Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, 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("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70152 | −1.91026 | −0.955132 | − | 0.296179i | \(-0.904287\pi\) | ||||
−0.955132 | + | 0.296179i | \(0.904287\pi\) | |||||||
\(3\) | −2.60067 | −1.50150 | −0.750749 | − | 0.660587i | \(-0.770307\pi\) | ||||
−0.750749 | + | 0.660587i | \(0.770307\pi\) | |||||||
\(4\) | 5.29822 | 2.64911 | ||||||||
\(5\) | −1.66030 | −0.742510 | −0.371255 | − | 0.928531i | \(-0.621072\pi\) | ||||
−0.371255 | + | 0.928531i | \(0.621072\pi\) | |||||||
\(6\) | 7.02577 | 2.86826 | ||||||||
\(7\) | 3.17610 | 1.20045 | 0.600226 | − | 0.799830i | \(-0.295077\pi\) | ||||
0.600226 | + | 0.799830i | \(0.295077\pi\) | |||||||
\(8\) | −8.91022 | −3.15024 | ||||||||
\(9\) | 3.76349 | 1.25450 | ||||||||
\(10\) | 4.48535 | 1.41839 | ||||||||
\(11\) | −4.43606 | −1.33752 | −0.668761 | − | 0.743477i | \(-0.733175\pi\) | ||||
−0.668761 | + | 0.743477i | \(0.733175\pi\) | |||||||
\(12\) | −13.7789 | −3.97764 | ||||||||
\(13\) | −5.94265 | −1.64820 | −0.824098 | − | 0.566448i | \(-0.808317\pi\) | ||||
−0.824098 | + | 0.566448i | \(0.808317\pi\) | |||||||
\(14\) | −8.58030 | −2.29318 | ||||||||
\(15\) | 4.31790 | 1.11488 | ||||||||
\(16\) | 13.4747 | 3.36868 | ||||||||
\(17\) | −5.95717 | −1.44483 | −0.722413 | − | 0.691462i | \(-0.756967\pi\) | ||||
−0.722413 | + | 0.691462i | \(0.756967\pi\) | |||||||
\(18\) | −10.1672 | −2.39642 | ||||||||
\(19\) | 0.924395 | 0.212071 | 0.106035 | − | 0.994362i | \(-0.466184\pi\) | ||||
0.106035 | + | 0.994362i | \(0.466184\pi\) | |||||||
\(20\) | −8.79665 | −1.96699 | ||||||||
\(21\) | −8.25999 | −1.80248 | ||||||||
\(22\) | 11.9841 | 2.55502 | ||||||||
\(23\) | 2.09388 | 0.436605 | 0.218302 | − | 0.975881i | \(-0.429948\pi\) | ||||
0.218302 | + | 0.975881i | \(0.429948\pi\) | |||||||
\(24\) | 23.1726 | 4.73008 | ||||||||
\(25\) | −2.24339 | −0.448679 | ||||||||
\(26\) | 16.0542 | 3.14849 | ||||||||
\(27\) | −1.98560 | −0.382128 | ||||||||
\(28\) | 16.8277 | 3.18013 | ||||||||
\(29\) | −8.93551 | −1.65928 | −0.829642 | − | 0.558296i | \(-0.811455\pi\) | ||||
−0.829642 | + | 0.558296i | \(0.811455\pi\) | |||||||
\(30\) | −11.6649 | −2.12971 | ||||||||
\(31\) | 0.505697 | 0.0908259 | 0.0454129 | − | 0.998968i | \(-0.485540\pi\) | ||||
0.0454129 | + | 0.998968i | \(0.485540\pi\) | |||||||
\(32\) | −18.5818 | −3.28483 | ||||||||
\(33\) | 11.5367 | 2.00829 | ||||||||
\(34\) | 16.0934 | 2.76000 | ||||||||
\(35\) | −5.27329 | −0.891348 | ||||||||
\(36\) | 19.9398 | 3.32330 | ||||||||
\(37\) | 11.4476 | 1.88198 | 0.940989 | − | 0.338437i | \(-0.109898\pi\) | ||||
0.940989 | + | 0.338437i | \(0.109898\pi\) | |||||||
\(38\) | −2.49727 | −0.405111 | ||||||||
\(39\) | 15.4549 | 2.47476 | ||||||||
\(40\) | 14.7937 | 2.33908 | ||||||||
\(41\) | 9.67385 | 1.51080 | 0.755400 | − | 0.655263i | \(-0.227442\pi\) | ||||
0.755400 | + | 0.655263i | \(0.227442\pi\) | |||||||
\(42\) | 22.3146 | 3.44321 | ||||||||
\(43\) | −2.55979 | −0.390365 | −0.195182 | − | 0.980767i | \(-0.562530\pi\) | ||||
−0.195182 | + | 0.980767i | \(0.562530\pi\) | |||||||
\(44\) | −23.5032 | −3.54325 | ||||||||
\(45\) | −6.24854 | −0.931477 | ||||||||
\(46\) | −5.65667 | −0.834030 | ||||||||
\(47\) | 7.56164 | 1.10298 | 0.551489 | − | 0.834182i | \(-0.314060\pi\) | ||||
0.551489 | + | 0.834182i | \(0.314060\pi\) | |||||||
\(48\) | −35.0433 | −5.05807 | ||||||||
\(49\) | 3.08761 | 0.441087 | ||||||||
\(50\) | 6.06058 | 0.857095 | ||||||||
\(51\) | 15.4926 | 2.16940 | ||||||||
\(52\) | −31.4855 | −4.36625 | ||||||||
\(53\) | −4.54872 | −0.624814 | −0.312407 | − | 0.949948i | \(-0.601135\pi\) | ||||
−0.312407 | + | 0.949948i | \(0.601135\pi\) | |||||||
\(54\) | 5.36413 | 0.729966 | ||||||||
\(55\) | 7.36520 | 0.993124 | ||||||||
\(56\) | −28.2998 | −3.78171 | ||||||||
\(57\) | −2.40405 | −0.318424 | ||||||||
\(58\) | 24.1395 | 3.16967 | ||||||||
\(59\) | −7.06044 | −0.919191 | −0.459596 | − | 0.888128i | \(-0.652006\pi\) | ||||
−0.459596 | + | 0.888128i | \(0.652006\pi\) | |||||||
\(60\) | 22.8772 | 2.95344 | ||||||||
\(61\) | 1.09734 | 0.140500 | 0.0702498 | − | 0.997529i | \(-0.477620\pi\) | ||||
0.0702498 | + | 0.997529i | \(0.477620\pi\) | |||||||
\(62\) | −1.36615 | −0.173502 | ||||||||
\(63\) | 11.9532 | 1.50597 | ||||||||
\(64\) | 23.2497 | 2.90622 | ||||||||
\(65\) | 9.86660 | 1.22380 | ||||||||
\(66\) | −31.1667 | −3.83636 | ||||||||
\(67\) | 4.19378 | 0.512352 | 0.256176 | − | 0.966630i | \(-0.417537\pi\) | ||||
0.256176 | + | 0.966630i | \(0.417537\pi\) | |||||||
\(68\) | −31.5624 | −3.82751 | ||||||||
\(69\) | −5.44550 | −0.655561 | ||||||||
\(70\) | 14.2459 | 1.70271 | ||||||||
\(71\) | 14.7479 | 1.75025 | 0.875126 | − | 0.483896i | \(-0.160779\pi\) | ||||
0.875126 | + | 0.483896i | \(0.160779\pi\) | |||||||
\(72\) | −33.5336 | −3.95197 | ||||||||
\(73\) | 2.30631 | 0.269933 | 0.134967 | − | 0.990850i | \(-0.456907\pi\) | ||||
0.134967 | + | 0.990850i | \(0.456907\pi\) | |||||||
\(74\) | −30.9260 | −3.59508 | ||||||||
\(75\) | 5.83433 | 0.673691 | ||||||||
\(76\) | 4.89765 | 0.561799 | ||||||||
\(77\) | −14.0894 | −1.60563 | ||||||||
\(78\) | −41.7517 | −4.72745 | ||||||||
\(79\) | 15.6561 | 1.76145 | 0.880726 | − | 0.473626i | \(-0.157055\pi\) | ||||
0.880726 | + | 0.473626i | \(0.157055\pi\) | |||||||
\(80\) | −22.3721 | −2.50128 | ||||||||
\(81\) | −6.12660 | −0.680733 | ||||||||
\(82\) | −26.1341 | −2.88603 | ||||||||
\(83\) | 3.16284 | 0.347167 | 0.173583 | − | 0.984819i | \(-0.444465\pi\) | ||||
0.173583 | + | 0.984819i | \(0.444465\pi\) | |||||||
\(84\) | −43.7633 | −4.77496 | ||||||||
\(85\) | 9.89071 | 1.07280 | ||||||||
\(86\) | 6.91534 | 0.745700 | ||||||||
\(87\) | 23.2383 | 2.49141 | ||||||||
\(88\) | 39.5263 | 4.21352 | ||||||||
\(89\) | 12.8782 | 1.36508 | 0.682541 | − | 0.730847i | \(-0.260875\pi\) | ||||
0.682541 | + | 0.730847i | \(0.260875\pi\) | |||||||
\(90\) | 16.8806 | 1.77937 | ||||||||
\(91\) | −18.8745 | −1.97858 | ||||||||
\(92\) | 11.0939 | 1.15661 | ||||||||
\(93\) | −1.31515 | −0.136375 | ||||||||
\(94\) | −20.4279 | −2.10698 | ||||||||
\(95\) | −1.53478 | −0.157465 | ||||||||
\(96\) | 48.3252 | 4.93217 | ||||||||
\(97\) | −18.7598 | −1.90477 | −0.952385 | − | 0.304899i | \(-0.901377\pi\) | ||||
−0.952385 | + | 0.304899i | \(0.901377\pi\) | |||||||
\(98\) | −8.34124 | −0.842592 | ||||||||
\(99\) | −16.6951 | −1.67792 | ||||||||
\(100\) | −11.8860 | −1.18860 | ||||||||
\(101\) | −8.16592 | −0.812540 | −0.406270 | − | 0.913753i | \(-0.633171\pi\) | ||||
−0.406270 | + | 0.913753i | \(0.633171\pi\) | |||||||
\(102\) | −41.8537 | −4.14414 | ||||||||
\(103\) | −3.64978 | −0.359623 | −0.179812 | − | 0.983701i | \(-0.557549\pi\) | ||||
−0.179812 | + | 0.983701i | \(0.557549\pi\) | |||||||
\(104\) | 52.9504 | 5.19221 | ||||||||
\(105\) | 13.7141 | 1.33836 | ||||||||
\(106\) | 12.2885 | 1.19356 | ||||||||
\(107\) | −16.0858 | −1.55507 | −0.777536 | − | 0.628838i | \(-0.783531\pi\) | ||||
−0.777536 | + | 0.628838i | \(0.783531\pi\) | |||||||
\(108\) | −10.5201 | −1.01230 | ||||||||
\(109\) | 2.55439 | 0.244666 | 0.122333 | − | 0.992489i | \(-0.460962\pi\) | ||||
0.122333 | + | 0.992489i | \(0.460962\pi\) | |||||||
\(110\) | −19.8973 | −1.89713 | ||||||||
\(111\) | −29.7715 | −2.82579 | ||||||||
\(112\) | 42.7970 | 4.04394 | ||||||||
\(113\) | −5.15003 | −0.484474 | −0.242237 | − | 0.970217i | \(-0.577881\pi\) | ||||
−0.242237 | + | 0.970217i | \(0.577881\pi\) | |||||||
\(114\) | 6.49459 | 0.608274 | ||||||||
\(115\) | −3.47648 | −0.324183 | ||||||||
\(116\) | −47.3423 | −4.39563 | ||||||||
\(117\) | −22.3651 | −2.06766 | ||||||||
\(118\) | 19.0739 | 1.75590 | ||||||||
\(119\) | −18.9206 | −1.73445 | ||||||||
\(120\) | −38.4735 | −3.51213 | ||||||||
\(121\) | 8.67863 | 0.788966 | ||||||||
\(122\) | −2.96448 | −0.268391 | ||||||||
\(123\) | −25.1585 | −2.26847 | ||||||||
\(124\) | 2.67930 | 0.240608 | ||||||||
\(125\) | 12.0262 | 1.07566 | ||||||||
\(126\) | −32.2919 | −2.87679 | ||||||||
\(127\) | −13.8140 | −1.22579 | −0.612897 | − | 0.790163i | \(-0.709996\pi\) | ||||
−0.612897 | + | 0.790163i | \(0.709996\pi\) | |||||||
\(128\) | −25.6461 | −2.26681 | ||||||||
\(129\) | 6.65718 | 0.586132 | ||||||||
\(130\) | −26.6549 | −2.33779 | ||||||||
\(131\) | 13.8494 | 1.21003 | 0.605014 | − | 0.796214i | \(-0.293167\pi\) | ||||
0.605014 | + | 0.796214i | \(0.293167\pi\) | |||||||
\(132\) | 61.1242 | 5.32018 | ||||||||
\(133\) | 2.93597 | 0.254581 | ||||||||
\(134\) | −11.3296 | −0.978728 | ||||||||
\(135\) | 3.29669 | 0.283734 | ||||||||
\(136\) | 53.0797 | 4.55155 | ||||||||
\(137\) | 1.91325 | 0.163460 | 0.0817300 | − | 0.996655i | \(-0.473955\pi\) | ||||
0.0817300 | + | 0.996655i | \(0.473955\pi\) | |||||||
\(138\) | 14.7111 | 1.25230 | ||||||||
\(139\) | 14.9315 | 1.26647 | 0.633236 | − | 0.773959i | \(-0.281726\pi\) | ||||
0.633236 | + | 0.773959i | \(0.281726\pi\) | |||||||
\(140\) | −27.9390 | −2.36128 | ||||||||
\(141\) | −19.6653 | −1.65612 | ||||||||
\(142\) | −39.8417 | −3.34344 | ||||||||
\(143\) | 26.3620 | 2.20450 | ||||||||
\(144\) | 50.7120 | 4.22600 | ||||||||
\(145\) | 14.8357 | 1.23203 | ||||||||
\(146\) | −6.23055 | −0.515644 | ||||||||
\(147\) | −8.02985 | −0.662291 | ||||||||
\(148\) | 60.6521 | 4.98557 | ||||||||
\(149\) | 8.74809 | 0.716671 | 0.358336 | − | 0.933593i | \(-0.383344\pi\) | ||||
0.358336 | + | 0.933593i | \(0.383344\pi\) | |||||||
\(150\) | −15.7616 | −1.28693 | ||||||||
\(151\) | 22.0545 | 1.79477 | 0.897387 | − | 0.441245i | \(-0.145463\pi\) | ||||
0.897387 | + | 0.441245i | \(0.145463\pi\) | |||||||
\(152\) | −8.23657 | −0.668074 | ||||||||
\(153\) | −22.4198 | −1.81253 | ||||||||
\(154\) | 38.0627 | 3.06718 | ||||||||
\(155\) | −0.839611 | −0.0674391 | ||||||||
\(156\) | 81.8835 | 6.55592 | ||||||||
\(157\) | −1.51570 | −0.120966 | −0.0604828 | − | 0.998169i | \(-0.519264\pi\) | ||||
−0.0604828 | + | 0.998169i | \(0.519264\pi\) | |||||||
\(158\) | −42.2954 | −3.36484 | ||||||||
\(159\) | 11.8297 | 0.938158 | ||||||||
\(160\) | 30.8514 | 2.43902 | ||||||||
\(161\) | 6.65038 | 0.524123 | ||||||||
\(162\) | 16.5511 | 1.30038 | ||||||||
\(163\) | −19.3959 | −1.51920 | −0.759601 | − | 0.650389i | \(-0.774606\pi\) | ||||
−0.759601 | + | 0.650389i | \(0.774606\pi\) | |||||||
\(164\) | 51.2542 | 4.00228 | ||||||||
\(165\) | −19.1545 | −1.49117 | ||||||||
\(166\) | −8.54448 | −0.663181 | ||||||||
\(167\) | 8.50159 | 0.657873 | 0.328937 | − | 0.944352i | \(-0.393310\pi\) | ||||
0.328937 | + | 0.944352i | \(0.393310\pi\) | |||||||
\(168\) | 73.5984 | 5.67824 | ||||||||
\(169\) | 22.3151 | 1.71655 | ||||||||
\(170\) | −26.7200 | −2.04933 | ||||||||
\(171\) | 3.47896 | 0.266042 | ||||||||
\(172\) | −13.5624 | −1.03412 | ||||||||
\(173\) | 9.42552 | 0.716609 | 0.358304 | − | 0.933605i | \(-0.383355\pi\) | ||||
0.358304 | + | 0.933605i | \(0.383355\pi\) | |||||||
\(174\) | −62.7789 | −4.75926 | ||||||||
\(175\) | −7.12524 | −0.538618 | ||||||||
\(176\) | −59.7747 | −4.50568 | ||||||||
\(177\) | 18.3619 | 1.38016 | ||||||||
\(178\) | −34.7906 | −2.60767 | ||||||||
\(179\) | 20.1117 | 1.50322 | 0.751608 | − | 0.659610i | \(-0.229278\pi\) | ||||
0.751608 | + | 0.659610i | \(0.229278\pi\) | |||||||
\(180\) | −33.1062 | −2.46759 | ||||||||
\(181\) | −11.3487 | −0.843544 | −0.421772 | − | 0.906702i | \(-0.638592\pi\) | ||||
−0.421772 | + | 0.906702i | \(0.638592\pi\) | |||||||
\(182\) | 50.9898 | 3.77961 | ||||||||
\(183\) | −2.85381 | −0.210960 | ||||||||
\(184\) | −18.6570 | −1.37541 | ||||||||
\(185\) | −19.0065 | −1.39739 | ||||||||
\(186\) | 3.55291 | 0.260512 | ||||||||
\(187\) | 26.4264 | 1.93249 | ||||||||
\(188\) | 40.0633 | 2.92191 | ||||||||
\(189\) | −6.30645 | −0.458727 | ||||||||
\(190\) | 4.14623 | 0.300799 | ||||||||
\(191\) | 18.6515 | 1.34958 | 0.674788 | − | 0.738012i | \(-0.264235\pi\) | ||||
0.674788 | + | 0.738012i | \(0.264235\pi\) | |||||||
\(192\) | −60.4649 | −4.36368 | ||||||||
\(193\) | −21.0126 | −1.51252 | −0.756259 | − | 0.654272i | \(-0.772975\pi\) | ||||
−0.756259 | + | 0.654272i | \(0.772975\pi\) | |||||||
\(194\) | 50.6800 | 3.63861 | ||||||||
\(195\) | −25.6598 | −1.83754 | ||||||||
\(196\) | 16.3588 | 1.16849 | ||||||||
\(197\) | −17.7277 | −1.26305 | −0.631524 | − | 0.775356i | \(-0.717570\pi\) | ||||
−0.631524 | + | 0.775356i | \(0.717570\pi\) | |||||||
\(198\) | 45.1021 | 3.20527 | ||||||||
\(199\) | −20.0982 | −1.42472 | −0.712362 | − | 0.701812i | \(-0.752375\pi\) | ||||
−0.712362 | + | 0.701812i | \(0.752375\pi\) | |||||||
\(200\) | 19.9891 | 1.41345 | ||||||||
\(201\) | −10.9067 | −0.769296 | ||||||||
\(202\) | 22.0604 | 1.55217 | ||||||||
\(203\) | −28.3801 | −1.99189 | ||||||||
\(204\) | 82.0835 | 5.74699 | ||||||||
\(205\) | −16.0615 | −1.12178 | ||||||||
\(206\) | 9.85996 | 0.686976 | ||||||||
\(207\) | 7.88031 | 0.547719 | ||||||||
\(208\) | −80.0756 | −5.55224 | ||||||||
\(209\) | −4.10067 | −0.283650 | ||||||||
\(210\) | −37.0489 | −2.55662 | ||||||||
\(211\) | 9.08607 | 0.625511 | 0.312755 | − | 0.949834i | \(-0.398748\pi\) | ||||
0.312755 | + | 0.949834i | \(0.398748\pi\) | |||||||
\(212\) | −24.1001 | −1.65520 | ||||||||
\(213\) | −38.3544 | −2.62800 | ||||||||
\(214\) | 43.4561 | 2.97060 | ||||||||
\(215\) | 4.25003 | 0.289850 | ||||||||
\(216\) | 17.6921 | 1.20379 | ||||||||
\(217\) | 1.60614 | 0.109032 | ||||||||
\(218\) | −6.90074 | −0.467377 | ||||||||
\(219\) | −5.99796 | −0.405305 | ||||||||
\(220\) | 39.0225 | 2.63090 | ||||||||
\(221\) | 35.4014 | 2.38136 | ||||||||
\(222\) | 80.4284 | 5.39800 | ||||||||
\(223\) | 19.8949 | 1.33226 | 0.666130 | − | 0.745836i | \(-0.267950\pi\) | ||||
0.666130 | + | 0.745836i | \(0.267950\pi\) | |||||||
\(224\) | −59.0177 | −3.94328 | ||||||||
\(225\) | −8.44300 | −0.562867 | ||||||||
\(226\) | 13.9129 | 0.925474 | ||||||||
\(227\) | 21.2188 | 1.40834 | 0.704171 | − | 0.710030i | \(-0.251319\pi\) | ||||
0.704171 | + | 0.710030i | \(0.251319\pi\) | |||||||
\(228\) | −12.7372 | −0.843541 | ||||||||
\(229\) | −0.117781 | −0.00778319 | −0.00389160 | − | 0.999992i | \(-0.501239\pi\) | ||||
−0.00389160 | + | 0.999992i | \(0.501239\pi\) | |||||||
\(230\) | 9.39178 | 0.619276 | ||||||||
\(231\) | 36.6418 | 2.41085 | ||||||||
\(232\) | 79.6174 | 5.22714 | ||||||||
\(233\) | 1.68147 | 0.110157 | 0.0550785 | − | 0.998482i | \(-0.482459\pi\) | ||||
0.0550785 | + | 0.998482i | \(0.482459\pi\) | |||||||
\(234\) | 60.4199 | 3.94977 | ||||||||
\(235\) | −12.5546 | −0.818973 | ||||||||
\(236\) | −37.4078 | −2.43504 | ||||||||
\(237\) | −40.7165 | −2.64482 | ||||||||
\(238\) | 51.1143 | 3.31325 | ||||||||
\(239\) | −20.4982 | −1.32592 | −0.662961 | − | 0.748654i | \(-0.730700\pi\) | ||||
−0.662961 | + | 0.748654i | \(0.730700\pi\) | |||||||
\(240\) | 58.1825 | 3.75567 | ||||||||
\(241\) | 12.1357 | 0.781731 | 0.390866 | − | 0.920448i | \(-0.372176\pi\) | ||||
0.390866 | + | 0.920448i | \(0.372176\pi\) | |||||||
\(242\) | −23.4455 | −1.50713 | ||||||||
\(243\) | 21.8901 | 1.40425 | ||||||||
\(244\) | 5.81393 | 0.372199 | ||||||||
\(245\) | −5.12636 | −0.327511 | ||||||||
\(246\) | 67.9662 | 4.33337 | ||||||||
\(247\) | −5.49336 | −0.349534 | ||||||||
\(248\) | −4.50587 | −0.286123 | ||||||||
\(249\) | −8.22551 | −0.521271 | ||||||||
\(250\) | −32.4891 | −2.05479 | ||||||||
\(251\) | 26.9484 | 1.70097 | 0.850484 | − | 0.526001i | \(-0.176309\pi\) | ||||
0.850484 | + | 0.526001i | \(0.176309\pi\) | |||||||
\(252\) | 63.3309 | 3.98947 | ||||||||
\(253\) | −9.28859 | −0.583968 | ||||||||
\(254\) | 37.3188 | 2.34159 | ||||||||
\(255\) | −25.7225 | −1.61080 | ||||||||
\(256\) | 22.7839 | 1.42400 | ||||||||
\(257\) | −1.79856 | −0.112191 | −0.0560955 | − | 0.998425i | \(-0.517865\pi\) | ||||
−0.0560955 | + | 0.998425i | \(0.517865\pi\) | |||||||
\(258\) | −17.9845 | −1.11967 | ||||||||
\(259\) | 36.3588 | 2.25923 | ||||||||
\(260\) | 52.2755 | 3.24199 | ||||||||
\(261\) | −33.6288 | −2.08157 | ||||||||
\(262\) | −37.4145 | −2.31148 | ||||||||
\(263\) | −16.3387 | −1.00749 | −0.503745 | − | 0.863853i | \(-0.668045\pi\) | ||||
−0.503745 | + | 0.863853i | \(0.668045\pi\) | |||||||
\(264\) | −102.795 | −6.32659 | ||||||||
\(265\) | 7.55225 | 0.463931 | ||||||||
\(266\) | −7.93159 | −0.486317 | ||||||||
\(267\) | −33.4919 | −2.04967 | ||||||||
\(268\) | 22.2196 | 1.35728 | ||||||||
\(269\) | −15.8975 | −0.969288 | −0.484644 | − | 0.874712i | \(-0.661051\pi\) | ||||
−0.484644 | + | 0.874712i | \(0.661051\pi\) | |||||||
\(270\) | −8.90608 | −0.542007 | ||||||||
\(271\) | 16.4572 | 0.999703 | 0.499851 | − | 0.866111i | \(-0.333388\pi\) | ||||
0.499851 | + | 0.866111i | \(0.333388\pi\) | |||||||
\(272\) | −80.2712 | −4.86716 | ||||||||
\(273\) | 49.0863 | 2.97084 | ||||||||
\(274\) | −5.16869 | −0.312252 | ||||||||
\(275\) | 9.95183 | 0.600118 | ||||||||
\(276\) | −28.8515 | −1.73665 | ||||||||
\(277\) | −8.71238 | −0.523476 | −0.261738 | − | 0.965139i | \(-0.584296\pi\) | ||||
−0.261738 | + | 0.965139i | \(0.584296\pi\) | |||||||
\(278\) | −40.3378 | −2.41930 | ||||||||
\(279\) | 1.90319 | 0.113941 | ||||||||
\(280\) | 46.9862 | 2.80796 | ||||||||
\(281\) | −4.47201 | −0.266778 | −0.133389 | − | 0.991064i | \(-0.542586\pi\) | ||||
−0.133389 | + | 0.991064i | \(0.542586\pi\) | |||||||
\(282\) | 53.1264 | 3.16363 | ||||||||
\(283\) | −9.70786 | −0.577073 | −0.288536 | − | 0.957469i | \(-0.593169\pi\) | ||||
−0.288536 | + | 0.957469i | \(0.593169\pi\) | |||||||
\(284\) | 78.1375 | 4.63661 | ||||||||
\(285\) | 3.99145 | 0.236433 | ||||||||
\(286\) | −71.2174 | −4.21118 | ||||||||
\(287\) | 30.7251 | 1.81364 | ||||||||
\(288\) | −69.9325 | −4.12081 | ||||||||
\(289\) | 18.4879 | 1.08752 | ||||||||
\(290\) | −40.0789 | −2.35351 | ||||||||
\(291\) | 48.7881 | 2.86001 | ||||||||
\(292\) | 12.2194 | 0.715084 | ||||||||
\(293\) | −0.113041 | −0.00660391 | −0.00330196 | − | 0.999995i | \(-0.501051\pi\) | ||||
−0.00330196 | + | 0.999995i | \(0.501051\pi\) | |||||||
\(294\) | 21.6928 | 1.26515 | ||||||||
\(295\) | 11.7225 | 0.682509 | ||||||||
\(296\) | −102.001 | −5.92868 | ||||||||
\(297\) | 8.80822 | 0.511105 | ||||||||
\(298\) | −23.6332 | −1.36903 | ||||||||
\(299\) | −12.4432 | −0.719610 | ||||||||
\(300\) | 30.9116 | 1.78468 | ||||||||
\(301\) | −8.13016 | −0.468615 | ||||||||
\(302\) | −59.5808 | −3.42849 | ||||||||
\(303\) | 21.2369 | 1.22003 | ||||||||
\(304\) | 12.4560 | 0.714399 | ||||||||
\(305\) | −1.82191 | −0.104322 | ||||||||
\(306\) | 60.5675 | 3.46241 | ||||||||
\(307\) | −14.3035 | −0.816343 | −0.408171 | − | 0.912905i | \(-0.633833\pi\) | ||||
−0.408171 | + | 0.912905i | \(0.633833\pi\) | |||||||
\(308\) | −74.6486 | −4.25350 | ||||||||
\(309\) | 9.49187 | 0.539974 | ||||||||
\(310\) | 2.26823 | 0.128827 | ||||||||
\(311\) | −33.1534 | −1.87995 | −0.939977 | − | 0.341237i | \(-0.889154\pi\) | ||||
−0.939977 | + | 0.341237i | \(0.889154\pi\) | |||||||
\(312\) | −137.707 | −7.79610 | ||||||||
\(313\) | 7.95116 | 0.449426 | 0.224713 | − | 0.974425i | \(-0.427856\pi\) | ||||
0.224713 | + | 0.974425i | \(0.427856\pi\) | |||||||
\(314\) | 4.09469 | 0.231076 | ||||||||
\(315\) | −19.8460 | −1.11819 | ||||||||
\(316\) | 82.9497 | 4.66628 | ||||||||
\(317\) | 0.186958 | 0.0105006 | 0.00525031 | − | 0.999986i | \(-0.498329\pi\) | ||||
0.00525031 | + | 0.999986i | \(0.498329\pi\) | |||||||
\(318\) | −31.9582 | −1.79213 | ||||||||
\(319\) | 39.6385 | 2.21933 | ||||||||
\(320\) | −38.6016 | −2.15790 | ||||||||
\(321\) | 41.8339 | 2.33494 | ||||||||
\(322\) | −17.9661 | −1.00121 | ||||||||
\(323\) | −5.50678 | −0.306405 | ||||||||
\(324\) | −32.4601 | −1.80334 | ||||||||
\(325\) | 13.3317 | 0.739510 | ||||||||
\(326\) | 52.3984 | 2.90208 | ||||||||
\(327\) | −6.64313 | −0.367366 | ||||||||
\(328\) | −86.1961 | −4.75938 | ||||||||
\(329\) | 24.0165 | 1.32407 | ||||||||
\(330\) | 51.7462 | 2.84854 | ||||||||
\(331\) | 3.00795 | 0.165332 | 0.0826659 | − | 0.996577i | \(-0.473657\pi\) | ||||
0.0826659 | + | 0.996577i | \(0.473657\pi\) | |||||||
\(332\) | 16.7574 | 0.919684 | ||||||||
\(333\) | 43.0831 | 2.36094 | ||||||||
\(334\) | −22.9672 | −1.25671 | ||||||||
\(335\) | −6.96295 | −0.380427 | ||||||||
\(336\) | −111.301 | −6.07197 | ||||||||
\(337\) | 31.6413 | 1.72361 | 0.861805 | − | 0.507240i | \(-0.169334\pi\) | ||||
0.861805 | + | 0.507240i | \(0.169334\pi\) | |||||||
\(338\) | −60.2848 | −3.27906 | ||||||||
\(339\) | 13.3935 | 0.727437 | ||||||||
\(340\) | 52.4032 | 2.84196 | ||||||||
\(341\) | −2.24330 | −0.121482 | ||||||||
\(342\) | −9.39848 | −0.508211 | ||||||||
\(343\) | −12.4262 | −0.670949 | ||||||||
\(344\) | 22.8083 | 1.22974 | ||||||||
\(345\) | 9.04118 | 0.486761 | ||||||||
\(346\) | −25.4633 | −1.36891 | ||||||||
\(347\) | −3.93576 | −0.211283 | −0.105641 | − | 0.994404i | \(-0.533690\pi\) | ||||
−0.105641 | + | 0.994404i | \(0.533690\pi\) | |||||||
\(348\) | 123.122 | 6.60003 | ||||||||
\(349\) | 9.95432 | 0.532843 | 0.266421 | − | 0.963857i | \(-0.414159\pi\) | ||||
0.266421 | + | 0.963857i | \(0.414159\pi\) | |||||||
\(350\) | 19.2490 | 1.02890 | ||||||||
\(351\) | 11.7997 | 0.629822 | ||||||||
\(352\) | 82.4300 | 4.39354 | ||||||||
\(353\) | −24.0736 | −1.28131 | −0.640653 | − | 0.767830i | \(-0.721336\pi\) | ||||
−0.640653 | + | 0.767830i | \(0.721336\pi\) | |||||||
\(354\) | −49.6050 | −2.63648 | ||||||||
\(355\) | −24.4859 | −1.29958 | ||||||||
\(356\) | 68.2314 | 3.61626 | ||||||||
\(357\) | 49.2062 | 2.60427 | ||||||||
\(358\) | −54.3321 | −2.87154 | ||||||||
\(359\) | 3.40516 | 0.179717 | 0.0898586 | − | 0.995955i | \(-0.471358\pi\) | ||||
0.0898586 | + | 0.995955i | \(0.471358\pi\) | |||||||
\(360\) | 55.6759 | 2.93438 | ||||||||
\(361\) | −18.1455 | −0.955026 | ||||||||
\(362\) | 30.6588 | 1.61139 | ||||||||
\(363\) | −22.5703 | −1.18463 | ||||||||
\(364\) | −100.001 | −5.24148 | ||||||||
\(365\) | −3.82918 | −0.200428 | ||||||||
\(366\) | 7.70964 | 0.402989 | ||||||||
\(367\) | 27.3963 | 1.43008 | 0.715038 | − | 0.699086i | \(-0.246409\pi\) | ||||
0.715038 | + | 0.699086i | \(0.246409\pi\) | |||||||
\(368\) | 28.2145 | 1.47078 | ||||||||
\(369\) | 36.4075 | 1.89530 | ||||||||
\(370\) | 51.3466 | 2.66938 | ||||||||
\(371\) | −14.4472 | −0.750060 | ||||||||
\(372\) | −6.96797 | −0.361272 | ||||||||
\(373\) | −6.49382 | −0.336237 | −0.168119 | − | 0.985767i | \(-0.553769\pi\) | ||||
−0.168119 | + | 0.985767i | \(0.553769\pi\) | |||||||
\(374\) | −71.3914 | −3.69156 | ||||||||
\(375\) | −31.2763 | −1.61510 | ||||||||
\(376\) | −67.3759 | −3.47465 | ||||||||
\(377\) | 53.1007 | 2.73482 | ||||||||
\(378\) | 17.0370 | 0.876289 | ||||||||
\(379\) | 21.4906 | 1.10390 | 0.551950 | − | 0.833877i | \(-0.313884\pi\) | ||||
0.551950 | + | 0.833877i | \(0.313884\pi\) | |||||||
\(380\) | −8.13159 | −0.417142 | ||||||||
\(381\) | 35.9257 | 1.84053 | ||||||||
\(382\) | −50.3875 | −2.57805 | ||||||||
\(383\) | 17.2400 | 0.880920 | 0.440460 | − | 0.897772i | \(-0.354815\pi\) | ||||
0.440460 | + | 0.897772i | \(0.354815\pi\) | |||||||
\(384\) | 66.6970 | 3.40362 | ||||||||
\(385\) | 23.3926 | 1.19220 | ||||||||
\(386\) | 56.7659 | 2.88931 | ||||||||
\(387\) | −9.63377 | −0.489712 | ||||||||
\(388\) | −99.3936 | −5.04595 | ||||||||
\(389\) | 0.378277 | 0.0191794 | 0.00958970 | − | 0.999954i | \(-0.496947\pi\) | ||||
0.00958970 | + | 0.999954i | \(0.496947\pi\) | |||||||
\(390\) | 69.3205 | 3.51018 | ||||||||
\(391\) | −12.4736 | −0.630818 | ||||||||
\(392\) | −27.5113 | −1.38953 | ||||||||
\(393\) | −36.0178 | −1.81686 | ||||||||
\(394\) | 47.8918 | 2.41276 | ||||||||
\(395\) | −25.9939 | −1.30790 | ||||||||
\(396\) | −88.4543 | −4.44499 | ||||||||
\(397\) | −18.6402 | −0.935523 | −0.467762 | − | 0.883855i | \(-0.654939\pi\) | ||||
−0.467762 | + | 0.883855i | \(0.654939\pi\) | |||||||
\(398\) | 54.2958 | 2.72160 | ||||||||
\(399\) | −7.63550 | −0.382253 | ||||||||
\(400\) | −30.2291 | −1.51146 | ||||||||
\(401\) | 19.9607 | 0.996791 | 0.498395 | − | 0.866950i | \(-0.333923\pi\) | ||||
0.498395 | + | 0.866950i | \(0.333923\pi\) | |||||||
\(402\) | 29.4646 | 1.46956 | ||||||||
\(403\) | −3.00518 | −0.149699 | ||||||||
\(404\) | −43.2649 | −2.15251 | ||||||||
\(405\) | 10.1720 | 0.505451 | ||||||||
\(406\) | 76.6694 | 3.80504 | ||||||||
\(407\) | −50.7824 | −2.51719 | ||||||||
\(408\) | −138.043 | −6.83414 | ||||||||
\(409\) | 2.48272 | 0.122762 | 0.0613812 | − | 0.998114i | \(-0.480449\pi\) | ||||
0.0613812 | + | 0.998114i | \(0.480449\pi\) | |||||||
\(410\) | 43.3905 | 2.14291 | ||||||||
\(411\) | −4.97574 | −0.245435 | ||||||||
\(412\) | −19.3373 | −0.952682 | ||||||||
\(413\) | −22.4247 | −1.10345 | ||||||||
\(414\) | −21.2888 | −1.04629 | ||||||||
\(415\) | −5.25127 | −0.257775 | ||||||||
\(416\) | 110.425 | 5.41404 | ||||||||
\(417\) | −38.8319 | −1.90161 | ||||||||
\(418\) | 11.0781 | 0.541846 | ||||||||
\(419\) | 0.0187896 | 0.000917933 0 | 0.000458967 | − | 1.00000i | \(-0.499854\pi\) | ||||
0.000458967 | 1.00000i | \(0.499854\pi\) | ||||||||
\(420\) | 72.6603 | 3.54546 | ||||||||
\(421\) | −8.09367 | −0.394462 | −0.197231 | − | 0.980357i | \(-0.563195\pi\) | ||||
−0.197231 | + | 0.980357i | \(0.563195\pi\) | |||||||
\(422\) | −24.5462 | −1.19489 | ||||||||
\(423\) | 28.4582 | 1.38368 | ||||||||
\(424\) | 40.5301 | 1.96831 | ||||||||
\(425\) | 13.3643 | 0.648263 | ||||||||
\(426\) | 103.615 | 5.02017 | ||||||||
\(427\) | 3.48525 | 0.168663 | ||||||||
\(428\) | −85.2261 | −4.11956 | ||||||||
\(429\) | −68.5588 | −3.31005 | ||||||||
\(430\) | −11.4816 | −0.553690 | ||||||||
\(431\) | −13.0687 | −0.629498 | −0.314749 | − | 0.949175i | \(-0.601920\pi\) | ||||
−0.314749 | + | 0.949175i | \(0.601920\pi\) | |||||||
\(432\) | −26.7553 | −1.28727 | ||||||||
\(433\) | 13.8960 | 0.667801 | 0.333901 | − | 0.942608i | \(-0.391635\pi\) | ||||
0.333901 | + | 0.942608i | \(0.391635\pi\) | |||||||
\(434\) | −4.33904 | −0.208280 | ||||||||
\(435\) | −38.5827 | −1.84990 | ||||||||
\(436\) | 13.5337 | 0.648148 | ||||||||
\(437\) | 1.93558 | 0.0925911 | ||||||||
\(438\) | 16.2036 | 0.774239 | ||||||||
\(439\) | −39.6689 | −1.89329 | −0.946646 | − | 0.322274i | \(-0.895553\pi\) | ||||
−0.946646 | + | 0.322274i | \(0.895553\pi\) | |||||||
\(440\) | −65.6256 | −3.12858 | ||||||||
\(441\) | 11.6202 | 0.553342 | ||||||||
\(442\) | −95.6377 | −4.54902 | ||||||||
\(443\) | −0.687120 | −0.0326460 | −0.0163230 | − | 0.999867i | \(-0.505196\pi\) | ||||
−0.0163230 | + | 0.999867i | \(0.505196\pi\) | |||||||
\(444\) | −157.736 | −7.48583 | ||||||||
\(445\) | −21.3817 | −1.01359 | ||||||||
\(446\) | −53.7465 | −2.54497 | ||||||||
\(447\) | −22.7509 | −1.07608 | ||||||||
\(448\) | 73.8435 | 3.48878 | ||||||||
\(449\) | −5.97951 | −0.282190 | −0.141095 | − | 0.989996i | \(-0.545062\pi\) | ||||
−0.141095 | + | 0.989996i | \(0.545062\pi\) | |||||||
\(450\) | 22.8090 | 1.07522 | ||||||||
\(451\) | −42.9138 | −2.02073 | ||||||||
\(452\) | −27.2860 | −1.28343 | ||||||||
\(453\) | −57.3566 | −2.69485 | ||||||||
\(454\) | −57.3231 | −2.69031 | ||||||||
\(455\) | 31.3373 | 1.46912 | ||||||||
\(456\) | 21.4206 | 1.00311 | ||||||||
\(457\) | 10.6755 | 0.499378 | 0.249689 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249689 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(458\) | 0.318188 | 0.0148680 | ||||||||
\(459\) | 11.8285 | 0.552109 | ||||||||
\(460\) | −18.4192 | −0.858798 | ||||||||
\(461\) | 28.8028 | 1.34148 | 0.670741 | − | 0.741692i | \(-0.265976\pi\) | ||||
0.670741 | + | 0.741692i | \(0.265976\pi\) | |||||||
\(462\) | −98.9887 | −4.60537 | ||||||||
\(463\) | 8.17095 | 0.379736 | 0.189868 | − | 0.981810i | \(-0.439194\pi\) | ||||
0.189868 | + | 0.981810i | \(0.439194\pi\) | |||||||
\(464\) | −120.404 | −5.58960 | ||||||||
\(465\) | 2.18355 | 0.101260 | ||||||||
\(466\) | −4.54254 | −0.210429 | ||||||||
\(467\) | −10.8314 | −0.501216 | −0.250608 | − | 0.968089i | \(-0.580631\pi\) | ||||
−0.250608 | + | 0.968089i | \(0.580631\pi\) | |||||||
\(468\) | −118.495 | −5.47746 | ||||||||
\(469\) | 13.3199 | 0.615054 | ||||||||
\(470\) | 33.9166 | 1.56446 | ||||||||
\(471\) | 3.94183 | 0.181630 | ||||||||
\(472\) | 62.9101 | 2.89567 | ||||||||
\(473\) | 11.3554 | 0.522122 | ||||||||
\(474\) | 109.996 | 5.05230 | ||||||||
\(475\) | −2.07378 | −0.0951517 | ||||||||
\(476\) | −100.245 | −4.59474 | ||||||||
\(477\) | −17.1191 | −0.783828 | ||||||||
\(478\) | 55.3765 | 2.53286 | ||||||||
\(479\) | −17.2868 | −0.789852 | −0.394926 | − | 0.918713i | \(-0.629230\pi\) | ||||
−0.394926 | + | 0.918713i | \(0.629230\pi\) | |||||||
\(480\) | −80.2345 | −3.66219 | ||||||||
\(481\) | −68.0293 | −3.10187 | ||||||||
\(482\) | −32.7850 | −1.49331 | ||||||||
\(483\) | −17.2954 | −0.786970 | ||||||||
\(484\) | 45.9813 | 2.09006 | ||||||||
\(485\) | 31.1470 | 1.41431 | ||||||||
\(486\) | −59.1365 | −2.68249 | ||||||||
\(487\) | 8.06575 | 0.365494 | 0.182747 | − | 0.983160i | \(-0.441501\pi\) | ||||
0.182747 | + | 0.983160i | \(0.441501\pi\) | |||||||
\(488\) | −9.77751 | −0.442607 | ||||||||
\(489\) | 50.4423 | 2.28108 | ||||||||
\(490\) | 13.8490 | 0.625633 | ||||||||
\(491\) | −32.8835 | −1.48401 | −0.742005 | − | 0.670394i | \(-0.766125\pi\) | ||||
−0.742005 | + | 0.670394i | \(0.766125\pi\) | |||||||
\(492\) | −133.295 | −6.00942 | ||||||||
\(493\) | 53.2304 | 2.39738 | ||||||||
\(494\) | 14.8404 | 0.667703 | ||||||||
\(495\) | 27.7189 | 1.24587 | ||||||||
\(496\) | 6.81413 | 0.305963 | ||||||||
\(497\) | 46.8407 | 2.10109 | ||||||||
\(498\) | 22.2214 | 0.995765 | ||||||||
\(499\) | 2.07468 | 0.0928752 | 0.0464376 | − | 0.998921i | \(-0.485213\pi\) | ||||
0.0464376 | + | 0.998921i | \(0.485213\pi\) | |||||||
\(500\) | 63.7176 | 2.84954 | ||||||||
\(501\) | −22.1099 | −0.987796 | ||||||||
\(502\) | −72.8017 | −3.24930 | ||||||||
\(503\) | 7.56513 | 0.337313 | 0.168656 | − | 0.985675i | \(-0.446057\pi\) | ||||
0.168656 | + | 0.985675i | \(0.446057\pi\) | |||||||
\(504\) | −106.506 | −4.74415 | ||||||||
\(505\) | 13.5579 | 0.603319 | ||||||||
\(506\) | 25.0933 | 1.11553 | ||||||||
\(507\) | −58.0343 | −2.57739 | ||||||||
\(508\) | −73.1896 | −3.24726 | ||||||||
\(509\) | 25.4583 | 1.12842 | 0.564210 | − | 0.825631i | \(-0.309181\pi\) | ||||
0.564210 | + | 0.825631i | \(0.309181\pi\) | |||||||
\(510\) | 69.4899 | 3.07706 | ||||||||
\(511\) | 7.32508 | 0.324042 | ||||||||
\(512\) | −10.2592 | −0.453397 | ||||||||
\(513\) | −1.83548 | −0.0810382 | ||||||||
\(514\) | 4.85884 | 0.214314 | ||||||||
\(515\) | 6.05974 | 0.267024 | ||||||||
\(516\) | 35.2712 | 1.55273 | ||||||||
\(517\) | −33.5439 | −1.47526 | ||||||||
\(518\) | −98.2241 | −4.31572 | ||||||||
\(519\) | −24.5127 | −1.07599 | ||||||||
\(520\) | −87.9136 | −3.85527 | ||||||||
\(521\) | 14.1063 | 0.618009 | 0.309005 | − | 0.951061i | \(-0.400004\pi\) | ||||
0.309005 | + | 0.951061i | \(0.400004\pi\) | |||||||
\(522\) | 90.8488 | 3.97634 | ||||||||
\(523\) | −22.9041 | −1.00153 | −0.500763 | − | 0.865585i | \(-0.666947\pi\) | ||||
−0.500763 | + | 0.865585i | \(0.666947\pi\) | |||||||
\(524\) | 73.3773 | 3.20550 | ||||||||
\(525\) | 18.5304 | 0.808734 | ||||||||
\(526\) | 44.1395 | 1.92457 | ||||||||
\(527\) | −3.01252 | −0.131228 | ||||||||
\(528\) | 155.454 | 6.76528 | ||||||||
\(529\) | −18.6157 | −0.809376 | ||||||||
\(530\) | −20.4026 | −0.886231 | ||||||||
\(531\) | −26.5719 | −1.15312 | ||||||||
\(532\) | 15.5554 | 0.674414 | ||||||||
\(533\) | −57.4883 | −2.49009 | ||||||||
\(534\) | 90.4790 | 3.91541 | ||||||||
\(535\) | 26.7073 | 1.15466 | ||||||||
\(536\) | −37.3675 | −1.61403 | ||||||||
\(537\) | −52.3038 | −2.25708 | ||||||||
\(538\) | 42.9475 | 1.85160 | ||||||||
\(539\) | −13.6968 | −0.589963 | ||||||||
\(540\) | 17.4666 | 0.751643 | ||||||||
\(541\) | −40.2549 | −1.73069 | −0.865346 | − | 0.501175i | \(-0.832901\pi\) | ||||
−0.865346 | + | 0.501175i | \(0.832901\pi\) | |||||||
\(542\) | −44.4594 | −1.90970 | ||||||||
\(543\) | 29.5143 | 1.26658 | ||||||||
\(544\) | 110.695 | 4.74601 | ||||||||
\(545\) | −4.24106 | −0.181667 | ||||||||
\(546\) | −132.608 | −5.67508 | ||||||||
\(547\) | −9.24781 | −0.395408 | −0.197704 | − | 0.980262i | \(-0.563348\pi\) | ||||
−0.197704 | + | 0.980262i | \(0.563348\pi\) | |||||||
\(548\) | 10.1368 | 0.433024 | ||||||||
\(549\) | 4.12982 | 0.176256 | ||||||||
\(550\) | −26.8851 | −1.14638 | ||||||||
\(551\) | −8.25995 | −0.351886 | ||||||||
\(552\) | 48.5206 | 2.06517 | ||||||||
\(553\) | 49.7254 | 2.11454 | ||||||||
\(554\) | 23.5367 | 0.999979 | ||||||||
\(555\) | 49.4297 | 2.09818 | ||||||||
\(556\) | 79.1104 | 3.35503 | ||||||||
\(557\) | 7.66751 | 0.324883 | 0.162441 | − | 0.986718i | \(-0.448063\pi\) | ||||
0.162441 | + | 0.986718i | \(0.448063\pi\) | |||||||
\(558\) | −5.14151 | −0.217657 | ||||||||
\(559\) | 15.2120 | 0.643398 | ||||||||
\(560\) | −71.0561 | −3.00267 | ||||||||
\(561\) | −68.7263 | −2.90163 | ||||||||
\(562\) | 12.0812 | 0.509616 | ||||||||
\(563\) | 16.4276 | 0.692341 | 0.346171 | − | 0.938172i | \(-0.387482\pi\) | ||||
0.346171 | + | 0.938172i | \(0.387482\pi\) | |||||||
\(564\) | −104.191 | −4.38725 | ||||||||
\(565\) | 8.55061 | 0.359727 | ||||||||
\(566\) | 26.2260 | 1.10236 | ||||||||
\(567\) | −19.4587 | −0.817188 | ||||||||
\(568\) | −131.407 | −5.51371 | ||||||||
\(569\) | −29.1778 | −1.22320 | −0.611598 | − | 0.791169i | \(-0.709473\pi\) | ||||
−0.611598 | + | 0.791169i | \(0.709473\pi\) | |||||||
\(570\) | −10.7830 | −0.451650 | ||||||||
\(571\) | −24.9364 | −1.04356 | −0.521779 | − | 0.853081i | \(-0.674731\pi\) | ||||
−0.521779 | + | 0.853081i | \(0.674731\pi\) | |||||||
\(572\) | 139.672 | 5.83996 | ||||||||
\(573\) | −48.5065 | −2.02639 | ||||||||
\(574\) | −83.0045 | −3.46454 | ||||||||
\(575\) | −4.69740 | −0.195895 | ||||||||
\(576\) | 87.5002 | 3.64584 | ||||||||
\(577\) | 41.1748 | 1.71413 | 0.857065 | − | 0.515208i | \(-0.172285\pi\) | ||||
0.857065 | + | 0.515208i | \(0.172285\pi\) | |||||||
\(578\) | −49.9454 | −2.07746 | ||||||||
\(579\) | 54.6468 | 2.27104 | ||||||||
\(580\) | 78.6026 | 3.26380 | ||||||||
\(581\) | 10.0455 | 0.416757 | ||||||||
\(582\) | −131.802 | −5.46337 | ||||||||
\(583\) | 20.1784 | 0.835703 | ||||||||
\(584\) | −20.5498 | −0.850355 | ||||||||
\(585\) | 37.1329 | 1.53526 | ||||||||
\(586\) | 0.305382 | 0.0126152 | ||||||||
\(587\) | 10.2758 | 0.424128 | 0.212064 | − | 0.977256i | \(-0.431981\pi\) | ||||
0.212064 | + | 0.977256i | \(0.431981\pi\) | |||||||
\(588\) | −42.5439 | −1.75448 | ||||||||
\(589\) | 0.467464 | 0.0192615 | ||||||||
\(590\) | −31.6685 | −1.30377 | ||||||||
\(591\) | 46.1040 | 1.89646 | ||||||||
\(592\) | 154.254 | 6.33978 | ||||||||
\(593\) | −14.6340 | −0.600946 | −0.300473 | − | 0.953790i | \(-0.597144\pi\) | ||||
−0.300473 | + | 0.953790i | \(0.597144\pi\) | |||||||
\(594\) | −23.7956 | −0.976346 | ||||||||
\(595\) | 31.4139 | 1.28784 | ||||||||
\(596\) | 46.3493 | 1.89854 | ||||||||
\(597\) | 52.2689 | 2.13922 | ||||||||
\(598\) | 33.6156 | 1.37465 | ||||||||
\(599\) | 28.5035 | 1.16462 | 0.582311 | − | 0.812966i | \(-0.302148\pi\) | ||||
0.582311 | + | 0.812966i | \(0.302148\pi\) | |||||||
\(600\) | −51.9852 | −2.12229 | ||||||||
\(601\) | −3.87714 | −0.158152 | −0.0790759 | − | 0.996869i | \(-0.525197\pi\) | ||||
−0.0790759 | + | 0.996869i | \(0.525197\pi\) | |||||||
\(602\) | 21.9638 | 0.895178 | ||||||||
\(603\) | 15.7833 | 0.642745 | ||||||||
\(604\) | 116.850 | 4.75455 | ||||||||
\(605\) | −14.4091 | −0.585815 | ||||||||
\(606\) | −57.3719 | −2.33058 | ||||||||
\(607\) | 12.0428 | 0.488803 | 0.244401 | − | 0.969674i | \(-0.421409\pi\) | ||||
0.244401 | + | 0.969674i | \(0.421409\pi\) | |||||||
\(608\) | −17.1769 | −0.696617 | ||||||||
\(609\) | 73.8073 | 2.99082 | ||||||||
\(610\) | 4.92193 | 0.199283 | ||||||||
\(611\) | −44.9362 | −1.81792 | ||||||||
\(612\) | −118.785 | −4.80160 | ||||||||
\(613\) | −14.6608 | −0.592145 | −0.296072 | − | 0.955166i | \(-0.595677\pi\) | ||||
−0.296072 | + | 0.955166i | \(0.595677\pi\) | |||||||
\(614\) | 38.6412 | 1.55943 | ||||||||
\(615\) | 41.7707 | 1.68436 | ||||||||
\(616\) | 125.539 | 5.05813 | ||||||||
\(617\) | 35.0503 | 1.41107 | 0.705536 | − | 0.708674i | \(-0.250706\pi\) | ||||
0.705536 | + | 0.708674i | \(0.250706\pi\) | |||||||
\(618\) | −25.6425 | −1.03149 | ||||||||
\(619\) | 41.5716 | 1.67090 | 0.835451 | − | 0.549565i | \(-0.185207\pi\) | ||||
0.835451 | + | 0.549565i | \(0.185207\pi\) | |||||||
\(620\) | −4.44844 | −0.178654 | ||||||||
\(621\) | −4.15760 | −0.166839 | ||||||||
\(622\) | 89.5645 | 3.59121 | ||||||||
\(623\) | 40.9023 | 1.63872 | ||||||||
\(624\) | 208.250 | 8.33668 | ||||||||
\(625\) | −8.75021 | −0.350008 | ||||||||
\(626\) | −21.4802 | −0.858523 | ||||||||
\(627\) | 10.6645 | 0.425899 | ||||||||
\(628\) | −8.03049 | −0.320452 | ||||||||
\(629\) | −68.1955 | −2.71913 | ||||||||
\(630\) | 53.6144 | 2.13605 | ||||||||
\(631\) | −33.2538 | −1.32381 | −0.661906 | − | 0.749587i | \(-0.730252\pi\) | ||||
−0.661906 | + | 0.749587i | \(0.730252\pi\) | |||||||
\(632\) | −139.500 | −5.54900 | ||||||||
\(633\) | −23.6299 | −0.939203 | ||||||||
\(634\) | −0.505071 | −0.0200589 | ||||||||
\(635\) | 22.9354 | 0.910164 | ||||||||
\(636\) | 62.6765 | 2.48528 | ||||||||
\(637\) | −18.3486 | −0.726997 | ||||||||
\(638\) | −107.084 | −4.23951 | ||||||||
\(639\) | 55.5035 | 2.19569 | ||||||||
\(640\) | 42.5802 | 1.68313 | ||||||||
\(641\) | −13.6559 | −0.539375 | −0.269687 | − | 0.962948i | \(-0.586920\pi\) | ||||
−0.269687 | + | 0.962948i | \(0.586920\pi\) | |||||||
\(642\) | −113.015 | −4.46035 | ||||||||
\(643\) | 17.6223 | 0.694955 | 0.347478 | − | 0.937688i | \(-0.387038\pi\) | ||||
0.347478 | + | 0.937688i | \(0.387038\pi\) | |||||||
\(644\) | 35.2352 | 1.38846 | ||||||||
\(645\) | −11.0529 | −0.435209 | ||||||||
\(646\) | 14.8767 | 0.585316 | ||||||||
\(647\) | 9.30266 | 0.365725 | 0.182863 | − | 0.983138i | \(-0.441464\pi\) | ||||
0.182863 | + | 0.983138i | \(0.441464\pi\) | |||||||
\(648\) | 54.5894 | 2.14447 | ||||||||
\(649\) | 31.3205 | 1.22944 | ||||||||
\(650\) | −36.0159 | −1.41266 | ||||||||
\(651\) | −4.17705 | −0.163712 | ||||||||
\(652\) | −102.764 | −4.02454 | ||||||||
\(653\) | 23.9780 | 0.938331 | 0.469166 | − | 0.883110i | \(-0.344555\pi\) | ||||
0.469166 | + | 0.883110i | \(0.344555\pi\) | |||||||
\(654\) | 17.9466 | 0.701766 | ||||||||
\(655\) | −22.9942 | −0.898459 | ||||||||
\(656\) | 130.352 | 5.08940 | ||||||||
\(657\) | 8.67979 | 0.338631 | ||||||||
\(658\) | −64.8812 | −2.52933 | ||||||||
\(659\) | −22.5794 | −0.879569 | −0.439784 | − | 0.898103i | \(-0.644945\pi\) | ||||
−0.439784 | + | 0.898103i | \(0.644945\pi\) | |||||||
\(660\) | −101.485 | −3.95029 | ||||||||
\(661\) | −4.18815 | −0.162900 | −0.0814501 | − | 0.996677i | \(-0.525955\pi\) | ||||
−0.0814501 | + | 0.996677i | \(0.525955\pi\) | |||||||
\(662\) | −8.12604 | −0.315827 | ||||||||
\(663\) | −92.0674 | −3.57560 | ||||||||
\(664\) | −28.1816 | −1.09366 | ||||||||
\(665\) | −4.87460 | −0.189029 | ||||||||
\(666\) | −116.390 | −4.51002 | ||||||||
\(667\) | −18.7099 | −0.724451 | ||||||||
\(668\) | 45.0433 | 1.74278 | ||||||||
\(669\) | −51.7400 | −2.00039 | ||||||||
\(670\) | 18.8106 | 0.726715 | ||||||||
\(671\) | −4.86785 | −0.187921 | ||||||||
\(672\) | 153.486 | 5.92084 | ||||||||
\(673\) | −2.58697 | −0.0997205 | −0.0498602 | − | 0.998756i | \(-0.515878\pi\) | ||||
−0.0498602 | + | 0.998756i | \(0.515878\pi\) | |||||||
\(674\) | −85.4796 | −3.29255 | ||||||||
\(675\) | 4.45447 | 0.171453 | ||||||||
\(676\) | 118.231 | 4.54733 | ||||||||
\(677\) | 32.4759 | 1.24815 | 0.624075 | − | 0.781364i | \(-0.285476\pi\) | ||||
0.624075 | + | 0.781364i | \(0.285476\pi\) | |||||||
\(678\) | −36.1830 | −1.38960 | ||||||||
\(679\) | −59.5830 | −2.28659 | ||||||||
\(680\) | −88.1284 | −3.37957 | ||||||||
\(681\) | −55.1832 | −2.11462 | ||||||||
\(682\) | 6.06033 | 0.232062 | ||||||||
\(683\) | −36.9000 | −1.41194 | −0.705969 | − | 0.708243i | \(-0.749488\pi\) | ||||
−0.705969 | + | 0.708243i | \(0.749488\pi\) | |||||||
\(684\) | 18.4323 | 0.704776 | ||||||||
\(685\) | −3.17657 | −0.121371 | ||||||||
\(686\) | 33.5695 | 1.28169 | ||||||||
\(687\) | 0.306310 | 0.0116864 | ||||||||
\(688\) | −34.4925 | −1.31501 | ||||||||
\(689\) | 27.0314 | 1.02982 | ||||||||
\(690\) | −24.4249 | −0.929842 | ||||||||
\(691\) | −12.7391 | −0.484616 | −0.242308 | − | 0.970199i | \(-0.577905\pi\) | ||||
−0.242308 | + | 0.970199i | \(0.577905\pi\) | |||||||
\(692\) | 49.9385 | 1.89838 | ||||||||
\(693\) | −53.0252 | −2.01426 | ||||||||
\(694\) | 10.6325 | 0.403606 | ||||||||
\(695\) | −24.7908 | −0.940368 | ||||||||
\(696\) | −207.059 | −7.84854 | ||||||||
\(697\) | −57.6287 | −2.18284 | ||||||||
\(698\) | −26.8918 | −1.01787 | ||||||||
\(699\) | −4.37296 | −0.165401 | ||||||||
\(700\) | −37.7511 | −1.42686 | ||||||||
\(701\) | −6.55587 | −0.247612 | −0.123806 | − | 0.992306i | \(-0.539510\pi\) | ||||
−0.123806 | + | 0.992306i | \(0.539510\pi\) | |||||||
\(702\) | −31.8772 | −1.20313 | ||||||||
\(703\) | 10.5821 | 0.399113 | ||||||||
\(704\) | −103.137 | −3.88713 | ||||||||
\(705\) | 32.6504 | 1.22969 | ||||||||
\(706\) | 65.0353 | 2.44763 | ||||||||
\(707\) | −25.9358 | −0.975415 | ||||||||
\(708\) | 97.2854 | 3.65621 | ||||||||
\(709\) | −15.6961 | −0.589481 | −0.294740 | − | 0.955577i | \(-0.595233\pi\) | ||||
−0.294740 | + | 0.955577i | \(0.595233\pi\) | |||||||
\(710\) | 66.1493 | 2.48254 | ||||||||
\(711\) | 58.9217 | 2.20974 | ||||||||
\(712\) | −114.747 | −4.30034 | ||||||||
\(713\) | 1.05887 | 0.0396550 | ||||||||
\(714\) | −132.932 | −4.97484 | ||||||||
\(715\) | −43.7688 | −1.63686 | ||||||||
\(716\) | 106.556 | 3.98219 | ||||||||
\(717\) | 53.3092 | 1.99087 | ||||||||
\(718\) | −9.19911 | −0.343308 | ||||||||
\(719\) | −32.9918 | −1.23039 | −0.615194 | − | 0.788376i | \(-0.710922\pi\) | ||||
−0.615194 | + | 0.788376i | \(0.710922\pi\) | |||||||
\(720\) | −84.1973 | −3.13785 | ||||||||
\(721\) | −11.5921 | −0.431711 | ||||||||
\(722\) | 49.0205 | 1.82435 | ||||||||
\(723\) | −31.5611 | −1.17377 | ||||||||
\(724\) | −60.1281 | −2.23464 | ||||||||
\(725\) | 20.0459 | 0.744485 | ||||||||
\(726\) | 60.9741 | 2.26296 | ||||||||
\(727\) | −42.2598 | −1.56733 | −0.783665 | − | 0.621184i | \(-0.786652\pi\) | ||||
−0.783665 | + | 0.621184i | \(0.786652\pi\) | |||||||
\(728\) | 168.176 | 6.23300 | ||||||||
\(729\) | −38.5491 | −1.42774 | ||||||||
\(730\) | 10.3446 | 0.382871 | ||||||||
\(731\) | 15.2491 | 0.564009 | ||||||||
\(732\) | −15.1201 | −0.558856 | ||||||||
\(733\) | 12.6849 | 0.468528 | 0.234264 | − | 0.972173i | \(-0.424732\pi\) | ||||
0.234264 | + | 0.972173i | \(0.424732\pi\) | |||||||
\(734\) | −74.0118 | −2.73182 | ||||||||
\(735\) | 13.3320 | 0.491758 | ||||||||
\(736\) | −38.9081 | −1.43417 | ||||||||
\(737\) | −18.6039 | −0.685282 | ||||||||
\(738\) | −98.3555 | −3.62052 | ||||||||
\(739\) | 31.5631 | 1.16107 | 0.580534 | − | 0.814236i | \(-0.302844\pi\) | ||||
0.580534 | + | 0.814236i | \(0.302844\pi\) | |||||||
\(740\) | −100.701 | −3.70184 | ||||||||
\(741\) | 14.2864 | 0.524825 | ||||||||
\(742\) | 39.0294 | 1.43281 | ||||||||
\(743\) | −36.3023 | −1.33180 | −0.665901 | − | 0.746040i | \(-0.731953\pi\) | ||||
−0.665901 | + | 0.746040i | \(0.731953\pi\) | |||||||
\(744\) | 11.7183 | 0.429614 | ||||||||
\(745\) | −14.5245 | −0.532136 | ||||||||
\(746\) | 17.5432 | 0.642302 | ||||||||
\(747\) | 11.9033 | 0.435520 | ||||||||
\(748\) | 140.013 | 5.11937 | ||||||||
\(749\) | −51.0901 | −1.86679 | ||||||||
\(750\) | 84.4935 | 3.08527 | ||||||||
\(751\) | −29.7824 | −1.08678 | −0.543388 | − | 0.839482i | \(-0.682859\pi\) | ||||
−0.543388 | + | 0.839482i | \(0.682859\pi\) | |||||||
\(752\) | 101.891 | 3.71558 | ||||||||
\(753\) | −70.0839 | −2.55400 | ||||||||
\(754\) | −143.453 | −5.22424 | ||||||||
\(755\) | −36.6172 | −1.33264 | ||||||||
\(756\) | −33.4130 | −1.21522 | ||||||||
\(757\) | 52.6604 | 1.91398 | 0.956988 | − | 0.290127i | \(-0.0936976\pi\) | ||||
0.956988 | + | 0.290127i | \(0.0936976\pi\) | |||||||
\(758\) | −58.0574 | −2.10874 | ||||||||
\(759\) | 24.1566 | 0.876828 | ||||||||
\(760\) | 13.6752 | 0.496052 | ||||||||
\(761\) | −52.0252 | −1.88591 | −0.942955 | − | 0.332920i | \(-0.891966\pi\) | ||||
−0.942955 | + | 0.332920i | \(0.891966\pi\) | |||||||
\(762\) | −97.0540 | −3.51589 | ||||||||
\(763\) | 8.11300 | 0.293710 | ||||||||
\(764\) | 98.8199 | 3.57518 | ||||||||
\(765\) | 37.2236 | 1.34582 | ||||||||
\(766\) | −46.5741 | −1.68279 | ||||||||
\(767\) | 41.9577 | 1.51501 | ||||||||
\(768\) | −59.2536 | −2.13813 | ||||||||
\(769\) | −11.7357 | −0.423199 | −0.211599 | − | 0.977356i | \(-0.567867\pi\) | ||||
−0.211599 | + | 0.977356i | \(0.567867\pi\) | |||||||
\(770\) | −63.1957 | −2.27741 | ||||||||
\(771\) | 4.67746 | 0.168455 | ||||||||
\(772\) | −111.329 | −4.00683 | ||||||||
\(773\) | 12.8279 | 0.461386 | 0.230693 | − | 0.973027i | \(-0.425901\pi\) | ||||
0.230693 | + | 0.973027i | \(0.425901\pi\) | |||||||
\(774\) | 26.0258 | 0.935480 | ||||||||
\(775\) | −1.13448 | −0.0407517 | ||||||||
\(776\) | 167.154 | 6.00048 | ||||||||
\(777\) | −94.5573 | −3.39222 | ||||||||
\(778\) | −1.02192 | −0.0366377 | ||||||||
\(779\) | 8.94246 | 0.320397 | ||||||||
\(780\) | −135.951 | −4.86784 | ||||||||
\(781\) | −65.4225 | −2.34100 | ||||||||
\(782\) | 33.6977 | 1.20503 | ||||||||
\(783\) | 17.7423 | 0.634059 | ||||||||
\(784\) | 41.6046 | 1.48588 | ||||||||
\(785\) | 2.51651 | 0.0898182 | ||||||||
\(786\) | 97.3028 | 3.47068 | ||||||||
\(787\) | −18.1850 | −0.648226 | −0.324113 | − | 0.946018i | \(-0.605066\pi\) | ||||
−0.324113 | + | 0.946018i | \(0.605066\pi\) | |||||||
\(788\) | −93.9254 | −3.34595 | ||||||||
\(789\) | 42.4917 | 1.51274 | ||||||||
\(790\) | 70.2231 | 2.49843 | ||||||||
\(791\) | −16.3570 | −0.581588 | ||||||||
\(792\) | 148.757 | 5.28585 | ||||||||
\(793\) | −6.52109 | −0.231571 | ||||||||
\(794\) | 50.3568 | 1.78710 | ||||||||
\(795\) | −19.6409 | −0.696591 | ||||||||
\(796\) | −106.485 | −3.77425 | ||||||||
\(797\) | 17.6620 | 0.625620 | 0.312810 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312810 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(798\) | 20.6275 | 0.730204 | ||||||||
\(799\) | −45.0460 | −1.59361 | ||||||||
\(800\) | 41.6863 | 1.47383 | ||||||||
\(801\) | 48.4669 | 1.71249 | ||||||||
\(802\) | −53.9243 | −1.90413 | ||||||||
\(803\) | −10.2309 | −0.361042 | ||||||||
\(804\) | −57.7859 | −2.03795 | ||||||||
\(805\) | −11.0416 | −0.389167 | ||||||||
\(806\) | 8.11857 | 0.285964 | ||||||||
\(807\) | 41.3442 | 1.45538 | ||||||||
\(808\) | 72.7602 | 2.55969 | ||||||||
\(809\) | 39.3413 | 1.38317 | 0.691584 | − | 0.722296i | \(-0.256913\pi\) | ||||
0.691584 | + | 0.722296i | \(0.256913\pi\) | |||||||
\(810\) | −27.4799 | −0.965545 | ||||||||
\(811\) | −19.1942 | −0.674000 | −0.337000 | − | 0.941505i | \(-0.609412\pi\) | ||||
−0.337000 | + | 0.941505i | \(0.609412\pi\) | |||||||
\(812\) | −150.364 | −5.27674 | ||||||||
\(813\) | −42.7997 | −1.50105 | ||||||||
\(814\) | 137.190 | 4.80849 | ||||||||
\(815\) | 32.2030 | 1.12802 | ||||||||
\(816\) | 208.759 | 7.30803 | ||||||||
\(817\) | −2.36626 | −0.0827850 | ||||||||
\(818\) | −6.70712 | −0.234509 | ||||||||
\(819\) | −71.0339 | −2.48212 | ||||||||
\(820\) | −85.0975 | −2.97173 | ||||||||
\(821\) | 21.0144 | 0.733407 | 0.366703 | − | 0.930338i | \(-0.380486\pi\) | ||||
0.366703 | + | 0.930338i | \(0.380486\pi\) | |||||||
\(822\) | 13.4421 | 0.468846 | ||||||||
\(823\) | 4.32938 | 0.150913 | 0.0754563 | − | 0.997149i | \(-0.475959\pi\) | ||||
0.0754563 | + | 0.997149i | \(0.475959\pi\) | |||||||
\(824\) | 32.5203 | 1.13290 | ||||||||
\(825\) | −25.8814 | −0.901076 | ||||||||
\(826\) | 60.5807 | 2.10787 | ||||||||
\(827\) | 41.2305 | 1.43372 | 0.716862 | − | 0.697215i | \(-0.245578\pi\) | ||||
0.716862 | + | 0.697215i | \(0.245578\pi\) | |||||||
\(828\) | 41.7516 | 1.45097 | ||||||||
\(829\) | 12.8129 | 0.445009 | 0.222505 | − | 0.974932i | \(-0.428577\pi\) | ||||
0.222505 | + | 0.974932i | \(0.428577\pi\) | |||||||
\(830\) | 14.1864 | 0.492418 | ||||||||
\(831\) | 22.6581 | 0.785999 | ||||||||
\(832\) | −138.165 | −4.79001 | ||||||||
\(833\) | −18.3934 | −0.637293 | ||||||||
\(834\) | 104.905 | 3.63257 | ||||||||
\(835\) | −14.1152 | −0.488477 | ||||||||
\(836\) | −21.7263 | −0.751419 | ||||||||
\(837\) | −1.00411 | −0.0347071 | ||||||||
\(838\) | −0.0507606 | −0.00175350 | ||||||||
\(839\) | 20.1927 | 0.697128 | 0.348564 | − | 0.937285i | \(-0.386669\pi\) | ||||
0.348564 | + | 0.937285i | \(0.386669\pi\) | |||||||
\(840\) | −122.196 | −4.21615 | ||||||||
\(841\) | 50.8434 | 1.75322 | ||||||||
\(842\) | 21.8652 | 0.753526 | ||||||||
\(843\) | 11.6302 | 0.400566 | ||||||||
\(844\) | 48.1400 | 1.65705 | ||||||||
\(845\) | −37.0499 | −1.27455 | ||||||||
\(846\) | −76.8804 | −2.64320 | ||||||||
\(847\) | 27.5642 | 0.947116 | ||||||||
\(848\) | −61.2927 | −2.10480 | ||||||||
\(849\) | 25.2470 | 0.866474 | ||||||||
\(850\) | −36.1039 | −1.23835 | ||||||||
\(851\) | 23.9700 | 0.821680 | ||||||||
\(852\) | −203.210 | −6.96186 | ||||||||
\(853\) | −37.4814 | −1.28334 | −0.641669 | − | 0.766982i | \(-0.721758\pi\) | ||||
−0.641669 | + | 0.766982i | \(0.721758\pi\) | |||||||
\(854\) | −9.41548 | −0.322191 | ||||||||
\(855\) | −5.77612 | −0.197539 | ||||||||
\(856\) | 143.328 | 4.89885 | ||||||||
\(857\) | 14.3079 | 0.488748 | 0.244374 | − | 0.969681i | \(-0.421418\pi\) | ||||
0.244374 | + | 0.969681i | \(0.421418\pi\) | |||||||
\(858\) | 185.213 | 6.32307 | ||||||||
\(859\) | 5.20329 | 0.177534 | 0.0887669 | − | 0.996052i | \(-0.471707\pi\) | ||||
0.0887669 | + | 0.996052i | \(0.471707\pi\) | |||||||
\(860\) | 22.5176 | 0.767845 | ||||||||
\(861\) | −79.9059 | −2.72318 | ||||||||
\(862\) | 35.3054 | 1.20251 | ||||||||
\(863\) | −15.0824 | −0.513409 | −0.256705 | − | 0.966490i | \(-0.582637\pi\) | ||||
−0.256705 | + | 0.966490i | \(0.582637\pi\) | |||||||
\(864\) | 36.8960 | 1.25523 | ||||||||
\(865\) | −15.6492 | −0.532089 | ||||||||
\(866\) | −37.5405 | −1.27568 | ||||||||
\(867\) | −48.0809 | −1.63291 | ||||||||
\(868\) | 8.50971 | 0.288838 | ||||||||
\(869\) | −69.4515 | −2.35598 | ||||||||
\(870\) | 104.232 | 3.53380 | ||||||||
\(871\) | −24.9222 | −0.844456 | ||||||||
\(872\) | −22.7602 | −0.770757 | ||||||||
\(873\) | −70.6024 | −2.38953 | ||||||||
\(874\) | −5.22900 | −0.176874 | ||||||||
\(875\) | 38.1965 | 1.29128 | ||||||||
\(876\) | −31.7785 | −1.07370 | ||||||||
\(877\) | 56.3955 | 1.90434 | 0.952170 | − | 0.305569i | \(-0.0988467\pi\) | ||||
0.952170 | + | 0.305569i | \(0.0988467\pi\) | |||||||
\(878\) | 107.166 | 3.61669 | ||||||||
\(879\) | 0.293982 | 0.00991576 | ||||||||
\(880\) | 99.2440 | 3.34552 | ||||||||
\(881\) | 0.612393 | 0.0206321 | 0.0103160 | − | 0.999947i | \(-0.496716\pi\) | ||||
0.0103160 | + | 0.999947i | \(0.496716\pi\) | |||||||
\(882\) | −31.3922 | −1.05703 | ||||||||
\(883\) | −49.2186 | −1.65634 | −0.828169 | − | 0.560478i | \(-0.810617\pi\) | ||||
−0.828169 | + | 0.560478i | \(0.810617\pi\) | |||||||
\(884\) | 187.564 | 6.30848 | ||||||||
\(885\) | −30.4863 | −1.02479 | ||||||||
\(886\) | 1.85627 | 0.0623626 | ||||||||
\(887\) | −30.9230 | −1.03829 | −0.519147 | − | 0.854685i | \(-0.673750\pi\) | ||||
−0.519147 | + | 0.854685i | \(0.673750\pi\) | |||||||
\(888\) | 265.271 | 8.90191 | ||||||||
\(889\) | −43.8746 | −1.47151 | ||||||||
\(890\) | 57.7630 | 1.93622 | ||||||||
\(891\) | 27.1780 | 0.910496 | ||||||||
\(892\) | 105.407 | 3.52930 | ||||||||
\(893\) | 6.98995 | 0.233910 | ||||||||
\(894\) | 61.4621 | 2.05560 | ||||||||
\(895\) | −33.3915 | −1.11615 | ||||||||
\(896\) | −81.4545 | −2.72120 | ||||||||
\(897\) | 32.3607 | 1.08049 | ||||||||
\(898\) | 16.1538 | 0.539058 | ||||||||
\(899\) | −4.51866 | −0.150706 | ||||||||
\(900\) | −44.7329 | −1.49110 | ||||||||
\(901\) | 27.0975 | 0.902748 | ||||||||
\(902\) | 115.932 | 3.86013 | ||||||||
\(903\) | 21.1439 | 0.703624 | ||||||||
\(904\) | 45.8879 | 1.52621 | ||||||||
\(905\) | 18.8423 | 0.626340 | ||||||||
\(906\) | 154.950 | 5.14788 | ||||||||
\(907\) | 32.6265 | 1.08335 | 0.541673 | − | 0.840589i | \(-0.317791\pi\) | ||||
0.541673 | + | 0.840589i | \(0.317791\pi\) | |||||||
\(908\) | 112.422 | 3.73086 | ||||||||
\(909\) | −30.7324 | −1.01933 | ||||||||
\(910\) | −84.6584 | −2.80640 | ||||||||
\(911\) | −38.4489 | −1.27387 | −0.636935 | − | 0.770918i | \(-0.719798\pi\) | ||||
−0.636935 | + | 0.770918i | \(0.719798\pi\) | |||||||
\(912\) | −32.3939 | −1.07267 | ||||||||
\(913\) | −14.0306 | −0.464343 | ||||||||
\(914\) | −28.8401 | −0.953944 | ||||||||
\(915\) | 4.73819 | 0.156640 | ||||||||
\(916\) | −0.624030 | −0.0206185 | ||||||||
\(917\) | 43.9871 | 1.45258 | ||||||||
\(918\) | −31.9550 | −1.05467 | ||||||||
\(919\) | −26.4208 | −0.871543 | −0.435771 | − | 0.900057i | \(-0.643524\pi\) | ||||
−0.435771 | + | 0.900057i | \(0.643524\pi\) | |||||||
\(920\) | 30.9762 | 1.02125 | ||||||||
\(921\) | 37.1987 | 1.22574 | ||||||||
\(922\) | −77.8115 | −2.56259 | ||||||||
\(923\) | −87.6415 | −2.88476 | ||||||||
\(924\) | 194.137 | 6.38662 | ||||||||
\(925\) | −25.6815 | −0.844404 | ||||||||
\(926\) | −22.0740 | −0.725396 | ||||||||
\(927\) | −13.7359 | −0.451147 | ||||||||
\(928\) | 166.038 | 5.45047 | ||||||||
\(929\) | 16.4854 | 0.540869 | 0.270434 | − | 0.962738i | \(-0.412833\pi\) | ||||
0.270434 | + | 0.962738i | \(0.412833\pi\) | |||||||
\(930\) | −5.89891 | −0.193433 | ||||||||
\(931\) | 2.85417 | 0.0935416 | ||||||||
\(932\) | 8.90883 | 0.291818 | ||||||||
\(933\) | 86.2210 | 2.82275 | ||||||||
\(934\) | 29.2612 | 0.957455 | ||||||||
\(935\) | −43.8758 | −1.43489 | ||||||||
\(936\) | 199.278 | 6.51362 | ||||||||
\(937\) | 4.93821 | 0.161324 | 0.0806621 | − | 0.996742i | \(-0.474297\pi\) | ||||
0.0806621 | + | 0.996742i | \(0.474297\pi\) | |||||||
\(938\) | −35.9839 | −1.17492 | ||||||||
\(939\) | −20.6784 | −0.674812 | ||||||||
\(940\) | −66.5172 | −2.16955 | ||||||||
\(941\) | −37.5893 | −1.22537 | −0.612687 | − | 0.790325i | \(-0.709911\pi\) | ||||
−0.612687 | + | 0.790325i | \(0.709911\pi\) | |||||||
\(942\) | −10.6489 | −0.346961 | ||||||||
\(943\) | 20.2559 | 0.659623 | ||||||||
\(944\) | −95.1375 | −3.09646 | ||||||||
\(945\) | 10.4706 | 0.340609 | ||||||||
\(946\) | −30.6769 | −0.997391 | ||||||||
\(947\) | −32.4830 | −1.05556 | −0.527779 | − | 0.849382i | \(-0.676975\pi\) | ||||
−0.527779 | + | 0.849382i | \(0.676975\pi\) | |||||||
\(948\) | −215.725 | −7.00642 | ||||||||
\(949\) | −13.7056 | −0.444903 | ||||||||
\(950\) | 5.60237 | 0.181765 | ||||||||
\(951\) | −0.486217 | −0.0157667 | ||||||||
\(952\) | 168.586 | 5.46392 | ||||||||
\(953\) | −25.6327 | −0.830324 | −0.415162 | − | 0.909747i | \(-0.636275\pi\) | ||||
−0.415162 | + | 0.909747i | \(0.636275\pi\) | |||||||
\(954\) | 46.2475 | 1.49732 | ||||||||
\(955\) | −30.9672 | −1.00207 | ||||||||
\(956\) | −108.604 | −3.51251 | ||||||||
\(957\) | −103.087 | −3.33232 | ||||||||
\(958\) | 46.7006 | 1.50883 | ||||||||
\(959\) | 6.07667 | 0.196226 | ||||||||
\(960\) | 100.390 | 3.24008 | ||||||||
\(961\) | −30.7443 | −0.991751 | ||||||||
\(962\) | 183.783 | 5.92539 | ||||||||
\(963\) | −60.5388 | −1.95083 | ||||||||
\(964\) | 64.2978 | 2.07089 | ||||||||
\(965\) | 34.8872 | 1.12306 | ||||||||
\(966\) | 46.7240 | 1.50332 | ||||||||
\(967\) | 40.1317 | 1.29055 | 0.645275 | − | 0.763950i | \(-0.276743\pi\) | ||||
0.645275 | + | 0.763950i | \(0.276743\pi\) | |||||||
\(968\) | −77.3285 | −2.48543 | ||||||||
\(969\) | 14.3213 | 0.460067 | ||||||||
\(970\) | −84.1442 | −2.70171 | ||||||||
\(971\) | −7.35583 | −0.236060 | −0.118030 | − | 0.993010i | \(-0.537658\pi\) | ||||
−0.118030 | + | 0.993010i | \(0.537658\pi\) | |||||||
\(972\) | 115.978 | 3.72001 | ||||||||
\(973\) | 47.4239 | 1.52034 | ||||||||
\(974\) | −21.7898 | −0.698190 | ||||||||
\(975\) | −34.6714 | −1.11037 | ||||||||
\(976\) | 14.7863 | 0.473298 | ||||||||
\(977\) | −33.1256 | −1.05978 | −0.529891 | − | 0.848066i | \(-0.677767\pi\) | ||||
−0.529891 | + | 0.848066i | \(0.677767\pi\) | |||||||
\(978\) | −136.271 | −4.35747 | ||||||||
\(979\) | −57.1283 | −1.82583 | ||||||||
\(980\) | −27.1606 | −0.867614 | ||||||||
\(981\) | 9.61343 | 0.306933 | ||||||||
\(982\) | 88.8354 | 2.83485 | ||||||||
\(983\) | 24.7113 | 0.788167 | 0.394083 | − | 0.919075i | \(-0.371062\pi\) | ||||
0.394083 | + | 0.919075i | \(0.371062\pi\) | |||||||
\(984\) | 224.168 | 7.14621 | ||||||||
\(985\) | 29.4334 | 0.937826 | ||||||||
\(986\) | −143.803 | −4.57962 | ||||||||
\(987\) | −62.4591 | −1.98810 | ||||||||
\(988\) | −29.1051 | −0.925955 | ||||||||
\(989\) | −5.35991 | −0.170435 | ||||||||
\(990\) | −74.8832 | −2.37994 | ||||||||
\(991\) | 7.84221 | 0.249116 | 0.124558 | − | 0.992212i | \(-0.460249\pi\) | ||||
0.124558 | + | 0.992212i | \(0.460249\pi\) | |||||||
\(992\) | −9.39677 | −0.298348 | ||||||||
\(993\) | −7.82268 | −0.248245 | ||||||||
\(994\) | −126.541 | −4.01364 | ||||||||
\(995\) | 33.3691 | 1.05787 | ||||||||
\(996\) | −43.5806 | −1.38090 | ||||||||
\(997\) | 49.9961 | 1.58339 | 0.791696 | − | 0.610915i | \(-0.209198\pi\) | ||||
0.791696 | + | 0.610915i | \(0.209198\pi\) | |||||||
\(998\) | −5.60478 | −0.177416 | ||||||||
\(999\) | −22.7304 | −0.719157 |
(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 | 6037.2.a.a.1.13 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.a.1.13 | ✓ | 243 | 1.1 | even | 1 | trivial |