Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65510 | −1.87744 | −0.938721 | − | 0.344679i | \(-0.887988\pi\) | ||||
−0.938721 | + | 0.344679i | \(0.887988\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.04957 | 2.52479 | ||||||||
\(5\) | −3.36488 | −1.50482 | −0.752411 | − | 0.658694i | \(-0.771109\pi\) | ||||
−0.752411 | + | 0.658694i | \(0.771109\pi\) | |||||||
\(6\) | 2.65510 | 1.08394 | ||||||||
\(7\) | 2.92058 | 1.10387 | 0.551937 | − | 0.833886i | \(-0.313889\pi\) | ||||
0.551937 | + | 0.833886i | \(0.313889\pi\) | |||||||
\(8\) | −8.09693 | −2.86270 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 8.93412 | 2.82522 | ||||||||
\(11\) | 6.58118 | 1.98430 | 0.992150 | − | 0.125053i | \(-0.0399102\pi\) | ||||
0.992150 | + | 0.125053i | \(0.0399102\pi\) | |||||||
\(12\) | −5.04957 | −1.45769 | ||||||||
\(13\) | −4.29464 | −1.19112 | −0.595560 | − | 0.803311i | \(-0.703070\pi\) | ||||
−0.595560 | + | 0.803311i | \(0.703070\pi\) | |||||||
\(14\) | −7.75443 | −2.07246 | ||||||||
\(15\) | 3.36488 | 0.868809 | ||||||||
\(16\) | 11.3990 | 2.84976 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.65510 | −0.625814 | ||||||||
\(19\) | −1.04245 | −0.239155 | −0.119578 | − | 0.992825i | \(-0.538154\pi\) | ||||
−0.119578 | + | 0.992825i | \(0.538154\pi\) | |||||||
\(20\) | −16.9912 | −3.79935 | ||||||||
\(21\) | −2.92058 | −0.637322 | ||||||||
\(22\) | −17.4737 | −3.72541 | ||||||||
\(23\) | −8.38753 | −1.74892 | −0.874461 | − | 0.485096i | \(-0.838785\pi\) | ||||
−0.874461 | + | 0.485096i | \(0.838785\pi\) | |||||||
\(24\) | 8.09693 | 1.65278 | ||||||||
\(25\) | 6.32245 | 1.26449 | ||||||||
\(26\) | 11.4027 | 2.23626 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 14.7477 | 2.78705 | ||||||||
\(29\) | −7.36681 | −1.36798 | −0.683991 | − | 0.729490i | \(-0.739757\pi\) | ||||
−0.683991 | + | 0.729490i | \(0.739757\pi\) | |||||||
\(30\) | −8.93412 | −1.63114 | ||||||||
\(31\) | 8.31935 | 1.49420 | 0.747100 | − | 0.664712i | \(-0.231446\pi\) | ||||
0.747100 | + | 0.664712i | \(0.231446\pi\) | |||||||
\(32\) | −14.0718 | −2.48756 | ||||||||
\(33\) | −6.58118 | −1.14564 | ||||||||
\(34\) | 2.65510 | 0.455346 | ||||||||
\(35\) | −9.82740 | −1.66113 | ||||||||
\(36\) | 5.04957 | 0.841596 | ||||||||
\(37\) | 7.07631 | 1.16334 | 0.581669 | − | 0.813426i | \(-0.302400\pi\) | ||||
0.581669 | + | 0.813426i | \(0.302400\pi\) | |||||||
\(38\) | 2.76782 | 0.449000 | ||||||||
\(39\) | 4.29464 | 0.687693 | ||||||||
\(40\) | 27.2452 | 4.30785 | ||||||||
\(41\) | 8.23725 | 1.28644 | 0.643221 | − | 0.765680i | \(-0.277598\pi\) | ||||
0.643221 | + | 0.765680i | \(0.277598\pi\) | |||||||
\(42\) | 7.75443 | 1.19653 | ||||||||
\(43\) | 6.39224 | 0.974808 | 0.487404 | − | 0.873177i | \(-0.337944\pi\) | ||||
0.487404 | + | 0.873177i | \(0.337944\pi\) | |||||||
\(44\) | 33.2321 | 5.00993 | ||||||||
\(45\) | −3.36488 | −0.501607 | ||||||||
\(46\) | 22.2698 | 3.28350 | ||||||||
\(47\) | 5.28278 | 0.770572 | 0.385286 | − | 0.922797i | \(-0.374103\pi\) | ||||
0.385286 | + | 0.922797i | \(0.374103\pi\) | |||||||
\(48\) | −11.3990 | −1.64531 | ||||||||
\(49\) | 1.52977 | 0.218538 | ||||||||
\(50\) | −16.7867 | −2.37400 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −21.6861 | −3.00732 | ||||||||
\(53\) | 0.314028 | 0.0431350 | 0.0215675 | − | 0.999767i | \(-0.493134\pi\) | ||||
0.0215675 | + | 0.999767i | \(0.493134\pi\) | |||||||
\(54\) | 2.65510 | 0.361314 | ||||||||
\(55\) | −22.1449 | −2.98602 | ||||||||
\(56\) | −23.6477 | −3.16006 | ||||||||
\(57\) | 1.04245 | 0.138076 | ||||||||
\(58\) | 19.5596 | 2.56831 | ||||||||
\(59\) | 12.4816 | 1.62496 | 0.812482 | − | 0.582987i | \(-0.198116\pi\) | ||||
0.812482 | + | 0.582987i | \(0.198116\pi\) | |||||||
\(60\) | 16.9912 | 2.19356 | ||||||||
\(61\) | −9.42298 | −1.20649 | −0.603245 | − | 0.797556i | \(-0.706126\pi\) | ||||
−0.603245 | + | 0.797556i | \(0.706126\pi\) | |||||||
\(62\) | −22.0887 | −2.80527 | ||||||||
\(63\) | 2.92058 | 0.367958 | ||||||||
\(64\) | 14.5639 | 1.82049 | ||||||||
\(65\) | 14.4510 | 1.79242 | ||||||||
\(66\) | 17.4737 | 2.15086 | ||||||||
\(67\) | 1.16403 | 0.142208 | 0.0711041 | − | 0.997469i | \(-0.477348\pi\) | ||||
0.0711041 | + | 0.997469i | \(0.477348\pi\) | |||||||
\(68\) | −5.04957 | −0.612351 | ||||||||
\(69\) | 8.38753 | 1.00974 | ||||||||
\(70\) | 26.0928 | 3.11868 | ||||||||
\(71\) | −9.32796 | −1.10702 | −0.553512 | − | 0.832841i | \(-0.686713\pi\) | ||||
−0.553512 | + | 0.832841i | \(0.686713\pi\) | |||||||
\(72\) | −8.09693 | −0.954233 | ||||||||
\(73\) | −3.35625 | −0.392819 | −0.196409 | − | 0.980522i | \(-0.562928\pi\) | ||||
−0.196409 | + | 0.980522i | \(0.562928\pi\) | |||||||
\(74\) | −18.7883 | −2.18410 | ||||||||
\(75\) | −6.32245 | −0.730053 | ||||||||
\(76\) | −5.26394 | −0.603815 | ||||||||
\(77\) | 19.2208 | 2.19042 | ||||||||
\(78\) | −11.4027 | −1.29110 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −38.3565 | −4.28838 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −21.8708 | −2.41522 | ||||||||
\(83\) | −6.00075 | −0.658668 | −0.329334 | − | 0.944213i | \(-0.606824\pi\) | ||||
−0.329334 | + | 0.944213i | \(0.606824\pi\) | |||||||
\(84\) | −14.7477 | −1.60910 | ||||||||
\(85\) | 3.36488 | 0.364973 | ||||||||
\(86\) | −16.9721 | −1.83014 | ||||||||
\(87\) | 7.36681 | 0.789805 | ||||||||
\(88\) | −53.2874 | −5.68045 | ||||||||
\(89\) | −0.846116 | −0.0896881 | −0.0448440 | − | 0.998994i | \(-0.514279\pi\) | ||||
−0.0448440 | + | 0.998994i | \(0.514279\pi\) | |||||||
\(90\) | 8.93412 | 0.941738 | ||||||||
\(91\) | −12.5428 | −1.31485 | ||||||||
\(92\) | −42.3535 | −4.41565 | ||||||||
\(93\) | −8.31935 | −0.862677 | ||||||||
\(94\) | −14.0263 | −1.44670 | ||||||||
\(95\) | 3.50773 | 0.359886 | ||||||||
\(96\) | 14.0718 | 1.43619 | ||||||||
\(97\) | 1.99768 | 0.202833 | 0.101417 | − | 0.994844i | \(-0.467662\pi\) | ||||
0.101417 | + | 0.994844i | \(0.467662\pi\) | |||||||
\(98\) | −4.06169 | −0.410293 | ||||||||
\(99\) | 6.58118 | 0.661433 | ||||||||
\(100\) | 31.9257 | 3.19257 | ||||||||
\(101\) | −1.00288 | −0.0997907 | −0.0498954 | − | 0.998754i | \(-0.515889\pi\) | ||||
−0.0498954 | + | 0.998754i | \(0.515889\pi\) | |||||||
\(102\) | −2.65510 | −0.262894 | ||||||||
\(103\) | −5.50565 | −0.542488 | −0.271244 | − | 0.962511i | \(-0.587435\pi\) | ||||
−0.271244 | + | 0.962511i | \(0.587435\pi\) | |||||||
\(104\) | 34.7734 | 3.40981 | ||||||||
\(105\) | 9.82740 | 0.959056 | ||||||||
\(106\) | −0.833776 | −0.0809835 | ||||||||
\(107\) | −2.49209 | −0.240920 | −0.120460 | − | 0.992718i | \(-0.538437\pi\) | ||||
−0.120460 | + | 0.992718i | \(0.538437\pi\) | |||||||
\(108\) | −5.04957 | −0.485895 | ||||||||
\(109\) | 8.18412 | 0.783897 | 0.391948 | − | 0.919987i | \(-0.371801\pi\) | ||||
0.391948 | + | 0.919987i | \(0.371801\pi\) | |||||||
\(110\) | 58.7970 | 5.60607 | ||||||||
\(111\) | −7.07631 | −0.671653 | ||||||||
\(112\) | 33.2918 | 3.14578 | ||||||||
\(113\) | −15.5682 | −1.46453 | −0.732266 | − | 0.681018i | \(-0.761537\pi\) | ||||
−0.732266 | + | 0.681018i | \(0.761537\pi\) | |||||||
\(114\) | −2.76782 | −0.259230 | ||||||||
\(115\) | 28.2231 | 2.63182 | ||||||||
\(116\) | −37.1992 | −3.45386 | ||||||||
\(117\) | −4.29464 | −0.397040 | ||||||||
\(118\) | −33.1399 | −3.05077 | ||||||||
\(119\) | −2.92058 | −0.267729 | ||||||||
\(120\) | −27.2452 | −2.48714 | ||||||||
\(121\) | 32.3119 | 2.93745 | ||||||||
\(122\) | 25.0190 | 2.26511 | ||||||||
\(123\) | −8.23725 | −0.742728 | ||||||||
\(124\) | 42.0092 | 3.77254 | ||||||||
\(125\) | −4.44988 | −0.398009 | ||||||||
\(126\) | −7.75443 | −0.690820 | ||||||||
\(127\) | −13.3078 | −1.18088 | −0.590438 | − | 0.807083i | \(-0.701045\pi\) | ||||
−0.590438 | + | 0.807083i | \(0.701045\pi\) | |||||||
\(128\) | −10.5252 | −0.930303 | ||||||||
\(129\) | −6.39224 | −0.562806 | ||||||||
\(130\) | −38.3688 | −3.36517 | ||||||||
\(131\) | 4.45114 | 0.388898 | 0.194449 | − | 0.980913i | \(-0.437708\pi\) | ||||
0.194449 | + | 0.980913i | \(0.437708\pi\) | |||||||
\(132\) | −33.2321 | −2.89249 | ||||||||
\(133\) | −3.04456 | −0.263997 | ||||||||
\(134\) | −3.09061 | −0.266988 | ||||||||
\(135\) | 3.36488 | 0.289603 | ||||||||
\(136\) | 8.09693 | 0.694306 | ||||||||
\(137\) | −10.9602 | −0.936394 | −0.468197 | − | 0.883624i | \(-0.655096\pi\) | ||||
−0.468197 | + | 0.883624i | \(0.655096\pi\) | |||||||
\(138\) | −22.2698 | −1.89573 | ||||||||
\(139\) | 4.74131 | 0.402153 | 0.201076 | − | 0.979576i | \(-0.435556\pi\) | ||||
0.201076 | + | 0.979576i | \(0.435556\pi\) | |||||||
\(140\) | −49.6242 | −4.19401 | ||||||||
\(141\) | −5.28278 | −0.444890 | ||||||||
\(142\) | 24.7667 | 2.07837 | ||||||||
\(143\) | −28.2638 | −2.36354 | ||||||||
\(144\) | 11.3990 | 0.949920 | ||||||||
\(145\) | 24.7885 | 2.05857 | ||||||||
\(146\) | 8.91118 | 0.737494 | ||||||||
\(147\) | −1.52977 | −0.126173 | ||||||||
\(148\) | 35.7323 | 2.93718 | ||||||||
\(149\) | 14.1244 | 1.15712 | 0.578558 | − | 0.815641i | \(-0.303616\pi\) | ||||
0.578558 | + | 0.815641i | \(0.303616\pi\) | |||||||
\(150\) | 16.7867 | 1.37063 | ||||||||
\(151\) | −19.7812 | −1.60977 | −0.804884 | − | 0.593432i | \(-0.797772\pi\) | ||||
−0.804884 | + | 0.593432i | \(0.797772\pi\) | |||||||
\(152\) | 8.44067 | 0.684629 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −51.0333 | −4.11238 | ||||||||
\(155\) | −27.9937 | −2.24851 | ||||||||
\(156\) | 21.6861 | 1.73628 | ||||||||
\(157\) | −15.2035 | −1.21337 | −0.606685 | − | 0.794942i | \(-0.707501\pi\) | ||||
−0.606685 | + | 0.794942i | \(0.707501\pi\) | |||||||
\(158\) | −2.65510 | −0.211229 | ||||||||
\(159\) | −0.314028 | −0.0249040 | ||||||||
\(160\) | 47.3499 | 3.74334 | ||||||||
\(161\) | −24.4964 | −1.93059 | ||||||||
\(162\) | −2.65510 | −0.208605 | ||||||||
\(163\) | −14.2436 | −1.11564 | −0.557821 | − | 0.829961i | \(-0.688363\pi\) | ||||
−0.557821 | + | 0.829961i | \(0.688363\pi\) | |||||||
\(164\) | 41.5946 | 3.24799 | ||||||||
\(165\) | 22.1449 | 1.72398 | ||||||||
\(166\) | 15.9326 | 1.23661 | ||||||||
\(167\) | 13.6600 | 1.05704 | 0.528522 | − | 0.848919i | \(-0.322746\pi\) | ||||
0.528522 | + | 0.848919i | \(0.322746\pi\) | |||||||
\(168\) | 23.6477 | 1.82446 | ||||||||
\(169\) | 5.44394 | 0.418765 | ||||||||
\(170\) | −8.93412 | −0.685215 | ||||||||
\(171\) | −1.04245 | −0.0797184 | ||||||||
\(172\) | 32.2781 | 2.46118 | ||||||||
\(173\) | 21.3641 | 1.62428 | 0.812142 | − | 0.583460i | \(-0.198302\pi\) | ||||
0.812142 | + | 0.583460i | \(0.198302\pi\) | |||||||
\(174\) | −19.5596 | −1.48281 | ||||||||
\(175\) | 18.4652 | 1.39584 | ||||||||
\(176\) | 75.0191 | 5.65478 | ||||||||
\(177\) | −12.4816 | −0.938173 | ||||||||
\(178\) | 2.24652 | 0.168384 | ||||||||
\(179\) | 14.5126 | 1.08472 | 0.542360 | − | 0.840146i | \(-0.317531\pi\) | ||||
0.542360 | + | 0.840146i | \(0.317531\pi\) | |||||||
\(180\) | −16.9912 | −1.26645 | ||||||||
\(181\) | 3.80550 | 0.282861 | 0.141430 | − | 0.989948i | \(-0.454830\pi\) | ||||
0.141430 | + | 0.989948i | \(0.454830\pi\) | |||||||
\(182\) | 33.3025 | 2.46855 | ||||||||
\(183\) | 9.42298 | 0.696567 | ||||||||
\(184\) | 67.9133 | 5.00663 | ||||||||
\(185\) | −23.8110 | −1.75062 | ||||||||
\(186\) | 22.0887 | 1.61963 | ||||||||
\(187\) | −6.58118 | −0.481263 | ||||||||
\(188\) | 26.6758 | 1.94553 | ||||||||
\(189\) | −2.92058 | −0.212441 | ||||||||
\(190\) | −9.31339 | −0.675665 | ||||||||
\(191\) | −12.1174 | −0.876785 | −0.438392 | − | 0.898784i | \(-0.644452\pi\) | ||||
−0.438392 | + | 0.898784i | \(0.644452\pi\) | |||||||
\(192\) | −14.5639 | −1.05106 | ||||||||
\(193\) | 19.5362 | 1.40625 | 0.703124 | − | 0.711067i | \(-0.251788\pi\) | ||||
0.703124 | + | 0.711067i | \(0.251788\pi\) | |||||||
\(194\) | −5.30404 | −0.380808 | ||||||||
\(195\) | −14.4510 | −1.03486 | ||||||||
\(196\) | 7.72467 | 0.551762 | ||||||||
\(197\) | 18.7785 | 1.33792 | 0.668958 | − | 0.743300i | \(-0.266741\pi\) | ||||
0.668958 | + | 0.743300i | \(0.266741\pi\) | |||||||
\(198\) | −17.4737 | −1.24180 | ||||||||
\(199\) | −16.7373 | −1.18647 | −0.593237 | − | 0.805028i | \(-0.702150\pi\) | ||||
−0.593237 | + | 0.805028i | \(0.702150\pi\) | |||||||
\(200\) | −51.1924 | −3.61985 | ||||||||
\(201\) | −1.16403 | −0.0821040 | ||||||||
\(202\) | 2.66276 | 0.187351 | ||||||||
\(203\) | −21.5153 | −1.51008 | ||||||||
\(204\) | 5.04957 | 0.353541 | ||||||||
\(205\) | −27.7174 | −1.93587 | ||||||||
\(206\) | 14.6181 | 1.01849 | ||||||||
\(207\) | −8.38753 | −0.582974 | ||||||||
\(208\) | −48.9548 | −3.39440 | ||||||||
\(209\) | −6.86057 | −0.474555 | ||||||||
\(210\) | −26.0928 | −1.80057 | ||||||||
\(211\) | 8.19938 | 0.564468 | 0.282234 | − | 0.959346i | \(-0.408924\pi\) | ||||
0.282234 | + | 0.959346i | \(0.408924\pi\) | |||||||
\(212\) | 1.58571 | 0.108907 | ||||||||
\(213\) | 9.32796 | 0.639141 | ||||||||
\(214\) | 6.61676 | 0.452313 | ||||||||
\(215\) | −21.5092 | −1.46691 | ||||||||
\(216\) | 8.09693 | 0.550926 | ||||||||
\(217\) | 24.2973 | 1.64941 | ||||||||
\(218\) | −21.7297 | −1.47172 | ||||||||
\(219\) | 3.35625 | 0.226794 | ||||||||
\(220\) | −111.822 | −7.53906 | ||||||||
\(221\) | 4.29464 | 0.288889 | ||||||||
\(222\) | 18.7883 | 1.26099 | ||||||||
\(223\) | 7.62776 | 0.510793 | 0.255396 | − | 0.966836i | \(-0.417794\pi\) | ||||
0.255396 | + | 0.966836i | \(0.417794\pi\) | |||||||
\(224\) | −41.0977 | −2.74595 | ||||||||
\(225\) | 6.32245 | 0.421496 | ||||||||
\(226\) | 41.3352 | 2.74957 | ||||||||
\(227\) | 23.9586 | 1.59019 | 0.795094 | − | 0.606487i | \(-0.207422\pi\) | ||||
0.795094 | + | 0.606487i | \(0.207422\pi\) | |||||||
\(228\) | 5.26394 | 0.348613 | ||||||||
\(229\) | 0.919568 | 0.0607668 | 0.0303834 | − | 0.999538i | \(-0.490327\pi\) | ||||
0.0303834 | + | 0.999538i | \(0.490327\pi\) | |||||||
\(230\) | −74.9352 | −4.94108 | ||||||||
\(231\) | −19.2208 | −1.26464 | ||||||||
\(232\) | 59.6485 | 3.91612 | ||||||||
\(233\) | −28.1339 | −1.84311 | −0.921556 | − | 0.388246i | \(-0.873081\pi\) | ||||
−0.921556 | + | 0.388246i | \(0.873081\pi\) | |||||||
\(234\) | 11.4027 | 0.745419 | ||||||||
\(235\) | −17.7759 | −1.15957 | ||||||||
\(236\) | 63.0267 | 4.10269 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 7.75443 | 0.502645 | ||||||||
\(239\) | −24.5036 | −1.58501 | −0.792504 | − | 0.609867i | \(-0.791223\pi\) | ||||
−0.792504 | + | 0.609867i | \(0.791223\pi\) | |||||||
\(240\) | 38.3565 | 2.47590 | ||||||||
\(241\) | −1.08480 | −0.0698781 | −0.0349391 | − | 0.999389i | \(-0.511124\pi\) | ||||
−0.0349391 | + | 0.999389i | \(0.511124\pi\) | |||||||
\(242\) | −85.7915 | −5.51488 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −47.5820 | −3.04613 | ||||||||
\(245\) | −5.14749 | −0.328861 | ||||||||
\(246\) | 21.8708 | 1.39443 | ||||||||
\(247\) | 4.47696 | 0.284862 | ||||||||
\(248\) | −67.3612 | −4.27744 | ||||||||
\(249\) | 6.00075 | 0.380282 | ||||||||
\(250\) | 11.8149 | 0.747239 | ||||||||
\(251\) | −5.96177 | −0.376303 | −0.188152 | − | 0.982140i | \(-0.560250\pi\) | ||||
−0.188152 | + | 0.982140i | \(0.560250\pi\) | |||||||
\(252\) | 14.7477 | 0.929016 | ||||||||
\(253\) | −55.1999 | −3.47038 | ||||||||
\(254\) | 35.3336 | 2.21703 | ||||||||
\(255\) | −3.36488 | −0.210717 | ||||||||
\(256\) | −1.18242 | −0.0739016 | ||||||||
\(257\) | 16.0042 | 0.998311 | 0.499156 | − | 0.866512i | \(-0.333644\pi\) | ||||
0.499156 | + | 0.866512i | \(0.333644\pi\) | |||||||
\(258\) | 16.9721 | 1.05663 | ||||||||
\(259\) | 20.6669 | 1.28418 | ||||||||
\(260\) | 72.9712 | 4.52548 | ||||||||
\(261\) | −7.36681 | −0.455994 | ||||||||
\(262\) | −11.8182 | −0.730133 | ||||||||
\(263\) | −15.8490 | −0.977294 | −0.488647 | − | 0.872482i | \(-0.662509\pi\) | ||||
−0.488647 | + | 0.872482i | \(0.662509\pi\) | |||||||
\(264\) | 53.2874 | 3.27961 | ||||||||
\(265\) | −1.05667 | −0.0649105 | ||||||||
\(266\) | 8.08363 | 0.495639 | ||||||||
\(267\) | 0.846116 | 0.0517814 | ||||||||
\(268\) | 5.87783 | 0.359046 | ||||||||
\(269\) | 17.2651 | 1.05267 | 0.526337 | − | 0.850276i | \(-0.323565\pi\) | ||||
0.526337 | + | 0.850276i | \(0.323565\pi\) | |||||||
\(270\) | −8.93412 | −0.543713 | ||||||||
\(271\) | 1.79677 | 0.109146 | 0.0545731 | − | 0.998510i | \(-0.482620\pi\) | ||||
0.0545731 | + | 0.998510i | \(0.482620\pi\) | |||||||
\(272\) | −11.3990 | −0.691168 | ||||||||
\(273\) | 12.5428 | 0.759127 | ||||||||
\(274\) | 29.1005 | 1.75802 | ||||||||
\(275\) | 41.6092 | 2.50913 | ||||||||
\(276\) | 42.3535 | 2.54938 | ||||||||
\(277\) | 20.6950 | 1.24344 | 0.621720 | − | 0.783240i | \(-0.286434\pi\) | ||||
0.621720 | + | 0.783240i | \(0.286434\pi\) | |||||||
\(278\) | −12.5887 | −0.755018 | ||||||||
\(279\) | 8.31935 | 0.498067 | ||||||||
\(280\) | 79.5718 | 4.75532 | ||||||||
\(281\) | 17.7871 | 1.06109 | 0.530545 | − | 0.847657i | \(-0.321987\pi\) | ||||
0.530545 | + | 0.847657i | \(0.321987\pi\) | |||||||
\(282\) | 14.0263 | 0.835255 | ||||||||
\(283\) | 7.33028 | 0.435740 | 0.217870 | − | 0.975978i | \(-0.430089\pi\) | ||||
0.217870 | + | 0.975978i | \(0.430089\pi\) | |||||||
\(284\) | −47.1022 | −2.79500 | ||||||||
\(285\) | −3.50773 | −0.207780 | ||||||||
\(286\) | 75.0433 | 4.43740 | ||||||||
\(287\) | 24.0575 | 1.42007 | ||||||||
\(288\) | −14.0718 | −0.829187 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −65.8159 | −3.86484 | ||||||||
\(291\) | −1.99768 | −0.117106 | ||||||||
\(292\) | −16.9476 | −0.991784 | ||||||||
\(293\) | 12.7741 | 0.746272 | 0.373136 | − | 0.927777i | \(-0.378282\pi\) | ||||
0.373136 | + | 0.927777i | \(0.378282\pi\) | |||||||
\(294\) | 4.06169 | 0.236883 | ||||||||
\(295\) | −41.9991 | −2.44528 | ||||||||
\(296\) | −57.2964 | −3.33028 | ||||||||
\(297\) | −6.58118 | −0.381879 | ||||||||
\(298\) | −37.5017 | −2.17242 | ||||||||
\(299\) | 36.0214 | 2.08317 | ||||||||
\(300\) | −31.9257 | −1.84323 | ||||||||
\(301\) | 18.6690 | 1.07607 | ||||||||
\(302\) | 52.5210 | 3.02225 | ||||||||
\(303\) | 1.00288 | 0.0576142 | ||||||||
\(304\) | −11.8830 | −0.681535 | ||||||||
\(305\) | 31.7072 | 1.81555 | ||||||||
\(306\) | 2.65510 | 0.151782 | ||||||||
\(307\) | 19.4378 | 1.10937 | 0.554687 | − | 0.832059i | \(-0.312838\pi\) | ||||
0.554687 | + | 0.832059i | \(0.312838\pi\) | |||||||
\(308\) | 97.0570 | 5.53034 | ||||||||
\(309\) | 5.50565 | 0.313205 | ||||||||
\(310\) | 74.3261 | 4.22144 | ||||||||
\(311\) | 2.49362 | 0.141400 | 0.0707001 | − | 0.997498i | \(-0.477477\pi\) | ||||
0.0707001 | + | 0.997498i | \(0.477477\pi\) | |||||||
\(312\) | −34.7734 | −1.96866 | ||||||||
\(313\) | −5.46325 | −0.308801 | −0.154401 | − | 0.988008i | \(-0.549345\pi\) | ||||
−0.154401 | + | 0.988008i | \(0.549345\pi\) | |||||||
\(314\) | 40.3668 | 2.27803 | ||||||||
\(315\) | −9.82740 | −0.553711 | ||||||||
\(316\) | 5.04957 | 0.284061 | ||||||||
\(317\) | 8.53332 | 0.479279 | 0.239639 | − | 0.970862i | \(-0.422971\pi\) | ||||
0.239639 | + | 0.970862i | \(0.422971\pi\) | |||||||
\(318\) | 0.833776 | 0.0467558 | ||||||||
\(319\) | −48.4823 | −2.71449 | ||||||||
\(320\) | −49.0059 | −2.73951 | ||||||||
\(321\) | 2.49209 | 0.139095 | ||||||||
\(322\) | 65.0406 | 3.62457 | ||||||||
\(323\) | 1.04245 | 0.0580036 | ||||||||
\(324\) | 5.04957 | 0.280532 | ||||||||
\(325\) | −27.1526 | −1.50616 | ||||||||
\(326\) | 37.8182 | 2.09455 | ||||||||
\(327\) | −8.18412 | −0.452583 | ||||||||
\(328\) | −66.6965 | −3.68270 | ||||||||
\(329\) | 15.4288 | 0.850615 | ||||||||
\(330\) | −58.7970 | −3.23667 | ||||||||
\(331\) | −9.15171 | −0.503023 | −0.251512 | − | 0.967854i | \(-0.580928\pi\) | ||||
−0.251512 | + | 0.967854i | \(0.580928\pi\) | |||||||
\(332\) | −30.3012 | −1.66300 | ||||||||
\(333\) | 7.07631 | 0.387779 | ||||||||
\(334\) | −36.2688 | −1.98454 | ||||||||
\(335\) | −3.91681 | −0.213998 | ||||||||
\(336\) | −33.2918 | −1.81622 | ||||||||
\(337\) | −22.5816 | −1.23010 | −0.615050 | − | 0.788488i | \(-0.710864\pi\) | ||||
−0.615050 | + | 0.788488i | \(0.710864\pi\) | |||||||
\(338\) | −14.4542 | −0.786207 | ||||||||
\(339\) | 15.5682 | 0.845548 | ||||||||
\(340\) | 16.9912 | 0.921479 | ||||||||
\(341\) | 54.7512 | 2.96494 | ||||||||
\(342\) | 2.76782 | 0.149667 | ||||||||
\(343\) | −15.9762 | −0.862635 | ||||||||
\(344\) | −51.7576 | −2.79058 | ||||||||
\(345\) | −28.2231 | −1.51948 | ||||||||
\(346\) | −56.7239 | −3.04950 | ||||||||
\(347\) | −19.8752 | −1.06696 | −0.533478 | − | 0.845814i | \(-0.679115\pi\) | ||||
−0.533478 | + | 0.845814i | \(0.679115\pi\) | |||||||
\(348\) | 37.1992 | 1.99409 | ||||||||
\(349\) | −6.31241 | −0.337895 | −0.168948 | − | 0.985625i | \(-0.554037\pi\) | ||||
−0.168948 | + | 0.985625i | \(0.554037\pi\) | |||||||
\(350\) | −49.0270 | −2.62060 | ||||||||
\(351\) | 4.29464 | 0.229231 | ||||||||
\(352\) | −92.6088 | −4.93607 | ||||||||
\(353\) | 8.21038 | 0.436995 | 0.218497 | − | 0.975838i | \(-0.429885\pi\) | ||||
0.218497 | + | 0.975838i | \(0.429885\pi\) | |||||||
\(354\) | 33.1399 | 1.76137 | ||||||||
\(355\) | 31.3875 | 1.66588 | ||||||||
\(356\) | −4.27252 | −0.226443 | ||||||||
\(357\) | 2.92058 | 0.154573 | ||||||||
\(358\) | −38.5323 | −2.03650 | ||||||||
\(359\) | 10.2711 | 0.542087 | 0.271043 | − | 0.962567i | \(-0.412631\pi\) | ||||
0.271043 | + | 0.962567i | \(0.412631\pi\) | |||||||
\(360\) | 27.2452 | 1.43595 | ||||||||
\(361\) | −17.9133 | −0.942805 | ||||||||
\(362\) | −10.1040 | −0.531054 | ||||||||
\(363\) | −32.3119 | −1.69594 | ||||||||
\(364\) | −63.3359 | −3.31970 | ||||||||
\(365\) | 11.2934 | 0.591122 | ||||||||
\(366\) | −25.0190 | −1.30776 | ||||||||
\(367\) | 23.1479 | 1.20831 | 0.604156 | − | 0.796866i | \(-0.293510\pi\) | ||||
0.604156 | + | 0.796866i | \(0.293510\pi\) | |||||||
\(368\) | −95.6098 | −4.98401 | ||||||||
\(369\) | 8.23725 | 0.428814 | ||||||||
\(370\) | 63.2205 | 3.28668 | ||||||||
\(371\) | 0.917142 | 0.0476156 | ||||||||
\(372\) | −42.0092 | −2.17807 | ||||||||
\(373\) | 13.2727 | 0.687237 | 0.343618 | − | 0.939109i | \(-0.388347\pi\) | ||||
0.343618 | + | 0.939109i | \(0.388347\pi\) | |||||||
\(374\) | 17.4737 | 0.903544 | ||||||||
\(375\) | 4.44988 | 0.229791 | ||||||||
\(376\) | −42.7743 | −2.20592 | ||||||||
\(377\) | 31.6378 | 1.62943 | ||||||||
\(378\) | 7.75443 | 0.398845 | ||||||||
\(379\) | −21.5358 | −1.10622 | −0.553109 | − | 0.833109i | \(-0.686559\pi\) | ||||
−0.553109 | + | 0.833109i | \(0.686559\pi\) | |||||||
\(380\) | 17.7126 | 0.908635 | ||||||||
\(381\) | 13.3078 | 0.681779 | ||||||||
\(382\) | 32.1730 | 1.64611 | ||||||||
\(383\) | 2.53977 | 0.129776 | 0.0648881 | − | 0.997893i | \(-0.479331\pi\) | ||||
0.0648881 | + | 0.997893i | \(0.479331\pi\) | |||||||
\(384\) | 10.5252 | 0.537110 | ||||||||
\(385\) | −64.6759 | −3.29619 | ||||||||
\(386\) | −51.8707 | −2.64015 | ||||||||
\(387\) | 6.39224 | 0.324936 | ||||||||
\(388\) | 10.0874 | 0.512111 | ||||||||
\(389\) | 2.85208 | 0.144606 | 0.0723030 | − | 0.997383i | \(-0.476965\pi\) | ||||
0.0723030 | + | 0.997383i | \(0.476965\pi\) | |||||||
\(390\) | 38.3688 | 1.94288 | ||||||||
\(391\) | 8.38753 | 0.424176 | ||||||||
\(392\) | −12.3864 | −0.625609 | ||||||||
\(393\) | −4.45114 | −0.224530 | ||||||||
\(394\) | −49.8590 | −2.51186 | ||||||||
\(395\) | −3.36488 | −0.169306 | ||||||||
\(396\) | 33.2321 | 1.66998 | ||||||||
\(397\) | 29.2386 | 1.46744 | 0.733722 | − | 0.679450i | \(-0.237782\pi\) | ||||
0.733722 | + | 0.679450i | \(0.237782\pi\) | |||||||
\(398\) | 44.4392 | 2.22754 | ||||||||
\(399\) | 3.04456 | 0.152419 | ||||||||
\(400\) | 72.0698 | 3.60349 | ||||||||
\(401\) | 9.36875 | 0.467853 | 0.233926 | − | 0.972254i | \(-0.424843\pi\) | ||||
0.233926 | + | 0.972254i | \(0.424843\pi\) | |||||||
\(402\) | 3.09061 | 0.154145 | ||||||||
\(403\) | −35.7286 | −1.77977 | ||||||||
\(404\) | −5.06414 | −0.251950 | ||||||||
\(405\) | −3.36488 | −0.167202 | ||||||||
\(406\) | 57.1254 | 2.83509 | ||||||||
\(407\) | 46.5704 | 2.30841 | ||||||||
\(408\) | −8.09693 | −0.400858 | ||||||||
\(409\) | 31.7885 | 1.57184 | 0.785920 | − | 0.618329i | \(-0.212190\pi\) | ||||
0.785920 | + | 0.618329i | \(0.212190\pi\) | |||||||
\(410\) | 73.5926 | 3.63448 | ||||||||
\(411\) | 10.9602 | 0.540627 | ||||||||
\(412\) | −27.8012 | −1.36967 | ||||||||
\(413\) | 36.4534 | 1.79376 | ||||||||
\(414\) | 22.2698 | 1.09450 | ||||||||
\(415\) | 20.1918 | 0.991178 | ||||||||
\(416\) | 60.4332 | 2.96298 | ||||||||
\(417\) | −4.74131 | −0.232183 | ||||||||
\(418\) | 18.2155 | 0.890950 | ||||||||
\(419\) | 24.8895 | 1.21593 | 0.607966 | − | 0.793963i | \(-0.291986\pi\) | ||||
0.607966 | + | 0.793963i | \(0.291986\pi\) | |||||||
\(420\) | 49.6242 | 2.42141 | ||||||||
\(421\) | −31.0362 | −1.51261 | −0.756306 | − | 0.654218i | \(-0.772998\pi\) | ||||
−0.756306 | + | 0.654218i | \(0.772998\pi\) | |||||||
\(422\) | −21.7702 | −1.05976 | ||||||||
\(423\) | 5.28278 | 0.256857 | ||||||||
\(424\) | −2.54266 | −0.123483 | ||||||||
\(425\) | −6.32245 | −0.306684 | ||||||||
\(426\) | −24.7667 | −1.19995 | ||||||||
\(427\) | −27.5205 | −1.33181 | ||||||||
\(428\) | −12.5840 | −0.608271 | ||||||||
\(429\) | 28.2638 | 1.36459 | ||||||||
\(430\) | 57.1090 | 2.75404 | ||||||||
\(431\) | −31.8529 | −1.53430 | −0.767151 | − | 0.641467i | \(-0.778326\pi\) | ||||
−0.767151 | + | 0.641467i | \(0.778326\pi\) | |||||||
\(432\) | −11.3990 | −0.548437 | ||||||||
\(433\) | 14.8952 | 0.715820 | 0.357910 | − | 0.933756i | \(-0.383490\pi\) | ||||
0.357910 | + | 0.933756i | \(0.383490\pi\) | |||||||
\(434\) | −64.5119 | −3.09667 | ||||||||
\(435\) | −24.7885 | −1.18852 | ||||||||
\(436\) | 41.3263 | 1.97917 | ||||||||
\(437\) | 8.74361 | 0.418263 | ||||||||
\(438\) | −8.91118 | −0.425793 | ||||||||
\(439\) | −0.624805 | −0.0298203 | −0.0149102 | − | 0.999889i | \(-0.504746\pi\) | ||||
−0.0149102 | + | 0.999889i | \(0.504746\pi\) | |||||||
\(440\) | 179.306 | 8.54807 | ||||||||
\(441\) | 1.52977 | 0.0728461 | ||||||||
\(442\) | −11.4027 | −0.542372 | ||||||||
\(443\) | 2.41810 | 0.114888 | 0.0574438 | − | 0.998349i | \(-0.481705\pi\) | ||||
0.0574438 | + | 0.998349i | \(0.481705\pi\) | |||||||
\(444\) | −35.7323 | −1.69578 | ||||||||
\(445\) | 2.84708 | 0.134965 | ||||||||
\(446\) | −20.2525 | −0.958983 | ||||||||
\(447\) | −14.1244 | −0.668061 | ||||||||
\(448\) | 42.5350 | 2.00959 | ||||||||
\(449\) | 11.1299 | 0.525254 | 0.262627 | − | 0.964897i | \(-0.415411\pi\) | ||||
0.262627 | + | 0.964897i | \(0.415411\pi\) | |||||||
\(450\) | −16.7867 | −0.791335 | ||||||||
\(451\) | 54.2108 | 2.55269 | ||||||||
\(452\) | −78.6128 | −3.69763 | ||||||||
\(453\) | 19.7812 | 0.929400 | ||||||||
\(454\) | −63.6125 | −2.98548 | ||||||||
\(455\) | 42.2052 | 1.97861 | ||||||||
\(456\) | −8.44067 | −0.395271 | ||||||||
\(457\) | 10.4726 | 0.489886 | 0.244943 | − | 0.969537i | \(-0.421231\pi\) | ||||
0.244943 | + | 0.969537i | \(0.421231\pi\) | |||||||
\(458\) | −2.44155 | −0.114086 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 142.514 | 6.64477 | ||||||||
\(461\) | −39.2782 | −1.82937 | −0.914684 | − | 0.404170i | \(-0.867560\pi\) | ||||
−0.914684 | + | 0.404170i | \(0.867560\pi\) | |||||||
\(462\) | 51.0333 | 2.37428 | ||||||||
\(463\) | −12.6819 | −0.589376 | −0.294688 | − | 0.955594i | \(-0.595216\pi\) | ||||
−0.294688 | + | 0.955594i | \(0.595216\pi\) | |||||||
\(464\) | −83.9746 | −3.89842 | ||||||||
\(465\) | 27.9937 | 1.29818 | ||||||||
\(466\) | 74.6983 | 3.46033 | ||||||||
\(467\) | 10.0949 | 0.467137 | 0.233568 | − | 0.972340i | \(-0.424960\pi\) | ||||
0.233568 | + | 0.972340i | \(0.424960\pi\) | |||||||
\(468\) | −21.6861 | −1.00244 | ||||||||
\(469\) | 3.39962 | 0.156980 | ||||||||
\(470\) | 47.1969 | 2.17703 | ||||||||
\(471\) | 15.2035 | 0.700539 | ||||||||
\(472\) | −101.063 | −4.65178 | ||||||||
\(473\) | 42.0685 | 1.93431 | ||||||||
\(474\) | 2.65510 | 0.121953 | ||||||||
\(475\) | −6.59085 | −0.302409 | ||||||||
\(476\) | −14.7477 | −0.675958 | ||||||||
\(477\) | 0.314028 | 0.0143783 | ||||||||
\(478\) | 65.0597 | 2.97576 | ||||||||
\(479\) | 42.1168 | 1.92436 | 0.962182 | − | 0.272408i | \(-0.0878202\pi\) | ||||
0.962182 | + | 0.272408i | \(0.0878202\pi\) | |||||||
\(480\) | −47.3499 | −2.16122 | ||||||||
\(481\) | −30.3902 | −1.38567 | ||||||||
\(482\) | 2.88026 | 0.131192 | ||||||||
\(483\) | 24.4964 | 1.11463 | ||||||||
\(484\) | 163.161 | 7.41643 | ||||||||
\(485\) | −6.72195 | −0.305228 | ||||||||
\(486\) | 2.65510 | 0.120438 | ||||||||
\(487\) | 5.85373 | 0.265258 | 0.132629 | − | 0.991166i | \(-0.457658\pi\) | ||||
0.132629 | + | 0.991166i | \(0.457658\pi\) | |||||||
\(488\) | 76.2972 | 3.45381 | ||||||||
\(489\) | 14.2436 | 0.644117 | ||||||||
\(490\) | 13.6671 | 0.617417 | ||||||||
\(491\) | 25.9625 | 1.17167 | 0.585835 | − | 0.810430i | \(-0.300767\pi\) | ||||
0.585835 | + | 0.810430i | \(0.300767\pi\) | |||||||
\(492\) | −41.5946 | −1.87523 | ||||||||
\(493\) | 7.36681 | 0.331784 | ||||||||
\(494\) | −11.8868 | −0.534812 | ||||||||
\(495\) | −22.1449 | −0.995339 | ||||||||
\(496\) | 94.8327 | 4.25811 | ||||||||
\(497\) | −27.2430 | −1.22202 | ||||||||
\(498\) | −15.9326 | −0.713958 | ||||||||
\(499\) | 8.40078 | 0.376070 | 0.188035 | − | 0.982162i | \(-0.439788\pi\) | ||||
0.188035 | + | 0.982162i | \(0.439788\pi\) | |||||||
\(500\) | −22.4700 | −1.00489 | ||||||||
\(501\) | −13.6600 | −0.610285 | ||||||||
\(502\) | 15.8291 | 0.706487 | ||||||||
\(503\) | 23.7472 | 1.05883 | 0.529417 | − | 0.848362i | \(-0.322411\pi\) | ||||
0.529417 | + | 0.848362i | \(0.322411\pi\) | |||||||
\(504\) | −23.6477 | −1.05335 | ||||||||
\(505\) | 3.37459 | 0.150167 | ||||||||
\(506\) | 146.561 | 6.51544 | ||||||||
\(507\) | −5.44394 | −0.241774 | ||||||||
\(508\) | −67.1987 | −2.98146 | ||||||||
\(509\) | 10.6551 | 0.472280 | 0.236140 | − | 0.971719i | \(-0.424118\pi\) | ||||
0.236140 | + | 0.971719i | \(0.424118\pi\) | |||||||
\(510\) | 8.93412 | 0.395609 | ||||||||
\(511\) | −9.80217 | −0.433622 | ||||||||
\(512\) | 24.1898 | 1.06905 | ||||||||
\(513\) | 1.04245 | 0.0460254 | ||||||||
\(514\) | −42.4927 | −1.87427 | ||||||||
\(515\) | 18.5259 | 0.816348 | ||||||||
\(516\) | −32.2781 | −1.42096 | ||||||||
\(517\) | 34.7669 | 1.52905 | ||||||||
\(518\) | −54.8727 | −2.41097 | ||||||||
\(519\) | −21.3641 | −0.937780 | ||||||||
\(520\) | −117.009 | −5.13116 | ||||||||
\(521\) | 23.2009 | 1.01645 | 0.508226 | − | 0.861224i | \(-0.330302\pi\) | ||||
0.508226 | + | 0.861224i | \(0.330302\pi\) | |||||||
\(522\) | 19.5596 | 0.856102 | ||||||||
\(523\) | 22.3541 | 0.977478 | 0.488739 | − | 0.872430i | \(-0.337457\pi\) | ||||
0.488739 | + | 0.872430i | \(0.337457\pi\) | |||||||
\(524\) | 22.4764 | 0.981885 | ||||||||
\(525\) | −18.4652 | −0.805887 | ||||||||
\(526\) | 42.0809 | 1.83481 | ||||||||
\(527\) | −8.31935 | −0.362397 | ||||||||
\(528\) | −75.0191 | −3.26479 | ||||||||
\(529\) | 47.3507 | 2.05873 | ||||||||
\(530\) | 2.80556 | 0.121866 | ||||||||
\(531\) | 12.4816 | 0.541655 | ||||||||
\(532\) | −15.3737 | −0.666536 | ||||||||
\(533\) | −35.3760 | −1.53231 | ||||||||
\(534\) | −2.24652 | −0.0972166 | ||||||||
\(535\) | 8.38561 | 0.362541 | ||||||||
\(536\) | −9.42503 | −0.407099 | ||||||||
\(537\) | −14.5126 | −0.626263 | ||||||||
\(538\) | −45.8407 | −1.97633 | ||||||||
\(539\) | 10.0677 | 0.433645 | ||||||||
\(540\) | 16.9912 | 0.731186 | ||||||||
\(541\) | −19.7725 | −0.850085 | −0.425042 | − | 0.905173i | \(-0.639741\pi\) | ||||
−0.425042 | + | 0.905173i | \(0.639741\pi\) | |||||||
\(542\) | −4.77062 | −0.204916 | ||||||||
\(543\) | −3.80550 | −0.163310 | ||||||||
\(544\) | 14.0718 | 0.603322 | ||||||||
\(545\) | −27.5386 | −1.17963 | ||||||||
\(546\) | −33.3025 | −1.42522 | ||||||||
\(547\) | −33.4523 | −1.43032 | −0.715159 | − | 0.698962i | \(-0.753646\pi\) | ||||
−0.715159 | + | 0.698962i | \(0.753646\pi\) | |||||||
\(548\) | −55.3444 | −2.36419 | ||||||||
\(549\) | −9.42298 | −0.402163 | ||||||||
\(550\) | −110.477 | −4.71074 | ||||||||
\(551\) | 7.67955 | 0.327160 | ||||||||
\(552\) | −67.9133 | −2.89058 | ||||||||
\(553\) | 2.92058 | 0.124196 | ||||||||
\(554\) | −54.9473 | −2.33449 | ||||||||
\(555\) | 23.8110 | 1.01072 | ||||||||
\(556\) | 23.9416 | 1.01535 | ||||||||
\(557\) | 2.10604 | 0.0892359 | 0.0446180 | − | 0.999004i | \(-0.485793\pi\) | ||||
0.0446180 | + | 0.999004i | \(0.485793\pi\) | |||||||
\(558\) | −22.0887 | −0.935091 | ||||||||
\(559\) | −27.4524 | −1.16111 | ||||||||
\(560\) | −112.023 | −4.73383 | ||||||||
\(561\) | 6.58118 | 0.277858 | ||||||||
\(562\) | −47.2266 | −1.99214 | ||||||||
\(563\) | 39.4165 | 1.66121 | 0.830605 | − | 0.556863i | \(-0.187995\pi\) | ||||
0.830605 | + | 0.556863i | \(0.187995\pi\) | |||||||
\(564\) | −26.6758 | −1.12325 | ||||||||
\(565\) | 52.3852 | 2.20386 | ||||||||
\(566\) | −19.4627 | −0.818077 | ||||||||
\(567\) | 2.92058 | 0.122653 | ||||||||
\(568\) | 75.5278 | 3.16908 | ||||||||
\(569\) | −21.1168 | −0.885264 | −0.442632 | − | 0.896703i | \(-0.645955\pi\) | ||||
−0.442632 | + | 0.896703i | \(0.645955\pi\) | |||||||
\(570\) | 9.31339 | 0.390095 | ||||||||
\(571\) | 45.7963 | 1.91652 | 0.958258 | − | 0.285906i | \(-0.0922944\pi\) | ||||
0.958258 | + | 0.285906i | \(0.0922944\pi\) | |||||||
\(572\) | −142.720 | −5.96743 | ||||||||
\(573\) | 12.1174 | 0.506212 | ||||||||
\(574\) | −63.8752 | −2.66610 | ||||||||
\(575\) | −53.0297 | −2.21149 | ||||||||
\(576\) | 14.5639 | 0.606830 | ||||||||
\(577\) | 13.3376 | 0.555251 | 0.277626 | − | 0.960689i | \(-0.410452\pi\) | ||||
0.277626 | + | 0.960689i | \(0.410452\pi\) | |||||||
\(578\) | −2.65510 | −0.110438 | ||||||||
\(579\) | −19.5362 | −0.811898 | ||||||||
\(580\) | 125.171 | 5.19745 | ||||||||
\(581\) | −17.5257 | −0.727087 | ||||||||
\(582\) | 5.30404 | 0.219859 | ||||||||
\(583\) | 2.06667 | 0.0855928 | ||||||||
\(584\) | 27.1753 | 1.12452 | ||||||||
\(585\) | 14.4510 | 0.597474 | ||||||||
\(586\) | −33.9166 | −1.40108 | ||||||||
\(587\) | 42.7337 | 1.76381 | 0.881905 | − | 0.471427i | \(-0.156261\pi\) | ||||
0.881905 | + | 0.471427i | \(0.156261\pi\) | |||||||
\(588\) | −7.72467 | −0.318560 | ||||||||
\(589\) | −8.67253 | −0.357345 | ||||||||
\(590\) | 111.512 | 4.59087 | ||||||||
\(591\) | −18.7785 | −0.772446 | ||||||||
\(592\) | 80.6631 | 3.31523 | ||||||||
\(593\) | −29.5411 | −1.21311 | −0.606554 | − | 0.795042i | \(-0.707449\pi\) | ||||
−0.606554 | + | 0.795042i | \(0.707449\pi\) | |||||||
\(594\) | 17.4737 | 0.716955 | ||||||||
\(595\) | 9.82740 | 0.402884 | ||||||||
\(596\) | 71.3222 | 2.92147 | ||||||||
\(597\) | 16.7373 | 0.685012 | ||||||||
\(598\) | −95.6407 | −3.91104 | ||||||||
\(599\) | 9.83650 | 0.401909 | 0.200954 | − | 0.979601i | \(-0.435596\pi\) | ||||
0.200954 | + | 0.979601i | \(0.435596\pi\) | |||||||
\(600\) | 51.1924 | 2.08992 | ||||||||
\(601\) | 20.0058 | 0.816052 | 0.408026 | − | 0.912970i | \(-0.366217\pi\) | ||||
0.408026 | + | 0.912970i | \(0.366217\pi\) | |||||||
\(602\) | −49.5682 | −2.02025 | ||||||||
\(603\) | 1.16403 | 0.0474028 | ||||||||
\(604\) | −99.8864 | −4.06432 | ||||||||
\(605\) | −108.726 | −4.42033 | ||||||||
\(606\) | −2.66276 | −0.108167 | ||||||||
\(607\) | 9.58695 | 0.389122 | 0.194561 | − | 0.980890i | \(-0.437672\pi\) | ||||
0.194561 | + | 0.980890i | \(0.437672\pi\) | |||||||
\(608\) | 14.6692 | 0.594913 | ||||||||
\(609\) | 21.5153 | 0.871845 | ||||||||
\(610\) | −84.1860 | −3.40859 | ||||||||
\(611\) | −22.6876 | −0.917844 | ||||||||
\(612\) | −5.04957 | −0.204117 | ||||||||
\(613\) | 28.6052 | 1.15535 | 0.577677 | − | 0.816265i | \(-0.303959\pi\) | ||||
0.577677 | + | 0.816265i | \(0.303959\pi\) | |||||||
\(614\) | −51.6093 | −2.08278 | ||||||||
\(615\) | 27.7174 | 1.11767 | ||||||||
\(616\) | −155.630 | −6.27050 | ||||||||
\(617\) | 19.0249 | 0.765916 | 0.382958 | − | 0.923766i | \(-0.374905\pi\) | ||||
0.382958 | + | 0.923766i | \(0.374905\pi\) | |||||||
\(618\) | −14.6181 | −0.588025 | ||||||||
\(619\) | 12.2797 | 0.493564 | 0.246782 | − | 0.969071i | \(-0.420627\pi\) | ||||
0.246782 | + | 0.969071i | \(0.420627\pi\) | |||||||
\(620\) | −141.356 | −5.67700 | ||||||||
\(621\) | 8.38753 | 0.336580 | ||||||||
\(622\) | −6.62082 | −0.265471 | ||||||||
\(623\) | −2.47115 | −0.0990044 | ||||||||
\(624\) | 48.9548 | 1.95976 | ||||||||
\(625\) | −16.6389 | −0.665556 | ||||||||
\(626\) | 14.5055 | 0.579756 | ||||||||
\(627\) | 6.86057 | 0.273985 | ||||||||
\(628\) | −76.7711 | −3.06350 | ||||||||
\(629\) | −7.07631 | −0.282151 | ||||||||
\(630\) | 26.0928 | 1.03956 | ||||||||
\(631\) | 31.0476 | 1.23598 | 0.617992 | − | 0.786184i | \(-0.287946\pi\) | ||||
0.617992 | + | 0.786184i | \(0.287946\pi\) | |||||||
\(632\) | −8.09693 | −0.322079 | ||||||||
\(633\) | −8.19938 | −0.325896 | ||||||||
\(634\) | −22.6568 | −0.899818 | ||||||||
\(635\) | 44.7792 | 1.77701 | ||||||||
\(636\) | −1.58571 | −0.0628773 | ||||||||
\(637\) | −6.56980 | −0.260305 | ||||||||
\(638\) | 128.725 | 5.09629 | ||||||||
\(639\) | −9.32796 | −0.369008 | ||||||||
\(640\) | 35.4160 | 1.39994 | ||||||||
\(641\) | 39.1331 | 1.54567 | 0.772833 | − | 0.634610i | \(-0.218839\pi\) | ||||
0.772833 | + | 0.634610i | \(0.218839\pi\) | |||||||
\(642\) | −6.61676 | −0.261143 | ||||||||
\(643\) | −33.2323 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727448\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727448\pi\) | |||||||
\(644\) | −123.697 | −4.87433 | ||||||||
\(645\) | 21.5092 | 0.846922 | ||||||||
\(646\) | −2.76782 | −0.108898 | ||||||||
\(647\) | −22.4668 | −0.883261 | −0.441630 | − | 0.897197i | \(-0.645600\pi\) | ||||
−0.441630 | + | 0.897197i | \(0.645600\pi\) | |||||||
\(648\) | −8.09693 | −0.318078 | ||||||||
\(649\) | 82.1435 | 3.22442 | ||||||||
\(650\) | 72.0931 | 2.82772 | ||||||||
\(651\) | −24.2973 | −0.952287 | ||||||||
\(652\) | −71.9240 | −2.81676 | ||||||||
\(653\) | 34.0925 | 1.33414 | 0.667072 | − | 0.744994i | \(-0.267548\pi\) | ||||
0.667072 | + | 0.744994i | \(0.267548\pi\) | |||||||
\(654\) | 21.7297 | 0.849698 | ||||||||
\(655\) | −14.9776 | −0.585222 | ||||||||
\(656\) | 93.8968 | 3.66605 | ||||||||
\(657\) | −3.35625 | −0.130940 | ||||||||
\(658\) | −40.9649 | −1.59698 | ||||||||
\(659\) | 17.4291 | 0.678940 | 0.339470 | − | 0.940617i | \(-0.389752\pi\) | ||||
0.339470 | + | 0.940617i | \(0.389752\pi\) | |||||||
\(660\) | 111.822 | 4.35268 | ||||||||
\(661\) | 9.05940 | 0.352370 | 0.176185 | − | 0.984357i | \(-0.443624\pi\) | ||||
0.176185 | + | 0.984357i | \(0.443624\pi\) | |||||||
\(662\) | 24.2987 | 0.944397 | ||||||||
\(663\) | −4.29464 | −0.166790 | ||||||||
\(664\) | 48.5877 | 1.88557 | ||||||||
\(665\) | 10.2446 | 0.397269 | ||||||||
\(666\) | −18.7883 | −0.728033 | ||||||||
\(667\) | 61.7893 | 2.39249 | ||||||||
\(668\) | 68.9773 | 2.66881 | ||||||||
\(669\) | −7.62776 | −0.294906 | ||||||||
\(670\) | 10.3995 | 0.401769 | ||||||||
\(671\) | −62.0143 | −2.39404 | ||||||||
\(672\) | 41.0977 | 1.58538 | ||||||||
\(673\) | −6.32183 | −0.243689 | −0.121844 | − | 0.992549i | \(-0.538881\pi\) | ||||
−0.121844 | + | 0.992549i | \(0.538881\pi\) | |||||||
\(674\) | 59.9566 | 2.30944 | ||||||||
\(675\) | −6.32245 | −0.243351 | ||||||||
\(676\) | 27.4896 | 1.05729 | ||||||||
\(677\) | −14.0424 | −0.539694 | −0.269847 | − | 0.962903i | \(-0.586973\pi\) | ||||
−0.269847 | + | 0.962903i | \(0.586973\pi\) | |||||||
\(678\) | −41.3352 | −1.58747 | ||||||||
\(679\) | 5.83437 | 0.223902 | ||||||||
\(680\) | −27.2452 | −1.04481 | ||||||||
\(681\) | −23.9586 | −0.918095 | ||||||||
\(682\) | −145.370 | −5.56650 | ||||||||
\(683\) | −38.0059 | −1.45426 | −0.727128 | − | 0.686502i | \(-0.759145\pi\) | ||||
−0.727128 | + | 0.686502i | \(0.759145\pi\) | |||||||
\(684\) | −5.26394 | −0.201272 | ||||||||
\(685\) | 36.8798 | 1.40911 | ||||||||
\(686\) | 42.4185 | 1.61955 | ||||||||
\(687\) | −0.919568 | −0.0350837 | ||||||||
\(688\) | 72.8654 | 2.77797 | ||||||||
\(689\) | −1.34864 | −0.0513790 | ||||||||
\(690\) | 74.9352 | 2.85273 | ||||||||
\(691\) | −5.32630 | −0.202622 | −0.101311 | − | 0.994855i | \(-0.532304\pi\) | ||||
−0.101311 | + | 0.994855i | \(0.532304\pi\) | |||||||
\(692\) | 107.880 | 4.10097 | ||||||||
\(693\) | 19.2208 | 0.730139 | ||||||||
\(694\) | 52.7707 | 2.00315 | ||||||||
\(695\) | −15.9540 | −0.605168 | ||||||||
\(696\) | −59.6485 | −2.26097 | ||||||||
\(697\) | −8.23725 | −0.312008 | ||||||||
\(698\) | 16.7601 | 0.634379 | ||||||||
\(699\) | 28.1339 | 1.06412 | ||||||||
\(700\) | 93.2413 | 3.52419 | ||||||||
\(701\) | 16.9542 | 0.640352 | 0.320176 | − | 0.947358i | \(-0.396258\pi\) | ||||
0.320176 | + | 0.947358i | \(0.396258\pi\) | |||||||
\(702\) | −11.4027 | −0.430368 | ||||||||
\(703\) | −7.37672 | −0.278218 | ||||||||
\(704\) | 95.8478 | 3.61240 | ||||||||
\(705\) | 17.7759 | 0.669481 | ||||||||
\(706\) | −21.7994 | −0.820432 | ||||||||
\(707\) | −2.92900 | −0.110156 | ||||||||
\(708\) | −63.0267 | −2.36869 | ||||||||
\(709\) | −3.77497 | −0.141772 | −0.0708860 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708860 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(710\) | −83.3371 | −3.12758 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 6.85094 | 0.256750 | ||||||||
\(713\) | −69.7788 | −2.61324 | ||||||||
\(714\) | −7.75443 | −0.290202 | ||||||||
\(715\) | 95.1044 | 3.55670 | ||||||||
\(716\) | 73.2822 | 2.73869 | ||||||||
\(717\) | 24.5036 | 0.915105 | ||||||||
\(718\) | −27.2708 | −1.01774 | ||||||||
\(719\) | −29.4620 | −1.09875 | −0.549373 | − | 0.835577i | \(-0.685134\pi\) | ||||
−0.549373 | + | 0.835577i | \(0.685134\pi\) | |||||||
\(720\) | −38.3565 | −1.42946 | ||||||||
\(721\) | −16.0797 | −0.598838 | ||||||||
\(722\) | 47.5616 | 1.77006 | ||||||||
\(723\) | 1.08480 | 0.0403441 | ||||||||
\(724\) | 19.2162 | 0.714163 | ||||||||
\(725\) | −46.5763 | −1.72980 | ||||||||
\(726\) | 85.7915 | 3.18402 | ||||||||
\(727\) | −3.28683 | −0.121902 | −0.0609509 | − | 0.998141i | \(-0.519413\pi\) | ||||
−0.0609509 | + | 0.998141i | \(0.519413\pi\) | |||||||
\(728\) | 101.558 | 3.76401 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −29.9851 | −1.10980 | ||||||||
\(731\) | −6.39224 | −0.236426 | ||||||||
\(732\) | 47.5820 | 1.75868 | ||||||||
\(733\) | −13.2649 | −0.489952 | −0.244976 | − | 0.969529i | \(-0.578780\pi\) | ||||
−0.244976 | + | 0.969529i | \(0.578780\pi\) | |||||||
\(734\) | −61.4602 | −2.26854 | ||||||||
\(735\) | 5.14749 | 0.189868 | ||||||||
\(736\) | 118.027 | 4.35055 | ||||||||
\(737\) | 7.66066 | 0.282184 | ||||||||
\(738\) | −21.8708 | −0.805074 | ||||||||
\(739\) | −22.4138 | −0.824504 | −0.412252 | − | 0.911070i | \(-0.635258\pi\) | ||||
−0.412252 | + | 0.911070i | \(0.635258\pi\) | |||||||
\(740\) | −120.235 | −4.41993 | ||||||||
\(741\) | −4.47696 | −0.164465 | ||||||||
\(742\) | −2.43511 | −0.0893956 | ||||||||
\(743\) | 41.7486 | 1.53161 | 0.765803 | − | 0.643075i | \(-0.222342\pi\) | ||||
0.765803 | + | 0.643075i | \(0.222342\pi\) | |||||||
\(744\) | 67.3612 | 2.46958 | ||||||||
\(745\) | −47.5270 | −1.74125 | ||||||||
\(746\) | −35.2405 | −1.29025 | ||||||||
\(747\) | −6.00075 | −0.219556 | ||||||||
\(748\) | −33.2321 | −1.21509 | ||||||||
\(749\) | −7.27835 | −0.265945 | ||||||||
\(750\) | −11.8149 | −0.431419 | ||||||||
\(751\) | −36.8217 | −1.34364 | −0.671821 | − | 0.740713i | \(-0.734488\pi\) | ||||
−0.671821 | + | 0.740713i | \(0.734488\pi\) | |||||||
\(752\) | 60.2186 | 2.19595 | ||||||||
\(753\) | 5.96177 | 0.217259 | ||||||||
\(754\) | −84.0016 | −3.05916 | ||||||||
\(755\) | 66.5613 | 2.42241 | ||||||||
\(756\) | −14.7477 | −0.536367 | ||||||||
\(757\) | 2.25723 | 0.0820405 | 0.0410203 | − | 0.999158i | \(-0.486939\pi\) | ||||
0.0410203 | + | 0.999158i | \(0.486939\pi\) | |||||||
\(758\) | 57.1797 | 2.07686 | ||||||||
\(759\) | 55.1999 | 2.00363 | ||||||||
\(760\) | −28.4019 | −1.03024 | ||||||||
\(761\) | 14.5837 | 0.528657 | 0.264329 | − | 0.964433i | \(-0.414850\pi\) | ||||
0.264329 | + | 0.964433i | \(0.414850\pi\) | |||||||
\(762\) | −35.3336 | −1.28000 | ||||||||
\(763\) | 23.9024 | 0.865324 | ||||||||
\(764\) | −61.1877 | −2.21369 | ||||||||
\(765\) | 3.36488 | 0.121658 | ||||||||
\(766\) | −6.74335 | −0.243647 | ||||||||
\(767\) | −53.6039 | −1.93553 | ||||||||
\(768\) | 1.18242 | 0.0426671 | ||||||||
\(769\) | 0.273702 | 0.00986995 | 0.00493498 | − | 0.999988i | \(-0.498429\pi\) | ||||
0.00493498 | + | 0.999988i | \(0.498429\pi\) | |||||||
\(770\) | 171.721 | 6.18840 | ||||||||
\(771\) | −16.0042 | −0.576375 | ||||||||
\(772\) | 98.6496 | 3.55048 | ||||||||
\(773\) | 44.7455 | 1.60938 | 0.804692 | − | 0.593692i | \(-0.202330\pi\) | ||||
0.804692 | + | 0.593692i | \(0.202330\pi\) | |||||||
\(774\) | −16.9721 | −0.610048 | ||||||||
\(775\) | 52.5987 | 1.88940 | ||||||||
\(776\) | −16.1750 | −0.580650 | ||||||||
\(777\) | −20.6669 | −0.741421 | ||||||||
\(778\) | −7.57256 | −0.271489 | ||||||||
\(779\) | −8.58695 | −0.307659 | ||||||||
\(780\) | −72.9712 | −2.61279 | ||||||||
\(781\) | −61.3890 | −2.19667 | ||||||||
\(782\) | −22.2698 | −0.796365 | ||||||||
\(783\) | 7.36681 | 0.263268 | ||||||||
\(784\) | 17.4379 | 0.622782 | ||||||||
\(785\) | 51.1579 | 1.82591 | ||||||||
\(786\) | 11.8182 | 0.421543 | ||||||||
\(787\) | −38.6654 | −1.37827 | −0.689137 | − | 0.724631i | \(-0.742010\pi\) | ||||
−0.689137 | + | 0.724631i | \(0.742010\pi\) | |||||||
\(788\) | 94.8236 | 3.37795 | ||||||||
\(789\) | 15.8490 | 0.564241 | ||||||||
\(790\) | 8.93412 | 0.317862 | ||||||||
\(791\) | −45.4681 | −1.61666 | ||||||||
\(792\) | −53.2874 | −1.89348 | ||||||||
\(793\) | 40.4683 | 1.43707 | ||||||||
\(794\) | −77.6315 | −2.75504 | ||||||||
\(795\) | 1.05667 | 0.0374761 | ||||||||
\(796\) | −84.5161 | −2.99560 | ||||||||
\(797\) | −54.2141 | −1.92036 | −0.960181 | − | 0.279377i | \(-0.909872\pi\) | ||||
−0.960181 | + | 0.279377i | \(0.909872\pi\) | |||||||
\(798\) | −8.08363 | −0.286157 | ||||||||
\(799\) | −5.28278 | −0.186891 | ||||||||
\(800\) | −88.9680 | −3.14549 | ||||||||
\(801\) | −0.846116 | −0.0298960 | ||||||||
\(802\) | −24.8750 | −0.878366 | ||||||||
\(803\) | −22.0880 | −0.779470 | ||||||||
\(804\) | −5.87783 | −0.207295 | ||||||||
\(805\) | 82.4277 | 2.90519 | ||||||||
\(806\) | 94.8632 | 3.34141 | ||||||||
\(807\) | −17.2651 | −0.607762 | ||||||||
\(808\) | 8.12029 | 0.285671 | ||||||||
\(809\) | −21.1087 | −0.742143 | −0.371071 | − | 0.928604i | \(-0.621009\pi\) | ||||
−0.371071 | + | 0.928604i | \(0.621009\pi\) | |||||||
\(810\) | 8.93412 | 0.313913 | ||||||||
\(811\) | 24.5967 | 0.863706 | 0.431853 | − | 0.901944i | \(-0.357860\pi\) | ||||
0.431853 | + | 0.901944i | \(0.357860\pi\) | |||||||
\(812\) | −108.643 | −3.81263 | ||||||||
\(813\) | −1.79677 | −0.0630156 | ||||||||
\(814\) | −123.649 | −4.33391 | ||||||||
\(815\) | 47.9280 | 1.67884 | ||||||||
\(816\) | 11.3990 | 0.399046 | ||||||||
\(817\) | −6.66361 | −0.233130 | ||||||||
\(818\) | −84.4017 | −2.95104 | ||||||||
\(819\) | −12.5428 | −0.438282 | ||||||||
\(820\) | −139.961 | −4.88765 | ||||||||
\(821\) | −1.02183 | −0.0356622 | −0.0178311 | − | 0.999841i | \(-0.505676\pi\) | ||||
−0.0178311 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(822\) | −29.1005 | −1.01500 | ||||||||
\(823\) | −27.0699 | −0.943597 | −0.471799 | − | 0.881706i | \(-0.656395\pi\) | ||||
−0.471799 | + | 0.881706i | \(0.656395\pi\) | |||||||
\(824\) | 44.5789 | 1.55298 | ||||||||
\(825\) | −41.6092 | −1.44864 | ||||||||
\(826\) | −96.7876 | −3.36767 | ||||||||
\(827\) | 0.444434 | 0.0154545 | 0.00772724 | − | 0.999970i | \(-0.497540\pi\) | ||||
0.00772724 | + | 0.999970i | \(0.497540\pi\) | |||||||
\(828\) | −42.3535 | −1.47188 | ||||||||
\(829\) | 38.8429 | 1.34907 | 0.674534 | − | 0.738244i | \(-0.264344\pi\) | ||||
0.674534 | + | 0.738244i | \(0.264344\pi\) | |||||||
\(830\) | −53.6114 | −1.86088 | ||||||||
\(831\) | −20.6950 | −0.717900 | ||||||||
\(832\) | −62.5468 | −2.16842 | ||||||||
\(833\) | −1.52977 | −0.0530033 | ||||||||
\(834\) | 12.5887 | 0.435910 | ||||||||
\(835\) | −45.9644 | −1.59066 | ||||||||
\(836\) | −34.6429 | −1.19815 | ||||||||
\(837\) | −8.31935 | −0.287559 | ||||||||
\(838\) | −66.0842 | −2.28284 | ||||||||
\(839\) | −13.4504 | −0.464360 | −0.232180 | − | 0.972673i | \(-0.574586\pi\) | ||||
−0.232180 | + | 0.972673i | \(0.574586\pi\) | |||||||
\(840\) | −79.5718 | −2.74549 | ||||||||
\(841\) | 25.2699 | 0.871375 | ||||||||
\(842\) | 82.4044 | 2.83984 | ||||||||
\(843\) | −17.7871 | −0.612621 | ||||||||
\(844\) | 41.4034 | 1.42516 | ||||||||
\(845\) | −18.3182 | −0.630167 | ||||||||
\(846\) | −14.0263 | −0.482235 | ||||||||
\(847\) | 94.3694 | 3.24257 | ||||||||
\(848\) | 3.57962 | 0.122924 | ||||||||
\(849\) | −7.33028 | −0.251575 | ||||||||
\(850\) | 16.7867 | 0.575781 | ||||||||
\(851\) | −59.3528 | −2.03459 | ||||||||
\(852\) | 47.1022 | 1.61369 | ||||||||
\(853\) | 22.8360 | 0.781889 | 0.390944 | − | 0.920414i | \(-0.372148\pi\) | ||||
0.390944 | + | 0.920414i | \(0.372148\pi\) | |||||||
\(854\) | 73.0699 | 2.50040 | ||||||||
\(855\) | 3.50773 | 0.119962 | ||||||||
\(856\) | 20.1783 | 0.689680 | ||||||||
\(857\) | −41.2584 | −1.40936 | −0.704680 | − | 0.709525i | \(-0.748909\pi\) | ||||
−0.704680 | + | 0.709525i | \(0.748909\pi\) | |||||||
\(858\) | −75.0433 | −2.56194 | ||||||||
\(859\) | −3.27100 | −0.111605 | −0.0558026 | − | 0.998442i | \(-0.517772\pi\) | ||||
−0.0558026 | + | 0.998442i | \(0.517772\pi\) | |||||||
\(860\) | −108.612 | −3.70364 | ||||||||
\(861\) | −24.0575 | −0.819878 | ||||||||
\(862\) | 84.5728 | 2.88056 | ||||||||
\(863\) | 36.8793 | 1.25538 | 0.627692 | − | 0.778462i | \(-0.284000\pi\) | ||||
0.627692 | + | 0.778462i | \(0.284000\pi\) | |||||||
\(864\) | 14.0718 | 0.478731 | ||||||||
\(865\) | −71.8878 | −2.44426 | ||||||||
\(866\) | −39.5484 | −1.34391 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 122.691 | 4.16441 | ||||||||
\(869\) | 6.58118 | 0.223251 | ||||||||
\(870\) | 65.8159 | 2.23137 | ||||||||
\(871\) | −4.99907 | −0.169387 | ||||||||
\(872\) | −66.2663 | −2.24406 | ||||||||
\(873\) | 1.99768 | 0.0676111 | ||||||||
\(874\) | −23.2152 | −0.785265 | ||||||||
\(875\) | −12.9962 | −0.439352 | ||||||||
\(876\) | 16.9476 | 0.572607 | ||||||||
\(877\) | 32.4616 | 1.09615 | 0.548076 | − | 0.836429i | \(-0.315361\pi\) | ||||
0.548076 | + | 0.836429i | \(0.315361\pi\) | |||||||
\(878\) | 1.65892 | 0.0559859 | ||||||||
\(879\) | −12.7741 | −0.430861 | ||||||||
\(880\) | −252.431 | −8.50944 | ||||||||
\(881\) | 6.32308 | 0.213030 | 0.106515 | − | 0.994311i | \(-0.466031\pi\) | ||||
0.106515 | + | 0.994311i | \(0.466031\pi\) | |||||||
\(882\) | −4.06169 | −0.136764 | ||||||||
\(883\) | 19.1139 | 0.643235 | 0.321618 | − | 0.946870i | \(-0.395773\pi\) | ||||
0.321618 | + | 0.946870i | \(0.395773\pi\) | |||||||
\(884\) | 21.6861 | 0.729383 | ||||||||
\(885\) | 41.9991 | 1.41178 | ||||||||
\(886\) | −6.42032 | −0.215695 | ||||||||
\(887\) | 22.7111 | 0.762564 | 0.381282 | − | 0.924459i | \(-0.375483\pi\) | ||||
0.381282 | + | 0.924459i | \(0.375483\pi\) | |||||||
\(888\) | 57.2964 | 1.92274 | ||||||||
\(889\) | −38.8665 | −1.30354 | ||||||||
\(890\) | −7.55930 | −0.253388 | ||||||||
\(891\) | 6.58118 | 0.220478 | ||||||||
\(892\) | 38.5169 | 1.28964 | ||||||||
\(893\) | −5.50705 | −0.184286 | ||||||||
\(894\) | 37.5017 | 1.25425 | ||||||||
\(895\) | −48.8331 | −1.63231 | ||||||||
\(896\) | −30.7396 | −1.02694 | ||||||||
\(897\) | −36.0214 | −1.20272 | ||||||||
\(898\) | −29.5511 | −0.986134 | ||||||||
\(899\) | −61.2871 | −2.04404 | ||||||||
\(900\) | 31.9257 | 1.06419 | ||||||||
\(901\) | −0.314028 | −0.0104618 | ||||||||
\(902\) | −143.935 | −4.79252 | ||||||||
\(903\) | −18.6690 | −0.621267 | ||||||||
\(904\) | 126.055 | 4.19251 | ||||||||
\(905\) | −12.8051 | −0.425655 | ||||||||
\(906\) | −52.5210 | −1.74489 | ||||||||
\(907\) | −40.1184 | −1.33211 | −0.666054 | − | 0.745903i | \(-0.732018\pi\) | ||||
−0.666054 | + | 0.745903i | \(0.732018\pi\) | |||||||
\(908\) | 120.981 | 4.01488 | ||||||||
\(909\) | −1.00288 | −0.0332636 | ||||||||
\(910\) | −112.059 | −3.71472 | ||||||||
\(911\) | −16.5464 | −0.548208 | −0.274104 | − | 0.961700i | \(-0.588381\pi\) | ||||
−0.274104 | + | 0.961700i | \(0.588381\pi\) | |||||||
\(912\) | 11.8830 | 0.393484 | ||||||||
\(913\) | −39.4920 | −1.30700 | ||||||||
\(914\) | −27.8057 | −0.919732 | ||||||||
\(915\) | −31.7072 | −1.04821 | ||||||||
\(916\) | 4.64343 | 0.153423 | ||||||||
\(917\) | 12.9999 | 0.429295 | ||||||||
\(918\) | −2.65510 | −0.0876315 | ||||||||
\(919\) | 58.0336 | 1.91435 | 0.957176 | − | 0.289507i | \(-0.0934915\pi\) | ||||
0.957176 | + | 0.289507i | \(0.0934915\pi\) | |||||||
\(920\) | −228.520 | −7.53409 | ||||||||
\(921\) | −19.4378 | −0.640497 | ||||||||
\(922\) | 104.288 | 3.43453 | ||||||||
\(923\) | 40.0602 | 1.31860 | ||||||||
\(924\) | −97.0570 | −3.19294 | ||||||||
\(925\) | 44.7396 | 1.47103 | ||||||||
\(926\) | 33.6716 | 1.10652 | ||||||||
\(927\) | −5.50565 | −0.180829 | ||||||||
\(928\) | 103.664 | 3.40294 | ||||||||
\(929\) | −18.6503 | −0.611897 | −0.305948 | − | 0.952048i | \(-0.598973\pi\) | ||||
−0.305948 | + | 0.952048i | \(0.598973\pi\) | |||||||
\(930\) | −74.3261 | −2.43725 | ||||||||
\(931\) | −1.59471 | −0.0522645 | ||||||||
\(932\) | −142.064 | −4.65346 | ||||||||
\(933\) | −2.49362 | −0.0816374 | ||||||||
\(934\) | −26.8030 | −0.877022 | ||||||||
\(935\) | 22.1449 | 0.724216 | ||||||||
\(936\) | 34.7734 | 1.13660 | ||||||||
\(937\) | −10.0582 | −0.328586 | −0.164293 | − | 0.986412i | \(-0.552534\pi\) | ||||
−0.164293 | + | 0.986412i | \(0.552534\pi\) | |||||||
\(938\) | −9.02635 | −0.294721 | ||||||||
\(939\) | 5.46325 | 0.178286 | ||||||||
\(940\) | −89.7609 | −2.92768 | ||||||||
\(941\) | −2.36206 | −0.0770010 | −0.0385005 | − | 0.999259i | \(-0.512258\pi\) | ||||
−0.0385005 | + | 0.999259i | \(0.512258\pi\) | |||||||
\(942\) | −40.3668 | −1.31522 | ||||||||
\(943\) | −69.0902 | −2.24989 | ||||||||
\(944\) | 142.278 | 4.63076 | ||||||||
\(945\) | 9.82740 | 0.319685 | ||||||||
\(946\) | −111.696 | −3.63156 | ||||||||
\(947\) | 16.7739 | 0.545080 | 0.272540 | − | 0.962144i | \(-0.412136\pi\) | ||||
0.272540 | + | 0.962144i | \(0.412136\pi\) | |||||||
\(948\) | −5.04957 | −0.164003 | ||||||||
\(949\) | 14.4139 | 0.467894 | ||||||||
\(950\) | 17.4994 | 0.567755 | ||||||||
\(951\) | −8.53332 | −0.276712 | ||||||||
\(952\) | 23.6477 | 0.766427 | ||||||||
\(953\) | 12.7004 | 0.411406 | 0.205703 | − | 0.978614i | \(-0.434052\pi\) | ||||
0.205703 | + | 0.978614i | \(0.434052\pi\) | |||||||
\(954\) | −0.833776 | −0.0269945 | ||||||||
\(955\) | 40.7737 | 1.31940 | ||||||||
\(956\) | −123.733 | −4.00181 | ||||||||
\(957\) | 48.4823 | 1.56721 | ||||||||
\(958\) | −111.824 | −3.61288 | ||||||||
\(959\) | −32.0101 | −1.03366 | ||||||||
\(960\) | 49.0059 | 1.58166 | ||||||||
\(961\) | 38.2116 | 1.23263 | ||||||||
\(962\) | 80.6891 | 2.60152 | ||||||||
\(963\) | −2.49209 | −0.0803066 | ||||||||
\(964\) | −5.47778 | −0.176427 | ||||||||
\(965\) | −65.7372 | −2.11615 | ||||||||
\(966\) | −65.0406 | −2.09265 | ||||||||
\(967\) | 46.6241 | 1.49933 | 0.749666 | − | 0.661817i | \(-0.230214\pi\) | ||||
0.749666 | + | 0.661817i | \(0.230214\pi\) | |||||||
\(968\) | −261.627 | −8.40902 | ||||||||
\(969\) | −1.04245 | −0.0334884 | ||||||||
\(970\) | 17.8475 | 0.573048 | ||||||||
\(971\) | 15.7122 | 0.504228 | 0.252114 | − | 0.967698i | \(-0.418874\pi\) | ||||
0.252114 | + | 0.967698i | \(0.418874\pi\) | |||||||
\(972\) | −5.04957 | −0.161965 | ||||||||
\(973\) | 13.8474 | 0.443926 | ||||||||
\(974\) | −15.5423 | −0.498006 | ||||||||
\(975\) | 27.1526 | 0.869580 | ||||||||
\(976\) | −107.413 | −3.43821 | ||||||||
\(977\) | 15.9999 | 0.511882 | 0.255941 | − | 0.966692i | \(-0.417615\pi\) | ||||
0.255941 | + | 0.966692i | \(0.417615\pi\) | |||||||
\(978\) | −37.8182 | −1.20929 | ||||||||
\(979\) | −5.56844 | −0.177968 | ||||||||
\(980\) | −25.9926 | −0.830304 | ||||||||
\(981\) | 8.18412 | 0.261299 | ||||||||
\(982\) | −68.9330 | −2.19974 | ||||||||
\(983\) | 26.0124 | 0.829666 | 0.414833 | − | 0.909898i | \(-0.363840\pi\) | ||||
0.414833 | + | 0.909898i | \(0.363840\pi\) | |||||||
\(984\) | 66.6965 | 2.12621 | ||||||||
\(985\) | −63.1876 | −2.01333 | ||||||||
\(986\) | −19.5596 | −0.622906 | ||||||||
\(987\) | −15.4288 | −0.491103 | ||||||||
\(988\) | 22.6067 | 0.719216 | ||||||||
\(989\) | −53.6151 | −1.70486 | ||||||||
\(990\) | 58.7970 | 1.86869 | ||||||||
\(991\) | 16.8593 | 0.535554 | 0.267777 | − | 0.963481i | \(-0.413711\pi\) | ||||
0.267777 | + | 0.963481i | \(0.413711\pi\) | |||||||
\(992\) | −117.068 | −3.71691 | ||||||||
\(993\) | 9.15171 | 0.290421 | ||||||||
\(994\) | 72.3330 | 2.29426 | ||||||||
\(995\) | 56.3190 | 1.78543 | ||||||||
\(996\) | 30.3012 | 0.960131 | ||||||||
\(997\) | 21.7364 | 0.688399 | 0.344199 | − | 0.938897i | \(-0.388150\pi\) | ||||
0.344199 | + | 0.938897i | \(0.388150\pi\) | |||||||
\(998\) | −22.3049 | −0.706050 | ||||||||
\(999\) | −7.07631 | −0.223884 |
(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 | 4029.2.a.l.1.2 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.2 | ✓ | 32 | 1.1 | even | 1 | trivial |