Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,4,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(13.5704393013\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{73}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 18 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 2.77200 | 0.533472 | 0.266736 | − | 0.963770i | \(-0.414055\pi\) | ||||
0.266736 | + | 0.963770i | \(0.414055\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −5.54400 | −0.377222 | ||||||||
\(7\) | −4.22800 | −0.228290 | −0.114145 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114145 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −19.3160 | −0.715408 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | −33.7200 | −0.924270 | −0.462135 | − | 0.886810i | \(-0.652916\pi\) | ||||
−0.462135 | + | 0.886810i | \(0.652916\pi\) | |||||||
\(12\) | 11.0880 | 0.266736 | ||||||||
\(13\) | −42.9480 | −0.916280 | −0.458140 | − | 0.888880i | \(-0.651484\pi\) | ||||
−0.458140 | + | 0.888880i | \(0.651484\pi\) | |||||||
\(14\) | 8.45600 | 0.161426 | ||||||||
\(15\) | 13.8600 | 0.238576 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 7.49202 | 0.106887 | 0.0534436 | − | 0.998571i | \(-0.482980\pi\) | ||||
0.0534436 | + | 0.998571i | \(0.482980\pi\) | |||||||
\(18\) | 38.6320 | 0.505870 | ||||||||
\(19\) | −25.7200 | −0.310557 | −0.155278 | − | 0.987871i | \(-0.549627\pi\) | ||||
−0.155278 | + | 0.987871i | \(0.549627\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | −11.7200 | −0.121787 | ||||||||
\(22\) | 67.4400 | 0.653557 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −22.1760 | −0.188611 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 85.8960 | 0.647908 | ||||||||
\(27\) | −128.388 | −0.915122 | ||||||||
\(28\) | −16.9120 | −0.114145 | ||||||||
\(29\) | −47.4560 | −0.303874 | −0.151937 | − | 0.988390i | \(-0.548551\pi\) | ||||
−0.151937 | + | 0.988390i | \(0.548551\pi\) | |||||||
\(30\) | −27.7200 | −0.168699 | ||||||||
\(31\) | 65.0720 | 0.377009 | 0.188505 | − | 0.982072i | \(-0.439636\pi\) | ||||
0.188505 | + | 0.982072i | \(0.439636\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −93.4720 | −0.493072 | ||||||||
\(34\) | −14.9840 | −0.0755806 | ||||||||
\(35\) | −21.1400 | −0.102095 | ||||||||
\(36\) | −77.2640 | −0.357704 | ||||||||
\(37\) | −215.596 | −0.957940 | −0.478970 | − | 0.877831i | \(-0.658990\pi\) | ||||
−0.478970 | + | 0.877831i | \(0.658990\pi\) | |||||||
\(38\) | 51.4400 | 0.219597 | ||||||||
\(39\) | −119.052 | −0.488810 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | 150.128 | 0.571856 | 0.285928 | − | 0.958251i | \(-0.407698\pi\) | ||||
0.285928 | + | 0.958251i | \(0.407698\pi\) | |||||||
\(42\) | 23.4400 | 0.0861161 | ||||||||
\(43\) | −83.0160 | −0.294414 | −0.147207 | − | 0.989106i | \(-0.547028\pi\) | ||||
−0.147207 | + | 0.989106i | \(0.547028\pi\) | |||||||
\(44\) | −134.880 | −0.462135 | ||||||||
\(45\) | −96.5800 | −0.319940 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | −278.140 | −0.863210 | −0.431605 | − | 0.902063i | \(-0.642053\pi\) | ||||
−0.431605 | + | 0.902063i | \(0.642053\pi\) | |||||||
\(48\) | 44.3520 | 0.133368 | ||||||||
\(49\) | −325.124 | −0.947883 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 20.7679 | 0.0570213 | ||||||||
\(52\) | −171.792 | −0.458140 | ||||||||
\(53\) | −182.404 | −0.472738 | −0.236369 | − | 0.971663i | \(-0.575957\pi\) | ||||
−0.236369 | + | 0.971663i | \(0.575957\pi\) | |||||||
\(54\) | 256.776 | 0.647089 | ||||||||
\(55\) | −168.600 | −0.413346 | ||||||||
\(56\) | 33.8240 | 0.0807129 | ||||||||
\(57\) | −71.2959 | −0.165673 | ||||||||
\(58\) | 94.9120 | 0.214872 | ||||||||
\(59\) | −270.060 | −0.595913 | −0.297956 | − | 0.954580i | \(-0.596305\pi\) | ||||
−0.297956 | + | 0.954580i | \(0.596305\pi\) | |||||||
\(60\) | 55.4400 | 0.119288 | ||||||||
\(61\) | −137.264 | −0.288112 | −0.144056 | − | 0.989570i | \(-0.546015\pi\) | ||||
−0.144056 | + | 0.989570i | \(0.546015\pi\) | |||||||
\(62\) | −130.144 | −0.266586 | ||||||||
\(63\) | 81.6680 | 0.163321 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −214.740 | −0.409773 | ||||||||
\(66\) | 186.944 | 0.348655 | ||||||||
\(67\) | −440.652 | −0.803496 | −0.401748 | − | 0.915750i | \(-0.631597\pi\) | ||||
−0.401748 | + | 0.915750i | \(0.631597\pi\) | |||||||
\(68\) | 29.9681 | 0.0534436 | ||||||||
\(69\) | −63.7560 | −0.111237 | ||||||||
\(70\) | 42.2800 | 0.0721918 | ||||||||
\(71\) | 1071.29 | 1.79068 | 0.895342 | − | 0.445380i | \(-0.146931\pi\) | ||||
0.895342 | + | 0.445380i | \(0.146931\pi\) | |||||||
\(72\) | 154.528 | 0.252935 | ||||||||
\(73\) | −269.756 | −0.432501 | −0.216250 | − | 0.976338i | \(-0.569383\pi\) | ||||
−0.216250 | + | 0.976338i | \(0.569383\pi\) | |||||||
\(74\) | 431.192 | 0.677366 | ||||||||
\(75\) | 69.3000 | 0.106694 | ||||||||
\(76\) | −102.880 | −0.155278 | ||||||||
\(77\) | 142.568 | 0.211002 | ||||||||
\(78\) | 238.104 | 0.345641 | ||||||||
\(79\) | 195.232 | 0.278042 | 0.139021 | − | 0.990289i | \(-0.455604\pi\) | ||||
0.139021 | + | 0.990289i | \(0.455604\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | 165.640 | 0.227216 | ||||||||
\(82\) | −300.256 | −0.404363 | ||||||||
\(83\) | 136.676 | 0.180748 | 0.0903742 | − | 0.995908i | \(-0.471194\pi\) | ||||
0.0903742 | + | 0.995908i | \(0.471194\pi\) | |||||||
\(84\) | −46.8801 | −0.0608933 | ||||||||
\(85\) | 37.4601 | 0.0478014 | ||||||||
\(86\) | 166.032 | 0.208182 | ||||||||
\(87\) | −131.548 | −0.162108 | ||||||||
\(88\) | 269.760 | 0.326779 | ||||||||
\(89\) | 629.896 | 0.750212 | 0.375106 | − | 0.926982i | \(-0.377606\pi\) | ||||
0.375106 | + | 0.926982i | \(0.377606\pi\) | |||||||
\(90\) | 193.160 | 0.226232 | ||||||||
\(91\) | 181.584 | 0.209178 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 180.380 | 0.201124 | ||||||||
\(94\) | 556.280 | 0.610382 | ||||||||
\(95\) | −128.600 | −0.138885 | ||||||||
\(96\) | −88.7041 | −0.0943054 | ||||||||
\(97\) | −419.392 | −0.438998 | −0.219499 | − | 0.975613i | \(-0.570442\pi\) | ||||
−0.219499 | + | 0.975613i | \(0.570442\pi\) | |||||||
\(98\) | 650.248 | 0.670255 | ||||||||
\(99\) | 651.336 | 0.661230 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 928.164 | 0.914414 | 0.457207 | − | 0.889360i | \(-0.348850\pi\) | ||||
0.457207 | + | 0.889360i | \(0.348850\pi\) | |||||||
\(102\) | −41.5358 | −0.0403202 | ||||||||
\(103\) | 1381.78 | 1.32185 | 0.660925 | − | 0.750452i | \(-0.270164\pi\) | ||||
0.660925 | + | 0.750452i | \(0.270164\pi\) | |||||||
\(104\) | 343.584 | 0.323954 | ||||||||
\(105\) | −58.6001 | −0.0544646 | ||||||||
\(106\) | 364.808 | 0.334276 | ||||||||
\(107\) | −763.820 | −0.690106 | −0.345053 | − | 0.938583i | \(-0.612139\pi\) | ||||
−0.345053 | + | 0.938583i | \(0.612139\pi\) | |||||||
\(108\) | −513.552 | −0.457561 | ||||||||
\(109\) | −156.736 | −0.137730 | −0.0688651 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688651 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(110\) | 337.200 | 0.292280 | ||||||||
\(111\) | −597.632 | −0.511034 | ||||||||
\(112\) | −67.6480 | −0.0570726 | ||||||||
\(113\) | 1036.12 | 0.862569 | 0.431285 | − | 0.902216i | \(-0.358060\pi\) | ||||
0.431285 | + | 0.902216i | \(0.358060\pi\) | |||||||
\(114\) | 142.592 | 0.117149 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | −189.824 | −0.151937 | ||||||||
\(117\) | 829.584 | 0.655514 | ||||||||
\(118\) | 540.120 | 0.421374 | ||||||||
\(119\) | −31.6762 | −0.0244013 | ||||||||
\(120\) | −110.880 | −0.0843493 | ||||||||
\(121\) | −193.960 | −0.145725 | ||||||||
\(122\) | 274.528 | 0.203726 | ||||||||
\(123\) | 416.155 | 0.305069 | ||||||||
\(124\) | 260.288 | 0.188505 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −163.336 | −0.115485 | ||||||||
\(127\) | −1228.31 | −0.858226 | −0.429113 | − | 0.903251i | \(-0.641174\pi\) | ||||
−0.429113 | + | 0.903251i | \(0.641174\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −230.120 | −0.157062 | ||||||||
\(130\) | 429.480 | 0.289753 | ||||||||
\(131\) | 1735.85 | 1.15773 | 0.578863 | − | 0.815425i | \(-0.303497\pi\) | ||||
0.578863 | + | 0.815425i | \(0.303497\pi\) | |||||||
\(132\) | −373.888 | −0.246536 | ||||||||
\(133\) | 108.744 | 0.0708971 | ||||||||
\(134\) | 881.304 | 0.568157 | ||||||||
\(135\) | −641.940 | −0.409255 | ||||||||
\(136\) | −59.9362 | −0.0377903 | ||||||||
\(137\) | −1307.40 | −0.815319 | −0.407660 | − | 0.913134i | \(-0.633655\pi\) | ||||
−0.407660 | + | 0.913134i | \(0.633655\pi\) | |||||||
\(138\) | 127.512 | 0.0786562 | ||||||||
\(139\) | 1073.82 | 0.655256 | 0.327628 | − | 0.944807i | \(-0.393751\pi\) | ||||
0.327628 | + | 0.944807i | \(0.393751\pi\) | |||||||
\(140\) | −84.5600 | −0.0510473 | ||||||||
\(141\) | −771.005 | −0.460499 | ||||||||
\(142\) | −2142.58 | −1.26620 | ||||||||
\(143\) | 1448.21 | 0.846890 | ||||||||
\(144\) | −309.056 | −0.178852 | ||||||||
\(145\) | −237.280 | −0.135897 | ||||||||
\(146\) | 539.512 | 0.305824 | ||||||||
\(147\) | −901.244 | −0.505669 | ||||||||
\(148\) | −862.384 | −0.478970 | ||||||||
\(149\) | 2309.08 | 1.26958 | 0.634789 | − | 0.772685i | \(-0.281087\pi\) | ||||
0.634789 | + | 0.772685i | \(0.281087\pi\) | |||||||
\(150\) | −138.600 | −0.0754443 | ||||||||
\(151\) | −87.6037 | −0.0472125 | −0.0236063 | − | 0.999721i | \(-0.507515\pi\) | ||||
−0.0236063 | + | 0.999721i | \(0.507515\pi\) | |||||||
\(152\) | 205.760 | 0.109798 | ||||||||
\(153\) | −144.716 | −0.0764679 | ||||||||
\(154\) | −285.136 | −0.149201 | ||||||||
\(155\) | 325.360 | 0.168604 | ||||||||
\(156\) | −476.208 | −0.244405 | ||||||||
\(157\) | −1862.30 | −0.946673 | −0.473337 | − | 0.880882i | \(-0.656951\pi\) | ||||
−0.473337 | + | 0.880882i | \(0.656951\pi\) | |||||||
\(158\) | −390.464 | −0.196605 | ||||||||
\(159\) | −505.624 | −0.252193 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | 97.2440 | 0.0476018 | ||||||||
\(162\) | −331.280 | −0.160666 | ||||||||
\(163\) | 76.7391 | 0.0368753 | 0.0184377 | − | 0.999830i | \(-0.494131\pi\) | ||||
0.0184377 | + | 0.999830i | \(0.494131\pi\) | |||||||
\(164\) | 600.513 | 0.285928 | ||||||||
\(165\) | −467.360 | −0.220509 | ||||||||
\(166\) | −273.352 | −0.127808 | ||||||||
\(167\) | −2324.96 | −1.07731 | −0.538655 | − | 0.842526i | \(-0.681068\pi\) | ||||
−0.538655 | + | 0.842526i | \(0.681068\pi\) | |||||||
\(168\) | 93.7601 | 0.0430581 | ||||||||
\(169\) | −352.468 | −0.160431 | ||||||||
\(170\) | −74.9202 | −0.0338007 | ||||||||
\(171\) | 496.808 | 0.222175 | ||||||||
\(172\) | −332.064 | −0.147207 | ||||||||
\(173\) | −2425.51 | −1.06594 | −0.532972 | − | 0.846133i | \(-0.678925\pi\) | ||||
−0.532972 | + | 0.846133i | \(0.678925\pi\) | |||||||
\(174\) | 263.096 | 0.114628 | ||||||||
\(175\) | −105.700 | −0.0456581 | ||||||||
\(176\) | −539.520 | −0.231067 | ||||||||
\(177\) | −748.607 | −0.317903 | ||||||||
\(178\) | −1259.79 | −0.530480 | ||||||||
\(179\) | 1911.86 | 0.798320 | 0.399160 | − | 0.916881i | \(-0.369302\pi\) | ||||
0.399160 | + | 0.916881i | \(0.369302\pi\) | |||||||
\(180\) | −386.320 | −0.159970 | ||||||||
\(181\) | −3990.39 | −1.63869 | −0.819345 | − | 0.573300i | \(-0.805663\pi\) | ||||
−0.819345 | + | 0.573300i | \(0.805663\pi\) | |||||||
\(182\) | −363.168 | −0.147911 | ||||||||
\(183\) | −380.496 | −0.153700 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −1077.98 | −0.428404 | ||||||||
\(186\) | −360.760 | −0.142216 | ||||||||
\(187\) | −252.631 | −0.0987926 | ||||||||
\(188\) | −1112.56 | −0.431605 | ||||||||
\(189\) | 542.824 | 0.208914 | ||||||||
\(190\) | 257.200 | 0.0982066 | ||||||||
\(191\) | 3212.75 | 1.21710 | 0.608550 | − | 0.793516i | \(-0.291752\pi\) | ||||
0.608550 | + | 0.793516i | \(0.291752\pi\) | |||||||
\(192\) | 177.408 | 0.0666840 | ||||||||
\(193\) | −2131.32 | −0.794899 | −0.397450 | − | 0.917624i | \(-0.630105\pi\) | ||||
−0.397450 | + | 0.917624i | \(0.630105\pi\) | |||||||
\(194\) | 838.783 | 0.310418 | ||||||||
\(195\) | −595.260 | −0.218602 | ||||||||
\(196\) | −1300.50 | −0.473942 | ||||||||
\(197\) | 3389.48 | 1.22584 | 0.612920 | − | 0.790145i | \(-0.289995\pi\) | ||||
0.612920 | + | 0.790145i | \(0.289995\pi\) | |||||||
\(198\) | −1302.67 | −0.467560 | ||||||||
\(199\) | −689.032 | −0.245448 | −0.122724 | − | 0.992441i | \(-0.539163\pi\) | ||||
−0.122724 | + | 0.992441i | \(0.539163\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | −1221.49 | −0.428643 | ||||||||
\(202\) | −1856.33 | −0.646588 | ||||||||
\(203\) | 200.644 | 0.0693716 | ||||||||
\(204\) | 83.0716 | 0.0285107 | ||||||||
\(205\) | 750.641 | 0.255742 | ||||||||
\(206\) | −2763.55 | −0.934689 | ||||||||
\(207\) | 444.268 | 0.149173 | ||||||||
\(208\) | −687.168 | −0.229070 | ||||||||
\(209\) | 867.280 | 0.287038 | ||||||||
\(210\) | 117.200 | 0.0385123 | ||||||||
\(211\) | 135.653 | 0.0442593 | 0.0221296 | − | 0.999755i | \(-0.492955\pi\) | ||||
0.0221296 | + | 0.999755i | \(0.492955\pi\) | |||||||
\(212\) | −729.616 | −0.236369 | ||||||||
\(213\) | 2969.61 | 0.955279 | ||||||||
\(214\) | 1527.64 | 0.487978 | ||||||||
\(215\) | −415.080 | −0.131666 | ||||||||
\(216\) | 1027.10 | 0.323544 | ||||||||
\(217\) | −275.124 | −0.0860676 | ||||||||
\(218\) | 313.472 | 0.0973899 | ||||||||
\(219\) | −747.764 | −0.230727 | ||||||||
\(220\) | −674.400 | −0.206673 | ||||||||
\(221\) | −321.767 | −0.0979385 | ||||||||
\(222\) | 1195.26 | 0.361356 | ||||||||
\(223\) | 205.321 | 0.0616560 | 0.0308280 | − | 0.999525i | \(-0.490186\pi\) | ||||
0.0308280 | + | 0.999525i | \(0.490186\pi\) | |||||||
\(224\) | 135.296 | 0.0403564 | ||||||||
\(225\) | −482.900 | −0.143082 | ||||||||
\(226\) | −2072.25 | −0.609929 | ||||||||
\(227\) | 1800.57 | 0.526467 | 0.263233 | − | 0.964732i | \(-0.415211\pi\) | ||||
0.263233 | + | 0.964732i | \(0.415211\pi\) | |||||||
\(228\) | −285.184 | −0.0828366 | ||||||||
\(229\) | −1265.24 | −0.365106 | −0.182553 | − | 0.983196i | \(-0.558436\pi\) | ||||
−0.182553 | + | 0.983196i | \(0.558436\pi\) | |||||||
\(230\) | 230.000 | 0.0659380 | ||||||||
\(231\) | 395.199 | 0.112564 | ||||||||
\(232\) | 379.648 | 0.107436 | ||||||||
\(233\) | 1252.76 | 0.352235 | 0.176118 | − | 0.984369i | \(-0.443646\pi\) | ||||
0.176118 | + | 0.984369i | \(0.443646\pi\) | |||||||
\(234\) | −1659.17 | −0.463518 | ||||||||
\(235\) | −1390.70 | −0.386039 | ||||||||
\(236\) | −1080.24 | −0.297956 | ||||||||
\(237\) | 541.184 | 0.148328 | ||||||||
\(238\) | 63.3525 | 0.0172543 | ||||||||
\(239\) | 4345.22 | 1.17602 | 0.588010 | − | 0.808854i | \(-0.299912\pi\) | ||||
0.588010 | + | 0.808854i | \(0.299912\pi\) | |||||||
\(240\) | 221.760 | 0.0596440 | ||||||||
\(241\) | 427.153 | 0.114171 | 0.0570857 | − | 0.998369i | \(-0.481819\pi\) | ||||
0.0570857 | + | 0.998369i | \(0.481819\pi\) | |||||||
\(242\) | 387.921 | 0.103043 | ||||||||
\(243\) | 3925.63 | 1.03634 | ||||||||
\(244\) | −549.056 | −0.144056 | ||||||||
\(245\) | −1625.62 | −0.423906 | ||||||||
\(246\) | −832.311 | −0.215716 | ||||||||
\(247\) | 1104.62 | 0.284557 | ||||||||
\(248\) | −520.576 | −0.133293 | ||||||||
\(249\) | 378.866 | 0.0964242 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | 3079.51 | 0.774411 | 0.387205 | − | 0.921993i | \(-0.373440\pi\) | ||||
0.387205 | + | 0.921993i | \(0.373440\pi\) | |||||||
\(252\) | 326.672 | 0.0816604 | ||||||||
\(253\) | 775.560 | 0.192724 | ||||||||
\(254\) | 2456.62 | 0.606857 | ||||||||
\(255\) | 103.839 | 0.0255007 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5829.41 | −1.41490 | −0.707448 | − | 0.706765i | \(-0.750154\pi\) | ||||
−0.707448 | + | 0.706765i | \(0.750154\pi\) | |||||||
\(258\) | 460.241 | 0.111059 | ||||||||
\(259\) | 911.539 | 0.218688 | ||||||||
\(260\) | −858.960 | −0.204886 | ||||||||
\(261\) | 916.660 | 0.217394 | ||||||||
\(262\) | −3471.71 | −0.818636 | ||||||||
\(263\) | 3528.99 | 0.827402 | 0.413701 | − | 0.910413i | \(-0.364236\pi\) | ||||
0.413701 | + | 0.910413i | \(0.364236\pi\) | |||||||
\(264\) | 747.776 | 0.174327 | ||||||||
\(265\) | −912.020 | −0.211415 | ||||||||
\(266\) | −217.488 | −0.0501318 | ||||||||
\(267\) | 1746.07 | 0.400217 | ||||||||
\(268\) | −1762.61 | −0.401748 | ||||||||
\(269\) | −4112.06 | −0.932032 | −0.466016 | − | 0.884776i | \(-0.654311\pi\) | ||||
−0.466016 | + | 0.884776i | \(0.654311\pi\) | |||||||
\(270\) | 1283.88 | 0.289387 | ||||||||
\(271\) | 1119.28 | 0.250890 | 0.125445 | − | 0.992101i | \(-0.459964\pi\) | ||||
0.125445 | + | 0.992101i | \(0.459964\pi\) | |||||||
\(272\) | 119.872 | 0.0267218 | ||||||||
\(273\) | 503.352 | 0.111591 | ||||||||
\(274\) | 2614.80 | 0.576518 | ||||||||
\(275\) | −843.000 | −0.184854 | ||||||||
\(276\) | −255.024 | −0.0556183 | ||||||||
\(277\) | −2919.79 | −0.633333 | −0.316666 | − | 0.948537i | \(-0.602564\pi\) | ||||
−0.316666 | + | 0.948537i | \(0.602564\pi\) | |||||||
\(278\) | −2147.65 | −0.463336 | ||||||||
\(279\) | −1256.93 | −0.269715 | ||||||||
\(280\) | 169.120 | 0.0360959 | ||||||||
\(281\) | 2925.91 | 0.621156 | 0.310578 | − | 0.950548i | \(-0.399477\pi\) | ||||
0.310578 | + | 0.950548i | \(0.399477\pi\) | |||||||
\(282\) | 1542.01 | 0.325622 | ||||||||
\(283\) | 7023.11 | 1.47520 | 0.737598 | − | 0.675240i | \(-0.235960\pi\) | ||||
0.737598 | + | 0.675240i | \(0.235960\pi\) | |||||||
\(284\) | 4285.15 | 0.895342 | ||||||||
\(285\) | −356.480 | −0.0740914 | ||||||||
\(286\) | −2896.42 | −0.598841 | ||||||||
\(287\) | −634.741 | −0.130549 | ||||||||
\(288\) | 618.112 | 0.126467 | ||||||||
\(289\) | −4856.87 | −0.988575 | ||||||||
\(290\) | 474.560 | 0.0960935 | ||||||||
\(291\) | −1162.55 | −0.234193 | ||||||||
\(292\) | −1079.02 | −0.216250 | ||||||||
\(293\) | 634.237 | 0.126459 | 0.0632296 | − | 0.997999i | \(-0.479860\pi\) | ||||
0.0632296 | + | 0.997999i | \(0.479860\pi\) | |||||||
\(294\) | 1802.49 | 0.357562 | ||||||||
\(295\) | −1350.30 | −0.266500 | ||||||||
\(296\) | 1724.77 | 0.338683 | ||||||||
\(297\) | 4329.25 | 0.845820 | ||||||||
\(298\) | −4618.16 | −0.897728 | ||||||||
\(299\) | 987.804 | 0.191058 | ||||||||
\(300\) | 277.200 | 0.0533472 | ||||||||
\(301\) | 350.991 | 0.0672120 | ||||||||
\(302\) | 175.207 | 0.0333843 | ||||||||
\(303\) | 2572.87 | 0.487814 | ||||||||
\(304\) | −411.520 | −0.0776392 | ||||||||
\(305\) | −686.320 | −0.128848 | ||||||||
\(306\) | 289.432 | 0.0540710 | ||||||||
\(307\) | 5365.54 | 0.997485 | 0.498742 | − | 0.866750i | \(-0.333795\pi\) | ||||
0.498742 | + | 0.866750i | \(0.333795\pi\) | |||||||
\(308\) | 570.273 | 0.105501 | ||||||||
\(309\) | 3830.29 | 0.705170 | ||||||||
\(310\) | −650.720 | −0.119221 | ||||||||
\(311\) | −9570.36 | −1.74497 | −0.872484 | − | 0.488642i | \(-0.837492\pi\) | ||||
−0.872484 | + | 0.488642i | \(0.837492\pi\) | |||||||
\(312\) | 952.416 | 0.172820 | ||||||||
\(313\) | −8376.76 | −1.51272 | −0.756361 | − | 0.654154i | \(-0.773025\pi\) | ||||
−0.756361 | + | 0.654154i | \(0.773025\pi\) | |||||||
\(314\) | 3724.60 | 0.669399 | ||||||||
\(315\) | 408.340 | 0.0730392 | ||||||||
\(316\) | 780.928 | 0.139021 | ||||||||
\(317\) | −5672.79 | −1.00510 | −0.502549 | − | 0.864549i | \(-0.667604\pi\) | ||||
−0.502549 | + | 0.864549i | \(0.667604\pi\) | |||||||
\(318\) | 1011.25 | 0.178327 | ||||||||
\(319\) | 1600.22 | 0.280862 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | −2117.31 | −0.368152 | ||||||||
\(322\) | −194.488 | −0.0336596 | ||||||||
\(323\) | −192.695 | −0.0331945 | ||||||||
\(324\) | 662.561 | 0.113608 | ||||||||
\(325\) | −1073.70 | −0.183256 | ||||||||
\(326\) | −153.478 | −0.0260748 | ||||||||
\(327\) | −434.472 | −0.0734752 | ||||||||
\(328\) | −1201.03 | −0.202181 | ||||||||
\(329\) | 1175.98 | 0.197063 | ||||||||
\(330\) | 934.720 | 0.155923 | ||||||||
\(331\) | 5436.79 | 0.902819 | 0.451410 | − | 0.892317i | \(-0.350921\pi\) | ||||
0.451410 | + | 0.892317i | \(0.350921\pi\) | |||||||
\(332\) | 546.703 | 0.0903742 | ||||||||
\(333\) | 4164.45 | 0.685317 | ||||||||
\(334\) | 4649.92 | 0.761774 | ||||||||
\(335\) | −2203.26 | −0.359334 | ||||||||
\(336\) | −187.520 | −0.0304466 | ||||||||
\(337\) | 6693.79 | 1.08200 | 0.541000 | − | 0.841022i | \(-0.318046\pi\) | ||||
0.541000 | + | 0.841022i | \(0.318046\pi\) | |||||||
\(338\) | 704.936 | 0.113442 | ||||||||
\(339\) | 2872.14 | 0.460157 | ||||||||
\(340\) | 149.840 | 0.0239007 | ||||||||
\(341\) | −2194.23 | −0.348458 | ||||||||
\(342\) | −993.616 | −0.157101 | ||||||||
\(343\) | 2824.83 | 0.444683 | ||||||||
\(344\) | 664.128 | 0.104091 | ||||||||
\(345\) | −318.780 | −0.0497465 | ||||||||
\(346\) | 4851.03 | 0.753736 | ||||||||
\(347\) | 2556.53 | 0.395509 | 0.197755 | − | 0.980252i | \(-0.436635\pi\) | ||||
0.197755 | + | 0.980252i | \(0.436635\pi\) | |||||||
\(348\) | −526.192 | −0.0810542 | ||||||||
\(349\) | −10566.7 | −1.62069 | −0.810344 | − | 0.585954i | \(-0.800720\pi\) | ||||
−0.810344 | + | 0.585954i | \(0.800720\pi\) | |||||||
\(350\) | 211.400 | 0.0322851 | ||||||||
\(351\) | 5514.01 | 0.838508 | ||||||||
\(352\) | 1079.04 | 0.163389 | ||||||||
\(353\) | 4561.90 | 0.687834 | 0.343917 | − | 0.939000i | \(-0.388246\pi\) | ||||
0.343917 | + | 0.939000i | \(0.388246\pi\) | |||||||
\(354\) | 1497.21 | 0.224791 | ||||||||
\(355\) | 5356.44 | 0.800818 | ||||||||
\(356\) | 2519.58 | 0.375106 | ||||||||
\(357\) | −87.8066 | −0.0130174 | ||||||||
\(358\) | −3823.72 | −0.564497 | ||||||||
\(359\) | −12107.3 | −1.77995 | −0.889974 | − | 0.456012i | \(-0.849278\pi\) | ||||
−0.889974 | + | 0.456012i | \(0.849278\pi\) | |||||||
\(360\) | 772.640 | 0.113116 | ||||||||
\(361\) | −6197.48 | −0.903555 | ||||||||
\(362\) | 7980.77 | 1.15873 | ||||||||
\(363\) | −537.658 | −0.0777404 | ||||||||
\(364\) | 726.337 | 0.104589 | ||||||||
\(365\) | −1348.78 | −0.193420 | ||||||||
\(366\) | 760.992 | 0.108682 | ||||||||
\(367\) | −2215.89 | −0.315174 | −0.157587 | − | 0.987505i | \(-0.550371\pi\) | ||||
−0.157587 | + | 0.987505i | \(0.550371\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −2899.88 | −0.409110 | ||||||||
\(370\) | 2155.96 | 0.302927 | ||||||||
\(371\) | 771.204 | 0.107922 | ||||||||
\(372\) | 721.519 | 0.100562 | ||||||||
\(373\) | −3872.34 | −0.537539 | −0.268770 | − | 0.963205i | \(-0.586617\pi\) | ||||
−0.268770 | + | 0.963205i | \(0.586617\pi\) | |||||||
\(374\) | 505.262 | 0.0698569 | ||||||||
\(375\) | 346.500 | 0.0477152 | ||||||||
\(376\) | 2225.12 | 0.305191 | ||||||||
\(377\) | 2038.14 | 0.278434 | ||||||||
\(378\) | −1085.65 | −0.147724 | ||||||||
\(379\) | −819.918 | −0.111125 | −0.0555625 | − | 0.998455i | \(-0.517695\pi\) | ||||
−0.0555625 | + | 0.998455i | \(0.517695\pi\) | |||||||
\(380\) | −514.400 | −0.0694426 | ||||||||
\(381\) | −3404.87 | −0.457840 | ||||||||
\(382\) | −6425.49 | −0.860620 | ||||||||
\(383\) | 6281.54 | 0.838046 | 0.419023 | − | 0.907976i | \(-0.362373\pi\) | ||||
0.419023 | + | 0.907976i | \(0.362373\pi\) | |||||||
\(384\) | −354.816 | −0.0471527 | ||||||||
\(385\) | 712.841 | 0.0943629 | ||||||||
\(386\) | 4262.63 | 0.562079 | ||||||||
\(387\) | 1603.54 | 0.210626 | ||||||||
\(388\) | −1677.57 | −0.219499 | ||||||||
\(389\) | −13939.3 | −1.81684 | −0.908419 | − | 0.418060i | \(-0.862710\pi\) | ||||
−0.908419 | + | 0.418060i | \(0.862710\pi\) | |||||||
\(390\) | 1190.52 | 0.154575 | ||||||||
\(391\) | −172.316 | −0.0222875 | ||||||||
\(392\) | 2600.99 | 0.335127 | ||||||||
\(393\) | 4811.79 | 0.617615 | ||||||||
\(394\) | −6778.96 | −0.866799 | ||||||||
\(395\) | 976.161 | 0.124344 | ||||||||
\(396\) | 2605.34 | 0.330615 | ||||||||
\(397\) | −2540.96 | −0.321227 | −0.160613 | − | 0.987017i | \(-0.551347\pi\) | ||||
−0.160613 | + | 0.987017i | \(0.551347\pi\) | |||||||
\(398\) | 1378.06 | 0.173558 | ||||||||
\(399\) | 301.439 | 0.0378216 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 4996.13 | 0.622181 | 0.311091 | − | 0.950380i | \(-0.399306\pi\) | ||||
0.311091 | + | 0.950380i | \(0.399306\pi\) | |||||||
\(402\) | 2442.98 | 0.303096 | ||||||||
\(403\) | −2794.72 | −0.345446 | ||||||||
\(404\) | 3712.66 | 0.457207 | ||||||||
\(405\) | 828.201 | 0.101614 | ||||||||
\(406\) | −401.288 | −0.0490531 | ||||||||
\(407\) | 7269.90 | 0.885395 | ||||||||
\(408\) | −166.143 | −0.0201601 | ||||||||
\(409\) | −1768.34 | −0.213787 | −0.106894 | − | 0.994270i | \(-0.534090\pi\) | ||||
−0.106894 | + | 0.994270i | \(0.534090\pi\) | |||||||
\(410\) | −1501.28 | −0.180837 | ||||||||
\(411\) | −3624.11 | −0.434950 | ||||||||
\(412\) | 5527.11 | 0.660925 | ||||||||
\(413\) | 1141.81 | 0.136041 | ||||||||
\(414\) | −888.536 | −0.105481 | ||||||||
\(415\) | 683.379 | 0.0808331 | ||||||||
\(416\) | 1374.34 | 0.161977 | ||||||||
\(417\) | 2976.64 | 0.349561 | ||||||||
\(418\) | −1734.56 | −0.202967 | ||||||||
\(419\) | 45.6353 | 0.00532083 | 0.00266042 | − | 0.999996i | \(-0.499153\pi\) | ||||
0.00266042 | + | 0.999996i | \(0.499153\pi\) | |||||||
\(420\) | −234.400 | −0.0272323 | ||||||||
\(421\) | −817.214 | −0.0946047 | −0.0473023 | − | 0.998881i | \(-0.515062\pi\) | ||||
−0.0473023 | + | 0.998881i | \(0.515062\pi\) | |||||||
\(422\) | −271.305 | −0.0312960 | ||||||||
\(423\) | 5372.55 | 0.617547 | ||||||||
\(424\) | 1459.23 | 0.167138 | ||||||||
\(425\) | 187.301 | 0.0213774 | ||||||||
\(426\) | −5939.23 | −0.675485 | ||||||||
\(427\) | 580.352 | 0.0657733 | ||||||||
\(428\) | −3055.28 | −0.345053 | ||||||||
\(429\) | 4014.44 | 0.451792 | ||||||||
\(430\) | 830.160 | 0.0931020 | ||||||||
\(431\) | 2475.30 | 0.276639 | 0.138319 | − | 0.990388i | \(-0.455830\pi\) | ||||
0.138319 | + | 0.990388i | \(0.455830\pi\) | |||||||
\(432\) | −2054.21 | −0.228780 | ||||||||
\(433\) | −59.6371 | −0.00661888 | −0.00330944 | − | 0.999995i | \(-0.501053\pi\) | ||||
−0.00330944 | + | 0.999995i | \(0.501053\pi\) | |||||||
\(434\) | 550.249 | 0.0608590 | ||||||||
\(435\) | −657.741 | −0.0724971 | ||||||||
\(436\) | −626.944 | −0.0688651 | ||||||||
\(437\) | 591.560 | 0.0647555 | ||||||||
\(438\) | 1495.53 | 0.163149 | ||||||||
\(439\) | −7258.27 | −0.789108 | −0.394554 | − | 0.918873i | \(-0.629101\pi\) | ||||
−0.394554 | + | 0.918873i | \(0.629101\pi\) | |||||||
\(440\) | 1348.80 | 0.146140 | ||||||||
\(441\) | 6280.10 | 0.678123 | ||||||||
\(442\) | 643.535 | 0.0692530 | ||||||||
\(443\) | −9721.43 | −1.04262 | −0.521308 | − | 0.853369i | \(-0.674556\pi\) | ||||
−0.521308 | + | 0.853369i | \(0.674556\pi\) | |||||||
\(444\) | −2390.53 | −0.255517 | ||||||||
\(445\) | 3149.48 | 0.335505 | ||||||||
\(446\) | −410.641 | −0.0435974 | ||||||||
\(447\) | 6400.78 | 0.677285 | ||||||||
\(448\) | −270.592 | −0.0285363 | ||||||||
\(449\) | −10662.3 | −1.12068 | −0.560340 | − | 0.828263i | \(-0.689329\pi\) | ||||
−0.560340 | + | 0.828263i | \(0.689329\pi\) | |||||||
\(450\) | 965.800 | 0.101174 | ||||||||
\(451\) | −5062.32 | −0.528549 | ||||||||
\(452\) | 4144.50 | 0.431285 | ||||||||
\(453\) | −242.838 | −0.0251866 | ||||||||
\(454\) | −3601.14 | −0.372268 | ||||||||
\(455\) | 907.921 | 0.0935472 | ||||||||
\(456\) | 570.368 | 0.0585744 | ||||||||
\(457\) | 4135.30 | 0.423284 | 0.211642 | − | 0.977347i | \(-0.432119\pi\) | ||||
0.211642 | + | 0.977347i | \(0.432119\pi\) | |||||||
\(458\) | 2530.48 | 0.258169 | ||||||||
\(459\) | −961.886 | −0.0978148 | ||||||||
\(460\) | −460.000 | −0.0466252 | ||||||||
\(461\) | −12080.6 | −1.22050 | −0.610249 | − | 0.792210i | \(-0.708931\pi\) | ||||
−0.610249 | + | 0.792210i | \(0.708931\pi\) | |||||||
\(462\) | −790.399 | −0.0795945 | ||||||||
\(463\) | −2114.39 | −0.212234 | −0.106117 | − | 0.994354i | \(-0.533842\pi\) | ||||
−0.106117 | + | 0.994354i | \(0.533842\pi\) | |||||||
\(464\) | −759.296 | −0.0759686 | ||||||||
\(465\) | 901.899 | 0.0899453 | ||||||||
\(466\) | −2505.51 | −0.249068 | ||||||||
\(467\) | −14182.0 | −1.40527 | −0.702637 | − | 0.711548i | \(-0.747994\pi\) | ||||
−0.702637 | + | 0.711548i | \(0.747994\pi\) | |||||||
\(468\) | 3318.34 | 0.327757 | ||||||||
\(469\) | 1863.08 | 0.183430 | ||||||||
\(470\) | 2781.40 | 0.272971 | ||||||||
\(471\) | −5162.30 | −0.505024 | ||||||||
\(472\) | 2160.48 | 0.210687 | ||||||||
\(473\) | 2799.30 | 0.272118 | ||||||||
\(474\) | −1082.37 | −0.104884 | ||||||||
\(475\) | −643.000 | −0.0621113 | ||||||||
\(476\) | −126.705 | −0.0122007 | ||||||||
\(477\) | 3523.32 | 0.338200 | ||||||||
\(478\) | −8690.43 | −0.831571 | ||||||||
\(479\) | −7546.93 | −0.719891 | −0.359946 | − | 0.932973i | \(-0.617205\pi\) | ||||
−0.359946 | + | 0.932973i | \(0.617205\pi\) | |||||||
\(480\) | −443.520 | −0.0421747 | ||||||||
\(481\) | 9259.42 | 0.877741 | ||||||||
\(482\) | −854.306 | −0.0807314 | ||||||||
\(483\) | 269.560 | 0.0253943 | ||||||||
\(484\) | −775.841 | −0.0728626 | ||||||||
\(485\) | −2096.96 | −0.196326 | ||||||||
\(486\) | −7851.26 | −0.732800 | ||||||||
\(487\) | −17109.7 | −1.59202 | −0.796010 | − | 0.605284i | \(-0.793060\pi\) | ||||
−0.796010 | + | 0.605284i | \(0.793060\pi\) | |||||||
\(488\) | 1098.11 | 0.101863 | ||||||||
\(489\) | 212.721 | 0.0196719 | ||||||||
\(490\) | 3251.24 | 0.299747 | ||||||||
\(491\) | 9833.66 | 0.903843 | 0.451922 | − | 0.892058i | \(-0.350739\pi\) | ||||
0.451922 | + | 0.892058i | \(0.350739\pi\) | |||||||
\(492\) | 1664.62 | 0.152534 | ||||||||
\(493\) | −355.541 | −0.0324803 | ||||||||
\(494\) | −2209.25 | −0.201212 | ||||||||
\(495\) | 3256.68 | 0.295711 | ||||||||
\(496\) | 1041.15 | 0.0942523 | ||||||||
\(497\) | −4529.40 | −0.408796 | ||||||||
\(498\) | −757.731 | −0.0681822 | ||||||||
\(499\) | −1705.54 | −0.153007 | −0.0765036 | − | 0.997069i | \(-0.524376\pi\) | ||||
−0.0765036 | + | 0.997069i | \(0.524376\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | −6444.80 | −0.574715 | ||||||||
\(502\) | −6159.03 | −0.547591 | ||||||||
\(503\) | −8705.79 | −0.771713 | −0.385857 | − | 0.922559i | \(-0.626094\pi\) | ||||
−0.385857 | + | 0.922559i | \(0.626094\pi\) | |||||||
\(504\) | −653.344 | −0.0577426 | ||||||||
\(505\) | 4640.82 | 0.408938 | ||||||||
\(506\) | −1551.12 | −0.136276 | ||||||||
\(507\) | −977.042 | −0.0855857 | ||||||||
\(508\) | −4913.23 | −0.429113 | ||||||||
\(509\) | −14926.4 | −1.29980 | −0.649902 | − | 0.760018i | \(-0.725190\pi\) | ||||
−0.649902 | + | 0.760018i | \(0.725190\pi\) | |||||||
\(510\) | −207.679 | −0.0180317 | ||||||||
\(511\) | 1140.53 | 0.0987358 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 3302.14 | 0.284197 | ||||||||
\(514\) | 11658.8 | 1.00048 | ||||||||
\(515\) | 6908.88 | 0.591149 | ||||||||
\(516\) | −920.482 | −0.0785309 | ||||||||
\(517\) | 9378.89 | 0.797839 | ||||||||
\(518\) | −1823.08 | −0.154636 | ||||||||
\(519\) | −6723.53 | −0.568651 | ||||||||
\(520\) | 1717.92 | 0.144877 | ||||||||
\(521\) | 17922.0 | 1.50706 | 0.753529 | − | 0.657415i | \(-0.228350\pi\) | ||||
0.753529 | + | 0.657415i | \(0.228350\pi\) | |||||||
\(522\) | −1833.32 | −0.153721 | ||||||||
\(523\) | −21926.5 | −1.83323 | −0.916615 | − | 0.399771i | \(-0.869090\pi\) | ||||
−0.916615 | + | 0.399771i | \(0.869090\pi\) | |||||||
\(524\) | 6943.41 | 0.578863 | ||||||||
\(525\) | −293.000 | −0.0243573 | ||||||||
\(526\) | −7057.98 | −0.585062 | ||||||||
\(527\) | 487.521 | 0.0402974 | ||||||||
\(528\) | −1495.55 | −0.123268 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 1824.04 | 0.149493 | ||||||||
\(531\) | 5216.48 | 0.426320 | ||||||||
\(532\) | 434.977 | 0.0354486 | ||||||||
\(533\) | −6447.71 | −0.523980 | ||||||||
\(534\) | −3492.15 | −0.282996 | ||||||||
\(535\) | −3819.10 | −0.308625 | ||||||||
\(536\) | 3525.22 | 0.284079 | ||||||||
\(537\) | 5299.68 | 0.425881 | ||||||||
\(538\) | 8224.12 | 0.659046 | ||||||||
\(539\) | 10963.2 | 0.876100 | ||||||||
\(540\) | −2567.76 | −0.204627 | ||||||||
\(541\) | −17623.6 | −1.40055 | −0.700275 | − | 0.713873i | \(-0.746939\pi\) | ||||
−0.700275 | + | 0.713873i | \(0.746939\pi\) | |||||||
\(542\) | −2238.55 | −0.177406 | ||||||||
\(543\) | −11061.4 | −0.874196 | ||||||||
\(544\) | −239.745 | −0.0188952 | ||||||||
\(545\) | −783.680 | −0.0615948 | ||||||||
\(546\) | −1006.70 | −0.0789064 | ||||||||
\(547\) | −9204.79 | −0.719504 | −0.359752 | − | 0.933048i | \(-0.617139\pi\) | ||||
−0.359752 | + | 0.933048i | \(0.617139\pi\) | |||||||
\(548\) | −5229.60 | −0.407660 | ||||||||
\(549\) | 2651.39 | 0.206118 | ||||||||
\(550\) | 1686.00 | 0.130711 | ||||||||
\(551\) | 1220.57 | 0.0943702 | ||||||||
\(552\) | 510.048 | 0.0393281 | ||||||||
\(553\) | −825.441 | −0.0634744 | ||||||||
\(554\) | 5839.58 | 0.447834 | ||||||||
\(555\) | −2988.16 | −0.228541 | ||||||||
\(556\) | 4295.30 | 0.327628 | ||||||||
\(557\) | 3584.33 | 0.272663 | 0.136331 | − | 0.990663i | \(-0.456469\pi\) | ||||
0.136331 | + | 0.990663i | \(0.456469\pi\) | |||||||
\(558\) | 2513.86 | 0.190717 | ||||||||
\(559\) | 3565.37 | 0.269766 | ||||||||
\(560\) | −338.240 | −0.0255236 | ||||||||
\(561\) | −700.294 | −0.0527031 | ||||||||
\(562\) | −5851.81 | −0.439224 | ||||||||
\(563\) | −9052.50 | −0.677651 | −0.338826 | − | 0.940849i | \(-0.610030\pi\) | ||||
−0.338826 | + | 0.940849i | \(0.610030\pi\) | |||||||
\(564\) | −3084.02 | −0.230249 | ||||||||
\(565\) | 5180.62 | 0.385753 | ||||||||
\(566\) | −14046.2 | −1.04312 | ||||||||
\(567\) | −700.327 | −0.0518712 | ||||||||
\(568\) | −8570.31 | −0.633102 | ||||||||
\(569\) | −13714.1 | −1.01042 | −0.505208 | − | 0.862998i | \(-0.668584\pi\) | ||||
−0.505208 | + | 0.862998i | \(0.668584\pi\) | |||||||
\(570\) | 712.959 | 0.0523905 | ||||||||
\(571\) | 1903.12 | 0.139480 | 0.0697398 | − | 0.997565i | \(-0.477783\pi\) | ||||
0.0697398 | + | 0.997565i | \(0.477783\pi\) | |||||||
\(572\) | 5792.83 | 0.423445 | ||||||||
\(573\) | 8905.74 | 0.649289 | ||||||||
\(574\) | 1269.48 | 0.0923122 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | −1236.22 | −0.0894260 | ||||||||
\(577\) | 14582.1 | 1.05210 | 0.526050 | − | 0.850454i | \(-0.323672\pi\) | ||||
0.526050 | + | 0.850454i | \(0.323672\pi\) | |||||||
\(578\) | 9713.74 | 0.699028 | ||||||||
\(579\) | −5908.02 | −0.424057 | ||||||||
\(580\) | −949.120 | −0.0679484 | ||||||||
\(581\) | −577.865 | −0.0412631 | ||||||||
\(582\) | 2325.11 | 0.165599 | ||||||||
\(583\) | 6150.67 | 0.436938 | ||||||||
\(584\) | 2158.05 | 0.152912 | ||||||||
\(585\) | 4147.92 | 0.293155 | ||||||||
\(586\) | −1268.47 | −0.0894201 | ||||||||
\(587\) | −13023.5 | −0.915734 | −0.457867 | − | 0.889021i | \(-0.651386\pi\) | ||||
−0.457867 | + | 0.889021i | \(0.651386\pi\) | |||||||
\(588\) | −3604.98 | −0.252835 | ||||||||
\(589\) | −1673.65 | −0.117083 | ||||||||
\(590\) | 2700.60 | 0.188444 | ||||||||
\(591\) | 9395.64 | 0.653951 | ||||||||
\(592\) | −3449.54 | −0.239485 | ||||||||
\(593\) | −17936.3 | −1.24209 | −0.621043 | − | 0.783776i | \(-0.713291\pi\) | ||||
−0.621043 | + | 0.783776i | \(0.713291\pi\) | |||||||
\(594\) | −8658.50 | −0.598085 | ||||||||
\(595\) | −158.381 | −0.0109126 | ||||||||
\(596\) | 9236.32 | 0.634789 | ||||||||
\(597\) | −1910.00 | −0.130940 | ||||||||
\(598\) | −1975.61 | −0.135098 | ||||||||
\(599\) | 18292.2 | 1.24774 | 0.623872 | − | 0.781526i | \(-0.285559\pi\) | ||||
0.623872 | + | 0.781526i | \(0.285559\pi\) | |||||||
\(600\) | −554.400 | −0.0377222 | ||||||||
\(601\) | 205.155 | 0.0139242 | 0.00696211 | − | 0.999976i | \(-0.497784\pi\) | ||||
0.00696211 | + | 0.999976i | \(0.497784\pi\) | |||||||
\(602\) | −701.983 | −0.0475260 | ||||||||
\(603\) | 8511.64 | 0.574827 | ||||||||
\(604\) | −350.415 | −0.0236063 | ||||||||
\(605\) | −969.802 | −0.0651703 | ||||||||
\(606\) | −5145.75 | −0.344937 | ||||||||
\(607\) | 23244.3 | 1.55429 | 0.777147 | − | 0.629319i | \(-0.216666\pi\) | ||||
0.777147 | + | 0.629319i | \(0.216666\pi\) | |||||||
\(608\) | 823.041 | 0.0548992 | ||||||||
\(609\) | 556.185 | 0.0370078 | ||||||||
\(610\) | 1372.64 | 0.0911091 | ||||||||
\(611\) | 11945.6 | 0.790942 | ||||||||
\(612\) | −578.864 | −0.0382339 | ||||||||
\(613\) | 15518.5 | 1.02249 | 0.511245 | − | 0.859435i | \(-0.329184\pi\) | ||||
0.511245 | + | 0.859435i | \(0.329184\pi\) | |||||||
\(614\) | −10731.1 | −0.705328 | ||||||||
\(615\) | 2080.78 | 0.136431 | ||||||||
\(616\) | −1140.55 | −0.0746005 | ||||||||
\(617\) | 26922.8 | 1.75668 | 0.878340 | − | 0.478036i | \(-0.158651\pi\) | ||||
0.878340 | + | 0.478036i | \(0.158651\pi\) | |||||||
\(618\) | −7660.57 | −0.498630 | ||||||||
\(619\) | 31.7390 | 0.00206090 | 0.00103045 | − | 0.999999i | \(-0.499672\pi\) | ||||
0.00103045 | + | 0.999999i | \(0.499672\pi\) | |||||||
\(620\) | 1301.44 | 0.0843018 | ||||||||
\(621\) | 2952.93 | 0.190816 | ||||||||
\(622\) | 19140.7 | 1.23388 | ||||||||
\(623\) | −2663.20 | −0.171266 | ||||||||
\(624\) | −1904.83 | −0.122202 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 16753.5 | 1.06966 | ||||||||
\(627\) | 2404.10 | 0.153127 | ||||||||
\(628\) | −7449.20 | −0.473337 | ||||||||
\(629\) | −1615.25 | −0.102391 | ||||||||
\(630\) | −816.680 | −0.0516465 | ||||||||
\(631\) | 16322.7 | 1.02979 | 0.514894 | − | 0.857254i | \(-0.327831\pi\) | ||||
0.514894 | + | 0.857254i | \(0.327831\pi\) | |||||||
\(632\) | −1561.86 | −0.0983027 | ||||||||
\(633\) | 376.029 | 0.0236111 | ||||||||
\(634\) | 11345.6 | 0.710711 | ||||||||
\(635\) | −6141.54 | −0.383810 | ||||||||
\(636\) | −2022.50 | −0.126096 | ||||||||
\(637\) | 13963.4 | 0.868526 | ||||||||
\(638\) | −3200.43 | −0.198599 | ||||||||
\(639\) | −20693.0 | −1.28107 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | 13384.6 | 0.824744 | 0.412372 | − | 0.911016i | \(-0.364700\pi\) | ||||
0.412372 | + | 0.911016i | \(0.364700\pi\) | |||||||
\(642\) | 4234.62 | 0.260323 | ||||||||
\(643\) | 9985.79 | 0.612443 | 0.306222 | − | 0.951960i | \(-0.400935\pi\) | ||||
0.306222 | + | 0.951960i | \(0.400935\pi\) | |||||||
\(644\) | 388.976 | 0.0238009 | ||||||||
\(645\) | −1150.60 | −0.0702402 | ||||||||
\(646\) | 385.390 | 0.0234721 | ||||||||
\(647\) | 1910.99 | 0.116119 | 0.0580593 | − | 0.998313i | \(-0.481509\pi\) | ||||
0.0580593 | + | 0.998313i | \(0.481509\pi\) | |||||||
\(648\) | −1325.12 | −0.0803329 | ||||||||
\(649\) | 9106.43 | 0.550784 | ||||||||
\(650\) | 2147.40 | 0.129582 | ||||||||
\(651\) | −762.646 | −0.0459147 | ||||||||
\(652\) | 306.957 | 0.0184377 | ||||||||
\(653\) | −18735.8 | −1.12280 | −0.561399 | − | 0.827545i | \(-0.689737\pi\) | ||||
−0.561399 | + | 0.827545i | \(0.689737\pi\) | |||||||
\(654\) | 868.945 | 0.0519548 | ||||||||
\(655\) | 8679.26 | 0.517751 | ||||||||
\(656\) | 2402.05 | 0.142964 | ||||||||
\(657\) | 5210.61 | 0.309414 | ||||||||
\(658\) | −2351.95 | −0.139344 | ||||||||
\(659\) | 1222.24 | 0.0722486 | 0.0361243 | − | 0.999347i | \(-0.488499\pi\) | ||||
0.0361243 | + | 0.999347i | \(0.488499\pi\) | |||||||
\(660\) | −1869.44 | −0.110254 | ||||||||
\(661\) | −14293.5 | −0.841076 | −0.420538 | − | 0.907275i | \(-0.638159\pi\) | ||||
−0.420538 | + | 0.907275i | \(0.638159\pi\) | |||||||
\(662\) | −10873.6 | −0.638390 | ||||||||
\(663\) | −891.940 | −0.0522475 | ||||||||
\(664\) | −1093.41 | −0.0639042 | ||||||||
\(665\) | 543.721 | 0.0317062 | ||||||||
\(666\) | −8328.91 | −0.484592 | ||||||||
\(667\) | 1091.49 | 0.0633622 | ||||||||
\(668\) | −9299.85 | −0.538655 | ||||||||
\(669\) | 569.149 | 0.0328917 | ||||||||
\(670\) | 4406.52 | 0.254088 | ||||||||
\(671\) | 4628.55 | 0.266294 | ||||||||
\(672\) | 375.041 | 0.0215290 | ||||||||
\(673\) | 11462.0 | 0.656506 | 0.328253 | − | 0.944590i | \(-0.393540\pi\) | ||||
0.328253 | + | 0.944590i | \(0.393540\pi\) | |||||||
\(674\) | −13387.6 | −0.765090 | ||||||||
\(675\) | −3209.70 | −0.183024 | ||||||||
\(676\) | −1409.87 | −0.0802157 | ||||||||
\(677\) | 12842.2 | 0.729046 | 0.364523 | − | 0.931194i | \(-0.381232\pi\) | ||||
0.364523 | + | 0.931194i | \(0.381232\pi\) | |||||||
\(678\) | −5744.28 | −0.325380 | ||||||||
\(679\) | 1773.19 | 0.100219 | ||||||||
\(680\) | −299.681 | −0.0169003 | ||||||||
\(681\) | 4991.18 | 0.280855 | ||||||||
\(682\) | 4388.46 | 0.246397 | ||||||||
\(683\) | 15416.5 | 0.863683 | 0.431841 | − | 0.901950i | \(-0.357864\pi\) | ||||
0.431841 | + | 0.901950i | \(0.357864\pi\) | |||||||
\(684\) | 1987.23 | 0.111087 | ||||||||
\(685\) | −6537.00 | −0.364622 | ||||||||
\(686\) | −5649.65 | −0.314438 | ||||||||
\(687\) | −3507.25 | −0.194774 | ||||||||
\(688\) | −1328.26 | −0.0736036 | ||||||||
\(689\) | 7833.89 | 0.433160 | ||||||||
\(690\) | 637.560 | 0.0351761 | ||||||||
\(691\) | 15247.1 | 0.839400 | 0.419700 | − | 0.907663i | \(-0.362135\pi\) | ||||
0.419700 | + | 0.907663i | \(0.362135\pi\) | |||||||
\(692\) | −9702.05 | −0.532972 | ||||||||
\(693\) | −2753.85 | −0.150952 | ||||||||
\(694\) | −5113.06 | −0.279667 | ||||||||
\(695\) | 5369.12 | 0.293039 | ||||||||
\(696\) | 1052.38 | 0.0573140 | ||||||||
\(697\) | 1124.76 | 0.0611240 | ||||||||
\(698\) | 21133.3 | 1.14600 | ||||||||
\(699\) | 3472.64 | 0.187908 | ||||||||
\(700\) | −422.800 | −0.0228290 | ||||||||
\(701\) | −8160.98 | −0.439709 | −0.219855 | − | 0.975533i | \(-0.570558\pi\) | ||||
−0.219855 | + | 0.975533i | \(0.570558\pi\) | |||||||
\(702\) | −11028.0 | −0.592914 | ||||||||
\(703\) | 5545.13 | 0.297495 | ||||||||
\(704\) | −2158.08 | −0.115534 | ||||||||
\(705\) | −3855.02 | −0.205941 | ||||||||
\(706\) | −9123.80 | −0.486372 | ||||||||
\(707\) | −3924.28 | −0.208752 | ||||||||
\(708\) | −2994.43 | −0.158951 | ||||||||
\(709\) | 14069.0 | 0.745235 | 0.372618 | − | 0.927985i | \(-0.378460\pi\) | ||||
0.372618 | + | 0.927985i | \(0.378460\pi\) | |||||||
\(710\) | −10712.9 | −0.566264 | ||||||||
\(711\) | −3771.10 | −0.198913 | ||||||||
\(712\) | −5039.17 | −0.265240 | ||||||||
\(713\) | −1496.66 | −0.0786119 | ||||||||
\(714\) | 175.613 | 0.00920471 | ||||||||
\(715\) | 7241.04 | 0.378741 | ||||||||
\(716\) | 7647.44 | 0.399160 | ||||||||
\(717\) | 12044.9 | 0.627374 | ||||||||
\(718\) | 24214.7 | 1.25861 | ||||||||
\(719\) | −19040.6 | −0.987613 | −0.493807 | − | 0.869572i | \(-0.664395\pi\) | ||||
−0.493807 | + | 0.869572i | \(0.664395\pi\) | |||||||
\(720\) | −1545.28 | −0.0799850 | ||||||||
\(721\) | −5842.15 | −0.301766 | ||||||||
\(722\) | 12395.0 | 0.638910 | ||||||||
\(723\) | 1184.07 | 0.0609073 | ||||||||
\(724\) | −15961.5 | −0.819345 | ||||||||
\(725\) | −1186.40 | −0.0607749 | ||||||||
\(726\) | 1075.32 | 0.0549707 | ||||||||
\(727\) | −25001.6 | −1.27546 | −0.637728 | − | 0.770262i | \(-0.720126\pi\) | ||||
−0.637728 | + | 0.770262i | \(0.720126\pi\) | |||||||
\(728\) | −1452.67 | −0.0739556 | ||||||||
\(729\) | 6409.57 | 0.325640 | ||||||||
\(730\) | 2697.56 | 0.136769 | ||||||||
\(731\) | −621.957 | −0.0314691 | ||||||||
\(732\) | −1521.98 | −0.0768500 | ||||||||
\(733\) | 7755.07 | 0.390778 | 0.195389 | − | 0.980726i | \(-0.437403\pi\) | ||||
0.195389 | + | 0.980726i | \(0.437403\pi\) | |||||||
\(734\) | 4431.79 | 0.222861 | ||||||||
\(735\) | −4506.22 | −0.226142 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 14858.8 | 0.742647 | ||||||||
\(738\) | 5799.75 | 0.289284 | ||||||||
\(739\) | 1304.33 | 0.0649265 | 0.0324632 | − | 0.999473i | \(-0.489665\pi\) | ||||
0.0324632 | + | 0.999473i | \(0.489665\pi\) | |||||||
\(740\) | −4311.92 | −0.214202 | ||||||||
\(741\) | 3062.02 | 0.151803 | ||||||||
\(742\) | −1542.41 | −0.0763121 | ||||||||
\(743\) | 2431.00 | 0.120033 | 0.0600165 | − | 0.998197i | \(-0.480885\pi\) | ||||
0.0600165 | + | 0.998197i | \(0.480885\pi\) | |||||||
\(744\) | −1443.04 | −0.0711080 | ||||||||
\(745\) | 11545.4 | 0.567773 | ||||||||
\(746\) | 7744.68 | 0.380098 | ||||||||
\(747\) | −2640.03 | −0.129309 | ||||||||
\(748\) | −1010.52 | −0.0493963 | ||||||||
\(749\) | 3229.43 | 0.157545 | ||||||||
\(750\) | −693.000 | −0.0337397 | ||||||||
\(751\) | 1841.29 | 0.0894667 | 0.0447334 | − | 0.998999i | \(-0.485756\pi\) | ||||
0.0447334 | + | 0.998999i | \(0.485756\pi\) | |||||||
\(752\) | −4450.24 | −0.215803 | ||||||||
\(753\) | 8536.42 | 0.413127 | ||||||||
\(754\) | −4076.28 | −0.196883 | ||||||||
\(755\) | −438.019 | −0.0211141 | ||||||||
\(756\) | 2171.30 | 0.104457 | ||||||||
\(757\) | 32667.3 | 1.56845 | 0.784223 | − | 0.620479i | \(-0.213062\pi\) | ||||
0.784223 | + | 0.620479i | \(0.213062\pi\) | |||||||
\(758\) | 1639.84 | 0.0785772 | ||||||||
\(759\) | 2149.85 | 0.102813 | ||||||||
\(760\) | 1028.80 | 0.0491033 | ||||||||
\(761\) | 20717.4 | 0.986864 | 0.493432 | − | 0.869784i | \(-0.335742\pi\) | ||||
0.493432 | + | 0.869784i | \(0.335742\pi\) | |||||||
\(762\) | 6809.74 | 0.323741 | ||||||||
\(763\) | 662.679 | 0.0314425 | ||||||||
\(764\) | 12851.0 | 0.608550 | ||||||||
\(765\) | −723.580 | −0.0341975 | ||||||||
\(766\) | −12563.1 | −0.592588 | ||||||||
\(767\) | 11598.5 | 0.546023 | ||||||||
\(768\) | 709.632 | 0.0333420 | ||||||||
\(769\) | 41399.2 | 1.94134 | 0.970671 | − | 0.240412i | \(-0.0772826\pi\) | ||||
0.970671 | + | 0.240412i | \(0.0772826\pi\) | |||||||
\(770\) | −1425.68 | −0.0667247 | ||||||||
\(771\) | −16159.1 | −0.754808 | ||||||||
\(772\) | −8525.27 | −0.397450 | ||||||||
\(773\) | −29071.8 | −1.35270 | −0.676352 | − | 0.736578i | \(-0.736440\pi\) | ||||
−0.676352 | + | 0.736578i | \(0.736440\pi\) | |||||||
\(774\) | −3207.07 | −0.148935 | ||||||||
\(775\) | 1626.80 | 0.0754018 | ||||||||
\(776\) | 3355.13 | 0.155209 | ||||||||
\(777\) | 2526.79 | 0.116664 | ||||||||
\(778\) | 27878.6 | 1.28470 | ||||||||
\(779\) | −3861.30 | −0.177594 | ||||||||
\(780\) | −2381.04 | −0.109301 | ||||||||
\(781\) | −36123.9 | −1.65507 | ||||||||
\(782\) | 344.633 | 0.0157597 | ||||||||
\(783\) | 6092.78 | 0.278082 | ||||||||
\(784\) | −5201.98 | −0.236971 | ||||||||
\(785\) | −9311.50 | −0.423365 | ||||||||
\(786\) | −9623.57 | −0.436719 | ||||||||
\(787\) | −13953.9 | −0.632026 | −0.316013 | − | 0.948755i | \(-0.602344\pi\) | ||||
−0.316013 | + | 0.948755i | \(0.602344\pi\) | |||||||
\(788\) | 13557.9 | 0.612920 | ||||||||
\(789\) | 9782.36 | 0.441396 | ||||||||
\(790\) | −1952.32 | −0.0879246 | ||||||||
\(791\) | −4380.73 | −0.196916 | ||||||||
\(792\) | −5210.69 | −0.233780 | ||||||||
\(793\) | 5895.22 | 0.263992 | ||||||||
\(794\) | 5081.91 | 0.227141 | ||||||||
\(795\) | −2528.12 | −0.112784 | ||||||||
\(796\) | −2756.13 | −0.122724 | ||||||||
\(797\) | −10192.3 | −0.452986 | −0.226493 | − | 0.974013i | \(-0.572726\pi\) | ||||
−0.226493 | + | 0.974013i | \(0.572726\pi\) | |||||||
\(798\) | −602.878 | −0.0267439 | ||||||||
\(799\) | −2083.83 | −0.0922661 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | −12167.1 | −0.536707 | ||||||||
\(802\) | −9992.26 | −0.439949 | ||||||||
\(803\) | 9096.18 | 0.399747 | ||||||||
\(804\) | −4885.95 | −0.214321 | ||||||||
\(805\) | 486.220 | 0.0212882 | ||||||||
\(806\) | 5589.43 | 0.244267 | ||||||||
\(807\) | −11398.6 | −0.497213 | ||||||||
\(808\) | −7425.31 | −0.323294 | ||||||||
\(809\) | −6977.15 | −0.303218 | −0.151609 | − | 0.988441i | \(-0.548445\pi\) | ||||
−0.151609 | + | 0.988441i | \(0.548445\pi\) | |||||||
\(810\) | −1656.40 | −0.0718519 | ||||||||
\(811\) | −26658.1 | −1.15424 | −0.577122 | − | 0.816658i | \(-0.695824\pi\) | ||||
−0.577122 | + | 0.816658i | \(0.695824\pi\) | |||||||
\(812\) | 802.575 | 0.0346858 | ||||||||
\(813\) | 3102.64 | 0.133843 | ||||||||
\(814\) | −14539.8 | −0.626069 | ||||||||
\(815\) | 383.696 | 0.0164911 | ||||||||
\(816\) | 332.286 | 0.0142553 | ||||||||
\(817\) | 2135.17 | 0.0914323 | ||||||||
\(818\) | 3536.69 | 0.151170 | ||||||||
\(819\) | −3507.48 | −0.149647 | ||||||||
\(820\) | 3002.56 | 0.127871 | ||||||||
\(821\) | −15664.5 | −0.665890 | −0.332945 | − | 0.942946i | \(-0.608042\pi\) | ||||
−0.332945 | + | 0.942946i | \(0.608042\pi\) | |||||||
\(822\) | 7248.23 | 0.307556 | ||||||||
\(823\) | −10077.6 | −0.426833 | −0.213417 | − | 0.976961i | \(-0.568459\pi\) | ||||
−0.213417 | + | 0.976961i | \(0.568459\pi\) | |||||||
\(824\) | −11054.2 | −0.467344 | ||||||||
\(825\) | −2336.80 | −0.0986144 | ||||||||
\(826\) | −2283.63 | −0.0961956 | ||||||||
\(827\) | −383.213 | −0.0161132 | −0.00805660 | − | 0.999968i | \(-0.502565\pi\) | ||||
−0.00805660 | + | 0.999968i | \(0.502565\pi\) | |||||||
\(828\) | 1777.07 | 0.0745864 | ||||||||
\(829\) | 36788.5 | 1.54128 | 0.770639 | − | 0.637272i | \(-0.219937\pi\) | ||||
0.770639 | + | 0.637272i | \(0.219937\pi\) | |||||||
\(830\) | −1366.76 | −0.0571577 | ||||||||
\(831\) | −8093.66 | −0.337865 | ||||||||
\(832\) | −2748.67 | −0.114535 | ||||||||
\(833\) | −2435.84 | −0.101317 | ||||||||
\(834\) | −5953.29 | −0.247177 | ||||||||
\(835\) | −11624.8 | −0.481788 | ||||||||
\(836\) | 3469.12 | 0.143519 | ||||||||
\(837\) | −8354.47 | −0.345009 | ||||||||
\(838\) | −91.2706 | −0.00376240 | ||||||||
\(839\) | −31031.6 | −1.27691 | −0.638457 | − | 0.769657i | \(-0.720427\pi\) | ||||
−0.638457 | + | 0.769657i | \(0.720427\pi\) | |||||||
\(840\) | 468.801 | 0.0192561 | ||||||||
\(841\) | −22136.9 | −0.907660 | ||||||||
\(842\) | 1634.43 | 0.0668956 | ||||||||
\(843\) | 8110.61 | 0.331369 | ||||||||
\(844\) | 542.610 | 0.0221296 | ||||||||
\(845\) | −1762.34 | −0.0717471 | ||||||||
\(846\) | −10745.1 | −0.436672 | ||||||||
\(847\) | 820.064 | 0.0332677 | ||||||||
\(848\) | −2918.46 | −0.118185 | ||||||||
\(849\) | 19468.1 | 0.786976 | ||||||||
\(850\) | −374.601 | −0.0151161 | ||||||||
\(851\) | 4958.71 | 0.199744 | ||||||||
\(852\) | 11878.5 | 0.477640 | ||||||||
\(853\) | 16764.1 | 0.672909 | 0.336454 | − | 0.941700i | \(-0.390772\pi\) | ||||
0.336454 | + | 0.941700i | \(0.390772\pi\) | |||||||
\(854\) | −1160.70 | −0.0465088 | ||||||||
\(855\) | 2484.04 | 0.0993595 | ||||||||
\(856\) | 6110.56 | 0.243989 | ||||||||
\(857\) | −10890.8 | −0.434101 | −0.217050 | − | 0.976160i | \(-0.569644\pi\) | ||||
−0.217050 | + | 0.976160i | \(0.569644\pi\) | |||||||
\(858\) | −8028.87 | −0.319465 | ||||||||
\(859\) | 31687.9 | 1.25864 | 0.629322 | − | 0.777144i | \(-0.283332\pi\) | ||||
0.629322 | + | 0.777144i | \(0.283332\pi\) | |||||||
\(860\) | −1660.32 | −0.0658330 | ||||||||
\(861\) | −1759.50 | −0.0696443 | ||||||||
\(862\) | −4950.61 | −0.195613 | ||||||||
\(863\) | −28981.6 | −1.14316 | −0.571580 | − | 0.820547i | \(-0.693669\pi\) | ||||
−0.571580 | + | 0.820547i | \(0.693669\pi\) | |||||||
\(864\) | 4108.42 | 0.161772 | ||||||||
\(865\) | −12127.6 | −0.476705 | ||||||||
\(866\) | 119.274 | 0.00468025 | ||||||||
\(867\) | −13463.3 | −0.527377 | ||||||||
\(868\) | −1100.50 | −0.0430338 | ||||||||
\(869\) | −6583.23 | −0.256986 | ||||||||
\(870\) | 1315.48 | 0.0512632 | ||||||||
\(871\) | 18925.1 | 0.736227 | ||||||||
\(872\) | 1253.89 | 0.0486950 | ||||||||
\(873\) | 8100.97 | 0.314062 | ||||||||
\(874\) | −1183.12 | −0.0457891 | ||||||||
\(875\) | −528.500 | −0.0204189 | ||||||||
\(876\) | −2991.06 | −0.115364 | ||||||||
\(877\) | −27450.6 | −1.05695 | −0.528473 | − | 0.848950i | \(-0.677235\pi\) | ||||
−0.528473 | + | 0.848950i | \(0.677235\pi\) | |||||||
\(878\) | 14516.5 | 0.557984 | ||||||||
\(879\) | 1758.11 | 0.0674624 | ||||||||
\(880\) | −2697.60 | −0.103337 | ||||||||
\(881\) | −34848.0 | −1.33264 | −0.666322 | − | 0.745664i | \(-0.732132\pi\) | ||||
−0.666322 | + | 0.745664i | \(0.732132\pi\) | |||||||
\(882\) | −12560.2 | −0.479505 | ||||||||
\(883\) | −45419.0 | −1.73100 | −0.865499 | − | 0.500911i | \(-0.832998\pi\) | ||||
−0.865499 | + | 0.500911i | \(0.832998\pi\) | |||||||
\(884\) | −1287.07 | −0.0489693 | ||||||||
\(885\) | −3743.04 | −0.142170 | ||||||||
\(886\) | 19442.9 | 0.737241 | ||||||||
\(887\) | −44670.7 | −1.69098 | −0.845488 | − | 0.533994i | \(-0.820691\pi\) | ||||
−0.845488 | + | 0.533994i | \(0.820691\pi\) | |||||||
\(888\) | 4781.06 | 0.180678 | ||||||||
\(889\) | 5193.28 | 0.195925 | ||||||||
\(890\) | −6298.96 | −0.237238 | ||||||||
\(891\) | −5585.39 | −0.210009 | ||||||||
\(892\) | 821.282 | 0.0308280 | ||||||||
\(893\) | 7153.77 | 0.268076 | ||||||||
\(894\) | −12801.6 | −0.478913 | ||||||||
\(895\) | 9559.30 | 0.357019 | ||||||||
\(896\) | 541.184 | 0.0201782 | ||||||||
\(897\) | 2738.20 | 0.101924 | ||||||||
\(898\) | 21324.6 | 0.792440 | ||||||||
\(899\) | −3088.06 | −0.114563 | ||||||||
\(900\) | −1931.60 | −0.0715408 | ||||||||
\(901\) | −1366.57 | −0.0505296 | ||||||||
\(902\) | 10124.6 | 0.373740 | ||||||||
\(903\) | 972.949 | 0.0358557 | ||||||||
\(904\) | −8288.99 | −0.304964 | ||||||||
\(905\) | −19951.9 | −0.732845 | ||||||||
\(906\) | 485.675 | 0.0178096 | ||||||||
\(907\) | −9483.83 | −0.347195 | −0.173597 | − | 0.984817i | \(-0.555539\pi\) | ||||
−0.173597 | + | 0.984817i | \(0.555539\pi\) | |||||||
\(908\) | 7202.27 | 0.263233 | ||||||||
\(909\) | −17928.4 | −0.654179 | ||||||||
\(910\) | −1815.84 | −0.0661479 | ||||||||
\(911\) | −10553.9 | −0.383827 | −0.191913 | − | 0.981412i | \(-0.561469\pi\) | ||||
−0.191913 | + | 0.981412i | \(0.561469\pi\) | |||||||
\(912\) | −1140.74 | −0.0414183 | ||||||||
\(913\) | −4608.71 | −0.167060 | ||||||||
\(914\) | −8270.59 | −0.299307 | ||||||||
\(915\) | −1902.48 | −0.0687367 | ||||||||
\(916\) | −5060.96 | −0.182553 | ||||||||
\(917\) | −7339.18 | −0.264298 | ||||||||
\(918\) | 1923.77 | 0.0691655 | ||||||||
\(919\) | −1949.12 | −0.0699624 | −0.0349812 | − | 0.999388i | \(-0.511137\pi\) | ||||
−0.0349812 | + | 0.999388i | \(0.511137\pi\) | |||||||
\(920\) | 920.000 | 0.0329690 | ||||||||
\(921\) | 14873.3 | 0.532130 | ||||||||
\(922\) | 24161.2 | 0.863023 | ||||||||
\(923\) | −46009.7 | −1.64077 | ||||||||
\(924\) | 1580.80 | 0.0562818 | ||||||||
\(925\) | −5389.90 | −0.191588 | ||||||||
\(926\) | 4228.79 | 0.150072 | ||||||||
\(927\) | −26690.4 | −0.945661 | ||||||||
\(928\) | 1518.59 | 0.0537179 | ||||||||
\(929\) | −7106.96 | −0.250992 | −0.125496 | − | 0.992094i | \(-0.540052\pi\) | ||||
−0.125496 | + | 0.992094i | \(0.540052\pi\) | |||||||
\(930\) | −1803.80 | −0.0636009 | ||||||||
\(931\) | 8362.20 | 0.294372 | ||||||||
\(932\) | 5011.03 | 0.176118 | ||||||||
\(933\) | −26529.1 | −0.930892 | ||||||||
\(934\) | 28363.9 | 0.993679 | ||||||||
\(935\) | −1263.16 | −0.0441814 | ||||||||
\(936\) | −6636.67 | −0.231759 | ||||||||
\(937\) | −44989.6 | −1.56857 | −0.784283 | − | 0.620403i | \(-0.786969\pi\) | ||||
−0.784283 | + | 0.620403i | \(0.786969\pi\) | |||||||
\(938\) | −3726.15 | −0.129705 | ||||||||
\(939\) | −23220.4 | −0.806995 | ||||||||
\(940\) | −5562.80 | −0.193020 | ||||||||
\(941\) | −9932.51 | −0.344092 | −0.172046 | − | 0.985089i | \(-0.555038\pi\) | ||||
−0.172046 | + | 0.985089i | \(0.555038\pi\) | |||||||
\(942\) | 10324.6 | 0.357106 | ||||||||
\(943\) | −3452.95 | −0.119240 | ||||||||
\(944\) | −4320.96 | −0.148978 | ||||||||
\(945\) | 2714.12 | 0.0934290 | ||||||||
\(946\) | −5598.60 | −0.192417 | ||||||||
\(947\) | −15455.2 | −0.530334 | −0.265167 | − | 0.964203i | \(-0.585427\pi\) | ||||
−0.265167 | + | 0.964203i | \(0.585427\pi\) | |||||||
\(948\) | 2164.74 | 0.0741638 | ||||||||
\(949\) | 11585.5 | 0.396292 | ||||||||
\(950\) | 1286.00 | 0.0439193 | ||||||||
\(951\) | −15725.0 | −0.536191 | ||||||||
\(952\) | 253.410 | 0.00862717 | ||||||||
\(953\) | 46941.7 | 1.59558 | 0.797792 | − | 0.602932i | \(-0.206001\pi\) | ||||
0.797792 | + | 0.602932i | \(0.206001\pi\) | |||||||
\(954\) | −7046.63 | −0.239144 | ||||||||
\(955\) | 16063.7 | 0.544304 | ||||||||
\(956\) | 17380.9 | 0.588010 | ||||||||
\(957\) | 4435.80 | 0.149832 | ||||||||
\(958\) | 15093.9 | 0.509040 | ||||||||
\(959\) | 5527.68 | 0.186130 | ||||||||
\(960\) | 887.041 | 0.0298220 | ||||||||
\(961\) | −25556.6 | −0.857864 | ||||||||
\(962\) | −18518.8 | −0.620656 | ||||||||
\(963\) | 14754.0 | 0.493707 | ||||||||
\(964\) | 1708.61 | 0.0570857 | ||||||||
\(965\) | −10656.6 | −0.355490 | ||||||||
\(966\) | −539.121 | −0.0179564 | ||||||||
\(967\) | 25323.3 | 0.842134 | 0.421067 | − | 0.907029i | \(-0.361656\pi\) | ||||
0.421067 | + | 0.907029i | \(0.361656\pi\) | |||||||
\(968\) | 1551.68 | 0.0515217 | ||||||||
\(969\) | −534.151 | −0.0177083 | ||||||||
\(970\) | 4193.92 | 0.138823 | ||||||||
\(971\) | 28679.0 | 0.947840 | 0.473920 | − | 0.880568i | \(-0.342839\pi\) | ||||
0.473920 | + | 0.880568i | \(0.342839\pi\) | |||||||
\(972\) | 15702.5 | 0.518168 | ||||||||
\(973\) | −4540.13 | −0.149589 | ||||||||
\(974\) | 34219.3 | 1.12573 | ||||||||
\(975\) | −2976.30 | −0.0977619 | ||||||||
\(976\) | −2196.22 | −0.0720281 | ||||||||
\(977\) | 7950.41 | 0.260344 | 0.130172 | − | 0.991491i | \(-0.458447\pi\) | ||||
0.130172 | + | 0.991491i | \(0.458447\pi\) | |||||||
\(978\) | −425.442 | −0.0139102 | ||||||||
\(979\) | −21240.1 | −0.693398 | ||||||||
\(980\) | −6502.48 | −0.211953 | ||||||||
\(981\) | 3027.51 | 0.0985332 | ||||||||
\(982\) | −19667.3 | −0.639114 | ||||||||
\(983\) | 6734.80 | 0.218522 | 0.109261 | − | 0.994013i | \(-0.465152\pi\) | ||||
0.109261 | + | 0.994013i | \(0.465152\pi\) | |||||||
\(984\) | −3329.24 | −0.107858 | ||||||||
\(985\) | 16947.4 | 0.548212 | ||||||||
\(986\) | 711.083 | 0.0229670 | ||||||||
\(987\) | 3259.81 | 0.105127 | ||||||||
\(988\) | 4418.50 | 0.142278 | ||||||||
\(989\) | 1909.37 | 0.0613896 | ||||||||
\(990\) | −6513.36 | −0.209099 | ||||||||
\(991\) | 46563.5 | 1.49257 | 0.746285 | − | 0.665626i | \(-0.231835\pi\) | ||||
0.746285 | + | 0.665626i | \(0.231835\pi\) | |||||||
\(992\) | −2082.31 | −0.0666464 | ||||||||
\(993\) | 15070.8 | 0.481629 | ||||||||
\(994\) | 9058.81 | 0.289062 | ||||||||
\(995\) | −3445.16 | −0.109768 | ||||||||
\(996\) | 1515.46 | 0.0482121 | ||||||||
\(997\) | 14783.7 | 0.469613 | 0.234806 | − | 0.972042i | \(-0.424554\pi\) | ||||
0.234806 | + | 0.972042i | \(0.424554\pi\) | |||||||
\(998\) | 3411.09 | 0.108192 | ||||||||
\(999\) | 27679.9 | 0.876631 |
(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 | 230.4.a.f.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2070.4.a.s.1.2 | 2 | |||
4.3 | odd | 2 | 1840.4.a.i.1.1 | 2 | |||
5.2 | odd | 4 | 1150.4.b.k.599.1 | 4 | |||
5.3 | odd | 4 | 1150.4.b.k.599.4 | 4 | |||
5.4 | even | 2 | 1150.4.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.f.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1150.4.a.l.1.1 | 2 | 5.4 | even | 2 | |||
1150.4.b.k.599.1 | 4 | 5.2 | odd | 4 | |||
1150.4.b.k.599.4 | 4 | 5.3 | odd | 4 | |||
1840.4.a.i.1.1 | 2 | 4.3 | odd | 2 | |||
2070.4.a.s.1.2 | 2 | 3.2 | odd | 2 |