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: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 | ||||||||
\(3\) | 7.00000 | 1.34715 | 0.673575 | − | 0.739119i | \(-0.264758\pi\) | ||||
0.673575 | + | 0.739119i | \(0.264758\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −14.0000 | −0.952579 | ||||||||
\(7\) | 20.0000 | 1.07990 | 0.539949 | − | 0.841698i | \(-0.318443\pi\) | ||||
0.539949 | + | 0.841698i | \(0.318443\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 22.0000 | 0.814815 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | 6.00000 | 0.164461 | 0.0822304 | − | 0.996613i | \(-0.473796\pi\) | ||||
0.0822304 | + | 0.996613i | \(0.473796\pi\) | |||||||
\(12\) | 28.0000 | 0.673575 | ||||||||
\(13\) | 47.0000 | 1.00273 | 0.501364 | − | 0.865237i | \(-0.332832\pi\) | ||||
0.501364 | + | 0.865237i | \(0.332832\pi\) | |||||||
\(14\) | −40.0000 | −0.763604 | ||||||||
\(15\) | 35.0000 | 0.602464 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −132.000 | −1.88322 | −0.941609 | − | 0.336709i | \(-0.890686\pi\) | ||||
−0.941609 | + | 0.336709i | \(0.890686\pi\) | |||||||
\(18\) | −44.0000 | −0.576161 | ||||||||
\(19\) | 146.000 | 1.76288 | 0.881439 | − | 0.472297i | \(-0.156575\pi\) | ||||
0.881439 | + | 0.472297i | \(0.156575\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 140.000 | 1.45479 | ||||||||
\(22\) | −12.0000 | −0.116291 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | −56.0000 | −0.476290 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −94.0000 | −0.709035 | ||||||||
\(27\) | −35.0000 | −0.249472 | ||||||||
\(28\) | 80.0000 | 0.539949 | ||||||||
\(29\) | −99.0000 | −0.633925 | −0.316963 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316963 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(30\) | −70.0000 | −0.426006 | ||||||||
\(31\) | −253.000 | −1.46581 | −0.732906 | − | 0.680330i | \(-0.761836\pi\) | ||||
−0.732906 | + | 0.680330i | \(0.761836\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 42.0000 | 0.221553 | ||||||||
\(34\) | 264.000 | 1.33164 | ||||||||
\(35\) | 100.000 | 0.482945 | ||||||||
\(36\) | 88.0000 | 0.407407 | ||||||||
\(37\) | −118.000 | −0.524299 | −0.262150 | − | 0.965027i | \(-0.584431\pi\) | ||||
−0.262150 | + | 0.965027i | \(0.584431\pi\) | |||||||
\(38\) | −292.000 | −1.24654 | ||||||||
\(39\) | 329.000 | 1.35082 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | 495.000 | 1.88551 | 0.942756 | − | 0.333483i | \(-0.108224\pi\) | ||||
0.942756 | + | 0.333483i | \(0.108224\pi\) | |||||||
\(42\) | −280.000 | −1.02869 | ||||||||
\(43\) | 272.000 | 0.964642 | 0.482321 | − | 0.875995i | \(-0.339794\pi\) | ||||
0.482321 | + | 0.875995i | \(0.339794\pi\) | |||||||
\(44\) | 24.0000 | 0.0822304 | ||||||||
\(45\) | 110.000 | 0.364396 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 639.000 | 1.98314 | 0.991572 | − | 0.129560i | \(-0.0413565\pi\) | ||||
0.991572 | + | 0.129560i | \(0.0413565\pi\) | |||||||
\(48\) | 112.000 | 0.336788 | ||||||||
\(49\) | 57.0000 | 0.166181 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | −924.000 | −2.53698 | ||||||||
\(52\) | 188.000 | 0.501364 | ||||||||
\(53\) | −342.000 | −0.886364 | −0.443182 | − | 0.896432i | \(-0.646151\pi\) | ||||
−0.443182 | + | 0.896432i | \(0.646151\pi\) | |||||||
\(54\) | 70.0000 | 0.176404 | ||||||||
\(55\) | 30.0000 | 0.0735491 | ||||||||
\(56\) | −160.000 | −0.381802 | ||||||||
\(57\) | 1022.00 | 2.37486 | ||||||||
\(58\) | 198.000 | 0.448253 | ||||||||
\(59\) | 240.000 | 0.529582 | 0.264791 | − | 0.964306i | \(-0.414697\pi\) | ||||
0.264791 | + | 0.964306i | \(0.414697\pi\) | |||||||
\(60\) | 140.000 | 0.301232 | ||||||||
\(61\) | −370.000 | −0.776617 | −0.388309 | − | 0.921529i | \(-0.626941\pi\) | ||||
−0.388309 | + | 0.921529i | \(0.626941\pi\) | |||||||
\(62\) | 506.000 | 1.03648 | ||||||||
\(63\) | 440.000 | 0.879917 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 235.000 | 0.448433 | ||||||||
\(66\) | −84.0000 | −0.156662 | ||||||||
\(67\) | 698.000 | 1.27275 | 0.636375 | − | 0.771380i | \(-0.280433\pi\) | ||||
0.636375 | + | 0.771380i | \(0.280433\pi\) | |||||||
\(68\) | −528.000 | −0.941609 | ||||||||
\(69\) | 161.000 | 0.280900 | ||||||||
\(70\) | −200.000 | −0.341494 | ||||||||
\(71\) | −357.000 | −0.596734 | −0.298367 | − | 0.954451i | \(-0.596442\pi\) | ||||
−0.298367 | + | 0.954451i | \(0.596442\pi\) | |||||||
\(72\) | −176.000 | −0.288081 | ||||||||
\(73\) | −259.000 | −0.415256 | −0.207628 | − | 0.978208i | \(-0.566574\pi\) | ||||
−0.207628 | + | 0.978208i | \(0.566574\pi\) | |||||||
\(74\) | 236.000 | 0.370736 | ||||||||
\(75\) | 175.000 | 0.269430 | ||||||||
\(76\) | 584.000 | 0.881439 | ||||||||
\(77\) | 120.000 | 0.177601 | ||||||||
\(78\) | −658.000 | −0.955177 | ||||||||
\(79\) | 542.000 | 0.771896 | 0.385948 | − | 0.922521i | \(-0.373874\pi\) | ||||
0.385948 | + | 0.922521i | \(0.373874\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | −990.000 | −1.33326 | ||||||||
\(83\) | −1248.00 | −1.65043 | −0.825216 | − | 0.564818i | \(-0.808946\pi\) | ||||
−0.825216 | + | 0.564818i | \(0.808946\pi\) | |||||||
\(84\) | 560.000 | 0.727393 | ||||||||
\(85\) | −660.000 | −0.842201 | ||||||||
\(86\) | −544.000 | −0.682105 | ||||||||
\(87\) | −693.000 | −0.853993 | ||||||||
\(88\) | −48.0000 | −0.0581456 | ||||||||
\(89\) | −828.000 | −0.986155 | −0.493078 | − | 0.869985i | \(-0.664128\pi\) | ||||
−0.493078 | + | 0.869985i | \(0.664128\pi\) | |||||||
\(90\) | −220.000 | −0.257667 | ||||||||
\(91\) | 940.000 | 1.08284 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | −1771.00 | −1.97467 | ||||||||
\(94\) | −1278.00 | −1.40229 | ||||||||
\(95\) | 730.000 | 0.788383 | ||||||||
\(96\) | −224.000 | −0.238145 | ||||||||
\(97\) | 992.000 | 1.03837 | 0.519187 | − | 0.854660i | \(-0.326235\pi\) | ||||
0.519187 | + | 0.854660i | \(0.326235\pi\) | |||||||
\(98\) | −114.000 | −0.117508 | ||||||||
\(99\) | 132.000 | 0.134005 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | −1542.00 | −1.51916 | −0.759578 | − | 0.650416i | \(-0.774594\pi\) | ||||
−0.759578 | + | 0.650416i | \(0.774594\pi\) | |||||||
\(102\) | 1848.00 | 1.79391 | ||||||||
\(103\) | 32.0000 | 0.0306122 | 0.0153061 | − | 0.999883i | \(-0.495128\pi\) | ||||
0.0153061 | + | 0.999883i | \(0.495128\pi\) | |||||||
\(104\) | −376.000 | −0.354518 | ||||||||
\(105\) | 700.000 | 0.650600 | ||||||||
\(106\) | 684.000 | 0.626754 | ||||||||
\(107\) | −834.000 | −0.753512 | −0.376756 | − | 0.926312i | \(-0.622961\pi\) | ||||
−0.376756 | + | 0.926312i | \(0.622961\pi\) | |||||||
\(108\) | −140.000 | −0.124736 | ||||||||
\(109\) | −1192.00 | −1.04746 | −0.523729 | − | 0.851885i | \(-0.675460\pi\) | ||||
−0.523729 | + | 0.851885i | \(0.675460\pi\) | |||||||
\(110\) | −60.0000 | −0.0520071 | ||||||||
\(111\) | −826.000 | −0.706310 | ||||||||
\(112\) | 320.000 | 0.269975 | ||||||||
\(113\) | −132.000 | −0.109890 | −0.0549448 | − | 0.998489i | \(-0.517498\pi\) | ||||
−0.0549448 | + | 0.998489i | \(0.517498\pi\) | |||||||
\(114\) | −2044.00 | −1.67928 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | −396.000 | −0.316963 | ||||||||
\(117\) | 1034.00 | 0.817037 | ||||||||
\(118\) | −480.000 | −0.374471 | ||||||||
\(119\) | −2640.00 | −2.03368 | ||||||||
\(120\) | −280.000 | −0.213003 | ||||||||
\(121\) | −1295.00 | −0.972953 | ||||||||
\(122\) | 740.000 | 0.549151 | ||||||||
\(123\) | 3465.00 | 2.54007 | ||||||||
\(124\) | −1012.00 | −0.732906 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −880.000 | −0.622195 | ||||||||
\(127\) | 89.0000 | 0.0621848 | 0.0310924 | − | 0.999517i | \(-0.490101\pi\) | ||||
0.0310924 | + | 0.999517i | \(0.490101\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 1904.00 | 1.29952 | ||||||||
\(130\) | −470.000 | −0.317090 | ||||||||
\(131\) | −1797.00 | −1.19851 | −0.599254 | − | 0.800559i | \(-0.704536\pi\) | ||||
−0.599254 | + | 0.800559i | \(0.704536\pi\) | |||||||
\(132\) | 168.000 | 0.110777 | ||||||||
\(133\) | 2920.00 | 1.90373 | ||||||||
\(134\) | −1396.00 | −0.899970 | ||||||||
\(135\) | −175.000 | −0.111567 | ||||||||
\(136\) | 1056.00 | 0.665818 | ||||||||
\(137\) | −1836.00 | −1.14496 | −0.572482 | − | 0.819917i | \(-0.694019\pi\) | ||||
−0.572482 | + | 0.819917i | \(0.694019\pi\) | |||||||
\(138\) | −322.000 | −0.198627 | ||||||||
\(139\) | −1027.00 | −0.626683 | −0.313342 | − | 0.949640i | \(-0.601449\pi\) | ||||
−0.313342 | + | 0.949640i | \(0.601449\pi\) | |||||||
\(140\) | 400.000 | 0.241473 | ||||||||
\(141\) | 4473.00 | 2.67159 | ||||||||
\(142\) | 714.000 | 0.421955 | ||||||||
\(143\) | 282.000 | 0.164909 | ||||||||
\(144\) | 352.000 | 0.203704 | ||||||||
\(145\) | −495.000 | −0.283500 | ||||||||
\(146\) | 518.000 | 0.293630 | ||||||||
\(147\) | 399.000 | 0.223871 | ||||||||
\(148\) | −472.000 | −0.262150 | ||||||||
\(149\) | 2310.00 | 1.27008 | 0.635042 | − | 0.772477i | \(-0.280983\pi\) | ||||
0.635042 | + | 0.772477i | \(0.280983\pi\) | |||||||
\(150\) | −350.000 | −0.190516 | ||||||||
\(151\) | −2149.00 | −1.15817 | −0.579083 | − | 0.815268i | \(-0.696589\pi\) | ||||
−0.579083 | + | 0.815268i | \(0.696589\pi\) | |||||||
\(152\) | −1168.00 | −0.623272 | ||||||||
\(153\) | −2904.00 | −1.53447 | ||||||||
\(154\) | −240.000 | −0.125583 | ||||||||
\(155\) | −1265.00 | −0.655531 | ||||||||
\(156\) | 1316.00 | 0.675412 | ||||||||
\(157\) | 1832.00 | 0.931271 | 0.465635 | − | 0.884977i | \(-0.345826\pi\) | ||||
0.465635 | + | 0.884977i | \(0.345826\pi\) | |||||||
\(158\) | −1084.00 | −0.545813 | ||||||||
\(159\) | −2394.00 | −1.19407 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | 460.000 | 0.225174 | ||||||||
\(162\) | 1678.00 | 0.813803 | ||||||||
\(163\) | 1217.00 | 0.584802 | 0.292401 | − | 0.956296i | \(-0.405546\pi\) | ||||
0.292401 | + | 0.956296i | \(0.405546\pi\) | |||||||
\(164\) | 1980.00 | 0.942756 | ||||||||
\(165\) | 210.000 | 0.0990817 | ||||||||
\(166\) | 2496.00 | 1.16703 | ||||||||
\(167\) | 3048.00 | 1.41234 | 0.706172 | − | 0.708041i | \(-0.250421\pi\) | ||||
0.706172 | + | 0.708041i | \(0.250421\pi\) | |||||||
\(168\) | −1120.00 | −0.514344 | ||||||||
\(169\) | 12.0000 | 0.00546199 | ||||||||
\(170\) | 1320.00 | 0.595526 | ||||||||
\(171\) | 3212.00 | 1.43642 | ||||||||
\(172\) | 1088.00 | 0.482321 | ||||||||
\(173\) | 774.000 | 0.340151 | 0.170076 | − | 0.985431i | \(-0.445599\pi\) | ||||
0.170076 | + | 0.985431i | \(0.445599\pi\) | |||||||
\(174\) | 1386.00 | 0.603864 | ||||||||
\(175\) | 500.000 | 0.215980 | ||||||||
\(176\) | 96.0000 | 0.0411152 | ||||||||
\(177\) | 1680.00 | 0.713427 | ||||||||
\(178\) | 1656.00 | 0.697317 | ||||||||
\(179\) | −1875.00 | −0.782928 | −0.391464 | − | 0.920193i | \(-0.628031\pi\) | ||||
−0.391464 | + | 0.920193i | \(0.628031\pi\) | |||||||
\(180\) | 440.000 | 0.182198 | ||||||||
\(181\) | −1606.00 | −0.659520 | −0.329760 | − | 0.944065i | \(-0.606968\pi\) | ||||
−0.329760 | + | 0.944065i | \(0.606968\pi\) | |||||||
\(182\) | −1880.00 | −0.765686 | ||||||||
\(183\) | −2590.00 | −1.04622 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | −590.000 | −0.234474 | ||||||||
\(186\) | 3542.00 | 1.39630 | ||||||||
\(187\) | −792.000 | −0.309715 | ||||||||
\(188\) | 2556.00 | 0.991572 | ||||||||
\(189\) | −700.000 | −0.269405 | ||||||||
\(190\) | −1460.00 | −0.557471 | ||||||||
\(191\) | 2982.00 | 1.12969 | 0.564843 | − | 0.825199i | \(-0.308937\pi\) | ||||
0.564843 | + | 0.825199i | \(0.308937\pi\) | |||||||
\(192\) | 448.000 | 0.168394 | ||||||||
\(193\) | 1385.00 | 0.516552 | 0.258276 | − | 0.966071i | \(-0.416846\pi\) | ||||
0.258276 | + | 0.966071i | \(0.416846\pi\) | |||||||
\(194\) | −1984.00 | −0.734242 | ||||||||
\(195\) | 1645.00 | 0.604107 | ||||||||
\(196\) | 228.000 | 0.0830904 | ||||||||
\(197\) | 957.000 | 0.346109 | 0.173054 | − | 0.984912i | \(-0.444636\pi\) | ||||
0.173054 | + | 0.984912i | \(0.444636\pi\) | |||||||
\(198\) | −264.000 | −0.0947559 | ||||||||
\(199\) | −358.000 | −0.127527 | −0.0637637 | − | 0.997965i | \(-0.520310\pi\) | ||||
−0.0637637 | + | 0.997965i | \(0.520310\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | 4886.00 | 1.71459 | ||||||||
\(202\) | 3084.00 | 1.07421 | ||||||||
\(203\) | −1980.00 | −0.684575 | ||||||||
\(204\) | −3696.00 | −1.26849 | ||||||||
\(205\) | 2475.00 | 0.843227 | ||||||||
\(206\) | −64.0000 | −0.0216461 | ||||||||
\(207\) | 506.000 | 0.169901 | ||||||||
\(208\) | 752.000 | 0.250682 | ||||||||
\(209\) | 876.000 | 0.289924 | ||||||||
\(210\) | −1400.00 | −0.460044 | ||||||||
\(211\) | −5380.00 | −1.75533 | −0.877665 | − | 0.479275i | \(-0.840900\pi\) | ||||
−0.877665 | + | 0.479275i | \(0.840900\pi\) | |||||||
\(212\) | −1368.00 | −0.443182 | ||||||||
\(213\) | −2499.00 | −0.803890 | ||||||||
\(214\) | 1668.00 | 0.532814 | ||||||||
\(215\) | 1360.00 | 0.431401 | ||||||||
\(216\) | 280.000 | 0.0882018 | ||||||||
\(217\) | −5060.00 | −1.58293 | ||||||||
\(218\) | 2384.00 | 0.740664 | ||||||||
\(219\) | −1813.00 | −0.559412 | ||||||||
\(220\) | 120.000 | 0.0367745 | ||||||||
\(221\) | −6204.00 | −1.88835 | ||||||||
\(222\) | 1652.00 | 0.499437 | ||||||||
\(223\) | 1040.00 | 0.312303 | 0.156151 | − | 0.987733i | \(-0.450091\pi\) | ||||
0.156151 | + | 0.987733i | \(0.450091\pi\) | |||||||
\(224\) | −640.000 | −0.190901 | ||||||||
\(225\) | 550.000 | 0.162963 | ||||||||
\(226\) | 264.000 | 0.0777036 | ||||||||
\(227\) | −3744.00 | −1.09470 | −0.547352 | − | 0.836902i | \(-0.684364\pi\) | ||||
−0.547352 | + | 0.836902i | \(0.684364\pi\) | |||||||
\(228\) | 4088.00 | 1.18743 | ||||||||
\(229\) | 2804.00 | 0.809142 | 0.404571 | − | 0.914507i | \(-0.367421\pi\) | ||||
0.404571 | + | 0.914507i | \(0.367421\pi\) | |||||||
\(230\) | −230.000 | −0.0659380 | ||||||||
\(231\) | 840.000 | 0.239255 | ||||||||
\(232\) | 792.000 | 0.224126 | ||||||||
\(233\) | −4869.00 | −1.36901 | −0.684504 | − | 0.729009i | \(-0.739981\pi\) | ||||
−0.684504 | + | 0.729009i | \(0.739981\pi\) | |||||||
\(234\) | −2068.00 | −0.577732 | ||||||||
\(235\) | 3195.00 | 0.886889 | ||||||||
\(236\) | 960.000 | 0.264791 | ||||||||
\(237\) | 3794.00 | 1.03986 | ||||||||
\(238\) | 5280.00 | 1.43803 | ||||||||
\(239\) | −2877.00 | −0.778651 | −0.389326 | − | 0.921100i | \(-0.627292\pi\) | ||||
−0.389326 | + | 0.921100i | \(0.627292\pi\) | |||||||
\(240\) | 560.000 | 0.150616 | ||||||||
\(241\) | 1622.00 | 0.433536 | 0.216768 | − | 0.976223i | \(-0.430448\pi\) | ||||
0.216768 | + | 0.976223i | \(0.430448\pi\) | |||||||
\(242\) | 2590.00 | 0.687981 | ||||||||
\(243\) | −4928.00 | −1.30095 | ||||||||
\(244\) | −1480.00 | −0.388309 | ||||||||
\(245\) | 285.000 | 0.0743183 | ||||||||
\(246\) | −6930.00 | −1.79610 | ||||||||
\(247\) | 6862.00 | 1.76769 | ||||||||
\(248\) | 2024.00 | 0.518242 | ||||||||
\(249\) | −8736.00 | −2.22338 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | −4752.00 | −1.19499 | −0.597497 | − | 0.801871i | \(-0.703838\pi\) | ||||
−0.597497 | + | 0.801871i | \(0.703838\pi\) | |||||||
\(252\) | 1760.00 | 0.439959 | ||||||||
\(253\) | 138.000 | 0.0342924 | ||||||||
\(254\) | −178.000 | −0.0439713 | ||||||||
\(255\) | −4620.00 | −1.13457 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5073.00 | −1.23130 | −0.615652 | − | 0.788018i | \(-0.711107\pi\) | ||||
−0.615652 | + | 0.788018i | \(0.711107\pi\) | |||||||
\(258\) | −3808.00 | −0.918898 | ||||||||
\(259\) | −2360.00 | −0.566190 | ||||||||
\(260\) | 940.000 | 0.224217 | ||||||||
\(261\) | −2178.00 | −0.516532 | ||||||||
\(262\) | 3594.00 | 0.847474 | ||||||||
\(263\) | 1314.00 | 0.308079 | 0.154039 | − | 0.988065i | \(-0.450772\pi\) | ||||
0.154039 | + | 0.988065i | \(0.450772\pi\) | |||||||
\(264\) | −336.000 | −0.0783309 | ||||||||
\(265\) | −1710.00 | −0.396394 | ||||||||
\(266\) | −5840.00 | −1.34614 | ||||||||
\(267\) | −5796.00 | −1.32850 | ||||||||
\(268\) | 2792.00 | 0.636375 | ||||||||
\(269\) | 5265.00 | 1.19336 | 0.596678 | − | 0.802481i | \(-0.296487\pi\) | ||||
0.596678 | + | 0.802481i | \(0.296487\pi\) | |||||||
\(270\) | 350.000 | 0.0788901 | ||||||||
\(271\) | −2488.00 | −0.557695 | −0.278847 | − | 0.960335i | \(-0.589952\pi\) | ||||
−0.278847 | + | 0.960335i | \(0.589952\pi\) | |||||||
\(272\) | −2112.00 | −0.470804 | ||||||||
\(273\) | 6580.00 | 1.45875 | ||||||||
\(274\) | 3672.00 | 0.809612 | ||||||||
\(275\) | 150.000 | 0.0328921 | ||||||||
\(276\) | 644.000 | 0.140450 | ||||||||
\(277\) | 5465.00 | 1.18542 | 0.592708 | − | 0.805418i | \(-0.298059\pi\) | ||||
0.592708 | + | 0.805418i | \(0.298059\pi\) | |||||||
\(278\) | 2054.00 | 0.443132 | ||||||||
\(279\) | −5566.00 | −1.19436 | ||||||||
\(280\) | −800.000 | −0.170747 | ||||||||
\(281\) | 8940.00 | 1.89792 | 0.948960 | − | 0.315396i | \(-0.102137\pi\) | ||||
0.948960 | + | 0.315396i | \(0.102137\pi\) | |||||||
\(282\) | −8946.00 | −1.88910 | ||||||||
\(283\) | 842.000 | 0.176861 | 0.0884306 | − | 0.996082i | \(-0.471815\pi\) | ||||
0.0884306 | + | 0.996082i | \(0.471815\pi\) | |||||||
\(284\) | −1428.00 | −0.298367 | ||||||||
\(285\) | 5110.00 | 1.06207 | ||||||||
\(286\) | −564.000 | −0.116608 | ||||||||
\(287\) | 9900.00 | 2.03616 | ||||||||
\(288\) | −704.000 | −0.144040 | ||||||||
\(289\) | 12511.0 | 2.54651 | ||||||||
\(290\) | 990.000 | 0.200465 | ||||||||
\(291\) | 6944.00 | 1.39885 | ||||||||
\(292\) | −1036.00 | −0.207628 | ||||||||
\(293\) | −4032.00 | −0.803932 | −0.401966 | − | 0.915655i | \(-0.631673\pi\) | ||||
−0.401966 | + | 0.915655i | \(0.631673\pi\) | |||||||
\(294\) | −798.000 | −0.158300 | ||||||||
\(295\) | 1200.00 | 0.236836 | ||||||||
\(296\) | 944.000 | 0.185368 | ||||||||
\(297\) | −210.000 | −0.0410284 | ||||||||
\(298\) | −4620.00 | −0.898085 | ||||||||
\(299\) | 1081.00 | 0.209083 | ||||||||
\(300\) | 700.000 | 0.134715 | ||||||||
\(301\) | 5440.00 | 1.04172 | ||||||||
\(302\) | 4298.00 | 0.818947 | ||||||||
\(303\) | −10794.0 | −2.04653 | ||||||||
\(304\) | 2336.00 | 0.440720 | ||||||||
\(305\) | −1850.00 | −0.347314 | ||||||||
\(306\) | 5808.00 | 1.08504 | ||||||||
\(307\) | −1096.00 | −0.203753 | −0.101876 | − | 0.994797i | \(-0.532485\pi\) | ||||
−0.101876 | + | 0.994797i | \(0.532485\pi\) | |||||||
\(308\) | 480.000 | 0.0888004 | ||||||||
\(309\) | 224.000 | 0.0412392 | ||||||||
\(310\) | 2530.00 | 0.463530 | ||||||||
\(311\) | −4653.00 | −0.848384 | −0.424192 | − | 0.905572i | \(-0.639442\pi\) | ||||
−0.424192 | + | 0.905572i | \(0.639442\pi\) | |||||||
\(312\) | −2632.00 | −0.477589 | ||||||||
\(313\) | 3440.00 | 0.621215 | 0.310608 | − | 0.950538i | \(-0.399468\pi\) | ||||
0.310608 | + | 0.950538i | \(0.399468\pi\) | |||||||
\(314\) | −3664.00 | −0.658508 | ||||||||
\(315\) | 2200.00 | 0.393511 | ||||||||
\(316\) | 2168.00 | 0.385948 | ||||||||
\(317\) | 3066.00 | 0.543229 | 0.271615 | − | 0.962406i | \(-0.412442\pi\) | ||||
0.271615 | + | 0.962406i | \(0.412442\pi\) | |||||||
\(318\) | 4788.00 | 0.844332 | ||||||||
\(319\) | −594.000 | −0.104256 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | −5838.00 | −1.01509 | ||||||||
\(322\) | −920.000 | −0.159222 | ||||||||
\(323\) | −19272.0 | −3.31988 | ||||||||
\(324\) | −3356.00 | −0.575446 | ||||||||
\(325\) | 1175.00 | 0.200545 | ||||||||
\(326\) | −2434.00 | −0.413518 | ||||||||
\(327\) | −8344.00 | −1.41108 | ||||||||
\(328\) | −3960.00 | −0.666629 | ||||||||
\(329\) | 12780.0 | 2.14159 | ||||||||
\(330\) | −420.000 | −0.0700613 | ||||||||
\(331\) | 1505.00 | 0.249916 | 0.124958 | − | 0.992162i | \(-0.460120\pi\) | ||||
0.124958 | + | 0.992162i | \(0.460120\pi\) | |||||||
\(332\) | −4992.00 | −0.825216 | ||||||||
\(333\) | −2596.00 | −0.427207 | ||||||||
\(334\) | −6096.00 | −0.998677 | ||||||||
\(335\) | 3490.00 | 0.569191 | ||||||||
\(336\) | 2240.00 | 0.363696 | ||||||||
\(337\) | −3268.00 | −0.528247 | −0.264124 | − | 0.964489i | \(-0.585083\pi\) | ||||
−0.264124 | + | 0.964489i | \(0.585083\pi\) | |||||||
\(338\) | −24.0000 | −0.00386221 | ||||||||
\(339\) | −924.000 | −0.148038 | ||||||||
\(340\) | −2640.00 | −0.421100 | ||||||||
\(341\) | −1518.00 | −0.241068 | ||||||||
\(342\) | −6424.00 | −1.01570 | ||||||||
\(343\) | −5720.00 | −0.900440 | ||||||||
\(344\) | −2176.00 | −0.341052 | ||||||||
\(345\) | 805.000 | 0.125622 | ||||||||
\(346\) | −1548.00 | −0.240523 | ||||||||
\(347\) | 4164.00 | 0.644194 | 0.322097 | − | 0.946707i | \(-0.395612\pi\) | ||||
0.322097 | + | 0.946707i | \(0.395612\pi\) | |||||||
\(348\) | −2772.00 | −0.426997 | ||||||||
\(349\) | −2911.00 | −0.446482 | −0.223241 | − | 0.974763i | \(-0.571664\pi\) | ||||
−0.223241 | + | 0.974763i | \(0.571664\pi\) | |||||||
\(350\) | −1000.00 | −0.152721 | ||||||||
\(351\) | −1645.00 | −0.250153 | ||||||||
\(352\) | −192.000 | −0.0290728 | ||||||||
\(353\) | 9753.00 | 1.47054 | 0.735269 | − | 0.677776i | \(-0.237056\pi\) | ||||
0.735269 | + | 0.677776i | \(0.237056\pi\) | |||||||
\(354\) | −3360.00 | −0.504469 | ||||||||
\(355\) | −1785.00 | −0.266868 | ||||||||
\(356\) | −3312.00 | −0.493078 | ||||||||
\(357\) | −18480.0 | −2.73968 | ||||||||
\(358\) | 3750.00 | 0.553614 | ||||||||
\(359\) | 3858.00 | 0.567180 | 0.283590 | − | 0.958946i | \(-0.408475\pi\) | ||||
0.283590 | + | 0.958946i | \(0.408475\pi\) | |||||||
\(360\) | −880.000 | −0.128834 | ||||||||
\(361\) | 14457.0 | 2.10774 | ||||||||
\(362\) | 3212.00 | 0.466351 | ||||||||
\(363\) | −9065.00 | −1.31071 | ||||||||
\(364\) | 3760.00 | 0.541422 | ||||||||
\(365\) | −1295.00 | −0.185708 | ||||||||
\(366\) | 5180.00 | 0.739789 | ||||||||
\(367\) | 7856.00 | 1.11738 | 0.558692 | − | 0.829375i | \(-0.311303\pi\) | ||||
0.558692 | + | 0.829375i | \(0.311303\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 10890.0 | 1.53634 | ||||||||
\(370\) | 1180.00 | 0.165798 | ||||||||
\(371\) | −6840.00 | −0.957184 | ||||||||
\(372\) | −7084.00 | −0.987334 | ||||||||
\(373\) | −34.0000 | −0.00471971 | −0.00235986 | − | 0.999997i | \(-0.500751\pi\) | ||||
−0.00235986 | + | 0.999997i | \(0.500751\pi\) | |||||||
\(374\) | 1584.00 | 0.219002 | ||||||||
\(375\) | 875.000 | 0.120493 | ||||||||
\(376\) | −5112.00 | −0.701147 | ||||||||
\(377\) | −4653.00 | −0.635654 | ||||||||
\(378\) | 1400.00 | 0.190498 | ||||||||
\(379\) | −6064.00 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 2920.00 | 0.394192 | ||||||||
\(381\) | 623.000 | 0.0837723 | ||||||||
\(382\) | −5964.00 | −0.798808 | ||||||||
\(383\) | 11868.0 | 1.58336 | 0.791679 | − | 0.610937i | \(-0.209207\pi\) | ||||
0.791679 | + | 0.610937i | \(0.209207\pi\) | |||||||
\(384\) | −896.000 | −0.119072 | ||||||||
\(385\) | 600.000 | 0.0794255 | ||||||||
\(386\) | −2770.00 | −0.365257 | ||||||||
\(387\) | 5984.00 | 0.786005 | ||||||||
\(388\) | 3968.00 | 0.519187 | ||||||||
\(389\) | 8616.00 | 1.12300 | 0.561502 | − | 0.827475i | \(-0.310224\pi\) | ||||
0.561502 | + | 0.827475i | \(0.310224\pi\) | |||||||
\(390\) | −3290.00 | −0.427168 | ||||||||
\(391\) | −3036.00 | −0.392678 | ||||||||
\(392\) | −456.000 | −0.0587538 | ||||||||
\(393\) | −12579.0 | −1.61457 | ||||||||
\(394\) | −1914.00 | −0.244736 | ||||||||
\(395\) | 2710.00 | 0.345202 | ||||||||
\(396\) | 528.000 | 0.0670025 | ||||||||
\(397\) | 3119.00 | 0.394303 | 0.197151 | − | 0.980373i | \(-0.436831\pi\) | ||||
0.197151 | + | 0.980373i | \(0.436831\pi\) | |||||||
\(398\) | 716.000 | 0.0901755 | ||||||||
\(399\) | 20440.0 | 2.56461 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 7986.00 | 0.994518 | 0.497259 | − | 0.867602i | \(-0.334340\pi\) | ||||
0.497259 | + | 0.867602i | \(0.334340\pi\) | |||||||
\(402\) | −9772.00 | −1.21240 | ||||||||
\(403\) | −11891.0 | −1.46981 | ||||||||
\(404\) | −6168.00 | −0.759578 | ||||||||
\(405\) | −4195.00 | −0.514694 | ||||||||
\(406\) | 3960.00 | 0.484068 | ||||||||
\(407\) | −708.000 | −0.0862267 | ||||||||
\(408\) | 7392.00 | 0.896957 | ||||||||
\(409\) | −3475.00 | −0.420117 | −0.210058 | − | 0.977689i | \(-0.567365\pi\) | ||||
−0.210058 | + | 0.977689i | \(0.567365\pi\) | |||||||
\(410\) | −4950.00 | −0.596251 | ||||||||
\(411\) | −12852.0 | −1.54244 | ||||||||
\(412\) | 128.000 | 0.0153061 | ||||||||
\(413\) | 4800.00 | 0.571895 | ||||||||
\(414\) | −1012.00 | −0.120138 | ||||||||
\(415\) | −6240.00 | −0.738095 | ||||||||
\(416\) | −1504.00 | −0.177259 | ||||||||
\(417\) | −7189.00 | −0.844237 | ||||||||
\(418\) | −1752.00 | −0.205007 | ||||||||
\(419\) | 10992.0 | 1.28161 | 0.640805 | − | 0.767704i | \(-0.278601\pi\) | ||||
0.640805 | + | 0.767704i | \(0.278601\pi\) | |||||||
\(420\) | 2800.00 | 0.325300 | ||||||||
\(421\) | 2012.00 | 0.232919 | 0.116459 | − | 0.993195i | \(-0.462845\pi\) | ||||
0.116459 | + | 0.993195i | \(0.462845\pi\) | |||||||
\(422\) | 10760.0 | 1.24121 | ||||||||
\(423\) | 14058.0 | 1.61589 | ||||||||
\(424\) | 2736.00 | 0.313377 | ||||||||
\(425\) | −3300.00 | −0.376644 | ||||||||
\(426\) | 4998.00 | 0.568436 | ||||||||
\(427\) | −7400.00 | −0.838668 | ||||||||
\(428\) | −3336.00 | −0.376756 | ||||||||
\(429\) | 1974.00 | 0.222158 | ||||||||
\(430\) | −2720.00 | −0.305047 | ||||||||
\(431\) | −9792.00 | −1.09435 | −0.547174 | − | 0.837019i | \(-0.684296\pi\) | ||||
−0.547174 | + | 0.837019i | \(0.684296\pi\) | |||||||
\(432\) | −560.000 | −0.0623681 | ||||||||
\(433\) | 5786.00 | 0.642165 | 0.321082 | − | 0.947051i | \(-0.395953\pi\) | ||||
0.321082 | + | 0.947051i | \(0.395953\pi\) | |||||||
\(434\) | 10120.0 | 1.11930 | ||||||||
\(435\) | −3465.00 | −0.381917 | ||||||||
\(436\) | −4768.00 | −0.523729 | ||||||||
\(437\) | 3358.00 | 0.367586 | ||||||||
\(438\) | 3626.00 | 0.395564 | ||||||||
\(439\) | 2549.00 | 0.277123 | 0.138562 | − | 0.990354i | \(-0.455752\pi\) | ||||
0.138562 | + | 0.990354i | \(0.455752\pi\) | |||||||
\(440\) | −240.000 | −0.0260035 | ||||||||
\(441\) | 1254.00 | 0.135407 | ||||||||
\(442\) | 12408.0 | 1.33527 | ||||||||
\(443\) | 1311.00 | 0.140604 | 0.0703019 | − | 0.997526i | \(-0.477604\pi\) | ||||
0.0703019 | + | 0.997526i | \(0.477604\pi\) | |||||||
\(444\) | −3304.00 | −0.353155 | ||||||||
\(445\) | −4140.00 | −0.441022 | ||||||||
\(446\) | −2080.00 | −0.220832 | ||||||||
\(447\) | 16170.0 | 1.71099 | ||||||||
\(448\) | 1280.00 | 0.134987 | ||||||||
\(449\) | −14610.0 | −1.53561 | −0.767805 | − | 0.640684i | \(-0.778651\pi\) | ||||
−0.767805 | + | 0.640684i | \(0.778651\pi\) | |||||||
\(450\) | −1100.00 | −0.115232 | ||||||||
\(451\) | 2970.00 | 0.310093 | ||||||||
\(452\) | −528.000 | −0.0549448 | ||||||||
\(453\) | −15043.0 | −1.56022 | ||||||||
\(454\) | 7488.00 | 0.774073 | ||||||||
\(455\) | 4700.00 | 0.484262 | ||||||||
\(456\) | −8176.00 | −0.839641 | ||||||||
\(457\) | 80.0000 | 0.00818871 | 0.00409436 | − | 0.999992i | \(-0.498697\pi\) | ||||
0.00409436 | + | 0.999992i | \(0.498697\pi\) | |||||||
\(458\) | −5608.00 | −0.572150 | ||||||||
\(459\) | 4620.00 | 0.469811 | ||||||||
\(460\) | 460.000 | 0.0466252 | ||||||||
\(461\) | −2343.00 | −0.236712 | −0.118356 | − | 0.992971i | \(-0.537762\pi\) | ||||
−0.118356 | + | 0.992971i | \(0.537762\pi\) | |||||||
\(462\) | −1680.00 | −0.169179 | ||||||||
\(463\) | −3400.00 | −0.341277 | −0.170639 | − | 0.985334i | \(-0.554583\pi\) | ||||
−0.170639 | + | 0.985334i | \(0.554583\pi\) | |||||||
\(464\) | −1584.00 | −0.158481 | ||||||||
\(465\) | −8855.00 | −0.883098 | ||||||||
\(466\) | 9738.00 | 0.968035 | ||||||||
\(467\) | −1374.00 | −0.136148 | −0.0680740 | − | 0.997680i | \(-0.521685\pi\) | ||||
−0.0680740 | + | 0.997680i | \(0.521685\pi\) | |||||||
\(468\) | 4136.00 | 0.408519 | ||||||||
\(469\) | 13960.0 | 1.37444 | ||||||||
\(470\) | −6390.00 | −0.627125 | ||||||||
\(471\) | 12824.0 | 1.25456 | ||||||||
\(472\) | −1920.00 | −0.187236 | ||||||||
\(473\) | 1632.00 | 0.158646 | ||||||||
\(474\) | −7588.00 | −0.735292 | ||||||||
\(475\) | 3650.00 | 0.352576 | ||||||||
\(476\) | −10560.0 | −1.01684 | ||||||||
\(477\) | −7524.00 | −0.722223 | ||||||||
\(478\) | 5754.00 | 0.550590 | ||||||||
\(479\) | 4536.00 | 0.432683 | 0.216341 | − | 0.976318i | \(-0.430588\pi\) | ||||
0.216341 | + | 0.976318i | \(0.430588\pi\) | |||||||
\(480\) | −1120.00 | −0.106502 | ||||||||
\(481\) | −5546.00 | −0.525729 | ||||||||
\(482\) | −3244.00 | −0.306556 | ||||||||
\(483\) | 3220.00 | 0.303344 | ||||||||
\(484\) | −5180.00 | −0.486476 | ||||||||
\(485\) | 4960.00 | 0.464375 | ||||||||
\(486\) | 9856.00 | 0.919912 | ||||||||
\(487\) | −11455.0 | −1.06586 | −0.532932 | − | 0.846158i | \(-0.678910\pi\) | ||||
−0.532932 | + | 0.846158i | \(0.678910\pi\) | |||||||
\(488\) | 2960.00 | 0.274576 | ||||||||
\(489\) | 8519.00 | 0.787817 | ||||||||
\(490\) | −570.000 | −0.0525510 | ||||||||
\(491\) | −10395.0 | −0.955437 | −0.477719 | − | 0.878513i | \(-0.658536\pi\) | ||||
−0.477719 | + | 0.878513i | \(0.658536\pi\) | |||||||
\(492\) | 13860.0 | 1.27003 | ||||||||
\(493\) | 13068.0 | 1.19382 | ||||||||
\(494\) | −13724.0 | −1.24994 | ||||||||
\(495\) | 660.000 | 0.0599289 | ||||||||
\(496\) | −4048.00 | −0.366453 | ||||||||
\(497\) | −7140.00 | −0.644412 | ||||||||
\(498\) | 17472.0 | 1.57217 | ||||||||
\(499\) | −5497.00 | −0.493145 | −0.246573 | − | 0.969124i | \(-0.579304\pi\) | ||||
−0.246573 | + | 0.969124i | \(0.579304\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | 21336.0 | 1.90264 | ||||||||
\(502\) | 9504.00 | 0.844989 | ||||||||
\(503\) | 7158.00 | 0.634512 | 0.317256 | − | 0.948340i | \(-0.397239\pi\) | ||||
0.317256 | + | 0.948340i | \(0.397239\pi\) | |||||||
\(504\) | −3520.00 | −0.311098 | ||||||||
\(505\) | −7710.00 | −0.679387 | ||||||||
\(506\) | −276.000 | −0.0242484 | ||||||||
\(507\) | 84.0000 | 0.00735813 | ||||||||
\(508\) | 356.000 | 0.0310924 | ||||||||
\(509\) | 12801.0 | 1.11472 | 0.557362 | − | 0.830270i | \(-0.311814\pi\) | ||||
0.557362 | + | 0.830270i | \(0.311814\pi\) | |||||||
\(510\) | 9240.00 | 0.802263 | ||||||||
\(511\) | −5180.00 | −0.448434 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −5110.00 | −0.439789 | ||||||||
\(514\) | 10146.0 | 0.870663 | ||||||||
\(515\) | 160.000 | 0.0136902 | ||||||||
\(516\) | 7616.00 | 0.649759 | ||||||||
\(517\) | 3834.00 | 0.326149 | ||||||||
\(518\) | 4720.00 | 0.400357 | ||||||||
\(519\) | 5418.00 | 0.458235 | ||||||||
\(520\) | −1880.00 | −0.158545 | ||||||||
\(521\) | 16788.0 | 1.41170 | 0.705850 | − | 0.708361i | \(-0.250565\pi\) | ||||
0.705850 | + | 0.708361i | \(0.250565\pi\) | |||||||
\(522\) | 4356.00 | 0.365243 | ||||||||
\(523\) | 19040.0 | 1.59189 | 0.795947 | − | 0.605366i | \(-0.206973\pi\) | ||||
0.795947 | + | 0.605366i | \(0.206973\pi\) | |||||||
\(524\) | −7188.00 | −0.599254 | ||||||||
\(525\) | 3500.00 | 0.290957 | ||||||||
\(526\) | −2628.00 | −0.217845 | ||||||||
\(527\) | 33396.0 | 2.76044 | ||||||||
\(528\) | 672.000 | 0.0553883 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 3420.00 | 0.280293 | ||||||||
\(531\) | 5280.00 | 0.431511 | ||||||||
\(532\) | 11680.0 | 0.951865 | ||||||||
\(533\) | 23265.0 | 1.89065 | ||||||||
\(534\) | 11592.0 | 0.939391 | ||||||||
\(535\) | −4170.00 | −0.336981 | ||||||||
\(536\) | −5584.00 | −0.449985 | ||||||||
\(537\) | −13125.0 | −1.05472 | ||||||||
\(538\) | −10530.0 | −0.843830 | ||||||||
\(539\) | 342.000 | 0.0273302 | ||||||||
\(540\) | −700.000 | −0.0557837 | ||||||||
\(541\) | −13339.0 | −1.06005 | −0.530026 | − | 0.847981i | \(-0.677818\pi\) | ||||
−0.530026 | + | 0.847981i | \(0.677818\pi\) | |||||||
\(542\) | 4976.00 | 0.394350 | ||||||||
\(543\) | −11242.0 | −0.888472 | ||||||||
\(544\) | 4224.00 | 0.332909 | ||||||||
\(545\) | −5960.00 | −0.468437 | ||||||||
\(546\) | −13160.0 | −1.03149 | ||||||||
\(547\) | −22975.0 | −1.79587 | −0.897934 | − | 0.440130i | \(-0.854932\pi\) | ||||
−0.897934 | + | 0.440130i | \(0.854932\pi\) | |||||||
\(548\) | −7344.00 | −0.572482 | ||||||||
\(549\) | −8140.00 | −0.632799 | ||||||||
\(550\) | −300.000 | −0.0232583 | ||||||||
\(551\) | −14454.0 | −1.11753 | ||||||||
\(552\) | −1288.00 | −0.0993133 | ||||||||
\(553\) | 10840.0 | 0.833569 | ||||||||
\(554\) | −10930.0 | −0.838215 | ||||||||
\(555\) | −4130.00 | −0.315872 | ||||||||
\(556\) | −4108.00 | −0.313342 | ||||||||
\(557\) | −17964.0 | −1.36653 | −0.683267 | − | 0.730169i | \(-0.739441\pi\) | ||||
−0.683267 | + | 0.730169i | \(0.739441\pi\) | |||||||
\(558\) | 11132.0 | 0.844543 | ||||||||
\(559\) | 12784.0 | 0.967273 | ||||||||
\(560\) | 1600.00 | 0.120736 | ||||||||
\(561\) | −5544.00 | −0.417233 | ||||||||
\(562\) | −17880.0 | −1.34203 | ||||||||
\(563\) | 12636.0 | 0.945904 | 0.472952 | − | 0.881088i | \(-0.343188\pi\) | ||||
0.472952 | + | 0.881088i | \(0.343188\pi\) | |||||||
\(564\) | 17892.0 | 1.33580 | ||||||||
\(565\) | −660.000 | −0.0491441 | ||||||||
\(566\) | −1684.00 | −0.125060 | ||||||||
\(567\) | −16780.0 | −1.24285 | ||||||||
\(568\) | 2856.00 | 0.210977 | ||||||||
\(569\) | −10302.0 | −0.759020 | −0.379510 | − | 0.925188i | \(-0.623907\pi\) | ||||
−0.379510 | + | 0.925188i | \(0.623907\pi\) | |||||||
\(570\) | −10220.0 | −0.750998 | ||||||||
\(571\) | 12380.0 | 0.907333 | 0.453666 | − | 0.891172i | \(-0.350116\pi\) | ||||
0.453666 | + | 0.891172i | \(0.350116\pi\) | |||||||
\(572\) | 1128.00 | 0.0824546 | ||||||||
\(573\) | 20874.0 | 1.52186 | ||||||||
\(574\) | −19800.0 | −1.43978 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 1408.00 | 0.101852 | ||||||||
\(577\) | 1913.00 | 0.138023 | 0.0690115 | − | 0.997616i | \(-0.478015\pi\) | ||||
0.0690115 | + | 0.997616i | \(0.478015\pi\) | |||||||
\(578\) | −25022.0 | −1.80065 | ||||||||
\(579\) | 9695.00 | 0.695873 | ||||||||
\(580\) | −1980.00 | −0.141750 | ||||||||
\(581\) | −24960.0 | −1.78230 | ||||||||
\(582\) | −13888.0 | −0.989134 | ||||||||
\(583\) | −2052.00 | −0.145772 | ||||||||
\(584\) | 2072.00 | 0.146815 | ||||||||
\(585\) | 5170.00 | 0.365390 | ||||||||
\(586\) | 8064.00 | 0.568465 | ||||||||
\(587\) | 16767.0 | 1.17896 | 0.589479 | − | 0.807784i | \(-0.299333\pi\) | ||||
0.589479 | + | 0.807784i | \(0.299333\pi\) | |||||||
\(588\) | 1596.00 | 0.111935 | ||||||||
\(589\) | −36938.0 | −2.58405 | ||||||||
\(590\) | −2400.00 | −0.167469 | ||||||||
\(591\) | 6699.00 | 0.466261 | ||||||||
\(592\) | −1888.00 | −0.131075 | ||||||||
\(593\) | −16722.0 | −1.15799 | −0.578997 | − | 0.815330i | \(-0.696556\pi\) | ||||
−0.578997 | + | 0.815330i | \(0.696556\pi\) | |||||||
\(594\) | 420.000 | 0.0290115 | ||||||||
\(595\) | −13200.0 | −0.909491 | ||||||||
\(596\) | 9240.00 | 0.635042 | ||||||||
\(597\) | −2506.00 | −0.171799 | ||||||||
\(598\) | −2162.00 | −0.147844 | ||||||||
\(599\) | −4200.00 | −0.286490 | −0.143245 | − | 0.989687i | \(-0.545754\pi\) | ||||
−0.143245 | + | 0.989687i | \(0.545754\pi\) | |||||||
\(600\) | −1400.00 | −0.0952579 | ||||||||
\(601\) | −19915.0 | −1.35166 | −0.675832 | − | 0.737056i | \(-0.736215\pi\) | ||||
−0.675832 | + | 0.737056i | \(0.736215\pi\) | |||||||
\(602\) | −10880.0 | −0.736604 | ||||||||
\(603\) | 15356.0 | 1.03706 | ||||||||
\(604\) | −8596.00 | −0.579083 | ||||||||
\(605\) | −6475.00 | −0.435118 | ||||||||
\(606\) | 21588.0 | 1.44712 | ||||||||
\(607\) | 24044.0 | 1.60777 | 0.803885 | − | 0.594785i | \(-0.202763\pi\) | ||||
0.803885 | + | 0.594785i | \(0.202763\pi\) | |||||||
\(608\) | −4672.00 | −0.311636 | ||||||||
\(609\) | −13860.0 | −0.922226 | ||||||||
\(610\) | 3700.00 | 0.245588 | ||||||||
\(611\) | 30033.0 | 1.98855 | ||||||||
\(612\) | −11616.0 | −0.767237 | ||||||||
\(613\) | 3452.00 | 0.227447 | 0.113723 | − | 0.993512i | \(-0.463722\pi\) | ||||
0.113723 | + | 0.993512i | \(0.463722\pi\) | |||||||
\(614\) | 2192.00 | 0.144075 | ||||||||
\(615\) | 17325.0 | 1.13595 | ||||||||
\(616\) | −960.000 | −0.0627914 | ||||||||
\(617\) | −16374.0 | −1.06838 | −0.534192 | − | 0.845363i | \(-0.679384\pi\) | ||||
−0.534192 | + | 0.845363i | \(0.679384\pi\) | |||||||
\(618\) | −448.000 | −0.0291605 | ||||||||
\(619\) | −12760.0 | −0.828542 | −0.414271 | − | 0.910154i | \(-0.635963\pi\) | ||||
−0.414271 | + | 0.910154i | \(0.635963\pi\) | |||||||
\(620\) | −5060.00 | −0.327765 | ||||||||
\(621\) | −805.000 | −0.0520186 | ||||||||
\(622\) | 9306.00 | 0.599898 | ||||||||
\(623\) | −16560.0 | −1.06495 | ||||||||
\(624\) | 5264.00 | 0.337706 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −6880.00 | −0.439265 | ||||||||
\(627\) | 6132.00 | 0.390572 | ||||||||
\(628\) | 7328.00 | 0.465635 | ||||||||
\(629\) | 15576.0 | 0.987370 | ||||||||
\(630\) | −4400.00 | −0.278254 | ||||||||
\(631\) | 29420.0 | 1.85609 | 0.928044 | − | 0.372470i | \(-0.121489\pi\) | ||||
0.928044 | + | 0.372470i | \(0.121489\pi\) | |||||||
\(632\) | −4336.00 | −0.272906 | ||||||||
\(633\) | −37660.0 | −2.36469 | ||||||||
\(634\) | −6132.00 | −0.384121 | ||||||||
\(635\) | 445.000 | 0.0278099 | ||||||||
\(636\) | −9576.00 | −0.597033 | ||||||||
\(637\) | 2679.00 | 0.166634 | ||||||||
\(638\) | 1188.00 | 0.0737200 | ||||||||
\(639\) | −7854.00 | −0.486228 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | −13692.0 | −0.843684 | −0.421842 | − | 0.906669i | \(-0.638616\pi\) | ||||
−0.421842 | + | 0.906669i | \(0.638616\pi\) | |||||||
\(642\) | 11676.0 | 0.717780 | ||||||||
\(643\) | 27398.0 | 1.68036 | 0.840180 | − | 0.542307i | \(-0.182449\pi\) | ||||
0.840180 | + | 0.542307i | \(0.182449\pi\) | |||||||
\(644\) | 1840.00 | 0.112587 | ||||||||
\(645\) | 9520.00 | 0.581162 | ||||||||
\(646\) | 38544.0 | 2.34751 | ||||||||
\(647\) | −6417.00 | −0.389920 | −0.194960 | − | 0.980811i | \(-0.562458\pi\) | ||||
−0.194960 | + | 0.980811i | \(0.562458\pi\) | |||||||
\(648\) | 6712.00 | 0.406902 | ||||||||
\(649\) | 1440.00 | 0.0870954 | ||||||||
\(650\) | −2350.00 | −0.141807 | ||||||||
\(651\) | −35420.0 | −2.13244 | ||||||||
\(652\) | 4868.00 | 0.292401 | ||||||||
\(653\) | 14583.0 | 0.873931 | 0.436965 | − | 0.899478i | \(-0.356053\pi\) | ||||
0.436965 | + | 0.899478i | \(0.356053\pi\) | |||||||
\(654\) | 16688.0 | 0.997787 | ||||||||
\(655\) | −8985.00 | −0.535989 | ||||||||
\(656\) | 7920.00 | 0.471378 | ||||||||
\(657\) | −5698.00 | −0.338356 | ||||||||
\(658\) | −25560.0 | −1.51434 | ||||||||
\(659\) | −9624.00 | −0.568889 | −0.284444 | − | 0.958693i | \(-0.591809\pi\) | ||||
−0.284444 | + | 0.958693i | \(0.591809\pi\) | |||||||
\(660\) | 840.000 | 0.0495408 | ||||||||
\(661\) | −24586.0 | −1.44672 | −0.723362 | − | 0.690469i | \(-0.757404\pi\) | ||||
−0.723362 | + | 0.690469i | \(0.757404\pi\) | |||||||
\(662\) | −3010.00 | −0.176717 | ||||||||
\(663\) | −43428.0 | −2.54390 | ||||||||
\(664\) | 9984.00 | 0.583516 | ||||||||
\(665\) | 14600.0 | 0.851374 | ||||||||
\(666\) | 5192.00 | 0.302081 | ||||||||
\(667\) | −2277.00 | −0.132183 | ||||||||
\(668\) | 12192.0 | 0.706172 | ||||||||
\(669\) | 7280.00 | 0.420719 | ||||||||
\(670\) | −6980.00 | −0.402479 | ||||||||
\(671\) | −2220.00 | −0.127723 | ||||||||
\(672\) | −4480.00 | −0.257172 | ||||||||
\(673\) | 14339.0 | 0.821289 | 0.410645 | − | 0.911795i | \(-0.365304\pi\) | ||||
0.410645 | + | 0.911795i | \(0.365304\pi\) | |||||||
\(674\) | 6536.00 | 0.373527 | ||||||||
\(675\) | −875.000 | −0.0498945 | ||||||||
\(676\) | 48.0000 | 0.00273100 | ||||||||
\(677\) | 14658.0 | 0.832131 | 0.416066 | − | 0.909335i | \(-0.363409\pi\) | ||||
0.416066 | + | 0.909335i | \(0.363409\pi\) | |||||||
\(678\) | 1848.00 | 0.104678 | ||||||||
\(679\) | 19840.0 | 1.12134 | ||||||||
\(680\) | 5280.00 | 0.297763 | ||||||||
\(681\) | −26208.0 | −1.47473 | ||||||||
\(682\) | 3036.00 | 0.170461 | ||||||||
\(683\) | 16797.0 | 0.941024 | 0.470512 | − | 0.882394i | \(-0.344069\pi\) | ||||
0.470512 | + | 0.882394i | \(0.344069\pi\) | |||||||
\(684\) | 12848.0 | 0.718210 | ||||||||
\(685\) | −9180.00 | −0.512043 | ||||||||
\(686\) | 11440.0 | 0.636707 | ||||||||
\(687\) | 19628.0 | 1.09004 | ||||||||
\(688\) | 4352.00 | 0.241161 | ||||||||
\(689\) | −16074.0 | −0.888782 | ||||||||
\(690\) | −1610.00 | −0.0888285 | ||||||||
\(691\) | 8132.00 | 0.447693 | 0.223846 | − | 0.974624i | \(-0.428139\pi\) | ||||
0.223846 | + | 0.974624i | \(0.428139\pi\) | |||||||
\(692\) | 3096.00 | 0.170076 | ||||||||
\(693\) | 2640.00 | 0.144712 | ||||||||
\(694\) | −8328.00 | −0.455514 | ||||||||
\(695\) | −5135.00 | −0.280261 | ||||||||
\(696\) | 5544.00 | 0.301932 | ||||||||
\(697\) | −65340.0 | −3.55083 | ||||||||
\(698\) | 5822.00 | 0.315711 | ||||||||
\(699\) | −34083.0 | −1.84426 | ||||||||
\(700\) | 2000.00 | 0.107990 | ||||||||
\(701\) | 19668.0 | 1.05970 | 0.529850 | − | 0.848091i | \(-0.322248\pi\) | ||||
0.529850 | + | 0.848091i | \(0.322248\pi\) | |||||||
\(702\) | 3290.00 | 0.176885 | ||||||||
\(703\) | −17228.0 | −0.924276 | ||||||||
\(704\) | 384.000 | 0.0205576 | ||||||||
\(705\) | 22365.0 | 1.19477 | ||||||||
\(706\) | −19506.0 | −1.03983 | ||||||||
\(707\) | −30840.0 | −1.64053 | ||||||||
\(708\) | 6720.00 | 0.356713 | ||||||||
\(709\) | 18200.0 | 0.964055 | 0.482028 | − | 0.876156i | \(-0.339900\pi\) | ||||
0.482028 | + | 0.876156i | \(0.339900\pi\) | |||||||
\(710\) | 3570.00 | 0.188704 | ||||||||
\(711\) | 11924.0 | 0.628952 | ||||||||
\(712\) | 6624.00 | 0.348659 | ||||||||
\(713\) | −5819.00 | −0.305643 | ||||||||
\(714\) | 36960.0 | 1.93725 | ||||||||
\(715\) | 1410.00 | 0.0737497 | ||||||||
\(716\) | −7500.00 | −0.391464 | ||||||||
\(717\) | −20139.0 | −1.04896 | ||||||||
\(718\) | −7716.00 | −0.401056 | ||||||||
\(719\) | −11880.0 | −0.616202 | −0.308101 | − | 0.951354i | \(-0.599693\pi\) | ||||
−0.308101 | + | 0.951354i | \(0.599693\pi\) | |||||||
\(720\) | 1760.00 | 0.0910991 | ||||||||
\(721\) | 640.000 | 0.0330580 | ||||||||
\(722\) | −28914.0 | −1.49040 | ||||||||
\(723\) | 11354.0 | 0.584038 | ||||||||
\(724\) | −6424.00 | −0.329760 | ||||||||
\(725\) | −2475.00 | −0.126785 | ||||||||
\(726\) | 18130.0 | 0.926815 | ||||||||
\(727\) | −2554.00 | −0.130292 | −0.0651462 | − | 0.997876i | \(-0.520751\pi\) | ||||
−0.0651462 | + | 0.997876i | \(0.520751\pi\) | |||||||
\(728\) | −7520.00 | −0.382843 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 2590.00 | 0.131315 | ||||||||
\(731\) | −35904.0 | −1.81663 | ||||||||
\(732\) | −10360.0 | −0.523110 | ||||||||
\(733\) | 6308.00 | 0.317860 | 0.158930 | − | 0.987290i | \(-0.449196\pi\) | ||||
0.158930 | + | 0.987290i | \(0.449196\pi\) | |||||||
\(734\) | −15712.0 | −0.790110 | ||||||||
\(735\) | 1995.00 | 0.100118 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 4188.00 | 0.209317 | ||||||||
\(738\) | −21780.0 | −1.08636 | ||||||||
\(739\) | 9557.00 | 0.475724 | 0.237862 | − | 0.971299i | \(-0.423553\pi\) | ||||
0.237862 | + | 0.971299i | \(0.423553\pi\) | |||||||
\(740\) | −2360.00 | −0.117237 | ||||||||
\(741\) | 48034.0 | 2.38134 | ||||||||
\(742\) | 13680.0 | 0.676831 | ||||||||
\(743\) | 19128.0 | 0.944466 | 0.472233 | − | 0.881474i | \(-0.343448\pi\) | ||||
0.472233 | + | 0.881474i | \(0.343448\pi\) | |||||||
\(744\) | 14168.0 | 0.698151 | ||||||||
\(745\) | 11550.0 | 0.567999 | ||||||||
\(746\) | 68.0000 | 0.00333734 | ||||||||
\(747\) | −27456.0 | −1.34480 | ||||||||
\(748\) | −3168.00 | −0.154858 | ||||||||
\(749\) | −16680.0 | −0.813717 | ||||||||
\(750\) | −1750.00 | −0.0852013 | ||||||||
\(751\) | −18448.0 | −0.896374 | −0.448187 | − | 0.893940i | \(-0.647930\pi\) | ||||
−0.448187 | + | 0.893940i | \(0.647930\pi\) | |||||||
\(752\) | 10224.0 | 0.495786 | ||||||||
\(753\) | −33264.0 | −1.60984 | ||||||||
\(754\) | 9306.00 | 0.449476 | ||||||||
\(755\) | −10745.0 | −0.517948 | ||||||||
\(756\) | −2800.00 | −0.134702 | ||||||||
\(757\) | −5602.00 | −0.268967 | −0.134484 | − | 0.990916i | \(-0.542938\pi\) | ||||
−0.134484 | + | 0.990916i | \(0.542938\pi\) | |||||||
\(758\) | 12128.0 | 0.581146 | ||||||||
\(759\) | 966.000 | 0.0461971 | ||||||||
\(760\) | −5840.00 | −0.278736 | ||||||||
\(761\) | 4005.00 | 0.190777 | 0.0953884 | − | 0.995440i | \(-0.469591\pi\) | ||||
0.0953884 | + | 0.995440i | \(0.469591\pi\) | |||||||
\(762\) | −1246.00 | −0.0592360 | ||||||||
\(763\) | −23840.0 | −1.13115 | ||||||||
\(764\) | 11928.0 | 0.564843 | ||||||||
\(765\) | −14520.0 | −0.686238 | ||||||||
\(766\) | −23736.0 | −1.11960 | ||||||||
\(767\) | 11280.0 | 0.531026 | ||||||||
\(768\) | 1792.00 | 0.0841969 | ||||||||
\(769\) | 41726.0 | 1.95667 | 0.978334 | − | 0.207032i | \(-0.0663803\pi\) | ||||
0.978334 | + | 0.207032i | \(0.0663803\pi\) | |||||||
\(770\) | −1200.00 | −0.0561623 | ||||||||
\(771\) | −35511.0 | −1.65875 | ||||||||
\(772\) | 5540.00 | 0.258276 | ||||||||
\(773\) | 34116.0 | 1.58741 | 0.793705 | − | 0.608303i | \(-0.208150\pi\) | ||||
0.793705 | + | 0.608303i | \(0.208150\pi\) | |||||||
\(774\) | −11968.0 | −0.555789 | ||||||||
\(775\) | −6325.00 | −0.293162 | ||||||||
\(776\) | −7936.00 | −0.367121 | ||||||||
\(777\) | −16520.0 | −0.762743 | ||||||||
\(778\) | −17232.0 | −0.794084 | ||||||||
\(779\) | 72270.0 | 3.32393 | ||||||||
\(780\) | 6580.00 | 0.302054 | ||||||||
\(781\) | −2142.00 | −0.0981393 | ||||||||
\(782\) | 6072.00 | 0.277665 | ||||||||
\(783\) | 3465.00 | 0.158147 | ||||||||
\(784\) | 912.000 | 0.0415452 | ||||||||
\(785\) | 9160.00 | 0.416477 | ||||||||
\(786\) | 25158.0 | 1.14167 | ||||||||
\(787\) | 1652.00 | 0.0748252 | 0.0374126 | − | 0.999300i | \(-0.488088\pi\) | ||||
0.0374126 | + | 0.999300i | \(0.488088\pi\) | |||||||
\(788\) | 3828.00 | 0.173054 | ||||||||
\(789\) | 9198.00 | 0.415028 | ||||||||
\(790\) | −5420.00 | −0.244095 | ||||||||
\(791\) | −2640.00 | −0.118670 | ||||||||
\(792\) | −1056.00 | −0.0473779 | ||||||||
\(793\) | −17390.0 | −0.778735 | ||||||||
\(794\) | −6238.00 | −0.278814 | ||||||||
\(795\) | −11970.0 | −0.534003 | ||||||||
\(796\) | −1432.00 | −0.0637637 | ||||||||
\(797\) | 12486.0 | 0.554927 | 0.277463 | − | 0.960736i | \(-0.410506\pi\) | ||||
0.277463 | + | 0.960736i | \(0.410506\pi\) | |||||||
\(798\) | −40880.0 | −1.81345 | ||||||||
\(799\) | −84348.0 | −3.73469 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | −18216.0 | −0.803534 | ||||||||
\(802\) | −15972.0 | −0.703231 | ||||||||
\(803\) | −1554.00 | −0.0682932 | ||||||||
\(804\) | 19544.0 | 0.857293 | ||||||||
\(805\) | 2300.00 | 0.100701 | ||||||||
\(806\) | 23782.0 | 1.03931 | ||||||||
\(807\) | 36855.0 | 1.60763 | ||||||||
\(808\) | 12336.0 | 0.537103 | ||||||||
\(809\) | 5490.00 | 0.238589 | 0.119294 | − | 0.992859i | \(-0.461937\pi\) | ||||
0.119294 | + | 0.992859i | \(0.461937\pi\) | |||||||
\(810\) | 8390.00 | 0.363944 | ||||||||
\(811\) | −14785.0 | −0.640162 | −0.320081 | − | 0.947390i | \(-0.603710\pi\) | ||||
−0.320081 | + | 0.947390i | \(0.603710\pi\) | |||||||
\(812\) | −7920.00 | −0.342288 | ||||||||
\(813\) | −17416.0 | −0.751299 | ||||||||
\(814\) | 1416.00 | 0.0609715 | ||||||||
\(815\) | 6085.00 | 0.261532 | ||||||||
\(816\) | −14784.0 | −0.634245 | ||||||||
\(817\) | 39712.0 | 1.70055 | ||||||||
\(818\) | 6950.00 | 0.297067 | ||||||||
\(819\) | 20680.0 | 0.882317 | ||||||||
\(820\) | 9900.00 | 0.421613 | ||||||||
\(821\) | −12486.0 | −0.530773 | −0.265386 | − | 0.964142i | \(-0.585500\pi\) | ||||
−0.265386 | + | 0.964142i | \(0.585500\pi\) | |||||||
\(822\) | 25704.0 | 1.09067 | ||||||||
\(823\) | −39805.0 | −1.68592 | −0.842962 | − | 0.537973i | \(-0.819190\pi\) | ||||
−0.842962 | + | 0.537973i | \(0.819190\pi\) | |||||||
\(824\) | −256.000 | −0.0108230 | ||||||||
\(825\) | 1050.00 | 0.0443107 | ||||||||
\(826\) | −9600.00 | −0.404391 | ||||||||
\(827\) | 15024.0 | 0.631724 | 0.315862 | − | 0.948805i | \(-0.397706\pi\) | ||||
0.315862 | + | 0.948805i | \(0.397706\pi\) | |||||||
\(828\) | 2024.00 | 0.0849503 | ||||||||
\(829\) | 14618.0 | 0.612430 | 0.306215 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306215 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(830\) | 12480.0 | 0.521912 | ||||||||
\(831\) | 38255.0 | 1.59693 | ||||||||
\(832\) | 3008.00 | 0.125341 | ||||||||
\(833\) | −7524.00 | −0.312955 | ||||||||
\(834\) | 14378.0 | 0.596966 | ||||||||
\(835\) | 15240.0 | 0.631619 | ||||||||
\(836\) | 3504.00 | 0.144962 | ||||||||
\(837\) | 8855.00 | 0.365679 | ||||||||
\(838\) | −21984.0 | −0.906235 | ||||||||
\(839\) | −10152.0 | −0.417743 | −0.208871 | − | 0.977943i | \(-0.566979\pi\) | ||||
−0.208871 | + | 0.977943i | \(0.566979\pi\) | |||||||
\(840\) | −5600.00 | −0.230022 | ||||||||
\(841\) | −14588.0 | −0.598139 | ||||||||
\(842\) | −4024.00 | −0.164699 | ||||||||
\(843\) | 62580.0 | 2.55678 | ||||||||
\(844\) | −21520.0 | −0.877665 | ||||||||
\(845\) | 60.0000 | 0.00244268 | ||||||||
\(846\) | −28116.0 | −1.14261 | ||||||||
\(847\) | −25900.0 | −1.05069 | ||||||||
\(848\) | −5472.00 | −0.221591 | ||||||||
\(849\) | 5894.00 | 0.238259 | ||||||||
\(850\) | 6600.00 | 0.266327 | ||||||||
\(851\) | −2714.00 | −0.109324 | ||||||||
\(852\) | −9996.00 | −0.401945 | ||||||||
\(853\) | −22306.0 | −0.895361 | −0.447680 | − | 0.894194i | \(-0.647750\pi\) | ||||
−0.447680 | + | 0.894194i | \(0.647750\pi\) | |||||||
\(854\) | 14800.0 | 0.593028 | ||||||||
\(855\) | 16060.0 | 0.642386 | ||||||||
\(856\) | 6672.00 | 0.266407 | ||||||||
\(857\) | 1731.00 | 0.0689963 | 0.0344982 | − | 0.999405i | \(-0.489017\pi\) | ||||
0.0344982 | + | 0.999405i | \(0.489017\pi\) | |||||||
\(858\) | −3948.00 | −0.157089 | ||||||||
\(859\) | −12649.0 | −0.502419 | −0.251210 | − | 0.967933i | \(-0.580828\pi\) | ||||
−0.251210 | + | 0.967933i | \(0.580828\pi\) | |||||||
\(860\) | 5440.00 | 0.215701 | ||||||||
\(861\) | 69300.0 | 2.74302 | ||||||||
\(862\) | 19584.0 | 0.773821 | ||||||||
\(863\) | −16143.0 | −0.636749 | −0.318374 | − | 0.947965i | \(-0.603137\pi\) | ||||
−0.318374 | + | 0.947965i | \(0.603137\pi\) | |||||||
\(864\) | 1120.00 | 0.0441009 | ||||||||
\(865\) | 3870.00 | 0.152120 | ||||||||
\(866\) | −11572.0 | −0.454079 | ||||||||
\(867\) | 87577.0 | 3.43053 | ||||||||
\(868\) | −20240.0 | −0.791464 | ||||||||
\(869\) | 3252.00 | 0.126947 | ||||||||
\(870\) | 6930.00 | 0.270056 | ||||||||
\(871\) | 32806.0 | 1.27622 | ||||||||
\(872\) | 9536.00 | 0.370332 | ||||||||
\(873\) | 21824.0 | 0.846083 | ||||||||
\(874\) | −6716.00 | −0.259922 | ||||||||
\(875\) | 2500.00 | 0.0965891 | ||||||||
\(876\) | −7252.00 | −0.279706 | ||||||||
\(877\) | 4094.00 | 0.157633 | 0.0788167 | − | 0.996889i | \(-0.474886\pi\) | ||||
0.0788167 | + | 0.996889i | \(0.474886\pi\) | |||||||
\(878\) | −5098.00 | −0.195956 | ||||||||
\(879\) | −28224.0 | −1.08302 | ||||||||
\(880\) | 480.000 | 0.0183873 | ||||||||
\(881\) | 30396.0 | 1.16239 | 0.581196 | − | 0.813764i | \(-0.302585\pi\) | ||||
0.581196 | + | 0.813764i | \(0.302585\pi\) | |||||||
\(882\) | −2508.00 | −0.0957469 | ||||||||
\(883\) | −21148.0 | −0.805987 | −0.402994 | − | 0.915203i | \(-0.632030\pi\) | ||||
−0.402994 | + | 0.915203i | \(0.632030\pi\) | |||||||
\(884\) | −24816.0 | −0.944177 | ||||||||
\(885\) | 8400.00 | 0.319054 | ||||||||
\(886\) | −2622.00 | −0.0994219 | ||||||||
\(887\) | 5031.00 | 0.190445 | 0.0952223 | − | 0.995456i | \(-0.469644\pi\) | ||||
0.0952223 | + | 0.995456i | \(0.469644\pi\) | |||||||
\(888\) | 6608.00 | 0.249718 | ||||||||
\(889\) | 1780.00 | 0.0671533 | ||||||||
\(890\) | 8280.00 | 0.311850 | ||||||||
\(891\) | −5034.00 | −0.189276 | ||||||||
\(892\) | 4160.00 | 0.156151 | ||||||||
\(893\) | 93294.0 | 3.49604 | ||||||||
\(894\) | −32340.0 | −1.20986 | ||||||||
\(895\) | −9375.00 | −0.350136 | ||||||||
\(896\) | −2560.00 | −0.0954504 | ||||||||
\(897\) | 7567.00 | 0.281666 | ||||||||
\(898\) | 29220.0 | 1.08584 | ||||||||
\(899\) | 25047.0 | 0.929215 | ||||||||
\(900\) | 2200.00 | 0.0814815 | ||||||||
\(901\) | 45144.0 | 1.66922 | ||||||||
\(902\) | −5940.00 | −0.219269 | ||||||||
\(903\) | 38080.0 | 1.40335 | ||||||||
\(904\) | 1056.00 | 0.0388518 | ||||||||
\(905\) | −8030.00 | −0.294946 | ||||||||
\(906\) | 30086.0 | 1.10325 | ||||||||
\(907\) | −538.000 | −0.0196957 | −0.00984785 | − | 0.999952i | \(-0.503135\pi\) | ||||
−0.00984785 | + | 0.999952i | \(0.503135\pi\) | |||||||
\(908\) | −14976.0 | −0.547352 | ||||||||
\(909\) | −33924.0 | −1.23783 | ||||||||
\(910\) | −9400.00 | −0.342425 | ||||||||
\(911\) | 3078.00 | 0.111941 | 0.0559707 | − | 0.998432i | \(-0.482175\pi\) | ||||
0.0559707 | + | 0.998432i | \(0.482175\pi\) | |||||||
\(912\) | 16352.0 | 0.593716 | ||||||||
\(913\) | −7488.00 | −0.271431 | ||||||||
\(914\) | −160.000 | −0.00579029 | ||||||||
\(915\) | −12950.0 | −0.467884 | ||||||||
\(916\) | 11216.0 | 0.404571 | ||||||||
\(917\) | −35940.0 | −1.29427 | ||||||||
\(918\) | −9240.00 | −0.332206 | ||||||||
\(919\) | 20288.0 | 0.728226 | 0.364113 | − | 0.931355i | \(-0.381372\pi\) | ||||
0.364113 | + | 0.931355i | \(0.381372\pi\) | |||||||
\(920\) | −920.000 | −0.0329690 | ||||||||
\(921\) | −7672.00 | −0.274485 | ||||||||
\(922\) | 4686.00 | 0.167381 | ||||||||
\(923\) | −16779.0 | −0.598361 | ||||||||
\(924\) | 3360.00 | 0.119628 | ||||||||
\(925\) | −2950.00 | −0.104860 | ||||||||
\(926\) | 6800.00 | 0.241320 | ||||||||
\(927\) | 704.000 | 0.0249433 | ||||||||
\(928\) | 3168.00 | 0.112063 | ||||||||
\(929\) | 28911.0 | 1.02103 | 0.510516 | − | 0.859868i | \(-0.329454\pi\) | ||||
0.510516 | + | 0.859868i | \(0.329454\pi\) | |||||||
\(930\) | 17710.0 | 0.624445 | ||||||||
\(931\) | 8322.00 | 0.292957 | ||||||||
\(932\) | −19476.0 | −0.684504 | ||||||||
\(933\) | −32571.0 | −1.14290 | ||||||||
\(934\) | 2748.00 | 0.0962712 | ||||||||
\(935\) | −3960.00 | −0.138509 | ||||||||
\(936\) | −8272.00 | −0.288866 | ||||||||
\(937\) | 14810.0 | 0.516352 | 0.258176 | − | 0.966098i | \(-0.416879\pi\) | ||||
0.258176 | + | 0.966098i | \(0.416879\pi\) | |||||||
\(938\) | −27920.0 | −0.971877 | ||||||||
\(939\) | 24080.0 | 0.836870 | ||||||||
\(940\) | 12780.0 | 0.443444 | ||||||||
\(941\) | −2544.00 | −0.0881318 | −0.0440659 | − | 0.999029i | \(-0.514031\pi\) | ||||
−0.0440659 | + | 0.999029i | \(0.514031\pi\) | |||||||
\(942\) | −25648.0 | −0.887109 | ||||||||
\(943\) | 11385.0 | 0.393157 | ||||||||
\(944\) | 3840.00 | 0.132396 | ||||||||
\(945\) | −3500.00 | −0.120481 | ||||||||
\(946\) | −3264.00 | −0.112179 | ||||||||
\(947\) | −11145.0 | −0.382433 | −0.191216 | − | 0.981548i | \(-0.561243\pi\) | ||||
−0.191216 | + | 0.981548i | \(0.561243\pi\) | |||||||
\(948\) | 15176.0 | 0.519930 | ||||||||
\(949\) | −12173.0 | −0.416388 | ||||||||
\(950\) | −7300.00 | −0.249309 | ||||||||
\(951\) | 21462.0 | 0.731812 | ||||||||
\(952\) | 21120.0 | 0.719016 | ||||||||
\(953\) | −4386.00 | −0.149083 | −0.0745417 | − | 0.997218i | \(-0.523749\pi\) | ||||
−0.0745417 | + | 0.997218i | \(0.523749\pi\) | |||||||
\(954\) | 15048.0 | 0.510689 | ||||||||
\(955\) | 14910.0 | 0.505211 | ||||||||
\(956\) | −11508.0 | −0.389326 | ||||||||
\(957\) | −4158.00 | −0.140448 | ||||||||
\(958\) | −9072.00 | −0.305953 | ||||||||
\(959\) | −36720.0 | −1.23644 | ||||||||
\(960\) | 2240.00 | 0.0753080 | ||||||||
\(961\) | 34218.0 | 1.14860 | ||||||||
\(962\) | 11092.0 | 0.371747 | ||||||||
\(963\) | −18348.0 | −0.613973 | ||||||||
\(964\) | 6488.00 | 0.216768 | ||||||||
\(965\) | 6925.00 | 0.231009 | ||||||||
\(966\) | −6440.00 | −0.214496 | ||||||||
\(967\) | 56381.0 | 1.87496 | 0.937482 | − | 0.348033i | \(-0.113150\pi\) | ||||
0.937482 | + | 0.348033i | \(0.113150\pi\) | |||||||
\(968\) | 10360.0 | 0.343991 | ||||||||
\(969\) | −134904. | −4.47238 | ||||||||
\(970\) | −9920.00 | −0.328363 | ||||||||
\(971\) | 43782.0 | 1.44699 | 0.723497 | − | 0.690327i | \(-0.242534\pi\) | ||||
0.723497 | + | 0.690327i | \(0.242534\pi\) | |||||||
\(972\) | −19712.0 | −0.650476 | ||||||||
\(973\) | −20540.0 | −0.676755 | ||||||||
\(974\) | 22910.0 | 0.753679 | ||||||||
\(975\) | 8225.00 | 0.270165 | ||||||||
\(976\) | −5920.00 | −0.194154 | ||||||||
\(977\) | 3714.00 | 0.121619 | 0.0608093 | − | 0.998149i | \(-0.480632\pi\) | ||||
0.0608093 | + | 0.998149i | \(0.480632\pi\) | |||||||
\(978\) | −17038.0 | −0.557071 | ||||||||
\(979\) | −4968.00 | −0.162184 | ||||||||
\(980\) | 1140.00 | 0.0371591 | ||||||||
\(981\) | −26224.0 | −0.853484 | ||||||||
\(982\) | 20790.0 | 0.675596 | ||||||||
\(983\) | −4662.00 | −0.151266 | −0.0756331 | − | 0.997136i | \(-0.524098\pi\) | ||||
−0.0756331 | + | 0.997136i | \(0.524098\pi\) | |||||||
\(984\) | −27720.0 | −0.898050 | ||||||||
\(985\) | 4785.00 | 0.154785 | ||||||||
\(986\) | −26136.0 | −0.844158 | ||||||||
\(987\) | 89460.0 | 2.88505 | ||||||||
\(988\) | 27448.0 | 0.883843 | ||||||||
\(989\) | 6256.00 | 0.201142 | ||||||||
\(990\) | −1320.00 | −0.0423761 | ||||||||
\(991\) | 51440.0 | 1.64889 | 0.824443 | − | 0.565945i | \(-0.191489\pi\) | ||||
0.824443 | + | 0.565945i | \(0.191489\pi\) | |||||||
\(992\) | 8096.00 | 0.259121 | ||||||||
\(993\) | 10535.0 | 0.336675 | ||||||||
\(994\) | 14280.0 | 0.455668 | ||||||||
\(995\) | −1790.00 | −0.0570320 | ||||||||
\(996\) | −34944.0 | −1.11169 | ||||||||
\(997\) | 686.000 | 0.0217912 | 0.0108956 | − | 0.999941i | \(-0.496532\pi\) | ||||
0.0108956 | + | 0.999941i | \(0.496532\pi\) | |||||||
\(998\) | 10994.0 | 0.348706 | ||||||||
\(999\) | 4130.00 | 0.130798 |
(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.c.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 2070.4.a.j.1.1 | 1 | |||
4.3 | odd | 2 | 1840.4.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 1150.4.b.b.599.1 | 2 | |||
5.3 | odd | 4 | 1150.4.b.b.599.2 | 2 | |||
5.4 | even | 2 | 1150.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.c.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
1150.4.a.e.1.1 | 1 | 5.4 | even | 2 | |||
1150.4.b.b.599.1 | 2 | 5.2 | odd | 4 | |||
1150.4.b.b.599.2 | 2 | 5.3 | odd | 4 | |||
1840.4.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
2070.4.a.j.1.1 | 1 | 3.2 | odd | 2 |