Newspace parameters
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(92.0429796090\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
Defining polynomial: |
\( x^{4} - x^{3} - 41x^{2} - 30x - 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.174957\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1 |
$q$-expansion
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −35.1436 | −1.89758 | −0.948789 | − | 0.315912i | \(-0.897690\pi\) | ||||
−0.948789 | + | 0.315912i | \(0.897690\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.7440 | 0.376724 | 0.188362 | − | 0.982100i | \(-0.439682\pi\) | ||||
0.188362 | + | 0.982100i | \(0.439682\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 87.1577 | 1.24346 | 0.621731 | − | 0.783231i | \(-0.286430\pi\) | ||||
0.621731 | + | 0.783231i | \(0.286430\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.6869 | 0.141114 | 0.0705568 | − | 0.997508i | \(-0.477522\pi\) | ||||
0.0705568 | + | 0.997508i | \(0.477522\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −105.431 | −1.09557 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −108.262 | −0.981485 | −0.490742 | − | 0.871305i | \(-0.663274\pi\) | ||||
−0.490742 | + | 0.871305i | \(0.663274\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −150.600 | −0.964337 | −0.482169 | − | 0.876078i | \(-0.660151\pi\) | ||||
−0.482169 | + | 0.876078i | \(0.660151\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −128.191 | −0.742701 | −0.371350 | − | 0.928493i | \(-0.621105\pi\) | ||||
−0.371350 | + | 0.928493i | \(0.621105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 41.2319 | 0.217502 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −175.718 | −0.848622 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.7756 | −0.0523216 | −0.0261608 | − | 0.999658i | \(-0.508328\pi\) | ||||
−0.0261608 | + | 0.999658i | \(0.508328\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 366.620 | 1.39650 | 0.698249 | − | 0.715855i | \(-0.253963\pi\) | ||||
0.698249 | + | 0.715855i | \(0.253963\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 301.237 | 1.06833 | 0.534165 | − | 0.845380i | \(-0.320626\pi\) | ||||
0.534165 | + | 0.845380i | \(0.320626\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −156.862 | −0.486822 | −0.243411 | − | 0.969923i | \(-0.578266\pi\) | ||||
−0.243411 | + | 0.969923i | \(0.578266\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 892.074 | 2.60080 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 261.473 | 0.717913 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −229.058 | −0.593651 | −0.296826 | − | 0.954932i | \(-0.595928\pi\) | ||||
−0.296826 | + | 0.954932i | \(0.595928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 68.7198 | 0.168476 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 35.0607 | 0.0814720 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −377.723 | −0.833482 | −0.416741 | − | 0.909025i | \(-0.636828\pi\) | ||||
−0.416741 | + | 0.909025i | \(0.636828\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −406.355 | −0.852925 | −0.426462 | − | 0.904505i | \(-0.640240\pi\) | ||||
−0.426462 | + | 0.904505i | \(0.640240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −316.293 | −0.632526 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 65.0000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −352.506 | −0.642768 | −0.321384 | − | 0.946949i | \(-0.604148\pi\) | ||||
−0.321384 | + | 0.946949i | \(0.604148\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −324.786 | −0.566661 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −842.944 | −1.40900 | −0.704500 | − | 0.709704i | \(-0.748829\pi\) | ||||
−0.704500 | + | 0.709704i | \(0.748829\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 50.4272 | 0.0808502 | 0.0404251 | − | 0.999183i | \(-0.487129\pi\) | ||||
0.0404251 | + | 0.999183i | \(0.487129\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −483.013 | −0.714862 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −695.344 | −0.990283 | −0.495141 | − | 0.868812i | \(-0.664884\pi\) | ||||
−0.495141 | + | 0.868812i | \(0.664884\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −675.845 | −0.893779 | −0.446889 | − | 0.894589i | \(-0.647468\pi\) | ||||
−0.446889 | + | 0.894589i | \(0.647468\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 435.789 | 0.556093 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −451.801 | −0.556760 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −943.389 | −1.12358 | −0.561792 | − | 0.827278i | \(-0.689888\pi\) | ||||
−0.561792 | + | 0.827278i | \(0.689888\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −456.867 | −0.526293 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −384.572 | −0.428798 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 58.4345 | 0.0631080 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 73.8249 | 0.0772761 | 0.0386381 | − | 0.999253i | \(-0.487698\pi\) | ||||
0.0386381 | + | 0.999253i | \(0.487698\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 123.696 | 0.125575 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.889523 | −0.000876345 0 | −0.000438172 | − | 1.00000i | \(-0.500139\pi\) | ||||
−0.000438172 | 1.00000i | \(0.500139\pi\) | ||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −458.408 | −0.438527 | −0.219263 | − | 0.975666i | \(-0.570365\pi\) | ||||
−0.219263 | + | 0.975666i | \(0.570365\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −527.154 | −0.489952 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 967.396 | 0.874035 | 0.437017 | − | 0.899453i | \(-0.356035\pi\) | ||||
0.437017 | + | 0.899453i | \(0.356035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 626.068 | 0.550151 | 0.275075 | − | 0.961423i | \(-0.411297\pi\) | ||||
0.275075 | + | 0.961423i | \(0.411297\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −35.3268 | −0.0302079 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2241.20 | −1.86579 | −0.932896 | − | 0.360146i | \(-0.882727\pi\) | ||||
−0.932896 | + | 0.360146i | \(0.882727\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −541.309 | −0.438933 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3063.04 | −2.35957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1142.10 | −0.858079 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1099.86 | 0.806268 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 895.939 | 0.625998 | 0.312999 | − | 0.949754i | \(-0.398666\pi\) | ||||
0.312999 | + | 0.949754i | \(0.398666\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 903.711 | 0.616801 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −636.783 | −0.424702 | −0.212351 | − | 0.977193i | \(-0.568112\pi\) | ||||
−0.212351 | + | 0.977193i | \(0.568112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −410.720 | −0.267774 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 505.892 | 0.315483 | 0.157742 | − | 0.987480i | \(-0.449579\pi\) | ||||
0.157742 | + | 0.987480i | \(0.449579\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1521.56 | −0.928470 | −0.464235 | − | 0.885712i | \(-0.653671\pi\) | ||||
−0.464235 | + | 0.885712i | \(0.653671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −470.585 | −0.281067 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 178.672 | 0.104484 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −753.002 | −0.431265 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2676.22 | 1.50157 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3105.92 | −1.70770 | −0.853849 | − | 0.520521i | \(-0.825738\pi\) | ||||
−0.853849 | + | 0.520521i | \(0.825738\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1634.44 | −0.880856 | −0.440428 | − | 0.897788i | \(-0.645173\pi\) | ||||
−0.440428 | + | 0.897788i | \(0.645173\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 784.420 | 0.414487 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −640.953 | −0.332146 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3132.82 | 1.59253 | 0.796263 | − | 0.604951i | \(-0.206807\pi\) | ||||
0.796263 | + | 0.604951i | \(0.206807\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −687.174 | −0.342745 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3804.71 | 1.86244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1419.27 | 0.681997 | 0.340999 | − | 0.940064i | \(-0.389235\pi\) | ||||
0.340999 | + | 0.940064i | \(0.389235\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 206.159 | 0.0972697 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3871.88 | 1.79410 | 0.897051 | − | 0.441927i | \(-0.145705\pi\) | ||||
0.897051 | + | 0.441927i | \(0.145705\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 105.182 | 0.0470379 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1619.92 | −0.711909 | −0.355955 | − | 0.934503i | \(-0.615844\pi\) | ||||
−0.355955 | + | 0.934503i | \(0.615844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −878.591 | −0.379515 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1133.17 | −0.481211 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2139.73 | −0.893470 | −0.446735 | − | 0.894666i | \(-0.647413\pi\) | ||||
−0.446735 | + | 0.894666i | \(0.647413\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −464.563 | −0.190777 | −0.0953887 | − | 0.995440i | \(-0.530409\pi\) | ||||
−0.0953887 | + | 0.995440i | \(0.530409\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1219.06 | −0.492436 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −58.8780 | −0.0233989 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1197.89 | 0.468442 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −948.878 | −0.365189 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2698.18 | 1.02216 | 0.511082 | − | 0.859532i | \(-0.329245\pi\) | ||||
0.511082 | + | 0.859532i | \(0.329245\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3896.41 | −1.45321 | −0.726606 | − | 0.687054i | \(-0.758903\pi\) | ||||
−0.726606 | + | 0.687054i | \(0.758903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 195.000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1213.46 | −0.438862 | −0.219431 | − | 0.975628i | \(-0.570420\pi\) | ||||
−0.219431 | + | 0.975628i | \(0.570420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4368.96 | −1.55632 | −0.778160 | − | 0.628066i | \(-0.783847\pi\) | ||||
−0.778160 | + | 0.628066i | \(0.783847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1057.52 | −0.371102 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5292.64 | 1.82990 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1833.10 | 0.624533 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −974.357 | −0.327162 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 160.624 | 0.0531609 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3107.39 | 1.01385 | 0.506923 | − | 0.861991i | \(-0.330783\pi\) | ||||
0.506923 | + | 0.861991i | \(0.330783\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2528.83 | −0.813486 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1506.19 | 0.477772 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4505.08 | 1.40933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 151.282 | 0.0466789 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1133.05 | 0.344874 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5594.97 | −1.68012 | −0.840060 | − | 0.542493i | \(-0.817480\pi\) | ||||
−0.840060 | + | 0.542493i | \(0.817480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2353.86 | −0.688244 | −0.344122 | − | 0.938925i | \(-0.611823\pi\) | ||||
−0.344122 | + | 0.938925i | \(0.611823\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1065.47 | −0.307459 | −0.153729 | − | 0.988113i | \(-0.549128\pi\) | ||||
−0.153729 | + | 0.988113i | \(0.549128\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1449.04 | −0.412726 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5318.61 | −1.49542 | −0.747712 | − | 0.664023i | \(-0.768848\pi\) | ||||
−0.747712 | + | 0.664023i | \(0.768848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −784.309 | −0.217713 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2086.03 | −0.571740 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 623.495 | 0.168747 | 0.0843735 | − | 0.996434i | \(-0.473111\pi\) | ||||
0.0843735 | + | 0.996434i | \(0.473111\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −955.412 | −0.255367 | −0.127684 | − | 0.991815i | \(-0.540754\pi\) | ||||
−0.127684 | + | 0.991815i | \(0.540754\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4460.37 | 1.16311 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 151.930 | 0.0391379 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2027.54 | −0.516023 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3310.75 | 0.832560 | 0.416280 | − | 0.909236i | \(-0.363334\pi\) | ||||
0.416280 | + | 0.909236i | \(0.363334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1487.95 | −0.369749 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1307.37 | 0.321061 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 125.710 | 0.0305119 | 0.0152560 | − | 0.999884i | \(-0.495144\pi\) | ||||
0.0152560 | + | 0.999884i | \(0.495144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 413.838 | 0.0992842 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1355.40 | −0.321446 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2980.02 | 0.698691 | 0.349346 | − | 0.936994i | \(-0.386404\pi\) | ||||
0.349346 | + | 0.936994i | \(0.386404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1145.29 | −0.265489 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2830.17 | −0.648702 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1769.95 | 0.401174 | 0.200587 | − | 0.979676i | \(-0.435715\pi\) | ||||
0.200587 | + | 0.979676i | \(0.435715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2492.03 | −0.558597 | −0.279299 | − | 0.960204i | \(-0.590102\pi\) | ||||
−0.279299 | + | 0.960204i | \(0.590102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1370.60 | −0.303856 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 343.599 | 0.0753448 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8647.77 | 1.87579 | 0.937896 | − | 0.346918i | \(-0.112772\pi\) | ||||
0.937896 | + | 0.346918i | \(0.112772\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1153.72 | −0.247567 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4778.49 | −1.01445 | −0.507226 | − | 0.861813i | \(-0.669329\pi\) | ||||
−0.507226 | + | 0.861813i | \(0.669329\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5654.65 | 1.18775 | 0.593877 | − | 0.804556i | \(-0.297597\pi\) | ||||
0.593877 | + | 0.804556i | \(0.297597\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 175.304 | 0.0364354 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12884.3 | −2.64996 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2683.47 | 0.546198 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 221.475 | 0.0446154 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1062.17 | 0.211783 | 0.105892 | − | 0.994378i | \(-0.466230\pi\) | ||||
0.105892 | + | 0.994378i | \(0.466230\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1888.62 | −0.372744 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 371.087 | 0.0725005 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1407.40 | −0.272215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10586.6 | −2.02724 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.66857 | −0.000505958 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2031.77 | −0.381440 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8643.05 | −1.60679 | −0.803396 | − | 0.595445i | \(-0.796976\pi\) | ||||
−0.803396 | + | 0.595445i | \(0.796976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1375.22 | −0.253184 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3893.30 | 0.709868 | 0.354934 | − | 0.934891i | \(-0.384503\pi\) | ||||
0.354934 | + | 0.934891i | \(0.384503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3637.44 | −0.656871 | −0.328435 | − | 0.944526i | \(-0.606521\pi\) | ||||
−0.328435 | + | 0.944526i | \(0.606521\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1581.46 | −0.282874 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6003.11 | 1.06362 | 0.531811 | − | 0.846863i | \(-0.321512\pi\) | ||||
0.531811 | + | 0.846863i | \(0.321512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2069.85 | −0.363289 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2902.19 | 0.504624 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1018.60 | 0.175470 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 325.000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1878.20 | 0.317630 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5512.69 | 0.923782 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6466.23 | −1.07377 | −0.536883 | − | 0.843657i | \(-0.680398\pi\) | ||||
−0.536883 | + | 0.843657i | \(0.680398\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −105.980 | −0.0174405 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1762.53 | −0.287455 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2923.30 | −0.472529 | −0.236265 | − | 0.971689i | \(-0.575923\pi\) | ||||
−0.236265 | + | 0.971689i | \(0.575923\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6723.60 | −1.07722 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1761.85 | −0.279793 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19296.5 | −3.03764 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1623.93 | −0.253418 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6051.65 | 0.936223 | 0.468112 | − | 0.883669i | \(-0.344934\pi\) | ||||
0.468112 | + | 0.883669i | \(0.344934\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4539.56 | −0.696267 | −0.348134 | − | 0.937445i | \(-0.613184\pi\) | ||||
−0.348134 | + | 0.937445i | \(0.613184\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5484.84 | 0.826993 | 0.413497 | − | 0.910506i | \(-0.364307\pi\) | ||||
0.413497 | + | 0.910506i | \(0.364307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4214.72 | −0.630124 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9189.12 | −1.36230 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8106.78 | −1.19181 | −0.595905 | − | 0.803055i | \(-0.703206\pi\) | ||||
−0.595905 | + | 0.803055i | \(0.703206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6722.42 | −0.980087 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3426.31 | −0.495412 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 252.136 | 0.0361573 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6563.94 | −0.933610 | −0.466805 | − | 0.884360i | \(-0.654595\pi\) | ||||
−0.466805 | + | 0.884360i | \(0.654595\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3299.58 | 0.465499 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8049.92 | 1.12650 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14069.6 | 1.95307 | 0.976535 | − | 0.215358i | \(-0.0690917\pi\) | ||||
0.976535 | + | 0.215358i | \(0.0690917\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1957.80 | −0.267459 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5008.62 | −0.678828 | −0.339414 | − | 0.940637i | \(-0.610229\pi\) | ||||
−0.339414 | + | 0.940637i | \(0.610229\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2687.82 | 0.361420 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6718.96 | −0.896405 | −0.448202 | − | 0.893932i | \(-0.647936\pi\) | ||||
−0.448202 | + | 0.893932i | \(0.647936\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2415.06 | −0.319696 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2711.13 | 0.356110 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12362.2 | 1.61128 | 0.805640 | − | 0.592406i | \(-0.201822\pi\) | ||||
0.805640 | + | 0.592406i | \(0.201822\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9435.86 | −1.22044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1910.35 | −0.245202 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3476.72 | −0.442868 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2905.75 | 0.367344 | 0.183672 | − | 0.982988i | \(-0.441202\pi\) | ||||
0.183672 | + | 0.982988i | \(0.441202\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1232.16 | −0.154599 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10275.9 | 1.27969 | 0.639844 | − | 0.768505i | \(-0.278999\pi\) | ||||
0.639844 | + | 0.768505i | \(0.278999\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1666.48 | −0.205988 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −161.844 | −0.0197108 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2615.14 | 0.316162 | 0.158081 | − | 0.987426i | \(-0.449469\pi\) | ||||
0.158081 | + | 0.987426i | \(0.449469\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1517.67 | 0.182144 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13274.6 | 1.58160 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3379.23 | −0.399710 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4564.69 | −0.536052 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 784.644 | 0.0914854 | 0.0457427 | − | 0.998953i | \(-0.485435\pi\) | ||||
0.0457427 | + | 0.998953i | \(0.485435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6500.38 | 0.752515 | 0.376258 | − | 0.926515i | \(-0.377211\pi\) | ||||
0.376258 | + | 0.926515i | \(0.377211\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1411.76 | −0.162274 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2178.94 | 0.248692 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14280.8 | 1.61849 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 536.015 | 0.0603241 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12519.0 | 1.39912 | 0.699558 | − | 0.714575i | \(-0.253380\pi\) | ||||
0.699558 | + | 0.714575i | \(0.253380\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13600.5 | 1.50947 | 0.754734 | − | 0.656030i | \(-0.227766\pi\) | ||||
0.754734 | + | 0.656030i | \(0.227766\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2259.01 | −0.248991 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1265.25 | −0.138501 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4044.70 | 0.439733 | 0.219867 | − | 0.975530i | \(-0.429438\pi\) | ||||
0.219867 | + | 0.975530i | \(0.429438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8028.67 | 0.866933 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12860.3 | −1.37926 | −0.689629 | − | 0.724162i | \(-0.742227\pi\) | ||||
−0.689629 | + | 0.724162i | \(0.742227\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4716.95 | −0.502482 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9317.76 | −0.985940 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16819.8 | 1.76788 | 0.883939 | − | 0.467602i | \(-0.154882\pi\) | ||||
0.883939 | + | 0.467602i | \(0.154882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5038.81 | 0.526094 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4903.33 | −0.508562 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2284.34 | −0.235365 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11489.0 | −1.17600 | −0.588000 | − | 0.808861i | \(-0.700084\pi\) | ||||
−0.588000 | + | 0.808861i | \(0.700084\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2353.26 | 0.239304 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9109.43 | 0.920322 | 0.460161 | − | 0.887836i | \(-0.347792\pi\) | ||||
0.460161 | + | 0.887836i | \(0.347792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12617.5 | 1.26649 | 0.633244 | − | 0.773952i | \(-0.281723\pi\) | ||||
0.633244 | + | 0.773952i | \(0.281723\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1922.86 | −0.191764 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13067.9 | −1.29488 | −0.647440 | − | 0.762116i | \(-0.724160\pi\) | ||||
−0.647440 | + | 0.762116i | \(0.724160\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12388.3 | 1.21970 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9398.47 | 0.919445 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4140.19 | 0.402466 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 292.173 | 0.0282227 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2061.52 | −0.197884 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10980.0 | −1.04737 | −0.523684 | − | 0.851913i | \(-0.675443\pi\) | ||||
−0.523684 | + | 0.851913i | \(0.675443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −153.083 | −0.0145114 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11414.1 | 1.07528 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 369.125 | 0.0345589 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12455.9 | −1.15899 | −0.579497 | − | 0.814975i | \(-0.696751\pi\) | ||||
−0.579497 | + | 0.814975i | \(0.696751\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4257.80 | 0.393751 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2632.88 | 0.241996 | 0.120998 | − | 0.992653i | \(-0.461391\pi\) | ||||
0.120998 | + | 0.992653i | \(0.461391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13126.0 | −1.19912 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 618.478 | 0.0561587 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29624.1 | 2.67369 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4716.61 | 0.423136 | 0.211568 | − | 0.977363i | \(-0.432143\pi\) | ||||
0.211568 | + | 0.977363i | \(0.432143\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11615.6 | 1.03583 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3448.42 | 0.305681 | 0.152841 | − | 0.988251i | \(-0.451158\pi\) | ||||
0.152841 | + | 0.988251i | \(0.451158\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.44761 | −0.000391913 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16933.1 | −1.47455 | −0.737274 | − | 0.675593i | \(-0.763888\pi\) | ||||
−0.737274 | + | 0.675593i | \(0.763888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1772.20 | −0.153419 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 315.546 | 0.0271573 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2292.04 | −0.196115 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2155.90 | −0.183397 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4859.76 | −0.411021 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5108.30 | −0.429556 | −0.214778 | − | 0.976663i | \(-0.568903\pi\) | ||||
−0.214778 | + | 0.976663i | \(0.568903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6314.75 | −0.527963 | −0.263981 | − | 0.964528i | \(-0.585036\pi\) | ||||
−0.263981 | + | 0.964528i | \(0.585036\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2635.77 | −0.219113 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11172.8 | −0.923520 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −446.375 | −0.0366874 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3399.51 | −0.277827 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4766.06 | 0.387319 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4836.98 | 0.390880 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6419.20 | −0.515845 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12260.6 | 0.979783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6811.49 | 0.541310 | 0.270655 | − | 0.962676i | \(-0.412760\pi\) | ||||
0.270655 | + | 0.962676i | \(0.412760\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1393.69 | −0.110145 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3130.34 | 0.246035 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5424.93 | 0.424046 | 0.212023 | − | 0.977265i | \(-0.431995\pi\) | ||||
0.212023 | + | 0.977265i | \(0.431995\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3657.19 | −0.284308 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1760.05 | −0.136081 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24436.9 | 1.87914 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −176.634 | −0.0135094 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14188.1 | −1.07930 | −0.539649 | − | 0.841890i | \(-0.681443\pi\) | ||||
−0.539649 | + | 0.841890i | \(0.681443\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3916.08 | 0.296302 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3593.68 | 0.270455 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3216.80 | 0.240803 | 0.120401 | − | 0.992725i | \(-0.461582\pi\) | ||||
0.120401 | + | 0.992725i | \(0.461582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11206.0 | −0.834407 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2846.63 | −0.210842 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5551.73 | −0.409034 | −0.204517 | − | 0.978863i | \(-0.565562\pi\) | ||||
−0.204517 | + | 0.978863i | \(0.565562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 381.117 | 0.0279322 | 0.0139661 | − | 0.999902i | \(-0.495554\pi\) | ||||
0.0139661 | + | 0.999902i | \(0.495554\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8094.54 | 0.590147 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2706.55 | −0.196297 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3178.27 | 0.229312 | 0.114656 | − | 0.993405i | \(-0.463423\pi\) | ||||
0.114656 | + | 0.993405i | \(0.463423\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11689.2 | −0.839012 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23751.6 | 1.69601 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3148.16 | −0.223643 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 585.000 | 0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 438.511 | 0.0308336 | 0.0154168 | − | 0.999881i | \(-0.495092\pi\) | ||||
0.0154168 | + | 0.999881i | \(0.495092\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1498.15 | −0.104805 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3640.39 | −0.253377 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7029.95 | −0.486822 | −0.243411 | − | 0.969923i | \(-0.578266\pi\) | ||||
−0.243411 | + | 0.969923i | \(0.578266\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15315.2 | −1.05523 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13106.9 | −0.898542 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14506.4 | −0.989507 | −0.494754 | − | 0.869033i | \(-0.664742\pi\) | ||||
−0.494754 | + | 0.869033i | \(0.664742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17430.6 | −1.18304 | −0.591520 | − | 0.806290i | \(-0.701472\pi\) | ||||
−0.591520 | + | 0.806290i | \(0.701472\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3172.56 | −0.214256 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5710.52 | −0.383745 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13330.5 | 0.891383 | 0.445691 | − | 0.895187i | \(-0.352958\pi\) | ||||
0.445691 | + | 0.895187i | \(0.352958\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15877.9 | 1.05650 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2039.20 | −0.135020 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14016.8 | −0.923542 | −0.461771 | − | 0.886999i | \(-0.652786\pi\) | ||||
−0.461771 | + | 0.886999i | \(0.652786\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5499.30 | 0.360574 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14539.6 | 0.948688 | 0.474344 | − | 0.880339i | \(-0.342685\pi\) | ||||
0.474344 | + | 0.880339i | \(0.342685\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21204.4 | −1.37686 | −0.688429 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688429 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2923.07 | −0.188887 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33154.1 | 2.13209 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 481.873 | 0.0306924 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1026.34 | −0.0650599 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27682.4 | 1.74646 | 0.873231 | − | 0.487307i | \(-0.162021\pi\) | ||||
0.873231 | + | 0.487307i | \(0.162021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9322.17 | 0.585345 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4479.69 | 0.279955 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11597.0 | 0.721332 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7586.49 | −0.469667 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25577.7 | −1.57606 | −0.788032 | − | 0.615634i | \(-0.788900\pi\) | ||||
−0.788032 | + | 0.615634i | \(0.788900\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13204.5 | 0.809852 | 0.404926 | − | 0.914349i | \(-0.367297\pi\) | ||||
0.404926 | + | 0.914349i | \(0.367297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4518.56 | 0.275842 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 969.924 | 0.0589361 | 0.0294680 | − | 0.999566i | \(-0.490619\pi\) | ||||
0.0294680 | + | 0.999566i | \(0.490619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5191.42 | −0.313992 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13515.3 | 0.813678 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9040.07 | −0.541754 | −0.270877 | − | 0.962614i | \(-0.587314\pi\) | ||||
−0.270877 | + | 0.962614i | \(0.587314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3183.92 | −0.189933 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 453.845 | 0.0269501 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27518.0 | 1.62663 | 0.813316 | − | 0.581822i | \(-0.197660\pi\) | ||||
0.813316 | + | 0.581822i | \(0.197660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22610.3 | 1.33047 | 0.665235 | − | 0.746634i | \(-0.268331\pi\) | ||||
0.665235 | + | 0.746634i | \(0.268331\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3399.15 | 0.199113 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2053.60 | −0.119752 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16304.3 | 0.946483 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16784.9 | −0.970018 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5584.93 | −0.321317 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −731.086 | −0.0418741 | −0.0209371 | − | 0.999781i | \(-0.506665\pi\) | ||||
−0.0209371 | + | 0.999781i | \(0.506665\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9436.61 | 0.535714 | 0.267857 | − | 0.963459i | \(-0.413685\pi\) | ||||
0.267857 | + | 0.963459i | \(0.413685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2594.48 | −0.146637 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7061.59 | −0.397358 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17455.9 | 0.977936 | 0.488968 | − | 0.872302i | \(-0.337373\pi\) | ||||
0.488968 | + | 0.872302i | \(0.337373\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2529.46 | 0.141088 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3196.40 | −0.177512 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2977.75 | −0.164649 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28075.1 | −1.54563 | −0.772814 | − | 0.634633i | \(-0.781151\pi\) | ||||
−0.772814 | + | 0.634633i | \(0.781151\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4347.11 | −0.238287 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7607.81 | −0.415224 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31953.8 | 1.73649 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15955.8 | −0.863384 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20427.0 | −1.10059 | −0.550297 | − | 0.834969i | \(-0.685486\pi\) | ||||
−0.550297 | + | 0.834969i | \(0.685486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −137.620 | −0.00738329 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2352.93 | −0.125697 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.2610 | 0.00166293 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10208.4 | 0.540737 | 0.270369 | − | 0.962757i | \(-0.412854\pi\) | ||||
0.270369 | + | 0.962757i | \(0.412854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6258.10 | −0.330094 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13878.2 | 0.728950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 893.358 | 0.0467268 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1870.49 | 0.0974261 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32325.4 | 1.67668 | 0.838341 | − | 0.545146i | \(-0.183526\pi\) | ||||
0.838341 | + | 0.545146i | \(0.183526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16110.1 | 0.832139 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2866.24 | −0.147436 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3765.01 | −0.192867 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −278.152 | −0.0141900 | −0.00709498 | − | 0.999975i | \(-0.502258\pi\) | ||||
−0.00709498 | + | 0.999975i | \(0.502258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26255.1 | 1.32843 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23210.0 | 1.16955 | 0.584775 | − | 0.811195i | \(-0.301183\pi\) | ||||
0.584775 | + | 0.811195i | \(0.301183\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13381.1 | 0.671524 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4844.83 | −0.242146 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28322.4 | −1.40982 | −0.704910 | − | 0.709296i | \(-0.749013\pi\) | ||||
−0.704910 | + | 0.709296i | \(0.749013\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 455.789 | 0.0225963 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13502.7 | −0.666710 | −0.333355 | − | 0.942801i | \(-0.608181\pi\) | ||||
−0.333355 | + | 0.942801i | \(0.608181\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15529.6 | −0.763706 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6082.61 | −0.297926 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33997.8 | −1.65855 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3344.10 | 0.162487 | 0.0812436 | − | 0.996694i | \(-0.474111\pi\) | ||||
0.0812436 | + | 0.996694i | \(0.474111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9932.25 | 0.480679 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8172.22 | −0.393931 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16645.4 | 0.799190 | 0.399595 | − | 0.916692i | \(-0.369151\pi\) | ||||
0.399595 | + | 0.916692i | \(0.369151\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4463.84 | −0.213475 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21705.9 | 1.03395 | 0.516977 | − | 0.855999i | \(-0.327057\pi\) | ||||
0.516977 | + | 0.855999i | \(0.327057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22002.3 | −1.04395 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3922.10 | 0.185364 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4910.41 | −0.231166 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27050.4 | −1.26848 | −0.634240 | − | 0.773136i | \(-0.718687\pi\) | ||||
−0.634240 | + | 0.773136i | \(0.718687\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 377.129 | 0.0176161 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22869.0 | 1.06409 | 0.532045 | − | 0.846716i | \(-0.321424\pi\) | ||||
0.532045 | + | 0.846716i | \(0.321424\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3204.77 | −0.148540 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1241.51 | 0.0573218 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4284.65 | 0.197065 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11585.4 | −0.530804 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4066.21 | −0.185587 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15664.1 | 0.712199 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35597.3 | −1.61234 | −0.806168 | − | 0.591687i | \(-0.798462\pi\) | ||||
−0.806168 | + | 0.591687i | \(0.798462\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8940.05 | 0.403390 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 78763.9 | 3.54048 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5282.61 | −0.236559 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3435.87 | −0.153280 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34475.5 | 1.53223 | 0.766114 | − | 0.642705i | \(-0.222188\pi\) | ||||
0.766114 | + | 0.642705i | \(0.222188\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13671.7 | −0.605345 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8490.50 | −0.374528 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 693.070 | 0.0304582 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19023.6 | 0.832910 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5309.85 | 0.231618 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15321.5 | 0.665855 | 0.332928 | − | 0.942952i | \(-0.391964\pi\) | ||||
0.332928 | + | 0.942952i | \(0.391964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38189.4 | −1.65353 | −0.826764 | − | 0.562548i | \(-0.809821\pi\) | ||||
−0.826764 | + | 0.562548i | \(0.809821\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7476.08 | −0.322506 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7096.33 | 0.304998 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3520.53 | 0.150756 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4111.80 | −0.175431 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2531.59 | −0.107616 | −0.0538082 | − | 0.998551i | \(-0.517136\pi\) | ||||
−0.0538082 | + | 0.998551i | \(0.517136\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41111.4 | 1.74126 | 0.870628 | − | 0.491942i | \(-0.163713\pi\) | ||||
0.870628 | + | 0.491942i | \(0.163713\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1030.80 | 0.0435003 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12919.5 | 0.543233 | 0.271617 | − | 0.962406i | \(-0.412442\pi\) | ||||
0.271617 | + | 0.962406i | \(0.412442\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17503.1 | 0.733303 | 0.366651 | − | 0.930358i | \(-0.380504\pi\) | ||||
0.366651 | + | 0.930358i | \(0.380504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25943.3 | 1.08299 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 77751.2 | 3.23400 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19359.4 | 0.802347 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3461.15 | −0.142933 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7315.80 | −0.301036 | −0.150518 | − | 0.988607i | \(-0.548094\pi\) | ||||
−0.150518 | + | 0.988607i | \(0.548094\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1708.53 | −0.0700535 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14335.5 | −0.585694 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 845.000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40137.7 | 1.62827 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16964.0 | 0.685750 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1274.85 | 0.0513528 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45161.1 | 1.81276 | 0.906382 | − | 0.422458i | \(-0.138833\pi\) | ||||
0.906382 | + | 0.422458i | \(0.138833\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 525.911 | 0.0210360 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11777.2 | −0.469431 | −0.234716 | − | 0.972064i | \(-0.575416\pi\) | ||||
−0.234716 | + | 0.972064i | \(0.575416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25218.0 | 1.00166 | 0.500830 | − | 0.865545i | \(-0.333028\pi\) | ||||
0.500830 | + | 0.865545i | \(0.333028\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38653.0 | −1.52996 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26065.2 | 1.02812 | 0.514062 | − | 0.857753i | \(-0.328140\pi\) | ||||
0.514062 | + | 0.857753i | \(0.328140\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8099.61 | −0.318376 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8050.42 | 0.315348 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9556.79 | −0.373063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4582.58 | −0.178272 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 664.424 | 0.0257587 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4392.95 | −0.169724 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20173.2 | −0.776740 | −0.388370 | − | 0.921504i | \(-0.626962\pi\) | ||||
−0.388370 | + | 0.921504i | \(0.626962\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3186.50 | 0.122273 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42933.8 | 1.64186 | 0.820929 | − | 0.571030i | \(-0.193456\pi\) | ||||
0.820929 | + | 0.571030i | \(0.193456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22251.5 | 0.848043 | 0.424022 | − | 0.905652i | \(-0.360618\pi\) | ||||
0.424022 | + | 0.905652i | \(0.360618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5665.85 | −0.215204 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36828.7 | 1.39412 | 0.697061 | − | 0.717012i | \(-0.254491\pi\) | ||||
0.697061 | + | 0.717012i | \(0.254491\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31486.5 | −1.18788 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1113.26 | 0.0418582 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1833.23 | −0.0686973 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10698.7 | −0.399572 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4222.21 | −0.157163 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19305.6 | 0.716214 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19964.2 | −0.738183 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31759.7 | −1.17043 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2322.82 | −0.0853183 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42790.0 | 1.56650 | 0.783252 | − | 0.621704i | \(-0.213559\pi\) | ||||
0.783252 | + | 0.621704i | \(0.213559\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.00570 | −0.000292115 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3041.01 | 0.110596 | 0.0552981 | − | 0.998470i | \(-0.482389\pi\) | ||||
0.0552981 | + | 0.998470i | \(0.482389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9288.79 | −0.336708 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6095.32 | −0.220224 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22378.9 | 0.805905 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24088.9 | −0.864656 | −0.432328 | − | 0.901716i | \(-0.642308\pi\) | ||||
−0.432328 | + | 0.901716i | \(0.642308\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25929.2 | −0.927682 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10958.3 | −0.390786 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −294.390 | −0.0104643 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4125.67 | −0.146176 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2324.68 | 0.0820992 | 0.0410496 | − | 0.999157i | \(-0.486930\pi\) | ||||
0.0410496 | + | 0.999157i | \(0.486930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10425.6 | 0.367008 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11679.9 | 0.409842 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5989.47 | 0.209494 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12489.1 | 0.435433 | 0.217717 | − | 0.976012i | \(-0.430139\pi\) | ||||
0.217717 | + | 0.976012i | \(0.430139\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10912.3 | −0.379244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25862.3 | −0.895949 | −0.447974 | − | 0.894046i | \(-0.647854\pi\) | ||||
−0.447974 | + | 0.894046i | \(0.647854\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39690.9 | −1.37064 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4744.39 | −0.163317 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14137.1 | 0.485104 | 0.242552 | − | 0.970138i | \(-0.422016\pi\) | ||||
0.242552 | + | 0.970138i | \(0.422016\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 655.554 | 0.0224238 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18009.3 | 0.614083 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7474.99 | 0.254081 | 0.127040 | − | 0.991898i | \(-0.459452\pi\) | ||||
0.127040 | + | 0.991898i | \(0.459452\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13490.9 | 0.457126 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6209.54 | −0.209745 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17778.9 | −0.598654 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13358.2 | −0.448396 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8706.56 | 0.291345 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19482.1 | −0.649896 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12889.8 | 0.428653 | 0.214327 | − | 0.976762i | \(-0.431244\pi\) | ||||
0.214327 | + | 0.976762i | \(0.431244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3055.81 | 0.101307 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11727.4 | −0.387591 | −0.193795 | − | 0.981042i | \(-0.562080\pi\) | ||||
−0.193795 | + | 0.981042i | \(0.562080\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 53473.2 | 1.76184 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 975.000 | 0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22896.3 | 0.749763 | 0.374882 | − | 0.927073i | \(-0.377683\pi\) | ||||
0.374882 | + | 0.927073i | \(0.377683\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12965.9 | −0.423281 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5634.61 | 0.183384 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36022.9 | −1.16882 | −0.584412 | − | 0.811457i | \(-0.698675\pi\) | ||||
−0.584412 | + | 0.811457i | \(0.698675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6067.32 | −0.196265 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16538.1 | 0.533346 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32612.5 | −1.04855 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −868.766 | −0.0278479 | −0.0139240 | − | 0.999903i | \(-0.504432\pi\) | ||||
−0.0139240 | + | 0.999903i | \(0.504432\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19398.7 | −0.619939 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21844.8 | −0.696007 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42992.0 | −1.36567 | −0.682834 | − | 0.730574i | \(-0.739253\pi\) | ||||
−0.682834 | + | 0.730574i | \(0.739253\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −317.941 | −0.0100693 |
(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 | 1560.4.a.n.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.4.a.n.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |