Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), not minimal) |
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: | no |
Analytic conductor: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 17.6 | ||
Character | \(\chi\) | \(=\) | 128.17 |
Dual form | 128.4.g.a.113.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.477813 | − | 1.15354i | 0.0919551 | − | 0.221999i | −0.871210 | − | 0.490911i | \(-0.836664\pi\) |
0.963165 | + | 0.268912i | \(0.0866640\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.3468 | + | 6.77105i | −1.46210 | + | 0.605621i | −0.965042 | − | 0.262096i | \(-0.915586\pi\) |
−0.497057 | + | 0.867718i | \(0.665586\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.0222 | − | 18.0222i | 0.973108 | − | 0.973108i | −0.0265394 | − | 0.999648i | \(-0.508449\pi\) |
0.999648 | + | 0.0265394i | \(0.00844875\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 17.9895 | + | 17.9895i | 0.666279 | + | 0.666279i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.1053 | + | 48.5384i | 0.551088 | + | 1.33044i | 0.916663 | + | 0.399662i | \(0.130872\pi\) |
−0.365575 | + | 0.930782i | \(0.619128\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 37.8086 | + | 15.6609i | 0.806633 | + | 0.334118i | 0.747610 | − | 0.664138i | \(-0.231201\pi\) |
0.0590233 | + | 0.998257i | \(0.481201\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 22.0920i | 0.380275i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 53.0615i | 0.757018i | 0.925598 | + | 0.378509i | \(0.123563\pi\) | ||||
−0.925598 | + | 0.378509i | \(0.876437\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.4427 | + | 13.4382i | 0.391730 | + | 0.162260i | 0.569850 | − | 0.821749i | \(-0.307001\pi\) |
−0.178120 | + | 0.984009i | \(0.557001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.1781 | − | 29.4006i | −0.126547 | − | 0.305512i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −32.1343 | − | 32.1343i | −0.291324 | − | 0.291324i | 0.546279 | − | 0.837603i | \(-0.316044\pi\) |
−0.837603 | + | 0.546279i | \(0.816044\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 132.981 | − | 132.981i | 1.06385 | − | 1.06385i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 60.4929 | − | 25.0570i | 0.431180 | − | 0.178601i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −52.0634 | + | 125.692i | −0.333377 | + | 0.804842i | 0.664943 | + | 0.746894i | \(0.268456\pi\) |
−0.998320 | + | 0.0579483i | \(0.981544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 53.3354 | 0.309010 | 0.154505 | − | 0.987992i | \(-0.450622\pi\) | ||||
0.154505 | + | 0.987992i | \(0.450622\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 65.5976 | 0.346033 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −172.576 | + | 416.634i | −0.833446 | + | 2.01212i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −57.3789 | + | 23.7671i | −0.254947 | + | 0.105602i | −0.506497 | − | 0.862242i | \(-0.669060\pi\) |
0.251550 | + | 0.967844i | \(0.419060\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 36.1309 | − | 36.1309i | 0.148348 | − | 0.148348i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 240.383 | + | 240.383i | 0.915647 | + | 0.915647i | 0.996709 | − | 0.0810624i | \(-0.0258313\pi\) |
−0.0810624 | + | 0.996709i | \(0.525831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −56.3244 | − | 135.979i | −0.199753 | − | 0.482247i | 0.791983 | − | 0.610544i | \(-0.209049\pi\) |
−0.991736 | + | 0.128297i | \(0.959049\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −415.879 | − | 172.263i | −1.37768 | − | 0.570653i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 314.904i | − | 0.977309i | −0.872477 | − | 0.488655i | \(-0.837488\pi\) | ||
0.872477 | − | 0.488655i | \(-0.162512\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 306.601i | − | 0.893880i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 61.2086 | + | 25.3534i | 0.168057 | + | 0.0696116i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −177.524 | − | 428.580i | −0.460089 | − | 1.11075i | −0.968360 | − | 0.249557i | \(-0.919715\pi\) |
0.508271 | − | 0.861197i | \(-0.330285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −657.312 | − | 657.312i | −1.61149 | − | 1.61149i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 31.0031 | − | 31.0031i | 0.0720431 | − | 0.0720431i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 133.963 | − | 55.4894i | 0.295602 | − | 0.122442i | −0.229954 | − | 0.973202i | \(-0.573857\pi\) |
0.525556 | + | 0.850759i | \(0.323857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −191.454 | + | 462.211i | −0.401855 | + | 0.970164i | 0.585360 | + | 0.810773i | \(0.300953\pi\) |
−0.987216 | + | 0.159391i | \(0.949047\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 648.422 | 1.29672 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −724.089 | −1.38173 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 55.4766 | − | 133.932i | 0.101157 | − | 0.244216i | −0.865196 | − | 0.501434i | \(-0.832806\pi\) |
0.966353 | + | 0.257218i | \(0.0828060\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −52.4224 | + | 21.7141i | −0.0914625 | + | 0.0378850i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −191.132 | + | 191.132i | −0.319482 | + | 0.319482i | −0.848568 | − | 0.529086i | \(-0.822535\pi\) |
0.529086 | + | 0.848568i | \(0.322535\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −175.452 | − | 175.452i | −0.281302 | − | 0.281302i | 0.552326 | − | 0.833628i | \(-0.313740\pi\) |
−0.833628 | + | 0.552326i | \(0.813740\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −89.8593 | − | 216.940i | −0.138347 | − | 0.334000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1237.11 | + | 512.428i | 1.83093 | + | 0.758398i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1222.08i | 1.74043i | 0.492668 | + | 0.870217i | \(0.336022\pi\) | ||||
−0.492668 | + | 0.870217i | \(0.663978\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 605.154i | 0.830116i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −896.581 | − | 371.376i | −1.18569 | − | 0.491131i | −0.299344 | − | 0.954145i | \(-0.596768\pi\) |
−0.886351 | + | 0.463015i | \(0.846768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −359.282 | − | 867.384i | −0.458466 | − | 1.10684i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 120.115 | + | 120.115i | 0.148019 | + | 0.148019i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 883.293 | − | 883.293i | 1.05201 | − | 1.05201i | 0.0534390 | − | 0.998571i | \(-0.482982\pi\) |
0.998571 | − | 0.0534390i | \(-0.0170183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 963.639 | − | 399.152i | 1.11007 | − | 0.459808i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 25.4843 | − | 61.5246i | 0.0284151 | − | 0.0686001i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −621.324 | −0.671016 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −682.976 | −0.714904 | −0.357452 | − | 0.933932i | \(-0.616354\pi\) | ||||
−0.357452 | + | 0.933932i | \(0.616354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −511.499 | + | 1234.87i | −0.519268 | + | 1.25362i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 919.967 | − | 381.063i | 0.906338 | − | 0.375417i | 0.119684 | − | 0.992812i | \(-0.461812\pi\) |
0.786654 | + | 0.617395i | \(0.211812\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 188.265 | − | 188.265i | 0.180100 | − | 0.180100i | −0.611299 | − | 0.791400i | \(-0.709353\pi\) |
0.791400 | + | 0.611299i | \(0.209353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 398.146 | + | 398.146i | 0.370049 | + | 0.370049i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 48.3932 | + | 116.832i | 0.0437229 | + | 0.105556i | 0.944232 | − | 0.329280i | \(-0.106806\pi\) |
−0.900509 | + | 0.434837i | \(0.856806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 394.289 | + | 163.320i | 0.346477 | + | 0.143516i | 0.549134 | − | 0.835734i | \(-0.314958\pi\) |
−0.202657 | + | 0.979250i | \(0.564958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 77.5452i | 0.0663087i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 914.060i | 0.760952i | 0.924791 | + | 0.380476i | \(0.124240\pi\) | ||||
−0.924791 | + | 0.380476i | \(0.875760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 742.874 | + | 307.709i | 0.602377 | + | 0.249513i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 398.428 | + | 961.891i | 0.314827 | + | 0.760059i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 956.286 | + | 956.286i | 0.736660 | + | 0.736660i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1010.60 | + | 1010.60i | −0.759276 | + | 0.759276i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 392.150 | − | 162.434i | 0.287471 | − | 0.119074i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −427.009 | + | 1030.89i | −0.305543 | + | 0.737645i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2159.36 | 1.50876 | 0.754379 | − | 0.656439i | \(-0.227938\pi\) | ||||
0.754379 | + | 0.656439i | \(0.227938\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −183.770 | −0.125427 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 896.246 | − | 2163.73i | 0.597751 | − | 1.44310i | −0.278116 | − | 0.960547i | \(-0.589710\pi\) |
0.875867 | − | 0.482552i | \(-0.160290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 826.876 | − | 342.503i | 0.539092 | − | 0.223299i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −819.201 | + | 819.201i | −0.522264 | + | 0.522264i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −118.307 | − | 118.307i | −0.0737786 | − | 0.0737786i | 0.669255 | − | 0.743033i | \(-0.266614\pi\) |
−0.743033 | + | 0.669255i | \(0.766614\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −924.203 | − | 2231.22i | −0.563956 | − | 1.36151i | −0.906579 | − | 0.422037i | \(-0.861315\pi\) |
0.342623 | − | 0.939473i | \(-0.388685\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −363.255 | − | 150.465i | −0.216962 | − | 0.0898686i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2150.04i | 1.25731i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2407.18i | − | 1.37866i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −353.677 | − | 146.498i | −0.198441 | − | 0.0821968i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 366.708 | + | 885.311i | 0.201623 | + | 0.486762i | 0.992058 | − | 0.125785i | \(-0.0401450\pi\) |
−0.790434 | + | 0.612547i | \(0.790145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1212.74 | − | 1212.74i | −0.653584 | − | 0.653584i | 0.300270 | − | 0.953854i | \(-0.402923\pi\) |
−0.953854 | + | 0.300270i | \(0.902923\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −954.551 | + | 954.551i | −0.504385 | + | 0.504385i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −871.861 | + | 361.137i | −0.451804 | + | 0.187143i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 896.752 | − | 2164.95i | 0.455851 | − | 1.10052i | −0.514211 | − | 0.857664i | \(-0.671915\pi\) |
0.970062 | − | 0.242858i | \(-0.0780848\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −579.208 | −0.288894 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1158.26 | −0.566980 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −363.960 | + | 878.678i | −0.174893 | + | 0.422229i | −0.986882 | − | 0.161444i | \(-0.948385\pi\) |
0.811989 | + | 0.583673i | \(0.198385\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1072.31 | + | 444.165i | −0.505934 | + | 0.209565i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −800.950 | + | 800.950i | −0.371134 | + | 0.371134i | −0.867890 | − | 0.496756i | \(-0.834524\pi\) |
0.496756 | + | 0.867890i | \(0.334524\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −369.282 | − | 369.282i | −0.168085 | − | 0.168085i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 341.882 | + | 825.376i | 0.152891 | + | 0.369112i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 217.486 | + | 90.0857i | 0.0955790 | + | 0.0395901i | 0.429961 | − | 0.902848i | \(-0.358527\pi\) |
−0.334382 | + | 0.942438i | \(0.608527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4793.23i | − | 2.07048i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 181.046i | − | 0.0768826i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1959.23 | + | 811.539i | 0.818099 | + | 0.338868i | 0.752180 | − | 0.658957i | \(-0.229002\pi\) |
0.0659185 | + | 0.997825i | \(0.479002\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −468.260 | − | 1130.48i | −0.192295 | − | 0.464242i | 0.798097 | − | 0.602529i | \(-0.205840\pi\) |
−0.990392 | + | 0.138287i | \(0.955840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 441.700 | + | 441.700i | 0.178423 | + | 0.178423i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 777.031 | − | 777.031i | 0.308803 | − | 0.308803i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2575.52 | + | 1066.82i | −1.00717 | + | 0.417183i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 638.634 | − | 1541.80i | 0.245787 | − | 0.593383i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5115.66 | −1.93799 | −0.968996 | − | 0.247078i | \(-0.920530\pi\) | ||||
−0.968996 | + | 0.247078i | \(0.920530\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4101.82 | 1.52982 | 0.764910 | − | 0.644137i | \(-0.222783\pi\) | ||||
0.764910 | + | 0.644137i | \(0.222783\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −345.979 | + | 835.267i | −0.127057 | + | 0.306742i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2365.10 | + | 979.657i | −0.855363 | + | 0.354303i | −0.766892 | − | 0.641776i | \(-0.778198\pi\) |
−0.0884706 | + | 0.996079i | \(0.528198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3419.40 | − | 3419.40i | 1.21807 | − | 1.21807i | 0.249757 | − | 0.968309i | \(-0.419649\pi\) |
0.968309 | − | 0.249757i | \(-0.0803506\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −127.989 | − | 127.989i | −0.0449138 | − | 0.0449138i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1326.95 | + | 3203.55i | 0.458787 | + | 1.10761i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5557.13 | − | 2301.84i | −1.89330 | − | 0.784231i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1156.16i | − | 0.388206i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1844.90i | 0.610594i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4175.73 | − | 1729.64i | −1.36241 | − | 0.564330i | −0.422692 | − | 0.906273i | \(-0.638915\pi\) |
−0.939720 | + | 0.341944i | \(0.888915\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 129.154 | + | 311.805i | 0.0415468 | + | 0.100303i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1841.44 | + | 1841.44i | 0.584118 | + | 0.584118i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 961.222 | − | 961.222i | 0.300701 | − | 0.300701i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −286.224 | + | 118.558i | −0.0883160 | + | 0.0365817i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −830.988 | + | 2006.18i | −0.252934 | + | 0.610636i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −717.256 | −0.215386 | −0.107693 | − | 0.994184i | \(-0.534346\pi\) | ||||
−0.107693 | + | 0.994184i | \(0.534346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4784.54 | 1.41764 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2316.16 | − | 5591.71i | 0.677221 | − | 1.63496i | −0.0918358 | − | 0.995774i | \(-0.529273\pi\) |
0.769056 | − | 0.639181i | \(-0.220727\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −197.065 | + | 81.6271i | −0.0568665 | + | 0.0235549i | −0.410935 | − | 0.911664i | \(-0.634798\pi\) |
0.354069 | + | 0.935219i | \(0.384798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1182.21 | − | 1182.21i | 0.336727 | − | 0.336727i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4600.59 | − | 4600.59i | −1.29354 | − | 1.29354i | −0.932583 | − | 0.360955i | \(-0.882451\pi\) |
−0.360955 | − | 0.932583i | \(-0.617549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2132.23 | + | 5147.67i | 0.591879 | + | 1.42892i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1409.72 | + | 583.924i | 0.386375 | + | 0.160042i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1366.19i | − | 0.369755i | −0.982762 | − | 0.184878i | \(-0.940811\pi\) | ||
0.982762 | − | 0.184878i | \(-0.0591889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1568.87i | 0.419336i | 0.977773 | + | 0.209668i | \(0.0672382\pi\) | ||||
−0.977773 | + | 0.209668i | \(0.932762\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2331.38 | + | 965.689i | 0.615465 | + | 0.254934i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2076.01 | + | 5011.93i | 0.541353 | + | 1.30694i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1016.16 | + | 1016.16i | 0.261768 | + | 0.261768i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −856.796 | + | 856.796i | −0.218061 | + | 0.218061i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1774.13 | + | 734.870i | −0.446144 | + | 0.184799i | −0.594433 | − | 0.804145i | \(-0.702623\pi\) |
0.148289 | + | 0.988944i | \(0.452623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 913.678 | − | 2205.81i | 0.227045 | − | 0.548136i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1172.23 | −0.287875 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 805.660 | 0.195547 | 0.0977737 | − | 0.995209i | \(-0.468828\pi\) | ||||
0.0977737 | + | 0.995209i | \(0.468828\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −605.759 | + | 1462.43i | −0.145328 | + | 0.350854i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3197.74 | + | 1324.55i | −0.758371 | + | 0.314128i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2159.44 | + | 2159.44i | −0.506300 | + | 0.506300i | −0.913389 | − | 0.407089i | \(-0.866544\pi\) |
0.407089 | + | 0.913389i | \(0.366544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5803.87 | + | 5803.87i | 1.34539 | + | 1.34539i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −596.867 | − | 1440.96i | −0.136808 | − | 0.330283i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2403.35 | + | 995.499i | 0.544738 | + | 0.225638i | 0.638045 | − | 0.769999i | \(-0.279744\pi\) |
−0.0933062 | + | 0.995637i | \(0.529744\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 363.916i | − | 0.0815731i | −0.999168 | − | 0.0407866i | \(-0.987014\pi\) | ||
0.999168 | − | 0.0407866i | \(-0.0129864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1302.32i | − | 0.288717i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9128.32 | + | 3781.08i | 2.00167 | + | 0.829118i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 236.874 | + | 571.865i | 0.0513805 | + | 0.124043i | 0.947486 | − | 0.319798i | \(-0.103615\pi\) |
−0.896105 | + | 0.443842i | \(0.853615\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 959.479 | + | 959.479i | 0.205887 | + | 0.205887i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5905.54 | + | 5905.54i | −1.25372 | + | 1.25372i | −0.299680 | + | 0.954040i | \(0.596880\pi\) |
−0.954040 | + | 0.299680i | \(0.903120\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2127.03 | − | 881.046i | 0.446781 | − | 0.185063i | −0.147938 | − | 0.988997i | \(-0.547264\pi\) |
0.594719 | + | 0.803934i | \(0.297264\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −296.877 | + | 716.723i | −0.0617033 | + | 0.148965i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8664.47 | 1.78205 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2097.48 | 0.426924 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −326.334 | + | 787.841i | −0.0657391 | + | 0.158708i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1783.51 | − | 738.755i | 0.355610 | − | 0.147299i | −0.197724 | − | 0.980258i | \(-0.563355\pi\) |
0.553335 | + | 0.832959i | \(0.313355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1814.14 | + | 1814.14i | −0.358046 | + | 0.358046i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2432.45 | + | 2432.45i | 0.475237 | + | 0.475237i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −711.703 | − | 1718.20i | −0.137655 | − | 0.332329i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3465.74 | − | 1435.56i | −0.663660 | − | 0.274897i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1243.30i | − | 0.235728i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8852.00i | − | 1.66185i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6622.54 | − | 2743.14i | −1.23117 | − | 0.509966i | −0.330223 | − | 0.943903i | \(-0.607124\pi\) |
−0.900943 | + | 0.433937i | \(0.857124\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −127.216 | − | 307.128i | −0.0234210 | − | 0.0565433i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −777.649 | − | 777.649i | −0.141789 | − | 0.141789i | 0.632649 | − | 0.774438i | \(-0.281967\pi\) |
−0.774438 | + | 0.632649i | \(0.781967\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3478.96 | − | 3478.96i | 0.628251 | − | 0.628251i | −0.319377 | − | 0.947628i | \(-0.603474\pi\) |
0.947628 | + | 0.319377i | \(0.103474\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10599.6 | + | 4390.50i | −1.89594 | + | 0.785323i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2639.41 | − | 6372.11i | 0.467648 | − | 1.12900i | −0.497540 | − | 0.867441i | \(-0.665763\pi\) |
0.965187 | − | 0.261560i | \(-0.0842369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7147.64 | −1.25452 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 157.893 | 0.0274540 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −713.052 | + | 1721.46i | −0.122834 | + | 0.296547i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7110.44 | − | 2945.24i | 1.21359 | − | 0.502685i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 376.792 | − | 376.792i | 0.0637207 | − | 0.0637207i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5675.28 | − | 5675.28i | −0.951028 | − | 0.951028i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1414.82 | − | 3415.68i | −0.234941 | − | 0.567198i | 0.761805 | − | 0.647807i | \(-0.224314\pi\) |
−0.996746 | + | 0.0806085i | \(0.974314\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1459.78 | − | 604.660i | −0.240226 | − | 0.0995050i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2565.00i | 0.418331i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5963.90i | 0.964018i | 0.876166 | + | 0.482009i | \(0.160093\pi\) | ||||
−0.876166 | + | 0.482009i | \(0.839907\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1054.41 | + | 436.750i | 0.168931 | + | 0.0699734i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1072.32 | + | 2588.82i | 0.170292 | + | 0.411121i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 655.996 | + | 655.996i | 0.103267 | + | 0.103267i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 709.909 | − | 709.909i | 0.110783 | − | 0.110783i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11609.9 | − | 4808.98i | 1.79612 | − | 0.743975i | 0.808214 | − | 0.588889i | \(-0.200434\pi\) |
0.987901 | − | 0.155086i | \(-0.0495656\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3007.79 | + | 7261.44i | −0.461327 | + | 1.11374i | 0.506525 | + | 0.862225i | \(0.330930\pi\) |
−0.967853 | + | 0.251518i | \(0.919070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2679.57 | 0.407478 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4646.74 | −0.700627 | −0.350313 | − | 0.936633i | \(-0.613925\pi\) | ||||
−0.350313 | + | 0.936633i | \(0.613925\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1830.23 | − | 4418.57i | 0.273630 | − | 0.660600i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1560.04 | − | 646.190i | 0.231278 | − | 0.0957983i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1380.53 | + | 1380.53i | −0.202957 | + | 0.202957i | −0.801266 | − | 0.598309i | \(-0.795840\pi\) |
0.598309 | + | 0.801266i | \(0.295840\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3978.10 | − | 3978.10i | −0.579983 | − | 0.579983i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 682.890 | + | 1648.64i | 0.0987394 | + | 0.238378i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4056.06 | + | 1680.07i | 0.581654 | + | 0.240929i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8418.93i | 1.19745i | 0.800954 | + | 0.598725i | \(0.204326\pi\) | ||||
−0.800954 | + | 0.598725i | \(0.795674\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8648.75i | 1.22015i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10923.3 | − | 4524.59i | −1.52860 | − | 0.633167i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2147.40 | − | 5184.27i | −0.298091 | − | 0.719655i | −0.999973 | − | 0.00736187i | \(-0.997657\pi\) |
0.701882 | − | 0.712293i | \(-0.252343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 985.145 | + | 985.145i | 0.135660 | + | 0.135660i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3936.89 | + | 3936.89i | −0.537825 | + | 0.537825i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7606.92 | − | 3150.89i | 1.03098 | − | 0.427046i | 0.197914 | − | 0.980219i | \(-0.436583\pi\) |
0.833066 | + | 0.553173i | \(0.186583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1031.77 | − | 2490.91i | 0.138738 | − | 0.334943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12379.9 | −1.65166 | −0.825828 | − | 0.563922i | \(-0.809292\pi\) | ||||
−0.825828 | + | 0.563922i | \(0.809292\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23692.5 | −3.13631 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1432.95 | − | 3459.45i | 0.188220 | − | 0.454402i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2056.29 | + | 851.744i | −0.268016 | + | 0.111016i | −0.512644 | − | 0.858601i | \(-0.671334\pi\) |
0.244629 | + | 0.969617i | \(0.421334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1705.09 | − | 1705.09i | 0.220538 | − | 0.220538i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2067.72 | − | 2067.72i | −0.265401 | − | 0.265401i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8274.74 | − | 19977.0i | −1.05404 | − | 2.54469i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10550.8 | + | 4370.29i | 1.33383 | + | 0.552490i | 0.931745 | − | 0.363114i | \(-0.118286\pi\) |
0.402083 | + | 0.915603i | \(0.368286\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 1117.49i | − | 0.140212i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3711.66i | − | 0.462224i | −0.972927 | − | 0.231112i | \(-0.925764\pi\) | ||
0.972927 | − | 0.231112i | \(-0.0742363\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2016.54 | + | 835.278i | 0.249258 | + | 0.103246i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4097.53 | − | 9892.32i | −0.502736 | − | 1.21371i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2307.24 | − | 2307.24i | −0.280996 | − | 0.280996i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6598.84 | − | 6598.84i | 0.797780 | − | 0.797780i | −0.184965 | − | 0.982745i | \(-0.559217\pi\) |
0.982745 | + | 0.184965i | \(0.0592173\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −193.001 | + | 79.9436i | −0.0231631 | + | 0.00959447i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1414.27 | − | 3414.36i | 0.168503 | − | 0.406803i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17170.8 | 2.03104 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3015.41 | −0.354113 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −866.138 | + | 2091.04i | −0.100987 | + | 0.243804i | −0.966296 | − | 0.257435i | \(-0.917123\pi\) |
0.865308 | + | 0.501240i | \(0.167123\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5360.95 | + | 2220.58i | −0.620610 | + | 0.257065i | −0.670757 | − | 0.741677i | \(-0.734031\pi\) |
0.0501475 | + | 0.998742i | \(0.484031\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5664.98 | − | 5664.98i | 0.651161 | − | 0.651161i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7056.18 | + | 7056.18i | 0.805353 | + | 0.805353i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4879.64 | + | 11780.5i | 0.553026 | + | 1.33512i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2480.16 | + | 1027.31i | 0.279122 | + | 0.115616i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3632.29i | 0.405943i | 0.979185 | + | 0.202971i | \(0.0650599\pi\) | ||||
−0.979185 | + | 0.202971i | \(0.934940\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4662.59i | − | 0.517482i | −0.965947 | − | 0.258741i | \(-0.916692\pi\) | ||
0.965947 | − | 0.258741i | \(-0.0833076\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2776.79 | − | 1150.18i | −0.306061 | − | 0.126775i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −610.696 | − | 1474.35i | −0.0668502 | − | 0.161391i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8537.50 | − | 8537.50i | −0.928184 | − | 0.928184i | 0.0694048 | − | 0.997589i | \(-0.477890\pi\) |
−0.997589 | + | 0.0694048i | \(0.977890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5515.60 | − | 5515.60i | 0.595573 | − | 0.595573i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4536.01 | + | 1878.88i | −0.486484 | + | 0.201508i | −0.612424 | − | 0.790530i | \(-0.709805\pi\) |
0.125940 | + | 0.992038i | \(0.459805\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8458.16 | + | 20419.8i | −0.901023 | + | 2.17526i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1196.46 | 0.126601 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17669.7 | 1.85720 | 0.928602 | − | 0.371077i | \(-0.121011\pi\) | ||||
0.928602 | + | 0.371077i | \(0.121011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6834.84 | + | 16500.8i | −0.713615 | + | 1.72282i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1978.41 | + | 819.482i | −0.205196 | + | 0.0849948i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13049.7 | + | 13049.7i | −1.34457 | + | 1.34457i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10783.5 | + | 10783.5i | 1.10378 | + | 1.10378i | 0.993950 | + | 0.109833i | \(0.0350317\pi\) |
0.109833 | + | 0.993950i | \(0.464968\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1329.56 | + | 3209.84i | 0.135204 | + | 0.326411i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −96.4913 | − | 39.9680i | −0.00974847 | − | 0.00403795i | 0.377804 | − | 0.925886i | \(-0.376679\pi\) |
−0.387552 | + | 0.921848i | \(0.626679\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16514.0i | 1.65761i | 0.559539 | + | 0.828804i | \(0.310978\pi\) | ||||
−0.559539 | + | 0.828804i | \(0.689022\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1178.28i | 0.117509i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4949.67 | + | 2050.22i | 0.490457 | + | 0.203154i | 0.614185 | − | 0.789162i | \(-0.289485\pi\) |
−0.123728 | + | 0.992316i | \(0.539485\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1413.95 | − | 3413.57i | −0.139211 | − | 0.336086i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2068.88 | − | 2068.88i | −0.202397 | − | 0.202397i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5467.80 | − | 5467.80i | 0.531521 | − | 0.531521i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6101.30 | − | 2527.24i | 0.589362 | − | 0.244122i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4516.38 | − | 10903.5i | 0.433524 | − | 1.04662i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19166.1 | 1.82823 | 0.914114 | − | 0.405456i | \(-0.132887\pi\) | ||||
0.914114 | + | 0.405456i | \(0.132887\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2541.63 | −0.240932 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −553.432 | + | 1336.10i | −0.0521367 | + | 0.125869i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11164.4 | − | 4624.46i | 1.04526 | − | 0.432961i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3738.42 | − | 3738.42i | 0.347852 | − | 0.347852i | −0.511457 | − | 0.859309i | \(-0.670894\pi\) |
0.859309 | + | 0.511457i | \(0.170894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 839.687 | + | 839.687i | 0.0776523 | + | 0.0776523i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1743.88 | + | 4210.09i | 0.160285 | + | 0.386963i | 0.983535 | − | 0.180716i | \(-0.0578416\pi\) |
−0.823250 | + | 0.567679i | \(0.807842\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6669.41 | − | 2762.56i | −0.609280 | − | 0.252372i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 23649.5i | − | 2.14740i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6889.26i | 0.621782i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6509.03 | + | 2696.13i | 0.583936 | + | 0.241874i | 0.655039 | − | 0.755595i | \(-0.272652\pi\) |
−0.0711034 | + | 0.997469i | \(0.522652\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 541.225 | + | 1306.63i | 0.0482638 | + | 0.116519i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3534.14 | − | 3534.14i | −0.313280 | − | 0.313280i | 0.532899 | − | 0.846179i | \(-0.321103\pi\) |
−0.846179 | + | 0.532899i | \(0.821103\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12458.3 | + | 12458.3i | −1.09780 | + | 1.09780i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −602.430 | + | 249.535i | −0.0527710 | + | 0.0218584i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4345.28 | + | 10490.4i | −0.378391 | + | 0.913518i | 0.613876 | + | 0.789402i | \(0.289609\pi\) |
−0.992268 | + | 0.124115i | \(0.960391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6324.05 | −0.547475 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2299.28 | 0.197886 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1802.78 | + | 4352.28i | −0.154252 | + | 0.372397i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15285.0 | − | 6331.24i | 1.30026 | − | 0.538583i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 207.835 | − | 207.835i | 0.0175779 | − | 0.0175779i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8864.19 | − | 8864.19i | −0.745388 | − | 0.745388i | 0.228221 | − | 0.973609i | \(-0.426709\pi\) |
−0.973609 | + | 0.228221i | \(0.926709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1505.26 | − | 3634.02i | −0.125852 | − | 0.303833i | 0.848378 | − | 0.529391i | \(-0.177579\pi\) |
−0.974230 | + | 0.225558i | \(0.927579\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5529.20 | − | 2290.27i | −0.459645 | − | 0.190391i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2830.06i | 0.233926i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 10101.8i | − | 0.830260i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3408.16 | + | 1411.71i | 0.278534 | + | 0.115373i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5323.95 | + | 12853.2i | 0.432657 | + | 1.04453i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1582.15 | − | 1582.15i | −0.127854 | − | 0.127854i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1872.29 | − | 1872.29i | 0.150457 | − | 0.150457i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14881.9 | − | 6164.29i | 1.18926 | − | 0.492606i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4671.40 | + | 11277.8i | −0.371237 | + | 0.896245i | 0.622305 | + | 0.782775i | \(0.286196\pi\) |
−0.993541 | + | 0.113470i | \(0.963804\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1527.80 | −0.120744 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7551.19 | −0.593500 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6749.10 | + | 16293.8i | −0.527552 | + | 1.27362i | 0.405571 | + | 0.914064i | \(0.367073\pi\) |
−0.933122 | + | 0.359559i | \(0.882927\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11759.1 | + | 4870.79i | −0.914148 | + | 0.378652i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3378.15 | + | 3378.15i | −0.261187 | + | 0.261187i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22024.5 | + | 22024.5i | 1.69363 | + | 1.69363i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −525.063 | − | 1267.61i | −0.0401580 | − | 0.0969499i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2590.39 | − | 1072.98i | −0.197053 | − | 0.0816220i | 0.281975 | − | 0.959422i | \(-0.409011\pi\) |
−0.479028 | + | 0.877800i | \(0.659011\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6023.28i | − | 0.455738i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3480.71i | 0.261953i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7377.58 | + | 3055.89i | 0.552270 | + | 0.228758i | 0.641325 | − | 0.767269i | \(-0.278385\pi\) |
−0.0890556 | + | 0.996027i | \(0.528385\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6189.15 | − | 14941.9i | −0.460849 | − | 1.11259i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10906.2 | + | 10906.2i | 0.807792 | + | 0.807792i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16799.5 | − | 16799.5i | 1.23773 | − | 1.23773i | 0.276810 | − | 0.960925i | \(-0.410723\pi\) |
0.960925 | − | 0.276810i | \(-0.0892773\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8801.25 | + | 3645.60i | −0.645045 | + | 0.267186i | −0.681130 | − | 0.732162i | \(-0.738511\pi\) |
0.0360851 | + | 0.999349i | \(0.488511\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2444.33 | + | 5901.13i | −0.178208 | + | 0.430232i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8546.51 | −0.619851 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11551.9 | 0.833472 | 0.416736 | − | 0.909028i | \(-0.363174\pi\) | ||||
0.416736 | + | 0.909028i | \(0.363174\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1959.90 | − | 4731.62i | 0.140675 | − | 0.339619i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22851.4 | + | 9465.36i | −1.63173 | + | 0.675886i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17233.4 | − | 17233.4i | 1.22425 | − | 1.22425i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13026.0 | − | 13026.0i | −0.920615 | − | 0.920615i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2507.65 | − | 6054.00i | −0.176323 | − | 0.425682i | 0.810867 | − | 0.585231i | \(-0.198996\pi\) |
−0.987190 | + | 0.159549i | \(0.948996\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1730.35 | + | 716.733i | 0.121049 | + | 0.0501400i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3196.34i | 0.222470i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7192.49i | 0.498078i | 0.968493 | + | 0.249039i | \(0.0801147\pi\) | ||||
−0.968493 | + | 0.249039i | \(0.919885\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22107.2 | − | 9157.12i | −1.52321 | − | 0.630933i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2310.59 | − | 5578.26i | −0.158402 | − | 0.382417i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8885.88 | − | 8885.88i | −0.606122 | − | 0.606122i | 0.335808 | − | 0.941930i | \(-0.390991\pi\) |
−0.941930 | + | 0.335808i | \(0.890991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1468.96 | − | 1468.96i | 0.0997009 | − | 0.0997009i | −0.655497 | − | 0.755198i | \(-0.727541\pi\) |
0.755198 | + | 0.655497i | \(0.227541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3407.38 | − | 1411.38i | 0.230115 | − | 0.0953167i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9677.19 | − | 23362.8i | 0.650303 | − | 1.56997i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1305.90 | 0.0873225 | 0.0436613 | − | 0.999046i | \(-0.486098\pi\) | ||||
0.0436613 | + | 0.999046i | \(0.486098\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4329.46 | 0.288076 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4931.67 | − | 11906.1i | 0.326537 | − | 0.788330i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15396.4 | + | 6377.39i | −1.01444 | + | 0.420196i | −0.827074 | − | 0.562093i | \(-0.809996\pi\) |
−0.187370 | + | 0.982289i | \(0.559996\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5310.53 | + | 5310.53i | −0.348197 | + | 0.348197i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14943.6 | − | 14943.6i | −0.975049 | − | 0.975049i | 0.0246473 | − | 0.999696i | \(-0.492154\pi\) |
−0.999696 | + | 0.0246473i | \(0.992154\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9902.61 | + | 23907.0i | 0.643004 | + | 1.55235i | 0.822608 | + | 0.568609i | \(0.192518\pi\) |
−0.179604 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2749.08 | − | 1138.71i | −0.177644 | − | 0.0735826i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 31837.8i | − | 2.04744i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3764.96i | 0.240957i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2128.17 | + | 881.515i | 0.135551 | + | 0.0561472i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1261.12 | − | 3044.61i | −0.0799429 | − | 0.192999i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11209.4 | − | 11209.4i | −0.707191 | − | 0.707191i | 0.258753 | − | 0.965944i | \(-0.416688\pi\) |
−0.965944 | + | 0.258753i | \(0.916688\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3990.43 | + | 3990.43i | −0.250561 | + | 0.250561i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35298.5 | + | 14621.1i | −2.20595 | + | 0.913736i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4801.63 | − | 11592.2i | 0.298662 | − | 0.721033i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6876.77 | −0.425729 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8922.84 | −0.549814 | −0.274907 | − | 0.961471i | \(-0.588647\pi\) | ||||
−0.274907 | + | 0.961471i | \(0.588647\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7149.00 | − | 17259.2i | 0.438459 | − | 1.05853i | −0.538022 | − | 0.842930i | \(-0.680828\pi\) |
0.976481 | − | 0.215603i | \(-0.0691715\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3004.05 | − | 1244.32i | 0.183386 | − | 0.0759611i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15074.6 | − | 15074.6i | 0.915985 | − | 0.915985i | −0.0807492 | − | 0.996734i | \(-0.525731\pi\) |
0.996734 | + | 0.0807492i | \(0.0257313\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5386.73 | + | 5386.73i | 0.325805 | + | 0.325805i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −649.526 | − | 1568.09i | −0.0391043 | − | 0.0944062i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 717.534 | + | 297.212i | 0.0430004 | + | 0.0178114i | 0.404080 | − | 0.914724i | \(-0.367592\pi\) |
−0.361080 | + | 0.932535i | \(0.617592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41438.5i | 2.47197i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6312.58i | − | 0.374851i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6945.56 | − | 2876.95i | −0.410562 | − | 0.170061i | 0.167836 | − | 0.985815i | \(-0.446322\pi\) |
−0.578398 | + | 0.815754i | \(0.696322\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −797.182 | − | 1924.57i | −0.0469089 | − | 0.113248i | 0.898688 | − | 0.438588i | \(-0.144521\pi\) |
−0.945597 | + | 0.325340i | \(0.894521\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1917.16 | + | 1917.16i | 0.112302 | + | 0.112302i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11197.6 | + | 11197.6i | −0.652971 | + | 0.652971i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5712.04 | − | 2366.01i | 0.331591 | − | 0.137349i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −342.714 | + | 827.385i | −0.0198058 | + | 0.0478155i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26284.2 | −1.51221 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6013.47 | 0.344431 | 0.172216 | − | 0.985059i | \(-0.444907\pi\) | ||||
0.172216 | + | 0.985059i | \(0.444907\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4712.31 | − | 11376.5i | 0.268707 | − | 0.648716i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19577.8 | − | 8109.41i | 1.11143 | − | 0.460369i | 0.250000 | − | 0.968246i | \(-0.419569\pi\) |
0.861430 | + | 0.507877i | \(0.169569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12308.7 | + | 12308.7i | −0.695679 | + | 0.695679i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5343.58 | − | 5343.58i | −0.300685 | − | 0.300685i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5715.60 | + | 13798.7i | 0.320207 | + | 0.773048i | 0.999241 | + | 0.0389416i | \(0.0123986\pi\) |
−0.679035 | + | 0.734106i | \(0.737601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2735.00 | + | 1132.88i | 0.152553 | + | 0.0631897i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 266.325i | 0.0147903i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 18984.2i | − | 1.04970i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8261.06 | + | 3421.84i | 0.454798 | + | 0.188384i | 0.598310 | − | 0.801265i | \(-0.295839\pi\) |
−0.143511 | + | 0.989649i | \(0.545839\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13036.7 | + | 31473.4i | 0.714608 | + | 1.72522i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30215.5 | + | 30215.5i | 1.64912 | + | 1.64912i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12755.1 | + | 12755.1i | −0.693161 | + | 0.693161i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7505.19 | + | 3108.75i | −0.406112 | + | 0.168217i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8530.14 | − | 20593.6i | 0.459599 | − | 1.10957i | −0.508961 | − | 0.860790i | \(-0.669970\pi\) |
0.968560 | − | 0.248780i | \(-0.0800298\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2180.92 | −0.117005 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6956.86 | 0.371646 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9712.25 | − | 23447.4i | 0.516643 | − | 1.24729i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11948.6 | − | 4949.27i | 0.632919 | − | 0.262163i | −0.0430740 | − | 0.999072i | \(-0.513715\pi\) |
0.675993 | + | 0.736908i | \(0.263715\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21984.6 | + | 21984.6i | −1.15962 | + | 1.15962i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1713.89 | − | 1713.89i | −0.0900222 | − | 0.0900222i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14558.0 | − | 35146.2i | −0.761453 | − | 1.83831i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1575.96 | − | 652.783i | −0.0820854 | − | 0.0340009i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 3624.32i | − | 0.187989i | −0.995573 | − | 0.0939947i | \(-0.970036\pi\) | ||
0.995573 | − | 0.0939947i | \(-0.0299637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6785.92i | − | 0.350514i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1809.76 | + | 749.626i | 0.0930921 | + | 0.0385600i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9791.24 | + | 23638.1i | 0.501569 | + | 1.21089i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24377.4 | + | 24377.4i | 1.24361 | + | 1.24361i | 0.958491 | + | 0.285123i | \(0.0920345\pi\) |
0.285123 | + | 0.958491i | \(0.407966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9325.61 | + | 9325.61i | −0.473790 | + | 0.473790i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7215.26 | − | 2988.66i | 0.365070 | − | 0.151217i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2874.93 | + | 6940.70i | −0.144868 | + | 0.349742i | −0.979613 | − | 0.200895i | \(-0.935615\pi\) |
0.834745 | + | 0.550637i | \(0.185615\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6773.41 | 0.339920 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7616.24 | 0.380662 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9423.24 | + | 22749.7i | −0.469066 | + | 1.13242i | 0.495506 | + | 0.868604i | \(0.334983\pi\) |
−0.964572 | + | 0.263820i | \(0.915017\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1657.72 | − | 686.650i | 0.0821833 | − | 0.0340414i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4515.42 | − | 4515.42i | 0.222954 | − | 0.222954i | −0.586787 | − | 0.809741i | \(-0.699607\pi\) |
0.809741 | + | 0.586787i | \(0.199607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11989.0 | − | 11989.0i | −0.589587 | − | 0.589587i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9448.20 | − | 22810.0i | −0.462773 | − | 1.11723i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2977.72 | + | 1233.41i | 0.145265 | + | 0.0601707i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 25582.2i | − | 1.24302i | −0.783406 | − | 0.621510i | \(-0.786519\pi\) | ||
0.783406 | − | 0.621510i | \(-0.213481\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2397.67i | 0.116037i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28035.9 | + | 11612.8i | 1.35143 | + | 0.559780i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7681.53 | + | 18544.9i | 0.368811 | + | 0.890389i | 0.993946 | + | 0.109872i | \(0.0350440\pi\) |
−0.625135 | + | 0.780517i | \(0.714956\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2107.93 | − | 2107.93i | −0.100808 | − | 0.100808i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9053.82 | + | 9053.82i | −0.431276 | + | 0.431276i | −0.889062 | − | 0.457786i | \(-0.848642\pi\) |
0.457786 | + | 0.889062i | \(0.348642\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10049.3 | − | 4162.58i | 0.476816 | − | 0.197504i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9140.51 | − | 22067.1i | 0.431995 | − | 1.04293i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5933.98 | 0.279353 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22171.5 | −1.03969 | −0.519847 | − | 0.854259i | \(-0.674011\pi\) | ||||
−0.519847 | + | 0.854259i | \(0.674011\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 384.954 | − | 929.362i | 0.0179816 | − | 0.0434113i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4511.27 | − | 1868.63i | 0.209908 | − | 0.0869469i | −0.275252 | − | 0.961372i | \(-0.588761\pi\) |
0.485160 | + | 0.874425i | \(0.338761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7092.61 | − | 7092.61i | 0.328741 | − | 0.328741i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1397.54 | + | 1397.54i | 0.0645255 | + | 0.0645255i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4568.36 | + | 11029.0i | 0.210114 | + | 0.507259i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13120.0 | − | 5434.50i | −0.601116 | − | 0.248991i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8908.03i | 0.406574i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41461.9i | 1.88514i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23455.4 | − | 9715.54i | −1.06238 | − | 0.440053i | −0.218086 | − | 0.975930i | \(-0.569981\pi\) |
−0.844296 | + | 0.535877i | \(0.819981\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1459.20 | + | 3522.81i | 0.0658413 | + | 0.158955i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16473.4 | + | 16473.4i | 0.740489 | + | 0.740489i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14477.2 | + | 14477.2i | −0.648300 | + | 0.648300i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9468.17 | − | 3921.84i | 0.422392 | − | 0.174960i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11912.1 | + | 28758.4i | −0.529421 | + | 1.27814i | 0.402482 | + | 0.915428i | \(0.368148\pi\) |
−0.931903 | + | 0.362708i | \(0.881852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16709.3 | 0.739841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31780.1 | 1.40186 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4988.64 | − | 12043.6i | 0.219234 | − | 0.529279i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18933.8 | − | 7842.65i | 0.828981 | − | 0.343375i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2296.70 | − | 2296.70i | 0.100183 | − | 0.100183i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2278.00 | + | 2278.00i | 0.0989992 | + | 0.0989992i | 0.754872 | − | 0.655873i | \(-0.227699\pi\) |
−0.655873 | + | 0.754872i | \(0.727699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11666.4 | + | 28165.2i | 0.505134 | + | 1.21950i | 0.946655 | + | 0.322250i | \(0.104439\pi\) |
−0.441521 | + | 0.897251i | \(0.645561\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −419.792 | − | 173.884i | −0.0181092 | − | 0.00750106i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 16827.9i | − | 0.723260i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5168.43i | − | 0.221323i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24516.0 | + | 10154.8i | 1.04598 | + | 0.433259i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12455.2 | − | 30069.5i | −0.529463 | − | 1.27824i | −0.931876 | − | 0.362778i | \(-0.881828\pi\) |
0.402413 | − | 0.915458i | \(-0.368172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18709.3 | − | 18709.3i | −0.792424 | − | 0.792424i | 0.189464 | − | 0.981888i | \(-0.439325\pi\) |
−0.981888 | + | 0.189464i | \(0.939325\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8723.26 | − | 8723.26i | 0.368127 | − | 0.368127i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31391.1 | + | 13002.6i | −1.31992 | + | 0.546730i | −0.927764 | − | 0.373167i | \(-0.878272\pi\) |
−0.392160 | + | 0.919897i | \(0.628272\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3317.38 | − | 8008.87i | 0.138984 | − | 0.335536i | −0.839027 | − | 0.544089i | \(-0.816875\pi\) |
0.978011 | + | 0.208553i | \(0.0668753\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 772.852 | 0.0322622 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16268.7 | 0.676683 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7669.66 | − | 18516.2i | 0.317868 | − | 0.767401i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3226.41 | − | 1336.42i | 0.133239 | − | 0.0551895i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13722.1 | + | 13722.1i | −0.564649 | + | 0.564649i | −0.930624 | − | 0.365976i | \(-0.880735\pi\) |
0.365976 | + | 0.930624i | \(0.380735\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4157.72 | + | 4157.72i | 0.170475 | + | 0.170475i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3990.55 | + | 9634.04i | 0.163039 | + | 0.393611i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8537.00 | + | 3536.14i | 0.347552 | + | 0.143961i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36426.4i | 1.47772i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 2874.60i | − | 0.116202i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2607.57 | + | 1080.09i | 0.105037 | + | 0.0435077i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8865.17 | + | 21402.4i | 0.355847 | + | 0.859092i | 0.995875 | + | 0.0907394i | \(0.0289230\pi\) |
−0.640027 | + | 0.768352i | \(0.721077\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11177.3 | − | 11177.3i | −0.447084 | − | 0.447084i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7933.81 | + | 7933.81i | −0.316236 | + | 0.316236i | −0.847319 | − | 0.531084i | \(-0.821785\pi\) |
0.531084 | + | 0.847319i | \(0.321785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3978.15 | − | 1647.80i | 0.158012 | − | 0.0654509i | −0.302275 | − | 0.953221i | \(-0.597746\pi\) |
0.460288 | + | 0.887770i | \(0.347746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4139.99 | − | 9994.83i | 0.163868 | − | 0.395613i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11315.5 | −0.446331 | −0.223166 | − | 0.974781i | \(-0.571639\pi\) | ||||
−0.223166 | + | 0.974781i | \(0.571639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4165.17 | −0.163723 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1002.20 | − | 2419.53i | 0.0392578 | − | 0.0947768i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59317.7 | + | 24570.2i | −2.31555 | + | 0.959133i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4194.99 | − | 4194.99i | 0.163194 | − | 0.163194i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12286.4 | − | 12286.4i | −0.476325 | − | 0.476325i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10883.3 | + | 26274.6i | 0.420483 | + | 1.01513i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7769.43 | + | 3218.20i | 0.299151 | + | 0.123912i | 0.527210 | − | 0.849735i | \(-0.323238\pi\) |
−0.228060 | + | 0.973647i | \(0.573238\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2410.34i | − | 0.0924901i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15431.2i | − | 0.590115i | −0.955479 | − | 0.295058i | \(-0.904661\pi\) | ||
0.955479 | − | 0.295058i | \(-0.0953389\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39311.6 | − | 16283.4i | −1.49824 | − | 0.620589i | −0.525145 | − | 0.851013i | \(-0.675989\pi\) |
−0.973090 | + | 0.230424i | \(0.925989\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1225.87 | + | 2959.51i | 0.0465618 | + | 0.112410i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24315.7 | + | 24315.7i | 0.920451 | + | 0.920451i | 0.997061 | − | 0.0766105i | \(-0.0244098\pi\) |
−0.0766105 | + | 0.997061i | \(0.524410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38916.5 | − | 38916.5i | 1.46818 | − | 1.46818i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29373.2 | + | 12166.8i | −1.10442 | + | 0.457467i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4231.75 | − | 10216.4i | 0.158578 | − | 0.382841i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37522.0 | −1.40137 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2322.08 | −0.0864348 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2776.82 | + | 6703.84i | −0.103017 | + | 0.248705i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22741.1 | − | 9419.66i | 0.840860 | − | 0.348296i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3311.95 | + | 3311.95i | −0.122054 | + | 0.122054i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15309.1 | + | 15309.1i | 0.562310 | + | 0.562310i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10871.5 | − | 26246.1i | −0.397996 | − | 0.960848i | −0.988141 | − | 0.153550i | \(-0.950929\pi\) |
0.590145 | − | 0.807297i | \(-0.299071\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23404.9 | + | 9694.63i | 0.854007 | + | 0.353741i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2752.62i | 0.100108i | 0.998747 | + | 0.0500540i | \(0.0159394\pi\) | ||||
−0.998747 | + | 0.0500540i | \(0.984061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 50985.3i | − | 1.84816i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10211.1 | − | 4229.60i | −0.368929 | − | 0.152815i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22842.9 | − | 55147.6i | −0.822615 | − | 1.98597i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27290.8 | − | 27290.8i | −0.979586 | − | 0.979586i | 0.0202098 | − | 0.999796i | \(-0.493567\pi\) |
−0.999796 | + | 0.0202098i | \(0.993567\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6328.66 | + | 6328.66i | −0.226424 | + | 0.226424i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10219.8 | + | 4233.16i | −0.364450 | + | 0.150960i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4469.74 | + | 10790.9i | −0.158880 | + | 0.383570i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6773.61 | 0.239994 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19815.1 | −0.699798 | −0.349899 | − | 0.936787i | \(-0.613784\pi\) | ||||
−0.349899 | + | 0.936787i | \(0.613784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4120.17 | − | 9946.96i | 0.145041 | − | 0.350159i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1268.62 | + | 525.480i | −0.0445153 | + | 0.0184388i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34878.0 | − | 34878.0i | 1.21993 | − | 1.21993i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19332.2 | − | 19332.2i | −0.674018 | − | 0.674018i | 0.284622 | − | 0.958640i | \(-0.408132\pi\) |
−0.958640 | + | 0.284622i | \(0.908132\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2350.83 | − | 5675.42i | −0.0817003 | − | 0.197242i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4000.39 | − | 1657.02i | −0.138586 | − | 0.0574041i | 0.312313 | − | 0.949979i | \(-0.398896\pi\) |
−0.450898 | + | 0.892575i | \(0.648896\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 15449.1i | − | 0.533500i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 29527.7i | 1.01644i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35953.4 | − | 14892.4i | −1.23372 | − | 0.511022i | −0.331970 | − | 0.943290i | \(-0.607713\pi\) |
−0.901745 | + | 0.432268i | \(0.857713\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3885.86 | − | 9381.31i | −0.132919 | − | 0.320896i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6089.35 | − | 6089.35i | −0.207635 | − | 0.207635i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1350.98 | − | 1350.98i | 0.0459208 | − | 0.0459208i | −0.683773 | − | 0.729694i | \(-0.739662\pi\) |
0.729694 | + | 0.683773i | \(0.239662\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 83624.5 | − | 34638.4i | 2.83354 | − | 1.17369i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3415.23 | + | 8245.10i | −0.115359 | + | 0.278502i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4264.31 | −0.143589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26946.3 | −0.904513 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1231.17 | + | 2972.32i | −0.0411984 | + | 0.0994616i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −67051.5 | + | 27773.6i | −2.23675 | + | 0.926492i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2303.21 | − | 2303.21i | 0.0765939 | − | 0.0765939i | −0.667772 | − | 0.744366i | \(-0.732752\pi\) |
0.744366 | + | 0.667772i | \(0.232752\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1645.07 | + | 1645.07i | 0.0545379 | + | 0.0545379i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3262.48 | − | 7876.32i | −0.107825 | − | 0.260312i | 0.860753 | − | 0.509023i | \(-0.169993\pi\) |
−0.968578 | + | 0.248711i | \(0.919993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −56867.8 | − | 23555.4i | −1.87369 | − | 0.776107i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 9609.46i | − | 0.315640i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43245.0i | 1.41610i | 0.706162 | + | 0.708050i | \(0.250425\pi\) | ||||
−0.706162 | + | 0.708050i | \(0.749575\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60632.5 | + | 25114.8i | 1.97939 | + | 0.819890i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4155.03 | + | 10031.1i | 0.135229 | + | 0.326472i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14901.6 | − | 14901.6i | −0.483506 | − | 0.483506i | 0.422743 | − | 0.906249i | \(-0.361067\pi\) |
−0.906249 | + | 0.422743i | \(0.861067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32028.4 | − | 32028.4i | 1.03605 | − | 1.03605i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9258.39 | + | 3834.95i | −0.298579 | + | 0.123676i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2559.65 | + | 6179.54i | −0.0822973 | + | 0.198683i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18330.8 | 0.587586 | 0.293793 | − | 0.955869i | \(-0.405082\pi\) | ||||
0.293793 | + | 0.955869i | \(0.405082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4616.15 | −0.147522 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32743.2 | + | 79049.1i | −1.04325 | + | 2.51862i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39601.9 | − | 16403.7i | 1.25798 | − | 0.521072i | 0.348690 | − | 0.937238i | \(-0.386626\pi\) |
0.909289 | + | 0.416166i | \(0.136626\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2875.49 | + | 2875.49i | −0.0910674 | + | 0.0910674i |
(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 | 128.4.g.a.17.6 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.13.1 | yes | 44 | ||
8.3 | odd | 2 | 256.4.g.b.33.6 | 44 | |||
8.5 | even | 2 | 256.4.g.a.33.6 | 44 | |||
32.5 | even | 8 | inner | 128.4.g.a.113.6 | 44 | ||
32.11 | odd | 8 | 256.4.g.b.225.6 | 44 | |||
32.21 | even | 8 | 256.4.g.a.225.6 | 44 | |||
32.27 | odd | 8 | 32.4.g.a.5.1 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.1 | ✓ | 44 | 32.27 | odd | 8 | ||
32.4.g.a.13.1 | yes | 44 | 4.3 | odd | 2 | ||
128.4.g.a.17.6 | 44 | 1.1 | even | 1 | trivial | ||
128.4.g.a.113.6 | 44 | 32.5 | even | 8 | inner | ||
256.4.g.a.33.6 | 44 | 8.5 | even | 2 | |||
256.4.g.a.225.6 | 44 | 32.21 | even | 8 | |||
256.4.g.b.33.6 | 44 | 8.3 | odd | 2 | |||
256.4.g.b.225.6 | 44 | 32.11 | odd | 8 |