Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,3,Mod(736,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.736");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.b (of order \(2\), degree \(1\), 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: | \(31.4714705336\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 736.3 | ||
Character | \(\chi\) | \(=\) | 1155.736 |
Dual form | 1155.3.b.a.736.94 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.79404i | − | 1.89702i | −0.316744 | − | 0.948511i | \(-0.602589\pi\) | ||
0.316744 | − | 0.948511i | \(-0.397411\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −10.3948 | −2.59869 | ||||||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | − | 6.57148i | − | 1.09525i | ||||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | 24.2621i | 3.03276i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 8.48374i | − | 0.848374i | ||||||
\(11\) | 10.8209 | + | 1.97674i | 0.983721 | + | 0.179704i | ||||
\(12\) | −18.0043 | −1.50036 | ||||||||
\(13\) | 11.4229i | 0.878687i | 0.898319 | + | 0.439343i | \(0.144789\pi\) | ||||
−0.898319 | + | 0.439343i | \(0.855211\pi\) | |||||||
\(14\) | −10.0381 | −0.717007 | ||||||||
\(15\) | 3.87298 | 0.258199 | ||||||||
\(16\) | 50.4723 | 3.15452 | ||||||||
\(17\) | 6.44081i | 0.378871i | 0.981893 | + | 0.189436i | \(0.0606658\pi\) | ||||
−0.981893 | + | 0.189436i | \(0.939334\pi\) | |||||||
\(18\) | − | 11.3821i | − | 0.632341i | ||||||
\(19\) | 15.1396i | 0.796820i | 0.917207 | + | 0.398410i | \(0.130438\pi\) | ||||
−0.917207 | + | 0.398410i | \(0.869562\pi\) | |||||||
\(20\) | −23.2434 | −1.16217 | ||||||||
\(21\) | − | 4.58258i | − | 0.218218i | ||||||
\(22\) | 7.49985 | − | 41.0551i | 0.340902 | − | 1.86614i | ||||
\(23\) | −12.3313 | −0.536143 | −0.268072 | − | 0.963399i | \(-0.586386\pi\) | ||||
−0.268072 | + | 0.963399i | \(0.586386\pi\) | |||||||
\(24\) | 42.0231i | 1.75096i | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 43.3391 | 1.66689 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | 27.5020i | 0.982214i | ||||||||
\(29\) | 36.9010i | 1.27245i | 0.771505 | + | 0.636224i | \(0.219504\pi\) | ||||
−0.771505 | + | 0.636224i | \(0.780496\pi\) | |||||||
\(30\) | − | 14.6943i | − | 0.489809i | ||||||
\(31\) | 37.4956 | 1.20953 | 0.604767 | − | 0.796402i | \(-0.293266\pi\) | ||||
0.604767 | + | 0.796402i | \(0.293266\pi\) | |||||||
\(32\) | − | 94.4457i | − | 2.95143i | ||||||
\(33\) | 18.7424 | + | 3.42382i | 0.567951 | + | 0.103752i | ||||
\(34\) | 24.4367 | 0.718727 | ||||||||
\(35\) | − | 5.91608i | − | 0.169031i | ||||||
\(36\) | −31.1843 | −0.866231 | ||||||||
\(37\) | 71.6335 | 1.93604 | 0.968020 | − | 0.250873i | \(-0.0807175\pi\) | ||||
0.968020 | + | 0.250873i | \(0.0807175\pi\) | |||||||
\(38\) | 57.4402 | 1.51159 | ||||||||
\(39\) | 19.7851i | 0.507310i | ||||||||
\(40\) | 54.2516i | 1.35629i | ||||||||
\(41\) | − | 46.2442i | − | 1.12791i | −0.825807 | − | 0.563953i | \(-0.809280\pi\) | ||
0.825807 | − | 0.563953i | \(-0.190720\pi\) | |||||||
\(42\) | −17.3865 | −0.413964 | ||||||||
\(43\) | 0.700871i | 0.0162993i | 0.999967 | + | 0.00814966i | \(0.00259415\pi\) | ||||
−0.999967 | + | 0.00814966i | \(0.997406\pi\) | |||||||
\(44\) | −112.481 | − | 20.5478i | −2.55639 | − | 0.466995i | ||||
\(45\) | 6.70820 | 0.149071 | ||||||||
\(46\) | 46.7855i | 1.01708i | ||||||||
\(47\) | 36.0339 | 0.766679 | 0.383339 | − | 0.923608i | \(-0.374774\pi\) | ||||
0.383339 | + | 0.923608i | \(0.374774\pi\) | |||||||
\(48\) | 87.4205 | 1.82126 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | − | 18.9702i | − | 0.379404i | ||||||
\(51\) | 11.1558i | 0.218741i | ||||||||
\(52\) | − | 118.739i | − | 2.28344i | ||||||
\(53\) | −21.6936 | −0.409313 | −0.204656 | − | 0.978834i | \(-0.565608\pi\) | ||||
−0.204656 | + | 0.978834i | \(0.565608\pi\) | |||||||
\(54\) | − | 19.7144i | − | 0.365082i | ||||||
\(55\) | 24.1963 | + | 4.42013i | 0.439933 | + | 0.0803660i | ||||
\(56\) | 64.1914 | 1.14627 | ||||||||
\(57\) | 26.2225i | 0.460044i | ||||||||
\(58\) | 140.004 | 2.41386 | ||||||||
\(59\) | 80.6121 | 1.36631 | 0.683154 | − | 0.730275i | \(-0.260608\pi\) | ||||
0.683154 | + | 0.730275i | \(0.260608\pi\) | |||||||
\(60\) | −40.2588 | −0.670980 | ||||||||
\(61\) | 21.0333i | 0.344808i | 0.985026 | + | 0.172404i | \(0.0551534\pi\) | ||||
−0.985026 | + | 0.172404i | \(0.944847\pi\) | |||||||
\(62\) | − | 142.260i | − | 2.29451i | ||||||
\(63\) | − | 7.93725i | − | 0.125988i | ||||||
\(64\) | −156.442 | −2.44441 | ||||||||
\(65\) | 25.5424i | 0.392961i | ||||||||
\(66\) | 12.9901 | − | 71.1095i | 0.196820 | − | 1.07742i | ||||
\(67\) | −18.1513 | −0.270914 | −0.135457 | − | 0.990783i | \(-0.543250\pi\) | ||||
−0.135457 | + | 0.990783i | \(0.543250\pi\) | |||||||
\(68\) | − | 66.9508i | − | 0.984570i | ||||||
\(69\) | −21.3584 | −0.309542 | ||||||||
\(70\) | −22.4459 | −0.320655 | ||||||||
\(71\) | −85.1196 | −1.19887 | −0.599434 | − | 0.800424i | \(-0.704607\pi\) | ||||
−0.599434 | + | 0.800424i | \(0.704607\pi\) | |||||||
\(72\) | 72.7862i | 1.01092i | ||||||||
\(73\) | 103.871i | 1.42289i | 0.702743 | + | 0.711444i | \(0.251958\pi\) | ||||
−0.702743 | + | 0.711444i | \(0.748042\pi\) | |||||||
\(74\) | − | 271.781i | − | 3.67271i | ||||||
\(75\) | 8.66025 | 0.115470 | ||||||||
\(76\) | − | 157.373i | − | 2.07069i | ||||||
\(77\) | 5.22997 | − | 28.6295i | 0.0679217 | − | 0.371811i | ||||
\(78\) | 75.0655 | 0.962378 | ||||||||
\(79\) | 43.5544i | 0.551321i | 0.961255 | + | 0.275661i | \(0.0888966\pi\) | ||||
−0.961255 | + | 0.275661i | \(0.911103\pi\) | |||||||
\(80\) | 112.859 | 1.41074 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −175.452 | −2.13966 | ||||||||
\(83\) | − | 33.9858i | − | 0.409467i | −0.978818 | − | 0.204734i | \(-0.934367\pi\) | ||
0.978818 | − | 0.204734i | \(-0.0656328\pi\) | |||||||
\(84\) | 47.6348i | 0.567081i | ||||||||
\(85\) | 14.4021i | 0.169436i | ||||||||
\(86\) | 2.65913 | 0.0309202 | ||||||||
\(87\) | 63.9144i | 0.734648i | ||||||||
\(88\) | −47.9599 | + | 262.538i | −0.544998 | + | 2.98339i | ||||
\(89\) | −125.375 | −1.40871 | −0.704355 | − | 0.709847i | \(-0.748764\pi\) | ||||
−0.704355 | + | 0.709847i | \(0.748764\pi\) | |||||||
\(90\) | − | 25.4512i | − | 0.282791i | ||||||
\(91\) | 30.2222 | 0.332112 | ||||||||
\(92\) | 128.181 | 1.39327 | ||||||||
\(93\) | 64.9443 | 0.698325 | ||||||||
\(94\) | − | 136.714i | − | 1.45441i | ||||||
\(95\) | 33.8531i | 0.356349i | ||||||||
\(96\) | − | 163.585i | − | 1.70401i | ||||||
\(97\) | −115.505 | −1.19077 | −0.595386 | − | 0.803440i | \(-0.703001\pi\) | ||||
−0.595386 | + | 0.803440i | \(0.703001\pi\) | |||||||
\(98\) | 26.5583i | 0.271003i | ||||||||
\(99\) | 32.4628 | + | 5.93023i | 0.327907 | + | 0.0599013i | ||||
\(100\) | −51.9739 | −0.519739 | ||||||||
\(101\) | − | 108.413i | − | 1.07339i | −0.843775 | − | 0.536696i | \(-0.819672\pi\) | ||
0.843775 | − | 0.536696i | \(-0.180328\pi\) | |||||||
\(102\) | 42.3256 | 0.414957 | ||||||||
\(103\) | −6.99136 | −0.0678772 | −0.0339386 | − | 0.999424i | \(-0.510805\pi\) | ||||
−0.0339386 | + | 0.999424i | \(0.510805\pi\) | |||||||
\(104\) | −277.144 | −2.66484 | ||||||||
\(105\) | − | 10.2470i | − | 0.0975900i | ||||||
\(106\) | 82.3064i | 0.776476i | ||||||||
\(107\) | 97.3371i | 0.909693i | 0.890570 | + | 0.454846i | \(0.150306\pi\) | ||||
−0.890570 | + | 0.454846i | \(0.849694\pi\) | |||||||
\(108\) | −54.0128 | −0.500119 | ||||||||
\(109\) | − | 178.540i | − | 1.63798i | −0.573807 | − | 0.818990i | \(-0.694534\pi\) | ||
0.573807 | − | 0.818990i | \(-0.305466\pi\) | |||||||
\(110\) | 16.7702 | − | 91.8020i | 0.152456 | − | 0.834563i | ||||
\(111\) | 124.073 | 1.11777 | ||||||||
\(112\) | − | 133.537i | − | 1.19229i | ||||||
\(113\) | 110.514 | 0.977999 | 0.488999 | − | 0.872284i | \(-0.337362\pi\) | ||||
0.488999 | + | 0.872284i | \(0.337362\pi\) | |||||||
\(114\) | 99.4894 | 0.872714 | ||||||||
\(115\) | −27.5736 | −0.239770 | ||||||||
\(116\) | − | 383.577i | − | 3.30670i | ||||||
\(117\) | 34.2688i | 0.292896i | ||||||||
\(118\) | − | 305.846i | − | 2.59192i | ||||||
\(119\) | 17.0408 | 0.143200 | ||||||||
\(120\) | 93.9666i | 0.783055i | ||||||||
\(121\) | 113.185 | + | 42.7804i | 0.935413 | + | 0.353557i | ||||
\(122\) | 79.8012 | 0.654108 | ||||||||
\(123\) | − | 80.0973i | − | 0.651197i | ||||||
\(124\) | −389.758 | −3.14321 | ||||||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | −30.1143 | −0.239002 | ||||||||
\(127\) | − | 163.597i | − | 1.28817i | −0.764955 | − | 0.644084i | \(-0.777239\pi\) | ||
0.764955 | − | 0.644084i | \(-0.222761\pi\) | |||||||
\(128\) | 215.766i | 1.68567i | ||||||||
\(129\) | 1.21394i | 0.00941041i | ||||||||
\(130\) | 96.9092 | 0.745455 | ||||||||
\(131\) | − | 50.4239i | − | 0.384915i | −0.981305 | − | 0.192457i | \(-0.938354\pi\) | ||
0.981305 | − | 0.192457i | \(-0.0616458\pi\) | |||||||
\(132\) | −194.823 | − | 35.5898i | −1.47593 | − | 0.269620i | ||||
\(133\) | 40.0556 | 0.301170 | ||||||||
\(134\) | 68.8667i | 0.513931i | ||||||||
\(135\) | 11.6190 | 0.0860663 | ||||||||
\(136\) | −156.267 | −1.14902 | ||||||||
\(137\) | 173.912 | 1.26943 | 0.634717 | − | 0.772745i | \(-0.281117\pi\) | ||||
0.634717 | + | 0.772745i | \(0.281117\pi\) | |||||||
\(138\) | 81.0348i | 0.587209i | ||||||||
\(139\) | − | 144.788i | − | 1.04164i | −0.853667 | − | 0.520819i | \(-0.825627\pi\) | ||
0.853667 | − | 0.520819i | \(-0.174373\pi\) | |||||||
\(140\) | 61.4963i | 0.439259i | ||||||||
\(141\) | 62.4126 | 0.442642 | ||||||||
\(142\) | 322.947i | 2.27428i | ||||||||
\(143\) | −22.5802 | + | 123.607i | −0.157903 | + | 0.864382i | ||||
\(144\) | 151.417 | 1.05151 | ||||||||
\(145\) | 82.5131i | 0.569056i | ||||||||
\(146\) | 394.090 | 2.69925 | ||||||||
\(147\) | −12.1244 | −0.0824786 | ||||||||
\(148\) | −744.614 | −5.03118 | ||||||||
\(149\) | 33.0981i | 0.222135i | 0.993813 | + | 0.111067i | \(0.0354269\pi\) | ||||
−0.993813 | + | 0.111067i | \(0.964573\pi\) | |||||||
\(150\) | − | 32.8574i | − | 0.219049i | ||||||
\(151\) | − | 31.0481i | − | 0.205616i | −0.994701 | − | 0.102808i | \(-0.967217\pi\) | ||
0.994701 | − | 0.102808i | \(-0.0327828\pi\) | |||||||
\(152\) | −367.317 | −2.41656 | ||||||||
\(153\) | 19.3224i | 0.126290i | ||||||||
\(154\) | −108.622 | − | 19.8427i | −0.705335 | − | 0.128849i | ||||
\(155\) | 83.8427 | 0.540920 | ||||||||
\(156\) | − | 205.662i | − | 1.31834i | ||||||
\(157\) | −223.833 | −1.42569 | −0.712845 | − | 0.701322i | \(-0.752594\pi\) | ||||
−0.712845 | + | 0.701322i | \(0.752594\pi\) | |||||||
\(158\) | 165.247 | 1.04587 | ||||||||
\(159\) | −37.5744 | −0.236317 | ||||||||
\(160\) | − | 211.187i | − | 1.31992i | ||||||
\(161\) | 32.6255i | 0.202643i | ||||||||
\(162\) | − | 34.1464i | − | 0.210780i | ||||||
\(163\) | −83.3361 | −0.511264 | −0.255632 | − | 0.966774i | \(-0.582284\pi\) | ||||
−0.255632 | + | 0.966774i | \(0.582284\pi\) | |||||||
\(164\) | 480.698i | 2.93108i | ||||||||
\(165\) | 41.9093 | + | 7.65589i | 0.253996 | + | 0.0463993i | ||||
\(166\) | −128.944 | −0.776768 | ||||||||
\(167\) | − | 57.1421i | − | 0.342168i | −0.985256 | − | 0.171084i | \(-0.945273\pi\) | ||
0.985256 | − | 0.171084i | \(-0.0547270\pi\) | |||||||
\(168\) | 111.183 | 0.661802 | ||||||||
\(169\) | 38.5167 | 0.227910 | ||||||||
\(170\) | 54.6422 | 0.321424 | ||||||||
\(171\) | 45.4187i | 0.265607i | ||||||||
\(172\) | − | 7.28539i | − | 0.0423569i | ||||||
\(173\) | 215.222i | 1.24406i | 0.782993 | + | 0.622030i | \(0.213692\pi\) | ||||
−0.782993 | + | 0.622030i | \(0.786308\pi\) | |||||||
\(174\) | 242.494 | 1.39364 | ||||||||
\(175\) | − | 13.2288i | − | 0.0755929i | ||||||
\(176\) | 546.157 | + | 99.7706i | 3.10316 | + | 0.566879i | ||||
\(177\) | 139.624 | 0.788838 | ||||||||
\(178\) | 475.679i | 2.67236i | ||||||||
\(179\) | 214.866 | 1.20037 | 0.600184 | − | 0.799862i | \(-0.295094\pi\) | ||||
0.600184 | + | 0.799862i | \(0.295094\pi\) | |||||||
\(180\) | −69.7303 | −0.387390 | ||||||||
\(181\) | −235.805 | −1.30279 | −0.651394 | − | 0.758739i | \(-0.725816\pi\) | ||||
−0.651394 | + | 0.758739i | \(0.725816\pi\) | |||||||
\(182\) | − | 114.664i | − | 0.630025i | ||||||
\(183\) | 36.4307i | 0.199075i | ||||||||
\(184\) | − | 299.183i | − | 1.62599i | ||||||
\(185\) | 160.177 | 0.865824 | ||||||||
\(186\) | − | 246.401i | − | 1.32474i | ||||||
\(187\) | −12.7318 | + | 69.6955i | −0.0680846 | + | 0.372703i | ||||
\(188\) | −374.564 | −1.99236 | ||||||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | 128.440 | 0.676002 | ||||||||
\(191\) | 186.716 | 0.977568 | 0.488784 | − | 0.872405i | \(-0.337441\pi\) | ||||
0.488784 | + | 0.872405i | \(0.337441\pi\) | |||||||
\(192\) | −270.966 | −1.41128 | ||||||||
\(193\) | 303.729i | 1.57372i | 0.617130 | + | 0.786862i | \(0.288295\pi\) | ||||
−0.617130 | + | 0.786862i | \(0.711705\pi\) | |||||||
\(194\) | 438.231i | 2.25892i | ||||||||
\(195\) | 44.2408i | 0.226876i | ||||||||
\(196\) | 72.7634 | 0.371242 | ||||||||
\(197\) | 220.622i | 1.11991i | 0.828523 | + | 0.559955i | \(0.189182\pi\) | ||||
−0.828523 | + | 0.559955i | \(0.810818\pi\) | |||||||
\(198\) | 22.4995 | − | 123.165i | 0.113634 | − | 0.622047i | ||||
\(199\) | 122.270 | 0.614425 | 0.307212 | − | 0.951641i | \(-0.400604\pi\) | ||||
0.307212 | + | 0.951641i | \(0.400604\pi\) | |||||||
\(200\) | 121.310i | 0.606552i | ||||||||
\(201\) | −31.4389 | −0.156413 | ||||||||
\(202\) | −411.322 | −2.03625 | ||||||||
\(203\) | 97.6308 | 0.480940 | ||||||||
\(204\) | − | 115.962i | − | 0.568442i | ||||||
\(205\) | − | 103.405i | − | 0.504415i | ||||||
\(206\) | 26.5255i | 0.128765i | ||||||||
\(207\) | −36.9939 | −0.178714 | ||||||||
\(208\) | 576.541i | 2.77183i | ||||||||
\(209\) | −29.9270 | + | 163.824i | −0.143192 | + | 0.783848i | ||||
\(210\) | −38.8774 | −0.185130 | ||||||||
\(211\) | 226.174i | 1.07192i | 0.844245 | + | 0.535958i | \(0.180049\pi\) | ||||
−0.844245 | + | 0.535958i | \(0.819951\pi\) | |||||||
\(212\) | 225.500 | 1.06368 | ||||||||
\(213\) | −147.431 | −0.692166 | ||||||||
\(214\) | 369.301 | 1.72571 | ||||||||
\(215\) | 1.56719i | 0.00728928i | ||||||||
\(216\) | 126.069i | 0.583655i | ||||||||
\(217\) | − | 99.2040i | − | 0.457161i | ||||||
\(218\) | −677.388 | −3.10729 | ||||||||
\(219\) | 179.909i | 0.821504i | ||||||||
\(220\) | −251.515 | − | 45.9463i | −1.14325 | − | 0.208847i | ||||
\(221\) | −73.5729 | −0.332909 | ||||||||
\(222\) | − | 470.738i | − | 2.12044i | ||||||
\(223\) | 343.952 | 1.54239 | 0.771193 | − | 0.636601i | \(-0.219660\pi\) | ||||
0.771193 | + | 0.636601i | \(0.219660\pi\) | |||||||
\(224\) | −249.880 | −1.11554 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | − | 419.294i | − | 1.85529i | ||||||
\(227\) | − | 40.9631i | − | 0.180454i | −0.995921 | − | 0.0902271i | \(-0.971241\pi\) | ||
0.995921 | − | 0.0902271i | \(-0.0287593\pi\) | |||||||
\(228\) | − | 272.577i | − | 1.19551i | ||||||
\(229\) | 34.1390 | 0.149079 | 0.0745394 | − | 0.997218i | \(-0.476251\pi\) | ||||
0.0745394 | + | 0.997218i | \(0.476251\pi\) | |||||||
\(230\) | 104.615i | 0.454850i | ||||||||
\(231\) | 9.05857 | − | 49.5877i | 0.0392146 | − | 0.214665i | ||||
\(232\) | −895.294 | −3.85902 | ||||||||
\(233\) | − | 356.584i | − | 1.53041i | −0.643790 | − | 0.765203i | \(-0.722639\pi\) | ||
0.643790 | − | 0.765203i | \(-0.277361\pi\) | |||||||
\(234\) | 130.017 | 0.555629 | ||||||||
\(235\) | 80.5743 | 0.342869 | ||||||||
\(236\) | −837.945 | −3.55061 | ||||||||
\(237\) | 75.4384i | 0.318305i | ||||||||
\(238\) | − | 64.6535i | − | 0.271653i | ||||||
\(239\) | − | 85.5789i | − | 0.358071i | −0.983843 | − | 0.179035i | \(-0.942702\pi\) | ||
0.983843 | − | 0.179035i | \(-0.0572977\pi\) | |||||||
\(240\) | 195.478 | 0.814493 | ||||||||
\(241\) | 57.4930i | 0.238560i | 0.992861 | + | 0.119280i | \(0.0380586\pi\) | ||||
−0.992861 | + | 0.119280i | \(0.961941\pi\) | |||||||
\(242\) | 162.311 | − | 429.429i | 0.670705 | − | 1.77450i | ||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 218.636i | − | 0.896050i | ||||||
\(245\) | −15.6525 | −0.0638877 | ||||||||
\(246\) | −303.893 | −1.23534 | ||||||||
\(247\) | −172.938 | −0.700155 | ||||||||
\(248\) | 909.720i | 3.66823i | ||||||||
\(249\) | − | 58.8651i | − | 0.236406i | ||||||
\(250\) | − | 42.4187i | − | 0.169675i | ||||||
\(251\) | −285.926 | −1.13915 | −0.569574 | − | 0.821940i | \(-0.692892\pi\) | ||||
−0.569574 | + | 0.821940i | \(0.692892\pi\) | |||||||
\(252\) | 82.5060i | 0.327405i | ||||||||
\(253\) | −133.436 | − | 24.3758i | −0.527415 | − | 0.0963470i | ||||
\(254\) | −620.695 | −2.44368 | ||||||||
\(255\) | 24.9451i | 0.0978241i | ||||||||
\(256\) | 192.858 | 0.753350 | ||||||||
\(257\) | 226.034 | 0.879510 | 0.439755 | − | 0.898118i | \(-0.355065\pi\) | ||||
0.439755 | + | 0.898118i | \(0.355065\pi\) | |||||||
\(258\) | 4.60576 | 0.0178518 | ||||||||
\(259\) | − | 189.524i | − | 0.731754i | ||||||
\(260\) | − | 265.508i | − | 1.02118i | ||||||
\(261\) | 110.703i | 0.424149i | ||||||||
\(262\) | −191.310 | −0.730192 | ||||||||
\(263\) | 339.512i | 1.29092i | 0.763794 | + | 0.645461i | \(0.223335\pi\) | ||||
−0.763794 | + | 0.645461i | \(0.776665\pi\) | |||||||
\(264\) | −83.0689 | + | 454.729i | −0.314655 | + | 1.72246i | ||||
\(265\) | −48.5083 | −0.183050 | ||||||||
\(266\) | − | 151.973i | − | 0.571326i | ||||||
\(267\) | −217.156 | −0.813320 | ||||||||
\(268\) | 188.678 | 0.704024 | ||||||||
\(269\) | 75.4600 | 0.280521 | 0.140260 | − | 0.990115i | \(-0.455206\pi\) | ||||
0.140260 | + | 0.990115i | \(0.455206\pi\) | |||||||
\(270\) | − | 44.0828i | − | 0.163270i | ||||||
\(271\) | 46.9854i | 0.173378i | 0.996235 | + | 0.0866889i | \(0.0276286\pi\) | ||||
−0.996235 | + | 0.0866889i | \(0.972371\pi\) | |||||||
\(272\) | 325.082i | 1.19515i | ||||||||
\(273\) | 52.3464 | 0.191745 | ||||||||
\(274\) | − | 659.831i | − | 2.40814i | ||||||
\(275\) | 54.1046 | + | 9.88371i | 0.196744 | + | 0.0359408i | ||||
\(276\) | 222.016 | 0.804406 | ||||||||
\(277\) | 482.230i | 1.74090i | 0.492255 | + | 0.870451i | \(0.336173\pi\) | ||||
−0.492255 | + | 0.870451i | \(0.663827\pi\) | |||||||
\(278\) | −549.331 | −1.97601 | ||||||||
\(279\) | 112.487 | 0.403178 | ||||||||
\(280\) | 143.536 | 0.512630 | ||||||||
\(281\) | − | 533.222i | − | 1.89759i | −0.315894 | − | 0.948794i | \(-0.602304\pi\) | ||
0.315894 | − | 0.948794i | \(-0.397696\pi\) | |||||||
\(282\) | − | 236.796i | − | 0.839702i | ||||||
\(283\) | 104.404i | 0.368920i | 0.982840 | + | 0.184460i | \(0.0590535\pi\) | ||||
−0.982840 | + | 0.184460i | \(0.940946\pi\) | |||||||
\(284\) | 884.799 | 3.11549 | ||||||||
\(285\) | 58.6353i | 0.205738i | ||||||||
\(286\) | 468.969 | + | 85.6702i | 1.63975 | + | 0.299546i | ||||
\(287\) | −122.351 | −0.426309 | ||||||||
\(288\) | − | 283.337i | − | 0.983810i | ||||||
\(289\) | 247.516 | 0.856457 | ||||||||
\(290\) | 313.058 | 1.07951 | ||||||||
\(291\) | −200.060 | −0.687492 | ||||||||
\(292\) | − | 1079.71i | − | 3.69765i | ||||||
\(293\) | − | 125.564i | − | 0.428545i | −0.976774 | − | 0.214272i | \(-0.931262\pi\) | ||
0.976774 | − | 0.214272i | \(-0.0687380\pi\) | |||||||
\(294\) | 46.0003i | 0.156464i | ||||||||
\(295\) | 180.254 | 0.611031 | ||||||||
\(296\) | 1737.98i | 5.87154i | ||||||||
\(297\) | 56.2272 | + | 10.2715i | 0.189317 | + | 0.0345840i | ||||
\(298\) | 125.576 | 0.421395 | ||||||||
\(299\) | − | 140.859i | − | 0.471102i | ||||||
\(300\) | −90.0214 | −0.300071 | ||||||||
\(301\) | 1.85433 | 0.00616056 | ||||||||
\(302\) | −117.798 | −0.390059 | ||||||||
\(303\) | − | 187.776i | − | 0.619724i | ||||||
\(304\) | 764.129i | 2.51358i | ||||||||
\(305\) | 47.0318i | 0.154203i | ||||||||
\(306\) | 73.3101 | 0.239576 | ||||||||
\(307\) | 357.902i | 1.16580i | 0.812543 | + | 0.582902i | \(0.198083\pi\) | ||||
−0.812543 | + | 0.582902i | \(0.801917\pi\) | |||||||
\(308\) | −54.3644 | + | 297.597i | −0.176508 | + | 0.966224i | ||||
\(309\) | −12.1094 | −0.0391889 | ||||||||
\(310\) | − | 318.103i | − | 1.02614i | ||||||
\(311\) | 497.178 | 1.59864 | 0.799321 | − | 0.600905i | \(-0.205193\pi\) | ||||
0.799321 | + | 0.600905i | \(0.205193\pi\) | |||||||
\(312\) | −480.027 | −1.53855 | ||||||||
\(313\) | 168.118 | 0.537118 | 0.268559 | − | 0.963263i | \(-0.413453\pi\) | ||||
0.268559 | + | 0.963263i | \(0.413453\pi\) | |||||||
\(314\) | 849.233i | 2.70456i | ||||||||
\(315\) | − | 17.7482i | − | 0.0563436i | ||||||
\(316\) | − | 452.738i | − | 1.43271i | ||||||
\(317\) | −81.4840 | −0.257047 | −0.128524 | − | 0.991706i | \(-0.541024\pi\) | ||||
−0.128524 | + | 0.991706i | \(0.541024\pi\) | |||||||
\(318\) | 142.559i | 0.448299i | ||||||||
\(319\) | −72.9437 | + | 399.303i | −0.228664 | + | 1.25173i | ||||
\(320\) | −349.816 | −1.09317 | ||||||||
\(321\) | 168.593i | 0.525211i | ||||||||
\(322\) | 123.783 | 0.384418 | ||||||||
\(323\) | −97.5111 | −0.301892 | ||||||||
\(324\) | −93.5530 | −0.288744 | ||||||||
\(325\) | 57.1146i | 0.175737i | ||||||||
\(326\) | 316.181i | 0.969880i | ||||||||
\(327\) | − | 309.240i | − | 0.945689i | ||||||
\(328\) | 1121.98 | 3.42067 | ||||||||
\(329\) | − | 95.3368i | − | 0.289777i | ||||||
\(330\) | 29.0468 | − | 159.006i | 0.0880206 | − | 0.481835i | ||||
\(331\) | −103.610 | −0.313020 | −0.156510 | − | 0.987676i | \(-0.550024\pi\) | ||||
−0.156510 | + | 0.987676i | \(0.550024\pi\) | |||||||
\(332\) | 353.274i | 1.06408i | ||||||||
\(333\) | 214.900 | 0.645347 | ||||||||
\(334\) | −216.800 | −0.649101 | ||||||||
\(335\) | −40.5875 | −0.121157 | ||||||||
\(336\) | − | 231.293i | − | 0.688372i | ||||||
\(337\) | 17.0836i | 0.0506932i | 0.999679 | + | 0.0253466i | \(0.00806894\pi\) | ||||
−0.999679 | + | 0.0253466i | \(0.991931\pi\) | |||||||
\(338\) | − | 146.134i | − | 0.432350i | ||||||
\(339\) | 191.416 | 0.564648 | ||||||||
\(340\) | − | 149.706i | − | 0.440313i | ||||||
\(341\) | 405.737 | + | 74.1191i | 1.18984 | + | 0.217358i | ||||
\(342\) | 172.321 | 0.503862 | ||||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | −17.0046 | −0.0494319 | ||||||||
\(345\) | −47.7589 | −0.138432 | ||||||||
\(346\) | 816.563 | 2.36001 | ||||||||
\(347\) | − | 649.237i | − | 1.87100i | −0.353327 | − | 0.935500i | \(-0.614950\pi\) | ||
0.353327 | − | 0.935500i | \(-0.385050\pi\) | |||||||
\(348\) | − | 664.375i | − | 1.90912i | ||||||
\(349\) | − | 276.848i | − | 0.793259i | −0.917979 | − | 0.396630i | \(-0.870180\pi\) | ||
0.917979 | − | 0.396630i | \(-0.129820\pi\) | |||||||
\(350\) | −50.1905 | −0.143401 | ||||||||
\(351\) | 59.3553i | 0.169103i | ||||||||
\(352\) | 186.695 | − | 1021.99i | 0.530383 | − | 2.90338i | ||||
\(353\) | 174.078 | 0.493138 | 0.246569 | − | 0.969125i | \(-0.420697\pi\) | ||||
0.246569 | + | 0.969125i | \(0.420697\pi\) | |||||||
\(354\) | − | 529.741i | − | 1.49644i | ||||||
\(355\) | −190.333 | −0.536150 | ||||||||
\(356\) | 1303.25 | 3.66081 | ||||||||
\(357\) | 29.5155 | 0.0826764 | ||||||||
\(358\) | − | 815.211i | − | 2.27712i | ||||||
\(359\) | − | 54.5892i | − | 0.152059i | −0.997106 | − | 0.0760295i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760295i | \(-0.0242243\pi\) | |||||||
\(360\) | 162.755i | 0.452097i | ||||||||
\(361\) | 131.793 | 0.365078 | ||||||||
\(362\) | 894.654i | 2.47142i | ||||||||
\(363\) | 196.042 | + | 74.0978i | 0.540061 | + | 0.204126i | ||||
\(364\) | −314.153 | −0.863058 | ||||||||
\(365\) | 232.262i | 0.636335i | ||||||||
\(366\) | 138.220 | 0.377650 | ||||||||
\(367\) | −720.700 | −1.96376 | −0.981880 | − | 0.189502i | \(-0.939313\pi\) | ||||
−0.981880 | + | 0.189502i | \(0.939313\pi\) | |||||||
\(368\) | −622.388 | −1.69127 | ||||||||
\(369\) | − | 138.733i | − | 0.375969i | ||||||
\(370\) | − | 607.720i | − | 1.64249i | ||||||
\(371\) | 57.3958i | 0.154706i | ||||||||
\(372\) | −675.081 | −1.81473 | ||||||||
\(373\) | − | 482.361i | − | 1.29319i | −0.762832 | − | 0.646596i | \(-0.776192\pi\) | ||
0.762832 | − | 0.646596i | \(-0.223808\pi\) | |||||||
\(374\) | 264.428 | + | 48.3051i | 0.707027 | + | 0.129158i | ||||
\(375\) | 19.3649 | 0.0516398 | ||||||||
\(376\) | 874.257i | 2.32515i | ||||||||
\(377\) | −421.517 | −1.11808 | ||||||||
\(378\) | −52.1595 | −0.137988 | ||||||||
\(379\) | −78.1531 | −0.206209 | −0.103104 | − | 0.994671i | \(-0.532878\pi\) | ||||
−0.103104 | + | 0.994671i | \(0.532878\pi\) | |||||||
\(380\) | − | 351.896i | − | 0.926041i | ||||||
\(381\) | − | 283.359i | − | 0.743724i | ||||||
\(382\) | − | 708.407i | − | 1.85447i | ||||||
\(383\) | −39.3013 | −0.102614 | −0.0513071 | − | 0.998683i | \(-0.516339\pi\) | ||||
−0.0513071 | + | 0.998683i | \(0.516339\pi\) | |||||||
\(384\) | 373.718i | 0.973224i | ||||||||
\(385\) | 11.6946 | − | 64.0175i | 0.0303755 | − | 0.166279i | ||||
\(386\) | 1152.36 | 2.98539 | ||||||||
\(387\) | 2.10261i | 0.00543311i | ||||||||
\(388\) | 1200.65 | 3.09445 | ||||||||
\(389\) | −185.063 | −0.475741 | −0.237870 | − | 0.971297i | \(-0.576449\pi\) | ||||
−0.237870 | + | 0.971297i | \(0.576449\pi\) | |||||||
\(390\) | 167.852 | 0.430389 | ||||||||
\(391\) | − | 79.4235i | − | 0.203129i | ||||||
\(392\) | − | 169.834i | − | 0.433251i | ||||||
\(393\) | − | 87.3367i | − | 0.222231i | ||||||
\(394\) | 837.051 | 2.12449 | ||||||||
\(395\) | 97.3905i | 0.246558i | ||||||||
\(396\) | −337.443 | − | 61.6434i | −0.852130 | − | 0.155665i | ||||
\(397\) | 647.463 | 1.63089 | 0.815445 | − | 0.578835i | \(-0.196492\pi\) | ||||
0.815445 | + | 0.578835i | \(0.196492\pi\) | |||||||
\(398\) | − | 463.900i | − | 1.16558i | ||||||
\(399\) | 69.3783 | 0.173880 | ||||||||
\(400\) | 252.361 | 0.630903 | ||||||||
\(401\) | 81.9779 | 0.204434 | 0.102217 | − | 0.994762i | \(-0.467406\pi\) | ||||
0.102217 | + | 0.994762i | \(0.467406\pi\) | |||||||
\(402\) | 119.281i | 0.296718i | ||||||||
\(403\) | 428.309i | 1.06280i | ||||||||
\(404\) | 1126.93i | 2.78942i | ||||||||
\(405\) | 20.1246 | 0.0496904 | ||||||||
\(406\) | − | 370.416i | − | 0.912354i | ||||||
\(407\) | 775.141 | + | 141.601i | 1.90452 | + | 0.347914i | ||||
\(408\) | −270.663 | −0.663389 | ||||||||
\(409\) | − | 618.678i | − | 1.51266i | −0.654190 | − | 0.756331i | \(-0.726990\pi\) | ||
0.654190 | − | 0.756331i | \(-0.273010\pi\) | |||||||
\(410\) | −392.324 | −0.956887 | ||||||||
\(411\) | 301.225 | 0.732908 | ||||||||
\(412\) | 72.6736 | 0.176392 | ||||||||
\(413\) | − | 213.280i | − | 0.516416i | ||||||
\(414\) | 140.356i | 0.339025i | ||||||||
\(415\) | − | 75.9945i | − | 0.183119i | ||||||
\(416\) | 1078.85 | 2.59338 | ||||||||
\(417\) | − | 250.780i | − | 0.601390i | ||||||
\(418\) | 621.557 | + | 113.545i | 1.48698 | + | 0.271638i | ||||
\(419\) | 360.854 | 0.861228 | 0.430614 | − | 0.902536i | \(-0.358297\pi\) | ||||
0.430614 | + | 0.902536i | \(0.358297\pi\) | |||||||
\(420\) | 106.515i | 0.253607i | ||||||||
\(421\) | −779.460 | −1.85145 | −0.925725 | − | 0.378197i | \(-0.876544\pi\) | ||||
−0.925725 | + | 0.378197i | \(0.876544\pi\) | |||||||
\(422\) | 858.115 | 2.03345 | ||||||||
\(423\) | 108.102 | 0.255560 | ||||||||
\(424\) | − | 526.331i | − | 1.24135i | ||||||
\(425\) | 32.2040i | 0.0757742i | ||||||||
\(426\) | 559.361i | 1.31305i | ||||||||
\(427\) | 55.6488 | 0.130325 | ||||||||
\(428\) | − | 1011.80i | − | 2.36401i | ||||||
\(429\) | −39.1100 | + | 214.093i | −0.0911656 | + | 0.499051i | ||||
\(430\) | 5.94600 | 0.0138279 | ||||||||
\(431\) | 282.147i | 0.654634i | 0.944915 | + | 0.327317i | \(0.106144\pi\) | ||||
−0.944915 | + | 0.327317i | \(0.893856\pi\) | |||||||
\(432\) | 262.262 | 0.607087 | ||||||||
\(433\) | −670.676 | −1.54891 | −0.774453 | − | 0.632631i | \(-0.781975\pi\) | ||||
−0.774453 | + | 0.632631i | \(0.781975\pi\) | |||||||
\(434\) | −376.384 | −0.867245 | ||||||||
\(435\) | 142.917i | 0.328544i | ||||||||
\(436\) | 1855.88i | 4.25661i | ||||||||
\(437\) | − | 186.691i | − | 0.427210i | ||||||
\(438\) | 682.584 | 1.55841 | ||||||||
\(439\) | 426.904i | 0.972447i | 0.873835 | + | 0.486223i | \(0.161626\pi\) | ||||
−0.873835 | + | 0.486223i | \(0.838374\pi\) | |||||||
\(440\) | −107.241 | + | 587.053i | −0.243731 | + | 1.33421i | ||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | 279.139i | 0.631536i | ||||||||
\(443\) | 11.0112 | 0.0248560 | 0.0124280 | − | 0.999923i | \(-0.496044\pi\) | ||||
0.0124280 | + | 0.999923i | \(0.496044\pi\) | |||||||
\(444\) | −1289.71 | −2.90475 | ||||||||
\(445\) | −280.348 | −0.629995 | ||||||||
\(446\) | − | 1304.97i | − | 2.92594i | ||||||
\(447\) | 57.3275i | 0.128250i | ||||||||
\(448\) | 413.908i | 0.923901i | ||||||||
\(449\) | 428.106 | 0.953464 | 0.476732 | − | 0.879049i | \(-0.341821\pi\) | ||||
0.476732 | + | 0.879049i | \(0.341821\pi\) | |||||||
\(450\) | − | 56.9107i | − | 0.126468i | ||||||
\(451\) | 91.4128 | − | 500.405i | 0.202689 | − | 1.10955i | ||||
\(452\) | −1148.77 | −2.54152 | ||||||||
\(453\) | − | 53.7768i | − | 0.118713i | ||||||
\(454\) | −155.416 | −0.342326 | ||||||||
\(455\) | 67.5789 | 0.148525 | ||||||||
\(456\) | −636.212 | −1.39520 | ||||||||
\(457\) | 419.530i | 0.918009i | 0.888434 | + | 0.459004i | \(0.151794\pi\) | ||||
−0.888434 | + | 0.459004i | \(0.848206\pi\) | |||||||
\(458\) | − | 129.525i | − | 0.282806i | ||||||
\(459\) | 33.4674i | 0.0729138i | ||||||||
\(460\) | 286.621 | 0.623090 | ||||||||
\(461\) | 50.8690i | 0.110345i | 0.998477 | + | 0.0551724i | \(0.0175708\pi\) | ||||
−0.998477 | + | 0.0551724i | \(0.982429\pi\) | |||||||
\(462\) | −188.138 | − | 34.3686i | −0.407225 | − | 0.0743910i | ||||
\(463\) | 213.799 | 0.461769 | 0.230884 | − | 0.972981i | \(-0.425838\pi\) | ||||
0.230884 | + | 0.972981i | \(0.425838\pi\) | |||||||
\(464\) | 1862.48i | 4.01396i | ||||||||
\(465\) | 145.220 | 0.312301 | ||||||||
\(466\) | −1352.90 | −2.90321 | ||||||||
\(467\) | −421.138 | −0.901794 | −0.450897 | − | 0.892576i | \(-0.648896\pi\) | ||||
−0.450897 | + | 0.892576i | \(0.648896\pi\) | |||||||
\(468\) | − | 356.216i | − | 0.761146i | ||||||
\(469\) | 48.0237i | 0.102396i | ||||||||
\(470\) | − | 305.702i | − | 0.650431i | ||||||
\(471\) | −387.691 | −0.823122 | ||||||||
\(472\) | 1955.82i | 4.14368i | ||||||||
\(473\) | −1.38544 | + | 7.58407i | −0.00292905 | + | 0.0160340i | ||||
\(474\) | 286.217 | 0.603832 | ||||||||
\(475\) | 75.6979i | 0.159364i | ||||||||
\(476\) | −177.135 | −0.372132 | ||||||||
\(477\) | −65.0808 | −0.136438 | ||||||||
\(478\) | −324.690 | −0.679268 | ||||||||
\(479\) | 465.160i | 0.971107i | 0.874207 | + | 0.485553i | \(0.161382\pi\) | ||||
−0.874207 | + | 0.485553i | \(0.838618\pi\) | |||||||
\(480\) | − | 365.787i | − | 0.762056i | ||||||
\(481\) | 818.264i | 1.70117i | ||||||||
\(482\) | 218.131 | 0.452554 | ||||||||
\(483\) | 56.5091i | 0.116996i | ||||||||
\(484\) | −1176.53 | − | 444.692i | −2.43085 | − | 0.918786i | ||||
\(485\) | −258.277 | −0.532529 | ||||||||
\(486\) | − | 59.1433i | − | 0.121694i | ||||||
\(487\) | 596.434 | 1.22471 | 0.612355 | − | 0.790583i | \(-0.290222\pi\) | ||||
0.612355 | + | 0.790583i | \(0.290222\pi\) | |||||||
\(488\) | −510.311 | −1.04572 | ||||||||
\(489\) | −144.342 | −0.295179 | ||||||||
\(490\) | 59.3862i | 0.121196i | ||||||||
\(491\) | 459.925i | 0.936710i | 0.883540 | + | 0.468355i | \(0.155153\pi\) | ||||
−0.883540 | + | 0.468355i | \(0.844847\pi\) | |||||||
\(492\) | 832.593i | 1.69226i | ||||||||
\(493\) | −237.672 | −0.482093 | ||||||||
\(494\) | 656.136i | 1.32821i | ||||||||
\(495\) | 72.5890 | + | 13.2604i | 0.146644 | + | 0.0267887i | ||||
\(496\) | 1892.49 | 3.81550 | ||||||||
\(497\) | 225.205i | 0.453129i | ||||||||
\(498\) | −223.337 | −0.448467 | ||||||||
\(499\) | −536.311 | −1.07477 | −0.537386 | − | 0.843336i | \(-0.680588\pi\) | ||||
−0.537386 | + | 0.843336i | \(0.680588\pi\) | |||||||
\(500\) | −116.217 | −0.232434 | ||||||||
\(501\) | − | 98.9730i | − | 0.197551i | ||||||
\(502\) | 1084.82i | 2.16099i | ||||||||
\(503\) | − | 706.964i | − | 1.40549i | −0.711439 | − | 0.702747i | \(-0.751956\pi\) | ||
0.711439 | − | 0.702747i | \(-0.248044\pi\) | |||||||
\(504\) | 192.574 | 0.382092 | ||||||||
\(505\) | − | 242.418i | − | 0.480036i | ||||||
\(506\) | −92.4828 | + | 506.262i | −0.182772 | + | 1.00052i | ||||
\(507\) | 66.7130 | 0.131584 | ||||||||
\(508\) | 1700.56i | 3.34755i | ||||||||
\(509\) | −716.152 | −1.40698 | −0.703490 | − | 0.710706i | \(-0.748376\pi\) | ||||
−0.703490 | + | 0.710706i | \(0.748376\pi\) | |||||||
\(510\) | 94.6430 | 0.185574 | ||||||||
\(511\) | 274.816 | 0.537801 | ||||||||
\(512\) | 131.355i | 0.256553i | ||||||||
\(513\) | 78.6676i | 0.153348i | ||||||||
\(514\) | − | 857.583i | − | 1.66845i | ||||||
\(515\) | −15.6331 | −0.0303556 | ||||||||
\(516\) | − | 12.6187i | − | 0.0244548i | ||||||
\(517\) | 389.920 | + | 71.2298i | 0.754198 | + | 0.137775i | ||||
\(518\) | −719.064 | −1.38815 | ||||||||
\(519\) | 372.776i | 0.718259i | ||||||||
\(520\) | −619.712 | −1.19175 | ||||||||
\(521\) | −540.716 | −1.03784 | −0.518921 | − | 0.854822i | \(-0.673666\pi\) | ||||
−0.518921 | + | 0.854822i | \(0.673666\pi\) | |||||||
\(522\) | 420.012 | 0.804620 | ||||||||
\(523\) | 830.514i | 1.58798i | 0.607930 | + | 0.793991i | \(0.292000\pi\) | ||||
−0.607930 | + | 0.793991i | \(0.708000\pi\) | |||||||
\(524\) | 524.145i | 1.00028i | ||||||||
\(525\) | − | 22.9129i | − | 0.0436436i | ||||||
\(526\) | 1288.12 | 2.44891 | ||||||||
\(527\) | 241.502i | 0.458258i | ||||||||
\(528\) | 945.971 | + | 172.808i | 1.79161 | + | 0.327288i | ||||
\(529\) | −376.939 | −0.712551 | ||||||||
\(530\) | 184.043i | 0.347251i | ||||||||
\(531\) | 241.836 | 0.455436 | ||||||||
\(532\) | −416.369 | −0.782648 | ||||||||
\(533\) | 528.244 | 0.991077 | ||||||||
\(534\) | 823.901i | 1.54289i | ||||||||
\(535\) | 217.652i | 0.406827i | ||||||||
\(536\) | − | 440.387i | − | 0.821618i | ||||||
\(537\) | 372.159 | 0.693033 | ||||||||
\(538\) | − | 286.299i | − | 0.532154i | ||||||
\(539\) | −75.7465 | − | 13.8372i | −0.140532 | − | 0.0256720i | ||||
\(540\) | −120.776 | −0.223660 | ||||||||
\(541\) | 563.661i | 1.04189i | 0.853591 | + | 0.520944i | \(0.174420\pi\) | ||||
−0.853591 | + | 0.520944i | \(0.825580\pi\) | |||||||
\(542\) | 178.265 | 0.328902 | ||||||||
\(543\) | −408.426 | −0.752166 | ||||||||
\(544\) | 608.307 | 1.11821 | ||||||||
\(545\) | − | 399.227i | − | 0.732527i | ||||||
\(546\) | − | 198.605i | − | 0.363745i | ||||||
\(547\) | − | 313.843i | − | 0.573753i | −0.957968 | − | 0.286877i | \(-0.907383\pi\) | ||
0.957968 | − | 0.286877i | \(-0.0926170\pi\) | |||||||
\(548\) | −1807.78 | −3.29887 | ||||||||
\(549\) | 63.0998i | 0.114936i | ||||||||
\(550\) | 37.4992 | − | 205.275i | 0.0681804 | − | 0.373228i | ||||
\(551\) | −558.665 | −1.01391 | ||||||||
\(552\) | − | 518.199i | − | 0.938767i | ||||||
\(553\) | 115.234 | 0.208380 | ||||||||
\(554\) | 1829.60 | 3.30253 | ||||||||
\(555\) | 277.435 | 0.499883 | ||||||||
\(556\) | 1505.03i | 2.70690i | ||||||||
\(557\) | − | 326.419i | − | 0.586031i | −0.956108 | − | 0.293016i | \(-0.905341\pi\) | ||
0.956108 | − | 0.293016i | \(-0.0946588\pi\) | |||||||
\(558\) | − | 426.780i | − | 0.764838i | ||||||
\(559\) | −8.00599 | −0.0143220 | ||||||||
\(560\) | − | 298.598i | − | 0.533211i | ||||||
\(561\) | −22.0522 | + | 120.716i | −0.0393087 | + | 0.215180i | ||||
\(562\) | −2023.07 | −3.59977 | ||||||||
\(563\) | − | 861.940i | − | 1.53098i | −0.643450 | − | 0.765488i | \(-0.722497\pi\) | ||
0.643450 | − | 0.765488i | \(-0.277503\pi\) | |||||||
\(564\) | −648.765 | −1.15029 | ||||||||
\(565\) | 247.116 | 0.437374 | ||||||||
\(566\) | 396.114 | 0.699849 | ||||||||
\(567\) | − | 23.8118i | − | 0.0419961i | ||||||
\(568\) | − | 2065.18i | − | 3.63587i | ||||||
\(569\) | − | 955.752i | − | 1.67971i | −0.542814 | − | 0.839853i | \(-0.682641\pi\) | ||
0.542814 | − | 0.839853i | \(-0.317359\pi\) | |||||||
\(570\) | 222.465 | 0.390290 | ||||||||
\(571\) | − | 601.731i | − | 1.05382i | −0.849921 | − | 0.526910i | \(-0.823351\pi\) | ||
0.849921 | − | 0.526910i | \(-0.176649\pi\) | |||||||
\(572\) | 234.716 | − | 1284.86i | 0.410343 | − | 2.24627i | ||||
\(573\) | 323.401 | 0.564399 | ||||||||
\(574\) | 464.204i | 0.808717i | ||||||||
\(575\) | −61.6565 | −0.107229 | ||||||||
\(576\) | −469.327 | −0.814804 | ||||||||
\(577\) | −861.319 | −1.49275 | −0.746377 | − | 0.665524i | \(-0.768208\pi\) | ||||
−0.746377 | + | 0.665524i | \(0.768208\pi\) | |||||||
\(578\) | − | 939.087i | − | 1.62472i | ||||||
\(579\) | 526.073i | 0.908590i | ||||||||
\(580\) | − | 857.705i | − | 1.47880i | ||||||
\(581\) | −89.9179 | −0.154764 | ||||||||
\(582\) | 759.038i | 1.30419i | ||||||||
\(583\) | −234.745 | − | 42.8826i | −0.402650 | − | 0.0735551i | ||||
\(584\) | −2520.12 | −4.31527 | ||||||||
\(585\) | 76.6273i | 0.130987i | ||||||||
\(586\) | −476.394 | −0.812959 | ||||||||
\(587\) | −354.226 | −0.603451 | −0.301726 | − | 0.953395i | \(-0.597563\pi\) | ||||
−0.301726 | + | 0.953395i | \(0.597563\pi\) | |||||||
\(588\) | 126.030 | 0.214337 | ||||||||
\(589\) | 567.667i | 0.963782i | ||||||||
\(590\) | − | 683.893i | − | 1.15914i | ||||||
\(591\) | 382.129i | 0.646580i | ||||||||
\(592\) | 3615.50 | 6.10727 | ||||||||
\(593\) | 297.046i | 0.500921i | 0.968127 | + | 0.250460i | \(0.0805820\pi\) | ||||
−0.968127 | + | 0.250460i | \(0.919418\pi\) | |||||||
\(594\) | 38.9704 | − | 213.328i | 0.0656067 | − | 0.359139i | ||||
\(595\) | 38.1043 | 0.0640409 | ||||||||
\(596\) | − | 344.047i | − | 0.577260i | ||||||
\(597\) | 211.779 | 0.354738 | ||||||||
\(598\) | −534.427 | −0.893691 | ||||||||
\(599\) | 1009.59 | 1.68547 | 0.842733 | − | 0.538332i | \(-0.180945\pi\) | ||||
0.842733 | + | 0.538332i | \(0.180945\pi\) | |||||||
\(600\) | 210.116i | 0.350193i | ||||||||
\(601\) | 619.434i | 1.03067i | 0.856988 | + | 0.515336i | \(0.172333\pi\) | ||||
−0.856988 | + | 0.515336i | \(0.827667\pi\) | |||||||
\(602\) | − | 7.03541i | − | 0.0116867i | ||||||
\(603\) | −54.4538 | −0.0903048 | ||||||||
\(604\) | 322.738i | 0.534334i | ||||||||
\(605\) | 253.089 | + | 95.6598i | 0.418329 | + | 0.158115i | ||||
\(606\) | −712.431 | −1.17563 | ||||||||
\(607\) | 65.3491i | 0.107659i | 0.998550 | + | 0.0538296i | \(0.0171428\pi\) | ||||
−0.998550 | + | 0.0538296i | \(0.982857\pi\) | |||||||
\(608\) | 1429.87 | 2.35176 | ||||||||
\(609\) | 169.101 | 0.277671 | ||||||||
\(610\) | 178.441 | 0.292526 | ||||||||
\(611\) | 411.613i | 0.673671i | ||||||||
\(612\) | − | 200.852i | − | 0.328190i | ||||||
\(613\) | − | 930.121i | − | 1.51733i | −0.651483 | − | 0.758663i | \(-0.725853\pi\) | ||
0.651483 | − | 0.758663i | \(-0.274147\pi\) | |||||||
\(614\) | 1357.89 | 2.21156 | ||||||||
\(615\) | − | 179.103i | − | 0.291224i | ||||||
\(616\) | 694.610 | + | 126.890i | 1.12761 | + | 0.205990i | ||||
\(617\) | −365.168 | −0.591844 | −0.295922 | − | 0.955212i | \(-0.595627\pi\) | ||||
−0.295922 | + | 0.955212i | \(0.595627\pi\) | |||||||
\(618\) | 45.9435i | 0.0743423i | ||||||||
\(619\) | −544.199 | −0.879159 | −0.439579 | − | 0.898204i | \(-0.644872\pi\) | ||||
−0.439579 | + | 0.898204i | \(0.644872\pi\) | |||||||
\(620\) | −871.526 | −1.40569 | ||||||||
\(621\) | −64.0753 | −0.103181 | ||||||||
\(622\) | − | 1886.31i | − | 3.03266i | ||||||
\(623\) | 331.712i | 0.532443i | ||||||||
\(624\) | 998.598i | 1.60032i | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 637.847i | − | 1.01893i | ||||||
\(627\) | −51.8352 | + | 283.752i | −0.0826717 | + | 0.452555i | ||||
\(628\) | 2326.70 | 3.70493 | ||||||||
\(629\) | 461.378i | 0.733510i | ||||||||
\(630\) | −67.3376 | −0.106885 | ||||||||
\(631\) | −548.112 | −0.868640 | −0.434320 | − | 0.900759i | \(-0.643011\pi\) | ||||
−0.434320 | + | 0.900759i | \(0.643011\pi\) | |||||||
\(632\) | −1056.72 | −1.67202 | ||||||||
\(633\) | 391.745i | 0.618871i | ||||||||
\(634\) | 309.154i | 0.487624i | ||||||||
\(635\) | − | 365.815i | − | 0.576086i | ||||||
\(636\) | 390.577 | 0.614115 | ||||||||
\(637\) | − | 79.9605i | − | 0.125527i | ||||||
\(638\) | 1514.97 | + | 276.752i | 2.37457 | + | 0.433780i | ||||
\(639\) | −255.359 | −0.399622 | ||||||||
\(640\) | 482.468i | 0.753856i | ||||||||
\(641\) | −169.697 | −0.264738 | −0.132369 | − | 0.991200i | \(-0.542258\pi\) | ||||
−0.132369 | + | 0.991200i | \(0.542258\pi\) | |||||||
\(642\) | 639.649 | 0.996338 | ||||||||
\(643\) | −1243.73 | −1.93426 | −0.967132 | − | 0.254274i | \(-0.918164\pi\) | ||||
−0.967132 | + | 0.254274i | \(0.918164\pi\) | |||||||
\(644\) | − | 339.135i | − | 0.526607i | ||||||
\(645\) | 2.71446i | 0.00420847i | ||||||||
\(646\) | 369.962i | 0.572696i | ||||||||
\(647\) | −477.079 | −0.737371 | −0.368685 | − | 0.929554i | \(-0.620192\pi\) | ||||
−0.368685 | + | 0.929554i | \(0.620192\pi\) | |||||||
\(648\) | 218.359i | 0.336973i | ||||||||
\(649\) | 872.298 | + | 159.349i | 1.34406 | + | 0.245531i | ||||
\(650\) | 216.695 | 0.333378 | ||||||||
\(651\) | − | 171.826i | − | 0.263942i | ||||||
\(652\) | 866.260 | 1.32862 | ||||||||
\(653\) | −80.0744 | −0.122625 | −0.0613127 | − | 0.998119i | \(-0.519529\pi\) | ||||
−0.0613127 | + | 0.998119i | \(0.519529\pi\) | |||||||
\(654\) | −1173.27 | −1.79399 | ||||||||
\(655\) | − | 112.751i | − | 0.172139i | ||||||
\(656\) | − | 2334.05i | − | 3.55800i | ||||||
\(657\) | 311.612i | 0.474296i | ||||||||
\(658\) | −361.712 | −0.549714 | ||||||||
\(659\) | − | 1258.14i | − | 1.90917i | −0.297941 | − | 0.954584i | \(-0.596300\pi\) | ||
0.297941 | − | 0.954584i | \(-0.403700\pi\) | |||||||
\(660\) | −435.638 | − | 79.5813i | −0.660057 | − | 0.120578i | ||||
\(661\) | 284.579 | 0.430528 | 0.215264 | − | 0.976556i | \(-0.430939\pi\) | ||||
0.215264 | + | 0.976556i | \(0.430939\pi\) | |||||||
\(662\) | 393.100i | 0.593806i | ||||||||
\(663\) | −127.432 | −0.192205 | ||||||||
\(664\) | 824.565 | 1.24181 | ||||||||
\(665\) | 89.5670 | 0.134687 | ||||||||
\(666\) | − | 815.342i | − | 1.22424i | ||||||
\(667\) | − | 455.037i | − | 0.682214i | ||||||
\(668\) | 593.979i | 0.889191i | ||||||||
\(669\) | 595.743 | 0.890497 | ||||||||
\(670\) | 153.991i | 0.229837i | ||||||||
\(671\) | −41.5774 | + | 227.600i | −0.0619633 | + | 0.339195i | ||||
\(672\) | −432.805 | −0.644055 | ||||||||
\(673\) | 577.479i | 0.858067i | 0.903289 | + | 0.429033i | \(0.141146\pi\) | ||||
−0.903289 | + | 0.429033i | \(0.858854\pi\) | |||||||
\(674\) | 64.8160 | 0.0961662 | ||||||||
\(675\) | 25.9808 | 0.0384900 | ||||||||
\(676\) | −400.373 | −0.592268 | ||||||||
\(677\) | 115.713i | 0.170921i | 0.996342 | + | 0.0854604i | \(0.0272361\pi\) | ||||
−0.996342 | + | 0.0854604i | \(0.972764\pi\) | |||||||
\(678\) | − | 726.239i | − | 1.07115i | ||||||
\(679\) | 305.597i | 0.450069i | ||||||||
\(680\) | −349.424 | −0.513859 | ||||||||
\(681\) | − | 70.9502i | − | 0.104185i | ||||||
\(682\) | 281.211 | − | 1539.38i | 0.412333 | − | 2.25716i | ||||
\(683\) | −64.0207 | −0.0937346 | −0.0468673 | − | 0.998901i | \(-0.514924\pi\) | ||||
−0.0468673 | + | 0.998901i | \(0.514924\pi\) | |||||||
\(684\) | − | 472.118i | − | 0.690230i | ||||||
\(685\) | 388.880 | 0.567708 | ||||||||
\(686\) | 70.2667 | 0.102430 | ||||||||
\(687\) | 59.1305 | 0.0860706 | ||||||||
\(688\) | 35.3745i | 0.0514164i | ||||||||
\(689\) | − | 247.804i | − | 0.359658i | ||||||
\(690\) | 181.199i | 0.262608i | ||||||||
\(691\) | −1183.60 | −1.71288 | −0.856440 | − | 0.516247i | \(-0.827329\pi\) | ||||
−0.856440 | + | 0.516247i | \(0.827329\pi\) | |||||||
\(692\) | − | 2237.19i | − | 3.23293i | ||||||
\(693\) | 15.6899 | − | 85.8885i | 0.0226406 | − | 0.123937i | ||||
\(694\) | −2463.23 | −3.54933 | ||||||||
\(695\) | − | 323.755i | − | 0.465834i | ||||||
\(696\) | −1550.69 | −2.22801 | ||||||||
\(697\) | 297.850 | 0.427331 | ||||||||
\(698\) | −1050.37 | −1.50483 | ||||||||
\(699\) | − | 617.622i | − | 0.883580i | ||||||
\(700\) | 137.510i | 0.196443i | ||||||||
\(701\) | − | 235.724i | − | 0.336268i | −0.985764 | − | 0.168134i | \(-0.946226\pi\) | ||
0.985764 | − | 0.168134i | \(-0.0537741\pi\) | |||||||
\(702\) | 225.197 | 0.320793 | ||||||||
\(703\) | 1084.50i | 1.54268i | ||||||||
\(704\) | −1692.85 | − | 309.246i | −2.40462 | − | 0.439270i | ||||
\(705\) | 139.559 | 0.197956 | ||||||||
\(706\) | − | 660.458i | − | 0.935493i | ||||||
\(707\) | −286.833 | −0.405704 | ||||||||
\(708\) | −1451.36 | −2.04995 | ||||||||
\(709\) | 480.239 | 0.677346 | 0.338673 | − | 0.940904i | \(-0.390022\pi\) | ||||
0.338673 | + | 0.940904i | \(0.390022\pi\) | |||||||
\(710\) | 722.132i | 1.01709i | ||||||||
\(711\) | 130.663i | 0.183774i | ||||||||
\(712\) | − | 3041.86i | − | 4.27228i | ||||||
\(713\) | −462.369 | −0.648484 | ||||||||
\(714\) | − | 111.983i | − | 0.156839i | ||||||
\(715\) | −50.4908 | + | 276.393i | −0.0706165 | + | 0.386564i | ||||
\(716\) | −2233.48 | −3.11939 | ||||||||
\(717\) | − | 148.227i | − | 0.206732i | ||||||
\(718\) | −207.114 | −0.288459 | ||||||||
\(719\) | 1258.52 | 1.75038 | 0.875191 | − | 0.483778i | \(-0.160736\pi\) | ||||
0.875191 | + | 0.483778i | \(0.160736\pi\) | |||||||
\(720\) | 338.578 | 0.470247 | ||||||||
\(721\) | 18.4974i | 0.0256552i | ||||||||
\(722\) | − | 500.029i | − | 0.692561i | ||||||
\(723\) | 99.5807i | 0.137733i | ||||||||
\(724\) | 2451.14 | 3.38555 | ||||||||
\(725\) | 184.505i | 0.254489i | ||||||||
\(726\) | 281.130 | − | 743.793i | 0.387232 | − | 1.02451i | ||||
\(727\) | 194.359 | 0.267344 | 0.133672 | − | 0.991026i | \(-0.457323\pi\) | ||||
0.133672 | + | 0.991026i | \(0.457323\pi\) | |||||||
\(728\) | 733.254i | 1.00722i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 881.213 | 1.20714 | ||||||||
\(731\) | −4.51417 | −0.00617534 | ||||||||
\(732\) | − | 378.689i | − | 0.517335i | ||||||
\(733\) | − | 351.523i | − | 0.479567i | −0.970826 | − | 0.239783i | \(-0.922924\pi\) | ||
0.970826 | − | 0.239783i | \(-0.0770764\pi\) | |||||||
\(734\) | 2734.37i | 3.72530i | ||||||||
\(735\) | −27.1109 | −0.0368856 | ||||||||
\(736\) | 1164.64i | 1.58239i | ||||||||
\(737\) | −196.414 | − | 35.8804i | −0.266504 | − | 0.0486844i | ||||
\(738\) | −526.357 | −0.713221 | ||||||||
\(739\) | − | 774.198i | − | 1.04763i | −0.851832 | − | 0.523815i | \(-0.824508\pi\) | ||
0.851832 | − | 0.523815i | \(-0.175492\pi\) | |||||||
\(740\) | −1665.01 | −2.25001 | ||||||||
\(741\) | −299.538 | −0.404235 | ||||||||
\(742\) | 217.762 | 0.293480 | ||||||||
\(743\) | 1409.74i | 1.89737i | 0.316226 | + | 0.948684i | \(0.397584\pi\) | ||||
−0.316226 | + | 0.948684i | \(0.602416\pi\) | |||||||
\(744\) | 1575.68i | 2.11785i | ||||||||
\(745\) | 74.0095i | 0.0993417i | ||||||||
\(746\) | −1830.10 | −2.45322 | ||||||||
\(747\) | − | 101.957i | − | 0.136489i | ||||||
\(748\) | 132.344 | − | 724.469i | 0.176931 | − | 0.968542i | ||||
\(749\) | 257.530 | 0.343831 | ||||||||
\(750\) | − | 73.4714i | − | 0.0979618i | ||||||
\(751\) | −274.755 | −0.365853 | −0.182926 | − | 0.983127i | \(-0.558557\pi\) | ||||
−0.182926 | + | 0.983127i | \(0.558557\pi\) | |||||||
\(752\) | 1818.71 | 2.41850 | ||||||||
\(753\) | −495.238 | −0.657687 | ||||||||
\(754\) | 1599.25i | 2.12103i | ||||||||
\(755\) | − | 69.4256i | − | 0.0919544i | ||||||
\(756\) | 142.905i | 0.189027i | ||||||||
\(757\) | 84.0067 | 0.110973 | 0.0554866 | − | 0.998459i | \(-0.482329\pi\) | ||||
0.0554866 | + | 0.998459i | \(0.482329\pi\) | |||||||
\(758\) | 296.516i | 0.391182i | ||||||||
\(759\) | −231.118 | − | 42.2201i | −0.304503 | − | 0.0556260i | ||||
\(760\) | −821.347 | −1.08072 | ||||||||
\(761\) | − | 197.644i | − | 0.259717i | −0.991533 | − | 0.129858i | \(-0.958548\pi\) | ||
0.991533 | − | 0.129858i | \(-0.0414522\pi\) | |||||||
\(762\) | −1075.08 | −1.41086 | ||||||||
\(763\) | −472.372 | −0.619099 | ||||||||
\(764\) | −1940.87 | −2.54040 | ||||||||
\(765\) | 43.2063i | 0.0564788i | ||||||||
\(766\) | 149.111i | 0.194662i | ||||||||
\(767\) | 920.826i | 1.20056i | ||||||||
\(768\) | 334.039 | 0.434947 | ||||||||
\(769\) | − | 735.394i | − | 0.956299i | −0.878279 | − | 0.478149i | \(-0.841308\pi\) | ||
0.878279 | − | 0.478149i | \(-0.158692\pi\) | |||||||
\(770\) | −242.885 | − | 44.3697i | −0.315435 | − | 0.0576230i | ||||
\(771\) | 391.503 | 0.507785 | ||||||||
\(772\) | − | 3157.19i | − | 4.08962i | ||||||
\(773\) | −580.926 | −0.751521 | −0.375761 | − | 0.926717i | \(-0.622619\pi\) | ||||
−0.375761 | + | 0.926717i | \(0.622619\pi\) | |||||||
\(774\) | 7.97740 | 0.0103067 | ||||||||
\(775\) | 187.478 | 0.241907 | ||||||||
\(776\) | − | 2802.39i | − | 3.61132i | ||||||
\(777\) | − | 328.266i | − | 0.422479i | ||||||
\(778\) | 702.138i | 0.902491i | ||||||||
\(779\) | 700.117 | 0.898739 | ||||||||
\(780\) | − | 459.873i | − | 0.589581i | ||||||
\(781\) | −921.073 | − | 168.259i | −1.17935 | − | 0.215441i | ||||
\(782\) | −301.336 | −0.385340 | ||||||||
\(783\) | 191.743i | 0.244883i | ||||||||
\(784\) | −353.306 | −0.450645 | ||||||||
\(785\) | −500.506 | −0.637588 | ||||||||
\(786\) | −331.359 | −0.421577 | ||||||||
\(787\) | 863.761i | 1.09754i | 0.835975 | + | 0.548768i | \(0.184903\pi\) | ||||
−0.835975 | + | 0.548768i | \(0.815097\pi\) | |||||||
\(788\) | − | 2293.32i | − | 2.91030i | ||||||
\(789\) | 588.053i | 0.745314i | ||||||||
\(790\) | 369.504 | 0.467727 | ||||||||
\(791\) | − | 292.392i | − | 0.369649i | ||||||
\(792\) | −143.880 | + | 787.614i | −0.181666 | + | 0.994462i | ||||
\(793\) | −240.262 | −0.302978 | ||||||||
\(794\) | − | 2456.50i | − | 3.09383i | ||||||
\(795\) | −84.0189 | −0.105684 | ||||||||
\(796\) | −1270.97 | −1.59670 | ||||||||
\(797\) | −557.124 | −0.699027 | −0.349513 | − | 0.936931i | \(-0.613653\pi\) | ||||
−0.349513 | + | 0.936931i | \(0.613653\pi\) | |||||||
\(798\) | − | 263.224i | − | 0.329855i | ||||||
\(799\) | 232.088i | 0.290472i | ||||||||
\(800\) | − | 472.229i | − | 0.590286i | ||||||
\(801\) | −376.126 | −0.469570 | ||||||||
\(802\) | − | 311.028i | − | 0.387815i | ||||||
\(803\) | −205.326 | + | 1123.98i | −0.255698 | + | 1.39972i | ||||
\(804\) | 326.801 | 0.406468 | ||||||||
\(805\) | 72.9529i | 0.0906247i | ||||||||
\(806\) | 1625.02 | 2.01616 | ||||||||
\(807\) | 130.701 | 0.161959 | ||||||||
\(808\) | 2630.31 | 3.25534 | ||||||||
\(809\) | − | 1364.17i | − | 1.68624i | −0.537722 | − | 0.843122i | \(-0.680715\pi\) | ||
0.537722 | − | 0.843122i | \(-0.319285\pi\) | |||||||
\(810\) | − | 76.3537i | − | 0.0942638i | ||||||
\(811\) | 872.097i | 1.07534i | 0.843157 | + | 0.537668i | \(0.180695\pi\) | ||||
−0.843157 | + | 0.537668i | \(0.819305\pi\) | |||||||
\(812\) | −1014.85 | −1.24982 | ||||||||
\(813\) | 81.3811i | 0.100100i | ||||||||
\(814\) | 537.240 | − | 2940.92i | 0.660000 | − | 3.61292i | ||||
\(815\) | −186.345 | −0.228644 | ||||||||
\(816\) | 563.059i | 0.690023i | ||||||||
\(817\) | −10.6109 | −0.0129876 | ||||||||
\(818\) | −2347.29 | −2.86955 | ||||||||
\(819\) | 90.6667 | 0.110704 | ||||||||
\(820\) | 1074.87i | 1.31082i | ||||||||
\(821\) | 433.155i | 0.527595i | 0.964578 | + | 0.263797i | \(0.0849750\pi\) | ||||
−0.964578 | + | 0.263797i | \(0.915025\pi\) | |||||||
\(822\) | − | 1142.86i | − | 1.39034i | ||||||
\(823\) | −1317.04 | −1.60029 | −0.800146 | − | 0.599806i | \(-0.795245\pi\) | ||||
−0.800146 | + | 0.599806i | \(0.795245\pi\) | |||||||
\(824\) | − | 169.625i | − | 0.205855i | ||||||
\(825\) | 93.7120 | + | 17.1191i | 0.113590 | + | 0.0207504i | ||||
\(826\) | −809.193 | −0.979652 | ||||||||
\(827\) | 167.202i | 0.202179i | 0.994877 | + | 0.101089i | \(0.0322328\pi\) | ||||
−0.994877 | + | 0.101089i | \(0.967767\pi\) | |||||||
\(828\) | 384.543 | 0.464424 | ||||||||
\(829\) | 1.28049 | 0.00154461 | 0.000772307 | − | 1.00000i | \(-0.499754\pi\) | ||||
0.000772307 | 1.00000i | \(0.499754\pi\) | ||||||||
\(830\) | −288.326 | −0.347381 | ||||||||
\(831\) | 835.246i | 1.00511i | ||||||||
\(832\) | − | 1787.03i | − | 2.14787i | ||||||
\(833\) | − | 45.0857i | − | 0.0541244i | ||||||
\(834\) | −951.469 | −1.14085 | ||||||||
\(835\) | − | 127.774i | − | 0.153022i | ||||||
\(836\) | 311.085 | − | 1702.92i | 0.372111 | − | 2.03698i | ||||
\(837\) | 194.833 | 0.232775 | ||||||||
\(838\) | − | 1369.10i | − | 1.63377i | ||||||
\(839\) | 985.680 | 1.17483 | 0.587413 | − | 0.809287i | \(-0.300146\pi\) | ||||
0.587413 | + | 0.809287i | \(0.300146\pi\) | |||||||
\(840\) | 248.612 | 0.295967 | ||||||||
\(841\) | −520.682 | −0.619122 | ||||||||
\(842\) | 2957.31i | 3.51224i | ||||||||
\(843\) | − | 923.568i | − | 1.09557i | ||||||
\(844\) | − | 2351.03i | − | 2.78558i | ||||||
\(845\) | 86.1261 | 0.101924 | ||||||||
\(846\) | − | 410.143i | − | 0.484802i | ||||||
\(847\) | 113.186 | − | 299.459i | 0.133632 | − | 0.353553i | ||||
\(848\) | −1094.92 | −1.29118 | ||||||||
\(849\) | 180.833i | 0.212996i | ||||||||
\(850\) | 122.184 | 0.143745 | ||||||||
\(851\) | −883.333 | −1.03799 | ||||||||
\(852\) | 1532.52 | 1.79873 | ||||||||
\(853\) | 824.902i | 0.967060i | 0.875328 | + | 0.483530i | \(0.160646\pi\) | ||||
−0.875328 | + | 0.483530i | \(0.839354\pi\) | |||||||
\(854\) | − | 211.134i | − | 0.247230i | ||||||
\(855\) | 101.559i | 0.118783i | ||||||||
\(856\) | −2361.60 | −2.75888 | ||||||||
\(857\) | − | 1101.72i | − | 1.28555i | −0.766054 | − | 0.642776i | \(-0.777783\pi\) | ||
0.766054 | − | 0.642776i | \(-0.222217\pi\) | |||||||
\(858\) | 812.279 | + | 148.385i | 0.946712 | + | 0.172943i | ||||
\(859\) | 1300.88 | 1.51441 | 0.757207 | − | 0.653174i | \(-0.226563\pi\) | ||||
0.757207 | + | 0.653174i | \(0.226563\pi\) | |||||||
\(860\) | − | 16.2906i | − | 0.0189426i | ||||||
\(861\) | −211.917 | −0.246129 | ||||||||
\(862\) | 1070.48 | 1.24185 | ||||||||
\(863\) | −1353.77 | −1.56868 | −0.784338 | − | 0.620334i | \(-0.786997\pi\) | ||||
−0.784338 | + | 0.620334i | \(0.786997\pi\) | |||||||
\(864\) | − | 490.754i | − | 0.568003i | ||||||
\(865\) | 481.252i | 0.556361i | ||||||||
\(866\) | 2544.58i | 2.93831i | ||||||||
\(867\) | 428.710 | 0.494476 | ||||||||
\(868\) | 1031.20i | 1.18802i | ||||||||
\(869\) | −86.0957 | + | 471.299i | −0.0990745 | + | 0.542346i | ||||
\(870\) | 542.233 | 0.623256 | ||||||||
\(871\) | − | 207.341i | − | 0.238049i | ||||||
\(872\) | 4331.75 | 4.96760 | ||||||||
\(873\) | −346.515 | −0.396924 | ||||||||
\(874\) | −708.312 | −0.810426 | ||||||||
\(875\) | − | 29.5804i | − | 0.0338062i | ||||||
\(876\) | − | 1870.12i | − | 2.13484i | ||||||
\(877\) | − | 341.336i | − | 0.389209i | −0.980882 | − | 0.194604i | \(-0.937658\pi\) | ||
0.980882 | − | 0.194604i | \(-0.0623423\pi\) | |||||||
\(878\) | 1619.69 | 1.84475 | ||||||||
\(879\) | − | 217.483i | − | 0.247420i | ||||||
\(880\) | 1221.24 | + | 223.094i | 1.38778 | + | 0.253516i | ||||
\(881\) | 1281.15 | 1.45420 | 0.727101 | − | 0.686531i | \(-0.240867\pi\) | ||||
0.727101 | + | 0.686531i | \(0.240867\pi\) | |||||||
\(882\) | 79.6749i | 0.0903344i | ||||||||
\(883\) | −1227.03 | −1.38961 | −0.694806 | − | 0.719197i | \(-0.744510\pi\) | ||||
−0.694806 | + | 0.719197i | \(0.744510\pi\) | |||||||
\(884\) | 764.774 | 0.865128 | ||||||||
\(885\) | 312.209 | 0.352779 | ||||||||
\(886\) | − | 41.7770i | − | 0.0471523i | ||||||
\(887\) | 902.044i | 1.01696i | 0.861074 | + | 0.508480i | \(0.169793\pi\) | ||||
−0.861074 | + | 0.508480i | \(0.830207\pi\) | |||||||
\(888\) | 3010.26i | 3.38994i | ||||||||
\(889\) | −432.838 | −0.486882 | ||||||||
\(890\) | 1063.65i | 1.19511i | ||||||||
\(891\) | 97.3884 | + | 17.7907i | 0.109302 | + | 0.0199671i | ||||
\(892\) | −3575.31 | −4.00819 | ||||||||
\(893\) | 545.538i | 0.610905i | ||||||||
\(894\) | 217.503 | 0.243292 | ||||||||
\(895\) | 480.455 | 0.536821 | ||||||||
\(896\) | 570.864 | 0.637125 | ||||||||
\(897\) | − | 243.976i | − | 0.271991i | ||||||
\(898\) | − | 1624.25i | − | 1.80874i | ||||||
\(899\) | 1383.62i | 1.53907i | ||||||||
\(900\) | −155.922 | −0.173246 | ||||||||
\(901\) | − | 139.724i | − | 0.155077i | ||||||
\(902\) | −1898.56 | − | 346.824i | −2.10483 | − | 0.384506i | ||||
\(903\) | 3.21179 | 0.00355680 | ||||||||
\(904\) | 2681.29i | 2.96603i | ||||||||
\(905\) | −527.276 | −0.582625 | ||||||||
\(906\) | −204.032 | −0.225201 | ||||||||
\(907\) | 202.474 | 0.223235 | 0.111617 | − | 0.993751i | \(-0.464397\pi\) | ||||
0.111617 | + | 0.993751i | \(0.464397\pi\) | |||||||
\(908\) | 425.802i | 0.468945i | ||||||||
\(909\) | − | 325.238i | − | 0.357798i | ||||||
\(910\) | − | 256.398i | − | 0.281756i | ||||||
\(911\) | 18.2211 | 0.0200012 | 0.0100006 | − | 0.999950i | \(-0.496817\pi\) | ||||
0.0100006 | + | 0.999950i | \(0.496817\pi\) | |||||||
\(912\) | 1323.51i | 1.45122i | ||||||||
\(913\) | 67.1811 | − | 367.758i | 0.0735828 | − | 0.402801i | ||||
\(914\) | 1591.72 | 1.74148 | ||||||||
\(915\) | 81.4615i | 0.0890290i | ||||||||
\(916\) | −354.868 | −0.387410 | ||||||||
\(917\) | −133.409 | −0.145484 | ||||||||
\(918\) | 126.977 | 0.138319 | ||||||||
\(919\) | − | 366.701i | − | 0.399021i | −0.979896 | − | 0.199511i | \(-0.936065\pi\) | ||
0.979896 | − | 0.199511i | \(-0.0639353\pi\) | |||||||
\(920\) | − | 668.993i | − | 0.727166i | ||||||
\(921\) | 619.904i | 0.673077i | ||||||||
\(922\) | 192.999 | 0.209327 | ||||||||
\(923\) | − | 972.315i | − | 1.05343i | ||||||
\(924\) | −94.1618 | + | 515.453i | −0.101907 | + | 0.557850i | ||||
\(925\) | 358.167 | 0.387208 | ||||||||
\(926\) | − | 811.162i | − | 0.875985i | ||||||
\(927\) | −20.9741 | −0.0226257 | ||||||||
\(928\) | 3485.14 | 3.75554 | ||||||||
\(929\) | 822.900 | 0.885791 | 0.442895 | − | 0.896573i | \(-0.353951\pi\) | ||||
0.442895 | + | 0.896573i | \(0.353951\pi\) | |||||||
\(930\) | − | 550.970i | − | 0.592441i | ||||||
\(931\) | − | 105.977i | − | 0.113831i | ||||||
\(932\) | 3706.61i | 3.97705i | ||||||||
\(933\) | 861.137 | 0.922976 | ||||||||
\(934\) | 1597.82i | 1.71072i | ||||||||
\(935\) | −28.4692 | + | 155.844i | −0.0304484 | + | 0.166678i | ||||
\(936\) | −831.431 | −0.888281 | ||||||||
\(937\) | − | 333.255i | − | 0.355662i | −0.984061 | − | 0.177831i | \(-0.943092\pi\) | ||
0.984061 | − | 0.177831i | \(-0.0569080\pi\) | |||||||
\(938\) | 182.204 | 0.194248 | ||||||||
\(939\) | 291.189 | 0.310105 | ||||||||
\(940\) | −837.552 | −0.891012 | ||||||||
\(941\) | − | 1394.00i | − | 1.48140i | −0.671834 | − | 0.740702i | \(-0.734493\pi\) | ||
0.671834 | − | 0.740702i | \(-0.265507\pi\) | |||||||
\(942\) | 1470.92i | 1.56148i | ||||||||
\(943\) | 570.250i | 0.604719i | ||||||||
\(944\) | 4068.68 | 4.31004 | ||||||||
\(945\) | − | 30.7409i | − | 0.0325300i | ||||||
\(946\) | 28.7743 | + | 5.25642i | 0.0304168 | + | 0.00555647i | ||||
\(947\) | −29.1583 | −0.0307902 | −0.0153951 | − | 0.999881i | \(-0.504901\pi\) | ||||
−0.0153951 | + | 0.999881i | \(0.504901\pi\) | |||||||
\(948\) | − | 784.165i | − | 0.827178i | ||||||
\(949\) | −1186.51 | −1.25027 | ||||||||
\(950\) | 287.201 | 0.302317 | ||||||||
\(951\) | −141.134 | −0.148406 | ||||||||
\(952\) | 413.444i | 0.434290i | ||||||||
\(953\) | − | 1138.36i | − | 1.19450i | −0.802055 | − | 0.597250i | \(-0.796260\pi\) | ||
0.802055 | − | 0.597250i | \(-0.203740\pi\) | |||||||
\(954\) | 246.919i | 0.258825i | ||||||||
\(955\) | 417.509 | 0.437182 | ||||||||
\(956\) | 889.574i | 0.930516i | ||||||||
\(957\) | −126.342 | + | 691.613i | −0.132019 | + | 0.722688i | ||||
\(958\) | 1764.84 | 1.84221 | ||||||||
\(959\) | − | 460.129i | − | 0.479801i | ||||||
\(960\) | −605.899 | −0.631144 | ||||||||
\(961\) | 444.919 | 0.462975 | ||||||||
\(962\) | 3104.53 | 3.22716 | ||||||||
\(963\) | 292.011i | 0.303231i | ||||||||
\(964\) | − | 597.626i | − | 0.619944i | ||||||
\(965\) | 679.158i | 0.703790i | ||||||||
\(966\) | 214.398 | 0.221944 | ||||||||
\(967\) | 169.986i | 0.175787i | 0.996130 | + | 0.0878937i | \(0.0280136\pi\) | ||||
−0.996130 | + | 0.0878937i | \(0.971986\pi\) | |||||||
\(968\) | −1037.94 | + | 2746.10i | −1.07225 | + | 2.83688i | ||||
\(969\) | −168.894 | −0.174297 | ||||||||
\(970\) | 979.913i | 1.01022i | ||||||||
\(971\) | 1098.16 | 1.13096 | 0.565479 | − | 0.824763i | \(-0.308691\pi\) | ||||
0.565479 | + | 0.824763i | \(0.308691\pi\) | |||||||
\(972\) | −162.039 | −0.166706 | ||||||||
\(973\) | −383.072 | −0.393702 | ||||||||
\(974\) | − | 2262.90i | − | 2.32330i | ||||||
\(975\) | 98.9254i | 0.101462i | ||||||||
\(976\) | 1061.60i | 1.08770i | ||||||||
\(977\) | −921.219 | −0.942906 | −0.471453 | − | 0.881891i | \(-0.656270\pi\) | ||||
−0.471453 | + | 0.881891i | \(0.656270\pi\) | |||||||
\(978\) | 547.641i | 0.559960i | ||||||||
\(979\) | −1356.68 | − | 247.835i | −1.38578 | − | 0.253151i | ||||
\(980\) | 162.704 | 0.166024 | ||||||||
\(981\) | − | 535.620i | − | 0.545994i | ||||||
\(982\) | 1744.97 | 1.77696 | ||||||||
\(983\) | −1261.35 | −1.28317 | −0.641583 | − | 0.767053i | \(-0.721722\pi\) | ||||
−0.641583 | + | 0.767053i | \(0.721722\pi\) | |||||||
\(984\) | 1943.32 | 1.97492 | ||||||||
\(985\) | 493.326i | 0.500839i | ||||||||
\(986\) | 901.739i | 0.914542i | ||||||||
\(987\) | − | 165.128i | − | 0.167303i | ||||||
\(988\) | 1797.65 | 1.81949 | ||||||||
\(989\) | − | 8.64264i | − | 0.00873876i | ||||||
\(990\) | 50.3105 | − | 275.406i | 0.0508187 | − | 0.278188i | ||||
\(991\) | 446.382 | 0.450436 | 0.225218 | − | 0.974308i | \(-0.427691\pi\) | ||||
0.225218 | + | 0.974308i | \(0.427691\pi\) | |||||||
\(992\) | − | 3541.30i | − | 3.56986i | ||||||
\(993\) | −179.457 | −0.180722 | ||||||||
\(994\) | 854.439 | 0.859596 | ||||||||
\(995\) | 273.405 | 0.274779 | ||||||||
\(996\) | 611.889i | 0.614347i | ||||||||
\(997\) | 584.900i | 0.586660i | 0.956011 | + | 0.293330i | \(0.0947634\pi\) | ||||
−0.956011 | + | 0.293330i | \(0.905237\pi\) | |||||||
\(998\) | 2034.79i | 2.03887i | ||||||||
\(999\) | 372.219 | 0.372591 |
(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 | 1155.3.b.a.736.3 | ✓ | 96 | |
11.10 | odd | 2 | inner | 1155.3.b.a.736.94 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.3.b.a.736.3 | ✓ | 96 | 1.1 | even | 1 | trivial | |
1155.3.b.a.736.94 | yes | 96 | 11.10 | odd | 2 | inner |