Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(474,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.474");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.d (of order \(2\), degree \(1\), 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: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 474.5 | ||
Character | \(\chi\) | \(=\) | 475.474 |
Dual form | 475.3.d.d.474.6 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.92865 | −1.46432 | −0.732162 | − | 0.681131i | \(-0.761489\pi\) | ||||
−0.732162 | + | 0.681131i | \(0.761489\pi\) | |||||||
\(3\) | 2.02259 | 0.674198 | 0.337099 | − | 0.941469i | \(-0.390554\pi\) | ||||
0.337099 | + | 0.941469i | \(0.390554\pi\) | |||||||
\(4\) | 4.57698 | 1.14424 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.92346 | −0.987243 | ||||||||
\(7\) | − | 8.32815i | − | 1.18974i | −0.803823 | − | 0.594868i | \(-0.797204\pi\) | ||
0.803823 | − | 0.594868i | \(-0.202796\pi\) | |||||||
\(8\) | −1.68976 | −0.211220 | ||||||||
\(9\) | −4.90912 | −0.545458 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.3372 | −1.57611 | −0.788053 | − | 0.615608i | \(-0.788911\pi\) | ||||
−0.788053 | + | 0.615608i | \(0.788911\pi\) | |||||||
\(12\) | 9.25736 | 0.771446 | ||||||||
\(13\) | 5.27368 | 0.405668 | 0.202834 | − | 0.979213i | \(-0.434985\pi\) | ||||
0.202834 | + | 0.979213i | \(0.434985\pi\) | |||||||
\(14\) | 24.3902i | 1.74216i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −13.3592 | −0.834950 | ||||||||
\(17\) | 19.0798i | 1.12234i | 0.827701 | + | 0.561170i | \(0.189649\pi\) | ||||
−0.827701 | + | 0.561170i | \(0.810351\pi\) | |||||||
\(18\) | 14.3771 | 0.798727 | ||||||||
\(19\) | 11.4291 | + | 15.1781i | 0.601534 | + | 0.798847i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 16.8445i | − | 0.802117i | ||||||
\(22\) | 50.7744 | 2.30793 | ||||||||
\(23\) | − | 3.32445i | − | 0.144541i | −0.997385 | − | 0.0722706i | \(-0.976975\pi\) | ||
0.997385 | − | 0.0722706i | \(-0.0230245\pi\) | |||||||
\(24\) | −3.41769 | −0.142404 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −15.4447 | −0.594029 | ||||||||
\(27\) | −28.1325 | −1.04194 | ||||||||
\(28\) | − | 38.1178i | − | 1.36135i | ||||||
\(29\) | 37.4537i | 1.29151i | 0.763546 | + | 0.645753i | \(0.223456\pi\) | ||||
−0.763546 | + | 0.645753i | \(0.776544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.86714i | − | 0.0924885i | −0.998930 | − | 0.0462443i | \(-0.985275\pi\) | ||
0.998930 | − | 0.0462443i | \(-0.0147253\pi\) | |||||||
\(32\) | 45.8834 | 1.43386 | ||||||||
\(33\) | −35.0660 | −1.06261 | ||||||||
\(34\) | − | 55.8779i | − | 1.64347i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −22.4689 | −0.624137 | ||||||||
\(37\) | 33.0085 | 0.892123 | 0.446061 | − | 0.895002i | \(-0.352826\pi\) | ||||
0.446061 | + | 0.895002i | \(0.352826\pi\) | |||||||
\(38\) | −33.4719 | − | 44.4513i | −0.880840 | − | 1.16977i | ||||
\(39\) | 10.6665 | 0.273500 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20.9092i | 0.509979i | 0.966944 | + | 0.254990i | \(0.0820721\pi\) | ||||
−0.966944 | + | 0.254990i | \(0.917928\pi\) | |||||||
\(42\) | 49.3315i | 1.17456i | ||||||||
\(43\) | 23.9545i | 0.557080i | 0.960425 | + | 0.278540i | \(0.0898505\pi\) | ||||
−0.960425 | + | 0.278540i | \(0.910149\pi\) | |||||||
\(44\) | −79.3518 | −1.80345 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.73613i | 0.211655i | ||||||||
\(47\) | − | 33.8351i | − | 0.719895i | −0.932973 | − | 0.359947i | \(-0.882795\pi\) | ||
0.932973 | − | 0.359947i | \(-0.117205\pi\) | |||||||
\(48\) | −27.0202 | −0.562921 | ||||||||
\(49\) | −20.3582 | −0.415473 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 38.5906i | 0.756679i | ||||||||
\(52\) | 24.1375 | 0.464183 | ||||||||
\(53\) | 37.4936 | 0.707426 | 0.353713 | − | 0.935354i | \(-0.384919\pi\) | ||||
0.353713 | + | 0.935354i | \(0.384919\pi\) | |||||||
\(54\) | 82.3901 | 1.52574 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 14.0726i | 0.251296i | ||||||||
\(57\) | 23.1165 | + | 30.6991i | 0.405553 | + | 0.538581i | ||||
\(58\) | − | 109.689i | − | 1.89118i | ||||||
\(59\) | 32.5574i | 0.551821i | 0.961183 | + | 0.275910i | \(0.0889793\pi\) | ||||
−0.961183 | + | 0.275910i | \(0.911021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.58141 | 0.107892 | 0.0539460 | − | 0.998544i | \(-0.482820\pi\) | ||||
0.0539460 | + | 0.998544i | \(0.482820\pi\) | |||||||
\(62\) | 8.39685i | 0.135433i | ||||||||
\(63\) | 40.8839i | 0.648951i | ||||||||
\(64\) | −80.9395 | −1.26468 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 102.696 | 1.55600 | ||||||||
\(67\) | −112.029 | −1.67208 | −0.836038 | − | 0.548671i | \(-0.815134\pi\) | ||||
−0.836038 | + | 0.548671i | \(0.815134\pi\) | |||||||
\(68\) | 87.3276i | 1.28423i | ||||||||
\(69\) | − | 6.72400i | − | 0.0974493i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 110.992i | 1.56327i | 0.623733 | + | 0.781637i | \(0.285615\pi\) | ||||
−0.623733 | + | 0.781637i | \(0.714385\pi\) | |||||||
\(72\) | 8.29522 | 0.115211 | ||||||||
\(73\) | 134.981i | 1.84906i | 0.381109 | + | 0.924530i | \(0.375542\pi\) | ||||
−0.381109 | + | 0.924530i | \(0.624458\pi\) | |||||||
\(74\) | −96.6704 | −1.30636 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 52.3109 | + | 69.4698i | 0.688301 | + | 0.914076i | ||||
\(77\) | 144.387i | 1.87515i | ||||||||
\(78\) | −31.2384 | −0.400493 | ||||||||
\(79\) | − | 48.8335i | − | 0.618145i | −0.951038 | − | 0.309072i | \(-0.899981\pi\) | ||
0.951038 | − | 0.309072i | \(-0.100019\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12.7185 | −0.157018 | ||||||||
\(82\) | − | 61.2355i | − | 0.746775i | ||||||
\(83\) | 44.2971i | 0.533700i | 0.963738 | + | 0.266850i | \(0.0859828\pi\) | ||||
−0.963738 | + | 0.266850i | \(0.914017\pi\) | |||||||
\(84\) | − | 77.0967i | − | 0.917818i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 70.1541i | − | 0.815746i | ||||||
\(87\) | 75.7535i | 0.870730i | ||||||||
\(88\) | 29.2956 | 0.332904 | ||||||||
\(89\) | 173.577i | 1.95030i | 0.221538 | + | 0.975152i | \(0.428892\pi\) | ||||
−0.221538 | + | 0.975152i | \(0.571108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 43.9200i | − | 0.482637i | ||||||
\(92\) | − | 15.2159i | − | 0.165390i | ||||||
\(93\) | − | 5.79906i | − | 0.0623555i | ||||||
\(94\) | 99.0910i | 1.05416i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 92.8034 | 0.966703 | ||||||||
\(97\) | 50.6952 | 0.522631 | 0.261315 | − | 0.965253i | \(-0.415844\pi\) | ||||
0.261315 | + | 0.965253i | \(0.415844\pi\) | |||||||
\(98\) | 59.6219 | 0.608386 | ||||||||
\(99\) | 85.1102 | 0.859699 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −100.261 | −0.992681 | −0.496340 | − | 0.868128i | \(-0.665323\pi\) | ||||
−0.496340 | + | 0.868128i | \(0.665323\pi\) | |||||||
\(102\) | − | 113.018i | − | 1.10802i | ||||||
\(103\) | 31.5721 | 0.306525 | 0.153263 | − | 0.988185i | \(-0.451022\pi\) | ||||
0.153263 | + | 0.988185i | \(0.451022\pi\) | |||||||
\(104\) | −8.91124 | −0.0856850 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −109.805 | −1.03590 | ||||||||
\(107\) | −71.5150 | −0.668365 | −0.334182 | − | 0.942508i | \(-0.608460\pi\) | ||||
−0.334182 | + | 0.942508i | \(0.608460\pi\) | |||||||
\(108\) | −128.762 | −1.19224 | ||||||||
\(109\) | − | 138.250i | − | 1.26835i | −0.773191 | − | 0.634174i | \(-0.781340\pi\) | ||
0.773191 | − | 0.634174i | \(-0.218660\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 66.7628 | 0.601467 | ||||||||
\(112\) | 111.257i | 0.993370i | ||||||||
\(113\) | −115.926 | −1.02590 | −0.512949 | − | 0.858419i | \(-0.671447\pi\) | ||||
−0.512949 | + | 0.858419i | \(0.671447\pi\) | |||||||
\(114\) | −67.7001 | − | 89.9069i | −0.593860 | − | 0.788657i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 171.425i | 1.47780i | ||||||||
\(117\) | −25.8891 | −0.221275 | ||||||||
\(118\) | − | 95.3492i | − | 0.808044i | ||||||
\(119\) | 158.899 | 1.33529 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 179.577 | 1.48411 | ||||||||
\(122\) | −19.2746 | −0.157989 | ||||||||
\(123\) | 42.2907i | 0.343827i | ||||||||
\(124\) | − | 13.1228i | − | 0.105829i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 119.735i | − | 0.950274i | ||||||
\(127\) | −114.758 | −0.903607 | −0.451804 | − | 0.892117i | \(-0.649219\pi\) | ||||
−0.451804 | + | 0.892117i | \(0.649219\pi\) | |||||||
\(128\) | 53.5097 | 0.418045 | ||||||||
\(129\) | 48.4501i | 0.375582i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −203.387 | −1.55257 | −0.776286 | − | 0.630381i | \(-0.782899\pi\) | ||||
−0.776286 | + | 0.630381i | \(0.782899\pi\) | |||||||
\(132\) | −160.496 | −1.21588 | ||||||||
\(133\) | 126.406 | − | 95.1837i | 0.950418 | − | 0.715667i | ||||
\(134\) | 328.094 | 2.44846 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 32.2402i | − | 0.237060i | ||||||
\(137\) | − | 152.757i | − | 1.11501i | −0.830172 | − | 0.557507i | \(-0.811758\pi\) | ||
0.830172 | − | 0.557507i | \(-0.188242\pi\) | |||||||
\(138\) | 19.6922i | 0.142697i | ||||||||
\(139\) | −155.284 | −1.11715 | −0.558575 | − | 0.829454i | \(-0.688652\pi\) | ||||
−0.558575 | + | 0.829454i | \(0.688652\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 68.4345i | − | 0.485351i | ||||||
\(142\) | − | 325.058i | − | 2.28914i | ||||||
\(143\) | −91.4306 | −0.639375 | ||||||||
\(144\) | 65.5819 | 0.455430 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 395.313i | − | 2.70762i | ||||||
\(147\) | −41.1763 | −0.280111 | ||||||||
\(148\) | 151.079 | 1.02081 | ||||||||
\(149\) | 106.711 | 0.716178 | 0.358089 | − | 0.933687i | \(-0.383428\pi\) | ||||
0.358089 | + | 0.933687i | \(0.383428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 262.585i | − | 1.73897i | −0.493955 | − | 0.869487i | \(-0.664449\pi\) | ||
0.493955 | − | 0.869487i | \(-0.335551\pi\) | |||||||
\(152\) | −19.3125 | − | 25.6473i | −0.127056 | − | 0.168732i | ||||
\(153\) | − | 93.6649i | − | 0.612189i | ||||||
\(154\) | − | 422.857i | − | 2.74583i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 48.8203 | 0.312951 | ||||||||
\(157\) | − | 238.486i | − | 1.51902i | −0.650496 | − | 0.759509i | \(-0.725439\pi\) | ||
0.650496 | − | 0.759509i | \(-0.274561\pi\) | |||||||
\(158\) | 143.016i | 0.905164i | ||||||||
\(159\) | 75.8343 | 0.476945 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.6865 | −0.171966 | ||||||||
\(162\) | 37.2479 | 0.229925 | ||||||||
\(163\) | 128.660i | 0.789328i | 0.918826 | + | 0.394664i | \(0.129139\pi\) | ||||
−0.918826 | + | 0.394664i | \(0.870861\pi\) | |||||||
\(164\) | 95.7007i | 0.583541i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 129.731i | − | 0.781510i | ||||||
\(167\) | 194.440 | 1.16431 | 0.582155 | − | 0.813078i | \(-0.302210\pi\) | ||||
0.582155 | + | 0.813078i | \(0.302210\pi\) | |||||||
\(168\) | 28.4631i | 0.169423i | ||||||||
\(169\) | −141.188 | −0.835434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −56.1070 | − | 74.5111i | −0.328111 | − | 0.435737i | ||||
\(172\) | 109.639i | 0.637436i | ||||||||
\(173\) | 253.484 | 1.46523 | 0.732613 | − | 0.680646i | \(-0.238301\pi\) | ||||
0.732613 | + | 0.680646i | \(0.238301\pi\) | |||||||
\(174\) | − | 221.855i | − | 1.27503i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 231.611 | 1.31597 | ||||||||
\(177\) | 65.8504i | 0.372036i | ||||||||
\(178\) | − | 508.346i | − | 2.85588i | ||||||
\(179\) | 262.044i | 1.46393i | 0.681341 | + | 0.731966i | \(0.261397\pi\) | ||||
−0.681341 | + | 0.731966i | \(0.738603\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 266.130i | 1.47033i | 0.677887 | + | 0.735166i | \(0.262896\pi\) | ||||
−0.677887 | + | 0.735166i | \(0.737104\pi\) | |||||||
\(182\) | 128.626i | 0.706737i | ||||||||
\(183\) | 13.3115 | 0.0727405 | ||||||||
\(184\) | 5.61751i | 0.0305299i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 16.9834i | 0.0913087i | ||||||||
\(187\) | − | 330.789i | − | 1.76893i | ||||||
\(188\) | − | 154.862i | − | 0.823735i | ||||||
\(189\) | 234.292i | 1.23964i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −204.892 | −1.07273 | −0.536366 | − | 0.843985i | \(-0.680203\pi\) | ||||
−0.536366 | + | 0.843985i | \(0.680203\pi\) | |||||||
\(192\) | −163.708 | −0.852644 | ||||||||
\(193\) | 239.909 | 1.24305 | 0.621526 | − | 0.783394i | \(-0.286513\pi\) | ||||
0.621526 | + | 0.783394i | \(0.286513\pi\) | |||||||
\(194\) | −148.468 | −0.765301 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −93.1788 | −0.475402 | ||||||||
\(197\) | 10.5701i | 0.0536555i | 0.999640 | + | 0.0268278i | \(0.00854057\pi\) | ||||
−0.999640 | + | 0.0268278i | \(0.991459\pi\) | |||||||
\(198\) | −249.258 | −1.25888 | ||||||||
\(199\) | 99.3795 | 0.499394 | 0.249697 | − | 0.968324i | \(-0.419669\pi\) | ||||
0.249697 | + | 0.968324i | \(0.419669\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −226.589 | −1.12731 | ||||||||
\(202\) | 293.628 | 1.45361 | ||||||||
\(203\) | 311.920 | 1.53655 | ||||||||
\(204\) | 176.628i | 0.865825i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −92.4635 | −0.448852 | ||||||||
\(207\) | 16.3201i | 0.0788411i | ||||||||
\(208\) | −70.4521 | −0.338712 | ||||||||
\(209\) | −198.149 | − | 263.145i | −0.948081 | − | 1.25907i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 89.7607i | 0.425406i | 0.977117 | + | 0.212703i | \(0.0682267\pi\) | ||||
−0.977117 | + | 0.212703i | \(0.931773\pi\) | |||||||
\(212\) | 171.607 | 0.809468 | ||||||||
\(213\) | 224.493i | 1.05396i | ||||||||
\(214\) | 209.442 | 0.978702 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 47.5371 | 0.220079 | ||||||||
\(217\) | −23.8780 | −0.110037 | ||||||||
\(218\) | 404.885i | 1.85727i | ||||||||
\(219\) | 273.012i | 1.24663i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 100.621i | 0.455297i | ||||||||
\(222\) | −195.525 | −0.880742 | ||||||||
\(223\) | −104.111 | −0.466866 | −0.233433 | − | 0.972373i | \(-0.574996\pi\) | ||||
−0.233433 | + | 0.972373i | \(0.574996\pi\) | |||||||
\(224\) | − | 382.124i | − | 1.70591i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 339.508 | 1.50225 | ||||||||
\(227\) | −254.689 | −1.12198 | −0.560990 | − | 0.827823i | \(-0.689579\pi\) | ||||
−0.560990 | + | 0.827823i | \(0.689579\pi\) | |||||||
\(228\) | 105.804 | + | 140.509i | 0.464051 | + | 0.616268i | ||||
\(229\) | −326.228 | −1.42457 | −0.712287 | − | 0.701888i | \(-0.752341\pi\) | ||||
−0.712287 | + | 0.701888i | \(0.752341\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 292.035i | 1.26422i | ||||||||
\(232\) | − | 63.2876i | − | 0.272791i | ||||||
\(233\) | − | 66.9003i | − | 0.287126i | −0.989641 | − | 0.143563i | \(-0.954144\pi\) | ||
0.989641 | − | 0.143563i | \(-0.0458559\pi\) | |||||||
\(234\) | 75.8201 | 0.324017 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 149.015i | 0.631417i | ||||||||
\(237\) | − | 98.7702i | − | 0.416752i | ||||||
\(238\) | −465.360 | −1.95529 | ||||||||
\(239\) | −246.601 | −1.03180 | −0.515902 | − | 0.856647i | \(-0.672543\pi\) | ||||
−0.515902 | + | 0.856647i | \(0.672543\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 39.9249i | − | 0.165663i | −0.996564 | − | 0.0828317i | \(-0.973604\pi\) | ||
0.996564 | − | 0.0828317i | \(-0.0263964\pi\) | |||||||
\(242\) | −525.918 | −2.17322 | ||||||||
\(243\) | 227.468 | 0.936082 | ||||||||
\(244\) | 30.1230 | 0.123455 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 123.855i | − | 0.503474i | ||||||
\(247\) | 60.2736 | + | 80.0444i | 0.244023 | + | 0.324066i | ||||
\(248\) | 4.84478i | 0.0195354i | ||||||||
\(249\) | 89.5950i | 0.359819i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 135.552 | 0.540046 | 0.270023 | − | 0.962854i | \(-0.412969\pi\) | ||||
0.270023 | + | 0.962854i | \(0.412969\pi\) | |||||||
\(252\) | 187.125i | 0.742558i | ||||||||
\(253\) | 57.6365i | 0.227812i | ||||||||
\(254\) | 336.086 | 1.32317 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 167.047 | 0.652528 | ||||||||
\(257\) | −315.240 | −1.22662 | −0.613308 | − | 0.789844i | \(-0.710162\pi\) | ||||
−0.613308 | + | 0.789844i | \(0.710162\pi\) | |||||||
\(258\) | − | 141.893i | − | 0.549974i | ||||||
\(259\) | − | 274.900i | − | 1.06139i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 183.865i | − | 0.704462i | ||||||
\(262\) | 595.649 | 2.27347 | ||||||||
\(263\) | 203.024i | 0.771956i | 0.922508 | + | 0.385978i | \(0.126136\pi\) | ||||
−0.922508 | + | 0.385978i | \(0.873864\pi\) | |||||||
\(264\) | 59.2530 | 0.224443 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −370.197 | + | 278.759i | −1.39172 | + | 1.04797i | ||||
\(267\) | 351.076i | 1.31489i | ||||||||
\(268\) | −512.755 | −1.91326 | ||||||||
\(269\) | − | 272.421i | − | 1.01272i | −0.862323 | − | 0.506359i | \(-0.830991\pi\) | ||
0.862323 | − | 0.506359i | \(-0.169009\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 225.743 | 0.833001 | 0.416501 | − | 0.909135i | \(-0.363256\pi\) | ||||
0.416501 | + | 0.909135i | \(0.363256\pi\) | |||||||
\(272\) | − | 254.890i | − | 0.937097i | ||||||
\(273\) | − | 88.8323i | − | 0.325393i | ||||||
\(274\) | 447.371i | 1.63274i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 30.7756i | − | 0.111506i | ||||||
\(277\) | 133.873i | 0.483296i | 0.970364 | + | 0.241648i | \(0.0776879\pi\) | ||||
−0.970364 | + | 0.241648i | \(0.922312\pi\) | |||||||
\(278\) | 454.772 | 1.63587 | ||||||||
\(279\) | 14.0752i | 0.0504486i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 272.283i | 0.968980i | 0.874797 | + | 0.484490i | \(0.160995\pi\) | ||||
−0.874797 | + | 0.484490i | \(0.839005\pi\) | |||||||
\(282\) | 200.421i | 0.710712i | ||||||||
\(283\) | − | 307.114i | − | 1.08521i | −0.839988 | − | 0.542605i | \(-0.817438\pi\) | ||
0.839988 | − | 0.542605i | \(-0.182562\pi\) | |||||||
\(284\) | 508.010i | 1.78877i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 267.768 | 0.936252 | ||||||||
\(287\) | 174.135 | 0.606741 | ||||||||
\(288\) | −225.247 | −0.782108 | ||||||||
\(289\) | −75.0377 | −0.259646 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 102.536 | 0.352356 | ||||||||
\(292\) | 617.807i | 2.11578i | ||||||||
\(293\) | −272.281 | −0.929287 | −0.464644 | − | 0.885498i | \(-0.653818\pi\) | ||||
−0.464644 | + | 0.885498i | \(0.653818\pi\) | |||||||
\(294\) | 120.591 | 0.410173 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −55.7764 | −0.188434 | ||||||||
\(297\) | 487.737 | 1.64221 | ||||||||
\(298\) | −312.518 | −1.04872 | ||||||||
\(299\) | − | 17.5321i | − | 0.0586357i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 199.496 | 0.662779 | ||||||||
\(302\) | 769.019i | 2.54642i | ||||||||
\(303\) | −202.787 | −0.669263 | ||||||||
\(304\) | −152.684 | − | 202.767i | −0.502251 | − | 0.666997i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 274.311i | 0.896443i | ||||||||
\(307\) | −41.8126 | −0.136198 | −0.0680988 | − | 0.997679i | \(-0.521693\pi\) | ||||
−0.0680988 | + | 0.997679i | \(0.521693\pi\) | |||||||
\(308\) | 660.854i | 2.14563i | ||||||||
\(309\) | 63.8575 | 0.206659 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 399.316 | 1.28398 | 0.641988 | − | 0.766715i | \(-0.278110\pi\) | ||||
0.641988 | + | 0.766715i | \(0.278110\pi\) | |||||||
\(312\) | −18.0238 | −0.0577686 | ||||||||
\(313\) | − | 273.543i | − | 0.873941i | −0.899476 | − | 0.436970i | \(-0.856051\pi\) | ||
0.899476 | − | 0.436970i | \(-0.143949\pi\) | |||||||
\(314\) | 698.441i | 2.22434i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 223.510i | − | 0.707309i | ||||||
\(317\) | 120.459 | 0.379996 | 0.189998 | − | 0.981784i | \(-0.439152\pi\) | ||||
0.189998 | + | 0.981784i | \(0.439152\pi\) | |||||||
\(318\) | −222.092 | −0.698402 | ||||||||
\(319\) | − | 649.340i | − | 2.03555i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −144.646 | −0.450610 | ||||||||
\(322\) | 81.0840 | 0.251814 | ||||||||
\(323\) | −289.595 | + | 218.065i | −0.896578 | + | 0.675125i | ||||
\(324\) | −58.2121 | −0.179667 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 376.801i | − | 1.15583i | ||||||
\(327\) | − | 279.623i | − | 0.855117i | ||||||
\(328\) | − | 35.3314i | − | 0.107718i | ||||||
\(329\) | −281.784 | −0.856485 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 55.2508i | 0.166921i | 0.996511 | + | 0.0834604i | \(0.0265972\pi\) | ||||
−0.996511 | + | 0.0834604i | \(0.973403\pi\) | |||||||
\(332\) | 202.747i | 0.610683i | ||||||||
\(333\) | −162.043 | −0.486615 | ||||||||
\(334\) | −569.445 | −1.70493 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 225.029i | 0.669728i | ||||||||
\(337\) | 480.908 | 1.42703 | 0.713513 | − | 0.700642i | \(-0.247103\pi\) | ||||
0.713513 | + | 0.700642i | \(0.247103\pi\) | |||||||
\(338\) | 413.491 | 1.22335 | ||||||||
\(339\) | −234.472 | −0.691658 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 49.7081i | 0.145772i | ||||||||
\(342\) | 164.318 | + | 218.217i | 0.480461 | + | 0.638061i | ||||
\(343\) | − | 238.534i | − | 0.695434i | ||||||
\(344\) | − | 40.4772i | − | 0.117666i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −742.365 | −2.14556 | ||||||||
\(347\) | − | 538.987i | − | 1.55328i | −0.629946 | − | 0.776639i | \(-0.716923\pi\) | ||
0.629946 | − | 0.776639i | \(-0.283077\pi\) | |||||||
\(348\) | 346.722i | 0.996327i | ||||||||
\(349\) | 21.5094 | 0.0616315 | 0.0308158 | − | 0.999525i | \(-0.490189\pi\) | ||||
0.0308158 | + | 0.999525i | \(0.490189\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −148.362 | −0.422683 | ||||||||
\(352\) | −795.488 | −2.25991 | ||||||||
\(353\) | − | 91.3380i | − | 0.258748i | −0.991596 | − | 0.129374i | \(-0.958703\pi\) | ||
0.991596 | − | 0.129374i | \(-0.0412968\pi\) | |||||||
\(354\) | − | 192.853i | − | 0.544781i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 794.458i | 2.23162i | ||||||||
\(357\) | 321.389 | 0.900248 | ||||||||
\(358\) | − | 767.434i | − | 2.14367i | ||||||
\(359\) | 673.203 | 1.87522 | 0.937609 | − | 0.347691i | \(-0.113034\pi\) | ||||
0.937609 | + | 0.347691i | \(0.113034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −99.7493 | + | 346.945i | −0.276314 | + | 0.961067i | ||||
\(362\) | − | 779.401i | − | 2.15304i | ||||||
\(363\) | 363.211 | 1.00058 | ||||||||
\(364\) | − | 201.021i | − | 0.552255i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −38.9847 | −0.106516 | ||||||||
\(367\) | 595.514i | 1.62265i | 0.584593 | + | 0.811327i | \(0.301254\pi\) | ||||
−0.584593 | + | 0.811327i | \(0.698746\pi\) | |||||||
\(368\) | 44.4120i | 0.120685i | ||||||||
\(369\) | − | 102.646i | − | 0.278172i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 312.252i | − | 0.841651i | ||||||
\(372\) | − | 26.5422i | − | 0.0713499i | ||||||
\(373\) | 228.595 | 0.612854 | 0.306427 | − | 0.951894i | \(-0.400866\pi\) | ||||
0.306427 | + | 0.951894i | \(0.400866\pi\) | |||||||
\(374\) | 968.765i | 2.59028i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 57.1730i | 0.152056i | ||||||||
\(377\) | 197.519i | 0.523922i | ||||||||
\(378\) | − | 686.158i | − | 1.81523i | ||||||
\(379\) | 725.490i | 1.91422i | 0.289723 | + | 0.957110i | \(0.406437\pi\) | ||||
−0.289723 | + | 0.957110i | \(0.593563\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −232.109 | −0.609210 | ||||||||
\(382\) | 600.056 | 1.57083 | ||||||||
\(383\) | 525.150 | 1.37115 | 0.685574 | − | 0.728003i | \(-0.259551\pi\) | ||||
0.685574 | + | 0.728003i | \(0.259551\pi\) | |||||||
\(384\) | 108.228 | 0.281845 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −702.609 | −1.82023 | ||||||||
\(387\) | − | 117.595i | − | 0.303864i | ||||||
\(388\) | 232.031 | 0.598017 | ||||||||
\(389\) | −135.008 | −0.347065 | −0.173533 | − | 0.984828i | \(-0.555518\pi\) | ||||
−0.173533 | + | 0.984828i | \(0.555518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 63.4297 | 0.162224 | ||||||||
\(392\) | 34.4003 | 0.0877560 | ||||||||
\(393\) | −411.369 | −1.04674 | ||||||||
\(394\) | − | 30.9562i | − | 0.0785691i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 389.547 | 0.983705 | ||||||||
\(397\) | − | 344.093i | − | 0.866733i | −0.901218 | − | 0.433366i | \(-0.857326\pi\) | ||
0.901218 | − | 0.433366i | \(-0.142674\pi\) | |||||||
\(398\) | −291.047 | −0.731275 | ||||||||
\(399\) | 255.667 | − | 192.518i | 0.640769 | − | 0.482501i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 66.2162i | 0.165128i | 0.996586 | + | 0.0825638i | \(0.0263108\pi\) | ||||
−0.996586 | + | 0.0825638i | \(0.973689\pi\) | |||||||
\(402\) | 663.600 | 1.65075 | ||||||||
\(403\) | − | 15.1204i | − | 0.0375196i | ||||||
\(404\) | −458.891 | −1.13587 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −913.503 | −2.25001 | ||||||||
\(407\) | −572.274 | −1.40608 | ||||||||
\(408\) | − | 65.2088i | − | 0.159825i | ||||||
\(409\) | 66.1891i | 0.161832i | 0.996721 | + | 0.0809158i | \(0.0257845\pi\) | ||||
−0.996721 | + | 0.0809158i | \(0.974216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 308.965i | − | 0.751739i | ||||||
\(412\) | 144.505 | 0.350740 | ||||||||
\(413\) | 271.143 | 0.656521 | ||||||||
\(414\) | − | 47.7958i | − | 0.115449i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 241.974 | 0.581669 | ||||||||
\(417\) | −314.076 | −0.753180 | ||||||||
\(418\) | 580.308 | + | 770.659i | 1.38830 | + | 1.84368i | ||||
\(419\) | −448.086 | −1.06942 | −0.534709 | − | 0.845036i | \(-0.679579\pi\) | ||||
−0.534709 | + | 0.845036i | \(0.679579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 728.066i | 1.72937i | 0.502312 | + | 0.864686i | \(0.332483\pi\) | ||||
−0.502312 | + | 0.864686i | \(0.667517\pi\) | |||||||
\(422\) | − | 262.877i | − | 0.622932i | ||||||
\(423\) | 166.100i | 0.392672i | ||||||||
\(424\) | −63.3551 | −0.149422 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 657.460i | − | 1.54333i | ||||||
\(427\) | − | 54.8110i | − | 0.128363i | ||||||
\(428\) | −327.323 | −0.764772 | ||||||||
\(429\) | −184.927 | −0.431065 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 623.890i | − | 1.44754i | −0.690042 | − | 0.723770i | \(-0.742408\pi\) | ||
0.690042 | − | 0.723770i | \(-0.257592\pi\) | |||||||
\(432\) | 375.827 | 0.869971 | ||||||||
\(433\) | −3.90352 | −0.00901505 | −0.00450752 | − | 0.999990i | \(-0.501435\pi\) | ||||
−0.00450752 | + | 0.999990i | \(0.501435\pi\) | |||||||
\(434\) | 69.9303 | 0.161130 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 632.766i | − | 1.45130i | ||||||
\(437\) | 50.4588 | − | 37.9956i | 0.115466 | − | 0.0869464i | ||||
\(438\) | − | 799.557i | − | 1.82547i | ||||||
\(439\) | − | 748.985i | − | 1.70612i | −0.521815 | − | 0.853059i | \(-0.674745\pi\) | ||
0.521815 | − | 0.853059i | \(-0.325255\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 99.9406 | 0.226623 | ||||||||
\(442\) | − | 294.682i | − | 0.666702i | ||||||
\(443\) | − | 77.7877i | − | 0.175593i | −0.996138 | − | 0.0877965i | \(-0.972017\pi\) | ||
0.996138 | − | 0.0877965i | \(-0.0279825\pi\) | |||||||
\(444\) | 305.572 | 0.688225 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 304.905 | 0.683642 | ||||||||
\(447\) | 215.832 | 0.482846 | ||||||||
\(448\) | 674.077i | 1.50464i | ||||||||
\(449\) | 112.043i | 0.249539i | 0.992186 | + | 0.124770i | \(0.0398192\pi\) | ||||
−0.992186 | + | 0.124770i | \(0.960181\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 362.505i | − | 0.803781i | ||||||
\(452\) | −530.593 | −1.17388 | ||||||||
\(453\) | − | 531.103i | − | 1.17241i | ||||||
\(454\) | 745.895 | 1.64294 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −39.0613 | − | 51.8740i | −0.0856607 | − | 0.113759i | ||||
\(457\) | 563.415i | 1.23286i | 0.787412 | + | 0.616428i | \(0.211421\pi\) | ||||
−0.787412 | + | 0.616428i | \(0.788579\pi\) | |||||||
\(458\) | 955.406 | 2.08604 | ||||||||
\(459\) | − | 536.761i | − | 1.16941i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −633.225 | −1.37359 | −0.686795 | − | 0.726851i | \(-0.740983\pi\) | ||||
−0.686795 | + | 0.726851i | \(0.740983\pi\) | |||||||
\(462\) | − | 855.268i | − | 1.85123i | ||||||
\(463\) | 547.595i | 1.18271i | 0.806411 | + | 0.591356i | \(0.201407\pi\) | ||||
−0.806411 | + | 0.591356i | \(0.798593\pi\) | |||||||
\(464\) | − | 500.351i | − | 1.07834i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 195.927i | 0.420445i | ||||||||
\(467\) | − | 856.723i | − | 1.83453i | −0.398283 | − | 0.917263i | \(-0.630394\pi\) | ||
0.398283 | − | 0.917263i | \(-0.369606\pi\) | |||||||
\(468\) | −118.494 | −0.253192 | ||||||||
\(469\) | 932.996i | 1.98933i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 482.360i | − | 1.02412i | ||||||
\(472\) | − | 55.0141i | − | 0.116555i | ||||||
\(473\) | − | 415.302i | − | 0.878017i | ||||||
\(474\) | 289.263i | 0.610260i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 727.278 | 1.52790 | ||||||||
\(477\) | −184.060 | −0.385871 | ||||||||
\(478\) | 722.208 | 1.51090 | ||||||||
\(479\) | −218.011 | −0.455137 | −0.227568 | − | 0.973762i | \(-0.573078\pi\) | ||||
−0.227568 | + | 0.973762i | \(0.573078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 174.076 | 0.361905 | ||||||||
\(482\) | 116.926i | 0.242585i | ||||||||
\(483\) | −55.9985 | −0.115939 | ||||||||
\(484\) | 821.920 | 1.69818 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −666.174 | −1.37073 | ||||||||
\(487\) | −782.514 | −1.60680 | −0.803402 | − | 0.595437i | \(-0.796979\pi\) | ||||
−0.803402 | + | 0.595437i | \(0.796979\pi\) | |||||||
\(488\) | −11.1210 | −0.0227889 | ||||||||
\(489\) | 260.228i | 0.532163i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.9182 | 0.0263100 | 0.0131550 | − | 0.999913i | \(-0.495813\pi\) | ||||
0.0131550 | + | 0.999913i | \(0.495813\pi\) | |||||||
\(492\) | 193.563i | 0.393422i | ||||||||
\(493\) | −714.607 | −1.44951 | ||||||||
\(494\) | −176.520 | − | 234.422i | −0.357328 | − | 0.474538i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 38.3027i | 0.0772233i | ||||||||
\(497\) | 924.363 | 1.85988 | ||||||||
\(498\) | − | 262.392i | − | 0.526892i | ||||||
\(499\) | −357.210 | −0.715851 | −0.357926 | − | 0.933750i | \(-0.616516\pi\) | ||||
−0.357926 | + | 0.933750i | \(0.616516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 393.272 | 0.784974 | ||||||||
\(502\) | −396.983 | −0.790802 | ||||||||
\(503\) | − | 317.657i | − | 0.631526i | −0.948838 | − | 0.315763i | \(-0.897740\pi\) | ||
0.948838 | − | 0.315763i | \(-0.102260\pi\) | |||||||
\(504\) | − | 69.0839i | − | 0.137071i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 168.797i | − | 0.333591i | ||||||
\(507\) | −285.566 | −0.563247 | ||||||||
\(508\) | −525.245 | −1.03395 | ||||||||
\(509\) | − | 386.897i | − | 0.760112i | −0.924964 | − | 0.380056i | \(-0.875905\pi\) | ||
0.924964 | − | 0.380056i | \(-0.124095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1124.15 | 2.19989 | ||||||||
\(512\) | −703.261 | −1.37356 | ||||||||
\(513\) | −321.530 | − | 426.998i | −0.626765 | − | 0.832354i | ||||
\(514\) | 923.228 | 1.79616 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 221.755i | 0.429758i | ||||||||
\(517\) | 586.604i | 1.13463i | ||||||||
\(518\) | 805.086i | 1.55422i | ||||||||
\(519\) | 512.695 | 0.987851 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 216.069i | 0.414719i | 0.978265 | + | 0.207359i | \(0.0664870\pi\) | ||||
−0.978265 | + | 0.207359i | \(0.933513\pi\) | |||||||
\(522\) | 538.474i | 1.03156i | ||||||||
\(523\) | −208.535 | −0.398728 | −0.199364 | − | 0.979926i | \(-0.563888\pi\) | ||||
−0.199364 | + | 0.979926i | \(0.563888\pi\) | |||||||
\(524\) | −930.897 | −1.77652 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 594.587i | − | 1.13039i | ||||||
\(527\) | 54.7045 | 0.103804 | ||||||||
\(528\) | 468.454 | 0.887223 | ||||||||
\(529\) | 517.948 | 0.979108 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 159.828i | − | 0.300995i | ||||||
\(532\) | 578.555 | − | 435.653i | 1.08751 | − | 0.818897i | ||||
\(533\) | 110.268i | 0.206882i | ||||||||
\(534\) | − | 1028.18i | − | 1.92542i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 189.302 | 0.353175 | ||||||||
\(537\) | 530.008i | 0.986979i | ||||||||
\(538\) | 797.826i | 1.48295i | ||||||||
\(539\) | 352.953 | 0.654829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −444.565 | −0.821746 | −0.410873 | − | 0.911693i | \(-0.634776\pi\) | ||||
−0.410873 | + | 0.911693i | \(0.634776\pi\) | |||||||
\(542\) | −661.123 | −1.21978 | ||||||||
\(543\) | 538.273i | 0.991294i | ||||||||
\(544\) | 875.445i | 1.60927i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 260.158i | 0.476481i | ||||||||
\(547\) | −57.5311 | −0.105176 | −0.0525879 | − | 0.998616i | \(-0.516747\pi\) | ||||
−0.0525879 | + | 0.998616i | \(0.516747\pi\) | |||||||
\(548\) | − | 699.164i | − | 1.27585i | ||||||
\(549\) | −32.3089 | −0.0588505 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −568.475 | + | 428.063i | −1.03172 | + | 0.776885i | ||||
\(552\) | 11.3619i | 0.0205832i | ||||||||
\(553\) | −406.693 | −0.735430 | ||||||||
\(554\) | − | 392.067i | − | 0.707702i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −710.731 | −1.27829 | ||||||||
\(557\) | 32.9110i | 0.0590861i | 0.999564 | + | 0.0295430i | \(0.00940521\pi\) | ||||
−0.999564 | + | 0.0295430i | \(0.990595\pi\) | |||||||
\(558\) | − | 41.2212i | − | 0.0738730i | ||||||
\(559\) | 126.328i | 0.225989i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 669.052i | − | 1.19261i | ||||||
\(562\) | − | 797.422i | − | 1.41890i | ||||||
\(563\) | −924.040 | −1.64128 | −0.820640 | − | 0.571446i | \(-0.806383\pi\) | ||||
−0.820640 | + | 0.571446i | \(0.806383\pi\) | |||||||
\(564\) | − | 313.223i | − | 0.555360i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 899.429i | 1.58910i | ||||||||
\(567\) | 105.921i | 0.186810i | ||||||||
\(568\) | − | 187.550i | − | 0.330194i | ||||||
\(569\) | 73.0173i | 0.128326i | 0.997939 | + | 0.0641628i | \(0.0204377\pi\) | ||||
−0.997939 | + | 0.0641628i | \(0.979562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 709.971 | 1.24338 | 0.621690 | − | 0.783263i | \(-0.286446\pi\) | ||||
0.621690 | + | 0.783263i | \(0.286446\pi\) | |||||||
\(572\) | −418.476 | −0.731601 | ||||||||
\(573\) | −414.413 | −0.723234 | ||||||||
\(574\) | −509.979 | −0.888465 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 397.342 | 0.689830 | ||||||||
\(577\) | 152.315i | 0.263978i | 0.991251 | + | 0.131989i | \(0.0421363\pi\) | ||||
−0.991251 | + | 0.131989i | \(0.957864\pi\) | |||||||
\(578\) | 219.759 | 0.380206 | ||||||||
\(579\) | 485.238 | 0.838062 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 368.913 | 0.634962 | ||||||||
\(582\) | −300.291 | −0.515964 | ||||||||
\(583\) | −650.032 | −1.11498 | ||||||||
\(584\) | − | 228.086i | − | 0.390558i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 797.415 | 1.36078 | ||||||||
\(587\) | − | 96.2527i | − | 0.163974i | −0.996633 | − | 0.0819870i | \(-0.973873\pi\) | ||
0.996633 | − | 0.0819870i | \(-0.0261266\pi\) | |||||||
\(588\) | −188.463 | −0.320515 | ||||||||
\(589\) | 43.5178 | − | 32.7690i | 0.0738842 | − | 0.0556350i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.3791i | 0.0361744i | ||||||||
\(592\) | −440.968 | −0.744878 | ||||||||
\(593\) | 707.928i | 1.19381i | 0.802313 | + | 0.596904i | \(0.203603\pi\) | ||||
−0.802313 | + | 0.596904i | \(0.796397\pi\) | |||||||
\(594\) | −1428.41 | −2.40473 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 488.412 | 0.819483 | ||||||||
\(597\) | 201.004 | 0.336690 | ||||||||
\(598\) | 51.3452i | 0.0858616i | ||||||||
\(599\) | 197.129i | 0.329097i | 0.986369 | + | 0.164549i | \(0.0526168\pi\) | ||||
−0.986369 | + | 0.164549i | \(0.947383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 828.260i | 1.37814i | 0.724697 | + | 0.689068i | \(0.241980\pi\) | ||||
−0.724697 | + | 0.689068i | \(0.758020\pi\) | |||||||
\(602\) | −584.255 | −0.970522 | ||||||||
\(603\) | 549.964 | 0.912047 | ||||||||
\(604\) | − | 1201.85i | − | 1.98981i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 593.891 | 0.980017 | ||||||||
\(607\) | −386.555 | −0.636829 | −0.318415 | − | 0.947952i | \(-0.603150\pi\) | ||||
−0.318415 | + | 0.947952i | \(0.603150\pi\) | |||||||
\(608\) | 524.408 | + | 696.423i | 0.862513 | + | 1.14543i | ||||
\(609\) | 630.887 | 1.03594 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 178.435i | − | 0.292038i | ||||||
\(612\) | − | 428.702i | − | 0.700493i | ||||||
\(613\) | 1061.04i | 1.73090i | 0.500993 | + | 0.865451i | \(0.332968\pi\) | ||||
−0.500993 | + | 0.865451i | \(0.667032\pi\) | |||||||
\(614\) | 122.454 | 0.199437 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 243.978i | − | 0.396068i | ||||||
\(617\) | 1188.74i | 1.92665i | 0.268337 | + | 0.963325i | \(0.413526\pi\) | ||||
−0.268337 | + | 0.963325i | \(0.586474\pi\) | |||||||
\(618\) | −187.016 | −0.302615 | ||||||||
\(619\) | 906.151 | 1.46390 | 0.731948 | − | 0.681361i | \(-0.238611\pi\) | ||||
0.731948 | + | 0.681361i | \(0.238611\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 93.5250i | 0.150604i | ||||||||
\(622\) | −1169.46 | −1.88016 | ||||||||
\(623\) | 1445.58 | 2.32035 | ||||||||
\(624\) | −142.496 | −0.228359 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 801.112i | 1.27973i | ||||||||
\(627\) | −400.775 | − | 532.235i | −0.639194 | − | 0.848860i | ||||
\(628\) | − | 1091.54i | − | 1.73813i | ||||||
\(629\) | 629.795i | 1.00126i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 310.563 | 0.492176 | 0.246088 | − | 0.969247i | \(-0.420855\pi\) | ||||
0.246088 | + | 0.969247i | \(0.420855\pi\) | |||||||
\(632\) | 82.5167i | 0.130564i | ||||||||
\(633\) | 181.549i | 0.286808i | ||||||||
\(634\) | −352.782 | −0.556438 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 347.091 | 0.545741 | ||||||||
\(637\) | −107.362 | −0.168544 | ||||||||
\(638\) | 1901.69i | 2.98070i | ||||||||
\(639\) | − | 544.875i | − | 0.852700i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 673.349i | − | 1.05047i | −0.850958 | − | 0.525233i | \(-0.823978\pi\) | ||
0.850958 | − | 0.525233i | \(-0.176022\pi\) | |||||||
\(642\) | 423.616 | 0.659839 | ||||||||
\(643\) | − | 454.931i | − | 0.707514i | −0.935337 | − | 0.353757i | \(-0.884904\pi\) | ||
0.935337 | − | 0.353757i | \(-0.115096\pi\) | |||||||
\(644\) | −126.720 | −0.196771 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 848.121 | − | 638.637i | 1.31288 | − | 0.988602i | ||||
\(647\) | − | 357.358i | − | 0.552331i | −0.961110 | − | 0.276166i | \(-0.910936\pi\) | ||
0.961110 | − | 0.276166i | \(-0.0890638\pi\) | |||||||
\(648\) | 21.4911 | 0.0331653 | ||||||||
\(649\) | − | 564.453i | − | 0.869728i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −48.2955 | −0.0741866 | ||||||||
\(652\) | 588.875i | 0.903183i | ||||||||
\(653\) | − | 859.520i | − | 1.31626i | −0.752903 | − | 0.658132i | \(-0.771347\pi\) | ||
0.752903 | − | 0.658132i | \(-0.228653\pi\) | |||||||
\(654\) | 818.918i | 1.25217i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 279.329i | − | 0.425807i | ||||||
\(657\) | − | 662.640i | − | 1.00858i | ||||||
\(658\) | 825.245 | 1.25417 | ||||||||
\(659\) | − | 103.485i | − | 0.157033i | −0.996913 | − | 0.0785166i | \(-0.974982\pi\) | ||
0.996913 | − | 0.0785166i | \(-0.0250183\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 520.372i | − | 0.787249i | −0.919271 | − | 0.393625i | \(-0.871221\pi\) | ||
0.919271 | − | 0.393625i | \(-0.128779\pi\) | |||||||
\(662\) | − | 161.810i | − | 0.244426i | ||||||
\(663\) | 203.514i | 0.306960i | ||||||||
\(664\) | − | 74.8513i | − | 0.112728i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 474.566 | 0.712562 | ||||||||
\(667\) | 124.513 | 0.186676 | ||||||||
\(668\) | 889.945 | 1.33225 | ||||||||
\(669\) | −210.574 | −0.314760 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −114.103 | −0.170049 | ||||||||
\(672\) | − | 772.881i | − | 1.15012i | ||||||
\(673\) | −687.475 | −1.02151 | −0.510754 | − | 0.859727i | \(-0.670634\pi\) | ||||
−0.510754 | + | 0.859727i | \(0.670634\pi\) | |||||||
\(674\) | −1408.41 | −2.08963 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −646.215 | −0.955940 | ||||||||
\(677\) | 540.624 | 0.798558 | 0.399279 | − | 0.916830i | \(-0.369261\pi\) | ||||
0.399279 | + | 0.916830i | \(0.369261\pi\) | |||||||
\(678\) | 686.686 | 1.01281 | ||||||||
\(679\) | − | 422.197i | − | 0.621793i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −515.133 | −0.756436 | ||||||||
\(682\) | − | 145.578i | − | 0.213457i | ||||||
\(683\) | 405.203 | 0.593270 | 0.296635 | − | 0.954991i | \(-0.404136\pi\) | ||||
0.296635 | + | 0.954991i | \(0.404136\pi\) | |||||||
\(684\) | −256.801 | − | 341.035i | −0.375439 | − | 0.498590i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 698.581i | 1.01834i | ||||||||
\(687\) | −659.826 | −0.960445 | ||||||||
\(688\) | − | 320.012i | − | 0.465134i | ||||||
\(689\) | 197.729 | 0.286980 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −252.865 | −0.365941 | −0.182970 | − | 0.983118i | \(-0.558571\pi\) | ||||
−0.182970 | + | 0.983118i | \(0.558571\pi\) | |||||||
\(692\) | 1160.19 | 1.67657 | ||||||||
\(693\) | − | 708.811i | − | 1.02282i | ||||||
\(694\) | 1578.50i | 2.27450i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 128.005i | − | 0.183915i | ||||||
\(697\) | −398.942 | −0.572370 | ||||||||
\(698\) | −62.9935 | −0.0902485 | ||||||||
\(699\) | − | 135.312i | − | 0.193579i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −77.0624 | −0.109932 | −0.0549660 | − | 0.998488i | \(-0.517505\pi\) | ||||
−0.0549660 | + | 0.998488i | \(0.517505\pi\) | |||||||
\(702\) | 434.499 | 0.618944 | ||||||||
\(703\) | 377.259 | + | 501.007i | 0.536642 | + | 0.712670i | ||||
\(704\) | 1403.26 | 1.99327 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 267.497i | 0.378891i | ||||||||
\(707\) | 834.987i | 1.18103i | ||||||||
\(708\) | 301.396i | 0.425700i | ||||||||
\(709\) | −876.024 | −1.23558 | −0.617788 | − | 0.786344i | \(-0.711971\pi\) | ||||
−0.617788 | + | 0.786344i | \(0.711971\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 239.729i | 0.337172i | ||||||||
\(712\) | − | 293.303i | − | 0.411942i | ||||||
\(713\) | −9.53167 | −0.0133684 | ||||||||
\(714\) | −941.234 | −1.31825 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1199.37i | 1.67510i | ||||||||
\(717\) | −498.774 | −0.695640 | ||||||||
\(718\) | −1971.58 | −2.74593 | ||||||||
\(719\) | −819.304 | −1.13950 | −0.569752 | − | 0.821816i | \(-0.692961\pi\) | ||||
−0.569752 | + | 0.821816i | \(0.692961\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 262.937i | − | 0.364684i | ||||||
\(722\) | 292.131 | − | 1016.08i | 0.404613 | − | 1.40731i | ||||
\(723\) | − | 80.7517i | − | 0.111690i | ||||||
\(724\) | 1218.07i | 1.68242i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1063.72 | −1.46518 | ||||||||
\(727\) | 140.643i | 0.193457i | 0.995311 | + | 0.0967286i | \(0.0308379\pi\) | ||||
−0.995311 | + | 0.0967286i | \(0.969162\pi\) | |||||||
\(728\) | 74.2141i | 0.101943i | ||||||||
\(729\) | 574.541 | 0.788123 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −457.046 | −0.625233 | ||||||||
\(732\) | 60.9265 | 0.0832329 | ||||||||
\(733\) | 693.708i | 0.946395i | 0.880956 | + | 0.473197i | \(0.156900\pi\) | ||||
−0.880956 | + | 0.473197i | \(0.843100\pi\) | |||||||
\(734\) | − | 1744.05i | − | 2.37609i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 152.537i | − | 0.207251i | ||||||
\(737\) | 1942.27 | 2.63537 | ||||||||
\(738\) | 300.613i | 0.407334i | ||||||||
\(739\) | 1424.83 | 1.92806 | 0.964028 | − | 0.265801i | \(-0.0856364\pi\) | ||||
0.964028 | + | 0.265801i | \(0.0856364\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 121.909 | + | 161.897i | 0.164520 | + | 0.218485i | ||||
\(742\) | 914.477i | 1.23245i | ||||||||
\(743\) | −1046.28 | −1.40818 | −0.704092 | − | 0.710109i | \(-0.748646\pi\) | ||||
−0.704092 | + | 0.710109i | \(0.748646\pi\) | |||||||
\(744\) | 9.79901i | 0.0131707i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −669.473 | −0.897417 | ||||||||
\(747\) | − | 217.460i | − | 0.291111i | ||||||
\(748\) | − | 1514.01i | − | 2.02408i | ||||||
\(749\) | 595.588i | 0.795178i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 70.9338i | 0.0944525i | 0.998884 | + | 0.0472262i | \(0.0150382\pi\) | ||||
−0.998884 | + | 0.0472262i | \(0.984962\pi\) | |||||||
\(752\) | 452.009i | 0.601076i | ||||||||
\(753\) | 274.166 | 0.364098 | ||||||||
\(754\) | − | 578.462i | − | 0.767191i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1072.35i | 1.41845i | ||||||||
\(757\) | 1422.41i | 1.87901i | 0.342532 | + | 0.939506i | \(0.388716\pi\) | ||||
−0.342532 | + | 0.939506i | \(0.611284\pi\) | |||||||
\(758\) | − | 2124.70i | − | 2.80304i | ||||||
\(759\) | 116.575i | 0.153590i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 110.061 | 0.144627 | 0.0723136 | − | 0.997382i | \(-0.476962\pi\) | ||||
0.0723136 | + | 0.997382i | \(0.476962\pi\) | |||||||
\(762\) | 679.765 | 0.892080 | ||||||||
\(763\) | −1151.37 | −1.50900 | ||||||||
\(764\) | −937.786 | −1.22747 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1537.98 | −2.00780 | ||||||||
\(767\) | 171.697i | 0.223856i | ||||||||
\(768\) | 337.868 | 0.439932 | ||||||||
\(769\) | −136.681 | −0.177739 | −0.0888693 | − | 0.996043i | \(-0.528325\pi\) | ||||
−0.0888693 | + | 0.996043i | \(0.528325\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −637.603 | −0.826981 | ||||||||
\(772\) | 1098.06 | 1.42235 | ||||||||
\(773\) | −177.135 | −0.229153 | −0.114576 | − | 0.993414i | \(-0.536551\pi\) | ||||
−0.114576 | + | 0.993414i | \(0.536551\pi\) | |||||||
\(774\) | 344.395i | 0.444955i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −85.6625 | −0.110390 | ||||||||
\(777\) | − | 556.011i | − | 0.715587i | ||||||
\(778\) | 395.392 | 0.508216 | ||||||||
\(779\) | −317.361 | + | 238.974i | −0.407396 | + | 0.306770i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1924.29i | − | 2.46389i | ||||||
\(782\) | −185.763 | −0.237549 | ||||||||
\(783\) | − | 1053.66i | − | 1.34568i | ||||||
\(784\) | 271.969 | 0.346899 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1204.75 | 1.53277 | ||||||||
\(787\) | −210.259 | −0.267166 | −0.133583 | − | 0.991038i | \(-0.542648\pi\) | ||||
−0.133583 | + | 0.991038i | \(0.542648\pi\) | |||||||
\(788\) | 48.3793i | 0.0613950i | ||||||||
\(789\) | 410.636i | 0.520451i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 965.453i | 1.22055i | ||||||||
\(792\) | −143.816 | −0.181585 | ||||||||
\(793\) | 34.7083 | 0.0437683 | ||||||||
\(794\) | 1007.73i | 1.26918i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 454.857 | 0.571429 | ||||||||
\(797\) | 474.092 | 0.594845 | 0.297423 | − | 0.954746i | \(-0.403873\pi\) | ||||
0.297423 | + | 0.954746i | \(0.403873\pi\) | |||||||
\(798\) | −748.758 | + | 563.817i | −0.938293 | + | 0.706537i | ||||
\(799\) | 645.565 | 0.807967 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 852.110i | − | 1.06381i | ||||||
\(802\) | − | 193.924i | − | 0.241800i | ||||||
\(803\) | − | 2340.19i | − | 2.91431i | ||||||
\(804\) | −1037.09 | −1.28992 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 44.2823i | 0.0549408i | ||||||||
\(807\) | − | 550.997i | − | 0.682772i | ||||||
\(808\) | 169.416 | 0.209674 | ||||||||
\(809\) | 1279.92 | 1.58210 | 0.791050 | − | 0.611751i | \(-0.209535\pi\) | ||||
0.791050 | + | 0.611751i | \(0.209535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 869.604i | − | 1.07226i | −0.844135 | − | 0.536130i | \(-0.819886\pi\) | ||
0.844135 | − | 0.536130i | \(-0.180114\pi\) | |||||||
\(812\) | 1427.65 | 1.75819 | ||||||||
\(813\) | 456.587 | 0.561607 | ||||||||
\(814\) | 1675.99 | 2.05896 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 515.540i | − | 0.631789i | ||||||
\(817\) | −363.583 | + | 273.779i | −0.445022 | + | 0.335103i | ||||
\(818\) | − | 193.845i | − | 0.236974i | ||||||
\(819\) | 215.609i | 0.263258i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1061.20 | −1.29257 | −0.646287 | − | 0.763094i | \(-0.723679\pi\) | ||||
−0.646287 | + | 0.763094i | \(0.723679\pi\) | |||||||
\(822\) | 904.849i | 1.10079i | ||||||||
\(823\) | 458.926i | 0.557626i | 0.960345 | + | 0.278813i | \(0.0899409\pi\) | ||||
−0.960345 | + | 0.278813i | \(0.910059\pi\) | |||||||
\(824\) | −53.3492 | −0.0647441 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −794.083 | −0.961359 | ||||||||
\(827\) | 746.165 | 0.902255 | 0.451128 | − | 0.892459i | \(-0.351022\pi\) | ||||
0.451128 | + | 0.892459i | \(0.351022\pi\) | |||||||
\(828\) | 74.6967i | 0.0902134i | ||||||||
\(829\) | − | 200.255i | − | 0.241562i | −0.992679 | − | 0.120781i | \(-0.961460\pi\) | ||
0.992679 | − | 0.120781i | \(-0.0385399\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 270.771i | 0.325837i | ||||||||
\(832\) | −426.849 | −0.513040 | ||||||||
\(833\) | − | 388.429i | − | 0.466301i | ||||||
\(834\) | 919.818 | 1.10290 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −906.923 | − | 1204.41i | −1.08484 | − | 1.44068i | ||||
\(837\) | 80.6599i | 0.0963678i | ||||||||
\(838\) | 1312.29 | 1.56597 | ||||||||
\(839\) | − | 247.657i | − | 0.295181i | −0.989049 | − | 0.147591i | \(-0.952848\pi\) | ||
0.989049 | − | 0.147591i | \(-0.0471518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −561.777 | −0.667987 | ||||||||
\(842\) | − | 2132.25i | − | 2.53236i | ||||||
\(843\) | 550.718i | 0.653284i | ||||||||
\(844\) | 410.832i | 0.486768i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 486.449i | − | 0.574999i | ||||||
\(847\) | − | 1495.55i | − | 1.76570i | ||||||
\(848\) | −500.884 | −0.590665 | ||||||||
\(849\) | − | 621.167i | − | 0.731645i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 109.735i | − | 0.128948i | ||||||
\(852\) | 1027.50i | 1.20598i | ||||||||
\(853\) | 172.802i | 0.202581i | 0.994857 | + | 0.101291i | \(0.0322972\pi\) | ||||
−0.994857 | + | 0.101291i | \(0.967703\pi\) | |||||||
\(854\) | 160.522i | 0.187965i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 120.843 | 0.141172 | ||||||||
\(857\) | 795.527 | 0.928270 | 0.464135 | − | 0.885765i | \(-0.346365\pi\) | ||||
0.464135 | + | 0.885765i | \(0.346365\pi\) | |||||||
\(858\) | 541.586 | 0.631219 | ||||||||
\(859\) | 104.671 | 0.121852 | 0.0609260 | − | 0.998142i | \(-0.480595\pi\) | ||||
0.0609260 | + | 0.998142i | \(0.480595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 352.203 | 0.409063 | ||||||||
\(862\) | 1827.15i | 2.11967i | ||||||||
\(863\) | −887.350 | −1.02822 | −0.514108 | − | 0.857725i | \(-0.671877\pi\) | ||||
−0.514108 | + | 0.857725i | \(0.671877\pi\) | |||||||
\(864\) | −1290.81 | −1.49400 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.4320 | 0.0132009 | ||||||||
\(867\) | −151.771 | −0.175053 | ||||||||
\(868\) | −109.289 | −0.125909 | ||||||||
\(869\) | 846.633i | 0.974262i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −590.806 | −0.678307 | ||||||||
\(872\) | 233.609i | 0.267900i | ||||||||
\(873\) | −248.869 | −0.285073 | ||||||||
\(874\) | −147.776 | + | 111.276i | −0.169080 | + | 0.127318i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1249.57i | 1.42645i | ||||||||
\(877\) | −82.4212 | −0.0939809 | −0.0469904 | − | 0.998895i | \(-0.514963\pi\) | ||||
−0.0469904 | + | 0.998895i | \(0.514963\pi\) | |||||||
\(878\) | 2193.51i | 2.49831i | ||||||||
\(879\) | −550.714 | −0.626523 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1311.40 | 1.48853 | 0.744267 | − | 0.667883i | \(-0.232799\pi\) | ||||
0.744267 | + | 0.667883i | \(0.232799\pi\) | |||||||
\(882\) | −292.691 | −0.331849 | ||||||||
\(883\) | 61.4085i | 0.0695453i | 0.999395 | + | 0.0347727i | \(0.0110707\pi\) | ||||
−0.999395 | + | 0.0347727i | \(0.988929\pi\) | |||||||
\(884\) | 460.538i | 0.520971i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 227.813i | 0.257125i | ||||||||
\(887\) | −70.9500 | −0.0799887 | −0.0399943 | − | 0.999200i | \(-0.512734\pi\) | ||||
−0.0399943 | + | 0.999200i | \(0.512734\pi\) | |||||||
\(888\) | −112.813 | −0.127042 | ||||||||
\(889\) | 955.723i | 1.07505i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 220.502 | 0.247477 | ||||||||
\(892\) | −476.514 | −0.534208 | ||||||||
\(893\) | 513.552 | − | 386.706i | 0.575086 | − | 0.433041i | ||||
\(894\) | −632.096 | −0.707042 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 445.637i | − | 0.497363i | ||||||
\(897\) | − | 35.4602i | − | 0.0395320i | ||||||
\(898\) | − | 328.135i | − | 0.365407i | ||||||
\(899\) | 107.385 | 0.119449 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 715.369i | 0.793972i | ||||||||
\(902\) | 1061.65i | 1.17700i | ||||||||
\(903\) | 403.500 | 0.446844 | ||||||||
\(904\) | 195.888 | 0.216690 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1555.41i | 1.71679i | ||||||||
\(907\) | 658.755 | 0.726301 | 0.363151 | − | 0.931730i | \(-0.381701\pi\) | ||||
0.363151 | + | 0.931730i | \(0.381701\pi\) | |||||||
\(908\) | −1165.71 | −1.28382 | ||||||||
\(909\) | 492.192 | 0.541465 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 445.396i | − | 0.488909i | −0.969661 | − | 0.244454i | \(-0.921391\pi\) | ||
0.969661 | − | 0.244454i | \(-0.0786089\pi\) | |||||||
\(912\) | −308.818 | − | 410.115i | −0.338616 | − | 0.449688i | ||||
\(913\) | − | 767.986i | − | 0.841168i | ||||||
\(914\) | − | 1650.04i | − | 1.80530i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1493.14 | −1.63006 | ||||||||
\(917\) | 1693.84i | 1.84715i | ||||||||
\(918\) | 1571.98i | 1.71240i | ||||||||
\(919\) | −423.867 | −0.461226 | −0.230613 | − | 0.973046i | \(-0.574073\pi\) | ||||
−0.230613 | + | 0.973046i | \(0.574073\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −84.5699 | −0.0918240 | ||||||||
\(922\) | 1854.49 | 2.01138 | ||||||||
\(923\) | 585.339i | 0.634170i | ||||||||
\(924\) | 1336.64i | 1.44658i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 1603.71i | − | 1.73187i | ||||||
\(927\) | −154.991 | −0.167197 | ||||||||
\(928\) | 1718.50i | 1.85183i | ||||||||
\(929\) | −976.138 | −1.05074 | −0.525370 | − | 0.850874i | \(-0.676073\pi\) | ||||
−0.525370 | + | 0.850874i | \(0.676073\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −232.676 | − | 308.998i | −0.249921 | − | 0.331899i | ||||
\(932\) | − | 306.201i | − | 0.328542i | ||||||
\(933\) | 807.654 | 0.865653 | ||||||||
\(934\) | 2509.04i | 2.68634i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 43.7463 | 0.0467375 | ||||||||
\(937\) | − | 383.017i | − | 0.408770i | −0.978891 | − | 0.204385i | \(-0.934481\pi\) | ||
0.978891 | − | 0.204385i | \(-0.0655194\pi\) | |||||||
\(938\) | − | 2732.42i | − | 2.91302i | ||||||
\(939\) | − | 553.267i | − | 0.589209i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1515.60i | 1.61062i | 0.592851 | + | 0.805312i | \(0.298002\pi\) | ||||
−0.592851 | + | 0.805312i | \(0.701998\pi\) | |||||||
\(942\) | 1412.66i | 1.49964i | ||||||||
\(943\) | 69.5114 | 0.0737130 | ||||||||
\(944\) | − | 434.941i | − | 0.460743i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1216.27i | 1.28570i | ||||||||
\(947\) | 33.4812i | 0.0353550i | 0.999844 | + | 0.0176775i | \(0.00562722\pi\) | ||||
−0.999844 | + | 0.0176775i | \(0.994373\pi\) | |||||||
\(948\) | − | 452.069i | − | 0.476866i | ||||||
\(949\) | 711.849i | 0.750104i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 243.639 | 0.256193 | ||||||||
\(952\) | −268.501 | −0.282039 | ||||||||
\(953\) | −1337.39 | −1.40335 | −0.701674 | − | 0.712499i | \(-0.747563\pi\) | ||||
−0.701674 | + | 0.712499i | \(0.747563\pi\) | |||||||
\(954\) | 539.048 | 0.565040 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1128.69 | −1.18064 | ||||||||
\(957\) | − | 1313.35i | − | 1.37236i | ||||||
\(958\) | 638.476 | 0.666468 | ||||||||
\(959\) | −1272.18 | −1.32657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 952.779 | 0.991446 | ||||||||
\(962\) | −509.808 | −0.529946 | ||||||||
\(963\) | 351.076 | 0.364565 | ||||||||
\(964\) | − | 182.735i | − | 0.189559i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 164.000 | 0.169772 | ||||||||
\(967\) | 146.380i | 0.151375i | 0.997132 | + | 0.0756877i | \(0.0241152\pi\) | ||||
−0.997132 | + | 0.0756877i | \(0.975885\pi\) | |||||||
\(968\) | −303.442 | −0.313473 | ||||||||
\(969\) | −585.732 | + | 441.058i | −0.604471 | + | 0.455168i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1118.48i | − | 1.15188i | −0.817492 | − | 0.575940i | \(-0.804636\pi\) | ||
0.817492 | − | 0.575940i | \(-0.195364\pi\) | |||||||
\(972\) | 1041.12 | 1.07111 | ||||||||
\(973\) | 1293.23i | 1.32912i | ||||||||
\(974\) | 2291.71 | 2.35288 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −87.9224 | −0.0900844 | ||||||||
\(977\) | −850.328 | −0.870346 | −0.435173 | − | 0.900347i | \(-0.643313\pi\) | ||||
−0.435173 | + | 0.900347i | \(0.643313\pi\) | |||||||
\(978\) | − | 762.115i | − | 0.779258i | ||||||
\(979\) | − | 3009.33i | − | 3.07388i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 678.685i | 0.691830i | ||||||||
\(982\) | −37.8328 | −0.0385263 | ||||||||
\(983\) | 1064.58 | 1.08299 | 0.541493 | − | 0.840705i | \(-0.317859\pi\) | ||||
0.541493 | + | 0.840705i | \(0.317859\pi\) | |||||||
\(984\) | − | 71.4610i | − | 0.0726230i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2092.83 | 2.12255 | ||||||||
\(987\) | −569.933 | −0.577440 | ||||||||
\(988\) | 275.871 | + | 366.361i | 0.279222 | + | 0.370811i | ||||
\(989\) | 79.6353 | 0.0805210 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1750.89i | 1.76679i | 0.468631 | + | 0.883394i | \(0.344747\pi\) | ||||
−0.468631 | + | 0.883394i | \(0.655253\pi\) | |||||||
\(992\) | − | 131.554i | − | 0.132615i | ||||||
\(993\) | 111.750i | 0.112538i | ||||||||
\(994\) | −2707.13 | −2.72347 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 410.074i | 0.411721i | ||||||||
\(997\) | − | 444.357i | − | 0.445695i | −0.974853 | − | 0.222847i | \(-0.928465\pi\) | ||
0.974853 | − | 0.222847i | \(-0.0715351\pi\) | |||||||
\(998\) | 1046.14 | 1.04824 | ||||||||
\(999\) | −928.612 | −0.929542 |
(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 | 475.3.d.d.474.5 | 28 | ||
5.2 | odd | 4 | 475.3.c.h.151.3 | ✓ | 14 | ||
5.3 | odd | 4 | 475.3.c.i.151.12 | yes | 14 | ||
5.4 | even | 2 | inner | 475.3.d.d.474.24 | 28 | ||
19.18 | odd | 2 | inner | 475.3.d.d.474.23 | 28 | ||
95.18 | even | 4 | 475.3.c.i.151.3 | yes | 14 | ||
95.37 | even | 4 | 475.3.c.h.151.12 | yes | 14 | ||
95.94 | odd | 2 | inner | 475.3.d.d.474.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.3.c.h.151.3 | ✓ | 14 | 5.2 | odd | 4 | ||
475.3.c.h.151.12 | yes | 14 | 95.37 | even | 4 | ||
475.3.c.i.151.3 | yes | 14 | 95.18 | even | 4 | ||
475.3.c.i.151.12 | yes | 14 | 5.3 | odd | 4 | ||
475.3.d.d.474.5 | 28 | 1.1 | even | 1 | trivial | ||
475.3.d.d.474.6 | 28 | 95.94 | odd | 2 | inner | ||
475.3.d.d.474.23 | 28 | 19.18 | odd | 2 | inner | ||
475.3.d.d.474.24 | 28 | 5.4 | even | 2 | inner |