Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(929,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("960.929");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.i (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: | \(26.1581053786\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 929.50 | ||
Character | \(\chi\) | \(=\) | 960.929 |
Dual form | 960.3.i.b.929.53 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.54191 | − | 1.59332i | 0.847305 | − | 0.531107i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.96076 | + | 0.625206i | −0.992152 | + | 0.125041i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.93744i | 0.848205i | 0.905614 | + | 0.424103i | \(0.139410\pi\) | ||||
−0.905614 | + | 0.424103i | \(0.860590\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.92266 | − | 8.10017i | 0.435851 | − | 0.900019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.99878 | −0.545344 | −0.272672 | − | 0.962107i | \(-0.587907\pi\) | ||||
−0.272672 | + | 0.962107i | \(0.587907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.6160 | 1.20123 | 0.600617 | − | 0.799537i | \(-0.294922\pi\) | ||||
0.600617 | + | 0.799537i | \(0.294922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.6137 | + | 9.49330i | −0.774245 | + | 0.632887i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.2275 | −0.836913 | −0.418457 | − | 0.908237i | \(-0.637429\pi\) | ||||
−0.418457 | + | 0.908237i | \(0.637429\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 29.6128i | − | 1.55857i | −0.626672 | − | 0.779283i | \(-0.715583\pi\) | ||
0.626672 | − | 0.779283i | \(-0.284417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.46024 | + | 15.0925i | 0.450488 | + | 0.718688i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 21.5275 | 0.935977 | 0.467989 | − | 0.883734i | \(-0.344979\pi\) | ||||
0.467989 | + | 0.883734i | \(0.344979\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.2182 | − | 6.20299i | 0.968729 | − | 0.248119i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.93512 | − | 26.8400i | −0.108708 | − | 0.994074i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 18.1383 | 0.625459 | 0.312729 | − | 0.949842i | \(-0.398757\pi\) | ||||
0.312729 | + | 0.949842i | \(0.398757\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.55847 | −0.276080 | −0.138040 | − | 0.990427i | \(-0.544080\pi\) | ||||
−0.138040 | + | 0.990427i | \(0.544080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.2484 | + | 9.55799i | −0.462072 | + | 0.289636i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.71212 | − | 29.4542i | −0.106060 | − | 0.841548i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −13.4855 | −0.364473 | −0.182236 | − | 0.983255i | \(-0.558334\pi\) | ||||
−0.182236 | + | 0.983255i | \(0.558334\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.6947 | − | 24.8814i | 1.01781 | − | 0.637984i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 18.8052i | − | 0.458664i | −0.973348 | − | 0.229332i | \(-0.926346\pi\) | ||
0.973348 | − | 0.229332i | \(-0.0736541\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 27.1036 | 0.630317 | 0.315158 | − | 0.949039i | \(-0.397942\pi\) | ||||
0.315158 | + | 0.949039i | \(0.397942\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.3951 | + | 42.6355i | −0.319891 | + | 0.947455i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 37.4498 | 0.796805 | 0.398403 | − | 0.917211i | \(-0.369565\pi\) | ||||
0.398403 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.7469 | 0.280548 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −36.1651 | + | 22.6690i | −0.709120 | + | 0.444490i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 93.5909i | − | 1.76587i | −0.469498 | − | 0.882933i | \(-0.655565\pi\) | ||
0.469498 | − | 0.882933i | \(-0.344435\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 29.7585 | − | 3.75047i | 0.541064 | − | 0.0681904i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −47.1827 | − | 75.2731i | −0.827766 | − | 1.32058i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 83.7790 | 1.41998 | 0.709992 | − | 0.704210i | \(-0.248699\pi\) | ||||
0.709992 | + | 0.704210i | \(0.248699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 39.3326i | − | 0.644797i | −0.946604 | − | 0.322398i | \(-0.895511\pi\) | ||
0.946604 | − | 0.322398i | \(-0.104489\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 48.0942 | + | 23.2905i | 0.763401 | + | 0.369691i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −77.4674 | + | 9.76324i | −1.19181 | + | 0.150204i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 103.540 | 1.54538 | 0.772688 | − | 0.634785i | \(-0.218912\pi\) | ||||
0.772688 | + | 0.634785i | \(0.218912\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 54.7210 | − | 34.3002i | 0.793058 | − | 0.497104i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5589i | 0.205054i | 0.994730 | + | 0.102527i | \(0.0326928\pi\) | ||||
−0.994730 | + | 0.102527i | \(0.967307\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 95.8968i | − | 1.31366i | −0.754041 | − | 0.656828i | \(-0.771898\pi\) | ||
0.754041 | − | 0.656828i | \(-0.228102\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 51.6773 | − | 54.3549i | 0.689031 | − | 0.724732i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 35.6174i | − | 0.462563i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −133.154 | −1.68549 | −0.842747 | − | 0.538310i | \(-0.819063\pi\) | ||||
−0.842747 | + | 0.538310i | \(0.819063\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −50.2255 | − | 63.5484i | −0.620068 | − | 0.784548i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 116.715i | − | 1.40621i | −0.711087 | − | 0.703104i | \(-0.751797\pi\) | ||
0.711087 | − | 0.703104i | \(-0.248203\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 70.5793 | − | 8.89513i | 0.830345 | − | 0.104649i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 46.1060 | − | 28.9001i | 0.529954 | − | 0.332185i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 146.524i | 1.64634i | 0.567794 | + | 0.823170i | \(0.307797\pi\) | ||||
−0.567794 | + | 0.823170i | \(0.692203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 92.7193i | 1.01889i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.7549 | + | 13.6364i | −0.233924 | + | 0.146628i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.5141 | + | 146.902i | 0.194885 | + | 1.54633i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 19.9818i | − | 0.205998i | −0.994681 | − | 0.102999i | \(-0.967156\pi\) | ||
0.994681 | − | 0.102999i | \(-0.0328439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −23.5312 | + | 48.5912i | −0.237688 | + | 0.490820i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −115.654 | −1.14509 | −0.572543 | − | 0.819874i | \(-0.694043\pi\) | ||||
−0.572543 | + | 0.819874i | \(0.694043\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 108.400i | 1.05243i | 0.850352 | + | 0.526214i | \(0.176389\pi\) | ||||
−0.850352 | + | 0.526214i | \(0.823611\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −56.3658 | − | 68.9554i | −0.536818 | − | 0.656718i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 74.1440i | − | 0.692935i | −0.938062 | − | 0.346467i | \(-0.887381\pi\) | ||
0.938062 | − | 0.346467i | \(-0.112619\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.0213i | − | 0.137810i | −0.997623 | − | 0.0689051i | \(-0.978049\pi\) | ||
0.997623 | − | 0.0689051i | \(-0.0219506\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −34.2790 | + | 21.4867i | −0.308820 | + | 0.193574i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −164.159 | −1.45273 | −0.726366 | − | 0.687308i | \(-0.758792\pi\) | ||||
−0.726366 | + | 0.687308i | \(0.758792\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −106.793 | + | 13.4591i | −0.928631 | + | 0.117036i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 61.2564 | − | 126.493i | 0.523559 | − | 1.08113i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 84.4750i | − | 0.709874i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.0146 | −0.702600 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −29.9627 | − | 47.8012i | −0.243600 | − | 0.388628i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −116.263 | + | 45.9129i | −0.930101 | + | 0.367303i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 68.6273i | − | 0.540372i | −0.962808 | − | 0.270186i | \(-0.912915\pi\) | ||
0.962808 | − | 0.270186i | \(-0.0870852\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 68.8951 | − | 43.1848i | 0.534070 | − | 0.334766i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 176.512 | 1.34742 | 0.673712 | − | 0.738994i | \(-0.264699\pi\) | ||||
0.673712 | + | 0.738994i | \(0.264699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 175.824 | 1.32198 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 31.3409 | + | 131.312i | 0.232155 | + | 0.972679i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −96.3424 | −0.703229 | −0.351615 | − | 0.936145i | \(-0.614367\pi\) | ||||
−0.351615 | + | 0.936145i | \(0.614367\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1883i | 0.145240i | 0.997360 | + | 0.0726198i | \(0.0231360\pi\) | ||||
−0.997360 | + | 0.0726198i | \(0.976864\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 95.1943 | − | 59.6696i | 0.675137 | − | 0.423189i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −93.6773 | −0.655086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −89.9797 | + | 11.3402i | −0.620550 | + | 0.0782080i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 34.9433 | − | 21.9032i | 0.237710 | − | 0.149001i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 138.759 | 0.931270 | 0.465635 | − | 0.884977i | \(-0.345826\pi\) | ||||
0.465635 | + | 0.884977i | \(0.345826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 123.501 | 0.817888 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −55.8097 | + | 115.245i | −0.364769 | + | 0.753238i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 42.4565 | − | 5.35080i | 0.273913 | − | 0.0345213i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −233.338 | −1.48623 | −0.743116 | − | 0.669162i | \(-0.766653\pi\) | ||||
−0.743116 | + | 0.669162i | \(0.766653\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −149.120 | − | 237.900i | −0.937864 | − | 1.49623i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 127.818i | 0.793901i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 98.7745 | 0.605979 | 0.302989 | − | 0.952994i | \(-0.402015\pi\) | ||||
0.302989 | + | 0.952994i | \(0.402015\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 69.6679 | − | 56.9482i | 0.422229 | − | 0.345141i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 133.070 | 0.796825 | 0.398412 | − | 0.917206i | \(-0.369561\pi\) | ||||
0.398412 | + | 0.917206i | \(0.369561\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 74.8609 | 0.442964 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −239.869 | − | 116.161i | −1.40274 | − | 0.679302i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 323.270i | 1.86861i | 0.356474 | + | 0.934305i | \(0.383979\pi\) | ||||
−0.356474 | + | 0.934305i | \(0.616021\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 36.8298 | + | 143.794i | 0.210456 | + | 0.821681i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 212.959 | − | 133.487i | 1.20316 | − | 0.754163i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 183.645 | 1.02595 | 0.512975 | − | 0.858403i | \(-0.328543\pi\) | ||||
0.512975 | + | 0.858403i | \(0.328543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 301.614i | 1.66637i | 0.552992 | + | 0.833187i | \(0.313486\pi\) | ||||
−0.552992 | + | 0.833187i | \(0.686514\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −62.6695 | − | 99.9801i | −0.342456 | − | 0.546339i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 66.8983 | − | 8.43121i | 0.361612 | − | 0.0455741i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 85.3478 | 0.456405 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 159.361 | − | 17.4271i | 0.843178 | − | 0.0922068i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 242.628i | 1.27030i | 0.772387 | + | 0.635152i | \(0.219063\pi\) | ||||
−0.772387 | + | 0.635152i | \(0.780937\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.6897i | − | 0.0709311i | −0.999371 | − | 0.0354656i | \(-0.988709\pi\) | ||
0.999371 | − | 0.0354656i | \(-0.0112914\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −181.360 | + | 148.248i | −0.930049 | + | 0.760245i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 361.518i | − | 1.83511i | −0.397604 | − | 0.917557i | \(-0.630158\pi\) | ||
0.397604 | − | 0.917557i | \(-0.369842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 196.862 | 0.989258 | 0.494629 | − | 0.869104i | \(-0.335304\pi\) | ||||
0.494629 | + | 0.869104i | \(0.335304\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 263.190 | − | 164.973i | 1.30941 | − | 0.820761i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 107.695i | 0.530517i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.7571 | + | 93.2881i | 0.0573518 | + | 0.455064i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 84.4449 | − | 174.376i | 0.407946 | − | 0.842397i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 177.641i | 0.849955i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 202.277i | − | 0.958658i | −0.877635 | − | 0.479329i | \(-0.840880\pi\) | ||
0.877635 | − | 0.479329i | \(-0.159120\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.1969 | + | 37.0073i | 0.108906 | + | 0.173743i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −134.454 | + | 16.9453i | −0.625370 | + | 0.0788155i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 50.8153i | − | 0.234172i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −152.794 | − | 243.762i | −0.697692 | − | 1.11307i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −222.178 | −1.00533 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 34.1739i | 0.153246i | 0.997060 | + | 0.0766232i | \(0.0244138\pi\) | ||||
−0.997060 | + | 0.0766232i | \(0.975586\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 44.7545 | − | 220.504i | 0.198909 | − | 0.980018i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 316.667i | 1.39501i | 0.716580 | + | 0.697505i | \(0.245706\pi\) | ||||
−0.716580 | + | 0.697505i | \(0.754294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 236.008i | − | 1.03060i | −0.857009 | − | 0.515301i | \(-0.827680\pi\) | ||
0.857009 | − | 0.515301i | \(-0.172320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −56.7499 | − | 90.5363i | −0.245671 | − | 0.391932i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 195.417 | 0.838698 | 0.419349 | − | 0.907825i | \(-0.362258\pi\) | ||||
0.419349 | + | 0.907825i | \(0.362258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −185.780 | + | 23.4138i | −0.790551 | + | 0.0996334i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −338.466 | + | 212.157i | −1.42813 | + | 0.895177i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.71717i | 0.0406576i | 0.999793 | + | 0.0203288i | \(0.00647130\pi\) | ||||
−0.999793 | + | 0.0203288i | \(0.993529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 200.592 | 0.832331 | 0.416166 | − | 0.909289i | \(-0.363374\pi\) | ||||
0.416166 | + | 0.909289i | \(0.363374\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −228.922 | − | 81.5091i | −0.942066 | − | 0.335428i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −68.1949 | + | 8.59462i | −0.278346 | + | 0.0350801i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 462.434i | − | 1.87220i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −185.965 | − | 296.680i | −0.746847 | − | 1.19149i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.8698 | 0.0831465 | 0.0415733 | − | 0.999135i | \(-0.486763\pi\) | ||||
0.0415733 | + | 0.999135i | \(0.486763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −129.139 | −0.510429 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 165.234 | − | 135.066i | 0.647975 | − | 0.529671i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 456.070 | 1.77459 | 0.887296 | − | 0.461199i | \(-0.152581\pi\) | ||||
0.887296 | + | 0.461199i | \(0.152581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 80.0693i | − | 0.309148i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 71.1503 | − | 146.923i | 0.272607 | − | 0.562925i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −161.431 | −0.613807 | −0.306904 | − | 0.951741i | \(-0.599293\pi\) | ||||
−0.306904 | + | 0.951741i | \(0.599293\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 58.5136 | + | 464.282i | 0.220806 | + | 1.75201i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 233.460 | + | 372.452i | 0.874383 | + | 1.39495i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −129.135 | −0.480054 | −0.240027 | − | 0.970766i | \(-0.577156\pi\) | ||||
−0.240027 | + | 0.970766i | \(0.577156\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 230.676 | 0.851203 | 0.425601 | − | 0.904911i | \(-0.360063\pi\) | ||||
0.425601 | + | 0.904911i | \(0.360063\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 147.732 | + | 235.684i | 0.541141 | + | 0.863313i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −145.280 | + | 37.2104i | −0.528291 | + | 0.135310i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −354.494 | −1.27976 | −0.639881 | − | 0.768474i | \(-0.721016\pi\) | ||||
−0.639881 | + | 0.768474i | \(0.721016\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −33.5719 | + | 69.3251i | −0.120329 | + | 0.248477i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 350.785i | 1.24834i | 0.781287 | + | 0.624172i | \(0.214564\pi\) | ||||
−0.781287 | + | 0.624172i | \(0.785436\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −254.054 | −0.897718 | −0.448859 | − | 0.893602i | \(-0.648170\pi\) | ||||
−0.448859 | + | 0.893602i | \(0.648170\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 281.123 | + | 343.913i | 0.986396 | + | 1.20671i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 111.655 | 0.389041 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −86.5776 | −0.299576 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −31.8375 | − | 50.7921i | −0.109407 | − | 0.174543i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 198.349i | − | 0.676958i | −0.940974 | − | 0.338479i | \(-0.890088\pi\) | ||
0.940974 | − | 0.338479i | \(-0.109912\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −415.608 | + | 52.3791i | −1.40884 | + | 0.177556i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.6071 | + | 161.007i | 0.0592833 | + | 0.542112i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 336.174 | 1.12433 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 160.926i | 0.534638i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −293.982 | + | 184.274i | −0.970237 | + | 0.608164i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.5910 | + | 195.120i | 0.0806261 | + | 0.639736i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −229.921 | −0.748927 | −0.374464 | − | 0.927242i | \(-0.622173\pi\) | ||||
−0.374464 | + | 0.927242i | \(0.622173\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 172.716 | + | 275.544i | 0.558952 | + | 0.891728i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 43.0855i | − | 0.138538i | −0.997598 | − | 0.0692692i | \(-0.977933\pi\) | ||
0.997598 | − | 0.0692692i | \(-0.0220668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 218.737i | 0.698841i | 0.936966 | + | 0.349420i | \(0.113622\pi\) | ||||
−0.936966 | + | 0.349420i | \(0.886378\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −253.145 | − | 85.4698i | −0.803636 | − | 0.271333i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 325.313i | 1.02622i | 0.858322 | + | 0.513111i | \(0.171507\pi\) | ||||
−0.858322 | + | 0.513111i | \(0.828493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −108.808 | −0.341090 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −118.135 | − | 188.468i | −0.368022 | − | 0.587127i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 421.316i | 1.30439i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 378.193 | − | 96.8661i | 1.16367 | − | 0.298050i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.9338 | − | 38.1829i | −0.0731919 | − | 0.116767i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 222.356i | 0.675854i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 314.138i | 0.949058i | 0.880240 | + | 0.474529i | \(0.157382\pi\) | ||||
−0.880240 | + | 0.474529i | \(0.842618\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −52.8990 | + | 109.235i | −0.158856 | + | 0.328033i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −513.638 | + | 64.7339i | −1.53325 | + | 0.193236i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 325.048i | − | 0.964534i | −0.876024 | − | 0.482267i | \(-0.839813\pi\) | ||
0.876024 | − | 0.482267i | \(-0.160187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −417.277 | + | 261.558i | −1.23091 | + | 0.771556i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 51.3404 | 0.150558 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.555i | 1.08617i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −250.013 | + | 204.367i | −0.724675 | + | 0.592367i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 415.143i | 1.19638i | 0.801355 | + | 0.598189i | \(0.204113\pi\) | ||||
−0.801355 | + | 0.598189i | \(0.795887\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 179.846i | − | 0.515318i | −0.966236 | − | 0.257659i | \(-0.917049\pi\) | ||
0.966236 | − | 0.257659i | \(-0.0829512\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −45.8350 | − | 419.135i | −0.130584 | − | 1.19412i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 103.250 | 0.292493 | 0.146246 | − | 0.989248i | \(-0.453281\pi\) | ||||
0.146246 | + | 0.989248i | \(0.453281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.10227 | − | 72.2229i | −0.0256402 | − | 0.203445i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −134.596 | − | 214.728i | −0.377019 | − | 0.601480i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 353.673i | 0.985161i | 0.870267 | + | 0.492580i | \(0.163946\pi\) | ||||
−0.870267 | + | 0.492580i | \(0.836054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −515.916 | −1.42913 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −216.100 | + | 135.456i | −0.595316 | + | 0.373156i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 59.9552 | + | 475.721i | 0.164261 | + | 1.30335i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 640.613i | − | 1.74554i | −0.488133 | − | 0.872769i | \(-0.662322\pi\) | ||
0.488133 | − | 0.872769i | \(-0.337678\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −152.325 | − | 73.7664i | −0.412806 | − | 0.199909i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 555.690 | 1.49782 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 503.724 | 1.35047 | 0.675233 | − | 0.737605i | \(-0.264043\pi\) | ||||
0.675233 | + | 0.737605i | \(0.264043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −222.376 | + | 301.950i | −0.593002 | + | 0.805201i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 283.249 | 0.751322 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 138.570i | 0.365620i | 0.983148 | + | 0.182810i | \(0.0585194\pi\) | ||||
−0.983148 | + | 0.182810i | \(0.941481\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −109.345 | − | 174.445i | −0.286995 | − | 0.457860i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 149.537 | 0.390437 | 0.195219 | − | 0.980760i | \(-0.437458\pi\) | ||||
0.195219 | + | 0.980760i | \(0.437458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22.2682 | + | 176.689i | 0.0578394 | + | 0.458933i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 106.318 | − | 219.544i | 0.274724 | − | 0.567297i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −585.106 | −1.50413 | −0.752064 | − | 0.659090i | \(-0.770942\pi\) | ||||
−0.752064 | + | 0.659090i | \(0.770942\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −306.283 | −0.783332 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 448.679 | − | 281.241i | 1.14168 | − | 0.715626i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 660.545 | − | 83.2486i | 1.67226 | − | 0.210756i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −529.718 | −1.33430 | −0.667151 | − | 0.744922i | \(-0.732487\pi\) | ||||
−0.667151 | + | 0.744922i | \(0.732487\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 446.929 | − | 280.144i | 1.12012 | − | 0.702115i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 134.714i | 0.335944i | 0.985792 | + | 0.167972i | \(0.0537219\pi\) | ||||
−0.985792 | + | 0.167972i | \(0.946278\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −133.649 | −0.331636 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 288.888 | + | 283.847i | 0.713303 | + | 0.700856i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 80.8966 | 0.198763 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 221.882 | 0.542499 | 0.271249 | − | 0.962509i | \(-0.412563\pi\) | ||||
0.271249 | + | 0.962509i | \(0.412563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −244.894 | + | 153.504i | −0.595850 | + | 0.373490i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 497.433i | 1.20444i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 72.9710 | + | 578.996i | 0.175834 | + | 1.39517i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.1664 | + | 51.3169i | 0.0771378 | + | 0.123062i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −358.418 | −0.855413 | −0.427707 | − | 0.903918i | \(-0.640678\pi\) | ||||
−0.427707 | + | 0.903918i | \(0.640678\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 572.660i | − | 1.36024i | −0.733102 | − | 0.680119i | \(-0.761928\pi\) | ||
0.733102 | − | 0.680119i | \(-0.238072\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 146.903 | − | 303.350i | 0.347288 | − | 0.717140i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −344.566 | + | 88.2531i | −0.810742 | + | 0.207654i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 233.535 | 0.546920 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −238.120 | + | 149.258i | −0.555057 | + | 0.347921i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 190.360i | 0.441672i | 0.975311 | + | 0.220836i | \(0.0708785\pi\) | ||||
−0.975311 | + | 0.220836i | \(0.929122\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 725.584i | 1.67571i | 0.545891 | + | 0.837857i | \(0.316191\pi\) | ||||
−0.545891 | + | 0.837857i | \(0.683809\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −210.652 | + | 172.192i | −0.484258 | + | 0.395844i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 637.488i | − | 1.45878i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −460.268 | −1.04845 | −0.524223 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524223 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 53.9242 | − | 111.352i | 0.122277 | − | 0.252499i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 121.292i | − | 0.273796i | −0.990585 | − | 0.136898i | \(-0.956287\pi\) | ||
0.990585 | − | 0.136898i | \(-0.0437133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −91.6078 | − | 726.872i | −0.205860 | − | 1.63342i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 352.714 | − | 221.088i | 0.789070 | − | 0.494604i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.4215i | 0.0276648i | 0.999904 | + | 0.0138324i | \(0.00440313\pi\) | ||||
−0.999904 | + | 0.0138324i | \(0.995597\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 112.808i | 0.250129i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 313.929 | − | 196.777i | 0.693000 | − | 0.434386i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −57.9686 | − | 459.958i | −0.127404 | − | 1.01090i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 438.321i | − | 0.959126i | −0.877507 | − | 0.479563i | \(-0.840795\pi\) | ||
0.877507 | − | 0.479563i | \(-0.159205\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 41.7595 | + | 381.867i | 0.0909792 | + | 0.831953i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 290.164 | 0.629424 | 0.314712 | − | 0.949187i | \(-0.398092\pi\) | ||||
0.314712 | + | 0.949187i | \(0.398092\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 342.841i | − | 0.740477i | −0.928937 | − | 0.370239i | \(-0.879276\pi\) | ||
0.928937 | − | 0.370239i | \(-0.120724\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 99.3952 | − | 81.2481i | 0.213753 | − | 0.174727i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 217.840i | 0.466466i | 0.972421 | + | 0.233233i | \(0.0749305\pi\) | ||||
−0.972421 | + | 0.233233i | \(0.925069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 614.764i | 1.31080i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −593.126 | + | 371.783i | −1.25929 | + | 0.789348i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −162.589 | −0.343739 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −183.688 | − | 717.169i | −0.386711 | − | 1.50983i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −758.103 | − | 367.125i | −1.58931 | − | 0.769654i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 577.121i | 1.20485i | 0.798177 | + | 0.602423i | \(0.205798\pi\) | ||||
−0.798177 | + | 0.602423i | \(0.794202\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −210.590 | −0.437817 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 203.655 | + | 324.902i | 0.421646 | + | 0.672676i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.4928 | + | 99.1251i | 0.0257583 | + | 0.204382i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 689.685i | − | 1.41619i | −0.706117 | − | 0.708095i | \(-0.749555\pi\) | ||
0.706117 | − | 0.708095i | \(-0.250445\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 251.076 | − | 157.380i | 0.513449 | − | 0.321840i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −834.980 | −1.70057 | −0.850285 | − | 0.526323i | \(-0.823570\pi\) | ||||
−0.850285 | + | 0.526323i | \(0.823570\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −258.063 | −0.523455 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 86.3529 | − | 255.761i | 0.174450 | − | 0.516688i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −86.4422 | −0.173928 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 145.508i | − | 0.291600i | −0.989314 | − | 0.145800i | \(-0.953424\pi\) | ||
0.989314 | − | 0.145800i | \(-0.0465755\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 338.252 | − | 212.023i | 0.675153 | − | 0.423199i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −244.686 | −0.486453 | −0.243227 | − | 0.969969i | \(-0.578206\pi\) | ||||
−0.243227 | + | 0.969969i | \(0.578206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 573.730 | − | 72.3074i | 1.13610 | − | 0.143183i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 190.290 | − | 119.278i | 0.375326 | − | 0.235261i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −413.015 | −0.811425 | −0.405713 | − | 0.914001i | \(-0.632977\pi\) | ||||
−0.405713 | + | 0.914001i | \(0.632977\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 569.381 | 1.11425 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −794.807 | + | 86.9170i | −1.54933 | + | 0.169429i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −67.7724 | − | 537.747i | −0.131597 | − | 1.04417i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −224.653 | −0.434533 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 515.072 | + | 821.724i | 0.992432 | + | 1.58328i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 189.285i | − | 0.363312i | −0.983362 | − | 0.181656i | \(-0.941854\pi\) | ||
0.983362 | − | 0.181656i | \(-0.0581457\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 235.324 | 0.449950 | 0.224975 | − | 0.974365i | \(-0.427770\pi\) | ||||
0.224975 | + | 0.974365i | \(0.427770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 322.729 | + | 306.831i | 0.614721 | + | 0.584440i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 121.766 | 0.231055 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −65.5678 | −0.123947 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 328.636 | − | 678.625i | 0.618901 | − | 1.27801i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 293.663i | − | 0.550963i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 46.3552 | + | 367.810i | 0.0866453 | + | 0.687496i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 466.810 | − | 292.606i | 0.869293 | − | 0.544890i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −82.4644 | −0.152995 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 789.168i | 1.45872i | 0.684130 | + | 0.729360i | \(0.260182\pi\) | ||||
−0.684130 | + | 0.729360i | \(0.739818\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 480.567 | + | 766.676i | 0.885022 | + | 1.41193i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.39140 | + | 74.5170i | 0.0172319 | + | 0.136729i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 905.745 | 1.65584 | 0.827921 | − | 0.560845i | \(-0.189524\pi\) | ||||
0.827921 | + | 0.560845i | \(0.189524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −318.601 | − | 154.288i | −0.580329 | − | 0.281035i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 537.125i | − | 0.974819i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 790.593i | − | 1.42964i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 156.616 | − | 128.022i | 0.282191 | − | 0.230670i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 352.250i | − | 0.632406i | −0.948692 | − | 0.316203i | \(-0.897592\pi\) | ||
0.948692 | − | 0.316203i | \(-0.102408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 423.251 | 0.757158 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 216.947 | − | 135.986i | 0.386714 | − | 0.242400i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1028.02i | − | 1.82597i | −0.407989 | − | 0.912987i | \(-0.633770\pi\) | ||
0.407989 | − | 0.912987i | \(-0.366230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 814.352 | − | 102.633i | 1.44133 | − | 0.181651i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 377.314 | − | 298.211i | 0.665457 | − | 0.525945i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 612.176i | − | 1.07588i | −0.842983 | − | 0.537941i | \(-0.819202\pi\) | ||
0.842983 | − | 0.537941i | \(-0.180798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 284.705i | 0.498607i | 0.968425 | + | 0.249304i | \(0.0802017\pi\) | ||||
−0.968425 | + | 0.249304i | \(0.919798\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 386.585 | + | 616.740i | 0.674668 | + | 1.07633i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 521.357 | − | 133.535i | 0.906709 | − | 0.232234i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 510.925i | − | 0.885485i | −0.896649 | − | 0.442743i | \(-0.854006\pi\) | ||
0.896649 | − | 0.442743i | \(-0.145994\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.8121 | − | 34.7981i | −0.0376720 | − | 0.0601003i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 692.989 | 1.19275 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 561.432i | 0.963005i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −224.794 | + | 665.797i | −0.384264 | + | 1.13811i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 425.221i | − | 0.724396i | −0.932101 | − | 0.362198i | \(-0.882026\pi\) | ||
0.932101 | − | 0.362198i | \(-0.117974\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 253.440i | 0.430289i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −576.014 | − | 918.947i | −0.974642 | − | 1.55490i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −639.053 | −1.07766 | −0.538831 | − | 0.842414i | \(-0.681134\pi\) | ||||
−0.538831 | + | 0.842414i | \(0.681134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 52.8142 | + | 419.060i | 0.0887634 | + | 0.704302i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 500.407 | − | 313.665i | 0.838203 | − | 0.525402i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 609.450i | − | 1.01745i | −0.860930 | − | 0.508723i | \(-0.830118\pi\) | ||
0.860930 | − | 0.508723i | \(-0.169882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 443.553 | 0.738025 | 0.369012 | − | 0.929425i | \(-0.379696\pi\) | ||||
0.369012 | + | 0.929425i | \(0.379696\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 406.153 | − | 838.694i | 0.673554 | − | 1.39087i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 421.737 | − | 53.1516i | 0.697086 | − | 0.0878539i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 483.158i | 0.795977i | 0.917390 | + | 0.397988i | \(0.130292\pi\) | ||||
−0.917390 | + | 0.397988i | \(0.869708\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 171.593 | + | 273.751i | 0.281761 | + | 0.449510i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 584.818 | 0.957150 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 115.677 | 0.188706 | 0.0943532 | − | 0.995539i | \(-0.469922\pi\) | ||||
0.0943532 | + | 0.995539i | \(0.469922\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 178.524 | + | 218.398i | 0.290282 | + | 0.355118i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −91.9068 | −0.148958 | −0.0744788 | − | 0.997223i | \(-0.523729\pi\) | ||||
−0.0744788 | + | 0.997223i | \(0.523729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 748.627i | − | 1.20941i | −0.796448 | − | 0.604706i | \(-0.793290\pi\) | ||
0.796448 | − | 0.604706i | \(-0.206710\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −63.1857 | − | 577.797i | −0.101748 | − | 0.930430i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −869.979 | −1.39643 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 548.046 | − | 300.451i | 0.876873 | − | 0.480721i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 283.038 | + | 451.547i | 0.451417 | + | 0.720171i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 191.865 | 0.305032 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 856.682 | 1.35766 | 0.678829 | − | 0.734296i | \(-0.262488\pi\) | ||||
0.678829 | + | 0.734296i | \(0.262488\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −322.292 | − | 514.170i | −0.509150 | − | 0.812276i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.9062 | + | 340.443i | 0.0675687 | + | 0.536131i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 214.672 | 0.337004 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 117.929 | + | 57.1094i | 0.184553 | + | 0.0893730i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.0978i | 0.0453944i | 0.999742 | + | 0.0226972i | \(0.00722536\pi\) | ||||
−0.999742 | + | 0.0226972i | \(0.992775\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −873.920 | −1.35913 | −0.679564 | − | 0.733616i | \(-0.737831\pi\) | ||||
−0.679564 | + | 0.733616i | \(0.737831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −314.772 | + | 257.303i | −0.488019 | + | 0.398919i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1152.62 | 1.78149 | 0.890743 | − | 0.454507i | \(-0.150184\pi\) | ||||
0.890743 | + | 0.454507i | \(0.150184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −502.572 | −0.774379 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −80.9652 | − | 129.168i | −0.124370 | − | 0.198415i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 143.894i | − | 0.220358i | −0.993912 | − | 0.110179i | \(-0.964858\pi\) | ||
0.993912 | − | 0.110179i | \(-0.0351424\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −875.635 | + | 110.357i | −1.33685 | + | 0.168483i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −776.781 | − | 376.170i | −1.18231 | − | 0.572557i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −410.806 | −0.623379 | −0.311689 | − | 0.950184i | \(-0.600895\pi\) | ||||
−0.311689 | + | 0.950184i | \(0.600895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1129.32i | 1.70851i | 0.519855 | + | 0.854254i | \(0.325986\pi\) | ||||
−0.519855 | + | 0.854254i | \(0.674014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −564.757 | + | 354.000i | −0.851820 | + | 0.533937i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −872.220 | + | 109.926i | −1.31161 | + | 0.165302i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 390.472 | 0.585415 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 54.4500 | + | 86.8672i | 0.0813902 | + | 0.129846i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 235.948i | 0.351636i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 630.561i | 0.936940i | 0.883479 | + | 0.468470i | \(0.155195\pi\) | ||||
−0.883479 | + | 0.468470i | \(0.844805\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −237.572 | − | 631.811i | −0.351958 | − | 0.936016i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 412.121i | − | 0.608746i | −0.952553 | − | 0.304373i | \(-0.901553\pi\) | ||
0.952553 | − | 0.304373i | \(-0.0984470\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 118.641 | 0.174729 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 504.552 | + | 804.941i | 0.740899 | + | 1.18200i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 538.782i | − | 0.788847i | −0.918929 | − | 0.394423i | \(-0.870944\pi\) | ||
0.918929 | − | 0.394423i | \(-0.129056\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 477.931 | − | 60.2338i | 0.697710 | − | 0.0879326i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −376.036 | − | 599.912i | −0.547360 | − | 0.873234i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1461.52i | − | 2.12122i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 617.899i | 0.894210i | 0.894482 | + | 0.447105i | \(0.147545\pi\) | ||||
−0.894482 | + | 0.447105i | \(0.852455\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −288.507 | − | 139.715i | −0.416316 | − | 0.201609i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.6218 | − | 100.149i | −0.0181609 | − | 0.144100i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 267.552i | 0.383862i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 496.732 | − | 311.361i | 0.710633 | − | 0.445438i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −583.091 | −0.831799 | −0.415900 | − | 0.909410i | \(-0.636533\pi\) | ||||
−0.415900 | + | 0.909410i | \(0.636533\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 399.343i | 0.568055i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −434.930 | + | 355.523i | −0.616922 | + | 0.504287i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 686.687i | − | 0.971268i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 291.529i | − | 0.411184i | −0.978638 | − | 0.205592i | \(-0.934088\pi\) | ||
0.978638 | − | 0.205592i | \(-0.0659119\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −522.317 | + | 1078.57i | −0.734623 | + | 1.51698i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −184.242 | −0.258404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 464.710 | − | 58.5675i | 0.649944 | − | 0.0819127i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.4826 | + | 24.7002i | 0.0215935 | + | 0.0344494i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1189.83i | 1.65483i | 0.561588 | + | 0.827417i | \(0.310191\pi\) | ||||
−0.561588 | + | 0.827417i | \(0.689809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −643.619 | −0.892675 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 509.887 | − | 319.607i | 0.705238 | − | 0.442057i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 439.278 | − | 112.512i | 0.605900 | − | 0.155188i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 332.813i | 0.457790i | 0.973451 | + | 0.228895i | \(0.0735112\pi\) | ||||
−0.973451 | + | 0.228895i | \(0.926489\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −711.770 | + | 157.557i | −0.976365 | + | 0.216128i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −385.617 | −0.527520 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 430.132 | 0.586810 | 0.293405 | − | 0.955988i | \(-0.405212\pi\) | ||||
0.293405 | + | 0.955988i | \(0.405212\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −159.652 | + | 130.503i | −0.217213 | + | 0.177555i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −621.115 | −0.842762 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 824.829i | 1.11614i | 0.829793 | + | 0.558071i | \(0.188458\pi\) | ||||
−0.829793 | + | 0.558071i | \(0.811542\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −736.807 | − | 1175.47i | −0.994341 | − | 1.58633i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 848.265 | 1.14168 | 0.570838 | − | 0.821063i | \(-0.306619\pi\) | ||||
0.570838 | + | 0.821063i | \(0.306619\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −688.351 | + | 86.7531i | −0.923961 | + | 0.116447i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −945.414 | − | 457.834i | −1.26561 | − | 0.612897i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 440.225 | 0.587751 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 63.2095 | 0.0841671 | 0.0420836 | − | 0.999114i | \(-0.486600\pi\) | ||||
0.0420836 | + | 0.999114i | \(0.486600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 53.0492 | − | 33.2522i | 0.0704504 | − | 0.0441597i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −612.659 | + | 77.2136i | −0.811469 | + | 0.102270i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1255.62 | −1.65868 | −0.829340 | − | 0.558744i | \(-0.811283\pi\) | ||||
−0.829340 | + | 0.558744i | \(0.811283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −328.259 | + | 205.759i | −0.432489 | + | 0.271093i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 819.598i | − | 1.07700i | −0.842625 | − | 0.538501i | \(-0.818991\pi\) | ||
0.842625 | − | 0.538501i | \(-0.181009\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 89.1880 | 0.116891 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 204.806 | − | 606.597i | 0.267721 | − | 0.792937i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1308.30 | 1.70573 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 275.299 | 0.357997 | 0.178998 | − | 0.983849i | \(-0.442714\pi\) | ||||
0.178998 | + | 0.983849i | \(0.442714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1159.29 | − | 726.667i | 1.50362 | − | 0.942499i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 310.696i | 0.401935i | 0.979598 | + | 0.200968i | \(0.0644086\pi\) | ||||
−0.979598 | + | 0.200968i | \(0.935591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −207.271 | + | 53.0881i | −0.267446 | + | 0.0685007i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −127.576 | − | 203.529i | −0.164191 | − | 0.261942i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −556.875 | −0.714858 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 87.3354i | − | 0.111825i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −53.2381 | − | 486.832i | −0.0679924 | − | 0.621752i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1157.54 | − | 145.885i | 1.47457 | − | 0.185840i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 882.041 | 1.12076 | 0.560382 | − | 0.828234i | \(-0.310654\pi\) | ||||
0.560382 | + | 0.828234i | \(0.310654\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −410.344 | + | 257.212i | −0.520082 | + | 0.325997i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 974.682i | − | 1.23221i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 614.220i | − | 0.774552i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 888.487 | + | 1086.93i | 1.11759 | + | 1.36721i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 572.739i | − | 0.718619i | −0.933218 | − | 0.359309i | \(-0.883012\pi\) | ||
0.933218 | − | 0.359309i | \(-0.116988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −532.818 | −0.666857 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1186.87 | + | 574.765i | 1.48174 | + | 0.717559i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 575.264i | 0.716394i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −79.9125 | − | 634.074i | −0.0992702 | − | 0.787670i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −328.249 | + | 205.753i | −0.406752 | + | 0.254960i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1122.50i | 1.38751i | 0.720210 | + | 0.693756i | \(0.244045\pi\) | ||||
−0.720210 | + | 0.693756i | \(0.755955\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 76.3000i | 0.0940814i | 0.998893 | + | 0.0470407i | \(0.0149791\pi\) | ||||
−0.998893 | + | 0.0470407i | \(0.985021\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 586.358 | − | 367.541i | 0.721228 | − | 0.452080i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −489.997 | + | 61.7544i | −0.601223 | + | 0.0757723i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 802.613i | − | 0.982391i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 751.042 | + | 363.706i | 0.917023 | + | 0.444085i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −499.762 | −0.608724 | −0.304362 | − | 0.952557i | \(-0.598443\pi\) | ||||
−0.304362 | + | 0.952557i | \(0.598443\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1081.64i | − | 1.31426i | −0.753777 | − | 0.657131i | \(-0.771770\pi\) | ||
0.753777 | − | 0.657131i | \(-0.228230\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −310.001 | + | 326.063i | −0.375759 | + | 0.395228i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 221.353i | 0.267658i | 0.991004 | + | 0.133829i | \(0.0427272\pi\) | ||||
−0.991004 | + | 0.133829i | \(0.957273\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1010.54i | − | 1.21899i | −0.792789 | − | 0.609496i | \(-0.791372\pi\) | ||
0.792789 | − | 0.609496i | \(-0.208628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −901.094 | + | 564.823i | −1.08435 | + | 0.679691i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −195.584 | −0.234794 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −660.127 | + | 83.1959i | −0.790571 | + | 0.0996358i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.1201 | + | 229.709i | 0.0300121 | + | 0.274443i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1554.32i | − | 1.85259i | −0.376803 | − | 0.926294i | \(-0.622976\pi\) | ||
0.376803 | − | 0.926294i | \(-0.377024\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −512.002 | −0.608802 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 558.913 | + | 891.665i | 0.663004 | + | 1.05773i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −371.367 | + | 46.8035i | −0.439488 | + | 0.0553887i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 504.769i | − | 0.595949i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −645.784 | + | 404.790i | −0.760641 | + | 0.476785i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −290.309 | −0.341138 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −79.6953 | −0.0934295 | −0.0467147 | − | 0.998908i | \(-0.514875\pi\) | ||||
−0.0467147 | + | 0.998908i | \(0.514875\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1262.55 | + | 426.278i | 1.47667 | + | 0.498571i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −169.805 | −0.198139 | −0.0990693 | − | 0.995081i | \(-0.531587\pi\) | ||||
−0.0990693 | + | 0.995081i | \(0.531587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 811.495i | 0.944698i | 0.881412 | + | 0.472349i | \(0.156594\pi\) | ||||
−0.881412 | + | 0.472349i | \(0.843406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 283.817 | − | 177.902i | 0.329636 | − | 0.206622i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 925.135 | 1.07200 | 0.535999 | − | 0.844218i | \(-0.319935\pi\) | ||||
0.535999 | + | 0.844218i | \(0.319935\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −202.110 | − | 1603.66i | −0.233653 | − | 1.85394i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −220.073 | + | 137.946i | −0.253833 | + | 0.159107i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 798.762 | 0.919173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1616.89 | 1.85636 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −161.856 | − | 78.3819i | −0.185402 | − | 0.0897845i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −272.605 | − | 690.302i | −0.311548 | − | 0.788917i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 425.026 | 0.484636 | 0.242318 | − | 0.970197i | \(-0.422092\pi\) | ||||
0.242318 | + | 0.970197i | \(0.422092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −316.033 | − | 504.185i | −0.359537 | − | 0.573590i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 41.8218i | − | 0.0474709i | −0.999718 | − | 0.0237354i | \(-0.992444\pi\) | ||
0.999718 | − | 0.0237354i | \(-0.00755593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 549.203 | 0.621973 | 0.310987 | − | 0.950414i | \(-0.399341\pi\) | ||||
0.310987 | + | 0.950414i | \(0.399341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −972.982 | + | 795.339i | −1.09941 | + | 0.898689i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1315.99 | −1.48364 | −0.741819 | − | 0.670600i | \(-0.766037\pi\) | ||||
−0.741819 | + | 0.670600i | \(0.766037\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 407.470 | 0.458346 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 301.292 | + | 381.213i | 0.338150 | + | 0.427848i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1108.99i | − | 1.24187i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −911.019 | + | 114.816i | −1.01790 | + | 0.128286i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 854.526 | − | 535.633i | 0.952648 | − | 0.597139i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −155.236 | −0.172676 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1331.57i | 1.47788i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 256.407 | + | 409.060i | 0.283950 | + | 0.453001i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −188.570 | − | 1496.23i | −0.208365 | − | 1.65329i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −103.221 | −0.113804 | −0.0569022 | − | 0.998380i | \(-0.518122\pi\) | ||||
−0.0569022 | + | 0.998380i | \(0.518122\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −453.670 | + | 936.815i | −0.499087 | + | 1.03060i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 937.234i | 1.02880i | 0.857551 | + | 0.514399i | \(0.171985\pi\) | ||||
−0.857551 | + | 0.514399i | \(0.828015\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 700.149i | 0.766867i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 373.396 | + | 456.796i | 0.408083 | + | 0.499230i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1048.03i | 1.14289i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −565.469 | −0.615309 | −0.307655 | − | 0.951498i | \(-0.599544\pi\) | ||||
−0.307655 | + | 0.951498i | \(0.599544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −584.439 | + | 366.337i | −0.634570 | + | 0.397761i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 227.352i | 0.246318i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −326.595 | + | 83.6504i | −0.353076 | + | 0.0904328i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 878.060 | + | 425.217i | 0.947206 | + | 0.458702i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 561.412i | 0.604318i | 0.953258 | + | 0.302159i | \(0.0977074\pi\) | ||||
−0.953258 | + | 0.302159i | \(0.902293\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 407.083i | − | 0.437253i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −68.6490 | − | 109.520i | −0.0735787 | − | 0.117384i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −423.390 | + | 53.3599i | −0.452823 | + | 0.0570694i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1293.38i | 1.38034i | 0.723647 | + | 0.690170i | \(0.242464\pi\) | ||||
−0.723647 | + | 0.690170i | \(0.757536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 348.519 | + | 556.011i | 0.371159 | + | 0.592131i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1509.76 | 1.60442 | 0.802209 | − | 0.597043i | \(-0.203658\pi\) | ||||
0.802209 | + | 0.597043i | \(0.203658\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 404.829i | − | 0.429299i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −779.654 | + | 186.085i | −0.825031 | + | 0.196915i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 368.756i | 0.389394i | 0.980863 | + | 0.194697i | \(0.0623723\pi\) | ||||
−0.980863 | + | 0.194697i | \(0.937628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1497.53i | − | 1.57801i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 518.327 | + | 826.917i | 0.545034 | + | 0.869523i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1580.92 | 1.65889 | 0.829443 | − | 0.558591i | \(-0.188658\pi\) | ||||
0.829443 | + | 0.558591i | \(0.188658\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −151.692 | − | 1203.62i | −0.158840 | − | 1.26033i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −276.580 | + | 173.366i | −0.289007 | + | 0.181155i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 572.027i | − | 0.596483i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −887.753 | −0.923780 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −600.579 | − | 290.841i | −0.623654 | − | 0.302016i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.55888 | + | 67.9113i | 0.00886931 | + | 0.0703744i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 653.389i | 0.675686i | 0.941202 | + | 0.337843i | \(0.109697\pi\) | ||||
−0.941202 | + | 0.337843i | \(0.890303\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 671.292 | + | 1070.95i | 0.692768 | + | 1.10521i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −414.882 | −0.427273 | −0.213636 | − | 0.976913i | \(-0.568531\pi\) | ||||
−0.213636 | + | 0.976913i | \(0.568531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −119.867 | −0.123193 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 806.996 | − | 848.808i | 0.827688 | − | 0.870573i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 829.934 | 0.849472 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 878.968i | − | 0.897822i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −121.675 | − | 58.9234i | −0.124032 | − | 0.0600646i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.3930 | 0.0441435 | 0.0220717 | − | 0.999756i | \(-0.492974\pi\) | ||||
0.0220717 | + | 0.999756i | \(0.492974\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 226.023 | + | 1793.40i | 0.229465 | + | 1.82071i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 354.284 | + | 565.210i | 0.358951 | + | 0.572654i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 583.472 | 0.589962 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −325.761 | −0.328719 | −0.164360 | − | 0.986400i | \(-0.552556\pi\) | ||||
−0.164360 | + | 0.986400i | \(0.552556\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 500.523 | + | 798.513i | 0.504052 | + | 0.804142i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −976.586 | + | 123.079i | −0.981493 | + | 0.123698i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 487.259 | 0.488725 | 0.244363 | − | 0.969684i | \(-0.421421\pi\) | ||||
0.244363 | + | 0.969684i | \(0.421421\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.5815 | + | 361.951i | 0.0396212 | + | 0.362313i |
(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 | 960.3.i.b.929.50 | yes | 64 | |
3.2 | odd | 2 | inner | 960.3.i.b.929.55 | yes | 64 | |
4.3 | odd | 2 | inner | 960.3.i.b.929.14 | yes | 64 | |
5.4 | even | 2 | inner | 960.3.i.b.929.13 | yes | 64 | |
8.3 | odd | 2 | inner | 960.3.i.b.929.51 | yes | 64 | |
8.5 | even | 2 | inner | 960.3.i.b.929.15 | yes | 64 | |
12.11 | even | 2 | inner | 960.3.i.b.929.11 | yes | 64 | |
15.14 | odd | 2 | inner | 960.3.i.b.929.12 | yes | 64 | |
20.19 | odd | 2 | inner | 960.3.i.b.929.49 | yes | 64 | |
24.5 | odd | 2 | inner | 960.3.i.b.929.10 | yes | 64 | |
24.11 | even | 2 | inner | 960.3.i.b.929.54 | yes | 64 | |
40.19 | odd | 2 | inner | 960.3.i.b.929.16 | yes | 64 | |
40.29 | even | 2 | inner | 960.3.i.b.929.52 | yes | 64 | |
60.59 | even | 2 | inner | 960.3.i.b.929.56 | yes | 64 | |
120.29 | odd | 2 | inner | 960.3.i.b.929.53 | yes | 64 | |
120.59 | even | 2 | inner | 960.3.i.b.929.9 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
960.3.i.b.929.9 | ✓ | 64 | 120.59 | even | 2 | inner | |
960.3.i.b.929.10 | yes | 64 | 24.5 | odd | 2 | inner | |
960.3.i.b.929.11 | yes | 64 | 12.11 | even | 2 | inner | |
960.3.i.b.929.12 | yes | 64 | 15.14 | odd | 2 | inner | |
960.3.i.b.929.13 | yes | 64 | 5.4 | even | 2 | inner | |
960.3.i.b.929.14 | yes | 64 | 4.3 | odd | 2 | inner | |
960.3.i.b.929.15 | yes | 64 | 8.5 | even | 2 | inner | |
960.3.i.b.929.16 | yes | 64 | 40.19 | odd | 2 | inner | |
960.3.i.b.929.49 | yes | 64 | 20.19 | odd | 2 | inner | |
960.3.i.b.929.50 | yes | 64 | 1.1 | even | 1 | trivial | |
960.3.i.b.929.51 | yes | 64 | 8.3 | odd | 2 | inner | |
960.3.i.b.929.52 | yes | 64 | 40.29 | even | 2 | inner | |
960.3.i.b.929.53 | yes | 64 | 120.29 | odd | 2 | inner | |
960.3.i.b.929.54 | yes | 64 | 24.11 | even | 2 | inner | |
960.3.i.b.929.55 | yes | 64 | 3.2 | odd | 2 | inner | |
960.3.i.b.929.56 | yes | 64 | 60.59 | even | 2 | inner |