Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,3,Mod(244,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.244");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.d (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: | \(15.4496309892\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 108x^{12} + 4395x^{10} + 83817x^{8} + 766449x^{6} + 3215376x^{4} + 5192667x^{2} + 964467 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 244.6 | ||
Root | \(0.460710i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.244 |
Dual form | 567.3.d.g.244.5 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90488 | −0.952438 | −0.476219 | − | 0.879327i | \(-0.657993\pi\) | ||||
−0.476219 | + | 0.879327i | \(0.657993\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.371447 | −0.0928617 | ||||||||
\(5\) | 8.23162i | 1.64632i | 0.567807 | + | 0.823162i | \(0.307792\pi\) | ||||
−0.567807 | + | 0.823162i | \(0.692208\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.18933 | − | 3.26989i | 0.884190 | − | 0.467127i | ||||
\(8\) | 8.32706 | 1.04088 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 15.6802i | − | 1.56802i | ||||||
\(11\) | 11.9301 | 1.08455 | 0.542276 | − | 0.840201i | \(-0.317563\pi\) | ||||
0.542276 | + | 0.840201i | \(0.317563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.58781i | − | 0.122139i | −0.998134 | − | 0.0610696i | \(-0.980549\pi\) | ||
0.998134 | − | 0.0610696i | \(-0.0194512\pi\) | |||||||
\(14\) | −11.7899 | + | 6.22874i | −0.842136 | + | 0.444910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.3762 | −0.898515 | ||||||||
\(17\) | − | 19.5020i | − | 1.14718i | −0.819143 | − | 0.573590i | \(-0.805550\pi\) | ||
0.819143 | − | 0.573590i | \(-0.194450\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.69545i | − | 0.352392i | −0.984355 | − | 0.176196i | \(-0.943621\pi\) | ||
0.984355 | − | 0.176196i | \(-0.0563793\pi\) | |||||||
\(20\) | − | 3.05761i | − | 0.152880i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −22.7253 | −1.03297 | ||||||||
\(23\) | 28.1484 | 1.22384 | 0.611922 | − | 0.790918i | \(-0.290396\pi\) | ||||
0.611922 | + | 0.790918i | \(0.290396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −42.7595 | −1.71038 | ||||||||
\(26\) | 3.02458i | 0.116330i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.29901 | + | 1.21459i | −0.0821073 | + | 0.0433782i | ||||
\(29\) | 10.9680 | 0.378207 | 0.189104 | − | 0.981957i | \(-0.439442\pi\) | ||||
0.189104 | + | 0.981957i | \(0.439442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 31.7080i | − | 1.02284i | −0.859331 | − | 0.511420i | \(-0.829120\pi\) | ||
0.859331 | − | 0.511420i | \(-0.170880\pi\) | |||||||
\(32\) | −5.92330 | −0.185103 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 37.1490i | 1.09262i | ||||||||
\(35\) | 26.9165 | + | 50.9482i | 0.769043 | + | 1.45566i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.88791 | −0.186160 | −0.0930798 | − | 0.995659i | \(-0.529671\pi\) | ||||
−0.0930798 | + | 0.995659i | \(0.529671\pi\) | |||||||
\(38\) | 12.7540i | 0.335632i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 68.5452i | 1.71363i | ||||||||
\(41\) | 1.56305i | 0.0381231i | 0.999818 | + | 0.0190615i | \(0.00606784\pi\) | ||||
−0.999818 | + | 0.0190615i | \(0.993932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 65.0484 | 1.51275 | 0.756377 | − | 0.654136i | \(-0.226968\pi\) | ||||
0.756377 | + | 0.654136i | \(0.226968\pi\) | |||||||
\(44\) | −4.43138 | −0.100713 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −53.6193 | −1.16564 | ||||||||
\(47\) | 55.2911i | 1.17641i | 0.808713 | + | 0.588203i | \(0.200164\pi\) | ||||
−0.808713 | + | 0.588203i | \(0.799836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 27.6156 | − | 40.4769i | 0.563584 | − | 0.826059i | ||||
\(50\) | 81.4516 | 1.62903 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.589787i | 0.0113420i | ||||||||
\(53\) | 33.9256 | 0.640106 | 0.320053 | − | 0.947400i | \(-0.396299\pi\) | ||||
0.320053 | + | 0.947400i | \(0.396299\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 98.2037i | 1.78552i | ||||||||
\(56\) | 51.5390 | − | 27.2286i | 0.920338 | − | 0.486225i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −20.8927 | −0.360219 | ||||||||
\(59\) | 6.57763i | 0.111485i | 0.998445 | + | 0.0557426i | \(0.0177526\pi\) | ||||
−0.998445 | + | 0.0557426i | \(0.982247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 76.1795i | − | 1.24884i | −0.781087 | − | 0.624422i | \(-0.785334\pi\) | ||
0.781087 | − | 0.624422i | \(-0.214666\pi\) | |||||||
\(62\) | 60.3999i | 0.974192i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 68.7881 | 1.07481 | ||||||||
\(65\) | 13.0702 | 0.201081 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −23.7171 | −0.353987 | −0.176993 | − | 0.984212i | \(-0.556637\pi\) | ||||
−0.176993 | + | 0.984212i | \(0.556637\pi\) | |||||||
\(68\) | 7.24397i | 0.106529i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −51.2726 | − | 97.0500i | −0.732466 | − | 1.38643i | ||||
\(71\) | 14.0551 | 0.197960 | 0.0989798 | − | 0.995089i | \(-0.468442\pi\) | ||||
0.0989798 | + | 0.995089i | \(0.468442\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 40.2281i | − | 0.551070i | −0.961291 | − | 0.275535i | \(-0.911145\pi\) | ||
0.961291 | − | 0.275535i | \(-0.0888549\pi\) | |||||||
\(74\) | 13.1206 | 0.177305 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.48700i | 0.0327237i | ||||||||
\(77\) | 73.8391 | − | 39.0100i | 0.958949 | − | 0.506624i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 63.7289 | 0.806695 | 0.403348 | − | 0.915047i | \(-0.367847\pi\) | ||||
0.403348 | + | 0.915047i | \(0.367847\pi\) | |||||||
\(80\) | − | 118.340i | − | 1.47925i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 2.97741i | − | 0.0363099i | ||||||
\(83\) | − | 2.24313i | − | 0.0270257i | −0.999909 | − | 0.0135129i | \(-0.995699\pi\) | ||
0.999909 | − | 0.0135129i | \(-0.00430141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 160.533 | 1.88863 | ||||||||
\(86\) | −123.909 | −1.44080 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 99.3424 | 1.12889 | ||||||||
\(89\) | 58.4246i | 0.656456i | 0.944599 | + | 0.328228i | \(0.106451\pi\) | ||||
−0.944599 | + | 0.328228i | \(0.893549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.19197 | − | 9.82748i | −0.0570546 | − | 0.107994i | ||||
\(92\) | −10.4556 | −0.113648 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 105.323i | − | 1.12045i | ||||||
\(95\) | 55.1144 | 0.580152 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 129.049i | 1.33041i | 0.746663 | + | 0.665203i | \(0.231655\pi\) | ||||
−0.746663 | + | 0.665203i | \(0.768345\pi\) | |||||||
\(98\) | −52.6043 | + | 77.1034i | −0.536779 | + | 0.786770i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 15.8829 | 0.158829 | ||||||||
\(101\) | 194.507i | 1.92581i | 0.269844 | + | 0.962904i | \(0.413028\pi\) | ||||
−0.269844 | + | 0.962904i | \(0.586972\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 95.2765i | 0.925015i | 0.886615 | + | 0.462507i | \(0.153050\pi\) | ||||
−0.886615 | + | 0.462507i | \(0.846950\pi\) | |||||||
\(104\) | − | 13.2218i | − | 0.127133i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −64.6242 | −0.609662 | ||||||||
\(107\) | 10.0507 | 0.0939319 | 0.0469660 | − | 0.998896i | \(-0.485045\pi\) | ||||
0.0469660 | + | 0.998896i | \(0.485045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 70.9967 | 0.651346 | 0.325673 | − | 0.945482i | \(-0.394409\pi\) | ||||
0.325673 | + | 0.945482i | \(0.394409\pi\) | |||||||
\(110\) | − | 187.066i | − | 1.70060i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −88.9793 | + | 47.0088i | −0.794458 | + | 0.419721i | ||||
\(113\) | −54.0265 | −0.478111 | −0.239055 | − | 0.971006i | \(-0.576838\pi\) | ||||
−0.239055 | + | 0.971006i | \(0.576838\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 231.707i | 2.01484i | ||||||||
\(116\) | −4.07403 | −0.0351209 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 12.5296i | − | 0.106183i | ||||||
\(119\) | −63.7696 | − | 120.705i | −0.535879 | − | 1.01432i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.3264 | 0.176251 | ||||||||
\(122\) | 145.113i | 1.18945i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.7778i | 0.0949826i | ||||||||
\(125\) | − | 146.189i | − | 1.16952i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 50.2162 | 0.395403 | 0.197701 | − | 0.980262i | \(-0.436652\pi\) | ||||
0.197701 | + | 0.980262i | \(0.436652\pi\) | |||||||
\(128\) | −107.340 | −0.838591 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −24.8972 | −0.191517 | ||||||||
\(131\) | − | 45.7188i | − | 0.348999i | −0.984657 | − | 0.174499i | \(-0.944169\pi\) | ||
0.984657 | − | 0.174499i | \(-0.0558307\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.8934 | − | 41.4404i | −0.164612 | − | 0.311582i | ||||
\(134\) | 45.1782 | 0.337151 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 162.395i | − | 1.19408i | ||||||
\(137\) | −31.4485 | −0.229551 | −0.114776 | − | 0.993391i | \(-0.536615\pi\) | ||||
−0.114776 | + | 0.993391i | \(0.536615\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 119.245i | 0.857879i | 0.903333 | + | 0.428939i | \(0.141113\pi\) | ||||
−0.903333 | + | 0.428939i | \(0.858887\pi\) | |||||||
\(140\) | −9.99804 | − | 18.9245i | −0.0714146 | − | 0.135175i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −26.7733 | −0.188544 | ||||||||
\(143\) | − | 18.9427i | − | 0.132466i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 90.2844i | 0.622651i | ||||||||
\(146\) | 76.6295i | 0.524860i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.55849 | 0.0172871 | ||||||||
\(149\) | −60.1447 | −0.403656 | −0.201828 | − | 0.979421i | \(-0.564688\pi\) | ||||
−0.201828 | + | 0.979421i | \(0.564688\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −207.625 | −1.37500 | −0.687499 | − | 0.726185i | \(-0.741292\pi\) | ||||
−0.687499 | + | 0.726185i | \(0.741292\pi\) | |||||||
\(152\) | − | 55.7535i | − | 0.366799i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −140.654 | + | 74.3092i | −0.913340 | + | 0.482528i | ||||
\(155\) | 261.008 | 1.68392 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 105.909i | − | 0.674579i | −0.941401 | − | 0.337289i | \(-0.890490\pi\) | ||
0.941401 | − | 0.337289i | \(-0.109510\pi\) | |||||||
\(158\) | −121.396 | −0.768327 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 48.7583i | − | 0.304740i | ||||||
\(161\) | 174.220 | − | 92.0423i | 1.08211 | − | 0.571692i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 56.2870 | 0.345319 | 0.172660 | − | 0.984982i | \(-0.444764\pi\) | ||||
0.172660 | + | 0.984982i | \(0.444764\pi\) | |||||||
\(164\) | − | 0.580588i | − | 0.00354017i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.27289i | 0.0257403i | ||||||||
\(167\) | 170.137i | 1.01879i | 0.860534 | + | 0.509394i | \(0.170130\pi\) | ||||
−0.860534 | + | 0.509394i | \(0.829870\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 166.479 | 0.985082 | ||||||||
\(170\) | −305.796 | −1.79880 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −24.1620 | −0.140477 | ||||||||
\(173\) | − | 95.7158i | − | 0.553270i | −0.960975 | − | 0.276635i | \(-0.910781\pi\) | ||
0.960975 | − | 0.276635i | \(-0.0892194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −264.653 | + | 139.819i | −1.51230 | + | 0.798965i | ||||
\(176\) | −171.509 | −0.974485 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 111.292i | − | 0.625233i | ||||||
\(179\) | −286.056 | −1.59808 | −0.799040 | − | 0.601277i | \(-0.794659\pi\) | ||||
−0.799040 | + | 0.601277i | \(0.794659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 246.704i | − | 1.36300i | −0.731816 | − | 0.681502i | \(-0.761327\pi\) | ||
0.731816 | − | 0.681502i | \(-0.238673\pi\) | |||||||
\(182\) | 9.89005 | + | 18.7201i | 0.0543409 | + | 0.102858i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 234.394 | 1.27388 | ||||||||
\(185\) | − | 56.6986i | − | 0.306479i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 232.661i | − | 1.24417i | ||||||
\(188\) | − | 20.5377i | − | 0.109243i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −104.986 | −0.552558 | ||||||||
\(191\) | −271.509 | −1.42152 | −0.710758 | − | 0.703437i | \(-0.751648\pi\) | ||||
−0.710758 | + | 0.703437i | \(0.751648\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −192.638 | −0.998123 | −0.499062 | − | 0.866566i | \(-0.666322\pi\) | ||||
−0.499062 | + | 0.866566i | \(0.666322\pi\) | |||||||
\(194\) | − | 245.823i | − | 1.26713i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.2577 | + | 15.0350i | −0.0523353 | + | 0.0767092i | ||||
\(197\) | 163.463 | 0.829763 | 0.414882 | − | 0.909875i | \(-0.363823\pi\) | ||||
0.414882 | + | 0.909875i | \(0.363823\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 297.225i | 1.49359i | 0.665053 | + | 0.746796i | \(0.268409\pi\) | ||||
−0.665053 | + | 0.746796i | \(0.731591\pi\) | |||||||
\(200\) | −356.061 | −1.78031 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 370.511i | − | 1.83421i | ||||||
\(203\) | 67.8846 | − | 35.8642i | 0.334407 | − | 0.176671i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.8664 | −0.0627629 | ||||||||
\(206\) | − | 181.490i | − | 0.881019i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 22.8267i | 0.109744i | ||||||||
\(209\) | − | 79.8772i | − | 0.382187i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 86.9972 | 0.412309 | 0.206155 | − | 0.978519i | \(-0.433905\pi\) | ||||
0.206155 | + | 0.978519i | \(0.433905\pi\) | |||||||
\(212\) | −12.6016 | −0.0594413 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −19.1454 | −0.0894643 | ||||||||
\(215\) | 535.453i | 2.49048i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −103.682 | − | 196.251i | −0.477796 | − | 0.904385i | ||||
\(218\) | −135.240 | −0.620367 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 36.4774i | − | 0.165806i | ||||||
\(221\) | −30.9655 | −0.140116 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 367.533i | − | 1.64813i | −0.566496 | − | 0.824065i | \(-0.691701\pi\) | ||
0.566496 | − | 0.824065i | \(-0.308299\pi\) | |||||||
\(224\) | −36.6613 | + | 19.3685i | −0.163666 | + | 0.0864667i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 102.914 | 0.455371 | ||||||||
\(227\) | − | 167.443i | − | 0.737633i | −0.929502 | − | 0.368817i | \(-0.879763\pi\) | ||
0.929502 | − | 0.368817i | \(-0.120237\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 437.899i | − | 1.91222i | −0.293001 | − | 0.956112i | \(-0.594654\pi\) | ||
0.293001 | − | 0.956112i | \(-0.405346\pi\) | |||||||
\(230\) | − | 441.373i | − | 1.91901i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 91.3313 | 0.393669 | ||||||||
\(233\) | −227.581 | −0.976740 | −0.488370 | − | 0.872637i | \(-0.662408\pi\) | ||||
−0.488370 | + | 0.872637i | \(0.662408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −455.135 | −1.93675 | ||||||||
\(236\) | − | 2.44324i | − | 0.0103527i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 121.473 | + | 229.927i | 0.510391 | + | 0.966081i | ||||
\(239\) | 355.290 | 1.48657 | 0.743285 | − | 0.668975i | \(-0.233267\pi\) | ||||
0.743285 | + | 0.668975i | \(0.233267\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 255.935i | 1.06197i | 0.847381 | + | 0.530985i | \(0.178178\pi\) | ||||
−0.847381 | + | 0.530985i | \(0.821822\pi\) | |||||||
\(242\) | −40.6241 | −0.167868 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 28.2966i | 0.115970i | ||||||||
\(245\) | 333.190 | + | 227.321i | 1.35996 | + | 0.927841i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.6311 | −0.0430409 | ||||||||
\(248\) | − | 264.035i | − | 1.06466i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 278.473i | 1.11389i | ||||||||
\(251\) | − | 200.521i | − | 0.798889i | −0.916757 | − | 0.399444i | \(-0.869203\pi\) | ||
0.916757 | − | 0.399444i | \(-0.130797\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 335.813 | 1.32732 | ||||||||
\(254\) | −95.6556 | −0.376597 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −70.6837 | −0.276108 | ||||||||
\(257\) | 151.654i | 0.590092i | 0.955483 | + | 0.295046i | \(0.0953349\pi\) | ||||
−0.955483 | + | 0.295046i | \(0.904665\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −42.6315 | + | 22.5227i | −0.164600 | + | 0.0869602i | ||||
\(260\) | −4.85490 | −0.0186727 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 87.0887i | 0.332400i | ||||||||
\(263\) | 356.262 | 1.35461 | 0.677305 | − | 0.735702i | \(-0.263148\pi\) | ||||
0.677305 | + | 0.735702i | \(0.263148\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 279.263i | 1.05382i | ||||||||
\(266\) | 41.7042 | + | 78.9388i | 0.156783 | + | 0.296762i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.80965 | 0.0328718 | ||||||||
\(269\) | 199.704i | 0.742395i | 0.928554 | + | 0.371198i | \(0.121053\pi\) | ||||
−0.928554 | + | 0.371198i | \(0.878947\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 151.831i | 0.560262i | 0.959962 | + | 0.280131i | \(0.0903779\pi\) | ||||
−0.959962 | + | 0.280131i | \(0.909622\pi\) | |||||||
\(272\) | 280.366i | 1.03076i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 59.9055 | 0.218633 | ||||||||
\(275\) | −510.123 | −1.85499 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −61.4847 | −0.221966 | −0.110983 | − | 0.993822i | \(-0.535400\pi\) | ||||
−0.110983 | + | 0.993822i | \(0.535400\pi\) | |||||||
\(278\) | − | 227.147i | − | 0.817077i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 224.135 | + | 424.249i | 0.800484 | + | 1.51517i | ||||
\(281\) | −121.844 | −0.433610 | −0.216805 | − | 0.976215i | \(-0.569564\pi\) | ||||
−0.216805 | + | 0.976215i | \(0.569564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 508.399i | 1.79646i | 0.439522 | + | 0.898232i | \(0.355148\pi\) | ||||
−0.439522 | + | 0.898232i | \(0.644852\pi\) | |||||||
\(284\) | −5.22073 | −0.0183829 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 36.0834i | 0.126166i | ||||||||
\(287\) | 5.11099 | + | 9.67420i | 0.0178083 | + | 0.0337080i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −91.3299 | −0.316020 | ||||||||
\(290\) | − | 171.981i | − | 0.593037i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.9426i | 0.0511732i | ||||||||
\(293\) | 442.511i | 1.51028i | 0.655565 | + | 0.755139i | \(0.272431\pi\) | ||||
−0.655565 | + | 0.755139i | \(0.727569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −54.1445 | −0.183541 | ||||||||
\(296\) | −57.3560 | −0.193770 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 114.568 | 0.384457 | ||||||||
\(299\) | − | 44.6944i | − | 0.149479i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 402.606 | − | 212.701i | 1.33756 | − | 0.706649i | ||||
\(302\) | 395.500 | 1.30960 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 96.2554i | 0.316630i | ||||||||
\(305\) | 627.081 | 2.05600 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 378.900i | − | 1.23420i | −0.786884 | − | 0.617101i | \(-0.788307\pi\) | ||
0.786884 | − | 0.617101i | \(-0.211693\pi\) | |||||||
\(308\) | −27.4273 | + | 14.4901i | −0.0890496 | + | 0.0470459i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −497.189 | −1.60383 | ||||||||
\(311\) | − | 76.8776i | − | 0.247195i | −0.992332 | − | 0.123597i | \(-0.960557\pi\) | ||
0.992332 | − | 0.123597i | \(-0.0394432\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 143.579i | − | 0.458719i | −0.973342 | − | 0.229360i | \(-0.926337\pi\) | ||
0.973342 | − | 0.229360i | \(-0.0736632\pi\) | |||||||
\(314\) | 201.743i | 0.642495i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.6719 | −0.0749110 | ||||||||
\(317\) | −94.7835 | −0.299002 | −0.149501 | − | 0.988762i | \(-0.547767\pi\) | ||||
−0.149501 | + | 0.988762i | \(0.547767\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 130.849 | 0.410185 | ||||||||
\(320\) | 566.237i | 1.76949i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −331.867 | + | 175.329i | −1.03064 | + | 0.544501i | ||||
\(323\) | −130.575 | −0.404257 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 67.8940i | 0.208904i | ||||||||
\(326\) | −107.220 | −0.328895 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.0156i | 0.0396816i | ||||||||
\(329\) | 180.796 | + | 342.215i | 0.549532 | + | 1.04017i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 468.332 | 1.41490 | 0.707451 | − | 0.706762i | \(-0.249845\pi\) | ||||
0.707451 | + | 0.706762i | \(0.249845\pi\) | |||||||
\(332\) | 0.833205i | 0.00250965i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 324.091i | − | 0.970332i | ||||||
\(335\) | − | 195.230i | − | 0.582777i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −331.311 | −0.983119 | −0.491560 | − | 0.870844i | \(-0.663573\pi\) | ||||
−0.491560 | + | 0.870844i | \(0.663573\pi\) | |||||||
\(338\) | −317.122 | −0.938230 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −59.6296 | −0.175381 | ||||||||
\(341\) | − | 378.279i | − | 1.10932i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 38.5671 | − | 340.825i | 0.112441 | − | 0.993658i | ||||
\(344\) | 541.662 | 1.57460 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 182.327i | 0.526956i | ||||||||
\(347\) | −372.049 | −1.07219 | −0.536094 | − | 0.844158i | \(-0.680101\pi\) | ||||
−0.536094 | + | 0.844158i | \(0.680101\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 7.82768i | − | 0.0224289i | −0.999937 | − | 0.0112144i | \(-0.996430\pi\) | ||
0.999937 | − | 0.0112144i | \(-0.00356974\pi\) | |||||||
\(350\) | 504.131 | − | 266.338i | 1.44037 | − | 0.760965i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −70.6653 | −0.200754 | ||||||||
\(353\) | − | 78.2312i | − | 0.221618i | −0.993842 | − | 0.110809i | \(-0.964656\pi\) | ||
0.993842 | − | 0.110809i | \(-0.0353442\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 115.696i | 0.325905i | ||||||||
\(356\) | − | 21.7016i | − | 0.0609596i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 544.902 | 1.52207 | ||||||||
\(359\) | 265.434 | 0.739370 | 0.369685 | − | 0.929157i | \(-0.379466\pi\) | ||||
0.369685 | + | 0.929157i | \(0.379466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 316.171 | 0.875820 | ||||||||
\(362\) | 469.940i | 1.29818i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.92854 | + | 3.65038i | 0.00529818 | + | 0.0100285i | ||||
\(365\) | 331.142 | 0.907239 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 440.261i | − | 1.19962i | −0.800142 | − | 0.599811i | \(-0.795243\pi\) | ||
0.800142 | − | 0.599811i | \(-0.204757\pi\) | |||||||
\(368\) | −404.669 | −1.09964 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 108.004i | 0.291902i | ||||||||
\(371\) | 209.977 | − | 110.933i | 0.565976 | − | 0.299011i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 150.712 | 0.404053 | 0.202026 | − | 0.979380i | \(-0.435247\pi\) | ||||
0.202026 | + | 0.979380i | \(0.435247\pi\) | |||||||
\(374\) | 443.190i | 1.18500i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 460.413i | 1.22450i | ||||||||
\(377\) | − | 17.4151i | − | 0.0461939i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 313.660 | 0.827599 | 0.413800 | − | 0.910368i | \(-0.364201\pi\) | ||||
0.413800 | + | 0.910368i | \(0.364201\pi\) | |||||||
\(380\) | −20.4721 | −0.0538738 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 517.192 | 1.35391 | ||||||||
\(383\) | − | 647.602i | − | 1.69087i | −0.534081 | − | 0.845434i | \(-0.679342\pi\) | ||
0.534081 | − | 0.845434i | \(-0.320658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 321.115 | + | 607.815i | 0.834066 | + | 1.57874i | ||||
\(386\) | 366.951 | 0.950651 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 47.9349i | − | 0.123544i | ||||||
\(389\) | 203.760 | 0.523806 | 0.261903 | − | 0.965094i | \(-0.415650\pi\) | ||||
0.261903 | + | 0.965094i | \(0.415650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 548.952i | − | 1.40397i | ||||||
\(392\) | 229.957 | − | 337.054i | 0.586625 | − | 0.859831i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −311.378 | −0.790298 | ||||||||
\(395\) | 524.592i | 1.32808i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 283.582i | − | 0.714312i | −0.934045 | − | 0.357156i | \(-0.883746\pi\) | ||
0.934045 | − | 0.357156i | \(-0.116254\pi\) | |||||||
\(398\) | − | 566.177i | − | 1.42255i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 614.721 | 1.53680 | ||||||||
\(401\) | 624.239 | 1.55671 | 0.778353 | − | 0.627827i | \(-0.216055\pi\) | ||||
0.778353 | + | 0.627827i | \(0.216055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −50.3463 | −0.124929 | ||||||||
\(404\) | − | 72.2488i | − | 0.178834i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −129.312 | + | 68.3169i | −0.318502 | + | 0.168268i | ||||
\(407\) | −82.1731 | −0.201900 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 29.9575i | − | 0.0732457i | −0.999329 | − | 0.0366228i | \(-0.988340\pi\) | ||
0.999329 | − | 0.0366228i | \(-0.0116600\pi\) | |||||||
\(410\) | 24.5089 | 0.0597778 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 35.3901i | − | 0.0858984i | ||||||
\(413\) | 21.5081 | + | 40.7111i | 0.0520778 | + | 0.0985741i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.4646 | 0.0444931 | ||||||||
\(416\) | 9.40507i | 0.0226083i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 152.156i | 0.364010i | ||||||||
\(419\) | − | 77.0775i | − | 0.183956i | −0.995761 | − | 0.0919779i | \(-0.970681\pi\) | ||
0.995761 | − | 0.0919779i | \(-0.0293189\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −593.516 | −1.40978 | −0.704888 | − | 0.709318i | \(-0.749003\pi\) | ||||
−0.704888 | + | 0.709318i | \(0.749003\pi\) | |||||||
\(422\) | −165.719 | −0.392699 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 282.501 | 0.666276 | ||||||||
\(425\) | 833.898i | 1.96211i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −249.099 | − | 471.500i | −0.583370 | − | 1.10422i | ||||
\(428\) | −3.73330 | −0.00872267 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 1019.97i | − | 2.37203i | ||||||
\(431\) | −420.280 | −0.975128 | −0.487564 | − | 0.873087i | \(-0.662114\pi\) | ||||
−0.487564 | + | 0.873087i | \(0.662114\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 686.056i | 1.58442i | 0.610246 | + | 0.792212i | \(0.291071\pi\) | ||||
−0.610246 | + | 0.792212i | \(0.708929\pi\) | |||||||
\(434\) | 197.501 | + | 373.835i | 0.455072 | + | 0.861370i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.3715 | −0.0604851 | ||||||||
\(437\) | − | 188.467i | − | 0.431274i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 82.9703i | 0.188998i | 0.995525 | + | 0.0944992i | \(0.0301250\pi\) | ||||
−0.995525 | + | 0.0944992i | \(0.969875\pi\) | |||||||
\(440\) | 817.748i | 1.85852i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 58.9855 | 0.133451 | ||||||||
\(443\) | −263.765 | −0.595405 | −0.297703 | − | 0.954659i | \(-0.596220\pi\) | ||||
−0.297703 | + | 0.954659i | \(0.596220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −480.929 | −1.08074 | ||||||||
\(446\) | 700.105i | 1.56974i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 425.752 | − | 224.930i | 0.950340 | − | 0.502075i | ||||
\(449\) | 781.684 | 1.74095 | 0.870473 | − | 0.492217i | \(-0.163813\pi\) | ||||
0.870473 | + | 0.492217i | \(0.163813\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.6472i | 0.0413464i | ||||||||
\(452\) | 20.0680 | 0.0443982 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 318.958i | 0.702550i | ||||||||
\(455\) | 80.8960 | − | 42.7383i | 0.177793 | − | 0.0939303i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −855.944 | −1.87296 | −0.936481 | − | 0.350718i | \(-0.885938\pi\) | ||||
−0.936481 | + | 0.350718i | \(0.885938\pi\) | |||||||
\(458\) | 834.144i | 1.82128i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 86.0668i | − | 0.187102i | ||||||
\(461\) | 440.539i | 0.955615i | 0.878465 | + | 0.477808i | \(0.158568\pi\) | ||||
−0.878465 | + | 0.477808i | \(0.841432\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −235.570 | −0.508791 | −0.254396 | − | 0.967100i | \(-0.581877\pi\) | ||||
−0.254396 | + | 0.967100i | \(0.581877\pi\) | |||||||
\(464\) | −157.679 | −0.339825 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 433.513 | 0.930285 | ||||||||
\(467\) | − | 929.249i | − | 1.98983i | −0.100735 | − | 0.994913i | \(-0.532120\pi\) | ||
0.100735 | − | 0.994913i | \(-0.467880\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −146.793 | + | 77.5524i | −0.312992 | + | 0.165357i | ||||
\(470\) | 866.976 | 1.84463 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 54.7723i | 0.116043i | ||||||||
\(473\) | 776.031 | 1.64066 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 286.294i | 0.602725i | ||||||||
\(476\) | 23.6870 | + | 44.8353i | 0.0497626 | + | 0.0941919i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −676.784 | −1.41587 | ||||||||
\(479\) | 26.6452i | 0.0556267i | 0.999613 | + | 0.0278134i | \(0.00885441\pi\) | ||||
−0.999613 | + | 0.0278134i | \(0.991146\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.9367i | 0.0227374i | ||||||||
\(482\) | − | 487.524i | − | 1.01146i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.92161 | −0.0163670 | ||||||||
\(485\) | −1062.28 | −2.19028 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −712.494 | −1.46303 | −0.731513 | − | 0.681827i | \(-0.761186\pi\) | ||||
−0.731513 | + | 0.681827i | \(0.761186\pi\) | |||||||
\(488\) | − | 634.352i | − | 1.29990i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −634.686 | − | 433.019i | −1.29528 | − | 0.883711i | ||||
\(491\) | −355.431 | −0.723893 | −0.361946 | − | 0.932199i | \(-0.617888\pi\) | ||||
−0.361946 | + | 0.932199i | \(0.617888\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 213.899i | − | 0.433872i | ||||||
\(494\) | 20.2509 | 0.0409938 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 455.842i | 0.919037i | ||||||||
\(497\) | 86.9918 | − | 45.9588i | 0.175034 | − | 0.0924723i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 236.886 | 0.474722 | 0.237361 | − | 0.971422i | \(-0.423718\pi\) | ||||
0.237361 | + | 0.971422i | \(0.423718\pi\) | |||||||
\(500\) | 54.3016i | 0.108603i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 381.968i | 0.760892i | ||||||||
\(503\) | 471.038i | 0.936457i | 0.883608 | + | 0.468228i | \(0.155108\pi\) | ||||
−0.883608 | + | 0.468228i | \(0.844892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1601.10 | −3.17050 | ||||||||
\(506\) | −639.681 | −1.26419 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.6526 | −0.0367178 | ||||||||
\(509\) | − | 477.868i | − | 0.938837i | −0.882976 | − | 0.469418i | \(-0.844464\pi\) | ||
0.882976 | − | 0.469418i | \(-0.155536\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −131.541 | − | 248.985i | −0.257420 | − | 0.487250i | ||||
\(512\) | 564.002 | 1.10157 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 288.881i | − | 0.562026i | ||||||
\(515\) | −784.280 | −1.52287 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 659.626i | 1.27587i | ||||||||
\(518\) | 81.2078 | − | 42.9030i | 0.156772 | − | 0.0828243i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 108.837 | 0.209301 | ||||||||
\(521\) | 85.6568i | 0.164408i | 0.996616 | + | 0.0822042i | \(0.0261960\pi\) | ||||
−0.996616 | + | 0.0822042i | \(0.973804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 575.874i | 1.10110i | 0.834803 | + | 0.550548i | \(0.185581\pi\) | ||||
−0.834803 | + | 0.550548i | \(0.814419\pi\) | |||||||
\(524\) | 16.9821i | 0.0324086i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −678.636 | −1.29018 | ||||||||
\(527\) | −618.372 | −1.17338 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 263.334 | 0.497797 | ||||||||
\(530\) | − | 531.961i | − | 1.00370i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.13223 | + | 15.3929i | 0.0152862 | + | 0.0289340i | ||||
\(533\) | 2.48182 | 0.00465632 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 82.7336i | 0.154642i | ||||||||
\(536\) | −197.494 | −0.368459 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 380.412i | − | 0.707086i | ||||||
\(539\) | 329.456 | − | 482.892i | 0.611236 | − | 0.895903i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 798.629 | 1.47621 | 0.738104 | − | 0.674687i | \(-0.235721\pi\) | ||||
0.738104 | + | 0.674687i | \(0.235721\pi\) | |||||||
\(542\) | − | 289.219i | − | 0.533615i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 115.516i | 0.212346i | ||||||||
\(545\) | 584.418i | 1.07233i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −273.484 | −0.499971 | −0.249986 | − | 0.968250i | \(-0.580426\pi\) | ||||
−0.249986 | + | 0.968250i | \(0.580426\pi\) | |||||||
\(548\) | 11.6814 | 0.0213165 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 971.722 | 1.76677 | ||||||||
\(551\) | − | 73.4358i | − | 0.133277i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 394.439 | − | 208.387i | 0.713272 | − | 0.376829i | ||||
\(554\) | 117.121 | 0.211409 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 44.2932i | − | 0.0796641i | ||||||
\(557\) | 526.108 | 0.944538 | 0.472269 | − | 0.881455i | \(-0.343435\pi\) | ||||
0.472269 | + | 0.881455i | \(0.343435\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 103.284i | − | 0.184767i | ||||||
\(560\) | −386.958 | − | 732.443i | −0.690996 | − | 1.30793i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 232.099 | 0.412987 | ||||||||
\(563\) | − | 386.727i | − | 0.686904i | −0.939170 | − | 0.343452i | \(-0.888404\pi\) | ||
0.939170 | − | 0.343452i | \(-0.111596\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 444.726i | − | 0.787125i | ||||||
\(566\) | − | 968.438i | − | 1.71102i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 117.038 | 0.206053 | ||||||||
\(569\) | 354.691 | 0.623359 | 0.311680 | − | 0.950187i | \(-0.399108\pi\) | ||||
0.311680 | + | 0.950187i | \(0.399108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 156.414 | 0.273929 | 0.136965 | − | 0.990576i | \(-0.456265\pi\) | ||||
0.136965 | + | 0.990576i | \(0.456265\pi\) | |||||||
\(572\) | 7.03619i | 0.0123010i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.73580 | − | 18.4282i | −0.0169613 | − | 0.0321048i | ||||
\(575\) | −1203.61 | −2.09324 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 199.310i | 0.345425i | 0.984972 | + | 0.172713i | \(0.0552532\pi\) | ||||
−0.984972 | + | 0.172713i | \(0.944747\pi\) | |||||||
\(578\) | 173.972 | 0.300990 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 33.5358i | − | 0.0578204i | ||||||
\(581\) | −7.33481 | − | 13.8835i | −0.0126245 | − | 0.0238959i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 404.735 | 0.694228 | ||||||||
\(584\) | − | 334.982i | − | 0.573599i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 842.929i | − | 1.43845i | ||||||
\(587\) | − | 144.214i | − | 0.245680i | −0.992426 | − | 0.122840i | \(-0.960800\pi\) | ||
0.992426 | − | 0.122840i | \(-0.0392002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −212.300 | −0.360441 | ||||||||
\(590\) | 103.139 | 0.174811 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 99.0222 | 0.167267 | ||||||||
\(593\) | 743.841i | 1.25437i | 0.778870 | + | 0.627185i | \(0.215793\pi\) | ||||
−0.778870 | + | 0.627185i | \(0.784207\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 993.594 | − | 524.927i | 1.66991 | − | 0.882230i | ||||
\(596\) | 22.3406 | 0.0374841 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 85.1372i | 0.142370i | ||||||||
\(599\) | 170.846 | 0.285218 | 0.142609 | − | 0.989779i | \(-0.454451\pi\) | ||||
0.142609 | + | 0.989779i | \(0.454451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1179.83i | 1.96311i | 0.191179 | + | 0.981555i | \(0.438769\pi\) | ||||
−0.191179 | + | 0.981555i | \(0.561231\pi\) | |||||||
\(602\) | −766.915 | + | 405.170i | −1.27394 | + | 0.673039i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 77.1215 | 0.127685 | ||||||||
\(605\) | 175.550i | 0.290166i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 484.623i | − | 0.798390i | −0.916866 | − | 0.399195i | \(-0.869290\pi\) | ||
0.916866 | − | 0.399195i | \(-0.130710\pi\) | |||||||
\(608\) | 39.6592i | 0.0652289i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1194.51 | −1.95822 | ||||||||
\(611\) | 87.7917 | 0.143685 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −201.948 | −0.329442 | −0.164721 | − | 0.986340i | \(-0.552672\pi\) | ||||
−0.164721 | + | 0.986340i | \(0.552672\pi\) | |||||||
\(614\) | 721.757i | 1.17550i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 614.863 | − | 324.839i | 0.998154 | − | 0.527336i | ||||
\(617\) | −968.557 | −1.56979 | −0.784893 | − | 0.619632i | \(-0.787282\pi\) | ||||
−0.784893 | + | 0.619632i | \(0.787282\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.0026i | − | 0.0452385i | −0.999744 | − | 0.0226193i | \(-0.992799\pi\) | ||
0.999744 | − | 0.0226193i | \(-0.00720055\pi\) | |||||||
\(620\) | −96.9507 | −0.156372 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 146.442i | 0.235438i | ||||||||
\(623\) | 191.042 | + | 361.609i | 0.306648 | + | 0.580432i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 134.387 | 0.215020 | ||||||||
\(626\) | 273.501i | 0.436902i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 39.3395i | 0.0626425i | ||||||||
\(629\) | 134.328i | 0.213558i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −322.046 | −0.510373 | −0.255187 | − | 0.966892i | \(-0.582137\pi\) | ||||
−0.255187 | + | 0.966892i | \(0.582137\pi\) | |||||||
\(632\) | 530.675 | 0.839675 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 180.551 | 0.284781 | ||||||||
\(635\) | 413.360i | 0.650961i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −64.2696 | − | 43.8483i | −0.100894 | − | 0.0688357i | ||||
\(638\) | −249.251 | −0.390676 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 883.579i | − | 1.38059i | ||||||
\(641\) | −467.164 | −0.728804 | −0.364402 | − | 0.931242i | \(-0.618727\pi\) | ||||
−0.364402 | + | 0.931242i | \(0.618727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 147.113i | − | 0.228791i | −0.993435 | − | 0.114396i | \(-0.963507\pi\) | ||
0.993435 | − | 0.114396i | \(-0.0364932\pi\) | |||||||
\(644\) | −64.7134 | + | 34.1888i | −0.100487 | + | 0.0530882i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 248.729 | 0.385030 | ||||||||
\(647\) | − | 688.665i | − | 1.06440i | −0.846620 | − | 0.532198i | \(-0.821366\pi\) | ||
0.846620 | − | 0.532198i | \(-0.178634\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 78.4715i | 0.120911i | ||||||||
\(650\) | − | 129.330i | − | 0.198969i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.9076 | −0.0320669 | ||||||||
\(653\) | −1170.28 | −1.79216 | −0.896081 | − | 0.443890i | \(-0.853598\pi\) | ||||
−0.896081 | + | 0.443890i | \(0.853598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 376.340 | 0.574565 | ||||||||
\(656\) | − | 22.4707i | − | 0.0342541i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −344.394 | − | 651.877i | −0.523395 | − | 0.990694i | ||||
\(659\) | −1010.50 | −1.53339 | −0.766694 | − | 0.642013i | \(-0.778100\pi\) | ||||
−0.766694 | + | 0.642013i | \(0.778100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 553.620i | − | 0.837549i | −0.908090 | − | 0.418774i | \(-0.862460\pi\) | ||
0.908090 | − | 0.418774i | \(-0.137540\pi\) | |||||||
\(662\) | −892.115 | −1.34761 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 18.6787i | − | 0.0281306i | ||||||
\(665\) | 341.121 | − | 180.218i | 0.512964 | − | 0.271005i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 308.732 | 0.462867 | ||||||||
\(668\) | − | 63.1970i | − | 0.0946063i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 371.890i | 0.555059i | ||||||||
\(671\) | − | 908.827i | − | 1.35444i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −155.458 | −0.230993 | −0.115496 | − | 0.993308i | \(-0.536846\pi\) | ||||
−0.115496 | + | 0.993308i | \(0.536846\pi\) | |||||||
\(674\) | 631.107 | 0.936360 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −61.8380 | −0.0914763 | ||||||||
\(677\) | − | 887.050i | − | 1.31027i | −0.755513 | − | 0.655133i | \(-0.772613\pi\) | ||
0.755513 | − | 0.655133i | \(-0.227387\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 421.977 | + | 798.729i | 0.621469 | + | 1.17633i | ||||
\(680\) | 1336.77 | 1.96584 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 720.574i | 1.05656i | ||||||||
\(683\) | −440.555 | −0.645030 | −0.322515 | − | 0.946564i | \(-0.604528\pi\) | ||||
−0.322515 | + | 0.946564i | \(0.604528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 258.872i | − | 0.377915i | ||||||
\(686\) | −73.4656 | + | 649.229i | −0.107093 | + | 0.946398i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −935.151 | −1.35923 | ||||||||
\(689\) | − | 53.8675i | − | 0.0781821i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 411.654i | 0.595736i | 0.954607 | + | 0.297868i | \(0.0962756\pi\) | ||||
−0.954607 | + | 0.297868i | \(0.903724\pi\) | |||||||
\(692\) | 35.5533i | 0.0513776i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 708.707 | 1.02119 | ||||||||
\(695\) | −981.580 | −1.41235 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.4826 | 0.0437340 | ||||||||
\(698\) | 14.9108i | 0.0213621i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 98.3043 | − | 51.9353i | 0.140435 | − | 0.0741932i | ||||
\(701\) | 61.6807 | 0.0879895 | 0.0439948 | − | 0.999032i | \(-0.485992\pi\) | ||||
0.0439948 | + | 0.999032i | \(0.485992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.1176i | 0.0656012i | ||||||||
\(704\) | 820.646 | 1.16569 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 149.021i | 0.211078i | ||||||||
\(707\) | 636.016 | + | 1203.87i | 0.899598 | + | 1.70278i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1094.43 | 1.54363 | 0.771814 | − | 0.635849i | \(-0.219350\pi\) | ||||
0.771814 | + | 0.635849i | \(0.219350\pi\) | |||||||
\(710\) | − | 220.387i | − | 0.310405i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 486.505i | 0.683294i | ||||||||
\(713\) | − | 892.531i | − | 1.25180i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 155.929 | 0.218082 | ||||||||
\(716\) | 106.255 | 0.148400 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −505.619 | −0.704204 | ||||||||
\(719\) | 577.350i | 0.802990i | 0.915861 | + | 0.401495i | \(0.131509\pi\) | ||||
−0.915861 | + | 0.401495i | \(0.868491\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 311.544 | + | 589.698i | 0.432100 | + | 0.817889i | ||||
\(722\) | −602.266 | −0.834164 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 91.6373i | 0.126571i | ||||||||
\(725\) | −468.987 | −0.646878 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 89.5790i | 0.123217i | 0.998100 | + | 0.0616087i | \(0.0196231\pi\) | ||||
−0.998100 | + | 0.0616087i | \(0.980377\pi\) | |||||||
\(728\) | −43.2338 | − | 81.8340i | −0.0593871 | − | 0.112409i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −630.785 | −0.864089 | ||||||||
\(731\) | − | 1268.58i | − | 1.73540i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 191.799i | − | 0.261663i | −0.991405 | − | 0.130832i | \(-0.958235\pi\) | ||
0.991405 | − | 0.130832i | \(-0.0417648\pi\) | |||||||
\(734\) | 838.643i | 1.14257i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −166.732 | −0.226538 | ||||||||
\(737\) | −282.947 | −0.383917 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1004.93 | 1.35985 | 0.679926 | − | 0.733281i | \(-0.262012\pi\) | ||||
0.679926 | + | 0.733281i | \(0.262012\pi\) | |||||||
\(740\) | 21.0605i | 0.0284601i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −399.980 | + | 211.314i | −0.539057 | + | 0.284790i | ||||
\(743\) | −319.379 | −0.429851 | −0.214925 | − | 0.976630i | \(-0.568951\pi\) | ||||
−0.214925 | + | 0.976630i | \(0.568951\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 495.088i | − | 0.664548i | ||||||
\(746\) | −287.087 | −0.384835 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 86.4210i | 0.115536i | ||||||||
\(749\) | 62.2072 | − | 32.8647i | 0.0830537 | − | 0.0438782i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 328.885 | 0.437930 | 0.218965 | − | 0.975733i | \(-0.429732\pi\) | ||||
0.218965 | + | 0.975733i | \(0.429732\pi\) | |||||||
\(752\) | − | 794.878i | − | 1.05702i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 33.1736i | 0.0439969i | ||||||||
\(755\) | − | 1709.09i | − | 2.26369i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −314.963 | −0.416068 | −0.208034 | − | 0.978122i | \(-0.566706\pi\) | ||||
−0.208034 | + | 0.978122i | \(0.566706\pi\) | |||||||
\(758\) | −597.484 | −0.788237 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 458.941 | 0.603870 | ||||||||
\(761\) | − | 1077.49i | − | 1.41589i | −0.706267 | − | 0.707946i | \(-0.749622\pi\) | ||
0.706267 | − | 0.707946i | \(-0.250378\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 439.422 | − | 232.152i | 0.575914 | − | 0.304262i | ||||
\(764\) | 100.851 | 0.132004 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1233.60i | 1.61045i | ||||||||
\(767\) | 10.4440 | 0.0136167 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1014.20i | 1.31885i | 0.751770 | + | 0.659426i | \(0.229200\pi\) | ||||
−0.751770 | + | 0.659426i | \(0.770800\pi\) | |||||||
\(770\) | −611.685 | − | 1157.81i | −0.794396 | − | 1.50365i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 71.5547 | 0.0926874 | ||||||||
\(773\) | − | 731.810i | − | 0.946714i | −0.880871 | − | 0.473357i | \(-0.843042\pi\) | ||
0.880871 | − | 0.473357i | \(-0.156958\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1355.82i | 1.74944i | ||||||||
\(776\) | 1074.60i | 1.38480i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −388.138 | −0.498893 | ||||||||
\(779\) | 10.4653 | 0.0134343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 167.679 | 0.214697 | ||||||||
\(782\) | 1045.69i | 1.33719i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −397.009 | + | 581.905i | −0.506389 | + | 0.742226i | ||||
\(785\) | 871.801 | 1.11057 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 151.096i | − | 0.191989i | −0.995382 | − | 0.0959947i | \(-0.969397\pi\) | ||
0.995382 | − | 0.0959947i | \(-0.0306032\pi\) | |||||||
\(788\) | −60.7179 | −0.0770532 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 999.283i | − | 1.26491i | ||||||
\(791\) | −334.388 | + | 176.661i | −0.422741 | + | 0.223339i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −120.959 | −0.152533 | ||||||||
\(794\) | 540.189i | 0.680338i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 110.403i | − | 0.138697i | ||||||
\(797\) | − | 157.062i | − | 0.197066i | −0.995134 | − | 0.0985330i | \(-0.968585\pi\) | ||
0.995134 | − | 0.0985330i | \(-0.0314150\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1078.29 | 1.34955 | ||||||||
\(800\) | 253.277 | 0.316597 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1189.10 | −1.48267 | ||||||||
\(803\) | − | 479.923i | − | 0.597663i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 757.657 | + | 1434.11i | 0.941189 | + | 1.78151i | ||||
\(806\) | 95.9035 | 0.118987 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1619.67i | 2.00454i | ||||||||
\(809\) | −428.194 | −0.529288 | −0.264644 | − | 0.964346i | \(-0.585254\pi\) | ||||
−0.264644 | + | 0.964346i | \(0.585254\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1167.08i | − | 1.43906i | −0.694459 | − | 0.719532i | \(-0.744356\pi\) | ||
0.694459 | − | 0.719532i | \(-0.255644\pi\) | |||||||
\(812\) | −25.2155 | + | 13.3216i | −0.0310536 | + | 0.0164060i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 156.530 | 0.192297 | ||||||||
\(815\) | 463.333i | 0.568507i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 435.529i | − | 0.533083i | ||||||
\(818\) | 57.0653i | 0.0697620i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.77918 | 0.00582826 | ||||||||
\(821\) | 862.850 | 1.05097 | 0.525487 | − | 0.850802i | \(-0.323883\pi\) | ||||
0.525487 | + | 0.850802i | \(0.323883\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 553.430 | 0.672454 | 0.336227 | − | 0.941781i | \(-0.390849\pi\) | ||||
0.336227 | + | 0.941781i | \(0.390849\pi\) | |||||||
\(824\) | 793.374i | 0.962832i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −40.9703 | − | 77.5496i | −0.0496009 | − | 0.0938857i | ||||
\(827\) | −726.434 | −0.878396 | −0.439198 | − | 0.898390i | \(-0.644737\pi\) | ||||
−0.439198 | + | 0.898390i | \(0.644737\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 153.336i | 0.184966i | 0.995714 | + | 0.0924828i | \(0.0294803\pi\) | ||||
−0.995714 | + | 0.0924828i | \(0.970520\pi\) | |||||||
\(830\) | −35.1728 | −0.0423769 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 109.222i | − | 0.131277i | ||||||
\(833\) | −789.382 | − | 538.561i | −0.947638 | − | 0.646532i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1400.51 | −1.67725 | ||||||||
\(836\) | 29.6701i | 0.0354906i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 146.823i | 0.175207i | ||||||||
\(839\) | 1568.32i | 1.86927i | 0.355608 | + | 0.934635i | \(0.384274\pi\) | ||||
−0.355608 | + | 0.934635i | \(0.615726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −720.703 | −0.856959 | ||||||||
\(842\) | 1130.57 | 1.34272 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −32.3148 | −0.0382877 | ||||||||
\(845\) | 1370.39i | 1.62176i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 131.996 | − | 69.7349i | 0.155839 | − | 0.0823317i | ||||
\(848\) | −487.723 | −0.575145 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 1588.47i | − | 1.86879i | ||||||
\(851\) | −193.884 | −0.227830 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 932.411i | − | 1.09310i | −0.837428 | − | 0.546548i | \(-0.815942\pi\) | ||
0.837428 | − | 0.546548i | \(-0.184058\pi\) | |||||||
\(854\) | 474.503 | + | 898.150i | 0.555624 | + | 1.05170i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 83.6929 | 0.0977721 | ||||||||
\(857\) | 1058.31i | 1.23490i | 0.786609 | + | 0.617451i | \(0.211835\pi\) | ||||
−0.786609 | + | 0.617451i | \(0.788165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 64.7528i | − | 0.0753816i | −0.999289 | − | 0.0376908i | \(-0.988000\pi\) | ||
0.999289 | − | 0.0376908i | \(-0.0120002\pi\) | |||||||
\(860\) | − | 198.892i | − | 0.231270i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 800.581 | 0.928749 | ||||||||
\(863\) | −1210.66 | −1.40285 | −0.701425 | − | 0.712743i | \(-0.747453\pi\) | ||||
−0.701425 | + | 0.712743i | \(0.747453\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 787.896 | 0.910862 | ||||||||
\(866\) | − | 1306.85i | − | 1.50907i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 38.5123 | + | 72.8969i | 0.0443690 | + | 0.0839827i | ||||
\(869\) | 760.290 | 0.874902 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.6583i | 0.0432357i | ||||||||
\(872\) | 591.194 | 0.677975 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 359.005i | 0.410761i | ||||||||
\(875\) | −478.023 | − | 904.814i | −0.546313 | − | 1.03407i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −834.997 | −0.952106 | −0.476053 | − | 0.879416i | \(-0.657933\pi\) | ||||
−0.476053 | + | 0.879416i | \(0.657933\pi\) | |||||||
\(878\) | − | 158.048i | − | 0.180009i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 1411.80i | − | 1.60432i | ||||||
\(881\) | 955.525i | 1.08459i | 0.840188 | + | 0.542296i | \(0.182445\pi\) | ||||
−0.840188 | + | 0.542296i | \(0.817555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 513.712 | 0.581780 | 0.290890 | − | 0.956757i | \(-0.406049\pi\) | ||||
0.290890 | + | 0.956757i | \(0.406049\pi\) | |||||||
\(884\) | 11.5020 | 0.0130114 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 502.439 | 0.567087 | ||||||||
\(887\) | − | 816.561i | − | 0.920587i | −0.887767 | − | 0.460294i | \(-0.847744\pi\) | ||
0.887767 | − | 0.460294i | \(-0.152256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 310.804 | − | 164.201i | 0.349611 | − | 0.184704i | ||||
\(890\) | 916.109 | 1.02934 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 136.519i | 0.153048i | ||||||||
\(893\) | 370.199 | 0.414556 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2354.71i | − | 2.63096i | ||||||
\(896\) | −664.361 | + | 350.989i | −0.741474 | + | 0.391729i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1489.01 | −1.65814 | ||||||||
\(899\) | − | 347.774i | − | 0.386845i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 661.620i | − | 0.734317i | ||||||
\(902\) | − | 35.5207i | − | 0.0393799i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −449.882 | −0.497657 | ||||||||
\(905\) | 2030.77 | 2.24395 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1001.84 | −1.10456 | −0.552280 | − | 0.833659i | \(-0.686242\pi\) | ||||
−0.552280 | + | 0.833659i | \(0.686242\pi\) | |||||||
\(908\) | 62.1960i | 0.0684978i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −154.097 | + | 81.4111i | −0.169337 | + | 0.0894628i | ||||
\(911\) | −243.326 | −0.267098 | −0.133549 | − | 0.991042i | \(-0.542637\pi\) | ||||
−0.133549 | + | 0.991042i | \(0.542637\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 26.7607i | − | 0.0293108i | ||||||
\(914\) | 1630.47 | 1.78388 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 162.656i | 0.177572i | ||||||||
\(917\) | −149.496 | − | 282.969i | −0.163027 | − | 0.308581i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1305.16 | −1.42020 | −0.710100 | − | 0.704101i | \(-0.751350\pi\) | ||||
−0.710100 | + | 0.704101i | \(0.751350\pi\) | |||||||
\(920\) | 1929.44i | 2.09722i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 839.171i | − | 0.910164i | ||||||
\(923\) | − | 22.3169i | − | 0.0241786i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 294.523 | 0.318404 | ||||||||
\(926\) | 448.732 | 0.484592 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −64.9668 | −0.0700073 | ||||||||
\(929\) | − | 90.9709i | − | 0.0979234i | −0.998801 | − | 0.0489617i | \(-0.984409\pi\) | ||
0.998801 | − | 0.0489617i | \(-0.0155912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −271.011 | − | 184.899i | −0.291097 | − | 0.198603i | ||||
\(932\) | 84.5340 | 0.0907017 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1770.10i | 1.89519i | ||||||||
\(935\) | 1915.17 | 2.04831 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1324.34i | − | 1.41338i | −0.707523 | − | 0.706690i | \(-0.750188\pi\) | ||
0.707523 | − | 0.706690i | \(-0.249812\pi\) | |||||||
\(938\) | 279.623 | − | 147.728i | 0.298105 | − | 0.157492i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 169.058 | 0.179849 | ||||||||
\(941\) | 1083.08i | 1.15099i | 0.817805 | + | 0.575495i | \(0.195191\pi\) | ||||
−0.817805 | + | 0.575495i | \(0.804809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.9973i | 0.0466567i | ||||||||
\(944\) | − | 94.5616i | − | 0.100171i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1478.24 | −1.56263 | ||||||||
\(947\) | 119.688 | 0.126386 | 0.0631931 | − | 0.998001i | \(-0.479872\pi\) | ||||
0.0631931 | + | 0.998001i | \(0.479872\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.8745 | −0.0673072 | ||||||||
\(950\) | − | 545.355i | − | 0.574058i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −531.014 | − | 1005.12i | −0.557787 | − | 1.05579i | ||||
\(953\) | −463.471 | −0.486329 | −0.243164 | − | 0.969985i | \(-0.578185\pi\) | ||||
−0.243164 | + | 0.969985i | \(0.578185\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2234.96i | − | 2.34027i | ||||||
\(956\) | −131.971 | −0.138045 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 50.7558i | − | 0.0529810i | ||||||
\(959\) | −194.645 | + | 102.833i | −0.202967 | + | 0.107230i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.3992 | −0.0462011 | ||||||||
\(962\) | − | 20.8330i | − | 0.0216560i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 95.0661i | − | 0.0986163i | ||||||
\(965\) | − | 1585.72i | − | 1.64323i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −519.927 | −0.537670 | −0.268835 | − | 0.963186i | \(-0.586639\pi\) | ||||
−0.268835 | + | 0.963186i | \(0.586639\pi\) | |||||||
\(968\) | 177.586 | 0.183457 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2023.52 | 2.08610 | ||||||||
\(971\) | 50.6835i | 0.0521972i | 0.999659 | + | 0.0260986i | \(0.00830839\pi\) | ||||
−0.999659 | + | 0.0260986i | \(0.991692\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 389.919 | + | 738.048i | 0.400739 | + | 0.758528i | ||||
\(974\) | 1357.21 | 1.39344 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1095.18i | 1.12211i | ||||||||
\(977\) | 493.117 | 0.504726 | 0.252363 | − | 0.967633i | \(-0.418792\pi\) | ||||
0.252363 | + | 0.967633i | \(0.418792\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 697.009i | 0.711960i | ||||||||
\(980\) | −123.762 | − | 84.4377i | −0.126288 | − | 0.0861609i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 677.053 | 0.689463 | ||||||||
\(983\) | 808.577i | 0.822561i | 0.911509 | + | 0.411281i | \(0.134918\pi\) | ||||
−0.911509 | + | 0.411281i | \(0.865082\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1345.57i | 1.36606i | ||||||||
\(986\) | 407.450i | 0.413236i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.94889 | 0.00399685 | ||||||||
\(989\) | 1831.01 | 1.85138 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −588.956 | −0.594305 | −0.297152 | − | 0.954830i | \(-0.596037\pi\) | ||||
−0.297152 | + | 0.954830i | \(0.596037\pi\) | |||||||
\(992\) | 187.816i | 0.189331i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −165.709 | + | 87.5457i | −0.166709 | + | 0.0880742i | ||||
\(995\) | −2446.64 | −2.45894 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 539.626i | 0.541250i | 0.962685 | + | 0.270625i | \(0.0872304\pi\) | ||||
−0.962685 | + | 0.270625i | \(0.912770\pi\) | |||||||
\(998\) | −451.239 | −0.452143 | ||||||||
\(999\) | 0 | 0 |
(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 | 567.3.d.g.244.6 | 14 | ||
3.2 | odd | 2 | 567.3.d.h.244.9 | 14 | |||
7.6 | odd | 2 | inner | 567.3.d.g.244.5 | 14 | ||
9.2 | odd | 6 | 63.3.l.a.13.6 | yes | 28 | ||
9.4 | even | 3 | 189.3.l.a.181.10 | 28 | |||
9.5 | odd | 6 | 63.3.l.a.34.5 | yes | 28 | ||
9.7 | even | 3 | 189.3.l.a.118.9 | 28 | |||
21.20 | even | 2 | 567.3.d.h.244.10 | 14 | |||
63.2 | odd | 6 | 441.3.k.a.31.6 | 28 | |||
63.5 | even | 6 | 441.3.t.b.178.9 | 28 | |||
63.11 | odd | 6 | 441.3.t.b.166.9 | 28 | |||
63.13 | odd | 6 | 189.3.l.a.181.9 | 28 | |||
63.20 | even | 6 | 63.3.l.a.13.5 | ✓ | 28 | ||
63.23 | odd | 6 | 441.3.t.b.178.10 | 28 | |||
63.32 | odd | 6 | 441.3.k.a.313.5 | 28 | |||
63.34 | odd | 6 | 189.3.l.a.118.10 | 28 | |||
63.38 | even | 6 | 441.3.t.b.166.10 | 28 | |||
63.41 | even | 6 | 63.3.l.a.34.6 | yes | 28 | ||
63.47 | even | 6 | 441.3.k.a.31.5 | 28 | |||
63.59 | even | 6 | 441.3.k.a.313.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.3.l.a.13.5 | ✓ | 28 | 63.20 | even | 6 | ||
63.3.l.a.13.6 | yes | 28 | 9.2 | odd | 6 | ||
63.3.l.a.34.5 | yes | 28 | 9.5 | odd | 6 | ||
63.3.l.a.34.6 | yes | 28 | 63.41 | even | 6 | ||
189.3.l.a.118.9 | 28 | 9.7 | even | 3 | |||
189.3.l.a.118.10 | 28 | 63.34 | odd | 6 | |||
189.3.l.a.181.9 | 28 | 63.13 | odd | 6 | |||
189.3.l.a.181.10 | 28 | 9.4 | even | 3 | |||
441.3.k.a.31.5 | 28 | 63.47 | even | 6 | |||
441.3.k.a.31.6 | 28 | 63.2 | odd | 6 | |||
441.3.k.a.313.5 | 28 | 63.32 | odd | 6 | |||
441.3.k.a.313.6 | 28 | 63.59 | even | 6 | |||
441.3.t.b.166.9 | 28 | 63.11 | odd | 6 | |||
441.3.t.b.166.10 | 28 | 63.38 | even | 6 | |||
441.3.t.b.178.9 | 28 | 63.5 | even | 6 | |||
441.3.t.b.178.10 | 28 | 63.23 | odd | 6 | |||
567.3.d.g.244.5 | 14 | 7.6 | odd | 2 | inner | ||
567.3.d.g.244.6 | 14 | 1.1 | even | 1 | trivial | ||
567.3.d.h.244.9 | 14 | 3.2 | odd | 2 | |||
567.3.d.h.244.10 | 14 | 21.20 | even | 2 |