Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,5,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.4244687775\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 996 x^{18} + 408854 x^{16} + 89661524 x^{14} + 11414409521 x^{12} + 861580608848 x^{10} + \cdots + 34\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{50} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.4 | ||
Root | \(-11.4302i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.5.e.f.113.17 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 11.4302i | − | 1.27003i | −0.772501 | − | 0.635014i | \(-0.780994\pi\) | ||
0.772501 | − | 0.635014i | \(-0.219006\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.10929 | −0.364372 | −0.182186 | − | 0.983264i | \(-0.558317\pi\) | ||||
−0.182186 | + | 0.983264i | \(0.558317\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −75.9168 | −1.54932 | −0.774661 | − | 0.632376i | \(-0.782080\pi\) | ||||
−0.774661 | + | 0.632376i | \(0.782080\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −49.6505 | −0.612969 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −149.183 | −1.23292 | −0.616460 | − | 0.787386i | \(-0.711434\pi\) | ||||
−0.616460 | + | 0.787386i | \(0.711434\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 188.468i | 1.11520i | 0.830111 | + | 0.557598i | \(0.188277\pi\) | ||||
−0.830111 | + | 0.557598i | \(0.811723\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 104.121i | 0.462762i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 322.296 | 1.11521 | 0.557605 | − | 0.830106i | \(-0.311720\pi\) | ||||
0.557605 | + | 0.830106i | \(0.311720\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 349.839 | − | 89.0705i | 0.969084 | − | 0.246733i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 867.748i | 1.96768i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 561.396 | 1.06124 | 0.530620 | − | 0.847610i | \(-0.321959\pi\) | ||||
0.530620 | + | 0.847610i | \(0.321959\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −542.021 | −0.867233 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 358.332i | − | 0.491539i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 260.782i | 0.310085i | 0.987908 | + | 0.155043i | \(0.0495515\pi\) | ||||
−0.987908 | + | 0.155043i | \(0.950448\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 167.262i | 0.174050i | 0.996206 | + | 0.0870248i | \(0.0277359\pi\) | ||||
−0.996206 | + | 0.0870248i | \(0.972264\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1705.20i | 1.56584i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 691.548 | 0.564529 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1800.56i | − | 1.31524i | −0.753352 | − | 0.657618i | \(-0.771564\pi\) | ||
0.753352 | − | 0.657618i | \(-0.228436\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2154.24 | 1.41633 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1423.75i | 0.846964i | 0.905904 | + | 0.423482i | \(0.139192\pi\) | ||||
−0.905904 | + | 0.423482i | \(0.860808\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −836.566 | −0.452442 | −0.226221 | − | 0.974076i | \(-0.572637\pi\) | ||||
−0.226221 | + | 0.974076i | \(0.572637\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 452.281 | 0.223349 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1086.54 | −0.491871 | −0.245935 | − | 0.969286i | \(-0.579095\pi\) | ||||
−0.245935 | + | 0.969286i | \(0.579095\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3362.36 | 1.40040 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3683.92i | − | 1.41635i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4337.45i | 1.54413i | 0.635545 | + | 0.772064i | \(0.280775\pi\) | ||||
−0.635545 | + | 0.772064i | \(0.719225\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1358.95 | 0.449241 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1018.10 | − | 3998.75i | −0.313357 | − | 1.23076i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5831.99i | − | 1.67538i | −0.546147 | − | 0.837690i | \(-0.683906\pi\) | ||
0.546147 | − | 0.837690i | \(-0.316094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5513.48 | 1.48172 | 0.740860 | − | 0.671660i | \(-0.234418\pi\) | ||||
0.740860 | + | 0.671660i | \(0.234418\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3769.31 | 0.949687 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1716.81i | − | 0.406346i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3107.22i | 0.692186i | 0.938200 | + | 0.346093i | \(0.112492\pi\) | ||||
−0.938200 | + | 0.346093i | \(0.887508\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6416.89i | − | 1.34780i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5926.54i | 1.17567i | 0.808982 | + | 0.587833i | \(0.200019\pi\) | ||||
−0.808982 | + | 0.587833i | \(0.799981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2350.54 | 0.441085 | 0.220543 | − | 0.975377i | \(-0.429217\pi\) | ||||
0.220543 | + | 0.975377i | \(0.429217\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6195.43i | 1.10141i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11325.5 | 1.91019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8365.30i | 1.34038i | 0.742190 | + | 0.670189i | \(0.233787\pi\) | ||||
−0.742190 | + | 0.670189i | \(0.766213\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8117.52 | −1.23724 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11086.6 | 1.60932 | 0.804660 | − | 0.593736i | \(-0.202348\pi\) | ||||
0.804660 | + | 0.593736i | \(0.202348\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2935.89 | −0.406351 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2980.80 | 0.393817 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 834.210i | 0.105316i | 0.998613 | + | 0.0526582i | \(0.0167694\pi\) | ||||
−0.998613 | + | 0.0526582i | \(0.983231\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 14307.9i | − | 1.72780i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1911.84 | 0.221048 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3186.79 | + | 811.369i | −0.353106 | + | 0.0899024i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2254.86i | − | 0.239649i | −0.992795 | − | 0.119825i | \(-0.961767\pi\) | ||
0.992795 | − | 0.119825i | \(-0.0382332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7407.03 | 0.755742 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 783.930 | 0.0768484 | 0.0384242 | − | 0.999262i | \(-0.487766\pi\) | ||||
0.0384242 | + | 0.999262i | \(0.487766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17833.0i | 1.68093i | 0.541862 | + | 0.840467i | \(0.317720\pi\) | ||||
−0.541862 | + | 0.840467i | \(0.682280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 7904.56i | − | 0.716967i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17730.5i | 1.54865i | 0.632787 | + | 0.774326i | \(0.281911\pi\) | ||||
−0.632787 | + | 0.774326i | \(0.718089\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13138.6i | 1.10585i | 0.833232 | + | 0.552924i | \(0.186488\pi\) | ||||
−0.833232 | + | 0.552924i | \(0.813512\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20580.8 | −1.67038 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4495.21i | 0.352041i | 0.984387 | + | 0.176021i | \(0.0563225\pi\) | ||||
−0.984387 | + | 0.176021i | \(0.943677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5113.92 | −0.386686 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 9357.55i | − | 0.683582i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24467.7 | −1.72782 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7614.66 | 0.520092 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16273.8 | 1.07567 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10630.7 | 0.680367 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3478.63i | − | 0.215676i | −0.994168 | − | 0.107838i | \(-0.965607\pi\) | ||
0.994168 | − | 0.107838i | \(-0.0343927\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9562.15i | 0.574614i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13454.4 | 0.784013 | 0.392006 | − | 0.919963i | \(-0.371781\pi\) | ||||
0.392006 | + | 0.919963i | \(0.371781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26558.7 | + | 6761.95i | −1.50142 | + | 0.382268i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3264.15i | 0.179103i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5102.78 | 0.271873 | 0.135936 | − | 0.990718i | \(-0.456596\pi\) | ||||
0.135936 | + | 0.990718i | \(0.456596\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17146.7 | −0.887464 | −0.443732 | − | 0.896160i | \(-0.646346\pi\) | ||||
−0.443732 | + | 0.896160i | \(0.646346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12419.4i | 0.624689i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 28116.3i | − | 1.37495i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2375.54i | − | 0.112986i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 38432.6i | − | 1.77855i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5776.87 | 0.260208 | 0.130104 | − | 0.991500i | \(-0.458469\pi\) | ||||
0.130104 | + | 0.991500i | \(0.458469\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2852.68i | − | 0.125112i | −0.998041 | − | 0.0625561i | \(-0.980075\pi\) | ||
0.998041 | − | 0.0625561i | \(-0.0199252\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16002.2 | −0.683590 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1523.63i | − | 0.0634187i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17754.0 | 0.720274 | 0.360137 | − | 0.932900i | \(-0.382730\pi\) | ||||
0.360137 | + | 0.932900i | \(0.382730\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 49578.2 | 1.96108 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −42619.4 | −1.64420 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −32885.4 | −1.23774 | −0.618868 | − | 0.785495i | \(-0.712408\pi\) | ||||
−0.618868 | + | 0.785495i | \(0.712408\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 15533.2i | − | 0.570548i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13740.4i | 0.492680i | 0.969183 | + | 0.246340i | \(0.0792280\pi\) | ||||
−0.969183 | + | 0.246340i | \(0.920772\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6959.29 | −0.243664 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17369.7 | + | 4422.40i | −0.594019 | + | 0.151240i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 10712.9i | − | 0.357944i | −0.983854 | − | 0.178972i | \(-0.942723\pi\) | ||
0.983854 | − | 0.178972i | \(-0.0572772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 41148.5 | 1.34362 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −66661.1 | −2.12778 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 39711.4i | − | 1.23939i | −0.784841 | − | 0.619697i | \(-0.787256\pi\) | ||
0.784841 | − | 0.619697i | \(-0.212744\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13456.0i | − | 0.410733i | −0.978685 | − | 0.205366i | \(-0.934161\pi\) | ||
0.978685 | − | 0.205366i | \(-0.0658386\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 63020.4i | − | 1.88182i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16401.8i | 0.479234i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −48081.2 | −1.37497 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27203.4i | 0.761553i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −59296.4 | −1.62541 | −0.812703 | − | 0.582678i | \(-0.802005\pi\) | ||||
−0.812703 | + | 0.582678i | \(0.802005\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 33032.9i | − | 0.886813i | −0.896321 | − | 0.443407i | \(-0.853770\pi\) | ||
0.896321 | − | 0.443407i | \(-0.146230\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19623.6 | −0.516071 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −29861.3 | −0.769442 | −0.384721 | − | 0.923033i | \(-0.625702\pi\) | ||||
−0.384721 | + | 0.923033i | \(0.625702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 30968.8 | 0.782021 | 0.391010 | − | 0.920386i | \(-0.372126\pi\) | ||||
0.391010 | + | 0.920386i | \(0.372126\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 35516.3 | 0.879095 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 19797.7i | − | 0.480422i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 12969.3i | − | 0.308610i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −27873.6 | −0.650508 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −52190.2 | + | 13287.8i | −1.19480 | + | 0.304202i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 76035.8i | 1.70786i | 0.520385 | + | 0.853932i | \(0.325788\pi\) | ||||
−0.520385 | + | 0.853932i | \(0.674212\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 67741.8 | 1.49313 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7620.52 | 0.164857 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 12698.0i | − | 0.269659i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 26867.3i | − | 0.560190i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 60742.6i | 1.24368i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 66035.2i | 1.32790i | 0.747777 | + | 0.663950i | \(0.231121\pi\) | ||||
−0.747777 | + | 0.663950i | \(0.768879\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26911.6 | 0.531588 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 70838.7i | 1.37473i | 0.726310 | + | 0.687367i | \(0.241234\pi\) | ||||
−0.726310 | + | 0.687367i | \(0.758766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 69086.9 | 1.31742 | 0.658710 | − | 0.752397i | \(-0.271102\pi\) | ||||
0.658710 | + | 0.752397i | \(0.271102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 129453.i | − | 2.42599i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −72230.6 | −1.33048 | −0.665242 | − | 0.746628i | \(-0.731672\pi\) | ||||
−0.665242 | + | 0.746628i | \(0.731672\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9897.63 | 0.179224 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 95617.4 | 1.70232 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14753.9 | −0.258292 | −0.129146 | − | 0.991626i | \(-0.541224\pi\) | ||||
−0.129146 | + | 0.991626i | \(0.541224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 45140.5i | − | 0.777198i | −0.921407 | − | 0.388599i | \(-0.872959\pi\) | ||
0.921407 | − | 0.388599i | \(-0.127041\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 63760.3i | 1.07979i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −30628.7 | −0.510266 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16787.0 | + | 65933.6i | 0.275155 | + | 1.08072i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 126723.i | − | 2.04388i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −46493.4 | −0.737980 | −0.368990 | − | 0.929433i | \(-0.620296\pi\) | ||||
−0.368990 | + | 0.929433i | \(0.620296\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −83750.9 | −1.30842 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 33557.9i | 0.516077i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 123613.i | 1.87154i | 0.352617 | + | 0.935768i | \(0.385292\pi\) | ||||
−0.352617 | + | 0.935768i | \(0.614708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 136693.i | 2.03772i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 12948.0i | − | 0.190073i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −51498.3 | −0.744528 | −0.372264 | − | 0.928127i | \(-0.621418\pi\) | ||||
−0.372264 | + | 0.928127i | \(0.621418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 39511.1i | − | 0.562636i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9535.23 | 0.133755 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 76030.5i | 1.05071i | 0.850883 | + | 0.525355i | \(0.176068\pi\) | ||||
−0.850883 | + | 0.525355i | \(0.823932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10469.5 | 0.142557 | 0.0712785 | − | 0.997456i | \(-0.477292\pi\) | ||||
0.0712785 | + | 0.997456i | \(0.477292\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −163543. | −2.19435 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 80860.5 | 1.06923 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 117299. | 1.52874 | 0.764369 | − | 0.644779i | \(-0.223050\pi\) | ||||
0.764369 | + | 0.644779i | \(0.223050\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 8304.63i | − | 0.106687i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 76392.4i | − | 0.967470i | −0.875215 | − | 0.483735i | \(-0.839280\pi\) | ||
0.875215 | − | 0.483735i | \(-0.160720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 133039. | 1.66114 | 0.830569 | − | 0.556916i | \(-0.188016\pi\) | ||||
0.830569 | + | 0.556916i | \(0.188016\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9274.14 | + | 36425.7i | 0.114178 | + | 0.448455i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 108086.i | − | 1.31222i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20353.6 | 0.243695 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25773.6 | −0.304361 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 132667.i | − | 1.54535i | −0.634800 | − | 0.772677i | \(-0.718917\pi\) | ||
0.634800 | − | 0.772677i | \(-0.281083\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 53125.3i | 0.610460i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 53457.2i | 0.606029i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 105805.i | 1.18349i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 63509.4 | 0.700979 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 8960.52i | − | 0.0975996i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −50223.9 | −0.539896 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 116528.i | − | 1.23638i | −0.786028 | − | 0.618192i | \(-0.787866\pi\) | ||
0.786028 | − | 0.618192i | \(-0.212134\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 203836. | 2.13483 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −74587.7 | −0.771164 | −0.385582 | − | 0.922674i | \(-0.625999\pi\) | ||||
−0.385582 | + | 0.922674i | \(0.625999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −140470. | −1.43383 | −0.716913 | − | 0.697163i | \(-0.754445\pi\) | ||||
−0.716913 | + | 0.697163i | \(0.754445\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −34335.7 | −0.346039 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 78316.2i | − | 0.779351i | −0.920952 | − | 0.389676i | \(-0.872587\pi\) | ||
0.920952 | − | 0.389676i | \(-0.127413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 38904.3i | − | 0.382310i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 202664. | 1.96683 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 112752. | − | 28707.1i | 1.08073 | − | 0.275159i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 102154.i | − | 0.967136i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 150177. | 1.40446 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 82486.8 | 0.762066 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 30840.1i | − | 0.281488i | −0.990046 | − | 0.140744i | \(-0.955051\pi\) | ||
0.990046 | − | 0.140744i | \(-0.0449494\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 89398.6i | 0.806199i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 28304.6i | − | 0.252213i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 179800.i | 1.58318i | 0.611052 | + | 0.791590i | \(0.290747\pi\) | ||||
−0.611052 | + | 0.791590i | \(0.709253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 51381.4 | 0.447102 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 24952.6i | − | 0.214589i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −72983.4 | −0.620349 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 58453.3i | 0.491101i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4348.77 | 0.0361166 | 0.0180583 | − | 0.999837i | \(-0.494252\pi\) | ||||
0.0180583 | + | 0.999837i | \(0.494252\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 165030. | 1.35492 | 0.677459 | − | 0.735561i | \(-0.263081\pi\) | ||||
0.677459 | + | 0.735561i | \(0.263081\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 67534.3 | 0.548163 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27708.9 | −0.222367 | −0.111183 | − | 0.993800i | \(-0.535464\pi\) | ||||
−0.111183 | + | 0.993800i | \(0.535464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 53986.5i | − | 0.428379i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 279672.i | 2.19438i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30040.7 | 0.233089 | 0.116544 | − | 0.993185i | \(-0.462818\pi\) | ||||
0.116544 | + | 0.993185i | \(0.462818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 114454. | − | 62320.7i | 0.878246 | − | 0.478209i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 87037.4i | − | 0.660530i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21411.8 | −0.160719 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 51235.7 | 0.380400 | 0.190200 | − | 0.981745i | \(-0.439086\pi\) | ||||
0.190200 | + | 0.981745i | \(0.439086\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 70689.8i | − | 0.519163i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 329286.i | − | 2.39235i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 75674.3i | 0.543914i | 0.962309 | + | 0.271957i | \(0.0876709\pi\) | ||||
−0.962309 | + | 0.271957i | \(0.912329\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 121512.i | − | 0.864084i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −49149.1 | −0.345806 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 216796.i | 1.50929i | 0.656132 | + | 0.754646i | \(0.272191\pi\) | ||||
−0.656132 | + | 0.754646i | \(0.727809\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39761.6 | −0.273914 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 56907.1i | − | 0.387944i | −0.981007 | − | 0.193972i | \(-0.937863\pi\) | ||
0.981007 | − | 0.193972i | \(-0.0621371\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −103167. | −0.696019 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 41535.9 | 0.277333 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −43485.7 | −0.287374 | −0.143687 | − | 0.989623i | \(-0.545896\pi\) | ||||
−0.143687 | + | 0.989623i | \(0.545896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 180936. | 1.18351 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 153788.i | − | 0.995718i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 76201.9i | − | 0.488396i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −148863. | −0.944507 | −0.472253 | − | 0.881463i | \(-0.656559\pi\) | ||||
−0.472253 | + | 0.881463i | \(0.656559\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 77290.7 | + | 303572.i | 0.485491 | + | 1.90685i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 54439.7i | 0.338553i | 0.985569 | + | 0.169277i | \(0.0541431\pi\) | ||||
−0.985569 | + | 0.169277i | \(0.945857\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31523.5 | −0.194100 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 73944.8 | 0.450814 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 268613.i | 1.62158i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 262595.i | − | 1.56978i | −0.619632 | − | 0.784892i | \(-0.712718\pi\) | ||
0.619632 | − | 0.784892i | \(-0.287282\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 58326.0i | − | 0.345286i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 442746.i | 2.59570i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −100991. | −0.586390 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 195991.i | 1.12710i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21837.6 | −0.124387 | −0.0621937 | − | 0.998064i | \(-0.519810\pi\) | ||||
−0.0621937 | + | 0.998064i | \(0.519810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 243876.i | − | 1.37596i | −0.725732 | − | 0.687978i | \(-0.758499\pi\) | ||
0.725732 | − | 0.687978i | \(-0.241501\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 53947.4 | 0.301502 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −174691. | −0.967148 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −418566. | −2.29566 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −321376. | −1.74622 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 150402.i | − | 0.809655i | −0.914393 | − | 0.404827i | \(-0.867332\pi\) | ||
0.914393 | − | 0.404827i | \(-0.132668\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 172534.i | 0.920237i | 0.887858 | + | 0.460118i | \(0.152193\pi\) | ||||
−0.887858 | + | 0.460118i | \(0.847807\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −27153.0 | −0.143496 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 196398. | − | 50003.8i | 1.02843 | − | 0.261843i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 339644.i | 1.76236i | 0.472781 | + | 0.881180i | \(0.343250\pi\) | ||||
−0.472781 | + | 0.881180i | \(0.656750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −166943. | −0.858402 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 69761.2 | 0.355473 | 0.177736 | − | 0.984078i | \(-0.443123\pi\) | ||||
0.177736 | + | 0.984078i | \(0.443123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 7599.06i | − | 0.0383743i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 66031.1i | − | 0.330471i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 105494.i | 0.523280i | 0.965166 | + | 0.261640i | \(0.0842633\pi\) | ||||
−0.965166 | + | 0.261640i | \(0.915737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 212399.i | − | 1.04424i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32606.9 | −0.158896 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 130335.i | 0.629561i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −134453. | −0.643781 | −0.321890 | − | 0.946777i | \(-0.604318\pi\) | ||||
−0.321890 | + | 0.946777i | \(0.604318\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 115489.i | − | 0.548170i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 196297. | 0.923657 | 0.461829 | − | 0.886969i | \(-0.347194\pi\) | ||||
0.461829 | + | 0.886969i | \(0.347194\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14619.6 | −0.0681982 | −0.0340991 | − | 0.999418i | \(-0.510856\pi\) | ||||
−0.0340991 | + | 0.999418i | \(0.510856\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17415.5 | −0.0805435 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −214407. | −0.983115 | −0.491557 | − | 0.870845i | \(-0.663572\pi\) | ||||
−0.491557 | + | 0.870845i | \(0.663572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 235890.i | − | 1.07242i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 202933.i | − | 0.914767i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 124802. | 0.557825 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −189620. | + | 48278.1i | −0.840422 | + | 0.213975i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 215357.i | − | 0.946503i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −349544. | −1.52346 | −0.761729 | − | 0.647895i | \(-0.775649\pi\) | ||||
−0.761729 | + | 0.647895i | \(0.775649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 339348. | 1.46675 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 487150.i | 2.08818i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20540.2i | 0.0873213i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 334987.i | 1.41244i | 0.707992 | + | 0.706220i | \(0.249601\pi\) | ||||
−0.707992 | + | 0.706220i | \(0.750399\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 375888.i | 1.57196i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 474897. | 1.96987 | 0.984933 | − | 0.172938i | \(-0.0553260\pi\) | ||||
0.984933 | + | 0.172938i | \(0.0553260\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 84048.9i | 0.345810i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −67472.8 | −0.275371 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 449924.i | − | 1.82149i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 422704. | 1.69760 | 0.848801 | − | 0.528713i | \(-0.177325\pi\) | ||||
0.848801 | + | 0.528713i | \(0.177325\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 157056. | 0.625717 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −341698. | −1.35054 | −0.675268 | − | 0.737572i | \(-0.735972\pi\) | ||||
−0.675268 | + | 0.737572i | \(0.735972\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7141.05 | −0.0280014 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 79546.4i | 0.309460i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 174479.i | − | 0.673452i | −0.941603 | − | 0.336726i | \(-0.890680\pi\) | ||
0.941603 | − | 0.336726i | \(-0.109320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −178446. | −0.683383 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −31916.8 | − | 125359.i | −0.121279 | − | 0.476343i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 162446.i | − | 0.612485i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 162094. | 0.606437 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −122451. | −0.454599 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 255132.i | − | 0.939917i | −0.882689 | − | 0.469958i | \(-0.844269\pi\) | ||
0.882689 | − | 0.469958i | \(-0.155731\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 440253.i | − | 1.60953i | −0.593593 | − | 0.804765i | \(-0.702291\pi\) | ||
0.593593 | − | 0.804765i | \(-0.297709\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 470337.i | − | 1.70644i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53907.7i | 0.194102i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35324.4 | 0.126230 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 289562.i | 1.02696i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −268331. | −0.944532 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 161512.i | − | 0.564285i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −453911. | −1.57406 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −501608. | −1.72658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −137088. | −0.468386 | −0.234193 | − | 0.972190i | \(-0.575245\pi\) | ||||
−0.234193 | + | 0.972190i | \(0.575245\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −153806. | −0.521642 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 119683.i | − | 0.402940i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 93456.1i | − | 0.312344i | −0.987730 | − | 0.156172i | \(-0.950085\pi\) | ||
0.987730 | − | 0.156172i | \(-0.0499154\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −273747. | −0.908249 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23228.0 | + | 91231.7i | 0.0765082 | + | 0.300499i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 635067.i | − | 2.07668i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 187477. | 0.608641 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −511715. | −1.64937 | −0.824684 | − | 0.565594i | \(-0.808647\pi\) | ||||
−0.824684 | + | 0.565594i | \(0.808647\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 157666.i | − | 0.504562i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 549580.i | 1.74624i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 27109.4i | − | 0.0855271i | −0.999085 | − | 0.0427636i | \(-0.986384\pi\) | ||
0.999085 | − | 0.0427636i | \(-0.0136162\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 40948.2i | − | 0.128274i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 616256. | 1.91688 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 90925.6i | − | 0.280842i | −0.990092 | − | 0.140421i | \(-0.955154\pi\) | ||
0.990092 | − | 0.140421i | \(-0.0448456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 374122. | 1.14747 | 0.573735 | − | 0.819041i | \(-0.305494\pi\) | ||||
0.573735 | + | 0.819041i | \(0.305494\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 677773.i | 2.06431i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −304288. | −0.920343 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 618133. | 1.85665 | 0.928325 | − | 0.371769i | \(-0.121249\pi\) | ||||
0.928325 | + | 0.371769i | \(0.121249\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −377574. | −1.12628 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −841659. | −2.49336 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 647076.i | − | 1.90379i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 85240.6i | 0.249078i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −546495. | −1.58603 | −0.793013 | − | 0.609205i | \(-0.791489\pi\) | ||||
−0.793013 | + | 0.609205i | \(0.791489\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14898.1 | + | 58514.7i | 0.0429437 | + | 0.168669i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 341322.i | 0.977212i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −126105. | −0.358610 | −0.179305 | − | 0.983794i | \(-0.557385\pi\) | ||||
−0.179305 | + | 0.983794i | \(0.557385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 222883. | 0.629569 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 353981.i | − | 0.993188i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 592405.i | − | 1.65107i | −0.564351 | − | 0.825535i | \(-0.690874\pi\) | ||
0.564351 | − | 0.825535i | \(-0.309126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 150697.i | 0.417211i | 0.978000 | + | 0.208606i | \(0.0668925\pi\) | ||||
−0.978000 | + | 0.208606i | \(0.933108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 154275.i | − | 0.424289i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −69364.1 | −0.189507 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 442114.i | 1.19993i | 0.800025 | + | 0.599967i | \(0.204820\pi\) | ||||
−0.800025 | + | 0.599967i | \(0.795180\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −226293. | −0.610149 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 204779.i | − | 0.548533i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 419179. | 1.11552 | 0.557761 | − | 0.830001i | \(-0.311660\pi\) | ||||
0.557761 | + | 0.830001i | \(0.311660\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −148243. | −0.391943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 104140. | 0.273558 | 0.136779 | − | 0.990602i | \(-0.456325\pi\) | ||||
0.136779 | + | 0.990602i | \(0.456325\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −184995. | −0.482812 | −0.241406 | − | 0.970424i | \(-0.577608\pi\) | ||||
−0.241406 | + | 0.970424i | \(0.577608\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 201166.i | − | 0.521641i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 63330.6i | − | 0.163169i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 241925. | 0.619327 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 151883. | + | 596546.i | 0.386344 | + | 1.51743i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 580312.i | − | 1.46676i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 677804. | 1.70234 | 0.851169 | − | 0.524892i | \(-0.175894\pi\) | ||||
0.851169 | + | 0.524892i | \(0.175894\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 869108. | 2.16903 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31687.9i | 0.0785861i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 633698.i | 1.56172i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 294256.i | − | 0.720648i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 272570.i | 0.663379i | 0.943389 | + | 0.331690i | \(0.107619\pi\) | ||||
−0.943389 | + | 0.331690i | \(0.892381\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 436968. | 1.05689 | 0.528443 | − | 0.848969i | \(-0.322776\pi\) | ||||
0.528443 | + | 0.848969i | \(0.322776\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 87104.4i | − | 0.209373i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 80856.5 | 0.193155 | 0.0965776 | − | 0.995325i | \(-0.469210\pi\) | ||||
0.0965776 | + | 0.995325i | \(0.469210\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 870036.i | 2.06561i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −145141. | −0.342474 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 252641. | 0.592485 | 0.296243 | − | 0.955113i | \(-0.404266\pi\) | ||||
0.296243 | + | 0.955113i | \(0.404266\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −122560. | −0.285672 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −116706. | −0.270372 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 290788.i | 0.669585i | 0.942292 | + | 0.334793i | \(0.108666\pi\) | ||||
−0.942292 | + | 0.334793i | \(0.891334\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 676941.i | 1.54934i | 0.632364 | + | 0.774672i | \(0.282085\pi\) | ||||
−0.632364 | + | 0.774672i | \(0.717915\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 694302. | 1.57951 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 241931. | − | 61596.5i | 0.547076 | − | 0.139288i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 146402.i | 0.329075i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 754798. | 1.68647 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −822519. | −1.82684 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 643778.i | 1.42137i | 0.703512 | + | 0.710683i | \(0.251614\pi\) | ||||
−0.703512 | + | 0.710683i | \(0.748386\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 194224.i | 0.426279i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 813059.i | 1.77396i | 0.461804 | + | 0.886982i | \(0.347202\pi\) | ||||
−0.461804 | + | 0.886982i | \(0.652798\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 171182.i | 0.371294i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 809704. | 1.74595 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 374698.i | − | 0.803231i | −0.915808 | − | 0.401615i | \(-0.868449\pi\) | ||
0.915808 | − | 0.401615i | \(-0.131551\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46482.7 | −0.0990626 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 789680.i | − | 1.67316i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −817472. | −1.72201 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 578886. | 1.21238 | 0.606188 | − | 0.795321i | \(-0.292698\pi\) | ||||
0.606188 | + | 0.795321i | \(0.292698\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −562318. | −1.17089 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 156194. | 0.323366 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 458868.i | 0.944543i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 825614.i | 1.68975i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −325316. | −0.662018 | −0.331009 | − | 0.943628i | \(-0.607389\pi\) | ||||
−0.331009 | + | 0.943628i | \(0.607389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −160376. | − | 629905.i | −0.324511 | − | 1.27457i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 113132.i | − | 0.227619i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −59513.5 | −0.119063 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −805646. | −1.60270 | −0.801350 | − | 0.598196i | \(-0.795884\pi\) | ||||
−0.801350 | + | 0.598196i | \(0.795884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 415342.i | − | 0.821611i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 93900.0i | 0.184708i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 256120.i | 0.500992i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 168641.i | 0.328038i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 234223. | 0.453077 | 0.226539 | − | 0.974002i | \(-0.427259\pi\) | ||||
0.226539 | + | 0.974002i | \(0.427259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1.35383e6i | − | 2.60431i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −515967. | −0.987063 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 141349.i | − | 0.268916i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 464219. | 0.878322 | 0.439161 | − | 0.898408i | \(-0.355276\pi\) | ||||
0.439161 | + | 0.898408i | \(0.355276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 71277.1 | 0.134121 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −269622. | −0.504568 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −82410.5 | −0.153382 | −0.0766910 | − | 0.997055i | \(-0.524435\pi\) | ||||
−0.0766910 | + | 0.997055i | \(0.524435\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 350094.i | 0.648052i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 463546.i | − | 0.853410i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 326895. | 0.598576 | 0.299288 | − | 0.954163i | \(-0.403251\pi\) | ||||
0.299288 | + | 0.954163i | \(0.403251\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 753637. | − | 191879.i | 1.37254 | − | 0.349455i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 735492.i | 1.33230i | 0.745820 | + | 0.666148i | \(0.232058\pi\) | ||||
−0.745820 | + | 0.666148i | \(0.767942\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −52623.2 | −0.0948123 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −550456. | −0.986464 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.34604e6i | − | 2.39936i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 30777.9i | − | 0.0545706i | −0.999628 | − | 0.0272853i | \(-0.991314\pi\) | ||
0.999628 | − | 0.0272853i | \(-0.00868626\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 531432.i | 0.937254i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25985.9i | 0.0455873i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −829936. | −1.44828 | −0.724141 | − | 0.689652i | \(-0.757763\pi\) | ||||
−0.724141 | + | 0.689652i | \(0.757763\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 957294.i | 1.66173i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −170283. | −0.294037 | −0.147018 | − | 0.989134i | \(-0.546968\pi\) | ||||
−0.147018 | + | 0.989134i | \(0.546968\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 997439.i | − | 1.71332i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 145768. | 0.249081 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.09915e6 | 1.86838 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 770218. | 1.30245 | 0.651225 | − | 0.758885i | \(-0.274255\pi\) | ||||
0.651225 | + | 0.758885i | \(0.274255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.41293e6 | 2.37690 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 23021.2i | − | 0.0385273i | −0.999814 | − | 0.0192637i | \(-0.993868\pi\) | ||
0.999814 | − | 0.0192637i | \(-0.00613219\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 90659.3i | − | 0.150942i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.56243e6 | 2.58796 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 126814. | + | 498082.i | 0.208974 | + | 0.820779i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 884140.i | − | 1.44950i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 93446.5 | 0.152419 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −161727. | −0.262447 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 67840.5i | 0.109532i | 0.998499 | + | 0.0547658i | \(0.0174412\pi\) | ||||
−0.998499 | + | 0.0547658i | \(0.982559\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 588638.i | 0.945571i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 341262.i | − | 0.545425i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.03912e6i | 1.65241i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −451622. | −0.714563 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 296624.i | 0.466971i | 0.972360 | + | 0.233485i | \(0.0750131\pi\) | ||||
−0.972360 | + | 0.233485i | \(0.924987\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −350188. | −0.548540 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 41419.0i | − | 0.0645557i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −350662. | −0.543823 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 388232. | 0.599101 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 869047. | 1.33443 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 822479. | 1.25669 | 0.628344 | − | 0.777935i | \(-0.283733\pi\) | ||||
0.628344 | + | 0.777935i | \(0.283733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 539509.i | 0.820270i | 0.912025 | + | 0.410135i | \(0.134518\pi\) | ||||
−0.912025 | + | 0.410135i | \(0.865482\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 119669.i | − | 0.181051i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 299562. | 0.450995 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −292663. | + | 74513.3i | −0.438454 | + | 0.111632i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 710395.i | 1.05909i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −443727. | −0.658309 | −0.329154 | − | 0.944276i | \(-0.606764\pi\) | ||||
−0.329154 | + | 0.944276i | \(0.606764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −171466. | −0.253150 | −0.126575 | − | 0.991957i | \(-0.540398\pi\) | ||||
−0.126575 | + | 0.991957i | \(0.540398\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 924255.i | − | 1.35795i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 62968.3i | − | 0.0920685i | −0.998940 | − | 0.0460342i | \(-0.985342\pi\) | ||
0.998940 | − | 0.0460342i | \(-0.0146583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.00097e6i | − | 1.45650i | −0.685312 | − | 0.728250i | \(-0.740334\pi\) | ||
0.685312 | − | 0.728250i | \(-0.259666\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.34075e6i | − | 1.94154i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.08367e6 | 1.56174 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 125165.i | − | 0.179519i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 59935.2 | 0.0855522 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 579085.i | 0.822656i | 0.911487 | + | 0.411328i | \(0.134935\pi\) | ||||
−0.911487 | + | 0.411328i | \(0.865065\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 639274. | 0.903847 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −873184. | −1.22871 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 63394.2 | 0.0887843 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −578081. | −0.805789 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.52067e6i | − | 2.10969i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.01083e6i | − | 1.39578i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 252867. | 0.347532 | 0.173766 | − | 0.984787i | \(-0.444406\pi\) | ||||
0.173766 | + | 0.984787i | \(0.444406\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 158226. | − | 40284.9i | 0.216443 | − | 0.0551074i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 466322.i | 0.634928i | 0.948270 | + | 0.317464i | \(0.102831\pi\) | ||||
−0.948270 | + | 0.317464i | \(0.897169\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 484650. | 0.656814 | 0.328407 | − | 0.944536i | \(-0.393488\pi\) | ||||
0.328407 | + | 0.944536i | \(0.393488\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.23545e6 | −1.66656 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.22166e6i | 1.64032i | 0.572137 | + | 0.820158i | \(0.306114\pi\) | ||||
−0.572137 | + | 0.820158i | \(0.693886\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 97587.0i | 0.130425i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 232647.i | − | 0.309499i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.24796e6i | − | 1.65258i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −585613. | −0.771923 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 111955.i | 0.146898i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −807051. | −1.05411 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 264511.i | − | 0.343910i | −0.985105 | − | 0.171955i | \(-0.944992\pi\) | ||
0.985105 | − | 0.171955i | \(-0.0550083\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.51642e6 | −1.96264 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −396673. | −0.511071 | −0.255535 | − | 0.966800i | \(-0.582252\pi\) | ||||
−0.255535 | + | 0.966800i | \(0.582252\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −380255. | −0.487701 | −0.243851 | − | 0.969813i | \(-0.578411\pi\) | ||||
−0.243851 | + | 0.969813i | \(0.578411\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 607235. | 0.775301 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.55369e6i | 1.97477i | 0.158334 | + | 0.987386i | \(0.449388\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 264087.i | 0.334151i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.21100e6 | 1.52542 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −380115. | + | 96778.9i | −0.476664 | + | 0.121361i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 361743.i | 0.451600i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.20938e6 | 1.50307 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −43618.8 | −0.0539702 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.39794e6i | 1.72203i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 725928.i | − | 0.890262i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 122575.i | 0.149659i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.19038e6i | − | 1.44701i | −0.690321 | − | 0.723503i | \(-0.742531\pi\) | ||
0.690321 | − | 0.723503i | \(-0.257469\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −38922.6 | −0.0471057 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 680660.i | − | 0.820150i | −0.912052 | − | 0.410075i | \(-0.865503\pi\) | ||
0.912052 | − | 0.410075i | \(-0.134497\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.65394e6 | −1.98416 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 574071.i | 0.685683i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.02142e6 | −1.21469 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 527917. | 0.625079 | 0.312539 | − | 0.949905i | \(-0.398820\pi\) | ||||
0.312539 | + | 0.949905i | \(0.398820\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.33194e6 | −1.57024 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.11696e6 | −1.31110 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 975939.i | 1.14062i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 885420.i | − | 1.03036i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28451.8 | −0.0329669 | −0.0164834 | − | 0.999864i | \(-0.505247\pi\) | ||||
−0.0164834 | + | 0.999864i | \(0.505247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.17629e6 | − | 299487.i | 1.35710 | − | 0.345524i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 852556.i | 0.979399i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 437985. | 0.500998 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.32816e6 | −1.51276 | −0.756380 | − | 0.654133i | \(-0.773034\pi\) | ||||
−0.756380 | + | 0.654133i | \(0.773034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.60561e6i | 1.82100i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 171072.i | − | 0.193196i | −0.995323 | − | 0.0965981i | \(-0.969204\pi\) | ||
0.995323 | − | 0.0965981i | \(-0.0307962\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 799286.i | 0.898832i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 247804.i | − | 0.277488i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 853096. | 0.951257 | 0.475628 | − | 0.879646i | \(-0.342221\pi\) | ||||
0.475628 | + | 0.879646i | \(0.342221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 443003.i | 0.491897i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −895174. | −0.989797 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 796329.i | 0.876812i | 0.898777 | + | 0.438406i | \(0.144457\pi\) | ||||
−0.898777 | + | 0.438406i | \(0.855543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 540148. | 0.592252 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −444686. | −0.485545 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −387386. | −0.421218 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 895545. | 0.969707 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 880330.i | − | 0.949277i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 300906.i | 0.323130i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −331903. | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −328129. | − | 1.28878e6i | −0.349459 | − | 1.37256i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 718821.i | 0.762399i | 0.924493 | + | 0.381200i | \(0.124489\pi\) | ||||
−0.924493 | + | 0.381200i | \(0.875511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.30172e6 | 1.37497 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.16764e6 | −1.22829 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 314771.i | 0.329765i | 0.986313 | + | 0.164883i | \(0.0527246\pi\) | ||||
−0.986313 | + | 0.164883i | \(0.947275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 124450.i | − | 0.129847i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 652338.i | − | 0.677851i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 641055.i | − | 0.663420i | −0.943381 | − | 0.331710i | \(-0.892374\pi\) | ||
0.943381 | − | 0.331710i | \(-0.107626\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 272015. | 0.280363 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 942845.i | − | 0.967845i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −469645. | −0.480150 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.36712e6i | 1.39207i | 0.718009 | + | 0.696034i | \(0.245054\pi\) | ||||
−0.718009 | + | 0.696034i | \(0.754946\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −352510. | −0.357497 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −282104. | −0.284946 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.66593e6 | −1.67597 | −0.837985 | − | 0.545694i | \(-0.816266\pi\) | ||||
−0.837985 | + | 0.545694i | \(0.816266\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −645198. | −0.646490 |
(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 | 304.5.e.f.113.4 | 20 | ||
4.3 | odd | 2 | 152.5.e.a.113.17 | yes | 20 | ||
12.11 | even | 2 | 1368.5.o.a.721.14 | 20 | |||
19.18 | odd | 2 | inner | 304.5.e.f.113.17 | 20 | ||
76.75 | even | 2 | 152.5.e.a.113.4 | ✓ | 20 | ||
228.227 | odd | 2 | 1368.5.o.a.721.13 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.5.e.a.113.4 | ✓ | 20 | 76.75 | even | 2 | ||
152.5.e.a.113.17 | yes | 20 | 4.3 | odd | 2 | ||
304.5.e.f.113.4 | 20 | 1.1 | even | 1 | trivial | ||
304.5.e.f.113.17 | 20 | 19.18 | odd | 2 | inner | ||
1368.5.o.a.721.13 | 20 | 228.227 | odd | 2 | |||
1368.5.o.a.721.14 | 20 | 12.11 | even | 2 |