Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2450,2,Mod(99,2450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2450.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2450.c (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: | \(19.5633484952\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 490) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2450.99 |
Dual form | 2450.2.c.w.99.2 |
$q$-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 \(\left(\mathbb{Z}/2450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 3.41421i | − 1.97120i | −0.169102 | − | 0.985599i | \(-0.554087\pi\) | ||||
0.169102 | − | 0.985599i | \(-0.445913\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.41421 | 1.39385 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −8.65685 | −2.88562 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.828427 | −0.249780 | −0.124890 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124890 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(12\) | 3.41421i | 0.985599i | ||||||||
\(13\) | 4.82843i | 1.33916i | 0.742738 | + | 0.669582i | \(0.233527\pi\) | ||||
−0.742738 | + | 0.669582i | \(0.766473\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.58579i | 0.627145i | 0.949564 | + | 0.313573i | \(0.101526\pi\) | ||||
−0.949564 | + | 0.313573i | \(0.898474\pi\) | |||||||
\(18\) | − 8.65685i | − 2.04044i | ||||||||
\(19\) | 0.585786 | 0.134389 | 0.0671943 | − | 0.997740i | \(-0.478595\pi\) | ||||
0.0671943 | + | 0.997740i | \(0.478595\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 0.828427i | − 0.176621i | ||||||||
\(23\) | − 1.17157i | − 0.244290i | −0.992512 | − | 0.122145i | \(-0.961023\pi\) | ||||
0.992512 | − | 0.122145i | \(-0.0389773\pi\) | |||||||
\(24\) | −3.41421 | −0.696923 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.82843 | −0.946932 | ||||||||
\(27\) | 19.3137i | 3.71692i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.82843 | 0.896616 | 0.448308 | − | 0.893879i | \(-0.352027\pi\) | ||||
0.448308 | + | 0.893879i | \(0.352027\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.82843 | 0.508001 | 0.254000 | − | 0.967204i | \(-0.418254\pi\) | ||||
0.254000 | + | 0.967204i | \(0.418254\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.82843i | 0.492366i | ||||||||
\(34\) | −2.58579 | −0.443459 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.65685 | 1.44281 | ||||||||
\(37\) | 7.65685i | 1.25878i | 0.777090 | + | 0.629390i | \(0.216695\pi\) | ||||
−0.777090 | + | 0.629390i | \(0.783305\pi\) | |||||||
\(38\) | 0.585786i | 0.0950271i | ||||||||
\(39\) | 16.4853 | 2.63976 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.07107 | 0.479620 | 0.239810 | − | 0.970820i | \(-0.422915\pi\) | ||||
0.239810 | + | 0.970820i | \(0.422915\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.82843i | − 1.34632i | −0.739496 | − | 0.673161i | \(-0.764936\pi\) | ||||
0.739496 | − | 0.673161i | \(-0.235064\pi\) | |||||||
\(44\) | 0.828427 | 0.124890 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.17157 | 0.172739 | ||||||||
\(47\) | 5.17157i | 0.754351i | 0.926142 | + | 0.377176i | \(0.123105\pi\) | ||||
−0.926142 | + | 0.377176i | \(0.876895\pi\) | |||||||
\(48\) | − 3.41421i | − 0.492799i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.82843 | 1.23623 | ||||||||
\(52\) | − 4.82843i | − 0.669582i | ||||||||
\(53\) | 6.48528i | 0.890822i | 0.895326 | + | 0.445411i | \(0.146942\pi\) | ||||
−0.895326 | + | 0.445411i | \(0.853058\pi\) | |||||||
\(54\) | −19.3137 | −2.62826 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 2.00000i | − 0.264906i | ||||||||
\(58\) | 4.82843i | 0.634004i | ||||||||
\(59\) | 8.58579 | 1.11777 | 0.558887 | − | 0.829244i | \(-0.311229\pi\) | ||||
0.558887 | + | 0.829244i | \(0.311229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.31371 | −1.19250 | −0.596249 | − | 0.802799i | \(-0.703343\pi\) | ||||
−0.596249 | + | 0.802799i | \(0.703343\pi\) | |||||||
\(62\) | 2.82843i | 0.359211i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.82843 | −0.348155 | ||||||||
\(67\) | − 1.65685i | − 0.202417i | −0.994865 | − | 0.101208i | \(-0.967729\pi\) | ||||
0.994865 | − | 0.101208i | \(-0.0322709\pi\) | |||||||
\(68\) | − 2.58579i | − 0.313573i | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.48528 | −0.532305 | −0.266152 | − | 0.963931i | \(-0.585752\pi\) | ||||
−0.266152 | + | 0.963931i | \(0.585752\pi\) | |||||||
\(72\) | 8.65685i | 1.02022i | ||||||||
\(73\) | 9.41421i | 1.10185i | 0.834555 | + | 0.550925i | \(0.185725\pi\) | ||||
−0.834555 | + | 0.550925i | \(0.814275\pi\) | |||||||
\(74\) | −7.65685 | −0.890091 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.585786 | −0.0671943 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 16.4853i | 1.86659i | ||||||||
\(79\) | 6.82843 | 0.768258 | 0.384129 | − | 0.923279i | \(-0.374502\pi\) | ||||
0.384129 | + | 0.923279i | \(0.374502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 39.9706 | 4.44117 | ||||||||
\(82\) | 3.07107i | 0.339143i | ||||||||
\(83\) | 2.24264i | 0.246162i | 0.992397 | + | 0.123081i | \(0.0392775\pi\) | ||||
−0.992397 | + | 0.123081i | \(0.960723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.82843 | 0.951994 | ||||||||
\(87\) | − 16.4853i | − 1.76741i | ||||||||
\(88\) | 0.828427i | 0.0883106i | ||||||||
\(89\) | 12.7279 | 1.34916 | 0.674579 | − | 0.738203i | \(-0.264325\pi\) | ||||
0.674579 | + | 0.738203i | \(0.264325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.17157i | 0.122145i | ||||||||
\(93\) | − 9.65685i | − 1.00137i | ||||||||
\(94\) | −5.17157 | −0.533407 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.41421 | 0.348462 | ||||||||
\(97\) | − 7.75736i | − 0.787641i | −0.919187 | − | 0.393820i | \(-0.871153\pi\) | ||||
0.919187 | − | 0.393820i | \(-0.128847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.17157 | 0.720770 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3137 | −1.32476 | −0.662382 | − | 0.749166i | \(-0.730454\pi\) | ||||
−0.662382 | + | 0.749166i | \(0.730454\pi\) | |||||||
\(102\) | 8.82843i | 0.874145i | ||||||||
\(103\) | 14.8284i | 1.46109i | 0.682865 | + | 0.730544i | \(0.260734\pi\) | ||||
−0.682865 | + | 0.730544i | \(0.739266\pi\) | |||||||
\(104\) | 4.82843 | 0.473466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.48528 | −0.629906 | ||||||||
\(107\) | − 9.65685i | − 0.933563i | −0.884373 | − | 0.466782i | \(-0.845413\pi\) | ||||
0.884373 | − | 0.466782i | \(-0.154587\pi\) | |||||||
\(108\) | − 19.3137i | − 1.85846i | ||||||||
\(109\) | −2.48528 | −0.238047 | −0.119023 | − | 0.992891i | \(-0.537976\pi\) | ||||
−0.119023 | + | 0.992891i | \(0.537976\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.1421 | 2.48130 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 15.3137i | − 1.44059i | −0.693667 | − | 0.720296i | \(-0.744006\pi\) | ||||
0.693667 | − | 0.720296i | \(-0.255994\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.82843 | −0.448308 | ||||||||
\(117\) | − 41.7990i | − 3.86432i | ||||||||
\(118\) | 8.58579i | 0.790386i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | − 9.31371i | − 0.843224i | ||||||||
\(123\) | − 10.4853i | − 0.945426i | ||||||||
\(124\) | −2.82843 | −0.254000 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.82843i | − 0.250982i | −0.992095 | − | 0.125491i | \(-0.959949\pi\) | ||||
0.992095 | − | 0.125491i | \(-0.0400507\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −30.1421 | −2.65387 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.24264 | 0.545422 | 0.272711 | − | 0.962096i | \(-0.412080\pi\) | ||||
0.272711 | + | 0.962096i | \(0.412080\pi\) | |||||||
\(132\) | − 2.82843i | − 0.246183i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.65685 | 0.143130 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.58579 | 0.221729 | ||||||||
\(137\) | 16.0000i | 1.36697i | 0.729964 | + | 0.683486i | \(0.239537\pi\) | ||||
−0.729964 | + | 0.683486i | \(0.760463\pi\) | |||||||
\(138\) | − 4.00000i | − 0.340503i | ||||||||
\(139\) | 19.8995 | 1.68785 | 0.843927 | − | 0.536459i | \(-0.180238\pi\) | ||||
0.843927 | + | 0.536459i | \(0.180238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.6569 | 1.48698 | ||||||||
\(142\) | − 4.48528i | − 0.376396i | ||||||||
\(143\) | − 4.00000i | − 0.334497i | ||||||||
\(144\) | −8.65685 | −0.721405 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.41421 | −0.779126 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 7.65685i | − 0.629390i | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.3137 | −0.920697 | −0.460348 | − | 0.887738i | \(-0.652275\pi\) | ||||
−0.460348 | + | 0.887738i | \(0.652275\pi\) | |||||||
\(152\) | − 0.585786i | − 0.0475136i | ||||||||
\(153\) | − 22.3848i | − 1.80970i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −16.4853 | −1.31988 | ||||||||
\(157\) | 6.48528i | 0.517582i | 0.965933 | + | 0.258791i | \(0.0833241\pi\) | ||||
−0.965933 | + | 0.258791i | \(0.916676\pi\) | |||||||
\(158\) | 6.82843i | 0.543240i | ||||||||
\(159\) | 22.1421 | 1.75599 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 39.9706i | 3.14038i | ||||||||
\(163\) | − 20.1421i | − 1.57765i | −0.614615 | − | 0.788827i | \(-0.710689\pi\) | ||||
0.614615 | − | 0.788827i | \(-0.289311\pi\) | |||||||
\(164\) | −3.07107 | −0.239810 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.24264 | −0.174063 | ||||||||
\(167\) | 15.7990i | 1.22256i | 0.791413 | + | 0.611281i | \(0.209346\pi\) | ||||
−0.791413 | + | 0.611281i | \(0.790654\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3137 | −0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.07107 | −0.387794 | ||||||||
\(172\) | 8.82843i | 0.673161i | ||||||||
\(173\) | 8.82843i | 0.671213i | 0.942002 | + | 0.335606i | \(0.108941\pi\) | ||||
−0.942002 | + | 0.335606i | \(0.891059\pi\) | |||||||
\(174\) | 16.4853 | 1.24975 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.828427 | −0.0624450 | ||||||||
\(177\) | − 29.3137i | − 2.20335i | ||||||||
\(178\) | 12.7279i | 0.953998i | ||||||||
\(179\) | −4.00000 | −0.298974 | −0.149487 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149487 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.48528 | 0.184730 | 0.0923648 | − | 0.995725i | \(-0.470557\pi\) | ||||
0.0923648 | + | 0.995725i | \(0.470557\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.7990i | 2.35065i | ||||||||
\(184\) | −1.17157 | −0.0863695 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.65685 | 0.708075 | ||||||||
\(187\) | − 2.14214i | − 0.156648i | ||||||||
\(188\) | − 5.17157i | − 0.377176i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1421 | 0.733859 | 0.366930 | − | 0.930249i | \(-0.380409\pi\) | ||||
0.366930 | + | 0.930249i | \(0.380409\pi\) | |||||||
\(192\) | 3.41421i | 0.246400i | ||||||||
\(193\) | 5.65685i | 0.407189i | 0.979055 | + | 0.203595i | \(0.0652625\pi\) | ||||
−0.979055 | + | 0.203595i | \(0.934738\pi\) | |||||||
\(194\) | 7.75736 | 0.556946 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.7990i | 1.83810i | 0.394139 | + | 0.919051i | \(0.371043\pi\) | ||||
−0.394139 | + | 0.919051i | \(0.628957\pi\) | |||||||
\(198\) | 7.17157i | 0.509661i | ||||||||
\(199\) | 16.4853 | 1.16861 | 0.584305 | − | 0.811534i | \(-0.301367\pi\) | ||||
0.584305 | + | 0.811534i | \(0.301367\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.65685 | −0.399004 | ||||||||
\(202\) | − 13.3137i | − 0.936749i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.82843 | −0.618114 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.8284 | −1.03315 | ||||||||
\(207\) | 10.1421i | 0.704927i | ||||||||
\(208\) | 4.82843i | 0.334791i | ||||||||
\(209\) | −0.485281 | −0.0335676 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.6274 | 1.28236 | 0.641182 | − | 0.767389i | \(-0.278444\pi\) | ||||
0.641182 | + | 0.767389i | \(0.278444\pi\) | |||||||
\(212\) | − 6.48528i | − 0.445411i | ||||||||
\(213\) | 15.3137i | 1.04928i | ||||||||
\(214\) | 9.65685 | 0.660129 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 19.3137 | 1.31413 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 2.48528i | − 0.168324i | ||||||||
\(219\) | 32.1421 | 2.17196 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.4853 | −0.839851 | ||||||||
\(222\) | 26.1421i | 1.75455i | ||||||||
\(223\) | 7.31371i | 0.489762i | 0.969553 | + | 0.244881i | \(0.0787489\pi\) | ||||
−0.969553 | + | 0.244881i | \(0.921251\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.3137 | 1.01865 | ||||||||
\(227\) | 18.2426i | 1.21081i | 0.795919 | + | 0.605403i | \(0.206988\pi\) | ||||
−0.795919 | + | 0.605403i | \(0.793012\pi\) | |||||||
\(228\) | 2.00000i | 0.132453i | ||||||||
\(229\) | −16.1421 | −1.06670 | −0.533351 | − | 0.845894i | \(-0.679068\pi\) | ||||
−0.533351 | + | 0.845894i | \(0.679068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 4.82843i | − 0.317002i | ||||||||
\(233\) | 23.3137i | 1.52733i | 0.645612 | + | 0.763666i | \(0.276603\pi\) | ||||
−0.645612 | + | 0.763666i | \(0.723397\pi\) | |||||||
\(234\) | 41.7990 | 2.73249 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.58579 | −0.558887 | ||||||||
\(237\) | − 23.3137i | − 1.51439i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.65685 | −0.107173 | −0.0535865 | − | 0.998563i | \(-0.517065\pi\) | ||||
−0.0535865 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4142 | 0.864085 | 0.432043 | − | 0.901853i | \(-0.357793\pi\) | ||||
0.432043 | + | 0.901853i | \(0.357793\pi\) | |||||||
\(242\) | − 10.3137i | − 0.662990i | ||||||||
\(243\) | − 78.5269i | − 5.03750i | ||||||||
\(244\) | 9.31371 | 0.596249 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.4853 | 0.668517 | ||||||||
\(247\) | 2.82843i | 0.179969i | ||||||||
\(248\) | − 2.82843i | − 0.179605i | ||||||||
\(249\) | 7.65685 | 0.485233 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.585786 | −0.0369745 | −0.0184873 | − | 0.999829i | \(-0.505885\pi\) | ||||
−0.0184873 | + | 0.999829i | \(0.505885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.970563i | 0.0610188i | ||||||||
\(254\) | 2.82843 | 0.177471 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 9.89949i | − 0.617514i | −0.951141 | − | 0.308757i | \(-0.900087\pi\) | ||||
0.951141 | − | 0.308757i | \(-0.0999129\pi\) | |||||||
\(258\) | − 30.1421i | − 1.87657i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −41.7990 | −2.58729 | ||||||||
\(262\) | 6.24264i | 0.385672i | ||||||||
\(263\) | 28.0000i | 1.72655i | 0.504730 | + | 0.863277i | \(0.331592\pi\) | ||||
−0.504730 | + | 0.863277i | \(0.668408\pi\) | |||||||
\(264\) | 2.82843 | 0.174078 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 43.4558i | − 2.65945i | ||||||||
\(268\) | 1.65685i | 0.101208i | ||||||||
\(269\) | 18.4853 | 1.12707 | 0.563534 | − | 0.826093i | \(-0.309441\pi\) | ||||
0.563534 | + | 0.826093i | \(0.309441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 2.58579i | 0.156786i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.0000 | −0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.00000 | 0.240772 | ||||||||
\(277\) | 8.14214i | 0.489214i | 0.969622 | + | 0.244607i | \(0.0786589\pi\) | ||||
−0.969622 | + | 0.244607i | \(0.921341\pi\) | |||||||
\(278\) | 19.8995i | 1.19349i | ||||||||
\(279\) | −24.4853 | −1.46590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.00000 | 0.477240 | 0.238620 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238620 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(282\) | 17.6569i | 1.05145i | ||||||||
\(283\) | 2.24264i | 0.133311i | 0.997776 | + | 0.0666556i | \(0.0212329\pi\) | ||||
−0.997776 | + | 0.0666556i | \(0.978767\pi\) | |||||||
\(284\) | 4.48528 | 0.266152 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − 8.65685i | − 0.510110i | ||||||||
\(289\) | 10.3137 | 0.606689 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −26.4853 | −1.55259 | ||||||||
\(292\) | − 9.41421i | − 0.550925i | ||||||||
\(293\) | 8.34315i | 0.487412i | 0.969849 | + | 0.243706i | \(0.0783632\pi\) | ||||
−0.969849 | + | 0.243706i | \(0.921637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.65685 | 0.445046 | ||||||||
\(297\) | − 16.0000i | − 0.928414i | ||||||||
\(298\) | 6.00000i | 0.347571i | ||||||||
\(299\) | 5.65685 | 0.327144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 11.3137i | − 0.651031i | ||||||||
\(303\) | 45.4558i | 2.61137i | ||||||||
\(304\) | 0.585786 | 0.0335972 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 22.3848 | 1.27965 | ||||||||
\(307\) | 14.9289i | 0.852039i | 0.904714 | + | 0.426020i | \(0.140085\pi\) | ||||
−0.904714 | + | 0.426020i | \(0.859915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 50.6274 | 2.88009 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.00000 | −0.226819 | −0.113410 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113410 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(312\) | − 16.4853i | − 0.933295i | ||||||||
\(313\) | − 14.3848i | − 0.813076i | −0.913634 | − | 0.406538i | \(-0.866736\pi\) | ||||
0.913634 | − | 0.406538i | \(-0.133264\pi\) | |||||||
\(314\) | −6.48528 | −0.365986 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.82843 | −0.384129 | ||||||||
\(317\) | − 10.4853i | − 0.588912i | −0.955665 | − | 0.294456i | \(-0.904862\pi\) | ||||
0.955665 | − | 0.294456i | \(-0.0951385\pi\) | |||||||
\(318\) | 22.1421i | 1.24167i | ||||||||
\(319\) | −4.00000 | −0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.9706 | −1.84024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.51472i | 0.0842812i | ||||||||
\(324\) | −39.9706 | −2.22059 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.1421 | 1.11557 | ||||||||
\(327\) | 8.48528i | 0.469237i | ||||||||
\(328\) | − 3.07107i | − 0.169571i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.7990 | 1.85776 | 0.928880 | − | 0.370380i | \(-0.120773\pi\) | ||||
0.928880 | + | 0.370380i | \(0.120773\pi\) | |||||||
\(332\) | − 2.24264i | − 0.123081i | ||||||||
\(333\) | − 66.2843i | − 3.63236i | ||||||||
\(334\) | −15.7990 | −0.864482 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 6.00000i | − 0.326841i | −0.986557 | − | 0.163420i | \(-0.947747\pi\) | ||||
0.986557 | − | 0.163420i | \(-0.0522527\pi\) | |||||||
\(338\) | − 10.3137i | − 0.560992i | ||||||||
\(339\) | −52.2843 | −2.83969 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.34315 | −0.126888 | ||||||||
\(342\) | − 5.07107i | − 0.274212i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.82843 | −0.475997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.82843 | −0.474619 | ||||||||
\(347\) | 3.17157i | 0.170259i | 0.996370 | + | 0.0851295i | \(0.0271304\pi\) | ||||
−0.996370 | + | 0.0851295i | \(0.972870\pi\) | |||||||
\(348\) | 16.4853i | 0.883704i | ||||||||
\(349\) | 2.48528 | 0.133034 | 0.0665170 | − | 0.997785i | \(-0.478811\pi\) | ||||
0.0665170 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −93.2548 | −4.97757 | ||||||||
\(352\) | − 0.828427i | − 0.0441553i | ||||||||
\(353\) | 2.38478i | 0.126929i | 0.997984 | + | 0.0634644i | \(0.0202149\pi\) | ||||
−0.997984 | + | 0.0634644i | \(0.979785\pi\) | |||||||
\(354\) | 29.3137 | 1.55801 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.7279 | −0.674579 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 4.00000i | − 0.211407i | ||||||||
\(359\) | −28.2843 | −1.49279 | −0.746393 | − | 0.665505i | \(-0.768216\pi\) | ||||
−0.746393 | + | 0.665505i | \(0.768216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6569 | −0.981940 | ||||||||
\(362\) | 2.48528i | 0.130623i | ||||||||
\(363\) | 35.2132i | 1.84821i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −31.7990 | −1.66216 | ||||||||
\(367\) | 24.9706i | 1.30345i | 0.758454 | + | 0.651726i | \(0.225955\pi\) | ||||
−0.758454 | + | 0.651726i | \(0.774045\pi\) | |||||||
\(368\) | − 1.17157i | − 0.0610725i | ||||||||
\(369\) | −26.5858 | −1.38400 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.65685i | 0.500685i | ||||||||
\(373\) | − 30.4853i | − 1.57847i | −0.614093 | − | 0.789234i | \(-0.710478\pi\) | ||||
0.614093 | − | 0.789234i | \(-0.289522\pi\) | |||||||
\(374\) | 2.14214 | 0.110767 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.17157 | 0.266704 | ||||||||
\(377\) | 23.3137i | 1.20072i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.4853 | −1.77139 | −0.885695 | − | 0.464268i | \(-0.846318\pi\) | ||||
−0.885695 | + | 0.464268i | \(0.846318\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.65685 | −0.494736 | ||||||||
\(382\) | 10.1421i | 0.518917i | ||||||||
\(383\) | 32.4853i | 1.65992i | 0.557823 | + | 0.829960i | \(0.311637\pi\) | ||||
−0.557823 | + | 0.829960i | \(0.688363\pi\) | |||||||
\(384\) | −3.41421 | −0.174231 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.65685 | −0.287926 | ||||||||
\(387\) | 76.4264i | 3.88497i | ||||||||
\(388\) | 7.75736i | 0.393820i | ||||||||
\(389\) | −28.1421 | −1.42686 | −0.713431 | − | 0.700725i | \(-0.752860\pi\) | ||||
−0.713431 | + | 0.700725i | \(0.752860\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.02944 | 0.153205 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 21.3137i | − 1.07513i | ||||||||
\(394\) | −25.7990 | −1.29973 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.17157 | −0.360385 | ||||||||
\(397\) | 33.7990i | 1.69632i | 0.529738 | + | 0.848161i | \(0.322290\pi\) | ||||
−0.529738 | + | 0.848161i | \(0.677710\pi\) | |||||||
\(398\) | 16.4853i | 0.826332i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | − 5.65685i | − 0.282138i | ||||||||
\(403\) | 13.6569i | 0.680296i | ||||||||
\(404\) | 13.3137 | 0.662382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6.34315i | − 0.314418i | ||||||||
\(408\) | − 8.82843i | − 0.437072i | ||||||||
\(409\) | −10.5858 | −0.523433 | −0.261717 | − | 0.965145i | \(-0.584289\pi\) | ||||
−0.261717 | + | 0.965145i | \(0.584289\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 54.6274 | 2.69457 | ||||||||
\(412\) | − 14.8284i | − 0.730544i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −10.1421 | −0.498459 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.82843 | −0.236733 | ||||||||
\(417\) | − 67.9411i | − 3.32709i | ||||||||
\(418\) | − 0.485281i | − 0.0237359i | ||||||||
\(419\) | −20.8701 | −1.01957 | −0.509785 | − | 0.860302i | \(-0.670275\pi\) | ||||
−0.509785 | + | 0.860302i | \(0.670275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.3137 | 0.843819 | 0.421909 | − | 0.906638i | \(-0.361360\pi\) | ||||
0.421909 | + | 0.906638i | \(0.361360\pi\) | |||||||
\(422\) | 18.6274i | 0.906768i | ||||||||
\(423\) | − 44.7696i | − 2.17677i | ||||||||
\(424\) | 6.48528 | 0.314953 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −15.3137 | −0.741952 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.65685i | 0.466782i | ||||||||
\(429\) | −13.6569 | −0.659359 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.3431 | −1.07623 | −0.538116 | − | 0.842871i | \(-0.680864\pi\) | ||||
−0.538116 | + | 0.842871i | \(0.680864\pi\) | |||||||
\(432\) | 19.3137i | 0.929231i | ||||||||
\(433\) | − 10.5858i | − 0.508720i | −0.967110 | − | 0.254360i | \(-0.918135\pi\) | ||||
0.967110 | − | 0.254360i | \(-0.0818649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.48528 | 0.119023 | ||||||||
\(437\) | − 0.686292i | − 0.0328298i | ||||||||
\(438\) | 32.1421i | 1.53581i | ||||||||
\(439\) | −24.9706 | −1.19178 | −0.595890 | − | 0.803066i | \(-0.703201\pi\) | ||||
−0.595890 | + | 0.803066i | \(0.703201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 12.4853i | − 0.593864i | ||||||||
\(443\) | 3.02944i | 0.143933i | 0.997407 | + | 0.0719665i | \(0.0229275\pi\) | ||||
−0.997407 | + | 0.0719665i | \(0.977073\pi\) | |||||||
\(444\) | −26.1421 | −1.24065 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.31371 | −0.346314 | ||||||||
\(447\) | − 20.4853i | − 0.968921i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.6274 | 0.784696 | 0.392348 | − | 0.919817i | \(-0.371663\pi\) | ||||
0.392348 | + | 0.919817i | \(0.371663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.54416 | −0.119800 | ||||||||
\(452\) | 15.3137i | 0.720296i | ||||||||
\(453\) | 38.6274i | 1.81487i | ||||||||
\(454\) | −18.2426 | −0.856170 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | − 21.6569i | − 1.01306i | −0.862221 | − | 0.506532i | \(-0.830927\pi\) | ||||
0.862221 | − | 0.506532i | \(-0.169073\pi\) | |||||||
\(458\) | − 16.1421i | − 0.754272i | ||||||||
\(459\) | −49.9411 | −2.33105 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.8284 | 0.597479 | 0.298740 | − | 0.954335i | \(-0.403434\pi\) | ||||
0.298740 | + | 0.954335i | \(0.403434\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 16.9706i | − 0.788689i | −0.918963 | − | 0.394344i | \(-0.870972\pi\) | ||||
0.918963 | − | 0.394344i | \(-0.129028\pi\) | |||||||
\(464\) | 4.82843 | 0.224154 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.3137 | −1.07999 | ||||||||
\(467\) | − 15.8995i | − 0.735741i | −0.929877 | − | 0.367870i | \(-0.880087\pi\) | ||||
0.929877 | − | 0.367870i | \(-0.119913\pi\) | |||||||
\(468\) | 41.7990i | 1.93216i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.1421 | 1.02026 | ||||||||
\(472\) | − 8.58579i | − 0.395193i | ||||||||
\(473\) | 7.31371i | 0.336285i | ||||||||
\(474\) | 23.3137 | 1.07083 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 56.1421i | − 2.57057i | ||||||||
\(478\) | − 1.65685i | − 0.0757827i | ||||||||
\(479\) | −17.1716 | −0.784589 | −0.392295 | − | 0.919840i | \(-0.628319\pi\) | ||||
−0.392295 | + | 0.919840i | \(0.628319\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.9706 | −1.68571 | ||||||||
\(482\) | 13.4142i | 0.611001i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.3137 | 0.468805 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 78.5269 | 3.56205 | ||||||||
\(487\) | − 31.7990i | − 1.44095i | −0.693481 | − | 0.720475i | \(-0.743924\pi\) | ||||
0.693481 | − | 0.720475i | \(-0.256076\pi\) | |||||||
\(488\) | 9.31371i | 0.421612i | ||||||||
\(489\) | −68.7696 | −3.10987 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.2843 | 1.45697 | 0.728484 | − | 0.685062i | \(-0.240225\pi\) | ||||
0.728484 | + | 0.685062i | \(0.240225\pi\) | |||||||
\(492\) | 10.4853i | 0.472713i | ||||||||
\(493\) | 12.4853i | 0.562309i | ||||||||
\(494\) | −2.82843 | −0.127257 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.82843 | 0.127000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.65685i | 0.343112i | ||||||||
\(499\) | −30.3431 | −1.35835 | −0.679173 | − | 0.733978i | \(-0.737661\pi\) | ||||
−0.679173 | + | 0.733978i | \(0.737661\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 53.9411 | 2.40991 | ||||||||
\(502\) | − 0.585786i | − 0.0261449i | ||||||||
\(503\) | − 17.6569i | − 0.787280i | −0.919265 | − | 0.393640i | \(-0.871216\pi\) | ||||
0.919265 | − | 0.393640i | \(-0.128784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.970563 | −0.0431468 | ||||||||
\(507\) | 35.2132i | 1.56387i | ||||||||
\(508\) | 2.82843i | 0.125491i | ||||||||
\(509\) | 5.79899 | 0.257036 | 0.128518 | − | 0.991707i | \(-0.458978\pi\) | ||||
0.128518 | + | 0.991707i | \(0.458978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 11.3137i | 0.499512i | ||||||||
\(514\) | 9.89949 | 0.436648 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 30.1421 | 1.32693 | ||||||||
\(517\) | − 4.28427i | − 0.188422i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.1421 | 1.32309 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.0711 | −0.835519 | −0.417759 | − | 0.908558i | \(-0.637184\pi\) | ||||
−0.417759 | + | 0.908558i | \(0.637184\pi\) | |||||||
\(522\) | − 41.7990i | − 1.82949i | ||||||||
\(523\) | − 23.8995i | − 1.04505i | −0.852623 | − | 0.522526i | \(-0.824990\pi\) | ||||
0.852623 | − | 0.522526i | \(-0.175010\pi\) | |||||||
\(524\) | −6.24264 | −0.272711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.0000 | −1.22086 | ||||||||
\(527\) | 7.31371i | 0.318590i | ||||||||
\(528\) | 2.82843i | 0.123091i | ||||||||
\(529\) | 21.6274 | 0.940322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −74.3259 | −3.22547 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.8284i | 0.642290i | ||||||||
\(534\) | 43.4558 | 1.88052 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.65685 | −0.0715652 | ||||||||
\(537\) | 13.6569i | 0.589337i | ||||||||
\(538\) | 18.4853i | 0.796957i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.9706 | −0.643635 | −0.321817 | − | 0.946802i | \(-0.604294\pi\) | ||||
−0.321817 | + | 0.946802i | \(0.604294\pi\) | |||||||
\(542\) | − 12.0000i | − 0.515444i | ||||||||
\(543\) | − 8.48528i | − 0.364138i | ||||||||
\(544\) | −2.58579 | −0.110865 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4853i | 0.448318i | 0.974553 | + | 0.224159i | \(0.0719635\pi\) | ||||
−0.974553 | + | 0.224159i | \(0.928036\pi\) | |||||||
\(548\) | − 16.0000i | − 0.683486i | ||||||||
\(549\) | 80.6274 | 3.44109 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.82843 | 0.120495 | ||||||||
\(552\) | 4.00000i | 0.170251i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.14214 | −0.345926 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.8995 | −0.843927 | ||||||||
\(557\) | − 15.1716i | − 0.642840i | −0.946937 | − | 0.321420i | \(-0.895840\pi\) | ||||
0.946937 | − | 0.321420i | \(-0.104160\pi\) | |||||||
\(558\) | − 24.4853i | − 1.03654i | ||||||||
\(559\) | 42.6274 | 1.80295 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.31371 | −0.308785 | ||||||||
\(562\) | 8.00000i | 0.337460i | ||||||||
\(563\) | 36.5858i | 1.54191i | 0.636891 | + | 0.770954i | \(0.280220\pi\) | ||||
−0.636891 | + | 0.770954i | \(0.719780\pi\) | |||||||
\(564\) | −17.6569 | −0.743488 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.24264 | −0.0942652 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.48528i | 0.188198i | ||||||||
\(569\) | 29.3137 | 1.22889 | 0.614447 | − | 0.788958i | \(-0.289379\pi\) | ||||
0.614447 | + | 0.788958i | \(0.289379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.20101 | −0.0921094 | −0.0460547 | − | 0.998939i | \(-0.514665\pi\) | ||||
−0.0460547 | + | 0.998939i | \(0.514665\pi\) | |||||||
\(572\) | 4.00000i | 0.167248i | ||||||||
\(573\) | − 34.6274i | − 1.44658i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.65685 | 0.360702 | ||||||||
\(577\) | 6.10051i | 0.253967i | 0.991905 | + | 0.126984i | \(0.0405296\pi\) | ||||
−0.991905 | + | 0.126984i | \(0.959470\pi\) | |||||||
\(578\) | 10.3137i | 0.428994i | ||||||||
\(579\) | 19.3137 | 0.802650 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − 26.4853i | − 1.09785i | ||||||||
\(583\) | − 5.37258i | − 0.222510i | ||||||||
\(584\) | 9.41421 | 0.389563 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.34315 | −0.344652 | ||||||||
\(587\) | 17.0711i | 0.704598i | 0.935887 | + | 0.352299i | \(0.114600\pi\) | ||||
−0.935887 | + | 0.352299i | \(0.885400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.65685 | 0.0682695 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 88.0833 | 3.62326 | ||||||||
\(592\) | 7.65685i | 0.314695i | ||||||||
\(593\) | − 3.27208i | − 0.134368i | −0.997741 | − | 0.0671841i | \(-0.978599\pi\) | ||||
0.997741 | − | 0.0671841i | \(-0.0214015\pi\) | |||||||
\(594\) | 16.0000 | 0.656488 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | − 56.2843i | − 2.30356i | ||||||||
\(598\) | 5.65685i | 0.231326i | ||||||||
\(599\) | 10.8284 | 0.442438 | 0.221219 | − | 0.975224i | \(-0.428997\pi\) | ||||
0.221219 | + | 0.975224i | \(0.428997\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.58579 | −0.268640 | −0.134320 | − | 0.990938i | \(-0.542885\pi\) | ||||
−0.134320 | + | 0.990938i | \(0.542885\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3431i | 0.584098i | ||||||||
\(604\) | 11.3137 | 0.460348 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −45.4558 | −1.84652 | ||||||||
\(607\) | 16.2843i | 0.660958i | 0.943813 | + | 0.330479i | \(0.107210\pi\) | ||||
−0.943813 | + | 0.330479i | \(0.892790\pi\) | |||||||
\(608\) | 0.585786i | 0.0237568i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.9706 | −1.01020 | ||||||||
\(612\) | 22.3848i | 0.904851i | ||||||||
\(613\) | − 12.3431i | − 0.498535i | −0.968435 | − | 0.249267i | \(-0.919810\pi\) | ||||
0.968435 | − | 0.249267i | \(-0.0801898\pi\) | |||||||
\(614\) | −14.9289 | −0.602483 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.3137i | 1.34116i | 0.741837 | + | 0.670580i | \(0.233955\pi\) | ||||
−0.741837 | + | 0.670580i | \(0.766045\pi\) | |||||||
\(618\) | 50.6274i | 2.03653i | ||||||||
\(619\) | 29.0711 | 1.16846 | 0.584232 | − | 0.811586i | \(-0.301396\pi\) | ||||
0.584232 | + | 0.811586i | \(0.301396\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.6274 | 0.908007 | ||||||||
\(622\) | − 4.00000i | − 0.160385i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 16.4853 | 0.659939 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.3848 | 0.574931 | ||||||||
\(627\) | 1.65685i | 0.0661684i | ||||||||
\(628\) | − 6.48528i | − 0.258791i | ||||||||
\(629\) | −19.7990 | −0.789437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4853 | −0.497031 | −0.248516 | − | 0.968628i | \(-0.579943\pi\) | ||||
−0.248516 | + | 0.968628i | \(0.579943\pi\) | |||||||
\(632\) | − 6.82843i | − 0.271620i | ||||||||
\(633\) | − 63.5980i | − 2.52779i | ||||||||
\(634\) | 10.4853 | 0.416424 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −22.1421 | −0.877993 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 4.00000i | − 0.158362i | ||||||||
\(639\) | 38.8284 | 1.53603 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.6274 | −0.972724 | −0.486362 | − | 0.873757i | \(-0.661676\pi\) | ||||
−0.486362 | + | 0.873757i | \(0.661676\pi\) | |||||||
\(642\) | − 32.9706i | − 1.30124i | ||||||||
\(643\) | − 4.78680i | − 0.188773i | −0.995536 | − | 0.0943864i | \(-0.969911\pi\) | ||||
0.995536 | − | 0.0943864i | \(-0.0300889\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.51472 | −0.0595958 | ||||||||
\(647\) | − 23.1127i | − 0.908654i | −0.890835 | − | 0.454327i | \(-0.849880\pi\) | ||||
0.890835 | − | 0.454327i | \(-0.150120\pi\) | |||||||
\(648\) | − 39.9706i | − 1.57019i | ||||||||
\(649\) | −7.11270 | −0.279198 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.1421i | 0.788827i | ||||||||
\(653\) | 4.34315i | 0.169960i | 0.996383 | + | 0.0849802i | \(0.0270827\pi\) | ||||
−0.996383 | + | 0.0849802i | \(0.972917\pi\) | |||||||
\(654\) | −8.48528 | −0.331801 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.07107 | 0.119905 | ||||||||
\(657\) | − 81.4975i | − 3.17952i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.1716 | 1.05845 | 0.529227 | − | 0.848480i | \(-0.322482\pi\) | ||||
0.529227 | + | 0.848480i | \(0.322482\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.2843 | 1.48909 | 0.744543 | − | 0.667575i | \(-0.232668\pi\) | ||||
0.744543 | + | 0.667575i | \(0.232668\pi\) | |||||||
\(662\) | 33.7990i | 1.31364i | ||||||||
\(663\) | 42.6274i | 1.65551i | ||||||||
\(664\) | 2.24264 | 0.0870313 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 66.2843 | 2.56846 | ||||||||
\(667\) | − 5.65685i | − 0.219034i | ||||||||
\(668\) | − 15.7990i | − 0.611281i | ||||||||
\(669\) | 24.9706 | 0.965418 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.71573 | 0.297862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 48.0000i | − 1.85026i | −0.379646 | − | 0.925132i | \(-0.623954\pi\) | ||||
0.379646 | − | 0.925132i | \(-0.376046\pi\) | |||||||
\(674\) | 6.00000 | 0.231111 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.3137 | 0.396681 | ||||||||
\(677\) | 39.4558i | 1.51641i | 0.652015 | + | 0.758206i | \(0.273924\pi\) | ||||
−0.652015 | + | 0.758206i | \(0.726076\pi\) | |||||||
\(678\) | − 52.2843i | − 2.00797i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 62.2843 | 2.38674 | ||||||||
\(682\) | − 2.34315i | − 0.0897237i | ||||||||
\(683\) | 33.6569i | 1.28784i | 0.765091 | + | 0.643922i | \(0.222694\pi\) | ||||
−0.765091 | + | 0.643922i | \(0.777306\pi\) | |||||||
\(684\) | 5.07107 | 0.193897 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 55.1127i | 2.10268i | ||||||||
\(688\) | − 8.82843i | − 0.336581i | ||||||||
\(689\) | −31.3137 | −1.19296 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.75736 | −0.0668531 | −0.0334265 | − | 0.999441i | \(-0.510642\pi\) | ||||
−0.0334265 | + | 0.999441i | \(0.510642\pi\) | |||||||
\(692\) | − 8.82843i | − 0.335606i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.17157 | −0.120391 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −16.4853 | −0.624873 | ||||||||
\(697\) | 7.94113i | 0.300792i | ||||||||
\(698\) | 2.48528i | 0.0940693i | ||||||||
\(699\) | 79.5980 | 3.01067 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.48528 | 0.0938678 | 0.0469339 | − | 0.998898i | \(-0.485055\pi\) | ||||
0.0469339 | + | 0.998898i | \(0.485055\pi\) | |||||||
\(702\) | − 93.2548i | − 3.51968i | ||||||||
\(703\) | 4.48528i | 0.169166i | ||||||||
\(704\) | 0.828427 | 0.0312225 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.38478 | −0.0897522 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 29.3137i | 1.10168i | ||||||||
\(709\) | −45.1127 | −1.69424 | −0.847121 | − | 0.531399i | \(-0.821666\pi\) | ||||
−0.847121 | + | 0.531399i | \(0.821666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −59.1127 | −2.21690 | ||||||||
\(712\) | − 12.7279i | − 0.476999i | ||||||||
\(713\) | − 3.31371i | − 0.124099i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | 5.65685i | 0.211259i | ||||||||
\(718\) | − 28.2843i | − 1.05556i | ||||||||
\(719\) | 41.4558 | 1.54604 | 0.773021 | − | 0.634380i | \(-0.218745\pi\) | ||||
0.773021 | + | 0.634380i | \(0.218745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 18.6569i | − 0.694336i | ||||||||
\(723\) | − 45.7990i | − 1.70328i | ||||||||
\(724\) | −2.48528 | −0.0923648 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −35.2132 | −1.30688 | ||||||||
\(727\) | − 3.51472i | − 0.130354i | −0.997874 | − | 0.0651768i | \(-0.979239\pi\) | ||||
0.997874 | − | 0.0651768i | \(-0.0207612\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −148.196 | −5.48874 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.8284 | 0.844340 | ||||||||
\(732\) | − 31.7990i | − 1.17532i | ||||||||
\(733\) | − 34.0000i | − 1.25582i | −0.778287 | − | 0.627909i | \(-0.783911\pi\) | ||||
0.778287 | − | 0.627909i | \(-0.216089\pi\) | |||||||
\(734\) | −24.9706 | −0.921680 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.17157 | 0.0431847 | ||||||||
\(737\) | 1.37258i | 0.0505597i | ||||||||
\(738\) | − 26.5858i | − 0.978636i | ||||||||
\(739\) | −3.17157 | −0.116668 | −0.0583341 | − | 0.998297i | \(-0.518579\pi\) | ||||
−0.0583341 | + | 0.998297i | \(0.518579\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.65685 | 0.354753 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 51.7990i | 1.90032i | 0.311762 | + | 0.950160i | \(0.399081\pi\) | ||||
−0.311762 | + | 0.950160i | \(0.600919\pi\) | |||||||
\(744\) | −9.65685 | −0.354037 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 30.4853 | 1.11615 | ||||||||
\(747\) | − 19.4142i | − 0.710329i | ||||||||
\(748\) | 2.14214i | 0.0783242i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.3137 | −1.43458 | −0.717289 | − | 0.696776i | \(-0.754617\pi\) | ||||
−0.717289 | + | 0.696776i | \(0.754617\pi\) | |||||||
\(752\) | 5.17157i | 0.188588i | ||||||||
\(753\) | 2.00000i | 0.0728841i | ||||||||
\(754\) | −23.3137 | −0.849035 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3.65685i | − 0.132911i | −0.997789 | − | 0.0664553i | \(-0.978831\pi\) | ||||
0.997789 | − | 0.0664553i | \(-0.0211690\pi\) | |||||||
\(758\) | − 34.4853i | − 1.25256i | ||||||||
\(759\) | 3.31371 | 0.120280 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.3848 | −0.811448 | −0.405724 | − | 0.913996i | \(-0.632980\pi\) | ||||
−0.405724 | + | 0.913996i | \(0.632980\pi\) | |||||||
\(762\) | − 9.65685i | − 0.349831i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.1421 | −0.366930 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.4853 | −1.17374 | ||||||||
\(767\) | 41.4558i | 1.49688i | ||||||||
\(768\) | − 3.41421i | − 0.123200i | ||||||||
\(769\) | 19.5563 | 0.705220 | 0.352610 | − | 0.935770i | \(-0.385294\pi\) | ||||
0.352610 | + | 0.935770i | \(0.385294\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.7990 | −1.21724 | ||||||||
\(772\) | − 5.65685i | − 0.203595i | ||||||||
\(773\) | 2.00000i | 0.0719350i | 0.999353 | + | 0.0359675i | \(0.0114513\pi\) | ||||
−0.999353 | + | 0.0359675i | \(0.988549\pi\) | |||||||
\(774\) | −76.4264 | −2.74709 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.75736 | −0.278473 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 28.1421i | − 1.00894i | ||||||||
\(779\) | 1.79899 | 0.0644555 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.71573 | 0.132959 | ||||||||
\(782\) | 3.02944i | 0.108332i | ||||||||
\(783\) | 93.2548i | 3.33266i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 21.3137 | 0.760235 | ||||||||
\(787\) | − 1.27208i | − 0.0453447i | −0.999743 | − | 0.0226723i | \(-0.992783\pi\) | ||||
0.999743 | − | 0.0226723i | \(-0.00721745\pi\) | |||||||
\(788\) | − 25.7990i | − 0.919051i | ||||||||
\(789\) | 95.5980 | 3.40338 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − 7.17157i | − 0.254831i | ||||||||
\(793\) | − 44.9706i | − 1.59695i | ||||||||
\(794\) | −33.7990 | −1.19948 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.4853 | −0.584305 | ||||||||
\(797\) | − 41.7990i | − 1.48060i | −0.672279 | − | 0.740298i | \(-0.734684\pi\) | ||||
0.672279 | − | 0.740298i | \(-0.265316\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.3726 | −0.473088 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −110.184 | −3.89315 | ||||||||
\(802\) | − 6.00000i | − 0.211867i | ||||||||
\(803\) | − 7.79899i | − 0.275220i | ||||||||
\(804\) | 5.65685 | 0.199502 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.6569 | −0.481042 | ||||||||
\(807\) | − 63.1127i | − 2.22167i | ||||||||
\(808\) | 13.3137i | 0.468375i | ||||||||
\(809\) | −3.02944 | −0.106509 | −0.0532547 | − | 0.998581i | \(-0.516960\pi\) | ||||
−0.0532547 | + | 0.998581i | \(0.516960\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.5858 | −1.14424 | −0.572121 | − | 0.820169i | \(-0.693879\pi\) | ||||
−0.572121 | + | 0.820169i | \(0.693879\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.9706i | 1.43690i | ||||||||
\(814\) | 6.34315 | 0.222327 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.82843 | 0.309057 | ||||||||
\(817\) | − 5.17157i | − 0.180930i | ||||||||
\(818\) | − 10.5858i | − 0.370123i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.3137 | 0.604253 | 0.302126 | − | 0.953268i | \(-0.402304\pi\) | ||||
0.302126 | + | 0.953268i | \(0.402304\pi\) | |||||||
\(822\) | 54.6274i | 1.90535i | ||||||||
\(823\) | 20.2843i | 0.707065i | 0.935422 | + | 0.353533i | \(0.115020\pi\) | ||||
−0.935422 | + | 0.353533i | \(0.884980\pi\) | |||||||
\(824\) | 14.8284 | 0.516573 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.37258i | 0.186823i | 0.995628 | + | 0.0934115i | \(0.0297772\pi\) | ||||
−0.995628 | + | 0.0934115i | \(0.970223\pi\) | |||||||
\(828\) | − 10.1421i | − 0.352464i | ||||||||
\(829\) | −5.02944 | −0.174680 | −0.0873398 | − | 0.996179i | \(-0.527837\pi\) | ||||
−0.0873398 | + | 0.996179i | \(0.527837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.7990 | 0.964336 | ||||||||
\(832\) | − 4.82843i | − 0.167396i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 67.9411 | 2.35261 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.485281 | 0.0167838 | ||||||||
\(837\) | 54.6274i | 1.88820i | ||||||||
\(838\) | − 20.8701i | − 0.720944i | ||||||||
\(839\) | −42.1421 | −1.45491 | −0.727454 | − | 0.686156i | \(-0.759297\pi\) | ||||
−0.727454 | + | 0.686156i | \(0.759297\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 17.3137i | 0.596670i | ||||||||
\(843\) | − 27.3137i | − 0.940734i | ||||||||
\(844\) | −18.6274 | −0.641182 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 44.7696 | 1.53921 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.48528i | 0.222705i | ||||||||
\(849\) | 7.65685 | 0.262783 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.97056 | 0.307507 | ||||||||
\(852\) | − 15.3137i | − 0.524639i | ||||||||
\(853\) | 43.1716i | 1.47817i | 0.673614 | + | 0.739083i | \(0.264741\pi\) | ||||
−0.673614 | + | 0.739083i | \(0.735259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.65685 | −0.330064 | ||||||||
\(857\) | − 4.92893i | − 0.168369i | −0.996450 | − | 0.0841846i | \(-0.973171\pi\) | ||||
0.996450 | − | 0.0841846i | \(-0.0268285\pi\) | |||||||
\(858\) | − 13.6569i | − 0.466237i | ||||||||
\(859\) | −7.21320 | −0.246111 | −0.123056 | − | 0.992400i | \(-0.539269\pi\) | ||||
−0.123056 | + | 0.992400i | \(0.539269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 22.3431i | − 0.761011i | ||||||||
\(863\) | − 4.97056i | − 0.169200i | −0.996415 | − | 0.0846000i | \(-0.973039\pi\) | ||||
0.996415 | − | 0.0846000i | \(-0.0269612\pi\) | |||||||
\(864\) | −19.3137 | −0.657066 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.5858 | 0.359720 | ||||||||
\(867\) | − 35.2132i | − 1.19590i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.65685 | −0.191896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | 0.271070 | ||||||||
\(872\) | 2.48528i | 0.0841622i | ||||||||
\(873\) | 67.1543i | 2.27283i | ||||||||
\(874\) | 0.686292 | 0.0232142 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32.1421 | −1.08598 | ||||||||
\(877\) | 30.2843i | 1.02263i | 0.859394 | + | 0.511314i | \(0.170841\pi\) | ||||
−0.859394 | + | 0.511314i | \(0.829159\pi\) | |||||||
\(878\) | − 24.9706i | − 0.842716i | ||||||||
\(879\) | 28.4853 | 0.960785 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.38478 | 0.0803452 | 0.0401726 | − | 0.999193i | \(-0.487209\pi\) | ||||
0.0401726 | + | 0.999193i | \(0.487209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 41.6569i | − 1.40186i | −0.713228 | − | 0.700932i | \(-0.752767\pi\) | ||||
0.713228 | − | 0.700932i | \(-0.247233\pi\) | |||||||
\(884\) | 12.4853 | 0.419925 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.02944 | −0.101776 | ||||||||
\(887\) | − 55.1127i | − 1.85050i | −0.379354 | − | 0.925252i | \(-0.623854\pi\) | ||||
0.379354 | − | 0.925252i | \(-0.376146\pi\) | |||||||
\(888\) | − 26.1421i | − 0.877273i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.1127 | −1.10932 | ||||||||
\(892\) | − 7.31371i | − 0.244881i | ||||||||
\(893\) | 3.02944i | 0.101376i | ||||||||
\(894\) | 20.4853 | 0.685130 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 19.3137i | − 0.644866i | ||||||||
\(898\) | 16.6274i | 0.554864i | ||||||||
\(899\) | 13.6569 | 0.455482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.7696 | −0.558675 | ||||||||
\(902\) | − 2.54416i | − 0.0847111i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.3137 | −0.509326 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −38.6274 | −1.28331 | ||||||||
\(907\) | − 0.284271i | − 0.00943907i | −0.999989 | − | 0.00471954i | \(-0.998498\pi\) | ||||
0.999989 | − | 0.00471954i | \(-0.00150228\pi\) | |||||||
\(908\) | − 18.2426i | − 0.605403i | ||||||||
\(909\) | 115.255 | 3.82276 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.2843 | 1.20215 | 0.601076 | − | 0.799192i | \(-0.294739\pi\) | ||||
0.601076 | + | 0.799192i | \(0.294739\pi\) | |||||||
\(912\) | − 2.00000i | − 0.0662266i | ||||||||
\(913\) | − 1.85786i | − 0.0614863i | ||||||||
\(914\) | 21.6569 | 0.716345 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.1421 | 0.533351 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − 49.9411i | − 1.64830i | ||||||||
\(919\) | −15.5147 | −0.511783 | −0.255892 | − | 0.966705i | \(-0.582369\pi\) | ||||
−0.255892 | + | 0.966705i | \(0.582369\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 50.9706 | 1.67954 | ||||||||
\(922\) | 12.8284i | 0.422482i | ||||||||
\(923\) | − 21.6569i | − 0.712844i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.9706 | 0.557687 | ||||||||
\(927\) | − 128.368i | − 4.21614i | ||||||||
\(928\) | 4.82843i | 0.158501i | ||||||||
\(929\) | −17.2132 | −0.564747 | −0.282373 | − | 0.959305i | \(-0.591122\pi\) | ||||
−0.282373 | + | 0.959305i | \(0.591122\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 23.3137i | − 0.763666i | ||||||||
\(933\) | 13.6569i | 0.447105i | ||||||||
\(934\) | 15.8995 | 0.520247 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −41.7990 | −1.36624 | ||||||||
\(937\) | 20.2426i | 0.661298i | 0.943754 | + | 0.330649i | \(0.107268\pi\) | ||||
−0.943754 | + | 0.330649i | \(0.892732\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −49.1127 | −1.60273 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.0000 | 1.62995 | 0.814977 | − | 0.579494i | \(-0.196750\pi\) | ||||
0.814977 | + | 0.579494i | \(0.196750\pi\) | |||||||
\(942\) | 22.1421i | 0.721430i | ||||||||
\(943\) | − 3.59798i | − 0.117166i | ||||||||
\(944\) | 8.58579 | 0.279444 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.31371 | −0.237789 | ||||||||
\(947\) | 4.82843i | 0.156903i | 0.996918 | + | 0.0784514i | \(0.0249975\pi\) | ||||
−0.996918 | + | 0.0784514i | \(0.975002\pi\) | |||||||
\(948\) | 23.3137i | 0.757194i | ||||||||
\(949\) | −45.4558 | −1.47556 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −35.7990 | −1.16086 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.343146i | 0.0111156i | 0.999985 | + | 0.00555779i | \(0.00176911\pi\) | ||||
−0.999985 | + | 0.00555779i | \(0.998231\pi\) | |||||||
\(954\) | 56.1421 | 1.81767 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.65685 | 0.0535865 | ||||||||
\(957\) | 13.6569i | 0.441463i | ||||||||
\(958\) | − 17.1716i | − 0.554788i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | − 36.9706i | − 1.19198i | ||||||||
\(963\) | 83.5980i | 2.69391i | ||||||||
\(964\) | −13.4142 | −0.432043 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.4558i | 1.20450i | 0.798308 | + | 0.602249i | \(0.205729\pi\) | ||||
−0.798308 | + | 0.602249i | \(0.794271\pi\) | |||||||
\(968\) | 10.3137i | 0.331495i | ||||||||
\(969\) | 5.17157 | 0.166135 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.3553 | 1.07042 | 0.535212 | − | 0.844718i | \(-0.320232\pi\) | ||||
0.535212 | + | 0.844718i | \(0.320232\pi\) | |||||||
\(972\) | 78.5269i | 2.51875i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31.7990 | 1.01891 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.31371 | −0.298125 | ||||||||
\(977\) | 12.6863i | 0.405870i | 0.979192 | + | 0.202935i | \(0.0650481\pi\) | ||||
−0.979192 | + | 0.202935i | \(0.934952\pi\) | |||||||
\(978\) | − 68.7696i | − 2.19901i | ||||||||
\(979\) | −10.5442 | −0.336993 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.5147 | 0.686912 | ||||||||
\(982\) | 32.2843i | 1.03023i | ||||||||
\(983\) | 12.2010i | 0.389152i | 0.980887 | + | 0.194576i | \(0.0623331\pi\) | ||||
−0.980887 | + | 0.194576i | \(0.937667\pi\) | |||||||
\(984\) | −10.4853 | −0.334259 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.4853 | −0.397612 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 2.82843i | − 0.0899843i | ||||||||
\(989\) | −10.3431 | −0.328893 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.7696 | 1.42215 | 0.711076 | − | 0.703115i | \(-0.248208\pi\) | ||||
0.711076 | + | 0.703115i | \(0.248208\pi\) | |||||||
\(992\) | 2.82843i | 0.0898027i | ||||||||
\(993\) | − 115.397i | − 3.66201i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.65685 | −0.242617 | ||||||||
\(997\) | − 18.2843i | − 0.579069i | −0.957168 | − | 0.289534i | \(-0.906500\pi\) | ||||
0.957168 | − | 0.289534i | \(-0.0935004\pi\) | |||||||
\(998\) | − 30.3431i | − 0.960495i | ||||||||
\(999\) | −147.882 | −4.67879 |
(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 | 2450.2.c.w.99.3 | 4 | ||
5.2 | odd | 4 | 490.2.a.l.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 2450.2.a.bs.1.2 | 2 | |||
5.4 | even | 2 | inner | 2450.2.c.w.99.2 | 4 | ||
7.6 | odd | 2 | 2450.2.c.t.99.4 | 4 | |||
15.2 | even | 4 | 4410.2.a.by.1.2 | 2 | |||
20.7 | even | 4 | 3920.2.a.ca.1.2 | 2 | |||
35.2 | odd | 12 | 490.2.e.j.361.2 | 4 | |||
35.12 | even | 12 | 490.2.e.i.361.1 | 4 | |||
35.13 | even | 4 | 2450.2.a.bn.1.1 | 2 | |||
35.17 | even | 12 | 490.2.e.i.471.1 | 4 | |||
35.27 | even | 4 | 490.2.a.m.1.2 | yes | 2 | ||
35.32 | odd | 12 | 490.2.e.j.471.2 | 4 | |||
35.34 | odd | 2 | 2450.2.c.t.99.1 | 4 | |||
105.62 | odd | 4 | 4410.2.a.bt.1.2 | 2 | |||
140.27 | odd | 4 | 3920.2.a.bm.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
490.2.a.l.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
490.2.a.m.1.2 | yes | 2 | 35.27 | even | 4 | ||
490.2.e.i.361.1 | 4 | 35.12 | even | 12 | |||
490.2.e.i.471.1 | 4 | 35.17 | even | 12 | |||
490.2.e.j.361.2 | 4 | 35.2 | odd | 12 | |||
490.2.e.j.471.2 | 4 | 35.32 | odd | 12 | |||
2450.2.a.bn.1.1 | 2 | 35.13 | even | 4 | |||
2450.2.a.bs.1.2 | 2 | 5.3 | odd | 4 | |||
2450.2.c.t.99.1 | 4 | 35.34 | odd | 2 | |||
2450.2.c.t.99.4 | 4 | 7.6 | odd | 2 | |||
2450.2.c.w.99.2 | 4 | 5.4 | even | 2 | inner | ||
2450.2.c.w.99.3 | 4 | 1.1 | even | 1 | trivial | ||
3920.2.a.bm.1.1 | 2 | 140.27 | odd | 4 | |||
3920.2.a.ca.1.2 | 2 | 20.7 | even | 4 | |||
4410.2.a.bt.1.2 | 2 | 105.62 | odd | 4 | |||
4410.2.a.by.1.2 | 2 | 15.2 | even | 4 |