Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2900,2,Mod(349,2900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2900.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2900.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: | \(23.1566165862\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5089536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 580) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.6 | ||
Root | \(1.66044 - 1.66044i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2900.349 |
Dual form | 2900.2.c.f.349.1 |
$q$-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 \(\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1277\) | \(1451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 3.32088i | 1.91731i | 0.284565 | + | 0.958657i | \(0.408151\pi\) | ||||
−0.284565 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.32088i | − 0.499247i | −0.968343 | − | 0.249624i | \(-0.919693\pi\) | ||||
0.968343 | − | 0.249624i | \(-0.0803069\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.02827 | −2.67609 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.32088 | 1.60431 | 0.802154 | − | 0.597118i | \(-0.203688\pi\) | ||||
0.802154 | + | 0.597118i | \(0.203688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.02827i | − 1.39459i | −0.716783 | − | 0.697296i | \(-0.754386\pi\) | ||||
0.716783 | − | 0.697296i | \(-0.245614\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.34916i | 1.53990i | 0.638106 | + | 0.769949i | \(0.279718\pi\) | ||||
−0.638106 | + | 0.769949i | \(0.720282\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.34916 | 0.997765 | 0.498883 | − | 0.866670i | \(-0.333744\pi\) | ||||
0.498883 | + | 0.866670i | \(0.333744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.38650 | 0.957214 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.70739i | − 0.356015i | −0.984029 | − | 0.178008i | \(-0.943035\pi\) | ||||
0.984029 | − | 0.178008i | \(-0.0569652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 16.6983i | − 3.21359i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.34916 | 1.49955 | 0.749777 | − | 0.661691i | \(-0.230161\pi\) | ||||
0.749777 | + | 0.661691i | \(0.230161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17.6700i | 3.07596i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.93438i | 1.14000i | 0.821643 | + | 0.570002i | \(0.193058\pi\) | ||||
−0.821643 | + | 0.570002i | \(0.806942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.6983 | 2.67387 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.02827 | −0.160589 | −0.0802947 | − | 0.996771i | \(-0.525586\pi\) | ||||
−0.0802947 | + | 0.996771i | \(0.525586\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7357i | 1.63717i | 0.574383 | + | 0.818587i | \(0.305242\pi\) | ||||
−0.574383 | + | 0.818587i | \(0.694758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.679116i | 0.0990592i | 0.998773 | + | 0.0495296i | \(0.0157722\pi\) | ||||
−0.998773 | + | 0.0495296i | \(0.984228\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.25526 | 0.750752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −21.0848 | −2.95247 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.38650i | 0.327812i | 0.986476 | + | 0.163906i | \(0.0524093\pi\) | ||||
−0.986476 | + | 0.163906i | \(0.947591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.4431i | 1.91303i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4431 | −1.35957 | −0.679785 | − | 0.733412i | \(-0.737927\pi\) | ||||
−0.679785 | + | 0.733412i | \(0.737927\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.38650 | −0.817708 | −0.408854 | − | 0.912600i | \(-0.634072\pi\) | ||||
−0.408854 | + | 0.912600i | \(0.634072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.6044i | 1.33603i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.70739i | 0.697269i | 0.937259 | + | 0.348634i | \(0.113354\pi\) | ||||
−0.937259 | + | 0.348634i | \(0.886646\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.67004 | 0.682593 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.61350 | −0.428843 | −0.214421 | − | 0.976741i | \(-0.568787\pi\) | ||||
−0.214421 | + | 0.976741i | \(0.568787\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 6.73566i | − 0.788350i | −0.919035 | − | 0.394175i | \(-0.871030\pi\) | ||||
0.919035 | − | 0.394175i | \(-0.128970\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.02827i | − 0.800946i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3774 | 1.28006 | 0.640031 | − | 0.768349i | \(-0.278922\pi\) | ||||
0.640031 | + | 0.768349i | \(0.278922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 31.3684 | 3.48537 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.96265i | − 0.434958i | −0.976065 | − | 0.217479i | \(-0.930217\pi\) | ||||
0.976065 | − | 0.217479i | \(-0.0697833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.32088i | 0.356036i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.58522 | −0.274033 | −0.137016 | − | 0.990569i | \(-0.543751\pi\) | ||||
−0.137016 | + | 0.990569i | \(0.543751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.64177 | −0.696247 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.7266i | 2.87511i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.3209i | 1.55560i | 0.628512 | + | 0.777800i | \(0.283664\pi\) | ||||
−0.628512 | + | 0.777800i | \(0.716336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −42.7175 | −4.29327 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8688 | 1.18099 | 0.590493 | − | 0.807043i | \(-0.298933\pi\) | ||||
0.590493 | + | 0.807043i | \(0.298933\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 3.65084i | − 0.359728i | −0.983691 | − | 0.179864i | \(-0.942434\pi\) | ||||
0.983691 | − | 0.179864i | \(-0.0575658\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.32088i | 0.514389i | 0.966360 | + | 0.257195i | \(0.0827982\pi\) | ||||
−0.966360 | + | 0.257195i | \(0.917202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.3118 | 1.37082 | 0.685411 | − | 0.728156i | \(-0.259622\pi\) | ||||
0.685411 | + | 0.728156i | \(0.259622\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.0283 | −2.18575 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.03735i | 0.191657i | 0.995398 | + | 0.0958287i | \(0.0305501\pi\) | ||||
−0.995398 | + | 0.0958287i | \(0.969450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 40.3684i | 3.73206i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.38650 | 0.768790 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.3118 | 1.57380 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 3.41478i | − 0.307900i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.26434i | 0.112192i | 0.998425 | + | 0.0560959i | \(0.0178652\pi\) | ||||
−0.998425 | + | 0.0560959i | \(0.982135\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −35.6519 | −3.13897 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.70739 | −0.149175 | −0.0745877 | − | 0.997214i | \(-0.523764\pi\) | ||||
−0.0745877 | + | 0.997214i | \(0.523764\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 5.74474i | − 0.498132i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 21.7639i | − 1.85942i | −0.368294 | − | 0.929709i | \(-0.620058\pi\) | ||||
0.368294 | − | 0.929709i | \(-0.379942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.6983 | 1.41633 | 0.708166 | − | 0.706046i | \(-0.249523\pi\) | ||||
0.708166 | + | 0.706046i | \(0.249523\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.25526 | −0.189928 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 26.7549i | − 2.23735i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.4521i | 1.43943i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.44305 | 0.524328 | 0.262164 | − | 0.965023i | \(-0.415564\pi\) | ||||
0.262164 | + | 0.965023i | \(0.415564\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 50.9728i | − 4.12091i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.7357i | − 0.856799i | −0.903589 | − | 0.428400i | \(-0.859078\pi\) | ||||
0.903589 | − | 0.428400i | \(-0.140922\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.92531 | −0.628518 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.25526 | −0.177740 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.90611i | 0.305950i | 0.988230 | + | 0.152975i | \(0.0488854\pi\) | ||||
−0.988230 | + | 0.152975i | \(0.951115\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.51960i | 0.427120i | 0.976930 | + | 0.213560i | \(0.0685058\pi\) | ||||
−0.976930 | + | 0.213560i | \(0.931494\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2835 | −0.944888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −34.9162 | −2.67011 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.80128i | 0.441063i | 0.975380 | + | 0.220532i | \(0.0707792\pi\) | ||||
−0.975380 | + | 0.220532i | \(0.929221\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 34.6802i | − 2.60672i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.0565 | −1.05064 | −0.525318 | − | 0.850906i | \(-0.676054\pi\) | ||||
−0.525318 | + | 0.850906i | \(0.676054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.08482 | −0.526611 | −0.263305 | − | 0.964713i | \(-0.584813\pi\) | ||||
−0.263305 | + | 0.964713i | \(0.584813\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 21.2088i | − 1.56780i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33.7831i | 2.47047i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.0565 | −1.60438 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.547875 | −0.0396428 | −0.0198214 | − | 0.999804i | \(-0.506310\pi\) | ||||
−0.0198214 | + | 0.999804i | \(0.506310\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.40571i | 0.317130i | 0.987349 | + | 0.158565i | \(0.0506867\pi\) | ||||
−0.987349 | + | 0.158565i | \(0.949313\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.64177i | 0.330712i | 0.986234 | + | 0.165356i | \(0.0528774\pi\) | ||||
−0.986234 | + | 0.165356i | \(0.947123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.4431 | −1.30739 | −0.653697 | − | 0.756757i | \(-0.726783\pi\) | ||||
−0.653697 | + | 0.756757i | \(0.726783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.9536 | −1.33688 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.32088i | − 0.0927079i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.7074i | 0.952729i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.1414 | 1.60072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.54787 | −0.313089 | −0.156544 | − | 0.987671i | \(-0.550035\pi\) | ||||
−0.156544 | + | 0.987671i | \(0.550035\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 12.0000i | − 0.822226i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 11.0283i | − 0.748648i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.3684 | 1.51151 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.9253 | 2.14753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.12217i | 0.0751459i | 0.999294 | + | 0.0375730i | \(0.0119627\pi\) | ||||
−0.999294 | + | 0.0375730i | \(0.988037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 9.63270i | − 0.639345i | −0.947528 | − | 0.319672i | \(-0.896427\pi\) | ||||
0.947528 | − | 0.319672i | \(-0.103573\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.3401 | 1.53566 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 8.05655i | − 0.527802i | −0.964550 | − | 0.263901i | \(-0.914991\pi\) | ||||
0.964550 | − | 0.263901i | \(-0.0850092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.7831i | 2.45428i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6135 | −1.00995 | −0.504977 | − | 0.863133i | \(-0.668499\pi\) | ||||
−0.504977 | + | 0.863133i | \(0.668499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.5105 | 1.19237 | 0.596184 | − | 0.802848i | \(-0.296683\pi\) | ||||
0.596184 | + | 0.802848i | \(0.296683\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 54.0757i | 3.46896i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 21.8688i | − 1.39148i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.1595 | 0.833950 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.67912 | −0.421582 | −0.210791 | − | 0.977531i | \(-0.567604\pi\) | ||||
−0.210791 | + | 0.977531i | \(0.567604\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.08482i | − 0.571158i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.4249i | 1.64834i | 0.566342 | + | 0.824170i | \(0.308358\pi\) | ||||
−0.566342 | + | 0.824170i | \(0.691642\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.15951 | 0.569145 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.02827 | −0.496938 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.4340i | 1.69165i | 0.533459 | + | 0.845826i | \(0.320892\pi\) | ||||
−0.533459 | + | 0.845826i | \(0.679108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 8.58522i | − 0.525407i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9717 | 0.668958 | 0.334479 | − | 0.942403i | \(-0.391440\pi\) | ||||
0.334479 | + | 0.942403i | \(0.391440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.1504 | 1.22405 | 0.612026 | − | 0.790838i | \(-0.290355\pi\) | ||||
0.612026 | + | 0.790838i | \(0.290355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 22.0565i | − 1.33492i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.15951i | − 0.189837i | −0.995485 | − | 0.0949184i | \(-0.969741\pi\) | ||||
0.995485 | − | 0.0949184i | \(-0.0302590\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −67.0293 | −4.01294 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3118 | −0.615151 | −0.307576 | − | 0.951524i | \(-0.599518\pi\) | ||||
−0.307576 | + | 0.951524i | \(0.599518\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.423851i | 0.0251953i | 0.999921 | + | 0.0125977i | \(0.00401007\pi\) | ||||
−0.999921 | + | 0.0125977i | \(0.995990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.35823i | 0.0801738i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23.3118 | −1.37128 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −50.8789 | −2.98257 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.2462i | 1.12437i | 0.827010 | + | 0.562187i | \(0.190040\pi\) | ||||
−0.827010 | + | 0.562187i | \(0.809960\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 88.8498i | − 5.15559i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.58522 | −0.496496 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.1806 | 0.817355 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 39.4148i | 2.26432i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 22.7357i | − 1.29759i | −0.760962 | − | 0.648796i | \(-0.775273\pi\) | ||||
0.760962 | − | 0.648796i | \(-0.224727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.1240 | 0.689712 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8031 | 0.839409 | 0.419704 | − | 0.907661i | \(-0.362134\pi\) | ||||
0.419704 | + | 0.907661i | \(0.362134\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 14.9717i | − 0.846252i | −0.906071 | − | 0.423126i | \(-0.860933\pi\) | ||||
0.906071 | − | 0.423126i | \(-0.139067\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 23.1222i | − 1.29867i | −0.760502 | − | 0.649335i | \(-0.775047\pi\) | ||||
0.760502 | − | 0.649335i | \(-0.224953\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.32088 | 0.297912 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.6700 | −0.986246 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.6135i | 1.53646i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 47.5279i | 2.62830i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.897033 | 0.0494550 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.82048 | −0.539783 | −0.269891 | − | 0.962891i | \(-0.586988\pi\) | ||||
−0.269891 | + | 0.962891i | \(0.586988\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 55.6711i | − 3.05076i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.09389i | 0.440903i | 0.975398 | + | 0.220451i | \(0.0707530\pi\) | ||||
−0.975398 | + | 0.220451i | \(0.929247\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.76579 | −0.367467 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 44.4249 | 2.40574 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 16.1878i | − 0.874058i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.37743i | 0.396041i | 0.980198 | + | 0.198021i | \(0.0634513\pi\) | ||||
−0.980198 | + | 0.198021i | \(0.936549\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.82956 | −0.472635 | −0.236318 | − | 0.971676i | \(-0.575941\pi\) | ||||
−0.236318 | + | 0.971676i | \(0.575941\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −83.9637 | −4.48165 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.7266i | 0.730593i | 0.930891 | + | 0.365296i | \(0.119032\pi\) | ||||
−0.930891 | + | 0.365296i | \(0.880968\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.8506i | 1.47401i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.70739 | 0.0901126 | 0.0450563 | − | 0.998984i | \(-0.485653\pi\) | ||||
0.0450563 | + | 0.998984i | \(0.485653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0848216 | −0.00446429 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 57.4905i | 3.01747i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.9627i | 1.35524i | 0.735412 | + | 0.677620i | \(0.236988\pi\) | ||||
−0.735412 | + | 0.677620i | \(0.763012\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.25526 | 0.429752 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.15230 | 0.163659 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.92531i | 0.513913i | 0.966423 | + | 0.256956i | \(0.0827197\pi\) | ||||
−0.966423 | + | 0.256956i | \(0.917280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 5.02827i | − 0.258969i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.2070 | −1.75710 | −0.878548 | − | 0.477655i | \(-0.841487\pi\) | ||||
−0.878548 | + | 0.477655i | \(0.841487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.19872 | −0.215107 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 21.4340i | − 1.09523i | −0.836732 | − | 0.547613i | \(-0.815537\pi\) | ||||
0.836732 | − | 0.547613i | \(-0.184463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 86.1888i | − 4.38123i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.3684 | 1.84395 | 0.921975 | − | 0.387251i | \(-0.126575\pi\) | ||||
0.921975 | + | 0.387251i | \(0.126575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8405 | 0.548227 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 5.67004i | − 0.286016i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.4713i | 1.37875i | 0.724406 | + | 0.689373i | \(0.242114\pi\) | ||||
−0.724406 | + | 0.689373i | \(0.757886\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.0776 | 0.955075 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.3118 | 1.11420 | 0.557099 | − | 0.830446i | \(-0.311914\pi\) | ||||
0.557099 | + | 0.830446i | \(0.311914\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 41.9819i | − 2.09127i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.8970i | 1.82892i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.95358 | −0.244939 | −0.122469 | − | 0.992472i | \(-0.539081\pi\) | ||||
−0.122469 | + | 0.992472i | \(0.539081\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 72.2755 | 3.56509 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.7941i | 0.678762i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 55.4532i | 2.71555i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.198716 | 0.00970793 | 0.00485397 | − | 0.999988i | \(-0.498455\pi\) | ||||
0.00485397 | + | 0.999988i | \(0.498455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4996 | 1.29151 | 0.645756 | − | 0.763544i | \(-0.276542\pi\) | ||||
0.645756 | + | 0.763544i | \(0.276542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 5.45213i | − 0.265091i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.43584i | 0.408239i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 88.8498 | 4.28971 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.2835 | −1.02519 | −0.512596 | − | 0.858630i | \(-0.671316\pi\) | ||||
−0.512596 | + | 0.858630i | \(0.671316\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 24.8031i | − 1.19196i | −0.802998 | − | 0.595981i | \(-0.796763\pi\) | ||||
0.802998 | − | 0.595981i | \(-0.203237\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.42571i | − 0.355220i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.3118 | 1.54216 | 0.771079 | − | 0.636739i | \(-0.219717\pi\) | ||||
0.771079 | + | 0.636739i | \(0.219717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.1907 | −2.00908 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3774i | 1.20572i | 0.797848 | + | 0.602859i | \(0.205972\pi\) | ||||
−0.797848 | + | 0.602859i | \(0.794028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 59.7759i | − 2.82730i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.7266 | −0.647798 | −0.323899 | − | 0.946092i | \(-0.604994\pi\) | ||||
−0.323899 | + | 0.946092i | \(0.604994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.47133 | −0.257635 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.3966i | 1.00530i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0101i | 0.702144i | 0.936348 | + | 0.351072i | \(0.114183\pi\) | ||||
−0.936348 | + | 0.351072i | \(0.885817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 106.020 | 4.94860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.7549 | 1.52555 | 0.762773 | − | 0.646666i | \(-0.223837\pi\) | ||||
0.762773 | + | 0.646666i | \(0.223837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 24.5369i | − 1.14033i | −0.821531 | − | 0.570164i | \(-0.806880\pi\) | ||||
0.821531 | − | 0.570164i | \(-0.193120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.60442i | 0.398165i | 0.979983 | + | 0.199083i | \(0.0637962\pi\) | ||||
−0.979983 | + | 0.199083i | \(0.936204\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.53880 | 0.348110 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 35.6519 | 1.64275 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 57.1232i | 2.62653i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 19.1595i | − 0.877254i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.26434 | −0.149151 | −0.0745757 | − | 0.997215i | \(-0.523760\pi\) | ||||
−0.0745757 | + | 0.997215i | \(0.523760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.8680 | 1.58984 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 7.48947i | − 0.340783i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 34.2070i | − 1.55007i | −0.631920 | − | 0.775033i | \(-0.717733\pi\) | ||||
0.631920 | − | 0.775033i | \(-0.282267\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.9717 | −0.586602 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.93438 | −0.403203 | −0.201601 | − | 0.979468i | \(-0.564615\pi\) | ||||
−0.201601 | + | 0.979468i | \(0.564615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.34916i | 0.285952i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.77301i | 0.214099i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.6236 | −1.28137 | −0.640685 | − | 0.767804i | \(-0.721349\pi\) | ||||
−0.640685 | + | 0.767804i | \(0.721349\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.3300 | −0.818922 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 0.0192012i | 0 0.000856140i | −1.00000 | 0.000428070i | \(-0.999864\pi\) | |||||
1.00000 | 0.000428070i | \(-0.000136259\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 40.7922i | − 1.81165i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.25526 | 0.365908 | 0.182954 | − | 0.983121i | \(-0.441434\pi\) | ||||
0.182954 | + | 0.983121i | \(0.441434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.89703 | −0.393582 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 72.6236i | − 3.20641i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.61350i | 0.158921i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.2654 | −0.845657 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.2553 | −0.887399 | −0.443700 | − | 0.896176i | \(-0.646334\pi\) | ||||
−0.443700 | + | 0.896176i | \(0.646334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.82048i | 0.0796042i | 0.999208 | + | 0.0398021i | \(0.0126728\pi\) | ||||
−0.999208 | + | 0.0398021i | \(0.987327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53.0101i | 2.30916i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.0848 | 0.873253 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 83.8397 | 3.63833 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.17044i | 0.223957i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 46.6802i | − 2.01440i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.9627 | 1.20444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.03920 | 0.0446788 | 0.0223394 | − | 0.999750i | \(-0.492889\pi\) | ||||
0.0223394 | + | 0.999750i | \(0.492889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 23.5279i | − 1.00968i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 37.7567i | − 1.61436i | −0.590305 | − | 0.807180i | \(-0.700992\pi\) | ||||
0.590305 | − | 0.807180i | \(-0.299008\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 51.2726 | 2.18826 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.34916 | 0.185280 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 15.0283i | − 0.639067i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 45.8506i | − 1.94275i | −0.237545 | − | 0.971376i | \(-0.576343\pi\) | ||||
0.237545 | − | 0.971376i | \(-0.423657\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 53.9819 | 2.28319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −112.190 | −4.73666 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.3027i | 1.40354i | 0.712402 | + | 0.701772i | \(0.247607\pi\) | ||||
−0.712402 | + | 0.701772i | \(0.752393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 41.4340i | − 1.74006i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.6700 | 0.992300 | 0.496150 | − | 0.868237i | \(-0.334747\pi\) | ||||
0.496150 | + | 0.868237i | \(0.334747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5671 | 0.609613 | 0.304807 | − | 0.952414i | \(-0.401408\pi\) | ||||
0.304807 | + | 0.952414i | \(0.401408\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.81943i | − 0.0760077i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.7639i | 0.573000i | 0.958080 | + | 0.286500i | \(0.0924919\pi\) | ||||
−0.958080 | + | 0.286500i | \(0.907508\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.6308 | −0.608037 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.23421 | −0.217152 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.6983i | 0.525911i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.04748i | 0.0432339i | 0.999766 | + | 0.0216170i | \(0.00688143\pi\) | ||||
−0.999766 | + | 0.0216170i | \(0.993119\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.3118 | 1.49620 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.4148 | −0.634079 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.3865i | 0.590783i | 0.955376 | + | 0.295391i | \(0.0954501\pi\) | ||||
−0.955376 | + | 0.295391i | \(0.904550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 61.2472i | − 2.50668i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.98080 | 0.244369 | 0.122184 | − | 0.992507i | \(-0.461010\pi\) | ||||
0.122184 | + | 0.992507i | \(0.461010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.08482 | −0.288996 | −0.144498 | − | 0.989505i | \(-0.546157\pi\) | ||||
−0.144498 | + | 0.989505i | \(0.546157\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 45.8205i | − 1.86595i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 32.7175i | − 1.32796i | −0.747749 | − | 0.663982i | \(-0.768865\pi\) | ||||
0.747749 | − | 0.663982i | \(-0.231135\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.38650 | 0.177750 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.41478 | 0.138147 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.22699i | 0.372675i | 0.982486 | + | 0.186337i | \(0.0596617\pi\) | ||||
−0.982486 | + | 0.186337i | \(0.940338\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 0.281683i | − 0.0113401i | −0.999984 | − | 0.00567006i | \(-0.998195\pi\) | ||||
0.999984 | − | 0.00567006i | \(-0.00180485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.2462 | −0.853957 | −0.426978 | − | 0.904262i | \(-0.640422\pi\) | ||||
−0.426978 | + | 0.904262i | \(0.640422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.5105 | −1.14409 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.41478i | 0.136810i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 76.8498i | 3.06909i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −44.0275 | −1.75549 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.8688 | 1.50753 | 0.753766 | − | 0.657143i | \(-0.228235\pi\) | ||||
0.753766 | + | 0.657143i | \(0.228235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 15.1030i | − 0.600289i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 26.4249i | − 1.04699i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.0101 | 1.14762 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.7658 | −1.45216 | −0.726081 | − | 0.687609i | \(-0.758660\pi\) | ||||
−0.726081 | + | 0.687609i | \(0.758660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 24.9728i | − 0.984830i | −0.870360 | − | 0.492415i | \(-0.836114\pi\) | ||||
0.870360 | − | 0.492415i | \(-0.163886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.56522i | 0.140163i | 0.997541 | + | 0.0700816i | \(0.0223260\pi\) | ||||
−0.997541 | + | 0.0700816i | \(0.977674\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −55.5663 | −2.18117 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.6236 | 1.43539 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 21.5652i | − 0.843912i | −0.906616 | − | 0.421956i | \(-0.861344\pi\) | ||||
0.906616 | − | 0.421956i | \(-0.138656\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 54.0757i | 2.10970i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.4623 | 1.57619 | 0.788093 | − | 0.615556i | \(-0.211069\pi\) | ||||
0.788093 | + | 0.615556i | \(0.211069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.1987 | 1.01901 | 0.509506 | − | 0.860467i | \(-0.329828\pi\) | ||||
0.509506 | + | 0.860467i | \(0.329828\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 106.020i | 4.11749i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.70739i | − 0.0661104i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.72659 | −0.144078 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.9819 | −1.31185 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.35823i | 0.129450i | 0.997903 | + | 0.0647251i | \(0.0206171\pi\) | ||||
−0.997903 | + | 0.0647251i | \(0.979383\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.6965i | 0.603264i | 0.953424 | + | 0.301632i | \(0.0975314\pi\) | ||||
−0.953424 | + | 0.301632i | \(0.902469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.2371 | 0.776629 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.9891 | 1.22582 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 40.1998i | − 1.53820i | −0.639128 | − | 0.769101i | \(-0.720704\pi\) | ||||
0.639128 | − | 0.769101i | \(-0.279296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 6.64177i | − 0.253399i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.7084 | 0.977995 | 0.488998 | − | 0.872285i | \(-0.337363\pi\) | ||||
0.488998 | + | 0.872285i | \(0.337363\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 56.4249i | 2.14340i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 6.52867i | − 0.247291i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.7549 | 1.01196 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.51775 | −0.321711 | −0.160855 | − | 0.986978i | \(-0.551425\pi\) | ||||
−0.160855 | + | 0.986978i | \(0.551425\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.1587i | 1.13746i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 15.6773i | − 0.589604i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.0848 | −1.31764 | −0.658819 | − | 0.752301i | \(-0.728944\pi\) | ||||
−0.658819 | + | 0.752301i | \(0.728944\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −91.3411 | −3.42556 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 14.2553i | − 0.533864i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 51.8506i | − 1.93640i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.3292 | −1.16838 | −0.584190 | − | 0.811617i | \(-0.698588\pi\) | ||||
−0.584190 | + | 0.811617i | \(0.698588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.82234 | −0.179593 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 61.4713i | 2.28614i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.9627i | 0.517846i | 0.965898 | + | 0.258923i | \(0.0833676\pi\) | ||||
−0.965898 | + | 0.258923i | \(0.916632\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −85.4742 | −3.16571 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −68.1624 | −2.52108 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 29.5761i | − 1.09242i | −0.837648 | − | 0.546210i | \(-0.816070\pi\) | ||||
0.837648 | − | 0.546210i | \(-0.183930\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.3684i | 1.11863i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.66819 | 0.245293 | 0.122647 | − | 0.992450i | \(-0.460862\pi\) | ||||
0.122647 | + | 0.992450i | \(0.460862\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 72.6236 | 2.66790 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 33.7002i | − 1.23634i | −0.786045 | − | 0.618170i | \(-0.787874\pi\) | ||||
0.786045 | − | 0.618170i | \(-0.212126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.8133i | 1.16399i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.02827 | 0.256808 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.3129 | −1.76296 | −0.881481 | − | 0.472220i | \(-0.843453\pi\) | ||||
−0.881481 | + | 0.472220i | \(0.843453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 22.1806i | − 0.808305i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 42.3985i | − 1.54100i | −0.637440 | − | 0.770500i | \(-0.720007\pi\) | ||||
0.637440 | − | 0.770500i | \(-0.279993\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 30.1696 | 1.09509 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.7933 | −1.62375 | −0.811877 | − | 0.583828i | \(-0.801554\pi\) | ||||
−0.811877 | + | 0.583828i | \(0.801554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 18.9043i | − 0.684380i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52.5105i | 1.89605i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.2080 | 1.88267 | 0.941335 | − | 0.337473i | \(-0.109572\pi\) | ||||
0.941335 | + | 0.337473i | \(0.109572\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −87.7541 | −3.16039 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 24.2179i | − 0.871058i | −0.900175 | − | 0.435529i | \(-0.856561\pi\) | ||||
0.900175 | − | 0.435529i | \(-0.143439\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.4177i | 1.09123i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.47213 | −0.160231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.2270 | −0.687996 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 16.6983i | − 0.596749i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.43398i | 0.0511159i | 0.999673 | + | 0.0255579i | \(0.00813623\pi\) | ||||
−0.999673 | + | 0.0255579i | \(0.991864\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −91.1051 | −3.24343 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.69110 | 0.0956845 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.1131i | 1.14037i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.4732i | 0.512666i | 0.966588 | + | 0.256333i | \(0.0825144\pi\) | ||||
−0.966588 | + | 0.256333i | \(0.917486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.31181 | −0.152541 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.7549 | 0.733337 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 35.8397i | − 1.26476i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 36.4358i | 1.28260i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.2654 | −1.73208 | −0.866039 | − | 0.499976i | \(-0.833342\pi\) | ||||
−0.866039 | + | 0.499976i | \(0.833342\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.69832 | −0.164980 | −0.0824901 | − | 0.996592i | \(-0.526287\pi\) | ||||
−0.0824901 | + | 0.996592i | \(0.526287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 66.9173i | 2.34689i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.6911i | 1.63351i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 53.3219 | 1.86322 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.7730 | 1.21359 | 0.606793 | − | 0.794860i | \(-0.292456\pi\) | ||||
0.606793 | + | 0.794860i | \(0.292456\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 44.1323i | − 1.53836i | −0.639035 | − | 0.769178i | \(-0.720666\pi\) | ||||
0.639035 | − | 0.769178i | \(-0.279334\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 22.6610i | − 0.787999i | −0.919111 | − | 0.394000i | \(-0.871091\pi\) | ||||
0.919111 | − | 0.394000i | \(-0.128909\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.9144 | 1.31682 | 0.658410 | − | 0.752659i | \(-0.271229\pi\) | ||||
0.658410 | + | 0.752659i | \(0.271229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.4924 | 0.363977 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.3665i | 1.15608i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 139.417i | − 4.81895i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.7175 | −1.06049 | −0.530243 | − | 0.847846i | \(-0.677899\pi\) | ||||
−0.530243 | + | 0.847846i | \(0.677899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 34.2443i | − 1.17944i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 22.8669i | − 0.785716i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.40756 | −0.0483074 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.8397 | 0.405859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.25341i | 0.0429159i | 0.999770 | + | 0.0214579i | \(0.00683080\pi\) | ||||
−0.999770 | + | 0.0214579i | \(0.993169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.85783i | 0.268418i | 0.990953 | + | 0.134209i | \(0.0428494\pi\) | ||||
−0.990953 | + | 0.134209i | \(0.957151\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4913 | 0.494438 | 0.247219 | − | 0.968960i | \(-0.420483\pi\) | ||||
0.247219 | + | 0.968960i | \(0.420483\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.51053 | −0.153718 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 9.69646i | − 0.330071i | −0.986288 | − | 0.165036i | \(-0.947226\pi\) | ||||
0.986288 | − | 0.165036i | \(-0.0527739\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 77.4158i | − 2.62918i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60.5380 | 2.05361 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.6983 | 0.972405 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 123.000i | − 4.16293i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 6.27341i | − 0.211838i | −0.994375 | − | 0.105919i | \(-0.966222\pi\) | ||||
0.994375 | − | 0.105919i | \(-0.0337784\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −63.9144 | −2.15578 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5953 | 0.660184 | 0.330092 | − | 0.943949i | \(-0.392920\pi\) | ||||
0.330092 | + | 0.943949i | \(0.392920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 5.24619i | − 0.176548i | −0.996096 | − | 0.0882742i | \(-0.971865\pi\) | ||||
0.996096 | − | 0.0882742i | \(-0.0281352\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.6044i | 1.09475i | 0.836888 | + | 0.547375i | \(0.184373\pi\) | ||||
−0.836888 | + | 0.547375i | \(0.815627\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.67004 | 0.0560114 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 166.907 | 5.59161 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.95358i | 0.0988378i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 28.5105i | − 0.951939i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.34916 | 0.278460 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.1523 | −0.504796 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 47.0920i | 1.56712i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.96265i | 0.0651688i | 0.999469 | + | 0.0325844i | \(0.0103738\pi\) | ||||
−0.999469 | + | 0.0325844i | \(0.989626\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −95.2856 | −3.16043 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.7066 | 1.67998 | 0.839992 | − | 0.542599i | \(-0.182560\pi\) | ||||
0.839992 | + | 0.542599i | \(0.182560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 21.0848i | − 0.697806i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.25526i | 0.0744754i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.2371 | −1.85509 | −0.927546 | − | 0.373710i | \(-0.878086\pi\) | ||||
−0.927546 | + | 0.373710i | \(0.878086\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 75.5025 | 2.48789 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.1696i | 0.598061i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.3100i | 0.962665i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.34009 | 0.175203 | 0.0876013 | − | 0.996156i | \(-0.472080\pi\) | ||||
0.0876013 | + | 0.996156i | \(0.472080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.8560 | 0.749074 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 49.1595i | 1.60941i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.01013i | 0.0983366i | 0.998791 | + | 0.0491683i | \(0.0156571\pi\) | ||||
−0.998791 | + | 0.0491683i | \(0.984343\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.7194 | 1.62253 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.829557 | −0.0270428 | −0.0135214 | − | 0.999909i | \(-0.504304\pi\) | ||||
−0.0135214 | + | 0.999909i | \(0.504304\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.75566i | 0.0571723i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 21.3027i | − 0.692246i | −0.938189 | − | 0.346123i | \(-0.887498\pi\) | ||||
0.938189 | − | 0.346123i | \(-0.112502\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.8688 | −1.09943 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 76.7860 | 2.48996 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 40.0203i | − 1.29638i | −0.761477 | − | 0.648192i | \(-0.775526\pi\) | ||||
0.761477 | − | 0.648192i | \(-0.224474\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.6700i | 0.571191i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.7476 | −0.928310 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.7084 | 1.24866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 42.7175i | − 1.37655i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.0365i | 0.998068i | 0.866582 | + | 0.499034i | \(0.166312\pi\) | ||||
−0.866582 | + | 0.499034i | \(0.833688\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −91.7012 | −2.94587 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.66819 | −0.0856262 | −0.0428131 | − | 0.999083i | \(-0.513632\pi\) | ||||
−0.0428131 | + | 0.999083i | \(0.513632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 22.0565i | − 0.707100i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 45.6519i | − 1.46053i | −0.683162 | − | 0.730267i | \(-0.739396\pi\) | ||||
0.683162 | − | 0.730267i | \(-0.260604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.7557 | −0.439633 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −114.899 | −3.66845 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 17.4521i | − 0.556636i | −0.960489 | − | 0.278318i | \(-0.910223\pi\) | ||||
0.960489 | − | 0.278318i | \(-0.0897770\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.97894i | 0.0948208i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.3300 | 0.582859 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.49960 | −0.142935 | −0.0714673 | − | 0.997443i | \(-0.522768\pi\) | ||||
−0.0714673 | + | 0.997443i | \(0.522768\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 32.6127i | − 1.03493i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.1896i | 0.671083i | 0.942025 | + | 0.335541i | \(0.108919\pi\) | ||||
−0.942025 | + | 0.335541i | \(0.891081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 115.792 | 3.66351 |
(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 | 2900.2.c.f.349.6 | 6 | ||
5.2 | odd | 4 | 580.2.a.c.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 2900.2.a.g.1.1 | 3 | |||
5.4 | even | 2 | inner | 2900.2.c.f.349.1 | 6 | ||
15.2 | even | 4 | 5220.2.a.x.1.3 | 3 | |||
20.7 | even | 4 | 2320.2.a.m.1.1 | 3 | |||
40.27 | even | 4 | 9280.2.a.bw.1.3 | 3 | |||
40.37 | odd | 4 | 9280.2.a.bk.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
580.2.a.c.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
2320.2.a.m.1.1 | 3 | 20.7 | even | 4 | |||
2900.2.a.g.1.1 | 3 | 5.3 | odd | 4 | |||
2900.2.c.f.349.1 | 6 | 5.4 | even | 2 | inner | ||
2900.2.c.f.349.6 | 6 | 1.1 | even | 1 | trivial | ||
5220.2.a.x.1.3 | 3 | 15.2 | even | 4 | |||
9280.2.a.bk.1.1 | 3 | 40.37 | odd | 4 | |||
9280.2.a.bw.1.3 | 3 | 40.27 | even | 4 |