Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(829,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, 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("2070.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} + 10x^{12} + 55x^{10} + 58x^{8} + 495x^{6} + 810x^{4} + 729x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.3 | ||
Root | \(1.13883 + 1.30502i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.829 |
Dual form | 2070.2.d.h.829.11 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.43942 | + | 1.71116i | −0.643726 | + | 0.765256i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.24894i | − | 0.472055i | −0.971746 | − | 0.236028i | \(-0.924154\pi\) | ||
0.971746 | − | 0.236028i | \(-0.0758456\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.71116 | + | 1.43942i | 0.541118 | + | 0.455183i | ||||
\(11\) | −2.41817 | −0.729104 | −0.364552 | − | 0.931183i | \(-0.618778\pi\) | ||||
−0.364552 | + | 0.931183i | \(0.618778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.80425i | 1.60981i | 0.593404 | + | 0.804905i | \(0.297784\pi\) | ||||
−0.593404 | + | 0.804905i | \(0.702216\pi\) | |||||||
\(14\) | −1.24894 | −0.333794 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 5.22007i | − | 1.26605i | −0.774130 | − | 0.633027i | \(-0.781812\pi\) | ||
0.774130 | − | 0.633027i | \(-0.218188\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.42233 | 0.326304 | 0.163152 | − | 0.986601i | \(-0.447834\pi\) | ||||
0.163152 | + | 0.986601i | \(0.447834\pi\) | |||||||
\(20\) | 1.43942 | − | 1.71116i | 0.321863 | − | 0.382628i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.41817i | 0.515555i | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.856164 | − | 4.92615i | −0.171233 | − | 0.985231i | ||||
\(26\) | 5.80425 | 1.13831 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.24894i | 0.236028i | ||||||||
\(29\) | 0.788275 | 0.146379 | 0.0731895 | − | 0.997318i | \(-0.476682\pi\) | ||||
0.0731895 | + | 0.997318i | \(0.476682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.287672 | 0.0516675 | 0.0258337 | − | 0.999666i | \(-0.491776\pi\) | ||||
0.0258337 | + | 0.999666i | \(0.491776\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.22007 | −0.895235 | ||||||||
\(35\) | 2.13714 | + | 1.79775i | 0.361243 | + | 0.303874i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.12777i | − | 0.678602i | −0.940678 | − | 0.339301i | \(-0.889810\pi\) | ||
0.940678 | − | 0.339301i | \(-0.110190\pi\) | |||||||
\(38\) | − | 1.42233i | − | 0.230732i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.71116 | − | 1.43942i | −0.270559 | − | 0.227592i | ||||
\(41\) | −5.01597 | −0.783364 | −0.391682 | − | 0.920101i | \(-0.628107\pi\) | ||||
−0.391682 | + | 0.920101i | \(0.628107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.09056i | − | 0.318807i | −0.987214 | − | 0.159403i | \(-0.949043\pi\) | ||
0.987214 | − | 0.159403i | \(-0.0509571\pi\) | |||||||
\(44\) | 2.41817 | 0.364552 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | − | 10.5570i | − | 1.53989i | −0.638108 | − | 0.769947i | \(-0.720283\pi\) | ||
0.638108 | − | 0.769947i | \(-0.279717\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.44015 | 0.777164 | ||||||||
\(50\) | −4.92615 | + | 0.856164i | −0.696663 | + | 0.121080i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 5.80425i | − | 0.804905i | ||||||
\(53\) | − | 3.42233i | − | 0.470093i | −0.971984 | − | 0.235046i | \(-0.924476\pi\) | ||
0.971984 | − | 0.235046i | \(-0.0755242\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.48075 | − | 4.13788i | 0.469344 | − | 0.557951i | ||||
\(56\) | 1.24894 | 0.166897 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 0.788275i | − | 0.103506i | ||||||
\(59\) | −5.01597 | −0.653024 | −0.326512 | − | 0.945193i | \(-0.605873\pi\) | ||||
−0.326512 | + | 0.945193i | \(0.605873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.0671 | 1.80110 | 0.900551 | − | 0.434750i | \(-0.143163\pi\) | ||||
0.900551 | + | 0.434750i | \(0.143163\pi\) | |||||||
\(62\) | − | 0.287672i | − | 0.0365344i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −9.93202 | − | 8.35473i | −1.23192 | − | 1.03628i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.42477i | − | 1.15142i | −0.817654 | − | 0.575709i | \(-0.804726\pi\) | ||
0.817654 | − | 0.575709i | \(-0.195274\pi\) | |||||||
\(68\) | 5.22007i | 0.633027i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.79775 | − | 2.13714i | 0.214872 | − | 0.255437i | ||||
\(71\) | −11.5619 | −1.37215 | −0.686073 | − | 0.727532i | \(-0.740667\pi\) | ||||
−0.686073 | + | 0.727532i | \(0.740667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.741689i | − | 0.0868081i | −0.999058 | − | 0.0434041i | \(-0.986180\pi\) | ||
0.999058 | − | 0.0434041i | \(-0.0138203\pi\) | |||||||
\(74\) | −4.12777 | −0.479844 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.42233 | −0.163152 | ||||||||
\(77\) | 3.02015i | 0.344178i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.375418 | −0.0422378 | −0.0211189 | − | 0.999777i | \(-0.506723\pi\) | ||||
−0.0211189 | + | 0.999777i | \(0.506723\pi\) | |||||||
\(80\) | −1.43942 | + | 1.71116i | −0.160932 | + | 0.191314i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.01597i | 0.553922i | ||||||||
\(83\) | − | 5.04691i | − | 0.553970i | −0.960874 | − | 0.276985i | \(-0.910665\pi\) | ||
0.960874 | − | 0.276985i | \(-0.0893353\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.93240 | + | 7.51386i | 0.968855 | + | 0.814992i | ||||
\(86\) | −2.09056 | −0.225431 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.41817i | − | 0.257777i | ||||||
\(89\) | 3.81362 | 0.404243 | 0.202121 | − | 0.979360i | \(-0.435216\pi\) | ||||
0.202121 | + | 0.979360i | \(0.435216\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.24916 | 0.759919 | ||||||||
\(92\) | − | 1.00000i | − | 0.104257i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.5570 | −1.08887 | ||||||||
\(95\) | −2.04732 | + | 2.43384i | −0.210051 | + | 0.249706i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.788275i | − | 0.0800372i | −0.999199 | − | 0.0400186i | \(-0.987258\pi\) | ||
0.999199 | − | 0.0400186i | \(-0.0127417\pi\) | |||||||
\(98\) | − | 5.44015i | − | 0.549538i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.856164 | + | 4.92615i | 0.0856164 | + | 0.492615i | ||||
\(101\) | −12.3036 | −1.22425 | −0.612127 | − | 0.790759i | \(-0.709686\pi\) | ||||
−0.612127 | + | 0.790759i | \(0.709686\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.52323i | − | 0.544220i | −0.962266 | − | 0.272110i | \(-0.912279\pi\) | ||
0.962266 | − | 0.272110i | \(-0.0877214\pi\) | |||||||
\(104\) | −5.80425 | −0.569153 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.42233 | −0.332406 | ||||||||
\(107\) | − | 12.4716i | − | 1.20567i | −0.797865 | − | 0.602836i | \(-0.794037\pi\) | ||
0.797865 | − | 0.602836i | \(-0.205963\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.79775 | −0.746889 | −0.373444 | − | 0.927653i | \(-0.621823\pi\) | ||||
−0.373444 | + | 0.927653i | \(0.621823\pi\) | |||||||
\(110\) | −4.13788 | − | 3.48075i | −0.394531 | − | 0.331876i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.24894i | − | 0.118014i | ||||||
\(113\) | − | 1.62458i | − | 0.152828i | −0.997076 | − | 0.0764139i | \(-0.975653\pi\) | ||
0.997076 | − | 0.0764139i | \(-0.0243470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.71116 | − | 1.43942i | −0.159567 | − | 0.134226i | ||||
\(116\) | −0.788275 | −0.0731895 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.01597i | 0.461758i | ||||||||
\(119\) | −6.51956 | −0.597647 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.15247 | −0.468407 | ||||||||
\(122\) | − | 14.0671i | − | 1.27357i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.287672 | −0.0258337 | ||||||||
\(125\) | 9.66183 | + | 5.62575i | 0.864180 | + | 0.503182i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 20.6725i | − | 1.83439i | −0.398438 | − | 0.917195i | \(-0.630448\pi\) | ||
0.398438 | − | 0.917195i | \(-0.369552\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.35473 | + | 9.93202i | −0.732758 | + | 0.871096i | ||||
\(131\) | 7.35442 | 0.642559 | 0.321280 | − | 0.946984i | \(-0.395887\pi\) | ||||
0.321280 | + | 0.946984i | \(0.395887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.77640i | − | 0.154034i | ||||||
\(134\) | −9.42477 | −0.814176 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.22007 | 0.447618 | ||||||||
\(137\) | − | 9.22007i | − | 0.787724i | −0.919170 | − | 0.393862i | \(-0.871139\pi\) | ||
0.919170 | − | 0.393862i | \(-0.128861\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | −2.13714 | − | 1.79775i | −0.180622 | − | 0.151937i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.5619i | 0.970254i | ||||||||
\(143\) | − | 14.0356i | − | 1.17372i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.13466 | + | 1.34887i | −0.0942280 | + | 0.112017i | ||||
\(146\) | −0.741689 | −0.0613826 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.12777i | 0.339301i | ||||||||
\(149\) | 15.4087 | 1.26233 | 0.631163 | − | 0.775650i | \(-0.282578\pi\) | ||||
0.631163 | + | 0.775650i | \(0.282578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1525 | 1.15171 | 0.575856 | − | 0.817551i | \(-0.304669\pi\) | ||||
0.575856 | + | 0.817551i | \(0.304669\pi\) | |||||||
\(152\) | 1.42233i | 0.115366i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.02015 | 0.243370 | ||||||||
\(155\) | −0.414080 | + | 0.492254i | −0.0332597 | + | 0.0395388i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0747i | 1.44252i | 0.692665 | + | 0.721260i | \(0.256437\pi\) | ||||
−0.692665 | + | 0.721260i | \(0.743563\pi\) | |||||||
\(158\) | 0.375418i | 0.0298666i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.71116 | + | 1.43942i | 0.135279 | + | 0.113796i | ||||
\(161\) | 1.24894 | 0.0984303 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.8640i | − | 1.55587i | −0.628344 | − | 0.777936i | \(-0.716267\pi\) | ||
0.628344 | − | 0.777936i | \(-0.283733\pi\) | |||||||
\(164\) | 5.01597 | 0.391682 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.04691 | −0.391716 | ||||||||
\(167\) | 2.55698i | 0.197865i | 0.995094 | + | 0.0989327i | \(0.0315428\pi\) | ||||
−0.995094 | + | 0.0989327i | \(0.968457\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.6893 | −1.59149 | ||||||||
\(170\) | 7.51386 | − | 8.93240i | 0.576286 | − | 0.685084i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.09056i | 0.159403i | ||||||||
\(173\) | − | 11.2848i | − | 0.857968i | −0.903312 | − | 0.428984i | \(-0.858872\pi\) | ||
0.903312 | − | 0.428984i | \(-0.141128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.15247 | + | 1.06930i | −0.465083 | + | 0.0808313i | ||||
\(176\) | −2.41817 | −0.182276 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 3.81362i | − | 0.285843i | ||||||
\(179\) | −11.4289 | −0.854233 | −0.427116 | − | 0.904197i | \(-0.640471\pi\) | ||||
−0.427116 | + | 0.904197i | \(0.640471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.21775 | 0.536491 | 0.268245 | − | 0.963351i | \(-0.413556\pi\) | ||||
0.268245 | + | 0.963351i | \(0.413556\pi\) | |||||||
\(182\) | − | 7.24916i | − | 0.537344i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 7.06330 | + | 5.94158i | 0.519304 | + | 0.436834i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.6230i | 0.923085i | ||||||||
\(188\) | 10.5570i | 0.769947i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.43384 | + | 2.04732i | 0.176569 | + | 0.148528i | ||||
\(191\) | −8.25555 | −0.597350 | −0.298675 | − | 0.954355i | \(-0.596545\pi\) | ||||
−0.298675 | + | 0.954355i | \(0.596545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 2.49788i | − | 0.179801i | −0.995951 | − | 0.0899007i | \(-0.971345\pi\) | ||
0.995951 | − | 0.0899007i | \(-0.0286550\pi\) | |||||||
\(194\) | −0.788275 | −0.0565948 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.44015 | −0.388582 | ||||||||
\(197\) | 15.1140i | 1.07683i | 0.842681 | + | 0.538413i | \(0.180976\pi\) | ||||
−0.842681 | + | 0.538413i | \(0.819024\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.37542 | −0.310165 | −0.155083 | − | 0.987902i | \(-0.549564\pi\) | ||||
−0.155083 | + | 0.987902i | \(0.549564\pi\) | |||||||
\(200\) | 4.92615 | − | 0.856164i | 0.348332 | − | 0.0605399i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.3036i | 0.865678i | ||||||||
\(203\) | − | 0.984509i | − | 0.0690990i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.22007 | − | 8.58315i | 0.504272 | − | 0.599474i | ||||
\(206\) | −5.52323 | −0.384821 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.80425i | 0.402452i | ||||||||
\(209\) | −3.43942 | −0.237910 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0356 | 1.24162 | 0.620812 | − | 0.783959i | \(-0.286803\pi\) | ||||
0.620812 | + | 0.783959i | \(0.286803\pi\) | |||||||
\(212\) | 3.42233i | 0.235046i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.4716 | −0.852539 | ||||||||
\(215\) | 3.57729 | + | 3.00918i | 0.243969 | + | 0.205224i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.359286i | − | 0.0243899i | ||||||
\(218\) | 7.79775i | 0.528130i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.48075 | + | 4.13788i | −0.234672 | + | 0.278976i | ||||
\(221\) | 30.2986 | 2.03810 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.7416i | 0.786273i | 0.919480 | + | 0.393136i | \(0.128610\pi\) | ||||
−0.919480 | + | 0.393136i | \(0.871390\pi\) | |||||||
\(224\) | −1.24894 | −0.0834484 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.62458 | −0.108066 | ||||||||
\(227\) | − | 9.21775i | − | 0.611803i | −0.952063 | − | 0.305902i | \(-0.901042\pi\) | ||
0.952063 | − | 0.305902i | \(-0.0989579\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.95309 | −0.591637 | −0.295818 | − | 0.955244i | \(-0.595592\pi\) | ||||
−0.295818 | + | 0.955244i | \(0.595592\pi\) | |||||||
\(230\) | −1.43942 | + | 1.71116i | −0.0949123 | + | 0.112831i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.788275i | 0.0517528i | ||||||||
\(233\) | 10.9971i | 0.720446i | 0.932866 | + | 0.360223i | \(0.117299\pi\) | ||||
−0.932866 | + | 0.360223i | \(0.882701\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.0647 | + | 15.1959i | 1.17841 | + | 0.991271i | ||||
\(236\) | 5.01597 | 0.326512 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.51956i | 0.422601i | ||||||||
\(239\) | −27.2651 | −1.76363 | −0.881815 | − | 0.471596i | \(-0.843678\pi\) | ||||
−0.881815 | + | 0.471596i | \(0.843678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.3988 | −1.82933 | −0.914663 | − | 0.404218i | \(-0.867544\pi\) | ||||
−0.914663 | + | 0.404218i | \(0.867544\pi\) | |||||||
\(242\) | 5.15247i | 0.331214i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.0671 | −0.900551 | ||||||||
\(245\) | −7.83063 | + | 9.30898i | −0.500281 | + | 0.594729i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.25555i | 0.525288i | ||||||||
\(248\) | 0.287672i | 0.0182672i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.62575 | − | 9.66183i | 0.355803 | − | 0.611068i | ||||
\(251\) | −0.734934 | −0.0463886 | −0.0231943 | − | 0.999731i | \(-0.507384\pi\) | ||||
−0.0231943 | + | 0.999731i | \(0.507384\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.41817i | − | 0.152029i | ||||||
\(254\) | −20.6725 | −1.29711 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 11.8648i | − | 0.740106i | −0.929011 | − | 0.370053i | \(-0.879340\pi\) | ||
0.929011 | − | 0.370053i | \(-0.120660\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.15534 | −0.320338 | ||||||||
\(260\) | 9.93202 | + | 8.35473i | 0.615958 | + | 0.518138i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 7.35442i | − | 0.454358i | ||||||
\(263\) | 23.5541i | 1.45241i | 0.687479 | + | 0.726204i | \(0.258717\pi\) | ||||
−0.687479 | + | 0.726204i | \(0.741283\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.85616 | + | 4.92615i | 0.359741 | + | 0.302611i | ||||
\(266\) | −1.77640 | −0.108918 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.42477i | 0.575709i | ||||||||
\(269\) | 29.6698 | 1.80900 | 0.904499 | − | 0.426476i | \(-0.140245\pi\) | ||||
0.904499 | + | 0.426476i | \(0.140245\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6738 | 0.891371 | 0.445686 | − | 0.895190i | \(-0.352960\pi\) | ||||
0.445686 | + | 0.895190i | \(0.352960\pi\) | |||||||
\(272\) | − | 5.22007i | − | 0.316513i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.22007 | −0.557005 | ||||||||
\(275\) | 2.07035 | + | 11.9123i | 0.124847 | + | 0.718336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2554i | 1.15695i | 0.815702 | + | 0.578473i | \(0.196351\pi\) | ||||
−0.815702 | + | 0.578473i | \(0.803649\pi\) | |||||||
\(278\) | 8.00000i | 0.479808i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.79775 | + | 2.13714i | −0.107436 | + | 0.127719i | ||||
\(281\) | −2.79912 | −0.166981 | −0.0834906 | − | 0.996509i | \(-0.526607\pi\) | ||||
−0.0834906 | + | 0.996509i | \(0.526607\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3118i | 1.20741i | 0.797208 | + | 0.603705i | \(0.206310\pi\) | ||||
−0.797208 | + | 0.603705i | \(0.793690\pi\) | |||||||
\(284\) | 11.5619 | 0.686073 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.0356 | −0.829945 | ||||||||
\(287\) | 6.26466i | 0.369791i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2492 | −0.602892 | ||||||||
\(290\) | 1.34887 | + | 1.13466i | 0.0792082 | + | 0.0666293i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.741689i | 0.0434041i | ||||||||
\(293\) | 2.84698i | 0.166323i | 0.996536 | + | 0.0831613i | \(0.0265017\pi\) | ||||
−0.996536 | + | 0.0831613i | \(0.973498\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.22007 | − | 8.58315i | 0.420369 | − | 0.499731i | ||||
\(296\) | 4.12777 | 0.239922 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 15.4087i | − | 0.892600i | ||||||
\(299\) | −5.80425 | −0.335668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.61098 | −0.150494 | ||||||||
\(302\) | − | 14.1525i | − | 0.814383i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.42233 | 0.0815761 | ||||||||
\(305\) | −20.2483 | + | 24.0710i | −1.15942 | + | 1.37830i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.25555i | 0.471169i | 0.971854 | + | 0.235584i | \(0.0757004\pi\) | ||||
−0.971854 | + | 0.235584i | \(0.924300\pi\) | |||||||
\(308\) | − | 3.02015i | − | 0.172089i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.492254 | + | 0.414080i | 0.0279582 | + | 0.0235182i | ||||
\(311\) | 22.2289 | 1.26048 | 0.630242 | − | 0.776399i | \(-0.282956\pi\) | ||||
0.630242 | + | 0.776399i | \(0.282956\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.9733i | − | 0.789819i | −0.918720 | − | 0.394909i | \(-0.870776\pi\) | ||
0.918720 | − | 0.394909i | \(-0.129224\pi\) | |||||||
\(314\) | 18.0747 | 1.02002 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.375418 | 0.0211189 | ||||||||
\(317\) | − | 5.82916i | − | 0.327398i | −0.986510 | − | 0.163699i | \(-0.947657\pi\) | ||
0.986510 | − | 0.163699i | \(-0.0523427\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.90618 | −0.106726 | ||||||||
\(320\) | 1.43942 | − | 1.71116i | 0.0804658 | − | 0.0956570i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 1.24894i | − | 0.0696008i | ||||||
\(323\) | − | 7.42466i | − | 0.413119i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.5926 | − | 4.96939i | 1.58603 | − | 0.275652i | ||||
\(326\) | −19.8640 | −1.10017 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.01597i | − | 0.276961i | ||||||
\(329\) | −13.1850 | −0.726915 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.7249 | 1.74376 | 0.871880 | − | 0.489719i | \(-0.162901\pi\) | ||||
0.871880 | + | 0.489719i | \(0.162901\pi\) | |||||||
\(332\) | 5.04691i | 0.276985i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.55698 | 0.139912 | ||||||||
\(335\) | 16.1273 | + | 13.5662i | 0.881130 | + | 0.741199i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.6753i | − | 0.635994i | −0.948092 | − | 0.317997i | \(-0.896990\pi\) | ||
0.948092 | − | 0.317997i | \(-0.103010\pi\) | |||||||
\(338\) | 20.6893i | 1.12535i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.93240 | − | 7.51386i | −0.484427 | − | 0.407496i | ||||
\(341\) | −0.695639 | −0.0376710 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.5370i | − | 0.838920i | ||||||
\(344\) | 2.09056 | 0.112715 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.2848 | −0.606675 | ||||||||
\(347\) | − | 7.59549i | − | 0.407747i | −0.978997 | − | 0.203874i | \(-0.934647\pi\) | ||
0.978997 | − | 0.203874i | \(-0.0653532\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.24916 | −0.495096 | −0.247548 | − | 0.968876i | \(-0.579625\pi\) | ||||
−0.247548 | + | 0.968876i | \(0.579625\pi\) | |||||||
\(350\) | 1.06930 | + | 6.15247i | 0.0571564 | + | 0.328864i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.41817i | 0.128889i | ||||||||
\(353\) | − | 26.2463i | − | 1.39695i | −0.715635 | − | 0.698475i | \(-0.753862\pi\) | ||
0.715635 | − | 0.698475i | \(-0.246138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6424 | − | 19.7843i | 0.883287 | − | 1.05004i | ||||
\(356\) | −3.81362 | −0.202121 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.4289i | 0.604034i | ||||||||
\(359\) | 17.2730 | 0.911634 | 0.455817 | − | 0.890074i | \(-0.349347\pi\) | ||||
0.455817 | + | 0.890074i | \(0.349347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.9770 | −0.893525 | ||||||||
\(362\) | − | 7.21775i | − | 0.379356i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.24916 | −0.379959 | ||||||||
\(365\) | 1.26915 | + | 1.06760i | 0.0664304 | + | 0.0558807i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 17.8005i | − | 0.929176i | −0.885527 | − | 0.464588i | \(-0.846202\pi\) | ||
0.885527 | − | 0.464588i | \(-0.153798\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.94158 | − | 7.06330i | 0.308888 | − | 0.367203i | ||||
\(371\) | −4.27429 | −0.221910 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.81918i | 0.508418i | 0.967149 | + | 0.254209i | \(0.0818151\pi\) | ||||
−0.967149 | + | 0.254209i | \(0.918185\pi\) | |||||||
\(374\) | 12.6230 | 0.652720 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.5570 | 0.544435 | ||||||||
\(377\) | 4.57534i | 0.235642i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.6715 | −0.856357 | −0.428179 | − | 0.903694i | \(-0.640845\pi\) | ||||
−0.428179 | + | 0.903694i | \(0.640845\pi\) | |||||||
\(380\) | 2.04732 | − | 2.43384i | 0.105025 | − | 0.124853i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.25555i | 0.422390i | ||||||||
\(383\) | 9.11397i | 0.465702i | 0.972512 | + | 0.232851i | \(0.0748054\pi\) | ||||
−0.972512 | + | 0.232851i | \(0.925195\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.16797 | − | 4.34725i | −0.263384 | − | 0.221556i | ||||
\(386\) | −2.49788 | −0.127139 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.788275i | 0.0400186i | ||||||||
\(389\) | 32.7086 | 1.65839 | 0.829195 | − | 0.558959i | \(-0.188799\pi\) | ||||
0.829195 | + | 0.558959i | \(0.188799\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.22007 | 0.263990 | ||||||||
\(392\) | 5.44015i | 0.274769i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.1140 | 0.761431 | ||||||||
\(395\) | 0.540382 | − | 0.642401i | 0.0271896 | − | 0.0323227i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 33.7644i | − | 1.69459i | −0.531125 | − | 0.847294i | \(-0.678231\pi\) | ||
0.531125 | − | 0.847294i | \(-0.321769\pi\) | |||||||
\(398\) | 4.37542i | 0.219320i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.856164 | − | 4.92615i | −0.0428082 | − | 0.246308i | ||||
\(401\) | 33.6164 | 1.67872 | 0.839362 | − | 0.543572i | \(-0.182929\pi\) | ||||
0.839362 | + | 0.543572i | \(0.182929\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.66972i | 0.0831748i | ||||||||
\(404\) | 12.3036 | 0.612127 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.984509 | −0.0488604 | ||||||||
\(407\) | 9.98164i | 0.494771i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.4401 | −1.20849 | −0.604244 | − | 0.796800i | \(-0.706525\pi\) | ||||
−0.604244 | + | 0.796800i | \(0.706525\pi\) | |||||||
\(410\) | −8.58315 | − | 7.22007i | −0.423892 | − | 0.356574i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.52323i | 0.272110i | ||||||||
\(413\) | 6.26466i | 0.308264i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.63609 | + | 7.26460i | 0.423929 | + | 0.356605i | ||||
\(416\) | 5.80425 | 0.284577 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.43942i | 0.168228i | ||||||||
\(419\) | 34.6526 | 1.69289 | 0.846445 | − | 0.532476i | \(-0.178738\pi\) | ||||
0.846445 | + | 0.532476i | \(0.178738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.72073 | −0.473759 | −0.236880 | − | 0.971539i | \(-0.576125\pi\) | ||||
−0.236880 | + | 0.971539i | \(0.576125\pi\) | |||||||
\(422\) | − | 18.0356i | − | 0.877961i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.42233 | 0.166203 | ||||||||
\(425\) | −25.7149 | + | 4.46924i | −1.24735 | + | 0.216790i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 17.5689i | − | 0.850220i | ||||||
\(428\) | 12.4716i | 0.602836i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.00918 | − | 3.57729i | 0.145116 | − | 0.172512i | ||||
\(431\) | 13.9469 | 0.671801 | 0.335900 | − | 0.941897i | \(-0.390959\pi\) | ||||
0.335900 | + | 0.941897i | \(0.390959\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.1608i | 0.728580i | 0.931286 | + | 0.364290i | \(0.118688\pi\) | ||||
−0.931286 | + | 0.364290i | \(0.881312\pi\) | |||||||
\(434\) | −0.359286 | −0.0172463 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.79775 | 0.373444 | ||||||||
\(437\) | 1.42233i | 0.0680392i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.1140 | 0.625895 | 0.312948 | − | 0.949770i | \(-0.398684\pi\) | ||||
0.312948 | + | 0.949770i | \(0.398684\pi\) | |||||||
\(440\) | 4.13788 | + | 3.48075i | 0.197266 | + | 0.165938i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 30.2986i | − | 1.44116i | ||||||
\(443\) | 4.00000i | 0.190046i | 0.995475 | + | 0.0950229i | \(0.0302924\pi\) | ||||
−0.995475 | + | 0.0950229i | \(0.969708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.48938 | + | 6.52573i | −0.260222 | + | 0.309349i | ||||
\(446\) | 11.7416 | 0.555979 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.24894i | 0.0590069i | ||||||||
\(449\) | −34.7121 | −1.63817 | −0.819083 | − | 0.573675i | \(-0.805517\pi\) | ||||
−0.819083 | + | 0.573675i | \(0.805517\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.1295 | 0.571154 | ||||||||
\(452\) | 1.62458i | 0.0764139i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.21775 | −0.432610 | ||||||||
\(455\) | −10.4346 | + | 12.4045i | −0.489180 | + | 0.581532i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5716i | 0.915519i | 0.889076 | + | 0.457759i | \(0.151348\pi\) | ||||
−0.889076 | + | 0.457759i | \(0.848652\pi\) | |||||||
\(458\) | 8.95309i | 0.418350i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.71116 | + | 1.43942i | 0.0797834 | + | 0.0671131i | ||||
\(461\) | −16.2186 | −0.755376 | −0.377688 | − | 0.925933i | \(-0.623281\pi\) | ||||
−0.377688 | + | 0.925933i | \(0.623281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.6496i | − | 1.37793i | −0.724794 | − | 0.688966i | \(-0.758065\pi\) | ||
0.724794 | − | 0.688966i | \(-0.241935\pi\) | |||||||
\(464\) | 0.788275 | 0.0365947 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.9971 | 0.509432 | ||||||||
\(467\) | 33.3519i | 1.54334i | 0.636023 | + | 0.771670i | \(0.280578\pi\) | ||||
−0.636023 | + | 0.771670i | \(0.719422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.7710 | −0.543533 | ||||||||
\(470\) | 15.1959 | − | 18.0647i | 0.700934 | − | 0.833264i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 5.01597i | − | 0.230879i | ||||||
\(473\) | 5.05531i | 0.232444i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.21775 | − | 7.00660i | −0.0558740 | − | 0.321485i | ||||
\(476\) | 6.51956 | 0.298824 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.2651i | 1.24707i | ||||||||
\(479\) | 2.49788 | 0.114131 | 0.0570656 | − | 0.998370i | \(-0.481826\pi\) | ||||
0.0570656 | + | 0.998370i | \(0.481826\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.9586 | 1.09242 | ||||||||
\(482\) | 28.3988i | 1.29353i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.15247 | 0.234203 | ||||||||
\(485\) | 1.34887 | + | 1.13466i | 0.0612489 | + | 0.0515221i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 3.37263i | − | 0.152828i | −0.997076 | − | 0.0764142i | \(-0.975653\pi\) | ||
0.997076 | − | 0.0764142i | \(-0.0243471\pi\) | |||||||
\(488\) | 14.0671i | 0.636786i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.30898 | + | 7.83063i | 0.420537 | + | 0.353752i | ||||
\(491\) | −26.3634 | −1.18976 | −0.594882 | − | 0.803813i | \(-0.702801\pi\) | ||||
−0.594882 | + | 0.803813i | \(0.702801\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.11485i | − | 0.185324i | ||||||
\(494\) | 8.25555 | 0.371435 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.287672 | 0.0129169 | ||||||||
\(497\) | 14.4401i | 0.647729i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.3833 | −1.76304 | −0.881519 | − | 0.472149i | \(-0.843478\pi\) | ||||
−0.881519 | + | 0.472149i | \(0.843478\pi\) | |||||||
\(500\) | −9.66183 | − | 5.62575i | −0.432090 | − | 0.251591i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.734934i | 0.0328017i | ||||||||
\(503\) | − | 5.15534i | − | 0.229865i | −0.993373 | − | 0.114933i | \(-0.963335\pi\) | ||
0.993373 | − | 0.114933i | \(-0.0366652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.7100 | − | 21.0535i | 0.788085 | − | 0.936868i | ||||
\(506\) | −2.41817 | −0.107501 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.6725i | 0.917195i | ||||||||
\(509\) | 5.46517 | 0.242240 | 0.121120 | − | 0.992638i | \(-0.461351\pi\) | ||||
0.121120 | + | 0.992638i | \(0.461351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.926326 | −0.0409782 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.8648 | −0.523334 | ||||||||
\(515\) | 9.45115 | + | 7.95022i | 0.416467 | + | 0.350329i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.5285i | 1.12274i | ||||||||
\(518\) | 5.15534i | 0.226513i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.35473 | − | 9.93202i | 0.366379 | − | 0.435548i | ||||
\(521\) | −2.07764 | −0.0910229 | −0.0455115 | − | 0.998964i | \(-0.514492\pi\) | ||||
−0.0455115 | + | 0.998964i | \(0.514492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.2569i | 0.842044i | 0.907050 | + | 0.421022i | \(0.138328\pi\) | ||||
−0.907050 | + | 0.421022i | \(0.861672\pi\) | |||||||
\(524\) | −7.35442 | −0.321280 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.5541 | 1.02701 | ||||||||
\(527\) | − | 1.50167i | − | 0.0654138i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 4.92615 | − | 5.85616i | 0.213978 | − | 0.254376i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.77640i | 0.0770169i | ||||||||
\(533\) | − | 29.1140i | − | 1.26107i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.3409 | + | 17.9518i | 0.922647 | + | 0.776123i | ||||
\(536\) | 9.42477 | 0.407088 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 29.6698i | − | 1.27915i | ||||||
\(539\) | −13.1552 | −0.566634 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.75084 | −0.290241 | −0.145121 | − | 0.989414i | \(-0.546357\pi\) | ||||
−0.145121 | + | 0.989414i | \(0.546357\pi\) | |||||||
\(542\) | − | 14.6738i | − | 0.630295i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.22007 | −0.223809 | ||||||||
\(545\) | 11.2242 | − | 13.3432i | 0.480792 | − | 0.571561i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 33.9704i | − | 1.45247i | −0.687446 | − | 0.726235i | \(-0.741268\pi\) | ||
0.687446 | − | 0.726235i | \(-0.258732\pi\) | |||||||
\(548\) | 9.22007i | 0.393862i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.9123 | − | 2.07035i | 0.507940 | − | 0.0882799i | ||||
\(551\) | 1.12119 | 0.0477641 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.468874i | 0.0199386i | ||||||||
\(554\) | 19.2554 | 0.818084 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.00000 | 0.339276 | ||||||||
\(557\) | 37.8625i | 1.60428i | 0.597133 | + | 0.802142i | \(0.296306\pi\) | ||||
−0.597133 | + | 0.802142i | \(0.703694\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.1341 | 0.513218 | ||||||||
\(560\) | 2.13714 | + | 1.79775i | 0.0903108 | + | 0.0759686i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.79912i | 0.118074i | ||||||||
\(563\) | − | 8.81789i | − | 0.371630i | −0.982585 | − | 0.185815i | \(-0.940508\pi\) | ||
0.982585 | − | 0.185815i | \(-0.0594925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.77993 | + | 2.33845i | 0.116952 | + | 0.0983793i | ||||
\(566\) | 20.3118 | 0.853768 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 11.5619i | − | 0.485127i | ||||||
\(569\) | −11.0547 | −0.463436 | −0.231718 | − | 0.972783i | \(-0.574435\pi\) | ||||
−0.231718 | + | 0.972783i | \(0.574435\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9822 | 0.459590 | 0.229795 | − | 0.973239i | \(-0.426194\pi\) | ||||
0.229795 | + | 0.973239i | \(0.426194\pi\) | |||||||
\(572\) | 14.0356i | 0.586859i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.26466 | 0.261482 | ||||||||
\(575\) | 4.92615 | − | 0.856164i | 0.205435 | − | 0.0357045i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.9761i | 1.37281i | 0.727217 | + | 0.686407i | \(0.240813\pi\) | ||||
−0.727217 | + | 0.686407i | \(0.759187\pi\) | |||||||
\(578\) | 10.2492i | 0.426309i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.13466 | − | 1.34887i | 0.0471140 | − | 0.0560087i | ||||
\(581\) | −6.30329 | −0.261505 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.27576i | 0.342747i | ||||||||
\(584\) | 0.741689 | 0.0306913 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.84698 | 0.117608 | ||||||||
\(587\) | − | 42.3988i | − | 1.74998i | −0.484137 | − | 0.874992i | \(-0.660866\pi\) | ||
0.484137 | − | 0.874992i | \(-0.339134\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.409164 | 0.0168593 | ||||||||
\(590\) | −8.58315 | − | 7.22007i | −0.353363 | − | 0.297246i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 4.12777i | − | 0.169650i | ||||||
\(593\) | − | 10.1755i | − | 0.417857i | −0.977931 | − | 0.208929i | \(-0.933002\pi\) | ||
0.977931 | − | 0.208929i | \(-0.0669976\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.38436 | − | 11.1560i | 0.384721 | − | 0.457353i | ||||
\(596\) | −15.4087 | −0.631163 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.80425i | 0.237353i | ||||||||
\(599\) | −33.8778 | −1.38421 | −0.692104 | − | 0.721797i | \(-0.743316\pi\) | ||||
−0.692104 | + | 0.721797i | \(0.743316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.5926 | −0.758409 | −0.379204 | − | 0.925313i | \(-0.623802\pi\) | ||||
−0.379204 | + | 0.925313i | \(0.623802\pi\) | |||||||
\(602\) | 2.61098i | 0.106416i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.1525 | −0.575856 | ||||||||
\(605\) | 7.41655 | − | 8.81673i | 0.301526 | − | 0.358451i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.7403i | − | 1.00418i | −0.864816 | − | 0.502088i | \(-0.832565\pi\) | ||
0.864816 | − | 0.502088i | \(-0.167435\pi\) | |||||||
\(608\) | − | 1.42233i | − | 0.0576830i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.0710 | + | 20.2483i | 0.974608 | + | 0.819832i | ||||
\(611\) | 61.2754 | 2.47894 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 13.9599i | − | 0.563834i | −0.959439 | − | 0.281917i | \(-0.909030\pi\) | ||
0.959439 | − | 0.281917i | \(-0.0909702\pi\) | |||||||
\(614\) | 8.25555 | 0.333167 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.02015 | −0.121685 | ||||||||
\(617\) | 14.9508i | 0.601895i | 0.953641 | + | 0.300948i | \(0.0973029\pi\) | ||||
−0.953641 | + | 0.300948i | \(0.902697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.5874 | 1.59115 | 0.795576 | − | 0.605853i | \(-0.207168\pi\) | ||||
0.795576 | + | 0.605853i | \(0.207168\pi\) | |||||||
\(620\) | 0.414080 | − | 0.492254i | 0.0166299 | − | 0.0197694i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 22.2289i | − | 0.891296i | ||||||
\(623\) | − | 4.76299i | − | 0.190825i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.5340 | + | 8.43519i | −0.941359 | + | 0.337408i | ||||
\(626\) | −13.9733 | −0.558486 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 18.0747i | − | 0.721260i | ||||||
\(629\) | −21.5473 | −0.859146 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.5250 | −1.57347 | −0.786733 | − | 0.617293i | \(-0.788229\pi\) | ||||
−0.786733 | + | 0.617293i | \(0.788229\pi\) | |||||||
\(632\) | − | 0.375418i | − | 0.0149333i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.82916 | −0.231506 | ||||||||
\(635\) | 35.3741 | + | 29.7564i | 1.40378 | + | 1.18085i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.5760i | 1.25109i | ||||||||
\(638\) | 1.90618i | 0.0754664i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.71116 | − | 1.43942i | −0.0676397 | − | 0.0568979i | ||||
\(641\) | 8.60953 | 0.340056 | 0.170028 | − | 0.985439i | \(-0.445614\pi\) | ||||
0.170028 | + | 0.985439i | \(0.445614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25.9359i | − | 1.02281i | −0.859340 | − | 0.511405i | \(-0.829125\pi\) | ||
0.859340 | − | 0.511405i | \(-0.170875\pi\) | |||||||
\(644\) | −1.24894 | −0.0492152 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.42466 | −0.292119 | ||||||||
\(647\) | 14.6156i | 0.574600i | 0.957841 | + | 0.287300i | \(0.0927577\pi\) | ||||
−0.957841 | + | 0.287300i | \(0.907242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.1295 | 0.476123 | ||||||||
\(650\) | −4.96939 | − | 28.5926i | −0.194915 | − | 1.12149i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.8640i | 0.777936i | ||||||||
\(653\) | 4.03564i | 0.157927i | 0.996878 | + | 0.0789633i | \(0.0251610\pi\) | ||||
−0.996878 | + | 0.0789633i | \(0.974839\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5861 | + | 12.5846i | −0.413632 | + | 0.491722i | ||||
\(656\) | −5.01597 | −0.195841 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.1850i | 0.514007i | ||||||||
\(659\) | 31.6859 | 1.23431 | 0.617153 | − | 0.786843i | \(-0.288286\pi\) | ||||
0.617153 | + | 0.786843i | \(0.288286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.98873 | 0.271830 | 0.135915 | − | 0.990721i | \(-0.456603\pi\) | ||||
0.135915 | + | 0.990721i | \(0.456603\pi\) | |||||||
\(662\) | − | 31.7249i | − | 1.23303i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.04691 | 0.195858 | ||||||||
\(665\) | 3.03972 | + | 2.55698i | 0.117875 | + | 0.0991556i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.788275i | 0.0305221i | ||||||||
\(668\) | − | 2.55698i | − | 0.0989327i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.5662 | − | 16.1273i | 0.524107 | − | 0.623053i | ||||
\(671\) | −34.0165 | −1.31319 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.9677i | 1.65628i | 0.560520 | + | 0.828141i | \(0.310601\pi\) | ||||
−0.560520 | + | 0.828141i | \(0.689399\pi\) | |||||||
\(674\) | −11.6753 | −0.449716 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.6893 | 0.795743 | ||||||||
\(677\) | 4.40218i | 0.169190i | 0.996415 | + | 0.0845948i | \(0.0269596\pi\) | ||||
−0.996415 | + | 0.0845948i | \(0.973040\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.984509 | −0.0377820 | ||||||||
\(680\) | −7.51386 | + | 8.93240i | −0.288143 | + | 0.342542i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.695639i | 0.0266374i | ||||||||
\(683\) | 40.0881i | 1.53393i | 0.641690 | + | 0.766964i | \(0.278233\pi\) | ||||
−0.641690 | + | 0.766964i | \(0.721767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.7771 | + | 13.2715i | 0.602810 | + | 0.507079i | ||||
\(686\) | −15.5370 | −0.593206 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 2.09056i | − | 0.0797017i | ||||||
\(689\) | 19.8640 | 0.756760 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.5340 | −0.476815 | −0.238407 | − | 0.971165i | \(-0.576625\pi\) | ||||
−0.238407 | + | 0.971165i | \(0.576625\pi\) | |||||||
\(692\) | 11.2848i | 0.428984i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.59549 | −0.288321 | ||||||||
\(695\) | 11.5153 | − | 13.6893i | 0.436801 | − | 0.519265i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.1838i | 0.991780i | ||||||||
\(698\) | 9.24916i | 0.350086i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.15247 | − | 1.06930i | 0.232542 | − | 0.0404157i | ||||
\(701\) | −24.4530 | −0.923578 | −0.461789 | − | 0.886990i | \(-0.652792\pi\) | ||||
−0.461789 | + | 0.886990i | \(0.652792\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.87105i | − | 0.221431i | ||||||
\(704\) | 2.41817 | 0.0911381 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.2463 | −0.987792 | ||||||||
\(707\) | 15.3665i | 0.577916i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.1764 | −1.47130 | −0.735650 | − | 0.677362i | \(-0.763123\pi\) | ||||
−0.735650 | + | 0.677362i | \(0.763123\pi\) | |||||||
\(710\) | −19.7843 | − | 16.6424i | −0.742493 | − | 0.624578i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.81362i | 0.142921i | ||||||||
\(713\) | 0.287672i | 0.0107734i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0173 | + | 20.2031i | 0.898195 | + | 0.755554i | ||||
\(716\) | 11.4289 | 0.427116 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 17.2730i | − | 0.644622i | ||||||
\(719\) | 43.7761 | 1.63257 | 0.816287 | − | 0.577646i | \(-0.196029\pi\) | ||||
0.816287 | + | 0.577646i | \(0.196029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.89818 | −0.256902 | ||||||||
\(722\) | 16.9770i | 0.631818i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.21775 | −0.268245 | ||||||||
\(725\) | −0.674893 | − | 3.88316i | −0.0250649 | − | 0.144217i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.3873i | 0.941562i | 0.882250 | + | 0.470781i | \(0.156028\pi\) | ||||
−0.882250 | + | 0.470781i | \(0.843972\pi\) | |||||||
\(728\) | 7.24916i | 0.268672i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.06760 | − | 1.26915i | 0.0395136 | − | 0.0469734i | ||||
\(731\) | −10.9129 | −0.403627 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 47.8775i | − | 1.76840i | −0.467111 | − | 0.884199i | \(-0.654705\pi\) | ||
0.467111 | − | 0.884199i | \(-0.345295\pi\) | |||||||
\(734\) | −17.8005 | −0.657027 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 22.7907i | 0.839505i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.8400 | 0.398756 | 0.199378 | − | 0.979923i | \(-0.436108\pi\) | ||||
0.199378 | + | 0.979923i | \(0.436108\pi\) | |||||||
\(740\) | −7.06330 | − | 5.94158i | −0.259652 | − | 0.218417i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.27429i | 0.156914i | ||||||||
\(743\) | − | 33.6893i | − | 1.23594i | −0.786201 | − | 0.617970i | \(-0.787955\pi\) | ||
0.786201 | − | 0.617970i | \(-0.212045\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.1795 | + | 26.3667i | −0.812593 | + | 0.966003i | ||||
\(746\) | 9.81918 | 0.359506 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 12.6230i | − | 0.461543i | ||||||
\(749\) | −15.5762 | −0.569144 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.7587 | −0.721005 | −0.360503 | − | 0.932758i | \(-0.617395\pi\) | ||||
−0.360503 | + | 0.932758i | \(0.617395\pi\) | |||||||
\(752\) | − | 10.5570i | − | 0.384974i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.57534 | 0.166624 | ||||||||
\(755\) | −20.3713 | + | 24.2172i | −0.741387 | + | 0.881354i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 9.03036i | − | 0.328214i | −0.986443 | − | 0.164107i | \(-0.947526\pi\) | ||
0.986443 | − | 0.164107i | \(-0.0524743\pi\) | |||||||
\(758\) | 16.6715i | 0.605536i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.43384 | − | 2.04732i | −0.0882845 | − | 0.0742641i | ||||
\(761\) | −8.65816 | −0.313858 | −0.156929 | − | 0.987610i | \(-0.550159\pi\) | ||||
−0.156929 | + | 0.987610i | \(0.550159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.73892i | 0.352573i | ||||||||
\(764\) | 8.25555 | 0.298675 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.11397 | 0.329301 | ||||||||
\(767\) | − | 29.1140i | − | 1.05124i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.65367 | −0.0596330 | −0.0298165 | − | 0.999555i | \(-0.509492\pi\) | ||||
−0.0298165 | + | 0.999555i | \(0.509492\pi\) | |||||||
\(770\) | −4.34725 | + | 5.16797i | −0.156664 | + | 0.186241i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.49788i | 0.0899007i | ||||||||
\(773\) | 13.5208i | 0.486309i | 0.969988 | + | 0.243155i | \(0.0781823\pi\) | ||||
−0.969988 | + | 0.243155i | \(0.921818\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.246295 | − | 1.41712i | −0.00884716 | − | 0.0509044i | ||||
\(776\) | 0.788275 | 0.0282974 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 32.7086i | − | 1.17266i | ||||||
\(779\) | −7.13436 | −0.255615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.9586 | 1.00044 | ||||||||
\(782\) | − | 5.22007i | − | 0.186669i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.44015 | 0.194291 | ||||||||
\(785\) | −30.9288 | − | 26.0170i | −1.10390 | − | 0.928588i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.9295i | − | 1.03123i | −0.856821 | − | 0.515613i | \(-0.827564\pi\) | ||
0.856821 | − | 0.515613i | \(-0.172436\pi\) | |||||||
\(788\) | − | 15.1140i | − | 0.538413i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.642401 | − | 0.540382i | −0.0228556 | − | 0.0192259i | ||||
\(791\) | −2.02901 | −0.0721432 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 81.6487i | 2.89943i | ||||||||
\(794\) | −33.7644 | −1.19825 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.37542 | 0.155083 | ||||||||
\(797\) | 14.6761i | 0.519856i | 0.965628 | + | 0.259928i | \(0.0836988\pi\) | ||||
−0.965628 | + | 0.259928i | \(0.916301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.1082 | −1.94959 | ||||||||
\(800\) | −4.92615 | + | 0.856164i | −0.174166 | + | 0.0302700i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 33.6164i | − | 1.18704i | ||||||
\(803\) | 1.79353i | 0.0632922i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.79775 | + | 2.13714i | −0.0633622 | + | 0.0753244i | ||||
\(806\) | 1.66972 | 0.0588134 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 12.3036i | − | 0.432839i | ||||||
\(809\) | 4.34055 | 0.152605 | 0.0763027 | − | 0.997085i | \(-0.475688\pi\) | ||||
0.0763027 | + | 0.997085i | \(0.475688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.580000 | 0.0203665 | 0.0101833 | − | 0.999948i | \(-0.496759\pi\) | ||||
0.0101833 | + | 0.999948i | \(0.496759\pi\) | |||||||
\(812\) | 0.984509i | 0.0345495i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.98164 | 0.349856 | ||||||||
\(815\) | 33.9906 | + | 28.5926i | 1.19064 | + | 1.00156i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.97346i | − | 0.104028i | ||||||
\(818\) | 24.4401i | 0.854530i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.22007 | + | 8.58315i | −0.252136 | + | 0.299737i | ||||
\(821\) | 5.46517 | 0.190736 | 0.0953679 | − | 0.995442i | \(-0.469597\pi\) | ||||
0.0953679 | + | 0.995442i | \(0.469597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 38.6209i | − | 1.34624i | −0.739533 | − | 0.673121i | \(-0.764953\pi\) | ||
0.739533 | − | 0.673121i | \(-0.235047\pi\) | |||||||
\(824\) | 5.52323 | 0.192411 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.26466 | 0.217975 | ||||||||
\(827\) | − | 5.79775i | − | 0.201607i | −0.994906 | − | 0.100804i | \(-0.967859\pi\) | ||
0.994906 | − | 0.100804i | \(-0.0321414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.2434 | −1.77976 | −0.889879 | − | 0.456197i | \(-0.849211\pi\) | ||||
−0.889879 | + | 0.456197i | \(0.849211\pi\) | |||||||
\(830\) | 7.26460 | − | 8.63609i | 0.252158 | − | 0.299763i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.80425i | − | 0.201226i | ||||||
\(833\) | − | 28.3980i | − | 0.983931i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.37542 | − | 3.68056i | −0.151418 | − | 0.127371i | ||||
\(836\) | 3.43942 | 0.118955 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 34.6526i | − | 1.19705i | ||||||
\(839\) | 43.0148 | 1.48504 | 0.742518 | − | 0.669827i | \(-0.233632\pi\) | ||||
0.742518 | + | 0.669827i | \(0.233632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3786 | −0.978573 | ||||||||
\(842\) | 9.72073i | 0.334998i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.0356 | −0.620812 | ||||||||
\(845\) | 29.7805 | − | 35.4028i | 1.02448 | − | 1.21789i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.43514i | 0.221114i | ||||||||
\(848\) | − | 3.42233i | − | 0.117523i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.46924 | + | 25.7149i | 0.153294 | + | 0.882013i | ||||
\(851\) | 4.12777 | 0.141498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12.3103i | − | 0.421497i | −0.977540 | − | 0.210748i | \(-0.932410\pi\) | ||
0.977540 | − | 0.210748i | \(-0.0675901\pi\) | |||||||
\(854\) | −17.5689 | −0.601196 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.4716 | 0.426269 | ||||||||
\(857\) | 21.3078i | 0.727861i | 0.931426 | + | 0.363931i | \(0.118565\pi\) | ||||
−0.931426 | + | 0.363931i | \(0.881435\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.1507 | −0.448696 | −0.224348 | − | 0.974509i | \(-0.572025\pi\) | ||||
−0.224348 | + | 0.974509i | \(0.572025\pi\) | |||||||
\(860\) | −3.57729 | − | 3.00918i | −0.121984 | − | 0.102612i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 13.9469i | − | 0.475035i | ||||||
\(863\) | − | 6.49833i | − | 0.221206i | −0.993865 | − | 0.110603i | \(-0.964722\pi\) | ||
0.993865 | − | 0.110603i | \(-0.0352782\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.3101 | + | 16.2435i | 0.656565 | + | 0.552296i | ||||
\(866\) | 15.1608 | 0.515184 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.359286i | 0.0121950i | ||||||||
\(869\) | 0.907822 | 0.0307958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.7037 | 1.85356 | ||||||||
\(872\) | − | 7.79775i | − | 0.264065i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.42233 | 0.0481110 | ||||||||
\(875\) | 7.02622 | − | 12.0671i | 0.237530 | − | 0.407941i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 42.0604i | − | 1.42028i | −0.704062 | − | 0.710139i | \(-0.748632\pi\) | ||
0.704062 | − | 0.710139i | \(-0.251368\pi\) | |||||||
\(878\) | − | 13.1140i | − | 0.442575i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.48075 | − | 4.13788i | 0.117336 | − | 0.139488i | ||||
\(881\) | 40.1225 | 1.35176 | 0.675881 | − | 0.737011i | \(-0.263763\pi\) | ||||
0.675881 | + | 0.737011i | \(0.263763\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.53197i | 0.186166i | 0.995658 | + | 0.0930828i | \(0.0296721\pi\) | ||||
−0.995658 | + | 0.0930828i | \(0.970328\pi\) | |||||||
\(884\) | −30.2986 | −1.01905 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.00000 | 0.134383 | ||||||||
\(887\) | − | 11.4833i | − | 0.385572i | −0.981241 | − | 0.192786i | \(-0.938248\pi\) | ||
0.981241 | − | 0.192786i | \(-0.0617523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.8188 | −0.865934 | ||||||||
\(890\) | 6.52573 | + | 5.48938i | 0.218743 | + | 0.184005i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 11.7416i | − | 0.393136i | ||||||
\(893\) | − | 15.0155i | − | 0.502474i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.4509 | − | 19.5566i | 0.549892 | − | 0.653707i | ||||
\(896\) | 1.24894 | 0.0417242 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.7121i | 1.15836i | ||||||||
\(899\) | 0.226765 | 0.00756303 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.8648 | −0.595163 | ||||||||
\(902\) | − | 12.1295i | − | 0.403867i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.62458 | 0.0540328 | ||||||||
\(905\) | −10.3893 | + | 12.3507i | −0.345353 | + | 0.410553i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.4998i | 1.37798i | 0.724772 | + | 0.688989i | \(0.241945\pi\) | ||||
−0.724772 | + | 0.688989i | \(0.758055\pi\) | |||||||
\(908\) | 9.21775i | 0.305902i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.4045 | + | 10.4346i | 0.411205 | + | 0.345902i | ||||
\(911\) | −25.9147 | −0.858593 | −0.429297 | − | 0.903164i | \(-0.641239\pi\) | ||||
−0.429297 | + | 0.903164i | \(0.641239\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.2043i | 0.403902i | ||||||||
\(914\) | 19.5716 | 0.647370 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.95309 | 0.295818 | ||||||||
\(917\) | − | 9.18524i | − | 0.303323i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2927 | 1.19718 | 0.598592 | − | 0.801054i | \(-0.295727\pi\) | ||||
0.598592 | + | 0.801054i | \(0.295727\pi\) | |||||||
\(920\) | 1.43942 | − | 1.71116i | 0.0474561 | − | 0.0564154i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.2186i | 0.534131i | ||||||||
\(923\) | − | 67.1082i | − | 2.20889i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.3340 | + | 3.53405i | −0.668579 | + | 0.116199i | ||||
\(926\) | −29.6496 | −0.974345 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 0.788275i | − | 0.0258764i | ||||||
\(929\) | −57.6102 | −1.89013 | −0.945065 | − | 0.326881i | \(-0.894002\pi\) | ||||
−0.945065 | + | 0.326881i | \(0.894002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.73767 | 0.253592 | ||||||||
\(932\) | − | 10.9971i | − | 0.360223i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.3519 | 1.09131 | ||||||||
\(935\) | −21.6000 | − | 18.1698i | −0.706396 | − | 0.594214i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.2358i | 1.54313i | 0.636153 | + | 0.771563i | \(0.280525\pi\) | ||||
−0.636153 | + | 0.771563i | \(0.719475\pi\) | |||||||
\(938\) | 11.7710i | 0.384336i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.0647 | − | 15.1959i | −0.589206 | − | 0.495635i | ||||
\(941\) | −32.6412 | −1.06407 | −0.532037 | − | 0.846721i | \(-0.678573\pi\) | ||||
−0.532037 | + | 0.846721i | \(0.678573\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.01597i | − | 0.163343i | ||||||
\(944\) | −5.01597 | −0.163256 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.05531 | 0.164362 | ||||||||
\(947\) | − | 23.5495i | − | 0.765255i | −0.923903 | − | 0.382627i | \(-0.875019\pi\) | ||
0.923903 | − | 0.382627i | \(-0.124981\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.30495 | 0.139745 | ||||||||
\(950\) | −7.00660 | + | 1.21775i | −0.227324 | + | 0.0395089i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 6.51956i | − | 0.211300i | ||||||
\(953\) | − | 29.3956i | − | 0.952216i | −0.879387 | − | 0.476108i | \(-0.842047\pi\) | ||
0.879387 | − | 0.476108i | \(-0.157953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.8832 | − | 14.1266i | 0.384530 | − | 0.457126i | ||||
\(956\) | 27.2651 | 0.881815 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 2.49788i | − | 0.0807029i | ||||||
\(959\) | −11.5153 | −0.371849 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9172 | −0.997330 | ||||||||
\(962\) | − | 23.9586i | − | 0.772457i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 28.3988 | 0.914663 | ||||||||
\(965\) | 4.27429 | + | 3.59549i | 0.137594 | + | 0.115743i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.5903i | − | 0.501350i | −0.968071 | − | 0.250675i | \(-0.919347\pi\) | ||
0.968071 | − | 0.250675i | \(-0.0806526\pi\) | |||||||
\(968\) | − | 5.15247i | − | 0.165607i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.13466 | − | 1.34887i | 0.0364316 | − | 0.0433095i | ||||
\(971\) | 3.43267 | 0.110160 | 0.0550798 | − | 0.998482i | \(-0.482459\pi\) | ||||
0.0550798 | + | 0.998482i | \(0.482459\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.99153i | 0.320314i | ||||||||
\(974\) | −3.37263 | −0.108066 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.0671 | 0.450276 | ||||||||
\(977\) | 54.1004i | 1.73082i | 0.501061 | + | 0.865412i | \(0.332943\pi\) | ||||
−0.501061 | + | 0.865412i | \(0.667057\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.22196 | −0.294735 | ||||||||
\(980\) | 7.83063 | − | 9.30898i | 0.250140 | − | 0.297365i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 26.3634i | 0.841290i | ||||||||
\(983\) | − | 53.9529i | − | 1.72083i | −0.509594 | − | 0.860415i | \(-0.670204\pi\) | ||
0.509594 | − | 0.860415i | \(-0.329796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.8625 | − | 21.7553i | −0.824047 | − | 0.693181i | ||||
\(986\) | −4.11485 | −0.131044 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 8.25555i | − | 0.262644i | ||||||
\(989\) | 2.09056 | 0.0664758 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.5156 | −1.35055 | −0.675276 | − | 0.737565i | \(-0.735976\pi\) | ||||
−0.675276 | + | 0.737565i | \(0.735976\pi\) | |||||||
\(992\) | − | 0.287672i | − | 0.00913360i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.4401 | 0.458014 | ||||||||
\(995\) | 6.29805 | − | 7.48706i | 0.199661 | − | 0.237356i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 50.1026i | − | 1.58676i | −0.608724 | − | 0.793382i | \(-0.708318\pi\) | ||
0.608724 | − | 0.793382i | \(-0.291682\pi\) | |||||||
\(998\) | 39.3833i | 1.24666i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2070.2.d.h.829.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 2070.2.d.h.829.14 | yes | 16 | |
5.4 | even | 2 | inner | 2070.2.d.h.829.11 | yes | 16 | |
15.14 | odd | 2 | inner | 2070.2.d.h.829.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.d.h.829.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
2070.2.d.h.829.6 | yes | 16 | 15.14 | odd | 2 | inner | |
2070.2.d.h.829.11 | yes | 16 | 5.4 | even | 2 | inner | |
2070.2.d.h.829.14 | yes | 16 | 3.2 | odd | 2 | inner |