Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [480,2,Mod(127,480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(480, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("480.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.w (of order \(4\), degree \(2\), 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: | \(3.83281929702\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 480.127 |
Dual form | 480.2.w.b.223.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/480\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(421\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.12132 | − | 0.707107i | −0.948683 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 1.00000i | 0.377964 | − | 0.377964i | −0.492403 | − | 0.870367i | \(-0.663881\pi\) |
0.870367 | + | 0.492403i | \(0.163881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.41421i | − | 1.63245i | −0.577736 | − | 0.816223i | \(-0.696064\pi\) | ||
0.577736 | − | 0.816223i | \(-0.303936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41421 | − | 3.41421i | 0.946932 | − | 0.946932i | −0.0517287 | − | 0.998661i | \(-0.516473\pi\) |
0.998661 | + | 0.0517287i | \(0.0164731\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | − | 2.00000i | −0.258199 | − | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.41421 | + | 5.41421i | 1.31314 | + | 1.31314i | 0.919089 | + | 0.394051i | \(0.128927\pi\) |
0.394051 | + | 0.919089i | \(0.371073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.82843 | 1.10772 | 0.553859 | − | 0.832611i | \(-0.313155\pi\) | ||||
0.553859 | + | 0.832611i | \(0.313155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421 | 0.308607 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.24264 | − | 4.24264i | −0.884652 | − | 0.884652i | 0.109351 | − | 0.994003i | \(-0.465123\pi\) |
−0.994003 | + | 0.109351i | \(0.965123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | + | 3.00000i | 0.800000 | + | 0.600000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.242641i | 0.0450572i | 0.999746 | + | 0.0225286i | \(0.00717169\pi\) | ||||
−0.999746 | + | 0.0225286i | \(0.992828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65685i | 0.297580i | 0.988869 | + | 0.148790i | \(0.0475378\pi\) | ||||
−0.988869 | + | 0.148790i | \(0.952462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.82843 | − | 3.82843i | 0.666444 | − | 0.666444i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.82843 | + | 1.41421i | −0.478091 | + | 0.239046i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.585786 | − | 0.585786i | −0.0963027 | − | 0.0963027i | 0.657314 | − | 0.753617i | \(-0.271693\pi\) |
−0.753617 | + | 0.657314i | \(0.771693\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.82843 | 0.773167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.48528 | −1.01283 | −0.506415 | − | 0.862290i | \(-0.669030\pi\) | ||||
−0.506415 | + | 0.862290i | \(0.669030\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.82843 | − | 4.82843i | −0.736328 | − | 0.736328i | 0.235537 | − | 0.971865i | \(-0.424315\pi\) |
−0.971865 | + | 0.235537i | \(0.924315\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.707107 | − | 2.12132i | 0.105409 | − | 0.316228i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.24264 | − | 6.24264i | 0.910583 | − | 0.910583i | −0.0857352 | − | 0.996318i | \(-0.527324\pi\) |
0.996318 | + | 0.0857352i | \(0.0273239\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.65685i | 1.07217i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.82843 | + | 2.82843i | −0.388514 | + | 0.388514i | −0.874157 | − | 0.485643i | \(-0.838586\pi\) |
0.485643 | + | 0.874157i | \(0.338586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.82843 | + | 11.4853i | −0.516225 | + | 1.54868i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.41421 | + | 3.41421i | 0.452224 | + | 0.452224i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.41421 | −0.184115 | −0.0920575 | − | 0.995754i | \(-0.529344\pi\) | ||||
−0.0920575 | + | 0.995754i | \(0.529344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.17157 | −0.406078 | −0.203039 | − | 0.979171i | \(-0.565082\pi\) | ||||
−0.203039 | + | 0.979171i | \(0.565082\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | + | 1.00000i | 0.125988 | + | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.65685 | + | 4.82843i | −1.19779 | + | 0.598893i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.65685 | − | 3.65685i | 0.446756 | − | 0.446756i | −0.447519 | − | 0.894275i | \(-0.647692\pi\) |
0.894275 | + | 0.447519i | \(0.147692\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.00000i | − | 0.722315i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.34315i | 0.278080i | 0.990287 | + | 0.139040i | \(0.0444017\pi\) | ||||
−0.990287 | + | 0.139040i | \(0.955598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.48528 | − | 7.48528i | 0.876086 | − | 0.876086i | −0.117041 | − | 0.993127i | \(-0.537341\pi\) |
0.993127 | + | 0.117041i | \(0.0373409\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.707107 | + | 4.94975i | 0.0816497 | + | 0.571548i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.41421 | − | 5.41421i | −0.617007 | − | 0.617007i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34315 | −0.263624 | −0.131812 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131812 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.07107 | − | 3.07107i | −0.337093 | − | 0.337093i | 0.518179 | − | 0.855272i | \(-0.326610\pi\) |
−0.855272 | + | 0.518179i | \(0.826610\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | − | 15.3137i | −0.830502 | − | 1.66100i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.171573 | + | 0.171573i | −0.0183945 | + | 0.0183945i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.65685i | 0.387626i | 0.981039 | + | 0.193813i | \(0.0620855\pi\) | ||||
−0.981039 | + | 0.193813i | \(0.937915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.82843i | − | 0.715814i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.17157 | + | 1.17157i | −0.121486 | + | 0.121486i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.2426 | − | 3.41421i | −1.05087 | − | 0.350291i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.656854 | + | 0.656854i | 0.0666934 | + | 0.0666934i | 0.739667 | − | 0.672973i | \(-0.234983\pi\) |
−0.672973 | + | 0.739667i | \(0.734983\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.41421 | 0.544149 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.41421 | −0.538734 | −0.269367 | − | 0.963038i | \(-0.586815\pi\) | ||||
−0.269367 | + | 0.963038i | \(0.586815\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8284 | + | 11.8284i | 1.16549 | + | 1.16549i | 0.983255 | + | 0.182234i | \(0.0583330\pi\) |
0.182234 | + | 0.983255i | \(0.441667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.00000 | − | 1.00000i | −0.292770 | − | 0.0975900i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.58579 | + | 6.58579i | −0.636672 | + | 0.636672i | −0.949733 | − | 0.313061i | \(-0.898646\pi\) |
0.313061 | + | 0.949733i | \(0.398646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.1421i | 1.92927i | 0.263595 | + | 0.964633i | \(0.415092\pi\) | ||||
−0.263595 | + | 0.964633i | \(0.584908\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.828427i | − | 0.0786308i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.07107 | − | 5.07107i | 0.477046 | − | 0.477046i | −0.427140 | − | 0.904186i | \(-0.640479\pi\) |
0.904186 | + | 0.427140i | \(0.140479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | + | 12.0000i | 0.559503 | + | 1.11901i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.41421 | + | 3.41421i | 0.315644 | + | 0.315644i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.8284 | 0.992640 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.3137 | −1.66488 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.58579 | − | 4.58579i | −0.413486 | − | 0.413486i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.36396 | − | 9.19239i | −0.569210 | − | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.48528 | + | 7.48528i | −0.664211 | + | 0.664211i | −0.956370 | − | 0.292159i | \(-0.905626\pi\) |
0.292159 | + | 0.956370i | \(0.405626\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.82843i | − | 0.601209i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.8995i | 1.91337i | 0.291129 | + | 0.956684i | \(0.405969\pi\) | ||||
−0.291129 | + | 0.956684i | \(0.594031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.82843 | − | 4.82843i | 0.418678 | − | 0.418678i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.00000 | − | 1.00000i | 0.172133 | − | 0.0860663i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.75736 | − | 1.75736i | −0.150141 | − | 0.150141i | 0.628040 | − | 0.778181i | \(-0.283857\pi\) |
−0.778181 | + | 0.628040i | \(0.783857\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.34315 | −0.707656 | −0.353828 | − | 0.935310i | \(-0.615120\pi\) | ||||
−0.353828 | + | 0.935310i | \(0.615120\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.82843 | 0.743488 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.4853 | − | 18.4853i | −1.54582 | − | 1.54582i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.171573 | − | 0.514719i | 0.0142484 | − | 0.0427451i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.53553 | + | 3.53553i | −0.291606 | + | 0.291606i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.7279i | 1.69810i | 0.528314 | + | 0.849049i | \(0.322824\pi\) | ||||
−0.528314 | + | 0.849049i | \(0.677176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3137i | 1.40897i | 0.709719 | + | 0.704485i | \(0.248822\pi\) | ||||
−0.709719 | + | 0.704485i | \(0.751178\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.41421 | + | 5.41421i | −0.437713 | + | 0.437713i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.17157 | − | 3.51472i | 0.0941030 | − | 0.282309i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.41421 | − | 1.41421i | −0.112867 | − | 0.112867i | 0.648418 | − | 0.761285i | \(-0.275431\pi\) |
−0.761285 | + | 0.648418i | \(0.775431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.48528 | −0.668734 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.48528 | − | 4.48528i | −0.351314 | − | 0.351314i | 0.509284 | − | 0.860598i | \(-0.329910\pi\) |
−0.860598 | + | 0.509284i | \(0.829910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.8284 | + | 5.41421i | −0.842992 | + | 0.421496i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.24264 | − | 4.24264i | 0.328305 | − | 0.328305i | −0.523636 | − | 0.851942i | \(-0.675425\pi\) |
0.851942 | + | 0.523636i | \(0.175425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 10.3137i | − | 0.793362i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.82843i | 0.369239i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.58579 | + | 2.58579i | −0.196594 | + | 0.196594i | −0.798538 | − | 0.601944i | \(-0.794393\pi\) |
0.601944 | + | 0.798538i | \(0.294393\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.00000 | − | 1.00000i | 0.529150 | − | 0.0755929i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00000 | − | 1.00000i | −0.0751646 | − | 0.0751646i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.7279 | 1.25030 | 0.625152 | − | 0.780503i | \(-0.285037\pi\) | ||||
0.625152 | + | 0.780503i | \(0.285037\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1421 | 1.49715 | 0.748577 | − | 0.663048i | \(-0.230738\pi\) | ||||
0.748577 | + | 0.663048i | \(0.230738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.24264 | − | 2.24264i | −0.165781 | − | 0.165781i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.828427 | + | 1.65685i | 0.0609072 | + | 0.121814i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.3137 | − | 29.3137i | 2.14363 | − | 2.14363i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.41421i | 0.102869i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.17157i | − | 0.0847720i | −0.999101 | − | 0.0423860i | \(-0.986504\pi\) | ||
0.999101 | − | 0.0423860i | \(-0.0134959\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.82843 | − | 9.82843i | 0.707466 | − | 0.707466i | −0.258536 | − | 0.966002i | \(-0.583240\pi\) |
0.966002 | + | 0.258536i | \(0.0832401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.2426 | − | 3.41421i | −0.733491 | − | 0.244497i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.8284 | + | 14.8284i | 1.05648 | + | 1.05648i | 0.998306 | + | 0.0581753i | \(0.0185282\pi\) |
0.0581753 | + | 0.998306i | \(0.481472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.3137 | −1.51089 | −0.755444 | − | 0.655213i | \(-0.772579\pi\) | ||||
−0.755444 | + | 0.655213i | \(0.772579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.17157 | 0.364775 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.242641 | + | 0.242641i | 0.0170300 | + | 0.0170300i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.7574 | + | 4.58579i | 0.960856 | + | 0.320285i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.24264 | − | 4.24264i | 0.294884 | − | 0.294884i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 26.1421i | − | 1.80829i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.3137i | − | 1.19192i | −0.803012 | − | 0.595962i | \(-0.796771\pi\) | ||
0.803012 | − | 0.595962i | \(-0.203229\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.65685 | + | 1.65685i | −0.113526 | + | 0.113526i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.82843 | + | 13.6569i | 0.465695 | + | 0.931390i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.65685 | + | 1.65685i | 0.112475 | + | 0.112475i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5858 | 0.715321 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.9706 | 2.48691 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6569 | − | 12.6569i | −0.847566 | − | 0.847566i | 0.142263 | − | 0.989829i | \(-0.454562\pi\) |
−0.989829 | + | 0.142263i | \(0.954562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | + | 4.00000i | −0.200000 | + | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.65685 | + | 9.65685i | −0.640948 | + | 0.640948i | −0.950789 | − | 0.309841i | \(-0.899724\pi\) |
0.309841 | + | 0.950789i | \(0.399724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3431i | 0.815658i | 0.913058 | + | 0.407829i | \(0.133714\pi\) | ||||
−0.913058 | + | 0.407829i | \(0.866286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 7.65685i | − | 0.503784i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.07107 | − | 7.07107i | 0.463241 | − | 0.463241i | −0.436475 | − | 0.899716i | \(-0.643773\pi\) |
0.899716 | + | 0.436475i | \(0.143773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.6569 | + | 8.82843i | −1.15181 | + | 0.575903i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.65685 | − | 1.65685i | −0.107624 | − | 0.107624i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.3137 | 1.50804 | 0.754019 | − | 0.656852i | \(-0.228113\pi\) | ||||
0.754019 | + | 0.656852i | \(0.228113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.9706 | −1.60850 | −0.804248 | − | 0.594294i | \(-0.797431\pi\) | ||||
−0.804248 | + | 0.594294i | \(0.797431\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.53553 | − | 10.6066i | 0.225877 | − | 0.677631i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4853 | − | 16.4853i | 1.04893 | − | 1.04893i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 4.34315i | − | 0.275236i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.7574i | − | 0.742118i | −0.928609 | − | 0.371059i | \(-0.878995\pi\) | ||
0.928609 | − | 0.371059i | \(-0.121005\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.9706 | + | 22.9706i | −1.44415 | + | 1.44415i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.41421 | − | 16.2426i | 0.339051 | − | 1.01715i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.41421 | + | 7.41421i | 0.462486 | + | 0.462486i | 0.899469 | − | 0.436984i | \(-0.143953\pi\) |
−0.436984 | + | 0.899469i | \(0.643953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.17157 | −0.0727980 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.242641 | −0.0150191 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.5563 | + | 11.5563i | 0.712595 | + | 0.712595i | 0.967077 | − | 0.254482i | \(-0.0819051\pi\) |
−0.254482 | + | 0.967077i | \(0.581905\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | − | 4.00000i | 0.491436 | − | 0.245718i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.58579 | + | 2.58579i | −0.158248 | + | 0.158248i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 13.8995i | − | 0.847467i | −0.905787 | − | 0.423734i | \(-0.860719\pi\) | ||
0.905787 | − | 0.423734i | \(-0.139281\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.3431i | − | 0.992775i | −0.868101 | − | 0.496388i | \(-0.834659\pi\) | ||
0.868101 | − | 0.496388i | \(-0.165341\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.82843 | − | 4.82843i | 0.292230 | − | 0.292230i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.2426 | − | 21.6569i | 0.979468 | − | 1.30596i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8995 | − | 11.8995i | −0.714971 | − | 0.714971i | 0.252600 | − | 0.967571i | \(-0.418714\pi\) |
−0.967571 | + | 0.252600i | \(0.918714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.65685 | −0.0991933 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.8284 | 0.765280 | 0.382640 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382640 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.828427 | + | 0.828427i | 0.0492449 | + | 0.0492449i | 0.731300 | − | 0.682056i | \(-0.238914\pi\) |
−0.682056 | + | 0.731300i | \(0.738914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.82843 | − | 9.65685i | −0.286011 | − | 0.572023i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.48528 | + | 6.48528i | −0.382814 | + | 0.382814i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274i | 2.44867i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.928932i | 0.0544550i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000 | − | 4.00000i | 0.233682 | − | 0.233682i | −0.580545 | − | 0.814228i | \(-0.697161\pi\) |
0.814228 | + | 0.580545i | \(0.197161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | + | 1.00000i | 0.174667 | + | 0.0582223i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.82843 | + | 3.82843i | 0.222148 | + | 0.222148i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −28.9706 | −1.67541 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.65685 | −0.556612 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.82843 | − | 3.82843i | −0.219937 | − | 0.219937i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.72792 | + | 2.24264i | 0.385240 | + | 0.128413i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.9706 | + | 10.9706i | −0.626123 | + | 0.626123i | −0.947090 | − | 0.320967i | \(-0.895992\pi\) |
0.320967 | + | 0.947090i | \(0.395992\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.7279i | 0.951618i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000i | 0.453638i | 0.973937 | + | 0.226819i | \(0.0728326\pi\) | ||||
−0.973937 | + | 0.226819i | \(0.927167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.82843 | − | 7.82843i | 0.442489 | − | 0.442489i | −0.450359 | − | 0.892848i | \(-0.648704\pi\) |
0.892848 | + | 0.450359i | \(0.148704\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.41421 | − | 2.82843i | −0.0796819 | − | 0.159364i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.75736 | + | 3.75736i | 0.211034 | + | 0.211034i | 0.804707 | − | 0.593672i | \(-0.202323\pi\) |
−0.593672 | + | 0.804707i | \(0.702323\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.31371 | 0.0735536 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.31371 | −0.519841 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.1421 | + | 26.1421i | 1.45459 | + | 1.45459i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.8995 | − | 3.41421i | 1.32571 | − | 0.189386i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.2426 | + | 14.2426i | −0.787620 | + | 0.787620i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 12.4853i | − | 0.688336i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.48528i | − | 0.136603i | −0.997665 | − | 0.0683017i | \(-0.978242\pi\) | ||
0.997665 | − | 0.0683017i | \(-0.0217580\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.585786 | − | 0.585786i | 0.0321009 | − | 0.0321009i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.3431 | + | 5.17157i | −0.565106 | + | 0.282553i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4853 | − | 11.4853i | −0.625643 | − | 0.625643i | 0.321326 | − | 0.946969i | \(-0.395872\pi\) |
−0.946969 | + | 0.321326i | \(0.895872\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.17157 | 0.389506 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.97056 | 0.485783 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.24264 | + | 12.7279i | −0.228416 | + | 0.685248i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.82843 | − | 6.82843i | 0.366569 | − | 0.366569i | −0.499655 | − | 0.866224i | \(-0.666540\pi\) |
0.866224 | + | 0.499655i | \(0.166540\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.48528i | 0.133034i | 0.997785 | + | 0.0665170i | \(0.0211887\pi\) | ||||
−0.997785 | + | 0.0665170i | \(0.978811\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.82843i | 0.257722i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.07107 | − | 7.07107i | 0.376355 | − | 0.376355i | −0.493430 | − | 0.869785i | \(-0.664257\pi\) |
0.869785 | + | 0.493430i | \(0.164257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.65685 | − | 4.97056i | 0.0879367 | − | 0.263810i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.65685 | + | 7.65685i | 0.405244 | + | 0.405244i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.79899 | −0.200503 | −0.100252 | − | 0.994962i | \(-0.531965\pi\) | ||||
−0.100252 | + | 0.994962i | \(0.531965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.31371 | 0.227037 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.9497 | − | 12.9497i | −0.679685 | − | 0.679685i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.1716 | + | 10.5858i | −1.10817 | + | 0.554085i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.82843 | + | 9.82843i | −0.513040 | + | 0.513040i | −0.915457 | − | 0.402417i | \(-0.868170\pi\) |
0.402417 | + | 0.915457i | \(0.368170\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.48528i | − | 0.337610i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.65685i | 0.293689i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.58579 | − | 2.58579i | 0.133887 | − | 0.133887i | −0.636987 | − | 0.770874i | \(-0.719820\pi\) |
0.770874 | + | 0.636987i | \(0.219820\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.00000 | − | 11.0000i | 0.103280 | − | 0.568038i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.828427 | + | 0.828427i | 0.0426662 | + | 0.0426662i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.2843 | −1.14467 | −0.572333 | − | 0.820021i | \(-0.693962\pi\) | ||||
−0.572333 | + | 0.820021i | \(0.693962\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5858 | −0.542326 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.89949 | + | 3.89949i | 0.199255 | + | 0.199255i | 0.799681 | − | 0.600426i | \(-0.205002\pi\) |
−0.600426 | + | 0.799681i | \(0.705002\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.65685 | + | 15.3137i | 0.390229 | + | 0.780459i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.82843 | − | 4.82843i | 0.245443 | − | 0.245443i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 19.7574i | − | 1.00174i | −0.865523 | − | 0.500869i | \(-0.833014\pi\) | ||
0.865523 | − | 0.500869i | \(-0.166986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 45.9411i | − | 2.32334i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.4853 | + | 15.4853i | −0.781129 | + | 0.781129i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.97056 | + | 1.65685i | 0.250096 | + | 0.0833654i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.10051 | − | 6.10051i | −0.306176 | − | 0.306176i | 0.537248 | − | 0.843424i | \(-0.319464\pi\) |
−0.843424 | + | 0.537248i | \(0.819464\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.82843 | 0.341849 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.343146 | −0.0171359 | −0.00856794 | − | 0.999963i | \(-0.502727\pi\) | ||||
−0.00856794 | + | 0.999963i | \(0.502727\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.65685 | + | 5.65685i | 0.281788 | + | 0.281788i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.12132 | + | 0.707107i | 0.105409 | + | 0.0351364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.17157 | + | 3.17157i | −0.157209 | + | 0.157209i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 29.9411i | − | 1.48049i | −0.672335 | − | 0.740247i | \(-0.734709\pi\) | ||
0.672335 | − | 0.740247i | \(-0.265291\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.48528i | − | 0.122590i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.41421 | + | 1.41421i | −0.0695889 | + | 0.0695889i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.34315 | + | 8.68629i | 0.213197 | + | 0.426393i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.89949 | − | 5.89949i | −0.288900 | − | 0.288900i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.7574 | −0.965210 | −0.482605 | − | 0.875838i | \(-0.660309\pi\) | ||||
−0.482605 | + | 0.875838i | \(0.660309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.24264 | + | 6.24264i | 0.303528 | + | 0.303528i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.41421 | + | 37.8995i | 0.262628 | + | 1.83840i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.17157 | + | 3.17157i | −0.153483 | + | 0.153483i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 26.1421i | − | 1.26215i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.1421i | 1.25922i | 0.776910 | + | 0.629611i | \(0.216786\pi\) | ||||
−0.776910 | + | 0.629611i | \(0.783214\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.7990 | + | 14.7990i | −0.711194 | + | 0.711194i | −0.966785 | − | 0.255591i | \(-0.917730\pi\) |
0.255591 | + | 0.966785i | \(0.417730\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.485281 | − | 0.242641i | 0.0232675 | − | 0.0116337i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.4853 | − | 20.4853i | −0.979944 | − | 0.979944i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.3137 | −1.20816 | −0.604079 | − | 0.796925i | \(-0.706459\pi\) | ||||
−0.604079 | + | 0.796925i | \(0.706459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | + | 24.0000i | 1.14027 | + | 1.14027i | 0.988400 | + | 0.151875i | \(0.0485310\pi\) |
0.151875 | + | 0.988400i | \(0.451469\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.58579 | − | 7.75736i | 0.122578 | − | 0.367734i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.6569 | + | 14.6569i | −0.693245 | + | 0.693245i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.1421i | − | 0.573023i | −0.958077 | − | 0.286511i | \(-0.907504\pi\) | ||
0.958077 | − | 0.286511i | \(-0.0924956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.1127i | 1.65339i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.2426 | + | 12.2426i | −0.575209 | + | 0.575209i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.82843 | + | 14.4853i | −0.226360 | + | 0.679080i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.31371 | − | 8.31371i | −0.388899 | − | 0.388899i | 0.485396 | − | 0.874295i | \(-0.338676\pi\) |
−0.874295 | + | 0.485396i | \(0.838676\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.65685 | −0.357391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.928932 | −0.0432647 | −0.0216323 | − | 0.999766i | \(-0.506886\pi\) | ||||
−0.0216323 | + | 0.999766i | \(0.506886\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8284 | + | 19.8284i | 0.921505 | + | 0.921505i | 0.997136 | − | 0.0756307i | \(-0.0240970\pi\) |
−0.0756307 | + | 0.997136i | \(0.524097\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.31371 | − | 1.65685i | 0.153670 | − | 0.0768348i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.41421 | + | 9.41421i | −0.435638 | + | 0.435638i | −0.890541 | − | 0.454903i | \(-0.849674\pi\) |
0.454903 | + | 0.890541i | \(0.349674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7.31371i | − | 0.337716i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2.00000i | − | 0.0921551i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.1421 | + | 26.1421i | −1.20202 | + | 1.20202i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.3137 | + | 14.4853i | 0.886174 | + | 0.664630i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.82843 | − | 2.82843i | −0.129505 | − | 0.129505i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.6274 | 1.76493 | 0.882466 | − | 0.470376i | \(-0.155882\pi\) | ||||
0.882466 | + | 0.470376i | \(0.155882\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.00000 | − | 6.00000i | −0.273009 | − | 0.273009i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.928932 | − | 1.85786i | −0.0421806 | − | 0.0843613i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.82843 | + | 9.82843i | −0.445369 | + | 0.445369i | −0.893811 | − | 0.448443i | \(-0.851979\pi\) |
0.448443 | + | 0.893811i | \(0.351979\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.34315i | − | 0.286847i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5.21320i | − | 0.235269i | −0.993057 | − | 0.117634i | \(-0.962469\pi\) | ||
0.993057 | − | 0.117634i | \(-0.0375311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.31371 | + | 1.31371i | −0.0591665 | + | 0.0591665i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.4853 | − | 3.82843i | −0.516225 | − | 0.172075i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.34315 | + | 2.34315i | 0.105104 | + | 0.105104i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.7990 | 1.15492 | 0.577461 | − | 0.816418i | \(-0.304044\pi\) | ||||
0.577461 | + | 0.816418i | \(0.304044\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | 0.268060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.2426 | − | 30.2426i | −1.34845 | − | 1.34845i | −0.887343 | − | 0.461109i | \(-0.847452\pi\) |
−0.461109 | − | 0.887343i | \(-0.652548\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.4853 | + | 3.82843i | 0.511088 | + | 0.170363i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.29289 | − | 7.29289i | 0.323889 | − | 0.323889i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 22.3848i | − | 0.992188i | −0.868269 | − | 0.496094i | \(-0.834767\pi\) | ||
0.868269 | − | 0.496094i | \(-0.165233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.9706i | − | 0.662259i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.41421 | + | 3.41421i | −0.150741 | + | 0.150741i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.7279 | − | 33.4558i | −0.737120 | − | 1.47424i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.7990 | − | 33.7990i | −1.48648 | − | 1.48648i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.65685 | −0.160518 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.82843 | −0.211537 | −0.105769 | − | 0.994391i | \(-0.533730\pi\) | ||||
−0.105769 | + | 0.994391i | \(0.533730\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9706 | + | 14.9706i | 0.654617 | + | 0.654617i | 0.954101 | − | 0.299484i | \(-0.0968146\pi\) |
−0.299484 | + | 0.954101i | \(0.596815\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.65685 | + | 4.24264i | 0.246885 | + | 0.185164i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.97056 | + | 8.97056i | −0.390764 | + | 0.390764i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000i | 0.565217i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.41421i | − | 0.0613716i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.1421 | + | 22.1421i | −0.959082 | + | 0.959082i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.6274 | − | 9.31371i | 0.805333 | − | 0.402667i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.8284 | + | 11.8284i | 0.510434 | + | 0.510434i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.0711 | 1.16603 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.14214 | 0.178084 | 0.0890422 | − | 0.996028i | \(-0.471619\pi\) | ||||
0.0890422 | + | 0.996028i | \(0.471619\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.2426 | + | 14.2426i | 0.611210 | + | 0.611210i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.2426 | − | 42.7279i | 0.610088 | − | 1.83026i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.9706 | + | 14.9706i | −0.640095 | + | 0.640095i | −0.950579 | − | 0.310484i | \(-0.899509\pi\) |
0.310484 | + | 0.950579i | \(0.399509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 3.17157i | − | 0.135359i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.17157i | 0.0499107i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.34315 | + | 2.34315i | −0.0996407 | + | 0.0996407i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.585786 | + | 1.75736i | −0.0248652 | + | 0.0745957i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.8284 | − | 14.8284i | −0.628301 | − | 0.628301i | 0.319340 | − | 0.947640i | \(-0.396539\pi\) |
−0.947640 | + | 0.319340i | \(0.896539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.9706 | −1.39451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 41.4558 | 1.75027 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.82843 | − | 2.82843i | −0.119204 | − | 0.119204i | 0.644988 | − | 0.764192i | \(-0.276862\pi\) |
−0.764192 | + | 0.644988i | \(0.776862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.3431 | + | 7.17157i | −0.603421 | + | 0.301710i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | + | 1.00000i | −0.0419961 | + | 0.0419961i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.3137i | 1.22889i | 0.788958 | + | 0.614447i | \(0.210621\pi\) | ||||
−0.788958 | + | 0.614447i | \(0.789379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.17157i | − | 0.132726i | −0.997796 | − | 0.0663631i | \(-0.978860\pi\) | ||
0.997796 | − | 0.0663631i | \(-0.0211396\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.828427 | − | 0.828427i | 0.0346080 | − | 0.0346080i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.24264 | − | 29.6985i | −0.176930 | − | 1.23851i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.2843 | + | 29.2843i | 1.21912 | + | 1.21912i | 0.967940 | + | 0.251180i | \(0.0808185\pi\) |
0.251180 | + | 0.967940i | \(0.419181\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.8995 | 0.577643 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.14214 | −0.254819 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.3137 | + | 15.3137i | 0.634229 | + | 0.634229i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.82843 | − | 9.65685i | −0.199631 | − | 0.399262i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.4142 | + | 29.4142i | −1.21405 | + | 1.21405i | −0.244373 | + | 0.969681i | \(0.578582\pi\) |
−0.969681 | + | 0.244373i | \(0.921418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000i | 0.329634i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.9706i | 0.862614i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.72792 | + | 6.72792i | −0.276283 | + | 0.276283i | −0.831623 | − | 0.555340i | \(-0.812588\pi\) |
0.555340 | + | 0.831623i | \(0.312588\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.9706 | − | 7.65685i | −0.941701 | − | 0.313900i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.0711 | − | 15.0711i | −0.616818 | − | 0.616818i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.7696 | −1.33893 | −0.669464 | − | 0.742845i | \(-0.733476\pi\) | ||||
−0.669464 | + | 0.742845i | \(0.733476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6569 | 0.801820 | 0.400910 | − | 0.916117i | \(-0.368694\pi\) | ||||
0.400910 | + | 0.916117i | \(0.368694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.65685 | + | 3.65685i | 0.148919 | + | 0.148919i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 38.8492 | + | 12.9497i | 1.57945 | + | 0.526482i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.3137 | − | 20.3137i | 0.824508 | − | 0.824508i | −0.162243 | − | 0.986751i | \(-0.551873\pi\) |
0.986751 | + | 0.162243i | \(0.0518728\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.343146i | 0.0139050i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 42.6274i | − | 1.72452i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.7279 | − | 28.7279i | 1.16031 | − | 1.16031i | 0.175902 | − | 0.984408i | \(-0.443716\pi\) |
0.984408 | − | 0.175902i | \(-0.0562842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.48528 | + | 12.9706i | 0.261512 | + | 0.523024i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.75736 | + | 3.75736i | 0.151266 | + | 0.151266i | 0.778683 | − | 0.627417i | \(-0.215888\pi\) |
−0.627417 | + | 0.778683i | \(0.715888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.2843 | −1.86032 | −0.930161 | − | 0.367152i | \(-0.880333\pi\) | ||||
−0.930161 | + | 0.367152i | \(0.880333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.00000 | 0.240772 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.65685 | + | 3.65685i | 0.146509 | + | 0.146509i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.4853 | − | 18.4853i | 0.738231 | − | 0.738231i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6.34315i | − | 0.252918i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 24.0000i | − | 0.955425i | −0.878516 | − | 0.477712i | \(-0.841466\pi\) | ||
0.878516 | − | 0.477712i | \(-0.158534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.2426 | − | 12.2426i | 0.486601 | − | 0.486601i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.1716 | − | 10.5858i | 0.840168 | − | 0.420084i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.0711 | + | 17.0711i | 0.676380 | + | 0.676380i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.34315 | −0.0926934 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.343146 | −0.0135534 | −0.00677672 | − | 0.999977i | \(-0.502157\pi\) | ||||
−0.00677672 | + | 0.999977i | \(0.502157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.3431 | − | 14.3431i | −0.565638 | − | 0.565638i | 0.365265 | − | 0.930904i | \(-0.380978\pi\) |
−0.930904 | + | 0.365265i | \(0.880978\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.82843 | + | 14.4853i | −0.190119 | + | 0.570357i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.5858 | − | 20.5858i | 0.809311 | − | 0.809311i | −0.175219 | − | 0.984530i | \(-0.556063\pi\) |
0.984530 | + | 0.175219i | \(0.0560633\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.65685i | 0.300558i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.34315i | 0.0918351i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.24264 | + | 4.24264i | −0.166027 | + | 0.166027i | −0.785231 | − | 0.619203i | \(-0.787456\pi\) |
0.619203 | + | 0.785231i | \(0.287456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.4853 | − | 46.4558i | 0.605060 | − | 1.81518i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.48528 | + | 7.48528i | 0.292029 | + | 0.292029i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3848 | −0.404533 | −0.202267 | − | 0.979330i | \(-0.564831\pi\) | ||||
−0.202267 | + | 0.979330i | \(0.564831\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.8284 | 0.810132 | 0.405066 | − | 0.914287i | \(-0.367249\pi\) | ||||
0.405066 | + | 0.914287i | \(0.367249\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.1421 | + | 26.1421i | 1.01528 | + | 1.01528i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.6569 | + | 6.82843i | −0.529590 | + | 0.264795i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.02944 | − | 1.02944i | 0.0398600 | − | 0.0398600i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 17.8995i | − | 0.692034i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.1716i | 0.662901i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.82843 | + | 7.82843i | −0.301764 | + | 0.301764i | −0.841704 | − | 0.539940i | \(-0.818447\pi\) |
0.539940 | + | 0.841704i | \(0.318447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.94975 | + | 0.707107i | −0.190516 | + | 0.0272166i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.2426 | + | 28.2426i | 1.08545 | + | 1.08545i | 0.995990 | + | 0.0894627i | \(0.0285150\pi\) |
0.0894627 | + | 0.995990i | \(0.471485\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.31371 | 0.0504155 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.6569 | −0.523332 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.2426 | + | 12.2426i | 0.468452 | + | 0.468452i | 0.901413 | − | 0.432961i | \(-0.142531\pi\) |
−0.432961 | + | 0.901413i | \(0.642531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.48528 | + | 4.97056i | 0.0949577 | + | 0.189915i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.72792 | + | 8.72792i | −0.332991 | + | 0.332991i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.3137i | 0.735794i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 7.85786i | − | 0.298927i | −0.988767 | − | 0.149464i | \(-0.952245\pi\) | ||
0.988767 | − | 0.149464i | \(-0.0477547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.41421 | − | 5.41421i | 0.205669 | − | 0.205669i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.6985 | + | 5.89949i | 0.671342 | + | 0.223781i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.1127 | − | 35.1127i | −1.32999 | − | 1.32999i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.0000 | 0.378235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.3553 | −1.18427 | −0.592137 | − | 0.805837i | \(-0.701716\pi\) | ||||
−0.592137 | + | 0.805837i | \(0.701716\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.82843 | − | 2.82843i | −0.106676 | − | 0.106676i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.7279 | − | 6.24264i | −0.705334 | − | 0.235111i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.41421 | + | 5.41421i | −0.203622 | + | 0.203622i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 14.2843i | − | 0.536457i | −0.963355 | − | 0.268229i | \(-0.913562\pi\) | ||
0.963355 | − | 0.268229i | \(-0.0864382\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2.34315i | − | 0.0878748i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.02944 | − | 7.02944i | 0.263254 | − | 0.263254i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.1421 | + | 52.2843i | 0.977660 | + | 1.95532i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.4853 | + | 16.4853i | 0.615654 | + | 0.615654i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.2843 | −0.607301 | −0.303650 | − | 0.952784i | \(-0.598205\pi\) | ||||
−0.303650 | + | 0.952784i | \(0.598205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.6569 | 0.881027 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.6569 | − | 17.6569i | −0.656665 | − | 0.656665i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.727922 | + | 0.970563i | −0.0270343 | + | 0.0360458i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.1421 | − | 15.1421i | 0.561591 | − | 0.561591i | −0.368168 | − | 0.929759i | \(-0.620015\pi\) |
0.929759 | + | 0.368168i | \(0.120015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 52.2843i | − | 1.93380i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.75736 | + | 9.75736i | −0.360396 | + | 0.360396i | −0.863959 | − | 0.503563i | \(-0.832022\pi\) |
0.503563 | + | 0.863959i | \(0.332022\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.0000 | − | 5.00000i | 0.368856 | − | 0.184428i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.7990 | − | 19.7990i | −0.729305 | − | 0.729305i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.51472 | −0.0557198 | −0.0278599 | − | 0.999612i | \(-0.508869\pi\) | ||||
−0.0278599 | + | 0.999612i | \(0.508869\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.3137 | 0.856450 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.4142 | − | 27.4142i | −1.00573 | − | 1.00573i | −0.999983 | − | 0.00574646i | \(-0.998171\pi\) |
−0.00574646 | − | 0.999983i | \(-0.501829\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.6569 | − | 43.9706i | 0.536986 | − | 1.61096i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.07107 | − | 3.07107i | 0.112364 | − | 0.112364i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.1716i | 0.481279i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.6569i | 1.22816i | 0.789245 | + | 0.614078i | \(0.210472\pi\) | ||||
−0.789245 | + | 0.614078i | \(0.789528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.31371 | − | 8.31371i | 0.302968 | − | 0.302968i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.2426 | − | 36.7279i | 0.445555 | − | 1.33667i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5563 | + | 33.5563i | 1.21963 | + | 1.21963i | 0.967763 | + | 0.251863i | \(0.0810434\pi\) |
0.251863 | + | 0.967763i | \(0.418957\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −32.4853 | −1.17914 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.4853 | 1.25009 | 0.625045 | − | 0.780589i | \(-0.285081\pi\) | ||||
0.625045 | + | 0.780589i | \(0.285081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.1421 | + | 20.1421i | 0.729194 | + | 0.729194i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.3137 | − | 7.65685i | 0.553668 | − | 0.276834i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.82843 | + | 4.82843i | −0.174344 | + | 0.174344i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 39.6569i | − | 1.43006i | −0.699092 | − | 0.715031i | \(-0.746412\pi\) | ||
0.699092 | − | 0.715031i | \(-0.253588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.4853i | 0.377618i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.0711 | + | 15.0711i | −0.542069 | + | 0.542069i | −0.924135 | − | 0.382066i | \(-0.875213\pi\) |
0.382066 | + | 0.924135i | \(0.375213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.97056 | + | 6.62742i | −0.178548 | + | 0.238064i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.828427 | − | 0.828427i | −0.0297197 | − | 0.0297197i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.3137 | −1.12193 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6863 | 0.453951 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.171573 | − | 0.171573i | −0.00613151 | − | 0.00613151i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.00000 | + | 4.00000i | 0.0713831 | + | 0.142766i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.8284 | − | 20.8284i | 0.742453 | − | 0.742453i | −0.230596 | − | 0.973050i | \(-0.574068\pi\) |
0.973050 | + | 0.230596i | \(0.0740677\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.3431i | 0.581831i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 10.1421i | − | 0.360613i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.8284 | + | 10.8284i | −0.384529 | + | 0.384529i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.48528 | + | 2.82843i | 0.300942 | + | 0.100314i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.75736 | − | 3.75736i | −0.133092 | − | 0.133092i | 0.637422 | − | 0.770515i | \(-0.280001\pi\) |
−0.770515 | + | 0.637422i | \(0.780001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 67.5980 | 2.39144 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.65685 | −0.129209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.5269 | − | 40.5269i | −1.43016 | − | 1.43016i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0000 | + | 6.00000i | 0.634417 | + | 0.211472i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.82843 | − | 9.82843i | 0.345977 | − | 0.345977i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.9706i | 0.385704i | 0.981228 | + | 0.192852i | \(0.0617738\pi\) | ||||
−0.981228 | + | 0.192852i | \(0.938226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000i | 1.05344i | 0.850038 | + | 0.526721i | \(0.176579\pi\) | ||||
−0.850038 | + | 0.526721i | \(0.823421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.5563 | − | 11.5563i | 0.405299 | − | 0.405299i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.34315 | + | 12.6863i | 0.222191 | + | 0.444381i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.3137 | − | 23.3137i | −0.815643 | − | 0.815643i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.82843 | 0.238605 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.2132 | −0.879947 | −0.439973 | − | 0.898011i | \(-0.645012\pi\) | ||||
−0.439973 | + | 0.898011i | \(0.645012\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.6569 | − | 28.6569i | −0.998915 | − | 0.998915i | 0.00108427 | − | 0.999999i | \(-0.499655\pi\) |
−0.999999 | + | 0.00108427i | \(0.999655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.7990 | − | 3.82843i | 0.933021 | − | 0.133289i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.4558 | − | 37.4558i | 1.30247 | − | 1.30247i | 0.375744 | − | 0.926724i | \(-0.377387\pi\) |
0.926724 | − | 0.375744i | \(-0.122613\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.7990i | 0.896036i | 0.894025 | + | 0.448018i | \(0.147870\pi\) | ||||
−0.894025 | + | 0.448018i | \(0.852130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 16.8284i | − | 0.583772i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.0711 | + | 27.0711i | −0.937957 | + | 0.937957i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0000 | + | 6.00000i | −0.415277 | + | 0.207639i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.17157 | − | 1.17157i | −0.0404955 | − | 0.0404955i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.1127 | 0.797939 | 0.398969 | − | 0.916964i | \(-0.369368\pi\) | ||||
0.398969 | + | 0.916964i | \(0.369368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9411 | 0.997970 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.07107 | + | 9.07107i | 0.312424 | + | 0.312424i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.29289 | + | 21.8787i | −0.250883 | + | 0.752649i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3137 | + | 18.3137i | −0.629266 | + | 0.629266i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.17157i | 0.0402083i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.97056i | 0.170389i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.5563 | − | 19.5563i | 0.669597 | − | 0.669597i | −0.288026 | − | 0.957623i | \(-0.592999\pi\) |
0.957623 | + | 0.288026i | \(0.0929989\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.41421 | − | 10.2426i | 0.116764 | − | 0.350291i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.0711 | − | 31.0711i | −1.06137 | − | 1.06137i | −0.997990 | − | 0.0633779i | \(-0.979813\pi\) |
−0.0633779 | − | 0.997990i | \(-0.520187\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.0000 | 1.70598 | 0.852989 | − | 0.521929i | \(-0.174787\pi\) | ||||
0.852989 | + | 0.521929i | \(0.174787\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.17157 | −0.312566 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.61522 | + | 1.61522i | 0.0549829 | + | 0.0549829i | 0.734064 | − | 0.679081i | \(-0.237621\pi\) |
−0.679081 | + | 0.734064i | \(0.737621\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.31371 | − | 3.65685i | 0.248674 | − | 0.124337i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.4350 | + | 29.4350i | −0.999666 | + | 0.999666i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.6863i | 0.430353i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 24.9706i | − | 0.846095i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.656854 | + | 0.656854i | −0.0222311 | + | 0.0222311i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.5563 | − | 2.82843i | −0.525901 | − | 0.0956183i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.92893 | + | 4.92893i | 0.166438 | + | 0.166438i | 0.785412 | − | 0.618974i | \(-0.212451\pi\) |
−0.618974 | + | 0.785412i | \(0.712451\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.65685 | 0.190801 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.31371 | 0.0442600 | 0.0221300 | − | 0.999755i | \(-0.492955\pi\) | ||||
0.0221300 | + | 0.999755i | \(0.492955\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.4853 | − | 16.4853i | −0.554774 | − | 0.554774i | 0.373041 | − | 0.927815i | \(-0.378315\pi\) |
−0.927815 | + | 0.373041i | \(0.878315\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.41421 | + | 2.82843i | 0.0475383 | + | 0.0950765i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.7279 | − | 32.7279i | 1.09890 | − | 1.09890i | 0.104356 | − | 0.994540i | \(-0.466722\pi\) |
0.994540 | − | 0.104356i | \(-0.0332782\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.9706i | 0.502097i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.41421i | 0.181383i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.1421 | − | 30.1421i | 1.00867 | − | 1.00867i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.4853 | − | 11.8284i | −1.18614 | − | 0.395381i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.4853 | − | 20.4853i | −0.683984 | − | 0.683984i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.402020 | −0.0134081 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.6274 | −1.02035 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.82843 | − | 6.82843i | −0.227236 | − | 0.227236i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42.7279 | − | 14.2426i | −1.42032 | − | 0.473441i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.5147 | + | 23.5147i | −0.780793 | + | 0.780793i | −0.979965 | − | 0.199171i | \(-0.936175\pi\) |
0.199171 | + | 0.979965i | \(0.436175\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 5.41421i | − | 0.179578i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.48528i | 0.148604i | 0.997236 | + | 0.0743020i | \(0.0236729\pi\) | ||||
−0.997236 | + | 0.0743020i | \(0.976327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.6274 | + | 16.6274i | −0.550287 | + | 0.550287i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.17157 | + | 6.34315i | 0.104849 | + | 0.209698i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.8995 | + | 21.8995i | 0.723185 | + | 0.723185i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.9411 | −0.723771 | −0.361885 | − | 0.932223i | \(-0.617867\pi\) | ||||
−0.361885 | + | 0.932223i | \(0.617867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.5147 | −0.511227 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.00000 | + | 8.00000i | 0.263323 | + | 0.263323i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.585786 | − | 4.10051i | −0.0192605 | − | 0.134824i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.8284 | + | 11.8284i | −0.388497 | + | 0.388497i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 10.2010i | − | 0.334684i | −0.985899 | − | 0.167342i | \(-0.946482\pi\) | ||
0.985899 | − | 0.167342i | \(-0.0535185\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.1421i | 0.791227i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.65685 | + | 5.65685i | −0.185197 | + | 0.185197i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −82.9117 | + | 41.4558i | −2.71150 | + | 1.35575i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.31371 | + | 4.31371i | 0.140923 | + | 0.140923i | 0.774049 | − | 0.633126i | \(-0.218229\pi\) |
−0.633126 | + | 0.774049i | \(0.718229\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.0711 | 0.361291 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.9289 | 0.812660 | 0.406330 | − | 0.913726i | \(-0.366808\pi\) | ||||
0.406330 | + | 0.913726i | \(0.366808\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.5147 | + | 27.5147i | 0.896003 | + | 0.896003i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | − | 3.00000i | 0.0325300 | − | 0.0975900i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.9706 | + | 16.9706i | −0.551469 | + | 0.551469i | −0.926865 | − | 0.375396i | \(-0.877507\pi\) |
0.375396 | + | 0.926865i | \(0.377507\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 51.1127i | − | 1.65919i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.31371i | 0.172309i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.0711 | − | 17.0711i | 0.552986 | − | 0.552986i | −0.374315 | − | 0.927301i | \(-0.622122\pi\) |
0.927301 | + | 0.374315i | \(0.122122\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.828427 | + | 2.48528i | −0.0268073 | + | 0.0804218i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.928932 | + | 0.928932i | 0.0300281 | + | 0.0300281i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.51472 | −0.113496 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.2548 | 0.911446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.58579 | − | 6.58579i | −0.212224 | − | 0.212224i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.7990 | + | 13.8995i | −0.894881 | + | 0.447441i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.34315 | + | 1.34315i | −0.0431927 | + | 0.0431927i | −0.728373 | − | 0.685181i | \(-0.759723\pi\) |
0.685181 | + | 0.728373i | \(0.259723\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.9706i | 1.18767i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 56.0416i | 1.79846i | 0.437475 | + | 0.899231i | \(0.355873\pi\) | ||||
−0.437475 | + | 0.899231i | \(0.644127\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.34315 | + | 8.34315i | −0.267469 | + | 0.267469i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.3137 | + | 14.4853i | 0.618534 | + | 0.463900i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.0416 | + | 20.0416i | 0.641189 | + | 0.641189i | 0.950848 | − | 0.309659i | \(-0.100215\pi\) |
−0.309659 | + | 0.950848i | \(0.600215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.7990 | 0.632778 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.1421 | −0.643089 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.8995 | + | 31.8995i | 1.01744 | + | 1.01744i | 0.999845 | + | 0.0175906i | \(0.00559955\pi\) |
0.0175906 | + | 0.999845i | \(0.494400\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.9706 | − | 41.9411i | −0.668178 | − | 1.33636i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.82843 | − | 8.82843i | 0.281012 | − | 0.281012i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.9706i | 1.30279i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.9706i | 1.49207i | 0.665907 | + | 0.746035i | \(0.268045\pi\) | ||||
−0.665907 | + | 0.746035i | \(0.731955\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.75736 | − | 1.75736i | 0.0557681 | − | 0.0557681i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 45.2132 | + | 15.0711i | 1.43335 | + | 0.477785i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.55635 | + | 5.55635i | 0.175971 | + | 0.175971i | 0.789597 | − | 0.613626i | \(-0.210290\pi\) |
−0.613626 | + | 0.789597i | \(0.710290\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.828427 | 0.0262103 |
(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 | 480.2.w.b.127.2 | yes | 4 | |
3.2 | odd | 2 | 1440.2.x.n.127.2 | 4 | |||
4.3 | odd | 2 | 480.2.w.a.127.1 | ✓ | 4 | ||
5.2 | odd | 4 | 2400.2.w.d.2143.2 | 4 | |||
5.3 | odd | 4 | 480.2.w.a.223.1 | yes | 4 | ||
5.4 | even | 2 | 2400.2.w.c.607.1 | 4 | |||
8.3 | odd | 2 | 960.2.w.a.127.2 | 4 | |||
8.5 | even | 2 | 960.2.w.b.127.1 | 4 | |||
12.11 | even | 2 | 1440.2.x.m.127.2 | 4 | |||
15.8 | even | 4 | 1440.2.x.m.703.2 | 4 | |||
20.3 | even | 4 | inner | 480.2.w.b.223.2 | yes | 4 | |
20.7 | even | 4 | 2400.2.w.c.2143.1 | 4 | |||
20.19 | odd | 2 | 2400.2.w.d.607.2 | 4 | |||
40.3 | even | 4 | 960.2.w.b.703.1 | 4 | |||
40.13 | odd | 4 | 960.2.w.a.703.2 | 4 | |||
60.23 | odd | 4 | 1440.2.x.n.703.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.2.w.a.127.1 | ✓ | 4 | 4.3 | odd | 2 | ||
480.2.w.a.223.1 | yes | 4 | 5.3 | odd | 4 | ||
480.2.w.b.127.2 | yes | 4 | 1.1 | even | 1 | trivial | |
480.2.w.b.223.2 | yes | 4 | 20.3 | even | 4 | inner | |
960.2.w.a.127.2 | 4 | 8.3 | odd | 2 | |||
960.2.w.a.703.2 | 4 | 40.13 | odd | 4 | |||
960.2.w.b.127.1 | 4 | 8.5 | even | 2 | |||
960.2.w.b.703.1 | 4 | 40.3 | even | 4 | |||
1440.2.x.m.127.2 | 4 | 12.11 | even | 2 | |||
1440.2.x.m.703.2 | 4 | 15.8 | even | 4 | |||
1440.2.x.n.127.2 | 4 | 3.2 | odd | 2 | |||
1440.2.x.n.703.2 | 4 | 60.23 | odd | 4 | |||
2400.2.w.c.607.1 | 4 | 5.4 | even | 2 | |||
2400.2.w.c.2143.1 | 4 | 20.7 | even | 4 | |||
2400.2.w.d.607.2 | 4 | 20.19 | odd | 2 | |||
2400.2.w.d.2143.2 | 4 | 5.2 | odd | 4 |