Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(406,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.406");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.k (of order \(3\), 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: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 285) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 676.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.676 |
Dual form | 855.2.k.a.406.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.707107 | + | 1.22474i | 0.258819 | + | 0.965926i | \(0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | − | 1.73205i | −0.316228 | − | 0.547723i | ||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 1.73205i | −0.277350 | − | 0.480384i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | 2.00000 | − | 3.46410i | 0.534522 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | + | 4.33013i | 0.114708 | + | 0.993399i | ||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | + | 3.46410i | 0.377964 | + | 0.654654i | ||||
\(29\) | −2.50000 | − | 4.33013i | −0.464238 | − | 0.804084i | 0.534928 | − | 0.844897i | \(-0.320339\pi\) |
−0.999167 | + | 0.0408130i | \(0.987005\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.00000 | 1.61645 | 0.808224 | − | 0.588875i | \(-0.200429\pi\) | ||||
0.808224 | + | 0.588875i | \(0.200429\pi\) | |||||||
\(32\) | 4.00000 | + | 6.92820i | 0.707107 | + | 1.22474i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | + | 3.46410i | 0.342997 | + | 0.594089i | ||||
\(35\) | 1.00000 | − | 1.73205i | 0.169031 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | −8.00000 | − | 3.46410i | −1.29777 | − | 0.561951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | − | 5.19615i | 0.468521 | − | 0.811503i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | − | 8.66025i | 0.762493 | − | 1.32068i | −0.179069 | − | 0.983836i | \(-0.557309\pi\) |
0.941562 | − | 0.336840i | \(-0.109358\pi\) | |||||||
\(44\) | 1.00000 | + | 1.73205i | 0.150756 | + | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 2.00000 | 0.282843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | + | 3.46410i | −0.277350 | + | 0.480384i | ||||
\(53\) | −1.00000 | − | 1.73205i | −0.137361 | − | 0.237915i | 0.789136 | − | 0.614218i | \(-0.210529\pi\) |
−0.926497 | + | 0.376303i | \(0.877195\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.500000 | − | 0.866025i | 0.0674200 | − | 0.116775i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.0000 | 1.31306 | ||||||||
\(59\) | 3.50000 | − | 6.06218i | 0.455661 | − | 0.789228i | −0.543065 | − | 0.839691i | \(-0.682736\pi\) |
0.998726 | + | 0.0504625i | \(0.0160695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | −9.00000 | + | 15.5885i | −1.14300 | + | 1.97974i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | − | 6.92820i | −0.488678 | − | 0.846415i | 0.511237 | − | 0.859440i | \(-0.329187\pi\) |
−0.999915 | + | 0.0130248i | \(0.995854\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.00000 | + | 3.46410i | 0.239046 | + | 0.414039i | ||||
\(71\) | 1.50000 | − | 2.59808i | 0.178017 | − | 0.308335i | −0.763184 | − | 0.646181i | \(-0.776365\pi\) |
0.941201 | + | 0.337846i | \(0.109698\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | − | 1.73205i | 0.117041 | − | 0.202721i | −0.801553 | − | 0.597924i | \(-0.795992\pi\) |
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | 6.00000 | − | 10.3923i | 0.697486 | − | 1.20808i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.00000 | − | 5.19615i | 0.802955 | − | 0.596040i | ||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50000 | − | 9.52628i | 0.618798 | − | 1.07179i | −0.370907 | − | 0.928670i | \(-0.620953\pi\) |
0.989705 | − | 0.143120i | \(-0.0457135\pi\) | |||||||
\(80\) | 2.00000 | + | 3.46410i | 0.223607 | + | 0.387298i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.00000 | + | 10.3923i | 0.662589 | + | 1.14764i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | + | 1.73205i | 0.108465 | + | 0.187867i | ||||
\(86\) | 10.0000 | + | 17.3205i | 1.07833 | + | 1.86772i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.50000 | + | 12.9904i | 0.794998 | + | 1.37698i | 0.922840 | + | 0.385183i | \(0.125862\pi\) |
−0.127842 | + | 0.991795i | \(0.540805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 3.46410i | 0.209657 | + | 0.363137i | ||||
\(92\) | −4.00000 | + | 6.92820i | −0.417029 | + | 0.722315i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | − | 1.73205i | −0.410391 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00000 | + | 6.92820i | −0.406138 | + | 0.703452i | −0.994453 | − | 0.105180i | \(-0.966458\pi\) |
0.588315 | + | 0.808632i | \(0.299792\pi\) | |||||||
\(98\) | 3.00000 | − | 5.19615i | 0.303046 | − | 0.524891i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | + | 1.73205i | −0.100000 | + | 0.173205i | ||||
\(101\) | −3.50000 | − | 6.06218i | −0.348263 | − | 0.603209i | 0.637678 | − | 0.770303i | \(-0.279895\pi\) |
−0.985941 | + | 0.167094i | \(0.946562\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00000 | 0.388514 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.50000 | + | 16.4545i | −0.909935 | + | 1.57605i | −0.0957826 | + | 0.995402i | \(0.530535\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 1.00000 | + | 1.73205i | 0.0953463 | + | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | + | 6.92820i | −0.377964 | + | 0.654654i | ||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | −5.00000 | + | 8.66025i | −0.464238 | + | 0.804084i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.00000 | + | 12.1244i | 0.644402 | + | 1.11614i | ||||
\(119\) | −2.00000 | + | 3.46410i | −0.183340 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −14.0000 | −1.26750 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.00000 | − | 15.5885i | −0.808224 | − | 1.39988i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | − | 3.46410i | −0.177471 | − | 0.307389i | 0.763542 | − | 0.645758i | \(-0.223458\pi\) |
−0.941014 | + | 0.338368i | \(0.890125\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.00000 | + | 3.46410i | −0.175412 | + | 0.303822i | ||||
\(131\) | 8.00000 | − | 13.8564i | 0.698963 | − | 1.21064i | −0.269863 | − | 0.962899i | \(-0.586978\pi\) |
0.968826 | − | 0.247741i | \(-0.0796882\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | − | 8.66025i | −0.0867110 | − | 0.750939i | ||||
\(134\) | 16.0000 | 1.38219 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | − | 5.19615i | −0.256307 | − | 0.443937i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | − | 17.3205i | −0.848189 | − | 1.46911i | −0.882823 | − | 0.469706i | \(-0.844360\pi\) |
0.0346338 | − | 0.999400i | \(-0.488974\pi\) | |||||||
\(140\) | −4.00000 | −0.338062 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00000 | + | 5.19615i | 0.251754 | + | 0.436051i | ||||
\(143\) | 1.00000 | + | 1.73205i | 0.0836242 | + | 0.144841i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.00000 | 0.415227 | ||||||||
\(146\) | 2.00000 | + | 3.46410i | 0.165521 | + | 0.286691i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | + | 10.3923i | 0.493197 | + | 0.854242i | ||||
\(149\) | 4.50000 | − | 7.79423i | 0.368654 | − | 0.638528i | −0.620701 | − | 0.784047i | \(-0.713152\pi\) |
0.989355 | + | 0.145519i | \(0.0464853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | −0.244137 | −0.122068 | − | 0.992522i | \(-0.538953\pi\) | ||||
−0.122068 | + | 0.992522i | \(0.538953\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.00000 | + | 3.46410i | −0.161165 | + | 0.279145i | ||||
\(155\) | −4.50000 | + | 7.79423i | −0.361449 | + | 0.626048i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | + | 10.3923i | −0.478852 | + | 0.829396i | −0.999706 | − | 0.0242497i | \(-0.992280\pi\) |
0.520854 | + | 0.853646i | \(0.325614\pi\) | |||||||
\(158\) | 11.0000 | + | 19.0526i | 0.875113 | + | 1.51574i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.00000 | −0.632456 | ||||||||
\(161\) | 4.00000 | + | 6.92820i | 0.315244 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.0000 | −1.40987 | −0.704934 | − | 0.709273i | \(-0.749024\pi\) | ||||
−0.704934 | + | 0.709273i | \(0.749024\pi\) | |||||||
\(164\) | −12.0000 | −0.937043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | − | 10.3923i | 0.465690 | − | 0.806599i | ||||
\(167\) | −1.00000 | − | 1.73205i | −0.0773823 | − | 0.134030i | 0.824737 | − | 0.565516i | \(-0.191323\pi\) |
−0.902120 | + | 0.431486i | \(0.857990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −20.0000 | −1.52499 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | + | 1.73205i | 0.0755929 | + | 0.130931i | ||||
\(176\) | −2.00000 | + | 3.46410i | −0.150756 | + | 0.261116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −30.0000 | −2.24860 | ||||||||
\(179\) | 3.00000 | 0.224231 | 0.112115 | − | 0.993695i | \(-0.464237\pi\) | ||||
0.112115 | + | 0.993695i | \(0.464237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.00000 | − | 8.66025i | −0.371647 | − | 0.643712i | 0.618172 | − | 0.786043i | \(-0.287874\pi\) |
−0.989819 | + | 0.142331i | \(0.954540\pi\) | |||||||
\(182\) | −8.00000 | −0.592999 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.00000 | + | 1.73205i | −0.0731272 | + | 0.126660i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.00000 | − | 5.19615i | 0.507833 | − | 0.376969i | ||||
\(191\) | −15.0000 | −1.08536 | −0.542681 | − | 0.839939i | \(-0.682591\pi\) | ||||
−0.542681 | + | 0.839939i | \(0.682591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0000 | − | 22.5167i | 0.935760 | − | 1.62078i | 0.162488 | − | 0.986710i | \(-0.448048\pi\) |
0.773272 | − | 0.634074i | \(-0.218619\pi\) | |||||||
\(194\) | −8.00000 | − | 13.8564i | −0.574367 | − | 0.994832i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | + | 5.19615i | 0.214286 | + | 0.371154i | ||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | + | 2.59808i | 0.106332 | + | 0.184173i | 0.914282 | − | 0.405079i | \(-0.132756\pi\) |
−0.807950 | + | 0.589252i | \(0.799423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.0000 | 0.985037 | ||||||||
\(203\) | 5.00000 | + | 8.66025i | 0.350931 | + | 0.607831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | 8.00000 | − | 13.8564i | 0.557386 | − | 0.965422i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.00000 | −0.554700 | ||||||||
\(209\) | −0.500000 | − | 4.33013i | −0.0345857 | − | 0.299521i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5000 | − | 23.3827i | 0.929378 | − | 1.60973i | 0.145014 | − | 0.989430i | \(-0.453677\pi\) |
0.784364 | − | 0.620301i | \(-0.212990\pi\) | |||||||
\(212\) | −2.00000 | + | 3.46410i | −0.137361 | + | 0.237915i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.00000 | + | 8.66025i | 0.340997 | + | 0.590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.0000 | −1.22192 | ||||||||
\(218\) | −19.0000 | − | 32.9090i | −1.28684 | − | 2.22888i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.00000 | − | 10.3923i | 0.401790 | − | 0.695920i | −0.592152 | − | 0.805826i | \(-0.701722\pi\) |
0.993942 | + | 0.109906i | \(0.0350549\pi\) | |||||||
\(224\) | −8.00000 | − | 13.8564i | −0.534522 | − | 0.925820i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.0000 | + | 17.3205i | −0.665190 | + | 1.15214i | ||||
\(227\) | −18.0000 | −1.19470 | −0.597351 | − | 0.801980i | \(-0.703780\pi\) | ||||
−0.597351 | + | 0.801980i | \(0.703780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0000 | −0.726900 | −0.363450 | − | 0.931614i | \(-0.618401\pi\) | ||||
−0.363450 | + | 0.931614i | \(0.618401\pi\) | |||||||
\(230\) | −4.00000 | + | 6.92820i | −0.263752 | + | 0.456832i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0000 | + | 20.7846i | −0.786146 | + | 1.36165i | 0.142166 | + | 0.989843i | \(0.454593\pi\) |
−0.928312 | + | 0.371802i | \(0.878740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14.0000 | −0.911322 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.00000 | − | 6.92820i | −0.259281 | − | 0.449089i | ||||
\(239\) | −27.0000 | −1.74648 | −0.873242 | − | 0.487286i | \(-0.837987\pi\) | ||||
−0.873242 | + | 0.487286i | \(0.837987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.50000 | − | 4.33013i | −0.161039 | − | 0.278928i | 0.774202 | − | 0.632938i | \(-0.218151\pi\) |
−0.935242 | + | 0.354010i | \(0.884818\pi\) | |||||||
\(242\) | 10.0000 | − | 17.3205i | 0.642824 | − | 1.11340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.00000 | − | 12.1244i | 0.448129 | − | 0.776182i | ||||
\(245\) | 1.50000 | − | 2.59808i | 0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.00000 | − | 5.19615i | 0.445399 | − | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | + | 1.73205i | −0.0632456 | + | 0.109545i | ||||
\(251\) | −8.50000 | − | 14.7224i | −0.536515 | − | 0.929272i | −0.999088 | − | 0.0426905i | \(-0.986407\pi\) |
0.462573 | − | 0.886581i | \(-0.346926\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | + | 3.46410i | 0.125739 | + | 0.217786i | ||||
\(254\) | 8.00000 | 0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 11.0000 | + | 19.0526i | 0.686161 | + | 1.18847i | 0.973070 | + | 0.230508i | \(0.0740389\pi\) |
−0.286909 | + | 0.957958i | \(0.592628\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0000 | 0.745644 | ||||||||
\(260\) | −2.00000 | − | 3.46410i | −0.124035 | − | 0.214834i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.0000 | + | 27.7128i | 0.988483 | + | 1.71210i | ||||
\(263\) | 10.0000 | − | 17.3205i | 0.616626 | − | 1.06803i | −0.373470 | − | 0.927642i | \(-0.621832\pi\) |
0.990097 | − | 0.140386i | \(-0.0448344\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 16.0000 | + | 6.92820i | 0.981023 | + | 0.424795i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.00000 | + | 13.8564i | −0.488678 | + | 0.846415i | ||||
\(269\) | 0.500000 | − | 0.866025i | 0.0304855 | − | 0.0528025i | −0.850380 | − | 0.526169i | \(-0.823628\pi\) |
0.880866 | + | 0.473366i | \(0.156961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.5000 | + | 23.3827i | −0.820067 | + | 1.42040i | 0.0855654 | + | 0.996333i | \(0.472730\pi\) |
−0.905632 | + | 0.424064i | \(0.860603\pi\) | |||||||
\(272\) | −4.00000 | − | 6.92820i | −0.242536 | − | 0.420084i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | 0.500000 | + | 0.866025i | 0.0301511 | + | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.00000 | −0.480673 | −0.240337 | − | 0.970690i | \(-0.577258\pi\) | ||||
−0.240337 | + | 0.970690i | \(0.577258\pi\) | |||||||
\(278\) | 40.0000 | 2.39904 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0000 | − | 22.5167i | −0.775515 | − | 1.34323i | −0.934505 | − | 0.355951i | \(-0.884157\pi\) |
0.158990 | − | 0.987280i | \(-0.449176\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.00000 | + | 1.73205i | −0.0594438 | + | 0.102960i | −0.894216 | − | 0.447636i | \(-0.852266\pi\) |
0.834772 | + | 0.550596i | \(0.185599\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | −6.00000 | + | 10.3923i | −0.354169 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | −5.00000 | + | 8.66025i | −0.293610 | + | 0.508548i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.00000 | −0.234082 | ||||||||
\(293\) | 4.00000 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.50000 | + | 6.06218i | 0.203778 | + | 0.352954i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.00000 | + | 15.5885i | 0.521356 | + | 0.903015i | ||||
\(299\) | −4.00000 | + | 6.92820i | −0.231326 | + | 0.400668i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | + | 17.3205i | −0.576390 | + | 0.998337i | ||||
\(302\) | 3.00000 | − | 5.19615i | 0.172631 | − | 0.299005i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0000 | + | 6.92820i | 0.917663 | + | 0.397360i | ||||
\(305\) | −7.00000 | −0.400819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | − | 20.7846i | 0.684876 | − | 1.18624i | −0.288600 | − | 0.957450i | \(-0.593190\pi\) |
0.973476 | − | 0.228790i | \(-0.0734771\pi\) | |||||||
\(308\) | −2.00000 | − | 3.46410i | −0.113961 | − | 0.197386i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.00000 | − | 15.5885i | −0.511166 | − | 0.885365i | ||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0000 | + | 17.3205i | 0.565233 | + | 0.979013i | 0.997028 | + | 0.0770410i | \(0.0245472\pi\) |
−0.431795 | + | 0.901972i | \(0.642119\pi\) | |||||||
\(314\) | −12.0000 | − | 20.7846i | −0.677199 | − | 1.17294i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.0000 | −1.23760 | ||||||||
\(317\) | 16.0000 | + | 27.7128i | 0.898650 | + | 1.55651i | 0.829222 | + | 0.558920i | \(0.188784\pi\) |
0.0694277 | + | 0.997587i | \(0.477883\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.50000 | + | 4.33013i | 0.139973 | + | 0.242441i | ||||
\(320\) | 4.00000 | − | 6.92820i | 0.223607 | − | 0.387298i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.0000 | −0.891645 | ||||||||
\(323\) | 8.00000 | + | 3.46410i | 0.445132 | + | 0.192748i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | + | 1.73205i | −0.0554700 | + | 0.0960769i | ||||
\(326\) | 18.0000 | − | 31.1769i | 0.996928 | − | 1.72673i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 6.00000 | + | 10.3923i | 0.329293 | + | 0.570352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.00000 | 0.218870 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.00000 | − | 6.92820i | 0.217894 | − | 0.377403i | −0.736270 | − | 0.676688i | \(-0.763415\pi\) |
0.954164 | + | 0.299285i | \(0.0967480\pi\) | |||||||
\(338\) | 9.00000 | + | 15.5885i | 0.489535 | + | 0.847900i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.00000 | − | 3.46410i | 0.108465 | − | 0.187867i | ||||
\(341\) | −9.00000 | −0.487377 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | + | 10.3923i | 0.322562 | + | 0.558694i | ||||
\(347\) | −11.0000 | + | 19.0526i | −0.590511 | + | 1.02279i | 0.403653 | + | 0.914912i | \(0.367740\pi\) |
−0.994164 | + | 0.107883i | \(0.965593\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.00000 | − | 6.92820i | −0.213201 | − | 0.369274i | ||||
\(353\) | 14.0000 | 0.745145 | 0.372572 | − | 0.928003i | \(-0.378476\pi\) | ||||
0.372572 | + | 0.928003i | \(0.378476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.50000 | + | 2.59808i | 0.0796117 | + | 0.137892i | ||||
\(356\) | 15.0000 | − | 25.9808i | 0.794998 | − | 1.37698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.00000 | + | 5.19615i | −0.158555 | + | 0.274625i | ||||
\(359\) | −4.00000 | + | 6.92820i | −0.211112 | + | 0.365657i | −0.952063 | − | 0.305903i | \(-0.901042\pi\) |
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | + | 4.33013i | −0.973684 | + | 0.227901i | ||||
\(362\) | 20.0000 | 1.05118 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | − | 6.92820i | 0.209657 | − | 0.363137i | ||||
\(365\) | 1.00000 | + | 1.73205i | 0.0523424 | + | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0000 | + | 17.3205i | 0.521996 | + | 0.904123i | 0.999673 | + | 0.0255875i | \(0.00814566\pi\) |
−0.477677 | + | 0.878536i | \(0.658521\pi\) | |||||||
\(368\) | −16.0000 | −0.834058 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | + | 10.3923i | 0.311925 | + | 0.540270i | ||||
\(371\) | 2.00000 | + | 3.46410i | 0.103835 | + | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.0000 | −1.65690 | −0.828449 | − | 0.560065i | \(-0.810776\pi\) | ||||
−0.828449 | + | 0.560065i | \(0.810776\pi\) | |||||||
\(374\) | −2.00000 | − | 3.46410i | −0.103418 | − | 0.179124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.00000 | + | 8.66025i | −0.257513 | + | 0.446026i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.0000 | 1.59236 | 0.796182 | − | 0.605058i | \(-0.206850\pi\) | ||||
0.796182 | + | 0.605058i | \(0.206850\pi\) | |||||||
\(380\) | 1.00000 | + | 8.66025i | 0.0512989 | + | 0.444262i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.0000 | − | 25.9808i | 0.767467 | − | 1.32929i | ||||
\(383\) | 13.0000 | − | 22.5167i | 0.664269 | − | 1.15055i | −0.315214 | − | 0.949021i | \(-0.602076\pi\) |
0.979483 | − | 0.201527i | \(-0.0645904\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | + | 1.73205i | −0.0509647 | + | 0.0882735i | ||||
\(386\) | 26.0000 | + | 45.0333i | 1.32337 | + | 2.29214i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.0000 | 0.812277 | ||||||||
\(389\) | 16.5000 | + | 28.5788i | 0.836583 | + | 1.44900i | 0.892735 | + | 0.450582i | \(0.148784\pi\) |
−0.0561516 | + | 0.998422i | \(0.517883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.0000 | − | 17.3205i | 0.503793 | − | 0.872595i | ||||
\(395\) | 5.50000 | + | 9.52628i | 0.276735 | + | 0.479319i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | − | 17.3205i | 0.501886 | − | 0.869291i | −0.498112 | − | 0.867113i | \(-0.665973\pi\) |
0.999998 | − | 0.00217869i | \(-0.000693499\pi\) | |||||||
\(398\) | −6.00000 | −0.300753 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −13.5000 | + | 23.3827i | −0.674158 | + | 1.16768i | 0.302556 | + | 0.953131i | \(0.402160\pi\) |
−0.976714 | + | 0.214544i | \(0.931173\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00000 | − | 15.5885i | −0.448322 | − | 0.776516i | ||||
\(404\) | −7.00000 | + | 12.1244i | −0.348263 | + | 0.603209i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.0000 | −0.992583 | ||||||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.5000 | + | 25.1147i | 0.716979 | + | 1.24184i | 0.962191 | + | 0.272374i | \(0.0878089\pi\) |
−0.245212 | + | 0.969469i | \(0.578858\pi\) | |||||||
\(410\) | −12.0000 | −0.592638 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000 | + | 13.8564i | 0.394132 | + | 0.682656i | ||||
\(413\) | −7.00000 | + | 12.1244i | −0.344447 | + | 0.596601i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.00000 | − | 5.19615i | 0.147264 | − | 0.255069i | ||||
\(416\) | 8.00000 | − | 13.8564i | 0.392232 | − | 0.679366i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.00000 | + | 3.46410i | 0.391293 | + | 0.169435i | ||||
\(419\) | 5.00000 | 0.244266 | 0.122133 | − | 0.992514i | \(-0.461027\pi\) | ||||
0.122133 | + | 0.992514i | \(0.461027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.50000 | − | 6.06218i | 0.170580 | − | 0.295452i | −0.768043 | − | 0.640398i | \(-0.778769\pi\) |
0.938623 | + | 0.344946i | \(0.112103\pi\) | |||||||
\(422\) | 27.0000 | + | 46.7654i | 1.31434 | + | 2.27650i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.00000 | − | 12.1244i | −0.338754 | − | 0.586739i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20.0000 | −0.964486 | ||||||||
\(431\) | 11.5000 | + | 19.9186i | 0.553936 | + | 0.959444i | 0.997985 | + | 0.0634424i | \(0.0202079\pi\) |
−0.444050 | + | 0.896002i | \(0.646459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.00000 | − | 5.19615i | −0.144171 | − | 0.249711i | 0.784892 | − | 0.619632i | \(-0.212718\pi\) |
−0.929063 | + | 0.369921i | \(0.879385\pi\) | |||||||
\(434\) | 18.0000 | − | 31.1769i | 0.864028 | − | 1.49654i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 38.0000 | 1.81987 | ||||||||
\(437\) | 14.0000 | − | 10.3923i | 0.669711 | − | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5000 | − | 21.6506i | 0.596592 | − | 1.03333i | −0.396728 | − | 0.917936i | \(-0.629854\pi\) |
0.993320 | − | 0.115392i | \(-0.0368124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000 | − | 6.92820i | 0.190261 | − | 0.329541i | ||||
\(443\) | −4.00000 | − | 6.92820i | −0.190046 | − | 0.329169i | 0.755219 | − | 0.655472i | \(-0.227530\pi\) |
−0.945265 | + | 0.326303i | \(0.894197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.0000 | −0.711068 | ||||||||
\(446\) | 12.0000 | + | 20.7846i | 0.568216 | + | 0.984180i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.0000 | 0.755929 | ||||||||
\(449\) | 39.0000 | 1.84052 | 0.920262 | − | 0.391303i | \(-0.127976\pi\) | ||||
0.920262 | + | 0.391303i | \(0.127976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.00000 | + | 5.19615i | −0.141264 | + | 0.244677i | ||||
\(452\) | −10.0000 | − | 17.3205i | −0.470360 | − | 0.814688i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.0000 | − | 31.1769i | 0.844782 | − | 1.46321i | ||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.00000 | −0.374224 | −0.187112 | − | 0.982339i | \(-0.559913\pi\) | ||||
−0.187112 | + | 0.982339i | \(0.559913\pi\) | |||||||
\(458\) | 11.0000 | − | 19.0526i | 0.513996 | − | 0.890268i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | − | 6.92820i | −0.186501 | − | 0.323029i | ||||
\(461\) | −1.50000 | + | 2.59808i | −0.0698620 | + | 0.121004i | −0.898840 | − | 0.438276i | \(-0.855589\pi\) |
0.828978 | + | 0.559281i | \(0.188923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0000 | −0.464739 | −0.232370 | − | 0.972628i | \(-0.574648\pi\) | ||||
−0.232370 | + | 0.972628i | \(0.574648\pi\) | |||||||
\(464\) | −20.0000 | −0.928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0000 | − | 41.5692i | −1.11178 | − | 1.92566i | ||||
\(467\) | 38.0000 | 1.75843 | 0.879215 | − | 0.476425i | \(-0.158068\pi\) | ||||
0.879215 | + | 0.476425i | \(0.158068\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | + | 13.8564i | 0.369406 | + | 0.639829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.00000 | + | 8.66025i | −0.229900 | + | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.50000 | − | 2.59808i | 0.160591 | − | 0.119208i | ||||
\(476\) | 8.00000 | 0.366679 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.0000 | − | 46.7654i | 1.23495 | − | 2.13900i | ||||
\(479\) | 2.50000 | + | 4.33013i | 0.114228 | + | 0.197849i | 0.917471 | − | 0.397803i | \(-0.130227\pi\) |
−0.803243 | + | 0.595652i | \(0.796894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | + | 10.3923i | 0.273576 | + | 0.473848i | ||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.0000 | + | 17.3205i | 0.454545 | + | 0.787296i | ||||
\(485\) | −4.00000 | − | 6.92820i | −0.181631 | − | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.0000 | 0.634401 | 0.317200 | − | 0.948359i | \(-0.397257\pi\) | ||||
0.317200 | + | 0.948359i | \(0.397257\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.00000 | + | 5.19615i | 0.135526 | + | 0.234738i | ||||
\(491\) | −16.5000 | + | 28.5788i | −0.744635 | + | 1.28974i | 0.205731 | + | 0.978609i | \(0.434043\pi\) |
−0.950365 | + | 0.311136i | \(0.899290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0000 | −0.450377 | ||||||||
\(494\) | 2.00000 | + | 17.3205i | 0.0899843 | + | 0.779287i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.0000 | − | 31.1769i | 0.808224 | − | 1.39988i | ||||
\(497\) | −3.00000 | + | 5.19615i | −0.134568 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0000 | + | 17.3205i | −0.447661 | + | 0.775372i | −0.998233 | − | 0.0594153i | \(-0.981076\pi\) |
0.550572 | + | 0.834788i | \(0.314410\pi\) | |||||||
\(500\) | −1.00000 | − | 1.73205i | −0.0447214 | − | 0.0774597i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 34.0000 | 1.51749 | ||||||||
\(503\) | −22.0000 | − | 38.1051i | −0.980932 | − | 1.69902i | −0.658781 | − | 0.752335i | \(-0.728928\pi\) |
−0.322151 | − | 0.946688i | \(-0.604406\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.00000 | 0.311496 | ||||||||
\(506\) | −8.00000 | −0.355643 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | + | 6.92820i | −0.177471 | + | 0.307389i | ||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | + | 3.46410i | −0.0884748 | + | 0.153243i | ||||
\(512\) | 32.0000 | 1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −44.0000 | −1.94076 | ||||||||
\(515\) | 4.00000 | − | 6.92820i | 0.176261 | − | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −12.0000 | + | 20.7846i | −0.527250 | + | 0.913223i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0000 | −0.920027 | −0.460013 | − | 0.887912i | \(-0.652155\pi\) | ||||
−0.460013 | + | 0.887912i | \(0.652155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0000 | + | 19.0526i | 0.480996 | + | 0.833110i | 0.999762 | − | 0.0218062i | \(-0.00694167\pi\) |
−0.518766 | + | 0.854916i | \(0.673608\pi\) | |||||||
\(524\) | −32.0000 | −1.39793 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.0000 | + | 34.6410i | 0.872041 | + | 1.51042i | ||||
\(527\) | 9.00000 | − | 15.5885i | 0.392046 | − | 0.679044i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −2.00000 | + | 3.46410i | −0.0868744 | + | 0.150471i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.0000 | + | 10.3923i | −0.606977 | + | 0.450564i | ||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.00000 | + | 1.73205i | 0.0431131 | + | 0.0746740i | ||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.50000 | − | 12.9904i | −0.322450 | − | 0.558500i | 0.658543 | − | 0.752543i | \(-0.271173\pi\) |
−0.980993 | + | 0.194043i | \(0.937840\pi\) | |||||||
\(542\) | −27.0000 | − | 46.7654i | −1.15975 | − | 2.00874i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.0000 | 0.685994 | ||||||||
\(545\) | −9.50000 | − | 16.4545i | −0.406935 | − | 0.704833i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | + | 6.92820i | 0.171028 | + | 0.296229i | 0.938779 | − | 0.344519i | \(-0.111958\pi\) |
−0.767752 | + | 0.640747i | \(0.778625\pi\) | |||||||
\(548\) | −6.00000 | + | 10.3923i | −0.256307 | + | 0.443937i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | 17.5000 | − | 12.9904i | 0.745525 | − | 0.553409i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0000 | + | 19.0526i | −0.467768 | + | 0.810197i | ||||
\(554\) | 8.00000 | − | 13.8564i | 0.339887 | − | 0.588702i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.0000 | + | 34.6410i | −0.848189 | + | 1.46911i | ||||
\(557\) | −16.0000 | − | 27.7128i | −0.677942 | − | 1.17423i | −0.975600 | − | 0.219557i | \(-0.929539\pi\) |
0.297658 | − | 0.954673i | \(-0.403795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.0000 | −0.845910 | ||||||||
\(560\) | −4.00000 | − | 6.92820i | −0.169031 | − | 0.292770i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 52.0000 | 2.19349 | ||||||||
\(563\) | 42.0000 | 1.77009 | 0.885044 | − | 0.465506i | \(-0.154128\pi\) | ||||
0.885044 | + | 0.465506i | \(0.154128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.00000 | + | 8.66025i | −0.210352 | + | 0.364340i | ||||
\(566\) | −2.00000 | − | 3.46410i | −0.0840663 | − | 0.145607i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.0000 | 1.63497 | 0.817483 | − | 0.575953i | \(-0.195369\pi\) | ||||
0.817483 | + | 0.575953i | \(0.195369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0000 | −0.627730 | −0.313865 | − | 0.949468i | \(-0.601624\pi\) | ||||
−0.313865 | + | 0.949468i | \(0.601624\pi\) | |||||||
\(572\) | 2.00000 | − | 3.46410i | 0.0836242 | − | 0.144841i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | − | 20.7846i | −0.500870 | − | 0.867533i | ||||
\(575\) | −2.00000 | + | 3.46410i | −0.0834058 | + | 0.144463i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.0000 | 0.499567 | 0.249783 | − | 0.968302i | \(-0.419641\pi\) | ||||
0.249783 | + | 0.968302i | \(0.419641\pi\) | |||||||
\(578\) | −26.0000 | −1.08146 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.00000 | − | 8.66025i | −0.207614 | − | 0.359597i | ||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.00000 | + | 1.73205i | 0.0414158 | + | 0.0717342i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.00000 | + | 6.92820i | −0.165238 | + | 0.286201i | ||||
\(587\) | 11.0000 | − | 19.0526i | 0.454019 | − | 0.786383i | −0.544613 | − | 0.838688i | \(-0.683323\pi\) |
0.998631 | + | 0.0523045i | \(0.0166566\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.50000 | + | 38.9711i | 0.185419 | + | 1.60578i | ||||
\(590\) | −14.0000 | −0.576371 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0000 | + | 20.7846i | −0.493197 | + | 0.854242i | ||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00000 | − | 3.46410i | −0.0819920 | − | 0.142014i | ||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.00000 | − | 13.8564i | −0.327144 | − | 0.566631i | ||||
\(599\) | −18.0000 | − | 31.1769i | −0.735460 | − | 1.27385i | −0.954521 | − | 0.298143i | \(-0.903633\pi\) |
0.219061 | − | 0.975711i | \(-0.429701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.0000 | −0.611863 | −0.305931 | − | 0.952054i | \(-0.598968\pi\) | ||||
−0.305931 | + | 0.952054i | \(0.598968\pi\) | |||||||
\(602\) | −20.0000 | − | 34.6410i | −0.815139 | − | 1.41186i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.00000 | + | 5.19615i | 0.122068 | + | 0.211428i | ||||
\(605\) | 5.00000 | − | 8.66025i | 0.203279 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0000 | −0.405887 | −0.202944 | − | 0.979190i | \(-0.565051\pi\) | ||||
−0.202944 | + | 0.979190i | \(0.565051\pi\) | |||||||
\(608\) | −28.0000 | + | 20.7846i | −1.13555 | + | 0.842927i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.00000 | − | 12.1244i | 0.283422 | − | 0.490901i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | − | 5.19615i | 0.121169 | − | 0.209871i | −0.799060 | − | 0.601251i | \(-0.794669\pi\) |
0.920229 | + | 0.391381i | \(0.128002\pi\) | |||||||
\(614\) | 24.0000 | + | 41.5692i | 0.968561 | + | 1.67760i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | − | 20.7846i | −0.483102 | − | 0.836757i | 0.516710 | − | 0.856161i | \(-0.327157\pi\) |
−0.999812 | + | 0.0194037i | \(0.993823\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.0000 | −1.28619 | −0.643094 | − | 0.765787i | \(-0.722350\pi\) | ||||
−0.643094 | + | 0.765787i | \(0.722350\pi\) | |||||||
\(620\) | 18.0000 | 0.722897 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000 | − | 41.5692i | 0.962312 | − | 1.66677i | ||||
\(623\) | −15.0000 | − | 25.9808i | −0.600962 | − | 1.04090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −40.0000 | −1.59872 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.0000 | 0.957704 | ||||||||
\(629\) | −6.00000 | + | 10.3923i | −0.239236 | + | 0.414368i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.50000 | + | 2.59808i | 0.0597141 | + | 0.103428i | 0.894337 | − | 0.447394i | \(-0.147648\pi\) |
−0.834623 | + | 0.550822i | \(0.814314\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −64.0000 | −2.54176 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | + | 5.19615i | 0.118864 | + | 0.205879i | ||||
\(638\) | −10.0000 | −0.395904 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.5000 | + | 28.5788i | −0.651711 | + | 1.12880i | 0.330997 | + | 0.943632i | \(0.392615\pi\) |
−0.982708 | + | 0.185164i | \(0.940718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0000 | + | 38.1051i | −0.867595 | + | 1.50272i | −0.00314839 | + | 0.999995i | \(0.501002\pi\) |
−0.864447 | + | 0.502724i | \(0.832331\pi\) | |||||||
\(644\) | 8.00000 | − | 13.8564i | 0.315244 | − | 0.546019i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.0000 | + | 10.3923i | −0.550823 | + | 0.408880i | ||||
\(647\) | −6.00000 | −0.235884 | −0.117942 | − | 0.993020i | \(-0.537630\pi\) | ||||
−0.117942 | + | 0.993020i | \(0.537630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.50000 | + | 6.06218i | −0.137387 | + | 0.237961i | ||||
\(650\) | −2.00000 | − | 3.46410i | −0.0784465 | − | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.0000 | + | 31.1769i | 0.704934 | + | 1.22098i | ||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000 | + | 13.8564i | 0.312586 | + | 0.541415i | ||||
\(656\) | −12.0000 | − | 20.7846i | −0.468521 | − | 0.811503i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.0000 | + | 34.6410i | 0.779089 | + | 1.34942i | 0.932467 | + | 0.361255i | \(0.117652\pi\) |
−0.153378 | + | 0.988168i | \(0.549015\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.50000 | − | 7.79423i | −0.175030 | − | 0.303160i | 0.765142 | − | 0.643862i | \(-0.222669\pi\) |
−0.940172 | + | 0.340701i | \(0.889335\pi\) | |||||||
\(662\) | −8.00000 | + | 13.8564i | −0.310929 | + | 0.538545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.00000 | + | 3.46410i | 0.310227 | + | 0.134332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0000 | + | 17.3205i | −0.387202 | + | 0.670653i | ||||
\(668\) | −2.00000 | + | 3.46410i | −0.0773823 | + | 0.134030i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.00000 | + | 13.8564i | −0.309067 | + | 0.535320i | ||||
\(671\) | −3.50000 | − | 6.06218i | −0.135116 | − | 0.234028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.0000 | 1.38770 | 0.693849 | − | 0.720121i | \(-0.255914\pi\) | ||||
0.693849 | + | 0.720121i | \(0.255914\pi\) | |||||||
\(674\) | 8.00000 | + | 13.8564i | 0.308148 | + | 0.533729i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.0000 | −0.692308 | ||||||||
\(677\) | −46.0000 | −1.76792 | −0.883962 | − | 0.467559i | \(-0.845134\pi\) | ||||
−0.883962 | + | 0.467559i | \(0.845134\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.00000 | − | 13.8564i | 0.307012 | − | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.00000 | − | 15.5885i | 0.344628 | − | 0.596913i | ||||
\(683\) | 24.0000 | 0.918334 | 0.459167 | − | 0.888350i | \(-0.348148\pi\) | ||||
0.459167 | + | 0.888350i | \(0.348148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | −20.0000 | + | 34.6410i | −0.763604 | + | 1.32260i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.0000 | − | 34.6410i | −0.762493 | − | 1.32068i | ||||
\(689\) | −2.00000 | + | 3.46410i | −0.0761939 | + | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.0000 | 0.874961 | 0.437481 | − | 0.899228i | \(-0.355871\pi\) | ||||
0.437481 | + | 0.899228i | \(0.355871\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.0000 | − | 38.1051i | −0.835109 | − | 1.44645i | ||||
\(695\) | 20.0000 | 0.758643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | − | 10.3923i | −0.227266 | − | 0.393637i | ||||
\(698\) | −6.00000 | + | 10.3923i | −0.227103 | + | 0.393355i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.00000 | − | 3.46410i | 0.0755929 | − | 0.130931i | ||||
\(701\) | −11.0000 | + | 19.0526i | −0.415464 | + | 0.719605i | −0.995477 | − | 0.0950021i | \(-0.969714\pi\) |
0.580013 | + | 0.814607i | \(0.303048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.00000 | − | 25.9808i | −0.113147 | − | 0.979883i | ||||
\(704\) | 8.00000 | 0.301511 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.0000 | + | 24.2487i | −0.526897 | + | 0.912612i | ||||
\(707\) | 7.00000 | + | 12.1244i | 0.263262 | + | 0.455983i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5000 | + | 23.3827i | 0.507003 | + | 0.878155i | 0.999967 | + | 0.00810550i | \(0.00258009\pi\) |
−0.492964 | + | 0.870050i | \(0.664087\pi\) | |||||||
\(710\) | −6.00000 | −0.225176 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.0000 | − | 31.1769i | −0.674105 | − | 1.16758i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.00000 | −0.0747958 | ||||||||
\(716\) | −3.00000 | − | 5.19615i | −0.112115 | − | 0.194189i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.00000 | − | 13.8564i | −0.298557 | − | 0.517116i | ||||
\(719\) | −13.5000 | + | 23.3827i | −0.503465 | + | 0.872027i | 0.496527 | + | 0.868021i | \(0.334608\pi\) |
−0.999992 | + | 0.00400572i | \(0.998725\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 11.0000 | − | 36.3731i | 0.409378 | − | 1.35367i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.0000 | + | 17.3205i | −0.371647 | + | 0.643712i | ||||
\(725\) | −2.50000 | + | 4.33013i | −0.0928477 | + | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.00000 | − | 1.73205i | 0.0370879 | − | 0.0642382i | −0.846886 | − | 0.531775i | \(-0.821525\pi\) |
0.883974 | + | 0.467537i | \(0.154858\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.00000 | −0.148047 | ||||||||
\(731\) | −10.0000 | − | 17.3205i | −0.369863 | − | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0000 | 0.369358 | 0.184679 | − | 0.982799i | \(-0.440875\pi\) | ||||
0.184679 | + | 0.982799i | \(0.440875\pi\) | |||||||
\(734\) | −40.0000 | −1.47643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | − | 27.7128i | 0.589768 | − | 1.02151i | ||||
\(737\) | 4.00000 | + | 6.92820i | 0.147342 | + | 0.255204i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.5000 | − | 45.8993i | 0.974818 | − | 1.68843i | 0.294285 | − | 0.955718i | \(-0.404919\pi\) |
0.680534 | − | 0.732717i | \(-0.261748\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.00000 | −0.293689 | ||||||||
\(743\) | 11.0000 | − | 19.0526i | 0.403551 | − | 0.698971i | −0.590601 | − | 0.806964i | \(-0.701109\pi\) |
0.994152 | + | 0.107993i | \(0.0344425\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.50000 | + | 7.79423i | 0.164867 | + | 0.285558i | ||||
\(746\) | 32.0000 | − | 55.4256i | 1.17160 | − | 2.02928i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.00000 | 0.146254 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.50000 | + | 2.59808i | 0.0547358 | + | 0.0948051i | 0.892095 | − | 0.451848i | \(-0.149235\pi\) |
−0.837359 | + | 0.546653i | \(0.815902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.0000 | − | 17.3205i | −0.364179 | − | 0.630776i | ||||
\(755\) | 1.50000 | − | 2.59808i | 0.0545906 | − | 0.0945537i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.00000 | − | 12.1244i | 0.254419 | − | 0.440667i | −0.710318 | − | 0.703881i | \(-0.751449\pi\) |
0.964738 | + | 0.263213i | \(0.0847823\pi\) | |||||||
\(758\) | −31.0000 | + | 53.6936i | −1.12597 | + | 1.95024i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.0000 | − | 32.9090i | 0.687846 | − | 1.19138i | ||||
\(764\) | 15.0000 | + | 25.9808i | 0.542681 | + | 0.939951i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.0000 | + | 45.0333i | 0.939418 | + | 1.62712i | ||||
\(767\) | −14.0000 | −0.505511 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.5000 | + | 37.2391i | 0.775310 | + | 1.34288i | 0.934620 | + | 0.355647i | \(0.115740\pi\) |
−0.159310 | + | 0.987229i | \(0.550927\pi\) | |||||||
\(770\) | −2.00000 | − | 3.46410i | −0.0720750 | − | 0.124838i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −52.0000 | −1.87152 | ||||||||
\(773\) | 10.0000 | + | 17.3205i | 0.359675 | + | 0.622975i | 0.987906 | − | 0.155051i | \(-0.0495542\pi\) |
−0.628231 | + | 0.778027i | \(0.716221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.50000 | − | 7.79423i | −0.161645 | − | 0.279977i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −66.0000 | −2.36621 | ||||||||
\(779\) | 24.0000 | + | 10.3923i | 0.859889 | + | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.50000 | + | 2.59808i | −0.0536742 | + | 0.0929665i | ||||
\(782\) | 8.00000 | − | 13.8564i | 0.286079 | − | 0.495504i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.00000 | + | 10.3923i | −0.214286 | + | 0.371154i | ||||
\(785\) | −6.00000 | − | 10.3923i | −0.214149 | − | 0.370917i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.00000 | −0.285169 | −0.142585 | − | 0.989783i | \(-0.545541\pi\) | ||||
−0.142585 | + | 0.989783i | \(0.545541\pi\) | |||||||
\(788\) | 10.0000 | + | 17.3205i | 0.356235 | + | 0.617018i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.0000 | −0.782725 | ||||||||
\(791\) | −20.0000 | −0.711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.00000 | − | 12.1244i | 0.248577 | − | 0.430548i | ||||
\(794\) | 20.0000 | + | 34.6410i | 0.709773 | + | 1.22936i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.00000 | − | 5.19615i | 0.106332 | − | 0.184173i | ||||
\(797\) | −10.0000 | −0.354218 | −0.177109 | − | 0.984191i | \(-0.556675\pi\) | ||||
−0.177109 | + | 0.984191i | \(0.556675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.00000 | − | 6.92820i | 0.141421 | − | 0.244949i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27.0000 | − | 46.7654i | −0.953403 | − | 1.65134i | ||||
\(803\) | −1.00000 | + | 1.73205i | −0.0352892 | + | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | −0.281963 | ||||||||
\(806\) | 36.0000 | 1.26805 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.00000 | 0.0351581 | 0.0175791 | − | 0.999845i | \(-0.494404\pi\) | ||||
0.0175791 | + | 0.999845i | \(0.494404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.5000 | − | 42.4352i | −0.860311 | − | 1.49010i | −0.871629 | − | 0.490167i | \(-0.836936\pi\) |
0.0113172 | − | 0.999936i | \(-0.496398\pi\) | |||||||
\(812\) | 10.0000 | − | 17.3205i | 0.350931 | − | 0.607831i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.00000 | + | 10.3923i | −0.210300 | + | 0.364250i | ||||
\(815\) | 9.00000 | − | 15.5885i | 0.315256 | − | 0.546040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.0000 | + | 17.3205i | 1.39942 | + | 0.605968i | ||||
\(818\) | −58.0000 | −2.02792 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | − | 10.3923i | 0.209529 | − | 0.362915i | ||||
\(821\) | −22.5000 | − | 38.9711i | −0.785255 | − | 1.36010i | −0.928846 | − | 0.370465i | \(-0.879198\pi\) |
0.143591 | − | 0.989637i | \(-0.454135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0000 | + | 17.3205i | 0.348578 | + | 0.603755i | 0.985997 | − | 0.166762i | \(-0.0533313\pi\) |
−0.637419 | + | 0.770517i | \(0.719998\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.0000 | − | 24.2487i | −0.487122 | − | 0.843721i | ||||
\(827\) | 6.00000 | + | 10.3923i | 0.208640 | + | 0.361376i | 0.951286 | − | 0.308308i | \(-0.0997628\pi\) |
−0.742646 | + | 0.669684i | \(0.766429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 6.00000 | + | 10.3923i | 0.208263 | + | 0.360722i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.00000 | + | 13.8564i | 0.277350 | + | 0.480384i | ||||
\(833\) | −3.00000 | + | 5.19615i | −0.103944 | + | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.00000 | 0.0692129 | ||||||||
\(836\) | −7.00000 | + | 5.19615i | −0.242100 | + | 0.179713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.00000 | + | 8.66025i | −0.172722 | + | 0.299164i | ||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | 7.00000 | + | 12.1244i | 0.241236 | + | 0.417833i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −54.0000 | −1.85876 | ||||||||
\(845\) | 4.50000 | + | 7.79423i | 0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.0000 | 0.687208 | ||||||||
\(848\) | −8.00000 | −0.274721 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.00000 | − | 3.46410i | 0.0685994 | − | 0.118818i | ||||
\(851\) | 12.0000 | + | 20.7846i | 0.411355 | + | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.00000 | − | 1.73205i | 0.0342393 | − | 0.0593043i | −0.848398 | − | 0.529359i | \(-0.822432\pi\) |
0.882637 | + | 0.470055i | \(0.155766\pi\) | |||||||
\(854\) | 28.0000 | 0.958140 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.00000 | − | 8.66025i | 0.170797 | − | 0.295829i | −0.767902 | − | 0.640567i | \(-0.778699\pi\) |
0.938699 | + | 0.344739i | \(0.112033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.5000 | − | 38.9711i | −0.767690 | − | 1.32968i | −0.938813 | − | 0.344428i | \(-0.888073\pi\) |
0.171122 | − | 0.985250i | \(-0.445261\pi\) | |||||||
\(860\) | 10.0000 | − | 17.3205i | 0.340997 | − | 0.590624i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −46.0000 | −1.56677 | ||||||||
\(863\) | 38.0000 | 1.29354 | 0.646768 | − | 0.762687i | \(-0.276120\pi\) | ||||
0.646768 | + | 0.762687i | \(0.276120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.00000 | + | 5.19615i | 0.102003 | + | 0.176674i | ||||
\(866\) | 12.0000 | 0.407777 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.0000 | + | 31.1769i | 0.610960 | + | 1.05821i | ||||
\(869\) | −5.50000 | + | 9.52628i | −0.186575 | + | 0.323157i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | + | 13.8564i | −0.271070 | + | 0.469506i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.00000 | + | 34.6410i | 0.135302 | + | 1.17175i | ||||
\(875\) | −2.00000 | −0.0676123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.0000 | + | 20.7846i | −0.405211 | + | 0.701846i | −0.994346 | − | 0.106188i | \(-0.966135\pi\) |
0.589135 | + | 0.808035i | \(0.299469\pi\) | |||||||
\(878\) | 25.0000 | + | 43.3013i | 0.843709 | + | 1.46135i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.00000 | − | 3.46410i | −0.0674200 | − | 0.116775i | ||||
\(881\) | 1.00000 | 0.0336909 | 0.0168454 | − | 0.999858i | \(-0.494638\pi\) | ||||
0.0168454 | + | 0.999858i | \(0.494638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.0000 | + | 24.2487i | 0.471138 | + | 0.816034i | 0.999455 | − | 0.0330128i | \(-0.0105102\pi\) |
−0.528317 | + | 0.849047i | \(0.677177\pi\) | |||||||
\(884\) | 4.00000 | + | 6.92820i | 0.134535 | + | 0.233021i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.0000 | 0.537531 | ||||||||
\(887\) | −6.00000 | − | 10.3923i | −0.201460 | − | 0.348939i | 0.747539 | − | 0.664218i | \(-0.231235\pi\) |
−0.948999 | + | 0.315279i | \(0.897902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00000 | + | 6.92820i | 0.134156 | + | 0.232364i | ||||
\(890\) | 15.0000 | − | 25.9808i | 0.502801 | − | 0.870877i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.0000 | −0.803579 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.50000 | + | 2.59808i | −0.0501395 | + | 0.0868441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.0000 | + | 67.5500i | −1.30145 | + | 2.25417i | ||||
\(899\) | −22.5000 | − | 38.9711i | −0.750417 | − | 1.29976i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | −6.00000 | − | 10.3923i | −0.199778 | − | 0.346026i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0000 | 0.332411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.00000 | + | 3.46410i | −0.0664089 | + | 0.115024i | −0.897318 | − | 0.441384i | \(-0.854488\pi\) |
0.830909 | + | 0.556408i | \(0.187821\pi\) | |||||||
\(908\) | 18.0000 | + | 31.1769i | 0.597351 | + | 1.03464i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.00000 | − | 6.92820i | 0.132599 | − | 0.229668i | ||||
\(911\) | 9.00000 | 0.298183 | 0.149092 | − | 0.988823i | \(-0.452365\pi\) | ||||
0.149092 | + | 0.988823i | \(0.452365\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 8.00000 | − | 13.8564i | 0.264616 | − | 0.458329i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.0000 | + | 19.0526i | 0.363450 | + | 0.629514i | ||||
\(917\) | −16.0000 | + | 27.7128i | −0.528367 | + | 0.915158i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000 | 1.05558 | 0.527791 | − | 0.849374i | \(-0.323020\pi\) | ||||
0.527791 | + | 0.849374i | \(0.323020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.00000 | − | 5.19615i | −0.0987997 | − | 0.171126i | ||||
\(923\) | −6.00000 | −0.197492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | + | 5.19615i | 0.0986394 | + | 0.170848i | ||||
\(926\) | 10.0000 | − | 17.3205i | 0.328620 | − | 0.569187i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.0000 | − | 34.6410i | 0.656532 | − | 1.13715i | ||||
\(929\) | −5.50000 | + | 9.52628i | −0.180449 | + | 0.312547i | −0.942034 | − | 0.335519i | \(-0.891088\pi\) |
0.761584 | + | 0.648066i | \(0.224422\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.50000 | − | 12.9904i | −0.0491605 | − | 0.425743i | ||||
\(932\) | 48.0000 | 1.57229 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38.0000 | + | 65.8179i | −1.24340 | + | 2.15363i | ||||
\(935\) | −1.00000 | − | 1.73205i | −0.0327035 | − | 0.0566441i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.00000 | + | 15.5885i | 0.294017 | + | 0.509253i | 0.974756 | − | 0.223274i | \(-0.0716744\pi\) |
−0.680739 | + | 0.732526i | \(0.738341\pi\) | |||||||
\(938\) | −32.0000 | −1.04484 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5000 | + | 18.1865i | 0.342290 | + | 0.592864i | 0.984858 | − | 0.173365i | \(-0.0554641\pi\) |
−0.642567 | + | 0.766229i | \(0.722131\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | −0.781548 | ||||||||
\(944\) | −14.0000 | − | 24.2487i | −0.455661 | − | 0.789228i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0000 | − | 17.3205i | −0.325128 | − | 0.563138i | ||||
\(947\) | 10.0000 | − | 17.3205i | 0.324956 | − | 0.562841i | −0.656547 | − | 0.754285i | \(-0.727984\pi\) |
0.981504 | + | 0.191444i | \(0.0613171\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 1.00000 | + | 8.66025i | 0.0324443 | + | 0.280976i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.00000 | + | 6.92820i | −0.129573 | + | 0.224427i | −0.923511 | − | 0.383572i | \(-0.874694\pi\) |
0.793938 | + | 0.607998i | \(0.208027\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.50000 | − | 12.9904i | 0.242694 | − | 0.420359i | ||||
\(956\) | 27.0000 | + | 46.7654i | 0.873242 | + | 1.51250i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.0000 | −0.323085 | ||||||||
\(959\) | 6.00000 | + | 10.3923i | 0.193750 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.0000 | 1.61290 | ||||||||
\(962\) | −24.0000 | −0.773791 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.00000 | + | 8.66025i | −0.161039 | + | 0.278928i | ||||
\(965\) | 13.0000 | + | 22.5167i | 0.418485 | + | 0.724837i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.00000 | + | 3.46410i | −0.0643157 | + | 0.111398i | −0.896390 | − | 0.443266i | \(-0.853820\pi\) |
0.832075 | + | 0.554664i | \(0.187153\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.0000 | 0.513729 | ||||||||
\(971\) | −12.0000 | + | 20.7846i | −0.385098 | + | 0.667010i | −0.991783 | − | 0.127933i | \(-0.959166\pi\) |
0.606685 | + | 0.794943i | \(0.292499\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000 | + | 34.6410i | 0.641171 | + | 1.11054i | ||||
\(974\) | −14.0000 | + | 24.2487i | −0.448589 | + | 0.776979i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.0000 | 0.896258 | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.50000 | − | 12.9904i | −0.239701 | − | 0.415174i | ||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33.0000 | − | 57.1577i | −1.05307 | − | 1.82397i | ||||
\(983\) | −7.00000 | + | 12.1244i | −0.223265 | + | 0.386707i | −0.955798 | − | 0.294025i | \(-0.905005\pi\) |
0.732532 | + | 0.680732i | \(0.238338\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.00000 | − | 8.66025i | 0.159313 | − | 0.275939i | ||||
\(986\) | 10.0000 | − | 17.3205i | 0.318465 | − | 0.551597i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.0000 | − | 6.92820i | −0.509028 | − | 0.220416i | ||||
\(989\) | −40.0000 | −1.27193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | − | 34.6410i | 0.635321 | − | 1.10041i | −0.351126 | − | 0.936328i | \(-0.614201\pi\) |
0.986447 | − | 0.164080i | \(-0.0524655\pi\) | |||||||
\(992\) | 36.0000 | + | 62.3538i | 1.14300 | + | 1.97974i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.00000 | − | 10.3923i | −0.190308 | − | 0.329624i | ||||
\(995\) | −3.00000 | −0.0951064 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.0000 | − | 45.0333i | −0.823428 | − | 1.42622i | −0.903115 | − | 0.429400i | \(-0.858725\pi\) |
0.0796863 | − | 0.996820i | \(-0.474608\pi\) | |||||||
\(998\) | −20.0000 | − | 34.6410i | −0.633089 | − | 1.09654i | ||||
\(999\) | 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 | 855.2.k.a.676.1 | 2 | ||
3.2 | odd | 2 | 285.2.i.c.106.1 | ✓ | 2 | ||
19.7 | even | 3 | inner | 855.2.k.a.406.1 | 2 | ||
57.8 | even | 6 | 5415.2.a.l.1.1 | 1 | |||
57.11 | odd | 6 | 5415.2.a.b.1.1 | 1 | |||
57.26 | odd | 6 | 285.2.i.c.121.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.i.c.106.1 | ✓ | 2 | 3.2 | odd | 2 | ||
285.2.i.c.121.1 | yes | 2 | 57.26 | odd | 6 | ||
855.2.k.a.406.1 | 2 | 19.7 | even | 3 | inner | ||
855.2.k.a.676.1 | 2 | 1.1 | even | 1 | trivial | ||
5415.2.a.b.1.1 | 1 | 57.11 | odd | 6 | |||
5415.2.a.l.1.1 | 1 | 57.8 | even | 6 |