Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.a (trivial) |
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: | yes |
Analytic conductor: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2541) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 2.23607 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.61803 | −1.14412 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.236068 | 0.0654735 | 0.0327367 | − | 0.999464i | \(-0.489578\pi\) | ||||
0.0327367 | + | 0.999464i | \(0.489578\pi\) | |||||||
\(14\) | −1.61803 | −0.432438 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.47214 | −0.337731 | −0.168866 | − | 0.985639i | \(-0.554010\pi\) | ||||
−0.168866 | + | 0.985639i | \(0.554010\pi\) | |||||||
\(20\) | 1.38197 | 0.309017 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.381966 | −0.0749097 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.618034 | 0.116797 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4721 | 1.88085 | 0.940426 | − | 0.340000i | \(-0.110427\pi\) | ||||
0.940426 | + | 0.340000i | \(0.110427\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.23607 | 0.554981 | ||||||||
\(35\) | 2.23607 | 0.377964 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.47214 | −0.242018 | −0.121009 | − | 0.992651i | \(-0.538613\pi\) | ||||
−0.121009 | + | 0.992651i | \(0.538613\pi\) | |||||||
\(38\) | 2.38197 | 0.386406 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.00000 | 0.790569 | ||||||||
\(41\) | −2.47214 | −0.386083 | −0.193041 | − | 0.981191i | \(-0.561835\pi\) | ||||
−0.193041 | + | 0.981191i | \(0.561835\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.47214 | −1.29199 | −0.645994 | − | 0.763342i | \(-0.723557\pi\) | ||||
−0.645994 | + | 0.763342i | \(0.723557\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.23607 | −0.477132 | ||||||||
\(47\) | −9.47214 | −1.38165 | −0.690827 | − | 0.723021i | \(-0.742753\pi\) | ||||
−0.690827 | + | 0.723021i | \(0.742753\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.145898 | 0.0202324 | ||||||||
\(53\) | −6.47214 | −0.889016 | −0.444508 | − | 0.895775i | \(-0.646622\pi\) | ||||
−0.444508 | + | 0.895775i | \(0.646622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.09017 | 1.06229 | ||||||||
\(59\) | −7.94427 | −1.03426 | −0.517128 | − | 0.855908i | \(-0.672999\pi\) | ||||
−0.517128 | + | 0.855908i | \(0.672999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4721 | 1.59689 | 0.798447 | − | 0.602066i | \(-0.205655\pi\) | ||||
0.798447 | + | 0.602066i | \(0.205655\pi\) | |||||||
\(62\) | −16.9443 | −2.15192 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0.527864 | 0.0654735 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.18034 | 1.12156 | 0.560779 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560779 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(68\) | −1.23607 | −0.149895 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.61803 | −0.432438 | ||||||||
\(71\) | 2.47214 | 0.293389 | 0.146694 | − | 0.989182i | \(-0.453137\pi\) | ||||
0.146694 | + | 0.989182i | \(0.453137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7082 | −1.25330 | −0.626650 | − | 0.779301i | \(-0.715575\pi\) | ||||
−0.626650 | + | 0.779301i | \(0.715575\pi\) | |||||||
\(74\) | 2.38197 | 0.276898 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.909830 | −0.104365 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.472136 | −0.0531194 | −0.0265597 | − | 0.999647i | \(-0.508455\pi\) | ||||
−0.0265597 | + | 0.999647i | \(0.508455\pi\) | |||||||
\(80\) | −10.8541 | −1.21353 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.00000 | 0.441726 | ||||||||
\(83\) | −7.52786 | −0.826290 | −0.413145 | − | 0.910665i | \(-0.635570\pi\) | ||||
−0.413145 | + | 0.910665i | \(0.635570\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.47214 | −0.485071 | ||||||||
\(86\) | 13.7082 | 1.47819 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.472136 | 0.0500463 | 0.0250232 | − | 0.999687i | \(-0.492034\pi\) | ||||
0.0250232 | + | 0.999687i | \(0.492034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.236068 | 0.0247466 | ||||||||
\(92\) | 1.23607 | 0.128869 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.3262 | 1.58078 | ||||||||
\(95\) | −3.29180 | −0.337731 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.41641 | 0.956091 | 0.478046 | − | 0.878335i | \(-0.341345\pi\) | ||||
0.478046 | + | 0.878335i | \(0.341345\pi\) | |||||||
\(98\) | −1.61803 | −0.163446 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.52786 | −0.948058 | −0.474029 | − | 0.880509i | \(-0.657201\pi\) | ||||
−0.474029 | + | 0.880509i | \(0.657201\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4721 | −1.03185 | −0.515925 | − | 0.856634i | \(-0.672552\pi\) | ||||
−0.515925 | + | 0.856634i | \(0.672552\pi\) | |||||||
\(104\) | 0.527864 | 0.0517613 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.4721 | 1.01714 | ||||||||
\(107\) | −19.6525 | −1.89988 | −0.949938 | − | 0.312438i | \(-0.898854\pi\) | ||||
−0.949938 | + | 0.312438i | \(0.898854\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4721 | −1.00305 | −0.501524 | − | 0.865144i | \(-0.667227\pi\) | ||||
−0.501524 | + | 0.865144i | \(0.667227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.85410 | −0.458670 | ||||||||
\(113\) | 5.52786 | 0.520018 | 0.260009 | − | 0.965606i | \(-0.416275\pi\) | ||||
0.260009 | + | 0.965606i | \(0.416275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.47214 | 0.417029 | ||||||||
\(116\) | −3.09017 | −0.286915 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.8541 | 1.18332 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −20.1803 | −1.82704 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.47214 | 0.581215 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.41641 | −0.835571 | −0.417786 | − | 0.908546i | \(-0.637194\pi\) | ||||
−0.417786 | + | 0.908546i | \(0.637194\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.854102 | −0.0749097 | ||||||||
\(131\) | −19.4164 | −1.69642 | −0.848210 | − | 0.529661i | \(-0.822319\pi\) | ||||
−0.848210 | + | 0.529661i | \(0.822319\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.47214 | −0.127650 | ||||||||
\(134\) | −14.8541 | −1.28320 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.47214 | −0.383482 | ||||||||
\(137\) | 9.41641 | 0.804498 | 0.402249 | − | 0.915530i | \(-0.368229\pi\) | ||||
0.402249 | + | 0.915530i | \(0.368229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.94427 | −0.758643 | −0.379322 | − | 0.925265i | \(-0.623843\pi\) | ||||
−0.379322 | + | 0.925265i | \(0.623843\pi\) | |||||||
\(140\) | 1.38197 | 0.116797 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | −0.335673 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.1803 | −0.928477 | ||||||||
\(146\) | 17.3262 | 1.43393 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.909830 | −0.0747876 | ||||||||
\(149\) | −21.0000 | −1.72039 | −0.860194 | − | 0.509968i | \(-0.829657\pi\) | ||||
−0.860194 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | −3.29180 | −0.267000 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.4164 | 1.88085 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.52786 | 0.281554 | 0.140777 | − | 0.990041i | \(-0.455040\pi\) | ||||
0.140777 | + | 0.990041i | \(0.455040\pi\) | |||||||
\(158\) | 0.763932 | 0.0607752 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.56231 | 0.597853 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.76393 | −0.294814 | −0.147407 | − | 0.989076i | \(-0.547093\pi\) | ||||
−0.147407 | + | 0.989076i | \(0.547093\pi\) | |||||||
\(164\) | −1.52786 | −0.119306 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.1803 | 0.945378 | ||||||||
\(167\) | 5.41641 | 0.419134 | 0.209567 | − | 0.977794i | \(-0.432795\pi\) | ||||
0.209567 | + | 0.977794i | \(0.432795\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9443 | −0.995713 | ||||||||
\(170\) | 7.23607 | 0.554981 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.23607 | −0.399246 | ||||||||
\(173\) | 7.52786 | 0.572333 | 0.286166 | − | 0.958180i | \(-0.407619\pi\) | ||||
0.286166 | + | 0.958180i | \(0.407619\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.763932 | −0.0572591 | ||||||||
\(179\) | 26.3607 | 1.97029 | 0.985145 | − | 0.171725i | \(-0.0549342\pi\) | ||||
0.985145 | + | 0.171725i | \(0.0549342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9443 | 0.962140 | 0.481070 | − | 0.876682i | \(-0.340248\pi\) | ||||
0.481070 | + | 0.876682i | \(0.340248\pi\) | |||||||
\(182\) | −0.381966 | −0.0283132 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.47214 | 0.329690 | ||||||||
\(185\) | −3.29180 | −0.242018 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.85410 | −0.426954 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.32624 | 0.386406 | ||||||||
\(191\) | −15.5279 | −1.12356 | −0.561778 | − | 0.827288i | \(-0.689883\pi\) | ||||
−0.561778 | + | 0.827288i | \(0.689883\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.52786 | 0.109978 | 0.0549890 | − | 0.998487i | \(-0.482488\pi\) | ||||
0.0549890 | + | 0.998487i | \(0.482488\pi\) | |||||||
\(194\) | −15.2361 | −1.09389 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.618034 | 0.0441453 | ||||||||
\(197\) | 23.8885 | 1.70199 | 0.850994 | − | 0.525175i | \(-0.176000\pi\) | ||||
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.8885 | −0.842757 | −0.421378 | − | 0.906885i | \(-0.638454\pi\) | ||||
−0.421378 | + | 0.906885i | \(0.638454\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.4164 | 1.08469 | ||||||||
\(203\) | −5.00000 | −0.350931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.52786 | −0.386083 | ||||||||
\(206\) | 16.9443 | 1.18056 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.14590 | −0.0794537 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.3607 | 1.81474 | 0.907372 | − | 0.420328i | \(-0.138085\pi\) | ||||
0.907372 | + | 0.420328i | \(0.138085\pi\) | |||||||
\(212\) | −4.00000 | −0.274721 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 31.7984 | 2.17369 | ||||||||
\(215\) | −18.9443 | −1.29199 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4721 | 0.710895 | ||||||||
\(218\) | 16.9443 | 1.14761 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.472136 | −0.0317593 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.8885 | −1.59970 | −0.799848 | − | 0.600203i | \(-0.795086\pi\) | ||||
−0.799848 | + | 0.600203i | \(0.795086\pi\) | |||||||
\(224\) | 3.38197 | 0.225967 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.94427 | −0.594964 | ||||||||
\(227\) | −3.52786 | −0.234153 | −0.117076 | − | 0.993123i | \(-0.537352\pi\) | ||||
−0.117076 | + | 0.993123i | \(0.537352\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | −7.23607 | −0.477132 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.1803 | −0.734025 | ||||||||
\(233\) | −14.9443 | −0.979032 | −0.489516 | − | 0.871994i | \(-0.662826\pi\) | ||||
−0.489516 | + | 0.871994i | \(0.662826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.1803 | −1.38165 | ||||||||
\(236\) | −4.90983 | −0.319603 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.23607 | 0.209763 | ||||||||
\(239\) | 26.1246 | 1.68986 | 0.844930 | − | 0.534876i | \(-0.179642\pi\) | ||||
0.844930 | + | 0.534876i | \(0.179642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.1803 | −1.23551 | −0.617757 | − | 0.786369i | \(-0.711959\pi\) | ||||
−0.617757 | + | 0.786369i | \(0.711959\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.70820 | 0.493467 | ||||||||
\(245\) | 2.23607 | 0.142857 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.347524 | −0.0221124 | ||||||||
\(248\) | 23.4164 | 1.48694 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.0902 | 1.14412 | ||||||||
\(251\) | 11.0000 | 0.694314 | 0.347157 | − | 0.937807i | \(-0.387147\pi\) | ||||
0.347157 | + | 0.937807i | \(0.387147\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 15.2361 | 0.955996 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 13.6525 | 0.851618 | 0.425809 | − | 0.904813i | \(-0.359990\pi\) | ||||
0.425809 | + | 0.904813i | \(0.359990\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.47214 | −0.0914741 | ||||||||
\(260\) | 0.326238 | 0.0202324 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 31.4164 | 1.94091 | ||||||||
\(263\) | −11.2918 | −0.696282 | −0.348141 | − | 0.937442i | \(-0.613187\pi\) | ||||
−0.348141 | + | 0.937442i | \(0.613187\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.4721 | −0.889016 | ||||||||
\(266\) | 2.38197 | 0.146048 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.67376 | 0.346580 | ||||||||
\(269\) | −13.4164 | −0.818013 | −0.409006 | − | 0.912532i | \(-0.634125\pi\) | ||||
−0.409006 | + | 0.912532i | \(0.634125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.88854 | 0.418449 | 0.209225 | − | 0.977868i | \(-0.432906\pi\) | ||||
0.209225 | + | 0.977868i | \(0.432906\pi\) | |||||||
\(272\) | 9.70820 | 0.588646 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.2361 | −0.920445 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.3607 | 1.82420 | 0.912098 | − | 0.409972i | \(-0.134461\pi\) | ||||
0.912098 | + | 0.409972i | \(0.134461\pi\) | |||||||
\(278\) | 14.4721 | 0.867981 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.00000 | 0.298807 | ||||||||
\(281\) | −11.4721 | −0.684370 | −0.342185 | − | 0.939633i | \(-0.611167\pi\) | ||||
−0.342185 | + | 0.939633i | \(0.611167\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.4164 | −1.09474 | −0.547371 | − | 0.836890i | \(-0.684371\pi\) | ||||
−0.547371 | + | 0.836890i | \(0.684371\pi\) | |||||||
\(284\) | 1.52786 | 0.0906621 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.47214 | −0.145926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 18.0902 | 1.06229 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.61803 | −0.387291 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.7639 | −1.03426 | ||||||||
\(296\) | −3.29180 | −0.191332 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 33.9787 | 1.96833 | ||||||||
\(299\) | 0.472136 | 0.0273043 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.47214 | −0.488326 | ||||||||
\(302\) | −16.1803 | −0.931074 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.14590 | 0.409845 | ||||||||
\(305\) | 27.8885 | 1.59689 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.8885 | 1.70583 | 0.852915 | − | 0.522050i | \(-0.174833\pi\) | ||||
0.852915 | + | 0.522050i | \(0.174833\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −37.8885 | −2.15192 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9443 | 0.844700 | 0.422350 | − | 0.906433i | \(-0.361205\pi\) | ||||
0.422350 | + | 0.906433i | \(0.361205\pi\) | |||||||
\(314\) | −5.70820 | −0.322133 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.291796 | −0.0164148 | ||||||||
\(317\) | 3.05573 | 0.171627 | 0.0858134 | − | 0.996311i | \(-0.472651\pi\) | ||||
0.0858134 | + | 0.996311i | \(0.472651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 9.47214 | 0.529508 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.23607 | −0.180339 | ||||||||
\(323\) | 2.94427 | 0.163824 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.09017 | 0.337303 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.52786 | −0.305225 | ||||||||
\(329\) | −9.47214 | −0.522216 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | −0.879440 | −0.439720 | − | 0.898135i | \(-0.644922\pi\) | ||||
−0.439720 | + | 0.898135i | \(0.644922\pi\) | |||||||
\(332\) | −4.65248 | −0.255338 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.76393 | −0.479541 | ||||||||
\(335\) | 20.5279 | 1.12156 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.5279 | −1.49954 | −0.749769 | − | 0.661699i | \(-0.769835\pi\) | ||||
−0.749769 | + | 0.661699i | \(0.769835\pi\) | |||||||
\(338\) | 20.9443 | 1.13922 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.76393 | −0.149895 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −18.9443 | −1.02141 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.1803 | −0.654819 | ||||||||
\(347\) | 4.94427 | 0.265422 | 0.132711 | − | 0.991155i | \(-0.457632\pi\) | ||||
0.132711 | + | 0.991155i | \(0.457632\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.1246 | 0.970188 | 0.485094 | − | 0.874462i | \(-0.338785\pi\) | ||||
0.485094 | + | 0.874462i | \(0.338785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.18034 | 0.275722 | 0.137861 | − | 0.990452i | \(-0.455977\pi\) | ||||
0.137861 | + | 0.990452i | \(0.455977\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.52786 | 0.293389 | ||||||||
\(356\) | 0.291796 | 0.0154652 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −42.6525 | −2.25425 | ||||||||
\(359\) | −28.9443 | −1.52762 | −0.763810 | − | 0.645441i | \(-0.776674\pi\) | ||||
−0.763810 | + | 0.645441i | \(0.776674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8328 | −0.885938 | ||||||||
\(362\) | −20.9443 | −1.10081 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.145898 | 0.00764713 | ||||||||
\(365\) | −23.9443 | −1.25330 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | −0.835193 | −0.417597 | − | 0.908633i | \(-0.637127\pi\) | ||||
−0.417597 | + | 0.908633i | \(0.637127\pi\) | |||||||
\(368\) | −9.70820 | −0.506075 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.32624 | 0.276898 | ||||||||
\(371\) | −6.47214 | −0.336017 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.1803 | −1.09229 | ||||||||
\(377\) | −1.18034 | −0.0607906 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7639 | 0.604273 | 0.302136 | − | 0.953265i | \(-0.402300\pi\) | ||||
0.302136 | + | 0.953265i | \(0.402300\pi\) | |||||||
\(380\) | −2.03444 | −0.104365 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 25.1246 | 1.28549 | ||||||||
\(383\) | 0.944272 | 0.0482500 | 0.0241250 | − | 0.999709i | \(-0.492320\pi\) | ||||
0.0241250 | + | 0.999709i | \(0.492320\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.47214 | −0.125828 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.81966 | 0.295448 | ||||||||
\(389\) | 25.5279 | 1.29431 | 0.647157 | − | 0.762357i | \(-0.275958\pi\) | ||||
0.647157 | + | 0.762357i | \(0.275958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −38.6525 | −1.94728 | ||||||||
\(395\) | −1.05573 | −0.0531194 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.9443 | 1.35229 | 0.676147 | − | 0.736767i | \(-0.263648\pi\) | ||||
0.676147 | + | 0.736767i | \(0.263648\pi\) | |||||||
\(398\) | 19.2361 | 0.964217 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.0000 | 1.29838 | 0.649189 | − | 0.760627i | \(-0.275108\pi\) | ||||
0.649189 | + | 0.760627i | \(0.275108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.47214 | 0.123146 | ||||||||
\(404\) | −5.88854 | −0.292966 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.09017 | 0.401508 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.52786 | −0.372229 | −0.186114 | − | 0.982528i | \(-0.559590\pi\) | ||||
−0.186114 | + | 0.982528i | \(0.559590\pi\) | |||||||
\(410\) | 8.94427 | 0.441726 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.47214 | −0.318859 | ||||||||
\(413\) | −7.94427 | −0.390912 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.8328 | −0.826290 | ||||||||
\(416\) | 0.798374 | 0.0391435 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.0000 | −0.830504 | −0.415252 | − | 0.909706i | \(-0.636307\pi\) | ||||
−0.415252 | + | 0.909706i | \(0.636307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.3607 | −1.82085 | −0.910424 | − | 0.413676i | \(-0.864245\pi\) | ||||
−0.910424 | + | 0.413676i | \(0.864245\pi\) | |||||||
\(422\) | −42.6525 | −2.07629 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.4721 | −0.702829 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4721 | 0.603569 | ||||||||
\(428\) | −12.1459 | −0.587094 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 30.6525 | 1.47819 | ||||||||
\(431\) | −20.2361 | −0.974737 | −0.487369 | − | 0.873196i | \(-0.662043\pi\) | ||||
−0.487369 | + | 0.873196i | \(0.662043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.58359 | 0.316387 | 0.158194 | − | 0.987408i | \(-0.449433\pi\) | ||||
0.158194 | + | 0.987408i | \(0.449433\pi\) | |||||||
\(434\) | −16.9443 | −0.813351 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.47214 | −0.309959 | ||||||||
\(437\) | −2.94427 | −0.140844 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.8885 | 1.28332 | 0.641660 | − | 0.766989i | \(-0.278246\pi\) | ||||
0.641660 | + | 0.766989i | \(0.278246\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.763932 | 0.0363365 | ||||||||
\(443\) | −14.0000 | −0.665160 | −0.332580 | − | 0.943075i | \(-0.607919\pi\) | ||||
−0.332580 | + | 0.943075i | \(0.607919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.05573 | 0.0500463 | ||||||||
\(446\) | 38.6525 | 1.83025 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.23607 | 0.200135 | ||||||||
\(449\) | −0.472136 | −0.0222815 | −0.0111407 | − | 0.999938i | \(-0.503546\pi\) | ||||
−0.0111407 | + | 0.999938i | \(0.503546\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.41641 | 0.160694 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.70820 | 0.267899 | ||||||||
\(455\) | 0.527864 | 0.0247466 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.36068 | 0.297540 | 0.148770 | − | 0.988872i | \(-0.452469\pi\) | ||||
0.148770 | + | 0.988872i | \(0.452469\pi\) | |||||||
\(458\) | −22.6525 | −1.05848 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.76393 | 0.128869 | ||||||||
\(461\) | −18.9443 | −0.882323 | −0.441161 | − | 0.897428i | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.70820 | 0.311757 | 0.155878 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155878 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(464\) | 24.2705 | 1.12673 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.1803 | 1.12013 | ||||||||
\(467\) | −10.0557 | −0.465324 | −0.232662 | − | 0.972558i | \(-0.574744\pi\) | ||||
−0.232662 | + | 0.972558i | \(0.574744\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.18034 | 0.423909 | ||||||||
\(470\) | 34.2705 | 1.58078 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17.7639 | −0.817651 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.23607 | −0.0566551 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −42.2705 | −1.93341 | ||||||||
\(479\) | 35.8885 | 1.63979 | 0.819895 | − | 0.572514i | \(-0.194032\pi\) | ||||
0.819895 | + | 0.572514i | \(0.194032\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.347524 | −0.0158457 | ||||||||
\(482\) | 31.0344 | 1.41358 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0557 | 0.956091 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.88854 | 0.266835 | 0.133418 | − | 0.991060i | \(-0.457405\pi\) | ||||
0.133418 | + | 0.991060i | \(0.457405\pi\) | |||||||
\(488\) | 27.8885 | 1.26246 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.61803 | −0.163446 | ||||||||
\(491\) | 12.1246 | 0.547176 | 0.273588 | − | 0.961847i | \(-0.411790\pi\) | ||||
0.273588 | + | 0.961847i | \(0.411790\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0000 | 0.450377 | ||||||||
\(494\) | 0.562306 | 0.0252993 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −50.8328 | −2.28246 | ||||||||
\(497\) | 2.47214 | 0.110890 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.7639 | 0.884755 | 0.442378 | − | 0.896829i | \(-0.354135\pi\) | ||||
0.442378 | + | 0.896829i | \(0.354135\pi\) | |||||||
\(500\) | −6.90983 | −0.309017 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.7984 | −0.794380 | ||||||||
\(503\) | −9.88854 | −0.440908 | −0.220454 | − | 0.975397i | \(-0.570754\pi\) | ||||
−0.220454 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.3050 | −0.948058 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.81966 | −0.258206 | ||||||||
\(509\) | −33.4164 | −1.48116 | −0.740578 | − | 0.671970i | \(-0.765448\pi\) | ||||
−0.740578 | + | 0.671970i | \(0.765448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.7082 | −0.473703 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.0902 | −0.974356 | ||||||||
\(515\) | −23.4164 | −1.03185 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.38197 | 0.104658 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.18034 | 0.0517613 | ||||||||
\(521\) | −10.1246 | −0.443567 | −0.221784 | − | 0.975096i | \(-0.571188\pi\) | ||||
−0.221784 | + | 0.975096i | \(0.571188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.58359 | −0.0692456 | −0.0346228 | − | 0.999400i | \(-0.511023\pi\) | ||||
−0.0346228 | + | 0.999400i | \(0.511023\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.2705 | 0.796632 | ||||||||
\(527\) | −20.9443 | −0.912347 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 23.4164 | 1.01714 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.909830 | −0.0394461 | ||||||||
\(533\) | −0.583592 | −0.0252782 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.9443 | −1.89988 | ||||||||
\(536\) | 20.5279 | 0.886669 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.7082 | 0.935907 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.3607 | −1.04735 | −0.523674 | − | 0.851919i | \(-0.675439\pi\) | ||||
−0.523674 | + | 0.851919i | \(0.675439\pi\) | |||||||
\(542\) | −11.1459 | −0.478757 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.76393 | −0.290001 | ||||||||
\(545\) | −23.4164 | −1.00305 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.0000 | 1.11168 | 0.555840 | − | 0.831289i | \(-0.312397\pi\) | ||||
0.555840 | + | 0.831289i | \(0.312397\pi\) | |||||||
\(548\) | 5.81966 | 0.248604 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.36068 | 0.313576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.472136 | −0.0200773 | ||||||||
\(554\) | −49.1246 | −2.08710 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.52786 | −0.234434 | ||||||||
\(557\) | −15.8328 | −0.670858 | −0.335429 | − | 0.942066i | \(-0.608881\pi\) | ||||
−0.335429 | + | 0.942066i | \(0.608881\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | −10.8541 | −0.458670 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.5623 | 0.783004 | ||||||||
\(563\) | −21.8885 | −0.922492 | −0.461246 | − | 0.887272i | \(-0.652597\pi\) | ||||
−0.461246 | + | 0.887272i | \(0.652597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.3607 | 0.520018 | ||||||||
\(566\) | 29.7984 | 1.25252 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.52786 | 0.231944 | ||||||||
\(569\) | 2.00000 | 0.0838444 | 0.0419222 | − | 0.999121i | \(-0.486652\pi\) | ||||
0.0419222 | + | 0.999121i | \(0.486652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.8328 | 1.87619 | 0.938097 | − | 0.346371i | \(-0.112586\pi\) | ||||
0.938097 | + | 0.346371i | \(0.112586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.4721 | 1.10205 | 0.551025 | − | 0.834489i | \(-0.314237\pi\) | ||||
0.551025 | + | 0.834489i | \(0.314237\pi\) | |||||||
\(578\) | 21.0344 | 0.874917 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.90983 | −0.286915 | ||||||||
\(581\) | −7.52786 | −0.312308 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −23.9443 | −0.990821 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.7771 | 1.43540 | 0.717702 | − | 0.696350i | \(-0.245194\pi\) | ||||
0.717702 | + | 0.696350i | \(0.245194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.4164 | −0.635222 | ||||||||
\(590\) | 28.7426 | 1.18332 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.14590 | 0.293695 | ||||||||
\(593\) | −4.11146 | −0.168837 | −0.0844186 | − | 0.996430i | \(-0.526903\pi\) | ||||
−0.0844186 | + | 0.996430i | \(0.526903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.47214 | −0.183340 | ||||||||
\(596\) | −12.9787 | −0.531629 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.763932 | −0.0312395 | ||||||||
\(599\) | −4.47214 | −0.182727 | −0.0913633 | − | 0.995818i | \(-0.529122\pi\) | ||||
−0.0913633 | + | 0.995818i | \(0.529122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7082 | −0.763124 | −0.381562 | − | 0.924343i | \(-0.624614\pi\) | ||||
−0.381562 | + | 0.924343i | \(0.624614\pi\) | |||||||
\(602\) | 13.7082 | 0.558705 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.18034 | 0.251474 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.9443 | −1.13422 | −0.567112 | − | 0.823641i | \(-0.691939\pi\) | ||||
−0.567112 | + | 0.823641i | \(0.691939\pi\) | |||||||
\(608\) | −4.97871 | −0.201914 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −45.1246 | −1.82704 | ||||||||
\(611\) | −2.23607 | −0.0904616 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.0000 | −0.969351 | −0.484675 | − | 0.874694i | \(-0.661062\pi\) | ||||
−0.484675 | + | 0.874694i | \(0.661062\pi\) | |||||||
\(614\) | −48.3607 | −1.95168 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.8328 | −1.08025 | −0.540124 | − | 0.841585i | \(-0.681623\pi\) | ||||
−0.540124 | + | 0.841585i | \(0.681623\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.88854 | 0.236681 | 0.118340 | − | 0.992973i | \(-0.462243\pi\) | ||||
0.118340 | + | 0.992973i | \(0.462243\pi\) | |||||||
\(620\) | 14.4721 | 0.581215 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.472136 | 0.0189157 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | −24.1803 | −0.966441 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.18034 | 0.0870050 | ||||||||
\(629\) | 2.94427 | 0.117396 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.8328 | 1.06820 | 0.534099 | − | 0.845422i | \(-0.320651\pi\) | ||||
0.534099 | + | 0.845422i | \(0.320651\pi\) | |||||||
\(632\) | −1.05573 | −0.0419946 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.94427 | −0.196362 | ||||||||
\(635\) | −21.0557 | −0.835571 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.236068 | 0.00935335 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −30.4508 | −1.20368 | ||||||||
\(641\) | −15.4164 | −0.608912 | −0.304456 | − | 0.952526i | \(-0.598475\pi\) | ||||
−0.304456 | + | 0.952526i | \(0.598475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.7771 | −1.48978 | −0.744891 | − | 0.667186i | \(-0.767499\pi\) | ||||
−0.744891 | + | 0.667186i | \(0.767499\pi\) | |||||||
\(644\) | 1.23607 | 0.0487079 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.76393 | −0.187434 | ||||||||
\(647\) | −50.3050 | −1.97769 | −0.988846 | − | 0.148942i | \(-0.952413\pi\) | ||||
−0.988846 | + | 0.148942i | \(0.952413\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.32624 | −0.0911025 | ||||||||
\(653\) | −36.9443 | −1.44574 | −0.722871 | − | 0.690983i | \(-0.757178\pi\) | ||||
−0.722871 | + | 0.690983i | \(0.757178\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −43.4164 | −1.69642 | ||||||||
\(656\) | 12.0000 | 0.468521 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.3262 | 0.597479 | ||||||||
\(659\) | 24.1246 | 0.939761 | 0.469881 | − | 0.882730i | \(-0.344297\pi\) | ||||
0.469881 | + | 0.882730i | \(0.344297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.3050 | −0.984249 | −0.492124 | − | 0.870525i | \(-0.663779\pi\) | ||||
−0.492124 | + | 0.870525i | \(0.663779\pi\) | |||||||
\(662\) | 25.8885 | 1.00619 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.8328 | −0.653240 | ||||||||
\(665\) | −3.29180 | −0.127650 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0000 | −0.387202 | ||||||||
\(668\) | 3.34752 | 0.129520 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −33.2148 | −1.28320 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.9443 | 0.961531 | 0.480766 | − | 0.876849i | \(-0.340359\pi\) | ||||
0.480766 | + | 0.876849i | \(0.340359\pi\) | |||||||
\(674\) | 44.5410 | 1.71566 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.00000 | −0.307692 | ||||||||
\(677\) | −17.5279 | −0.673651 | −0.336825 | − | 0.941567i | \(-0.609353\pi\) | ||||
−0.336825 | + | 0.941567i | \(0.609353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.41641 | 0.361369 | ||||||||
\(680\) | −10.0000 | −0.383482 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.9443 | −1.71974 | −0.859872 | − | 0.510509i | \(-0.829457\pi\) | ||||
−0.859872 | + | 0.510509i | \(0.829457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.0557 | 0.804498 | ||||||||
\(686\) | −1.61803 | −0.0617768 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 41.1246 | 1.56786 | ||||||||
\(689\) | −1.52786 | −0.0582070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.8328 | −0.564267 | −0.282133 | − | 0.959375i | \(-0.591042\pi\) | ||||
−0.282133 | + | 0.959375i | \(0.591042\pi\) | |||||||
\(692\) | 4.65248 | 0.176861 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.00000 | −0.303676 | ||||||||
\(695\) | −20.0000 | −0.758643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.94427 | 0.187278 | ||||||||
\(698\) | −29.3262 | −1.11001 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1115 | 0.457443 | 0.228722 | − | 0.973492i | \(-0.426545\pi\) | ||||
0.228722 | + | 0.973492i | \(0.426545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.16718 | 0.0817369 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.38197 | −0.315459 | ||||||||
\(707\) | −9.52786 | −0.358332 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.5279 | −1.29672 | −0.648361 | − | 0.761333i | \(-0.724545\pi\) | ||||
−0.648361 | + | 0.761333i | \(0.724545\pi\) | |||||||
\(710\) | −8.94427 | −0.335673 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.05573 | 0.0395651 | ||||||||
\(713\) | 20.9443 | 0.784369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.2918 | 0.608853 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 46.8328 | 1.74779 | ||||||||
\(719\) | −21.3607 | −0.796619 | −0.398309 | − | 0.917251i | \(-0.630403\pi\) | ||||
−0.398309 | + | 0.917251i | \(0.630403\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.4721 | −0.390003 | ||||||||
\(722\) | 27.2361 | 1.01362 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.00000 | 0.297318 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.52786 | −0.130841 | −0.0654206 | − | 0.997858i | \(-0.520839\pi\) | ||||
−0.0654206 | + | 0.997858i | \(0.520839\pi\) | |||||||
\(728\) | 0.527864 | 0.0195639 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 38.7426 | 1.43393 | ||||||||
\(731\) | 16.9443 | 0.626707 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.3607 | −0.973654 | −0.486827 | − | 0.873498i | \(-0.661846\pi\) | ||||
−0.486827 | + | 0.873498i | \(0.661846\pi\) | |||||||
\(734\) | 25.8885 | 0.955564 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.76393 | 0.249322 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.8885 | 1.90875 | 0.954375 | − | 0.298609i | \(-0.0965227\pi\) | ||||
0.954375 | + | 0.298609i | \(0.0965227\pi\) | |||||||
\(740\) | −2.03444 | −0.0747876 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.4721 | 0.384444 | ||||||||
\(743\) | 30.5967 | 1.12249 | 0.561243 | − | 0.827651i | \(-0.310323\pi\) | ||||
0.561243 | + | 0.827651i | \(0.310323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −46.9574 | −1.72039 | ||||||||
\(746\) | −9.70820 | −0.355443 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.6525 | −0.718086 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.18034 | −0.262014 | −0.131007 | − | 0.991381i | \(-0.541821\pi\) | ||||
−0.131007 | + | 0.991381i | \(0.541821\pi\) | |||||||
\(752\) | 45.9787 | 1.67667 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.90983 | 0.0695519 | ||||||||
\(755\) | 22.3607 | 0.813788 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.5836 | −0.566395 | −0.283198 | − | 0.959062i | \(-0.591395\pi\) | ||||
−0.283198 | + | 0.959062i | \(0.591395\pi\) | |||||||
\(758\) | −19.0344 | −0.691362 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.36068 | −0.267000 | ||||||||
\(761\) | −24.4721 | −0.887114 | −0.443557 | − | 0.896246i | \(-0.646284\pi\) | ||||
−0.443557 | + | 0.896246i | \(0.646284\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.4721 | −0.379117 | ||||||||
\(764\) | −9.59675 | −0.347198 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.52786 | −0.0552040 | ||||||||
\(767\) | −1.87539 | −0.0677163 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.1803 | −0.547417 | −0.273709 | − | 0.961813i | \(-0.588250\pi\) | ||||
−0.273709 | + | 0.961813i | \(0.588250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.944272 | 0.0339851 | ||||||||
\(773\) | 19.1803 | 0.689869 | 0.344934 | − | 0.938627i | \(-0.387901\pi\) | ||||
0.344934 | + | 0.938627i | \(0.387901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 21.0557 | 0.755857 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.3050 | −1.48085 | ||||||||
\(779\) | 3.63932 | 0.130392 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.47214 | 0.231443 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.85410 | −0.173361 | ||||||||
\(785\) | 7.88854 | 0.281554 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.2492 | 1.61296 | 0.806480 | − | 0.591261i | \(-0.201370\pi\) | ||||
0.806480 | + | 0.591261i | \(0.201370\pi\) | |||||||
\(788\) | 14.7639 | 0.525943 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.70820 | 0.0607752 | ||||||||
\(791\) | 5.52786 | 0.196548 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.94427 | 0.104554 | ||||||||
\(794\) | −43.5967 | −1.54719 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.34752 | −0.260426 | ||||||||
\(797\) | 37.7639 | 1.33767 | 0.668834 | − | 0.743412i | \(-0.266794\pi\) | ||||
0.668834 | + | 0.743412i | \(0.266794\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.9443 | 0.670200 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −42.0689 | −1.48550 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.47214 | 0.157622 | ||||||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.3050 | −0.749506 | ||||||||
\(809\) | −49.3607 | −1.73543 | −0.867715 | − | 0.497063i | \(-0.834412\pi\) | ||||
−0.867715 | + | 0.497063i | \(0.834412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.5279 | 1.42313 | 0.711563 | − | 0.702622i | \(-0.247988\pi\) | ||||
0.711563 | + | 0.702622i | \(0.247988\pi\) | |||||||
\(812\) | −3.09017 | −0.108444 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.41641 | −0.294814 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.4721 | 0.436345 | ||||||||
\(818\) | 12.1803 | 0.425876 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.41641 | −0.119306 | ||||||||
\(821\) | −1.83282 | −0.0639657 | −0.0319829 | − | 0.999488i | \(-0.510182\pi\) | ||||
−0.0319829 | + | 0.999488i | \(0.510182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.0689 | −1.15271 | −0.576354 | − | 0.817200i | \(-0.695525\pi\) | ||||
−0.576354 | + | 0.817200i | \(0.695525\pi\) | |||||||
\(824\) | −23.4164 | −0.815749 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.8541 | 0.447251 | ||||||||
\(827\) | 26.2361 | 0.912317 | 0.456159 | − | 0.889898i | \(-0.349225\pi\) | ||||
0.456159 | + | 0.889898i | \(0.349225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.9443 | −0.727425 | −0.363712 | − | 0.931511i | \(-0.618491\pi\) | ||||
−0.363712 | + | 0.931511i | \(0.618491\pi\) | |||||||
\(830\) | 27.2361 | 0.945378 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.1115 | 0.419134 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.5066 | 0.950199 | ||||||||
\(839\) | −29.2492 | −1.00980 | −0.504898 | − | 0.863179i | \(-0.668470\pi\) | ||||
−0.504898 | + | 0.863179i | \(0.668470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 60.4508 | 2.08327 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.2918 | 0.560787 | ||||||||
\(845\) | −28.9443 | −0.995713 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 31.4164 | 1.07884 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.94427 | −0.100928 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.4164 | −1.00720 | −0.503599 | − | 0.863937i | \(-0.667991\pi\) | ||||
−0.503599 | + | 0.863937i | \(0.667991\pi\) | |||||||
\(854\) | −20.1803 | −0.690557 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −43.9443 | −1.50198 | ||||||||
\(857\) | 14.5836 | 0.498166 | 0.249083 | − | 0.968482i | \(-0.419871\pi\) | ||||
0.249083 | + | 0.968482i | \(0.419871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.05573 | 0.308977 | 0.154489 | − | 0.987995i | \(-0.450627\pi\) | ||||
0.154489 | + | 0.987995i | \(0.450627\pi\) | |||||||
\(860\) | −11.7082 | −0.399246 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.7426 | 1.11522 | ||||||||
\(863\) | −25.8885 | −0.881256 | −0.440628 | − | 0.897690i | \(-0.645244\pi\) | ||||
−0.440628 | + | 0.897690i | \(0.645244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.8328 | 0.572333 | ||||||||
\(866\) | −10.6525 | −0.361986 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.47214 | 0.219679 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.16718 | 0.0734322 | ||||||||
\(872\) | −23.4164 | −0.792980 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.76393 | 0.161142 | ||||||||
\(875\) | −11.1803 | −0.377964 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.0000 | −0.945493 | −0.472746 | − | 0.881199i | \(-0.656737\pi\) | ||||
−0.472746 | + | 0.881199i | \(0.656737\pi\) | |||||||
\(878\) | −43.5066 | −1.46828 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.2361 | −1.35559 | −0.677794 | − | 0.735252i | \(-0.737064\pi\) | ||||
−0.677794 | + | 0.735252i | \(0.737064\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.1803 | −0.847386 | −0.423693 | − | 0.905806i | \(-0.639266\pi\) | ||||
−0.423693 | + | 0.905806i | \(0.639266\pi\) | |||||||
\(884\) | −0.291796 | −0.00981416 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.6525 | 0.761025 | ||||||||
\(887\) | −16.9443 | −0.568933 | −0.284466 | − | 0.958686i | \(-0.591816\pi\) | ||||
−0.284466 | + | 0.958686i | \(0.591816\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.41641 | −0.315816 | ||||||||
\(890\) | −1.70820 | −0.0572591 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.7639 | −0.494333 | ||||||||
\(893\) | 13.9443 | 0.466627 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 58.9443 | 1.97029 | ||||||||
\(896\) | −13.6180 | −0.454947 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.763932 | 0.0254927 | ||||||||
\(899\) | −52.3607 | −1.74633 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9443 | 0.431236 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.3607 | 0.411110 | ||||||||
\(905\) | 28.9443 | 0.962140 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.7771 | 1.85205 | 0.926024 | − | 0.377465i | \(-0.123204\pi\) | ||||
0.926024 | + | 0.377465i | \(0.123204\pi\) | |||||||
\(908\) | −2.18034 | −0.0723571 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.854102 | −0.0283132 | ||||||||
\(911\) | 54.2492 | 1.79736 | 0.898678 | − | 0.438608i | \(-0.144528\pi\) | ||||
0.898678 | + | 0.438608i | \(0.144528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −10.2918 | −0.340422 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.65248 | 0.285886 | ||||||||
\(917\) | −19.4164 | −0.641186 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.4721 | 0.741287 | 0.370644 | − | 0.928775i | \(-0.379137\pi\) | ||||
0.370644 | + | 0.928775i | \(0.379137\pi\) | |||||||
\(920\) | 10.0000 | 0.329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.6525 | 1.00949 | ||||||||
\(923\) | 0.583592 | 0.0192092 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −10.8541 | −0.356688 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.9098 | −0.555092 | ||||||||
\(929\) | −12.7082 | −0.416943 | −0.208471 | − | 0.978028i | \(-0.566849\pi\) | ||||
−0.208471 | + | 0.978028i | \(0.566849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.47214 | −0.0482473 | ||||||||
\(932\) | −9.23607 | −0.302537 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.2705 | 0.532387 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.3607 | −1.25319 | −0.626594 | − | 0.779346i | \(-0.715552\pi\) | ||||
−0.626594 | + | 0.779346i | \(0.715552\pi\) | |||||||
\(938\) | −14.8541 | −0.485004 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.0902 | −0.426954 | ||||||||
\(941\) | −26.5836 | −0.866600 | −0.433300 | − | 0.901250i | \(-0.642651\pi\) | ||||
−0.433300 | + | 0.901250i | \(0.642651\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.94427 | −0.161008 | ||||||||
\(944\) | 38.5623 | 1.25510 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.0000 | 1.42981 | 0.714904 | − | 0.699223i | \(-0.246470\pi\) | ||||
0.714904 | + | 0.699223i | \(0.246470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.52786 | −0.0820579 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.47214 | −0.144943 | ||||||||
\(953\) | −8.41641 | −0.272634 | −0.136317 | − | 0.990665i | \(-0.543527\pi\) | ||||
−0.136317 | + | 0.990665i | \(0.543527\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.7214 | −1.12356 | ||||||||
\(956\) | 16.1459 | 0.522196 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −58.0689 | −1.87612 | ||||||||
\(959\) | 9.41641 | 0.304072 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.6656 | 2.53760 | ||||||||
\(962\) | 0.562306 | 0.0181295 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.8541 | −0.381795 | ||||||||
\(965\) | 3.41641 | 0.109978 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.3050 | 0.427858 | 0.213929 | − | 0.976849i | \(-0.431374\pi\) | ||||
0.213929 | + | 0.976849i | \(0.431374\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34.0689 | −1.09389 | ||||||||
\(971\) | −12.0557 | −0.386887 | −0.193443 | − | 0.981111i | \(-0.561966\pi\) | ||||
−0.193443 | + | 0.981111i | \(0.561966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.94427 | −0.286740 | ||||||||
\(974\) | −9.52786 | −0.305292 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −60.5410 | −1.93787 | ||||||||
\(977\) | −16.4721 | −0.526990 | −0.263495 | − | 0.964661i | \(-0.584875\pi\) | ||||
−0.263495 | + | 0.964661i | \(0.584875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.38197 | 0.0441453 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.6180 | −0.626037 | ||||||||
\(983\) | 40.0000 | 1.27580 | 0.637901 | − | 0.770118i | \(-0.279803\pi\) | ||||
0.637901 | + | 0.770118i | \(0.279803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53.4164 | 1.70199 | ||||||||
\(986\) | −16.1803 | −0.515287 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.214782 | −0.00683312 | ||||||||
\(989\) | −16.9443 | −0.538797 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1803 | −0.355155 | −0.177578 | − | 0.984107i | \(-0.556826\pi\) | ||||
−0.177578 | + | 0.984107i | \(0.556826\pi\) | |||||||
\(992\) | 35.4164 | 1.12447 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.00000 | −0.126872 | ||||||||
\(995\) | −26.5836 | −0.842757 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.1935 | −1.81134 | −0.905668 | − | 0.423987i | \(-0.860630\pi\) | ||||
−0.905668 | + | 0.423987i | \(0.860630\pi\) | |||||||
\(998\) | −31.9787 | −1.01227 | ||||||||
\(999\) | 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 | 7623.2.a.y.1.1 | 2 | ||
3.2 | odd | 2 | 2541.2.a.y.1.2 | yes | 2 | ||
11.10 | odd | 2 | 7623.2.a.bn.1.2 | 2 | |||
33.32 | even | 2 | 2541.2.a.q.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.q.1.1 | ✓ | 2 | 33.32 | even | 2 | ||
2541.2.a.y.1.2 | yes | 2 | 3.2 | odd | 2 | ||
7623.2.a.y.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7623.2.a.bn.1.2 | 2 | 11.10 | odd | 2 |