Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7360,2,Mod(1,7360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7360 = 2^{6} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7360.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: | \(58.7698958877\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3680) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7360.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | −0.288675 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288675 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.64575 | 0.622036 | 0.311018 | − | 0.950404i | \(-0.399330\pi\) | ||||
0.311018 | + | 0.950404i | \(0.399330\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.64575 | 0.496213 | 0.248106 | − | 0.968733i | \(-0.420192\pi\) | ||||
0.248106 | + | 0.968733i | \(0.420192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.64575 | −0.733799 | −0.366900 | − | 0.930261i | \(-0.619581\pi\) | ||||
−0.366900 | + | 0.930261i | \(0.619581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.29150 | −1.76845 | −0.884225 | − | 0.467062i | \(-0.845312\pi\) | ||||
−0.884225 | + | 0.467062i | \(0.845312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.64575 | 1.29522 | 0.647612 | − | 0.761970i | \(-0.275768\pi\) | ||||
0.647612 | + | 0.761970i | \(0.275768\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.64575 | −0.359132 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.645751 | −0.115980 | −0.0579902 | − | 0.998317i | \(-0.518469\pi\) | ||||
−0.0579902 | + | 0.998317i | \(0.518469\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.64575 | −0.286489 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.64575 | −0.278183 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.64575 | 1.58575 | 0.792876 | − | 0.609383i | \(-0.208583\pi\) | ||||
0.792876 | + | 0.609383i | \(0.208583\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.64575 | 0.423659 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.29150 | 0.670220 | 0.335110 | − | 0.942179i | \(-0.391226\pi\) | ||||
0.335110 | + | 0.942179i | \(0.391226\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.64575 | 0.250975 | 0.125487 | − | 0.992095i | \(-0.459951\pi\) | ||||
0.125487 | + | 0.992095i | \(0.459951\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.29150 | −0.613072 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.29150 | 1.02101 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.29150 | −0.726844 | −0.363422 | − | 0.931625i | \(-0.618392\pi\) | ||||
−0.363422 | + | 0.931625i | \(0.618392\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.64575 | −0.221913 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.64575 | −0.747798 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.29150 | 0.688895 | 0.344447 | − | 0.938806i | \(-0.388066\pi\) | ||||
0.344447 | + | 0.938806i | \(0.388066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.35425 | 1.06965 | 0.534826 | − | 0.844962i | \(-0.320377\pi\) | ||||
0.534826 | + | 0.844962i | \(0.320377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.29150 | −0.414690 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.64575 | 0.328165 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.93725 | −0.847520 | −0.423760 | − | 0.905774i | \(-0.639290\pi\) | ||||
−0.423760 | + | 0.905774i | \(0.639290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.35425 | −0.160720 | −0.0803599 | − | 0.996766i | \(-0.525607\pi\) | ||||
−0.0803599 | + | 0.996766i | \(0.525607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.64575 | −0.543744 | −0.271872 | − | 0.962333i | \(-0.587643\pi\) | ||||
−0.271872 | + | 0.962333i | \(0.587643\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.70850 | 0.308662 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.64575 | −0.185161 | −0.0925807 | − | 0.995705i | \(-0.529512\pi\) | ||||
−0.0925807 | + | 0.995705i | \(0.529512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.5830 | −1.60069 | −0.800346 | − | 0.599538i | \(-0.795351\pi\) | ||||
−0.800346 | + | 0.599538i | \(0.795351\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.29150 | 0.790875 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.00000 | −0.321634 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.64575 | −0.174449 | −0.0872246 | − | 0.996189i | \(-0.527800\pi\) | ||||
−0.0872246 | + | 0.996189i | \(0.527800\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.35425 | −0.456449 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.645751 | 0.0669613 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.64575 | −0.579242 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.93725 | 0.298233 | 0.149116 | − | 0.988820i | \(-0.452357\pi\) | ||||
0.149116 | + | 0.988820i | \(0.452357\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.29150 | −0.330808 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.00000 | 0.796030 | 0.398015 | − | 0.917379i | \(-0.369699\pi\) | ||||
0.398015 | + | 0.917379i | \(0.369699\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.29150 | 0.718453 | 0.359227 | − | 0.933250i | \(-0.383041\pi\) | ||||
0.359227 | + | 0.933250i | \(0.383041\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.64575 | 0.160609 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.2288 | −1.76224 | −0.881120 | − | 0.472892i | \(-0.843210\pi\) | ||||
−0.881120 | + | 0.472892i | \(0.843210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.35425 | 0.225496 | 0.112748 | − | 0.993624i | \(-0.464035\pi\) | ||||
0.112748 | + | 0.993624i | \(0.464035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.64575 | −0.915534 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.354249 | −0.0333249 | −0.0166625 | − | 0.999861i | \(-0.505304\pi\) | ||||
−0.0166625 | + | 0.999861i | \(0.505304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.29150 | 0.489200 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.0000 | −1.10004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.29150 | −0.753773 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.29150 | −0.386952 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | 0.0443678 | − | 0.999015i | \(-0.485873\pi\) | ||||
0.0443678 | + | 0.999015i | \(0.485873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.64575 | −0.144900 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.35425 | −0.467803 | −0.233901 | − | 0.972260i | \(-0.575149\pi\) | ||||
−0.233901 | + | 0.972260i | \(0.575149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.29150 | 0.805675 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.00000 | −0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.87451 | 0.843636 | 0.421818 | − | 0.906680i | \(-0.361392\pi\) | ||||
0.421818 | + | 0.906680i | \(0.361392\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.93725 | −0.503591 | −0.251796 | − | 0.967780i | \(-0.581021\pi\) | ||||
−0.251796 | + | 0.967780i | \(0.581021\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.35425 | −0.364121 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00000 | −0.249136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.29150 | 0.353957 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.2288 | −1.40206 | −0.701028 | − | 0.713134i | \(-0.747275\pi\) | ||||
−0.701028 | + | 0.713134i | \(0.747275\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.5830 | 1.17897 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.645751 | 0.0518680 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.2288 | 1.45481 | 0.727407 | − | 0.686207i | \(-0.240725\pi\) | ||||
0.727407 | + | 0.686207i | \(0.240725\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.29150 | 0.419643 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.64575 | −0.129703 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.87451 | 0.538453 | 0.269227 | − | 0.963077i | \(-0.413232\pi\) | ||||
0.269227 | + | 0.963077i | \(0.413232\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.64575 | 0.128122 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.58301 | 0.354644 | 0.177322 | − | 0.984153i | \(-0.443257\pi\) | ||||
0.177322 | + | 0.984153i | \(0.443257\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | −0.461538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.2915 | −0.863483 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.5830 | −0.956668 | −0.478334 | − | 0.878178i | \(-0.658759\pi\) | ||||
−0.478334 | + | 0.878178i | \(0.658759\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.64575 | 0.124407 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.29150 | −0.397734 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.35425 | 0.549682 | 0.274841 | − | 0.961490i | \(-0.411375\pi\) | ||||
0.274841 | + | 0.961490i | \(0.411375\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.93725 | 0.218324 | 0.109162 | − | 0.994024i | \(-0.465183\pi\) | ||||
0.109162 | + | 0.994024i | \(0.465183\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.35425 | −0.617564 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.64575 | −0.709170 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.22876 | 0.598554 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.8745 | 1.43807 | 0.719034 | − | 0.694974i | \(-0.244584\pi\) | ||||
0.719034 | + | 0.694974i | \(0.244584\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.2288 | −1.52808 | −0.764040 | − | 0.645169i | \(-0.776787\pi\) | ||||
−0.764040 | + | 0.645169i | \(0.776787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.64575 | −0.189466 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0627461 | 0.00447047 | 0.00223524 | − | 0.999998i | \(-0.499289\pi\) | ||||
0.00223524 | + | 0.999998i | \(0.499289\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.64575 | 0.400217 | 0.200108 | − | 0.979774i | \(-0.435871\pi\) | ||||
0.200108 | + | 0.979774i | \(0.435871\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.93725 | 0.489316 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.93725 | 0.346527 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.29150 | −0.299732 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.29150 | 0.642707 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.87451 | 0.679789 | 0.339895 | − | 0.940464i | \(-0.389609\pi\) | ||||
0.339895 | + | 0.940464i | \(0.389609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.35425 | 0.0927916 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.64575 | −0.112239 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.06275 | −0.0721439 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.64575 | 0.313931 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.2915 | 1.29769 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000 | 0.937509 | 0.468755 | − | 0.883328i | \(-0.344703\pi\) | ||||
0.468755 | + | 0.883328i | \(0.344703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.9373 | −1.12417 | −0.562083 | − | 0.827081i | \(-0.690000\pi\) | ||||
−0.562083 | + | 0.827081i | \(0.690000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.937254 | −0.0619355 | −0.0309677 | − | 0.999520i | \(-0.509859\pi\) | ||||
−0.0309677 | + | 0.999520i | \(0.509859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.70850 | −0.178206 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.22876 | −0.342547 | −0.171274 | − | 0.985224i | \(-0.554788\pi\) | ||||
−0.171274 | + | 0.985224i | \(0.554788\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.64575 | 0.106903 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.35425 | 0.346338 | 0.173169 | − | 0.984892i | \(-0.444599\pi\) | ||||
0.173169 | + | 0.984892i | \(0.444599\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.8745 | −1.02257 | −0.511283 | − | 0.859412i | \(-0.670830\pi\) | ||||
−0.511283 | + | 0.859412i | \(0.670830\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.29150 | 0.274174 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.9373 | −0.950435 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.5830 | 0.924160 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.64575 | −0.103467 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.29150 | −0.456612 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.6458 | −1.53736 | −0.768680 | − | 0.639634i | \(-0.779086\pi\) | ||||
−0.768680 | + | 0.639634i | \(0.779086\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8745 | 0.986394 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.2288 | −1.61733 | −0.808667 | − | 0.588266i | \(-0.799811\pi\) | ||||
−0.808667 | + | 0.588266i | \(0.799811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.29150 | 0.325054 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.64575 | 0.100718 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.00000 | −0.304855 | −0.152428 | − | 0.988315i | \(-0.548709\pi\) | ||||
−0.152428 | + | 0.988315i | \(0.548709\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.70850 | 0.286021 | 0.143010 | − | 0.989721i | \(-0.454322\pi\) | ||||
0.143010 | + | 0.989721i | \(0.454322\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.35425 | 0.263531 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.64575 | 0.0992425 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.64575 | 0.279136 | 0.139568 | − | 0.990212i | \(-0.455429\pi\) | ||||
0.139568 | + | 0.990212i | \(0.455429\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.29150 | 0.0773202 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.22876 | −0.490886 | −0.245443 | − | 0.969411i | \(-0.578933\pi\) | ||||
−0.245443 | + | 0.969411i | \(0.578933\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.70850 | −0.398779 | −0.199389 | − | 0.979920i | \(-0.563896\pi\) | ||||
−0.199389 | + | 0.979920i | \(0.563896\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.64575 | 0.334425 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.06275 | 0.416901 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.1660 | 2.12741 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.93725 | −0.172185 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.29150 | −0.308083 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.22876 | 0.477481 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.64575 | 0.153008 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.70850 | 0.156115 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.00000 | −0.459588 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.35425 | −0.478363 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8745 | 1.36259 | 0.681295 | − | 0.732009i | \(-0.261417\pi\) | ||||
0.681295 | + | 0.732009i | \(0.261417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.29150 | −0.414799 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0627 | −0.570606 | −0.285303 | − | 0.958437i | \(-0.592094\pi\) | ||||
−0.285303 | + | 0.958437i | \(0.592094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.29150 | 0.185455 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0000 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.93725 | 0.276433 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.2288 | 1.01743 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −41.1660 | −2.29054 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.64575 | −0.146760 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.35425 | −0.130190 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.93725 | −0.272200 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.9373 | −1.86536 | −0.932680 | − | 0.360705i | \(-0.882536\pi\) | ||||
−0.932680 | + | 0.360705i | \(0.882536\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.2915 | −1.05717 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.93725 | 0.379023 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.77124 | −0.0964858 | −0.0482429 | − | 0.998836i | \(-0.515362\pi\) | ||||
−0.0482429 | + | 0.998836i | \(0.515362\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.354249 | 0.0192401 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.06275 | −0.0575509 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5830 | −1.00339 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.58301 | 0.460760 | 0.230380 | − | 0.973101i | \(-0.426003\pi\) | ||||
0.230380 | + | 0.973101i | \(0.426003\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.1660 | −0.972404 | −0.486202 | − | 0.873846i | \(-0.661618\pi\) | ||||
−0.486202 | + | 0.873846i | \(0.661618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.2288 | −0.706099 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.6458 | −1.52466 | −0.762330 | − | 0.647189i | \(-0.775945\pi\) | ||||
−0.762330 | + | 0.647189i | \(0.775945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.35425 | 0.0718761 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.0000 | 0.635107 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.2288 | −0.645409 | −0.322705 | − | 0.946500i | \(-0.604592\pi\) | ||||
−0.322705 | + | 0.946500i | \(0.604592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.8745 | 0.677606 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.29150 | 0.435191 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.64575 | 0.243170 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.8745 | −1.35064 | −0.675319 | − | 0.737526i | \(-0.735994\pi\) | ||||
−0.675319 | + | 0.737526i | \(0.735994\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.58301 | −0.446813 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.70850 | −0.452123 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.1660 | 0.578154 | 0.289077 | − | 0.957306i | \(-0.406652\pi\) | ||||
0.289077 | + | 0.957306i | \(0.406652\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.93725 | −0.408789 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.8745 | −1.12362 | −0.561809 | − | 0.827267i | \(-0.689894\pi\) | ||||
−0.561809 | + | 0.827267i | \(0.689894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.00000 | −0.0512316 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.2288 | 0.829251 | 0.414625 | − | 0.909992i | \(-0.363913\pi\) | ||||
0.414625 | + | 0.909992i | \(0.363913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.70850 | −0.138038 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.29150 | −0.167316 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.29150 | −0.369694 | −0.184847 | − | 0.982767i | \(-0.559179\pi\) | ||||
−0.184847 | + | 0.982767i | \(0.559179\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.29150 | 0.368747 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.35425 | 0.270086 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.64575 | 0.0828067 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.9373 | 0.799868 | 0.399934 | − | 0.916544i | \(-0.369033\pi\) | ||||
0.399934 | + | 0.916544i | \(0.369033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.29150 | −0.465157 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.7490 | −1.88510 | −0.942548 | − | 0.334071i | \(-0.891577\pi\) | ||||
−0.942548 | + | 0.334071i | \(0.891577\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.70850 | 0.0851063 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.8745 | 0.786870 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | 0.247234 | 0.123617 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123617 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.87451 | −0.487074 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.70850 | 0.428517 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.5830 | 0.715852 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.93725 | 0.290749 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.9373 | 1.51138 | 0.755692 | − | 0.654927i | \(-0.227301\pi\) | ||||
0.755692 | + | 0.654927i | \(0.227301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.22876 | −0.206097 | −0.103048 | − | 0.994676i | \(-0.532860\pi\) | ||||
−0.103048 | + | 0.994676i | \(0.532860\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.00000 | 0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.29150 | −0.353690 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.7490 | 0.665362 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.35425 | 0.210225 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.6458 | −1.33165 | −0.665824 | − | 0.746108i | \(-0.731920\pi\) | ||||
−0.665824 | + | 0.746108i | \(0.731920\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.00000 | 0.143839 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.64575 | −0.270073 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.6458 | −0.699004 | −0.349502 | − | 0.936936i | \(-0.613649\pi\) | ||||
−0.349502 | + | 0.936936i | \(0.613649\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.58301 | 0.408715 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.8745 | −1.56192 | −0.780958 | − | 0.624584i | \(-0.785268\pi\) | ||||
−0.780958 | + | 0.624584i | \(0.785268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.64575 | 0.0780161 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.41699 | 0.444415 | 0.222208 | − | 0.974999i | \(-0.428674\pi\) | ||||
0.222208 | + | 0.974999i | \(0.428674\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.06275 | 0.332572 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.2288 | 0.809478 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.35425 | 0.204130 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.7490 | −1.29804 | −0.649022 | − | 0.760770i | \(-0.724822\pi\) | ||||
−0.649022 | + | 0.760770i | \(0.724822\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −36.4575 | −1.70169 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.7085 | −0.917916 | −0.458958 | − | 0.888458i | \(-0.651777\pi\) | ||||
−0.458958 | + | 0.888458i | \(0.651777\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4575 | 0.857793 | 0.428897 | − | 0.903354i | \(-0.358902\pi\) | ||||
0.428897 | + | 0.903354i | \(0.358902\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.645751 | −0.0299460 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.58301 | 0.212076 | 0.106038 | − | 0.994362i | \(-0.466183\pi\) | ||||
0.106038 | + | 0.994362i | \(0.466183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.4170 | −0.527188 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.2288 | −0.839937 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.70850 | 0.124537 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.64575 | 0.259045 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.5830 | 0.484563 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.29150 | 0.333157 | 0.166579 | − | 0.986028i | \(-0.446728\pi\) | ||||
0.166579 | + | 0.986028i | \(0.446728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.5203 | −1.16362 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.64575 | 0.0748843 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.93725 | −0.133374 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.7085 | −0.711820 | −0.355910 | − | 0.934520i | \(-0.615829\pi\) | ||||
−0.355910 | + | 0.934520i | \(0.615829\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.87451 | −0.310876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3542 | 0.783186 | 0.391593 | − | 0.920138i | \(-0.371924\pi\) | ||||
0.391593 | + | 0.920138i | \(0.371924\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.8745 | −0.985178 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.29150 | 0.147942 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.22876 | −0.0999734 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.06275 | 0.0923412 | 0.0461706 | − | 0.998934i | \(-0.485298\pi\) | ||||
0.0461706 | + | 0.998934i | \(0.485298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.58301 | −0.204754 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.4575 | −1.89309 | −0.946543 | − | 0.322576i | \(-0.895451\pi\) | ||||
−0.946543 | + | 0.322576i | \(0.895451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | 0.266469 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.8745 | 0.925246 | 0.462623 | − | 0.886555i | \(-0.346908\pi\) | ||||
0.462623 | + | 0.886555i | \(0.346908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.64575 | −0.338228 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28.2288 | 1.24633 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.29150 | −0.321302 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.93725 | −0.217140 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.5830 | 0.552333 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.4575 | 1.77248 | 0.886238 | − | 0.463230i | \(-0.153310\pi\) | ||||
0.886238 | + | 0.463230i | \(0.153310\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.8118 | −0.997489 | −0.498744 | − | 0.866749i | \(-0.666205\pi\) | ||||
−0.498744 | + | 0.866749i | \(0.666205\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.64575 | −0.0718265 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.70850 | 0.205105 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.5830 | −0.459263 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.3542 | −0.491807 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.2288 | 0.788098 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.35425 | −0.317359 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.06275 | −0.304214 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.0405 | −1.72148 | −0.860738 | − | 0.509048i | \(-0.829998\pi\) | ||||
−0.860738 | + | 0.509048i | \(0.829998\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.93725 | −0.126050 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.35425 | −0.100845 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1660 | −0.691209 | −0.345604 | − | 0.938380i | \(-0.612326\pi\) | ||||
−0.345604 | + | 0.938380i | \(0.612326\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.7085 | −0.713101 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9373 | 0.721551 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.70850 | −0.115177 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.64575 | 0.409439 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.5203 | 1.08133 | 0.540664 | − | 0.841239i | \(-0.318173\pi\) | ||||
0.540664 | + | 0.841239i | \(0.318173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.35425 | −0.184165 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.5830 | −1.79466 | −0.897330 | − | 0.441361i | \(-0.854496\pi\) | ||||
−0.897330 | + | 0.441361i | \(0.854496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.354249 | 0.0149034 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.64575 | 0.0691151 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.4170 | 0.478625 | 0.239313 | − | 0.970943i | \(-0.423078\pi\) | ||||
0.239313 | + | 0.970943i | \(0.423078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.4575 | −1.02352 | −0.511758 | − | 0.859130i | \(-0.671005\pi\) | ||||
−0.511758 | + | 0.859130i | \(0.671005\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.8745 | −0.830269 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.3542 | −0.888989 | −0.444495 | − | 0.895782i | \(-0.646617\pi\) | ||||
−0.444495 | + | 0.895782i | \(0.646617\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.2288 | 0.882237 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | −0.995688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.70850 | −0.360669 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.29150 | −0.218777 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.8745 | 0.861583 | 0.430792 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430792 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.64575 | −0.150221 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0627461 | −0.00258103 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.7490 | 0.810995 | 0.405497 | − | 0.914096i | \(-0.367098\pi\) | ||||
0.405497 | + | 0.914096i | \(0.367098\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | 0.491952 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.64575 | −0.231065 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.8745 | −1.62923 | −0.814614 | − | 0.580003i | \(-0.803051\pi\) | ||||
−0.814614 | + | 0.580003i | \(0.803051\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0000 | 0.775026 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.8745 | 0.565014 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.29150 | 0.337098 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.7085 | 0.759354 | 0.379677 | − | 0.925119i | \(-0.376035\pi\) | ||||
0.379677 | + | 0.925119i | \(0.376035\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.93725 | −0.200068 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.93725 | 0.321107 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.2915 | −1.91009 | −0.955043 | − | 0.296468i | \(-0.904191\pi\) | ||||
−0.955043 | + | 0.296468i | \(0.904191\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.29150 | 0.173050 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.9373 | 1.48704 | 0.743519 | − | 0.668715i | \(-0.233155\pi\) | ||||
0.743519 | + | 0.668715i | \(0.233155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2915 | 0.614617 | 0.307309 | − | 0.951610i | \(-0.400572\pi\) | ||||
0.307309 | + | 0.951610i | \(0.400572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.00000 | −0.200643 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.70850 | −0.108514 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.29150 | −0.371067 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −70.3320 | −2.80432 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.5203 | 0.856708 | 0.428354 | − | 0.903611i | \(-0.359094\pi\) | ||||
0.428354 | + | 0.903611i | \(0.359094\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.87451 | −0.392476 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.00000 | −0.0396838 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.3542 | 0.449872 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.70850 | 0.107147 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.9373 | 1.61692 | 0.808462 | − | 0.588548i | \(-0.200300\pi\) | ||||
0.808462 | + | 0.588548i | \(0.200300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.2915 | 0.681910 | 0.340955 | − | 0.940080i | \(-0.389250\pi\) | ||||
0.340955 | + | 0.940080i | \(0.389250\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.64575 | 0.0648014 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.2915 | −0.876369 | −0.438185 | − | 0.898885i | \(-0.644378\pi\) | ||||
−0.438185 | + | 0.898885i | \(0.644378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.70850 | 0.341838 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.06275 | 0.0416523 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.520259 | 0.0203593 | 0.0101797 | − | 0.999948i | \(-0.496760\pi\) | ||||
0.0101797 | + | 0.999948i | \(0.496760\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.35425 | 0.209208 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.29150 | 0.362496 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.16601 | 0.278726 | 0.139363 | − | 0.990241i | \(-0.455495\pi\) | ||||
0.139363 | + | 0.990241i | \(0.455495\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.2915 | −0.749220 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.29150 | −0.360309 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.00000 | −0.116160 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.0000 | −0.541271 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.7490 | 0.530775 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.1033 | 0.505094 | 0.252547 | − | 0.967585i | \(-0.418732\pi\) | ||||
0.252547 | + | 0.967585i | \(0.418732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.83399 | 0.185511 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.9373 | 0.649037 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.0405 | 1.14947 | 0.574734 | − | 0.818340i | \(-0.305105\pi\) | ||||
0.574734 | + | 0.818340i | \(0.305105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.87451 | −0.377286 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.937254 | 0.0357585 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.0000 | 0.533358 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8745 | 0.527811 | 0.263906 | − | 0.964549i | \(-0.414989\pi\) | ||||
0.263906 | + | 0.964549i | \(0.414989\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.41699 | −0.205775 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.93725 | 0.225213 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.2915 | −1.18525 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.22876 | 0.197770 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.0627 | −0.417834 | −0.208917 | − | 0.977933i | \(-0.566994\pi\) | ||||
−0.208917 | + | 0.977933i | \(0.566994\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.4575 | 2.05390 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.00000 | −0.112987 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.1660 | 0.495159 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.3542 | −1.29020 | −0.645100 | − | 0.764098i | \(-0.723184\pi\) | ||||
−0.645100 | + | 0.764098i | \(0.723184\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.29150 | 0.123441 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.645751 | 0.0241836 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.35425 | 0.162840 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.35425 | −0.199958 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.1255 | 0.526792 | 0.263396 | − | 0.964688i | \(-0.415157\pi\) | ||||
0.263396 | + | 0.964688i | \(0.415157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.8745 | 0.590379 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | 0.111417 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.4575 | −0.684551 | −0.342276 | − | 0.939600i | \(-0.611198\pi\) | ||||
−0.342276 | + | 0.939600i | \(0.611198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | −0.443836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5830 | 0.390892 | 0.195446 | − | 0.980714i | \(-0.437385\pi\) | ||||
0.195446 | + | 0.980714i | \(0.437385\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.29150 | −0.158294 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.4170 | −0.420550 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.06275 | 0.296593 | 0.148296 | − | 0.988943i | \(-0.452621\pi\) | ||||
0.148296 | + | 0.988943i | \(0.452621\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.9373 | 0.548734 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.2915 | −1.58821 | −0.794106 | − | 0.607780i | \(-0.792060\pi\) | ||||
−0.794106 | + | 0.607780i | \(0.792060\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0000 | 0.366372 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 29.1660 | 1.06713 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.0000 | −1.09618 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.9778 | −1.96968 | −0.984838 | − | 0.173474i | \(-0.944501\pi\) | ||||
−0.984838 | + | 0.173474i | \(0.944501\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.0000 | 0.874609 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.2288 | 0.627019 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.6458 | 1.94979 | 0.974894 | − | 0.222669i | \(-0.0714771\pi\) | ||||
0.974894 | + | 0.222669i | \(0.0714771\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.64575 | 0.0597370 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.1660 | 0.586017 | 0.293009 | − | 0.956110i | \(-0.405344\pi\) | ||||
0.293009 | + | 0.956110i | \(0.405344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.87451 | 0.140267 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.5830 | −0.527250 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.0000 | −0.505511 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.1660 | 0.546900 | 0.273450 | − | 0.961886i | \(-0.411835\pi\) | ||||
0.273450 | + | 0.961886i | \(0.411835\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.6458 | 0.887595 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.2288 | −1.37499 | −0.687496 | − | 0.726188i | \(-0.741290\pi\) | ||||
−0.687496 | + | 0.726188i | \(0.741290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.645751 | −0.0231961 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.8745 | −0.569495 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.2288 | 0.868085 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.22876 | −0.0797512 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.0000 | 0.536056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.2288 | −0.650612 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.5830 | −0.377243 | −0.188622 | − | 0.982050i | \(-0.560402\pi\) | ||||
−0.188622 | + | 0.982050i | \(0.560402\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.2288 | 0.933768 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.583005 | −0.0207293 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.1033 | −0.784910 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.29150 | −0.187670 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.2288 | −1.14160 | −0.570801 | − | 0.821089i | \(-0.693367\pi\) | ||||
−0.570801 | + | 0.821089i | \(0.693367\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.8745 | 0.773864 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.29150 | 0.116300 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.64575 | −0.269813 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.64575 | 0.0580051 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.00000 | 0.176008 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.7490 | −1.53813 | −0.769067 | − | 0.639168i | \(-0.779279\pi\) | ||||
−0.769067 | + | 0.639168i | \(0.779279\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.2288 | 0.464524 | 0.232262 | − | 0.972653i | \(-0.425387\pi\) | ||||
0.232262 | + | 0.972653i | \(0.425387\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.70850 | −0.165134 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.87451 | −0.240804 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.29150 | 0.325069 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.70850 | 0.304300 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.5830 | 0.648551 | 0.324276 | − | 0.945963i | \(-0.394879\pi\) | ||||
0.324276 | + | 0.945963i | \(0.394879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.5830 | −0.891768 | −0.445884 | − | 0.895091i | \(-0.647111\pi\) | ||||
−0.445884 | + | 0.895091i | \(0.647111\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.64575 | −0.0572977 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.4575 | −1.82413 | −0.912063 | − | 0.410050i | \(-0.865511\pi\) | ||||
−0.912063 | + | 0.410050i | \(0.865511\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.0405 | 1.21701 | 0.608504 | − | 0.793551i | \(-0.291770\pi\) | ||||
0.608504 | + | 0.793551i | \(0.291770\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.64575 | −0.161159 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.2915 | 1.08419 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.58301 | −0.158601 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.22876 | −0.111602 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.06275 | 0.312881 | 0.156440 | − | 0.987687i | \(-0.449998\pi\) | ||||
0.156440 | + | 0.987687i | \(0.449998\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.22876 | 0.283413 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00000 | 0.206406 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.6458 | −0.468874 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.70850 | 0.230235 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.64575 | −0.330652 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.7490 | 0.607715 | 0.303857 | − | 0.952718i | \(-0.401725\pi\) | ||||
0.303857 | + | 0.952718i | \(0.401725\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.2915 | 0.386161 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.0627 | 0.753649 | 0.376825 | − | 0.926285i | \(-0.377016\pi\) | ||||
0.376825 | + | 0.926285i | \(0.377016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.7712 | 0.572227 | 0.286114 | − | 0.958196i | \(-0.407636\pi\) | ||||
0.286114 | + | 0.958196i | \(0.407636\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.06275 | −0.240698 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.8745 | −1.45947 | −0.729733 | − | 0.683733i | \(-0.760355\pi\) | ||||
−0.729733 | + | 0.683733i | \(0.760355\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.5830 | 0.427835 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.1660 | −1.22826 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.70850 | −0.0918795 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.3542 | 0.621910 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.87451 | −0.198822 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.64575 | −0.0556365 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.8745 | 0.806185 | 0.403092 | − | 0.915159i | \(-0.367935\pi\) | ||||
0.403092 | + | 0.915159i | \(0.367935\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.8745 | 1.27602 | 0.638012 | − | 0.770026i | \(-0.279757\pi\) | ||||
0.638012 | + | 0.770026i | \(0.279757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.58301 | −0.154230 | −0.0771152 | − | 0.997022i | \(-0.524571\pi\) | ||||
−0.0771152 | + | 0.997022i | \(0.524571\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.29150 | 0.177872 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.0405 | 0.874355 | 0.437178 | − | 0.899375i | \(-0.355978\pi\) | ||||
0.437178 | + | 0.899375i | \(0.355978\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.64575 | 0.0551967 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.64575 | 0.0551347 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.9373 | −0.566784 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.35425 | −0.245825 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.64575 | −0.0883391 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.93725 | −0.0646110 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.5830 | 1.28539 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.70850 | −0.0901331 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.93725 | −0.0976376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.3948 | −1.57372 | −0.786859 | − | 0.617133i | \(-0.788294\pi\) | ||||
−0.786859 | + | 0.617133i | \(0.788294\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.0000 | −0.530687 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5203 | 0.779261 | 0.389630 | − | 0.920971i | \(-0.372603\pi\) | ||||
0.389630 | + | 0.920971i | \(0.372603\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0000 | −0.794284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.35425 | 0.276183 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.81176 | −0.290990 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.0627 | 0.958692 | 0.479346 | − | 0.877626i | \(-0.340874\pi\) | ||||
0.479346 | + | 0.877626i | \(0.340874\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.8745 | −0.786692 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.58301 | 0.117936 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.64575 | 0.317150 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.5830 | −0.478969 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.4575 | 0.835234 | 0.417617 | − | 0.908623i | \(-0.362865\pi\) | ||||
0.417617 | + | 0.908623i | \(0.362865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.2288 | −0.794065 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.0627 | 0.329440 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | 0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.9373 | −0.422642 | −0.211321 | − | 0.977417i | \(-0.567776\pi\) | ||||
−0.211321 | + | 0.977417i | \(0.567776\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.7490 | 0.643800 | 0.321900 | − | 0.946774i | \(-0.395679\pi\) | ||||
0.321900 | + | 0.946774i | \(0.395679\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.29150 | −0.139751 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.22876 | −0.267681 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.4575 | −0.502302 | −0.251151 | − | 0.967948i | \(-0.580809\pi\) | ||||
−0.251151 | + | 0.967948i | \(0.580809\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.2915 | 0.398999 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.0000 | −0.453981 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.2915 | 0.689699 | 0.344850 | − | 0.938658i | \(-0.387930\pi\) | ||||
0.344850 | + | 0.938658i | \(0.387930\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.8745 | −0.643124 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.93725 | −0.159599 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.2510 | 0.524772 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5830 | −0.986549 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.4575 | 1.17483 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.2288 | 0.683378 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.8745 | −1.70033 | −0.850165 | − | 0.526517i | \(-0.823498\pi\) | ||||
−0.850165 | + | 0.526517i | \(0.823498\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.1660 | 1.32244 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.7490 | 0.697959 | 0.348980 | − | 0.937130i | \(-0.386528\pi\) | ||||
0.348980 | + | 0.937130i | \(0.386528\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.77124 | −0.313252 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.64575 | 0.0847319 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.6458 | −0.692509 | −0.346254 | − | 0.938141i | \(-0.612547\pi\) | ||||
−0.346254 | + | 0.938141i | \(0.612547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.70850 | −0.0865640 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.70850 | −0.150331 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.54249 | −0.0491977 | −0.0245988 | − | 0.999697i | \(-0.507831\pi\) | ||||
−0.0245988 | + | 0.999697i | \(0.507831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.0627461 | −0.00199926 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.93725 | 0.157155 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.64575 | −0.0523318 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.7490 | 1.51680 | 0.758399 | − | 0.651791i | \(-0.225982\pi\) | ||||
0.758399 | + | 0.651791i | \(0.225982\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.9373 | 1.07697 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.64575 | −0.178982 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.6235 | −1.63493 | −0.817467 | − | 0.575976i | \(-0.804622\pi\) | ||||
−0.817467 | + | 0.575976i | \(0.804622\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 48.2288 | 1.52589 |
(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 | 7360.2.a.be.1.2 | 2 | ||
4.3 | odd | 2 | 7360.2.a.br.1.1 | 2 | |||
8.3 | odd | 2 | 3680.2.a.m.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 3680.2.a.o.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3680.2.a.m.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
3680.2.a.o.1.2 | yes | 2 | 8.5 | even | 2 | ||
7360.2.a.be.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7360.2.a.br.1.1 | 2 | 4.3 | odd | 2 |