Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + \cdots + 1552 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.937159\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.937159 | −0.419110 | −0.209555 | − | 0.977797i | \(-0.567202\pi\) | ||||
−0.209555 | + | 0.977797i | \(0.567202\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.792704 | −0.299614 | −0.149807 | − | 0.988715i | \(-0.547865\pi\) | ||||
−0.149807 | + | 0.988715i | \(0.547865\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.937159 | 0.296356 | ||||||||
\(11\) | −4.70314 | −1.41805 | −0.709025 | − | 0.705183i | \(-0.750865\pi\) | ||||
−0.709025 | + | 0.705183i | \(0.750865\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.792704 | 0.211859 | ||||||||
\(15\) | 0.937159 | 0.241973 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.60442 | −0.874199 | −0.437100 | − | 0.899413i | \(-0.643994\pi\) | ||||
−0.437100 | + | 0.899413i | \(0.643994\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.803399 | −0.184312 | −0.0921562 | − | 0.995745i | \(-0.529376\pi\) | ||||
−0.0921562 | + | 0.995745i | \(0.529376\pi\) | |||||||
\(20\) | −0.937159 | −0.209555 | ||||||||
\(21\) | 0.792704 | 0.172982 | ||||||||
\(22\) | 4.70314 | 1.00271 | ||||||||
\(23\) | −4.68922 | −0.977770 | −0.488885 | − | 0.872348i | \(-0.662596\pi\) | ||||
−0.488885 | + | 0.872348i | \(0.662596\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.12173 | −0.824347 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.792704 | −0.149807 | ||||||||
\(29\) | −3.11482 | −0.578408 | −0.289204 | − | 0.957268i | \(-0.593391\pi\) | ||||
−0.289204 | + | 0.957268i | \(0.593391\pi\) | |||||||
\(30\) | −0.937159 | −0.171101 | ||||||||
\(31\) | −3.57843 | −0.642704 | −0.321352 | − | 0.946960i | \(-0.604137\pi\) | ||||
−0.321352 | + | 0.946960i | \(0.604137\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.70314 | 0.818712 | ||||||||
\(34\) | 3.60442 | 0.618152 | ||||||||
\(35\) | 0.742890 | 0.125571 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.63083 | 0.268107 | 0.134054 | − | 0.990974i | \(-0.457201\pi\) | ||||
0.134054 | + | 0.990974i | \(0.457201\pi\) | |||||||
\(38\) | 0.803399 | 0.130329 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0.937159 | 0.148178 | ||||||||
\(41\) | −7.48219 | −1.16852 | −0.584261 | − | 0.811566i | \(-0.698616\pi\) | ||||
−0.584261 | + | 0.811566i | \(0.698616\pi\) | |||||||
\(42\) | −0.792704 | −0.122317 | ||||||||
\(43\) | 3.98449 | 0.607629 | 0.303815 | − | 0.952731i | \(-0.401740\pi\) | ||||
0.303815 | + | 0.952731i | \(0.401740\pi\) | |||||||
\(44\) | −4.70314 | −0.709025 | ||||||||
\(45\) | −0.937159 | −0.139703 | ||||||||
\(46\) | 4.68922 | 0.691387 | ||||||||
\(47\) | 0.579710 | 0.0845593 | 0.0422797 | − | 0.999106i | \(-0.486538\pi\) | ||||
0.0422797 | + | 0.999106i | \(0.486538\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.37162 | −0.910231 | ||||||||
\(50\) | 4.12173 | 0.582901 | ||||||||
\(51\) | 3.60442 | 0.504719 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 5.61866 | 0.771782 | 0.385891 | − | 0.922544i | \(-0.373894\pi\) | ||||
0.385891 | + | 0.922544i | \(0.373894\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.40759 | 0.594320 | ||||||||
\(56\) | 0.792704 | 0.105930 | ||||||||
\(57\) | 0.803399 | 0.106413 | ||||||||
\(58\) | 3.11482 | 0.408996 | ||||||||
\(59\) | −1.93187 | −0.251508 | −0.125754 | − | 0.992061i | \(-0.540135\pi\) | ||||
−0.125754 | + | 0.992061i | \(0.540135\pi\) | |||||||
\(60\) | 0.937159 | 0.120987 | ||||||||
\(61\) | −14.8337 | −1.89926 | −0.949628 | − | 0.313380i | \(-0.898539\pi\) | ||||
−0.949628 | + | 0.313380i | \(0.898539\pi\) | |||||||
\(62\) | 3.57843 | 0.454461 | ||||||||
\(63\) | −0.792704 | −0.0998713 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.937159 | −0.116240 | ||||||||
\(66\) | −4.70314 | −0.578917 | ||||||||
\(67\) | 5.77582 | 0.705629 | 0.352815 | − | 0.935693i | \(-0.385225\pi\) | ||||
0.352815 | + | 0.935693i | \(0.385225\pi\) | |||||||
\(68\) | −3.60442 | −0.437100 | ||||||||
\(69\) | 4.68922 | 0.564516 | ||||||||
\(70\) | −0.742890 | −0.0887923 | ||||||||
\(71\) | −5.96557 | −0.707983 | −0.353991 | − | 0.935249i | \(-0.615176\pi\) | ||||
−0.353991 | + | 0.935249i | \(0.615176\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 0.810762 | 0.0948925 | 0.0474462 | − | 0.998874i | \(-0.484892\pi\) | ||||
0.0474462 | + | 0.998874i | \(0.484892\pi\) | |||||||
\(74\) | −1.63083 | −0.189580 | ||||||||
\(75\) | 4.12173 | 0.475937 | ||||||||
\(76\) | −0.803399 | −0.0921562 | ||||||||
\(77\) | 3.72820 | 0.424868 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 6.43093 | 0.723536 | 0.361768 | − | 0.932268i | \(-0.382173\pi\) | ||||
0.361768 | + | 0.932268i | \(0.382173\pi\) | |||||||
\(80\) | −0.937159 | −0.104778 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.48219 | 0.826270 | ||||||||
\(83\) | −5.41646 | −0.594534 | −0.297267 | − | 0.954794i | \(-0.596075\pi\) | ||||
−0.297267 | + | 0.954794i | \(0.596075\pi\) | |||||||
\(84\) | 0.792704 | 0.0864911 | ||||||||
\(85\) | 3.37791 | 0.366386 | ||||||||
\(86\) | −3.98449 | −0.429659 | ||||||||
\(87\) | 3.11482 | 0.333944 | ||||||||
\(88\) | 4.70314 | 0.501357 | ||||||||
\(89\) | −18.2668 | −1.93628 | −0.968141 | − | 0.250406i | \(-0.919436\pi\) | ||||
−0.968141 | + | 0.250406i | \(0.919436\pi\) | |||||||
\(90\) | 0.937159 | 0.0987852 | ||||||||
\(91\) | −0.792704 | −0.0830979 | ||||||||
\(92\) | −4.68922 | −0.488885 | ||||||||
\(93\) | 3.57843 | 0.371066 | ||||||||
\(94\) | −0.579710 | −0.0597925 | ||||||||
\(95\) | 0.752913 | 0.0772472 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 10.4350 | 1.05951 | 0.529755 | − | 0.848151i | \(-0.322284\pi\) | ||||
0.529755 | + | 0.848151i | \(0.322284\pi\) | |||||||
\(98\) | 6.37162 | 0.643631 | ||||||||
\(99\) | −4.70314 | −0.472684 | ||||||||
\(100\) | −4.12173 | −0.412173 | ||||||||
\(101\) | −1.41189 | −0.140488 | −0.0702441 | − | 0.997530i | \(-0.522378\pi\) | ||||
−0.0702441 | + | 0.997530i | \(0.522378\pi\) | |||||||
\(102\) | −3.60442 | −0.356890 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −0.742890 | −0.0724986 | ||||||||
\(106\) | −5.61866 | −0.545732 | ||||||||
\(107\) | 0.502970 | 0.0486240 | 0.0243120 | − | 0.999704i | \(-0.492260\pi\) | ||||
0.0243120 | + | 0.999704i | \(0.492260\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 17.7539 | 1.70052 | 0.850259 | − | 0.526365i | \(-0.176445\pi\) | ||||
0.850259 | + | 0.526365i | \(0.176445\pi\) | |||||||
\(110\) | −4.40759 | −0.420247 | ||||||||
\(111\) | −1.63083 | −0.154792 | ||||||||
\(112\) | −0.792704 | −0.0749035 | ||||||||
\(113\) | 8.02786 | 0.755198 | 0.377599 | − | 0.925969i | \(-0.376750\pi\) | ||||
0.377599 | + | 0.925969i | \(0.376750\pi\) | |||||||
\(114\) | −0.803399 | −0.0752453 | ||||||||
\(115\) | 4.39454 | 0.409793 | ||||||||
\(116\) | −3.11482 | −0.289204 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 1.93187 | 0.177843 | ||||||||
\(119\) | 2.85724 | 0.261922 | ||||||||
\(120\) | −0.937159 | −0.0855505 | ||||||||
\(121\) | 11.1196 | 1.01087 | ||||||||
\(122\) | 14.8337 | 1.34298 | ||||||||
\(123\) | 7.48219 | 0.674646 | ||||||||
\(124\) | −3.57843 | −0.321352 | ||||||||
\(125\) | 8.54851 | 0.764602 | ||||||||
\(126\) | 0.792704 | 0.0706197 | ||||||||
\(127\) | −8.03716 | −0.713183 | −0.356591 | − | 0.934260i | \(-0.616061\pi\) | ||||
−0.356591 | + | 0.934260i | \(0.616061\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.98449 | −0.350815 | ||||||||
\(130\) | 0.937159 | 0.0821943 | ||||||||
\(131\) | 4.13397 | 0.361186 | 0.180593 | − | 0.983558i | \(-0.442198\pi\) | ||||
0.180593 | + | 0.983558i | \(0.442198\pi\) | |||||||
\(132\) | 4.70314 | 0.409356 | ||||||||
\(133\) | 0.636858 | 0.0552226 | ||||||||
\(134\) | −5.77582 | −0.498955 | ||||||||
\(135\) | 0.937159 | 0.0806578 | ||||||||
\(136\) | 3.60442 | 0.309076 | ||||||||
\(137\) | −17.8896 | −1.52842 | −0.764208 | − | 0.644970i | \(-0.776870\pi\) | ||||
−0.764208 | + | 0.644970i | \(0.776870\pi\) | |||||||
\(138\) | −4.68922 | −0.399173 | ||||||||
\(139\) | −17.3454 | −1.47122 | −0.735608 | − | 0.677407i | \(-0.763104\pi\) | ||||
−0.735608 | + | 0.677407i | \(0.763104\pi\) | |||||||
\(140\) | 0.742890 | 0.0627856 | ||||||||
\(141\) | −0.579710 | −0.0488204 | ||||||||
\(142\) | 5.96557 | 0.500619 | ||||||||
\(143\) | −4.70314 | −0.393297 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.91908 | 0.242417 | ||||||||
\(146\) | −0.810762 | −0.0670991 | ||||||||
\(147\) | 6.37162 | 0.525522 | ||||||||
\(148\) | 1.63083 | 0.134054 | ||||||||
\(149\) | −9.59017 | −0.785657 | −0.392829 | − | 0.919612i | \(-0.628503\pi\) | ||||
−0.392829 | + | 0.919612i | \(0.628503\pi\) | |||||||
\(150\) | −4.12173 | −0.336538 | ||||||||
\(151\) | 8.93579 | 0.727184 | 0.363592 | − | 0.931558i | \(-0.381550\pi\) | ||||
0.363592 | + | 0.931558i | \(0.381550\pi\) | |||||||
\(152\) | 0.803399 | 0.0651643 | ||||||||
\(153\) | −3.60442 | −0.291400 | ||||||||
\(154\) | −3.72820 | −0.300427 | ||||||||
\(155\) | 3.35355 | 0.269364 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −18.9333 | −1.51104 | −0.755521 | − | 0.655125i | \(-0.772616\pi\) | ||||
−0.755521 | + | 0.655125i | \(0.772616\pi\) | |||||||
\(158\) | −6.43093 | −0.511617 | ||||||||
\(159\) | −5.61866 | −0.445588 | ||||||||
\(160\) | 0.937159 | 0.0740889 | ||||||||
\(161\) | 3.71716 | 0.292953 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −9.61838 | −0.753370 | −0.376685 | − | 0.926341i | \(-0.622936\pi\) | ||||
−0.376685 | + | 0.926341i | \(0.622936\pi\) | |||||||
\(164\) | −7.48219 | −0.584261 | ||||||||
\(165\) | −4.40759 | −0.343131 | ||||||||
\(166\) | 5.41646 | 0.420399 | ||||||||
\(167\) | −25.2414 | −1.95324 | −0.976621 | − | 0.214970i | \(-0.931035\pi\) | ||||
−0.976621 | + | 0.214970i | \(0.931035\pi\) | |||||||
\(168\) | −0.792704 | −0.0611584 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −3.37791 | −0.259074 | ||||||||
\(171\) | −0.803399 | −0.0614375 | ||||||||
\(172\) | 3.98449 | 0.303815 | ||||||||
\(173\) | 0.222644 | 0.0169273 | 0.00846364 | − | 0.999964i | \(-0.497306\pi\) | ||||
0.00846364 | + | 0.999964i | \(0.497306\pi\) | |||||||
\(174\) | −3.11482 | −0.236134 | ||||||||
\(175\) | 3.26731 | 0.246986 | ||||||||
\(176\) | −4.70314 | −0.354513 | ||||||||
\(177\) | 1.93187 | 0.145208 | ||||||||
\(178\) | 18.2668 | 1.36916 | ||||||||
\(179\) | 25.3993 | 1.89843 | 0.949217 | − | 0.314623i | \(-0.101878\pi\) | ||||
0.949217 | + | 0.314623i | \(0.101878\pi\) | |||||||
\(180\) | −0.937159 | −0.0698517 | ||||||||
\(181\) | −6.58007 | −0.489093 | −0.244546 | − | 0.969638i | \(-0.578639\pi\) | ||||
−0.244546 | + | 0.969638i | \(0.578639\pi\) | |||||||
\(182\) | 0.792704 | 0.0587591 | ||||||||
\(183\) | 14.8337 | 1.09654 | ||||||||
\(184\) | 4.68922 | 0.345694 | ||||||||
\(185\) | −1.52835 | −0.112366 | ||||||||
\(186\) | −3.57843 | −0.262383 | ||||||||
\(187\) | 16.9521 | 1.23966 | ||||||||
\(188\) | 0.579710 | 0.0422797 | ||||||||
\(189\) | 0.792704 | 0.0576607 | ||||||||
\(190\) | −0.752913 | −0.0546220 | ||||||||
\(191\) | 11.0853 | 0.802105 | 0.401052 | − | 0.916055i | \(-0.368644\pi\) | ||||
0.401052 | + | 0.916055i | \(0.368644\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 6.80068 | 0.489524 | 0.244762 | − | 0.969583i | \(-0.421290\pi\) | ||||
0.244762 | + | 0.969583i | \(0.421290\pi\) | |||||||
\(194\) | −10.4350 | −0.749186 | ||||||||
\(195\) | 0.937159 | 0.0671113 | ||||||||
\(196\) | −6.37162 | −0.455116 | ||||||||
\(197\) | −5.08227 | −0.362096 | −0.181048 | − | 0.983474i | \(-0.557949\pi\) | ||||
−0.181048 | + | 0.983474i | \(0.557949\pi\) | |||||||
\(198\) | 4.70314 | 0.334238 | ||||||||
\(199\) | 15.9413 | 1.13005 | 0.565024 | − | 0.825074i | \(-0.308867\pi\) | ||||
0.565024 | + | 0.825074i | \(0.308867\pi\) | |||||||
\(200\) | 4.12173 | 0.291451 | ||||||||
\(201\) | −5.77582 | −0.407395 | ||||||||
\(202\) | 1.41189 | 0.0993401 | ||||||||
\(203\) | 2.46913 | 0.173299 | ||||||||
\(204\) | 3.60442 | 0.252360 | ||||||||
\(205\) | 7.01200 | 0.489740 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −4.68922 | −0.325923 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 3.77850 | 0.261364 | ||||||||
\(210\) | 0.742890 | 0.0512643 | ||||||||
\(211\) | 10.7284 | 0.738571 | 0.369285 | − | 0.929316i | \(-0.379603\pi\) | ||||
0.369285 | + | 0.929316i | \(0.379603\pi\) | |||||||
\(212\) | 5.61866 | 0.385891 | ||||||||
\(213\) | 5.96557 | 0.408754 | ||||||||
\(214\) | −0.502970 | −0.0343824 | ||||||||
\(215\) | −3.73410 | −0.254664 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.83663 | 0.192563 | ||||||||
\(218\) | −17.7539 | −1.20245 | ||||||||
\(219\) | −0.810762 | −0.0547862 | ||||||||
\(220\) | 4.40759 | 0.297160 | ||||||||
\(221\) | −3.60442 | −0.242459 | ||||||||
\(222\) | 1.63083 | 0.109454 | ||||||||
\(223\) | −19.7800 | −1.32457 | −0.662284 | − | 0.749253i | \(-0.730413\pi\) | ||||
−0.662284 | + | 0.749253i | \(0.730413\pi\) | |||||||
\(224\) | 0.792704 | 0.0529648 | ||||||||
\(225\) | −4.12173 | −0.274782 | ||||||||
\(226\) | −8.02786 | −0.534006 | ||||||||
\(227\) | 13.3566 | 0.886507 | 0.443254 | − | 0.896396i | \(-0.353824\pi\) | ||||
0.443254 | + | 0.896396i | \(0.353824\pi\) | |||||||
\(228\) | 0.803399 | 0.0532064 | ||||||||
\(229\) | −1.87870 | −0.124148 | −0.0620741 | − | 0.998072i | \(-0.519772\pi\) | ||||
−0.0620741 | + | 0.998072i | \(0.519772\pi\) | |||||||
\(230\) | −4.39454 | −0.289768 | ||||||||
\(231\) | −3.72820 | −0.245298 | ||||||||
\(232\) | 3.11482 | 0.204498 | ||||||||
\(233\) | 16.0079 | 1.04871 | 0.524356 | − | 0.851499i | \(-0.324306\pi\) | ||||
0.524356 | + | 0.851499i | \(0.324306\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −0.543280 | −0.0354397 | ||||||||
\(236\) | −1.93187 | −0.125754 | ||||||||
\(237\) | −6.43093 | −0.417734 | ||||||||
\(238\) | −2.85724 | −0.185207 | ||||||||
\(239\) | 17.4394 | 1.12806 | 0.564031 | − | 0.825754i | \(-0.309250\pi\) | ||||
0.564031 | + | 0.825754i | \(0.309250\pi\) | |||||||
\(240\) | 0.937159 | 0.0604933 | ||||||||
\(241\) | −6.56601 | −0.422954 | −0.211477 | − | 0.977383i | \(-0.567827\pi\) | ||||
−0.211477 | + | 0.977383i | \(0.567827\pi\) | |||||||
\(242\) | −11.1196 | −0.714792 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −14.8337 | −0.949628 | ||||||||
\(245\) | 5.97122 | 0.381487 | ||||||||
\(246\) | −7.48219 | −0.477047 | ||||||||
\(247\) | −0.803399 | −0.0511191 | ||||||||
\(248\) | 3.57843 | 0.227230 | ||||||||
\(249\) | 5.41646 | 0.343254 | ||||||||
\(250\) | −8.54851 | −0.540655 | ||||||||
\(251\) | 18.8493 | 1.18976 | 0.594878 | − | 0.803816i | \(-0.297200\pi\) | ||||
0.594878 | + | 0.803816i | \(0.297200\pi\) | |||||||
\(252\) | −0.792704 | −0.0499357 | ||||||||
\(253\) | 22.0541 | 1.38653 | ||||||||
\(254\) | 8.03716 | 0.504296 | ||||||||
\(255\) | −3.37791 | −0.211533 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.0916 | −0.941389 | −0.470694 | − | 0.882296i | \(-0.655997\pi\) | ||||
−0.470694 | + | 0.882296i | \(0.655997\pi\) | |||||||
\(258\) | 3.98449 | 0.248064 | ||||||||
\(259\) | −1.29277 | −0.0803287 | ||||||||
\(260\) | −0.937159 | −0.0581201 | ||||||||
\(261\) | −3.11482 | −0.192803 | ||||||||
\(262\) | −4.13397 | −0.255397 | ||||||||
\(263\) | 2.51843 | 0.155293 | 0.0776465 | − | 0.996981i | \(-0.475259\pi\) | ||||
0.0776465 | + | 0.996981i | \(0.475259\pi\) | |||||||
\(264\) | −4.70314 | −0.289458 | ||||||||
\(265\) | −5.26557 | −0.323462 | ||||||||
\(266\) | −0.636858 | −0.0390483 | ||||||||
\(267\) | 18.2668 | 1.11791 | ||||||||
\(268\) | 5.77582 | 0.352815 | ||||||||
\(269\) | −26.3178 | −1.60462 | −0.802312 | − | 0.596905i | \(-0.796397\pi\) | ||||
−0.802312 | + | 0.596905i | \(0.796397\pi\) | |||||||
\(270\) | −0.937159 | −0.0570337 | ||||||||
\(271\) | 6.11955 | 0.371736 | 0.185868 | − | 0.982575i | \(-0.440490\pi\) | ||||
0.185868 | + | 0.982575i | \(0.440490\pi\) | |||||||
\(272\) | −3.60442 | −0.218550 | ||||||||
\(273\) | 0.792704 | 0.0479766 | ||||||||
\(274\) | 17.8896 | 1.08075 | ||||||||
\(275\) | 19.3851 | 1.16897 | ||||||||
\(276\) | 4.68922 | 0.282258 | ||||||||
\(277\) | −31.2379 | −1.87690 | −0.938451 | − | 0.345413i | \(-0.887739\pi\) | ||||
−0.938451 | + | 0.345413i | \(0.887739\pi\) | |||||||
\(278\) | 17.3454 | 1.04031 | ||||||||
\(279\) | −3.57843 | −0.214235 | ||||||||
\(280\) | −0.742890 | −0.0443961 | ||||||||
\(281\) | −18.1874 | −1.08497 | −0.542484 | − | 0.840066i | \(-0.682516\pi\) | ||||
−0.542484 | + | 0.840066i | \(0.682516\pi\) | |||||||
\(282\) | 0.579710 | 0.0345212 | ||||||||
\(283\) | 1.52975 | 0.0909343 | 0.0454671 | − | 0.998966i | \(-0.485522\pi\) | ||||
0.0454671 | + | 0.998966i | \(0.485522\pi\) | |||||||
\(284\) | −5.96557 | −0.353991 | ||||||||
\(285\) | −0.752913 | −0.0445987 | ||||||||
\(286\) | 4.70314 | 0.278103 | ||||||||
\(287\) | 5.93116 | 0.350105 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −4.00818 | −0.235775 | ||||||||
\(290\) | −2.91908 | −0.171414 | ||||||||
\(291\) | −10.4350 | −0.611708 | ||||||||
\(292\) | 0.810762 | 0.0474462 | ||||||||
\(293\) | −9.77976 | −0.571340 | −0.285670 | − | 0.958328i | \(-0.592216\pi\) | ||||
−0.285670 | + | 0.958328i | \(0.592216\pi\) | |||||||
\(294\) | −6.37162 | −0.371600 | ||||||||
\(295\) | 1.81047 | 0.105409 | ||||||||
\(296\) | −1.63083 | −0.0947902 | ||||||||
\(297\) | 4.70314 | 0.272904 | ||||||||
\(298\) | 9.59017 | 0.555543 | ||||||||
\(299\) | −4.68922 | −0.271184 | ||||||||
\(300\) | 4.12173 | 0.237968 | ||||||||
\(301\) | −3.15852 | −0.182054 | ||||||||
\(302\) | −8.93579 | −0.514197 | ||||||||
\(303\) | 1.41189 | 0.0811108 | ||||||||
\(304\) | −0.803399 | −0.0460781 | ||||||||
\(305\) | 13.9015 | 0.795997 | ||||||||
\(306\) | 3.60442 | 0.206051 | ||||||||
\(307\) | −17.1789 | −0.980451 | −0.490225 | − | 0.871596i | \(-0.663086\pi\) | ||||
−0.490225 | + | 0.871596i | \(0.663086\pi\) | |||||||
\(308\) | 3.72820 | 0.212434 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −3.35355 | −0.190469 | ||||||||
\(311\) | 28.7706 | 1.63143 | 0.815715 | − | 0.578454i | \(-0.196344\pi\) | ||||
0.815715 | + | 0.578454i | \(0.196344\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 26.0073 | 1.47002 | 0.735010 | − | 0.678057i | \(-0.237178\pi\) | ||||
0.735010 | + | 0.678057i | \(0.237178\pi\) | |||||||
\(314\) | 18.9333 | 1.06847 | ||||||||
\(315\) | 0.742890 | 0.0418571 | ||||||||
\(316\) | 6.43093 | 0.361768 | ||||||||
\(317\) | −0.494041 | −0.0277481 | −0.0138741 | − | 0.999904i | \(-0.504416\pi\) | ||||
−0.0138741 | + | 0.999904i | \(0.504416\pi\) | |||||||
\(318\) | 5.61866 | 0.315079 | ||||||||
\(319\) | 14.6494 | 0.820212 | ||||||||
\(320\) | −0.937159 | −0.0523888 | ||||||||
\(321\) | −0.502970 | −0.0280731 | ||||||||
\(322\) | −3.71716 | −0.207149 | ||||||||
\(323\) | 2.89579 | 0.161126 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.12173 | −0.228633 | ||||||||
\(326\) | 9.61838 | 0.532713 | ||||||||
\(327\) | −17.7539 | −0.981794 | ||||||||
\(328\) | 7.48219 | 0.413135 | ||||||||
\(329\) | −0.459538 | −0.0253352 | ||||||||
\(330\) | 4.40759 | 0.242630 | ||||||||
\(331\) | 13.2952 | 0.730768 | 0.365384 | − | 0.930857i | \(-0.380938\pi\) | ||||
0.365384 | + | 0.930857i | \(0.380938\pi\) | |||||||
\(332\) | −5.41646 | −0.297267 | ||||||||
\(333\) | 1.63083 | 0.0893691 | ||||||||
\(334\) | 25.2414 | 1.38115 | ||||||||
\(335\) | −5.41287 | −0.295736 | ||||||||
\(336\) | 0.792704 | 0.0432455 | ||||||||
\(337\) | −1.04274 | −0.0568015 | −0.0284007 | − | 0.999597i | \(-0.509041\pi\) | ||||
−0.0284007 | + | 0.999597i | \(0.509041\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −8.02786 | −0.436014 | ||||||||
\(340\) | 3.37791 | 0.183193 | ||||||||
\(341\) | 16.8299 | 0.911388 | ||||||||
\(342\) | 0.803399 | 0.0434429 | ||||||||
\(343\) | 10.5997 | 0.572332 | ||||||||
\(344\) | −3.98449 | −0.214829 | ||||||||
\(345\) | −4.39454 | −0.236594 | ||||||||
\(346\) | −0.222644 | −0.0119694 | ||||||||
\(347\) | 25.2951 | 1.35791 | 0.678956 | − | 0.734179i | \(-0.262433\pi\) | ||||
0.678956 | + | 0.734179i | \(0.262433\pi\) | |||||||
\(348\) | 3.11482 | 0.166972 | ||||||||
\(349\) | 17.3267 | 0.927475 | 0.463737 | − | 0.885973i | \(-0.346508\pi\) | ||||
0.463737 | + | 0.885973i | \(0.346508\pi\) | |||||||
\(350\) | −3.26731 | −0.174645 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 4.70314 | 0.250678 | ||||||||
\(353\) | −16.7368 | −0.890811 | −0.445406 | − | 0.895329i | \(-0.646941\pi\) | ||||
−0.445406 | + | 0.895329i | \(0.646941\pi\) | |||||||
\(354\) | −1.93187 | −0.102678 | ||||||||
\(355\) | 5.59068 | 0.296723 | ||||||||
\(356\) | −18.2668 | −0.968141 | ||||||||
\(357\) | −2.85724 | −0.151221 | ||||||||
\(358\) | −25.3993 | −1.34240 | ||||||||
\(359\) | 6.34619 | 0.334939 | 0.167470 | − | 0.985877i | \(-0.446440\pi\) | ||||
0.167470 | + | 0.985877i | \(0.446440\pi\) | |||||||
\(360\) | 0.937159 | 0.0493926 | ||||||||
\(361\) | −18.3545 | −0.966029 | ||||||||
\(362\) | 6.58007 | 0.345841 | ||||||||
\(363\) | −11.1196 | −0.583625 | ||||||||
\(364\) | −0.792704 | −0.0415490 | ||||||||
\(365\) | −0.759812 | −0.0397704 | ||||||||
\(366\) | −14.8337 | −0.775368 | ||||||||
\(367\) | 30.8119 | 1.60837 | 0.804185 | − | 0.594379i | \(-0.202602\pi\) | ||||
0.804185 | + | 0.594379i | \(0.202602\pi\) | |||||||
\(368\) | −4.68922 | −0.244442 | ||||||||
\(369\) | −7.48219 | −0.389507 | ||||||||
\(370\) | 1.52835 | 0.0794551 | ||||||||
\(371\) | −4.45393 | −0.231237 | ||||||||
\(372\) | 3.57843 | 0.185533 | ||||||||
\(373\) | −26.3688 | −1.36533 | −0.682663 | − | 0.730734i | \(-0.739178\pi\) | ||||
−0.682663 | + | 0.730734i | \(0.739178\pi\) | |||||||
\(374\) | −16.9521 | −0.876571 | ||||||||
\(375\) | −8.54851 | −0.441443 | ||||||||
\(376\) | −0.579710 | −0.0298962 | ||||||||
\(377\) | −3.11482 | −0.160421 | ||||||||
\(378\) | −0.792704 | −0.0407723 | ||||||||
\(379\) | 9.77930 | 0.502329 | 0.251165 | − | 0.967944i | \(-0.419186\pi\) | ||||
0.251165 | + | 0.967944i | \(0.419186\pi\) | |||||||
\(380\) | 0.752913 | 0.0386236 | ||||||||
\(381\) | 8.03716 | 0.411756 | ||||||||
\(382\) | −11.0853 | −0.567174 | ||||||||
\(383\) | −32.4570 | −1.65847 | −0.829237 | − | 0.558897i | \(-0.811225\pi\) | ||||
−0.829237 | + | 0.558897i | \(0.811225\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −3.49392 | −0.178066 | ||||||||
\(386\) | −6.80068 | −0.346146 | ||||||||
\(387\) | 3.98449 | 0.202543 | ||||||||
\(388\) | 10.4350 | 0.529755 | ||||||||
\(389\) | 7.67508 | 0.389142 | 0.194571 | − | 0.980888i | \(-0.437669\pi\) | ||||
0.194571 | + | 0.980888i | \(0.437669\pi\) | |||||||
\(390\) | −0.937159 | −0.0474549 | ||||||||
\(391\) | 16.9019 | 0.854766 | ||||||||
\(392\) | 6.37162 | 0.321815 | ||||||||
\(393\) | −4.13397 | −0.208531 | ||||||||
\(394\) | 5.08227 | 0.256041 | ||||||||
\(395\) | −6.02680 | −0.303241 | ||||||||
\(396\) | −4.70314 | −0.236342 | ||||||||
\(397\) | −7.64131 | −0.383506 | −0.191753 | − | 0.981443i | \(-0.561417\pi\) | ||||
−0.191753 | + | 0.981443i | \(0.561417\pi\) | |||||||
\(398\) | −15.9413 | −0.799065 | ||||||||
\(399\) | −0.636858 | −0.0318828 | ||||||||
\(400\) | −4.12173 | −0.206087 | ||||||||
\(401\) | −12.6513 | −0.631777 | −0.315888 | − | 0.948796i | \(-0.602303\pi\) | ||||
−0.315888 | + | 0.948796i | \(0.602303\pi\) | |||||||
\(402\) | 5.77582 | 0.288072 | ||||||||
\(403\) | −3.57843 | −0.178254 | ||||||||
\(404\) | −1.41189 | −0.0702441 | ||||||||
\(405\) | −0.937159 | −0.0465678 | ||||||||
\(406\) | −2.46913 | −0.122541 | ||||||||
\(407\) | −7.67004 | −0.380190 | ||||||||
\(408\) | −3.60442 | −0.178445 | ||||||||
\(409\) | 24.4350 | 1.20823 | 0.604115 | − | 0.796897i | \(-0.293527\pi\) | ||||
0.604115 | + | 0.796897i | \(0.293527\pi\) | |||||||
\(410\) | −7.01200 | −0.346298 | ||||||||
\(411\) | 17.8896 | 0.882431 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 1.53140 | 0.0753552 | ||||||||
\(414\) | 4.68922 | 0.230462 | ||||||||
\(415\) | 5.07609 | 0.249175 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 17.3454 | 0.849407 | ||||||||
\(418\) | −3.77850 | −0.184813 | ||||||||
\(419\) | −23.6809 | −1.15689 | −0.578444 | − | 0.815722i | \(-0.696340\pi\) | ||||
−0.578444 | + | 0.815722i | \(0.696340\pi\) | |||||||
\(420\) | −0.742890 | −0.0362493 | ||||||||
\(421\) | −12.5451 | −0.611411 | −0.305705 | − | 0.952126i | \(-0.598892\pi\) | ||||
−0.305705 | + | 0.952126i | \(0.598892\pi\) | |||||||
\(422\) | −10.7284 | −0.522248 | ||||||||
\(423\) | 0.579710 | 0.0281864 | ||||||||
\(424\) | −5.61866 | −0.272866 | ||||||||
\(425\) | 14.8564 | 0.720643 | ||||||||
\(426\) | −5.96557 | −0.289033 | ||||||||
\(427\) | 11.7587 | 0.569043 | ||||||||
\(428\) | 0.502970 | 0.0243120 | ||||||||
\(429\) | 4.70314 | 0.227070 | ||||||||
\(430\) | 3.73410 | 0.180074 | ||||||||
\(431\) | −18.7049 | −0.900984 | −0.450492 | − | 0.892780i | \(-0.648751\pi\) | ||||
−0.450492 | + | 0.892780i | \(0.648751\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 32.1566 | 1.54535 | 0.772673 | − | 0.634805i | \(-0.218919\pi\) | ||||
0.772673 | + | 0.634805i | \(0.218919\pi\) | |||||||
\(434\) | −2.83663 | −0.136163 | ||||||||
\(435\) | −2.91908 | −0.139959 | ||||||||
\(436\) | 17.7539 | 0.850259 | ||||||||
\(437\) | 3.76732 | 0.180215 | ||||||||
\(438\) | 0.810762 | 0.0387397 | ||||||||
\(439\) | 31.5854 | 1.50749 | 0.753745 | − | 0.657167i | \(-0.228245\pi\) | ||||
0.753745 | + | 0.657167i | \(0.228245\pi\) | |||||||
\(440\) | −4.40759 | −0.210124 | ||||||||
\(441\) | −6.37162 | −0.303410 | ||||||||
\(442\) | 3.60442 | 0.171445 | ||||||||
\(443\) | 26.8464 | 1.27551 | 0.637756 | − | 0.770238i | \(-0.279863\pi\) | ||||
0.637756 | + | 0.770238i | \(0.279863\pi\) | |||||||
\(444\) | −1.63083 | −0.0773959 | ||||||||
\(445\) | 17.1189 | 0.811515 | ||||||||
\(446\) | 19.7800 | 0.936611 | ||||||||
\(447\) | 9.59017 | 0.453599 | ||||||||
\(448\) | −0.792704 | −0.0374517 | ||||||||
\(449\) | −1.58098 | −0.0746108 | −0.0373054 | − | 0.999304i | \(-0.511877\pi\) | ||||
−0.0373054 | + | 0.999304i | \(0.511877\pi\) | |||||||
\(450\) | 4.12173 | 0.194300 | ||||||||
\(451\) | 35.1898 | 1.65702 | ||||||||
\(452\) | 8.02786 | 0.377599 | ||||||||
\(453\) | −8.93579 | −0.419840 | ||||||||
\(454\) | −13.3566 | −0.626855 | ||||||||
\(455\) | 0.742890 | 0.0348272 | ||||||||
\(456\) | −0.803399 | −0.0376226 | ||||||||
\(457\) | −13.8693 | −0.648777 | −0.324389 | − | 0.945924i | \(-0.605159\pi\) | ||||
−0.324389 | + | 0.945924i | \(0.605159\pi\) | |||||||
\(458\) | 1.87870 | 0.0877861 | ||||||||
\(459\) | 3.60442 | 0.168240 | ||||||||
\(460\) | 4.39454 | 0.204897 | ||||||||
\(461\) | 2.70162 | 0.125827 | 0.0629136 | − | 0.998019i | \(-0.479961\pi\) | ||||
0.0629136 | + | 0.998019i | \(0.479961\pi\) | |||||||
\(462\) | 3.72820 | 0.173452 | ||||||||
\(463\) | −30.6401 | −1.42396 | −0.711982 | − | 0.702198i | \(-0.752202\pi\) | ||||
−0.711982 | + | 0.702198i | \(0.752202\pi\) | |||||||
\(464\) | −3.11482 | −0.144602 | ||||||||
\(465\) | −3.35355 | −0.155517 | ||||||||
\(466\) | −16.0079 | −0.741551 | ||||||||
\(467\) | −20.2536 | −0.937223 | −0.468612 | − | 0.883404i | \(-0.655246\pi\) | ||||
−0.468612 | + | 0.883404i | \(0.655246\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −4.57852 | −0.211416 | ||||||||
\(470\) | 0.543280 | 0.0250596 | ||||||||
\(471\) | 18.9333 | 0.872400 | ||||||||
\(472\) | 1.93187 | 0.0889214 | ||||||||
\(473\) | −18.7396 | −0.861649 | ||||||||
\(474\) | 6.43093 | 0.295382 | ||||||||
\(475\) | 3.31140 | 0.151937 | ||||||||
\(476\) | 2.85724 | 0.130961 | ||||||||
\(477\) | 5.61866 | 0.257261 | ||||||||
\(478\) | −17.4394 | −0.797660 | ||||||||
\(479\) | 20.6640 | 0.944162 | 0.472081 | − | 0.881555i | \(-0.343503\pi\) | ||||
0.472081 | + | 0.881555i | \(0.343503\pi\) | |||||||
\(480\) | −0.937159 | −0.0427753 | ||||||||
\(481\) | 1.63083 | 0.0743596 | ||||||||
\(482\) | 6.56601 | 0.299074 | ||||||||
\(483\) | −3.71716 | −0.169137 | ||||||||
\(484\) | 11.1196 | 0.505434 | ||||||||
\(485\) | −9.77921 | −0.444051 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −21.3896 | −0.969257 | −0.484628 | − | 0.874720i | \(-0.661045\pi\) | ||||
−0.484628 | + | 0.874720i | \(0.661045\pi\) | |||||||
\(488\) | 14.8337 | 0.671488 | ||||||||
\(489\) | 9.61838 | 0.434958 | ||||||||
\(490\) | −5.97122 | −0.269752 | ||||||||
\(491\) | −42.5182 | −1.91882 | −0.959409 | − | 0.282017i | \(-0.908996\pi\) | ||||
−0.959409 | + | 0.282017i | \(0.908996\pi\) | |||||||
\(492\) | 7.48219 | 0.337323 | ||||||||
\(493\) | 11.2271 | 0.505644 | ||||||||
\(494\) | 0.803399 | 0.0361466 | ||||||||
\(495\) | 4.40759 | 0.198107 | ||||||||
\(496\) | −3.57843 | −0.160676 | ||||||||
\(497\) | 4.72893 | 0.212121 | ||||||||
\(498\) | −5.41646 | −0.242718 | ||||||||
\(499\) | 10.6374 | 0.476196 | 0.238098 | − | 0.971241i | \(-0.423476\pi\) | ||||
0.238098 | + | 0.971241i | \(0.423476\pi\) | |||||||
\(500\) | 8.54851 | 0.382301 | ||||||||
\(501\) | 25.2414 | 1.12770 | ||||||||
\(502\) | −18.8493 | −0.841285 | ||||||||
\(503\) | 5.29457 | 0.236073 | 0.118037 | − | 0.993009i | \(-0.462340\pi\) | ||||
0.118037 | + | 0.993009i | \(0.462340\pi\) | |||||||
\(504\) | 0.792704 | 0.0353098 | ||||||||
\(505\) | 1.32316 | 0.0588800 | ||||||||
\(506\) | −22.0541 | −0.980423 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −8.03716 | −0.356591 | ||||||||
\(509\) | 26.7767 | 1.18686 | 0.593428 | − | 0.804887i | \(-0.297774\pi\) | ||||
0.593428 | + | 0.804887i | \(0.297774\pi\) | |||||||
\(510\) | 3.37791 | 0.149576 | ||||||||
\(511\) | −0.642694 | −0.0284311 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.803399 | 0.0354710 | ||||||||
\(514\) | 15.0916 | 0.665662 | ||||||||
\(515\) | 0.937159 | 0.0412962 | ||||||||
\(516\) | −3.98449 | −0.175407 | ||||||||
\(517\) | −2.72646 | −0.119909 | ||||||||
\(518\) | 1.29277 | 0.0568009 | ||||||||
\(519\) | −0.222644 | −0.00977297 | ||||||||
\(520\) | 0.937159 | 0.0410971 | ||||||||
\(521\) | 29.6848 | 1.30052 | 0.650258 | − | 0.759714i | \(-0.274661\pi\) | ||||
0.650258 | + | 0.759714i | \(0.274661\pi\) | |||||||
\(522\) | 3.11482 | 0.136332 | ||||||||
\(523\) | −1.23849 | −0.0541553 | −0.0270777 | − | 0.999633i | \(-0.508620\pi\) | ||||
−0.0270777 | + | 0.999633i | \(0.508620\pi\) | |||||||
\(524\) | 4.13397 | 0.180593 | ||||||||
\(525\) | −3.26731 | −0.142597 | ||||||||
\(526\) | −2.51843 | −0.109809 | ||||||||
\(527\) | 12.8981 | 0.561852 | ||||||||
\(528\) | 4.70314 | 0.204678 | ||||||||
\(529\) | −1.01123 | −0.0439667 | ||||||||
\(530\) | 5.26557 | 0.228722 | ||||||||
\(531\) | −1.93187 | −0.0838359 | ||||||||
\(532\) | 0.636858 | 0.0276113 | ||||||||
\(533\) | −7.48219 | −0.324090 | ||||||||
\(534\) | −18.2668 | −0.790484 | ||||||||
\(535\) | −0.471363 | −0.0203788 | ||||||||
\(536\) | −5.77582 | −0.249478 | ||||||||
\(537\) | −25.3993 | −1.09606 | ||||||||
\(538\) | 26.3178 | 1.13464 | ||||||||
\(539\) | 29.9666 | 1.29075 | ||||||||
\(540\) | 0.937159 | 0.0403289 | ||||||||
\(541\) | 24.2953 | 1.04454 | 0.522268 | − | 0.852781i | \(-0.325086\pi\) | ||||
0.522268 | + | 0.852781i | \(0.325086\pi\) | |||||||
\(542\) | −6.11955 | −0.262857 | ||||||||
\(543\) | 6.58007 | 0.282378 | ||||||||
\(544\) | 3.60442 | 0.154538 | ||||||||
\(545\) | −16.6383 | −0.712704 | ||||||||
\(546\) | −0.792704 | −0.0339246 | ||||||||
\(547\) | −21.1912 | −0.906069 | −0.453035 | − | 0.891493i | \(-0.649659\pi\) | ||||
−0.453035 | + | 0.891493i | \(0.649659\pi\) | |||||||
\(548\) | −17.8896 | −0.764208 | ||||||||
\(549\) | −14.8337 | −0.633085 | ||||||||
\(550\) | −19.3851 | −0.826583 | ||||||||
\(551\) | 2.50244 | 0.106608 | ||||||||
\(552\) | −4.68922 | −0.199586 | ||||||||
\(553\) | −5.09782 | −0.216781 | ||||||||
\(554\) | 31.2379 | 1.32717 | ||||||||
\(555\) | 1.52835 | 0.0648748 | ||||||||
\(556\) | −17.3454 | −0.735608 | ||||||||
\(557\) | 21.2459 | 0.900217 | 0.450108 | − | 0.892974i | \(-0.351385\pi\) | ||||
0.450108 | + | 0.892974i | \(0.351385\pi\) | |||||||
\(558\) | 3.57843 | 0.151487 | ||||||||
\(559\) | 3.98449 | 0.168526 | ||||||||
\(560\) | 0.742890 | 0.0313928 | ||||||||
\(561\) | −16.9521 | −0.715718 | ||||||||
\(562\) | 18.1874 | 0.767188 | ||||||||
\(563\) | −29.5654 | −1.24603 | −0.623017 | − | 0.782209i | \(-0.714093\pi\) | ||||
−0.623017 | + | 0.782209i | \(0.714093\pi\) | |||||||
\(564\) | −0.579710 | −0.0244102 | ||||||||
\(565\) | −7.52339 | −0.316511 | ||||||||
\(566\) | −1.52975 | −0.0643002 | ||||||||
\(567\) | −0.792704 | −0.0332904 | ||||||||
\(568\) | 5.96557 | 0.250310 | ||||||||
\(569\) | 24.0452 | 1.00803 | 0.504013 | − | 0.863696i | \(-0.331856\pi\) | ||||
0.504013 | + | 0.863696i | \(0.331856\pi\) | |||||||
\(570\) | 0.752913 | 0.0315361 | ||||||||
\(571\) | 20.1068 | 0.841443 | 0.420721 | − | 0.907190i | \(-0.361777\pi\) | ||||
0.420721 | + | 0.907190i | \(0.361777\pi\) | |||||||
\(572\) | −4.70314 | −0.196648 | ||||||||
\(573\) | −11.0853 | −0.463096 | ||||||||
\(574\) | −5.93116 | −0.247562 | ||||||||
\(575\) | 19.3277 | 0.806021 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 9.84511 | 0.409857 | 0.204929 | − | 0.978777i | \(-0.434304\pi\) | ||||
0.204929 | + | 0.978777i | \(0.434304\pi\) | |||||||
\(578\) | 4.00818 | 0.166718 | ||||||||
\(579\) | −6.80068 | −0.282627 | ||||||||
\(580\) | 2.91908 | 0.121208 | ||||||||
\(581\) | 4.29365 | 0.178131 | ||||||||
\(582\) | 10.4350 | 0.432543 | ||||||||
\(583\) | −26.4253 | −1.09443 | ||||||||
\(584\) | −0.810762 | −0.0335496 | ||||||||
\(585\) | −0.937159 | −0.0387468 | ||||||||
\(586\) | 9.77976 | 0.403998 | ||||||||
\(587\) | −31.2144 | −1.28836 | −0.644179 | − | 0.764875i | \(-0.722801\pi\) | ||||
−0.644179 | + | 0.764875i | \(0.722801\pi\) | |||||||
\(588\) | 6.37162 | 0.262761 | ||||||||
\(589\) | 2.87491 | 0.118458 | ||||||||
\(590\) | −1.81047 | −0.0745358 | ||||||||
\(591\) | 5.08227 | 0.209056 | ||||||||
\(592\) | 1.63083 | 0.0670268 | ||||||||
\(593\) | 31.3049 | 1.28554 | 0.642769 | − | 0.766060i | \(-0.277785\pi\) | ||||
0.642769 | + | 0.766060i | \(0.277785\pi\) | |||||||
\(594\) | −4.70314 | −0.192972 | ||||||||
\(595\) | −2.67768 | −0.109774 | ||||||||
\(596\) | −9.59017 | −0.392829 | ||||||||
\(597\) | −15.9413 | −0.652434 | ||||||||
\(598\) | 4.68922 | 0.191756 | ||||||||
\(599\) | 8.02028 | 0.327700 | 0.163850 | − | 0.986485i | \(-0.447609\pi\) | ||||
0.163850 | + | 0.986485i | \(0.447609\pi\) | |||||||
\(600\) | −4.12173 | −0.168269 | ||||||||
\(601\) | 24.6819 | 1.00680 | 0.503398 | − | 0.864055i | \(-0.332083\pi\) | ||||
0.503398 | + | 0.864055i | \(0.332083\pi\) | |||||||
\(602\) | 3.15852 | 0.128732 | ||||||||
\(603\) | 5.77582 | 0.235210 | ||||||||
\(604\) | 8.93579 | 0.363592 | ||||||||
\(605\) | −10.4208 | −0.423665 | ||||||||
\(606\) | −1.41189 | −0.0573540 | ||||||||
\(607\) | 35.6610 | 1.44744 | 0.723718 | − | 0.690095i | \(-0.242431\pi\) | ||||
0.723718 | + | 0.690095i | \(0.242431\pi\) | |||||||
\(608\) | 0.803399 | 0.0325821 | ||||||||
\(609\) | −2.46913 | −0.100054 | ||||||||
\(610\) | −13.9015 | −0.562855 | ||||||||
\(611\) | 0.579710 | 0.0234525 | ||||||||
\(612\) | −3.60442 | −0.145700 | ||||||||
\(613\) | 26.1783 | 1.05733 | 0.528665 | − | 0.848830i | \(-0.322693\pi\) | ||||
0.528665 | + | 0.848830i | \(0.322693\pi\) | |||||||
\(614\) | 17.1789 | 0.693283 | ||||||||
\(615\) | −7.01200 | −0.282751 | ||||||||
\(616\) | −3.72820 | −0.150213 | ||||||||
\(617\) | −11.4978 | −0.462884 | −0.231442 | − | 0.972849i | \(-0.574344\pi\) | ||||
−0.231442 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 2.45533 | 0.0986879 | 0.0493440 | − | 0.998782i | \(-0.484287\pi\) | ||||
0.0493440 | + | 0.998782i | \(0.484287\pi\) | |||||||
\(620\) | 3.35355 | 0.134682 | ||||||||
\(621\) | 4.68922 | 0.188172 | ||||||||
\(622\) | −28.7706 | −1.15360 | ||||||||
\(623\) | 14.4802 | 0.580137 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 12.5973 | 0.503894 | ||||||||
\(626\) | −26.0073 | −1.03946 | ||||||||
\(627\) | −3.77850 | −0.150899 | ||||||||
\(628\) | −18.9333 | −0.755521 | ||||||||
\(629\) | −5.87820 | −0.234379 | ||||||||
\(630\) | −0.742890 | −0.0295974 | ||||||||
\(631\) | −18.3325 | −0.729807 | −0.364904 | − | 0.931045i | \(-0.618898\pi\) | ||||
−0.364904 | + | 0.931045i | \(0.618898\pi\) | |||||||
\(632\) | −6.43093 | −0.255809 | ||||||||
\(633\) | −10.7284 | −0.426414 | ||||||||
\(634\) | 0.494041 | 0.0196209 | ||||||||
\(635\) | 7.53210 | 0.298902 | ||||||||
\(636\) | −5.61866 | −0.222794 | ||||||||
\(637\) | −6.37162 | −0.252453 | ||||||||
\(638\) | −14.6494 | −0.579977 | ||||||||
\(639\) | −5.96557 | −0.235994 | ||||||||
\(640\) | 0.937159 | 0.0370445 | ||||||||
\(641\) | 42.7020 | 1.68663 | 0.843313 | − | 0.537423i | \(-0.180602\pi\) | ||||
0.843313 | + | 0.537423i | \(0.180602\pi\) | |||||||
\(642\) | 0.502970 | 0.0198507 | ||||||||
\(643\) | 32.3813 | 1.27699 | 0.638496 | − | 0.769625i | \(-0.279557\pi\) | ||||
0.638496 | + | 0.769625i | \(0.279557\pi\) | |||||||
\(644\) | 3.71716 | 0.146477 | ||||||||
\(645\) | 3.73410 | 0.147030 | ||||||||
\(646\) | −2.89579 | −0.113933 | ||||||||
\(647\) | −33.6185 | −1.32168 | −0.660839 | − | 0.750527i | \(-0.729800\pi\) | ||||
−0.660839 | + | 0.750527i | \(0.729800\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 9.08585 | 0.356651 | ||||||||
\(650\) | 4.12173 | 0.161668 | ||||||||
\(651\) | −2.83663 | −0.111176 | ||||||||
\(652\) | −9.61838 | −0.376685 | ||||||||
\(653\) | 7.01542 | 0.274535 | 0.137267 | − | 0.990534i | \(-0.456168\pi\) | ||||
0.137267 | + | 0.990534i | \(0.456168\pi\) | |||||||
\(654\) | 17.7539 | 0.694233 | ||||||||
\(655\) | −3.87418 | −0.151377 | ||||||||
\(656\) | −7.48219 | −0.292131 | ||||||||
\(657\) | 0.810762 | 0.0316308 | ||||||||
\(658\) | 0.459538 | 0.0179147 | ||||||||
\(659\) | 19.1360 | 0.745433 | 0.372716 | − | 0.927945i | \(-0.378426\pi\) | ||||
0.372716 | + | 0.927945i | \(0.378426\pi\) | |||||||
\(660\) | −4.40759 | −0.171565 | ||||||||
\(661\) | −24.9601 | −0.970836 | −0.485418 | − | 0.874282i | \(-0.661333\pi\) | ||||
−0.485418 | + | 0.874282i | \(0.661333\pi\) | |||||||
\(662\) | −13.2952 | −0.516731 | ||||||||
\(663\) | 3.60442 | 0.139984 | ||||||||
\(664\) | 5.41646 | 0.210200 | ||||||||
\(665\) | −0.596837 | −0.0231443 | ||||||||
\(666\) | −1.63083 | −0.0631935 | ||||||||
\(667\) | 14.6061 | 0.565549 | ||||||||
\(668\) | −25.2414 | −0.976621 | ||||||||
\(669\) | 19.7800 | 0.764739 | ||||||||
\(670\) | 5.41287 | 0.209117 | ||||||||
\(671\) | 69.7648 | 2.69324 | ||||||||
\(672\) | −0.792704 | −0.0305792 | ||||||||
\(673\) | 30.0790 | 1.15946 | 0.579731 | − | 0.814808i | \(-0.303158\pi\) | ||||
0.579731 | + | 0.814808i | \(0.303158\pi\) | |||||||
\(674\) | 1.04274 | 0.0401647 | ||||||||
\(675\) | 4.12173 | 0.158646 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 15.5954 | 0.599378 | 0.299689 | − | 0.954037i | \(-0.403117\pi\) | ||||
0.299689 | + | 0.954037i | \(0.403117\pi\) | |||||||
\(678\) | 8.02786 | 0.308308 | ||||||||
\(679\) | −8.27183 | −0.317444 | ||||||||
\(680\) | −3.37791 | −0.129537 | ||||||||
\(681\) | −13.3566 | −0.511825 | ||||||||
\(682\) | −16.8299 | −0.644448 | ||||||||
\(683\) | −29.5061 | −1.12902 | −0.564509 | − | 0.825427i | \(-0.690935\pi\) | ||||
−0.564509 | + | 0.825427i | \(0.690935\pi\) | |||||||
\(684\) | −0.803399 | −0.0307187 | ||||||||
\(685\) | 16.7654 | 0.640575 | ||||||||
\(686\) | −10.5997 | −0.404700 | ||||||||
\(687\) | 1.87870 | 0.0716770 | ||||||||
\(688\) | 3.98449 | 0.151907 | ||||||||
\(689\) | 5.61866 | 0.214054 | ||||||||
\(690\) | 4.39454 | 0.167297 | ||||||||
\(691\) | 40.5561 | 1.54283 | 0.771414 | − | 0.636333i | \(-0.219550\pi\) | ||||
0.771414 | + | 0.636333i | \(0.219550\pi\) | |||||||
\(692\) | 0.222644 | 0.00846364 | ||||||||
\(693\) | 3.72820 | 0.141623 | ||||||||
\(694\) | −25.2951 | −0.960189 | ||||||||
\(695\) | 16.2554 | 0.616602 | ||||||||
\(696\) | −3.11482 | −0.118067 | ||||||||
\(697\) | 26.9689 | 1.02152 | ||||||||
\(698\) | −17.3267 | −0.655824 | ||||||||
\(699\) | −16.0079 | −0.605474 | ||||||||
\(700\) | 3.26731 | 0.123493 | ||||||||
\(701\) | 24.4791 | 0.924564 | 0.462282 | − | 0.886733i | \(-0.347031\pi\) | ||||
0.462282 | + | 0.886733i | \(0.347031\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −1.31021 | −0.0494155 | ||||||||
\(704\) | −4.70314 | −0.177256 | ||||||||
\(705\) | 0.543280 | 0.0204611 | ||||||||
\(706\) | 16.7368 | 0.629899 | ||||||||
\(707\) | 1.11921 | 0.0420922 | ||||||||
\(708\) | 1.93187 | 0.0726041 | ||||||||
\(709\) | 29.0564 | 1.09124 | 0.545618 | − | 0.838034i | \(-0.316295\pi\) | ||||
0.545618 | + | 0.838034i | \(0.316295\pi\) | |||||||
\(710\) | −5.59068 | −0.209815 | ||||||||
\(711\) | 6.43093 | 0.241179 | ||||||||
\(712\) | 18.2668 | 0.684579 | ||||||||
\(713\) | 16.7800 | 0.628417 | ||||||||
\(714\) | 2.85724 | 0.106929 | ||||||||
\(715\) | 4.40759 | 0.164835 | ||||||||
\(716\) | 25.3993 | 0.949217 | ||||||||
\(717\) | −17.4394 | −0.651286 | ||||||||
\(718\) | −6.34619 | −0.236838 | ||||||||
\(719\) | 38.6846 | 1.44269 | 0.721347 | − | 0.692574i | \(-0.243523\pi\) | ||||
0.721347 | + | 0.692574i | \(0.243523\pi\) | |||||||
\(720\) | −0.937159 | −0.0349259 | ||||||||
\(721\) | 0.792704 | 0.0295218 | ||||||||
\(722\) | 18.3545 | 0.683086 | ||||||||
\(723\) | 6.56601 | 0.244193 | ||||||||
\(724\) | −6.58007 | −0.244546 | ||||||||
\(725\) | 12.8385 | 0.476808 | ||||||||
\(726\) | 11.1196 | 0.412685 | ||||||||
\(727\) | 21.4901 | 0.797024 | 0.398512 | − | 0.917163i | \(-0.369527\pi\) | ||||
0.398512 | + | 0.917163i | \(0.369527\pi\) | |||||||
\(728\) | 0.792704 | 0.0293796 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.759812 | 0.0281219 | ||||||||
\(731\) | −14.3618 | −0.531189 | ||||||||
\(732\) | 14.8337 | 0.548268 | ||||||||
\(733\) | −33.9224 | −1.25295 | −0.626475 | − | 0.779441i | \(-0.715503\pi\) | ||||
−0.626475 | + | 0.779441i | \(0.715503\pi\) | |||||||
\(734\) | −30.8119 | −1.13729 | ||||||||
\(735\) | −5.97122 | −0.220252 | ||||||||
\(736\) | 4.68922 | 0.172847 | ||||||||
\(737\) | −27.1645 | −1.00062 | ||||||||
\(738\) | 7.48219 | 0.275423 | ||||||||
\(739\) | 3.01425 | 0.110881 | 0.0554406 | − | 0.998462i | \(-0.482344\pi\) | ||||
0.0554406 | + | 0.998462i | \(0.482344\pi\) | |||||||
\(740\) | −1.52835 | −0.0561832 | ||||||||
\(741\) | 0.803399 | 0.0295136 | ||||||||
\(742\) | 4.45393 | 0.163509 | ||||||||
\(743\) | −6.72363 | −0.246666 | −0.123333 | − | 0.992365i | \(-0.539358\pi\) | ||||
−0.123333 | + | 0.992365i | \(0.539358\pi\) | |||||||
\(744\) | −3.57843 | −0.131191 | ||||||||
\(745\) | 8.98751 | 0.329277 | ||||||||
\(746\) | 26.3688 | 0.965431 | ||||||||
\(747\) | −5.41646 | −0.198178 | ||||||||
\(748\) | 16.9521 | 0.619830 | ||||||||
\(749\) | −0.398707 | −0.0145684 | ||||||||
\(750\) | 8.54851 | 0.312148 | ||||||||
\(751\) | 45.2545 | 1.65136 | 0.825679 | − | 0.564140i | \(-0.190792\pi\) | ||||
0.825679 | + | 0.564140i | \(0.190792\pi\) | |||||||
\(752\) | 0.579710 | 0.0211398 | ||||||||
\(753\) | −18.8493 | −0.686906 | ||||||||
\(754\) | 3.11482 | 0.113435 | ||||||||
\(755\) | −8.37425 | −0.304770 | ||||||||
\(756\) | 0.792704 | 0.0288304 | ||||||||
\(757\) | 8.39311 | 0.305053 | 0.152526 | − | 0.988299i | \(-0.451259\pi\) | ||||
0.152526 | + | 0.988299i | \(0.451259\pi\) | |||||||
\(758\) | −9.77930 | −0.355200 | ||||||||
\(759\) | −22.0541 | −0.800512 | ||||||||
\(760\) | −0.752913 | −0.0273110 | ||||||||
\(761\) | 14.2758 | 0.517496 | 0.258748 | − | 0.965945i | \(-0.416690\pi\) | ||||
0.258748 | + | 0.965945i | \(0.416690\pi\) | |||||||
\(762\) | −8.03716 | −0.291156 | ||||||||
\(763\) | −14.0736 | −0.509499 | ||||||||
\(764\) | 11.0853 | 0.401052 | ||||||||
\(765\) | 3.37791 | 0.122129 | ||||||||
\(766\) | 32.4570 | 1.17272 | ||||||||
\(767\) | −1.93187 | −0.0697557 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −29.7150 | −1.07155 | −0.535776 | − | 0.844360i | \(-0.679981\pi\) | ||||
−0.535776 | + | 0.844360i | \(0.679981\pi\) | |||||||
\(770\) | 3.49392 | 0.125912 | ||||||||
\(771\) | 15.0916 | 0.543511 | ||||||||
\(772\) | 6.80068 | 0.244762 | ||||||||
\(773\) | −32.4335 | −1.16655 | −0.583277 | − | 0.812274i | \(-0.698230\pi\) | ||||
−0.583277 | + | 0.812274i | \(0.698230\pi\) | |||||||
\(774\) | −3.98449 | −0.143220 | ||||||||
\(775\) | 14.7493 | 0.529811 | ||||||||
\(776\) | −10.4350 | −0.374593 | ||||||||
\(777\) | 1.29277 | 0.0463778 | ||||||||
\(778\) | −7.67508 | −0.275165 | ||||||||
\(779\) | 6.01119 | 0.215373 | ||||||||
\(780\) | 0.937159 | 0.0335557 | ||||||||
\(781\) | 28.0569 | 1.00396 | ||||||||
\(782\) | −16.9019 | −0.604411 | ||||||||
\(783\) | 3.11482 | 0.111315 | ||||||||
\(784\) | −6.37162 | −0.227558 | ||||||||
\(785\) | 17.7435 | 0.633293 | ||||||||
\(786\) | 4.13397 | 0.147454 | ||||||||
\(787\) | 7.44005 | 0.265209 | 0.132605 | − | 0.991169i | \(-0.457666\pi\) | ||||
0.132605 | + | 0.991169i | \(0.457666\pi\) | |||||||
\(788\) | −5.08227 | −0.181048 | ||||||||
\(789\) | −2.51843 | −0.0896584 | ||||||||
\(790\) | 6.02680 | 0.214424 | ||||||||
\(791\) | −6.36372 | −0.226268 | ||||||||
\(792\) | 4.70314 | 0.167119 | ||||||||
\(793\) | −14.8337 | −0.526759 | ||||||||
\(794\) | 7.64131 | 0.271180 | ||||||||
\(795\) | 5.26557 | 0.186751 | ||||||||
\(796\) | 15.9413 | 0.565024 | ||||||||
\(797\) | 23.0552 | 0.816658 | 0.408329 | − | 0.912835i | \(-0.366112\pi\) | ||||
0.408329 | + | 0.912835i | \(0.366112\pi\) | |||||||
\(798\) | 0.636858 | 0.0225445 | ||||||||
\(799\) | −2.08951 | −0.0739217 | ||||||||
\(800\) | 4.12173 | 0.145725 | ||||||||
\(801\) | −18.2668 | −0.645427 | ||||||||
\(802\) | 12.6513 | 0.446734 | ||||||||
\(803\) | −3.81313 | −0.134562 | ||||||||
\(804\) | −5.77582 | −0.203698 | ||||||||
\(805\) | −3.48357 | −0.122780 | ||||||||
\(806\) | 3.57843 | 0.126045 | ||||||||
\(807\) | 26.3178 | 0.926430 | ||||||||
\(808\) | 1.41189 | 0.0496700 | ||||||||
\(809\) | −24.4161 | −0.858423 | −0.429211 | − | 0.903204i | \(-0.641208\pi\) | ||||
−0.429211 | + | 0.903204i | \(0.641208\pi\) | |||||||
\(810\) | 0.937159 | 0.0329284 | ||||||||
\(811\) | 1.52704 | 0.0536217 | 0.0268108 | − | 0.999641i | \(-0.491465\pi\) | ||||
0.0268108 | + | 0.999641i | \(0.491465\pi\) | |||||||
\(812\) | 2.46913 | 0.0866495 | ||||||||
\(813\) | −6.11955 | −0.214622 | ||||||||
\(814\) | 7.67004 | 0.268835 | ||||||||
\(815\) | 9.01395 | 0.315745 | ||||||||
\(816\) | 3.60442 | 0.126180 | ||||||||
\(817\) | −3.20114 | −0.111994 | ||||||||
\(818\) | −24.4350 | −0.854348 | ||||||||
\(819\) | −0.792704 | −0.0276993 | ||||||||
\(820\) | 7.01200 | 0.244870 | ||||||||
\(821\) | 8.57849 | 0.299392 | 0.149696 | − | 0.988732i | \(-0.452171\pi\) | ||||
0.149696 | + | 0.988732i | \(0.452171\pi\) | |||||||
\(822\) | −17.8896 | −0.623973 | ||||||||
\(823\) | −2.61365 | −0.0911059 | −0.0455530 | − | 0.998962i | \(-0.514505\pi\) | ||||
−0.0455530 | + | 0.998962i | \(0.514505\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −19.3851 | −0.674903 | ||||||||
\(826\) | −1.53140 | −0.0532842 | ||||||||
\(827\) | −17.7252 | −0.616366 | −0.308183 | − | 0.951327i | \(-0.599721\pi\) | ||||
−0.308183 | + | 0.951327i | \(0.599721\pi\) | |||||||
\(828\) | −4.68922 | −0.162962 | ||||||||
\(829\) | 45.1815 | 1.56922 | 0.784610 | − | 0.619990i | \(-0.212863\pi\) | ||||
0.784610 | + | 0.619990i | \(0.212863\pi\) | |||||||
\(830\) | −5.07609 | −0.176194 | ||||||||
\(831\) | 31.2379 | 1.08363 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 22.9660 | 0.795724 | ||||||||
\(834\) | −17.3454 | −0.600622 | ||||||||
\(835\) | 23.6552 | 0.818623 | ||||||||
\(836\) | 3.77850 | 0.130682 | ||||||||
\(837\) | 3.57843 | 0.123689 | ||||||||
\(838\) | 23.6809 | 0.818043 | ||||||||
\(839\) | −52.4895 | −1.81214 | −0.906069 | − | 0.423129i | \(-0.860932\pi\) | ||||
−0.906069 | + | 0.423129i | \(0.860932\pi\) | |||||||
\(840\) | 0.742890 | 0.0256321 | ||||||||
\(841\) | −19.2979 | −0.665445 | ||||||||
\(842\) | 12.5451 | 0.432333 | ||||||||
\(843\) | 18.1874 | 0.626406 | ||||||||
\(844\) | 10.7284 | 0.369285 | ||||||||
\(845\) | −0.937159 | −0.0322392 | ||||||||
\(846\) | −0.579710 | −0.0199308 | ||||||||
\(847\) | −8.81451 | −0.302870 | ||||||||
\(848\) | 5.61866 | 0.192945 | ||||||||
\(849\) | −1.52975 | −0.0525009 | ||||||||
\(850\) | −14.8564 | −0.509572 | ||||||||
\(851\) | −7.64733 | −0.262147 | ||||||||
\(852\) | 5.96557 | 0.204377 | ||||||||
\(853\) | −41.2017 | −1.41072 | −0.705359 | − | 0.708850i | \(-0.749214\pi\) | ||||
−0.705359 | + | 0.708850i | \(0.749214\pi\) | |||||||
\(854\) | −11.7587 | −0.402374 | ||||||||
\(855\) | 0.752913 | 0.0257491 | ||||||||
\(856\) | −0.502970 | −0.0171912 | ||||||||
\(857\) | −35.6191 | −1.21673 | −0.608363 | − | 0.793659i | \(-0.708173\pi\) | ||||
−0.608363 | + | 0.793659i | \(0.708173\pi\) | |||||||
\(858\) | −4.70314 | −0.160563 | ||||||||
\(859\) | 7.62712 | 0.260234 | 0.130117 | − | 0.991499i | \(-0.458465\pi\) | ||||
0.130117 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(860\) | −3.73410 | −0.127332 | ||||||||
\(861\) | −5.93116 | −0.202133 | ||||||||
\(862\) | 18.7049 | 0.637092 | ||||||||
\(863\) | −4.07478 | −0.138707 | −0.0693536 | − | 0.997592i | \(-0.522094\pi\) | ||||
−0.0693536 | + | 0.997592i | \(0.522094\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −0.208653 | −0.00709440 | ||||||||
\(866\) | −32.1566 | −1.09272 | ||||||||
\(867\) | 4.00818 | 0.136125 | ||||||||
\(868\) | 2.83663 | 0.0962816 | ||||||||
\(869\) | −30.2456 | −1.02601 | ||||||||
\(870\) | 2.91908 | 0.0989661 | ||||||||
\(871\) | 5.77582 | 0.195706 | ||||||||
\(872\) | −17.7539 | −0.601224 | ||||||||
\(873\) | 10.4350 | 0.353170 | ||||||||
\(874\) | −3.76732 | −0.127431 | ||||||||
\(875\) | −6.77644 | −0.229085 | ||||||||
\(876\) | −0.810762 | −0.0273931 | ||||||||
\(877\) | −1.87904 | −0.0634506 | −0.0317253 | − | 0.999497i | \(-0.510100\pi\) | ||||
−0.0317253 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(878\) | −31.5854 | −1.06596 | ||||||||
\(879\) | 9.77976 | 0.329863 | ||||||||
\(880\) | 4.40759 | 0.148580 | ||||||||
\(881\) | −14.0026 | −0.471759 | −0.235879 | − | 0.971782i | \(-0.575797\pi\) | ||||
−0.235879 | + | 0.971782i | \(0.575797\pi\) | |||||||
\(882\) | 6.37162 | 0.214544 | ||||||||
\(883\) | −17.2474 | −0.580422 | −0.290211 | − | 0.956963i | \(-0.593726\pi\) | ||||
−0.290211 | + | 0.956963i | \(0.593726\pi\) | |||||||
\(884\) | −3.60442 | −0.121230 | ||||||||
\(885\) | −1.81047 | −0.0608582 | ||||||||
\(886\) | −26.8464 | −0.901923 | ||||||||
\(887\) | 1.85975 | 0.0624443 | 0.0312222 | − | 0.999512i | \(-0.490060\pi\) | ||||
0.0312222 | + | 0.999512i | \(0.490060\pi\) | |||||||
\(888\) | 1.63083 | 0.0547272 | ||||||||
\(889\) | 6.37109 | 0.213679 | ||||||||
\(890\) | −17.1189 | −0.573828 | ||||||||
\(891\) | −4.70314 | −0.157561 | ||||||||
\(892\) | −19.7800 | −0.662284 | ||||||||
\(893\) | −0.465738 | −0.0155853 | ||||||||
\(894\) | −9.59017 | −0.320743 | ||||||||
\(895\) | −23.8032 | −0.795653 | ||||||||
\(896\) | 0.792704 | 0.0264824 | ||||||||
\(897\) | 4.68922 | 0.156568 | ||||||||
\(898\) | 1.58098 | 0.0527578 | ||||||||
\(899\) | 11.1462 | 0.371745 | ||||||||
\(900\) | −4.12173 | −0.137391 | ||||||||
\(901\) | −20.2520 | −0.674691 | ||||||||
\(902\) | −35.1898 | −1.17169 | ||||||||
\(903\) | 3.15852 | 0.105109 | ||||||||
\(904\) | −8.02786 | −0.267003 | ||||||||
\(905\) | 6.16657 | 0.204984 | ||||||||
\(906\) | 8.93579 | 0.296872 | ||||||||
\(907\) | 31.3348 | 1.04046 | 0.520228 | − | 0.854028i | \(-0.325847\pi\) | ||||
0.520228 | + | 0.854028i | \(0.325847\pi\) | |||||||
\(908\) | 13.3566 | 0.443254 | ||||||||
\(909\) | −1.41189 | −0.0468294 | ||||||||
\(910\) | −0.742890 | −0.0246265 | ||||||||
\(911\) | −5.22797 | −0.173210 | −0.0866051 | − | 0.996243i | \(-0.527602\pi\) | ||||
−0.0866051 | + | 0.996243i | \(0.527602\pi\) | |||||||
\(912\) | 0.803399 | 0.0266032 | ||||||||
\(913\) | 25.4744 | 0.843080 | ||||||||
\(914\) | 13.8693 | 0.458755 | ||||||||
\(915\) | −13.9015 | −0.459569 | ||||||||
\(916\) | −1.87870 | −0.0620741 | ||||||||
\(917\) | −3.27701 | −0.108216 | ||||||||
\(918\) | −3.60442 | −0.118963 | ||||||||
\(919\) | 39.1606 | 1.29179 | 0.645894 | − | 0.763427i | \(-0.276485\pi\) | ||||
0.645894 | + | 0.763427i | \(0.276485\pi\) | |||||||
\(920\) | −4.39454 | −0.144884 | ||||||||
\(921\) | 17.1789 | 0.566064 | ||||||||
\(922\) | −2.70162 | −0.0889732 | ||||||||
\(923\) | −5.96557 | −0.196359 | ||||||||
\(924\) | −3.72820 | −0.122649 | ||||||||
\(925\) | −6.72186 | −0.221013 | ||||||||
\(926\) | 30.6401 | 1.00689 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 3.11482 | 0.102249 | ||||||||
\(929\) | 27.1936 | 0.892194 | 0.446097 | − | 0.894985i | \(-0.352814\pi\) | ||||
0.446097 | + | 0.894985i | \(0.352814\pi\) | |||||||
\(930\) | 3.35355 | 0.109967 | ||||||||
\(931\) | 5.11896 | 0.167767 | ||||||||
\(932\) | 16.0079 | 0.524356 | ||||||||
\(933\) | −28.7706 | −0.941907 | ||||||||
\(934\) | 20.2536 | 0.662717 | ||||||||
\(935\) | −15.8868 | −0.519554 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 30.3989 | 0.993089 | 0.496545 | − | 0.868011i | \(-0.334602\pi\) | ||||
0.496545 | + | 0.868011i | \(0.334602\pi\) | |||||||
\(938\) | 4.57852 | 0.149494 | ||||||||
\(939\) | −26.0073 | −0.848716 | ||||||||
\(940\) | −0.543280 | −0.0177198 | ||||||||
\(941\) | −38.1436 | −1.24345 | −0.621723 | − | 0.783237i | \(-0.713567\pi\) | ||||
−0.621723 | + | 0.783237i | \(0.713567\pi\) | |||||||
\(942\) | −18.9333 | −0.616880 | ||||||||
\(943\) | 35.0856 | 1.14255 | ||||||||
\(944\) | −1.93187 | −0.0628770 | ||||||||
\(945\) | −0.742890 | −0.0241662 | ||||||||
\(946\) | 18.7396 | 0.609278 | ||||||||
\(947\) | −18.8645 | −0.613014 | −0.306507 | − | 0.951868i | \(-0.599160\pi\) | ||||
−0.306507 | + | 0.951868i | \(0.599160\pi\) | |||||||
\(948\) | −6.43093 | −0.208867 | ||||||||
\(949\) | 0.810762 | 0.0263184 | ||||||||
\(950\) | −3.31140 | −0.107436 | ||||||||
\(951\) | 0.494041 | 0.0160204 | ||||||||
\(952\) | −2.85724 | −0.0926035 | ||||||||
\(953\) | −22.5227 | −0.729582 | −0.364791 | − | 0.931089i | \(-0.618860\pi\) | ||||
−0.364791 | + | 0.931089i | \(0.618860\pi\) | |||||||
\(954\) | −5.61866 | −0.181911 | ||||||||
\(955\) | −10.3887 | −0.336170 | ||||||||
\(956\) | 17.4394 | 0.564031 | ||||||||
\(957\) | −14.6494 | −0.473549 | ||||||||
\(958\) | −20.6640 | −0.667623 | ||||||||
\(959\) | 14.1812 | 0.457935 | ||||||||
\(960\) | 0.937159 | 0.0302467 | ||||||||
\(961\) | −18.1949 | −0.586931 | ||||||||
\(962\) | −1.63083 | −0.0525801 | ||||||||
\(963\) | 0.502970 | 0.0162080 | ||||||||
\(964\) | −6.56601 | −0.211477 | ||||||||
\(965\) | −6.37332 | −0.205164 | ||||||||
\(966\) | 3.71716 | 0.119598 | ||||||||
\(967\) | −38.8121 | −1.24811 | −0.624057 | − | 0.781379i | \(-0.714517\pi\) | ||||
−0.624057 | + | 0.781379i | \(0.714517\pi\) | |||||||
\(968\) | −11.1196 | −0.357396 | ||||||||
\(969\) | −2.89579 | −0.0930261 | ||||||||
\(970\) | 9.77921 | 0.313992 | ||||||||
\(971\) | 30.7021 | 0.985276 | 0.492638 | − | 0.870234i | \(-0.336033\pi\) | ||||
0.492638 | + | 0.870234i | \(0.336033\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 13.7498 | 0.440797 | ||||||||
\(974\) | 21.3896 | 0.685368 | ||||||||
\(975\) | 4.12173 | 0.132001 | ||||||||
\(976\) | −14.8337 | −0.474814 | ||||||||
\(977\) | −28.5714 | −0.914081 | −0.457040 | − | 0.889446i | \(-0.651091\pi\) | ||||
−0.457040 | + | 0.889446i | \(0.651091\pi\) | |||||||
\(978\) | −9.61838 | −0.307562 | ||||||||
\(979\) | 85.9116 | 2.74575 | ||||||||
\(980\) | 5.97122 | 0.190744 | ||||||||
\(981\) | 17.7539 | 0.566839 | ||||||||
\(982\) | 42.5182 | 1.35681 | ||||||||
\(983\) | 32.6252 | 1.04058 | 0.520291 | − | 0.853989i | \(-0.325823\pi\) | ||||
0.520291 | + | 0.853989i | \(0.325823\pi\) | |||||||
\(984\) | −7.48219 | −0.238524 | ||||||||
\(985\) | 4.76289 | 0.151758 | ||||||||
\(986\) | −11.2271 | −0.357544 | ||||||||
\(987\) | 0.459538 | 0.0146273 | ||||||||
\(988\) | −0.803399 | −0.0255595 | ||||||||
\(989\) | −18.6842 | −0.594121 | ||||||||
\(990\) | −4.40759 | −0.140082 | ||||||||
\(991\) | −13.3840 | −0.425156 | −0.212578 | − | 0.977144i | \(-0.568186\pi\) | ||||
−0.212578 | + | 0.977144i | \(0.568186\pi\) | |||||||
\(992\) | 3.57843 | 0.113615 | ||||||||
\(993\) | −13.2952 | −0.421909 | ||||||||
\(994\) | −4.72893 | −0.149993 | ||||||||
\(995\) | −14.9395 | −0.473615 | ||||||||
\(996\) | 5.41646 | 0.171627 | ||||||||
\(997\) | −47.8225 | −1.51455 | −0.757276 | − | 0.653094i | \(-0.773470\pi\) | ||||
−0.757276 | + | 0.653094i | \(0.773470\pi\) | |||||||
\(998\) | −10.6374 | −0.336722 | ||||||||
\(999\) | −1.63083 | −0.0515973 |
(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 | 8034.2.a.z.1.6 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.z.1.6 | ✓ | 14 | 1.1 | even | 1 | trivial |