Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(37,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.7 | ||
Root | \(0.120370 - 0.120370i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.37 |
Dual form | 570.2.m.a.493.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.66396 | + | 1.49373i | −0.744146 | + | 0.668017i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.170229 | − | 0.170229i | −0.0643405 | − | 0.0643405i | 0.674204 | − | 0.738545i | \(-0.264487\pi\) |
−0.738545 | + | 0.674204i | \(0.764487\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −0.120370 | + | 2.23283i | −0.0380644 | + | 0.706082i | ||||
\(11\) | 3.43349 | 1.03524 | 0.517618 | − | 0.855612i | \(-0.326819\pi\) | ||||
0.517618 | + | 0.855612i | \(0.326819\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 4.54030 | + | 4.54030i | 1.25925 | + | 1.25925i | 0.951450 | + | 0.307803i | \(0.0995936\pi\) |
0.307803 | + | 0.951450i | \(0.400406\pi\) | |||||||
\(14\) | −0.240740 | −0.0643405 | ||||||||
\(15\) | −2.23283 | − | 0.120370i | −0.576513 | − | 0.0310794i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.537531 | + | 0.537531i | 0.130370 | + | 0.130370i | 0.769281 | − | 0.638911i | \(-0.220615\pi\) |
−0.638911 | + | 0.769281i | \(0.720615\pi\) | |||||||
\(18\) | 0.707107 | + | 0.707107i | 0.166667 | + | 0.166667i | ||||
\(19\) | 2.42784 | + | 3.62016i | 0.556986 | + | 0.830522i | ||||
\(20\) | 1.49373 | + | 1.66396i | 0.334009 | + | 0.372073i | ||||
\(21\) | − | 0.240740i | − | 0.0525338i | ||||||
\(22\) | 2.42784 | − | 2.42784i | 0.517618 | − | 0.517618i | ||||
\(23\) | 5.15769 | − | 5.15769i | 1.07545 | − | 1.07545i | 0.0785425 | − | 0.996911i | \(-0.474973\pi\) |
0.996911 | − | 0.0785425i | \(-0.0250266\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | 0.537531 | − | 4.97102i | 0.107506 | − | 0.994204i | ||||
\(26\) | 6.42095 | 1.25925 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −0.170229 | + | 0.170229i | −0.0321703 | + | 0.0321703i | ||||
\(29\) | −5.37513 | −0.998137 | −0.499069 | − | 0.866562i | \(-0.666324\pi\) | ||||
−0.499069 | + | 0.866562i | \(0.666324\pi\) | |||||||
\(30\) | −1.66396 | + | 1.49373i | −0.303796 | + | 0.272717i | ||||
\(31\) | 5.37513i | 0.965402i | 0.875785 | + | 0.482701i | \(0.160344\pi\) | ||||
−0.875785 | + | 0.482701i | \(0.839656\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 2.42784 | + | 2.42784i | 0.422634 | + | 0.422634i | ||||
\(34\) | 0.760184 | 0.130370 | ||||||||
\(35\) | 0.537531 | + | 0.0289779i | 0.0908593 | + | 0.00489816i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.54122 | + | 5.54122i | −0.910972 | + | 0.910972i | −0.996349 | − | 0.0853770i | \(-0.972791\pi\) |
0.0853770 | + | 0.996349i | \(0.472791\pi\) | |||||||
\(38\) | 4.27659 | + | 0.843095i | 0.693754 | + | 0.136768i | ||||
\(39\) | 6.42095i | 1.02818i | ||||||||
\(40\) | 2.23283 | + | 0.120370i | 0.353041 | + | 0.0190322i | ||||
\(41\) | 3.68222i | 0.575066i | 0.957771 | + | 0.287533i | \(0.0928350\pi\) | ||||
−0.957771 | + | 0.287533i | \(0.907165\pi\) | |||||||
\(42\) | −0.170229 | − | 0.170229i | −0.0262669 | − | 0.0262669i | ||||
\(43\) | 2.29224 | − | 2.29224i | 0.349563 | − | 0.349563i | −0.510384 | − | 0.859947i | \(-0.670497\pi\) |
0.859947 | + | 0.510384i | \(0.170497\pi\) | |||||||
\(44\) | − | 3.43349i | − | 0.517618i | ||||||
\(45\) | −1.49373 | − | 1.66396i | −0.222672 | − | 0.248049i | ||||
\(46\) | − | 7.29408i | − | 1.07545i | ||||||
\(47\) | −9.57865 | − | 9.57865i | −1.39719 | − | 1.39719i | −0.807982 | − | 0.589208i | \(-0.799440\pi\) |
−0.589208 | − | 0.807982i | \(-0.700560\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 6.94204i | − | 0.991721i | ||||||
\(50\) | −3.13495 | − | 3.89514i | −0.443349 | − | 0.550855i | ||||
\(51\) | 0.760184i | 0.106447i | ||||||||
\(52\) | 4.54030 | − | 4.54030i | 0.629626 | − | 0.629626i | ||||
\(53\) | −1.93366 | − | 1.93366i | −0.265608 | − | 0.265608i | 0.561720 | − | 0.827328i | \(-0.310140\pi\) |
−0.827328 | + | 0.561720i | \(0.810140\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −5.71319 | + | 5.12871i | −0.770367 | + | 0.691556i | ||||
\(56\) | 0.240740i | 0.0321703i | ||||||||
\(57\) | −0.843095 | + | 4.27659i | −0.111671 | + | 0.566448i | ||||
\(58\) | −3.80079 | + | 3.80079i | −0.499069 | + | 0.499069i | ||||
\(59\) | −4.20166 | −0.547010 | −0.273505 | − | 0.961871i | \(-0.588183\pi\) | ||||
−0.273505 | + | 0.961871i | \(0.588183\pi\) | |||||||
\(60\) | −0.120370 | + | 2.23283i | −0.0155397 | + | 0.288257i | ||||
\(61\) | 1.65954 | 0.212483 | 0.106241 | − | 0.994340i | \(-0.466118\pi\) | ||||
0.106241 | + | 0.994340i | \(0.466118\pi\) | |||||||
\(62\) | 3.80079 | + | 3.80079i | 0.482701 | + | 0.482701i | ||||
\(63\) | 0.170229 | − | 0.170229i | 0.0214468 | − | 0.0214468i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −14.3369 | − | 0.772891i | −1.77827 | − | 0.0958653i | ||||
\(66\) | 3.43349 | 0.422634 | ||||||||
\(67\) | 0.481480 | − | 0.481480i | 0.0588222 | − | 0.0588222i | −0.677084 | − | 0.735906i | \(-0.736757\pi\) |
0.735906 | + | 0.677084i | \(0.236757\pi\) | |||||||
\(68\) | 0.537531 | − | 0.537531i | 0.0651852 | − | 0.0651852i | ||||
\(69\) | 7.29408 | 0.878104 | ||||||||
\(70\) | 0.400582 | − | 0.359601i | 0.0478787 | − | 0.0429806i | ||||
\(71\) | − | 8.93130i | − | 1.05995i | −0.848013 | − | 0.529975i | \(-0.822201\pi\) | ||
0.848013 | − | 0.529975i | \(-0.177799\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 8.74888 | − | 8.74888i | 1.02398 | − | 1.02398i | 0.0242731 | − | 0.999705i | \(-0.492273\pi\) |
0.999705 | − | 0.0242731i | \(-0.00772714\pi\) | |||||||
\(74\) | 7.83647i | 0.910972i | ||||||||
\(75\) | 3.89514 | − | 3.13495i | 0.449771 | − | 0.361993i | ||||
\(76\) | 3.62016 | − | 2.42784i | 0.415261 | − | 0.278493i | ||||
\(77\) | −0.584480 | − | 0.584480i | −0.0666077 | − | 0.0666077i | ||||
\(78\) | 4.54030 | + | 4.54030i | 0.514088 | + | 0.514088i | ||||
\(79\) | 1.15022 | 0.129410 | 0.0647050 | − | 0.997904i | \(-0.479389\pi\) | ||||
0.0647050 | + | 0.997904i | \(0.479389\pi\) | |||||||
\(80\) | 1.66396 | − | 1.49373i | 0.186036 | − | 0.167004i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 2.60372 | + | 2.60372i | 0.287533 | + | 0.287533i | ||||
\(83\) | −9.97102 | + | 9.97102i | −1.09446 | + | 1.09446i | −0.0994159 | + | 0.995046i | \(0.531697\pi\) |
−0.995046 | + | 0.0994159i | \(0.968303\pi\) | |||||||
\(84\) | −0.240740 | −0.0262669 | ||||||||
\(85\) | −1.69736 | − | 0.0915034i | −0.184104 | − | 0.00992494i | ||||
\(86\) | − | 3.24172i | − | 0.349563i | ||||||
\(87\) | −3.80079 | − | 3.80079i | −0.407488 | − | 0.407488i | ||||
\(88\) | −2.42784 | − | 2.42784i | −0.258809 | − | 0.258809i | ||||
\(89\) | 2.10098 | 0.222703 | 0.111351 | − | 0.993781i | \(-0.464482\pi\) | ||||
0.111351 | + | 0.993781i | \(0.464482\pi\) | |||||||
\(90\) | −2.23283 | − | 0.120370i | −0.235361 | − | 0.0126881i | ||||
\(91\) | − | 1.54578i | − | 0.162042i | ||||||
\(92\) | −5.15769 | − | 5.15769i | −0.537727 | − | 0.537727i | ||||
\(93\) | −3.80079 | + | 3.80079i | −0.394124 | + | 0.394124i | ||||
\(94\) | −13.5463 | −1.39719 | ||||||||
\(95\) | −9.44739 | − | 2.39726i | −0.969282 | − | 0.245953i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 10.8544 | − | 10.8544i | 1.10210 | − | 1.10210i | 0.107942 | − | 0.994157i | \(-0.465574\pi\) |
0.994157 | − | 0.107942i | \(-0.0344260\pi\) | |||||||
\(98\) | −4.90877 | − | 4.90877i | −0.495860 | − | 0.495860i | ||||
\(99\) | 3.43349i | 0.345079i | ||||||||
\(100\) | −4.97102 | − | 0.537531i | −0.497102 | − | 0.0537531i | ||||
\(101\) | 8.90870 | 0.886449 | 0.443225 | − | 0.896411i | \(-0.353834\pi\) | ||||
0.443225 | + | 0.896411i | \(0.353834\pi\) | |||||||
\(102\) | 0.537531 | + | 0.537531i | 0.0532235 | + | 0.0532235i | ||||
\(103\) | 6.26365 | + | 6.26365i | 0.617176 | + | 0.617176i | 0.944806 | − | 0.327630i | \(-0.106250\pi\) |
−0.327630 | + | 0.944806i | \(0.606250\pi\) | |||||||
\(104\) | − | 6.42095i | − | 0.629626i | ||||||
\(105\) | 0.359601 | + | 0.400582i | 0.0350935 | + | 0.0390928i | ||||
\(106\) | −2.73460 | −0.265608 | ||||||||
\(107\) | 5.59814 | − | 5.59814i | 0.541193 | − | 0.541193i | −0.382686 | − | 0.923879i | \(-0.625001\pi\) |
0.923879 | + | 0.382686i | \(0.125001\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | −10.7123 | −1.02605 | −0.513026 | − | 0.858373i | \(-0.671476\pi\) | ||||
−0.513026 | + | 0.858373i | \(0.671476\pi\) | |||||||
\(110\) | −0.413290 | + | 7.66639i | −0.0394056 | + | 0.730961i | ||||
\(111\) | −7.83647 | −0.743805 | ||||||||
\(112\) | 0.170229 | + | 0.170229i | 0.0160851 | + | 0.0160851i | ||||
\(113\) | −6.81260 | − | 6.81260i | −0.640875 | − | 0.640875i | 0.309895 | − | 0.950771i | \(-0.399706\pi\) |
−0.950771 | + | 0.309895i | \(0.899706\pi\) | |||||||
\(114\) | 2.42784 | + | 3.62016i | 0.227389 | + | 0.339059i | ||||
\(115\) | −0.877989 | + | 16.2864i | −0.0818729 | + | 1.51872i | ||||
\(116\) | 5.37513i | 0.499069i | ||||||||
\(117\) | −4.54030 | + | 4.54030i | −0.419751 | + | 0.419751i | ||||
\(118\) | −2.97102 | + | 2.97102i | −0.273505 | + | 0.273505i | ||||
\(119\) | − | 0.183007i | − | 0.0167762i | ||||||
\(120\) | 1.49373 | + | 1.66396i | 0.136358 | + | 0.151898i | ||||
\(121\) | 0.788861 | 0.0717146 | ||||||||
\(122\) | 1.17347 | − | 1.17347i | 0.106241 | − | 0.106241i | ||||
\(123\) | −2.60372 | + | 2.60372i | −0.234770 | + | 0.234770i | ||||
\(124\) | 5.37513 | 0.482701 | ||||||||
\(125\) | 6.53094 | + | 9.07451i | 0.584145 | + | 0.811649i | ||||
\(126\) | − | 0.240740i | − | 0.0214468i | ||||||
\(127\) | 5.19935 | − | 5.19935i | 0.461368 | − | 0.461368i | −0.437736 | − | 0.899104i | \(-0.644219\pi\) |
0.899104 | + | 0.437736i | \(0.144219\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 3.24172 | 0.285417 | ||||||||
\(130\) | −10.6842 | + | 9.59118i | −0.937068 | + | 0.841202i | ||||
\(131\) | 2.14729 | 0.187610 | 0.0938048 | − | 0.995591i | \(-0.470097\pi\) | ||||
0.0938048 | + | 0.995591i | \(0.470097\pi\) | |||||||
\(132\) | 2.42784 | − | 2.42784i | 0.211317 | − | 0.211317i | ||||
\(133\) | 0.202967 | − | 1.02955i | 0.0175995 | − | 0.0892730i | ||||
\(134\) | − | 0.680916i | − | 0.0588222i | ||||||
\(135\) | 0.120370 | − | 2.23283i | 0.0103598 | − | 0.192171i | ||||
\(136\) | − | 0.760184i | − | 0.0651852i | ||||||
\(137\) | −13.5518 | − | 13.5518i | −1.15781 | − | 1.15781i | −0.984946 | − | 0.172863i | \(-0.944698\pi\) |
−0.172863 | − | 0.984946i | \(-0.555302\pi\) | |||||||
\(138\) | 5.15769 | − | 5.15769i | 0.439052 | − | 0.439052i | ||||
\(139\) | 10.5015i | 0.890721i | 0.895351 | + | 0.445361i | \(0.146925\pi\) | ||||
−0.895351 | + | 0.445361i | \(0.853075\pi\) | |||||||
\(140\) | 0.0289779 | − | 0.537531i | 0.00244908 | − | 0.0454297i | ||||
\(141\) | − | 13.5463i | − | 1.14080i | ||||||
\(142\) | −6.31539 | − | 6.31539i | −0.529975 | − | 0.529975i | ||||
\(143\) | 15.5891 | + | 15.5891i | 1.30362 | + | 1.30362i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 8.94401 | − | 8.02901i | 0.742760 | − | 0.666773i | ||||
\(146\) | − | 12.3728i | − | 1.02398i | ||||||
\(147\) | 4.90877 | − | 4.90877i | 0.404868 | − | 0.404868i | ||||
\(148\) | 5.54122 | + | 5.54122i | 0.455486 | + | 0.455486i | ||||
\(149\) | − | 1.02035i | − | 0.0835900i | −0.999126 | − | 0.0417950i | \(-0.986692\pi\) | ||
0.999126 | − | 0.0417950i | \(-0.0133076\pi\) | |||||||
\(150\) | 0.537531 | − | 4.97102i | 0.0438892 | − | 0.405882i | ||||
\(151\) | 19.8394i | 1.61451i | 0.590204 | + | 0.807254i | \(0.299047\pi\) | ||||
−0.590204 | + | 0.807254i | \(0.700953\pi\) | |||||||
\(152\) | 0.843095 | − | 4.27659i | 0.0683841 | − | 0.346877i | ||||
\(153\) | −0.537531 | + | 0.537531i | −0.0434568 | + | 0.0434568i | ||||
\(154\) | −0.826579 | −0.0666077 | ||||||||
\(155\) | −8.02901 | − | 8.94401i | −0.644905 | − | 0.718400i | ||||
\(156\) | 6.42095 | 0.514088 | ||||||||
\(157\) | −13.1863 | − | 13.1863i | −1.05238 | − | 1.05238i | −0.998550 | − | 0.0538289i | \(-0.982857\pi\) |
−0.0538289 | − | 0.998550i | \(-0.517143\pi\) | |||||||
\(158\) | 0.813330 | − | 0.813330i | 0.0647050 | − | 0.0647050i | ||||
\(159\) | − | 2.73460i | − | 0.216868i | ||||||
\(160\) | 0.120370 | − | 2.23283i | 0.00951609 | − | 0.176520i | ||||
\(161\) | −1.75598 | −0.138390 | ||||||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 1.19921 | − | 1.19921i | 0.0939291 | − | 0.0939291i | −0.658581 | − | 0.752510i | \(-0.728843\pi\) |
0.752510 | + | 0.658581i | \(0.228843\pi\) | |||||||
\(164\) | 3.68222 | 0.287533 | ||||||||
\(165\) | −7.66639 | − | 0.413290i | −0.596827 | − | 0.0321746i | ||||
\(166\) | 14.1012i | 1.09446i | ||||||||
\(167\) | −11.1290 | + | 11.1290i | −0.861184 | + | 0.861184i | −0.991476 | − | 0.130292i | \(-0.958409\pi\) |
0.130292 | + | 0.991476i | \(0.458409\pi\) | |||||||
\(168\) | −0.170229 | + | 0.170229i | −0.0131335 | + | 0.0131335i | ||||
\(169\) | 28.2287i | 2.17144i | ||||||||
\(170\) | −1.26492 | + | 1.13551i | −0.0970146 | + | 0.0870897i | ||||
\(171\) | −3.62016 | + | 2.42784i | −0.276841 | + | 0.185662i | ||||
\(172\) | −2.29224 | − | 2.29224i | −0.174782 | − | 0.174782i | ||||
\(173\) | −15.2012 | − | 15.2012i | −1.15573 | − | 1.15573i | −0.985385 | − | 0.170341i | \(-0.945513\pi\) |
−0.170341 | − | 0.985385i | \(-0.554487\pi\) | |||||||
\(174\) | −5.37513 | −0.407488 | ||||||||
\(175\) | −0.937716 | + | 0.754709i | −0.0708846 | + | 0.0570506i | ||||
\(176\) | −3.43349 | −0.258809 | ||||||||
\(177\) | −2.97102 | − | 2.97102i | −0.223316 | − | 0.223316i | ||||
\(178\) | 1.48561 | − | 1.48561i | 0.111351 | − | 0.111351i | ||||
\(179\) | 24.9536 | 1.86512 | 0.932559 | − | 0.361019i | \(-0.117571\pi\) | ||||
0.932559 | + | 0.361019i | \(0.117571\pi\) | |||||||
\(180\) | −1.66396 | + | 1.49373i | −0.124024 | + | 0.111336i | ||||
\(181\) | 15.9721i | 1.18720i | 0.804762 | + | 0.593598i | \(0.202293\pi\) | ||||
−0.804762 | + | 0.593598i | \(0.797707\pi\) | |||||||
\(182\) | −1.09303 | − | 1.09303i | −0.0810210 | − | 0.0810210i | ||||
\(183\) | 1.17347 | + | 1.17347i | 0.0867456 | + | 0.0867456i | ||||
\(184\) | −7.29408 | −0.537727 | ||||||||
\(185\) | 0.943277 | − | 17.4975i | 0.0693511 | − | 1.28644i | ||||
\(186\) | 5.37513i | 0.394124i | ||||||||
\(187\) | 1.84561 | + | 1.84561i | 0.134964 | + | 0.134964i | ||||
\(188\) | −9.57865 | + | 9.57865i | −0.698595 | + | 0.698595i | ||||
\(189\) | 0.240740 | 0.0175113 | ||||||||
\(190\) | −8.37543 | + | 4.98520i | −0.607618 | + | 0.361664i | ||||
\(191\) | 2.91580 | 0.210980 | 0.105490 | − | 0.994420i | \(-0.466359\pi\) | ||||
0.105490 | + | 0.994420i | \(0.466359\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −6.67601 | − | 6.67601i | −0.480550 | − | 0.480550i | 0.424758 | − | 0.905307i | \(-0.360359\pi\) |
−0.905307 | + | 0.424758i | \(0.860359\pi\) | |||||||
\(194\) | − | 15.3505i | − | 1.10210i | ||||||
\(195\) | −9.59118 | − | 10.6842i | −0.686839 | − | 0.765113i | ||||
\(196\) | −6.94204 | −0.495860 | ||||||||
\(197\) | −4.08263 | − | 4.08263i | −0.290875 | − | 0.290875i | 0.546551 | − | 0.837426i | \(-0.315941\pi\) |
−0.837426 | + | 0.546551i | \(0.815941\pi\) | |||||||
\(198\) | 2.42784 | + | 2.42784i | 0.172539 | + | 0.172539i | ||||
\(199\) | − | 8.23662i | − | 0.583879i | −0.956437 | − | 0.291939i | \(-0.905699\pi\) | ||
0.956437 | − | 0.291939i | \(-0.0943006\pi\) | |||||||
\(200\) | −3.89514 | + | 3.13495i | −0.275428 | + | 0.221675i | ||||
\(201\) | 0.680916 | 0.0480281 | ||||||||
\(202\) | 6.29940 | − | 6.29940i | 0.443225 | − | 0.443225i | ||||
\(203\) | 0.915004 | + | 0.915004i | 0.0642207 | + | 0.0642207i | ||||
\(204\) | 0.760184 | 0.0532235 | ||||||||
\(205\) | −5.50024 | − | 6.12706i | −0.384154 | − | 0.427933i | ||||
\(206\) | 8.85814 | 0.617176 | ||||||||
\(207\) | 5.15769 | + | 5.15769i | 0.358484 | + | 0.358484i | ||||
\(208\) | −4.54030 | − | 4.54030i | −0.314813 | − | 0.314813i | ||||
\(209\) | 8.33598 | + | 12.4298i | 0.576612 | + | 0.859787i | ||||
\(210\) | 0.537531 | + | 0.0289779i | 0.0370932 | + | 0.00199967i | ||||
\(211\) | 14.6136i | 1.00604i | 0.864275 | + | 0.503020i | \(0.167778\pi\) | ||||
−0.864275 | + | 0.503020i | \(0.832222\pi\) | |||||||
\(212\) | −1.93366 | + | 1.93366i | −0.132804 | + | 0.132804i | ||||
\(213\) | 6.31539 | − | 6.31539i | 0.432723 | − | 0.432723i | ||||
\(214\) | − | 7.91697i | − | 0.541193i | ||||||
\(215\) | −0.390206 | + | 7.23819i | −0.0266118 | + | 0.493640i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0.915004 | − | 0.915004i | 0.0621145 | − | 0.0621145i | ||||
\(218\) | −7.57474 | + | 7.57474i | −0.513026 | + | 0.513026i | ||||
\(219\) | 12.3728 | 0.836075 | ||||||||
\(220\) | 5.12871 | + | 5.71319i | 0.345778 | + | 0.385183i | ||||
\(221\) | 4.88110i | 0.328339i | ||||||||
\(222\) | −5.54122 | + | 5.54122i | −0.371903 | + | 0.371903i | ||||
\(223\) | −15.9582 | − | 15.9582i | −1.06864 | − | 1.06864i | −0.997464 | − | 0.0711734i | \(-0.977326\pi\) |
−0.0711734 | − | 0.997464i | \(-0.522674\pi\) | |||||||
\(224\) | 0.240740 | 0.0160851 | ||||||||
\(225\) | 4.97102 | + | 0.537531i | 0.331401 | + | 0.0358354i | ||||
\(226\) | −9.63447 | −0.640875 | ||||||||
\(227\) | 5.87132 | − | 5.87132i | 0.389694 | − | 0.389694i | −0.484885 | − | 0.874578i | \(-0.661138\pi\) |
0.874578 | + | 0.484885i | \(0.161138\pi\) | |||||||
\(228\) | 4.27659 | + | 0.843095i | 0.283224 | + | 0.0558353i | ||||
\(229\) | − | 10.2825i | − | 0.679487i | −0.940518 | − | 0.339743i | \(-0.889660\pi\) | ||
0.940518 | − | 0.339743i | \(-0.110340\pi\) | |||||||
\(230\) | 10.8954 | + | 12.1371i | 0.718421 | + | 0.800294i | ||||
\(231\) | − | 0.826579i | − | 0.0543849i | ||||||
\(232\) | 3.80079 | + | 3.80079i | 0.249534 | + | 0.249534i | ||||
\(233\) | 14.4725 | − | 14.4725i | 0.948123 | − | 0.948123i | −0.0505960 | − | 0.998719i | \(-0.516112\pi\) |
0.998719 | + | 0.0505960i | \(0.0161121\pi\) | |||||||
\(234\) | 6.42095i | 0.419751i | ||||||||
\(235\) | 30.2464 | + | 1.63056i | 1.97306 | + | 0.106366i | ||||
\(236\) | 4.20166i | 0.273505i | ||||||||
\(237\) | 0.813330 | + | 0.813330i | 0.0528314 | + | 0.0528314i | ||||
\(238\) | −0.129405 | − | 0.129405i | −0.00838810 | − | 0.00838810i | ||||
\(239\) | 21.4459i | 1.38722i | 0.720352 | + | 0.693609i | \(0.243980\pi\) | ||||
−0.720352 | + | 0.693609i | \(0.756020\pi\) | |||||||
\(240\) | 2.23283 | + | 0.120370i | 0.144128 | + | 0.00776986i | ||||
\(241\) | 1.51636i | 0.0976773i | 0.998807 | + | 0.0488387i | \(0.0155520\pi\) | ||||
−0.998807 | + | 0.0488387i | \(0.984448\pi\) | |||||||
\(242\) | 0.557809 | − | 0.557809i | 0.0358573 | − | 0.0358573i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 1.65954i | − | 0.106241i | ||||||
\(245\) | 10.3696 | + | 11.5513i | 0.662486 | + | 0.737985i | ||||
\(246\) | 3.68222i | 0.234770i | ||||||||
\(247\) | −5.41348 | + | 27.4598i | −0.344451 | + | 1.74722i | ||||
\(248\) | 3.80079 | − | 3.80079i | 0.241351 | − | 0.241351i | ||||
\(249\) | −14.1012 | −0.893624 | ||||||||
\(250\) | 11.0347 | + | 1.79858i | 0.697897 | + | 0.113752i | ||||
\(251\) | 11.6524 | 0.735495 | 0.367748 | − | 0.929926i | \(-0.380129\pi\) | ||||
0.367748 | + | 0.929926i | \(0.380129\pi\) | |||||||
\(252\) | −0.170229 | − | 0.170229i | −0.0107234 | − | 0.0107234i | ||||
\(253\) | 17.7089 | − | 17.7089i | 1.11335 | − | 1.11335i | ||||
\(254\) | − | 7.35299i | − | 0.461368i | ||||||
\(255\) | −1.13551 | − | 1.26492i | −0.0711084 | − | 0.0792121i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.00645 | + | 1.00645i | −0.0627804 | + | 0.0627804i | −0.737800 | − | 0.675020i | \(-0.764135\pi\) |
0.675020 | + | 0.737800i | \(0.264135\pi\) | |||||||
\(258\) | 2.29224 | − | 2.29224i | 0.142709 | − | 0.142709i | ||||
\(259\) | 1.88655 | 0.117225 | ||||||||
\(260\) | −0.772891 | + | 14.3369i | −0.0479327 | + | 0.889135i | ||||
\(261\) | − | 5.37513i | − | 0.332712i | ||||||
\(262\) | 1.51836 | − | 1.51836i | 0.0938048 | − | 0.0938048i | ||||
\(263\) | 0.396280 | − | 0.396280i | 0.0244357 | − | 0.0244357i | −0.694783 | − | 0.719219i | \(-0.744500\pi\) |
0.719219 | + | 0.694783i | \(0.244500\pi\) | |||||||
\(264\) | − | 3.43349i | − | 0.211317i | ||||||
\(265\) | 6.10589 | + | 0.329165i | 0.375082 | + | 0.0202204i | ||||
\(266\) | −0.584480 | − | 0.871519i | −0.0358368 | − | 0.0534362i | ||||
\(267\) | 1.48561 | + | 1.48561i | 0.0909181 | + | 0.0909181i | ||||
\(268\) | −0.481480 | − | 0.481480i | −0.0294111 | − | 0.0294111i | ||||
\(269\) | −20.9263 | −1.27590 | −0.637948 | − | 0.770079i | \(-0.720217\pi\) | ||||
−0.637948 | + | 0.770079i | \(0.720217\pi\) | |||||||
\(270\) | −1.49373 | − | 1.66396i | −0.0909056 | − | 0.101265i | ||||
\(271\) | −16.9175 | −1.02767 | −0.513834 | − | 0.857890i | \(-0.671775\pi\) | ||||
−0.513834 | + | 0.857890i | \(0.671775\pi\) | |||||||
\(272\) | −0.537531 | − | 0.537531i | −0.0325926 | − | 0.0325926i | ||||
\(273\) | 1.09303 | − | 1.09303i | 0.0661534 | − | 0.0661534i | ||||
\(274\) | −19.1651 | −1.15781 | ||||||||
\(275\) | 1.84561 | − | 17.0680i | 0.111294 | − | 1.02924i | ||||
\(276\) | − | 7.29408i | − | 0.439052i | ||||||
\(277\) | 15.6769 | + | 15.6769i | 0.941931 | + | 0.941931i | 0.998404 | − | 0.0564732i | \(-0.0179856\pi\) |
−0.0564732 | + | 0.998404i | \(0.517986\pi\) | |||||||
\(278\) | 7.42565 | + | 7.42565i | 0.445361 | + | 0.445361i | ||||
\(279\) | −5.37513 | −0.321801 | ||||||||
\(280\) | −0.359601 | − | 0.400582i | −0.0214903 | − | 0.0239394i | ||||
\(281\) | 10.3485i | 0.617342i | 0.951169 | + | 0.308671i | \(0.0998842\pi\) | ||||
−0.951169 | + | 0.308671i | \(0.900116\pi\) | |||||||
\(282\) | −9.57865 | − | 9.57865i | −0.570400 | − | 0.570400i | ||||
\(283\) | 6.03331 | − | 6.03331i | 0.358643 | − | 0.358643i | −0.504670 | − | 0.863313i | \(-0.668386\pi\) |
0.863313 | + | 0.504670i | \(0.168386\pi\) | |||||||
\(284\) | −8.93130 | −0.529975 | ||||||||
\(285\) | −4.98520 | − | 8.37543i | −0.295297 | − | 0.496118i | ||||
\(286\) | 22.0463 | 1.30362 | ||||||||
\(287\) | 0.626820 | − | 0.626820i | 0.0370000 | − | 0.0370000i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 16.4221i | − | 0.966007i | ||||||
\(290\) | 0.647005 | − | 12.0017i | 0.0379935 | − | 0.704766i | ||||
\(291\) | 15.3505 | 0.899860 | ||||||||
\(292\) | −8.74888 | − | 8.74888i | −0.511989 | − | 0.511989i | ||||
\(293\) | 6.64005 | + | 6.64005i | 0.387916 | + | 0.387916i | 0.873943 | − | 0.486028i | \(-0.161555\pi\) |
−0.486028 | + | 0.873943i | \(0.661555\pi\) | |||||||
\(294\) | − | 6.94204i | − | 0.404868i | ||||||
\(295\) | 6.99140 | − | 6.27615i | 0.407055 | − | 0.365412i | ||||
\(296\) | 7.83647 | 0.455486 | ||||||||
\(297\) | −2.42784 | + | 2.42784i | −0.140878 | + | 0.140878i | ||||
\(298\) | −0.721494 | − | 0.721494i | −0.0417950 | − | 0.0417950i | ||||
\(299\) | 46.8349 | 2.70853 | ||||||||
\(300\) | −3.13495 | − | 3.89514i | −0.180997 | − | 0.224886i | ||||
\(301\) | −0.780412 | −0.0449822 | ||||||||
\(302\) | 14.0286 | + | 14.0286i | 0.807254 | + | 0.807254i | ||||
\(303\) | 6.29940 | + | 6.29940i | 0.361891 | + | 0.361891i | ||||
\(304\) | −2.42784 | − | 3.62016i | −0.139246 | − | 0.207631i | ||||
\(305\) | −2.76141 | + | 2.47891i | −0.158118 | + | 0.141942i | ||||
\(306\) | 0.760184i | 0.0434568i | ||||||||
\(307\) | 6.21426 | − | 6.21426i | 0.354667 | − | 0.354667i | −0.507176 | − | 0.861843i | \(-0.669311\pi\) |
0.861843 | + | 0.507176i | \(0.169311\pi\) | |||||||
\(308\) | −0.584480 | + | 0.584480i | −0.0333038 | + | 0.0333038i | ||||
\(309\) | 8.85814i | 0.503922i | ||||||||
\(310\) | −12.0017 | − | 0.647005i | −0.681653 | − | 0.0367474i | ||||
\(311\) | −4.55027 | −0.258022 | −0.129011 | − | 0.991643i | \(-0.541180\pi\) | ||||
−0.129011 | + | 0.991643i | \(0.541180\pi\) | |||||||
\(312\) | 4.54030 | − | 4.54030i | 0.257044 | − | 0.257044i | ||||
\(313\) | 20.0429 | − | 20.0429i | 1.13289 | − | 1.13289i | 0.143197 | − | 0.989694i | \(-0.454262\pi\) |
0.989694 | − | 0.143197i | \(-0.0457382\pi\) | |||||||
\(314\) | −18.6482 | −1.05238 | ||||||||
\(315\) | −0.0289779 | + | 0.537531i | −0.00163272 | + | 0.0302864i | ||||
\(316\) | − | 1.15022i | − | 0.0647050i | ||||||
\(317\) | 21.4280 | − | 21.4280i | 1.20351 | − | 1.20351i | 0.230424 | − | 0.973090i | \(-0.425989\pi\) |
0.973090 | − | 0.230424i | \(-0.0740114\pi\) | |||||||
\(318\) | −1.93366 | − | 1.93366i | −0.108434 | − | 0.108434i | ||||
\(319\) | −18.4555 | −1.03331 | ||||||||
\(320\) | −1.49373 | − | 1.66396i | −0.0835021 | − | 0.0930182i | ||||
\(321\) | 7.91697 | 0.441882 | ||||||||
\(322\) | −1.24166 | + | 1.24166i | −0.0691952 | + | 0.0691952i | ||||
\(323\) | −0.640907 | + | 3.25099i | −0.0356610 | + | 0.180890i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | 25.0105 | − | 20.1294i | 1.38733 | − | 1.11658i | ||||
\(326\) | − | 1.69593i | − | 0.0939291i | ||||||
\(327\) | −7.57474 | − | 7.57474i | −0.418884 | − | 0.418884i | ||||
\(328\) | 2.60372 | − | 2.60372i | 0.143766 | − | 0.143766i | ||||
\(329\) | 3.26113i | 0.179792i | ||||||||
\(330\) | −5.71319 | + | 5.12871i | −0.314501 | + | 0.282326i | ||||
\(331\) | − | 31.9582i | − | 1.75658i | −0.478125 | − | 0.878292i | \(-0.658683\pi\) | ||
0.478125 | − | 0.878292i | \(-0.341317\pi\) | |||||||
\(332\) | 9.97102 | + | 9.97102i | 0.547231 | + | 0.547231i | ||||
\(333\) | −5.54122 | − | 5.54122i | −0.303657 | − | 0.303657i | ||||
\(334\) | 15.7387i | 0.861184i | ||||||||
\(335\) | −0.0819620 | + | 1.52037i | −0.00447806 | + | 0.0830665i | ||||
\(336\) | 0.240740i | 0.0131335i | ||||||||
\(337\) | −6.27191 | + | 6.27191i | −0.341653 | + | 0.341653i | −0.856988 | − | 0.515336i | \(-0.827667\pi\) |
0.515336 | + | 0.856988i | \(0.327667\pi\) | |||||||
\(338\) | 19.9607 | + | 19.9607i | 1.08572 | + | 1.08572i | ||||
\(339\) | − | 9.63447i | − | 0.523273i | ||||||
\(340\) | −0.0915034 | + | 1.69736i | −0.00496247 | + | 0.0920521i | ||||
\(341\) | 18.4555i | 0.999420i | ||||||||
\(342\) | −0.843095 | + | 4.27659i | −0.0455894 | + | 0.231251i | ||||
\(343\) | −2.37334 | + | 2.37334i | −0.128148 | + | 0.128148i | ||||
\(344\) | −3.24172 | −0.174782 | ||||||||
\(345\) | −12.1371 | + | 10.8954i | −0.653437 | + | 0.586588i | ||||
\(346\) | −21.4978 | −1.15573 | ||||||||
\(347\) | −9.84922 | − | 9.84922i | −0.528734 | − | 0.528734i | 0.391461 | − | 0.920195i | \(-0.371970\pi\) |
−0.920195 | + | 0.391461i | \(0.871970\pi\) | |||||||
\(348\) | −3.80079 | + | 3.80079i | −0.203744 | + | 0.203744i | ||||
\(349\) | − | 23.7919i | − | 1.27355i | −0.771049 | − | 0.636776i | \(-0.780268\pi\) | ||
0.771049 | − | 0.636776i | \(-0.219732\pi\) | |||||||
\(350\) | −0.129405 | + | 1.19672i | −0.00691701 | + | 0.0639676i | ||||
\(351\) | −6.42095 | −0.342725 | ||||||||
\(352\) | −2.42784 | + | 2.42784i | −0.129405 | + | 0.129405i | ||||
\(353\) | −16.4474 | + | 16.4474i | −0.875407 | + | 0.875407i | −0.993055 | − | 0.117649i | \(-0.962464\pi\) |
0.117649 | + | 0.993055i | \(0.462464\pi\) | |||||||
\(354\) | −4.20166 | −0.223316 | ||||||||
\(355\) | 13.3410 | + | 14.8613i | 0.708065 | + | 0.788758i | ||||
\(356\) | − | 2.10098i | − | 0.111351i | ||||||
\(357\) | 0.129405 | − | 0.129405i | 0.00684886 | − | 0.00684886i | ||||
\(358\) | 17.6448 | − | 17.6448i | 0.932559 | − | 0.932559i | ||||
\(359\) | − | 9.08979i | − | 0.479741i | −0.970805 | − | 0.239870i | \(-0.922895\pi\) | ||
0.970805 | − | 0.239870i | \(-0.0771050\pi\) | |||||||
\(360\) | −0.120370 | + | 2.23283i | −0.00634406 | + | 0.117680i | ||||
\(361\) | −7.21114 | + | 17.5784i | −0.379534 | + | 0.925178i | ||||
\(362\) | 11.2940 | + | 11.2940i | 0.593598 | + | 0.593598i | ||||
\(363\) | 0.557809 | + | 0.557809i | 0.0292774 | + | 0.0292774i | ||||
\(364\) | −1.54578 | −0.0810210 | ||||||||
\(365\) | −1.48931 | + | 27.6263i | −0.0779542 | + | 1.44602i | ||||
\(366\) | 1.65954 | 0.0867456 | ||||||||
\(367\) | 17.6931 | + | 17.6931i | 0.923570 | + | 0.923570i | 0.997280 | − | 0.0737098i | \(-0.0234839\pi\) |
−0.0737098 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(368\) | −5.15769 | + | 5.15769i | −0.268863 | + | 0.268863i | ||||
\(369\) | −3.68222 | −0.191689 | ||||||||
\(370\) | −11.7056 | − | 13.0396i | −0.608545 | − | 0.677896i | ||||
\(371\) | 0.658329i | 0.0341787i | ||||||||
\(372\) | 3.80079 | + | 3.80079i | 0.197062 | + | 0.197062i | ||||
\(373\) | −4.93586 | − | 4.93586i | −0.255569 | − | 0.255569i | 0.567680 | − | 0.823249i | \(-0.307841\pi\) |
−0.823249 | + | 0.567680i | \(0.807841\pi\) | |||||||
\(374\) | 2.61008 | 0.134964 | ||||||||
\(375\) | −1.79858 | + | 11.0347i | −0.0928780 | + | 0.569831i | ||||
\(376\) | 13.5463i | 0.698595i | ||||||||
\(377\) | −24.4047 | − | 24.4047i | −1.25691 | − | 1.25691i | ||||
\(378\) | 0.170229 | − | 0.170229i | 0.00875564 | − | 0.00875564i | ||||
\(379\) | 9.44824 | 0.485324 | 0.242662 | − | 0.970111i | \(-0.421979\pi\) | ||||
0.242662 | + | 0.970111i | \(0.421979\pi\) | |||||||
\(380\) | −2.39726 | + | 9.44739i | −0.122977 | + | 0.484641i | ||||
\(381\) | 7.35299 | 0.376705 | ||||||||
\(382\) | 2.06179 | − | 2.06179i | 0.105490 | − | 0.105490i | ||||
\(383\) | 17.3196 | + | 17.3196i | 0.884991 | + | 0.884991i | 0.994037 | − | 0.109046i | \(-0.0347794\pi\) |
−0.109046 | + | 0.994037i | \(0.534779\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 1.84561 | + | 0.0994955i | 0.0940609 | + | 0.00507076i | ||||
\(386\) | −9.44130 | −0.480550 | ||||||||
\(387\) | 2.29224 | + | 2.29224i | 0.116521 | + | 0.116521i | ||||
\(388\) | −10.8544 | − | 10.8544i | −0.551049 | − | 0.551049i | ||||
\(389\) | − | 20.3705i | − | 1.03283i | −0.856340 | − | 0.516413i | \(-0.827267\pi\) | ||
0.856340 | − | 0.516413i | \(-0.172733\pi\) | |||||||
\(390\) | −14.3369 | − | 0.772891i | −0.725976 | − | 0.0391369i | ||||
\(391\) | 5.54484 | 0.280415 | ||||||||
\(392\) | −4.90877 | + | 4.90877i | −0.247930 | + | 0.247930i | ||||
\(393\) | 1.51836 | + | 1.51836i | 0.0765913 | + | 0.0765913i | ||||
\(394\) | −5.77371 | −0.290875 | ||||||||
\(395\) | −1.91392 | + | 1.71812i | −0.0963000 | + | 0.0864481i | ||||
\(396\) | 3.43349 | 0.172539 | ||||||||
\(397\) | 13.9251 | + | 13.9251i | 0.698883 | + | 0.698883i | 0.964170 | − | 0.265287i | \(-0.0854666\pi\) |
−0.265287 | + | 0.964170i | \(0.585467\pi\) | |||||||
\(398\) | −5.82417 | − | 5.82417i | −0.291939 | − | 0.291939i | ||||
\(399\) | 0.871519 | − | 0.584480i | 0.0436305 | − | 0.0292606i | ||||
\(400\) | −0.537531 | + | 4.97102i | −0.0268765 | + | 0.248551i | ||||
\(401\) | 0.407767i | 0.0203629i | 0.999948 | + | 0.0101815i | \(0.00324092\pi\) | ||||
−0.999948 | + | 0.0101815i | \(0.996759\pi\) | |||||||
\(402\) | 0.481480 | − | 0.481480i | 0.0240141 | − | 0.0240141i | ||||
\(403\) | −24.4047 | + | 24.4047i | −1.21569 | + | 1.21569i | ||||
\(404\) | − | 8.90870i | − | 0.443225i | ||||||
\(405\) | 1.66396 | − | 1.49373i | 0.0826829 | − | 0.0742241i | ||||
\(406\) | 1.29401 | 0.0642207 | ||||||||
\(407\) | −19.0257 | + | 19.0257i | −0.943071 | + | 0.943071i | ||||
\(408\) | 0.537531 | − | 0.537531i | 0.0266117 | − | 0.0266117i | ||||
\(409\) | 6.82208 | 0.337330 | 0.168665 | − | 0.985673i | \(-0.446054\pi\) | ||||
0.168665 | + | 0.985673i | \(0.446054\pi\) | |||||||
\(410\) | −8.22175 | − | 0.443229i | −0.406043 | − | 0.0218895i | ||||
\(411\) | − | 19.1651i | − | 0.945347i | ||||||
\(412\) | 6.26365 | − | 6.26365i | 0.308588 | − | 0.308588i | ||||
\(413\) | 0.715245 | + | 0.715245i | 0.0351949 | + | 0.0351949i | ||||
\(414\) | 7.29408 | 0.358484 | ||||||||
\(415\) | 1.69736 | − | 31.4854i | 0.0833200 | − | 1.54556i | ||||
\(416\) | −6.42095 | −0.314813 | ||||||||
\(417\) | −7.42565 | + | 7.42565i | −0.363636 | + | 0.363636i | ||||
\(418\) | 14.6836 | + | 2.89476i | 0.718199 | + | 0.141587i | ||||
\(419\) | 30.8811i | 1.50864i | 0.656507 | + | 0.754320i | \(0.272033\pi\) | ||||
−0.656507 | + | 0.754320i | \(0.727967\pi\) | |||||||
\(420\) | 0.400582 | − | 0.359601i | 0.0195464 | − | 0.0175467i | ||||
\(421\) | 5.62994i | 0.274386i | 0.990544 | + | 0.137193i | \(0.0438081\pi\) | ||||
−0.990544 | + | 0.137193i | \(0.956192\pi\) | |||||||
\(422\) | 10.3334 | + | 10.3334i | 0.503020 | + | 0.503020i | ||||
\(423\) | 9.57865 | − | 9.57865i | 0.465730 | − | 0.465730i | ||||
\(424\) | 2.73460i | 0.132804i | ||||||||
\(425\) | 2.96102 | − | 2.38314i | 0.143630 | − | 0.115599i | ||||
\(426\) | − | 8.93130i | − | 0.432723i | ||||||
\(427\) | −0.282502 | − | 0.282502i | −0.0136712 | − | 0.0136712i | ||||
\(428\) | −5.59814 | − | 5.59814i | −0.270597 | − | 0.270597i | ||||
\(429\) | 22.0463i | 1.06440i | ||||||||
\(430\) | 4.84226 | + | 5.39409i | 0.233514 | + | 0.260126i | ||||
\(431\) | 8.03322i | 0.386947i | 0.981106 | + | 0.193473i | \(0.0619753\pi\) | ||||
−0.981106 | + | 0.193473i | \(0.938025\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −27.5643 | − | 27.5643i | −1.32466 | − | 1.32466i | −0.909960 | − | 0.414695i | \(-0.863888\pi\) |
−0.414695 | − | 0.909960i | \(-0.636112\pi\) | |||||||
\(434\) | − | 1.29401i | − | 0.0621145i | ||||||
\(435\) | 12.0017 | + | 0.647005i | 0.575439 | + | 0.0310215i | ||||
\(436\) | 10.7123i | 0.513026i | ||||||||
\(437\) | 31.1938 | + | 6.14960i | 1.49220 | + | 0.294175i | ||||
\(438\) | 8.74888 | − | 8.74888i | 0.418037 | − | 0.418037i | ||||
\(439\) | −2.72959 | −0.130276 | −0.0651381 | − | 0.997876i | \(-0.520749\pi\) | ||||
−0.0651381 | + | 0.997876i | \(0.520749\pi\) | |||||||
\(440\) | 7.66639 | + | 0.413290i | 0.365481 | + | 0.0197028i | ||||
\(441\) | 6.94204 | 0.330574 | ||||||||
\(442\) | 3.45146 | + | 3.45146i | 0.164169 | + | 0.164169i | ||||
\(443\) | −21.7450 | + | 21.7450i | −1.03313 | + | 1.03313i | −0.0337029 | + | 0.999432i | \(0.510730\pi\) |
−0.999432 | + | 0.0337029i | \(0.989270\pi\) | |||||||
\(444\) | 7.83647i | 0.371903i | ||||||||
\(445\) | −3.49594 | + | 3.13829i | −0.165723 | + | 0.148769i | ||||
\(446\) | −22.5682 | −1.06864 | ||||||||
\(447\) | 0.721494 | − | 0.721494i | 0.0341255 | − | 0.0341255i | ||||
\(448\) | 0.170229 | − | 0.170229i | 0.00804257 | − | 0.00804257i | ||||
\(449\) | 6.33780 | 0.299099 | 0.149550 | − | 0.988754i | \(-0.452218\pi\) | ||||
0.149550 | + | 0.988754i | \(0.452218\pi\) | |||||||
\(450\) | 3.89514 | − | 3.13495i | 0.183618 | − | 0.147783i | ||||
\(451\) | 12.6429i | 0.595329i | ||||||||
\(452\) | −6.81260 | + | 6.81260i | −0.320438 | + | 0.320438i | ||||
\(453\) | −14.0286 | + | 14.0286i | −0.659120 | + | 0.659120i | ||||
\(454\) | − | 8.30331i | − | 0.389694i | ||||||
\(455\) | 2.30898 | + | 2.57212i | 0.108247 | + | 0.120583i | ||||
\(456\) | 3.62016 | − | 2.42784i | 0.169530 | − | 0.113694i | ||||
\(457\) | −14.1287 | − | 14.1287i | −0.660915 | − | 0.660915i | 0.294681 | − | 0.955596i | \(-0.404787\pi\) |
−0.955596 | + | 0.294681i | \(0.904787\pi\) | |||||||
\(458\) | −7.27083 | − | 7.27083i | −0.339743 | − | 0.339743i | ||||
\(459\) | −0.760184 | −0.0354823 | ||||||||
\(460\) | 16.2864 | + | 0.877989i | 0.759358 | + | 0.0409365i | ||||
\(461\) | −10.3701 | −0.482984 | −0.241492 | − | 0.970403i | \(-0.577637\pi\) | ||||
−0.241492 | + | 0.970403i | \(0.577637\pi\) | |||||||
\(462\) | −0.584480 | − | 0.584480i | −0.0271925 | − | 0.0271925i | ||||
\(463\) | −21.5966 | + | 21.5966i | −1.00368 | + | 1.00368i | −0.00368676 | + | 0.999993i | \(0.501174\pi\) |
−0.999993 | + | 0.00368676i | \(0.998826\pi\) | |||||||
\(464\) | 5.37513 | 0.249534 | ||||||||
\(465\) | 0.647005 | − | 12.0017i | 0.0300042 | − | 0.556567i | ||||
\(466\) | − | 20.4672i | − | 0.948123i | ||||||
\(467\) | 5.68112 | + | 5.68112i | 0.262891 | + | 0.262891i | 0.826228 | − | 0.563337i | \(-0.190483\pi\) |
−0.563337 | + | 0.826228i | \(0.690483\pi\) | |||||||
\(468\) | 4.54030 | + | 4.54030i | 0.209875 | + | 0.209875i | ||||
\(469\) | −0.163924 | −0.00756930 | ||||||||
\(470\) | 22.5404 | − | 20.2345i | 1.03971 | − | 0.933346i | ||||
\(471\) | − | 18.6482i | − | 0.859264i | ||||||
\(472\) | 2.97102 | + | 2.97102i | 0.136752 | + | 0.136752i | ||||
\(473\) | 7.87039 | − | 7.87039i | 0.361881 | − | 0.361881i | ||||
\(474\) | 1.15022 | 0.0528314 | ||||||||
\(475\) | 19.3009 | − | 10.1229i | 0.885588 | − | 0.464471i | ||||
\(476\) | −0.183007 | −0.00838810 | ||||||||
\(477\) | 1.93366 | − | 1.93366i | 0.0885361 | − | 0.0885361i | ||||
\(478\) | 15.1645 | + | 15.1645i | 0.693609 | + | 0.693609i | ||||
\(479\) | 18.3301i | 0.837524i | 0.908096 | + | 0.418762i | \(0.137536\pi\) | ||||
−0.908096 | + | 0.418762i | \(0.862464\pi\) | |||||||
\(480\) | 1.66396 | − | 1.49373i | 0.0759491 | − | 0.0681792i | ||||
\(481\) | −50.3176 | −2.29429 | ||||||||
\(482\) | 1.07223 | + | 1.07223i | 0.0488387 | + | 0.0488387i | ||||
\(483\) | −1.24166 | − | 1.24166i | −0.0564977 | − | 0.0564977i | ||||
\(484\) | − | 0.788861i | − | 0.0358573i | ||||||
\(485\) | −1.84774 | + | 34.2749i | −0.0839014 | + | 1.55634i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −8.21504 | + | 8.21504i | −0.372259 | + | 0.372259i | −0.868299 | − | 0.496040i | \(-0.834787\pi\) |
0.496040 | + | 0.868299i | \(0.334787\pi\) | |||||||
\(488\) | −1.17347 | − | 1.17347i | −0.0531206 | − | 0.0531206i | ||||
\(489\) | 1.69593 | 0.0766928 | ||||||||
\(490\) | 15.5004 | + | 0.835615i | 0.700236 | + | 0.0377492i | ||||
\(491\) | 5.85271 | 0.264129 | 0.132065 | − | 0.991241i | \(-0.457839\pi\) | ||||
0.132065 | + | 0.991241i | \(0.457839\pi\) | |||||||
\(492\) | 2.60372 | + | 2.60372i | 0.117385 | + | 0.117385i | ||||
\(493\) | −2.88930 | − | 2.88930i | −0.130128 | − | 0.130128i | ||||
\(494\) | 15.5891 | + | 23.2449i | 0.701386 | + | 1.04584i | ||||
\(495\) | −5.12871 | − | 5.71319i | −0.230519 | − | 0.256789i | ||||
\(496\) | − | 5.37513i | − | 0.241351i | ||||||
\(497\) | −1.52037 | + | 1.52037i | −0.0681978 | + | 0.0681978i | ||||
\(498\) | −9.97102 | + | 9.97102i | −0.446812 | + | 0.446812i | ||||
\(499\) | − | 24.4054i | − | 1.09254i | −0.837610 | − | 0.546268i | \(-0.816048\pi\) | ||
0.837610 | − | 0.546268i | \(-0.183952\pi\) | |||||||
\(500\) | 9.07451 | − | 6.53094i | 0.405825 | − | 0.292073i | ||||
\(501\) | −15.7387 | −0.703154 | ||||||||
\(502\) | 8.23952 | − | 8.23952i | 0.367748 | − | 0.367748i | ||||
\(503\) | 19.8672 | − | 19.8672i | 0.885836 | − | 0.885836i | −0.108284 | − | 0.994120i | \(-0.534536\pi\) |
0.994120 | + | 0.108284i | \(0.0345357\pi\) | |||||||
\(504\) | −0.240740 | −0.0107234 | ||||||||
\(505\) | −14.8237 | + | 13.3072i | −0.659647 | + | 0.592163i | ||||
\(506\) | − | 25.0442i | − | 1.11335i | ||||||
\(507\) | −19.9607 | + | 19.9607i | −0.886485 | + | 0.886485i | ||||
\(508\) | −5.19935 | − | 5.19935i | −0.230684 | − | 0.230684i | ||||
\(509\) | −19.2340 | −0.852534 | −0.426267 | − | 0.904597i | \(-0.640172\pi\) | ||||
−0.426267 | + | 0.904597i | \(0.640172\pi\) | |||||||
\(510\) | −1.69736 | − | 0.0915034i | −0.0751603 | − | 0.00405184i | ||||
\(511\) | −2.97863 | −0.131767 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −4.27659 | − | 0.843095i | −0.188816 | − | 0.0372236i | ||||
\(514\) | 1.42333i | 0.0627804i | ||||||||
\(515\) | −19.7787 | − | 1.06626i | −0.871553 | − | 0.0469848i | ||||
\(516\) | − | 3.24172i | − | 0.142709i | ||||||
\(517\) | −32.8882 | − | 32.8882i | −1.44642 | − | 1.44642i | ||||
\(518\) | 1.33400 | − | 1.33400i | 0.0586124 | − | 0.0586124i | ||||
\(519\) | − | 21.4978i | − | 0.943647i | ||||||
\(520\) | 9.59118 | + | 10.6842i | 0.420601 | + | 0.468534i | ||||
\(521\) | 19.1370i | 0.838407i | 0.907892 | + | 0.419204i | \(0.137691\pi\) | ||||
−0.907892 | + | 0.419204i | \(0.862309\pi\) | |||||||
\(522\) | −3.80079 | − | 3.80079i | −0.166356 | − | 0.166356i | ||||
\(523\) | −13.3664 | − | 13.3664i | −0.584471 | − | 0.584471i | 0.351657 | − | 0.936129i | \(-0.385618\pi\) |
−0.936129 | + | 0.351657i | \(0.885618\pi\) | |||||||
\(524\) | − | 2.14729i | − | 0.0938048i | ||||||
\(525\) | −1.19672 | − | 0.129405i | −0.0522294 | − | 0.00564771i | ||||
\(526\) | − | 0.560424i | − | 0.0244357i | ||||||
\(527\) | −2.88930 | + | 2.88930i | −0.125860 | + | 0.125860i | ||||
\(528\) | −2.42784 | − | 2.42784i | −0.105658 | − | 0.105658i | ||||
\(529\) | − | 30.2036i | − | 1.31320i | ||||||
\(530\) | 4.55027 | − | 4.08476i | 0.197651 | − | 0.177431i | ||||
\(531\) | − | 4.20166i | − | 0.182337i | ||||||
\(532\) | −1.02955 | − | 0.202967i | −0.0446365 | − | 0.00879973i | ||||
\(533\) | −16.7184 | + | 16.7184i | −0.724153 | + | 0.724153i | ||||
\(534\) | 2.10098 | 0.0909181 | ||||||||
\(535\) | −0.952967 | + | 17.6772i | −0.0412003 | + | 0.764253i | ||||
\(536\) | −0.680916 | −0.0294111 | ||||||||
\(537\) | 17.6448 | + | 17.6448i | 0.761431 | + | 0.761431i | ||||
\(538\) | −14.7971 | + | 14.7971i | −0.637948 | + | 0.637948i | ||||
\(539\) | − | 23.8354i | − | 1.02667i | ||||||
\(540\) | −2.23283 | − | 0.120370i | −0.0960855 | − | 0.00517990i | ||||
\(541\) | −36.4227 | −1.56593 | −0.782967 | − | 0.622063i | \(-0.786295\pi\) | ||||
−0.782967 | + | 0.622063i | \(0.786295\pi\) | |||||||
\(542\) | −11.9625 | + | 11.9625i | −0.513834 | + | 0.513834i | ||||
\(543\) | −11.2940 | + | 11.2940i | −0.484671 | + | 0.484671i | ||||
\(544\) | −0.760184 | −0.0325926 | ||||||||
\(545\) | 17.8249 | − | 16.0013i | 0.763533 | − | 0.685421i | ||||
\(546\) | − | 1.54578i | − | 0.0661534i | ||||||
\(547\) | 7.49691 | − | 7.49691i | 0.320545 | − | 0.320545i | −0.528431 | − | 0.848976i | \(-0.677220\pi\) |
0.848976 | + | 0.528431i | \(0.177220\pi\) | |||||||
\(548\) | −13.5518 | + | 13.5518i | −0.578904 | + | 0.578904i | ||||
\(549\) | 1.65954i | 0.0708275i | ||||||||
\(550\) | −10.7638 | − | 13.3739i | −0.458971 | − | 0.570266i | ||||
\(551\) | −13.0500 | − | 19.4588i | −0.555948 | − | 0.828975i | ||||
\(552\) | −5.15769 | − | 5.15769i | −0.219526 | − | 0.219526i | ||||
\(553\) | −0.195801 | − | 0.195801i | −0.00832631 | − | 0.00832631i | ||||
\(554\) | 22.1704 | 0.941931 | ||||||||
\(555\) | 13.0396 | − | 11.7056i | 0.553500 | − | 0.496875i | ||||
\(556\) | 10.5015 | 0.445361 | ||||||||
\(557\) | 6.66081 | + | 6.66081i | 0.282228 | + | 0.282228i | 0.833997 | − | 0.551769i | \(-0.186047\pi\) |
−0.551769 | + | 0.833997i | \(0.686047\pi\) | |||||||
\(558\) | −3.80079 | + | 3.80079i | −0.160900 | + | 0.160900i | ||||
\(559\) | 20.8149 | 0.880377 | ||||||||
\(560\) | −0.537531 | − | 0.0289779i | −0.0227148 | − | 0.00122454i | ||||
\(561\) | 2.61008i | 0.110198i | ||||||||
\(562\) | 7.31752 | + | 7.31752i | 0.308671 | + | 0.308671i | ||||
\(563\) | −18.2264 | − | 18.2264i | −0.768150 | − | 0.768150i | 0.209631 | − | 0.977781i | \(-0.432774\pi\) |
−0.977781 | + | 0.209631i | \(0.932774\pi\) | |||||||
\(564\) | −13.5463 | −0.570400 | ||||||||
\(565\) | 21.5121 | + | 1.15970i | 0.905020 | + | 0.0487890i | ||||
\(566\) | − | 8.53238i | − | 0.358643i | ||||||
\(567\) | 0.170229 | + | 0.170229i | 0.00714895 | + | 0.00714895i | ||||
\(568\) | −6.31539 | + | 6.31539i | −0.264988 | + | 0.264988i | ||||
\(569\) | 12.9797 | 0.544138 | 0.272069 | − | 0.962278i | \(-0.412292\pi\) | ||||
0.272069 | + | 0.962278i | \(0.412292\pi\) | |||||||
\(570\) | −9.44739 | − | 2.39726i | −0.395708 | − | 0.100410i | ||||
\(571\) | −4.34400 | −0.181791 | −0.0908954 | − | 0.995860i | \(-0.528973\pi\) | ||||
−0.0908954 | + | 0.995860i | \(0.528973\pi\) | |||||||
\(572\) | 15.5891 | − | 15.5891i | 0.651812 | − | 0.651812i | ||||
\(573\) | 2.06179 | + | 2.06179i | 0.0861323 | + | 0.0861323i | ||||
\(574\) | − | 0.886458i | − | 0.0370000i | ||||||
\(575\) | −22.8666 | − | 28.4114i | −0.953602 | − | 1.18484i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 22.6630 | + | 22.6630i | 0.943474 | + | 0.943474i | 0.998486 | − | 0.0550121i | \(-0.0175197\pi\) |
−0.0550121 | + | 0.998486i | \(0.517520\pi\) | |||||||
\(578\) | −11.6122 | − | 11.6122i | −0.483004 | − | 0.483004i | ||||
\(579\) | − | 9.44130i | − | 0.392367i | ||||||
\(580\) | −8.02901 | − | 8.94401i | −0.333386 | − | 0.371380i | ||||
\(581\) | 3.39472 | 0.140837 | ||||||||
\(582\) | 10.8544 | − | 10.8544i | 0.449930 | − | 0.449930i | ||||
\(583\) | −6.63919 | − | 6.63919i | −0.274967 | − | 0.274967i | ||||
\(584\) | −12.3728 | −0.511989 | ||||||||
\(585\) | 0.772891 | − | 14.3369i | 0.0319551 | − | 0.592757i | ||||
\(586\) | 9.39045 | 0.387916 | ||||||||
\(587\) | −1.52632 | − | 1.52632i | −0.0629979 | − | 0.0629979i | 0.674906 | − | 0.737904i | \(-0.264184\pi\) |
−0.737904 | + | 0.674906i | \(0.764184\pi\) | |||||||
\(588\) | −4.90877 | − | 4.90877i | −0.202434 | − | 0.202434i | ||||
\(589\) | −19.4588 | + | 13.0500i | −0.801788 | + | 0.537715i | ||||
\(590\) | 0.505754 | − | 9.38157i | 0.0208216 | − | 0.386233i | ||||
\(591\) | − | 5.77371i | − | 0.237499i | ||||||
\(592\) | 5.54122 | − | 5.54122i | 0.227743 | − | 0.227743i | ||||
\(593\) | 2.34436 | − | 2.34436i | 0.0962714 | − | 0.0962714i | −0.657331 | − | 0.753602i | \(-0.728315\pi\) |
0.753602 | + | 0.657331i | \(0.228315\pi\) | |||||||
\(594\) | 3.43349i | 0.140878i | ||||||||
\(595\) | 0.273363 | + | 0.304516i | 0.0112068 | + | 0.0124839i | ||||
\(596\) | −1.02035 | −0.0417950 | ||||||||
\(597\) | 5.82417 | − | 5.82417i | 0.238368 | − | 0.238368i | ||||
\(598\) | 33.1173 | − | 33.1173i | 1.35427 | − | 1.35427i | ||||
\(599\) | −20.2744 | −0.828391 | −0.414195 | − | 0.910188i | \(-0.635937\pi\) | ||||
−0.414195 | + | 0.910188i | \(0.635937\pi\) | |||||||
\(600\) | −4.97102 | − | 0.537531i | −0.202941 | − | 0.0219446i | ||||
\(601\) | − | 18.2726i | − | 0.745354i | −0.927961 | − | 0.372677i | \(-0.878440\pi\) | ||
0.927961 | − | 0.372677i | \(-0.121560\pi\) | |||||||
\(602\) | −0.551834 | + | 0.551834i | −0.0224911 | + | 0.0224911i | ||||
\(603\) | 0.481480 | + | 0.481480i | 0.0196074 | + | 0.0196074i | ||||
\(604\) | 19.8394 | 0.807254 | ||||||||
\(605\) | −1.31263 | + | 1.17835i | −0.0533662 | + | 0.0479066i | ||||
\(606\) | 8.90870 | 0.361891 | ||||||||
\(607\) | −21.4067 | + | 21.4067i | −0.868872 | + | 0.868872i | −0.992348 | − | 0.123476i | \(-0.960596\pi\) |
0.123476 | + | 0.992348i | \(0.460596\pi\) | |||||||
\(608\) | −4.27659 | − | 0.843095i | −0.173438 | − | 0.0341920i | ||||
\(609\) | 1.29401i | 0.0524360i | ||||||||
\(610\) | −0.199759 | + | 3.70547i | −0.00808802 | + | 0.150030i | ||||
\(611\) | − | 86.9799i | − | 3.51883i | ||||||
\(612\) | 0.537531 | + | 0.537531i | 0.0217284 | + | 0.0217284i | ||||
\(613\) | −21.6012 | + | 21.6012i | −0.872462 | + | 0.872462i | −0.992740 | − | 0.120278i | \(-0.961621\pi\) |
0.120278 | + | 0.992740i | \(0.461621\pi\) | |||||||
\(614\) | − | 8.78829i | − | 0.354667i | ||||||
\(615\) | 0.443229 | − | 8.22175i | 0.0178727 | − | 0.331533i | ||||
\(616\) | 0.826579i | 0.0333038i | ||||||||
\(617\) | 13.3582 | + | 13.3582i | 0.537782 | + | 0.537782i | 0.922877 | − | 0.385095i | \(-0.125831\pi\) |
−0.385095 | + | 0.922877i | \(0.625831\pi\) | |||||||
\(618\) | 6.26365 | + | 6.26365i | 0.251961 | + | 0.251961i | ||||
\(619\) | 35.7297i | 1.43610i | 0.695993 | + | 0.718049i | \(0.254965\pi\) | ||||
−0.695993 | + | 0.718049i | \(0.745035\pi\) | |||||||
\(620\) | −8.94401 | + | 8.02901i | −0.359200 | + | 0.322453i | ||||
\(621\) | 7.29408i | 0.292701i | ||||||||
\(622\) | −3.21753 | + | 3.21753i | −0.129011 | + | 0.129011i | ||||
\(623\) | −0.357647 | − | 0.357647i | −0.0143288 | − | 0.0143288i | ||||
\(624\) | − | 6.42095i | − | 0.257044i | ||||||
\(625\) | −24.4221 | − | 5.34416i | −0.976885 | − | 0.213766i | ||||
\(626\) | − | 28.3449i | − | 1.13289i | ||||||
\(627\) | −2.89476 | + | 14.6836i | −0.115606 | + | 0.586407i | ||||
\(628\) | −13.1863 | + | 13.1863i | −0.526190 | + | 0.526190i | ||||
\(629\) | −5.95716 | −0.237528 | ||||||||
\(630\) | 0.359601 | + | 0.400582i | 0.0143269 | + | 0.0159596i | ||||
\(631\) | −5.92905 | −0.236032 | −0.118016 | − | 0.993012i | \(-0.537653\pi\) | ||||
−0.118016 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(632\) | −0.813330 | − | 0.813330i | −0.0323525 | − | 0.0323525i | ||||
\(633\) | −10.3334 | + | 10.3334i | −0.410714 | + | 0.410714i | ||||
\(634\) | − | 30.3037i | − | 1.20351i | ||||||
\(635\) | −0.885081 | + | 16.4180i | −0.0351234 | + | 0.651527i | ||||
\(636\) | −2.73460 | −0.108434 | ||||||||
\(637\) | 31.5190 | − | 31.5190i | 1.24883 | − | 1.24883i | ||||
\(638\) | −13.0500 | + | 13.0500i | −0.516654 | + | 0.516654i | ||||
\(639\) | 8.93130 | 0.353317 | ||||||||
\(640\) | −2.23283 | − | 0.120370i | −0.0882602 | − | 0.00475805i | ||||
\(641\) | 6.60094i | 0.260721i | 0.991467 | + | 0.130361i | \(0.0416135\pi\) | ||||
−0.991467 | + | 0.130361i | \(0.958386\pi\) | |||||||
\(642\) | 5.59814 | − | 5.59814i | 0.220941 | − | 0.220941i | ||||
\(643\) | 13.4065 | − | 13.4065i | 0.528700 | − | 0.528700i | −0.391484 | − | 0.920185i | \(-0.628038\pi\) |
0.920185 | + | 0.391484i | \(0.128038\pi\) | |||||||
\(644\) | 1.75598i | 0.0691952i | ||||||||
\(645\) | −5.39409 | + | 4.84226i | −0.212392 | + | 0.190664i | ||||
\(646\) | 1.84561 | + | 2.75199i | 0.0726145 | + | 0.108275i | ||||
\(647\) | 10.3980 | + | 10.3980i | 0.408788 | + | 0.408788i | 0.881316 | − | 0.472528i | \(-0.156658\pi\) |
−0.472528 | + | 0.881316i | \(0.656658\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | −14.4264 | −0.566284 | ||||||||
\(650\) | 3.45146 | − | 31.9187i | 0.135377 | − | 1.25195i | ||||
\(651\) | 1.29401 | 0.0507163 | ||||||||
\(652\) | −1.19921 | − | 1.19921i | −0.0469646 | − | 0.0469646i | ||||
\(653\) | −9.88773 | + | 9.88773i | −0.386937 | + | 0.386937i | −0.873593 | − | 0.486657i | \(-0.838216\pi\) |
0.486657 | + | 0.873593i | \(0.338216\pi\) | |||||||
\(654\) | −10.7123 | −0.418884 | ||||||||
\(655\) | −3.57301 | + | 3.20748i | −0.139609 | + | 0.125326i | ||||
\(656\) | − | 3.68222i | − | 0.143766i | ||||||
\(657\) | 8.74888 | + | 8.74888i | 0.341326 | + | 0.341326i | ||||
\(658\) | 2.30597 | + | 2.30597i | 0.0898959 | + | 0.0898959i | ||||
\(659\) | −13.1768 | −0.513294 | −0.256647 | − | 0.966505i | \(-0.582618\pi\) | ||||
−0.256647 | + | 0.966505i | \(0.582618\pi\) | |||||||
\(660\) | −0.413290 | + | 7.66639i | −0.0160873 | + | 0.298414i | ||||
\(661\) | 27.6493i | 1.07543i | 0.843126 | + | 0.537716i | \(0.180713\pi\) | ||||
−0.843126 | + | 0.537716i | \(0.819287\pi\) | |||||||
\(662\) | −22.5979 | − | 22.5979i | −0.878292 | − | 0.878292i | ||||
\(663\) | −3.45146 | + | 3.45146i | −0.134044 | + | 0.134044i | ||||
\(664\) | 14.1012 | 0.547231 | ||||||||
\(665\) | 1.20014 | + | 2.01630i | 0.0465393 | + | 0.0781889i | ||||
\(666\) | −7.83647 | −0.303657 | ||||||||
\(667\) | −27.7233 | + | 27.7233i | −1.07345 | + | 1.07345i | ||||
\(668\) | 11.1290 | + | 11.1290i | 0.430592 | + | 0.430592i | ||||
\(669\) | − | 22.5682i | − | 0.872539i | ||||||
\(670\) | 1.01711 | + | 1.13302i | 0.0392942 | + | 0.0437723i | ||||
\(671\) | 5.69802 | 0.219970 | ||||||||
\(672\) | 0.170229 | + | 0.170229i | 0.00656673 | + | 0.00656673i | ||||
\(673\) | 15.0414 | + | 15.0414i | 0.579804 | + | 0.579804i | 0.934849 | − | 0.355045i | \(-0.115535\pi\) |
−0.355045 | + | 0.934849i | \(0.615535\pi\) | |||||||
\(674\) | 8.86982i | 0.341653i | ||||||||
\(675\) | 3.13495 | + | 3.89514i | 0.120664 | + | 0.149924i | ||||
\(676\) | 28.2287 | 1.08572 | ||||||||
\(677\) | −32.6303 | + | 32.6303i | −1.25408 | + | 1.25408i | −0.300211 | + | 0.953873i | \(0.597057\pi\) |
−0.953873 | + | 0.300211i | \(0.902943\pi\) | |||||||
\(678\) | −6.81260 | − | 6.81260i | −0.261636 | − | 0.261636i | ||||
\(679\) | −3.69547 | −0.141819 | ||||||||
\(680\) | 1.13551 | + | 1.26492i | 0.0435448 | + | 0.0485073i | ||||
\(681\) | 8.30331 | 0.318183 | ||||||||
\(682\) | 13.0500 | + | 13.0500i | 0.499710 | + | 0.499710i | ||||
\(683\) | 19.7427 | + | 19.7427i | 0.755435 | + | 0.755435i | 0.975488 | − | 0.220053i | \(-0.0706231\pi\) |
−0.220053 | + | 0.975488i | \(0.570623\pi\) | |||||||
\(684\) | 2.42784 | + | 3.62016i | 0.0928310 | + | 0.138420i | ||||
\(685\) | 42.7924 | + | 2.30691i | 1.63501 | + | 0.0881425i | ||||
\(686\) | 3.35641i | 0.128148i | ||||||||
\(687\) | 7.27083 | − | 7.27083i | 0.277399 | − | 0.277399i | ||||
\(688\) | −2.29224 | + | 2.29224i | −0.0873908 | + | 0.0873908i | ||||
\(689\) | − | 17.5588i | − | 0.668936i | ||||||
\(690\) | −0.877989 | + | 16.2864i | −0.0334245 | + | 0.620013i | ||||
\(691\) | −1.07506 | −0.0408973 | −0.0204486 | − | 0.999791i | \(-0.506509\pi\) | ||||
−0.0204486 | + | 0.999791i | \(0.506509\pi\) | |||||||
\(692\) | −15.2012 | + | 15.2012i | −0.577863 | + | 0.577863i | ||||
\(693\) | 0.584480 | − | 0.584480i | 0.0222026 | − | 0.0222026i | ||||
\(694\) | −13.9289 | −0.528734 | ||||||||
\(695\) | −15.6864 | − | 17.4740i | −0.595017 | − | 0.662827i | ||||
\(696\) | 5.37513i | 0.203744i | ||||||||
\(697\) | −1.97931 | + | 1.97931i | −0.0749715 | + | 0.0749715i | ||||
\(698\) | −16.8234 | − | 16.8234i | −0.636776 | − | 0.636776i | ||||
\(699\) | 20.4672 | 0.774139 | ||||||||
\(700\) | 0.754709 | + | 0.937716i | 0.0285253 | + | 0.0354423i | ||||
\(701\) | 49.0251 | 1.85165 | 0.925827 | − | 0.377947i | \(-0.123370\pi\) | ||||
0.925827 | + | 0.377947i | \(0.123370\pi\) | |||||||
\(702\) | −4.54030 | + | 4.54030i | −0.171363 | + | 0.171363i | ||||
\(703\) | −33.5134 | − | 6.60689i | −1.26398 | − | 0.249184i | ||||
\(704\) | 3.43349i | 0.129405i | ||||||||
\(705\) | 20.2345 | + | 22.5404i | 0.762074 | + | 0.848922i | ||||
\(706\) | 23.2601i | 0.875407i | ||||||||
\(707\) | −1.51652 | − | 1.51652i | −0.0570346 | − | 0.0570346i | ||||
\(708\) | −2.97102 | + | 2.97102i | −0.111658 | + | 0.111658i | ||||
\(709\) | − | 1.20397i | − | 0.0452160i | −0.999744 | − | 0.0226080i | \(-0.992803\pi\) | ||
0.999744 | − | 0.0226080i | \(-0.00719696\pi\) | |||||||
\(710\) | 19.9420 | + | 1.07506i | 0.748412 | + | 0.0403464i | ||||
\(711\) | 1.15022i | 0.0431367i | ||||||||
\(712\) | −1.48561 | − | 1.48561i | −0.0556757 | − | 0.0556757i | ||||
\(713\) | 27.7233 | + | 27.7233i | 1.03825 | + | 1.03825i | ||||
\(714\) | − | 0.183007i | − | 0.00684886i | ||||||
\(715\) | −49.2255 | − | 2.65371i | −1.84093 | − | 0.0992433i | ||||
\(716\) | − | 24.9536i | − | 0.932559i | ||||||
\(717\) | −15.1645 | + | 15.1645i | −0.566329 | + | 0.566329i | ||||
\(718\) | −6.42745 | − | 6.42745i | −0.239870 | − | 0.239870i | ||||
\(719\) | − | 13.0396i | − | 0.486297i | −0.969989 | − | 0.243148i | \(-0.921820\pi\) | ||
0.969989 | − | 0.243148i | \(-0.0781802\pi\) | |||||||
\(720\) | 1.49373 | + | 1.66396i | 0.0556681 | + | 0.0620122i | ||||
\(721\) | − | 2.13251i | − | 0.0794189i | ||||||
\(722\) | 7.33075 | + | 17.5288i | 0.272822 | + | 0.652356i | ||||
\(723\) | −1.07223 | + | 1.07223i | −0.0398766 | + | 0.0398766i | ||||
\(724\) | 15.9721 | 0.593598 | ||||||||
\(725\) | −2.88930 | + | 26.7199i | −0.107306 | + | 0.992352i | ||||
\(726\) | 0.788861 | 0.0292774 | ||||||||
\(727\) | −11.3275 | − | 11.3275i | −0.420115 | − | 0.420115i | 0.465129 | − | 0.885243i | \(-0.346008\pi\) |
−0.885243 | + | 0.465129i | \(0.846008\pi\) | |||||||
\(728\) | −1.09303 | + | 1.09303i | −0.0405105 | + | 0.0405105i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 18.4816 | + | 20.5878i | 0.684035 | + | 0.761989i | ||||
\(731\) | 2.46430 | 0.0911454 | ||||||||
\(732\) | 1.17347 | − | 1.17347i | 0.0433728 | − | 0.0433728i | ||||
\(733\) | 30.7800 | − | 30.7800i | 1.13689 | − | 1.13689i | 0.147882 | − | 0.989005i | \(-0.452754\pi\) |
0.989005 | − | 0.147882i | \(-0.0472456\pi\) | |||||||
\(734\) | 25.0218 | 0.923570 | ||||||||
\(735\) | −0.835615 | + | 15.5004i | −0.0308221 | + | 0.571740i | ||||
\(736\) | 7.29408i | 0.268863i | ||||||||
\(737\) | 1.65316 | − | 1.65316i | 0.0608949 | − | 0.0608949i | ||||
\(738\) | −2.60372 | + | 2.60372i | −0.0958443 | + | 0.0958443i | ||||
\(739\) | 44.9834i | 1.65474i | 0.561656 | + | 0.827371i | \(0.310165\pi\) | ||||
−0.561656 | + | 0.827371i | \(0.689835\pi\) | |||||||
\(740\) | −17.4975 | − | 0.943277i | −0.643220 | − | 0.0346756i | ||||
\(741\) | −23.2449 | + | 15.5891i | −0.853922 | + | 0.572679i | ||||
\(742\) | 0.465509 | + | 0.465509i | 0.0170894 | + | 0.0170894i | ||||
\(743\) | 16.4071 | + | 16.4071i | 0.601917 | + | 0.601917i | 0.940821 | − | 0.338904i | \(-0.110056\pi\) |
−0.338904 | + | 0.940821i | \(0.610056\pi\) | |||||||
\(744\) | 5.37513 | 0.197062 | ||||||||
\(745\) | 1.52412 | + | 1.69782i | 0.0558396 | + | 0.0622032i | ||||
\(746\) | −6.98036 | −0.255569 | ||||||||
\(747\) | −9.97102 | − | 9.97102i | −0.364821 | − | 0.364821i | ||||
\(748\) | 1.84561 | − | 1.84561i | 0.0674821 | − | 0.0674821i | ||||
\(749\) | −1.90593 | −0.0696413 | ||||||||
\(750\) | 6.53094 | + | 9.07451i | 0.238476 | + | 0.331354i | ||||
\(751\) | 10.0580i | 0.367021i | 0.983018 | + | 0.183510i | \(0.0587461\pi\) | ||||
−0.983018 | + | 0.183510i | \(0.941254\pi\) | |||||||
\(752\) | 9.57865 | + | 9.57865i | 0.349297 | + | 0.349297i | ||||
\(753\) | 8.23952 | + | 8.23952i | 0.300265 | + | 0.300265i | ||||
\(754\) | −34.5135 | −1.25691 | ||||||||
\(755\) | −29.6348 | − | 33.0120i | −1.07852 | − | 1.20143i | ||||
\(756\) | − | 0.240740i | − | 0.00875564i | ||||||
\(757\) | −0.0674583 | − | 0.0674583i | −0.00245182 | − | 0.00245182i | 0.705880 | − | 0.708332i | \(-0.250552\pi\) |
−0.708332 | + | 0.705880i | \(0.750552\pi\) | |||||||
\(758\) | 6.68092 | − | 6.68092i | 0.242662 | − | 0.242662i | ||||
\(759\) | 25.0442 | 0.909045 | ||||||||
\(760\) | 4.98520 | + | 8.37543i | 0.180832 | + | 0.303809i | ||||
\(761\) | 15.9170 | 0.576990 | 0.288495 | − | 0.957481i | \(-0.406845\pi\) | ||||
0.288495 | + | 0.957481i | \(0.406845\pi\) | |||||||
\(762\) | 5.19935 | − | 5.19935i | 0.188353 | − | 0.188353i | ||||
\(763\) | 1.82355 | + | 1.82355i | 0.0660168 | + | 0.0660168i | ||||
\(764\) | − | 2.91580i | − | 0.105490i | ||||||
\(765\) | 0.0915034 | − | 1.69736i | 0.00330831 | − | 0.0613681i | ||||
\(766\) | 24.4936 | 0.884991 | ||||||||
\(767\) | −19.0768 | − | 19.0768i | −0.688823 | − | 0.688823i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 4.99203i | − | 0.180017i | −0.995941 | − | 0.0900087i | \(-0.971311\pi\) | ||
0.995941 | − | 0.0900087i | \(-0.0286895\pi\) | |||||||
\(770\) | 1.37540 | − | 1.23469i | 0.0495658 | − | 0.0444951i | ||||
\(771\) | −1.42333 | −0.0512600 | ||||||||
\(772\) | −6.67601 | + | 6.67601i | −0.240275 | + | 0.240275i | ||||
\(773\) | −0.387825 | − | 0.387825i | −0.0139491 | − | 0.0139491i | 0.700098 | − | 0.714047i | \(-0.253140\pi\) |
−0.714047 | + | 0.700098i | \(0.753140\pi\) | |||||||
\(774\) | 3.24172 | 0.116521 | ||||||||
\(775\) | 26.7199 | + | 2.88930i | 0.959807 | + | 0.103787i | ||||
\(776\) | −15.3505 | −0.551049 | ||||||||
\(777\) | 1.33400 | + | 1.33400i | 0.0478568 | + | 0.0478568i | ||||
\(778\) | −14.4041 | − | 14.4041i | −0.516413 | − | 0.516413i | ||||
\(779\) | −13.3302 | + | 8.93985i | −0.477605 | + | 0.320303i | ||||
\(780\) | −10.6842 | + | 9.59118i | −0.382556 | + | 0.343419i | ||||
\(781\) | − | 30.6655i | − | 1.09730i | ||||||
\(782\) | 3.92079 | − | 3.92079i | 0.140207 | − | 0.140207i | ||||
\(783\) | 3.80079 | − | 3.80079i | 0.135829 | − | 0.135829i | ||||
\(784\) | 6.94204i | 0.247930i | ||||||||
\(785\) | 41.6382 | + | 2.24469i | 1.48613 | + | 0.0801163i | ||||
\(786\) | 2.14729 | 0.0765913 | ||||||||
\(787\) | 33.2308 | − | 33.2308i | 1.18455 | − | 1.18455i | 0.205999 | − | 0.978552i | \(-0.433956\pi\) |
0.978552 | − | 0.205999i | \(-0.0660445\pi\) | |||||||
\(788\) | −4.08263 | + | 4.08263i | −0.145438 | + | 0.145438i | ||||
\(789\) | 0.560424 | 0.0199516 | ||||||||
\(790\) | −0.138452 | + | 2.56824i | −0.00492591 | + | 0.0913740i | ||||
\(791\) | 2.31940i | 0.0824685i | ||||||||
\(792\) | 2.42784 | − | 2.42784i | 0.0862697 | − | 0.0862697i | ||||
\(793\) | 7.53482 | + | 7.53482i | 0.267569 | + | 0.267569i | ||||
\(794\) | 19.6931 | 0.698883 | ||||||||
\(795\) | 4.08476 | + | 4.55027i | 0.144872 | + | 0.161382i | ||||
\(796\) | −8.23662 | −0.291939 | ||||||||
\(797\) | 12.3179 | − | 12.3179i | 0.436324 | − | 0.436324i | −0.454449 | − | 0.890773i | \(-0.650164\pi\) |
0.890773 | + | 0.454449i | \(0.150164\pi\) | |||||||
\(798\) | 0.202967 | − | 1.02955i | 0.00718495 | − | 0.0364455i | ||||
\(799\) | − | 10.2976i | − | 0.364304i | ||||||
\(800\) | 3.13495 | + | 3.89514i | 0.110837 | + | 0.137714i | ||||
\(801\) | 2.10098i | 0.0742343i | ||||||||
\(802\) | 0.288335 | + | 0.288335i | 0.0101815 | + | 0.0101815i | ||||
\(803\) | 30.0392 | − | 30.0392i | 1.06006 | − | 1.06006i | ||||
\(804\) | − | 0.680916i | − | 0.0240141i | ||||||
\(805\) | 2.92188 | − | 2.62296i | 0.102983 | − | 0.0924472i | ||||
\(806\) | 34.5135i | 1.21569i | ||||||||
\(807\) | −14.7971 | − | 14.7971i | −0.520882 | − | 0.520882i | ||||
\(808\) | −6.29940 | − | 6.29940i | −0.221612 | − | 0.221612i | ||||
\(809\) | 9.46048i | 0.332613i | 0.986074 | + | 0.166306i | \(0.0531841\pi\) | ||||
−0.986074 | + | 0.166306i | \(0.946816\pi\) | |||||||
\(810\) | 0.120370 | − | 2.23283i | 0.00422937 | − | 0.0784535i | ||||
\(811\) | − | 3.82726i | − | 0.134393i | −0.997740 | − | 0.0671967i | \(-0.978594\pi\) | ||
0.997740 | − | 0.0671967i | \(-0.0214055\pi\) | |||||||
\(812\) | 0.915004 | − | 0.915004i | 0.0321103 | − | 0.0321103i | ||||
\(813\) | −11.9625 | − | 11.9625i | −0.419543 | − | 0.419543i | ||||
\(814\) | 26.9065i | 0.943071i | ||||||||
\(815\) | −0.204140 | + | 3.78673i | −0.00715071 | + | 0.132643i | ||||
\(816\) | − | 0.760184i | − | 0.0266117i | ||||||
\(817\) | 13.8635 | + | 2.73308i | 0.485022 | + | 0.0956182i | ||||
\(818\) | 4.82394 | − | 4.82394i | 0.168665 | − | 0.168665i | ||||
\(819\) | 1.54578 | 0.0540140 | ||||||||
\(820\) | −6.12706 | + | 5.50024i | −0.213966 | + | 0.192077i | ||||
\(821\) | 2.99180 | 0.104415 | 0.0522073 | − | 0.998636i | \(-0.483374\pi\) | ||||
0.0522073 | + | 0.998636i | \(0.483374\pi\) | |||||||
\(822\) | −13.5518 | − | 13.5518i | −0.472673 | − | 0.472673i | ||||
\(823\) | −32.6466 | + | 32.6466i | −1.13799 | + | 1.13799i | −0.149179 | + | 0.988810i | \(0.547663\pi\) |
−0.988810 | + | 0.149179i | \(0.952337\pi\) | |||||||
\(824\) | − | 8.85814i | − | 0.308588i | ||||||
\(825\) | 13.3739 | − | 10.7638i | 0.465620 | − | 0.374748i | ||||
\(826\) | 1.01151 | 0.0351949 | ||||||||
\(827\) | −24.8297 | + | 24.8297i | −0.863413 | + | 0.863413i | −0.991733 | − | 0.128320i | \(-0.959042\pi\) |
0.128320 | + | 0.991733i | \(0.459042\pi\) | |||||||
\(828\) | 5.15769 | − | 5.15769i | 0.179242 | − | 0.179242i | ||||
\(829\) | 24.2255 | 0.841388 | 0.420694 | − | 0.907203i | \(-0.361787\pi\) | ||||
0.420694 | + | 0.907203i | \(0.361787\pi\) | |||||||
\(830\) | −21.0633 | − | 23.4638i | −0.731119 | − | 0.814439i | ||||
\(831\) | 22.1704i | 0.769083i | ||||||||
\(832\) | −4.54030 | + | 4.54030i | −0.157407 | + | 0.157407i | ||||
\(833\) | 3.73156 | − | 3.73156i | 0.129291 | − | 0.129291i | ||||
\(834\) | 10.5015i | 0.363636i | ||||||||
\(835\) | 1.89447 | − | 35.1418i | 0.0655609 | − | 1.21613i | ||||
\(836\) | 12.4298 | − | 8.33598i | 0.429893 | − | 0.288306i | ||||
\(837\) | −3.80079 | − | 3.80079i | −0.131375 | − | 0.131375i | ||||
\(838\) | 21.8362 | + | 21.8362i | 0.754320 | + | 0.754320i | ||||
\(839\) | 14.8623 | 0.513105 | 0.256552 | − | 0.966530i | \(-0.417413\pi\) | ||||
0.256552 | + | 0.966530i | \(0.417413\pi\) | |||||||
\(840\) | 0.0289779 | − | 0.537531i | 0.000999834 | − | 0.0185466i | ||||
\(841\) | −0.107945 | −0.00372223 | ||||||||
\(842\) | 3.98097 | + | 3.98097i | 0.137193 | + | 0.137193i | ||||
\(843\) | −7.31752 | + | 7.31752i | −0.252029 | + | 0.252029i | ||||
\(844\) | 14.6136 | 0.503020 | ||||||||
\(845\) | −42.1660 | − | 46.9714i | −1.45056 | − | 1.61586i | ||||
\(846\) | − | 13.5463i | − | 0.465730i | ||||||
\(847\) | −0.134287 | − | 0.134287i | −0.00461416 | − | 0.00461416i | ||||
\(848\) | 1.93366 | + | 1.93366i | 0.0664021 | + | 0.0664021i | ||||
\(849\) | 8.53238 | 0.292831 | ||||||||
\(850\) | 0.408622 | − | 3.77889i | 0.0140156 | − | 0.129615i | ||||
\(851\) | 57.1599i | 1.95941i | ||||||||
\(852\) | −6.31539 | − | 6.31539i | −0.216362 | − | 0.216362i | ||||
\(853\) | 2.50921 | − | 2.50921i | 0.0859138 | − | 0.0859138i | −0.662844 | − | 0.748758i | \(-0.730651\pi\) |
0.748758 | + | 0.662844i | \(0.230651\pi\) | |||||||
\(854\) | −0.399518 | −0.0136712 | ||||||||
\(855\) | 2.39726 | − | 9.44739i | 0.0819845 | − | 0.323094i | ||||
\(856\) | −7.91697 | −0.270597 | ||||||||
\(857\) | −3.30288 | + | 3.30288i | −0.112824 | + | 0.112824i | −0.761265 | − | 0.648441i | \(-0.775421\pi\) |
0.648441 | + | 0.761265i | \(0.275421\pi\) | |||||||
\(858\) | 15.5891 | + | 15.5891i | 0.532202 | + | 0.532202i | ||||
\(859\) | − | 9.52716i | − | 0.325063i | −0.986703 | − | 0.162531i | \(-0.948034\pi\) | ||
0.986703 | − | 0.162531i | \(-0.0519659\pi\) | |||||||
\(860\) | 7.23819 | + | 0.390206i | 0.246820 | + | 0.0133059i | ||||
\(861\) | 0.886458 | 0.0302104 | ||||||||
\(862\) | 5.68035 | + | 5.68035i | 0.193473 | + | 0.193473i | ||||
\(863\) | 14.4388 | + | 14.4388i | 0.491503 | + | 0.491503i | 0.908779 | − | 0.417277i | \(-0.137015\pi\) |
−0.417277 | + | 0.908779i | \(0.637015\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 48.0007 | + | 2.58769i | 1.63207 | + | 0.0879840i | ||||
\(866\) | −38.9818 | −1.32466 | ||||||||
\(867\) | 11.6122 | − | 11.6122i | 0.394371 | − | 0.394371i | ||||
\(868\) | −0.915004 | − | 0.915004i | −0.0310573 | − | 0.0310573i | ||||
\(869\) | 3.94928 | 0.133970 | ||||||||
\(870\) | 8.94401 | − | 8.02901i | 0.303230 | − | 0.272209i | ||||
\(871\) | 4.37213 | 0.148144 | ||||||||
\(872\) | 7.57474 | + | 7.57474i | 0.256513 | + | 0.256513i | ||||
\(873\) | 10.8544 | + | 10.8544i | 0.367366 | + | 0.367366i | ||||
\(874\) | 26.4057 | − | 17.7089i | 0.893188 | − | 0.599012i | ||||
\(875\) | 0.432989 | − | 2.65650i | 0.0146377 | − | 0.0898062i | ||||
\(876\) | − | 12.3728i | − | 0.418037i | ||||||
\(877\) | −27.0374 | + | 27.0374i | −0.912987 | + | 0.912987i | −0.996506 | − | 0.0835187i | \(-0.973384\pi\) |
0.0835187 | + | 0.996506i | \(0.473384\pi\) | |||||||
\(878\) | −1.93011 | + | 1.93011i | −0.0651381 | + | 0.0651381i | ||||
\(879\) | 9.39045i | 0.316732i | ||||||||
\(880\) | 5.71319 | − | 5.12871i | 0.192592 | − | 0.172889i | ||||
\(881\) | −15.9706 | −0.538063 | −0.269031 | − | 0.963131i | \(-0.586704\pi\) | ||||
−0.269031 | + | 0.963131i | \(0.586704\pi\) | |||||||
\(882\) | 4.90877 | − | 4.90877i | 0.165287 | − | 0.165287i | ||||
\(883\) | −8.39528 | + | 8.39528i | −0.282524 | + | 0.282524i | −0.834115 | − | 0.551591i | \(-0.814021\pi\) |
0.551591 | + | 0.834115i | \(0.314021\pi\) | |||||||
\(884\) | 4.88110 | 0.164169 | ||||||||
\(885\) | 9.38157 | + | 0.505754i | 0.315358 | + | 0.0170007i | ||||
\(886\) | 30.7520i | 1.03313i | ||||||||
\(887\) | 18.4894 | − | 18.4894i | 0.620814 | − | 0.620814i | −0.324925 | − | 0.945740i | \(-0.605339\pi\) |
0.945740 | + | 0.324925i | \(0.105339\pi\) | |||||||
\(888\) | 5.54122 | + | 5.54122i | 0.185951 | + | 0.185951i | ||||
\(889\) | −1.77016 | −0.0593693 | ||||||||
\(890\) | −0.252895 | + | 4.69111i | −0.00847705 | + | 0.157246i | ||||
\(891\) | −3.43349 | −0.115026 | ||||||||
\(892\) | −15.9582 | + | 15.9582i | −0.534319 | + | 0.534319i | ||||
\(893\) | 11.4208 | − | 57.9317i | 0.382182 | − | 1.93861i | ||||
\(894\) | − | 1.02035i | − | 0.0341255i | ||||||
\(895\) | −41.5218 | + | 37.2739i | −1.38792 | + | 1.24593i | ||||
\(896\) | − | 0.240740i | − | 0.00804257i | ||||||
\(897\) | 33.1173 | + | 33.1173i | 1.10575 | + | 1.10575i | ||||
\(898\) | 4.48150 | − | 4.48150i | 0.149550 | − | 0.149550i | ||||
\(899\) | − | 28.8921i | − | 0.963604i | ||||||
\(900\) | 0.537531 | − | 4.97102i | 0.0179177 | − | 0.165701i | ||||
\(901\) | − | 2.07880i | − | 0.0692549i | ||||||
\(902\) | 8.93985 | + | 8.93985i | 0.297664 | + | 0.297664i | ||||
\(903\) | −0.551834 | − | 0.551834i | −0.0183639 | − | 0.0183639i | ||||
\(904\) | 9.63447i | 0.320438i | ||||||||
\(905\) | −23.8580 | − | 26.5769i | −0.793068 | − | 0.883447i | ||||
\(906\) | 19.8394i | 0.659120i | ||||||||
\(907\) | −15.6355 | + | 15.6355i | −0.519169 | + | 0.519169i | −0.917320 | − | 0.398151i | \(-0.869652\pi\) |
0.398151 | + | 0.917320i | \(0.369652\pi\) | |||||||
\(908\) | −5.87132 | − | 5.87132i | −0.194847 | − | 0.194847i | ||||
\(909\) | 8.90870i | 0.295483i | ||||||||
\(910\) | 3.45146 | + | 0.186066i | 0.114415 | + | 0.00616803i | ||||
\(911\) | − | 21.2778i | − | 0.704964i | −0.935819 | − | 0.352482i | \(-0.885338\pi\) | ||
0.935819 | − | 0.352482i | \(-0.114662\pi\) | |||||||
\(912\) | 0.843095 | − | 4.27659i | 0.0279177 | − | 0.141612i | ||||
\(913\) | −34.2354 | + | 34.2354i | −1.13303 | + | 1.13303i | ||||
\(914\) | −19.9811 | −0.660915 | ||||||||
\(915\) | −3.70547 | − | 0.199759i | −0.122499 | − | 0.00660384i | ||||
\(916\) | −10.2825 | −0.339743 | ||||||||
\(917\) | −0.365531 | − | 0.365531i | −0.0120709 | − | 0.0120709i | ||||
\(918\) | −0.537531 | + | 0.537531i | −0.0177412 | + | 0.0177412i | ||||
\(919\) | − | 19.7132i | − | 0.650277i | −0.945666 | − | 0.325139i | \(-0.894589\pi\) | ||
0.945666 | − | 0.325139i | \(-0.105411\pi\) | |||||||
\(920\) | 12.1371 | − | 10.8954i | 0.400147 | − | 0.359211i | ||||
\(921\) | 8.78829 | 0.289584 | ||||||||
\(922\) | −7.33277 | + | 7.33277i | −0.241492 | + | 0.241492i | ||||
\(923\) | 40.5508 | − | 40.5508i | 1.33475 | − | 1.33475i | ||||
\(924\) | −0.826579 | −0.0271925 | ||||||||
\(925\) | 24.5670 | + | 30.5241i | 0.807757 | + | 1.00363i | ||||
\(926\) | 30.5422i | 1.00368i | ||||||||
\(927\) | −6.26365 | + | 6.26365i | −0.205725 | + | 0.205725i | ||||
\(928\) | 3.80079 | − | 3.80079i | 0.124767 | − | 0.124767i | ||||
\(929\) | 44.9199i | 1.47377i | 0.676016 | + | 0.736887i | \(0.263705\pi\) | ||||
−0.676016 | + | 0.736887i | \(0.736295\pi\) | |||||||
\(930\) | −8.02901 | − | 8.94401i | −0.263282 | − | 0.293286i | ||||
\(931\) | 25.1313 | − | 16.8542i | 0.823646 | − | 0.552374i | ||||
\(932\) | −14.4725 | − | 14.4725i | −0.474062 | − | 0.474062i | ||||
\(933\) | −3.21753 | − | 3.21753i | −0.105337 | − | 0.105337i | ||||
\(934\) | 8.03432 | 0.262891 | ||||||||
\(935\) | −5.82786 | − | 0.314176i | −0.190591 | − | 0.0102747i | ||||
\(936\) | 6.42095 | 0.209875 | ||||||||
\(937\) | 11.9641 | + | 11.9641i | 0.390851 | + | 0.390851i | 0.874991 | − | 0.484140i | \(-0.160867\pi\) |
−0.484140 | + | 0.874991i | \(0.660867\pi\) | |||||||
\(938\) | −0.115912 | + | 0.115912i | −0.00378465 | + | 0.00378465i | ||||
\(939\) | 28.3449 | 0.925002 | ||||||||
\(940\) | 1.63056 | − | 30.2464i | 0.0531831 | − | 0.986530i | ||||
\(941\) | − | 37.3163i | − | 1.21648i | −0.793755 | − | 0.608238i | \(-0.791877\pi\) | ||
0.793755 | − | 0.608238i | \(-0.208123\pi\) | |||||||
\(942\) | −13.1863 | − | 13.1863i | −0.429632 | − | 0.429632i | ||||
\(943\) | 18.9917 | + | 18.9917i | 0.618456 | + | 0.618456i | ||||
\(944\) | 4.20166 | 0.136752 | ||||||||
\(945\) | −0.400582 | + | 0.359601i | −0.0130309 | + | 0.0116978i | ||||
\(946\) | − | 11.1304i | − | 0.361881i | ||||||
\(947\) | 21.4508 | + | 21.4508i | 0.697057 | + | 0.697057i | 0.963775 | − | 0.266717i | \(-0.0859390\pi\) |
−0.266717 | + | 0.963775i | \(0.585939\pi\) | |||||||
\(948\) | 0.813330 | − | 0.813330i | 0.0264157 | − | 0.0264157i | ||||
\(949\) | 79.4451 | 2.57890 | ||||||||
\(950\) | 6.48984 | − | 20.8058i | 0.210558 | − | 0.675030i | ||||
\(951\) | 30.3037 | 0.982665 | ||||||||
\(952\) | −0.129405 | + | 0.129405i | −0.00419405 | + | 0.00419405i | ||||
\(953\) | −24.4941 | − | 24.4941i | −0.793442 | − | 0.793442i | 0.188610 | − | 0.982052i | \(-0.439602\pi\) |
−0.982052 | + | 0.188610i | \(0.939602\pi\) | |||||||
\(954\) | − | 2.73460i | − | 0.0885361i | ||||||
\(955\) | −4.85178 | + | 4.35543i | −0.157000 | + | 0.140938i | ||||
\(956\) | 21.4459 | 0.693609 | ||||||||
\(957\) | −13.0500 | − | 13.0500i | −0.421846 | − | 0.421846i | ||||
\(958\) | 12.9613 | + | 12.9613i | 0.418762 | + | 0.418762i | ||||
\(959\) | 4.61382i | 0.148988i | ||||||||
\(960\) | 0.120370 | − | 2.23283i | 0.00388493 | − | 0.0720641i | ||||
\(961\) | 2.10794 | 0.0679982 | ||||||||
\(962\) | −35.5799 | + | 35.5799i | −1.14714 | + | 1.14714i | ||||
\(963\) | 5.59814 | + | 5.59814i | 0.180398 | + | 0.180398i | ||||
\(964\) | 1.51636 | 0.0488387 | ||||||||
\(965\) | 21.0808 | + | 1.13645i | 0.678614 | + | 0.0365836i | ||||
\(966\) | −1.75598 | −0.0564977 | ||||||||
\(967\) | 34.3368 | + | 34.3368i | 1.10420 | + | 1.10420i | 0.993898 | + | 0.110299i | \(0.0351809\pi\) |
0.110299 | + | 0.993898i | \(0.464819\pi\) | |||||||
\(968\) | −0.557809 | − | 0.557809i | −0.0179287 | − | 0.0179287i | ||||
\(969\) | −2.75199 | + | 1.84561i | −0.0884066 | + | 0.0592895i | ||||
\(970\) | 22.9295 | + | 25.5426i | 0.736221 | + | 0.820122i | ||||
\(971\) | − | 23.0276i | − | 0.738992i | −0.929232 | − | 0.369496i | \(-0.879530\pi\) | ||
0.929232 | − | 0.369496i | \(-0.120470\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 1.78765 | − | 1.78765i | 0.0573095 | − | 0.0573095i | ||||
\(974\) | 11.6178i | 0.372259i | ||||||||
\(975\) | 31.9187 | + | 3.45146i | 1.02222 | + | 0.110535i | ||||
\(976\) | −1.65954 | −0.0531206 | ||||||||
\(977\) | −32.7527 | + | 32.7527i | −1.04785 | + | 1.04785i | −0.0490563 | + | 0.998796i | \(0.515621\pi\) |
−0.998796 | + | 0.0490563i | \(0.984379\pi\) | |||||||
\(978\) | 1.19921 | − | 1.19921i | 0.0383464 | − | 0.0383464i | ||||
\(979\) | 7.21368 | 0.230550 | ||||||||
\(980\) | 11.5513 | − | 10.3696i | 0.368992 | − | 0.331243i | ||||
\(981\) | − | 10.7123i | − | 0.342018i | ||||||
\(982\) | 4.13849 | − | 4.13849i | 0.132065 | − | 0.132065i | ||||
\(983\) | −4.11107 | − | 4.11107i | −0.131123 | − | 0.131123i | 0.638499 | − | 0.769622i | \(-0.279555\pi\) |
−0.769622 | + | 0.638499i | \(0.779555\pi\) | |||||||
\(984\) | 3.68222 | 0.117385 | ||||||||
\(985\) | 12.8917 | + | 0.694982i | 0.410763 | + | 0.0221440i | ||||
\(986\) | −4.08609 | −0.130128 | ||||||||
\(987\) | −2.30597 | + | 2.30597i | −0.0733997 | + | 0.0733997i | ||||
\(988\) | 27.4598 | + | 5.41348i | 0.873612 | + | 0.172226i | ||||
\(989\) | − | 23.6453i | − | 0.751878i | ||||||
\(990\) | −7.66639 | − | 0.413290i | −0.243654 | − | 0.0131352i | ||||
\(991\) | − | 39.6215i | − | 1.25862i | −0.777155 | − | 0.629309i | \(-0.783338\pi\) | ||
0.777155 | − | 0.629309i | \(-0.216662\pi\) | |||||||
\(992\) | −3.80079 | − | 3.80079i | −0.120675 | − | 0.120675i | ||||
\(993\) | 22.5979 | − | 22.5979i | 0.717122 | − | 0.717122i | ||||
\(994\) | 2.15012i | 0.0681978i | ||||||||
\(995\) | 12.3033 | + | 13.7054i | 0.390041 | + | 0.434491i | ||||
\(996\) | 14.1012i | 0.446812i | ||||||||
\(997\) | 23.8300 | + | 23.8300i | 0.754705 | + | 0.754705i | 0.975353 | − | 0.220649i | \(-0.0708174\pi\) |
−0.220649 | + | 0.975353i | \(0.570817\pi\) | |||||||
\(998\) | −17.2572 | − | 17.2572i | −0.546268 | − | 0.546268i | ||||
\(999\) | − | 7.83647i | − | 0.247935i |
(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 | 570.2.m.a.37.7 | yes | 20 | |
3.2 | odd | 2 | 1710.2.p.d.37.4 | 20 | |||
5.3 | odd | 4 | inner | 570.2.m.a.493.2 | yes | 20 | |
15.8 | even | 4 | 1710.2.p.d.1063.9 | 20 | |||
19.18 | odd | 2 | inner | 570.2.m.a.37.2 | ✓ | 20 | |
57.56 | even | 2 | 1710.2.p.d.37.9 | 20 | |||
95.18 | even | 4 | inner | 570.2.m.a.493.7 | yes | 20 | |
285.113 | odd | 4 | 1710.2.p.d.1063.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.m.a.37.2 | ✓ | 20 | 19.18 | odd | 2 | inner | |
570.2.m.a.37.7 | yes | 20 | 1.1 | even | 1 | trivial | |
570.2.m.a.493.2 | yes | 20 | 5.3 | odd | 4 | inner | |
570.2.m.a.493.7 | yes | 20 | 95.18 | even | 4 | inner | |
1710.2.p.d.37.4 | 20 | 3.2 | odd | 2 | |||
1710.2.p.d.37.9 | 20 | 57.56 | even | 2 | |||
1710.2.p.d.1063.4 | 20 | 285.113 | odd | 4 | |||
1710.2.p.d.1063.9 | 20 | 15.8 | even | 4 |