Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(265,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.265");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.o (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.836829184.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 265.3 | ||
Root | \(2.63640i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.265 |
Dual form | 546.2.o.b.307.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.15711 | − | 1.15711i | −0.517477 | − | 0.517477i | 0.399330 | − | 0.916807i | \(-0.369243\pi\) |
−0.916807 | + | 0.399330i | \(0.869243\pi\) | |||||||
\(6\) | −0.707107 | − | 0.707107i | −0.288675 | − | 0.288675i | ||||
\(7\) | 2.02133 | − | 1.70711i | 0.763992 | − | 0.645226i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.63640 | −0.517477 | ||||||||
\(11\) | 1.37930 | + | 1.37930i | 0.415876 | + | 0.415876i | 0.883780 | − | 0.467904i | \(-0.154991\pi\) |
−0.467904 | + | 0.883780i | \(0.654991\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.50062 | − | 3.27843i | −0.416198 | − | 0.909274i | ||||
\(14\) | 0.222191 | − | 2.63640i | 0.0593831 | − | 0.704609i | ||||
\(15\) | −1.15711 | + | 1.15711i | −0.298765 | + | 0.298765i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.50625 | −0.365319 | −0.182659 | − | 0.983176i | \(-0.558471\pi\) | ||||
−0.182659 | + | 0.983176i | \(0.558471\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | −0.934922 | − | 0.934922i | −0.214486 | − | 0.214486i | 0.591684 | − | 0.806170i | \(-0.298463\pi\) |
−0.806170 | + | 0.591684i | \(0.798463\pi\) | |||||||
\(20\) | −1.15711 | + | 1.15711i | −0.258738 | + | 0.258738i | ||||
\(21\) | −1.70711 | − | 2.02133i | −0.372521 | − | 0.441091i | ||||
\(22\) | 1.95063 | 0.415876 | ||||||||
\(23\) | 4.19327i | 0.874358i | 0.899375 | + | 0.437179i | \(0.144022\pi\) | ||||
−0.899375 | + | 0.437179i | \(0.855978\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | − | 2.32218i | − | 0.464436i | ||||||
\(26\) | −3.37930 | − | 1.25710i | −0.662736 | − | 0.246538i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.70711 | − | 2.02133i | −0.322613 | − | 0.381996i | ||||
\(29\) | −0.406261 | −0.0754407 | −0.0377204 | − | 0.999288i | \(-0.512010\pi\) | ||||
−0.0377204 | + | 0.999288i | \(0.512010\pi\) | |||||||
\(30\) | 1.63640i | 0.298765i | ||||||||
\(31\) | −2.31423 | − | 2.31423i | −0.415647 | − | 0.415647i | 0.468053 | − | 0.883700i | \(-0.344956\pi\) |
−0.883700 | + | 0.468053i | \(0.844956\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 1.37930 | − | 1.37930i | 0.240106 | − | 0.240106i | ||||
\(34\) | −1.06508 | + | 1.06508i | −0.182659 | + | 0.182659i | ||||
\(35\) | −4.31423 | − | 0.363595i | −0.729237 | − | 0.0614588i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | 0.257101 | + | 0.257101i | 0.0422671 | + | 0.0422671i | 0.727924 | − | 0.685657i | \(-0.240485\pi\) |
−0.685657 | + | 0.727924i | \(0.740485\pi\) | |||||||
\(38\) | −1.32218 | −0.214486 | ||||||||
\(39\) | −3.27843 | + | 1.50062i | −0.524969 | + | 0.240292i | ||||
\(40\) | 1.63640i | 0.258738i | ||||||||
\(41\) | 3.60624 | + | 3.60624i | 0.563199 | + | 0.563199i | 0.930215 | − | 0.367015i | \(-0.119620\pi\) |
−0.367015 | + | 0.930215i | \(0.619620\pi\) | |||||||
\(42\) | −2.63640 | − | 0.222191i | −0.406806 | − | 0.0342849i | ||||
\(43\) | − | 2.46483i | − | 0.375883i | −0.982180 | − | 0.187942i | \(-0.939818\pi\) | ||
0.982180 | − | 0.187942i | \(-0.0601816\pi\) | |||||||
\(44\) | 1.37930 | − | 1.37930i | 0.207938 | − | 0.207938i | ||||
\(45\) | 1.15711 | + | 1.15711i | 0.172492 | + | 0.172492i | ||||
\(46\) | 2.96509 | + | 2.96509i | 0.437179 | + | 0.437179i | ||||
\(47\) | −1.41421 | + | 1.41421i | −0.206284 | + | 0.206284i | −0.802686 | − | 0.596402i | \(-0.796597\pi\) |
0.596402 | + | 0.802686i | \(0.296597\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 1.17157 | − | 6.90126i | 0.167368 | − | 0.985895i | ||||
\(50\) | −1.64203 | − | 1.64203i | −0.232218 | − | 0.232218i | ||||
\(51\) | 1.50625i | 0.210917i | ||||||||
\(52\) | −3.27843 | + | 1.50062i | −0.454637 | + | 0.208099i | ||||
\(53\) | 13.4456 | 1.84690 | 0.923450 | − | 0.383719i | \(-0.125357\pi\) | ||||
0.923450 | + | 0.383719i | \(0.125357\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | − | 3.19202i | − | 0.430412i | ||||||
\(56\) | −2.63640 | − | 0.222191i | −0.352304 | − | 0.0296916i | ||||
\(57\) | −0.934922 | + | 0.934922i | −0.123833 | + | 0.123833i | ||||
\(58\) | −0.287270 | + | 0.287270i | −0.0377204 | + | 0.0377204i | ||||
\(59\) | 8.75986 | − | 8.75986i | 1.14044 | − | 1.14044i | 0.152066 | − | 0.988370i | \(-0.451407\pi\) |
0.988370 | − | 0.152066i | \(-0.0485927\pi\) | |||||||
\(60\) | 1.15711 | + | 1.15711i | 0.149383 | + | 0.149383i | ||||
\(61\) | 11.7394i | 1.50308i | 0.659689 | + | 0.751539i | \(0.270688\pi\) | ||||
−0.659689 | + | 0.751539i | \(0.729312\pi\) | |||||||
\(62\) | −3.27281 | −0.415647 | ||||||||
\(63\) | −2.02133 | + | 1.70711i | −0.254664 | + | 0.215075i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −2.05713 | + | 5.52991i | −0.255155 | + | 0.685901i | ||||
\(66\) | − | 1.95063i | − | 0.240106i | ||||||
\(67\) | 11.1012 | − | 11.1012i | 1.35623 | − | 1.35623i | 0.477720 | − | 0.878512i | \(-0.341464\pi\) |
0.878512 | − | 0.477720i | \(-0.158536\pi\) | |||||||
\(68\) | 1.50625i | 0.182659i | ||||||||
\(69\) | 4.19327 | 0.504811 | ||||||||
\(70\) | −3.30772 | + | 2.79352i | −0.395348 | + | 0.333889i | ||||
\(71\) | −5.18078 | + | 5.18078i | −0.614845 | + | 0.614845i | −0.944205 | − | 0.329360i | \(-0.893167\pi\) |
0.329360 | + | 0.944205i | \(0.393167\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −2.56008 | + | 2.56008i | −0.299635 | + | 0.299635i | −0.840871 | − | 0.541236i | \(-0.817957\pi\) |
0.541236 | + | 0.840871i | \(0.317957\pi\) | |||||||
\(74\) | 0.363595 | 0.0422671 | ||||||||
\(75\) | −2.32218 | −0.268142 | ||||||||
\(76\) | −0.934922 | + | 0.934922i | −0.107243 | + | 0.107243i | ||||
\(77\) | 5.14265 | + | 0.433413i | 0.586060 | + | 0.0493920i | ||||
\(78\) | −1.25710 | + | 3.37930i | −0.142339 | + | 0.382631i | ||||
\(79\) | 1.42546 | 0.160377 | 0.0801884 | − | 0.996780i | \(-0.474448\pi\) | ||||
0.0801884 | + | 0.996780i | \(0.474448\pi\) | |||||||
\(80\) | 1.15711 | + | 1.15711i | 0.129369 | + | 0.129369i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.09999 | 0.563199 | ||||||||
\(83\) | 4.90797 | + | 4.90797i | 0.538719 | + | 0.538719i | 0.923153 | − | 0.384434i | \(-0.125603\pi\) |
−0.384434 | + | 0.923153i | \(0.625603\pi\) | |||||||
\(84\) | −2.02133 | + | 1.70711i | −0.220545 | + | 0.186261i | ||||
\(85\) | 1.74290 | + | 1.74290i | 0.189044 | + | 0.189044i | ||||
\(86\) | −1.74290 | − | 1.74290i | −0.187942 | − | 0.187942i | ||||
\(87\) | 0.406261i | 0.0435557i | ||||||||
\(88\) | − | 1.95063i | − | 0.207938i | ||||||
\(89\) | 2.03017 | − | 2.03017i | 0.215198 | − | 0.215198i | −0.591274 | − | 0.806471i | \(-0.701375\pi\) |
0.806471 | + | 0.591274i | \(0.201375\pi\) | |||||||
\(90\) | 1.63640 | 0.172492 | ||||||||
\(91\) | −8.62990 | − | 4.06508i | −0.904659 | − | 0.426136i | ||||
\(92\) | 4.19327 | 0.437179 | ||||||||
\(93\) | −2.31423 | + | 2.31423i | −0.239974 | + | 0.239974i | ||||
\(94\) | 2.00000i | 0.206284i | ||||||||
\(95\) | 2.16362i | 0.221983i | ||||||||
\(96\) | 0.707107 | + | 0.707107i | 0.0721688 | + | 0.0721688i | ||||
\(97\) | 10.2741 | + | 10.2741i | 1.04317 | + | 1.04317i | 0.999025 | + | 0.0441477i | \(0.0140572\pi\) |
0.0441477 | + | 0.999025i | \(0.485943\pi\) | |||||||
\(98\) | −4.05150 | − | 5.70836i | −0.409264 | − | 0.576631i | ||||
\(99\) | −1.37930 | − | 1.37930i | −0.138625 | − | 0.138625i | ||||
\(100\) | −2.32218 | −0.232218 | ||||||||
\(101\) | −1.93018 | −0.192060 | −0.0960301 | − | 0.995378i | \(-0.530615\pi\) | ||||
−0.0960301 | + | 0.995378i | \(0.530615\pi\) | |||||||
\(102\) | 1.06508 | + | 1.06508i | 0.105458 | + | 0.105458i | ||||
\(103\) | 7.94886 | 0.783225 | 0.391612 | − | 0.920130i | \(-0.371917\pi\) | ||||
0.391612 | + | 0.920130i | \(0.371917\pi\) | |||||||
\(104\) | −1.25710 | + | 3.37930i | −0.123269 | + | 0.331368i | ||||
\(105\) | −0.363595 | + | 4.31423i | −0.0354832 | + | 0.421025i | ||||
\(106\) | 9.50750 | − | 9.50750i | 0.923450 | − | 0.923450i | ||||
\(107\) | −3.33315 | −0.322228 | −0.161114 | − | 0.986936i | \(-0.551509\pi\) | ||||
−0.161114 | + | 0.986936i | \(0.551509\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 9.58382 | − | 9.58382i | 0.917964 | − | 0.917964i | −0.0789174 | − | 0.996881i | \(-0.525146\pi\) |
0.996881 | + | 0.0789174i | \(0.0251463\pi\) | |||||||
\(110\) | −2.25710 | − | 2.25710i | −0.215206 | − | 0.215206i | ||||
\(111\) | 0.257101 | − | 0.257101i | 0.0244029 | − | 0.0244029i | ||||
\(112\) | −2.02133 | + | 1.70711i | −0.190998 | + | 0.161306i | ||||
\(113\) | −10.3865 | −0.977084 | −0.488542 | − | 0.872540i | \(-0.662471\pi\) | ||||
−0.488542 | + | 0.872540i | \(0.662471\pi\) | |||||||
\(114\) | 1.32218i | 0.123833i | ||||||||
\(115\) | 4.85209 | − | 4.85209i | 0.452460 | − | 0.452460i | ||||
\(116\) | 0.406261i | 0.0377204i | ||||||||
\(117\) | 1.50062 | + | 3.27843i | 0.138733 | + | 0.303091i | ||||
\(118\) | − | 12.3883i | − | 1.14044i | ||||||
\(119\) | −3.04463 | + | 2.57133i | −0.279101 | + | 0.235713i | ||||
\(120\) | 1.63640 | 0.149383 | ||||||||
\(121\) | − | 7.19504i | − | 0.654094i | ||||||
\(122\) | 8.30102 | + | 8.30102i | 0.751539 | + | 0.751539i | ||||
\(123\) | 3.60624 | − | 3.60624i | 0.325163 | − | 0.325163i | ||||
\(124\) | −2.31423 | + | 2.31423i | −0.207824 | + | 0.207824i | ||||
\(125\) | −8.47259 | + | 8.47259i | −0.757811 | + | 0.757811i | ||||
\(126\) | −0.222191 | + | 2.63640i | −0.0197944 | + | 0.234870i | ||||
\(127\) | − | 9.12016i | − | 0.809283i | −0.914475 | − | 0.404642i | \(-0.867396\pi\) | ||
0.914475 | − | 0.404642i | \(-0.132604\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −2.46483 | −0.217016 | ||||||||
\(130\) | 2.45563 | + | 5.36484i | 0.215373 | + | 0.470528i | ||||
\(131\) | − | 3.98205i | − | 0.347913i | −0.984753 | − | 0.173957i | \(-0.944345\pi\) | ||
0.984753 | − | 0.173957i | \(-0.0556553\pi\) | |||||||
\(132\) | −1.37930 | − | 1.37930i | −0.120053 | − | 0.120053i | ||||
\(133\) | −3.48580 | − | 0.293777i | −0.302257 | − | 0.0254737i | ||||
\(134\) | − | 15.6995i | − | 1.35623i | ||||||
\(135\) | 1.15711 | − | 1.15711i | 0.0995884 | − | 0.0995884i | ||||
\(136\) | 1.06508 | + | 1.06508i | 0.0913297 | + | 0.0913297i | ||||
\(137\) | 13.8868 | + | 13.8868i | 1.18643 | + | 1.18643i | 0.978047 | + | 0.208382i | \(0.0668197\pi\) |
0.208382 | + | 0.978047i | \(0.433180\pi\) | |||||||
\(138\) | 2.96509 | − | 2.96509i | 0.252405 | − | 0.252405i | ||||
\(139\) | − | 7.37155i | − | 0.625247i | −0.949877 | − | 0.312623i | \(-0.898792\pi\) | ||
0.949877 | − | 0.312623i | \(-0.101208\pi\) | |||||||
\(140\) | −0.363595 | + | 4.31423i | −0.0307294 | + | 0.364619i | ||||
\(141\) | 1.41421 | + | 1.41421i | 0.119098 | + | 0.119098i | ||||
\(142\) | 7.32672i | 0.614845i | ||||||||
\(143\) | 2.45214 | − | 6.59178i | 0.205058 | − | 0.551232i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.470090 | + | 0.470090i | 0.0390388 | + | 0.0390388i | ||||
\(146\) | 3.62050i | 0.299635i | ||||||||
\(147\) | −6.90126 | − | 1.17157i | −0.569206 | − | 0.0966297i | ||||
\(148\) | 0.257101 | − | 0.257101i | 0.0211335 | − | 0.0211335i | ||||
\(149\) | −11.7376 | + | 11.7376i | −0.961585 | + | 0.961585i | −0.999289 | − | 0.0377039i | \(-0.987996\pi\) |
0.0377039 | + | 0.999289i | \(0.487996\pi\) | |||||||
\(150\) | −1.64203 | + | 1.64203i | −0.134071 | + | 0.134071i | ||||
\(151\) | 2.79529 | + | 2.79529i | 0.227477 | + | 0.227477i | 0.811638 | − | 0.584161i | \(-0.198576\pi\) |
−0.584161 | + | 0.811638i | \(0.698576\pi\) | |||||||
\(152\) | 1.32218i | 0.107243i | ||||||||
\(153\) | 1.50625 | 0.121773 | ||||||||
\(154\) | 3.94287 | − | 3.32994i | 0.317726 | − | 0.268334i | ||||
\(155\) | 5.35564i | 0.430176i | ||||||||
\(156\) | 1.50062 | + | 3.27843i | 0.120146 | + | 0.262485i | ||||
\(157\) | 10.4472i | 0.833774i | 0.908958 | + | 0.416887i | \(0.136879\pi\) | ||||
−0.908958 | + | 0.416887i | \(0.863121\pi\) | |||||||
\(158\) | 1.00795 | − | 1.00795i | 0.0801884 | − | 0.0801884i | ||||
\(159\) | − | 13.4456i | − | 1.06631i | ||||||
\(160\) | 1.63640 | 0.129369 | ||||||||
\(161\) | 7.15836 | + | 8.47600i | 0.564158 | + | 0.668002i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 9.07232 | + | 9.07232i | 0.710599 | + | 0.710599i | 0.966660 | − | 0.256062i | \(-0.0824250\pi\) |
−0.256062 | + | 0.966660i | \(0.582425\pi\) | |||||||
\(164\) | 3.60624 | − | 3.60624i | 0.281600 | − | 0.281600i | ||||
\(165\) | −3.19202 | −0.248499 | ||||||||
\(166\) | 6.94091 | 0.538719 | ||||||||
\(167\) | −9.04741 | + | 9.04741i | −0.700109 | + | 0.700109i | −0.964434 | − | 0.264325i | \(-0.914851\pi\) |
0.264325 | + | 0.964434i | \(0.414851\pi\) | |||||||
\(168\) | −0.222191 | + | 2.63640i | −0.0171424 | + | 0.203403i | ||||
\(169\) | −8.49625 | + | 9.83940i | −0.653558 | + | 0.756877i | ||||
\(170\) | 2.46483 | 0.189044 | ||||||||
\(171\) | 0.934922 | + | 0.934922i | 0.0714952 | + | 0.0714952i | ||||
\(172\) | −2.46483 | −0.187942 | ||||||||
\(173\) | −0.0159057 | −0.00120928 | −0.000604642 | − | 1.00000i | \(-0.500192\pi\) | ||||
−0.000604642 | 1.00000i | \(0.500192\pi\) | ||||||||
\(174\) | 0.287270 | + | 0.287270i | 0.0217779 | + | 0.0217779i | ||||
\(175\) | −3.96421 | − | 4.69390i | −0.299666 | − | 0.354825i | ||||
\(176\) | −1.37930 | − | 1.37930i | −0.103969 | − | 0.103969i | ||||
\(177\) | −8.75986 | − | 8.75986i | −0.658431 | − | 0.658431i | ||||
\(178\) | − | 2.87109i | − | 0.215198i | ||||||
\(179\) | − | 10.3710i | − | 0.775167i | −0.921835 | − | 0.387584i | \(-0.873310\pi\) | ||
0.921835 | − | 0.387584i | \(-0.126690\pi\) | |||||||
\(180\) | 1.15711 | − | 1.15711i | 0.0862461 | − | 0.0862461i | ||||
\(181\) | 1.42973 | 0.106271 | 0.0531354 | − | 0.998587i | \(-0.483079\pi\) | ||||
0.0531354 | + | 0.998587i | \(0.483079\pi\) | |||||||
\(182\) | −8.97670 | + | 3.22781i | −0.665398 | + | 0.239262i | ||||
\(183\) | 11.7394 | 0.867802 | ||||||||
\(184\) | 2.96509 | − | 2.96509i | 0.218589 | − | 0.218589i | ||||
\(185\) | − | 0.594989i | − | 0.0437444i | ||||||
\(186\) | 3.27281i | 0.239974i | ||||||||
\(187\) | −2.07757 | − | 2.07757i | −0.151927 | − | 0.151927i | ||||
\(188\) | 1.41421 | + | 1.41421i | 0.103142 | + | 0.103142i | ||||
\(189\) | 1.70711 | + | 2.02133i | 0.124174 | + | 0.147030i | ||||
\(190\) | 1.52991 | + | 1.52991i | 0.110991 | + | 0.110991i | ||||
\(191\) | −23.1833 | −1.67748 | −0.838741 | − | 0.544530i | \(-0.816708\pi\) | ||||
−0.838741 | + | 0.544530i | \(0.816708\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 13.6264 | + | 13.6264i | 0.980850 | + | 0.980850i | 0.999820 | − | 0.0189698i | \(-0.00603863\pi\) |
−0.0189698 | + | 0.999820i | \(0.506039\pi\) | |||||||
\(194\) | 14.5297 | 1.04317 | ||||||||
\(195\) | 5.52991 | + | 2.05713i | 0.396005 | + | 0.147314i | ||||
\(196\) | −6.90126 | − | 1.17157i | −0.492947 | − | 0.0836838i | ||||
\(197\) | 10.1950 | − | 10.1950i | 0.726366 | − | 0.726366i | −0.243528 | − | 0.969894i | \(-0.578305\pi\) |
0.969894 | + | 0.243528i | \(0.0783046\pi\) | |||||||
\(198\) | −1.95063 | −0.138625 | ||||||||
\(199\) | −1.42518 | −0.101029 | −0.0505143 | − | 0.998723i | \(-0.516086\pi\) | ||||
−0.0505143 | + | 0.998723i | \(0.516086\pi\) | |||||||
\(200\) | −1.64203 | + | 1.64203i | −0.116109 | + | 0.116109i | ||||
\(201\) | −11.1012 | − | 11.1012i | −0.783021 | − | 0.783021i | ||||
\(202\) | −1.36484 | + | 1.36484i | −0.0960301 | + | 0.0960301i | ||||
\(203\) | −0.821188 | + | 0.693530i | −0.0576361 | + | 0.0486763i | ||||
\(204\) | 1.50625 | 0.105458 | ||||||||
\(205\) | − | 8.34564i | − | 0.582885i | ||||||
\(206\) | 5.62070 | − | 5.62070i | 0.391612 | − | 0.391612i | ||||
\(207\) | − | 4.19327i | − | 0.291453i | ||||||
\(208\) | 1.50062 | + | 3.27843i | 0.104050 | + | 0.227318i | ||||
\(209\) | − | 2.57908i | − | 0.178399i | ||||||
\(210\) | 2.79352 | + | 3.30772i | 0.192771 | + | 0.228254i | ||||
\(211\) | 5.45234 | 0.375354 | 0.187677 | − | 0.982231i | \(-0.439904\pi\) | ||||
0.187677 | + | 0.982231i | \(0.439904\pi\) | |||||||
\(212\) | − | 13.4456i | − | 0.923450i | ||||||
\(213\) | 5.18078 | + | 5.18078i | 0.354981 | + | 0.354981i | ||||
\(214\) | −2.35689 | + | 2.35689i | −0.161114 | + | 0.161114i | ||||
\(215\) | −2.85209 | + | 2.85209i | −0.194511 | + | 0.194511i | ||||
\(216\) | 0.707107 | − | 0.707107i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | −8.62845 | − | 0.727190i | −0.585737 | − | 0.0493649i | ||||
\(218\) | − | 13.5536i | − | 0.917964i | ||||||
\(219\) | 2.56008 | + | 2.56008i | 0.172994 | + | 0.172994i | ||||
\(220\) | −3.19202 | −0.215206 | ||||||||
\(221\) | 2.26031 | + | 4.93813i | 0.152045 | + | 0.332175i | ||||
\(222\) | − | 0.363595i | − | 0.0244029i | ||||||
\(223\) | −18.3548 | − | 18.3548i | −1.22913 | − | 1.22913i | −0.964293 | − | 0.264839i | \(-0.914681\pi\) |
−0.264839 | − | 0.964293i | \(-0.585319\pi\) | |||||||
\(224\) | −0.222191 | + | 2.63640i | −0.0148458 | + | 0.176152i | ||||
\(225\) | 2.32218i | 0.154812i | ||||||||
\(226\) | −7.34440 | + | 7.34440i | −0.488542 | + | 0.488542i | ||||
\(227\) | −6.91251 | − | 6.91251i | −0.458799 | − | 0.458799i | 0.439462 | − | 0.898261i | \(-0.355169\pi\) |
−0.898261 | + | 0.439462i | \(0.855169\pi\) | |||||||
\(228\) | 0.934922 | + | 0.934922i | 0.0619167 | + | 0.0619167i | ||||
\(229\) | −2.96035 | + | 2.96035i | −0.195625 | + | 0.195625i | −0.798122 | − | 0.602496i | \(-0.794173\pi\) |
0.602496 | + | 0.798122i | \(0.294173\pi\) | |||||||
\(230\) | − | 6.86189i | − | 0.452460i | ||||||
\(231\) | 0.433413 | − | 5.14265i | 0.0285165 | − | 0.338362i | ||||
\(232\) | 0.287270 | + | 0.287270i | 0.0188602 | + | 0.0188602i | ||||
\(233\) | − | 6.59953i | − | 0.432350i | −0.976355 | − | 0.216175i | \(-0.930642\pi\) | ||
0.976355 | − | 0.216175i | \(-0.0693581\pi\) | |||||||
\(234\) | 3.37930 | + | 1.25710i | 0.220912 | + | 0.0821792i | ||||
\(235\) | 3.27281 | 0.213495 | ||||||||
\(236\) | −8.75986 | − | 8.75986i | −0.570218 | − | 0.570218i | ||||
\(237\) | − | 1.42546i | − | 0.0925936i | ||||||
\(238\) | −0.334675 | + | 3.97108i | −0.0216938 | + | 0.257407i | ||||
\(239\) | −10.9611 | + | 10.9611i | −0.709014 | + | 0.709014i | −0.966328 | − | 0.257314i | \(-0.917162\pi\) |
0.257314 | + | 0.966328i | \(0.417162\pi\) | |||||||
\(240\) | 1.15711 | − | 1.15711i | 0.0746913 | − | 0.0746913i | ||||
\(241\) | −20.1598 | + | 20.1598i | −1.29861 | + | 1.29861i | −0.369295 | + | 0.929312i | \(0.620401\pi\) |
−0.929312 | + | 0.369295i | \(0.879599\pi\) | |||||||
\(242\) | −5.08766 | − | 5.08766i | −0.327047 | − | 0.327047i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 11.7394 | 0.751539 | ||||||||
\(245\) | −9.34118 | + | 6.62990i | −0.596786 | + | 0.423569i | ||||
\(246\) | − | 5.09999i | − | 0.325163i | ||||||
\(247\) | −1.66211 | + | 4.46804i | −0.105758 | + | 0.284295i | ||||
\(248\) | 3.27281i | 0.207824i | ||||||||
\(249\) | 4.90797 | − | 4.90797i | 0.311030 | − | 0.311030i | ||||
\(250\) | 11.9820i | 0.757811i | ||||||||
\(251\) | −6.62641 | −0.418255 | −0.209128 | − | 0.977888i | \(-0.567062\pi\) | ||||
−0.209128 | + | 0.977888i | \(0.567062\pi\) | |||||||
\(252\) | 1.70711 | + | 2.02133i | 0.107538 | + | 0.127332i | ||||
\(253\) | −5.78380 | + | 5.78380i | −0.363624 | + | 0.363624i | ||||
\(254\) | −6.44893 | − | 6.44893i | −0.404642 | − | 0.404642i | ||||
\(255\) | 1.74290 | − | 1.74290i | 0.109145 | − | 0.109145i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.5297 | −0.656826 | −0.328413 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328413 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(258\) | −1.74290 | + | 1.74290i | −0.108508 | + | 0.108508i | ||||
\(259\) | 0.958584 | + | 0.0807877i | 0.0595635 | + | 0.00501990i | ||||
\(260\) | 5.52991 | + | 2.05713i | 0.342950 | + | 0.127578i | ||||
\(261\) | 0.406261 | 0.0251469 | ||||||||
\(262\) | −2.81573 | − | 2.81573i | −0.173957 | − | 0.173957i | ||||
\(263\) | 11.3310 | 0.698699 | 0.349349 | − | 0.936993i | \(-0.386403\pi\) | ||||
0.349349 | + | 0.936993i | \(0.386403\pi\) | |||||||
\(264\) | −1.95063 | −0.120053 | ||||||||
\(265\) | −15.5581 | − | 15.5581i | −0.955727 | − | 0.955727i | ||||
\(266\) | −2.67256 | + | 2.25710i | −0.163865 | + | 0.138392i | ||||
\(267\) | −2.03017 | − | 2.03017i | −0.124244 | − | 0.124244i | ||||
\(268\) | −11.1012 | − | 11.1012i | −0.678116 | − | 0.678116i | ||||
\(269\) | − | 11.6504i | − | 0.710339i | −0.934802 | − | 0.355170i | \(-0.884423\pi\) | ||
0.934802 | − | 0.355170i | \(-0.115577\pi\) | |||||||
\(270\) | − | 1.63640i | − | 0.0995884i | ||||||
\(271\) | −9.41876 | + | 9.41876i | −0.572149 | + | 0.572149i | −0.932728 | − | 0.360580i | \(-0.882579\pi\) |
0.360580 | + | 0.932728i | \(0.382579\pi\) | |||||||
\(272\) | 1.50625 | 0.0913297 | ||||||||
\(273\) | −4.06508 | + | 8.62990i | −0.246030 | + | 0.522305i | ||||
\(274\) | 19.6389 | 1.18643 | ||||||||
\(275\) | 3.20299 | − | 3.20299i | 0.193148 | − | 0.193148i | ||||
\(276\) | − | 4.19327i | − | 0.252405i | ||||||
\(277\) | 5.99357i | 0.360119i | 0.983656 | + | 0.180059i | \(0.0576290\pi\) | ||||
−0.983656 | + | 0.180059i | \(0.942371\pi\) | |||||||
\(278\) | −5.21247 | − | 5.21247i | −0.312623 | − | 0.312623i | ||||
\(279\) | 2.31423 | + | 2.31423i | 0.138549 | + | 0.138549i | ||||
\(280\) | 2.79352 | + | 3.30772i | 0.166945 | + | 0.197674i | ||||
\(281\) | 12.4581 | + | 12.4581i | 0.743190 | + | 0.743190i | 0.973190 | − | 0.230001i | \(-0.0738729\pi\) |
−0.230001 | + | 0.973190i | \(0.573873\pi\) | |||||||
\(282\) | 2.00000 | 0.119098 | ||||||||
\(283\) | 12.9995 | 0.772739 | 0.386370 | − | 0.922344i | \(-0.373729\pi\) | ||||
0.386370 | + | 0.922344i | \(0.373729\pi\) | |||||||
\(284\) | 5.18078 | + | 5.18078i | 0.307422 | + | 0.307422i | ||||
\(285\) | 2.16362 | 0.128162 | ||||||||
\(286\) | −2.92717 | − | 6.39501i | −0.173087 | − | 0.378145i | ||||
\(287\) | 13.4456 | + | 1.13317i | 0.793671 | + | 0.0668891i | ||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | −14.7312 | −0.866542 | ||||||||
\(290\) | 0.664807 | 0.0390388 | ||||||||
\(291\) | 10.2741 | − | 10.2741i | 0.602276 | − | 0.602276i | ||||
\(292\) | 2.56008 | + | 2.56008i | 0.149817 | + | 0.149817i | ||||
\(293\) | −1.51545 | + | 1.51545i | −0.0885336 | + | 0.0885336i | −0.749987 | − | 0.661453i | \(-0.769940\pi\) |
0.661453 | + | 0.749987i | \(0.269940\pi\) | |||||||
\(294\) | −5.70836 | + | 4.05150i | −0.332918 | + | 0.236288i | ||||
\(295\) | −20.2723 | −1.18030 | ||||||||
\(296\) | − | 0.363595i | − | 0.0211335i | ||||||
\(297\) | −1.37930 | + | 1.37930i | −0.0800354 | + | 0.0800354i | ||||
\(298\) | 16.5995i | 0.961585i | ||||||||
\(299\) | 13.7474 | − | 6.29253i | 0.795030 | − | 0.363906i | ||||
\(300\) | 2.32218i | 0.134071i | ||||||||
\(301\) | −4.20773 | − | 4.98225i | −0.242530 | − | 0.287172i | ||||
\(302\) | 3.95313 | 0.227477 | ||||||||
\(303\) | 1.93018i | 0.110886i | ||||||||
\(304\) | 0.934922 | + | 0.934922i | 0.0536214 | + | 0.0536214i | ||||
\(305\) | 13.5838 | − | 13.5838i | 0.777807 | − | 0.777807i | ||||
\(306\) | 1.06508 | − | 1.06508i | 0.0608865 | − | 0.0608865i | ||||
\(307\) | 4.87286 | − | 4.87286i | 0.278109 | − | 0.278109i | −0.554245 | − | 0.832354i | \(-0.686993\pi\) |
0.832354 | + | 0.554245i | \(0.186993\pi\) | |||||||
\(308\) | 0.433413 | − | 5.14265i | 0.0246960 | − | 0.293030i | ||||
\(309\) | − | 7.94886i | − | 0.452195i | ||||||
\(310\) | 3.78701 | + | 3.78701i | 0.215088 | + | 0.215088i | ||||
\(311\) | −26.8179 | −1.52070 | −0.760352 | − | 0.649511i | \(-0.774974\pi\) | ||||
−0.760352 | + | 0.649511i | \(0.774974\pi\) | |||||||
\(312\) | 3.37930 | + | 1.25710i | 0.191315 | + | 0.0711693i | ||||
\(313\) | 1.96858i | 0.111271i | 0.998451 | + | 0.0556354i | \(0.0177184\pi\) | ||||
−0.998451 | + | 0.0556354i | \(0.982282\pi\) | |||||||
\(314\) | 7.38726 | + | 7.38726i | 0.416887 | + | 0.416887i | ||||
\(315\) | 4.31423 | + | 0.363595i | 0.243079 | + | 0.0204863i | ||||
\(316\) | − | 1.42546i | − | 0.0801884i | ||||||
\(317\) | 9.47705 | − | 9.47705i | 0.532284 | − | 0.532284i | −0.388967 | − | 0.921252i | \(-0.627168\pi\) |
0.921252 | + | 0.388967i | \(0.127168\pi\) | |||||||
\(318\) | −9.50750 | − | 9.50750i | −0.533154 | − | 0.533154i | ||||
\(319\) | −0.560357 | − | 0.560357i | −0.0313740 | − | 0.0313740i | ||||
\(320\) | 1.15711 | − | 1.15711i | 0.0646846 | − | 0.0646846i | ||||
\(321\) | 3.33315i | 0.186038i | ||||||||
\(322\) | 11.0552 | + | 0.931709i | 0.616080 | + | 0.0519221i | ||||
\(323\) | 1.40822 | + | 1.40822i | 0.0783557 | + | 0.0783557i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −7.61311 | + | 3.48472i | −0.422299 | + | 0.193297i | ||||
\(326\) | 12.8302 | 0.710599 | ||||||||
\(327\) | −9.58382 | − | 9.58382i | −0.529987 | − | 0.529987i | ||||
\(328\) | − | 5.09999i | − | 0.281600i | ||||||
\(329\) | −0.444383 | + | 5.27281i | −0.0244996 | + | 0.290699i | ||||
\(330\) | −2.25710 | + | 2.25710i | −0.124249 | + | 0.124249i | ||||
\(331\) | −13.2853 | + | 13.2853i | −0.730226 | + | 0.730226i | −0.970664 | − | 0.240438i | \(-0.922709\pi\) |
0.240438 | + | 0.970664i | \(0.422709\pi\) | |||||||
\(332\) | 4.90797 | − | 4.90797i | 0.269360 | − | 0.269360i | ||||
\(333\) | −0.257101 | − | 0.257101i | −0.0140890 | − | 0.0140890i | ||||
\(334\) | 12.7950i | 0.700109i | ||||||||
\(335\) | −25.6908 | −1.40364 | ||||||||
\(336\) | 1.70711 | + | 2.02133i | 0.0931303 | + | 0.110273i | ||||
\(337\) | 10.6200i | 0.578507i | 0.957252 | + | 0.289254i | \(0.0934071\pi\) | ||||
−0.957252 | + | 0.289254i | \(0.906593\pi\) | |||||||
\(338\) | 0.949747 | + | 12.9653i | 0.0516595 | + | 0.705217i | ||||
\(339\) | 10.3865i | 0.564120i | ||||||||
\(340\) | 1.74290 | − | 1.74290i | 0.0945220 | − | 0.0945220i | ||||
\(341\) | − | 6.38404i | − | 0.345715i | ||||||
\(342\) | 1.32218 | 0.0714952 | ||||||||
\(343\) | −9.41305 | − | 15.9497i | −0.508257 | − | 0.861205i | ||||
\(344\) | −1.74290 | + | 1.74290i | −0.0939708 | + | 0.0939708i | ||||
\(345\) | −4.85209 | − | 4.85209i | −0.261228 | − | 0.261228i | ||||
\(346\) | −0.0112470 | + | 0.0112470i | −0.000604642 | + | 0.000604642i | ||||
\(347\) | −33.6050 | −1.80401 | −0.902007 | − | 0.431722i | \(-0.857906\pi\) | ||||
−0.902007 | + | 0.431722i | \(0.857906\pi\) | |||||||
\(348\) | 0.406261 | 0.0217779 | ||||||||
\(349\) | 22.5833 | − | 22.5833i | 1.20886 | − | 1.20886i | 0.237462 | − | 0.971397i | \(-0.423684\pi\) |
0.971397 | − | 0.237462i | \(-0.0763156\pi\) | |||||||
\(350\) | −6.12220 | − | 0.515968i | −0.327246 | − | 0.0275797i | ||||
\(351\) | 3.27843 | − | 1.50062i | 0.174990 | − | 0.0800974i | ||||
\(352\) | −1.95063 | −0.103969 | ||||||||
\(353\) | 10.4681 | + | 10.4681i | 0.557162 | + | 0.557162i | 0.928498 | − | 0.371336i | \(-0.121100\pi\) |
−0.371336 | + | 0.928498i | \(0.621100\pi\) | |||||||
\(354\) | −12.3883 | −0.658431 | ||||||||
\(355\) | 11.9895 | 0.636336 | ||||||||
\(356\) | −2.03017 | − | 2.03017i | −0.107599 | − | 0.107599i | ||||
\(357\) | 2.57133 | + | 3.04463i | 0.136089 | + | 0.161139i | ||||
\(358\) | −7.33343 | − | 7.33343i | −0.387584 | − | 0.387584i | ||||
\(359\) | −2.68248 | − | 2.68248i | −0.141576 | − | 0.141576i | 0.632767 | − | 0.774343i | \(-0.281919\pi\) |
−0.774343 | + | 0.632767i | \(0.781919\pi\) | |||||||
\(360\) | − | 1.63640i | − | 0.0862461i | ||||||
\(361\) | − | 17.2518i | − | 0.907992i | ||||||
\(362\) | 1.01097 | − | 1.01097i | 0.0531354 | − | 0.0531354i | ||||
\(363\) | −7.19504 | −0.377642 | ||||||||
\(364\) | −4.06508 | + | 8.62990i | −0.213068 | + | 0.452330i | ||||
\(365\) | 5.92460 | 0.310108 | ||||||||
\(366\) | 8.30102 | − | 8.30102i | 0.433901 | − | 0.433901i | ||||
\(367\) | 8.08749i | 0.422164i | 0.977468 | + | 0.211082i | \(0.0676986\pi\) | ||||
−0.977468 | + | 0.211082i | \(0.932301\pi\) | |||||||
\(368\) | − | 4.19327i | − | 0.218589i | ||||||
\(369\) | −3.60624 | − | 3.60624i | −0.187733 | − | 0.187733i | ||||
\(370\) | −0.420721 | − | 0.420721i | −0.0218722 | − | 0.0218722i | ||||
\(371\) | 27.1781 | − | 22.9531i | 1.41102 | − | 1.19167i | ||||
\(372\) | 2.31423 | + | 2.31423i | 0.119987 | + | 0.119987i | ||||
\(373\) | −27.5920 | −1.42866 | −0.714331 | − | 0.699808i | \(-0.753269\pi\) | ||||
−0.714331 | + | 0.699808i | \(0.753269\pi\) | |||||||
\(374\) | −2.93813 | −0.151927 | ||||||||
\(375\) | 8.47259 | + | 8.47259i | 0.437523 | + | 0.437523i | ||||
\(376\) | 2.00000 | 0.103142 | ||||||||
\(377\) | 0.609645 | + | 1.33190i | 0.0313983 | + | 0.0685963i | ||||
\(378\) | 2.63640 | + | 0.222191i | 0.135602 | + | 0.0114283i | ||||
\(379\) | −7.79457 | + | 7.79457i | −0.400380 | + | 0.400380i | −0.878367 | − | 0.477987i | \(-0.841367\pi\) |
0.477987 | + | 0.878367i | \(0.341367\pi\) | |||||||
\(380\) | 2.16362 | 0.110991 | ||||||||
\(381\) | −9.12016 | −0.467240 | ||||||||
\(382\) | −16.3931 | + | 16.3931i | −0.838741 | + | 0.838741i | ||||
\(383\) | −11.3366 | − | 11.3366i | −0.579275 | − | 0.579275i | 0.355428 | − | 0.934704i | \(-0.384335\pi\) |
−0.934704 | + | 0.355428i | \(0.884335\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | −5.44912 | − | 6.45214i | −0.277713 | − | 0.328831i | ||||
\(386\) | 19.2707 | 0.980850 | ||||||||
\(387\) | 2.46483i | 0.125294i | ||||||||
\(388\) | 10.2741 | − | 10.2741i | 0.521586 | − | 0.521586i | ||||
\(389\) | − | 17.5669i | − | 0.890675i | −0.895363 | − | 0.445338i | \(-0.853084\pi\) | ||
0.895363 | − | 0.445338i | \(-0.146916\pi\) | |||||||
\(390\) | 5.36484 | − | 2.45563i | 0.271659 | − | 0.124346i | ||||
\(391\) | − | 6.31611i | − | 0.319419i | ||||||
\(392\) | −5.70836 | + | 4.05150i | −0.288316 | + | 0.204632i | ||||
\(393\) | −3.98205 | −0.200868 | ||||||||
\(394\) | − | 14.4180i | − | 0.726366i | ||||||
\(395\) | −1.64942 | − | 1.64942i | −0.0829913 | − | 0.0829913i | ||||
\(396\) | −1.37930 | + | 1.37930i | −0.0693127 | + | 0.0693127i | ||||
\(397\) | −24.6394 | + | 24.6394i | −1.23662 | + | 1.23662i | −0.275242 | + | 0.961375i | \(0.588758\pi\) |
−0.961375 | + | 0.275242i | \(0.911242\pi\) | |||||||
\(398\) | −1.00776 | + | 1.00776i | −0.0505143 | + | 0.0505143i | ||||
\(399\) | −0.293777 | + | 3.48580i | −0.0147072 | + | 0.174508i | ||||
\(400\) | 2.32218i | 0.116109i | ||||||||
\(401\) | 20.8486 | + | 20.8486i | 1.04113 | + | 1.04113i | 0.999117 | + | 0.0420122i | \(0.0133769\pi\) |
0.0420122 | + | 0.999117i | \(0.486623\pi\) | |||||||
\(402\) | −15.6995 | −0.783021 | ||||||||
\(403\) | −4.11425 | + | 11.0598i | −0.204945 | + | 0.550929i | ||||
\(404\) | 1.93018i | 0.0960301i | ||||||||
\(405\) | −1.15711 | − | 1.15711i | −0.0574974 | − | 0.0574974i | ||||
\(406\) | −0.0902676 | + | 1.07107i | −0.00447991 | + | 0.0531562i | ||||
\(407\) | 0.709240i | 0.0351557i | ||||||||
\(408\) | 1.06508 | − | 1.06508i | 0.0527292 | − | 0.0527292i | ||||
\(409\) | 13.8170 | + | 13.8170i | 0.683206 | + | 0.683206i | 0.960721 | − | 0.277515i | \(-0.0895109\pi\) |
−0.277515 | + | 0.960721i | \(0.589511\pi\) | |||||||
\(410\) | −5.90126 | − | 5.90126i | −0.291443 | − | 0.291443i | ||||
\(411\) | 13.8868 | − | 13.8868i | 0.684985 | − | 0.684985i | ||||
\(412\) | − | 7.94886i | − | 0.391612i | ||||||
\(413\) | 2.75258 | − | 32.6606i | 0.135445 | − | 1.60712i | ||||
\(414\) | −2.96509 | − | 2.96509i | −0.145726 | − | 0.145726i | ||||
\(415\) | − | 11.3581i | − | 0.557549i | ||||||
\(416\) | 3.37930 | + | 1.25710i | 0.165684 | + | 0.0616344i | ||||
\(417\) | −7.37155 | −0.360986 | ||||||||
\(418\) | −1.82369 | − | 1.82369i | −0.0891995 | − | 0.0891995i | ||||
\(419\) | − | 16.3845i | − | 0.800435i | −0.916420 | − | 0.400218i | \(-0.868935\pi\) | ||
0.916420 | − | 0.400218i | \(-0.131065\pi\) | |||||||
\(420\) | 4.31423 | + | 0.363595i | 0.210513 | + | 0.0177416i | ||||
\(421\) | −17.2214 | + | 17.2214i | −0.839319 | + | 0.839319i | −0.988769 | − | 0.149450i | \(-0.952250\pi\) |
0.149450 | + | 0.988769i | \(0.452250\pi\) | |||||||
\(422\) | 3.85538 | − | 3.85538i | 0.187677 | − | 0.187677i | ||||
\(423\) | 1.41421 | − | 1.41421i | 0.0687614 | − | 0.0687614i | ||||
\(424\) | −9.50750 | − | 9.50750i | −0.461725 | − | 0.461725i | ||||
\(425\) | 3.49778i | 0.169667i | ||||||||
\(426\) | 7.32672 | 0.354981 | ||||||||
\(427\) | 20.0404 | + | 23.7293i | 0.969824 | + | 1.14834i | ||||
\(428\) | 3.33315i | 0.161114i | ||||||||
\(429\) | −6.59178 | − | 2.45214i | −0.318254 | − | 0.118390i | ||||
\(430\) | 4.03346i | 0.194511i | ||||||||
\(431\) | 22.5749 | − | 22.5749i | 1.08739 | − | 1.08739i | 0.0915975 | − | 0.995796i | \(-0.470803\pi\) |
0.995796 | − | 0.0915975i | \(-0.0291973\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 35.8075 | 1.72080 | 0.860400 | − | 0.509620i | \(-0.170214\pi\) | ||||
0.860400 | + | 0.509620i | \(0.170214\pi\) | |||||||
\(434\) | −6.61544 | + | 5.58704i | −0.317551 | + | 0.268186i | ||||
\(435\) | 0.470090 | − | 0.470090i | 0.0225391 | − | 0.0225391i | ||||
\(436\) | −9.58382 | − | 9.58382i | −0.458982 | − | 0.458982i | ||||
\(437\) | 3.92038 | − | 3.92038i | 0.187537 | − | 0.187537i | ||||
\(438\) | 3.62050 | 0.172994 | ||||||||
\(439\) | 9.78979 | 0.467241 | 0.233621 | − | 0.972328i | \(-0.424943\pi\) | ||||
0.233621 | + | 0.972328i | \(0.424943\pi\) | |||||||
\(440\) | −2.25710 | + | 2.25710i | −0.107603 | + | 0.107603i | ||||
\(441\) | −1.17157 | + | 6.90126i | −0.0557892 | + | 0.328632i | ||||
\(442\) | 5.09007 | + | 1.89351i | 0.242110 | + | 0.0900649i | ||||
\(443\) | −2.71378 | −0.128936 | −0.0644679 | − | 0.997920i | \(-0.520535\pi\) | ||||
−0.0644679 | + | 0.997920i | \(0.520535\pi\) | |||||||
\(444\) | −0.257101 | − | 0.257101i | −0.0122015 | − | 0.0122015i | ||||
\(445\) | −4.69827 | −0.222719 | ||||||||
\(446\) | −25.9577 | −1.22913 | ||||||||
\(447\) | 11.7376 | + | 11.7376i | 0.555171 | + | 0.555171i | ||||
\(448\) | 1.70711 | + | 2.02133i | 0.0806532 | + | 0.0954990i | ||||
\(449\) | 14.7825 | + | 14.7825i | 0.697632 | + | 0.697632i | 0.963899 | − | 0.266268i | \(-0.0857905\pi\) |
−0.266268 | + | 0.963899i | \(0.585790\pi\) | |||||||
\(450\) | 1.64203 | + | 1.64203i | 0.0774060 | + | 0.0774060i | ||||
\(451\) | 9.94819i | 0.468442i | ||||||||
\(452\) | 10.3865i | 0.488542i | ||||||||
\(453\) | 2.79529 | − | 2.79529i | 0.131334 | − | 0.131334i | ||||
\(454\) | −9.77576 | −0.458799 | ||||||||
\(455\) | 5.28201 | + | 14.6895i | 0.247625 | + | 0.688655i | ||||
\(456\) | 1.32218 | 0.0619167 | ||||||||
\(457\) | −17.9920 | + | 17.9920i | −0.841632 | + | 0.841632i | −0.989071 | − | 0.147439i | \(-0.952897\pi\) |
0.147439 | + | 0.989071i | \(0.452897\pi\) | |||||||
\(458\) | 4.18657i | 0.195625i | ||||||||
\(459\) | − | 1.50625i | − | 0.0703056i | ||||||
\(460\) | −4.85209 | − | 4.85209i | −0.226230 | − | 0.226230i | ||||
\(461\) | 23.4424 | + | 23.4424i | 1.09182 | + | 1.09182i | 0.995334 | + | 0.0964882i | \(0.0307610\pi\) |
0.0964882 | + | 0.995334i | \(0.469239\pi\) | |||||||
\(462\) | −3.32994 | − | 3.94287i | −0.154923 | − | 0.183439i | ||||
\(463\) | 12.4486 | + | 12.4486i | 0.578536 | + | 0.578536i | 0.934500 | − | 0.355964i | \(-0.115847\pi\) |
−0.355964 | + | 0.934500i | \(0.615847\pi\) | |||||||
\(464\) | 0.406261 | 0.0188602 | ||||||||
\(465\) | 5.35564 | 0.248362 | ||||||||
\(466\) | −4.66657 | − | 4.66657i | −0.216175 | − | 0.216175i | ||||
\(467\) | 27.6932 | 1.28149 | 0.640744 | − | 0.767754i | \(-0.278626\pi\) | ||||
0.640744 | + | 0.767754i | \(0.278626\pi\) | |||||||
\(468\) | 3.27843 | − | 1.50062i | 0.151546 | − | 0.0693664i | ||||
\(469\) | 3.48830 | − | 41.3903i | 0.161075 | − | 1.91123i | ||||
\(470\) | 2.31423 | − | 2.31423i | 0.106747 | − | 0.106747i | ||||
\(471\) | 10.4472 | 0.481380 | ||||||||
\(472\) | −12.3883 | −0.570218 | ||||||||
\(473\) | 3.39975 | − | 3.39975i | 0.156321 | − | 0.156321i | ||||
\(474\) | −1.00795 | − | 1.00795i | −0.0462968 | − | 0.0462968i | ||||
\(475\) | −2.17106 | + | 2.17106i | −0.0996148 | + | 0.0996148i | ||||
\(476\) | 2.57133 | + | 3.04463i | 0.117857 | + | 0.139550i | ||||
\(477\) | −13.4456 | −0.615633 | ||||||||
\(478\) | 15.5013i | 0.709014i | ||||||||
\(479\) | 7.69426 | − | 7.69426i | 0.351560 | − | 0.351560i | −0.509130 | − | 0.860690i | \(-0.670033\pi\) |
0.860690 | + | 0.509130i | \(0.170033\pi\) | |||||||
\(480\) | − | 1.63640i | − | 0.0746913i | ||||||
\(481\) | 0.457076 | − | 1.22870i | 0.0208409 | − | 0.0560238i | ||||
\(482\) | 28.5103i | 1.29861i | ||||||||
\(483\) | 8.47600 | − | 7.15836i | 0.385671 | − | 0.325717i | ||||
\(484\) | −7.19504 | −0.327047 | ||||||||
\(485\) | − | 23.7765i | − | 1.07964i | ||||||
\(486\) | −0.707107 | − | 0.707107i | −0.0320750 | − | 0.0320750i | ||||
\(487\) | −3.65436 | + | 3.65436i | −0.165595 | + | 0.165595i | −0.785040 | − | 0.619445i | \(-0.787358\pi\) |
0.619445 | + | 0.785040i | \(0.287358\pi\) | |||||||
\(488\) | 8.30102 | − | 8.30102i | 0.375769 | − | 0.375769i | ||||
\(489\) | 9.07232 | − | 9.07232i | 0.410264 | − | 0.410264i | ||||
\(490\) | −1.91717 | + | 11.2933i | −0.0866088 | + | 0.510177i | ||||
\(491\) | 12.9652i | 0.585110i | 0.956249 | + | 0.292555i | \(0.0945055\pi\) | ||||
−0.956249 | + | 0.292555i | \(0.905495\pi\) | |||||||
\(492\) | −3.60624 | − | 3.60624i | −0.162582 | − | 0.162582i | ||||
\(493\) | 0.611930 | 0.0275599 | ||||||||
\(494\) | 1.98409 | + | 4.33468i | 0.0892686 | + | 0.195026i | ||||
\(495\) | 3.19202i | 0.143471i | ||||||||
\(496\) | 2.31423 | + | 2.31423i | 0.103912 | + | 0.103912i | ||||
\(497\) | −1.62793 | + | 19.3162i | −0.0730228 | + | 0.866450i | ||||
\(498\) | − | 6.94091i | − | 0.311030i | ||||||
\(499\) | 15.8982 | − | 15.8982i | 0.711703 | − | 0.711703i | −0.255188 | − | 0.966891i | \(-0.582137\pi\) |
0.966891 | + | 0.255188i | \(0.0821374\pi\) | |||||||
\(500\) | 8.47259 | + | 8.47259i | 0.378906 | + | 0.378906i | ||||
\(501\) | 9.04741 | + | 9.04741i | 0.404208 | + | 0.404208i | ||||
\(502\) | −4.68558 | + | 4.68558i | −0.209128 | + | 0.209128i | ||||
\(503\) | 7.72073i | 0.344250i | 0.985075 | + | 0.172125i | \(0.0550633\pi\) | ||||
−0.985075 | + | 0.172125i | \(0.944937\pi\) | |||||||
\(504\) | 2.63640 | + | 0.222191i | 0.117435 | + | 0.00989719i | ||||
\(505\) | 2.23344 | + | 2.23344i | 0.0993867 | + | 0.0993867i | ||||
\(506\) | 8.17953i | 0.363624i | ||||||||
\(507\) | 9.83940 | + | 8.49625i | 0.436983 | + | 0.377332i | ||||
\(508\) | −9.12016 | −0.404642 | ||||||||
\(509\) | 23.7432 | + | 23.7432i | 1.05240 | + | 1.05240i | 0.998549 | + | 0.0538516i | \(0.0171498\pi\) |
0.0538516 | + | 0.998549i | \(0.482850\pi\) | |||||||
\(510\) | − | 2.46483i | − | 0.109145i | ||||||
\(511\) | −0.804444 | + | 9.54510i | −0.0355865 | + | 0.422250i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0.934922 | − | 0.934922i | 0.0412778 | − | 0.0412778i | ||||
\(514\) | −7.44563 | + | 7.44563i | −0.328413 | + | 0.328413i | ||||
\(515\) | −9.19773 | − | 9.19773i | −0.405301 | − | 0.405301i | ||||
\(516\) | 2.46483i | 0.108508i | ||||||||
\(517\) | −3.90126 | −0.171577 | ||||||||
\(518\) | 0.734947 | − | 0.620696i | 0.0322917 | − | 0.0272718i | ||||
\(519\) | 0.0159057i | 0.000698181i | ||||||||
\(520\) | 5.36484 | − | 2.45563i | 0.235264 | − | 0.107686i | ||||
\(521\) | − | 11.2520i | − | 0.492958i | −0.969148 | − | 0.246479i | \(-0.920726\pi\) | ||
0.969148 | − | 0.246479i | \(-0.0792736\pi\) | |||||||
\(522\) | 0.287270 | − | 0.287270i | 0.0125735 | − | 0.0125735i | ||||
\(523\) | 39.7356i | 1.73752i | 0.495237 | + | 0.868758i | \(0.335081\pi\) | ||||
−0.495237 | + | 0.868758i | \(0.664919\pi\) | |||||||
\(524\) | −3.98205 | −0.173957 | ||||||||
\(525\) | −4.69390 | + | 3.96421i | −0.204858 | + | 0.173012i | ||||
\(526\) | 8.01222 | − | 8.01222i | 0.349349 | − | 0.349349i | ||||
\(527\) | 3.48580 | + | 3.48580i | 0.151844 | + | 0.151844i | ||||
\(528\) | −1.37930 | + | 1.37930i | −0.0600265 | + | 0.0600265i | ||||
\(529\) | 5.41647 | 0.235499 | ||||||||
\(530\) | −22.0025 | −0.955727 | ||||||||
\(531\) | −8.75986 | + | 8.75986i | −0.380145 | + | 0.380145i | ||||
\(532\) | −0.293777 | + | 3.48580i | −0.0127368 | + | 0.151129i | ||||
\(533\) | 6.41120 | − | 17.2344i | 0.277700 | − | 0.746505i | ||||
\(534\) | −2.87109 | −0.124244 | ||||||||
\(535\) | 3.85683 | + | 3.85683i | 0.166745 | + | 0.166745i | ||||
\(536\) | −15.6995 | −0.678116 | ||||||||
\(537\) | −10.3710 | −0.447543 | ||||||||
\(538\) | −8.23810 | − | 8.23810i | −0.355170 | − | 0.355170i | ||||
\(539\) | 11.1349 | − | 7.90299i | 0.479614 | − | 0.340406i | ||||
\(540\) | −1.15711 | − | 1.15711i | −0.0497942 | − | 0.0497942i | ||||
\(541\) | −10.4751 | − | 10.4751i | −0.450359 | − | 0.450359i | 0.445114 | − | 0.895474i | \(-0.353163\pi\) |
−0.895474 | + | 0.445114i | \(0.853163\pi\) | |||||||
\(542\) | 13.3201i | 0.572149i | ||||||||
\(543\) | − | 1.42973i | − | 0.0613554i | ||||||
\(544\) | 1.06508 | − | 1.06508i | 0.0456649 | − | 0.0456649i | ||||
\(545\) | −22.1791 | −0.950050 | ||||||||
\(546\) | 3.22781 | + | 8.97670i | 0.138138 | + | 0.384167i | ||||
\(547\) | 17.4124 | 0.744502 | 0.372251 | − | 0.928132i | \(-0.378586\pi\) | ||||
0.372251 | + | 0.928132i | \(0.378586\pi\) | |||||||
\(548\) | 13.8868 | − | 13.8868i | 0.593215 | − | 0.593215i | ||||
\(549\) | − | 11.7394i | − | 0.501026i | ||||||
\(550\) | − | 4.52971i | − | 0.193148i | ||||||
\(551\) | 0.379822 | + | 0.379822i | 0.0161810 | + | 0.0161810i | ||||
\(552\) | −2.96509 | − | 2.96509i | −0.126203 | − | 0.126203i | ||||
\(553\) | 2.88133 | − | 2.43341i | 0.122527 | − | 0.103479i | ||||
\(554\) | 4.23810 | + | 4.23810i | 0.180059 | + | 0.180059i | ||||
\(555\) | −0.594989 | −0.0252559 | ||||||||
\(556\) | −7.37155 | −0.312623 | ||||||||
\(557\) | 6.23417 | + | 6.23417i | 0.264150 | + | 0.264150i | 0.826738 | − | 0.562587i | \(-0.190194\pi\) |
−0.562587 | + | 0.826738i | \(0.690194\pi\) | |||||||
\(558\) | 3.27281 | 0.138549 | ||||||||
\(559\) | −8.08079 | + | 3.69879i | −0.341781 | + | 0.156442i | ||||
\(560\) | 4.31423 | + | 0.363595i | 0.182309 | + | 0.0153647i | ||||
\(561\) | −2.07757 | + | 2.07757i | −0.0877153 | + | 0.0877153i | ||||
\(562\) | 17.6185 | 0.743190 | ||||||||
\(563\) | 32.2131 | 1.35762 | 0.678809 | − | 0.734315i | \(-0.262496\pi\) | ||||
0.678809 | + | 0.734315i | \(0.262496\pi\) | |||||||
\(564\) | 1.41421 | − | 1.41421i | 0.0595491 | − | 0.0595491i | ||||
\(565\) | 12.0184 | + | 12.0184i | 0.505618 | + | 0.505618i | ||||
\(566\) | 9.19202 | − | 9.19202i | 0.386370 | − | 0.386370i | ||||
\(567\) | 2.02133 | − | 1.70711i | 0.0848880 | − | 0.0716917i | ||||
\(568\) | 7.32672 | 0.307422 | ||||||||
\(569\) | − | 25.5422i | − | 1.07079i | −0.844603 | − | 0.535393i | \(-0.820164\pi\) | ||
0.844603 | − | 0.535393i | \(-0.179836\pi\) | |||||||
\(570\) | 1.52991 | − | 1.52991i | 0.0640809 | − | 0.0640809i | ||||
\(571\) | − | 34.8620i | − | 1.45893i | −0.684020 | − | 0.729464i | \(-0.739770\pi\) | ||
0.684020 | − | 0.729464i | \(-0.260230\pi\) | |||||||
\(572\) | −6.59178 | − | 2.45214i | −0.275616 | − | 0.102529i | ||||
\(573\) | 23.1833i | 0.968495i | ||||||||
\(574\) | 10.3088 | − | 8.70622i | 0.430280 | − | 0.363391i | ||||
\(575\) | 9.73753 | 0.406083 | ||||||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 11.7404 | + | 11.7404i | 0.488760 | + | 0.488760i | 0.907915 | − | 0.419155i | \(-0.137674\pi\) |
−0.419155 | + | 0.907915i | \(0.637674\pi\) | |||||||
\(578\) | −10.4165 | + | 10.4165i | −0.433271 | + | 0.433271i | ||||
\(579\) | 13.6264 | − | 13.6264i | 0.566294 | − | 0.566294i | ||||
\(580\) | 0.470090 | − | 0.470090i | 0.0195194 | − | 0.0195194i | ||||
\(581\) | 18.2991 | + | 1.54221i | 0.759173 | + | 0.0639817i | ||||
\(582\) | − | 14.5297i | − | 0.602276i | ||||||
\(583\) | 18.5456 | + | 18.5456i | 0.768081 | + | 0.768081i | ||||
\(584\) | 3.62050 | 0.149817 | ||||||||
\(585\) | 2.05713 | − | 5.52991i | 0.0850517 | − | 0.228634i | ||||
\(586\) | 2.14317i | 0.0885336i | ||||||||
\(587\) | 25.6920 | + | 25.6920i | 1.06042 | + | 1.06042i | 0.998053 | + | 0.0623701i | \(0.0198659\pi\) |
0.0623701 | + | 0.998053i | \(0.480134\pi\) | |||||||
\(588\) | −1.17157 | + | 6.90126i | −0.0483149 | + | 0.284603i | ||||
\(589\) | 4.32724i | 0.178301i | ||||||||
\(590\) | −14.3347 | + | 14.3347i | −0.590149 | + | 0.590149i | ||||
\(591\) | −10.1950 | − | 10.1950i | −0.419368 | − | 0.419368i | ||||
\(592\) | −0.257101 | − | 0.257101i | −0.0105668 | − | 0.0105668i | ||||
\(593\) | 6.06857 | − | 6.06857i | 0.249206 | − | 0.249206i | −0.571439 | − | 0.820645i | \(-0.693614\pi\) |
0.820645 | + | 0.571439i | \(0.193614\pi\) | |||||||
\(594\) | 1.95063i | 0.0800354i | ||||||||
\(595\) | 6.49830 | + | 0.547664i | 0.266404 | + | 0.0224521i | ||||
\(596\) | 11.7376 | + | 11.7376i | 0.480793 | + | 0.480793i | ||||
\(597\) | 1.42518i | 0.0583289i | ||||||||
\(598\) | 5.27136 | − | 14.1703i | 0.215562 | − | 0.579468i | ||||
\(599\) | −42.6492 | −1.74260 | −0.871300 | − | 0.490750i | \(-0.836723\pi\) | ||||
−0.871300 | + | 0.490750i | \(0.836723\pi\) | |||||||
\(600\) | 1.64203 | + | 1.64203i | 0.0670355 | + | 0.0670355i | ||||
\(601\) | − | 4.02249i | − | 0.164081i | −0.996629 | − | 0.0820405i | \(-0.973856\pi\) | ||
0.996629 | − | 0.0820405i | \(-0.0261437\pi\) | |||||||
\(602\) | −6.49830 | − | 0.547664i | −0.264851 | − | 0.0223211i | ||||
\(603\) | −11.1012 | + | 11.1012i | −0.452077 | + | 0.452077i | ||||
\(604\) | 2.79529 | − | 2.79529i | 0.113739 | − | 0.113739i | ||||
\(605\) | −8.32547 | + | 8.32547i | −0.338479 | + | 0.338479i | ||||
\(606\) | 1.36484 | + | 1.36484i | 0.0554430 | + | 0.0554430i | ||||
\(607\) | 39.1674i | 1.58975i | 0.606770 | + | 0.794877i | \(0.292465\pi\) | ||||
−0.606770 | + | 0.794877i | \(0.707535\pi\) | |||||||
\(608\) | 1.32218 | 0.0536214 | ||||||||
\(609\) | 0.693530 | + | 0.821188i | 0.0281033 | + | 0.0332762i | ||||
\(610\) | − | 19.2104i | − | 0.777807i | ||||||
\(611\) | 6.75861 | + | 2.51420i | 0.273424 | + | 0.101714i | ||||
\(612\) | − | 1.50625i | − | 0.0608865i | ||||||
\(613\) | −15.7609 | + | 15.7609i | −0.636577 | + | 0.636577i | −0.949710 | − | 0.313132i | \(-0.898622\pi\) |
0.313132 | + | 0.949710i | \(0.398622\pi\) | |||||||
\(614\) | − | 6.89126i | − | 0.278109i | ||||||
\(615\) | −8.34564 | −0.336529 | ||||||||
\(616\) | −3.32994 | − | 3.94287i | −0.134167 | − | 0.158863i | ||||
\(617\) | −19.4135 | + | 19.4135i | −0.781558 | + | 0.781558i | −0.980094 | − | 0.198536i | \(-0.936381\pi\) |
0.198536 | + | 0.980094i | \(0.436381\pi\) | |||||||
\(618\) | −5.62070 | − | 5.62070i | −0.226098 | − | 0.226098i | ||||
\(619\) | 28.9913 | − | 28.9913i | 1.16526 | − | 1.16526i | 0.181953 | − | 0.983307i | \(-0.441758\pi\) |
0.983307 | − | 0.181953i | \(-0.0582418\pi\) | |||||||
\(620\) | 5.35564 | 0.215088 | ||||||||
\(621\) | −4.19327 | −0.168270 | ||||||||
\(622\) | −18.9631 | + | 18.9631i | −0.760352 | + | 0.760352i | ||||
\(623\) | 0.637932 | − | 7.56936i | 0.0255582 | − | 0.303260i | ||||
\(624\) | 3.27843 | − | 1.50062i | 0.131242 | − | 0.0600731i | ||||
\(625\) | 7.99659 | 0.319864 | ||||||||
\(626\) | 1.39200 | + | 1.39200i | 0.0556354 | + | 0.0556354i | ||||
\(627\) | −2.57908 | −0.102999 | ||||||||
\(628\) | 10.4472 | 0.416887 | ||||||||
\(629\) | −0.387257 | − | 0.387257i | −0.0154410 | − | 0.0154410i | ||||
\(630\) | 3.30772 | − | 2.79352i | 0.131783 | − | 0.111296i | ||||
\(631\) | −14.3025 | − | 14.3025i | −0.569375 | − | 0.569375i | 0.362578 | − | 0.931953i | \(-0.381897\pi\) |
−0.931953 | + | 0.362578i | \(0.881897\pi\) | |||||||
\(632\) | −1.00795 | − | 1.00795i | −0.0400942 | − | 0.0400942i | ||||
\(633\) | − | 5.45234i | − | 0.216711i | ||||||
\(634\) | − | 13.4026i | − | 0.532284i | ||||||
\(635\) | −10.5531 | + | 10.5531i | −0.418785 | + | 0.418785i | ||||
\(636\) | −13.4456 | −0.533154 | ||||||||
\(637\) | −24.3834 | + | 6.51528i | −0.966106 | + | 0.258145i | ||||
\(638\) | −0.792465 | −0.0313740 | ||||||||
\(639\) | 5.18078 | − | 5.18078i | 0.204948 | − | 0.204948i | ||||
\(640\) | − | 1.63640i | − | 0.0646846i | ||||||
\(641\) | 41.5501i | 1.64113i | 0.571553 | + | 0.820565i | \(0.306341\pi\) | ||||
−0.571553 | + | 0.820565i | \(0.693659\pi\) | |||||||
\(642\) | 2.35689 | + | 2.35689i | 0.0930191 | + | 0.0930191i | ||||
\(643\) | 23.7094 | + | 23.7094i | 0.935009 | + | 0.935009i | 0.998013 | − | 0.0630044i | \(-0.0200682\pi\) |
−0.0630044 | + | 0.998013i | \(0.520068\pi\) | |||||||
\(644\) | 8.47600 | − | 7.15836i | 0.334001 | − | 0.282079i | ||||
\(645\) | 2.85209 | + | 2.85209i | 0.112301 | + | 0.112301i | ||||
\(646\) | 1.99153 | 0.0783557 | ||||||||
\(647\) | −26.3735 | −1.03685 | −0.518425 | − | 0.855123i | \(-0.673482\pi\) | ||||
−0.518425 | + | 0.855123i | \(0.673482\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 24.1650 | 0.948560 | ||||||||
\(650\) | −2.91921 | + | 7.84735i | −0.114501 | + | 0.307798i | ||||
\(651\) | −0.727190 | + | 8.62845i | −0.0285008 | + | 0.338176i | ||||
\(652\) | 9.07232 | − | 9.07232i | 0.355299 | − | 0.355299i | ||||
\(653\) | −12.3520 | −0.483369 | −0.241685 | − | 0.970355i | \(-0.577700\pi\) | ||||
−0.241685 | + | 0.970355i | \(0.577700\pi\) | |||||||
\(654\) | −13.5536 | −0.529987 | ||||||||
\(655\) | −4.60768 | + | 4.60768i | −0.180037 | + | 0.180037i | ||||
\(656\) | −3.60624 | − | 3.60624i | −0.140800 | − | 0.140800i | ||||
\(657\) | 2.56008 | − | 2.56008i | 0.0998782 | − | 0.0998782i | ||||
\(658\) | 3.41421 | + | 4.04267i | 0.133100 | + | 0.157600i | ||||
\(659\) | −40.1732 | −1.56492 | −0.782462 | − | 0.622698i | \(-0.786036\pi\) | ||||
−0.782462 | + | 0.622698i | \(0.786036\pi\) | |||||||
\(660\) | 3.19202i | 0.124249i | ||||||||
\(661\) | 26.5576 | − | 26.5576i | 1.03297 | − | 1.03297i | 0.0335333 | − | 0.999438i | \(-0.489324\pi\) |
0.999438 | − | 0.0335333i | \(-0.0106760\pi\) | |||||||
\(662\) | 18.7883i | 0.730226i | ||||||||
\(663\) | 4.93813 | − | 2.26031i | 0.191781 | − | 0.0877833i | ||||
\(664\) | − | 6.94091i | − | 0.269360i | ||||||
\(665\) | 3.69353 | + | 4.37340i | 0.143229 | + | 0.169593i | ||||
\(666\) | −0.363595 | −0.0140890 | ||||||||
\(667\) | − | 1.70356i | − | 0.0659622i | ||||||
\(668\) | 9.04741 | + | 9.04741i | 0.350055 | + | 0.350055i | ||||
\(669\) | −18.3548 | + | 18.3548i | −0.709639 | + | 0.709639i | ||||
\(670\) | −18.1661 | + | 18.1661i | −0.701818 | + | 0.701818i | ||||
\(671\) | −16.1922 | + | 16.1922i | −0.625094 | + | 0.625094i | ||||
\(672\) | 2.63640 | + | 0.222191i | 0.101702 | + | 0.00857122i | ||||
\(673\) | − | 3.49388i | − | 0.134679i | −0.997730 | − | 0.0673395i | \(-0.978549\pi\) | ||
0.997730 | − | 0.0673395i | \(-0.0214511\pi\) | |||||||
\(674\) | 7.50946 | + | 7.50946i | 0.289254 | + | 0.289254i | ||||
\(675\) | 2.32218 | 0.0893807 | ||||||||
\(676\) | 9.83940 | + | 8.49625i | 0.378438 | + | 0.326779i | ||||
\(677\) | − | 25.1586i | − | 0.966922i | −0.875366 | − | 0.483461i | \(-0.839380\pi\) | ||
0.875366 | − | 0.483461i | \(-0.160620\pi\) | |||||||
\(678\) | 7.34440 | + | 7.34440i | 0.282060 | + | 0.282060i | ||||
\(679\) | 38.3062 | + | 3.22838i | 1.47006 | + | 0.123894i | ||||
\(680\) | − | 2.46483i | − | 0.0945220i | ||||||
\(681\) | −6.91251 | + | 6.91251i | −0.264888 | + | 0.264888i | ||||
\(682\) | −4.51420 | − | 4.51420i | −0.172858 | − | 0.172858i | ||||
\(683\) | −26.5689 | − | 26.5689i | −1.01663 | − | 1.01663i | −0.999859 | − | 0.0167709i | \(-0.994661\pi\) |
−0.0167709 | − | 0.999859i | \(-0.505339\pi\) | |||||||
\(684\) | 0.934922 | − | 0.934922i | 0.0357476 | − | 0.0357476i | ||||
\(685\) | − | 32.1372i | − | 1.22790i | ||||||
\(686\) | −17.9342 | − | 4.62214i | −0.684731 | − | 0.176474i | ||||
\(687\) | 2.96035 | + | 2.96035i | 0.112944 | + | 0.112944i | ||||
\(688\) | 2.46483i | 0.0939708i | ||||||||
\(689\) | −20.1768 | − | 44.0806i | −0.768677 | − | 1.67934i | ||||
\(690\) | −6.86189 | −0.261228 | ||||||||
\(691\) | −1.14265 | − | 1.14265i | −0.0434686 | − | 0.0434686i | 0.685038 | − | 0.728507i | \(-0.259785\pi\) |
−0.728507 | + | 0.685038i | \(0.759785\pi\) | |||||||
\(692\) | 0.0159057i | 0.000604642i | ||||||||
\(693\) | −5.14265 | − | 0.433413i | −0.195353 | − | 0.0164640i | ||||
\(694\) | −23.7624 | + | 23.7624i | −0.902007 | + | 0.902007i | ||||
\(695\) | −8.52971 | + | 8.52971i | −0.323550 | + | 0.323550i | ||||
\(696\) | 0.287270 | − | 0.287270i | 0.0108889 | − | 0.0108889i | ||||
\(697\) | −5.43189 | − | 5.43189i | −0.205747 | − | 0.205747i | ||||
\(698\) | − | 31.9377i | − | 1.20886i | ||||||
\(699\) | −6.59953 | −0.249617 | ||||||||
\(700\) | −4.69390 | + | 3.96421i | −0.177413 | + | 0.149833i | ||||
\(701\) | − | 21.5853i | − | 0.815264i | −0.913146 | − | 0.407632i | \(-0.866355\pi\) | ||
0.913146 | − | 0.407632i | \(-0.133645\pi\) | |||||||
\(702\) | 1.25710 | − | 3.37930i | 0.0474462 | − | 0.127544i | ||||
\(703\) | − | 0.480738i | − | 0.0181314i | ||||||
\(704\) | −1.37930 | + | 1.37930i | −0.0519845 | + | 0.0519845i | ||||
\(705\) | − | 3.27281i | − | 0.123261i | ||||||
\(706\) | 14.8042 | 0.557162 | ||||||||
\(707\) | −3.90154 | + | 3.29503i | −0.146732 | + | 0.123922i | ||||
\(708\) | −8.75986 | + | 8.75986i | −0.329216 | + | 0.329216i | ||||
\(709\) | 29.2210 | + | 29.2210i | 1.09742 | + | 1.09742i | 0.994712 | + | 0.102706i | \(0.0327501\pi\) |
0.102706 | + | 0.994712i | \(0.467250\pi\) | |||||||
\(710\) | 8.47785 | − | 8.47785i | 0.318168 | − | 0.318168i | ||||
\(711\) | −1.42546 | −0.0534589 | ||||||||
\(712\) | −2.87109 | −0.107599 | ||||||||
\(713\) | 9.70418 | − | 9.70418i | 0.363424 | − | 0.363424i | ||||
\(714\) | 3.97108 | + | 0.334675i | 0.148614 | + | 0.0125249i | ||||
\(715\) | −10.4648 | + | 4.79003i | −0.391363 | + | 0.179137i | ||||
\(716\) | −10.3710 | −0.387584 | ||||||||
\(717\) | 10.9611 | + | 10.9611i | 0.409349 | + | 0.409349i | ||||
\(718\) | −3.79360 | −0.141576 | ||||||||
\(719\) | −13.2373 | −0.493668 | −0.246834 | − | 0.969058i | \(-0.579390\pi\) | ||||
−0.246834 | + | 0.969058i | \(0.579390\pi\) | |||||||
\(720\) | −1.15711 | − | 1.15711i | −0.0431231 | − | 0.0431231i | ||||
\(721\) | 16.0673 | − | 13.5696i | 0.598378 | − | 0.505357i | ||||
\(722\) | −12.1989 | − | 12.1989i | −0.453996 | − | 0.453996i | ||||
\(723\) | 20.1598 | + | 20.1598i | 0.749751 | + | 0.749751i | ||||
\(724\) | − | 1.42973i | − | 0.0531354i | ||||||
\(725\) | 0.943410i | 0.0350374i | ||||||||
\(726\) | −5.08766 | + | 5.08766i | −0.188821 | + | 0.188821i | ||||
\(727\) | −17.2911 | −0.641291 | −0.320646 | − | 0.947199i | \(-0.603900\pi\) | ||||
−0.320646 | + | 0.947199i | \(0.603900\pi\) | |||||||
\(728\) | 3.22781 | + | 8.97670i | 0.119631 | + | 0.332699i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 4.18933 | − | 4.18933i | 0.155054 | − | 0.155054i | ||||
\(731\) | 3.71265i | 0.137317i | ||||||||
\(732\) | − | 11.7394i | − | 0.433901i | ||||||
\(733\) | −14.5279 | − | 14.5279i | −0.536602 | − | 0.536602i | 0.385927 | − | 0.922529i | \(-0.373882\pi\) |
−0.922529 | + | 0.385927i | \(0.873882\pi\) | |||||||
\(734\) | 5.71872 | + | 5.71872i | 0.211082 | + | 0.211082i | ||||
\(735\) | 6.62990 | + | 9.34118i | 0.244547 | + | 0.344555i | ||||
\(736\) | −2.96509 | − | 2.96509i | −0.109295 | − | 0.109295i | ||||
\(737\) | 30.6240 | 1.12805 | ||||||||
\(738\) | −5.09999 | −0.187733 | ||||||||
\(739\) | −12.3646 | − | 12.3646i | −0.454838 | − | 0.454838i | 0.442119 | − | 0.896957i | \(-0.354227\pi\) |
−0.896957 | + | 0.442119i | \(0.854227\pi\) | |||||||
\(740\) | −0.594989 | −0.0218722 | ||||||||
\(741\) | 4.46804 | + | 1.66211i | 0.164138 | + | 0.0610592i | ||||
\(742\) | 2.98750 | − | 35.4481i | 0.109675 | − | 1.30134i | ||||
\(743\) | −12.6873 | + | 12.6873i | −0.465452 | + | 0.465452i | −0.900437 | − | 0.434986i | \(-0.856753\pi\) |
0.434986 | + | 0.900437i | \(0.356753\pi\) | |||||||
\(744\) | 3.27281 | 0.119987 | ||||||||
\(745\) | 27.1636 | 0.995196 | ||||||||
\(746\) | −19.5105 | + | 19.5105i | −0.714331 | + | 0.714331i | ||||
\(747\) | −4.90797 | − | 4.90797i | −0.179573 | − | 0.179573i | ||||
\(748\) | −2.07757 | + | 2.07757i | −0.0759637 | + | 0.0759637i | ||||
\(749\) | −6.73740 | + | 5.69004i | −0.246179 | + | 0.207910i | ||||
\(750\) | 11.9820 | 0.437523 | ||||||||
\(751\) | − | 15.8031i | − | 0.576663i | −0.957531 | − | 0.288331i | \(-0.906900\pi\) | ||
0.957531 | − | 0.288331i | \(-0.0931004\pi\) | |||||||
\(752\) | 1.41421 | − | 1.41421i | 0.0515711 | − | 0.0515711i | ||||
\(753\) | 6.62641i | 0.241480i | ||||||||
\(754\) | 1.37288 | + | 0.510711i | 0.0499973 | + | 0.0185990i | ||||
\(755\) | − | 6.46892i | − | 0.235428i | ||||||
\(756\) | 2.02133 | − | 1.70711i | 0.0735152 | − | 0.0620869i | ||||
\(757\) | 36.8200 | 1.33825 | 0.669123 | − | 0.743152i | \(-0.266670\pi\) | ||||
0.669123 | + | 0.743152i | \(0.266670\pi\) | |||||||
\(758\) | 11.0232i | 0.400380i | ||||||||
\(759\) | 5.78380 | + | 5.78380i | 0.209939 | + | 0.209939i | ||||
\(760\) | 1.52991 | − | 1.52991i | 0.0554957 | − | 0.0554957i | ||||
\(761\) | 29.9773 | − | 29.9773i | 1.08668 | − | 1.08668i | 0.0908090 | − | 0.995868i | \(-0.471055\pi\) |
0.995868 | − | 0.0908090i | \(-0.0289453\pi\) | |||||||
\(762\) | −6.44893 | + | 6.44893i | −0.233620 | + | 0.233620i | ||||
\(763\) | 3.01149 | − | 35.7327i | 0.109023 | − | 1.29361i | ||||
\(764\) | 23.1833i | 0.838741i | ||||||||
\(765\) | −1.74290 | − | 1.74290i | −0.0630147 | − | 0.0630147i | ||||
\(766\) | −16.0324 | −0.579275 | ||||||||
\(767\) | −41.8639 | − | 15.5734i | −1.51162 | − | 0.562321i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −28.6613 | − | 28.6613i | −1.03355 | − | 1.03355i | −0.999417 | − | 0.0341363i | \(-0.989132\pi\) |
−0.0341363 | − | 0.999417i | \(-0.510868\pi\) | |||||||
\(770\) | −8.41546 | − | 0.709240i | −0.303272 | − | 0.0255592i | ||||
\(771\) | 10.5297i | 0.379218i | ||||||||
\(772\) | 13.6264 | − | 13.6264i | 0.490425 | − | 0.490425i | ||||
\(773\) | −31.7211 | − | 31.7211i | −1.14093 | − | 1.14093i | −0.988280 | − | 0.152650i | \(-0.951219\pi\) |
−0.152650 | − | 0.988280i | \(-0.548781\pi\) | |||||||
\(774\) | 1.74290 | + | 1.74290i | 0.0626472 | + | 0.0626472i | ||||
\(775\) | −5.37405 | + | 5.37405i | −0.193041 | + | 0.193041i | ||||
\(776\) | − | 14.5297i | − | 0.521586i | ||||||
\(777\) | 0.0807877 | − | 0.958584i | 0.00289824 | − | 0.0343890i | ||||
\(778\) | −12.4216 | − | 12.4216i | −0.445338 | − | 0.445338i | ||||
\(779\) | − | 6.74310i | − | 0.241596i | ||||||
\(780\) | 2.05713 | − | 5.52991i | 0.0736569 | − | 0.198003i | ||||
\(781\) | −14.2917 | −0.511398 | ||||||||
\(782\) | −4.46616 | − | 4.46616i | −0.159710 | − | 0.159710i | ||||
\(783\) | − | 0.406261i | − | 0.0145186i | ||||||
\(784\) | −1.17157 | + | 6.90126i | −0.0418419 | + | 0.246474i | ||||
\(785\) | 12.0885 | − | 12.0885i | 0.431459 | − | 0.431459i | ||||
\(786\) | −2.81573 | + | 2.81573i | −0.100434 | + | 0.100434i | ||||
\(787\) | −33.6855 | + | 33.6855i | −1.20076 | + | 1.20076i | −0.226823 | + | 0.973936i | \(0.572834\pi\) |
−0.973936 | + | 0.226823i | \(0.927166\pi\) | |||||||
\(788\) | −10.1950 | − | 10.1950i | −0.363183 | − | 0.363183i | ||||
\(789\) | − | 11.3310i | − | 0.403394i | ||||||
\(790\) | −2.33263 | −0.0829913 | ||||||||
\(791\) | −20.9947 | + | 17.7309i | −0.746484 | + | 0.630440i | ||||
\(792\) | 1.95063i | 0.0693127i | ||||||||
\(793\) | 38.4869 | − | 17.6164i | 1.36671 | − | 0.625578i | ||||
\(794\) | 34.8454i | 1.23662i | ||||||||
\(795\) | −15.5581 | + | 15.5581i | −0.551790 | + | 0.551790i | ||||
\(796\) | 1.42518i | 0.0505143i | ||||||||
\(797\) | −36.5386 | −1.29426 | −0.647132 | − | 0.762378i | \(-0.724032\pi\) | ||||
−0.647132 | + | 0.762378i | \(0.724032\pi\) | |||||||
\(798\) | 2.25710 | + | 2.67256i | 0.0799005 | + | 0.0946077i | ||||
\(799\) | 2.13016 | − | 2.13016i | 0.0753595 | − | 0.0753595i | ||||
\(800\) | 1.64203 | + | 1.64203i | 0.0580545 | + | 0.0580545i | ||||
\(801\) | −2.03017 | + | 2.03017i | −0.0717325 | + | 0.0717325i | ||||
\(802\) | 29.4844 | 1.04113 | ||||||||
\(803\) | −7.06226 | −0.249222 | ||||||||
\(804\) | −11.1012 | + | 11.1012i | −0.391510 | + | 0.391510i | ||||
\(805\) | 1.52465 | − | 18.0907i | 0.0537370 | − | 0.637614i | ||||
\(806\) | 4.91126 | + | 10.7297i | 0.172992 | + | 0.377937i | ||||
\(807\) | −11.6504 | −0.410115 | ||||||||
\(808\) | 1.36484 | + | 1.36484i | 0.0480151 | + | 0.0480151i | ||||
\(809\) | 19.7133 | 0.693082 | 0.346541 | − | 0.938035i | \(-0.387356\pi\) | ||||
0.346541 | + | 0.938035i | \(0.387356\pi\) | |||||||
\(810\) | −1.63640 | −0.0574974 | ||||||||
\(811\) | −0.988834 | − | 0.988834i | −0.0347227 | − | 0.0347227i | 0.689532 | − | 0.724255i | \(-0.257816\pi\) |
−0.724255 | + | 0.689532i | \(0.757816\pi\) | |||||||
\(812\) | 0.693530 | + | 0.821188i | 0.0243381 | + | 0.0288181i | ||||
\(813\) | 9.41876 | + | 9.41876i | 0.330330 | + | 0.330330i | ||||
\(814\) | 0.501508 | + | 0.501508i | 0.0175779 | + | 0.0175779i | ||||
\(815\) | − | 20.9954i | − | 0.735437i | ||||||
\(816\) | − | 1.50625i | − | 0.0527292i | ||||||
\(817\) | −2.30442 | + | 2.30442i | −0.0806216 | + | 0.0806216i | ||||
\(818\) | 19.5402 | 0.683206 | ||||||||
\(819\) | 8.62990 | + | 4.06508i | 0.301553 | + | 0.142045i | ||||
\(820\) | −8.34564 | −0.291443 | ||||||||
\(821\) | −7.22975 | + | 7.22975i | −0.252320 | + | 0.252320i | −0.821921 | − | 0.569601i | \(-0.807098\pi\) |
0.569601 | + | 0.821921i | \(0.307098\pi\) | |||||||
\(822\) | − | 19.6389i | − | 0.684985i | ||||||
\(823\) | − | 1.41848i | − | 0.0494451i | −0.999694 | − | 0.0247225i | \(-0.992130\pi\) | ||
0.999694 | − | 0.0247225i | \(-0.00787023\pi\) | |||||||
\(824\) | −5.62070 | − | 5.62070i | −0.195806 | − | 0.195806i | ||||
\(825\) | −3.20299 | − | 3.20299i | −0.111514 | − | 0.111514i | ||||
\(826\) | −21.1482 | − | 25.0409i | −0.735839 | − | 0.871284i | ||||
\(827\) | −18.4680 | − | 18.4680i | −0.642197 | − | 0.642197i | 0.308898 | − | 0.951095i | \(-0.400040\pi\) |
−0.951095 | + | 0.308898i | \(0.900040\pi\) | |||||||
\(828\) | −4.19327 | −0.145726 | ||||||||
\(829\) | 2.23560 | 0.0776455 | 0.0388228 | − | 0.999246i | \(-0.487639\pi\) | ||||
0.0388228 | + | 0.999246i | \(0.487639\pi\) | |||||||
\(830\) | −8.03142 | − | 8.03142i | −0.278775 | − | 0.278775i | ||||
\(831\) | 5.99357 | 0.207915 | ||||||||
\(832\) | 3.27843 | − | 1.50062i | 0.113659 | − | 0.0520248i | ||||
\(833\) | −1.76468 | + | 10.3950i | −0.0611425 | + | 0.360166i | ||||
\(834\) | −5.21247 | + | 5.21247i | −0.180493 | + | 0.180493i | ||||
\(835\) | 20.9377 | 0.724580 | ||||||||
\(836\) | −2.57908 | −0.0891995 | ||||||||
\(837\) | 2.31423 | − | 2.31423i | 0.0799914 | − | 0.0799914i | ||||
\(838\) | −11.5856 | − | 11.5856i | −0.400218 | − | 0.400218i | ||||
\(839\) | 18.5594 | − | 18.5594i | 0.640740 | − | 0.640740i | −0.309997 | − | 0.950738i | \(-0.600328\pi\) |
0.950738 | + | 0.309997i | \(0.100328\pi\) | |||||||
\(840\) | 3.30772 | − | 2.79352i | 0.114127 | − | 0.0963855i | ||||
\(841\) | −28.8350 | −0.994309 | ||||||||
\(842\) | 24.3547i | 0.839319i | ||||||||
\(843\) | 12.4581 | − | 12.4581i | 0.429081 | − | 0.429081i | ||||
\(844\) | − | 5.45234i | − | 0.187677i | ||||||
\(845\) | 21.2164 | − | 1.55417i | 0.729867 | − | 0.0534651i | ||||
\(846\) | − | 2.00000i | − | 0.0687614i | ||||||
\(847\) | −12.2827 | − | 14.5436i | −0.422039 | − | 0.499723i | ||||
\(848\) | −13.4456 | −0.461725 | ||||||||
\(849\) | − | 12.9995i | − | 0.446141i | ||||||
\(850\) | 2.47330 | + | 2.47330i | 0.0848336 | + | 0.0848336i | ||||
\(851\) | −1.07809 | + | 1.07809i | −0.0369565 | + | 0.0369565i | ||||
\(852\) | 5.18078 | − | 5.18078i | 0.177490 | − | 0.177490i | ||||
\(853\) | −14.9138 | + | 14.9138i | −0.510637 | + | 0.510637i | −0.914722 | − | 0.404084i | \(-0.867590\pi\) |
0.404084 | + | 0.914722i | \(0.367590\pi\) | |||||||
\(854\) | 30.9498 | + | 2.60840i | 1.05908 | + | 0.0892575i | ||||
\(855\) | − | 2.16362i | − | 0.0739942i | ||||||
\(856\) | 2.35689 | + | 2.35689i | 0.0805569 | + | 0.0805569i | ||||
\(857\) | −54.4574 | −1.86023 | −0.930115 | − | 0.367268i | \(-0.880293\pi\) | ||||
−0.930115 | + | 0.367268i | \(0.880293\pi\) | |||||||
\(858\) | −6.39501 | + | 2.92717i | −0.218322 | + | 0.0999318i | ||||
\(859\) | − | 39.4294i | − | 1.34531i | −0.739954 | − | 0.672657i | \(-0.765153\pi\) | ||
0.739954 | − | 0.672657i | \(-0.234847\pi\) | |||||||
\(860\) | 2.85209 | + | 2.85209i | 0.0972554 | + | 0.0972554i | ||||
\(861\) | 1.13317 | − | 13.4456i | 0.0386184 | − | 0.458226i | ||||
\(862\) | − | 31.9257i | − | 1.08739i | ||||||
\(863\) | 18.5773 | − | 18.5773i | 0.632379 | − | 0.632379i | −0.316285 | − | 0.948664i | \(-0.602436\pi\) |
0.948664 | + | 0.316285i | \(0.102436\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | 0.0184046 | + | 0.0184046i | 0.000625776 | + | 0.000625776i | ||||
\(866\) | 25.3197 | − | 25.3197i | 0.860400 | − | 0.860400i | ||||
\(867\) | 14.7312i | 0.500298i | ||||||||
\(868\) | −0.727190 | + | 8.62845i | −0.0246824 | + | 0.292869i | ||||
\(869\) | 1.96614 | + | 1.96614i | 0.0666969 | + | 0.0666969i | ||||
\(870\) | − | 0.664807i | − | 0.0225391i | ||||||
\(871\) | −53.0535 | − | 19.7359i | −1.79765 | − | 0.668725i | ||||
\(872\) | −13.5536 | −0.458982 | ||||||||
\(873\) | −10.2741 | − | 10.2741i | −0.347724 | − | 0.347724i | ||||
\(874\) | − | 5.54426i | − | 0.187537i | ||||||
\(875\) | −2.66231 | + | 31.5895i | −0.0900024 | + | 1.06792i | ||||
\(876\) | 2.56008 | − | 2.56008i | 0.0864971 | − | 0.0864971i | ||||
\(877\) | 5.10175 | − | 5.10175i | 0.172274 | − | 0.172274i | −0.615704 | − | 0.787978i | \(-0.711128\pi\) |
0.787978 | + | 0.615704i | \(0.211128\pi\) | |||||||
\(878\) | 6.92243 | − | 6.92243i | 0.233621 | − | 0.233621i | ||||
\(879\) | 1.51545 | + | 1.51545i | 0.0511149 | + | 0.0511149i | ||||
\(880\) | 3.19202i | 0.107603i | ||||||||
\(881\) | 3.68123 | 0.124024 | 0.0620119 | − | 0.998075i | \(-0.480248\pi\) | ||||
0.0620119 | + | 0.998075i | \(0.480248\pi\) | |||||||
\(882\) | 4.05150 | + | 5.70836i | 0.136421 | + | 0.192210i | ||||
\(883\) | − | 51.2530i | − | 1.72480i | −0.506226 | − | 0.862401i | \(-0.668960\pi\) | ||
0.506226 | − | 0.862401i | \(-0.331040\pi\) | |||||||
\(884\) | 4.93813 | − | 2.26031i | 0.166087 | − | 0.0760226i | ||||
\(885\) | 20.2723i | 0.681446i | ||||||||
\(886\) | −1.91893 | + | 1.91893i | −0.0644679 | + | 0.0644679i | ||||
\(887\) | 35.1063i | 1.17875i | 0.807858 | + | 0.589377i | \(0.200627\pi\) | ||||
−0.807858 | + | 0.589377i | \(0.799373\pi\) | |||||||
\(888\) | −0.363595 | −0.0122015 | ||||||||
\(889\) | −15.5691 | − | 18.4349i | −0.522170 | − | 0.618286i | ||||
\(890\) | −3.32218 | + | 3.32218i | −0.111360 | + | 0.111360i | ||||
\(891\) | 1.37930 | + | 1.37930i | 0.0462084 | + | 0.0462084i | ||||
\(892\) | −18.3548 | + | 18.3548i | −0.614566 | + | 0.614566i | ||||
\(893\) | 2.64436 | 0.0884901 | ||||||||
\(894\) | 16.5995 | 0.555171 | ||||||||
\(895\) | −12.0005 | + | 12.0005i | −0.401131 | + | 0.401131i | ||||
\(896\) | 2.63640 | + | 0.222191i | 0.0880761 | + | 0.00742289i | ||||
\(897\) | −6.29253 | − | 13.7474i | −0.210101 | − | 0.459011i | ||||
\(898\) | 20.9057 | 0.697632 | ||||||||
\(899\) | 0.940179 | + | 0.940179i | 0.0313567 | + | 0.0313567i | ||||
\(900\) | 2.32218 | 0.0774060 | ||||||||
\(901\) | −20.2525 | −0.674707 | ||||||||
\(902\) | 7.03444 | + | 7.03444i | 0.234221 | + | 0.234221i | ||||
\(903\) | −4.98225 | + | 4.20773i | −0.165799 | + | 0.140025i | ||||
\(904\) | 7.34440 | + | 7.34440i | 0.244271 | + | 0.244271i | ||||
\(905\) | −1.65436 | − | 1.65436i | −0.0549926 | − | 0.0549926i | ||||
\(906\) | − | 3.95313i | − | 0.131334i | ||||||
\(907\) | 39.1741i | 1.30075i | 0.759612 | + | 0.650377i | \(0.225389\pi\) | ||||
−0.759612 | + | 0.650377i | \(0.774611\pi\) | |||||||
\(908\) | −6.91251 | + | 6.91251i | −0.229400 | + | 0.229400i | ||||
\(909\) | 1.93018 | 0.0640201 | ||||||||
\(910\) | 14.1220 | + | 6.65211i | 0.468140 | + | 0.220515i | ||||
\(911\) | −36.7864 | −1.21879 | −0.609394 | − | 0.792868i | \(-0.708587\pi\) | ||||
−0.609394 | + | 0.792868i | \(0.708587\pi\) | |||||||
\(912\) | 0.934922 | − | 0.934922i | 0.0309583 | − | 0.0309583i | ||||
\(913\) | 13.5392i | 0.448081i | ||||||||
\(914\) | 25.4446i | 0.841632i | ||||||||
\(915\) | −13.5838 | − | 13.5838i | −0.449067 | − | 0.449067i | ||||
\(916\) | 2.96035 | + | 2.96035i | 0.0978127 | + | 0.0978127i | ||||
\(917\) | −6.79778 | − | 8.04905i | −0.224483 | − | 0.265803i | ||||
\(918\) | −1.06508 | − | 1.06508i | −0.0351528 | − | 0.0351528i | ||||
\(919\) | 38.3072 | 1.26364 | 0.631820 | − | 0.775115i | \(-0.282308\pi\) | ||||
0.631820 | + | 0.775115i | \(0.282308\pi\) | |||||||
\(920\) | −6.86189 | −0.226230 | ||||||||
\(921\) | −4.87286 | − | 4.87286i | −0.160566 | − | 0.160566i | ||||
\(922\) | 33.1526 | 1.09182 | ||||||||
\(923\) | 24.7592 | + | 9.21043i | 0.814960 | + | 0.303165i | ||||
\(924\) | −5.14265 | − | 0.433413i | −0.169181 | − | 0.0142583i | ||||
\(925\) | 0.597033 | − | 0.597033i | 0.0196303 | − | 0.0196303i | ||||
\(926\) | 17.6050 | 0.578536 | ||||||||
\(927\) | −7.94886 | −0.261075 | ||||||||
\(928\) | 0.287270 | − | 0.287270i | 0.00943009 | − | 0.00943009i | ||||
\(929\) | −30.8995 | − | 30.8995i | −1.01378 | − | 1.01378i | −0.999904 | − | 0.0138758i | \(-0.995583\pi\) |
−0.0138758 | − | 0.999904i | \(-0.504417\pi\) | |||||||
\(930\) | 3.78701 | − | 3.78701i | 0.124181 | − | 0.124181i | ||||
\(931\) | −7.54747 | + | 5.35681i | −0.247358 | + | 0.175562i | ||||
\(932\) | −6.59953 | −0.216175 | ||||||||
\(933\) | 26.8179i | 0.877979i | ||||||||
\(934\) | 19.5821 | − | 19.5821i | 0.640744 | − | 0.640744i | ||||
\(935\) | 4.80798i | 0.157238i | ||||||||
\(936\) | 1.25710 | − | 3.37930i | 0.0410896 | − | 0.110456i | ||||
\(937\) | − | 23.1904i | − | 0.757596i | −0.925479 | − | 0.378798i | \(-0.876337\pi\) | ||
0.925479 | − | 0.378798i | \(-0.123663\pi\) | |||||||
\(938\) | −26.8008 | − | 31.7340i | −0.875076 | − | 1.03615i | ||||
\(939\) | 1.96858 | 0.0642422 | ||||||||
\(940\) | − | 3.27281i | − | 0.106747i | ||||||
\(941\) | 21.8417 | + | 21.8417i | 0.712018 | + | 0.712018i | 0.966957 | − | 0.254939i | \(-0.0820555\pi\) |
−0.254939 | + | 0.966957i | \(0.582056\pi\) | |||||||
\(942\) | 7.38726 | − | 7.38726i | 0.240690 | − | 0.240690i | ||||
\(943\) | −15.1219 | + | 15.1219i | −0.492438 | + | 0.492438i | ||||
\(944\) | −8.75986 | + | 8.75986i | −0.285109 | + | 0.285109i | ||||
\(945\) | 0.363595 | − | 4.31423i | 0.0118277 | − | 0.140342i | ||||
\(946\) | − | 4.80798i | − | 0.156321i | ||||||
\(947\) | 18.1943 | + | 18.1943i | 0.591236 | + | 0.591236i | 0.937965 | − | 0.346729i | \(-0.112708\pi\) |
−0.346729 | + | 0.937965i | \(0.612708\pi\) | |||||||
\(948\) | −1.42546 | −0.0462968 | ||||||||
\(949\) | 12.2348 | + | 4.55133i | 0.397157 | + | 0.147742i | ||||
\(950\) | 3.07034i | 0.0996148i | ||||||||
\(951\) | −9.47705 | − | 9.47705i | −0.307314 | − | 0.307314i | ||||
\(952\) | 3.97108 | + | 0.334675i | 0.128703 | + | 0.0108469i | ||||
\(953\) | − | 10.2539i | − | 0.332156i | −0.986113 | − | 0.166078i | \(-0.946890\pi\) | ||
0.986113 | − | 0.166078i | \(-0.0531104\pi\) | |||||||
\(954\) | −9.50750 | + | 9.50750i | −0.307817 | + | 0.307817i | ||||
\(955\) | 26.8257 | + | 26.8257i | 0.868058 | + | 0.868058i | ||||
\(956\) | 10.9611 | + | 10.9611i | 0.354507 | + | 0.354507i | ||||
\(957\) | −0.560357 | + | 0.560357i | −0.0181138 | + | 0.0181138i | ||||
\(958\) | − | 10.8813i | − | 0.351560i | ||||||
\(959\) | 51.7761 | + | 4.36360i | 1.67194 | + | 0.140908i | ||||
\(960\) | −1.15711 | − | 1.15711i | −0.0373457 | − | 0.0373457i | ||||
\(961\) | − | 20.2887i | − | 0.654475i | ||||||
\(962\) | −0.545620 | − | 1.19202i | −0.0175915 | − | 0.0384323i | ||||
\(963\) | 3.33315 | 0.107409 | ||||||||
\(964\) | 20.1598 | + | 20.1598i | 0.649304 | + | 0.649304i | ||||
\(965\) | − | 31.5346i | − | 1.01513i | ||||||
\(966\) | 0.931709 | − | 11.0552i | 0.0299772 | − | 0.355694i | ||||
\(967\) | 21.4696 | − | 21.4696i | 0.690417 | − | 0.690417i | −0.271907 | − | 0.962324i | \(-0.587654\pi\) |
0.962324 | + | 0.271907i | \(0.0876542\pi\) | |||||||
\(968\) | −5.08766 | + | 5.08766i | −0.163524 | + | 0.163524i | ||||
\(969\) | 1.40822 | − | 1.40822i | 0.0452387 | − | 0.0452387i | ||||
\(970\) | −16.8125 | − | 16.8125i | −0.539818 | − | 0.539818i | ||||
\(971\) | 43.1357i | 1.38429i | 0.721759 | + | 0.692145i | \(0.243334\pi\) | ||||
−0.721759 | + | 0.692145i | \(0.756666\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −12.5840 | − | 14.9004i | −0.403425 | − | 0.477683i | ||||
\(974\) | 5.16804i | 0.165595i | ||||||||
\(975\) | 3.48472 | + | 7.61311i | 0.111600 | + | 0.243815i | ||||
\(976\) | − | 11.7394i | − | 0.375769i | ||||||
\(977\) | −17.7281 | + | 17.7281i | −0.567173 | + | 0.567173i | −0.931335 | − | 0.364163i | \(-0.881355\pi\) |
0.364163 | + | 0.931335i | \(0.381355\pi\) | |||||||
\(978\) | − | 12.8302i | − | 0.410264i | ||||||
\(979\) | 5.60044 | 0.178991 | ||||||||
\(980\) | 6.62990 | + | 9.34118i | 0.211784 | + | 0.298393i | ||||
\(981\) | −9.58382 | + | 9.58382i | −0.305988 | + | 0.305988i | ||||
\(982\) | 9.16776 | + | 9.16776i | 0.292555 | + | 0.292555i | ||||
\(983\) | −30.2120 | + | 30.2120i | −0.963613 | + | 0.963613i | −0.999361 | − | 0.0357478i | \(-0.988619\pi\) |
0.0357478 | + | 0.999361i | \(0.488619\pi\) | |||||||
\(984\) | −5.09999 | −0.162582 | ||||||||
\(985\) | −23.5936 | −0.751755 | ||||||||
\(986\) | 0.432700 | − | 0.432700i | 0.0137800 | − | 0.0137800i | ||||
\(987\) | 5.27281 | + | 0.444383i | 0.167835 | + | 0.0141449i | ||||
\(988\) | 4.46804 | + | 1.66211i | 0.142147 | + | 0.0528788i | ||||
\(989\) | 10.3357 | 0.328656 | ||||||||
\(990\) | 2.25710 | + | 2.25710i | 0.0717354 | + | 0.0717354i | ||||
\(991\) | −45.3635 | −1.44102 | −0.720510 | − | 0.693445i | \(-0.756092\pi\) | ||||
−0.720510 | + | 0.693445i | \(0.756092\pi\) | |||||||
\(992\) | 3.27281 | 0.103912 | ||||||||
\(993\) | 13.2853 | + | 13.2853i | 0.421596 | + | 0.421596i | ||||
\(994\) | 12.5075 | + | 14.8097i | 0.396714 | + | 0.469737i | ||||
\(995\) | 1.64910 | + | 1.64910i | 0.0522799 | + | 0.0522799i | ||||
\(996\) | −4.90797 | − | 4.90797i | −0.155515 | − | 0.155515i | ||||
\(997\) | − | 29.1744i | − | 0.923963i | −0.886890 | − | 0.461981i | \(-0.847139\pi\) | ||
0.886890 | − | 0.461981i | \(-0.152861\pi\) | |||||||
\(998\) | − | 22.4835i | − | 0.711703i | ||||||
\(999\) | −0.257101 | + | 0.257101i | −0.00813430 | + | 0.00813430i |
(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 | 546.2.o.b.265.3 | ✓ | 8 | |
3.2 | odd | 2 | 1638.2.x.c.811.2 | 8 | |||
7.6 | odd | 2 | 546.2.o.c.265.4 | yes | 8 | ||
13.8 | odd | 4 | 546.2.o.c.307.4 | yes | 8 | ||
21.20 | even | 2 | 1638.2.x.a.811.1 | 8 | |||
39.8 | even | 4 | 1638.2.x.a.307.1 | 8 | |||
91.34 | even | 4 | inner | 546.2.o.b.307.3 | yes | 8 | |
273.125 | odd | 4 | 1638.2.x.c.307.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.o.b.265.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
546.2.o.b.307.3 | yes | 8 | 91.34 | even | 4 | inner | |
546.2.o.c.265.4 | yes | 8 | 7.6 | odd | 2 | ||
546.2.o.c.307.4 | yes | 8 | 13.8 | odd | 4 | ||
1638.2.x.a.307.1 | 8 | 39.8 | even | 4 | |||
1638.2.x.a.811.1 | 8 | 21.20 | even | 2 | |||
1638.2.x.c.307.2 | 8 | 273.125 | odd | 4 | |||
1638.2.x.c.811.2 | 8 | 3.2 | odd | 2 |