Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1650,2,Mod(1649,1650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1650, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1650.1649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1650.f (of order \(2\), degree \(1\), not 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: | \(13.1753163335\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2051727616.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 37x^{4} + 36x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 330) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1649.5 | ||
Root | \(-1.18994i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1650.1649 |
Dual form | 1650.2.f.f.1649.1 |
$q$-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 \(\left(\mathbb{Z}/1650\mathbb{Z}\right)^\times\).
\(n\) | \(551\) | \(727\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.03743 | − | 1.38699i | −0.598959 | − | 0.800780i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.38699 | − | 1.03743i | 0.566237 | − | 0.423528i | ||||
\(7\) | 0.394100 | 0.148956 | 0.0744779 | − | 0.997223i | \(-0.476271\pi\) | ||||
0.0744779 | + | 0.997223i | \(0.476271\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.847487 | + | 2.87781i | −0.282496 | + | 0.959269i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.26480 | + | 0.584041i | −0.984373 | + | 0.176095i | ||||
\(12\) | 1.03743 | + | 1.38699i | 0.299480 | + | 0.400390i | ||||
\(13\) | 2.37988 | 0.660060 | 0.330030 | − | 0.943970i | \(-0.392941\pi\) | ||||
0.330030 | + | 0.943970i | \(0.392941\pi\) | |||||||
\(14\) | 0.394100i | 0.105328i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.906774i | 0.219925i | 0.993936 | + | 0.109963i | \(0.0350731\pi\) | ||||
−0.993936 | + | 0.109963i | \(0.964927\pi\) | |||||||
\(18\) | −2.87781 | − | 0.847487i | −0.678305 | − | 0.199755i | ||||
\(19\) | − | 3.69497i | − | 0.847685i | −0.905736 | − | 0.423843i | \(-0.860681\pi\) | ||
0.905736 | − | 0.423843i | \(-0.139319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.408850 | − | 0.546613i | −0.0892184 | − | 0.119281i | ||||
\(22\) | −0.584041 | − | 3.26480i | −0.124518 | − | 0.696057i | ||||
\(23\) | 3.54796 | 0.739801 | 0.369901 | − | 0.929071i | \(-0.379392\pi\) | ||||
0.369901 | + | 0.929071i | \(0.379392\pi\) | |||||||
\(24\) | −1.38699 | + | 1.03743i | −0.283118 | + | 0.211764i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.37988i | 0.466733i | ||||||||
\(27\) | 4.87070 | − | 1.81006i | 0.937366 | − | 0.348346i | ||||
\(28\) | −0.394100 | −0.0744779 | ||||||||
\(29\) | −3.37573 | −0.626857 | −0.313429 | − | 0.949612i | \(-0.601478\pi\) | ||||
−0.313429 | + | 0.949612i | \(0.601478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.66654 | 0.658530 | 0.329265 | − | 0.944238i | \(-0.393199\pi\) | ||||
0.329265 | + | 0.944238i | \(0.393199\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 4.19705 | + | 3.92234i | 0.730613 | + | 0.682792i | ||||
\(34\) | −0.906774 | −0.155510 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.847487 | − | 2.87781i | 0.141248 | − | 0.479634i | ||||
\(37\) | − | 4.58753i | − | 0.754185i | −0.926176 | − | 0.377093i | \(-0.876924\pi\) | ||
0.926176 | − | 0.377093i | \(-0.123076\pi\) | |||||||
\(38\) | 3.69497 | 0.599404 | ||||||||
\(39\) | −2.46896 | − | 3.30087i | −0.395349 | − | 0.528563i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.14971 | −1.27277 | −0.636386 | − | 0.771371i | \(-0.719571\pi\) | ||||
−0.636386 | + | 0.771371i | \(0.719571\pi\) | |||||||
\(42\) | 0.546613 | − | 0.408850i | 0.0843442 | − | 0.0630870i | ||||
\(43\) | 2.60175 | 0.396763 | 0.198381 | − | 0.980125i | \(-0.436432\pi\) | ||||
0.198381 | + | 0.980125i | \(0.436432\pi\) | |||||||
\(44\) | 3.26480 | − | 0.584041i | 0.492187 | − | 0.0880475i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.54796i | 0.523119i | ||||||||
\(47\) | 3.39825 | 0.495686 | 0.247843 | − | 0.968800i | \(-0.420278\pi\) | ||||
0.247843 | + | 0.968800i | \(0.420278\pi\) | |||||||
\(48\) | −1.03743 | − | 1.38699i | −0.149740 | − | 0.200195i | ||||
\(49\) | −6.84469 | −0.977812 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.25769 | − | 0.940713i | 0.176111 | − | 0.131726i | ||||
\(52\) | −2.37988 | −0.330030 | ||||||||
\(53\) | 6.45474 | 0.886626 | 0.443313 | − | 0.896367i | \(-0.353803\pi\) | ||||
0.443313 | + | 0.896367i | \(0.353803\pi\) | |||||||
\(54\) | 1.81006 | + | 4.87070i | 0.246318 | + | 0.662818i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 0.394100i | − | 0.0526638i | ||||||
\(57\) | −5.12489 | + | 3.83327i | −0.678809 | + | 0.507729i | ||||
\(58\) | − | 3.37573i | − | 0.443255i | ||||||
\(59\) | − | 7.76983i | − | 1.01155i | −0.862667 | − | 0.505773i | \(-0.831207\pi\) | ||
0.862667 | − | 0.505773i | \(-0.168793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.8346i | − | 1.64330i | −0.569989 | − | 0.821652i | \(-0.693053\pi\) | ||
0.569989 | − | 0.821652i | \(-0.306947\pi\) | |||||||
\(62\) | 3.66654i | 0.465651i | ||||||||
\(63\) | −0.333995 | + | 1.13414i | −0.0420794 | + | 0.142889i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.92234 | + | 4.19705i | −0.482807 | + | 0.516621i | ||||
\(67\) | − | 11.9195i | − | 1.45620i | −0.685469 | − | 0.728102i | \(-0.740403\pi\) | ||
0.685469 | − | 0.728102i | \(-0.259597\pi\) | |||||||
\(68\) | − | 0.906774i | − | 0.109963i | ||||||
\(69\) | −3.68076 | − | 4.92099i | −0.443111 | − | 0.592418i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.58753i | 0.307083i | 0.988142 | + | 0.153542i | \(0.0490679\pi\) | ||||
−0.988142 | + | 0.153542i | \(0.950932\pi\) | |||||||
\(72\) | 2.87781 | + | 0.847487i | 0.339153 | + | 0.0998773i | ||||
\(73\) | −11.8911 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(74\) | 4.58753 | 0.533290 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.69497i | 0.423843i | ||||||||
\(77\) | −1.28666 | + | 0.230170i | −0.146628 | + | 0.0262303i | ||||
\(78\) | 3.30087 | − | 2.46896i | 0.373750 | − | 0.279554i | ||||
\(79\) | − | 2.56633i | − | 0.288735i | −0.989524 | − | 0.144368i | \(-0.953885\pi\) | ||
0.989524 | − | 0.144368i | \(-0.0461148\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.56353 | − | 4.87781i | −0.840392 | − | 0.541978i | ||||
\(82\) | − | 8.14971i | − | 0.899985i | ||||||
\(83\) | − | 1.69767i | − | 0.186344i | −0.995650 | − | 0.0931720i | \(-0.970299\pi\) | ||
0.995650 | − | 0.0931720i | \(-0.0297006\pi\) | |||||||
\(84\) | 0.408850 | + | 0.546613i | 0.0446092 | + | 0.0596404i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.60175i | 0.280554i | ||||||||
\(87\) | 3.50208 | + | 4.68211i | 0.375462 | + | 0.501974i | ||||
\(88\) | 0.584041 | + | 3.26480i | 0.0622590 | + | 0.348028i | ||||
\(89\) | − | 15.3036i | − | 1.62218i | −0.584924 | − | 0.811088i | \(-0.698876\pi\) | ||
0.584924 | − | 0.811088i | \(-0.301124\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.937911 | 0.0983198 | ||||||||
\(92\) | −3.54796 | −0.369901 | ||||||||
\(93\) | −3.80377 | − | 5.08545i | −0.394432 | − | 0.527337i | ||||
\(94\) | 3.39825i | 0.350503i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.38699 | − | 1.03743i | 0.141559 | − | 0.105882i | ||||
\(97\) | − | 10.1213i | − | 1.02766i | −0.857892 | − | 0.513830i | \(-0.828226\pi\) | ||
0.857892 | − | 0.513830i | \(-0.171774\pi\) | |||||||
\(98\) | − | 6.84469i | − | 0.691418i | ||||||
\(99\) | 1.08612 | − | 9.89042i | 0.109159 | − | 0.994024i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.01837 | 0.300339 | 0.150170 | − | 0.988660i | \(-0.452018\pi\) | ||||
0.150170 | + | 0.988660i | \(0.452018\pi\) | |||||||
\(102\) | 0.940713 | + | 1.25769i | 0.0931444 | + | 0.124530i | ||||
\(103\) | − | 0.601748i | − | 0.0592920i | −0.999560 | − | 0.0296460i | \(-0.990562\pi\) | ||
0.999560 | − | 0.0296460i | \(-0.00943800\pi\) | |||||||
\(104\) | − | 2.37988i | − | 0.233367i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.45474i | 0.626940i | ||||||||
\(107\) | − | 15.2456i | − | 1.47385i | −0.675974 | − | 0.736926i | \(-0.736277\pi\) | ||
0.675974 | − | 0.736926i | \(-0.263723\pi\) | |||||||
\(108\) | −4.87070 | + | 1.81006i | −0.468683 | + | 0.174173i | ||||
\(109\) | 18.3770i | 1.76020i | 0.474793 | + | 0.880098i | \(0.342523\pi\) | ||||
−0.474793 | + | 0.880098i | \(0.657477\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.36286 | + | 4.75923i | −0.603936 | + | 0.451726i | ||||
\(112\) | 0.394100 | 0.0372389 | ||||||||
\(113\) | −6.37988 | −0.600169 | −0.300084 | − | 0.953913i | \(-0.597015\pi\) | ||||
−0.300084 | + | 0.953913i | \(0.597015\pi\) | |||||||
\(114\) | −3.83327 | − | 5.12489i | −0.359019 | − | 0.479990i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.37573 | 0.313429 | ||||||||
\(117\) | −2.01692 | + | 6.84884i | −0.186464 | + | 0.633175i | ||||
\(118\) | 7.76983 | 0.715271 | ||||||||
\(119\) | 0.357360i | 0.0327591i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3178 | − | 3.81355i | 0.937981 | − | 0.346686i | ||||
\(122\) | 12.8346 | 1.16199 | ||||||||
\(123\) | 8.45474 | + | 11.3036i | 0.762338 | + | 1.01921i | ||||
\(124\) | −3.66654 | −0.329265 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.13414 | − | 0.333995i | −0.101037 | − | 0.0297546i | ||||
\(127\) | 22.0338 | 1.95519 | 0.977593 | − | 0.210502i | \(-0.0675098\pi\) | ||||
0.977593 | + | 0.210502i | \(0.0675098\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −2.69913 | − | 3.60860i | −0.237645 | − | 0.317720i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.97748 | 0.172773 | 0.0863865 | − | 0.996262i | \(-0.472468\pi\) | ||||
0.0863865 | + | 0.996262i | \(0.472468\pi\) | |||||||
\(132\) | −4.19705 | − | 3.92234i | −0.365306 | − | 0.341396i | ||||
\(133\) | − | 1.45619i | − | 0.126268i | ||||||
\(134\) | 11.9195 | 1.02969 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.906774 | 0.0777552 | ||||||||
\(137\) | 19.6172 | 1.67601 | 0.838006 | − | 0.545661i | \(-0.183721\pi\) | ||||
0.838006 | + | 0.545661i | \(0.183721\pi\) | |||||||
\(138\) | 4.92099 | − | 3.68076i | 0.418903 | − | 0.313327i | ||||
\(139\) | − | 18.7230i | − | 1.58807i | −0.607875 | − | 0.794033i | \(-0.707978\pi\) | ||
0.607875 | − | 0.794033i | \(-0.292022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.52544 | − | 4.71334i | −0.296896 | − | 0.396935i | ||||
\(142\) | −2.58753 | −0.217141 | ||||||||
\(143\) | −7.76983 | + | 1.38995i | −0.649746 | + | 0.116233i | ||||
\(144\) | −0.847487 | + | 2.87781i | −0.0706239 | + | 0.239817i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 11.8911i | − | 0.984115i | ||||||
\(147\) | 7.10087 | + | 9.49352i | 0.585670 | + | 0.783012i | ||||
\(148\) | 4.58753i | 0.377093i | ||||||||
\(149\) | −22.0113 | −1.80324 | −0.901619 | − | 0.432532i | \(-0.857620\pi\) | ||||
−0.901619 | + | 0.432532i | \(0.857620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.9278i | 1.13343i | 0.823913 | + | 0.566716i | \(0.191786\pi\) | ||||
−0.823913 | + | 0.566716i | \(0.808214\pi\) | |||||||
\(152\) | −3.69497 | −0.299702 | ||||||||
\(153\) | −2.60952 | − | 0.768479i | −0.210967 | − | 0.0621279i | ||||
\(154\) | −0.230170 | − | 1.28666i | −0.0185477 | − | 0.103682i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.46896 | + | 3.30087i | 0.197675 | + | 0.264281i | ||||
\(157\) | 2.62427i | 0.209440i | 0.994502 | + | 0.104720i | \(0.0333946\pi\) | ||||
−0.994502 | + | 0.104720i | \(0.966605\pi\) | |||||||
\(158\) | 2.56633 | 0.204167 | ||||||||
\(159\) | −6.69632 | − | 8.95266i | −0.531053 | − | 0.709992i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.39825 | 0.110198 | ||||||||
\(162\) | 4.87781 | − | 7.56353i | 0.383237 | − | 0.594247i | ||||
\(163\) | − | 6.77398i | − | 0.530579i | −0.964169 | − | 0.265290i | \(-0.914532\pi\) | ||
0.964169 | − | 0.265290i | \(-0.0854676\pi\) | |||||||
\(164\) | 8.14971 | 0.636386 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.69767 | 0.131765 | ||||||||
\(167\) | − | 16.7542i | − | 1.29648i | −0.761438 | − | 0.648238i | \(-0.775506\pi\) | ||
0.761438 | − | 0.648238i | \(-0.224494\pi\) | |||||||
\(168\) | −0.546613 | + | 0.408850i | −0.0421721 | + | 0.0315435i | ||||
\(169\) | −7.33616 | −0.564320 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.6334 | + | 3.13144i | 0.813158 | + | 0.239467i | ||||
\(172\) | −2.60175 | −0.198381 | ||||||||
\(173\) | − | 13.0959i | − | 0.995665i | −0.867273 | − | 0.497832i | \(-0.834129\pi\) | ||
0.867273 | − | 0.497832i | \(-0.165871\pi\) | |||||||
\(174\) | −4.68211 | + | 3.50208i | −0.354950 | + | 0.265492i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.26480 | + | 0.584041i | −0.246093 | + | 0.0440237i | ||||
\(177\) | −10.7767 | + | 8.06064i | −0.810025 | + | 0.605875i | ||||
\(178\) | 15.3036 | 1.14705 | ||||||||
\(179\) | 14.9816i | 1.11978i | 0.828567 | + | 0.559890i | \(0.189157\pi\) | ||||
−0.828567 | + | 0.559890i | \(0.810843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.9687 | 1.78158 | 0.890788 | − | 0.454419i | \(-0.150153\pi\) | ||||
0.890788 | + | 0.454419i | \(0.150153\pi\) | |||||||
\(182\) | 0.937911i | 0.0695226i | ||||||||
\(183\) | −17.8015 | + | 13.3150i | −1.31592 | + | 0.984272i | ||||
\(184\) | − | 3.54796i | − | 0.261559i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.08545 | − | 3.80377i | 0.372884 | − | 0.278906i | ||||
\(187\) | −0.529593 | − | 2.96043i | −0.0387277 | − | 0.216488i | ||||
\(188\) | −3.39825 | −0.247843 | ||||||||
\(189\) | 1.91954 | − | 0.713344i | 0.139626 | − | 0.0518881i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 21.9249i | − | 1.58643i | −0.608940 | − | 0.793217i | \(-0.708405\pi\) | ||
0.608940 | − | 0.793217i | \(-0.291595\pi\) | |||||||
\(192\) | 1.03743 | + | 1.38699i | 0.0748699 | + | 0.100097i | ||||
\(193\) | −21.8699 | −1.57423 | −0.787115 | − | 0.616806i | \(-0.788426\pi\) | ||||
−0.787115 | + | 0.616806i | \(0.788426\pi\) | |||||||
\(194\) | 10.1213 | 0.726665 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.84469 | 0.488906 | ||||||||
\(197\) | 18.0338i | 1.28486i | 0.766345 | + | 0.642429i | \(0.222073\pi\) | ||||
−0.766345 | + | 0.642429i | \(0.777927\pi\) | |||||||
\(198\) | 9.89042 | + | 1.08612i | 0.702881 | + | 0.0771870i | ||||
\(199\) | 3.81625 | 0.270527 | 0.135263 | − | 0.990810i | \(-0.456812\pi\) | ||||
0.135263 | + | 0.990810i | \(0.456812\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.5323 | + | 12.3657i | −1.16610 | + | 0.872207i | ||||
\(202\) | 3.01837i | 0.212372i | ||||||||
\(203\) | −1.33037 | −0.0933740 | ||||||||
\(204\) | −1.25769 | + | 0.940713i | −0.0880557 | + | 0.0658631i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.601748 | 0.0419258 | ||||||||
\(207\) | −3.00685 | + | 10.2103i | −0.208991 | + | 0.709668i | ||||
\(208\) | 2.37988 | 0.165015 | ||||||||
\(209\) | 2.15802 | + | 12.0633i | 0.149273 | + | 0.834439i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0903i | 1.31423i | 0.753789 | + | 0.657116i | \(0.228224\pi\) | ||||
−0.753789 | + | 0.657116i | \(0.771776\pi\) | |||||||
\(212\) | −6.45474 | −0.443313 | ||||||||
\(213\) | 3.58888 | − | 2.68438i | 0.245906 | − | 0.183930i | ||||
\(214\) | 15.2456 | 1.04217 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.81006 | − | 4.87070i | −0.123159 | − | 0.331409i | ||||
\(217\) | 1.44498 | 0.0980918 | ||||||||
\(218\) | −18.3770 | −1.24465 | ||||||||
\(219\) | 12.3362 | + | 16.4929i | 0.833601 | + | 1.11448i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.15802i | 0.145164i | ||||||||
\(222\) | −4.75923 | − | 6.36286i | −0.319419 | − | 0.427047i | ||||
\(223\) | 2.17815i | 0.145860i | 0.997337 | + | 0.0729298i | \(0.0232349\pi\) | ||||
−0.997337 | + | 0.0729298i | \(0.976765\pi\) | |||||||
\(224\) | 0.394100i | 0.0263319i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 6.37988i | − | 0.424383i | ||||||
\(227\) | − | 6.83890i | − | 0.453914i | −0.973905 | − | 0.226957i | \(-0.927122\pi\) | ||
0.973905 | − | 0.226957i | \(-0.0728776\pi\) | |||||||
\(228\) | 5.12489 | − | 3.83327i | 0.339404 | − | 0.253864i | ||||
\(229\) | 23.8474 | 1.57588 | 0.787940 | − | 0.615752i | \(-0.211148\pi\) | ||||
0.787940 | + | 0.615752i | \(0.211148\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.65406 | + | 1.54579i | 0.108829 | + | 0.101706i | ||||
\(232\) | 3.37573i | 0.221628i | ||||||||
\(233\) | 10.5760i | 0.692858i | 0.938076 | + | 0.346429i | \(0.112606\pi\) | ||||
−0.938076 | + | 0.346429i | \(0.887394\pi\) | |||||||
\(234\) | −6.84884 | − | 2.01692i | −0.447722 | − | 0.131850i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.76983i | 0.505773i | ||||||||
\(237\) | −3.55948 | + | 2.66239i | −0.231213 | + | 0.172941i | ||||
\(238\) | −0.357360 | −0.0231642 | ||||||||
\(239\) | −22.4290 | −1.45081 | −0.725406 | − | 0.688322i | \(-0.758348\pi\) | ||||
−0.725406 | + | 0.688322i | \(0.758348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.78820i | − | 0.308435i | −0.988037 | − | 0.154218i | \(-0.950714\pi\) | ||
0.988037 | − | 0.154218i | \(-0.0492857\pi\) | |||||||
\(242\) | 3.81355 | + | 10.3178i | 0.245144 | + | 0.663253i | ||||
\(243\) | 1.08115 | + | 15.5509i | 0.0693556 | + | 0.997592i | ||||
\(244\) | 12.8346i | 0.821652i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.3036 | + | 8.45474i | −0.720690 | + | 0.539054i | ||||
\(247\) | − | 8.79360i | − | 0.559523i | ||||||
\(248\) | − | 3.66654i | − | 0.232825i | ||||||
\(249\) | −2.35466 | + | 1.76121i | −0.149220 | + | 0.111612i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5042i | 0.726141i | 0.931762 | + | 0.363071i | \(0.118272\pi\) | ||||
−0.931762 | + | 0.363071i | \(0.881728\pi\) | |||||||
\(252\) | 0.333995 | − | 1.13414i | 0.0210397 | − | 0.0714443i | ||||
\(253\) | −11.5834 | + | 2.07216i | −0.728241 | + | 0.130275i | ||||
\(254\) | 22.0338i | 1.38253i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.3431 | −1.01946 | −0.509729 | − | 0.860335i | \(-0.670254\pi\) | ||||
−0.509729 | + | 0.860335i | \(0.670254\pi\) | |||||||
\(258\) | 3.60860 | − | 2.69913i | 0.224662 | − | 0.168040i | ||||
\(259\) | − | 1.80795i | − | 0.112340i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.86089 | − | 9.71469i | 0.177084 | − | 0.601324i | ||||
\(262\) | 1.97748i | 0.122169i | ||||||||
\(263\) | − | 3.23463i | − | 0.199456i | −0.995015 | − | 0.0997280i | \(-0.968203\pi\) | ||
0.995015 | − | 0.0997280i | \(-0.0317973\pi\) | |||||||
\(264\) | 3.92234 | − | 4.19705i | 0.241404 | − | 0.258311i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.45619 | 0.0892847 | ||||||||
\(267\) | −21.2259 | + | 15.8764i | −1.29901 | + | 0.971617i | ||||
\(268\) | 11.9195i | 0.728102i | ||||||||
\(269\) | 8.94622i | 0.545460i | 0.962091 | + | 0.272730i | \(0.0879266\pi\) | ||||
−0.962091 | + | 0.272730i | \(0.912073\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.38297i | 0.205501i | 0.994707 | + | 0.102750i | \(0.0327643\pi\) | ||||
−0.994707 | + | 0.102750i | \(0.967236\pi\) | |||||||
\(272\) | 0.906774i | 0.0549813i | ||||||||
\(273\) | −0.973015 | − | 1.30087i | −0.0588896 | − | 0.0787325i | ||||
\(274\) | 19.6172i | 1.18512i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.68076 | + | 4.92099i | 0.221555 | + | 0.296209i | ||||
\(277\) | −5.76983 | −0.346675 | −0.173338 | − | 0.984862i | \(-0.555455\pi\) | ||||
−0.173338 | + | 0.984862i | \(0.555455\pi\) | |||||||
\(278\) | 18.7230 | 1.12293 | ||||||||
\(279\) | −3.10734 | + | 10.5516i | −0.186032 | + | 0.631707i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.115874 | −0.00691245 | −0.00345623 | − | 0.999994i | \(-0.501100\pi\) | ||||
−0.00345623 | + | 0.999994i | \(0.501100\pi\) | |||||||
\(282\) | 4.71334 | − | 3.52544i | 0.280676 | − | 0.209937i | ||||
\(283\) | 21.1805 | 1.25905 | 0.629524 | − | 0.776981i | \(-0.283250\pi\) | ||||
0.629524 | + | 0.776981i | \(0.283250\pi\) | |||||||
\(284\) | − | 2.58753i | − | 0.153542i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.38995 | − | 7.76983i | −0.0821893 | − | 0.459440i | ||||
\(287\) | −3.21180 | −0.189587 | ||||||||
\(288\) | −2.87781 | − | 0.847487i | −0.169576 | − | 0.0499386i | ||||
\(289\) | 16.1778 | 0.951633 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.0381 | + | 10.5001i | −0.822929 | + | 0.615526i | ||||
\(292\) | 11.8911 | 0.695874 | ||||||||
\(293\) | 16.5143i | 0.964776i | 0.875958 | + | 0.482388i | \(0.160231\pi\) | ||||
−0.875958 | + | 0.482388i | \(0.839769\pi\) | |||||||
\(294\) | −9.49352 | + | 7.10087i | −0.553673 | + | 0.414131i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.58753 | −0.266645 | ||||||||
\(297\) | −14.8447 | + | 8.75416i | −0.861376 | + | 0.507968i | ||||
\(298\) | − | 22.0113i | − | 1.27508i | ||||||
\(299\) | 8.44373 | 0.488314 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.02535 | 0.0591001 | ||||||||
\(302\) | −13.9278 | −0.801457 | ||||||||
\(303\) | −3.13134 | − | 4.18645i | −0.179891 | − | 0.240505i | ||||
\(304\) | − | 3.69497i | − | 0.211921i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.768479 | − | 2.60952i | 0.0439310 | − | 0.149176i | ||||
\(307\) | −17.6526 | −1.00749 | −0.503744 | − | 0.863853i | \(-0.668045\pi\) | ||||
−0.503744 | + | 0.863853i | \(0.668045\pi\) | |||||||
\(308\) | 1.28666 | − | 0.230170i | 0.0733140 | − | 0.0131152i | ||||
\(309\) | −0.834619 | + | 0.624270i | −0.0474798 | + | 0.0355135i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.13549i | 0.234502i | 0.993102 | + | 0.117251i | \(0.0374083\pi\) | ||||
−0.993102 | + | 0.117251i | \(0.962592\pi\) | |||||||
\(312\) | −3.30087 | + | 2.46896i | −0.186875 | + | 0.139777i | ||||
\(313\) | 12.1580i | 0.687212i | 0.939114 | + | 0.343606i | \(0.111648\pi\) | ||||
−0.939114 | + | 0.343606i | \(0.888352\pi\) | |||||||
\(314\) | −2.62427 | −0.148096 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.56633i | 0.144368i | ||||||||
\(317\) | −6.97195 | −0.391584 | −0.195792 | − | 0.980645i | \(-0.562728\pi\) | ||||
−0.195792 | + | 0.980645i | \(0.562728\pi\) | |||||||
\(318\) | 8.95266 | − | 6.69632i | 0.502040 | − | 0.375511i | ||||
\(319\) | 11.0211 | − | 1.97156i | 0.617061 | − | 0.110386i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.1456 | + | 15.8162i | −1.18023 | + | 0.882777i | ||||
\(322\) | 1.39825i | 0.0779215i | ||||||||
\(323\) | 3.35051 | 0.186427 | ||||||||
\(324\) | 7.56353 | + | 4.87781i | 0.420196 | + | 0.270989i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.77398 | 0.375176 | ||||||||
\(327\) | 25.4887 | − | 19.0648i | 1.40953 | − | 1.05429i | ||||
\(328\) | 8.14971i | 0.449993i | ||||||||
\(329\) | 1.33925 | 0.0738353 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.39825 | −0.296715 | −0.148357 | − | 0.988934i | \(-0.547399\pi\) | ||||
−0.148357 | + | 0.988934i | \(0.547399\pi\) | |||||||
\(332\) | 1.69767i | 0.0931720i | ||||||||
\(333\) | 13.2020 | + | 3.88787i | 0.723466 | + | 0.213054i | ||||
\(334\) | 16.7542 | 0.916747 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.408850 | − | 0.546613i | −0.0223046 | − | 0.0298202i | ||||
\(337\) | −24.7657 | −1.34907 | −0.674536 | − | 0.738242i | \(-0.735656\pi\) | ||||
−0.674536 | + | 0.738242i | \(0.735656\pi\) | |||||||
\(338\) | − | 7.33616i | − | 0.399035i | ||||||
\(339\) | 6.61867 | + | 8.84884i | 0.359477 | + | 0.480603i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.9705 | + | 2.14141i | −0.648239 | + | 0.115964i | ||||
\(342\) | −3.13144 | + | 10.6334i | −0.169329 | + | 0.574989i | ||||
\(343\) | −5.45619 | −0.294607 | ||||||||
\(344\) | − | 2.60175i | − | 0.140277i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.0959 | 0.704041 | ||||||||
\(347\) | − | 30.3416i | − | 1.62882i | −0.580290 | − | 0.814410i | \(-0.697061\pi\) | ||
0.580290 | − | 0.814410i | \(-0.302939\pi\) | |||||||
\(348\) | −3.50208 | − | 4.68211i | −0.187731 | − | 0.250987i | ||||
\(349\) | − | 21.6172i | − | 1.15714i | −0.815632 | − | 0.578572i | \(-0.803610\pi\) | ||
0.815632 | − | 0.578572i | \(-0.196390\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.5917 | − | 4.30773i | 0.618718 | − | 0.229929i | ||||
\(352\) | −0.584041 | − | 3.26480i | −0.0311295 | − | 0.174014i | ||||
\(353\) | −7.70465 | −0.410077 | −0.205039 | − | 0.978754i | \(-0.565732\pi\) | ||||
−0.205039 | + | 0.978754i | \(0.565732\pi\) | |||||||
\(354\) | −8.06064 | − | 10.7767i | −0.428418 | − | 0.572774i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.3036i | 0.811088i | ||||||||
\(357\) | 0.495654 | − | 0.370735i | 0.0262328 | − | 0.0196214i | ||||
\(358\) | −14.9816 | −0.791804 | ||||||||
\(359\) | 0.344467 | 0.0181803 | 0.00909014 | − | 0.999959i | \(-0.497106\pi\) | ||||
0.00909014 | + | 0.999959i | \(0.497106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.34717 | 0.281430 | ||||||||
\(362\) | 23.9687i | 1.25976i | ||||||||
\(363\) | −15.9933 | − | 10.3544i | −0.839432 | − | 0.543465i | ||||
\(364\) | −0.937911 | −0.0491599 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13.3150 | − | 17.8015i | −0.695986 | − | 0.930499i | ||||
\(367\) | 27.9687i | 1.45995i | 0.683473 | + | 0.729976i | \(0.260469\pi\) | ||||
−0.683473 | + | 0.729976i | \(0.739531\pi\) | |||||||
\(368\) | 3.54796 | 0.184950 | ||||||||
\(369\) | 6.90677 | − | 23.4533i | 0.359552 | − | 1.22093i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.54381 | 0.132068 | ||||||||
\(372\) | 3.80377 | + | 5.08545i | 0.197216 | + | 0.263669i | ||||
\(373\) | 21.8911 | 1.13348 | 0.566739 | − | 0.823897i | \(-0.308205\pi\) | ||||
0.566739 | + | 0.823897i | \(0.308205\pi\) | |||||||
\(374\) | 2.96043 | − | 0.529593i | 0.153080 | − | 0.0273846i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 3.39825i | − | 0.175251i | ||||||
\(377\) | −8.03384 | −0.413764 | ||||||||
\(378\) | 0.713344 | + | 1.91954i | 0.0366905 | + | 0.0987305i | ||||
\(379\) | 29.8023 | 1.53084 | 0.765422 | − | 0.643529i | \(-0.222530\pi\) | ||||
0.765422 | + | 0.643529i | \(0.222530\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.8585 | − | 30.5607i | −1.17108 | − | 1.56567i | ||||
\(382\) | 21.9249 | 1.12178 | ||||||||
\(383\) | 31.3017 | 1.59944 | 0.799722 | − | 0.600370i | \(-0.204980\pi\) | ||||
0.799722 | + | 0.600370i | \(0.204980\pi\) | |||||||
\(384\) | −1.38699 | + | 1.03743i | −0.0707796 | + | 0.0529410i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 21.8699i | − | 1.11315i | ||||||
\(387\) | −2.20495 | + | 7.48733i | −0.112084 | + | 0.380602i | ||||
\(388\) | 10.1213i | 0.513830i | ||||||||
\(389\) | 16.5733i | 0.840300i | 0.907455 | + | 0.420150i | \(0.138023\pi\) | ||||
−0.907455 | + | 0.420150i | \(0.861977\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.21720i | 0.162701i | ||||||||
\(392\) | 6.84469i | 0.345709i | ||||||||
\(393\) | −2.05149 | − | 2.74274i | −0.103484 | − | 0.138353i | ||||
\(394\) | −18.0338 | −0.908532 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.08612 | + | 9.89042i | −0.0545794 | + | 0.497012i | ||||
\(397\) | 3.94798i | 0.198143i | 0.995080 | + | 0.0990716i | \(0.0315873\pi\) | ||||
−0.995080 | + | 0.0990716i | \(0.968413\pi\) | |||||||
\(398\) | 3.81625i | 0.191291i | ||||||||
\(399\) | −2.01972 | + | 1.51069i | −0.101112 | + | 0.0756291i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4.72486i | − | 0.235948i | −0.993017 | − | 0.117974i | \(-0.962360\pi\) | ||
0.993017 | − | 0.117974i | \(-0.0376400\pi\) | |||||||
\(402\) | −12.3657 | − | 16.5323i | −0.616743 | − | 0.824556i | ||||
\(403\) | 8.72593 | 0.434669 | ||||||||
\(404\) | −3.01837 | −0.150170 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 1.33037i | − | 0.0660254i | ||||||
\(407\) | 2.67930 | + | 14.9774i | 0.132808 | + | 0.742400i | ||||
\(408\) | −0.940713 | − | 1.25769i | −0.0465722 | − | 0.0622648i | ||||
\(409\) | 12.1497i | 0.600765i | 0.953819 | + | 0.300382i | \(0.0971143\pi\) | ||||
−0.953819 | + | 0.300382i | \(0.902886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.3514 | − | 27.2089i | −1.00386 | − | 1.34212i | ||||
\(412\) | 0.601748i | 0.0296460i | ||||||||
\(413\) | − | 3.06209i | − | 0.150676i | ||||||
\(414\) | −10.2103 | − | 3.00685i | −0.501811 | − | 0.147779i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.37988i | 0.116683i | ||||||||
\(417\) | −25.9687 | + | 19.4238i | −1.27169 | + | 0.951187i | ||||
\(418\) | −12.0633 | + | 2.15802i | −0.590037 | + | 0.105552i | ||||
\(419\) | − | 7.01547i | − | 0.342728i | −0.985208 | − | 0.171364i | \(-0.945183\pi\) | ||
0.985208 | − | 0.171364i | \(-0.0548174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0085 | −0.633995 | −0.316997 | − | 0.948426i | \(-0.602675\pi\) | ||||
−0.316997 | + | 0.948426i | \(0.602675\pi\) | |||||||
\(422\) | −19.0903 | −0.929302 | ||||||||
\(423\) | −2.87997 | + | 9.77951i | −0.140029 | + | 0.475496i | ||||
\(424\) | − | 6.45474i | − | 0.313470i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.68438 | + | 3.58888i | 0.130058 | + | 0.173882i | ||||
\(427\) | − | 5.05812i | − | 0.244780i | ||||||
\(428\) | 15.2456i | 0.736926i | ||||||||
\(429\) | 9.98848 | + | 9.33471i | 0.482248 | + | 0.450684i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.5397 | 1.13387 | 0.566933 | − | 0.823764i | \(-0.308130\pi\) | ||||
0.566933 | + | 0.823764i | \(0.308130\pi\) | |||||||
\(432\) | 4.87070 | − | 1.81006i | 0.234342 | − | 0.0870865i | ||||
\(433\) | − | 3.05919i | − | 0.147015i | −0.997295 | − | 0.0735076i | \(-0.976581\pi\) | ||
0.997295 | − | 0.0735076i | \(-0.0234193\pi\) | |||||||
\(434\) | 1.44498i | 0.0693614i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 18.3770i | − | 0.880098i | ||||||
\(437\) | − | 13.1096i | − | 0.627119i | ||||||
\(438\) | −16.4929 | + | 12.3362i | −0.788059 | + | 0.589445i | ||||
\(439\) | 27.8461i | 1.32902i | 0.747279 | + | 0.664510i | \(0.231360\pi\) | ||||
−0.747279 | + | 0.664510i | \(0.768640\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.80078 | − | 19.6977i | 0.276228 | − | 0.937985i | ||||
\(442\) | −2.15802 | −0.102646 | ||||||||
\(443\) | −28.5213 | −1.35509 | −0.677544 | − | 0.735483i | \(-0.736956\pi\) | ||||
−0.677544 | + | 0.735483i | \(0.736956\pi\) | |||||||
\(444\) | 6.36286 | − | 4.75923i | 0.301968 | − | 0.225863i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.17815 | −0.103138 | ||||||||
\(447\) | 22.8352 | + | 30.5295i | 1.08007 | + | 1.44400i | ||||
\(448\) | −0.394100 | −0.0186195 | ||||||||
\(449\) | − | 4.00000i | − | 0.188772i | −0.995536 | − | 0.0943858i | \(-0.969911\pi\) | ||
0.995536 | − | 0.0943858i | \(-0.0300887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.6071 | − | 4.75976i | 1.25288 | − | 0.224129i | ||||
\(452\) | 6.37988 | 0.300084 | ||||||||
\(453\) | 19.3178 | − | 14.4491i | 0.907629 | − | 0.678880i | ||||
\(454\) | 6.83890 | 0.320965 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.83327 | + | 5.12489i | 0.179509 | + | 0.239995i | ||||
\(457\) | 13.0651 | 0.611160 | 0.305580 | − | 0.952166i | \(-0.401150\pi\) | ||||
0.305580 | + | 0.952166i | \(0.401150\pi\) | |||||||
\(458\) | 23.8474i | 1.11432i | ||||||||
\(459\) | 1.64131 | + | 4.41662i | 0.0766100 | + | 0.206150i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.1355 | −0.937803 | −0.468902 | − | 0.883250i | \(-0.655350\pi\) | ||||
−0.468902 | + | 0.883250i | \(0.655350\pi\) | |||||||
\(462\) | −1.54579 | + | 1.65406i | −0.0719169 | + | 0.0769537i | ||||
\(463\) | 12.6071i | 0.585904i | 0.956127 | + | 0.292952i | \(0.0946376\pi\) | ||||
−0.956127 | + | 0.292952i | \(0.905362\pi\) | |||||||
\(464\) | −3.37573 | −0.156714 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.5760 | −0.489924 | ||||||||
\(467\) | −14.9843 | −0.693392 | −0.346696 | − | 0.937978i | \(-0.612696\pi\) | ||||
−0.346696 | + | 0.937978i | \(0.612696\pi\) | |||||||
\(468\) | 2.01692 | − | 6.84884i | 0.0932321 | − | 0.316588i | ||||
\(469\) | − | 4.69749i | − | 0.216910i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.63984 | − | 2.72249i | 0.167715 | − | 0.125446i | ||||
\(472\) | −7.76983 | −0.357635 | ||||||||
\(473\) | −8.49418 | + | 1.51953i | −0.390563 | + | 0.0698679i | ||||
\(474\) | −2.66239 | − | 3.55948i | −0.122287 | − | 0.163492i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 0.357360i | − | 0.0163796i | ||||||
\(477\) | −5.47031 | + | 18.5755i | −0.250468 | + | 0.850513i | ||||
\(478\) | − | 22.4290i | − | 1.02588i | ||||||
\(479\) | −23.7060 | −1.08315 | −0.541577 | − | 0.840651i | \(-0.682173\pi\) | ||||
−0.541577 | + | 0.840651i | \(0.682173\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 10.9178i | − | 0.497808i | ||||||
\(482\) | 4.78820 | 0.218097 | ||||||||
\(483\) | −1.45059 | − | 1.93936i | −0.0660039 | − | 0.0882440i | ||||
\(484\) | −10.3178 | + | 3.81355i | −0.468991 | + | 0.173343i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −15.5509 | + | 1.08115i | −0.705404 | + | 0.0490418i | ||||
\(487\) | 10.3279i | 0.468000i | 0.972237 | + | 0.234000i | \(0.0751816\pi\) | ||||
−0.972237 | + | 0.234000i | \(0.924818\pi\) | |||||||
\(488\) | −12.8346 | −0.580996 | ||||||||
\(489\) | −9.39545 | + | 7.02752i | −0.424877 | + | 0.317795i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.1608 | 0.954975 | 0.477488 | − | 0.878638i | \(-0.341548\pi\) | ||||
0.477488 | + | 0.878638i | \(0.341548\pi\) | |||||||
\(492\) | −8.45474 | − | 11.3036i | −0.381169 | − | 0.509605i | ||||
\(493\) | − | 3.06102i | − | 0.137862i | ||||||
\(494\) | 8.79360 | 0.395643 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.66654 | 0.164632 | ||||||||
\(497\) | 1.01975i | 0.0457418i | ||||||||
\(498\) | −1.76121 | − | 2.35466i | −0.0789219 | − | 0.105515i | ||||
\(499\) | −23.6325 | −1.05794 | −0.528968 | − | 0.848642i | \(-0.677421\pi\) | ||||
−0.528968 | + | 0.848642i | \(0.677421\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.2379 | + | 17.3812i | −1.03819 | + | 0.776536i | ||||
\(502\) | −11.5042 | −0.513460 | ||||||||
\(503\) | − | 13.5195i | − | 0.602806i | −0.953497 | − | 0.301403i | \(-0.902545\pi\) | ||
0.953497 | − | 0.301403i | \(-0.0974549\pi\) | |||||||
\(504\) | 1.13414 | + | 0.333995i | 0.0505187 | + | 0.0148773i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.07216 | − | 11.5834i | −0.0921185 | − | 0.514944i | ||||
\(507\) | 7.61074 | + | 10.1752i | 0.338005 | + | 0.451896i | ||||
\(508\) | −22.0338 | −0.977593 | ||||||||
\(509\) | − | 31.0930i | − | 1.37817i | −0.724679 | − | 0.689087i | \(-0.758012\pi\) | ||
0.724679 | − | 0.689087i | \(-0.241988\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.68628 | −0.207309 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −6.68812 | − | 17.9971i | −0.295288 | − | 0.794591i | ||||
\(514\) | − | 16.3431i | − | 0.720865i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.69913 | + | 3.60860i | 0.118822 | + | 0.158860i | ||||
\(517\) | −11.0946 | + | 1.98472i | −0.487940 | + | 0.0872878i | ||||
\(518\) | 1.80795 | 0.0794365 | ||||||||
\(519\) | −18.1639 | + | 13.5861i | −0.797308 | + | 0.596363i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.40699i | − | 0.105452i | −0.998609 | − | 0.0527261i | \(-0.983209\pi\) | ||
0.998609 | − | 0.0527261i | \(-0.0167910\pi\) | |||||||
\(522\) | 9.71469 | + | 2.86089i | 0.425201 | + | 0.125218i | ||||
\(523\) | 11.7967 | 0.515833 | 0.257917 | − | 0.966167i | \(-0.416964\pi\) | ||||
0.257917 | + | 0.966167i | \(0.416964\pi\) | |||||||
\(524\) | −1.97748 | −0.0863865 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.23463 | 0.141037 | ||||||||
\(527\) | 3.32472i | 0.144827i | ||||||||
\(528\) | 4.19705 | + | 3.92234i | 0.182653 | + | 0.170698i | ||||
\(529\) | −10.4120 | −0.452694 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.3601 | + | 6.58483i | 0.970344 | + | 0.285757i | ||||
\(532\) | 1.45619i | 0.0631338i | ||||||||
\(533\) | −19.3953 | −0.840106 | ||||||||
\(534\) | −15.8764 | − | 21.2259i | −0.687037 | − | 0.918535i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −11.9195 | −0.514846 | ||||||||
\(537\) | 20.7794 | − | 15.5424i | 0.896697 | − | 0.670702i | ||||
\(538\) | −8.94622 | −0.385699 | ||||||||
\(539\) | 22.3465 | − | 3.99758i | 0.962532 | − | 0.172188i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 28.7472i | − | 1.23594i | −0.786203 | − | 0.617969i | \(-0.787956\pi\) | ||
0.786203 | − | 0.617969i | \(-0.212044\pi\) | |||||||
\(542\) | −3.38297 | −0.145311 | ||||||||
\(543\) | −24.8658 | − | 33.2443i | −1.06709 | − | 1.42665i | ||||
\(544\) | −0.906774 | −0.0388776 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.30087 | − | 0.973015i | 0.0556723 | − | 0.0416412i | ||||
\(547\) | 19.6663 | 0.840872 | 0.420436 | − | 0.907322i | \(-0.361877\pi\) | ||||
0.420436 | + | 0.907322i | \(0.361877\pi\) | |||||||
\(548\) | −19.6172 | −0.838006 | ||||||||
\(549\) | 36.9355 | + | 10.8772i | 1.57637 | + | 0.464226i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.4732i | 0.531378i | ||||||||
\(552\) | −4.92099 | + | 3.68076i | −0.209451 | + | 0.156663i | ||||
\(553\) | − | 1.01139i | − | 0.0430087i | ||||||
\(554\) | − | 5.76983i | − | 0.245137i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.7230i | 0.794033i | ||||||||
\(557\) | 14.2710i | 0.604681i | 0.953200 | + | 0.302341i | \(0.0977680\pi\) | ||||
−0.953200 | + | 0.302341i | \(0.902232\pi\) | |||||||
\(558\) | −10.5516 | − | 3.10734i | −0.446684 | − | 0.131544i | ||||
\(559\) | 6.19185 | 0.261887 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.55668 | + | 3.80578i | −0.150163 | + | 0.160680i | ||||
\(562\) | − | 0.115874i | − | 0.00488784i | ||||||
\(563\) | − | 40.9573i | − | 1.72614i | −0.505082 | − | 0.863072i | \(-0.668538\pi\) | ||
0.505082 | − | 0.863072i | \(-0.331462\pi\) | |||||||
\(564\) | 3.52544 | + | 4.71334i | 0.148448 | + | 0.198468i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.1805i | 0.890281i | ||||||||
\(567\) | −2.98079 | − | 1.92234i | −0.125181 | − | 0.0807308i | ||||
\(568\) | 2.58753 | 0.108570 | ||||||||
\(569\) | −29.3162 | −1.22900 | −0.614500 | − | 0.788917i | \(-0.710642\pi\) | ||||
−0.614500 | + | 0.788917i | \(0.710642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.6381i | 0.821829i | 0.911674 | + | 0.410914i | \(0.134791\pi\) | ||||
−0.911674 | + | 0.410914i | \(0.865209\pi\) | |||||||
\(572\) | 7.76983 | − | 1.38995i | 0.324873 | − | 0.0581166i | ||||
\(573\) | −30.4097 | + | 22.7455i | −1.27038 | + | 0.950209i | ||||
\(574\) | − | 3.21180i | − | 0.134058i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.847487 | − | 2.87781i | 0.0353120 | − | 0.119909i | ||||
\(577\) | 4.75146i | 0.197806i | 0.995097 | + | 0.0989029i | \(0.0315333\pi\) | ||||
−0.995097 | + | 0.0989029i | \(0.968467\pi\) | |||||||
\(578\) | 16.1778i | 0.672906i | ||||||||
\(579\) | 22.6885 | + | 30.3334i | 0.942900 | + | 1.26061i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.669053i | − | 0.0277570i | ||||||
\(582\) | −10.5001 | − | 14.0381i | −0.435243 | − | 0.581899i | ||||
\(583\) | −21.0734 | + | 3.76983i | −0.872771 | + | 0.156130i | ||||
\(584\) | 11.8911i | 0.492057i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.5143 | −0.682200 | ||||||||
\(587\) | 23.3572 | 0.964056 | 0.482028 | − | 0.876156i | \(-0.339900\pi\) | ||||
0.482028 | + | 0.876156i | \(0.339900\pi\) | |||||||
\(588\) | −7.10087 | − | 9.49352i | −0.292835 | − | 0.391506i | ||||
\(589\) | − | 13.5478i | − | 0.558226i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.0128 | − | 18.7088i | 1.02889 | − | 0.769577i | ||||
\(592\) | − | 4.58753i | − | 0.188546i | ||||||
\(593\) | 27.7315i | 1.13880i | 0.822062 | + | 0.569398i | \(0.192824\pi\) | ||||
−0.822062 | + | 0.569398i | \(0.807176\pi\) | |||||||
\(594\) | −8.75416 | − | 14.8447i | −0.359188 | − | 0.609085i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.0113 | 0.901619 | ||||||||
\(597\) | −3.95908 | − | 5.29310i | −0.162034 | − | 0.216632i | ||||
\(598\) | 8.44373i | 0.345290i | ||||||||
\(599\) | − | 9.59602i | − | 0.392083i | −0.980596 | − | 0.196041i | \(-0.937191\pi\) | ||
0.980596 | − | 0.196041i | \(-0.0628087\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.8503i | 0.483383i | 0.970353 | + | 0.241692i | \(0.0777023\pi\) | ||||
−0.970353 | + | 0.241692i | \(0.922298\pi\) | |||||||
\(602\) | 1.02535i | 0.0417901i | ||||||||
\(603\) | 34.3021 | + | 10.1017i | 1.39689 | + | 0.411371i | ||||
\(604\) | − | 13.9278i | − | 0.566716i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.18645 | − | 3.13134i | 0.170063 | − | 0.127202i | ||||
\(607\) | 23.9338 | 0.971441 | 0.485721 | − | 0.874114i | \(-0.338557\pi\) | ||||
0.485721 | + | 0.874114i | \(0.338557\pi\) | |||||||
\(608\) | 3.69497 | 0.149851 | ||||||||
\(609\) | 1.38017 | + | 1.84522i | 0.0559272 | + | 0.0747720i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.08744 | 0.327183 | ||||||||
\(612\) | 2.60952 | + | 0.768479i | 0.105484 | + | 0.0310639i | ||||
\(613\) | 38.0977 | 1.53875 | 0.769376 | − | 0.638797i | \(-0.220568\pi\) | ||||
0.769376 | + | 0.638797i | \(0.220568\pi\) | |||||||
\(614\) | − | 17.6526i | − | 0.712402i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.230170 | + | 1.28666i | 0.00927383 | + | 0.0518408i | ||||
\(617\) | −42.1905 | −1.69853 | −0.849263 | − | 0.527969i | \(-0.822954\pi\) | ||||
−0.849263 | + | 0.527969i | \(0.822954\pi\) | |||||||
\(618\) | −0.624270 | − | 0.834619i | −0.0251118 | − | 0.0335733i | ||||
\(619\) | −23.2596 | −0.934882 | −0.467441 | − | 0.884024i | \(-0.654824\pi\) | ||||
−0.467441 | + | 0.884024i | \(0.654824\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.2811 | − | 6.42202i | 0.693465 | − | 0.257707i | ||||
\(622\) | −4.13549 | −0.165818 | ||||||||
\(623\) | − | 6.03114i | − | 0.241632i | ||||||
\(624\) | −2.46896 | − | 3.30087i | −0.0988373 | − | 0.132141i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.1580 | −0.485932 | ||||||||
\(627\) | 14.4930 | − | 15.5080i | 0.578793 | − | 0.619329i | ||||
\(628\) | − | 2.62427i | − | 0.104720i | ||||||
\(629\) | 4.15985 | 0.165864 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.8902 | 0.433531 | 0.216765 | − | 0.976224i | \(-0.430449\pi\) | ||||
0.216765 | + | 0.976224i | \(0.430449\pi\) | |||||||
\(632\) | −2.56633 | −0.102083 | ||||||||
\(633\) | 26.4781 | − | 19.8048i | 1.05241 | − | 0.787171i | ||||
\(634\) | − | 6.97195i | − | 0.276892i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.69632 | + | 8.95266i | 0.265527 | + | 0.354996i | ||||
\(637\) | −16.2895 | −0.645415 | ||||||||
\(638\) | 1.97156 | + | 11.0211i | 0.0780550 | + | 0.436328i | ||||
\(639\) | −7.44641 | − | 2.19290i | −0.294575 | − | 0.0867497i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.2076i | − | 0.798154i | −0.916917 | − | 0.399077i | \(-0.869331\pi\) | ||
0.916917 | − | 0.399077i | \(-0.130669\pi\) | |||||||
\(642\) | −15.8162 | − | 21.1456i | −0.624218 | − | 0.834549i | ||||
\(643\) | 37.2937i | 1.47072i | 0.677677 | + | 0.735360i | \(0.262987\pi\) | ||||
−0.677677 | + | 0.735360i | \(0.737013\pi\) | |||||||
\(644\) | −1.39825 | −0.0550988 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.35051i | 0.131824i | ||||||||
\(647\) | 21.5681 | 0.847929 | 0.423965 | − | 0.905679i | \(-0.360638\pi\) | ||||
0.423965 | + | 0.905679i | \(0.360638\pi\) | |||||||
\(648\) | −4.87781 | + | 7.56353i | −0.191618 | + | 0.297124i | ||||
\(649\) | 4.53790 | + | 25.3669i | 0.178128 | + | 0.995738i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.49906 | − | 2.00418i | −0.0587530 | − | 0.0785499i | ||||
\(652\) | 6.77398i | 0.265290i | ||||||||
\(653\) | 32.8837 | 1.28684 | 0.643420 | − | 0.765513i | \(-0.277515\pi\) | ||||
0.643420 | + | 0.765513i | \(0.277515\pi\) | |||||||
\(654\) | 19.0648 | + | 25.4887i | 0.745492 | + | 0.996687i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.14971 | −0.318193 | ||||||||
\(657\) | 10.0776 | − | 34.2203i | 0.393163 | − | 1.33506i | ||||
\(658\) | 1.33925i | 0.0522094i | ||||||||
\(659\) | 36.5278 | 1.42292 | 0.711460 | − | 0.702727i | \(-0.248034\pi\) | ||||
0.711460 | + | 0.702727i | \(0.248034\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.7936 | −1.19773 | −0.598866 | − | 0.800849i | \(-0.704382\pi\) | ||||
−0.598866 | + | 0.800849i | \(0.704382\pi\) | |||||||
\(662\) | − | 5.39825i | − | 0.209809i | ||||||
\(663\) | 2.99315 | − | 2.23879i | 0.116244 | − | 0.0869472i | ||||
\(664\) | −1.69767 | −0.0658825 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.88787 | + | 13.2020i | −0.150652 | + | 0.511568i | ||||
\(667\) | −11.9770 | −0.463750 | ||||||||
\(668\) | 16.7542i | 0.648238i | ||||||||
\(669\) | 3.02107 | − | 2.25967i | 0.116801 | − | 0.0873639i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.49594 | + | 41.9024i | 0.289378 | + | 1.61762i | ||||
\(672\) | 0.546613 | − | 0.408850i | 0.0210861 | − | 0.0157717i | ||||
\(673\) | −13.8699 | −0.534646 | −0.267323 | − | 0.963607i | \(-0.586139\pi\) | ||||
−0.267323 | + | 0.963607i | \(0.586139\pi\) | |||||||
\(674\) | − | 24.7657i | − | 0.953938i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.33616 | 0.282160 | ||||||||
\(677\) | − | 36.4913i | − | 1.40247i | −0.712928 | − | 0.701237i | \(-0.752632\pi\) | ||
0.712928 | − | 0.701237i | \(-0.247368\pi\) | |||||||
\(678\) | −8.84884 | + | 6.61867i | −0.339838 | + | 0.254188i | ||||
\(679\) | − | 3.98879i | − | 0.153076i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.48549 | + | 7.09486i | −0.363485 | + | 0.271876i | ||||
\(682\) | −2.14141 | − | 11.9705i | −0.0819987 | − | 0.458374i | ||||
\(683\) | 11.3518 | 0.434366 | 0.217183 | − | 0.976131i | \(-0.430313\pi\) | ||||
0.217183 | + | 0.976131i | \(0.430313\pi\) | |||||||
\(684\) | −10.6334 | − | 3.13144i | −0.406579 | − | 0.119734i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 5.45619i | − | 0.208318i | ||||||
\(687\) | −24.7399 | − | 33.0761i | −0.943888 | − | 1.26193i | ||||
\(688\) | 2.60175 | 0.0991907 | ||||||||
\(689\) | 15.3615 | 0.585227 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.6578 | −1.39453 | −0.697265 | − | 0.716813i | \(-0.745600\pi\) | ||||
−0.697265 | + | 0.716813i | \(0.745600\pi\) | |||||||
\(692\) | 13.0959i | 0.497832i | ||||||||
\(693\) | 0.428038 | − | 3.89781i | 0.0162598 | − | 0.148066i | ||||
\(694\) | 30.3416 | 1.15175 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.68211 | − | 3.50208i | 0.177475 | − | 0.132746i | ||||
\(697\) | − | 7.38995i | − | 0.279914i | ||||||
\(698\) | 21.6172 | 0.818224 | ||||||||
\(699\) | 14.6688 | − | 10.9718i | 0.554826 | − | 0.414993i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.64422 | −0.0621012 | −0.0310506 | − | 0.999518i | \(-0.509885\pi\) | ||||
−0.0310506 | + | 0.999518i | \(0.509885\pi\) | |||||||
\(702\) | 4.30773 | + | 11.5917i | 0.162585 | + | 0.437500i | ||||
\(703\) | −16.9508 | −0.639312 | ||||||||
\(704\) | 3.26480 | − | 0.584041i | 0.123047 | − | 0.0220119i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 7.70465i | − | 0.289968i | ||||||
\(707\) | 1.18954 | 0.0447372 | ||||||||
\(708\) | 10.7767 | − | 8.06064i | 0.405013 | − | 0.302937i | ||||
\(709\) | −48.7172 | −1.82961 | −0.914807 | − | 0.403892i | \(-0.867657\pi\) | ||||
−0.914807 | + | 0.403892i | \(0.867657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.38541 | + | 2.17493i | 0.276974 | + | 0.0815664i | ||||
\(712\) | −15.3036 | −0.573526 | ||||||||
\(713\) | 13.0087 | 0.487181 | ||||||||
\(714\) | 0.370735 | + | 0.495654i | 0.0138744 | + | 0.0185494i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 14.9816i | − | 0.559890i | ||||||
\(717\) | 23.2685 | + | 31.1088i | 0.868977 | + | 1.16178i | ||||
\(718\) | 0.344467i | 0.0128554i | ||||||||
\(719\) | − | 22.9460i | − | 0.855740i | −0.903840 | − | 0.427870i | \(-0.859264\pi\) | ||
0.903840 | − | 0.427870i | \(-0.140736\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 0.237149i | − | 0.00883189i | ||||||
\(722\) | 5.34717i | 0.199001i | ||||||||
\(723\) | −6.64119 | + | 4.96741i | −0.246988 | + | 0.184740i | ||||
\(724\) | −23.9687 | −0.890788 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.3544 | − | 15.9933i | 0.384288 | − | 0.593568i | ||||
\(727\) | − | 22.0623i | − | 0.818244i | −0.912480 | − | 0.409122i | \(-0.865835\pi\) | ||
0.912480 | − | 0.409122i | \(-0.134165\pi\) | |||||||
\(728\) | − | 0.937911i | − | 0.0347613i | ||||||
\(729\) | 20.4474 | − | 17.6325i | 0.757310 | − | 0.653055i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.35920i | 0.0872581i | ||||||||
\(732\) | 17.8015 | − | 13.3150i | 0.657962 | − | 0.492136i | ||||
\(733\) | 27.0522 | 0.999196 | 0.499598 | − | 0.866257i | \(-0.333481\pi\) | ||||
0.499598 | + | 0.866257i | \(0.333481\pi\) | |||||||
\(734\) | −27.9687 | −1.03234 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.54796i | 0.130780i | ||||||||
\(737\) | 6.96150 | + | 38.9149i | 0.256430 | + | 1.43345i | ||||
\(738\) | 23.4533 | + | 6.90677i | 0.863327 | + | 0.254242i | ||||
\(739\) | 28.2286i | 1.03841i | 0.854651 | + | 0.519203i | \(0.173771\pi\) | ||||
−0.854651 | + | 0.519203i | \(0.826229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.1966 | + | 9.12273i | −0.448055 | + | 0.335132i | ||||
\(742\) | 2.54381i | 0.0933862i | ||||||||
\(743\) | 4.98591i | 0.182915i | 0.995809 | + | 0.0914576i | \(0.0291526\pi\) | ||||
−0.995809 | + | 0.0914576i | \(0.970847\pi\) | |||||||
\(744\) | −5.08545 | + | 3.80377i | −0.186442 | + | 0.139453i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21.8911i | 0.801490i | ||||||||
\(747\) | 4.88558 | + | 1.43876i | 0.178754 | + | 0.0526414i | ||||
\(748\) | 0.529593 | + | 2.96043i | 0.0193638 | + | 0.108244i | ||||
\(749\) | − | 6.00830i | − | 0.219539i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.87312 | 0.287294 | 0.143647 | − | 0.989629i | \(-0.454117\pi\) | ||||
0.143647 | + | 0.989629i | \(0.454117\pi\) | |||||||
\(752\) | 3.39825 | 0.123921 | ||||||||
\(753\) | 15.9563 | − | 11.9348i | 0.581479 | − | 0.434929i | ||||
\(754\) | − | 8.03384i | − | 0.292575i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.91954 | + | 0.713344i | −0.0698130 | + | 0.0259441i | ||||
\(757\) | − | 13.2250i | − | 0.480669i | −0.970690 | − | 0.240335i | \(-0.922743\pi\) | ||
0.970690 | − | 0.240335i | \(-0.0772572\pi\) | |||||||
\(758\) | 29.8023i | 1.08247i | ||||||||
\(759\) | 14.8910 | + | 13.9163i | 0.540508 | + | 0.505131i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.3923 | 1.46422 | 0.732109 | − | 0.681187i | \(-0.238536\pi\) | ||||
0.732109 | + | 0.681187i | \(0.238536\pi\) | |||||||
\(762\) | 30.5607 | − | 22.8585i | 1.10710 | − | 0.828077i | ||||
\(763\) | 7.24237i | 0.262191i | ||||||||
\(764\) | 21.9249i | 0.793217i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.3017i | 1.13098i | ||||||||
\(767\) | − | 18.4913i | − | 0.667681i | ||||||
\(768\) | −1.03743 | − | 1.38699i | −0.0374350 | − | 0.0500487i | ||||
\(769\) | − | 14.2433i | − | 0.513627i | −0.966461 | − | 0.256814i | \(-0.917327\pi\) | ||
0.966461 | − | 0.256814i | \(-0.0826727\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.9548 | + | 22.6678i | 0.610613 | + | 0.816360i | ||||
\(772\) | 21.8699 | 0.787115 | ||||||||
\(773\) | 7.21450 | 0.259488 | 0.129744 | − | 0.991548i | \(-0.458585\pi\) | ||||
0.129744 | + | 0.991548i | \(0.458585\pi\) | |||||||
\(774\) | −7.48733 | − | 2.20495i | −0.269126 | − | 0.0792552i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.1213 | −0.363333 | ||||||||
\(777\) | −2.50760 | + | 1.87561i | −0.0899598 | + | 0.0672872i | ||||
\(778\) | −16.5733 | −0.594182 | ||||||||
\(779\) | 30.1130i | 1.07891i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.51122 | − | 8.44776i | −0.0540758 | − | 0.302285i | ||||
\(782\) | −3.21720 | −0.115047 | ||||||||
\(783\) | −16.4422 | + | 6.11027i | −0.587595 | + | 0.218363i | ||||
\(784\) | −6.84469 | −0.244453 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.74274 | − | 2.05149i | 0.0978304 | − | 0.0731742i | ||||
\(787\) | 8.68088 | 0.309440 | 0.154720 | − | 0.987958i | \(-0.450552\pi\) | ||||
0.154720 | + | 0.987958i | \(0.450552\pi\) | |||||||
\(788\) | − | 18.0338i | − | 0.642429i | ||||||
\(789\) | −4.48641 | + | 3.35570i | −0.159720 | + | 0.119466i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.51431 | −0.0893986 | ||||||||
\(792\) | −9.89042 | − | 1.08612i | −0.351441 | − | 0.0385935i | ||||
\(793\) | − | 30.5449i | − | 1.08468i | ||||||
\(794\) | −3.94798 | −0.140108 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.81625 | −0.135263 | ||||||||
\(797\) | 41.6239 | 1.47440 | 0.737198 | − | 0.675677i | \(-0.236149\pi\) | ||||
0.737198 | + | 0.675677i | \(0.236149\pi\) | |||||||
\(798\) | −1.51069 | − | 2.01972i | −0.0534779 | − | 0.0714973i | ||||
\(799\) | 3.08145i | 0.109014i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44.0407 | + | 12.9696i | 1.55610 | + | 0.458258i | ||||
\(802\) | 4.72486 | 0.166841 | ||||||||
\(803\) | 38.8220 | − | 6.94489i | 1.37000 | − | 0.245080i | ||||
\(804\) | 16.5323 | − | 12.3657i | 0.583049 | − | 0.436103i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.72593i | 0.307358i | ||||||||
\(807\) | 12.4083 | − | 9.28105i | 0.436793 | − | 0.326709i | ||||
\(808\) | − | 3.01837i | − | 0.106186i | ||||||
\(809\) | −7.92917 | −0.278775 | −0.139387 | − | 0.990238i | \(-0.544513\pi\) | ||||
−0.139387 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.9743i | 1.05254i | 0.850318 | + | 0.526269i | \(0.176410\pi\) | ||||
−0.850318 | + | 0.526269i | \(0.823590\pi\) | |||||||
\(812\) | 1.33037 | 0.0466870 | ||||||||
\(813\) | 4.69215 | − | 3.50959i | 0.164561 | − | 0.123087i | ||||
\(814\) | −14.9774 | + | 2.67930i | −0.524956 | + | 0.0939096i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.25769 | − | 0.940713i | 0.0440279 | − | 0.0329315i | ||||
\(817\) | − | 9.61339i | − | 0.336330i | ||||||
\(818\) | −12.1497 | −0.424805 | ||||||||
\(819\) | −0.794867 | + | 2.69913i | −0.0277749 | + | 0.0943151i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.46210 | 0.260429 | 0.130215 | − | 0.991486i | \(-0.458433\pi\) | ||||
0.130215 | + | 0.991486i | \(0.458433\pi\) | |||||||
\(822\) | 27.2089 | − | 20.3514i | 0.949019 | − | 0.709838i | ||||
\(823\) | − | 45.0224i | − | 1.56938i | −0.619886 | − | 0.784692i | \(-0.712821\pi\) | ||
0.619886 | − | 0.784692i | \(-0.287179\pi\) | |||||||
\(824\) | −0.601748 | −0.0209629 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.06209 | 0.106544 | ||||||||
\(827\) | − | 35.9716i | − | 1.25085i | −0.780283 | − | 0.625427i | \(-0.784925\pi\) | ||
0.780283 | − | 0.625427i | \(-0.215075\pi\) | |||||||
\(828\) | 3.00685 | − | 10.2103i | 0.104495 | − | 0.354834i | ||||
\(829\) | 7.50832 | 0.260775 | 0.130387 | − | 0.991463i | \(-0.458378\pi\) | ||||
0.130387 | + | 0.991463i | \(0.458378\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.98578 | + | 8.00270i | 0.207644 | + | 0.277611i | ||||
\(832\) | −2.37988 | −0.0825076 | ||||||||
\(833\) | − | 6.20658i | − | 0.215045i | ||||||
\(834\) | −19.4238 | − | 25.9687i | −0.672591 | − | 0.899221i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.15802 | − | 12.0633i | −0.0746365 | − | 0.417219i | ||||
\(837\) | 17.8586 | − | 6.63665i | 0.617283 | − | 0.229396i | ||||
\(838\) | 7.01547 | 0.242345 | ||||||||
\(839\) | 41.7806i | 1.44243i | 0.692713 | + | 0.721214i | \(0.256415\pi\) | ||||
−0.692713 | + | 0.721214i | \(0.743585\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.6044 | −0.607050 | ||||||||
\(842\) | − | 13.0085i | − | 0.448302i | ||||||
\(843\) | 0.120211 | + | 0.160716i | 0.00414028 | + | 0.00553535i | ||||
\(844\) | − | 19.0903i | − | 0.657116i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.77951 | − | 2.87997i | −0.336226 | − | 0.0990156i | ||||
\(847\) | 4.06624 | − | 1.50292i | 0.139718 | − | 0.0516409i | ||||
\(848\) | 6.45474 | 0.221657 | ||||||||
\(849\) | −21.9732 | − | 29.3771i | −0.754118 | − | 1.00822i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 16.2764i | − | 0.557947i | ||||||
\(852\) | −3.58888 | + | 2.68438i | −0.122953 | + | 0.0919652i | ||||
\(853\) | 35.6816 | 1.22172 | 0.610858 | − | 0.791740i | \(-0.290825\pi\) | ||||
0.610858 | + | 0.791740i | \(0.290825\pi\) | |||||||
\(854\) | 5.05812 | 0.173085 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.2456 | −0.521085 | ||||||||
\(857\) | 39.8584i | 1.36154i | 0.732499 | + | 0.680768i | \(0.238354\pi\) | ||||
−0.732499 | + | 0.680768i | \(0.761646\pi\) | |||||||
\(858\) | −9.33471 | + | 9.98848i | −0.318682 | + | 0.341001i | ||||
\(859\) | −44.9857 | −1.53489 | −0.767446 | − | 0.641113i | \(-0.778473\pi\) | ||||
−0.767446 | + | 0.641113i | \(0.778473\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.33201 | + | 4.45474i | 0.113555 | + | 0.151817i | ||||
\(862\) | 23.5397i | 0.801764i | ||||||||
\(863\) | −18.8644 | −0.642153 | −0.321076 | − | 0.947053i | \(-0.604045\pi\) | ||||
−0.321076 | + | 0.947053i | \(0.604045\pi\) | |||||||
\(864\) | 1.81006 | + | 4.87070i | 0.0615795 | + | 0.165704i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.05919 | 0.103955 | ||||||||
\(867\) | −16.7833 | − | 22.4384i | −0.569989 | − | 0.762048i | ||||
\(868\) | −1.44498 | −0.0490459 | ||||||||
\(869\) | 1.49884 | + | 8.37856i | 0.0508448 | + | 0.284223i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 28.3671i | − | 0.961182i | ||||||
\(872\) | 18.3770 | 0.622323 | ||||||||
\(873\) | 29.1271 | + | 8.57765i | 0.985802 | + | 0.290309i | ||||
\(874\) | 13.1096 | 0.443440 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.3362 | − | 16.4929i | −0.416800 | − | 0.557242i | ||||
\(877\) | 39.1853 | 1.32319 | 0.661597 | − | 0.749860i | \(-0.269879\pi\) | ||||
0.661597 | + | 0.749860i | \(0.269879\pi\) | |||||||
\(878\) | −27.8461 | −0.939759 | ||||||||
\(879\) | 22.9052 | − | 17.1324i | 0.772573 | − | 0.577862i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.2286i | 1.08581i | 0.839794 | + | 0.542904i | \(0.182675\pi\) | ||||
−0.839794 | + | 0.542904i | \(0.817325\pi\) | |||||||
\(882\) | 19.6977 | + | 5.80078i | 0.663255 | + | 0.195322i | ||||
\(883\) | − | 44.2593i | − | 1.48944i | −0.667375 | − | 0.744721i | \(-0.732582\pi\) | ||
0.667375 | − | 0.744721i | \(-0.267418\pi\) | |||||||
\(884\) | − | 2.15802i | − | 0.0725819i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 28.5213i | − | 0.958191i | ||||||
\(887\) | − | 28.6557i | − | 0.962165i | −0.876675 | − | 0.481082i | \(-0.840244\pi\) | ||
0.876675 | − | 0.481082i | \(-0.159756\pi\) | |||||||
\(888\) | 4.75923 | + | 6.36286i | 0.159709 | + | 0.213524i | ||||
\(889\) | 8.68353 | 0.291236 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.5422 | + | 11.5076i | 0.922699 | + | 0.385520i | ||||
\(892\) | − | 2.17815i | − | 0.0729298i | ||||||
\(893\) | − | 12.5565i | − | 0.420186i | ||||||
\(894\) | −30.5295 | + | 22.8352i | −1.02106 | + | 0.763722i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 0.394100i | − | 0.0131660i | ||||||
\(897\) | −8.75976 | − | 11.7114i | −0.292480 | − | 0.391032i | ||||
\(898\) | 4.00000 | 0.133482 | ||||||||
\(899\) | −12.3772 | −0.412804 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.85299i | 0.194991i | ||||||||
\(902\) | 4.75976 | + | 26.6071i | 0.158483 | + | 0.885921i | ||||
\(903\) | −1.06373 | − | 1.42215i | −0.0353986 | − | 0.0473262i | ||||
\(904\) | 6.37988i | 0.212192i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 14.4491 | + | 19.3178i | 0.480040 | + | 0.641791i | ||||
\(907\) | 7.17532i | 0.238253i | 0.992879 | + | 0.119126i | \(0.0380093\pi\) | ||||
−0.992879 | + | 0.119126i | \(0.961991\pi\) | |||||||
\(908\) | 6.83890i | 0.226957i | ||||||||
\(909\) | −2.55803 | + | 8.68628i | −0.0848445 | + | 0.288106i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.0314i | − | 1.06125i | −0.847607 | − | 0.530625i | \(-0.821957\pi\) | ||
0.847607 | − | 0.530625i | \(-0.178043\pi\) | |||||||
\(912\) | −5.12489 | + | 3.83327i | −0.169702 | + | 0.126932i | ||||
\(913\) | 0.991511 | + | 5.54256i | 0.0328142 | + | 0.183432i | ||||
\(914\) | 13.0651i | 0.432155i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.8474 | −0.787940 | ||||||||
\(917\) | 0.779324 | 0.0257355 | ||||||||
\(918\) | −4.41662 | + | 1.64131i | −0.145770 | + | 0.0541715i | ||||
\(919\) | − | 8.61703i | − | 0.284250i | −0.989849 | − | 0.142125i | \(-0.954607\pi\) | ||
0.989849 | − | 0.142125i | \(-0.0453934\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.3133 | + | 24.4840i | 0.603445 | + | 0.806776i | ||||
\(922\) | − | 20.1355i | − | 0.663127i | ||||||
\(923\) | 6.15802i | 0.202694i | ||||||||
\(924\) | −1.65406 | − | 1.54579i | −0.0544145 | − | 0.0508529i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.6071 | −0.414297 | ||||||||
\(927\) | 1.73171 | + | 0.509974i | 0.0568770 | + | 0.0167497i | ||||
\(928\) | − | 3.37573i | − | 0.110814i | ||||||
\(929\) | − | 2.05503i | − | 0.0674235i | −0.999432 | − | 0.0337117i | \(-0.989267\pi\) | ||
0.999432 | − | 0.0337117i | \(-0.0107328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.2909i | 0.828877i | ||||||||
\(932\) | − | 10.5760i | − | 0.346429i | ||||||
\(933\) | 5.73589 | − | 4.29028i | 0.187785 | − | 0.140457i | ||||
\(934\) | − | 14.9843i | − | 0.490302i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.84884 | + | 2.01692i | 0.223861 | + | 0.0659251i | ||||
\(937\) | 19.8342 | 0.647956 | 0.323978 | − | 0.946065i | \(-0.394980\pi\) | ||||
0.323978 | + | 0.946065i | \(0.394980\pi\) | |||||||
\(938\) | 4.69749 | 0.153378 | ||||||||
\(939\) | 16.8631 | − | 12.6131i | 0.550305 | − | 0.411612i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.98887 | 0.227831 | 0.113915 | − | 0.993490i | \(-0.463661\pi\) | ||||
0.113915 | + | 0.993490i | \(0.463661\pi\) | |||||||
\(942\) | 2.72249 | + | 3.63984i | 0.0887036 | + | 0.118592i | ||||
\(943\) | −28.9149 | −0.941598 | ||||||||
\(944\) | − | 7.76983i | − | 0.252886i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.51953 | − | 8.49418i | −0.0494041 | − | 0.276170i | ||||
\(947\) | 29.3913 | 0.955090 | 0.477545 | − | 0.878607i | \(-0.341527\pi\) | ||||
0.477545 | + | 0.878607i | \(0.341527\pi\) | |||||||
\(948\) | 3.55948 | − | 2.66239i | 0.115607 | − | 0.0864703i | ||||
\(949\) | −28.2994 | −0.918638 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.23290 | + | 9.67003i | 0.234543 | + | 0.313572i | ||||
\(952\) | 0.357360 | 0.0115821 | ||||||||
\(953\) | − | 0.203883i | − | 0.00660443i | −0.999995 | − | 0.00330221i | \(-0.998949\pi\) | ||
0.999995 | − | 0.00330221i | \(-0.00105113\pi\) | |||||||
\(954\) | −18.5755 | − | 5.47031i | −0.601403 | − | 0.177108i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22.4290 | 0.725406 | ||||||||
\(957\) | −14.1681 | − | 13.2408i | −0.457990 | − | 0.428013i | ||||
\(958\) | − | 23.7060i | − | 0.765905i | ||||||
\(959\) | 7.73114 | 0.249652 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.5565 | −0.566339 | ||||||||
\(962\) | 10.9178 | 0.352003 | ||||||||
\(963\) | 43.8740 | + | 12.9205i | 1.41382 | + | 0.416357i | ||||
\(964\) | 4.78820i | 0.154218i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.93936 | − | 1.45059i | 0.0623980 | − | 0.0466718i | ||||
\(967\) | −55.4842 | −1.78425 | −0.892126 | − | 0.451786i | \(-0.850787\pi\) | ||||
−0.892126 | + | 0.451786i | \(0.850787\pi\) | |||||||
\(968\) | −3.81355 | − | 10.3178i | −0.122572 | − | 0.331626i | ||||
\(969\) | −3.47591 | − | 4.64712i | −0.111662 | − | 0.149287i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 15.0321i | − | 0.482402i | −0.970475 | − | 0.241201i | \(-0.922459\pi\) | ||
0.970475 | − | 0.241201i | \(-0.0775413\pi\) | |||||||
\(972\) | −1.08115 | − | 15.5509i | −0.0346778 | − | 0.498796i | ||||
\(973\) | − | 7.37874i | − | 0.236552i | ||||||
\(974\) | −10.3279 | −0.330926 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 12.8346i | − | 0.410826i | ||||||
\(977\) | 44.5267 | 1.42454 | 0.712268 | − | 0.701908i | \(-0.247668\pi\) | ||||
0.712268 | + | 0.701908i | \(0.247668\pi\) | |||||||
\(978\) | −7.02752 | − | 9.39545i | −0.224715 | − | 0.300433i | ||||
\(979\) | 8.93791 | + | 49.9631i | 0.285657 | + | 1.59683i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −52.8854 | − | 15.5743i | −1.68850 | − | 0.497248i | ||||
\(982\) | 21.1608i | 0.675270i | ||||||||
\(983\) | −20.2004 | −0.644293 | −0.322146 | − | 0.946690i | \(-0.604404\pi\) | ||||
−0.322146 | + | 0.946690i | \(0.604404\pi\) | |||||||
\(984\) | 11.3036 | − | 8.45474i | 0.360345 | − | 0.269527i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.06102 | 0.0974829 | ||||||||
\(987\) | −1.38938 | − | 1.85753i | −0.0442243 | − | 0.0591258i | ||||
\(988\) | 8.79360i | 0.279762i | ||||||||
\(989\) | 9.23091 | 0.293526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.1668 | −1.24417 | −0.622087 | − | 0.782949i | \(-0.713715\pi\) | ||||
−0.622087 | + | 0.782949i | \(0.713715\pi\) | |||||||
\(992\) | 3.66654i | 0.116413i | ||||||||
\(993\) | 5.60030 | + | 7.48733i | 0.177720 | + | 0.237603i | ||||
\(994\) | −1.01975 | −0.0323444 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.35466 | − | 1.76121i | 0.0746102 | − | 0.0558062i | ||||
\(997\) | −20.6426 | −0.653757 | −0.326878 | − | 0.945066i | \(-0.605997\pi\) | ||||
−0.326878 | + | 0.945066i | \(0.605997\pi\) | |||||||
\(998\) | − | 23.6325i | − | 0.748074i | ||||||
\(999\) | −8.30370 | − | 22.3445i | −0.262717 | − | 0.706948i |
(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 | 1650.2.f.f.1649.5 | 8 | ||
3.2 | odd | 2 | 1650.2.f.c.1649.4 | 8 | |||
5.2 | odd | 4 | 1650.2.d.c.1451.2 | 8 | |||
5.3 | odd | 4 | 330.2.d.b.131.7 | yes | 8 | ||
5.4 | even | 2 | 1650.2.f.d.1649.4 | 8 | |||
11.10 | odd | 2 | 1650.2.f.e.1649.1 | 8 | |||
15.2 | even | 4 | 1650.2.d.f.1451.1 | 8 | |||
15.8 | even | 4 | 330.2.d.a.131.8 | yes | 8 | ||
15.14 | odd | 2 | 1650.2.f.e.1649.5 | 8 | |||
20.3 | even | 4 | 2640.2.f.a.1121.2 | 8 | |||
33.32 | even | 2 | 1650.2.f.d.1649.8 | 8 | |||
55.32 | even | 4 | 1650.2.d.f.1451.2 | 8 | |||
55.43 | even | 4 | 330.2.d.a.131.7 | ✓ | 8 | ||
55.54 | odd | 2 | 1650.2.f.c.1649.8 | 8 | |||
60.23 | odd | 4 | 2640.2.f.b.1121.1 | 8 | |||
165.32 | odd | 4 | 1650.2.d.c.1451.1 | 8 | |||
165.98 | odd | 4 | 330.2.d.b.131.8 | yes | 8 | ||
165.164 | even | 2 | inner | 1650.2.f.f.1649.1 | 8 | ||
220.43 | odd | 4 | 2640.2.f.b.1121.2 | 8 | |||
660.263 | even | 4 | 2640.2.f.a.1121.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.d.a.131.7 | ✓ | 8 | 55.43 | even | 4 | ||
330.2.d.a.131.8 | yes | 8 | 15.8 | even | 4 | ||
330.2.d.b.131.7 | yes | 8 | 5.3 | odd | 4 | ||
330.2.d.b.131.8 | yes | 8 | 165.98 | odd | 4 | ||
1650.2.d.c.1451.1 | 8 | 165.32 | odd | 4 | |||
1650.2.d.c.1451.2 | 8 | 5.2 | odd | 4 | |||
1650.2.d.f.1451.1 | 8 | 15.2 | even | 4 | |||
1650.2.d.f.1451.2 | 8 | 55.32 | even | 4 | |||
1650.2.f.c.1649.4 | 8 | 3.2 | odd | 2 | |||
1650.2.f.c.1649.8 | 8 | 55.54 | odd | 2 | |||
1650.2.f.d.1649.4 | 8 | 5.4 | even | 2 | |||
1650.2.f.d.1649.8 | 8 | 33.32 | even | 2 | |||
1650.2.f.e.1649.1 | 8 | 11.10 | odd | 2 | |||
1650.2.f.e.1649.5 | 8 | 15.14 | odd | 2 | |||
1650.2.f.f.1649.1 | 8 | 165.164 | even | 2 | inner | ||
1650.2.f.f.1649.5 | 8 | 1.1 | even | 1 | trivial | ||
2640.2.f.a.1121.1 | 8 | 660.263 | even | 4 | |||
2640.2.f.a.1121.2 | 8 | 20.3 | even | 4 | |||
2640.2.f.b.1121.1 | 8 | 60.23 | odd | 4 | |||
2640.2.f.b.1121.2 | 8 | 220.43 | odd | 4 |