Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), degree \(2\), 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: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.21913473024.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 11x^{6} - 2x^{5} + 51x^{4} + 162x^{2} + 112x + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(-0.591990 - 1.02536i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.961 |
Dual form | 1960.2.q.x.361.3 |
$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.591990 | + | 1.02536i | 0.341785 | + | 0.591990i | 0.984764 | − | 0.173894i | \(-0.0556351\pi\) |
−0.642979 | + | 0.765884i | \(0.722302\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.799096 | − | 1.38408i | 0.266365 | − | 0.461359i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.115117 | − | 0.199389i | −0.0347091 | − | 0.0601179i | 0.848149 | − | 0.529758i | \(-0.177717\pi\) |
−0.882858 | + | 0.469640i | \(0.844384\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.27259 | −0.630304 | −0.315152 | − | 0.949041i | \(-0.602055\pi\) | ||||
−0.315152 | + | 0.949041i | \(0.602055\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.18398 | −0.305702 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.26639 | − | 5.65755i | −0.792216 | − | 1.37216i | −0.924592 | − | 0.380958i | \(-0.875594\pi\) |
0.132376 | − | 0.991200i | \(-0.457739\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.130093 | − | 0.225328i | 0.0298454 | − | 0.0516937i | −0.850717 | − | 0.525624i | \(-0.823832\pi\) |
0.880562 | + | 0.473930i | \(0.157165\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.43539 | − | 7.68233i | 0.924843 | − | 1.60188i | 0.133030 | − | 0.991112i | \(-0.457529\pi\) |
0.791813 | − | 0.610764i | \(-0.209137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.44417 | 1.04773 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.42662 | 1.00770 | 0.503849 | − | 0.863792i | \(-0.331917\pi\) | ||||
0.503849 | + | 0.863792i | \(0.331917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.43539 | − | 4.21822i | −0.437409 | − | 0.757615i | 0.560079 | − | 0.828439i | \(-0.310771\pi\) |
−0.997489 | + | 0.0708235i | \(0.977437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.136296 | − | 0.236072i | 0.0237261 | − | 0.0410949i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.577014 | − | 0.999417i | 0.0948605 | − | 0.164303i | −0.814690 | − | 0.579897i | \(-0.803093\pi\) |
0.909550 | + | 0.415594i | \(0.136426\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.34535 | − | 2.33022i | −0.215429 | − | 0.373133i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.43337 | 0.692377 | 0.346188 | − | 0.938165i | \(-0.387476\pi\) | ||||
0.346188 | + | 0.938165i | \(0.387476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.17723 | 0.637021 | 0.318511 | − | 0.947919i | \(-0.396817\pi\) | ||||
0.318511 | + | 0.947919i | \(0.396817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.799096 | + | 1.38408i | 0.119122 | + | 0.206326i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.461897 | + | 0.800028i | −0.0673745 | + | 0.116696i | −0.897745 | − | 0.440516i | \(-0.854796\pi\) |
0.830370 | + | 0.557212i | \(0.188129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.86734 | − | 6.69843i | 0.541536 | − | 0.937967i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.06743 | + | 1.84885i | 0.146623 | + | 0.253959i | 0.929977 | − | 0.367617i | \(-0.119826\pi\) |
−0.783354 | + | 0.621576i | \(0.786493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.230234 | 0.0310448 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.308055 | 0.0408029 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.53553 | + | 4.39167i | 0.330098 | + | 0.571747i | 0.982531 | − | 0.186100i | \(-0.0595847\pi\) |
−0.652432 | + | 0.757847i | \(0.726251\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.44417 | + | 7.69752i | −0.569017 | + | 0.985566i | 0.427646 | + | 0.903946i | \(0.359343\pi\) |
−0.996663 | + | 0.0816204i | \(0.973990\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.13630 | − | 1.96812i | 0.140940 | − | 0.244116i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.07984 | − | 7.06649i | −0.498432 | − | 0.863309i | 0.501567 | − | 0.865119i | \(-0.332757\pi\) |
−0.999998 | + | 0.00180980i | \(0.999424\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.5028 | 1.26439 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.06556 | −1.07588 | −0.537942 | − | 0.842982i | \(-0.680798\pi\) | ||||
−0.537942 | + | 0.842982i | \(0.680798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00478 | − | 5.20442i | −0.351682 | − | 0.609132i | 0.634862 | − | 0.772626i | \(-0.281057\pi\) |
−0.986544 | + | 0.163494i | \(0.947724\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.591990 | − | 1.02536i | 0.0683571 | − | 0.118398i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0564558 | + | 0.0977843i | −0.00635177 | + | 0.0110016i | −0.869184 | − | 0.494489i | \(-0.835355\pi\) |
0.862832 | + | 0.505491i | \(0.168689\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.825600 | + | 1.42998i | 0.0917334 | + | 0.158887i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.72065 | 0.957216 | 0.478608 | − | 0.878029i | \(-0.341141\pi\) | ||||
0.478608 | + | 0.878029i | \(0.341141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.53278 | 0.708579 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.21250 | + | 5.56422i | 0.344416 | + | 0.596547i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.95852 | + | 13.7846i | −0.843601 | + | 1.46116i | 0.0432288 | + | 0.999065i | \(0.486236\pi\) |
−0.886830 | + | 0.462095i | \(0.847098\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.88345 | − | 4.99429i | 0.299000 | − | 0.517884i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.130093 | + | 0.225328i | 0.0133473 | + | 0.0231181i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.29565 | 0.436157 | 0.218079 | − | 0.975931i | \(-0.430021\pi\) | ||||
0.218079 | + | 0.975931i | \(0.430021\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.367959 | −0.0369812 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.69356 | − | 6.39743i | −0.367523 | − | 0.636568i | 0.621655 | − | 0.783291i | \(-0.286461\pi\) |
−0.989178 | + | 0.146723i | \(0.953127\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.29032 | − | 9.16311i | 0.521271 | − | 0.902868i | −0.478423 | − | 0.878130i | \(-0.658791\pi\) |
0.999694 | − | 0.0247384i | \(-0.00787529\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.73306 | − | 11.6620i | 0.650910 | − | 1.12741i | −0.331993 | − | 0.943282i | \(-0.607721\pi\) |
0.982903 | − | 0.184127i | \(-0.0589456\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.25284 | − | 7.36614i | −0.407348 | − | 0.705548i | 0.587243 | − | 0.809410i | \(-0.300213\pi\) |
−0.994592 | + | 0.103862i | \(0.966880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.36634 | 0.129688 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.3968 | 1.73063 | 0.865313 | − | 0.501232i | \(-0.167120\pi\) | ||||
0.865313 | + | 0.501232i | \(0.167120\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.43539 | + | 7.68233i | 0.413603 | + | 0.716381i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.81602 | + | 3.14544i | −0.167891 | + | 0.290796i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.47350 | − | 9.48037i | 0.497591 | − | 0.861852i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.62451 | + | 4.54579i | 0.236644 | + | 0.409880i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.41032 | 0.746295 | 0.373147 | − | 0.927772i | \(-0.378279\pi\) | ||||
0.373147 | + | 0.927772i | \(0.378279\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.47287 | + | 4.28314i | 0.217724 | + | 0.377110i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.891086 | − | 1.54341i | 0.0778546 | − | 0.134848i | −0.824470 | − | 0.565906i | \(-0.808526\pi\) |
0.902324 | + | 0.431058i | \(0.141860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.72208 | + | 4.71479i | −0.234280 | + | 0.405784i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.65685 | + | 9.79796i | 0.483298 | + | 0.837096i | 0.999816 | − | 0.0191800i | \(-0.00610555\pi\) |
−0.516518 | + | 0.856276i | \(0.672772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4390 | 1.30952 | 0.654761 | − | 0.755836i | \(-0.272769\pi\) | ||||
0.654761 | + | 0.755836i | \(0.272769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.09375 | −0.0921105 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.261614 | + | 0.453129i | 0.0218773 | + | 0.0378926i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.71331 | + | 4.69959i | −0.225328 | + | 0.390280i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.6406 | + | 20.1620i | −0.953631 | + | 1.65174i | −0.216161 | + | 0.976358i | \(0.569354\pi\) |
−0.737470 | + | 0.675380i | \(0.763980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1699 | − | 19.3468i | −0.908992 | − | 1.57442i | −0.815467 | − | 0.578804i | \(-0.803520\pi\) |
−0.0935251 | − | 0.995617i | \(-0.529814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.4406 | −0.844076 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.87079 | 0.391231 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.76301 | + | 3.05363i | 0.140704 | + | 0.243706i | 0.927762 | − | 0.373173i | \(-0.121730\pi\) |
−0.787058 | + | 0.616879i | \(0.788397\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.26382 | + | 2.18900i | −0.100227 | + | 0.173599i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.12610 | − | 14.0748i | 0.636485 | − | 1.10242i | −0.349714 | − | 0.936857i | \(-0.613721\pi\) |
0.986198 | − | 0.165568i | \(-0.0529456\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.136296 | + | 0.236072i | 0.0106107 | + | 0.0183782i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.99714 | −0.309308 | −0.154654 | − | 0.987969i | \(-0.549426\pi\) | ||||
−0.154654 | + | 0.987969i | \(0.549426\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.83532 | −0.602717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.207914 | − | 0.360117i | −0.0158996 | − | 0.0275389i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.81070 | + | 15.2606i | −0.669865 | + | 1.16024i | 0.308077 | + | 0.951361i | \(0.400315\pi\) |
−0.977942 | + | 0.208878i | \(0.933019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.00202 | + | 5.19965i | −0.225646 | + | 0.390830i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.6406 | − | 21.8941i | −0.944799 | − | 1.63644i | −0.756153 | − | 0.654395i | \(-0.772923\pi\) |
−0.188646 | − | 0.982045i | \(-0.560410\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.4950 | 1.37473 | 0.687363 | − | 0.726315i | \(-0.258768\pi\) | ||||
0.687363 | + | 0.726315i | \(0.258768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.5236 | −0.777927 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.577014 | + | 0.999417i | 0.0424229 | + | 0.0734786i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.752035 | + | 1.30256i | −0.0549942 | + | 0.0952528i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.93289 | + | 17.2043i | −0.718719 | + | 1.24486i | 0.242788 | + | 0.970079i | \(0.421938\pi\) |
−0.961508 | + | 0.274779i | \(0.911395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.71676 | + | 9.90172i | 0.411501 | + | 0.712741i | 0.995054 | − | 0.0993341i | \(-0.0316712\pi\) |
−0.583553 | + | 0.812075i | \(0.698338\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.69070 | 0.192685 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.56273 | −0.325081 | −0.162541 | − | 0.986702i | \(-0.551969\pi\) | ||||
−0.162541 | + | 0.986702i | \(0.551969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.22146 | + | 12.5079i | 0.511916 | + | 0.886664i | 0.999905 | + | 0.0138143i | \(0.00439737\pi\) |
−0.487989 | + | 0.872850i | \(0.662269\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.83045 | − | 8.36658i | 0.340713 | − | 0.590133i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.21669 | + | 3.83941i | −0.154820 | + | 0.268156i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.08861 | − | 12.2778i | −0.492693 | − | 0.853369i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0599037 | −0.00414363 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.63651 | 0.456876 | 0.228438 | − | 0.973558i | \(-0.426638\pi\) | ||||
0.228438 | + | 0.973558i | \(0.426638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.36672 | − | 9.29543i | −0.367721 | − | 0.636912i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.08861 | + | 3.61758i | −0.142442 | + | 0.246717i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.55759 | − | 6.16193i | 0.240400 | − | 0.416385i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.42317 | + | 12.8573i | 0.499337 | + | 0.864876i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.3325 | −1.36156 | −0.680782 | − | 0.732486i | \(-0.738360\pi\) | ||||
−0.680782 | + | 0.732486i | \(0.738360\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.59819 | −0.106546 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.9656 | − | 20.7250i | −0.794185 | − | 1.37557i | −0.923355 | − | 0.383946i | \(-0.874565\pi\) |
0.129171 | − | 0.991622i | \(-0.458769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.29767 | + | 2.24763i | −0.0857523 | + | 0.148527i | −0.905712 | − | 0.423895i | \(-0.860663\pi\) |
0.819959 | + | 0.572422i | \(0.193996\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.58189 | − | 13.1322i | 0.496706 | − | 0.860320i | −0.503287 | − | 0.864120i | \(-0.667876\pi\) |
0.999993 | + | 0.00379927i | \(0.00120935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.461897 | − | 0.800028i | −0.0301308 | − | 0.0521881i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.133685 | −0.00868377 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5656 | 0.683431 | 0.341716 | − | 0.939803i | \(-0.388992\pi\) | ||||
0.341716 | + | 0.939803i | \(0.388992\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.83808 | − | 17.0401i | −0.633726 | − | 1.09765i | −0.986783 | − | 0.162044i | \(-0.948191\pi\) |
0.353057 | − | 0.935602i | \(-0.385142\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.18875 | − | 12.4513i | 0.461159 | − | 0.798750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.295648 | + | 0.512078i | −0.0188117 | + | 0.0325828i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.16254 | + | 8.94178i | 0.327163 | + | 0.566662i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.0498 | −1.58113 | −0.790564 | − | 0.612380i | \(-0.790212\pi\) | ||||
−0.790564 | + | 0.612380i | \(0.790212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.04236 | −0.128402 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.86734 | + | 6.69843i | 0.242182 | + | 0.419472i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.857500 | + | 1.48523i | −0.0534894 | + | 0.0926464i | −0.891530 | − | 0.452961i | \(-0.850368\pi\) |
0.838041 | + | 0.545607i | \(0.183701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.33639 | − | 7.51085i | 0.268416 | − | 0.464910i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0587 | + | 19.1542i | 0.681906 | + | 1.18110i | 0.974398 | + | 0.224828i | \(0.0721821\pi\) |
−0.292492 | + | 0.956268i | \(0.594485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.13487 | −0.131144 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.8454 | −1.15332 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.9630 | + | 27.6488i | 0.973283 | + | 1.68578i | 0.685488 | + | 0.728084i | \(0.259589\pi\) |
0.287796 | + | 0.957692i | \(0.407078\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8883 | − | 22.3232i | 0.782910 | − | 1.35604i | −0.147329 | − | 0.989088i | \(-0.547068\pi\) |
0.930239 | − | 0.366953i | \(-0.119599\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.115117 | + | 0.199389i | −0.00694182 | + | 0.0120236i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00877 | + | 6.94340i | 0.240864 | + | 0.417188i | 0.960961 | − | 0.276685i | \(-0.0892360\pi\) |
−0.720097 | + | 0.693874i | \(0.755903\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.78445 | −0.466043 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.13207 | −0.186844 | −0.0934218 | − | 0.995627i | \(-0.529781\pi\) | ||||
−0.0934218 | + | 0.995627i | \(0.529781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.58524 | − | 2.74571i | −0.0942325 | − | 0.163216i | 0.815056 | − | 0.579383i | \(-0.196706\pi\) |
−0.909288 | + | 0.416167i | \(0.863373\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.154027 | + | 0.266783i | −0.00912380 | + | 0.0158029i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8386 | + | 22.2371i | −0.755212 | + | 1.30806i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.54298 | + | 4.40457i | 0.149072 | + | 0.258200i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.5264 | −1.02390 | −0.511952 | − | 0.859014i | \(-0.671077\pi\) | ||||
−0.511952 | + | 0.859014i | \(0.671077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.07107 | −0.295249 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.626717 | − | 1.08550i | −0.0363658 | − | 0.0629874i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.0798 | + | 17.4588i | −0.582932 | + | 1.00967i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.37310 | − | 7.57443i | 0.251228 | − | 0.435139i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.44417 | − | 7.69752i | −0.254472 | − | 0.440759i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.11063 | 0.120460 | 0.0602300 | − | 0.998185i | \(-0.480817\pi\) | ||||
0.0602300 | + | 0.998185i | \(0.480817\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.5273 | 0.712651 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.4075 | − | 18.0263i | −0.590153 | − | 1.02217i | −0.994211 | − | 0.107442i | \(-0.965734\pi\) |
0.404058 | − | 0.914733i | \(-0.367599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6930 | − | 18.5208i | 0.604405 | − | 1.04686i | −0.387741 | − | 0.921769i | \(-0.626744\pi\) |
0.992145 | − | 0.125091i | \(-0.0399223\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.74547 | + | 13.4155i | −0.435029 | + | 0.753492i | −0.997298 | − | 0.0734623i | \(-0.976595\pi\) |
0.562269 | + | 0.826954i | \(0.309928\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.624697 | − | 1.08201i | −0.0349763 | − | 0.0605807i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.9436 | 0.889886 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.69974 | −0.0945760 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.13630 | + | 1.96812i | 0.0630304 | + | 0.109172i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.03528 | − | 8.72135i | 0.278451 | − | 0.482292i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.26180 | − | 7.38165i | 0.234250 | − | 0.405732i | −0.724805 | − | 0.688954i | \(-0.758070\pi\) |
0.959054 | + | 0.283222i | \(0.0914033\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.922179 | − | 1.59726i | −0.0505351 | − | 0.0875294i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.15968 | 0.445811 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.1246 | −0.987309 | −0.493655 | − | 0.869658i | \(-0.664339\pi\) | ||||
−0.493655 | + | 0.869658i | \(0.664339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.8907 | + | 18.8633i | 0.591503 | + | 1.02451i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.560711 | + | 0.971179i | −0.0303642 | + | 0.0525923i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.25141 | + | 9.09571i | −0.282727 | + | 0.489697i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.05113 | − | 3.55266i | −0.110110 | − | 0.190717i | 0.805704 | − | 0.592318i | \(-0.201787\pi\) |
−0.915815 | + | 0.401601i | \(0.868454\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.67850 | −0.464549 | −0.232275 | − | 0.972650i | \(-0.574617\pi\) | ||||
−0.232275 | + | 0.972650i | \(0.574617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.3724 | −0.660388 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0581 | − | 26.0814i | −0.801462 | − | 1.38817i | −0.918653 | − | 0.395064i | \(-0.870722\pi\) |
0.117191 | − | 0.993109i | \(-0.462611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.53278 | − | 7.85100i | 0.240575 | − | 0.416688i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.1421 | + | 31.4231i | −0.957505 | + | 1.65845i | −0.228977 | + | 0.973432i | \(0.573538\pi\) |
−0.728528 | + | 0.685016i | \(0.759795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.46615 | + | 16.3959i | 0.498219 | + | 0.862940i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.9610 | 0.680277 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00955 | 0.314554 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.35574 | + | 9.27641i | 0.279567 | + | 0.484225i | 0.971277 | − | 0.237951i | \(-0.0764757\pi\) |
−0.691710 | + | 0.722175i | \(0.743142\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.54269 | − | 6.13612i | 0.184425 | − | 0.319434i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.82167 | + | 4.88728i | −0.146101 | + | 0.253054i | −0.929783 | − | 0.368108i | \(-0.880006\pi\) |
0.783682 | + | 0.621162i | \(0.213339\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.591990 | + | 1.02536i | 0.0305702 | + | 0.0529492i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.3325 | −0.635156 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.59944 | −0.0821575 | −0.0410787 | − | 0.999156i | \(-0.513079\pi\) | ||||
−0.0410787 | + | 0.999156i | \(0.513079\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.97882 | + | 8.62357i | 0.255073 | + | 0.441799i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.4447 | − | 25.0189i | 0.738089 | − | 1.27841i | −0.215266 | − | 0.976555i | \(-0.569062\pi\) |
0.953355 | − | 0.301852i | \(-0.0976047\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.33801 | − | 5.78160i | 0.169680 | − | 0.293895i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.7613 | + | 20.3712i | 0.596323 | + | 1.03286i | 0.993359 | + | 0.115058i | \(0.0367055\pi\) |
−0.397036 | + | 0.917803i | \(0.629961\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −57.9509 | −2.93070 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.11006 | 0.106438 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.0564558 | − | 0.0977843i | −0.00284060 | − | 0.00492006i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.29032 | − | 14.3593i | 0.416079 | − | 0.720671i | −0.579462 | − | 0.814999i | \(-0.696737\pi\) |
0.995541 | + | 0.0943288i | \(0.0300705\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.760807 | − | 1.31776i | 0.0379929 | − | 0.0658056i | −0.846404 | − | 0.532542i | \(-0.821237\pi\) |
0.884397 | + | 0.466736i | \(0.154570\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.53466 | + | 9.58630i | 0.275701 | + | 0.477528i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.65120 | −0.0820488 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.265697 | −0.0131701 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.71464 | + | 4.70189i | 0.134230 | + | 0.232493i | 0.925303 | − | 0.379228i | \(-0.123811\pi\) |
−0.791073 | + | 0.611722i | \(0.790477\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.69760 | + | 11.6006i | −0.330368 | + | 0.572214i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.36033 | + | 7.55231i | −0.214040 | + | 0.370728i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.13974 | + | 15.8305i | 0.447575 | + | 0.775223i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.4199 | 0.606750 | 0.303375 | − | 0.952871i | \(-0.401886\pi\) | ||||
0.303375 | + | 0.952871i | \(0.401886\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.6804 | −1.00790 | −0.503951 | − | 0.863732i | \(-0.668121\pi\) | ||||
−0.503951 | + | 0.863732i | \(0.668121\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.738200 | + | 1.27860i | 0.0358925 | + | 0.0621676i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.26639 | + | 5.65755i | −0.158443 | + | 0.274432i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.309746 | + | 0.536496i | −0.0149547 | + | 0.0259023i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.8076 | + | 27.3795i | 0.761424 | + | 1.31883i | 0.942117 | + | 0.335286i | \(0.108833\pi\) |
−0.180692 | + | 0.983540i | \(0.557834\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.1247 | −1.49576 | −0.747880 | − | 0.663834i | \(-0.768928\pi\) | ||||
−0.747880 | + | 0.663834i | \(0.768928\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.42501 | −0.308055 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.15403 | − | 1.99883i | −0.0552046 | − | 0.0956172i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.122199 | + | 0.211655i | −0.00583223 | + | 0.0101017i | −0.868927 | − | 0.494941i | \(-0.835190\pi\) |
0.863095 | + | 0.505042i | \(0.168523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.72741 | − | 2.99196i | 0.0820716 | − | 0.142152i | −0.822068 | − | 0.569389i | \(-0.807180\pi\) |
0.904140 | + | 0.427237i | \(0.140513\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.95852 | − | 13.7846i | −0.377270 | − | 0.653451i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.5643 | −1.30375 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.5329 | −0.733044 | −0.366522 | − | 0.930409i | \(-0.619452\pi\) | ||||
−0.366522 | + | 0.930409i | \(0.619452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.510357 | − | 0.883964i | −0.0240318 | − | 0.0416243i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.2249 | − | 22.9062i | 0.621360 | − | 1.07623i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.26896 | − | 9.12610i | 0.246471 | − | 0.426901i | −0.716073 | − | 0.698026i | \(-0.754062\pi\) |
0.962544 | + | 0.271124i | \(0.0873955\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.7828 | − | 30.8007i | −0.830028 | − | 1.43765i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.98972 | 0.278969 | 0.139485 | − | 0.990224i | \(-0.455455\pi\) | ||||
0.139485 | + | 0.990224i | \(0.455455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.3601 | −1.55038 | −0.775188 | − | 0.631731i | \(-0.782345\pi\) | ||||
−0.775188 | + | 0.631731i | \(0.782345\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.88345 | + | 4.99429i | 0.133717 | + | 0.231605i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.85379 | + | 17.0673i | −0.455979 | + | 0.789779i | −0.998744 | − | 0.0501059i | \(-0.984044\pi\) |
0.542765 | + | 0.839885i | \(0.317377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.08737 | + | 3.61543i | −0.0961810 | + | 0.166590i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.480870 | − | 0.832892i | −0.0221104 | − | 0.0382964i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.260186 | −0.0119382 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.41193 | 0.156222 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.162800 | − | 0.281978i | −0.00743853 | − | 0.0128839i | 0.862282 | − | 0.506428i | \(-0.169034\pi\) |
−0.869721 | + | 0.493544i | \(0.835701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.31132 | + | 2.27127i | −0.0597909 | + | 0.103561i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.14782 | + | 3.72014i | −0.0975277 | + | 0.168923i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.46021 | + | 14.6535i | 0.383369 | + | 0.664014i | 0.991541 | − | 0.129791i | \(-0.0414306\pi\) |
−0.608173 | + | 0.793805i | \(0.708097\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.2423 | 0.870165 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0203 | 0.677859 | 0.338929 | − | 0.940812i | \(-0.389935\pi\) | ||||
0.338929 | + | 0.940812i | \(0.389935\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.7255 | − | 30.7014i | −0.798314 | − | 1.38272i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.183979 | − | 0.318662i | 0.00826926 | − | 0.0143228i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.5215 | + | 35.5443i | −0.918670 | + | 1.59118i | −0.117233 | + | 0.993104i | \(0.537402\pi\) |
−0.801437 | + | 0.598079i | \(0.795931\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.36627 | − | 4.09850i | −0.105717 | − | 0.183107i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.29741 | 0.369963 | 0.184982 | − | 0.982742i | \(-0.440777\pi\) | ||||
0.184982 | + | 0.982742i | \(0.440777\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.38712 | 0.328722 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.63843 | − | 8.03400i | −0.206000 | − | 0.356802i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.35633 | + | 7.54538i | −0.193091 | + | 0.334443i | −0.946273 | − | 0.323369i | \(-0.895185\pi\) |
0.753182 | + | 0.657812i | \(0.228518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.708248 | − | 1.22672i | 0.0312699 | − | 0.0541611i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.29032 | + | 9.16311i | 0.233120 | + | 0.403775i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.212689 | 0.00935404 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.8634 | −0.915800 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.5528 | + | 23.4742i | 0.593760 | + | 1.02842i | 0.993721 | + | 0.111890i | \(0.0356903\pi\) |
−0.399961 | + | 0.916532i | \(0.630976\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.685928 | − | 1.18806i | 0.0299935 | − | 0.0519503i | −0.850639 | − | 0.525750i | \(-0.823785\pi\) |
0.880633 | + | 0.473800i | \(0.157118\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.9099 | + | 27.5567i | −0.693045 | + | 1.20039i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.8454 | − | 48.2297i | −1.21067 | − | 2.09694i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.10454 | 0.351707 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.0753 | −0.436408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.73306 | + | 11.6620i | 0.291096 | + | 0.504192i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.9662 | − | 25.9221i | 0.645837 | − | 1.11862i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.28279 | + | 7.41802i | −0.184132 | + | 0.318925i | −0.943284 | − | 0.331988i | \(-0.892281\pi\) |
0.759152 | + | 0.650913i | \(0.225614\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.9489 | + | 18.9640i | 0.469861 | + | 0.813823i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.50568 | 0.364343 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.2056 | 1.89009 | 0.945046 | − | 0.326936i | \(-0.106016\pi\) | ||||
0.945046 | + | 0.326936i | \(0.106016\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.10263 | + | 12.3021i | 0.303133 | + | 0.525042i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.705966 | − | 1.22277i | 0.0300751 | − | 0.0520917i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.683172 | + | 1.18329i | −0.0289991 | + | 0.0502278i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.66926 | + | 11.5515i | 0.282586 | + | 0.489453i | 0.972021 | − | 0.234895i | \(-0.0754745\pi\) |
−0.689435 | + | 0.724347i | \(0.742141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.49313 | −0.401517 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.78079 | −0.0751849 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.8660 | − | 25.7487i | −0.626528 | − | 1.08518i | −0.988243 | − | 0.152889i | \(-0.951142\pi\) |
0.361716 | − | 0.932288i | \(-0.382191\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.19841 | + | 15.9321i | −0.386980 | + | 0.670269i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.7930 | + | 20.4260i | −0.494387 | + | 0.856303i | −0.999979 | − | 0.00646948i | \(-0.997941\pi\) |
0.505592 | + | 0.862773i | \(0.331274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.3217 | − | 28.2700i | −0.683042 | − | 1.18306i | −0.974048 | − | 0.226342i | \(-0.927323\pi\) |
0.291006 | − | 0.956721i | \(-0.406010\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.5207 | −0.982591 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.87079 | −0.369937 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.4098 | + | 24.9584i | 0.599886 | + | 1.03903i | 0.992837 | + | 0.119474i | \(0.0381209\pi\) |
−0.392951 | + | 0.919559i | \(0.628546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.76852 | + | 11.7234i | −0.281290 | + | 0.487209i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.245760 | − | 0.425669i | 0.0101783 | − | 0.0176294i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.81602 | − | 3.14544i | −0.0750832 | − | 0.130048i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.82205 | −0.0752039 | −0.0376019 | − | 0.999293i | \(-0.511972\pi\) | ||||
−0.0376019 | + | 0.999293i | \(0.511972\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.26731 | −0.0522186 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.70109 | − | 4.67842i | −0.111108 | − | 0.192445i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.4684 | + | 26.7921i | −0.635212 | + | 1.10022i | 0.351258 | + | 0.936279i | \(0.385754\pi\) |
−0.986470 | + | 0.163941i | \(0.947579\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.55006 | + | 14.8091i | −0.349931 | + | 0.606098i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.1456 | + | 27.9650i | 0.659691 | + | 1.14262i | 0.980696 | + | 0.195540i | \(0.0626460\pi\) |
−0.321005 | + | 0.947077i | \(0.604021\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.2829 | −1.03131 | −0.515655 | − | 0.856797i | \(-0.672451\pi\) | ||||
−0.515655 | + | 0.856797i | \(0.672451\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0407 | −0.531060 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.47350 | + | 9.48037i | 0.222529 | + | 0.385432i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.64426 | − | 8.04410i | 0.188505 | − | 0.326500i | −0.756247 | − | 0.654286i | \(-0.772969\pi\) |
0.944752 | + | 0.327786i | \(0.106303\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.04970 | − | 1.81814i | 0.0424664 | − | 0.0735540i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.0305 | − | 34.6938i | −0.809023 | − | 1.40127i | −0.913541 | − | 0.406746i | \(-0.866663\pi\) |
0.104518 | − | 0.994523i | \(-0.466670\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.24902 | −0.211661 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.9860 | 1.12667 | 0.563336 | − | 0.826228i | \(-0.309518\pi\) | ||||
0.563336 | + | 0.826228i | \(0.309518\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9024 | + | 39.6681i | 0.920525 | + | 1.59440i | 0.798605 | + | 0.601856i | \(0.205572\pi\) |
0.121920 | + | 0.992540i | \(0.461095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.1470 | − | 41.8239i | 0.968986 | − | 1.67833i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0354624 | − | 0.0614227i | −0.00141623 | − | 0.00245299i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.53901 | −0.300600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5847 | 0.899082 | 0.449541 | − | 0.893260i | \(-0.351588\pi\) | ||||
0.449541 | + | 0.893260i | \(0.351588\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.92875 | + | 6.80479i | 0.156154 | + | 0.270466i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.20516 | + | 7.28355i | −0.166877 | + | 0.289039i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.24425 | + | 12.5474i | −0.286578 | + | 0.496368i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.7563 | + | 29.0227i | 0.661832 | + | 1.14633i | 0.980134 | + | 0.198338i | \(0.0635543\pi\) |
−0.318301 | + | 0.947990i | \(0.603112\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.4980 | 1.83370 | 0.916851 | − | 0.399231i | \(-0.130723\pi\) | ||||
0.916851 | + | 0.399231i | \(0.130723\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.94575 | −0.194739 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.787826 | + | 1.36455i | 0.0309726 | + | 0.0536462i | 0.881096 | − | 0.472937i | \(-0.156806\pi\) |
−0.850124 | + | 0.526583i | \(0.823473\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.583767 | − | 1.01111i | 0.0229148 | − | 0.0396897i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.06556 | + | 10.5059i | −0.237364 | + | 0.411126i | −0.959957 | − | 0.280148i | \(-0.909617\pi\) |
0.722593 | + | 0.691273i | \(0.242950\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.891086 | + | 1.54341i | 0.0348176 | + | 0.0603059i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.60442 | −0.374704 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.1682 | 1.36996 | 0.684979 | − | 0.728563i | \(-0.259811\pi\) | ||||
0.684979 | + | 0.728563i | \(0.259811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.812124 | + | 1.40664i | 0.0315880 | + | 0.0547120i | 0.881387 | − | 0.472395i | \(-0.156610\pi\) |
−0.849799 | + | 0.527106i | \(0.823277\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.78888 | + | 15.2228i | −0.341332 | + | 0.591204i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.0692 | − | 41.6891i | 0.931963 | − | 1.61421i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.0366 | − | 20.8481i | −0.465363 | − | 0.806032i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.04640 | 0.0790003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.3194 | −0.937443 | −0.468721 | − | 0.883346i | \(-0.655285\pi\) | ||||
−0.468721 | + | 0.883346i | \(0.655285\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.72208 | − | 4.71479i | −0.104773 | − | 0.181472i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.07763 | + | 10.5268i | −0.233582 | + | 0.404577i | −0.958860 | − | 0.283880i | \(-0.908378\pi\) |
0.725277 | + | 0.688457i | \(0.241712\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.1670 | − | 24.5380i | 0.542882 | − | 0.940299i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.2579 | + | 28.1595i | 0.622091 | + | 1.07749i | 0.989096 | + | 0.147275i | \(0.0470501\pi\) |
−0.367004 | + | 0.930219i | \(0.619617\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.3137 | −0.432275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.07282 | −0.117236 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.42584 | − | 4.20168i | −0.0924172 | − | 0.160071i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.1656 | + | 17.6073i | −0.386716 | + | 0.669812i | −0.992006 | − | 0.126194i | \(-0.959724\pi\) |
0.605290 | + | 0.796005i | \(0.293057\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.71951 | + | 13.3706i | −0.292818 | + | 0.507175i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.4811 | − | 25.0820i | −0.548512 | − | 0.950050i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.9536 | 0.679068 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.35321 | 0.277727 | 0.138863 | − | 0.990312i | \(-0.455655\pi\) | ||||
0.138863 | + | 0.990312i | \(0.455655\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.150131 | − | 0.260034i | −0.00566230 | − | 0.00980738i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.546876 | − | 0.947217i | 0.0205965 | − | 0.0356743i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.83188 | − | 10.1011i | 0.219021 | − | 0.379355i | −0.735488 | − | 0.677538i | \(-0.763047\pi\) |
0.954509 | + | 0.298183i | \(0.0963805\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0902272 | + | 0.156278i | 0.00338378 | + | 0.00586089i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.2077 | −1.61814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.523229 | −0.0195676 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.25472 | + | 10.8335i | 0.233587 | + | 0.404584i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.84285 | − | 4.92397i | 0.106021 | − | 0.183633i | −0.808134 | − | 0.588998i | \(-0.799522\pi\) |
0.914155 | + | 0.405365i | \(0.132856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6481 | − | 20.1751i | 0.433197 | − | 0.750319i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.71331 | − | 4.69959i | −0.100770 | − | 0.174538i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.6873 | 0.693074 | 0.346537 | − | 0.938036i | \(-0.387357\pi\) | ||||
0.346537 | + | 0.938036i | \(0.387357\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.9763 | 0.813936 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.6444 | − | 23.6329i | −0.504658 | − | 0.874094i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.918469 | + | 1.59083i | −0.0339244 | + | 0.0587588i | −0.882489 | − | 0.470333i | \(-0.844134\pi\) |
0.848565 | + | 0.529092i | \(0.177467\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.939319 | + | 1.62695i | −0.0346003 | + | 0.0599294i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.2817 | + | 21.2725i | 0.451789 | + | 0.782522i | 0.998497 | − | 0.0548012i | \(-0.0174525\pi\) |
−0.546708 | + | 0.837323i | \(0.684119\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.700083 | −0.0257182 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.1926 | −0.997601 | −0.498800 | − | 0.866717i | \(-0.666226\pi\) | ||||
−0.498800 | + | 0.866717i | \(0.666226\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.6406 | − | 20.1620i | −0.426477 | − | 0.738679i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.96864 | − | 12.0700i | 0.254969 | − | 0.441620i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.164228 | + | 0.284452i | −0.00599278 | + | 0.0103798i | −0.869006 | − | 0.494801i | \(-0.835241\pi\) |
0.863013 | + | 0.505181i | \(0.168574\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.8292 | − | 25.6849i | −0.540406 | − | 0.936011i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.3398 | 0.813027 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.6331 | −1.76760 | −0.883801 | − | 0.467864i | \(-0.845024\pi\) | ||||
−0.883801 | + | 0.467864i | \(0.845024\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.20906 | − | 2.09414i | −0.0438859 | − | 0.0760126i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.01127 | − | 6.94772i | 0.145408 | − | 0.251854i | −0.784117 | − | 0.620613i | \(-0.786884\pi\) |
0.929525 | + | 0.368759i | \(0.120217\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.22032 | − | 9.04186i | 0.188741 | − | 0.326909i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.76224 | − | 9.98048i | −0.208062 | − | 0.360374i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.6370 | 1.28510 | 0.642552 | − | 0.766242i | \(-0.277876\pi\) | ||||
0.642552 | + | 0.766242i | \(0.277876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.03053 | −0.0731276 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.7978 | − | 42.9510i | −0.891914 | − | 1.54484i | −0.837579 | − | 0.546317i | \(-0.816029\pi\) |
−0.0543350 | − | 0.998523i | \(-0.517304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.43539 | + | 4.21822i | −0.0874819 | + | 0.151523i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.576751 | − | 0.998962i | 0.0206642 | − | 0.0357915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.04360 | + | 1.80757i | 0.0373430 | + | 0.0646799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29.5434 | 1.05580 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.52603 | −0.125849 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.7217 | − | 18.5706i | −0.382188 | − | 0.661969i | 0.609187 | − | 0.793027i | \(-0.291496\pi\) |
−0.991375 | + | 0.131058i | \(0.958163\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.0932 | + | 22.6781i | −0.466131 | + | 0.807363i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0998 | − | 17.4933i | 0.358654 | − | 0.621206i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.26382 | − | 2.18900i | −0.0448231 | − | 0.0776358i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.1429 | 1.24482 | 0.622412 | − | 0.782690i | \(-0.286153\pi\) | ||||
0.622412 | + | 0.782690i | \(0.286153\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.03494 | 0.213501 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.7193 | + | 22.0304i | 0.449413 | + | 0.778405i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.691802 | + | 1.19824i | −0.0244132 | + | 0.0422848i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.8999 | + | 32.7356i | −0.665308 | + | 1.15235i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.16299 | + | 2.01435i | 0.0408884 | + | 0.0708208i | 0.885745 | − | 0.464171i | \(-0.153648\pi\) |
−0.844857 | + | 0.534992i | \(0.820315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.8045 | −0.414512 | −0.207256 | − | 0.978287i | \(-0.566453\pi\) | ||||
−0.207256 | + | 0.978287i | \(0.566453\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.5190 | 1.07035 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.12610 | + | 14.0748i | 0.284645 | + | 0.493019i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.543428 | − | 0.941245i | 0.0190121 | − | 0.0329300i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.8895 | − | 44.8419i | 0.903550 | − | 1.56499i | 0.0806973 | − | 0.996739i | \(-0.474285\pi\) |
0.822852 | − | 0.568255i | \(-0.192381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.3129 | + | 35.1830i | 0.708064 | + | 1.22640i | 0.965574 | + | 0.260128i | \(0.0837646\pi\) |
−0.257510 | + | 0.966276i | \(0.582902\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.272593 | −0.00949045 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.6201 | 0.438846 | 0.219423 | − | 0.975630i | \(-0.429583\pi\) | ||||
0.219423 | + | 0.975630i | \(0.429583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.2452 | + | 43.7260i | 0.876803 | + | 1.51867i | 0.854829 | + | 0.518909i | \(0.173662\pi\) |
0.0219739 | + | 0.999759i | \(0.493005\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.74630 | + | 8.22084i | −0.164647 | + | 0.285178i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.99857 | − | 3.46163i | 0.0691634 | − | 0.119795i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.2587 | − | 22.9647i | −0.458287 | − | 0.793776i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.41032 | −0.152261 | −0.0761305 | − | 0.997098i | \(-0.524257\pi\) | ||||
−0.0761305 | + | 0.997098i | \(0.524257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.448205 | 0.0154553 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.85415 | − | 3.21149i | −0.0638604 | − | 0.110610i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.91766 | − | 6.78559i | 0.134772 | − | 0.233431i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.87689 | − | 3.25086i | 0.0644146 | − | 0.111569i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.11857 | − | 8.86561i | −0.175462 | − | 0.303909i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.6785 | 0.708018 | 0.354009 | − | 0.935242i | \(-0.384818\pi\) | ||||
0.354009 | + | 0.935242i | \(0.384818\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.415828 | 0.0142210 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.96527 | + | 5.13600i | 0.101292 | + | 0.175443i | 0.912217 | − | 0.409707i | \(-0.134369\pi\) |
−0.810925 | + | 0.585150i | \(0.801036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.6916 | + | 27.1786i | −0.535390 | + | 0.927322i | 0.463755 | + | 0.885964i | \(0.346502\pi\) |
−0.999144 | + | 0.0413587i | \(0.986831\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.0855 | + | 22.6647i | −0.445435 | + | 0.771517i | −0.998082 | − | 0.0618987i | \(-0.980284\pi\) |
0.552647 | + | 0.833415i | \(0.313618\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.81070 | − | 15.2606i | −0.299573 | − | 0.518875i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.4013 | −1.03248 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0259961 | 0.000881857 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.27182 | + | 16.0593i | 0.314163 | + | 0.544147i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.43264 | − | 5.94550i | 0.116177 | − | 0.201225i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.1152 | − | 45.2328i | 0.881847 | − | 1.52740i | 0.0325618 | − | 0.999470i | \(-0.489633\pi\) |
0.849285 | − | 0.527934i | \(-0.177033\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.3754 | − | 17.9708i | −0.349955 | − | 0.606140i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.5930 | 1.13178 | 0.565888 | − | 0.824482i | \(-0.308533\pi\) | ||||
0.565888 | + | 0.824482i | \(0.308533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.5923 | 1.02951 | 0.514757 | − | 0.857336i | \(-0.327882\pi\) | ||||
0.514757 | + | 0.857336i | \(0.327882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.00202 | − | 5.19965i | −0.100912 | − | 0.174784i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.5152 | + | 42.4616i | −0.823141 | + | 1.42572i | 0.0801908 | + | 0.996780i | \(0.474447\pi\) |
−0.903332 | + | 0.428942i | \(0.858886\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.190081 | − | 0.329231i | 0.00636797 | − | 0.0110296i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.120179 | + | 0.208156i | 0.00402164 | + | 0.00696568i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.2811 | 0.845054 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.8686 | −0.796951 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.2160 | − | 22.8907i | −0.440777 | − | 0.763448i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.97331 | − | 12.0781i | 0.232315 | − | 0.402381i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.24752 | + | 16.0172i | −0.307398 | + | 0.532429i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.4507 | + | 31.9575i | 0.612644 | + | 1.06113i | 0.990793 | + | 0.135386i | \(0.0432274\pi\) |
−0.378149 | + | 0.925745i | \(0.623439\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.8060 | −0.391582 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.6118 | 1.14674 | 0.573371 | − | 0.819296i | \(-0.305636\pi\) | ||||
0.573371 | + | 0.819296i | \(0.305636\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.00390 | − | 1.73880i | −0.0332241 | − | 0.0575459i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.26180 | − | 9.11371i | 0.173950 | − | 0.301290i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.4085 | − | 26.6883i | 0.508279 | − | 0.880365i | −0.491675 | − | 0.870779i | \(-0.663615\pi\) |
0.999954 | − | 0.00958624i | \(-0.00305144\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.24947 | + | 2.16415i | 0.0411715 | + | 0.0713111i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.6023 | 0.678134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.15403 | −0.0379442 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.45496 | − | 14.6444i | −0.277697 | − | 0.480986i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.66936 | − | 15.0158i | 0.284433 | − | 0.492652i | −0.688039 | − | 0.725674i | \(-0.741528\pi\) |
0.972471 | + | 0.233022i | \(0.0748615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.3222 | − | 21.3427i | 0.403411 | − | 0.698729i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.752035 | − | 1.30256i | −0.0245942 | − | 0.0425983i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.3736 | 1.44962 | 0.724811 | − | 0.688948i | \(-0.241927\pi\) | ||||
0.724811 | + | 0.688948i | \(0.241927\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.3206 | 0.826307 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.829670 | − | 1.43703i | −0.0270465 | − | 0.0468458i | 0.852185 | − | 0.523240i | \(-0.175277\pi\) |
−0.879232 | + | 0.476394i | \(0.841944\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.6638 | − | 34.0586i | 0.640340 | − | 1.10910i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.7243 | − | 32.4314i | 0.608458 | − | 1.05388i | −0.383037 | − | 0.923733i | \(-0.625122\pi\) |
0.991495 | − | 0.130147i | \(-0.0415448\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.82863 | + | 11.8275i | 0.221667 | + | 0.383938i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.3409 | −0.594746 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.5875 | 1.21758 | 0.608789 | − | 0.793332i | \(-0.291656\pi\) | ||||
0.608789 | + | 0.793332i | \(0.291656\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.93289 | − | 17.2043i | −0.321421 | − | 0.556717i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.739628 | − | 1.28107i | 0.0239088 | − | 0.0414112i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.63772 | − | 6.30072i | 0.117346 | − | 0.203249i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.7607 | − | 18.6381i | −0.346760 | − | 0.600605i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.4335 | −0.368058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.5757 | −0.790302 | −0.395151 | − | 0.918616i | \(-0.629308\pi\) | ||||
−0.395151 | + | 0.918616i | \(0.629308\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.00623 | − | 1.74284i | −0.0323247 | − | 0.0559880i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.3177 | + | 42.1195i | −0.780392 | + | 1.35168i | 0.151321 | + | 0.988485i | \(0.451647\pi\) |
−0.931713 | + | 0.363194i | \(0.881686\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.34535 | + | 2.33022i | −0.0430857 | + | 0.0746267i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.16872 | − | 2.02428i | −0.0373906 | − | 0.0647623i | 0.846725 | − | 0.532032i | \(-0.178571\pi\) |
−0.884115 | + | 0.467269i | \(0.845238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.66465 | 0.117123 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.5937 | −0.434014 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.3665 | − | 24.8836i | −0.458221 | − | 0.793662i | 0.540646 | − | 0.841250i | \(-0.318180\pi\) |
−0.998867 | + | 0.0475879i | \(0.984847\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.28137 | − | 3.95144i | 0.0726903 | − | 0.125903i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.5276 | − | 32.0908i | 0.589145 | − | 1.02043i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.92394 | + | 6.79646i | 0.124648 | + | 0.215897i | 0.921595 | − | 0.388152i | \(-0.126887\pi\) |
−0.796947 | + | 0.604049i | \(0.793553\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.0918 | 0.320253 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.4429 | −0.457871 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.2262 | − | 29.8366i | −0.545558 | − | 0.944934i | −0.998572 | − | 0.0534302i | \(-0.982985\pi\) |
0.453014 | − | 0.891503i | \(-0.350349\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.14136 | − | 5.44099i | 0.0993882 | − | 0.172145i |
(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 | 1960.2.q.x.961.3 | 8 | ||
7.2 | even | 3 | 1960.2.a.y.1.2 | yes | 4 | ||
7.3 | odd | 6 | 1960.2.q.y.361.2 | 8 | |||
7.4 | even | 3 | inner | 1960.2.q.x.361.3 | 8 | ||
7.5 | odd | 6 | 1960.2.a.x.1.3 | ✓ | 4 | ||
7.6 | odd | 2 | 1960.2.q.y.961.2 | 8 | |||
28.19 | even | 6 | 3920.2.a.ce.1.2 | 4 | |||
28.23 | odd | 6 | 3920.2.a.cd.1.3 | 4 | |||
35.9 | even | 6 | 9800.2.a.cl.1.3 | 4 | |||
35.19 | odd | 6 | 9800.2.a.cs.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.x.1.3 | ✓ | 4 | 7.5 | odd | 6 | ||
1960.2.a.y.1.2 | yes | 4 | 7.2 | even | 3 | ||
1960.2.q.x.361.3 | 8 | 7.4 | even | 3 | inner | ||
1960.2.q.x.961.3 | 8 | 1.1 | even | 1 | trivial | ||
1960.2.q.y.361.2 | 8 | 7.3 | odd | 6 | |||
1960.2.q.y.961.2 | 8 | 7.6 | odd | 2 | |||
3920.2.a.cd.1.3 | 4 | 28.23 | odd | 6 | |||
3920.2.a.ce.1.2 | 4 | 28.19 | even | 6 | |||
9800.2.a.cl.1.3 | 4 | 35.9 | even | 6 | |||
9800.2.a.cs.1.2 | 4 | 35.19 | odd | 6 |