Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(157,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.bc (of order \(12\), degree \(4\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 28x^{14} + 519x^{12} - 5404x^{10} + 40705x^{8} - 194544x^{6} + 672624x^{4} - 1306368x^{2} + 1679616 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 607.3 | ||
Root | \(-1.90899 + 1.10215i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.607 |
Dual form | 1050.2.bc.e.493.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | − | 0.258819i | 0.683013 | − | 0.183013i | ||||
\(3\) | 0.258819 | − | 0.965926i | 0.149429 | − | 0.557678i | ||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −0.965926 | − | 2.46313i | −0.365086 | − | 0.930974i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.55868 | − | 2.69971i | −0.469960 | − | 0.813994i | 0.529450 | − | 0.848341i | \(-0.322398\pi\) |
−0.999410 | + | 0.0343469i | \(0.989065\pi\) | |||||||
\(12\) | −0.258819 | − | 0.965926i | −0.0747146 | − | 0.278839i | ||||
\(13\) | −2.30403 | − | 2.30403i | −0.639023 | − | 0.639023i | 0.311291 | − | 0.950315i | \(-0.399239\pi\) |
−0.950315 | + | 0.311291i | \(0.899239\pi\) | |||||||
\(14\) | −1.57052 | − | 2.12920i | −0.419738 | − | 0.569052i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −1.10215 | − | 0.295321i | −0.267311 | − | 0.0716259i | 0.122674 | − | 0.992447i | \(-0.460853\pi\) |
−0.389985 | + | 0.920821i | \(0.627520\pi\) | |||||||
\(18\) | −0.965926 | − | 0.258819i | −0.227671 | − | 0.0610042i | ||||
\(19\) | −2.99522 | + | 5.18788i | −0.687151 | + | 1.19018i | 0.285605 | + | 0.958348i | \(0.407806\pi\) |
−0.972756 | + | 0.231833i | \(0.925528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.62920 | + | 0.295509i | −0.573738 | + | 0.0644853i | ||||
\(22\) | −2.20431 | − | 2.20431i | −0.469960 | − | 0.469960i | ||||
\(23\) | −0.295321 | − | 1.10215i | −0.0615787 | − | 0.229815i | 0.928277 | − | 0.371889i | \(-0.121290\pi\) |
−0.989856 | + | 0.142074i | \(0.954623\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.82185 | − | 1.62920i | −0.553411 | − | 0.319512i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −2.06808 | − | 1.65017i | −0.390830 | − | 0.311852i | ||||
\(29\) | 5.39943i | 1.00265i | 0.865260 | + | 0.501324i | \(0.167154\pi\) | ||||
−0.865260 | + | 0.501324i | \(0.832846\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.68788 | − | 2.12920i | 0.662362 | − | 0.382415i | −0.130814 | − | 0.991407i | \(-0.541759\pi\) |
0.793176 | + | 0.608992i | \(0.208426\pi\) | |||||||
\(32\) | 0.258819 | − | 0.965926i | 0.0457532 | − | 0.170753i | ||||
\(33\) | −3.01114 | + | 0.806832i | −0.524172 | + | 0.140451i | ||||
\(34\) | −1.14103 | −0.195686 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 5.55960 | − | 1.48969i | 0.913993 | − | 0.244904i | 0.228977 | − | 0.973432i | \(-0.426462\pi\) |
0.685016 | + | 0.728528i | \(0.259795\pi\) | |||||||
\(38\) | −1.55044 | + | 5.78632i | −0.251515 | + | 0.938666i | ||||
\(39\) | −2.82185 | + | 1.62920i | −0.451858 | + | 0.260880i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.2584i | − | 1.60209i | −0.598603 | − | 0.801046i | \(-0.704277\pi\) | ||
0.598603 | − | 0.801046i | \(-0.295723\pi\) | |||||||
\(42\) | −2.46313 | + | 0.965926i | −0.380069 | + | 0.149046i | ||||
\(43\) | 6.44695 | − | 6.44695i | 0.983150 | − | 0.983150i | −0.0167102 | − | 0.999860i | \(-0.505319\pi\) |
0.999860 | + | 0.0167102i | \(0.00531925\pi\) | |||||||
\(44\) | −2.69971 | − | 1.55868i | −0.406997 | − | 0.234980i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.570516 | − | 0.988164i | −0.0841181 | − | 0.145697i | ||||
\(47\) | −1.10215 | − | 4.11329i | −0.160766 | − | 0.599985i | −0.998542 | − | 0.0539725i | \(-0.982812\pi\) |
0.837777 | − | 0.546013i | \(-0.183855\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | −5.13397 | + | 4.75839i | −0.733425 | + | 0.679770i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.570516 | + | 0.988164i | −0.0798883 | + | 0.138371i | ||||
\(52\) | −3.14737 | − | 0.843334i | −0.436461 | − | 0.116949i | ||||
\(53\) | −2.78442 | − | 0.746082i | −0.382469 | − | 0.102482i | 0.0624615 | − | 0.998047i | \(-0.480105\pi\) |
−0.444930 | + | 0.895565i | \(0.646772\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.42471 | − | 1.05868i | −0.324015 | − | 0.141472i | ||||
\(57\) | 4.23588 | + | 4.23588i | 0.561056 | + | 0.561056i | ||||
\(58\) | 1.39747 | + | 5.21545i | 0.183497 | + | 0.684821i | ||||
\(59\) | 0.117360 | + | 0.203274i | 0.0152790 | + | 0.0264640i | 0.873564 | − | 0.486710i | \(-0.161803\pi\) |
−0.858285 | + | 0.513174i | \(0.828470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.38403 | + | 4.26317i | 0.945428 | + | 0.545843i | 0.891658 | − | 0.452710i | \(-0.149543\pi\) |
0.0537703 | + | 0.998553i | \(0.482876\pi\) | |||||||
\(62\) | 3.01114 | − | 3.01114i | 0.382415 | − | 0.382415i | ||||
\(63\) | −0.395046 | + | 2.61609i | −0.0497712 | + | 0.329597i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.69971 | + | 1.55868i | −0.332312 | + | 0.191860i | ||||
\(67\) | 3.60425 | − | 13.4513i | 0.440330 | − | 1.64333i | −0.287651 | − | 0.957735i | \(-0.592874\pi\) |
0.727981 | − | 0.685598i | \(-0.240459\pi\) | |||||||
\(68\) | −1.10215 | + | 0.295321i | −0.133656 | + | 0.0358129i | ||||
\(69\) | −1.14103 | −0.137364 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.74161 | 0.206691 | 0.103345 | − | 0.994646i | \(-0.467045\pi\) | ||||
0.103345 | + | 0.994646i | \(0.467045\pi\) | |||||||
\(72\) | −0.965926 | + | 0.258819i | −0.113835 | + | 0.0305021i | ||||
\(73\) | −0.293478 | + | 1.09527i | −0.0343490 | + | 0.128192i | −0.980971 | − | 0.194152i | \(-0.937804\pi\) |
0.946622 | + | 0.322345i | \(0.104471\pi\) | |||||||
\(74\) | 4.98460 | − | 2.87786i | 0.579448 | − | 0.334545i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.99044i | 0.687151i | ||||||||
\(77\) | −5.14416 | + | 6.44695i | −0.586232 | + | 0.734698i | ||||
\(78\) | −2.30403 | + | 2.30403i | −0.260880 | + | 0.260880i | ||||
\(79\) | −8.76189 | − | 5.05868i | −0.985790 | − | 0.569146i | −0.0817766 | − | 0.996651i | \(-0.526059\pi\) |
−0.904013 | + | 0.427505i | \(0.859393\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.65507 | − | 9.90885i | −0.293203 | − | 1.09425i | ||||
\(83\) | 8.06061 | + | 8.06061i | 0.884767 | + | 0.884767i | 0.994015 | − | 0.109248i | \(-0.0348441\pi\) |
−0.109248 | + | 0.994015i | \(0.534844\pi\) | |||||||
\(84\) | −2.12920 | + | 1.57052i | −0.232314 | + | 0.171357i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.55868 | − | 7.89587i | 0.491575 | − | 0.851433i | ||||
\(87\) | 5.21545 | + | 1.39747i | 0.559154 | + | 0.149825i | ||||
\(88\) | −3.01114 | − | 0.806832i | −0.320988 | − | 0.0860086i | ||||
\(89\) | −9.18432 | + | 15.9077i | −0.973536 | + | 1.68621i | −0.288850 | + | 0.957374i | \(0.593273\pi\) |
−0.684685 | + | 0.728839i | \(0.740060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.44960 | + | 7.90064i | −0.361616 | + | 0.828212i | ||||
\(92\) | −0.806832 | − | 0.806832i | −0.0841181 | − | 0.0841181i | ||||
\(93\) | −1.10215 | − | 4.11329i | −0.114288 | − | 0.426528i | ||||
\(94\) | −2.12920 | − | 3.68788i | −0.219610 | − | 0.380375i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | −0.740585 | + | 0.740585i | −0.0751950 | + | 0.0751950i | −0.743704 | − | 0.668509i | \(-0.766933\pi\) |
0.668509 | + | 0.743704i | \(0.266933\pi\) | |||||||
\(98\) | −3.72748 | + | 5.92503i | −0.376532 | + | 0.598518i | ||||
\(99\) | 3.11736i | 0.313306i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0755 | + | 5.81707i | −1.00255 | + | 0.578820i | −0.909001 | − | 0.416795i | \(-0.863153\pi\) |
−0.0935457 | + | 0.995615i | \(0.529820\pi\) | |||||||
\(102\) | −0.295321 | + | 1.10215i | −0.0292411 | + | 0.109129i | ||||
\(103\) | 10.2718 | − | 2.75232i | 1.01211 | − | 0.271194i | 0.285599 | − | 0.958349i | \(-0.407807\pi\) |
0.726511 | + | 0.687155i | \(0.241141\pi\) | |||||||
\(104\) | −3.25839 | −0.319512 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.88264 | −0.279987 | ||||||||
\(107\) | 16.0605 | − | 4.30339i | 1.55262 | − | 0.416024i | 0.622305 | − | 0.782775i | \(-0.286196\pi\) |
0.930319 | + | 0.366750i | \(0.119530\pi\) | |||||||
\(108\) | −0.258819 | + | 0.965926i | −0.0249049 | + | 0.0929463i | ||||
\(109\) | 12.3420 | − | 7.12564i | 1.18215 | − | 0.682512i | 0.225636 | − | 0.974212i | \(-0.427554\pi\) |
0.956510 | + | 0.291700i | \(0.0942208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5.75572i | − | 0.546309i | ||||||
\(112\) | −2.61609 | − | 0.395046i | −0.247197 | − | 0.0373284i | ||||
\(113\) | 7.08781 | − | 7.08781i | 0.666765 | − | 0.666765i | −0.290201 | − | 0.956966i | \(-0.593722\pi\) |
0.956966 | + | 0.290201i | \(0.0937221\pi\) | |||||||
\(114\) | 5.18788 | + | 2.99522i | 0.485889 | + | 0.280528i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.69971 | + | 4.67604i | 0.250662 | + | 0.434159i | ||||
\(117\) | 0.843334 | + | 3.14737i | 0.0779663 | + | 0.290974i | ||||
\(118\) | 0.165972 | + | 0.165972i | 0.0152790 | + | 0.0152790i | ||||
\(119\) | 0.337185 | + | 3.00000i | 0.0309097 | + | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.641033 | − | 1.11030i | 0.0582757 | − | 0.100937i | ||||
\(122\) | 8.23581 | + | 2.20678i | 0.745636 | + | 0.199792i | ||||
\(123\) | −9.90885 | − | 2.65507i | −0.893451 | − | 0.239399i | ||||
\(124\) | 2.12920 | − | 3.68788i | 0.191207 | − | 0.331181i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.295509 | + | 2.62920i | 0.0263260 | + | 0.234227i | ||||
\(127\) | −0.705385 | − | 0.705385i | −0.0625928 | − | 0.0625928i | 0.675117 | − | 0.737710i | \(-0.264093\pi\) |
−0.737710 | + | 0.675117i | \(0.764093\pi\) | |||||||
\(128\) | −0.258819 | − | 0.965926i | −0.0228766 | − | 0.0853766i | ||||
\(129\) | −4.55868 | − | 7.89587i | −0.401369 | − | 0.695192i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.6997 | − | 6.75483i | −1.02221 | − | 0.590172i | −0.107466 | − | 0.994209i | \(-0.534274\pi\) |
−0.914743 | + | 0.404036i | \(0.867607\pi\) | |||||||
\(132\) | −2.20431 | + | 2.20431i | −0.191860 | + | 0.191860i | ||||
\(133\) | 15.6716 | + | 2.36650i | 1.35890 | + | 0.205202i | ||||
\(134\) | − | 13.9258i | − | 1.20300i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.988164 | + | 0.570516i | −0.0847343 | + | 0.0489214i | ||||
\(137\) | −4.44327 | + | 16.5825i | −0.379614 | + | 1.41674i | 0.466870 | + | 0.884326i | \(0.345382\pi\) |
−0.846484 | + | 0.532414i | \(0.821285\pi\) | |||||||
\(138\) | −1.10215 | + | 0.295321i | −0.0938215 | + | 0.0251394i | ||||
\(139\) | 11.1551 | 0.946167 | 0.473084 | − | 0.881017i | \(-0.343141\pi\) | ||||
0.473084 | + | 0.881017i | \(0.343141\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.25839 | −0.358621 | ||||||||
\(142\) | 1.68226 | − | 0.450761i | 0.141172 | − | 0.0378270i | ||||
\(143\) | −2.62898 | + | 9.81147i | −0.219846 | + | 0.820477i | ||||
\(144\) | −0.866025 | + | 0.500000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.13391i | 0.0938432i | ||||||||
\(147\) | 3.26748 | + | 6.19060i | 0.269498 | + | 0.510592i | ||||
\(148\) | 4.06991 | − | 4.06991i | 0.334545 | − | 0.334545i | ||||
\(149\) | 16.5790 | + | 9.57191i | 1.35821 | + | 0.784161i | 0.989382 | − | 0.145338i | \(-0.0464269\pi\) |
0.368825 | + | 0.929499i | \(0.379760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.74656 | + | 15.1495i | 0.711785 | + | 1.23285i | 0.964187 | + | 0.265225i | \(0.0854462\pi\) |
−0.252402 | + | 0.967622i | \(0.581221\pi\) | |||||||
\(152\) | 1.55044 | + | 5.78632i | 0.125757 | + | 0.469333i | ||||
\(153\) | 0.806832 | + | 0.806832i | 0.0652285 | + | 0.0652285i | ||||
\(154\) | −3.30029 | + | 7.55868i | −0.265945 | + | 0.609096i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.62920 | + | 2.82185i | −0.130440 | + | 0.225929i | ||||
\(157\) | −12.1063 | − | 3.24387i | −0.966186 | − | 0.258889i | −0.258969 | − | 0.965886i | \(-0.583383\pi\) |
−0.707217 | + | 0.706997i | \(0.750049\pi\) | |||||||
\(158\) | −9.77262 | − | 2.61857i | −0.777468 | − | 0.208322i | ||||
\(159\) | −1.44132 | + | 2.49644i | −0.114304 | + | 0.197981i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.42948 | + | 1.79201i | −0.191470 | + | 0.141230i | ||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −3.91019 | − | 14.5930i | −0.306270 | − | 1.14301i | −0.931847 | − | 0.362851i | \(-0.881803\pi\) |
0.625578 | − | 0.780162i | \(-0.284863\pi\) | |||||||
\(164\) | −5.12920 | − | 8.88403i | −0.400523 | − | 0.693726i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.87219 | + | 5.69971i | 0.766231 | + | 0.442384i | ||||
\(167\) | 1.44769 | − | 1.44769i | 0.112026 | − | 0.112026i | −0.648872 | − | 0.760898i | \(-0.724759\pi\) |
0.760898 | + | 0.648872i | \(0.224759\pi\) | |||||||
\(168\) | −1.65017 | + | 2.06808i | −0.127313 | + | 0.159556i | ||||
\(169\) | − | 2.38287i | − | 0.183298i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.18788 | − | 2.99522i | 0.396727 | − | 0.229050i | ||||
\(172\) | 2.35975 | − | 8.80669i | 0.179929 | − | 0.671504i | ||||
\(173\) | −11.8178 | + | 3.16658i | −0.898493 | + | 0.240751i | −0.678369 | − | 0.734721i | \(-0.737313\pi\) |
−0.220124 | + | 0.975472i | \(0.570646\pi\) | |||||||
\(174\) | 5.39943 | 0.409329 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.11736 | −0.234980 | ||||||||
\(177\) | 0.226722 | − | 0.0607501i | 0.0170415 | − | 0.00456625i | ||||
\(178\) | −4.75415 | + | 17.7427i | −0.356339 | + | 1.32987i | ||||
\(179\) | 16.5790 | − | 9.57191i | 1.23917 | − | 0.715438i | 0.270249 | − | 0.962790i | \(-0.412894\pi\) |
0.968926 | + | 0.247353i | \(0.0795606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.22760i | − | 0.388564i | −0.980946 | − | 0.194282i | \(-0.937762\pi\) | ||
0.980946 | − | 0.194282i | \(-0.0622377\pi\) | |||||||
\(182\) | −1.28722 | + | 8.52426i | −0.0954148 | + | 0.631860i | ||||
\(183\) | 6.02903 | − | 6.02903i | 0.445679 | − | 0.445679i | ||||
\(184\) | −0.988164 | − | 0.570516i | −0.0728484 | − | 0.0420590i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.12920 | − | 3.68788i | −0.156120 | − | 0.270408i | ||||
\(187\) | 0.920622 | + | 3.43581i | 0.0673226 | + | 0.251251i | ||||
\(188\) | −3.01114 | − | 3.01114i | −0.219610 | − | 0.219610i | ||||
\(189\) | 2.42471 | + | 1.05868i | 0.176371 | + | 0.0770076i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.12920 | + | 8.88403i | −0.371136 | + | 0.642826i | −0.989741 | − | 0.142876i | \(-0.954365\pi\) |
0.618605 | + | 0.785702i | \(0.287698\pi\) | |||||||
\(192\) | −0.965926 | − | 0.258819i | −0.0697097 | − | 0.0186787i | ||||
\(193\) | −4.69340 | − | 1.25759i | −0.337838 | − | 0.0905235i | 0.0859114 | − | 0.996303i | \(-0.472620\pi\) |
−0.423750 | + | 0.905779i | \(0.639286\pi\) | |||||||
\(194\) | −0.523673 | + | 0.907028i | −0.0375975 | + | 0.0651208i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.06696 | + | 6.68788i | −0.147640 | + | 0.477705i | ||||
\(197\) | 4.53011 | + | 4.53011i | 0.322757 | + | 0.322757i | 0.849824 | − | 0.527067i | \(-0.176708\pi\) |
−0.527067 | + | 0.849824i | \(0.676708\pi\) | |||||||
\(198\) | 0.806832 | + | 3.01114i | 0.0573391 | + | 0.213992i | ||||
\(199\) | −1.28367 | − | 2.22339i | −0.0909971 | − | 0.157612i | 0.816934 | − | 0.576731i | \(-0.195672\pi\) |
−0.907931 | + | 0.419120i | \(0.862339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0601 | − | 6.96288i | −0.850652 | − | 0.491124i | ||||
\(202\) | −8.22658 | + | 8.22658i | −0.578820 | + | 0.578820i | ||||
\(203\) | 13.2995 | − | 5.21545i | 0.933439 | − | 0.366052i | ||||
\(204\) | 1.14103i | 0.0798883i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.20944 | − | 5.31707i | 0.641652 | − | 0.370458i | ||||
\(207\) | −0.295321 | + | 1.10215i | −0.0205262 | + | 0.0766049i | ||||
\(208\) | −3.14737 | + | 0.843334i | −0.218231 | + | 0.0584747i | ||||
\(209\) | 18.6744 | 1.29173 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.1746 | 1.73309 | 0.866546 | − | 0.499098i | \(-0.166335\pi\) | ||||
0.866546 | + | 0.499098i | \(0.166335\pi\) | |||||||
\(212\) | −2.78442 | + | 0.746082i | −0.191234 | + | 0.0512411i | ||||
\(213\) | 0.450761 | − | 1.68226i | 0.0308856 | − | 0.115267i | ||||
\(214\) | 14.3994 | − | 8.31351i | 0.984325 | − | 0.568300i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −8.80669 | − | 7.02706i | −0.597837 | − | 0.477028i | ||||
\(218\) | 10.0772 | − | 10.0772i | 0.682512 | − | 0.682512i | ||||
\(219\) | 0.981996 | + | 0.566956i | 0.0663572 | + | 0.0383113i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.85897 | + | 3.21983i | 0.125048 | + | 0.216589i | ||||
\(222\) | −1.48969 | − | 5.55960i | −0.0999815 | − | 0.373136i | ||||
\(223\) | 7.35350 | + | 7.35350i | 0.492427 | + | 0.492427i | 0.909070 | − | 0.416643i | \(-0.136794\pi\) |
−0.416643 | + | 0.909070i | \(0.636794\pi\) | |||||||
\(224\) | −2.62920 | + | 0.295509i | −0.175671 | + | 0.0197445i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.01184 | − | 8.68076i | 0.333382 | − | 0.577435i | ||||
\(227\) | −19.6517 | − | 5.26566i | −1.30433 | − | 0.349494i | −0.461245 | − | 0.887273i | \(-0.652597\pi\) |
−0.843086 | + | 0.537779i | \(0.819264\pi\) | |||||||
\(228\) | 5.78632 | + | 1.55044i | 0.383209 | + | 0.102680i | ||||
\(229\) | 3.91643 | − | 6.78346i | 0.258805 | − | 0.448263i | −0.707117 | − | 0.707096i | \(-0.750005\pi\) |
0.965922 | + | 0.258833i | \(0.0833380\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.89587 | + | 6.63747i | 0.322124 | + | 0.436714i | ||||
\(232\) | 3.81797 | + | 3.81797i | 0.250662 | + | 0.250662i | ||||
\(233\) | −1.44769 | − | 5.40286i | −0.0948415 | − | 0.353953i | 0.902154 | − | 0.431414i | \(-0.141985\pi\) |
−0.996995 | + | 0.0774612i | \(0.975319\pi\) | |||||||
\(234\) | 1.62920 | + | 2.82185i | 0.106504 | + | 0.184470i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.203274 | + | 0.117360i | 0.0132320 | + | 0.00763949i | ||||
\(237\) | −7.15405 | + | 7.15405i | −0.464706 | + | 0.464706i | ||||
\(238\) | 1.10215 | + | 2.81051i | 0.0714420 | + | 0.182178i | ||||
\(239\) | 12.3686i | 0.800060i | 0.916502 | + | 0.400030i | \(0.131000\pi\) | ||||
−0.916502 | + | 0.400030i | \(0.869000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1145 | − | 6.99433i | 0.780366 | − | 0.450544i | −0.0561941 | − | 0.998420i | \(-0.517897\pi\) |
0.836560 | + | 0.547875i | \(0.184563\pi\) | |||||||
\(242\) | 0.331823 | − | 1.23838i | 0.0213304 | − | 0.0796061i | ||||
\(243\) | 0.965926 | − | 0.258819i | 0.0619642 | − | 0.0166032i | ||||
\(244\) | 8.52634 | 0.545843 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.2584 | −0.654051 | ||||||||
\(247\) | 18.8541 | − | 5.05195i | 1.19966 | − | 0.321448i | ||||
\(248\) | 1.10215 | − | 4.11329i | 0.0699868 | − | 0.261194i | ||||
\(249\) | 9.87219 | − | 5.69971i | 0.625625 | − | 0.361205i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.0336i | 1.07515i | 0.843216 | + | 0.537575i | \(0.180659\pi\) | ||||
−0.843216 | + | 0.537575i | \(0.819341\pi\) | |||||||
\(252\) | 0.965926 | + | 2.46313i | 0.0608476 | + | 0.155162i | ||||
\(253\) | −2.51519 | + | 2.51519i | −0.158128 | + | 0.158128i | ||||
\(254\) | −0.863917 | − | 0.498783i | −0.0542070 | − | 0.0312964i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 5.43164 | + | 20.2711i | 0.338816 | + | 1.26448i | 0.899672 | + | 0.436566i | \(0.143805\pi\) |
−0.560856 | + | 0.827913i | \(0.689528\pi\) | |||||||
\(258\) | −6.44695 | − | 6.44695i | −0.401369 | − | 0.401369i | ||||
\(259\) | −9.03946 | − | 12.2551i | −0.561685 | − | 0.761493i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.69971 | − | 4.67604i | 0.167108 | − | 0.289440i | ||||
\(262\) | −13.0493 | − | 3.49656i | −0.806191 | − | 0.216018i | ||||
\(263\) | −18.4888 | − | 4.95406i | −1.14007 | − | 0.305481i | −0.361090 | − | 0.932531i | \(-0.617595\pi\) |
−0.778979 | + | 0.627050i | \(0.784262\pi\) | |||||||
\(264\) | −1.55868 | + | 2.69971i | −0.0959301 | + | 0.166156i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.7501 | − | 1.77023i | 0.965698 | − | 0.108540i | ||||
\(267\) | 12.9886 | + | 12.9886i | 0.794888 | + | 0.794888i | ||||
\(268\) | −3.60425 | − | 13.4513i | −0.220165 | − | 0.821666i | ||||
\(269\) | −14.6138 | − | 25.3118i | −0.891019 | − | 1.54329i | −0.838656 | − | 0.544662i | \(-0.816658\pi\) |
−0.0523636 | − | 0.998628i | \(-0.516675\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4796 | + | 11.2466i | 1.18330 | + | 0.683180i | 0.956776 | − | 0.290826i | \(-0.0939299\pi\) |
0.226526 | + | 0.974005i | \(0.427263\pi\) | |||||||
\(272\) | −0.806832 | + | 0.806832i | −0.0489214 | + | 0.0489214i | ||||
\(273\) | 6.73861 | + | 5.37689i | 0.407840 | + | 0.325424i | ||||
\(274\) | 17.1675i | 1.03713i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.988164 | + | 0.570516i | −0.0594805 | + | 0.0343411i | ||||
\(277\) | −5.60865 | + | 20.9318i | −0.336991 | + | 1.25767i | 0.564703 | + | 0.825294i | \(0.308991\pi\) |
−0.901694 | + | 0.432374i | \(0.857676\pi\) | |||||||
\(278\) | 10.7750 | − | 2.88717i | 0.646244 | − | 0.173161i | ||||
\(279\) | −4.25839 | −0.254943 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.3758 | 1.15586 | 0.577930 | − | 0.816086i | \(-0.303861\pi\) | ||||
0.577930 | + | 0.816086i | \(0.303861\pi\) | |||||||
\(282\) | −4.11329 | + | 1.10215i | −0.244943 | + | 0.0656323i | ||||
\(283\) | −4.82531 | + | 18.0083i | −0.286835 | + | 1.07048i | 0.660653 | + | 0.750692i | \(0.270280\pi\) |
−0.947488 | + | 0.319792i | \(0.896387\pi\) | |||||||
\(284\) | 1.50828 | − | 0.870803i | 0.0894997 | − | 0.0516727i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.1576i | 0.600631i | ||||||||
\(287\) | −25.2677 | + | 9.90885i | −1.49151 | + | 0.584901i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | −13.5949 | − | 7.84902i | −0.799700 | − | 0.461707i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.523673 | + | 0.907028i | 0.0306982 | + | 0.0531709i | ||||
\(292\) | 0.293478 | + | 1.09527i | 0.0171745 | + | 0.0640961i | ||||
\(293\) | −11.4539 | − | 11.4539i | −0.669145 | − | 0.669145i | 0.288373 | − | 0.957518i | \(-0.406886\pi\) |
−0.957518 | + | 0.288373i | \(0.906886\pi\) | |||||||
\(294\) | 4.75839 | + | 5.13397i | 0.277515 | + | 0.299419i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.87786 | − | 4.98460i | 0.167272 | − | 0.289724i | ||||
\(297\) | 3.01114 | + | 0.806832i | 0.174724 | + | 0.0468172i | ||||
\(298\) | 18.4915 | + | 4.95478i | 1.07118 | + | 0.287023i | ||||
\(299\) | −1.85897 | + | 3.21983i | −0.107507 | + | 0.186207i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.1069 | − | 9.65237i | −1.27422 | − | 0.556353i | ||||
\(302\) | 12.3695 | + | 12.3695i | 0.711785 | + | 0.711785i | ||||
\(303\) | 3.01114 | + | 11.2377i | 0.172985 | + | 0.645590i | ||||
\(304\) | 2.99522 | + | 5.18788i | 0.171788 | + | 0.297545i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.988164 | + | 0.570516i | 0.0564896 | + | 0.0326143i | ||||
\(307\) | 0.398902 | − | 0.398902i | 0.0227665 | − | 0.0227665i | −0.695632 | − | 0.718398i | \(-0.744876\pi\) |
0.718398 | + | 0.695632i | \(0.244876\pi\) | |||||||
\(308\) | −1.23150 | + | 8.15530i | −0.0701713 | + | 0.464691i | ||||
\(309\) | − | 10.6341i | − | 0.604955i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.2317 | + | 6.48460i | −0.636889 | + | 0.367708i | −0.783415 | − | 0.621499i | \(-0.786524\pi\) |
0.146526 | + | 0.989207i | \(0.453191\pi\) | |||||||
\(312\) | −0.843334 | + | 3.14737i | −0.0477444 | + | 0.178185i | ||||
\(313\) | 1.78875 | − | 0.479293i | 0.101106 | − | 0.0270912i | −0.207911 | − | 0.978148i | \(-0.566667\pi\) |
0.309017 | + | 0.951056i | \(0.400000\pi\) | |||||||
\(314\) | −12.5333 | −0.707297 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.1174 | −0.569146 | ||||||||
\(317\) | −31.2821 | + | 8.38202i | −1.75698 | + | 0.470781i | −0.986094 | − | 0.166191i | \(-0.946853\pi\) |
−0.770886 | + | 0.636973i | \(0.780186\pi\) | |||||||
\(318\) | −0.746082 | + | 2.78442i | −0.0418382 | + | 0.156142i | ||||
\(319\) | 14.5769 | − | 8.41598i | 0.816150 | − | 0.471204i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 16.6270i | − | 0.928030i | ||||||
\(322\) | −1.88289 | + | 2.35975i | −0.104930 | + | 0.131504i | ||||
\(323\) | 4.83328 | − | 4.83328i | 0.268931 | − | 0.268931i | ||||
\(324\) | 0.866025 | + | 0.500000i | 0.0481125 | + | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.55390 | − | 13.0837i | −0.418372 | − | 0.724641i | ||||
\(327\) | −3.68850 | − | 13.7657i | −0.203975 | − | 0.761243i | ||||
\(328\) | −7.25378 | − | 7.25378i | −0.400523 | − | 0.400523i | ||||
\(329\) | −9.06696 | + | 6.68788i | −0.499877 | + | 0.368715i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.80168 | − | 10.0488i | 0.318889 | − | 0.552332i | −0.661368 | − | 0.750062i | \(-0.730024\pi\) |
0.980257 | + | 0.197730i | \(0.0633570\pi\) | |||||||
\(332\) | 11.0110 | + | 2.95039i | 0.604307 | + | 0.161924i | ||||
\(333\) | −5.55960 | − | 1.48969i | −0.304664 | − | 0.0816346i | ||||
\(334\) | 1.02367 | − | 1.77305i | 0.0560129 | − | 0.0970172i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.05868 | + | 2.42471i | −0.0577557 | + | 0.132279i | ||||
\(337\) | 9.45809 | + | 9.45809i | 0.515215 | + | 0.515215i | 0.916120 | − | 0.400905i | \(-0.131304\pi\) |
−0.400905 | + | 0.916120i | \(0.631304\pi\) | |||||||
\(338\) | −0.616733 | − | 2.30168i | −0.0335459 | − | 0.125195i | ||||
\(339\) | −5.01184 | − | 8.68076i | −0.272206 | − | 0.471474i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.4964 | − | 6.63747i | −0.622567 | − | 0.359439i | ||||
\(342\) | 4.23588 | − | 4.23588i | 0.229050 | − | 0.229050i | ||||
\(343\) | 16.6796 | + | 8.04937i | 0.900611 | + | 0.434625i | ||||
\(344\) | − | 9.11736i | − | 0.491575i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.5956 | + | 6.11736i | −0.569622 | + | 0.328871i | ||||
\(347\) | 5.58708 | − | 20.8512i | 0.299930 | − | 1.11935i | −0.637293 | − | 0.770622i | \(-0.719946\pi\) |
0.937223 | − | 0.348732i | \(-0.113388\pi\) | |||||||
\(348\) | 5.21545 | − | 1.39747i | 0.279577 | − | 0.0749125i | ||||
\(349\) | 14.9455 | 0.800016 | 0.400008 | − | 0.916512i | \(-0.369007\pi\) | ||||
0.400008 | + | 0.916512i | \(0.369007\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.25839 | 0.173920 | ||||||||
\(352\) | −3.01114 | + | 0.806832i | −0.160494 | + | 0.0430043i | ||||
\(353\) | −9.43970 | + | 35.2295i | −0.502425 | + | 1.87507i | −0.0187553 | + | 0.999824i | \(0.505970\pi\) |
−0.483669 | + | 0.875251i | \(0.660696\pi\) | |||||||
\(354\) | 0.203274 | − | 0.117360i | 0.0108039 | − | 0.00623762i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.3686i | 0.973536i | ||||||||
\(357\) | 2.98505 | + | 0.450761i | 0.157985 | + | 0.0238568i | ||||
\(358\) | 13.5367 | − | 13.5367i | 0.715438 | − | 0.715438i | ||||
\(359\) | −3.77518 | − | 2.17960i | −0.199246 | − | 0.115035i | 0.397058 | − | 0.917794i | \(-0.370031\pi\) |
−0.596304 | + | 0.802759i | \(0.703365\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.44271 | − | 14.6232i | −0.444353 | − | 0.769642i | ||||
\(362\) | −1.35300 | − | 5.04947i | −0.0711122 | − | 0.265394i | ||||
\(363\) | −0.906558 | − | 0.906558i | −0.0475819 | − | 0.0475819i | ||||
\(364\) | 0.962884 | + | 8.56696i | 0.0504688 | + | 0.449030i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.26317 | − | 7.38403i | 0.222840 | − | 0.385969i | ||||
\(367\) | −17.9178 | − | 4.80106i | −0.935302 | − | 0.250614i | −0.241188 | − | 0.970478i | \(-0.577537\pi\) |
−0.694114 | + | 0.719865i | \(0.744204\pi\) | |||||||
\(368\) | −1.10215 | − | 0.295321i | −0.0574537 | − | 0.0153947i | ||||
\(369\) | −5.12920 | + | 8.88403i | −0.267015 | + | 0.462484i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.851846 | + | 7.57903i | 0.0442256 | + | 0.393483i | ||||
\(372\) | −3.01114 | − | 3.01114i | −0.156120 | − | 0.156120i | ||||
\(373\) | −5.05195 | − | 18.8541i | −0.261580 | − | 0.976229i | −0.964311 | − | 0.264773i | \(-0.914703\pi\) |
0.702731 | − | 0.711456i | \(-0.251964\pi\) | |||||||
\(374\) | 1.77851 | + | 3.08046i | 0.0919643 | + | 0.159287i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.68788 | − | 2.12920i | −0.190188 | − | 0.109805i | ||||
\(377\) | 12.4404 | − | 12.4404i | 0.640716 | − | 0.640716i | ||||
\(378\) | 2.61609 | + | 0.395046i | 0.134557 | + | 0.0203190i | ||||
\(379\) | 37.4424i | 1.92329i | 0.274300 | + | 0.961644i | \(0.411554\pi\) | ||||
−0.274300 | + | 0.961644i | \(0.588446\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.863917 | + | 0.498783i | −0.0442598 | + | 0.0255534i | ||||
\(382\) | −2.65507 | + | 9.90885i | −0.135845 | + | 0.506981i | ||||
\(383\) | 0.582793 | − | 0.156159i | 0.0297794 | − | 0.00797935i | −0.243899 | − | 0.969801i | \(-0.578426\pi\) |
0.273678 | + | 0.961821i | \(0.411760\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.85897 | −0.247315 | ||||||||
\(387\) | −8.80669 | + | 2.35975i | −0.447669 | + | 0.119953i | ||||
\(388\) | −0.271073 | + | 1.01166i | −0.0137616 | + | 0.0513592i | ||||
\(389\) | −17.6000 | + | 10.1614i | −0.892357 | + | 0.515202i | −0.874713 | − | 0.484642i | \(-0.838950\pi\) |
−0.0176441 | + | 0.999844i | \(0.505617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.30196i | 0.0658428i | ||||||||
\(392\) | −0.265576 | + | 6.99496i | −0.0134136 | + | 0.353299i | ||||
\(393\) | −9.55278 | + | 9.55278i | −0.481874 | + | 0.481874i | ||||
\(394\) | 5.54823 | + | 3.20327i | 0.279516 | + | 0.161379i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.55868 | + | 2.69971i | 0.0783266 | + | 0.135666i | ||||
\(397\) | 3.10214 | + | 11.5774i | 0.155692 | + | 0.581051i | 0.999045 | + | 0.0436908i | \(0.0139116\pi\) |
−0.843353 | + | 0.537360i | \(0.819422\pi\) | |||||||
\(398\) | −1.81539 | − | 1.81539i | −0.0909971 | − | 0.0909971i | ||||
\(399\) | 6.34196 | − | 14.5251i | 0.317495 | − | 0.727163i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.2584 | + | 17.7681i | −0.512280 | + | 0.887294i | 0.487619 | + | 0.873057i | \(0.337866\pi\) |
−0.999899 | + | 0.0142379i | \(0.995468\pi\) | |||||||
\(402\) | −13.4513 | − | 3.60425i | −0.670888 | − | 0.179764i | ||||
\(403\) | −13.4027 | − | 3.59125i | −0.667637 | − | 0.178893i | ||||
\(404\) | −5.81707 | + | 10.0755i | −0.289410 | + | 0.501273i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.4964 | − | 8.47989i | 0.570559 | − | 0.420850i | ||||
\(407\) | −12.6874 | − | 12.6874i | −0.628890 | − | 0.628890i | ||||
\(408\) | 0.295321 | + | 1.10215i | 0.0146206 | + | 0.0545647i | ||||
\(409\) | −6.61219 | − | 11.4527i | −0.326952 | − | 0.566297i | 0.654954 | − | 0.755669i | \(-0.272688\pi\) |
−0.981905 | + | 0.189372i | \(0.939355\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.8675 | + | 8.58374i | 0.733359 | + | 0.423405i | ||||
\(412\) | 7.51948 | − | 7.51948i | 0.370458 | − | 0.370458i | ||||
\(413\) | 0.387327 | − | 0.485420i | 0.0190591 | − | 0.0238860i | ||||
\(414\) | 1.14103i | 0.0560787i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.82185 | + | 1.62920i | −0.138353 | + | 0.0798779i | ||||
\(417\) | 2.88717 | − | 10.7750i | 0.141385 | − | 0.527656i | ||||
\(418\) | 18.0381 | − | 4.83328i | 0.882270 | − | 0.236404i | ||||
\(419\) | 19.9791 | 0.976043 | 0.488022 | − | 0.872832i | \(-0.337719\pi\) | ||||
0.488022 | + | 0.872832i | \(0.337719\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.2920 | −0.988970 | −0.494485 | − | 0.869186i | \(-0.664643\pi\) | ||||
−0.494485 | + | 0.869186i | \(0.664643\pi\) | |||||||
\(422\) | 24.3168 | − | 6.51567i | 1.18372 | − | 0.317178i | ||||
\(423\) | −1.10215 | + | 4.11329i | −0.0535885 | + | 0.199995i | ||||
\(424\) | −2.49644 | + | 1.44132i | −0.121238 | + | 0.0699967i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 1.74161i | − | 0.0843811i | ||||||
\(427\) | 3.36830 | − | 22.3057i | 0.163004 | − | 1.07945i | ||||
\(428\) | 11.7571 | − | 11.7571i | 0.568300 | − | 0.568300i | ||||
\(429\) | 8.79673 | + | 5.07879i | 0.424710 | + | 0.245206i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.167764 | + | 0.290576i | 0.00808092 | + | 0.0139966i | 0.870038 | − | 0.492985i | \(-0.164094\pi\) |
−0.861957 | + | 0.506982i | \(0.830761\pi\) | |||||||
\(432\) | 0.258819 | + | 0.965926i | 0.0124524 | + | 0.0464731i | ||||
\(433\) | −4.53678 | − | 4.53678i | −0.218024 | − | 0.218024i | 0.589641 | − | 0.807665i | \(-0.299269\pi\) |
−0.807665 | + | 0.589641i | \(0.799269\pi\) | |||||||
\(434\) | −10.3253 | − | 4.50828i | −0.495633 | − | 0.216404i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.12564 | − | 12.3420i | 0.341256 | − | 0.591073i | ||||
\(437\) | 6.60239 | + | 1.76910i | 0.315835 | + | 0.0846277i | ||||
\(438\) | 1.09527 | + | 0.293478i | 0.0523342 | + | 0.0140229i | ||||
\(439\) | 13.6209 | − | 23.5920i | 0.650088 | − | 1.12599i | −0.333013 | − | 0.942922i | \(-0.608065\pi\) |
0.983101 | − | 0.183063i | \(-0.0586013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.82535 | − | 1.55390i | 0.325017 | − | 0.0739953i | ||||
\(442\) | 2.62898 | + | 2.62898i | 0.125048 | + | 0.125048i | ||||
\(443\) | −1.33672 | − | 4.98872i | −0.0635097 | − | 0.237021i | 0.926873 | − | 0.375374i | \(-0.122486\pi\) |
−0.990383 | + | 0.138353i | \(0.955819\pi\) | |||||||
\(444\) | −2.87786 | − | 4.98460i | −0.136577 | − | 0.236559i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.00617 | + | 5.19971i | 0.426454 | + | 0.246214i | ||||
\(447\) | 13.5367 | − | 13.5367i | 0.640265 | − | 0.640265i | ||||
\(448\) | −2.46313 | + | 0.965926i | −0.116372 | + | 0.0456357i | ||||
\(449\) | 26.0501i | 1.22938i | 0.788768 | + | 0.614691i | \(0.210719\pi\) | ||||
−0.788768 | + | 0.614691i | \(0.789281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.6947 | + | 15.9896i | −1.30409 | + | 0.752919i | ||||
\(452\) | 2.59432 | − | 9.68212i | 0.122026 | − | 0.455409i | ||||
\(453\) | 16.8970 | − | 4.52755i | 0.793893 | − | 0.212723i | ||||
\(454\) | −20.3450 | −0.954836 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.99044 | 0.280528 | ||||||||
\(457\) | 29.2530 | − | 7.83833i | 1.36840 | − | 0.366661i | 0.501506 | − | 0.865154i | \(-0.332780\pi\) |
0.866894 | + | 0.498493i | \(0.166113\pi\) | |||||||
\(458\) | 2.02729 | − | 7.56596i | 0.0947292 | − | 0.353534i | ||||
\(459\) | 0.988164 | − | 0.570516i | 0.0461235 | − | 0.0266294i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.71793i | 0.173161i | 0.996245 | + | 0.0865807i | \(0.0275940\pi\) | ||||
−0.996245 | + | 0.0865807i | \(0.972406\pi\) | |||||||
\(462\) | 6.44695 | + | 5.14416i | 0.299939 | + | 0.239328i | ||||
\(463\) | −16.3674 | + | 16.3674i | −0.760658 | + | 0.760658i | −0.976441 | − | 0.215783i | \(-0.930770\pi\) |
0.215783 | + | 0.976441i | \(0.430770\pi\) | |||||||
\(464\) | 4.67604 | + | 2.69971i | 0.217080 | + | 0.125331i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.79673 | − | 4.84407i | −0.129556 | − | 0.224397i | ||||
\(467\) | −7.00365 | − | 26.1380i | −0.324090 | − | 1.20952i | −0.915223 | − | 0.402947i | \(-0.867986\pi\) |
0.591133 | − | 0.806574i | \(-0.298681\pi\) | |||||||
\(468\) | 2.30403 | + | 2.30403i | 0.106504 | + | 0.106504i | ||||
\(469\) | −36.6136 | + | 4.11519i | −1.69066 | + | 0.190022i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.26667 | + | 10.8542i | −0.288753 | + | 0.500135i | ||||
\(472\) | 0.226722 | + | 0.0607501i | 0.0104357 | + | 0.00279625i | ||||
\(473\) | −27.4536 | − | 7.35618i | −1.26232 | − | 0.338237i | ||||
\(474\) | −5.05868 | + | 8.76189i | −0.232353 | + | 0.402447i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.79201 | + | 2.42948i | 0.0821367 | + | 0.111355i | ||||
\(477\) | 2.03833 | + | 2.03833i | 0.0933289 | + | 0.0933289i | ||||
\(478\) | 3.20124 | + | 11.9472i | 0.146421 | + | 0.546451i | ||||
\(479\) | −21.0873 | − | 36.5243i | −0.963503 | − | 1.66884i | −0.713583 | − | 0.700571i | \(-0.752929\pi\) |
−0.249920 | − | 0.968266i | \(-0.580404\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.2418 | − | 9.37721i | −0.740562 | − | 0.427564i | ||||
\(482\) | 9.89148 | − | 9.89148i | 0.450544 | − | 0.450544i | ||||
\(483\) | 1.10215 | + | 2.81051i | 0.0501497 | + | 0.127883i | ||||
\(484\) | − | 1.28207i | − | 0.0582757i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 8.09527 | − | 30.2120i | 0.366832 | − | 1.36903i | −0.498089 | − | 0.867126i | \(-0.665965\pi\) |
0.864921 | − | 0.501909i | \(-0.167369\pi\) | |||||||
\(488\) | 8.23581 | − | 2.20678i | 0.372818 | − | 0.0998962i | ||||
\(489\) | −15.1078 | −0.683199 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.7108 | 1.20544 | 0.602721 | − | 0.797952i | \(-0.294083\pi\) | ||||
0.602721 | + | 0.797952i | \(0.294083\pi\) | |||||||
\(492\) | −9.90885 | + | 2.65507i | −0.446725 | + | 0.119700i | ||||
\(493\) | 1.59456 | − | 5.95099i | 0.0718156 | − | 0.268019i | ||||
\(494\) | 16.9041 | − | 9.75961i | 0.760553 | − | 0.439106i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.25839i | − | 0.191207i | ||||||
\(497\) | −1.68226 | − | 4.28980i | −0.0754598 | − | 0.192424i | ||||
\(498\) | 8.06061 | − | 8.06061i | 0.361205 | − | 0.361205i | ||||
\(499\) | −6.79373 | − | 3.92236i | −0.304129 | − | 0.175589i | 0.340167 | − | 0.940365i | \(-0.389516\pi\) |
−0.644296 | + | 0.764776i | \(0.722850\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.02367 | − | 1.77305i | −0.0457343 | − | 0.0792142i | ||||
\(502\) | 4.40861 | + | 16.4532i | 0.196766 | + | 0.734341i | ||||
\(503\) | 23.4463 | + | 23.4463i | 1.04542 | + | 1.04542i | 0.998918 | + | 0.0464999i | \(0.0148067\pi\) |
0.0464999 | + | 0.998918i | \(0.485193\pi\) | |||||||
\(504\) | 1.57052 | + | 2.12920i | 0.0699564 | + | 0.0948420i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.77851 | + | 3.08046i | −0.0790642 | + | 0.136943i | ||||
\(507\) | −2.30168 | − | 0.616733i | −0.102221 | − | 0.0273901i | ||||
\(508\) | −0.963574 | − | 0.258189i | −0.0427517 | − | 0.0114553i | ||||
\(509\) | −6.72339 | + | 11.6452i | −0.298009 | + | 0.516166i | −0.975680 | − | 0.219198i | \(-0.929656\pi\) |
0.677671 | + | 0.735365i | \(0.262989\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.98128 | − | 0.335081i | 0.131884 | − | 0.0148231i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.55044 | − | 5.78632i | −0.0684536 | − | 0.255472i | ||||
\(514\) | 10.4931 | + | 18.1746i | 0.462831 | + | 0.801647i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.89587 | − | 4.55868i | −0.347596 | − | 0.200685i | ||||
\(517\) | −9.38680 | + | 9.38680i | −0.412831 | + | 0.412831i | ||||
\(518\) | −11.9033 | − | 9.49790i | −0.523001 | − | 0.417314i | ||||
\(519\) | 12.2347i | 0.537045i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.28346 | − | 3.05040i | 0.231472 | − | 0.133641i | −0.379779 | − | 0.925077i | \(-0.624000\pi\) |
0.611251 | + | 0.791437i | \(0.290667\pi\) | |||||||
\(522\) | 1.39747 | − | 5.21545i | 0.0611658 | − | 0.228274i | ||||
\(523\) | −11.3122 | + | 3.03110i | −0.494649 | + | 0.132541i | −0.497516 | − | 0.867455i | \(-0.665754\pi\) |
0.00286635 | + | 0.999996i | \(0.499088\pi\) | |||||||
\(524\) | −13.5097 | −0.590172 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1410 | −0.834589 | ||||||||
\(527\) | −4.69340 | + | 1.25759i | −0.204448 | + | 0.0547816i | ||||
\(528\) | −0.806832 | + | 3.01114i | −0.0351129 | + | 0.131043i | ||||
\(529\) | 18.7911 | − | 10.8490i | 0.817002 | − | 0.471697i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 0.234720i | − | 0.0101860i | ||||||
\(532\) | 14.7552 | − | 5.78632i | 0.639720 | − | 0.250869i | ||||
\(533\) | −23.6357 | + | 23.6357i | −1.02377 | + | 1.02377i | ||||
\(534\) | 15.9077 | + | 9.18432i | 0.688394 | + | 0.397444i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.96288 | − | 12.0601i | −0.300751 | − | 0.520916i | ||||
\(537\) | −4.95478 | − | 18.4915i | −0.213815 | − | 0.797967i | ||||
\(538\) | −20.6670 | − | 20.6670i | −0.891019 | − | 0.891019i | ||||
\(539\) | 20.8485 | + | 6.44345i | 0.898009 | + | 0.277539i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.354252 | + | 0.613582i | −0.0152305 | + | 0.0263800i | −0.873540 | − | 0.486752i | \(-0.838182\pi\) |
0.858310 | + | 0.513132i | \(0.171515\pi\) | |||||||
\(542\) | 21.7267 | + | 5.82165i | 0.933241 | + | 0.250061i | ||||
\(543\) | −5.04947 | − | 1.35300i | −0.216694 | − | 0.0580629i | ||||
\(544\) | −0.570516 | + | 0.988164i | −0.0244607 | + | 0.0423672i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.90064 | + | 3.44960i | 0.338116 | + | 0.147629i | ||||
\(547\) | 24.3712 | + | 24.3712i | 1.04204 | + | 1.04204i | 0.999077 | + | 0.0429611i | \(0.0136792\pi\) |
0.0429611 | + | 0.999077i | \(0.486321\pi\) | |||||||
\(548\) | 4.44327 | + | 16.5825i | 0.189807 | + | 0.708370i | ||||
\(549\) | −4.26317 | − | 7.38403i | −0.181948 | − | 0.315143i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.0116 | − | 16.1725i | −1.19333 | − | 0.688971i | ||||
\(552\) | −0.806832 | + | 0.806832i | −0.0343411 | + | 0.0343411i | ||||
\(553\) | −3.99683 | + | 26.4679i | −0.169962 | + | 1.12553i | ||||
\(554\) | 21.6702i | 0.920677i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.66064 | − | 5.57757i | 0.409703 | − | 0.236542i | ||||
\(557\) | 5.47611 | − | 20.4371i | 0.232030 | − | 0.865948i | −0.747435 | − | 0.664335i | \(-0.768715\pi\) |
0.979465 | − | 0.201613i | \(-0.0646184\pi\) | |||||||
\(558\) | −4.11329 | + | 1.10215i | −0.174130 | + | 0.0466579i | ||||
\(559\) | −29.7079 | −1.25651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.55701 | 0.150177 | ||||||||
\(562\) | 18.7155 | − | 5.01481i | 0.789467 | − | 0.211537i | ||||
\(563\) | 8.98894 | − | 33.5472i | 0.378839 | − | 1.41385i | −0.468815 | − | 0.883296i | \(-0.655319\pi\) |
0.847654 | − | 0.530549i | \(-0.178014\pi\) | |||||||
\(564\) | −3.68788 | + | 2.12920i | −0.155288 | + | 0.0896553i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.6436i | 0.783648i | ||||||||
\(567\) | 1.65017 | − | 2.06808i | 0.0693005 | − | 0.0868512i | ||||
\(568\) | 1.23150 | − | 1.23150i | 0.0516727 | − | 0.0516727i | ||||
\(569\) | 4.58874 | + | 2.64931i | 0.192370 | + | 0.111065i | 0.593092 | − | 0.805135i | \(-0.297907\pi\) |
−0.400722 | + | 0.916200i | \(0.631241\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9427 | − | 22.4174i | −0.541636 | − | 0.938140i | −0.998810 | − | 0.0487634i | \(-0.984472\pi\) |
0.457175 | − | 0.889377i | \(-0.348861\pi\) | |||||||
\(572\) | 2.62898 | + | 9.81147i | 0.109923 | + | 0.410238i | ||||
\(573\) | 7.25378 | + | 7.25378i | 0.303031 | + | 0.303031i | ||||
\(574\) | −21.8421 | + | 16.1110i | −0.911673 | + | 0.672459i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −20.2574 | − | 5.42795i | −0.843326 | − | 0.225968i | −0.188807 | − | 0.982014i | \(-0.560462\pi\) |
−0.654519 | + | 0.756046i | \(0.727129\pi\) | |||||||
\(578\) | −15.1631 | − | 4.06295i | −0.630704 | − | 0.168997i | ||||
\(579\) | −2.42948 | + | 4.20799i | −0.100966 | + | 0.174878i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0683 | − | 27.6403i | 0.500679 | − | 1.14671i | ||||
\(582\) | 0.740585 | + | 0.740585i | 0.0306982 | + | 0.0306982i | ||||
\(583\) | 2.32581 | + | 8.68003i | 0.0963251 | + | 0.359490i | ||||
\(584\) | 0.566956 | + | 0.981996i | 0.0234608 | + | 0.0406353i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0281 | − | 8.09914i | −0.579496 | − | 0.334572i | ||||
\(587\) | 21.0917 | − | 21.0917i | 0.870548 | − | 0.870548i | −0.121984 | − | 0.992532i | \(-0.538926\pi\) |
0.992532 | + | 0.121984i | \(0.0389257\pi\) | |||||||
\(588\) | 5.92503 | + | 3.72748i | 0.244344 | + | 0.153719i | ||||
\(589\) | 25.5097i | 1.05111i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.54823 | − | 3.20327i | 0.228224 | − | 0.131765i | ||||
\(592\) | 1.48969 | − | 5.55960i | 0.0612259 | − | 0.228498i | ||||
\(593\) | −23.1242 | + | 6.19610i | −0.949595 | + | 0.254443i | −0.700190 | − | 0.713956i | \(-0.746902\pi\) |
−0.249405 | + | 0.968399i | \(0.580235\pi\) | |||||||
\(594\) | 3.11736 | 0.127907 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.1438 | 0.784161 | ||||||||
\(597\) | −2.47986 | + | 0.664478i | −0.101494 | + | 0.0271953i | ||||
\(598\) | −0.962272 | + | 3.59125i | −0.0393502 | + | 0.146857i | ||||
\(599\) | −22.3474 | + | 12.9022i | −0.913088 | + | 0.527172i | −0.881423 | − | 0.472327i | \(-0.843414\pi\) |
−0.0316646 | + | 0.999499i | \(0.510081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26.1745i | − | 1.06768i | −0.845586 | − | 0.533840i | \(-0.820749\pi\) | ||
0.845586 | − | 0.533840i | \(-0.179251\pi\) | |||||||
\(602\) | −23.8519 | − | 3.60178i | −0.972129 | − | 0.146798i | ||||
\(603\) | −9.84701 | + | 9.84701i | −0.401001 | + | 0.401001i | ||||
\(604\) | 15.1495 | + | 8.74656i | 0.616424 | + | 0.355892i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.81707 | + | 10.0755i | 0.236302 | + | 0.409288i | ||||
\(607\) | 8.50340 | + | 31.7351i | 0.345142 | + | 1.28809i | 0.892446 | + | 0.451155i | \(0.148988\pi\) |
−0.547303 | + | 0.836934i | \(0.684346\pi\) | |||||||
\(608\) | 4.23588 | + | 4.23588i | 0.171788 | + | 0.171788i | ||||
\(609\) | −1.59558 | − | 14.1962i | −0.0646561 | − | 0.575257i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.93776 | + | 12.0166i | −0.280672 | + | 0.486138i | ||||
\(612\) | 1.10215 | + | 0.295321i | 0.0445519 | + | 0.0119376i | ||||
\(613\) | −37.5024 | − | 10.0487i | −1.51471 | − | 0.405864i | −0.596711 | − | 0.802456i | \(-0.703526\pi\) |
−0.917995 | + | 0.396592i | \(0.870193\pi\) | |||||||
\(614\) | 0.282066 | − | 0.488553i | 0.0113833 | − | 0.0197164i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.921208 | + | 8.19615i | 0.0371165 | + | 0.330232i | ||||
\(617\) | −16.2604 | − | 16.2604i | −0.654618 | − | 0.654618i | 0.299483 | − | 0.954102i | \(-0.403186\pi\) |
−0.954102 | + | 0.299483i | \(0.903186\pi\) | |||||||
\(618\) | −2.75232 | − | 10.2718i | −0.110715 | − | 0.413192i | ||||
\(619\) | 13.8100 | + | 23.9195i | 0.555069 | + | 0.961407i | 0.997898 | + | 0.0648015i | \(0.0206414\pi\) |
−0.442829 | + | 0.896606i | \(0.646025\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.988164 | + | 0.570516i | 0.0396536 | + | 0.0228940i | ||||
\(622\) | −9.17061 | + | 9.17061i | −0.367708 | + | 0.367708i | ||||
\(623\) | 48.0540 | + | 7.25646i | 1.92524 | + | 0.290724i | ||||
\(624\) | 3.25839i | 0.130440i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.60375 | − | 0.925923i | 0.0640986 | − | 0.0370073i | ||||
\(627\) | 4.83328 | − | 18.0381i | 0.193023 | − | 0.720371i | ||||
\(628\) | −12.1063 | + | 3.24387i | −0.483093 | + | 0.129444i | ||||
\(629\) | −6.56747 | −0.261862 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.7151 | −0.784844 | −0.392422 | − | 0.919785i | \(-0.628363\pi\) | ||||
−0.392422 | + | 0.919785i | \(0.628363\pi\) | |||||||
\(632\) | −9.77262 | + | 2.61857i | −0.388734 | + | 0.104161i | ||||
\(633\) | 6.51567 | − | 24.3168i | 0.258975 | − | 0.966506i | ||||
\(634\) | −28.0468 | + | 16.1928i | −1.11388 | + | 0.643099i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.88264i | 0.114304i | ||||||||
\(637\) | 22.7923 | + | 0.865352i | 0.903065 | + | 0.0342865i | ||||
\(638\) | 11.9020 | − | 11.9020i | 0.471204 | − | 0.471204i | ||||
\(639\) | −1.50828 | − | 0.870803i | −0.0596665 | − | 0.0344485i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.453156 | + | 0.784890i | 0.0178986 | + | 0.0310013i | 0.874836 | − | 0.484419i | \(-0.160969\pi\) |
−0.856937 | + | 0.515421i | \(0.827636\pi\) | |||||||
\(642\) | −4.30339 | − | 16.0605i | −0.169841 | − | 0.633856i | ||||
\(643\) | −4.52704 | − | 4.52704i | −0.178529 | − | 0.178529i | 0.612185 | − | 0.790714i | \(-0.290291\pi\) |
−0.790714 | + | 0.612185i | \(0.790291\pi\) | |||||||
\(644\) | −1.20799 | + | 2.76667i | −0.0476014 | + | 0.109022i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.41765 | − | 5.91954i | 0.134466 | − | 0.232901i | ||||
\(647\) | −10.1722 | − | 2.72563i | −0.399910 | − | 0.107156i | 0.0532577 | − | 0.998581i | \(-0.483040\pi\) |
−0.453168 | + | 0.891425i | \(0.649706\pi\) | |||||||
\(648\) | 0.965926 | + | 0.258819i | 0.0379452 | + | 0.0101674i | ||||
\(649\) | 0.365854 | − | 0.633677i | 0.0143610 | − | 0.0248740i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.06696 | + | 6.68788i | −0.355362 | + | 0.262119i | ||||
\(652\) | −10.6828 | − | 10.6828i | −0.418372 | − | 0.418372i | ||||
\(653\) | −5.97781 | − | 22.3095i | −0.233930 | − | 0.873037i | −0.978628 | − | 0.205636i | \(-0.934074\pi\) |
0.744699 | − | 0.667401i | \(-0.232593\pi\) | |||||||
\(654\) | −7.12564 | − | 12.3420i | −0.278634 | − | 0.482609i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.88403 | − | 5.12920i | −0.346863 | − | 0.200261i | ||||
\(657\) | 0.801797 | − | 0.801797i | 0.0312811 | − | 0.0312811i | ||||
\(658\) | −7.02706 | + | 8.80669i | −0.273943 | + | 0.343321i | ||||
\(659\) | − | 43.2474i | − | 1.68468i | −0.538947 | − | 0.842340i | \(-0.681178\pi\) | ||
0.538947 | − | 0.842340i | \(-0.318822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0787 | + | 9.86042i | −0.664286 | + | 0.383526i | −0.793908 | − | 0.608038i | \(-0.791957\pi\) |
0.129622 | + | 0.991563i | \(0.458624\pi\) | |||||||
\(662\) | 3.00317 | − | 11.2080i | 0.116721 | − | 0.435610i | ||||
\(663\) | 3.59125 | − | 0.962272i | 0.139473 | − | 0.0373716i | ||||
\(664\) | 11.3994 | 0.442384 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.75572 | −0.223030 | ||||||||
\(667\) | 5.95099 | − | 1.59456i | 0.230423 | − | 0.0617418i | ||||
\(668\) | 0.529892 | − | 1.97758i | 0.0205021 | − | 0.0765150i | ||||
\(669\) | 9.00617 | − | 5.19971i | 0.348199 | − | 0.201033i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 26.5797i | − | 1.02610i | ||||||
\(672\) | −0.395046 | + | 2.61609i | −0.0152392 | + | 0.100918i | ||||
\(673\) | −15.0859 | + | 15.0859i | −0.581517 | + | 0.581517i | −0.935320 | − | 0.353803i | \(-0.884888\pi\) |
0.353803 | + | 0.935320i | \(0.384888\pi\) | |||||||
\(674\) | 11.5837 | + | 6.68788i | 0.446189 | + | 0.257607i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.19144 | − | 2.06363i | −0.0458245 | − | 0.0793704i | ||||
\(677\) | −3.45209 | − | 12.8834i | −0.132674 | − | 0.495148i | 0.867322 | − | 0.497747i | \(-0.165839\pi\) |
−0.999997 | + | 0.00259937i | \(0.999173\pi\) | |||||||
\(678\) | −7.08781 | − | 7.08781i | −0.272206 | − | 0.272206i | ||||
\(679\) | 2.53951 | + | 1.10880i | 0.0974573 | + | 0.0425520i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1725 | + | 17.6193i | −0.389810 | + | 0.675171i | ||||
\(682\) | −12.8226 | − | 3.43581i | −0.491003 | − | 0.131564i | ||||
\(683\) | 31.8622 | + | 8.53746i | 1.21918 | + | 0.326677i | 0.810356 | − | 0.585938i | \(-0.199274\pi\) |
0.408819 | + | 0.912615i | \(0.365941\pi\) | |||||||
\(684\) | 2.99522 | − | 5.18788i | 0.114525 | − | 0.198363i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.1945 | + | 3.45811i | 0.694671 | + | 0.132031i | ||||
\(687\) | −5.53867 | − | 5.53867i | −0.211313 | − | 0.211313i | ||||
\(688\) | −2.35975 | − | 8.80669i | −0.0899645 | − | 0.335752i | ||||
\(689\) | 4.69639 | + | 8.13438i | 0.178918 | + | 0.309895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.0104 | + | 18.4812i | 1.21773 | + | 0.703059i | 0.964433 | − | 0.264329i | \(-0.0851505\pi\) |
0.253301 | + | 0.967388i | \(0.418484\pi\) | |||||||
\(692\) | −8.65125 | + | 8.65125i | −0.328871 | + | 0.328871i | ||||
\(693\) | 7.67845 | − | 3.01114i | 0.291680 | − | 0.114384i | ||||
\(694\) | − | 21.5868i | − | 0.819424i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.67604 | − | 2.69971i | 0.177245 | − | 0.102332i | ||||
\(697\) | −3.02952 | + | 11.3063i | −0.114751 | + | 0.428257i | ||||
\(698\) | 14.4363 | − | 3.86819i | 0.546421 | − | 0.146413i | ||||
\(699\) | −5.59345 | −0.211564 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.4397 | 0.696456 | 0.348228 | − | 0.937410i | \(-0.386784\pi\) | ||||
0.348228 | + | 0.937410i | \(0.386784\pi\) | |||||||
\(702\) | 3.14737 | − | 0.843334i | 0.118790 | − | 0.0318296i | ||||
\(703\) | −8.92391 | + | 33.3045i | −0.336572 | + | 1.25610i | ||||
\(704\) | −2.69971 | + | 1.55868i | −0.101749 | + | 0.0587450i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.4722i | 1.37265i | ||||||||
\(707\) | 24.0603 | + | 19.1983i | 0.904882 | + | 0.722026i | ||||
\(708\) | 0.165972 | − | 0.165972i | 0.00623762 | − | 0.00623762i | ||||
\(709\) | −33.7593 | − | 19.4909i | −1.26786 | − | 0.731998i | −0.293275 | − | 0.956028i | \(-0.594745\pi\) |
−0.974582 | + | 0.224030i | \(0.928078\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.05868 | + | 8.76189i | 0.189715 | + | 0.328597i | ||||
\(712\) | 4.75415 | + | 17.7427i | 0.178169 | + | 0.664937i | ||||
\(713\) | −3.43581 | − | 3.43581i | −0.128672 | − | 0.128672i | ||||
\(714\) | 3.00000 | − | 0.337185i | 0.112272 | − | 0.0126188i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.57191 | − | 16.5790i | 0.357719 | − | 0.619587i | ||||
\(717\) | 11.9472 | + | 3.20124i | 0.446176 | + | 0.119552i | ||||
\(718\) | −4.21067 | − | 1.12824i | −0.157141 | − | 0.0421057i | ||||
\(719\) | 9.01794 | − | 15.6195i | 0.336312 | − | 0.582510i | −0.647424 | − | 0.762130i | \(-0.724154\pi\) |
0.983736 | + | 0.179620i | \(0.0574869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.7011 | − | 22.6422i | −0.621982 | − | 0.843239i | ||||
\(722\) | −11.9398 | − | 11.9398i | −0.444353 | − | 0.444353i | ||||
\(723\) | −3.62053 | − | 13.5120i | −0.134649 | − | 0.502517i | ||||
\(724\) | −2.61380 | − | 4.52723i | −0.0971411 | − | 0.168253i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.11030 | − | 0.641033i | −0.0412072 | − | 0.0237910i | ||||
\(727\) | −34.0615 | + | 34.0615i | −1.26327 | + | 1.26327i | −0.313774 | + | 0.949498i | \(0.601593\pi\) |
−0.949498 | + | 0.313774i | \(0.898407\pi\) | |||||||
\(728\) | 3.14737 | + | 8.02583i | 0.116649 | + | 0.297457i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.00944 | + | 5.20160i | −0.333226 | + | 0.192388i | ||||
\(732\) | 2.20678 | − | 8.23581i | 0.0815649 | − | 0.304404i | ||||
\(733\) | 32.6701 | − | 8.75391i | 1.20670 | − | 0.323333i | 0.401231 | − | 0.915977i | \(-0.368582\pi\) |
0.805465 | + | 0.592644i | \(0.201916\pi\) | |||||||
\(734\) | −18.5499 | −0.684689 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.14103 | −0.0420590 | ||||||||
\(737\) | −41.9324 | + | 11.2358i | −1.54460 | + | 0.413874i | ||||
\(738\) | −2.65507 | + | 9.90885i | −0.0977344 | + | 0.364750i | ||||
\(739\) | −15.9959 | + | 9.23522i | −0.588418 | + | 0.339723i | −0.764472 | − | 0.644657i | \(-0.777000\pi\) |
0.176054 | + | 0.984381i | \(0.443667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 19.5192i | − | 0.717057i | ||||||
\(742\) | 2.78442 | + | 7.10030i | 0.102219 | + | 0.260660i | ||||
\(743\) | 32.1999 | − | 32.1999i | 1.18130 | − | 1.18130i | 0.201894 | − | 0.979407i | \(-0.435290\pi\) |
0.979407 | − | 0.201894i | \(-0.0647096\pi\) | |||||||
\(744\) | −3.68788 | − | 2.12920i | −0.135204 | − | 0.0780601i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.75961 | − | 16.9041i | −0.357325 | − | 0.618905i | ||||
\(747\) | −2.95039 | − | 11.0110i | −0.107949 | − | 0.402871i | ||||
\(748\) | 2.51519 | + | 2.51519i | 0.0919643 | + | 0.0919643i | ||||
\(749\) | −26.1130 | − | 35.4022i | −0.954149 | − | 1.29357i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.62208 | − | 8.00567i | 0.168662 | − | 0.292131i | −0.769288 | − | 0.638902i | \(-0.779389\pi\) |
0.937950 | + | 0.346771i | \(0.112722\pi\) | |||||||
\(752\) | −4.11329 | − | 1.10215i | −0.149996 | − | 0.0401914i | ||||
\(753\) | 16.4532 | + | 4.40861i | 0.599587 | + | 0.160659i | ||||
\(754\) | 8.79673 | − | 15.2364i | 0.320358 | − | 0.554876i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.62920 | − | 0.295509i | 0.0956230 | − | 0.0107476i | ||||
\(757\) | −15.1284 | − | 15.1284i | −0.549850 | − | 0.549850i | 0.376548 | − | 0.926397i | \(-0.377111\pi\) |
−0.926397 | + | 0.376548i | \(0.877111\pi\) | |||||||
\(758\) | 9.69081 | + | 36.1666i | 0.351986 | + | 1.31363i | ||||
\(759\) | 1.77851 | + | 3.08046i | 0.0645557 | + | 0.111814i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.4867 | + | 18.7562i | 1.17764 | + | 0.679913i | 0.955468 | − | 0.295094i | \(-0.0953511\pi\) |
0.222175 | + | 0.975007i | \(0.428684\pi\) | |||||||
\(762\) | −0.705385 | + | 0.705385i | −0.0255534 | + | 0.0255534i | ||||
\(763\) | −29.4728 | − | 23.5170i | −1.06699 | − | 0.851371i | ||||
\(764\) | 10.2584i | 0.371136i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.522518 | − | 0.301676i | 0.0188794 | − | 0.0109000i | ||||
\(767\) | 0.197948 | − | 0.738750i | 0.00714747 | − | 0.0266747i | ||||
\(768\) | −0.965926 | + | 0.258819i | −0.0348548 | + | 0.00933933i | ||||
\(769\) | −0.469440 | −0.0169285 | −0.00846423 | − | 0.999964i | \(-0.502694\pi\) | ||||
−0.00846423 | + | 0.999964i | \(0.502694\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.9862 | 0.755800 | ||||||||
\(772\) | −4.69340 | + | 1.25759i | −0.168919 | + | 0.0452618i | ||||
\(773\) | −6.66314 | + | 24.8672i | −0.239656 | + | 0.894410i | 0.736338 | + | 0.676614i | \(0.236553\pi\) |
−0.975994 | + | 0.217796i | \(0.930113\pi\) | |||||||
\(774\) | −7.89587 | + | 4.55868i | −0.283811 | + | 0.163858i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.04735i | 0.0375975i | ||||||||
\(777\) | −14.1771 | + | 5.55960i | −0.508600 | + | 0.199450i | ||||
\(778\) | −14.3704 | + | 14.3704i | −0.515202 | + | 0.515202i | ||||
\(779\) | 53.2193 | + | 30.7262i | 1.90678 | + | 1.10088i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.71461 | − | 4.70184i | −0.0971363 | − | 0.168245i | ||||
\(782\) | 0.336971 | + | 1.25759i | 0.0120501 | + | 0.0449714i | ||||
\(783\) | −3.81797 | − | 3.81797i | −0.136443 | − | 0.136443i | ||||
\(784\) | 1.55390 | + | 6.82535i | 0.0554965 | + | 0.243762i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.75483 | + | 11.6997i | −0.240937 | + | 0.417315i | ||||
\(787\) | −24.9641 | − | 6.68911i | −0.889874 | − | 0.238441i | −0.215211 | − | 0.976567i | \(-0.569044\pi\) |
−0.674662 | + | 0.738127i | \(0.735711\pi\) | |||||||
\(788\) | 6.18825 | + | 1.65814i | 0.220447 | + | 0.0590687i | ||||
\(789\) | −9.57052 | + | 16.5766i | −0.340719 | + | 0.590143i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.3045 | − | 10.6119i | −0.864167 | − | 0.377314i | ||||
\(792\) | 2.20431 | + | 2.20431i | 0.0783266 | + | 0.0783266i | ||||
\(793\) | −7.19056 | − | 26.8355i | −0.255344 | − | 0.952957i | ||||
\(794\) | 5.99288 | + | 10.3800i | 0.212679 | + | 0.368371i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.22339 | − | 1.28367i | −0.0788058 | − | 0.0454986i | ||||
\(797\) | 30.2041 | − | 30.2041i | 1.06988 | − | 1.06988i | 0.0725174 | − | 0.997367i | \(-0.476897\pi\) |
0.997367 | − | 0.0725174i | \(-0.0231033\pi\) | |||||||
\(798\) | 2.36650 | − | 15.6716i | 0.0837733 | − | 0.554767i | ||||
\(799\) | 4.85897i | 0.171898i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.9077 | − | 9.18432i | 0.562071 | − | 0.324512i | ||||
\(802\) | −5.31014 | + | 19.8177i | −0.187507 | + | 0.699787i | ||||
\(803\) | 3.41437 | − | 0.914876i | 0.120490 | − | 0.0322853i | ||||
\(804\) | −13.9258 | −0.491124 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.8755 | −0.488744 | ||||||||
\(807\) | −28.2317 | + | 7.56466i | −0.993803 | + | 0.266289i | ||||
\(808\) | −3.01114 | + | 11.2377i | −0.105931 | + | 0.395342i | ||||
\(809\) | 11.3829 | − | 6.57191i | 0.400201 | − | 0.231056i | −0.286370 | − | 0.958119i | \(-0.592449\pi\) |
0.686571 | + | 0.727063i | \(0.259115\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.45633i | − | 0.0511386i | −0.999673 | − | 0.0255693i | \(-0.991860\pi\) | ||
0.999673 | − | 0.0255693i | \(-0.00813985\pi\) | |||||||
\(812\) | 8.90995 | − | 11.1664i | 0.312678 | − | 0.391865i | ||||
\(813\) | 15.9050 | − | 15.9050i | 0.557814 | − | 0.557814i | ||||
\(814\) | −15.5388 | − | 8.97133i | −0.544635 | − | 0.314445i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.570516 | + | 0.988164i | 0.0199721 | + | 0.0345926i | ||||
\(817\) | 14.1359 | + | 52.7560i | 0.494554 | + | 1.84570i | ||||
\(818\) | −9.35105 | − | 9.35105i | −0.326952 | − | 0.326952i | ||||
\(819\) | 6.93776 | − | 5.11736i | 0.242425 | − | 0.178815i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.43420 | + | 5.94821i | −0.119854 | + | 0.207594i | −0.919710 | − | 0.392599i | \(-0.871576\pi\) |
0.799855 | + | 0.600193i | \(0.204909\pi\) | |||||||
\(822\) | 16.5825 | + | 4.44327i | 0.578382 | + | 0.154977i | ||||
\(823\) | −5.25665 | − | 1.40852i | −0.183235 | − | 0.0490978i | 0.166035 | − | 0.986120i | \(-0.446904\pi\) |
−0.349270 | + | 0.937022i | \(0.613570\pi\) | |||||||
\(824\) | 5.31707 | − | 9.20944i | 0.185229 | − | 0.320826i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.248494 | − | 0.569127i | 0.00864620 | − | 0.0198025i | ||||
\(827\) | 4.02842 | + | 4.02842i | 0.140082 | + | 0.140082i | 0.773670 | − | 0.633589i | \(-0.218419\pi\) |
−0.633589 | + | 0.773670i | \(0.718419\pi\) | |||||||
\(828\) | 0.295321 | + | 1.10215i | 0.0102631 | + | 0.0383025i | ||||
\(829\) | 9.72816 | + | 16.8497i | 0.337873 | + | 0.585213i | 0.984032 | − | 0.177989i | \(-0.0569592\pi\) |
−0.646159 | + | 0.763203i | \(0.723626\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.7669 | + | 10.8351i | 0.651017 | + | 0.375865i | ||||
\(832\) | −2.30403 | + | 2.30403i | −0.0798779 | + | 0.0798779i | ||||
\(833\) | 7.06368 | − | 3.72831i | 0.244742 | − | 0.129178i | ||||
\(834\) | − | 11.1551i | − | 0.386271i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.1725 | − | 9.33719i | 0.559337 | − | 0.322933i | ||||
\(837\) | −1.10215 | + | 4.11329i | −0.0380960 | + | 0.142176i | ||||
\(838\) | 19.2983 | − | 5.17097i | 0.666650 | − | 0.178628i | ||||
\(839\) | −10.1273 | −0.349632 | −0.174816 | − | 0.984601i | \(-0.555933\pi\) | ||||
−0.174816 | + | 0.984601i | \(0.555933\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.153802 | −0.00530352 | ||||||||
\(842\) | −19.6005 | + | 5.25195i | −0.675479 | + | 0.180994i | ||||
\(843\) | 5.01481 | − | 18.7155i | 0.172719 | − | 0.644597i | ||||
\(844\) | 21.8018 | − | 12.5873i | 0.750451 | − | 0.433273i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.25839i | 0.146407i | ||||||||
\(847\) | −3.35400 | − | 0.506476i | −0.115245 | − | 0.0174027i | ||||
\(848\) | −2.03833 | + | 2.03833i | −0.0699967 | + | 0.0699967i | ||||
\(849\) | 16.1458 | + | 9.32179i | 0.554123 | + | 0.319923i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.28374 | − | 5.68760i | −0.112565 | − | 0.194968i | ||||
\(852\) | −0.450761 | − | 1.68226i | −0.0154428 | − | 0.0576334i | ||||
\(853\) | 27.6531 | + | 27.6531i | 0.946824 | + | 0.946824i | 0.998656 | − | 0.0518322i | \(-0.0165061\pi\) |
−0.0518322 | + | 0.998656i | \(0.516506\pi\) | |||||||
\(854\) | −2.51961 | − | 22.4174i | −0.0862193 | − | 0.767109i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.31351 | − | 14.3994i | 0.284150 | − | 0.492162i | ||||
\(857\) | 29.4312 | + | 7.88607i | 1.00535 | + | 0.269383i | 0.723686 | − | 0.690130i | \(-0.242446\pi\) |
0.281665 | + | 0.959513i | \(0.409113\pi\) | |||||||
\(858\) | 9.81147 | + | 2.62898i | 0.334958 | + | 0.0897518i | ||||
\(859\) | 17.6997 | − | 30.6568i | 0.603906 | − | 1.04600i | −0.388317 | − | 0.921526i | \(-0.626943\pi\) |
0.992223 | − | 0.124471i | \(-0.0397233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.03145 | + | 26.9713i | 0.103311 | + | 0.919181i | ||||
\(862\) | 0.237255 | + | 0.237255i | 0.00808092 | + | 0.00808092i | ||||
\(863\) | −1.05194 | − | 3.92588i | −0.0358083 | − | 0.133638i | 0.945708 | − | 0.325018i | \(-0.105370\pi\) |
−0.981516 | + | 0.191380i | \(0.938704\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.55640 | − | 3.20799i | −0.188814 | − | 0.109012i | ||||
\(867\) | −11.1002 | + | 11.1002i | −0.376982 | + | 0.376982i | ||||
\(868\) | −11.1403 | − | 1.68226i | −0.378128 | − | 0.0570997i | ||||
\(869\) | 31.5395i | 1.06990i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.2964 | + | 22.6878i | −1.33151 | + | 0.768747i | ||||
\(872\) | 3.68850 | − | 13.7657i | 0.124908 | − | 0.466164i | ||||
\(873\) | 1.01166 | − | 0.271073i | 0.0342394 | − | 0.00917443i | ||||
\(874\) | 6.83529 | 0.231207 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.13391 | 0.0383113 | ||||||||
\(877\) | −24.7603 | + | 6.63449i | −0.836095 | + | 0.224031i | −0.651371 | − | 0.758760i | \(-0.725806\pi\) |
−0.184724 | + | 0.982790i | \(0.559139\pi\) | |||||||
\(878\) | 7.05067 | − | 26.3135i | 0.237949 | − | 0.888037i | ||||
\(879\) | −14.0281 | + | 8.09914i | −0.473157 | + | 0.273177i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.74161i | 0.0586762i | 0.999570 | + | 0.0293381i | \(0.00933995\pi\) | ||||
−0.999570 | + | 0.0293381i | \(0.990660\pi\) | |||||||
\(882\) | 6.19060 | − | 3.26748i | 0.208448 | − | 0.110022i | ||||
\(883\) | 3.58173 | − | 3.58173i | 0.120535 | − | 0.120535i | −0.644266 | − | 0.764801i | \(-0.722837\pi\) |
0.764801 | + | 0.644266i | \(0.222837\pi\) | |||||||
\(884\) | 3.21983 | + | 1.85897i | 0.108294 | + | 0.0625238i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.58235 | − | 4.47277i | −0.0867558 | − | 0.150266i | ||||
\(887\) | 5.68177 | + | 21.2046i | 0.190775 | + | 0.711982i | 0.993320 | + | 0.115391i | \(0.0368120\pi\) |
−0.802545 | + | 0.596591i | \(0.796521\pi\) | |||||||
\(888\) | −4.06991 | − | 4.06991i | −0.136577 | − | 0.136577i | ||||
\(889\) | −1.05610 | + | 2.41880i | −0.0354205 | + | 0.0811240i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.55868 | − | 2.69971i | 0.0522177 | − | 0.0904438i | ||||
\(892\) | 10.0451 | + | 2.69157i | 0.336334 | + | 0.0901204i | ||||
\(893\) | 24.6404 | + | 6.60239i | 0.824561 | + | 0.220940i | ||||
\(894\) | 9.57191 | − | 16.5790i | 0.320132 | − | 0.554486i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.12920 | + | 1.57052i | −0.0711315 | + | 0.0524673i | ||||
\(897\) | 2.62898 | + | 2.62898i | 0.0877790 | + | 0.0877790i | ||||
\(898\) | 6.74227 | + | 25.1625i | 0.224992 | + | 0.839683i | ||||
\(899\) | 11.4964 | + | 19.9124i | 0.383428 | + | 0.664116i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.84852 | + | 1.64459i | 0.0948979 | + | 0.0547894i | ||||
\(902\) | −22.6126 | + | 22.6126i | −0.752919 | + | 0.752919i | ||||
\(903\) | −15.0452 | + | 18.8554i | −0.500672 | + | 0.627469i | ||||
\(904\) | − | 10.0237i | − | 0.333382i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 15.1495 | − | 8.74656i | 0.503308 | − | 0.290585i | ||||
\(907\) | −0.178339 | + | 0.665569i | −0.00592164 | + | 0.0220999i | −0.968823 | − | 0.247752i | \(-0.920308\pi\) |
0.962902 | + | 0.269852i | \(0.0869748\pi\) | |||||||
\(908\) | −19.6517 | + | 5.26566i | −0.652165 | + | 0.174747i | ||||
\(909\) | 11.6341 | 0.385880 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.8225 | 0.689881 | 0.344941 | − | 0.938625i | \(-0.387899\pi\) | ||||
0.344941 | + | 0.938625i | \(0.387899\pi\) | |||||||
\(912\) | 5.78632 | − | 1.55044i | 0.191604 | − | 0.0513402i | ||||
\(913\) | 9.19742 | − | 34.3253i | 0.304390 | − | 1.13600i | ||||
\(914\) | 26.2276 | − | 15.1425i | 0.867530 | − | 0.500869i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 7.83286i | − | 0.258805i | ||||||
\(917\) | −5.33695 | + | 35.3425i | −0.176241 | + | 1.16711i | ||||
\(918\) | 0.806832 | − | 0.806832i | 0.0266294 | − | 0.0266294i | ||||
\(919\) | −38.5703 | − | 22.2686i | −1.27232 | − | 0.734572i | −0.296893 | − | 0.954911i | \(-0.595950\pi\) |
−0.975423 | + | 0.220339i | \(0.929284\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.282066 | − | 0.488553i | −0.00929439 | − | 0.0160984i | ||||
\(922\) | 0.962272 | + | 3.59125i | 0.0316907 | + | 0.118271i | ||||
\(923\) | −4.01272 | − | 4.01272i | −0.132080 | − | 0.132080i | ||||
\(924\) | 7.55868 | + | 3.30029i | 0.248662 | + | 0.108571i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.5735 | + | 20.0459i | −0.380329 | + | 0.658750i | ||||
\(927\) | −10.2718 | − | 2.75232i | −0.337370 | − | 0.0903980i | ||||
\(928\) | 5.21545 | + | 1.39747i | 0.171205 | + | 0.0458743i | ||||
\(929\) | 7.68149 | − | 13.3047i | 0.252022 | − | 0.436514i | −0.712061 | − | 0.702118i | \(-0.752238\pi\) |
0.964082 | + | 0.265604i | \(0.0855713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.30856 | − | 40.8869i | −0.305076 | − | 1.34001i | ||||
\(932\) | −3.95517 | − | 3.95517i | −0.129556 | − | 0.129556i | ||||
\(933\) | 3.35668 | + | 12.5273i | 0.109893 | + | 0.410125i | ||||
\(934\) | −13.5300 | − | 23.4347i | −0.442716 | − | 0.766806i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.82185 | + | 1.62920i | 0.0922351 | + | 0.0532520i | ||||
\(937\) | −14.8294 | + | 14.8294i | −0.484456 | + | 0.484456i | −0.906552 | − | 0.422095i | \(-0.861295\pi\) |
0.422095 | + | 0.906552i | \(0.361295\pi\) | |||||||
\(938\) | −34.3009 | + | 13.4513i | −1.11996 | + | 0.439199i | ||||
\(939\) | − | 1.85185i | − | 0.0604327i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0066 | − | 15.5923i | 0.880389 | − | 0.508293i | 0.00960244 | − | 0.999954i | \(-0.496943\pi\) |
0.870787 | + | 0.491661i | \(0.163610\pi\) | |||||||
\(942\) | −3.24387 | + | 12.1063i | −0.105691 | + | 0.394444i | ||||
\(943\) | −11.3063 | + | 3.02952i | −0.368184 | + | 0.0986547i | ||||
\(944\) | 0.234720 | 0.00763949 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.4221 | −0.924082 | ||||||||
\(947\) | 18.7182 | − | 5.01553i | 0.608261 | − | 0.162983i | 0.0584752 | − | 0.998289i | \(-0.481376\pi\) |
0.549785 | + | 0.835306i | \(0.314709\pi\) | |||||||
\(948\) | −2.61857 | + | 9.77262i | −0.0850471 | + | 0.317400i | ||||
\(949\) | 3.19973 | − | 1.84737i | 0.103868 | − | 0.0599680i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.3857i | 1.05018i | ||||||||
\(952\) | 2.35975 | + | 1.88289i | 0.0764798 | + | 0.0610250i | ||||
\(953\) | −22.0009 | + | 22.0009i | −0.712680 | + | 0.712680i | −0.967095 | − | 0.254415i | \(-0.918117\pi\) |
0.254415 | + | 0.967095i | \(0.418117\pi\) | |||||||
\(954\) | 2.49644 | + | 1.44132i | 0.0808252 | + | 0.0466645i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.18432 | + | 10.7115i | 0.200015 | + | 0.346436i | ||||
\(957\) | −4.35643 | − | 16.2584i | −0.140823 | − | 0.525560i | ||||
\(958\) | −29.8219 | − | 29.8219i | −0.963503 | − | 0.963503i | ||||
\(959\) | 45.1367 | − | 5.07314i | 1.45754 | − | 0.163820i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.43304 | + | 11.1424i | −0.207518 | + | 0.359431i | ||||
\(962\) | −18.1154 | − | 4.85400i | −0.584063 | − | 0.156499i | ||||
\(963\) | −16.0605 | − | 4.30339i | −0.517542 | − | 0.138675i | ||||
\(964\) | 6.99433 | − | 12.1145i | 0.225272 | − | 0.390183i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.79201 | + | 2.42948i | 0.0576570 | + | 0.0781674i | ||||
\(967\) | 14.6687 | + | 14.6687i | 0.471715 | + | 0.471715i | 0.902469 | − | 0.430754i | \(-0.141752\pi\) |
−0.430754 | + | 0.902469i | \(0.641752\pi\) | |||||||
\(968\) | −0.331823 | − | 1.23838i | −0.0106652 | − | 0.0398031i | ||||
\(969\) | −3.41765 | − | 5.91954i | −0.109791 | − | 0.190163i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.11356 | + | 5.26172i | 0.292468 | + | 0.168857i | 0.639054 | − | 0.769162i | \(-0.279326\pi\) |
−0.346586 | + | 0.938018i | \(0.612659\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −10.7750 | − | 27.4765i | −0.345432 | − | 0.880857i | ||||
\(974\) | − | 31.2777i | − | 1.00220i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.38403 | − | 4.26317i | 0.236357 | − | 0.136461i | ||||
\(977\) | −12.7095 | + | 47.4327i | −0.406614 | + | 1.51751i | 0.394445 | + | 0.918920i | \(0.370937\pi\) |
−0.801059 | + | 0.598585i | \(0.795730\pi\) | |||||||
\(978\) | −14.5930 | + | 3.91019i | −0.466633 | + | 0.125034i | ||||
\(979\) | 57.2616 | 1.83009 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.2513 | −0.455008 | ||||||||
\(982\) | 25.8007 | − | 6.91327i | 0.823332 | − | 0.220611i | ||||
\(983\) | −14.9681 | + | 55.8618i | −0.477409 | + | 1.78172i | 0.134638 | + | 0.990895i | \(0.457013\pi\) |
−0.612048 | + | 0.790821i | \(0.709654\pi\) | |||||||
\(984\) | −8.88403 | + | 5.12920i | −0.283213 | + | 0.163513i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 6.16092i | − | 0.196204i | ||||||
\(987\) | 4.11329 | + | 10.4890i | 0.130928 | + | 0.333867i | ||||
\(988\) | 13.8022 | − | 13.8022i | 0.439106 | − | 0.439106i | ||||
\(989\) | −9.00944 | − | 5.20160i | −0.286484 | − | 0.165401i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.8317 | + | 51.6700i | 0.947635 | + | 1.64135i | 0.750388 | + | 0.660998i | \(0.229867\pi\) |
0.197247 | + | 0.980354i | \(0.436800\pi\) | |||||||
\(992\) | −1.10215 | − | 4.11329i | −0.0349934 | − | 0.130597i | ||||
\(993\) | −8.20481 | − | 8.20481i | −0.260372 | − | 0.260372i | ||||
\(994\) | −2.73522 | − | 3.70822i | −0.0867560 | − | 0.117618i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.69971 | − | 9.87219i | 0.180602 | − | 0.312812i | ||||
\(997\) | 51.2361 | + | 13.7287i | 1.62266 | + | 0.434791i | 0.951782 | − | 0.306775i | \(-0.0992498\pi\) |
0.670880 | + | 0.741566i | \(0.265916\pi\) | |||||||
\(998\) | −7.57742 | − | 2.03036i | −0.239859 | − | 0.0642701i | ||||
\(999\) | −2.87786 | + | 4.98460i | −0.0910515 | + | 0.157706i |
(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 | 1050.2.bc.e.607.3 | yes | 16 | |
5.2 | odd | 4 | 1050.2.bc.f.943.4 | yes | 16 | ||
5.3 | odd | 4 | 1050.2.bc.f.943.1 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.2.bc.e.607.2 | yes | 16 | |
7.3 | odd | 6 | 1050.2.bc.f.157.1 | yes | 16 | ||
35.3 | even | 12 | inner | 1050.2.bc.e.493.4 | yes | 16 | |
35.17 | even | 12 | inner | 1050.2.bc.e.493.1 | ✓ | 16 | |
35.24 | odd | 6 | 1050.2.bc.f.157.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.bc.e.493.1 | ✓ | 16 | 35.17 | even | 12 | inner | |
1050.2.bc.e.493.4 | yes | 16 | 35.3 | even | 12 | inner | |
1050.2.bc.e.607.2 | yes | 16 | 5.4 | even | 2 | inner | |
1050.2.bc.e.607.3 | yes | 16 | 1.1 | even | 1 | trivial | |
1050.2.bc.f.157.1 | yes | 16 | 7.3 | odd | 6 | ||
1050.2.bc.f.157.4 | yes | 16 | 35.24 | odd | 6 | ||
1050.2.bc.f.943.1 | yes | 16 | 5.3 | odd | 4 | ||
1050.2.bc.f.943.4 | yes | 16 | 5.2 | odd | 4 |