Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,3,Mod(7,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.g (of order \(10\), 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: | \(0.899184872389\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 13.2 | ||
Root | \(-1.29715 + 0.104262i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.13 |
Dual form | 33.3.g.a.28.2 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.40785 | − | 0.782357i | −1.20392 | − | 0.391179i | −0.362721 | − | 0.931898i | \(-0.618152\pi\) |
−0.841203 | + | 0.540719i | \(0.818152\pi\) | |||||||
\(3\) | 1.40126 | − | 1.01807i | 0.467086 | − | 0.339358i | ||||
\(4\) | 1.94958 | + | 1.41645i | 0.487395 | + | 0.354113i | ||||
\(5\) | −2.61024 | − | 8.03348i | −0.522047 | − | 1.60670i | −0.770082 | − | 0.637945i | \(-0.779785\pi\) |
0.248034 | − | 0.968751i | \(-0.420215\pi\) | |||||||
\(6\) | −4.17052 | + | 1.35508i | −0.695086 | + | 0.225847i | ||||
\(7\) | 1.43445 | − | 1.97435i | 0.204921 | − | 0.282050i | −0.694170 | − | 0.719811i | \(-0.744228\pi\) |
0.899091 | + | 0.437761i | \(0.144228\pi\) | |||||||
\(8\) | 2.36641 | + | 3.25708i | 0.295801 | + | 0.407135i | ||||
\(9\) | 0.927051 | − | 2.85317i | 0.103006 | − | 0.317019i | ||||
\(10\) | 21.3855i | 2.13855i | ||||||||
\(11\) | 2.51703 | + | 10.7082i | 0.228821 | + | 0.973469i | ||||
\(12\) | 4.17392 | 0.347827 | ||||||||
\(13\) | 11.1993 | + | 3.63888i | 0.861485 | + | 0.279914i | 0.706249 | − | 0.707964i | \(-0.250386\pi\) |
0.155236 | + | 0.987877i | \(0.450386\pi\) | |||||||
\(14\) | −4.99858 | + | 3.63168i | −0.357041 | + | 0.259406i | ||||
\(15\) | −11.8363 | − | 8.59957i | −0.789086 | − | 0.573305i | ||||
\(16\) | −6.12844 | − | 18.8614i | −0.383028 | − | 1.17884i | ||||
\(17\) | −1.93053 | + | 0.627268i | −0.113561 | + | 0.0368981i | −0.365246 | − | 0.930911i | \(-0.619015\pi\) |
0.251685 | + | 0.967809i | \(0.419015\pi\) | |||||||
\(18\) | −4.46440 | + | 6.14471i | −0.248022 | + | 0.341373i | ||||
\(19\) | −4.97861 | − | 6.85246i | −0.262032 | − | 0.360656i | 0.657648 | − | 0.753326i | \(-0.271552\pi\) |
−0.919680 | + | 0.392670i | \(0.871552\pi\) | |||||||
\(20\) | 6.29019 | − | 19.3592i | 0.314509 | − | 0.967960i | ||||
\(21\) | − | 4.22695i | − | 0.201283i | ||||||
\(22\) | 2.31697 | − | 27.7528i | 0.105317 | − | 1.26149i | ||||
\(23\) | 41.9571 | 1.82422 | 0.912110 | − | 0.409946i | \(-0.134452\pi\) | ||||
0.912110 | + | 0.409946i | \(0.134452\pi\) | |||||||
\(24\) | 6.63189 | + | 2.15483i | 0.276329 | + | 0.0897847i | ||||
\(25\) | −37.4981 | + | 27.2440i | −1.49992 | + | 1.08976i | ||||
\(26\) | −24.1193 | − | 17.5237i | −0.927667 | − | 0.673989i | ||||
\(27\) | −1.60570 | − | 4.94183i | −0.0594703 | − | 0.183031i | ||||
\(28\) | 5.59314 | − | 1.81732i | 0.199755 | − | 0.0649044i | ||||
\(29\) | −14.4679 | + | 19.9133i | −0.498893 | + | 0.686667i | −0.981997 | − | 0.188896i | \(-0.939509\pi\) |
0.483105 | + | 0.875563i | \(0.339509\pi\) | |||||||
\(30\) | 21.7721 | + | 29.9667i | 0.725736 | + | 0.998889i | ||||
\(31\) | 6.74074 | − | 20.7459i | 0.217443 | − | 0.669222i | −0.781528 | − | 0.623870i | \(-0.785559\pi\) |
0.998971 | − | 0.0453514i | \(-0.0144407\pi\) | |||||||
\(32\) | 34.1061i | 1.06582i | ||||||||
\(33\) | 14.4287 | + | 12.4424i | 0.437233 | + | 0.377041i | ||||
\(34\) | 5.13918 | 0.151152 | ||||||||
\(35\) | −19.6051 | − | 6.37010i | −0.560147 | − | 0.182003i | ||||
\(36\) | 5.84874 | − | 4.24936i | 0.162465 | − | 0.118038i | ||||
\(37\) | 12.9478 | + | 9.40714i | 0.349941 | + | 0.254247i | 0.748844 | − | 0.662746i | \(-0.230609\pi\) |
−0.398903 | + | 0.916993i | \(0.630609\pi\) | |||||||
\(38\) | 6.62665 | + | 20.3947i | 0.174386 | + | 0.536704i | ||||
\(39\) | 19.3978 | − | 6.30272i | 0.497379 | − | 0.161608i | ||||
\(40\) | 19.9888 | − | 27.5122i | 0.499720 | − | 0.687806i | ||||
\(41\) | −30.9272 | − | 42.5677i | −0.754323 | − | 1.03824i | −0.997665 | − | 0.0682958i | \(-0.978244\pi\) |
0.243342 | − | 0.969940i | \(-0.421756\pi\) | |||||||
\(42\) | −3.30698 | + | 10.1778i | −0.0787377 | + | 0.242330i | ||||
\(43\) | 42.3507i | 0.984900i | 0.870341 | + | 0.492450i | \(0.163899\pi\) | ||||
−0.870341 | + | 0.492450i | \(0.836101\pi\) | |||||||
\(44\) | −10.2604 | + | 24.4417i | −0.233192 | + | 0.555493i | ||||
\(45\) | −25.3407 | −0.563127 | ||||||||
\(46\) | −101.026 | − | 32.8254i | −2.19622 | − | 0.713596i | ||||
\(47\) | 13.0910 | − | 9.51117i | 0.278532 | − | 0.202365i | −0.439745 | − | 0.898123i | \(-0.644931\pi\) |
0.718277 | + | 0.695757i | \(0.244931\pi\) | |||||||
\(48\) | −27.7898 | − | 20.1905i | −0.578955 | − | 0.420635i | ||||
\(49\) | 13.3014 | + | 40.9376i | 0.271458 | + | 0.835461i | ||||
\(50\) | 111.604 | − | 36.2624i | 2.23208 | − | 0.725248i | ||||
\(51\) | −2.06657 | + | 2.84439i | −0.0405210 | + | 0.0557723i | ||||
\(52\) | 16.6797 | + | 22.9576i | 0.320763 | + | 0.441492i | ||||
\(53\) | −15.3065 | + | 47.1085i | −0.288802 | + | 0.888840i | 0.696432 | + | 0.717623i | \(0.254770\pi\) |
−0.985233 | + | 0.171217i | \(0.945230\pi\) | |||||||
\(54\) | 13.1554i | 0.243619i | ||||||||
\(55\) | 79.4537 | − | 48.1714i | 1.44461 | − | 0.875843i | ||||
\(56\) | 9.82509 | 0.175448 | ||||||||
\(57\) | −13.9526 | − | 4.53348i | −0.244783 | − | 0.0795348i | ||||
\(58\) | 50.4158 | − | 36.6292i | 0.869238 | − | 0.631538i | ||||
\(59\) | −16.1257 | − | 11.7160i | −0.273317 | − | 0.198576i | 0.442680 | − | 0.896679i | \(-0.354028\pi\) |
−0.715997 | + | 0.698103i | \(0.754028\pi\) | |||||||
\(60\) | −10.8949 | − | 33.5311i | −0.181582 | − | 0.558852i | ||||
\(61\) | −113.086 | + | 36.7440i | −1.85387 | + | 0.602360i | −0.857784 | + | 0.514011i | \(0.828159\pi\) |
−0.996090 | + | 0.0883491i | \(0.971841\pi\) | |||||||
\(62\) | −32.4614 | + | 44.6792i | −0.523571 | + | 0.720633i | ||||
\(63\) | −4.30334 | − | 5.92304i | −0.0683070 | − | 0.0940166i | ||||
\(64\) | 2.16942 | − | 6.67679i | 0.0338972 | − | 0.104325i | ||||
\(65\) | − | 99.4678i | − | 1.53027i | ||||||
\(66\) | −25.0077 | − | 41.2477i | −0.378905 | − | 0.624966i | ||||
\(67\) | −4.41442 | −0.0658869 | −0.0329434 | − | 0.999457i | \(-0.510488\pi\) | ||||
−0.0329434 | + | 0.999457i | \(0.510488\pi\) | |||||||
\(68\) | −4.65223 | − | 1.51160i | −0.0684151 | − | 0.0222294i | ||||
\(69\) | 58.7927 | − | 42.7154i | 0.852068 | − | 0.619064i | ||||
\(70\) | 42.2225 | + | 30.6764i | 0.603179 | + | 0.438235i | ||||
\(71\) | 1.86520 | + | 5.74049i | 0.0262704 | + | 0.0808520i | 0.963332 | − | 0.268312i | \(-0.0864657\pi\) |
−0.937062 | + | 0.349164i | \(0.886466\pi\) | |||||||
\(72\) | 11.4868 | − | 3.73228i | 0.159539 | − | 0.0518372i | ||||
\(73\) | −3.57399 | + | 4.91917i | −0.0489588 | + | 0.0673859i | −0.832794 | − | 0.553582i | \(-0.813260\pi\) |
0.783836 | + | 0.620968i | \(0.213260\pi\) | |||||||
\(74\) | −23.8166 | − | 32.7808i | −0.321847 | − | 0.442984i | ||||
\(75\) | −24.8082 | + | 76.3517i | −0.330775 | + | 1.01802i | ||||
\(76\) | − | 20.4114i | − | 0.268571i | ||||||
\(77\) | 24.7522 | + | 10.3908i | 0.321457 | + | 0.134945i | ||||
\(78\) | −51.6379 | −0.662024 | ||||||||
\(79\) | 98.3988 | + | 31.9717i | 1.24555 | + | 0.404705i | 0.856326 | − | 0.516436i | \(-0.172742\pi\) |
0.389229 | + | 0.921141i | \(0.372742\pi\) | |||||||
\(80\) | −135.526 | + | 98.4655i | −1.69408 | + | 1.23082i | ||||
\(81\) | −7.28115 | − | 5.29007i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 41.1649 | + | 126.693i | 0.502011 | + | 1.54503i | ||||
\(83\) | 28.6898 | − | 9.32189i | 0.345660 | − | 0.112312i | −0.131041 | − | 0.991377i | \(-0.541832\pi\) |
0.476702 | + | 0.879065i | \(0.341832\pi\) | |||||||
\(84\) | 5.98727 | − | 8.24077i | 0.0712771 | − | 0.0981045i | ||||
\(85\) | 10.0783 | + | 13.8716i | 0.118568 | + | 0.163195i | ||||
\(86\) | 33.1334 | − | 101.974i | 0.385272 | − | 1.18574i | ||||
\(87\) | 42.6331i | 0.490036i | ||||||||
\(88\) | −28.9210 | + | 33.5380i | −0.328647 | + | 0.381114i | ||||
\(89\) | −60.4650 | −0.679382 | −0.339691 | − | 0.940537i | \(-0.610323\pi\) | ||||
−0.339691 | + | 0.940537i | \(0.610323\pi\) | |||||||
\(90\) | 61.0166 | + | 19.8255i | 0.677962 | + | 0.220283i | ||||
\(91\) | 23.2492 | − | 16.8916i | 0.255486 | − | 0.185621i | ||||
\(92\) | 81.7987 | + | 59.4302i | 0.889116 | + | 0.645981i | ||||
\(93\) | −11.6753 | − | 35.9329i | −0.125541 | − | 0.386375i | ||||
\(94\) | −38.9623 | + | 12.6596i | −0.414492 | + | 0.134677i | ||||
\(95\) | −42.0538 | + | 57.8821i | −0.442672 | + | 0.609285i | ||||
\(96\) | 34.7226 | + | 47.7915i | 0.361693 | + | 0.497828i | ||||
\(97\) | 11.3376 | − | 34.8935i | 0.116882 | − | 0.359727i | −0.875453 | − | 0.483304i | \(-0.839437\pi\) |
0.992335 | + | 0.123577i | \(0.0394366\pi\) | |||||||
\(98\) | − | 108.978i | − | 1.11202i | ||||||
\(99\) | 32.8856 | + | 2.74549i | 0.332178 | + | 0.0277322i | ||||
\(100\) | −111.695 | −1.11695 | ||||||||
\(101\) | 134.816 | + | 43.8043i | 1.33481 | + | 0.433706i | 0.887556 | − | 0.460700i | \(-0.152402\pi\) |
0.447255 | + | 0.894406i | \(0.352402\pi\) | |||||||
\(102\) | 7.20131 | − | 5.23206i | 0.0706011 | − | 0.0512947i | ||||
\(103\) | −31.5689 | − | 22.9361i | −0.306494 | − | 0.222681i | 0.423897 | − | 0.905711i | \(-0.360662\pi\) |
−0.730391 | + | 0.683030i | \(0.760662\pi\) | |||||||
\(104\) | 14.6500 | + | 45.0881i | 0.140865 | + | 0.433539i | ||||
\(105\) | −33.9571 | + | 11.0333i | −0.323401 | + | 0.105079i | ||||
\(106\) | 73.7114 | − | 101.455i | 0.695391 | − | 0.957123i | ||||
\(107\) | −68.5495 | − | 94.3503i | −0.640650 | − | 0.881779i | 0.358000 | − | 0.933721i | \(-0.383459\pi\) |
−0.998650 | + | 0.0519427i | \(0.983459\pi\) | |||||||
\(108\) | 3.86944 | − | 11.9089i | 0.0358281 | − | 0.110268i | ||||
\(109\) | − | 81.2670i | − | 0.745569i | −0.927918 | − | 0.372784i | \(-0.878403\pi\) | ||
0.927918 | − | 0.372784i | \(-0.121597\pi\) | |||||||
\(110\) | −229.000 | + | 53.8281i | −2.08182 | + | 0.489346i | ||||
\(111\) | 27.7204 | 0.249733 | ||||||||
\(112\) | −46.0299 | − | 14.9560i | −0.410981 | − | 0.133536i | ||||
\(113\) | 61.8457 | − | 44.9335i | 0.547307 | − | 0.397642i | −0.279485 | − | 0.960150i | \(-0.590164\pi\) |
0.826791 | + | 0.562509i | \(0.190164\pi\) | |||||||
\(114\) | 30.0490 | + | 21.8319i | 0.263588 | + | 0.191508i | ||||
\(115\) | −109.518 | − | 337.061i | −0.952329 | − | 2.93097i | ||||
\(116\) | −56.4126 | + | 18.3296i | −0.486316 | + | 0.158014i | ||||
\(117\) | 20.7647 | − | 28.5801i | 0.177476 | − | 0.244274i | ||||
\(118\) | 29.6621 | + | 40.8264i | 0.251374 | + | 0.345986i | ||||
\(119\) | −1.53080 | + | 4.71133i | −0.0128639 | + | 0.0395910i | ||||
\(120\) | − | 58.9018i | − | 0.490848i | ||||||
\(121\) | −108.329 | + | 53.9055i | −0.895282 | + | 0.445500i | ||||
\(122\) | 301.041 | 2.46755 | ||||||||
\(123\) | −86.6741 | − | 28.1621i | −0.704668 | − | 0.228960i | ||||
\(124\) | 42.5272 | − | 30.8978i | 0.342961 | − | 0.249176i | ||||
\(125\) | 145.901 | + | 106.003i | 1.16720 | + | 0.848024i | ||||
\(126\) | 5.72786 | + | 17.6285i | 0.0454592 | + | 0.139909i | ||||
\(127\) | −20.0314 | + | 6.50861i | −0.157728 | + | 0.0512489i | −0.386817 | − | 0.922157i | \(-0.626425\pi\) |
0.229089 | + | 0.973406i | \(0.426425\pi\) | |||||||
\(128\) | 69.7411 | − | 95.9903i | 0.544852 | − | 0.749925i | ||||
\(129\) | 43.1162 | + | 59.3443i | 0.334234 | + | 0.460033i | ||||
\(130\) | −77.8193 | + | 239.503i | −0.598610 | + | 1.84233i | ||||
\(131\) | 106.847i | 0.815628i | 0.913065 | + | 0.407814i | \(0.133709\pi\) | ||||
−0.913065 | + | 0.407814i | \(0.866291\pi\) | |||||||
\(132\) | 10.5059 | + | 44.6950i | 0.0795901 | + | 0.338598i | ||||
\(133\) | −20.6707 | −0.155419 | ||||||||
\(134\) | 10.6293 | + | 3.45365i | 0.0793228 | + | 0.0257735i | ||||
\(135\) | −35.5089 | + | 25.7987i | −0.263029 | + | 0.191102i | ||||
\(136\) | −6.61148 | − | 4.80352i | −0.0486138 | − | 0.0353200i | ||||
\(137\) | 36.8295 | + | 113.349i | 0.268828 | + | 0.827368i | 0.990787 | + | 0.135432i | \(0.0432421\pi\) |
−0.721959 | + | 0.691936i | \(0.756758\pi\) | |||||||
\(138\) | −174.983 | + | 56.8553i | −1.26799 | + | 0.411995i | ||||
\(139\) | −4.36390 | + | 6.00639i | −0.0313950 | + | 0.0432115i | −0.824426 | − | 0.565970i | \(-0.808502\pi\) |
0.793031 | + | 0.609181i | \(0.208502\pi\) | |||||||
\(140\) | −29.1989 | − | 40.1888i | −0.208563 | − | 0.287063i | ||||
\(141\) | 8.66081 | − | 26.6552i | 0.0614242 | − | 0.189044i | ||||
\(142\) | − | 15.2815i | − | 0.107616i | ||||||
\(143\) | −10.7766 | + | 129.083i | −0.0753610 | + | 0.902679i | ||||
\(144\) | −59.4962 | −0.413168 | ||||||||
\(145\) | 197.738 | + | 64.2490i | 1.36371 | + | 0.443096i | ||||
\(146\) | 12.4542 | − | 9.04849i | 0.0853026 | − | 0.0619759i | ||||
\(147\) | 60.3162 | + | 43.8223i | 0.410314 | + | 0.298111i | ||||
\(148\) | 11.9180 | + | 36.6800i | 0.0805274 | + | 0.247838i | ||||
\(149\) | −134.349 | + | 43.6527i | −0.901673 | + | 0.292971i | −0.722927 | − | 0.690924i | \(-0.757204\pi\) |
−0.178746 | + | 0.983895i | \(0.557204\pi\) | |||||||
\(150\) | 119.469 | − | 164.434i | 0.796457 | − | 1.09623i | ||||
\(151\) | 37.4614 | + | 51.5612i | 0.248089 | + | 0.341465i | 0.914841 | − | 0.403815i | \(-0.132316\pi\) |
−0.666752 | + | 0.745280i | \(0.732316\pi\) | |||||||
\(152\) | 10.5376 | − | 32.4314i | 0.0693264 | − | 0.213365i | ||||
\(153\) | 6.08965i | 0.0398016i | ||||||||
\(154\) | −51.4702 | − | 44.3845i | −0.334222 | − | 0.288211i | ||||
\(155\) | −184.257 | −1.18875 | ||||||||
\(156\) | 46.7450 | + | 15.1884i | 0.299648 | + | 0.0973614i | ||||
\(157\) | −29.8448 | + | 21.6835i | −0.190094 | + | 0.138111i | −0.678762 | − | 0.734359i | \(-0.737483\pi\) |
0.488668 | + | 0.872470i | \(0.337483\pi\) | |||||||
\(158\) | −211.916 | − | 153.966i | −1.34124 | − | 0.974469i | ||||
\(159\) | 26.5116 | + | 81.5944i | 0.166740 | + | 0.513172i | ||||
\(160\) | 273.991 | − | 89.0251i | 1.71244 | − | 0.556407i | ||||
\(161\) | 60.1852 | − | 82.8378i | 0.373821 | − | 0.514521i | ||||
\(162\) | 13.3932 | + | 18.4341i | 0.0826740 | + | 0.113791i | ||||
\(163\) | −16.5744 | + | 51.0109i | −0.101684 | + | 0.312950i | −0.988938 | − | 0.148331i | \(-0.952610\pi\) |
0.887254 | + | 0.461281i | \(0.152610\pi\) | |||||||
\(164\) | − | 126.796i | − | 0.773147i | ||||||
\(165\) | 62.2932 | − | 148.390i | 0.377535 | − | 0.899335i | ||||
\(166\) | −76.3738 | −0.460083 | ||||||||
\(167\) | −125.534 | − | 40.7886i | −0.751703 | − | 0.244243i | −0.0919892 | − | 0.995760i | \(-0.529323\pi\) |
−0.659714 | + | 0.751517i | \(0.729323\pi\) | |||||||
\(168\) | 13.7675 | − | 10.0027i | 0.0819494 | − | 0.0595397i | ||||
\(169\) | −24.5408 | − | 17.8299i | −0.145212 | − | 0.105503i | ||||
\(170\) | −13.4145 | − | 41.2855i | −0.0789086 | − | 0.242856i | ||||
\(171\) | −24.1667 | + | 7.85222i | −0.141326 | + | 0.0459194i | ||||
\(172\) | −59.9878 | + | 82.5661i | −0.348766 | + | 0.480036i | ||||
\(173\) | −39.1282 | − | 53.8553i | −0.226174 | − | 0.311302i | 0.680815 | − | 0.732455i | \(-0.261626\pi\) |
−0.906990 | + | 0.421153i | \(0.861626\pi\) | |||||||
\(174\) | 33.3543 | − | 102.654i | 0.191691 | − | 0.589966i | ||||
\(175\) | 113.114i | 0.646368i | ||||||||
\(176\) | 186.545 | − | 113.099i | 1.05992 | − | 0.642608i | ||||
\(177\) | −34.5240 | −0.195051 | ||||||||
\(178\) | 145.591 | + | 47.3052i | 0.817925 | + | 0.265760i | ||||
\(179\) | −144.418 | + | 104.926i | −0.806807 | + | 0.586179i | −0.912903 | − | 0.408177i | \(-0.866165\pi\) |
0.106096 | + | 0.994356i | \(0.466165\pi\) | |||||||
\(180\) | −49.4038 | − | 35.8939i | −0.274465 | − | 0.199411i | ||||
\(181\) | −16.1042 | − | 49.5637i | −0.0889736 | − | 0.273833i | 0.896663 | − | 0.442714i | \(-0.145984\pi\) |
−0.985636 | + | 0.168882i | \(0.945984\pi\) | |||||||
\(182\) | −69.1958 | + | 22.4831i | −0.380197 | + | 0.123533i | ||||
\(183\) | −121.055 | + | 166.618i | −0.661503 | + | 0.910481i | ||||
\(184\) | 99.2874 | + | 136.657i | 0.539605 | + | 0.742703i | ||||
\(185\) | 41.7753 | − | 128.571i | 0.225812 | − | 0.694978i | ||||
\(186\) | 95.6553i | 0.514276i | ||||||||
\(187\) | −11.5761 | − | 19.0936i | −0.0619042 | − | 0.102105i | ||||
\(188\) | 38.9941 | 0.207415 | ||||||||
\(189\) | −12.0602 | − | 3.91859i | −0.0638105 | − | 0.0207333i | ||||
\(190\) | 146.544 | − | 106.470i | 0.771282 | − | 0.560370i | ||||
\(191\) | 289.898 | + | 210.623i | 1.51779 | + | 1.10274i | 0.962569 | + | 0.271035i | \(0.0873660\pi\) |
0.555220 | + | 0.831703i | \(0.312634\pi\) | |||||||
\(192\) | −3.75755 | − | 11.5645i | −0.0195706 | − | 0.0602320i | ||||
\(193\) | 203.430 | − | 66.0985i | 1.05404 | − | 0.342479i | 0.269789 | − | 0.962920i | \(-0.413046\pi\) |
0.784254 | + | 0.620440i | \(0.213046\pi\) | |||||||
\(194\) | −54.5984 | + | 75.1482i | −0.281435 | + | 0.387362i | ||||
\(195\) | −101.266 | − | 139.380i | −0.519311 | − | 0.714770i | ||||
\(196\) | −32.0540 | + | 98.6520i | −0.163541 | + | 0.503326i | ||||
\(197\) | − | 276.568i | − | 1.40390i | −0.712227 | − | 0.701949i | \(-0.752313\pi\) | ||
0.712227 | − | 0.701949i | \(-0.247687\pi\) | |||||||
\(198\) | −77.0356 | − | 32.3390i | −0.389068 | − | 0.163328i | ||||
\(199\) | 78.8085 | 0.396022 | 0.198011 | − | 0.980200i | \(-0.436552\pi\) | ||||
0.198011 | + | 0.980200i | \(0.436552\pi\) | |||||||
\(200\) | −177.471 | − | 57.6640i | −0.887357 | − | 0.288320i | ||||
\(201\) | −6.18574 | + | 4.49421i | −0.0307748 | + | 0.0223592i | ||||
\(202\) | −290.346 | − | 210.948i | −1.43735 | − | 1.04430i | ||||
\(203\) | 18.5624 | + | 57.1293i | 0.0914405 | + | 0.281425i | ||||
\(204\) | −8.05789 | + | 2.61817i | −0.0394995 | + | 0.0128342i | ||||
\(205\) | −261.239 | + | 359.565i | −1.27434 | + | 1.75398i | ||||
\(206\) | 58.0688 | + | 79.9249i | 0.281888 | + | 0.387985i | ||||
\(207\) | 38.8963 | − | 119.711i | 0.187905 | − | 0.578312i | ||||
\(208\) | − | 233.535i | − | 1.12277i | ||||||
\(209\) | 60.8459 | − | 70.5595i | 0.291129 | − | 0.337605i | ||||
\(210\) | 90.3955 | 0.430455 | ||||||||
\(211\) | −208.249 | − | 67.6643i | −0.986964 | − | 0.320684i | −0.229319 | − | 0.973351i | \(-0.573650\pi\) |
−0.757645 | + | 0.652667i | \(0.773650\pi\) | |||||||
\(212\) | −96.5683 | + | 70.1610i | −0.455511 | + | 0.330948i | ||||
\(213\) | 8.45787 | + | 6.14500i | 0.0397083 | + | 0.0288498i | ||||
\(214\) | 91.2412 | + | 280.811i | 0.426361 | + | 1.31220i | ||||
\(215\) | 340.224 | − | 110.545i | 1.58244 | − | 0.514165i | ||||
\(216\) | 12.2962 | − | 16.9243i | 0.0569269 | − | 0.0783531i | ||||
\(217\) | −31.2903 | − | 43.0675i | −0.144195 | − | 0.198468i | ||||
\(218\) | −63.5798 | + | 195.679i | −0.291650 | + | 0.897608i | ||||
\(219\) | 10.5316i | 0.0480896i | ||||||||
\(220\) | 223.134 | + | 18.6286i | 1.01425 | + | 0.0846753i | ||||
\(221\) | −23.9032 | −0.108159 | ||||||||
\(222\) | −66.7465 | − | 21.6873i | −0.300660 | − | 0.0976904i | ||||
\(223\) | 169.528 | − | 123.169i | 0.760216 | − | 0.552329i | −0.138761 | − | 0.990326i | \(-0.544312\pi\) |
0.898977 | + | 0.437997i | \(0.144312\pi\) | |||||||
\(224\) | 67.3374 | + | 48.9235i | 0.300613 | + | 0.218408i | ||||
\(225\) | 42.9690 | + | 132.245i | 0.190973 | + | 0.587755i | ||||
\(226\) | −184.069 | + | 59.8076i | −0.814465 | + | 0.264636i | ||||
\(227\) | −48.9868 | + | 67.4246i | −0.215801 | + | 0.297025i | −0.903169 | − | 0.429284i | \(-0.858766\pi\) |
0.687368 | + | 0.726309i | \(0.258766\pi\) | |||||||
\(228\) | −20.7803 | − | 28.6016i | −0.0911417 | − | 0.125446i | ||||
\(229\) | 102.180 | − | 314.478i | 0.446201 | − | 1.37327i | −0.434959 | − | 0.900450i | \(-0.643237\pi\) |
0.881161 | − | 0.472817i | \(-0.156763\pi\) | |||||||
\(230\) | 897.274i | 3.90119i | ||||||||
\(231\) | 45.2628 | − | 10.6394i | 0.195943 | − | 0.0460578i | ||||
\(232\) | −99.0962 | −0.427139 | ||||||||
\(233\) | −157.314 | − | 51.1146i | −0.675169 | − | 0.219376i | −0.0486901 | − | 0.998814i | \(-0.515505\pi\) |
−0.626479 | + | 0.779438i | \(0.715505\pi\) | |||||||
\(234\) | −72.3580 | + | 52.5712i | −0.309222 | + | 0.224663i | ||||
\(235\) | −110.578 | − | 80.3400i | −0.470547 | − | 0.341872i | ||||
\(236\) | −14.8432 | − | 45.6826i | −0.0628948 | − | 0.193570i | ||||
\(237\) | 170.432 | − | 55.3766i | 0.719121 | − | 0.233657i | ||||
\(238\) | 7.37188 | − | 10.1465i | 0.0309743 | − | 0.0426324i | ||||
\(239\) | −105.769 | − | 145.579i | −0.442550 | − | 0.609117i | 0.528227 | − | 0.849103i | \(-0.322857\pi\) |
−0.970776 | + | 0.239986i | \(0.922857\pi\) | |||||||
\(240\) | −89.6620 | + | 275.951i | −0.373591 | + | 1.14980i | ||||
\(241\) | 226.632i | 0.940380i | 0.882565 | + | 0.470190i | \(0.155815\pi\) | ||||
−0.882565 | + | 0.470190i | \(0.844185\pi\) | |||||||
\(242\) | 303.013 | − | 45.0442i | 1.25212 | − | 0.186133i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | −272.517 | − | 88.5461i | −1.11687 | − | 0.362894i | ||||
\(245\) | 294.151 | − | 213.714i | 1.20062 | − | 0.872300i | ||||
\(246\) | 186.665 | + | 135.620i | 0.758802 | + | 0.551302i | ||||
\(247\) | −30.8217 | − | 94.8594i | −0.124784 | − | 0.384046i | ||||
\(248\) | 83.5223 | − | 27.1380i | 0.336783 | − | 0.109428i | ||||
\(249\) | 30.7115 | − | 42.2707i | 0.123339 | − | 0.169762i | ||||
\(250\) | −268.374 | − | 369.385i | −1.07350 | − | 1.47754i | ||||
\(251\) | −24.4520 | + | 75.2554i | −0.0974181 | + | 0.299822i | −0.987876 | − | 0.155243i | \(-0.950384\pi\) |
0.890458 | + | 0.455065i | \(0.150384\pi\) | |||||||
\(252\) | − | 17.6429i | − | 0.0700117i | ||||||
\(253\) | 105.607 | + | 449.283i | 0.417420 | + | 1.77582i | ||||
\(254\) | 53.3247 | 0.209940 | ||||||||
\(255\) | 28.2446 | + | 9.17722i | 0.110763 | + | 0.0359891i | ||||
\(256\) | −265.743 | + | 193.074i | −1.03806 | + | 0.754194i | ||||
\(257\) | −241.518 | − | 175.473i | −0.939758 | − | 0.682774i | 0.00860422 | − | 0.999963i | \(-0.497261\pi\) |
−0.948362 | + | 0.317189i | \(0.897261\pi\) | |||||||
\(258\) | −57.3887 | − | 176.624i | −0.222437 | − | 0.684590i | ||||
\(259\) | 37.1460 | − | 12.0695i | 0.143421 | − | 0.0466002i | ||||
\(260\) | 140.891 | − | 193.920i | 0.541890 | − | 0.745848i | ||||
\(261\) | 43.4037 | + | 59.7400i | 0.166298 | + | 0.228889i | ||||
\(262\) | 83.5928 | − | 257.272i | 0.319056 | − | 0.981955i | ||||
\(263\) | − | 60.3285i | − | 0.229386i | −0.993401 | − | 0.114693i | \(-0.963412\pi\) | ||
0.993401 | − | 0.114693i | \(-0.0365884\pi\) | |||||||
\(264\) | −6.38159 | + | 76.4391i | −0.0241727 | + | 0.289542i | ||||
\(265\) | 418.399 | 1.57887 | ||||||||
\(266\) | 49.7719 | + | 16.1719i | 0.187112 | + | 0.0607965i | ||||
\(267\) | −84.7271 | + | 61.5579i | −0.317330 | + | 0.230554i | ||||
\(268\) | −8.60627 | − | 6.25282i | −0.0321130 | − | 0.0233314i | ||||
\(269\) | −60.5588 | − | 186.381i | −0.225126 | − | 0.692866i | −0.998279 | − | 0.0586463i | \(-0.981322\pi\) |
0.773153 | − | 0.634219i | \(-0.218678\pi\) | |||||||
\(270\) | 105.684 | − | 34.3388i | 0.391422 | − | 0.127181i | ||||
\(271\) | 200.141 | − | 275.470i | 0.738527 | − | 1.01650i | −0.260175 | − | 0.965561i | \(-0.583780\pi\) |
0.998702 | − | 0.0509339i | \(-0.0162198\pi\) | |||||||
\(272\) | 23.6623 | + | 32.5684i | 0.0869938 | + | 0.119737i | ||||
\(273\) | 15.3813 | − | 47.3389i | 0.0563419 | − | 0.173402i | ||||
\(274\) | − | 301.742i | − | 1.10125i | ||||||
\(275\) | −386.116 | − | 332.961i | −1.40406 | − | 1.21077i | ||||
\(276\) | 175.125 | 0.634513 | ||||||||
\(277\) | −333.579 | − | 108.386i | −1.20426 | − | 0.391287i | −0.362932 | − | 0.931816i | \(-0.618224\pi\) |
−0.841326 | + | 0.540529i | \(0.818224\pi\) | |||||||
\(278\) | 15.2067 | − | 11.0483i | 0.0547005 | − | 0.0397423i | ||||
\(279\) | −52.9425 | − | 38.4650i | −0.189758 | − | 0.137867i | ||||
\(280\) | −25.6458 | − | 78.9297i | −0.0915922 | − | 0.281892i | ||||
\(281\) | −388.450 | + | 126.215i | −1.38238 | + | 0.449164i | −0.903452 | − | 0.428689i | \(-0.858976\pi\) |
−0.478931 | + | 0.877853i | \(0.658976\pi\) | |||||||
\(282\) | −41.7078 | + | 57.4059i | −0.147900 | + | 0.203567i | ||||
\(283\) | 188.772 | + | 259.822i | 0.667039 | + | 0.918100i | 0.999689 | − | 0.0249503i | \(-0.00794275\pi\) |
−0.332650 | + | 0.943050i | \(0.607943\pi\) | |||||||
\(284\) | −4.49478 | + | 13.8335i | −0.0158267 | + | 0.0487096i | ||||
\(285\) | 123.922i | 0.434813i | ||||||||
\(286\) | 126.938 | − | 302.381i | 0.443838 | − | 1.05728i | ||||
\(287\) | −128.407 | −0.447411 | ||||||||
\(288\) | 97.3106 | + | 31.6181i | 0.337884 | + | 0.109785i | ||||
\(289\) | −230.472 | + | 167.448i | −0.797482 | + | 0.579405i | ||||
\(290\) | −425.858 | − | 309.404i | −1.46847 | − | 1.06691i | ||||
\(291\) | −19.6373 | − | 60.4373i | −0.0674820 | − | 0.207688i | ||||
\(292\) | −13.9356 | + | 4.52794i | −0.0477245 | + | 0.0155066i | ||||
\(293\) | −221.635 | + | 305.055i | −0.756435 | + | 1.04114i | 0.241067 | + | 0.970508i | \(0.422503\pi\) |
−0.997502 | + | 0.0706350i | \(0.977497\pi\) | |||||||
\(294\) | −110.948 | − | 152.706i | −0.377373 | − | 0.519409i | ||||
\(295\) | −52.0284 | + | 160.127i | −0.176367 | + | 0.542803i | ||||
\(296\) | 64.4332i | 0.217680i | ||||||||
\(297\) | 48.8763 | − | 29.6328i | 0.164567 | − | 0.0997738i | ||||
\(298\) | 357.645 | 1.20015 | ||||||||
\(299\) | 469.890 | + | 152.677i | 1.57154 | + | 0.510624i | ||||
\(300\) | −156.514 | + | 113.714i | −0.521714 | + | 0.379047i | ||||
\(301\) | 83.6150 | + | 60.7499i | 0.277791 | + | 0.201827i | ||||
\(302\) | −49.8621 | − | 153.460i | −0.165106 | − | 0.508144i | ||||
\(303\) | 233.508 | − | 75.8714i | 0.770654 | − | 0.250401i | ||||
\(304\) | −98.7360 | + | 135.898i | −0.324789 | + | 0.447034i | ||||
\(305\) | 590.364 | + | 812.566i | 1.93562 | + | 2.66415i | ||||
\(306\) | 4.76428 | − | 14.6629i | 0.0155695 | − | 0.0479181i | ||||
\(307\) | 505.973i | 1.64812i | 0.566502 | + | 0.824060i | \(0.308296\pi\) | ||||
−0.566502 | + | 0.824060i | \(0.691704\pi\) | |||||||
\(308\) | 33.5383 | + | 55.3180i | 0.108891 | + | 0.179604i | ||||
\(309\) | −67.5869 | −0.218728 | ||||||||
\(310\) | 443.662 | + | 144.154i | 1.43117 | + | 0.465014i | ||||
\(311\) | 134.356 | − | 97.6152i | 0.432012 | − | 0.313875i | −0.350441 | − | 0.936585i | \(-0.613968\pi\) |
0.782453 | + | 0.622710i | \(0.213968\pi\) | |||||||
\(312\) | 66.4314 | + | 48.2653i | 0.212921 | + | 0.154696i | ||||
\(313\) | 28.9379 | + | 89.0616i | 0.0924533 | + | 0.284542i | 0.986582 | − | 0.163269i | \(-0.0522038\pi\) |
−0.894128 | + | 0.447811i | \(0.852204\pi\) | |||||||
\(314\) | 88.8259 | − | 28.8613i | 0.282885 | − | 0.0919149i | ||||
\(315\) | −36.3499 | + | 50.0314i | −0.115397 | + | 0.158830i | ||||
\(316\) | 146.550 | + | 201.709i | 0.463766 | + | 0.638319i | ||||
\(317\) | 46.2133 | − | 142.230i | 0.145783 | − | 0.448675i | −0.851328 | − | 0.524634i | \(-0.824202\pi\) |
0.997111 | + | 0.0759598i | \(0.0242021\pi\) | |||||||
\(318\) | − | 217.208i | − | 0.683045i | ||||||
\(319\) | −249.651 | − | 104.802i | −0.782606 | − | 0.328532i | ||||
\(320\) | −59.3006 | −0.185314 | ||||||||
\(321\) | −192.111 | − | 62.4207i | −0.598477 | − | 0.194457i | ||||
\(322\) | −209.726 | + | 152.375i | −0.651322 | + | 0.473213i | ||||
\(323\) | 13.9097 | + | 10.1060i | 0.0430641 | + | 0.0312879i | ||||
\(324\) | −6.70206 | − | 20.6268i | −0.0206854 | − | 0.0636631i | ||||
\(325\) | −519.090 | + | 168.663i | −1.59720 | + | 0.518962i | ||||
\(326\) | 79.8175 | − | 109.859i | 0.244839 | − | 0.336992i | ||||
\(327\) | −82.7358 | − | 113.876i | −0.253015 | − | 0.348245i | ||||
\(328\) | 65.4599 | − | 201.465i | 0.199573 | − | 0.614222i | ||||
\(329\) | − | 39.4895i | − | 0.120029i | ||||||
\(330\) | −266.087 | + | 308.566i | −0.806324 | + | 0.935048i | ||||
\(331\) | −271.711 | −0.820880 | −0.410440 | − | 0.911888i | \(-0.634625\pi\) | ||||
−0.410440 | + | 0.911888i | \(0.634625\pi\) | |||||||
\(332\) | 69.1371 | + | 22.4640i | 0.208244 | + | 0.0676627i | ||||
\(333\) | 38.8435 | − | 28.2214i | 0.116647 | − | 0.0847491i | ||||
\(334\) | 270.357 | + | 196.426i | 0.809451 | + | 0.588100i | ||||
\(335\) | 11.5227 | + | 35.4632i | 0.0343961 | + | 0.105860i | ||||
\(336\) | −79.7261 | + | 25.9046i | −0.237280 | + | 0.0770970i | ||||
\(337\) | 294.136 | − | 404.843i | 0.872807 | − | 1.20132i | −0.105555 | − | 0.994413i | \(-0.533662\pi\) |
0.978362 | − | 0.206902i | \(-0.0663380\pi\) | |||||||
\(338\) | 45.1411 | + | 62.1314i | 0.133554 | + | 0.183821i | ||||
\(339\) | 40.9161 | − | 125.927i | 0.120697 | − | 0.371466i | ||||
\(340\) | 41.3192i | 0.121527i | ||||||||
\(341\) | 239.117 | + | 19.9629i | 0.701222 | + | 0.0585422i | ||||
\(342\) | 64.3329 | 0.188108 | ||||||||
\(343\) | 213.633 | + | 69.4137i | 0.622838 | + | 0.202372i | ||||
\(344\) | −137.940 | + | 100.219i | −0.400987 | + | 0.291334i | ||||
\(345\) | −496.616 | − | 360.813i | −1.43947 | − | 1.04583i | ||||
\(346\) | 52.0806 | + | 160.288i | 0.150522 | + | 0.463259i | ||||
\(347\) | −230.849 | + | 75.0075i | −0.665272 | + | 0.216160i | −0.622136 | − | 0.782909i | \(-0.713735\pi\) |
−0.0431362 | + | 0.999069i | \(0.513735\pi\) | |||||||
\(348\) | −60.3878 | + | 83.1167i | −0.173528 | + | 0.238841i | ||||
\(349\) | −262.931 | − | 361.893i | −0.753383 | − | 1.03694i | −0.997736 | − | 0.0672560i | \(-0.978576\pi\) |
0.244353 | − | 0.969686i | \(-0.421424\pi\) | |||||||
\(350\) | 88.4958 | − | 272.362i | 0.252845 | − | 0.778178i | ||||
\(351\) | − | 61.1881i | − | 0.174325i | ||||||
\(352\) | −365.214 | + | 85.8462i | −1.03754 | + | 0.243881i | ||||
\(353\) | −226.910 | −0.642805 | −0.321403 | − | 0.946943i | \(-0.604154\pi\) | ||||
−0.321403 | + | 0.946943i | \(0.604154\pi\) | |||||||
\(354\) | 83.1286 | + | 27.0101i | 0.234826 | + | 0.0762997i | ||||
\(355\) | 41.2475 | − | 29.9681i | 0.116190 | − | 0.0844171i | ||||
\(356\) | −117.881 | − | 85.6459i | −0.331128 | − | 0.240578i | ||||
\(357\) | 2.65143 | + | 8.16026i | 0.00742697 | + | 0.0228579i | ||||
\(358\) | 429.827 | − | 139.659i | 1.20063 | − | 0.390110i | ||||
\(359\) | 377.742 | − | 519.917i | 1.05221 | − | 1.44824i | 0.165324 | − | 0.986239i | \(-0.447133\pi\) |
0.886881 | − | 0.461997i | \(-0.152867\pi\) | |||||||
\(360\) | −59.9664 | − | 82.5367i | −0.166573 | − | 0.229269i | ||||
\(361\) | 89.3854 | − | 275.100i | 0.247605 | − | 0.762050i | ||||
\(362\) | 131.941i | 0.364478i | ||||||||
\(363\) | −96.9173 | + | 185.823i | −0.266990 | + | 0.511908i | ||||
\(364\) | 69.2524 | 0.190254 | ||||||||
\(365\) | 48.8471 | + | 15.8714i | 0.133828 | + | 0.0434832i | ||||
\(366\) | 421.837 | − | 306.482i | 1.15256 | − | 0.837384i | ||||
\(367\) | 580.779 | + | 421.960i | 1.58250 | + | 1.14976i | 0.913755 | + | 0.406267i | \(0.133170\pi\) |
0.668748 | + | 0.743489i | \(0.266830\pi\) | |||||||
\(368\) | −257.131 | − | 791.369i | −0.698726 | − | 2.15046i | ||||
\(369\) | −150.124 | + | 48.7782i | −0.406840 | + | 0.132190i | ||||
\(370\) | −201.177 | + | 276.896i | −0.543721 | + | 0.748368i | ||||
\(371\) | 71.0523 | + | 97.7951i | 0.191516 | + | 0.263599i | ||||
\(372\) | 28.1353 | − | 86.5917i | 0.0756326 | − | 0.232773i | ||||
\(373\) | 18.1857i | 0.0487552i | 0.999703 | + | 0.0243776i | \(0.00776040\pi\) | ||||
−0.999703 | + | 0.0243776i | \(0.992240\pi\) | |||||||
\(374\) | 12.9355 | + | 55.0311i | 0.0345868 | + | 0.147142i | ||||
\(375\) | 312.363 | 0.832969 | ||||||||
\(376\) | 61.9572 | + | 20.1311i | 0.164780 | + | 0.0535402i | ||||
\(377\) | −234.492 | + | 170.369i | −0.621996 | + | 0.451906i | ||||
\(378\) | 25.9734 | + | 18.8708i | 0.0687126 | + | 0.0499226i | ||||
\(379\) | −48.1193 | − | 148.096i | −0.126964 | − | 0.390755i | 0.867290 | − | 0.497803i | \(-0.165860\pi\) |
−0.994254 | + | 0.107049i | \(0.965860\pi\) | |||||||
\(380\) | −163.975 | + | 53.2786i | −0.431512 | + | 0.140207i | ||||
\(381\) | −21.4430 | + | 29.5137i | −0.0562808 | + | 0.0774638i | ||||
\(382\) | −533.247 | − | 733.952i | −1.39594 | − | 1.92134i | ||||
\(383\) | −222.614 | + | 685.137i | −0.581239 | + | 1.78887i | 0.0326387 | + | 0.999467i | \(0.489609\pi\) |
−0.613877 | + | 0.789401i | \(0.710391\pi\) | |||||||
\(384\) | − | 205.509i | − | 0.535179i | ||||||
\(385\) | 18.8652 | − | 225.969i | 0.0490005 | − | 0.586931i | ||||
\(386\) | −541.542 | −1.40296 | ||||||||
\(387\) | 120.834 | + | 39.2613i | 0.312232 | + | 0.101450i | ||||
\(388\) | 71.5286 | − | 51.9685i | 0.184352 | − | 0.133940i | ||||
\(389\) | −7.19093 | − | 5.22452i | −0.0184857 | − | 0.0134306i | 0.578504 | − | 0.815680i | \(-0.303637\pi\) |
−0.596990 | + | 0.802249i | \(0.703637\pi\) | |||||||
\(390\) | 134.787 | + | 414.832i | 0.345608 | + | 1.06367i | ||||
\(391\) | −80.9995 | + | 26.3183i | −0.207160 | + | 0.0673103i | ||||
\(392\) | −101.860 | + | 140.199i | −0.259848 | + | 0.357650i | ||||
\(393\) | 108.778 | + | 149.721i | 0.276790 | + | 0.380969i | ||||
\(394\) | −216.375 | + | 665.933i | −0.549175 | + | 1.69019i | ||||
\(395\) | − | 873.939i | − | 2.21250i | ||||||
\(396\) | 60.2243 | + | 51.9335i | 0.152082 | + | 0.131145i | ||||
\(397\) | 513.254 | 1.29283 | 0.646416 | − | 0.762985i | \(-0.276267\pi\) | ||||
0.646416 | + | 0.762985i | \(0.276267\pi\) | |||||||
\(398\) | −189.759 | − | 61.6564i | −0.476781 | − | 0.154915i | ||||
\(399\) | −28.9650 | + | 21.0443i | −0.0725940 | + | 0.0527426i | ||||
\(400\) | 743.664 | + | 540.304i | 1.85916 | + | 1.35076i | ||||
\(401\) | 169.595 | + | 521.961i | 0.422931 | + | 1.30165i | 0.904961 | + | 0.425494i | \(0.139900\pi\) |
−0.482030 | + | 0.876155i | \(0.660100\pi\) | |||||||
\(402\) | 18.4104 | − | 5.98190i | 0.0457970 | − | 0.0148804i | ||||
\(403\) | 150.983 | − | 207.811i | 0.374648 | − | 0.515659i | ||||
\(404\) | 200.788 | + | 276.361i | 0.496999 | + | 0.684061i | ||||
\(405\) | −23.4921 | + | 72.3014i | −0.0580053 | + | 0.178522i | ||||
\(406\) | − | 152.081i | − | 0.374584i | ||||||
\(407\) | −68.1431 | + | 162.325i | −0.167428 | + | 0.398834i | ||||
\(408\) | −14.1547 | −0.0346930 | ||||||||
\(409\) | −481.308 | − | 156.386i | −1.17679 | − | 0.382363i | −0.345618 | − | 0.938375i | \(-0.612331\pi\) |
−0.831174 | + | 0.556013i | \(0.812331\pi\) | |||||||
\(410\) | 910.333 | − | 661.396i | 2.22032 | − | 1.61316i | ||||
\(411\) | 167.006 | + | 121.337i | 0.406340 | + | 0.295223i | ||||
\(412\) | −29.0581 | − | 89.4317i | −0.0705294 | − | 0.217067i | ||||
\(413\) | −46.2629 | + | 15.0317i | −0.112017 | + | 0.0363964i | ||||
\(414\) | −187.313 | + | 257.814i | −0.452447 | + | 0.622739i | ||||
\(415\) | −149.774 | − | 206.147i | −0.360902 | − | 0.496739i | ||||
\(416\) | −124.108 | + | 381.965i | −0.298337 | + | 0.918185i | ||||
\(417\) | 12.8593i | 0.0308376i | ||||||||
\(418\) | −201.711 | + | 122.293i | −0.482561 | + | 0.292568i | ||||
\(419\) | −111.580 | −0.266300 | −0.133150 | − | 0.991096i | \(-0.542509\pi\) | ||||
−0.133150 | + | 0.991096i | \(0.542509\pi\) | |||||||
\(420\) | −81.8303 | − | 26.5883i | −0.194834 | − | 0.0633054i | ||||
\(421\) | −302.005 | + | 219.420i | −0.717352 | + | 0.521187i | −0.885537 | − | 0.464569i | \(-0.846209\pi\) |
0.168185 | + | 0.985755i | \(0.446209\pi\) | |||||||
\(422\) | 448.495 | + | 325.851i | 1.06278 | + | 0.772158i | ||||
\(423\) | −15.0010 | − | 46.1682i | −0.0354633 | − | 0.109145i | ||||
\(424\) | −189.658 | + | 61.6235i | −0.447306 | + | 0.145338i | ||||
\(425\) | 55.3020 | − | 76.1167i | 0.130122 | − | 0.179098i | ||||
\(426\) | −15.5577 | − | 21.4133i | −0.0365204 | − | 0.0502660i | ||||
\(427\) | −89.6710 | + | 275.979i | −0.210002 | + | 0.646321i | ||||
\(428\) | − | 281.041i | − | 0.656637i | ||||||
\(429\) | 116.315 | + | 191.850i | 0.271131 | + | 0.447203i | ||||
\(430\) | −905.693 | −2.10626 | ||||||||
\(431\) | −74.2514 | − | 24.1257i | −0.172277 | − | 0.0559762i | 0.221608 | − | 0.975136i | \(-0.428869\pi\) |
−0.393885 | + | 0.919160i | \(0.628869\pi\) | |||||||
\(432\) | −83.3695 | + | 60.5715i | −0.192985 | + | 0.140212i | ||||
\(433\) | −575.600 | − | 418.198i | −1.32933 | − | 0.965816i | −0.999765 | − | 0.0216834i | \(-0.993097\pi\) |
−0.329567 | − | 0.944132i | \(-0.606903\pi\) | |||||||
\(434\) | 41.6482 | + | 128.180i | 0.0959637 | + | 0.295346i | ||||
\(435\) | 342.492 | − | 111.283i | 0.787339 | − | 0.255822i | ||||
\(436\) | 115.111 | − | 158.437i | 0.264016 | − | 0.363387i | ||||
\(437\) | −208.888 | − | 287.509i | −0.478004 | − | 0.657916i | ||||
\(438\) | 8.23949 | − | 25.3585i | 0.0188116 | − | 0.0578962i | ||||
\(439\) | − | 262.674i | − | 0.598347i | −0.954199 | − | 0.299173i | \(-0.903289\pi\) | ||
0.954199 | − | 0.299173i | \(-0.0967109\pi\) | |||||||
\(440\) | 344.918 | + | 144.794i | 0.783904 | + | 0.329077i | ||||
\(441\) | 129.133 | 0.292818 | ||||||||
\(442\) | 57.5552 | + | 18.7008i | 0.130215 | + | 0.0423096i | ||||
\(443\) | 427.731 | − | 310.765i | 0.965533 | − | 0.701501i | 0.0111036 | − | 0.999938i | \(-0.496466\pi\) |
0.954429 | + | 0.298438i | \(0.0964655\pi\) | |||||||
\(444\) | 54.0432 | + | 39.2647i | 0.121719 | + | 0.0884340i | ||||
\(445\) | 157.828 | + | 485.745i | 0.354670 | + | 1.09156i | ||||
\(446\) | −504.560 | + | 163.942i | −1.13130 | + | 0.367582i | ||||
\(447\) | −143.816 | + | 197.946i | −0.321737 | + | 0.442833i | ||||
\(448\) | −10.0704 | − | 13.8607i | −0.0224786 | − | 0.0309391i | ||||
\(449\) | −88.9372 | + | 273.721i | −0.198078 | + | 0.609623i | 0.801848 | + | 0.597528i | \(0.203850\pi\) |
−0.999927 | + | 0.0120953i | \(0.996150\pi\) | |||||||
\(450\) | − | 352.043i | − | 0.782318i | ||||||
\(451\) | 377.976 | − | 438.318i | 0.838085 | − | 0.971880i | ||||
\(452\) | 184.219 | 0.407565 | ||||||||
\(453\) | 104.986 | + | 34.1121i | 0.231758 | + | 0.0753026i | ||||
\(454\) | 170.703 | − | 124.023i | 0.375998 | − | 0.273178i | ||||
\(455\) | −196.384 | − | 142.681i | −0.431613 | − | 0.313585i | ||||
\(456\) | −18.2517 | − | 56.1729i | −0.0400256 | − | 0.123186i | ||||
\(457\) | 786.473 | − | 255.540i | 1.72095 | − | 0.559169i | 0.728853 | − | 0.684670i | \(-0.240054\pi\) |
0.992094 | + | 0.125501i | \(0.0400537\pi\) | |||||||
\(458\) | −492.068 | + | 677.274i | −1.07439 | + | 1.47876i | ||||
\(459\) | 6.19971 | + | 8.53317i | 0.0135070 | + | 0.0185908i | ||||
\(460\) | 263.918 | − | 812.255i | 0.573734 | − | 1.76577i | ||||
\(461\) | 325.354i | 0.705756i | 0.935669 | + | 0.352878i | \(0.114797\pi\) | ||||
−0.935669 | + | 0.352878i | \(0.885203\pi\) | |||||||
\(462\) | −117.310 | − | 9.79371i | −0.253917 | − | 0.0211985i | ||||
\(463\) | −711.656 | −1.53705 | −0.768527 | − | 0.639818i | \(-0.779010\pi\) | ||||
−0.768527 | + | 0.639818i | \(0.779010\pi\) | |||||||
\(464\) | 464.259 | + | 150.847i | 1.00056 | + | 0.325101i | ||||
\(465\) | −258.191 | + | 187.587i | −0.555250 | + | 0.403413i | ||||
\(466\) | 338.799 | + | 246.152i | 0.727037 | + | 0.528224i | ||||
\(467\) | 141.566 | + | 435.697i | 0.303140 | + | 0.932970i | 0.980365 | + | 0.197193i | \(0.0631826\pi\) |
−0.677225 | + | 0.735776i | \(0.736817\pi\) | |||||||
\(468\) | 80.9648 | − | 26.3070i | 0.173002 | − | 0.0562116i | ||||
\(469\) | −6.33226 | + | 8.71560i | −0.0135016 | + | 0.0185834i | ||||
\(470\) | 203.402 | + | 279.958i | 0.432769 | + | 0.595656i | ||||
\(471\) | −19.7448 | + | 60.7683i | −0.0419211 | + | 0.129020i | ||||
\(472\) | − | 80.2474i | − | 0.170016i | ||||||
\(473\) | −453.498 | + | 106.598i | −0.958769 | + | 0.225366i | ||||
\(474\) | −453.698 | −0.957169 | ||||||||
\(475\) | 373.377 | + | 121.317i | 0.786056 | + | 0.255405i | ||||
\(476\) | −9.65780 | + | 7.01680i | −0.0202895 | + | 0.0147412i | ||||
\(477\) | 120.219 | + | 87.3440i | 0.252031 | + | 0.183111i | ||||
\(478\) | 140.782 | + | 433.282i | 0.294523 | + | 0.906447i | ||||
\(479\) | 563.437 | − | 183.072i | 1.17628 | − | 0.382196i | 0.345295 | − | 0.938494i | \(-0.387779\pi\) |
0.830983 | + | 0.556298i | \(0.187779\pi\) | |||||||
\(480\) | 293.298 | − | 403.690i | 0.611038 | − | 0.841022i | ||||
\(481\) | 110.775 | + | 152.469i | 0.230302 | + | 0.316983i | ||||
\(482\) | 177.307 | − | 545.694i | 0.367857 | − | 1.13215i | ||||
\(483\) | − | 177.350i | − | 0.367185i | ||||||
\(484\) | −287.551 | − | 48.3500i | −0.594114 | − | 0.0998966i | ||||
\(485\) | −309.910 | −0.638990 | ||||||||
\(486\) | 37.5346 | + | 12.1957i | 0.0772318 | + | 0.0250941i | ||||
\(487\) | −354.198 | + | 257.340i | −0.727307 | + | 0.528419i | −0.888710 | − | 0.458469i | \(-0.848398\pi\) |
0.161403 | + | 0.986889i | \(0.448398\pi\) | |||||||
\(488\) | −387.286 | − | 281.380i | −0.793619 | − | 0.576598i | ||||
\(489\) | 28.7078 | + | 88.3535i | 0.0587071 | + | 0.180682i | ||||
\(490\) | −875.472 | + | 284.458i | −1.78668 | + | 0.580527i | ||||
\(491\) | 455.377 | − | 626.773i | 0.927449 | − | 1.27652i | −0.0333976 | − | 0.999442i | \(-0.510633\pi\) |
0.960846 | − | 0.277082i | \(-0.0893672\pi\) | |||||||
\(492\) | −129.088 | − | 177.674i | −0.262374 | − | 0.361126i | ||||
\(493\) | 15.4397 | − | 47.5186i | 0.0313179 | − | 0.0963866i | ||||
\(494\) | 252.521i | 0.511175i | ||||||||
\(495\) | −63.7834 | − | 271.352i | −0.128855 | − | 0.548186i | ||||
\(496\) | −432.607 | −0.872191 | ||||||||
\(497\) | 14.0093 | + | 4.55188i | 0.0281876 | + | 0.00915872i | ||||
\(498\) | −107.019 | + | 77.7541i | −0.214898 | + | 0.156133i | ||||
\(499\) | −212.052 | − | 154.065i | −0.424953 | − | 0.308747i | 0.354674 | − | 0.934990i | \(-0.384592\pi\) |
−0.779628 | + | 0.626243i | \(0.784592\pi\) | |||||||
\(500\) | 134.297 | + | 413.323i | 0.268593 | + | 0.826646i | ||||
\(501\) | −217.432 | + | 70.6479i | −0.433996 | + | 0.141014i | ||||
\(502\) | 117.753 | − | 162.073i | 0.234568 | − | 0.322855i | ||||
\(503\) | −90.2264 | − | 124.186i | −0.179377 | − | 0.246891i | 0.709855 | − | 0.704348i | \(-0.248760\pi\) |
−0.889232 | + | 0.457457i | \(0.848760\pi\) | |||||||
\(504\) | 9.10836 | − | 28.0326i | 0.0180721 | − | 0.0556203i | ||||
\(505\) | − | 1197.38i | − | 2.37105i | ||||||
\(506\) | 97.2133 | − | 1164.43i | 0.192121 | − | 2.30124i | ||||
\(507\) | −52.5402 | −0.103630 | ||||||||
\(508\) | −48.2720 | − | 15.6845i | −0.0950237 | − | 0.0308751i | ||||
\(509\) | 633.283 | − | 460.107i | 1.24417 | − | 0.903943i | 0.246302 | − | 0.969193i | \(-0.420785\pi\) |
0.997869 | + | 0.0652505i | \(0.0207846\pi\) | |||||||
\(510\) | −60.8288 | − | 44.1947i | −0.119272 | − | 0.0866563i | ||||
\(511\) | 4.58546 | + | 14.1126i | 0.00897350 | + | 0.0276176i | ||||
\(512\) | 339.548 | − | 110.326i | 0.663180 | − | 0.215480i | ||||
\(513\) | −25.8696 | + | 35.6064i | −0.0504281 | + | 0.0694083i | ||||
\(514\) | 444.256 | + | 611.466i | 0.864311 | + | 1.18962i | ||||
\(515\) | −101.855 | + | 313.477i | −0.197776 | + | 0.608693i | ||||
\(516\) | 176.769i | 0.342575i | ||||||||
\(517\) | 134.798 | + | 116.241i | 0.260730 | + | 0.224837i | ||||
\(518\) | −98.8844 | −0.190897 | ||||||||
\(519\) | −109.657 | − | 35.6298i | −0.211286 | − | 0.0686509i | ||||
\(520\) | 323.974 | − | 235.381i | 0.623027 | − | 0.452656i | ||||
\(521\) | 146.048 | + | 106.110i | 0.280323 | + | 0.203667i | 0.719058 | − | 0.694950i | \(-0.244573\pi\) |
−0.438735 | + | 0.898616i | \(0.644573\pi\) | |||||||
\(522\) | −57.7714 | − | 177.802i | −0.110673 | − | 0.340617i | ||||
\(523\) | 144.402 | − | 46.9189i | 0.276103 | − | 0.0897112i | −0.167693 | − | 0.985839i | \(-0.553632\pi\) |
0.443795 | + | 0.896128i | \(0.353632\pi\) | |||||||
\(524\) | −151.344 | + | 208.308i | −0.288825 | + | 0.397533i | ||||
\(525\) | 115.159 | + | 158.502i | 0.219350 | + | 0.301909i | ||||
\(526\) | −47.1985 | + | 145.262i | −0.0897309 | + | 0.276163i | ||||
\(527\) | 44.2788i | 0.0840206i | ||||||||
\(528\) | 146.255 | − | 348.398i | 0.276998 | − | 0.659845i | ||||
\(529\) | 1231.39 | 2.32778 | ||||||||
\(530\) | −1007.44 | − | 327.338i | −1.90083 | − | 0.617618i | ||||
\(531\) | −48.3771 | + | 35.1480i | −0.0911056 | + | 0.0661921i | ||||
\(532\) | −40.2992 | − | 29.2791i | −0.0757504 | − | 0.0550359i | ||||
\(533\) | −191.465 | − | 589.269i | −0.359222 | − | 1.10557i | ||||
\(534\) | 252.170 | − | 81.9351i | 0.472229 | − | 0.153437i | ||||
\(535\) | −579.031 | + | 796.968i | −1.08230 | + | 1.48966i | ||||
\(536\) | −10.4463 | − | 14.3781i | −0.0194894 | − | 0.0268248i | ||||
\(537\) | −95.5450 | + | 294.057i | −0.177924 | + | 0.547592i | ||||
\(538\) | 496.155i | 0.922222i | ||||||||
\(539\) | −404.886 | + | 245.475i | −0.751179 | + | 0.455426i | ||||
\(540\) | −105.770 | −0.195871 | ||||||||
\(541\) | −273.764 | − | 88.9514i | −0.506034 | − | 0.164420i | 0.0448639 | − | 0.998993i | \(-0.485715\pi\) |
−0.550898 | + | 0.834573i | \(0.685715\pi\) | |||||||
\(542\) | −697.425 | + | 506.709i | −1.28676 | + | 0.934887i | ||||
\(543\) | −73.0257 | − | 53.0563i | −0.134486 | − | 0.0977095i | ||||
\(544\) | −21.3937 | − | 65.8430i | −0.0393266 | − | 0.121035i | ||||
\(545\) | −652.857 | + | 212.126i | −1.19790 | + | 0.389222i | ||||
\(546\) | −74.0718 | + | 101.951i | −0.135663 | + | 0.186724i | ||||
\(547\) | 71.9684 | + | 99.0560i | 0.131569 | + | 0.181090i | 0.869719 | − | 0.493548i | \(-0.164300\pi\) |
−0.738150 | + | 0.674637i | \(0.764300\pi\) | |||||||
\(548\) | −88.7522 | + | 273.151i | −0.161956 | + | 0.498451i | ||||
\(549\) | 356.718i | 0.649759i | ||||||||
\(550\) | 669.215 | + | 1103.80i | 1.21675 | + | 2.00691i | ||||
\(551\) | 208.485 | 0.378376 | ||||||||
\(552\) | 278.255 | + | 90.4104i | 0.504085 | + | 0.163787i | ||||
\(553\) | 204.271 | − | 148.412i | 0.369387 | − | 0.268376i | ||||
\(554\) | 718.411 | + | 521.956i | 1.29677 | + | 0.942159i | ||||
\(555\) | −72.3569 | − | 222.692i | −0.130373 | − | 0.401246i | ||||
\(556\) | −17.0155 | + | 5.52869i | −0.0306035 | + | 0.00994368i | ||||
\(557\) | 329.379 | − | 453.352i | 0.591345 | − | 0.813917i | −0.403536 | − | 0.914964i | \(-0.632219\pi\) |
0.994882 | + | 0.101047i | \(0.0322191\pi\) | |||||||
\(558\) | 97.3841 | + | 134.038i | 0.174524 | + | 0.240211i | ||||
\(559\) | −154.109 | + | 474.299i | −0.275687 | + | 0.848477i | ||||
\(560\) | 408.819i | 0.730034i | ||||||||
\(561\) | −35.6598 | − | 14.9697i | −0.0635647 | − | 0.0266840i | ||||
\(562\) | 1034.07 | 1.83999 | ||||||||
\(563\) | 438.838 | + | 142.587i | 0.779464 | + | 0.253263i | 0.671611 | − | 0.740904i | \(-0.265603\pi\) |
0.107853 | + | 0.994167i | \(0.465603\pi\) | |||||||
\(564\) | 54.6408 | − | 39.6989i | 0.0968809 | − | 0.0703881i | ||||
\(565\) | −522.404 | − | 379.549i | −0.924609 | − | 0.671768i | ||||
\(566\) | −251.260 | − | 773.300i | −0.443923 | − | 1.36625i | ||||
\(567\) | −20.8889 | + | 6.78720i | −0.0368410 | + | 0.0119704i | ||||
\(568\) | −14.2834 | + | 19.6594i | −0.0251468 | + | 0.0346117i | ||||
\(569\) | −500.191 | − | 688.453i | −0.879070 | − | 1.20994i | −0.976678 | − | 0.214711i | \(-0.931119\pi\) |
0.0976081 | − | 0.995225i | \(-0.468881\pi\) | |||||||
\(570\) | 96.9510 | − | 298.385i | 0.170090 | − | 0.523482i | ||||
\(571\) | 558.153i | 0.977500i | 0.872424 | + | 0.488750i | \(0.162547\pi\) | ||||
−0.872424 | + | 0.488750i | \(0.837453\pi\) | |||||||
\(572\) | −203.850 | + | 236.393i | −0.356381 | + | 0.413275i | ||||
\(573\) | 620.652 | 1.08316 | ||||||||
\(574\) | 309.184 | + | 100.460i | 0.538649 | + | 0.175018i | ||||
\(575\) | −1573.31 | + | 1143.08i | −2.73619 | + | 1.98796i | ||||
\(576\) | −17.0389 | − | 12.3795i | −0.0295814 | − | 0.0214921i | ||||
\(577\) | 328.715 | + | 1011.68i | 0.569697 | + | 1.75335i | 0.653565 | + | 0.756870i | \(0.273272\pi\) |
−0.0838684 | + | 0.996477i | \(0.526728\pi\) | |||||||
\(578\) | 685.947 | − | 222.878i | 1.18676 | − | 0.385601i | ||||
\(579\) | 217.765 | − | 299.728i | 0.376106 | − | 0.517665i | ||||
\(580\) | 294.501 | + | 405.345i | 0.507760 | + | 0.698871i | ||||
\(581\) | 22.7494 | − | 70.0154i | 0.0391556 | − | 0.120509i | ||||
\(582\) | 160.887i | 0.276439i | ||||||||
\(583\) | −542.972 | − | 45.3306i | −0.931342 | − | 0.0777540i | ||||
\(584\) | −24.4796 | −0.0419172 | ||||||||
\(585\) | −283.798 | − | 92.2117i | −0.485126 | − | 0.157627i | ||||
\(586\) | 772.326 | − | 561.128i | 1.31796 | − | 0.957556i | ||||
\(587\) | 111.426 | + | 80.9556i | 0.189822 | + | 0.137914i | 0.678638 | − | 0.734473i | \(-0.262571\pi\) |
−0.488815 | + | 0.872387i | \(0.662571\pi\) | |||||||
\(588\) | 55.5191 | + | 170.870i | 0.0944202 | + | 0.290596i | ||||
\(589\) | −175.720 | + | 57.0948i | −0.298336 | + | 0.0969352i | ||||
\(590\) | 250.553 | − | 344.857i | 0.424666 | − | 0.584503i | ||||
\(591\) | −281.567 | − | 387.543i | −0.476424 | − | 0.655741i | ||||
\(592\) | 98.0820 | − | 301.865i | 0.165679 | − | 0.509908i | ||||
\(593\) | 42.1576i | 0.0710921i | 0.999368 | + | 0.0355461i | \(0.0113170\pi\) | ||||
−0.999368 | + | 0.0355461i | \(0.988683\pi\) | |||||||
\(594\) | −140.870 | + | 33.1126i | −0.237155 | + | 0.0557451i | ||||
\(595\) | 41.8441 | 0.0703263 | ||||||||
\(596\) | −323.757 | − | 105.195i | −0.543216 | − | 0.176502i | ||||
\(597\) | 110.431 | − | 80.2328i | 0.184977 | − | 0.134393i | ||||
\(598\) | −1011.98 | − | 735.244i | −1.69227 | − | 1.22950i | ||||
\(599\) | −99.8140 | − | 307.196i | −0.166634 | − | 0.512848i | 0.832519 | − | 0.553997i | \(-0.186898\pi\) |
−0.999153 | + | 0.0411491i | \(0.986898\pi\) | |||||||
\(600\) | −307.389 | + | 99.8769i | −0.512316 | + | 0.166461i | ||||
\(601\) | 401.291 | − | 552.330i | 0.667706 | − | 0.919018i | −0.332000 | − | 0.943279i | \(-0.607723\pi\) |
0.999706 | + | 0.0242612i | \(0.00772333\pi\) | |||||||
\(602\) | −153.804 | − | 211.693i | −0.255489 | − | 0.351650i | ||||
\(603\) | −4.09239 | + | 12.5951i | −0.00678672 | + | 0.0208874i | ||||
\(604\) | 153.585i | 0.254280i | ||||||||
\(605\) | 715.814 | + | 729.554i | 1.18316 | + | 1.20587i | ||||
\(606\) | −621.610 | −1.02576 | ||||||||
\(607\) | 209.112 | + | 67.9445i | 0.344500 | + | 0.111935i | 0.476157 | − | 0.879361i | \(-0.342030\pi\) |
−0.131656 | + | 0.991295i | \(0.542030\pi\) | |||||||
\(608\) | 233.711 | − | 169.801i | 0.384393 | − | 0.279278i | ||||
\(609\) | 84.1726 | + | 61.1550i | 0.138214 | + | 0.100419i | ||||
\(610\) | −785.790 | − | 2418.41i | −1.28818 | − | 3.96461i | ||||
\(611\) | 181.220 | − | 58.8820i | 0.296596 | − | 0.0963699i | ||||
\(612\) | −8.62570 | + | 11.8723i | −0.0140943 | + | 0.0193991i | ||||
\(613\) | 116.415 | + | 160.231i | 0.189910 | + | 0.261389i | 0.893346 | − | 0.449370i | \(-0.148352\pi\) |
−0.703436 | + | 0.710759i | \(0.748352\pi\) | |||||||
\(614\) | 395.852 | − | 1218.31i | 0.644709 | − | 1.98421i | ||||
\(615\) | 769.805i | 1.25172i | ||||||||
\(616\) | 24.7301 | + | 105.209i | 0.0401462 | + | 0.170793i | ||||
\(617\) | 666.299 | 1.07990 | 0.539951 | − | 0.841697i | \(-0.318443\pi\) | ||||
0.539951 | + | 0.841697i | \(0.318443\pi\) | |||||||
\(618\) | 162.739 | + | 52.8771i | 0.263332 | + | 0.0855616i | ||||
\(619\) | −409.934 | + | 297.834i | −0.662252 | + | 0.481154i | −0.867423 | − | 0.497572i | \(-0.834225\pi\) |
0.205171 | + | 0.978726i | \(0.434225\pi\) | |||||||
\(620\) | −359.223 | − | 260.991i | −0.579392 | − | 0.420953i | ||||
\(621\) | −67.3704 | − | 207.345i | −0.108487 | − | 0.333889i | ||||
\(622\) | −399.878 | + | 129.928i | −0.642891 | + | 0.208888i | ||||
\(623\) | −86.7339 | + | 119.379i | −0.139220 | + | 0.191620i | ||||
\(624\) | −237.756 | − | 327.243i | −0.381020 | − | 0.524428i | ||||
\(625\) | 112.663 | − | 346.742i | 0.180261 | − | 0.554787i | ||||
\(626\) | − | 237.087i | − | 0.378733i | ||||||
\(627\) | 13.4260 | − | 160.818i | 0.0214131 | − | 0.256488i | ||||
\(628\) | −88.8984 | −0.141558 | ||||||||
\(629\) | −30.8970 | − | 10.0390i | −0.0491208 | − | 0.0159603i | ||||
\(630\) | 126.668 | − | 92.0293i | 0.201060 | − | 0.146078i | ||||
\(631\) | −615.691 | − | 447.325i | −0.975738 | − | 0.708915i | −0.0189857 | − | 0.999820i | \(-0.506044\pi\) |
−0.956752 | + | 0.290905i | \(0.906044\pi\) | |||||||
\(632\) | 128.717 | + | 396.151i | 0.203666 | + | 0.626821i | ||||
\(633\) | −360.698 | + | 117.198i | −0.569824 | + | 0.185147i | ||||
\(634\) | −222.549 | + | 306.313i | −0.351024 | + | 0.483143i | ||||
\(635\) | 104.574 | + | 143.933i | 0.164683 | + | 0.226666i | ||||
\(636\) | −63.8881 | + | 196.627i | −0.100453 | + | 0.309162i | ||||
\(637\) | 506.875i | 0.795722i | ||||||||
\(638\) | 519.130 | + | 447.663i | 0.813683 | + | 0.701667i | ||||
\(639\) | 18.1077 | 0.0283376 | ||||||||
\(640\) | −953.178 | − | 309.706i | −1.48934 | − | 0.483916i | ||||
\(641\) | −164.241 | + | 119.328i | −0.256227 | + | 0.186160i | −0.708482 | − | 0.705729i | \(-0.750620\pi\) |
0.452255 | + | 0.891889i | \(0.350620\pi\) | |||||||
\(642\) | 413.739 | + | 300.599i | 0.644454 | + | 0.468223i | ||||
\(643\) | −140.650 | − | 432.877i | −0.218741 | − | 0.673215i | −0.998867 | − | 0.0475925i | \(-0.984845\pi\) |
0.780126 | − | 0.625622i | \(-0.215155\pi\) | |||||||
\(644\) | 234.672 | − | 76.2495i | 0.364397 | − | 0.118400i | ||||
\(645\) | 364.198 | − | 501.276i | 0.564648 | − | 0.777171i | ||||
\(646\) | −25.5859 | − | 35.2160i | −0.0396067 | − | 0.0545140i | ||||
\(647\) | 165.477 | − | 509.287i | 0.255761 | − | 0.787151i | −0.737918 | − | 0.674890i | \(-0.764191\pi\) |
0.993679 | − | 0.112260i | \(-0.0358091\pi\) | |||||||
\(648\) | − | 36.2337i | − | 0.0559162i | ||||||
\(649\) | 84.8678 | − | 202.166i | 0.130767 | − | 0.311504i | ||||
\(650\) | 1381.84 | 2.12591 | ||||||||
\(651\) | −87.6917 | − | 28.4928i | −0.134703 | − | 0.0437677i | ||||
\(652\) | −104.568 | + | 75.9730i | −0.160380 | + | 0.116523i | ||||
\(653\) | 670.730 | + | 487.314i | 1.02715 | + | 0.746269i | 0.967736 | − | 0.251965i | \(-0.0810766\pi\) |
0.0594144 | + | 0.998233i | \(0.481077\pi\) | |||||||
\(654\) | 110.123 | + | 338.925i | 0.168384 | + | 0.518234i | ||||
\(655\) | 858.356 | − | 278.897i | 1.31047 | − | 0.425797i | ||||
\(656\) | −613.351 | + | 844.205i | −0.934986 | + | 1.28690i | ||||
\(657\) | 10.7220 | + | 14.7575i | 0.0163196 | + | 0.0224620i | ||||
\(658\) | −30.8949 | + | 95.0847i | −0.0469527 | + | 0.144506i | ||||
\(659\) | 1089.67i | 1.65353i | 0.562551 | + | 0.826763i | \(0.309820\pi\) | ||||
−0.562551 | + | 0.826763i | \(0.690180\pi\) | |||||||
\(660\) | 331.634 | − | 201.063i | 0.502475 | − | 0.304642i | ||||
\(661\) | −920.151 | −1.39206 | −0.696029 | − | 0.718013i | \(-0.745052\pi\) | ||||
−0.696029 | + | 0.718013i | \(0.745052\pi\) | |||||||
\(662\) | 654.239 | + | 212.575i | 0.988277 | + | 0.321111i | ||||
\(663\) | −33.4945 | + | 24.3352i | −0.0505197 | + | 0.0367047i | ||||
\(664\) | 98.2538 | + | 71.3856i | 0.147973 | + | 0.107508i | ||||
\(665\) | 53.9554 | + | 166.058i | 0.0811360 | + | 0.249711i | ||||
\(666\) | −115.608 | + | 37.5635i | −0.173586 | + | 0.0564016i | ||||
\(667\) | −607.030 | + | 835.505i | −0.910090 | + | 1.25263i | ||||
\(668\) | −186.964 | − | 257.334i | −0.279887 | − | 0.385231i | ||||
\(669\) | 112.157 | − | 345.184i | 0.167649 | − | 0.515971i | ||||
\(670\) | − | 94.4048i | − | 0.140903i | ||||||
\(671\) | −678.102 | − | 1118.46i | −1.01058 | − | 1.66685i | ||||
\(672\) | 144.165 | 0.214531 | ||||||||
\(673\) | 614.204 | + | 199.567i | 0.912636 | + | 0.296533i | 0.727442 | − | 0.686169i | \(-0.240709\pi\) |
0.185193 | + | 0.982702i | \(0.440709\pi\) | |||||||
\(674\) | −1024.97 | + | 744.682i | −1.52072 | + | 1.10487i | ||||
\(675\) | 194.846 | + | 141.564i | 0.288660 | + | 0.209724i | ||||
\(676\) | −22.5890 | − | 69.5218i | −0.0334157 | − | 0.102843i | ||||
\(677\) | −701.518 | + | 227.937i | −1.03622 | + | 0.336687i | −0.777245 | − | 0.629198i | \(-0.783383\pi\) |
−0.258971 | + | 0.965885i | \(0.583383\pi\) | |||||||
\(678\) | −197.040 | + | 271.202i | −0.290619 | + | 0.400003i | ||||
\(679\) | −52.6287 | − | 72.4372i | −0.0775092 | − | 0.106682i | ||||
\(680\) | −21.3315 | + | 65.6516i | −0.0313698 | + | 0.0965464i | ||||
\(681\) | 144.352i | 0.211970i | ||||||||
\(682\) | −560.139 | − | 235.142i | −0.821318 | − | 0.344783i | ||||
\(683\) | 527.576 | 0.772440 | 0.386220 | − | 0.922407i | \(-0.373781\pi\) | ||||
0.386220 | + | 0.922407i | \(0.373781\pi\) | |||||||
\(684\) | −58.2372 | − | 18.9224i | −0.0851421 | − | 0.0276643i | ||||
\(685\) | 814.457 | − | 591.738i | 1.18899 | − | 0.863851i | ||||
\(686\) | −460.091 | − | 334.275i | −0.670686 | − | 0.487282i | ||||
\(687\) | −176.981 | − | 544.692i | −0.257614 | − | 0.792856i | ||||
\(688\) | 798.794 | − | 259.544i | 1.16104 | − | 0.377244i | ||||
\(689\) | −342.844 | + | 471.885i | −0.497597 | + | 0.684883i | ||||
\(690\) | 913.492 | + | 1257.31i | 1.32390 | + | 1.82219i | ||||
\(691\) | −159.667 | + | 491.405i | −0.231067 | + | 0.711151i | 0.766552 | + | 0.642182i | \(0.221971\pi\) |
−0.997619 | + | 0.0689685i | \(0.978029\pi\) | |||||||
\(692\) | − | 160.419i | − | 0.231819i | ||||||
\(693\) | 52.5932 | − | 60.9894i | 0.0758921 | − | 0.0880077i | ||||
\(694\) | 614.533 | 0.885494 | ||||||||
\(695\) | 59.6431 | + | 19.3792i | 0.0858174 | + | 0.0278837i | ||||
\(696\) | −138.859 | + | 100.887i | −0.199511 | + | 0.144953i | ||||
\(697\) | 86.4074 | + | 62.7786i | 0.123970 | + | 0.0900698i | ||||
\(698\) | 349.967 | + | 1077.09i | 0.501386 | + | 1.54311i | ||||
\(699\) | −272.477 | + | 88.5330i | −0.389809 | + | 0.126657i | ||||
\(700\) | −160.221 | + | 220.526i | −0.228887 | + | 0.315037i | ||||
\(701\) | 411.442 | + | 566.302i | 0.586936 | + | 0.807848i | 0.994434 | − | 0.105358i | \(-0.0335988\pi\) |
−0.407498 | + | 0.913206i | \(0.633599\pi\) | |||||||
\(702\) | −47.8709 | + | 147.332i | −0.0681922 | + | 0.209874i | ||||
\(703\) | − | 135.559i | − | 0.192829i | ||||||
\(704\) | 76.9566 | + | 6.42480i | 0.109313 | + | 0.00912614i | ||||
\(705\) | −236.741 | −0.335803 | ||||||||
\(706\) | 546.365 | + | 177.525i | 0.773888 | + | 0.251452i | ||||
\(707\) | 279.871 | − | 203.338i | 0.395858 | − | 0.287607i | ||||
\(708\) | −67.3074 | − | 48.9017i | −0.0950669 | − | 0.0690701i | ||||
\(709\) | −200.757 | − | 617.867i | −0.283155 | − | 0.871463i | −0.986945 | − | 0.161055i | \(-0.948510\pi\) |
0.703790 | − | 0.710408i | \(-0.251490\pi\) | |||||||
\(710\) | −122.763 | + | 39.8883i | −0.172906 | + | 0.0561807i | ||||
\(711\) | 182.441 | − | 251.109i | 0.256598 | − | 0.353177i | ||||
\(712\) | −143.085 | − | 196.939i | −0.200962 | − | 0.276600i | ||||
\(713\) | 282.822 | − | 870.436i | 0.396664 | − | 1.22081i | ||||
\(714\) | − | 21.7230i | − | 0.0304244i | ||||||
\(715\) | 1065.12 | − | 250.364i | 1.48967 | − | 0.350159i | ||||
\(716\) | −430.178 | −0.600808 | ||||||||
\(717\) | −296.421 | − | 96.3129i | −0.413418 | − | 0.134328i | ||||
\(718\) | −1316.31 | + | 956.352i | −1.83329 | + | 1.33197i | ||||
\(719\) | −561.880 | − | 408.230i | −0.781474 | − | 0.567774i | 0.123947 | − | 0.992289i | \(-0.460445\pi\) |
−0.905421 | + | 0.424515i | \(0.860445\pi\) | |||||||
\(720\) | 155.299 | + | 477.961i | 0.215693 | + | 0.663835i | ||||
\(721\) | −90.5678 | + | 29.4273i | −0.125614 | + | 0.0408145i | ||||
\(722\) | −430.453 | + | 592.468i | −0.596195 | + | 0.820592i | ||||
\(723\) | 230.728 | + | 317.569i | 0.319125 | + | 0.439239i | ||||
\(724\) | 38.8082 | − | 119.439i | 0.0536025 | − | 0.164972i | ||||
\(725\) | − | 1140.87i | − | 1.57362i | ||||||
\(726\) | 378.742 | − | 371.609i | 0.521683 | − | 0.511858i | ||||
\(727\) | −970.108 | −1.33440 | −0.667200 | − | 0.744879i | \(-0.732507\pi\) | ||||
−0.667200 | + | 0.744879i | \(0.732507\pi\) | |||||||
\(728\) | 110.034 | + | 35.7523i | 0.151146 | + | 0.0491103i | ||||
\(729\) | −21.8435 | + | 15.8702i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | −105.199 | − | 76.4317i | −0.144109 | − | 0.104701i | ||||
\(731\) | −26.5652 | − | 81.7594i | −0.0363410 | − | 0.111846i | ||||
\(732\) | −472.013 | + | 153.366i | −0.644827 | + | 0.209517i | ||||
\(733\) | −92.6359 | + | 127.502i | −0.126379 | + | 0.173946i | −0.867518 | − | 0.497406i | \(-0.834286\pi\) |
0.741139 | + | 0.671352i | \(0.234286\pi\) | |||||||
\(734\) | −1068.30 | − | 1470.39i | −1.45545 | − | 2.00326i | ||||
\(735\) | 194.606 | − | 598.936i | 0.264770 | − | 0.814879i | ||||
\(736\) | 1430.99i | 1.94428i | ||||||||
\(737\) | −11.1112 | − | 47.2703i | −0.0150763 | − | 0.0641388i | ||||
\(738\) | 399.638 | 0.541514 | ||||||||
\(739\) | −651.979 | − | 211.841i | −0.882244 | − | 0.286659i | −0.167355 | − | 0.985897i | \(-0.553523\pi\) |
−0.714889 | + | 0.699238i | \(0.753523\pi\) | |||||||
\(740\) | 263.559 | − | 191.487i | 0.356161 | − | 0.258766i | ||||
\(741\) | −139.763 | − | 101.544i | −0.188614 | − | 0.137036i | ||||
\(742\) | −94.5724 | − | 291.064i | −0.127456 | − | 0.392270i | ||||
\(743\) | 490.820 | − | 159.477i | 0.660592 | − | 0.214639i | 0.0405134 | − | 0.999179i | \(-0.487101\pi\) |
0.620079 | + | 0.784540i | \(0.287101\pi\) | |||||||
\(744\) | 89.4078 | − | 123.059i | 0.120172 | − | 0.165402i | ||||
\(745\) | 701.367 | + | 965.349i | 0.941432 | + | 1.29577i | ||||
\(746\) | 14.2277 | − | 43.7884i | 0.0190720 | − | 0.0586976i | ||||
\(747\) | − | 90.4988i | − | 0.121150i | ||||||
\(748\) | 4.47664 | − | 53.6215i | 0.00598482 | − | 0.0716865i | ||||
\(749\) | −284.611 | −0.379988 | ||||||||
\(750\) | −752.123 | − | 244.380i | −1.00283 | − | 0.325840i | ||||
\(751\) | 690.649 | − | 501.786i | 0.919640 | − | 0.668157i | −0.0237947 | − | 0.999717i | \(-0.507575\pi\) |
0.943434 | + | 0.331560i | \(0.107575\pi\) | |||||||
\(752\) | −259.621 | − | 188.626i | −0.345241 | − | 0.250832i | ||||
\(753\) | 42.3520 | + | 130.346i | 0.0562444 | + | 0.173102i | ||||
\(754\) | 697.911 | − | 226.765i | 0.925612 | − | 0.300750i | ||||
\(755\) | 316.433 | − | 435.532i | 0.419116 | − | 0.576864i | ||||
\(756\) | −17.9618 | − | 24.7223i | −0.0237590 | − | 0.0327015i | ||||
\(757\) | −153.287 | + | 471.770i | −0.202493 | + | 0.623210i | 0.797314 | + | 0.603565i | \(0.206254\pi\) |
−0.999807 | + | 0.0196452i | \(0.993746\pi\) | |||||||
\(758\) | 394.239i | 0.520104i | ||||||||
\(759\) | 605.386 | + | 522.045i | 0.797610 | + | 0.687806i | ||||
\(760\) | −288.043 | −0.379004 | ||||||||
\(761\) | −1.23010 | − | 0.399683i | −0.00161642 | − | 0.000525208i | 0.308209 | − | 0.951319i | \(-0.400271\pi\) |
−0.309825 | + | 0.950794i | \(0.600271\pi\) | |||||||
\(762\) | 74.7217 | − | 54.2885i | 0.0980599 | − | 0.0712447i | ||||
\(763\) | −160.449 | − | 116.573i | −0.210287 | − | 0.152783i | ||||
\(764\) | 266.841 | + | 821.254i | 0.349269 | + | 1.07494i | ||||
\(765\) | 48.9211 | − | 15.8954i | 0.0639491 | − | 0.0207783i | ||||
\(766\) | 1072.04 | − | 1475.54i | 1.39953 | − | 1.92629i | ||||
\(767\) | −137.963 | − | 189.890i | −0.179874 | − | 0.247576i | ||||
\(768\) | −175.812 | + | 541.092i | −0.228921 | + | 0.704547i | ||||
\(769\) | − | 398.342i | − | 0.518000i | −0.965877 | − | 0.259000i | \(-0.916607\pi\) | ||
0.965877 | − | 0.259000i | \(-0.0833929\pi\) | |||||||
\(770\) | −222.213 | + | 529.339i | −0.288588 | + | 0.687453i | ||||
\(771\) | −517.073 | −0.670653 | ||||||||
\(772\) | 490.229 | + | 159.285i | 0.635012 | + | 0.206328i | ||||
\(773\) | 515.743 | − | 374.709i | 0.667196 | − | 0.484747i | −0.201889 | − | 0.979408i | \(-0.564708\pi\) |
0.869086 | + | 0.494662i | \(0.164708\pi\) | |||||||
\(774\) | −260.233 | − | 189.070i | −0.336218 | − | 0.244277i | ||||
\(775\) | 312.435 | + | 961.575i | 0.403142 | + | 1.24074i | ||||
\(776\) | 140.480 | − | 45.6448i | 0.181031 | − | 0.0588206i | ||||
\(777\) | 39.7635 | − | 54.7298i | 0.0511757 | − | 0.0704373i | ||||
\(778\) | 13.2272 | + | 18.2057i | 0.0170016 | + | 0.0234007i | ||||
\(779\) | −137.719 | + | 423.855i | −0.176789 | + | 0.544102i | ||||
\(780\) | − | 415.171i | − | 0.532270i | ||||||
\(781\) | −56.7753 | + | 34.4218i | −0.0726956 | + | 0.0440740i | ||||
\(782\) | 215.625 | 0.275735 | ||||||||
\(783\) | 121.639 | + | 39.5231i | 0.155351 | + | 0.0504765i | ||||
\(784\) | 690.623 | − | 501.767i | 0.880897 | − | 0.640009i | ||||
\(785\) | 252.096 | + | 183.158i | 0.321141 | + | 0.233323i | ||||
\(786\) | −144.787 | − | 445.608i | −0.184207 | − | 0.566932i | ||||
\(787\) | 1018.20 | − | 330.835i | 1.29378 | − | 0.420375i | 0.420367 | − | 0.907354i | \(-0.361901\pi\) |
0.873413 | + | 0.486980i | \(0.161901\pi\) | |||||||
\(788\) | 391.746 | − | 539.191i | 0.497139 | − | 0.684253i | ||||
\(789\) | −61.4189 | − | 84.5359i | −0.0778440 | − | 0.107143i | ||||
\(790\) | −683.733 | + | 2104.31i | −0.865484 | + | 2.66369i | ||||
\(791\) | − | 186.560i | − | 0.235853i | ||||||
\(792\) | 68.8784 | + | 113.608i | 0.0869677 | + | 0.143444i | ||||
\(793\) | −1400.19 | −1.76569 | ||||||||
\(794\) | −1235.84 | − | 401.548i | −1.55647 | − | 0.505728i | ||||
\(795\) | 586.286 | − | 425.961i | 0.737466 | − | 0.535800i | ||||
\(796\) | 153.643 | + | 111.629i | 0.193019 | + | 0.140237i | ||||
\(797\) | 113.056 | + | 347.952i | 0.141852 | + | 0.436577i | 0.996593 | − | 0.0824789i | \(-0.0262837\pi\) |
−0.854740 | + | 0.519056i | \(0.826284\pi\) | |||||||
\(798\) | 86.2075 | − | 28.0105i | 0.108029 | − | 0.0351009i | ||||
\(799\) | −19.3066 | + | 26.5732i | −0.0241634 | + | 0.0332581i | ||||
\(800\) | −929.186 | − | 1278.92i | −1.16148 | − | 1.59864i | ||||
\(801\) | −56.0542 | + | 172.517i | −0.0699802 | + | 0.215377i | ||||
\(802\) | − | 1389.49i | − | 1.73253i | ||||||
\(803\) | −61.6711 | − | 25.8891i | −0.0768009 | − | 0.0322405i | ||||
\(804\) | −18.4254 | −0.0229172 | ||||||||
\(805\) | −822.574 | − | 267.271i | −1.02183 | − | 0.332013i | ||||
\(806\) | −526.127 | + | 382.254i | −0.652763 | + | 0.474260i | ||||
\(807\) | −274.608 | − | 199.514i | −0.340283 | − | 0.247230i | ||||
\(808\) | 176.355 | + | 542.765i | 0.218261 | + | 0.671739i | ||||
\(809\) | 168.019 | − | 54.5926i | 0.207687 | − | 0.0674816i | −0.203326 | − | 0.979111i | \(-0.565175\pi\) |
0.411013 | + | 0.911629i | \(0.365175\pi\) | |||||||
\(810\) | 113.131 | − | 155.711i | 0.139668 | − | 0.192236i | ||||
\(811\) | 150.709 | + | 207.434i | 0.185832 | + | 0.255775i | 0.891761 | − | 0.452507i | \(-0.149470\pi\) |
−0.705929 | + | 0.708282i | \(0.749470\pi\) | |||||||
\(812\) | −44.7320 | + | 137.671i | −0.0550887 | + | 0.169546i | ||||
\(813\) | − | 589.763i | − | 0.725416i | ||||||
\(814\) | 291.075 | − | 337.543i | 0.357585 | − | 0.414671i | ||||
\(815\) | 453.058 | 0.555900 | ||||||||
\(816\) | 66.3140 | + | 21.5467i | 0.0812672 | + | 0.0264053i | ||||
\(817\) | 290.207 | − | 210.847i | 0.355210 | − | 0.258075i | ||||
\(818\) | 1036.57 | + | 753.109i | 1.26720 | + | 0.920672i | ||||
\(819\) | −26.6412 | − | 81.9933i | −0.0325290 | − | 0.100114i | ||||
\(820\) | −1018.61 | + | 330.968i | −1.24221 | + | 0.403620i | ||||
\(821\) | −551.722 | + | 759.381i | −0.672013 | + | 0.924946i | −0.999804 | − | 0.0198041i | \(-0.993696\pi\) |
0.327791 | + | 0.944750i | \(0.393696\pi\) | |||||||
\(822\) | −307.196 | − | 422.818i | −0.373717 | − | 0.514378i | ||||
\(823\) | 172.552 | − | 531.062i | 0.209663 | − | 0.645275i | −0.789827 | − | 0.613330i | \(-0.789830\pi\) |
0.999490 | − | 0.0319455i | \(-0.0101703\pi\) | |||||||
\(824\) | − | 157.099i | − | 0.190654i | ||||||
\(825\) | −880.028 | − | 73.4700i | −1.06670 | − | 0.0890546i | ||||
\(826\) | 123.154 | 0.149097 | ||||||||
\(827\) | −1261.70 | − | 409.950i | −1.52563 | − | 0.495708i | −0.578262 | − | 0.815851i | \(-0.696269\pi\) |
−0.947369 | + | 0.320144i | \(0.896269\pi\) | |||||||
\(828\) | 245.396 | − | 178.291i | 0.296372 | − | 0.215327i | ||||
\(829\) | 727.620 | + | 528.647i | 0.877709 | + | 0.637693i | 0.932644 | − | 0.360797i | \(-0.117495\pi\) |
−0.0549356 | + | 0.998490i | \(0.517495\pi\) | |||||||
\(830\) | 199.354 | + | 613.547i | 0.240185 | + | 0.739214i | ||||
\(831\) | −577.776 | + | 187.731i | −0.695278 | + | 0.225910i | ||||
\(832\) | 48.5920 | − | 66.8812i | 0.0584039 | − | 0.0803861i | ||||
\(833\) | −51.3577 | − | 70.6877i | −0.0616538 | − | 0.0848592i | ||||
\(834\) | 10.0606 | − | 30.9632i | 0.0120630 | − | 0.0371261i | ||||
\(835\) | 1114.95i | 1.33527i | ||||||||
\(836\) | 218.568 | − | 51.3761i | 0.261445 | − | 0.0614547i | ||||
\(837\) | −113.346 | −0.135420 | ||||||||
\(838\) | 268.667 | + | 87.2953i | 0.320605 | + | 0.104171i | ||||
\(839\) | −229.444 | + | 166.701i | −0.273473 | + | 0.198690i | −0.716066 | − | 0.698033i | \(-0.754059\pi\) |
0.442592 | + | 0.896723i | \(0.354059\pi\) | |||||||
\(840\) | −116.293 | − | 84.4916i | −0.138444 | − | 0.100585i | ||||
\(841\) | 72.6621 | + | 223.631i | 0.0863996 | + | 0.265911i | ||||
\(842\) | 898.847 | − | 292.053i | 1.06751 | − | 0.346856i | ||||
\(843\) | −415.822 | + | 572.330i | −0.493265 | + | 0.678921i | ||||
\(844\) | −310.156 | − | 426.893i | −0.367483 | − | 0.505797i | ||||
\(845\) | −79.1792 | + | 243.688i | −0.0937032 | + | 0.288389i | ||||
\(846\) | 122.902i | 0.145274i | ||||||||
\(847\) | −48.9642 | + | 291.204i | −0.0578090 | + | 0.343806i | ||||
\(848\) | 982.338 | 1.15842 | ||||||||
\(849\) | 529.037 | + | 171.894i | 0.623129 | + | 0.202467i | ||||
\(850\) | −192.709 | + | 140.012i | −0.226717 | + | 0.164719i | ||||
\(851\) | 543.253 | + | 394.696i | 0.638370 | + | 0.463803i | ||||
\(852\) | 7.78519 | + | 23.9603i | 0.00913755 | + | 0.0281225i | ||||
\(853\) | −419.377 | + | 136.264i | −0.491650 | + | 0.159747i | −0.544341 | − | 0.838864i | \(-0.683220\pi\) |
0.0526910 | + | 0.998611i | \(0.483220\pi\) | |||||||
\(854\) | 431.828 | − | 594.361i | 0.505654 | − | 0.695973i | ||||
\(855\) | 126.161 | + | 173.646i | 0.147557 | + | 0.203095i | ||||
\(856\) | 145.090 | − | 446.542i | 0.169498 | − | 0.521662i | ||||
\(857\) | − | 1378.52i | − | 1.60854i | −0.594264 | − | 0.804270i | \(-0.702557\pi\) | ||
0.594264 | − | 0.804270i | \(-0.297443\pi\) | |||||||
\(858\) | −129.974 | − | 552.946i | −0.151485 | − | 0.644459i | ||||
\(859\) | 1387.60 | 1.61537 | 0.807685 | − | 0.589614i | \(-0.200720\pi\) | ||||
0.807685 | + | 0.589614i | \(0.200720\pi\) | |||||||
\(860\) | 819.876 | + | 266.394i | 0.953344 | + | 0.309760i | ||||
\(861\) | −179.931 | + | 130.728i | −0.208979 | + | 0.151832i | ||||
\(862\) | 159.911 | + | 116.182i | 0.185512 | + | 0.134782i | ||||
\(863\) | −159.131 | − | 489.755i | −0.184393 | − | 0.567503i | 0.815544 | − | 0.578695i | \(-0.196438\pi\) |
−0.999937 | + | 0.0111912i | \(0.996438\pi\) | |||||||
\(864\) | 168.547 | − | 54.7642i | 0.195077 | − | 0.0633845i | ||||
\(865\) | −330.512 | + | 454.911i | −0.382095 | + | 0.525908i | ||||
\(866\) | 1058.78 | + | 1457.28i | 1.22261 | + | 1.68277i | ||||
\(867\) | −152.477 | + | 469.276i | −0.175867 | + | 0.541264i | ||||
\(868\) | − | 128.285i | − | 0.147794i | ||||||
\(869\) | −94.6851 | + | 1134.14i | −0.108959 | + | 1.30511i | ||||
\(870\) | −911.732 | −1.04797 | ||||||||
\(871\) | −49.4385 | − | 16.0635i | −0.0567606 | − | 0.0184426i | ||||
\(872\) | 264.693 | − | 192.311i | 0.303547 | − | 0.220540i | ||||
\(873\) | −89.0465 | − | 64.6961i | −0.102001 | − | 0.0741078i | ||||
\(874\) | 278.035 | + | 855.703i | 0.318118 | + | 0.979065i | ||||
\(875\) | 418.574 | − | 136.003i | 0.478370 | − | 0.155432i | ||||
\(876\) | −14.9176 | + | 20.5322i | −0.0170292 | + | 0.0234386i | ||||
\(877\) | −436.200 | − | 600.377i | −0.497377 | − | 0.684581i | 0.484350 | − | 0.874874i | \(-0.339056\pi\) |
−0.981727 | + | 0.190293i | \(0.939056\pi\) | |||||||
\(878\) | −205.505 | + | 632.479i | −0.234060 | + | 0.720364i | ||||
\(879\) | 653.102i | 0.743006i | ||||||||
\(880\) | −1395.51 | − | 1203.39i | −1.58580 | − | 1.36749i | ||||
\(881\) | −620.478 | −0.704288 | −0.352144 | − | 0.935946i | \(-0.614547\pi\) | ||||
−0.352144 | + | 0.935946i | \(0.614547\pi\) | |||||||
\(882\) | −310.932 | − | 101.028i | −0.352531 | − | 0.114544i | ||||
\(883\) | −545.414 | + | 396.266i | −0.617683 | + | 0.448773i | −0.852111 | − | 0.523361i | \(-0.824678\pi\) |
0.234429 | + | 0.972133i | \(0.424678\pi\) | |||||||
\(884\) | −46.6012 | − | 33.8577i | −0.0527163 | − | 0.0383006i | ||||
\(885\) | 90.1159 | + | 277.348i | 0.101826 | + | 0.313388i | ||||
\(886\) | −1273.04 | + | 413.636i | −1.43684 | + | 0.466858i | ||||
\(887\) | −645.643 | + | 888.652i | −0.727895 | + | 1.00186i | 0.271329 | + | 0.962487i | \(0.412537\pi\) |
−0.999224 | + | 0.0393755i | \(0.987463\pi\) | |||||||
\(888\) | 65.5977 | + | 90.2876i | 0.0738713 | + | 0.101675i | ||||
\(889\) | −15.8838 | + | 48.8853i | −0.0178670 | + | 0.0549891i | ||||
\(890\) | − | 1293.08i | − | 1.45290i | ||||||
\(891\) | 38.3200 | − | 91.2830i | 0.0430078 | − | 0.102450i | ||||
\(892\) | 504.973 | 0.566113 | ||||||||
\(893\) | −130.350 | − | 42.3533i | −0.145969 | − | 0.0474281i | ||||
\(894\) | 501.153 | − | 364.109i | 0.560573 | − | 0.407280i | ||||
\(895\) | 1219.89 | + | 886.301i | 1.36300 | + | 0.990280i | ||||
\(896\) | −89.4784 | − | 275.386i | −0.0998643 | − | 0.307351i | ||||
\(897\) | 813.873 | − | 264.443i | 0.907328 | − | 0.294809i | ||||
\(898\) | 428.295 | − | 589.497i | 0.476943 | − | 0.656456i | ||||
\(899\) | 315.595 | + | 434.380i | 0.351051 | + | 0.483181i | ||||
\(900\) | −103.547 | + | 318.686i | −0.115053 | + | 0.354095i | ||||
\(901\) | − | 100.546i | − | 0.111594i | ||||||
\(902\) | −1253.03 | + | 759.690i | −1.38917 | + | 0.842228i | ||||
\(903\) | 179.014 | 0.198244 | ||||||||
\(904\) | 292.704 | + | 95.1052i | 0.323787 | + | 0.105205i | ||||
\(905\) | −356.133 | + | 258.746i | −0.393518 | + | 0.285907i | ||||
\(906\) | −226.103 | − | 164.273i | −0.249562 | − | 0.181317i | ||||
\(907\) | 76.3752 | + | 235.059i | 0.0842064 | + | 0.259161i | 0.984291 | − | 0.176555i | \(-0.0564953\pi\) |
−0.900084 | + | 0.435716i | \(0.856495\pi\) | |||||||
\(908\) | −191.008 | + | 62.0621i | −0.210361 | + | 0.0683504i | ||||
\(909\) | 249.962 | − | 344.044i | 0.274986 | − | 0.378486i | ||||
\(910\) | 361.235 | + | 497.197i | 0.396962 | + | 0.546371i | ||||
\(911\) | 212.218 | − | 653.140i | 0.232951 | − | 0.716948i | −0.764436 | − | 0.644700i | \(-0.776982\pi\) |
0.997387 | − | 0.0722488i | \(-0.0230176\pi\) | |||||||
\(912\) | 290.949i | 0.319023i | ||||||||
\(913\) | 172.033 | + | 283.751i | 0.188426 | + | 0.310790i | ||||
\(914\) | −2093.63 | −2.29062 | ||||||||
\(915\) | 1654.51 | + | 537.581i | 1.80820 | + | 0.587521i | ||||
\(916\) | 644.652 | − | 468.367i | 0.703769 | − | 0.511318i | ||||
\(917\) | 210.954 | + | 153.267i | 0.230048 | + | 0.167140i | ||||
\(918\) | −8.25197 | − | 25.3970i | −0.00898908 | − | 0.0276655i | ||||
\(919\) | −1412.55 | + | 458.966i | −1.53705 | + | 0.499419i | −0.950562 | − | 0.310536i | \(-0.899491\pi\) |
−0.586492 | + | 0.809955i | \(0.699491\pi\) | |||||||
\(920\) | 838.671 | − | 1154.33i | 0.911599 | − | 1.25471i | ||||
\(921\) | 515.118 | + | 708.999i | 0.559303 | + | 0.769814i | ||||
\(922\) | 254.543 | − | 783.402i | 0.276077 | − | 0.849677i | ||||
\(923\) | 71.0767i | 0.0770062i | ||||||||
\(924\) | 103.314 | + | 43.3703i | 0.111811 | + | 0.0469376i | ||||
\(925\) | −741.807 | −0.801953 | ||||||||
\(926\) | 1713.56 | + | 556.769i | 1.85050 | + | 0.601262i | ||||
\(927\) | −94.7067 | + | 68.8084i | −0.102165 | + | 0.0742270i | ||||
\(928\) | −679.167 | − | 493.444i | −0.731861 | − | 0.531728i | ||||
\(929\) | −210.565 | − | 648.052i | −0.226658 | − | 0.697580i | −0.998119 | − | 0.0613042i | \(-0.980474\pi\) |
0.771462 | − | 0.636276i | \(-0.219526\pi\) | |||||||
\(930\) | 768.445 | − | 249.683i | 0.826285 | − | 0.268476i | ||||
\(931\) | 214.301 | − | 294.960i | 0.230183 | − | 0.316820i | ||||
\(932\) | −234.296 | − | 322.481i | −0.251390 | − | 0.346009i | ||||
\(933\) | 88.8877 | − | 273.568i | 0.0952709 | − | 0.293214i | ||||
\(934\) | − | 1159.85i | − | 1.24181i | ||||||
\(935\) | −123.172 | + | 142.835i | −0.131734 | + | 0.152765i | ||||
\(936\) | 142.225 | 0.151950 | ||||||||
\(937\) | 84.2017 | + | 27.3588i | 0.0898630 | + | 0.0291983i | 0.353603 | − | 0.935395i | \(-0.384956\pi\) |
−0.263740 | + | 0.964594i | \(0.584956\pi\) | |||||||
\(938\) | 22.0658 | − | 16.0318i | 0.0235243 | − | 0.0170914i | ||||
\(939\) | 131.221 | + | 95.3374i | 0.139745 | + | 0.101531i | ||||
\(940\) | −101.784 | − | 313.258i | −0.108281 | − | 0.333254i | ||||
\(941\) | −553.577 | + | 179.868i | −0.588286 | + | 0.191146i | −0.588009 | − | 0.808854i | \(-0.700088\pi\) |
−0.000276616 | 1.00000i | \(0.500088\pi\) | ||||||||
\(942\) | 95.0851 | − | 130.873i | 0.100940 | − | 0.138931i | ||||
\(943\) | −1297.62 | − | 1786.01i | −1.37605 | − | 1.89397i | ||||
\(944\) | −122.155 | + | 375.954i | −0.129401 | + | 0.398256i | ||||
\(945\) | 107.114i | 0.113348i | ||||||||
\(946\) | 1175.35 | + | 98.1254i | 1.24244 | + | 0.103727i | ||||
\(947\) | −912.836 | −0.963924 | −0.481962 | − | 0.876192i | \(-0.660076\pi\) | ||||
−0.481962 | + | 0.876192i | \(0.660076\pi\) | |||||||
\(948\) | 410.709 | + | 133.447i | 0.433237 | + | 0.140767i | ||||
\(949\) | −57.9265 | + | 42.0860i | −0.0610395 | + | 0.0443478i | ||||
\(950\) | −804.120 | − | 584.228i | −0.846442 | − | 0.614976i | ||||
\(951\) | −80.0437 | − | 246.349i | −0.0841680 | − | 0.259042i | ||||
\(952\) | −18.9677 | + | 6.16296i | −0.0199240 | + | 0.00647370i | ||||
\(953\) | −326.027 | + | 448.738i | −0.342106 | + | 0.470869i | −0.945055 | − | 0.326911i | \(-0.893992\pi\) |
0.602949 | + | 0.797780i | \(0.293992\pi\) | |||||||
\(954\) | −221.134 | − | 304.365i | −0.231797 | − | 0.319041i | ||||
\(955\) | 935.335 | − | 2878.67i | 0.979409 | − | 3.01431i | ||||
\(956\) | − | 433.636i | − | 0.453594i | ||||||
\(957\) | −456.522 | + | 107.309i | −0.477034 | + | 0.112130i | ||||
\(958\) | −1499.90 | −1.56566 | ||||||||
\(959\) | 276.621 | + | 89.8796i | 0.288447 | + | 0.0937223i | ||||
\(960\) | −83.0955 | + | 60.3724i | −0.0865578 | + | 0.0628879i | ||||
\(961\) | 392.512 | + | 285.176i | 0.408441 | + | 0.296750i | ||||
\(962\) | −147.445 | − | 453.788i | −0.153269 | − | 0.471713i | ||||
\(963\) | −332.746 | + | 108.116i | −0.345531 | + | 0.112270i | ||||
\(964\) | −321.013 | + | 441.837i | −0.333001 | + | 0.458337i | ||||
\(965\) | −1062.00 | − | 1461.72i | −1.10052 | − | 1.51474i | ||||
\(966\) | −138.751 | + | 427.032i | −0.143635 | + | 0.442062i | ||||
\(967\) | − | 1781.13i | − | 1.84191i | −0.389667 | − | 0.920956i | \(-0.627410\pi\) | ||
0.389667 | − | 0.920956i | \(-0.372590\pi\) | |||||||
\(968\) | −431.925 | − | 225.274i | −0.446204 | − | 0.232721i | ||||
\(969\) | 29.7797 | 0.0307324 | ||||||||
\(970\) | 746.216 | + | 242.460i | 0.769295 | + | 0.249959i | ||||
\(971\) | 801.707 | − | 582.474i | 0.825651 | − | 0.599870i | −0.0926749 | − | 0.995696i | \(-0.529542\pi\) |
0.918325 | + | 0.395826i | \(0.129542\pi\) | |||||||
\(972\) | −30.3910 | − | 22.0803i | −0.0312664 | − | 0.0227164i | ||||
\(973\) | 5.59892 | + | 17.2317i | 0.00575429 | + | 0.0177099i | ||||
\(974\) | 1054.19 | − | 342.526i | 1.08233 | − | 0.351670i | ||||
\(975\) | −555.668 | + | 764.812i | −0.569916 | + | 0.784423i | ||||
\(976\) | 1386.09 | + | 1907.78i | 1.42017 | + | 1.95470i | ||||
\(977\) | 233.282 | − | 717.969i | 0.238774 | − | 0.734871i | −0.757824 | − | 0.652459i | \(-0.773738\pi\) |
0.996598 | − | 0.0824121i | \(-0.0262624\pi\) | |||||||
\(978\) | − | 235.201i | − | 0.240492i | ||||||
\(979\) | −152.192 | − | 647.469i | −0.155457 | − | 0.661357i | ||||
\(980\) | 876.187 | 0.894069 | ||||||||
\(981\) | −231.868 | − | 75.3386i | −0.236359 | − | 0.0767978i | ||||
\(982\) | −1586.84 | + | 1152.91i | −1.61593 | + | 1.17404i | ||||
\(983\) | 167.072 | + | 121.385i | 0.169961 | + | 0.123484i | 0.669514 | − | 0.742799i | \(-0.266502\pi\) |
−0.499553 | + | 0.866283i | \(0.666502\pi\) | |||||||
\(984\) | −113.380 | − | 348.947i | −0.115223 | − | 0.354621i | ||||
\(985\) | −2221.80 | + | 721.908i | −2.25564 | + | 0.732901i | ||||
\(986\) | −74.3530 | + | 102.338i | −0.0754087 | + | 0.103791i | ||||
\(987\) | −40.2032 | − | 55.3350i | −0.0407327 | − | 0.0560638i | ||||
\(988\) | 74.2745 | − | 228.594i | 0.0751767 | − | 0.231370i | ||||
\(989\) | 1776.91i | 1.79667i | ||||||||
\(990\) | −58.7137 | + | 703.276i | −0.0593068 | + | 0.710380i | ||||
\(991\) | 852.133 | 0.859872 | 0.429936 | − | 0.902859i | \(-0.358536\pi\) | ||||
0.429936 | + | 0.902859i | \(0.358536\pi\) | |||||||
\(992\) | 707.562 | + | 229.901i | 0.713268 | + | 0.231755i | ||||
\(993\) | −380.738 | + | 276.622i | −0.383422 | + | 0.278572i | ||||
\(994\) | −30.1710 | − | 21.9205i | −0.0303531 | − | 0.0220528i | ||||
\(995\) | −205.709 | − | 633.106i | −0.206742 | − | 0.636288i | ||||
\(996\) | 119.749 | − | 38.9088i | 0.120230 | − | 0.0390651i | ||||
\(997\) | 686.595 | − | 945.017i | 0.688661 | − | 0.947861i | −0.311336 | − | 0.950300i | \(-0.600776\pi\) |
0.999997 | + | 0.00243927i | \(0.000776445\pi\) | |||||||
\(998\) | 390.055 | + | 536.864i | 0.390836 | + | 0.537940i | ||||
\(999\) | 25.6982 | − | 79.0910i | 0.0257240 | − | 0.0791702i |
(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 | 33.3.g.a.13.2 | ✓ | 16 | |
3.2 | odd | 2 | 99.3.k.c.46.3 | 16 | |||
4.3 | odd | 2 | 528.3.bf.b.145.1 | 16 | |||
11.2 | odd | 10 | 363.3.g.a.118.2 | 16 | |||
11.3 | even | 5 | 363.3.g.a.40.2 | 16 | |||
11.4 | even | 5 | 363.3.c.e.241.3 | 16 | |||
11.5 | even | 5 | 363.3.g.f.94.3 | 16 | |||
11.6 | odd | 10 | inner | 33.3.g.a.28.2 | yes | 16 | |
11.7 | odd | 10 | 363.3.c.e.241.14 | 16 | |||
11.8 | odd | 10 | 363.3.g.g.40.3 | 16 | |||
11.9 | even | 5 | 363.3.g.g.118.3 | 16 | |||
11.10 | odd | 2 | 363.3.g.f.112.3 | 16 | |||
33.17 | even | 10 | 99.3.k.c.28.3 | 16 | |||
33.26 | odd | 10 | 1089.3.c.m.604.14 | 16 | |||
33.29 | even | 10 | 1089.3.c.m.604.3 | 16 | |||
44.39 | even | 10 | 528.3.bf.b.193.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.13.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
33.3.g.a.28.2 | yes | 16 | 11.6 | odd | 10 | inner | |
99.3.k.c.28.3 | 16 | 33.17 | even | 10 | |||
99.3.k.c.46.3 | 16 | 3.2 | odd | 2 | |||
363.3.c.e.241.3 | 16 | 11.4 | even | 5 | |||
363.3.c.e.241.14 | 16 | 11.7 | odd | 10 | |||
363.3.g.a.40.2 | 16 | 11.3 | even | 5 | |||
363.3.g.a.118.2 | 16 | 11.2 | odd | 10 | |||
363.3.g.f.94.3 | 16 | 11.5 | even | 5 | |||
363.3.g.f.112.3 | 16 | 11.10 | odd | 2 | |||
363.3.g.g.40.3 | 16 | 11.8 | odd | 10 | |||
363.3.g.g.118.3 | 16 | 11.9 | even | 5 | |||
528.3.bf.b.145.1 | 16 | 4.3 | odd | 2 | |||
528.3.bf.b.193.1 | 16 | 44.39 | even | 10 | |||
1089.3.c.m.604.3 | 16 | 33.29 | even | 10 | |||
1089.3.c.m.604.14 | 16 | 33.26 | odd | 10 |