Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [92,2,Mod(9,92)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(92, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("92.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 92 = 2^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 92.e (of order \(11\), degree \(10\), 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: | \(0.734623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{11})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + 14788 x^{12} - 23925 x^{11} + 35080 x^{10} - 43945 x^{9} + 57269 x^{8} + \cdots + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 85.1 | ||
Root | \(-0.420431 + 0.123450i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 92.85 |
Dual form | 92.2.e.a.13.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/92\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(47\) |
\(\chi(n)\) | \(e\left(\frac{4}{11}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.368621 | + | 0.236898i | −0.212823 | + | 0.136773i | −0.642710 | − | 0.766110i | \(-0.722190\pi\) |
0.429887 | + | 0.902883i | \(0.358554\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.781296 | + | 1.71080i | 0.349406 | + | 0.765093i | 0.999984 | + | 0.00565324i | \(0.00179949\pi\) |
−0.650578 | + | 0.759440i | \(0.725473\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.72847 | − | 1.38840i | 1.78719 | − | 0.524767i | 0.790991 | − | 0.611828i | \(-0.209566\pi\) |
0.996203 | + | 0.0870608i | \(0.0277474\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.16648 | + | 2.55425i | −0.388828 | + | 0.851415i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.86466 | − | 3.30599i | −0.863727 | − | 0.996794i | −0.999981 | − | 0.00611985i | \(-0.998052\pi\) |
0.136255 | − | 0.990674i | \(-0.456493\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.72299 | − | 1.09317i | −1.03257 | − | 0.303190i | −0.278816 | − | 0.960345i | \(-0.589942\pi\) |
−0.753756 | + | 0.657154i | \(0.771760\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.693287 | − | 0.445548i | −0.179006 | − | 0.115040i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.170460 | + | 1.18558i | −0.0413426 | + | 0.287544i | 0.958653 | + | 0.284578i | \(0.0918534\pi\) |
−0.999996 | + | 0.00296653i | \(0.999056\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.220090 | − | 1.53076i | −0.0504922 | − | 0.351181i | −0.999369 | − | 0.0355329i | \(-0.988687\pi\) |
0.948876 | − | 0.315648i | \(-0.102222\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41410 | + | 1.63196i | −0.308582 | + | 0.356123i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.25781 | + | 2.20705i | −0.887815 | + | 0.460201i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.957892 | − | 1.10547i | 0.191578 | − | 0.221093i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.362184 | − | 2.51905i | −0.0697024 | − | 0.484790i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.772612 | − | 5.37364i | 0.143471 | − | 0.997859i | −0.783142 | − | 0.621843i | \(-0.786384\pi\) |
0.926613 | − | 0.376017i | \(-0.122707\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.63810 | − | 1.69540i | −0.473817 | − | 0.304504i | 0.281851 | − | 0.959458i | \(-0.409051\pi\) |
−0.755668 | + | 0.654954i | \(0.772688\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.83915 | + | 0.540024i | 0.320156 | + | 0.0940062i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.06962 | + | 7.00471i | 1.02595 | + | 1.18401i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.08028 | + | 2.36547i | −0.177596 | + | 0.388882i | −0.977406 | − | 0.211373i | \(-0.932207\pi\) |
0.799809 | + | 0.600254i | \(0.204934\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.63134 | − | 0.479005i | 0.261224 | − | 0.0767022i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.38557 | + | 9.60306i | 0.684911 | + | 1.49975i | 0.857354 | + | 0.514727i | \(0.172107\pi\) |
−0.172443 | + | 0.985019i | \(0.555166\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.09254 | − | 2.63012i | 0.624107 | − | 0.401089i | −0.190017 | − | 0.981781i | \(-0.560854\pi\) |
0.814123 | + | 0.580692i | \(0.197218\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.28117 | −0.787270 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.40483 | −0.350781 | −0.175391 | − | 0.984499i | \(-0.556119\pi\) | ||||
−0.175391 | + | 0.984499i | \(0.556119\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.5420 | − | 9.34557i | 2.07743 | − | 1.33508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.218025 | − | 0.477409i | −0.0305297 | − | 0.0668506i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.1568 | + | 2.98231i | −1.39514 | + | 0.409651i | −0.891014 | − | 0.453977i | \(-0.850005\pi\) |
−0.504130 | + | 0.863628i | \(0.668187\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.41774 | − | 7.48381i | 0.460848 | − | 1.00912i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.443765 | + | 0.512132i | 0.0587781 | + | 0.0678335i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.25467 | + | 1.54291i | 0.684100 | + | 0.200870i | 0.605272 | − | 0.796018i | \(-0.293064\pi\) |
0.0788275 | + | 0.996888i | \(0.474882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.58911 | + | 5.51989i | 1.09972 | + | 0.706749i | 0.959030 | − | 0.283304i | \(-0.0914305\pi\) |
0.140693 | + | 0.990053i | \(0.455067\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.96936 | + | 13.6972i | −0.248116 | + | 1.72569i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.03857 | − | 7.22338i | −0.128818 | − | 0.895950i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.95204 | + | 8.02308i | −0.849327 | + | 0.980175i | −0.999965 | − | 0.00841372i | \(-0.997322\pi\) |
0.150638 | + | 0.988589i | \(0.451867\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.04667 | − | 1.82223i | 0.126004 | − | 0.219371i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.461121 | − | 0.532163i | 0.0547250 | − | 0.0631561i | −0.727727 | − | 0.685867i | \(-0.759423\pi\) |
0.782452 | + | 0.622711i | \(0.213969\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.964609 | − | 6.70901i | −0.112899 | − | 0.785230i | −0.965075 | − | 0.261974i | \(-0.915626\pi\) |
0.852176 | − | 0.523255i | \(-0.175283\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0912159 | + | 0.634420i | −0.0105327 | + | 0.0732565i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.1355 | − | 11.6550i | −2.06673 | − | 1.32821i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.13462 | − | 0.333154i | −0.127655 | − | 0.0374828i | 0.217281 | − | 0.976109i | \(-0.430281\pi\) |
−0.344936 | + | 0.938626i | \(0.612099\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.78628 | − | 5.52366i | −0.531809 | − | 0.613740i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.80407 | + | 6.14005i | −0.307786 | + | 0.673958i | −0.998805 | − | 0.0488792i | \(-0.984435\pi\) |
0.691018 | + | 0.722837i | \(0.257162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.16146 | + | 0.634662i | −0.234443 | + | 0.0688388i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.988203 | + | 2.16386i | 0.105947 | + | 0.231991i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.29920 | − | 5.97623i | 0.985713 | − | 0.633479i | 0.0547144 | − | 0.998502i | \(-0.482575\pi\) |
0.930999 | + | 0.365023i | \(0.118939\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.1218 | −2.00451 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.37410 | 0.142487 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.44687 | − | 1.57251i | 0.251044 | − | 0.161336i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.84506 | + | 8.41951i | 0.390407 | + | 0.854872i | 0.998154 | + | 0.0607409i | \(0.0193464\pi\) |
−0.607747 | + | 0.794131i | \(0.707926\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.7859 | − | 3.46065i | 1.18453 | − | 0.347808i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.68544 | − | 3.69059i | 0.167707 | − | 0.367228i | −0.807054 | − | 0.590478i | \(-0.798939\pi\) |
0.974761 | + | 0.223250i | \(0.0716666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.25438 | − | 4.90982i | −0.419197 | − | 0.483779i | 0.506395 | − | 0.862302i | \(-0.330978\pi\) |
−0.925592 | + | 0.378522i | \(0.876432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.89679 | − | 1.14420i | −0.380288 | − | 0.111662i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.61218 | − | 1.03608i | −0.155855 | − | 0.100162i | 0.460389 | − | 0.887717i | \(-0.347710\pi\) |
−0.616244 | + | 0.787555i | \(0.711346\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.90076 | + | 13.2201i | −0.182060 | + | 1.26625i | 0.669822 | + | 0.742522i | \(0.266370\pi\) |
−0.851882 | + | 0.523733i | \(0.824539\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.162164 | − | 1.12788i | −0.0153920 | − | 0.107053i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.82059 | + | 4.40920i | −0.359411 | + | 0.414782i | −0.906442 | − | 0.422330i | \(-0.861212\pi\) |
0.547031 | + | 0.837112i | \(0.315758\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.10242 | − | 5.55990i | −0.662304 | − | 0.518464i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.13503 | − | 8.23427i | 0.659634 | − | 0.761258i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.840043 | + | 5.84262i | 0.0770066 | + | 0.535592i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.15785 | + | 8.05302i | −0.105259 | + | 0.732093i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.89156 | − | 2.50095i | −0.350890 | − | 0.225503i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.6625 | + | 3.42442i | 1.04313 | + | 0.306290i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.93614 | + | 10.3129i | 0.792955 | + | 0.915118i | 0.997973 | − | 0.0636398i | \(-0.0202709\pi\) |
−0.205018 | + | 0.978758i | \(0.565725\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.885525 | + | 1.93903i | −0.0779662 | + | 0.170722i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0487 | − | 4.71232i | 1.40218 | − | 0.411718i | 0.508749 | − | 0.860915i | \(-0.330108\pi\) |
0.893433 | + | 0.449197i | \(0.148290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.16601 | − | 6.93259i | −0.274528 | − | 0.601132i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.02661 | − | 2.58774i | 0.346555 | − | 0.222718i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.3511 | 1.31154 | 0.655768 | − | 0.754963i | \(-0.272345\pi\) | ||||
0.655768 | + | 0.754963i | \(0.272345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.33601 | 0.791870 | 0.395935 | − | 0.918278i | \(-0.370420\pi\) | ||||
0.395935 | + | 0.918278i | \(0.370420\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.886472 | − | 0.569701i | 0.0746544 | − | 0.0479774i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.05109 | + | 15.4397i | 0.589642 | + | 1.29113i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.79685 | − | 2.87662i | 0.813585 | − | 0.238890i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.14653 | + | 6.88994i | −0.259521 | + | 0.568272i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.3736 | − | 15.4339i | −1.09561 | − | 1.26440i | −0.961908 | − | 0.273375i | \(-0.911860\pi\) |
−0.133699 | − | 0.991022i | \(-0.542685\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.1954 | − | 5.04901i | −1.39934 | − | 0.410883i | −0.506882 | − | 0.862016i | \(-0.669202\pi\) |
−0.892457 | + | 0.451133i | \(0.851020\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.82941 | − | 1.81835i | −0.228744 | − | 0.147005i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.839360 | − | 5.83788i | 0.0674190 | − | 0.468909i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.85221 | + | 12.8824i | 0.147823 | + | 1.02813i | 0.919774 | + | 0.392448i | \(0.128372\pi\) |
−0.771952 | + | 0.635681i | \(0.780719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.03750 | − | 3.50546i | 0.240890 | − | 0.278001i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.0687 | + | 16.3475i | −1.34520 | + | 1.28836i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.19935 | + | 4.84631i | −0.328919 | + | 0.379593i | −0.895988 | − | 0.444077i | \(-0.853532\pi\) |
0.567070 | + | 0.823670i | \(0.308077\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.513050 | + | 3.56834i | 0.0399409 | + | 0.277795i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.51397 | − | 24.4402i | 0.271919 | − | 1.89124i | −0.156527 | − | 0.987674i | \(-0.550030\pi\) |
0.428446 | − | 0.903567i | \(-0.359061\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.72935 | + | 1.11138i | 0.133027 | + | 0.0854911i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.16668 | + | 1.22345i | 0.318634 | + | 0.0935593i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.17919 | + | 5.97710i | 0.393766 | + | 0.454430i | 0.917668 | − | 0.397348i | \(-0.130070\pi\) |
−0.523902 | + | 0.851779i | \(0.675524\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.99453 | − | 6.55710i | 0.226365 | − | 0.495671i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.30249 | + | 0.676073i | −0.173066 | + | 0.0508167i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.49842 | + | 3.28107i | 0.111997 | + | 0.245239i | 0.957328 | − | 0.289004i | \(-0.0933240\pi\) |
−0.845331 | + | 0.534243i | \(0.820597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.707821 | + | 0.454889i | −0.0526119 | + | 0.0338116i | −0.566682 | − | 0.823936i | \(-0.691773\pi\) |
0.514070 | + | 0.857748i | \(0.328137\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.47378 | −0.330711 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.89087 | −0.359584 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.40781 | − | 2.83273i | 0.322331 | − | 0.207150i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.21003 | − | 11.4084i | −0.378974 | − | 0.829837i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2099 | + | 2.99788i | −0.738759 | + | 0.216919i | −0.629398 | − | 0.777083i | \(-0.716699\pi\) |
−0.109361 | + | 0.994002i | \(0.534880\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.62373 | + | 12.3142i | −0.404805 | + | 0.886399i | 0.591956 | + | 0.805970i | \(0.298356\pi\) |
−0.996760 | + | 0.0804281i | \(0.974371\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.09404 | + | 2.41665i | 0.149957 | + | 0.173060i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.29705 | + | 1.84898i | 0.448646 | + | 0.131734i | 0.498248 | − | 0.867035i | \(-0.333977\pi\) |
−0.0496017 | + | 0.998769i | \(0.515795\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7385 | − | 9.47187i | −1.04479 | − | 0.671443i | −0.0986200 | − | 0.995125i | \(-0.531443\pi\) |
−0.946166 | + | 0.323682i | \(0.895079\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.662012 | − | 4.60440i | 0.0466947 | − | 0.324769i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.80751 | − | 26.4818i | −0.267234 | − | 1.85866i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.0025 | + | 15.0057i | −0.908133 | + | 1.04804i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.670664 | − | 13.4500i | −0.0466144 | − | 0.934838i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.43020 | + | 5.11273i | −0.306444 | + | 0.353655i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.413560 | + | 2.87637i | 0.0284706 | + | 0.198017i | 0.999093 | − | 0.0425924i | \(-0.0135617\pi\) |
−0.970622 | + | 0.240610i | \(0.922653\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0439106 | + | 0.305405i | −0.00300870 | + | 0.0209260i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.69709 | + | 4.94662i | 0.524937 | + | 0.337357i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.8281 | − | 4.35392i | −1.00660 | − | 0.295563i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.94493 | + | 2.24456i | 0.131426 | + | 0.151674i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.93065 | − | 4.22754i | 0.129870 | − | 0.284375i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.98602 | + | 2.63853i | −0.601748 | + | 0.176689i | −0.568397 | − | 0.822755i | \(-0.692436\pi\) |
−0.0333512 | + | 0.999444i | \(0.510618\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.70627 | + | 3.73620i | 0.113751 | + | 0.249080i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.5483 | + | 9.99227i | −1.03197 | + | 0.663210i | −0.942989 | − | 0.332823i | \(-0.891999\pi\) |
−0.0889855 | + | 0.996033i | \(0.528362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.98568 | 0.527709 | 0.263854 | − | 0.964563i | \(-0.415006\pi\) | ||||
0.263854 | + | 0.964563i | \(0.415006\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.44616 | 0.621512 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.03131 | + | 2.59077i | −0.264100 | + | 0.169727i | −0.665989 | − | 0.745962i | \(-0.731990\pi\) |
0.401889 | + | 0.915688i | \(0.368354\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.87889 | − | 4.11419i | −0.122565 | − | 0.268380i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.497167 | − | 0.145982i | 0.0322945 | − | 0.00948252i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.35978 | − | 9.54659i | 0.282011 | − | 0.617517i | −0.714622 | − | 0.699511i | \(-0.753401\pi\) |
0.996633 | + | 0.0819934i | \(0.0261286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.200330 | − | 0.231193i | −0.0129044 | − | 0.0148924i | 0.749261 | − | 0.662275i | \(-0.230409\pi\) |
−0.762165 | + | 0.647383i | \(0.775864\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.3984 | + | 3.05326i | 0.667061 | + | 0.195867i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.3500 | + | 17.5768i | 1.74733 | + | 1.12294i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.853987 | + | 5.93961i | −0.0543379 | + | 0.377929i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.420929 | − | 2.92763i | −0.0266753 | − | 0.185531i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.59046 | − | 11.0680i | 0.605345 | − | 0.698605i | −0.367511 | − | 0.930019i | \(-0.619790\pi\) |
0.972855 | + | 0.231414i | \(0.0743353\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.4936 | + | 7.75385i | 1.22555 | + | 0.487481i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.646409 | − | 0.745995i | 0.0404797 | − | 0.0467161i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.87846 | − | 26.9753i | −0.241932 | − | 1.68267i | −0.642405 | − | 0.766365i | \(-0.722063\pi\) |
0.400473 | − | 0.916309i | \(-0.368846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.82382 | + | 12.6849i | −0.113327 | + | 0.788203i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.8243 | + | 8.24171i | 0.793807 | + | 0.510149i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.56887 | − | 2.22242i | −0.466717 | − | 0.137040i | 0.0399148 | − | 0.999203i | \(-0.487291\pi\) |
−0.506631 | + | 0.862163i | \(0.669110\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.0376 | − | 15.0462i | −0.800893 | − | 0.924280i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.01212 | + | 4.40592i | −0.123140 | + | 0.269638i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.92411 | + | 1.15222i | −0.239257 | + | 0.0702523i | −0.399163 | − | 0.916880i | \(-0.630699\pi\) |
0.159906 | + | 0.987132i | \(0.448881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.94666 | + | 21.7801i | 0.604216 | + | 1.32305i | 0.926460 | + | 0.376393i | \(0.122836\pi\) |
−0.322244 | + | 0.946657i | \(0.604437\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.04869 | − | 4.52992i | 0.426606 | − | 0.274163i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.39869 | −0.385856 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.86931 | −0.412737 | −0.206368 | − | 0.978474i | \(-0.566165\pi\) | ||||
−0.206368 | + | 0.978474i | \(0.566165\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.40778 | − | 4.76069i | 0.443492 | − | 0.285015i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.09904 | − | 11.1653i | −0.304183 | − | 0.666069i | 0.694382 | − | 0.719606i | \(-0.255678\pi\) |
−0.998566 | + | 0.0535373i | \(0.982950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.44911 | + | 0.719124i | −0.145585 | + | 0.0427475i | −0.353713 | − | 0.935354i | \(-0.615081\pi\) |
0.208128 | + | 0.978102i | \(0.433263\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.529443 | + | 1.15932i | −0.0313615 | + | 0.0686721i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.0700 | + | 39.3188i | 2.01109 | + | 2.32092i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9348 | + | 4.38527i | 0.878521 | + | 0.257957i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.41194 | − | 2.19272i | −0.200011 | − | 0.128539i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.943729 | − | 6.56378i | 0.0551333 | − | 0.383460i | −0.943508 | − | 0.331350i | \(-0.892496\pi\) |
0.998641 | − | 0.0521107i | \(-0.0165949\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.46584 | + | 10.1952i | 0.0853447 | + | 0.593585i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.29041 | + | 8.41358i | −0.423032 | + | 0.488205i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.2645 | − | 3.56230i | 1.05626 | − | 0.206013i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6998 | − | 18.1185i | 0.904921 | − | 1.04433i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.253008 | + | 1.75971i | 0.0145349 | + | 0.101092i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.73278 | + | 19.0069i | −0.156479 | + | 1.08833i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.69823 | − | 2.37671i | −0.211069 | − | 0.135646i | 0.430835 | − | 0.902431i | \(-0.358219\pi\) |
−0.641904 | + | 0.766785i | \(0.721855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.73138 | + | 0.802006i | 0.155383 | + | 0.0456245i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0320 | − | 12.7317i | −0.625570 | − | 0.721946i | 0.351185 | − | 0.936306i | \(-0.385779\pi\) |
−0.976755 | + | 0.214360i | \(0.931233\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.67930 | − | 5.86686i | 0.151443 | − | 0.331614i | −0.818671 | − | 0.574263i | \(-0.805289\pi\) |
0.970114 | + | 0.242648i | \(0.0780161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.9719 | + | 7.33240i | −1.40700 | + | 0.413134i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.7314 | − | 27.8778i | −0.715064 | − | 1.56577i | −0.820694 | − | 0.571367i | \(-0.806413\pi\) |
0.105630 | − | 0.994406i | \(-0.466314\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.9785 | + | 12.8394i | −1.11858 | + | 0.718867i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.839728 | 0.0468690 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.85235 | 0.103068 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.77468 | + | 3.06850i | −0.264852 | + | 0.170210i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.43115 | − | 5.32348i | −0.134443 | − | 0.294389i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3712 | + | 3.33888i | −0.626914 | + | 0.184079i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6296 | − | 27.6549i | 0.694184 | − | 1.52005i | −0.152700 | − | 0.988273i | \(-0.548797\pi\) |
0.846884 | − | 0.531778i | \(-0.178476\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.78187 | − | 5.51858i | −0.262045 | − | 0.302416i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.1575 | − | 5.62514i | −1.04669 | − | 0.307334i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.2067 | − | 11.7007i | −0.991781 | − | 0.637379i | −0.0591647 | − | 0.998248i | \(-0.518844\pi\) |
−0.932616 | + | 0.360869i | \(0.882480\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.363818 | − | 2.53041i | 0.0197599 | − | 0.137433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.95226 | + | 13.5783i | 0.105721 | + | 0.735306i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 33.1954 | − | 38.3096i | 1.79238 | − | 2.06852i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.93523 | + | 0.366945i | 0.211866 | + | 0.0197557i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.7458 | + | 14.7094i | −0.684229 | + | 0.789642i | −0.986532 | − | 0.163569i | \(-0.947699\pi\) |
0.302303 | + | 0.953212i | \(0.402245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.04180 | + | 21.1562i | 0.162824 | + | 1.13247i | 0.893278 | + | 0.449504i | \(0.148399\pi\) |
−0.730454 | + | 0.682962i | \(0.760692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.40533 | + | 9.77431i | −0.0750112 | + | 0.521714i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.94762 | + | 3.17964i | 0.263335 | + | 0.169235i | 0.665645 | − | 0.746268i | \(-0.268156\pi\) |
−0.402310 | + | 0.915503i | \(0.631793\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.27070 | + | 0.373110i | 0.0674415 | + | 0.0198026i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.69376 | − | 1.95471i | −0.0896435 | − | 0.103454i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.7559 | + | 25.7417i | −0.620450 | + | 1.35860i | 0.294741 | + | 0.955577i | \(0.404767\pi\) |
−0.915191 | + | 0.403020i | \(0.867961\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9356 | − | 4.67911i | 0.838714 | − | 0.246269i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.48094 | − | 3.24280i | −0.0777291 | − | 0.170203i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.7241 | − | 6.89197i | 0.561326 | − | 0.360742i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.82639 | 0.408534 | 0.204267 | − | 0.978915i | \(-0.434519\pi\) | ||||
0.204267 | + | 0.978915i | \(0.434519\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −29.6443 | −1.54322 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −43.8855 | + | 28.2035i | −2.27842 | + | 1.46425i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.01953 | − | 10.9912i | −0.259901 | − | 0.569105i | 0.734029 | − | 0.679118i | \(-0.237638\pi\) |
−0.993930 | + | 0.110014i | \(0.964910\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.11028 | + | 1.50051i | −0.263894 | + | 0.0774862i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.75072 | + | 19.1614i | −0.450685 | + | 0.986863i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.29294 | − | 6.10838i | −0.271880 | − | 0.313766i | 0.603347 | − | 0.797479i | \(-0.293833\pi\) |
−0.875227 | + | 0.483713i | \(0.839288\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.73714 | − | 1.68458i | −0.293923 | − | 0.0863035i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.34988 | + | 0.867513i | 0.0689755 | + | 0.0443279i | 0.574674 | − | 0.818382i | \(-0.305129\pi\) |
−0.505699 | + | 0.862710i | \(0.668765\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.77014 | − | 40.1322i | 0.294073 | − | 2.04533i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.94408 | + | 13.5213i | 0.0988229 | + | 0.687329i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.4321 | − | 13.1934i | 0.579632 | − | 0.668930i | −0.387894 | − | 0.921704i | \(-0.626797\pi\) |
0.967525 | + | 0.252774i | \(0.0813428\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.89083 | − | 5.42417i | −0.0956235 | − | 0.274312i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.79954 | + | 5.53897i | −0.242105 | + | 0.279404i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.316513 | − | 2.20140i | −0.0159255 | − | 0.110764i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.43126 | − | 16.9098i | 0.122021 | − | 0.848677i | −0.833239 | − | 0.552912i | \(-0.813516\pi\) |
0.955261 | − | 0.295765i | \(-0.0955744\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.80937 | + | 1.80547i | 0.140645 | + | 0.0903868i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.01219 | + | 0.297205i | 0.0505463 | + | 0.0148417i | 0.306908 | − | 0.951739i | \(-0.400706\pi\) |
−0.256362 | + | 0.966581i | \(0.582524\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.96826 | + | 9.19587i | 0.396927 | + | 0.458079i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.71037 | − | 12.5040i | 0.283751 | − | 0.621328i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.9149 | − | 3.20489i | 0.541029 | − | 0.158861i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.51568 | − | 18.6467i | −0.421073 | − | 0.922022i | −0.994692 | − | 0.102899i | \(-0.967188\pi\) |
0.573619 | − | 0.819123i | \(-0.305539\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.65874 | + | 3.63665i | −0.279125 | + | 0.179383i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.9887 | 1.32803 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.6952 | −0.623183 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.44145 | + | 2.21168i | −0.168528 | + | 0.108307i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.76828 | + | 17.0102i | 0.379505 | + | 0.831000i | 0.998944 | + | 0.0459551i | \(0.0146331\pi\) |
−0.619438 | + | 0.785045i | \(0.712640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.92934 | + | 0.566505i | −0.0940303 | + | 0.0276098i | −0.328409 | − | 0.944536i | \(-0.606513\pi\) |
0.234379 | + | 0.972145i | \(0.424694\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.80520 | − | 6.14254i | 0.136394 | − | 0.298660i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.14733 | + | 1.32409i | 0.0556537 | + | 0.0642278i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.2772 | + | 14.1755i | 2.33630 | + | 0.685999i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.25682 | − | 4.02101i | −0.302082 | − | 0.194136i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.08461 | − | 14.4988i | 0.100412 | − | 0.698383i | −0.875975 | − | 0.482356i | \(-0.839781\pi\) |
0.976387 | − | 0.216027i | \(-0.0693099\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.18739 | + | 36.0791i | 0.249290 | + | 1.73385i | 0.602333 | + | 0.798245i | \(0.294238\pi\) |
−0.353043 | + | 0.935607i | \(0.614853\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.92986 | + | 3.38124i | −0.140476 | + | 0.162118i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.31557 | + | 6.03195i | 0.206442 | + | 0.288547i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.9843 | + | 14.9846i | −0.619705 | + | 0.715178i | −0.975651 | − | 0.219328i | \(-0.929613\pi\) |
0.355946 | + | 0.934507i | \(0.384159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.90787 | + | 48.0453i | 0.328946 | + | 2.28787i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.130477 | + | 0.907490i | −0.00619917 | + | 0.0431161i | −0.992686 | − | 0.120723i | \(-0.961479\pi\) |
0.986487 | + | 0.163839i | \(0.0523878\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.4896 | + | 11.2399i | 0.829085 | + | 0.532820i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.58604 | + | 2.52109i | 0.406106 | + | 0.119243i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1257 | − | 20.9182i | −0.855404 | − | 0.987189i | 0.144593 | − | 0.989491i | \(-0.453813\pi\) |
−0.999997 | + | 0.00230182i | \(0.999267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1845 | − | 42.0081i | 0.903362 | − | 1.97809i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.53466 | − | 2.21238i | 0.354009 | − | 0.103947i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.9398 | − | 32.7136i | −0.700388 | − | 1.53364i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.915093 | − | 0.588094i | 0.0428062 | − | 0.0275099i | −0.519063 | − | 0.854736i | \(-0.673719\pi\) |
0.561869 | + | 0.827226i | \(0.310083\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.04826 | 0.142280 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.7366 | 1.24525 | 0.622624 | − | 0.782521i | \(-0.286066\pi\) | ||||
0.622624 | + | 0.782521i | \(0.286066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.7874 | + | 11.4312i | −0.826649 | + | 0.531255i | −0.884211 | − | 0.467087i | \(-0.845303\pi\) |
0.0575626 | + | 0.998342i | \(0.481667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.07358 | + | 2.35080i | 0.0497859 | + | 0.109016i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.0957 | − | 7.07515i | 1.11502 | − | 0.327399i | 0.328215 | − | 0.944603i | \(-0.393553\pi\) |
0.786803 | + | 0.617204i | \(0.211735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.7332 | + | 47.5891i | −1.00355 | + | 2.19746i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.73458 | − | 4.30994i | −0.172081 | − | 0.198592i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.4189 | − | 5.99552i | −0.938861 | − | 0.275674i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.90303 | − | 1.22300i | −0.0873170 | − | 0.0561152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.23021 | − | 29.4218i | 0.193688 | − | 1.34713i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.465539 | + | 3.23790i | 0.0212710 | + | 0.147943i | 0.997689 | − | 0.0679453i | \(-0.0216443\pi\) |
−0.976418 | + | 0.215888i | \(0.930735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.60772 | − | 7.62571i | 0.301286 | − | 0.347703i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.41917 | − | 10.0696i | 0.110076 | − | 0.458181i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.4000 | + | 13.1563i | −0.517646 | + | 0.597395i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.07399 | + | 7.46975i | 0.0486670 | + | 0.338487i | 0.999579 | + | 0.0290243i | \(0.00924001\pi\) |
−0.950912 | + | 0.309462i | \(0.899851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.399886 | − | 2.78127i | 0.0180835 | − | 0.125773i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.8706 | + | 16.6260i | 1.16753 | + | 0.750323i | 0.973052 | − | 0.230585i | \(-0.0740640\pi\) |
0.194473 | + | 0.980908i | \(0.437700\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.23915 | + | 1.83198i | 0.280997 | + | 0.0825082i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.1287 | + | 17.4595i | 0.679987 | + | 0.784746i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.44154 | − | 3.15654i | 0.0646620 | − | 0.141590i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8788 | − | 3.19429i | 0.487000 | − | 0.142996i | −0.0290090 | − | 0.999579i | \(-0.509235\pi\) |
0.516009 | + | 0.856583i | \(0.327417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.49452 | + | 9.84162i | 0.200800 | + | 0.439691i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.248763 | − | 0.159871i | 0.0110918 | − | 0.00712828i | −0.535083 | − | 0.844799i | \(-0.679720\pi\) |
0.546175 | + | 0.837671i | \(0.316083\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.63069 | 0.339561 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.900758 | −0.0400041 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.5602 | + | 17.7118i | −1.22158 | + | 0.785064i | −0.982559 | − | 0.185950i | \(-0.940464\pi\) |
−0.239024 | + | 0.971014i | \(0.576827\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8759 | − | 30.3841i | −0.613835 | − | 1.34411i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.77635 | + | 1.10884i | −0.166730 | + | 0.0489563i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.07579 | − | 11.1144i | 0.223666 | − | 0.489760i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.88903 | + | 7.95036i | 0.302979 | + | 0.349656i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.32512 | − | 0.976343i | −0.145956 | − | 0.0428567i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.1264 | + | 17.4331i | 1.18843 | + | 0.763758i | 0.976917 | − | 0.213617i | \(-0.0685246\pi\) |
0.211513 | + | 0.977375i | \(0.432161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.486415 | + | 3.38309i | −0.0212695 | + | 0.147932i | −0.997689 | − | 0.0679508i | \(-0.978354\pi\) |
0.976419 | + | 0.215883i | \(0.0692630\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.449520 | + | 3.12648i | 0.0196187 | + | 0.136451i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.45972 | − | 2.83867i | 0.107147 | − | 0.123654i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.2579 | − | 18.7944i | 0.576431 | − | 0.817146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0705 | + | 11.6219i | −0.437021 | + | 0.504349i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.82967 | − | 40.5463i | −0.252511 | − | 1.75625i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.512944 | − | 3.56760i | 0.0221765 | − | 0.154241i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.32963 | − | 0.854500i | −0.0573777 | − | 0.0368744i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −72.5542 | − | 21.3038i | −3.12513 | − | 0.917621i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.3348 | − | 23.4676i | −0.874261 | − | 1.00895i | −0.999858 | − | 0.0168698i | \(-0.994630\pi\) |
0.125597 | − | 0.992081i | \(-0.459916\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.153155 | − | 0.335363i | 0.00657251 | − | 0.0143918i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.1020 | + | 7.07698i | −1.03242 | + | 0.303145i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.67952 | − | 3.67764i | −0.0718111 | − | 0.157244i | 0.870322 | − | 0.492483i | \(-0.163910\pi\) |
−0.942133 | + | 0.335238i | \(0.891183\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.1182 | + | 15.4998i | −1.02934 | + | 0.661517i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.39581 | −0.357674 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.82756 | −0.247813 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.80287 | − | 1.15864i | 0.0765277 | − | 0.0491814i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.65168 | + | 14.5652i | 0.281841 | + | 0.617145i | 0.996615 | − | 0.0822100i | \(-0.0261978\pi\) |
−0.714774 | + | 0.699355i | \(0.753471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.1117 | + | 5.31806i | −0.766041 | + | 0.224930i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.953742 | + | 2.08840i | −0.0402670 | + | 0.0881724i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.7618 | + | 18.1901i | 0.664282 | + | 0.766622i | 0.983470 | − | 0.181069i | \(-0.0579559\pi\) |
−0.319189 | + | 0.947691i | \(0.603410\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.5283 | − | 3.09138i | −0.442927 | − | 0.130055i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −30.3008 | − | 19.4732i | −1.27252 | − | 0.817796i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.07405 | + | 21.3805i | −0.128871 | + | 0.896315i | 0.818118 | + | 0.575050i | \(0.195017\pi\) |
−0.946989 | + | 0.321266i | \(0.895892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.76443 | − | 33.1373i | −0.199385 | − | 1.38675i | −0.806074 | − | 0.591815i | \(-0.798412\pi\) |
0.606689 | − | 0.794939i | \(-0.292497\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.05337 | − | 3.52378i | 0.127556 | − | 0.147208i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.63871 | + | 6.82098i | −0.0683389 | + | 0.284454i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.4595 | − | 16.6872i | 0.601958 | − | 0.694697i | −0.370219 | − | 0.928945i | \(-0.620717\pi\) |
0.972177 | + | 0.234248i | \(0.0752628\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.844199 | − | 5.87153i | −0.0350837 | − | 0.244013i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.73408 | + | 32.9262i | −0.196403 | + | 1.36601i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.9552 | + | 25.0350i | 1.61336 | + | 1.03684i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.6618 | + | 5.77321i | 0.812913 | + | 0.238693i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.0521 | − | 24.2955i | −0.868915 | − | 1.00278i | −0.999935 | − | 0.0114017i | \(-0.996371\pi\) |
0.131020 | − | 0.991380i | \(-0.458175\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.01464 | + | 4.41145i | −0.0830119 | + | 0.181771i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.75924 | + | 0.810186i | −0.113500 | + | 0.0333266i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.32781 | + | 2.90751i | 0.0545268 | + | 0.119397i | 0.934934 | − | 0.354821i | \(-0.115458\pi\) |
−0.880408 | + | 0.474218i | \(0.842731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.33924 | + | 6.00196i | −0.382871 | + | 0.246056i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.67679 | 0.314190 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.8422 | 1.05588 | 0.527942 | − | 0.849280i | \(-0.322964\pi\) | ||||
0.527942 | + | 0.849280i | \(0.322964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.8313 | − | 13.3874i | 0.849725 | − | 0.546085i | −0.0417643 | − | 0.999127i | \(-0.513298\pi\) |
0.891489 | + | 0.453043i | \(0.149661\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.3835 | − | 27.1160i | −0.504294 | − | 1.10425i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.6817 | + | 4.31095i | −0.596897 | + | 0.175265i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.09301 | − | 13.3418i | 0.247308 | − | 0.541528i | −0.744745 | − | 0.667349i | \(-0.767429\pi\) |
0.992053 | + | 0.125820i | \(0.0401563\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.67701 | + | 8.85974i | 0.311088 | + | 0.359015i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.95318 | + | 2.62889i | 0.362207 | + | 0.106354i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.3237 | − | 13.0613i | −0.820867 | − | 0.527539i | 0.0614967 | − | 0.998107i | \(-0.480413\pi\) |
−0.882364 | + | 0.470568i | \(0.844049\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.23817 | − | 8.61166i | 0.0499278 | − | 0.347256i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.991474 | + | 6.89585i | 0.0399152 | + | 0.277617i | 0.999998 | − | 0.00210023i | \(-0.000668525\pi\) |
−0.960083 | + | 0.279717i | \(0.909759\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.1549 | + | 11.7194i | −0.408160 | + | 0.471042i | −0.922194 | − | 0.386728i | \(-0.873605\pi\) |
0.514034 | + | 0.857770i | \(0.328151\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.10176 | + | 9.92626i | 0.284984 | + | 0.398327i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.6736 | − | 41.1695i | 1.42923 | − | 1.64942i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.21252 | + | 15.3884i | 0.0885009 | + | 0.615538i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.421869 | − | 2.93416i | 0.0168478 | − | 0.117179i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.62030 | − | 1.68397i | −0.104478 | − | 0.0671442i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.0925 | + | 7.95506i | 1.07853 | + | 0.316686i | 0.772292 | − | 0.635268i | \(-0.219110\pi\) |
0.306242 | + | 0.951954i | \(0.400928\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.833853 | − | 0.962318i | −0.0331427 | − | 0.0382487i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.6615 | + | 23.3453i | −0.423087 | + | 0.926432i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −64.3560 | + | 18.8966i | −2.54988 | + | 0.748711i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.821382 | + | 1.79858i | 0.0324934 | + | 0.0711506i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.94192 | + | 5.74662i | −0.353185 | + | 0.226978i | −0.705187 | − | 0.709021i | \(-0.749137\pi\) |
0.352003 | + | 0.935999i | \(0.385501\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.25974 | 0.128551 | 0.0642757 | − | 0.997932i | \(-0.479526\pi\) | ||||
0.0642757 | + | 0.997932i | \(0.479526\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.00915 | −0.157860 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.6085 | + | 8.74564i | −0.535005 | + | 0.343827i | −0.780082 | − | 0.625677i | \(-0.784823\pi\) |
0.245078 | + | 0.969503i | \(0.421187\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.95198 | − | 21.7918i | −0.390650 | − | 0.855403i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.49737 | − | 1.90780i | 0.254652 | − | 0.0747726i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.69174 | − | 16.8426i | 0.301001 | − | 0.659100i | −0.697336 | − | 0.716744i | \(-0.745632\pi\) |
0.998337 | + | 0.0576440i | \(0.0183588\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.6006 | + | 23.7744i | 0.804933 | + | 0.928942i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.2616 | + | 5.36210i | 0.712455 | + | 0.209196i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.1248 | + | 16.1467i | 0.978724 | + | 0.628988i | 0.929119 | − | 0.369781i | \(-0.120567\pi\) |
0.0496051 | + | 0.998769i | \(0.484204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.53664 | + | 10.6876i | −0.0597685 | + | 0.415699i | 0.937868 | + | 0.346991i | \(0.112797\pi\) |
−0.997637 | + | 0.0687078i | \(0.978112\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.289818 | + | 2.01573i | 0.0112556 | + | 0.0782844i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.38669 | − | 10.8328i | 0.364000 | − | 0.420078i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.57022 | + | 24.5851i | 0.331840 | + | 0.951940i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.68737 | − | 3.10139i | 0.103900 | − | 0.119907i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.35617 | − | 44.2081i | −0.245377 | − | 1.70664i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.42944 | + | 9.94197i | −0.0551008 | + | 0.383235i | 0.943547 | + | 0.331240i | \(0.107467\pi\) |
−0.998647 | + | 0.0519947i | \(0.983442\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.13165 | − | 2.01259i | −0.120537 | − | 0.0774647i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.79281 | − | 1.99455i | −0.261069 | − | 0.0766567i | 0.148579 | − | 0.988901i | \(-0.452530\pi\) |
−0.409648 | + | 0.912244i | \(0.634348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.8709 | + | 34.4729i | 1.14634 | + | 1.32295i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.36426 | − | 7.36671i | 0.128919 | − | 0.282293i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.3356 | − | 8.61372i | 1.12250 | − | 0.329595i | 0.332742 | − | 0.943018i | \(-0.392026\pi\) |
0.789754 | + | 0.613423i | \(0.210208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.9938 | + | 26.2627i | 0.458259 | + | 1.00345i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.94369 | + | 1.89179i | −0.112309 | + | 0.0721764i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41.0738 | 1.56479 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.7392 | −1.47371 | −0.736854 | − | 0.676052i | \(-0.763690\pi\) | ||||
−0.736854 | + | 0.676052i | \(0.763690\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 50.9244 | − | 32.7272i | 1.93446 | − | 1.24320i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.29419 | + | 15.9720i | 0.276684 | + | 0.605854i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.1327 | + | 3.56249i | −0.459559 | + | 0.134939i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.872276 | − | 1.91002i | 0.0329925 | − | 0.0722436i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.49305 | + | 7.49338i | 0.245239 | + | 0.283021i | 0.865002 | − | 0.501768i | \(-0.167317\pi\) |
−0.619763 | + | 0.784789i | \(0.712771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.85874 | + | 1.13303i | 0.145535 | + | 0.0427330i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.66724 | + | 1.07147i | 0.0627919 | + | 0.0403539i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.84551 | − | 19.7909i | 0.107016 | − | 0.744315i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.17957 | − | 42.9799i | −0.232079 | − | 1.61414i | −0.689085 | − | 0.724680i | \(-0.741988\pi\) |
0.457007 | − | 0.889463i | \(-0.348922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.17447 | − | 2.50948i | 0.0815491 | − | 0.0941127i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.9744 | + | 1.39630i | 0.560795 | + | 0.0522920i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.9053 | + | 24.1260i | −0.781814 | + | 0.902261i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.654463 | + | 4.55189i | 0.0244414 | + | 0.169993i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.66577 | + | 18.5408i | −0.0994163 | + | 0.691455i | 0.877772 | + | 0.479079i | \(0.159029\pi\) |
−0.977188 | + | 0.212376i | \(0.931880\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.9335 | − | 17.3091i | −1.00306 | − | 0.644626i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.128615 | + | 0.0377647i | 0.00478324 | + | 0.00140449i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.20029 | − | 6.00146i | −0.193134 | − | 0.222889i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.2504 | + | 26.8247i | −0.454343 | + | 0.994872i | 0.534398 | + | 0.845233i | \(0.320538\pi\) |
−0.988741 | + | 0.149639i | \(0.952189\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.4820 | − | 4.83954i | 0.610443 | − | 0.179242i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.42059 | + | 5.30035i | 0.0895286 | + | 0.196040i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.0771 | + | 11.6174i | −0.667693 | + | 0.429100i | −0.830093 | − | 0.557625i | \(-0.811713\pi\) |
0.162400 | + | 0.986725i | \(0.448076\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.2457 | −0.525460 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 46.4394 | 1.71062 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.12581 | + | 4.57948i | −0.262127 | + | 0.168459i | −0.665103 | − | 0.746752i | \(-0.731612\pi\) |
0.402976 | + | 0.915211i | \(0.367976\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.09229 | − | 2.39177i | −0.0401261 | − | 0.0878639i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.0803 | + | 4.13436i | −0.516557 | + | 0.151675i | −0.529612 | − | 0.848240i | \(-0.677663\pi\) |
0.0130549 | + | 0.999915i | \(0.495844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.9556 | − | 34.9380i | 0.584569 | − | 1.28003i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.4123 | − | 14.3245i | −0.454142 | − | 0.524108i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.06164 | − | 2.66074i | −0.331105 | − | 0.0972212i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5806 | − | 13.2264i | −0.750998 | − | 0.482637i | 0.108296 | − | 0.994119i | \(-0.465460\pi\) |
−0.859294 | + | 0.511482i | \(0.829097\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.913258 | + | 6.35185i | −0.0332810 | + | 0.231474i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.79682 | − | 33.3626i | −0.174574 | − | 1.21419i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.25536 | + | 10.6813i | −0.336392 | + | 0.388217i | −0.898593 | − | 0.438784i | \(-0.855409\pi\) |
0.562201 | + | 0.827001i | \(0.309955\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.02263 | + | 1.75978i | −0.327501 | + | 0.0638758i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.37866 | + | 1.59106i | −0.0499765 | + | 0.0576759i | −0.780187 | − | 0.625546i | \(-0.784876\pi\) |
0.730211 | + | 0.683222i | \(0.239422\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.36713 | + | 65.1498i | 0.339113 | + | 2.35858i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.900228 | − | 6.26123i | 0.0325478 | − | 0.226375i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.8764 | − | 11.4885i | −0.645481 | − | 0.414825i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.1904 | + | 7.39656i | 0.908388 | + | 0.266727i | 0.702362 | − | 0.711820i | \(-0.252129\pi\) |
0.206026 | + | 0.978547i | \(0.433947\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.82008 | + | 9.02486i | 0.281633 | + | 0.325022i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.38626 | − | 16.1737i | 0.265665 | − | 0.581726i | −0.729043 | − | 0.684468i | \(-0.760034\pi\) |
0.994708 | + | 0.102742i | \(0.0327617\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.40123 | + | 1.29232i | −0.158097 | + | 0.0464214i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.33274 | − | 5.10799i | −0.0836865 | − | 0.183248i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.7348 | − | 8.82681i | 0.492100 | − | 0.316253i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.08028 | −0.110221 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.8163 | −0.493753 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.5921 | + | 13.2337i | −0.734964 | + | 0.472333i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.1874 | + | 28.8765i | 0.470082 | + | 1.02934i | 0.985073 | + | 0.172140i | \(0.0550681\pi\) |
−0.514991 | + | 0.857196i | \(0.672205\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.31653 | − | 0.973821i | 0.118072 | − | 0.0346689i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.9438 | + | 26.1533i | −0.424673 | + | 0.929903i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.9430 | − | 29.9398i | −0.921264 | − | 1.06320i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.37034 | + | 2.45775i | 0.296865 | + | 0.0871675i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.25548 | − | 4.66282i | −0.257002 | − | 0.165165i | 0.405795 | − | 0.913964i | \(-0.366995\pi\) |
−0.662798 | + | 0.748799i | \(0.730631\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.409928 | − | 2.85111i | 0.0145022 | − | 0.100865i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.41739 | + | 30.7236i | 0.156081 | + | 1.08557i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.4166 | + | 22.4080i | −0.685198 | + | 0.790761i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41.3030 | − | 16.4288i | −1.45574 | − | 0.579040i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.17355 | − | 1.35435i | 0.0413109 | − | 0.0476753i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.59346 | − | 24.9931i | −0.126339 | − | 0.878710i | −0.950138 | − | 0.311828i | \(-0.899059\pi\) |
0.823799 | − | 0.566882i | \(-0.191850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.24877 | − | 22.5957i | 0.114080 | − | 0.793442i | −0.849800 | − | 0.527105i | \(-0.823278\pi\) |
0.963880 | − | 0.266337i | \(-0.0858134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.82622 | − | 5.67227i | −0.309549 | − | 0.198935i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.5720 | − | 3.39785i | −0.405350 | − | 0.119021i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.92681 | − | 5.68585i | −0.172367 | − | 0.198923i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22.3053 | − | 48.8418i | 0.779410 | − | 1.70667i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.3969 | − | 4.81455i | 0.572254 | − | 0.168029i | 0.0172130 | − | 0.999852i | \(-0.494521\pi\) |
0.555041 | + | 0.831823i | \(0.312702\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.15836 | − | 13.4849i | −0.214667 | − | 0.470055i | 0.771411 | − | 0.636337i | \(-0.219551\pi\) |
−0.986078 | + | 0.166282i | \(0.946824\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.35869 | − | 1.51584i | 0.0821190 | − | 0.0527747i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.6981 | −1.24135 | −0.620673 | − | 0.784070i | \(-0.713141\pi\) | ||||
−0.620673 | + | 0.784070i | \(0.713141\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.6807 | −1.69075 | −0.845376 | − | 0.534172i | \(-0.820623\pi\) | ||||
−0.845376 | + | 0.534172i | \(0.820623\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.53217 | − | 1.62733i | 0.0878399 | − | 0.0564513i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.60105 | + | 18.8337i | 0.298009 | + | 0.652548i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.5578 | − | 13.0833i | 1.54199 | − | 0.452768i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.31532 | + | 7.25955i | −0.114594 | + | 0.250927i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.1538 | − | 30.1831i | −0.902930 | − | 1.04204i | −0.998911 | − | 0.0466532i | \(-0.985144\pi\) |
0.0959815 | − | 0.995383i | \(-0.469401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.453748 | − | 0.133232i | −0.0156465 | − | 0.00459422i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.52466 | + | 2.90782i | 0.155838 | + | 0.100151i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.550223 | + | 3.82689i | −0.0189283 | + | 0.131649i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.70599 | + | 39.6861i | 0.196060 | + | 1.36363i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.732434 | − | 0.845274i | 0.0251371 | − | 0.0290097i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.621098 | − | 12.4560i | −0.0212910 | − | 0.426985i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.9783 | + | 14.9777i | −0.444368 | + | 0.512828i | −0.933105 | − | 0.359603i | \(-0.882912\pi\) |
0.488738 | + | 0.872431i | \(0.337458\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.16234 | + | 8.08422i | 0.0397510 | + | 0.276475i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.96630 | − | 55.4068i | 0.272124 | − | 1.89266i | −0.154119 | − | 0.988052i | \(-0.549254\pi\) |
0.426243 | − | 0.904609i | \(-0.359837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.2351 | − | 14.2896i | −0.758650 | − | 0.487555i | 0.103236 | − | 0.994657i | \(-0.467080\pi\) |
−0.861886 | + | 0.507102i | \(0.830717\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.8734 | − | 6.42262i | −0.745445 | − | 0.218882i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.75417 | + | 4.33254i | 0.127793 | + | 0.147481i | 0.816040 | − | 0.577995i | \(-0.196165\pi\) |
−0.688247 | + | 0.725477i | \(0.741619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.17914 | + | 13.5304i | −0.210097 | + | 0.460049i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.54415 | + | 1.92154i | −0.222251 | + | 0.0652588i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.14889 | + | 4.70541i | 0.0728961 | + | 0.159620i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.6530 | − | 22.2701i | 1.17417 | − | 0.754594i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.9907 | −0.879652 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 59.9003 | 2.02500 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.4023 | − | 8.61310i | 0.452562 | − | 0.290844i | −0.294435 | − | 0.955672i | \(-0.595131\pi\) |
0.746997 | + | 0.664828i | \(0.231495\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.20707 | + | 2.64311i | 0.0407134 | + | 0.0891500i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.1413 | + | 3.56502i | −0.409052 | + | 0.120108i | −0.479783 | − | 0.877387i | \(-0.659285\pi\) |
0.0707316 | + | 0.997495i | \(0.477467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.1509 | + | 46.3141i | −0.711786 | + | 1.55859i | 0.113284 | + | 0.993563i | \(0.463863\pi\) |
−0.825070 | + | 0.565031i | \(0.808864\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.95555 | − | 3.41089i | −0.0993498 | − | 0.114656i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.6085 | − | 10.7492i | −1.22919 | − | 0.360923i | −0.398247 | − | 0.917278i | \(-0.630381\pi\) |
−0.830945 | + | 0.556355i | \(0.812200\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 56.5727 | + | 36.3571i | 1.89739 | + | 1.21938i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.55012 | + | 31.6468i | −0.152435 | + | 1.06021i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.529281 | + | 3.68123i | 0.0177117 | + | 0.123188i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.44255 | + | 5.12698i | −0.148498 | + | 0.171376i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.88875 | + | 5.63995i | −0.196620 | + | 0.188313i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.1487 | + | 12.8663i | −0.371831 | + | 0.429115i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.80442 | − | 12.5500i | −0.0601139 | − | 0.418102i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.49502 | + | 10.3981i | −0.0497512 | + | 0.346028i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.33124 | − | 0.855536i | −0.0442519 | − | 0.0284390i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.1722 | + | 14.7319i | 1.66594 | + | 0.489164i | 0.972802 | − | 0.231639i | \(-0.0744089\pi\) |
0.693139 | + | 0.720804i | \(0.256227\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.46064 | + | 8.61004i | 0.247454 | + | 0.285577i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.2870 | + | 40.0430i | −0.605876 | + | 1.32668i | 0.319484 | + | 0.947592i | \(0.396491\pi\) |
−0.925359 | + | 0.379091i | \(0.876237\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.3316 | − | 8.31892i | 0.937640 | − | 0.275316i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.49534 | − | 7.65373i | −0.115552 | − | 0.253025i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 69.3432 | − | 44.5642i | 2.28991 | − | 1.47164i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.28315 | 0.108301 | 0.0541506 | − | 0.998533i | \(-0.482755\pi\) | ||||
0.0541506 | + | 0.998533i | \(0.482755\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.92628 | 0.0634730 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.29849 | + | 1.47715i | −0.0756559 | + | 0.0486211i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.58016 | + | 3.46008i | 0.0519555 | + | 0.113767i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.5036 | − | 5.13951i | 0.574892 | − | 0.168804i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.83159 | − | 6.20032i | 0.0929015 | − | 0.203426i | −0.857477 | − | 0.514523i | \(-0.827969\pi\) |
0.950378 | + | 0.311097i | \(0.100696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.5064 | − | 20.2035i | −0.573749 | − | 0.662142i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.08274 | + | 2.07968i | 0.231878 | + | 0.0680857i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.29003 | + | 5.32768i | 0.271113 | + | 0.174234i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.62857 | + | 39.1475i | −0.183877 | + | 1.27889i | 0.663610 | + | 0.748079i | \(0.269023\pi\) |
−0.847487 | + | 0.530816i | \(0.821886\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.402201 | + | 2.79737i | 0.0131253 | + | 0.0912886i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.78856 | + | 2.06411i | −0.0583055 | + | 0.0672882i | −0.784153 | − | 0.620567i | \(-0.786902\pi\) |
0.725848 | + | 0.687856i | \(0.241448\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.8673 | − | 31.2089i | −1.29826 | − | 1.01630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.4469 | − | 17.8266i | 0.502487 | − | 0.579900i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.370338 | − | 2.57576i | −0.0120344 | − | 0.0837010i | 0.982919 | − | 0.184038i | \(-0.0589170\pi\) |
−0.994954 | + | 0.100337i | \(0.968008\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.74284 | + | 26.0320i | −0.121498 | + | 0.845036i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.2972 | + | 7.26029i | 0.366338 | + | 0.235431i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.8091 | − | 6.40372i | −0.706465 | − | 0.207437i | −0.0912867 | − | 0.995825i | \(-0.529098\pi\) |
−0.615179 | + | 0.788388i | \(0.710916\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.1057 | − | 15.1248i | −0.424090 | − | 0.489426i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.32285 | − | 9.46572i | 0.139738 | − | 0.305983i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 72.5873 | − | 21.3136i | 2.34397 | − | 0.688251i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.79268 | − | 19.2533i | −0.283635 | − | 0.621074i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.52699 | − | 2.90932i | 0.145880 | − | 0.0937516i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.4610 | −0.819618 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.9400 | 0.769858 | 0.384929 | − | 0.922946i | \(-0.374226\pi\) | ||||
0.384929 | + | 0.922946i | \(0.374226\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.682815 | + | 0.438818i | −0.0219352 | + | 0.0140969i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.2660 | + | 46.5659i | 0.682457 | + | 1.49437i | 0.860019 | + | 0.510262i | \(0.170452\pi\) |
−0.177562 | + | 0.984110i | \(0.556821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44.1451 | − | 12.9622i | 1.41523 | − | 0.415548i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.03312 | − | 2.26223i | 0.0330865 | − | 0.0724492i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.82983 | + | 4.41985i | 0.122527 | + | 0.141404i | 0.813699 | − | 0.581287i | \(-0.197451\pi\) |
−0.691172 | + | 0.722691i | \(0.742905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46.3964 | − | 13.6232i | −1.48283 | − | 0.435400i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.5501 | − | 20.2760i | −1.00732 | − | 0.647364i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.25276 | + | 36.5338i | −0.167537 | + | 1.16525i | 0.716417 | + | 0.697673i | \(0.245781\pi\) |
−0.883954 | + | 0.467574i | \(0.845128\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.75662 | + | 12.2176i | 0.0559707 | + | 0.389285i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.40068 | − | 3.92459i | 0.108245 | − | 0.124921i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.6205 | + | 20.2310i | −0.369510 | + | 0.643307i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.7157 | − | 29.6775i | 0.816885 | − | 0.942736i | −0.182294 | − | 0.983244i | \(-0.558352\pi\) |
0.999179 | + | 0.0405085i | \(0.0128978\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.89587 | + | 13.1861i | 0.0601637 | + | 0.418448i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.68933 | − | 32.6150i | 0.148662 | − | 1.03396i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.8118 | + | 16.5882i | 0.817468 | + | 0.525354i | 0.881273 | − | 0.472608i | \(-0.156687\pi\) |
−0.0638053 | + | 0.997962i | \(0.520324\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.34999 | + | 1.86453i | 0.200905 | + | 0.0589910i |
(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 | 92.2.e.a.85.1 | yes | 20 | |
3.2 | odd | 2 | 828.2.q.a.361.1 | 20 | |||
4.3 | odd | 2 | 368.2.m.d.177.2 | 20 | |||
23.6 | even | 11 | 2116.2.a.j.1.5 | 10 | |||
23.13 | even | 11 | inner | 92.2.e.a.13.1 | ✓ | 20 | |
23.17 | odd | 22 | 2116.2.a.i.1.5 | 10 | |||
69.59 | odd | 22 | 828.2.q.a.289.1 | 20 | |||
92.59 | odd | 22 | 368.2.m.d.289.2 | 20 | |||
92.63 | even | 22 | 8464.2.a.cd.1.6 | 10 | |||
92.75 | odd | 22 | 8464.2.a.ce.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
92.2.e.a.13.1 | ✓ | 20 | 23.13 | even | 11 | inner | |
92.2.e.a.85.1 | yes | 20 | 1.1 | even | 1 | trivial | |
368.2.m.d.177.2 | 20 | 4.3 | odd | 2 | |||
368.2.m.d.289.2 | 20 | 92.59 | odd | 22 | |||
828.2.q.a.289.1 | 20 | 69.59 | odd | 22 | |||
828.2.q.a.361.1 | 20 | 3.2 | odd | 2 | |||
2116.2.a.i.1.5 | 10 | 23.17 | odd | 22 | |||
2116.2.a.j.1.5 | 10 | 23.6 | even | 11 | |||
8464.2.a.cd.1.6 | 10 | 92.63 | even | 22 | |||
8464.2.a.ce.1.6 | 10 | 92.75 | odd | 22 |