Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(361,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.do (of order \(6\), degree \(2\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(1.21245 - 0.727987i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.361 |
Dual form | 819.2.do.e.667.1 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99469 | − | 1.15163i | −1.41046 | − | 0.814328i | −0.415026 | − | 0.909810i | \(-0.636227\pi\) |
−0.995431 | + | 0.0954820i | \(0.969561\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.65252 | + | 2.86225i | 0.826259 | + | 1.43112i | ||||
\(5\) | 0.733776 | − | 0.423646i | 0.328155 | − | 0.189460i | −0.326867 | − | 0.945070i | \(-0.605993\pi\) |
0.655022 | + | 0.755610i | \(0.272660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.09135 | − | 1.62057i | 0.790457 | − | 0.612517i | ||||
\(8\) | − | 3.00585i | − | 1.06273i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.95154 | −0.617131 | ||||||||
\(11\) | 1.50340i | 0.453293i | 0.973977 | + | 0.226646i | \(0.0727762\pi\) | ||||
−0.973977 | + | 0.226646i | \(0.927224\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.92329 | − | 2.11054i | −0.810774 | − | 0.585360i | ||||
\(14\) | −6.03790 | + | 0.824057i | −1.61370 | + | 0.220238i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.156597 | + | 0.271234i | −0.0391492 | + | 0.0678085i | ||||
\(17\) | −1.03570 | − | 1.79389i | −0.251194 | − | 0.435081i | 0.712661 | − | 0.701509i | \(-0.247490\pi\) |
−0.963855 | + | 0.266428i | \(0.914157\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0474272i | 0.0108805i | 0.999985 | + | 0.00544027i | \(0.00173170\pi\) | ||||
−0.999985 | + | 0.00544027i | \(0.998268\pi\) | |||||||
\(20\) | 2.42516 | + | 1.40016i | 0.542282 | + | 0.313086i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.73137 | − | 2.99882i | 0.369129 | − | 0.639350i | ||||
\(23\) | 3.90935 | − | 6.77119i | 0.815156 | − | 1.41189i | −0.0940598 | − | 0.995567i | \(-0.529984\pi\) |
0.909216 | − | 0.416325i | \(-0.136682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.14105 | + | 3.70840i | −0.428210 | + | 0.741681i | ||||
\(26\) | 3.40047 | + | 7.57643i | 0.666887 | + | 1.48586i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.09446 | + | 3.30795i | 1.52971 | + | 0.625143i | ||||
\(29\) | 0.679854 | + | 1.17754i | 0.126246 | + | 0.218664i | 0.922219 | − | 0.386668i | \(-0.126374\pi\) |
−0.795973 | + | 0.605331i | \(0.793041\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.80787 | + | 3.93052i | 1.22273 | + | 0.705943i | 0.965499 | − | 0.260407i | \(-0.0838567\pi\) |
0.257230 | + | 0.966350i | \(0.417190\pi\) | |||||||
\(32\) | −4.58156 | + | 2.64516i | −0.809912 | + | 0.467603i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.77099i | 0.818218i | ||||||||
\(35\) | 0.848038 | − | 2.07513i | 0.143345 | − | 0.350761i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.80427 | − | 3.35110i | −0.954216 | − | 0.550917i | −0.0598278 | − | 0.998209i | \(-0.519055\pi\) |
−0.894388 | + | 0.447292i | \(0.852388\pi\) | |||||||
\(38\) | 0.0546187 | − | 0.0946024i | 0.00886032 | − | 0.0153465i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.27341 | − | 2.20562i | −0.201345 | − | 0.348739i | ||||
\(41\) | 8.67622 | − | 5.00922i | 1.35500 | − | 0.782309i | 0.366054 | − | 0.930594i | \(-0.380709\pi\) |
0.988945 | + | 0.148285i | \(0.0473754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.63283 | − | 8.02430i | 0.706500 | − | 1.22369i | −0.259647 | − | 0.965704i | \(-0.583606\pi\) |
0.966147 | − | 0.257991i | \(-0.0830604\pi\) | |||||||
\(44\) | −4.30311 | + | 2.48440i | −0.648718 | + | 0.374537i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15.5959 | + | 9.00428i | −2.29948 | + | 1.32761i | ||||
\(47\) | −0.311781 | + | 0.180007i | −0.0454779 | + | 0.0262567i | −0.522567 | − | 0.852598i | \(-0.675025\pi\) |
0.477089 | + | 0.878855i | \(0.341692\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.74751 | − | 6.77836i | 0.249645 | − | 0.968337i | ||||
\(50\) | 8.54144 | − | 4.93141i | 1.20794 | − | 0.697406i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.21011 | − | 11.8549i | 0.167813 | − | 1.64398i | ||||
\(53\) | 1.35591 | − | 2.34850i | 0.186248 | − | 0.322591i | −0.757748 | − | 0.652547i | \(-0.773701\pi\) |
0.943996 | + | 0.329956i | \(0.107034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.636910 | + | 1.10316i | 0.0858809 | + | 0.148750i | ||||
\(56\) | −4.87118 | − | 6.28629i | −0.650939 | − | 0.840040i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 3.13177i | − | 0.411222i | ||||||
\(59\) | −1.42132 | + | 0.820598i | −0.185040 | + | 0.106833i | −0.589658 | − | 0.807653i | \(-0.700738\pi\) |
0.404619 | + | 0.914486i | \(0.367404\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.52194 | 0.578975 | 0.289488 | − | 0.957182i | \(-0.406515\pi\) | ||||
0.289488 | + | 0.957182i | \(0.406515\pi\) | |||||||
\(62\) | −9.05305 | − | 15.6803i | −1.14974 | − | 1.99140i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.8114 | 1.60143 | ||||||||
\(65\) | −3.03916 | − | 0.310229i | −0.376962 | − | 0.0384792i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.04266i | 0.249551i | 0.992185 | + | 0.124775i | \(0.0398210\pi\) | ||||
−0.992185 | + | 0.124775i | \(0.960179\pi\) | |||||||
\(68\) | 3.42303 | − | 5.92886i | 0.415103 | − | 0.718980i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.08136 | + | 3.16260i | −0.487815 | + | 0.378003i | ||||
\(71\) | −12.3096 | − | 7.10697i | −1.46088 | − | 0.843442i | −0.461832 | − | 0.886967i | \(-0.652808\pi\) |
−0.999052 | + | 0.0435255i | \(0.986141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.85563 | − | 3.38075i | −0.685349 | − | 0.395687i | 0.116518 | − | 0.993189i | \(-0.462827\pi\) |
−0.801867 | + | 0.597502i | \(0.796160\pi\) | |||||||
\(74\) | 7.71847 | + | 13.3688i | 0.897253 | + | 1.55409i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.135748 | + | 0.0783743i | −0.0155714 | + | 0.00899015i | ||||
\(77\) | 2.43637 | + | 3.14414i | 0.277650 | + | 0.358308i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.82952 | − | 10.0970i | −0.655873 | − | 1.13600i | −0.981674 | − | 0.190567i | \(-0.938967\pi\) |
0.325801 | − | 0.945438i | \(-0.394366\pi\) | |||||||
\(80\) | 0.265367i | 0.0296689i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −23.0751 | −2.54822 | ||||||||
\(83\) | 11.5362i | 1.26627i | 0.774043 | + | 0.633133i | \(0.218232\pi\) | ||||
−0.774043 | + | 0.633133i | \(0.781768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.51994 | − | 0.877541i | −0.164861 | − | 0.0951826i | ||||
\(86\) | −18.4821 | + | 10.6706i | −1.99298 | + | 1.15065i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.51900 | 0.481727 | ||||||||
\(89\) | −15.1652 | − | 8.75561i | −1.60750 | − | 0.928093i | −0.989927 | − | 0.141582i | \(-0.954781\pi\) |
−0.617577 | − | 0.786510i | \(-0.711886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.53391 | + | 0.323492i | −0.999425 | + | 0.0339112i | ||||
\(92\) | 25.8411 | 2.69412 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.829208 | 0.0855262 | ||||||||
\(95\) | 0.0200923 | + | 0.0348009i | 0.00206143 | + | 0.00357050i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.369125 | + | 0.213115i | 0.0374790 | + | 0.0216385i | 0.518622 | − | 0.855003i | \(-0.326445\pi\) |
−0.481143 | + | 0.876642i | \(0.659778\pi\) | |||||||
\(98\) | −11.2919 | + | 11.5082i | −1.14066 | + | 1.16251i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.1525 | −1.41525 | ||||||||
\(101\) | 9.66997 | 0.962198 | 0.481099 | − | 0.876666i | \(-0.340238\pi\) | ||||
0.481099 | + | 0.876666i | \(0.340238\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.98912 | − | 8.64140i | −0.491592 | − | 0.851463i | 0.508361 | − | 0.861144i | \(-0.330252\pi\) |
−0.999953 | + | 0.00968129i | \(0.996918\pi\) | |||||||
\(104\) | −6.34397 | + | 8.78695i | −0.622078 | + | 0.861631i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.40922 | + | 3.12301i | −0.525390 | + | 0.303334i | ||||
\(107\) | 4.93111 | − | 8.54094i | 0.476709 | − | 0.825684i | −0.522935 | − | 0.852373i | \(-0.675163\pi\) |
0.999644 | + | 0.0266888i | \(0.00849631\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0507 | + | 5.80275i | 0.962679 | + | 0.555803i | 0.896996 | − | 0.442038i | \(-0.145744\pi\) |
0.0656822 | + | 0.997841i | \(0.479078\pi\) | |||||||
\(110\) | − | 2.93395i | − | 0.279741i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.112054 | + | 0.821022i | 0.0105881 | + | 0.0775793i | ||||
\(113\) | −1.73879 | + | 3.01167i | −0.163572 | + | 0.283314i | −0.936147 | − | 0.351609i | \(-0.885635\pi\) |
0.772576 | + | 0.634923i | \(0.218968\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.62472i | − | 0.617758i | ||||||
\(116\) | −2.24694 | + | 3.89182i | −0.208623 | + | 0.361346i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.78011 | 0.347987 | ||||||||
\(119\) | −5.07313 | − | 2.07322i | −0.465053 | − | 0.190052i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.73978 | 0.794526 | ||||||||
\(122\) | −9.01986 | − | 5.20762i | −0.816620 | − | 0.471476i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 25.9811i | 2.33317i | ||||||||
\(125\) | 7.86464i | 0.703435i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.84992 | − | 13.5965i | −0.696567 | − | 1.20649i | −0.969649 | − | 0.244499i | \(-0.921376\pi\) |
0.273082 | − | 0.961991i | \(-0.411957\pi\) | |||||||
\(128\) | −16.3917 | − | 9.46373i | −1.44883 | − | 0.836483i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.70491 | + | 4.11881i | 0.500353 | + | 0.361243i | ||||
\(131\) | −1.27259 | − | 2.20418i | −0.111186 | − | 0.192580i | 0.805063 | − | 0.593190i | \(-0.202132\pi\) |
−0.916249 | + | 0.400610i | \(0.868798\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0768590 | + | 0.0991869i | 0.00666452 | + | 0.00860060i | ||||
\(134\) | 2.35240 | − | 4.07447i | 0.203216 | − | 0.351981i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.39215 | + | 3.11316i | −0.462373 | + | 0.266951i | ||||
\(137\) | 1.61490 | − | 0.932362i | 0.137970 | − | 0.0796571i | −0.429426 | − | 0.903102i | \(-0.641284\pi\) |
0.567396 | + | 0.823445i | \(0.307951\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.80462 | + | 13.5180i | −0.661979 | + | 1.14658i | 0.318116 | + | 0.948052i | \(0.396950\pi\) |
−0.980095 | + | 0.198530i | \(0.936383\pi\) | |||||||
\(140\) | 7.34092 | − | 1.00189i | 0.620421 | − | 0.0846755i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.3692 | + | 28.3524i | 1.37368 | + | 2.37928i | ||||
\(143\) | 3.17300 | − | 4.39487i | 0.265339 | − | 0.367518i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.997721 | + | 0.576035i | 0.0828562 | + | 0.0478371i | ||||
\(146\) | 7.78676 | + | 13.4871i | 0.644437 | + | 1.11620i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 22.1510i | − | 1.82080i | ||||||
\(149\) | − | 6.36363i | − | 0.521329i | −0.965429 | − | 0.260664i | \(-0.916058\pi\) | ||
0.965429 | − | 0.260664i | \(-0.0839416\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.575122 | − | 0.332047i | −0.0468028 | − | 0.0270216i | 0.476416 | − | 0.879220i | \(-0.341936\pi\) |
−0.523219 | + | 0.852198i | \(0.675269\pi\) | |||||||
\(152\) | 0.142559 | 0.0115630 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.23889 | − | 9.07739i | −0.0998325 | − | 0.731477i | ||||
\(155\) | 6.66060 | 0.534992 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.28798 | − | 14.3552i | 0.661453 | − | 1.14567i | −0.318781 | − | 0.947828i | \(-0.603273\pi\) |
0.980234 | − | 0.197842i | \(-0.0633933\pi\) | |||||||
\(158\) | 26.8539i | 2.13638i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.24122 | + | 3.88191i | −0.177184 | + | 0.306892i | ||||
\(161\) | −2.79735 | − | 20.4963i | −0.220462 | − | 1.61534i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.05127i | 0.708950i | 0.935065 | + | 0.354475i | \(0.115340\pi\) | ||||
−0.935065 | + | 0.354475i | \(0.884660\pi\) | |||||||
\(164\) | 28.6752 | + | 16.5557i | 2.23916 | + | 1.29278i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.2855 | − | 23.0112i | 1.03116 | − | 1.78601i | ||||
\(167\) | 2.30156 | − | 1.32880i | 0.178100 | − | 0.102826i | −0.408300 | − | 0.912848i | \(-0.633878\pi\) |
0.586400 | + | 0.810022i | \(0.300545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.09120 | + | 12.3395i | 0.314708 | + | 0.949189i | ||||
\(170\) | 2.02121 | + | 3.50084i | 0.155020 | + | 0.268502i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 30.6234 | 2.33501 | ||||||||
\(173\) | 19.5870 | 1.48918 | 0.744588 | − | 0.667525i | \(-0.232646\pi\) | ||||
0.744588 | + | 0.667525i | \(0.232646\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.53204 | + | 11.2253i | 0.115811 | + | 0.848553i | ||||
\(176\) | −0.407774 | − | 0.235428i | −0.0307371 | − | 0.0177461i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 20.1665 | + | 34.9294i | 1.51154 | + | 2.61807i | ||||
\(179\) | −2.89332 | −0.216257 | −0.108129 | − | 0.994137i | \(-0.534486\pi\) | ||||
−0.108129 | + | 0.994137i | \(0.534486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.36804 | −0.101686 | −0.0508429 | − | 0.998707i | \(-0.516191\pi\) | ||||
−0.0508429 | + | 0.998707i | \(0.516191\pi\) | |||||||
\(182\) | 19.3897 | + | 10.3343i | 1.43726 | + | 0.766029i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −20.3532 | − | 11.7509i | −1.50046 | − | 0.866289i | ||||
\(185\) | −5.67871 | −0.417507 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.69693 | − | 1.55707i | 0.197219 | − | 0.113865i | ||||
\(188\) | −1.03045 | − | 0.594929i | −0.0751531 | − | 0.0433897i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 0.0925559i | − | 0.00671471i | ||||||
\(191\) | 1.51325 | 0.109495 | 0.0547475 | − | 0.998500i | \(-0.482565\pi\) | ||||
0.0547475 | + | 0.998500i | \(0.482565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.95394i | 0.500556i | 0.968174 | + | 0.250278i | \(0.0805220\pi\) | ||||
−0.968174 | + | 0.250278i | \(0.919478\pi\) | |||||||
\(194\) | −0.490860 | − | 0.850194i | −0.0352417 | − | 0.0610404i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.2891 | − | 6.19955i | 1.59208 | − | 0.442825i | ||||
\(197\) | 13.4037 | − | 7.73860i | 0.954971 | − | 0.551353i | 0.0603494 | − | 0.998177i | \(-0.480779\pi\) |
0.894622 | + | 0.446825i | \(0.147445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.30764 | + | 5.72901i | 0.234473 | + | 0.406118i | 0.959119 | − | 0.283002i | \(-0.0913304\pi\) |
−0.724647 | + | 0.689121i | \(0.757997\pi\) | |||||||
\(200\) | 11.1469 | + | 6.43566i | 0.788205 | + | 0.455070i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.2886 | − | 11.1363i | −1.35714 | − | 0.783545i | ||||
\(203\) | 3.33010 | + | 1.36090i | 0.233727 | + | 0.0955168i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.24427 | − | 7.35129i | 0.296433 | − | 0.513436i | ||||
\(206\) | 22.9825i | 1.60127i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.03023 | − | 0.462389i | 0.0714335 | − | 0.0320609i | ||||
\(209\) | −0.0713021 | −0.00493207 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.04714 | + | 7.00986i | 0.278617 | + | 0.482578i | 0.971041 | − | 0.238912i | \(-0.0767907\pi\) |
−0.692424 | + | 0.721490i | \(0.743457\pi\) | |||||||
\(212\) | 8.96264 | 0.615557 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −19.6721 | + | 11.3577i | −1.34475 | + | 0.776394i | ||||
\(215\) | − | 7.85072i | − | 0.535415i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.6073 | − | 2.81251i | 1.39892 | − | 0.190925i | ||||
\(218\) | −13.3653 | − | 23.1493i | −0.905211 | − | 1.56787i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.10501 | + | 3.64599i | −0.141920 | + | 0.245812i | ||||
\(221\) | −0.758428 | + | 7.42993i | −0.0510174 | + | 0.499791i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9067 | − | 8.02903i | 0.931261 | − | 0.537664i | 0.0440506 | − | 0.999029i | \(-0.485974\pi\) |
0.887210 | + | 0.461366i | \(0.152640\pi\) | |||||||
\(224\) | −5.29498 | + | 12.9567i | −0.353786 | + | 0.865706i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.93668 | − | 4.00490i | 0.461421 | − | 0.266402i | ||||
\(227\) | 1.12220 | − | 0.647903i | 0.0744831 | − | 0.0430029i | −0.462296 | − | 0.886726i | \(-0.652974\pi\) |
0.536779 | + | 0.843723i | \(0.319641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.0285 | + | 10.4088i | −1.19136 | + | 0.687831i | −0.958614 | − | 0.284707i | \(-0.908104\pi\) |
−0.232743 | + | 0.972538i | \(0.574770\pi\) | |||||||
\(230\) | −7.62925 | + | 13.2142i | −0.503058 | + | 0.871322i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.53951 | − | 2.04354i | 0.232380 | − | 0.134165i | ||||
\(233\) | 6.65213 | + | 11.5218i | 0.435796 | + | 0.754820i | 0.997360 | − | 0.0726127i | \(-0.0231337\pi\) |
−0.561565 | + | 0.827433i | \(0.689800\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.152518 | + | 0.264169i | −0.00994920 | + | 0.0172325i | ||||
\(236\) | −4.69751 | − | 2.71211i | −0.305782 | − | 0.176543i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.73172 | + | 9.97782i | 0.501173 | + | 0.646766i | ||||
\(239\) | 13.3652i | 0.864525i | 0.901748 | + | 0.432263i | \(0.142285\pi\) | ||||
−0.901748 | + | 0.432263i | \(0.857715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.722398 | + | 0.417076i | −0.0465337 | + | 0.0268663i | −0.523086 | − | 0.852280i | \(-0.675219\pi\) |
0.476553 | + | 0.879146i | \(0.341886\pi\) | |||||||
\(242\) | −17.4331 | − | 10.0650i | −1.12064 | − | 0.647004i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.47259 | + | 12.9429i | 0.478384 | + | 0.828585i | ||||
\(245\) | −1.58934 | − | 5.71413i | −0.101539 | − | 0.365062i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.100097 | − | 0.138643i | 0.00636903 | − | 0.00882165i | ||||
\(248\) | 11.8146 | − | 20.4634i | 0.750225 | − | 1.29943i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.05718 | − | 15.6875i | 0.572827 | − | 0.992165i | ||||
\(251\) | −13.6360 | + | 23.6183i | −0.860699 | + | 1.49078i | 0.0105555 | + | 0.999944i | \(0.496640\pi\) |
−0.871255 | + | 0.490831i | \(0.836693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.1798 | + | 5.87733i | 0.640000 | + | 0.369504i | ||||
\(254\) | 36.1609i | 2.26894i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.98607 | + | 15.5643i | 0.561630 | + | 0.972771i | ||||
\(257\) | −3.27594 | + | 5.67409i | −0.204348 | + | 0.353940i | −0.949925 | − | 0.312479i | \(-0.898841\pi\) |
0.745577 | + | 0.666419i | \(0.232174\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.5695 | + | 2.39789i | −1.09171 | + | 0.148998i | ||||
\(260\) | −4.13432 | − | 9.21148i | −0.256399 | − | 0.571272i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.86221i | 0.362168i | ||||||||
\(263\) | 22.5891 | 1.39290 | 0.696450 | − | 0.717605i | \(-0.254762\pi\) | ||||
0.696450 | + | 0.717605i | \(0.254762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.29770i | − | 0.141146i | ||||||
\(266\) | −0.0390827 | − | 0.286360i | −0.00239631 | − | 0.0175579i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.84660 | + | 3.37553i | −0.357138 | + | 0.206194i | ||||
\(269\) | 8.00065 | + | 13.8575i | 0.487808 | + | 0.844909i | 0.999902 | − | 0.0140210i | \(-0.00446317\pi\) |
−0.512093 | + | 0.858930i | \(0.671130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.58582 | − | 4.37967i | −0.460806 | − | 0.266046i | 0.251577 | − | 0.967837i | \(-0.419051\pi\) |
−0.712383 | + | 0.701791i | \(0.752384\pi\) | |||||||
\(272\) | 0.648750 | 0.0393363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29496 | −0.259468 | ||||||||
\(275\) | −5.57522 | − | 3.21886i | −0.336199 | − | 0.194104i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.95914 | − | 17.2497i | −0.598387 | − | 1.03644i | −0.993059 | − | 0.117614i | \(-0.962475\pi\) |
0.394673 | − | 0.918822i | \(-0.370858\pi\) | |||||||
\(278\) | 31.1355 | − | 17.9761i | 1.86739 | − | 1.07814i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.23752 | − | 2.54907i | −0.372763 | − | 0.152336i | ||||
\(281\) | − | 14.0234i | − | 0.836566i | −0.908317 | − | 0.418283i | \(-0.862632\pi\) | ||
0.908317 | − | 0.418283i | \(-0.137368\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.01259 | −0.0601922 | −0.0300961 | − | 0.999547i | \(-0.509581\pi\) | ||||
−0.0300961 | + | 0.999547i | \(0.509581\pi\) | |||||||
\(284\) | − | 46.9776i | − | 2.78761i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.3904 | + | 5.11227i | −0.673530 | + | 0.302295i | ||||
\(287\) | 10.0273 | − | 24.5365i | 0.591890 | − | 1.44834i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.35465 | − | 11.0066i | 0.373803 | − | 0.647446i | ||||
\(290\) | −1.32676 | − | 2.29802i | −0.0779101 | − | 0.134944i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 22.3470i | − | 1.30776i | ||||||
\(293\) | 0.172543 | + | 0.0996176i | 0.0100801 | + | 0.00581972i | 0.505032 | − | 0.863101i | \(-0.331481\pi\) |
−0.494952 | + | 0.868921i | \(0.664814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.695286 | + | 1.20427i | −0.0404811 | + | 0.0701153i | ||||
\(296\) | −10.0729 | + | 17.4467i | −0.585474 | + | 1.01407i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.32857 | + | 12.6935i | −0.424532 | + | 0.735312i | ||||
\(299\) | −25.7191 | + | 11.5433i | −1.48737 | + | 0.667565i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.31504 | − | 24.2895i | −0.191076 | − | 1.40002i | ||||
\(302\) | 0.764792 | + | 1.32466i | 0.0440088 | + | 0.0762256i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0128639 | − | 0.00742695i | −0.000737793 | − | 0.000425965i | ||||
\(305\) | 3.31809 | − | 1.91570i | 0.189993 | − | 0.109693i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.2004i | 1.55241i | 0.630482 | + | 0.776204i | \(0.282857\pi\) | ||||
−0.630482 | + | 0.776204i | \(0.717143\pi\) | |||||||
\(308\) | −4.97317 | + | 12.1692i | −0.283373 | + | 0.693407i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.2858 | − | 7.67057i | −0.754584 | − | 0.435659i | ||||
\(311\) | −13.5505 | + | 23.4701i | −0.768376 | + | 1.33087i | 0.170067 | + | 0.985432i | \(0.445602\pi\) |
−0.938443 | + | 0.345434i | \(0.887732\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0392 | + | 19.1205i | 0.623975 | + | 1.08076i | 0.988738 | + | 0.149656i | \(0.0478165\pi\) |
−0.364763 | + | 0.931100i | \(0.618850\pi\) | |||||||
\(314\) | −33.0639 | + | 19.0894i | −1.86590 | + | 1.07728i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.2668 | − | 33.3711i | 1.08384 | − | 1.87727i | ||||
\(317\) | −6.12126 | + | 3.53411i | −0.343804 | + | 0.198496i | −0.661953 | − | 0.749545i | \(-0.730272\pi\) |
0.318149 | + | 0.948041i | \(0.396939\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.77032 | + | 1.02209i | −0.0991188 | + | 0.0572263i | ||||
\(320\) | 9.40071 | − | 5.42750i | 0.525516 | − | 0.303407i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −18.0244 | + | 44.1053i | −1.00446 | + | 2.45789i | ||||
\(323\) | 0.0850789 | − | 0.0491204i | 0.00473392 | − | 0.00273313i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0857 | − | 6.32195i | 0.781331 | − | 0.350679i | ||||
\(326\) | 10.4237 | − | 18.0544i | 0.577318 | − | 0.999943i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.0569 | − | 26.0794i | −0.831381 | − | 1.43999i | ||||
\(329\) | −0.360331 | + | 0.881721i | −0.0198657 | + | 0.0486108i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.58858i | 0.362141i | 0.983470 | + | 0.181071i | \(0.0579563\pi\) | ||||
−0.983470 | + | 0.181071i | \(0.942044\pi\) | |||||||
\(332\) | −33.0195 | + | 19.0638i | −1.81218 | + | 1.04626i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.12118 | −0.334936 | ||||||||
\(335\) | 0.865365 | + | 1.49886i | 0.0472799 | + | 0.0818912i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.22290 | −0.230036 | −0.115018 | − | 0.993363i | \(-0.536693\pi\) | ||||
−0.115018 | + | 0.993363i | \(0.536693\pi\) | |||||||
\(338\) | 6.04985 | − | 29.3249i | 0.329069 | − | 1.59506i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 5.80061i | − | 0.314582i | ||||||
\(341\) | −5.90916 | + | 10.2350i | −0.319999 | + | 0.554254i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.33014 | − | 17.0079i | −0.395790 | − | 0.918341i | ||||
\(344\) | −24.1198 | − | 13.9256i | −1.30045 | − | 0.750817i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −39.0700 | − | 22.5571i | −2.10042 | − | 1.21268i | ||||
\(347\) | −4.54739 | − | 7.87631i | −0.244117 | − | 0.422822i | 0.717766 | − | 0.696284i | \(-0.245165\pi\) |
−0.961883 | + | 0.273462i | \(0.911831\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.98521 | − | 4.61026i | 0.427439 | − | 0.246782i | −0.270816 | − | 0.962631i | \(-0.587294\pi\) |
0.698255 | + | 0.715849i | \(0.253960\pi\) | |||||||
\(350\) | 9.87149 | − | 24.1553i | 0.527653 | − | 1.29116i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.97674 | − | 6.88792i | −0.211961 | − | 0.367127i | ||||
\(353\) | 2.15449i | 0.114672i | 0.998355 | + | 0.0573359i | \(0.0182606\pi\) | ||||
−0.998355 | + | 0.0573359i | \(0.981739\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0433 | −0.639195 | ||||||||
\(356\) | − | 57.8752i | − | 3.06738i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.77128 | + | 3.33205i | 0.305021 | + | 0.176104i | ||||
\(359\) | −7.41107 | + | 4.27878i | −0.391141 | + | 0.225825i | −0.682654 | − | 0.730741i | \(-0.739175\pi\) |
0.291513 | + | 0.956567i | \(0.405841\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9978 | 0.999882 | ||||||||
\(362\) | 2.72881 | + | 1.57548i | 0.143423 | + | 0.0828055i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.6809 | − | 26.7538i | −0.874315 | − | 1.40228i | ||||
\(365\) | −5.72896 | −0.299867 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.29823 | 0.119967 | 0.0599833 | − | 0.998199i | \(-0.480895\pi\) | ||||
0.0599833 | + | 0.998199i | \(0.480895\pi\) | |||||||
\(368\) | 1.22438 | + | 2.12070i | 0.0638255 | + | 0.110549i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.3273 | + | 6.53979i | 0.588876 | + | 0.339988i | ||||
\(371\) | −0.970225 | − | 7.10888i | −0.0503716 | − | 0.369075i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7684 | 0.609343 | 0.304672 | − | 0.952457i | \(-0.401453\pi\) | ||||
0.304672 | + | 0.952457i | \(0.401453\pi\) | |||||||
\(374\) | −7.17271 | −0.370892 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.541073 | + | 0.937166i | 0.0279037 | + | 0.0483307i | ||||
\(377\) | 0.497847 | − | 4.87715i | 0.0256404 | − | 0.251186i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.92034 | + | 3.99546i | −0.355474 | + | 0.205233i | −0.667094 | − | 0.744974i | \(-0.732462\pi\) |
0.311619 | + | 0.950207i | \(0.399129\pi\) | |||||||
\(380\) | −0.0664059 | + | 0.115018i | −0.00340655 | + | 0.00590032i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.01846 | − | 1.74271i | −0.154438 | − | 0.0891647i | ||||
\(383\) | 28.2446i | 1.44323i | 0.692294 | + | 0.721616i | \(0.256600\pi\) | ||||
−0.692294 | + | 0.721616i | \(0.743400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.11975 | + | 1.27494i | 0.158997 | + | 0.0649770i | ||||
\(386\) | 8.00839 | − | 13.8709i | 0.407616 | − | 0.706012i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.40870i | 0.0715161i | ||||||||
\(389\) | −3.84043 | + | 6.65182i | −0.194717 | + | 0.337261i | −0.946808 | − | 0.321799i | \(-0.895712\pi\) |
0.752090 | + | 0.659060i | \(0.229046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1957 | −0.819050 | ||||||||
\(392\) | −20.3747 | − | 5.25276i | −1.02908 | − | 0.265304i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −35.6481 | −1.79593 | ||||||||
\(395\) | −8.55513 | − | 4.93931i | −0.430455 | − | 0.248524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.45281i | 0.374046i | 0.982356 | + | 0.187023i | \(0.0598839\pi\) | ||||
−0.982356 | + | 0.187023i | \(0.940116\pi\) | |||||||
\(398\) | − | 15.2368i | − | 0.763750i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.670563 | − | 1.16145i | −0.0335282 | − | 0.0580725i | ||||
\(401\) | 15.7601 | + | 9.09912i | 0.787024 | + | 0.454389i | 0.838914 | − | 0.544264i | \(-0.183191\pi\) |
−0.0518898 | + | 0.998653i | \(0.516524\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.6058 | − | 25.8584i | −0.578126 | − | 1.28810i | ||||
\(404\) | 15.9798 | + | 27.6778i | 0.795025 | + | 1.37702i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.07525 | − | 6.54964i | −0.251880 | − | 0.325053i | ||||
\(407\) | 5.03804 | − | 8.72615i | 0.249727 | − | 0.432539i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.3594 | + | 14.6413i | −1.25394 | + | 0.723964i | −0.971890 | − | 0.235435i | \(-0.924349\pi\) |
−0.282053 | + | 0.959399i | \(0.591015\pi\) | |||||||
\(410\) | −16.9320 | + | 9.77568i | −0.836211 | + | 0.482787i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.4892 | − | 28.5602i | 0.812365 | − | 1.40706i | ||||
\(413\) | −1.64264 | + | 4.01950i | −0.0808291 | + | 0.197787i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.88728 | + | 8.46502i | 0.239907 | + | 0.415531i | ||||
\(416\) | 18.9759 | + | 1.93701i | 0.930372 | + | 0.0949698i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.142225 | + | 0.0821139i | 0.00695647 | + | 0.00401632i | ||||
\(419\) | −10.3697 | − | 17.9608i | −0.506591 | − | 0.877441i | −0.999971 | − | 0.00762733i | \(-0.997572\pi\) |
0.493380 | − | 0.869814i | \(-0.335761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.8696i | 1.21207i | 0.795437 | + | 0.606036i | \(0.207241\pi\) | ||||
−0.795437 | + | 0.606036i | \(0.792759\pi\) | |||||||
\(422\) | − | 18.6433i | − | 0.907541i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.05923 | − | 4.07565i | −0.342826 | − | 0.197931i | ||||
\(425\) | 8.86994 | 0.430255 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.45698 | − | 7.32812i | 0.457655 | − | 0.354632i | ||||
\(428\) | 32.5950 | 1.57554 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.04115 | + | 15.6597i | −0.436003 | + | 0.755179i | ||||
\(431\) | − | 21.1688i | − | 1.01966i | −0.860274 | − | 0.509832i | \(-0.829708\pi\) | ||
0.860274 | − | 0.509832i | \(-0.170292\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7148 | + | 20.2906i | −0.562977 | + | 0.975105i | 0.434258 | + | 0.900789i | \(0.357011\pi\) |
−0.997235 | + | 0.0743163i | \(0.976323\pi\) | |||||||
\(434\) | −44.3442 | − | 18.1220i | −2.12859 | − | 0.869885i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 38.3566i | 1.83695i | ||||||||
\(437\) | 0.321139 | + | 0.185409i | 0.0153621 | + | 0.00886934i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.01919 | + | 10.4256i | −0.287280 | + | 0.497584i | −0.973160 | − | 0.230131i | \(-0.926085\pi\) |
0.685879 | + | 0.727715i | \(0.259418\pi\) | |||||||
\(440\) | 3.31593 | − | 1.91445i | 0.158081 | − | 0.0912680i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0694 | − | 13.9470i | 0.478952 | − | 0.663390i | ||||
\(443\) | 7.86656 | + | 13.6253i | 0.373752 | + | 0.647357i | 0.990139 | − | 0.140086i | \(-0.0447379\pi\) |
−0.616388 | + | 0.787443i | \(0.711405\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.8371 | −0.703346 | ||||||||
\(446\) | −36.9860 | −1.75134 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 26.7932 | − | 20.7618i | 1.26586 | − | 0.980902i | ||||
\(449\) | −22.5177 | − | 13.0006i | −1.06268 | − | 0.613536i | −0.136504 | − | 0.990640i | \(-0.543587\pi\) |
−0.926171 | + | 0.377104i | \(0.876920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.53087 | + | 13.0438i | 0.354615 | + | 0.614211i | ||||
\(452\) | −11.4935 | −0.540610 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.98459 | −0.140074 | ||||||||
\(455\) | −6.85871 | + | 4.27637i | −0.321541 | + | 0.200479i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.6700 | + | 15.3979i | 1.24757 | + | 0.720284i | 0.970624 | − | 0.240602i | \(-0.0773448\pi\) |
0.276945 | + | 0.960886i | \(0.410678\pi\) | |||||||
\(458\) | 47.9483 | 2.24048 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.9616 | − | 10.9475i | 0.884088 | − | 0.510429i | ||||
\(461\) | 29.5278 | + | 17.0479i | 1.37525 | + | 0.794000i | 0.991583 | − | 0.129472i | \(-0.0413284\pi\) |
0.383665 | + | 0.923472i | \(0.374662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.69184i | − | 0.0786263i | −0.999227 | − | 0.0393131i | \(-0.987483\pi\) | ||
0.999227 | − | 0.0393131i | \(-0.0125170\pi\) | |||||||
\(464\) | −0.425852 | −0.0197697 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 30.6433i | − | 1.41952i | ||||||
\(467\) | −14.1762 | − | 24.5539i | −0.655996 | − | 1.13622i | −0.981643 | − | 0.190727i | \(-0.938916\pi\) |
0.325647 | − | 0.945491i | \(-0.394418\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.31027 | + | 4.27192i | 0.152854 | + | 0.197259i | ||||
\(470\) | 0.608453 | − | 0.351290i | 0.0280658 | − | 0.0162038i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.46659 | + | 4.27226i | 0.113534 | + | 0.196647i | ||||
\(473\) | 12.0637 | + | 6.96501i | 0.554692 | + | 0.320251i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.175879 | − | 0.101544i | −0.00806989 | − | 0.00465915i | ||||
\(476\) | −2.44936 | − | 17.9466i | −0.112266 | − | 0.822581i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.3918 | − | 26.6595i | 0.704007 | − | 1.21938i | ||||
\(479\) | 6.28246i | 0.287053i | 0.989646 | + | 0.143526i | \(0.0458442\pi\) | ||||
−0.989646 | + | 0.143526i | \(0.954156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.89490 | + | 22.0464i | 0.451169 | + | 1.00523i | ||||
\(482\) | 1.92128 | 0.0875117 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.4427 | + | 25.0154i | 0.656484 | + | 1.13706i | ||||
\(485\) | 0.361140 | 0.0163985 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2736 | + | 6.50879i | −0.510854 | + | 0.294942i | −0.733185 | − | 0.680030i | \(-0.761967\pi\) |
0.222331 | + | 0.974971i | \(0.428634\pi\) | |||||||
\(488\) | − | 13.5923i | − | 0.615293i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.41034 | + | 13.2282i | −0.154063 | + | 0.597591i | ||||
\(491\) | 6.17616 | + | 10.6974i | 0.278726 | + | 0.482768i | 0.971068 | − | 0.238801i | \(-0.0767544\pi\) |
−0.692342 | + | 0.721569i | \(0.743421\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.40825 | − | 2.43916i | 0.0634244 | − | 0.109854i | ||||
\(494\) | −0.359329 | + | 0.161275i | −0.0161670 | + | 0.00725609i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.13218 | + | 1.23102i | −0.0957378 | + | 0.0552743i | ||||
\(497\) | −37.2611 | + | 5.08542i | −1.67139 | + | 0.228112i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.92708 | + | 4.57670i | −0.354865 | + | 0.204881i | −0.666826 | − | 0.745214i | \(-0.732348\pi\) |
0.311961 | + | 0.950095i | \(0.399014\pi\) | |||||||
\(500\) | −22.5105 | + | 12.9965i | −1.00670 | + | 0.581220i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 54.3993 | − | 31.4074i | 2.42796 | − | 1.40178i | ||||
\(503\) | 11.2519 | − | 19.4888i | 0.501696 | − | 0.868963i | −0.498302 | − | 0.867003i | \(-0.666043\pi\) |
0.999998 | − | 0.00195935i | \(-0.000623680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.09559 | − | 4.09664i | 0.315750 | − | 0.182298i | ||||
\(506\) | −13.5370 | − | 23.4469i | −0.601795 | − | 1.04234i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.9443 | − | 44.9368i | 1.15109 | − | 1.99375i | ||||
\(509\) | 33.4811 | + | 19.3303i | 1.48402 | + | 0.856800i | 0.999835 | − | 0.0181646i | \(-0.00578229\pi\) |
0.484187 | + | 0.874965i | \(0.339116\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.7249 | + | 2.41911i | −0.784104 | + | 0.107015i | ||||
\(512\) | − | 3.53972i | − | 0.156435i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.0690 | − | 7.54536i | 0.576447 | − | 0.332812i | ||||
\(515\) | −7.32179 | − | 4.22724i | −0.322637 | − | 0.186274i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.270623 | − | 0.468732i | −0.0119020 | − | 0.0206148i | ||||
\(518\) | 37.8071 | + | 15.4505i | 1.66115 | + | 0.678857i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.932502 | + | 9.13525i | −0.0408929 | + | 0.400607i | ||||
\(521\) | 20.1176 | − | 34.8446i | 0.881366 | − | 1.52657i | 0.0315430 | − | 0.999502i | \(-0.489958\pi\) |
0.849823 | − | 0.527068i | \(-0.176709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.366073 | − | 0.634057i | 0.0160073 | − | 0.0277254i | −0.857911 | − | 0.513799i | \(-0.828238\pi\) |
0.873918 | + | 0.486073i | \(0.161571\pi\) | |||||||
\(524\) | 4.20594 | − | 7.28491i | 0.183737 | − | 0.318243i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.0581 | − | 26.0143i | −1.96463 | − | 1.13428i | ||||
\(527\) | − | 16.2834i | − | 0.709316i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0660 | − | 33.0234i | −0.828959 | − | 1.43580i | ||||
\(530\) | −2.64610 | + | 4.58319i | −0.114939 | + | 0.199081i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.156887 | + | 0.383898i | −0.00680189 | + | 0.0166441i | ||||
\(533\) | −35.9353 | − | 3.66817i | −1.55653 | − | 0.158886i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8.35618i | − | 0.361269i | ||||||
\(536\) | 6.13993 | 0.265204 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 36.8553i | − | 1.58894i | ||||||
\(539\) | 10.1906 | + | 2.62722i | 0.438940 | + | 0.113162i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4847 | − | 11.8268i | 0.880705 | − | 0.508476i | 0.00981448 | − | 0.999952i | \(-0.496876\pi\) |
0.870891 | + | 0.491476i | \(0.163543\pi\) | |||||||
\(542\) | 10.0876 | + | 17.4722i | 0.433298 | + | 0.750494i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.49024 | + | 5.47919i | 0.406891 | + | 0.234918i | ||||
\(545\) | 9.83325 | 0.421210 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9472 | −0.553582 | −0.276791 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276791 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(548\) | 5.33730 | + | 3.08149i | 0.227998 | + | 0.131635i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.41388 | + | 12.8412i | 0.316129 | + | 0.547552i | ||||
\(551\) | −0.0558475 | + | 0.0322436i | −0.00237918 | + | 0.00137362i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.5545 | − | 11.6693i | −1.21426 | − | 0.496230i | ||||
\(554\) | 45.8771i | 1.94913i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −51.5891 | −2.18787 | ||||||||
\(557\) | 6.40680i | 0.271465i | 0.990746 | + | 0.135732i | \(0.0433388\pi\) | ||||
−0.990746 | + | 0.135732i | \(0.956661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.4787 | + | 13.6795i | −1.28911 | + | 0.578582i | ||||
\(560\) | 0.430045 | + | 0.554975i | 0.0181727 | + | 0.0234520i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.1498 | + | 27.9723i | −0.681239 | + | 1.17994i | ||||
\(563\) | −3.66042 | − | 6.34004i | −0.154268 | − | 0.267201i | 0.778524 | − | 0.627615i | \(-0.215969\pi\) |
−0.932792 | + | 0.360414i | \(0.882635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.94652i | 0.123961i | ||||||||
\(566\) | 2.01980 | + | 1.16613i | 0.0848986 | + | 0.0490162i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.3625 | + | 37.0009i | −0.896349 | + | 1.55252i | ||||
\(569\) | 2.15872 | − | 3.73901i | 0.0904981 | − | 0.156747i | −0.817223 | − | 0.576322i | \(-0.804487\pi\) |
0.907721 | + | 0.419575i | \(0.137821\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.0847 | − | 29.5916i | 0.714974 | − | 1.23837i | −0.247996 | − | 0.968761i | \(-0.579772\pi\) |
0.962970 | − | 0.269610i | \(-0.0868946\pi\) | |||||||
\(572\) | 17.8226 | + | 1.81929i | 0.745202 | + | 0.0760682i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −48.2582 | + | 37.3948i | −2.01426 | + | 1.56083i | ||||
\(575\) | 16.7402 | + | 28.9949i | 0.698115 | + | 1.20917i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.50494 | + | 3.17828i | 0.229174 | + | 0.132314i | 0.610191 | − | 0.792254i | \(-0.291093\pi\) |
−0.381017 | + | 0.924568i | \(0.624426\pi\) | |||||||
\(578\) | −25.3511 | + | 14.6364i | −1.05447 | + | 0.608796i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.80763i | 0.158103i | ||||||||
\(581\) | 18.6953 | + | 24.1263i | 0.775610 | + | 1.00093i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.53074 | + | 2.03847i | 0.146228 | + | 0.0844249i | ||||
\(584\) | −10.1620 | + | 17.6011i | −0.420507 | + | 0.728339i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.229446 | − | 0.397412i | −0.00947832 | − | 0.0164169i | ||||
\(587\) | −27.2036 | + | 15.7060i | −1.12281 | + | 0.648256i | −0.942118 | − | 0.335283i | \(-0.891168\pi\) |
−0.180695 | + | 0.983539i | \(0.557835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.186414 | + | 0.322878i | −0.00768104 | + | 0.0133040i | ||||
\(590\) | 2.77376 | − | 1.60143i | 0.114194 | − | 0.0659298i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.81786 | − | 1.04954i | 0.0747136 | − | 0.0431359i | ||||
\(593\) | 0.409641 | − | 0.236506i | 0.0168219 | − | 0.00971215i | −0.491565 | − | 0.870841i | \(-0.663575\pi\) |
0.508387 | + | 0.861128i | \(0.330242\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.60086 | + | 0.627928i | −0.188617 | + | 0.0257425i | ||||
\(596\) | 18.2143 | − | 10.5160i | 0.746086 | − | 0.430753i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 64.5951 | + | 6.59369i | 2.64149 | + | 0.269636i | ||||
\(599\) | −4.81348 | + | 8.33719i | −0.196673 | + | 0.340648i | −0.947448 | − | 0.319910i | \(-0.896347\pi\) |
0.750774 | + | 0.660559i | \(0.229680\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5399 | + | 35.5762i | 0.837842 | + | 1.45118i | 0.891696 | + | 0.452635i | \(0.149516\pi\) |
−0.0538542 | + | 0.998549i | \(0.517151\pi\) | |||||||
\(602\) | −21.3601 | + | 52.2676i | −0.870572 | + | 2.13027i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 2.19485i | − | 0.0893073i | ||||||
\(605\) | 6.41304 | − | 3.70257i | 0.260727 | − | 0.150531i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0858 | 0.774668 | 0.387334 | − | 0.921939i | \(-0.373396\pi\) | ||||
0.387334 | + | 0.921939i | \(0.373396\pi\) | |||||||
\(608\) | −0.125453 | − | 0.217290i | −0.00508777 | − | 0.00881228i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.82474 | −0.357303 | ||||||||
\(611\) | 1.29134 | + | 0.131816i | 0.0522419 | + | 0.00533271i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.0048i | 1.53500i | 0.641049 | + | 0.767500i | \(0.278499\pi\) | ||||
−0.641049 | + | 0.767500i | \(0.721501\pi\) | |||||||
\(614\) | 31.3249 | − | 54.2563i | 1.26417 | − | 2.18961i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.45082 | − | 7.32335i | 0.380784 | − | 0.295066i | ||||
\(617\) | −7.20117 | − | 4.15759i | −0.289908 | − | 0.167378i | 0.347992 | − | 0.937497i | \(-0.386864\pi\) |
−0.637900 | + | 0.770119i | \(0.720197\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.5146 | + | 22.2364i | 1.54803 | + | 0.893756i | 0.998292 | + | 0.0584199i | \(0.0186062\pi\) |
0.549739 | + | 0.835336i | \(0.314727\pi\) | |||||||
\(620\) | 11.0068 | + | 19.0643i | 0.442042 | + | 0.765640i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 54.0579 | − | 31.2103i | 2.16752 | − | 1.25142i | ||||
\(623\) | −45.9048 | + | 6.26512i | −1.83914 | + | 0.251007i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.37342 | − | 12.7711i | −0.294937 | − | 0.510845i | ||||
\(626\) | − | 50.8526i | − | 2.03248i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 54.7842 | 2.18613 | ||||||||
\(629\) | 13.8829i | 0.553549i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.1779 | − | 5.87622i | −0.405177 | − | 0.233929i | 0.283539 | − | 0.958961i | \(-0.408492\pi\) |
−0.688715 | + | 0.725032i | \(0.741825\pi\) | |||||||
\(632\) | −30.3501 | + | 17.5227i | −1.20726 | + | 0.697014i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.2800 | 0.646562 | ||||||||
\(635\) | −11.5202 | − | 6.65117i | −0.457164 | − | 0.263944i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.4145 | + | 16.1269i | −0.769231 | + | 0.638971i | ||||
\(638\) | 4.70831 | 0.186404 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.0371 | −0.633921 | ||||||||
\(641\) | −5.24342 | − | 9.08186i | −0.207102 | − | 0.358712i | 0.743698 | − | 0.668516i | \(-0.233070\pi\) |
−0.950801 | + | 0.309804i | \(0.899737\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.0912 | + | 15.6411i | 1.06837 | + | 0.616825i | 0.927736 | − | 0.373237i | \(-0.121752\pi\) |
0.140635 | + | 0.990061i | \(0.455085\pi\) | |||||||
\(644\) | 54.0428 | − | 41.8773i | 2.12959 | − | 1.65020i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.226275 | −0.00890265 | ||||||||
\(647\) | −26.8675 | −1.05627 | −0.528135 | − | 0.849160i | \(-0.677109\pi\) | ||||
−0.528135 | + | 0.849160i | \(0.677109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.23369 | − | 2.13681i | −0.0484265 | − | 0.0838772i | ||||
\(650\) | −35.3770 | − | 3.61119i | −1.38760 | − | 0.141643i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.9070 | + | 14.9574i | −1.01459 | + | 0.585776i | ||||
\(653\) | −2.07081 | + | 3.58674i | −0.0810369 | + | 0.140360i | −0.903696 | − | 0.428176i | \(-0.859156\pi\) |
0.822659 | + | 0.568536i | \(0.192490\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.86759 | − | 1.07825i | −0.0729726 | − | 0.0421308i | ||||
\(656\) | 3.13771i | 0.122507i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.73417 | − | 1.34379i | 0.0676048 | − | 0.0523863i | ||||
\(659\) | 10.7276 | − | 18.5807i | 0.417887 | − | 0.723801i | −0.577840 | − | 0.816150i | \(-0.696104\pi\) |
0.995727 | + | 0.0923492i | \(0.0294376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3872i | 1.64867i | 0.566102 | + | 0.824335i | \(0.308451\pi\) | ||||
−0.566102 | + | 0.824335i | \(0.691549\pi\) | |||||||
\(662\) | 7.58763 | − | 13.1422i | 0.294902 | − | 0.510785i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 34.6762 | 1.34570 | ||||||||
\(665\) | 0.0984174 | + | 0.0402200i | 0.00381646 | + | 0.00155967i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.6312 | 0.411640 | ||||||||
\(668\) | 7.60673 | + | 4.39175i | 0.294313 | + | 0.169922i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 3.98633i | − | 0.154005i | ||||||
\(671\) | 6.79830i | 0.262445i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7928 | − | 25.6219i | −0.570220 | − | 0.987650i | −0.996543 | − | 0.0830790i | \(-0.973525\pi\) |
0.426323 | − | 0.904571i | \(-0.359809\pi\) | |||||||
\(674\) | 8.42336 | + | 4.86323i | 0.324456 | + | 0.187324i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.5578 | + | 32.1012i | −1.09838 | + | 1.23466i | ||||
\(677\) | 16.0830 | + | 27.8565i | 0.618118 | + | 1.07061i | 0.989829 | + | 0.142263i | \(0.0454380\pi\) |
−0.371711 | + | 0.928349i | \(0.621229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.11734 | − | 0.152495i | 0.0428795 | − | 0.00585223i | ||||
\(680\) | −2.63775 | + | 4.56872i | −0.101153 | + | 0.175202i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.5738 | − | 13.6104i | 0.902689 | − | 0.521168i | ||||
\(683\) | 7.44986 | − | 4.30118i | 0.285061 | − | 0.164580i | −0.350651 | − | 0.936506i | \(-0.614040\pi\) |
0.635712 | + | 0.771926i | \(0.280706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.789983 | − | 1.36829i | 0.0301837 | − | 0.0522797i | ||||
\(686\) | −4.96555 | + | 42.3671i | −0.189586 | + | 1.61758i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.45097 | + | 2.51316i | 0.0553179 | + | 0.0958134i | ||||
\(689\) | −8.92031 | + | 4.00363i | −0.339837 | + | 0.152526i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.7033 | + | 10.2210i | 0.673466 | + | 0.388826i | 0.797388 | − | 0.603466i | \(-0.206214\pi\) |
−0.123923 | + | 0.992292i | \(0.539548\pi\) | |||||||
\(692\) | 32.3680 | + | 56.0629i | 1.23044 | + | 2.13119i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.9477i | 0.795164i | ||||||||
\(695\) | 13.2256i | 0.501675i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.9719 | − | 10.3761i | −0.680736 | − | 0.393023i | ||||
\(698\) | −21.2373 | −0.803845 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −29.5978 | + | 22.9351i | −1.11869 | + | 0.866864i | ||||
\(701\) | 25.1373 | 0.949422 | 0.474711 | − | 0.880142i | \(-0.342553\pi\) | ||||
0.474711 | + | 0.880142i | \(0.342553\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.158933 | − | 0.275280i | 0.00599427 | − | 0.0103824i | ||||
\(704\) | 19.2607i | 0.725915i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.48118 | − | 4.29753i | 0.0933804 | − | 0.161740i | ||||
\(707\) | 20.2233 | − | 15.6709i | 0.760576 | − | 0.589363i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 29.4929i | − | 1.10763i | −0.832640 | − | 0.553814i | \(-0.813172\pi\) | ||
0.832640 | − | 0.553814i | \(-0.186828\pi\) | |||||||
\(710\) | 24.0227 | + | 13.8695i | 0.901556 | + | 0.520514i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −26.3180 | + | 45.5841i | −0.986309 | + | 1.70834i | ||||
\(713\) | 53.2287 | − | 30.7316i | 1.99343 | − | 1.15091i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.466399 | − | 4.56908i | 0.0174423 | − | 0.170874i | ||||
\(716\) | −4.78127 | − | 8.28140i | −0.178684 | − | 0.309491i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.7104 | 0.735584 | ||||||||
\(719\) | −8.33153 | −0.310713 | −0.155357 | − | 0.987858i | \(-0.549653\pi\) | ||||
−0.155357 | + | 0.987858i | \(0.549653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.4380 | − | 9.98702i | −0.910118 | − | 0.371936i | ||||
\(722\) | −37.8946 | − | 21.8784i | −1.41029 | − | 0.814231i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.26071 | − | 3.91567i | −0.0840188 | − | 0.145525i | ||||
\(725\) | −5.82240 | −0.216239 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.66141 | 0.358322 | 0.179161 | − | 0.983820i | \(-0.442662\pi\) | ||||
0.179161 | + | 0.983820i | \(0.442662\pi\) | |||||||
\(728\) | 0.972369 | + | 28.6575i | 0.0360384 | + | 1.06212i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.4275 | + | 6.59766i | 0.422950 | + | 0.244190i | ||||
\(731\) | −19.1929 | −0.709875 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.1398 | − | 7.00894i | 0.448395 | − | 0.258881i | −0.258757 | − | 0.965942i | \(-0.583313\pi\) |
0.707152 | + | 0.707061i | \(0.249980\pi\) | |||||||
\(734\) | −4.58425 | − | 2.64672i | −0.169208 | − | 0.0976921i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.3635i | 1.52468i | ||||||||
\(737\) | −3.07094 | −0.113120 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 38.8147i | − | 1.42782i | −0.700237 | − | 0.713910i | \(-0.746923\pi\) | ||
0.700237 | − | 0.713910i | \(-0.253077\pi\) | |||||||
\(740\) | −9.38417 | − | 16.2539i | −0.344969 | − | 0.597504i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.25153 | + | 15.2973i | −0.229501 | + | 0.561583i | ||||
\(743\) | −29.7863 | + | 17.1971i | −1.09275 | + | 0.630901i | −0.934308 | − | 0.356467i | \(-0.883981\pi\) |
−0.158445 | + | 0.987368i | \(0.550648\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.69592 | − | 4.66948i | −0.0987710 | − | 0.171076i | ||||
\(746\) | −23.4742 | − | 13.5528i | −0.859452 | − | 0.496205i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.91346 | + | 5.14619i | 0.325908 | + | 0.188163i | ||||
\(749\) | −3.52848 | − | 25.8533i | −0.128928 | − | 0.944660i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0735 | − | 41.6965i | 0.878454 | − | 1.52153i | 0.0254165 | − | 0.999677i | \(-0.491909\pi\) |
0.853037 | − | 0.521850i | \(-0.174758\pi\) | |||||||
\(752\) | − | 0.112754i | − | 0.00411172i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.60974 | + | 9.15506i | −0.240713 | + | 0.333408i | ||||
\(755\) | −0.562681 | −0.0204781 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.45319 | + | 5.98110i | 0.125508 | + | 0.217387i | 0.921931 | − | 0.387353i | \(-0.126611\pi\) |
−0.796423 | + | 0.604740i | \(0.793277\pi\) | |||||||
\(758\) | 18.4052 | 0.668508 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.104606 | − | 0.0603945i | 0.00379447 | − | 0.00219074i | ||||
\(761\) | 31.9730i | 1.15902i | 0.814965 | + | 0.579511i | \(0.196756\pi\) | ||||
−0.814965 | + | 0.579511i | \(0.803244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.4232 | − | 4.15219i | 1.10139 | − | 0.150319i | ||||
\(764\) | 2.50067 | + | 4.33129i | 0.0904712 | + | 0.156701i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.5274 | − | 56.3391i | 1.17526 | − | 2.03562i | ||||
\(767\) | 5.88683 | + | 0.600911i | 0.212561 | + | 0.0216976i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.4665 | − | 7.19752i | 0.449553 | − | 0.259549i | −0.258089 | − | 0.966121i | \(-0.583093\pi\) |
0.707641 | + | 0.706572i | \(0.249759\pi\) | |||||||
\(770\) | −4.75466 | − | 6.13592i | −0.171346 | − | 0.221123i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.9039 | + | 11.4915i | −0.716357 | + | 0.413589i | ||||
\(773\) | 32.2829 | − | 18.6385i | 1.16114 | − | 0.670382i | 0.209560 | − | 0.977796i | \(-0.432797\pi\) |
0.951576 | + | 0.307414i | \(0.0994636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.1520 | + | 16.8309i | −1.04717 | + | 0.604583i | ||||
\(776\) | 0.640590 | − | 1.10953i | 0.0229958 | − | 0.0398300i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.3209 | − | 8.84553i | 0.549281 | − | 0.317128i | ||||
\(779\) | 0.237573 | + | 0.411489i | 0.00851194 | + | 0.0147431i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.6846 | − | 18.5063i | 0.382326 | − | 0.662208i | ||||
\(782\) | 32.3053 | + | 18.6515i | 1.15524 | + | 0.666975i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.56487 | + | 1.53546i | 0.0558881 | + | 0.0548377i | ||||
\(785\) | − | 14.0447i | − | 0.501276i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.4263 | + | 7.17430i | −0.442948 | + | 0.255736i | −0.704847 | − | 0.709359i | \(-0.748985\pi\) |
0.261899 | + | 0.965095i | \(0.415651\pi\) | |||||||
\(788\) | 44.2996 | + | 25.5764i | 1.57811 | + | 0.911120i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.3765 | + | 19.7047i | 0.404759 | + | 0.701064i | ||||
\(791\) | 1.24420 | + | 9.11630i | 0.0442386 | + | 0.324138i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.2189 | − | 9.54376i | −0.469418 | − | 0.338909i | ||||
\(794\) | 8.58291 | − | 14.8660i | 0.304596 | − | 0.527576i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.9319 | + | 18.9346i | −0.387470 | + | 0.671118i | ||||
\(797\) | −5.54219 | + | 9.59935i | −0.196314 | + | 0.340026i | −0.947331 | − | 0.320257i | \(-0.896231\pi\) |
0.751016 | + | 0.660284i | \(0.229564\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.645824 | + | 0.372866i | 0.0228476 | + | 0.0131911i | ||||
\(800\) | − | 22.6537i | − | 0.800929i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.9577 | − | 36.2998i | −0.740042 | − | 1.28179i | ||||
\(803\) | 5.08262 | − | 8.80336i | 0.179362 | − | 0.310664i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.7358 | − | 13.8546i | −0.378388 | − | 0.488312i | ||||
\(806\) | −6.62941 | + | 64.9450i | −0.233511 | + | 2.28759i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 29.0665i | − | 1.02255i | ||||||
\(809\) | 42.5536 | 1.49610 | 0.748052 | − | 0.663640i | \(-0.230989\pi\) | ||||
0.748052 | + | 0.663640i | \(0.230989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.3622i | 0.574554i | 0.957848 | + | 0.287277i | \(0.0927500\pi\) | ||||
−0.957848 | + | 0.287277i | \(0.907250\pi\) | |||||||
\(812\) | 1.60781 | + | 11.7805i | 0.0564231 | + | 0.413414i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.0986 | + | 11.6040i | −0.704457 | + | 0.406719i | ||||
\(815\) | 3.83453 | + | 6.64160i | 0.134318 | + | 0.232645i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.380570 | + | 0.219722i | 0.0133145 | + | 0.00768710i | ||||
\(818\) | 67.4455 | 2.35818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.0549 | 0.979721 | ||||||||
\(821\) | −2.68944 | − | 1.55275i | −0.0938621 | − | 0.0541913i | 0.452334 | − | 0.891848i | \(-0.350591\pi\) |
−0.546196 | + | 0.837657i | \(0.683925\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5082 | + | 42.4494i | 0.854301 | + | 1.47969i | 0.877292 | + | 0.479958i | \(0.159348\pi\) |
−0.0229903 | + | 0.999736i | \(0.507319\pi\) | |||||||
\(824\) | −25.9747 | + | 14.9965i | −0.904873 | + | 0.522429i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.90555 | − | 6.12593i | 0.275069 | − | 0.213148i | ||||
\(827\) | 13.0887i | 0.455140i | 0.973762 | + | 0.227570i | \(0.0730780\pi\) | ||||
−0.973762 | + | 0.227570i | \(0.926922\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.2565 | −1.71075 | −0.855374 | − | 0.518010i | \(-0.826673\pi\) | ||||
−0.855374 | + | 0.518010i | \(0.826673\pi\) | |||||||
\(830\) | − | 22.5134i | − | 0.781452i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.4514 | − | 27.0391i | −1.29839 | − | 0.937411i | ||||
\(833\) | −13.9695 | + | 3.88551i | −0.484015 | + | 0.134625i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.12588 | − | 1.95009i | 0.0389629 | − | 0.0674856i | ||||
\(836\) | −0.117828 | − | 0.204084i | −0.00407517 | − | 0.00705840i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 47.7682i | 1.65012i | ||||||||
\(839\) | −14.9508 | − | 8.63182i | −0.516157 | − | 0.298004i | 0.219204 | − | 0.975679i | \(-0.429654\pi\) |
−0.735361 | + | 0.677676i | \(0.762987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5756 | − | 23.5136i | 0.468124 | − | 0.810815i | ||||
\(842\) | 28.6407 | − | 49.6071i | 0.987024 | − | 1.70957i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.3760 | + | 23.1678i | −0.460419 | + | 0.797470i | ||||
\(845\) | 8.22958 | + | 7.32117i | 0.283106 | + | 0.251856i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.2780 | − | 14.1634i | 0.628038 | − | 0.486661i | ||||
\(848\) | 0.424662 | + | 0.735535i | 0.0145829 | + | 0.0252584i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.6928 | − | 10.2149i | −0.606857 | − | 0.350369i | ||||
\(851\) | −45.3818 | + | 26.2012i | −1.55567 | + | 0.898166i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 52.4163i | − | 1.79470i | −0.441319 | − | 0.897350i | \(-0.645489\pi\) | ||
0.441319 | − | 0.897350i | \(-0.354511\pi\) | |||||||
\(854\) | −27.3030 | + | 3.72634i | −0.934290 | + | 0.127513i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.6728 | − | 14.8222i | −0.877477 | − | 0.506611i | ||||
\(857\) | −5.06355 | + | 8.77032i | −0.172967 | + | 0.299588i | −0.939456 | − | 0.342670i | \(-0.888669\pi\) |
0.766489 | + | 0.642258i | \(0.222002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.255118 | + | 0.441878i | 0.00870452 | + | 0.0150767i | 0.870345 | − | 0.492443i | \(-0.163896\pi\) |
−0.861640 | + | 0.507519i | \(0.830563\pi\) | |||||||
\(860\) | 22.4707 | − | 12.9735i | 0.766244 | − | 0.442391i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.3787 | + | 42.2251i | −0.830341 | + | 1.43819i | ||||
\(863\) | −17.7527 | + | 10.2495i | −0.604310 | + | 0.348898i | −0.770735 | − | 0.637156i | \(-0.780111\pi\) |
0.166426 | + | 0.986054i | \(0.446777\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.3725 | − | 8.29797i | 0.488680 | − | 0.282139i | ||||
\(866\) | 46.7347 | − | 26.9823i | 1.58811 | − | 0.916896i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 42.1041 | + | 54.3356i | 1.42911 | + | 1.84427i | ||||
\(869\) | 15.1799 | − | 8.76412i | 0.514943 | − | 0.297302i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.31113 | − | 5.97128i | 0.146077 | − | 0.202329i | ||||
\(872\) | 17.4422 | − | 30.2107i | 0.590667 | − | 1.02306i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.427047 | − | 0.739668i | −0.0144451 | − | 0.0250196i | ||||
\(875\) | 12.7452 | + | 16.4477i | 0.430866 | + | 0.556035i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 11.2906i | − | 0.381256i | −0.981662 | − | 0.190628i | \(-0.938948\pi\) | ||
0.981662 | − | 0.190628i | \(-0.0610525\pi\) | |||||||
\(878\) | 24.0128 | − | 13.8638i | 0.810394 | − | 0.467881i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.398953 | −0.0134487 | ||||||||
\(881\) | −11.2634 | − | 19.5088i | −0.379474 | − | 0.657268i | 0.611512 | − | 0.791235i | \(-0.290562\pi\) |
−0.990986 | + | 0.133967i | \(0.957228\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0268 | −0.943178 | −0.471589 | − | 0.881819i | \(-0.656319\pi\) | ||||
−0.471589 | + | 0.881819i | \(0.656319\pi\) | |||||||
\(884\) | −22.5196 | + | 10.1073i | −0.757417 | + | 0.339945i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 36.2376i | − | 1.21743i | ||||||
\(887\) | −10.3118 | + | 17.8605i | −0.346235 | + | 0.599696i | −0.985577 | − | 0.169226i | \(-0.945873\pi\) |
0.639342 | + | 0.768922i | \(0.279207\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.4509 | − | 15.7137i | −1.28960 | − | 0.527019i | ||||
\(890\) | 29.5954 | + | 17.0869i | 0.992040 | + | 0.572754i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 45.9621 | + | 26.5362i | 1.53893 | + | 0.888499i | ||||
\(893\) | −0.00853722 | − | 0.0147869i | −0.000285687 | − | 0.000494824i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.12305 | + | 1.22574i | −0.0709658 | + | 0.0409721i | ||||
\(896\) | −49.6174 | + | 6.77181i | −1.65760 | + | 0.226230i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.9438 | + | 51.8642i | 0.999238 | + | 1.73073i | ||||
\(899\) | 10.6887i | 0.356489i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.61725 | −0.187138 | ||||||||
\(902\) | − | 34.6912i | − | 1.15509i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.05263 | + | 5.22654i | 0.301086 | + | 0.173832i | ||||
\(905\) | −1.00384 | + | 0.579565i | −0.0333686 | + | 0.0192654i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.4631 | −1.37676 | −0.688379 | − | 0.725351i | \(-0.741678\pi\) | ||||
−0.688379 | + | 0.725351i | \(0.741678\pi\) | |||||||
\(908\) | 3.70892 | + | 2.14134i | 0.123085 | + | 0.0710630i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18.6058 | − | 0.631308i | 0.616776 | − | 0.0209277i | ||||
\(911\) | −40.8187 | −1.35239 | −0.676193 | − | 0.736725i | \(-0.736371\pi\) | ||||
−0.676193 | + | 0.736725i | \(0.736371\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.3436 | −0.573990 | ||||||||
\(914\) | −35.4655 | − | 61.4280i | −1.17309 | − | 2.03186i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −59.5849 | − | 34.4014i | −1.96874 | − | 1.13665i | ||||
\(917\) | −6.23346 | − | 2.54741i | −0.205847 | − | 0.0841230i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.7678 | −1.60870 | −0.804350 | − | 0.594155i | \(-0.797486\pi\) | ||||
−0.804350 | + | 0.594155i | \(0.797486\pi\) | |||||||
\(920\) | −19.9129 | −0.656509 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.2659 | − | 68.0105i | −1.29315 | − | 2.23981i | ||||
\(923\) | 20.9850 | + | 46.7557i | 0.690730 | + | 1.53898i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.8544 | − | 14.3497i | 0.817209 | − | 0.471816i | ||||
\(926\) | −1.94837 | + | 3.37468i | −0.0640275 | + | 0.110899i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.22958 | − | 3.59665i | −0.204496 | − | 0.118066i | ||||
\(929\) | 29.3829i | 0.964023i | 0.876165 | + | 0.482012i | \(0.160094\pi\) | ||||
−0.876165 | + | 0.482012i | \(0.839906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.321479 | + | 0.0828796i | 0.0105360 | + | 0.00271627i | ||||
\(932\) | −21.9855 | + | 38.0801i | −0.720160 | + | 1.24735i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 65.3031i | 2.13678i | ||||||||
\(935\) | 1.31930 | − | 2.28509i | 0.0431456 | − | 0.0747304i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0196 | −0.686681 | −0.343340 | − | 0.939211i | \(-0.611558\pi\) | ||||
−0.343340 | + | 0.939211i | \(0.611558\pi\) | |||||||
\(938\) | −1.68327 | − | 12.3334i | −0.0549606 | − | 0.402699i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.00816 | −0.0328825 | ||||||||
\(941\) | −20.8740 | − | 12.0516i | −0.680474 | − | 0.392872i | 0.119560 | − | 0.992827i | \(-0.461852\pi\) |
−0.800034 | + | 0.599955i | \(0.795185\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 78.3312i | − | 2.55081i | ||||||
\(944\) | − | 0.514013i | − | 0.0167297i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0423 | − | 27.7860i | −0.521579 | − | 0.903402i | ||||
\(947\) | 2.89292 | + | 1.67023i | 0.0940072 | + | 0.0542751i | 0.546267 | − | 0.837611i | \(-0.316049\pi\) |
−0.452259 | + | 0.891886i | \(0.649382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.98245 | + | 22.2415i | 0.324044 | + | 0.721988i | ||||
\(950\) | 0.233883 | + | 0.405097i | 0.00758815 | + | 0.0131431i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.23180 | + | 15.2491i | −0.201974 | + | 0.494225i | ||||
\(953\) | 2.48562 | − | 4.30522i | 0.0805171 | − | 0.139460i | −0.822955 | − | 0.568106i | \(-0.807676\pi\) |
0.903472 | + | 0.428647i | \(0.141009\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.11039 | − | 0.641082i | 0.0359313 | − | 0.0207449i | ||||
\(956\) | −38.2546 | + | 22.0863i | −1.23724 | + | 0.714322i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.23509 | − | 12.5315i | 0.233755 | − | 0.404876i | ||||
\(959\) | 1.86637 | − | 4.56695i | 0.0602681 | − | 0.147475i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3981 | + | 26.6702i | 0.496711 | + | 0.860329i | ||||
\(962\) | 5.65211 | − | 55.3709i | 0.182231 | − | 1.78523i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.38755 | − | 1.37845i | −0.0768978 | − | 0.0443970i | ||||
\(965\) | 2.94601 | + | 5.10264i | 0.0948354 | + | 0.164260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.4943i | 1.52731i | 0.645623 | + | 0.763657i | \(0.276598\pi\) | ||||
−0.645623 | + | 0.763657i | \(0.723402\pi\) | |||||||
\(968\) | − | 26.2705i | − | 0.844364i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.720362 | − | 0.415901i | −0.0231294 | − | 0.0133538i | ||||
\(971\) | −34.4715 | −1.10624 | −0.553121 | − | 0.833101i | \(-0.686563\pi\) | ||||
−0.553121 | + | 0.833101i | \(0.686563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.58463 | + | 40.9188i | 0.179035 | + | 1.31180i | ||||
\(974\) | 29.9830 | 0.960717 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.708122 | + | 1.22650i | −0.0226664 | + | 0.0392594i | ||||
\(977\) | 13.3481i | 0.427044i | 0.976938 | + | 0.213522i | \(0.0684936\pi\) | ||||
−0.976938 | + | 0.213522i | \(0.931506\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.1632 | − | 22.7993i | 0.420698 | − | 0.728670i | ||||
\(980\) | 13.7288 | − | 13.9918i | 0.438551 | − | 0.446951i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 28.4507i | − | 0.907898i | ||||||
\(983\) | −10.8551 | − | 6.26720i | −0.346224 | − | 0.199893i | 0.316797 | − | 0.948493i | \(-0.397393\pi\) |
−0.663021 | + | 0.748601i | \(0.730726\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.55685 | − | 11.3568i | 0.208919 | − | 0.361858i | ||||
\(986\) | −5.61804 | + | 3.24358i | −0.178915 | + | 0.103297i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.562243 | + | 0.0573923i | 0.0178873 | + | 0.00182589i | ||||
\(989\) | −36.2227 | − | 62.7396i | −1.15182 | − | 1.99500i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4119 | −0.330745 | −0.165373 | − | 0.986231i | \(-0.552883\pi\) | ||||
−0.165373 | + | 0.986231i | \(0.552883\pi\) | |||||||
\(992\) | −41.5875 | −1.32040 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 80.1808 | + | 32.7673i | 2.54318 | + | 1.03932i | ||||
\(995\) | 4.85414 | + | 2.80254i | 0.153887 | + | 0.0888464i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.87635 | − | 4.98198i | −0.0910949 | − | 0.157781i | 0.816877 | − | 0.576812i | \(-0.195703\pi\) |
−0.907972 | + | 0.419031i | \(0.862370\pi\) | |||||||
\(998\) | 21.0827 | 0.667362 | ||||||||
\(999\) | 0 | 0 |
(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 | 819.2.do.e.361.1 | 12 | ||
3.2 | odd | 2 | 91.2.u.b.88.6 | yes | 12 | ||
7.2 | even | 3 | 819.2.bm.f.478.6 | 12 | |||
13.4 | even | 6 | 819.2.bm.f.550.1 | 12 | |||
21.2 | odd | 6 | 91.2.k.b.23.1 | yes | 12 | ||
21.5 | even | 6 | 637.2.k.i.569.1 | 12 | |||
21.11 | odd | 6 | 637.2.q.g.491.1 | 12 | |||
21.17 | even | 6 | 637.2.q.i.491.1 | 12 | |||
21.20 | even | 2 | 637.2.u.g.361.6 | 12 | |||
39.2 | even | 12 | 1183.2.e.j.508.11 | 24 | |||
39.11 | even | 12 | 1183.2.e.j.508.2 | 24 | |||
39.17 | odd | 6 | 91.2.k.b.4.6 | ✓ | 12 | ||
91.30 | even | 6 | inner | 819.2.do.e.667.1 | 12 | ||
273.2 | even | 12 | 1183.2.e.j.170.11 | 24 | |||
273.11 | even | 12 | 8281.2.a.cp.1.11 | 12 | |||
273.17 | even | 6 | 637.2.q.i.589.1 | 12 | |||
273.80 | odd | 12 | 8281.2.a.co.1.2 | 12 | |||
273.95 | odd | 6 | 637.2.q.g.589.1 | 12 | |||
273.128 | even | 12 | 1183.2.e.j.170.2 | 24 | |||
273.158 | even | 12 | 8281.2.a.cp.1.2 | 12 | |||
273.173 | even | 6 | 637.2.u.g.30.6 | 12 | |||
273.206 | odd | 12 | 8281.2.a.co.1.11 | 12 | |||
273.212 | odd | 6 | 91.2.u.b.30.6 | yes | 12 | ||
273.251 | even | 6 | 637.2.k.i.459.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.6 | ✓ | 12 | 39.17 | odd | 6 | ||
91.2.k.b.23.1 | yes | 12 | 21.2 | odd | 6 | ||
91.2.u.b.30.6 | yes | 12 | 273.212 | odd | 6 | ||
91.2.u.b.88.6 | yes | 12 | 3.2 | odd | 2 | ||
637.2.k.i.459.6 | 12 | 273.251 | even | 6 | |||
637.2.k.i.569.1 | 12 | 21.5 | even | 6 | |||
637.2.q.g.491.1 | 12 | 21.11 | odd | 6 | |||
637.2.q.g.589.1 | 12 | 273.95 | odd | 6 | |||
637.2.q.i.491.1 | 12 | 21.17 | even | 6 | |||
637.2.q.i.589.1 | 12 | 273.17 | even | 6 | |||
637.2.u.g.30.6 | 12 | 273.173 | even | 6 | |||
637.2.u.g.361.6 | 12 | 21.20 | even | 2 | |||
819.2.bm.f.478.6 | 12 | 7.2 | even | 3 | |||
819.2.bm.f.550.1 | 12 | 13.4 | even | 6 | |||
819.2.do.e.361.1 | 12 | 1.1 | even | 1 | trivial | ||
819.2.do.e.667.1 | 12 | 91.30 | even | 6 | inner | ||
1183.2.e.j.170.2 | 24 | 273.128 | even | 12 | |||
1183.2.e.j.170.11 | 24 | 273.2 | even | 12 | |||
1183.2.e.j.508.2 | 24 | 39.11 | even | 12 | |||
1183.2.e.j.508.11 | 24 | 39.2 | even | 12 | |||
8281.2.a.co.1.2 | 12 | 273.80 | odd | 12 | |||
8281.2.a.co.1.11 | 12 | 273.206 | odd | 12 | |||
8281.2.a.cp.1.2 | 12 | 273.158 | even | 12 | |||
8281.2.a.cp.1.11 | 12 | 273.11 | even | 12 |