Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 459.6 | ||
Root | \(1.21245 + 0.727987i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.459 |
Dual form | 637.2.k.i.569.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.30327i | 1.62866i | 0.580405 | + | 0.814328i | \(0.302894\pi\) | ||||
−0.580405 | + | 0.814328i | \(0.697106\pi\) | |||||||
\(3\) | −0.736680 | − | 1.27597i | −0.425323 | − | 0.736680i | 0.571128 | − | 0.820861i | \(-0.306506\pi\) |
−0.996451 | + | 0.0841807i | \(0.973173\pi\) | |||||||
\(4\) | −3.30504 | −1.65252 | ||||||||
\(5\) | −0.733776 | + | 0.423646i | −0.328155 | + | 0.189460i | −0.655022 | − | 0.755610i | \(-0.727340\pi\) |
0.326867 | + | 0.945070i | \(0.394007\pi\) | |||||||
\(6\) | 2.93889 | − | 1.69677i | 1.19980 | − | 0.692704i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 3.00585i | − | 1.06273i | ||||||
\(9\) | 0.414604 | − | 0.718115i | 0.138201 | − | 0.239372i | ||||
\(10\) | −0.975769 | − | 1.69008i | −0.308565 | − | 0.534451i | ||||
\(11\) | 1.30198 | − | 0.751701i | 0.392563 | − | 0.226646i | −0.290707 | − | 0.956812i | \(-0.593890\pi\) |
0.683270 | + | 0.730166i | \(0.260557\pi\) | |||||||
\(12\) | 2.43476 | + | 4.21712i | 0.702853 | + | 1.21738i | ||||
\(13\) | 2.92329 | − | 2.11054i | 0.810774 | − | 0.585360i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.08112 | + | 0.624183i | 0.279143 | + | 0.161163i | ||||
\(16\) | 0.313194 | 0.0782985 | ||||||||
\(17\) | 2.07140 | 0.502389 | 0.251194 | − | 0.967937i | \(-0.419177\pi\) | ||||
0.251194 | + | 0.967937i | \(0.419177\pi\) | |||||||
\(18\) | 1.65401 | + | 0.954943i | 0.389854 | + | 0.225082i | ||||
\(19\) | −0.0410731 | − | 0.0237136i | −0.00942282 | − | 0.00544027i | 0.495281 | − | 0.868733i | \(-0.335065\pi\) |
−0.504704 | + | 0.863292i | \(0.668398\pi\) | |||||||
\(20\) | 2.42516 | − | 1.40016i | 0.542282 | − | 0.313086i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.73137 | + | 2.99882i | 0.369129 | + | 0.639350i | ||||
\(23\) | 7.81870 | 1.63031 | 0.815156 | − | 0.579241i | \(-0.196651\pi\) | ||||
0.815156 | + | 0.579241i | \(0.196651\pi\) | |||||||
\(24\) | −3.83536 | + | 2.21435i | −0.782891 | + | 0.452002i | ||||
\(25\) | −2.14105 | + | 3.70840i | −0.428210 | + | 0.741681i | ||||
\(26\) | 4.86115 | + | 6.73311i | 0.953349 | + | 1.32047i | ||||
\(27\) | −5.64180 | −1.08577 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.679854 | + | 1.17754i | −0.126246 | + | 0.218664i | −0.922219 | − | 0.386668i | \(-0.873626\pi\) |
0.795973 | + | 0.605331i | \(0.206959\pi\) | |||||||
\(30\) | −1.43766 | + | 2.49010i | −0.262480 | + | 0.454628i | ||||
\(31\) | 6.80787 | + | 3.93052i | 1.22273 | + | 0.705943i | 0.965499 | − | 0.260407i | \(-0.0838567\pi\) |
0.257230 | + | 0.966350i | \(0.417190\pi\) | |||||||
\(32\) | − | 5.29033i | − | 0.935206i | ||||||
\(33\) | −1.91829 | − | 1.10753i | −0.333932 | − | 0.192796i | ||||
\(34\) | 4.77099i | 0.818218i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.37028 | + | 2.37340i | −0.228380 | + | 0.395566i | ||||
\(37\) | − | 6.70219i | − | 1.10183i | −0.834560 | − | 0.550917i | \(-0.814278\pi\) | ||
0.834560 | − | 0.550917i | \(-0.185722\pi\) | |||||||
\(38\) | 0.0546187 | − | 0.0946024i | 0.00886032 | − | 0.0153465i | ||||
\(39\) | −4.84652 | − | 2.17522i | −0.776064 | − | 0.348314i | ||||
\(40\) | 1.27341 | + | 2.20562i | 0.201345 | + | 0.348739i | ||||
\(41\) | 8.67622 | + | 5.00922i | 1.35500 | + | 0.782309i | 0.988945 | − | 0.148285i | \(-0.0473754\pi\) |
0.366054 | + | 0.930594i | \(0.380709\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.63283 | + | 8.02430i | 0.706500 | + | 1.22369i | 0.966147 | + | 0.257991i | \(0.0830604\pi\) |
−0.259647 | + | 0.965704i | \(0.583606\pi\) | |||||||
\(44\) | −4.30311 | + | 2.48440i | −0.648718 | + | 0.374537i | ||||
\(45\) | 0.702581i | 0.104735i | ||||||||
\(46\) | 18.0086i | 2.65522i | ||||||||
\(47\) | 0.311781 | − | 0.180007i | 0.0454779 | − | 0.0262567i | −0.477089 | − | 0.878855i | \(-0.658308\pi\) |
0.522567 | + | 0.852598i | \(0.324975\pi\) | |||||||
\(48\) | −0.230724 | − | 0.399625i | −0.0333021 | − | 0.0576810i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.54144 | − | 4.93141i | −1.20794 | − | 0.697406i | ||||
\(51\) | −1.52596 | − | 2.64304i | −0.213677 | − | 0.370100i | ||||
\(52\) | −9.66157 | + | 6.97543i | −1.33982 | + | 0.967318i | ||||
\(53\) | −1.35591 | + | 2.34850i | −0.186248 | + | 0.322591i | −0.943996 | − | 0.329956i | \(-0.892966\pi\) |
0.757748 | + | 0.652547i | \(0.226299\pi\) | |||||||
\(54\) | − | 12.9946i | − | 1.76834i | ||||||
\(55\) | −0.636910 | + | 1.10316i | −0.0858809 | + | 0.148750i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0698773i | 0.00925548i | ||||||||
\(58\) | −2.71219 | − | 1.56588i | −0.356128 | − | 0.205611i | ||||
\(59\) | 1.64120i | 0.213666i | 0.994277 | + | 0.106833i | \(0.0340709\pi\) | ||||
−0.994277 | + | 0.106833i | \(0.965929\pi\) | |||||||
\(60\) | −3.57313 | − | 2.06295i | −0.461289 | − | 0.266325i | ||||
\(61\) | 2.26097 | − | 3.91612i | 0.289488 | − | 0.501407i | −0.684200 | − | 0.729295i | \(-0.739848\pi\) |
0.973688 | + | 0.227887i | \(0.0731817\pi\) | |||||||
\(62\) | −9.05305 | + | 15.6803i | −1.14974 | + | 1.99140i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.8114 | 1.60143 | ||||||||
\(65\) | −1.25091 | + | 2.78711i | −0.155157 | + | 0.345698i | ||||
\(66\) | 2.55093 | − | 4.41834i | 0.313998 | − | 0.543860i | ||||
\(67\) | −1.76900 | + | 1.02133i | −0.216117 | + | 0.124775i | −0.604151 | − | 0.796870i | \(-0.706488\pi\) |
0.388034 | + | 0.921645i | \(0.373154\pi\) | |||||||
\(68\) | −6.84606 | −0.830206 | ||||||||
\(69\) | −5.75988 | − | 9.97641i | −0.693409 | − | 1.20102i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3096 | − | 7.10697i | 1.46088 | − | 0.843442i | 0.461832 | − | 0.886967i | \(-0.347192\pi\) |
0.999052 | + | 0.0435255i | \(0.0138590\pi\) | |||||||
\(72\) | −2.15854 | − | 1.24624i | −0.254387 | − | 0.146870i | ||||
\(73\) | −5.85563 | − | 3.38075i | −0.685349 | − | 0.395687i | 0.116518 | − | 0.993189i | \(-0.462827\pi\) |
−0.801867 | + | 0.597502i | \(0.796160\pi\) | |||||||
\(74\) | 15.4369 | 1.79451 | ||||||||
\(75\) | 6.30907 | 0.728509 | ||||||||
\(76\) | 0.135748 | + | 0.0783743i | 0.0155714 | + | 0.00899015i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.01012 | − | 11.1628i | 0.567284 | − | 1.26394i | ||||
\(79\) | −5.82952 | − | 10.0970i | −0.655873 | − | 1.13600i | −0.981674 | − | 0.190567i | \(-0.938967\pi\) |
0.325801 | − | 0.945438i | \(-0.394366\pi\) | |||||||
\(80\) | −0.229814 | + | 0.132683i | −0.0256940 | + | 0.0148344i | ||||
\(81\) | 2.91240 | + | 5.04442i | 0.323600 | + | 0.560491i | ||||
\(82\) | −11.5376 | + | 19.9837i | −1.27411 | + | 2.20683i | ||||
\(83\) | − | 11.5362i | − | 1.26627i | −0.774043 | − | 0.633133i | \(-0.781768\pi\) | ||
0.774043 | − | 0.633133i | \(-0.218232\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.51994 | + | 0.877541i | −0.164861 | + | 0.0951826i | ||||
\(86\) | −18.4821 | + | 10.6706i | −1.99298 | + | 1.15065i | ||||
\(87\) | 2.00334 | 0.214781 | ||||||||
\(88\) | −2.25950 | − | 3.91357i | −0.240863 | − | 0.417188i | ||||
\(89\) | − | 17.5112i | − | 1.85619i | −0.372350 | − | 0.928093i | \(-0.621448\pi\) | ||
0.372350 | − | 0.928093i | \(-0.378552\pi\) | |||||||
\(90\) | −1.61823 | −0.170576 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −25.8411 | −2.69412 | ||||||||
\(93\) | − | 11.5822i | − | 1.20101i | ||||||
\(94\) | 0.414604 | + | 0.718115i | 0.0427631 | + | 0.0740679i | ||||
\(95\) | 0.0401846 | 0.00412286 | ||||||||
\(96\) | −6.75029 | + | 3.89728i | −0.688948 | + | 0.397764i | ||||
\(97\) | −0.369125 | + | 0.213115i | −0.0374790 | + | 0.0216385i | −0.518622 | − | 0.855003i | \(-0.673555\pi\) |
0.481143 | + | 0.876642i | \(0.340222\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.24663i | − | 0.125291i | ||||||
\(100\) | 7.07624 | − | 12.2564i | 0.707624 | − | 1.22564i | ||||
\(101\) | −4.83499 | − | 8.37444i | −0.481099 | − | 0.833288i | 0.518666 | − | 0.854977i | \(-0.326429\pi\) |
−0.999765 | + | 0.0216891i | \(0.993096\pi\) | |||||||
\(102\) | 6.08763 | − | 3.51469i | 0.602765 | − | 0.348007i | ||||
\(103\) | 4.98912 | + | 8.64140i | 0.491592 | + | 0.851463i | 0.999953 | − | 0.00968129i | \(-0.00308170\pi\) |
−0.508361 | + | 0.861144i | \(0.669748\pi\) | |||||||
\(104\) | −6.34397 | − | 8.78695i | −0.622078 | − | 0.861631i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.40922 | − | 3.12301i | −0.525390 | − | 0.303334i | ||||
\(107\) | 9.86223 | 0.953417 | 0.476709 | − | 0.879061i | \(-0.341830\pi\) | ||||
0.476709 | + | 0.879061i | \(0.341830\pi\) | |||||||
\(108\) | 18.6464 | 1.79425 | ||||||||
\(109\) | −10.0507 | − | 5.80275i | −0.962679 | − | 0.555803i | −0.0656822 | − | 0.997841i | \(-0.520922\pi\) |
−0.896996 | + | 0.442038i | \(0.854256\pi\) | |||||||
\(110\) | −2.54087 | − | 1.46697i | −0.242263 | − | 0.139870i | ||||
\(111\) | −8.55178 | + | 4.93737i | −0.811699 | + | 0.468635i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.73879 | + | 3.01167i | 0.163572 | + | 0.283314i | 0.936147 | − | 0.351609i | \(-0.114365\pi\) |
−0.772576 | + | 0.634923i | \(0.781032\pi\) | |||||||
\(114\) | −0.160946 | −0.0150740 | ||||||||
\(115\) | −5.73718 | + | 3.31236i | −0.534994 | + | 0.308879i | ||||
\(116\) | 2.24694 | − | 3.89182i | 0.208623 | − | 0.361346i | ||||
\(117\) | −0.303608 | − | 2.97429i | −0.0280686 | − | 0.274974i | ||||
\(118\) | −3.78011 | −0.347987 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.87620 | − | 3.24967i | 0.171273 | − | 0.296653i | ||||
\(121\) | −4.36989 | + | 7.56887i | −0.397263 | + | 0.688079i | ||||
\(122\) | 9.01986 | + | 5.20762i | 0.816620 | + | 0.471476i | ||||
\(123\) | − | 14.7608i | − | 1.33093i | ||||||
\(124\) | −22.5003 | − | 12.9905i | −2.02058 | − | 1.16658i | ||||
\(125\) | − | 7.86464i | − | 0.703435i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.84992 | + | 13.5965i | −0.696567 | + | 1.20649i | 0.273082 | + | 0.961991i | \(0.411957\pi\) |
−0.969649 | + | 0.244499i | \(0.921376\pi\) | |||||||
\(128\) | 18.9275i | 1.67297i | ||||||||
\(129\) | 6.82583 | − | 11.8227i | 0.600981 | − | 1.04093i | ||||
\(130\) | −6.41945 | − | 2.88119i | −0.563023 | − | 0.252697i | ||||
\(131\) | −1.27259 | − | 2.20418i | −0.111186 | − | 0.192580i | 0.805063 | − | 0.593190i | \(-0.202132\pi\) |
−0.916249 | + | 0.400610i | \(0.868798\pi\) | |||||||
\(132\) | 6.34003 | + | 3.66042i | 0.551829 | + | 0.318598i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.35240 | − | 4.07447i | −0.203216 | − | 0.351981i | ||||
\(135\) | 4.13982 | − | 2.39013i | 0.356299 | − | 0.205709i | ||||
\(136\) | − | 6.22632i | − | 0.533902i | ||||||
\(137\) | 1.86472i | 0.159314i | 0.996822 | + | 0.0796571i | \(0.0253825\pi\) | ||||
−0.996822 | + | 0.0796571i | \(0.974617\pi\) | |||||||
\(138\) | 22.9783 | − | 13.2665i | 1.95605 | − | 1.12932i | ||||
\(139\) | 7.80462 | + | 13.5180i | 0.661979 | + | 1.14658i | 0.980095 | + | 0.198530i | \(0.0636166\pi\) |
−0.318116 | + | 0.948052i | \(0.603050\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.459366 | − | 0.265215i | −0.0386856 | − | 0.0223351i | ||||
\(142\) | 16.3692 | + | 28.3524i | 1.37368 | + | 2.37928i | ||||
\(143\) | 2.21957 | − | 4.94533i | 0.185610 | − | 0.413550i | ||||
\(144\) | 0.129851 | − | 0.224909i | 0.0108209 | − | 0.0187424i | ||||
\(145\) | − | 1.15207i | − | 0.0956741i | ||||||
\(146\) | 7.78676 | − | 13.4871i | 0.644437 | − | 1.11620i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 22.1510i | 1.82080i | ||||||||
\(149\) | 5.51106 | + | 3.18181i | 0.451484 | + | 0.260664i | 0.708457 | − | 0.705754i | \(-0.249392\pi\) |
−0.256973 | + | 0.966419i | \(0.582725\pi\) | |||||||
\(150\) | 14.5315i | 1.18649i | ||||||||
\(151\) | 0.575122 | + | 0.332047i | 0.0468028 | + | 0.0270216i | 0.523219 | − | 0.852198i | \(-0.324731\pi\) |
−0.476416 | + | 0.879220i | \(0.658064\pi\) | |||||||
\(152\) | −0.0712794 | + | 0.123460i | −0.00578152 | + | 0.0100139i | ||||
\(153\) | 0.858811 | − | 1.48750i | 0.0694307 | − | 0.120258i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.66060 | −0.534992 | ||||||||
\(156\) | 16.0179 | + | 7.18919i | 1.28246 | + | 0.575596i | ||||
\(157\) | −8.28798 | + | 14.3552i | −0.661453 | + | 1.14567i | 0.318781 | + | 0.947828i | \(0.396727\pi\) |
−0.980234 | + | 0.197842i | \(0.936607\pi\) | |||||||
\(158\) | 23.2562 | − | 13.4269i | 1.85016 | − | 1.06819i | ||||
\(159\) | 3.99548 | 0.316862 | ||||||||
\(160\) | 2.24122 | + | 3.88191i | 0.177184 | + | 0.306892i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.6186 | + | 6.70802i | −0.912846 | + | 0.527032i | ||||
\(163\) | 7.83863 | + | 4.52563i | 0.613969 | + | 0.354475i | 0.774517 | − | 0.632553i | \(-0.217993\pi\) |
−0.160548 | + | 0.987028i | \(0.551326\pi\) | |||||||
\(164\) | −28.6752 | − | 16.5557i | −2.23916 | − | 1.29278i | ||||
\(165\) | 1.87680 | 0.146108 | ||||||||
\(166\) | 26.5710 | 2.06231 | ||||||||
\(167\) | 2.30156 | + | 1.32880i | 0.178100 | + | 0.102826i | 0.586400 | − | 0.810022i | \(-0.300545\pi\) |
−0.408300 | + | 0.912848i | \(0.633878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.09120 | − | 12.3395i | 0.314708 | − | 0.949189i | ||||
\(170\) | −2.02121 | − | 3.50084i | −0.155020 | − | 0.268502i | ||||
\(171\) | −0.0340582 | + | 0.0196635i | −0.00260449 | + | 0.00150370i | ||||
\(172\) | −15.3117 | − | 26.5206i | −1.16750 | − | 2.02218i | ||||
\(173\) | −9.79352 | + | 16.9629i | −0.744588 | + | 1.28966i | 0.205799 | + | 0.978594i | \(0.434021\pi\) |
−0.950387 | + | 0.311070i | \(0.899313\pi\) | |||||||
\(174\) | 4.61423i | 0.349804i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.407774 | − | 0.235428i | 0.0307371 | − | 0.0177461i | ||||
\(177\) | 2.09411 | − | 1.20904i | 0.157403 | − | 0.0908768i | ||||
\(178\) | 40.3330 | 3.02309 | ||||||||
\(179\) | −1.44666 | − | 2.50569i | −0.108129 | − | 0.187284i | 0.806884 | − | 0.590711i | \(-0.201152\pi\) |
−0.915012 | + | 0.403426i | \(0.867819\pi\) | |||||||
\(180\) | − | 2.32205i | − | 0.173076i | ||||||
\(181\) | 1.36804 | 0.101686 | 0.0508429 | − | 0.998707i | \(-0.483809\pi\) | ||||
0.0508429 | + | 0.998707i | \(0.483809\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.66245 | −0.492503 | ||||||||
\(184\) | − | 23.5018i | − | 1.73258i | ||||||
\(185\) | 2.83936 | + | 4.91791i | 0.208754 | + | 0.361572i | ||||
\(186\) | 26.6768 | 1.95604 | ||||||||
\(187\) | 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 | ||||||||
\(191\) | 0.756625 | − | 1.31051i | 0.0547475 | − | 0.0948254i | −0.837353 | − | 0.546663i | \(-0.815898\pi\) |
0.892100 | + | 0.451837i | \(0.149231\pi\) | |||||||
\(192\) | −9.43792 | − | 16.3470i | −0.681123 | − | 1.17974i | ||||
\(193\) | −6.02229 | + | 3.47697i | −0.433494 | + | 0.250278i | −0.700834 | − | 0.713324i | \(-0.747189\pi\) |
0.267340 | + | 0.963602i | \(0.413855\pi\) | |||||||
\(194\) | −0.490860 | − | 0.850194i | −0.0352417 | − | 0.0610404i | ||||
\(195\) | 4.47778 | − | 0.457080i | 0.320661 | − | 0.0327322i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.4037 | − | 7.73860i | −0.954971 | − | 0.551353i | −0.0603494 | − | 0.998177i | \(-0.519221\pi\) |
−0.894622 | + | 0.446825i | \(0.852555\pi\) | |||||||
\(198\) | 2.87133 | 0.204056 | ||||||||
\(199\) | 6.61529 | 0.468945 | 0.234473 | − | 0.972123i | \(-0.424664\pi\) | ||||
0.234473 | + | 0.972123i | \(0.424664\pi\) | |||||||
\(200\) | 11.1469 | + | 6.43566i | 0.788205 | + | 0.455070i | ||||
\(201\) | 2.60637 | + | 1.50479i | 0.183839 | + | 0.106140i | ||||
\(202\) | 19.2886 | − | 11.1363i | 1.35714 | − | 0.783545i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.04336 | + | 8.73535i | 0.353106 | + | 0.611597i | ||||
\(205\) | −8.48854 | −0.592865 | ||||||||
\(206\) | −19.9035 | + | 11.4913i | −1.38674 | + | 0.800634i | ||||
\(207\) | 3.24166 | − | 5.61473i | 0.225311 | − | 0.390250i | ||||
\(208\) | 0.915555 | − | 0.661010i | 0.0634823 | − | 0.0458328i | ||||
\(209\) | −0.0713021 | −0.00493207 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.04714 | − | 7.00986i | 0.278617 | − | 0.482578i | −0.692424 | − | 0.721490i | \(-0.743457\pi\) |
0.971041 | + | 0.238912i | \(0.0767907\pi\) | |||||||
\(212\) | 4.48132 | − | 7.76187i | 0.307778 | − | 0.533088i | ||||
\(213\) | −18.1365 | − | 10.4711i | −1.24269 | − | 0.717470i | ||||
\(214\) | 22.7153i | 1.55279i | ||||||||
\(215\) | −6.79892 | − | 3.92536i | −0.463683 | − | 0.267707i | ||||
\(216\) | 16.9584i | 1.15387i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.3653 | − | 23.1493i | 0.905211 | − | 1.56787i | ||||
\(219\) | 9.96212i | 0.673178i | ||||||||
\(220\) | 2.10501 | − | 3.64599i | 0.141920 | − | 0.245812i | ||||
\(221\) | 6.05530 | − | 4.37178i | 0.407323 | − | 0.294078i | ||||
\(222\) | −11.3721 | − | 19.6970i | −0.763244 | − | 1.32198i | ||||
\(223\) | −13.9067 | − | 8.02903i | −0.931261 | − | 0.537664i | −0.0440506 | − | 0.999029i | \(-0.514026\pi\) |
−0.887210 | + | 0.461366i | \(0.847360\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.77537 | + | 3.07504i | 0.118358 | + | 0.205002i | ||||
\(226\) | −6.93668 | + | 4.00490i | −0.461421 | + | 0.266402i | ||||
\(227\) | − | 1.29581i | − | 0.0860057i | −0.999075 | − | 0.0430029i | \(-0.986308\pi\) | ||
0.999075 | − | 0.0430029i | \(-0.0136925\pi\) | |||||||
\(228\) | − | 0.230947i | − | 0.0152948i | ||||||
\(229\) | −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 | 0.561565 | − | 0.827433i | \(-0.310200\pi\) |
−0.997360 | + | 0.0726127i | \(0.976866\pi\) | |||||||
\(234\) | 6.85059 | − | 0.699290i | 0.447837 | − | 0.0457140i | ||||
\(235\) | −0.152518 | + | 0.264169i | −0.00994920 | + | 0.0172325i | ||||
\(236\) | − | 5.42421i | − | 0.353086i | ||||||
\(237\) | −8.58899 | + | 14.8766i | −0.557915 | + | 0.966337i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3652i | 0.864525i | 0.901748 | + | 0.432263i | \(0.142285\pi\) | ||||
−0.901748 | + | 0.432263i | \(0.857715\pi\) | |||||||
\(240\) | 0.338599 | + | 0.195490i | 0.0218565 | + | 0.0126188i | ||||
\(241\) | − | 0.834153i | − | 0.0537325i | −0.999639 | − | 0.0268663i | \(-0.991447\pi\) | ||
0.999639 | − | 0.0268663i | \(-0.00855282\pi\) | |||||||
\(242\) | −17.4331 | − | 10.0650i | −1.12064 | − | 0.647004i | ||||
\(243\) | −4.17170 | + | 7.22559i | −0.267614 | + | 0.463522i | ||||
\(244\) | −7.47259 | + | 12.9429i | −0.478384 | + | 0.828585i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 33.9980 | 2.16763 | ||||||||
\(247\) | −0.170117 | + | 0.0173651i | −0.0108243 | + | 0.00110491i | ||||
\(248\) | 11.8146 | − | 20.4634i | 0.750225 | − | 1.29943i | ||||
\(249\) | −14.7199 | + | 8.49852i | −0.932834 | + | 0.538572i | ||||
\(250\) | 18.1144 | 1.14565 | ||||||||
\(251\) | −13.6360 | − | 23.6183i | −0.860699 | − | 1.49078i | −0.871255 | − | 0.490831i | \(-0.836693\pi\) |
0.0105555 | − | 0.999944i | \(-0.496640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.1798 | − | 5.87733i | 0.640000 | − | 0.369504i | ||||
\(254\) | −31.3163 | − | 18.0804i | −1.96496 | − | 1.13447i | ||||
\(255\) | 2.23943 | + | 1.29293i | 0.140238 | + | 0.0809667i | ||||
\(256\) | −17.9721 | −1.12326 | ||||||||
\(257\) | 6.55188 | 0.408695 | 0.204348 | − | 0.978898i | \(-0.434493\pi\) | ||||
0.204348 | + | 0.978898i | \(0.434493\pi\) | |||||||
\(258\) | 27.2308 | + | 15.7217i | 1.69532 | + | 0.978791i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.13432 | − | 9.21148i | 0.256399 | − | 0.571272i | ||||
\(261\) | 0.563740 | + | 0.976426i | 0.0348946 | + | 0.0604393i | ||||
\(262\) | 5.07682 | − | 2.93110i | 0.313647 | − | 0.181084i | ||||
\(263\) | 11.2945 | + | 19.5627i | 0.696450 | + | 1.20629i | 0.969689 | + | 0.244341i | \(0.0785717\pi\) |
−0.273239 | + | 0.961946i | \(0.588095\pi\) | |||||||
\(264\) | −3.32906 | + | 5.76610i | −0.204889 | + | 0.354879i | ||||
\(265\) | − | 2.29770i | − | 0.141146i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.3437 | + | 12.9002i | −1.36742 | + | 0.789478i | ||||
\(268\) | 5.84660 | − | 3.37553i | 0.357138 | − | 0.206194i | ||||
\(269\) | −16.0013 | −0.975617 | −0.487808 | − | 0.872951i | \(-0.662203\pi\) | ||||
−0.487808 | + | 0.872951i | \(0.662203\pi\) | |||||||
\(270\) | 5.50510 | + | 9.53511i | 0.335030 | + | 0.580288i | ||||
\(271\) | 8.75935i | 0.532093i | 0.963960 | + | 0.266046i | \(0.0857174\pi\) | ||||
−0.963960 | + | 0.266046i | \(0.914283\pi\) | |||||||
\(272\) | 0.648750 | 0.0393363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29496 | −0.259468 | ||||||||
\(275\) | 6.43771i | 0.388209i | ||||||||
\(276\) | 19.0366 | + | 32.9724i | 1.14587 | + | 1.98471i | ||||
\(277\) | 19.9183 | 1.19677 | 0.598387 | − | 0.801208i | \(-0.295809\pi\) | ||||
0.598387 | + | 0.801208i | \(0.295809\pi\) | |||||||
\(278\) | −31.1355 | + | 17.9761i | −1.86739 | + | 1.07814i | ||||
\(279\) | 5.64514 | − | 3.25922i | 0.337965 | − | 0.195124i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.0234i | − | 0.836566i | −0.908317 | − | 0.418283i | \(-0.862632\pi\) | ||
0.908317 | − | 0.418283i | \(-0.137368\pi\) | |||||||
\(282\) | 0.610861 | − | 1.05804i | 0.0363762 | − | 0.0630055i | ||||
\(283\) | −0.506295 | − | 0.876929i | −0.0300961 | − | 0.0521280i | 0.850585 | − | 0.525838i | \(-0.176248\pi\) |
−0.880681 | + | 0.473710i | \(0.842915\pi\) | |||||||
\(284\) | −40.6838 | + | 23.4888i | −2.41414 | + | 1.39380i | ||||
\(285\) | −0.0296032 | − | 0.0512743i | −0.00175354 | − | 0.00303723i | ||||
\(286\) | 11.3904 | + | 5.11227i | 0.673530 | + | 0.302295i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.79906 | − | 2.19339i | −0.223862 | − | 0.129247i | ||||
\(289\) | −12.7093 | −0.747606 | ||||||||
\(290\) | 2.65352 | 0.155820 | ||||||||
\(291\) | 0.543855 | + | 0.313995i | 0.0318813 | + | 0.0184067i | ||||
\(292\) | 19.3531 | + | 11.1735i | 1.13255 | + | 0.653879i | ||||
\(293\) | 0.172543 | − | 0.0996176i | 0.0100801 | − | 0.00581972i | −0.494952 | − | 0.868921i | \(-0.664814\pi\) |
0.505032 | + | 0.863101i | \(0.331481\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.695286 | − | 1.20427i | −0.0404811 | − | 0.0701153i | ||||
\(296\) | −20.1458 | −1.17095 | ||||||||
\(297\) | −7.34554 | + | 4.24095i | −0.426232 | + | 0.246085i | ||||
\(298\) | −7.32857 | + | 12.6935i | −0.424532 | + | 0.735312i | ||||
\(299\) | 22.8563 | − | 16.5017i | 1.32181 | − | 0.954319i | ||||
\(300\) | −20.8517 | −1.20387 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.764792 | + | 1.32466i | −0.0440088 | + | 0.0762256i | ||||
\(303\) | −7.12368 | + | 12.3386i | −0.409245 | + | 0.708833i | ||||
\(304\) | −0.0128639 | − | 0.00742695i | −0.000737793 | − | 0.000425965i | ||||
\(305\) | 3.83140i | 0.219386i | ||||||||
\(306\) | 3.42612 | + | 1.97807i | 0.195858 | + | 0.113079i | ||||
\(307\) | 27.2004i | 1.55241i | 0.630482 | + | 0.776204i | \(0.282857\pi\) | ||||
−0.630482 | + | 0.776204i | \(0.717143\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.35077 | − | 12.7319i | 0.418171 | − | 0.724293i | ||||
\(310\) | − | 15.3411i | − | 0.871318i | ||||||
\(311\) | −13.5505 | + | 23.4701i | −0.768376 | + | 1.33087i | 0.170067 | + | 0.985432i | \(0.445602\pi\) |
−0.938443 | + | 0.345434i | \(0.887732\pi\) | |||||||
\(312\) | −6.53839 | + | 14.5679i | −0.370163 | + | 0.824744i | ||||
\(313\) | −11.0392 | − | 19.1205i | −0.623975 | − | 1.08076i | −0.988738 | − | 0.149656i | \(-0.952183\pi\) |
0.364763 | − | 0.931100i | \(-0.381150\pi\) | |||||||
\(314\) | −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 | \(0.396939\pi\) | |||||||
\(318\) | 9.20265i | 0.516059i | ||||||||
\(319\) | 2.04419i | 0.114453i | ||||||||
\(320\) | −9.40071 | + | 5.42750i | −0.525516 | + | 0.303407i | ||||
\(321\) | −7.26531 | − | 12.5839i | −0.405510 | − | 0.702364i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0850789 | − | 0.0491204i | −0.00473392 | − | 0.00273313i | ||||
\(324\) | −9.62558 | − | 16.6720i | −0.534754 | − | 0.926221i | ||||
\(325\) | 1.56786 | + | 15.3595i | 0.0869690 | + | 0.851992i | ||||
\(326\) | −10.4237 | + | 18.0544i | −0.577318 | + | 0.999943i | ||||
\(327\) | 17.0991i | 0.945582i | ||||||||
\(328\) | 15.0569 | − | 26.0794i | 0.831381 | − | 1.43999i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.32276i | 0.237960i | ||||||||
\(331\) | 5.70588 | + | 3.29429i | 0.313623 | + | 0.181071i | 0.648547 | − | 0.761175i | \(-0.275377\pi\) |
−0.334923 | + | 0.942245i | \(0.608710\pi\) | |||||||
\(332\) | 38.1277i | 2.09253i | ||||||||
\(333\) | −4.81294 | − | 2.77875i | −0.263748 | − | 0.152275i | ||||
\(334\) | −3.06059 | + | 5.30110i | −0.167468 | + | 0.290063i | ||||
\(335\) | 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 | \(0.536693\pi\) | |||||||
\(338\) | 28.4210 | + | 9.42313i | 1.54590 | + | 0.512551i | ||||
\(339\) | 2.56187 | − | 4.43728i | 0.139141 | − | 0.241000i | ||||
\(340\) | 5.02347 | − | 2.90030i | 0.272436 | − | 0.157291i | ||||
\(341\) | 11.8183 | 0.639998 | ||||||||
\(342\) | −0.0452902 | − | 0.0784450i | −0.00244902 | − | 0.00424182i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 24.1198 | − | 13.9256i | 1.30045 | − | 0.750817i | ||||
\(345\) | 8.45293 | + | 4.88030i | 0.455091 | + | 0.262747i | ||||
\(346\) | −39.0700 | − | 22.5571i | −2.10042 | − | 1.21268i | ||||
\(347\) | −9.09478 | −0.488233 | −0.244117 | − | 0.969746i | \(-0.578498\pi\) | ||||
−0.244117 | + | 0.969746i | \(0.578498\pi\) | |||||||
\(348\) | −6.62111 | −0.354929 | ||||||||
\(349\) | −7.98521 | − | 4.61026i | −0.427439 | − | 0.246782i | 0.270816 | − | 0.962631i | \(-0.412706\pi\) |
−0.698255 | + | 0.715849i | \(0.746040\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.4926 | + | 11.9073i | −0.880310 | + | 0.635564i | ||||
\(352\) | −3.97674 | − | 6.88792i | −0.211961 | − | 0.367127i | ||||
\(353\) | −1.86584 | + | 1.07724i | −0.0993087 | + | 0.0573359i | −0.548832 | − | 0.835933i | \(-0.684927\pi\) |
0.449523 | + | 0.893269i | \(0.351594\pi\) | |||||||
\(354\) | 2.78473 | + | 4.82330i | 0.148007 | + | 0.256356i | ||||
\(355\) | −6.02167 | + | 10.4298i | −0.319597 | + | 0.553559i | ||||
\(356\) | 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 | \(0.405841\pi\) | |||||||
\(360\) | 2.11185 | 0.111304 | ||||||||
\(361\) | −9.49888 | − | 16.4525i | −0.499941 | − | 0.865923i | ||||
\(362\) | 3.15096i | 0.165611i | ||||||||
\(363\) | 12.8769 | 0.675860 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.72896 | 0.299867 | ||||||||
\(366\) | − | 15.3454i | − | 0.802117i | ||||||
\(367\) | 1.14912 | + | 1.99033i | 0.0599833 | + | 0.103894i | 0.894458 | − | 0.447153i | \(-0.147562\pi\) |
−0.834474 | + | 0.551047i | \(0.814229\pi\) | |||||||
\(368\) | 2.44877 | 0.127651 | ||||||||
\(369\) | 7.19439 | − | 4.15368i | 0.374525 | − | 0.216232i | ||||
\(370\) | −11.3273 | + | 6.53979i | −0.588876 | + | 0.339988i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 38.2795i | 1.98470i | ||||||||
\(373\) | −5.88418 | + | 10.1917i | −0.304672 | + | 0.527707i | −0.977188 | − | 0.212375i | \(-0.931880\pi\) |
0.672517 | + | 0.740082i | \(0.265213\pi\) | |||||||
\(374\) | 3.58636 | + | 6.21175i | 0.185446 | + | 0.321202i | ||||
\(375\) | −10.0350 | + | 5.79373i | −0.518207 | + | 0.299187i | ||||
\(376\) | −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 | 0.311619 | − | 0.950207i | \(-0.399129\pi\) |
−0.667094 | + | 0.744974i | \(0.732462\pi\) | |||||||
\(380\) | −0.132812 | −0.00681310 | ||||||||
\(381\) | 23.1315 | 1.18506 | ||||||||
\(382\) | 3.01846 | + | 1.74271i | 0.154438 | + | 0.0891647i | ||||
\(383\) | 24.4605 | + | 14.1223i | 1.24988 | + | 0.721616i | 0.971084 | − | 0.238736i | \(-0.0767331\pi\) |
0.278791 | + | 0.960352i | \(0.410066\pi\) | |||||||
\(384\) | 24.1508 | − | 13.9435i | 1.23244 | − | 0.711551i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.00839 | − | 13.8709i | −0.407616 | − | 0.706012i | ||||
\(387\) | 7.68316 | 0.390557 | ||||||||
\(388\) | 1.21997 | − | 0.704352i | 0.0619347 | − | 0.0357580i | ||||
\(389\) | 3.84043 | − | 6.65182i | 0.194717 | − | 0.337261i | −0.752090 | − | 0.659060i | \(-0.770954\pi\) |
0.946808 | + | 0.321799i | \(0.104288\pi\) | |||||||
\(390\) | 1.05278 | + | 10.3135i | 0.0533094 | + | 0.522246i | ||||
\(391\) | 16.1957 | 0.819050 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.87498 | + | 3.24756i | −0.0945801 | + | 0.163818i | ||||
\(394\) | 17.8241 | − | 30.8722i | 0.897964 | − | 1.55532i | ||||
\(395\) | 8.55513 | + | 4.93931i | 0.430455 | + | 0.248524i | ||||
\(396\) | 4.12017i | 0.207046i | ||||||||
\(397\) | −6.45433 | − | 3.72641i | −0.323933 | − | 0.187023i | 0.329211 | − | 0.944256i | \(-0.393217\pi\) |
−0.653144 | + | 0.757233i | \(0.726551\pi\) | |||||||
\(398\) | 15.2368i | 0.763750i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.670563 | + | 1.16145i | −0.0335282 | + | 0.0580725i | ||||
\(401\) | − | 18.1982i | − | 0.908777i | −0.890804 | − | 0.454389i | \(-0.849858\pi\) | ||
0.890804 | − | 0.454389i | \(-0.150142\pi\) | |||||||
\(402\) | −3.46593 | + | 6.00316i | −0.172865 | + | 0.299411i | ||||
\(403\) | 28.1969 | − | 2.87826i | 1.40459 | − | 0.143376i | ||||
\(404\) | 15.9798 | + | 27.6778i | 0.795025 | + | 1.37702i | ||||
\(405\) | −4.27409 | − | 2.46765i | −0.212381 | − | 0.122618i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.03804 | − | 8.72615i | −0.249727 | − | 0.432539i | ||||
\(408\) | −7.94458 | + | 4.58681i | −0.393315 | + | 0.227081i | ||||
\(409\) | − | 29.2825i | − | 1.44793i | −0.689838 | − | 0.723964i | \(-0.742318\pi\) | ||
0.689838 | − | 0.723964i | \(-0.257682\pi\) | |||||||
\(410\) | − | 19.5514i | − | 0.965573i | ||||||
\(411\) | 2.37933 | − | 1.37371i | 0.117364 | − | 0.0677599i | ||||
\(412\) | −16.4892 | − | 28.5602i | −0.812365 | − | 1.40706i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.9322 | + | 7.46641i | 0.635583 | + | 0.366954i | ||||
\(415\) | 4.88728 | + | 8.46502i | 0.239907 | + | 0.415531i | ||||
\(416\) | −11.1655 | − | 15.4651i | −0.547432 | − | 0.758241i | ||||
\(417\) | 11.4990 | − | 19.9169i | 0.563109 | − | 0.975334i | ||||
\(418\) | − | 0.164228i | − | 0.00803264i | ||||||
\(419\) | −10.3697 | + | 17.9608i | −0.506591 | + | 0.877441i | 0.493380 | + | 0.869814i | \(0.335761\pi\) |
−0.999971 | + | 0.00762733i | \(0.997572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 24.8696i | − | 1.21207i | −0.795437 | − | 0.606036i | \(-0.792759\pi\) | ||
0.795437 | − | 0.606036i | \(-0.207241\pi\) | |||||||
\(422\) | 16.1456 | + | 9.32165i | 0.785954 | + | 0.453771i | ||||
\(423\) | − | 0.298526i | − | 0.0145148i | ||||||
\(424\) | 7.05923 | + | 4.07565i | 0.342826 | + | 0.197931i | ||||
\(425\) | −4.43497 | + | 7.68159i | −0.215128 | + | 0.372612i | ||||
\(426\) | 24.1178 | − | 41.7733i | 1.16851 | − | 2.02392i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −32.5950 | −1.57554 | ||||||||
\(429\) | −7.94520 | + | 0.811025i | −0.383598 | + | 0.0391566i | ||||
\(430\) | 9.04115 | − | 15.6597i | 0.436003 | − | 0.755179i | ||||
\(431\) | −18.3327 | + | 10.5844i | −0.883055 | + | 0.509832i | −0.871665 | − | 0.490103i | \(-0.836959\pi\) |
−0.0113906 | + | 0.999935i | \(0.503626\pi\) | |||||||
\(432\) | −1.76698 | −0.0850138 | ||||||||
\(433\) | 11.7148 | + | 20.2906i | 0.562977 | + | 0.975105i | 0.997235 | + | 0.0743163i | \(0.0236774\pi\) |
−0.434258 | + | 0.900789i | \(0.642989\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.47000 | + | 0.848707i | −0.0704813 | + | 0.0406924i | ||||
\(436\) | 33.2178 | + | 19.1783i | 1.59084 | + | 0.918474i | ||||
\(437\) | −0.321139 | − | 0.185409i | −0.0153621 | − | 0.00886934i | ||||
\(438\) | −22.9454 | −1.09637 | ||||||||
\(439\) | −12.0384 | −0.574561 | −0.287280 | − | 0.957847i | \(-0.592751\pi\) | ||||
−0.287280 | + | 0.957847i | \(0.592751\pi\) | |||||||
\(440\) | 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 | 0.616388 | − | 0.787443i | \(-0.288595\pi\) |
−0.990139 | + | 0.140086i | \(0.955262\pi\) | |||||||
\(444\) | 28.2640 | − | 16.3182i | 1.34135 | − | 0.774427i | ||||
\(445\) | 7.41855 | + | 12.8493i | 0.351673 | + | 0.609116i | ||||
\(446\) | 18.4930 | − | 32.0308i | 0.875669 | − | 1.51670i | ||||
\(447\) | − | 9.37592i | − | 0.443466i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5177 | − | 13.0006i | 1.06268 | − | 0.613536i | 0.136504 | − | 0.990640i | \(-0.456413\pi\) |
0.926171 | + | 0.377104i | \(0.123080\pi\) | |||||||
\(450\) | −7.08263 | + | 4.08916i | −0.333878 | + | 0.192765i | ||||
\(451\) | 15.0617 | 0.709230 | ||||||||
\(452\) | −5.74676 | − | 9.95369i | −0.270305 | − | 0.468182i | ||||
\(453\) | − | 0.978449i | − | 0.0459716i | ||||||
\(454\) | 2.98459 | 0.140074 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.210041 | 0.00983605 | ||||||||
\(457\) | 30.7958i | 1.44057i | 0.693679 | + | 0.720284i | \(0.255989\pi\) | ||||
−0.693679 | + | 0.720284i | \(0.744011\pi\) | |||||||
\(458\) | −23.9742 | − | 41.5245i | −1.12024 | − | 1.94031i | ||||
\(459\) | −11.6864 | −0.545476 | ||||||||
\(460\) | 18.9616 | − | 10.9475i | 0.884088 | − | 0.510429i | ||||
\(461\) | 29.5278 | − | 17.0479i | 1.37525 | − | 0.794000i | 0.383665 | − | 0.923472i | \(-0.374662\pi\) |
0.991583 | + | 0.129472i | \(0.0413284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.69184i | 0.0786263i | 0.999227 | + | 0.0393131i | \(0.0125170\pi\) | ||||
−0.999227 | + | 0.0393131i | \(0.987483\pi\) | |||||||
\(464\) | −0.212926 | + | 0.368799i | −0.00988485 | + | 0.0171211i | ||||
\(465\) | 4.90674 | + | 8.49871i | 0.227544 | + | 0.394118i | ||||
\(466\) | 26.5378 | − | 15.3216i | 1.22934 | − | 0.709761i | ||||
\(467\) | −14.1762 | − | 24.5539i | −0.655996 | − | 1.13622i | −0.981643 | − | 0.190727i | \(-0.938916\pi\) |
0.325647 | − | 0.945491i | \(-0.394418\pi\) | |||||||
\(468\) | 1.00344 | + | 9.83015i | 0.0463838 | + | 0.454399i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.608453 | − | 0.351290i | −0.0280658 | − | 0.0162038i | ||||
\(471\) | 24.4224 | 1.12532 | ||||||||
\(472\) | 4.93318 | 0.227068 | ||||||||
\(473\) | 12.0637 | + | 6.96501i | 0.554692 | + | 0.320251i | ||||
\(474\) | −34.2647 | − | 19.7827i | −1.57383 | − | 0.908651i | ||||
\(475\) | 0.175879 | − | 0.101544i | 0.00806989 | − | 0.00465915i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.12433 | + | 1.94739i | 0.0514794 | + | 0.0891650i | ||||
\(478\) | −30.7837 | −1.40801 | ||||||||
\(479\) | −5.44077 | + | 3.14123i | −0.248595 | + | 0.143526i | −0.619121 | − | 0.785296i | \(-0.712511\pi\) |
0.370526 | + | 0.928822i | \(0.379178\pi\) | |||||||
\(480\) | 3.30213 | − | 5.71946i | 0.150721 | − | 0.261056i | ||||
\(481\) | −14.1453 | − | 19.5924i | −0.644969 | − | 0.893338i | ||||
\(482\) | 1.92128 | 0.0875117 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.4427 | − | 25.0154i | 0.656484 | − | 1.13706i | ||||
\(485\) | 0.180570 | − | 0.312757i | 0.00819927 | − | 0.0142016i | ||||
\(486\) | −16.6425 | − | 9.60853i | −0.754917 | − | 0.435852i | ||||
\(487\) | 13.0176i | 0.589883i | 0.955515 | + | 0.294942i | \(0.0953002\pi\) | ||||
−0.955515 | + | 0.294942i | \(0.904700\pi\) | |||||||
\(488\) | −11.7712 | − | 6.79613i | −0.532859 | − | 0.307647i | ||||
\(489\) | − | 13.3358i | − | 0.603065i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.17616 | + | 10.6974i | −0.278726 | + | 0.482768i | −0.971068 | − | 0.238801i | \(-0.923246\pi\) |
0.692342 | + | 0.721569i | \(0.256579\pi\) | |||||||
\(492\) | 48.7849i | 2.19939i | ||||||||
\(493\) | −1.40825 | + | 2.43916i | −0.0634244 | + | 0.109854i | ||||
\(494\) | −0.0399964 | − | 0.391825i | −0.00179952 | − | 0.0176290i | ||||
\(495\) | 0.528131 | + | 0.914749i | 0.0237377 | + | 0.0411149i | ||||
\(496\) | 2.13218 | + | 1.23102i | 0.0957378 | + | 0.0552743i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −19.5744 | − | 33.9038i | −0.877148 | − | 1.51926i | ||||
\(499\) | 7.92708 | − | 4.57670i | 0.354865 | − | 0.204881i | −0.311961 | − | 0.950095i | \(-0.600986\pi\) |
0.666826 | + | 0.745214i | \(0.267652\pi\) | |||||||
\(500\) | 25.9929i | 1.16244i | ||||||||
\(501\) | − | 3.91562i | − | 0.174937i | ||||||
\(502\) | 54.3993 | − | 31.4074i | 2.42796 | − | 1.40178i | ||||
\(503\) | 11.2519 | + | 19.4888i | 0.501696 | + | 0.868963i | 0.999998 | + | 0.00195935i | \(0.000623680\pi\) |
−0.498302 | + | 0.867003i | \(0.666043\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.09559 | + | 4.09664i | 0.315750 | + | 0.182298i | ||||
\(506\) | 13.5370 | + | 23.4469i | 0.601795 | + | 1.04234i | ||||
\(507\) | −18.7587 | + | 3.86999i | −0.833101 | + | 0.171872i | ||||
\(508\) | 25.9443 | − | 44.9368i | 1.15109 | − | 1.99375i | ||||
\(509\) | 38.6606i | 1.71360i | 0.515649 | + | 0.856800i | \(0.327551\pi\) | ||||
−0.515649 | + | 0.856800i | \(0.672449\pi\) | |||||||
\(510\) | −2.97797 | + | 5.15800i | −0.131867 | + | 0.228400i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 3.53972i | − | 0.156435i | ||||||
\(513\) | 0.231727 | + | 0.133787i | 0.0102310 | + | 0.00590686i | ||||
\(514\) | 15.0907i | 0.665623i | ||||||||
\(515\) | −7.32179 | − | 4.22724i | −0.322637 | − | 0.186274i | ||||
\(516\) | −22.5596 | + | 39.0744i | −0.993132 | + | 1.72016i | ||||
\(517\) | 0.270623 | − | 0.468732i | 0.0119020 | − | 0.0206148i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 28.8588 | 1.26676 | ||||||||
\(520\) | 8.37761 | + | 3.76006i | 0.367383 | + | 0.164889i | ||||
\(521\) | 20.1176 | − | 34.8446i | 0.881366 | − | 1.52657i | 0.0315430 | − | 0.999502i | \(-0.489958\pi\) |
0.849823 | − | 0.527068i | \(-0.176709\pi\) | |||||||
\(522\) | −2.24897 | + | 1.29844i | −0.0984348 | + | 0.0568313i | ||||
\(523\) | 0.732146 | 0.0320145 | 0.0160073 | − | 0.999872i | \(-0.494905\pi\) | ||||
0.0160073 | + | 0.999872i | \(0.494905\pi\) | |||||||
\(524\) | 4.20594 | + | 7.28491i | 0.183737 | + | 0.318243i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.0581 | + | 26.0143i | −1.96463 | + | 1.13428i | ||||
\(527\) | 14.1018 | + | 8.14169i | 0.614285 | + | 0.354658i | ||||
\(528\) | −0.600798 | − | 0.346871i | −0.0261464 | − | 0.0150956i | ||||
\(529\) | 38.1321 | 1.65792 | ||||||||
\(530\) | 5.29221 | 0.229879 | ||||||||
\(531\) | 1.17857 | + | 0.680446i | 0.0511455 | + | 0.0295288i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.9353 | − | 3.66817i | 1.55653 | − | 0.158886i | ||||
\(534\) | −29.7125 | − | 51.4636i | −1.28579 | − | 2.22705i | ||||
\(535\) | −7.23667 | + | 4.17809i | −0.312868 | + | 0.180635i | ||||
\(536\) | 3.06996 | + | 5.31733i | 0.132602 | + | 0.229674i | ||||
\(537\) | −2.13146 | + | 3.69179i | −0.0919791 | + | 0.159312i | ||||
\(538\) | − | 36.8553i | − | 1.58894i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −13.6823 | + | 7.89946i | −0.588791 | + | 0.339939i | ||||
\(541\) | −20.4847 | + | 11.8268i | −0.880705 | + | 0.508476i | −0.870891 | − | 0.491476i | \(-0.836457\pi\) |
−0.00981448 | + | 0.999952i | \(0.503124\pi\) | |||||||
\(542\) | −20.1751 | −0.866595 | ||||||||
\(543\) | −1.00781 | − | 1.74558i | −0.0432492 | − | 0.0749099i | ||||
\(544\) | − | 10.9584i | − | 0.469837i | ||||||
\(545\) | 9.83325 | 0.421210 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9472 | −0.553582 | −0.276791 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276791 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(548\) | − | 6.16298i | − | 0.263270i | ||||||
\(549\) | −1.87481 | − | 3.24727i | −0.0800151 | − | 0.138590i | ||||
\(550\) | −14.8278 | −0.632258 | ||||||||
\(551\) | 0.0558475 | − | 0.0322436i | 0.00237918 | − | 0.00137362i | ||||
\(552\) | −29.9876 | + | 17.3133i | −1.27636 | + | 0.736904i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 45.8771i | 1.94913i | ||||||||
\(555\) | 4.18340 | − | 7.24585i | 0.177575 | − | 0.307569i | ||||
\(556\) | −25.7946 | − | 44.6775i | −1.09393 | − | 1.89475i | ||||
\(557\) | 5.54845 | − | 3.20340i | 0.235096 | − | 0.135732i | −0.377825 | − | 0.925877i | \(-0.623328\pi\) |
0.612921 | + | 0.790145i | \(0.289995\pi\) | |||||||
\(558\) | 7.50685 | + | 13.0023i | 0.317790 | + | 0.550429i | ||||
\(559\) | 30.4787 | + | 13.6795i | 1.28911 | + | 0.578582i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.97355 | − | 2.29413i | −0.167764 | − | 0.0968584i | ||||
\(562\) | 32.2996 | 1.36248 | ||||||||
\(563\) | 7.32084 | 0.308537 | 0.154268 | − | 0.988029i | \(-0.450698\pi\) | ||||
0.154268 | + | 0.988029i | \(0.450698\pi\) | |||||||
\(564\) | 1.51822 | + | 0.876546i | 0.0639287 | + | 0.0369092i | ||||
\(565\) | −2.55176 | − | 1.47326i | −0.107354 | − | 0.0619806i | ||||
\(566\) | 2.01980 | − | 1.16613i | 0.0848986 | − | 0.0490162i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.3625 | − | 37.0009i | −0.896349 | − | 1.55252i | ||||
\(569\) | 4.31743 | 0.180996 | 0.0904981 | − | 0.995897i | \(-0.471154\pi\) | ||||
0.0904981 | + | 0.995897i | \(0.471154\pi\) | |||||||
\(570\) | 0.118098 | − | 0.0681842i | 0.00494660 | − | 0.00285592i | ||||
\(571\) | 17.0847 | − | 29.5916i | 0.714974 | − | 1.23837i | −0.247996 | − | 0.968761i | \(-0.579772\pi\) |
0.962970 | − | 0.269610i | \(-0.0868946\pi\) | |||||||
\(572\) | −7.33577 | + | 16.3445i | −0.306724 | + | 0.683398i | ||||
\(573\) | −2.22956 | −0.0931413 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.7402 | + | 28.9949i | −0.698115 | + | 1.20917i | ||||
\(576\) | 5.31166 | − | 9.20007i | 0.221319 | − | 0.383336i | ||||
\(577\) | 5.50494 | + | 3.17828i | 0.229174 | + | 0.132314i | 0.610191 | − | 0.792254i | \(-0.291093\pi\) |
−0.381017 | + | 0.924568i | \(0.624426\pi\) | |||||||
\(578\) | − | 29.2729i | − | 1.21759i | ||||||
\(579\) | 8.87301 | + | 5.12283i | 0.368750 | + | 0.212898i | ||||
\(580\) | 3.80763i | 0.158103i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.723214 | + | 1.25264i | −0.0299782 | + | 0.0519237i | ||||
\(583\) | 4.07695i | 0.168850i | ||||||||
\(584\) | −10.1620 | + | 17.6011i | −0.420507 | + | 0.728339i | ||||
\(585\) | 1.48283 | + | 2.05384i | 0.0613074 | + | 0.0849160i | ||||
\(586\) | 0.229446 | + | 0.397412i | 0.00947832 | + | 0.0164169i | ||||
\(587\) | −27.2036 | − | 15.7060i | −1.12281 | − | 0.648256i | −0.180695 | − | 0.983539i | \(-0.557835\pi\) |
−0.942118 | + | 0.335283i | \(0.891168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.186414 | − | 0.322878i | −0.00768104 | − | 0.0133040i | ||||
\(590\) | 2.77376 | − | 1.60143i | 0.114194 | − | 0.0659298i | ||||
\(591\) | 22.8035i | 0.938011i | ||||||||
\(592\) | − | 2.09909i | − | 0.0862719i | ||||||
\(593\) | −0.409641 | + | 0.236506i | −0.0168219 | + | 0.00971215i | −0.508387 | − | 0.861128i | \(-0.669758\pi\) |
0.491565 | + | 0.870841i | \(0.336425\pi\) | |||||||
\(594\) | −9.76804 | − | 16.9187i | −0.400787 | − | 0.694184i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.2143 | − | 10.5160i | −0.746086 | − | 0.430753i | ||||
\(597\) | −4.87335 | − | 8.44089i | −0.199453 | − | 0.345463i | ||||
\(598\) | 38.0079 | + | 52.6442i | 1.55426 | + | 2.15278i | ||||
\(599\) | 4.81348 | − | 8.33719i | 0.196673 | − | 0.340648i | −0.750774 | − | 0.660559i | \(-0.770320\pi\) |
0.947448 | + | 0.319910i | \(0.103653\pi\) | |||||||
\(600\) | − | 18.9641i | − | 0.774207i | ||||||
\(601\) | −20.5399 | + | 35.5762i | −0.837842 | + | 1.45118i | 0.0538542 | + | 0.998549i | \(0.482849\pi\) |
−0.891696 | + | 0.452635i | \(0.850484\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.69379i | 0.0689765i | ||||||||
\(604\) | −1.90080 | − | 1.09743i | −0.0773424 | − | 0.0446537i | ||||
\(605\) | − | 7.40514i | − | 0.301062i | ||||||
\(606\) | −28.4190 | − | 16.4077i | −1.15444 | − | 0.666518i | ||||
\(607\) | 9.54289 | − | 16.5288i | 0.387334 | − | 0.670882i | −0.604756 | − | 0.796411i | \(-0.706729\pi\) |
0.992090 | + | 0.125529i | \(0.0400627\pi\) | |||||||
\(608\) | −0.125453 | + | 0.217290i | −0.00508777 | + | 0.00881228i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.82474 | −0.357303 | ||||||||
\(611\) | 0.531513 | − | 1.18424i | 0.0215027 | − | 0.0479092i | ||||
\(612\) | −2.83840 | + | 4.91626i | −0.114736 | + | 0.198728i | ||||
\(613\) | −32.9131 | + | 19.0024i | −1.32935 | + | 0.767500i | −0.985199 | − | 0.171415i | \(-0.945166\pi\) |
−0.344149 | + | 0.938915i | \(0.611833\pi\) | |||||||
\(614\) | −62.6498 | −2.52834 | ||||||||
\(615\) | 6.25334 | + | 10.8311i | 0.252159 | + | 0.436752i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.20117 | − | 4.15759i | 0.289908 | − | 0.167378i | −0.347992 | − | 0.937497i | \(-0.613136\pi\) |
0.637900 | + | 0.770119i | \(0.279803\pi\) | |||||||
\(618\) | 29.3250 | + | 16.9308i | 1.17962 | + | 0.681056i | ||||
\(619\) | 38.5146 | + | 22.2364i | 1.54803 | + | 0.893756i | 0.998292 | + | 0.0584199i | \(0.0186062\pi\) |
0.549739 | + | 0.835336i | \(0.314727\pi\) | |||||||
\(620\) | 22.0135 | 0.884085 | ||||||||
\(621\) | −44.1116 | −1.77014 | ||||||||
\(622\) | −54.0579 | − | 31.2103i | −2.16752 | − | 1.25142i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.51790 | − | 0.681266i | −0.0607646 | − | 0.0272725i | ||||
\(625\) | −7.37342 | − | 12.7711i | −0.294937 | − | 0.510845i | ||||
\(626\) | 44.0397 | − | 25.4263i | 1.76018 | − | 1.01624i | ||||
\(627\) | 0.0525269 | + | 0.0909792i | 0.00209772 | + | 0.00363336i | ||||
\(628\) | 27.3921 | − | 47.4445i | 1.09306 | − | 1.89324i | ||||
\(629\) | − | 13.8829i | − | 0.553549i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.1779 | + | 5.87622i | −0.405177 | + | 0.233929i | −0.688715 | − | 0.725032i | \(-0.741825\pi\) |
0.283539 | + | 0.958961i | \(0.408492\pi\) | |||||||
\(632\) | −30.3501 | + | 17.5227i | −1.20726 | + | 0.697014i | ||||
\(633\) | −11.9258 | −0.474008 | ||||||||
\(634\) | −8.14001 | − | 14.0989i | −0.323281 | − | 0.559939i | ||||
\(635\) | − | 13.3023i | − | 0.527887i | ||||||
\(636\) | −13.2052 | −0.523620 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.70831 | −0.186404 | ||||||||
\(639\) | − | 11.7863i | − | 0.466259i | ||||||
\(640\) | −8.01854 | − | 13.8885i | −0.316961 | − | 0.548992i | ||||
\(641\) | −10.4868 | −0.414205 | −0.207102 | − | 0.978319i | \(-0.566403\pi\) | ||||
−0.207102 | + | 0.978319i | \(0.566403\pi\) | |||||||
\(642\) | 28.9840 | − | 16.7339i | 1.14391 | − | 0.660436i | ||||
\(643\) | −27.0912 | + | 15.6411i | −1.06837 | + | 0.616825i | −0.927736 | − | 0.373237i | \(-0.878248\pi\) |
−0.140635 | + | 0.990061i | \(0.544915\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.5669i | 0.455448i | ||||||||
\(646\) | 0.113137 | − | 0.195959i | 0.00445133 | − | 0.00770992i | ||||
\(647\) | 13.4337 | + | 23.2679i | 0.528135 | + | 0.914757i | 0.999462 | + | 0.0327983i | \(0.0104419\pi\) |
−0.471327 | + | 0.881959i | \(0.656225\pi\) | |||||||
\(648\) | 15.1627 | − | 8.75422i | 0.595649 | − | 0.343898i | ||||
\(649\) | 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 | ||||
\(653\) | −4.14161 | −0.162074 | −0.0810369 | − | 0.996711i | \(-0.525823\pi\) | ||||
−0.0810369 | + | 0.996711i | \(0.525823\pi\) | |||||||
\(654\) | −39.3838 | −1.54003 | ||||||||
\(655\) | 1.86759 | + | 1.07825i | 0.0729726 | + | 0.0421308i | ||||
\(656\) | 2.71734 | + | 1.56886i | 0.106094 | + | 0.0612536i | ||||
\(657\) | −4.85553 | + | 2.80334i | −0.189432 | + | 0.109369i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.7276 | − | 18.5807i | −0.417887 | − | 0.723801i | 0.577840 | − | 0.816150i | \(-0.303896\pi\) |
−0.995727 | + | 0.0923492i | \(0.970562\pi\) | |||||||
\(660\) | −6.20288 | −0.241447 | ||||||||
\(661\) | 36.7084 | − | 21.1936i | 1.42779 | − | 0.824335i | 0.430844 | − | 0.902426i | \(-0.358216\pi\) |
0.996946 | + | 0.0780909i | \(0.0248824\pi\) | |||||||
\(662\) | −7.58763 | + | 13.1422i | −0.294902 | + | 0.510785i | ||||
\(663\) | −10.0391 | − | 4.50576i | −0.389885 | − | 0.174989i | ||||
\(664\) | −34.6762 | −1.34570 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.40021 | − | 11.0855i | 0.248003 | − | 0.429554i | ||||
\(667\) | −5.31558 | + | 9.20685i | −0.205820 | + | 0.356491i | ||||
\(668\) | −7.60673 | − | 4.39175i | −0.294313 | − | 0.169922i | ||||
\(669\) | 23.6593i | 0.914722i | ||||||||
\(670\) | 3.45226 | + | 1.99317i | 0.133373 | + | 0.0770027i | ||||
\(671\) | − | 6.79830i | − | 0.262445i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7928 | + | 25.6219i | −0.570220 | + | 0.987650i | 0.426323 | + | 0.904571i | \(0.359809\pi\) |
−0.996543 | + | 0.0830790i | \(0.973525\pi\) | |||||||
\(674\) | − | 9.72645i | − | 0.374649i | ||||||
\(675\) | 12.0794 | − | 20.9221i | 0.464935 | − | 0.805292i | ||||
\(676\) | −13.5216 | + | 40.7823i | −0.520061 | + | 1.56855i | ||||
\(677\) | 16.0830 | + | 27.8565i | 0.618118 | + | 1.07061i | 0.989829 | + | 0.142263i | \(0.0454380\pi\) |
−0.371711 | + | 0.928349i | \(0.621229\pi\) | |||||||
\(678\) | 10.2202 | + | 5.90066i | 0.392506 | + | 0.226613i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.63775 | + | 4.56872i | 0.101153 | + | 0.175202i | ||||
\(681\) | −1.65341 | + | 0.954596i | −0.0633587 | + | 0.0365802i | ||||
\(682\) | 27.2207i | 1.04234i | ||||||||
\(683\) | 8.60236i | 0.329160i | 0.986364 | + | 0.164580i | \(0.0526269\pi\) | ||||
−0.986364 | + | 0.164580i | \(0.947373\pi\) | |||||||
\(684\) | 0.112563 | − | 0.0649885i | 0.00430397 | − | 0.00248490i | ||||
\(685\) | −0.789983 | − | 1.36829i | −0.0301837 | − | 0.0522797i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.5625 | + | 15.3359i | 1.01342 | + | 0.585100i | ||||
\(688\) | 1.45097 | + | 2.51316i | 0.0553179 | + | 0.0958134i | ||||
\(689\) | 0.992909 | + | 9.72704i | 0.0378268 | + | 0.370571i | ||||
\(690\) | −11.2406 | + | 19.4694i | −0.427924 | + | 0.741186i | ||||
\(691\) | − | 20.4420i | − | 0.777651i | −0.921311 | − | 0.388826i | \(-0.872881\pi\) | ||
0.921311 | − | 0.388826i | \(-0.127119\pi\) | |||||||
\(692\) | 32.3680 | − | 56.0629i | 1.23044 | − | 2.13119i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 20.9477i | − | 0.795164i | ||||||
\(695\) | −11.4537 | − | 6.61279i | −0.434463 | − | 0.250837i | ||||
\(696\) | − | 6.02174i | − | 0.228253i | ||||||
\(697\) | 17.9719 | + | 10.3761i | 0.680736 | + | 0.393023i | ||||
\(698\) | 10.6187 | − | 18.3921i | 0.401922 | − | 0.696150i | ||||
\(699\) | −9.80099 | + | 16.9758i | −0.370708 | + | 0.642084i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.1373 | −0.949422 | −0.474711 | − | 0.880142i | \(-0.657447\pi\) | ||||
−0.474711 | + | 0.880142i | \(0.657447\pi\) | |||||||
\(702\) | −27.4256 | − | 37.9869i | −1.03511 | − | 1.43372i | ||||
\(703\) | −0.158933 | + | 0.275280i | −0.00599427 | + | 0.0103824i | ||||
\(704\) | 16.6803 | − | 9.63036i | 0.628661 | − | 0.362958i | ||||
\(705\) | 0.449429 | 0.0169265 | ||||||||
\(706\) | −2.48118 | − | 4.29753i | −0.0933804 | − | 0.161740i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.92112 | + | 3.99591i | −0.260112 | + | 0.150176i | ||||
\(709\) | −25.5416 | − | 14.7464i | −0.959234 | − | 0.553814i | −0.0632970 | − | 0.997995i | \(-0.520162\pi\) |
−0.895937 | + | 0.444181i | \(0.853495\pi\) | |||||||
\(710\) | −24.0227 | − | 13.8695i | −0.901556 | − | 0.520514i | ||||
\(711\) | −9.66777 | −0.362570 | ||||||||
\(712\) | −52.6360 | −1.97262 | ||||||||
\(713\) | 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 | ||||
\(717\) | 17.0536 | − | 9.84591i | 0.636879 | − | 0.367702i | ||||
\(718\) | −9.85518 | − | 17.0697i | −0.367792 | − | 0.637034i | ||||
\(719\) | 4.16576 | − | 7.21531i | 0.155357 | − | 0.269086i | −0.777832 | − | 0.628472i | \(-0.783681\pi\) |
0.933189 | + | 0.359386i | \(0.117014\pi\) | |||||||
\(720\) | 0.220044i | 0.00820055i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37.8946 | − | 21.8784i | 1.41029 | − | 0.814231i | ||||
\(723\) | −1.06435 | + | 0.614504i | −0.0395837 | + | 0.0228537i | ||||
\(724\) | −4.52143 | −0.168038 | ||||||||
\(725\) | −2.91120 | − | 5.04235i | −0.108119 | − | 0.187268i | ||||
\(726\) | 29.6588i | 1.10074i | ||||||||
\(727\) | −9.66141 | −0.358322 | −0.179161 | − | 0.983820i | \(-0.557338\pi\) | ||||
−0.179161 | + | 0.983820i | \(0.557338\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7672 | 1.10249 | ||||||||
\(730\) | 13.1953i | 0.488381i | ||||||||
\(731\) | 9.59645 | + | 16.6215i | 0.354938 | + | 0.614770i | ||||
\(732\) | 22.0197 | 0.813870 | ||||||||
\(733\) | 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 | ||||||
\(737\) | −1.53547 | + | 2.65951i | −0.0565598 | + | 0.0979644i | ||||
\(738\) | 9.56704 | + | 16.5706i | 0.352168 | + | 0.609972i | ||||
\(739\) | 33.6145 | − | 19.4073i | 1.23653 | − | 0.713910i | 0.268146 | − | 0.963378i | \(-0.413589\pi\) |
0.968383 | + | 0.249468i | \(0.0802559\pi\) | |||||||
\(740\) | −9.38417 | − | 16.2539i | −0.344969 | − | 0.597504i | ||||
\(741\) | 0.147479 | + | 0.204271i | 0.00541779 | + | 0.00750410i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.7863 | + | 17.1971i | 1.09275 | + | 0.630901i | 0.934308 | − | 0.356467i | \(-0.116019\pi\) |
0.158445 | + | 0.987368i | \(0.449352\pi\) | |||||||
\(744\) | −34.8142 | −1.27635 | ||||||||
\(745\) | −5.39185 | −0.197542 | ||||||||
\(746\) | −23.4742 | − | 13.5528i | −0.859452 | − | 0.496205i | ||||
\(747\) | −8.28434 | − | 4.78297i | −0.303108 | − | 0.175000i | ||||
\(748\) | −8.91346 | + | 5.14619i | −0.325908 | + | 0.188163i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.3445 | − | 23.1134i | −0.487272 | − | 0.843980i | ||||
\(751\) | −48.1470 | −1.75691 | −0.878454 | − | 0.477827i | \(-0.841425\pi\) | ||||
−0.878454 | + | 0.477827i | \(0.841425\pi\) | |||||||
\(752\) | 0.0976479 | − | 0.0563770i | 0.00356085 | − | 0.00205586i | ||||
\(753\) | −20.0908 | + | 34.7983i | −0.732150 | + | 1.26812i | ||||
\(754\) | −11.2334 | + | 1.14667i | −0.409096 | + | 0.0417594i | ||||
\(755\) | −0.562681 | −0.0204781 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.45319 | − | 5.98110i | 0.125508 | − | 0.217387i | −0.796423 | − | 0.604740i | \(-0.793277\pi\) |
0.921931 | + | 0.387353i | \(0.126611\pi\) | |||||||
\(758\) | 9.20262 | − | 15.9394i | 0.334254 | − | 0.578945i | ||||
\(759\) | −14.9986 | − | 8.65942i | −0.544413 | − | 0.314317i | ||||
\(760\) | − | 0.120789i | − | 0.00438147i | ||||||
\(761\) | 27.6895 | + | 15.9865i | 1.00374 | + | 0.579511i | 0.909353 | − | 0.416025i | \(-0.136577\pi\) |
0.0943888 | + | 0.995535i | \(0.469910\pi\) | |||||||
\(762\) | 53.2781i | 1.93006i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.50067 | + | 4.33129i | −0.0904712 | + | 0.156701i | ||||
\(765\) | 1.45533i | 0.0526174i | ||||||||
\(766\) | −32.5274 | + | 56.3391i | −1.17526 | + | 2.03562i | ||||
\(767\) | 3.46382 | + | 4.79769i | 0.125071 | + | 0.173234i | ||||
\(768\) | 13.2397 | + | 22.9319i | 0.477748 | + | 0.827483i | ||||
\(769\) | −12.4665 | − | 7.19752i | −0.449553 | − | 0.259549i | 0.258089 | − | 0.966121i | \(-0.416907\pi\) |
−0.707641 | + | 0.706572i | \(0.750241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.82664 | − | 8.35999i | −0.173827 | − | 0.301078i | ||||
\(772\) | 19.9039 | − | 11.4915i | 0.716357 | − | 0.413589i | ||||
\(773\) | − | 37.2771i | − | 1.34076i | −0.742016 | − | 0.670382i | \(-0.766130\pi\) | ||
0.742016 | − | 0.670382i | \(-0.233870\pi\) | |||||||
\(774\) | 17.6964i | 0.636083i | ||||||||
\(775\) | −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 | ||||
\(780\) | −14.7992 | + | 1.51067i | −0.529897 | + | 0.0540905i | ||||
\(781\) | 10.6846 | − | 18.5063i | 0.382326 | − | 0.662208i | ||||
\(782\) | 37.3029i | 1.33395i | ||||||||
\(783\) | 3.83560 | − | 6.64346i | 0.137073 | − | 0.237418i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 14.0447i | − | 0.501276i | ||||||
\(786\) | −7.47999 | − | 4.31857i | −0.266802 | − | 0.154038i | ||||
\(787\) | − | 14.3486i | − | 0.511472i | −0.966747 | − | 0.255736i | \(-0.917682\pi\) | ||
0.966747 | − | 0.255736i | \(-0.0823178\pi\) | |||||||
\(788\) | 44.2996 | + | 25.5764i | 1.57811 | + | 0.911120i | ||||
\(789\) | 16.6409 | − | 28.8229i | 0.592432 | − | 1.02612i | ||||
\(790\) | −11.3765 | + | 19.7047i | −0.404759 | + | 0.701064i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.74719 | −0.133150 | ||||||||
\(793\) | −1.65567 | − | 16.2198i | −0.0587947 | − | 0.575982i | ||||
\(794\) | 8.58291 | − | 14.8660i | 0.304596 | − | 0.527576i | ||||
\(795\) | −2.93179 | + | 1.69267i | −0.103980 | + | 0.0600328i | ||||
\(796\) | −21.8638 | −0.774940 | ||||||||
\(797\) | −5.54219 | − | 9.59935i | −0.196314 | − | 0.340026i | 0.751016 | − | 0.660284i | \(-0.229564\pi\) |
−0.947331 | + | 0.320257i | \(0.896231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.645824 | − | 0.372866i | 0.0228476 | − | 0.0131911i | ||||
\(800\) | 19.6187 | + | 11.3268i | 0.693625 | + | 0.400464i | ||||
\(801\) | −12.5751 | − | 7.26022i | −0.444318 | − | 0.256527i | ||||
\(802\) | 41.9154 | 1.48008 | ||||||||
\(803\) | −10.1652 | −0.358724 | ||||||||
\(804\) | −8.61415 | − | 4.97338i | −0.303798 | − | 0.175398i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.62941 | + | 64.9450i | 0.233511 | + | 2.28759i | ||||
\(807\) | 11.7878 | + | 20.4171i | 0.414952 | + | 0.718718i | ||||
\(808\) | −25.1723 | + | 14.5332i | −0.885558 | + | 0.511277i | ||||
\(809\) | 21.2768 | + | 36.8525i | 0.748052 | + | 1.29566i | 0.948755 | + | 0.316013i | \(0.102344\pi\) |
−0.200703 | + | 0.979652i | \(0.564323\pi\) | |||||||
\(810\) | 5.68365 | − | 9.84438i | 0.199703 | − | 0.345896i | ||||
\(811\) | 16.3622i | 0.574554i | 0.957848 | + | 0.287277i | \(0.0927500\pi\) | ||||
−0.957848 | + | 0.287277i | \(0.907250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.1766 | − | 6.45284i | 0.391982 | − | 0.226311i | ||||
\(814\) | 20.0986 | − | 11.6040i | 0.704457 | − | 0.406719i | ||||
\(815\) | −7.66906 | −0.268636 | ||||||||
\(816\) | −0.477922 | − | 0.827785i | −0.0167306 | − | 0.0289783i | ||||
\(817\) | − | 0.439444i | − | 0.0153742i | ||||||
\(818\) | 67.4455 | 2.35818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.0549 | 0.979721 | ||||||||
\(821\) | 3.10550i | 0.108383i | 0.998531 | + | 0.0541913i | \(0.0172581\pi\) | ||||
−0.998531 | + | 0.0541913i | \(0.982742\pi\) | |||||||
\(822\) | 3.16401 | + | 5.48023i | 0.110358 | + | 0.191145i | ||||
\(823\) | −49.0164 | −1.70860 | −0.854301 | − | 0.519778i | \(-0.826015\pi\) | ||||
−0.854301 | + | 0.519778i | \(0.826015\pi\) | |||||||
\(824\) | 25.9747 | − | 14.9965i | 0.904873 | − | 0.522429i | ||||
\(825\) | 8.21432 | − | 4.74254i | 0.285986 | − | 0.165114i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.0887i | 0.455140i | 0.973762 | + | 0.227570i | \(0.0730780\pi\) | ||||
−0.973762 | + | 0.227570i | \(0.926922\pi\) | |||||||
\(828\) | −10.7138 | + | 18.5569i | −0.372331 | + | 0.644896i | ||||
\(829\) | −24.6282 | − | 42.6574i | −0.855374 | − | 1.48155i | −0.876297 | − | 0.481771i | \(-0.839994\pi\) |
0.0209227 | − | 0.999781i | \(-0.493340\pi\) | |||||||
\(830\) | −19.4972 | + | 11.2567i | −0.676757 | + | 0.390726i | ||||
\(831\) | −14.6734 | − | 25.4151i | −0.509015 | − | 0.881639i | ||||
\(832\) | 37.4514 | − | 27.0391i | 1.29839 | − | 0.937411i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 45.8739 | + | 26.4853i | 1.58848 | + | 0.917111i | ||||
\(835\) | −2.25177 | −0.0779257 | ||||||||
\(836\) | 0.235656 | 0.00815034 | ||||||||
\(837\) | −38.4087 | − | 22.1753i | −1.32760 | − | 0.766489i | ||||
\(838\) | −41.3684 | − | 23.8841i | −1.42905 | − | 0.825062i | ||||
\(839\) | −14.9508 | + | 8.63182i | −0.516157 | + | 0.298004i | −0.735361 | − | 0.677676i | \(-0.762987\pi\) |
0.219204 | + | 0.975679i | \(0.429654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5756 | + | 23.5136i | 0.468124 | + | 0.810815i | ||||
\(842\) | 57.2814 | 1.97405 | ||||||||
\(843\) | −17.8934 | + | 10.3308i | −0.616282 | + | 0.355810i | ||||
\(844\) | −13.3760 | + | 23.1678i | −0.460419 | + | 0.797470i | ||||
\(845\) | 2.22553 | + | 10.7876i | 0.0765606 | + | 0.371105i | ||||
\(846\) | 0.687585 | 0.0236397 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.424662 | + | 0.735535i | −0.0145829 | + | 0.0252584i | ||||
\(849\) | −0.745955 | + | 1.29203i | −0.0256011 | + | 0.0443424i | ||||
\(850\) | −17.6928 | − | 10.2149i | −0.606857 | − | 0.350369i | ||||
\(851\) | − | 52.4024i | − | 1.79633i | ||||||
\(852\) | 59.9419 | + | 34.6075i | 2.05358 | + | 1.18563i | ||||
\(853\) | − | 52.4163i | − | 1.79470i | −0.441319 | − | 0.897350i | \(-0.645489\pi\) | ||
0.441319 | − | 0.897350i | \(-0.354511\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0166607 | − | 0.0288572i | 0.000569784 | − | 0.000986895i | ||||
\(856\) | − | 29.6443i | − | 1.01322i | ||||||
\(857\) | −5.06355 | + | 8.77032i | −0.172967 | + | 0.299588i | −0.939456 | − | 0.342670i | \(-0.888669\pi\) |
0.766489 | + | 0.642258i | \(0.222002\pi\) | |||||||
\(858\) | −1.86801 | − | 18.2999i | −0.0637727 | − | 0.624749i | ||||
\(859\) | −0.255118 | − | 0.441878i | −0.00870452 | − | 0.0150767i | 0.861640 | − | 0.507519i | \(-0.169437\pi\) |
−0.870345 | + | 0.492443i | \(0.836104\pi\) | |||||||
\(860\) | 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 | \(0.446777\pi\) | |||||||
\(864\) | 29.8470i | 1.01541i | ||||||||
\(865\) | − | 16.5959i | − | 0.564279i | ||||||
\(866\) | −46.7347 | + | 26.9823i | −1.58811 | + | 0.916896i | ||||
\(867\) | 9.36269 | + | 16.2167i | 0.317974 | + | 0.550747i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.1799 | − | 8.76412i | −0.514943 | − | 0.297302i | ||||
\(870\) | −1.95480 | − | 3.38581i | −0.0662739 | − | 0.114790i | ||||
\(871\) | −3.01572 | + | 6.71919i | −0.102184 | + | 0.227671i | ||||
\(872\) | −17.4422 | + | 30.2107i | −0.590667 | + | 1.02306i | ||||
\(873\) | 0.353433i | 0.0119619i | ||||||||
\(874\) | 0.427047 | − | 0.739668i | 0.0144451 | − | 0.0250196i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 32.9252i | − | 1.11244i | ||||||
\(877\) | −9.77794 | − | 5.64530i | −0.330178 | − | 0.190628i | 0.325742 | − | 0.945459i | \(-0.394386\pi\) |
−0.655920 | + | 0.754830i | \(0.727719\pi\) | |||||||
\(878\) | − | 27.7276i | − | 0.935762i | ||||||
\(879\) | −0.254218 | − | 0.146773i | −0.00857455 | − | 0.00495052i | ||||
\(880\) | −0.199476 | + | 0.345503i | −0.00672435 | + | 0.0116469i | ||||
\(881\) | −11.2634 | + | 19.5088i | −0.379474 | + | 0.657268i | −0.990986 | − | 0.133967i | \(-0.957228\pi\) |
0.611512 | + | 0.791235i | \(0.290562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0268 | −0.943178 | −0.471589 | − | 0.881819i | \(-0.656319\pi\) | ||||
−0.471589 | + | 0.881819i | \(0.656319\pi\) | |||||||
\(884\) | −20.0130 | + | 14.4489i | −0.673109 | + | 0.485969i | ||||
\(885\) | −1.02441 | + | 1.77432i | −0.0344351 | + | 0.0596433i | ||||
\(886\) | 31.3827 | − | 18.1188i | 1.05432 | − | 0.608713i | ||||
\(887\) | 20.6235 | 0.692470 | 0.346235 | − | 0.938148i | \(-0.387460\pi\) | ||||
0.346235 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(888\) | 14.8410 | + | 25.7053i | 0.498031 | + | 0.862615i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −29.5954 | + | 17.0869i | −0.992040 | + | 0.572754i | ||||
\(891\) | 7.58379 | + | 4.37850i | 0.254066 | + | 0.146685i | ||||
\(892\) | 45.9621 | + | 26.5362i | 1.53893 | + | 0.888499i | ||||
\(893\) | −0.0170744 | −0.000571374 | ||||||||
\(894\) | 21.5952 | 0.722253 | ||||||||
\(895\) | 2.12305 | + | 1.22574i | 0.0709658 | + | 0.0409721i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −37.8935 | − | 17.0074i | −1.26523 | − | 0.567861i | ||||
\(898\) | 29.9438 | + | 51.8642i | 0.999238 | + | 1.73073i | ||||
\(899\) | −9.25671 | + | 5.34437i | −0.308729 | + | 0.178245i | ||||
\(900\) | −5.86767 | − | 10.1631i | −0.195589 | − | 0.338770i | ||||
\(901\) | −2.80863 | + | 4.86468i | −0.0935689 | + | 0.162066i | ||||
\(902\) | 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 | ||||
\(906\) | 2.25363 | 0.0748718 | ||||||||
\(907\) | 20.7315 | + | 35.9081i | 0.688379 | + | 1.19231i | 0.972362 | + | 0.233479i | \(0.0750109\pi\) |
−0.283982 | + | 0.958829i | \(0.591656\pi\) | |||||||
\(908\) | 4.28269i | 0.142126i | ||||||||
\(909\) | −8.01841 | −0.265954 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.8187 | 1.35239 | 0.676193 | − | 0.736725i | \(-0.263629\pi\) | ||||
0.676193 | + | 0.736725i | \(0.263629\pi\) | |||||||
\(912\) | 0.0218852i | 0.000724690i | ||||||||
\(913\) | −8.67180 | − | 15.0200i | −0.286995 | − | 0.497090i | ||||
\(914\) | −70.9310 | −2.34619 | ||||||||
\(915\) | 4.88875 | − | 2.82252i | 0.161617 | − | 0.0933096i | ||||
\(916\) | 59.5849 | − | 34.4014i | 1.96874 | − | 1.13665i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 26.9170i | − | 0.888393i | ||||||
\(919\) | 24.3839 | − | 42.2341i | 0.804350 | − | 1.39318i | −0.112379 | − | 0.993665i | \(-0.535847\pi\) |
0.916729 | − | 0.399510i | \(-0.130820\pi\) | |||||||
\(920\) | 9.95645 | + | 17.2451i | 0.328254 | + | 0.568553i | ||||
\(921\) | 34.7068 | − | 20.0380i | 1.14363 | − | 0.660274i | ||||
\(922\) | 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 | ||||
\(926\) | −3.89675 | −0.128055 | ||||||||
\(927\) | 8.27403 | 0.271755 | ||||||||
\(928\) | 6.22958 | + | 3.59665i | 0.204496 | + | 0.118066i | ||||
\(929\) | 25.4464 | + | 14.6915i | 0.834868 | + | 0.482012i | 0.855517 | − | 0.517775i | \(-0.173240\pi\) |
−0.0206482 | + | 0.999787i | \(0.506573\pi\) | |||||||
\(930\) | −19.5748 | + | 11.3015i | −0.641883 | + | 0.370591i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.9855 | + | 38.0801i | 0.720160 | + | 1.24735i | ||||
\(933\) | 39.9294 | 1.30723 | ||||||||
\(934\) | 56.5541 | − | 32.6515i | 1.85051 | − | 1.06839i | ||||
\(935\) | −1.31930 | + | 2.28509i | −0.0431456 | + | 0.0747304i | ||||
\(936\) | −8.94028 | + | 0.912599i | −0.292222 | + | 0.0298292i | ||||
\(937\) | 21.0196 | 0.686681 | 0.343340 | − | 0.939211i | \(-0.388442\pi\) | ||||
0.343340 | + | 0.939211i | \(0.388442\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.2648 | + | 28.1714i | −0.530781 | + | 0.919340i | ||||
\(940\) | 0.504079 | − | 0.873090i | 0.0164412 | − | 0.0284770i | ||||
\(941\) | 20.8740 | + | 12.0516i | 0.680474 | + | 0.392872i | 0.800034 | − | 0.599955i | \(-0.204815\pi\) |
−0.119560 | + | 0.992827i | \(0.538148\pi\) | |||||||
\(942\) | 56.2513i | 1.83277i | ||||||||
\(943\) | 67.8368 | + | 39.1656i | 2.20907 | + | 1.27541i | ||||
\(944\) | 0.514013i | 0.0167297i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0423 | + | 27.7860i | −0.521579 | + | 0.903402i | ||||
\(947\) | − | 3.34046i | − | 0.108550i | −0.998526 | − | 0.0542751i | \(-0.982715\pi\) | ||
0.998526 | − | 0.0542751i | \(-0.0172848\pi\) | |||||||
\(948\) | 28.3869 | − | 49.1676i | 0.921965 | − | 1.59689i | ||||
\(949\) | −24.2529 | + | 2.47567i | −0.787282 | + | 0.0803636i | ||||
\(950\) | 0.233883 | + | 0.405097i | 0.00758815 | + | 0.0131431i | ||||
\(951\) | 9.01883 | + | 5.20703i | 0.292456 | + | 0.168849i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.48562 | − | 4.30522i | −0.0805171 | − | 0.139460i | 0.822955 | − | 0.568106i | \(-0.192324\pi\) |
−0.903472 | + | 0.428647i | \(0.858991\pi\) | |||||||
\(954\) | −4.48537 | + | 2.58963i | −0.145219 | + | 0.0838423i | ||||
\(955\) | 1.28216i | 0.0414898i | ||||||||
\(956\) | − | 44.1726i | − | 1.42864i | ||||||
\(957\) | 2.60832 | − | 1.50591i | 0.0843150 | − | 0.0486793i | ||||
\(958\) | −7.23509 | − | 12.5315i | −0.233755 | − | 0.404876i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.8506 | + | 7.99667i | 0.447028 | + | 0.258091i | ||||
\(961\) | 15.3981 | + | 26.6702i | 0.496711 | + | 0.860329i | ||||
\(962\) | 45.1266 | − | 32.5803i | 1.45494 | − | 1.05043i | ||||
\(963\) | 4.08892 | − | 7.08221i | 0.131763 | − | 0.228221i | ||||
\(964\) | 2.75691i | 0.0887939i | ||||||||
\(965\) | 2.94601 | − | 5.10264i | 0.0948354 | − | 0.164260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 47.4943i | − | 1.52731i | −0.645623 | − | 0.763657i | \(-0.723402\pi\) | ||
0.645623 | − | 0.763657i | \(-0.276598\pi\) | |||||||
\(968\) | 22.7509 | + | 13.1352i | 0.731241 | + | 0.422182i | ||||
\(969\) | 0.144744i | 0.00464985i | ||||||||
\(970\) | 0.720362 | + | 0.415901i | 0.0231294 | + | 0.0133538i | ||||
\(971\) | 17.2357 | − | 29.8532i | 0.553121 | − | 0.958033i | −0.444926 | − | 0.895567i | \(-0.646770\pi\) |
0.998047 | − | 0.0624662i | \(-0.0198966\pi\) | |||||||
\(972\) | 13.7876 | − | 23.8808i | 0.442238 | − | 0.765978i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.9830 | −0.960717 | ||||||||
\(975\) | 18.4432 | − | 13.3156i | 0.590656 | − | 0.426440i | ||||
\(976\) | 0.708122 | − | 1.22650i | 0.0226664 | − | 0.0392594i | ||||
\(977\) | 11.5598 | − | 6.67406i | 0.369831 | − | 0.213522i | −0.303553 | − | 0.952814i | \(-0.598173\pi\) |
0.673385 | + | 0.739292i | \(0.264840\pi\) | |||||||
\(978\) | 30.7159 | 0.982185 | ||||||||
\(979\) | −13.1632 | − | 22.7993i | −0.420698 | − | 0.728670i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.33408 | + | 4.81169i | −0.266087 | + | 0.153625i | ||||
\(982\) | −24.6390 | − | 14.2253i | −0.786263 | − | 0.453949i | ||||
\(983\) | 10.8551 | + | 6.26720i | 0.346224 | + | 0.199893i | 0.663021 | − | 0.748601i | \(-0.269274\pi\) |
−0.316797 | + | 0.948493i | \(0.602607\pi\) | |||||||
\(984\) | −44.3686 | −1.41442 | ||||||||
\(985\) | 13.1137 | 0.417838 | ||||||||
\(986\) | −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 | ||||
\(990\) | −2.10691 | + | 1.21643i | −0.0669620 | + | 0.0386605i | ||||
\(991\) | 5.20596 | + | 9.01698i | 0.165373 | + | 0.286434i | 0.936788 | − | 0.349899i | \(-0.113784\pi\) |
−0.771415 | + | 0.636332i | \(0.780451\pi\) | |||||||
\(992\) | 20.7938 | − | 36.0158i | 0.660202 | − | 1.14350i | ||||
\(993\) | − | 9.70736i | − | 0.308054i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.85414 | + | 2.80254i | −0.153887 | + | 0.0888464i | ||||
\(996\) | 48.6497 | − | 28.0879i | 1.54153 | − | 0.890000i | ||||
\(997\) | −5.75270 | −0.182190 | −0.0910949 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910949 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(998\) | 10.5414 | + | 18.2582i | 0.333681 | + | 0.577953i | ||||
\(999\) | 37.8125i | 1.19633i |
(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 | 637.2.k.i.459.6 | 12 | ||
7.2 | even | 3 | 637.2.u.g.30.6 | 12 | |||
7.3 | odd | 6 | 637.2.q.g.589.1 | 12 | |||
7.4 | even | 3 | 637.2.q.i.589.1 | 12 | |||
7.5 | odd | 6 | 91.2.u.b.30.6 | yes | 12 | ||
7.6 | odd | 2 | 91.2.k.b.4.6 | ✓ | 12 | ||
13.10 | even | 6 | 637.2.u.g.361.6 | 12 | |||
21.5 | even | 6 | 819.2.do.e.667.1 | 12 | |||
21.20 | even | 2 | 819.2.bm.f.550.1 | 12 | |||
91.6 | even | 12 | 1183.2.e.j.508.2 | 24 | |||
91.10 | odd | 6 | 637.2.q.g.491.1 | 12 | |||
91.19 | even | 12 | 1183.2.e.j.170.2 | 24 | |||
91.20 | even | 12 | 1183.2.e.j.508.11 | 24 | |||
91.23 | even | 6 | inner | 637.2.k.i.569.1 | 12 | ||
91.32 | odd | 12 | 8281.2.a.co.1.11 | 12 | |||
91.33 | even | 12 | 1183.2.e.j.170.11 | 24 | |||
91.45 | even | 12 | 8281.2.a.cp.1.11 | 12 | |||
91.46 | odd | 12 | 8281.2.a.co.1.2 | 12 | |||
91.59 | even | 12 | 8281.2.a.cp.1.2 | 12 | |||
91.62 | odd | 6 | 91.2.u.b.88.6 | yes | 12 | ||
91.75 | odd | 6 | 91.2.k.b.23.1 | yes | 12 | ||
91.88 | even | 6 | 637.2.q.i.491.1 | 12 | |||
273.62 | even | 6 | 819.2.do.e.361.1 | 12 | |||
273.257 | even | 6 | 819.2.bm.f.478.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.6 | ✓ | 12 | 7.6 | odd | 2 | ||
91.2.k.b.23.1 | yes | 12 | 91.75 | odd | 6 | ||
91.2.u.b.30.6 | yes | 12 | 7.5 | odd | 6 | ||
91.2.u.b.88.6 | yes | 12 | 91.62 | odd | 6 | ||
637.2.k.i.459.6 | 12 | 1.1 | even | 1 | trivial | ||
637.2.k.i.569.1 | 12 | 91.23 | even | 6 | inner | ||
637.2.q.g.491.1 | 12 | 91.10 | odd | 6 | |||
637.2.q.g.589.1 | 12 | 7.3 | odd | 6 | |||
637.2.q.i.491.1 | 12 | 91.88 | even | 6 | |||
637.2.q.i.589.1 | 12 | 7.4 | even | 3 | |||
637.2.u.g.30.6 | 12 | 7.2 | even | 3 | |||
637.2.u.g.361.6 | 12 | 13.10 | even | 6 | |||
819.2.bm.f.478.6 | 12 | 273.257 | even | 6 | |||
819.2.bm.f.550.1 | 12 | 21.20 | even | 2 | |||
819.2.do.e.361.1 | 12 | 273.62 | even | 6 | |||
819.2.do.e.667.1 | 12 | 21.5 | even | 6 | |||
1183.2.e.j.170.2 | 24 | 91.19 | even | 12 | |||
1183.2.e.j.170.11 | 24 | 91.33 | even | 12 | |||
1183.2.e.j.508.2 | 24 | 91.6 | even | 12 | |||
1183.2.e.j.508.11 | 24 | 91.20 | even | 12 | |||
8281.2.a.co.1.2 | 12 | 91.46 | odd | 12 | |||
8281.2.a.co.1.11 | 12 | 91.32 | odd | 12 | |||
8281.2.a.cp.1.2 | 12 | 91.59 | even | 12 | |||
8281.2.a.cp.1.11 | 12 | 91.45 | even | 12 |