Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(30,637)]
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([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.u (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 | 361.6 | ||
Root | \(1.21245 - 0.727987i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.361 |
Dual form | 637.2.u.g.30.6 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0.995431 | − | 0.0954820i | \(-0.0304392\pi\) |
0.415026 | + | 0.909810i | \(0.363773\pi\) | |||||||
\(3\) | 1.47336 | 0.850645 | 0.425323 | − | 0.905042i | \(-0.360161\pi\) | ||||
0.425323 | + | 0.905042i | \(0.360161\pi\) | |||||||
\(4\) | 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 | \(0.272660\pi\) | |||||||
\(6\) | 2.93889 | + | 1.69677i | 1.19980 | + | 0.692704i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.00585i | 1.06273i | ||||||||
\(9\) | −0.829208 | −0.276403 | ||||||||
\(10\) | 1.95154 | 0.617131 | ||||||||
\(11\) | − | 1.50340i | − | 0.453293i | −0.973977 | − | 0.226646i | \(-0.927224\pi\) | ||
0.973977 | − | 0.226646i | \(-0.0727762\pi\) | |||||||
\(12\) | 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 | ||||
\(16\) | −0.156597 | + | 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 | \(0.914157\pi\) | |||||||
\(18\) | −1.65401 | − | 0.954943i | −0.389854 | − | 0.225082i | ||||
\(19\) | − | 0.0474272i | − | 0.0108805i | −0.999985 | − | 0.00544027i | \(-0.998268\pi\) | ||
0.999985 | − | 0.00544027i | \(-0.00173170\pi\) | |||||||
\(20\) | 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 | \(0.470016\pi\) |
−0.909216 | + | 0.416325i | \(0.863318\pi\) | |||||||
\(24\) | 4.42870i | 0.904004i | ||||||||
\(25\) | −2.14105 | + | 3.70840i | −0.428210 | + | 0.741681i | ||||
\(26\) | 3.40047 | + | 7.57643i | 0.666887 | + | 1.48586i | ||||
\(27\) | −5.64180 | −1.08577 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.679854 | − | 1.17754i | −0.126246 | − | 0.218664i | 0.795973 | − | 0.605331i | \(-0.206959\pi\) |
−0.922219 | + | 0.386668i | \(0.873626\pi\) | |||||||
\(30\) | 2.87532 | 0.524959 | ||||||||
\(31\) | −6.80787 | − | 3.93052i | −1.22273 | − | 0.705943i | −0.257230 | − | 0.966350i | \(-0.582810\pi\) |
−0.965499 | + | 0.260407i | \(0.916143\pi\) | |||||||
\(32\) | 4.58156 | − | 2.64516i | 0.809912 | − | 0.467603i | ||||
\(33\) | − | 2.21505i | − | 0.385591i | ||||||
\(34\) | − | 4.77099i | − | 0.818218i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.37028 | − | 2.37340i | −0.228380 | − | 0.395566i | ||||
\(37\) | −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 | ||||
\(39\) | 4.30706 | + | 3.10959i | 0.689681 | + | 0.497934i | ||||
\(40\) | 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 | ||||
\(45\) | −0.608453 | + | 0.351290i | −0.0907028 | + | 0.0523673i | ||||
\(46\) | −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 | \(0.341692\pi\) | |||||||
\(48\) | −0.230724 | + | 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 | ||||
\(52\) | −1.21011 | + | 11.8549i | −0.167813 | + | 1.64398i | ||||
\(53\) | −1.35591 | + | 2.34850i | −0.186248 | + | 0.322591i | −0.943996 | − | 0.329956i | \(-0.892966\pi\) |
0.757748 | + | 0.652547i | \(0.226299\pi\) | |||||||
\(54\) | −11.2536 | − | 6.49729i | −1.53143 | − | 0.884169i | ||||
\(55\) | −0.636910 | − | 1.10316i | −0.0858809 | − | 0.148750i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.0698773i | − | 0.00925548i | ||||||
\(58\) | − | 3.13177i | − | 0.411222i | ||||||
\(59\) | −1.42132 | + | 0.820598i | −0.185040 | + | 0.106833i | −0.589658 | − | 0.807653i | \(-0.700738\pi\) |
0.404619 | + | 0.914486i | \(0.367404\pi\) | |||||||
\(60\) | 3.57313 | + | 2.06295i | 0.461289 | + | 0.266325i | ||||
\(61\) | −4.52194 | −0.578975 | −0.289488 | − | 0.957182i | \(-0.593485\pi\) | ||||
−0.289488 | + | 0.957182i | \(0.593485\pi\) | |||||||
\(62\) | −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 | ||||
\(66\) | 2.55093 | − | 4.41834i | 0.313998 | − | 0.543860i | ||||
\(67\) | 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 | ||||
\(69\) | −5.75988 | + | 9.97641i | −0.693409 | + | 1.20102i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3096 | + | 7.10697i | 1.46088 | + | 0.843442i | 0.999052 | − | 0.0435255i | \(-0.0138590\pi\) |
0.461832 | + | 0.886967i | \(0.347192\pi\) | |||||||
\(72\) | − | 2.49247i | − | 0.293741i | ||||||
\(73\) | 5.85563 | + | 3.38075i | 0.685349 | + | 0.395687i | 0.801867 | − | 0.597502i | \(-0.203840\pi\) |
−0.116518 | + | 0.993189i | \(0.537173\pi\) | |||||||
\(74\) | −7.71847 | − | 13.3688i | −0.897253 | − | 1.55409i | ||||
\(75\) | −3.15454 | + | 5.46382i | −0.364255 | + | 0.630907i | ||||
\(76\) | 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 | \(-0.394366\pi\) | |||||||
\(80\) | 0.265367i | 0.0296689i | ||||||||
\(81\) | −5.82479 | −0.647199 | ||||||||
\(82\) | 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 | ||||
\(87\) | −1.00167 | − | 1.73494i | −0.107390 | − | 0.186006i | ||||
\(88\) | 4.51900 | 0.481727 | ||||||||
\(89\) | −15.1652 | − | 8.75561i | −1.60750 | − | 0.928093i | −0.989927 | − | 0.141582i | \(-0.954781\pi\) |
−0.617577 | − | 0.786510i | \(-0.711886\pi\) | |||||||
\(90\) | −1.61823 | −0.170576 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −25.8411 | −2.69412 | ||||||||
\(93\) | −10.0304 | − | 5.79108i | −1.04011 | − | 0.600507i | ||||
\(94\) | −0.829208 | −0.0855262 | ||||||||
\(95\) | −0.0200923 | − | 0.0348009i | −0.00206143 | − | 0.00357050i | ||||
\(96\) | 6.75029 | − | 3.89728i | 0.688948 | − | 0.397764i | ||||
\(97\) | −0.369125 | − | 0.213115i | −0.0374790 | − | 0.0216385i | 0.481143 | − | 0.876642i | \(-0.340222\pi\) |
−0.518622 | + | 0.855003i | \(0.673555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.24663i | 0.125291i | ||||||||
\(100\) | −14.1525 | −1.41525 | ||||||||
\(101\) | 9.66997 | 0.962198 | 0.481099 | − | 0.876666i | \(-0.340238\pi\) | ||||
0.481099 | + | 0.876666i | \(0.340238\pi\) | |||||||
\(102\) | − | 7.02939i | − | 0.696013i | ||||||
\(103\) | 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 | ||||
\(107\) | −4.93111 | + | 8.54094i | −0.476709 | + | 0.825684i | −0.999644 | − | 0.0266888i | \(-0.991504\pi\) |
0.522935 | + | 0.852373i | \(0.324837\pi\) | |||||||
\(108\) | −9.32319 | − | 16.1482i | −0.897124 | − | 1.55386i | ||||
\(109\) | 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 | ||||||
\(111\) | −8.55178 | − | 4.93737i | −0.811699 | − | 0.468635i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.73879 | − | 3.01167i | 0.163572 | − | 0.283314i | −0.772576 | − | 0.634923i | \(-0.781032\pi\) |
0.936147 | + | 0.351609i | \(0.114365\pi\) | |||||||
\(114\) | 0.0804731 | − | 0.139383i | 0.00753699 | − | 0.0130545i | ||||
\(115\) | 6.62472i | 0.617758i | ||||||||
\(116\) | 2.24694 | − | 3.89182i | 0.208623 | − | 0.361346i | ||||
\(117\) | −2.42401 | − | 1.75008i | −0.224100 | − | 0.161795i | ||||
\(118\) | −3.78011 | −0.347987 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.87620 | + | 3.24967i | 0.171273 | + | 0.296653i | ||||
\(121\) | 8.73978 | 0.794526 | ||||||||
\(122\) | −9.01986 | − | 5.20762i | −0.816620 | − | 0.471476i | ||||
\(123\) | 12.7832 | − | 7.38039i | 1.15262 | − | 0.665467i | ||||
\(124\) | − | 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 | ||||
\(129\) | 6.82583 | − | 11.8227i | 0.600981 | − | 1.04093i | ||||
\(130\) | 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 | \(0.868798\pi\) | |||||||
\(132\) | 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 | ||||
\(136\) | 5.39215 | − | 3.11316i | 0.462373 | − | 0.266951i | ||||
\(137\) | −1.61490 | + | 0.932362i | −0.137970 | + | 0.0796571i | −0.567396 | − | 0.823445i | \(-0.692049\pi\) |
0.429426 | + | 0.903102i | \(0.358716\pi\) | |||||||
\(138\) | −22.9783 | + | 13.2665i | −1.95605 | + | 1.12932i | ||||
\(139\) | 7.80462 | − | 13.5180i | 0.661979 | − | 1.14658i | −0.318116 | − | 0.948052i | \(-0.603050\pi\) |
0.980095 | − | 0.198530i | \(-0.0636166\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.459366 | + | 0.265215i | −0.0386856 | + | 0.0223351i | ||||
\(142\) | 16.3692 | + | 28.3524i | 1.37368 | + | 2.37928i | ||||
\(143\) | 3.17300 | − | 4.39487i | 0.265339 | − | 0.367518i | ||||
\(144\) | 0.129851 | − | 0.224909i | 0.0108209 | − | 0.0187424i | ||||
\(145\) | −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 | \(0.0839416\pi\) | ||||
−0.965429 | + | 0.260664i | \(0.916058\pi\) | |||||||
\(150\) | −12.5846 | + | 7.26574i | −1.02753 | + | 0.593245i | ||||
\(151\) | −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 | ||||||||
\(153\) | 0.858811 | + | 1.48750i | 0.0694307 | + | 0.120258i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.66060 | −0.534992 | ||||||||
\(156\) | −1.78293 | + | 17.4665i | −0.142749 | + | 1.39844i | ||||
\(157\) | −8.28798 | + | 14.3552i | −0.661453 | + | 1.14567i | 0.318781 | + | 0.947828i | \(0.396727\pi\) |
−0.980234 | + | 0.197842i | \(0.936607\pi\) | |||||||
\(158\) | − | 26.8539i | − | 2.13638i | ||||||
\(159\) | −1.99774 | + | 3.46019i | −0.158431 | + | 0.274411i | ||||
\(160\) | 2.24122 | − | 3.88191i | 0.177184 | − | 0.306892i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.6186 | − | 6.70802i | −0.912846 | − | 0.527032i | ||||
\(163\) | 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 | ||||
\(165\) | −0.938398 | − | 1.62535i | −0.0730542 | − | 0.126534i | ||||
\(166\) | −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 | ||||
\(171\) | 0.0393270i | 0.00300741i | ||||||||
\(172\) | 30.6234 | 2.33501 | ||||||||
\(173\) | 19.5870 | 1.48918 | 0.744588 | − | 0.667525i | \(-0.232646\pi\) | ||||
0.744588 | + | 0.667525i | \(0.232646\pi\) | |||||||
\(174\) | − | 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 | ||||
\(178\) | −20.1665 | − | 34.9294i | −1.51154 | − | 2.61807i | ||||
\(179\) | 2.89332 | 0.216257 | 0.108129 | − | 0.994137i | \(-0.465514\pi\) | ||||
0.108129 | + | 0.994137i | \(0.465514\pi\) | |||||||
\(180\) | −2.01096 | − | 1.16103i | −0.149888 | − | 0.0865379i | ||||
\(181\) | 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 | ||||||||
\(184\) | −20.3532 | − | 11.7509i | −1.50046 | − | 0.866289i | ||||
\(185\) | −5.67871 | −0.417507 | ||||||||
\(186\) | −13.3384 | − | 23.1028i | −0.978019 | − | 1.69398i | ||||
\(187\) | −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 | \(-0.517435\pi\) | ||||
−0.0547475 | + | 0.998500i | \(0.517435\pi\) | |||||||
\(192\) | 18.8758 | 1.36225 | ||||||||
\(193\) | 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 | ||||
\(195\) | 4.47778 | + | 0.457080i | 0.320661 | + | 0.0327322i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.4037 | + | 7.73860i | −0.954971 | + | 0.551353i | −0.894622 | − | 0.446825i | \(-0.852555\pi\) |
−0.0603494 | + | 0.998177i | \(0.519221\pi\) | |||||||
\(198\) | −1.43566 | + | 2.48664i | −0.102028 | + | 0.176718i | ||||
\(199\) | −3.30764 | − | 5.72901i | −0.234473 | − | 0.406118i | 0.724647 | − | 0.689121i | \(-0.242003\pi\) |
−0.959119 | + | 0.283002i | \(0.908670\pi\) | |||||||
\(200\) | −11.1469 | − | 6.43566i | −0.788205 | − | 0.455070i | ||||
\(201\) | 3.00958i | 0.212279i | ||||||||
\(202\) | 19.2886 | + | 11.1363i | 1.35714 | + | 0.783545i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.04336 | − | 8.73535i | 0.353106 | − | 0.611597i | ||||
\(205\) | 4.24427 | − | 7.35129i | 0.296433 | − | 0.513436i | ||||
\(206\) | 22.9825i | 1.60127i | ||||||||
\(207\) | 3.24166 | − | 5.61473i | 0.225311 | − | 0.390250i | ||||
\(208\) | −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 | ||||||||
\(213\) | 18.1365 | + | 10.4711i | 1.24269 | + | 0.717470i | ||||
\(214\) | −19.6721 | + | 11.3577i | −1.34475 | + | 0.776394i | ||||
\(215\) | − | 7.85072i | − | 0.535415i | ||||||
\(216\) | − | 16.9584i | − | 1.15387i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.3653 | + | 23.1493i | 0.905211 | + | 1.56787i | ||||
\(219\) | 8.62745 | + | 4.98106i | 0.582989 | + | 0.336589i | ||||
\(220\) | 2.10501 | − | 3.64599i | 0.141920 | − | 0.245812i | ||||
\(221\) | 0.758428 | − | 7.42993i | 0.0510174 | − | 0.499791i | ||||
\(222\) | −11.3721 | − | 19.6970i | −0.763244 | − | 1.32198i | ||||
\(223\) | −13.9067 | + | 8.02903i | −0.931261 | + | 0.537664i | −0.887210 | − | 0.461366i | \(-0.847360\pi\) |
−0.0440506 | + | 0.999029i | \(0.514026\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.77537 | − | 3.07504i | 0.118358 | − | 0.205002i | ||||
\(226\) | 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 | \(0.319641\pi\) | |||||||
\(228\) | 0.200006 | − | 0.115474i | 0.0132457 | − | 0.00764742i | ||||
\(229\) | 18.0285 | − | 10.4088i | 1.19136 | − | 0.687831i | 0.232743 | − | 0.972538i | \(-0.425230\pi\) |
0.958614 | + | 0.284707i | \(0.0918965\pi\) | |||||||
\(230\) | −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 | \(0.976866\pi\) | |||||||
\(234\) | −2.81969 | − | 6.28243i | −0.184329 | − | 0.410696i | ||||
\(235\) | −0.152518 | + | 0.264169i | −0.00994920 | + | 0.0172325i | ||||
\(236\) | −4.69751 | − | 2.71211i | −0.305782 | − | 0.176543i | ||||
\(237\) | −8.58899 | − | 14.8766i | −0.557915 | − | 0.966337i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 13.3652i | − | 0.864525i | −0.901748 | − | 0.432263i | \(-0.857715\pi\) | ||
0.901748 | − | 0.432263i | \(-0.142285\pi\) | |||||||
\(240\) | 0.390981i | 0.0252377i | ||||||||
\(241\) | 0.722398 | − | 0.417076i | 0.0465337 | − | 0.0268663i | −0.476553 | − | 0.879146i | \(-0.658114\pi\) |
0.523086 | + | 0.852280i | \(0.324781\pi\) | |||||||
\(242\) | 17.4331 | + | 10.0650i | 1.12064 | + | 0.647004i | ||||
\(243\) | 8.34339 | 0.535229 | ||||||||
\(244\) | −7.47259 | − | 12.9429i | −0.478384 | − | 0.828585i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 33.9980 | 2.16763 | ||||||||
\(247\) | 0.100097 | − | 0.138643i | 0.00636903 | − | 0.00882165i | ||||
\(248\) | 11.8146 | − | 20.4634i | 0.750225 | − | 1.29943i | ||||
\(249\) | 16.9970i | 1.07714i | ||||||||
\(250\) | −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 | ||||||
\(255\) | −2.23943 | − | 1.29293i | −0.140238 | − | 0.0809667i | ||||
\(256\) | 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 | \(0.232174\pi\) | |||||||
\(258\) | 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 | ||||
\(262\) | − | 5.86221i | − | 0.362168i | ||||||
\(263\) | −22.5891 | −1.39290 | −0.696450 | − | 0.717605i | \(-0.745238\pi\) | ||||
−0.696450 | + | 0.717605i | \(0.745238\pi\) | |||||||
\(264\) | 6.65811 | 0.409779 | ||||||||
\(265\) | 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 | ||||
\(269\) | 8.00065 | + | 13.8575i | 0.487808 | + | 0.844909i | 0.999902 | − | 0.0140210i | \(-0.00446317\pi\) |
−0.512093 | + | 0.858930i | \(0.671130\pi\) | |||||||
\(270\) | −11.0102 | −0.670059 | ||||||||
\(271\) | 7.58582 | + | 4.37967i | 0.460806 | + | 0.266046i | 0.712383 | − | 0.701791i | \(-0.247616\pi\) |
−0.251577 | + | 0.967837i | \(0.580949\pi\) | |||||||
\(272\) | 0.648750 | 0.0393363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29496 | −0.259468 | ||||||||
\(275\) | 5.57522 | + | 3.21886i | 0.336199 | + | 0.194104i | ||||
\(276\) | −38.0733 | −2.29174 | ||||||||
\(277\) | −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 | ||||
\(279\) | 5.64514 | + | 3.25922i | 0.337965 | + | 0.195124i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0234i | 0.836566i | 0.908317 | + | 0.418283i | \(0.137368\pi\) | ||||
−0.908317 | + | 0.418283i | \(0.862632\pi\) | |||||||
\(282\) | −1.22172 | −0.0727525 | ||||||||
\(283\) | 1.01259 | 0.0601922 | 0.0300961 | − | 0.999547i | \(-0.490419\pi\) | ||||
0.0300961 | + | 0.999547i | \(0.490419\pi\) | |||||||
\(284\) | 46.9776i | 2.78761i | ||||||||
\(285\) | −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 | ||||
\(289\) | 6.35465 | − | 11.0066i | 0.373803 | − | 0.647446i | ||||
\(290\) | −1.32676 | − | 2.29802i | −0.0779101 | − | 0.134944i | ||||
\(291\) | −0.543855 | − | 0.313995i | −0.0318813 | − | 0.0184067i | ||||
\(292\) | 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 | ||||
\(297\) | 8.48190i | 0.492170i | ||||||||
\(298\) | −7.32857 | + | 12.6935i | −0.424532 | + | 0.735312i | ||||
\(299\) | −25.7191 | + | 11.5433i | −1.48737 | + | 0.667565i | ||||
\(300\) | −20.8517 | −1.20387 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.764792 | − | 1.32466i | −0.0440088 | − | 0.0762256i | ||||
\(303\) | 14.2474 | 0.818489 | ||||||||
\(304\) | 0.0128639 | + | 0.00742695i | 0.000737793 | + | 0.000425965i | ||||
\(305\) | −3.31809 | + | 1.91570i | −0.189993 | + | 0.109693i | ||||
\(306\) | 3.95614i | 0.226157i | ||||||||
\(307\) | − | 27.2004i | − | 1.55241i | −0.630482 | − | 0.776204i | \(-0.717143\pi\) | ||
0.630482 | − | 0.776204i | \(-0.282857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.35077 | + | 12.7319i | 0.418171 | + | 0.724293i | ||||
\(310\) | −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 | \(0.887732\pi\) | |||||||
\(312\) | −9.34696 | + | 12.9464i | −0.529168 | + | 0.732943i | ||||
\(313\) | −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 | −0.318149 | − | 0.948041i | \(-0.603061\pi\) |
0.661953 | + | 0.749545i | \(0.269728\pi\) | |||||||
\(318\) | −7.96973 | + | 4.60133i | −0.446920 | + | 0.258030i | ||||
\(319\) | −1.77032 | + | 1.02209i | −0.0991188 | + | 0.0572263i | ||||
\(320\) | 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 | ||||
\(325\) | −14.0857 | + | 6.32195i | −0.781331 | + | 0.350679i | ||||
\(326\) | −10.4237 | + | 18.0544i | −0.577318 | + | 0.999943i | ||||
\(327\) | 14.8082 | + | 8.54955i | 0.818898 | + | 0.472791i | ||||
\(328\) | 15.0569 | + | 26.0794i | 0.831381 | + | 1.43999i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 4.32276i | − | 0.237960i | ||||||
\(331\) | 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 | ||||
\(333\) | 4.81294 | + | 2.77875i | 0.263748 | + | 0.152275i | ||||
\(334\) | 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 | ||||
\(339\) | 2.56187 | − | 4.43728i | 0.139141 | − | 0.241000i | ||||
\(340\) | − | 5.80061i | − | 0.314582i | ||||||
\(341\) | −5.90916 | + | 10.2350i | −0.319999 | + | 0.554254i | ||||
\(342\) | −0.0452902 | + | 0.0784450i | −0.00244902 | + | 0.00424182i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 24.1198 | + | 13.9256i | 1.30045 | + | 0.750817i | ||||
\(345\) | 9.76060i | 0.525493i | ||||||||
\(346\) | 39.0700 | + | 22.5571i | 2.10042 | + | 1.21268i | ||||
\(347\) | 4.54739 | + | 7.87631i | 0.244117 | + | 0.422822i | 0.961883 | − | 0.273462i | \(-0.0881687\pi\) |
−0.717766 | + | 0.696284i | \(0.754835\pi\) | |||||||
\(348\) | 3.31056 | − | 5.73405i | 0.177464 | − | 0.307378i | ||||
\(349\) | −7.98521 | + | 4.61026i | −0.427439 | + | 0.246782i | −0.698255 | − | 0.715849i | \(-0.746040\pi\) |
0.270816 | + | 0.962631i | \(0.412706\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.4926 | − | 11.9073i | −0.880310 | − | 0.635564i | ||||
\(352\) | −3.97674 | − | 6.88792i | −0.211961 | − | 0.367127i | ||||
\(353\) | 2.15449i | 0.114672i | 0.998355 | + | 0.0573359i | \(0.0182606\pi\) | ||||
−0.998355 | + | 0.0573359i | \(0.981739\pi\) | |||||||
\(354\) | −5.56947 | −0.296014 | ||||||||
\(355\) | 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 | −0.291513 | − | 0.956567i | \(-0.594159\pi\) |
0.682654 | + | 0.730741i | \(0.260825\pi\) | |||||||
\(360\) | −1.05593 | − | 1.82892i | −0.0556521 | − | 0.0963923i | ||||
\(361\) | 18.9978 | 0.999882 | ||||||||
\(362\) | 2.72881 | + | 1.57548i | 0.143423 | + | 0.0828055i | ||||
\(363\) | 12.8769 | 0.675860 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.72896 | 0.299867 | ||||||||
\(366\) | −13.2895 | − | 7.67270i | −0.694654 | − | 0.401059i | ||||
\(367\) | −2.29823 | −0.119967 | −0.0599833 | − | 0.998199i | \(-0.519105\pi\) | ||||
−0.0599833 | + | 0.998199i | \(0.519105\pi\) | |||||||
\(368\) | −1.22438 | − | 2.12070i | −0.0638255 | − | 0.110549i | ||||
\(369\) | −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 | ||||||
\(373\) | 11.7684 | 0.609343 | 0.304672 | − | 0.952457i | \(-0.401453\pi\) | ||||
0.304672 | + | 0.952457i | \(0.401453\pi\) | |||||||
\(374\) | −7.17271 | −0.370892 | ||||||||
\(375\) | 11.5875i | 0.598374i | ||||||||
\(376\) | −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 | ||||
\(381\) | −11.5658 | − | 20.0325i | −0.592532 | − | 1.02630i | ||||
\(382\) | −3.01846 | − | 1.74271i | −0.154438 | − | 0.0891647i | ||||
\(383\) | 28.2446i | 1.44323i | 0.692294 | + | 0.721616i | \(0.256600\pi\) | ||||
−0.692294 | + | 0.721616i | \(0.743400\pi\) | |||||||
\(384\) | 24.1508 | + | 13.9435i | 1.23244 | + | 0.711551i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.00839 | + | 13.8709i | −0.407616 | + | 0.706012i | ||||
\(387\) | −3.84158 | + | 6.65381i | −0.195278 | + | 0.338232i | ||||
\(388\) | − | 1.40870i | − | 0.0715161i | ||||||
\(389\) | 3.84043 | − | 6.65182i | 0.194717 | − | 0.337261i | −0.752090 | − | 0.659060i | \(-0.770954\pi\) |
0.946808 | + | 0.321799i | \(0.104288\pi\) | |||||||
\(390\) | 8.40538 | + | 6.06849i | 0.425623 | + | 0.307290i | ||||
\(391\) | 16.1957 | 0.819050 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.87498 | − | 3.24756i | −0.0945801 | − | 0.163818i | ||||
\(394\) | −35.6481 | −1.79593 | ||||||||
\(395\) | −8.55513 | − | 4.93931i | −0.430455 | − | 0.248524i | ||||
\(396\) | −3.56817 | + | 2.06008i | −0.179307 | + | 0.103523i | ||||
\(397\) | − | 7.45281i | − | 0.374046i | −0.982356 | − | 0.187023i | \(-0.940116\pi\) | ||
0.982356 | − | 0.187023i | \(-0.0598839\pi\) | |||||||
\(398\) | − | 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 | 0.0518898 | − | 0.998653i | \(-0.483476\pi\) |
−0.838914 | + | 0.544264i | \(0.816809\pi\) | |||||||
\(402\) | −3.46593 | + | 6.00316i | −0.172865 | + | 0.299411i | ||||
\(403\) | −11.6058 | − | 25.8584i | −0.578126 | − | 1.28810i | ||||
\(404\) | 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 | ||||
\(409\) | 25.3594 | − | 14.6413i | 1.25394 | − | 0.723964i | 0.282053 | − | 0.959399i | \(-0.408985\pi\) |
0.971890 | + | 0.235435i | \(0.0756514\pi\) | |||||||
\(410\) | 16.9320 | − | 9.77568i | 0.836211 | − | 0.482787i | ||||
\(411\) | −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 | ||||
\(416\) | 18.9759 | + | 1.93701i | 0.930372 | + | 0.0949698i | ||||
\(417\) | 11.4990 | − | 19.9169i | 0.563109 | − | 0.975334i | ||||
\(418\) | −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 | ||||||||
\(423\) | 0.258531 | − | 0.149263i | 0.0125702 | − | 0.00725742i | ||||
\(424\) | −7.05923 | − | 4.07565i | −0.342826 | − | 0.197931i | ||||
\(425\) | 8.86994 | 0.430255 | ||||||||
\(426\) | 24.1178 | + | 41.7733i | 1.16851 | + | 2.02392i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −32.5950 | −1.57554 | ||||||||
\(429\) | 4.67497 | − | 6.47524i | 0.225710 | − | 0.312627i | ||||
\(430\) | 9.04115 | − | 15.6597i | 0.436003 | − | 0.755179i | ||||
\(431\) | 21.1688i | 1.01966i | 0.860274 | + | 0.509832i | \(0.170292\pi\) | ||||
−0.860274 | + | 0.509832i | \(0.829708\pi\) | |||||||
\(432\) | 0.883489 | − | 1.53025i | 0.0425069 | − | 0.0736241i | ||||
\(433\) | 11.7148 | − | 20.2906i | 0.562977 | − | 0.975105i | −0.434258 | − | 0.900789i | \(-0.642989\pi\) |
0.997235 | − | 0.0743163i | \(-0.0236774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.47000 | − | 0.848707i | −0.0704813 | − | 0.0406924i | ||||
\(436\) | 38.3566i | 1.83695i | ||||||||
\(437\) | 0.321139 | + | 0.185409i | 0.0153621 | + | 0.00886934i | ||||
\(438\) | 11.4727 | + | 19.8713i | 0.548187 | + | 0.949488i | ||||
\(439\) | 6.01919 | − | 10.4256i | 0.287280 | − | 0.497584i | −0.685879 | − | 0.727715i | \(-0.740582\pi\) |
0.973160 | + | 0.230131i | \(0.0739155\pi\) | |||||||
\(440\) | 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 | \(0.955262\pi\) | |||||||
\(444\) | − | 32.6364i | − | 1.54885i | ||||||
\(445\) | −14.8371 | −0.703346 | ||||||||
\(446\) | −36.9860 | −1.75134 | ||||||||
\(447\) | 9.37592i | 0.443466i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5177 | + | 13.0006i | 1.06268 | + | 0.613536i | 0.926171 | − | 0.377104i | \(-0.123080\pi\) |
0.136504 | + | 0.990640i | \(0.456413\pi\) | |||||||
\(450\) | 7.08263 | − | 4.08916i | 0.333878 | − | 0.192765i | ||||
\(451\) | −7.53087 | − | 13.0438i | −0.354615 | − | 0.614211i | ||||
\(452\) | 11.4935 | 0.540610 | ||||||||
\(453\) | −0.847362 | − | 0.489225i | −0.0398125 | − | 0.0229858i | ||||
\(454\) | 2.98459 | 0.140074 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.210041 | 0.00983605 | ||||||||
\(457\) | 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 | ||||||||
\(459\) | 5.84322 | + | 10.1208i | 0.272738 | + | 0.472396i | ||||
\(460\) | −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 | ||||||||
\(465\) | −9.81347 | −0.455089 | ||||||||
\(466\) | − | 30.6433i | − | 1.41952i | ||||||
\(467\) | −14.1762 | − | 24.5539i | −0.655996 | − | 1.13622i | −0.981643 | − | 0.190727i | \(-0.938916\pi\) |
0.325647 | − | 0.945491i | \(-0.394418\pi\) | |||||||
\(468\) | 1.00344 | − | 9.83015i | 0.0463838 | − | 0.454399i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.608453 | + | 0.351290i | −0.0280658 | + | 0.0162038i | ||||
\(471\) | −12.2112 | + | 21.1504i | −0.562662 | + | 0.974559i | ||||
\(472\) | −2.46659 | − | 4.27226i | −0.113534 | − | 0.196647i | ||||
\(473\) | −12.0637 | − | 6.96501i | −0.554692 | − | 0.320251i | ||||
\(474\) | − | 39.5655i | − | 1.81730i | ||||||
\(475\) | 0.175879 | + | 0.101544i | 0.00806989 | + | 0.00465915i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.12433 | − | 1.94739i | 0.0514794 | − | 0.0891650i | ||||
\(478\) | 15.3918 | − | 26.6595i | 0.704007 | − | 1.21938i | ||||
\(479\) | 6.28246i | 0.287053i | 0.989646 | + | 0.143526i | \(0.0458442\pi\) | ||||
−0.989646 | + | 0.143526i | \(0.954156\pi\) | |||||||
\(480\) | 3.30213 | − | 5.71946i | 0.150721 | − | 0.261056i | ||||
\(481\) | −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 | ||||||||
\(486\) | 16.6425 | + | 9.60853i | 0.754917 | + | 0.435852i | ||||
\(487\) | −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 | ||||||
\(489\) | 13.3358i | 0.603065i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.17616 | − | 10.6974i | −0.278726 | − | 0.482768i | 0.692342 | − | 0.721569i | \(-0.256579\pi\) |
−0.971068 | + | 0.238801i | \(0.923246\pi\) | |||||||
\(492\) | 42.2490 | + | 24.3925i | 1.90473 | + | 1.09970i | ||||
\(493\) | −1.40825 | + | 2.43916i | −0.0634244 | + | 0.109854i | ||||
\(494\) | 0.359329 | − | 0.161275i | 0.0161670 | − | 0.00725609i | ||||
\(495\) | 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 | −0.666826 | − | 0.745214i | \(-0.732348\pi\) |
0.311961 | + | 0.950095i | \(0.399014\pi\) | |||||||
\(500\) | −22.5105 | + | 12.9965i | −1.00670 | + | 0.581220i | ||||
\(501\) | 3.39102 | − | 1.95781i | 0.151500 | − | 0.0874684i | ||||
\(502\) | −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 | ||||
\(507\) | 6.02782 | + | 18.1805i | 0.267705 | + | 0.807423i | ||||
\(508\) | 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 | \(0.339116\pi\) | |||||||
\(510\) | −2.97797 | − | 5.15800i | −0.131867 | − | 0.228400i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.53972i | 0.156435i | ||||||||
\(513\) | 0.267575i | 0.0118137i | ||||||||
\(514\) | −13.0690 | + | 7.54536i | −0.576447 | + | 0.332812i | ||||
\(515\) | 7.32179 | + | 4.22724i | 0.322637 | + | 0.186274i | ||||
\(516\) | 45.1193 | 1.98626 | ||||||||
\(517\) | 0.270623 | + | 0.468732i | 0.0119020 | + | 0.0206148i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 28.8588 | 1.26676 | ||||||||
\(520\) | −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 | \(-0.176709\pi\) | |||||||
\(522\) | 2.59689i | 0.113663i | ||||||||
\(523\) | −0.366073 | + | 0.634057i | −0.0160073 | + | 0.0277254i | −0.873918 | − | 0.486073i | \(-0.838429\pi\) |
0.857911 | + | 0.513799i | \(0.171762\pi\) | |||||||
\(524\) | 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 | ||||||||
\(528\) | 0.600798 | + | 0.346871i | 0.0261464 | + | 0.0150956i | ||||
\(529\) | −19.0660 | − | 33.0234i | −0.828959 | − | 1.43580i | ||||
\(530\) | −2.64610 | + | 4.58319i | −0.114939 | + | 0.199081i | ||||
\(531\) | 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 | ||||
\(535\) | 8.35618i | 0.361269i | ||||||||
\(536\) | −6.13993 | −0.265204 | ||||||||
\(537\) | 4.26291 | 0.183958 | ||||||||
\(538\) | 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 | 0.00981448 | − | 0.999952i | \(-0.496876\pi\) |
0.870891 | + | 0.491476i | \(0.163543\pi\) | |||||||
\(542\) | 10.0876 | + | 17.4722i | 0.433298 | + | 0.750494i | ||||
\(543\) | 2.01562 | 0.0864985 | ||||||||
\(544\) | −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 | ||||
\(549\) | 3.74963 | 0.160030 | ||||||||
\(550\) | 7.41388 | + | 12.8412i | 0.316129 | + | 0.547552i | ||||
\(551\) | −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 | ||||||
\(555\) | −8.36679 | −0.355150 | ||||||||
\(556\) | 51.5891 | 2.18787 | ||||||||
\(557\) | − | 6.40680i | − | 0.271465i | −0.990746 | − | 0.135732i | \(-0.956661\pi\) | ||
0.990746 | − | 0.135732i | \(-0.0433388\pi\) | |||||||
\(558\) | 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 | ||||
\(562\) | −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 | \(0.882635\pi\) | |||||||
\(564\) | −1.51822 | − | 0.876546i | −0.0639287 | − | 0.0369092i | ||||
\(565\) | − | 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 | −0.907721 | − | 0.419575i | \(-0.862179\pi\) |
0.817223 | + | 0.576322i | \(0.195513\pi\) | |||||||
\(570\) | − | 0.136368i | − | 0.00571184i | ||||||
\(571\) | 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 | ||||
\(573\) | −2.22956 | −0.0931413 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.7402 | − | 28.9949i | −0.698115 | − | 1.20917i | ||||
\(576\) | −10.6233 | −0.442639 | ||||||||
\(577\) | −5.50494 | − | 3.17828i | −0.229174 | − | 0.132314i | 0.381017 | − | 0.924568i | \(-0.375574\pi\) |
−0.610191 | + | 0.792254i | \(0.708907\pi\) | |||||||
\(578\) | 25.3511 | − | 14.6364i | 1.05447 | − | 0.608796i | ||||
\(579\) | 10.2457i | 0.425795i | ||||||||
\(580\) | − | 3.80763i | − | 0.158103i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.723214 | − | 1.25264i | −0.0299782 | − | 0.0519237i | ||||
\(583\) | 3.53074 | + | 2.03847i | 0.146228 | + | 0.0844249i | ||||
\(584\) | −10.1620 | + | 17.6011i | −0.420507 | + | 0.728339i | ||||
\(585\) | −2.52010 | − | 0.257244i | −0.104193 | − | 0.0106358i | ||||
\(586\) | 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 | ||||
\(591\) | −19.7484 | + | 11.4018i | −0.812342 | + | 0.469006i | ||||
\(592\) | 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 | \(0.330242\pi\) | |||||||
\(594\) | −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 | ||||
\(598\) | −64.5951 | − | 6.59369i | −2.64149 | − | 0.269636i | ||||
\(599\) | 4.81348 | − | 8.33719i | 0.196673 | − | 0.340648i | −0.750774 | − | 0.660559i | \(-0.770320\pi\) |
0.947448 | + | 0.319910i | \(0.103653\pi\) | |||||||
\(600\) | −16.4234 | − | 9.48206i | −0.670483 | − | 0.387103i | ||||
\(601\) | −20.5399 | − | 35.5762i | −0.837842 | − | 1.45118i | −0.891696 | − | 0.452635i | \(-0.850484\pi\) |
0.0538542 | − | 0.998549i | \(-0.482849\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.69379i | − | 0.0689765i | ||||||
\(604\) | − | 2.19485i | − | 0.0893073i | ||||||
\(605\) | 6.41304 | − | 3.70257i | 0.260727 | − | 0.150531i | ||||
\(606\) | 28.4190 | + | 16.4077i | 1.15444 | + | 0.666518i | ||||
\(607\) | −19.0858 | −0.774668 | −0.387334 | − | 0.921939i | \(-0.626604\pi\) | ||||
−0.387334 | + | 0.921939i | \(0.626604\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | −2.83840 | + | 4.91626i | −0.114736 | + | 0.198728i | ||||
\(613\) | 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 | ||||
\(615\) | 6.25334 | − | 10.8311i | 0.252159 | − | 0.436752i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.20117 | + | 4.15759i | 0.289908 | + | 0.167378i | 0.637900 | − | 0.770119i | \(-0.279803\pi\) |
−0.347992 | + | 0.937497i | \(0.613136\pi\) | |||||||
\(618\) | 33.8616i | 1.36211i | ||||||||
\(619\) | −38.5146 | − | 22.2364i | −1.54803 | − | 0.893756i | −0.998292 | − | 0.0584199i | \(-0.981394\pi\) |
−0.549739 | − | 0.835336i | \(-0.685273\pi\) | |||||||
\(620\) | −11.0068 | − | 19.0643i | −0.442042 | − | 0.765640i | ||||
\(621\) | 22.0558 | − | 38.2018i | 0.885069 | − | 1.53298i | ||||
\(622\) | −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 | ||||
\(626\) | − | 50.8526i | − | 2.03248i | ||||||
\(627\) | −0.105054 | −0.00419544 | ||||||||
\(628\) | −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 | ||||
\(633\) | 5.96290 | + | 10.3280i | 0.237004 | + | 0.410503i | ||||
\(634\) | 16.2800 | 0.646562 | ||||||||
\(635\) | −11.5202 | − | 6.65117i | −0.457164 | − | 0.263944i | ||||
\(636\) | −13.2052 | −0.523620 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.70831 | −0.186404 | ||||||||
\(639\) | −10.2072 | − | 5.89315i | −0.403792 | − | 0.233129i | ||||
\(640\) | 16.0371 | 0.633921 | ||||||||
\(641\) | 5.24342 | + | 9.08186i | 0.207102 | + | 0.358712i | 0.950801 | − | 0.309804i | \(-0.100263\pi\) |
−0.743698 | + | 0.668516i | \(0.766930\pi\) | |||||||
\(642\) | −28.9840 | + | 16.7339i | −1.14391 | + | 0.660436i | ||||
\(643\) | −27.0912 | − | 15.6411i | −1.06837 | − | 0.616825i | −0.140635 | − | 0.990061i | \(-0.544915\pi\) |
−0.927736 | + | 0.373237i | \(0.878248\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 11.5669i | − | 0.455448i | ||||||
\(646\) | −0.226275 | −0.00890265 | ||||||||
\(647\) | −26.8675 | −1.05627 | −0.528135 | − | 0.849160i | \(-0.677109\pi\) | ||||
−0.528135 | + | 0.849160i | \(0.677109\pi\) | |||||||
\(648\) | − | 17.5084i | − | 0.687796i | ||||||
\(649\) | 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 | −0.822659 | − | 0.568536i | \(-0.807510\pi\) |
0.903696 | + | 0.428176i | \(0.140844\pi\) | |||||||
\(654\) | 19.6919 | + | 34.1073i | 0.770014 | + | 1.33370i | ||||
\(655\) | −1.86759 | − | 1.07825i | −0.0729726 | − | 0.0421308i | ||||
\(656\) | 3.13771i | 0.122507i | ||||||||
\(657\) | −4.85553 | − | 2.80334i | −0.189432 | − | 0.109369i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.7276 | + | 18.5807i | −0.417887 | + | 0.723801i | −0.995727 | − | 0.0923492i | \(-0.970562\pi\) |
0.577840 | + | 0.816150i | \(0.303896\pi\) | |||||||
\(660\) | 3.10144 | − | 5.37185i | 0.120723 | − | 0.209099i | ||||
\(661\) | − | 42.3872i | − | 1.64867i | −0.566102 | − | 0.824335i | \(-0.691549\pi\) | ||
0.566102 | − | 0.824335i | \(-0.308451\pi\) | |||||||
\(662\) | −7.58763 | + | 13.1422i | −0.294902 | + | 0.510785i | ||||
\(663\) | 1.11744 | − | 10.9470i | 0.0433977 | − | 0.425145i | ||||
\(664\) | −34.6762 | −1.34570 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.40021 | + | 11.0855i | 0.248003 | + | 0.429554i | ||||
\(667\) | 10.6312 | 0.411640 | ||||||||
\(668\) | 7.60673 | + | 4.39175i | 0.294313 | + | 0.169922i | ||||
\(669\) | −20.4896 | + | 11.8297i | −0.792173 | + | 0.457361i | ||||
\(670\) | 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 | ||||
\(675\) | 12.0794 | − | 20.9221i | 0.464935 | − | 0.805292i | ||||
\(676\) | −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 | \(0.621229\pi\) | |||||||
\(678\) | 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 | ||||
\(682\) | −23.5738 | + | 13.6104i | −0.902689 | + | 0.521168i | ||||
\(683\) | −7.44986 | + | 4.30118i | −0.285061 | + | 0.164580i | −0.635712 | − | 0.771926i | \(-0.719294\pi\) |
0.350651 | + | 0.936506i | \(0.385960\pi\) | |||||||
\(684\) | −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 | ||||
\(689\) | −8.92031 | + | 4.00363i | −0.339837 | + | 0.152526i | ||||
\(690\) | −11.2406 | + | 19.4694i | −0.427924 | + | 0.741186i | ||||
\(691\) | −17.7033 | − | 10.2210i | −0.673466 | − | 0.388826i | 0.123923 | − | 0.992292i | \(-0.460452\pi\) |
−0.797388 | + | 0.603466i | \(0.793786\pi\) | |||||||
\(692\) | 32.3680 | + | 56.0629i | 1.23044 | + | 2.13119i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.9477i | 0.795164i | ||||||||
\(695\) | − | 13.2256i | − | 0.501675i | ||||||
\(696\) | 5.21498 | − | 3.01087i | 0.197673 | − | 0.114127i | ||||
\(697\) | −17.9719 | − | 10.3761i | −0.680736 | − | 0.393023i | ||||
\(698\) | −21.2373 | −0.803845 | ||||||||
\(699\) | −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 | \(0.657447\pi\) | |||||||
\(702\) | −19.1848 | − | 42.7447i | −0.724083 | − | 1.61330i | ||||
\(703\) | −0.158933 | + | 0.275280i | −0.00599427 | + | 0.0103824i | ||||
\(704\) | − | 19.2607i | − | 0.725915i | ||||||
\(705\) | −0.224715 | + | 0.389217i | −0.00846324 | + | 0.0146588i | ||||
\(706\) | −2.48118 | + | 4.29753i | −0.0933804 | + | 0.161740i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.92112 | − | 3.99591i | −0.260112 | − | 0.150176i | ||||
\(709\) | − | 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 | ||||
\(711\) | 4.83389 | + | 8.37254i | 0.181285 | + | 0.313995i | ||||
\(712\) | 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 | ||||
\(717\) | − | 19.6918i | − | 0.735404i | ||||||
\(718\) | 19.7104 | 0.735584 | ||||||||
\(719\) | −8.33153 | −0.310713 | −0.155357 | − | 0.987858i | \(-0.549653\pi\) | ||||
−0.155357 | + | 0.987858i | \(0.549653\pi\) | |||||||
\(720\) | − | 0.220044i | − | 0.00820055i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37.8946 | + | 21.8784i | 1.41029 | + | 0.814231i | ||||
\(723\) | 1.06435 | − | 0.614504i | 0.0395837 | − | 0.0228537i | ||||
\(724\) | 2.26071 | + | 3.91567i | 0.0840188 | + | 0.145525i | ||||
\(725\) | 5.82240 | 0.216239 | ||||||||
\(726\) | 25.6853 | + | 14.8294i | 0.953271 | + | 0.550371i | ||||
\(727\) | −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 | ||||||||
\(730\) | 11.4275 | + | 6.59766i | 0.422950 | + | 0.244190i | ||||
\(731\) | −19.1929 | −0.709875 | ||||||||
\(732\) | −11.0098 | − | 19.0696i | −0.406935 | − | 0.704832i | ||||
\(733\) | −12.1398 | + | 7.00894i | −0.448395 | + | 0.258881i | −0.707152 | − | 0.707061i | \(-0.750020\pi\) |
0.258757 | + | 0.965942i | \(0.416687\pi\) | |||||||
\(734\) | −4.58425 | − | 2.64672i | −0.169208 | − | 0.0976921i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.3635i | 1.52468i | ||||||||
\(737\) | 3.07094 | 0.113120 | ||||||||
\(738\) | −19.1341 | −0.704335 | ||||||||
\(739\) | − | 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 | ||||
\(741\) | 0.147479 | − | 0.204271i | 0.00541779 | − | 0.00750410i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.7863 | − | 17.1971i | 1.09275 | − | 0.630901i | 0.158445 | − | 0.987368i | \(-0.449352\pi\) |
0.934308 | + | 0.356467i | \(0.116019\pi\) | |||||||
\(744\) | 17.4071 | − | 30.1500i | 0.638175 | − | 1.10535i | ||||
\(745\) | 2.69592 | + | 4.66948i | 0.0987710 | + | 0.171076i | ||||
\(746\) | 23.4742 | + | 13.5528i | 0.859452 | + | 0.496205i | ||||
\(747\) | − | 9.56594i | − | 0.349999i | ||||||
\(748\) | −8.91346 | − | 5.14619i | −0.325908 | − | 0.188163i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.3445 | + | 23.1134i | −0.487272 | + | 0.843980i | ||||
\(751\) | 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 | ||||||
\(753\) | −20.0908 | + | 34.7983i | −0.732150 | + | 1.26812i | ||||
\(754\) | 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 | ||||||||
\(759\) | 14.9986 | + | 8.65942i | 0.544413 | + | 0.314317i | ||||
\(760\) | 0.104606 | − | 0.0603945i | 0.00379447 | − | 0.00219074i | ||||
\(761\) | 31.9730i | 1.15902i | 0.814965 | + | 0.579511i | \(0.196756\pi\) | ||||
−0.814965 | + | 0.579511i | \(0.803244\pi\) | |||||||
\(762\) | − | 53.2781i | − | 1.93006i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.50067 | − | 4.33129i | −0.0904712 | − | 0.156701i | ||||
\(765\) | 1.26035 | + | 0.727663i | 0.0455680 | + | 0.0263087i | ||||
\(766\) | −32.5274 | + | 56.3391i | −1.17526 | + | 2.03562i | ||||
\(767\) | −5.88683 | − | 0.600911i | −0.212561 | − | 0.0216976i | ||||
\(768\) | 13.2397 | + | 22.9319i | 0.477748 | + | 0.827483i | ||||
\(769\) | −12.4665 | + | 7.19752i | −0.449553 | + | 0.259549i | −0.707641 | − | 0.706572i | \(-0.750241\pi\) |
0.258089 | + | 0.966121i | \(0.416907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.82664 | + | 8.35999i | −0.173827 | + | 0.301078i | ||||
\(772\) | −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 | \(0.0994636\pi\) | |||||||
\(774\) | −15.3255 | + | 8.84818i | −0.550864 | + | 0.318041i | ||||
\(775\) | 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 | ||||
\(780\) | 6.09134 | + | 13.5718i | 0.218105 | + | 0.485950i | ||||
\(781\) | 10.6846 | − | 18.5063i | 0.382326 | − | 0.662208i | ||||
\(782\) | 32.3053 | + | 18.6515i | 1.15524 | + | 0.666975i | ||||
\(783\) | 3.83560 | + | 6.64346i | 0.137073 | + | 0.237418i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0447i | 0.501276i | ||||||||
\(786\) | − | 8.63715i | − | 0.308077i | ||||||
\(787\) | 12.4263 | − | 7.17430i | 0.442948 | − | 0.255736i | −0.261899 | − | 0.965095i | \(-0.584349\pi\) |
0.704847 | + | 0.709359i | \(0.251015\pi\) | |||||||
\(788\) | −44.2996 | − | 25.5764i | −1.57811 | − | 0.911120i | ||||
\(789\) | −33.2818 | −1.18486 | ||||||||
\(790\) | −11.3765 | − | 19.7047i | −0.404759 | − | 0.701064i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.74719 | −0.133150 | ||||||||
\(793\) | −13.2189 | − | 9.54376i | −0.469418 | − | 0.338909i | ||||
\(794\) | 8.58291 | − | 14.8660i | 0.304596 | − | 0.527576i | ||||
\(795\) | 3.38534i | 0.120066i | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 12.5751 | + | 7.26022i | 0.444318 | + | 0.256527i | ||||
\(802\) | −20.9577 | − | 36.2998i | −0.740042 | − | 1.28179i | ||||
\(803\) | 5.08262 | − | 8.80336i | 0.179362 | − | 0.310664i | ||||
\(804\) | −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 | ||||
\(808\) | 29.0665i | 1.02255i | ||||||||
\(809\) | −42.5536 | −1.49610 | −0.748052 | − | 0.663640i | \(-0.769011\pi\) | ||||
−0.748052 | + | 0.663640i | \(0.769011\pi\) | |||||||
\(810\) | −11.3673 | −0.399406 | ||||||||
\(811\) | − | 16.3622i | − | 0.574554i | −0.957848 | − | 0.287277i | \(-0.907250\pi\) | ||
0.957848 | − | 0.287277i | \(-0.0927500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.1766 | + | 6.45284i | 0.391982 | + | 0.226311i | ||||
\(814\) | −20.0986 | + | 11.6040i | −0.704457 | + | 0.406719i | ||||
\(815\) | 3.83453 | + | 6.64160i | 0.134318 | + | 0.232645i | ||||
\(816\) | 0.955843 | 0.0334612 | ||||||||
\(817\) | −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 | 0.546196 | − | 0.837657i | \(-0.316075\pi\) |
−0.452334 | + | 0.891848i | \(0.649409\pi\) | |||||||
\(822\) | −6.32802 | −0.220715 | ||||||||
\(823\) | 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 | ||||
\(825\) | 8.21432 | + | 4.74254i | 0.285986 | + | 0.165114i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.0887i | − | 0.455140i | −0.973762 | − | 0.227570i | \(-0.926922\pi\) | ||
0.973762 | − | 0.227570i | \(-0.0730780\pi\) | |||||||
\(828\) | 21.4276 | 0.744662 | ||||||||
\(829\) | 49.2565 | 1.71075 | 0.855374 | − | 0.518010i | \(-0.173327\pi\) | ||||
0.855374 | + | 0.518010i | \(0.173327\pi\) | |||||||
\(830\) | 22.5134i | 0.781452i | ||||||||
\(831\) | −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 | ||||
\(835\) | 1.12588 | − | 1.95009i | 0.0389629 | − | 0.0674856i | ||||
\(836\) | −0.117828 | − | 0.204084i | −0.00407517 | − | 0.00705840i | ||||
\(837\) | 38.4087 | + | 22.1753i | 1.32760 | + | 0.766489i | ||||
\(838\) | − | 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 | ||||
\(843\) | 20.6615i | 0.711621i | ||||||||
\(844\) | −13.3760 | + | 23.1678i | −0.460419 | + | 0.797470i | ||||
\(845\) | 8.22958 | + | 7.32117i | 0.283106 | + | 0.251856i | ||||
\(846\) | 0.687585 | 0.0236397 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.424662 | − | 0.735535i | −0.0145829 | − | 0.0252584i | ||||
\(849\) | 1.49191 | 0.0512022 | ||||||||
\(850\) | 17.6928 | + | 10.2149i | 0.606857 | + | 0.350369i | ||||
\(851\) | 45.3818 | − | 26.2012i | 1.55567 | − | 0.898166i | ||||
\(852\) | 69.2149i | 2.37126i | ||||||||
\(853\) | 52.4163i | 1.79470i | 0.441319 | + | 0.897350i | \(0.354511\pi\) | ||||
−0.441319 | + | 0.897350i | \(0.645489\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0166607 | + | 0.0288572i | 0.000569784 | + | 0.000986895i | ||||
\(856\) | −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 | \(0.222002\pi\) | |||||||
\(858\) | 16.7822 | − | 7.53222i | 0.572935 | − | 0.257146i | ||||
\(859\) | −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 | −0.166426 | − | 0.986054i | \(-0.553223\pi\) |
0.770735 | + | 0.637156i | \(0.219889\pi\) | |||||||
\(864\) | −25.8482 | + | 14.9235i | −0.879375 | + | 0.507707i | ||||
\(865\) | 14.3725 | − | 8.29797i | 0.488680 | − | 0.282139i | ||||
\(866\) | 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 | ||||
\(871\) | −4.31113 | + | 5.97128i | −0.146077 | + | 0.202329i | ||||
\(872\) | −17.4422 | + | 30.2107i | −0.590667 | + | 1.02306i | ||||
\(873\) | 0.306082 | + | 0.176716i | 0.0103593 | + | 0.00598094i | ||||
\(874\) | 0.427047 | + | 0.739668i | 0.0144451 | + | 0.0250196i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 32.9252i | 1.11244i | ||||||||
\(877\) | − | 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 | ||||
\(879\) | 0.254218 | + | 0.146773i | 0.00857455 | + | 0.00495052i | ||||
\(880\) | 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 | ||||
\(885\) | −1.02441 | + | 1.77432i | −0.0344351 | + | 0.0596433i | ||||
\(886\) | − | 36.2376i | − | 1.21743i | ||||||
\(887\) | −10.3118 | + | 17.8605i | −0.346235 | + | 0.599696i | −0.985577 | − | 0.169226i | \(-0.945873\pi\) |
0.639342 | + | 0.768922i | \(0.279207\pi\) | |||||||
\(888\) | 14.8410 | − | 25.7053i | 0.498031 | − | 0.862615i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −29.5954 | − | 17.0869i | −0.992040 | − | 0.572754i | ||||
\(891\) | 8.75700i | 0.293371i | ||||||||
\(892\) | −45.9621 | − | 26.5362i | −1.53893 | − | 0.888499i | ||||
\(893\) | 0.00853722 | + | 0.0147869i | 0.000285687 | + | 0.000494824i | ||||
\(894\) | −10.7976 | + | 18.7020i | −0.361127 | + | 0.625490i | ||||
\(895\) | 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 | ||||
\(899\) | 10.6887i | 0.356489i | ||||||||
\(900\) | 11.7353 | 0.391178 | ||||||||
\(901\) | 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 | ||||
\(906\) | −1.12681 | − | 1.95170i | −0.0374359 | − | 0.0648409i | ||||
\(907\) | −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 | ||||
\(909\) | −8.01841 | −0.265954 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.8187 | 1.35239 | 0.676193 | − | 0.736725i | \(-0.263629\pi\) | ||||
0.676193 | + | 0.736725i | \(0.263629\pi\) | |||||||
\(912\) | 0.0189531 | + | 0.0109426i | 0.000627600 | + | 0.000362345i | ||||
\(913\) | 17.3436 | 0.573990 | ||||||||
\(914\) | 35.4655 | + | 61.4280i | 1.17309 | + | 2.03186i | ||||
\(915\) | −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 | ||||||||
\(919\) | −48.7678 | −1.60870 | −0.804350 | − | 0.594155i | \(-0.797486\pi\) | ||||
−0.804350 | + | 0.594155i | \(0.797486\pi\) | |||||||
\(920\) | −19.9129 | −0.656509 | ||||||||
\(921\) | − | 40.0760i | − | 1.32055i | ||||||
\(922\) | 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 | ||||
\(927\) | −4.13701 | − | 7.16552i | −0.135877 | − | 0.235346i | ||||
\(928\) | −6.22958 | − | 3.59665i | −0.204496 | − | 0.118066i | ||||
\(929\) | 29.3829i | 0.964023i | 0.876165 | + | 0.482012i | \(0.160094\pi\) | ||||
−0.876165 | + | 0.482012i | \(0.839906\pi\) | |||||||
\(930\) | −19.5748 | − | 11.3015i | −0.641883 | − | 0.370591i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.9855 | − | 38.0801i | 0.720160 | − | 1.24735i | ||||
\(933\) | −19.9647 | + | 34.5799i | −0.653615 | + | 1.13210i | ||||
\(934\) | − | 65.3031i | − | 2.13678i | ||||||
\(935\) | −1.31930 | + | 2.28509i | −0.0431456 | + | 0.0747304i | ||||
\(936\) | 5.26047 | − | 7.28621i | 0.171944 | − | 0.238157i | ||||
\(937\) | 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 | ||||
\(940\) | −1.00816 | −0.0328825 | ||||||||
\(941\) | −20.8740 | − | 12.0516i | −0.680474 | − | 0.392872i | 0.119560 | − | 0.992827i | \(-0.461852\pi\) |
−0.800034 | + | 0.599955i | \(0.795185\pi\) | |||||||
\(942\) | −48.7150 | + | 28.1256i | −1.58722 | + | 0.916383i | ||||
\(943\) | 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 | 0.452259 | − | 0.891886i | \(-0.350618\pi\) |
−0.546267 | + | 0.837611i | \(0.683951\pi\) | |||||||
\(948\) | 28.3869 | − | 49.1676i | 0.921965 | − | 1.59689i | ||||
\(949\) | 9.98245 | + | 22.2415i | 0.324044 | + | 0.721988i | ||||
\(950\) | 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 | −0.903472 | − | 0.428647i | \(-0.858991\pi\) |
0.822955 | + | 0.568106i | \(0.192324\pi\) | |||||||
\(954\) | 4.48537 | − | 2.58963i | 0.145219 | − | 0.0838423i | ||||
\(955\) | −1.11039 | + | 0.641082i | −0.0359313 | + | 0.0207449i | ||||
\(956\) | 38.2546 | − | 22.0863i | 1.23724 | − | 0.714322i | ||||
\(957\) | −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 | ||||
\(962\) | 5.65211 | − | 55.3709i | 0.182231 | − | 1.78523i | ||||
\(963\) | 4.08892 | − | 7.08221i | 0.131763 | − | 0.228221i | ||||
\(964\) | 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 | ||||||||
\(969\) | −0.125352 | + | 0.0723720i | −0.00402689 | + | 0.00232492i | ||||
\(970\) | −0.720362 | − | 0.415901i | −0.0231294 | − | 0.0133538i | ||||
\(971\) | −34.4715 | −1.10624 | −0.553121 | − | 0.833101i | \(-0.686563\pi\) | ||||
−0.553121 | + | 0.833101i | \(0.686563\pi\) | |||||||
\(972\) | 13.7876 | + | 23.8808i | 0.442238 | + | 0.765978i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.9830 | −0.960717 | ||||||||
\(975\) | −20.7532 | + | 9.31451i | −0.664636 | + | 0.298303i | ||||
\(976\) | 0.708122 | − | 1.22650i | 0.0226664 | − | 0.0392594i | ||||
\(977\) | − | 13.3481i | − | 0.427044i | −0.976938 | − | 0.213522i | \(-0.931506\pi\) | ||
0.976938 | − | 0.213522i | \(-0.0684936\pi\) | |||||||
\(978\) | −15.3579 | + | 26.6007i | −0.491093 | + | 0.850597i | ||||
\(979\) | −13.1632 | + | 22.7993i | −0.420698 | + | 0.728670i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.33408 | − | 4.81169i | −0.266087 | − | 0.153625i | ||||
\(982\) | − | 28.4507i | − | 0.907898i | ||||||
\(983\) | −10.8551 | − | 6.26720i | −0.346224 | − | 0.199893i | 0.316797 | − | 0.948493i | \(-0.397393\pi\) |
−0.663021 | + | 0.748601i | \(0.730726\pi\) | |||||||
\(984\) | 22.1843 | + | 38.4244i | 0.707210 | + | 1.22492i | ||||
\(985\) | −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 | ||||
\(990\) | 2.43285i | 0.0773211i | ||||||||
\(991\) | −10.4119 | −0.330745 | −0.165373 | − | 0.986231i | \(-0.552883\pi\) | ||||
−0.165373 | + | 0.986231i | \(0.552883\pi\) | |||||||
\(992\) | −41.5875 | −1.32040 | ||||||||
\(993\) | 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 | ||||
\(997\) | 2.87635 | + | 4.98198i | 0.0910949 | + | 0.157781i | 0.907972 | − | 0.419031i | \(-0.137630\pi\) |
−0.816877 | + | 0.576812i | \(0.804297\pi\) | |||||||
\(998\) | −21.0827 | −0.667362 | ||||||||
\(999\) | 32.7465 | + | 18.9062i | 1.03605 | + | 0.598167i |
(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.u.g.361.6 | 12 | ||
7.2 | even | 3 | 637.2.k.i.569.1 | 12 | |||
7.3 | odd | 6 | 637.2.q.g.491.1 | 12 | |||
7.4 | even | 3 | 637.2.q.i.491.1 | 12 | |||
7.5 | odd | 6 | 91.2.k.b.23.1 | yes | 12 | ||
7.6 | odd | 2 | 91.2.u.b.88.6 | yes | 12 | ||
13.4 | even | 6 | 637.2.k.i.459.6 | 12 | |||
21.5 | even | 6 | 819.2.bm.f.478.6 | 12 | |||
21.20 | even | 2 | 819.2.do.e.361.1 | 12 | |||
91.4 | even | 6 | 637.2.q.i.589.1 | 12 | |||
91.11 | odd | 12 | 8281.2.a.co.1.11 | 12 | |||
91.17 | odd | 6 | 637.2.q.g.589.1 | 12 | |||
91.24 | even | 12 | 8281.2.a.cp.1.11 | 12 | |||
91.30 | even | 6 | inner | 637.2.u.g.30.6 | 12 | ||
91.41 | even | 12 | 1183.2.e.j.508.11 | 24 | |||
91.54 | even | 12 | 1183.2.e.j.170.11 | 24 | |||
91.67 | odd | 12 | 8281.2.a.co.1.2 | 12 | |||
91.69 | odd | 6 | 91.2.k.b.4.6 | ✓ | 12 | ||
91.76 | even | 12 | 1183.2.e.j.508.2 | 24 | |||
91.80 | even | 12 | 8281.2.a.cp.1.2 | 12 | |||
91.82 | odd | 6 | 91.2.u.b.30.6 | yes | 12 | ||
91.89 | even | 12 | 1183.2.e.j.170.2 | 24 | |||
273.173 | even | 6 | 819.2.do.e.667.1 | 12 | |||
273.251 | even | 6 | 819.2.bm.f.550.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.6 | ✓ | 12 | 91.69 | odd | 6 | ||
91.2.k.b.23.1 | yes | 12 | 7.5 | odd | 6 | ||
91.2.u.b.30.6 | yes | 12 | 91.82 | odd | 6 | ||
91.2.u.b.88.6 | yes | 12 | 7.6 | odd | 2 | ||
637.2.k.i.459.6 | 12 | 13.4 | even | 6 | |||
637.2.k.i.569.1 | 12 | 7.2 | even | 3 | |||
637.2.q.g.491.1 | 12 | 7.3 | odd | 6 | |||
637.2.q.g.589.1 | 12 | 91.17 | odd | 6 | |||
637.2.q.i.491.1 | 12 | 7.4 | even | 3 | |||
637.2.q.i.589.1 | 12 | 91.4 | even | 6 | |||
637.2.u.g.30.6 | 12 | 91.30 | even | 6 | inner | ||
637.2.u.g.361.6 | 12 | 1.1 | even | 1 | trivial | ||
819.2.bm.f.478.6 | 12 | 21.5 | even | 6 | |||
819.2.bm.f.550.1 | 12 | 273.251 | even | 6 | |||
819.2.do.e.361.1 | 12 | 21.20 | even | 2 | |||
819.2.do.e.667.1 | 12 | 273.173 | even | 6 | |||
1183.2.e.j.170.2 | 24 | 91.89 | even | 12 | |||
1183.2.e.j.170.11 | 24 | 91.54 | even | 12 | |||
1183.2.e.j.508.2 | 24 | 91.76 | even | 12 | |||
1183.2.e.j.508.11 | 24 | 91.41 | even | 12 | |||
8281.2.a.co.1.2 | 12 | 91.67 | odd | 12 | |||
8281.2.a.co.1.11 | 12 | 91.11 | odd | 12 | |||
8281.2.a.cp.1.2 | 12 | 91.80 | even | 12 | |||
8281.2.a.cp.1.11 | 12 | 91.24 | even | 12 |