Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
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([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
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 | 589.1 | ||
Root | \(1.21245 - 0.727987i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.589 |
Dual form | 637.2.q.i.491.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99469 | − | 1.15163i | −1.41046 | − | 0.814328i | −0.415026 | − | 0.909810i | \(-0.636227\pi\) |
−0.995431 | + | 0.0954820i | \(0.969561\pi\) | |||||||
\(3\) | −0.736680 | + | 1.27597i | −0.425323 | + | 0.736680i | −0.996451 | − | 0.0841807i | \(-0.973173\pi\) |
0.571128 | + | 0.820861i | \(0.306506\pi\) | |||||||
\(4\) | 1.65252 | + | 2.86225i | 0.826259 | + | 1.43112i | ||||
\(5\) | − | 0.847292i | − | 0.378920i | −0.981888 | − | 0.189460i | \(-0.939326\pi\) | ||
0.981888 | − | 0.189460i | \(-0.0606738\pi\) | |||||||
\(6\) | 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 | \(-0.406110\pi\) |
−0.683270 | + | 0.730166i | \(0.739443\pi\) | |||||||
\(12\) | −4.86951 | −1.40571 | ||||||||
\(13\) | 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 | \(0.914157\pi\) | |||||||
\(18\) | − | 1.90989i | − | 0.450164i | ||||||
\(19\) | 0.0410731 | − | 0.0237136i | 0.00942282 | − | 0.00544027i | −0.495281 | − | 0.868733i | \(-0.664935\pi\) |
0.504704 | + | 0.863292i | \(0.331602\pi\) | |||||||
\(20\) | 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 | \(0.863318\pi\) | |||||||
\(24\) | 3.83536 | + | 2.21435i | 0.782891 | + | 0.452002i | ||||
\(25\) | 4.28210 | 0.856419 | ||||||||
\(26\) | −8.26161 | + | 0.843323i | −1.62024 | + | 0.165389i | ||||
\(27\) | −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 | ||||
\(31\) | − | 7.86105i | − | 1.41189i | −0.708269 | − | 0.705943i | \(-0.750523\pi\) | ||
0.708269 | − | 0.705943i | \(-0.249477\pi\) | |||||||
\(32\) | −4.58156 | + | 2.64516i | −0.809912 | + | 0.467603i | ||||
\(33\) | 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 | ||||
\(37\) | 5.80427 | + | 3.35110i | 0.954216 | + | 0.550917i | 0.894388 | − | 0.447292i | \(-0.147612\pi\) |
0.0598278 | + | 0.998209i | \(0.480945\pi\) | |||||||
\(38\) | −0.109237 | −0.0177206 | ||||||||
\(39\) | 0.539460 | + | 5.28482i | 0.0863827 | + | 0.846248i | ||||
\(40\) | −2.54683 | −0.402689 | ||||||||
\(41\) | 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 | \(0.583606\pi\) | |||||||
\(44\) | − | 4.96880i | − | 0.749075i | ||||||
\(45\) | 0.608453 | − | 0.351290i | 0.0907028 | − | 0.0523673i | ||||
\(46\) | 15.5959 | − | 9.00428i | 2.29948 | − | 1.32761i | ||||
\(47\) | 0.360014i | 0.0525134i | 0.999655 | + | 0.0262567i | \(0.00835873\pi\) | ||||
−0.999655 | + | 0.0262567i | \(0.991641\pi\) | |||||||
\(48\) | −0.230724 | − | 0.399625i | −0.0333021 | − | 0.0576810i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.54144 | − | 4.93141i | −1.20794 | − | 0.697406i | ||||
\(51\) | 3.05192 | 0.427355 | ||||||||
\(52\) | 10.8717 | + | 4.87945i | 1.50763 | + | 0.676658i | ||||
\(53\) | 2.71181 | 0.372496 | 0.186248 | − | 0.982503i | \(-0.440367\pi\) | ||||
0.186248 | + | 0.982503i | \(0.440367\pi\) | |||||||
\(54\) | 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 | ||||||||
\(58\) | 2.71219 | − | 1.56588i | 0.356128 | − | 0.205611i | ||||
\(59\) | 1.42132 | − | 0.820598i | 0.185040 | − | 0.106833i | −0.404619 | − | 0.914486i | \(-0.632596\pi\) |
0.589658 | + | 0.807653i | \(0.299262\pi\) | |||||||
\(60\) | 4.12590i | 0.532651i | ||||||||
\(61\) | 2.26097 | + | 3.91612i | 0.289488 | + | 0.501407i | 0.973688 | − | 0.227887i | \(-0.0731817\pi\) |
−0.684200 | + | 0.729295i | \(0.739848\pi\) | |||||||
\(62\) | −9.05305 | + | 15.6803i | −1.14974 | + | 1.99140i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.8114 | 1.60143 | ||||||||
\(65\) | −1.78825 | − | 2.47688i | −0.221805 | − | 0.307219i | ||||
\(66\) | −5.10186 | −0.627995 | ||||||||
\(67\) | 1.76900 | + | 1.02133i | 0.216117 | + | 0.124775i | 0.604151 | − | 0.796870i | \(-0.293512\pi\) |
−0.388034 | + | 0.921645i | \(0.626846\pi\) | |||||||
\(68\) | 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 | 0.461832 | − | 0.886967i | \(-0.347192\pi\) |
0.999052 | + | 0.0435255i | \(0.0138590\pi\) | |||||||
\(72\) | 2.15854 | − | 1.24624i | 0.254387 | − | 0.146870i | ||||
\(73\) | 6.76150i | 0.791373i | 0.918386 | + | 0.395687i | \(0.129493\pi\) | ||||
−0.918386 | + | 0.395687i | \(0.870507\pi\) | |||||||
\(74\) | −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 | ||||
\(79\) | 11.6590 | 1.31175 | 0.655873 | − | 0.754871i | \(-0.272301\pi\) | ||||
0.655873 | + | 0.754871i | \(0.272301\pi\) | |||||||
\(80\) | 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 | ||||
\(86\) | − | 21.3413i | − | 2.30129i | ||||||
\(87\) | −1.00167 | − | 1.73494i | −0.107390 | − | 0.186006i | ||||
\(88\) | −2.25950 | + | 3.91357i | −0.240863 | + | 0.417188i | ||||
\(89\) | 15.1652 | + | 8.75561i | 1.60750 | + | 0.928093i | 0.989927 | + | 0.141582i | \(0.0452189\pi\) |
0.617577 | + | 0.786510i | \(0.288114\pi\) | |||||||
\(90\) | −1.61823 | −0.170576 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −25.8411 | −2.69412 | ||||||||
\(93\) | 10.0304 | + | 5.79108i | 1.04011 | + | 0.600507i | ||||
\(94\) | 0.414604 | − | 0.718115i | 0.0427631 | − | 0.0740679i | ||||
\(95\) | −0.0200923 | − | 0.0348009i | −0.00206143 | − | 0.00357050i | ||||
\(96\) | − | 7.79456i | − | 0.795529i | ||||||
\(97\) | −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 | −0.999765 | − | 0.0216891i | \(-0.993096\pi\) |
0.518666 | + | 0.854977i | \(0.326429\pi\) | |||||||
\(102\) | −6.08763 | − | 3.51469i | −0.602765 | − | 0.348007i | ||||
\(103\) | −9.97823 | −0.983185 | −0.491592 | − | 0.870825i | \(-0.663585\pi\) | ||||
−0.491592 | + | 0.870825i | \(0.663585\pi\) | |||||||
\(104\) | −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 | ||||
\(109\) | 11.6055i | 1.11161i | 0.831314 | + | 0.555803i | \(0.187589\pi\) | ||||
−0.831314 | + | 0.555803i | \(0.812411\pi\) | |||||||
\(110\) | 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 | \(0.781032\pi\) | |||||||
\(114\) | 0.0804731 | − | 0.139383i | 0.00753699 | − | 0.0130545i | ||||
\(115\) | 5.73718 | + | 3.31236i | 0.534994 | + | 0.308879i | ||||
\(116\) | −4.49388 | −0.417247 | ||||||||
\(117\) | 2.72762 | + | 1.22422i | 0.252168 | + | 0.113179i | ||||
\(118\) | −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 | ||||
\(122\) | − | 10.4152i | − | 0.942951i | ||||||
\(123\) | −12.7832 | + | 7.38039i | −1.15262 | + | 0.665467i | ||||
\(124\) | 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 | \(0.921376\pi\) | |||||||
\(128\) | −16.3917 | − | 9.46373i | −1.44883 | − | 0.836483i | ||||
\(129\) | −13.6517 | −1.20196 | ||||||||
\(130\) | 0.714541 | + | 7.00000i | 0.0626694 | + | 0.613940i | ||||
\(131\) | 2.54517 | 0.222373 | 0.111186 | − | 0.993800i | \(-0.464535\pi\) | ||||
0.111186 | + | 0.993800i | \(0.464535\pi\) | |||||||
\(132\) | 6.34003 | + | 3.66042i | 0.551829 | + | 0.318598i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.35240 | − | 4.07447i | −0.203216 | − | 0.351981i | ||||
\(135\) | 4.78025i | 0.411419i | ||||||||
\(136\) | −5.39215 | + | 3.11316i | −0.462373 | + | 0.266951i | ||||
\(137\) | 1.61490 | − | 0.932362i | 0.137970 | − | 0.0796571i | −0.429426 | − | 0.903102i | \(-0.641284\pi\) |
0.567396 | + | 0.823445i | \(0.307951\pi\) | |||||||
\(138\) | 26.5331i | 2.25865i | ||||||||
\(139\) | 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 | ||||
\(142\) | −32.7385 | −2.74735 | ||||||||
\(143\) | −5.39257 | + | 0.550459i | −0.450949 | + | 0.0460317i | ||||
\(144\) | −0.259703 | −0.0216419 | ||||||||
\(145\) | 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 | ||||||||
\(149\) | −5.51106 | + | 3.18181i | −0.451484 | + | 0.260664i | −0.708457 | − | 0.705754i | \(-0.750608\pi\) |
0.256973 | + | 0.966419i | \(0.417275\pi\) | |||||||
\(150\) | 12.5846 | − | 7.26574i | 1.02753 | − | 0.593245i | ||||
\(151\) | − | 0.664094i | − | 0.0540432i | −0.999635 | − | 0.0270216i | \(-0.991398\pi\) | ||
0.999635 | − | 0.0270216i | \(-0.00860228\pi\) | |||||||
\(152\) | −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 | ||||||||
\(156\) | −14.2350 | + | 10.2773i | −1.13971 | + | 0.822844i | ||||
\(157\) | 16.5760 | 1.32291 | 0.661453 | − | 0.749986i | \(-0.269940\pi\) | ||||
0.661453 | + | 0.749986i | \(0.269940\pi\) | |||||||
\(158\) | −23.2562 | − | 13.4269i | −1.85016 | − | 1.06819i | ||||
\(159\) | −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 | ||||
\(163\) | −7.83863 | + | 4.52563i | −0.613969 | + | 0.354475i | −0.774517 | − | 0.632553i | \(-0.782007\pi\) |
0.160548 | + | 0.987028i | \(0.448674\pi\) | |||||||
\(164\) | 33.1113i | 2.58556i | ||||||||
\(165\) | −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 | 0.586400 | − | 0.810022i | \(-0.300545\pi\) |
−0.408300 | + | 0.912848i | \(0.633878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.09120 | − | 12.3395i | 0.314708 | − | 0.949189i | ||||
\(170\) | 4.04242 | 0.310039 | ||||||||
\(171\) | 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 | −0.950387 | − | 0.311070i | \(-0.899313\pi\) |
0.205799 | − | 0.978594i | \(-0.434021\pi\) | |||||||
\(174\) | 4.61423i | 0.349804i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.407774 | − | 0.235428i | 0.0307371 | − | 0.0177461i | ||||
\(177\) | 2.41807i | 0.181754i | ||||||||
\(178\) | −20.1665 | − | 34.9294i | −1.51154 | − | 2.61807i | ||||
\(179\) | −1.44666 | + | 2.50569i | −0.108129 | + | 0.187284i | −0.915012 | − | 0.403426i | \(-0.867819\pi\) |
0.806884 | + | 0.590711i | \(0.201152\pi\) | |||||||
\(180\) | 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 | ||||
\(185\) | 2.83936 | − | 4.91791i | 0.208754 | − | 0.361572i | ||||
\(186\) | −13.3384 | − | 23.1028i | −0.978019 | − | 1.69398i | ||||
\(187\) | 3.11415i | 0.227729i | ||||||||
\(188\) | −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 | 0.892100 | − | 0.451837i | \(-0.149231\pi\) |
−0.837353 | + | 0.546663i | \(0.815898\pi\) | |||||||
\(192\) | −9.43792 | + | 16.3470i | −0.681123 | + | 1.17974i | ||||
\(193\) | 6.02229 | + | 3.47697i | 0.433494 | + | 0.250278i | 0.700834 | − | 0.713324i | \(-0.252811\pi\) |
−0.267340 | + | 0.963602i | \(0.586145\pi\) | |||||||
\(194\) | 0.981719 | 0.0704834 | ||||||||
\(195\) | 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 | \(0.852555\pi\) | |||||||
\(198\) | −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 | \(0.908670\pi\) | |||||||
\(200\) | − | 12.8713i | − | 0.910140i | ||||||
\(201\) | −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 | ||||
\(205\) | 4.24427 | − | 7.35129i | 0.296433 | − | 0.513436i | ||||
\(206\) | 19.9035 | + | 11.4913i | 1.38674 | + | 0.800634i | ||||
\(207\) | −6.48333 | −0.450622 | ||||||||
\(208\) | 0.114674 | + | 1.12340i | 0.00795118 | + | 0.0778937i | ||||
\(209\) | −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 | ||||
\(213\) | 20.9423i | 1.43494i | ||||||||
\(214\) | 19.6721 | − | 11.3577i | 1.34475 | − | 0.776394i | ||||
\(215\) | 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 | ||||
\(219\) | −8.62745 | − | 4.98106i | −0.582989 | − | 0.336589i | ||||
\(220\) | −4.21002 | −0.283840 | ||||||||
\(221\) | −6.81373 | − | 3.05815i | −0.458341 | − | 0.205713i | ||||
\(222\) | 22.7442 | 1.52649 | ||||||||
\(223\) | −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 | ||||
\(226\) | − | 8.00979i | − | 0.532804i | ||||||
\(227\) | −1.12220 | + | 0.647903i | −0.0744831 | + | 0.0430029i | −0.536779 | − | 0.843723i | \(-0.680359\pi\) |
0.462296 | + | 0.886726i | \(0.347026\pi\) | |||||||
\(228\) | −0.200006 | + | 0.115474i | −0.0132457 | + | 0.00764742i | ||||
\(229\) | − | 20.8175i | − | 1.37566i | −0.725871 | − | 0.687831i | \(-0.758563\pi\) | ||
0.725871 | − | 0.687831i | \(-0.241437\pi\) | |||||||
\(230\) | −7.62925 | − | 13.2142i | −0.503058 | − | 0.871322i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.53951 | + | 2.04354i | 0.232380 | + | 0.134165i | ||||
\(233\) | 13.3043 | 0.871591 | 0.435796 | − | 0.900046i | \(-0.356467\pi\) | ||||
0.435796 | + | 0.900046i | \(0.356467\pi\) | |||||||
\(234\) | −4.03090 | − | 5.58314i | −0.263508 | − | 0.364981i | ||||
\(235\) | 0.305037 | 0.0198984 | ||||||||
\(236\) | 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 | \(0.142285\pi\) | ||||
−0.901748 | + | 0.432263i | \(0.857715\pi\) | |||||||
\(240\) | −0.338599 | + | 0.195490i | −0.0218565 | + | 0.0126188i | ||||
\(241\) | −0.722398 | + | 0.417076i | −0.0465337 | + | 0.0268663i | −0.523086 | − | 0.852280i | \(-0.675219\pi\) |
0.476553 | + | 0.879146i | \(0.341886\pi\) | |||||||
\(242\) | 20.1300i | 1.29401i | ||||||||
\(243\) | −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 | ||||||||
\(247\) | 0.0700199 | − | 0.156008i | 0.00445526 | − | 0.00992657i | ||||
\(248\) | −23.6291 | −1.50045 | ||||||||
\(249\) | 14.7199 | + | 8.49852i | 0.932834 | + | 0.538572i | ||||
\(250\) | −9.05718 | + | 15.6875i | −0.572827 | + | 0.992165i | ||||
\(251\) | −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 | ||||
\(255\) | − | 2.58587i | − | 0.161933i | ||||||
\(256\) | 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 | ||||
\(261\) | −1.12748 | −0.0697893 | ||||||||
\(262\) | −5.07682 | − | 2.93110i | −0.313647 | − | 0.181084i | ||||
\(263\) | 11.2945 | − | 19.5627i | 0.696450 | − | 1.20629i | −0.273239 | − | 0.961946i | \(-0.588095\pi\) |
0.969689 | − | 0.244341i | \(-0.0785717\pi\) | |||||||
\(264\) | −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 | ||||
\(268\) | 6.75107i | 0.412387i | ||||||||
\(269\) | 8.00065 | + | 13.8575i | 0.487808 | + | 0.844909i | 0.999902 | − | 0.0140210i | \(-0.00446317\pi\) |
−0.512093 | + | 0.858930i | \(0.671130\pi\) | |||||||
\(270\) | 5.50510 | − | 9.53511i | 0.335030 | − | 0.580288i | ||||
\(271\) | −7.58582 | − | 4.37967i | −0.460806 | − | 0.266046i | 0.251577 | − | 0.967837i | \(-0.419051\pi\) |
−0.712383 | + | 0.701791i | \(0.752384\pi\) | |||||||
\(272\) | 0.648750 | 0.0393363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29496 | −0.259468 | ||||||||
\(275\) | −5.57522 | − | 3.21886i | −0.336199 | − | 0.194104i | ||||
\(276\) | 19.0366 | − | 32.9724i | 1.14587 | − | 1.98471i | ||||
\(277\) | −9.95914 | − | 17.2497i | −0.598387 | − | 1.03644i | −0.993059 | − | 0.117614i | \(-0.962475\pi\) |
0.394673 | − | 0.918822i | \(-0.370858\pi\) | |||||||
\(278\) | − | 35.9522i | − | 2.15627i | ||||||
\(279\) | 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 | −0.880681 | − | 0.473710i | \(-0.842915\pi\) |
0.850585 | + | 0.525838i | \(0.176248\pi\) | |||||||
\(284\) | 40.6838 | + | 23.4888i | 2.41414 | + | 1.39380i | ||||
\(285\) | 0.0592065 | 0.00350709 | ||||||||
\(286\) | 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 | ||||
\(291\) | − | 0.627989i | − | 0.0368134i | ||||||
\(292\) | −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 | ||||
\(296\) | 10.0729 | − | 17.4467i | 0.585474 | − | 1.01407i | ||||
\(297\) | 7.34554 | + | 4.24095i | 0.426232 | + | 0.246085i | ||||
\(298\) | 14.6571 | 0.849065 | ||||||||
\(299\) | 2.86276 | + | 28.0450i | 0.165558 | + | 1.62188i | ||||
\(300\) | −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 | ||||
\(304\) | 0.0148539i | 0.000851930i | ||||||||
\(305\) | 3.31809 | − | 1.91570i | 0.189993 | − | 0.109693i | ||||
\(306\) | −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 | ||||
\(310\) | 13.2858 | + | 7.67057i | 0.754584 | + | 0.435659i | ||||
\(311\) | 27.1009 | 1.53675 | 0.768376 | − | 0.639999i | \(-0.221065\pi\) | ||||
0.768376 | + | 0.639999i | \(0.221065\pi\) | |||||||
\(312\) | 15.8854 | − | 1.62153i | 0.899331 | − | 0.0918013i | ||||
\(313\) | 22.0785 | 1.24795 | 0.623975 | − | 0.781445i | \(-0.285517\pi\) | ||||
0.623975 | + | 0.781445i | \(0.285517\pi\) | |||||||
\(314\) | −33.0639 | − | 19.0894i | −1.86590 | − | 1.07728i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.2668 | + | 33.3711i | 1.08384 | + | 1.87727i | ||||
\(317\) | − | 7.06823i | − | 0.396991i | −0.980102 | − | 0.198496i | \(-0.936394\pi\) | ||
0.980102 | − | 0.198496i | \(-0.0636056\pi\) | |||||||
\(318\) | 7.96973 | − | 4.60133i | 0.446920 | − | 0.258030i | ||||
\(319\) | 1.77032 | − | 1.02209i | 0.0991188 | − | 0.0572263i | ||||
\(320\) | − | 10.8550i | − | 0.606813i | ||||||
\(321\) | −7.26531 | − | 12.5839i | −0.405510 | − | 0.702364i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0850789 | − | 0.0491204i | −0.00473392 | − | 0.00273313i | ||||
\(324\) | 19.2512 | 1.06951 | ||||||||
\(325\) | 12.5178 | − | 9.03756i | 0.694362 | − | 0.501313i | ||||
\(326\) | 20.8475 | 1.15464 | ||||||||
\(327\) | −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 | ||||||||
\(331\) | −5.70588 | + | 3.29429i | −0.313623 | + | 0.181071i | −0.648547 | − | 0.761175i | \(-0.724623\pi\) |
0.334923 | + | 0.942245i | \(0.391290\pi\) | |||||||
\(332\) | 33.0195 | − | 19.0638i | 1.81218 | − | 1.04626i | ||||
\(333\) | 5.55751i | 0.304550i | ||||||||
\(334\) | −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 | \(0.536693\pi\) | |||||||
\(338\) | −22.3712 | + | 19.9018i | −1.21683 | + | 1.08251i | ||||
\(339\) | −5.12373 | −0.278283 | ||||||||
\(340\) | −5.02347 | − | 2.90030i | −0.272436 | − | 0.157291i | ||||
\(341\) | −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 | ||||
\(345\) | −8.45293 | + | 4.88030i | −0.455091 | + | 0.262747i | ||||
\(346\) | 45.1142i | 2.42535i | ||||||||
\(347\) | 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 | 0.270816 | − | 0.962631i | \(-0.412706\pi\) |
−0.698255 | + | 0.715849i | \(0.746040\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.4926 | + | 11.9073i | −0.880310 | + | 0.635564i | ||||
\(352\) | 7.95349 | 0.423922 | ||||||||
\(353\) | 1.86584 | + | 1.07724i | 0.0993087 | + | 0.0573359i | 0.548832 | − | 0.835933i | \(-0.315073\pi\) |
−0.449523 | + | 0.893269i | \(0.648406\pi\) | |||||||
\(354\) | 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 | ||||
\(359\) | − | 8.55756i | − | 0.451651i | −0.974168 | − | 0.225825i | \(-0.927492\pi\) | ||
0.974168 | − | 0.225825i | \(-0.0725079\pi\) | |||||||
\(360\) | −1.05593 | − | 1.82892i | −0.0556521 | − | 0.0963923i | ||||
\(361\) | −9.49888 | + | 16.4525i | −0.499941 | + | 0.865923i | ||||
\(362\) | −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 | ||||
\(367\) | 1.14912 | − | 1.99033i | 0.0599833 | − | 0.103894i | −0.834474 | − | 0.551047i | \(-0.814229\pi\) |
0.894458 | + | 0.447153i | \(0.147562\pi\) | |||||||
\(368\) | −1.22438 | − | 2.12070i | −0.0638255 | − | 0.110549i | ||||
\(369\) | 8.30736i | 0.432464i | ||||||||
\(370\) | −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 | 0.672517 | − | 0.740082i | \(-0.265213\pi\) |
−0.977188 | + | 0.212375i | \(0.931880\pi\) | |||||||
\(374\) | 3.58636 | − | 6.21175i | 0.185446 | − | 0.321202i | ||||
\(375\) | 10.0350 | + | 5.79373i | 0.518207 | + | 0.299187i | ||||
\(376\) | 1.08215 | 0.0558074 | ||||||||
\(377\) | 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 | \(0.732462\pi\) | |||||||
\(380\) | 0.0664059 | − | 0.115018i | 0.00340655 | − | 0.00590032i | ||||
\(381\) | −11.5658 | − | 20.0325i | −0.592532 | − | 1.02630i | ||||
\(382\) | − | 3.48542i | − | 0.178329i | ||||||
\(383\) | −24.4605 | + | 14.1223i | −1.24988 | + | 0.721616i | −0.971084 | − | 0.238736i | \(-0.923267\pi\) |
−0.278791 | + | 0.960352i | \(0.589934\pi\) | |||||||
\(384\) | 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 | ||||
\(388\) | −1.21997 | − | 0.704352i | −0.0619347 | − | 0.0357580i | ||||
\(389\) | −7.68086 | −0.389435 | −0.194717 | − | 0.980859i | \(-0.562379\pi\) | ||||
−0.194717 | + | 0.980859i | \(0.562379\pi\) | |||||||
\(390\) | −9.45816 | − | 4.24503i | −0.478933 | − | 0.214955i | ||||
\(391\) | 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 | ||||
\(395\) | − | 9.87862i | − | 0.497047i | ||||||
\(396\) | 3.56817 | − | 2.06008i | 0.179307 | − | 0.103523i | ||||
\(397\) | 6.45433 | − | 3.72641i | 0.323933 | − | 0.187023i | −0.329211 | − | 0.944256i | \(-0.606783\pi\) |
0.653144 | + | 0.757233i | \(0.273449\pi\) | |||||||
\(398\) | 15.2368i | 0.763750i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.670563 | + | 1.16145i | −0.0335282 | + | 0.0580725i | ||||
\(401\) | 15.7601 | + | 9.09912i | 0.787024 | + | 0.454389i | 0.838914 | − | 0.544264i | \(-0.183191\pi\) |
−0.0518898 | + | 0.998653i | \(0.516524\pi\) | |||||||
\(402\) | 6.93186 | 0.345730 | ||||||||
\(403\) | −16.5911 | − | 22.9801i | −0.826461 | − | 1.14472i | ||||
\(404\) | −31.9596 | −1.59005 | ||||||||
\(405\) | −4.27409 | − | 2.46765i | −0.212381 | − | 0.122618i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.03804 | − | 8.72615i | −0.249727 | − | 0.432539i | ||||
\(408\) | − | 9.17361i | − | 0.454161i | ||||||
\(409\) | −25.3594 | + | 14.6413i | −1.25394 | + | 0.723964i | −0.971890 | − | 0.235435i | \(-0.924349\pi\) |
−0.282053 | + | 0.959399i | \(0.591015\pi\) | |||||||
\(410\) | −16.9320 | + | 9.77568i | −0.836211 | + | 0.482787i | ||||
\(411\) | 2.74741i | 0.135520i | ||||||||
\(412\) | −16.4892 | − | 28.5602i | −0.812365 | − | 1.40706i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.9322 | + | 7.46641i | 0.635583 | + | 0.366954i | ||||
\(415\) | −9.77456 | −0.479814 | ||||||||
\(416\) | −7.81047 | + | 17.4021i | −0.382940 | + | 0.853210i | ||||
\(417\) | −22.9980 | −1.12622 | ||||||||
\(418\) | 0.142225 | + | 0.0821139i | 0.00695647 | + | 0.00401632i | ||||
\(419\) | −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 | ||||
\(423\) | −0.258531 | + | 0.149263i | −0.0125702 | + | 0.00725742i | ||||
\(424\) | − | 8.15130i | − | 0.395862i | ||||||
\(425\) | −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 | ||||||||
\(429\) | 3.27023 | − | 7.28626i | 0.157888 | − | 0.351784i | ||||
\(430\) | −18.0823 | −0.872006 | ||||||||
\(431\) | 18.3327 | + | 10.5844i | 0.883055 | + | 0.509832i | 0.871665 | − | 0.490103i | \(-0.163041\pi\) |
0.0113906 | + | 0.999935i | \(0.496374\pi\) | |||||||
\(432\) | 0.883489 | − | 1.53025i | 0.0425069 | − | 0.0736241i | ||||
\(433\) | 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 | ||||
\(437\) | 0.370819i | 0.0177387i | ||||||||
\(438\) | 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 | ||||
\(443\) | 15.7331 | 0.747503 | 0.373752 | − | 0.927529i | \(-0.378071\pi\) | ||||
0.373752 | + | 0.927529i | \(0.378071\pi\) | |||||||
\(444\) | −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 | \(0.123080\pi\) | |||||||
\(450\) | − | 8.17832i | − | 0.385530i | ||||||
\(451\) | −7.53087 | − | 13.0438i | −0.354615 | − | 0.614211i | ||||
\(452\) | −5.74676 | + | 9.95369i | −0.270305 | + | 0.468182i | ||||
\(453\) | 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 | −0.276945 | − | 0.960886i | \(-0.589322\pi\) |
−0.970624 | + | 0.240602i | \(0.922655\pi\) | |||||||
\(458\) | −23.9742 | + | 41.5245i | −1.12024 | + | 1.94031i | ||||
\(459\) | 5.84322 | + | 10.1208i | 0.272738 | + | 0.472396i | ||||
\(460\) | 21.8949i | 1.02086i | ||||||||
\(461\) | 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 | ||||
\(467\) | 28.3524 | 1.31199 | 0.655996 | − | 0.754764i | \(-0.272249\pi\) | ||||
0.655996 | + | 0.754764i | \(0.272249\pi\) | |||||||
\(468\) | 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 | ||||
\(473\) | − | 13.9300i | − | 0.640503i | ||||||
\(474\) | 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 | ||||
\(478\) | 15.3918 | − | 26.6595i | 0.704007 | − | 1.21938i | ||||
\(479\) | 5.44077 | + | 3.14123i | 0.248595 | + | 0.143526i | 0.619121 | − | 0.785296i | \(-0.287489\pi\) |
−0.370526 | + | 0.928822i | \(0.620822\pi\) | |||||||
\(480\) | −6.60426 | −0.301442 | ||||||||
\(481\) | 24.0402 | − | 2.45396i | 1.09614 | − | 0.111891i | ||||
\(482\) | 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 | ||||
\(486\) | 19.2171i | 0.871703i | ||||||||
\(487\) | 11.2736 | − | 6.50879i | 0.510854 | − | 0.294942i | −0.222331 | − | 0.974971i | \(-0.571366\pi\) |
0.733185 | + | 0.680030i | \(0.238033\pi\) | |||||||
\(488\) | 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 | \(0.256579\pi\) | |||||||
\(492\) | −42.2490 | − | 24.3925i | −1.90473 | − | 1.09970i | ||||
\(493\) | 2.81650 | 0.126849 | ||||||||
\(494\) | −0.319332 | + | 0.230550i | −0.0143674 | + | 0.0103730i | ||||
\(495\) | −1.05626 | −0.0474754 | ||||||||
\(496\) | 2.13218 | + | 1.23102i | 0.0957378 | + | 0.0552743i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −19.5744 | − | 33.9038i | −0.877148 | − | 1.51926i | ||||
\(499\) | 9.15340i | 0.409763i | 0.978787 | + | 0.204881i | \(0.0656808\pi\) | ||||
−0.978787 | + | 0.204881i | \(0.934319\pi\) | |||||||
\(500\) | 22.5105 | − | 12.9965i | 1.00670 | − | 0.581220i | ||||
\(501\) | −3.39102 | + | 1.95781i | −0.151500 | + | 0.0874684i | ||||
\(502\) | 62.8149i | 2.80357i | ||||||||
\(503\) | 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 | ||||
\(506\) | −27.0741 | −1.20359 | ||||||||
\(507\) | 12.7308 | + | 14.3105i | 0.565396 | + | 0.635551i | ||||
\(508\) | −51.8885 | −2.30218 | ||||||||
\(509\) | −33.4811 | − | 19.3303i | −1.48402 | − | 0.856800i | −0.484187 | − | 0.874965i | \(-0.660884\pi\) |
−0.999835 | + | 0.0181646i | \(0.994218\pi\) | |||||||
\(510\) | −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 | ||||
\(514\) | 13.0690 | − | 7.54536i | 0.576447 | − | 0.332812i | ||||
\(515\) | 8.45447i | 0.372549i | ||||||||
\(516\) | −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 | ||||||||
\(520\) | −7.44511 | + | 5.37520i | −0.326490 | + | 0.235718i | ||||
\(521\) | −40.2351 | −1.76273 | −0.881366 | − | 0.472434i | \(-0.843375\pi\) | ||||
−0.881366 | + | 0.472434i | \(0.843375\pi\) | |||||||
\(522\) | 2.24897 | + | 1.29844i | 0.0984348 | + | 0.0568313i | ||||
\(523\) | −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 | ||||
\(527\) | −14.1018 | + | 8.14169i | −0.614285 | + | 0.354658i | ||||
\(528\) | 0.693741i | 0.0301912i | ||||||||
\(529\) | −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 | ||||
\(534\) | 59.4251 | 2.57157 | ||||||||
\(535\) | 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 | ||||
\(541\) | − | 23.6537i | − | 1.01695i | −0.861076 | − | 0.508476i | \(-0.830209\pi\) | ||
0.861076 | − | 0.508476i | \(-0.169791\pi\) | |||||||
\(542\) | 10.0876 | + | 17.4722i | 0.433298 | + | 0.750494i | ||||
\(543\) | −1.00781 | + | 1.74558i | −0.0432492 | + | 0.0749099i | ||||
\(544\) | 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 | ||||
\(549\) | −1.87481 | + | 3.24727i | −0.0800151 | + | 0.138590i | ||||
\(550\) | 7.41388 | + | 12.8412i | 0.316129 | + | 0.547552i | ||||
\(551\) | 0.0644871i | 0.00274724i | ||||||||
\(552\) | −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 | \(-0.376672\pi\) |
−0.612921 | + | 0.790145i | \(0.710005\pi\) | |||||||
\(558\) | −15.0137 | −0.635581 | ||||||||
\(559\) | 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 | \(0.882635\pi\) | |||||||
\(564\) | − | 1.75309i | − | 0.0738185i | ||||||
\(565\) | 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 | ||||
\(569\) | −2.15872 | + | 3.73901i | −0.0904981 | + | 0.156747i | −0.907721 | − | 0.419575i | \(-0.862179\pi\) |
0.817223 | + | 0.576322i | \(0.195513\pi\) | |||||||
\(570\) | −0.118098 | − | 0.0681842i | −0.00494660 | − | 0.00285592i | ||||
\(571\) | −34.1695 | −1.42995 | −0.714974 | − | 0.699152i | \(-0.753561\pi\) | ||||
−0.714974 | + | 0.699152i | \(0.753561\pi\) | |||||||
\(572\) | −10.4869 | − | 14.5252i | −0.438478 | − | 0.607330i | ||||
\(573\) | −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 | ||||
\(577\) | − | 6.35656i | − | 0.264627i | −0.991208 | − | 0.132314i | \(-0.957759\pi\) | ||
0.991208 | − | 0.132314i | \(-0.0422406\pi\) | |||||||
\(578\) | −25.3511 | + | 14.6364i | −1.05447 | + | 0.608796i | ||||
\(579\) | −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 | ||||
\(583\) | −3.53074 | − | 2.03847i | −0.146228 | − | 0.0844249i | ||||
\(584\) | 20.3240 | 0.841014 | ||||||||
\(585\) | 1.03727 | − | 2.31109i | 0.0428857 | − | 0.0955518i | ||||
\(586\) | −0.458892 | −0.0189566 | ||||||||
\(587\) | −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 | ||||
\(590\) | 3.20286i | 0.131860i | ||||||||
\(591\) | 19.7484 | − | 11.4018i | 0.812342 | − | 0.469006i | ||||
\(592\) | −1.81786 | + | 1.04954i | −0.0747136 | + | 0.0431359i | ||||
\(593\) | − | 0.473013i | − | 0.0194243i | −0.999953 | − | 0.00971215i | \(-0.996908\pi\) | ||
0.999953 | − | 0.00971215i | \(-0.00309152\pi\) | |||||||
\(594\) | −9.76804 | − | 16.9187i | −0.400787 | − | 0.694184i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.2143 | − | 10.5160i | −0.746086 | − | 0.430753i | ||||
\(597\) | 9.74670 | 0.398906 | ||||||||
\(598\) | 26.5872 | − | 59.2378i | 1.08723 | − | 2.42242i | ||||
\(599\) | −9.62695 | −0.393347 | −0.196673 | − | 0.980469i | \(-0.563014\pi\) | ||||
−0.196673 | + | 0.980469i | \(0.563014\pi\) | |||||||
\(600\) | 16.4234 | + | 9.48206i | 0.670483 | + | 0.387103i | ||||
\(601\) | −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 | ||||
\(605\) | −6.41304 | + | 3.70257i | −0.260727 | + | 0.150531i | ||||
\(606\) | 32.8155i | 1.33304i | ||||||||
\(607\) | 9.54289 | + | 16.5288i | 0.387334 | + | 0.670882i | 0.992090 | − | 0.125529i | \(-0.0400627\pi\) |
−0.604756 | + | 0.796411i | \(0.706729\pi\) | |||||||
\(608\) | −0.125453 | + | 0.217290i | −0.00508777 | + | 0.00881228i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.82474 | −0.357303 | ||||||||
\(611\) | 0.759825 | + | 1.05242i | 0.0307392 | + | 0.0425765i | ||||
\(612\) | 5.67680 | 0.229471 | ||||||||
\(613\) | 32.9131 | + | 19.0024i | 1.32935 | + | 0.767500i | 0.985199 | − | 0.171415i | \(-0.0548340\pi\) |
0.344149 | + | 0.938915i | \(0.388167\pi\) | |||||||
\(614\) | 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 | −0.347992 | − | 0.937497i | \(-0.613136\pi\) |
0.637900 | + | 0.770119i | \(0.279803\pi\) | |||||||
\(618\) | −29.3250 | + | 16.9308i | −1.17962 | + | 0.681056i | ||||
\(619\) | − | 44.4728i | − | 1.78751i | −0.448553 | − | 0.893756i | \(-0.648060\pi\) | ||
0.448553 | − | 0.893756i | \(-0.351940\pi\) | |||||||
\(620\) | −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 | ||||
\(625\) | 14.7468 | 0.589874 | ||||||||
\(626\) | −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 | \(0.408492\pi\) | |||||||
\(632\) | − | 35.0453i | − | 1.39403i | ||||||
\(633\) | 5.96290 | + | 10.3280i | 0.237004 | + | 0.410503i | ||||
\(634\) | −8.14001 | + | 14.0989i | −0.323281 | + | 0.559939i | ||||
\(635\) | 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 | ||||
\(640\) | −8.01854 | + | 13.8885i | −0.316961 | + | 0.548992i | ||||
\(641\) | 5.24342 | + | 9.08186i | 0.207102 | + | 0.358712i | 0.950801 | − | 0.309804i | \(-0.100263\pi\) |
−0.743698 | + | 0.668516i | \(0.766930\pi\) | |||||||
\(642\) | 33.4679i | 1.32087i | ||||||||
\(643\) | −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 | −0.471327 | − | 0.881959i | \(-0.656225\pi\) |
0.999462 | − | 0.0327983i | \(-0.0104419\pi\) | |||||||
\(648\) | −15.1627 | − | 8.75422i | −0.595649 | − | 0.343898i | ||||
\(649\) | −2.46738 | −0.0968530 | ||||||||
\(650\) | −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 | ||||
\(655\) | − | 2.15650i | − | 0.0842615i | ||||||
\(656\) | −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 | \(0.970562\pi\) | |||||||
\(660\) | 3.10144 | − | 5.37185i | 0.120723 | − | 0.209099i | ||||
\(661\) | −36.7084 | − | 21.1936i | −1.42779 | − | 0.824335i | −0.430844 | − | 0.902426i | \(-0.641784\pi\) |
−0.996946 | + | 0.0780909i | \(0.975118\pi\) | |||||||
\(662\) | 15.1753 | 0.589803 | ||||||||
\(663\) | 8.92164 | − | 6.44122i | 0.346488 | − | 0.250156i | ||||
\(664\) | −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 | ||||
\(668\) | 8.78349i | 0.339844i | ||||||||
\(669\) | 20.4896 | − | 11.8297i | 0.792173 | − | 0.457361i | ||||
\(670\) | −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 | \(0.973525\pi\) | |||||||
\(674\) | 8.42336 | + | 4.86323i | 0.324456 | + | 0.187324i | ||||
\(675\) | −24.1588 | −0.929871 | ||||||||
\(676\) | 42.0793 | − | 8.68114i | 1.61844 | − | 0.333890i | ||||
\(677\) | −32.1659 | −1.23624 | −0.618118 | − | 0.786085i | \(-0.712105\pi\) | ||||
−0.618118 | + | 0.786085i | \(0.712105\pi\) | |||||||
\(678\) | 10.2202 | + | 5.90066i | 0.392506 | + | 0.226613i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.63775 | + | 4.56872i | 0.101153 | + | 0.175202i | ||||
\(681\) | − | 1.90919i | − | 0.0731604i | ||||||
\(682\) | 23.5738 | − | 13.6104i | 0.902689 | − | 0.521168i | ||||
\(683\) | 7.44986 | − | 4.30118i | 0.285061 | − | 0.164580i | −0.350651 | − | 0.936506i | \(-0.614040\pi\) |
0.635712 | + | 0.771926i | \(0.280706\pi\) | |||||||
\(684\) | 0.129977i | 0.00496980i | ||||||||
\(685\) | −0.789983 | − | 1.36829i | −0.0301837 | − | 0.0522797i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.5625 | + | 15.3359i | 1.01342 | + | 0.585100i | ||||
\(688\) | −2.90195 | −0.110636 | ||||||||
\(689\) | 7.92740 | − | 5.72340i | 0.302010 | − | 0.218044i | ||||
\(690\) | 22.4813 | 0.855847 | ||||||||
\(691\) | 17.7033 | + | 10.2210i | 0.673466 | + | 0.388826i | 0.797388 | − | 0.603466i | \(-0.206214\pi\) |
−0.123923 | + | 0.992292i | \(0.539548\pi\) | |||||||
\(692\) | 32.3680 | − | 56.0629i | 1.23044 | − | 2.13119i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 20.9477i | − | 0.795164i | ||||||
\(695\) | 11.4537 | − | 6.61279i | 0.434463 | − | 0.250837i | ||||
\(696\) | −5.21498 | + | 3.01087i | −0.197673 | + | 0.114127i | ||||
\(697\) | − | 20.7522i | − | 0.786046i | ||||||
\(698\) | 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 | \(0.657447\pi\) | |||||||
\(702\) | 46.6104 | − | 4.75787i | 1.75920 | − | 0.179574i | ||||
\(703\) | 0.317866 | 0.0119885 | ||||||||
\(704\) | −16.6803 | − | 9.63036i | −0.628661 | − | 0.362958i | ||||
\(705\) | −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 | ||||
\(709\) | 25.5416 | − | 14.7464i | 0.959234 | − | 0.553814i | 0.0632970 | − | 0.997995i | \(-0.479838\pi\) |
0.895937 | + | 0.444181i | \(0.146505\pi\) | |||||||
\(710\) | 27.7390i | 1.04103i | ||||||||
\(711\) | 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 | ||||
\(716\) | −9.56254 | −0.357369 | ||||||||
\(717\) | −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 | 0.933189 | − | 0.359386i | \(-0.117014\pi\) |
−0.777832 | + | 0.628472i | \(0.783681\pi\) | |||||||
\(720\) | 0.220044i | 0.00820055i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37.8946 | − | 21.8784i | 1.41029 | − | 0.814231i | ||||
\(723\) | − | 1.22901i | − | 0.0457073i | ||||||
\(724\) | 2.26071 | + | 3.91567i | 0.0840188 | + | 0.145525i | ||||
\(725\) | −2.91120 | + | 5.04235i | −0.108119 | + | 0.187268i | ||||
\(726\) | −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 | ||||
\(731\) | 9.59645 | − | 16.6215i | 0.354938 | − | 0.614770i | ||||
\(732\) | −11.0098 | − | 19.0696i | −0.406935 | − | 0.704832i | ||||
\(733\) | 14.0179i | 0.517762i | 0.965909 | + | 0.258881i | \(0.0833538\pi\) | ||||
−0.965909 | + | 0.258881i | \(0.916646\pi\) | |||||||
\(734\) | −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 | \(-0.586411\pi\) |
−0.968383 | + | 0.249468i | \(0.919744\pi\) | |||||||
\(740\) | 18.7683 | 0.689938 | ||||||||
\(741\) | 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 | \(0.449352\pi\) | |||||||
\(744\) | 17.4071 | − | 30.1500i | 0.638175 | − | 1.10535i | ||||
\(745\) | 2.69592 | + | 4.66948i | 0.0987710 | + | 0.171076i | ||||
\(746\) | 27.1057i | 0.992410i | ||||||||
\(747\) | 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 | ||||
\(751\) | 24.0735 | − | 41.6965i | 0.878454 | − | 1.52153i | 0.0254165 | − | 0.999677i | \(-0.491909\pi\) |
0.853037 | − | 0.521850i | \(-0.174758\pi\) | |||||||
\(752\) | −0.0976479 | − | 0.0563770i | −0.00356085 | − | 0.00205586i | ||||
\(753\) | 40.1816 | 1.46430 | ||||||||
\(754\) | 4.62364 | − | 10.3017i | 0.168383 | − | 0.375167i | ||||
\(755\) | −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 | ||||
\(759\) | 17.3188i | 0.628634i | ||||||||
\(760\) | −0.104606 | + | 0.0603945i | −0.00379447 | + | 0.00219074i | ||||
\(761\) | −27.6895 | + | 15.9865i | −1.00374 | + | 0.579511i | −0.909353 | − | 0.416025i | \(-0.863423\pi\) |
−0.0943888 | + | 0.995535i | \(0.530090\pi\) | |||||||
\(762\) | 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 | ||||
\(766\) | 65.0548 | 2.35053 | ||||||||
\(767\) | 2.42301 | − | 5.39860i | 0.0874898 | − | 0.194932i | ||||
\(768\) | −26.4795 | −0.955495 | ||||||||
\(769\) | −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 | ||||
\(772\) | 22.9830i | 0.827177i | ||||||||
\(773\) | −32.2829 | + | 18.6385i | −1.16114 | + | 0.670382i | −0.951576 | − | 0.307414i | \(-0.900536\pi\) |
−0.209560 | + | 0.977796i | \(0.567203\pi\) | |||||||
\(774\) | 15.3255 | − | 8.84818i | 0.550864 | − | 0.318041i | ||||
\(775\) | − | 33.6618i | − | 1.20917i | ||||||
\(776\) | 0.640590 | + | 1.10953i | 0.0229958 | + | 0.0398300i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.3209 | + | 8.84553i | 0.549281 | + | 0.317128i | ||||
\(779\) | 0.475146 | 0.0170239 | ||||||||
\(780\) | 8.70789 | + | 12.0612i | 0.311792 | + | 0.431859i | ||||
\(781\) | −21.3693 | −0.764652 | ||||||||
\(782\) | −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 | ||||||
\(786\) | 7.47999 | − | 4.31857i | 0.266802 | − | 0.154038i | ||||
\(787\) | −12.4263 | + | 7.17430i | −0.442948 | + | 0.255736i | −0.704847 | − | 0.709359i | \(-0.748985\pi\) |
0.261899 | + | 0.965095i | \(0.415651\pi\) | |||||||
\(788\) | − | 51.1527i | − | 1.82224i | ||||||
\(789\) | 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 | ||||||||
\(793\) | 14.8746 | + | 6.67605i | 0.528213 | + | 0.237073i | ||||
\(794\) | −17.1658 | −0.609192 | ||||||||
\(795\) | 2.93179 | + | 1.69267i | 0.103980 | + | 0.0600328i | ||||
\(796\) | 10.9319 | − | 18.9346i | 0.387470 | − | 0.671118i | ||||
\(797\) | −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 | ||||
\(801\) | 14.5204i | 0.513054i | ||||||||
\(802\) | −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 | ||||
\(807\) | −23.5757 | −0.829904 | ||||||||
\(808\) | 25.1723 | + | 14.5332i | 0.885558 | + | 0.511277i | ||||
\(809\) | 21.2768 | − | 36.8525i | 0.748052 | − | 1.29566i | −0.200703 | − | 0.979652i | \(-0.564323\pi\) |
0.948755 | − | 0.316013i | \(-0.102344\pi\) | |||||||
\(810\) | 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 | ||||
\(814\) | 23.2079i | 0.813437i | ||||||||
\(815\) | 3.83453 | + | 6.64160i | 0.134318 | + | 0.232645i | ||||
\(816\) | −0.477922 | + | 0.827785i | −0.0167306 | + | 0.0289783i | ||||
\(817\) | 0.380570 | + | 0.219722i | 0.0133145 | + | 0.00768710i | ||||
\(818\) | 67.4455 | 2.35818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.0549 | 0.979721 | ||||||||
\(821\) | −2.68944 | − | 1.55275i | −0.0938621 | − | 0.0541913i | 0.452334 | − | 0.891848i | \(-0.350591\pi\) |
−0.546196 | + | 0.837657i | \(0.683925\pi\) | |||||||
\(822\) | 3.16401 | − | 5.48023i | 0.110358 | − | 0.191145i | ||||
\(823\) | 24.5082 | + | 42.4494i | 0.854301 | + | 1.47969i | 0.877292 | + | 0.479958i | \(0.159348\pi\) |
−0.0229903 | + | 0.999736i | \(0.507319\pi\) | |||||||
\(824\) | 29.9930i | 1.04486i | ||||||||
\(825\) | 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 | 0.0209227 | + | 0.999781i | \(0.493340\pi\) |
−0.876297 | + | 0.481771i | \(0.839994\pi\) | |||||||
\(830\) | 19.4972 | + | 11.2567i | 0.676757 | + | 0.390726i | ||||
\(831\) | 29.3468 | 1.01803 | ||||||||
\(832\) | 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 | ||||
\(837\) | 44.3505i | 1.53298i | ||||||||
\(838\) | 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 | ||||
\(842\) | −28.6407 | + | 49.6071i | −0.987024 | + | 1.70957i | ||||
\(843\) | 17.8934 | + | 10.3308i | 0.616282 | + | 0.355810i | ||||
\(844\) | 26.7519 | 0.920839 | ||||||||
\(845\) | −10.4551 | − | 3.46644i | −0.359667 | − | 0.119249i | ||||
\(846\) | 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 | ||||
\(850\) | 20.4298i | 0.700738i | ||||||||
\(851\) | −45.3818 | + | 26.2012i | −1.55567 | + | 0.898166i | ||||
\(852\) | −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 | ||||
\(856\) | 25.6728 | + | 14.8222i | 0.877477 | + | 0.506611i | ||||
\(857\) | 10.1271 | 0.345935 | 0.172967 | − | 0.984928i | \(-0.444664\pi\) | ||||
0.172967 | + | 0.984928i | \(0.444664\pi\) | |||||||
\(858\) | −14.9142 | + | 10.7677i | −0.509162 | + | 0.367603i | ||||
\(859\) | 0.510237 | 0.0174090 | 0.00870452 | − | 0.999962i | \(-0.497229\pi\) | ||||
0.00870452 | + | 0.999962i | \(0.497229\pi\) | |||||||
\(860\) | 22.4707 | + | 12.9735i | 0.766244 | + | 0.442391i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.3787 | − | 42.2251i | −0.830341 | − | 1.43819i | ||||
\(863\) | − | 20.4991i | − | 0.697797i | −0.937161 | − | 0.348898i | \(-0.886556\pi\) | ||
0.937161 | − | 0.348898i | \(-0.113444\pi\) | |||||||
\(864\) | 25.8482 | − | 14.9235i | 0.879375 | − | 0.507707i | ||||
\(865\) | −14.3725 | + | 8.29797i | −0.488680 | + | 0.282139i | ||||
\(866\) | − | 53.9646i | − | 1.83379i | ||||||
\(867\) | 9.36269 | + | 16.2167i | 0.317974 | + | 0.550747i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.1799 | − | 8.76412i | −0.514943 | − | 0.297302i | ||||
\(870\) | 3.90960 | 0.132548 | ||||||||
\(871\) | 7.32685 | − | 0.747905i | 0.248261 | − | 0.0253418i | ||||
\(872\) | 34.8844 | 1.18133 | ||||||||
\(873\) | −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 | ||||||
\(877\) | 9.77794 | − | 5.64530i | 0.330178 | − | 0.190628i | −0.325742 | − | 0.945459i | \(-0.605614\pi\) |
0.655920 | + | 0.754830i | \(0.272281\pi\) | |||||||
\(878\) | −24.0128 | + | 13.8638i | −0.810394 | + | 0.467881i | ||||
\(879\) | 0.293545i | 0.00990103i | ||||||||
\(880\) | −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 | \(0.656319\pi\) | |||||||
\(884\) | −2.50663 | − | 24.5562i | −0.0843071 | − | 0.825915i | ||||
\(885\) | 2.04881 | 0.0688701 | ||||||||
\(886\) | −31.3827 | − | 18.1188i | −1.05432 | − | 0.608713i | ||||
\(887\) | −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 | ||||
\(891\) | −7.58379 | + | 4.37850i | −0.254066 | + | 0.146685i | ||||
\(892\) | − | 53.0725i | − | 1.77700i | ||||||
\(893\) | 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 | ||||
\(898\) | −59.8876 | −1.99848 | ||||||||
\(899\) | 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 | ||||
\(905\) | − | 1.15913i | − | 0.0385308i | ||||||
\(906\) | −1.12681 | − | 1.95170i | −0.0374359 | − | 0.0648409i | ||||
\(907\) | 20.7315 | − | 35.9081i | 0.688379 | − | 1.19231i | −0.283982 | − | 0.958829i | \(-0.591656\pi\) |
0.972362 | − | 0.233479i | \(-0.0750109\pi\) | |||||||
\(908\) | −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 | ||||
\(913\) | −8.67180 | + | 15.0200i | −0.286995 | + | 0.497090i | ||||
\(914\) | 35.4655 | + | 61.4280i | 1.17309 | + | 2.03186i | ||||
\(915\) | 5.64504i | 0.186619i | ||||||||
\(916\) | 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 | 0.916729 | + | 0.399510i | \(0.130820\pi\) |
−0.112379 | + | 0.993665i | \(0.535847\pi\) | |||||||
\(920\) | 9.95645 | − | 17.2451i | 0.328254 | − | 0.568553i | ||||
\(921\) | −34.7068 | − | 20.0380i | −1.14363 | − | 0.660274i | ||||
\(922\) | −78.5317 | −2.58630 | ||||||||
\(923\) | 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 | ||||
\(928\) | − | 7.19330i | − | 0.236132i | ||||||
\(929\) | −25.4464 | + | 14.6915i | −0.834868 | + | 0.482012i | −0.855517 | − | 0.517775i | \(-0.826760\pi\) |
0.0206482 | + | 0.999787i | \(0.493427\pi\) | |||||||
\(930\) | −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 | ||||
\(934\) | −56.5541 | − | 32.6515i | −1.85051 | − | 1.06839i | ||||
\(935\) | 2.63859 | 0.0862912 | ||||||||
\(936\) | 3.67980 | − | 8.19881i | 0.120278 | − | 0.267986i | ||||
\(937\) | 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 | ||||
\(941\) | − | 24.1033i | − | 0.785744i | −0.919593 | − | 0.392872i | \(-0.871482\pi\) | ||
0.919593 | − | 0.392872i | \(-0.128518\pi\) | |||||||
\(942\) | 48.7150 | − | 28.1256i | 1.58722 | − | 0.916383i | ||||
\(943\) | −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 | ||||
\(947\) | 2.89292 | + | 1.67023i | 0.0940072 | + | 0.0542751i | 0.546267 | − | 0.837611i | \(-0.316049\pi\) |
−0.452259 | + | 0.891886i | \(0.649382\pi\) | |||||||
\(948\) | −56.7739 | −1.84393 | ||||||||
\(949\) | 14.2704 | + | 19.7658i | 0.463238 | + | 0.641624i | ||||
\(950\) | −0.467765 | −0.0151763 | ||||||||
\(951\) | 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 | \(0.858991\pi\) | |||||||
\(954\) | − | 5.17925i | − | 0.167685i | ||||||
\(955\) | 1.11039 | − | 0.641082i | 0.0359313 | − | 0.0207449i | ||||
\(956\) | −38.2546 | + | 22.0863i | −1.23724 | + | 0.714322i | ||||
\(957\) | 3.01183i | 0.0973585i | ||||||||
\(958\) | −7.23509 | − | 12.5315i | −0.233755 | − | 0.404876i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13.8506 | + | 7.99667i | 0.447028 | + | 0.258091i | ||||
\(961\) | −30.7961 | −0.993423 | ||||||||
\(962\) | −50.7787 | − | 22.7906i | −1.63717 | − | 0.734798i | ||||
\(963\) | −8.17783 | −0.263527 | ||||||||
\(964\) | −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 | \(-0.723402\pi\) | ||
0.645623 | − | 0.763657i | \(-0.276598\pi\) | |||||||
\(968\) | −22.7509 | + | 13.1352i | −0.731241 | + | 0.422182i | ||||
\(969\) | 0.125352 | − | 0.0723720i | 0.00402689 | − | 0.00232492i | ||||
\(970\) | − | 0.831803i | − | 0.0267076i | ||||||
\(971\) | 17.2357 | + | 29.8532i | 0.553121 | + | 0.958033i | 0.998047 | + | 0.0624662i | \(0.0198966\pi\) |
−0.444926 | + | 0.895567i | \(0.646770\pi\) | |||||||
\(972\) | 13.7876 | − | 23.8808i | 0.442238 | − | 0.765978i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.9830 | −0.960717 | ||||||||
\(975\) | 2.31002 | + | 22.6301i | 0.0739798 | + | 0.724743i | ||||
\(976\) | −1.41624 | −0.0453329 | ||||||||
\(977\) | −11.5598 | − | 6.67406i | −0.369831 | − | 0.213522i | 0.303553 | − | 0.952814i | \(-0.401827\pi\) |
−0.673385 | + | 0.739292i | \(0.735160\pi\) | |||||||
\(978\) | −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 | ||||
\(982\) | 24.6390 | − | 14.2253i | 0.786263 | − | 0.453949i | ||||
\(983\) | − | 12.5344i | − | 0.399785i | −0.979818 | − | 0.199893i | \(-0.935941\pi\) | ||
0.979818 | − | 0.199893i | \(-0.0640594\pi\) | |||||||
\(984\) | 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 | ||||
\(989\) | −72.4455 | −2.30363 | ||||||||
\(990\) | 2.10691 | + | 1.21643i | 0.0669620 | + | 0.0386605i | ||||
\(991\) | 5.20596 | − | 9.01698i | 0.165373 | − | 0.286434i | −0.771415 | − | 0.636332i | \(-0.780451\pi\) |
0.936788 | + | 0.349899i | \(0.113784\pi\) | |||||||
\(992\) | 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 | ||||
\(996\) | 56.1759i | 1.78000i | ||||||||
\(997\) | 2.87635 | + | 4.98198i | 0.0910949 | + | 0.157781i | 0.907972 | − | 0.419031i | \(-0.137630\pi\) |
−0.816877 | + | 0.576812i | \(0.804297\pi\) | |||||||
\(998\) | 10.5414 | − | 18.2582i | 0.333681 | − | 0.577953i | ||||
\(999\) | −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.q.i.589.1 | 12 | ||
7.2 | even | 3 | 637.2.k.i.459.6 | 12 | |||
7.3 | odd | 6 | 91.2.u.b.30.6 | yes | 12 | ||
7.4 | even | 3 | 637.2.u.g.30.6 | 12 | |||
7.5 | odd | 6 | 91.2.k.b.4.6 | ✓ | 12 | ||
7.6 | odd | 2 | 637.2.q.g.589.1 | 12 | |||
13.6 | odd | 12 | 8281.2.a.co.1.11 | 12 | |||
13.7 | odd | 12 | 8281.2.a.co.1.2 | 12 | |||
13.10 | even | 6 | inner | 637.2.q.i.491.1 | 12 | ||
21.5 | even | 6 | 819.2.bm.f.550.1 | 12 | |||
21.17 | even | 6 | 819.2.do.e.667.1 | 12 | |||
91.6 | even | 12 | 8281.2.a.cp.1.11 | 12 | |||
91.10 | odd | 6 | 91.2.k.b.23.1 | yes | 12 | ||
91.19 | even | 12 | 1183.2.e.j.508.2 | 24 | |||
91.20 | even | 12 | 8281.2.a.cp.1.2 | 12 | |||
91.23 | even | 6 | 637.2.u.g.361.6 | 12 | |||
91.33 | even | 12 | 1183.2.e.j.508.11 | 24 | |||
91.45 | even | 12 | 1183.2.e.j.170.2 | 24 | |||
91.59 | even | 12 | 1183.2.e.j.170.11 | 24 | |||
91.62 | odd | 6 | 637.2.q.g.491.1 | 12 | |||
91.75 | odd | 6 | 91.2.u.b.88.6 | yes | 12 | ||
91.88 | even | 6 | 637.2.k.i.569.1 | 12 | |||
273.101 | even | 6 | 819.2.bm.f.478.6 | 12 | |||
273.257 | even | 6 | 819.2.do.e.361.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.6 | ✓ | 12 | 7.5 | odd | 6 | ||
91.2.k.b.23.1 | yes | 12 | 91.10 | odd | 6 | ||
91.2.u.b.30.6 | yes | 12 | 7.3 | odd | 6 | ||
91.2.u.b.88.6 | yes | 12 | 91.75 | odd | 6 | ||
637.2.k.i.459.6 | 12 | 7.2 | even | 3 | |||
637.2.k.i.569.1 | 12 | 91.88 | even | 6 | |||
637.2.q.g.491.1 | 12 | 91.62 | odd | 6 | |||
637.2.q.g.589.1 | 12 | 7.6 | odd | 2 | |||
637.2.q.i.491.1 | 12 | 13.10 | even | 6 | inner | ||
637.2.q.i.589.1 | 12 | 1.1 | even | 1 | trivial | ||
637.2.u.g.30.6 | 12 | 7.4 | even | 3 | |||
637.2.u.g.361.6 | 12 | 91.23 | even | 6 | |||
819.2.bm.f.478.6 | 12 | 273.101 | even | 6 | |||
819.2.bm.f.550.1 | 12 | 21.5 | even | 6 | |||
819.2.do.e.361.1 | 12 | 273.257 | even | 6 | |||
819.2.do.e.667.1 | 12 | 21.17 | even | 6 | |||
1183.2.e.j.170.2 | 24 | 91.45 | even | 12 | |||
1183.2.e.j.170.11 | 24 | 91.59 | even | 12 | |||
1183.2.e.j.508.2 | 24 | 91.19 | even | 12 | |||
1183.2.e.j.508.11 | 24 | 91.33 | even | 12 | |||
8281.2.a.co.1.2 | 12 | 13.7 | odd | 12 | |||
8281.2.a.co.1.11 | 12 | 13.6 | odd | 12 | |||
8281.2.a.cp.1.2 | 12 | 91.20 | even | 12 | |||
8281.2.a.cp.1.11 | 12 | 91.6 | even | 12 |