Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.2 | ||
Character | \(\chi\) | \(=\) | 1183.508 |
Dual form | 1183.2.e.j.170.2 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.15163 | − | 1.99469i | −0.814328 | − | 1.41046i | −0.909810 | − | 0.415026i | \(-0.863773\pi\) |
0.0954820 | − | 0.995431i | \(-0.469561\pi\) | |||||||
\(3\) | 0.736680 | − | 1.27597i | 0.425323 | − | 0.736680i | −0.571128 | − | 0.820861i | \(-0.693494\pi\) |
0.996451 | + | 0.0841807i | \(0.0268273\pi\) | |||||||
\(4\) | −1.65252 | + | 2.86225i | −0.826259 | + | 1.43112i | ||||
\(5\) | −0.423646 | − | 0.733776i | −0.189460 | − | 0.328155i | 0.755610 | − | 0.655022i | \(-0.227340\pi\) |
−0.945070 | + | 0.326867i | \(0.894007\pi\) | |||||||
\(6\) | −3.39354 | −1.38541 | ||||||||
\(7\) | −1.00088 | + | 2.44913i | −0.378297 | + | 0.925684i | ||||
\(8\) | 3.00585 | 1.06273 | ||||||||
\(9\) | 0.414604 | + | 0.718115i | 0.138201 | + | 0.239372i | ||||
\(10\) | −0.975769 | + | 1.69008i | −0.308565 | + | 0.534451i | ||||
\(11\) | 0.751701 | − | 1.30198i | 0.226646 | − | 0.392563i | −0.730166 | − | 0.683270i | \(-0.760557\pi\) |
0.956812 | + | 0.290707i | \(0.0938905\pi\) | |||||||
\(12\) | 2.43476 | + | 4.21712i | 0.702853 | + | 1.21738i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 6.03790 | − | 0.824057i | 1.61370 | − | 0.220238i | ||||
\(15\) | −1.24837 | −0.322327 | ||||||||
\(16\) | −0.156597 | − | 0.271234i | −0.0391492 | − | 0.0678085i | ||||
\(17\) | −1.03570 | + | 1.79389i | −0.251194 | + | 0.435081i | −0.963855 | − | 0.266428i | \(-0.914157\pi\) |
0.712661 | + | 0.701509i | \(0.247490\pi\) | |||||||
\(18\) | 0.954943 | − | 1.65401i | 0.225082 | − | 0.389854i | ||||
\(19\) | 0.0237136 | + | 0.0410731i | 0.00544027 | + | 0.00942282i | 0.868733 | − | 0.495281i | \(-0.164935\pi\) |
−0.863292 | + | 0.504704i | \(0.831602\pi\) | |||||||
\(20\) | 2.80033 | 0.626173 | ||||||||
\(21\) | 2.38768 | + | 3.08132i | 0.521035 | + | 0.672399i | ||||
\(22\) | −3.46274 | −0.738258 | ||||||||
\(23\) | 3.90935 | + | 6.77119i | 0.815156 | + | 1.41189i | 0.909216 | + | 0.416325i | \(0.136682\pi\) |
−0.0940598 | + | 0.995567i | \(0.529984\pi\) | |||||||
\(24\) | 2.21435 | − | 3.83536i | 0.452002 | − | 0.782891i | ||||
\(25\) | 2.14105 | − | 3.70840i | 0.428210 | − | 0.741681i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64180 | 1.08577 | ||||||||
\(28\) | −5.35604 | − | 6.91200i | −1.01220 | − | 1.30624i | ||||
\(29\) | 1.35971 | 0.252491 | 0.126246 | − | 0.991999i | \(-0.459707\pi\) | ||||
0.126246 | + | 0.991999i | \(0.459707\pi\) | |||||||
\(30\) | 1.43766 | + | 2.49010i | 0.262480 | + | 0.454628i | ||||
\(31\) | −3.93052 | + | 6.80787i | −0.705943 | + | 1.22273i | 0.260407 | + | 0.965499i | \(0.416143\pi\) |
−0.966350 | + | 0.257230i | \(0.917190\pi\) | |||||||
\(32\) | 2.64516 | − | 4.58156i | 0.467603 | − | 0.809912i | ||||
\(33\) | −1.10753 | − | 1.91829i | −0.192796 | − | 0.333932i | ||||
\(34\) | 4.77099 | 0.818218 | ||||||||
\(35\) | 2.22113 | − | 0.303142i | 0.375440 | − | 0.0512403i | ||||
\(36\) | −2.74056 | −0.456760 | ||||||||
\(37\) | −3.35110 | − | 5.80427i | −0.550917 | − | 0.954216i | −0.998209 | − | 0.0598278i | \(-0.980945\pi\) |
0.447292 | − | 0.894388i | \(-0.352388\pi\) | |||||||
\(38\) | 0.0546187 | − | 0.0946024i | 0.00886032 | − | 0.0153465i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.27341 | − | 2.20562i | −0.201345 | − | 0.348739i | ||||
\(41\) | 10.0184 | 1.56462 | 0.782309 | − | 0.622891i | \(-0.214042\pi\) | ||||
0.782309 | + | 0.622891i | \(0.214042\pi\) | |||||||
\(42\) | 3.39653 | − | 8.31123i | 0.524096 | − | 1.28245i | ||||
\(43\) | 9.26566 | 1.41300 | 0.706500 | − | 0.707713i | \(-0.250273\pi\) | ||||
0.706500 | + | 0.707713i | \(0.250273\pi\) | |||||||
\(44\) | 2.48440 | + | 4.30311i | 0.374537 | + | 0.648718i | ||||
\(45\) | 0.351290 | − | 0.608453i | 0.0523673 | − | 0.0907028i | ||||
\(46\) | 9.00428 | − | 15.5959i | 1.32761 | − | 2.29948i | ||||
\(47\) | −0.180007 | − | 0.311781i | −0.0262567 | − | 0.0454779i | 0.852598 | − | 0.522567i | \(-0.175025\pi\) |
−0.878855 | + | 0.477089i | \(0.841692\pi\) | |||||||
\(48\) | −0.461448 | −0.0666042 | ||||||||
\(49\) | −4.99648 | − | 4.90257i | −0.713782 | − | 0.700367i | ||||
\(50\) | −9.86281 | −1.39481 | ||||||||
\(51\) | 1.52596 | + | 2.64304i | 0.213677 | + | 0.370100i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.35591 | + | 2.34850i | −0.186248 | + | 0.322591i | −0.943996 | − | 0.329956i | \(-0.892966\pi\) |
0.757748 | + | 0.652547i | \(0.226299\pi\) | |||||||
\(54\) | −6.49729 | − | 11.2536i | −0.884169 | − | 1.53143i | ||||
\(55\) | −1.27382 | −0.171762 | ||||||||
\(56\) | −3.00849 | + | 7.36171i | −0.402027 | + | 0.983750i | ||||
\(57\) | 0.0698773 | 0.00925548 | ||||||||
\(58\) | −1.56588 | − | 2.71219i | −0.205611 | − | 0.356128i | ||||
\(59\) | −0.820598 | + | 1.42132i | −0.106833 | + | 0.185040i | −0.914486 | − | 0.404619i | \(-0.867404\pi\) |
0.807653 | + | 0.589658i | \(0.200738\pi\) | |||||||
\(60\) | 2.06295 | − | 3.57313i | 0.266325 | − | 0.461289i | ||||
\(61\) | −2.26097 | − | 3.91612i | −0.289488 | − | 0.501407i | 0.684200 | − | 0.729295i | \(-0.260152\pi\) |
−0.973688 | + | 0.227887i | \(0.926818\pi\) | |||||||
\(62\) | 18.1061 | 2.29948 | ||||||||
\(63\) | −2.17373 | + | 0.296672i | −0.273864 | + | 0.0373771i | ||||
\(64\) | −12.8114 | −1.60143 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.55093 | + | 4.41834i | −0.313998 | + | 0.543860i | ||||
\(67\) | 1.02133 | − | 1.76900i | 0.124775 | − | 0.216117i | −0.796870 | − | 0.604151i | \(-0.793512\pi\) |
0.921645 | + | 0.388034i | \(0.126846\pi\) | |||||||
\(68\) | −3.42303 | − | 5.92886i | −0.415103 | − | 0.718980i | ||||
\(69\) | 11.5198 | 1.38682 | ||||||||
\(70\) | −3.16260 | − | 4.08136i | −0.378003 | − | 0.487815i | ||||
\(71\) | 14.2139 | 1.68688 | 0.843442 | − | 0.537220i | \(-0.180526\pi\) | ||||
0.843442 | + | 0.537220i | \(0.180526\pi\) | |||||||
\(72\) | 1.24624 | + | 2.15854i | 0.146870 | + | 0.254387i | ||||
\(73\) | −3.38075 | + | 5.85563i | −0.395687 | + | 0.685349i | −0.993189 | − | 0.116518i | \(-0.962827\pi\) |
0.597502 | + | 0.801867i | \(0.296160\pi\) | |||||||
\(74\) | −7.71847 | + | 13.3688i | −0.897253 | + | 1.55409i | ||||
\(75\) | −3.15454 | − | 5.46382i | −0.364255 | − | 0.630907i | ||||
\(76\) | −0.156749 | −0.0179803 | ||||||||
\(77\) | 2.43637 | + | 3.14414i | 0.277650 | + | 0.358308i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.82952 | − | 10.0970i | −0.655873 | − | 1.13600i | −0.981674 | − | 0.190567i | \(-0.938967\pi\) |
0.325801 | − | 0.945438i | \(-0.394366\pi\) | |||||||
\(80\) | −0.132683 | + | 0.229814i | −0.0148344 | + | 0.0256940i | ||||
\(81\) | 2.91240 | − | 5.04442i | 0.323600 | − | 0.560491i | ||||
\(82\) | −11.5376 | − | 19.9837i | −1.27411 | − | 2.20683i | ||||
\(83\) | 11.5362 | 1.26627 | 0.633133 | − | 0.774043i | \(-0.281768\pi\) | ||||
0.633133 | + | 0.774043i | \(0.281768\pi\) | |||||||
\(84\) | −12.7652 | + | 1.74220i | −1.39280 | + | 0.190090i | ||||
\(85\) | 1.75508 | 0.190365 | ||||||||
\(86\) | −10.6706 | − | 18.4821i | −1.15065 | − | 1.99298i | ||||
\(87\) | 1.00167 | − | 1.73494i | 0.107390 | − | 0.186006i | ||||
\(88\) | 2.25950 | − | 3.91357i | 0.240863 | − | 0.417188i | ||||
\(89\) | 8.75561 | + | 15.1652i | 0.928093 | + | 1.60750i | 0.786510 | + | 0.617577i | \(0.211886\pi\) |
0.141582 | + | 0.989927i | \(0.454781\pi\) | |||||||
\(90\) | −1.61823 | −0.170576 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −25.8411 | −2.69412 | ||||||||
\(93\) | 5.79108 | + | 10.0304i | 0.600507 | + | 1.04011i | ||||
\(94\) | −0.414604 | + | 0.718115i | −0.0427631 | + | 0.0740679i | ||||
\(95\) | 0.0200923 | − | 0.0348009i | 0.00206143 | − | 0.00357050i | ||||
\(96\) | −3.89728 | − | 6.75029i | −0.397764 | − | 0.688948i | ||||
\(97\) | 0.426229 | 0.0432770 | 0.0216385 | − | 0.999766i | \(-0.493112\pi\) | ||||
0.0216385 | + | 0.999766i | \(0.493112\pi\) | |||||||
\(98\) | −4.02499 | + | 15.6124i | −0.406585 | + | 1.57709i | ||||
\(99\) | 1.24663 | 0.125291 | ||||||||
\(100\) | 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 | \(0.326429\pi\) | |||||||
\(102\) | 3.51469 | − | 6.08763i | 0.348007 | − | 0.602765i | ||||
\(103\) | 4.98912 | + | 8.64140i | 0.491592 | + | 0.851463i | 0.999953 | − | 0.00968129i | \(-0.00308170\pi\) |
−0.508361 | + | 0.861144i | \(0.669748\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.24947 | − | 3.05741i | 0.121935 | − | 0.298373i | ||||
\(106\) | 6.24603 | 0.606668 | ||||||||
\(107\) | −4.93111 | − | 8.54094i | −0.476709 | − | 0.825684i | 0.522935 | − | 0.852373i | \(-0.324837\pi\) |
−0.999644 | + | 0.0266888i | \(0.991504\pi\) | |||||||
\(108\) | −9.32319 | + | 16.1482i | −0.897124 | + | 1.55386i | ||||
\(109\) | −5.80275 | + | 10.0507i | −0.555803 | + | 0.962679i | 0.442038 | + | 0.896996i | \(0.354256\pi\) |
−0.997841 | + | 0.0656822i | \(0.979078\pi\) | |||||||
\(110\) | 1.46697 | + | 2.54087i | 0.139870 | + | 0.242263i | ||||
\(111\) | −9.87475 | −0.937269 | ||||||||
\(112\) | 0.821022 | − | 0.112054i | 0.0775793 | − | 0.0105881i | ||||
\(113\) | −3.47758 | −0.327143 | −0.163572 | − | 0.986531i | \(-0.552301\pi\) | ||||
−0.163572 | + | 0.986531i | \(0.552301\pi\) | |||||||
\(114\) | −0.0804731 | − | 0.139383i | −0.00753699 | − | 0.0130545i | ||||
\(115\) | 3.31236 | − | 5.73718i | 0.308879 | − | 0.534994i | ||||
\(116\) | −2.24694 | + | 3.89182i | −0.208623 | + | 0.361346i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.78011 | 0.347987 | ||||||||
\(119\) | −3.35685 | − | 4.33203i | −0.307722 | − | 0.397117i | ||||
\(120\) | −3.75240 | −0.342546 | ||||||||
\(121\) | 4.36989 | + | 7.56887i | 0.397263 | + | 0.688079i | ||||
\(122\) | −5.20762 | + | 9.01986i | −0.471476 | + | 0.816620i | ||||
\(123\) | 7.38039 | − | 12.7832i | 0.665467 | − | 1.15262i | ||||
\(124\) | −12.9905 | − | 22.5003i | −1.16658 | − | 2.02058i | ||||
\(125\) | −7.86464 | −0.703435 | ||||||||
\(126\) | 3.09510 | + | 3.99425i | 0.275734 | + | 0.355836i | ||||
\(127\) | −15.6998 | −1.39313 | −0.696567 | − | 0.717491i | \(-0.745290\pi\) | ||||
−0.696567 | + | 0.717491i | \(0.745290\pi\) | |||||||
\(128\) | 9.46373 | + | 16.3917i | 0.836483 | + | 1.44883i | ||||
\(129\) | 6.82583 | − | 11.8227i | 0.600981 | − | 1.04093i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.27259 | + | 2.20418i | 0.111186 | + | 0.192580i | 0.916249 | − | 0.400610i | \(-0.131202\pi\) |
−0.805063 | + | 0.593190i | \(0.797868\pi\) | |||||||
\(132\) | 7.32083 | 0.637197 | ||||||||
\(133\) | −0.124328 | + | 0.0169684i | −0.0107806 | + | 0.00147134i | ||||
\(134\) | −4.70479 | −0.406432 | ||||||||
\(135\) | −2.39013 | − | 4.13982i | −0.205709 | − | 0.356299i | ||||
\(136\) | −3.11316 | + | 5.39215i | −0.266951 | + | 0.462373i | ||||
\(137\) | 0.932362 | − | 1.61490i | 0.0796571 | − | 0.137970i | −0.823445 | − | 0.567396i | \(-0.807951\pi\) |
0.903102 | + | 0.429426i | \(0.141284\pi\) | |||||||
\(138\) | −13.2665 | − | 22.9783i | −1.12932 | − | 1.95605i | ||||
\(139\) | 15.6092 | 1.32396 | 0.661979 | − | 0.749522i | \(-0.269717\pi\) | ||||
0.661979 | + | 0.749522i | \(0.269717\pi\) | |||||||
\(140\) | −2.80280 | + | 6.85837i | −0.236879 | + | 0.579638i | ||||
\(141\) | −0.530430 | −0.0446703 | ||||||||
\(142\) | −16.3692 | − | 28.3524i | −1.37368 | − | 2.37928i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.129851 | − | 0.224909i | 0.0108209 | − | 0.0187424i | ||||
\(145\) | −0.576035 | − | 0.997721i | −0.0478371 | − | 0.0828562i | ||||
\(146\) | 15.5735 | 1.28887 | ||||||||
\(147\) | −9.93633 | + | 2.76372i | −0.819535 | + | 0.227947i | ||||
\(148\) | 22.1510 | 1.82080 | ||||||||
\(149\) | 3.18181 | + | 5.51106i | 0.260664 | + | 0.451484i | 0.966419 | − | 0.256973i | \(-0.0827251\pi\) |
−0.705754 | + | 0.708457i | \(0.749392\pi\) | |||||||
\(150\) | −7.26574 | + | 12.5846i | −0.593245 | + | 1.02753i | ||||
\(151\) | −0.332047 | + | 0.575122i | −0.0270216 | + | 0.0468028i | −0.879220 | − | 0.476416i | \(-0.841936\pi\) |
0.852198 | + | 0.523219i | \(0.175269\pi\) | |||||||
\(152\) | 0.0712794 | + | 0.123460i | 0.00578152 | + | 0.0100139i | ||||
\(153\) | −1.71762 | −0.138861 | ||||||||
\(154\) | 3.46578 | − | 8.48069i | 0.279281 | − | 0.683393i | ||||
\(155\) | 6.66060 | 0.534992 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.28798 | − | 14.3552i | 0.661453 | − | 1.14567i | −0.318781 | − | 0.947828i | \(-0.603273\pi\) |
0.980234 | − | 0.197842i | \(-0.0633933\pi\) | |||||||
\(158\) | −13.4269 | + | 23.2562i | −1.06819 | + | 1.85016i | ||||
\(159\) | 1.99774 | + | 3.46019i | 0.158431 | + | 0.274411i | ||||
\(160\) | −4.48245 | −0.354369 | ||||||||
\(161\) | −20.4963 | + | 2.79735i | −1.61534 | + | 0.220462i | ||||
\(162\) | −13.4160 | −1.05406 | ||||||||
\(163\) | −4.52563 | − | 7.83863i | −0.354475 | − | 0.613969i | 0.632553 | − | 0.774517i | \(-0.282007\pi\) |
−0.987028 | + | 0.160548i | \(0.948674\pi\) | |||||||
\(164\) | −16.5557 | + | 28.6752i | −1.29278 | + | 2.23916i | ||||
\(165\) | −0.938398 | + | 1.62535i | −0.0730542 | + | 0.126534i | ||||
\(166\) | −13.2855 | − | 23.0112i | −1.03116 | − | 1.78601i | ||||
\(167\) | −2.65761 | −0.205652 | −0.102826 | − | 0.994699i | \(-0.532788\pi\) | ||||
−0.102826 | + | 0.994699i | \(0.532788\pi\) | |||||||
\(168\) | 7.17701 | + | 9.26197i | 0.553718 | + | 0.714576i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.02121 | − | 3.50084i | −0.155020 | − | 0.268502i | ||||
\(171\) | −0.0196635 | + | 0.0340582i | −0.00150370 | + | 0.00260449i | ||||
\(172\) | −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 | \(-0.434021\pi\) | |||||||
\(174\) | −4.61423 | −0.349804 | ||||||||
\(175\) | 6.93943 | + | 8.95538i | 0.524572 | + | 0.676963i | ||||
\(176\) | −0.470856 | −0.0354921 | ||||||||
\(177\) | 1.20904 | + | 2.09411i | 0.0908768 | + | 0.157403i | ||||
\(178\) | 20.1665 | − | 34.9294i | 1.51154 | − | 2.61807i | ||||
\(179\) | 1.44666 | − | 2.50569i | 0.108129 | − | 0.187284i | −0.806884 | − | 0.590711i | \(-0.798848\pi\) |
0.915012 | + | 0.403426i | \(0.132181\pi\) | |||||||
\(180\) | 1.16103 | + | 2.01096i | 0.0865379 | + | 0.149888i | ||||
\(181\) | 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 | ||||||||
\(184\) | 11.7509 | + | 20.3532i | 0.866289 | + | 1.50046i | ||||
\(185\) | −2.83936 | + | 4.91791i | −0.208754 | + | 0.361572i | ||||
\(186\) | 13.3384 | − | 23.1028i | 0.978019 | − | 1.69398i | ||||
\(187\) | 1.55707 | + | 2.69693i | 0.113865 | + | 0.197219i | ||||
\(188\) | 1.18986 | 0.0867794 | ||||||||
\(189\) | −5.64677 | + | 13.8175i | −0.410742 | + | 1.00508i | ||||
\(190\) | −0.0925559 | −0.00671471 | ||||||||
\(191\) | 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 | ||||
\(193\) | −3.47697 | + | 6.02229i | −0.250278 | + | 0.433494i | −0.963602 | − | 0.267340i | \(-0.913855\pi\) |
0.713324 | + | 0.700834i | \(0.247189\pi\) | |||||||
\(194\) | −0.490860 | − | 0.850194i | −0.0352417 | − | 0.0610404i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.2891 | − | 6.19955i | 1.59208 | − | 0.442825i | ||||
\(197\) | 15.4772 | 1.10271 | 0.551353 | − | 0.834272i | \(-0.314112\pi\) | ||||
0.551353 | + | 0.834272i | \(0.314112\pi\) | |||||||
\(198\) | −1.43566 | − | 2.48664i | −0.102028 | − | 0.176718i | ||||
\(199\) | −3.30764 | + | 5.72901i | −0.234473 | + | 0.406118i | −0.959119 | − | 0.283002i | \(-0.908670\pi\) |
0.724647 | + | 0.689121i | \(0.242003\pi\) | |||||||
\(200\) | 6.43566 | − | 11.1469i | 0.455070 | − | 0.788205i | ||||
\(201\) | −1.50479 | − | 2.60637i | −0.106140 | − | 0.183839i | ||||
\(202\) | 22.2725 | 1.56709 | ||||||||
\(203\) | −1.36090 | + | 3.33010i | −0.0955168 | + | 0.233727i | ||||
\(204\) | −10.0867 | −0.706211 | ||||||||
\(205\) | −4.24427 | − | 7.35129i | −0.296433 | − | 0.513436i | ||||
\(206\) | 11.4913 | − | 19.9035i | 0.800634 | − | 1.38674i | ||||
\(207\) | −3.24166 | + | 5.61473i | −0.225311 | + | 0.390250i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0713021 | 0.00493207 | ||||||||
\(210\) | −7.53751 | + | 1.02872i | −0.520137 | + | 0.0709887i | ||||
\(211\) | −8.09428 | −0.557234 | −0.278617 | − | 0.960402i | \(-0.589876\pi\) | ||||
−0.278617 | + | 0.960402i | \(0.589876\pi\) | |||||||
\(212\) | −4.48132 | − | 7.76187i | −0.307778 | − | 0.533088i | ||||
\(213\) | 10.4711 | − | 18.1365i | 0.717470 | − | 1.24269i | ||||
\(214\) | −11.3577 | + | 19.6721i | −0.776394 | + | 1.34475i | ||||
\(215\) | −3.92536 | − | 6.79892i | −0.267707 | − | 0.463683i | ||||
\(216\) | 16.9584 | 1.15387 | ||||||||
\(217\) | −12.7394 | − | 16.4402i | −0.864805 | − | 1.11604i | ||||
\(218\) | 26.7306 | 1.81042 | ||||||||
\(219\) | 4.98106 | + | 8.62745i | 0.336589 | + | 0.582989i | ||||
\(220\) | 2.10501 | − | 3.64599i | 0.141920 | − | 0.245812i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 11.3721 | + | 19.6970i | 0.763244 | + | 1.32198i | ||||
\(223\) | −16.0581 | −1.07533 | −0.537664 | − | 0.843159i | \(-0.680693\pi\) | ||||
−0.537664 | + | 0.843159i | \(0.680693\pi\) | |||||||
\(224\) | 8.57334 | + | 11.0639i | 0.572830 | + | 0.739240i | ||||
\(225\) | 3.55075 | 0.236716 | ||||||||
\(226\) | 4.00490 | + | 6.93668i | 0.266402 | + | 0.461421i | ||||
\(227\) | −0.647903 | + | 1.12220i | −0.0430029 | + | 0.0744831i | −0.886726 | − | 0.462296i | \(-0.847026\pi\) |
0.843723 | + | 0.536779i | \(0.180359\pi\) | |||||||
\(228\) | −0.115474 | + | 0.200006i | −0.00764742 | + | 0.0132457i | ||||
\(229\) | 10.4088 | + | 18.0285i | 0.687831 | + | 1.19136i | 0.972538 | + | 0.232743i | \(0.0747702\pi\) |
−0.284707 | + | 0.958614i | \(0.591896\pi\) | |||||||
\(230\) | −15.2585 | −1.00612 | ||||||||
\(231\) | 5.80665 | − | 0.792496i | 0.382050 | − | 0.0521424i | ||||
\(232\) | 4.08707 | 0.268330 | ||||||||
\(233\) | 6.65213 | + | 11.5218i | 0.435796 | + | 0.754820i | 0.997360 | − | 0.0726127i | \(-0.0231337\pi\) |
−0.561565 | + | 0.827433i | \(0.689800\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.152518 | + | 0.264169i | −0.00994920 | + | 0.0172325i | ||||
\(236\) | −2.71211 | − | 4.69751i | −0.176543 | − | 0.305782i | ||||
\(237\) | −17.1780 | −1.11583 | ||||||||
\(238\) | −4.77519 | + | 11.6848i | −0.309530 | + | 0.757411i | ||||
\(239\) | 13.3652 | 0.864525 | 0.432263 | − | 0.901748i | \(-0.357715\pi\) | ||||
0.432263 | + | 0.901748i | \(0.357715\pi\) | |||||||
\(240\) | 0.195490 | + | 0.338599i | 0.0126188 | + | 0.0218565i | ||||
\(241\) | 0.417076 | − | 0.722398i | 0.0268663 | − | 0.0465337i | −0.852280 | − | 0.523086i | \(-0.824781\pi\) |
0.879146 | + | 0.476553i | \(0.158114\pi\) | |||||||
\(242\) | 10.0650 | − | 17.4331i | 0.647004 | − | 1.12064i | ||||
\(243\) | 4.17170 | + | 7.22559i | 0.267614 | + | 0.463522i | ||||
\(244\) | 14.9452 | 0.956767 | ||||||||
\(245\) | −1.48065 | + | 5.74325i | −0.0945955 | + | 0.366923i | ||||
\(246\) | −33.9980 | −2.16763 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −11.8146 | + | 20.4634i | −0.750225 | + | 1.29943i | ||||
\(249\) | 8.49852 | − | 14.7199i | 0.538572 | − | 0.932834i | ||||
\(250\) | 9.05718 | + | 15.6875i | 0.572827 | + | 0.992165i | ||||
\(251\) | 27.2721 | 1.72140 | 0.860699 | − | 0.509114i | \(-0.170027\pi\) | ||||
0.860699 | + | 0.509114i | \(0.170027\pi\) | |||||||
\(252\) | 2.74297 | − | 6.71199i | 0.172791 | − | 0.422816i | ||||
\(253\) | 11.7547 | 0.739009 | ||||||||
\(254\) | 18.0804 | + | 31.3163i | 1.13447 | + | 1.96496i | ||||
\(255\) | 1.29293 | − | 2.23943i | 0.0809667 | − | 0.140238i | ||||
\(256\) | 8.98607 | − | 15.5643i | 0.561630 | − | 0.972771i | ||||
\(257\) | −3.27594 | − | 5.67409i | −0.204348 | − | 0.353940i | 0.745577 | − | 0.666419i | \(-0.232174\pi\) |
−0.949925 | + | 0.312479i | \(0.898841\pi\) | |||||||
\(258\) | −31.4434 | −1.95758 | ||||||||
\(259\) | 17.5695 | − | 2.39789i | 1.09171 | − | 0.148998i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.563740 | + | 0.976426i | 0.0348946 | + | 0.0604393i | ||||
\(262\) | 2.93110 | − | 5.07682i | 0.181084 | − | 0.313647i | ||||
\(263\) | 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 | ||||
\(265\) | 2.29770 | 0.141146 | ||||||||
\(266\) | 0.177027 | + | 0.228454i | 0.0108542 | + | 0.0140074i | ||||
\(267\) | 25.8003 | 1.57896 | ||||||||
\(268\) | 3.37553 | + | 5.84660i | 0.206194 | + | 0.357138i | ||||
\(269\) | −8.00065 | + | 13.8575i | −0.487808 | + | 0.844909i | −0.999902 | − | 0.0140210i | \(-0.995537\pi\) |
0.512093 | + | 0.858930i | \(0.328870\pi\) | |||||||
\(270\) | −5.50510 | + | 9.53511i | −0.335030 | + | 0.580288i | ||||
\(271\) | −4.37967 | − | 7.58582i | −0.266046 | − | 0.460806i | 0.701791 | − | 0.712383i | \(-0.252384\pi\) |
−0.967837 | + | 0.251577i | \(0.919051\pi\) | |||||||
\(272\) | 0.648750 | 0.0393363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29496 | −0.259468 | ||||||||
\(275\) | −3.21886 | − | 5.57522i | −0.194104 | − | 0.336199i | ||||
\(276\) | −19.0366 | + | 32.9724i | −1.14587 | + | 1.98471i | ||||
\(277\) | 9.95914 | − | 17.2497i | 0.598387 | − | 1.03644i | −0.394673 | − | 0.918822i | \(-0.629142\pi\) |
0.993059 | − | 0.117614i | \(-0.0375246\pi\) | |||||||
\(278\) | −17.9761 | − | 31.1355i | −1.07814 | − | 1.86739i | ||||
\(279\) | −6.51844 | −0.390249 | ||||||||
\(280\) | 6.67638 | − | 0.911198i | 0.398990 | − | 0.0544545i | ||||
\(281\) | 14.0234 | 0.836566 | 0.418283 | − | 0.908317i | \(-0.362632\pi\) | ||||
0.418283 | + | 0.908317i | \(0.362632\pi\) | |||||||
\(282\) | 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 | \(0.176248\pi\) | |||||||
\(284\) | −23.4888 | + | 40.6838i | −1.39380 | + | 2.41414i | ||||
\(285\) | −0.0296032 | − | 0.0512743i | −0.00175354 | − | 0.00303723i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0273 | + | 24.5365i | −0.591890 | + | 1.44834i | ||||
\(288\) | 4.38678 | 0.258493 | ||||||||
\(289\) | 6.35465 | + | 11.0066i | 0.373803 | + | 0.647446i | ||||
\(290\) | −1.32676 | + | 2.29802i | −0.0779101 | + | 0.134944i | ||||
\(291\) | 0.313995 | − | 0.543855i | 0.0184067 | − | 0.0318813i | ||||
\(292\) | −11.1735 | − | 19.3531i | −0.653879 | − | 1.13255i | ||||
\(293\) | 0.199235 | 0.0116394 | 0.00581972 | − | 0.999983i | \(-0.498148\pi\) | ||||
0.00581972 | + | 0.999983i | \(0.498148\pi\) | |||||||
\(294\) | 16.9558 | + | 16.6371i | 0.988880 | + | 0.970295i | ||||
\(295\) | 1.39057 | 0.0809622 | ||||||||
\(296\) | −10.0729 | − | 17.4467i | −0.585474 | − | 1.01407i | ||||
\(297\) | 4.24095 | − | 7.34554i | 0.246085 | − | 0.426232i | ||||
\(298\) | 7.32857 | − | 12.6935i | 0.424532 | − | 0.735312i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 20.8517 | 1.20387 | ||||||||
\(301\) | −9.27382 | + | 22.6928i | −0.534534 | + | 1.30799i | ||||
\(302\) | 1.52958 | 0.0880177 | ||||||||
\(303\) | 7.12368 | + | 12.3386i | 0.409245 | + | 0.708833i | ||||
\(304\) | 0.00742695 | − | 0.0128639i | 0.000425965 | − | 0.000737793i | ||||
\(305\) | −1.91570 | + | 3.31809i | −0.109693 | + | 0.189993i | ||||
\(306\) | 1.97807 | + | 3.42612i | 0.113079 | + | 0.195858i | ||||
\(307\) | 27.2004 | 1.55241 | 0.776204 | − | 0.630482i | \(-0.217143\pi\) | ||||
0.776204 | + | 0.630482i | \(0.217143\pi\) | |||||||
\(308\) | −13.0255 | + | 1.77772i | −0.742194 | + | 0.101295i | ||||
\(309\) | 14.7015 | 0.836341 | ||||||||
\(310\) | −7.67057 | − | 13.2858i | −0.435659 | − | 0.754584i | ||||
\(311\) | −13.5505 | + | 23.4701i | −0.768376 | + | 1.33087i | 0.170067 | + | 0.985432i | \(0.445602\pi\) |
−0.938443 | + | 0.345434i | \(0.887732\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0392 | + | 19.1205i | 0.623975 | + | 1.08076i | 0.988738 | + | 0.149656i | \(0.0478165\pi\) |
−0.364763 | + | 0.931100i | \(0.618850\pi\) | |||||||
\(314\) | −38.1789 | −2.15456 | ||||||||
\(315\) | 1.13858 | + | 1.46934i | 0.0641517 | + | 0.0827882i | ||||
\(316\) | 38.5336 | 2.16768 | ||||||||
\(317\) | 3.53411 | + | 6.12126i | 0.198496 | + | 0.343804i | 0.948041 | − | 0.318149i | \(-0.103061\pi\) |
−0.749545 | + | 0.661953i | \(0.769728\pi\) | |||||||
\(318\) | 4.60133 | − | 7.96973i | 0.258030 | − | 0.446920i | ||||
\(319\) | 1.02209 | − | 1.77032i | 0.0572263 | − | 0.0991188i | ||||
\(320\) | 5.42750 | + | 9.40071i | 0.303407 | + | 0.525516i | ||||
\(321\) | −14.5306 | −0.811020 | ||||||||
\(322\) | 29.1841 | + | 37.6622i | 1.62637 | + | 2.09883i | ||||
\(323\) | −0.0982407 | −0.00546626 | ||||||||
\(324\) | 9.62558 | + | 16.6720i | 0.534754 | + | 0.926221i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.4237 | + | 18.0544i | −0.577318 | + | 0.999943i | ||||
\(327\) | 8.54955 | + | 14.8082i | 0.472791 | + | 0.818898i | ||||
\(328\) | 30.1139 | 1.66276 | ||||||||
\(329\) | 0.943758 | − | 0.128805i | 0.0520310 | − | 0.00710124i | ||||
\(330\) | 4.32276 | 0.237960 | ||||||||
\(331\) | 3.29429 | + | 5.70588i | 0.181071 | + | 0.313623i | 0.942245 | − | 0.334923i | \(-0.108710\pi\) |
−0.761175 | + | 0.648547i | \(0.775377\pi\) | |||||||
\(332\) | −19.0638 | + | 33.0195i | −1.04626 | + | 1.81218i | ||||
\(333\) | 2.77875 | − | 4.81294i | 0.152275 | − | 0.263748i | ||||
\(334\) | 3.06059 | + | 5.30110i | 0.167468 | + | 0.290063i | ||||
\(335\) | −1.73073 | −0.0945599 | ||||||||
\(336\) | 0.461854 | − | 1.13015i | 0.0251962 | − | 0.0616545i | ||||
\(337\) | 4.22290 | 0.230036 | 0.115018 | − | 0.993363i | \(-0.463307\pi\) | ||||
0.115018 | + | 0.993363i | \(0.463307\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.56187 | + | 4.43728i | −0.139141 | + | 0.241000i | ||||
\(340\) | −2.90030 | + | 5.02347i | −0.157291 | + | 0.272436i | ||||
\(341\) | 5.90916 | + | 10.2350i | 0.319999 | + | 0.554254i | ||||
\(342\) | 0.0905805 | 0.00489803 | ||||||||
\(343\) | 17.0079 | − | 7.33014i | 0.918341 | − | 0.395790i | ||||
\(344\) | 27.8512 | 1.50163 | ||||||||
\(345\) | −4.88030 | − | 8.45293i | −0.262747 | − | 0.455091i | ||||
\(346\) | −22.5571 | + | 39.0700i | −1.21268 | + | 2.10042i | ||||
\(347\) | 4.54739 | − | 7.87631i | 0.244117 | − | 0.422822i | −0.717766 | − | 0.696284i | \(-0.754835\pi\) |
0.961883 | + | 0.273462i | \(0.0881687\pi\) | |||||||
\(348\) | 3.31056 | + | 5.73405i | 0.177464 | + | 0.307378i | ||||
\(349\) | 9.22053 | 0.493564 | 0.246782 | − | 0.969071i | \(-0.420627\pi\) | ||||
0.246782 | + | 0.969071i | \(0.420627\pi\) | |||||||
\(350\) | 9.87149 | − | 24.1553i | 0.527653 | − | 1.29116i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.97674 | − | 6.88792i | −0.211961 | − | 0.367127i | ||||
\(353\) | −1.07724 | + | 1.86584i | −0.0573359 | + | 0.0993087i | −0.893269 | − | 0.449523i | \(-0.851594\pi\) |
0.835933 | + | 0.548832i | \(0.184927\pi\) | |||||||
\(354\) | 2.78473 | − | 4.82330i | 0.148007 | − | 0.256356i | ||||
\(355\) | −6.02167 | − | 10.4298i | −0.319597 | − | 0.553559i | ||||
\(356\) | −57.8752 | −3.06738 | ||||||||
\(357\) | −8.00046 | + | 1.09191i | −0.423429 | + | 0.0577899i | ||||
\(358\) | −6.66410 | −0.352208 | ||||||||
\(359\) | −4.27878 | − | 7.41107i | −0.225825 | − | 0.391141i | 0.730741 | − | 0.682654i | \(-0.239175\pi\) |
−0.956567 | + | 0.291513i | \(0.905841\pi\) | |||||||
\(360\) | 1.05593 | − | 1.82892i | 0.0556521 | − | 0.0963923i | ||||
\(361\) | 9.49888 | − | 16.4525i | 0.499941 | − | 0.865923i | ||||
\(362\) | −1.57548 | − | 2.72881i | −0.0828055 | − | 0.143423i | ||||
\(363\) | 12.8769 | 0.675860 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.72896 | 0.299867 | ||||||||
\(366\) | 7.67270 | + | 13.2895i | 0.401059 | + | 0.694654i | ||||
\(367\) | −1.14912 | + | 1.99033i | −0.0599833 | + | 0.103894i | −0.894458 | − | 0.447153i | \(-0.852438\pi\) |
0.834474 | + | 0.551047i | \(0.185771\pi\) | |||||||
\(368\) | 1.22438 | − | 2.12070i | 0.0638255 | − | 0.110549i | ||||
\(369\) | 4.15368 | + | 7.19439i | 0.216232 | + | 0.374525i | ||||
\(370\) | 13.0796 | 0.679975 | ||||||||
\(371\) | −4.39468 | − | 5.67136i | −0.228160 | − | 0.294442i | ||||
\(372\) | −38.2795 | −1.98470 | ||||||||
\(373\) | −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 | ||||
\(375\) | −5.79373 | + | 10.0350i | −0.299187 | + | 0.518207i | ||||
\(376\) | −0.541073 | − | 0.937166i | −0.0279037 | − | 0.0483307i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 34.0646 | − | 4.64917i | 1.75210 | − | 0.239127i | ||||
\(379\) | 7.99093 | 0.410466 | 0.205233 | − | 0.978713i | \(-0.434205\pi\) | ||||
0.205233 | + | 0.978713i | \(0.434205\pi\) | |||||||
\(380\) | 0.0664059 | + | 0.115018i | 0.00340655 | + | 0.00590032i | ||||
\(381\) | −11.5658 | + | 20.0325i | −0.592532 | + | 1.02630i | ||||
\(382\) | 1.74271 | − | 3.01846i | 0.0891647 | − | 0.154438i | ||||
\(383\) | −14.1223 | − | 24.4605i | −0.721616 | − | 1.24988i | −0.960352 | − | 0.278791i | \(-0.910066\pi\) |
0.238736 | − | 0.971084i | \(-0.423267\pi\) | |||||||
\(384\) | 27.8870 | 1.42310 | ||||||||
\(385\) | 1.27494 | − | 3.11975i | 0.0649770 | − | 0.158997i | ||||
\(386\) | 16.0168 | 0.815233 | ||||||||
\(387\) | 3.84158 | + | 6.65381i | 0.195278 | + | 0.338232i | ||||
\(388\) | −0.704352 | + | 1.21997i | −0.0357580 | + | 0.0619347i | ||||
\(389\) | −3.84043 | + | 6.65182i | −0.194717 | + | 0.337261i | −0.946808 | − | 0.321799i | \(-0.895712\pi\) |
0.752090 | + | 0.659060i | \(0.229046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1957 | −0.819050 | ||||||||
\(392\) | −15.0186 | − | 14.7364i | −0.758556 | − | 0.744300i | ||||
\(393\) | 3.74996 | 0.189160 | ||||||||
\(394\) | −17.8241 | − | 30.8722i | −0.897964 | − | 1.55532i | ||||
\(395\) | −4.93931 | + | 8.55513i | −0.248524 | + | 0.430455i | ||||
\(396\) | −2.06008 | + | 3.56817i | −0.103523 | + | 0.179307i | ||||
\(397\) | −3.72641 | − | 6.45433i | −0.187023 | − | 0.323933i | 0.757233 | − | 0.653144i | \(-0.226551\pi\) |
−0.944256 | + | 0.329211i | \(0.893217\pi\) | |||||||
\(398\) | 15.2368 | 0.763750 | ||||||||
\(399\) | −0.0699389 | + | 0.171139i | −0.00350132 | + | 0.00856765i | ||||
\(400\) | −1.34113 | −0.0670563 | ||||||||
\(401\) | −9.09912 | − | 15.7601i | −0.454389 | − | 0.787024i | 0.544264 | − | 0.838914i | \(-0.316809\pi\) |
−0.998653 | + | 0.0518898i | \(0.983476\pi\) | |||||||
\(402\) | −3.46593 | + | 6.00316i | −0.172865 | + | 0.299411i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −15.9798 | − | 27.6778i | −0.795025 | − | 1.37702i | ||||
\(405\) | −4.93530 | −0.245237 | ||||||||
\(406\) | 8.20978 | − | 1.12048i | 0.407444 | − | 0.0556083i | ||||
\(407\) | −10.0761 | −0.499453 | ||||||||
\(408\) | 4.58681 | + | 7.94458i | 0.227081 | + | 0.393315i | ||||
\(409\) | −14.6413 | + | 25.3594i | −0.723964 | + | 1.25394i | 0.235435 | + | 0.971890i | \(0.424349\pi\) |
−0.959399 | + | 0.282053i | \(0.908985\pi\) | |||||||
\(410\) | −9.77568 | + | 16.9320i | −0.482787 | + | 0.836211i | ||||
\(411\) | −1.37371 | − | 2.37933i | −0.0677599 | − | 0.117364i | ||||
\(412\) | −32.9784 | −1.62473 | ||||||||
\(413\) | −2.65967 | − | 3.43232i | −0.130874 | − | 0.168893i | ||||
\(414\) | 14.9328 | 0.733909 | ||||||||
\(415\) | −4.88728 | − | 8.46502i | −0.239907 | − | 0.415531i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.4990 | − | 19.9169i | 0.563109 | − | 0.975334i | ||||
\(418\) | −0.0821139 | − | 0.142225i | −0.00401632 | − | 0.00695647i | ||||
\(419\) | −20.7393 | −1.01318 | −0.506591 | − | 0.862187i | \(-0.669095\pi\) | ||||
−0.506591 | + | 0.862187i | \(0.669095\pi\) | |||||||
\(420\) | 6.68630 | + | 8.62871i | 0.326258 | + | 0.421038i | ||||
\(421\) | −24.8696 | −1.21207 | −0.606036 | − | 0.795437i | \(-0.707241\pi\) | ||||
−0.606036 | + | 0.795437i | \(0.707241\pi\) | |||||||
\(422\) | 9.32165 | + | 16.1456i | 0.453771 | + | 0.785954i | ||||
\(423\) | 0.149263 | − | 0.258531i | 0.00725742 | − | 0.0125702i | ||||
\(424\) | −4.07565 | + | 7.05923i | −0.197931 | + | 0.342826i | ||||
\(425\) | 4.43497 | + | 7.68159i | 0.215128 | + | 0.372612i | ||||
\(426\) | −48.2356 | −2.33702 | ||||||||
\(427\) | 11.8540 | − | 1.61785i | 0.573657 | − | 0.0782932i | ||||
\(428\) | 32.5950 | 1.57554 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.04115 | + | 15.6597i | −0.436003 | + | 0.755179i | ||||
\(431\) | 10.5844 | − | 18.3327i | 0.509832 | − | 0.883055i | −0.490103 | − | 0.871665i | \(-0.663041\pi\) |
0.999935 | − | 0.0113906i | \(-0.00362583\pi\) | |||||||
\(432\) | −0.883489 | − | 1.53025i | −0.0425069 | − | 0.0736241i | ||||
\(433\) | −23.4296 | −1.12595 | −0.562977 | − | 0.826472i | \(-0.690344\pi\) | ||||
−0.562977 | + | 0.826472i | \(0.690344\pi\) | |||||||
\(434\) | −18.1220 | + | 44.3442i | −0.869885 | + | 2.12859i | ||||
\(435\) | −1.69741 | −0.0813848 | ||||||||
\(436\) | −19.1783 | − | 33.2178i | −0.918474 | − | 1.59084i | ||||
\(437\) | −0.185409 | + | 0.321139i | −0.00886934 | + | 0.0153621i | ||||
\(438\) | 11.4727 | − | 19.8713i | 0.548187 | − | 0.949488i | ||||
\(439\) | 6.01919 | + | 10.4256i | 0.287280 | + | 0.497584i | 0.973160 | − | 0.230131i | \(-0.0739155\pi\) |
−0.685879 | + | 0.727715i | \(0.740582\pi\) | |||||||
\(440\) | −3.82891 | −0.182536 | ||||||||
\(441\) | 1.44905 | − | 5.62067i | 0.0690025 | − | 0.267651i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.86656 | − | 13.6253i | −0.373752 | − | 0.647357i | 0.616388 | − | 0.787443i | \(-0.288595\pi\) |
−0.990139 | + | 0.140086i | \(0.955262\pi\) | |||||||
\(444\) | 16.3182 | − | 28.2640i | 0.774427 | − | 1.34135i | ||||
\(445\) | 7.41855 | − | 12.8493i | 0.351673 | − | 0.609116i | ||||
\(446\) | 18.4930 | + | 32.0308i | 0.875669 | + | 1.51670i | ||||
\(447\) | 9.37592 | 0.443466 | ||||||||
\(448\) | 12.8227 | − | 31.3768i | 0.605815 | − | 1.48242i | ||||
\(449\) | −26.0012 | −1.22707 | −0.613536 | − | 0.789667i | \(-0.710253\pi\) | ||||
−0.613536 | + | 0.789667i | \(0.710253\pi\) | |||||||
\(450\) | −4.08916 | − | 7.08263i | −0.192765 | − | 0.333878i | ||||
\(451\) | 7.53087 | − | 13.0438i | 0.354615 | − | 0.614211i | ||||
\(452\) | 5.74676 | − | 9.95369i | 0.270305 | − | 0.468182i | ||||
\(453\) | 0.489225 | + | 0.847362i | 0.0229858 | + | 0.0398125i | ||||
\(454\) | 2.98459 | 0.140074 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.210041 | 0.00983605 | ||||||||
\(457\) | −15.3979 | − | 26.6700i | −0.720284 | − | 1.24757i | −0.960886 | − | 0.276945i | \(-0.910678\pi\) |
0.240602 | − | 0.970624i | \(-0.422655\pi\) | |||||||
\(458\) | 23.9742 | − | 41.5245i | 1.12024 | − | 1.94031i | ||||
\(459\) | −5.84322 | + | 10.1208i | −0.272738 | + | 0.472396i | ||||
\(460\) | 10.9475 | + | 18.9616i | 0.510429 | + | 0.884088i | ||||
\(461\) | −34.0958 | −1.58800 | −0.794000 | − | 0.607918i | \(-0.792005\pi\) | ||||
−0.794000 | + | 0.607918i | \(0.792005\pi\) | |||||||
\(462\) | −8.26791 | − | 10.6698i | −0.384658 | − | 0.496403i | ||||
\(463\) | −1.69184 | −0.0786263 | −0.0393131 | − | 0.999227i | \(-0.512517\pi\) | ||||
−0.0393131 | + | 0.999227i | \(0.512517\pi\) | |||||||
\(464\) | −0.212926 | − | 0.368799i | −0.00988485 | − | 0.0171211i | ||||
\(465\) | 4.90674 | − | 8.49871i | 0.227544 | − | 0.394118i | ||||
\(466\) | 15.3216 | − | 26.5378i | 0.709761 | − | 1.22934i | ||||
\(467\) | −14.1762 | − | 24.5539i | −0.655996 | − | 1.13622i | −0.981643 | − | 0.190727i | \(-0.938916\pi\) |
0.325647 | − | 0.945491i | \(-0.394418\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.31027 | + | 4.27192i | 0.152854 | + | 0.197259i | ||||
\(470\) | 0.702581 | 0.0324076 | ||||||||
\(471\) | −12.2112 | − | 21.1504i | −0.562662 | − | 0.974559i | ||||
\(472\) | −2.46659 | + | 4.27226i | −0.113534 | + | 0.196647i | ||||
\(473\) | 6.96501 | − | 12.0637i | 0.320251 | − | 0.554692i | ||||
\(474\) | 19.7827 | + | 34.2647i | 0.908651 | + | 1.57383i | ||||
\(475\) | 0.203088 | 0.00931830 | ||||||||
\(476\) | 17.9466 | − | 2.44936i | 0.822581 | − | 0.112266i | ||||
\(477\) | −2.24866 | −0.102959 | ||||||||
\(478\) | −15.3918 | − | 26.6595i | −0.704007 | − | 1.21938i | ||||
\(479\) | 3.14123 | − | 5.44077i | 0.143526 | − | 0.248595i | −0.785296 | − | 0.619121i | \(-0.787489\pi\) |
0.928822 | + | 0.370526i | \(0.120822\pi\) | |||||||
\(480\) | −3.30213 | + | 5.71946i | −0.150721 | + | 0.261056i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.92128 | −0.0875117 | ||||||||
\(483\) | −11.5299 | + | 28.2134i | −0.524629 | + | 1.28375i | ||||
\(484\) | −28.8853 | −1.31297 | ||||||||
\(485\) | −0.180570 | − | 0.312757i | −0.00819927 | − | 0.0142016i | ||||
\(486\) | 9.60853 | − | 16.6425i | 0.435852 | − | 0.754917i | ||||
\(487\) | −6.50879 | + | 11.2736i | −0.294942 | + | 0.510854i | −0.974971 | − | 0.222331i | \(-0.928634\pi\) |
0.680030 | + | 0.733185i | \(0.261967\pi\) | |||||||
\(488\) | −6.79613 | − | 11.7712i | −0.307647 | − | 0.532859i | ||||
\(489\) | −13.3358 | −0.603065 | ||||||||
\(490\) | 13.1612 | − | 3.66068i | 0.594560 | − | 0.165373i | ||||
\(491\) | −12.3523 | −0.557453 | −0.278726 | − | 0.960371i | \(-0.589912\pi\) | ||||
−0.278726 | + | 0.960371i | \(0.589912\pi\) | |||||||
\(492\) | 24.3925 | + | 42.2490i | 1.09970 | + | 1.90473i | ||||
\(493\) | −1.40825 | + | 2.43916i | −0.0634244 | + | 0.109854i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.528131 | − | 0.914749i | −0.0237377 | − | 0.0411149i | ||||
\(496\) | 2.46203 | 0.110549 | ||||||||
\(497\) | −14.2264 | + | 34.8118i | −0.638143 | + | 1.56152i | ||||
\(498\) | −39.1487 | −1.75430 | ||||||||
\(499\) | −4.57670 | − | 7.92708i | −0.204881 | − | 0.354865i | 0.745214 | − | 0.666826i | \(-0.232348\pi\) |
−0.950095 | + | 0.311961i | \(0.899014\pi\) | |||||||
\(500\) | 12.9965 | − | 22.5105i | 0.581220 | − | 1.00670i | ||||
\(501\) | −1.95781 | + | 3.39102i | −0.0874684 | + | 0.151500i | ||||
\(502\) | −31.4074 | − | 54.3993i | −1.40178 | − | 2.42796i | ||||
\(503\) | 22.5037 | 1.00339 | 0.501696 | − | 0.865044i | \(-0.332710\pi\) | ||||
0.501696 | + | 0.865044i | \(0.332710\pi\) | |||||||
\(504\) | −6.53389 | + | 0.891750i | −0.291042 | + | 0.0397217i | ||||
\(505\) | 8.19329 | 0.364596 | ||||||||
\(506\) | −13.5370 | − | 23.4469i | −0.601795 | − | 1.04234i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.9443 | − | 44.9368i | 1.15109 | − | 1.99375i | ||||
\(509\) | 19.3303 | + | 33.4811i | 0.856800 | + | 1.48402i | 0.874965 | + | 0.484187i | \(0.160884\pi\) |
−0.0181646 | + | 0.999835i | \(0.505782\pi\) | |||||||
\(510\) | −5.95594 | −0.263734 | ||||||||
\(511\) | −10.9575 | − | 14.1407i | −0.484730 | − | 0.625546i | ||||
\(512\) | −3.53972 | −0.156435 | ||||||||
\(513\) | 0.133787 | + | 0.231727i | 0.00590686 | + | 0.0102310i | ||||
\(514\) | −7.54536 | + | 13.0690i | −0.332812 | + | 0.576447i | ||||
\(515\) | 4.22724 | − | 7.32179i | 0.186274 | − | 0.322637i | ||||
\(516\) | 22.5596 | + | 39.0744i | 0.993132 | + | 1.72016i | ||||
\(517\) | −0.541245 | −0.0238039 | ||||||||
\(518\) | −25.0166 | − | 32.2841i | −1.09917 | − | 1.41848i | ||||
\(519\) | −28.8588 | −1.26676 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.1176 | + | 34.8446i | −0.881366 | + | 1.52657i | −0.0315430 | + | 0.999502i | \(0.510042\pi\) |
−0.849823 | + | 0.527068i | \(0.823291\pi\) | |||||||
\(522\) | 1.29844 | − | 2.24897i | 0.0568313 | − | 0.0984348i | ||||
\(523\) | 0.366073 | + | 0.634057i | 0.0160073 | + | 0.0277254i | 0.873918 | − | 0.486073i | \(-0.161571\pi\) |
−0.857911 | + | 0.513799i | \(0.828238\pi\) | |||||||
\(524\) | −8.41189 | −0.367475 | ||||||||
\(525\) | 16.5389 | − | 2.25724i | 0.721818 | − | 0.0985142i | ||||
\(526\) | −52.0286 | −2.26856 | ||||||||
\(527\) | −8.14169 | − | 14.1018i | −0.354658 | − | 0.614285i | ||||
\(528\) | −0.346871 | + | 0.600798i | −0.0150956 | + | 0.0261464i | ||||
\(529\) | −19.0660 | + | 33.0234i | −0.828959 | + | 1.43580i | ||||
\(530\) | −2.64610 | − | 4.58319i | −0.114939 | − | 0.199081i | ||||
\(531\) | −1.36089 | −0.0590577 | ||||||||
\(532\) | 0.156887 | − | 0.383898i | 0.00680189 | − | 0.0166441i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −29.7125 | − | 51.4636i | −1.28579 | − | 2.22705i | ||||
\(535\) | −4.17809 | + | 7.23667i | −0.180635 | + | 0.312868i | ||||
\(536\) | 3.06996 | − | 5.31733i | 0.132602 | − | 0.229674i | ||||
\(537\) | −2.13146 | − | 3.69179i | −0.0919791 | − | 0.159312i | ||||
\(538\) | 36.8553 | 1.58894 | ||||||||
\(539\) | −10.1389 | + | 2.82007i | −0.436715 | + | 0.121469i | ||||
\(540\) | 15.7989 | 0.679877 | ||||||||
\(541\) | −11.8268 | − | 20.4847i | −0.508476 | − | 0.880705i | −0.999952 | − | 0.00981448i | \(-0.996876\pi\) |
0.491476 | − | 0.870891i | \(-0.336457\pi\) | |||||||
\(542\) | −10.0876 | + | 17.4722i | −0.433298 | + | 0.750494i | ||||
\(543\) | 1.00781 | − | 1.74558i | 0.0432492 | − | 0.0749099i | ||||
\(544\) | 5.47919 | + | 9.49024i | 0.234918 | + | 0.406891i | ||||
\(545\) | 9.83325 | 0.421210 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9472 | −0.553582 | −0.276791 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276791 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(548\) | 3.08149 | + | 5.33730i | 0.131635 | + | 0.227998i | ||||
\(549\) | 1.87481 | − | 3.24727i | 0.0800151 | − | 0.138590i | ||||
\(550\) | −7.41388 | + | 12.8412i | −0.316129 | + | 0.547552i | ||||
\(551\) | 0.0322436 | + | 0.0558475i | 0.00137362 | + | 0.00237918i | ||||
\(552\) | 34.6267 | 1.47381 | ||||||||
\(553\) | 30.5636 | − | 4.17134i | 1.29970 | − | 0.177384i | ||||
\(554\) | −45.8771 | −1.94913 | ||||||||
\(555\) | 4.18340 | + | 7.24585i | 0.177575 | + | 0.307569i | ||||
\(556\) | −25.7946 | + | 44.6775i | −1.09393 | + | 1.89475i | ||||
\(557\) | 3.20340 | − | 5.54845i | 0.135732 | − | 0.235096i | −0.790145 | − | 0.612921i | \(-0.789995\pi\) |
0.925877 | + | 0.377825i | \(0.123328\pi\) | |||||||
\(558\) | 7.50685 | + | 13.0023i | 0.317790 | + | 0.550429i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.430045 | − | 0.554975i | −0.0181727 | − | 0.0234520i | ||||
\(561\) | 4.58827 | 0.193717 | ||||||||
\(562\) | −16.1498 | − | 27.9723i | −0.681239 | − | 1.17994i | ||||
\(563\) | −3.66042 | + | 6.34004i | −0.154268 | + | 0.267201i | −0.932792 | − | 0.360414i | \(-0.882635\pi\) |
0.778524 | + | 0.627615i | \(0.215969\pi\) | |||||||
\(564\) | 0.876546 | − | 1.51822i | 0.0369092 | − | 0.0639287i | ||||
\(565\) | 1.47326 | + | 2.55176i | 0.0619806 | + | 0.107354i | ||||
\(566\) | 2.33226 | 0.0980324 | ||||||||
\(567\) | 9.43948 | + | 12.1817i | 0.396421 | + | 0.511583i | ||||
\(568\) | 42.7249 | 1.79270 | ||||||||
\(569\) | 2.15872 | + | 3.73901i | 0.0904981 | + | 0.156747i | 0.907721 | − | 0.419575i | \(-0.137821\pi\) |
−0.817223 | + | 0.576322i | \(0.804487\pi\) | |||||||
\(570\) | −0.0681842 | + | 0.118098i | −0.00285592 | + | 0.00494660i | ||||
\(571\) | −17.0847 | + | 29.5916i | −0.714974 | + | 1.23837i | 0.247996 | + | 0.968761i | \(0.420228\pi\) |
−0.962970 | + | 0.269610i | \(0.913105\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.22956 | 0.0931413 | ||||||||
\(574\) | 60.4903 | − | 8.25576i | 2.52482 | − | 0.344589i | ||||
\(575\) | 33.4804 | 1.39623 | ||||||||
\(576\) | −5.31166 | − | 9.20007i | −0.221319 | − | 0.383336i | ||||
\(577\) | −3.17828 | + | 5.50494i | −0.132314 | + | 0.229174i | −0.924568 | − | 0.381017i | \(-0.875574\pi\) |
0.792254 | + | 0.610191i | \(0.208907\pi\) | |||||||
\(578\) | 14.6364 | − | 25.3511i | 0.608796 | − | 1.05447i | ||||
\(579\) | 5.12283 | + | 8.87301i | 0.212898 | + | 0.368750i | ||||
\(580\) | 3.80763 | 0.158103 | ||||||||
\(581\) | −11.5464 | + | 28.2537i | −0.479025 | + | 1.17216i | ||||
\(582\) | −1.44643 | −0.0599563 | ||||||||
\(583\) | 2.03847 | + | 3.53074i | 0.0844249 | + | 0.146228i | ||||
\(584\) | −10.1620 | + | 17.6011i | −0.420507 | + | 0.728339i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.229446 | − | 0.397412i | −0.00947832 | − | 0.0164169i | ||||
\(587\) | −31.4120 | −1.29651 | −0.648256 | − | 0.761422i | \(-0.724501\pi\) | ||||
−0.648256 | + | 0.761422i | \(0.724501\pi\) | |||||||
\(588\) | 8.50954 | − | 33.0073i | 0.350927 | − | 1.36120i | ||||
\(589\) | −0.372827 | −0.0153621 | ||||||||
\(590\) | −1.60143 | − | 2.77376i | −0.0659298 | − | 0.114194i | ||||
\(591\) | 11.4018 | − | 19.7484i | 0.469006 | − | 0.812342i | ||||
\(592\) | −1.04954 | + | 1.81786i | −0.0431359 | + | 0.0747136i | ||||
\(593\) | 0.236506 | + | 0.409641i | 0.00971215 | + | 0.0168219i | 0.870841 | − | 0.491565i | \(-0.163575\pi\) |
−0.861128 | + | 0.508387i | \(0.830242\pi\) | |||||||
\(594\) | −19.5361 | −0.801575 | ||||||||
\(595\) | −1.75663 | + | 4.29842i | −0.0720146 | + | 0.176218i | ||||
\(596\) | −21.0320 | −0.861505 | ||||||||
\(597\) | 4.87335 | + | 8.44089i | 0.199453 | + | 0.345463i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.81348 | − | 8.33719i | 0.196673 | − | 0.340648i | −0.750774 | − | 0.660559i | \(-0.770320\pi\) |
0.947448 | + | 0.319910i | \(0.103653\pi\) | |||||||
\(600\) | −9.48206 | − | 16.4234i | −0.387103 | − | 0.670483i | ||||
\(601\) | −41.0799 | −1.67568 | −0.837842 | − | 0.545914i | \(-0.816183\pi\) | ||||
−0.837842 | + | 0.545914i | \(0.816183\pi\) | |||||||
\(602\) | 55.9451 | − | 7.63543i | 2.28015 | − | 0.311197i | ||||
\(603\) | 1.69379 | 0.0689765 | ||||||||
\(604\) | −1.09743 | − | 1.90080i | −0.0446537 | − | 0.0773424i | ||||
\(605\) | 3.70257 | − | 6.41304i | 0.150531 | − | 0.260727i | ||||
\(606\) | 16.4077 | − | 28.4190i | 0.666518 | − | 1.15444i | ||||
\(607\) | −9.54289 | − | 16.5288i | −0.387334 | − | 0.670882i | 0.604756 | − | 0.796411i | \(-0.293271\pi\) |
−0.992090 | + | 0.125529i | \(0.959937\pi\) | |||||||
\(608\) | 0.250905 | 0.0101755 | ||||||||
\(609\) | 3.24655 | + | 4.18969i | 0.131557 | + | 0.169775i | ||||
\(610\) | 8.82474 | 0.357303 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.83840 | − | 4.91626i | 0.114736 | − | 0.198728i | ||||
\(613\) | 19.0024 | − | 32.9131i | 0.767500 | − | 1.32935i | −0.171415 | − | 0.985199i | \(-0.554834\pi\) |
0.938915 | − | 0.344149i | \(-0.111833\pi\) | |||||||
\(614\) | −31.3249 | − | 54.2563i | −1.26417 | − | 2.18961i | ||||
\(615\) | −12.5067 | −0.504318 | ||||||||
\(616\) | 7.32335 | + | 9.45082i | 0.295066 | + | 0.380784i | ||||
\(617\) | 8.31519 | 0.334757 | 0.167378 | − | 0.985893i | \(-0.446470\pi\) | ||||
0.167378 | + | 0.985893i | \(0.446470\pi\) | |||||||
\(618\) | −16.9308 | − | 29.3250i | −0.681056 | − | 1.17962i | ||||
\(619\) | 22.2364 | − | 38.5146i | 0.893756 | − | 1.54803i | 0.0584199 | − | 0.998292i | \(-0.481394\pi\) |
0.835336 | − | 0.549739i | \(-0.185273\pi\) | |||||||
\(620\) | −11.0068 | + | 19.0643i | −0.442042 | + | 0.765640i | ||||
\(621\) | 22.0558 | + | 38.2018i | 0.885069 | + | 1.53298i | ||||
\(622\) | 62.4206 | 2.50284 | ||||||||
\(623\) | −45.9048 | + | 6.26512i | −1.83914 | + | 0.251007i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.37342 | − | 12.7711i | −0.294937 | − | 0.510845i | ||||
\(626\) | 25.4263 | − | 44.0397i | 1.01624 | − | 1.76018i | ||||
\(627\) | 0.0525269 | − | 0.0909792i | 0.00209772 | − | 0.00363336i | ||||
\(628\) | 27.3921 | + | 47.4445i | 1.09306 | + | 1.89324i | ||||
\(629\) | 13.8829 | 0.553549 | ||||||||
\(630\) | 1.61966 | − | 3.96326i | 0.0645286 | − | 0.157900i | ||||
\(631\) | 11.7524 | 0.467858 | 0.233929 | − | 0.972254i | \(-0.424842\pi\) | ||||
0.233929 | + | 0.972254i | \(0.424842\pi\) | |||||||
\(632\) | −17.5227 | − | 30.3501i | −0.697014 | − | 1.20726i | ||||
\(633\) | −5.96290 | + | 10.3280i | −0.237004 | + | 0.410503i | ||||
\(634\) | 8.14001 | − | 14.0989i | 0.323281 | − | 0.559939i | ||||
\(635\) | 6.65117 | + | 11.5202i | 0.263944 | + | 0.457164i | ||||
\(636\) | −13.2052 | −0.523620 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.70831 | −0.186404 | ||||||||
\(639\) | 5.89315 | + | 10.2072i | 0.233129 | + | 0.403792i | ||||
\(640\) | 8.01854 | − | 13.8885i | 0.316961 | − | 0.548992i | ||||
\(641\) | −5.24342 | + | 9.08186i | −0.207102 | + | 0.358712i | −0.950801 | − | 0.309804i | \(-0.899737\pi\) |
0.743698 | + | 0.668516i | \(0.233070\pi\) | |||||||
\(642\) | 16.7339 | + | 28.9840i | 0.660436 | + | 1.14391i | ||||
\(643\) | 31.2822 | 1.23365 | 0.616825 | − | 0.787101i | \(-0.288419\pi\) | ||||
0.616825 | + | 0.787101i | \(0.288419\pi\) | |||||||
\(644\) | 25.8638 | − | 63.2882i | 1.01918 | − | 2.49390i | ||||
\(645\) | −11.5669 | −0.455448 | ||||||||
\(646\) | 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 | \(-0.0104419\pi\) | |||||||
\(648\) | 8.75422 | − | 15.1627i | 0.343898 | − | 0.595649i | ||||
\(649\) | 1.23369 | + | 2.13681i | 0.0484265 | + | 0.0838772i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30.3621 | + | 4.14384i | −1.18998 | + | 0.162410i | ||||
\(652\) | 29.9148 | 1.17155 | ||||||||
\(653\) | 2.07081 | + | 3.58674i | 0.0810369 | + | 0.140360i | 0.903696 | − | 0.428176i | \(-0.140844\pi\) |
−0.822659 | + | 0.568536i | \(0.807510\pi\) | |||||||
\(654\) | 19.6919 | − | 34.1073i | 0.770014 | − | 1.33370i | ||||
\(655\) | 1.07825 | − | 1.86759i | 0.0421308 | − | 0.0729726i | ||||
\(656\) | −1.56886 | − | 2.71734i | −0.0612536 | − | 0.106094i | ||||
\(657\) | −5.60668 | −0.218738 | ||||||||
\(658\) | −1.34379 | − | 1.73417i | −0.0523863 | − | 0.0676048i | ||||
\(659\) | 21.4551 | 0.835773 | 0.417887 | − | 0.908499i | \(-0.362771\pi\) | ||||
0.417887 | + | 0.908499i | \(0.362771\pi\) | |||||||
\(660\) | −3.10144 | − | 5.37185i | −0.120723 | − | 0.209099i | ||||
\(661\) | −21.1936 | + | 36.7084i | −0.824335 | + | 1.42779i | 0.0780909 | + | 0.996946i | \(0.475118\pi\) |
−0.902426 | + | 0.430844i | \(0.858216\pi\) | |||||||
\(662\) | 7.58763 | − | 13.1422i | 0.294902 | − | 0.510785i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 34.6762 | 1.34570 | ||||||||
\(665\) | 0.0651220 | + | 0.0840403i | 0.00252532 | + | 0.00325894i | ||||
\(666\) | −12.8004 | −0.496006 | ||||||||
\(667\) | 5.31558 | + | 9.20685i | 0.205820 | + | 0.356491i | ||||
\(668\) | 4.39175 | − | 7.60673i | 0.169922 | − | 0.294313i | ||||
\(669\) | −11.8297 | + | 20.4896i | −0.457361 | + | 0.792173i | ||||
\(670\) | 1.99317 | + | 3.45226i | 0.0770027 | + | 0.133373i | ||||
\(671\) | −6.79830 | −0.262445 | ||||||||
\(672\) | 20.4330 | − | 2.78872i | 0.788222 | − | 0.107577i | ||||
\(673\) | −29.5856 | −1.14044 | −0.570220 | − | 0.821492i | \(-0.693142\pi\) | ||||
−0.570220 | + | 0.821492i | \(0.693142\pi\) | |||||||
\(674\) | −4.86323 | − | 8.42336i | −0.187324 | − | 0.324456i | ||||
\(675\) | 12.0794 | − | 20.9221i | 0.464935 | − | 0.805292i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.0830 | − | 27.8565i | −0.618118 | − | 1.07061i | −0.989829 | − | 0.142263i | \(-0.954562\pi\) |
0.371711 | − | 0.928349i | \(-0.378771\pi\) | |||||||
\(678\) | 11.8013 | 0.453227 | ||||||||
\(679\) | −0.426604 | + | 1.04389i | −0.0163716 | + | 0.0400609i | ||||
\(680\) | 5.27551 | 0.202306 | ||||||||
\(681\) | 0.954596 | + | 1.65341i | 0.0365802 | + | 0.0633587i | ||||
\(682\) | 13.6104 | − | 23.5738i | 0.521168 | − | 0.902689i | ||||
\(683\) | 4.30118 | − | 7.44986i | 0.164580 | − | 0.285061i | −0.771926 | − | 0.635712i | \(-0.780706\pi\) |
0.936506 | + | 0.350651i | \(0.114040\pi\) | |||||||
\(684\) | −0.0649885 | − | 0.112563i | −0.00248490 | − | 0.00430397i | ||||
\(685\) | −1.57997 | −0.0603674 | ||||||||
\(686\) | −34.2082 | − | 25.4838i | −1.30608 | − | 0.972978i | ||||
\(687\) | 30.6717 | 1.17020 | ||||||||
\(688\) | −1.45097 | − | 2.51316i | −0.0553179 | − | 0.0958134i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −11.2406 | + | 19.4694i | −0.427924 | + | 0.741186i | ||||
\(691\) | −10.2210 | − | 17.7033i | −0.388826 | − | 0.673466i | 0.603466 | − | 0.797388i | \(-0.293786\pi\) |
−0.992292 | + | 0.123923i | \(0.960452\pi\) | |||||||
\(692\) | 64.7359 | 2.46089 | ||||||||
\(693\) | −1.24773 | + | 3.05316i | −0.0473973 | + | 0.115980i | ||||
\(694\) | −20.9477 | −0.795164 | ||||||||
\(695\) | −6.61279 | − | 11.4537i | −0.250837 | − | 0.434463i | ||||
\(696\) | 3.01087 | − | 5.21498i | 0.114127 | − | 0.197673i | ||||
\(697\) | −10.3761 | + | 17.9719i | −0.393023 | + | 0.680736i | ||||
\(698\) | −10.6187 | − | 18.3921i | −0.401922 | − | 0.696150i | ||||
\(699\) | 19.6020 | 0.741415 | ||||||||
\(700\) | −37.1000 | + | 5.06344i | −1.40225 | + | 0.191380i | ||||
\(701\) | 25.1373 | 0.949422 | 0.474711 | − | 0.880142i | \(-0.342553\pi\) | ||||
0.474711 | + | 0.880142i | \(0.342553\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.158933 | − | 0.275280i | 0.00599427 | − | 0.0103824i | ||||
\(704\) | −9.63036 | + | 16.6803i | −0.362958 | + | 0.628661i | ||||
\(705\) | 0.224715 | + | 0.389217i | 0.00846324 | + | 0.0146588i | ||||
\(706\) | 4.96236 | 0.186761 | ||||||||
\(707\) | −15.6709 | − | 20.2233i | −0.589363 | − | 0.760576i | ||||
\(708\) | −7.99182 | −0.300351 | ||||||||
\(709\) | 14.7464 | + | 25.5416i | 0.553814 | + | 0.959234i | 0.997995 | + | 0.0632970i | \(0.0201615\pi\) |
−0.444181 | + | 0.895937i | \(0.646505\pi\) | |||||||
\(710\) | −13.8695 | + | 24.0227i | −0.520514 | + | 0.901556i | ||||
\(711\) | 4.83389 | − | 8.37254i | 0.181285 | − | 0.313995i | ||||
\(712\) | 26.3180 | + | 45.5841i | 0.986309 | + | 1.70834i | ||||
\(713\) | −61.4632 | −2.30182 | ||||||||
\(714\) | 11.3916 | + | 14.7009i | 0.426320 | + | 0.550169i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.78127 | + | 8.28140i | 0.178684 | + | 0.309491i | ||||
\(717\) | 9.84591 | − | 17.0536i | 0.367702 | − | 0.636879i | ||||
\(718\) | −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 | \(0.783681\pi\) | |||||||
\(720\) | −0.220044 | −0.00820055 | ||||||||
\(721\) | −26.1574 | + | 3.56999i | −0.974154 | + | 0.132953i | ||||
\(722\) | −43.7569 | −1.62846 | ||||||||
\(723\) | −0.614504 | − | 1.06435i | −0.0228537 | − | 0.0395837i | ||||
\(724\) | −2.26071 | + | 3.91567i | −0.0840188 | + | 0.145525i | ||||
\(725\) | 2.91120 | − | 5.04235i | 0.108119 | − | 0.187268i | ||||
\(726\) | −14.8294 | − | 25.6853i | −0.550371 | − | 0.953271i | ||||
\(727\) | −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 | ||||||||
\(730\) | −6.59766 | − | 11.4275i | −0.244190 | − | 0.422950i | ||||
\(731\) | −9.59645 | + | 16.6215i | −0.354938 | + | 0.614770i | ||||
\(732\) | 11.0098 | − | 19.0696i | 0.406935 | − | 0.704832i | ||||
\(733\) | 7.00894 | + | 12.1398i | 0.258881 | + | 0.448395i | 0.965942 | − | 0.258757i | \(-0.0833129\pi\) |
−0.707061 | + | 0.707152i | \(0.749980\pi\) | |||||||
\(734\) | 5.29344 | 0.195384 | ||||||||
\(735\) | 6.23743 | + | 6.12021i | 0.230071 | + | 0.225747i | ||||
\(736\) | 41.3635 | 1.52468 | ||||||||
\(737\) | −1.53547 | − | 2.65951i | −0.0565598 | − | 0.0979644i | ||||
\(738\) | 9.56704 | − | 16.5706i | 0.352168 | − | 0.609972i | ||||
\(739\) | 19.4073 | − | 33.6145i | 0.713910 | − | 1.23653i | −0.249468 | − | 0.968383i | \(-0.580256\pi\) |
0.963378 | − | 0.268146i | \(-0.0864108\pi\) | |||||||
\(740\) | −9.38417 | − | 16.2539i | −0.344969 | − | 0.597504i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.25153 | + | 15.2973i | −0.229501 | + | 0.561583i | ||||
\(743\) | −34.3942 | −1.26180 | −0.630901 | − | 0.775863i | \(-0.717315\pi\) | ||||
−0.630901 | + | 0.775863i | \(0.717315\pi\) | |||||||
\(744\) | 17.4071 | + | 30.1500i | 0.638175 | + | 1.10535i | ||||
\(745\) | 2.69592 | − | 4.66948i | 0.0987710 | − | 0.171076i | ||||
\(746\) | −13.5528 | + | 23.4742i | −0.496205 | + | 0.859452i | ||||
\(747\) | 4.78297 | + | 8.28434i | 0.175000 | + | 0.303108i | ||||
\(748\) | −10.2924 | −0.376327 | ||||||||
\(749\) | 25.8533 | − | 3.52848i | 0.944660 | − | 0.128928i | ||||
\(750\) | 26.6890 | 0.974545 | ||||||||
\(751\) | −24.0735 | − | 41.6965i | −0.878454 | − | 1.52153i | −0.853037 | − | 0.521850i | \(-0.825242\pi\) |
−0.0254165 | − | 0.999677i | \(-0.508091\pi\) | |||||||
\(752\) | −0.0563770 | + | 0.0976479i | −0.00205586 | + | 0.00356085i | ||||
\(753\) | 20.0908 | − | 34.7983i | 0.732150 | − | 1.26812i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.562681 | 0.0204781 | ||||||||
\(756\) | −30.2177 | − | 38.9961i | −1.09901 | − | 1.41828i | ||||
\(757\) | −6.90638 | −0.251016 | −0.125508 | − | 0.992093i | \(-0.540056\pi\) | ||||
−0.125508 | + | 0.992093i | \(0.540056\pi\) | |||||||
\(758\) | −9.20262 | − | 15.9394i | −0.334254 | − | 0.578945i | ||||
\(759\) | 8.65942 | − | 14.9986i | 0.314317 | − | 0.544413i | ||||
\(760\) | 0.0603945 | − | 0.104606i | 0.00219074 | − | 0.00379447i | ||||
\(761\) | 15.9865 | + | 27.6895i | 0.579511 | + | 1.00374i | 0.995535 | + | 0.0943888i | \(0.0300897\pi\) |
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(762\) | 53.2781 | 1.93006 | ||||||||
\(763\) | −18.8075 | − | 24.2712i | −0.680878 | − | 0.878676i | ||||
\(764\) | −5.00135 | −0.180942 | ||||||||
\(765\) | 0.727663 | + | 1.26035i | 0.0263087 | + | 0.0455680i | ||||
\(766\) | −32.5274 | + | 56.3391i | −1.17526 | + | 2.03562i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −13.2397 | − | 22.9319i | −0.477748 | − | 0.827483i | ||||
\(769\) | −14.3950 | −0.519099 | −0.259549 | − | 0.965730i | \(-0.583574\pi\) | ||||
−0.259549 | + | 0.965730i | \(0.583574\pi\) | |||||||
\(770\) | −7.69119 | + | 1.04970i | −0.277171 | + | 0.0378285i | ||||
\(771\) | −9.65328 | −0.347654 | ||||||||
\(772\) | −11.4915 | − | 19.9039i | −0.413589 | − | 0.716357i | ||||
\(773\) | −18.6385 | + | 32.2829i | −0.670382 | + | 1.16114i | 0.307414 | + | 0.951576i | \(0.400536\pi\) |
−0.977796 | + | 0.209560i | \(0.932797\pi\) | |||||||
\(774\) | 8.84818 | − | 15.3255i | 0.318041 | − | 0.550864i | ||||
\(775\) | 16.8309 | + | 29.1520i | 0.604583 | + | 1.04717i | ||||
\(776\) | 1.28118 | 0.0459917 | ||||||||
\(777\) | 9.88344 | − | 24.1845i | 0.354566 | − | 0.867616i | ||||
\(778\) | 17.6911 | 0.634255 | ||||||||
\(779\) | 0.237573 | + | 0.411489i | 0.00851194 | + | 0.0147431i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.6846 | − | 18.5063i | 0.382326 | − | 0.662208i | ||||
\(782\) | 18.6515 | + | 32.3053i | 0.666975 | + | 1.15524i | ||||
\(783\) | 7.67121 | 0.274147 | ||||||||
\(784\) | −0.547311 | + | 2.12294i | −0.0195468 | + | 0.0758193i | ||||
\(785\) | −14.0447 | −0.501276 | ||||||||
\(786\) | −4.31857 | − | 7.47999i | −0.154038 | − | 0.266802i | ||||
\(787\) | 7.17430 | − | 12.4263i | 0.255736 | − | 0.442948i | −0.709359 | − | 0.704847i | \(-0.751015\pi\) |
0.965095 | + | 0.261899i | \(0.0843488\pi\) | |||||||
\(788\) | −25.5764 | + | 44.2996i | −0.911120 | + | 1.57811i | ||||
\(789\) | −16.6409 | − | 28.8229i | −0.592432 | − | 1.02612i | ||||
\(790\) | 22.7531 | 0.809518 | ||||||||
\(791\) | 3.48064 | − | 8.51705i | 0.123757 | − | 0.302831i | ||||
\(792\) | 3.74719 | 0.133150 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −8.58291 | + | 14.8660i | −0.304596 | + | 0.527576i | ||||
\(795\) | 1.69267 | − | 2.93179i | 0.0600328 | − | 0.103980i | ||||
\(796\) | −10.9319 | − | 18.9346i | −0.387470 | − | 0.671118i | ||||
\(797\) | 11.0844 | 0.392629 | 0.196314 | − | 0.980541i | \(-0.437103\pi\) | ||||
0.196314 | + | 0.980541i | \(0.437103\pi\) | |||||||
\(798\) | 0.421912 | − | 0.0575829i | 0.0149355 | − | 0.00203841i | ||||
\(799\) | 0.745733 | 0.0263821 | ||||||||
\(800\) | −11.3268 | − | 19.6187i | −0.400464 | − | 0.693625i | ||||
\(801\) | −7.26022 | + | 12.5751i | −0.256527 | + | 0.444318i | ||||
\(802\) | −20.9577 | + | 36.2998i | −0.740042 | + | 1.28179i | ||||
\(803\) | 5.08262 | + | 8.80336i | 0.179362 | + | 0.310664i | ||||
\(804\) | 9.94676 | 0.350795 | ||||||||
\(805\) | 10.7358 | + | 13.8546i | 0.378388 | + | 0.488312i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.7878 | + | 20.4171i | 0.414952 | + | 0.718718i | ||||
\(808\) | −14.5332 | + | 25.1723i | −0.511277 | + | 0.885558i | ||||
\(809\) | 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 | ||||
\(811\) | −16.3622 | −0.574554 | −0.287277 | − | 0.957848i | \(-0.592750\pi\) | ||||
−0.287277 | + | 0.957848i | \(0.592750\pi\) | |||||||
\(812\) | −7.28265 | − | 9.39830i | −0.255571 | − | 0.329816i | ||||
\(813\) | −12.9057 | −0.452622 | ||||||||
\(814\) | 11.6040 | + | 20.0986i | 0.406719 | + | 0.704457i | ||||
\(815\) | −3.83453 | + | 6.64160i | −0.134318 | + | 0.232645i | ||||
\(816\) | 0.477922 | − | 0.827785i | 0.0167306 | − | 0.0289783i | ||||
\(817\) | 0.219722 | + | 0.380570i | 0.00768710 | + | 0.0133145i | ||||
\(818\) | 67.4455 | 2.35818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.0549 | 0.979721 | ||||||||
\(821\) | −1.55275 | − | 2.68944i | −0.0541913 | − | 0.0938621i | 0.837657 | − | 0.546196i | \(-0.183925\pi\) |
−0.891848 | + | 0.452334i | \(0.850591\pi\) | |||||||
\(822\) | −3.16401 | + | 5.48023i | −0.110358 | + | 0.191145i | ||||
\(823\) | −24.5082 | + | 42.4494i | −0.854301 | + | 1.47969i | 0.0229903 | + | 0.999736i | \(0.492681\pi\) |
−0.877292 | + | 0.479958i | \(0.840652\pi\) | |||||||
\(824\) | 14.9965 | + | 25.9747i | 0.522429 | + | 0.904873i | ||||
\(825\) | −9.48507 | −0.330228 | ||||||||
\(826\) | −3.78344 | + | 9.25799i | −0.131643 | + | 0.322127i | ||||
\(827\) | −13.0887 | −0.455140 | −0.227570 | − | 0.973762i | \(-0.573078\pi\) | ||||
−0.227570 | + | 0.973762i | \(0.573078\pi\) | |||||||
\(828\) | −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 | \(0.839994\pi\) | |||||||
\(830\) | −11.2567 | + | 19.4972i | −0.390726 | + | 0.676757i | ||||
\(831\) | −14.6734 | − | 25.4151i | −0.509015 | − | 0.881639i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.9695 | − | 3.88551i | 0.484015 | − | 0.134625i | ||||
\(834\) | −52.9706 | −1.83422 | ||||||||
\(835\) | 1.12588 | + | 1.95009i | 0.0389629 | + | 0.0674856i | ||||
\(836\) | −0.117828 | + | 0.204084i | −0.00407517 | + | 0.00705840i | ||||
\(837\) | −22.1753 | + | 38.4087i | −0.766489 | + | 1.32760i | ||||
\(838\) | 23.8841 | + | 41.3684i | 0.825062 | + | 1.42905i | ||||
\(839\) | −17.2636 | −0.596007 | −0.298004 | − | 0.954565i | \(-0.596321\pi\) | ||||
−0.298004 | + | 0.954565i | \(0.596321\pi\) | |||||||
\(840\) | 3.75570 | − | 9.19011i | 0.129584 | − | 0.317089i | ||||
\(841\) | −27.1512 | −0.936248 | ||||||||
\(842\) | 28.6407 | + | 49.6071i | 0.987024 | + | 1.70957i | ||||
\(843\) | 10.3308 | − | 17.8934i | 0.355810 | − | 0.616282i | ||||
\(844\) | 13.3760 | − | 23.1678i | 0.460419 | − | 0.797470i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.687585 | −0.0236397 | ||||||||
\(847\) | −22.9109 | + | 3.12690i | −0.787228 | + | 0.107441i | ||||
\(848\) | 0.849323 | 0.0291659 | ||||||||
\(849\) | 0.745955 | + | 1.29203i | 0.0256011 | + | 0.0443424i | ||||
\(850\) | 10.2149 | − | 17.6928i | 0.350369 | − | 0.606857i | ||||
\(851\) | 26.2012 | − | 45.3818i | 0.898166 | − | 1.55567i | ||||
\(852\) | 34.6075 | + | 59.9419i | 1.18563 | + | 2.05358i | ||||
\(853\) | −52.4163 | −1.79470 | −0.897350 | − | 0.441319i | \(-0.854511\pi\) | ||||
−0.897350 | + | 0.441319i | \(0.854511\pi\) | |||||||
\(854\) | −16.8786 | − | 21.7819i | −0.577574 | − | 0.745363i | ||||
\(855\) | 0.0333214 | 0.00113957 | ||||||||
\(856\) | −14.8222 | − | 25.6728i | −0.506611 | − | 0.877477i | ||||
\(857\) | −5.06355 | + | 8.77032i | −0.172967 | + | 0.299588i | −0.939456 | − | 0.342670i | \(-0.888669\pi\) |
0.766489 | + | 0.642258i | \(0.222002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.255118 | + | 0.441878i | 0.00870452 | + | 0.0150767i | 0.870345 | − | 0.492443i | \(-0.163896\pi\) |
−0.861640 | + | 0.507519i | \(0.830563\pi\) | |||||||
\(860\) | 25.9469 | 0.884782 | ||||||||
\(861\) | 23.9209 | + | 30.8700i | 0.815220 | + | 1.05205i | ||||
\(862\) | −48.7573 | −1.66068 | ||||||||
\(863\) | 10.2495 | + | 17.7527i | 0.348898 | + | 0.604310i | 0.986054 | − | 0.166426i | \(-0.0532225\pi\) |
−0.637156 | + | 0.770735i | \(0.719889\pi\) | |||||||
\(864\) | 14.9235 | − | 25.8482i | 0.507707 | − | 0.879375i | ||||
\(865\) | −8.29797 | + | 14.3725i | −0.282139 | + | 0.488680i | ||||
\(866\) | 26.9823 | + | 46.7347i | 0.916896 | + | 1.58811i | ||||
\(867\) | 18.7254 | 0.635947 | ||||||||
\(868\) | 68.1080 | − | 9.29543i | 2.31174 | − | 0.315508i | ||||
\(869\) | −17.5282 | −0.594605 | ||||||||
\(870\) | 1.95480 | + | 3.38581i | 0.0662739 | + | 0.114790i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17.4422 | + | 30.2107i | −0.590667 | + | 1.02306i | ||||
\(873\) | 0.176716 | + | 0.306082i | 0.00598094 | + | 0.0103593i | ||||
\(874\) | 0.854095 | 0.0288902 | ||||||||
\(875\) | 7.87157 | − | 19.2615i | 0.266108 | − | 0.651159i | ||||
\(876\) | −32.9252 | −1.11244 | ||||||||
\(877\) | −5.64530 | − | 9.77794i | −0.190628 | − | 0.330178i | 0.754830 | − | 0.655920i | \(-0.227719\pi\) |
−0.945459 | + | 0.325742i | \(0.894386\pi\) | |||||||
\(878\) | 13.8638 | − | 24.0128i | 0.467881 | − | 0.810394i | ||||
\(879\) | 0.146773 | − | 0.254218i | 0.00495052 | − | 0.00857455i | ||||
\(880\) | 0.199476 | + | 0.345503i | 0.00672435 | + | 0.0116469i | ||||
\(881\) | 22.5268 | 0.758947 | 0.379474 | − | 0.925203i | \(-0.376105\pi\) | ||||
0.379474 | + | 0.925203i | \(0.376105\pi\) | |||||||
\(882\) | −12.8803 | + | 3.58255i | −0.433701 | + | 0.120631i | ||||
\(883\) | 28.0268 | 0.943178 | 0.471589 | − | 0.881819i | \(-0.343681\pi\) | ||||
0.471589 | + | 0.881819i | \(0.343681\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.02441 | − | 1.77432i | 0.0344351 | − | 0.0596433i | ||||
\(886\) | −18.1188 | + | 31.3827i | −0.608713 | + | 1.05432i | ||||
\(887\) | 10.3118 | + | 17.8605i | 0.346235 | + | 0.599696i | 0.985577 | − | 0.169226i | \(-0.0541267\pi\) |
−0.639342 | + | 0.768922i | \(0.720793\pi\) | |||||||
\(888\) | −29.6820 | −0.996062 | ||||||||
\(889\) | 15.7137 | − | 38.4509i | 0.527019 | − | 1.28960i | ||||
\(890\) | −34.1738 | −1.14551 | ||||||||
\(891\) | −4.37850 | − | 7.58379i | −0.146685 | − | 0.254066i | ||||
\(892\) | 26.5362 | − | 45.9621i | 0.888499 | − | 1.53893i | ||||
\(893\) | 0.00853722 | − | 0.0147869i | 0.000285687 | − | 0.000494824i | ||||
\(894\) | −10.7976 | − | 18.7020i | −0.361127 | − | 0.625490i | ||||
\(895\) | −2.45149 | −0.0819443 | ||||||||
\(896\) | −49.6174 | + | 6.77181i | −1.65760 | + | 0.226230i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.9438 | + | 51.8642i | 0.999238 | + | 1.73073i | ||||
\(899\) | −5.34437 | + | 9.25671i | −0.178245 | + | 0.308729i | ||||
\(900\) | −5.86767 | + | 10.1631i | −0.195589 | + | 0.338770i | ||||
\(901\) | −2.80863 | − | 4.86468i | −0.0935689 | − | 0.162066i | ||||
\(902\) | −34.6912 | −1.15509 | ||||||||
\(903\) | 22.1235 | + | 28.5504i | 0.736223 | + | 0.950099i | ||||
\(904\) | −10.4531 | −0.347664 | ||||||||
\(905\) | −0.579565 | − | 1.00384i | −0.0192654 | − | 0.0333686i | ||||
\(906\) | 1.12681 | − | 1.95170i | 0.0374359 | − | 0.0648409i | ||||
\(907\) | −20.7315 | + | 35.9081i | −0.688379 | + | 1.19231i | 0.283982 | + | 0.958829i | \(0.408344\pi\) |
−0.972362 | + | 0.233479i | \(0.924989\pi\) | |||||||
\(908\) | −2.14134 | − | 3.70892i | −0.0710630 | − | 0.123085i | ||||
\(909\) | −8.01841 | −0.265954 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.8187 | 1.35239 | 0.676193 | − | 0.736725i | \(-0.263629\pi\) | ||||
0.676193 | + | 0.736725i | \(0.263629\pi\) | |||||||
\(912\) | −0.0109426 | − | 0.0189531i | −0.000362345 | − | 0.000627600i | ||||
\(913\) | 8.67180 | − | 15.0200i | 0.286995 | − | 0.497090i | ||||
\(914\) | −35.4655 | + | 61.4280i | −1.17309 | + | 2.03186i | ||||
\(915\) | 2.82252 | + | 4.88875i | 0.0933096 | + | 0.161617i | ||||
\(916\) | −68.8027 | −2.27331 | ||||||||
\(917\) | −6.67204 | + | 0.910605i | −0.220330 | + | 0.0300708i | ||||
\(918\) | 26.9170 | 0.888393 | ||||||||
\(919\) | 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 | ||||
\(921\) | 20.0380 | − | 34.7068i | 0.660274 | − | 1.14363i | ||||
\(922\) | 39.2659 | + | 68.0105i | 1.29315 | + | 2.23981i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −7.32728 | + | 17.9297i | −0.241050 | + | 0.589843i | ||||
\(925\) | −28.6994 | −0.943631 | ||||||||
\(926\) | 1.94837 | + | 3.37468i | 0.0640275 | + | 0.110899i | ||||
\(927\) | −4.13701 | + | 7.16552i | −0.135877 | + | 0.235346i | ||||
\(928\) | 3.59665 | − | 6.22958i | 0.118066 | − | 0.204496i | ||||
\(929\) | −14.6915 | − | 25.4464i | −0.482012 | − | 0.834868i | 0.517775 | − | 0.855517i | \(-0.326760\pi\) |
−0.999787 | + | 0.0206482i | \(0.993427\pi\) | |||||||
\(930\) | −22.6030 | −0.741183 | ||||||||
\(931\) | 0.0828796 | − | 0.321479i | 0.00271627 | − | 0.0105360i | ||||
\(932\) | −43.9711 | −1.44032 | ||||||||
\(933\) | 19.9647 | + | 34.5799i | 0.653615 | + | 1.13210i | ||||
\(934\) | −32.6515 | + | 56.5541i | −1.06839 | + | 1.85051i | ||||
\(935\) | 1.31930 | − | 2.28509i | 0.0431456 | − | 0.0747304i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0196 | −0.686681 | −0.343340 | − | 0.939211i | \(-0.611558\pi\) | ||||
−0.343340 | + | 0.939211i | \(0.611558\pi\) | |||||||
\(938\) | 4.70893 | − | 11.5226i | 0.153752 | − | 0.376228i | ||||
\(939\) | 32.5296 | 1.06156 | ||||||||
\(940\) | −0.504079 | − | 0.873090i | −0.0164412 | − | 0.0284770i | ||||
\(941\) | −12.0516 | + | 20.8740i | −0.392872 | + | 0.680474i | −0.992827 | − | 0.119560i | \(-0.961852\pi\) |
0.599955 | + | 0.800034i | \(0.295185\pi\) | |||||||
\(942\) | −28.1256 | + | 48.7150i | −0.916383 | + | 1.58722i | ||||
\(943\) | 39.1656 | + | 67.8368i | 1.27541 | + | 2.20907i | ||||
\(944\) | 0.514013 | 0.0167297 | ||||||||
\(945\) | 12.5312 | − | 1.71027i | 0.407640 | − | 0.0556350i | ||||
\(946\) | −32.0845 | −1.04316 | ||||||||
\(947\) | −1.67023 | − | 2.89292i | −0.0542751 | − | 0.0940072i | 0.837611 | − | 0.546267i | \(-0.183951\pi\) |
−0.891886 | + | 0.452259i | \(0.850618\pi\) | |||||||
\(948\) | 28.3869 | − | 49.1676i | 0.921965 | − | 1.59689i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.233883 | − | 0.405097i | −0.00758815 | − | 0.0131431i | ||||
\(951\) | 10.4141 | 0.337699 | ||||||||
\(952\) | −10.0902 | − | 13.0214i | −0.327024 | − | 0.422027i | ||||
\(953\) | −4.97124 | −0.161034 | −0.0805171 | − | 0.996753i | \(-0.525657\pi\) | ||||
−0.0805171 | + | 0.996753i | \(0.525657\pi\) | |||||||
\(954\) | 2.58963 | + | 4.48537i | 0.0838423 | + | 0.145219i | ||||
\(955\) | 0.641082 | − | 1.11039i | 0.0207449 | − | 0.0359313i | ||||
\(956\) | −22.0863 | + | 38.2546i | −0.714322 | + | 1.23724i | ||||
\(957\) | −1.50591 | − | 2.60832i | −0.0486793 | − | 0.0843150i | ||||
\(958\) | −14.4702 | −0.467510 | ||||||||
\(959\) | 3.02191 | + | 3.89980i | 0.0975827 | + | 0.125931i | ||||
\(960\) | 15.9933 | 0.516183 | ||||||||
\(961\) | −15.3981 | − | 26.6702i | −0.496711 | − | 0.860329i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.08892 | − | 7.08221i | 0.131763 | − | 0.228221i | ||||
\(964\) | 1.37845 | + | 2.38755i | 0.0443970 | + | 0.0768978i | ||||
\(965\) | 5.89202 | 0.189671 | ||||||||
\(966\) | 69.5552 | − | 9.49294i | 2.23790 | − | 0.305430i | ||||
\(967\) | −47.4943 | −1.52731 | −0.763657 | − | 0.645623i | \(-0.776598\pi\) | ||||
−0.763657 | + | 0.645623i | \(0.776598\pi\) | |||||||
\(968\) | 13.1352 | + | 22.7509i | 0.422182 | + | 0.731241i | ||||
\(969\) | −0.0723720 | + | 0.125352i | −0.00232492 | + | 0.00402689i | ||||
\(970\) | −0.415901 | + | 0.720362i | −0.0133538 | + | 0.0231294i | ||||
\(971\) | −17.2357 | − | 29.8532i | −0.553121 | − | 0.958033i | −0.998047 | − | 0.0624662i | \(-0.980103\pi\) |
0.444926 | − | 0.895567i | \(-0.353230\pi\) | |||||||
\(972\) | −27.5752 | −0.884476 | ||||||||
\(973\) | −15.6230 | + | 38.2291i | −0.500850 | + | 1.22557i | ||||
\(974\) | 29.9830 | 0.960717 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.708122 | + | 1.22650i | −0.0226664 | + | 0.0392594i | ||||
\(977\) | −6.67406 | + | 11.5598i | −0.213522 | + | 0.369831i | −0.952814 | − | 0.303553i | \(-0.901827\pi\) |
0.739292 | + | 0.673385i | \(0.235160\pi\) | |||||||
\(978\) | 15.3579 | + | 26.6007i | 0.491093 | + | 0.850597i | ||||
\(979\) | 26.3264 | 0.841395 | ||||||||
\(980\) | −13.9918 | − | 13.7288i | −0.446951 | − | 0.438551i | ||||
\(981\) | −9.62337 | −0.307251 | ||||||||
\(982\) | 14.2253 | + | 24.6390i | 0.453949 | + | 0.786263i | ||||
\(983\) | 6.26720 | − | 10.8551i | 0.199893 | − | 0.346224i | −0.748601 | − | 0.663021i | \(-0.769274\pi\) |
0.948493 | + | 0.316797i | \(0.102607\pi\) | |||||||
\(984\) | 22.1843 | − | 38.4244i | 0.707210 | − | 1.22492i | ||||
\(985\) | −6.55685 | − | 11.3568i | −0.208919 | − | 0.361858i | ||||
\(986\) | 6.48715 | 0.206593 | ||||||||
\(987\) | 0.530897 | − | 1.29909i | 0.0168986 | − | 0.0413506i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.2227 | + | 62.7396i | 1.15182 | + | 1.99500i | ||||
\(990\) | −1.21643 | + | 2.10691i | −0.0386605 | + | 0.0669620i | ||||
\(991\) | 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 | ||||
\(993\) | 9.70736 | 0.308054 | ||||||||
\(994\) | 85.8223 | − | 11.7131i | 2.72212 | − | 0.371517i | ||||
\(995\) | 5.60508 | 0.177693 | ||||||||
\(996\) | 28.0879 | + | 48.6497i | 0.890000 | + | 1.54153i | ||||
\(997\) | −2.87635 | + | 4.98198i | −0.0910949 | + | 0.157781i | −0.907972 | − | 0.419031i | \(-0.862370\pi\) |
0.816877 | + | 0.576812i | \(0.195703\pi\) | |||||||
\(998\) | −10.5414 | + | 18.2582i | −0.333681 | + | 0.577953i | ||||
\(999\) | −18.9062 | − | 32.7465i | −0.598167 | − | 1.03605i |
(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 | 1183.2.e.j.508.2 | 24 | ||
7.2 | even | 3 | inner | 1183.2.e.j.170.2 | 24 | ||
7.3 | odd | 6 | 8281.2.a.co.1.11 | 12 | |||
7.4 | even | 3 | 8281.2.a.cp.1.11 | 12 | |||
13.6 | odd | 12 | 91.2.u.b.88.6 | yes | 12 | ||
13.11 | odd | 12 | 91.2.k.b.4.6 | ✓ | 12 | ||
13.12 | even | 2 | inner | 1183.2.e.j.508.11 | 24 | ||
39.11 | even | 12 | 819.2.bm.f.550.1 | 12 | |||
39.32 | even | 12 | 819.2.do.e.361.1 | 12 | |||
91.6 | even | 12 | 637.2.u.g.361.6 | 12 | |||
91.11 | odd | 12 | 637.2.q.g.589.1 | 12 | |||
91.19 | even | 12 | 637.2.k.i.569.1 | 12 | |||
91.24 | even | 12 | 637.2.q.i.589.1 | 12 | |||
91.25 | even | 6 | 8281.2.a.cp.1.2 | 12 | |||
91.32 | odd | 12 | 637.2.q.g.491.1 | 12 | |||
91.37 | odd | 12 | 91.2.u.b.30.6 | yes | 12 | ||
91.38 | odd | 6 | 8281.2.a.co.1.2 | 12 | |||
91.45 | even | 12 | 637.2.q.i.491.1 | 12 | |||
91.51 | even | 6 | inner | 1183.2.e.j.170.11 | 24 | ||
91.58 | odd | 12 | 91.2.k.b.23.1 | yes | 12 | ||
91.76 | even | 12 | 637.2.k.i.459.6 | 12 | |||
91.89 | even | 12 | 637.2.u.g.30.6 | 12 | |||
273.128 | even | 12 | 819.2.do.e.667.1 | 12 | |||
273.149 | even | 12 | 819.2.bm.f.478.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.6 | ✓ | 12 | 13.11 | odd | 12 | ||
91.2.k.b.23.1 | yes | 12 | 91.58 | odd | 12 | ||
91.2.u.b.30.6 | yes | 12 | 91.37 | odd | 12 | ||
91.2.u.b.88.6 | yes | 12 | 13.6 | odd | 12 | ||
637.2.k.i.459.6 | 12 | 91.76 | even | 12 | |||
637.2.k.i.569.1 | 12 | 91.19 | even | 12 | |||
637.2.q.g.491.1 | 12 | 91.32 | odd | 12 | |||
637.2.q.g.589.1 | 12 | 91.11 | odd | 12 | |||
637.2.q.i.491.1 | 12 | 91.45 | even | 12 | |||
637.2.q.i.589.1 | 12 | 91.24 | even | 12 | |||
637.2.u.g.30.6 | 12 | 91.89 | even | 12 | |||
637.2.u.g.361.6 | 12 | 91.6 | even | 12 | |||
819.2.bm.f.478.6 | 12 | 273.149 | even | 12 | |||
819.2.bm.f.550.1 | 12 | 39.11 | even | 12 | |||
819.2.do.e.361.1 | 12 | 39.32 | even | 12 | |||
819.2.do.e.667.1 | 12 | 273.128 | even | 12 | |||
1183.2.e.j.170.2 | 24 | 7.2 | even | 3 | inner | ||
1183.2.e.j.170.11 | 24 | 91.51 | even | 6 | inner | ||
1183.2.e.j.508.2 | 24 | 1.1 | even | 1 | trivial | ||
1183.2.e.j.508.11 | 24 | 13.12 | even | 2 | inner | ||
8281.2.a.co.1.2 | 12 | 91.38 | odd | 6 | |||
8281.2.a.co.1.11 | 12 | 7.3 | odd | 6 | |||
8281.2.a.cp.1.2 | 12 | 91.25 | even | 6 | |||
8281.2.a.cp.1.11 | 12 | 7.4 | even | 3 |