Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [875,2,Mod(82,875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(875, base_ring=CyclotomicField(60))
chi = DirichletCharacter(H, H._module([27, 50]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("875.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 875 = 5^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 875.bb (of order \(60\), degree \(16\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.98691017686\) |
Analytic rank: | \(0\) |
Dimension: | \(288\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{60})\) |
Twist minimal: | no (minimal twist has level 175) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{60}]$ |
Embedding invariants
Embedding label | 243.9 | ||
Character | \(\chi\) | \(=\) | 875.243 |
Dual form | 875.2.bb.a.857.9 |
$q$-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 \(\left(\mathbb{Z}/875\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(626\) |
\(\chi(n)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0171512 | 0.000898858i | 0.0121278 | 0.000635588i | 0.0583989 | − | 0.998293i | \(-0.481400\pi\) | ||
−0.0462711 | + | 0.998929i | \(0.514734\pi\) | |||||||
\(3\) | −0.711812 | − | 0.879015i | −0.410965 | − | 0.507499i | 0.529070 | − | 0.848578i | \(-0.322541\pi\) |
−0.940035 | + | 0.341079i | \(0.889208\pi\) | |||||||
\(4\) | −1.98875 | − | 0.209026i | −0.994375 | − | 0.104513i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.0114183 | − | 0.0157160i | −0.00466152 | − | 0.00641603i | ||||
\(7\) | 0.822022 | − | 2.51481i | 0.310695 | − | 0.950510i | ||||
\(8\) | −0.0678483 | − | 0.0107461i | −0.0239880 | − | 0.00379932i | ||||
\(9\) | 0.357745 | − | 1.68306i | 0.119248 | − | 0.561019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.96090 | + | 1.05447i | −1.49577 | + | 0.317935i | −0.881886 | − | 0.471463i | \(-0.843726\pi\) |
−0.613882 | + | 0.789398i | \(0.710393\pi\) | |||||||
\(12\) | 1.23188 | + | 1.89693i | 0.355613 | + | 0.547596i | ||||
\(13\) | −0.286147 | − | 0.145799i | −0.0793630 | − | 0.0404375i | 0.413859 | − | 0.910341i | \(-0.364181\pi\) |
−0.493222 | + | 0.869904i | \(0.664181\pi\) | |||||||
\(14\) | 0.0163592 | − | 0.0423932i | 0.00437217 | − | 0.0113301i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.91086 | + | 0.831279i | 0.977715 | + | 0.207820i | ||||
\(17\) | 1.33924 | + | 3.48884i | 0.324814 | + | 0.846169i | 0.994616 | + | 0.103629i | \(0.0330455\pi\) |
−0.669802 | + | 0.742540i | \(0.733621\pi\) | |||||||
\(18\) | 0.00764859 | − | 0.0285449i | 0.00180279 | − | 0.00672810i | ||||
\(19\) | −0.698358 | − | 6.64443i | −0.160214 | − | 1.52434i | −0.718991 | − | 0.695019i | \(-0.755396\pi\) |
0.558777 | − | 0.829318i | \(-0.311271\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.79568 | + | 1.06750i | −0.610068 | + | 0.232948i | ||||
\(22\) | −0.0860334 | + | 0.0136263i | −0.0183424 | + | 0.00290515i | ||||
\(23\) | −0.178896 | + | 3.41354i | −0.0373024 | + | 0.711772i | 0.914412 | + | 0.404786i | \(0.132654\pi\) |
−0.951714 | + | 0.306986i | \(0.900679\pi\) | |||||||
\(24\) | 0.0388492 | + | 0.0672888i | 0.00793006 | + | 0.0137353i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.00477673 | − | 0.00275784i | −0.000936793 | − | 0.000540858i | ||||
\(27\) | −4.75748 | + | 2.42406i | −0.915577 | + | 0.466510i | ||||
\(28\) | −2.16046 | + | 4.82951i | −0.408288 | + | 0.912691i | ||||
\(29\) | −1.99592 | + | 2.74715i | −0.370633 | + | 0.510133i | −0.953073 | − | 0.302741i | \(-0.902098\pi\) |
0.582440 | + | 0.812874i | \(0.302098\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.305449 | − | 0.686049i | 0.0548602 | − | 0.123218i | −0.884036 | − | 0.467420i | \(-0.845184\pi\) |
0.938896 | + | 0.344202i | \(0.111850\pi\) | |||||||
\(32\) | 0.199035 | + | 0.0533314i | 0.0351848 | + | 0.00942775i | ||||
\(33\) | 4.45813 | + | 3.61012i | 0.776060 | + | 0.628441i | ||||
\(34\) | 0.0198337 | + | 0.0610417i | 0.00340145 | + | 0.0104686i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.06327 | + | 3.27240i | −0.177211 | + | 0.545400i | ||||
\(37\) | −2.76416 | + | 1.79507i | −0.454426 | + | 0.295107i | −0.751483 | − | 0.659752i | \(-0.770661\pi\) |
0.297058 | + | 0.954860i | \(0.403995\pi\) | |||||||
\(38\) | −0.00600530 | − | 0.114588i | −0.000974188 | − | 0.0185886i | ||||
\(39\) | 0.0755233 | + | 0.355309i | 0.0120934 | + | 0.0568950i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.88534 | + | 2.56210i | −1.23148 | + | 0.400133i | −0.851252 | − | 0.524758i | \(-0.824156\pi\) |
−0.380232 | + | 0.924891i | \(0.624156\pi\) | |||||||
\(42\) | −0.0489089 | + | 0.0157961i | −0.00754681 | + | 0.00243739i | ||||
\(43\) | 3.99562 | + | 3.99562i | 0.609326 | + | 0.609326i | 0.942770 | − | 0.333444i | \(-0.108211\pi\) |
−0.333444 | + | 0.942770i | \(0.608211\pi\) | |||||||
\(44\) | 10.0864 | − | 1.06012i | 1.52058 | − | 0.159820i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.00613657 | + | 0.0583856i | −0.000904788 | + | 0.00860849i | ||||
\(47\) | 5.87681 | + | 2.25590i | 0.857221 | + | 0.329056i | 0.746978 | − | 0.664849i | \(-0.231504\pi\) |
0.110242 | + | 0.993905i | \(0.464837\pi\) | |||||||
\(48\) | −2.05309 | − | 4.02942i | −0.296338 | − | 0.581596i | ||||
\(49\) | −5.64856 | − | 4.13446i | −0.806937 | − | 0.590638i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.11346 | − | 3.66061i | 0.295943 | − | 0.512588i | ||||
\(52\) | 0.538600 | + | 0.349771i | 0.0746903 | + | 0.0485045i | ||||
\(53\) | −8.77763 | + | 7.10798i | −1.20570 | + | 0.976356i | −0.999997 | − | 0.00225825i | \(-0.999281\pi\) |
−0.205702 | + | 0.978615i | \(0.565948\pi\) | |||||||
\(54\) | −0.0837755 | + | 0.0372993i | −0.0114004 | + | 0.00507579i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.0827972 | + | 0.161792i | −0.0110642 | + | 0.0216204i | ||||
\(57\) | −5.34345 | + | 5.34345i | −0.707757 | + | 0.707757i | ||||
\(58\) | −0.0367018 | + | 0.0453229i | −0.00481918 | + | 0.00595119i | ||||
\(59\) | −6.39870 | + | 7.10647i | −0.833039 | + | 0.925184i | −0.998132 | − | 0.0610943i | \(-0.980541\pi\) |
0.165093 | + | 0.986278i | \(0.447208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.03745 | + | 1.83453i | −0.260869 | + | 0.234887i | −0.789178 | − | 0.614165i | \(-0.789493\pi\) |
0.528309 | + | 0.849052i | \(0.322826\pi\) | |||||||
\(62\) | 0.00585548 | − | 0.0114920i | 0.000743647 | − | 0.00145949i | ||||
\(63\) | −3.93850 | − | 2.28317i | −0.496204 | − | 0.287652i | ||||
\(64\) | −7.60172 | − | 2.46995i | −0.950215 | − | 0.308744i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0732173 | + | 0.0659252i | 0.00901243 | + | 0.00811483i | ||||
\(67\) | 6.09544 | − | 2.33982i | 0.744676 | − | 0.285854i | 0.0437055 | − | 0.999044i | \(-0.486084\pi\) |
0.700971 | + | 0.713190i | \(0.252750\pi\) | |||||||
\(68\) | −1.93416 | − | 7.21837i | −0.234551 | − | 0.875357i | ||||
\(69\) | 3.12789 | − | 2.27255i | 0.376554 | − | 0.273582i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.66851 | − | 2.66533i | −0.435372 | − | 0.316316i | 0.348422 | − | 0.937338i | \(-0.386718\pi\) |
−0.783793 | + | 0.621022i | \(0.786718\pi\) | |||||||
\(72\) | −0.0423587 | + | 0.110348i | −0.00499202 | + | 0.0130046i | ||||
\(73\) | −5.50292 | + | 8.47376i | −0.644069 | + | 0.991779i | 0.354325 | + | 0.935122i | \(0.384711\pi\) |
−0.998394 | + | 0.0566564i | \(0.981956\pi\) | |||||||
\(74\) | −0.0490223 | + | 0.0283030i | −0.00569873 | + | 0.00329016i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.3601i | 1.53251i | ||||||||
\(77\) | −1.42617 | + | 13.3425i | −0.162528 | + | 1.52052i | ||||
\(78\) | 0.000975946 | 0.00616188i | 0.000110504 | 0.000697695i | ||||||
\(79\) | −3.33735 | − | 7.49580i | −0.375481 | − | 0.843344i | −0.998147 | − | 0.0608557i | \(-0.980617\pi\) |
0.622666 | − | 0.782488i | \(-0.286050\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.801517 | + | 0.356859i | 0.0890575 | + | 0.0396510i | ||||
\(82\) | −0.137546 | + | 0.0368554i | −0.0151894 | + | 0.00407000i | ||||
\(83\) | 0.203179 | − | 1.28282i | 0.0223018 | − | 0.140808i | −0.974025 | − | 0.226441i | \(-0.927291\pi\) |
0.996327 | + | 0.0856324i | \(0.0272911\pi\) | |||||||
\(84\) | 5.78305 | − | 1.53863i | 0.630983 | − | 0.167878i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.0649383 | + | 0.0721212i | 0.00700247 | + | 0.00777703i | ||||
\(87\) | 3.83550 | − | 0.201010i | 0.411209 | − | 0.0215506i | ||||
\(88\) | 0.347920 | − | 0.0182337i | 0.0370884 | − | 0.00194372i | ||||
\(89\) | 0.663356 | + | 0.736732i | 0.0703156 | + | 0.0780934i | 0.777276 | − | 0.629160i | \(-0.216601\pi\) |
−0.706960 | + | 0.707253i | \(0.749934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.601877 | + | 0.599756i | −0.0630939 | + | 0.0628715i | ||||
\(92\) | 1.06930 | − | 6.75128i | 0.111482 | − | 0.703870i | ||||
\(93\) | −0.820470 | + | 0.219844i | −0.0850787 | + | 0.0227968i | ||||
\(94\) | 0.0987668 | + | 0.0439738i | 0.0101870 | + | 0.00453555i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.0947968 | − | 0.212917i | −0.00967515 | − | 0.0217308i | ||||
\(97\) | 1.94322 | + | 12.2690i | 0.197304 | + | 1.24573i | 0.865183 | + | 0.501457i | \(0.167202\pi\) |
−0.667879 | + | 0.744270i | \(0.732798\pi\) | |||||||
\(98\) | −0.0931634 | − | 0.0759884i | −0.00941093 | − | 0.00767599i | ||||
\(99\) | 8.72671i | 0.877067i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1944 | − | 5.88575i | 1.01438 | − | 0.585654i | 0.101911 | − | 0.994794i | \(-0.467504\pi\) |
0.912472 | + | 0.409139i | \(0.134171\pi\) | |||||||
\(102\) | 0.0395387 | − | 0.0608843i | 0.00391492 | − | 0.00602845i | ||||
\(103\) | 5.28346 | − | 13.7639i | 0.520595 | − | 1.35620i | −0.381384 | − | 0.924417i | \(-0.624552\pi\) |
0.901979 | − | 0.431780i | \(-0.142114\pi\) | |||||||
\(104\) | 0.0178478 | + | 0.0129672i | 0.00175012 | + | 0.00127154i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.156936 | + | 0.114021i | −0.0152430 | + | 0.0110747i | ||||
\(107\) | −2.68589 | − | 10.0239i | −0.259655 | − | 0.969046i | −0.965441 | − | 0.260621i | \(-0.916073\pi\) |
0.705786 | − | 0.708425i | \(-0.250594\pi\) | |||||||
\(108\) | 9.96813 | − | 3.82641i | 0.959184 | − | 0.368196i | ||||
\(109\) | 6.76285 | + | 6.08930i | 0.647763 | + | 0.583249i | 0.926120 | − | 0.377229i | \(-0.123123\pi\) |
−0.278357 | + | 0.960478i | \(0.589790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.54546 | + | 1.15199i | 0.336520 | + | 0.109342i | ||||
\(112\) | 5.30532 | − | 9.15175i | 0.501306 | − | 0.864759i | ||||
\(113\) | 3.87378 | − | 7.60273i | 0.364415 | − | 0.715204i | −0.633889 | − | 0.773424i | \(-0.718542\pi\) |
0.998304 | + | 0.0582196i | \(0.0185424\pi\) | |||||||
\(114\) | −0.0964498 | + | 0.0868438i | −0.00903335 | + | 0.00813366i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.54361 | − | 5.04619i | 0.421864 | − | 0.468527i | ||||
\(117\) | −0.347756 | + | 0.429443i | −0.0321501 | + | 0.0397020i | ||||
\(118\) | −0.116133 | + | 0.116133i | −0.0106909 | + | 0.0106909i | ||||
\(119\) | 9.87467 | − | 0.500033i | 0.905210 | − | 0.0458379i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.4496 | − | 5.98816i | 1.22269 | − | 0.544378i | ||||
\(122\) | −0.0365938 | + | 0.0296330i | −0.00331304 | + | 0.00268285i | ||||
\(123\) | 7.86501 | + | 5.10760i | 0.709164 | + | 0.460536i | ||||
\(124\) | −0.750864 | + | 1.30053i | −0.0674296 | + | 0.116791i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.0654978 | − | 0.0426993i | −0.00583501 | − | 0.00380396i | ||||
\(127\) | −7.32616 | − | 14.3784i | −0.650091 | − | 1.27588i | −0.947081 | − | 0.320996i | \(-0.895983\pi\) |
0.296989 | − | 0.954881i | \(-0.404017\pi\) | |||||||
\(128\) | −0.512900 | − | 0.196884i | −0.0453344 | − | 0.0174022i | ||||
\(129\) | 0.668078 | − | 6.35633i | 0.0588210 | − | 0.559644i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.96375 | + | 0.311503i | −0.258944 | + | 0.0272161i | −0.233111 | − | 0.972450i | \(-0.574891\pi\) |
−0.0258332 | + | 0.999666i | \(0.508224\pi\) | |||||||
\(132\) | −8.11149 | − | 8.11149i | −0.706015 | − | 0.706015i | ||||
\(133\) | −17.2836 | − | 3.70563i | −1.49867 | − | 0.321319i | ||||
\(134\) | 0.106647 | − | 0.0346518i | 0.00921293 | − | 0.00299346i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0533737 | − | 0.251104i | −0.00457676 | − | 0.0215320i | ||||
\(137\) | −0.809052 | − | 15.4376i | −0.0691220 | − | 1.31893i | −0.784474 | − | 0.620162i | \(-0.787067\pi\) |
0.715352 | − | 0.698764i | \(-0.246266\pi\) | |||||||
\(138\) | 0.0556899 | − | 0.0361654i | 0.00474064 | − | 0.00307861i | ||||
\(139\) | −5.70394 | + | 17.5549i | −0.483801 | + | 1.48899i | 0.349908 | + | 0.936784i | \(0.386213\pi\) |
−0.833709 | + | 0.552204i | \(0.813787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.20022 | − | 6.77157i | −0.185292 | − | 0.570269i | ||||
\(142\) | −0.0605237 | − | 0.0490111i | −0.00507903 | − | 0.00411292i | ||||
\(143\) | 1.57329 | + | 0.421562i | 0.131565 | + | 0.0352528i | ||||
\(144\) | 2.79818 | − | 6.28481i | 0.233182 | − | 0.523734i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.101999 | + | 0.140389i | −0.00844147 | + | 0.0116187i | ||||
\(147\) | 0.386457 | + | 7.90813i | 0.0318745 | + | 0.652251i | ||||
\(148\) | 5.87245 | − | 2.99216i | 0.482712 | − | 0.245954i | ||||
\(149\) | −12.7732 | − | 7.37458i | −1.04642 | − | 0.604149i | −0.124773 | − | 0.992185i | \(-0.539820\pi\) |
−0.921644 | + | 0.388036i | \(0.873154\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.80622 | − | 4.86051i | −0.228367 | − | 0.395543i | 0.728957 | − | 0.684559i | \(-0.240005\pi\) |
−0.957324 | + | 0.289016i | \(0.906672\pi\) | |||||||
\(152\) | −0.0240194 | + | 0.458318i | −0.00194823 | + | 0.0371745i | ||||
\(153\) | 6.35103 | − | 1.00590i | 0.513450 | − | 0.0813225i | ||||
\(154\) | −0.0364537 | + | 0.227559i | −0.00293752 | + | 0.0183372i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0759281 | − | 0.722408i | −0.00607912 | − | 0.0578389i | ||||
\(157\) | −1.35782 | + | 5.06744i | −0.108366 | + | 0.404426i | −0.998705 | − | 0.0508712i | \(-0.983800\pi\) |
0.890340 | + | 0.455297i | \(0.150467\pi\) | |||||||
\(158\) | −0.0505019 | − | 0.131562i | −0.00401772 | − | 0.0104665i | ||||
\(159\) | 12.4960 | + | 2.65612i | 0.991000 | + | 0.210644i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.43735 | + | 3.25590i | 0.664957 | + | 0.256601i | ||||
\(162\) | 0.0134262 | + | 0.00684101i | 0.00105487 | + | 0.000537481i | ||||
\(163\) | 9.67348 | + | 14.8958i | 0.757685 | + | 1.16673i | 0.981381 | + | 0.192074i | \(0.0615212\pi\) |
−0.223695 | + | 0.974659i | \(0.571812\pi\) | |||||||
\(164\) | 16.2175 | − | 3.44714i | 1.26638 | − | 0.269177i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.00463785 | − | 0.0218194i | 0.000359967 | − | 0.00169351i | ||||
\(167\) | 5.68050 | + | 0.899703i | 0.439571 | + | 0.0696211i | 0.372297 | − | 0.928113i | \(-0.378570\pi\) |
0.0672731 | + | 0.997735i | \(0.478570\pi\) | |||||||
\(168\) | 0.201154 | − | 0.0423856i | 0.0155193 | − | 0.00327012i | ||||
\(169\) | −7.58059 | − | 10.4338i | −0.583122 | − | 0.802599i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.4328 | − | 1.20163i | −0.874287 | − | 0.0918912i | ||||
\(172\) | −7.11110 | − | 8.78147i | −0.542216 | − | 0.669581i | ||||
\(173\) | 2.25614 | + | 0.118239i | 0.171531 | + | 0.00898956i | 0.137908 | − | 0.990445i | \(-0.455962\pi\) |
0.0336229 | + | 0.999435i | \(0.489295\pi\) | |||||||
\(174\) | 0.0659643 | 0.00500074 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.2779 | −1.52851 | ||||||||
\(177\) | 10.8014 | + | 0.566075i | 0.811880 | + | 0.0425488i | ||||
\(178\) | 0.0107152 | + | 0.0132321i | 0.000803135 | + | 0.000991789i | ||||
\(179\) | −23.0769 | − | 2.42548i | −1.72485 | − | 0.181289i | −0.810369 | − | 0.585920i | \(-0.800733\pi\) |
−0.914480 | + | 0.404631i | \(0.867400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.07470 | − | 1.47920i | −0.0798820 | − | 0.109948i | 0.767206 | − | 0.641401i | \(-0.221646\pi\) |
−0.847088 | + | 0.531453i | \(0.821646\pi\) | |||||||
\(182\) | −0.0108620 | + | 0.00974556i | −0.000805147 | + | 0.000722389i | ||||
\(183\) | 3.06286 | + | 0.485109i | 0.226413 | + | 0.0358603i | ||||
\(184\) | 0.0488201 | − | 0.229680i | 0.00359906 | − | 0.0169323i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0142697 | + | 0.00303311i | −0.00104630 | + | 0.000222399i | ||||
\(187\) | −10.3227 | − | 15.8956i | −0.754873 | − | 1.16240i | ||||
\(188\) | −11.2160 | − | 5.71482i | −0.818008 | − | 0.416796i | ||||
\(189\) | 2.18529 | + | 13.9568i | 0.158957 | + | 1.01521i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.720510 | + | 0.153149i | 0.0521342 | + | 0.0110815i | 0.233905 | − | 0.972259i | \(-0.424850\pi\) |
−0.181771 | + | 0.983341i | \(0.558183\pi\) | |||||||
\(192\) | 3.23987 | + | 8.44016i | 0.233818 | + | 0.609116i | ||||
\(193\) | 3.73619 | − | 13.9437i | 0.268937 | − | 1.00369i | −0.690860 | − | 0.722989i | \(-0.742768\pi\) |
0.959796 | − | 0.280697i | \(-0.0905656\pi\) | |||||||
\(194\) | 0.0223005 | + | 0.212175i | 0.00160108 | + | 0.0152333i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.3694 | + | 9.40311i | 0.740669 | + | 0.671651i | ||||
\(197\) | −9.93010 | + | 1.57277i | −0.707490 | + | 0.112055i | −0.499802 | − | 0.866140i | \(-0.666594\pi\) |
−0.207688 | + | 0.978195i | \(0.566594\pi\) | |||||||
\(198\) | −0.00784407 | + | 0.149674i | −0.000557454 | + | 0.0106368i | ||||
\(199\) | 3.19046 | + | 5.52604i | 0.226166 | + | 0.391731i | 0.956669 | − | 0.291179i | \(-0.0940475\pi\) |
−0.730503 | + | 0.682910i | \(0.760714\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.39554 | − | 3.69247i | −0.451107 | − | 0.260447i | ||||
\(202\) | 0.180137 | − | 0.0917845i | 0.0126744 | − | 0.00645794i | ||||
\(203\) | 5.26787 | + | 7.27758i | 0.369732 | + | 0.510786i | ||||
\(204\) | −4.96830 | + | 6.83828i | −0.347851 | + | 0.478775i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.102990 | − | 0.231319i | 0.00717563 | − | 0.0161167i | ||||
\(207\) | 5.68118 | + | 1.52227i | 0.394869 | + | 0.105805i | ||||
\(208\) | −0.997882 | − | 0.808069i | −0.0691907 | − | 0.0560295i | ||||
\(209\) | 10.4708 | + | 32.2260i | 0.724284 | + | 2.22912i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.73583 | − | 26.8861i | 0.601399 | − | 1.85092i | 0.0815311 | − | 0.996671i | \(-0.474019\pi\) |
0.519868 | − | 0.854246i | \(-0.325981\pi\) | |||||||
\(212\) | 18.9423 | − | 12.3012i | 1.30096 | − | 0.844853i | ||||
\(213\) | 0.268427 | + | 5.12188i | 0.0183923 | + | 0.350946i | ||||
\(214\) | −0.0370563 | − | 0.174336i | −0.00253312 | − | 0.0119174i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.348836 | − | 0.113344i | 0.0237353 | − | 0.00771206i | ||||
\(217\) | −1.47420 | − | 1.33209i | −0.100075 | − | 0.0904285i | ||||
\(218\) | 0.110518 | + | 0.110518i | 0.00748521 | + | 0.00748521i | ||||
\(219\) | 11.3656 | − | 1.19457i | 0.768017 | − | 0.0807218i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.125451 | − | 1.19358i | 0.00843873 | − | 0.0802891i | ||||
\(222\) | 0.0597735 | + | 0.0229449i | 0.00401173 | + | 0.00153996i | ||||
\(223\) | −9.61132 | − | 18.8633i | −0.643622 | − | 1.26318i | −0.950291 | − | 0.311362i | \(-0.899215\pi\) |
0.306670 | − | 0.951816i | \(-0.400785\pi\) | |||||||
\(224\) | 0.297730 | − | 0.456697i | 0.0198929 | − | 0.0305144i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.0732739 | − | 0.126914i | 0.00487411 | − | 0.00844220i | ||||
\(227\) | −16.7245 | − | 10.8610i | −1.11004 | − | 0.720872i | −0.146712 | − | 0.989179i | \(-0.546869\pi\) |
−0.963333 | + | 0.268308i | \(0.913536\pi\) | |||||||
\(228\) | 11.7437 | − | 9.50987i | 0.777746 | − | 0.629807i | ||||
\(229\) | −9.17427 | + | 4.08465i | −0.606253 | + | 0.269921i | −0.686819 | − | 0.726828i | \(-0.740994\pi\) |
0.0805667 | + | 0.996749i | \(0.474327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.7434 | − | 8.24375i | 0.838457 | − | 0.542399i | ||||
\(232\) | 0.164941 | − | 0.164941i | 0.0108289 | − | 0.0108289i | ||||
\(233\) | −1.75658 | + | 2.16919i | −0.115077 | + | 0.142108i | −0.831429 | − | 0.555630i | \(-0.812477\pi\) |
0.716352 | + | 0.697739i | \(0.245810\pi\) | |||||||
\(234\) | −0.00635045 | + | 0.00705289i | −0.000415142 | + | 0.000461062i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 14.2108 | − | 12.7955i | 0.925047 | − | 0.832916i | ||||
\(237\) | −4.21336 | + | 8.26918i | −0.273687 | + | 0.537141i | ||||
\(238\) | 0.169812 | 0.000299749i | 0.0110073 | 1.94298e-5i | ||||||
\(239\) | 3.96154 | + | 1.28718i | 0.256251 | + | 0.0832609i | 0.434325 | − | 0.900756i | \(-0.356987\pi\) |
−0.178075 | + | 0.984017i | \(0.556987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.27483 | + | 4.74948i | 0.339782 | + | 0.305941i | 0.821301 | − | 0.570494i | \(-0.193248\pi\) |
−0.481520 | + | 0.876435i | \(0.659915\pi\) | |||||||
\(242\) | 0.236060 | − | 0.0906150i | 0.0151745 | − | 0.00582495i | ||||
\(243\) | 3.88900 | + | 14.5140i | 0.249480 | + | 0.931071i | ||||
\(244\) | 4.43544 | − | 3.22254i | 0.283950 | − | 0.206302i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.130304 | + | 0.0946711i | 0.00830785 | + | 0.00603601i | ||||
\(247\) | −0.768920 | + | 2.00311i | −0.0489252 | + | 0.127455i | ||||
\(248\) | −0.0280965 | + | 0.0432649i | −0.00178413 | + | 0.00274732i | ||||
\(249\) | −1.27225 | + | 0.734532i | −0.0806254 | + | 0.0465491i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.67076i | 0.231697i | 0.993267 | + | 0.115848i | \(0.0369586\pi\) | ||||
−0.993267 | + | 0.115848i | \(0.963041\pi\) | |||||||
\(252\) | 7.35544 | + | 5.36390i | 0.463349 | + | 0.337894i | ||||
\(253\) | −2.71200 | − | 17.1229i | −0.170502 | − | 1.07651i | ||||
\(254\) | −0.112728 | − | 0.253192i | −0.00707321 | − | 0.0158867i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.5952 | + | 6.49819i | 0.912198 | + | 0.406137i | ||||
\(257\) | −5.31329 | + | 1.42369i | −0.331434 | + | 0.0888074i | −0.420698 | − | 0.907201i | \(-0.638215\pi\) |
0.0892647 | + | 0.996008i | \(0.471548\pi\) | |||||||
\(258\) | 0.0171718 | − | 0.108418i | 0.00106907 | − | 0.00674984i | ||||
\(259\) | 2.24206 | + | 8.42694i | 0.139315 | + | 0.523624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.90958 | + | 4.34202i | 0.241997 | + | 0.268765i | ||||
\(262\) | −0.0511120 | + | 0.00267867i | −0.00315771 | + | 0.000165489i | ||||
\(263\) | 20.7708 | − | 1.08855i | 1.28078 | − | 0.0671229i | 0.600232 | − | 0.799826i | \(-0.295075\pi\) |
0.680549 | + | 0.732703i | \(0.261741\pi\) | |||||||
\(264\) | −0.263681 | − | 0.292848i | −0.0162285 | − | 0.0180235i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.293103 | − | 0.0790916i | −0.0179713 | − | 0.00484942i | ||||
\(267\) | 0.175413 | − | 1.10751i | 0.0107351 | − | 0.0677788i | ||||
\(268\) | −12.6114 | + | 3.37921i | −0.770363 | + | 0.206418i | ||||
\(269\) | −0.143111 | − | 0.0637171i | −0.00872562 | − | 0.00388490i | 0.402369 | − | 0.915477i | \(-0.368187\pi\) |
−0.411095 | + | 0.911593i | \(0.634853\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.567128 | + | 1.27379i | 0.0344506 | + | 0.0773772i | 0.929951 | − | 0.367683i | \(-0.119849\pi\) |
−0.895501 | + | 0.445060i | \(0.853182\pi\) | |||||||
\(272\) | 2.33738 | + | 14.7577i | 0.141725 | + | 0.894814i | ||||
\(273\) | 0.955618 | + | 0.102145i | 0.0578366 | + | 0.00618212i | ||||
\(274\) | − | 0.265502i | − | 0.0160395i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.69562 | + | 3.86572i | −0.403029 | + | 0.232689i | ||||
\(277\) | −16.3574 | + | 25.1881i | −0.982819 | + | 1.51341i | −0.129792 | + | 0.991541i | \(0.541431\pi\) |
−0.853027 | + | 0.521867i | \(0.825236\pi\) | |||||||
\(278\) | −0.113609 | + | 0.295961i | −0.00681381 | + | 0.0177506i | ||||
\(279\) | −1.04539 | − | 0.759518i | −0.0625857 | − | 0.0454712i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.1092 | + | 16.7898i | −1.37858 | + | 1.00160i | −0.381567 | + | 0.924341i | \(0.624616\pi\) |
−0.997011 | + | 0.0772549i | \(0.975384\pi\) | |||||||
\(282\) | −0.0316498 | − | 0.118119i | −0.00188472 | − | 0.00703385i | ||||
\(283\) | −26.2719 | + | 10.0848i | −1.56170 | + | 0.599482i | −0.977277 | − | 0.211965i | \(-0.932014\pi\) |
−0.584426 | + | 0.811447i | \(0.698680\pi\) | |||||||
\(284\) | 6.73862 | + | 6.06748i | 0.399864 | + | 0.360039i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0266049 | + | 0.00864446i | 0.00157318 | + | 0.000511158i | ||||
\(287\) | −0.0387214 | + | 21.9363i | −0.00228565 | + | 1.29486i | ||||
\(288\) | 0.160964 | − | 0.315909i | 0.00948487 | − | 0.0186151i | ||||
\(289\) | 2.25500 | − | 2.03041i | 0.132647 | − | 0.119436i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.40141 | − | 10.4413i | 0.551120 | − | 0.612081i | ||||
\(292\) | 12.7152 | − | 15.7019i | 0.744100 | − | 0.918887i | ||||
\(293\) | 4.56757 | − | 4.56757i | 0.266840 | − | 0.266840i | −0.560986 | − | 0.827826i | \(-0.689578\pi\) |
0.827826 | + | 0.560986i | \(0.189578\pi\) | |||||||
\(294\) | −0.000480065 | 0.135981i | −2.79979e−5 | 0.00793060i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.206834 | − | 0.0920883i | 0.0120220 | − | 0.00535252i | ||||
\(297\) | 21.0453 | − | 17.0421i | 1.22117 | − | 0.988885i | ||||
\(298\) | −0.212447 | − | 0.137964i | −0.0123067 | − | 0.00799207i | ||||
\(299\) | 0.548882 | − | 0.950692i | 0.0317427 | − | 0.0549799i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.3327 | − | 6.76374i | 0.768485 | − | 0.389855i | ||||
\(302\) | −0.0437612 | − | 0.0858861i | −0.00251817 | − | 0.00494219i | ||||
\(303\) | −12.4302 | − | 4.77150i | −0.714095 | − | 0.274115i | ||||
\(304\) | 2.79219 | − | 26.5660i | 0.160143 | − | 1.52366i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.109832 | − | 0.0115438i | 0.00627868 | − | 0.000659916i | ||||
\(307\) | −12.4946 | − | 12.4946i | −0.713104 | − | 0.713104i | 0.254080 | − | 0.967183i | \(-0.418227\pi\) |
−0.967183 | + | 0.254080i | \(0.918227\pi\) | |||||||
\(308\) | 5.62524 | − | 26.2369i | 0.320528 | − | 1.49498i | ||||
\(309\) | −15.8595 | + | 5.15306i | −0.902215 | + | 0.293148i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.55465 | + | 7.31407i | 0.0881563 | + | 0.414743i | 0.999991 | + | 0.00418591i | \(0.00133242\pi\) |
−0.911835 | + | 0.410557i | \(0.865334\pi\) | |||||||
\(312\) | −0.00130593 | − | 0.0249187i | −7.39340e−5 | − | 0.00141074i | ||||
\(313\) | −23.3423 | + | 15.1587i | −1.31939 | + | 0.856819i | −0.995992 | − | 0.0894451i | \(-0.971491\pi\) |
−0.323394 | + | 0.946264i | \(0.604824\pi\) | |||||||
\(314\) | −0.0278431 | + | 0.0856923i | −0.00157128 | + | 0.00483590i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.07033 | + | 15.6049i | 0.285228 | + | 0.877843i | ||||
\(317\) | 22.2075 | + | 17.9833i | 1.24730 | + | 1.01004i | 0.999146 | + | 0.0413185i | \(0.0131558\pi\) |
0.248150 | + | 0.968722i | \(0.420177\pi\) | |||||||
\(318\) | 0.211935 | + | 0.0567878i | 0.0118847 | + | 0.00318450i | ||||
\(319\) | 7.00477 | − | 15.7330i | 0.392192 | − | 0.880878i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.89929 | + | 9.49606i | −0.385081 | + | 0.530019i | ||||
\(322\) | 0.141784 | + | 0.0634266i | 0.00790134 | + | 0.00353463i | ||||
\(323\) | 22.2461 | − | 11.3350i | 1.23781 | − | 0.630694i | ||||
\(324\) | −1.51943 | − | 0.877241i | −0.0844125 | − | 0.0487356i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.152523 | + | 0.264177i | 0.00844745 | + | 0.0146314i | ||||
\(327\) | 0.538704 | − | 10.2791i | 0.0297904 | − | 0.568434i | ||||
\(328\) | 0.562539 | − | 0.0890975i | 0.0310610 | − | 0.00491959i | ||||
\(329\) | 10.5040 | − | 12.9247i | 0.579105 | − | 0.712560i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.74558 | − | 16.6081i | −0.0959457 | − | 0.912863i | −0.931570 | − | 0.363561i | \(-0.881561\pi\) |
0.835624 | − | 0.549301i | \(-0.185106\pi\) | |||||||
\(332\) | −0.672217 | + | 2.50875i | −0.0368927 | + | 0.137685i | ||||
\(333\) | 2.03234 | + | 5.29442i | 0.111371 | + | 0.290132i | ||||
\(334\) | 0.0966189 | + | 0.0205370i | 0.00528675 | + | 0.00112373i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −11.8209 | + | 1.85087i | −0.644884 | + | 0.100973i | ||||
\(337\) | −21.2946 | − | 10.8501i | −1.15999 | − | 0.591044i | −0.235358 | − | 0.971909i | \(-0.575626\pi\) |
−0.924631 | + | 0.380865i | \(0.875626\pi\) | |||||||
\(338\) | −0.120638 | − | 0.185766i | −0.00656184 | − | 0.0101043i | ||||
\(339\) | −9.44031 | + | 2.00660i | −0.512728 | + | 0.108984i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.791882 | + | 3.72551i | −0.0428828 | + | 0.201748i | ||||
\(342\) | −0.195006 | − | 0.0308859i | −0.0105447 | − | 0.00167012i | ||||
\(343\) | −15.0406 | + | 10.8064i | −0.812118 | + | 0.583493i | ||||
\(344\) | −0.228158 | − | 0.314033i | −0.0123015 | − | 0.0169315i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.0385893 | + | 0.00405590i | 0.00207457 | + | 0.000218046i | ||||
\(347\) | 2.31115 | + | 2.85404i | 0.124069 | + | 0.153213i | 0.835396 | − | 0.549649i | \(-0.185239\pi\) |
−0.711326 | + | 0.702862i | \(0.751905\pi\) | |||||||
\(348\) | −7.66988 | − | 0.401961i | −0.411149 | − | 0.0215474i | ||||
\(349\) | 1.21897 | 0.0652497 | 0.0326249 | − | 0.999468i | \(-0.489613\pi\) | ||||
0.0326249 | + | 0.999468i | \(0.489613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.71477 | 0.0915274 | ||||||||
\(352\) | −1.04363 | − | 0.0546944i | −0.0556258 | − | 0.00291522i | ||||
\(353\) | 15.9851 | + | 19.7399i | 0.850799 | + | 1.05065i | 0.998103 | + | 0.0615584i | \(0.0196070\pi\) |
−0.147304 | + | 0.989091i | \(0.547060\pi\) | |||||||
\(354\) | 0.184748 | + | 0.0194178i | 0.00981924 | + | 0.00103204i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.16525 | − | 1.60383i | −0.0617583 | − | 0.0850031i | ||||
\(357\) | −7.46845 | − | 8.32405i | −0.395272 | − | 0.440556i | ||||
\(358\) | −0.393617 | − | 0.0623428i | −0.0208033 | − | 0.00329492i | ||||
\(359\) | 2.33682 | − | 10.9939i | 0.123333 | − | 0.580235i | −0.872467 | − | 0.488674i | \(-0.837481\pi\) |
0.995799 | − | 0.0915616i | \(-0.0291858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −25.0759 | + | 5.33005i | −1.31979 | + | 0.280529i | ||||
\(362\) | −0.0171029 | − | 0.0263361i | −0.000898908 | − | 0.00138420i | ||||
\(363\) | −14.8373 | − | 7.55997i | −0.778755 | − | 0.396796i | ||||
\(364\) | 1.32235 | − | 1.06696i | 0.0693099 | − | 0.0559238i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.0520958 | + | 0.0110733i | 0.00272309 | + | 0.000578810i | ||||
\(367\) | −2.58488 | − | 6.73383i | −0.134929 | − | 0.351503i | 0.849423 | − | 0.527712i | \(-0.176950\pi\) |
−0.984353 | + | 0.176209i | \(0.943617\pi\) | |||||||
\(368\) | −3.53724 | + | 13.2012i | −0.184391 | + | 0.688158i | ||||
\(369\) | 1.49122 | + | 14.1881i | 0.0776301 | + | 0.738601i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6598 | + | 27.9170i | 0.553431 | + | 1.44938i | ||||
\(372\) | 1.67766 | − | 0.265716i | 0.0869827 | − | 0.0137767i | ||||
\(373\) | −0.204078 | + | 3.89404i | −0.0105667 | + | 0.201626i | 0.988245 | + | 0.152881i | \(0.0488552\pi\) |
−0.998811 | + | 0.0487442i | \(0.984478\pi\) | |||||||
\(374\) | −0.162760 | − | 0.281908i | −0.00841610 | − | 0.0145771i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.374489 | − | 0.216211i | −0.0193128 | − | 0.0111503i | ||||
\(377\) | 0.971660 | − | 0.495085i | 0.0500430 | − | 0.0254982i | ||||
\(378\) | 0.0249353 | + | 0.241340i | 0.00128253 | + | 0.0124132i | ||||
\(379\) | 2.70772 | − | 3.72686i | 0.139086 | − | 0.191436i | −0.733792 | − | 0.679375i | \(-0.762251\pi\) |
0.872878 | + | 0.487939i | \(0.162251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.42397 | + | 16.6745i | −0.380342 | + | 0.854261i | ||||
\(382\) | 0.0122200 | + | 0.00327433i | 0.000625228 | + | 0.000167529i | ||||
\(383\) | 22.1000 | + | 17.8962i | 1.12926 | + | 0.914454i | 0.997049 | − | 0.0767678i | \(-0.0244600\pi\) |
0.132208 | + | 0.991222i | \(0.457793\pi\) | |||||||
\(384\) | 0.192024 | + | 0.590991i | 0.00979921 | + | 0.0301589i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0766136 | − | 0.235792i | 0.00389953 | − | 0.0120015i | ||||
\(387\) | 8.15426 | − | 5.29544i | 0.414504 | − | 0.269182i | ||||
\(388\) | −1.30003 | − | 24.8061i | −0.0659992 | − | 1.25934i | ||||
\(389\) | −6.09298 | − | 28.6652i | −0.308926 | − | 1.45338i | −0.809208 | − | 0.587522i | \(-0.800104\pi\) |
0.500282 | − | 0.865863i | \(-0.333230\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.1489 | + | 3.94741i | −0.614396 | + | 0.199629i | ||||
\(392\) | 0.338815 | + | 0.341216i | 0.0171128 | + | 0.0172340i | ||||
\(393\) | 2.38345 | + | 2.38345i | 0.120229 | + | 0.120229i | ||||
\(394\) | −0.171727 | + | 0.0180493i | −0.00865149 | + | 0.000909308i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.82411 | − | 17.3552i | 0.0916649 | − | 0.872134i | ||||
\(397\) | 1.04017 | + | 0.399283i | 0.0522045 | + | 0.0200394i | 0.384330 | − | 0.923196i | \(-0.374432\pi\) |
−0.332126 | + | 0.943235i | \(0.607766\pi\) | |||||||
\(398\) | 0.0497532 | + | 0.0976462i | 0.00249390 | + | 0.00489456i | ||||
\(399\) | 9.04534 | + | 17.8302i | 0.452833 | + | 0.892627i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.29812 | + | 7.44456i | −0.214638 | + | 0.371764i | −0.953160 | − | 0.302465i | \(-0.902190\pi\) |
0.738523 | + | 0.674229i | \(0.235524\pi\) | |||||||
\(402\) | −0.106372 | − | 0.0690790i | −0.00530537 | − | 0.00344535i | ||||
\(403\) | −0.187429 | + | 0.151777i | −0.00933650 | + | 0.00756055i | ||||
\(404\) | −21.5044 | + | 9.57439i | −1.06989 | + | 0.476344i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0838090 | + | 0.129555i | 0.00415937 | + | 0.00642969i | ||||
\(407\) | 11.8199 | − | 11.8199i | 0.585890 | − | 0.585890i | ||||
\(408\) | −0.182732 | + | 0.225655i | −0.00904657 | + | 0.0111716i | ||||
\(409\) | 10.3987 | − | 11.5490i | 0.514185 | − | 0.571060i | −0.429010 | − | 0.903300i | \(-0.641138\pi\) |
0.943195 | + | 0.332240i | \(0.107804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.9940 | + | 11.6999i | −0.640947 | + | 0.577112i | ||||
\(412\) | −13.3845 | + | 26.2686i | −0.659407 | + | 1.29416i | ||||
\(413\) | 12.6116 | + | 21.9332i | 0.620575 | + | 1.07926i | ||||
\(414\) | 0.0960709 | + | 0.0312153i | 0.00472163 | + | 0.00153415i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.0491778 | − | 0.0442799i | −0.00241114 | − | 0.00217100i | ||||
\(417\) | 19.4912 | − | 7.48195i | 0.954486 | − | 0.366393i | ||||
\(418\) | 0.150621 | + | 0.562127i | 0.00736713 | + | 0.0274945i | ||||
\(419\) | −5.12758 | + | 3.72540i | −0.250499 | + | 0.181998i | −0.705948 | − | 0.708264i | \(-0.749479\pi\) |
0.455449 | + | 0.890262i | \(0.349479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9408 | − | 13.0347i | −0.874380 | − | 0.635274i | 0.0573790 | − | 0.998352i | \(-0.481726\pi\) |
−0.931759 | + | 0.363079i | \(0.881726\pi\) | |||||||
\(422\) | 0.173997 | − | 0.453278i | 0.00847004 | − | 0.0220652i | ||||
\(423\) | 5.89920 | − | 9.08396i | 0.286829 | − | 0.441677i | ||||
\(424\) | 0.671930 | − | 0.387939i | 0.0326318 | − | 0.0188400i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.0880879i | 0.00426787i | ||||||||
\(427\) | 2.93866 | + | 6.63183i | 0.142212 | + | 0.320937i | ||||
\(428\) | 3.24632 | + | 20.4964i | 0.156917 | + | 0.990732i | ||||
\(429\) | −0.749328 | − | 1.68302i | −0.0361779 | − | 0.0812568i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.89080 | − | 3.95844i | −0.428255 | − | 0.190671i | 0.181279 | − | 0.983432i | \(-0.441976\pi\) |
−0.609533 | + | 0.792761i | \(0.708643\pi\) | |||||||
\(432\) | −20.6209 | + | 5.52535i | −0.992123 | + | 0.265839i | ||||
\(433\) | −1.94672 | + | 12.2911i | −0.0935535 | + | 0.590674i | 0.895722 | + | 0.444614i | \(0.146659\pi\) |
−0.989276 | + | 0.146060i | \(0.953341\pi\) | |||||||
\(434\) | −0.0240870 | − | 0.0241722i | −0.00115621 | − | 0.00116030i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1768 | − | 13.5237i | −0.583163 | − | 0.647668i | ||||
\(437\) | 22.8060 | − | 1.19521i | 1.09096 | − | 0.0571746i | ||||
\(438\) | 0.196008 | − | 0.0102723i | 0.00936562 | − | 0.000490831i | ||||
\(439\) | −16.4159 | − | 18.2318i | −0.783490 | − | 0.870154i | 0.210727 | − | 0.977545i | \(-0.432417\pi\) |
−0.994217 | + | 0.107391i | \(0.965750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.97928 | + | 8.02776i | −0.427585 | + | 0.382274i | ||||
\(442\) | 0.00322450 | − | 0.0203587i | 0.000153374 | − | 0.000968363i | ||||
\(443\) | 6.76871 | − | 1.81367i | 0.321591 | − | 0.0861701i | −0.0944121 | − | 0.995533i | \(-0.530097\pi\) |
0.416003 | + | 0.909363i | \(0.363430\pi\) | |||||||
\(444\) | −6.81023 | − | 3.03211i | −0.323199 | − | 0.143898i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.147891 | − | 0.332168i | −0.00700282 | − | 0.0157286i | ||||
\(447\) | 2.60972 | + | 16.4771i | 0.123435 | + | 0.779340i | ||||
\(448\) | −12.4602 | + | 17.0865i | −0.588691 | + | 0.807263i | ||||
\(449\) | − | 11.3776i | − | 0.536943i | −0.963288 | − | 0.268472i | \(-0.913481\pi\) | ||
0.963288 | − | 0.268472i | \(-0.0865186\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.4167 | − | 21.0252i | 1.71480 | − | 0.990039i | ||||
\(452\) | −9.29316 | + | 14.3102i | −0.437113 | + | 0.673095i | ||||
\(453\) | −2.27496 | + | 5.92648i | −0.106887 | + | 0.278450i | ||||
\(454\) | −0.277083 | − | 0.201313i | −0.0130042 | − | 0.00944808i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.419965 | − | 0.305123i | 0.0196667 | − | 0.0142887i | ||||
\(457\) | 1.77469 | + | 6.62325i | 0.0830167 | + | 0.309822i | 0.994931 | − | 0.100558i | \(-0.0320627\pi\) |
−0.911915 | + | 0.410380i | \(0.865396\pi\) | |||||||
\(458\) | −0.161021 | + | 0.0618104i | −0.00752404 | + | 0.00288821i | ||||
\(459\) | −14.8286 | − | 13.3517i | −0.692138 | − | 0.623204i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.19822 | + | 2.01392i | 0.288680 | + | 0.0937978i | 0.449777 | − | 0.893141i | \(-0.351503\pi\) |
−0.161097 | + | 0.986939i | \(0.551503\pi\) | |||||||
\(462\) | 0.225976 | − | 0.129936i | 0.0105133 | − | 0.00604516i | ||||
\(463\) | 2.03589 | − | 3.99566i | 0.0946158 | − | 0.185694i | −0.838848 | − | 0.544366i | \(-0.816770\pi\) |
0.933464 | + | 0.358672i | \(0.116770\pi\) | |||||||
\(464\) | −10.0894 | + | 9.08455i | −0.468389 | + | 0.421740i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.0320772 | + | 0.0356254i | −0.00148595 | + | 0.00165031i | ||||
\(467\) | −25.2819 | + | 31.2205i | −1.16991 | + | 1.44471i | −0.298322 | + | 0.954465i | \(0.596427\pi\) |
−0.871583 | + | 0.490248i | \(0.836906\pi\) | |||||||
\(468\) | 0.781365 | − | 0.781365i | 0.0361186 | − | 0.0361186i | ||||
\(469\) | −0.873619 | − | 17.2523i | −0.0403400 | − | 0.796636i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.42086 | − | 2.41352i | 0.249780 | − | 0.111209i | ||||
\(472\) | 0.510507 | − | 0.413401i | 0.0234980 | − | 0.0190283i | ||||
\(473\) | −24.0351 | − | 15.6086i | −1.10514 | − | 0.717684i | ||||
\(474\) | −0.0796971 | + | 0.138039i | −0.00366061 | + | 0.00634036i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −19.7428 | − | 1.06962i | −0.904909 | − | 0.0490261i | ||||
\(477\) | 8.82298 | + | 17.3161i | 0.403977 | + | 0.792849i | ||||
\(478\) | 0.0667882 | + | 0.0256376i | 0.00305482 | + | 0.00117264i | ||||
\(479\) | −2.16757 | + | 20.6230i | −0.0990386 | + | 0.942290i | 0.826321 | + | 0.563199i | \(0.190430\pi\) |
−0.925360 | + | 0.379090i | \(0.876237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.05268 | − | 0.110641i | 0.0479980 | − | 0.00504479i | ||||
\(482\) | 0.0862007 | + | 0.0862007i | 0.00392633 | + | 0.00392633i | ||||
\(483\) | −3.14383 | − | 9.73414i | −0.143049 | − | 0.442919i | ||||
\(484\) | −27.9996 | + | 9.09763i | −1.27271 | + | 0.413529i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.0536552 | + | 0.252428i | 0.00243385 | + | 0.0114504i | ||||
\(487\) | −0.389033 | − | 7.42319i | −0.0176288 | − | 0.336377i | −0.993179 | − | 0.116600i | \(-0.962800\pi\) |
0.975550 | − | 0.219777i | \(-0.0705329\pi\) | |||||||
\(488\) | 0.157952 | − | 0.102575i | 0.00715013 | − | 0.00464335i | ||||
\(489\) | 6.20797 | − | 19.1062i | 0.280734 | − | 0.864011i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.27403 | − | 19.3095i | −0.283143 | − | 0.871425i | −0.986949 | − | 0.161033i | \(-0.948518\pi\) |
0.703806 | − | 0.710392i | \(-0.251482\pi\) | |||||||
\(492\) | −14.5739 | − | 11.8017i | −0.657043 | − | 0.532063i | ||||
\(493\) | −12.2574 | − | 3.28436i | −0.552045 | − | 0.147920i | ||||
\(494\) | −0.0149884 | + | 0.0336646i | −0.000674362 | + | 0.00151464i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.76487 | − | 2.42913i | 0.0792448 | − | 0.109071i | ||||
\(497\) | −9.71839 | + | 7.03465i | −0.435929 | + | 0.315547i | ||||
\(498\) | −0.0224808 | + | 0.0114546i | −0.00100739 | + | 0.000513291i | ||||
\(499\) | −7.97198 | − | 4.60262i | −0.356875 | − | 0.206042i | 0.310834 | − | 0.950464i | \(-0.399392\pi\) |
−0.667709 | + | 0.744422i | \(0.732725\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.25260 | − | 5.63367i | −0.145315 | − | 0.251694i | ||||
\(502\) | −0.00329950 | + | 0.0629581i | −0.000147264 | + | 0.00280996i | ||||
\(503\) | −20.6686 | + | 3.27358i | −0.921565 | + | 0.145962i | −0.599150 | − | 0.800637i | \(-0.704495\pi\) |
−0.322415 | + | 0.946598i | \(0.604495\pi\) | |||||||
\(504\) | 0.242685 | + | 0.197233i | 0.0108100 | + | 0.00878544i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.0311230 | − | 0.296116i | −0.00138359 | − | 0.0131640i | ||||
\(507\) | −3.77549 | + | 14.0903i | −0.167676 | + | 0.625774i | ||||
\(508\) | 11.5644 | + | 30.1264i | 0.513089 | + | 1.33664i | ||||
\(509\) | −6.93922 | − | 1.47498i | −0.307575 | − | 0.0653772i | 0.0515382 | − | 0.998671i | \(-0.483588\pi\) |
−0.359114 | + | 0.933294i | \(0.616921\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.7864 | + | 20.8044i | 0.742586 | + | 0.920334i | ||||
\(512\) | 1.22350 | + | 0.623407i | 0.0540718 | + | 0.0275509i | ||||
\(513\) | 19.4289 | + | 29.9179i | 0.857807 | + | 1.32091i | ||||
\(514\) | −0.0924091 | + | 0.0196422i | −0.00407599 | + | 0.000866379i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.65728 | + | 12.5015i | −0.116980 | + | 0.550349i | ||||
\(517\) | −31.5330 | − | 4.99434i | −1.38682 | − | 0.219651i | ||||
\(518\) | 0.0308794 | + | 0.146548i | 0.00135676 | + | 0.00643893i | ||||
\(519\) | −1.50201 | − | 2.06734i | −0.0659310 | − | 0.0907463i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.1966 | − | 1.59723i | −0.665775 | − | 0.0699757i | −0.234388 | − | 0.972143i | \(-0.575309\pi\) |
−0.431386 | + | 0.902167i | \(0.641975\pi\) | |||||||
\(522\) | 0.0631512 | + | 0.0779852i | 0.00276405 | + | 0.00341332i | ||||
\(523\) | −4.63114 | − | 0.242708i | −0.202506 | − | 0.0106129i | −0.0491867 | − | 0.998790i | \(-0.515663\pi\) |
−0.153319 | + | 0.988177i | \(0.548996\pi\) | |||||||
\(524\) | 5.95927 | 0.260332 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.357223 | 0.0155757 | ||||||||
\(527\) | 2.80259 | + | 0.146877i | 0.122083 | + | 0.00639808i | ||||
\(528\) | 14.4341 | + | 17.8246i | 0.628163 | + | 0.775717i | ||||
\(529\) | 11.2538 | + | 1.18282i | 0.489294 | + | 0.0514268i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.67149 | + | 13.3117i | 0.419707 | + | 0.577677i | ||||
\(532\) | 33.5981 | + | 10.9823i | 1.45666 | + | 0.476143i | ||||
\(533\) | 2.62992 | + | 0.416539i | 0.113915 | + | 0.0180423i | ||||
\(534\) | 0.00400405 | − | 0.0188376i | 0.000173272 | − | 0.000815181i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.438709 | + | 0.0932504i | −0.0189493 | + | 0.00402781i | ||||
\(537\) | 14.2944 | + | 22.0114i | 0.616848 | + | 0.949863i | ||||
\(538\) | −0.00239725 | − | 0.00122146i | −0.000103353 | − | 5.26610e-5i | ||||
\(539\) | 32.3816 | + | 14.5544i | 1.39477 | + | 0.626903i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.8117 | − | 5.27390i | −1.06674 | − | 0.226743i | −0.359088 | − | 0.933304i | \(-0.616912\pi\) |
−0.707652 | + | 0.706561i | \(0.750246\pi\) | |||||||
\(542\) | 0.00858198 | + | 0.0223568i | 0.000368628 | + | 0.000960308i | ||||
\(543\) | −0.535254 | + | 1.99759i | −0.0229699 | + | 0.0857249i | ||||
\(544\) | 0.0804917 | + | 0.765827i | 0.00345105 | + | 0.0328346i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.0162982 | + | 0.00261088i | 0.000697499 | + | 0.000111735i | ||||
\(547\) | 8.90589 | − | 1.41055i | 0.380788 | − | 0.0603110i | 0.0368938 | − | 0.999319i | \(-0.488254\pi\) |
0.343895 | + | 0.939008i | \(0.388254\pi\) | |||||||
\(548\) | −1.61787 | + | 30.8707i | −0.0691118 | + | 1.31873i | ||||
\(549\) | 2.35873 | + | 4.08544i | 0.100668 | + | 0.174362i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.6471 | + | 11.3433i | 0.836995 | + | 0.483239i | ||||
\(552\) | −0.236643 | + | 0.120576i | −0.0100722 | + | 0.00513204i | ||||
\(553\) | −21.5939 | + | 2.23108i | −0.918266 | + | 0.0948752i | ||||
\(554\) | −0.303190 | + | 0.417305i | −0.0128813 | + | 0.0177296i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.0131 | − | 33.7201i | 0.636699 | − | 1.43005i | ||||
\(557\) | 16.3666 | + | 4.38542i | 0.693475 | + | 0.185816i | 0.588306 | − | 0.808638i | \(-0.299795\pi\) |
0.105169 | + | 0.994454i | \(0.466462\pi\) | |||||||
\(558\) | −0.0172470 | − | 0.0139663i | −0.000730123 | − | 0.000591242i | ||||
\(559\) | −0.560777 | − | 1.72589i | −0.0237183 | − | 0.0729975i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.62463 | + | 20.3885i | −0.279692 | + | 0.860804i | ||||
\(562\) | −0.411443 | + | 0.267194i | −0.0173557 | + | 0.0112709i | ||||
\(563\) | −2.26896 | − | 43.2943i | −0.0956252 | − | 1.82464i | −0.453935 | − | 0.891035i | \(-0.649980\pi\) |
0.358310 | − | 0.933603i | \(-0.383353\pi\) | |||||||
\(564\) | 2.96025 | + | 13.9269i | 0.124649 | + | 0.586427i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.459661 | + | 0.149353i | −0.0193210 | + | 0.00627776i | ||||
\(567\) | 1.55630 | − | 1.72232i | 0.0653584 | − | 0.0723306i | ||||
\(568\) | 0.220260 | + | 0.220260i | 0.00924190 | + | 0.00924190i | ||||
\(569\) | 9.81623 | − | 1.03173i | 0.411518 | − | 0.0432522i | 0.103492 | − | 0.994630i | \(-0.466998\pi\) |
0.308026 | + | 0.951378i | \(0.400332\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.152474 | − | 1.45070i | 0.00638085 | − | 0.0607098i | −0.990868 | − | 0.134835i | \(-0.956950\pi\) |
0.997249 | + | 0.0741249i | \(0.0236163\pi\) | |||||||
\(572\) | −3.04076 | − | 1.16724i | −0.127141 | − | 0.0488047i | ||||
\(573\) | −0.378247 | − | 0.742352i | −0.0158015 | − | 0.0310122i | ||||
\(574\) | −0.0203817 | + | 0.376199i | −0.000850716 | + | 0.0157022i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.87654 | + | 11.9105i | −0.286522 | + | 0.496271i | ||||
\(577\) | −4.72112 | − | 3.06593i | −0.196543 | − | 0.127636i | 0.442616 | − | 0.896711i | \(-0.354051\pi\) |
−0.639159 | + | 0.769075i | \(0.720717\pi\) | |||||||
\(578\) | 0.0405011 | − | 0.0327972i | 0.00168462 | − | 0.00136418i | ||||
\(579\) | −14.9161 | + | 6.64109i | −0.619894 | + | 0.275994i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.05904 | − | 1.56547i | −0.126911 | − | 0.0649466i | ||||
\(582\) | 0.170631 | − | 0.170631i | 0.00707288 | − | 0.00707288i | ||||
\(583\) | 36.0498 | − | 44.5177i | 1.49303 | − | 1.84374i | ||||
\(584\) | 0.464424 | − | 0.515795i | 0.0192180 | − | 0.0213437i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.0824450 | − | 0.0742338i | 0.00340577 | − | 0.00306657i | ||||
\(587\) | 9.42678 | − | 18.5011i | 0.389085 | − | 0.763622i | −0.610512 | − | 0.792007i | \(-0.709036\pi\) |
0.999597 | + | 0.0283850i | \(0.00903644\pi\) | |||||||
\(588\) | 0.884438 | − | 15.8081i | 0.0364736 | − | 0.651914i | ||||
\(589\) | −4.77172 | − | 1.55043i | −0.196615 | − | 0.0638842i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.45086 | + | 7.60919i | 0.347622 | + | 0.313000i | ||||
\(592\) | −12.3025 | + | 4.72247i | −0.505628 | + | 0.194092i | ||||
\(593\) | −3.80233 | − | 14.1905i | −0.156143 | − | 0.582733i | −0.999005 | − | 0.0446033i | \(-0.985798\pi\) |
0.842862 | − | 0.538130i | \(-0.180869\pi\) | |||||||
\(594\) | 0.376271 | − | 0.273377i | 0.0154386 | − | 0.0112168i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23.8611 | + | 17.3361i | 0.977390 | + | 0.710116i | ||||
\(597\) | 2.58646 | − | 6.73797i | 0.105857 | − | 0.275767i | ||||
\(598\) | 0.0102685 | − | 0.0158122i | 0.000419912 | − | 0.000646608i | ||||
\(599\) | −8.74982 | + | 5.05171i | −0.357508 | + | 0.206407i | −0.667987 | − | 0.744173i | \(-0.732844\pi\) |
0.310479 | + | 0.950580i | \(0.399511\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.6515i | 0.923974i | 0.886887 | + | 0.461987i | \(0.152863\pi\) | ||||
−0.886887 | + | 0.461987i | \(0.847137\pi\) | |||||||
\(602\) | 0.234752 | − | 0.104022i | 0.00956778 | − | 0.00423963i | ||||
\(603\) | −1.75744 | − | 11.0960i | −0.0715684 | − | 0.451865i | ||||
\(604\) | 4.56489 | + | 10.2529i | 0.185743 | + | 0.417185i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.208904 | − | 0.0930100i | −0.00848614 | − | 0.00377827i | ||||
\(607\) | 19.2701 | − | 5.16341i | 0.782150 | − | 0.209576i | 0.154418 | − | 0.988006i | \(-0.450650\pi\) |
0.627732 | + | 0.778429i | \(0.283983\pi\) | |||||||
\(608\) | 0.215359 | − | 1.35972i | 0.00873395 | − | 0.0551440i | ||||
\(609\) | 2.64737 | − | 9.81081i | 0.107277 | − | 0.397554i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.35272 | − | 1.50235i | −0.0547254 | − | 0.0607787i | ||||
\(612\) | −12.8409 | + | 0.672961i | −0.519061 | + | 0.0272028i | ||||
\(613\) | −38.3266 | + | 2.00861i | −1.54800 | + | 0.0811272i | −0.807070 | − | 0.590456i | \(-0.798948\pi\) |
−0.740929 | + | 0.671584i | \(0.765614\pi\) | |||||||
\(614\) | −0.203067 | − | 0.225528i | −0.00819510 | − | 0.00910158i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.240144 | − | 0.889942i | 0.00967566 | − | 0.0358568i | ||||
\(617\) | 0.0933065 | − | 0.589114i | 0.00375638 | − | 0.0237168i | −0.985739 | − | 0.168282i | \(-0.946178\pi\) |
0.989495 | + | 0.144565i | \(0.0461782\pi\) | |||||||
\(618\) | −0.276642 | + | 0.0741259i | −0.0111282 | + | 0.00298178i | ||||
\(619\) | −2.53843 | − | 1.13018i | −0.102028 | − | 0.0454258i | 0.355088 | − | 0.934833i | \(-0.384451\pi\) |
−0.457116 | + | 0.889407i | \(0.651118\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.42352 | − | 16.6735i | −0.297896 | − | 0.669084i | ||||
\(622\) | 0.0200899 | + | 0.126843i | 0.000805532 | + | 0.00508593i | ||||
\(623\) | 2.39804 | − | 1.06261i | 0.0960753 | − | 0.0425724i | ||||
\(624\) | 1.45235i | 0.0581404i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.413975 | + | 0.239009i | −0.0165458 | + | 0.00955270i | ||||
\(627\) | 20.8738 | − | 32.1429i | 0.833620 | − | 1.28366i | ||||
\(628\) | 3.75958 | − | 9.79405i | 0.150024 | − | 0.390825i | ||||
\(629\) | −9.96459 | − | 7.23970i | −0.397314 | − | 0.288666i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.3034 | − | 16.2043i | 0.887883 | − | 0.645085i | −0.0474420 | − | 0.998874i | \(-0.515107\pi\) |
0.935325 | + | 0.353789i | \(0.115107\pi\) | |||||||
\(632\) | 0.145882 | + | 0.544441i | 0.00580289 | + | 0.0216567i | ||||
\(633\) | −29.8516 | + | 11.4589i | −1.18649 | + | 0.455452i | ||||
\(634\) | 0.364721 | + | 0.328396i | 0.0144849 | + | 0.0130423i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.2963 | − | 7.89435i | −0.963411 | − | 0.313031i | ||||
\(637\) | 1.01352 | + | 2.00662i | 0.0401570 | + | 0.0795052i | ||||
\(638\) | 0.134282 | − | 0.263544i | 0.00531628 | − | 0.0104338i | ||||
\(639\) | −5.79828 | + | 5.22080i | −0.229377 | + | 0.206532i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.01518 | − | 1.12747i | 0.0400971 | − | 0.0445323i | −0.722763 | − | 0.691096i | \(-0.757128\pi\) |
0.762860 | + | 0.646564i | \(0.223795\pi\) | |||||||
\(642\) | −0.126867 | + | 0.156668i | −0.00500704 | + | 0.00618318i | ||||
\(643\) | 18.1864 | − | 18.1864i | 0.717201 | − | 0.717201i | −0.250830 | − | 0.968031i | \(-0.580703\pi\) |
0.968031 | + | 0.250830i | \(0.0807034\pi\) | |||||||
\(644\) | −16.0992 | − | 8.23879i | −0.634398 | − | 0.324654i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.391737 | − | 0.174412i | 0.0154127 | − | 0.00686216i | ||||
\(647\) | −5.86608 | + | 4.75026i | −0.230620 | + | 0.186752i | −0.737664 | − | 0.675168i | \(-0.764071\pi\) |
0.507045 | + | 0.861920i | \(0.330738\pi\) | |||||||
\(648\) | −0.0505467 | − | 0.0328254i | −0.00198566 | − | 0.00128950i | ||||
\(649\) | 24.2497 | − | 42.0017i | 0.951885 | − | 1.64871i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.121578 | + | 2.24404i | −0.00476501 | + | 0.0879510i | ||||
\(652\) | −16.1245 | − | 31.6461i | −0.631484 | − | 1.23936i | ||||
\(653\) | −32.2034 | − | 12.3617i | −1.26022 | − | 0.483751i | −0.365677 | − | 0.930742i | \(-0.619162\pi\) |
−0.894539 | + | 0.446990i | \(0.852496\pi\) | |||||||
\(654\) | 0.0184789 | − | 0.175815i | 0.000722581 | − | 0.00687489i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −32.9683 | + | 3.46511i | −1.28720 | + | 0.135290i | ||||
\(657\) | 12.2932 | + | 12.2932i | 0.479602 | + | 0.479602i | ||||
\(658\) | 0.191774 | − | 0.212232i | 0.00747614 | − | 0.00827368i | ||||
\(659\) | 16.9511 | − | 5.50773i | 0.660319 | − | 0.214551i | 0.0403605 | − | 0.999185i | \(-0.487149\pi\) |
0.619959 | + | 0.784634i | \(0.287149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.15962 | + | 38.3880i | 0.317372 | + | 1.49312i | 0.790684 | + | 0.612225i | \(0.209725\pi\) |
−0.473311 | + | 0.880895i | \(0.656941\pi\) | |||||||
\(662\) | −0.0150105 | − | 0.286418i | −0.000583401 | − | 0.0111320i | ||||
\(663\) | −1.13847 | + | 0.739334i | −0.0442147 | + | 0.0287134i | ||||
\(664\) | −0.0275707 | + | 0.0848540i | −0.00106995 | + | 0.00329297i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0300981 | + | 0.0926326i | 0.00116628 | + | 0.00358944i | ||||
\(667\) | −9.02044 | − | 7.30461i | −0.349273 | − | 0.282836i | ||||
\(668\) | −11.1090 | − | 2.97666i | −0.429822 | − | 0.115170i | ||||
\(669\) | −9.73964 | + | 21.8756i | −0.376556 | + | 0.845760i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.17313 | − | 11.2493i | 0.315520 | − | 0.434276i | ||||
\(672\) | −0.613371 | + | 0.0633735i | −0.0236613 | + | 0.00244468i | ||||
\(673\) | 15.3295 | − | 7.81076i | 0.590908 | − | 0.301083i | −0.132850 | − | 0.991136i | \(-0.542413\pi\) |
0.723759 | + | 0.690053i | \(0.242413\pi\) | |||||||
\(674\) | −0.355475 | − | 0.205234i | −0.0136924 | − | 0.00790531i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.8950 | + | 22.3347i | 0.495960 | + | 0.859028i | ||||
\(677\) | 0.0333362 | − | 0.636093i | 0.00128122 | − | 0.0244470i | −0.997914 | − | 0.0645556i | \(-0.979437\pi\) |
0.999195 | + | 0.0401085i | \(0.0127704\pi\) | |||||||
\(678\) | −0.163717 | + | 0.0259302i | −0.00628750 | + | 0.000995842i | ||||
\(679\) | 32.4515 | + | 5.19856i | 1.24538 | + | 0.199502i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.35771 | + | 22.4321i | 0.0903476 | + | 0.859600i | ||||
\(682\) | −0.0169304 | + | 0.0631853i | −0.000648300 | + | 0.00241949i | ||||
\(683\) | 6.51343 | + | 16.9681i | 0.249229 | + | 0.649265i | 0.999935 | − | 0.0113716i | \(-0.00361978\pi\) |
−0.750706 | + | 0.660637i | \(0.770286\pi\) | |||||||
\(684\) | 22.4858 | + | 4.77950i | 0.859765 | + | 0.182749i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.267679 | + | 0.171824i | −0.0102200 | + | 0.00656028i | ||||
\(687\) | 10.1208 | + | 5.15681i | 0.386133 | + | 0.196745i | ||||
\(688\) | 12.3048 | + | 18.9478i | 0.469117 | + | 0.722377i | ||||
\(689\) | 3.54803 | − | 0.754158i | 0.135169 | − | 0.0287311i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.16326 | − | 24.2912i | 0.196420 | − | 0.924081i | −0.763934 | − | 0.645295i | \(-0.776735\pi\) |
0.960353 | − | 0.278786i | \(-0.0899322\pi\) | |||||||
\(692\) | −4.46218 | − | 0.706740i | −0.169627 | − | 0.0268662i | ||||
\(693\) | 21.9460 | + | 7.17355i | 0.833661 | + | 0.272501i | ||||
\(694\) | 0.0370737 | + | 0.0510276i | 0.00140730 | + | 0.00193698i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.262392 | − | 0.0275786i | −0.00994596 | − | 0.00104536i | ||||
\(697\) | −19.4992 | − | 24.0795i | −0.738583 | − | 0.912074i | ||||
\(698\) | 0.0209068 | + | 0.00109568i | 0.000791333 | + | 4.14720e-5i | ||||
\(699\) | 3.15710 | 0.119413 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.79098 | −0.294261 | −0.147131 | − | 0.989117i | \(-0.547004\pi\) | ||||
−0.147131 | + | 0.989117i | \(0.547004\pi\) | |||||||
\(702\) | 0.0294103 | + | 0.00154133i | 0.00111002 | + | 5.81738e-5i | ||||
\(703\) | 13.8576 | + | 17.1127i | 0.522648 | + | 0.645417i | ||||
\(704\) | 40.3159 | + | 4.23737i | 1.51946 | + | 0.159702i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.256420 | + | 0.352932i | 0.00965050 | + | 0.0132828i | ||||
\(707\) | −6.42152 | − | 30.4753i | −0.241506 | − | 1.14614i | ||||
\(708\) | −21.3629 | − | 3.38355i | −0.802866 | − | 0.127162i | ||||
\(709\) | 9.38432 | − | 44.1498i | 0.352436 | − | 1.65808i | −0.342884 | − | 0.939378i | \(-0.611404\pi\) |
0.695319 | − | 0.718701i | \(-0.255263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.8098 | + | 2.93536i | −0.517907 | + | 0.110085i | ||||
\(712\) | −0.0370906 | − | 0.0571145i | −0.00139003 | − | 0.00214046i | ||||
\(713\) | 2.28721 | + | 1.16539i | 0.0856568 | + | 0.0436443i | ||||
\(714\) | −0.120611 | − | 0.149481i | −0.00451375 | − | 0.00559418i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 45.3872 | + | 9.64735i | 1.69620 | + | 0.360539i | ||||
\(717\) | −1.68842 | − | 4.39848i | −0.0630552 | − | 0.164264i | ||||
\(718\) | 0.0499613 | − | 0.186458i | 0.00186454 | − | 0.00695856i | ||||
\(719\) | 3.25147 | + | 30.9356i | 0.121259 | + | 1.15370i | 0.870762 | + | 0.491704i | \(0.163626\pi\) |
−0.749503 | + | 0.662001i | \(0.769708\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.2705 | − | 24.6012i | −1.12733 | − | 0.916195i | ||||
\(722\) | −0.434874 | + | 0.0688773i | −0.0161843 | + | 0.00256335i | ||||
\(723\) | 0.420174 | − | 8.01739i | 0.0156264 | − | 0.298170i | ||||
\(724\) | 1.82812 | + | 3.16640i | 0.0679417 | + | 0.117678i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.247682 | − | 0.142999i | −0.00919235 | − | 0.00530721i | ||||
\(727\) | 19.4572 | − | 9.91394i | 0.721628 | − | 0.367688i | −0.0542869 | − | 0.998525i | \(-0.517289\pi\) |
0.775915 | + | 0.630838i | \(0.217289\pi\) | |||||||
\(728\) | 0.0472814 | − | 0.0342246i | 0.00175236 | − | 0.00126845i | ||||
\(729\) | 11.5369 | − | 15.8791i | 0.427291 | − | 0.588116i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.58899 | + | 19.2912i | −0.317675 | + | 0.713510i | ||||
\(732\) | −5.98986 | − | 1.60498i | −0.221392 | − | 0.0593217i | ||||
\(733\) | −0.175122 | − | 0.141811i | −0.00646830 | − | 0.00523792i | 0.626081 | − | 0.779758i | \(-0.284658\pi\) |
−0.632549 | + | 0.774520i | \(0.717991\pi\) | |||||||
\(734\) | −0.0382810 | − | 0.117817i | −0.00141298 | − | 0.00434870i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.217655 | + | 0.669875i | −0.00802289 | + | 0.0246919i | ||||
\(737\) | −27.7716 | + | 18.0351i | −1.02298 | + | 0.664331i | ||||
\(738\) | 0.0128233 | + | 0.244683i | 0.000472032 | + | 0.00900691i | ||||
\(739\) | 8.38752 | + | 39.4602i | 0.308540 | + | 1.45157i | 0.810023 | + | 0.586398i | \(0.199455\pi\) |
−0.501483 | + | 0.865167i | \(0.667212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.30809 | − | 0.749943i | 0.0847897 | − | 0.0275498i | ||||
\(742\) | 0.157736 | + | 0.488393i | 0.00579066 | + | 0.0179295i | ||||
\(743\) | 1.97911 | + | 1.97911i | 0.0726064 | + | 0.0726064i | 0.742477 | − | 0.669871i | \(-0.233651\pi\) |
−0.669871 | + | 0.742477i | \(0.733651\pi\) | |||||||
\(744\) | 0.0580299 | − | 0.00609919i | 0.00212748 | − | 0.000223607i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.00700037 | + | 0.0666041i | −0.000256302 | + | 0.00243855i | ||||
\(747\) | −2.08638 | − | 0.800886i | −0.0763366 | − | 0.0293029i | ||||
\(748\) | 17.2067 | + | 33.7701i | 0.629141 | + | 1.23476i | ||||
\(749\) | −27.4161 | − | 1.48535i | −1.00176 | − | 0.0542734i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9793 | − | 25.9449i | 0.546602 | − | 0.946743i | −0.451902 | − | 0.892068i | \(-0.649254\pi\) |
0.998504 | − | 0.0546754i | \(-0.0174124\pi\) | |||||||
\(752\) | 21.1081 | + | 13.7078i | 0.769733 | + | 0.499870i | ||||
\(753\) | 3.22666 | − | 2.61289i | 0.117586 | − | 0.0952192i | ||||
\(754\) | 0.0171102 | − | 0.00761794i | 0.000623116 | − | 0.000277429i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.42867 | − | 28.2134i | −0.0519601 | − | 1.02611i | ||||
\(757\) | −29.2442 | + | 29.2442i | −1.06290 | + | 1.06290i | −0.0650131 | + | 0.997884i | \(0.520709\pi\) |
−0.997884 | + | 0.0650131i | \(0.979291\pi\) | |||||||
\(758\) | 0.0497906 | − | 0.0614863i | 0.00180848 | − | 0.00223328i | ||||
\(759\) | −13.1208 | + | 14.5721i | −0.476256 | + | 0.528936i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.3614 | − | 31.8396i | 1.28185 | − | 1.15418i | 0.302250 | − | 0.953229i | \(-0.402262\pi\) |
0.979601 | − | 0.200954i | \(-0.0644043\pi\) | |||||||
\(762\) | −0.142318 | + | 0.279315i | −0.00515565 | + | 0.0101185i | ||||
\(763\) | 20.8726 | − | 12.0018i | 0.755641 | − | 0.434493i | ||||
\(764\) | −1.40090 | − | 0.455180i | −0.0506828 | − | 0.0164679i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.362956 | + | 0.326807i | 0.0131141 | + | 0.0118080i | ||||
\(767\) | 2.86709 | − | 1.10057i | 0.103525 | − | 0.0397394i | ||||
\(768\) | −4.67702 | − | 17.4549i | −0.168767 | − | 0.629848i | ||||
\(769\) | −30.0966 | + | 21.8665i | −1.08531 | + | 0.788525i | −0.978601 | − | 0.205765i | \(-0.934032\pi\) |
−0.106710 | + | 0.994290i | \(0.534032\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.03351 | + | 3.65706i | 0.181277 | + | 0.131706i | ||||
\(772\) | −10.3449 | + | 26.9495i | −0.372322 | + | 0.969933i | ||||
\(773\) | 0.188996 | − | 0.291029i | 0.00679773 | − | 0.0104676i | −0.835255 | − | 0.549862i | \(-0.814680\pi\) |
0.842053 | + | 0.539395i | \(0.181347\pi\) | |||||||
\(774\) | 0.144615 | − | 0.0834938i | 0.00519809 | − | 0.00300112i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 0.853311i | − | 0.0306321i | ||||||
\(777\) | 5.81148 | − | 7.96919i | 0.208486 | − | 0.285893i | ||||
\(778\) | −0.0787362 | − | 0.497121i | −0.00282283 | − | 0.0178226i | ||||
\(779\) | 22.5305 | + | 50.6043i | 0.807239 | + | 1.81309i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.0096 | + | 9.35408i | 0.751783 | + | 0.334715i | ||||
\(782\) | −0.211917 | + | 0.0567829i | −0.00757812 | + | 0.00203055i | ||||
\(783\) | 2.83631 | − | 17.9077i | 0.101361 | − | 0.639970i | ||||
\(784\) | −18.6538 | − | 20.8648i | −0.666208 | − | 0.745173i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.0387367 | + | 0.0430215i | 0.00138169 | + | 0.00153453i | ||||
\(787\) | −9.65966 | + | 0.506241i | −0.344330 | + | 0.0180456i | −0.223717 | − | 0.974654i | \(-0.571819\pi\) |
−0.120613 | + | 0.992700i | \(0.538486\pi\) | |||||||
\(788\) | 20.0772 | − | 1.05220i | 0.715222 | − | 0.0374832i | ||||
\(789\) | −15.7417 | − | 17.4830i | −0.560421 | − | 0.622410i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.9351 | − | 15.9914i | −0.566587 | − | 0.568590i | ||||
\(792\) | 0.0937781 | − | 0.592092i | 0.00333226 | − | 0.0210391i | ||||
\(793\) | 0.850484 | − | 0.227886i | 0.0302016 | − | 0.00809249i | ||||
\(794\) | 0.0174813 | + | 0.00778316i | 0.000620387 | + | 0.000276214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.18995 | − | 11.6568i | −0.183953 | − | 0.413165i | ||||
\(797\) | −7.51322 | − | 47.4366i | −0.266132 | − | 1.68029i | −0.652377 | − | 0.757895i | \(-0.726228\pi\) |
0.386245 | − | 0.922396i | \(-0.373772\pi\) | |||||||
\(798\) | 0.139112 | + | 0.313941i | 0.00492451 | + | 0.0111134i | ||||
\(799\) | 23.5245i | 0.832235i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.47727 | − | 0.852904i | 0.0521969 | − | 0.0301359i | ||||
\(802\) | −0.0804096 | + | 0.123820i | −0.00283936 | + | 0.00437224i | ||||
\(803\) | 18.3641 | − | 47.8402i | 0.648056 | − | 1.68824i | ||||
\(804\) | 11.9473 | + | 8.68023i | 0.421349 | + | 0.306128i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.00335106 | + | 0.00243469i | −0.000118036 | + | 8.57583e-5i | ||||
\(807\) | 0.0458598 | + | 0.171151i | 0.00161434 | + | 0.00602480i | ||||
\(808\) | −0.754923 | + | 0.289788i | −0.0265581 | + | 0.0101947i | ||||
\(809\) | −24.0016 | − | 21.6112i | −0.843852 | − | 0.759808i | 0.128899 | − | 0.991658i | \(-0.458856\pi\) |
−0.972752 | + | 0.231850i | \(0.925522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.8661 | + | 8.40440i | 0.908281 | + | 0.295118i | 0.725651 | − | 0.688063i | \(-0.241539\pi\) |
0.182630 | + | 0.983182i | \(0.441539\pi\) | |||||||
\(812\) | −8.95528 | − | 15.5744i | −0.314269 | − | 0.546555i | ||||
\(813\) | 0.715992 | − | 1.40521i | 0.0251109 | − | 0.0492830i | ||||
\(814\) | 0.213350 | − | 0.192101i | 0.00747791 | − | 0.00673314i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11.3084 | − | 12.5593i | 0.395874 | − | 0.439663i | ||||
\(817\) | 23.7582 | − | 29.3390i | 0.831195 | − | 1.02644i | ||||
\(818\) | 0.188732 | − | 0.188732i | 0.00659886 | − | 0.00659886i | ||||
\(819\) | 0.794105 | + | 1.22755i | 0.0277483 | + | 0.0428942i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.432586 | − | 0.192600i | 0.0150974 | − | 0.00672177i | −0.399174 | − | 0.916875i | \(-0.630703\pi\) |
0.414271 | + | 0.910153i | \(0.364036\pi\) | |||||||
\(822\) | −0.233380 | + | 0.188987i | −0.00814006 | + | 0.00659169i | ||||
\(823\) | −13.5690 | − | 8.81180i | −0.472985 | − | 0.307160i | 0.286044 | − | 0.958216i | \(-0.407660\pi\) |
−0.759030 | + | 0.651056i | \(0.774326\pi\) | |||||||
\(824\) | −0.506382 | + | 0.877080i | −0.0176407 | + | 0.0305545i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.196589 | + | 0.387517i | 0.00684021 | + | 0.0134835i | ||||
\(827\) | 6.12078 | + | 12.0127i | 0.212841 | + | 0.417723i | 0.972601 | − | 0.232480i | \(-0.0746839\pi\) |
−0.759761 | + | 0.650203i | \(0.774684\pi\) | |||||||
\(828\) | −10.9803 | − | 4.21492i | −0.381590 | − | 0.146479i | ||||
\(829\) | −0.359804 | + | 3.42331i | −0.0124965 | + | 0.118896i | −0.998992 | − | 0.0448933i | \(-0.985705\pi\) |
0.986495 | + | 0.163790i | \(0.0523719\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.7841 | − | 3.55085i | 1.17196 | − | 0.123178i | ||||
\(832\) | 1.81509 | + | 1.81509i | 0.0629271 | + | 0.0629271i | ||||
\(833\) | 6.85971 | − | 25.2440i | 0.237675 | − | 0.874652i | ||||
\(834\) | 0.341022 | − | 0.110805i | 0.0118086 | − | 0.00383686i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −14.0878 | − | 66.2781i | −0.487238 | − | 2.29227i | ||||
\(837\) | 0.209856 | + | 4.00429i | 0.00725368 | + | 0.138409i | ||||
\(838\) | −0.0912929 | + | 0.0592863i | −0.00315366 | + | 0.00204801i | ||||
\(839\) | 8.56984 | − | 26.3753i | 0.295864 | − | 0.910575i | −0.687066 | − | 0.726595i | \(-0.741102\pi\) |
0.982930 | − | 0.183980i | \(-0.0588982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.39836 | + | 16.6145i | 0.186150 | + | 0.572912i | ||||
\(842\) | −0.295990 | − | 0.239688i | −0.0102005 | − | 0.00826019i | ||||
\(843\) | 31.2079 | + | 8.36213i | 1.07486 | + | 0.288007i | ||||
\(844\) | −22.9933 | + | 51.6438i | −0.791462 | + | 1.77765i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.109344 | − | 0.150499i | 0.00375931 | − | 0.00517425i | ||||
\(847\) | −4.00320 | − | 38.7457i | −0.137552 | − | 1.33132i | ||||
\(848\) | −40.2368 | + | 20.5017i | −1.38174 | + | 0.704030i | ||||
\(849\) | 27.5654 | + | 15.9149i | 0.946042 | + | 0.546198i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.63304 | − | 9.75671i | −0.193098 | − | 0.334456i | ||||
\(852\) | 0.536774 | − | 10.2423i | 0.0183896 | − | 0.350894i | ||||
\(853\) | 30.3919 | − | 4.81360i | 1.04060 | − | 0.164815i | 0.387330 | − | 0.921941i | \(-0.373397\pi\) |
0.653268 | + | 0.757126i | \(0.273397\pi\) | |||||||
\(854\) | 0.0444406 | + | 0.116385i | 0.00152073 | + | 0.00398263i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0745154 | + | 0.708966i | 0.00254688 | + | 0.0242320i | ||||
\(857\) | 1.08695 | − | 4.05654i | 0.0371294 | − | 0.138569i | −0.944873 | − | 0.327437i | \(-0.893815\pi\) |
0.982002 | + | 0.188868i | \(0.0604818\pi\) | |||||||
\(858\) | −0.0113391 | − | 0.0295394i | −0.000387110 | − | 0.00100846i | ||||
\(859\) | 7.03428 | + | 1.49518i | 0.240006 | + | 0.0510149i | 0.326344 | − | 0.945251i | \(-0.394183\pi\) |
−0.0863379 | + | 0.996266i | \(0.527516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.3099 | − | 15.5805i | 0.658078 | − | 0.530981i | ||||
\(862\) | −0.148930 | − | 0.0758837i | −0.00507258 | − | 0.00258461i | ||||
\(863\) | 5.37498 | + | 8.27674i | 0.182966 | + | 0.281743i | 0.918238 | − | 0.396029i | \(-0.129612\pi\) |
−0.735272 | + | 0.677773i | \(0.762945\pi\) | |||||||
\(864\) | −1.07619 | + | 0.228750i | −0.0366126 | + | 0.00778224i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.0444367 | + | 0.209058i | −0.00151002 | + | 0.00710408i | ||||
\(867\) | −3.38990 | − | 0.536908i | −0.115127 | − | 0.0182343i | ||||
\(868\) | 2.65337 | + | 2.95735i | 0.0900613 | + | 0.100379i | ||||
\(869\) | 24.4604 | + | 33.6668i | 0.829761 | + | 1.14207i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.08534 | − | 0.219178i | −0.0706589 | − | 0.00742655i | ||||
\(872\) | −0.393411 | − | 0.485822i | −0.0133226 | − | 0.0164520i | ||||
\(873\) | 21.3446 | + | 1.11862i | 0.722404 | + | 0.0378596i | ||||
\(874\) | 0.392224 | 0.0132672 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.8531 | −0.772133 | ||||||||
\(877\) | 32.6864 | + | 1.71302i | 1.10374 | + | 0.0578445i | 0.595488 | − | 0.803364i | \(-0.296959\pi\) |
0.508252 | + | 0.861209i | \(0.330292\pi\) | |||||||
\(878\) | −0.265166 | − | 0.327453i | −0.00894891 | − | 0.0110510i | ||||
\(879\) | −7.26621 | − | 0.763709i | −0.245083 | − | 0.0257593i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3837 | − | 15.6683i | −0.383527 | − | 0.527880i | 0.572988 | − | 0.819564i | \(-0.305784\pi\) |
−0.956515 | + | 0.291684i | \(0.905784\pi\) | |||||||
\(882\) | −0.161221 | + | 0.129615i | −0.00542861 | + | 0.00436436i | ||||
\(883\) | −36.1203 | − | 5.72089i | −1.21554 | − | 0.192523i | −0.484461 | − | 0.874813i | \(-0.660984\pi\) |
−0.731082 | + | 0.682289i | \(0.760984\pi\) | |||||||
\(884\) | −0.498980 | + | 2.34752i | −0.0167825 | + | 0.0789556i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.117722 | − | 0.0250226i | 0.00395495 | − | 0.000840650i | ||||
\(887\) | 6.23155 | + | 9.59574i | 0.209235 | + | 0.322194i | 0.927670 | − | 0.373400i | \(-0.121808\pi\) |
−0.718435 | + | 0.695594i | \(0.755141\pi\) | |||||||
\(888\) | −0.228174 | − | 0.116260i | −0.00765701 | − | 0.00390144i | ||||
\(889\) | −42.1812 | + | 6.60455i | −1.41471 | + | 0.221509i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.35255 | − | 0.925162i | −0.145816 | − | 0.0309941i | ||||
\(892\) | 15.1716 | + | 39.5234i | 0.507983 | + | 1.32334i | ||||
\(893\) | 10.8850 | − | 40.6235i | 0.364253 | − | 1.35941i | ||||
\(894\) | 0.0299493 | + | 0.284948i | 0.00100165 | + | 0.00953010i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.916741 | + | 1.12800i | −0.0306262 | + | 0.0376839i | ||||
\(897\) | −1.22637 | + | 0.194238i | −0.0409474 | + | 0.00648543i | ||||
\(898\) | 0.0102269 | − | 0.195140i | 0.000341275 | − | 0.00651192i | ||||
\(899\) | 1.27503 | + | 2.20841i | 0.0425246 | + | 0.0736547i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.5540 | − | 21.1045i | −1.21779 | − | 0.703091i | ||||
\(902\) | 0.643490 | − | 0.327875i | 0.0214259 | − | 0.0109170i | ||||
\(903\) | −15.4358 | − | 6.90514i | −0.513672 | − | 0.229789i | ||||
\(904\) | −0.344529 | + | 0.474204i | −0.0114589 | + | 0.0157718i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.0443454 | + | 0.0996015i | −0.00147328 | + | 0.00330904i | ||||
\(907\) | 0.668595 | + | 0.179150i | 0.0222003 | + | 0.00594856i | 0.269902 | − | 0.962888i | \(-0.413009\pi\) |
−0.247702 | + | 0.968836i | \(0.579675\pi\) | |||||||
\(908\) | 30.9906 | + | 25.0957i | 1.02846 | + | 0.832831i | ||||
\(909\) | −6.25905 | − | 19.2634i | −0.207600 | − | 0.638926i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.30607 | − | 22.4858i | 0.242061 | − | 0.744987i | −0.754045 | − | 0.656823i | \(-0.771900\pi\) |
0.996106 | − | 0.0881643i | \(-0.0281000\pi\) | |||||||
\(912\) | −25.3394 | + | 16.4556i | −0.839071 | + | 0.544899i | ||||
\(913\) | 0.344749 | + | 6.57821i | 0.0114095 | + | 0.217707i | ||||
\(914\) | 0.0244848 | + | 0.115192i | 0.000809886 | + | 0.00381021i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.0991 | − | 6.20568i | 0.631053 | − | 0.205042i | ||||
\(917\) | −1.65290 | + | 7.70934i | −0.0545835 | + | 0.254585i | ||||
\(918\) | −0.242327 | − | 0.242327i | −0.00799798 | − | 0.00799798i | ||||
\(919\) | −7.72720 | + | 0.812161i | −0.254897 | + | 0.0267907i | −0.231115 | − | 0.972926i | \(-0.574237\pi\) |
−0.0237818 | + | 0.999717i | \(0.507571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.08913 | + | 19.8767i | −0.0688391 | + | 0.654960i | ||||
\(922\) | 0.104497 | + | 0.0401126i | 0.00344142 | + | 0.00132104i | ||||
\(923\) | 0.661131 | + | 1.29754i | 0.0217614 | + | 0.0427091i | ||||
\(924\) | −27.0667 | + | 13.7310i | −0.890429 | + | 0.451718i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.0385095 | − | 0.0667005i | 0.00126550 | − | 0.00219191i | ||||
\(927\) | −21.2753 | − | 13.8163i | −0.698772 | − | 0.453788i | ||||
\(928\) | −0.543768 | + | 0.440335i | −0.0178501 | + | 0.0144547i | ||||
\(929\) | 50.4013 | − | 22.4401i | 1.65361 | − | 0.736236i | 0.653822 | − | 0.756648i | \(-0.273164\pi\) |
0.999792 | + | 0.0204117i | \(0.00649769\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.5264 | + | 40.4188i | −0.771048 | + | 1.32467i | ||||
\(932\) | 3.94681 | − | 3.94681i | 0.129282 | − | 0.129282i | ||||
\(933\) | 5.32256 | − | 6.57281i | 0.174253 | − | 0.215184i | ||||
\(934\) | −0.461678 | + | 0.512745i | −0.0151066 | + | 0.0167775i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.0282095 | − | 0.0253999i | 0.000922056 | − | 0.000830223i | ||||
\(937\) | 15.4139 | − | 30.2515i | 0.503551 | − | 0.988274i | −0.489657 | − | 0.871915i | \(-0.662878\pi\) |
0.993207 | − | 0.116358i | \(-0.0371221\pi\) | |||||||
\(938\) | 0.000523698 | − | 0.296683i | 1.70994e−5 | − | 0.00968704i | ||||
\(939\) | 29.9400 | + | 9.72811i | 0.977057 | + | 0.317465i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.2943 | − | 15.5719i | −0.563779 | − | 0.507629i | 0.337234 | − | 0.941421i | \(-0.390509\pi\) |
−0.901013 | + | 0.433792i | \(0.857175\pi\) | |||||||
\(942\) | 0.0951439 | − | 0.0365223i | 0.00309995 | − | 0.00118996i | ||||
\(943\) | −7.33518 | − | 27.3753i | −0.238866 | − | 0.891462i | ||||
\(944\) | −30.9319 | + | 22.4733i | −1.00675 | + | 0.731444i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.398202 | − | 0.289311i | −0.0129467 | − | 0.00940630i | ||||
\(947\) | 11.5591 | − | 30.1124i | 0.375619 | − | 0.978521i | −0.607298 | − | 0.794474i | \(-0.707747\pi\) |
0.982917 | − | 0.184047i | \(-0.0589200\pi\) | |||||||
\(948\) | 10.1078 | − | 15.5646i | 0.328286 | − | 0.505516i | ||||
\(949\) | 2.81012 | − | 1.62242i | 0.0912202 | − | 0.0526660i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 32.3214i | − | 1.04809i | ||||||
\(952\) | −0.675353 | − | 0.0721879i | −0.0218883 | − | 0.00233962i | ||||
\(953\) | 4.45329 | + | 28.1170i | 0.144256 | + | 0.910797i | 0.948564 | + | 0.316585i | \(0.102536\pi\) |
−0.804308 | + | 0.594213i | \(0.797464\pi\) | |||||||
\(954\) | 0.135760 | + | 0.304923i | 0.00439540 | + | 0.00987224i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.60946 | − | 3.38795i | −0.246107 | − | 0.109574i | ||||
\(957\) | −18.8156 | + | 5.04162i | −0.608222 | + | 0.162973i | ||||
\(958\) | −0.0557136 | + | 0.351762i | −0.00180002 | + | 0.0113649i | ||||
\(959\) | −39.4878 | − | 10.6555i | −1.27513 | − | 0.344083i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.3657 | + | 22.6184i | 0.656958 | + | 0.729625i | ||||
\(962\) | 0.0181542 | 0.000951419i | 0.000585314 | 3.06750e-5i | ||||||
\(963\) | −17.8316 | + | 0.934516i | −0.574616 | + | 0.0301144i | ||||
\(964\) | −9.49755 | − | 10.5481i | −0.305896 | − | 0.339732i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.0451709 | − | 0.169778i | −0.00145335 | − | 0.00546253i | ||||
\(967\) | −3.33883 | + | 21.0805i | −0.107369 | + | 0.677904i | 0.874022 | + | 0.485886i | \(0.161503\pi\) |
−0.981391 | + | 0.192018i | \(0.938497\pi\) | |||||||
\(968\) | −0.976883 | + | 0.261755i | −0.0313982 | + | 0.00841312i | ||||
\(969\) | −25.7986 | − | 11.4863i | −0.828772 | − | 0.368993i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.6561 | + | 48.6404i | 0.694978 | + | 1.56095i | 0.822281 | + | 0.569082i | \(0.192701\pi\) |
−0.127302 | + | 0.991864i | \(0.540632\pi\) | |||||||
\(972\) | −4.70046 | − | 29.6775i | −0.150767 | − | 0.951908i | ||||
\(973\) | 39.4585 | + | 28.7749i | 1.26498 | + | 0.922479i | ||||
\(974\) | − | 0.127666i | − | 0.00409070i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.49319 | + | 5.48089i | −0.303870 | + | 0.175439i | ||||
\(977\) | 20.2636 | − | 31.2032i | 0.648289 | − | 0.998278i | −0.349820 | − | 0.936817i | \(-0.613757\pi\) |
0.998109 | − | 0.0614611i | \(-0.0195760\pi\) | |||||||
\(978\) | 0.123648 | − | 0.322114i | 0.00395383 | − | 0.0103001i | ||||
\(979\) | −4.06771 | − | 2.95536i | −0.130005 | − | 0.0944538i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.6680 | − | 9.20384i | 0.404458 | − | 0.293856i | ||||
\(982\) | −0.0902509 | − | 0.336821i | −0.00288002 | − | 0.0107484i | ||||
\(983\) | −18.7129 | + | 7.18320i | −0.596848 | + | 0.229109i | −0.637990 | − | 0.770045i | \(-0.720234\pi\) |
0.0411417 | + | 0.999153i | \(0.486900\pi\) | |||||||
\(984\) | −0.478740 | − | 0.431060i | −0.0152617 | − | 0.0137417i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.207277 | − | 0.0673484i | −0.00660105 | − | 0.00214481i | ||||
\(987\) | −18.8379 | − | 0.0332522i | −0.599616 | − | 0.00105843i | ||||
\(988\) | 1.94789 | − | 3.82295i | 0.0619707 | − | 0.121624i | ||||
\(989\) | −14.3540 | + | 12.9244i | −0.456431 | + | 0.410972i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.5931 | + | 29.5346i | −0.844756 | + | 0.938197i | −0.998756 | − | 0.0498742i | \(-0.984118\pi\) |
0.153999 | + | 0.988071i | \(0.450785\pi\) | |||||||
\(992\) | 0.0973831 | − | 0.120258i | 0.00309192 | − | 0.00381820i | ||||
\(993\) | −13.3562 | + | 13.3562i | −0.423847 | + | 0.423847i | ||||
\(994\) | −0.173005 | + | 0.111917i | −0.00548740 | + | 0.00354980i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.68372 | − | 1.19487i | 0.0850369 | − | 0.0378609i | ||||
\(997\) | −8.84910 | + | 7.16586i | −0.280254 | + | 0.226945i | −0.759133 | − | 0.650936i | \(-0.774377\pi\) |
0.478879 | + | 0.877881i | \(0.341043\pi\) | |||||||
\(998\) | −0.132592 | − | 0.0861063i | −0.00419713 | − | 0.00272565i | ||||
\(999\) | 8.79910 | − | 15.2405i | 0.278391 | − | 0.482188i |
(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 | 875.2.bb.a.243.9 | 288 | ||
5.2 | odd | 4 | 875.2.bb.c.257.10 | 288 | |||
5.3 | odd | 4 | 175.2.x.a.47.9 | yes | 288 | ||
5.4 | even | 2 | 875.2.bb.b.243.10 | 288 | |||
7.3 | odd | 6 | inner | 875.2.bb.a.493.10 | 288 | ||
25.6 | even | 5 | 875.2.bb.c.768.10 | 288 | |||
25.8 | odd | 20 | 875.2.bb.b.607.9 | 288 | |||
25.17 | odd | 20 | inner | 875.2.bb.a.607.10 | 288 | ||
25.19 | even | 10 | 175.2.x.a.33.9 | ✓ | 288 | ||
35.3 | even | 12 | 175.2.x.a.122.9 | yes | 288 | ||
35.17 | even | 12 | 875.2.bb.c.507.10 | 288 | |||
35.24 | odd | 6 | 875.2.bb.b.493.9 | 288 | |||
175.17 | even | 60 | inner | 875.2.bb.a.857.9 | 288 | ||
175.31 | odd | 30 | 875.2.bb.c.143.10 | 288 | |||
175.94 | odd | 30 | 175.2.x.a.108.9 | yes | 288 | ||
175.108 | even | 60 | 875.2.bb.b.857.10 | 288 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.x.a.33.9 | ✓ | 288 | 25.19 | even | 10 | ||
175.2.x.a.47.9 | yes | 288 | 5.3 | odd | 4 | ||
175.2.x.a.108.9 | yes | 288 | 175.94 | odd | 30 | ||
175.2.x.a.122.9 | yes | 288 | 35.3 | even | 12 | ||
875.2.bb.a.243.9 | 288 | 1.1 | even | 1 | trivial | ||
875.2.bb.a.493.10 | 288 | 7.3 | odd | 6 | inner | ||
875.2.bb.a.607.10 | 288 | 25.17 | odd | 20 | inner | ||
875.2.bb.a.857.9 | 288 | 175.17 | even | 60 | inner | ||
875.2.bb.b.243.10 | 288 | 5.4 | even | 2 | |||
875.2.bb.b.493.9 | 288 | 35.24 | odd | 6 | |||
875.2.bb.b.607.9 | 288 | 25.8 | odd | 20 | |||
875.2.bb.b.857.10 | 288 | 175.108 | even | 60 | |||
875.2.bb.c.143.10 | 288 | 175.31 | odd | 30 | |||
875.2.bb.c.257.10 | 288 | 5.2 | odd | 4 | |||
875.2.bb.c.507.10 | 288 | 35.17 | even | 12 | |||
875.2.bb.c.768.10 | 288 | 25.6 | even | 5 |