Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [430,2,Mod(221,430)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(430, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("430.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 430 = 2 \cdot 5 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 430.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: | \(3.43356728692\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 221.2 | ||
Root | \(-1.62241 + 0.606458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 430.221 |
Dual form | 430.2.e.e.251.2 |
$q$-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 \(\left(\mathbb{Z}/430\mathbb{Z}\right)^\times\).
\(n\) | \(87\) | \(261\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.285997 | − | 0.495361i | 0.165120 | − | 0.285997i | −0.771578 | − | 0.636135i | \(-0.780532\pi\) |
0.936698 | + | 0.350138i | \(0.113865\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0.285997 | − | 0.495361i | 0.116758 | − | 0.202230i | ||||
\(7\) | 2.33641 | + | 4.04678i | 0.883081 | + | 1.52954i | 0.847898 | + | 0.530160i | \(0.177868\pi\) |
0.0351829 | + | 0.999381i | \(0.488799\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.33641 | + | 2.31473i | 0.445471 | + | 0.771578i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −1.57199 | −0.473974 | −0.236987 | − | 0.971513i | \(-0.576160\pi\) | ||||
−0.236987 | + | 0.971513i | \(0.576160\pi\) | |||||||
\(12\) | 0.285997 | − | 0.495361i | 0.0825601 | − | 0.142998i | ||||
\(13\) | −2.45882 | − | 4.25880i | −0.681954 | − | 1.18118i | −0.974384 | − | 0.224892i | \(-0.927797\pi\) |
0.292430 | − | 0.956287i | \(-0.405536\pi\) | |||||||
\(14\) | 2.33641 | + | 4.04678i | 0.624432 | + | 1.08155i | ||||
\(15\) | −0.285997 | − | 0.495361i | −0.0738440 | − | 0.127902i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 1.33641 | + | 2.31473i | 0.314995 | + | 0.545588i | ||||
\(19\) | −0.214003 | + | 0.370665i | −0.0490957 | + | 0.0850363i | −0.889529 | − | 0.456879i | \(-0.848967\pi\) |
0.840433 | + | 0.541915i | \(0.182301\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 2.67282 | 0.583258 | ||||||||
\(22\) | −1.57199 | −0.335150 | ||||||||
\(23\) | 0.336412 | − | 0.582682i | 0.0701467 | − | 0.121498i | −0.828819 | − | 0.559517i | \(-0.810987\pi\) |
0.898965 | + | 0.438020i | \(0.144320\pi\) | |||||||
\(24\) | 0.285997 | − | 0.495361i | 0.0583788 | − | 0.101115i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −2.45882 | − | 4.25880i | −0.482214 | − | 0.835220i | ||||
\(27\) | 3.24482 | 0.624465 | ||||||||
\(28\) | 2.33641 | + | 4.04678i | 0.441540 | + | 0.764770i | ||||
\(29\) | −2.47842 | − | 4.29275i | −0.460231 | − | 0.797144i | 0.538741 | − | 0.842472i | \(-0.318900\pi\) |
−0.998972 | + | 0.0453274i | \(0.985567\pi\) | |||||||
\(30\) | −0.285997 | − | 0.495361i | −0.0522156 | − | 0.0904401i | ||||
\(31\) | 3.12241 | − | 5.40817i | 0.560801 | − | 0.971336i | −0.436626 | − | 0.899643i | \(-0.643827\pi\) |
0.997427 | − | 0.0716927i | \(-0.0228401\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.449585 | + | 0.778704i | −0.0782627 | + | 0.135555i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.67282 | 0.789851 | ||||||||
\(36\) | 1.33641 | + | 2.31473i | 0.222735 | + | 0.385789i | ||||
\(37\) | 2.78600 | − | 4.82549i | 0.458015 | − | 0.793305i | −0.540841 | − | 0.841125i | \(-0.681894\pi\) |
0.998856 | + | 0.0478196i | \(0.0152273\pi\) | |||||||
\(38\) | −0.214003 | + | 0.370665i | −0.0347159 | + | 0.0601298i | ||||
\(39\) | −2.81286 | −0.450418 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −7.48963 | −1.16968 | −0.584842 | − | 0.811147i | \(-0.698844\pi\) | ||||
−0.584842 | + | 0.811147i | \(0.698844\pi\) | |||||||
\(42\) | 2.67282 | 0.412426 | ||||||||
\(43\) | 1.90643 | + | 6.27420i | 0.290728 | + | 0.956806i | ||||
\(44\) | −1.57199 | −0.236987 | ||||||||
\(45\) | 2.67282 | 0.398441 | ||||||||
\(46\) | 0.336412 | − | 0.582682i | 0.0496012 | − | 0.0859118i | ||||
\(47\) | −10.6336 | −1.55107 | −0.775536 | − | 0.631303i | \(-0.782521\pi\) | ||||
−0.775536 | + | 0.631303i | \(0.782521\pi\) | |||||||
\(48\) | 0.285997 | − | 0.495361i | 0.0412801 | − | 0.0714992i | ||||
\(49\) | −7.41764 | + | 12.8477i | −1.05966 | + | 1.83539i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.45882 | − | 4.25880i | −0.340977 | − | 0.590590i | ||||
\(53\) | −2.24482 | + | 3.88814i | −0.308349 | + | 0.534077i | −0.978001 | − | 0.208598i | \(-0.933110\pi\) |
0.669652 | + | 0.742675i | \(0.266443\pi\) | |||||||
\(54\) | 3.24482 | 0.441564 | ||||||||
\(55\) | −0.785997 | + | 1.36139i | −0.105984 | + | 0.183569i | ||||
\(56\) | 2.33641 | + | 4.04678i | 0.312216 | + | 0.540774i | ||||
\(57\) | 0.122408 | + | 0.212018i | 0.0162134 | + | 0.0280824i | ||||
\(58\) | −2.47842 | − | 4.29275i | −0.325433 | − | 0.563666i | ||||
\(59\) | −10.2017 | −1.32814 | −0.664072 | − | 0.747669i | \(-0.731173\pi\) | ||||
−0.664072 | + | 0.747669i | \(0.731173\pi\) | |||||||
\(60\) | −0.285997 | − | 0.495361i | −0.0369220 | − | 0.0639508i | ||||
\(61\) | 3.90841 | + | 6.76956i | 0.500420 | + | 0.866753i | 1.00000 | 0.000485039i | \(0.000154393\pi\) | |
−0.499580 | + | 0.866268i | \(0.666512\pi\) | |||||||
\(62\) | 3.12241 | − | 5.40817i | 0.396546 | − | 0.686838i | ||||
\(63\) | −6.24482 | + | 10.8163i | −0.786773 | + | 1.36273i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.91764 | −0.609958 | ||||||||
\(66\) | −0.449585 | + | 0.778704i | −0.0553401 | + | 0.0958518i | ||||
\(67\) | 5.63164 | − | 9.75429i | 0.688015 | − | 1.19168i | −0.284464 | − | 0.958687i | \(-0.591816\pi\) |
0.972479 | − | 0.232990i | \(-0.0748509\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.192425 | − | 0.333290i | −0.0231653 | − | 0.0401235i | ||||
\(70\) | 4.67282 | 0.558509 | ||||||||
\(71\) | −0.449585 | − | 0.778704i | −0.0533559 | − | 0.0924151i | 0.838114 | − | 0.545495i | \(-0.183658\pi\) |
−0.891470 | + | 0.453080i | \(0.850325\pi\) | |||||||
\(72\) | 1.33641 | + | 2.31473i | 0.157498 | + | 0.272794i | ||||
\(73\) | −7.22324 | − | 12.5110i | −0.845416 | − | 1.46430i | −0.885259 | − | 0.465098i | \(-0.846019\pi\) |
0.0398431 | − | 0.999206i | \(-0.487314\pi\) | |||||||
\(74\) | 2.78600 | − | 4.82549i | 0.323866 | − | 0.560952i | ||||
\(75\) | −0.571993 | −0.0660481 | ||||||||
\(76\) | −0.214003 | + | 0.370665i | −0.0245479 | + | 0.0425182i | ||||
\(77\) | −3.67282 | − | 6.36152i | −0.418557 | − | 0.724962i | ||||
\(78\) | −2.81286 | −0.318493 | ||||||||
\(79\) | 6.48963 | + | 11.2404i | 0.730141 | + | 1.26464i | 0.956823 | + | 0.290672i | \(0.0938789\pi\) |
−0.226682 | + | 0.973969i | \(0.572788\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −3.08123 | + | 5.33684i | −0.342359 | + | 0.592983i | ||||
\(82\) | −7.48963 | −0.827092 | ||||||||
\(83\) | 7.86723 | − | 13.6264i | 0.863540 | − | 1.49570i | −0.00494923 | − | 0.999988i | \(-0.501575\pi\) |
0.868489 | − | 0.495708i | \(-0.165091\pi\) | |||||||
\(84\) | 2.67282 | 0.291629 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.90643 | + | 6.27420i | 0.205575 | + | 0.676564i | ||||
\(87\) | −2.83528 | −0.303974 | ||||||||
\(88\) | −1.57199 | −0.167575 | ||||||||
\(89\) | −3.21598 | + | 5.57024i | −0.340893 | + | 0.590444i | −0.984599 | − | 0.174829i | \(-0.944063\pi\) |
0.643706 | + | 0.765273i | \(0.277396\pi\) | |||||||
\(90\) | 2.67282 | 0.281740 | ||||||||
\(91\) | 11.4896 | − | 19.9006i | 1.20444 | − | 2.08615i | ||||
\(92\) | 0.336412 | − | 0.582682i | 0.0350734 | − | 0.0607488i | ||||
\(93\) | −1.78600 | − | 3.09344i | −0.185199 | − | 0.320774i | ||||
\(94\) | −10.6336 | −1.09677 | ||||||||
\(95\) | 0.214003 | + | 0.370665i | 0.0219563 | + | 0.0380294i | ||||
\(96\) | 0.285997 | − | 0.495361i | 0.0291894 | − | 0.0505575i | ||||
\(97\) | −4.28797 | −0.435378 | −0.217689 | − | 0.976018i | \(-0.569852\pi\) | ||||
−0.217689 | + | 0.976018i | \(0.569852\pi\) | |||||||
\(98\) | −7.41764 | + | 12.8477i | −0.749295 | + | 1.29782i | ||||
\(99\) | −2.10083 | − | 3.63875i | −0.211141 | − | 0.365708i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −0.570017 | − | 0.987298i | −0.0567188 | − | 0.0982398i | 0.836272 | − | 0.548315i | \(-0.184731\pi\) |
−0.892991 | + | 0.450075i | \(0.851397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.98040 | + | 6.89425i | 0.392200 | + | 0.679311i | 0.992739 | − | 0.120284i | \(-0.0383807\pi\) |
−0.600539 | + | 0.799595i | \(0.705047\pi\) | |||||||
\(104\) | −2.45882 | − | 4.25880i | −0.241107 | − | 0.417610i | ||||
\(105\) | 1.33641 | − | 2.31473i | 0.130420 | − | 0.225895i | ||||
\(106\) | −2.24482 | + | 3.88814i | −0.218036 | + | 0.377649i | ||||
\(107\) | 6.30249 | 0.609285 | 0.304642 | − | 0.952467i | \(-0.401463\pi\) | ||||
0.304642 | + | 0.952467i | \(0.401463\pi\) | |||||||
\(108\) | 3.24482 | 0.312233 | ||||||||
\(109\) | −10.1512 | + | 17.5825i | −0.972313 | + | 1.68410i | −0.283782 | + | 0.958889i | \(0.591589\pi\) |
−0.688531 | + | 0.725207i | \(0.741744\pi\) | |||||||
\(110\) | −0.785997 | + | 1.36139i | −0.0749418 | + | 0.129803i | ||||
\(111\) | −1.59357 | − | 2.76015i | −0.151255 | − | 0.261982i | ||||
\(112\) | 2.33641 | + | 4.04678i | 0.220770 | + | 0.382385i | ||||
\(113\) | −1.95684 | −0.184084 | −0.0920422 | − | 0.995755i | \(-0.529339\pi\) | ||||
−0.0920422 | + | 0.995755i | \(0.529339\pi\) | |||||||
\(114\) | 0.122408 | + | 0.212018i | 0.0114646 | + | 0.0198573i | ||||
\(115\) | −0.336412 | − | 0.582682i | −0.0313706 | − | 0.0543354i | ||||
\(116\) | −2.47842 | − | 4.29275i | −0.230116 | − | 0.398572i | ||||
\(117\) | 6.57199 | − | 11.3830i | 0.607581 | − | 1.05236i | ||||
\(118\) | −10.2017 | −0.939139 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.285997 | − | 0.495361i | −0.0261078 | − | 0.0452200i | ||||
\(121\) | −8.52884 | −0.775349 | ||||||||
\(122\) | 3.90841 | + | 6.76956i | 0.353850 | + | 0.612887i | ||||
\(123\) | −2.14201 | + | 3.71007i | −0.193139 | + | 0.334526i | ||||
\(124\) | 3.12241 | − | 5.40817i | 0.280401 | − | 0.485668i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −6.24482 | + | 10.8163i | −0.556333 | + | 0.963596i | ||||
\(127\) | −1.00000 | −0.0887357 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.65322 | + | 0.850029i | 0.321648 | + | 0.0748409i | ||||
\(130\) | −4.91764 | −0.431306 | ||||||||
\(131\) | 7.05767 | 0.616632 | 0.308316 | − | 0.951284i | \(-0.400235\pi\) | ||||
0.308316 | + | 0.951284i | \(0.400235\pi\) | |||||||
\(132\) | −0.449585 | + | 0.778704i | −0.0391313 | + | 0.0677775i | ||||
\(133\) | −2.00000 | −0.173422 | ||||||||
\(134\) | 5.63164 | − | 9.75429i | 0.486500 | − | 0.842643i | ||||
\(135\) | 1.62241 | − | 2.81009i | 0.139635 | − | 0.241854i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.7921 | 1.17834 | 0.589170 | − | 0.808009i | \(-0.299455\pi\) | ||||
0.589170 | + | 0.808009i | \(0.299455\pi\) | |||||||
\(138\) | −0.192425 | − | 0.333290i | −0.0163803 | − | 0.0283716i | ||||
\(139\) | −4.52884 | + | 7.84418i | −0.384131 | + | 0.665334i | −0.991648 | − | 0.128972i | \(-0.958832\pi\) |
0.607517 | + | 0.794306i | \(0.292166\pi\) | |||||||
\(140\) | 4.67282 | 0.394926 | ||||||||
\(141\) | −3.04118 | + | 5.26748i | −0.256114 | + | 0.443602i | ||||
\(142\) | −0.449585 | − | 0.778704i | −0.0377283 | − | 0.0653474i | ||||
\(143\) | 3.86525 | + | 6.69481i | 0.323228 | + | 0.559848i | ||||
\(144\) | 1.33641 | + | 2.31473i | 0.111368 | + | 0.192894i | ||||
\(145\) | −4.95684 | −0.411643 | ||||||||
\(146\) | −7.22324 | − | 12.5110i | −0.597800 | − | 1.03542i | ||||
\(147\) | 4.24284 | + | 7.34882i | 0.349944 | + | 0.606120i | ||||
\(148\) | 2.78600 | − | 4.82549i | 0.229008 | − | 0.396653i | ||||
\(149\) | 4.72324 | − | 8.18089i | 0.386943 | − | 0.670205i | −0.605094 | − | 0.796154i | \(-0.706864\pi\) |
0.992037 | + | 0.125950i | \(0.0401977\pi\) | |||||||
\(150\) | −0.571993 | −0.0467031 | ||||||||
\(151\) | 5.75518 | 0.468350 | 0.234175 | − | 0.972194i | \(-0.424761\pi\) | ||||
0.234175 | + | 0.972194i | \(0.424761\pi\) | |||||||
\(152\) | −0.214003 | + | 0.370665i | −0.0173580 | + | 0.0300649i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.67282 | − | 6.36152i | −0.295965 | − | 0.512626i | ||||
\(155\) | −3.12241 | − | 5.40817i | −0.250798 | − | 0.434395i | ||||
\(156\) | −2.81286 | −0.225209 | ||||||||
\(157\) | −3.35799 | − | 5.81621i | −0.267997 | − | 0.464184i | 0.700348 | − | 0.713802i | \(-0.253028\pi\) |
−0.968344 | + | 0.249618i | \(0.919695\pi\) | |||||||
\(158\) | 6.48963 | + | 11.2404i | 0.516288 | + | 0.894236i | ||||
\(159\) | 1.28402 | + | 2.22399i | 0.101829 | + | 0.176374i | ||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | 3.14399 | 0.247781 | ||||||||
\(162\) | −3.08123 | + | 5.33684i | −0.242084 | + | 0.419302i | ||||
\(163\) | 6.30447 | + | 10.9197i | 0.493804 | + | 0.855294i | 0.999975 | − | 0.00713978i | \(-0.00227268\pi\) |
−0.506170 | + | 0.862433i | \(0.668939\pi\) | |||||||
\(164\) | −7.48963 | −0.584842 | ||||||||
\(165\) | 0.449585 | + | 0.778704i | 0.0350001 | + | 0.0606220i | ||||
\(166\) | 7.86723 | − | 13.6264i | 0.610615 | − | 1.05762i | ||||
\(167\) | 12.6625 | − | 21.9320i | 0.979850 | − | 1.69715i | 0.316951 | − | 0.948442i | \(-0.397341\pi\) |
0.662899 | − | 0.748709i | \(-0.269326\pi\) | |||||||
\(168\) | 2.67282 | 0.206213 | ||||||||
\(169\) | −5.59159 | + | 9.68493i | −0.430123 | + | 0.744994i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.14399 | −0.0874828 | ||||||||
\(172\) | 1.90643 | + | 6.27420i | 0.145364 | + | 0.478403i | ||||
\(173\) | 9.91369 | 0.753724 | 0.376862 | − | 0.926269i | \(-0.377003\pi\) | ||||
0.376862 | + | 0.926269i | \(0.377003\pi\) | |||||||
\(174\) | −2.83528 | −0.214942 | ||||||||
\(175\) | 2.33641 | − | 4.04678i | 0.176616 | − | 0.305908i | ||||
\(176\) | −1.57199 | −0.118493 | ||||||||
\(177\) | −2.91764 | + | 5.05350i | −0.219303 | + | 0.379844i | ||||
\(178\) | −3.21598 | + | 5.57024i | −0.241048 | + | 0.417507i | ||||
\(179\) | −1.95684 | − | 3.38935i | −0.146261 | − | 0.253332i | 0.783581 | − | 0.621289i | \(-0.213391\pi\) |
−0.929843 | + | 0.367957i | \(0.880057\pi\) | |||||||
\(180\) | 2.67282 | 0.199221 | ||||||||
\(181\) | −1.28797 | − | 2.23083i | −0.0957343 | − | 0.165817i | 0.814181 | − | 0.580612i | \(-0.197187\pi\) |
−0.909915 | + | 0.414795i | \(0.863853\pi\) | |||||||
\(182\) | 11.4896 | − | 19.9006i | 0.851668 | − | 1.47513i | ||||
\(183\) | 4.47116 | 0.330518 | ||||||||
\(184\) | 0.336412 | − | 0.582682i | 0.0248006 | − | 0.0429559i | ||||
\(185\) | −2.78600 | − | 4.82549i | −0.204831 | − | 0.354777i | ||||
\(186\) | −1.78600 | − | 3.09344i | −0.130956 | − | 0.226822i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −10.6336 | −0.775536 | ||||||||
\(189\) | 7.58123 | + | 13.1311i | 0.551453 | + | 0.955145i | ||||
\(190\) | 0.214003 | + | 0.370665i | 0.0155254 | + | 0.0268908i | ||||
\(191\) | −5.91764 | + | 10.2497i | −0.428185 | + | 0.741639i | −0.996712 | − | 0.0810260i | \(-0.974180\pi\) |
0.568527 | + | 0.822665i | \(0.307514\pi\) | |||||||
\(192\) | 0.285997 | − | 0.495361i | 0.0206400 | − | 0.0357496i | ||||
\(193\) | −9.25934 | −0.666502 | −0.333251 | − | 0.942838i | \(-0.608146\pi\) | ||||
−0.333251 | + | 0.942838i | \(0.608146\pi\) | |||||||
\(194\) | −4.28797 | −0.307859 | ||||||||
\(195\) | −1.40643 | + | 2.43601i | −0.100716 | + | 0.174446i | ||||
\(196\) | −7.41764 | + | 12.8477i | −0.529831 | + | 0.917695i | ||||
\(197\) | 0.528837 | + | 0.915973i | 0.0376781 | + | 0.0652604i | 0.884250 | − | 0.467015i | \(-0.154671\pi\) |
−0.846571 | + | 0.532275i | \(0.821337\pi\) | |||||||
\(198\) | −2.10083 | − | 3.63875i | −0.149300 | − | 0.258594i | ||||
\(199\) | 10.5328 | 0.746650 | 0.373325 | − | 0.927701i | \(-0.378218\pi\) | ||||
0.373325 | + | 0.927701i | \(0.378218\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | −3.22126 | − | 5.57939i | −0.227210 | − | 0.393540i | ||||
\(202\) | −0.570017 | − | 0.987298i | −0.0401062 | − | 0.0694661i | ||||
\(203\) | 11.5812 | − | 20.0593i | 0.812843 | − | 1.40789i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.74482 | + | 6.48621i | −0.261549 | + | 0.453017i | ||||
\(206\) | 3.98040 | + | 6.89425i | 0.277327 | + | 0.480345i | ||||
\(207\) | 1.79834 | 0.124993 | ||||||||
\(208\) | −2.45882 | − | 4.25880i | −0.170489 | − | 0.295295i | ||||
\(209\) | 0.336412 | − | 0.582682i | 0.0232701 | − | 0.0403050i | ||||
\(210\) | 1.33641 | − | 2.31473i | 0.0922212 | − | 0.159732i | ||||
\(211\) | 3.85997 | 0.265731 | 0.132866 | − | 0.991134i | \(-0.457582\pi\) | ||||
0.132866 | + | 0.991134i | \(0.457582\pi\) | |||||||
\(212\) | −2.24482 | + | 3.88814i | −0.154175 | + | 0.267038i | ||||
\(213\) | −0.514319 | −0.0352406 | ||||||||
\(214\) | 6.30249 | 0.430829 | ||||||||
\(215\) | 6.38683 | + | 1.48608i | 0.435578 | + | 0.101350i | ||||
\(216\) | 3.24482 | 0.220782 | ||||||||
\(217\) | 29.1809 | 1.98093 | ||||||||
\(218\) | −10.1512 | + | 17.5825i | −0.687529 | + | 1.19084i | ||||
\(219\) | −8.26329 | −0.558381 | ||||||||
\(220\) | −0.785997 | + | 1.36139i | −0.0529919 | + | 0.0917846i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.59357 | − | 2.76015i | −0.106954 | − | 0.185249i | ||||
\(223\) | 25.0185 | 1.67536 | 0.837680 | − | 0.546161i | \(-0.183911\pi\) | ||||
0.837680 | + | 0.546161i | \(0.183911\pi\) | |||||||
\(224\) | 2.33641 | + | 4.04678i | 0.156108 | + | 0.270387i | ||||
\(225\) | 1.33641 | − | 2.31473i | 0.0890941 | − | 0.154316i | ||||
\(226\) | −1.95684 | −0.130167 | ||||||||
\(227\) | −6.48766 | + | 11.2370i | −0.430601 | + | 0.745823i | −0.996925 | − | 0.0783598i | \(-0.975032\pi\) |
0.566324 | + | 0.824183i | \(0.308365\pi\) | |||||||
\(228\) | 0.122408 | + | 0.212018i | 0.00810670 | + | 0.0140412i | ||||
\(229\) | −10.3569 | − | 17.9386i | −0.684401 | − | 1.18542i | −0.973625 | − | 0.228155i | \(-0.926731\pi\) |
0.289224 | − | 0.957261i | \(-0.406603\pi\) | |||||||
\(230\) | −0.336412 | − | 0.582682i | −0.0221823 | − | 0.0384209i | ||||
\(231\) | −4.20166 | −0.276449 | ||||||||
\(232\) | −2.47842 | − | 4.29275i | −0.162716 | − | 0.281833i | ||||
\(233\) | −11.1625 | − | 19.3339i | −0.731277 | − | 1.26661i | −0.956338 | − | 0.292264i | \(-0.905591\pi\) |
0.225061 | − | 0.974345i | \(-0.427742\pi\) | |||||||
\(234\) | 6.57199 | − | 11.3830i | 0.429625 | − | 0.744132i | ||||
\(235\) | −5.31681 | + | 9.20899i | −0.346830 | + | 0.600728i | ||||
\(236\) | −10.2017 | −0.664072 | ||||||||
\(237\) | 7.42405 | 0.482244 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3857 | + | 19.7206i | −0.736479 | + | 1.27562i | 0.217592 | + | 0.976040i | \(0.430180\pi\) |
−0.954071 | + | 0.299580i | \(0.903153\pi\) | |||||||
\(240\) | −0.285997 | − | 0.495361i | −0.0184610 | − | 0.0319754i | ||||
\(241\) | 12.4793 | + | 21.6147i | 0.803860 | + | 1.39233i | 0.917058 | + | 0.398754i | \(0.130557\pi\) |
−0.113197 | + | 0.993573i | \(0.536109\pi\) | |||||||
\(242\) | −8.52884 | −0.548254 | ||||||||
\(243\) | 6.62967 | + | 11.4829i | 0.425293 | + | 0.736630i | ||||
\(244\) | 3.90841 | + | 6.76956i | 0.250210 | + | 0.433376i | ||||
\(245\) | 7.41764 | + | 12.8477i | 0.473896 | + | 0.820811i | ||||
\(246\) | −2.14201 | + | 3.71007i | −0.136570 | + | 0.236545i | ||||
\(247\) | 2.10478 | 0.133924 | ||||||||
\(248\) | 3.12241 | − | 5.40817i | 0.198273 | − | 0.343419i | ||||
\(249\) | −4.50000 | − | 7.79423i | −0.285176 | − | 0.493939i | ||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −0.929983 | − | 1.61078i | −0.0587000 | − | 0.101671i | 0.835182 | − | 0.549974i | \(-0.185362\pi\) |
−0.893882 | + | 0.448302i | \(0.852029\pi\) | |||||||
\(252\) | −6.24482 | + | 10.8163i | −0.393386 | + | 0.681365i | ||||
\(253\) | −0.528837 | + | 0.915973i | −0.0332477 | + | 0.0575867i | ||||
\(254\) | −1.00000 | −0.0627456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.3681 | −1.64480 | −0.822398 | − | 0.568913i | \(-0.807364\pi\) | ||||
−0.822398 | + | 0.568913i | \(0.807364\pi\) | |||||||
\(258\) | 3.65322 | + | 0.850029i | 0.227440 | + | 0.0529205i | ||||
\(259\) | 26.0369 | 1.61786 | ||||||||
\(260\) | −4.91764 | −0.304979 | ||||||||
\(261\) | 6.62438 | − | 11.4738i | 0.410039 | − | 0.710209i | ||||
\(262\) | 7.05767 | 0.436025 | ||||||||
\(263\) | 3.40841 | − | 5.90353i | 0.210171 | − | 0.364027i | −0.741597 | − | 0.670846i | \(-0.765931\pi\) |
0.951768 | + | 0.306819i | \(0.0992645\pi\) | |||||||
\(264\) | −0.449585 | + | 0.778704i | −0.0276700 | + | 0.0479259i | ||||
\(265\) | 2.24482 | + | 3.88814i | 0.137898 | + | 0.238846i | ||||
\(266\) | −2.00000 | −0.122628 | ||||||||
\(267\) | 1.83952 | + | 3.18614i | 0.112577 | + | 0.194989i | ||||
\(268\) | 5.63164 | − | 9.75429i | 0.344007 | − | 0.595838i | ||||
\(269\) | −3.22635 | −0.196714 | −0.0983569 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983569 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(270\) | 1.62241 | − | 2.81009i | 0.0987366 | − | 0.171017i | ||||
\(271\) | 13.1008 | + | 22.6913i | 0.795819 | + | 1.37840i | 0.922318 | + | 0.386432i | \(0.126293\pi\) |
−0.126499 | + | 0.991967i | \(0.540374\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.57199 | − | 11.3830i | −0.397755 | − | 0.688932i | ||||
\(274\) | 13.7921 | 0.833213 | ||||||||
\(275\) | 0.785997 | + | 1.36139i | 0.0473974 | + | 0.0820947i | ||||
\(276\) | −0.192425 | − | 0.333290i | −0.0115826 | − | 0.0200617i | ||||
\(277\) | 0.715980 | − | 1.24011i | 0.0430191 | − | 0.0745112i | −0.843714 | − | 0.536793i | \(-0.819636\pi\) |
0.886733 | + | 0.462282i | \(0.152969\pi\) | |||||||
\(278\) | −4.52884 | + | 7.84418i | −0.271622 | + | 0.470462i | ||||
\(279\) | 16.6913 | 0.999282 | ||||||||
\(280\) | 4.67282 | 0.279255 | ||||||||
\(281\) | −0.0823593 | + | 0.142651i | −0.00491315 | + | 0.00850982i | −0.868472 | − | 0.495739i | \(-0.834897\pi\) |
0.863558 | + | 0.504249i | \(0.168231\pi\) | |||||||
\(282\) | −3.04118 | + | 5.26748i | −0.181100 | + | 0.313674i | ||||
\(283\) | −10.0000 | − | 17.3205i | −0.594438 | − | 1.02960i | −0.993626 | − | 0.112728i | \(-0.964041\pi\) |
0.399188 | − | 0.916869i | \(-0.369292\pi\) | |||||||
\(284\) | −0.449585 | − | 0.778704i | −0.0266779 | − | 0.0462076i | ||||
\(285\) | 0.244817 | 0.0145017 | ||||||||
\(286\) | 3.86525 | + | 6.69481i | 0.228557 | + | 0.395872i | ||||
\(287\) | −17.4989 | − | 30.3089i | −1.03293 | − | 1.78908i | ||||
\(288\) | 1.33641 | + | 2.31473i | 0.0787488 | + | 0.136397i | ||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | −4.95684 | −0.291076 | ||||||||
\(291\) | −1.22635 | + | 2.12409i | −0.0718897 | + | 0.124517i | ||||
\(292\) | −7.22324 | − | 12.5110i | −0.422708 | − | 0.732152i | ||||
\(293\) | 26.1153 | 1.52567 | 0.762837 | − | 0.646590i | \(-0.223806\pi\) | ||||
0.762837 | + | 0.646590i | \(0.223806\pi\) | |||||||
\(294\) | 4.24284 | + | 7.34882i | 0.247447 | + | 0.428592i | ||||
\(295\) | −5.10083 | + | 8.83490i | −0.296982 | + | 0.514388i | ||||
\(296\) | 2.78600 | − | 4.82549i | 0.161933 | − | 0.280476i | ||||
\(297\) | −5.10083 | −0.295980 | ||||||||
\(298\) | 4.72324 | − | 8.18089i | 0.273610 | − | 0.473906i | ||||
\(299\) | −3.30871 | −0.191347 | ||||||||
\(300\) | −0.571993 | −0.0330240 | ||||||||
\(301\) | −20.9361 | + | 22.3740i | −1.20674 | + | 1.28962i | ||||
\(302\) | 5.75518 | 0.331174 | ||||||||
\(303\) | −0.652092 | −0.0374617 | ||||||||
\(304\) | −0.214003 | + | 0.370665i | −0.0122739 | + | 0.0212591i | ||||
\(305\) | 7.81681 | 0.447589 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.112042 | − | 0.194063i | 0.00639460 | − | 0.0110758i | −0.862810 | − | 0.505528i | \(-0.831298\pi\) |
0.869205 | + | 0.494452i | \(0.164631\pi\) | |||||||
\(308\) | −3.67282 | − | 6.36152i | −0.209279 | − | 0.362481i | ||||
\(309\) | 4.55352 | 0.259041 | ||||||||
\(310\) | −3.12241 | − | 5.40817i | −0.177341 | − | 0.307163i | ||||
\(311\) | 9.00000 | − | 15.5885i | 0.510343 | − | 0.883940i | −0.489585 | − | 0.871956i | \(-0.662852\pi\) |
0.999928 | − | 0.0119847i | \(-0.00381495\pi\) | |||||||
\(312\) | −2.81286 | −0.159247 | ||||||||
\(313\) | 6.71287 | − | 11.6270i | 0.379434 | − | 0.657199i | −0.611546 | − | 0.791209i | \(-0.709452\pi\) |
0.990980 | + | 0.134010i | \(0.0427854\pi\) | |||||||
\(314\) | −3.35799 | − | 5.81621i | −0.189502 | − | 0.328228i | ||||
\(315\) | 6.24482 | + | 10.8163i | 0.351856 | + | 0.609432i | ||||
\(316\) | 6.48963 | + | 11.2404i | 0.365070 | + | 0.632321i | ||||
\(317\) | 19.6952 | 1.10620 | 0.553098 | − | 0.833116i | \(-0.313446\pi\) | ||||
0.553098 | + | 0.833116i | \(0.313446\pi\) | |||||||
\(318\) | 1.28402 | + | 2.22399i | 0.0720043 | + | 0.124715i | ||||
\(319\) | 3.89606 | + | 6.74818i | 0.218138 | + | 0.377825i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 1.80249 | − | 3.12201i | 0.100605 | − | 0.174253i | ||||
\(322\) | 3.14399 | 0.175208 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3.08123 | + | 5.33684i | −0.171179 | + | 0.296491i | ||||
\(325\) | −2.45882 | + | 4.25880i | −0.136391 | + | 0.236236i | ||||
\(326\) | 6.30447 | + | 10.9197i | 0.349172 | + | 0.604784i | ||||
\(327\) | 5.80644 | + | 10.0571i | 0.321097 | + | 0.556156i | ||||
\(328\) | −7.48963 | −0.413546 | ||||||||
\(329\) | −24.8445 | − | 43.0320i | −1.36972 | − | 2.37243i | ||||
\(330\) | 0.449585 | + | 0.778704i | 0.0247488 | + | 0.0428662i | ||||
\(331\) | −4.96080 | − | 8.59235i | −0.272670 | − | 0.472278i | 0.696875 | − | 0.717193i | \(-0.254573\pi\) |
−0.969545 | + | 0.244915i | \(0.921240\pi\) | |||||||
\(332\) | 7.86723 | − | 13.6264i | 0.431770 | − | 0.747848i | ||||
\(333\) | 14.8930 | 0.816129 | ||||||||
\(334\) | 12.6625 | − | 21.9320i | 0.692859 | − | 1.20007i | ||||
\(335\) | −5.63164 | − | 9.75429i | −0.307690 | − | 0.532934i | ||||
\(336\) | 2.67282 | 0.145814 | ||||||||
\(337\) | −6.18008 | − | 10.7042i | −0.336651 | − | 0.583096i | 0.647150 | − | 0.762363i | \(-0.275961\pi\) |
−0.983800 | + | 0.179267i | \(0.942627\pi\) | |||||||
\(338\) | −5.59159 | + | 9.68493i | −0.304143 | + | 0.526791i | ||||
\(339\) | −0.559651 | + | 0.969344i | −0.0303961 | + | 0.0526475i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.90841 | + | 8.50161i | −0.265805 | + | 0.460388i | ||||
\(342\) | −1.14399 | −0.0618597 | ||||||||
\(343\) | −36.6129 | −1.97691 | ||||||||
\(344\) | 1.90643 | + | 6.27420i | 0.102788 | + | 0.338282i | ||||
\(345\) | −0.384851 | −0.0207197 | ||||||||
\(346\) | 9.91369 | 0.532963 | ||||||||
\(347\) | −15.2468 | + | 26.4082i | −0.818491 | + | 1.41767i | 0.0883033 | + | 0.996094i | \(0.471856\pi\) |
−0.906794 | + | 0.421574i | \(0.861478\pi\) | |||||||
\(348\) | −2.83528 | −0.151987 | ||||||||
\(349\) | 0.901146 | − | 1.56083i | 0.0482372 | − | 0.0835494i | −0.840899 | − | 0.541193i | \(-0.817973\pi\) |
0.889136 | + | 0.457643i | \(0.151306\pi\) | |||||||
\(350\) | 2.33641 | − | 4.04678i | 0.124886 | − | 0.216310i | ||||
\(351\) | −7.97842 | − | 13.8190i | −0.425857 | − | 0.737605i | ||||
\(352\) | −1.57199 | −0.0837875 | ||||||||
\(353\) | 10.7129 | + | 18.5552i | 0.570189 | + | 0.987596i | 0.996546 | + | 0.0830410i | \(0.0264632\pi\) |
−0.426357 | + | 0.904555i | \(0.640203\pi\) | |||||||
\(354\) | −2.91764 | + | 5.05350i | −0.155071 | + | 0.268591i | ||||
\(355\) | −0.899170 | −0.0477230 | ||||||||
\(356\) | −3.21598 | + | 5.57024i | −0.170447 | + | 0.295222i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.95684 | − | 3.38935i | −0.103422 | − | 0.179133i | ||||
\(359\) | 4.18404 | + | 7.24696i | 0.220825 | + | 0.382480i | 0.955059 | − | 0.296417i | \(-0.0957917\pi\) |
−0.734234 | + | 0.678897i | \(0.762458\pi\) | |||||||
\(360\) | 2.67282 | 0.140870 | ||||||||
\(361\) | 9.40841 | + | 16.2958i | 0.495179 | + | 0.857676i | ||||
\(362\) | −1.28797 | − | 2.23083i | −0.0676944 | − | 0.117250i | ||||
\(363\) | −2.43922 | + | 4.22485i | −0.128026 | + | 0.221747i | ||||
\(364\) | 11.4896 | − | 19.9006i | 0.602220 | − | 1.04308i | ||||
\(365\) | −14.4465 | −0.756163 | ||||||||
\(366\) | 4.47116 | 0.233711 | ||||||||
\(367\) | −10.1585 | + | 17.5950i | −0.530270 | + | 0.918454i | 0.469107 | + | 0.883142i | \(0.344576\pi\) |
−0.999376 | + | 0.0353124i | \(0.988757\pi\) | |||||||
\(368\) | 0.336412 | − | 0.582682i | 0.0175367 | − | 0.0303744i | ||||
\(369\) | −10.0092 | − | 17.3365i | −0.521060 | − | 0.902502i | ||||
\(370\) | −2.78600 | − | 4.82549i | −0.144837 | − | 0.250865i | ||||
\(371\) | −20.9793 | −1.08919 | ||||||||
\(372\) | −1.78600 | − | 3.09344i | −0.0925996 | − | 0.160387i | ||||
\(373\) | 14.2056 | + | 24.6048i | 0.735539 | + | 1.27399i | 0.954487 | + | 0.298254i | \(0.0964042\pi\) |
−0.218948 | + | 0.975737i | \(0.570262\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.285997 | + | 0.495361i | −0.0147688 | + | 0.0255803i | ||||
\(376\) | −10.6336 | −0.548387 | ||||||||
\(377\) | −12.1880 | + | 21.1102i | −0.627713 | + | 1.08723i | ||||
\(378\) | 7.58123 | + | 13.1311i | 0.389936 | + | 0.675390i | ||||
\(379\) | 6.42801 | 0.330185 | 0.165092 | − | 0.986278i | \(-0.447208\pi\) | ||||
0.165092 | + | 0.986278i | \(0.447208\pi\) | |||||||
\(380\) | 0.214003 | + | 0.370665i | 0.0109781 | + | 0.0190147i | ||||
\(381\) | −0.285997 | + | 0.495361i | −0.0146521 | + | 0.0253781i | ||||
\(382\) | −5.91764 | + | 10.2497i | −0.302773 | + | 0.524418i | ||||
\(383\) | 17.3064 | 0.884318 | 0.442159 | − | 0.896937i | \(-0.354213\pi\) | ||||
0.442159 | + | 0.896937i | \(0.354213\pi\) | |||||||
\(384\) | 0.285997 | − | 0.495361i | 0.0145947 | − | 0.0252788i | ||||
\(385\) | −7.34565 | −0.374369 | ||||||||
\(386\) | −9.25934 | −0.471288 | ||||||||
\(387\) | −11.9753 | + | 12.7978i | −0.608739 | + | 0.650548i | ||||
\(388\) | −4.28797 | −0.217689 | ||||||||
\(389\) | −20.2386 | −1.02614 | −0.513069 | − | 0.858347i | \(-0.671491\pi\) | ||||
−0.513069 | + | 0.858347i | \(0.671491\pi\) | |||||||
\(390\) | −1.40643 | + | 2.43601i | −0.0712173 | + | 0.123352i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −7.41764 | + | 12.8477i | −0.374647 | + | 0.648908i | ||||
\(393\) | 2.01847 | − | 3.49609i | 0.101818 | − | 0.176355i | ||||
\(394\) | 0.528837 | + | 0.915973i | 0.0266424 | + | 0.0461460i | ||||
\(395\) | 12.9793 | 0.653058 | ||||||||
\(396\) | −2.10083 | − | 3.63875i | −0.105571 | − | 0.182854i | ||||
\(397\) | −4.75518 | + | 8.23622i | −0.238656 | + | 0.413364i | −0.960329 | − | 0.278870i | \(-0.910040\pi\) |
0.721673 | + | 0.692234i | \(0.243373\pi\) | |||||||
\(398\) | 10.5328 | 0.527961 | ||||||||
\(399\) | −0.571993 | + | 0.990721i | −0.0286355 | + | 0.0495981i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −15.1101 | − | 26.1714i | −0.754561 | − | 1.30694i | −0.945592 | − | 0.325354i | \(-0.894517\pi\) |
0.191032 | − | 0.981584i | \(-0.438817\pi\) | |||||||
\(402\) | −3.22126 | − | 5.57939i | −0.160662 | − | 0.278275i | ||||
\(403\) | −30.7098 | −1.52976 | ||||||||
\(404\) | −0.570017 | − | 0.987298i | −0.0283594 | − | 0.0491199i | ||||
\(405\) | 3.08123 | + | 5.33684i | 0.153107 | + | 0.265190i | ||||
\(406\) | 11.5812 | − | 20.0593i | 0.574767 | − | 0.995525i | ||||
\(407\) | −4.37957 | + | 7.58563i | −0.217087 | + | 0.376006i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.4712 | 0.666106 | 0.333053 | − | 0.942908i | \(-0.391921\pi\) | ||||
0.333053 | + | 0.942908i | \(0.391921\pi\) | |||||||
\(410\) | −3.74482 | + | 6.48621i | −0.184943 | + | 0.320331i | ||||
\(411\) | 3.94450 | − | 6.83208i | 0.194568 | − | 0.337001i | ||||
\(412\) | 3.98040 | + | 6.89425i | 0.196100 | + | 0.339655i | ||||
\(413\) | −23.8353 | − | 41.2839i | −1.17286 | − | 2.03145i | ||||
\(414\) | 1.79834 | 0.0883835 | ||||||||
\(415\) | −7.86723 | − | 13.6264i | −0.386187 | − | 0.668895i | ||||
\(416\) | −2.45882 | − | 4.25880i | −0.120554 | − | 0.208805i | ||||
\(417\) | 2.59046 | + | 4.48682i | 0.126856 | + | 0.219720i | ||||
\(418\) | 0.336412 | − | 0.582682i | 0.0164544 | − | 0.0284999i | ||||
\(419\) | −18.5759 | −0.907494 | −0.453747 | − | 0.891130i | \(-0.649913\pi\) | ||||
−0.453747 | + | 0.891130i | \(0.649913\pi\) | |||||||
\(420\) | 1.33641 | − | 2.31473i | 0.0652102 | − | 0.112947i | ||||
\(421\) | −10.1028 | − | 17.4986i | −0.492381 | − | 0.852828i | 0.507581 | − | 0.861604i | \(-0.330540\pi\) |
−0.999961 | + | 0.00877580i | \(0.997207\pi\) | |||||||
\(422\) | 3.85997 | 0.187900 | ||||||||
\(423\) | −14.2109 | − | 24.6140i | −0.690957 | − | 1.19677i | ||||
\(424\) | −2.24482 | + | 3.88814i | −0.109018 | + | 0.188825i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.514319 | −0.0249188 | ||||||||
\(427\) | −18.2633 | + | 31.6329i | −0.883822 | + | 1.53083i | ||||
\(428\) | 6.30249 | 0.304642 | ||||||||
\(429\) | 4.42179 | 0.213486 | ||||||||
\(430\) | 6.38683 | + | 1.48608i | 0.308000 | + | 0.0716652i | ||||
\(431\) | 36.7345 | 1.76944 | 0.884718 | − | 0.466126i | \(-0.154351\pi\) | ||||
0.884718 | + | 0.466126i | \(0.154351\pi\) | |||||||
\(432\) | 3.24482 | 0.156116 | ||||||||
\(433\) | −16.5728 | + | 28.7050i | −0.796440 | + | 1.37947i | 0.125481 | + | 0.992096i | \(0.459953\pi\) |
−0.921921 | + | 0.387378i | \(0.873381\pi\) | |||||||
\(434\) | 29.1809 | 1.40073 | ||||||||
\(435\) | −1.41764 | + | 2.45543i | −0.0679707 | + | 0.117729i | ||||
\(436\) | −10.1512 | + | 17.5825i | −0.486156 | + | 0.842048i | ||||
\(437\) | 0.143987 | + | 0.249392i | 0.00688781 | + | 0.0119300i | ||||
\(438\) | −8.26329 | −0.394835 | ||||||||
\(439\) | −1.52884 | − | 2.64802i | −0.0729674 | − | 0.126383i | 0.827233 | − | 0.561859i | \(-0.189914\pi\) |
−0.900201 | + | 0.435476i | \(0.856580\pi\) | |||||||
\(440\) | −0.785997 | + | 1.36139i | −0.0374709 | + | 0.0649015i | ||||
\(441\) | −39.6521 | −1.88819 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.38683 | − | 7.59821i | −0.208424 | − | 0.361002i | 0.742794 | − | 0.669520i | \(-0.233500\pi\) |
−0.951218 | + | 0.308518i | \(0.900167\pi\) | |||||||
\(444\) | −1.59357 | − | 2.76015i | −0.0756275 | − | 0.130991i | ||||
\(445\) | 3.21598 | + | 5.57024i | 0.152452 | + | 0.264055i | ||||
\(446\) | 25.0185 | 1.18466 | ||||||||
\(447\) | −2.70166 | − | 4.67941i | −0.127784 | − | 0.221329i | ||||
\(448\) | 2.33641 | + | 4.04678i | 0.110385 | + | 0.191193i | ||||
\(449\) | −8.74877 | + | 15.1533i | −0.412880 | + | 0.715129i | −0.995203 | − | 0.0978282i | \(-0.968810\pi\) |
0.582323 | + | 0.812957i | \(0.302144\pi\) | |||||||
\(450\) | 1.33641 | − | 2.31473i | 0.0629991 | − | 0.109118i | ||||
\(451\) | 11.7737 | 0.554400 | ||||||||
\(452\) | −1.95684 | −0.0920422 | ||||||||
\(453\) | 1.64596 | − | 2.85089i | 0.0773341 | − | 0.133947i | ||||
\(454\) | −6.48766 | + | 11.2370i | −0.304481 | + | 0.527376i | ||||
\(455\) | −11.4896 | − | 19.9006i | −0.538642 | − | 0.932956i | ||||
\(456\) | 0.122408 | + | 0.212018i | 0.00573230 | + | 0.00992864i | ||||
\(457\) | −2.07841 | −0.0972238 | −0.0486119 | − | 0.998818i | \(-0.515480\pi\) | ||||
−0.0486119 | + | 0.998818i | \(0.515480\pi\) | |||||||
\(458\) | −10.3569 | − | 17.9386i | −0.483944 | − | 0.838216i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.336412 | − | 0.582682i | −0.0156853 | − | 0.0271677i | ||||
\(461\) | −0.151246 | + | 0.261965i | −0.00704421 | + | 0.0122009i | −0.869526 | − | 0.493887i | \(-0.835576\pi\) |
0.862482 | + | 0.506088i | \(0.168909\pi\) | |||||||
\(462\) | −4.20166 | −0.195479 | ||||||||
\(463\) | 2.85488 | − | 4.94480i | 0.132678 | − | 0.229804i | −0.792030 | − | 0.610482i | \(-0.790976\pi\) |
0.924708 | + | 0.380677i | \(0.124309\pi\) | |||||||
\(464\) | −2.47842 | − | 4.29275i | −0.115058 | − | 0.199286i | ||||
\(465\) | −3.57199 | −0.165647 | ||||||||
\(466\) | −11.1625 | − | 19.3339i | −0.517091 | − | 0.895628i | ||||
\(467\) | 3.87844 | − | 6.71765i | 0.179473 | − | 0.310856i | −0.762227 | − | 0.647309i | \(-0.775894\pi\) |
0.941700 | + | 0.336454i | \(0.109228\pi\) | |||||||
\(468\) | 6.57199 | − | 11.3830i | 0.303790 | − | 0.526181i | ||||
\(469\) | 52.6314 | 2.43029 | ||||||||
\(470\) | −5.31681 | + | 9.20899i | −0.245246 | + | 0.424779i | ||||
\(471\) | −3.84150 | −0.177007 | ||||||||
\(472\) | −10.2017 | −0.469570 | ||||||||
\(473\) | −2.99689 | − | 9.86299i | −0.137797 | − | 0.453501i | ||||
\(474\) | 7.42405 | 0.340998 | ||||||||
\(475\) | 0.428007 | 0.0196383 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | −11.3857 | + | 19.7206i | −0.520770 | + | 0.901999i | ||||
\(479\) | −14.5944 | + | 25.2783i | −0.666836 | + | 1.15499i | 0.311948 | + | 0.950099i | \(0.399018\pi\) |
−0.978784 | + | 0.204895i | \(0.934315\pi\) | |||||||
\(480\) | −0.285997 | − | 0.495361i | −0.0130539 | − | 0.0226100i | ||||
\(481\) | −27.4011 | −1.24938 | ||||||||
\(482\) | 12.4793 | + | 21.6147i | 0.568415 | + | 0.984524i | ||||
\(483\) | 0.899170 | − | 1.55741i | 0.0409136 | − | 0.0708645i | ||||
\(484\) | −8.52884 | −0.387674 | ||||||||
\(485\) | −2.14399 | + | 3.71349i | −0.0973534 | + | 0.168621i | ||||
\(486\) | 6.62967 | + | 11.4829i | 0.300728 | + | 0.520876i | ||||
\(487\) | 0.705614 | + | 1.22216i | 0.0319744 | + | 0.0553813i | 0.881570 | − | 0.472054i | \(-0.156487\pi\) |
−0.849595 | + | 0.527435i | \(0.823154\pi\) | |||||||
\(488\) | 3.90841 | + | 6.76956i | 0.176925 | + | 0.306443i | ||||
\(489\) | 7.21223 | 0.326148 | ||||||||
\(490\) | 7.41764 | + | 12.8477i | 0.335095 | + | 0.580401i | ||||
\(491\) | −7.45882 | − | 12.9191i | −0.336612 | − | 0.583029i | 0.647181 | − | 0.762336i | \(-0.275948\pi\) |
−0.983793 | + | 0.179307i | \(0.942614\pi\) | |||||||
\(492\) | −2.14201 | + | 3.71007i | −0.0965693 | + | 0.167263i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.10478 | 0.0946987 | ||||||||
\(495\) | −4.20166 | −0.188851 | ||||||||
\(496\) | 3.12241 | − | 5.40817i | 0.140200 | − | 0.242834i | ||||
\(497\) | 2.10083 | − | 3.63875i | 0.0942351 | − | 0.163220i | ||||
\(498\) | −4.50000 | − | 7.79423i | −0.201650 | − | 0.349268i | ||||
\(499\) | −10.4157 | − | 18.0405i | −0.466269 | − | 0.807602i | 0.532989 | − | 0.846122i | \(-0.321069\pi\) |
−0.999258 | + | 0.0385205i | \(0.987736\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −7.24284 | − | 12.5450i | −0.323586 | − | 0.560468i | ||||
\(502\) | −0.929983 | − | 1.61078i | −0.0415072 | − | 0.0718925i | ||||
\(503\) | 3.01037 | + | 5.21411i | 0.134226 | + | 0.232486i | 0.925301 | − | 0.379233i | \(-0.123812\pi\) |
−0.791076 | + | 0.611718i | \(0.790479\pi\) | |||||||
\(504\) | −6.24482 | + | 10.8163i | −0.278166 | + | 0.481798i | ||||
\(505\) | −1.14003 | −0.0507308 | ||||||||
\(506\) | −0.528837 | + | 0.915973i | −0.0235097 | + | 0.0407200i | ||||
\(507\) | 3.19835 | + | 5.53971i | 0.142044 | + | 0.246027i | ||||
\(508\) | −1.00000 | −0.0443678 | ||||||||
\(509\) | −3.05437 | − | 5.29032i | −0.135382 | − | 0.234489i | 0.790361 | − | 0.612641i | \(-0.209893\pi\) |
−0.925744 | + | 0.378152i | \(0.876560\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.7529 | − | 58.4618i | 1.49314 | − | 2.58620i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.694402 | + | 1.20274i | −0.0306586 | + | 0.0531022i | ||||
\(514\) | −26.3681 | −1.16305 | ||||||||
\(515\) | 7.96080 | 0.350795 | ||||||||
\(516\) | 3.65322 | + | 0.850029i | 0.160824 | + | 0.0374204i | ||||
\(517\) | 16.7160 | 0.735168 | ||||||||
\(518\) | 26.0369 | 1.14400 | ||||||||
\(519\) | 2.83528 | − | 4.91085i | 0.124455 | − | 0.215562i | ||||
\(520\) | −4.91764 | −0.215653 | ||||||||
\(521\) | −2.72522 | + | 4.72021i | −0.119394 | + | 0.206796i | −0.919528 | − | 0.393025i | \(-0.871428\pi\) |
0.800134 | + | 0.599822i | \(0.204762\pi\) | |||||||
\(522\) | 6.62438 | − | 11.4738i | 0.289941 | − | 0.502193i | ||||
\(523\) | −18.1081 | − | 31.3641i | −0.791811 | − | 1.37146i | −0.924844 | − | 0.380346i | \(-0.875805\pi\) |
0.133033 | − | 0.991112i | \(-0.457528\pi\) | |||||||
\(524\) | 7.05767 | 0.308316 | ||||||||
\(525\) | −1.33641 | − | 2.31473i | −0.0583258 | − | 0.101023i | ||||
\(526\) | 3.40841 | − | 5.90353i | 0.148614 | − | 0.257406i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.449585 | + | 0.778704i | −0.0195657 | + | 0.0338887i | ||||
\(529\) | 11.2737 | + | 19.5265i | 0.490159 | + | 0.848980i | ||||
\(530\) | 2.24482 | + | 3.88814i | 0.0975086 | + | 0.168890i | ||||
\(531\) | −13.6336 | − | 23.6141i | −0.591649 | − | 1.02477i | ||||
\(532\) | −2.00000 | −0.0867110 | ||||||||
\(533\) | 18.4157 | + | 31.8969i | 0.797671 | + | 1.38161i | ||||
\(534\) | 1.83952 | + | 3.18614i | 0.0796038 | + | 0.137878i | ||||
\(535\) | 3.15125 | − | 5.45812i | 0.136240 | − | 0.235975i | ||||
\(536\) | 5.63164 | − | 9.75429i | 0.243250 | − | 0.421321i | ||||
\(537\) | −2.23860 | −0.0966029 | ||||||||
\(538\) | −3.22635 | −0.139098 | ||||||||
\(539\) | 11.6605 | − | 20.1965i | 0.502252 | − | 0.869927i | ||||
\(540\) | 1.62241 | − | 2.81009i | 0.0698173 | − | 0.120927i | ||||
\(541\) | 0.854037 | + | 1.47924i | 0.0367179 | + | 0.0635973i | 0.883800 | − | 0.467864i | \(-0.154976\pi\) |
−0.847082 | + | 0.531461i | \(0.821643\pi\) | |||||||
\(542\) | 13.1008 | + | 22.6913i | 0.562729 | + | 0.974675i | ||||
\(543\) | −1.47342 | −0.0632307 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.1512 | + | 17.5825i | 0.434832 | + | 0.753150i | ||||
\(546\) | −6.57199 | − | 11.3830i | −0.281255 | − | 0.487149i | ||||
\(547\) | −20.4145 | + | 35.3590i | −0.872862 | + | 1.51184i | −0.0138399 | + | 0.999904i | \(0.504406\pi\) |
−0.859022 | + | 0.511938i | \(0.828928\pi\) | |||||||
\(548\) | 13.7921 | 0.589170 | ||||||||
\(549\) | −10.4465 | + | 18.0938i | −0.445845 | + | 0.772226i | ||||
\(550\) | 0.785997 | + | 1.36139i | 0.0335150 | + | 0.0580497i | ||||
\(551\) | 2.12156 | 0.0903816 | ||||||||
\(552\) | −0.192425 | − | 0.333290i | −0.00819017 | − | 0.0141858i | ||||
\(553\) | −30.3249 | + | 52.5243i | −1.28955 | + | 2.23356i | ||||
\(554\) | 0.715980 | − | 1.24011i | 0.0304191 | − | 0.0526874i | ||||
\(555\) | −3.18714 | −0.135287 | ||||||||
\(556\) | −4.52884 | + | 7.84418i | −0.192065 | + | 0.332667i | ||||
\(557\) | −36.6050 | −1.55100 | −0.775501 | − | 0.631346i | \(-0.782503\pi\) | ||||
−0.775501 | + | 0.631346i | \(0.782503\pi\) | |||||||
\(558\) | 16.6913 | 0.706599 | ||||||||
\(559\) | 22.0330 | − | 23.5462i | 0.931896 | − | 0.995899i | ||||
\(560\) | 4.67282 | 0.197463 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.0823593 | + | 0.142651i | −0.00347412 | + | 0.00601735i | ||||
\(563\) | 31.8946 | 1.34420 | 0.672100 | − | 0.740461i | \(-0.265393\pi\) | ||||
0.672100 | + | 0.740461i | \(0.265393\pi\) | |||||||
\(564\) | −3.04118 | + | 5.26748i | −0.128057 | + | 0.221801i | ||||
\(565\) | −0.978422 | + | 1.69468i | −0.0411625 | + | 0.0712956i | ||||
\(566\) | −10.0000 | − | 17.3205i | −0.420331 | − | 0.728035i | ||||
\(567\) | −28.7961 | −1.20932 | ||||||||
\(568\) | −0.449585 | − | 0.778704i | −0.0188642 | − | 0.0326737i | ||||
\(569\) | 13.7056 | − | 23.7388i | 0.574569 | − | 0.995183i | −0.421519 | − | 0.906820i | \(-0.638503\pi\) |
0.996088 | − | 0.0883635i | \(-0.0281637\pi\) | |||||||
\(570\) | 0.244817 | 0.0102543 | ||||||||
\(571\) | −20.1501 | + | 34.9010i | −0.843256 | + | 1.46056i | 0.0438710 | + | 0.999037i | \(0.486031\pi\) |
−0.887127 | + | 0.461525i | \(0.847302\pi\) | |||||||
\(572\) | 3.86525 | + | 6.69481i | 0.161614 | + | 0.279924i | ||||
\(573\) | 3.38485 | + | 5.86273i | 0.141404 | + | 0.244919i | ||||
\(574\) | −17.4989 | − | 30.3089i | −0.730389 | − | 1.26507i | ||||
\(575\) | −0.672824 | −0.0280587 | ||||||||
\(576\) | 1.33641 | + | 2.31473i | 0.0556838 | + | 0.0964472i | ||||
\(577\) | 8.69045 | + | 15.0523i | 0.361788 | + | 0.626635i | 0.988255 | − | 0.152812i | \(-0.0488330\pi\) |
−0.626467 | + | 0.779448i | \(0.715500\pi\) | |||||||
\(578\) | 8.50000 | − | 14.7224i | 0.353553 | − | 0.612372i | ||||
\(579\) | −2.64814 | + | 4.58671i | −0.110053 | + | 0.190617i | ||||
\(580\) | −4.95684 | −0.205822 | ||||||||
\(581\) | 73.5243 | 3.05030 | ||||||||
\(582\) | −1.22635 | + | 2.12409i | −0.0508337 | + | 0.0880465i | ||||
\(583\) | 3.52884 | − | 6.11213i | 0.146150 | − | 0.253138i | ||||
\(584\) | −7.22324 | − | 12.5110i | −0.298900 | − | 0.517710i | ||||
\(585\) | −6.57199 | − | 11.3830i | −0.271718 | − | 0.470630i | ||||
\(586\) | 26.1153 | 1.07882 | ||||||||
\(587\) | 3.72719 | + | 6.45569i | 0.153838 | + | 0.266455i | 0.932635 | − | 0.360821i | \(-0.117503\pi\) |
−0.778798 | + | 0.627275i | \(0.784170\pi\) | |||||||
\(588\) | 4.24284 | + | 7.34882i | 0.174972 | + | 0.303060i | ||||
\(589\) | 1.33641 | + | 2.31473i | 0.0550659 | + | 0.0953769i | ||||
\(590\) | −5.10083 | + | 8.83490i | −0.209998 | + | 0.363727i | ||||
\(591\) | 0.604983 | 0.0248857 | ||||||||
\(592\) | 2.78600 | − | 4.82549i | 0.114504 | − | 0.198326i | ||||
\(593\) | 8.48568 | + | 14.6976i | 0.348465 | + | 0.603559i | 0.985977 | − | 0.166881i | \(-0.0533696\pi\) |
−0.637512 | + | 0.770441i | \(0.720036\pi\) | |||||||
\(594\) | −5.10083 | −0.209290 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.72324 | − | 8.18089i | 0.193471 | − | 0.335102i | ||||
\(597\) | 3.01234 | − | 5.21753i | 0.123287 | − | 0.213539i | ||||
\(598\) | −3.30871 | −0.135303 | ||||||||
\(599\) | −6.69045 | + | 11.5882i | −0.273364 | + | 0.473481i | −0.969721 | − | 0.244215i | \(-0.921470\pi\) |
0.696357 | + | 0.717696i | \(0.254803\pi\) | |||||||
\(600\) | −0.571993 | −0.0233515 | ||||||||
\(601\) | 34.9585 | 1.42599 | 0.712994 | − | 0.701170i | \(-0.247339\pi\) | ||||
0.712994 | + | 0.701170i | \(0.247339\pi\) | |||||||
\(602\) | −20.9361 | + | 22.3740i | −0.853292 | + | 0.911897i | ||||
\(603\) | 30.1048 | 1.22596 | ||||||||
\(604\) | 5.75518 | 0.234175 | ||||||||
\(605\) | −4.26442 | + | 7.38619i | −0.173373 | + | 0.300291i | ||||
\(606\) | −0.652092 | −0.0264894 | ||||||||
\(607\) | 1.28289 | − | 2.22203i | 0.0520709 | − | 0.0901894i | −0.838815 | − | 0.544416i | \(-0.816751\pi\) |
0.890886 | + | 0.454227i | \(0.150084\pi\) | |||||||
\(608\) | −0.214003 | + | 0.370665i | −0.00867898 | + | 0.0150324i | ||||
\(609\) | −6.62438 | − | 11.4738i | −0.268434 | − | 0.464941i | ||||
\(610\) | 7.81681 | 0.316493 | ||||||||
\(611\) | 26.1462 | + | 45.2865i | 1.05776 | + | 1.83209i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.7120 | 0.553824 | 0.276912 | − | 0.960895i | \(-0.410689\pi\) | ||||
0.276912 | + | 0.960895i | \(0.410689\pi\) | |||||||
\(614\) | 0.112042 | − | 0.194063i | 0.00452166 | − | 0.00783175i | ||||
\(615\) | 2.14201 | + | 3.71007i | 0.0863742 | + | 0.149604i | ||||
\(616\) | −3.67282 | − | 6.36152i | −0.147982 | − | 0.256313i | ||||
\(617\) | −20.0832 | − | 34.7851i | −0.808519 | − | 1.40040i | −0.913889 | − | 0.405964i | \(-0.866936\pi\) |
0.105370 | − | 0.994433i | \(-0.466397\pi\) | |||||||
\(618\) | 4.55352 | 0.183170 | ||||||||
\(619\) | −8.29410 | − | 14.3658i | −0.333368 | − | 0.577410i | 0.649802 | − | 0.760104i | \(-0.274852\pi\) |
−0.983170 | + | 0.182693i | \(0.941519\pi\) | |||||||
\(620\) | −3.12241 | − | 5.40817i | −0.125399 | − | 0.217197i | ||||
\(621\) | 1.09159 | − | 1.89070i | 0.0438042 | − | 0.0758711i | ||||
\(622\) | 9.00000 | − | 15.5885i | 0.360867 | − | 0.625040i | ||||
\(623\) | −30.0554 | −1.20414 | ||||||||
\(624\) | −2.81286 | −0.112604 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 6.71287 | − | 11.6270i | 0.268300 | − | 0.464710i | ||||
\(627\) | −0.192425 | − | 0.333290i | −0.00768473 | − | 0.0133103i | ||||
\(628\) | −3.35799 | − | 5.81621i | −0.133998 | − | 0.232092i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 6.24482 | + | 10.8163i | 0.248799 | + | 0.430933i | ||||
\(631\) | 14.5081 | + | 25.1288i | 0.577559 | + | 1.00036i | 0.995758 | + | 0.0920057i | \(0.0293278\pi\) |
−0.418200 | + | 0.908355i | \(0.637339\pi\) | |||||||
\(632\) | 6.48963 | + | 11.2404i | 0.258144 | + | 0.447118i | ||||
\(633\) | 1.10394 | − | 1.91208i | 0.0438776 | − | 0.0759982i | ||||
\(634\) | 19.6952 | 0.782198 | ||||||||
\(635\) | −0.500000 | + | 0.866025i | −0.0198419 | + | 0.0343672i | ||||
\(636\) | 1.28402 | + | 2.22399i | 0.0509147 | + | 0.0881869i | ||||
\(637\) | 72.9546 | 2.89057 | ||||||||
\(638\) | 3.89606 | + | 6.74818i | 0.154247 | + | 0.267163i | ||||
\(639\) | 1.20166 | − | 2.08134i | 0.0475370 | − | 0.0823364i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −49.6419 | −1.96074 | −0.980369 | − | 0.197171i | \(-0.936825\pi\) | ||||
−0.980369 | + | 0.197171i | \(0.936825\pi\) | |||||||
\(642\) | 1.80249 | − | 3.12201i | 0.0711387 | − | 0.123216i | ||||
\(643\) | −5.81286 | −0.229237 | −0.114618 | − | 0.993410i | \(-0.536565\pi\) | ||||
−0.114618 | + | 0.993410i | \(0.536565\pi\) | |||||||
\(644\) | 3.14399 | 0.123890 | ||||||||
\(645\) | 2.56276 | − | 2.73877i | 0.100908 | − | 0.107839i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2122 | −0.676682 | −0.338341 | − | 0.941023i | \(-0.609866\pi\) | ||||
−0.338341 | + | 0.941023i | \(0.609866\pi\) | |||||||
\(648\) | −3.08123 | + | 5.33684i | −0.121042 | + | 0.209651i | ||||
\(649\) | 16.0369 | 0.629505 | ||||||||
\(650\) | −2.45882 | + | 4.25880i | −0.0964429 | + | 0.167044i | ||||
\(651\) | 8.34565 | − | 14.4551i | 0.327092 | − | 0.566539i | ||||
\(652\) | 6.30447 | + | 10.9197i | 0.246902 | + | 0.427647i | ||||
\(653\) | 38.4033 | 1.50284 | 0.751419 | − | 0.659825i | \(-0.229370\pi\) | ||||
0.751419 | + | 0.659825i | \(0.229370\pi\) | |||||||
\(654\) | 5.80644 | + | 10.0571i | 0.227050 | + | 0.393262i | ||||
\(655\) | 3.52884 | − | 6.11213i | 0.137883 | − | 0.238820i | ||||
\(656\) | −7.48963 | −0.292421 | ||||||||
\(657\) | 19.3064 | − | 33.4397i | 0.753216 | − | 1.30461i | ||||
\(658\) | −24.8445 | − | 43.0320i | −0.968540 | − | 1.67756i | ||||
\(659\) | 6.22635 | + | 10.7843i | 0.242544 | + | 0.420099i | 0.961438 | − | 0.275021i | \(-0.0886848\pi\) |
−0.718894 | + | 0.695119i | \(0.755351\pi\) | |||||||
\(660\) | 0.449585 | + | 0.778704i | 0.0175001 | + | 0.0303110i | ||||
\(661\) | 46.7177 | 1.81711 | 0.908553 | − | 0.417769i | \(-0.137188\pi\) | ||||
0.908553 | + | 0.417769i | \(0.137188\pi\) | |||||||
\(662\) | −4.96080 | − | 8.59235i | −0.192807 | − | 0.333951i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.86723 | − | 13.6264i | 0.305308 | − | 0.528808i | ||||
\(665\) | −1.00000 | + | 1.73205i | −0.0387783 | + | 0.0671660i | ||||
\(666\) | 14.8930 | 0.577090 | ||||||||
\(667\) | −3.33508 | −0.129135 | ||||||||
\(668\) | 12.6625 | − | 21.9320i | 0.489925 | − | 0.848575i | ||||
\(669\) | 7.15520 | − | 12.3932i | 0.276636 | − | 0.479148i | ||||
\(670\) | −5.63164 | − | 9.75429i | −0.217569 | − | 0.376841i | ||||
\(671\) | −6.14399 | − | 10.6417i | −0.237186 | − | 0.410818i | ||||
\(672\) | 2.67282 | 0.103106 | ||||||||
\(673\) | 11.4936 | + | 19.9075i | 0.443045 | + | 0.767377i | 0.997914 | − | 0.0645612i | \(-0.0205648\pi\) |
−0.554869 | + | 0.831938i | \(0.687231\pi\) | |||||||
\(674\) | −6.18008 | − | 10.7042i | −0.238048 | − | 0.412311i | ||||
\(675\) | −1.62241 | − | 2.81009i | −0.0624465 | − | 0.108161i | ||||
\(676\) | −5.59159 | + | 9.68493i | −0.215061 | + | 0.372497i | ||||
\(677\) | −13.6010 | −0.522730 | −0.261365 | − | 0.965240i | \(-0.584173\pi\) | ||||
−0.261365 | + | 0.965240i | \(0.584173\pi\) | |||||||
\(678\) | −0.559651 | + | 0.969344i | −0.0214933 | + | 0.0372274i | ||||
\(679\) | −10.0185 | − | 17.3525i | −0.384474 | − | 0.665928i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.71090 | + | 6.42746i | 0.142202 | + | 0.246301i | ||||
\(682\) | −4.90841 | + | 8.50161i | −0.187953 | + | 0.325543i | ||||
\(683\) | 7.18714 | − | 12.4485i | 0.275008 | − | 0.476328i | −0.695129 | − | 0.718885i | \(-0.744653\pi\) |
0.970137 | + | 0.242557i | \(0.0779860\pi\) | |||||||
\(684\) | −1.14399 | −0.0437414 | ||||||||
\(685\) | 6.89606 | − | 11.9443i | 0.263485 | − | 0.456369i | ||||
\(686\) | −36.6129 | −1.39789 | ||||||||
\(687\) | −11.8481 | −0.452034 | ||||||||
\(688\) | 1.90643 | + | 6.27420i | 0.0726819 | + | 0.239201i | ||||
\(689\) | 22.0784 | 0.841120 | ||||||||
\(690\) | −0.384851 | −0.0146510 | ||||||||
\(691\) | 10.8868 | − | 18.8565i | 0.414154 | − | 0.717336i | −0.581185 | − | 0.813772i | \(-0.697411\pi\) |
0.995339 | + | 0.0964351i | \(0.0307440\pi\) | |||||||
\(692\) | 9.91369 | 0.376862 | ||||||||
\(693\) | 9.81681 | − | 17.0032i | 0.372910 | − | 0.645899i | ||||
\(694\) | −15.2468 | + | 26.4082i | −0.578760 | + | 1.00244i | ||||
\(695\) | 4.52884 | + | 7.84418i | 0.171789 | + | 0.297547i | ||||
\(696\) | −2.83528 | −0.107471 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.901146 | − | 1.56083i | 0.0341089 | − | 0.0590783i | ||||
\(699\) | −12.7697 | −0.482994 | ||||||||
\(700\) | 2.33641 | − | 4.04678i | 0.0883081 | − | 0.152954i | ||||
\(701\) | 22.8672 | + | 39.6072i | 0.863683 | + | 1.49594i | 0.868349 | + | 0.495954i | \(0.165182\pi\) |
−0.00466559 | + | 0.999989i | \(0.501485\pi\) | |||||||
\(702\) | −7.97842 | − | 13.8190i | −0.301126 | − | 0.521566i | ||||
\(703\) | 1.19243 | + | 2.06534i | 0.0449732 | + | 0.0778958i | ||||
\(704\) | −1.57199 | −0.0592467 | ||||||||
\(705\) | 3.04118 | + | 5.26748i | 0.114537 | + | 0.198385i | ||||
\(706\) | 10.7129 | + | 18.5552i | 0.403184 | + | 0.698336i | ||||
\(707\) | 2.66359 | − | 4.61347i | 0.100175 | − | 0.173507i | ||||
\(708\) | −2.91764 | + | 5.05350i | −0.109652 | + | 0.189922i | ||||
\(709\) | 24.5042 | 0.920273 | 0.460136 | − | 0.887848i | \(-0.347801\pi\) | ||||
0.460136 | + | 0.887848i | \(0.347801\pi\) | |||||||
\(710\) | −0.899170 | −0.0337452 | ||||||||
\(711\) | −17.3456 | + | 30.0435i | −0.650513 | + | 1.12672i | ||||
\(712\) | −3.21598 | + | 5.57024i | −0.120524 | + | 0.208754i | ||||
\(713\) | −2.10083 | − | 3.63875i | −0.0786767 | − | 0.136272i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.73050 | 0.289104 | ||||||||
\(716\) | −1.95684 | − | 3.38935i | −0.0731307 | − | 0.126666i | ||||
\(717\) | 6.51254 | + | 11.2801i | 0.243215 | + | 0.421261i | ||||
\(718\) | 4.18404 | + | 7.24696i | 0.156147 | + | 0.270454i | ||||
\(719\) | −2.30644 | + | 3.99488i | −0.0860159 | + | 0.148984i | −0.905824 | − | 0.423655i | \(-0.860747\pi\) |
0.819808 | + | 0.572639i | \(0.194080\pi\) | |||||||
\(720\) | 2.67282 | 0.0996103 | ||||||||
\(721\) | −18.5997 | + | 32.2156i | −0.692689 | + | 1.19977i | ||||
\(722\) | 9.40841 | + | 16.2958i | 0.350145 | + | 0.606468i | ||||
\(723\) | 14.2761 | 0.530934 | ||||||||
\(724\) | −1.28797 | − | 2.23083i | −0.0478671 | − | 0.0829083i | ||||
\(725\) | −2.47842 | + | 4.29275i | −0.0920463 | + | 0.159429i | ||||
\(726\) | −2.43922 | + | 4.22485i | −0.0905279 | + | 0.156799i | ||||
\(727\) | −12.4297 | −0.460992 | −0.230496 | − | 0.973073i | \(-0.574035\pi\) | ||||
−0.230496 | + | 0.973073i | \(0.574035\pi\) | |||||||
\(728\) | 11.4896 | − | 19.9006i | 0.425834 | − | 0.737566i | ||||
\(729\) | −10.9031 | −0.403819 | ||||||||
\(730\) | −14.4465 | −0.534688 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4.47116 | 0.165259 | ||||||||
\(733\) | 13.1272 | 0.484864 | 0.242432 | − | 0.970168i | \(-0.422055\pi\) | ||||
0.242432 | + | 0.970168i | \(0.422055\pi\) | |||||||
\(734\) | −10.1585 | + | 17.5950i | −0.374957 | + | 0.649445i | ||||
\(735\) | 8.48568 | 0.312999 | ||||||||
\(736\) | 0.336412 | − | 0.582682i | 0.0124003 | − | 0.0214780i | ||||
\(737\) | −8.85291 | + | 15.3337i | −0.326101 | + | 0.564824i | ||||
\(738\) | −10.0092 | − | 17.3365i | −0.368445 | − | 0.638166i | ||||
\(739\) | −35.2426 | −1.29642 | −0.648209 | − | 0.761462i | \(-0.724482\pi\) | ||||
−0.648209 | + | 0.761462i | \(0.724482\pi\) | |||||||
\(740\) | −2.78600 | − | 4.82549i | −0.102415 | − | 0.177388i | ||||
\(741\) | 0.601961 | − | 1.04263i | 0.0221136 | − | 0.0383019i | ||||
\(742\) | −20.9793 | −0.770173 | ||||||||
\(743\) | −20.4033 | + | 35.3396i | −0.748525 | + | 1.29648i | 0.200004 | + | 0.979795i | \(0.435904\pi\) |
−0.948530 | + | 0.316689i | \(0.897429\pi\) | |||||||
\(744\) | −1.78600 | − | 3.09344i | −0.0654778 | − | 0.113411i | ||||
\(745\) | −4.72324 | − | 8.18089i | −0.173046 | − | 0.299725i | ||||
\(746\) | 14.2056 | + | 24.6048i | 0.520104 | + | 0.900847i | ||||
\(747\) | 42.0554 | 1.53873 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.7252 | + | 25.5048i | 0.538048 | + | 0.931926i | ||||
\(750\) | −0.285997 | + | 0.495361i | −0.0104431 | + | 0.0180880i | ||||
\(751\) | 1.34480 | − | 2.32926i | 0.0490725 | − | 0.0849961i | −0.840446 | − | 0.541896i | \(-0.817707\pi\) |
0.889518 | + | 0.456900i | \(0.151040\pi\) | |||||||
\(752\) | −10.6336 | −0.387768 | ||||||||
\(753\) | −1.06389 | −0.0387702 | ||||||||
\(754\) | −12.1880 | + | 21.1102i | −0.443860 | + | 0.768789i | ||||
\(755\) | 2.87759 | − | 4.98413i | 0.104726 | − | 0.181391i | ||||
\(756\) | 7.58123 | + | 13.1311i | 0.275727 | + | 0.477573i | ||||
\(757\) | −26.3412 | − | 45.6243i | −0.957388 | − | 1.65824i | −0.728807 | − | 0.684719i | \(-0.759925\pi\) |
−0.228580 | − | 0.973525i | \(-0.573408\pi\) | |||||||
\(758\) | 6.42801 | 0.233476 | ||||||||
\(759\) | 0.302491 | + | 0.523930i | 0.0109797 | + | 0.0190175i | ||||
\(760\) | 0.214003 | + | 0.370665i | 0.00776272 | + | 0.0134454i | ||||
\(761\) | −1.45156 | − | 2.51418i | −0.0526191 | − | 0.0911389i | 0.838516 | − | 0.544877i | \(-0.183424\pi\) |
−0.891135 | + | 0.453738i | \(0.850090\pi\) | |||||||
\(762\) | −0.285997 | + | 0.495361i | −0.0103606 | + | 0.0179450i | ||||
\(763\) | −94.8700 | −3.43452 | ||||||||
\(764\) | −5.91764 | + | 10.2497i | −0.214093 | + | 0.370819i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.3064 | 0.625307 | ||||||||
\(767\) | 25.0841 | + | 43.4469i | 0.905733 | + | 1.56877i | ||||
\(768\) | 0.285997 | − | 0.495361i | 0.0103200 | − | 0.0178748i | ||||
\(769\) | 6.23558 | − | 10.8003i | 0.224861 | − | 0.389470i | −0.731417 | − | 0.681931i | \(-0.761141\pi\) |
0.956278 | + | 0.292460i | \(0.0944739\pi\) | |||||||
\(770\) | −7.34565 | −0.264719 | ||||||||
\(771\) | −7.54118 | + | 13.0617i | −0.271589 | + | 0.470406i | ||||
\(772\) | −9.25934 | −0.333251 | ||||||||
\(773\) | 4.71598 | 0.169622 | 0.0848110 | − | 0.996397i | \(-0.472971\pi\) | ||||
0.0848110 | + | 0.996397i | \(0.472971\pi\) | |||||||
\(774\) | −11.9753 | + | 12.7978i | −0.430444 | + | 0.460007i | ||||
\(775\) | −6.24482 | −0.224320 | ||||||||
\(776\) | −4.28797 | −0.153929 | ||||||||
\(777\) | 7.44648 | − | 12.8977i | 0.267141 | − | 0.462702i | ||||
\(778\) | −20.2386 | −0.725589 | ||||||||
\(779\) | 1.60281 | − | 2.77614i | 0.0574265 | − | 0.0994656i | ||||
\(780\) | −1.40643 | + | 2.43601i | −0.0503582 | + | 0.0872230i | ||||
\(781\) | 0.706744 | + | 1.22412i | 0.0252893 | + | 0.0438023i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.04203 | − | 13.9292i | −0.287399 | − | 0.497789i | ||||
\(784\) | −7.41764 | + | 12.8477i | −0.264916 | + | 0.458848i | ||||
\(785\) | −6.71598 | −0.239704 | ||||||||
\(786\) | 2.01847 | − | 3.49609i | 0.0719965 | − | 0.124702i | ||||
\(787\) | 14.6933 | + | 25.4495i | 0.523759 | + | 0.907176i | 0.999618 | + | 0.0276548i | \(0.00880393\pi\) |
−0.475859 | + | 0.879522i | \(0.657863\pi\) | |||||||
\(788\) | 0.528837 | + | 0.915973i | 0.0188390 | + | 0.0326302i | ||||
\(789\) | −1.94958 | − | 3.37678i | −0.0694071 | − | 0.120217i | ||||
\(790\) | 12.9793 | 0.461782 | ||||||||
\(791\) | −4.57199 | − | 7.91892i | −0.162561 | − | 0.281565i | ||||
\(792\) | −2.10083 | − | 3.63875i | −0.0746498 | − | 0.129297i | ||||
\(793\) | 19.2201 | − | 33.2902i | 0.682527 | − | 1.18217i | ||||
\(794\) | −4.75518 | + | 8.23622i | −0.168755 | + | 0.292292i | ||||
\(795\) | 2.56804 | 0.0910790 | ||||||||
\(796\) | 10.5328 | 0.373325 | ||||||||
\(797\) | 25.7406 | − | 44.5840i | 0.911778 | − | 1.57925i | 0.100227 | − | 0.994965i | \(-0.468043\pi\) |
0.811551 | − | 0.584281i | \(-0.198624\pi\) | |||||||
\(798\) | −0.571993 | + | 0.990721i | −0.0202483 | + | 0.0350712i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −17.1915 | −0.607432 | ||||||||
\(802\) | −15.1101 | − | 26.1714i | −0.533555 | − | 0.924144i | ||||
\(803\) | 11.3549 | + | 19.6672i | 0.400705 | + | 0.694042i | ||||
\(804\) | −3.22126 | − | 5.57939i | −0.113605 | − | 0.196770i | ||||
\(805\) | 1.57199 | − | 2.72277i | 0.0554055 | − | 0.0959651i | ||||
\(806\) | −30.7098 | −1.08171 | ||||||||
\(807\) | −0.922724 | + | 1.59820i | −0.0324814 | + | 0.0562595i | ||||
\(808\) | −0.570017 | − | 0.987298i | −0.0200531 | − | 0.0347330i | ||||
\(809\) | 29.9793 | 1.05401 | 0.527007 | − | 0.849861i | \(-0.323314\pi\) | ||||
0.527007 | + | 0.849861i | \(0.323314\pi\) | |||||||
\(810\) | 3.08123 | + | 5.33684i | 0.108263 | + | 0.187518i | ||||
\(811\) | 21.4896 | − | 37.2211i | 0.754603 | − | 1.30701i | −0.190968 | − | 0.981596i | \(-0.561163\pi\) |
0.945571 | − | 0.325415i | \(-0.105504\pi\) | |||||||
\(812\) | 11.5812 | − | 20.0593i | 0.406421 | − | 0.703943i | ||||
\(813\) | 14.9872 | 0.525623 | ||||||||
\(814\) | −4.37957 | + | 7.58563i | −0.153504 | + | 0.265876i | ||||
\(815\) | 12.6089 | 0.441672 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.73360 | − | 0.636053i | −0.0956367 | − | 0.0222527i | ||||
\(818\) | 13.4712 | 0.471008 | ||||||||
\(819\) | 61.4195 | 2.14617 | ||||||||
\(820\) | −3.74482 | + | 6.48621i | −0.130775 | + | 0.226508i | ||||
\(821\) | −7.53940 | −0.263127 | −0.131563 | − | 0.991308i | \(-0.542000\pi\) | ||||
−0.131563 | + | 0.991308i | \(0.542000\pi\) | |||||||
\(822\) | 3.94450 | − | 6.83208i | 0.137580 | − | 0.238296i | ||||
\(823\) | −3.49472 | + | 6.05303i | −0.121818 | + | 0.210995i | −0.920485 | − | 0.390779i | \(-0.872206\pi\) |
0.798667 | + | 0.601774i | \(0.205539\pi\) | |||||||
\(824\) | 3.98040 | + | 6.89425i | 0.138664 | + | 0.240173i | ||||
\(825\) | 0.899170 | 0.0313051 | ||||||||
\(826\) | −23.8353 | − | 41.2839i | −0.829336 | − | 1.43645i | ||||
\(827\) | −17.6429 | + | 30.5583i | −0.613502 | + | 1.06262i | 0.377143 | + | 0.926155i | \(0.376906\pi\) |
−0.990645 | + | 0.136462i | \(0.956427\pi\) | |||||||
\(828\) | 1.79834 | 0.0624966 | ||||||||
\(829\) | 18.4969 | − | 32.0376i | 0.642424 | − | 1.11271i | −0.342466 | − | 0.939530i | \(-0.611262\pi\) |
0.984890 | − | 0.173180i | \(-0.0554044\pi\) | |||||||
\(830\) | −7.86723 | − | 13.6264i | −0.273075 | − | 0.472980i | ||||
\(831\) | −0.409536 | − | 0.709337i | −0.0142066 | − | 0.0246066i | ||||
\(832\) | −2.45882 | − | 4.25880i | −0.0852443 | − | 0.147647i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.59046 | + | 4.48682i | 0.0897004 | + | 0.155366i | ||||
\(835\) | −12.6625 | − | 21.9320i | −0.438202 | − | 0.758989i | ||||
\(836\) | 0.336412 | − | 0.582682i | 0.0116350 | − | 0.0201525i | ||||
\(837\) | 10.1316 | − | 17.5485i | 0.350201 | − | 0.606566i | ||||
\(838\) | −18.5759 | −0.641695 | ||||||||
\(839\) | −16.0722 | −0.554874 | −0.277437 | − | 0.960744i | \(-0.589485\pi\) | ||||
−0.277437 | + | 0.960744i | \(0.589485\pi\) | |||||||
\(840\) | 1.33641 | − | 2.31473i | 0.0461106 | − | 0.0798659i | ||||
\(841\) | 2.21485 | − | 3.83623i | 0.0763741 | − | 0.132284i | ||||
\(842\) | −10.1028 | − | 17.4986i | −0.348166 | − | 0.603041i | ||||
\(843\) | 0.0471090 | + | 0.0815952i | 0.00162252 | + | 0.00281029i | ||||
\(844\) | 3.85997 | 0.132866 | ||||||||
\(845\) | 5.59159 | + | 9.68493i | 0.192357 | + | 0.333172i | ||||
\(846\) | −14.2109 | − | 24.6140i | −0.488581 | − | 0.846247i | ||||
\(847\) | −19.9269 | − | 34.5144i | −0.684696 | − | 1.18593i | ||||
\(848\) | −2.24482 | + | 3.88814i | −0.0770873 | + | 0.133519i | ||||
\(849\) | −11.4399 | −0.392615 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.87448 | − | 3.24670i | −0.0642565 | − | 0.111296i | ||||
\(852\) | −0.514319 | −0.0176203 | ||||||||
\(853\) | −24.4812 | − | 42.4028i | −0.838222 | − | 1.45184i | −0.891380 | − | 0.453257i | \(-0.850262\pi\) |
0.0531582 | − | 0.998586i | \(-0.483071\pi\) | |||||||
\(854\) | −18.2633 | + | 31.6329i | −0.624957 | + | 1.08246i | ||||
\(855\) | −0.571993 | + | 0.990721i | −0.0195618 | + | 0.0338820i | ||||
\(856\) | 6.30249 | 0.215415 | ||||||||
\(857\) | −15.4496 | + | 26.7595i | −0.527748 | + | 0.914086i | 0.471729 | + | 0.881744i | \(0.343630\pi\) |
−0.999477 | + | 0.0323424i | \(0.989703\pi\) | |||||||
\(858\) | 4.42179 | 0.150958 | ||||||||
\(859\) | −35.6336 | −1.21580 | −0.607902 | − | 0.794012i | \(-0.707989\pi\) | ||||
−0.607902 | + | 0.794012i | \(0.707989\pi\) | |||||||
\(860\) | 6.38683 | + | 1.48608i | 0.217789 | + | 0.0506750i | ||||
\(861\) | −20.0185 | −0.682228 | ||||||||
\(862\) | 36.7345 | 1.25118 | ||||||||
\(863\) | 4.88767 | − | 8.46570i | 0.166378 | − | 0.288176i | −0.770766 | − | 0.637119i | \(-0.780126\pi\) |
0.937144 | + | 0.348943i | \(0.113459\pi\) | |||||||
\(864\) | 3.24482 | 0.110391 | ||||||||
\(865\) | 4.95684 | − | 8.58551i | 0.168538 | − | 0.291916i | ||||
\(866\) | −16.5728 | + | 28.7050i | −0.563168 | + | 0.975436i | ||||
\(867\) | −4.86194 | − | 8.42113i | −0.165120 | − | 0.285997i | ||||
\(868\) | 29.1809 | 0.990465 | ||||||||
\(869\) | −10.2017 | − | 17.6698i | −0.346068 | − | 0.599407i | ||||
\(870\) | −1.41764 | + | 2.45543i | −0.0480625 | + | 0.0832467i | ||||
\(871\) | −55.3888 | −1.87678 | ||||||||
\(872\) | −10.1512 | + | 17.5825i | −0.343765 | + | 0.595418i | ||||
\(873\) | −5.73050 | − | 9.92551i | −0.193948 | − | 0.335928i | ||||
\(874\) | 0.143987 | + | 0.249392i | 0.00487042 | + | 0.00843581i | ||||
\(875\) | −2.33641 | − | 4.04678i | −0.0789851 | − | 0.136806i | ||||
\(876\) | −8.26329 | −0.279191 | ||||||||
\(877\) | 16.9322 | + | 29.3274i | 0.571758 | + | 0.990315i | 0.996386 | + | 0.0849463i | \(0.0270719\pi\) |
−0.424627 | + | 0.905368i | \(0.639595\pi\) | |||||||
\(878\) | −1.52884 | − | 2.64802i | −0.0515958 | − | 0.0893665i | ||||
\(879\) | 7.46890 | − | 12.9365i | 0.251920 | − | 0.436338i | ||||
\(880\) | −0.785997 | + | 1.36139i | −0.0264959 | + | 0.0458923i | ||||
\(881\) | 6.77535 | 0.228267 | 0.114134 | − | 0.993465i | \(-0.463591\pi\) | ||||
0.114134 | + | 0.993465i | \(0.463591\pi\) | |||||||
\(882\) | −39.6521 | −1.33516 | ||||||||
\(883\) | −16.2600 | + | 28.1631i | −0.547192 | + | 0.947764i | 0.451273 | + | 0.892386i | \(0.350970\pi\) |
−0.998465 | + | 0.0553786i | \(0.982363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.91764 | + | 5.05350i | 0.0980754 | + | 0.169872i | ||||
\(886\) | −4.38683 | − | 7.59821i | −0.147378 | − | 0.255267i | ||||
\(887\) | −13.3720 | −0.448989 | −0.224494 | − | 0.974475i | \(-0.572073\pi\) | ||||
−0.224494 | + | 0.974475i | \(0.572073\pi\) | |||||||
\(888\) | −1.59357 | − | 2.76015i | −0.0534768 | − | 0.0926245i | ||||
\(889\) | −2.33641 | − | 4.04678i | −0.0783607 | − | 0.135725i | ||||
\(890\) | 3.21598 | + | 5.57024i | 0.107800 | + | 0.186715i | ||||
\(891\) | 4.84367 | − | 8.38948i | 0.162269 | − | 0.281058i | ||||
\(892\) | 25.0185 | 0.837680 | ||||||||
\(893\) | 2.27563 | − | 3.94151i | 0.0761511 | − | 0.131898i | ||||
\(894\) | −2.70166 | − | 4.67941i | −0.0903571 | − | 0.156503i | ||||
\(895\) | −3.91369 | −0.130820 | ||||||||
\(896\) | 2.33641 | + | 4.04678i | 0.0780540 | + | 0.135194i | ||||
\(897\) | −0.946279 | + | 1.63900i | −0.0315953 | + | 0.0547247i | ||||
\(898\) | −8.74877 | + | 15.1533i | −0.291950 | + | 0.505673i | ||||
\(899\) | −30.9546 | −1.03239 | ||||||||
\(900\) | 1.33641 | − | 2.31473i | 0.0445471 | − | 0.0771578i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 11.7737 | 0.392020 | ||||||||
\(903\) | 5.09555 | + | 16.7698i | 0.169569 | + | 0.558065i | ||||
\(904\) | −1.95684 | −0.0650837 | ||||||||
\(905\) | −2.57595 | −0.0856273 | ||||||||
\(906\) | 1.64596 | − | 2.85089i | 0.0546835 | − | 0.0947145i | ||||
\(907\) | −14.6544 | −0.486590 | −0.243295 | − | 0.969952i | \(-0.578228\pi\) | ||||
−0.243295 | + | 0.969952i | \(0.578228\pi\) | |||||||
\(908\) | −6.48766 | + | 11.2370i | −0.215300 | + | 0.372911i | ||||
\(909\) | 1.52355 | − | 2.63887i | 0.0505331 | − | 0.0875259i | ||||
\(910\) | −11.4896 | − | 19.9006i | −0.380878 | − | 0.659699i | ||||
\(911\) | −15.1792 | −0.502911 | −0.251455 | − | 0.967869i | \(-0.580909\pi\) | ||||
−0.251455 | + | 0.967869i | \(0.580909\pi\) | |||||||
\(912\) | 0.122408 | + | 0.212018i | 0.00405335 | + | 0.00702061i | ||||
\(913\) | −12.3672 | + | 21.4207i | −0.409295 | + | 0.708920i | ||||
\(914\) | −2.07841 | −0.0687476 | ||||||||
\(915\) | 2.23558 | − | 3.87214i | 0.0739060 | − | 0.128009i | ||||
\(916\) | −10.3569 | − | 17.9386i | −0.342200 | − | 0.592708i | ||||
\(917\) | 16.4896 | + | 28.5609i | 0.544536 | + | 0.943163i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.3905 | −0.837555 | −0.418778 | − | 0.908089i | \(-0.637541\pi\) | ||||
−0.418778 | + | 0.908089i | \(0.637541\pi\) | |||||||
\(920\) | −0.336412 | − | 0.582682i | −0.0110912 | − | 0.0192105i | ||||
\(921\) | −0.0640875 | − | 0.111003i | −0.00211176 | − | 0.00365767i | ||||
\(922\) | −0.151246 | + | 0.261965i | −0.00498101 | + | 0.00862736i | ||||
\(923\) | −2.21090 | + | 3.82938i | −0.0727725 | + | 0.126046i | ||||
\(924\) | −4.20166 | −0.138224 | ||||||||
\(925\) | −5.57199 | −0.183206 | ||||||||
\(926\) | 2.85488 | − | 4.94480i | 0.0938173 | − | 0.162496i | ||||
\(927\) | −10.6389 | + | 18.4271i | −0.349427 | + | 0.605226i | ||||
\(928\) | −2.47842 | − | 4.29275i | −0.0813582 | − | 0.140917i | ||||
\(929\) | −13.4764 | − | 23.3419i | −0.442148 | − | 0.765823i | 0.555701 | − | 0.831382i | \(-0.312450\pi\) |
−0.997849 | + | 0.0655598i | \(0.979117\pi\) | |||||||
\(930\) | −3.57199 | −0.117130 | ||||||||
\(931\) | −3.17480 | − | 5.49892i | −0.104050 | − | 0.180220i | ||||
\(932\) | −11.1625 | − | 19.3339i | −0.365638 | − | 0.633304i | ||||
\(933\) | −5.14794 | − | 8.91649i | −0.168536 | − | 0.291913i | ||||
\(934\) | 3.87844 | − | 6.71765i | 0.126906 | − | 0.219808i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.57199 | − | 11.3830i | 0.214812 | − | 0.372066i | ||||
\(937\) | −7.28797 | − | 12.6231i | −0.238088 | − | 0.412380i | 0.722078 | − | 0.691812i | \(-0.243187\pi\) |
−0.960166 | + | 0.279432i | \(0.909854\pi\) | |||||||
\(938\) | 52.6314 | 1.71847 | ||||||||
\(939\) | −3.83972 | − | 6.65059i | −0.125304 | − | 0.217034i | ||||
\(940\) | −5.31681 | + | 9.20899i | −0.173415 | + | 0.300364i | ||||
\(941\) | −20.0317 | + | 34.6959i | −0.653013 | + | 1.13105i | 0.329374 | + | 0.944199i | \(0.393162\pi\) |
−0.982388 | + | 0.186853i | \(0.940171\pi\) | |||||||
\(942\) | −3.84150 | −0.125163 | ||||||||
\(943\) | −2.51960 | + | 4.36408i | −0.0820495 | + | 0.142114i | ||||
\(944\) | −10.2017 | −0.332036 | ||||||||
\(945\) | 15.1625 | 0.493235 | ||||||||
\(946\) | −2.99689 | − | 9.86299i | −0.0974374 | − | 0.320674i | ||||
\(947\) | 37.2751 | 1.21128 | 0.605640 | − | 0.795739i | \(-0.292917\pi\) | ||||
0.605640 | + | 0.795739i | \(0.292917\pi\) | |||||||
\(948\) | 7.42405 | 0.241122 | ||||||||
\(949\) | −35.5213 | + | 61.5247i | −1.15307 | + | 1.99718i | ||||
\(950\) | 0.428007 | 0.0138864 | ||||||||
\(951\) | 5.63277 | − | 9.75625i | 0.182655 | − | 0.316368i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.8137 | + | 22.1940i | 0.415077 | + | 0.718934i | 0.995436 | − | 0.0954264i | \(-0.0304215\pi\) |
−0.580360 | + | 0.814360i | \(0.697088\pi\) | |||||||
\(954\) | −12.0000 | −0.388514 | ||||||||
\(955\) | 5.91764 | + | 10.2497i | 0.191490 | + | 0.331671i | ||||
\(956\) | −11.3857 | + | 19.7206i | −0.368240 | + | 0.637810i | ||||
\(957\) | 4.45704 | 0.144076 | ||||||||
\(958\) | −14.5944 | + | 25.2783i | −0.471524 | + | 0.816704i | ||||
\(959\) | 32.2241 | + | 55.8138i | 1.04057 | + | 1.80232i | ||||
\(960\) | −0.285997 | − | 0.495361i | −0.00923050 | − | 0.0159877i | ||||
\(961\) | −3.99887 | − | 6.92625i | −0.128996 | − | 0.223427i | ||||
\(962\) | −27.4011 | −0.883446 | ||||||||
\(963\) | 8.42272 | + | 14.5886i | 0.271418 | + | 0.470111i | ||||
\(964\) | 12.4793 | + | 21.6147i | 0.401930 | + | 0.696163i | ||||
\(965\) | −4.62967 | + | 8.01882i | −0.149034 | + | 0.258135i | ||||
\(966\) | 0.899170 | − | 1.55741i | 0.0289303 | − | 0.0501088i | ||||
\(967\) | 43.6442 | 1.40350 | 0.701751 | − | 0.712422i | \(-0.252402\pi\) | ||||
0.701751 | + | 0.712422i | \(0.252402\pi\) | |||||||
\(968\) | −8.52884 | −0.274127 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.14399 | + | 3.71349i | −0.0688393 | + | 0.119233i | ||||
\(971\) | −18.4773 | − | 32.0036i | −0.592965 | − | 1.02704i | −0.993831 | − | 0.110908i | \(-0.964624\pi\) |
0.400866 | − | 0.916137i | \(-0.368709\pi\) | |||||||
\(972\) | 6.62967 | + | 11.4829i | 0.212647 | + | 0.368315i | ||||
\(973\) | −42.3249 | −1.35687 | ||||||||
\(974\) | 0.705614 | + | 1.22216i | 0.0226093 | + | 0.0391605i | ||||
\(975\) | 1.40643 | + | 2.43601i | 0.0450418 | + | 0.0780146i | ||||
\(976\) | 3.90841 | + | 6.76956i | 0.125105 | + | 0.216688i | ||||
\(977\) | 30.5257 | − | 52.8721i | 0.976605 | − | 1.69153i | 0.302070 | − | 0.953286i | \(-0.402322\pi\) |
0.674535 | − | 0.738243i | \(-0.264344\pi\) | |||||||
\(978\) | 7.21223 | 0.230622 | ||||||||
\(979\) | 5.05550 | − | 8.75638i | 0.161574 | − | 0.279855i | ||||
\(980\) | 7.41764 | + | 12.8477i | 0.236948 | + | 0.410406i | ||||
\(981\) | −54.2650 | −1.73255 | ||||||||
\(982\) | −7.45882 | − | 12.9191i | −0.238021 | − | 0.412264i | ||||
\(983\) | −21.6964 | + | 37.5792i | −0.692007 | + | 1.19859i | 0.279172 | + | 0.960241i | \(0.409940\pi\) |
−0.971179 | + | 0.238350i | \(0.923393\pi\) | |||||||
\(984\) | −2.14201 | + | 3.71007i | −0.0682848 | + | 0.118273i | ||||
\(985\) | 1.05767 | 0.0337003 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.4218 | −0.904676 | ||||||||
\(988\) | 2.10478 | 0.0669621 | ||||||||
\(989\) | 4.29721 | + | 0.999871i | 0.136643 | + | 0.0317941i | ||||
\(990\) | −4.20166 | −0.133538 | ||||||||
\(991\) | −6.52658 | −0.207324 | −0.103662 | − | 0.994613i | \(-0.533056\pi\) | ||||
−0.103662 | + | 0.994613i | \(0.533056\pi\) | |||||||
\(992\) | 3.12241 | − | 5.40817i | 0.0991366 | − | 0.171710i | ||||
\(993\) | −5.67508 | −0.180093 | ||||||||
\(994\) | 2.10083 | − | 3.63875i | 0.0666343 | − | 0.115414i | ||||
\(995\) | 5.26640 | − | 9.12166i | 0.166956 | − | 0.289176i | ||||
\(996\) | −4.50000 | − | 7.79423i | −0.142588 | − | 0.246970i | ||||
\(997\) | 20.0000 | 0.633406 | 0.316703 | − | 0.948525i | \(-0.397424\pi\) | ||||
0.316703 | + | 0.948525i | \(0.397424\pi\) | |||||||
\(998\) | −10.4157 | − | 18.0405i | −0.329702 | − | 0.571061i | ||||
\(999\) | 9.04005 | − | 15.6578i | 0.286014 | − | 0.495392i |
(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 | 430.2.e.e.221.2 | ✓ | 6 | |
43.36 | even | 3 | inner | 430.2.e.e.251.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
430.2.e.e.221.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
430.2.e.e.251.2 | yes | 6 | 43.36 | even | 3 | inner |