Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(121,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.i (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.121 |
Dual form | 570.2.i.e.391.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −5.00000 | −1.88982 | −0.944911 | − | 0.327327i | \(-0.893852\pi\) | ||||
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.00000 | + | 5.19615i | −0.832050 | + | 1.44115i | 0.0643593 | + | 0.997927i | \(0.479500\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | −2.50000 | − | 4.33013i | −0.668153 | − | 1.15728i | ||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.00000 | − | 3.46410i | −0.485071 | − | 0.840168i | 0.514782 | − | 0.857321i | \(-0.327873\pi\) |
−0.999853 | + | 0.0171533i | \(0.994540\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.500000 | − | 4.33013i | −0.114708 | − | 0.993399i | ||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.50000 | − | 4.33013i | −0.545545 | − | 0.944911i | ||||
\(22\) | 0.500000 | + | 0.866025i | 0.106600 | + | 0.184637i | ||||
\(23\) | −3.50000 | + | 6.06218i | −0.729800 | + | 1.26405i | 0.227167 | + | 0.973856i | \(0.427054\pi\) |
−0.956967 | + | 0.290196i | \(0.906280\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −6.00000 | −1.17670 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.50000 | − | 4.33013i | 0.472456 | − | 0.818317i | ||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0.500000 | + | 0.866025i | 0.0870388 | + | 0.150756i | ||||
\(34\) | 2.00000 | − | 3.46410i | 0.342997 | − | 0.594089i | ||||
\(35\) | 2.50000 | + | 4.33013i | 0.422577 | + | 0.731925i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 7.00000 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(38\) | 3.50000 | − | 2.59808i | 0.567775 | − | 0.421464i | ||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 2.50000 | + | 4.33013i | 0.390434 | + | 0.676252i | 0.992507 | − | 0.122189i | \(-0.0389915\pi\) |
−0.602072 | + | 0.798441i | \(0.705658\pi\) | |||||||
\(42\) | 2.50000 | − | 4.33013i | 0.385758 | − | 0.668153i | ||||
\(43\) | −3.00000 | − | 5.19615i | −0.457496 | − | 0.792406i | 0.541332 | − | 0.840809i | \(-0.317920\pi\) |
−0.998828 | + | 0.0484030i | \(0.984587\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −7.00000 | −1.03209 | ||||||||
\(47\) | 4.00000 | − | 6.92820i | 0.583460 | − | 1.01058i | −0.411606 | − | 0.911362i | \(-0.635032\pi\) |
0.995066 | − | 0.0992202i | \(-0.0316348\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 18.0000 | 2.57143 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 2.00000 | − | 3.46410i | 0.280056 | − | 0.485071i | ||||
\(52\) | −3.00000 | − | 5.19615i | −0.416025 | − | 0.720577i | ||||
\(53\) | −5.50000 | + | 9.52628i | −0.755483 | + | 1.30854i | 0.189651 | + | 0.981852i | \(0.439264\pi\) |
−0.945134 | + | 0.326683i | \(0.894069\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −0.500000 | − | 0.866025i | −0.0674200 | − | 0.116775i | ||||
\(56\) | 5.00000 | 0.668153 | ||||||||
\(57\) | 3.50000 | − | 2.59808i | 0.463586 | − | 0.344124i | ||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | 4.00000 | + | 6.92820i | 0.520756 | + | 0.901975i | 0.999709 | + | 0.0241347i | \(0.00768307\pi\) |
−0.478953 | + | 0.877841i | \(0.658984\pi\) | |||||||
\(60\) | 0.500000 | + | 0.866025i | 0.0645497 | + | 0.111803i | ||||
\(61\) | 2.00000 | − | 3.46410i | 0.256074 | − | 0.443533i | −0.709113 | − | 0.705095i | \(-0.750904\pi\) |
0.965187 | + | 0.261562i | \(0.0842377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.50000 | − | 4.33013i | 0.314970 | − | 0.545545i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | −0.500000 | + | 0.866025i | −0.0615457 | + | 0.106600i | ||||
\(67\) | −6.00000 | + | 10.3923i | −0.733017 | + | 1.26962i | 0.222571 | + | 0.974916i | \(0.428555\pi\) |
−0.955588 | + | 0.294706i | \(0.904778\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | −7.00000 | −0.842701 | ||||||||
\(70\) | −2.50000 | + | 4.33013i | −0.298807 | + | 0.517549i | ||||
\(71\) | −1.00000 | − | 1.73205i | −0.118678 | − | 0.205557i | 0.800566 | − | 0.599245i | \(-0.204532\pi\) |
−0.919244 | + | 0.393688i | \(0.871199\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 1.00000 | + | 1.73205i | 0.117041 | + | 0.202721i | 0.918594 | − | 0.395203i | \(-0.129326\pi\) |
−0.801553 | + | 0.597924i | \(0.795992\pi\) | |||||||
\(74\) | 3.50000 | + | 6.06218i | 0.406867 | + | 0.704714i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 4.00000 | + | 1.73205i | 0.458831 | + | 0.198680i | ||||
\(77\) | −5.00000 | −0.569803 | ||||||||
\(78\) | −3.00000 | − | 5.19615i | −0.339683 | − | 0.588348i | ||||
\(79\) | −5.00000 | − | 8.66025i | −0.562544 | − | 0.974355i | −0.997274 | − | 0.0737937i | \(-0.976489\pi\) |
0.434730 | − | 0.900561i | \(-0.356844\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.50000 | + | 4.33013i | −0.276079 | + | 0.478183i | ||||
\(83\) | −10.0000 | −1.09764 | −0.548821 | − | 0.835940i | \(-0.684923\pi\) | ||||
−0.548821 | + | 0.835940i | \(0.684923\pi\) | |||||||
\(84\) | 5.00000 | 0.545545 | ||||||||
\(85\) | −2.00000 | + | 3.46410i | −0.216930 | + | 0.375735i | ||||
\(86\) | 3.00000 | − | 5.19615i | 0.323498 | − | 0.560316i | ||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −6.50000 | + | 11.2583i | −0.688999 | + | 1.19338i | 0.283164 | + | 0.959072i | \(0.408616\pi\) |
−0.972162 | + | 0.234309i | \(0.924717\pi\) | |||||||
\(90\) | 0.500000 | + | 0.866025i | 0.0527046 | + | 0.0912871i | ||||
\(91\) | 15.0000 | − | 25.9808i | 1.57243 | − | 2.72352i | ||||
\(92\) | −3.50000 | − | 6.06218i | −0.364900 | − | 0.632026i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | −3.50000 | + | 2.59808i | −0.359092 | + | 0.266557i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.00000 | − | 1.73205i | −0.101535 | − | 0.175863i | 0.810782 | − | 0.585348i | \(-0.199042\pi\) |
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(98\) | 9.00000 | + | 15.5885i | 0.909137 | + | 1.57467i | ||||
\(99\) | −0.500000 | + | 0.866025i | −0.0502519 | + | 0.0870388i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | 15.0000 | 1.47799 | 0.738997 | − | 0.673709i | \(-0.235300\pi\) | ||||
0.738997 | + | 0.673709i | \(0.235300\pi\) | |||||||
\(104\) | 3.00000 | − | 5.19615i | 0.294174 | − | 0.509525i | ||||
\(105\) | −2.50000 | + | 4.33013i | −0.243975 | + | 0.422577i | ||||
\(106\) | −11.0000 | −1.06841 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 8.00000 | + | 13.8564i | 0.766261 | + | 1.32720i | 0.939577 | + | 0.342337i | \(0.111218\pi\) |
−0.173316 | + | 0.984866i | \(0.555448\pi\) | |||||||
\(110\) | 0.500000 | − | 0.866025i | 0.0476731 | − | 0.0825723i | ||||
\(111\) | 3.50000 | + | 6.06218i | 0.332205 | + | 0.575396i | ||||
\(112\) | 2.50000 | + | 4.33013i | 0.236228 | + | 0.409159i | ||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 4.00000 | + | 1.73205i | 0.374634 | + | 0.162221i | ||||
\(115\) | 7.00000 | 0.652753 | ||||||||
\(116\) | −3.00000 | − | 5.19615i | −0.278543 | − | 0.482451i | ||||
\(117\) | −3.00000 | − | 5.19615i | −0.277350 | − | 0.480384i | ||||
\(118\) | −4.00000 | + | 6.92820i | −0.368230 | + | 0.637793i | ||||
\(119\) | 10.0000 | + | 17.3205i | 0.916698 | + | 1.58777i | ||||
\(120\) | −0.500000 | + | 0.866025i | −0.0456435 | + | 0.0790569i | ||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 4.00000 | 0.362143 | ||||||||
\(123\) | −2.50000 | + | 4.33013i | −0.225417 | + | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 5.00000 | 0.445435 | ||||||||
\(127\) | 2.50000 | − | 4.33013i | 0.221839 | − | 0.384237i | −0.733527 | − | 0.679660i | \(-0.762127\pi\) |
0.955366 | + | 0.295423i | \(0.0954607\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 3.00000 | − | 5.19615i | 0.264135 | − | 0.457496i | ||||
\(130\) | 3.00000 | + | 5.19615i | 0.263117 | + | 0.455733i | ||||
\(131\) | 1.50000 | + | 2.59808i | 0.131056 | + | 0.226995i | 0.924084 | − | 0.382190i | \(-0.124830\pi\) |
−0.793028 | + | 0.609185i | \(0.791497\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 2.50000 | + | 21.6506i | 0.216777 | + | 1.87735i | ||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | 6.00000 | − | 10.3923i | 0.512615 | − | 0.887875i | −0.487278 | − | 0.873247i | \(-0.662010\pi\) |
0.999893 | − | 0.0146279i | \(-0.00465636\pi\) | |||||||
\(138\) | −3.50000 | − | 6.06218i | −0.297940 | − | 0.516047i | ||||
\(139\) | 8.00000 | − | 13.8564i | 0.678551 | − | 1.17529i | −0.296866 | − | 0.954919i | \(-0.595942\pi\) |
0.975417 | − | 0.220366i | \(-0.0707252\pi\) | |||||||
\(140\) | −5.00000 | −0.422577 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 1.00000 | − | 1.73205i | 0.0839181 | − | 0.145350i | ||||
\(143\) | −3.00000 | + | 5.19615i | −0.250873 | + | 0.434524i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | −1.00000 | + | 1.73205i | −0.0827606 | + | 0.143346i | ||||
\(147\) | 9.00000 | + | 15.5885i | 0.742307 | + | 1.28571i | ||||
\(148\) | −3.50000 | + | 6.06218i | −0.287698 | + | 0.498308i | ||||
\(149\) | 2.00000 | + | 3.46410i | 0.163846 | + | 0.283790i | 0.936245 | − | 0.351348i | \(-0.114277\pi\) |
−0.772399 | + | 0.635138i | \(0.780943\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | 0.500000 | + | 4.33013i | 0.0405554 | + | 0.351220i | ||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | −2.50000 | − | 4.33013i | −0.201456 | − | 0.348932i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | −4.50000 | − | 7.79423i | −0.359139 | − | 0.622047i | 0.628678 | − | 0.777666i | \(-0.283596\pi\) |
−0.987817 | + | 0.155618i | \(0.950263\pi\) | |||||||
\(158\) | 5.00000 | − | 8.66025i | 0.397779 | − | 0.688973i | ||||
\(159\) | −11.0000 | −0.872357 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 17.5000 | − | 30.3109i | 1.37919 | − | 2.38883i | ||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | −5.00000 | −0.390434 | ||||||||
\(165\) | 0.500000 | − | 0.866025i | 0.0389249 | − | 0.0674200i | ||||
\(166\) | −5.00000 | − | 8.66025i | −0.388075 | − | 0.672166i | ||||
\(167\) | −10.5000 | + | 18.1865i | −0.812514 | + | 1.40732i | 0.0985846 | + | 0.995129i | \(0.468568\pi\) |
−0.911099 | + | 0.412188i | \(0.864765\pi\) | |||||||
\(168\) | 2.50000 | + | 4.33013i | 0.192879 | + | 0.334077i | ||||
\(169\) | −11.5000 | − | 19.9186i | −0.884615 | − | 1.53220i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 4.00000 | + | 1.73205i | 0.305888 | + | 0.132453i | ||||
\(172\) | 6.00000 | 0.457496 | ||||||||
\(173\) | 4.50000 | + | 7.79423i | 0.342129 | + | 0.592584i | 0.984828 | − | 0.173534i | \(-0.0555188\pi\) |
−0.642699 | + | 0.766119i | \(0.722185\pi\) | |||||||
\(174\) | −3.00000 | − | 5.19615i | −0.227429 | − | 0.393919i | ||||
\(175\) | 2.50000 | − | 4.33013i | 0.188982 | − | 0.327327i | ||||
\(176\) | −0.500000 | − | 0.866025i | −0.0376889 | − | 0.0652791i | ||||
\(177\) | −4.00000 | + | 6.92820i | −0.300658 | + | 0.520756i | ||||
\(178\) | −13.0000 | −0.974391 | ||||||||
\(179\) | 7.00000 | 0.523205 | 0.261602 | − | 0.965176i | \(-0.415749\pi\) | ||||
0.261602 | + | 0.965176i | \(0.415749\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | −9.00000 | + | 15.5885i | −0.668965 | + | 1.15868i | 0.309229 | + | 0.950988i | \(0.399929\pi\) |
−0.978194 | + | 0.207693i | \(0.933404\pi\) | |||||||
\(182\) | 30.0000 | 2.22375 | ||||||||
\(183\) | 4.00000 | 0.295689 | ||||||||
\(184\) | 3.50000 | − | 6.06218i | 0.258023 | − | 0.446910i | ||||
\(185\) | −3.50000 | − | 6.06218i | −0.257325 | − | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | − | 3.46410i | −0.146254 | − | 0.253320i | ||||
\(188\) | 4.00000 | + | 6.92820i | 0.291730 | + | 0.505291i | ||||
\(189\) | 5.00000 | 0.363696 | ||||||||
\(190\) | −4.00000 | − | 1.73205i | −0.290191 | − | 0.125656i | ||||
\(191\) | −14.0000 | −1.01300 | −0.506502 | − | 0.862239i | \(-0.669062\pi\) | ||||
−0.506502 | + | 0.862239i | \(0.669062\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | 1.00000 | − | 1.73205i | 0.0717958 | − | 0.124354i | ||||
\(195\) | 3.00000 | + | 5.19615i | 0.214834 | + | 0.372104i | ||||
\(196\) | −9.00000 | + | 15.5885i | −0.642857 | + | 1.11346i | ||||
\(197\) | 1.00000 | 0.0712470 | 0.0356235 | − | 0.999365i | \(-0.488658\pi\) | ||||
0.0356235 | + | 0.999365i | \(0.488658\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | −12.0000 | −0.846415 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | 15.0000 | − | 25.9808i | 1.05279 | − | 1.82349i | ||||
\(204\) | 2.00000 | + | 3.46410i | 0.140028 | + | 0.242536i | ||||
\(205\) | 2.50000 | − | 4.33013i | 0.174608 | − | 0.302429i | ||||
\(206\) | 7.50000 | + | 12.9904i | 0.522550 | + | 0.905083i | ||||
\(207\) | −3.50000 | − | 6.06218i | −0.243267 | − | 0.421350i | ||||
\(208\) | 6.00000 | 0.416025 | ||||||||
\(209\) | −0.500000 | − | 4.33013i | −0.0345857 | − | 0.299521i | ||||
\(210\) | −5.00000 | −0.345033 | ||||||||
\(211\) | −6.50000 | − | 11.2583i | −0.447478 | − | 0.775055i | 0.550743 | − | 0.834675i | \(-0.314345\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | −5.50000 | − | 9.52628i | −0.377742 | − | 0.654268i | ||||
\(213\) | 1.00000 | − | 1.73205i | 0.0685189 | − | 0.118678i | ||||
\(214\) | −2.00000 | − | 3.46410i | −0.136717 | − | 0.236801i | ||||
\(215\) | −3.00000 | + | 5.19615i | −0.204598 | + | 0.354375i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.00000 | + | 13.8564i | −0.541828 | + | 0.938474i | ||||
\(219\) | −1.00000 | + | 1.73205i | −0.0675737 | + | 0.117041i | ||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 24.0000 | 1.61441 | ||||||||
\(222\) | −3.50000 | + | 6.06218i | −0.234905 | + | 0.406867i | ||||
\(223\) | 10.5000 | + | 18.1865i | 0.703132 | + | 1.21786i | 0.967361 | + | 0.253401i | \(0.0815490\pi\) |
−0.264229 | + | 0.964460i | \(0.585118\pi\) | |||||||
\(224\) | −2.50000 | + | 4.33013i | −0.167038 | + | 0.289319i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 2.00000 | + | 3.46410i | 0.133038 | + | 0.230429i | ||||
\(227\) | 2.00000 | 0.132745 | 0.0663723 | − | 0.997795i | \(-0.478857\pi\) | ||||
0.0663723 | + | 0.997795i | \(0.478857\pi\) | |||||||
\(228\) | 0.500000 | + | 4.33013i | 0.0331133 | + | 0.286770i | ||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 3.50000 | + | 6.06218i | 0.230783 | + | 0.399728i | ||||
\(231\) | −2.50000 | − | 4.33013i | −0.164488 | − | 0.284901i | ||||
\(232\) | 3.00000 | − | 5.19615i | 0.196960 | − | 0.341144i | ||||
\(233\) | 9.00000 | + | 15.5885i | 0.589610 | + | 1.02123i | 0.994283 | + | 0.106773i | \(0.0340517\pi\) |
−0.404674 | + | 0.914461i | \(0.632615\pi\) | |||||||
\(234\) | 3.00000 | − | 5.19615i | 0.196116 | − | 0.339683i | ||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | 5.00000 | − | 8.66025i | 0.324785 | − | 0.562544i | ||||
\(238\) | −10.0000 | + | 17.3205i | −0.648204 | + | 1.12272i | ||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 13.0000 | − | 22.5167i | 0.837404 | − | 1.45043i | −0.0546547 | − | 0.998505i | \(-0.517406\pi\) |
0.892058 | − | 0.451920i | \(-0.149261\pi\) | |||||||
\(242\) | −5.00000 | − | 8.66025i | −0.321412 | − | 0.556702i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 2.00000 | + | 3.46410i | 0.128037 | + | 0.221766i | ||||
\(245\) | −9.00000 | − | 15.5885i | −0.574989 | − | 0.995910i | ||||
\(246\) | −5.00000 | −0.318788 | ||||||||
\(247\) | 24.0000 | + | 10.3923i | 1.52708 | + | 0.661247i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.00000 | − | 8.66025i | −0.316862 | − | 0.548821i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | −6.00000 | + | 10.3923i | −0.378717 | + | 0.655956i | −0.990876 | − | 0.134778i | \(-0.956968\pi\) |
0.612159 | + | 0.790735i | \(0.290301\pi\) | |||||||
\(252\) | 2.50000 | + | 4.33013i | 0.157485 | + | 0.272772i | ||||
\(253\) | −3.50000 | + | 6.06218i | −0.220043 | + | 0.381126i | ||||
\(254\) | 5.00000 | 0.313728 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 6.00000 | 0.373544 | ||||||||
\(259\) | −35.0000 | −2.17479 | ||||||||
\(260\) | −3.00000 | + | 5.19615i | −0.186052 | + | 0.322252i | ||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | −1.50000 | + | 2.59808i | −0.0926703 | + | 0.160510i | ||||
\(263\) | −10.5000 | − | 18.1865i | −0.647458 | − | 1.12143i | −0.983728 | − | 0.179664i | \(-0.942499\pi\) |
0.336270 | − | 0.941766i | \(-0.390834\pi\) | |||||||
\(264\) | −0.500000 | − | 0.866025i | −0.0307729 | − | 0.0533002i | ||||
\(265\) | 11.0000 | 0.675725 | ||||||||
\(266\) | −17.5000 | + | 12.9904i | −1.07299 | + | 0.796491i | ||||
\(267\) | −13.0000 | −0.795587 | ||||||||
\(268\) | −6.00000 | − | 10.3923i | −0.366508 | − | 0.634811i | ||||
\(269\) | −16.0000 | − | 27.7128i | −0.975537 | − | 1.68968i | −0.678151 | − | 0.734923i | \(-0.737218\pi\) |
−0.297386 | − | 0.954757i | \(-0.596115\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | −2.00000 | + | 3.46410i | −0.121268 | + | 0.210042i | ||||
\(273\) | 30.0000 | 1.81568 | ||||||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | −0.500000 | + | 0.866025i | −0.0301511 | + | 0.0522233i | ||||
\(276\) | 3.50000 | − | 6.06218i | 0.210675 | − | 0.364900i | ||||
\(277\) | −14.0000 | −0.841178 | −0.420589 | − | 0.907251i | \(-0.638177\pi\) | ||||
−0.420589 | + | 0.907251i | \(0.638177\pi\) | |||||||
\(278\) | 16.0000 | 0.959616 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.50000 | − | 4.33013i | −0.149404 | − | 0.258775i | ||||
\(281\) | 5.50000 | − | 9.52628i | 0.328102 | − | 0.568290i | −0.654033 | − | 0.756466i | \(-0.726924\pi\) |
0.982135 | + | 0.188176i | \(0.0602575\pi\) | |||||||
\(282\) | 4.00000 | + | 6.92820i | 0.238197 | + | 0.412568i | ||||
\(283\) | −11.0000 | − | 19.0526i | −0.653882 | − | 1.13256i | −0.982173 | − | 0.187980i | \(-0.939806\pi\) |
0.328291 | − | 0.944577i | \(-0.393527\pi\) | |||||||
\(284\) | 2.00000 | 0.118678 | ||||||||
\(285\) | −4.00000 | − | 1.73205i | −0.236940 | − | 0.102598i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | −12.5000 | − | 21.6506i | −0.737852 | − | 1.27800i | ||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 3.00000 | + | 5.19615i | 0.176166 | + | 0.305129i | ||||
\(291\) | 1.00000 | − | 1.73205i | 0.0586210 | − | 0.101535i | ||||
\(292\) | −2.00000 | −0.117041 | ||||||||
\(293\) | 5.00000 | 0.292103 | 0.146052 | − | 0.989277i | \(-0.453343\pi\) | ||||
0.146052 | + | 0.989277i | \(0.453343\pi\) | |||||||
\(294\) | −9.00000 | + | 15.5885i | −0.524891 | + | 0.909137i | ||||
\(295\) | 4.00000 | − | 6.92820i | 0.232889 | − | 0.403376i | ||||
\(296\) | −7.00000 | −0.406867 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −2.00000 | + | 3.46410i | −0.115857 | + | 0.200670i | ||||
\(299\) | −21.0000 | − | 36.3731i | −1.21446 | − | 2.10351i | ||||
\(300\) | 0.500000 | − | 0.866025i | 0.0288675 | − | 0.0500000i | ||||
\(301\) | 15.0000 | + | 25.9808i | 0.864586 | + | 1.49751i | ||||
\(302\) | −10.0000 | − | 17.3205i | −0.575435 | − | 0.996683i | ||||
\(303\) | −2.00000 | −0.114897 | ||||||||
\(304\) | −3.50000 | + | 2.59808i | −0.200739 | + | 0.149010i | ||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 2.00000 | + | 3.46410i | 0.114332 | + | 0.198030i | ||||
\(307\) | −9.00000 | − | 15.5885i | −0.513657 | − | 0.889680i | −0.999875 | − | 0.0158424i | \(-0.994957\pi\) |
0.486217 | − | 0.873838i | \(-0.338376\pi\) | |||||||
\(308\) | 2.50000 | − | 4.33013i | 0.142451 | − | 0.246732i | ||||
\(309\) | 7.50000 | + | 12.9904i | 0.426660 | + | 0.738997i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.0000 | −1.13410 | −0.567048 | − | 0.823685i | \(-0.691915\pi\) | ||||
−0.567048 | + | 0.823685i | \(0.691915\pi\) | |||||||
\(312\) | 6.00000 | 0.339683 | ||||||||
\(313\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(314\) | 4.50000 | − | 7.79423i | 0.253950 | − | 0.439854i | ||||
\(315\) | −5.00000 | −0.281718 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | −1.50000 | + | 2.59808i | −0.0842484 | + | 0.145922i | −0.905071 | − | 0.425261i | \(-0.860182\pi\) |
0.820822 | + | 0.571184i | \(0.193516\pi\) | |||||||
\(318\) | −5.50000 | − | 9.52628i | −0.308425 | − | 0.534207i | ||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | −2.00000 | − | 3.46410i | −0.111629 | − | 0.193347i | ||||
\(322\) | 35.0000 | 1.95047 | ||||||||
\(323\) | −14.0000 | + | 10.3923i | −0.778981 | + | 0.578243i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.00000 | − | 5.19615i | −0.166410 | − | 0.288231i | ||||
\(326\) | −5.00000 | − | 8.66025i | −0.276924 | − | 0.479647i | ||||
\(327\) | −8.00000 | + | 13.8564i | −0.442401 | + | 0.766261i | ||||
\(328\) | −2.50000 | − | 4.33013i | −0.138039 | − | 0.239091i | ||||
\(329\) | −20.0000 | + | 34.6410i | −1.10264 | + | 1.90982i | ||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | 15.0000 | 0.824475 | 0.412237 | − | 0.911077i | \(-0.364747\pi\) | ||||
0.412237 | + | 0.911077i | \(0.364747\pi\) | |||||||
\(332\) | 5.00000 | − | 8.66025i | 0.274411 | − | 0.475293i | ||||
\(333\) | −3.50000 | + | 6.06218i | −0.191799 | + | 0.332205i | ||||
\(334\) | −21.0000 | −1.14907 | ||||||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | −2.50000 | + | 4.33013i | −0.136386 | + | 0.236228i | ||||
\(337\) | −1.00000 | − | 1.73205i | −0.0544735 | − | 0.0943508i | 0.837503 | − | 0.546433i | \(-0.184015\pi\) |
−0.891976 | + | 0.452082i | \(0.850681\pi\) | |||||||
\(338\) | 11.5000 | − | 19.9186i | 0.625518 | − | 1.08343i | ||||
\(339\) | 2.00000 | + | 3.46410i | 0.108625 | + | 0.188144i | ||||
\(340\) | −2.00000 | − | 3.46410i | −0.108465 | − | 0.187867i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.500000 | + | 4.33013i | 0.0270369 | + | 0.234146i | ||||
\(343\) | −55.0000 | −2.96972 | ||||||||
\(344\) | 3.00000 | + | 5.19615i | 0.161749 | + | 0.280158i | ||||
\(345\) | 3.50000 | + | 6.06218i | 0.188434 | + | 0.326377i | ||||
\(346\) | −4.50000 | + | 7.79423i | −0.241921 | + | 0.419020i | ||||
\(347\) | 1.00000 | + | 1.73205i | 0.0536828 | + | 0.0929814i | 0.891618 | − | 0.452788i | \(-0.149571\pi\) |
−0.837935 | + | 0.545770i | \(0.816237\pi\) | |||||||
\(348\) | 3.00000 | − | 5.19615i | 0.160817 | − | 0.278543i | ||||
\(349\) | 16.0000 | 0.856460 | 0.428230 | − | 0.903670i | \(-0.359137\pi\) | ||||
0.428230 | + | 0.903670i | \(0.359137\pi\) | |||||||
\(350\) | 5.00000 | 0.267261 | ||||||||
\(351\) | 3.00000 | − | 5.19615i | 0.160128 | − | 0.277350i | ||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 36.0000 | 1.91609 | 0.958043 | − | 0.286623i | \(-0.0925328\pi\) | ||||
0.958043 | + | 0.286623i | \(0.0925328\pi\) | |||||||
\(354\) | −8.00000 | −0.425195 | ||||||||
\(355\) | −1.00000 | + | 1.73205i | −0.0530745 | + | 0.0919277i | ||||
\(356\) | −6.50000 | − | 11.2583i | −0.344499 | − | 0.596690i | ||||
\(357\) | −10.0000 | + | 17.3205i | −0.529256 | + | 0.916698i | ||||
\(358\) | 3.50000 | + | 6.06218i | 0.184981 | + | 0.320396i | ||||
\(359\) | 9.00000 | + | 15.5885i | 0.475002 | + | 0.822727i | 0.999590 | − | 0.0286287i | \(-0.00911406\pi\) |
−0.524588 | + | 0.851356i | \(0.675781\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −18.5000 | + | 4.33013i | −0.973684 | + | 0.227901i | ||||
\(362\) | −18.0000 | −0.946059 | ||||||||
\(363\) | −5.00000 | − | 8.66025i | −0.262432 | − | 0.454545i | ||||
\(364\) | 15.0000 | + | 25.9808i | 0.786214 | + | 1.36176i | ||||
\(365\) | 1.00000 | − | 1.73205i | 0.0523424 | − | 0.0906597i | ||||
\(366\) | 2.00000 | + | 3.46410i | 0.104542 | + | 0.181071i | ||||
\(367\) | 2.00000 | − | 3.46410i | 0.104399 | − | 0.180825i | −0.809093 | − | 0.587680i | \(-0.800041\pi\) |
0.913493 | + | 0.406855i | \(0.133375\pi\) | |||||||
\(368\) | 7.00000 | 0.364900 | ||||||||
\(369\) | −5.00000 | −0.260290 | ||||||||
\(370\) | 3.50000 | − | 6.06218i | 0.181956 | − | 0.315158i | ||||
\(371\) | 27.5000 | − | 47.6314i | 1.42773 | − | 2.47290i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | 0.258890 | 0.129445 | − | 0.991587i | \(-0.458680\pi\) | ||||
0.129445 | + | 0.991587i | \(0.458680\pi\) | |||||||
\(374\) | 2.00000 | − | 3.46410i | 0.103418 | − | 0.179124i | ||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | −4.00000 | + | 6.92820i | −0.206284 | + | 0.357295i | ||||
\(377\) | −18.0000 | − | 31.1769i | −0.927047 | − | 1.60569i | ||||
\(378\) | 2.50000 | + | 4.33013i | 0.128586 | + | 0.222718i | ||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | −0.500000 | − | 4.33013i | −0.0256495 | − | 0.222131i | ||||
\(381\) | 5.00000 | 0.256158 | ||||||||
\(382\) | −7.00000 | − | 12.1244i | −0.358151 | − | 0.620336i | ||||
\(383\) | −16.0000 | − | 27.7128i | −0.817562 | − | 1.41606i | −0.907474 | − | 0.420109i | \(-0.861992\pi\) |
0.0899119 | − | 0.995950i | \(-0.471341\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 2.50000 | + | 4.33013i | 0.127412 | + | 0.220684i | ||||
\(386\) | −2.00000 | + | 3.46410i | −0.101797 | + | 0.176318i | ||||
\(387\) | 6.00000 | 0.304997 | ||||||||
\(388\) | 2.00000 | 0.101535 | ||||||||
\(389\) | 5.00000 | − | 8.66025i | 0.253510 | − | 0.439092i | −0.710980 | − | 0.703213i | \(-0.751748\pi\) |
0.964490 | + | 0.264120i | \(0.0850816\pi\) | |||||||
\(390\) | −3.00000 | + | 5.19615i | −0.151911 | + | 0.263117i | ||||
\(391\) | 28.0000 | 1.41602 | ||||||||
\(392\) | −18.0000 | −0.909137 | ||||||||
\(393\) | −1.50000 | + | 2.59808i | −0.0756650 | + | 0.131056i | ||||
\(394\) | 0.500000 | + | 0.866025i | 0.0251896 | + | 0.0436297i | ||||
\(395\) | −5.00000 | + | 8.66025i | −0.251577 | + | 0.435745i | ||||
\(396\) | −0.500000 | − | 0.866025i | −0.0251259 | − | 0.0435194i | ||||
\(397\) | 16.5000 | + | 28.5788i | 0.828111 | + | 1.43433i | 0.899518 | + | 0.436884i | \(0.143918\pi\) |
−0.0714068 | + | 0.997447i | \(0.522749\pi\) | |||||||
\(398\) | 4.00000 | 0.200502 | ||||||||
\(399\) | −17.5000 | + | 12.9904i | −0.876096 | + | 0.650332i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | −6.00000 | − | 10.3923i | −0.299253 | − | 0.518321i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.00000 | − | 1.73205i | −0.0497519 | − | 0.0861727i | ||||
\(405\) | −0.500000 | + | 0.866025i | −0.0248452 | + | 0.0430331i | ||||
\(406\) | 30.0000 | 1.48888 | ||||||||
\(407\) | 7.00000 | 0.346977 | ||||||||
\(408\) | −2.00000 | + | 3.46410i | −0.0990148 | + | 0.171499i | ||||
\(409\) | 1.50000 | − | 2.59808i | 0.0741702 | − | 0.128467i | −0.826555 | − | 0.562856i | \(-0.809703\pi\) |
0.900725 | + | 0.434389i | \(0.143036\pi\) | |||||||
\(410\) | 5.00000 | 0.246932 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | −7.50000 | + | 12.9904i | −0.369498 | + | 0.639990i | ||||
\(413\) | −20.0000 | − | 34.6410i | −0.984136 | − | 1.70457i | ||||
\(414\) | 3.50000 | − | 6.06218i | 0.172016 | − | 0.297940i | ||||
\(415\) | 5.00000 | + | 8.66025i | 0.245440 | + | 0.425115i | ||||
\(416\) | 3.00000 | + | 5.19615i | 0.147087 | + | 0.254762i | ||||
\(417\) | 16.0000 | 0.783523 | ||||||||
\(418\) | 3.50000 | − | 2.59808i | 0.171191 | − | 0.127076i | ||||
\(419\) | −3.00000 | −0.146560 | −0.0732798 | − | 0.997311i | \(-0.523347\pi\) | ||||
−0.0732798 | + | 0.997311i | \(0.523347\pi\) | |||||||
\(420\) | −2.50000 | − | 4.33013i | −0.121988 | − | 0.211289i | ||||
\(421\) | 4.00000 | + | 6.92820i | 0.194948 | + | 0.337660i | 0.946883 | − | 0.321577i | \(-0.104213\pi\) |
−0.751935 | + | 0.659237i | \(0.770879\pi\) | |||||||
\(422\) | 6.50000 | − | 11.2583i | 0.316415 | − | 0.548047i | ||||
\(423\) | 4.00000 | + | 6.92820i | 0.194487 | + | 0.336861i | ||||
\(424\) | 5.50000 | − | 9.52628i | 0.267104 | − | 0.462637i | ||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 2.00000 | 0.0969003 | ||||||||
\(427\) | −10.0000 | + | 17.3205i | −0.483934 | + | 0.838198i | ||||
\(428\) | 2.00000 | − | 3.46410i | 0.0966736 | − | 0.167444i | ||||
\(429\) | −6.00000 | −0.289683 | ||||||||
\(430\) | −6.00000 | −0.289346 | ||||||||
\(431\) | 2.00000 | − | 3.46410i | 0.0963366 | − | 0.166860i | −0.813829 | − | 0.581104i | \(-0.802621\pi\) |
0.910166 | + | 0.414244i | \(0.135954\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −3.00000 | + | 5.19615i | −0.144171 | + | 0.249711i | −0.929063 | − | 0.369921i | \(-0.879385\pi\) |
0.784892 | + | 0.619632i | \(0.212718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.00000 | + | 5.19615i | 0.143839 | + | 0.249136i | ||||
\(436\) | −16.0000 | −0.766261 | ||||||||
\(437\) | 28.0000 | + | 12.1244i | 1.33942 | + | 0.579987i | ||||
\(438\) | −2.00000 | −0.0955637 | ||||||||
\(439\) | 16.0000 | + | 27.7128i | 0.763638 | + | 1.32266i | 0.940963 | + | 0.338508i | \(0.109922\pi\) |
−0.177325 | + | 0.984152i | \(0.556744\pi\) | |||||||
\(440\) | 0.500000 | + | 0.866025i | 0.0238366 | + | 0.0412861i | ||||
\(441\) | −9.00000 | + | 15.5885i | −0.428571 | + | 0.742307i | ||||
\(442\) | 12.0000 | + | 20.7846i | 0.570782 | + | 0.988623i | ||||
\(443\) | −12.0000 | + | 20.7846i | −0.570137 | + | 0.987507i | 0.426414 | + | 0.904528i | \(0.359777\pi\) |
−0.996551 | + | 0.0829786i | \(0.973557\pi\) | |||||||
\(444\) | −7.00000 | −0.332205 | ||||||||
\(445\) | 13.0000 | 0.616259 | ||||||||
\(446\) | −10.5000 | + | 18.1865i | −0.497189 | + | 0.861157i | ||||
\(447\) | −2.00000 | + | 3.46410i | −0.0945968 | + | 0.163846i | ||||
\(448\) | −5.00000 | −0.236228 | ||||||||
\(449\) | −39.0000 | −1.84052 | −0.920262 | − | 0.391303i | \(-0.872024\pi\) | ||||
−0.920262 | + | 0.391303i | \(0.872024\pi\) | |||||||
\(450\) | 0.500000 | − | 0.866025i | 0.0235702 | − | 0.0408248i | ||||
\(451\) | 2.50000 | + | 4.33013i | 0.117720 | + | 0.203898i | ||||
\(452\) | −2.00000 | + | 3.46410i | −0.0940721 | + | 0.162938i | ||||
\(453\) | −10.0000 | − | 17.3205i | −0.469841 | − | 0.813788i | ||||
\(454\) | 1.00000 | + | 1.73205i | 0.0469323 | + | 0.0812892i | ||||
\(455\) | −30.0000 | −1.40642 | ||||||||
\(456\) | −3.50000 | + | 2.59808i | −0.163903 | + | 0.121666i | ||||
\(457\) | 8.00000 | 0.374224 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | 5.00000 | + | 8.66025i | 0.233635 | + | 0.404667i | ||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | −3.50000 | + | 6.06218i | −0.163188 | + | 0.282650i | ||||
\(461\) | 3.00000 | + | 5.19615i | 0.139724 | + | 0.242009i | 0.927392 | − | 0.374091i | \(-0.122045\pi\) |
−0.787668 | + | 0.616100i | \(0.788712\pi\) | |||||||
\(462\) | 2.50000 | − | 4.33013i | 0.116311 | − | 0.201456i | ||||
\(463\) | −9.00000 | −0.418265 | −0.209133 | − | 0.977887i | \(-0.567064\pi\) | ||||
−0.209133 | + | 0.977887i | \(0.567064\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.00000 | + | 15.5885i | −0.416917 | + | 0.722121i | ||||
\(467\) | 38.0000 | 1.75843 | 0.879215 | − | 0.476425i | \(-0.158068\pi\) | ||||
0.879215 | + | 0.476425i | \(0.158068\pi\) | |||||||
\(468\) | 6.00000 | 0.277350 | ||||||||
\(469\) | 30.0000 | − | 51.9615i | 1.38527 | − | 2.39936i | ||||
\(470\) | −4.00000 | − | 6.92820i | −0.184506 | − | 0.319574i | ||||
\(471\) | 4.50000 | − | 7.79423i | 0.207349 | − | 0.359139i | ||||
\(472\) | −4.00000 | − | 6.92820i | −0.184115 | − | 0.318896i | ||||
\(473\) | −3.00000 | − | 5.19615i | −0.137940 | − | 0.238919i | ||||
\(474\) | 10.0000 | 0.459315 | ||||||||
\(475\) | 4.00000 | + | 1.73205i | 0.183533 | + | 0.0794719i | ||||
\(476\) | −20.0000 | −0.916698 | ||||||||
\(477\) | −5.50000 | − | 9.52628i | −0.251828 | − | 0.436178i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.0000 | + | 36.3731i | −0.959514 | + | 1.66193i | −0.235833 | + | 0.971794i | \(0.575782\pi\) |
−0.723681 | + | 0.690134i | \(0.757551\pi\) | |||||||
\(480\) | −0.500000 | − | 0.866025i | −0.0228218 | − | 0.0395285i | ||||
\(481\) | −21.0000 | + | 36.3731i | −0.957518 | + | 1.65847i | ||||
\(482\) | 26.0000 | 1.18427 | ||||||||
\(483\) | 35.0000 | 1.59256 | ||||||||
\(484\) | 5.00000 | − | 8.66025i | 0.227273 | − | 0.393648i | ||||
\(485\) | −1.00000 | + | 1.73205i | −0.0454077 | + | 0.0786484i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −13.0000 | −0.589086 | −0.294543 | − | 0.955638i | \(-0.595167\pi\) | ||||
−0.294543 | + | 0.955638i | \(0.595167\pi\) | |||||||
\(488\) | −2.00000 | + | 3.46410i | −0.0905357 | + | 0.156813i | ||||
\(489\) | −5.00000 | − | 8.66025i | −0.226108 | − | 0.391630i | ||||
\(490\) | 9.00000 | − | 15.5885i | 0.406579 | − | 0.704215i | ||||
\(491\) | 16.5000 | + | 28.5788i | 0.744635 | + | 1.28974i | 0.950365 | + | 0.311136i | \(0.100710\pi\) |
−0.205731 | + | 0.978609i | \(0.565957\pi\) | |||||||
\(492\) | −2.50000 | − | 4.33013i | −0.112709 | − | 0.195217i | ||||
\(493\) | 24.0000 | 1.08091 | ||||||||
\(494\) | 3.00000 | + | 25.9808i | 0.134976 | + | 1.16893i | ||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.00000 | + | 8.66025i | 0.224281 | + | 0.388465i | ||||
\(498\) | 5.00000 | − | 8.66025i | 0.224055 | − | 0.388075i | ||||
\(499\) | 3.50000 | + | 6.06218i | 0.156682 | + | 0.271380i | 0.933670 | − | 0.358134i | \(-0.116587\pi\) |
−0.776989 | + | 0.629515i | \(0.783254\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | −21.0000 | −0.938211 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | −0.500000 | + | 0.866025i | −0.0222939 | + | 0.0386142i | −0.876957 | − | 0.480569i | \(-0.840430\pi\) |
0.854663 | + | 0.519183i | \(0.173764\pi\) | |||||||
\(504\) | −2.50000 | + | 4.33013i | −0.111359 | + | 0.192879i | ||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | −7.00000 | −0.311188 | ||||||||
\(507\) | 11.5000 | − | 19.9186i | 0.510733 | − | 0.884615i | ||||
\(508\) | 2.50000 | + | 4.33013i | 0.110920 | + | 0.192118i | ||||
\(509\) | −1.00000 | + | 1.73205i | −0.0443242 | + | 0.0767718i | −0.887336 | − | 0.461123i | \(-0.847447\pi\) |
0.843012 | + | 0.537895i | \(0.180780\pi\) | |||||||
\(510\) | −2.00000 | − | 3.46410i | −0.0885615 | − | 0.153393i | ||||
\(511\) | −5.00000 | − | 8.66025i | −0.221187 | − | 0.383107i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.500000 | + | 4.33013i | 0.0220755 | + | 0.191180i | ||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | −7.50000 | − | 12.9904i | −0.330489 | − | 0.572425i | ||||
\(516\) | 3.00000 | + | 5.19615i | 0.132068 | + | 0.228748i | ||||
\(517\) | 4.00000 | − | 6.92820i | 0.175920 | − | 0.304702i | ||||
\(518\) | −17.5000 | − | 30.3109i | −0.768906 | − | 1.33178i | ||||
\(519\) | −4.50000 | + | 7.79423i | −0.197528 | + | 0.342129i | ||||
\(520\) | −6.00000 | −0.263117 | ||||||||
\(521\) | −14.0000 | −0.613351 | −0.306676 | − | 0.951814i | \(-0.599217\pi\) | ||||
−0.306676 | + | 0.951814i | \(0.599217\pi\) | |||||||
\(522\) | 3.00000 | − | 5.19615i | 0.131306 | − | 0.227429i | ||||
\(523\) | 7.00000 | − | 12.1244i | 0.306089 | − | 0.530161i | −0.671414 | − | 0.741082i | \(-0.734313\pi\) |
0.977503 | + | 0.210921i | \(0.0676463\pi\) | |||||||
\(524\) | −3.00000 | −0.131056 | ||||||||
\(525\) | 5.00000 | 0.218218 | ||||||||
\(526\) | 10.5000 | − | 18.1865i | 0.457822 | − | 0.792971i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.500000 | − | 0.866025i | 0.0217597 | − | 0.0376889i | ||||
\(529\) | −13.0000 | − | 22.5167i | −0.565217 | − | 0.978985i | ||||
\(530\) | 5.50000 | + | 9.52628i | 0.238905 | + | 0.413795i | ||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | −20.0000 | − | 8.66025i | −0.867110 | − | 0.375470i | ||||
\(533\) | −30.0000 | −1.29944 | ||||||||
\(534\) | −6.50000 | − | 11.2583i | −0.281283 | − | 0.487196i | ||||
\(535\) | 2.00000 | + | 3.46410i | 0.0864675 | + | 0.149766i | ||||
\(536\) | 6.00000 | − | 10.3923i | 0.259161 | − | 0.448879i | ||||
\(537\) | 3.50000 | + | 6.06218i | 0.151036 | + | 0.261602i | ||||
\(538\) | 16.0000 | − | 27.7128i | 0.689809 | − | 1.19478i | ||||
\(539\) | 18.0000 | 0.775315 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −4.00000 | + | 6.92820i | −0.171973 | + | 0.297867i | −0.939110 | − | 0.343617i | \(-0.888348\pi\) |
0.767136 | + | 0.641484i | \(0.221681\pi\) | |||||||
\(542\) | 1.00000 | − | 1.73205i | 0.0429537 | − | 0.0743980i | ||||
\(543\) | −18.0000 | −0.772454 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 8.00000 | − | 13.8564i | 0.342682 | − | 0.593543i | ||||
\(546\) | 15.0000 | + | 25.9808i | 0.641941 | + | 1.11187i | ||||
\(547\) | −7.00000 | + | 12.1244i | −0.299298 | + | 0.518400i | −0.975976 | − | 0.217880i | \(-0.930086\pi\) |
0.676677 | + | 0.736280i | \(0.263419\pi\) | |||||||
\(548\) | 6.00000 | + | 10.3923i | 0.256307 | + | 0.443937i | ||||
\(549\) | 2.00000 | + | 3.46410i | 0.0853579 | + | 0.147844i | ||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 24.0000 | + | 10.3923i | 1.02243 | + | 0.442727i | ||||
\(552\) | 7.00000 | 0.297940 | ||||||||
\(553\) | 25.0000 | + | 43.3013i | 1.06311 | + | 1.84136i | ||||
\(554\) | −7.00000 | − | 12.1244i | −0.297402 | − | 0.515115i | ||||
\(555\) | 3.50000 | − | 6.06218i | 0.148567 | − | 0.257325i | ||||
\(556\) | 8.00000 | + | 13.8564i | 0.339276 | + | 0.587643i | ||||
\(557\) | −0.500000 | + | 0.866025i | −0.0211857 | + | 0.0366947i | −0.876424 | − | 0.481540i | \(-0.840077\pi\) |
0.855238 | + | 0.518235i | \(0.173411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.0000 | 1.52264 | ||||||||
\(560\) | 2.50000 | − | 4.33013i | 0.105644 | − | 0.182981i | ||||
\(561\) | 2.00000 | − | 3.46410i | 0.0844401 | − | 0.146254i | ||||
\(562\) | 11.0000 | 0.464007 | ||||||||
\(563\) | 24.0000 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331220\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(564\) | −4.00000 | + | 6.92820i | −0.168430 | + | 0.291730i | ||||
\(565\) | −2.00000 | − | 3.46410i | −0.0841406 | − | 0.145736i | ||||
\(566\) | 11.0000 | − | 19.0526i | 0.462364 | − | 0.800839i | ||||
\(567\) | 2.50000 | + | 4.33013i | 0.104990 | + | 0.181848i | ||||
\(568\) | 1.00000 | + | 1.73205i | 0.0419591 | + | 0.0726752i | ||||
\(569\) | 33.0000 | 1.38343 | 0.691716 | − | 0.722170i | \(-0.256855\pi\) | ||||
0.691716 | + | 0.722170i | \(0.256855\pi\) | |||||||
\(570\) | −0.500000 | − | 4.33013i | −0.0209427 | − | 0.181369i | ||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | −3.00000 | − | 5.19615i | −0.125436 | − | 0.217262i | ||||
\(573\) | −7.00000 | − | 12.1244i | −0.292429 | − | 0.506502i | ||||
\(574\) | 12.5000 | − | 21.6506i | 0.521740 | − | 0.903680i | ||||
\(575\) | −3.50000 | − | 6.06218i | −0.145960 | − | 0.252810i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −32.0000 | −1.33218 | −0.666089 | − | 0.745873i | \(-0.732033\pi\) | ||||
−0.666089 | + | 0.745873i | \(0.732033\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −2.00000 | + | 3.46410i | −0.0831172 | + | 0.143963i | ||||
\(580\) | −3.00000 | + | 5.19615i | −0.124568 | + | 0.215758i | ||||
\(581\) | 50.0000 | 2.07435 | ||||||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | −5.50000 | + | 9.52628i | −0.227787 | + | 0.394538i | ||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | −3.00000 | + | 5.19615i | −0.124035 | + | 0.214834i | ||||
\(586\) | 2.50000 | + | 4.33013i | 0.103274 | + | 0.178876i | ||||
\(587\) | 10.0000 | + | 17.3205i | 0.412744 | + | 0.714894i | 0.995189 | − | 0.0979766i | \(-0.0312370\pi\) |
−0.582445 | + | 0.812870i | \(0.697904\pi\) | |||||||
\(588\) | −18.0000 | −0.742307 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 8.00000 | 0.329355 | ||||||||
\(591\) | 0.500000 | + | 0.866025i | 0.0205673 | + | 0.0356235i | ||||
\(592\) | −3.50000 | − | 6.06218i | −0.143849 | − | 0.249154i | ||||
\(593\) | −11.0000 | + | 19.0526i | −0.451716 | + | 0.782395i | −0.998493 | − | 0.0548835i | \(-0.982521\pi\) |
0.546777 | + | 0.837278i | \(0.315855\pi\) | |||||||
\(594\) | −0.500000 | − | 0.866025i | −0.0205152 | − | 0.0355335i | ||||
\(595\) | 10.0000 | − | 17.3205i | 0.409960 | − | 0.710072i | ||||
\(596\) | −4.00000 | −0.163846 | ||||||||
\(597\) | 4.00000 | 0.163709 | ||||||||
\(598\) | 21.0000 | − | 36.3731i | 0.858754 | − | 1.48741i | ||||
\(599\) | −4.00000 | + | 6.92820i | −0.163436 | + | 0.283079i | −0.936099 | − | 0.351738i | \(-0.885591\pi\) |
0.772663 | + | 0.634816i | \(0.218924\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −3.00000 | −0.122373 | −0.0611863 | − | 0.998126i | \(-0.519488\pi\) | ||||
−0.0611863 | + | 0.998126i | \(0.519488\pi\) | |||||||
\(602\) | −15.0000 | + | 25.9808i | −0.611354 | + | 1.05890i | ||||
\(603\) | −6.00000 | − | 10.3923i | −0.244339 | − | 0.423207i | ||||
\(604\) | 10.0000 | − | 17.3205i | 0.406894 | − | 0.704761i | ||||
\(605\) | 5.00000 | + | 8.66025i | 0.203279 | + | 0.352089i | ||||
\(606\) | −1.00000 | − | 1.73205i | −0.0406222 | − | 0.0703598i | ||||
\(607\) | −1.00000 | −0.0405887 | −0.0202944 | − | 0.999794i | \(-0.506460\pi\) | ||||
−0.0202944 | + | 0.999794i | \(0.506460\pi\) | |||||||
\(608\) | −4.00000 | − | 1.73205i | −0.162221 | − | 0.0702439i | ||||
\(609\) | 30.0000 | 1.21566 | ||||||||
\(610\) | −2.00000 | − | 3.46410i | −0.0809776 | − | 0.140257i | ||||
\(611\) | 24.0000 | + | 41.5692i | 0.970936 | + | 1.68171i | ||||
\(612\) | −2.00000 | + | 3.46410i | −0.0808452 | + | 0.140028i | ||||
\(613\) | −17.5000 | − | 30.3109i | −0.706818 | − | 1.22425i | −0.966031 | − | 0.258425i | \(-0.916796\pi\) |
0.259213 | − | 0.965820i | \(-0.416537\pi\) | |||||||
\(614\) | 9.00000 | − | 15.5885i | 0.363210 | − | 0.629099i | ||||
\(615\) | 5.00000 | 0.201619 | ||||||||
\(616\) | 5.00000 | 0.201456 | ||||||||
\(617\) | −24.0000 | + | 41.5692i | −0.966204 | + | 1.67351i | −0.259858 | + | 0.965647i | \(0.583676\pi\) |
−0.706346 | + | 0.707867i | \(0.749658\pi\) | |||||||
\(618\) | −7.50000 | + | 12.9904i | −0.301694 | + | 0.522550i | ||||
\(619\) | 43.0000 | 1.72832 | 0.864158 | − | 0.503221i | \(-0.167852\pi\) | ||||
0.864158 | + | 0.503221i | \(0.167852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.50000 | − | 6.06218i | 0.140450 | − | 0.243267i | ||||
\(622\) | −10.0000 | − | 17.3205i | −0.400963 | − | 0.694489i | ||||
\(623\) | 32.5000 | − | 56.2917i | 1.30209 | − | 2.25528i | ||||
\(624\) | 3.00000 | + | 5.19615i | 0.120096 | + | 0.208013i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.50000 | − | 2.59808i | 0.139777 | − | 0.103757i | ||||
\(628\) | 9.00000 | 0.359139 | ||||||||
\(629\) | −14.0000 | − | 24.2487i | −0.558217 | − | 0.966859i | ||||
\(630\) | −2.50000 | − | 4.33013i | −0.0996024 | − | 0.172516i | ||||
\(631\) | −19.0000 | + | 32.9090i | −0.756378 | + | 1.31009i | 0.188308 | + | 0.982110i | \(0.439700\pi\) |
−0.944686 | + | 0.327975i | \(0.893634\pi\) | |||||||
\(632\) | 5.00000 | + | 8.66025i | 0.198889 | + | 0.344486i | ||||
\(633\) | 6.50000 | − | 11.2583i | 0.258352 | − | 0.447478i | ||||
\(634\) | −3.00000 | −0.119145 | ||||||||
\(635\) | −5.00000 | −0.198419 | ||||||||
\(636\) | 5.50000 | − | 9.52628i | 0.218089 | − | 0.377742i | ||||
\(637\) | −54.0000 | + | 93.5307i | −2.13956 | + | 3.70582i | ||||
\(638\) | −6.00000 | −0.237542 | ||||||||
\(639\) | 2.00000 | 0.0791188 | ||||||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | 13.0000 | + | 22.5167i | 0.513469 | + | 0.889355i | 0.999878 | + | 0.0156233i | \(0.00497325\pi\) |
−0.486409 | + | 0.873731i | \(0.661693\pi\) | |||||||
\(642\) | 2.00000 | − | 3.46410i | 0.0789337 | − | 0.136717i | ||||
\(643\) | 22.0000 | + | 38.1051i | 0.867595 | + | 1.50272i | 0.864447 | + | 0.502724i | \(0.167669\pi\) |
0.00314839 | + | 0.999995i | \(0.498998\pi\) | |||||||
\(644\) | 17.5000 | + | 30.3109i | 0.689597 | + | 1.19442i | ||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | −16.0000 | − | 6.92820i | −0.629512 | − | 0.272587i | ||||
\(647\) | 3.00000 | 0.117942 | 0.0589711 | − | 0.998260i | \(-0.481218\pi\) | ||||
0.0589711 | + | 0.998260i | \(0.481218\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 4.00000 | + | 6.92820i | 0.157014 | + | 0.271956i | ||||
\(650\) | 3.00000 | − | 5.19615i | 0.117670 | − | 0.203810i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.00000 | − | 8.66025i | 0.195815 | − | 0.339162i | ||||
\(653\) | 9.00000 | 0.352197 | 0.176099 | − | 0.984373i | \(-0.443652\pi\) | ||||
0.176099 | + | 0.984373i | \(0.443652\pi\) | |||||||
\(654\) | −16.0000 | −0.625650 | ||||||||
\(655\) | 1.50000 | − | 2.59808i | 0.0586098 | − | 0.101515i | ||||
\(656\) | 2.50000 | − | 4.33013i | 0.0976086 | − | 0.169063i | ||||
\(657\) | −2.00000 | −0.0780274 | ||||||||
\(658\) | −40.0000 | −1.55936 | ||||||||
\(659\) | 5.50000 | − | 9.52628i | 0.214250 | − | 0.371091i | −0.738791 | − | 0.673935i | \(-0.764603\pi\) |
0.953040 | + | 0.302844i | \(0.0979361\pi\) | |||||||
\(660\) | 0.500000 | + | 0.866025i | 0.0194625 | + | 0.0337100i | ||||
\(661\) | 10.0000 | − | 17.3205i | 0.388955 | − | 0.673690i | −0.603354 | − | 0.797473i | \(-0.706170\pi\) |
0.992309 | + | 0.123784i | \(0.0395028\pi\) | |||||||
\(662\) | 7.50000 | + | 12.9904i | 0.291496 | + | 0.504885i | ||||
\(663\) | 12.0000 | + | 20.7846i | 0.466041 | + | 0.807207i | ||||
\(664\) | 10.0000 | 0.388075 | ||||||||
\(665\) | 17.5000 | − | 12.9904i | 0.678621 | − | 0.503745i | ||||
\(666\) | −7.00000 | −0.271244 | ||||||||
\(667\) | −21.0000 | − | 36.3731i | −0.813123 | − | 1.40837i | ||||
\(668\) | −10.5000 | − | 18.1865i | −0.406257 | − | 0.703658i | ||||
\(669\) | −10.5000 | + | 18.1865i | −0.405953 | + | 0.703132i | ||||
\(670\) | 6.00000 | + | 10.3923i | 0.231800 | + | 0.401490i | ||||
\(671\) | 2.00000 | − | 3.46410i | 0.0772091 | − | 0.133730i | ||||
\(672\) | −5.00000 | −0.192879 | ||||||||
\(673\) | −40.0000 | −1.54189 | −0.770943 | − | 0.636904i | \(-0.780215\pi\) | ||||
−0.770943 | + | 0.636904i | \(0.780215\pi\) | |||||||
\(674\) | 1.00000 | − | 1.73205i | 0.0385186 | − | 0.0667161i | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | 21.0000 | 0.807096 | 0.403548 | − | 0.914959i | \(-0.367777\pi\) | ||||
0.403548 | + | 0.914959i | \(0.367777\pi\) | |||||||
\(678\) | −2.00000 | + | 3.46410i | −0.0768095 | + | 0.133038i | ||||
\(679\) | 5.00000 | + | 8.66025i | 0.191882 | + | 0.332350i | ||||
\(680\) | 2.00000 | − | 3.46410i | 0.0766965 | − | 0.132842i | ||||
\(681\) | 1.00000 | + | 1.73205i | 0.0383201 | + | 0.0663723i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | −3.50000 | + | 2.59808i | −0.133826 | + | 0.0993399i | ||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | −27.5000 | − | 47.6314i | −1.04995 | − | 1.81858i | ||||
\(687\) | 5.00000 | + | 8.66025i | 0.190762 | + | 0.330409i | ||||
\(688\) | −3.00000 | + | 5.19615i | −0.114374 | + | 0.198101i | ||||
\(689\) | −33.0000 | − | 57.1577i | −1.25720 | − | 2.17753i | ||||
\(690\) | −3.50000 | + | 6.06218i | −0.133243 | + | 0.230783i | ||||
\(691\) | 1.00000 | 0.0380418 | 0.0190209 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190209 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(692\) | −9.00000 | −0.342129 | ||||||||
\(693\) | 2.50000 | − | 4.33013i | 0.0949671 | − | 0.164488i | ||||
\(694\) | −1.00000 | + | 1.73205i | −0.0379595 | + | 0.0657477i | ||||
\(695\) | −16.0000 | −0.606915 | ||||||||
\(696\) | 6.00000 | 0.227429 | ||||||||
\(697\) | 10.0000 | − | 17.3205i | 0.378777 | − | 0.656061i | ||||
\(698\) | 8.00000 | + | 13.8564i | 0.302804 | + | 0.524473i | ||||
\(699\) | −9.00000 | + | 15.5885i | −0.340411 | + | 0.589610i | ||||
\(700\) | 2.50000 | + | 4.33013i | 0.0944911 | + | 0.163663i | ||||
\(701\) | −17.0000 | − | 29.4449i | −0.642081 | − | 1.11212i | −0.984967 | − | 0.172740i | \(-0.944738\pi\) |
0.342886 | − | 0.939377i | \(-0.388595\pi\) | |||||||
\(702\) | 6.00000 | 0.226455 | ||||||||
\(703\) | −3.50000 | − | 30.3109i | −0.132005 | − | 1.14320i | ||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −4.00000 | − | 6.92820i | −0.150649 | − | 0.260931i | ||||
\(706\) | 18.0000 | + | 31.1769i | 0.677439 | + | 1.17336i | ||||
\(707\) | 5.00000 | − | 8.66025i | 0.188044 | − | 0.325702i | ||||
\(708\) | −4.00000 | − | 6.92820i | −0.150329 | − | 0.260378i | ||||
\(709\) | 2.00000 | − | 3.46410i | 0.0751116 | − | 0.130097i | −0.826023 | − | 0.563636i | \(-0.809402\pi\) |
0.901135 | + | 0.433539i | \(0.142735\pi\) | |||||||
\(710\) | −2.00000 | −0.0750587 | ||||||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | 6.50000 | − | 11.2583i | 0.243598 | − | 0.421924i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −20.0000 | −0.748481 | ||||||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | −3.50000 | + | 6.06218i | −0.130801 | + | 0.226554i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.00000 | + | 15.5885i | −0.335877 | + | 0.581756i | ||||
\(719\) | 22.0000 | + | 38.1051i | 0.820462 | + | 1.42108i | 0.905339 | + | 0.424690i | \(0.139617\pi\) |
−0.0848774 | + | 0.996391i | \(0.527050\pi\) | |||||||
\(720\) | −0.500000 | − | 0.866025i | −0.0186339 | − | 0.0322749i | ||||
\(721\) | −75.0000 | −2.79315 | ||||||||
\(722\) | −13.0000 | − | 13.8564i | −0.483810 | − | 0.515682i | ||||
\(723\) | 26.0000 | 0.966950 | ||||||||
\(724\) | −9.00000 | − | 15.5885i | −0.334482 | − | 0.579340i | ||||
\(725\) | −3.00000 | − | 5.19615i | −0.111417 | − | 0.192980i | ||||
\(726\) | 5.00000 | − | 8.66025i | 0.185567 | − | 0.321412i | ||||
\(727\) | −16.0000 | − | 27.7128i | −0.593407 | − | 1.02781i | −0.993770 | − | 0.111454i | \(-0.964449\pi\) |
0.400362 | − | 0.916357i | \(-0.368884\pi\) | |||||||
\(728\) | −15.0000 | + | 25.9808i | −0.555937 | + | 0.962911i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.00000 | 0.0740233 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | −2.00000 | + | 3.46410i | −0.0739221 | + | 0.128037i | ||||
\(733\) | 19.0000 | 0.701781 | 0.350891 | − | 0.936416i | \(-0.385879\pi\) | ||||
0.350891 | + | 0.936416i | \(0.385879\pi\) | |||||||
\(734\) | 4.00000 | 0.147643 | ||||||||
\(735\) | 9.00000 | − | 15.5885i | 0.331970 | − | 0.574989i | ||||
\(736\) | 3.50000 | + | 6.06218i | 0.129012 | + | 0.223455i | ||||
\(737\) | −6.00000 | + | 10.3923i | −0.221013 | + | 0.382805i | ||||
\(738\) | −2.50000 | − | 4.33013i | −0.0920263 | − | 0.159394i | ||||
\(739\) | 23.5000 | + | 40.7032i | 0.864461 | + | 1.49729i | 0.867581 | + | 0.497296i | \(0.165674\pi\) |
−0.00311943 | + | 0.999995i | \(0.500993\pi\) | |||||||
\(740\) | 7.00000 | 0.257325 | ||||||||
\(741\) | 3.00000 | + | 25.9808i | 0.110208 | + | 0.954427i | ||||
\(742\) | 55.0000 | 2.01911 | ||||||||
\(743\) | −7.50000 | − | 12.9904i | −0.275148 | − | 0.476571i | 0.695024 | − | 0.718986i | \(-0.255394\pi\) |
−0.970173 | + | 0.242415i | \(0.922060\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | − | 3.46410i | 0.0732743 | − | 0.126915i | ||||
\(746\) | 2.50000 | + | 4.33013i | 0.0915315 | + | 0.158537i | ||||
\(747\) | 5.00000 | − | 8.66025i | 0.182940 | − | 0.316862i | ||||
\(748\) | 4.00000 | 0.146254 | ||||||||
\(749\) | 20.0000 | 0.730784 | ||||||||
\(750\) | −0.500000 | + | 0.866025i | −0.0182574 | + | 0.0316228i | ||||
\(751\) | −20.0000 | + | 34.6410i | −0.729810 | + | 1.26407i | 0.227153 | + | 0.973859i | \(0.427058\pi\) |
−0.956963 | + | 0.290209i | \(0.906275\pi\) | |||||||
\(752\) | −8.00000 | −0.291730 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 18.0000 | − | 31.1769i | 0.655521 | − | 1.13540i | ||||
\(755\) | 10.0000 | + | 17.3205i | 0.363937 | + | 0.630358i | ||||
\(756\) | −2.50000 | + | 4.33013i | −0.0909241 | + | 0.157485i | ||||
\(757\) | 6.50000 | + | 11.2583i | 0.236247 | + | 0.409191i | 0.959634 | − | 0.281251i | \(-0.0907494\pi\) |
−0.723388 | + | 0.690442i | \(0.757416\pi\) | |||||||
\(758\) | −2.00000 | − | 3.46410i | −0.0726433 | − | 0.125822i | ||||
\(759\) | −7.00000 | −0.254084 | ||||||||
\(760\) | 3.50000 | − | 2.59808i | 0.126958 | − | 0.0942421i | ||||
\(761\) | −31.0000 | −1.12375 | −0.561875 | − | 0.827222i | \(-0.689920\pi\) | ||||
−0.561875 | + | 0.827222i | \(0.689920\pi\) | |||||||
\(762\) | 2.50000 | + | 4.33013i | 0.0905654 | + | 0.156864i | ||||
\(763\) | −40.0000 | − | 69.2820i | −1.44810 | − | 2.50818i | ||||
\(764\) | 7.00000 | − | 12.1244i | 0.253251 | − | 0.438644i | ||||
\(765\) | −2.00000 | − | 3.46410i | −0.0723102 | − | 0.125245i | ||||
\(766\) | 16.0000 | − | 27.7128i | 0.578103 | − | 1.00130i | ||||
\(767\) | −48.0000 | −1.73318 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −3.00000 | + | 5.19615i | −0.108183 | + | 0.187378i | −0.915034 | − | 0.403376i | \(-0.867837\pi\) |
0.806851 | + | 0.590755i | \(0.201170\pi\) | |||||||
\(770\) | −2.50000 | + | 4.33013i | −0.0900937 | + | 0.156047i | ||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | −4.00000 | −0.143963 | ||||||||
\(773\) | 10.5000 | − | 18.1865i | 0.377659 | − | 0.654124i | −0.613062 | − | 0.790034i | \(-0.710063\pi\) |
0.990721 | + | 0.135910i | \(0.0433959\pi\) | |||||||
\(774\) | 3.00000 | + | 5.19615i | 0.107833 | + | 0.186772i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.00000 | + | 1.73205i | 0.0358979 | + | 0.0621770i | ||||
\(777\) | −17.5000 | − | 30.3109i | −0.627809 | − | 1.08740i | ||||
\(778\) | 10.0000 | 0.358517 | ||||||||
\(779\) | 17.5000 | − | 12.9904i | 0.627003 | − | 0.465429i | ||||
\(780\) | −6.00000 | −0.214834 | ||||||||
\(781\) | −1.00000 | − | 1.73205i | −0.0357828 | − | 0.0619777i | ||||
\(782\) | 14.0000 | + | 24.2487i | 0.500639 | + | 0.867132i | ||||
\(783\) | 3.00000 | − | 5.19615i | 0.107211 | − | 0.185695i | ||||
\(784\) | −9.00000 | − | 15.5885i | −0.321429 | − | 0.556731i | ||||
\(785\) | −4.50000 | + | 7.79423i | −0.160612 | + | 0.278188i | ||||
\(786\) | −3.00000 | −0.107006 | ||||||||
\(787\) | −26.0000 | −0.926800 | −0.463400 | − | 0.886149i | \(-0.653371\pi\) | ||||
−0.463400 | + | 0.886149i | \(0.653371\pi\) | |||||||
\(788\) | −0.500000 | + | 0.866025i | −0.0178118 | + | 0.0308509i | ||||
\(789\) | 10.5000 | − | 18.1865i | 0.373810 | − | 0.647458i | ||||
\(790\) | −10.0000 | −0.355784 | ||||||||
\(791\) | −20.0000 | −0.711118 | ||||||||
\(792\) | 0.500000 | − | 0.866025i | 0.0177667 | − | 0.0307729i | ||||
\(793\) | 12.0000 | + | 20.7846i | 0.426132 | + | 0.738083i | ||||
\(794\) | −16.5000 | + | 28.5788i | −0.585563 | + | 1.01423i | ||||
\(795\) | 5.50000 | + | 9.52628i | 0.195065 | + | 0.337862i | ||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | 47.0000 | 1.66483 | 0.832413 | − | 0.554156i | \(-0.186959\pi\) | ||||
0.832413 | + | 0.554156i | \(0.186959\pi\) | |||||||
\(798\) | −20.0000 | − | 8.66025i | −0.707992 | − | 0.306570i | ||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −6.50000 | − | 11.2583i | −0.229666 | − | 0.397794i | ||||
\(802\) | −9.00000 | + | 15.5885i | −0.317801 | + | 0.550448i | ||||
\(803\) | 1.00000 | + | 1.73205i | 0.0352892 | + | 0.0611227i | ||||
\(804\) | 6.00000 | − | 10.3923i | 0.211604 | − | 0.366508i | ||||
\(805\) | −35.0000 | −1.23359 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.0000 | − | 27.7128i | 0.563227 | − | 0.975537i | ||||
\(808\) | 1.00000 | − | 1.73205i | 0.0351799 | − | 0.0609333i | ||||
\(809\) | −18.0000 | −0.632846 | −0.316423 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316423 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −21.5000 | + | 37.2391i | −0.754967 | + | 1.30764i | 0.190424 | + | 0.981702i | \(0.439014\pi\) |
−0.945391 | + | 0.325939i | \(0.894319\pi\) | |||||||
\(812\) | 15.0000 | + | 25.9808i | 0.526397 | + | 0.911746i | ||||
\(813\) | 1.00000 | − | 1.73205i | 0.0350715 | − | 0.0607457i | ||||
\(814\) | 3.50000 | + | 6.06218i | 0.122675 | + | 0.212479i | ||||
\(815\) | 5.00000 | + | 8.66025i | 0.175142 | + | 0.303355i | ||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | −21.0000 | + | 15.5885i | −0.734697 | + | 0.545371i | ||||
\(818\) | 3.00000 | 0.104893 | ||||||||
\(819\) | 15.0000 | + | 25.9808i | 0.524142 | + | 0.907841i | ||||
\(820\) | 2.50000 | + | 4.33013i | 0.0873038 | + | 0.151215i | ||||
\(821\) | −21.0000 | + | 36.3731i | −0.732905 | + | 1.26943i | 0.222731 | + | 0.974880i | \(0.428503\pi\) |
−0.955636 | + | 0.294549i | \(0.904831\pi\) | |||||||
\(822\) | 6.00000 | + | 10.3923i | 0.209274 | + | 0.362473i | ||||
\(823\) | 11.5000 | − | 19.9186i | 0.400865 | − | 0.694318i | −0.592966 | − | 0.805228i | \(-0.702043\pi\) |
0.993831 | + | 0.110910i | \(0.0353764\pi\) | |||||||
\(824\) | −15.0000 | −0.522550 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 20.0000 | − | 34.6410i | 0.695889 | − | 1.20532i | ||||
\(827\) | 15.0000 | − | 25.9808i | 0.521601 | − | 0.903440i | −0.478083 | − | 0.878315i | \(-0.658668\pi\) |
0.999684 | − | 0.0251251i | \(-0.00799840\pi\) | |||||||
\(828\) | 7.00000 | 0.243267 | ||||||||
\(829\) | −28.0000 | −0.972480 | −0.486240 | − | 0.873825i | \(-0.661632\pi\) | ||||
−0.486240 | + | 0.873825i | \(0.661632\pi\) | |||||||
\(830\) | −5.00000 | + | 8.66025i | −0.173553 | + | 0.300602i | ||||
\(831\) | −7.00000 | − | 12.1244i | −0.242827 | − | 0.420589i | ||||
\(832\) | −3.00000 | + | 5.19615i | −0.104006 | + | 0.180144i | ||||
\(833\) | −36.0000 | − | 62.3538i | −1.24733 | − | 2.16043i | ||||
\(834\) | 8.00000 | + | 13.8564i | 0.277017 | + | 0.479808i | ||||
\(835\) | 21.0000 | 0.726735 | ||||||||
\(836\) | 4.00000 | + | 1.73205i | 0.138343 | + | 0.0599042i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.50000 | − | 2.59808i | −0.0518166 | − | 0.0897491i | ||||
\(839\) | 9.00000 | + | 15.5885i | 0.310715 | + | 0.538173i | 0.978517 | − | 0.206165i | \(-0.0660984\pi\) |
−0.667803 | + | 0.744338i | \(0.732765\pi\) | |||||||
\(840\) | 2.50000 | − | 4.33013i | 0.0862582 | − | 0.149404i | ||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −4.00000 | + | 6.92820i | −0.137849 | + | 0.238762i | ||||
\(843\) | 11.0000 | 0.378860 | ||||||||
\(844\) | 13.0000 | 0.447478 | ||||||||
\(845\) | −11.5000 | + | 19.9186i | −0.395612 | + | 0.685220i | ||||
\(846\) | −4.00000 | + | 6.92820i | −0.137523 | + | 0.238197i | ||||
\(847\) | 50.0000 | 1.71802 | ||||||||
\(848\) | 11.0000 | 0.377742 | ||||||||
\(849\) | 11.0000 | − | 19.0526i | 0.377519 | − | 0.653882i | ||||
\(850\) | 2.00000 | + | 3.46410i | 0.0685994 | + | 0.118818i | ||||
\(851\) | −24.5000 | + | 42.4352i | −0.839849 | + | 1.45466i | ||||
\(852\) | 1.00000 | + | 1.73205i | 0.0342594 | + | 0.0593391i | ||||
\(853\) | −9.00000 | − | 15.5885i | −0.308154 | − | 0.533739i | 0.669804 | − | 0.742538i | \(-0.266378\pi\) |
−0.977959 | + | 0.208799i | \(0.933045\pi\) | |||||||
\(854\) | −20.0000 | −0.684386 | ||||||||
\(855\) | −0.500000 | − | 4.33013i | −0.0170996 | − | 0.148087i | ||||
\(856\) | 4.00000 | 0.136717 | ||||||||
\(857\) | 18.0000 | + | 31.1769i | 0.614868 | + | 1.06498i | 0.990408 | + | 0.138177i | \(0.0441242\pi\) |
−0.375539 | + | 0.926806i | \(0.622542\pi\) | |||||||
\(858\) | −3.00000 | − | 5.19615i | −0.102418 | − | 0.177394i | ||||
\(859\) | 8.50000 | − | 14.7224i | 0.290016 | − | 0.502323i | −0.683797 | − | 0.729672i | \(-0.739673\pi\) |
0.973813 | + | 0.227349i | \(0.0730059\pi\) | |||||||
\(860\) | −3.00000 | − | 5.19615i | −0.102299 | − | 0.177187i | ||||
\(861\) | 12.5000 | − | 21.6506i | 0.425999 | − | 0.737852i | ||||
\(862\) | 4.00000 | 0.136241 | ||||||||
\(863\) | −1.00000 | −0.0340404 | −0.0170202 | − | 0.999855i | \(-0.505418\pi\) | ||||
−0.0170202 | + | 0.999855i | \(0.505418\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 4.50000 | − | 7.79423i | 0.153005 | − | 0.265012i | ||||
\(866\) | −6.00000 | −0.203888 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.00000 | − | 8.66025i | −0.169613 | − | 0.293779i | ||||
\(870\) | −3.00000 | + | 5.19615i | −0.101710 | + | 0.176166i | ||||
\(871\) | −36.0000 | − | 62.3538i | −1.21981 | − | 2.11278i | ||||
\(872\) | −8.00000 | − | 13.8564i | −0.270914 | − | 0.469237i | ||||
\(873\) | 2.00000 | 0.0676897 | ||||||||
\(874\) | 3.50000 | + | 30.3109i | 0.118389 | + | 1.02528i | ||||
\(875\) | −5.00000 | −0.169031 | ||||||||
\(876\) | −1.00000 | − | 1.73205i | −0.0337869 | − | 0.0585206i | ||||
\(877\) | 3.50000 | + | 6.06218i | 0.118187 | + | 0.204705i | 0.919049 | − | 0.394143i | \(-0.128959\pi\) |
−0.800862 | + | 0.598848i | \(0.795625\pi\) | |||||||
\(878\) | −16.0000 | + | 27.7128i | −0.539974 | + | 0.935262i | ||||
\(879\) | 2.50000 | + | 4.33013i | 0.0843229 | + | 0.146052i | ||||
\(880\) | −0.500000 | + | 0.866025i | −0.0168550 | + | 0.0291937i | ||||
\(881\) | 33.0000 | 1.11180 | 0.555899 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555899 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(882\) | −18.0000 | −0.606092 | ||||||||
\(883\) | 18.0000 | − | 31.1769i | 0.605748 | − | 1.04919i | −0.386185 | − | 0.922422i | \(-0.626207\pi\) |
0.991933 | − | 0.126765i | \(-0.0404595\pi\) | |||||||
\(884\) | −12.0000 | + | 20.7846i | −0.403604 | + | 0.699062i | ||||
\(885\) | 8.00000 | 0.268917 | ||||||||
\(886\) | −24.0000 | −0.806296 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | −3.50000 | − | 6.06218i | −0.117452 | − | 0.203433i | ||||
\(889\) | −12.5000 | + | 21.6506i | −0.419237 | + | 0.726139i | ||||
\(890\) | 6.50000 | + | 11.2583i | 0.217880 | + | 0.377380i | ||||
\(891\) | −0.500000 | − | 0.866025i | −0.0167506 | − | 0.0290129i | ||||
\(892\) | −21.0000 | −0.703132 | ||||||||
\(893\) | −32.0000 | − | 13.8564i | −1.07084 | − | 0.463687i | ||||
\(894\) | −4.00000 | −0.133780 | ||||||||
\(895\) | −3.50000 | − | 6.06218i | −0.116992 | − | 0.202636i | ||||
\(896\) | −2.50000 | − | 4.33013i | −0.0835191 | − | 0.144659i | ||||
\(897\) | 21.0000 | − | 36.3731i | 0.701170 | − | 1.21446i | ||||
\(898\) | −19.5000 | − | 33.7750i | −0.650723 | − | 1.12709i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 44.0000 | 1.46585 | ||||||||
\(902\) | −2.50000 | + | 4.33013i | −0.0832409 | + | 0.144177i | ||||
\(903\) | −15.0000 | + | 25.9808i | −0.499169 | + | 0.864586i | ||||
\(904\) | −4.00000 | −0.133038 | ||||||||
\(905\) | 18.0000 | 0.598340 | ||||||||
\(906\) | 10.0000 | − | 17.3205i | 0.332228 | − | 0.575435i | ||||
\(907\) | −11.0000 | − | 19.0526i | −0.365249 | − | 0.632630i | 0.623567 | − | 0.781770i | \(-0.285683\pi\) |
−0.988816 | + | 0.149140i | \(0.952349\pi\) | |||||||
\(908\) | −1.00000 | + | 1.73205i | −0.0331862 | + | 0.0574801i | ||||
\(909\) | −1.00000 | − | 1.73205i | −0.0331679 | − | 0.0574485i | ||||
\(910\) | −15.0000 | − | 25.9808i | −0.497245 | − | 0.861254i | ||||
\(911\) | −18.0000 | −0.596367 | −0.298183 | − | 0.954509i | \(-0.596381\pi\) | ||||
−0.298183 | + | 0.954509i | \(0.596381\pi\) | |||||||
\(912\) | −4.00000 | − | 1.73205i | −0.132453 | − | 0.0573539i | ||||
\(913\) | −10.0000 | −0.330952 | ||||||||
\(914\) | 4.00000 | + | 6.92820i | 0.132308 | + | 0.229165i | ||||
\(915\) | −2.00000 | − | 3.46410i | −0.0661180 | − | 0.114520i | ||||
\(916\) | −5.00000 | + | 8.66025i | −0.165205 | + | 0.286143i | ||||
\(917\) | −7.50000 | − | 12.9904i | −0.247672 | − | 0.428980i | ||||
\(918\) | −2.00000 | + | 3.46410i | −0.0660098 | + | 0.114332i | ||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | −7.00000 | −0.230783 | ||||||||
\(921\) | 9.00000 | − | 15.5885i | 0.296560 | − | 0.513657i | ||||
\(922\) | −3.00000 | + | 5.19615i | −0.0987997 | + | 0.171126i | ||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 5.00000 | 0.164488 | ||||||||
\(925\) | −3.50000 | + | 6.06218i | −0.115079 | + | 0.199323i | ||||
\(926\) | −4.50000 | − | 7.79423i | −0.147879 | − | 0.256134i | ||||
\(927\) | −7.50000 | + | 12.9904i | −0.246332 | + | 0.426660i | ||||
\(928\) | 3.00000 | + | 5.19615i | 0.0984798 | + | 0.170572i | ||||
\(929\) | 7.50000 | + | 12.9904i | 0.246067 | + | 0.426201i | 0.962431 | − | 0.271526i | \(-0.0875283\pi\) |
−0.716364 | + | 0.697727i | \(0.754195\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.00000 | − | 77.9423i | −0.294963 | − | 2.55446i | ||||
\(932\) | −18.0000 | −0.589610 | ||||||||
\(933\) | −10.0000 | − | 17.3205i | −0.327385 | − | 0.567048i | ||||
\(934\) | 19.0000 | + | 32.9090i | 0.621699 | + | 1.07681i | ||||
\(935\) | −2.00000 | + | 3.46410i | −0.0654070 | + | 0.113288i | ||||
\(936\) | 3.00000 | + | 5.19615i | 0.0980581 | + | 0.169842i | ||||
\(937\) | 11.0000 | − | 19.0526i | 0.359354 | − | 0.622420i | −0.628499 | − | 0.777811i | \(-0.716330\pi\) |
0.987853 | + | 0.155391i | \(0.0496636\pi\) | |||||||
\(938\) | 60.0000 | 1.95907 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.00000 | − | 6.92820i | 0.130466 | − | 0.225973i | ||||
\(941\) | −23.0000 | + | 39.8372i | −0.749779 | + | 1.29865i | 0.198150 | + | 0.980172i | \(0.436507\pi\) |
−0.947929 | + | 0.318483i | \(0.896827\pi\) | |||||||
\(942\) | 9.00000 | 0.293236 | ||||||||
\(943\) | −35.0000 | −1.13976 | ||||||||
\(944\) | 4.00000 | − | 6.92820i | 0.130189 | − | 0.225494i | ||||
\(945\) | −2.50000 | − | 4.33013i | −0.0813250 | − | 0.140859i | ||||
\(946\) | 3.00000 | − | 5.19615i | 0.0975384 | − | 0.168941i | ||||
\(947\) | 16.0000 | + | 27.7128i | 0.519930 | + | 0.900545i | 0.999732 | + | 0.0231683i | \(0.00737536\pi\) |
−0.479801 | + | 0.877377i | \(0.659291\pi\) | |||||||
\(948\) | 5.00000 | + | 8.66025i | 0.162392 | + | 0.281272i | ||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | 0.500000 | + | 4.33013i | 0.0162221 | + | 0.140488i | ||||
\(951\) | −3.00000 | −0.0972817 | ||||||||
\(952\) | −10.0000 | − | 17.3205i | −0.324102 | − | 0.561361i | ||||
\(953\) | 18.0000 | + | 31.1769i | 0.583077 | + | 1.00992i | 0.995112 | + | 0.0987513i | \(0.0314848\pi\) |
−0.412035 | + | 0.911168i | \(0.635182\pi\) | |||||||
\(954\) | 5.50000 | − | 9.52628i | 0.178069 | − | 0.308425i | ||||
\(955\) | 7.00000 | + | 12.1244i | 0.226515 | + | 0.392335i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.00000 | −0.193952 | ||||||||
\(958\) | −42.0000 | −1.35696 | ||||||||
\(959\) | −30.0000 | + | 51.9615i | −0.968751 | + | 1.67793i | ||||
\(960\) | 0.500000 | − | 0.866025i | 0.0161374 | − | 0.0279508i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −42.0000 | −1.35413 | ||||||||
\(963\) | 2.00000 | − | 3.46410i | 0.0644491 | − | 0.111629i | ||||
\(964\) | 13.0000 | + | 22.5167i | 0.418702 | + | 0.725213i | ||||
\(965\) | 2.00000 | − | 3.46410i | 0.0643823 | − | 0.111513i | ||||
\(966\) | 17.5000 | + | 30.3109i | 0.563053 | + | 0.975237i | ||||
\(967\) | −12.0000 | − | 20.7846i | −0.385894 | − | 0.668388i | 0.605999 | − | 0.795466i | \(-0.292774\pi\) |
−0.991893 | + | 0.127078i | \(0.959440\pi\) | |||||||
\(968\) | 10.0000 | 0.321412 | ||||||||
\(969\) | −16.0000 | − | 6.92820i | −0.513994 | − | 0.222566i | ||||
\(970\) | −2.00000 | −0.0642161 | ||||||||
\(971\) | −6.00000 | − | 10.3923i | −0.192549 | − | 0.333505i | 0.753545 | − | 0.657396i | \(-0.228342\pi\) |
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −40.0000 | + | 69.2820i | −1.28234 | + | 2.22108i | ||||
\(974\) | −6.50000 | − | 11.2583i | −0.208273 | − | 0.360740i | ||||
\(975\) | 3.00000 | − | 5.19615i | 0.0960769 | − | 0.166410i | ||||
\(976\) | −4.00000 | −0.128037 | ||||||||
\(977\) | −6.00000 | −0.191957 | −0.0959785 | − | 0.995383i | \(-0.530598\pi\) | ||||
−0.0959785 | + | 0.995383i | \(0.530598\pi\) | |||||||
\(978\) | 5.00000 | − | 8.66025i | 0.159882 | − | 0.276924i | ||||
\(979\) | −6.50000 | + | 11.2583i | −0.207741 | + | 0.359818i | ||||
\(980\) | 18.0000 | 0.574989 | ||||||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | −16.5000 | + | 28.5788i | −0.526536 | + | 0.911987i | ||||
\(983\) | −1.50000 | − | 2.59808i | −0.0478426 | − | 0.0828658i | 0.841112 | − | 0.540860i | \(-0.181901\pi\) |
−0.888955 | + | 0.457995i | \(0.848568\pi\) | |||||||
\(984\) | 2.50000 | − | 4.33013i | 0.0796971 | − | 0.138039i | ||||
\(985\) | −0.500000 | − | 0.866025i | −0.0159313 | − | 0.0275939i | ||||
\(986\) | 12.0000 | + | 20.7846i | 0.382158 | + | 0.661917i | ||||
\(987\) | −40.0000 | −1.27321 | ||||||||
\(988\) | −21.0000 | + | 15.5885i | −0.668099 | + | 0.495935i | ||||
\(989\) | 42.0000 | 1.33552 | ||||||||
\(990\) | 0.500000 | + | 0.866025i | 0.0158910 | + | 0.0275241i | ||||
\(991\) | −5.00000 | − | 8.66025i | −0.158830 | − | 0.275102i | 0.775617 | − | 0.631204i | \(-0.217439\pi\) |
−0.934447 | + | 0.356102i | \(0.884106\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.50000 | + | 12.9904i | 0.238005 | + | 0.412237i | ||||
\(994\) | −5.00000 | + | 8.66025i | −0.158590 | + | 0.274687i | ||||
\(995\) | −4.00000 | −0.126809 | ||||||||
\(996\) | 10.0000 | 0.316862 | ||||||||
\(997\) | 15.5000 | − | 26.8468i | 0.490890 | − | 0.850246i | −0.509055 | − | 0.860734i | \(-0.670005\pi\) |
0.999945 | + | 0.0104877i | \(0.00333839\pi\) | |||||||
\(998\) | −3.50000 | + | 6.06218i | −0.110791 | + | 0.191895i | ||||
\(999\) | −7.00000 | −0.221470 |
(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 | 570.2.i.e.121.1 | ✓ | 2 | |
3.2 | odd | 2 | 1710.2.l.c.1261.1 | 2 | |||
19.11 | even | 3 | inner | 570.2.i.e.391.1 | yes | 2 | |
57.11 | odd | 6 | 1710.2.l.c.1531.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.e.121.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
570.2.i.e.391.1 | yes | 2 | 19.11 | even | 3 | inner | |
1710.2.l.c.1261.1 | 2 | 3.2 | odd | 2 | |||
1710.2.l.c.1531.1 | 2 | 57.11 | odd | 6 |