Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(21,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.21");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.l (of order \(4\), 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: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 21.20 | ||
Character | \(\chi\) | \(=\) | 80.21 |
Dual form | 80.6.l.a.61.20 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0219870 | + | 5.65681i | −0.00388679 | + | 0.999992i | ||||
\(3\) | 9.88924 | − | 9.88924i | 0.634395 | − | 0.634395i | −0.314772 | − | 0.949167i | \(-0.601928\pi\) |
0.949167 | + | 0.314772i | \(0.101928\pi\) | |||||||
\(4\) | −31.9990 | − | 0.248752i | −0.999970 | − | 0.00777351i | ||||
\(5\) | −17.6777 | − | 17.6777i | −0.316228 | − | 0.316228i | ||||
\(6\) | 55.7241 | + | 56.1590i | 0.631925 | + | 0.636856i | ||||
\(7\) | 122.335i | 0.943641i | 0.881695 | + | 0.471820i | \(0.156403\pi\) | ||||
−0.881695 | + | 0.471820i | \(0.843597\pi\) | |||||||
\(8\) | 2.11071 | − | 181.007i | 0.0116601 | − | 0.999932i | ||||
\(9\) | 47.4058i | 0.195086i | ||||||||
\(10\) | 100.388 | − | 99.6106i | 0.317454 | − | 0.314996i | ||||
\(11\) | −301.232 | − | 301.232i | −0.750618 | − | 0.750618i | 0.223976 | − | 0.974595i | \(-0.428096\pi\) |
−0.974595 | + | 0.223976i | \(0.928096\pi\) | |||||||
\(12\) | −318.906 | + | 313.986i | −0.639307 | + | 0.629444i | ||||
\(13\) | −384.386 | + | 384.386i | −0.630826 | + | 0.630826i | −0.948275 | − | 0.317449i | \(-0.897174\pi\) |
0.317449 | + | 0.948275i | \(0.397174\pi\) | |||||||
\(14\) | −692.028 | − | 2.68978i | −0.943633 | − | 0.00366773i | ||||
\(15\) | −349.637 | −0.401227 | ||||||||
\(16\) | 1023.88 | + | 15.9197i | 0.999879 | + | 0.0155466i | ||||
\(17\) | −1558.08 | −1.30758 | −0.653791 | − | 0.756676i | \(-0.726822\pi\) | ||||
−0.653791 | + | 0.756676i | \(0.726822\pi\) | |||||||
\(18\) | −268.166 | − | 1.04231i | −0.195084 | − | 0.000758256i | ||||
\(19\) | −2096.85 | + | 2096.85i | −1.33255 | + | 1.33255i | −0.429462 | + | 0.903085i | \(0.641297\pi\) |
−0.903085 | + | 0.429462i | \(0.858703\pi\) | |||||||
\(20\) | 561.271 | + | 570.066i | 0.313760 | + | 0.318676i | ||||
\(21\) | 1209.80 | + | 1209.80i | 0.598641 | + | 0.598641i | ||||
\(22\) | 1710.63 | − | 1697.39i | 0.753530 | − | 0.747695i | ||||
\(23\) | − | 4768.93i | − | 1.87975i | −0.341513 | − | 0.939877i | \(-0.610939\pi\) | ||
0.341513 | − | 0.939877i | \(-0.389061\pi\) | |||||||
\(24\) | −1769.15 | − | 1810.90i | −0.626955 | − | 0.641749i | ||||
\(25\) | 625.000i | 0.200000i | ||||||||
\(26\) | −2165.95 | − | 2182.85i | −0.628370 | − | 0.633273i | ||||
\(27\) | 2871.89 | + | 2871.89i | 0.758157 | + | 0.758157i | ||||
\(28\) | 30.4312 | − | 3914.61i | 0.00733540 | − | 0.943612i | ||||
\(29\) | −1907.21 | + | 1907.21i | −0.421117 | + | 0.421117i | −0.885588 | − | 0.464471i | \(-0.846244\pi\) |
0.464471 | + | 0.885588i | \(0.346244\pi\) | |||||||
\(30\) | 7.68747 | − | 1977.83i | 0.00155948 | − | 0.401224i | ||||
\(31\) | 1152.69 | 0.215431 | 0.107715 | − | 0.994182i | \(-0.465646\pi\) | ||||
0.107715 | + | 0.994182i | \(0.465646\pi\) | |||||||
\(32\) | −112.567 | + | 5791.52i | −0.0194328 | + | 0.999811i | ||||
\(33\) | −5957.91 | −0.952377 | ||||||||
\(34\) | 34.2576 | − | 8813.79i | 0.00508229 | − | 1.30757i | ||||
\(35\) | 2162.60 | − | 2162.60i | 0.298405 | − | 0.298405i | ||||
\(36\) | 11.7923 | − | 1516.94i | 0.00151650 | − | 0.195080i | ||||
\(37\) | −7429.66 | − | 7429.66i | −0.892205 | − | 0.892205i | 0.102525 | − | 0.994730i | \(-0.467308\pi\) |
−0.994730 | + | 0.102525i | \(0.967308\pi\) | |||||||
\(38\) | −11815.4 | − | 11907.6i | −1.32736 | − | 1.33772i | ||||
\(39\) | 7602.58i | 0.800386i | ||||||||
\(40\) | −3237.09 | + | 3162.47i | −0.319894 | + | 0.312519i | ||||
\(41\) | − | 4115.54i | − | 0.382356i | −0.981555 | − | 0.191178i | \(-0.938769\pi\) | ||
0.981555 | − | 0.191178i | \(-0.0612307\pi\) | |||||||
\(42\) | −6870.23 | + | 6817.03i | −0.600963 | + | 0.596310i | ||||
\(43\) | 8400.86 | + | 8400.86i | 0.692871 | + | 0.692871i | 0.962863 | − | 0.269992i | \(-0.0870210\pi\) |
−0.269992 | + | 0.962863i | \(0.587021\pi\) | |||||||
\(44\) | 9564.19 | + | 9714.06i | 0.744761 | + | 0.756430i | ||||
\(45\) | 838.025 | − | 838.025i | 0.0616915 | − | 0.0616915i | ||||
\(46\) | 26976.9 | + | 104.854i | 1.87974 | + | 0.00730620i | ||||
\(47\) | −8941.71 | −0.590441 | −0.295220 | − | 0.955429i | \(-0.595393\pi\) | ||||
−0.295220 | + | 0.955429i | \(0.595393\pi\) | |||||||
\(48\) | 10282.8 | − | 9967.93i | 0.644181 | − | 0.624456i | ||||
\(49\) | 1841.08 | 0.109543 | ||||||||
\(50\) | −3535.51 | − | 13.7419i | −0.199998 | − | 0.000777357i | ||||
\(51\) | −15408.3 | + | 15408.3i | −0.829523 | + | 0.829523i | ||||
\(52\) | 12395.6 | − | 12204.4i | 0.635711 | − | 0.625903i | ||||
\(53\) | 24969.5 | + | 24969.5i | 1.22101 | + | 1.22101i | 0.967273 | + | 0.253738i | \(0.0816601\pi\) |
0.253738 | + | 0.967273i | \(0.418340\pi\) | |||||||
\(54\) | −16308.9 | + | 16182.6i | −0.761098 | + | 0.755204i | ||||
\(55\) | 10650.2i | 0.474733i | ||||||||
\(56\) | 22143.5 | + | 258.214i | 0.943576 | + | 0.0110030i | ||||
\(57\) | 41472.4i | 1.69072i | ||||||||
\(58\) | −10746.8 | − | 10830.6i | −0.419477 | − | 0.422751i | ||||
\(59\) | 23257.6 | + | 23257.6i | 0.869831 | + | 0.869831i | 0.992453 | − | 0.122622i | \(-0.0391303\pi\) |
−0.122622 | + | 0.992453i | \(0.539130\pi\) | |||||||
\(60\) | 11188.1 | + | 86.9731i | 0.401215 | + | 0.00311894i | ||||
\(61\) | 14305.9 | − | 14305.9i | 0.492257 | − | 0.492257i | −0.416760 | − | 0.909017i | \(-0.636834\pi\) |
0.909017 | + | 0.416760i | \(0.136834\pi\) | |||||||
\(62\) | −25.3441 | + | 6520.54i | −0.000837333 | + | 0.215429i | ||||
\(63\) | −5799.41 | −0.184091 | ||||||||
\(64\) | −32759.1 | − | 764.106i | −0.999728 | − | 0.0233187i | ||||
\(65\) | 13590.1 | 0.398970 | ||||||||
\(66\) | 130.996 | − | 33702.8i | 0.00370168 | − | 0.952370i | ||||
\(67\) | −38864.6 | + | 38864.6i | −1.05771 | + | 1.05771i | −0.0594820 | + | 0.998229i | \(0.518945\pi\) |
−0.998229 | + | 0.0594820i | \(0.981055\pi\) | |||||||
\(68\) | 49857.2 | + | 387.577i | 1.30754 | + | 0.0101645i | ||||
\(69\) | −47161.1 | − | 47161.1i | −1.19251 | − | 1.19251i | ||||
\(70\) | 12185.9 | + | 12281.0i | 0.297243 | + | 0.299563i | ||||
\(71\) | − | 12843.7i | − | 0.302373i | −0.988505 | − | 0.151187i | \(-0.951691\pi\) | ||
0.988505 | − | 0.151187i | \(-0.0483094\pi\) | |||||||
\(72\) | 8580.79 | + | 100.060i | 0.195073 | + | 0.00227472i | ||||
\(73\) | − | 28584.7i | − | 0.627807i | −0.949455 | − | 0.313904i | \(-0.898363\pi\) | ||
0.949455 | − | 0.313904i | \(-0.101637\pi\) | |||||||
\(74\) | 42191.5 | − | 41864.8i | 0.895666 | − | 0.888731i | ||||
\(75\) | 6180.78 | + | 6180.78i | 0.126879 | + | 0.126879i | ||||
\(76\) | 67618.6 | − | 66575.4i | 1.34287 | − | 1.32215i | ||||
\(77\) | 36851.3 | − | 36851.3i | 0.708314 | − | 0.708314i | ||||
\(78\) | −43006.4 | − | 167.158i | −0.800380 | − | 0.00311093i | ||||
\(79\) | −50757.6 | −0.915025 | −0.457513 | − | 0.889203i | \(-0.651260\pi\) | ||||
−0.457513 | + | 0.889203i | \(0.651260\pi\) | |||||||
\(80\) | −17818.3 | − | 18381.2i | −0.311273 | − | 0.321106i | ||||
\(81\) | 45282.1 | 0.766856 | ||||||||
\(82\) | 23280.9 | + | 90.4884i | 0.382353 | + | 0.00148613i | ||||
\(83\) | −39493.3 | + | 39493.3i | −0.629257 | + | 0.629257i | −0.947881 | − | 0.318624i | \(-0.896779\pi\) |
0.318624 | + | 0.947881i | \(0.396779\pi\) | |||||||
\(84\) | −38411.6 | − | 39013.5i | −0.593969 | − | 0.603276i | ||||
\(85\) | 27543.3 | + | 27543.3i | 0.413493 | + | 0.413493i | ||||
\(86\) | −47706.8 | + | 47337.3i | −0.695559 | + | 0.690173i | ||||
\(87\) | 37721.7i | 0.534309i | ||||||||
\(88\) | −55160.9 | + | 53889.3i | −0.759319 | + | 0.741815i | ||||
\(89\) | − | 97259.4i | − | 1.30154i | −0.759276 | − | 0.650768i | \(-0.774447\pi\) | ||
0.759276 | − | 0.650768i | \(-0.225553\pi\) | |||||||
\(90\) | 4722.12 | + | 4758.97i | 0.0614513 | + | 0.0619309i | ||||
\(91\) | −47024.0 | − | 47024.0i | −0.595273 | − | 0.595273i | ||||
\(92\) | −1186.28 | + | 152601.i | −0.0146123 | + | 1.87970i | ||||
\(93\) | 11399.2 | − | 11399.2i | 0.136668 | − | 0.136668i | ||||
\(94\) | 196.601 | − | 50581.6i | 0.00229492 | − | 0.590436i | ||||
\(95\) | 74134.7 | 0.842777 | ||||||||
\(96\) | 56160.6 | + | 58387.0i | 0.621947 | + | 0.646603i | ||||
\(97\) | −46757.9 | −0.504575 | −0.252287 | − | 0.967652i | \(-0.581183\pi\) | ||||
−0.252287 | + | 0.967652i | \(0.581183\pi\) | |||||||
\(98\) | −40.4798 | + | 10414.6i | −0.000425768 | + | 0.109542i | ||||
\(99\) | 14280.1 | − | 14280.1i | 0.146435 | − | 0.146435i | ||||
\(100\) | 155.470 | − | 19999.4i | 0.00155470 | − | 0.199994i | ||||
\(101\) | −62869.3 | − | 62869.3i | −0.613247 | − | 0.613247i | 0.330544 | − | 0.943791i | \(-0.392768\pi\) |
−0.943791 | + | 0.330544i | \(0.892768\pi\) | |||||||
\(102\) | −86822.9 | − | 87500.5i | −0.826293 | − | 0.832741i | ||||
\(103\) | 8850.12i | 0.0821971i | 0.999155 | + | 0.0410985i | \(0.0130858\pi\) | ||||
−0.999155 | + | 0.0410985i | \(0.986914\pi\) | |||||||
\(104\) | 68765.3 | + | 70388.0i | 0.623428 | + | 0.638139i | ||||
\(105\) | − | 42773.0i | − | 0.378614i | ||||||
\(106\) | −141797. | + | 140699.i | −1.22575 | + | 1.21626i | ||||
\(107\) | 119180. | + | 119180.i | 1.00634 | + | 1.00634i | 0.999980 | + | 0.00636140i | \(0.00202491\pi\) |
0.00636140 | + | 0.999980i | \(0.497975\pi\) | |||||||
\(108\) | −91183.4 | − | 92612.2i | −0.752240 | − | 0.764027i | ||||
\(109\) | 118189. | − | 118189.i | 0.952819 | − | 0.952819i | −0.0461173 | − | 0.998936i | \(-0.514685\pi\) |
0.998936 | + | 0.0461173i | \(0.0146848\pi\) | |||||||
\(110\) | −60245.9 | − | 234.165i | −0.474729 | − | 0.00184518i | ||||
\(111\) | −146947. | −1.13202 | ||||||||
\(112\) | −1947.54 | + | 125256.i | −0.0146704 | + | 0.943526i | ||||
\(113\) | 72392.2 | 0.533329 | 0.266665 | − | 0.963789i | \(-0.414078\pi\) | ||||
0.266665 | + | 0.963789i | \(0.414078\pi\) | |||||||
\(114\) | −234602. | − | 911.853i | −1.69071 | − | 0.00657147i | ||||
\(115\) | −84303.5 | + | 84303.5i | −0.594430 | + | 0.594430i | ||||
\(116\) | 61503.2 | − | 60554.4i | 0.424378 | − | 0.417831i | ||||
\(117\) | −18222.2 | − | 18222.2i | −0.123065 | − | 0.123065i | ||||
\(118\) | −132075. | + | 131053.i | −0.873206 | + | 0.866444i | ||||
\(119\) | − | 190609.i | − | 1.23389i | ||||||
\(120\) | −737.982 | + | 63286.8i | −0.00467835 | + | 0.401199i | ||||
\(121\) | 20430.2i | 0.126855i | ||||||||
\(122\) | 80611.4 | + | 81240.5i | 0.490340 | + | 0.494166i | ||||
\(123\) | −40699.6 | − | 40699.6i | −0.242565 | − | 0.242565i | ||||
\(124\) | −36884.9 | − | 286.734i | −0.215424 | − | 0.00167465i | ||||
\(125\) | 11048.5 | − | 11048.5i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 127.511 | − | 32806.1i | 0.000715522 | − | 0.184089i | ||||
\(127\) | 122901. | 0.676153 | 0.338076 | − | 0.941119i | \(-0.390224\pi\) | ||||
0.338076 | + | 0.941119i | \(0.390224\pi\) | |||||||
\(128\) | 5042.68 | − | 185295.i | 0.0272042 | − | 0.999630i | ||||
\(129\) | 166156. | 0.879108 | ||||||||
\(130\) | −298.806 | + | 76876.7i | −0.00155071 | + | 0.398967i | ||||
\(131\) | −75109.1 | + | 75109.1i | −0.382397 | + | 0.382397i | −0.871965 | − | 0.489568i | \(-0.837154\pi\) |
0.489568 | + | 0.871965i | \(0.337154\pi\) | |||||||
\(132\) | 190647. | + | 1482.04i | 0.952348 | + | 0.00740331i | ||||
\(133\) | −256518. | − | 256518.i | −1.25745 | − | 1.25745i | ||||
\(134\) | −218995. | − | 220704.i | −1.05359 | − | 1.06181i | ||||
\(135\) | − | 101537.i | − | 0.479500i | ||||||
\(136\) | −3288.66 | + | 282024.i | −0.0152466 | + | 1.30749i | ||||
\(137\) | − | 73685.1i | − | 0.335412i | −0.985837 | − | 0.167706i | \(-0.946364\pi\) | ||
0.985837 | − | 0.167706i | \(-0.0536359\pi\) | |||||||
\(138\) | 267818. | − | 265744.i | 1.19713 | − | 1.18786i | ||||
\(139\) | 18908.2 | + | 18908.2i | 0.0830067 | + | 0.0830067i | 0.747391 | − | 0.664384i | \(-0.231306\pi\) |
−0.664384 | + | 0.747391i | \(0.731306\pi\) | |||||||
\(140\) | −69739.1 | + | 68663.2i | −0.300716 | + | 0.296077i | ||||
\(141\) | −88426.8 | + | 88426.8i | −0.374573 | + | 0.374573i | ||||
\(142\) | 72654.2 | + | 282.393i | 0.302371 | + | 0.00117526i | ||||
\(143\) | 231579. | 0.947019 | ||||||||
\(144\) | −754.685 | + | 48537.7i | −0.00303291 | + | 0.195062i | ||||
\(145\) | 67430.0 | 0.266338 | ||||||||
\(146\) | 161698. | + | 628.491i | 0.627803 | + | 0.00244015i | ||||
\(147\) | 18206.9 | − | 18206.9i | 0.0694932 | − | 0.0694932i | ||||
\(148\) | 235894. | + | 239590.i | 0.885243 | + | 0.899114i | ||||
\(149\) | −147704. | − | 147704.i | −0.545039 | − | 0.545039i | 0.379963 | − | 0.925002i | \(-0.375937\pi\) |
−0.925002 | + | 0.379963i | \(0.875937\pi\) | |||||||
\(150\) | −35099.4 | + | 34827.6i | −0.127371 | + | 0.126385i | ||||
\(151\) | 86096.9i | 0.307288i | 0.988126 | + | 0.153644i | \(0.0491008\pi\) | ||||
−0.988126 | + | 0.153644i | \(0.950899\pi\) | |||||||
\(152\) | 375118. | + | 383970.i | 1.31692 | + | 1.34799i | ||||
\(153\) | − | 73862.3i | − | 0.255090i | ||||||
\(154\) | 207650. | + | 209271.i | 0.705555 | + | 0.711061i | ||||
\(155\) | −20376.8 | − | 20376.8i | −0.0681251 | − | 0.0681251i | ||||
\(156\) | 1891.16 | − | 243275.i | 0.00622181 | − | 0.800362i | ||||
\(157\) | −141259. | + | 141259.i | −0.457370 | + | 0.457370i | −0.897791 | − | 0.440421i | \(-0.854829\pi\) |
0.440421 | + | 0.897791i | \(0.354829\pi\) | |||||||
\(158\) | 1116.01 | − | 287126.i | 0.00355651 | − | 0.915018i | ||||
\(159\) | 493858. | 1.54921 | ||||||||
\(160\) | 104371. | − | 100391.i | 0.322313 | − | 0.310023i | ||||
\(161\) | 583408. | 1.77381 | ||||||||
\(162\) | −995.616 | + | 256152.i | −0.00298060 | + | 0.766850i | ||||
\(163\) | −283813. | + | 283813.i | −0.836687 | + | 0.836687i | −0.988421 | − | 0.151734i | \(-0.951514\pi\) |
0.151734 | + | 0.988421i | \(0.451514\pi\) | |||||||
\(164\) | −1023.75 | + | 131693.i | −0.00297225 | + | 0.382344i | ||||
\(165\) | 105322. | + | 105322.i | 0.301168 | + | 0.301168i | ||||
\(166\) | −222538. | − | 224274.i | −0.626806 | − | 0.631698i | ||||
\(167\) | − | 15467.8i | − | 0.0429178i | −0.999770 | − | 0.0214589i | \(-0.993169\pi\) | ||
0.999770 | − | 0.0214589i | \(-0.00683110\pi\) | |||||||
\(168\) | 221536. | − | 216429.i | 0.605580 | − | 0.591620i | ||||
\(169\) | 75787.0i | 0.204117i | ||||||||
\(170\) | −156413. | + | 155202.i | −0.415097 | + | 0.411883i | ||||
\(171\) | −99402.7 | − | 99402.7i | −0.259961 | − | 0.259961i | ||||
\(172\) | −266730. | − | 270909.i | −0.687464 | − | 0.698236i | ||||
\(173\) | −433381. | + | 433381.i | −1.10092 | + | 1.10092i | −0.106617 | + | 0.994300i | \(0.534002\pi\) |
−0.994300 | + | 0.106617i | \(0.965998\pi\) | |||||||
\(174\) | −213384. | − | 829.386i | −0.534305 | − | 0.00207675i | ||||
\(175\) | −76459.5 | −0.188728 | ||||||||
\(176\) | −303629. | − | 313220.i | −0.738858 | − | 0.762197i | ||||
\(177\) | 460000. | 1.10363 | ||||||||
\(178\) | 550178. | + | 2138.44i | 1.30153 | + | 0.00505879i | ||||
\(179\) | 197142. | − | 197142.i | 0.459883 | − | 0.459883i | −0.438734 | − | 0.898617i | \(-0.644573\pi\) |
0.898617 | + | 0.438734i | \(0.144573\pi\) | |||||||
\(180\) | −27024.4 | + | 26607.5i | −0.0621692 | + | 0.0612101i | ||||
\(181\) | −86411.6 | − | 86411.6i | −0.196054 | − | 0.196054i | 0.602252 | − | 0.798306i | \(-0.294270\pi\) |
−0.798306 | + | 0.602252i | \(0.794270\pi\) | |||||||
\(182\) | 267040. | − | 264972.i | 0.597582 | − | 0.592955i | ||||
\(183\) | − | 282950.i | − | 0.624570i | ||||||
\(184\) | −863209. | − | 10065.8i | −1.87963 | − | 0.0219182i | ||||
\(185\) | 262678.i | 0.564280i | ||||||||
\(186\) | 64232.5 | + | 64733.8i | 0.136136 | + | 0.137198i | ||||
\(187\) | 469344. | + | 469344.i | 0.981494 | + | 0.981494i | ||||
\(188\) | 286126. | + | 2224.27i | 0.590423 | + | 0.00458980i | ||||
\(189\) | −351334. | + | 351334.i | −0.715427 | + | 0.715427i | ||||
\(190\) | −1630.00 | + | 419366.i | −0.00327569 | + | 0.842770i | ||||
\(191\) | −697785. | −1.38401 | −0.692003 | − | 0.721895i | \(-0.743271\pi\) | ||||
−0.692003 | + | 0.721895i | \(0.743271\pi\) | |||||||
\(192\) | −331519. | + | 316406.i | −0.649016 | + | 0.619429i | ||||
\(193\) | −573139. | −1.10756 | −0.553779 | − | 0.832663i | \(-0.686815\pi\) | ||||
−0.553779 | + | 0.832663i | \(0.686815\pi\) | |||||||
\(194\) | 1028.06 | − | 264501.i | 0.00196117 | − | 0.504571i | ||||
\(195\) | 134396. | − | 134396.i | 0.253104 | − | 0.253104i | ||||
\(196\) | −58912.8 | − | 457.973i | −0.109539 | − | 0.000851530i | ||||
\(197\) | −259965. | − | 259965.i | −0.477254 | − | 0.477254i | 0.426999 | − | 0.904252i | \(-0.359571\pi\) |
−0.904252 | + | 0.426999i | \(0.859571\pi\) | |||||||
\(198\) | 80466.1 | + | 81094.1i | 0.145865 | + | 0.147003i | ||||
\(199\) | 80858.1i | 0.144741i | 0.997378 | + | 0.0723704i | \(0.0230564\pi\) | ||||
−0.997378 | + | 0.0723704i | \(0.976944\pi\) | |||||||
\(200\) | 113129. | + | 1319.19i | 0.199986 | + | 0.00233202i | ||||
\(201\) | 768683.i | 1.34201i | ||||||||
\(202\) | 357022. | − | 354258.i | 0.615626 | − | 0.610859i | ||||
\(203\) | −233319. | − | 233319.i | −0.397383 | − | 0.397383i | ||||
\(204\) | 496883. | − | 489217.i | 0.835946 | − | 0.823050i | ||||
\(205\) | −72753.2 | + | 72753.2i | −0.120912 | + | 0.120912i | ||||
\(206\) | −50063.5 | − | 194.587i | −0.0821964 | − | 0.000319482i | ||||
\(207\) | 226075. | 0.366713 | ||||||||
\(208\) | −399684. | + | 387445.i | −0.640557 | + | 0.620943i | ||||
\(209\) | 1.26327e6 | 2.00047 | ||||||||
\(210\) | 241959. | + | 940.449i | 0.378611 | + | 0.00147159i | ||||
\(211\) | −520212. | + | 520212.i | −0.804404 | + | 0.804404i | −0.983780 | − | 0.179377i | \(-0.942592\pi\) |
0.179377 | + | 0.983780i | \(0.442592\pi\) | |||||||
\(212\) | −792788. | − | 805210.i | −1.21148 | − | 1.23047i | ||||
\(213\) | −127014. | − | 127014.i | −0.191824 | − | 0.191824i | ||||
\(214\) | −676801. | + | 671560.i | −1.01024 | + | 1.00242i | ||||
\(215\) | − | 297015.i | − | 0.438210i | ||||||
\(216\) | 525895. | − | 513771.i | 0.766945 | − | 0.749265i | ||||
\(217\) | 141014.i | 0.203289i | ||||||||
\(218\) | 665973. | + | 671171.i | 0.949108 | + | 0.956515i | ||||
\(219\) | −282681. | − | 282681.i | −0.398278 | − | 0.398278i | ||||
\(220\) | 2649.25 | − | 340795.i | 0.00369034 | − | 0.474718i | ||||
\(221\) | 598907. | − | 598907.i | 0.824856 | − | 0.824856i | ||||
\(222\) | 3230.93 | − | 831254.i | 0.00439992 | − | 1.13201i | ||||
\(223\) | −126355. | −0.170150 | −0.0850749 | − | 0.996375i | \(-0.527113\pi\) | ||||
−0.0850749 | + | 0.996375i | \(0.527113\pi\) | |||||||
\(224\) | −708508. | − | 13770.9i | −0.943462 | − | 0.0183375i | ||||
\(225\) | −29628.7 | −0.0390172 | ||||||||
\(226\) | −1591.69 | + | 409509.i | −0.00207294 | + | 0.533325i | ||||
\(227\) | −918677. | + | 918677.i | −1.18331 | + | 1.18331i | −0.204427 | + | 0.978882i | \(0.565533\pi\) |
−0.978882 | + | 0.204427i | \(0.934467\pi\) | |||||||
\(228\) | 10316.4 | − | 1.32708e6i | 0.0131428 | − | 1.69067i | ||||
\(229\) | −347876. | − | 347876.i | −0.438365 | − | 0.438365i | 0.453097 | − | 0.891461i | \(-0.350319\pi\) |
−0.891461 | + | 0.453097i | \(0.850319\pi\) | |||||||
\(230\) | −475035. | − | 478743.i | −0.592116 | − | 0.596736i | ||||
\(231\) | − | 728862.i | − | 0.898702i | ||||||
\(232\) | 341192. | + | 349244.i | 0.416178 | + | 0.425999i | ||||
\(233\) | 728178.i | 0.878714i | 0.898313 | + | 0.439357i | \(0.144794\pi\) | ||||
−0.898313 | + | 0.439357i | \(0.855206\pi\) | |||||||
\(234\) | 103480. | − | 102679.i | 0.123543 | − | 0.122586i | ||||
\(235\) | 158069. | + | 158069.i | 0.186714 | + | 0.186714i | ||||
\(236\) | −738436. | − | 750007.i | −0.863044 | − | 0.876567i | ||||
\(237\) | −501954. | + | 501954.i | −0.580488 | + | 0.580488i | ||||
\(238\) | 1.07824e6 | + | 4190.91i | 1.23388 | + | 0.00479585i | ||||
\(239\) | 203434. | 0.230372 | 0.115186 | − | 0.993344i | \(-0.463254\pi\) | ||||
0.115186 | + | 0.993344i | \(0.463254\pi\) | |||||||
\(240\) | −357985. | − | 5566.11i | −0.401178 | − | 0.00623769i | ||||
\(241\) | −131370. | −0.145698 | −0.0728490 | − | 0.997343i | \(-0.523209\pi\) | ||||
−0.0728490 | + | 0.997343i | \(0.523209\pi\) | |||||||
\(242\) | −115570. | − | 449.198i | −0.126854 | − | 0.000493059i | ||||
\(243\) | −250065. | + | 250065.i | −0.271667 | + | 0.271667i | ||||
\(244\) | −461335. | + | 454217.i | −0.496068 | + | 0.488415i | ||||
\(245\) | −32546.0 | − | 32546.0i | −0.0346404 | − | 0.0346404i | ||||
\(246\) | 231125. | − | 229335.i | 0.243506 | − | 0.241620i | ||||
\(247\) | − | 1.61200e6i | − | 1.68121i | ||||||
\(248\) | 2432.99 | − | 208645.i | 0.00251195 | − | 0.215416i | ||||
\(249\) | 781117.i | 0.798395i | ||||||||
\(250\) | 62256.6 | + | 62742.5i | 0.0629993 | + | 0.0634909i | ||||
\(251\) | 487551. | + | 487551.i | 0.488467 | + | 0.488467i | 0.907822 | − | 0.419355i | \(-0.137744\pi\) |
−0.419355 | + | 0.907822i | \(0.637744\pi\) | |||||||
\(252\) | 185575. | + | 1442.62i | 0.184085 | + | 0.00143103i | ||||
\(253\) | −1.43655e6 | + | 1.43655e6i | −1.41098 | + | 1.41098i | ||||
\(254\) | −2702.21 | + | 695226.i | −0.00262806 | + | 0.676148i | ||||
\(255\) | 544765. | 0.524636 | ||||||||
\(256\) | 1.04807e6 | + | 32599.5i | 0.999517 | + | 0.0310893i | ||||
\(257\) | −1.90822e6 | −1.80217 | −0.901084 | − | 0.433645i | \(-0.857227\pi\) | ||||
−0.901084 | + | 0.433645i | \(0.857227\pi\) | |||||||
\(258\) | −3653.27 | + | 939914.i | −0.00341690 | + | 0.879101i | ||||
\(259\) | 908910. | − | 908910.i | 0.841921 | − | 0.841921i | ||||
\(260\) | −434871. | − | 3380.57i | −0.398957 | − | 0.00310139i | ||||
\(261\) | −90412.8 | − | 90412.8i | −0.0821540 | − | 0.0821540i | ||||
\(262\) | −423226. | − | 426529.i | −0.380908 | − | 0.383880i | ||||
\(263\) | − | 484503.i | − | 0.431924i | −0.976402 | − | 0.215962i | \(-0.930711\pi\) | ||
0.976402 | − | 0.215962i | \(-0.0692887\pi\) | |||||||
\(264\) | −12575.4 | + | 1.07842e6i | −0.0111048 | + | 0.952312i | ||||
\(265\) | − | 882804.i | − | 0.772235i | ||||||
\(266\) | 1.45672e6 | − | 1.44543e6i | 1.26232 | − | 1.25255i | ||||
\(267\) | −961821. | − | 961821.i | −0.825689 | − | 0.825689i | ||||
\(268\) | 1.25330e6 | − | 1.23396e6i | 1.06590 | − | 1.04946i | ||||
\(269\) | 986492. | − | 986492.i | 0.831214 | − | 0.831214i | −0.156469 | − | 0.987683i | \(-0.550011\pi\) |
0.987683 | + | 0.156469i | \(0.0500110\pi\) | |||||||
\(270\) | 574374. | + | 2232.49i | 0.479497 | + | 0.00186371i | ||||
\(271\) | 1.22694e6 | 1.01484 | 0.507422 | − | 0.861698i | \(-0.330599\pi\) | ||||
0.507422 | + | 0.861698i | \(0.330599\pi\) | |||||||
\(272\) | −1.59529e6 | − | 24804.2i | −1.30742 | − | 0.0203284i | ||||
\(273\) | −930064. | −0.755277 | ||||||||
\(274\) | 416823. | + | 1620.11i | 0.335409 | + | 0.00130367i | ||||
\(275\) | 188270. | − | 188270.i | 0.150124 | − | 0.150124i | ||||
\(276\) | 1.49738e6 | + | 1.52084e6i | 1.18320 | + | 1.20174i | ||||
\(277\) | 1.69007e6 | + | 1.69007e6i | 1.32344 | + | 1.32344i | 0.910970 | + | 0.412473i | \(0.135335\pi\) |
0.412473 | + | 0.910970i | \(0.364665\pi\) | |||||||
\(278\) | −107376. | + | 106544.i | −0.0833287 | + | 0.0826834i | ||||
\(279\) | 54644.1i | 0.0420275i | ||||||||
\(280\) | −386882. | − | 396011.i | −0.294906 | − | 0.301864i | ||||
\(281\) | 1.34620e6i | 1.01705i | 0.861046 | + | 0.508527i | \(0.169810\pi\) | ||||
−0.861046 | + | 0.508527i | \(0.830190\pi\) | |||||||
\(282\) | −498269. | − | 502158.i | −0.373114 | − | 0.376026i | ||||
\(283\) | 944602. | + | 944602.i | 0.701104 | + | 0.701104i | 0.964648 | − | 0.263543i | \(-0.0848912\pi\) |
−0.263543 | + | 0.964648i | \(0.584891\pi\) | |||||||
\(284\) | −3194.89 | + | 410985.i | −0.00235050 | + | 0.302364i | ||||
\(285\) | 733136. | − | 733136.i | 0.534653 | − | 0.534653i | ||||
\(286\) | −5091.72 | + | 1.31000e6i | −0.00368086 | + | 0.947012i | ||||
\(287\) | 503476. | 0.360806 | ||||||||
\(288\) | −274552. | − | 5336.31i | −0.195049 | − | 0.00379105i | ||||
\(289\) | 1.00777e6 | 0.709768 | ||||||||
\(290\) | −1482.58 | + | 381439.i | −0.00103520 | + | 0.266336i | ||||
\(291\) | −462400. | + | 462400.i | −0.320100 | + | 0.320100i | ||||
\(292\) | −7110.51 | + | 914683.i | −0.00488027 | + | 0.627788i | ||||
\(293\) | −838880. | − | 838880.i | −0.570862 | − | 0.570862i | 0.361508 | − | 0.932369i | \(-0.382262\pi\) |
−0.932369 | + | 0.361508i | \(0.882262\pi\) | |||||||
\(294\) | 102593. | + | 103393.i | 0.0692226 | + | 0.0697628i | ||||
\(295\) | − | 822281.i | − | 0.550130i | ||||||
\(296\) | −1.36050e6 | + | 1.32914e6i | −0.902548 | + | 0.881741i | ||||
\(297\) | − | 1.73021e6i | − | 1.13817i | ||||||
\(298\) | 838783. | − | 832288.i | 0.547153 | − | 0.542916i | ||||
\(299\) | 1.83311e6 | + | 1.83311e6i | 1.18580 | + | 1.18580i | ||||
\(300\) | −196241. | − | 199316.i | −0.125889 | − | 0.127861i | ||||
\(301\) | −1.02772e6 | + | 1.02772e6i | −0.653821 | + | 0.653821i | ||||
\(302\) | −487034. | − | 1893.01i | −0.307285 | − | 0.00119436i | ||||
\(303\) | −1.24346e6 | −0.778082 | ||||||||
\(304\) | −2.18029e6 | + | 2.11353e6i | −1.35310 | + | 1.31167i | ||||
\(305\) | −505791. | −0.311330 | ||||||||
\(306\) | 417825. | + | 1624.01i | 0.255089 | + | 0.000991482i | ||||
\(307\) | −521897. | + | 521897.i | −0.316038 | + | 0.316038i | −0.847243 | − | 0.531205i | \(-0.821739\pi\) |
0.531205 | + | 0.847243i | \(0.321739\pi\) | |||||||
\(308\) | −1.18837e6 | + | 1.17004e6i | −0.713798 | + | 0.702786i | ||||
\(309\) | 87521.0 | + | 87521.0i | 0.0521454 | + | 0.0521454i | ||||
\(310\) | 115716. | − | 114820.i | 0.0683894 | − | 0.0678598i | ||||
\(311\) | − | 1.29428e6i | − | 0.758798i | −0.925233 | − | 0.379399i | \(-0.876131\pi\) | ||
0.925233 | − | 0.379399i | \(-0.123869\pi\) | |||||||
\(312\) | 1.37612e6 | + | 16046.8i | 0.800332 | + | 0.00933260i | ||||
\(313\) | 2.45861e6i | 1.41850i | 0.704957 | + | 0.709251i | \(0.250966\pi\) | ||||
−0.704957 | + | 0.709251i | \(0.749034\pi\) | |||||||
\(314\) | −795970. | − | 802182.i | −0.455589 | − | 0.459144i | ||||
\(315\) | 102520. | + | 102520.i | 0.0582146 | + | 0.0582146i | ||||
\(316\) | 1.62419e6 | + | 12626.1i | 0.914998 | + | 0.00711296i | ||||
\(317\) | 1.88035e6 | − | 1.88035e6i | 1.05097 | − | 1.05097i | 0.0523414 | − | 0.998629i | \(-0.483332\pi\) |
0.998629 | − | 0.0523414i | \(-0.0166684\pi\) | |||||||
\(318\) | −10858.4 | + | 2.79366e6i | −0.00602143 | + | 1.54920i | ||||
\(319\) | 1.14902e6 | 0.632197 | ||||||||
\(320\) | 565597. | + | 592612.i | 0.308768 | + | 0.323516i | ||||
\(321\) | 2.35721e6 | 1.27684 | ||||||||
\(322\) | −12827.4 | + | 3.30023e6i | −0.00689443 | + | 1.77380i | ||||
\(323\) | 3.26706e6 | − | 3.26706e6i | 1.74241 | − | 1.74241i | ||||
\(324\) | −1.44898e6 | − | 11264.0i | −0.766833 | − | 0.00596116i | ||||
\(325\) | −240242. | − | 240242.i | −0.126165 | − | 0.126165i | ||||
\(326\) | −1.59924e6 | − | 1.61172e6i | −0.833429 | − | 0.839933i | ||||
\(327\) | − | 2.33760e6i | − | 1.20893i | ||||||
\(328\) | −744943. | − | 8686.71i | −0.382330 | − | 0.00445831i | ||||
\(329\) | − | 1.09389e6i | − | 0.557164i | ||||||
\(330\) | −598102. | + | 593471.i | −0.302336 | + | 0.299995i | ||||
\(331\) | −2.05885e6 | − | 2.05885e6i | −1.03289 | − | 1.03289i | −0.999440 | − | 0.0334519i | \(-0.989350\pi\) |
−0.0334519 | − | 0.999440i | \(-0.510650\pi\) | |||||||
\(332\) | 1.27357e6 | − | 1.25392e6i | 0.634129 | − | 0.624346i | ||||
\(333\) | 352209. | − | 352209.i | 0.174057 | − | 0.174057i | ||||
\(334\) | 87498.4 | + | 340.090i | 0.0429175 | + | 0.000166812i | ||||
\(335\) | 1.37407e6 | 0.668955 | ||||||||
\(336\) | 1.21943e6 | + | 1.25795e6i | 0.589262 | + | 0.607875i | ||||
\(337\) | −256497. | −0.123029 | −0.0615145 | − | 0.998106i | \(-0.519593\pi\) | ||||
−0.0615145 | + | 0.998106i | \(0.519593\pi\) | |||||||
\(338\) | −428713. | − | 1666.33i | −0.204115 | − | 0.000793357i | ||||
\(339\) | 715904. | − | 715904.i | 0.338342 | − | 0.338342i | ||||
\(340\) | −874507. | − | 888210.i | −0.410267 | − | 0.416695i | ||||
\(341\) | −347226. | − | 347226.i | −0.161706 | − | 0.161706i | ||||
\(342\) | 564488. | − | 560117.i | 0.260969 | − | 0.258949i | ||||
\(343\) | 2.28132e6i | 1.04701i | ||||||||
\(344\) | 1.53835e6 | − | 1.50288e6i | 0.700903 | − | 0.684745i | ||||
\(345\) | 1.66740e6i | 0.754207i | ||||||||
\(346\) | −2.44203e6 | − | 2.46108e6i | −1.09663 | − | 1.10519i | ||||
\(347\) | −297841. | − | 297841.i | −0.132789 | − | 0.132789i | 0.637589 | − | 0.770377i | \(-0.279932\pi\) |
−0.770377 | + | 0.637589i | \(0.779932\pi\) | |||||||
\(348\) | 9383.36 | − | 1.20706e6i | 0.00415346 | − | 0.534293i | ||||
\(349\) | −1.06398e6 | + | 1.06398e6i | −0.467597 | + | 0.467597i | −0.901135 | − | 0.433538i | \(-0.857265\pi\) |
0.433538 | + | 0.901135i | \(0.357265\pi\) | |||||||
\(350\) | 1681.11 | − | 432517.i | 0.000733546 | − | 0.188727i | ||||
\(351\) | −2.20783e6 | −0.956530 | ||||||||
\(352\) | 1.77850e6 | − | 1.71068e6i | 0.765063 | − | 0.735890i | ||||
\(353\) | 2.71943e6 | 1.16156 | 0.580780 | − | 0.814060i | \(-0.302748\pi\) | ||||
0.580780 | + | 0.814060i | \(0.302748\pi\) | |||||||
\(354\) | −10114.0 | + | 2.60213e6i | −0.00428959 | + | 1.10363i | ||||
\(355\) | −227046. | + | 227046.i | −0.0956187 | + | 0.0956187i | ||||
\(356\) | −24193.5 | + | 3.11221e6i | −0.0101175 | + | 1.30150i | ||||
\(357\) | −1.88497e6 | − | 1.88497e6i | −0.782771 | − | 0.782771i | ||||
\(358\) | 1.11086e6 | + | 1.11953e6i | 0.458092 | + | 0.461667i | ||||
\(359\) | 1.93088e6i | 0.790714i | 0.918528 | + | 0.395357i | \(0.129379\pi\) | ||||
−0.918528 | + | 0.395357i | \(0.870621\pi\) | |||||||
\(360\) | −149920. | − | 153457.i | −0.0609680 | − | 0.0624067i | ||||
\(361\) | − | 6.31742e6i | − | 2.55136i | ||||||
\(362\) | 490714. | − | 486914.i | 0.196814 | − | 0.195290i | ||||
\(363\) | 202039. | + | 202039.i | 0.0804764 | + | 0.0804764i | ||||
\(364\) | 1.49303e6 | + | 1.51642e6i | 0.590628 | + | 0.599883i | ||||
\(365\) | −505311. | + | 505311.i | −0.198530 | + | 0.198530i | ||||
\(366\) | 1.60059e6 | + | 6221.21i | 0.624566 | + | 0.00242757i | ||||
\(367\) | −4.26731e6 | −1.65382 | −0.826911 | − | 0.562332i | \(-0.809904\pi\) | ||||
−0.826911 | + | 0.562332i | \(0.809904\pi\) | |||||||
\(368\) | 75919.7 | − | 4.88279e6i | 0.0292237 | − | 1.87953i | ||||
\(369\) | 195101. | 0.0745922 | ||||||||
\(370\) | −1.48592e6 | − | 5775.50i | −0.564276 | − | 0.00219324i | ||||
\(371\) | −3.05465e6 | + | 3.05465e6i | −1.15220 | + | 1.15220i | ||||
\(372\) | −367599. | + | 361928.i | −0.137726 | + | 0.135602i | ||||
\(373\) | −1.60230e6 | − | 1.60230e6i | −0.596311 | − | 0.596311i | 0.343018 | − | 0.939329i | \(-0.388551\pi\) |
−0.939329 | + | 0.343018i | \(0.888551\pi\) | |||||||
\(374\) | −2.66531e6 | + | 2.64467e6i | −0.985302 | + | 0.977672i | ||||
\(375\) | − | 218523.i | − | 0.0802453i | ||||||
\(376\) | −18873.3 | + | 1.61851e6i | −0.00688461 | + | 0.590400i | ||||
\(377\) | − | 1.46621e6i | − | 0.531304i | ||||||
\(378\) | −1.97970e6 | − | 1.99515e6i | −0.712641 | − | 0.718203i | ||||
\(379\) | −1.32305e6 | − | 1.32305e6i | −0.473127 | − | 0.473127i | 0.429798 | − | 0.902925i | \(-0.358585\pi\) |
−0.902925 | + | 0.429798i | \(0.858585\pi\) | |||||||
\(380\) | −2.37224e6 | − | 18441.2i | −0.842751 | − | 0.00655133i | ||||
\(381\) | 1.21539e6 | − | 1.21539e6i | 0.428948 | − | 0.428948i | ||||
\(382\) | 15342.2 | − | 3.94724e6i | 0.00537933 | − | 1.38400i | ||||
\(383\) | 2.69607e6 | 0.939149 | 0.469574 | − | 0.882893i | \(-0.344407\pi\) | ||||
0.469574 | + | 0.882893i | \(0.344407\pi\) | |||||||
\(384\) | −1.78256e6 | − | 1.88230e6i | −0.616902 | − | 0.651419i | ||||
\(385\) | −1.30289e6 | −0.447977 | ||||||||
\(386\) | 12601.6 | − | 3.24214e6i | 0.00430484 | − | 1.10755i | ||||
\(387\) | −398250. | + | 398250.i | −0.135169 | + | 0.135169i | ||||
\(388\) | 1.49621e6 | + | 11631.1i | 0.504560 | + | 0.00392232i | ||||
\(389\) | 2.79493e6 | + | 2.79493e6i | 0.936475 | + | 0.936475i | 0.998099 | − | 0.0616242i | \(-0.0196280\pi\) |
−0.0616242 | + | 0.998099i | \(0.519628\pi\) | |||||||
\(390\) | 757297. | + | 763207.i | 0.252119 | + | 0.254086i | ||||
\(391\) | 7.43039e6i | 2.45793i | ||||||||
\(392\) | 3885.98 | − | 333249.i | 0.00127728 | − | 0.109535i | ||||
\(393\) | 1.48554e6i | 0.485181i | ||||||||
\(394\) | 1.47629e6 | − | 1.46486e6i | 0.479105 | − | 0.475395i | ||||
\(395\) | 897276. | + | 897276.i | 0.289356 | + | 0.289356i | ||||
\(396\) | −460503. | + | 453399.i | −0.147569 | + | 0.145292i | ||||
\(397\) | 2.49038e6 | − | 2.49038e6i | 0.793030 | − | 0.793030i | −0.188956 | − | 0.981986i | \(-0.560510\pi\) |
0.981986 | + | 0.188956i | \(0.0605103\pi\) | |||||||
\(398\) | −457399. | − | 1777.83i | −0.144740 | − | 0.000562576i | ||||
\(399\) | −5.07354e6 | −1.59543 | ||||||||
\(400\) | −9949.79 | + | 639923.i | −0.00310931 | + | 0.199976i | ||||
\(401\) | −4.48252e6 | −1.39207 | −0.696036 | − | 0.718007i | \(-0.745054\pi\) | ||||
−0.696036 | + | 0.718007i | \(0.745054\pi\) | |||||||
\(402\) | −4.34829e6 | − | 16901.0i | −1.34200 | − | 0.00521612i | ||||
\(403\) | −443078. | + | 443078.i | −0.135899 | + | 0.135899i | ||||
\(404\) | 1.99612e6 | + | 2.02740e6i | 0.608461 | + | 0.617995i | ||||
\(405\) | −800481. | − | 800481.i | −0.242501 | − | 0.242501i | ||||
\(406\) | 1.32497e6 | − | 1.31471e6i | 0.398925 | − | 0.395836i | ||||
\(407\) | 4.47610e6i | 1.33941i | ||||||||
\(408\) | 2.75648e6 | + | 2.82153e6i | 0.819794 | + | 0.839139i | ||||
\(409\) | − | 2.36608e6i | − | 0.699393i | −0.936863 | − | 0.349696i | \(-0.886285\pi\) | ||
0.936863 | − | 0.349696i | \(-0.113715\pi\) | |||||||
\(410\) | −409952. | − | 413151.i | −0.120441 | − | 0.121381i | ||||
\(411\) | −728690. | − | 728690.i | −0.212784 | − | 0.212784i | ||||
\(412\) | 2201.49 | − | 283195.i | 0.000638960 | − | 0.0821946i | ||||
\(413\) | −2.84523e6 | + | 2.84523e6i | −0.820808 | + | 0.820808i | ||||
\(414\) | −4970.71 | + | 1.27886e6i | −0.00142534 | + | 0.366711i | ||||
\(415\) | 1.39630e6 | 0.397977 | ||||||||
\(416\) | −2.18291e6 | − | 2.26945e6i | −0.618448 | − | 0.642966i | ||||
\(417\) | 373975. | 0.105318 | ||||||||
\(418\) | −27775.6 | + | 7.14610e6i | −0.00777539 | + | 2.00045i | ||||
\(419\) | −1.04928e6 | + | 1.04928e6i | −0.291983 | + | 0.291983i | −0.837863 | − | 0.545880i | \(-0.816195\pi\) |
0.545880 | + | 0.837863i | \(0.316195\pi\) | |||||||
\(420\) | −10639.9 | + | 1.36869e6i | −0.00294316 | + | 0.378602i | ||||
\(421\) | −83315.8 | − | 83315.8i | −0.0229099 | − | 0.0229099i | 0.695559 | − | 0.718469i | \(-0.255157\pi\) |
−0.718469 | + | 0.695559i | \(0.755157\pi\) | |||||||
\(422\) | −2.93130e6 | − | 2.95418e6i | −0.801271 | − | 0.807524i | ||||
\(423\) | − | 423890.i | − | 0.115187i | ||||||
\(424\) | 4.57235e6 | − | 4.46695e6i | 1.23517 | − | 1.20669i | ||||
\(425\) | − | 973803.i | − | 0.261516i | ||||||
\(426\) | 721287. | − | 715702.i | 0.192568 | − | 0.191077i | ||||
\(427\) | 1.75012e6 | + | 1.75012e6i | 0.464513 | + | 0.464513i | ||||
\(428\) | −3.78401e6 | − | 3.84330e6i | −0.998488 | − | 1.01413i | ||||
\(429\) | 2.29014e6 | − | 2.29014e6i | 0.600784 | − | 0.600784i | ||||
\(430\) | 1.68016e6 | + | 6530.46i | 0.438207 | + | 0.00170323i | ||||
\(431\) | 1.89615e6 | 0.491676 | 0.245838 | − | 0.969311i | \(-0.420937\pi\) | ||||
0.245838 | + | 0.969311i | \(0.420937\pi\) | |||||||
\(432\) | 2.89474e6 | + | 2.98618e6i | 0.746278 | + | 0.769852i | ||||
\(433\) | −6.49433e6 | −1.66462 | −0.832309 | − | 0.554312i | \(-0.812982\pi\) | ||||
−0.832309 | + | 0.554312i | \(0.812982\pi\) | |||||||
\(434\) | −797692. | − | 3100.48i | −0.203288 | − | 0.000790141i | ||||
\(435\) | 666831. | − | 666831.i | 0.168963 | − | 0.168963i | ||||
\(436\) | −3.81133e6 | + | 3.75253e6i | −0.960197 | + | 0.945383i | ||||
\(437\) | 9.99970e6 | + | 9.99970e6i | 2.50486 | + | 2.50486i | ||||
\(438\) | 1.60529e6 | − | 1.59286e6i | 0.399823 | − | 0.396727i | ||||
\(439\) | 2.58577e6i | 0.640365i | 0.947356 | + | 0.320183i | \(0.103744\pi\) | ||||
−0.947356 | + | 0.320183i | \(0.896256\pi\) | |||||||
\(440\) | 1.92775e6 | + | 22479.4i | 0.474700 | + | 0.00553544i | ||||
\(441\) | 87278.0i | 0.0213702i | ||||||||
\(442\) | 3.37473e6 | + | 3.40107e6i | 0.821644 | + | 0.828056i | ||||
\(443\) | −562901. | − | 562901.i | −0.136277 | − | 0.136277i | 0.635678 | − | 0.771955i | \(-0.280721\pi\) |
−0.771955 | + | 0.635678i | \(0.780721\pi\) | |||||||
\(444\) | 4.70217e6 | + | 36553.5i | 1.13199 | + | 0.00879978i | ||||
\(445\) | −1.71932e6 | + | 1.71932e6i | −0.411582 | + | 0.411582i | ||||
\(446\) | 2778.17 | − | 714768.i | 0.000661335 | − | 0.170148i | ||||
\(447\) | −2.92137e6 | −0.691540 | ||||||||
\(448\) | 93477.1 | − | 4.00759e6i | 0.0220044 | − | 0.943384i | ||||
\(449\) | 6.62708e6 | 1.55134 | 0.775669 | − | 0.631141i | \(-0.217413\pi\) | ||||
0.775669 | + | 0.631141i | \(0.217413\pi\) | |||||||
\(450\) | 651.444 | − | 167604.i | 0.000151651 | − | 0.0390169i | ||||
\(451\) | −1.23973e6 | + | 1.23973e6i | −0.287003 | + | 0.287003i | ||||
\(452\) | −2.31648e6 | − | 18007.7i | −0.533313 | − | 0.00414584i | ||||
\(453\) | 851433. | + | 851433.i | 0.194942 | + | 0.194942i | ||||
\(454\) | −5.17658e6 | − | 5.21698e6i | −1.17870 | − | 1.18790i | ||||
\(455\) | 1.66255e6i | 0.376484i | ||||||||
\(456\) | 7.50680e6 | + | 87536.1i | 1.69061 | + | 0.0197140i | ||||
\(457\) | − | 2.47813e6i | − | 0.555052i | −0.960718 | − | 0.277526i | \(-0.910485\pi\) | ||
0.960718 | − | 0.277526i | \(-0.0895145\pi\) | |||||||
\(458\) | 1.97552e6 | − | 1.96022e6i | 0.440065 | − | 0.436658i | ||||
\(459\) | −4.47465e6 | − | 4.47465e6i | −0.991351 | − | 0.991351i | ||||
\(460\) | 2.71860e6 | − | 2.67666e6i | 0.599033 | − | 0.589792i | ||||
\(461\) | 2.88325e6 | − | 2.88325e6i | 0.631872 | − | 0.631872i | −0.316665 | − | 0.948537i | \(-0.602563\pi\) |
0.948537 | + | 0.316665i | \(0.102563\pi\) | |||||||
\(462\) | 4.12304e6 | + | 16025.5i | 0.898695 | + | 0.00349306i | ||||
\(463\) | 4.18992e6 | 0.908351 | 0.454175 | − | 0.890912i | \(-0.349934\pi\) | ||||
0.454175 | + | 0.890912i | \(0.349934\pi\) | |||||||
\(464\) | −1.98311e6 | + | 1.92238e6i | −0.427613 | + | 0.414519i | ||||
\(465\) | −403023. | −0.0864365 | ||||||||
\(466\) | −4.11916e6 | − | 16010.4i | −0.878707 | − | 0.00341537i | ||||
\(467\) | −1.38927e6 | + | 1.38927e6i | −0.294777 | + | 0.294777i | −0.838964 | − | 0.544187i | \(-0.816838\pi\) |
0.544187 | + | 0.838964i | \(0.316838\pi\) | |||||||
\(468\) | 578559. | + | 587624.i | 0.122105 | + | 0.124018i | ||||
\(469\) | −4.75451e6 | − | 4.75451e6i | −0.998099 | − | 0.998099i | ||||
\(470\) | −897640. | + | 890689.i | −0.187438 | + | 0.185987i | ||||
\(471\) | 2.79389e6i | 0.580306i | ||||||||
\(472\) | 4.25888e6 | − | 4.16070e6i | 0.879915 | − | 0.859630i | ||||
\(473\) | − | 5.06121e6i | − | 1.04016i | ||||||
\(474\) | −2.82842e6 | − | 2.85049e6i | −0.578227 | − | 0.582739i | ||||
\(475\) | −1.31053e6 | − | 1.31053e6i | −0.266509 | − | 0.266509i | ||||
\(476\) | −47414.4 | + | 6.09929e6i | −0.00959163 | + | 1.23385i | ||||
\(477\) | −1.18370e6 | + | 1.18370e6i | −0.238202 | + | 0.238202i | ||||
\(478\) | −4472.90 | + | 1.15079e6i | −0.000895405 | + | 0.230370i | ||||
\(479\) | −3.01097e6 | −0.599609 | −0.299804 | − | 0.954001i | \(-0.596921\pi\) | ||||
−0.299804 | + | 0.954001i | \(0.596921\pi\) | |||||||
\(480\) | 39357.5 | − | 2.02493e6i | 0.00779694 | − | 0.401151i | ||||
\(481\) | 5.71172e6 | 1.12565 | ||||||||
\(482\) | 2888.43 | − | 743135.i | 0.000566297 | − | 0.145697i | ||||
\(483\) | 5.76946e6 | − | 5.76946e6i | 1.12530 | − | 1.12530i | ||||
\(484\) | 5082.05 | − | 653746.i | 0.000986111 | − | 0.126851i | ||||
\(485\) | 826570. | + | 826570.i | 0.159561 | + | 0.159561i | ||||
\(486\) | −1.40907e6 | − | 1.42007e6i | −0.270609 | − | 0.272721i | ||||
\(487\) | 1.73420e6i | 0.331341i | 0.986181 | + | 0.165671i | \(0.0529789\pi\) | ||||
−0.986181 | + | 0.165671i | \(0.947021\pi\) | |||||||
\(488\) | −2.55928e6 | − | 2.61967e6i | −0.486483 | − | 0.497963i | ||||
\(489\) | 5.61339e6i | 1.06158i | ||||||||
\(490\) | 184822. | − | 183391.i | 0.0347748 | − | 0.0345055i | ||||
\(491\) | 2.65718e6 | + | 2.65718e6i | 0.497414 | + | 0.497414i | 0.910632 | − | 0.413218i | \(-0.135595\pi\) |
−0.413218 | + | 0.910632i | \(0.635595\pi\) | |||||||
\(492\) | 1.29222e6 | + | 1.31247e6i | 0.240672 | + | 0.244443i | ||||
\(493\) | 2.97159e6 | − | 2.97159e6i | 0.550645 | − | 0.550645i | ||||
\(494\) | 9.11877e6 | + | 35443.0i | 1.68120 | + | 0.00653451i | ||||
\(495\) | −504879. | −0.0926136 | ||||||||
\(496\) | 1.18021e6 | + | 18350.4i | 0.215405 | + | 0.00334920i | ||||
\(497\) | 1.57123e6 | 0.285331 | ||||||||
\(498\) | −4.41863e6 | − | 17174.4i | −0.798389 | − | 0.00310319i | ||||
\(499\) | 7.30951e6 | − | 7.30951e6i | 1.31413 | − | 1.31413i | 0.395781 | − | 0.918345i | \(-0.370474\pi\) |
0.918345 | − | 0.395781i | \(-0.129526\pi\) | |||||||
\(500\) | −356291. | + | 350794.i | −0.0637353 | + | 0.0627520i | ||||
\(501\) | −152965. | − | 152965.i | −0.0272268 | − | 0.0272268i | ||||
\(502\) | −2.76870e6 | + | 2.74726e6i | −0.490362 | + | 0.486565i | ||||
\(503\) | 5.49766e6i | 0.968853i | 0.874832 | + | 0.484426i | \(0.160972\pi\) | ||||
−0.874832 | + | 0.484426i | \(0.839028\pi\) | |||||||
\(504\) | −12240.8 | + | 1.04973e6i | −0.00214652 | + | 0.184078i | ||||
\(505\) | 2.22277e6i | 0.387851i | ||||||||
\(506\) | −8.09472e6 | − | 8.15789e6i | −1.40548 | − | 1.41645i | ||||
\(507\) | 749476. | + | 749476.i | 0.129491 | + | 0.129491i | ||||
\(508\) | −3.93270e6 | − | 30571.8i | −0.676132 | − | 0.00525608i | ||||
\(509\) | −2.60875e6 | + | 2.60875e6i | −0.446311 | + | 0.446311i | −0.894126 | − | 0.447815i | \(-0.852202\pi\) |
0.447815 | + | 0.894126i | \(0.352202\pi\) | |||||||
\(510\) | −11977.7 | + | 3.08163e6i | −0.00203915 | + | 0.524632i | ||||
\(511\) | 3.49692e6 | 0.592424 | ||||||||
\(512\) | −207453. | + | 5.92801e6i | −0.0349740 | + | 0.999388i | ||||
\(513\) | −1.20438e7 | −2.02056 | ||||||||
\(514\) | 41955.9 | − | 1.07944e7i | 0.00700464 | − | 1.80215i | ||||
\(515\) | 156450. | − | 156450.i | 0.0259930 | − | 0.0259930i | ||||
\(516\) | −5.31684e6 | − | 41331.7i | −0.879081 | − | 0.00683375i | ||||
\(517\) | 2.69353e6 | + | 2.69353e6i | 0.443195 | + | 0.443195i | ||||
\(518\) | 5.12155e6 | + | 5.16151e6i | 0.838642 | + | 0.845187i | ||||
\(519\) | 8.57162e6i | 1.39683i | ||||||||
\(520\) | 28684.8 | − | 2.45991e6i | 0.00465203 | − | 0.398942i | ||||
\(521\) | 9.50774e6i | 1.53456i | 0.641314 | + | 0.767279i | \(0.278390\pi\) | ||||
−0.641314 | + | 0.767279i | \(0.721610\pi\) | |||||||
\(522\) | 513436. | − | 509460.i | 0.0824727 | − | 0.0818341i | ||||
\(523\) | 2.12191e6 | + | 2.12191e6i | 0.339213 | + | 0.339213i | 0.856071 | − | 0.516858i | \(-0.172898\pi\) |
−0.516858 | + | 0.856071i | \(0.672898\pi\) | |||||||
\(524\) | 2.42210e6 | − | 2.38473e6i | 0.385358 | − | 0.379413i | ||||
\(525\) | −756127. | + | 756127.i | −0.119728 | + | 0.119728i | ||||
\(526\) | 2.74074e6 | + | 10652.8i | 0.431920 | + | 0.00167879i | ||||
\(527\) | −1.79598e6 | −0.281693 | ||||||||
\(528\) | −6.10016e6 | − | 94847.9i | −0.952262 | − | 0.0148062i | ||||
\(529\) | −1.63063e7 | −2.53348 | ||||||||
\(530\) | 4.99386e6 | + | 19410.2i | 0.772229 | + | 0.00300151i | ||||
\(531\) | −1.10255e6 | + | 1.10255e6i | −0.169692 | + | 0.169692i | ||||
\(532\) | 8.14452e6 | + | 8.27214e6i | 1.24763 | + | 1.26718i | ||||
\(533\) | 1.58196e6 | + | 1.58196e6i | 0.241200 | + | 0.241200i | ||||
\(534\) | 5.46199e6 | − | 5.41969e6i | 0.828892 | − | 0.822473i | ||||
\(535\) | − | 4.21366e6i | − | 0.636466i | ||||||
\(536\) | 6.95273e6 | + | 7.11680e6i | 1.04531 | + | 1.06997i | ||||
\(537\) | − | 3.89918e6i | − | 0.583495i | ||||||
\(538\) | 5.55871e6 | + | 5.60209e6i | 0.827977 | + | 0.834439i | ||||
\(539\) | −554592. | − | 554592.i | −0.0822246 | − | 0.0822246i | ||||
\(540\) | −25257.5 | + | 3.24908e6i | −0.00372740 | + | 0.479486i | ||||
\(541\) | 7.92767e6 | − | 7.92767e6i | 1.16454 | − | 1.16454i | 0.181064 | − | 0.983471i | \(-0.442046\pi\) |
0.983471 | − | 0.181064i | \(-0.0579541\pi\) | |||||||
\(542\) | −26976.6 | + | 6.94055e6i | −0.00394448 | + | 1.01484i | ||||
\(543\) | −1.70909e6 | −0.248751 | ||||||||
\(544\) | 175388. | − | 9.02368e6i | 0.0254099 | − | 1.30733i | ||||
\(545\) | −4.17861e6 | −0.602615 | ||||||||
\(546\) | 20449.3 | − | 5.26120e6i | 0.00293560 | − | 0.755271i | ||||
\(547\) | 2.38242e6 | − | 2.38242e6i | 0.340447 | − | 0.340447i | −0.516088 | − | 0.856535i | \(-0.672612\pi\) |
0.856535 | + | 0.516088i | \(0.172612\pi\) | |||||||
\(548\) | −18329.3 | + | 2.35785e6i | −0.00260733 | + | 0.335402i | ||||
\(549\) | 678185. | + | 678185.i | 0.0960323 | + | 0.0960323i | ||||
\(550\) | 1.06087e6 | + | 1.06915e6i | 0.149539 | + | 0.150706i | ||||
\(551\) | − | 7.99824e6i | − | 1.12232i | ||||||
\(552\) | −8.63603e6 | + | 8.43694e6i | −1.20633 | + | 1.17852i | ||||
\(553\) | − | 6.20944e6i | − | 0.863455i | ||||||
\(554\) | −9.59757e6 | + | 9.52325e6i | −1.32858 | + | 1.31829i | ||||
\(555\) | 2.59769e6 | + | 2.59769e6i | 0.357976 | + | 0.357976i | ||||
\(556\) | −600341. | − | 609747.i | −0.0823589 | − | 0.0836494i | ||||
\(557\) | −2.36995e6 | + | 2.36995e6i | −0.323669 | + | 0.323669i | −0.850173 | − | 0.526504i | \(-0.823503\pi\) |
0.526504 | + | 0.850173i | \(0.323503\pi\) | |||||||
\(558\) | −309112. | − | 1201.46i | −0.0420271 | − | 0.000163352i | ||||
\(559\) | −6.45835e6 | −0.874162 | ||||||||
\(560\) | 2.24867e6 | − | 2.17981e6i | 0.303008 | − | 0.293730i | ||||
\(561\) | 9.28292e6 | 1.24531 | ||||||||
\(562\) | −7.61521e6 | − | 29598.9i | −1.01705 | − | 0.00395307i | ||||
\(563\) | 6.69440e6 | − | 6.69440e6i | 0.890104 | − | 0.890104i | −0.104429 | − | 0.994532i | \(-0.533301\pi\) |
0.994532 | + | 0.104429i | \(0.0333014\pi\) | |||||||
\(564\) | 2.85157e6 | − | 2.80757e6i | 0.377473 | − | 0.371650i | ||||
\(565\) | −1.27973e6 | − | 1.27973e6i | −0.168654 | − | 0.168654i | ||||
\(566\) | −5.36420e6 | + | 5.32266e6i | −0.703824 | + | 0.698374i | ||||
\(567\) | 5.53959e6i | 0.723636i | ||||||||
\(568\) | −2.32479e6 | − | 27109.2i | −0.302352 | − | 0.00352571i | ||||
\(569\) | − | 6.90268e6i | − | 0.893793i | −0.894586 | − | 0.446897i | \(-0.852529\pi\) | ||
0.894586 | − | 0.446897i | \(-0.147471\pi\) | |||||||
\(570\) | 4.13109e6 | + | 4.16333e6i | 0.532571 | + | 0.536727i | ||||
\(571\) | −6.09499e6 | − | 6.09499e6i | −0.782317 | − | 0.782317i | 0.197904 | − | 0.980221i | \(-0.436586\pi\) |
−0.980221 | + | 0.197904i | \(0.936586\pi\) | |||||||
\(572\) | −7.41030e6 | − | 57605.8i | −0.946991 | − | 0.00736167i | ||||
\(573\) | −6.90056e6 | + | 6.90056e6i | −0.878006 | + | 0.878006i | ||||
\(574\) | −11069.9 | + | 2.84807e6i | −0.00140238 | + | 0.360804i | ||||
\(575\) | 2.98058e6 | 0.375951 | ||||||||
\(576\) | 36223.1 | − | 1.55297e6i | 0.00454914 | − | 0.195033i | ||||
\(577\) | −6.40682e6 | −0.801130 | −0.400565 | − | 0.916268i | \(-0.631186\pi\) | ||||
−0.400565 | + | 0.916268i | \(0.631186\pi\) | |||||||
\(578\) | −22157.8 | + | 5.70076e6i | −0.00275872 | + | 0.709763i | ||||
\(579\) | −5.66791e6 | + | 5.66791e6i | −0.702630 | + | 0.702630i | ||||
\(580\) | −2.15769e6 | − | 16773.4i | −0.266330 | − | 0.00207038i | ||||
\(581\) | −4.83142e6 | − | 4.83142e6i | −0.593792 | − | 0.593792i | ||||
\(582\) | −2.60554e6 | − | 2.62588e6i | −0.318853 | − | 0.321341i | ||||
\(583\) | − | 1.50432e7i | − | 1.83303i | ||||||
\(584\) | −5.17403e6 | − | 60333.9i | −0.627765 | − | 0.00732031i | ||||
\(585\) | 644251.i | 0.0778333i | ||||||||
\(586\) | 4.76383e6 | − | 4.72694e6i | 0.573076 | − | 0.568638i | ||||
\(587\) | −3.17862e6 | − | 3.17862e6i | −0.380754 | − | 0.380754i | 0.490620 | − | 0.871374i | \(-0.336770\pi\) |
−0.871374 | + | 0.490620i | \(0.836770\pi\) | |||||||
\(588\) | −587132. | + | 578074.i | −0.0700313 | + | 0.0689509i | ||||
\(589\) | −2.41701e6 | + | 2.41701e6i | −0.287071 | + | 0.287071i | ||||
\(590\) | 4.65149e6 | + | 18079.5i | 0.550126 | + | 0.00213824i | ||||
\(591\) | −5.14171e6 | −0.605535 | ||||||||
\(592\) | −7.48878e6 | − | 7.72533e6i | −0.878227 | − | 0.905968i | ||||
\(593\) | 6.93794e6 | 0.810203 | 0.405102 | − | 0.914272i | \(-0.367236\pi\) | ||||
0.405102 | + | 0.914272i | \(0.367236\pi\) | |||||||
\(594\) | 9.78748e6 | + | 38042.1i | 1.13816 | + | 0.00442383i | ||||
\(595\) | −3.36952e6 | + | 3.36952e6i | −0.390189 | + | 0.390189i | ||||
\(596\) | 4.68965e6 | + | 4.76314e6i | 0.540785 | + | 0.549259i | ||||
\(597\) | 799625. | + | 799625.i | 0.0918228 | + | 0.0918228i | ||||
\(598\) | −1.04099e7 | + | 1.03293e7i | −1.19040 | + | 1.18118i | ||||
\(599\) | − | 1.29586e7i | − | 1.47568i | −0.674978 | − | 0.737838i | \(-0.735847\pi\) | ||
0.674978 | − | 0.737838i | \(-0.264153\pi\) | |||||||
\(600\) | 1.13181e6 | − | 1.10572e6i | 0.128350 | − | 0.125391i | ||||
\(601\) | 3.22149e6i | 0.363806i | 0.983316 | + | 0.181903i | \(0.0582257\pi\) | ||||
−0.983316 | + | 0.181903i | \(0.941774\pi\) | |||||||
\(602\) | −5.79103e6 | − | 5.83622e6i | −0.651275 | − | 0.656357i | ||||
\(603\) | −1.84241e6 | − | 1.84241e6i | −0.206344 | − | 0.206344i | ||||
\(604\) | 21416.8 | − | 2.75502e6i | 0.00238870 | − | 0.307278i | ||||
\(605\) | 361158. | − | 361158.i | 0.0401152 | − | 0.0401152i | ||||
\(606\) | 27339.9 | − | 7.03402e6i | 0.00302424 | − | 0.778076i | ||||
\(607\) | −2.77321e6 | −0.305500 | −0.152750 | − | 0.988265i | \(-0.548813\pi\) | ||||
−0.152750 | + | 0.988265i | \(0.548813\pi\) | |||||||
\(608\) | −1.19079e7 | − | 1.23800e7i | −1.30640 | − | 1.35819i | ||||
\(609\) | −4.61469e6 | −0.504196 | ||||||||
\(610\) | 11120.8 | − | 2.86117e6i | 0.00121007 | − | 0.311328i | ||||
\(611\) | 3.43707e6 | − | 3.43707e6i | 0.372465 | − | 0.372465i | ||||
\(612\) | −18373.4 | + | 2.36352e6i | −0.00198295 | + | 0.255083i | ||||
\(613\) | 3.18104e6 | + | 3.18104e6i | 0.341915 | + | 0.341915i | 0.857087 | − | 0.515172i | \(-0.172272\pi\) |
−0.515172 | + | 0.857087i | \(0.672272\pi\) | |||||||
\(614\) | −2.94080e6 | − | 2.96375e6i | −0.314807 | − | 0.317264i | ||||
\(615\) | 1.43895e6i | 0.153411i | ||||||||
\(616\) | −6.59256e6 | − | 6.74812e6i | −0.700007 | − | 0.716525i | ||||
\(617\) | − | 2.69222e6i | − | 0.284707i | −0.989816 | − | 0.142353i | \(-0.954533\pi\) | ||
0.989816 | − | 0.142353i | \(-0.0454669\pi\) | |||||||
\(618\) | −497014. | + | 493165.i | −0.0523477 | + | 0.0519423i | ||||
\(619\) | 1.97397e6 | + | 1.97397e6i | 0.207069 | + | 0.207069i | 0.803020 | − | 0.595952i | \(-0.203225\pi\) |
−0.595952 | + | 0.803020i | \(0.703225\pi\) | |||||||
\(620\) | 646970. | + | 657108.i | 0.0675935 | + | 0.0686527i | ||||
\(621\) | 1.36958e7 | − | 1.36958e7i | 1.42515 | − | 1.42515i | ||||
\(622\) | 7.32148e6 | + | 28457.2i | 0.758792 | + | 0.00294928i | ||||
\(623\) | 1.18983e7 | 1.22818 | ||||||||
\(624\) | −121031. | + | 7.78410e6i | −0.0124432 | + | 0.800289i | ||||
\(625\) | −390625. | −0.0400000 | ||||||||
\(626\) | −1.39079e7 | − | 54057.5i | −1.41849 | − | 0.00551341i | ||||
\(627\) | 1.24928e7 | − | 1.24928e7i | 1.26909 | − | 1.26909i | ||||
\(628\) | 4.55529e6 | − | 4.48502e6i | 0.460911 | − | 0.453801i | ||||
\(629\) | 1.15760e7 | + | 1.15760e7i | 1.16663 | + | 1.16663i | ||||
\(630\) | −582190. | + | 577682.i | −0.0584405 | + | 0.0579879i | ||||
\(631\) | − | 7.74739e6i | − | 0.774608i | −0.921952 | − | 0.387304i | \(-0.873406\pi\) | ||
0.921952 | − | 0.387304i | \(-0.126594\pi\) | |||||||
\(632\) | −107134. | + | 9.18748e6i | −0.0106693 | + | 0.914963i | ||||
\(633\) | 1.02890e7i | 1.02062i | ||||||||
\(634\) | 1.05954e7 | + | 1.06781e7i | 1.04688 | + | 1.05505i | ||||
\(635\) | −2.17260e6 | − | 2.17260e6i | −0.213818 | − | 0.213818i | ||||
\(636\) | −1.58030e7 | − | 122848.i | −1.54916 | − | 0.0120428i | ||||
\(637\) | −707687. | + | 707687.i | −0.0691023 | + | 0.0691023i | ||||
\(638\) | −25263.5 | + | 6.49981e6i | −0.00245721 | + | 0.632192i | ||||
\(639\) | 608865. | 0.0589887 | ||||||||
\(640\) | −3.36473e6 | + | 3.18644e6i | −0.324713 | + | 0.307508i | ||||
\(641\) | 1.28304e7 | 1.23337 | 0.616687 | − | 0.787209i | \(-0.288475\pi\) | ||||
0.616687 | + | 0.787209i | \(0.288475\pi\) | |||||||
\(642\) | −51827.8 | + | 1.33343e7i | −0.00496279 | + | 1.27683i | ||||
\(643\) | 4.34386e6 | − | 4.34386e6i | 0.414332 | − | 0.414332i | −0.468912 | − | 0.883245i | \(-0.655354\pi\) |
0.883245 | + | 0.468912i | \(0.155354\pi\) | |||||||
\(644\) | −1.86685e7 | − | 145124.i | −1.77376 | − | 0.0137887i | ||||
\(645\) | −2.93725e6 | − | 2.93725e6i | −0.277998 | − | 0.277998i | ||||
\(646\) | 1.84093e7 | + | 1.85530e7i | 1.73563 | + | 1.74917i | ||||
\(647\) | 4.82724e6i | 0.453355i | 0.973970 | + | 0.226678i | \(0.0727863\pi\) | ||||
−0.973970 | + | 0.226678i | \(0.927214\pi\) | |||||||
\(648\) | 95577.2 | − | 8.19637e6i | 0.00894163 | − | 0.766804i | ||||
\(649\) | − | 1.40119e7i | − | 1.30582i | ||||||
\(650\) | 1.36428e6 | − | 1.35372e6i | 0.126655 | − | 0.125674i | ||||
\(651\) | 1.39453e6 | + | 1.39453e6i | 0.128966 | + | 0.128966i | ||||
\(652\) | 9.15234e6 | − | 9.01114e6i | 0.843166 | − | 0.830158i | ||||
\(653\) | 4.17503e6 | − | 4.17503e6i | 0.383157 | − | 0.383157i | −0.489081 | − | 0.872238i | \(-0.662668\pi\) |
0.872238 | + | 0.489081i | \(0.162668\pi\) | |||||||
\(654\) | 1.32233e7 | + | 51396.7i | 1.20892 | + | 0.00469884i | ||||
\(655\) | 2.65551e6 | 0.241849 | ||||||||
\(656\) | 65518.1 | − | 4.21381e6i | 0.00594431 | − | 0.382310i | ||||
\(657\) | 1.35508e6 | 0.122476 | ||||||||
\(658\) | 6.18791e6 | + | 24051.3i | 0.557159 | + | 0.00216558i | ||||
\(659\) | −1.12655e7 | + | 1.12655e7i | −1.01051 | + | 1.01051i | −0.0105615 | + | 0.999944i | \(0.503362\pi\) |
−0.999944 | + | 0.0105615i | \(0.996638\pi\) | |||||||
\(660\) | −3.34400e6 | − | 3.39640e6i | −0.298818 | − | 0.303500i | ||||
\(661\) | 6.22807e6 | + | 6.22807e6i | 0.554434 | + | 0.554434i | 0.927717 | − | 0.373284i | \(-0.121768\pi\) |
−0.373284 | + | 0.927717i | \(0.621768\pi\) | |||||||
\(662\) | 1.16918e7 | − | 1.16013e7i | 1.03690 | − | 1.02887i | ||||
\(663\) | − | 1.18455e7i | − | 1.04657i | ||||||
\(664\) | 7.06520e6 | + | 7.23192e6i | 0.621877 | + | 0.636551i | ||||
\(665\) | 9.06929e6i | 0.795278i | ||||||||
\(666\) | 1.98464e6 | + | 2.00013e6i | 0.173379 | + | 0.174732i | ||||
\(667\) | 9.09533e6 | + | 9.09533e6i | 0.791597 | + | 0.791597i | ||||
\(668\) | −3847.65 | + | 494955.i | −0.000333622 | + | 0.0429165i | ||||
\(669\) | −1.24956e6 | + | 1.24956e6i | −0.107942 | + | 0.107942i | ||||
\(670\) | −30211.7 | + | 7.77286e6i | −0.00260009 | + | 0.668950i | ||||
\(671\) | −8.61880e6 | −0.738994 | ||||||||
\(672\) | −7.14279e6 | + | 6.87042e6i | −0.610161 | + | 0.586895i | ||||
\(673\) | −5.79021e6 | −0.492784 | −0.246392 | − | 0.969170i | \(-0.579245\pi\) | ||||
−0.246392 | + | 0.969170i | \(0.579245\pi\) | |||||||
\(674\) | 5639.59 | − | 1.45095e6i | 0.000478187 | − | 0.123028i | ||||
\(675\) | −1.79493e6 | + | 1.79493e6i | −0.151631 | + | 0.151631i | ||||
\(676\) | 18852.2 | − | 2.42511e6i | 0.00158670 | − | 0.204110i | ||||
\(677\) | −1.96617e6 | − | 1.96617e6i | −0.164873 | − | 0.164873i | 0.619849 | − | 0.784721i | \(-0.287194\pi\) |
−0.784721 | + | 0.619849i | \(0.787194\pi\) | |||||||
\(678\) | 4.03399e6 | + | 4.06547e6i | 0.337024 | + | 0.339654i | ||||
\(679\) | − | 5.72014e6i | − | 0.476137i | ||||||
\(680\) | 5.04367e6 | − | 4.92739e6i | 0.418287 | − | 0.408644i | ||||
\(681\) | 1.81700e7i | 1.50137i | ||||||||
\(682\) | 1.97183e6 | − | 1.95656e6i | 0.162333 | − | 0.161076i | ||||
\(683\) | −554999. | − | 554999.i | −0.0455240 | − | 0.0455240i | 0.683978 | − | 0.729502i | \(-0.260248\pi\) |
−0.729502 | + | 0.683978i | \(0.760248\pi\) | |||||||
\(684\) | 3.15606e6 | + | 3.20552e6i | 0.257932 | + | 0.261974i | ||||
\(685\) | −1.30258e6 | + | 1.30258e6i | −0.106067 | + | 0.106067i | ||||
\(686\) | −1.29050e7 | − | 50159.3i | −1.04700 | − | 0.00406950i | ||||
\(687\) | −6.88046e6 | −0.556193 | ||||||||
\(688\) | 8.46770e6 | + | 8.73517e6i | 0.682015 | + | 0.703559i | ||||
\(689\) | −1.91959e7 | −1.54049 | ||||||||
\(690\) | −9.43214e6 | − | 36661.0i | −0.754202 | − | 0.00293144i | ||||
\(691\) | −1.32042e7 | + | 1.32042e7i | −1.05200 | + | 1.05200i | −0.0534279 | + | 0.998572i | \(0.517015\pi\) |
−0.998572 | + | 0.0534279i | \(0.982985\pi\) | |||||||
\(692\) | 1.39756e7 | − | 1.37600e7i | 1.10944 | − | 1.09233i | ||||
\(693\) | 1.74697e6 | + | 1.74697e6i | 0.138182 | + | 0.138182i | ||||
\(694\) | 1.69138e6 | − | 1.67828e6i | 0.133304 | − | 0.132271i | ||||
\(695\) | − | 668506.i | − | 0.0524980i | ||||||
\(696\) | 6.82789e6 | + | 79619.4i | 0.534273 | + | 0.00623011i | ||||
\(697\) | 6.41236e6i | 0.499961i | ||||||||
\(698\) | −5.99536e6 | − | 6.04215e6i | −0.465776 | − | 0.469411i | ||||
\(699\) | 7.20112e6 | + | 7.20112e6i | 0.557452 | + | 0.557452i | ||||
\(700\) | 2.44663e6 | + | 19019.5i | 0.188722 | + | 0.00146708i | ||||
\(701\) | −1.03528e7 | + | 1.03528e7i | −0.795723 | + | 0.795723i | −0.982418 | − | 0.186695i | \(-0.940222\pi\) |
0.186695 | + | 0.982418i | \(0.440222\pi\) | |||||||
\(702\) | 48543.6 | − | 1.24893e7i | 0.00371783 | − | 0.956523i | ||||
\(703\) | 3.11577e7 | 2.37781 | ||||||||
\(704\) | 9.63791e6 | + | 1.00983e7i | 0.732911 | + | 0.767917i | ||||
\(705\) | 3.12636e6 | 0.236900 | ||||||||
\(706\) | −59792.1 | + | 1.53833e7i | −0.00451473 | + | 1.16155i | ||||
\(707\) | 7.69114e6 | − | 7.69114e6i | 0.578685 | − | 0.578685i | ||||
\(708\) | −1.47196e7 | − | 114426.i | −1.10360 | − | 0.00857911i | ||||
\(709\) | −2.20601e6 | − | 2.20601e6i | −0.164813 | − | 0.164813i | 0.619882 | − | 0.784695i | \(-0.287181\pi\) |
−0.784695 | + | 0.619882i | \(0.787181\pi\) | |||||||
\(710\) | −1.27936e6 | − | 1.28935e6i | −0.0952464 | − | 0.0959897i | ||||
\(711\) | − | 2.40621e6i | − | 0.178508i | ||||||
\(712\) | −1.76046e7 | − | 205286.i | −1.30145 | − | 0.0151761i | ||||
\(713\) | − | 5.49708e6i | − | 0.404957i | ||||||
\(714\) | 1.07044e7 | − | 1.06215e7i | 0.785808 | − | 0.779723i | ||||
\(715\) | −4.09377e6 | − | 4.09377e6i | −0.299474 | − | 0.299474i | ||||
\(716\) | −6.35741e6 | + | 6.25933e6i | −0.463444 | + | 0.456294i | ||||
\(717\) | 2.01181e6 | − | 2.01181e6i | 0.146147 | − | 0.146147i | ||||
\(718\) | −1.09226e7 | − | 42454.2i | −0.790708 | − | 0.00307333i | ||||
\(719\) | −7.60007e6 | −0.548271 | −0.274136 | − | 0.961691i | \(-0.588392\pi\) | ||||
−0.274136 | + | 0.961691i | \(0.588392\pi\) | |||||||
\(720\) | 871375. | − | 844693.i | 0.0626432 | − | 0.0607250i | ||||
\(721\) | −1.08268e6 | −0.0775645 | ||||||||
\(722\) | 3.57365e7 | + | 138901.i | 2.55134 | + | 0.00991660i | ||||
\(723\) | −1.29915e6 | + | 1.29915e6i | −0.0924301 | + | 0.0924301i | ||||
\(724\) | 2.74359e6 | + | 2.78658e6i | 0.194524 | + | 0.197572i | ||||
\(725\) | −1.19200e6 | − | 1.19200e6i | −0.0842235 | − | 0.0842235i | ||||
\(726\) | −1.14734e6 | + | 1.13845e6i | −0.0807886 | + | 0.0801630i | ||||
\(727\) | 1.18770e7i | 0.833432i | 0.909037 | + | 0.416716i | \(0.136819\pi\) | ||||
−0.909037 | + | 0.416716i | \(0.863181\pi\) | |||||||
\(728\) | −8.61093e6 | + | 8.41243e6i | −0.602174 | + | 0.588292i | ||||
\(729\) | 1.59494e7i | 1.11154i | ||||||||
\(730\) | −2.84734e6 | − | 2.86956e6i | −0.197757 | − | 0.199300i | ||||
\(731\) | −1.30892e7 | − | 1.30892e7i | −0.905985 | − | 0.905985i | ||||
\(732\) | −70384.4 | + | 9.05412e6i | −0.00485511 | + | 0.624552i | ||||
\(733\) | −1.72162e7 | + | 1.72162e7i | −1.18352 | + | 1.18352i | −0.204698 | + | 0.978825i | \(0.565621\pi\) |
−0.978825 | + | 0.204698i | \(0.934379\pi\) | |||||||
\(734\) | 93825.2 | − | 2.41394e7i | 0.00642805 | − | 1.65381i | ||||
\(735\) | −643711. | −0.0439514 | ||||||||
\(736\) | 2.76194e7 | + | 536821.i | 1.87940 | + | 0.0365288i | ||||
\(737\) | 2.34145e7 | 1.58787 | ||||||||
\(738\) | −4289.68 | + | 1.10365e6i | −0.000289924 | + | 0.0745916i | ||||
\(739\) | 7.02153e6 | − | 7.02153e6i | 0.472956 | − | 0.472956i | −0.429914 | − | 0.902870i | \(-0.641456\pi\) |
0.902870 | + | 0.429914i | \(0.141456\pi\) | |||||||
\(740\) | 65341.8 | − | 8.40545e6i | 0.00438644 | − | 0.564263i | ||||
\(741\) | −1.59414e7 | − | 1.59414e7i | −1.06655 | − | 1.06655i | ||||
\(742\) | −1.72124e7 | − | 1.73467e7i | −1.14771 | − | 1.15667i | ||||
\(743\) | − | 3.78191e6i | − | 0.251327i | −0.992073 | − | 0.125664i | \(-0.959894\pi\) | ||
0.992073 | − | 0.125664i | \(-0.0401060\pi\) | |||||||
\(744\) | −2.03928e6 | − | 2.08740e6i | −0.135065 | − | 0.138252i | ||||
\(745\) | 5.22214e6i | 0.344713i | ||||||||
\(746\) | 9.09916e6 | − | 9.02870e6i | 0.598624 | − | 0.593989i | ||||
\(747\) | −1.87221e6 | − | 1.87221e6i | −0.122759 | − | 0.122759i | ||||
\(748\) | −1.49018e7 | − | 1.51353e7i | −0.973835 | − | 0.989094i | ||||
\(749\) | −1.45800e7 | + | 1.45800e7i | −0.949624 | + | 0.949624i | ||||
\(750\) | 1.23615e6 | + | 4804.67i | 0.0802447 | + | 0.000311896i | ||||
\(751\) | 1.35554e7 | 0.877027 | 0.438514 | − | 0.898725i | \(-0.355505\pi\) | ||||
0.438514 | + | 0.898725i | \(0.355505\pi\) | |||||||
\(752\) | −9.15521e6 | − | 142349.i | −0.590369 | − | 0.00917932i | ||||
\(753\) | 9.64301e6 | 0.619762 | ||||||||
\(754\) | 8.29407e6 | + | 32237.5i | 0.531300 | + | 0.00206506i | ||||
\(755\) | 1.52199e6 | − | 1.52199e6i | 0.0971729 | − | 0.0971729i | ||||
\(756\) | 1.13297e7 | − | 1.11549e7i | 0.720967 | − | 0.709844i | ||||
\(757\) | −1.42526e7 | − | 1.42526e7i | −0.903974 | − | 0.903974i | 0.0918036 | − | 0.995777i | \(-0.470737\pi\) |
−0.995777 | + | 0.0918036i | \(0.970737\pi\) | |||||||
\(758\) | 7.51332e6 | − | 7.45514e6i | 0.474962 | − | 0.471284i | ||||
\(759\) | 2.84128e7i | 1.79023i | ||||||||
\(760\) | 156477. | − | 1.34189e7i | 0.00982688 | − | 0.842719i | ||||
\(761\) | − | 5.64585e6i | − | 0.353401i | −0.984265 | − | 0.176701i | \(-0.943458\pi\) | ||
0.984265 | − | 0.176701i | \(-0.0565424\pi\) | |||||||
\(762\) | 6.84853e6 | + | 6.90198e6i | 0.427278 | + | 0.430612i | ||||
\(763\) | 1.44587e7 | + | 1.44587e7i | 0.899118 | + | 0.899118i | ||||
\(764\) | 2.23284e7 | + | 173576.i | 1.38396 | + | 0.0107586i | ||||
\(765\) | −1.30571e6 | + | 1.30571e6i | −0.0806667 | + | 0.0806667i | ||||
\(766\) | −59278.4 | + | 1.52512e7i | −0.00365027 | + | 0.939141i | ||||
\(767\) | −1.78798e7 | −1.09743 | ||||||||
\(768\) | 1.06870e7 | − | 1.00422e7i | 0.653811 | − | 0.614365i | ||||
\(769\) | 1.87425e7 | 1.14291 | 0.571455 | − | 0.820633i | \(-0.306379\pi\) | ||||
0.571455 | + | 0.820633i | \(0.306379\pi\) | |||||||
\(770\) | 28646.6 | − | 7.37020e6i | 0.00174119 | − | 0.447974i | ||||
\(771\) | −1.88708e7 | + | 1.88708e7i | −1.14329 | + | 1.14329i | ||||
\(772\) | 1.83399e7 | + | 142570.i | 1.10753 | + | 0.00860962i | ||||
\(773\) | 5.14466e6 | + | 5.14466e6i | 0.309676 | + | 0.309676i | 0.844784 | − | 0.535108i | \(-0.179729\pi\) |
−0.535108 | + | 0.844784i | \(0.679729\pi\) | |||||||
\(774\) | −2.24407e6 | − | 2.26158e6i | −0.134643 | − | 0.135694i | ||||
\(775\) | 720430.i | 0.0430861i | ||||||||
\(776\) | −98692.2 | + | 8.46351e6i | −0.00588340 | + | 0.504540i | ||||
\(777\) | − | 1.79769e7i | − | 1.06822i | ||||||
\(778\) | −1.58718e7 | + | 1.57489e7i | −0.940108 | + | 0.932828i | ||||
\(779\) | 8.62966e6 | + | 8.62966e6i | 0.509507 | + | 0.509507i | ||||
\(780\) | −4.33397e6 | + | 4.26711e6i | −0.255064 | + | 0.251129i | ||||
\(781\) | −3.86892e6 | + | 3.86892e6i | −0.226967 | + | 0.226967i | ||||
\(782\) | −4.20323e7 | − | 163372.i | −2.45791 | − | 0.00955345i | ||||
\(783\) | −1.09546e7 | −0.638546 | ||||||||
\(784\) | 1.88504e6 | + | 29309.4i | 0.109529 | + | 0.00170301i | ||||
\(785\) | 4.99426e6 | 0.289266 | ||||||||
\(786\) | −8.40344e6 | − | 32662.6i | −0.485178 | − | 0.00188580i | ||||
\(787\) | 3.76779e6 | − | 3.76779e6i | 0.216845 | − | 0.216845i | −0.590322 | − | 0.807168i | \(-0.700999\pi\) |
0.807168 | + | 0.590322i | \(0.200999\pi\) | |||||||
\(788\) | 8.25396e6 | + | 8.38329e6i | 0.473529 | + | 0.480949i | ||||
\(789\) | −4.79136e6 | − | 4.79136e6i | −0.274010 | − | 0.274010i | ||||
\(790\) | −5.09545e6 | + | 5.05599e6i | −0.290479 | + | 0.288230i | ||||
\(791\) | 8.85612e6i | 0.503271i | ||||||||
\(792\) | −2.55467e6 | − | 2.61495e6i | −0.144718 | − | 0.148132i | ||||
\(793\) | 1.09980e7i | 0.621057i | ||||||||
\(794\) | 1.40329e7 | + | 1.41424e7i | 0.789941 | + | 0.796106i | ||||
\(795\) | −8.73026e6 | − | 8.73026e6i | −0.489902 | − | 0.489902i | ||||
\(796\) | 20113.6 | − | 2.58738e6i | 0.00112514 | − | 0.144736i | ||||
\(797\) | −1.12687e7 | + | 1.12687e7i | −0.628388 | + | 0.628388i | −0.947662 | − | 0.319274i | \(-0.896561\pi\) |
0.319274 | + | 0.947662i | \(0.396561\pi\) | |||||||
\(798\) | 111552. | − | 2.87001e7i | 0.00620111 | − | 1.59542i | ||||
\(799\) | 1.39319e7 | 0.772049 | ||||||||
\(800\) | −3.61970e6 | − | 70354.1i | −0.199962 | − | 0.00388655i | ||||
\(801\) | 4.61066e6 | 0.253911 | ||||||||
\(802\) | 98557.1 | − | 2.53568e7i | 0.00541068 | − | 1.39206i | ||||
\(803\) | −8.61062e6 | + | 8.61062e6i | −0.471244 | + | 0.471244i | ||||
\(804\) | 191212. | − | 2.45971e7i | 0.0104322 | − | 1.34197i | ||||
\(805\) | −1.03133e7 | − | 1.03133e7i | −0.560929 | − | 0.560929i | ||||
\(806\) | −2.49666e6 | − | 2.51615e6i | −0.135370 | − | 0.136426i | ||||
\(807\) | − | 1.95113e7i | − | 1.05464i | ||||||
\(808\) | −1.15125e7 | + | 1.12471e7i | −0.620356 | + | 0.606055i | ||||
\(809\) | − | 3.50449e6i | − | 0.188258i | −0.995560 | − | 0.0941291i | \(-0.969993\pi\) | ||
0.995560 | − | 0.0941291i | \(-0.0300066\pi\) | |||||||
\(810\) | 4.54577e6 | − | 4.51057e6i | 0.243442 | − | 0.241557i | ||||
\(811\) | −3.02322e6 | − | 3.02322e6i | −0.161405 | − | 0.161405i | 0.621784 | − | 0.783189i | \(-0.286408\pi\) |
−0.783189 | + | 0.621784i | \(0.786408\pi\) | |||||||
\(812\) | 7.40794e6 | + | 7.52401e6i | 0.394282 | + | 0.400460i | ||||
\(813\) | 1.21335e7 | − | 1.21335e7i | 0.643812 | − | 0.643812i | ||||
\(814\) | −2.53205e7 | − | 98415.9i | −1.33940 | − | 0.00520600i | ||||
\(815\) | 1.00343e7 | 0.529167 | ||||||||
\(816\) | −1.60215e7 | + | 1.55309e7i | −0.842319 | + | 0.816526i | ||||
\(817\) | −3.52306e7 | −1.84657 | ||||||||
\(818\) | 1.33845e7 | + | 52022.9i | 0.699387 | + | 0.00271839i | ||||
\(819\) | 2.22921e6 | − | 2.22921e6i | 0.116129 | − | 0.116129i | ||||
\(820\) | 2.34613e6 | − | 2.30994e6i | 0.121848 | − | 0.119968i | ||||
\(821\) | 247372. | + | 247372.i | 0.0128083 | + | 0.0128083i | 0.713482 | − | 0.700674i | \(-0.247117\pi\) |
−0.700674 | + | 0.713482i | \(0.747117\pi\) | |||||||
\(822\) | 4.13808e6 | − | 4.10604e6i | 0.213609 | − | 0.211955i | ||||
\(823\) | 2.01832e7i | 1.03870i | 0.854562 | + | 0.519350i | \(0.173826\pi\) | ||||
−0.854562 | + | 0.519350i | \(0.826174\pi\) | |||||||
\(824\) | 1.60193e6 | + | 18680.0i | 0.0821915 | + | 0.000958428i | ||||
\(825\) | − | 3.72369e6i | − | 0.190475i | ||||||
\(826\) | −1.60324e7 | − | 1.61575e7i | −0.817612 | − | 0.823992i | ||||
\(827\) | −1.59793e7 | − | 1.59793e7i | −0.812445 | − | 0.812445i | 0.172555 | − | 0.985000i | \(-0.444798\pi\) |
−0.985000 | + | 0.172555i | \(0.944798\pi\) | |||||||
\(828\) | −7.23418e6 | − | 56236.7i | −0.366702 | − | 0.00285065i | ||||
\(829\) | 1.10547e7 | − | 1.10547e7i | 0.558675 | − | 0.558675i | −0.370255 | − | 0.928930i | \(-0.620730\pi\) |
0.928930 | + | 0.370255i | \(0.120730\pi\) | |||||||
\(830\) | −30700.4 | + | 7.89860e6i | −0.00154685 | + | 0.397974i | ||||
\(831\) | 3.34270e7 | 1.67917 | ||||||||
\(832\) | 1.28859e7 | − | 1.22984e7i | 0.645365 | − | 0.615945i | ||||
\(833\) | −2.86856e6 | −0.143236 | ||||||||
\(834\) | −8222.59 | + | 2.11551e6i | −0.000409349 | + | 0.105317i | ||||
\(835\) | −273435. | + | 273435.i | −0.0135718 | + | 0.0135718i | ||||
\(836\) | −4.04235e7 | − | 314242.i | −2.00041 | − | 0.0155507i | ||||
\(837\) | 3.31040e6 | + | 3.31040e6i | 0.163330 | + | 0.163330i | ||||
\(838\) | −5.91252e6 | − | 5.95866e6i | −0.290846 | − | 0.293115i | ||||
\(839\) | − | 3.34841e7i | − | 1.64223i | −0.570762 | − | 0.821116i | \(-0.693352\pi\) | ||
0.570762 | − | 0.821116i | \(-0.306648\pi\) | |||||||
\(840\) | −7.74221e6 | − | 90281.3i | −0.378588 | − | 0.00441468i | ||||
\(841\) | 1.32363e7i | 0.645320i | ||||||||
\(842\) | 473134. | − | 469470.i | 0.0229987 | − | 0.0228206i | ||||
\(843\) | 1.33129e7 | + | 1.33129e7i | 0.645215 | + | 0.645215i | ||||
\(844\) | 1.67757e7 | − | 1.65169e7i | 0.810632 | − | 0.798126i | ||||
\(845\) | 1.33974e6 | − | 1.33974e6i | 0.0645473 | − | 0.0645473i | ||||
\(846\) | 2.39786e6 | + | 9320.05i | 0.115186 | + | 0.000447705i | ||||
\(847\) | −2.49933e6 | −0.119706 | ||||||||
\(848\) | 2.51681e7 | + | 2.59631e7i | 1.20188 | + | 1.23985i | ||||
\(849\) | 1.86828e7 | 0.889554 | ||||||||
\(850\) | 5.50862e6 | + | 21411.0i | 0.261514 | + | 0.00101646i | ||||
\(851\) | −3.54315e7 | + | 3.54315e7i | −1.67713 | + | 1.67713i | ||||
\(852\) | 4.03273e6 | + | 4.09592e6i | 0.190327 | + | 0.193309i | ||||
\(853\) | −1.30905e7 | − | 1.30905e7i | −0.616004 | − | 0.616004i | 0.328500 | − | 0.944504i | \(-0.393457\pi\) |
−0.944504 | + | 0.328500i | \(0.893457\pi\) | |||||||
\(854\) | −9.93858e6 | + | 9.86162e6i | −0.466315 | + | 0.462704i | ||||
\(855\) | 3.51442e6i | 0.164414i | ||||||||
\(856\) | 2.18240e7 | − | 2.13209e7i | 1.01801 | − | 0.994539i | ||||
\(857\) | − | 3.48281e7i | − | 1.61986i | −0.586525 | − | 0.809931i | \(-0.699504\pi\) | ||
0.586525 | − | 0.809931i | \(-0.300496\pi\) | |||||||
\(858\) | 1.29045e7 | + | 1.30052e7i | 0.598445 | + | 0.603115i | ||||
\(859\) | −9.28672e6 | − | 9.28672e6i | −0.429417 | − | 0.429417i | 0.459013 | − | 0.888430i | \(-0.348203\pi\) |
−0.888430 | + | 0.459013i | \(0.848203\pi\) | |||||||
\(860\) | −73883.2 | + | 9.50420e6i | −0.00340643 | + | 0.438197i | ||||
\(861\) | 4.97900e6 | − | 4.97900e6i | 0.228894 | − | 0.228894i | ||||
\(862\) | −41690.5 | + | 1.07261e7i | −0.00191104 | + | 0.491672i | ||||
\(863\) | −3.92643e7 | −1.79462 | −0.897308 | − | 0.441406i | \(-0.854480\pi\) | ||||
−0.897308 | + | 0.441406i | \(0.854480\pi\) | |||||||
\(864\) | −1.69559e7 | + | 1.63094e7i | −0.772746 | + | 0.743280i | ||||
\(865\) | 1.53223e7 | 0.696281 | ||||||||
\(866\) | 142791. | − | 3.67372e7i | 0.00647001 | − | 1.66461i | ||||
\(867\) | 9.96607e6 | − | 9.96607e6i | 0.450273 | − | 0.450273i | ||||
\(868\) | 35077.7 | − | 4.51232e6i | 0.00158027 | − | 0.203283i | ||||
\(869\) | 1.52898e7 | + | 1.52898e7i | 0.686835 | + | 0.686835i | ||||
\(870\) | 3.75748e6 | + | 3.78680e6i | 0.168305 | + | 0.169619i | ||||
\(871\) | − | 2.98781e7i | − | 1.33446i | ||||||
\(872\) | −2.11436e7 | − | 2.16425e7i | −0.941644 | − | 0.963864i | ||||
\(873\) | − | 2.21660e6i | − | 0.0984354i | ||||||
\(874\) | −5.67863e7 | + | 5.63466e7i | −2.51458 | + | 2.49511i | ||||
\(875\) | 1.35163e6 | + | 1.35163e6i | 0.0596811 | + | 0.0596811i | ||||
\(876\) | 8.97520e6 | + | 9.11583e6i | 0.395170 | + | 0.401362i | ||||
\(877\) | −1.40868e7 | + | 1.40868e7i | −0.618462 | + | 0.618462i | −0.945137 | − | 0.326675i | \(-0.894072\pi\) |
0.326675 | + | 0.945137i | \(0.394072\pi\) | |||||||
\(878\) | −1.46272e7 | − | 56853.2i | −0.640361 | − | 0.00248896i | ||||
\(879\) | −1.65918e7 | −0.724303 | ||||||||
\(880\) | −169547. | + | 1.09044e7i | −0.00738046 | + | 0.474675i | ||||
\(881\) | 4.17564e7 | 1.81252 | 0.906261 | − | 0.422718i | \(-0.138924\pi\) | ||||
0.906261 | + | 0.422718i | \(0.138924\pi\) | |||||||
\(882\) | −493715. | − | 1918.98i | −0.0213700 | − | 8.30613e-5i | ||||
\(883\) | −1.75653e7 | + | 1.75653e7i | −0.758148 | + | 0.758148i | −0.975985 | − | 0.217837i | \(-0.930100\pi\) |
0.217837 | + | 0.975985i | \(0.430100\pi\) | |||||||
\(884\) | −1.93134e7 | + | 1.90154e7i | −0.831244 | + | 0.818419i | ||||
\(885\) | −8.13173e6 | − | 8.13173e6i | −0.349000 | − | 0.349000i | ||||
\(886\) | 3.19660e6 | − | 3.17185e6i | 0.136806 | − | 0.135746i | ||||
\(887\) | 1.97380e7i | 0.842353i | 0.906979 | + | 0.421177i | \(0.138383\pi\) | ||||
−0.906979 | + | 0.421177i | \(0.861617\pi\) | |||||||
\(888\) | −310163. | + | 2.65985e7i | −0.0131995 | + | 1.13194i | ||||
\(889\) | 1.50351e7i | 0.638045i | ||||||||
\(890\) | −9.68806e6 | − | 9.76367e6i | −0.409979 | − | 0.413179i | ||||
\(891\) | −1.36404e7 | − | 1.36404e7i | −0.575616 | − | 0.575616i | ||||
\(892\) | 4.04325e6 | + | 31431.2i | 0.170145 | + | 0.00132266i | ||||
\(893\) | 1.87494e7 | − | 1.87494e7i | 0.786790 | − | 0.786790i | ||||
\(894\) | 64232.0 | − | 1.65256e7i | 0.00268787 | − | 0.691535i | ||||
\(895\) | −6.97004e6 | −0.290856 | ||||||||
\(896\) | 2.26681e7 | + | 616897.i | 0.943291 | + | 0.0256710i | ||||
\(897\) | 3.62562e7 | 1.50453 | ||||||||
\(898\) | −145709. | + | 3.74881e7i | −0.00602971 | + | 1.55133i | ||||
\(899\) | −2.19842e6 | + | 2.19842e6i | −0.0907216 | + | 0.0907216i | ||||
\(900\) | 948088. | + | 7370.20i | 0.0390160 | + | 0.000303300i | ||||
\(901\) | −3.89045e7 | − | 3.89045e7i | −1.59657 | − | 1.59657i | ||||
\(902\) | −6.98568e6 | − | 7.04019e6i | −0.285886 | − | 0.288117i | ||||
\(903\) | 2.03268e7i | 0.829562i | ||||||||
\(904\) | 152799. | − | 1.31035e7i | 0.00621869 | − | 0.533293i | ||||
\(905\) | 3.05511e6i | 0.123995i | ||||||||
\(906\) | −4.83511e6 | + | 4.79767e6i | −0.195698 | + | 0.194183i | ||||
\(907\) | 3.47142e7 | + | 3.47142e7i | 1.40116 | + | 1.40116i | 0.796424 | + | 0.604738i | \(0.206722\pi\) |
0.604738 | + | 0.796424i | \(0.293278\pi\) | |||||||
\(908\) | 2.96253e7 | − | 2.91683e7i | 1.19247 | − | 1.17407i | ||||
\(909\) | 2.98037e6 | − | 2.98037e6i | 0.119636 | − | 0.119636i | ||||
\(910\) | −9.40473e6 | − | 36554.5i | −0.376481 | − | 0.00146331i | ||||
\(911\) | 3.91881e7 | 1.56444 | 0.782220 | − | 0.623003i | \(-0.214087\pi\) | ||||
0.782220 | + | 0.623003i | \(0.214087\pi\) | |||||||
\(912\) | −660227. | + | 4.24626e7i | −0.0262849 | + | 1.69052i | ||||
\(913\) | 2.37933e7 | 0.944663 | ||||||||
\(914\) | 1.40183e7 | + | 54486.6i | 0.555048 | + | 0.00215737i | ||||
\(915\) | −5.00189e6 | + | 5.00189e6i | −0.197507 | + | 0.197507i | ||||
\(916\) | 1.10452e7 | + | 1.12182e7i | 0.434944 | + | 0.441759i | ||||
\(917\) | −9.18849e6 | − | 9.18849e6i | −0.360845 | − | 0.360845i | ||||
\(918\) | 2.54106e7 | − | 2.52139e7i | 0.995197 | − | 0.987490i | ||||
\(919\) | 1.20777e7i | 0.471732i | 0.971786 | + | 0.235866i | \(0.0757926\pi\) | ||||
−0.971786 | + | 0.235866i | \(0.924207\pi\) | |||||||
\(920\) | 1.50816e7 | + | 1.54375e7i | 0.587459 | + | 0.601321i | ||||
\(921\) | 1.03223e7i | 0.400985i | ||||||||
\(922\) | 1.62466e7 | + | 1.63734e7i | 0.629412 | + | 0.634323i | ||||
\(923\) | 4.93693e6 | + | 4.93693e6i | 0.190745 | + | 0.190745i | ||||
\(924\) | −181306. | + | 2.33229e7i | −0.00698607 | + | 0.898674i | ||||
\(925\) | 4.64354e6 | − | 4.64354e6i | 0.178441 | − | 0.178441i | ||||
\(926\) | −92123.7 | + | 2.37016e7i | −0.00353056 | + | 0.908344i | ||||
\(927\) | −419548. | −0.0160355 | ||||||||
\(928\) | −1.08310e7 | − | 1.12603e7i | −0.412854 | − | 0.429221i | ||||
\(929\) | −2.07335e7 | −0.788196 | −0.394098 | − | 0.919068i | \(-0.628943\pi\) | ||||
−0.394098 | + | 0.919068i | \(0.628943\pi\) | |||||||
\(930\) | 8861.25 | − | 2.27982e6i | 0.000335960 | − | 0.0864359i | ||||
\(931\) | −3.86046e6 | + | 3.86046e6i | −0.145971 | + | 0.145971i | ||||
\(932\) | 181136. | − | 2.33010e7i | 0.00683069 | − | 0.878687i | ||||
\(933\) | −1.27994e7 | − | 1.27994e7i | −0.481377 | − | 0.481377i | ||||
\(934\) | −7.82828e6 | − | 7.88937e6i | −0.293629 | − | 0.295921i | ||||
\(935\) | − | 1.65938e7i | − | 0.620751i | ||||||
\(936\) | −3.33680e6 | + | 3.25988e6i | −0.124492 | + | 0.121622i | ||||
\(937\) | − | 2.96264e6i | − | 0.110238i | −0.998480 | − | 0.0551188i | \(-0.982446\pi\) | ||
0.998480 | − | 0.0551188i | \(-0.0175538\pi\) | |||||||
\(938\) | 2.69999e7 | − | 2.67908e7i | 1.00197 | − | 0.994212i | ||||
\(939\) | 2.43138e7 | + | 2.43138e7i | 0.899890 | + | 0.899890i | ||||
\(940\) | −5.01873e6 | − | 5.09736e6i | −0.185257 | − | 0.188159i | ||||
\(941\) | −3.93651e6 | + | 3.93651e6i | −0.144923 | + | 0.144923i | −0.775846 | − | 0.630923i | \(-0.782676\pi\) |
0.630923 | + | 0.775846i | \(0.282676\pi\) | |||||||
\(942\) | −1.58045e7 | − | 61429.2i | −0.580302 | − | 0.00225553i | ||||
\(943\) | −1.96267e7 | −0.718735 | ||||||||
\(944\) | 2.34427e7 | + | 2.41832e7i | 0.856203 | + | 0.883249i | ||||
\(945\) | 1.24215e7 | 0.452476 | ||||||||
\(946\) | 2.86303e7 | + | 111281.i | 1.04016 | + | 0.00404289i | ||||
\(947\) | 3.98729e6 | − | 3.98729e6i | 0.144478 | − | 0.144478i | −0.631168 | − | 0.775646i | \(-0.717424\pi\) |
0.775646 | + | 0.631168i | \(0.217424\pi\) | |||||||
\(948\) | 1.61869e7 | − | 1.59372e7i | 0.584982 | − | 0.575958i | ||||
\(949\) | 1.09876e7 | + | 1.09876e7i | 0.396037 | + | 0.396037i | ||||
\(950\) | 7.44223e6 | − | 7.38460e6i | 0.267543 | − | 0.265471i | ||||
\(951\) | − | 3.71905e7i | − | 1.33346i | ||||||
\(952\) | −3.45015e7 | − | 402319.i | −1.23380 | − | 0.0143873i | ||||
\(953\) | − | 2.98015e7i | − | 1.06293i | −0.847079 | − | 0.531467i | \(-0.821641\pi\) | ||
0.847079 | − | 0.531467i | \(-0.178359\pi\) | |||||||
\(954\) | −6.66993e6 | − | 6.72199e6i | −0.237274 | − | 0.239126i | ||||
\(955\) | 1.23352e7 | + | 1.23352e7i | 0.437661 | + | 0.437661i | ||||
\(956\) | −6.50970e6 | − | 50604.7i | −0.230365 | − | 0.00179080i | ||||
\(957\) | 1.13630e7 | − | 1.13630e7i | 0.401062 | − | 0.401062i | ||||
\(958\) | 66202.2 | − | 1.70325e7i | 0.00233055 | − | 0.599604i | ||||
\(959\) | 9.01429e6 | 0.316508 | ||||||||
\(960\) | 1.14538e7 | + | 267160.i | 0.401118 | + | 0.00935607i | ||||
\(961\) | −2.73005e7 | −0.953590 | ||||||||
\(962\) | −125584. | + | 3.23101e7i | −0.00437517 | + | 1.12564i | ||||
\(963\) | −5.64985e6 | + | 5.64985e6i | −0.196323 | + | 0.196323i | ||||
\(964\) | 4.20371e6 | + | 32678.6i | 0.145694 | + | 0.00113258i | ||||
\(965\) | 1.01318e7 | + | 1.01318e7i | 0.350241 | + | 0.350241i | ||||
\(966\) | 3.25099e7 | + | 3.27636e7i | 1.12092 | + | 1.12966i | ||||
\(967\) | 1.00777e7i | 0.346574i | 0.984871 | + | 0.173287i | \(0.0554388\pi\) | ||||
−0.984871 | + | 0.173287i | \(0.944561\pi\) | |||||||
\(968\) | 3.69800e6 | + | 43122.1i | 0.126847 | + | 0.00147915i | ||||
\(969\) | − | 6.46175e7i | − | 2.21076i | ||||||
\(970\) | −4.69393e6 | + | 4.65758e6i | −0.160180 | + | 0.158939i | ||||
\(971\) | 1.87643e7 | + | 1.87643e7i | 0.638683 | + | 0.638683i | 0.950231 | − | 0.311548i | \(-0.100847\pi\) |
−0.311548 | + | 0.950231i | \(0.600847\pi\) | |||||||
\(972\) | 8.06404e6 | − | 7.93963e6i | 0.273771 | − | 0.269547i | ||||
\(973\) | −2.31314e6 | + | 2.31314e6i | −0.0783285 | + | 0.0783285i | ||||
\(974\) | −9.81002e6 | − | 38129.7i | −0.331339 | − | 0.00128785i | ||||
\(975\) | −4.75161e6 | −0.160077 | ||||||||
\(976\) | 1.48753e7 | − | 1.44198e7i | 0.499850 | − | 0.484544i | ||||
\(977\) | 2.26099e6 | 0.0757812 | 0.0378906 | − | 0.999282i | \(-0.487936\pi\) | ||||
0.0378906 | + | 0.999282i | \(0.487936\pi\) | |||||||
\(978\) | −3.17539e7 | − | 123421.i | −1.06157 | − | 0.00412613i | ||||
\(979\) | −2.92976e7 | + | 2.92976e7i | −0.976957 | + | 0.976957i | ||||
\(980\) | 1.03335e6 | + | 1.04954e6i | 0.0343701 | + | 0.0349086i | ||||
\(981\) | 5.60284e6 | + | 5.60284e6i | 0.185881 | + | 0.185881i | ||||
\(982\) | −1.50896e7 | + | 1.49728e7i | −0.499343 | + | 0.495477i | ||||
\(983\) | − | 3.91938e7i | − | 1.29370i | −0.762618 | − | 0.646849i | \(-0.776086\pi\) | ||
0.762618 | − | 0.646849i | \(-0.223914\pi\) | |||||||
\(984\) | −7.45282e6 | + | 7.28101e6i | −0.245376 | + | 0.239720i | ||||
\(985\) | 9.19115e6i | 0.301842i | ||||||||
\(986\) | 1.67444e7 | + | 1.68751e7i | 0.548501 | + | 0.552781i | ||||
\(987\) | −1.08177e7 | − | 1.08177e7i | −0.353462 | − | 0.353462i | ||||
\(988\) | −400988. | + | 5.15824e7i | −0.0130689 | + | 1.68116i | ||||
\(989\) | 4.00631e7 | − | 4.00631e7i | 1.30243 | − | 1.30243i | ||||
\(990\) | 11100.8 | − | 2.85601e6i | 0.000359969 | − | 0.0926129i | ||||
\(991\) | 5.81615e7 | 1.88127 | 0.940635 | − | 0.339420i | \(-0.110231\pi\) | ||||
0.940635 | + | 0.339420i | \(0.110231\pi\) | |||||||
\(992\) | −129754. | + | 6.67582e6i | −0.00418641 | + | 0.215390i | ||||
\(993\) | −4.07210e7 | −1.31052 | ||||||||
\(994\) | −34546.7 | + | 8.88817e6i | −0.00110902 | + | 0.285329i | ||||
\(995\) | 1.42938e6 | − | 1.42938e6i | 0.0457710 | − | 0.0457710i | ||||
\(996\) | 194305. | − | 2.49950e7i | 0.00620633 | − | 0.798371i | ||||
\(997\) | 4.33030e7 | + | 4.33030e7i | 1.37969 | + | 1.37969i | 0.845139 | + | 0.534546i | \(0.179517\pi\) |
0.534546 | + | 0.845139i | \(0.320483\pi\) | |||||||
\(998\) | 4.11878e7 | + | 4.15092e7i | 1.30901 | + | 1.31922i | ||||
\(999\) | − | 4.26744e7i | − | 1.35286i |
(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 | 80.6.l.a.21.20 | ✓ | 80 | |
4.3 | odd | 2 | 320.6.l.a.241.11 | 80 | |||
16.3 | odd | 4 | 320.6.l.a.81.11 | 80 | |||
16.13 | even | 4 | inner | 80.6.l.a.61.20 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.l.a.21.20 | ✓ | 80 | 1.1 | even | 1 | trivial | |
80.6.l.a.61.20 | yes | 80 | 16.13 | even | 4 | inner | |
320.6.l.a.81.11 | 80 | 16.3 | odd | 4 | |||
320.6.l.a.241.11 | 80 | 4.3 | odd | 2 |