Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,4,Mod(11,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.b (of order \(2\), degree \(1\), 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: | \(0.708022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-0.866025 - 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.11 |
Dual form | 12.4.b.a.11.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | − | 2.23607i | −0.612372 | − | 0.790569i | ||||
\(3\) | 3.46410 | − | 3.87298i | 0.666667 | − | 0.745356i | ||||
\(4\) | −2.00000 | + | 7.74597i | −0.250000 | + | 0.968246i | ||||
\(5\) | 8.94427i | 0.800000i | 0.916515 | + | 0.400000i | \(0.130990\pi\) | ||||
−0.916515 | + | 0.400000i | \(0.869010\pi\) | |||||||
\(6\) | −14.6603 | − | 1.03776i | −0.997504 | − | 0.0706108i | ||||
\(7\) | 7.74597i | 0.418243i | 0.977890 | + | 0.209121i | \(0.0670604\pi\) | ||||
−0.977890 | + | 0.209121i | \(0.932940\pi\) | |||||||
\(8\) | 20.7846 | − | 8.94427i | 0.918559 | − | 0.395285i | ||||
\(9\) | −3.00000 | − | 26.8328i | −0.111111 | − | 0.993808i | ||||
\(10\) | 20.0000 | − | 15.4919i | 0.632456 | − | 0.489898i | ||||
\(11\) | −34.6410 | −0.949514 | −0.474757 | − | 0.880117i | \(-0.657464\pi\) | ||||
−0.474757 | + | 0.880117i | \(0.657464\pi\) | |||||||
\(12\) | 23.0718 | + | 34.5788i | 0.555021 | + | 0.831836i | ||||
\(13\) | −10.0000 | −0.213346 | −0.106673 | − | 0.994294i | \(-0.534020\pi\) | ||||
−0.106673 | + | 0.994294i | \(0.534020\pi\) | |||||||
\(14\) | 17.3205 | − | 13.4164i | 0.330650 | − | 0.256120i | ||||
\(15\) | 34.6410 | + | 30.9839i | 0.596285 | + | 0.533333i | ||||
\(16\) | −56.0000 | − | 30.9839i | −0.875000 | − | 0.484123i | ||||
\(17\) | 35.7771i | 0.510425i | 0.966885 | + | 0.255212i | \(0.0821454\pi\) | ||||
−0.966885 | + | 0.255212i | \(0.917855\pi\) | |||||||
\(18\) | −54.8038 | + | 53.1840i | −0.717633 | + | 0.696422i | ||||
\(19\) | − | 69.7137i | − | 0.841759i | −0.907117 | − | 0.420879i | \(-0.861722\pi\) | ||
0.907117 | − | 0.420879i | \(-0.138278\pi\) | |||||||
\(20\) | −69.2820 | − | 17.8885i | −0.774597 | − | 0.200000i | ||||
\(21\) | 30.0000 | + | 26.8328i | 0.311740 | + | 0.278829i | ||||
\(22\) | 60.0000 | + | 77.4597i | 0.581456 | + | 0.750657i | ||||
\(23\) | 96.9948 | 0.879340 | 0.439670 | − | 0.898159i | \(-0.355095\pi\) | ||||
0.439670 | + | 0.898159i | \(0.355095\pi\) | |||||||
\(24\) | 37.3590 | − | 111.482i | 0.317745 | − | 0.948176i | ||||
\(25\) | 45.0000 | 0.360000 | ||||||||
\(26\) | 17.3205 | + | 22.3607i | 0.130647 | + | 0.168665i | ||||
\(27\) | −114.315 | − | 81.3327i | −0.814815 | − | 0.579721i | ||||
\(28\) | −60.0000 | − | 15.4919i | −0.404962 | − | 0.104561i | ||||
\(29\) | − | 152.053i | − | 0.973637i | −0.873503 | − | 0.486818i | \(-0.838157\pi\) | ||
0.873503 | − | 0.486818i | \(-0.161843\pi\) | |||||||
\(30\) | 9.28203 | − | 131.125i | 0.0564886 | − | 0.798003i | ||||
\(31\) | 224.633i | 1.30146i | 0.759309 | + | 0.650730i | \(0.225537\pi\) | ||||
−0.759309 | + | 0.650730i | \(0.774463\pi\) | |||||||
\(32\) | 27.7128 | + | 178.885i | 0.153093 | + | 0.988212i | ||||
\(33\) | −120.000 | + | 134.164i | −0.633010 | + | 0.707726i | ||||
\(34\) | 80.0000 | − | 61.9677i | 0.403526 | − | 0.312570i | ||||
\(35\) | −69.2820 | −0.334594 | ||||||||
\(36\) | 213.846 | + | 30.4277i | 0.990028 | + | 0.140869i | ||||
\(37\) | −130.000 | −0.577618 | −0.288809 | − | 0.957387i | \(-0.593259\pi\) | ||||
−0.288809 | + | 0.957387i | \(0.593259\pi\) | |||||||
\(38\) | −155.885 | + | 120.748i | −0.665469 | + | 0.515470i | ||||
\(39\) | −34.6410 | + | 38.7298i | −0.142231 | + | 0.159019i | ||||
\(40\) | 80.0000 | + | 185.903i | 0.316228 | + | 0.734847i | ||||
\(41\) | − | 125.220i | − | 0.476977i | −0.971145 | − | 0.238488i | \(-0.923348\pi\) | ||
0.971145 | − | 0.238488i | \(-0.0766519\pi\) | |||||||
\(42\) | 8.03848 | − | 113.558i | 0.0295325 | − | 0.417199i | ||||
\(43\) | − | 224.633i | − | 0.796656i | −0.917243 | − | 0.398328i | \(-0.869591\pi\) | ||
0.917243 | − | 0.398328i | \(-0.130409\pi\) | |||||||
\(44\) | 69.2820 | − | 268.328i | 0.237379 | − | 0.919363i | ||||
\(45\) | 240.000 | − | 26.8328i | 0.795046 | − | 0.0888889i | ||||
\(46\) | −168.000 | − | 216.887i | −0.538484 | − | 0.695179i | ||||
\(47\) | 193.990 | 0.602049 | 0.301025 | − | 0.953616i | \(-0.402671\pi\) | ||||
0.301025 | + | 0.953616i | \(0.402671\pi\) | |||||||
\(48\) | −313.990 | + | 109.556i | −0.944177 | + | 0.329438i | ||||
\(49\) | 283.000 | 0.825073 | ||||||||
\(50\) | −77.9423 | − | 100.623i | −0.220454 | − | 0.284605i | ||||
\(51\) | 138.564 | + | 123.935i | 0.380448 | + | 0.340283i | ||||
\(52\) | 20.0000 | − | 77.4597i | 0.0533366 | − | 0.206572i | ||||
\(53\) | 545.601i | 1.41404i | 0.707195 | + | 0.707019i | \(0.249960\pi\) | ||||
−0.707195 | + | 0.707019i | \(0.750040\pi\) | |||||||
\(54\) | 16.1347 | + | 396.489i | 0.0406602 | + | 0.999173i | ||||
\(55\) | − | 309.839i | − | 0.759612i | ||||||
\(56\) | 69.2820 | + | 160.997i | 0.165325 | + | 0.384181i | ||||
\(57\) | −270.000 | − | 241.495i | −0.627410 | − | 0.561173i | ||||
\(58\) | −340.000 | + | 263.363i | −0.769727 | + | 0.596228i | ||||
\(59\) | −173.205 | −0.382193 | −0.191096 | − | 0.981571i | \(-0.561204\pi\) | ||||
−0.191096 | + | 0.981571i | \(0.561204\pi\) | |||||||
\(60\) | −309.282 | + | 206.360i | −0.665469 | + | 0.444017i | ||||
\(61\) | −442.000 | −0.927743 | −0.463871 | − | 0.885903i | \(-0.653540\pi\) | ||||
−0.463871 | + | 0.885903i | \(0.653540\pi\) | |||||||
\(62\) | 502.295 | − | 389.076i | 1.02890 | − | 0.796979i | ||||
\(63\) | 207.846 | − | 23.2379i | 0.415653 | − | 0.0464714i | ||||
\(64\) | 352.000 | − | 371.806i | 0.687500 | − | 0.726184i | ||||
\(65\) | − | 89.4427i | − | 0.170677i | ||||||
\(66\) | 507.846 | + | 35.9492i | 0.947144 | + | 0.0670460i | ||||
\(67\) | 735.867i | 1.34180i | 0.741549 | + | 0.670899i | \(0.234092\pi\) | ||||
−0.741549 | + | 0.670899i | \(0.765908\pi\) | |||||||
\(68\) | −277.128 | − | 71.5542i | −0.494217 | − | 0.127606i | ||||
\(69\) | 336.000 | − | 375.659i | 0.586227 | − | 0.655421i | ||||
\(70\) | 120.000 | + | 154.919i | 0.204896 | + | 0.264520i | ||||
\(71\) | −1039.23 | −1.73710 | −0.868549 | − | 0.495603i | \(-0.834947\pi\) | ||||
−0.868549 | + | 0.495603i | \(0.834947\pi\) | |||||||
\(72\) | −302.354 | − | 530.877i | −0.494899 | − | 0.868950i | ||||
\(73\) | 410.000 | 0.657354 | 0.328677 | − | 0.944442i | \(-0.393397\pi\) | ||||
0.328677 | + | 0.944442i | \(0.393397\pi\) | |||||||
\(74\) | 225.167 | + | 290.689i | 0.353717 | + | 0.456647i | ||||
\(75\) | 155.885 | − | 174.284i | 0.240000 | − | 0.268328i | ||||
\(76\) | 540.000 | + | 139.427i | 0.815030 | + | 0.210440i | ||||
\(77\) | − | 268.328i | − | 0.397128i | ||||||
\(78\) | 146.603 | + | 10.3776i | 0.212814 | + | 0.0150646i | ||||
\(79\) | − | 85.2056i | − | 0.121347i | −0.998158 | − | 0.0606733i | \(-0.980675\pi\) | ||
0.998158 | − | 0.0606733i | \(-0.0193248\pi\) | |||||||
\(80\) | 277.128 | − | 500.879i | 0.387298 | − | 0.700000i | ||||
\(81\) | −711.000 | + | 160.997i | −0.975309 | + | 0.220846i | ||||
\(82\) | −280.000 | + | 216.887i | −0.377083 | + | 0.292087i | ||||
\(83\) | 1254.00 | 1.65837 | 0.829186 | − | 0.558973i | \(-0.188804\pi\) | ||||
0.829186 | + | 0.558973i | \(0.188804\pi\) | |||||||
\(84\) | −267.846 | + | 178.713i | −0.347910 | + | 0.232134i | ||||
\(85\) | −320.000 | −0.408340 | ||||||||
\(86\) | −502.295 | + | 389.076i | −0.629812 | + | 0.487850i | ||||
\(87\) | −588.897 | − | 526.726i | −0.725706 | − | 0.649091i | ||||
\(88\) | −720.000 | + | 309.839i | −0.872185 | + | 0.375329i | ||||
\(89\) | 840.762i | 1.00135i | 0.865634 | + | 0.500677i | \(0.166916\pi\) | ||||
−0.865634 | + | 0.500677i | \(0.833084\pi\) | |||||||
\(90\) | −475.692 | − | 490.181i | −0.557137 | − | 0.574106i | ||||
\(91\) | − | 77.4597i | − | 0.0892305i | ||||||
\(92\) | −193.990 | + | 751.319i | −0.219835 | + | 0.851417i | ||||
\(93\) | 870.000 | + | 778.152i | 0.970052 | + | 0.867641i | ||||
\(94\) | −336.000 | − | 433.774i | −0.368678 | − | 0.475962i | ||||
\(95\) | 623.538 | 0.673407 | ||||||||
\(96\) | 788.820 | + | 512.346i | 0.838632 | + | 0.544699i | ||||
\(97\) | 770.000 | 0.805996 | 0.402998 | − | 0.915201i | \(-0.367968\pi\) | ||||
0.402998 | + | 0.915201i | \(0.367968\pi\) | |||||||
\(98\) | −490.170 | − | 632.807i | −0.505252 | − | 0.652277i | ||||
\(99\) | 103.923 | + | 929.516i | 0.105502 | + | 0.943635i | ||||
\(100\) | −90.0000 | + | 348.569i | −0.0900000 | + | 0.348569i | ||||
\(101\) | − | 1493.69i | − | 1.47156i | −0.677218 | − | 0.735782i | \(-0.736815\pi\) | ||
0.677218 | − | 0.735782i | \(-0.263185\pi\) | |||||||
\(102\) | 37.1281 | − | 524.501i | 0.0360415 | − | 0.509151i | ||||
\(103\) | − | 1355.54i | − | 1.29675i | −0.761319 | − | 0.648377i | \(-0.775448\pi\) | ||
0.761319 | − | 0.648377i | \(-0.224552\pi\) | |||||||
\(104\) | −207.846 | + | 89.4427i | −0.195971 | + | 0.0843325i | ||||
\(105\) | −240.000 | + | 268.328i | −0.223063 | + | 0.249392i | ||||
\(106\) | 1220.00 | − | 945.008i | 1.11790 | − | 0.865918i | ||||
\(107\) | −644.323 | −0.582141 | −0.291070 | − | 0.956702i | \(-0.594011\pi\) | ||||
−0.291070 | + | 0.956702i | \(0.594011\pi\) | |||||||
\(108\) | 858.631 | − | 722.818i | 0.765016 | − | 0.644011i | ||||
\(109\) | −1066.00 | −0.936737 | −0.468368 | − | 0.883533i | \(-0.655158\pi\) | ||||
−0.468368 | + | 0.883533i | \(0.655158\pi\) | |||||||
\(110\) | −692.820 | + | 536.656i | −0.600526 | + | 0.465165i | ||||
\(111\) | −450.333 | + | 503.488i | −0.385079 | + | 0.430531i | ||||
\(112\) | 240.000 | − | 433.774i | 0.202481 | − | 0.365963i | ||||
\(113\) | − | 1037.54i | − | 0.863745i | −0.901935 | − | 0.431872i | \(-0.857853\pi\) | ||
0.901935 | − | 0.431872i | \(-0.142147\pi\) | |||||||
\(114\) | −72.3463 | + | 1022.02i | −0.0594373 | + | 0.839658i | ||||
\(115\) | 867.548i | 0.703472i | ||||||||
\(116\) | 1177.79 | + | 304.105i | 0.942720 | + | 0.243409i | ||||
\(117\) | 30.0000 | + | 268.328i | 0.0237051 | + | 0.212025i | ||||
\(118\) | 300.000 | + | 387.298i | 0.234044 | + | 0.302150i | ||||
\(119\) | −277.128 | −0.213481 | ||||||||
\(120\) | 997.128 | + | 334.149i | 0.758541 | + | 0.254196i | ||||
\(121\) | −131.000 | −0.0984222 | ||||||||
\(122\) | 765.566 | + | 988.342i | 0.568124 | + | 0.733445i | ||||
\(123\) | −484.974 | − | 433.774i | −0.355518 | − | 0.317985i | ||||
\(124\) | −1740.00 | − | 449.266i | −1.26013 | − | 0.325365i | ||||
\(125\) | 1520.53i | 1.08800i | ||||||||
\(126\) | −411.962 | − | 424.509i | −0.291273 | − | 0.300145i | ||||
\(127\) | 1835.79i | 1.28268i | 0.767257 | + | 0.641340i | \(0.221621\pi\) | ||||
−0.767257 | + | 0.641340i | \(0.778379\pi\) | |||||||
\(128\) | −1441.07 | − | 143.108i | −0.995105 | − | 0.0988212i | ||||
\(129\) | −870.000 | − | 778.152i | −0.593792 | − | 0.531104i | ||||
\(130\) | −200.000 | + | 154.919i | −0.134932 | + | 0.104518i | ||||
\(131\) | 450.333 | 0.300350 | 0.150175 | − | 0.988659i | \(-0.452016\pi\) | ||||
0.150175 | + | 0.988659i | \(0.452016\pi\) | |||||||
\(132\) | −799.230 | − | 1197.84i | −0.527001 | − | 0.789841i | ||||
\(133\) | 540.000 | 0.352060 | ||||||||
\(134\) | 1645.45 | − | 1274.56i | 1.06078 | − | 0.821680i | ||||
\(135\) | 727.461 | − | 1022.47i | 0.463777 | − | 0.651852i | ||||
\(136\) | 320.000 | + | 743.613i | 0.201763 | + | 0.468855i | ||||
\(137\) | 89.4427i | 0.0557782i | 0.999611 | + | 0.0278891i | \(0.00887852\pi\) | ||||
−0.999611 | + | 0.0278891i | \(0.991121\pi\) | |||||||
\(138\) | −1421.97 | − | 100.658i | −0.877145 | − | 0.0620909i | ||||
\(139\) | − | 1959.73i | − | 1.19584i | −0.801555 | − | 0.597921i | \(-0.795994\pi\) | ||
0.801555 | − | 0.597921i | \(-0.204006\pi\) | |||||||
\(140\) | 138.564 | − | 536.656i | 0.0836486 | − | 0.323970i | ||||
\(141\) | 672.000 | − | 751.319i | 0.401366 | − | 0.448741i | ||||
\(142\) | 1800.00 | + | 2323.79i | 1.06375 | + | 1.37330i | ||||
\(143\) | 346.410 | 0.202575 | ||||||||
\(144\) | −663.384 | + | 1595.59i | −0.383903 | + | 0.923373i | ||||
\(145\) | 1360.00 | 0.778909 | ||||||||
\(146\) | −710.141 | − | 916.788i | −0.402546 | − | 0.519684i | ||||
\(147\) | 980.341 | − | 1096.05i | 0.550049 | − | 0.614973i | ||||
\(148\) | 260.000 | − | 1006.98i | 0.144405 | − | 0.559276i | ||||
\(149\) | 1618.91i | 0.890111i | 0.895503 | + | 0.445055i | \(0.146816\pi\) | ||||
−0.895503 | + | 0.445055i | \(0.853184\pi\) | |||||||
\(150\) | −659.711 | − | 46.6993i | −0.359101 | − | 0.0254199i | ||||
\(151\) | 565.456i | 0.304743i | 0.988323 | + | 0.152371i | \(0.0486909\pi\) | ||||
−0.988323 | + | 0.152371i | \(0.951309\pi\) | |||||||
\(152\) | −623.538 | − | 1448.97i | −0.332734 | − | 0.773205i | ||||
\(153\) | 960.000 | − | 107.331i | 0.507264 | − | 0.0567138i | ||||
\(154\) | −600.000 | + | 464.758i | −0.313957 | + | 0.243190i | ||||
\(155\) | −2009.18 | −1.04117 | ||||||||
\(156\) | −230.718 | − | 345.788i | −0.118412 | − | 0.177469i | ||||
\(157\) | −730.000 | −0.371085 | −0.185542 | − | 0.982636i | \(-0.559404\pi\) | ||||
−0.185542 | + | 0.982636i | \(0.559404\pi\) | |||||||
\(158\) | −190.526 | + | 147.580i | −0.0959329 | + | 0.0743093i | ||||
\(159\) | 2113.10 | + | 1890.02i | 1.05396 | + | 0.942692i | ||||
\(160\) | −1600.00 | + | 247.871i | −0.790569 | + | 0.122474i | ||||
\(161\) | 751.319i | 0.367778i | ||||||||
\(162\) | 1591.49 | + | 1310.99i | 0.771846 | + | 0.635809i | ||||
\(163\) | − | 255.617i | − | 0.122831i | −0.998112 | − | 0.0614155i | \(-0.980439\pi\) | ||
0.998112 | − | 0.0614155i | \(-0.0195615\pi\) | |||||||
\(164\) | 969.948 | + | 250.440i | 0.461831 | + | 0.119244i | ||||
\(165\) | −1200.00 | − | 1073.31i | −0.566181 | − | 0.506408i | ||||
\(166\) | −2172.00 | − | 2804.04i | −1.01554 | − | 1.31106i | ||||
\(167\) | 13.8564 | 0.00642060 | 0.00321030 | − | 0.999995i | \(-0.498978\pi\) | ||||
0.00321030 | + | 0.999995i | \(0.498978\pi\) | |||||||
\(168\) | 863.538 | + | 289.381i | 0.396568 | + | 0.132894i | ||||
\(169\) | −2097.00 | −0.954483 | ||||||||
\(170\) | 554.256 | + | 715.542i | 0.250056 | + | 0.322821i | ||||
\(171\) | −1870.61 | + | 209.141i | −0.836547 | + | 0.0935288i | ||||
\(172\) | 1740.00 | + | 449.266i | 0.771359 | + | 0.199164i | ||||
\(173\) | − | 1118.03i | − | 0.491344i | −0.969353 | − | 0.245672i | \(-0.920991\pi\) | ||
0.969353 | − | 0.245672i | \(-0.0790086\pi\) | |||||||
\(174\) | −157.795 | + | 2229.13i | −0.0687493 | + | 0.971206i | ||||
\(175\) | 348.569i | 0.150567i | ||||||||
\(176\) | 1939.90 | + | 1073.31i | 0.830825 | + | 0.459682i | ||||
\(177\) | −600.000 | + | 670.820i | −0.254795 | + | 0.284870i | ||||
\(178\) | 1880.00 | − | 1456.24i | 0.791640 | − | 0.613202i | ||||
\(179\) | −1351.00 | −0.564125 | −0.282063 | − | 0.959396i | \(-0.591019\pi\) | ||||
−0.282063 | + | 0.959396i | \(0.591019\pi\) | |||||||
\(180\) | −272.154 | + | 1912.70i | −0.112695 | + | 0.792023i | ||||
\(181\) | 1262.00 | 0.518253 | 0.259126 | − | 0.965843i | \(-0.416565\pi\) | ||||
0.259126 | + | 0.965843i | \(0.416565\pi\) | |||||||
\(182\) | −173.205 | + | 134.164i | −0.0705429 | + | 0.0546423i | ||||
\(183\) | −1531.13 | + | 1711.86i | −0.618495 | + | 0.691499i | ||||
\(184\) | 2016.00 | − | 867.548i | 0.807725 | − | 0.347590i | ||||
\(185\) | − | 1162.76i | − | 0.462094i | ||||||
\(186\) | 233.116 | − | 3293.18i | 0.0918972 | − | 1.29821i | ||||
\(187\) | − | 1239.35i | − | 0.484656i | ||||||
\(188\) | −387.979 | + | 1502.64i | −0.150512 | + | 0.582931i | ||||
\(189\) | 630.000 | − | 885.483i | 0.242464 | − | 0.340791i | ||||
\(190\) | −1080.00 | − | 1394.27i | −0.412376 | − | 0.532375i | ||||
\(191\) | 2771.28 | 1.04986 | 0.524929 | − | 0.851146i | \(-0.324092\pi\) | ||||
0.524929 | + | 0.851146i | \(0.324092\pi\) | |||||||
\(192\) | −220.636 | − | 2651.27i | −0.0829325 | − | 0.996555i | ||||
\(193\) | −190.000 | −0.0708627 | −0.0354313 | − | 0.999372i | \(-0.511281\pi\) | ||||
−0.0354313 | + | 0.999372i | \(0.511281\pi\) | |||||||
\(194\) | −1333.68 | − | 1721.77i | −0.493570 | − | 0.637196i | ||||
\(195\) | −346.410 | − | 309.839i | −0.127215 | − | 0.113785i | ||||
\(196\) | −566.000 | + | 2192.11i | −0.206268 | + | 0.798873i | ||||
\(197\) | − | 2137.68i | − | 0.773114i | −0.922266 | − | 0.386557i | \(-0.873664\pi\) | ||
0.922266 | − | 0.386557i | \(-0.126336\pi\) | |||||||
\(198\) | 1898.46 | − | 1842.35i | 0.681403 | − | 0.661262i | ||||
\(199\) | 255.617i | 0.0910563i | 0.998963 | + | 0.0455281i | \(0.0144971\pi\) | ||||
−0.998963 | + | 0.0455281i | \(0.985503\pi\) | |||||||
\(200\) | 935.307 | − | 402.492i | 0.330681 | − | 0.142302i | ||||
\(201\) | 2850.00 | + | 2549.12i | 1.00012 | + | 0.894532i | ||||
\(202\) | −3340.00 | + | 2587.15i | −1.16337 | + | 0.901146i | ||||
\(203\) | 1177.79 | 0.407217 | ||||||||
\(204\) | −1237.13 | + | 825.442i | −0.424590 | + | 0.283296i | ||||
\(205\) | 1120.00 | 0.381581 | ||||||||
\(206\) | −3031.09 | + | 2347.87i | −1.02517 | + | 0.794097i | ||||
\(207\) | −290.985 | − | 2602.64i | −0.0977045 | − | 0.873895i | ||||
\(208\) | 560.000 | + | 309.839i | 0.186678 | + | 0.103286i | ||||
\(209\) | 2414.95i | 0.799262i | ||||||||
\(210\) | 1015.69 | + | 71.8983i | 0.333759 | + | 0.0236260i | ||||
\(211\) | 549.964i | 0.179436i | 0.995967 | + | 0.0897181i | \(0.0285966\pi\) | ||||
−0.995967 | + | 0.0897181i | \(0.971403\pi\) | |||||||
\(212\) | −4226.20 | − | 1091.20i | −1.36914 | − | 0.353509i | ||||
\(213\) | −3600.00 | + | 4024.92i | −1.15807 | + | 1.29476i | ||||
\(214\) | 1116.00 | + | 1440.75i | 0.356487 | + | 0.460223i | ||||
\(215\) | 2009.18 | 0.637325 | ||||||||
\(216\) | −3103.46 | − | 668.000i | −0.977610 | − | 0.210424i | ||||
\(217\) | −1740.00 | −0.544327 | ||||||||
\(218\) | 1846.37 | + | 2383.65i | 0.573632 | + | 0.740555i | ||||
\(219\) | 1420.28 | − | 1587.92i | 0.438236 | − | 0.489963i | ||||
\(220\) | 2400.00 | + | 619.677i | 0.735491 | + | 0.189903i | ||||
\(221\) | − | 357.771i | − | 0.108897i | ||||||
\(222\) | 1905.83 | + | 134.909i | 0.576176 | + | 0.0407861i | ||||
\(223\) | 472.504i | 0.141889i | 0.997480 | + | 0.0709444i | \(0.0226013\pi\) | ||||
−0.997480 | + | 0.0709444i | \(0.977399\pi\) | |||||||
\(224\) | −1385.64 | + | 214.663i | −0.413313 | + | 0.0640301i | ||||
\(225\) | −135.000 | − | 1207.48i | −0.0400000 | − | 0.357771i | ||||
\(226\) | −2320.00 | + | 1797.06i | −0.682850 | + | 0.528933i | ||||
\(227\) | 505.759 | 0.147878 | 0.0739392 | − | 0.997263i | \(-0.476443\pi\) | ||||
0.0739392 | + | 0.997263i | \(0.476443\pi\) | |||||||
\(228\) | 2410.61 | − | 1608.42i | 0.700206 | − | 0.467194i | ||||
\(229\) | 4094.00 | 1.18139 | 0.590697 | − | 0.806894i | \(-0.298853\pi\) | ||||
0.590697 | + | 0.806894i | \(0.298853\pi\) | |||||||
\(230\) | 1939.90 | − | 1502.64i | 0.556144 | − | 0.430787i | ||||
\(231\) | −1039.23 | − | 929.516i | −0.296001 | − | 0.264752i | ||||
\(232\) | −1360.00 | − | 3160.35i | −0.384864 | − | 0.894342i | ||||
\(233\) | − | 5277.12i | − | 1.48376i | −0.670534 | − | 0.741879i | \(-0.733935\pi\) | ||
0.670534 | − | 0.741879i | \(-0.266065\pi\) | |||||||
\(234\) | 548.038 | − | 531.840i | 0.153104 | − | 0.148579i | ||||
\(235\) | 1735.10i | 0.481639i | ||||||||
\(236\) | 346.410 | − | 1341.64i | 0.0955482 | − | 0.370057i | ||||
\(237\) | −330.000 | − | 295.161i | −0.0904464 | − | 0.0808977i | ||||
\(238\) | 480.000 | + | 619.677i | 0.130730 | + | 0.168772i | ||||
\(239\) | −5681.13 | −1.53758 | −0.768790 | − | 0.639502i | \(-0.779141\pi\) | ||||
−0.768790 | + | 0.639502i | \(0.779141\pi\) | |||||||
\(240\) | −979.897 | − | 2808.41i | −0.263550 | − | 0.755342i | ||||
\(241\) | −1198.00 | −0.320207 | −0.160104 | − | 0.987100i | \(-0.551183\pi\) | ||||
−0.160104 | + | 0.987100i | \(0.551183\pi\) | |||||||
\(242\) | 226.899 | + | 292.925i | 0.0602711 | + | 0.0778096i | ||||
\(243\) | −1839.44 | + | 3311.40i | −0.485597 | + | 0.874183i | ||||
\(244\) | 884.000 | − | 3423.72i | 0.231936 | − | 0.898283i | ||||
\(245\) | 2531.23i | 0.660058i | ||||||||
\(246\) | −129.948 | + | 1835.75i | −0.0336797 | + | 0.475786i | ||||
\(247\) | 697.137i | 0.179586i | ||||||||
\(248\) | 2009.18 | + | 4668.91i | 0.514448 | + | 1.19547i | ||||
\(249\) | 4344.00 | − | 4856.74i | 1.10558 | − | 1.23608i | ||||
\(250\) | 3400.00 | − | 2633.63i | 0.860140 | − | 0.666261i | ||||
\(251\) | 4260.84 | 1.07148 | 0.535741 | − | 0.844382i | \(-0.320032\pi\) | ||||
0.535741 | + | 0.844382i | \(0.320032\pi\) | |||||||
\(252\) | −235.692 | + | 1656.44i | −0.0589175 | + | 0.414072i | ||||
\(253\) | −3360.00 | −0.834946 | ||||||||
\(254\) | 4104.96 | − | 3179.69i | 1.01405 | − | 0.785478i | ||||
\(255\) | −1108.51 | + | 1239.35i | −0.272226 | + | 0.304358i | ||||
\(256\) | 2176.00 | + | 3470.19i | 0.531250 | + | 0.847215i | ||||
\(257\) | 3148.38i | 0.764166i | 0.924128 | + | 0.382083i | \(0.124793\pi\) | ||||
−0.924128 | + | 0.382083i | \(0.875207\pi\) | |||||||
\(258\) | −233.116 | + | 3293.18i | −0.0562525 | + | 0.794668i | ||||
\(259\) | − | 1006.98i | − | 0.241585i | ||||||
\(260\) | 692.820 | + | 178.885i | 0.165257 | + | 0.0426692i | ||||
\(261\) | −4080.00 | + | 456.158i | −0.967608 | + | 0.108182i | ||||
\(262\) | −780.000 | − | 1006.98i | −0.183926 | − | 0.237447i | ||||
\(263\) | −4253.92 | −0.997368 | −0.498684 | − | 0.866784i | \(-0.666183\pi\) | ||||
−0.498684 | + | 0.866784i | \(0.666183\pi\) | |||||||
\(264\) | −1294.15 | + | 3861.86i | −0.301703 | + | 0.900307i | ||||
\(265\) | −4880.00 | −1.13123 | ||||||||
\(266\) | −935.307 | − | 1207.48i | −0.215592 | − | 0.278328i | ||||
\(267\) | 3256.26 | + | 2912.48i | 0.746366 | + | 0.667570i | ||||
\(268\) | −5700.00 | − | 1471.73i | −1.29919 | − | 0.335449i | ||||
\(269\) | − | 44.7214i | − | 0.0101365i | −0.999987 | − | 0.00506823i | \(-0.998387\pi\) | ||
0.999987 | − | 0.00506823i | \(-0.00161328\pi\) | |||||||
\(270\) | −3546.31 | + | 144.313i | −0.799338 | + | 0.0325281i | ||||
\(271\) | − | 8760.69i | − | 1.96374i | −0.189552 | − | 0.981871i | \(-0.560704\pi\) | ||
0.189552 | − | 0.981871i | \(-0.439296\pi\) | |||||||
\(272\) | 1108.51 | − | 2003.52i | 0.247108 | − | 0.446622i | ||||
\(273\) | −300.000 | − | 268.328i | −0.0665085 | − | 0.0594870i | ||||
\(274\) | 200.000 | − | 154.919i | 0.0440965 | − | 0.0341570i | ||||
\(275\) | −1558.85 | −0.341825 | ||||||||
\(276\) | 2237.85 | + | 3353.96i | 0.488052 | + | 0.731467i | ||||
\(277\) | 6350.00 | 1.37738 | 0.688690 | − | 0.725055i | \(-0.258186\pi\) | ||||
0.688690 | + | 0.725055i | \(0.258186\pi\) | |||||||
\(278\) | −4382.09 | + | 3394.35i | −0.945396 | + | 0.732301i | ||||
\(279\) | 6027.54 | − | 673.899i | 1.29340 | − | 0.144607i | ||||
\(280\) | −1440.00 | + | 619.677i | −0.307344 | + | 0.132260i | ||||
\(281\) | 5563.34i | 1.18107i | 0.807012 | + | 0.590535i | \(0.201083\pi\) | ||||
−0.807012 | + | 0.590535i | \(0.798917\pi\) | |||||||
\(282\) | −2843.94 | − | 201.315i | −0.600546 | − | 0.0425112i | ||||
\(283\) | 6777.72i | 1.42365i | 0.702356 | + | 0.711826i | \(0.252132\pi\) | ||||
−0.702356 | + | 0.711826i | \(0.747868\pi\) | |||||||
\(284\) | 2078.46 | − | 8049.84i | 0.434275 | − | 1.68194i | ||||
\(285\) | 2160.00 | − | 2414.95i | 0.448938 | − | 0.501928i | ||||
\(286\) | −600.000 | − | 774.597i | −0.124052 | − | 0.160150i | ||||
\(287\) | 969.948 | 0.199492 | ||||||||
\(288\) | 4716.86 | − | 1280.27i | 0.965082 | − | 0.261946i | ||||
\(289\) | 3633.00 | 0.739467 | ||||||||
\(290\) | −2355.59 | − | 3041.05i | −0.476983 | − | 0.615782i | ||||
\(291\) | 2667.36 | − | 2982.20i | 0.537331 | − | 0.600754i | ||||
\(292\) | −820.000 | + | 3175.85i | −0.164339 | + | 0.636481i | ||||
\(293\) | 652.932i | 0.130187i | 0.997879 | + | 0.0650933i | \(0.0207345\pi\) | ||||
−0.997879 | + | 0.0650933i | \(0.979265\pi\) | |||||||
\(294\) | −4148.85 | − | 293.687i | −0.823013 | − | 0.0582591i | ||||
\(295\) | − | 1549.19i | − | 0.305754i | ||||||
\(296\) | −2702.00 | + | 1162.76i | −0.530576 | + | 0.228324i | ||||
\(297\) | 3960.00 | + | 2817.45i | 0.773678 | + | 0.550454i | ||||
\(298\) | 3620.00 | − | 2804.04i | 0.703695 | − | 0.545079i | ||||
\(299\) | −969.948 | −0.187604 | ||||||||
\(300\) | 1038.23 | + | 1556.05i | 0.199808 | + | 0.299461i | ||||
\(301\) | 1740.00 | 0.333196 | ||||||||
\(302\) | 1264.40 | − | 979.398i | 0.240920 | − | 0.186616i | ||||
\(303\) | −5785.05 | − | 5174.31i | −1.09684 | − | 0.981043i | ||||
\(304\) | −2160.00 | + | 3903.97i | −0.407515 | + | 0.736539i | ||||
\(305\) | − | 3953.37i | − | 0.742194i | ||||||
\(306\) | −1902.77 | − | 1960.72i | −0.355471 | − | 0.366297i | ||||
\(307\) | − | 1556.94i | − | 0.289444i | −0.989472 | − | 0.144722i | \(-0.953771\pi\) | ||
0.989472 | − | 0.144722i | \(-0.0462287\pi\) | |||||||
\(308\) | 2078.46 | + | 536.656i | 0.384517 | + | 0.0992819i | ||||
\(309\) | −5250.00 | − | 4695.74i | −0.966544 | − | 0.864503i | ||||
\(310\) | 3480.00 | + | 4492.66i | 0.637583 | + | 0.823116i | ||||
\(311\) | 3256.26 | 0.593715 | 0.296857 | − | 0.954922i | \(-0.404061\pi\) | ||||
0.296857 | + | 0.954922i | \(0.404061\pi\) | |||||||
\(312\) | −373.590 | + | 1114.82i | −0.0677896 | + | 0.202290i | ||||
\(313\) | −7030.00 | −1.26952 | −0.634759 | − | 0.772710i | \(-0.718901\pi\) | ||||
−0.634759 | + | 0.772710i | \(0.718901\pi\) | |||||||
\(314\) | 1264.40 | + | 1632.33i | 0.227242 | + | 0.293368i | ||||
\(315\) | 207.846 | + | 1859.03i | 0.0371771 | + | 0.332522i | ||||
\(316\) | 660.000 | + | 170.411i | 0.117493 | + | 0.0303367i | ||||
\(317\) | 491.935i | 0.0871603i | 0.999050 | + | 0.0435802i | \(0.0138764\pi\) | ||||
−0.999050 | + | 0.0435802i | \(0.986124\pi\) | |||||||
\(318\) | 566.204 | − | 7998.64i | 0.0998464 | − | 1.41051i | ||||
\(319\) | 5267.26i | 0.924482i | ||||||||
\(320\) | 3325.54 | + | 3148.38i | 0.580948 | + | 0.550000i | ||||
\(321\) | −2232.00 | + | 2495.45i | −0.388094 | + | 0.433902i | ||||
\(322\) | 1680.00 | − | 1301.32i | 0.290754 | − | 0.225217i | ||||
\(323\) | 2494.15 | 0.429654 | ||||||||
\(324\) | 174.923 | − | 5829.38i | 0.0299937 | − | 0.999550i | ||||
\(325\) | −450.000 | −0.0768046 | ||||||||
\(326\) | −571.577 | + | 442.741i | −0.0971065 | + | 0.0752183i | ||||
\(327\) | −3692.73 | + | 4128.60i | −0.624491 | + | 0.698202i | ||||
\(328\) | −1120.00 | − | 2602.64i | −0.188542 | − | 0.438131i | ||||
\(329\) | 1502.64i | 0.251803i | ||||||||
\(330\) | −321.539 | + | 4542.31i | −0.0536368 | + | 0.757716i | ||||
\(331\) | 4237.04i | 0.703592i | 0.936077 | + | 0.351796i | \(0.114429\pi\) | ||||
−0.936077 | + | 0.351796i | \(0.885571\pi\) | |||||||
\(332\) | −2508.01 | + | 9713.48i | −0.414593 | + | 1.60571i | ||||
\(333\) | 390.000 | + | 3488.27i | 0.0641798 | + | 0.574041i | ||||
\(334\) | −24.0000 | − | 30.9839i | −0.00393180 | − | 0.00507593i | ||||
\(335\) | −6581.79 | −1.07344 | ||||||||
\(336\) | −848.616 | − | 2432.15i | −0.137785 | − | 0.394895i | ||||
\(337\) | 1490.00 | 0.240847 | 0.120424 | − | 0.992723i | \(-0.461575\pi\) | ||||
0.120424 | + | 0.992723i | \(0.461575\pi\) | |||||||
\(338\) | 3632.11 | + | 4689.03i | 0.584499 | + | 0.754585i | ||||
\(339\) | −4018.36 | − | 3594.13i | −0.643797 | − | 0.575830i | ||||
\(340\) | 640.000 | − | 2478.71i | 0.102085 | − | 0.395373i | ||||
\(341\) | − | 7781.52i | − | 1.23576i | ||||||
\(342\) | 3707.65 | + | 3820.58i | 0.586219 | + | 0.604074i | ||||
\(343\) | 4848.98i | 0.763324i | ||||||||
\(344\) | −2009.18 | − | 4668.91i | −0.314906 | − | 0.731775i | ||||
\(345\) | 3360.00 | + | 3005.28i | 0.524337 | + | 0.468981i | ||||
\(346\) | −2500.00 | + | 1936.49i | −0.388442 | + | 0.300886i | ||||
\(347\) | 1988.39 | 0.307616 | 0.153808 | − | 0.988101i | \(-0.450846\pi\) | ||||
0.153808 | + | 0.988101i | \(0.450846\pi\) | |||||||
\(348\) | 5257.79 | − | 3508.13i | 0.809906 | − | 0.540389i | ||||
\(349\) | −2074.00 | −0.318105 | −0.159053 | − | 0.987270i | \(-0.550844\pi\) | ||||
−0.159053 | + | 0.987270i | \(0.550844\pi\) | |||||||
\(350\) | 779.423 | − | 603.738i | 0.119034 | − | 0.0922033i | ||||
\(351\) | 1143.15 | + | 813.327i | 0.173838 | + | 0.123681i | ||||
\(352\) | −960.000 | − | 6196.77i | −0.145364 | − | 0.938321i | ||||
\(353\) | − | 8658.06i | − | 1.30544i | −0.757597 | − | 0.652722i | \(-0.773627\pi\) | ||
0.757597 | − | 0.652722i | \(-0.226373\pi\) | |||||||
\(354\) | 2539.23 | + | 179.746i | 0.381239 | + | 0.0269870i | ||||
\(355\) | − | 9295.16i | − | 1.38968i | ||||||
\(356\) | −6512.51 | − | 1681.52i | −0.969557 | − | 0.250339i | ||||
\(357\) | −960.000 | + | 1073.31i | −0.142321 | + | 0.159120i | ||||
\(358\) | 2340.00 | + | 3020.93i | 0.345455 | + | 0.445980i | ||||
\(359\) | 8106.00 | 1.19169 | 0.595847 | − | 0.803098i | \(-0.296816\pi\) | ||||
0.595847 | + | 0.803098i | \(0.296816\pi\) | |||||||
\(360\) | 4748.31 | − | 2704.33i | 0.695160 | − | 0.395919i | ||||
\(361\) | 1999.00 | 0.291442 | ||||||||
\(362\) | −2185.85 | − | 2821.92i | −0.317364 | − | 0.409715i | ||||
\(363\) | −453.797 | + | 507.361i | −0.0656148 | + | 0.0733596i | ||||
\(364\) | 600.000 | + | 154.919i | 0.0863971 | + | 0.0223076i | ||||
\(365\) | 3667.15i | 0.525884i | ||||||||
\(366\) | 6479.83 | + | 458.691i | 0.925427 | + | 0.0655087i | ||||
\(367\) | − | 7893.14i | − | 1.12267i | −0.827590 | − | 0.561333i | \(-0.810289\pi\) | ||
0.827590 | − | 0.561333i | \(-0.189711\pi\) | |||||||
\(368\) | −5431.71 | − | 3005.28i | −0.769423 | − | 0.425709i | ||||
\(369\) | −3360.00 | + | 375.659i | −0.474023 | + | 0.0529974i | ||||
\(370\) | −2600.00 | + | 2013.95i | −0.365318 | + | 0.282974i | ||||
\(371\) | −4226.20 | −0.591411 | ||||||||
\(372\) | −7767.54 | + | 5182.69i | −1.08260 | + | 0.722338i | ||||
\(373\) | 4910.00 | 0.681582 | 0.340791 | − | 0.940139i | \(-0.389305\pi\) | ||||
0.340791 | + | 0.940139i | \(0.389305\pi\) | |||||||
\(374\) | −2771.28 | + | 2146.63i | −0.383154 | + | 0.296790i | ||||
\(375\) | 5888.97 | + | 5267.26i | 0.810947 | + | 0.725333i | ||||
\(376\) | 4032.00 | − | 1735.10i | 0.553017 | − | 0.237981i | ||||
\(377\) | 1520.53i | 0.207722i | ||||||||
\(378\) | −3071.19 | + | 124.979i | −0.417897 | + | 0.0170058i | ||||
\(379\) | − | 3137.12i | − | 0.425179i | −0.977142 | − | 0.212590i | \(-0.931810\pi\) | ||
0.977142 | − | 0.212590i | \(-0.0681897\pi\) | |||||||
\(380\) | −1247.08 | + | 4829.91i | −0.168352 | + | 0.652024i | ||||
\(381\) | 7110.00 | + | 6359.38i | 0.956053 | + | 0.855120i | ||||
\(382\) | −4800.00 | − | 6196.77i | −0.642904 | − | 0.829986i | ||||
\(383\) | 6207.67 | 0.828191 | 0.414095 | − | 0.910233i | \(-0.364098\pi\) | ||||
0.414095 | + | 0.910233i | \(0.364098\pi\) | |||||||
\(384\) | −5546.26 | + | 5085.48i | −0.737060 | + | 0.675827i | ||||
\(385\) | 2400.00 | 0.317702 | ||||||||
\(386\) | 329.090 | + | 424.853i | 0.0433944 | + | 0.0560219i | ||||
\(387\) | −6027.54 | + | 673.899i | −0.791723 | + | 0.0885174i | ||||
\(388\) | −1540.00 | + | 5964.39i | −0.201499 | + | 0.780403i | ||||
\(389\) | 9454.10i | 1.23224i | 0.787652 | + | 0.616120i | \(0.211297\pi\) | ||||
−0.787652 | + | 0.616120i | \(0.788703\pi\) | |||||||
\(390\) | −92.8203 | + | 1311.25i | −0.0120516 | + | 0.170251i | ||||
\(391\) | 3470.19i | 0.448837i | ||||||||
\(392\) | 5882.04 | − | 2531.23i | 0.757878 | − | 0.326139i | ||||
\(393\) | 1560.00 | − | 1744.13i | 0.200233 | − | 0.223867i | ||||
\(394\) | −4780.00 | + | 3702.57i | −0.611200 | + | 0.473434i | ||||
\(395\) | 762.102 | 0.0970773 | ||||||||
\(396\) | −7407.85 | − | 1054.05i | −0.940046 | − | 0.133757i | ||||
\(397\) | −10570.0 | −1.33625 | −0.668127 | − | 0.744047i | \(-0.732904\pi\) | ||||
−0.668127 | + | 0.744047i | \(0.732904\pi\) | |||||||
\(398\) | 571.577 | − | 442.741i | 0.0719863 | − | 0.0557604i | ||||
\(399\) | 1870.61 | − | 2091.41i | 0.234706 | − | 0.262410i | ||||
\(400\) | −2520.00 | − | 1394.27i | −0.315000 | − | 0.174284i | ||||
\(401\) | − | 1681.52i | − | 0.209405i | −0.994504 | − | 0.104702i | \(-0.966611\pi\) | ||
0.994504 | − | 0.104702i | \(-0.0333890\pi\) | |||||||
\(402\) | 763.655 | − | 10788.0i | 0.0947454 | − | 1.33845i | ||||
\(403\) | − | 2246.33i | − | 0.277662i | ||||||
\(404\) | 11570.1 | + | 2987.39i | 1.42484 | + | 0.367891i | ||||
\(405\) | −1440.00 | − | 6359.38i | −0.176677 | − | 0.780247i | ||||
\(406\) | −2040.00 | − | 2633.63i | −0.249368 | − | 0.321933i | ||||
\(407\) | 4503.33 | 0.548457 | ||||||||
\(408\) | 3988.51 | + | 1336.60i | 0.483973 | + | 0.162185i | ||||
\(409\) | −3574.00 | −0.432085 | −0.216043 | − | 0.976384i | \(-0.569315\pi\) | ||||
−0.216043 | + | 0.976384i | \(0.569315\pi\) | |||||||
\(410\) | −1939.90 | − | 2504.40i | −0.233670 | − | 0.301667i | ||||
\(411\) | 346.410 | + | 309.839i | 0.0415746 | + | 0.0371854i | ||||
\(412\) | 10500.0 | + | 2711.09i | 1.25558 | + | 0.324189i | ||||
\(413\) | − | 1341.64i | − | 0.159849i | ||||||
\(414\) | −5315.69 | + | 5158.57i | −0.631043 | + | 0.612392i | ||||
\(415\) | 11216.2i | 1.32670i | ||||||||
\(416\) | −277.128 | − | 1788.85i | −0.0326618 | − | 0.210831i | ||||
\(417\) | −7590.00 | − | 6788.70i | −0.891328 | − | 0.797228i | ||||
\(418\) | 5400.00 | − | 4182.82i | 0.631872 | − | 0.489446i | ||||
\(419\) | −15346.0 | −1.78926 | −0.894630 | − | 0.446808i | \(-0.852561\pi\) | ||||
−0.894630 | + | 0.446808i | \(0.852561\pi\) | |||||||
\(420\) | −1598.46 | − | 2395.69i | −0.185707 | − | 0.278328i | ||||
\(421\) | 3518.00 | 0.407261 | 0.203630 | − | 0.979048i | \(-0.434726\pi\) | ||||
0.203630 | + | 0.979048i | \(0.434726\pi\) | |||||||
\(422\) | 1229.76 | − | 952.565i | 0.141857 | − | 0.109882i | ||||
\(423\) | −581.969 | − | 5205.29i | −0.0668943 | − | 0.598321i | ||||
\(424\) | 4880.00 | + | 11340.1i | 0.558948 | + | 1.29888i | ||||
\(425\) | 1609.97i | 0.183753i | ||||||||
\(426\) | 15235.4 | + | 1078.47i | 1.73276 | + | 0.122658i | ||||
\(427\) | − | 3423.72i | − | 0.388022i | ||||||
\(428\) | 1288.65 | − | 4990.90i | 0.145535 | − | 0.563655i | ||||
\(429\) | 1200.00 | − | 1341.64i | 0.135050 | − | 0.150991i | ||||
\(430\) | −3480.00 | − | 4492.66i | −0.390280 | − | 0.503850i | ||||
\(431\) | −12886.5 | −1.44018 | −0.720091 | − | 0.693879i | \(-0.755900\pi\) | ||||
−0.720091 | + | 0.693879i | \(0.755900\pi\) | |||||||
\(432\) | 3881.66 | + | 8096.56i | 0.432307 | + | 0.901727i | ||||
\(433\) | 14450.0 | 1.60375 | 0.801874 | − | 0.597493i | \(-0.203837\pi\) | ||||
0.801874 | + | 0.597493i | \(0.203837\pi\) | |||||||
\(434\) | 3013.77 | + | 3890.76i | 0.333331 | + | 0.430328i | ||||
\(435\) | 4711.18 | − | 5267.26i | 0.519273 | − | 0.580565i | ||||
\(436\) | 2132.00 | − | 8257.20i | 0.234184 | − | 0.906991i | ||||
\(437\) | − | 6761.87i | − | 0.740192i | ||||||
\(438\) | −6010.70 | − | 425.483i | −0.655714 | − | 0.0464163i | ||||
\(439\) | 15065.9i | 1.63794i | 0.573835 | + | 0.818971i | \(0.305455\pi\) | ||||
−0.573835 | + | 0.818971i | \(0.694545\pi\) | |||||||
\(440\) | −2771.28 | − | 6439.88i | −0.300263 | − | 0.697748i | ||||
\(441\) | −849.000 | − | 7593.69i | −0.0916748 | − | 0.819964i | ||||
\(442\) | −800.000 | + | 619.677i | −0.0860908 | + | 0.0666856i | ||||
\(443\) | 3041.48 | 0.326197 | 0.163098 | − | 0.986610i | \(-0.447851\pi\) | ||||
0.163098 | + | 0.986610i | \(0.447851\pi\) | |||||||
\(444\) | −2999.33 | − | 4495.24i | −0.320590 | − | 0.480484i | ||||
\(445\) | −7520.00 | −0.801084 | ||||||||
\(446\) | 1056.55 | − | 818.401i | 0.112173 | − | 0.0868888i | ||||
\(447\) | 6270.02 | + | 5608.08i | 0.663450 | + | 0.593407i | ||||
\(448\) | 2880.00 | + | 2726.58i | 0.303721 | + | 0.287542i | ||||
\(449\) | 14310.8i | 1.50416i | 0.659069 | + | 0.752082i | \(0.270951\pi\) | ||||
−0.659069 | + | 0.752082i | \(0.729049\pi\) | |||||||
\(450\) | −2466.17 | + | 2393.28i | −0.258348 | + | 0.250712i | ||||
\(451\) | 4337.74i | 0.452896i | ||||||||
\(452\) | 8036.72 | + | 2075.07i | 0.836317 | + | 0.215936i | ||||
\(453\) | 2190.00 | + | 1958.80i | 0.227142 | + | 0.203162i | ||||
\(454\) | −876.000 | − | 1130.91i | −0.0905566 | − | 0.116908i | ||||
\(455\) | 692.820 | 0.0713844 | ||||||||
\(456\) | −7771.84 | − | 2604.43i | −0.798136 | − | 0.267464i | ||||
\(457\) | −3430.00 | −0.351091 | −0.175546 | − | 0.984471i | \(-0.556169\pi\) | ||||
−0.175546 | + | 0.984471i | \(0.556169\pi\) | |||||||
\(458\) | −7091.02 | − | 9154.46i | −0.723453 | − | 0.933974i | ||||
\(459\) | 2909.85 | − | 4089.87i | 0.295904 | − | 0.415902i | ||||
\(460\) | −6720.00 | − | 1735.10i | −0.681134 | − | 0.175868i | ||||
\(461\) | − | 3908.65i | − | 0.394889i | −0.980314 | − | 0.197445i | \(-0.936736\pi\) | ||
0.980314 | − | 0.197445i | \(-0.0632642\pi\) | |||||||
\(462\) | −278.461 | + | 3933.76i | −0.0280415 | + | 0.396136i | ||||
\(463\) | − | 18179.8i | − | 1.82481i | −0.409291 | − | 0.912404i | \(-0.634224\pi\) | ||
0.409291 | − | 0.912404i | \(-0.365776\pi\) | |||||||
\(464\) | −4711.18 | + | 8514.95i | −0.471360 | + | 0.851932i | ||||
\(465\) | −6960.00 | + | 7781.52i | −0.694112 | + | 0.776041i | ||||
\(466\) | −11800.0 | + | 9140.24i | −1.17301 | + | 0.908613i | ||||
\(467\) | −1849.83 | −0.183298 | −0.0916488 | − | 0.995791i | \(-0.529214\pi\) | ||||
−0.0916488 | + | 0.995791i | \(0.529214\pi\) | |||||||
\(468\) | −2138.46 | − | 304.277i | −0.211219 | − | 0.0300539i | ||||
\(469\) | −5700.00 | −0.561197 | ||||||||
\(470\) | 3879.79 | − | 3005.28i | 0.380769 | − | 0.294943i | ||||
\(471\) | −2528.79 | + | 2827.28i | −0.247390 | + | 0.276590i | ||||
\(472\) | −3600.00 | + | 1549.19i | −0.351067 | + | 0.151075i | ||||
\(473\) | 7781.52i | 0.756437i | ||||||||
\(474\) | −88.4232 | + | 1249.14i | −0.00856838 | + | 0.121044i | ||||
\(475\) | − | 3137.12i | − | 0.303033i | ||||||
\(476\) | 554.256 | − | 2146.63i | 0.0533704 | − | 0.206703i | ||||
\(477\) | 14640.0 | − | 1636.80i | 1.40528 | − | 0.157115i | ||||
\(478\) | 9840.00 | + | 12703.4i | 0.941571 | + | 1.21556i | ||||
\(479\) | 15242.0 | 1.45392 | 0.726959 | − | 0.686681i | \(-0.240933\pi\) | ||||
0.726959 | + | 0.686681i | \(0.240933\pi\) | |||||||
\(480\) | −4582.56 | + | 7055.42i | −0.435759 | + | 0.670905i | ||||
\(481\) | 1300.00 | 0.123233 | ||||||||
\(482\) | 2075.00 | + | 2678.81i | 0.196086 | + | 0.253146i | ||||
\(483\) | 2909.85 | + | 2602.64i | 0.274125 | + | 0.245185i | ||||
\(484\) | 262.000 | − | 1014.72i | 0.0246056 | − | 0.0952969i | ||||
\(485\) | 6887.09i | 0.644797i | ||||||||
\(486\) | 10590.5 | − | 1622.41i | 0.988468 | − | 0.151428i | ||||
\(487\) | − | 9783.16i | − | 0.910302i | −0.890414 | − | 0.455151i | \(-0.849585\pi\) | ||
0.890414 | − | 0.455151i | \(-0.150415\pi\) | |||||||
\(488\) | −9186.80 | + | 3953.37i | −0.852186 | + | 0.366722i | ||||
\(489\) | −990.000 | − | 885.483i | −0.0915529 | − | 0.0818874i | ||||
\(490\) | 5660.00 | − | 4384.22i | 0.521822 | − | 0.404202i | ||||
\(491\) | 6893.56 | 0.633609 | 0.316805 | − | 0.948491i | \(-0.397390\pi\) | ||||
0.316805 | + | 0.948491i | \(0.397390\pi\) | |||||||
\(492\) | 4329.95 | − | 2889.05i | 0.396767 | − | 0.264732i | ||||
\(493\) | 5440.00 | 0.496968 | ||||||||
\(494\) | 1558.85 | − | 1207.48i | 0.141975 | − | 0.109974i | ||||
\(495\) | −8313.84 | + | 929.516i | −0.754908 | + | 0.0844013i | ||||
\(496\) | 6960.00 | − | 12579.4i | 0.630067 | − | 1.13878i | ||||
\(497\) | − | 8049.84i | − | 0.726529i | ||||||
\(498\) | −18384.0 | − | 1301.36i | −1.65423 | − | 0.117099i | ||||
\(499\) | − | 1309.07i | − | 0.117439i | −0.998275 | − | 0.0587194i | \(-0.981298\pi\) | ||
0.998275 | − | 0.0587194i | \(-0.0187017\pi\) | |||||||
\(500\) | −11777.9 | − | 3041.05i | −1.05345 | − | 0.272000i | ||||
\(501\) | 48.0000 | − | 53.6656i | 0.00428040 | − | 0.00478564i | ||||
\(502\) | −7380.00 | − | 9527.54i | −0.656146 | − | 0.847081i | ||||
\(503\) | −7939.72 | −0.703806 | −0.351903 | − | 0.936036i | \(-0.614465\pi\) | ||||
−0.351903 | + | 0.936036i | \(0.614465\pi\) | |||||||
\(504\) | 4112.15 | − | 2342.02i | 0.363432 | − | 0.206988i | ||||
\(505\) | 13360.0 | 1.17725 | ||||||||
\(506\) | 5819.69 | + | 7513.19i | 0.511298 | + | 0.660083i | ||||
\(507\) | −7264.22 | + | 8121.65i | −0.636322 | + | 0.711430i | ||||
\(508\) | −14220.0 | − | 3671.59i | −1.24195 | − | 0.320670i | ||||
\(509\) | − | 14534.4i | − | 1.26567i | −0.774285 | − | 0.632837i | \(-0.781890\pi\) | ||
0.774285 | − | 0.632837i | \(-0.218110\pi\) | |||||||
\(510\) | 4691.28 | + | 332.084i | 0.407320 | + | 0.0288332i | ||||
\(511\) | 3175.85i | 0.274934i | ||||||||
\(512\) | 3990.65 | − | 10876.2i | 0.344459 | − | 0.938801i | ||||
\(513\) | −5670.00 | + | 7969.35i | −0.487986 | + | 0.685878i | ||||
\(514\) | 7040.00 | − | 5453.16i | 0.604127 | − | 0.467954i | ||||
\(515\) | 12124.4 | 1.03740 | ||||||||
\(516\) | 7767.54 | − | 5182.69i | 0.662687 | − | 0.442161i | ||||
\(517\) | −6720.00 | −0.571654 | ||||||||
\(518\) | −2251.67 | + | 1744.13i | −0.190989 | + | 0.147940i | ||||
\(519\) | −4330.13 | − | 3872.98i | −0.366226 | − | 0.327563i | ||||
\(520\) | −800.000 | − | 1859.03i | −0.0674660 | − | 0.156777i | ||||
\(521\) | − | 9355.71i | − | 0.786720i | −0.919385 | − | 0.393360i | \(-0.871313\pi\) | ||
0.919385 | − | 0.393360i | \(-0.128687\pi\) | |||||||
\(522\) | 8086.77 | + | 8333.07i | 0.678062 | + | 0.698714i | ||||
\(523\) | 10062.0i | 0.841264i | 0.907231 | + | 0.420632i | \(0.138192\pi\) | ||||
−0.907231 | + | 0.420632i | \(0.861808\pi\) | |||||||
\(524\) | −900.666 | + | 3488.27i | −0.0750874 | + | 0.290812i | ||||
\(525\) | 1350.00 | + | 1207.48i | 0.112226 | + | 0.100378i | ||||
\(526\) | 7368.00 | + | 9512.05i | 0.610761 | + | 0.788489i | ||||
\(527\) | −8036.72 | −0.664298 | ||||||||
\(528\) | 10876.9 | − | 3795.12i | 0.896510 | − | 0.312806i | ||||
\(529\) | −2759.00 | −0.226761 | ||||||||
\(530\) | 8452.41 | + | 10912.0i | 0.692734 | + | 0.894316i | ||||
\(531\) | 519.615 | + | 4647.58i | 0.0424659 | + | 0.379826i | ||||
\(532\) | −1080.00 | + | 4182.82i | −0.0880149 | + | 0.340880i | ||||
\(533\) | 1252.20i | 0.101761i | ||||||||
\(534\) | 872.511 | − | 12325.8i | 0.0707065 | − | 0.998855i | ||||
\(535\) | − | 5763.00i | − | 0.465712i | ||||||
\(536\) | 6581.79 | + | 15294.7i | 0.530392 | + | 1.23252i | ||||
\(537\) | −4680.00 | + | 5232.40i | −0.376084 | + | 0.420474i | ||||
\(538\) | −100.000 | + | 77.4597i | −0.00801358 | + | 0.00620729i | ||||
\(539\) | −9803.41 | −0.783419 | ||||||||
\(540\) | 6465.08 | + | 7679.83i | 0.515209 | + | 0.612013i | ||||
\(541\) | −23962.0 | −1.90426 | −0.952132 | − | 0.305687i | \(-0.901114\pi\) | ||||
−0.952132 | + | 0.305687i | \(0.901114\pi\) | |||||||
\(542\) | −19589.5 | + | 15174.0i | −1.55247 | + | 1.20254i | ||||
\(543\) | 4371.70 | − | 4887.70i | 0.345502 | − | 0.386283i | ||||
\(544\) | −6400.00 | + | 991.484i | −0.504408 | + | 0.0781425i | ||||
\(545\) | − | 9534.59i | − | 0.749389i | ||||||
\(546\) | −80.3848 | + | 1135.58i | −0.00630064 | + | 0.0890078i | ||||
\(547\) | 15112.4i | 1.18128i | 0.806936 | + | 0.590639i | \(0.201124\pi\) | ||||
−0.806936 | + | 0.590639i | \(0.798876\pi\) | |||||||
\(548\) | −692.820 | − | 178.885i | −0.0540070 | − | 0.0139445i | ||||
\(549\) | 1326.00 | + | 11860.1i | 0.103083 | + | 0.921998i | ||||
\(550\) | 2700.00 | + | 3485.69i | 0.209324 | + | 0.270237i | ||||
\(551\) | −10600.2 | −0.819567 | ||||||||
\(552\) | 3623.63 | − | 10813.2i | 0.279406 | − | 0.833770i | ||||
\(553\) | 660.000 | 0.0507524 | ||||||||
\(554\) | −10998.5 | − | 14199.0i | −0.843470 | − | 1.08892i | ||||
\(555\) | −4503.33 | − | 4027.90i | −0.344425 | − | 0.308063i | ||||
\(556\) | 15180.0 | + | 3919.46i | 1.15787 | + | 0.298961i | ||||
\(557\) | 16055.0i | 1.22131i | 0.791896 | + | 0.610656i | \(0.209094\pi\) | ||||
−0.791896 | + | 0.610656i | \(0.790906\pi\) | |||||||
\(558\) | −11946.9 | − | 12310.8i | −0.906365 | − | 0.933971i | ||||
\(559\) | 2246.33i | 0.169964i | ||||||||
\(560\) | 3879.79 | + | 2146.63i | 0.292770 | + | 0.161985i | ||||
\(561\) | −4800.00 | − | 4293.25i | −0.361241 | − | 0.323104i | ||||
\(562\) | 12440.0 | − | 9635.98i | 0.933718 | − | 0.723255i | ||||
\(563\) | 25142.4 | 1.88211 | 0.941055 | − | 0.338254i | \(-0.109836\pi\) | ||||
0.941055 | + | 0.338254i | \(0.109836\pi\) | |||||||
\(564\) | 4475.69 | + | 6707.93i | 0.334150 | + | 0.500806i | ||||
\(565\) | 9280.00 | 0.690996 | ||||||||
\(566\) | 15155.4 | − | 11739.4i | 1.12550 | − | 0.871806i | ||||
\(567\) | −1247.08 | − | 5507.38i | −0.0923674 | − | 0.407916i | ||||
\(568\) | −21600.0 | + | 9295.16i | −1.59563 | + | 0.686648i | ||||
\(569\) | − | 23416.1i | − | 1.72523i | −0.505864 | − | 0.862613i | \(-0.668826\pi\) | ||
0.505864 | − | 0.862613i | \(-0.331174\pi\) | |||||||
\(570\) | −9141.23 | − | 647.085i | −0.671726 | − | 0.0475498i | ||||
\(571\) | 4918.69i | 0.360492i | 0.983622 | + | 0.180246i | \(0.0576893\pi\) | ||||
−0.983622 | + | 0.180246i | \(0.942311\pi\) | |||||||
\(572\) | −692.820 | + | 2683.28i | −0.0506438 | + | 0.196143i | ||||
\(573\) | 9600.00 | − | 10733.1i | 0.699905 | − | 0.782518i | ||||
\(574\) | −1680.00 | − | 2168.87i | −0.122163 | − | 0.157712i | ||||
\(575\) | 4364.77 | 0.316562 | ||||||||
\(576\) | −11032.6 | − | 8329.73i | −0.798077 | − | 0.602556i | ||||
\(577\) | 19490.0 | 1.40620 | 0.703102 | − | 0.711089i | \(-0.251798\pi\) | ||||
0.703102 | + | 0.711089i | \(0.251798\pi\) | |||||||
\(578\) | −6292.54 | − | 8123.63i | −0.452829 | − | 0.584600i | ||||
\(579\) | −658.179 | + | 735.867i | −0.0472418 | + | 0.0528179i | ||||
\(580\) | −2720.00 | + | 10534.5i | −0.194727 | + | 0.754176i | ||||
\(581\) | 9713.48i | 0.693602i | ||||||||
\(582\) | −11288.4 | − | 799.077i | −0.803985 | − | 0.0569121i | ||||
\(583\) | − | 18900.2i | − | 1.34265i | ||||||
\(584\) | 8521.69 | − | 3667.15i | 0.603819 | − | 0.259842i | ||||
\(585\) | −2400.00 | + | 268.328i | −0.169620 | + | 0.0189641i | ||||
\(586\) | 1460.00 | − | 1130.91i | 0.102922 | − | 0.0797227i | ||||
\(587\) | −1364.86 | −0.0959687 | −0.0479844 | − | 0.998848i | \(-0.515280\pi\) | ||||
−0.0479844 | + | 0.998848i | \(0.515280\pi\) | |||||||
\(588\) | 6529.32 | + | 9785.80i | 0.457933 | + | 0.686326i | ||||
\(589\) | 15660.0 | 1.09552 | ||||||||
\(590\) | −3464.10 | + | 2683.28i | −0.241720 | + | 0.187236i | ||||
\(591\) | −8279.20 | − | 7405.14i | −0.576245 | − | 0.515409i | ||||
\(592\) | 7280.00 | + | 4027.90i | 0.505416 | + | 0.279638i | ||||
\(593\) | 25795.3i | 1.78632i | 0.449743 | + | 0.893158i | \(0.351515\pi\) | ||||
−0.449743 | + | 0.893158i | \(0.648485\pi\) | |||||||
\(594\) | −558.921 | − | 13734.8i | −0.0386074 | − | 0.948729i | ||||
\(595\) | − | 2478.71i | − | 0.170785i | ||||||
\(596\) | −12540.0 | − | 3237.83i | −0.861846 | − | 0.222528i | ||||
\(597\) | 990.000 | + | 885.483i | 0.0678694 | + | 0.0607042i | ||||
\(598\) | 1680.00 | + | 2168.87i | 0.114883 | + | 0.148314i | ||||
\(599\) | 2424.87 | 0.165405 | 0.0827025 | − | 0.996574i | \(-0.473645\pi\) | ||||
0.0827025 | + | 0.996574i | \(0.473645\pi\) | |||||||
\(600\) | 1681.15 | − | 5016.70i | 0.114388 | − | 0.341343i | ||||
\(601\) | −8758.00 | −0.594420 | −0.297210 | − | 0.954812i | \(-0.596056\pi\) | ||||
−0.297210 | + | 0.954812i | \(0.596056\pi\) | |||||||
\(602\) | −3013.77 | − | 3890.76i | −0.204040 | − | 0.263414i | ||||
\(603\) | 19745.4 | − | 2207.60i | 1.33349 | − | 0.149089i | ||||
\(604\) | −4380.00 | − | 1130.91i | −0.295066 | − | 0.0761856i | ||||
\(605\) | − | 1171.70i | − | 0.0787378i | ||||||
\(606\) | −1550.10 | + | 21897.9i | −0.103908 | + | 1.46789i | ||||
\(607\) | 19558.6i | 1.30784i | 0.756565 | + | 0.653919i | \(0.226876\pi\) | ||||
−0.756565 | + | 0.653919i | \(0.773124\pi\) | |||||||
\(608\) | 12470.8 | − | 1931.96i | 0.831836 | − | 0.128867i | ||||
\(609\) | 4080.00 | − | 4561.58i | 0.271478 | − | 0.303521i | ||||
\(610\) | −8840.00 | + | 6847.43i | −0.586756 | + | 0.454499i | ||||
\(611\) | −1939.90 | −0.128445 | ||||||||
\(612\) | −1088.62 | + | 7650.79i | −0.0719031 | + | 0.505335i | ||||
\(613\) | −16450.0 | −1.08386 | −0.541932 | − | 0.840422i | \(-0.682307\pi\) | ||||
−0.541932 | + | 0.840422i | \(0.682307\pi\) | |||||||
\(614\) | −3481.42 | + | 2696.70i | −0.228825 | + | 0.177247i | ||||
\(615\) | 3879.79 | − | 4337.74i | 0.254388 | − | 0.284414i | ||||
\(616\) | −2400.00 | − | 5577.10i | −0.156978 | − | 0.364785i | ||||
\(617\) | 8461.28i | 0.552088i | 0.961145 | + | 0.276044i | \(0.0890236\pi\) | ||||
−0.961145 | + | 0.276044i | \(0.910976\pi\) | |||||||
\(618\) | −1406.73 | + | 19872.6i | −0.0915649 | + | 1.29352i | ||||
\(619\) | − | 19930.4i | − | 1.29413i | −0.762433 | − | 0.647067i | \(-0.775995\pi\) | ||
0.762433 | − | 0.647067i | \(-0.224005\pi\) | |||||||
\(620\) | 4018.36 | − | 15563.0i | 0.260292 | − | 1.00811i | ||||
\(621\) | −11088.0 | − | 7888.85i | −0.716499 | − | 0.509772i | ||||
\(622\) | −5640.00 | − | 7281.21i | −0.363575 | − | 0.469373i | ||||
\(623\) | −6512.51 | −0.418809 | ||||||||
\(624\) | 3139.90 | − | 1095.56i | 0.201437 | − | 0.0702843i | ||||
\(625\) | −7975.00 | −0.510400 | ||||||||
\(626\) | 12176.3 | + | 15719.6i | 0.777418 | + | 1.00364i | ||||
\(627\) | 9353.07 | + | 8365.64i | 0.595735 | + | 0.532842i | ||||
\(628\) | 1460.00 | − | 5654.56i | 0.0927712 | − | 0.359301i | ||||
\(629\) | − | 4651.02i | − | 0.294830i | ||||||
\(630\) | 3796.92 | − | 3684.70i | 0.240116 | − | 0.233019i | ||||
\(631\) | − | 12199.9i | − | 0.769683i | −0.922983 | − | 0.384842i | \(-0.874256\pi\) | ||
0.922983 | − | 0.384842i | \(-0.125744\pi\) | |||||||
\(632\) | −762.102 | − | 1770.97i | −0.0479665 | − | 0.111464i | ||||
\(633\) | 2130.00 | + | 1905.13i | 0.133744 | + | 0.119624i | ||||
\(634\) | 1100.00 | − | 852.056i | 0.0689063 | − | 0.0533746i | ||||
\(635\) | −16419.8 | −1.02614 | ||||||||
\(636\) | −18866.2 | + | 12588.0i | −1.17625 | + | 0.784821i | ||||
\(637\) | −2830.00 | −0.176026 | ||||||||
\(638\) | 11777.9 | − | 9123.16i | 0.730867 | − | 0.566127i | ||||
\(639\) | 3117.69 | + | 27885.5i | 0.193011 | + | 1.72634i | ||||
\(640\) | 1280.00 | − | 12889.3i | 0.0790569 | − | 0.796084i | ||||
\(641\) | 7012.31i | 0.432090i | 0.976383 | + | 0.216045i | \(0.0693158\pi\) | ||||
−0.976383 | + | 0.216045i | \(0.930684\pi\) | |||||||
\(642\) | 9445.94 | + | 668.654i | 0.580688 | + | 0.0411054i | ||||
\(643\) | 15979.9i | 0.980073i | 0.871702 | + | 0.490036i | \(0.163017\pi\) | ||||
−0.871702 | + | 0.490036i | \(0.836983\pi\) | |||||||
\(644\) | −5819.69 | − | 1502.64i | −0.356099 | − | 0.0919444i | ||||
\(645\) | 6960.00 | − | 7781.52i | 0.424883 | − | 0.475034i | ||||
\(646\) | −4320.00 | − | 5577.10i | −0.263109 | − | 0.339672i | ||||
\(647\) | −17999.5 | −1.09371 | −0.546856 | − | 0.837226i | \(-0.684176\pi\) | ||||
−0.546856 | + | 0.837226i | \(0.684176\pi\) | |||||||
\(648\) | −13337.9 | + | 9705.63i | −0.808581 | + | 0.588385i | ||||
\(649\) | 6000.00 | 0.362898 | ||||||||
\(650\) | 779.423 | + | 1006.23i | 0.0470330 | + | 0.0607194i | ||||
\(651\) | −6027.54 | + | 6738.99i | −0.362884 | + | 0.405717i | ||||
\(652\) | 1980.00 | + | 511.234i | 0.118931 | + | 0.0307078i | ||||
\(653\) | − | 5196.62i | − | 0.311423i | −0.987803 | − | 0.155712i | \(-0.950233\pi\) | ||
0.987803 | − | 0.155712i | \(-0.0497671\pi\) | |||||||
\(654\) | 15627.8 | + | 1106.26i | 0.934398 | + | 0.0661437i | ||||
\(655\) | 4027.90i | 0.240280i | ||||||||
\(656\) | −3879.79 | + | 7012.31i | −0.230915 | + | 0.417355i | ||||
\(657\) | −1230.00 | − | 11001.5i | −0.0730394 | − | 0.653284i | ||||
\(658\) | 3360.00 | − | 2602.64i | 0.199068 | − | 0.154197i | ||||
\(659\) | −6062.18 | −0.358344 | −0.179172 | − | 0.983818i | \(-0.557342\pi\) | ||||
−0.179172 | + | 0.983818i | \(0.557342\pi\) | |||||||
\(660\) | 10713.8 | − | 7148.53i | 0.631872 | − | 0.421601i | ||||
\(661\) | 9422.00 | 0.554423 | 0.277211 | − | 0.960809i | \(-0.410590\pi\) | ||||
0.277211 | + | 0.960809i | \(0.410590\pi\) | |||||||
\(662\) | 9474.32 | − | 7338.78i | 0.556238 | − | 0.430860i | ||||
\(663\) | −1385.64 | − | 1239.35i | −0.0811672 | − | 0.0725981i | ||||
\(664\) | 26064.0 | − | 11216.2i | 1.52331 | − | 0.655529i | ||||
\(665\) | 4829.91i | 0.281648i | ||||||||
\(666\) | 7124.50 | − | 6913.92i | 0.414518 | − | 0.402266i | ||||
\(667\) | − | 14748.3i | − | 0.856158i | ||||||
\(668\) | −27.7128 | + | 107.331i | −0.00160515 | + | 0.00621672i | ||||
\(669\) | 1830.00 | + | 1636.80i | 0.105758 | + | 0.0945925i | ||||
\(670\) | 11400.0 | + | 14717.3i | 0.657344 | + | 0.848627i | ||||
\(671\) | 15311.3 | 0.880905 | ||||||||
\(672\) | −3968.62 | + | 6110.18i | −0.227816 | + | 0.350752i | ||||
\(673\) | −17470.0 | −1.00062 | −0.500311 | − | 0.865846i | \(-0.666781\pi\) | ||||
−0.500311 | + | 0.865846i | \(0.666781\pi\) | |||||||
\(674\) | −2580.76 | − | 3331.74i | −0.147488 | − | 0.190406i | ||||
\(675\) | −5144.19 | − | 3659.97i | −0.293333 | − | 0.208700i | ||||
\(676\) | 4194.00 | − | 16243.3i | 0.238621 | − | 0.924175i | ||||
\(677\) | − | 20813.3i | − | 1.18157i | −0.806830 | − | 0.590784i | \(-0.798819\pi\) | ||
0.806830 | − | 0.590784i | \(-0.201181\pi\) | |||||||
\(678\) | −1076.72 | + | 15210.5i | −0.0609897 | + | 0.861589i | ||||
\(679\) | 5964.39i | 0.337102i | ||||||||
\(680\) | −6651.08 | + | 2862.17i | −0.375084 | + | 0.161410i | ||||
\(681\) | 1752.00 | − | 1958.80i | 0.0985856 | − | 0.110222i | ||||
\(682\) | −17400.0 | + | 13478.0i | −0.976951 | + | 0.756743i | ||||
\(683\) | −12616.3 | −0.706805 | −0.353402 | − | 0.935471i | \(-0.614975\pi\) | ||||
−0.353402 | + | 0.935471i | \(0.614975\pi\) | |||||||
\(684\) | 2121.23 | − | 14908.0i | 0.118578 | − | 0.833365i | ||||
\(685\) | −800.000 | −0.0446225 | ||||||||
\(686\) | 10842.6 | − | 8398.67i | 0.603460 | − | 0.467438i | ||||
\(687\) | 14182.0 | − | 15856.0i | 0.787596 | − | 0.880559i | ||||
\(688\) | −6960.00 | + | 12579.4i | −0.385680 | + | 0.697074i | ||||
\(689\) | − | 5456.01i | − | 0.301680i | ||||||
\(690\) | 900.309 | − | 12718.5i | 0.0496727 | − | 0.701716i | ||||
\(691\) | 3028.67i | 0.166738i | 0.996519 | + | 0.0833691i | \(0.0265681\pi\) | ||||
−0.996519 | + | 0.0833691i | \(0.973432\pi\) | |||||||
\(692\) | 8660.25 | + | 2236.07i | 0.475742 | + | 0.122836i | ||||
\(693\) | −7200.00 | + | 804.984i | −0.394669 | + | 0.0441253i | ||||
\(694\) | −3444.00 | − | 4446.18i | −0.188375 | − | 0.243191i | ||||
\(695\) | 17528.4 | 0.956674 | ||||||||
\(696\) | −16951.2 | − | 5680.53i | −0.923179 | − | 0.309368i | ||||
\(697\) | 4480.00 | 0.243461 | ||||||||
\(698\) | 3592.27 | + | 4637.60i | 0.194799 | + | 0.251484i | ||||
\(699\) | −20438.2 | − | 18280.5i | −1.10593 | − | 0.989172i | ||||
\(700\) | −2700.00 | − | 697.137i | −0.145786 | − | 0.0376419i | ||||
\(701\) | 17664.9i | 0.951777i | 0.879506 | + | 0.475888i | \(0.157873\pi\) | ||||
−0.879506 | + | 0.475888i | \(0.842127\pi\) | |||||||
\(702\) | −161.347 | − | 3964.89i | −0.00867470 | − | 0.213170i | ||||
\(703\) | 9062.78i | 0.486215i | ||||||||
\(704\) | −12193.6 | + | 12879.8i | −0.652791 | + | 0.689523i | ||||
\(705\) | 6720.00 | + | 6010.55i | 0.358993 | + | 0.321093i | ||||
\(706\) | −19360.0 | + | 14996.2i | −1.03204 | + | 0.799418i | ||||
\(707\) | 11570.1 | 0.615472 | ||||||||
\(708\) | −3996.15 | − | 5989.22i | −0.212125 | − | 0.317922i | ||||
\(709\) | 14174.0 | 0.750798 | 0.375399 | − | 0.926863i | \(-0.377506\pi\) | ||||
0.375399 | + | 0.926863i | \(0.377506\pi\) | |||||||
\(710\) | −20784.6 | + | 16099.7i | −1.09864 | + | 0.851001i | ||||
\(711\) | −2286.31 | + | 255.617i | −0.120595 | + | 0.0134830i | ||||
\(712\) | 7520.00 | + | 17474.9i | 0.395820 | + | 0.919803i | ||||
\(713\) | 21788.2i | 1.14443i | ||||||||
\(714\) | 4062.77 | + | 287.593i | 0.212949 | + | 0.0150741i | ||||
\(715\) | 3098.39i | 0.162060i | ||||||||
\(716\) | 2702.00 | − | 10464.8i | 0.141031 | − | 0.546212i | ||||
\(717\) | −19680.0 | + | 22002.9i | −1.02505 | + | 1.14604i | ||||
\(718\) | −14040.0 | − | 18125.6i | −0.729761 | − | 0.942117i | ||||
\(719\) | 32839.7 | 1.70336 | 0.851678 | − | 0.524065i | \(-0.175585\pi\) | ||||
0.851678 | + | 0.524065i | \(0.175585\pi\) | |||||||
\(720\) | −14271.4 | − | 5933.49i | −0.738699 | − | 0.307122i | ||||
\(721\) | 10500.0 | 0.542358 | ||||||||
\(722\) | −3462.37 | − | 4469.90i | −0.178471 | − | 0.230405i | ||||
\(723\) | −4149.99 | + | 4639.83i | −0.213472 | + | 0.238668i | ||||
\(724\) | −2524.00 | + | 9775.41i | −0.129563 | + | 0.501796i | ||||
\(725\) | − | 6842.37i | − | 0.350509i | ||||||
\(726\) | 1920.49 | + | 135.947i | 0.0981766 | + | 0.00694967i | ||||
\(727\) | 8001.58i | 0.408201i | 0.978950 | + | 0.204101i | \(0.0654270\pi\) | ||||
−0.978950 | + | 0.204101i | \(0.934573\pi\) | |||||||
\(728\) | −692.820 | − | 1609.97i | −0.0352715 | − | 0.0819635i | ||||
\(729\) | 6453.00 | + | 18595.1i | 0.327846 | + | 0.944731i | ||||
\(730\) | 8200.00 | − | 6351.69i | 0.415747 | − | 0.322037i | ||||
\(731\) | 8036.72 | 0.406633 | ||||||||
\(732\) | −10197.7 | − | 15283.8i | −0.514917 | − | 0.771730i | ||||
\(733\) | 11750.0 | 0.592082 | 0.296041 | − | 0.955175i | \(-0.404333\pi\) | ||||
0.296041 | + | 0.955175i | \(0.404333\pi\) | |||||||
\(734\) | −17649.6 | + | 13671.3i | −0.887546 | + | 0.687490i | ||||
\(735\) | 9803.41 | + | 8768.43i | 0.491978 | + | 0.440039i | ||||
\(736\) | 2688.00 | + | 17351.0i | 0.134621 | + | 0.868974i | ||||
\(737\) | − | 25491.2i | − | 1.27406i | ||||||
\(738\) | 6659.69 | + | 6862.53i | 0.332177 | + | 0.342294i | ||||
\(739\) | − | 19961.4i | − | 0.993627i | −0.867857 | − | 0.496814i | \(-0.834503\pi\) | ||
0.867857 | − | 0.496814i | \(-0.165497\pi\) | |||||||
\(740\) | 9006.66 | + | 2325.51i | 0.447421 | + | 0.115524i | ||||
\(741\) | 2700.00 | + | 2414.95i | 0.133856 | + | 0.119724i | ||||
\(742\) | 7320.00 | + | 9450.08i | 0.362164 | + | 0.467552i | ||||
\(743\) | −25592.8 | −1.26367 | −0.631836 | − | 0.775102i | \(-0.717698\pi\) | ||||
−0.631836 | + | 0.775102i | \(0.717698\pi\) | |||||||
\(744\) | 25042.6 | + | 8392.06i | 1.23401 | + | 0.413532i | ||||
\(745\) | −14480.0 | −0.712089 | ||||||||
\(746\) | −8504.37 | − | 10979.1i | −0.417382 | − | 0.538838i | ||||
\(747\) | −3762.01 | − | 33648.5i | −0.184264 | − | 1.64810i | ||||
\(748\) | 9600.00 | + | 2478.71i | 0.469266 | + | 0.121164i | ||||
\(749\) | − | 4990.90i | − | 0.243476i | ||||||
\(750\) | 1577.95 | − | 22291.3i | 0.0768246 | − | 1.08528i | ||||
\(751\) | 5244.02i | 0.254803i | 0.991851 | + | 0.127401i | \(0.0406637\pi\) | ||||
−0.991851 | + | 0.127401i | \(0.959336\pi\) | |||||||
\(752\) | −10863.4 | − | 6010.55i | −0.526793 | − | 0.291466i | ||||
\(753\) | 14760.0 | − | 16502.2i | 0.714322 | − | 0.798636i | ||||
\(754\) | 3400.00 | − | 2633.63i | 0.164218 | − | 0.127203i | ||||
\(755\) | −5057.59 | −0.243794 | ||||||||
\(756\) | 5598.92 | + | 6650.92i | 0.269353 | + | 0.319963i | ||||
\(757\) | −14290.0 | −0.686102 | −0.343051 | − | 0.939317i | \(-0.611460\pi\) | ||||
−0.343051 | + | 0.939317i | \(0.611460\pi\) | |||||||
\(758\) | −7014.81 | + | 5433.65i | −0.336134 | + | 0.260368i | ||||
\(759\) | −11639.4 | + | 13013.2i | −0.556631 | + | 0.622332i | ||||
\(760\) | 12960.0 | − | 5577.10i | 0.618564 | − | 0.266188i | ||||
\(761\) | − | 16976.2i | − | 0.808657i | −0.914614 | − | 0.404328i | \(-0.867505\pi\) | ||
0.914614 | − | 0.404328i | \(-0.132495\pi\) | |||||||
\(762\) | 1905.12 | − | 26913.2i | 0.0905711 | − | 1.27948i | ||||
\(763\) | − | 8257.20i | − | 0.391783i | ||||||
\(764\) | −5542.56 | + | 21466.3i | −0.262464 | + | 1.01652i | ||||
\(765\) | 960.000 | + | 8586.50i | 0.0453711 | + | 0.405811i | ||||
\(766\) | −10752.0 | − | 13880.8i | −0.507161 | − | 0.654742i | ||||
\(767\) | 1732.05 | 0.0815394 | ||||||||
\(768\) | 20977.9 | + | 3593.49i | 0.985644 | + | 0.168840i | ||||
\(769\) | −29566.0 | −1.38645 | −0.693223 | − | 0.720723i | \(-0.743810\pi\) | ||||
−0.693223 | + | 0.720723i | \(0.743810\pi\) | |||||||
\(770\) | −4156.92 | − | 5366.56i | −0.194552 | − | 0.251166i | ||||
\(771\) | 12193.6 | + | 10906.3i | 0.569576 | + | 0.509444i | ||||
\(772\) | 380.000 | − | 1471.73i | 0.0177157 | − | 0.0686125i | ||||
\(773\) | − | 21457.3i | − | 0.998403i | −0.866486 | − | 0.499202i | \(-0.833627\pi\) | ||
0.866486 | − | 0.499202i | \(-0.166373\pi\) | |||||||
\(774\) | 11946.9 | + | 12310.8i | 0.554809 | + | 0.571707i | ||||
\(775\) | 10108.5i | 0.468526i | ||||||||
\(776\) | 16004.1 | − | 6887.09i | 0.740355 | − | 0.318598i | ||||
\(777\) | −3900.00 | − | 3488.27i | −0.180067 | − | 0.161056i | ||||
\(778\) | 21140.0 | − | 16375.0i | 0.974172 | − | 0.754590i | ||||
\(779\) | −8729.54 | −0.401499 | ||||||||
\(780\) | 3092.82 | − | 2063.60i | 0.141975 | − | 0.0947293i | ||||
\(781\) | 36000.0 | 1.64940 | ||||||||
\(782\) | 7759.59 | − | 6010.55i | 0.354837 | − | 0.274855i | ||||
\(783\) | −12366.8 | + | 17381.9i | −0.564438 | + | 0.793334i | ||||
\(784\) | −15848.0 | − | 8768.43i | −0.721939 | − | 0.399437i | ||||
\(785\) | − | 6529.32i | − | 0.296868i | ||||||
\(786\) | −6602.00 | − | 467.339i | −0.299600 | − | 0.0212079i | ||||
\(787\) | 3896.22i | 0.176474i | 0.996099 | + | 0.0882372i | \(0.0281233\pi\) | ||||
−0.996099 | + | 0.0882372i | \(0.971877\pi\) | |||||||
\(788\) | 16558.4 | + | 4275.36i | 0.748564 | + | 0.193279i | ||||
\(789\) | −14736.0 | + | 16475.3i | −0.664912 | + | 0.743394i | ||||
\(790\) | −1320.00 | − | 1704.11i | −0.0594475 | − | 0.0767463i | ||||
\(791\) | 8036.72 | 0.361255 | ||||||||
\(792\) | 10473.8 | + | 18390.1i | 0.469914 | + | 0.825081i | ||||
\(793\) | 4420.00 | 0.197930 | ||||||||
\(794\) | 18307.8 | + | 23635.2i | 0.818286 | + | 1.05640i | ||||
\(795\) | −16904.8 | + | 18900.2i | −0.754154 | + | 0.843169i | ||||
\(796\) | −1980.00 | − | 511.234i | −0.0881649 | − | 0.0227641i | ||||
\(797\) | 30759.4i | 1.36707i | 0.729919 | + | 0.683533i | \(0.239558\pi\) | ||||
−0.729919 | + | 0.683533i | \(0.760442\pi\) | |||||||
\(798\) | −7916.54 | − | 560.392i | −0.351181 | − | 0.0248592i | ||||
\(799\) | 6940.39i | 0.307301i | ||||||||
\(800\) | 1247.08 | + | 8049.84i | 0.0551135 | + | 0.355756i | ||||
\(801\) | 22560.0 | − | 2522.28i | 0.995154 | − | 0.111262i | ||||
\(802\) | −3760.00 | + | 2912.48i | −0.165549 | + | 0.128234i | ||||
\(803\) | −14202.8 | −0.624168 | ||||||||
\(804\) | −25445.4 | + | 16977.8i | −1.11616 | + | 0.744726i | ||||
\(805\) | −6720.00 | −0.294222 | ||||||||
\(806\) | −5022.95 | + | 3890.76i | −0.219511 | + | 0.170032i | ||||
\(807\) | −173.205 | − | 154.919i | −0.00755528 | − | 0.00675764i | ||||
\(808\) | −13360.0 | − | 31045.8i | −0.581687 | − | 1.35172i | ||||
\(809\) | − | 10429.0i | − | 0.453232i | −0.973984 | − | 0.226616i | \(-0.927234\pi\) | ||
0.973984 | − | 0.226616i | \(-0.0727663\pi\) | |||||||
\(810\) | −11725.8 | + | 14234.7i | −0.508647 | + | 0.617477i | ||||
\(811\) | − | 8156.50i | − | 0.353161i | −0.984286 | − | 0.176580i | \(-0.943496\pi\) | ||
0.984286 | − | 0.176580i | \(-0.0565036\pi\) | |||||||
\(812\) | −2355.59 | + | 9123.16i | −0.101804 | + | 0.394286i | ||||
\(813\) | −33930.0 | − | 30347.9i | −1.46369 | − | 1.30916i | ||||
\(814\) | −7800.00 | − | 10069.8i | −0.335860 | − | 0.433593i | ||||
\(815\) | 2286.31 | 0.0982648 | ||||||||
\(816\) | −3919.59 | − | 11233.6i | −0.168153 | − | 0.481931i | ||||
\(817\) | −15660.0 | −0.670592 | ||||||||
\(818\) | 6190.35 | + | 7991.71i | 0.264597 | + | 0.341593i | ||||
\(819\) | −2078.46 | + | 232.379i | −0.0886780 | + | 0.00991450i | ||||
\(820\) | −2240.00 | + | 8675.48i | −0.0953954 | + | 0.369465i | ||||
\(821\) | 35750.3i | 1.51972i | 0.650085 | + | 0.759861i | \(0.274733\pi\) | ||||
−0.650085 | + | 0.759861i | \(0.725267\pi\) | |||||||
\(822\) | 92.8203 | − | 1311.25i | 0.00393854 | − | 0.0556389i | ||||
\(823\) | − | 20875.4i | − | 0.884168i | −0.896974 | − | 0.442084i | \(-0.854239\pi\) | ||
0.896974 | − | 0.442084i | \(-0.145761\pi\) | |||||||
\(824\) | −12124.4 | − | 28174.5i | −0.512587 | − | 1.19115i | ||||
\(825\) | −5400.00 | + | 6037.38i | −0.227883 | + | 0.254781i | ||||
\(826\) | −3000.00 | + | 2323.79i | −0.126372 | + | 0.0978874i | ||||
\(827\) | 12907.2 | 0.542719 | 0.271360 | − | 0.962478i | \(-0.412527\pi\) | ||||
0.271360 | + | 0.962478i | \(0.412527\pi\) | |||||||
\(828\) | 20742.0 | + | 2951.33i | 0.870572 | + | 0.123872i | ||||
\(829\) | −14074.0 | −0.589638 | −0.294819 | − | 0.955553i | \(-0.595259\pi\) | ||||
−0.294819 | + | 0.955553i | \(0.595259\pi\) | |||||||
\(830\) | 25080.1 | − | 19427.0i | 1.04885 | − | 0.812433i | ||||
\(831\) | 21997.0 | − | 24593.4i | 0.918254 | − | 1.02664i | ||||
\(832\) | −3520.00 | + | 3718.06i | −0.146676 | + | 0.154929i | ||||
\(833\) | 10124.9i | 0.421138i | ||||||||
\(834\) | −2033.73 | + | 28730.1i | −0.0844394 | + | 1.19286i | ||||
\(835\) | 123.935i | 0.00513648i | ||||||||
\(836\) | −18706.1 | − | 4829.91i | −0.773882 | − | 0.199816i | ||||
\(837\) | 18270.0 | − | 25679.0i | 0.754485 | − | 1.06045i | ||||
\(838\) | 26580.0 | + | 34314.6i | 1.09569 | + | 1.41453i | ||||
\(839\) | 16697.0 | 0.687060 | 0.343530 | − | 0.939142i | \(-0.388377\pi\) | ||||
0.343530 | + | 0.939142i | \(0.388377\pi\) | |||||||
\(840\) | −2588.31 | + | 7723.72i | −0.106316 | + | 0.317254i | ||||
\(841\) | 1269.00 | 0.0520317 | ||||||||
\(842\) | −6093.35 | − | 7866.49i | −0.249395 | − | 0.321968i | ||||
\(843\) | 21546.7 | + | 19272.0i | 0.880318 | + | 0.787380i | ||||
\(844\) | −4260.00 | − | 1099.93i | −0.173738 | − | 0.0448591i | ||||
\(845\) | − | 18756.1i | − | 0.763587i | ||||||
\(846\) | −10631.4 | + | 10317.1i | −0.432050 | + | 0.419280i | ||||
\(847\) | − | 1014.72i | − | 0.0411644i | ||||||
\(848\) | 16904.8 | − | 30553.6i | 0.684568 | − | 1.23728i | ||||
\(849\) | 26250.0 | + | 23478.7i | 1.06113 | + | 0.949102i | ||||
\(850\) | 3600.00 | − | 2788.55i | 0.145269 | − | 0.112525i | ||||
\(851\) | −12609.3 | −0.507923 | ||||||||
\(852\) | −23976.9 | − | 35935.3i | −0.964126 | − | 1.44498i | ||||
\(853\) | 23630.0 | 0.948506 | 0.474253 | − | 0.880389i | \(-0.342718\pi\) | ||||
0.474253 | + | 0.880389i | \(0.342718\pi\) | |||||||
\(854\) | −7655.66 | + | 5930.05i | −0.306758 | + | 0.237614i | ||||
\(855\) | −1870.61 | − | 16731.3i | −0.0748230 | − | 0.669237i | ||||
\(856\) | −13392.0 | + | 5763.00i | −0.534730 | + | 0.230111i | ||||
\(857\) | 31322.8i | 1.24850i | 0.781223 | + | 0.624252i | \(0.214596\pi\) | ||||
−0.781223 | + | 0.624252i | \(0.785404\pi\) | |||||||
\(858\) | −5078.46 | − | 359.492i | −0.202070 | − | 0.0143040i | ||||
\(859\) | − | 13671.6i | − | 0.543038i | −0.962433 | − | 0.271519i | \(-0.912474\pi\) | ||
0.962433 | − | 0.271519i | \(-0.0875261\pi\) | |||||||
\(860\) | −4018.36 | + | 15563.0i | −0.159331 | + | 0.617087i | ||||
\(861\) | 3360.00 | − | 3756.59i | 0.132995 | − | 0.148693i | ||||
\(862\) | 22320.0 | + | 28815.0i | 0.881928 | + | 1.13856i | ||||
\(863\) | −25107.8 | −0.990359 | −0.495179 | − | 0.868791i | \(-0.664898\pi\) | ||||
−0.495179 | + | 0.868791i | \(0.664898\pi\) | |||||||
\(864\) | 11381.2 | − | 22703.3i | 0.448145 | − | 0.893961i | ||||
\(865\) | 10000.0 | 0.393075 | ||||||||
\(866\) | −25028.1 | − | 32311.2i | −0.982091 | − | 1.26787i | ||||
\(867\) | 12585.1 | − | 14070.5i | 0.492978 | − | 0.551166i | ||||
\(868\) | 3480.00 | − | 13478.0i | 0.136082 | − | 0.527042i | ||||
\(869\) | 2951.61i | 0.115220i | ||||||||
\(870\) | −19937.9 | − | 1411.36i | −0.776965 | − | 0.0549994i | ||||
\(871\) | − | 7358.67i | − | 0.286267i | ||||||
\(872\) | −22156.4 | + | 9534.59i | −0.860447 | + | 0.370278i | ||||
\(873\) | −2310.00 | − | 20661.3i | −0.0895552 | − | 0.801006i | ||||
\(874\) | −15120.0 | + | 11711.9i | −0.585173 | + | 0.453273i | ||||
\(875\) | −11777.9 | −0.455048 | ||||||||
\(876\) | 9459.44 | + | 14177.3i | 0.364846 | + | 0.546811i | ||||
\(877\) | 41750.0 | 1.60752 | 0.803761 | − | 0.594952i | \(-0.202829\pi\) | ||||
0.803761 | + | 0.594952i | \(0.202829\pi\) | |||||||
\(878\) | 33688.4 | − | 26094.9i | 1.29491 | − | 1.00303i | ||||
\(879\) | 2528.79 | + | 2261.82i | 0.0970354 | + | 0.0867911i | ||||
\(880\) | −9600.00 | + | 17351.0i | −0.367745 | + | 0.664660i | ||||
\(881\) | 2397.06i | 0.0916676i | 0.998949 | + | 0.0458338i | \(0.0145945\pi\) | ||||
−0.998949 | + | 0.0458338i | \(0.985406\pi\) | |||||||
\(882\) | −15509.5 | + | 15051.1i | −0.592099 | + | 0.574599i | ||||
\(883\) | 43431.6i | 1.65526i | 0.561277 | + | 0.827628i | \(0.310310\pi\) | ||||
−0.561277 | + | 0.827628i | \(0.689690\pi\) | |||||||
\(884\) | 2771.28 | + | 715.542i | 0.105439 | + | 0.0272243i | ||||
\(885\) | −6000.00 | − | 5366.56i | −0.227896 | − | 0.203836i | ||||
\(886\) | −5268.00 | − | 6800.96i | −0.199754 | − | 0.257881i | ||||
\(887\) | −6387.80 | −0.241805 | −0.120903 | − | 0.992664i | \(-0.538579\pi\) | ||||
−0.120903 | + | 0.992664i | \(0.538579\pi\) | |||||||
\(888\) | −4856.67 | + | 14492.7i | −0.183535 | + | 0.547684i | ||||
\(889\) | −14220.0 | −0.536472 | ||||||||
\(890\) | 13025.0 | + | 16815.2i | 0.490561 | + | 0.633312i | ||||
\(891\) | 24629.8 | − | 5577.10i | 0.926070 | − | 0.209697i | ||||
\(892\) | −3660.00 | − | 945.008i | −0.137383 | − | 0.0354722i | ||||
\(893\) | − | 13523.7i | − | 0.506780i | ||||||
\(894\) | 1680.05 | − | 23733.7i | 0.0628515 | − | 0.887889i | ||||
\(895\) | − | 12083.7i | − | 0.451300i | ||||||
\(896\) | 1108.51 | − | 11162.5i | 0.0413313 | − | 0.416196i | ||||
\(897\) | −3360.00 | + | 3756.59i | −0.125069 | + | 0.139832i | ||||
\(898\) | 32000.0 | − | 24787.1i | 1.18915 | − | 0.921109i | ||||
\(899\) | 34156.0 | 1.26715 | ||||||||
\(900\) | 9623.07 | + | 1369.25i | 0.356410 | + | 0.0507129i | ||||
\(901\) | −19520.0 | −0.721760 | ||||||||
\(902\) | 9699.48 | − | 7513.19i | 0.358046 | − | 0.277341i | ||||
\(903\) | 6027.54 | − | 6738.99i | 0.222131 | − | 0.248349i | ||||
\(904\) | −9280.00 | − | 21564.8i | −0.341425 | − | 0.793400i | ||||
\(905\) | 11287.7i | 0.414602i | ||||||||
\(906\) | 586.809 | − | 8289.72i | 0.0215181 | − | 0.303982i | ||||
\(907\) | 37327.8i | 1.36654i | 0.730167 | + | 0.683269i | \(0.239442\pi\) | ||||
−0.730167 | + | 0.683269i | \(0.760558\pi\) | |||||||
\(908\) | −1011.52 | + | 3917.59i | −0.0369696 | + | 0.143183i | ||||
\(909\) | −40080.0 | + | 4481.08i | −1.46245 | + | 0.163507i | ||||
\(910\) | −1200.00 | − | 1549.19i | −0.0437139 | − | 0.0564344i | ||||
\(911\) | −50853.0 | −1.84944 | −0.924718 | − | 0.380654i | \(-0.875699\pi\) | ||||
−0.924718 | + | 0.380654i | \(0.875699\pi\) | |||||||
\(912\) | 7637.54 | + | 21889.4i | 0.277307 | + | 0.794770i | ||||
\(913\) | −43440.0 | −1.57465 | ||||||||
\(914\) | 5940.93 | + | 7669.71i | 0.214999 | + | 0.277562i | ||||
\(915\) | −15311.3 | − | 13694.9i | −0.553199 | − | 0.494796i | ||||
\(916\) | −8188.00 | + | 31712.0i | −0.295348 | + | 1.14388i | ||||
\(917\) | 3488.27i | 0.125619i | ||||||||
\(918\) | −14185.2 | + | 577.251i | −0.510003 | + | 0.0207540i | ||||
\(919\) | 14198.4i | 0.509642i | 0.966988 | + | 0.254821i | \(0.0820165\pi\) | ||||
−0.966988 | + | 0.254821i | \(0.917984\pi\) | |||||||
\(920\) | 7759.59 | + | 18031.7i | 0.278072 | + | 0.646180i | ||||
\(921\) | −6030.00 | − | 5393.40i | −0.215739 | − | 0.192962i | ||||
\(922\) | −8740.00 | + | 6769.97i | −0.312187 | + | 0.241819i | ||||
\(923\) | 10392.3 | 0.370603 | ||||||||
\(924\) | 9278.46 | − | 6190.81i | 0.330345 | − | 0.220414i | ||||
\(925\) | −5850.00 | −0.207943 | ||||||||
\(926\) | −40651.2 | + | 31488.3i | −1.44264 | + | 1.11746i | ||||
\(927\) | −36373.1 | + | 4066.63i | −1.28873 | + | 0.144084i | ||||
\(928\) | 27200.0 | − | 4213.81i | 0.962159 | − | 0.149057i | ||||
\(929\) | 10232.2i | 0.361366i | 0.983541 | + | 0.180683i | \(0.0578308\pi\) | ||||
−0.983541 | + | 0.180683i | \(0.942169\pi\) | |||||||
\(930\) | 29455.1 | + | 2085.05i | 1.03857 | + | 0.0735178i | ||||
\(931\) | − | 19729.0i | − | 0.694512i | ||||||
\(932\) | 40876.4 | + | 10554.2i | 1.43664 | + | 0.370940i | ||||
\(933\) | 11280.0 | − | 12611.4i | 0.395810 | − | 0.442529i | ||||
\(934\) | 3204.00 | + | 4136.35i | 0.112246 | + | 0.144909i | ||||
\(935\) | 11085.1 | 0.387724 | ||||||||
\(936\) | 3023.54 | + | 5308.77i | 0.105585 | + | 0.185387i | ||||
\(937\) | 37850.0 | 1.31964 | 0.659822 | − | 0.751422i | \(-0.270632\pi\) | ||||
0.659822 | + | 0.751422i | \(0.270632\pi\) | |||||||
\(938\) | 9872.69 | + | 12745.6i | 0.343662 | + | 0.443665i | ||||
\(939\) | −24352.6 | + | 27227.1i | −0.846345 | + | 0.946243i | ||||
\(940\) | −13440.0 | − | 3470.19i | −0.466345 | − | 0.120410i | ||||
\(941\) | − | 13997.8i | − | 0.484925i | −0.970161 | − | 0.242463i | \(-0.922045\pi\) | ||
0.970161 | − | 0.242463i | \(-0.0779552\pi\) | |||||||
\(942\) | 10702.0 | + | 757.567i | 0.370159 | + | 0.0262026i | ||||
\(943\) | − | 12145.7i | − | 0.419425i | ||||||
\(944\) | 9699.48 | + | 5366.56i | 0.334419 | + | 0.185028i | ||||
\(945\) | 7920.00 | + | 5634.89i | 0.272632 | + | 0.193971i | ||||
\(946\) | 17400.0 | − | 13478.0i | 0.598016 | − | 0.463221i | ||||
\(947\) | 7738.80 | 0.265552 | 0.132776 | − | 0.991146i | \(-0.457611\pi\) | ||||
0.132776 | + | 0.991146i | \(0.457611\pi\) | |||||||
\(948\) | 2946.31 | − | 1965.85i | 0.100941 | − | 0.0673499i | ||||
\(949\) | −4100.00 | −0.140244 | ||||||||
\(950\) | −7014.81 | + | 5433.65i | −0.239569 | + | 0.185569i | ||||
\(951\) | 1905.26 | + | 1704.11i | 0.0649655 | + | 0.0581069i | ||||
\(952\) | −5760.00 | + | 2478.71i | −0.196095 | + | 0.0843860i | ||||
\(953\) | − | 44882.4i | − | 1.52558i | −0.646644 | − | 0.762792i | \(-0.723828\pi\) | ||
0.646644 | − | 0.762792i | \(-0.276172\pi\) | |||||||
\(954\) | −29017.2 | − | 29901.0i | −0.984767 | − | 1.01476i | ||||
\(955\) | 24787.1i | 0.839886i | ||||||||
\(956\) | 11362.3 | − | 44005.8i | 0.384395 | − | 1.48876i | ||||
\(957\) | 20400.0 | + | 18246.3i | 0.689068 | + | 0.616321i | ||||
\(958\) | −26400.0 | − | 34082.3i | −0.890340 | − | 1.14942i | ||||
\(959\) | −692.820 | −0.0233288 | ||||||||
\(960\) | 23713.6 | − | 1973.43i | 0.797244 | − | 0.0663460i | ||||
\(961\) | −20669.0 | −0.693800 | ||||||||
\(962\) | −2251.67 | − | 2906.89i | −0.0754643 | − | 0.0974240i | ||||
\(963\) | 1932.97 | + | 17289.0i | 0.0646823 | + | 0.578536i | ||||
\(964\) | 2396.00 | − | 9279.67i | 0.0800518 | − | 0.310039i | ||||
\(965\) | − | 1699.41i | − | 0.0566902i | ||||||
\(966\) | 779.691 | − | 11014.5i | 0.0259691 | − | 0.366860i | ||||
\(967\) | − | 15856.0i | − | 0.527295i | −0.964619 | − | 0.263648i | \(-0.915074\pi\) | ||
0.964619 | − | 0.263648i | \(-0.0849256\pi\) | |||||||
\(968\) | −2722.78 | + | 1171.70i | −0.0904066 | + | 0.0389048i | ||||
\(969\) | 8640.00 | − | 9659.81i | 0.286436 | − | 0.320246i | ||||
\(970\) | 15400.0 | − | 11928.8i | 0.509757 | − | 0.394856i | ||||
\(971\) | 40426.1 | 1.33608 | 0.668040 | − | 0.744125i | \(-0.267133\pi\) | ||||
0.668040 | + | 0.744125i | \(0.267133\pi\) | |||||||
\(972\) | −21971.1 | − | 20871.0i | −0.725025 | − | 0.688723i | ||||
\(973\) | 15180.0 | 0.500153 | ||||||||
\(974\) | −21875.8 | + | 16944.9i | −0.719657 | + | 0.557444i | ||||
\(975\) | −1558.85 | + | 1742.84i | −0.0512031 | + | 0.0572468i | ||||
\(976\) | 24752.0 | + | 13694.9i | 0.811775 | + | 0.449141i | ||||
\(977\) | − | 6404.10i | − | 0.209709i | −0.994488 | − | 0.104854i | \(-0.966562\pi\) | ||
0.994488 | − | 0.104854i | \(-0.0334376\pi\) | |||||||
\(978\) | −265.270 | + | 3747.41i | −0.00867320 | + | 0.122524i | ||||
\(979\) | − | 29124.8i | − | 0.950801i | ||||||
\(980\) | −19606.8 | − | 5062.46i | −0.639099 | − | 0.165015i | ||||
\(981\) | 3198.00 | + | 28603.8i | 0.104082 | + | 0.930936i | ||||
\(982\) | −11940.0 | − | 15414.5i | −0.388005 | − | 0.500912i | ||||
\(983\) | −25953.0 | −0.842089 | −0.421045 | − | 0.907040i | \(-0.638336\pi\) | ||||
−0.421045 | + | 0.907040i | \(0.638336\pi\) | |||||||
\(984\) | −13959.8 | − | 4678.08i | −0.452258 | − | 0.151557i | ||||
\(985\) | 19120.0 | 0.618491 | ||||||||
\(986\) | −9422.36 | − | 12164.2i | −0.304330 | − | 0.392888i | ||||
\(987\) | 5819.69 | + | 5205.29i | 0.187683 | + | 0.167868i | ||||
\(988\) | −5400.00 | − | 1394.27i | −0.173883 | − | 0.0448965i | ||||
\(989\) | − | 21788.2i | − | 0.700532i | ||||||
\(990\) | 16478.5 | + | 16980.4i | 0.529010 | + | 0.545122i | ||||
\(991\) | − | 48358.1i | − | 1.55010i | −0.631903 | − | 0.775048i | \(-0.717726\pi\) | ||
0.631903 | − | 0.775048i | \(-0.282274\pi\) | |||||||
\(992\) | −40183.6 | + | 6225.21i | −1.28612 | + | 0.199245i | ||||
\(993\) | 16410.0 | + | 14677.6i | 0.524427 | + | 0.469061i | ||||
\(994\) | −18000.0 | + | 13942.7i | −0.574372 | + | 0.444906i | ||||
\(995\) | −2286.31 | −0.0728450 | ||||||||
\(996\) | 28932.1 | + | 43362.0i | 0.920432 | + | 1.37949i | ||||
\(997\) | −18370.0 | −0.583534 | −0.291767 | − | 0.956489i | \(-0.594243\pi\) | ||||
−0.291767 | + | 0.956489i | \(0.594243\pi\) | |||||||
\(998\) | −2927.17 | + | 2267.37i | −0.0928435 | + | 0.0719163i | ||||
\(999\) | 14861.0 | + | 10573.2i | 0.470652 | + | 0.334858i |
(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 | 12.4.b.a.11.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 12.4.b.a.11.4 | yes | 4 | |
4.3 | odd | 2 | inner | 12.4.b.a.11.3 | yes | 4 | |
8.3 | odd | 2 | 192.4.c.b.191.3 | 4 | |||
8.5 | even | 2 | 192.4.c.b.191.2 | 4 | |||
12.11 | even | 2 | inner | 12.4.b.a.11.2 | yes | 4 | |
16.3 | odd | 4 | 768.4.f.c.383.2 | 8 | |||
16.5 | even | 4 | 768.4.f.c.383.1 | 8 | |||
16.11 | odd | 4 | 768.4.f.c.383.7 | 8 | |||
16.13 | even | 4 | 768.4.f.c.383.8 | 8 | |||
24.5 | odd | 2 | 192.4.c.b.191.4 | 4 | |||
24.11 | even | 2 | 192.4.c.b.191.1 | 4 | |||
48.5 | odd | 4 | 768.4.f.c.383.4 | 8 | |||
48.11 | even | 4 | 768.4.f.c.383.6 | 8 | |||
48.29 | odd | 4 | 768.4.f.c.383.5 | 8 | |||
48.35 | even | 4 | 768.4.f.c.383.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.4.b.a.11.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
12.4.b.a.11.2 | yes | 4 | 12.11 | even | 2 | inner | |
12.4.b.a.11.3 | yes | 4 | 4.3 | odd | 2 | inner | |
12.4.b.a.11.4 | yes | 4 | 3.2 | odd | 2 | inner | |
192.4.c.b.191.1 | 4 | 24.11 | even | 2 | |||
192.4.c.b.191.2 | 4 | 8.5 | even | 2 | |||
192.4.c.b.191.3 | 4 | 8.3 | odd | 2 | |||
192.4.c.b.191.4 | 4 | 24.5 | odd | 2 | |||
768.4.f.c.383.1 | 8 | 16.5 | even | 4 | |||
768.4.f.c.383.2 | 8 | 16.3 | odd | 4 | |||
768.4.f.c.383.3 | 8 | 48.35 | even | 4 | |||
768.4.f.c.383.4 | 8 | 48.5 | odd | 4 | |||
768.4.f.c.383.5 | 8 | 48.29 | odd | 4 | |||
768.4.f.c.383.6 | 8 | 48.11 | even | 4 | |||
768.4.f.c.383.7 | 8 | 16.11 | odd | 4 | |||
768.4.f.c.383.8 | 8 | 16.13 | even | 4 |