Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,4,Mod(4,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.23904011012\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.16 |
Dual form | 21.4.e.a.4.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50000 | − | 2.59808i | 0.530330 | − | 0.918559i | −0.469044 | − | 0.883175i | \(-0.655401\pi\) |
0.999374 | − | 0.0353837i | \(-0.0112653\pi\) | |||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(5\) | 1.50000 | − | 2.59808i | 0.134164 | − | 0.232379i | −0.791114 | − | 0.611669i | \(-0.790498\pi\) |
0.925278 | + | 0.379290i | \(0.123832\pi\) | |||||||
\(6\) | −9.00000 | −0.612372 | ||||||||
\(7\) | −3.50000 | + | 18.1865i | −0.188982 | + | 0.981981i | ||||
\(8\) | 21.0000 | 0.928078 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | −4.50000 | − | 7.79423i | −0.142302 | − | 0.246475i | ||||
\(11\) | 7.50000 | + | 12.9904i | 0.205576 | + | 0.356068i | 0.950316 | − | 0.311287i | \(-0.100760\pi\) |
−0.744740 | + | 0.667355i | \(0.767427\pi\) | |||||||
\(12\) | −1.50000 | + | 2.59808i | −0.0360844 | + | 0.0625000i | ||||
\(13\) | −64.0000 | −1.36542 | −0.682708 | − | 0.730691i | \(-0.739198\pi\) | ||||
−0.682708 | + | 0.730691i | \(0.739198\pi\) | |||||||
\(14\) | 42.0000 | + | 36.3731i | 0.801784 | + | 0.694365i | ||||
\(15\) | −9.00000 | −0.154919 | ||||||||
\(16\) | 35.5000 | − | 61.4878i | 0.554688 | − | 0.960747i | ||||
\(17\) | −42.0000 | − | 72.7461i | −0.599206 | − | 1.03785i | −0.992939 | − | 0.118630i | \(-0.962150\pi\) |
0.393733 | − | 0.919225i | \(-0.371183\pi\) | |||||||
\(18\) | 13.5000 | + | 23.3827i | 0.176777 | + | 0.306186i | ||||
\(19\) | 8.00000 | − | 13.8564i | 0.0965961 | − | 0.167309i | −0.813678 | − | 0.581317i | \(-0.802538\pi\) |
0.910274 | + | 0.414007i | \(0.135871\pi\) | |||||||
\(20\) | −3.00000 | −0.0335410 | ||||||||
\(21\) | 52.5000 | − | 18.1865i | 0.545545 | − | 0.188982i | ||||
\(22\) | 45.0000 | 0.436092 | ||||||||
\(23\) | 42.0000 | − | 72.7461i | 0.380765 | − | 0.659505i | −0.610406 | − | 0.792088i | \(-0.708994\pi\) |
0.991172 | + | 0.132583i | \(0.0423272\pi\) | |||||||
\(24\) | −31.5000 | − | 54.5596i | −0.267913 | − | 0.464039i | ||||
\(25\) | 58.0000 | + | 100.459i | 0.464000 | + | 0.803672i | ||||
\(26\) | −96.0000 | + | 166.277i | −0.724121 | + | 1.25421i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 17.5000 | − | 6.06218i | 0.118114 | − | 0.0409159i | ||||
\(29\) | −297.000 | −1.90178 | −0.950888 | − | 0.309535i | \(-0.899827\pi\) | ||||
−0.950888 | + | 0.309535i | \(0.899827\pi\) | |||||||
\(30\) | −13.5000 | + | 23.3827i | −0.0821584 | + | 0.142302i | ||||
\(31\) | 126.500 | + | 219.104i | 0.732906 | + | 1.26943i | 0.955636 | + | 0.294550i | \(0.0951696\pi\) |
−0.222731 | + | 0.974880i | \(0.571497\pi\) | |||||||
\(32\) | −22.5000 | − | 38.9711i | −0.124296 | − | 0.215287i | ||||
\(33\) | 22.5000 | − | 38.9711i | 0.118689 | − | 0.205576i | ||||
\(34\) | −252.000 | −1.27111 | ||||||||
\(35\) | 42.0000 | + | 36.3731i | 0.202837 | + | 0.175662i | ||||
\(36\) | 9.00000 | 0.0416667 | ||||||||
\(37\) | 158.000 | − | 273.664i | 0.702028 | − | 1.21595i | −0.265725 | − | 0.964049i | \(-0.585611\pi\) |
0.967753 | − | 0.251900i | \(-0.0810553\pi\) | |||||||
\(38\) | −24.0000 | − | 41.5692i | −0.102456 | − | 0.177458i | ||||
\(39\) | 96.0000 | + | 166.277i | 0.394162 | + | 0.682708i | ||||
\(40\) | 31.5000 | − | 54.5596i | 0.124515 | − | 0.215666i | ||||
\(41\) | 360.000 | 1.37128 | 0.685641 | − | 0.727940i | \(-0.259522\pi\) | ||||
0.685641 | + | 0.727940i | \(0.259522\pi\) | |||||||
\(42\) | 31.5000 | − | 163.679i | 0.115728 | − | 0.601338i | ||||
\(43\) | 26.0000 | 0.0922084 | 0.0461042 | − | 0.998937i | \(-0.485319\pi\) | ||||
0.0461042 | + | 0.998937i | \(0.485319\pi\) | |||||||
\(44\) | 7.50000 | − | 12.9904i | 0.0256970 | − | 0.0445085i | ||||
\(45\) | 13.5000 | + | 23.3827i | 0.0447214 | + | 0.0774597i | ||||
\(46\) | −126.000 | − | 218.238i | −0.403863 | − | 0.699511i | ||||
\(47\) | 15.0000 | − | 25.9808i | 0.0465527 | − | 0.0806316i | −0.841810 | − | 0.539774i | \(-0.818510\pi\) |
0.888363 | + | 0.459142i | \(0.151843\pi\) | |||||||
\(48\) | −213.000 | −0.640498 | ||||||||
\(49\) | −318.500 | − | 127.306i | −0.928571 | − | 0.371154i | ||||
\(50\) | 348.000 | 0.984293 | ||||||||
\(51\) | −126.000 | + | 218.238i | −0.345952 | + | 0.599206i | ||||
\(52\) | 32.0000 | + | 55.4256i | 0.0853385 | + | 0.147811i | ||||
\(53\) | −181.500 | − | 314.367i | −0.470395 | − | 0.814748i | 0.529032 | − | 0.848602i | \(-0.322555\pi\) |
−0.999427 | + | 0.0338538i | \(0.989222\pi\) | |||||||
\(54\) | 40.5000 | − | 70.1481i | 0.102062 | − | 0.176777i | ||||
\(55\) | 45.0000 | 0.110324 | ||||||||
\(56\) | −73.5000 | + | 381.917i | −0.175390 | + | 0.911354i | ||||
\(57\) | −48.0000 | −0.111540 | ||||||||
\(58\) | −445.500 | + | 771.629i | −1.00857 | + | 1.74689i | ||||
\(59\) | 7.50000 | + | 12.9904i | 0.0165494 | + | 0.0286645i | 0.874182 | − | 0.485599i | \(-0.161399\pi\) |
−0.857632 | + | 0.514264i | \(0.828065\pi\) | |||||||
\(60\) | 4.50000 | + | 7.79423i | 0.00968246 | + | 0.0167705i | ||||
\(61\) | 59.0000 | − | 102.191i | 0.123839 | − | 0.214495i | −0.797440 | − | 0.603399i | \(-0.793813\pi\) |
0.921279 | + | 0.388903i | \(0.127146\pi\) | |||||||
\(62\) | 759.000 | 1.55473 | ||||||||
\(63\) | −126.000 | − | 109.119i | −0.251976 | − | 0.218218i | ||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | −96.0000 | + | 166.277i | −0.183190 | + | 0.317294i | ||||
\(66\) | −67.5000 | − | 116.913i | −0.125889 | − | 0.218046i | ||||
\(67\) | 185.000 | + | 320.429i | 0.337334 | + | 0.584279i | 0.983930 | − | 0.178553i | \(-0.0571417\pi\) |
−0.646597 | + | 0.762832i | \(0.723808\pi\) | |||||||
\(68\) | −42.0000 | + | 72.7461i | −0.0749007 | + | 0.129732i | ||||
\(69\) | −252.000 | −0.439670 | ||||||||
\(70\) | 157.500 | − | 54.5596i | 0.268926 | − | 0.0931589i | ||||
\(71\) | −342.000 | −0.571661 | −0.285831 | − | 0.958280i | \(-0.592269\pi\) | ||||
−0.285831 | + | 0.958280i | \(0.592269\pi\) | |||||||
\(72\) | −94.5000 | + | 163.679i | −0.154680 | + | 0.267913i | ||||
\(73\) | −181.000 | − | 313.501i | −0.290198 | − | 0.502638i | 0.683658 | − | 0.729802i | \(-0.260388\pi\) |
−0.973856 | + | 0.227165i | \(0.927054\pi\) | |||||||
\(74\) | −474.000 | − | 820.992i | −0.744613 | − | 1.28971i | ||||
\(75\) | 174.000 | − | 301.377i | 0.267891 | − | 0.464000i | ||||
\(76\) | −16.0000 | −0.0241490 | ||||||||
\(77\) | −262.500 | + | 90.9327i | −0.388502 | + | 0.134581i | ||||
\(78\) | 576.000 | 0.836143 | ||||||||
\(79\) | −233.500 | + | 404.434i | −0.332542 | + | 0.575979i | −0.983010 | − | 0.183555i | \(-0.941240\pi\) |
0.650468 | + | 0.759534i | \(0.274573\pi\) | |||||||
\(80\) | −106.500 | − | 184.463i | −0.148838 | − | 0.257795i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 540.000 | − | 935.307i | 0.727232 | − | 1.25960i | ||||
\(83\) | 477.000 | 0.630814 | 0.315407 | − | 0.948957i | \(-0.397859\pi\) | ||||
0.315407 | + | 0.948957i | \(0.397859\pi\) | |||||||
\(84\) | −42.0000 | − | 36.3731i | −0.0545545 | − | 0.0472456i | ||||
\(85\) | −252.000 | −0.321568 | ||||||||
\(86\) | 39.0000 | − | 67.5500i | 0.0489009 | − | 0.0846989i | ||||
\(87\) | 445.500 | + | 771.629i | 0.548996 | + | 0.950888i | ||||
\(88\) | 157.500 | + | 272.798i | 0.190790 | + | 0.330459i | ||||
\(89\) | −453.000 | + | 784.619i | −0.539527 | + | 0.934488i | 0.459402 | + | 0.888228i | \(0.348064\pi\) |
−0.998929 | + | 0.0462600i | \(0.985270\pi\) | |||||||
\(90\) | 81.0000 | 0.0948683 | ||||||||
\(91\) | 224.000 | − | 1163.94i | 0.258039 | − | 1.34081i | ||||
\(92\) | −84.0000 | −0.0951914 | ||||||||
\(93\) | 379.500 | − | 657.313i | 0.423143 | − | 0.732906i | ||||
\(94\) | −45.0000 | − | 77.9423i | −0.0493765 | − | 0.0855227i | ||||
\(95\) | −24.0000 | − | 41.5692i | −0.0259195 | − | 0.0448938i | ||||
\(96\) | −67.5000 | + | 116.913i | −0.0717624 | + | 0.124296i | ||||
\(97\) | 503.000 | 0.526515 | 0.263257 | − | 0.964726i | \(-0.415203\pi\) | ||||
0.263257 | + | 0.964726i | \(0.415203\pi\) | |||||||
\(98\) | −808.500 | + | 636.529i | −0.833376 | + | 0.656113i | ||||
\(99\) | −135.000 | −0.137051 | ||||||||
\(100\) | 58.0000 | − | 100.459i | 0.0580000 | − | 0.100459i | ||||
\(101\) | 543.000 | + | 940.504i | 0.534956 | + | 0.926570i | 0.999165 | + | 0.0408451i | \(0.0130050\pi\) |
−0.464210 | + | 0.885725i | \(0.653662\pi\) | |||||||
\(102\) | 378.000 | + | 654.715i | 0.366937 | + | 0.635554i | ||||
\(103\) | −868.000 | + | 1503.42i | −0.830355 | + | 1.43822i | 0.0674017 | + | 0.997726i | \(0.478529\pi\) |
−0.897757 | + | 0.440491i | \(0.854804\pi\) | |||||||
\(104\) | −1344.00 | −1.26721 | ||||||||
\(105\) | 31.5000 | − | 163.679i | 0.0292770 | − | 0.152128i | ||||
\(106\) | −1089.00 | −0.997859 | ||||||||
\(107\) | 676.500 | − | 1171.73i | 0.611212 | − | 1.05865i | −0.379824 | − | 0.925059i | \(-0.624015\pi\) |
0.991036 | − | 0.133592i | \(-0.0426512\pi\) | |||||||
\(108\) | −13.5000 | − | 23.3827i | −0.0120281 | − | 0.0208333i | ||||
\(109\) | 185.000 | + | 320.429i | 0.162567 | + | 0.281574i | 0.935789 | − | 0.352562i | \(-0.114689\pi\) |
−0.773222 | + | 0.634136i | \(0.781356\pi\) | |||||||
\(110\) | 67.5000 | − | 116.913i | 0.0585079 | − | 0.101339i | ||||
\(111\) | −948.000 | −0.810632 | ||||||||
\(112\) | 994.000 | + | 860.829i | 0.838609 | + | 0.726256i | ||||
\(113\) | −648.000 | −0.539458 | −0.269729 | − | 0.962936i | \(-0.586934\pi\) | ||||
−0.269729 | + | 0.962936i | \(0.586934\pi\) | |||||||
\(114\) | −72.0000 | + | 124.708i | −0.0591528 | + | 0.102456i | ||||
\(115\) | −126.000 | − | 218.238i | −0.102170 | − | 0.176964i | ||||
\(116\) | 148.500 | + | 257.210i | 0.118861 | + | 0.205873i | ||||
\(117\) | 288.000 | − | 498.831i | 0.227569 | − | 0.394162i | ||||
\(118\) | 45.0000 | 0.0351067 | ||||||||
\(119\) | 1470.00 | − | 509.223i | 1.13239 | − | 0.392272i | ||||
\(120\) | −189.000 | −0.143777 | ||||||||
\(121\) | 553.000 | − | 957.824i | 0.415477 | − | 0.719627i | ||||
\(122\) | −177.000 | − | 306.573i | −0.131351 | − | 0.227507i | ||||
\(123\) | −540.000 | − | 935.307i | −0.395855 | − | 0.685641i | ||||
\(124\) | 126.500 | − | 219.104i | 0.0916132 | − | 0.158679i | ||||
\(125\) | 723.000 | 0.517337 | ||||||||
\(126\) | −472.500 | + | 163.679i | −0.334077 | + | 0.115728i | ||||
\(127\) | 377.000 | 0.263412 | 0.131706 | − | 0.991289i | \(-0.457954\pi\) | ||||
0.131706 | + | 0.991289i | \(0.457954\pi\) | |||||||
\(128\) | 829.500 | − | 1436.74i | 0.572798 | − | 0.992115i | ||||
\(129\) | −39.0000 | − | 67.5500i | −0.0266183 | − | 0.0461042i | ||||
\(130\) | 288.000 | + | 498.831i | 0.194302 | + | 0.336541i | ||||
\(131\) | 325.500 | − | 563.783i | 0.217092 | − | 0.376015i | −0.736826 | − | 0.676083i | \(-0.763676\pi\) |
0.953918 | + | 0.300068i | \(0.0970095\pi\) | |||||||
\(132\) | −45.0000 | −0.0296723 | ||||||||
\(133\) | 224.000 | + | 193.990i | 0.146040 | + | 0.126474i | ||||
\(134\) | 1110.00 | 0.715593 | ||||||||
\(135\) | 40.5000 | − | 70.1481i | 0.0258199 | − | 0.0447214i | ||||
\(136\) | −882.000 | − | 1527.67i | −0.556109 | − | 0.963210i | ||||
\(137\) | 885.000 | + | 1532.86i | 0.551903 | + | 0.955923i | 0.998137 | + | 0.0610074i | \(0.0194313\pi\) |
−0.446235 | + | 0.894916i | \(0.647235\pi\) | |||||||
\(138\) | −378.000 | + | 654.715i | −0.233170 | + | 0.403863i | ||||
\(139\) | −1558.00 | −0.950704 | −0.475352 | − | 0.879796i | \(-0.657679\pi\) | ||||
−0.475352 | + | 0.879796i | \(0.657679\pi\) | |||||||
\(140\) | 10.5000 | − | 54.5596i | 0.00633866 | − | 0.0329366i | ||||
\(141\) | −90.0000 | −0.0537544 | ||||||||
\(142\) | −513.000 | + | 888.542i | −0.303169 | + | 0.525104i | ||||
\(143\) | −480.000 | − | 831.384i | −0.280697 | − | 0.486181i | ||||
\(144\) | 319.500 | + | 553.390i | 0.184896 | + | 0.320249i | ||||
\(145\) | −445.500 | + | 771.629i | −0.255150 | + | 0.441933i | ||||
\(146\) | −1086.00 | −0.615603 | ||||||||
\(147\) | 147.000 | + | 1018.45i | 0.0824786 | + | 0.571429i | ||||
\(148\) | −316.000 | −0.175507 | ||||||||
\(149\) | −1227.00 | + | 2125.23i | −0.674629 | + | 1.16849i | 0.301948 | + | 0.953324i | \(0.402363\pi\) |
−0.976577 | + | 0.215168i | \(0.930970\pi\) | |||||||
\(150\) | −522.000 | − | 904.131i | −0.284141 | − | 0.492146i | ||||
\(151\) | −629.500 | − | 1090.33i | −0.339258 | − | 0.587612i | 0.645035 | − | 0.764153i | \(-0.276843\pi\) |
−0.984293 | + | 0.176540i | \(0.943509\pi\) | |||||||
\(152\) | 168.000 | − | 290.985i | 0.0896487 | − | 0.155276i | ||||
\(153\) | 756.000 | 0.399470 | ||||||||
\(154\) | −157.500 | + | 818.394i | −0.0824137 | + | 0.428234i | ||||
\(155\) | 759.000 | 0.393318 | ||||||||
\(156\) | 96.0000 | − | 166.277i | 0.0492702 | − | 0.0853385i | ||||
\(157\) | 98.0000 | + | 169.741i | 0.0498169 | + | 0.0862854i | 0.889859 | − | 0.456236i | \(-0.150803\pi\) |
−0.840042 | + | 0.542522i | \(0.817470\pi\) | |||||||
\(158\) | 700.500 | + | 1213.30i | 0.352714 | + | 0.610918i | ||||
\(159\) | −544.500 | + | 943.102i | −0.271583 | + | 0.470395i | ||||
\(160\) | −135.000 | −0.0667043 | ||||||||
\(161\) | 1176.00 | + | 1018.45i | 0.575663 | + | 0.498539i | ||||
\(162\) | −243.000 | −0.117851 | ||||||||
\(163\) | 626.000 | − | 1084.26i | 0.300810 | − | 0.521019i | −0.675509 | − | 0.737351i | \(-0.736076\pi\) |
0.976320 | + | 0.216332i | \(0.0694095\pi\) | |||||||
\(164\) | −180.000 | − | 311.769i | −0.0857051 | − | 0.148446i | ||||
\(165\) | −67.5000 | − | 116.913i | −0.0318477 | − | 0.0551618i | ||||
\(166\) | 715.500 | − | 1239.28i | 0.334540 | − | 0.579440i | ||||
\(167\) | −2646.00 | −1.22607 | −0.613035 | − | 0.790056i | \(-0.710051\pi\) | ||||
−0.613035 | + | 0.790056i | \(0.710051\pi\) | |||||||
\(168\) | 1102.50 | − | 381.917i | 0.506308 | − | 0.175390i | ||||
\(169\) | 1899.00 | 0.864360 | ||||||||
\(170\) | −378.000 | + | 654.715i | −0.170537 | + | 0.295379i | ||||
\(171\) | 72.0000 | + | 124.708i | 0.0321987 | + | 0.0557698i | ||||
\(172\) | −13.0000 | − | 22.5167i | −0.00576303 | − | 0.00998186i | ||||
\(173\) | 393.000 | − | 680.696i | 0.172712 | − | 0.299147i | −0.766655 | − | 0.642059i | \(-0.778080\pi\) |
0.939367 | + | 0.342913i | \(0.111414\pi\) | |||||||
\(174\) | 2673.00 | 1.16460 | ||||||||
\(175\) | −2030.00 | + | 703.213i | −0.876878 | + | 0.303759i | ||||
\(176\) | 1065.00 | 0.456122 | ||||||||
\(177\) | 22.5000 | − | 38.9711i | 0.00955482 | − | 0.0165494i | ||||
\(178\) | 1359.00 | + | 2353.86i | 0.572255 | + | 0.991174i | ||||
\(179\) | −1446.00 | − | 2504.55i | −0.603794 | − | 1.04580i | −0.992241 | − | 0.124331i | \(-0.960322\pi\) |
0.388447 | − | 0.921471i | \(-0.373012\pi\) | |||||||
\(180\) | 13.5000 | − | 23.3827i | 0.00559017 | − | 0.00968246i | ||||
\(181\) | 1352.00 | 0.555212 | 0.277606 | − | 0.960695i | \(-0.410459\pi\) | ||||
0.277606 | + | 0.960695i | \(0.410459\pi\) | |||||||
\(182\) | −2688.00 | − | 2327.88i | −1.09477 | − | 0.948097i | ||||
\(183\) | −354.000 | −0.142997 | ||||||||
\(184\) | 882.000 | − | 1527.67i | 0.353380 | − | 0.612072i | ||||
\(185\) | −474.000 | − | 820.992i | −0.188374 | − | 0.326273i | ||||
\(186\) | −1138.50 | − | 1971.94i | −0.448811 | − | 0.777364i | ||||
\(187\) | 630.000 | − | 1091.19i | 0.246365 | − | 0.426716i | ||||
\(188\) | −30.0000 | −0.0116382 | ||||||||
\(189\) | −94.5000 | + | 491.036i | −0.0363696 | + | 0.188982i | ||||
\(190\) | −144.000 | −0.0549835 | ||||||||
\(191\) | −1956.00 | + | 3387.89i | −0.741001 | + | 1.28345i | 0.211039 | + | 0.977478i | \(0.432315\pi\) |
−0.952040 | + | 0.305974i | \(0.901018\pi\) | |||||||
\(192\) | −649.500 | − | 1124.97i | −0.244133 | − | 0.422852i | ||||
\(193\) | −746.500 | − | 1292.98i | −0.278416 | − | 0.482230i | 0.692575 | − | 0.721345i | \(-0.256476\pi\) |
−0.970991 | + | 0.239115i | \(0.923143\pi\) | |||||||
\(194\) | 754.500 | − | 1306.83i | 0.279227 | − | 0.483635i | ||||
\(195\) | 576.000 | 0.211529 | ||||||||
\(196\) | 49.0000 | + | 339.482i | 0.0178571 | + | 0.123718i | ||||
\(197\) | −4086.00 | −1.47774 | −0.738872 | − | 0.673846i | \(-0.764641\pi\) | ||||
−0.738872 | + | 0.673846i | \(0.764641\pi\) | |||||||
\(198\) | −202.500 | + | 350.740i | −0.0726821 | + | 0.125889i | ||||
\(199\) | 1778.00 | + | 3079.59i | 0.633362 | + | 1.09702i | 0.986860 | + | 0.161580i | \(0.0516590\pi\) |
−0.353497 | + | 0.935436i | \(0.615008\pi\) | |||||||
\(200\) | 1218.00 | + | 2109.64i | 0.430628 | + | 0.745870i | ||||
\(201\) | 555.000 | − | 961.288i | 0.194760 | − | 0.337334i | ||||
\(202\) | 3258.00 | 1.13481 | ||||||||
\(203\) | 1039.50 | − | 5401.40i | 0.359402 | − | 1.86751i | ||||
\(204\) | 252.000 | 0.0864879 | ||||||||
\(205\) | 540.000 | − | 935.307i | 0.183977 | − | 0.318657i | ||||
\(206\) | 2604.00 | + | 4510.26i | 0.880725 | + | 1.52546i | ||||
\(207\) | 378.000 | + | 654.715i | 0.126922 | + | 0.219835i | ||||
\(208\) | −2272.00 | + | 3935.22i | −0.757379 | + | 1.31182i | ||||
\(209\) | 240.000 | 0.0794313 | ||||||||
\(210\) | −378.000 | − | 327.358i | −0.124212 | − | 0.107571i | ||||
\(211\) | 1250.00 | 0.407837 | 0.203918 | − | 0.978988i | \(-0.434632\pi\) | ||||
0.203918 | + | 0.978988i | \(0.434632\pi\) | |||||||
\(212\) | −181.500 | + | 314.367i | −0.0587994 | + | 0.101844i | ||||
\(213\) | 513.000 | + | 888.542i | 0.165024 | + | 0.285831i | ||||
\(214\) | −2029.50 | − | 3515.20i | −0.648289 | − | 1.12287i | ||||
\(215\) | 39.0000 | − | 67.5500i | 0.0123711 | − | 0.0214273i | ||||
\(216\) | 567.000 | 0.178609 | ||||||||
\(217\) | −4427.50 | + | 1533.73i | −1.38506 | + | 0.479799i | ||||
\(218\) | 1110.00 | 0.344856 | ||||||||
\(219\) | −543.000 | + | 940.504i | −0.167546 | + | 0.290198i | ||||
\(220\) | −22.5000 | − | 38.9711i | −0.00689523 | − | 0.0119429i | ||||
\(221\) | 2688.00 | + | 4655.75i | 0.818165 | + | 1.41710i | ||||
\(222\) | −1422.00 | + | 2462.98i | −0.429903 | + | 0.744613i | ||||
\(223\) | 425.000 | 0.127624 | 0.0638119 | − | 0.997962i | \(-0.479674\pi\) | ||||
0.0638119 | + | 0.997962i | \(0.479674\pi\) | |||||||
\(224\) | 787.500 | − | 272.798i | 0.234898 | − | 0.0813709i | ||||
\(225\) | −1044.00 | −0.309333 | ||||||||
\(226\) | −972.000 | + | 1683.55i | −0.286091 | + | 0.495523i | ||||
\(227\) | −1927.50 | − | 3338.53i | −0.563580 | − | 0.976149i | −0.997180 | − | 0.0750439i | \(-0.976090\pi\) |
0.433600 | − | 0.901105i | \(-0.357243\pi\) | |||||||
\(228\) | 24.0000 | + | 41.5692i | 0.00697122 | + | 0.0120745i | ||||
\(229\) | 1094.00 | − | 1894.86i | 0.315692 | − | 0.546795i | −0.663892 | − | 0.747828i | \(-0.731097\pi\) |
0.979584 | + | 0.201033i | \(0.0644299\pi\) | |||||||
\(230\) | −756.000 | −0.216735 | ||||||||
\(231\) | 630.000 | + | 545.596i | 0.179441 | + | 0.155401i | ||||
\(232\) | −6237.00 | −1.76500 | ||||||||
\(233\) | −426.000 | + | 737.854i | −0.119778 | + | 0.207461i | −0.919679 | − | 0.392670i | \(-0.871551\pi\) |
0.799902 | + | 0.600131i | \(0.204885\pi\) | |||||||
\(234\) | −864.000 | − | 1496.49i | −0.241374 | − | 0.418072i | ||||
\(235\) | −45.0000 | − | 77.9423i | −0.0124914 | − | 0.0216357i | ||||
\(236\) | 7.50000 | − | 12.9904i | 0.00206868 | − | 0.00358306i | ||||
\(237\) | 1401.00 | 0.383986 | ||||||||
\(238\) | 882.000 | − | 4583.01i | 0.240217 | − | 1.24820i | ||||
\(239\) | 5508.00 | 1.49072 | 0.745362 | − | 0.666660i | \(-0.232277\pi\) | ||||
0.745362 | + | 0.666660i | \(0.232277\pi\) | |||||||
\(240\) | −319.500 | + | 553.390i | −0.0859318 | + | 0.148838i | ||||
\(241\) | −395.500 | − | 685.026i | −0.105711 | − | 0.183097i | 0.808317 | − | 0.588747i | \(-0.200379\pi\) |
−0.914029 | + | 0.405650i | \(0.867045\pi\) | |||||||
\(242\) | −1659.00 | − | 2873.47i | −0.440680 | − | 0.763280i | ||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −118.000 | −0.0309597 | ||||||||
\(245\) | −808.500 | + | 636.529i | −0.210829 | + | 0.165985i | ||||
\(246\) | −3240.00 | −0.839735 | ||||||||
\(247\) | −512.000 | + | 886.810i | −0.131894 | + | 0.228447i | ||||
\(248\) | 2656.50 | + | 4601.19i | 0.680193 | + | 1.17813i | ||||
\(249\) | −715.500 | − | 1239.28i | −0.182100 | − | 0.315407i | ||||
\(250\) | 1084.50 | − | 1878.41i | 0.274359 | − | 0.475204i | ||||
\(251\) | 5265.00 | 1.32400 | 0.662000 | − | 0.749504i | \(-0.269708\pi\) | ||||
0.662000 | + | 0.749504i | \(0.269708\pi\) | |||||||
\(252\) | −31.5000 | + | 163.679i | −0.00787426 | + | 0.0409159i | ||||
\(253\) | 1260.00 | 0.313105 | ||||||||
\(254\) | 565.500 | − | 979.475i | 0.139695 | − | 0.241959i | ||||
\(255\) | 378.000 | + | 654.715i | 0.0928285 | + | 0.160784i | ||||
\(256\) | −756.500 | − | 1310.30i | −0.184692 | − | 0.319897i | ||||
\(257\) | 3435.00 | − | 5949.59i | 0.833733 | − | 1.44407i | −0.0613246 | − | 0.998118i | \(-0.519532\pi\) |
0.895058 | − | 0.445950i | \(-0.147134\pi\) | |||||||
\(258\) | −234.000 | −0.0564659 | ||||||||
\(259\) | 4424.00 | + | 3831.30i | 1.06137 | + | 0.919171i | ||||
\(260\) | 192.000 | 0.0457974 | ||||||||
\(261\) | 1336.50 | − | 2314.89i | 0.316963 | − | 0.548996i | ||||
\(262\) | −976.500 | − | 1691.35i | −0.230261 | − | 0.398824i | ||||
\(263\) | 111.000 | + | 192.258i | 0.0260249 | + | 0.0450765i | 0.878745 | − | 0.477292i | \(-0.158382\pi\) |
−0.852720 | + | 0.522369i | \(0.825048\pi\) | |||||||
\(264\) | 472.500 | − | 818.394i | 0.110153 | − | 0.190790i | ||||
\(265\) | −1089.00 | −0.252441 | ||||||||
\(266\) | 840.000 | − | 290.985i | 0.193623 | − | 0.0670730i | ||||
\(267\) | 2718.00 | 0.622992 | ||||||||
\(268\) | 185.000 | − | 320.429i | 0.0421667 | − | 0.0730349i | ||||
\(269\) | −3925.50 | − | 6799.17i | −0.889747 | − | 1.54109i | −0.840174 | − | 0.542317i | \(-0.817547\pi\) |
−0.0495729 | − | 0.998771i | \(-0.515786\pi\) | |||||||
\(270\) | −121.500 | − | 210.444i | −0.0273861 | − | 0.0474342i | ||||
\(271\) | −2591.50 | + | 4488.61i | −0.580895 | + | 1.00614i | 0.414479 | + | 0.910059i | \(0.363964\pi\) |
−0.995374 | + | 0.0960800i | \(0.969370\pi\) | |||||||
\(272\) | −5964.00 | −1.32949 | ||||||||
\(273\) | −3360.00 | + | 1163.94i | −0.744895 | + | 0.258039i | ||||
\(274\) | 5310.00 | 1.17076 | ||||||||
\(275\) | −870.000 | + | 1506.88i | −0.190774 | + | 0.330431i | ||||
\(276\) | 126.000 | + | 218.238i | 0.0274794 | + | 0.0475957i | ||||
\(277\) | 2480.00 | + | 4295.49i | 0.537938 | + | 0.931736i | 0.999015 | + | 0.0443755i | \(0.0141298\pi\) |
−0.461077 | + | 0.887360i | \(0.652537\pi\) | |||||||
\(278\) | −2337.00 | + | 4047.80i | −0.504187 | + | 0.873277i | ||||
\(279\) | −2277.00 | −0.488604 | ||||||||
\(280\) | 882.000 | + | 763.834i | 0.188249 | + | 0.163028i | ||||
\(281\) | −774.000 | −0.164317 | −0.0821583 | − | 0.996619i | \(-0.526181\pi\) | ||||
−0.0821583 | + | 0.996619i | \(0.526181\pi\) | |||||||
\(282\) | −135.000 | + | 233.827i | −0.0285076 | + | 0.0493765i | ||||
\(283\) | −1849.00 | − | 3202.56i | −0.388380 | − | 0.672695i | 0.603852 | − | 0.797097i | \(-0.293632\pi\) |
−0.992232 | + | 0.124402i | \(0.960299\pi\) | |||||||
\(284\) | 171.000 | + | 296.181i | 0.0357288 | + | 0.0618841i | ||||
\(285\) | −72.0000 | + | 124.708i | −0.0149646 | + | 0.0259195i | ||||
\(286\) | −2880.00 | −0.595447 | ||||||||
\(287\) | −1260.00 | + | 6547.15i | −0.259148 | + | 1.34657i | ||||
\(288\) | 405.000 | 0.0828641 | ||||||||
\(289\) | −1071.50 | + | 1855.89i | −0.218095 | + | 0.377751i | ||||
\(290\) | 1336.50 | + | 2314.89i | 0.270628 | + | 0.468741i | ||||
\(291\) | −754.500 | − | 1306.83i | −0.151992 | − | 0.263257i | ||||
\(292\) | −181.000 | + | 313.501i | −0.0362747 | + | 0.0628297i | ||||
\(293\) | −6273.00 | −1.25076 | −0.625380 | − | 0.780321i | \(-0.715056\pi\) | ||||
−0.625380 | + | 0.780321i | \(0.715056\pi\) | |||||||
\(294\) | 2866.50 | + | 1145.75i | 0.568632 | + | 0.227284i | ||||
\(295\) | 45.0000 | 0.00888136 | ||||||||
\(296\) | 3318.00 | − | 5746.94i | 0.651537 | − | 1.12849i | ||||
\(297\) | 202.500 | + | 350.740i | 0.0395631 | + | 0.0685253i | ||||
\(298\) | 3681.00 | + | 6375.68i | 0.715552 | + | 1.23937i | ||||
\(299\) | −2688.00 | + | 4655.75i | −0.519903 | + | 0.900499i | ||||
\(300\) | −348.000 | −0.0669726 | ||||||||
\(301\) | −91.0000 | + | 472.850i | −0.0174258 | + | 0.0905469i | ||||
\(302\) | −3777.00 | −0.719675 | ||||||||
\(303\) | 1629.00 | − | 2821.51i | 0.308857 | − | 0.534956i | ||||
\(304\) | −568.000 | − | 983.805i | −0.107161 | − | 0.185609i | ||||
\(305\) | −177.000 | − | 306.573i | −0.0332295 | − | 0.0575551i | ||||
\(306\) | 1134.00 | − | 1964.15i | 0.211851 | − | 0.366937i | ||||
\(307\) | −1684.00 | −0.313065 | −0.156533 | − | 0.987673i | \(-0.550032\pi\) | ||||
−0.156533 | + | 0.987673i | \(0.550032\pi\) | |||||||
\(308\) | 210.000 | + | 181.865i | 0.0388502 | + | 0.0336453i | ||||
\(309\) | 5208.00 | 0.958812 | ||||||||
\(310\) | 1138.50 | − | 1971.94i | 0.208589 | − | 0.361286i | ||||
\(311\) | 660.000 | + | 1143.15i | 0.120338 | + | 0.208432i | 0.919901 | − | 0.392151i | \(-0.128269\pi\) |
−0.799563 | + | 0.600582i | \(0.794935\pi\) | |||||||
\(312\) | 2016.00 | + | 3491.81i | 0.365813 | + | 0.633606i | ||||
\(313\) | 4251.50 | − | 7363.81i | 0.767760 | − | 1.32980i | −0.171014 | − | 0.985269i | \(-0.554704\pi\) |
0.938775 | − | 0.344531i | \(-0.111962\pi\) | |||||||
\(314\) | 588.000 | 0.105678 | ||||||||
\(315\) | −472.500 | + | 163.679i | −0.0845154 | + | 0.0292770i | ||||
\(316\) | 467.000 | 0.0831355 | ||||||||
\(317\) | 1288.50 | − | 2231.75i | 0.228295 | − | 0.395418i | −0.729008 | − | 0.684505i | \(-0.760018\pi\) |
0.957303 | + | 0.289087i | \(0.0933517\pi\) | |||||||
\(318\) | 1633.50 | + | 2829.30i | 0.288057 | + | 0.498929i | ||||
\(319\) | −2227.50 | − | 3858.14i | −0.390959 | − | 0.677162i | ||||
\(320\) | 649.500 | − | 1124.97i | 0.113463 | − | 0.196524i | ||||
\(321\) | −4059.00 | −0.705767 | ||||||||
\(322\) | 4410.00 | − | 1527.67i | 0.763229 | − | 0.264390i | ||||
\(323\) | −1344.00 | −0.231524 | ||||||||
\(324\) | −40.5000 | + | 70.1481i | −0.00694444 | + | 0.0120281i | ||||
\(325\) | −3712.00 | − | 6429.37i | −0.633553 | − | 1.09735i | ||||
\(326\) | −1878.00 | − | 3252.79i | −0.319058 | − | 0.552624i | ||||
\(327\) | 555.000 | − | 961.288i | 0.0938580 | − | 0.162567i | ||||
\(328\) | 7560.00 | 1.27266 | ||||||||
\(329\) | 420.000 | + | 363.731i | 0.0703810 | + | 0.0609517i | ||||
\(330\) | −405.000 | −0.0675591 | ||||||||
\(331\) | 242.000 | − | 419.156i | 0.0401859 | − | 0.0696040i | −0.845233 | − | 0.534398i | \(-0.820538\pi\) |
0.885419 | + | 0.464794i | \(0.153872\pi\) | |||||||
\(332\) | −238.500 | − | 413.094i | −0.0394259 | − | 0.0682876i | ||||
\(333\) | 1422.00 | + | 2462.98i | 0.234009 | + | 0.405316i | ||||
\(334\) | −3969.00 | + | 6874.51i | −0.650222 | + | 1.12622i | ||||
\(335\) | 1110.00 | 0.181032 | ||||||||
\(336\) | 745.500 | − | 3873.73i | 0.121043 | − | 0.628957i | ||||
\(337\) | −8359.00 | −1.35117 | −0.675584 | − | 0.737283i | \(-0.736109\pi\) | ||||
−0.675584 | + | 0.737283i | \(0.736109\pi\) | |||||||
\(338\) | 2848.50 | − | 4933.75i | 0.458396 | − | 0.793966i | ||||
\(339\) | 972.000 | + | 1683.55i | 0.155728 | + | 0.269729i | ||||
\(340\) | 126.000 | + | 218.238i | 0.0200980 | + | 0.0348107i | ||||
\(341\) | −1897.50 | + | 3286.57i | −0.301335 | + | 0.521928i | ||||
\(342\) | 432.000 | 0.0683038 | ||||||||
\(343\) | 3430.00 | − | 5346.84i | 0.539949 | − | 0.841698i | ||||
\(344\) | 546.000 | 0.0855766 | ||||||||
\(345\) | −378.000 | + | 654.715i | −0.0589879 | + | 0.102170i | ||||
\(346\) | −1179.00 | − | 2042.09i | −0.183189 | − | 0.317293i | ||||
\(347\) | 930.000 | + | 1610.81i | 0.143876 | + | 0.249201i | 0.928953 | − | 0.370197i | \(-0.120710\pi\) |
−0.785077 | + | 0.619398i | \(0.787377\pi\) | |||||||
\(348\) | 445.500 | − | 771.629i | 0.0686244 | − | 0.118861i | ||||
\(349\) | −1918.00 | −0.294178 | −0.147089 | − | 0.989123i | \(-0.546990\pi\) | ||||
−0.147089 | + | 0.989123i | \(0.546990\pi\) | |||||||
\(350\) | −1218.00 | + | 6328.91i | −0.186014 | + | 0.966556i | ||||
\(351\) | −1728.00 | −0.262774 | ||||||||
\(352\) | 337.500 | − | 584.567i | 0.0511046 | − | 0.0885157i | ||||
\(353\) | 1524.00 | + | 2639.65i | 0.229786 | + | 0.398000i | 0.957744 | − | 0.287620i | \(-0.0928642\pi\) |
−0.727959 | + | 0.685621i | \(0.759531\pi\) | |||||||
\(354\) | −67.5000 | − | 116.913i | −0.0101344 | − | 0.0175533i | ||||
\(355\) | −513.000 | + | 888.542i | −0.0766964 | + | 0.132842i | ||||
\(356\) | 906.000 | 0.134882 | ||||||||
\(357\) | −3528.00 | − | 3055.34i | −0.523030 | − | 0.452957i | ||||
\(358\) | −8676.00 | −1.28084 | ||||||||
\(359\) | 15.0000 | − | 25.9808i | 0.00220521 | − | 0.00381953i | −0.864921 | − | 0.501909i | \(-0.832631\pi\) |
0.867126 | + | 0.498089i | \(0.165965\pi\) | |||||||
\(360\) | 283.500 | + | 491.036i | 0.0415049 | + | 0.0718886i | ||||
\(361\) | 3301.50 | + | 5718.37i | 0.481338 | + | 0.833703i | ||||
\(362\) | 2028.00 | − | 3512.60i | 0.294446 | − | 0.509995i | ||||
\(363\) | −3318.00 | −0.479752 | ||||||||
\(364\) | −1120.00 | + | 387.979i | −0.161275 | + | 0.0558672i | ||||
\(365\) | −1086.00 | −0.155737 | ||||||||
\(366\) | −531.000 | + | 919.719i | −0.0758356 | + | 0.131351i | ||||
\(367\) | 5655.50 | + | 9795.61i | 0.804400 | + | 1.39326i | 0.916696 | + | 0.399586i | \(0.130846\pi\) |
−0.112296 | + | 0.993675i | \(0.535820\pi\) | |||||||
\(368\) | −2982.00 | − | 5164.98i | −0.422412 | − | 0.731638i | ||||
\(369\) | −1620.00 | + | 2805.92i | −0.228547 | + | 0.395855i | ||||
\(370\) | −2844.00 | −0.399601 | ||||||||
\(371\) | 6352.50 | − | 2200.57i | 0.888963 | − | 0.307946i | ||||
\(372\) | −759.000 | −0.105786 | ||||||||
\(373\) | −604.000 | + | 1046.16i | −0.0838443 | + | 0.145223i | −0.904898 | − | 0.425628i | \(-0.860053\pi\) |
0.821054 | + | 0.570851i | \(0.193387\pi\) | |||||||
\(374\) | −1890.00 | − | 3273.58i | −0.261309 | − | 0.452600i | ||||
\(375\) | −1084.50 | − | 1878.41i | −0.149342 | − | 0.258668i | ||||
\(376\) | 315.000 | − | 545.596i | 0.0432045 | − | 0.0748324i | ||||
\(377\) | 19008.0 | 2.59672 | ||||||||
\(378\) | 1134.00 | + | 982.073i | 0.154303 | + | 0.133631i | ||||
\(379\) | 7640.00 | 1.03546 | 0.517731 | − | 0.855543i | \(-0.326777\pi\) | ||||
0.517731 | + | 0.855543i | \(0.326777\pi\) | |||||||
\(380\) | −24.0000 | + | 41.5692i | −0.00323993 | + | 0.00561173i | ||||
\(381\) | −565.500 | − | 979.475i | −0.0760405 | − | 0.131706i | ||||
\(382\) | 5868.00 | + | 10163.7i | 0.785950 | + | 1.36131i | ||||
\(383\) | −6375.00 | + | 11041.8i | −0.850515 | + | 1.47314i | 0.0302291 | + | 0.999543i | \(0.490376\pi\) |
−0.880744 | + | 0.473592i | \(0.842957\pi\) | |||||||
\(384\) | −4977.00 | −0.661410 | ||||||||
\(385\) | −157.500 | + | 818.394i | −0.0208492 | + | 0.108336i | ||||
\(386\) | −4479.00 | −0.590609 | ||||||||
\(387\) | −117.000 | + | 202.650i | −0.0153681 | + | 0.0266183i | ||||
\(388\) | −251.500 | − | 435.611i | −0.0329072 | − | 0.0569969i | ||||
\(389\) | −1563.00 | − | 2707.20i | −0.203720 | − | 0.352854i | 0.746004 | − | 0.665942i | \(-0.231970\pi\) |
−0.949724 | + | 0.313087i | \(0.898637\pi\) | |||||||
\(390\) | 864.000 | − | 1496.49i | 0.112180 | − | 0.194302i | ||||
\(391\) | −7056.00 | −0.912627 | ||||||||
\(392\) | −6688.50 | − | 2673.42i | −0.861786 | − | 0.344459i | ||||
\(393\) | −1953.00 | −0.250676 | ||||||||
\(394\) | −6129.00 | + | 10615.7i | −0.783692 | + | 1.35739i | ||||
\(395\) | 700.500 | + | 1213.30i | 0.0892303 | + | 0.154551i | ||||
\(396\) | 67.5000 | + | 116.913i | 0.00856566 | + | 0.0148362i | ||||
\(397\) | 2966.00 | − | 5137.26i | 0.374960 | − | 0.649450i | −0.615361 | − | 0.788246i | \(-0.710990\pi\) |
0.990321 | + | 0.138795i | \(0.0443230\pi\) | |||||||
\(398\) | 10668.0 | 1.34356 | ||||||||
\(399\) | 168.000 | − | 872.954i | 0.0210790 | − | 0.109530i | ||||
\(400\) | 8236.00 | 1.02950 | ||||||||
\(401\) | −804.000 | + | 1392.57i | −0.100124 | + | 0.173420i | −0.911736 | − | 0.410777i | \(-0.865257\pi\) |
0.811611 | + | 0.584198i | \(0.198591\pi\) | |||||||
\(402\) | −1665.00 | − | 2883.86i | −0.206574 | − | 0.357796i | ||||
\(403\) | −8096.00 | − | 14022.7i | −1.00072 | − | 1.73330i | ||||
\(404\) | 543.000 | − | 940.504i | 0.0668695 | − | 0.115821i | ||||
\(405\) | −243.000 | −0.0298142 | ||||||||
\(406\) | −12474.0 | − | 10802.8i | −1.52481 | − | 1.32053i | ||||
\(407\) | 4740.00 | 0.577280 | ||||||||
\(408\) | −2646.00 | + | 4583.01i | −0.321070 | + | 0.556109i | ||||
\(409\) | 2232.50 | + | 3866.80i | 0.269902 | + | 0.467484i | 0.968836 | − | 0.247702i | \(-0.0796753\pi\) |
−0.698934 | + | 0.715186i | \(0.746342\pi\) | |||||||
\(410\) | −1620.00 | − | 2805.92i | −0.195137 | − | 0.337987i | ||||
\(411\) | 2655.00 | − | 4598.59i | 0.318641 | − | 0.551903i | ||||
\(412\) | 1736.00 | 0.207589 | ||||||||
\(413\) | −262.500 | + | 90.9327i | −0.0312755 | + | 0.0108342i | ||||
\(414\) | 2268.00 | 0.269242 | ||||||||
\(415\) | 715.500 | − | 1239.28i | 0.0846326 | − | 0.146588i | ||||
\(416\) | 1440.00 | + | 2494.15i | 0.169716 | + | 0.293957i | ||||
\(417\) | 2337.00 | + | 4047.80i | 0.274445 | + | 0.475352i | ||||
\(418\) | 360.000 | − | 623.538i | 0.0421248 | − | 0.0729623i | ||||
\(419\) | −1584.00 | −0.184686 | −0.0923430 | − | 0.995727i | \(-0.529436\pi\) | ||||
−0.0923430 | + | 0.995727i | \(0.529436\pi\) | |||||||
\(420\) | −157.500 | + | 54.5596i | −0.0182981 | + | 0.00633866i | ||||
\(421\) | −1330.00 | −0.153967 | −0.0769837 | − | 0.997032i | \(-0.524529\pi\) | ||||
−0.0769837 | + | 0.997032i | \(0.524529\pi\) | |||||||
\(422\) | 1875.00 | − | 3247.60i | 0.216288 | − | 0.374622i | ||||
\(423\) | 135.000 | + | 233.827i | 0.0155176 | + | 0.0268772i | ||||
\(424\) | −3811.50 | − | 6601.71i | −0.436563 | − | 0.756150i | ||||
\(425\) | 4872.00 | − | 8438.55i | 0.556063 | − | 0.963129i | ||||
\(426\) | 3078.00 | 0.350069 | ||||||||
\(427\) | 1652.00 | + | 1430.67i | 0.187227 | + | 0.162143i | ||||
\(428\) | −1353.00 | −0.152803 | ||||||||
\(429\) | −1440.00 | + | 2494.15i | −0.162060 | + | 0.280697i | ||||
\(430\) | −117.000 | − | 202.650i | −0.0131215 | − | 0.0227271i | ||||
\(431\) | −4794.00 | − | 8303.45i | −0.535775 | − | 0.927989i | −0.999125 | − | 0.0418139i | \(-0.986686\pi\) |
0.463351 | − | 0.886175i | \(-0.346647\pi\) | |||||||
\(432\) | 958.500 | − | 1660.17i | 0.106750 | − | 0.184896i | ||||
\(433\) | 494.000 | 0.0548271 | 0.0274135 | − | 0.999624i | \(-0.491273\pi\) | ||||
0.0274135 | + | 0.999624i | \(0.491273\pi\) | |||||||
\(434\) | −2656.50 | + | 13803.6i | −0.293816 | + | 1.52671i | ||||
\(435\) | 2673.00 | 0.294622 | ||||||||
\(436\) | 185.000 | − | 320.429i | 0.0203209 | − | 0.0351968i | ||||
\(437\) | −672.000 | − | 1163.94i | −0.0735609 | − | 0.127411i | ||||
\(438\) | 1629.00 | + | 2821.51i | 0.177709 | + | 0.307801i | ||||
\(439\) | 8004.50 | − | 13864.2i | 0.870237 | − | 1.50729i | 0.00848508 | − | 0.999964i | \(-0.497299\pi\) |
0.861752 | − | 0.507330i | \(-0.169368\pi\) | |||||||
\(440\) | 945.000 | 0.102389 | ||||||||
\(441\) | 2425.50 | − | 1909.59i | 0.261905 | − | 0.206197i | ||||
\(442\) | 16128.0 | 1.73559 | ||||||||
\(443\) | −3886.50 | + | 6731.62i | −0.416824 | + | 0.721961i | −0.995618 | − | 0.0935130i | \(-0.970190\pi\) |
0.578794 | + | 0.815474i | \(0.303524\pi\) | |||||||
\(444\) | 474.000 | + | 820.992i | 0.0506645 | + | 0.0877535i | ||||
\(445\) | 1359.00 | + | 2353.86i | 0.144770 | + | 0.250749i | ||||
\(446\) | 637.500 | − | 1104.18i | 0.0676827 | − | 0.117230i | ||||
\(447\) | 7362.00 | 0.778995 | ||||||||
\(448\) | −1515.50 | + | 7874.77i | −0.159823 | + | 0.830464i | ||||
\(449\) | 864.000 | 0.0908122 | 0.0454061 | − | 0.998969i | \(-0.485542\pi\) | ||||
0.0454061 | + | 0.998969i | \(0.485542\pi\) | |||||||
\(450\) | −1566.00 | + | 2712.39i | −0.164049 | + | 0.284141i | ||||
\(451\) | 2700.00 | + | 4676.54i | 0.281903 | + | 0.488269i | ||||
\(452\) | 324.000 | + | 561.184i | 0.0337161 | + | 0.0583980i | ||||
\(453\) | −1888.50 | + | 3270.98i | −0.195871 | + | 0.339258i | ||||
\(454\) | −11565.0 | −1.19553 | ||||||||
\(455\) | −2688.00 | − | 2327.88i | −0.276957 | − | 0.239852i | ||||
\(456\) | −1008.00 | −0.103517 | ||||||||
\(457\) | −1259.50 | + | 2181.52i | −0.128921 | + | 0.223298i | −0.923259 | − | 0.384179i | \(-0.874485\pi\) |
0.794338 | + | 0.607476i | \(0.207818\pi\) | |||||||
\(458\) | −3282.00 | − | 5684.59i | −0.334842 | − | 0.579964i | ||||
\(459\) | −1134.00 | − | 1964.15i | −0.115317 | − | 0.199735i | ||||
\(460\) | −126.000 | + | 218.238i | −0.0127713 | + | 0.0221205i | ||||
\(461\) | −342.000 | −0.0345521 | −0.0172761 | − | 0.999851i | \(-0.505499\pi\) | ||||
−0.0172761 | + | 0.999851i | \(0.505499\pi\) | |||||||
\(462\) | 2362.50 | − | 818.394i | 0.237908 | − | 0.0824137i | ||||
\(463\) | −4336.00 | −0.435229 | −0.217614 | − | 0.976035i | \(-0.569828\pi\) | ||||
−0.217614 | + | 0.976035i | \(0.569828\pi\) | |||||||
\(464\) | −10543.5 | + | 18261.9i | −1.05489 | + | 1.82713i | ||||
\(465\) | −1138.50 | − | 1971.94i | −0.113541 | − | 0.196659i | ||||
\(466\) | 1278.00 | + | 2213.56i | 0.127043 | + | 0.220046i | ||||
\(467\) | −9318.00 | + | 16139.2i | −0.923310 | + | 1.59922i | −0.129052 | + | 0.991638i | \(0.541194\pi\) |
−0.794257 | + | 0.607581i | \(0.792140\pi\) | |||||||
\(468\) | −576.000 | −0.0568923 | ||||||||
\(469\) | −6475.00 | + | 2243.01i | −0.637500 | + | 0.220837i | ||||
\(470\) | −270.000 | −0.0264982 | ||||||||
\(471\) | 294.000 | − | 509.223i | 0.0287618 | − | 0.0498169i | ||||
\(472\) | 157.500 | + | 272.798i | 0.0153592 | + | 0.0266029i | ||||
\(473\) | 195.000 | + | 337.750i | 0.0189558 | + | 0.0328325i | ||||
\(474\) | 2101.50 | − | 3639.90i | 0.203639 | − | 0.352714i | ||||
\(475\) | 1856.00 | 0.179282 | ||||||||
\(476\) | −1176.00 | − | 1018.45i | −0.113239 | − | 0.0980680i | ||||
\(477\) | 3267.00 | 0.313597 | ||||||||
\(478\) | 8262.00 | − | 14310.2i | 0.790575 | − | 1.36932i | ||||
\(479\) | −7539.00 | − | 13057.9i | −0.719135 | − | 1.24558i | −0.961343 | − | 0.275354i | \(-0.911205\pi\) |
0.242208 | − | 0.970224i | \(-0.422128\pi\) | |||||||
\(480\) | 202.500 | + | 350.740i | 0.0192559 | + | 0.0333521i | ||||
\(481\) | −10112.0 | + | 17514.5i | −0.958560 | + | 1.66028i | ||||
\(482\) | −2373.00 | −0.224247 | ||||||||
\(483\) | 882.000 | − | 4583.01i | 0.0830898 | − | 0.431747i | ||||
\(484\) | −1106.00 | −0.103869 | ||||||||
\(485\) | 754.500 | − | 1306.83i | 0.0706393 | − | 0.122351i | ||||
\(486\) | 364.500 | + | 631.333i | 0.0340207 | + | 0.0589256i | ||||
\(487\) | −3110.50 | − | 5387.54i | −0.289425 | − | 0.501300i | 0.684247 | − | 0.729250i | \(-0.260131\pi\) |
−0.973673 | + | 0.227950i | \(0.926798\pi\) | |||||||
\(488\) | 1239.00 | − | 2146.01i | 0.114932 | − | 0.199068i | ||||
\(489\) | −3756.00 | −0.347346 | ||||||||
\(490\) | 441.000 | + | 3055.34i | 0.0406579 | + | 0.281686i | ||||
\(491\) | −7371.00 | −0.677492 | −0.338746 | − | 0.940878i | \(-0.610003\pi\) | ||||
−0.338746 | + | 0.940878i | \(0.610003\pi\) | |||||||
\(492\) | −540.000 | + | 935.307i | −0.0494819 | + | 0.0857051i | ||||
\(493\) | 12474.0 | + | 21605.6i | 1.13956 | + | 1.97377i | ||||
\(494\) | 1536.00 | + | 2660.43i | 0.139895 | + | 0.242304i | ||||
\(495\) | −202.500 | + | 350.740i | −0.0183873 | + | 0.0318477i | ||||
\(496\) | 17963.0 | 1.62613 | ||||||||
\(497\) | 1197.00 | − | 6219.79i | 0.108034 | − | 0.561360i | ||||
\(498\) | −4293.00 | −0.386293 | ||||||||
\(499\) | −2137.00 | + | 3701.39i | −0.191714 | + | 0.332058i | −0.945818 | − | 0.324696i | \(-0.894738\pi\) |
0.754104 | + | 0.656755i | \(0.228071\pi\) | |||||||
\(500\) | −361.500 | − | 626.136i | −0.0323335 | − | 0.0560033i | ||||
\(501\) | 3969.00 | + | 6874.51i | 0.353936 | + | 0.613035i | ||||
\(502\) | 7897.50 | − | 13678.9i | 0.702157 | − | 1.21617i | ||||
\(503\) | −2520.00 | −0.223382 | −0.111691 | − | 0.993743i | \(-0.535627\pi\) | ||||
−0.111691 | + | 0.993743i | \(0.535627\pi\) | |||||||
\(504\) | −2646.00 | − | 2291.50i | −0.233854 | − | 0.202523i | ||||
\(505\) | 3258.00 | 0.287087 | ||||||||
\(506\) | 1890.00 | − | 3273.58i | 0.166049 | − | 0.287605i | ||||
\(507\) | −2848.50 | − | 4933.75i | −0.249519 | − | 0.432180i | ||||
\(508\) | −188.500 | − | 326.492i | −0.0164633 | − | 0.0285152i | ||||
\(509\) | 7138.50 | − | 12364.2i | 0.621628 | − | 1.07669i | −0.367555 | − | 0.930002i | \(-0.619805\pi\) |
0.989183 | − | 0.146689i | \(-0.0468616\pi\) | |||||||
\(510\) | 2268.00 | 0.196919 | ||||||||
\(511\) | 6335.00 | − | 2194.51i | 0.548423 | − | 0.189979i | ||||
\(512\) | 8733.00 | 0.753804 | ||||||||
\(513\) | 216.000 | − | 374.123i | 0.0185899 | − | 0.0321987i | ||||
\(514\) | −10305.0 | − | 17848.8i | −0.884308 | − | 1.53167i | ||||
\(515\) | 2604.00 | + | 4510.26i | 0.222808 | + | 0.385914i | ||||
\(516\) | −39.0000 | + | 67.5500i | −0.00332729 | + | 0.00576303i | ||||
\(517\) | 450.000 | 0.0382804 | ||||||||
\(518\) | 16590.0 | − | 5746.94i | 1.40719 | − | 0.487464i | ||||
\(519\) | −2358.00 | −0.199431 | ||||||||
\(520\) | −2016.00 | + | 3491.81i | −0.170014 | + | 0.294473i | ||||
\(521\) | 3153.00 | + | 5461.16i | 0.265135 | + | 0.459228i | 0.967599 | − | 0.252492i | \(-0.0812501\pi\) |
−0.702464 | + | 0.711719i | \(0.747917\pi\) | |||||||
\(522\) | −4009.50 | − | 6944.66i | −0.336190 | − | 0.582298i | ||||
\(523\) | −4036.00 | + | 6990.56i | −0.337442 | + | 0.584466i | −0.983951 | − | 0.178440i | \(-0.942895\pi\) |
0.646509 | + | 0.762906i | \(0.276228\pi\) | |||||||
\(524\) | −651.000 | −0.0542730 | ||||||||
\(525\) | 4872.00 | + | 4219.28i | 0.405012 | + | 0.350751i | ||||
\(526\) | 666.000 | 0.0552072 | ||||||||
\(527\) | 10626.0 | − | 18404.8i | 0.878322 | − | 1.52130i | ||||
\(528\) | −1597.50 | − | 2766.95i | −0.131671 | − | 0.228061i | ||||
\(529\) | 2555.50 | + | 4426.26i | 0.210035 | + | 0.363792i | ||||
\(530\) | −1633.50 | + | 2829.30i | −0.133877 | + | 0.231881i | ||||
\(531\) | −135.000 | −0.0110330 | ||||||||
\(532\) | 56.0000 | − | 290.985i | 0.00456374 | − | 0.0237139i | ||||
\(533\) | −23040.0 | −1.87237 | ||||||||
\(534\) | 4077.00 | − | 7061.57i | 0.330391 | − | 0.572255i | ||||
\(535\) | −2029.50 | − | 3515.20i | −0.164005 | − | 0.284066i | ||||
\(536\) | 3885.00 | + | 6729.02i | 0.313072 | + | 0.542256i | ||||
\(537\) | −4338.00 | + | 7513.64i | −0.348601 | + | 0.603794i | ||||
\(538\) | −23553.0 | −1.88744 | ||||||||
\(539\) | −735.000 | − | 5092.23i | −0.0587360 | − | 0.406935i | ||||
\(540\) | −81.0000 | −0.00645497 | ||||||||
\(541\) | 11429.0 | − | 19795.6i | 0.908264 | − | 1.57316i | 0.0917903 | − | 0.995778i | \(-0.470741\pi\) |
0.816474 | − | 0.577382i | \(-0.195926\pi\) | |||||||
\(542\) | 7774.50 | + | 13465.8i | 0.616132 | + | 1.06717i | ||||
\(543\) | −2028.00 | − | 3512.60i | −0.160276 | − | 0.277606i | ||||
\(544\) | −1890.00 | + | 3273.58i | −0.148958 | + | 0.258003i | ||||
\(545\) | 1110.00 | 0.0872425 | ||||||||
\(546\) | −2016.00 | + | 10475.4i | −0.158016 | + | 0.821076i | ||||
\(547\) | −24724.0 | −1.93258 | −0.966291 | − | 0.257454i | \(-0.917116\pi\) | ||||
−0.966291 | + | 0.257454i | \(0.917116\pi\) | |||||||
\(548\) | 885.000 | − | 1532.86i | 0.0689878 | − | 0.119490i | ||||
\(549\) | 531.000 | + | 919.719i | 0.0412796 | + | 0.0714985i | ||||
\(550\) | 2610.00 | + | 4520.65i | 0.202347 | + | 0.350475i | ||||
\(551\) | −2376.00 | + | 4115.35i | −0.183704 | + | 0.318185i | ||||
\(552\) | −5292.00 | −0.408048 | ||||||||
\(553\) | −6538.00 | − | 5662.07i | −0.502756 | − | 0.435399i | ||||
\(554\) | 14880.0 | 1.14114 | ||||||||
\(555\) | −1422.00 | + | 2462.98i | −0.108758 | + | 0.188374i | ||||
\(556\) | 779.000 | + | 1349.27i | 0.0594190 | + | 0.102917i | ||||
\(557\) | 4921.50 | + | 8524.29i | 0.374382 | + | 0.648448i | 0.990234 | − | 0.139413i | \(-0.0445216\pi\) |
−0.615853 | + | 0.787861i | \(0.711188\pi\) | |||||||
\(558\) | −3415.50 | + | 5915.82i | −0.259121 | + | 0.448811i | ||||
\(559\) | −1664.00 | −0.125903 | ||||||||
\(560\) | 3727.50 | − | 1291.24i | 0.281278 | − | 0.0974375i | ||||
\(561\) | −3780.00 | −0.284477 | ||||||||
\(562\) | −1161.00 | + | 2010.91i | −0.0871420 | + | 0.150934i | ||||
\(563\) | 6685.50 | + | 11579.6i | 0.500462 | + | 0.866826i | 1.00000 | 0.000533812i | \(0.000169918\pi\) | |
−0.499538 | + | 0.866292i | \(0.666497\pi\) | |||||||
\(564\) | 45.0000 | + | 77.9423i | 0.00335965 | + | 0.00581908i | ||||
\(565\) | −972.000 | + | 1683.55i | −0.0723758 | + | 0.125359i | ||||
\(566\) | −11094.0 | −0.823879 | ||||||||
\(567\) | 1417.50 | − | 491.036i | 0.104990 | − | 0.0363696i | ||||
\(568\) | −7182.00 | −0.530546 | ||||||||
\(569\) | 2616.00 | − | 4531.04i | 0.192739 | − | 0.333834i | −0.753418 | − | 0.657542i | \(-0.771596\pi\) |
0.946157 | + | 0.323708i | \(0.104930\pi\) | |||||||
\(570\) | 216.000 | + | 374.123i | 0.0158724 | + | 0.0274917i | ||||
\(571\) | 7199.00 | + | 12469.0i | 0.527616 | + | 0.913858i | 0.999482 | + | 0.0321874i | \(0.0102474\pi\) |
−0.471866 | + | 0.881670i | \(0.656419\pi\) | |||||||
\(572\) | −480.000 | + | 831.384i | −0.0350871 | + | 0.0607726i | ||||
\(573\) | 11736.0 | 0.855634 | ||||||||
\(574\) | 15120.0 | + | 13094.3i | 1.09947 | + | 0.952170i | ||||
\(575\) | 9744.00 | 0.706701 | ||||||||
\(576\) | −1948.50 | + | 3374.90i | −0.140951 | + | 0.244133i | ||||
\(577\) | −9935.50 | − | 17208.8i | −0.716846 | − | 1.24161i | −0.962243 | − | 0.272191i | \(-0.912252\pi\) |
0.245397 | − | 0.969423i | \(-0.421082\pi\) | |||||||
\(578\) | 3214.50 | + | 5567.68i | 0.231325 | + | 0.400666i | ||||
\(579\) | −2239.50 | + | 3878.93i | −0.160743 | + | 0.278416i | ||||
\(580\) | 891.000 | 0.0637875 | ||||||||
\(581\) | −1669.50 | + | 8674.98i | −0.119213 | + | 0.619447i | ||||
\(582\) | −4527.00 | −0.322423 | ||||||||
\(583\) | 2722.50 | − | 4715.51i | 0.193404 | − | 0.334985i | ||||
\(584\) | −3801.00 | − | 6583.53i | −0.269326 | − | 0.466487i | ||||
\(585\) | −864.000 | − | 1496.49i | −0.0610633 | − | 0.105765i | ||||
\(586\) | −9409.50 | + | 16297.7i | −0.663315 | + | 1.14890i | ||||
\(587\) | −16137.0 | −1.13466 | −0.567330 | − | 0.823491i | \(-0.692024\pi\) | ||||
−0.567330 | + | 0.823491i | \(0.692024\pi\) | |||||||
\(588\) | 808.500 | − | 636.529i | 0.0567040 | − | 0.0446429i | ||||
\(589\) | 4048.00 | 0.283183 | ||||||||
\(590\) | 67.5000 | − | 116.913i | 0.00471005 | − | 0.00815805i | ||||
\(591\) | 6129.00 | + | 10615.7i | 0.426588 | + | 0.738872i | ||||
\(592\) | −11218.0 | − | 19430.1i | −0.778812 | − | 1.34894i | ||||
\(593\) | 10662.0 | − | 18467.1i | 0.738340 | − | 1.27884i | −0.214902 | − | 0.976636i | \(-0.568943\pi\) |
0.953242 | − | 0.302207i | \(-0.0977235\pi\) | |||||||
\(594\) | 1215.00 | 0.0839260 | ||||||||
\(595\) | 882.000 | − | 4583.01i | 0.0607705 | − | 0.315773i | ||||
\(596\) | 2454.00 | 0.168657 | ||||||||
\(597\) | 5334.00 | − | 9238.76i | 0.365672 | − | 0.633362i | ||||
\(598\) | 8064.00 | + | 13967.3i | 0.551441 | + | 0.955123i | ||||
\(599\) | 4323.00 | + | 7487.66i | 0.294880 | + | 0.510747i | 0.974957 | − | 0.222394i | \(-0.0713871\pi\) |
−0.680077 | + | 0.733141i | \(0.738054\pi\) | |||||||
\(600\) | 3654.00 | − | 6328.91i | 0.248623 | − | 0.430628i | ||||
\(601\) | 11195.0 | 0.759823 | 0.379911 | − | 0.925023i | \(-0.375954\pi\) | ||||
0.379911 | + | 0.925023i | \(0.375954\pi\) | |||||||
\(602\) | 1092.00 | + | 945.700i | 0.0739312 | + | 0.0640263i | ||||
\(603\) | −3330.00 | −0.224889 | ||||||||
\(604\) | −629.500 | + | 1090.33i | −0.0424073 | + | 0.0734515i | ||||
\(605\) | −1659.00 | − | 2873.47i | −0.111484 | − | 0.193096i | ||||
\(606\) | −4887.00 | − | 8464.53i | −0.327592 | − | 0.567406i | ||||
\(607\) | 4485.50 | − | 7769.11i | 0.299935 | − | 0.519503i | −0.676185 | − | 0.736731i | \(-0.736368\pi\) |
0.976121 | + | 0.217228i | \(0.0697015\pi\) | |||||||
\(608\) | −720.000 | −0.0480261 | ||||||||
\(609\) | −15592.5 | + | 5401.40i | −1.03750 | + | 0.359402i | ||||
\(610\) | −1062.00 | −0.0704904 | ||||||||
\(611\) | −960.000 | + | 1662.77i | −0.0635637 | + | 0.110096i | ||||
\(612\) | −378.000 | − | 654.715i | −0.0249669 | − | 0.0432439i | ||||
\(613\) | 6386.00 | + | 11060.9i | 0.420764 | + | 0.728784i | 0.996014 | − | 0.0891932i | \(-0.0284288\pi\) |
−0.575251 | + | 0.817977i | \(0.695096\pi\) | |||||||
\(614\) | −2526.00 | + | 4375.16i | −0.166028 | + | 0.287569i | ||||
\(615\) | −3240.00 | −0.212438 | ||||||||
\(616\) | −5512.50 | + | 1909.59i | −0.360560 | + | 0.124902i | ||||
\(617\) | 12762.0 | 0.832705 | 0.416352 | − | 0.909203i | \(-0.363308\pi\) | ||||
0.416352 | + | 0.909203i | \(0.363308\pi\) | |||||||
\(618\) | 7812.00 | − | 13530.8i | 0.508487 | − | 0.880725i | ||||
\(619\) | −6421.00 | − | 11121.5i | −0.416933 | − | 0.722150i | 0.578696 | − | 0.815543i | \(-0.303562\pi\) |
−0.995629 | + | 0.0933936i | \(0.970229\pi\) | |||||||
\(620\) | −379.500 | − | 657.313i | −0.0245824 | − | 0.0425780i | ||||
\(621\) | 1134.00 | − | 1964.15i | 0.0732783 | − | 0.126922i | ||||
\(622\) | 3960.00 | 0.255276 | ||||||||
\(623\) | −12684.0 | − | 10984.7i | −0.815688 | − | 0.706407i | ||||
\(624\) | 13632.0 | 0.874546 | ||||||||
\(625\) | −6165.50 | + | 10679.0i | −0.394592 | + | 0.683453i | ||||
\(626\) | −12754.5 | − | 22091.4i | −0.814333 | − | 1.41047i | ||||
\(627\) | −360.000 | − | 623.538i | −0.0229298 | − | 0.0397157i | ||||
\(628\) | 98.0000 | − | 169.741i | 0.00622711 | − | 0.0107857i | ||||
\(629\) | −26544.0 | −1.68264 | ||||||||
\(630\) | −283.500 | + | 1473.11i | −0.0179284 | + | 0.0931589i | ||||
\(631\) | 21365.0 | 1.34790 | 0.673952 | − | 0.738775i | \(-0.264596\pi\) | ||||
0.673952 | + | 0.738775i | \(0.264596\pi\) | |||||||
\(632\) | −4903.50 | + | 8493.11i | −0.308625 | + | 0.534554i | ||||
\(633\) | −1875.00 | − | 3247.60i | −0.117732 | − | 0.203918i | ||||
\(634\) | −3865.50 | − | 6695.24i | −0.242143 | − | 0.419404i | ||||
\(635\) | 565.500 | − | 979.475i | 0.0353404 | − | 0.0612114i | ||||
\(636\) | 1089.00 | 0.0678957 | ||||||||
\(637\) | 20384.0 | + | 8147.57i | 1.26789 | + | 0.506779i | ||||
\(638\) | −13365.0 | −0.829350 | ||||||||
\(639\) | 1539.00 | − | 2665.63i | 0.0952768 | − | 0.165024i | ||||
\(640\) | −2488.50 | − | 4310.21i | −0.153698 | − | 0.266212i | ||||
\(641\) | −4137.00 | − | 7165.49i | −0.254917 | − | 0.441529i | 0.709956 | − | 0.704246i | \(-0.248715\pi\) |
−0.964873 | + | 0.262717i | \(0.915381\pi\) | |||||||
\(642\) | −6088.50 | + | 10545.6i | −0.374290 | + | 0.648289i | ||||
\(643\) | 27998.0 | 1.71716 | 0.858580 | − | 0.512680i | \(-0.171347\pi\) | ||||
0.858580 | + | 0.512680i | \(0.171347\pi\) | |||||||
\(644\) | 294.000 | − | 1527.67i | 0.0179895 | − | 0.0934761i | ||||
\(645\) | −234.000 | −0.0142849 | ||||||||
\(646\) | −2016.00 | + | 3491.81i | −0.122784 | + | 0.212668i | ||||
\(647\) | 8733.00 | + | 15126.0i | 0.530649 | + | 0.919110i | 0.999360 | + | 0.0357592i | \(0.0113849\pi\) |
−0.468712 | + | 0.883351i | \(0.655282\pi\) | |||||||
\(648\) | −850.500 | − | 1473.11i | −0.0515599 | − | 0.0893043i | ||||
\(649\) | −112.500 | + | 194.856i | −0.00680433 | + | 0.0117854i | ||||
\(650\) | −22272.0 | −1.34397 | ||||||||
\(651\) | 10626.0 | + | 9202.39i | 0.639732 | + | 0.554024i | ||||
\(652\) | −1252.00 | −0.0752026 | ||||||||
\(653\) | −1078.50 | + | 1868.02i | −0.0646324 | + | 0.111947i | −0.896531 | − | 0.442981i | \(-0.853921\pi\) |
0.831898 | + | 0.554928i | \(0.187254\pi\) | |||||||
\(654\) | −1665.00 | − | 2883.86i | −0.0995515 | − | 0.172428i | ||||
\(655\) | −976.500 | − | 1691.35i | −0.0582519 | − | 0.100895i | ||||
\(656\) | 12780.0 | − | 22135.6i | 0.760633 | − | 1.31745i | ||||
\(657\) | 3258.00 | 0.193465 | ||||||||
\(658\) | 1575.00 | − | 545.596i | 0.0933129 | − | 0.0323245i | ||||
\(659\) | 19944.0 | 1.17892 | 0.589460 | − | 0.807798i | \(-0.299341\pi\) | ||||
0.589460 | + | 0.807798i | \(0.299341\pi\) | |||||||
\(660\) | −67.5000 | + | 116.913i | −0.00398096 | + | 0.00689523i | ||||
\(661\) | −13753.0 | − | 23820.9i | −0.809273 | − | 1.40170i | −0.913368 | − | 0.407135i | \(-0.866528\pi\) |
0.104095 | − | 0.994567i | \(-0.466806\pi\) | |||||||
\(662\) | −726.000 | − | 1257.47i | −0.0426236 | − | 0.0738262i | ||||
\(663\) | 8064.00 | − | 13967.3i | 0.472368 | − | 0.818165i | ||||
\(664\) | 10017.0 | 0.585444 | ||||||||
\(665\) | 840.000 | − | 290.985i | 0.0489832 | − | 0.0169683i | ||||
\(666\) | 8532.00 | 0.496409 | ||||||||
\(667\) | −12474.0 | + | 21605.6i | −0.724131 | + | 1.25423i | ||||
\(668\) | 1323.00 | + | 2291.50i | 0.0766294 | + | 0.132726i | ||||
\(669\) | −637.500 | − | 1104.18i | −0.0368418 | − | 0.0638119i | ||||
\(670\) | 1665.00 | − | 2883.86i | 0.0960068 | − | 0.166289i | ||||
\(671\) | 1770.00 | 0.101833 | ||||||||
\(672\) | −1890.00 | − | 1636.79i | −0.108495 | − | 0.0939590i | ||||
\(673\) | −19123.0 | −1.09530 | −0.547650 | − | 0.836707i | \(-0.684478\pi\) | ||||
−0.547650 | + | 0.836707i | \(0.684478\pi\) | |||||||
\(674\) | −12538.5 | + | 21717.3i | −0.716565 | + | 1.24113i | ||||
\(675\) | 1566.00 | + | 2712.39i | 0.0892968 | + | 0.154667i | ||||
\(676\) | −949.500 | − | 1644.58i | −0.0540225 | − | 0.0935698i | ||||
\(677\) | −6928.50 | + | 12000.5i | −0.393329 | + | 0.681266i | −0.992886 | − | 0.119066i | \(-0.962010\pi\) |
0.599557 | + | 0.800332i | \(0.295343\pi\) | |||||||
\(678\) | 5832.00 | 0.330349 | ||||||||
\(679\) | −1760.50 | + | 9147.83i | −0.0995019 | + | 0.517027i | ||||
\(680\) | −5292.00 | −0.298440 | ||||||||
\(681\) | −5782.50 | + | 10015.6i | −0.325383 | + | 0.563580i | ||||
\(682\) | 5692.50 | + | 9859.70i | 0.319615 | + | 0.553589i | ||||
\(683\) | 11122.5 | + | 19264.7i | 0.623120 | + | 1.07927i | 0.988901 | + | 0.148574i | \(0.0474683\pi\) |
−0.365782 | + | 0.930701i | \(0.619198\pi\) | |||||||
\(684\) | 72.0000 | − | 124.708i | 0.00402484 | − | 0.00697122i | ||||
\(685\) | 5310.00 | 0.296182 | ||||||||
\(686\) | −8746.50 | − | 16931.7i | −0.486797 | − | 0.942353i | ||||
\(687\) | −6564.00 | −0.364530 | ||||||||
\(688\) | 923.000 | − | 1598.68i | 0.0511469 | − | 0.0885890i | ||||
\(689\) | 11616.0 | + | 20119.5i | 0.642285 | + | 1.11247i | ||||
\(690\) | 1134.00 | + | 1964.15i | 0.0625661 | + | 0.108368i | ||||
\(691\) | 320.000 | − | 554.256i | 0.0176170 | − | 0.0305136i | −0.857082 | − | 0.515179i | \(-0.827725\pi\) |
0.874700 | + | 0.484666i | \(0.161059\pi\) | |||||||
\(692\) | −786.000 | −0.0431781 | ||||||||
\(693\) | 472.500 | − | 2455.18i | 0.0259001 | − | 0.134581i | ||||
\(694\) | 5580.00 | 0.305207 | ||||||||
\(695\) | −2337.00 | + | 4047.80i | −0.127550 | + | 0.220924i | ||||
\(696\) | 9355.50 | + | 16204.2i | 0.509511 | + | 0.882498i | ||||
\(697\) | −15120.0 | − | 26188.6i | −0.821680 | − | 1.42319i | ||||
\(698\) | −2877.00 | + | 4983.11i | −0.156012 | + | 0.270220i | ||||
\(699\) | 2556.00 | 0.138307 | ||||||||
\(700\) | 1624.00 | + | 1406.43i | 0.0876878 | + | 0.0759398i | ||||
\(701\) | −15561.0 | −0.838418 | −0.419209 | − | 0.907890i | \(-0.637693\pi\) | ||||
−0.419209 | + | 0.907890i | \(0.637693\pi\) | |||||||
\(702\) | −2592.00 | + | 4489.48i | −0.139357 | + | 0.241374i | ||||
\(703\) | −2528.00 | − | 4378.62i | −0.135626 | − | 0.234912i | ||||
\(704\) | 3247.50 | + | 5624.83i | 0.173856 | + | 0.301128i | ||||
\(705\) | −135.000 | + | 233.827i | −0.00721191 | + | 0.0124914i | ||||
\(706\) | 9144.00 | 0.487449 | ||||||||
\(707\) | −19005.0 | + | 6583.53i | −1.01097 | + | 0.350211i | ||||
\(708\) | −45.0000 | −0.00238871 | ||||||||
\(709\) | −2767.00 | + | 4792.58i | −0.146568 | + | 0.253864i | −0.929957 | − | 0.367668i | \(-0.880156\pi\) |
0.783389 | + | 0.621532i | \(0.213489\pi\) | |||||||
\(710\) | 1539.00 | + | 2665.63i | 0.0813488 | + | 0.140900i | ||||
\(711\) | −2101.50 | − | 3639.90i | −0.110847 | − | 0.191993i | ||||
\(712\) | −9513.00 | + | 16477.0i | −0.500723 | + | 0.867278i | ||||
\(713\) | 21252.0 | 1.11626 | ||||||||
\(714\) | −13230.0 | + | 4583.01i | −0.693446 | + | 0.240217i | ||||
\(715\) | −2880.00 | −0.150638 | ||||||||
\(716\) | −1446.00 | + | 2504.55i | −0.0754742 | + | 0.130725i | ||||
\(717\) | −8262.00 | − | 14310.2i | −0.430335 | − | 0.745362i | ||||
\(718\) | −45.0000 | − | 77.9423i | −0.00233898 | − | 0.00405123i | ||||
\(719\) | 10923.0 | − | 18919.2i | 0.566564 | − | 0.981317i | −0.430339 | − | 0.902667i | \(-0.641606\pi\) |
0.996902 | − | 0.0786494i | \(-0.0250607\pi\) | |||||||
\(720\) | 1917.00 | 0.0992255 | ||||||||
\(721\) | −24304.0 | − | 21047.9i | −1.25538 | − | 1.08719i | ||||
\(722\) | 19809.0 | 1.02107 | ||||||||
\(723\) | −1186.50 | + | 2055.08i | −0.0610324 | + | 0.105711i | ||||
\(724\) | −676.000 | − | 1170.87i | −0.0347007 | − | 0.0601035i | ||||
\(725\) | −17226.0 | − | 29836.3i | −0.882424 | − | 1.52840i | ||||
\(726\) | −4977.00 | + | 8620.42i | −0.254427 | + | 0.440680i | ||||
\(727\) | −11089.0 | −0.565706 | −0.282853 | − | 0.959163i | \(-0.591281\pi\) | ||||
−0.282853 | + | 0.959163i | \(0.591281\pi\) | |||||||
\(728\) | 4704.00 | − | 24442.7i | 0.239481 | − | 1.24438i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −1629.00 | + | 2821.51i | −0.0825918 | + | 0.143053i | ||||
\(731\) | −1092.00 | − | 1891.40i | −0.0552518 | − | 0.0956990i | ||||
\(732\) | 177.000 | + | 306.573i | 0.00893731 | + | 0.0154799i | ||||
\(733\) | −5881.00 | + | 10186.2i | −0.296343 | + | 0.513282i | −0.975296 | − | 0.220900i | \(-0.929101\pi\) |
0.678953 | + | 0.734182i | \(0.262434\pi\) | |||||||
\(734\) | 33933.0 | 1.70639 | ||||||||
\(735\) | 2866.50 | + | 1145.75i | 0.143854 | + | 0.0574989i | ||||
\(736\) | −3780.00 | −0.189311 | ||||||||
\(737\) | −2775.00 | + | 4806.44i | −0.138695 | + | 0.240227i | ||||
\(738\) | 4860.00 | + | 8417.77i | 0.242411 | + | 0.419868i | ||||
\(739\) | 11363.0 | + | 19681.3i | 0.565622 | + | 0.979686i | 0.996992 | + | 0.0775108i | \(0.0246972\pi\) |
−0.431369 | + | 0.902175i | \(0.641969\pi\) | |||||||
\(740\) | −474.000 | + | 820.992i | −0.0235467 | + | 0.0407841i | ||||
\(741\) | 3072.00 | 0.152298 | ||||||||
\(742\) | 3811.50 | − | 19805.1i | 0.188578 | − | 0.979878i | ||||
\(743\) | 6678.00 | 0.329734 | 0.164867 | − | 0.986316i | \(-0.447281\pi\) | ||||
0.164867 | + | 0.986316i | \(0.447281\pi\) | |||||||
\(744\) | 7969.50 | − | 13803.6i | 0.392710 | − | 0.680193i | ||||
\(745\) | 3681.00 | + | 6375.68i | 0.181022 | + | 0.313539i | ||||
\(746\) | 1812.00 | + | 3138.48i | 0.0889303 | + | 0.154032i | ||||
\(747\) | −2146.50 | + | 3717.85i | −0.105136 | + | 0.182100i | ||||
\(748\) | −1260.00 | −0.0615911 | ||||||||
\(749\) | 18942.0 | + | 16404.3i | 0.924066 | + | 0.800265i | ||||
\(750\) | −6507.00 | −0.316803 | ||||||||
\(751\) | 9993.50 | − | 17309.2i | 0.485577 | − | 0.841043i | −0.514286 | − | 0.857619i | \(-0.671943\pi\) |
0.999863 | + | 0.0165754i | \(0.00527637\pi\) | |||||||
\(752\) | −1065.00 | − | 1844.63i | −0.0516444 | − | 0.0894506i | ||||
\(753\) | −7897.50 | − | 13678.9i | −0.382206 | − | 0.662000i | ||||
\(754\) | 28512.0 | − | 49384.2i | 1.37712 | − | 2.38524i | ||||
\(755\) | −3777.00 | −0.182065 | ||||||||
\(756\) | 472.500 | − | 163.679i | 0.0227310 | − | 0.00787426i | ||||
\(757\) | 314.000 | 0.0150760 | 0.00753799 | − | 0.999972i | \(-0.497601\pi\) | ||||
0.00753799 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(758\) | 11460.0 | − | 19849.3i | 0.549137 | − | 0.951133i | ||||
\(759\) | −1890.00 | − | 3273.58i | −0.0903856 | − | 0.156552i | ||||
\(760\) | −504.000 | − | 872.954i | −0.0240553 | − | 0.0416649i | ||||
\(761\) | 5748.00 | − | 9955.83i | 0.273804 | − | 0.474242i | −0.696029 | − | 0.718014i | \(-0.745051\pi\) |
0.969833 | + | 0.243772i | \(0.0783847\pi\) | |||||||
\(762\) | −3393.00 | −0.161306 | ||||||||
\(763\) | −6475.00 | + | 2243.01i | −0.307222 | + | 0.106425i | ||||
\(764\) | 3912.00 | 0.185250 | ||||||||
\(765\) | 1134.00 | − | 1964.15i | 0.0535946 | − | 0.0928285i | ||||
\(766\) | 19125.0 | + | 33125.5i | 0.902107 | + | 1.56250i | ||||
\(767\) | −480.000 | − | 831.384i | −0.0225969 | − | 0.0391389i | ||||
\(768\) | −2269.50 | + | 3930.89i | −0.106632 | + | 0.184692i | ||||
\(769\) | 2765.00 | 0.129660 | 0.0648299 | − | 0.997896i | \(-0.479350\pi\) | ||||
0.0648299 | + | 0.997896i | \(0.479350\pi\) | |||||||
\(770\) | 1890.00 | + | 1636.79i | 0.0884557 | + | 0.0766049i | ||||
\(771\) | −20610.0 | −0.962712 | ||||||||
\(772\) | −746.500 | + | 1292.98i | −0.0348020 | + | 0.0602788i | ||||
\(773\) | 7023.00 | + | 12164.2i | 0.326778 | + | 0.565997i | 0.981871 | − | 0.189552i | \(-0.0607036\pi\) |
−0.655092 | + | 0.755549i | \(0.727370\pi\) | |||||||
\(774\) | 351.000 | + | 607.950i | 0.0163003 | + | 0.0282330i | ||||
\(775\) | −14674.0 | + | 25416.1i | −0.680136 | + | 1.17803i | ||||
\(776\) | 10563.0 | 0.488646 | ||||||||
\(777\) | 3318.00 | − | 17240.8i | 0.153195 | − | 0.796025i | ||||
\(778\) | −9378.00 | −0.432156 | ||||||||
\(779\) | 2880.00 | − | 4988.31i | 0.132460 | − | 0.229428i | ||||
\(780\) | −288.000 | − | 498.831i | −0.0132206 | − | 0.0228987i | ||||
\(781\) | −2565.00 | − | 4442.71i | −0.117520 | − | 0.203550i | ||||
\(782\) | −10584.0 | + | 18332.0i | −0.483994 | + | 0.838302i | ||||
\(783\) | −8019.00 | −0.365997 | ||||||||
\(784\) | −19134.5 | + | 15064.5i | −0.871652 | + | 0.686248i | ||||
\(785\) | 588.000 | 0.0267345 | ||||||||
\(786\) | −2929.50 | + | 5074.04i | −0.132941 | + | 0.230261i | ||||
\(787\) | 9257.00 | + | 16033.6i | 0.419284 | + | 0.726221i | 0.995868 | − | 0.0908171i | \(-0.0289479\pi\) |
−0.576584 | + | 0.817038i | \(0.695615\pi\) | |||||||
\(788\) | 2043.00 | + | 3538.58i | 0.0923590 | + | 0.159970i | ||||
\(789\) | 333.000 | − | 576.773i | 0.0150255 | − | 0.0260249i | ||||
\(790\) | 4203.00 | 0.189286 | ||||||||
\(791\) | 2268.00 | − | 11784.9i | 0.101948 | − | 0.529737i | ||||
\(792\) | −2835.00 | −0.127194 | ||||||||
\(793\) | −3776.00 | + | 6540.22i | −0.169092 | + | 0.292875i | ||||
\(794\) | −8898.00 | − | 15411.8i | −0.397706 | − | 0.688846i | ||||
\(795\) | 1633.50 | + | 2829.30i | 0.0728733 | + | 0.126220i | ||||
\(796\) | 1778.00 | − | 3079.59i | 0.0791703 | − | 0.137127i | ||||
\(797\) | −27495.0 | −1.22199 | −0.610993 | − | 0.791636i | \(-0.709230\pi\) | ||||
−0.610993 | + | 0.791636i | \(0.709230\pi\) | |||||||
\(798\) | −2016.00 | − | 1745.91i | −0.0894306 | − | 0.0774492i | ||||
\(799\) | −2520.00 | −0.111578 | ||||||||
\(800\) | 2610.00 | − | 4520.65i | 0.115347 | − | 0.199787i | ||||
\(801\) | −4077.00 | − | 7061.57i | −0.179842 | − | 0.311496i | ||||
\(802\) | 2412.00 | + | 4177.71i | 0.106198 | + | 0.183940i | ||||
\(803\) | 2715.00 | − | 4702.52i | 0.119315 | − | 0.206660i | ||||
\(804\) | −1110.00 | −0.0486899 | ||||||||
\(805\) | 4410.00 | − | 1527.67i | 0.193083 | − | 0.0668860i | ||||
\(806\) | −48576.0 | −2.12285 | ||||||||
\(807\) | −11776.5 | + | 20397.5i | −0.513696 | + | 0.889747i | ||||
\(808\) | 11403.0 | + | 19750.6i | 0.496480 | + | 0.859929i | ||||
\(809\) | 3972.00 | + | 6879.71i | 0.172618 | + | 0.298983i | 0.939334 | − | 0.343003i | \(-0.111444\pi\) |
−0.766716 | + | 0.641986i | \(0.778111\pi\) | |||||||
\(810\) | −364.500 | + | 631.333i | −0.0158114 | + | 0.0273861i | ||||
\(811\) | −28942.0 | −1.25313 | −0.626567 | − | 0.779368i | \(-0.715540\pi\) | ||||
−0.626567 | + | 0.779368i | \(0.715540\pi\) | |||||||
\(812\) | −5197.50 | + | 1800.47i | −0.224626 | + | 0.0778128i | ||||
\(813\) | 15549.0 | 0.670759 | ||||||||
\(814\) | 7110.00 | − | 12314.9i | 0.306149 | − | 0.530266i | ||||
\(815\) | −1878.00 | − | 3252.79i | −0.0807159 | − | 0.139804i | ||||
\(816\) | 8946.00 | + | 15494.9i | 0.383790 | + | 0.664744i | ||||
\(817\) | 208.000 | − | 360.267i | 0.00890698 | − | 0.0154273i | ||||
\(818\) | 13395.0 | 0.572549 | ||||||||
\(819\) | 8064.00 | + | 6983.63i | 0.344052 | + | 0.297958i | ||||
\(820\) | −1080.00 | −0.0459942 | ||||||||
\(821\) | −4093.50 | + | 7090.15i | −0.174012 | + | 0.301398i | −0.939819 | − | 0.341673i | \(-0.889007\pi\) |
0.765807 | + | 0.643071i | \(0.222340\pi\) | |||||||
\(822\) | −7965.00 | − | 13795.8i | −0.337970 | − | 0.585381i | ||||
\(823\) | 140.000 | + | 242.487i | 0.00592964 | + | 0.0102704i | 0.868975 | − | 0.494856i | \(-0.164779\pi\) |
−0.863045 | + | 0.505126i | \(0.831446\pi\) | |||||||
\(824\) | −18228.0 | + | 31571.8i | −0.770634 | + | 1.33478i | ||||
\(825\) | 5220.00 | 0.220287 | ||||||||
\(826\) | −157.500 | + | 818.394i | −0.00663453 | + | 0.0344741i | ||||
\(827\) | 25317.0 | 1.06452 | 0.532260 | − | 0.846581i | \(-0.321343\pi\) | ||||
0.532260 | + | 0.846581i | \(0.321343\pi\) | |||||||
\(828\) | 378.000 | − | 654.715i | 0.0158652 | − | 0.0274794i | ||||
\(829\) | −7660.00 | − | 13267.5i | −0.320920 | − | 0.555850i | 0.659758 | − | 0.751478i | \(-0.270659\pi\) |
−0.980678 | + | 0.195628i | \(0.937325\pi\) | |||||||
\(830\) | −2146.50 | − | 3717.85i | −0.0897664 | − | 0.155480i | ||||
\(831\) | 7440.00 | − | 12886.5i | 0.310579 | − | 0.537938i | ||||
\(832\) | −27712.0 | −1.15474 | ||||||||
\(833\) | 4116.00 | + | 28516.5i | 0.171202 | + | 1.18612i | ||||
\(834\) | 14022.0 | 0.582185 | ||||||||
\(835\) | −3969.00 | + | 6874.51i | −0.164495 | + | 0.284913i | ||||
\(836\) | −120.000 | − | 207.846i | −0.00496446 | − | 0.00859869i | ||||
\(837\) | 3415.50 | + | 5915.82i | 0.141048 | + | 0.244302i | ||||
\(838\) | −2376.00 | + | 4115.35i | −0.0979446 | + | 0.169645i | ||||
\(839\) | 34092.0 | 1.40284 | 0.701422 | − | 0.712746i | \(-0.252549\pi\) | ||||
0.701422 | + | 0.712746i | \(0.252549\pi\) | |||||||
\(840\) | 661.500 | − | 3437.25i | 0.0271713 | − | 0.141186i | ||||
\(841\) | 63820.0 | 2.61675 | ||||||||
\(842\) | −1995.00 | + | 3455.44i | −0.0816535 | + | 0.141428i | ||||
\(843\) | 1161.00 | + | 2010.91i | 0.0474341 | + | 0.0821583i | ||||
\(844\) | −625.000 | − | 1082.53i | −0.0254898 | − | 0.0441496i | ||||
\(845\) | 2848.50 | − | 4933.75i | 0.115966 | − | 0.200859i | ||||
\(846\) | 810.000 | 0.0329177 | ||||||||
\(847\) | 15484.0 | + | 13409.5i | 0.628142 | + | 0.543987i | ||||
\(848\) | −25773.0 | −1.04369 | ||||||||
\(849\) | −5547.00 | + | 9607.69i | −0.224232 | + | 0.388380i | ||||
\(850\) | −14616.0 | − | 25315.7i | −0.589794 | − | 1.02155i | ||||
\(851\) | −13272.0 | − | 22987.8i | −0.534616 | − | 0.925982i | ||||
\(852\) | 513.000 | − | 888.542i | 0.0206280 | − | 0.0357288i | ||||
\(853\) | −7378.00 | −0.296152 | −0.148076 | − | 0.988976i | \(-0.547308\pi\) | ||||
−0.148076 | + | 0.988976i | \(0.547308\pi\) | |||||||
\(854\) | 6195.00 | − | 2146.01i | 0.248230 | − | 0.0859894i | ||||
\(855\) | 432.000 | 0.0172796 | ||||||||
\(856\) | 14206.5 | − | 24606.4i | 0.567253 | − | 0.982510i | ||||
\(857\) | 7797.00 | + | 13504.8i | 0.310782 | + | 0.538291i | 0.978532 | − | 0.206095i | \(-0.0660757\pi\) |
−0.667750 | + | 0.744386i | \(0.732742\pi\) | |||||||
\(858\) | 4320.00 | + | 7482.46i | 0.171891 | + | 0.297724i | ||||
\(859\) | 15269.0 | − | 26446.7i | 0.606486 | − | 1.05046i | −0.385329 | − | 0.922779i | \(-0.625912\pi\) |
0.991815 | − | 0.127685i | \(-0.0407548\pi\) | |||||||
\(860\) | −78.0000 | −0.00309277 | ||||||||
\(861\) | 18900.0 | − | 6547.15i | 0.748096 | − | 0.259148i | ||||
\(862\) | −28764.0 | −1.13655 | ||||||||
\(863\) | 411.000 | − | 711.873i | 0.0162116 | − | 0.0280793i | −0.857806 | − | 0.513974i | \(-0.828173\pi\) |
0.874017 | + | 0.485895i | \(0.161506\pi\) | |||||||
\(864\) | −607.500 | − | 1052.22i | −0.0239208 | − | 0.0414320i | ||||
\(865\) | −1179.00 | − | 2042.09i | −0.0463436 | − | 0.0802694i | ||||
\(866\) | 741.000 | − | 1283.45i | 0.0290764 | − | 0.0503619i | ||||
\(867\) | 6429.00 | 0.251834 | ||||||||
\(868\) | 3542.00 | + | 3067.46i | 0.138506 | + | 0.119950i | ||||
\(869\) | −7005.00 | −0.273450 | ||||||||
\(870\) | 4009.50 | − | 6944.66i | 0.156247 | − | 0.270628i | ||||
\(871\) | −11840.0 | − | 20507.5i | −0.460601 | − | 0.797784i | ||||
\(872\) | 3885.00 | + | 6729.02i | 0.150875 | + | 0.261323i | ||||
\(873\) | −2263.50 | + | 3920.50i | −0.0877524 | + | 0.151992i | ||||
\(874\) | −4032.00 | −0.156046 | ||||||||
\(875\) | −2530.50 | + | 13148.9i | −0.0977674 | + | 0.508015i | ||||
\(876\) | 1086.00 | 0.0418865 | ||||||||
\(877\) | 20912.0 | − | 36220.6i | 0.805186 | − | 1.39462i | −0.110980 | − | 0.993823i | \(-0.535399\pi\) |
0.916165 | − | 0.400800i | \(-0.131268\pi\) | |||||||
\(878\) | −24013.5 | − | 41592.6i | −0.923025 | − | 1.59873i | ||||
\(879\) | 9409.50 | + | 16297.7i | 0.361063 | + | 0.625380i | ||||
\(880\) | 1597.50 | − | 2766.95i | 0.0611951 | − | 0.105993i | ||||
\(881\) | −46098.0 | −1.76286 | −0.881431 | − | 0.472313i | \(-0.843419\pi\) | ||||
−0.881431 | + | 0.472313i | \(0.843419\pi\) | |||||||
\(882\) | −1323.00 | − | 9166.01i | −0.0505076 | − | 0.349927i | ||||
\(883\) | 21008.0 | 0.800652 | 0.400326 | − | 0.916373i | \(-0.368897\pi\) | ||||
0.400326 | + | 0.916373i | \(0.368897\pi\) | |||||||
\(884\) | 2688.00 | − | 4655.75i | 0.102271 | − | 0.177138i | ||||
\(885\) | −67.5000 | − | 116.913i | −0.00256383 | − | 0.00444068i | ||||
\(886\) | 11659.5 | + | 20194.8i | 0.442109 | + | 0.765755i | ||||
\(887\) | −12018.0 | + | 20815.8i | −0.454932 | + | 0.787966i | −0.998684 | − | 0.0512801i | \(-0.983670\pi\) |
0.543752 | + | 0.839246i | \(0.317003\pi\) | |||||||
\(888\) | −19908.0 | −0.752330 | ||||||||
\(889\) | −1319.50 | + | 6856.32i | −0.0497802 | + | 0.258666i | ||||
\(890\) | 8154.00 | 0.307104 | ||||||||
\(891\) | 607.500 | − | 1052.22i | 0.0228418 | − | 0.0395631i | ||||
\(892\) | −212.500 | − | 368.061i | −0.00797649 | − | 0.0138157i | ||||
\(893\) | −240.000 | − | 415.692i | −0.00899361 | − | 0.0155774i | ||||
\(894\) | 11043.0 | − | 19127.0i | 0.413124 | − | 0.715552i | ||||
\(895\) | −8676.00 | −0.324030 | ||||||||
\(896\) | 23226.0 | + | 20114.3i | 0.865989 | + | 0.749969i | ||||
\(897\) | 16128.0 | 0.600332 | ||||||||
\(898\) | 1296.00 | − | 2244.74i | 0.0481604 | − | 0.0834163i | ||||
\(899\) | −37570.5 | − | 65074.0i | −1.39382 | − | 2.41417i | ||||
\(900\) | 522.000 | + | 904.131i | 0.0193333 | + | 0.0334863i | ||||
\(901\) | −15246.0 | + | 26406.8i | −0.563727 | + | 0.976404i | ||||
\(902\) | 16200.0 | 0.598006 | ||||||||
\(903\) | 1365.00 | − | 472.850i | 0.0503038 | − | 0.0174258i | ||||
\(904\) | −13608.0 | −0.500659 | ||||||||
\(905\) | 2028.00 | − | 3512.60i | 0.0744895 | − | 0.129020i | ||||
\(906\) | 5665.50 | + | 9812.93i | 0.207752 | + | 0.359838i | ||||
\(907\) | −6646.00 | − | 11511.2i | −0.243304 | − | 0.421415i | 0.718349 | − | 0.695683i | \(-0.244898\pi\) |
−0.961653 | + | 0.274268i | \(0.911565\pi\) | |||||||
\(908\) | −1927.50 | + | 3338.53i | −0.0704475 | + | 0.122019i | ||||
\(909\) | −9774.00 | −0.356637 | ||||||||
\(910\) | −10080.0 | + | 3491.81i | −0.367196 | + | 0.127201i | ||||
\(911\) | −9306.00 | −0.338443 | −0.169221 | − | 0.985578i | \(-0.554125\pi\) | ||||
−0.169221 | + | 0.985578i | \(0.554125\pi\) | |||||||
\(912\) | −1704.00 | + | 2951.41i | −0.0618696 | + | 0.107161i | ||||
\(913\) | 3577.50 | + | 6196.41i | 0.129680 | + | 0.224613i | ||||
\(914\) | 3778.50 | + | 6544.55i | 0.136741 | + | 0.236843i | ||||
\(915\) | −531.000 | + | 919.719i | −0.0191850 | + | 0.0332295i | ||||
\(916\) | −2188.00 | −0.0789231 | ||||||||
\(917\) | 9114.00 | + | 7892.96i | 0.328212 | + | 0.284240i | ||||
\(918\) | −6804.00 | −0.244625 | ||||||||
\(919\) | −8248.00 | + | 14286.0i | −0.296057 | + | 0.512786i | −0.975230 | − | 0.221192i | \(-0.929005\pi\) |
0.679173 | + | 0.733978i | \(0.262339\pi\) | |||||||
\(920\) | −2646.00 | − | 4583.01i | −0.0948218 | − | 0.164236i | ||||
\(921\) | 2526.00 | + | 4375.16i | 0.0903741 | + | 0.156533i | ||||
\(922\) | −513.000 | + | 888.542i | −0.0183240 | + | 0.0317382i | ||||
\(923\) | 21888.0 | 0.780555 | ||||||||
\(924\) | 157.500 | − | 818.394i | 0.00560754 | − | 0.0291376i | ||||
\(925\) | 36656.0 | 1.30296 | ||||||||
\(926\) | −6504.00 | + | 11265.3i | −0.230815 | + | 0.399783i | ||||
\(927\) | −7812.00 | − | 13530.8i | −0.276785 | − | 0.479406i | ||||
\(928\) | 6682.50 | + | 11574.4i | 0.236383 | + | 0.409428i | ||||
\(929\) | −7077.00 | + | 12257.7i | −0.249934 | + | 0.432899i | −0.963507 | − | 0.267682i | \(-0.913742\pi\) |
0.713573 | + | 0.700581i | \(0.247076\pi\) | |||||||
\(930\) | −6831.00 | −0.240857 | ||||||||
\(931\) | −4312.00 | + | 3394.82i | −0.151794 | + | 0.119507i | ||||
\(932\) | 852.000 | 0.0299444 | ||||||||
\(933\) | 1980.00 | − | 3429.46i | 0.0694773 | − | 0.120338i | ||||
\(934\) | 27954.0 | + | 48417.7i | 0.979318 | + | 1.69623i | ||||
\(935\) | −1890.00 | − | 3273.58i | −0.0661065 | − | 0.114500i | ||||
\(936\) | 6048.00 | − | 10475.4i | 0.211202 | − | 0.365813i | ||||
\(937\) | −3781.00 | −0.131825 | −0.0659124 | − | 0.997825i | \(-0.520996\pi\) | ||||
−0.0659124 | + | 0.997825i | \(0.520996\pi\) | |||||||
\(938\) | −3885.00 | + | 20187.1i | −0.135234 | + | 0.702698i | ||||
\(939\) | −25509.0 | −0.886533 | ||||||||
\(940\) | −45.0000 | + | 77.9423i | −0.00156142 | + | 0.00270446i | ||||
\(941\) | 12931.5 | + | 22398.0i | 0.447986 | + | 0.775935i | 0.998255 | − | 0.0590530i | \(-0.0188081\pi\) |
−0.550269 | + | 0.834988i | \(0.685475\pi\) | |||||||
\(942\) | −882.000 | − | 1527.67i | −0.0305065 | − | 0.0528388i | ||||
\(943\) | 15120.0 | − | 26188.6i | 0.522137 | − | 0.904367i | ||||
\(944\) | 1065.00 | 0.0367191 | ||||||||
\(945\) | 1134.00 | + | 982.073i | 0.0390360 | + | 0.0338062i | ||||
\(946\) | 1170.00 | 0.0402114 | ||||||||
\(947\) | 21192.0 | − | 36705.6i | 0.727188 | − | 1.25953i | −0.230878 | − | 0.972983i | \(-0.574160\pi\) |
0.958067 | − | 0.286545i | \(-0.0925067\pi\) | |||||||
\(948\) | −700.500 | − | 1213.30i | −0.0239991 | − | 0.0415677i | ||||
\(949\) | 11584.0 | + | 20064.1i | 0.396241 | + | 0.686309i | ||||
\(950\) | 2784.00 | − | 4822.03i | 0.0950788 | − | 0.164681i | ||||
\(951\) | −7731.00 | −0.263612 | ||||||||
\(952\) | 30870.0 | − | 10693.7i | 1.05095 | − | 0.364059i | ||||
\(953\) | 10530.0 | 0.357923 | 0.178961 | − | 0.983856i | \(-0.442726\pi\) | ||||
0.178961 | + | 0.983856i | \(0.442726\pi\) | |||||||
\(954\) | 4900.50 | − | 8487.91i | 0.166310 | − | 0.288057i | ||||
\(955\) | 5868.00 | + | 10163.7i | 0.198831 | + | 0.344386i | ||||
\(956\) | −2754.00 | − | 4770.07i | −0.0931702 | − | 0.161376i | ||||
\(957\) | −6682.50 | + | 11574.4i | −0.225721 | + | 0.390959i | ||||
\(958\) | −45234.0 | −1.52552 | ||||||||
\(959\) | −30975.0 | + | 10730.1i | −1.04300 | + | 0.361305i | ||||
\(960\) | −3897.00 | −0.131016 | ||||||||
\(961\) | −17109.0 | + | 29633.7i | −0.574301 | + | 0.994718i | ||||
\(962\) | 30336.0 | + | 52543.5i | 1.01671 | + | 1.76099i | ||||
\(963\) | 6088.50 | + | 10545.6i | 0.203737 | + | 0.352884i | ||||
\(964\) | −395.500 | + | 685.026i | −0.0132139 | + | 0.0228871i | ||||
\(965\) | −4479.00 | −0.149414 | ||||||||
\(966\) | −10584.0 | − | 9166.01i | −0.352520 | − | 0.305292i | ||||
\(967\) | −38341.0 | −1.27504 | −0.637520 | − | 0.770434i | \(-0.720040\pi\) | ||||
−0.637520 | + | 0.770434i | \(0.720040\pi\) | |||||||
\(968\) | 11613.0 | − | 20114.3i | 0.385595 | − | 0.667870i | ||||
\(969\) | 2016.00 | + | 3491.81i | 0.0668351 | + | 0.115762i | ||||
\(970\) | −2263.50 | − | 3920.50i | −0.0749243 | − | 0.129773i | ||||
\(971\) | −961.500 | + | 1665.37i | −0.0317776 | + | 0.0550403i | −0.881477 | − | 0.472227i | \(-0.843450\pi\) |
0.849699 | + | 0.527268i | \(0.176783\pi\) | |||||||
\(972\) | 243.000 | 0.00801875 | ||||||||
\(973\) | 5453.00 | − | 28334.6i | 0.179666 | − | 0.933573i | ||||
\(974\) | −18663.0 | −0.613964 | ||||||||
\(975\) | −11136.0 | + | 19288.1i | −0.365782 | + | 0.633553i | ||||
\(976\) | −4189.00 | − | 7255.56i | −0.137384 | − | 0.237956i | ||||
\(977\) | −28545.0 | − | 49441.4i | −0.934734 | − | 1.61901i | −0.775107 | − | 0.631830i | \(-0.782304\pi\) |
−0.159627 | − | 0.987177i | \(-0.551029\pi\) | |||||||
\(978\) | −5634.00 | + | 9758.37i | −0.184208 | + | 0.319058i | ||||
\(979\) | −13590.0 | −0.443655 | ||||||||
\(980\) | 955.500 | + | 381.917i | 0.0311452 | + | 0.0124489i | ||||
\(981\) | −3330.00 | −0.108378 | ||||||||
\(982\) | −11056.5 | + | 19150.4i | −0.359294 | + | 0.622316i | ||||
\(983\) | −2742.00 | − | 4749.28i | −0.0889687 | − | 0.154098i | 0.818107 | − | 0.575066i | \(-0.195024\pi\) |
−0.907075 | + | 0.420968i | \(0.861690\pi\) | |||||||
\(984\) | −11340.0 | − | 19641.5i | −0.367384 | − | 0.636328i | ||||
\(985\) | −6129.00 | + | 10615.7i | −0.198260 | + | 0.343397i | ||||
\(986\) | 74844.0 | 2.41736 | ||||||||
\(987\) | 315.000 | − | 1636.79i | 0.0101586 | − | 0.0527858i | ||||
\(988\) | 1024.00 | 0.0329735 | ||||||||
\(989\) | 1092.00 | − | 1891.40i | 0.0351098 | − | 0.0608119i | ||||
\(990\) | 607.500 | + | 1052.22i | 0.0195026 | + | 0.0337796i | ||||
\(991\) | 11232.5 | + | 19455.3i | 0.360053 | + | 0.623629i | 0.987969 | − | 0.154651i | \(-0.0494254\pi\) |
−0.627917 | + | 0.778281i | \(0.716092\pi\) | |||||||
\(992\) | 5692.50 | − | 9859.70i | 0.182195 | − | 0.315570i | ||||
\(993\) | −1452.00 | −0.0464026 | ||||||||
\(994\) | −14364.0 | − | 12439.6i | −0.458349 | − | 0.396941i | ||||
\(995\) | 10668.0 | 0.339898 | ||||||||
\(996\) | −715.500 | + | 1239.28i | −0.0227625 | + | 0.0394259i | ||||
\(997\) | −14683.0 | − | 25431.7i | −0.466415 | − | 0.807854i | 0.532850 | − | 0.846210i | \(-0.321121\pi\) |
−0.999264 | + | 0.0383563i | \(0.987788\pi\) | |||||||
\(998\) | 6411.00 | + | 11104.2i | 0.203343 | + | 0.352201i | ||||
\(999\) | 4266.00 | − | 7388.93i | 0.135105 | − | 0.234009i |
(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 | 21.4.e.a.16.1 | yes | 2 | |
3.2 | odd | 2 | 63.4.e.a.37.1 | 2 | |||
4.3 | odd | 2 | 336.4.q.e.289.1 | 2 | |||
7.2 | even | 3 | 147.4.a.b.1.1 | 1 | |||
7.3 | odd | 6 | 147.4.e.h.67.1 | 2 | |||
7.4 | even | 3 | inner | 21.4.e.a.4.1 | ✓ | 2 | |
7.5 | odd | 6 | 147.4.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 147.4.e.h.79.1 | 2 | |||
21.2 | odd | 6 | 441.4.a.l.1.1 | 1 | |||
21.5 | even | 6 | 441.4.a.k.1.1 | 1 | |||
21.11 | odd | 6 | 63.4.e.a.46.1 | 2 | |||
21.17 | even | 6 | 441.4.e.c.361.1 | 2 | |||
21.20 | even | 2 | 441.4.e.c.226.1 | 2 | |||
28.11 | odd | 6 | 336.4.q.e.193.1 | 2 | |||
28.19 | even | 6 | 2352.4.a.bd.1.1 | 1 | |||
28.23 | odd | 6 | 2352.4.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.a.4.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
21.4.e.a.16.1 | yes | 2 | 1.1 | even | 1 | trivial | |
63.4.e.a.37.1 | 2 | 3.2 | odd | 2 | |||
63.4.e.a.46.1 | 2 | 21.11 | odd | 6 | |||
147.4.a.a.1.1 | 1 | 7.5 | odd | 6 | |||
147.4.a.b.1.1 | 1 | 7.2 | even | 3 | |||
147.4.e.h.67.1 | 2 | 7.3 | odd | 6 | |||
147.4.e.h.79.1 | 2 | 7.6 | odd | 2 | |||
336.4.q.e.193.1 | 2 | 28.11 | odd | 6 | |||
336.4.q.e.289.1 | 2 | 4.3 | odd | 2 | |||
441.4.a.k.1.1 | 1 | 21.5 | even | 6 | |||
441.4.a.l.1.1 | 1 | 21.2 | odd | 6 | |||
441.4.e.c.226.1 | 2 | 21.20 | even | 2 | |||
441.4.e.c.361.1 | 2 | 21.17 | even | 6 | |||
2352.4.a.i.1.1 | 1 | 28.23 | odd | 6 | |||
2352.4.a.bd.1.1 | 1 | 28.19 | even | 6 |