Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,3,Mod(79,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.79");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.f (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: | \(4.25069212402\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 79.6 | ||
Character | \(\chi\) | \(=\) | 156.79 |
Dual form | 156.3.f.a.79.5 |
$q$-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 \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.66943 | + | 1.10137i | −0.834713 | + | 0.550685i | ||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 1.57397 | − | 3.67731i | 0.393492 | − | 0.919328i | ||||
\(5\) | −0.251667 | −0.0503334 | −0.0251667 | − | 0.999683i | \(-0.508012\pi\) | ||||
−0.0251667 | + | 0.999683i | \(0.508012\pi\) | |||||||
\(6\) | −1.90763 | − | 2.89153i | −0.317938 | − | 0.481922i | ||||
\(7\) | 2.33352i | 0.333360i | 0.986011 | + | 0.166680i | \(0.0533046\pi\) | ||||
−0.986011 | + | 0.166680i | \(0.946695\pi\) | |||||||
\(8\) | 1.42246 | + | 7.87252i | 0.177807 | + | 0.984065i | ||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0.420139 | − | 0.277178i | 0.0420139 | − | 0.0277178i | ||||
\(11\) | 17.3946i | 1.58133i | 0.612252 | + | 0.790663i | \(0.290264\pi\) | ||||
−0.612252 | + | 0.790663i | \(0.709736\pi\) | |||||||
\(12\) | 6.36929 | + | 2.72619i | 0.530774 | + | 0.227183i | ||||
\(13\) | −3.60555 | −0.277350 | ||||||||
\(14\) | −2.57007 | − | 3.89564i | −0.183576 | − | 0.278260i | ||||
\(15\) | − | 0.435900i | − | 0.0290600i | ||||||
\(16\) | −11.0452 | − | 11.5759i | −0.690328 | − | 0.723497i | ||||
\(17\) | −17.8176 | −1.04809 | −0.524047 | − | 0.851689i | \(-0.675578\pi\) | ||||
−0.524047 | + | 0.851689i | \(0.675578\pi\) | |||||||
\(18\) | 5.00828 | − | 3.30411i | 0.278238 | − | 0.183562i | ||||
\(19\) | − | 5.49823i | − | 0.289381i | −0.989477 | − | 0.144690i | \(-0.953781\pi\) | ||
0.989477 | − | 0.144690i | \(-0.0462186\pi\) | |||||||
\(20\) | −0.396116 | + | 0.925457i | −0.0198058 | + | 0.0462729i | ||||
\(21\) | −4.04177 | −0.192465 | ||||||||
\(22\) | −19.1579 | − | 29.0390i | −0.870812 | − | 1.31995i | ||||
\(23\) | 30.7733i | 1.33797i | 0.743275 | + | 0.668985i | \(0.233271\pi\) | ||||
−0.743275 | + | 0.668985i | \(0.766729\pi\) | |||||||
\(24\) | −13.6356 | + | 2.46376i | −0.568150 | + | 0.102657i | ||||
\(25\) | −24.9367 | −0.997467 | ||||||||
\(26\) | 6.01920 | − | 3.97105i | 0.231508 | − | 0.152733i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 8.58107 | + | 3.67288i | 0.306467 | + | 0.131174i | ||||
\(29\) | −22.8908 | −0.789338 | −0.394669 | − | 0.918823i | \(-0.629141\pi\) | ||||
−0.394669 | + | 0.918823i | \(0.629141\pi\) | |||||||
\(30\) | 0.480087 | + | 0.727702i | 0.0160029 | + | 0.0242567i | ||||
\(31\) | − | 0.174889i | − | 0.00564158i | −0.999996 | − | 0.00282079i | \(-0.999102\pi\) | ||
0.999996 | − | 0.00282079i | \(-0.000897886\pi\) | |||||||
\(32\) | 31.1886 | + | 7.16029i | 0.974644 | + | 0.223759i | ||||
\(33\) | −30.1283 | −0.912979 | ||||||||
\(34\) | 29.7452 | − | 19.6238i | 0.874858 | − | 0.577170i | ||||
\(35\) | − | 0.587269i | − | 0.0167791i | ||||||
\(36\) | −4.72191 | + | 11.0319i | −0.131164 | + | 0.306443i | ||||
\(37\) | 38.6830 | 1.04549 | 0.522743 | − | 0.852490i | \(-0.324909\pi\) | ||||
0.522743 | + | 0.852490i | \(0.324909\pi\) | |||||||
\(38\) | 6.05559 | + | 9.17890i | 0.159358 | + | 0.241550i | ||||
\(39\) | − | 6.24500i | − | 0.160128i | ||||||
\(40\) | −0.357985 | − | 1.98125i | −0.00894962 | − | 0.0495313i | ||||
\(41\) | 10.7622 | 0.262492 | 0.131246 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131246 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(42\) | 6.74744 | − | 4.45149i | 0.160653 | − | 0.105988i | ||||
\(43\) | 42.8900i | 0.997443i | 0.866762 | + | 0.498721i | \(0.166197\pi\) | ||||
−0.866762 | + | 0.498721i | \(0.833803\pi\) | |||||||
\(44\) | 63.9653 | + | 27.3785i | 1.45376 | + | 0.622239i | ||||
\(45\) | 0.755000 | 0.0167778 | ||||||||
\(46\) | −33.8928 | − | 51.3738i | −0.736800 | − | 1.11682i | ||||
\(47\) | 36.2920i | 0.772170i | 0.922463 | + | 0.386085i | \(0.126173\pi\) | ||||
−0.922463 | + | 0.386085i | \(0.873827\pi\) | |||||||
\(48\) | 20.0501 | − | 19.1309i | 0.417711 | − | 0.398561i | ||||
\(49\) | 43.5547 | 0.888871 | ||||||||
\(50\) | 41.6299 | − | 27.4645i | 0.832598 | − | 0.549290i | ||||
\(51\) | − | 30.8610i | − | 0.605117i | ||||||
\(52\) | −5.67503 | + | 13.2587i | −0.109135 | + | 0.254976i | ||||
\(53\) | 87.4625 | 1.65023 | 0.825117 | − | 0.564961i | \(-0.191109\pi\) | ||||
0.825117 | + | 0.564961i | \(0.191109\pi\) | |||||||
\(54\) | 5.72289 | + | 8.67459i | 0.105979 | + | 0.160641i | ||||
\(55\) | − | 4.37764i | − | 0.0795934i | ||||||
\(56\) | −18.3707 | + | 3.31932i | −0.328048 | + | 0.0592737i | ||||
\(57\) | 9.52322 | 0.167074 | ||||||||
\(58\) | 38.2145 | − | 25.2112i | 0.658871 | − | 0.434677i | ||||
\(59\) | − | 94.5210i | − | 1.60205i | −0.598630 | − | 0.801025i | \(-0.704288\pi\) | ||
0.598630 | − | 0.801025i | \(-0.295712\pi\) | |||||||
\(60\) | −1.60294 | − | 0.686092i | −0.0267156 | − | 0.0114349i | ||||
\(61\) | −26.2640 | −0.430557 | −0.215278 | − | 0.976553i | \(-0.569066\pi\) | ||||
−0.215278 | + | 0.976553i | \(0.569066\pi\) | |||||||
\(62\) | 0.192617 | + | 0.291964i | 0.00310673 | + | 0.00470910i | ||||
\(63\) | − | 7.00055i | − | 0.111120i | ||||||
\(64\) | −59.9532 | + | 22.3966i | −0.936769 | + | 0.349947i | ||||
\(65\) | 0.907397 | 0.0139600 | ||||||||
\(66\) | 50.2970 | − | 33.1824i | 0.762076 | − | 0.502764i | ||||
\(67\) | 32.3753i | 0.483214i | 0.970374 | + | 0.241607i | \(0.0776745\pi\) | ||||
−0.970374 | + | 0.241607i | \(0.922326\pi\) | |||||||
\(68\) | −28.0443 | + | 65.5209i | −0.412417 | + | 0.963542i | ||||
\(69\) | −53.3010 | −0.772478 | ||||||||
\(70\) | 0.646800 | + | 0.980402i | 0.00924000 | + | 0.0140057i | ||||
\(71\) | 13.5128i | 0.190321i | 0.995462 | + | 0.0951603i | \(0.0303364\pi\) | ||||
−0.995462 | + | 0.0951603i | \(0.969664\pi\) | |||||||
\(72\) | −4.26737 | − | 23.6176i | −0.0592690 | − | 0.328022i | ||||
\(73\) | 110.236 | 1.51008 | 0.755041 | − | 0.655678i | \(-0.227617\pi\) | ||||
0.755041 | + | 0.655678i | \(0.227617\pi\) | |||||||
\(74\) | −64.5784 | + | 42.6043i | −0.872681 | + | 0.575733i | ||||
\(75\) | − | 43.1916i | − | 0.575888i | ||||||
\(76\) | −20.2187 | − | 8.65405i | −0.266036 | − | 0.113869i | ||||
\(77\) | −40.5906 | −0.527150 | ||||||||
\(78\) | 6.87805 | + | 10.4256i | 0.0881802 | + | 0.133661i | ||||
\(79\) | 8.46854i | 0.107197i | 0.998563 | + | 0.0535984i | \(0.0170691\pi\) | ||||
−0.998563 | + | 0.0535984i | \(0.982931\pi\) | |||||||
\(80\) | 2.77972 | + | 2.91328i | 0.0347465 | + | 0.0364160i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −17.9666 | + | 11.8531i | −0.219105 | + | 0.144550i | ||||
\(83\) | 1.61619i | 0.0194721i | 0.999953 | + | 0.00973606i | \(0.00309913\pi\) | ||||
−0.999953 | + | 0.00973606i | \(0.996901\pi\) | |||||||
\(84\) | −6.36162 | + | 14.8629i | −0.0757336 | + | 0.176939i | ||||
\(85\) | 4.48410 | 0.0527541 | ||||||||
\(86\) | −47.2378 | − | 71.6018i | −0.549277 | − | 0.832579i | ||||
\(87\) | − | 39.6480i | − | 0.455725i | ||||||
\(88\) | −136.939 | + | 24.7430i | −1.55613 | + | 0.281171i | ||||
\(89\) | −104.620 | −1.17551 | −0.587753 | − | 0.809040i | \(-0.699987\pi\) | ||||
−0.587753 | + | 0.809040i | \(0.699987\pi\) | |||||||
\(90\) | −1.26042 | + | 0.831535i | −0.0140046 | + | 0.00923927i | ||||
\(91\) | − | 8.41362i | − | 0.0924573i | ||||||
\(92\) | 113.163 | + | 48.4363i | 1.23003 | + | 0.526481i | ||||
\(93\) | 0.302916 | 0.00325716 | ||||||||
\(94\) | −39.9709 | − | 60.5868i | −0.425223 | − | 0.644541i | ||||
\(95\) | 1.38372i | 0.0145655i | ||||||||
\(96\) | −12.4020 | + | 54.0203i | −0.129187 | + | 0.562711i | ||||
\(97\) | 77.5982 | 0.799981 | 0.399991 | − | 0.916519i | \(-0.369013\pi\) | ||||
0.399991 | + | 0.916519i | \(0.369013\pi\) | |||||||
\(98\) | −72.7114 | + | 47.9698i | −0.741953 | + | 0.489488i | ||||
\(99\) | − | 52.1838i | − | 0.527109i | ||||||
\(100\) | −39.2495 | + | 91.6999i | −0.392495 | + | 0.916999i | ||||
\(101\) | −4.14702 | −0.0410596 | −0.0205298 | − | 0.999789i | \(-0.506535\pi\) | ||||
−0.0205298 | + | 0.999789i | \(0.506535\pi\) | |||||||
\(102\) | 33.9894 | + | 51.5201i | 0.333229 | + | 0.505099i | ||||
\(103\) | 73.5402i | 0.713983i | 0.934108 | + | 0.356991i | \(0.116197\pi\) | ||||
−0.934108 | + | 0.356991i | \(0.883803\pi\) | |||||||
\(104\) | −5.12874 | − | 28.3848i | −0.0493148 | − | 0.272931i | ||||
\(105\) | 1.01718 | 0.00968742 | ||||||||
\(106\) | −146.012 | + | 96.3285i | −1.37747 | + | 0.908760i | ||||
\(107\) | − | 81.6012i | − | 0.762628i | −0.924446 | − | 0.381314i | \(-0.875472\pi\) | ||
0.924446 | − | 0.381314i | \(-0.124528\pi\) | |||||||
\(108\) | −19.1079 | − | 8.17858i | −0.176925 | − | 0.0757276i | ||||
\(109\) | 111.967 | 1.02722 | 0.513610 | − | 0.858024i | \(-0.328308\pi\) | ||||
0.513610 | + | 0.858024i | \(0.328308\pi\) | |||||||
\(110\) | 4.82140 | + | 7.30815i | 0.0438309 | + | 0.0664377i | ||||
\(111\) | 67.0009i | 0.603611i | ||||||||
\(112\) | 27.0127 | − | 25.7743i | 0.241185 | − | 0.230127i | ||||
\(113\) | −166.707 | −1.47529 | −0.737643 | − | 0.675190i | \(-0.764061\pi\) | ||||
−0.737643 | + | 0.675190i | \(0.764061\pi\) | |||||||
\(114\) | −15.8983 | + | 10.4886i | −0.139459 | + | 0.0920052i | ||||
\(115\) | − | 7.74462i | − | 0.0673446i | ||||||
\(116\) | −36.0294 | + | 84.1766i | −0.310598 | + | 0.725661i | ||||
\(117\) | 10.8167 | 0.0924500 | ||||||||
\(118\) | 104.103 | + | 157.796i | 0.882225 | + | 1.33725i | ||||
\(119\) | − | 41.5777i | − | 0.349392i | ||||||
\(120\) | 3.43163 | − | 0.620048i | 0.0285969 | − | 0.00516706i | ||||
\(121\) | −181.572 | −1.50059 | ||||||||
\(122\) | 43.8458 | − | 28.9263i | 0.359391 | − | 0.237101i | ||||
\(123\) | 18.6406i | 0.151550i | ||||||||
\(124\) | −0.643121 | − | 0.275270i | −0.00518646 | − | 0.00221992i | ||||
\(125\) | 12.5674 | 0.100539 | ||||||||
\(126\) | 7.71020 | + | 11.6869i | 0.0611921 | + | 0.0927532i | ||||
\(127\) | − | 94.8943i | − | 0.747199i | −0.927590 | − | 0.373600i | \(-0.878123\pi\) | ||
0.927590 | − | 0.373600i | \(-0.121877\pi\) | |||||||
\(128\) | 75.4206 | − | 103.420i | 0.589223 | − | 0.807970i | ||||
\(129\) | −74.2877 | −0.575874 | ||||||||
\(130\) | −1.51483 | + | 0.999380i | −0.0116526 | + | 0.00768754i | ||||
\(131\) | − | 223.567i | − | 1.70662i | −0.521405 | − | 0.853310i | \(-0.674592\pi\) | ||
0.521405 | − | 0.853310i | \(-0.325408\pi\) | |||||||
\(132\) | −47.4210 | + | 110.791i | −0.359250 | + | 0.839327i | ||||
\(133\) | 12.8302 | 0.0964679 | ||||||||
\(134\) | −35.6572 | − | 54.0482i | −0.266099 | − | 0.403345i | ||||
\(135\) | 1.30770i | 0.00968666i | ||||||||
\(136\) | −25.3447 | − | 140.269i | −0.186358 | − | 1.03139i | ||||
\(137\) | 189.094 | 1.38025 | 0.690124 | − | 0.723692i | \(-0.257556\pi\) | ||||
0.690124 | + | 0.723692i | \(0.257556\pi\) | |||||||
\(138\) | 88.9821 | − | 58.7041i | 0.644797 | − | 0.425392i | ||||
\(139\) | − | 114.967i | − | 0.827098i | −0.910482 | − | 0.413549i | \(-0.864289\pi\) | ||
0.910482 | − | 0.413549i | \(-0.135711\pi\) | |||||||
\(140\) | −2.15957 | − | 0.924343i | −0.0154255 | − | 0.00660245i | ||||
\(141\) | −62.8596 | −0.445813 | ||||||||
\(142\) | −14.8826 | − | 22.5586i | −0.104807 | − | 0.158863i | ||||
\(143\) | − | 62.7171i | − | 0.438581i | ||||||
\(144\) | 33.1357 | + | 34.7278i | 0.230109 | + | 0.241166i | ||||
\(145\) | 5.76085 | 0.0397300 | ||||||||
\(146\) | −184.031 | + | 121.411i | −1.26049 | + | 0.831579i | ||||
\(147\) | 75.4389i | 0.513190i | ||||||||
\(148\) | 60.8858 | − | 142.249i | 0.411390 | − | 0.961144i | ||||
\(149\) | 148.971 | 0.999807 | 0.499903 | − | 0.866081i | \(-0.333369\pi\) | ||||
0.499903 | + | 0.866081i | \(0.333369\pi\) | |||||||
\(150\) | 47.5699 | + | 72.1051i | 0.317133 | + | 0.480701i | ||||
\(151\) | 253.205i | 1.67685i | 0.545014 | + | 0.838427i | \(0.316524\pi\) | ||||
−0.545014 | + | 0.838427i | \(0.683476\pi\) | |||||||
\(152\) | 43.2850 | − | 7.82099i | 0.284770 | − | 0.0514539i | ||||
\(153\) | 53.4528 | 0.349365 | ||||||||
\(154\) | 67.7630 | − | 44.7052i | 0.440019 | − | 0.290294i | ||||
\(155\) | 0.0440137i | 0.000283959i | ||||||||
\(156\) | −22.9648 | − | 9.82943i | −0.147210 | − | 0.0630092i | ||||
\(157\) | 274.330 | 1.74732 | 0.873662 | − | 0.486534i | \(-0.161739\pi\) | ||||
0.873662 | + | 0.486534i | \(0.161739\pi\) | |||||||
\(158\) | −9.32700 | − | 14.1376i | −0.0590316 | − | 0.0894785i | ||||
\(159\) | 151.489i | 0.952764i | ||||||||
\(160\) | −7.84914 | − | 1.80201i | −0.0490571 | − | 0.0112626i | ||||
\(161\) | −71.8101 | −0.446026 | ||||||||
\(162\) | −15.0248 | + | 9.91233i | −0.0927459 | + | 0.0611872i | ||||
\(163\) | 157.871i | 0.968533i | 0.874920 | + | 0.484267i | \(0.160914\pi\) | ||||
−0.874920 | + | 0.484267i | \(0.839086\pi\) | |||||||
\(164\) | 16.9393 | − | 39.5758i | 0.103288 | − | 0.241316i | ||||
\(165\) | 7.58229 | 0.0459533 | ||||||||
\(166\) | −1.78002 | − | 2.69810i | −0.0107230 | − | 0.0162536i | ||||
\(167\) | 95.1205i | 0.569584i | 0.958589 | + | 0.284792i | \(0.0919245\pi\) | ||||
−0.958589 | + | 0.284792i | \(0.908076\pi\) | |||||||
\(168\) | −5.74924 | − | 31.8189i | −0.0342217 | − | 0.189398i | ||||
\(169\) | 13.0000 | 0.0769231 | ||||||||
\(170\) | −7.48587 | + | 4.93865i | −0.0440345 | + | 0.0290509i | ||||
\(171\) | 16.4947i | 0.0964602i | ||||||||
\(172\) | 157.720 | + | 67.5076i | 0.916977 | + | 0.392486i | ||||
\(173\) | −129.298 | −0.747386 | −0.373693 | − | 0.927552i | \(-0.621909\pi\) | ||||
−0.373693 | + | 0.927552i | \(0.621909\pi\) | |||||||
\(174\) | 43.6672 | + | 66.1895i | 0.250961 | + | 0.380399i | ||||
\(175\) | − | 58.1901i | − | 0.332515i | ||||||
\(176\) | 201.359 | − | 192.127i | 1.14408 | − | 1.09163i | ||||
\(177\) | 163.715 | 0.924945 | ||||||||
\(178\) | 174.656 | − | 115.225i | 0.981211 | − | 0.647334i | ||||
\(179\) | − | 32.4167i | − | 0.181099i | −0.995892 | − | 0.0905494i | \(-0.971138\pi\) | ||
0.995892 | − | 0.0905494i | \(-0.0288623\pi\) | |||||||
\(180\) | 1.18835 | − | 2.77637i | 0.00660193 | − | 0.0154243i | ||||
\(181\) | −88.3270 | −0.487995 | −0.243997 | − | 0.969776i | \(-0.578459\pi\) | ||||
−0.243997 | + | 0.969776i | \(0.578459\pi\) | |||||||
\(182\) | 9.26651 | + | 14.0459i | 0.0509149 | + | 0.0771754i | ||||
\(183\) | − | 45.4905i | − | 0.248582i | ||||||
\(184\) | −242.264 | + | 43.7737i | −1.31665 | + | 0.237900i | ||||
\(185\) | −9.73522 | −0.0526228 | ||||||||
\(186\) | −0.505697 | + | 0.333623i | −0.00271880 | + | 0.00179367i | ||||
\(187\) | − | 309.930i | − | 1.65738i | ||||||
\(188\) | 133.457 | + | 57.1225i | 0.709878 | + | 0.303843i | ||||
\(189\) | 12.1253 | 0.0641551 | ||||||||
\(190\) | −1.52399 | − | 2.31002i | −0.00802100 | − | 0.0121580i | ||||
\(191\) | 195.231i | 1.02215i | 0.859536 | + | 0.511076i | \(0.170753\pi\) | ||||
−0.859536 | + | 0.511076i | \(0.829247\pi\) | |||||||
\(192\) | −38.7921 | − | 103.842i | −0.202042 | − | 0.540844i | ||||
\(193\) | −88.5332 | −0.458721 | −0.229361 | − | 0.973341i | \(-0.573664\pi\) | ||||
−0.229361 | + | 0.973341i | \(0.573664\pi\) | |||||||
\(194\) | −129.544 | + | 85.4643i | −0.667755 | + | 0.440538i | ||||
\(195\) | 1.57166i | 0.00805979i | ||||||||
\(196\) | 68.5537 | − | 160.164i | 0.349764 | − | 0.817164i | ||||
\(197\) | −193.536 | −0.982415 | −0.491208 | − | 0.871043i | \(-0.663444\pi\) | ||||
−0.491208 | + | 0.871043i | \(0.663444\pi\) | |||||||
\(198\) | 57.4736 | + | 87.1169i | 0.290271 | + | 0.439985i | ||||
\(199\) | 372.542i | 1.87207i | 0.351904 | + | 0.936036i | \(0.385534\pi\) | ||||
−0.351904 | + | 0.936036i | \(0.614466\pi\) | |||||||
\(200\) | −35.4713 | − | 196.314i | −0.177356 | − | 0.981572i | ||||
\(201\) | −56.0757 | −0.278984 | ||||||||
\(202\) | 6.92315 | − | 4.56741i | 0.0342730 | − | 0.0226109i | ||||
\(203\) | − | 53.4161i | − | 0.263134i | ||||||
\(204\) | −113.485 | − | 48.5742i | −0.556301 | − | 0.238109i | ||||
\(205\) | −2.70848 | −0.0132121 | ||||||||
\(206\) | −80.9950 | − | 122.770i | −0.393179 | − | 0.595971i | ||||
\(207\) | − | 92.3200i | − | 0.445990i | ||||||
\(208\) | 39.8242 | + | 41.7377i | 0.191462 | + | 0.200662i | ||||
\(209\) | 95.6395 | 0.457605 | ||||||||
\(210\) | −1.69811 | + | 1.12029i | −0.00808622 | + | 0.00533472i | ||||
\(211\) | − | 284.334i | − | 1.34755i | −0.738935 | − | 0.673777i | \(-0.764671\pi\) | ||
0.738935 | − | 0.673777i | \(-0.235329\pi\) | |||||||
\(212\) | 137.663 | − | 321.627i | 0.649355 | − | 1.51711i | ||||
\(213\) | −23.4048 | −0.109882 | ||||||||
\(214\) | 89.8731 | + | 136.227i | 0.419968 | + | 0.636576i | ||||
\(215\) | − | 10.7940i | − | 0.0502046i | ||||||
\(216\) | 40.9068 | − | 7.39129i | 0.189383 | − | 0.0342190i | ||||
\(217\) | 0.408106 | 0.00188067 | ||||||||
\(218\) | −186.921 | + | 123.317i | −0.857434 | + | 0.565675i | ||||
\(219\) | 190.934i | 0.871846i | ||||||||
\(220\) | −16.0979 | − | 6.89027i | −0.0731725 | − | 0.0313194i | ||||
\(221\) | 64.2423 | 0.290689 | ||||||||
\(222\) | −73.7927 | − | 111.853i | −0.332400 | − | 0.503842i | ||||
\(223\) | − | 21.0036i | − | 0.0941863i | −0.998891 | − | 0.0470932i | \(-0.985004\pi\) | ||
0.998891 | − | 0.0470932i | \(-0.0149958\pi\) | |||||||
\(224\) | −16.7087 | + | 72.7792i | −0.0745923 | + | 0.324907i | ||||
\(225\) | 74.8100 | 0.332489 | ||||||||
\(226\) | 278.306 | − | 183.607i | 1.23144 | − | 0.812418i | ||||
\(227\) | 428.034i | 1.88561i | 0.333340 | + | 0.942807i | \(0.391824\pi\) | ||||
−0.333340 | + | 0.942807i | \(0.608176\pi\) | |||||||
\(228\) | 14.9893 | − | 35.0199i | 0.0657423 | − | 0.153596i | ||||
\(229\) | −299.946 | −1.30981 | −0.654903 | − | 0.755713i | \(-0.727291\pi\) | ||||
−0.654903 | + | 0.755713i | \(0.727291\pi\) | |||||||
\(230\) | 8.52970 | + | 12.9291i | 0.0370856 | + | 0.0562134i | ||||
\(231\) | − | 70.3049i | − | 0.304350i | ||||||
\(232\) | −32.5611 | − | 180.208i | −0.140350 | − | 0.776760i | ||||
\(233\) | −343.608 | −1.47471 | −0.737356 | − | 0.675504i | \(-0.763926\pi\) | ||||
−0.737356 | + | 0.675504i | \(0.763926\pi\) | |||||||
\(234\) | −18.0576 | + | 11.9131i | −0.0771693 | + | 0.0509108i | ||||
\(235\) | − | 9.13349i | − | 0.0388659i | ||||||
\(236\) | −347.583 | − | 148.773i | −1.47281 | − | 0.630395i | ||||
\(237\) | −14.6679 | −0.0618901 | ||||||||
\(238\) | 45.7924 | + | 69.4109i | 0.192405 | + | 0.291642i | ||||
\(239\) | − | 11.0123i | − | 0.0460765i | −0.999735 | − | 0.0230383i | \(-0.992666\pi\) | ||
0.999735 | − | 0.0230383i | \(-0.00733396\pi\) | |||||||
\(240\) | −5.04595 | + | 4.81462i | −0.0210248 | + | 0.0200609i | ||||
\(241\) | 273.663 | 1.13553 | 0.567766 | − | 0.823190i | \(-0.307808\pi\) | ||||
0.567766 | + | 0.823190i | \(0.307808\pi\) | |||||||
\(242\) | 303.120 | − | 199.977i | 1.25256 | − | 0.826353i | ||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | −41.3387 | + | 96.5808i | −0.169421 | + | 0.395823i | ||||
\(245\) | −10.9613 | −0.0447399 | ||||||||
\(246\) | −20.5302 | − | 31.1191i | −0.0834561 | − | 0.126500i | ||||
\(247\) | 19.8242i | 0.0802598i | ||||||||
\(248\) | 1.37682 | − | 0.248772i | 0.00555168 | − | 0.00100311i | ||||
\(249\) | −2.79932 | −0.0112422 | ||||||||
\(250\) | −20.9803 | + | 13.8414i | −0.0839214 | + | 0.0553654i | ||||
\(251\) | 184.717i | 0.735926i | 0.929840 | + | 0.367963i | \(0.119945\pi\) | ||||
−0.929840 | + | 0.367963i | \(0.880055\pi\) | |||||||
\(252\) | −25.7432 | − | 11.0187i | −0.102156 | − | 0.0437248i | ||||
\(253\) | −535.289 | −2.11577 | ||||||||
\(254\) | 104.514 | + | 158.419i | 0.411471 | + | 0.623697i | ||||
\(255\) | 7.76669i | 0.0304576i | ||||||||
\(256\) | −12.0052 | + | 255.718i | −0.0468952 | + | 0.998900i | ||||
\(257\) | 426.793 | 1.66067 | 0.830337 | − | 0.557261i | \(-0.188148\pi\) | ||||
0.830337 | + | 0.557261i | \(0.188148\pi\) | |||||||
\(258\) | 124.018 | − | 81.8183i | 0.480690 | − | 0.317125i | ||||
\(259\) | 90.2674i | 0.348523i | ||||||||
\(260\) | 1.42822 | − | 3.33678i | 0.00549314 | − | 0.0128338i | ||||
\(261\) | 68.6724 | 0.263113 | ||||||||
\(262\) | 246.230 | + | 373.229i | 0.939809 | + | 1.42454i | ||||
\(263\) | 173.214i | 0.658609i | 0.944224 | + | 0.329304i | \(0.106814\pi\) | ||||
−0.944224 | + | 0.329304i | \(0.893186\pi\) | |||||||
\(264\) | −42.8562 | − | 237.186i | −0.162334 | − | 0.898431i | ||||
\(265\) | −22.0114 | −0.0830619 | ||||||||
\(266\) | −21.4191 | + | 14.1308i | −0.0805230 | + | 0.0531234i | ||||
\(267\) | − | 181.207i | − | 0.678679i | ||||||
\(268\) | 119.054 | + | 50.9578i | 0.444232 | + | 0.190141i | ||||
\(269\) | 375.485 | 1.39585 | 0.697927 | − | 0.716169i | \(-0.254106\pi\) | ||||
0.697927 | + | 0.716169i | \(0.254106\pi\) | |||||||
\(270\) | −1.44026 | − | 2.18311i | −0.00533430 | − | 0.00808558i | ||||
\(271\) | 451.566i | 1.66629i | 0.553051 | + | 0.833147i | \(0.313463\pi\) | ||||
−0.553051 | + | 0.833147i | \(0.686537\pi\) | |||||||
\(272\) | 196.800 | + | 206.256i | 0.723528 | + | 0.758293i | ||||
\(273\) | 14.5728 | 0.0533803 | ||||||||
\(274\) | −315.678 | + | 208.262i | −1.15211 | + | 0.760081i | ||||
\(275\) | − | 433.763i | − | 1.57732i | ||||||
\(276\) | −83.8941 | + | 196.004i | −0.303964 | + | 0.710161i | ||||
\(277\) | −480.894 | −1.73608 | −0.868039 | − | 0.496496i | \(-0.834620\pi\) | ||||
−0.868039 | + | 0.496496i | \(0.834620\pi\) | |||||||
\(278\) | 126.621 | + | 191.928i | 0.455470 | + | 0.690389i | ||||
\(279\) | 0.524666i | 0.00188053i | ||||||||
\(280\) | 4.62329 | − | 0.835364i | 0.0165117 | − | 0.00298344i | ||||
\(281\) | −251.688 | −0.895688 | −0.447844 | − | 0.894112i | \(-0.647808\pi\) | ||||
−0.447844 | + | 0.894112i | \(0.647808\pi\) | |||||||
\(282\) | 104.939 | − | 69.2317i | 0.372126 | − | 0.245502i | ||||
\(283\) | − | 366.709i | − | 1.29579i | −0.761729 | − | 0.647896i | \(-0.775649\pi\) | ||
0.761729 | − | 0.647896i | \(-0.224351\pi\) | |||||||
\(284\) | 49.6906 | + | 21.2687i | 0.174967 | + | 0.0748897i | ||||
\(285\) | −2.39668 | −0.00840940 | ||||||||
\(286\) | 69.0747 | + | 104.702i | 0.241520 | + | 0.366089i | ||||
\(287\) | 25.1137i | 0.0875041i | ||||||||
\(288\) | −93.5659 | − | 21.4809i | −0.324881 | − | 0.0745864i | ||||
\(289\) | 28.4669 | 0.0985012 | ||||||||
\(290\) | −9.61732 | + | 6.34483i | −0.0331632 | + | 0.0218787i | ||||
\(291\) | 134.404i | 0.461869i | ||||||||
\(292\) | 173.508 | − | 405.372i | 0.594205 | − | 1.38826i | ||||
\(293\) | −84.9216 | −0.289835 | −0.144917 | − | 0.989444i | \(-0.546292\pi\) | ||||
−0.144917 | + | 0.989444i | \(0.546292\pi\) | |||||||
\(294\) | −83.0862 | − | 125.940i | −0.282606 | − | 0.428367i | ||||
\(295\) | 23.7878i | 0.0806366i | ||||||||
\(296\) | 55.0248 | + | 304.533i | 0.185895 | + | 1.02883i | ||||
\(297\) | 90.3849 | 0.304326 | ||||||||
\(298\) | −248.696 | + | 164.072i | −0.834552 | + | 0.550578i | ||||
\(299\) | − | 110.955i | − | 0.371086i | ||||||
\(300\) | −158.829 | − | 67.9822i | −0.529430 | − | 0.226607i | ||||
\(301\) | −100.085 | −0.332507 | ||||||||
\(302\) | −278.872 | − | 422.707i | −0.923418 | − | 1.39969i | ||||
\(303\) | − | 7.18285i | − | 0.0237058i | ||||||
\(304\) | −63.6473 | + | 60.7293i | −0.209366 | + | 0.199768i | ||||
\(305\) | 6.60977 | 0.0216714 | ||||||||
\(306\) | −89.2355 | + | 58.8713i | −0.291619 | + | 0.192390i | ||||
\(307\) | 146.019i | 0.475633i | 0.971310 | + | 0.237816i | \(0.0764316\pi\) | ||||
−0.971310 | + | 0.237816i | \(0.923568\pi\) | |||||||
\(308\) | −63.8883 | + | 149.264i | −0.207430 | + | 0.484624i | ||||
\(309\) | −127.375 | −0.412218 | ||||||||
\(310\) | −0.0484754 | − | 0.0734776i | −0.000156372 | − | 0.000237025i | ||||
\(311\) | 193.433i | 0.621971i | 0.950415 | + | 0.310985i | \(0.100659\pi\) | ||||
−0.950415 | + | 0.310985i | \(0.899341\pi\) | |||||||
\(312\) | 49.1639 | − | 8.88323i | 0.157577 | − | 0.0284719i | ||||
\(313\) | −328.534 | −1.04963 | −0.524814 | − | 0.851217i | \(-0.675865\pi\) | ||||
−0.524814 | + | 0.851217i | \(0.675865\pi\) | |||||||
\(314\) | −457.973 | + | 302.139i | −1.45851 | + | 0.962225i | ||||
\(315\) | 1.76181i | 0.00559304i | ||||||||
\(316\) | 31.1415 | + | 13.3292i | 0.0985489 | + | 0.0421811i | ||||
\(317\) | 516.505 | 1.62935 | 0.814676 | − | 0.579916i | \(-0.196915\pi\) | ||||
0.814676 | + | 0.579916i | \(0.196915\pi\) | |||||||
\(318\) | −166.846 | − | 252.900i | −0.524673 | − | 0.795284i | ||||
\(319\) | − | 398.176i | − | 1.24820i | ||||||
\(320\) | 15.0882 | − | 5.63649i | 0.0471507 | − | 0.0176140i | ||||
\(321\) | 141.337 | 0.440303 | ||||||||
\(322\) | 119.882 | − | 79.0895i | 0.372303 | − | 0.245620i | ||||
\(323\) | 97.9653i | 0.303298i | ||||||||
\(324\) | 14.1657 | − | 33.0958i | 0.0437214 | − | 0.102148i | ||||
\(325\) | 89.9104 | 0.276647 | ||||||||
\(326\) | −173.874 | − | 263.554i | −0.533357 | − | 0.808447i | ||||
\(327\) | 193.932i | 0.593066i | ||||||||
\(328\) | 15.3087 | + | 84.7253i | 0.0466728 | + | 0.258309i | ||||
\(329\) | −84.6881 | −0.257411 | ||||||||
\(330\) | −12.6581 | + | 8.35091i | −0.0383578 | + | 0.0253058i | ||||
\(331\) | − | 525.675i | − | 1.58814i | −0.607824 | − | 0.794071i | \(-0.707958\pi\) | ||
0.607824 | − | 0.794071i | \(-0.292042\pi\) | |||||||
\(332\) | 5.94322 | + | 2.54383i | 0.0179013 | + | 0.00766213i | ||||
\(333\) | −116.049 | −0.348495 | ||||||||
\(334\) | −104.763 | − | 158.797i | −0.313661 | − | 0.475439i | ||||
\(335\) | − | 8.14780i | − | 0.0243218i | ||||||
\(336\) | 44.6424 | + | 46.7873i | 0.132864 | + | 0.139248i | ||||
\(337\) | 201.872 | 0.599026 | 0.299513 | − | 0.954092i | \(-0.403176\pi\) | ||||
0.299513 | + | 0.954092i | \(0.403176\pi\) | |||||||
\(338\) | −21.7025 | + | 14.3178i | −0.0642087 | + | 0.0423604i | ||||
\(339\) | − | 288.746i | − | 0.851757i | ||||||
\(340\) | 7.05783 | − | 16.4894i | 0.0207583 | − | 0.0484983i | ||||
\(341\) | 3.04212 | 0.00892117 | ||||||||
\(342\) | −18.1668 | − | 27.5367i | −0.0531192 | − | 0.0805166i | ||||
\(343\) | 215.978i | 0.629674i | ||||||||
\(344\) | −337.653 | + | 61.0092i | −0.981549 | + | 0.177352i | ||||
\(345\) | 13.4141 | 0.0388814 | ||||||||
\(346\) | 215.853 | − | 142.405i | 0.623853 | − | 0.411574i | ||||
\(347\) | − | 23.9745i | − | 0.0690907i | −0.999403 | − | 0.0345453i | \(-0.989002\pi\) | ||
0.999403 | − | 0.0345453i | \(-0.0109983\pi\) | |||||||
\(348\) | −145.798 | − | 62.4048i | −0.418960 | − | 0.179324i | ||||
\(349\) | −0.403468 | −0.00115607 | −0.000578035 | − | 1.00000i | \(-0.500184\pi\) | ||||
−0.000578035 | 1.00000i | \(0.500184\pi\) | ||||||||
\(350\) | 64.0889 | + | 97.1442i | 0.183111 | + | 0.277555i | ||||
\(351\) | 18.7350i | 0.0533761i | ||||||||
\(352\) | −124.550 | + | 542.513i | −0.353836 | + | 1.54123i | ||||
\(353\) | 174.107 | 0.493221 | 0.246610 | − | 0.969115i | \(-0.420683\pi\) | ||||
0.246610 | + | 0.969115i | \(0.420683\pi\) | |||||||
\(354\) | −273.310 | + | 180.311i | −0.772063 | + | 0.509353i | ||||
\(355\) | − | 3.40071i | − | 0.00957947i | ||||||
\(356\) | −164.669 | + | 384.721i | −0.462553 | + | 1.08068i | ||||
\(357\) | 72.0147 | 0.201722 | ||||||||
\(358\) | 35.7028 | + | 54.1173i | 0.0997284 | + | 0.151166i | ||||
\(359\) | − | 200.471i | − | 0.558415i | −0.960231 | − | 0.279208i | \(-0.909928\pi\) | ||
0.960231 | − | 0.279208i | \(-0.0900718\pi\) | |||||||
\(360\) | 1.07395 | + | 5.94376i | 0.00298321 | + | 0.0165104i | ||||
\(361\) | 330.769 | 0.916259 | ||||||||
\(362\) | 147.455 | − | 97.2807i | 0.407335 | − | 0.268731i | ||||
\(363\) | − | 314.491i | − | 0.866367i | ||||||
\(364\) | −30.9395 | − | 13.2428i | −0.0849986 | − | 0.0363812i | ||||
\(365\) | −27.7427 | −0.0760075 | ||||||||
\(366\) | 50.1019 | + | 75.9431i | 0.136890 | + | 0.207495i | ||||
\(367\) | − | 661.977i | − | 1.80375i | −0.431995 | − | 0.901876i | \(-0.642190\pi\) | ||
0.431995 | − | 0.901876i | \(-0.357810\pi\) | |||||||
\(368\) | 356.230 | − | 339.899i | 0.968018 | − | 0.923638i | ||||
\(369\) | −32.2865 | −0.0874972 | ||||||||
\(370\) | 16.2522 | − | 10.7221i | 0.0439249 | − | 0.0289786i | ||||
\(371\) | 204.095i | 0.550122i | ||||||||
\(372\) | 0.476781 | − | 1.11392i | 0.00128167 | − | 0.00299440i | ||||
\(373\) | −136.647 | −0.366346 | −0.183173 | − | 0.983081i | \(-0.558637\pi\) | ||||
−0.183173 | + | 0.983081i | \(0.558637\pi\) | |||||||
\(374\) | 341.347 | + | 517.405i | 0.912693 | + | 1.38344i | ||||
\(375\) | 21.7674i | 0.0580463i | ||||||||
\(376\) | −285.710 | + | 51.6238i | −0.759866 | + | 0.137297i | ||||
\(377\) | 82.5340 | 0.218923 | ||||||||
\(378\) | −20.2423 | + | 13.3545i | −0.0535511 | + | 0.0353292i | ||||
\(379\) | − | 171.247i | − | 0.451838i | −0.974146 | − | 0.225919i | \(-0.927462\pi\) | ||
0.974146 | − | 0.225919i | \(-0.0725384\pi\) | |||||||
\(380\) | 5.08838 | + | 2.17794i | 0.0133905 | + | 0.00573141i | ||||
\(381\) | 164.362 | 0.431396 | ||||||||
\(382\) | −215.022 | − | 325.924i | −0.562884 | − | 0.853204i | ||||
\(383\) | 488.106i | 1.27443i | 0.770687 | + | 0.637214i | \(0.219913\pi\) | ||||
−0.770687 | + | 0.637214i | \(0.780087\pi\) | |||||||
\(384\) | 179.129 | + | 130.632i | 0.466482 | + | 0.340188i | ||||
\(385\) | 10.2153 | 0.0265332 | ||||||||
\(386\) | 147.800 | − | 97.5078i | 0.382901 | − | 0.252611i | ||||
\(387\) | − | 128.670i | − | 0.332481i | ||||||
\(388\) | 122.137 | − | 285.353i | 0.314786 | − | 0.735445i | ||||
\(389\) | 741.544 | 1.90628 | 0.953141 | − | 0.302525i | \(-0.0978296\pi\) | ||||
0.953141 | + | 0.302525i | \(0.0978296\pi\) | |||||||
\(390\) | −1.73098 | − | 2.62377i | −0.00443840 | − | 0.00672761i | ||||
\(391\) | − | 548.307i | − | 1.40232i | ||||||
\(392\) | 61.9546 | + | 342.885i | 0.158047 | + | 0.874708i | ||||
\(393\) | 387.230 | 0.985317 | ||||||||
\(394\) | 323.094 | − | 213.155i | 0.820035 | − | 0.541001i | ||||
\(395\) | − | 2.13125i | − | 0.00539557i | ||||||
\(396\) | −191.896 | − | 82.1356i | −0.484586 | − | 0.207413i | ||||
\(397\) | 344.631 | 0.868088 | 0.434044 | − | 0.900892i | \(-0.357086\pi\) | ||||
0.434044 | + | 0.900892i | \(0.357086\pi\) | |||||||
\(398\) | −410.307 | − | 621.932i | −1.03092 | − | 1.56264i | ||||
\(399\) | 22.2226i | 0.0556958i | ||||||||
\(400\) | 275.432 | + | 288.666i | 0.688579 | + | 0.721664i | ||||
\(401\) | −401.952 | −1.00237 | −0.501187 | − | 0.865339i | \(-0.667103\pi\) | ||||
−0.501187 | + | 0.865339i | \(0.667103\pi\) | |||||||
\(402\) | 93.6143 | − | 61.7601i | 0.232871 | − | 0.153632i | ||||
\(403\) | 0.630571i | 0.00156469i | ||||||||
\(404\) | −6.52728 | + | 15.2499i | −0.0161566 | + | 0.0377473i | ||||
\(405\) | −2.26500 | −0.00559259 | ||||||||
\(406\) | 58.8309 | + | 89.1742i | 0.144904 | + | 0.219641i | ||||
\(407\) | 672.874i | 1.65325i | ||||||||
\(408\) | 242.954 | − | 43.8984i | 0.595475 | − | 0.107594i | ||||
\(409\) | −251.492 | −0.614895 | −0.307447 | − | 0.951565i | \(-0.599475\pi\) | ||||
−0.307447 | + | 0.951565i | \(0.599475\pi\) | |||||||
\(410\) | 4.52160 | − | 2.98303i | 0.0110283 | − | 0.00727569i | ||||
\(411\) | 327.520i | 0.796886i | ||||||||
\(412\) | 270.430 | + | 115.750i | 0.656384 | + | 0.280947i | ||||
\(413\) | 220.566 | 0.534059 | ||||||||
\(414\) | 101.678 | + | 154.121i | 0.245600 | + | 0.372274i | ||||
\(415\) | − | 0.406740i | − | 0.000980098i | ||||||
\(416\) | −112.452 | − | 25.8168i | −0.270318 | − | 0.0620596i | ||||
\(417\) | 199.128 | 0.477525 | ||||||||
\(418\) | −159.663 | + | 105.334i | −0.381969 | + | 0.251996i | ||||
\(419\) | − | 453.214i | − | 1.08166i | −0.841133 | − | 0.540829i | \(-0.818111\pi\) | ||
0.841133 | − | 0.540829i | \(-0.181889\pi\) | |||||||
\(420\) | 1.60101 | − | 3.74049i | 0.00381193 | − | 0.00890592i | ||||
\(421\) | 239.355 | 0.568539 | 0.284270 | − | 0.958744i | \(-0.408249\pi\) | ||||
0.284270 | + | 0.958744i | \(0.408249\pi\) | |||||||
\(422\) | 313.157 | + | 474.675i | 0.742078 | + | 1.12482i | ||||
\(423\) | − | 108.876i | − | 0.257390i | ||||||
\(424\) | 124.411 | + | 688.550i | 0.293423 | + | 1.62394i | ||||
\(425\) | 444.311 | 1.04544 | ||||||||
\(426\) | 39.0726 | − | 25.7773i | 0.0917197 | − | 0.0605102i | ||||
\(427\) | − | 61.2874i | − | 0.143530i | ||||||
\(428\) | −300.073 | − | 128.438i | −0.701105 | − | 0.300088i | ||||
\(429\) | 108.629 | 0.253215 | ||||||||
\(430\) | 11.8882 | + | 18.0198i | 0.0276469 | + | 0.0419065i | ||||
\(431\) | − | 582.956i | − | 1.35257i | −0.736642 | − | 0.676283i | \(-0.763590\pi\) | ||
0.736642 | − | 0.676283i | \(-0.236410\pi\) | |||||||
\(432\) | −60.1504 | + | 57.3928i | −0.139237 | + | 0.132854i | ||||
\(433\) | −38.8680 | −0.0897643 | −0.0448822 | − | 0.998992i | \(-0.514291\pi\) | ||||
−0.0448822 | + | 0.998992i | \(0.514291\pi\) | |||||||
\(434\) | −0.681303 | + | 0.449476i | −0.00156982 | + | 0.00103566i | ||||
\(435\) | 9.97809i | 0.0229381i | ||||||||
\(436\) | 176.233 | − | 411.737i | 0.404203 | − | 0.944352i | ||||
\(437\) | 169.199 | 0.387183 | ||||||||
\(438\) | −210.289 | − | 318.751i | −0.480112 | − | 0.727741i | ||||
\(439\) | − | 374.232i | − | 0.852464i | −0.904614 | − | 0.426232i | \(-0.859841\pi\) | ||
0.904614 | − | 0.426232i | \(-0.140159\pi\) | |||||||
\(440\) | 34.4631 | − | 6.22700i | 0.0783251 | − | 0.0141523i | ||||
\(441\) | −130.664 | −0.296290 | ||||||||
\(442\) | −107.248 | + | 70.7545i | −0.242642 | + | 0.160078i | ||||
\(443\) | − | 196.055i | − | 0.442562i | −0.975210 | − | 0.221281i | \(-0.928976\pi\) | ||
0.975210 | − | 0.221281i | \(-0.0710238\pi\) | |||||||
\(444\) | 246.383 | + | 105.457i | 0.554917 | + | 0.237516i | ||||
\(445\) | 26.3294 | 0.0591672 | ||||||||
\(446\) | 23.1327 | + | 35.0639i | 0.0518670 | + | 0.0786186i | ||||
\(447\) | 258.026i | 0.577239i | ||||||||
\(448\) | −52.2629 | − | 139.902i | −0.116658 | − | 0.312281i | ||||
\(449\) | −858.959 | −1.91305 | −0.956524 | − | 0.291653i | \(-0.905795\pi\) | ||||
−0.956524 | + | 0.291653i | \(0.905795\pi\) | |||||||
\(450\) | −124.890 | + | 82.3935i | −0.277533 | + | 0.183097i | ||||
\(451\) | 187.203i | 0.415085i | ||||||||
\(452\) | −262.392 | + | 613.035i | −0.580514 | + | 1.35627i | ||||
\(453\) | −438.564 | −0.968132 | ||||||||
\(454\) | −471.424 | − | 714.572i | −1.03838 | − | 1.57395i | ||||
\(455\) | 2.11743i | 0.00465369i | ||||||||
\(456\) | 13.5464 | + | 74.9718i | 0.0297069 | + | 0.164412i | ||||
\(457\) | 356.728 | 0.780586 | 0.390293 | − | 0.920691i | \(-0.372374\pi\) | ||||
0.390293 | + | 0.920691i | \(0.372374\pi\) | |||||||
\(458\) | 500.737 | − | 330.351i | 1.09331 | − | 0.721291i | ||||
\(459\) | 92.5830i | 0.201706i | ||||||||
\(460\) | −28.4794 | − | 12.1898i | −0.0619117 | − | 0.0264996i | ||||
\(461\) | −9.54824 | −0.0207120 | −0.0103560 | − | 0.999946i | \(-0.503296\pi\) | ||||
−0.0103560 | + | 0.999946i | \(0.503296\pi\) | |||||||
\(462\) | 77.4317 | + | 117.369i | 0.167601 | + | 0.254045i | ||||
\(463\) | 767.584i | 1.65785i | 0.559360 | + | 0.828925i | \(0.311047\pi\) | ||||
−0.559360 | + | 0.828925i | \(0.688953\pi\) | |||||||
\(464\) | 252.835 | + | 264.983i | 0.544902 | + | 0.571084i | ||||
\(465\) | −0.0762340 | −0.000163944 | ||||||||
\(466\) | 573.628 | − | 378.439i | 1.23096 | − | 0.812102i | ||||
\(467\) | 11.3023i | 0.0242019i | 0.999927 | + | 0.0121009i | \(0.00385194\pi\) | ||||
−0.999927 | + | 0.0121009i | \(0.996148\pi\) | |||||||
\(468\) | 17.0251 | − | 39.7762i | 0.0363784 | − | 0.0849919i | ||||
\(469\) | −75.5484 | −0.161084 | ||||||||
\(470\) | 10.0594 | + | 15.2477i | 0.0214029 | + | 0.0324419i | ||||
\(471\) | 475.153i | 1.00882i | ||||||||
\(472\) | 744.119 | − | 134.452i | 1.57652 | − | 0.284856i | ||||
\(473\) | −746.055 | −1.57728 | ||||||||
\(474\) | 24.4870 | − | 16.1548i | 0.0516604 | − | 0.0340819i | ||||
\(475\) | 137.108i | 0.288648i | ||||||||
\(476\) | −152.894 | − | 65.4420i | −0.321206 | − | 0.137483i | ||||
\(477\) | −262.387 | −0.550078 | ||||||||
\(478\) | 12.1286 | + | 18.3842i | 0.0253737 | + | 0.0384607i | ||||
\(479\) | − | 418.204i | − | 0.873077i | −0.899686 | − | 0.436538i | \(-0.856204\pi\) | ||
0.899686 | − | 0.436538i | \(-0.143796\pi\) | |||||||
\(480\) | 3.12117 | − | 13.5951i | 0.00650244 | − | 0.0283231i | ||||
\(481\) | −139.473 | −0.289966 | ||||||||
\(482\) | −456.861 | + | 301.405i | −0.947844 | + | 0.625321i | ||||
\(483\) | − | 124.379i | − | 0.257513i | ||||||
\(484\) | −285.788 | + | 667.695i | −0.590471 | + | 1.37954i | ||||
\(485\) | −19.5289 | −0.0402657 | ||||||||
\(486\) | −17.1687 | − | 26.0238i | −0.0353265 | − | 0.0535469i | ||||
\(487\) | − | 422.152i | − | 0.866842i | −0.901192 | − | 0.433421i | \(-0.857306\pi\) | ||
0.901192 | − | 0.433421i | \(-0.142694\pi\) | |||||||
\(488\) | −37.3593 | − | 206.764i | −0.0765560 | − | 0.423696i | ||||
\(489\) | −273.440 | −0.559183 | ||||||||
\(490\) | 18.2990 | − | 12.0724i | 0.0373450 | − | 0.0246376i | ||||
\(491\) | − | 13.0273i | − | 0.0265321i | −0.999912 | − | 0.0132661i | \(-0.995777\pi\) | ||
0.999912 | − | 0.0132661i | \(-0.00422285\pi\) | |||||||
\(492\) | 68.5473 | + | 29.3397i | 0.139324 | + | 0.0596336i | ||||
\(493\) | 407.859 | 0.827301 | ||||||||
\(494\) | −21.8337 | − | 33.0950i | −0.0441978 | − | 0.0669939i | ||||
\(495\) | 13.1329i | 0.0265311i | ||||||||
\(496\) | −2.02450 | + | 1.93169i | −0.00408166 | + | 0.00389454i | ||||
\(497\) | −31.5323 | −0.0634452 | ||||||||
\(498\) | 4.67325 | − | 3.08308i | 0.00938405 | − | 0.00619093i | ||||
\(499\) | 354.534i | 0.710489i | 0.934773 | + | 0.355245i | \(0.115602\pi\) | ||||
−0.934773 | + | 0.355245i | \(0.884398\pi\) | |||||||
\(500\) | 19.7807 | − | 46.2142i | 0.0395614 | − | 0.0924285i | ||||
\(501\) | −164.753 | −0.328849 | ||||||||
\(502\) | −203.442 | − | 308.372i | −0.405263 | − | 0.614287i | ||||
\(503\) | − | 290.412i | − | 0.577360i | −0.957426 | − | 0.288680i | \(-0.906784\pi\) | ||
0.957426 | − | 0.288680i | \(-0.0932164\pi\) | |||||||
\(504\) | 55.1120 | − | 9.95797i | 0.109349 | − | 0.0197579i | ||||
\(505\) | 1.04367 | 0.00206667 | ||||||||
\(506\) | 893.626 | − | 589.552i | 1.76606 | − | 1.16512i | ||||
\(507\) | 22.5167i | 0.0444116i | ||||||||
\(508\) | −348.956 | − | 149.361i | −0.686921 | − | 0.294017i | ||||
\(509\) | 4.57807 | 0.00899424 | 0.00449712 | − | 0.999990i | \(-0.498569\pi\) | ||||
0.00449712 | + | 0.999990i | \(0.498569\pi\) | |||||||
\(510\) | −8.55399 | − | 12.9659i | −0.0167725 | − | 0.0254234i | ||||
\(511\) | 257.238i | 0.503400i | ||||||||
\(512\) | −261.599 | − | 440.125i | −0.510935 | − | 0.859619i | ||||
\(513\) | −28.5697 | −0.0556913 | ||||||||
\(514\) | −712.500 | + | 470.057i | −1.38619 | + | 0.914508i | ||||
\(515\) | − | 18.5076i | − | 0.0359371i | ||||||
\(516\) | −116.927 | + | 273.179i | −0.226602 | + | 0.529417i | ||||
\(517\) | −631.284 | −1.22105 | ||||||||
\(518\) | −99.4178 | − | 150.695i | −0.191926 | − | 0.290917i | ||||
\(519\) | − | 223.950i | − | 0.431503i | ||||||
\(520\) | 1.29073 | + | 7.14351i | 0.00248218 | + | 0.0137375i | ||||
\(521\) | −162.675 | −0.312235 | −0.156118 | − | 0.987738i | \(-0.549898\pi\) | ||||
−0.156118 | + | 0.987738i | \(0.549898\pi\) | |||||||
\(522\) | −114.644 | + | 75.6337i | −0.219624 | + | 0.144892i | ||||
\(523\) | 655.375i | 1.25311i | 0.779379 | + | 0.626553i | \(0.215535\pi\) | ||||
−0.779379 | + | 0.626553i | \(0.784465\pi\) | |||||||
\(524\) | −822.126 | − | 351.888i | −1.56894 | − | 0.671541i | ||||
\(525\) | 100.788 | 0.191978 | ||||||||
\(526\) | −190.773 | − | 289.168i | −0.362686 | − | 0.549749i | ||||
\(527\) | 3.11610i | 0.00591290i | ||||||||
\(528\) | 332.774 | + | 348.764i | 0.630255 | + | 0.660537i | ||||
\(529\) | −417.998 | −0.790166 | ||||||||
\(530\) | 36.7464 | − | 24.2427i | 0.0693328 | − | 0.0457409i | ||||
\(531\) | 283.563i | 0.534017i | ||||||||
\(532\) | 20.1944 | − | 47.1807i | 0.0379594 | − | 0.0886856i | ||||
\(533\) | −38.8035 | −0.0728021 | ||||||||
\(534\) | 199.576 | + | 302.512i | 0.373738 | + | 0.566502i | ||||
\(535\) | 20.5363i | 0.0383856i | ||||||||
\(536\) | −254.876 | + | 46.0525i | −0.475514 | + | 0.0859188i | ||||
\(537\) | 56.1473 | 0.104557 | ||||||||
\(538\) | −626.844 | + | 413.548i | −1.16514 | + | 0.768676i | ||||
\(539\) | 757.616i | 1.40560i | ||||||||
\(540\) | 4.80882 | + | 2.05828i | 0.00890522 | + | 0.00381162i | ||||
\(541\) | −447.595 | −0.827347 | −0.413673 | − | 0.910425i | \(-0.635754\pi\) | ||||
−0.413673 | + | 0.910425i | \(0.635754\pi\) | |||||||
\(542\) | −497.341 | − | 753.856i | −0.917603 | − | 1.39088i | ||||
\(543\) | − | 152.987i | − | 0.281744i | ||||||
\(544\) | −555.706 | − | 127.579i | −1.02152 | − | 0.234521i | ||||
\(545\) | −28.1784 | −0.0517034 | ||||||||
\(546\) | −24.3282 | + | 16.0501i | −0.0445572 | + | 0.0293957i | ||||
\(547\) | 1066.95i | 1.95056i | 0.220980 | + | 0.975278i | \(0.429074\pi\) | ||||
−0.220980 | + | 0.975278i | \(0.570926\pi\) | |||||||
\(548\) | 297.628 | − | 695.357i | 0.543117 | − | 1.26890i | ||||
\(549\) | 78.7919 | 0.143519 | ||||||||
\(550\) | 477.733 | + | 724.135i | 0.868606 | + | 1.31661i | ||||
\(551\) | 125.859i | 0.228419i | ||||||||
\(552\) | −75.8183 | − | 419.613i | −0.137352 | − | 0.760169i | ||||
\(553\) | −19.7615 | −0.0357351 | ||||||||
\(554\) | 802.817 | − | 529.642i | 1.44913 | − | 0.956032i | ||||
\(555\) | − | 16.8619i | − | 0.0303818i | ||||||
\(556\) | −422.768 | − | 180.954i | −0.760374 | − | 0.325457i | ||||
\(557\) | −617.405 | −1.10845 | −0.554224 | − | 0.832368i | \(-0.686985\pi\) | ||||
−0.554224 | + | 0.832368i | \(0.686985\pi\) | |||||||
\(558\) | −0.577852 | − | 0.875892i | −0.00103558 | − | 0.00156970i | ||||
\(559\) | − | 154.642i | − | 0.276641i | ||||||
\(560\) | −6.79819 | + | 6.48653i | −0.0121396 | + | 0.0115831i | ||||
\(561\) | 536.814 | 0.956888 | ||||||||
\(562\) | 420.175 | − | 277.202i | 0.747643 | − | 0.493242i | ||||
\(563\) | 372.544i | 0.661713i | 0.943681 | + | 0.330856i | \(0.107338\pi\) | ||||
−0.943681 | + | 0.330856i | \(0.892662\pi\) | |||||||
\(564\) | −98.9391 | + | 231.154i | −0.175424 | + | 0.409848i | ||||
\(565\) | 41.9547 | 0.0742561 | ||||||||
\(566\) | 403.882 | + | 612.193i | 0.713573 | + | 1.08161i | ||||
\(567\) | 21.0017i | 0.0370400i | ||||||||
\(568\) | −106.380 | + | 19.2213i | −0.187288 | + | 0.0338403i | ||||
\(569\) | −87.3586 | −0.153530 | −0.0767650 | − | 0.997049i | \(-0.524459\pi\) | ||||
−0.0767650 | + | 0.997049i | \(0.524459\pi\) | |||||||
\(570\) | 4.00108 | − | 2.63963i | 0.00701943 | − | 0.00463093i | ||||
\(571\) | 603.066i | 1.05616i | 0.849195 | + | 0.528079i | \(0.177087\pi\) | ||||
−0.849195 | + | 0.528079i | \(0.822913\pi\) | |||||||
\(572\) | −230.630 | − | 98.7147i | −0.403200 | − | 0.172578i | ||||
\(573\) | −338.150 | −0.590140 | ||||||||
\(574\) | −27.6594 | − | 41.9254i | −0.0481872 | − | 0.0730408i | ||||
\(575\) | − | 767.384i | − | 1.33458i | ||||||
\(576\) | 179.860 | − | 67.1899i | 0.312256 | − | 0.116649i | ||||
\(577\) | 245.153 | 0.424875 | 0.212437 | − | 0.977175i | \(-0.431860\pi\) | ||||
0.212437 | + | 0.977175i | \(0.431860\pi\) | |||||||
\(578\) | −47.5233 | + | 31.3525i | −0.0822203 | + | 0.0542431i | ||||
\(579\) | − | 153.344i | − | 0.264843i | ||||||
\(580\) | 9.06741 | − | 21.1845i | 0.0156335 | − | 0.0365249i | ||||
\(581\) | −3.77140 | −0.00649122 | ||||||||
\(582\) | −148.029 | − | 224.378i | −0.254345 | − | 0.385528i | ||||
\(583\) | 1521.37i | 2.60956i | ||||||||
\(584\) | 156.806 | + | 867.835i | 0.268503 | + | 1.48602i | ||||
\(585\) | −2.72219 | −0.00465332 | ||||||||
\(586\) | 141.770 | − | 93.5301i | 0.241929 | − | 0.159608i | ||||
\(587\) | − | 751.196i | − | 1.27972i | −0.768491 | − | 0.639860i | \(-0.778992\pi\) | ||
0.768491 | − | 0.639860i | \(-0.221008\pi\) | |||||||
\(588\) | 277.413 | + | 118.739i | 0.471790 | + | 0.201936i | ||||
\(589\) | −0.961580 | −0.00163256 | ||||||||
\(590\) | −26.1992 | − | 39.7120i | −0.0444054 | − | 0.0673084i | ||||
\(591\) | − | 335.214i | − | 0.567198i | ||||||
\(592\) | −427.263 | − | 447.792i | −0.721728 | − | 0.756405i | ||||
\(593\) | −820.636 | −1.38387 | −0.691936 | − | 0.721959i | \(-0.743242\pi\) | ||||
−0.691936 | + | 0.721959i | \(0.743242\pi\) | |||||||
\(594\) | −150.891 | + | 99.5472i | −0.254025 | + | 0.167588i | ||||
\(595\) | 10.4637i | 0.0175861i | ||||||||
\(596\) | 234.476 | − | 547.814i | 0.393416 | − | 0.919150i | ||||
\(597\) | −645.262 | −1.08084 | ||||||||
\(598\) | 122.202 | + | 185.231i | 0.204352 | + | 0.309751i | ||||
\(599\) | 370.633i | 0.618752i | 0.950940 | + | 0.309376i | \(0.100120\pi\) | ||||
−0.950940 | + | 0.309376i | \(0.899880\pi\) | |||||||
\(600\) | 340.027 | − | 61.4381i | 0.566711 | − | 0.102397i | ||||
\(601\) | 282.638 | 0.470279 | 0.235139 | − | 0.971962i | \(-0.424445\pi\) | ||||
0.235139 | + | 0.971962i | \(0.424445\pi\) | |||||||
\(602\) | 167.084 | − | 110.230i | 0.277548 | − | 0.183107i | ||||
\(603\) | − | 97.1260i | − | 0.161071i | ||||||
\(604\) | 931.113 | + | 398.537i | 1.54158 | + | 0.659829i | ||||
\(605\) | 45.6955 | 0.0755298 | ||||||||
\(606\) | 7.91098 | + | 11.9912i | 0.0130544 | + | 0.0197875i | ||||
\(607\) | − | 878.042i | − | 1.44653i | −0.690572 | − | 0.723263i | \(-0.742641\pi\) | ||
0.690572 | − | 0.723263i | \(-0.257359\pi\) | |||||||
\(608\) | 39.3690 | − | 171.482i | 0.0647516 | − | 0.282043i | ||||
\(609\) | 92.5194 | 0.151920 | ||||||||
\(610\) | −11.0345 | + | 7.27980i | −0.0180894 | + | 0.0119341i | ||||
\(611\) | − | 130.853i | − | 0.214162i | ||||||
\(612\) | 84.1330 | − | 196.563i | 0.137472 | − | 0.321181i | ||||
\(613\) | 748.062 | 1.22033 | 0.610164 | − | 0.792275i | \(-0.291103\pi\) | ||||
0.610164 | + | 0.792275i | \(0.291103\pi\) | |||||||
\(614\) | −160.821 | − | 243.768i | −0.261924 | − | 0.397017i | ||||
\(615\) | − | 4.69122i | − | 0.00762800i | ||||||
\(616\) | −57.7383 | − | 319.550i | −0.0937310 | − | 0.518750i | ||||
\(617\) | −66.8574 | −0.108359 | −0.0541794 | − | 0.998531i | \(-0.517254\pi\) | ||||
−0.0541794 | + | 0.998531i | \(0.517254\pi\) | |||||||
\(618\) | 212.644 | − | 140.287i | 0.344084 | − | 0.227002i | ||||
\(619\) | − | 419.308i | − | 0.677396i | −0.940895 | − | 0.338698i | \(-0.890014\pi\) | ||
0.940895 | − | 0.338698i | \(-0.109986\pi\) | |||||||
\(620\) | 0.161852 | + | 0.0692762i | 0.000261052 | + | 0.000111736i | ||||
\(621\) | 159.903 | 0.257493 | ||||||||
\(622\) | −213.041 | − | 322.922i | −0.342510 | − | 0.519167i | ||||
\(623\) | − | 244.133i | − | 0.391867i | ||||||
\(624\) | −72.2918 | + | 68.9775i | −0.115852 | + | 0.110541i | ||||
\(625\) | 620.254 | 0.992406 | ||||||||
\(626\) | 548.463 | − | 361.837i | 0.876139 | − | 0.578015i | ||||
\(627\) | 165.652i | 0.264199i | ||||||||
\(628\) | 431.786 | − | 1008.80i | 0.687558 | − | 1.60636i | ||||
\(629\) | −689.238 | −1.09577 | ||||||||
\(630\) | −1.94040 | − | 2.94121i | −0.00308000 | − | 0.00466858i | ||||
\(631\) | 1104.22i | 1.74996i | 0.484163 | + | 0.874978i | \(0.339124\pi\) | ||||
−0.484163 | + | 0.874978i | \(0.660876\pi\) | |||||||
\(632\) | −66.6688 | + | 12.0461i | −0.105489 | + | 0.0190603i | ||||
\(633\) | 492.481 | 0.778011 | ||||||||
\(634\) | −862.267 | + | 568.863i | −1.36004 | + | 0.897260i | ||||
\(635\) | 23.8817i | 0.0376090i | ||||||||
\(636\) | 557.074 | + | 238.440i | 0.875902 | + | 0.374905i | ||||
\(637\) | −157.039 | −0.246529 | ||||||||
\(638\) | 438.539 | + | 664.726i | 0.687365 | + | 1.04189i | ||||
\(639\) | − | 40.5383i | − | 0.0634402i | ||||||
\(640\) | −18.9808 | + | 26.0274i | −0.0296576 | + | 0.0406679i | ||||
\(641\) | 257.680 | 0.401996 | 0.200998 | − | 0.979592i | \(-0.435581\pi\) | ||||
0.200998 | + | 0.979592i | \(0.435581\pi\) | |||||||
\(642\) | −235.952 | + | 155.665i | −0.367527 | + | 0.242468i | ||||
\(643\) | 288.864i | 0.449244i | 0.974446 | + | 0.224622i | \(0.0721147\pi\) | ||||
−0.974446 | + | 0.224622i | \(0.927885\pi\) | |||||||
\(644\) | −113.027 | + | 264.068i | −0.175508 | + | 0.410044i | ||||
\(645\) | 18.6958 | 0.0289857 | ||||||||
\(646\) | −107.896 | − | 163.546i | −0.167022 | − | 0.253167i | ||||
\(647\) | − | 83.0624i | − | 0.128381i | −0.997938 | − | 0.0641904i | \(-0.979553\pi\) | ||
0.997938 | − | 0.0641904i | \(-0.0204465\pi\) | |||||||
\(648\) | 12.8021 | + | 70.8527i | 0.0197563 | + | 0.109341i | ||||
\(649\) | 1644.15 | 2.53336 | ||||||||
\(650\) | −150.099 | + | 99.0246i | −0.230921 | + | 0.152346i | ||||
\(651\) | 0.706861i | 0.00108581i | ||||||||
\(652\) | 580.541 | + | 248.484i | 0.890400 | + | 0.381110i | ||||
\(653\) | 763.163 | 1.16870 | 0.584352 | − | 0.811501i | \(-0.301349\pi\) | ||||
0.584352 | + | 0.811501i | \(0.301349\pi\) | |||||||
\(654\) | −213.591 | − | 323.756i | −0.326592 | − | 0.495040i | ||||
\(655\) | 56.2644i | 0.0858999i | ||||||||
\(656\) | −118.871 | − | 124.582i | −0.181205 | − | 0.189912i | ||||
\(657\) | −330.708 | −0.503361 | ||||||||
\(658\) | 141.380 | − | 93.2729i | 0.214864 | − | 0.141752i | ||||
\(659\) | 901.575i | 1.36810i | 0.729437 | + | 0.684048i | \(0.239782\pi\) | ||||
−0.729437 | + | 0.684048i | \(0.760218\pi\) | |||||||
\(660\) | 11.9343 | − | 27.8825i | 0.0180823 | − | 0.0422461i | ||||
\(661\) | 1056.46 | 1.59828 | 0.799141 | − | 0.601144i | \(-0.205288\pi\) | ||||
0.799141 | + | 0.601144i | \(0.205288\pi\) | |||||||
\(662\) | 578.963 | + | 877.576i | 0.874566 | + | 1.32564i | ||||
\(663\) | 111.271i | 0.167829i | ||||||||
\(664\) | −12.7235 | + | 2.29895i | −0.0191618 | + | 0.00346228i | ||||
\(665\) | −3.22894 | −0.00485555 | ||||||||
\(666\) | 193.735 | − | 127.813i | 0.290894 | − | 0.191911i | ||||
\(667\) | − | 704.426i | − | 1.05611i | ||||||
\(668\) | 349.788 | + | 149.717i | 0.523634 | + | 0.224127i | ||||
\(669\) | 36.3792 | 0.0543785 | ||||||||
\(670\) | 8.97374 | + | 13.6021i | 0.0133936 | + | 0.0203017i | ||||
\(671\) | − | 456.851i | − | 0.680851i | ||||||
\(672\) | −126.057 | − | 28.9403i | −0.187585 | − | 0.0430659i | ||||
\(673\) | −748.492 | −1.11217 | −0.556086 | − | 0.831124i | \(-0.687698\pi\) | ||||
−0.556086 | + | 0.831124i | \(0.687698\pi\) | |||||||
\(674\) | −337.010 | + | 222.335i | −0.500015 | + | 0.329875i | ||||
\(675\) | 129.575i | 0.191963i | ||||||||
\(676\) | 20.4616 | − | 47.8051i | 0.0302686 | − | 0.0707175i | ||||
\(677\) | 918.698 | 1.35701 | 0.678507 | − | 0.734594i | \(-0.262627\pi\) | ||||
0.678507 | + | 0.734594i | \(0.262627\pi\) | |||||||
\(678\) | 318.016 | + | 482.040i | 0.469050 | + | 0.710973i | ||||
\(679\) | 181.077i | 0.266682i | ||||||||
\(680\) | 6.37843 | + | 35.3012i | 0.00938004 | + | 0.0519135i | ||||
\(681\) | −741.377 | −1.08866 | ||||||||
\(682\) | −5.07859 | + | 3.35050i | −0.00744662 | + | 0.00491275i | ||||
\(683\) | − | 711.777i | − | 1.04213i | −0.853516 | − | 0.521066i | \(-0.825534\pi\) | ||
0.853516 | − | 0.521066i | \(-0.174466\pi\) | |||||||
\(684\) | 60.6562 | + | 25.9621i | 0.0886786 | + | 0.0379564i | ||||
\(685\) | −47.5886 | −0.0694725 | ||||||||
\(686\) | −237.872 | − | 360.559i | −0.346752 | − | 0.525597i | ||||
\(687\) | − | 519.521i | − | 0.756217i | ||||||
\(688\) | 496.493 | − | 473.731i | 0.721647 | − | 0.688563i | ||||
\(689\) | −315.350 | −0.457693 | ||||||||
\(690\) | −22.3938 | + | 14.7739i | −0.0324548 | + | 0.0214114i | ||||
\(691\) | 55.6041i | 0.0804690i | 0.999190 | + | 0.0402345i | \(0.0128105\pi\) | ||||
−0.999190 | + | 0.0402345i | \(0.987190\pi\) | |||||||
\(692\) | −203.511 | + | 475.468i | −0.294091 | + | 0.687093i | ||||
\(693\) | 121.772 | 0.175717 | ||||||||
\(694\) | 26.4048 | + | 40.0236i | 0.0380472 | + | 0.0576709i | ||||
\(695\) | 28.9333i | 0.0416306i | ||||||||
\(696\) | 312.130 | − | 56.3976i | 0.448463 | − | 0.0810310i | ||||
\(697\) | −191.756 | −0.275116 | ||||||||
\(698\) | 0.673561 | − | 0.444368i | 0.000964987 | − | 0.000636630i | ||||
\(699\) | − | 595.146i | − | 0.851425i | ||||||
\(700\) | −213.983 | − | 91.5895i | −0.305690 | − | 0.130842i | ||||
\(701\) | −398.266 | −0.568140 | −0.284070 | − | 0.958803i | \(-0.591685\pi\) | ||||
−0.284070 | + | 0.958803i | \(0.591685\pi\) | |||||||
\(702\) | −20.6342 | − | 31.2767i | −0.0293934 | − | 0.0445537i | ||||
\(703\) | − | 212.688i | − | 0.302543i | ||||||
\(704\) | −389.580 | − | 1042.86i | −0.553381 | − | 1.48134i | ||||
\(705\) | 15.8197 | 0.0224393 | ||||||||
\(706\) | −290.659 | + | 191.756i | −0.411698 | + | 0.271609i | ||||
\(707\) | − | 9.67715i | − | 0.0136876i | ||||||
\(708\) | 257.683 | − | 602.032i | 0.363958 | − | 0.850327i | ||||
\(709\) | 194.214 | 0.273927 | 0.136964 | − | 0.990576i | \(-0.456266\pi\) | ||||
0.136964 | + | 0.990576i | \(0.456266\pi\) | |||||||
\(710\) | 3.74544 | + | 5.67724i | 0.00527527 | + | 0.00799611i | ||||
\(711\) | − | 25.4056i | − | 0.0357322i | ||||||
\(712\) | −148.817 | − | 823.624i | −0.209013 | − | 1.15678i | ||||
\(713\) | 5.38191 | 0.00754826 | ||||||||
\(714\) | −120.223 | + | 79.3148i | −0.168380 | + | 0.111085i | ||||
\(715\) | 15.7838i | 0.0220752i | ||||||||
\(716\) | −119.206 | − | 51.0229i | −0.166489 | − | 0.0712610i | ||||
\(717\) | 19.0738 | 0.0266023 | ||||||||
\(718\) | 220.793 | + | 334.672i | 0.307511 | + | 0.466117i | ||||
\(719\) | − | 798.804i | − | 1.11099i | −0.831519 | − | 0.555496i | \(-0.812528\pi\) | ||
0.831519 | − | 0.555496i | \(-0.187472\pi\) | |||||||
\(720\) | −8.33916 | − | 8.73984i | −0.0115822 | − | 0.0121387i | ||||
\(721\) | −171.607 | −0.238013 | ||||||||
\(722\) | −552.195 | + | 364.299i | −0.764813 | + | 0.504570i | ||||
\(723\) | 473.999i | 0.655600i | ||||||||
\(724\) | −139.024 | + | 324.806i | −0.192022 | + | 0.448627i | ||||
\(725\) | 570.820 | 0.787338 | ||||||||
\(726\) | 346.371 | + | 525.020i | 0.477095 | + | 0.723168i | ||||
\(727\) | − | 1133.48i | − | 1.55912i | −0.626325 | − | 0.779562i | \(-0.715442\pi\) | ||
0.626325 | − | 0.779562i | \(-0.284558\pi\) | |||||||
\(728\) | 66.2364 | − | 11.9680i | 0.0909841 | − | 0.0164396i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 46.3144 | − | 30.5550i | 0.0634444 | − | 0.0418562i | ||||
\(731\) | − | 764.198i | − | 1.04541i | ||||||
\(732\) | −167.283 | − | 71.6007i | −0.228528 | − | 0.0978151i | ||||
\(733\) | −582.095 | −0.794126 | −0.397063 | − | 0.917791i | \(-0.629971\pi\) | ||||
−0.397063 | + | 0.917791i | \(0.629971\pi\) | |||||||
\(734\) | 729.081 | + | 1105.12i | 0.993299 | + | 1.50562i | ||||
\(735\) | − | 18.9855i | − | 0.0258306i | ||||||
\(736\) | −220.346 | + | 959.778i | −0.299383 | + | 1.30405i | ||||
\(737\) | −563.156 | −0.764119 | ||||||||
\(738\) | 53.8999 | − | 35.5593i | 0.0730350 | − | 0.0481834i | ||||
\(739\) | − | 373.621i | − | 0.505576i | −0.967522 | − | 0.252788i | \(-0.918653\pi\) | ||
0.967522 | − | 0.252788i | \(-0.0813475\pi\) | |||||||
\(740\) | −15.3229 | + | 35.7994i | −0.0207067 | + | 0.0483776i | ||||
\(741\) | −34.3365 | −0.0463380 | ||||||||
\(742\) | −224.784 | − | 340.722i | −0.302944 | − | 0.459194i | ||||
\(743\) | 529.876i | 0.713158i | 0.934265 | + | 0.356579i | \(0.116057\pi\) | ||||
−0.934265 | + | 0.356579i | \(0.883943\pi\) | |||||||
\(744\) | 0.430885 | + | 2.38472i | 0.000579146 | + | 0.00320526i | ||||
\(745\) | −37.4911 | −0.0503236 | ||||||||
\(746\) | 228.122 | − | 150.499i | 0.305793 | − | 0.201741i | ||||
\(747\) | − | 4.84856i | − | 0.00649071i | ||||||
\(748\) | −1139.71 | − | 487.820i | −1.52367 | − | 0.652165i | ||||
\(749\) | 190.418 | 0.254229 | ||||||||
\(750\) | −23.9739 | − | 36.3390i | −0.0319652 | − | 0.0484520i | ||||
\(751\) | − | 925.306i | − | 1.23210i | −0.787707 | − | 0.616050i | \(-0.788732\pi\) | ||
0.787707 | − | 0.616050i | \(-0.211268\pi\) | |||||||
\(752\) | 420.114 | − | 400.854i | 0.558663 | − | 0.533051i | ||||
\(753\) | −319.940 | −0.424887 | ||||||||
\(754\) | −137.784 | + | 90.9004i | −0.182738 | + | 0.120558i | ||||
\(755\) | − | 63.7233i | − | 0.0844017i | ||||||
\(756\) | 19.0849 | − | 44.5886i | 0.0252445 | − | 0.0589796i | ||||
\(757\) | −1082.42 | −1.42988 | −0.714940 | − | 0.699186i | \(-0.753546\pi\) | ||||
−0.714940 | + | 0.699186i | \(0.753546\pi\) | |||||||
\(758\) | 188.606 | + | 285.883i | 0.248820 | + | 0.377155i | ||||
\(759\) | − | 927.148i | − | 1.22154i | ||||||
\(760\) | −10.8934 | + | 1.96828i | −0.0143334 | + | 0.00258985i | ||||
\(761\) | −505.561 | −0.664338 | −0.332169 | − | 0.943220i | \(-0.607780\pi\) | ||||
−0.332169 | + | 0.943220i | \(0.607780\pi\) | |||||||
\(762\) | −274.390 | + | 181.023i | −0.360092 | + | 0.237563i | ||||
\(763\) | 261.277i | 0.342434i | ||||||||
\(764\) | 717.925 | + | 307.288i | 0.939693 | + | 0.402209i | ||||
\(765\) | −13.4523 | −0.0175847 | ||||||||
\(766\) | −537.585 | − | 814.857i | −0.701808 | − | 1.06378i | ||||
\(767\) | 340.800i | 0.444329i | ||||||||
\(768\) | −442.917 | − | 20.7936i | −0.576715 | − | 0.0270749i | ||||
\(769\) | 1500.21 | 1.95086 | 0.975430 | − | 0.220311i | \(-0.0707072\pi\) | ||||
0.975430 | + | 0.220311i | \(0.0707072\pi\) | |||||||
\(770\) | −17.0537 | + | 11.2508i | −0.0221476 | + | 0.0146115i | ||||
\(771\) | 739.228i | 0.958791i | ||||||||
\(772\) | −139.349 | + | 325.564i | −0.180503 | + | 0.421715i | ||||
\(773\) | 1376.68 | 1.78096 | 0.890478 | − | 0.455025i | \(-0.150370\pi\) | ||||
0.890478 | + | 0.455025i | \(0.150370\pi\) | |||||||
\(774\) | 141.713 | + | 214.805i | 0.183092 | + | 0.277526i | ||||
\(775\) | 4.36114i | 0.00562728i | ||||||||
\(776\) | 110.380 | + | 610.894i | 0.142242 | + | 0.787234i | ||||
\(777\) | −156.348 | −0.201220 | ||||||||
\(778\) | −1237.95 | + | 816.714i | −1.59120 | + | 1.04976i | ||||
\(779\) | − | 59.1728i | − | 0.0759600i | ||||||
\(780\) | 5.77948 | + | 2.47374i | 0.00740959 | + | 0.00317146i | ||||
\(781\) | −235.049 | −0.300959 | ||||||||
\(782\) | 603.889 | + | 915.358i | 0.772236 | + | 1.17053i | ||||
\(783\) | 118.944i | 0.151908i | ||||||||
\(784\) | −481.072 | − | 504.187i | −0.613613 | − | 0.643096i | ||||
\(785\) | −69.0397 | −0.0879486 | ||||||||
\(786\) | −646.451 | + | 426.483i | −0.822457 | + | 0.542599i | ||||
\(787\) | 401.463i | 0.510119i | 0.966925 | + | 0.255059i | \(0.0820950\pi\) | ||||
−0.966925 | + | 0.255059i | \(0.917905\pi\) | |||||||
\(788\) | −304.619 | + | 711.692i | −0.386573 | + | 0.903162i | ||||
\(789\) | −300.016 | −0.380248 | ||||||||
\(790\) | 2.34729 | + | 3.55797i | 0.00297126 | + | 0.00450375i | ||||
\(791\) | − | 389.015i | − | 0.491801i | ||||||
\(792\) | 410.818 | − | 74.2291i | 0.518709 | − | 0.0937236i | ||||
\(793\) | 94.6961 | 0.119415 | ||||||||
\(794\) | −575.336 | + | 379.566i | −0.724604 | + | 0.478043i | ||||
\(795\) | − | 38.1249i | − | 0.0479558i | ||||||
\(796\) | 1369.95 | + | 586.370i | 1.72105 | + | 0.736646i | ||||
\(797\) | 8.24350 | 0.0103432 | 0.00517158 | − | 0.999987i | \(-0.498354\pi\) | ||||
0.00517158 | + | 0.999987i | \(0.498354\pi\) | |||||||
\(798\) | −24.4753 | − | 37.0990i | −0.0306708 | − | 0.0464900i | ||||
\(799\) | − | 646.637i | − | 0.809307i | ||||||
\(800\) | −777.740 | − | 178.554i | −0.972175 | − | 0.223192i | ||||
\(801\) | 313.860 | 0.391836 | ||||||||
\(802\) | 671.029 | − | 442.698i | 0.836695 | − | 0.551992i | ||||
\(803\) | 1917.51i | 2.38793i | ||||||||
\(804\) | −88.2615 | + | 206.208i | −0.109778 | + | 0.256478i | ||||
\(805\) | 18.0722 | 0.0224500 | ||||||||
\(806\) | −0.694492 | − | 1.05269i | −0.000861652 | − | 0.00130607i | ||||
\(807\) | 650.359i | 0.805897i | ||||||||
\(808\) | −5.89895 | − | 32.6475i | −0.00730069 | − | 0.0404054i | ||||
\(809\) | −34.8089 | −0.0430270 | −0.0215135 | − | 0.999769i | \(-0.506848\pi\) | ||||
−0.0215135 | + | 0.999769i | \(0.506848\pi\) | |||||||
\(810\) | 3.78125 | − | 2.49460i | 0.00466821 | − | 0.00307976i | ||||
\(811\) | 209.233i | 0.257994i | 0.991645 | + | 0.128997i | \(0.0411757\pi\) | ||||
−0.991645 | + | 0.128997i | \(0.958824\pi\) | |||||||
\(812\) | −196.428 | − | 84.0753i | −0.241906 | − | 0.103541i | ||||
\(813\) | −782.135 | −0.962035 | ||||||||
\(814\) | −741.083 | − | 1123.31i | −0.910422 | − | 1.37999i | ||||
\(815\) | − | 39.7309i | − | 0.0487495i | ||||||
\(816\) | −357.245 | + | 340.867i | −0.437800 | + | 0.417729i | ||||
\(817\) | 235.819 | 0.288641 | ||||||||
\(818\) | 419.847 | − | 276.986i | 0.513261 | − | 0.338613i | ||||
\(819\) | 25.2409i | 0.0308191i | ||||||||
\(820\) | −4.26306 | + | 9.95991i | −0.00519885 | + | 0.0121462i | ||||
\(821\) | 789.296 | 0.961384 | 0.480692 | − | 0.876889i | \(-0.340386\pi\) | ||||
0.480692 | + | 0.876889i | \(0.340386\pi\) | |||||||
\(822\) | −360.721 | − | 546.771i | −0.438833 | − | 0.665171i | ||||
\(823\) | − | 591.495i | − | 0.718706i | −0.933202 | − | 0.359353i | \(-0.882997\pi\) | ||
0.933202 | − | 0.359353i | \(-0.117003\pi\) | |||||||
\(824\) | −578.947 | + | 104.608i | −0.702605 | + | 0.126951i | ||||
\(825\) | 751.299 | 0.910666 | ||||||||
\(826\) | −368.219 | + | 242.925i | −0.445786 | + | 0.294098i | ||||
\(827\) | 623.715i | 0.754189i | 0.926175 | + | 0.377095i | \(0.123077\pi\) | ||||
−0.926175 | + | 0.377095i | \(0.876923\pi\) | |||||||
\(828\) | −339.489 | − | 145.309i | −0.410011 | − | 0.175494i | ||||
\(829\) | 1315.38 | 1.58671 | 0.793353 | − | 0.608762i | \(-0.208334\pi\) | ||||
0.793353 | + | 0.608762i | \(0.208334\pi\) | |||||||
\(830\) | 0.447972 | + | 0.679023i | 0.000539725 | + | 0.000818100i | ||||
\(831\) | − | 832.932i | − | 1.00233i | ||||||
\(832\) | 216.164 | − | 80.7522i | 0.259813 | − | 0.0970579i | ||||
\(833\) | −776.040 | −0.931621 | ||||||||
\(834\) | −332.429 | + | 219.314i | −0.398596 | + | 0.262966i | ||||
\(835\) | − | 23.9387i | − | 0.0286691i | ||||||
\(836\) | 150.534 | − | 351.696i | 0.180064 | − | 0.420689i | ||||
\(837\) | −0.908749 | −0.00108572 | ||||||||
\(838\) | 499.157 | + | 756.608i | 0.595652 | + | 0.902874i | ||||
\(839\) | − | 379.400i | − | 0.452205i | −0.974104 | − | 0.226103i | \(-0.927402\pi\) | ||
0.974104 | − | 0.226103i | \(-0.0725984\pi\) | |||||||
\(840\) | 1.44689 | + | 8.00777i | 0.00172249 | + | 0.00953306i | ||||
\(841\) | −317.011 | −0.376945 | ||||||||
\(842\) | −399.586 | + | 263.618i | −0.474567 | + | 0.313086i | ||||
\(843\) | − | 435.937i | − | 0.517126i | ||||||
\(844\) | −1045.58 | − | 447.533i | −1.23884 | − | 0.530252i | ||||
\(845\) | −3.27167 | −0.00387180 | ||||||||
\(846\) | 119.913 | + | 181.761i | 0.141741 | + | 0.214847i | ||||
\(847\) | − | 423.701i | − | 0.500237i | ||||||
\(848\) | −966.044 | − | 1012.46i | −1.13920 | − | 1.19394i | ||||
\(849\) | 635.158 | 0.748125 | ||||||||
\(850\) | −741.745 | + | 489.351i | −0.872642 | + | 0.575707i | ||||
\(851\) | 1190.40i | 1.39883i | ||||||||
\(852\) | −36.8384 | + | 86.0667i | −0.0432376 | + | 0.101017i | ||||
\(853\) | 1112.16 | 1.30382 | 0.651909 | − | 0.758297i | \(-0.273969\pi\) | ||||
0.651909 | + | 0.758297i | \(0.273969\pi\) | |||||||
\(854\) | 67.5001 | + | 102.315i | 0.0790400 | + | 0.119807i | ||||
\(855\) | − | 4.15117i | − | 0.00485517i | ||||||
\(856\) | 642.407 | − | 116.074i | 0.750476 | − | 0.135601i | ||||
\(857\) | 384.695 | 0.448886 | 0.224443 | − | 0.974487i | \(-0.427944\pi\) | ||||
0.224443 | + | 0.974487i | \(0.427944\pi\) | |||||||
\(858\) | −181.348 | + | 119.641i | −0.211362 | + | 0.139442i | ||||
\(859\) | − | 1229.85i | − | 1.43172i | −0.698242 | − | 0.715861i | \(-0.746034\pi\) | ||
0.698242 | − | 0.715861i | \(-0.253966\pi\) | |||||||
\(860\) | −39.6929 | − | 16.9894i | −0.0461545 | − | 0.0197551i | ||||
\(861\) | −43.4982 | −0.0505205 | ||||||||
\(862\) | 642.050 | + | 973.202i | 0.744838 | + | 1.12900i | ||||
\(863\) | − | 274.288i | − | 0.317831i | −0.987292 | − | 0.158915i | \(-0.949200\pi\) | ||
0.987292 | − | 0.158915i | \(-0.0507997\pi\) | |||||||
\(864\) | 37.2060 | − | 162.061i | 0.0430625 | − | 0.187570i | ||||
\(865\) | 32.5399 | 0.0376184 | ||||||||
\(866\) | 64.8872 | − | 42.8080i | 0.0749275 | − | 0.0494319i | ||||
\(867\) | 49.3060i | 0.0568697i | ||||||||
\(868\) | 0.642346 | − | 1.50073i | 0.000740030 | − | 0.00172896i | ||||
\(869\) | −147.307 | −0.169513 | ||||||||
\(870\) | −10.9896 | − | 16.6577i | −0.0126317 | − | 0.0191468i | ||||
\(871\) | − | 116.731i | − | 0.134019i | ||||||
\(872\) | 159.268 | + | 881.463i | 0.182647 | + | 1.01085i | ||||
\(873\) | −232.795 | −0.266660 | ||||||||
\(874\) | −282.465 | + | 186.351i | −0.323187 | + | 0.213216i | ||||
\(875\) | 29.3262i | 0.0335157i | ||||||||
\(876\) | 702.125 | + | 300.525i | 0.801512 | + | 0.343065i | ||||
\(877\) | −1335.73 | −1.52307 | −0.761535 | − | 0.648124i | \(-0.775554\pi\) | ||||
−0.761535 | + | 0.648124i | \(0.775554\pi\) | |||||||
\(878\) | 412.168 | + | 624.753i | 0.469439 | + | 0.711563i | ||||
\(879\) | − | 147.089i | − | 0.167336i | ||||||
\(880\) | −50.6753 | + | 48.3521i | −0.0575856 | + | 0.0549456i | ||||
\(881\) | −1187.95 | −1.34841 | −0.674206 | − | 0.738544i | \(-0.735514\pi\) | ||||
−0.674206 | + | 0.738544i | \(0.735514\pi\) | |||||||
\(882\) | 218.134 | − | 143.909i | 0.247318 | − | 0.163163i | ||||
\(883\) | 397.325i | 0.449972i | 0.974362 | + | 0.224986i | \(0.0722337\pi\) | ||||
−0.974362 | + | 0.224986i | \(0.927766\pi\) | |||||||
\(884\) | 101.115 | − | 236.239i | 0.114384 | − | 0.267239i | ||||
\(885\) | −41.2017 | −0.0465556 | ||||||||
\(886\) | 215.929 | + | 327.299i | 0.243712 | + | 0.369412i | ||||
\(887\) | 435.697i | 0.491203i | 0.969371 | + | 0.245602i | \(0.0789855\pi\) | ||||
−0.969371 | + | 0.245602i | \(0.921015\pi\) | |||||||
\(888\) | −527.466 | + | 95.3057i | −0.593993 | + | 0.107326i | ||||
\(889\) | 221.438 | 0.249086 | ||||||||
\(890\) | −43.9550 | + | 28.9984i | −0.0493876 | + | 0.0325825i | ||||
\(891\) | 156.551i | 0.175703i | ||||||||
\(892\) | −77.2366 | − | 33.0589i | −0.0865881 | − | 0.0370616i | ||||
\(893\) | 199.542 | 0.223451 | ||||||||
\(894\) | −284.182 | − | 430.755i | −0.317877 | − | 0.481829i | ||||
\(895\) | 8.15820i | 0.00911531i | ||||||||
\(896\) | 241.333 | + | 175.995i | 0.269345 | + | 0.196423i | ||||
\(897\) | 192.179 | 0.214247 | ||||||||
\(898\) | 1433.97 | − | 946.031i | 1.59685 | − | 1.05349i | ||||
\(899\) | 4.00335i | 0.00445311i | ||||||||
\(900\) | 117.749 | − | 275.100i | 0.130832 | − | 0.305666i | ||||
\(901\) | −1558.37 | −1.72960 | ||||||||
\(902\) | −206.180 | − | 312.522i | −0.228581 | − | 0.346477i | ||||
\(903\) | − | 173.352i | − | 0.191973i | ||||||
\(904\) | −237.134 | − | 1312.41i | −0.262316 | − | 1.45178i | ||||
\(905\) | 22.2290 | 0.0245624 | ||||||||
\(906\) | 732.150 | − | 483.021i | 0.808112 | − | 0.533136i | ||||
\(907\) | 1247.02i | 1.37489i | 0.726238 | + | 0.687444i | \(0.241267\pi\) | ||||
−0.726238 | + | 0.687444i | \(0.758733\pi\) | |||||||
\(908\) | 1574.02 | + | 673.712i | 1.73350 | + | 0.741974i | ||||
\(909\) | 12.4411 | 0.0136865 | ||||||||
\(910\) | −2.33207 | − | 3.53489i | −0.00256272 | − | 0.00388449i | ||||
\(911\) | − | 547.306i | − | 0.600775i | −0.953817 | − | 0.300387i | \(-0.902884\pi\) | ||
0.953817 | − | 0.300387i | \(-0.0971159\pi\) | |||||||
\(912\) | −105.186 | − | 110.240i | −0.115336 | − | 0.120878i | ||||
\(913\) | −28.1129 | −0.0307918 | ||||||||
\(914\) | −595.531 | + | 392.889i | −0.651566 | + | 0.429857i | ||||
\(915\) | 11.4485i | 0.0125120i | ||||||||
\(916\) | −472.105 | + | 1102.99i | −0.515399 | + | 1.20414i | ||||
\(917\) | 521.698 | 0.568918 | ||||||||
\(918\) | −101.968 | − | 154.560i | −0.111076 | − | 0.168366i | ||||
\(919\) | − | 315.834i | − | 0.343672i | −0.985126 | − | 0.171836i | \(-0.945030\pi\) | ||
0.985126 | − | 0.171836i | \(-0.0549698\pi\) | |||||||
\(920\) | 60.9697 | − | 11.0164i | 0.0662715 | − | 0.0119743i | ||||
\(921\) | −252.913 | −0.274607 | ||||||||
\(922\) | 15.9401 | − | 10.5161i | 0.0172886 | − | 0.0114058i | ||||
\(923\) | − | 48.7210i | − | 0.0527854i | ||||||
\(924\) | −258.533 | − | 110.658i | −0.279798 | − | 0.119760i | ||||
\(925\) | −964.624 | −1.04284 | ||||||||
\(926\) | −845.394 | − | 1281.43i | −0.912953 | − | 1.38383i | ||||
\(927\) | − | 220.621i | − | 0.237994i | ||||||
\(928\) | −713.933 | − | 163.905i | −0.769324 | − | 0.176622i | ||||
\(929\) | 1106.19 | 1.19073 | 0.595366 | − | 0.803455i | \(-0.297007\pi\) | ||||
0.595366 | + | 0.803455i | \(0.297007\pi\) | |||||||
\(930\) | 0.127267 | − | 0.0839618i | 0.000136846 | − | 9.02815e-5i | ||||
\(931\) | − | 239.474i | − | 0.257222i | ||||||
\(932\) | −540.828 | + | 1263.55i | −0.580288 | + | 1.35574i | ||||
\(933\) | −335.036 | −0.359095 | ||||||||
\(934\) | −12.4480 | − | 18.8683i | −0.0133276 | − | 0.0202016i | ||||
\(935\) | 77.9990i | 0.0834214i | ||||||||
\(936\) | 15.3862 | + | 85.1544i | 0.0164383 | + | 0.0909769i | ||||
\(937\) | −1597.85 | −1.70528 | −0.852641 | − | 0.522496i | \(-0.825001\pi\) | ||||
−0.852641 | + | 0.522496i | \(0.825001\pi\) | |||||||
\(938\) | 126.123 | − | 83.2068i | 0.134459 | − | 0.0887066i | ||||
\(939\) | − | 569.037i | − | 0.606003i | ||||||
\(940\) | −33.5867 | − | 14.3758i | −0.0357305 | − | 0.0152934i | ||||
\(941\) | −15.4424 | −0.0164106 | −0.00820529 | − | 0.999966i | \(-0.502612\pi\) | ||||
−0.00820529 | + | 0.999966i | \(0.502612\pi\) | |||||||
\(942\) | −523.319 | − | 793.233i | −0.555541 | − | 0.842073i | ||||
\(943\) | 331.187i | 0.351206i | ||||||||
\(944\) | −1094.17 | + | 1044.01i | −1.15908 | + | 1.10594i | ||||
\(945\) | −3.05154 | −0.00322914 | ||||||||
\(946\) | 1245.48 | − | 821.682i | 1.31658 | − | 0.868586i | ||||
\(947\) | 145.749i | 0.153906i | 0.997035 | + | 0.0769531i | \(0.0245192\pi\) | ||||
−0.997035 | + | 0.0769531i | \(0.975481\pi\) | |||||||
\(948\) | −23.0869 | + | 53.9386i | −0.0243533 | + | 0.0568973i | ||||
\(949\) | −397.461 | −0.418821 | ||||||||
\(950\) | −151.006 | − | 228.891i | −0.158954 | − | 0.240938i | ||||
\(951\) | 894.613i | 0.940707i | ||||||||
\(952\) | 327.321 | − | 59.1424i | 0.343825 | − | 0.0621244i | ||||
\(953\) | 1507.81 | 1.58217 | 0.791086 | − | 0.611705i | \(-0.209516\pi\) | ||||
0.791086 | + | 0.611705i | \(0.209516\pi\) | |||||||
\(954\) | 438.036 | − | 288.986i | 0.459158 | − | 0.302920i | ||||
\(955\) | − | 49.1332i | − | 0.0514483i | ||||||
\(956\) | −40.4956 | − | 17.3330i | −0.0423594 | − | 0.0181308i | ||||
\(957\) | 689.661 | 0.720649 | ||||||||
\(958\) | 460.597 | + | 698.160i | 0.480790 | + | 0.728769i | ||||
\(959\) | 441.254i | 0.460119i | ||||||||
\(960\) | 9.76268 | + | 26.1336i | 0.0101695 | + | 0.0272225i | ||||
\(961\) | 960.969 | 0.999968 | ||||||||
\(962\) | 232.841 | − | 153.612i | 0.242038 | − | 0.159680i | ||||
\(963\) | 244.804i | 0.254209i | ||||||||
\(964\) | 430.738 | − | 1006.35i | 0.446823 | − | 1.04393i | ||||
\(965\) | 22.2809 | 0.0230890 | ||||||||
\(966\) | 136.987 | + | 207.641i | 0.141809 | + | 0.214949i | ||||
\(967\) | 900.400i | 0.931127i | 0.885015 | + | 0.465563i | \(0.154148\pi\) | ||||
−0.885015 | + | 0.465563i | \(0.845852\pi\) | |||||||
\(968\) | −258.277 | − | 1429.43i | −0.266816 | − | 1.47668i | ||||
\(969\) | −169.681 | −0.175109 | ||||||||
\(970\) | 32.6020 | − | 21.5085i | 0.0336103 | − | 0.0221737i | ||||
\(971\) | − | 253.545i | − | 0.261118i | −0.991441 | − | 0.130559i | \(-0.958323\pi\) | ||
0.991441 | − | 0.130559i | \(-0.0416772\pi\) | |||||||
\(972\) | 57.3236 | + | 24.5357i | 0.0589749 | + | 0.0252425i | ||||
\(973\) | 268.277 | 0.275721 | ||||||||
\(974\) | 464.945 | + | 704.752i | 0.477357 | + | 0.723564i | ||||
\(975\) | 155.729i | 0.159722i | ||||||||
\(976\) | 290.092 | + | 304.030i | 0.297225 | + | 0.311506i | ||||
\(977\) | −421.348 | −0.431267 | −0.215634 | − | 0.976474i | \(-0.569182\pi\) | ||||
−0.215634 | + | 0.976474i | \(0.569182\pi\) | |||||||
\(978\) | 456.489 | − | 301.159i | 0.466757 | − | 0.307934i | ||||
\(979\) | − | 1819.82i | − | 1.85886i | ||||||
\(980\) | −17.2527 | + | 40.3080i | −0.0176048 | + | 0.0411306i | ||||
\(981\) | −335.901 | −0.342407 | ||||||||
\(982\) | 14.3479 | + | 21.7481i | 0.0146109 | + | 0.0221467i | ||||
\(983\) | 587.872i | 0.598038i | 0.954247 | + | 0.299019i | \(0.0966594\pi\) | ||||
−0.954247 | + | 0.299019i | \(0.903341\pi\) | |||||||
\(984\) | −146.749 | + | 26.5154i | −0.149135 | + | 0.0269466i | ||||
\(985\) | 48.7065 | 0.0494483 | ||||||||
\(986\) | −680.891 | + | 449.204i | −0.690559 | + | 0.455582i | ||||
\(987\) | − | 146.684i | − | 0.148616i | ||||||
\(988\) | 72.8996 | + | 31.2026i | 0.0737851 | + | 0.0315816i | ||||
\(989\) | −1319.87 | −1.33455 | ||||||||
\(990\) | −14.4642 | − | 21.9244i | −0.0146103 | − | 0.0221459i | ||||
\(991\) | 555.559i | 0.560604i | 0.959912 | + | 0.280302i | \(0.0904346\pi\) | ||||
−0.959912 | + | 0.280302i | \(0.909565\pi\) | |||||||
\(992\) | 1.25226 | − | 5.45454i | 0.00126235 | − | 0.00549853i | ||||
\(993\) | 910.496 | 0.916915 | ||||||||
\(994\) | 52.6408 | − | 34.7287i | 0.0529586 | − | 0.0349383i | ||||
\(995\) | − | 93.7565i | − | 0.0942277i | ||||||
\(996\) | −4.40604 | + | 10.2940i | −0.00442373 | + | 0.0103353i | ||||
\(997\) | −1312.59 | −1.31654 | −0.658272 | − | 0.752780i | \(-0.728712\pi\) | ||||
−0.658272 | + | 0.752780i | \(0.728712\pi\) | |||||||
\(998\) | −390.473 | − | 591.868i | −0.391256 | − | 0.593055i | ||||
\(999\) | − | 201.003i | − | 0.201204i |
(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 | 156.3.f.a.79.6 | yes | 24 | |
3.2 | odd | 2 | 468.3.f.b.235.19 | 24 | |||
4.3 | odd | 2 | inner | 156.3.f.a.79.5 | ✓ | 24 | |
8.3 | odd | 2 | 2496.3.k.e.703.14 | 24 | |||
8.5 | even | 2 | 2496.3.k.e.703.13 | 24 | |||
12.11 | even | 2 | 468.3.f.b.235.20 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.3.f.a.79.5 | ✓ | 24 | 4.3 | odd | 2 | inner | |
156.3.f.a.79.6 | yes | 24 | 1.1 | even | 1 | trivial | |
468.3.f.b.235.19 | 24 | 3.2 | odd | 2 | |||
468.3.f.b.235.20 | 24 | 12.11 | even | 2 | |||
2496.3.k.e.703.13 | 24 | 8.5 | even | 2 | |||
2496.3.k.e.703.14 | 24 | 8.3 | odd | 2 |