Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(22,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Character | \(\chi\) | \(=\) | 105.43 |
Dual form | 105.3.l.a.22.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.59930 | + | 1.59930i | −0.799651 | + | 0.799651i | −0.983040 | − | 0.183389i | \(-0.941293\pi\) |
0.183389 | + | 0.983040i | \(0.441293\pi\) | |||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | − | 1.11554i | − | 0.278884i | ||||||
\(5\) | −1.35929 | + | 4.81169i | −0.271859 | + | 0.962337i | ||||
\(6\) | 3.91747 | 0.652912 | ||||||||
\(7\) | 1.87083 | − | 1.87083i | 0.267261 | − | 0.267261i | ||||
\(8\) | −4.61313 | − | 4.61313i | −0.576641 | − | 0.576641i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | −5.52142 | − | 9.86926i | −0.552142 | − | 0.986926i | ||||
\(11\) | −13.7143 | −1.24675 | −0.623376 | − | 0.781922i | \(-0.714239\pi\) | ||||
−0.623376 | + | 0.781922i | \(0.714239\pi\) | |||||||
\(12\) | −1.36625 | + | 1.36625i | −0.113854 | + | 0.113854i | ||||
\(13\) | −16.4959 | − | 16.4959i | −1.26891 | − | 1.26891i | −0.946650 | − | 0.322263i | \(-0.895557\pi\) |
−0.322263 | − | 0.946650i | \(-0.604443\pi\) | |||||||
\(14\) | 5.98404i | 0.427432i | ||||||||
\(15\) | 7.55788 | − | 4.22830i | 0.503858 | − | 0.281887i | ||||
\(16\) | 19.2177 | 1.20111 | ||||||||
\(17\) | −3.05243 | + | 3.05243i | −0.179555 | + | 0.179555i | −0.791162 | − | 0.611607i | \(-0.790523\pi\) |
0.611607 | + | 0.791162i | \(0.290523\pi\) | |||||||
\(18\) | −4.79791 | − | 4.79791i | −0.266550 | − | 0.266550i | ||||
\(19\) | 4.66410i | 0.245479i | 0.992439 | + | 0.122740i | \(0.0391680\pi\) | ||||
−0.992439 | + | 0.122740i | \(0.960832\pi\) | |||||||
\(20\) | 5.36761 | + | 1.51634i | 0.268380 | + | 0.0758171i | ||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | 21.9333 | − | 21.9333i | 0.996966 | − | 0.996966i | ||||
\(23\) | −4.61681 | − | 4.61681i | −0.200731 | − | 0.200731i | 0.599582 | − | 0.800313i | \(-0.295333\pi\) |
−0.800313 | + | 0.599582i | \(0.795333\pi\) | |||||||
\(24\) | 11.2998i | 0.470826i | ||||||||
\(25\) | −21.3046 | − | 13.0810i | −0.852186 | − | 0.523240i | ||||
\(26\) | 52.7638 | 2.02938 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | −2.08698 | − | 2.08698i | −0.0745349 | − | 0.0745349i | ||||
\(29\) | 50.3467i | 1.73609i | 0.496481 | + | 0.868047i | \(0.334625\pi\) | ||||
−0.496481 | + | 0.868047i | \(0.665375\pi\) | |||||||
\(30\) | −5.32500 | + | 18.8497i | −0.177500 | + | 0.628322i | ||||
\(31\) | 11.0632 | 0.356877 | 0.178438 | − | 0.983951i | \(-0.442896\pi\) | ||||
0.178438 | + | 0.983951i | \(0.442896\pi\) | |||||||
\(32\) | −12.2824 | + | 12.2824i | −0.383826 | + | 0.383826i | ||||
\(33\) | 16.7965 | + | 16.7965i | 0.508984 | + | 0.508984i | ||||
\(34\) | − | 9.76351i | − | 0.287162i | ||||||
\(35\) | 6.45883 | + | 11.5448i | 0.184538 | + | 0.329853i | ||||
\(36\) | 3.34661 | 0.0929613 | ||||||||
\(37\) | −44.4533 | + | 44.4533i | −1.20144 | + | 1.20144i | −0.227712 | + | 0.973729i | \(0.573124\pi\) |
−0.973729 | + | 0.227712i | \(0.926876\pi\) | |||||||
\(38\) | −7.45931 | − | 7.45931i | −0.196298 | − | 0.196298i | ||||
\(39\) | 40.4065i | 1.03606i | ||||||||
\(40\) | 28.4675 | − | 15.9263i | 0.711688 | − | 0.398158i | ||||
\(41\) | −20.5922 | −0.502249 | −0.251124 | − | 0.967955i | \(-0.580800\pi\) | ||||
−0.251124 | + | 0.967955i | \(0.580800\pi\) | |||||||
\(42\) | 7.32892 | − | 7.32892i | 0.174498 | − | 0.174498i | ||||
\(43\) | 41.9068 | + | 41.9068i | 0.974578 | + | 0.974578i | 0.999685 | − | 0.0251070i | \(-0.00799264\pi\) |
−0.0251070 | + | 0.999685i | \(0.507993\pi\) | |||||||
\(44\) | 15.2988i | 0.347699i | ||||||||
\(45\) | −14.4351 | − | 4.07788i | −0.320779 | − | 0.0906196i | ||||
\(46\) | 14.7673 | 0.321029 | ||||||||
\(47\) | 20.4247 | − | 20.4247i | 0.434569 | − | 0.434569i | −0.455610 | − | 0.890179i | \(-0.650579\pi\) |
0.890179 | + | 0.455610i | \(0.150579\pi\) | |||||||
\(48\) | −23.5368 | − | 23.5368i | −0.490350 | − | 0.490350i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | 54.9930 | − | 13.1521i | 1.09986 | − | 0.263042i | ||||
\(51\) | 7.47689 | 0.146606 | ||||||||
\(52\) | −18.4017 | + | 18.4017i | −0.353879 | + | 0.353879i | ||||
\(53\) | −46.1212 | − | 46.1212i | −0.870212 | − | 0.870212i | 0.122283 | − | 0.992495i | \(-0.460978\pi\) |
−0.992495 | + | 0.122283i | \(0.960978\pi\) | |||||||
\(54\) | 11.7524i | 0.217637i | ||||||||
\(55\) | 18.6417 | − | 65.9888i | 0.338941 | − | 1.19980i | ||||
\(56\) | −17.2608 | −0.308228 | ||||||||
\(57\) | 5.71233 | − | 5.71233i | 0.100216 | − | 0.100216i | ||||
\(58\) | −80.5197 | − | 80.5197i | −1.38827 | − | 1.38827i | ||||
\(59\) | − | 47.2598i | − | 0.801014i | −0.916294 | − | 0.400507i | \(-0.868834\pi\) | ||
0.916294 | − | 0.400507i | \(-0.131166\pi\) | |||||||
\(60\) | −4.71682 | − | 8.43108i | −0.0786136 | − | 0.140518i | ||||
\(61\) | 33.7814 | 0.553793 | 0.276896 | − | 0.960900i | \(-0.410694\pi\) | ||||
0.276896 | + | 0.960900i | \(0.410694\pi\) | |||||||
\(62\) | −17.6934 | + | 17.6934i | −0.285377 | + | 0.285377i | ||||
\(63\) | 5.61249 | + | 5.61249i | 0.0890871 | + | 0.0890871i | ||||
\(64\) | 37.5843i | 0.587254i | ||||||||
\(65\) | 101.796 | − | 56.9502i | 1.56609 | − | 0.876157i | ||||
\(66\) | −53.7253 | −0.814020 | ||||||||
\(67\) | −63.1243 | + | 63.1243i | −0.942154 | + | 0.942154i | −0.998416 | − | 0.0562621i | \(-0.982082\pi\) |
0.0562621 | + | 0.998416i | \(0.482082\pi\) | |||||||
\(68\) | 3.40509 | + | 3.40509i | 0.0500749 | + | 0.0500749i | ||||
\(69\) | 11.3088i | 0.163896i | ||||||||
\(70\) | −28.7933 | − | 8.13407i | −0.411333 | − | 0.116201i | ||||
\(71\) | −31.1884 | −0.439273 | −0.219637 | − | 0.975582i | \(-0.570487\pi\) | ||||
−0.219637 | + | 0.975582i | \(0.570487\pi\) | |||||||
\(72\) | 13.8394 | − | 13.8394i | 0.192214 | − | 0.192214i | ||||
\(73\) | −19.0978 | − | 19.0978i | −0.261614 | − | 0.261614i | 0.564096 | − | 0.825709i | \(-0.309225\pi\) |
−0.825709 | + | 0.564096i | \(0.809225\pi\) | |||||||
\(74\) | − | 142.189i | − | 1.92147i | ||||||
\(75\) | 10.0719 | + | 42.1136i | 0.134292 | + | 0.561515i | ||||
\(76\) | 5.20297 | 0.0684601 | ||||||||
\(77\) | −25.6570 | + | 25.6570i | −0.333208 | + | 0.333208i | ||||
\(78\) | −64.6221 | − | 64.6221i | −0.828489 | − | 0.828489i | ||||
\(79\) | 53.2345i | 0.673854i | 0.941531 | + | 0.336927i | \(0.109388\pi\) | ||||
−0.941531 | + | 0.336927i | \(0.890612\pi\) | |||||||
\(80\) | −26.1225 | + | 92.4696i | −0.326532 | + | 1.15587i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 32.9332 | − | 32.9332i | 0.401624 | − | 0.401624i | ||||
\(83\) | 97.3590 | + | 97.3590i | 1.17300 | + | 1.17300i | 0.981491 | + | 0.191510i | \(0.0613384\pi\) |
0.191510 | + | 0.981491i | \(0.438662\pi\) | |||||||
\(84\) | 5.11203i | 0.0608575i | ||||||||
\(85\) | −10.5382 | − | 18.8365i | −0.123979 | − | 0.221606i | ||||
\(86\) | −134.043 | −1.55864 | ||||||||
\(87\) | 61.6619 | − | 61.6619i | 0.708758 | − | 0.708758i | ||||
\(88\) | 63.2657 | + | 63.2657i | 0.718929 | + | 0.718929i | ||||
\(89\) | − | 156.139i | − | 1.75437i | −0.480154 | − | 0.877184i | \(-0.659419\pi\) | ||
0.480154 | − | 0.877184i | \(-0.340581\pi\) | |||||||
\(90\) | 29.6078 | − | 16.5643i | 0.328975 | − | 0.184047i | ||||
\(91\) | −61.7219 | −0.678263 | ||||||||
\(92\) | −5.15021 | + | 5.15021i | −0.0559806 | + | 0.0559806i | ||||
\(93\) | −13.5496 | − | 13.5496i | −0.145694 | − | 0.145694i | ||||
\(94\) | 65.3306i | 0.695007i | ||||||||
\(95\) | −22.4422 | − | 6.33989i | −0.236234 | − | 0.0667356i | ||||
\(96\) | 30.0857 | 0.313392 | ||||||||
\(97\) | −76.2395 | + | 76.2395i | −0.785974 | + | 0.785974i | −0.980832 | − | 0.194857i | \(-0.937576\pi\) |
0.194857 | + | 0.980832i | \(0.437576\pi\) | |||||||
\(98\) | 11.1951 | + | 11.1951i | 0.114236 | + | 0.114236i | ||||
\(99\) | − | 41.1428i | − | 0.415584i | ||||||
\(100\) | −14.5923 | + | 23.7661i | −0.145923 | + | 0.237661i | ||||
\(101\) | −70.4622 | −0.697646 | −0.348823 | − | 0.937189i | \(-0.613418\pi\) | ||||
−0.348823 | + | 0.937189i | \(0.613418\pi\) | |||||||
\(102\) | −11.9578 | + | 11.9578i | −0.117233 | + | 0.117233i | ||||
\(103\) | 60.8151 | + | 60.8151i | 0.590438 | + | 0.590438i | 0.937750 | − | 0.347312i | \(-0.112905\pi\) |
−0.347312 | + | 0.937750i | \(0.612905\pi\) | |||||||
\(104\) | 152.195i | 1.46342i | ||||||||
\(105\) | 6.22907 | − | 22.0499i | 0.0593245 | − | 0.209999i | ||||
\(106\) | 147.524 | 1.39173 | ||||||||
\(107\) | −52.5369 | + | 52.5369i | −0.490999 | + | 0.490999i | −0.908621 | − | 0.417622i | \(-0.862864\pi\) |
0.417622 | + | 0.908621i | \(0.362864\pi\) | |||||||
\(108\) | −4.09874 | − | 4.09874i | −0.0379513 | − | 0.0379513i | ||||
\(109\) | − | 38.7375i | − | 0.355390i | −0.984086 | − | 0.177695i | \(-0.943136\pi\) | ||
0.984086 | − | 0.177695i | \(-0.0568640\pi\) | |||||||
\(110\) | 75.7222 | + | 135.350i | 0.688384 | + | 1.23045i | ||||
\(111\) | 108.888 | 0.980972 | ||||||||
\(112\) | 35.9531 | − | 35.9531i | 0.321010 | − | 0.321010i | ||||
\(113\) | −40.5307 | − | 40.5307i | −0.358679 | − | 0.358679i | 0.504647 | − | 0.863326i | \(-0.331623\pi\) |
−0.863326 | + | 0.504647i | \(0.831623\pi\) | |||||||
\(114\) | 18.2715i | 0.160276i | ||||||||
\(115\) | 28.4902 | − | 15.9390i | 0.247741 | − | 0.138600i | ||||
\(116\) | 56.1636 | 0.484169 | ||||||||
\(117\) | 49.4876 | − | 49.4876i | 0.422971 | − | 0.422971i | ||||
\(118\) | 75.5827 | + | 75.5827i | 0.640532 | + | 0.640532i | ||||
\(119\) | 11.4211i | 0.0959760i | ||||||||
\(120\) | −54.3712 | − | 15.3598i | −0.453093 | − | 0.127998i | ||||
\(121\) | 67.0812 | 0.554390 | ||||||||
\(122\) | −54.0266 | + | 54.0266i | −0.442841 | + | 0.442841i | ||||
\(123\) | 25.2202 | + | 25.2202i | 0.205042 | + | 0.205042i | ||||
\(124\) | − | 12.3414i | − | 0.0995271i | ||||||
\(125\) | 91.9009 | − | 84.7303i | 0.735207 | − | 0.677842i | ||||
\(126\) | −17.9521 | −0.142477 | ||||||||
\(127\) | −3.98961 | + | 3.98961i | −0.0314143 | + | 0.0314143i | −0.722639 | − | 0.691225i | \(-0.757071\pi\) |
0.691225 | + | 0.722639i | \(0.257071\pi\) | |||||||
\(128\) | −109.238 | − | 109.238i | −0.853424 | − | 0.853424i | ||||
\(129\) | − | 102.650i | − | 0.795739i | ||||||
\(130\) | −71.7215 | + | 253.883i | −0.551704 | + | 1.95294i | ||||
\(131\) | −72.5637 | −0.553921 | −0.276961 | − | 0.960881i | \(-0.589327\pi\) | ||||
−0.276961 | + | 0.960881i | \(0.589327\pi\) | |||||||
\(132\) | 18.7371 | − | 18.7371i | 0.141948 | − | 0.141948i | ||||
\(133\) | 8.72573 | + | 8.72573i | 0.0656070 | + | 0.0656070i | ||||
\(134\) | − | 201.910i | − | 1.50679i | ||||||
\(135\) | 12.6849 | + | 22.6736i | 0.0939622 | + | 0.167953i | ||||
\(136\) | 28.1625 | 0.207077 | ||||||||
\(137\) | 67.6559 | − | 67.6559i | 0.493838 | − | 0.493838i | −0.415675 | − | 0.909513i | \(-0.636455\pi\) |
0.909513 | + | 0.415675i | \(0.136455\pi\) | |||||||
\(138\) | −18.0862 | − | 18.0862i | −0.131060 | − | 0.131060i | ||||
\(139\) | − | 132.992i | − | 0.956777i | −0.878148 | − | 0.478388i | \(-0.841221\pi\) | ||
0.878148 | − | 0.478388i | \(-0.158779\pi\) | |||||||
\(140\) | 12.8787 | − | 7.20506i | 0.0919906 | − | 0.0514647i | ||||
\(141\) | −50.0302 | −0.354824 | ||||||||
\(142\) | 49.8797 | − | 49.8797i | 0.351265 | − | 0.351265i | ||||
\(143\) | 226.229 | + | 226.229i | 1.58202 | + | 1.58202i | ||||
\(144\) | 57.6532i | 0.400369i | ||||||||
\(145\) | −242.253 | − | 68.4361i | −1.67071 | − | 0.471973i | ||||
\(146\) | 61.0863 | 0.418399 | ||||||||
\(147\) | −8.57321 | + | 8.57321i | −0.0583212 | + | 0.0583212i | ||||
\(148\) | 49.5892 | + | 49.5892i | 0.335062 | + | 0.335062i | ||||
\(149\) | 46.6022i | 0.312767i | 0.987696 | + | 0.156383i | \(0.0499835\pi\) | ||||
−0.987696 | + | 0.156383i | \(0.950016\pi\) | |||||||
\(150\) | −83.4604 | − | 51.2445i | −0.556403 | − | 0.341630i | ||||
\(151\) | 162.417 | 1.07561 | 0.537803 | − | 0.843071i | \(-0.319254\pi\) | ||||
0.537803 | + | 0.843071i | \(0.319254\pi\) | |||||||
\(152\) | 21.5161 | − | 21.5161i | 0.141553 | − | 0.141553i | ||||
\(153\) | −9.15729 | − | 9.15729i | −0.0598515 | − | 0.0598515i | ||||
\(154\) | − | 82.0667i | − | 0.532901i | ||||||
\(155\) | −15.0381 | + | 53.2325i | −0.0970201 | + | 0.343436i | ||||
\(156\) | 45.0748 | 0.288941 | ||||||||
\(157\) | 108.835 | − | 108.835i | 0.693219 | − | 0.693219i | −0.269720 | − | 0.962939i | \(-0.586931\pi\) |
0.962939 | + | 0.269720i | \(0.0869312\pi\) | |||||||
\(158\) | −85.1380 | − | 85.1380i | −0.538848 | − | 0.538848i | ||||
\(159\) | 112.973i | 0.710525i | ||||||||
\(160\) | −42.4037 | − | 75.7946i | −0.265023 | − | 0.473716i | ||||
\(161\) | −17.2745 | −0.107295 | ||||||||
\(162\) | 14.3937 | − | 14.3937i | 0.0888501 | − | 0.0888501i | ||||
\(163\) | −201.498 | − | 201.498i | −1.23619 | − | 1.23619i | −0.961548 | − | 0.274638i | \(-0.911442\pi\) |
−0.274638 | − | 0.961548i | \(-0.588558\pi\) | |||||||
\(164\) | 22.9713i | 0.140069i | ||||||||
\(165\) | −103.651 | + | 57.9880i | −0.628186 | + | 0.351443i | ||||
\(166\) | −311.413 | −1.87598 | ||||||||
\(167\) | −41.4832 | + | 41.4832i | −0.248402 | + | 0.248402i | −0.820315 | − | 0.571912i | \(-0.806202\pi\) |
0.571912 | + | 0.820315i | \(0.306202\pi\) | |||||||
\(168\) | 21.1400 | + | 21.1400i | 0.125833 | + | 0.125833i | ||||
\(169\) | 375.227i | 2.22028i | ||||||||
\(170\) | 46.9790 | + | 13.2715i | 0.276347 | + | 0.0780676i | ||||
\(171\) | −13.9923 | −0.0818263 | ||||||||
\(172\) | 46.7486 | − | 46.7486i | 0.271794 | − | 0.271794i | ||||
\(173\) | 130.020 | + | 130.020i | 0.751561 | + | 0.751561i | 0.974771 | − | 0.223209i | \(-0.0716534\pi\) |
−0.223209 | + | 0.974771i | \(0.571653\pi\) | |||||||
\(174\) | 197.232i | 1.13352i | ||||||||
\(175\) | −64.3296 | + | 15.3850i | −0.367598 | + | 0.0879144i | ||||
\(176\) | −263.557 | −1.49748 | ||||||||
\(177\) | −57.8812 | + | 57.8812i | −0.327013 | + | 0.327013i | ||||
\(178\) | 249.713 | + | 249.713i | 1.40288 | + | 1.40288i | ||||
\(179\) | − | 95.2857i | − | 0.532322i | −0.963929 | − | 0.266161i | \(-0.914245\pi\) | ||
0.963929 | − | 0.266161i | \(-0.0857553\pi\) | |||||||
\(180\) | −4.54902 | + | 16.1028i | −0.0252724 | + | 0.0894601i | ||||
\(181\) | −189.309 | −1.04590 | −0.522952 | − | 0.852362i | \(-0.675169\pi\) | ||||
−0.522952 | + | 0.852362i | \(0.675169\pi\) | |||||||
\(182\) | 98.7120 | − | 98.7120i | 0.542373 | − | 0.542373i | ||||
\(183\) | −41.3736 | − | 41.3736i | −0.226085 | − | 0.226085i | ||||
\(184\) | 42.5959i | 0.231499i | ||||||||
\(185\) | −153.470 | − | 274.320i | −0.829569 | − | 1.48281i | ||||
\(186\) | 43.3397 | 0.233009 | ||||||||
\(187\) | 41.8618 | − | 41.8618i | 0.223860 | − | 0.223860i | ||||
\(188\) | −22.7845 | − | 22.7845i | −0.121194 | − | 0.121194i | ||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | 46.0312 | − | 25.7524i | 0.242270 | − | 0.135539i | ||||
\(191\) | 324.784 | 1.70044 | 0.850219 | − | 0.526430i | \(-0.176470\pi\) | ||||
0.850219 | + | 0.526430i | \(0.176470\pi\) | |||||||
\(192\) | 46.0311 | − | 46.0311i | 0.239746 | − | 0.239746i | ||||
\(193\) | −24.7283 | − | 24.7283i | −0.128126 | − | 0.128126i | 0.640136 | − | 0.768262i | \(-0.278878\pi\) |
−0.768262 | + | 0.640136i | \(0.778878\pi\) | |||||||
\(194\) | − | 243.860i | − | 1.25701i | ||||||
\(195\) | −194.423 | − | 54.9243i | −0.997042 | − | 0.281663i | ||||
\(196\) | −7.80875 | −0.0398406 | ||||||||
\(197\) | 9.08901 | − | 9.08901i | 0.0461371 | − | 0.0461371i | −0.683662 | − | 0.729799i | \(-0.739614\pi\) |
0.729799 | + | 0.683662i | \(0.239614\pi\) | |||||||
\(198\) | 65.7998 | + | 65.7998i | 0.332322 | + | 0.332322i | ||||
\(199\) | − | 119.192i | − | 0.598953i | −0.954104 | − | 0.299476i | \(-0.903188\pi\) | ||
0.954104 | − | 0.299476i | \(-0.0968120\pi\) | |||||||
\(200\) | 37.9367 | + | 158.625i | 0.189684 | + | 0.793127i | ||||
\(201\) | 154.622 | 0.769265 | ||||||||
\(202\) | 112.690 | − | 112.690i | 0.557873 | − | 0.557873i | ||||
\(203\) | 94.1901 | + | 94.1901i | 0.463991 | + | 0.463991i | ||||
\(204\) | − | 8.34074i | − | 0.0408860i | ||||||
\(205\) | 27.9909 | − | 99.0832i | 0.136541 | − | 0.483333i | ||||
\(206\) | −194.524 | −0.944289 | ||||||||
\(207\) | 13.8504 | − | 13.8504i | 0.0669103 | − | 0.0669103i | ||||
\(208\) | −317.013 | − | 317.013i | −1.52410 | − | 1.52410i | ||||
\(209\) | − | 63.9647i | − | 0.306051i | ||||||
\(210\) | 25.3023 | + | 45.2266i | 0.120487 | + | 0.215365i | ||||
\(211\) | −35.9417 | −0.170340 | −0.0851699 | − | 0.996366i | \(-0.527143\pi\) | ||||
−0.0851699 | + | 0.996366i | \(0.527143\pi\) | |||||||
\(212\) | −51.4499 | + | 51.4499i | −0.242688 | + | 0.242688i | ||||
\(213\) | 38.1978 | + | 38.1978i | 0.179333 | + | 0.179333i | ||||
\(214\) | − | 168.045i | − | 0.785256i | ||||||
\(215\) | −258.606 | + | 144.679i | −1.20282 | + | 0.672925i | ||||
\(216\) | −33.8994 | −0.156942 | ||||||||
\(217\) | 20.6973 | − | 20.6973i | 0.0953793 | − | 0.0953793i | ||||
\(218\) | 61.9529 | + | 61.9529i | 0.284188 | + | 0.284188i | ||||
\(219\) | 46.7798i | 0.213607i | ||||||||
\(220\) | −73.6128 | − | 20.7955i | −0.334604 | − | 0.0945251i | ||||
\(221\) | 100.705 | 0.455678 | ||||||||
\(222\) | −174.145 | + | 174.145i | −0.784435 | + | 0.784435i | ||||
\(223\) | −230.412 | − | 230.412i | −1.03324 | − | 1.03324i | −0.999428 | − | 0.0338071i | \(-0.989237\pi\) |
−0.0338071 | − | 0.999428i | \(-0.510763\pi\) | |||||||
\(224\) | 45.9566i | 0.205164i | ||||||||
\(225\) | 39.2430 | − | 63.9139i | 0.174413 | − | 0.284062i | ||||
\(226\) | 129.642 | 0.573636 | ||||||||
\(227\) | 99.4972 | − | 99.4972i | 0.438314 | − | 0.438314i | −0.453130 | − | 0.891444i | \(-0.649693\pi\) |
0.891444 | + | 0.453130i | \(0.149693\pi\) | |||||||
\(228\) | −6.37231 | − | 6.37231i | −0.0279487 | − | 0.0279487i | ||||
\(229\) | 12.3627i | 0.0539854i | 0.999636 | + | 0.0269927i | \(0.00859309\pi\) | ||||
−0.999636 | + | 0.0269927i | \(0.991407\pi\) | |||||||
\(230\) | −20.0732 | + | 71.0558i | −0.0872746 | + | 0.308938i | ||||
\(231\) | 62.8467 | 0.272064 | ||||||||
\(232\) | 232.256 | − | 232.256i | 1.00110 | − | 1.00110i | ||||
\(233\) | 214.583 | + | 214.583i | 0.920959 | + | 0.920959i | 0.997097 | − | 0.0761385i | \(-0.0242591\pi\) |
−0.0761385 | + | 0.997097i | \(0.524259\pi\) | |||||||
\(234\) | 158.291i | 0.676458i | ||||||||
\(235\) | 70.5142 | + | 126.041i | 0.300060 | + | 0.536343i | ||||
\(236\) | −52.7200 | −0.223390 | ||||||||
\(237\) | 65.1987 | − | 65.1987i | 0.275100 | − | 0.275100i | ||||
\(238\) | −18.2659 | − | 18.2659i | −0.0767473 | − | 0.0767473i | ||||
\(239\) | 10.6709i | 0.0446481i | 0.999751 | + | 0.0223240i | \(0.00710655\pi\) | ||||
−0.999751 | + | 0.0223240i | \(0.992893\pi\) | |||||||
\(240\) | 145.245 | − | 81.2583i | 0.605188 | − | 0.338576i | ||||
\(241\) | −217.027 | −0.900526 | −0.450263 | − | 0.892896i | \(-0.648670\pi\) | ||||
−0.450263 | + | 0.892896i | \(0.648670\pi\) | |||||||
\(242\) | −107.283 | + | 107.283i | −0.443318 | + | 0.443318i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 37.6843i | − | 0.154444i | ||||||
\(245\) | 33.6818 | + | 9.51506i | 0.137477 | + | 0.0388370i | ||||
\(246\) | −80.6694 | −0.327924 | ||||||||
\(247\) | 76.9384 | − | 76.9384i | 0.311492 | − | 0.311492i | ||||
\(248\) | −51.0359 | − | 51.0359i | −0.205790 | − | 0.205790i | ||||
\(249\) | − | 238.480i | − | 0.957751i | ||||||
\(250\) | −11.4680 | + | 282.487i | −0.0458719 | + | 1.12995i | ||||
\(251\) | −59.6693 | −0.237726 | −0.118863 | − | 0.992911i | \(-0.537925\pi\) | ||||
−0.118863 | + | 0.992911i | \(0.537925\pi\) | |||||||
\(252\) | 6.26093 | − | 6.26093i | 0.0248450 | − | 0.0248450i | ||||
\(253\) | 63.3161 | + | 63.3161i | 0.250261 | + | 0.250261i | ||||
\(254\) | − | 12.7612i | − | 0.0502409i | ||||||
\(255\) | −10.1633 | + | 35.9765i | −0.0398561 | + | 0.141084i | ||||
\(256\) | 199.073 | 0.777629 | ||||||||
\(257\) | −224.525 | + | 224.525i | −0.873639 | + | 0.873639i | −0.992867 | − | 0.119228i | \(-0.961958\pi\) |
0.119228 | + | 0.992867i | \(0.461958\pi\) | |||||||
\(258\) | 164.169 | + | 164.169i | 0.636314 | + | 0.636314i | ||||
\(259\) | 166.329i | 0.642197i | ||||||||
\(260\) | −63.5300 | − | 113.557i | −0.244346 | − | 0.436757i | ||||
\(261\) | −151.040 | −0.578698 | ||||||||
\(262\) | 116.051 | − | 116.051i | 0.442944 | − | 0.442944i | ||||
\(263\) | −0.00150876 | − | 0.00150876i | −5.73673e−6 | − | 5.73673e-6i | 0.707104 | − | 0.707110i | \(-0.250001\pi\) |
−0.707110 | + | 0.707104i | \(0.750001\pi\) | |||||||
\(264\) | − | 154.969i | − | 0.587003i | ||||||
\(265\) | 284.613 | − | 159.229i | 1.07401 | − | 0.600862i | ||||
\(266\) | −27.9102 | −0.104925 | ||||||||
\(267\) | −191.230 | + | 191.230i | −0.716218 | + | 0.716218i | ||||
\(268\) | 70.4174 | + | 70.4174i | 0.262752 | + | 0.262752i | ||||
\(269\) | − | 10.8410i | − | 0.0403011i | −0.999797 | − | 0.0201506i | \(-0.993585\pi\) | ||
0.999797 | − | 0.0201506i | \(-0.00641456\pi\) | |||||||
\(270\) | −56.5490 | − | 15.9750i | −0.209441 | − | 0.0591667i | ||||
\(271\) | 423.331 | 1.56211 | 0.781054 | − | 0.624464i | \(-0.214682\pi\) | ||||
0.781054 | + | 0.624464i | \(0.214682\pi\) | |||||||
\(272\) | −58.6607 | + | 58.6607i | −0.215664 | + | 0.215664i | ||||
\(273\) | 75.5936 | + | 75.5936i | 0.276900 | + | 0.276900i | ||||
\(274\) | 216.404i | 0.789797i | ||||||||
\(275\) | 292.178 | + | 179.396i | 1.06246 | + | 0.652350i | ||||
\(276\) | 12.6154 | 0.0457079 | ||||||||
\(277\) | 43.6341 | − | 43.6341i | 0.157524 | − | 0.157524i | −0.623945 | − | 0.781469i | \(-0.714471\pi\) |
0.781469 | + | 0.623945i | \(0.214471\pi\) | |||||||
\(278\) | 212.694 | + | 212.694i | 0.765088 | + | 0.765088i | ||||
\(279\) | 33.1895i | 0.118959i | ||||||||
\(280\) | 23.4624 | − | 83.0533i | 0.0837944 | − | 0.296619i | ||||
\(281\) | −173.395 | −0.617065 | −0.308532 | − | 0.951214i | \(-0.599838\pi\) | ||||
−0.308532 | + | 0.951214i | \(0.599838\pi\) | |||||||
\(282\) | 80.0134 | − | 80.0134i | 0.283735 | − | 0.283735i | ||||
\(283\) | 205.636 | + | 205.636i | 0.726630 | + | 0.726630i | 0.969947 | − | 0.243317i | \(-0.0782354\pi\) |
−0.243317 | + | 0.969947i | \(0.578235\pi\) | |||||||
\(284\) | 34.7918i | 0.122506i | ||||||||
\(285\) | 19.7212 | + | 35.2507i | 0.0691972 | + | 0.123687i | ||||
\(286\) | −723.616 | −2.53013 | ||||||||
\(287\) | −38.5245 | + | 38.5245i | −0.134232 | + | 0.134232i | ||||
\(288\) | −36.8473 | − | 36.8473i | −0.127942 | − | 0.127942i | ||||
\(289\) | 270.365i | 0.935520i | ||||||||
\(290\) | 496.885 | − | 277.985i | 1.71340 | − | 0.958570i | ||||
\(291\) | 186.748 | 0.641745 | ||||||||
\(292\) | −21.3043 | + | 21.3043i | −0.0729598 | + | 0.0729598i | ||||
\(293\) | −240.660 | − | 240.660i | −0.821366 | − | 0.821366i | 0.164938 | − | 0.986304i | \(-0.447258\pi\) |
−0.986304 | + | 0.164938i | \(0.947258\pi\) | |||||||
\(294\) | − | 27.4223i | − | 0.0932732i | ||||||
\(295\) | 227.399 | + | 64.2400i | 0.770845 | + | 0.217763i | ||||
\(296\) | 410.138 | 1.38560 | ||||||||
\(297\) | −50.3894 | + | 50.3894i | −0.169661 | + | 0.169661i | ||||
\(298\) | −74.5311 | − | 74.5311i | −0.250104 | − | 0.250104i | ||||
\(299\) | 152.316i | 0.509420i | ||||||||
\(300\) | 46.9793 | − | 11.2355i | 0.156598 | − | 0.0374517i | ||||
\(301\) | 156.801 | 0.520934 | ||||||||
\(302\) | −259.753 | + | 259.753i | −0.860110 | + | 0.860110i | ||||
\(303\) | 86.2982 | + | 86.2982i | 0.284813 | + | 0.284813i | ||||
\(304\) | 89.6334i | 0.294847i | ||||||||
\(305\) | −45.9188 | + | 162.545i | −0.150554 | + | 0.532936i | ||||
\(306\) | 29.2905 | 0.0957207 | ||||||||
\(307\) | −334.742 | + | 334.742i | −1.09037 | + | 1.09037i | −0.0948775 | + | 0.995489i | \(0.530246\pi\) |
−0.995489 | + | 0.0948775i | \(0.969754\pi\) | |||||||
\(308\) | 28.6214 | + | 28.6214i | 0.0929265 | + | 0.0929265i | ||||
\(309\) | − | 148.966i | − | 0.482091i | ||||||
\(310\) | −61.0844 | − | 109.185i | −0.197046 | − | 0.352211i | ||||
\(311\) | −29.4564 | −0.0947151 | −0.0473575 | − | 0.998878i | \(-0.515080\pi\) | ||||
−0.0473575 | + | 0.998878i | \(0.515080\pi\) | |||||||
\(312\) | 186.400 | − | 186.400i | 0.597437 | − | 0.597437i | ||||
\(313\) | −375.133 | − | 375.133i | −1.19851 | − | 1.19851i | −0.974613 | − | 0.223895i | \(-0.928123\pi\) |
−0.223895 | − | 0.974613i | \(-0.571877\pi\) | |||||||
\(314\) | 348.121i | 1.10867i | ||||||||
\(315\) | −34.6345 | + | 19.3765i | −0.109951 | + | 0.0615127i | ||||
\(316\) | 59.3850 | 0.187927 | ||||||||
\(317\) | −409.594 | + | 409.594i | −1.29209 | + | 1.29209i | −0.358605 | + | 0.933489i | \(0.616748\pi\) |
−0.933489 | + | 0.358605i | \(0.883252\pi\) | |||||||
\(318\) | −180.679 | − | 180.679i | −0.568172 | − | 0.568172i | ||||
\(319\) | − | 690.469i | − | 2.16448i | ||||||
\(320\) | −180.844 | − | 51.0881i | −0.565136 | − | 0.159650i | ||||
\(321\) | 128.689 | 0.400899 | ||||||||
\(322\) | 27.6272 | − | 27.6272i | 0.0857987 | − | 0.0857987i | ||||
\(323\) | −14.2368 | − | 14.2368i | −0.0440769 | − | 0.0440769i | ||||
\(324\) | 10.0398i | 0.0309871i | ||||||||
\(325\) | 135.656 | + | 567.221i | 0.417403 | + | 1.74530i | ||||
\(326\) | 644.513 | 1.97703 | ||||||||
\(327\) | −47.4435 | + | 47.4435i | −0.145087 | + | 0.145087i | ||||
\(328\) | 94.9945 | + | 94.9945i | 0.289617 | + | 0.289617i | ||||
\(329\) | − | 76.4224i | − | 0.232287i | ||||||
\(330\) | 73.0285 | − | 258.509i | 0.221298 | − | 0.783361i | ||||
\(331\) | −71.9385 | −0.217337 | −0.108668 | − | 0.994078i | \(-0.534659\pi\) | ||||
−0.108668 | + | 0.994078i | \(0.534659\pi\) | |||||||
\(332\) | 108.607 | − | 108.607i | 0.327131 | − | 0.327131i | ||||
\(333\) | −133.360 | − | 133.360i | −0.400480 | − | 0.400480i | ||||
\(334\) | − | 132.688i | − | 0.397270i | ||||||
\(335\) | −217.930 | − | 389.539i | −0.650537 | − | 1.16280i | ||||
\(336\) | −88.0667 | −0.262103 | ||||||||
\(337\) | −302.137 | + | 302.137i | −0.896548 | + | 0.896548i | −0.995129 | − | 0.0985809i | \(-0.968570\pi\) |
0.0985809 | + | 0.995129i | \(0.468570\pi\) | |||||||
\(338\) | −600.102 | − | 600.102i | −1.77545 | − | 1.77545i | ||||
\(339\) | 99.2796i | 0.292860i | ||||||||
\(340\) | −21.0128 | + | 11.7557i | −0.0618022 | + | 0.0345756i | ||||
\(341\) | −151.723 | −0.444937 | ||||||||
\(342\) | 22.3779 | − | 22.3779i | 0.0654325 | − | 0.0654325i | ||||
\(343\) | −13.0958 | − | 13.0958i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 386.643i | − | 1.12396i | ||||||
\(345\) | −54.4145 | − | 15.3720i | −0.157723 | − | 0.0445566i | ||||
\(346\) | −415.883 | −1.20197 | ||||||||
\(347\) | −346.764 | + | 346.764i | −0.999320 | + | 0.999320i | −1.00000 | 0.000679298i | \(-0.999784\pi\) | |
0.000679298 | 1.00000i | \(0.499784\pi\) | ||||||||
\(348\) | −68.7861 | − | 68.7861i | −0.197661 | − | 0.197661i | ||||
\(349\) | − | 29.7025i | − | 0.0851075i | −0.999094 | − | 0.0425537i | \(-0.986451\pi\) | ||
0.999094 | − | 0.0425537i | \(-0.0135494\pi\) | |||||||
\(350\) | 78.2772 | − | 127.488i | 0.223649 | − | 0.364251i | ||||
\(351\) | −121.219 | −0.345354 | ||||||||
\(352\) | 168.444 | − | 168.444i | 0.478535 | − | 0.478535i | ||||
\(353\) | −368.835 | − | 368.835i | −1.04486 | − | 1.04486i | −0.998945 | − | 0.0459136i | \(-0.985380\pi\) |
−0.0459136 | − | 0.998945i | \(-0.514620\pi\) | |||||||
\(354\) | − | 185.139i | − | 0.522992i | ||||||
\(355\) | 42.3942 | − | 150.069i | 0.119420 | − | 0.422729i | ||||
\(356\) | −174.178 | −0.489265 | ||||||||
\(357\) | 13.9880 | − | 13.9880i | 0.0391820 | − | 0.0391820i | ||||
\(358\) | 152.391 | + | 152.391i | 0.425672 | + | 0.425672i | ||||
\(359\) | − | 610.662i | − | 1.70101i | −0.525969 | − | 0.850504i | \(-0.676297\pi\) | ||
0.525969 | − | 0.850504i | \(-0.323703\pi\) | |||||||
\(360\) | 47.7790 | + | 85.4026i | 0.132719 | + | 0.237229i | ||||
\(361\) | 339.246 | 0.939740 | ||||||||
\(362\) | 302.762 | − | 302.762i | 0.836358 | − | 0.836358i | ||||
\(363\) | −82.1573 | − | 82.1573i | −0.226329 | − | 0.226329i | ||||
\(364\) | 68.8530i | 0.189157i | ||||||||
\(365\) | 117.852 | − | 65.9331i | 0.322882 | − | 0.180639i | ||||
\(366\) | 132.338 | 0.361578 | ||||||||
\(367\) | 72.5232 | − | 72.5232i | 0.197611 | − | 0.197611i | −0.601364 | − | 0.798975i | \(-0.705376\pi\) |
0.798975 | + | 0.601364i | \(0.205376\pi\) | |||||||
\(368\) | −88.7245 | − | 88.7245i | −0.241099 | − | 0.241099i | ||||
\(369\) | − | 61.7766i | − | 0.167416i | ||||||
\(370\) | 684.167 | + | 193.276i | 1.84910 | + | 0.522368i | ||||
\(371\) | −172.570 | −0.465148 | ||||||||
\(372\) | −15.1150 | + | 15.1150i | −0.0406318 | + | 0.0406318i | ||||
\(373\) | 6.51685 | + | 6.51685i | 0.0174714 | + | 0.0174714i | 0.715789 | − | 0.698317i | \(-0.246067\pi\) |
−0.698317 | + | 0.715789i | \(0.746067\pi\) | |||||||
\(374\) | 133.899i | 0.358020i | ||||||||
\(375\) | −216.328 | − | 8.78217i | −0.576875 | − | 0.0234191i | ||||
\(376\) | −188.444 | −0.501181 | ||||||||
\(377\) | 830.513 | − | 830.513i | 2.20295 | − | 2.20295i | ||||
\(378\) | 21.9868 | + | 21.9868i | 0.0581661 | + | 0.0581661i | ||||
\(379\) | 224.357i | 0.591970i | 0.955193 | + | 0.295985i | \(0.0956479\pi\) | ||||
−0.955193 | + | 0.295985i | \(0.904352\pi\) | |||||||
\(380\) | −7.07237 | + | 25.0351i | −0.0186115 | + | 0.0658817i | ||||
\(381\) | 9.77251 | 0.0256496 | ||||||||
\(382\) | −519.427 | + | 519.427i | −1.35976 | + | 1.35976i | ||||
\(383\) | 82.5720 | + | 82.5720i | 0.215593 | + | 0.215593i | 0.806638 | − | 0.591045i | \(-0.201285\pi\) |
−0.591045 | + | 0.806638i | \(0.701285\pi\) | |||||||
\(384\) | 267.578i | 0.696818i | ||||||||
\(385\) | −88.5782 | − | 158.329i | −0.230073 | − | 0.411244i | ||||
\(386\) | 79.0961 | 0.204912 | ||||||||
\(387\) | −125.721 | + | 125.721i | −0.324859 | + | 0.324859i | ||||
\(388\) | 85.0479 | + | 85.0479i | 0.219196 | + | 0.219196i | ||||
\(389\) | 711.444i | 1.82891i | 0.404693 | + | 0.914453i | \(0.367378\pi\) | ||||
−0.404693 | + | 0.914453i | \(0.632622\pi\) | |||||||
\(390\) | 398.782 | − | 223.101i | 1.02252 | − | 0.572054i | ||||
\(391\) | 28.1850 | 0.0720843 | ||||||||
\(392\) | −32.2919 | + | 32.2919i | −0.0823773 | + | 0.0823773i | ||||
\(393\) | 88.8720 | + | 88.8720i | 0.226137 | + | 0.226137i | ||||
\(394\) | 29.0721i | 0.0737871i | ||||||||
\(395\) | −256.148 | − | 72.3613i | −0.648475 | − | 0.183193i | ||||
\(396\) | −45.8963 | −0.115900 | ||||||||
\(397\) | −333.858 | + | 333.858i | −0.840951 | + | 0.840951i | −0.988983 | − | 0.148032i | \(-0.952706\pi\) |
0.148032 | + | 0.988983i | \(0.452706\pi\) | |||||||
\(398\) | 190.623 | + | 190.623i | 0.478953 | + | 0.478953i | ||||
\(399\) | − | 21.3736i | − | 0.0535679i | ||||||
\(400\) | −409.427 | − | 251.387i | −1.02357 | − | 0.628467i | ||||
\(401\) | −125.123 | −0.312027 | −0.156014 | − | 0.987755i | \(-0.549864\pi\) | ||||
−0.156014 | + | 0.987755i | \(0.549864\pi\) | |||||||
\(402\) | −247.288 | + | 247.288i | −0.615144 | + | 0.615144i | ||||
\(403\) | −182.497 | − | 182.497i | −0.452845 | − | 0.452845i | ||||
\(404\) | 78.6031i | 0.194562i | ||||||||
\(405\) | 12.2336 | − | 43.3052i | 0.0302065 | − | 0.106926i | ||||
\(406\) | −301.277 | −0.742062 | ||||||||
\(407\) | 609.645 | − | 609.645i | 1.49790 | − | 1.49790i | ||||
\(408\) | −34.4919 | − | 34.4919i | −0.0845389 | − | 0.0845389i | ||||
\(409\) | 313.700i | 0.766993i | 0.923542 | + | 0.383496i | \(0.125280\pi\) | ||||
−0.923542 | + | 0.383496i | \(0.874720\pi\) | |||||||
\(410\) | 113.698 | + | 203.230i | 0.277313 | + | 0.495683i | ||||
\(411\) | −165.722 | −0.403217 | ||||||||
\(412\) | 67.8414 | − | 67.8414i | 0.164664 | − | 0.164664i | ||||
\(413\) | −88.4150 | − | 88.4150i | −0.214080 | − | 0.214080i | ||||
\(414\) | 44.3020i | 0.107010i | ||||||||
\(415\) | −600.801 | + | 336.121i | −1.44771 | + | 0.809931i | ||||
\(416\) | 405.219 | 0.974083 | ||||||||
\(417\) | −162.881 | + | 162.881i | −0.390602 | + | 0.390602i | ||||
\(418\) | 102.299 | + | 102.299i | 0.244734 | + | 0.244734i | ||||
\(419\) | 182.061i | 0.434514i | 0.976114 | + | 0.217257i | \(0.0697110\pi\) | ||||
−0.976114 | + | 0.217257i | \(0.930289\pi\) | |||||||
\(420\) | −24.5975 | − | 6.94875i | −0.0585654 | − | 0.0165446i | ||||
\(421\) | 444.013 | 1.05466 | 0.527331 | − | 0.849660i | \(-0.323193\pi\) | ||||
0.527331 | + | 0.849660i | \(0.323193\pi\) | |||||||
\(422\) | 57.4817 | − | 57.4817i | 0.136212 | − | 0.136212i | ||||
\(423\) | 61.2742 | + | 61.2742i | 0.144856 | + | 0.144856i | ||||
\(424\) | 425.527i | 1.00360i | ||||||||
\(425\) | 104.960 | − | 25.1021i | 0.246964 | − | 0.0590637i | ||||
\(426\) | −122.180 | −0.286807 | ||||||||
\(427\) | 63.1992 | − | 63.1992i | 0.148007 | − | 0.148007i | ||||
\(428\) | 58.6068 | + | 58.6068i | 0.136932 | + | 0.136932i | ||||
\(429\) | − | 554.145i | − | 1.29171i | ||||||
\(430\) | 182.204 | − | 644.975i | 0.423731 | − | 1.49994i | ||||
\(431\) | −209.687 | −0.486514 | −0.243257 | − | 0.969962i | \(-0.578216\pi\) | ||||
−0.243257 | + | 0.969962i | \(0.578216\pi\) | |||||||
\(432\) | 70.6104 | − | 70.6104i | 0.163450 | − | 0.163450i | ||||
\(433\) | 593.138 | + | 593.138i | 1.36983 | + | 1.36983i | 0.860668 | + | 0.509167i | \(0.170046\pi\) |
0.509167 | + | 0.860668i | \(0.329954\pi\) | |||||||
\(434\) | 66.2025i | 0.152540i | ||||||||
\(435\) | 212.881 | + | 380.514i | 0.489382 | + | 0.874746i | ||||
\(436\) | −43.2130 | −0.0991124 | ||||||||
\(437\) | 21.5333 | − | 21.5333i | 0.0492752 | − | 0.0492752i | ||||
\(438\) | −74.8151 | − | 74.8151i | −0.170811 | − | 0.170811i | ||||
\(439\) | 91.5547i | 0.208553i | 0.994548 | + | 0.104276i | \(0.0332527\pi\) | ||||
−0.994548 | + | 0.104276i | \(0.966747\pi\) | |||||||
\(440\) | −390.411 | + | 218.418i | −0.887299 | + | 0.496405i | ||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −161.058 | + | 161.058i | −0.364384 | + | 0.364384i | ||||
\(443\) | 302.352 | + | 302.352i | 0.682511 | + | 0.682511i | 0.960565 | − | 0.278054i | \(-0.0896895\pi\) |
−0.278054 | + | 0.960565i | \(0.589689\pi\) | |||||||
\(444\) | − | 121.468i | − | 0.273577i | ||||||
\(445\) | 751.291 | + | 212.239i | 1.68829 | + | 0.476941i | ||||
\(446\) | 736.995 | 1.65246 | ||||||||
\(447\) | 57.0759 | − | 57.0759i | 0.127686 | − | 0.127686i | ||||
\(448\) | 70.3137 | + | 70.3137i | 0.156950 | + | 0.156950i | ||||
\(449\) | 190.141i | 0.423477i | 0.977326 | + | 0.211738i | \(0.0679125\pi\) | ||||
−0.977326 | + | 0.211738i | \(0.932088\pi\) | |||||||
\(450\) | 39.4563 | + | 164.979i | 0.0876806 | + | 0.366620i | ||||
\(451\) | 282.407 | 0.626180 | ||||||||
\(452\) | −45.2135 | + | 45.2135i | −0.100030 | + | 0.100030i | ||||
\(453\) | −198.919 | − | 198.919i | −0.439114 | − | 0.439114i | ||||
\(454\) | 318.252i | 0.700996i | ||||||||
\(455\) | 83.8982 | − | 296.986i | 0.184392 | − | 0.652717i | ||||
\(456\) | −52.7035 | −0.115578 | ||||||||
\(457\) | −83.0275 | + | 83.0275i | −0.181680 | + | 0.181680i | −0.792087 | − | 0.610408i | \(-0.791006\pi\) |
0.610408 | + | 0.792087i | \(0.291006\pi\) | |||||||
\(458\) | −19.7716 | − | 19.7716i | −0.0431695 | − | 0.0431695i | ||||
\(459\) | 22.4307i | 0.0488686i | ||||||||
\(460\) | −17.7806 | − | 31.7819i | −0.0386534 | − | 0.0690910i | ||||
\(461\) | 231.095 | 0.501290 | 0.250645 | − | 0.968079i | \(-0.419357\pi\) | ||||
0.250645 | + | 0.968079i | \(0.419357\pi\) | |||||||
\(462\) | −100.511 | + | 100.511i | −0.217556 | + | 0.217556i | ||||
\(463\) | −584.068 | − | 584.068i | −1.26149 | − | 1.26149i | −0.950373 | − | 0.311112i | \(-0.899299\pi\) |
−0.311112 | − | 0.950373i | \(-0.600701\pi\) | |||||||
\(464\) | 967.550i | 2.08524i | ||||||||
\(465\) | 83.6141 | − | 46.7784i | 0.179815 | − | 0.100599i | ||||
\(466\) | −686.367 | −1.47289 | ||||||||
\(467\) | −50.5678 | + | 50.5678i | −0.108282 | + | 0.108282i | −0.759172 | − | 0.650890i | \(-0.774396\pi\) |
0.650890 | + | 0.759172i | \(0.274396\pi\) | |||||||
\(468\) | −55.2052 | − | 55.2052i | −0.117960 | − | 0.117960i | ||||
\(469\) | 236.190i | 0.503602i | ||||||||
\(470\) | −314.351 | − | 88.8036i | −0.668831 | − | 0.188944i | ||||
\(471\) | −266.591 | −0.566011 | ||||||||
\(472\) | −218.016 | + | 218.016i | −0.461898 | + | 0.461898i | ||||
\(473\) | −574.722 | − | 574.722i | −1.21506 | − | 1.21506i | ||||
\(474\) | 208.545i | 0.439968i | ||||||||
\(475\) | 61.0111 | − | 99.3670i | 0.128444 | − | 0.209194i | ||||
\(476\) | 12.7407 | 0.0267662 | ||||||||
\(477\) | 138.364 | − | 138.364i | 0.290071 | − | 0.290071i | ||||
\(478\) | −17.0660 | − | 17.0660i | −0.0357029 | − | 0.0357029i | ||||
\(479\) | 479.014i | 1.00003i | 0.866017 | + | 0.500015i | \(0.166672\pi\) | ||||
−0.866017 | + | 0.500015i | \(0.833328\pi\) | |||||||
\(480\) | −40.8953 | + | 144.763i | −0.0851985 | + | 0.301589i | ||||
\(481\) | 1466.59 | 3.04905 | ||||||||
\(482\) | 347.092 | − | 347.092i | 0.720107 | − | 0.720107i | ||||
\(483\) | 21.1569 | + | 21.1569i | 0.0438030 | + | 0.0438030i | ||||
\(484\) | − | 74.8314i | − | 0.154610i | ||||||
\(485\) | −263.209 | − | 470.473i | −0.542698 | − | 0.970046i | ||||
\(486\) | −35.2573 | −0.0725458 | ||||||||
\(487\) | 533.369 | − | 533.369i | 1.09521 | − | 1.09521i | 0.100250 | − | 0.994962i | \(-0.468036\pi\) |
0.994962 | − | 0.100250i | \(-0.0319644\pi\) | |||||||
\(488\) | −155.838 | − | 155.838i | −0.319340 | − | 0.319340i | ||||
\(489\) | 493.568i | 1.00934i | ||||||||
\(490\) | −69.0848 | + | 38.6499i | −0.140989 | + | 0.0788774i | ||||
\(491\) | −348.294 | −0.709356 | −0.354678 | − | 0.934989i | \(-0.615409\pi\) | ||||
−0.354678 | + | 0.934989i | \(0.615409\pi\) | |||||||
\(492\) | 28.1340 | − | 28.1340i | 0.0571830 | − | 0.0571830i | ||||
\(493\) | −153.680 | − | 153.680i | −0.311724 | − | 0.311724i | ||||
\(494\) | 246.096i | 0.498169i | ||||||||
\(495\) | 197.966 | + | 55.9252i | 0.399932 | + | 0.112980i | ||||
\(496\) | 212.609 | 0.428647 | ||||||||
\(497\) | −58.3481 | + | 58.3481i | −0.117401 | + | 0.117401i | ||||
\(498\) | 381.402 | + | 381.402i | 0.765867 | + | 0.765867i | ||||
\(499\) | − | 665.697i | − | 1.33406i | −0.745030 | − | 0.667031i | \(-0.767565\pi\) | ||
0.745030 | − | 0.667031i | \(-0.232435\pi\) | |||||||
\(500\) | −94.5197 | − | 102.519i | −0.189039 | − | 0.205037i | ||||
\(501\) | 101.613 | 0.202820 | ||||||||
\(502\) | 95.4292 | − | 95.4292i | 0.190098 | − | 0.190098i | ||||
\(503\) | 462.086 | + | 462.086i | 0.918660 | + | 0.918660i | 0.996932 | − | 0.0782724i | \(-0.0249404\pi\) |
−0.0782724 | + | 0.996932i | \(0.524940\pi\) | |||||||
\(504\) | − | 51.7823i | − | 0.102743i | ||||||
\(505\) | 95.7789 | − | 339.042i | 0.189661 | − | 0.671370i | ||||
\(506\) | −202.523 | −0.400244 | ||||||||
\(507\) | 459.558 | − | 459.558i | 0.906426 | − | 0.906426i | ||||
\(508\) | 4.45055 | + | 4.45055i | 0.00876093 | + | 0.00876093i | ||||
\(509\) | − | 75.7747i | − | 0.148870i | −0.997226 | − | 0.0744348i | \(-0.976285\pi\) | ||
0.997226 | − | 0.0744348i | \(-0.0237153\pi\) | |||||||
\(510\) | −41.2830 | − | 73.7914i | −0.0809471 | − | 0.144689i | ||||
\(511\) | −71.4574 | −0.139838 | ||||||||
\(512\) | 118.575 | − | 118.575i | 0.231592 | − | 0.231592i | ||||
\(513\) | 17.1370 | + | 17.1370i | 0.0334055 | + | 0.0334055i | ||||
\(514\) | − | 718.167i | − | 1.39721i | ||||||
\(515\) | −375.289 | + | 209.958i | −0.728716 | + | 0.407685i | ||||
\(516\) | −114.510 | −0.221919 | ||||||||
\(517\) | −280.110 | + | 280.110i | −0.541799 | + | 0.541799i | ||||
\(518\) | −266.010 | − | 266.010i | −0.513534 | − | 0.513534i | ||||
\(519\) | − | 318.483i | − | 0.613647i | ||||||
\(520\) | −732.315 | − | 206.878i | −1.40830 | − | 0.397842i | ||||
\(521\) | −493.508 | −0.947231 | −0.473616 | − | 0.880732i | \(-0.657051\pi\) | ||||
−0.473616 | + | 0.880732i | \(0.657051\pi\) | |||||||
\(522\) | 241.559 | − | 241.559i | 0.462757 | − | 0.462757i | ||||
\(523\) | 88.8615 | + | 88.8615i | 0.169907 | + | 0.169907i | 0.786939 | − | 0.617031i | \(-0.211665\pi\) |
−0.617031 | + | 0.786939i | \(0.711665\pi\) | |||||||
\(524\) | 80.9474i | 0.154480i | ||||||||
\(525\) | 97.6301 | + | 59.9446i | 0.185962 | + | 0.114180i | ||||
\(526\) | 0.00482592 | 9.17476e−6 | ||||||||
\(527\) | −33.7696 | + | 33.7696i | −0.0640789 | + | 0.0640789i | ||||
\(528\) | 322.790 | + | 322.790i | 0.611345 | + | 0.611345i | ||||
\(529\) | − | 486.370i | − | 0.919414i | ||||||
\(530\) | −200.528 | + | 709.837i | −0.378355 | + | 1.33932i | ||||
\(531\) | 141.779 | 0.267005 | ||||||||
\(532\) | 9.73387 | − | 9.73387i | 0.0182967 | − | 0.0182967i | ||||
\(533\) | 339.686 | + | 339.686i | 0.637310 | + | 0.637310i | ||||
\(534\) | − | 611.670i | − | 1.14545i | ||||||
\(535\) | −181.378 | − | 324.204i | −0.339024 | − | 0.605989i | ||||
\(536\) | 582.401 | 1.08657 | ||||||||
\(537\) | −116.701 | + | 116.701i | −0.217320 | + | 0.217320i | ||||
\(538\) | 17.3380 | + | 17.3380i | 0.0322268 | + | 0.0322268i | ||||
\(539\) | 95.9999i | 0.178107i | ||||||||
\(540\) | 25.2932 | − | 14.1505i | 0.0468393 | − | 0.0262045i | ||||
\(541\) | 95.0854 | 0.175759 | 0.0878793 | − | 0.996131i | \(-0.471991\pi\) | ||||
0.0878793 | + | 0.996131i | \(0.471991\pi\) | |||||||
\(542\) | −677.035 | + | 677.035i | −1.24914 | + | 1.24914i | ||||
\(543\) | 231.855 | + | 231.855i | 0.426988 | + | 0.426988i | ||||
\(544\) | − | 74.9825i | − | 0.137835i | ||||||
\(545\) | 186.392 | + | 52.6556i | 0.342005 | + | 0.0966158i | ||||
\(546\) | −241.794 | −0.442846 | ||||||||
\(547\) | 638.590 | − | 638.590i | 1.16744 | − | 1.16744i | 0.184634 | − | 0.982807i | \(-0.440890\pi\) |
0.982807 | − | 0.184634i | \(-0.0591100\pi\) | |||||||
\(548\) | −75.4725 | − | 75.4725i | −0.137724 | − | 0.137724i | ||||
\(549\) | 101.344i | 0.184598i | ||||||||
\(550\) | −754.189 | + | 180.371i | −1.37125 | + | 0.327948i | ||||
\(551\) | −234.822 | −0.426175 | ||||||||
\(552\) | 52.1691 | − | 52.1691i | 0.0945092 | − | 0.0945092i | ||||
\(553\) | 99.5926 | + | 99.5926i | 0.180095 | + | 0.180095i | ||||
\(554\) | 139.568i | 0.251928i | ||||||||
\(555\) | −148.011 | + | 523.934i | −0.266686 | + | 0.944026i | ||||
\(556\) | −148.357 | −0.266830 | ||||||||
\(557\) | 368.475 | − | 368.475i | 0.661534 | − | 0.661534i | −0.294207 | − | 0.955742i | \(-0.595056\pi\) |
0.955742 | + | 0.294207i | \(0.0950556\pi\) | |||||||
\(558\) | −53.0801 | − | 53.0801i | −0.0951256 | − | 0.0951256i | ||||
\(559\) | − | 1382.58i | − | 2.47331i | ||||||
\(560\) | 124.124 | + | 221.866i | 0.221650 | + | 0.396189i | ||||
\(561\) | −102.540 | −0.182781 | ||||||||
\(562\) | 277.311 | − | 277.311i | 0.493436 | − | 0.493436i | ||||
\(563\) | −229.051 | − | 229.051i | −0.406840 | − | 0.406840i | 0.473795 | − | 0.880635i | \(-0.342884\pi\) |
−0.880635 | + | 0.473795i | \(0.842884\pi\) | |||||||
\(564\) | 55.8104i | 0.0989547i | ||||||||
\(565\) | 250.114 | − | 139.928i | 0.442680 | − | 0.247660i | ||||
\(566\) | −657.749 | −1.16210 | ||||||||
\(567\) | −16.8375 | + | 16.8375i | −0.0296957 | + | 0.0296957i | ||||
\(568\) | 143.876 | + | 143.876i | 0.253303 | + | 0.253303i | ||||
\(569\) | 156.076i | 0.274298i | 0.990550 | + | 0.137149i | \(0.0437940\pi\) | ||||
−0.990550 | + | 0.137149i | \(0.956206\pi\) | |||||||
\(570\) | −87.9167 | − | 24.8363i | −0.154240 | − | 0.0435725i | ||||
\(571\) | −689.495 | −1.20752 | −0.603761 | − | 0.797166i | \(-0.706332\pi\) | ||||
−0.603761 | + | 0.797166i | \(0.706332\pi\) | |||||||
\(572\) | 252.366 | − | 252.366i | 0.441200 | − | 0.441200i | ||||
\(573\) | −397.777 | − | 397.777i | −0.694201 | − | 0.694201i | ||||
\(574\) | − | 123.225i | − | 0.214677i | ||||||
\(575\) | 37.9670 | + | 158.752i | 0.0660295 | + | 0.276090i | ||||
\(576\) | −112.753 | −0.195751 | ||||||||
\(577\) | −613.020 | + | 613.020i | −1.06243 | + | 1.06243i | −0.0645083 | + | 0.997917i | \(0.520548\pi\) |
−0.997917 | + | 0.0645083i | \(0.979452\pi\) | |||||||
\(578\) | −432.396 | − | 432.396i | −0.748090 | − | 0.748090i | ||||
\(579\) | 60.5718i | 0.104614i | ||||||||
\(580\) | −76.3429 | + | 270.242i | −0.131626 | + | 0.465934i | ||||
\(581\) | 364.284 | 0.626995 | ||||||||
\(582\) | −298.666 | + | 298.666i | −0.513172 | + | 0.513172i | ||||
\(583\) | 632.519 | + | 632.519i | 1.08494 | + | 1.08494i | ||||
\(584\) | 176.201i | 0.301714i | ||||||||
\(585\) | 170.851 | + | 305.387i | 0.292052 | + | 0.522029i | ||||
\(586\) | 769.777 | 1.31361 | ||||||||
\(587\) | −100.105 | + | 100.105i | −0.170536 | + | 0.170536i | −0.787215 | − | 0.616679i | \(-0.788478\pi\) |
0.616679 | + | 0.787215i | \(0.288478\pi\) | |||||||
\(588\) | 9.56373 | + | 9.56373i | 0.0162648 | + | 0.0162648i | ||||
\(589\) | 51.5998i | 0.0876057i | ||||||||
\(590\) | −466.420 | + | 260.941i | −0.790542 | + | 0.442273i | ||||
\(591\) | −22.2634 | −0.0376708 | ||||||||
\(592\) | −854.291 | + | 854.291i | −1.44306 | + | 1.44306i | ||||
\(593\) | 436.401 | + | 436.401i | 0.735920 | + | 0.735920i | 0.971786 | − | 0.235866i | \(-0.0757925\pi\) |
−0.235866 | + | 0.971786i | \(0.575793\pi\) | |||||||
\(594\) | − | 161.176i | − | 0.271340i | ||||||
\(595\) | −54.9549 | − | 15.5247i | −0.0923613 | − | 0.0260919i | ||||
\(596\) | 51.9865 | 0.0872256 | ||||||||
\(597\) | −145.979 | + | 145.979i | −0.244521 | + | 0.244521i | ||||
\(598\) | −243.600 | − | 243.600i | −0.407358 | − | 0.407358i | ||||
\(599\) | − | 30.2472i | − | 0.0504962i | −0.999681 | − | 0.0252481i | \(-0.991962\pi\) | ||
0.999681 | − | 0.0252481i | \(-0.00803757\pi\) | |||||||
\(600\) | 147.813 | − | 240.738i | 0.246355 | − | 0.401231i | ||||
\(601\) | −880.877 | −1.46569 | −0.732843 | − | 0.680398i | \(-0.761807\pi\) | ||||
−0.732843 | + | 0.680398i | \(0.761807\pi\) | |||||||
\(602\) | −250.772 | + | 250.772i | −0.416565 | + | 0.416565i | ||||
\(603\) | −189.373 | − | 189.373i | −0.314051 | − | 0.314051i | ||||
\(604\) | − | 181.181i | − | 0.299969i | ||||||
\(605\) | −91.1831 | + | 322.773i | −0.150716 | + | 0.533510i | ||||
\(606\) | −276.034 | −0.455501 | ||||||||
\(607\) | 313.283 | − | 313.283i | 0.516117 | − | 0.516117i | −0.400277 | − | 0.916394i | \(-0.631086\pi\) |
0.916394 | + | 0.400277i | \(0.131086\pi\) | |||||||
\(608\) | −57.2865 | − | 57.2865i | −0.0942212 | − | 0.0942212i | ||||
\(609\) | − | 230.718i | − | 0.378847i | ||||||
\(610\) | −186.521 | − | 333.397i | −0.305772 | − | 0.546553i | ||||
\(611\) | −673.847 | −1.10286 | ||||||||
\(612\) | −10.2153 | + | 10.2153i | −0.0166916 | + | 0.0166916i | ||||
\(613\) | −83.0520 | − | 83.0520i | −0.135485 | − | 0.135485i | 0.636112 | − | 0.771597i | \(-0.280542\pi\) |
−0.771597 | + | 0.636112i | \(0.780542\pi\) | |||||||
\(614\) | − | 1070.71i | − | 1.74383i | ||||||
\(615\) | −155.633 | + | 87.0700i | −0.253062 | + | 0.141577i | ||||
\(616\) | 236.719 | 0.384283 | ||||||||
\(617\) | 238.533 | − | 238.533i | 0.386602 | − | 0.386602i | −0.486872 | − | 0.873473i | \(-0.661862\pi\) |
0.873473 | + | 0.486872i | \(0.161862\pi\) | |||||||
\(618\) | 238.242 | + | 238.242i | 0.385504 | + | 0.385504i | ||||
\(619\) | 26.3818i | 0.0426201i | 0.999773 | + | 0.0213100i | \(0.00678371\pi\) | ||||
−0.999773 | + | 0.0213100i | \(0.993216\pi\) | |||||||
\(620\) | 59.3828 | + | 16.7756i | 0.0957787 | + | 0.0270573i | ||||
\(621\) | −33.9265 | −0.0546320 | ||||||||
\(622\) | 47.1097 | − | 47.1097i | 0.0757390 | − | 0.0757390i | ||||
\(623\) | −292.109 | − | 292.109i | −0.468875 | − | 0.468875i | ||||
\(624\) | 776.520i | 1.24442i | ||||||||
\(625\) | 282.775 | + | 557.372i | 0.452440 | + | 0.891795i | ||||
\(626\) | 1199.90 | 1.91678 | ||||||||
\(627\) | −78.3405 | + | 78.3405i | −0.124945 | + | 0.124945i | ||||
\(628\) | −121.410 | − | 121.410i | −0.193328 | − | 0.193328i | ||||
\(629\) | − | 271.381i | − | 0.431448i | ||||||
\(630\) | 24.4022 | − | 86.3800i | 0.0387337 | − | 0.137111i | ||||
\(631\) | −672.112 | −1.06515 | −0.532577 | − | 0.846382i | \(-0.678776\pi\) | ||||
−0.532577 | + | 0.846382i | \(0.678776\pi\) | |||||||
\(632\) | 245.578 | − | 245.578i | 0.388572 | − | 0.388572i | ||||
\(633\) | 44.0194 | + | 44.0194i | 0.0695410 | + | 0.0695410i | ||||
\(634\) | − | 1310.13i | − | 2.06645i | ||||||
\(635\) | −13.7737 | − | 24.6198i | −0.0216909 | − | 0.0387713i | ||||
\(636\) | 126.026 | 0.198154 | ||||||||
\(637\) | −115.471 | + | 115.471i | −0.181273 | + | 0.181273i | ||||
\(638\) | 1104.27 | + | 1104.27i | 1.73083 | + | 1.73083i | ||||
\(639\) | − | 93.5652i | − | 0.146424i | ||||||
\(640\) | 674.107 | − | 377.133i | 1.05329 | − | 0.589271i | ||||
\(641\) | 582.851 | 0.909284 | 0.454642 | − | 0.890674i | \(-0.349767\pi\) | ||||
0.454642 | + | 0.890674i | \(0.349767\pi\) | |||||||
\(642\) | −205.812 | + | 205.812i | −0.320580 | + | 0.320580i | ||||
\(643\) | 488.888 | + | 488.888i | 0.760324 | + | 0.760324i | 0.976381 | − | 0.216057i | \(-0.0693196\pi\) |
−0.216057 | + | 0.976381i | \(0.569320\pi\) | |||||||
\(644\) | 19.2703i | 0.0299229i | ||||||||
\(645\) | 493.921 | + | 139.532i | 0.765770 | + | 0.216329i | ||||
\(646\) | 45.5380 | 0.0704923 | ||||||||
\(647\) | 501.243 | − | 501.243i | 0.774718 | − | 0.774718i | −0.204209 | − | 0.978927i | \(-0.565462\pi\) |
0.978927 | + | 0.204209i | \(0.0654623\pi\) | |||||||
\(648\) | 41.5182 | + | 41.5182i | 0.0640713 | + | 0.0640713i | ||||
\(649\) | 648.134i | 0.998665i | ||||||||
\(650\) | −1124.11 | − | 690.202i | −1.72940 | − | 1.06185i | ||||
\(651\) | −50.6978 | −0.0778769 | ||||||||
\(652\) | −224.778 | + | 224.778i | −0.344752 | + | 0.344752i | ||||
\(653\) | 385.795 | + | 385.795i | 0.590805 | + | 0.590805i | 0.937849 | − | 0.347044i | \(-0.112815\pi\) |
−0.347044 | + | 0.937849i | \(0.612815\pi\) | |||||||
\(654\) | − | 151.753i | − | 0.232038i | ||||||
\(655\) | 98.6354 | − | 349.154i | 0.150588 | − | 0.533059i | ||||
\(656\) | −395.735 | −0.603255 | ||||||||
\(657\) | 57.2934 | − | 57.2934i | 0.0872045 | − | 0.0872045i | ||||
\(658\) | 122.222 | + | 122.222i | 0.185748 | + | 0.185748i | ||||
\(659\) | 232.235i | 0.352405i | 0.984354 | + | 0.176203i | \(0.0563814\pi\) | ||||
−0.984354 | + | 0.176203i | \(0.943619\pi\) | |||||||
\(660\) | 64.6877 | + | 115.626i | 0.0980117 | + | 0.175191i | ||||
\(661\) | −1126.09 | −1.70361 | −0.851804 | − | 0.523860i | \(-0.824491\pi\) | ||||
−0.851804 | + | 0.523860i | \(0.824491\pi\) | |||||||
\(662\) | 115.051 | − | 115.051i | 0.173794 | − | 0.173794i | ||||
\(663\) | −123.338 | − | 123.338i | −0.186030 | − | 0.186030i | ||||
\(664\) | − | 898.260i | − | 1.35280i | ||||||
\(665\) | −53.8463 | + | 30.1246i | −0.0809719 | + | 0.0453002i | ||||
\(666\) | 426.566 | 0.640489 | ||||||||
\(667\) | 232.441 | − | 232.441i | 0.348488 | − | 0.348488i | ||||
\(668\) | 46.2760 | + | 46.2760i | 0.0692754 | + | 0.0692754i | ||||
\(669\) | 564.391i | 0.843633i | ||||||||
\(670\) | 971.526 | + | 274.455i | 1.45004 | + | 0.409634i | ||||
\(671\) | −463.287 | −0.690442 | ||||||||
\(672\) | 56.2851 | − | 56.2851i | 0.0837577 | − | 0.0837577i | ||||
\(673\) | 146.969 | + | 146.969i | 0.218379 | + | 0.218379i | 0.807815 | − | 0.589436i | \(-0.200650\pi\) |
−0.589436 | + | 0.807815i | \(0.700650\pi\) | |||||||
\(674\) | − | 966.416i | − | 1.43385i | ||||||
\(675\) | −126.341 | + | 30.2156i | −0.187172 | + | 0.0447638i | ||||
\(676\) | 418.580 | 0.619200 | ||||||||
\(677\) | 312.515 | − | 312.515i | 0.461617 | − | 0.461617i | −0.437568 | − | 0.899185i | \(-0.644160\pi\) |
0.899185 | + | 0.437568i | \(0.144160\pi\) | |||||||
\(678\) | −158.778 | − | 158.778i | −0.234186 | − | 0.234186i | ||||
\(679\) | 285.262i | 0.420121i | ||||||||
\(680\) | −38.2811 | + | 135.509i | −0.0562958 | + | 0.199278i | ||||
\(681\) | −243.717 | −0.357882 | ||||||||
\(682\) | 242.652 | − | 242.652i | 0.355794 | − | 0.355794i | ||||
\(683\) | −660.747 | − | 660.747i | −0.967419 | − | 0.967419i | 0.0320664 | − | 0.999486i | \(-0.489791\pi\) |
−0.999486 | + | 0.0320664i | \(0.989791\pi\) | |||||||
\(684\) | 15.6089i | 0.0228200i | ||||||||
\(685\) | 233.575 | + | 417.503i | 0.340985 | + | 0.609493i | ||||
\(686\) | 41.8883 | 0.0610616 | ||||||||
\(687\) | 15.1411 | − | 15.1411i | 0.0220395 | − | 0.0220395i | ||||
\(688\) | 805.354 | + | 805.354i | 1.17057 | + | 1.17057i | ||||
\(689\) | 1521.62i | 2.20845i | ||||||||
\(690\) | 111.610 | − | 62.4407i | 0.161753 | − | 0.0904938i | ||||
\(691\) | −1000.24 | −1.44752 | −0.723759 | − | 0.690053i | \(-0.757587\pi\) | ||||
−0.723759 | + | 0.690053i | \(0.757587\pi\) | |||||||
\(692\) | 145.042 | − | 145.042i | 0.209598 | − | 0.209598i | ||||
\(693\) | −76.9711 | − | 76.9711i | −0.111069 | − | 0.111069i | ||||
\(694\) | − | 1109.16i | − | 1.59822i | ||||||
\(695\) | 639.916 | + | 180.775i | 0.920742 | + | 0.260108i | ||||
\(696\) | −568.909 | −0.817398 | ||||||||
\(697\) | 62.8562 | − | 62.8562i | 0.0901811 | − | 0.0901811i | ||||
\(698\) | 47.5033 | + | 47.5033i | 0.0680563 | + | 0.0680563i | ||||
\(699\) | − | 525.620i | − | 0.751960i | ||||||
\(700\) | 17.1625 | + | 71.7620i | 0.0245179 | + | 0.102517i | ||||
\(701\) | 440.221 | 0.627989 | 0.313995 | − | 0.949425i | \(-0.398333\pi\) | ||||
0.313995 | + | 0.949425i | \(0.398333\pi\) | |||||||
\(702\) | 193.866 | − | 193.866i | 0.276163 | − | 0.276163i | ||||
\(703\) | −207.335 | − | 207.335i | −0.294928 | − | 0.294928i | ||||
\(704\) | − | 515.441i | − | 0.732160i | ||||||
\(705\) | 68.0057 | − | 240.729i | 0.0964620 | − | 0.341460i | ||||
\(706\) | 1179.76 | 1.67105 | ||||||||
\(707\) | −131.823 | + | 131.823i | −0.186454 | + | 0.186454i | ||||
\(708\) | 64.5686 | + | 64.5686i | 0.0911985 | + | 0.0911985i | ||||
\(709\) | 63.2033i | 0.0891443i | 0.999006 | + | 0.0445721i | \(0.0141925\pi\) | ||||
−0.999006 | + | 0.0445721i | \(0.985808\pi\) | |||||||
\(710\) | 172.204 | + | 307.806i | 0.242541 | + | 0.433530i | ||||
\(711\) | −159.703 | −0.224618 | ||||||||
\(712\) | −720.289 | + | 720.289i | −1.01164 | + | 1.01164i | ||||
\(713\) | −51.0766 | − | 51.0766i | −0.0716361 | − | 0.0716361i | ||||
\(714\) | 44.7420i | 0.0626639i | ||||||||
\(715\) | −1396.05 | + | 781.030i | −1.95252 | + | 1.09235i | ||||
\(716\) | −106.295 | −0.148456 | ||||||||
\(717\) | 13.0691 | − | 13.0691i | 0.0182275 | − | 0.0182275i | ||||
\(718\) | 976.633 | + | 976.633i | 1.36021 | + | 1.36021i | ||||
\(719\) | − | 934.275i | − | 1.29941i | −0.760187 | − | 0.649704i | \(-0.774893\pi\) | ||
0.760187 | − | 0.649704i | \(-0.225107\pi\) | |||||||
\(720\) | −277.409 | − | 78.3676i | −0.385290 | − | 0.108844i | ||||
\(721\) | 227.549 | 0.315602 | ||||||||
\(722\) | −542.557 | + | 542.557i | −0.751464 | + | 0.751464i | ||||
\(723\) | 265.802 | + | 265.802i | 0.367638 | + | 0.367638i | ||||
\(724\) | 211.180i | 0.291686i | ||||||||
\(725\) | 658.586 | − | 1072.62i | 0.908394 | − | 1.47947i | ||||
\(726\) | 262.789 | 0.361968 | ||||||||
\(727\) | −584.907 | + | 584.907i | −0.804548 | + | 0.804548i | −0.983803 | − | 0.179254i | \(-0.942631\pi\) |
0.179254 | + | 0.983803i | \(0.442631\pi\) | |||||||
\(728\) | 284.731 | + | 284.731i | 0.391114 | + | 0.391114i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −83.0342 | + | 293.928i | −0.113746 | + | 0.402641i | ||||
\(731\) | −255.835 | −0.349980 | ||||||||
\(732\) | −46.1537 | + | 46.1537i | −0.0630515 | + | 0.0630515i | ||||
\(733\) | −281.681 | − | 281.681i | −0.384285 | − | 0.384285i | 0.488358 | − | 0.872643i | \(-0.337596\pi\) |
−0.872643 | + | 0.488358i | \(0.837596\pi\) | |||||||
\(734\) | 231.973i | 0.316040i | ||||||||
\(735\) | −29.5981 | − | 52.9051i | −0.0402695 | − | 0.0719798i | ||||
\(736\) | 113.411 | 0.154091 | ||||||||
\(737\) | 865.704 | − | 865.704i | 1.17463 | − | 1.17463i | ||||
\(738\) | 98.7995 | + | 98.7995i | 0.133875 | + | 0.133875i | ||||
\(739\) | 892.992i | 1.20838i | 0.796841 | + | 0.604189i | \(0.206503\pi\) | ||||
−0.796841 | + | 0.604189i | \(0.793497\pi\) | |||||||
\(740\) | −306.014 | + | 171.201i | −0.413533 | + | 0.231353i | ||||
\(741\) | −188.460 | −0.254332 | ||||||||
\(742\) | 275.991 | − | 275.991i | 0.371956 | − | 0.371956i | ||||
\(743\) | 305.538 | + | 305.538i | 0.411222 | + | 0.411222i | 0.882164 | − | 0.470942i | \(-0.156086\pi\) |
−0.470942 | + | 0.882164i | \(0.656086\pi\) | |||||||
\(744\) | 125.012i | 0.168027i | ||||||||
\(745\) | −224.235 | − | 63.3462i | −0.300987 | − | 0.0850284i | ||||
\(746\) | −20.8448 | −0.0279421 | ||||||||
\(747\) | −292.077 | + | 292.077i | −0.391000 | + | 0.391000i | ||||
\(748\) | −46.6984 | − | 46.6984i | −0.0624310 | − | 0.0624310i | ||||
\(749\) | 196.575i | 0.262450i | ||||||||
\(750\) | 360.019 | − | 331.929i | 0.480026 | − | 0.442572i | ||||
\(751\) | 562.121 | 0.748496 | 0.374248 | − | 0.927329i | \(-0.377901\pi\) | ||||
0.374248 | + | 0.927329i | \(0.377901\pi\) | |||||||
\(752\) | 392.517 | − | 392.517i | 0.521964 | − | 0.521964i | ||||
\(753\) | 73.0796 | + | 73.0796i | 0.0970513 | + | 0.0970513i | ||||
\(754\) | 2656.48i | 3.52319i | ||||||||
\(755\) | −220.772 | + | 781.497i | −0.292413 | + | 1.03510i | ||||
\(756\) | −15.3361 | −0.0202858 | ||||||||
\(757\) | 370.109 | − | 370.109i | 0.488915 | − | 0.488915i | −0.419048 | − | 0.907964i | \(-0.637636\pi\) |
0.907964 | + | 0.419048i | \(0.137636\pi\) | |||||||
\(758\) | −358.814 | − | 358.814i | −0.473370 | − | 0.473370i | ||||
\(759\) | − | 155.092i | − | 0.204338i | ||||||
\(760\) | 74.2820 | + | 132.775i | 0.0977395 | + | 0.174705i | ||||
\(761\) | −466.002 | −0.612354 | −0.306177 | − | 0.951975i | \(-0.599050\pi\) | ||||
−0.306177 | + | 0.951975i | \(0.599050\pi\) | |||||||
\(762\) | −15.6292 | + | 15.6292i | −0.0205108 | + | 0.0205108i | ||||
\(763\) | −72.4712 | − | 72.4712i | −0.0949819 | − | 0.0949819i | ||||
\(764\) | − | 362.308i | − | 0.474225i | ||||||
\(765\) | 56.5094 | − | 31.6145i | 0.0738685 | − | 0.0413262i | ||||
\(766\) | −264.115 | −0.344798 | ||||||||
\(767\) | −779.592 | + | 779.592i | −1.01642 | + | 1.01642i | ||||
\(768\) | −243.814 | − | 243.814i | −0.317466 | − | 0.317466i | ||||
\(769\) | 216.013i | 0.280901i | 0.990088 | + | 0.140451i | \(0.0448551\pi\) | ||||
−0.990088 | + | 0.140451i | \(0.955145\pi\) | |||||||
\(770\) | 394.879 | + | 111.553i | 0.512830 | + | 0.144874i | ||||
\(771\) | 549.972 | 0.713323 | ||||||||
\(772\) | −27.5853 | + | 27.5853i | −0.0357323 | + | 0.0357323i | ||||
\(773\) | −290.907 | − | 290.907i | −0.376335 | − | 0.376335i | 0.493443 | − | 0.869778i | \(-0.335738\pi\) |
−0.869778 | + | 0.493443i | \(0.835738\pi\) | |||||||
\(774\) | − | 402.130i | − | 0.519548i | ||||||
\(775\) | −235.697 | − | 144.717i | −0.304125 | − | 0.186732i | ||||
\(776\) | 703.406 | 0.906451 | ||||||||
\(777\) | 203.711 | − | 203.711i | 0.262176 | − | 0.262176i | ||||
\(778\) | −1137.81 | − | 1137.81i | −1.46249 | − | 1.46249i | ||||
\(779\) | − | 96.0441i | − | 0.123292i | ||||||
\(780\) | −61.2700 | + | 216.886i | −0.0785513 | + | 0.278059i | ||||
\(781\) | 427.726 | 0.547665 | ||||||||
\(782\) | −45.0763 | + | 45.0763i | −0.0576423 | + | 0.0576423i | ||||
\(783\) | 184.986 | + | 184.986i | 0.236253 | + | 0.236253i | ||||
\(784\) | − | 134.524i | − | 0.171587i | ||||||
\(785\) | 375.742 | + | 671.621i | 0.478652 | + | 0.855568i | ||||
\(786\) | −284.266 | −0.361662 | ||||||||
\(787\) | 310.573 | − | 310.573i | 0.394629 | − | 0.394629i | −0.481705 | − | 0.876334i | \(-0.659982\pi\) |
0.876334 | + | 0.481705i | \(0.159982\pi\) | |||||||
\(788\) | −10.1391 | − | 10.1391i | −0.0128669 | − | 0.0128669i | ||||
\(789\) | 0.00369569i | 4.68402e-6i | ||||||||
\(790\) | 525.385 | − | 293.930i | 0.665044 | − | 0.372063i | ||||
\(791\) | −151.652 | −0.191722 | ||||||||
\(792\) | −189.797 | + | 189.797i | −0.239643 | + | 0.239643i | ||||
\(793\) | −557.253 | − | 557.253i | −0.702715 | − | 0.702715i | ||||
\(794\) | − | 1067.88i | − | 1.34494i | ||||||
\(795\) | −543.593 | − | 153.564i | −0.683765 | − | 0.193163i | ||||
\(796\) | −132.962 | −0.167038 | ||||||||
\(797\) | −762.912 | + | 762.912i | −0.957230 | + | 0.957230i | −0.999122 | − | 0.0418921i | \(-0.986661\pi\) |
0.0418921 | + | 0.999122i | \(0.486661\pi\) | |||||||
\(798\) | 34.1828 | + | 34.1828i | 0.0428356 | + | 0.0428356i | ||||
\(799\) | 124.690i | 0.156058i | ||||||||
\(800\) | 422.339 | − | 101.006i | 0.527924 | − | 0.126258i | ||||
\(801\) | 468.416 | 0.584789 | ||||||||
\(802\) | 200.109 | − | 200.109i | 0.249513 | − | 0.249513i | ||||
\(803\) | 261.912 | + | 261.912i | 0.326167 | + | 0.326167i | ||||
\(804\) | − | 172.487i | − | 0.214536i | ||||||
\(805\) | 23.4811 | − | 83.1195i | 0.0291691 | − | 0.103254i | ||||
\(806\) | 583.735 | 0.724237 | ||||||||
\(807\) | −13.2775 | + | 13.2775i | −0.0164529 | + | 0.0164529i | ||||
\(808\) | 325.051 | + | 325.051i | 0.402291 | + | 0.402291i | ||||
\(809\) | 1212.68i | 1.49898i | 0.662015 | + | 0.749490i | \(0.269701\pi\) | ||||
−0.662015 | + | 0.749490i | \(0.730299\pi\) | |||||||
\(810\) | 49.6928 | + | 88.8234i | 0.0613491 | + | 0.109658i | ||||
\(811\) | −971.089 | −1.19740 | −0.598699 | − | 0.800974i | \(-0.704315\pi\) | ||||
−0.598699 | + | 0.800974i | \(0.704315\pi\) | |||||||
\(812\) | 105.072 | − | 105.072i | 0.129400 | − | 0.129400i | ||||
\(813\) | −518.473 | − | 518.473i | −0.637728 | − | 0.637728i | ||||
\(814\) | 1950.01i | 2.39559i | ||||||||
\(815\) | 1243.44 | − | 695.651i | 1.52570 | − | 0.853559i | ||||
\(816\) | 143.689 | 0.176089 | ||||||||
\(817\) | −195.458 | + | 195.458i | −0.239238 | + | 0.239238i | ||||
\(818\) | −501.701 | − | 501.701i | −0.613327 | − | 0.613327i | ||||
\(819\) | − | 185.166i | − | 0.226088i | ||||||
\(820\) | −110.531 | − | 31.2248i | −0.134794 | − | 0.0380790i | ||||
\(821\) | −997.382 | −1.21484 | −0.607419 | − | 0.794382i | \(-0.707795\pi\) | ||||
−0.607419 | + | 0.794382i | \(0.707795\pi\) | |||||||
\(822\) | 265.040 | − | 265.040i | 0.322433 | − | 0.322433i | ||||
\(823\) | 475.439 | + | 475.439i | 0.577690 | + | 0.577690i | 0.934266 | − | 0.356576i | \(-0.116056\pi\) |
−0.356576 | + | 0.934266i | \(0.616056\pi\) | |||||||
\(824\) | − | 561.096i | − | 0.680942i | ||||||
\(825\) | −138.128 | − | 577.558i | −0.167428 | − | 0.700070i | ||||
\(826\) | 282.805 | 0.342379 | ||||||||
\(827\) | −302.620 | + | 302.620i | −0.365925 | + | 0.365925i | −0.865989 | − | 0.500064i | \(-0.833310\pi\) |
0.500064 | + | 0.865989i | \(0.333310\pi\) | |||||||
\(828\) | −15.4506 | − | 15.4506i | −0.0186602 | − | 0.0186602i | ||||
\(829\) | − | 317.984i | − | 0.383576i | −0.981436 | − | 0.191788i | \(-0.938571\pi\) | ||
0.981436 | − | 0.191788i | \(-0.0614286\pi\) | |||||||
\(830\) | 423.302 | − | 1498.42i | 0.510002 | − | 1.80533i | ||||
\(831\) | −106.881 | −0.128618 | ||||||||
\(832\) | 619.985 | − | 619.985i | 0.745174 | − | 0.745174i | ||||
\(833\) | 21.3670 | + | 21.3670i | 0.0256507 | + | 0.0256507i | ||||
\(834\) | − | 520.993i | − | 0.624691i | ||||||
\(835\) | −143.216 | − | 255.992i | −0.171516 | − | 0.306577i | ||||
\(836\) | −71.3549 | −0.0853528 | ||||||||
\(837\) | 40.6487 | − | 40.6487i | 0.0485648 | − | 0.0485648i | ||||
\(838\) | −291.171 | − | 291.171i | −0.347460 | − | 0.347460i | ||||
\(839\) | 755.271i | 0.900204i | 0.892977 | + | 0.450102i | \(0.148612\pi\) | ||||
−0.892977 | + | 0.450102i | \(0.851388\pi\) | |||||||
\(840\) | −130.455 | + | 72.9836i | −0.155303 | + | 0.0868853i | ||||
\(841\) | −1693.80 | −2.01403 | ||||||||
\(842\) | −710.110 | + | 710.110i | −0.843361 | + | 0.843361i | ||||
\(843\) | 212.365 | + | 212.365i | 0.251916 | + | 0.251916i | ||||
\(844\) | 40.0943i | 0.0475051i | ||||||||
\(845\) | −1805.48 | − | 510.044i | −2.13666 | − | 0.603603i | ||||
\(846\) | −195.992 | −0.231669 | ||||||||
\(847\) | 125.497 | − | 125.497i | 0.148167 | − | 0.148167i | ||||
\(848\) | −886.345 | − | 886.345i | −1.04522 | − | 1.04522i | ||||
\(849\) | − | 503.704i | − | 0.593291i | ||||||
\(850\) | −127.716 | + | 208.008i | −0.150255 | + | 0.244715i | ||||
\(851\) | 410.465 | 0.482332 | ||||||||
\(852\) | 42.6110 | − | 42.6110i | 0.0500130 | − | 0.0500130i | ||||
\(853\) | 672.027 | + | 672.027i | 0.787840 | + | 0.787840i | 0.981140 | − | 0.193300i | \(-0.0619190\pi\) |
−0.193300 | + | 0.981140i | \(0.561919\pi\) | |||||||
\(854\) | 202.149i | 0.236709i | ||||||||
\(855\) | 19.0197 | − | 67.3266i | 0.0222452 | − | 0.0787445i | ||||
\(856\) | 484.719 | 0.566261 | ||||||||
\(857\) | 101.904 | − | 101.904i | 0.118907 | − | 0.118907i | −0.645149 | − | 0.764057i | \(-0.723205\pi\) |
0.764057 | + | 0.645149i | \(0.223205\pi\) | |||||||
\(858\) | 886.245 | + | 886.245i | 1.03292 | + | 1.03292i | ||||
\(859\) | − | 152.886i | − | 0.177982i | −0.996032 | − | 0.0889909i | \(-0.971636\pi\) | ||
0.996032 | − | 0.0889909i | \(-0.0283642\pi\) | |||||||
\(860\) | 161.394 | + | 288.485i | 0.187668 | + | 0.335447i | ||||
\(861\) | 94.3653 | 0.109600 | ||||||||
\(862\) | 335.353 | − | 335.353i | 0.389041 | − | 0.389041i | ||||
\(863\) | 181.809 | + | 181.809i | 0.210671 | + | 0.210671i | 0.804553 | − | 0.593881i | \(-0.202405\pi\) |
−0.593881 | + | 0.804553i | \(0.702405\pi\) | |||||||
\(864\) | 90.2570i | 0.104464i | ||||||||
\(865\) | −802.351 | + | 448.880i | −0.927574 | + | 0.518937i | ||||
\(866\) | −1897.22 | −2.19078 | ||||||||
\(867\) | 331.129 | − | 331.129i | 0.381925 | − | 0.381925i | ||||
\(868\) | −23.0886 | − | 23.0886i | −0.0265997 | − | 0.0265997i | ||||
\(869\) | − | 730.072i | − | 0.840129i | ||||||
\(870\) | −949.019 | − | 268.096i | −1.09083 | − | 0.308157i | ||||
\(871\) | 2082.58 | 2.39102 | ||||||||
\(872\) | −178.701 | + | 178.701i | −0.204932 | + | 0.204932i | ||||
\(873\) | −228.719 | − | 228.719i | −0.261991 | − | 0.261991i | ||||
\(874\) | 68.8764i | 0.0788059i | ||||||||
\(875\) | 13.4150 | − | 330.447i | 0.0153314 | − | 0.377653i | ||||
\(876\) | 52.1846 | 0.0595714 | ||||||||
\(877\) | 342.206 | − | 342.206i | 0.390201 | − | 0.390201i | −0.484558 | − | 0.874759i | \(-0.661020\pi\) |
0.874759 | + | 0.484558i | \(0.161020\pi\) | |||||||
\(878\) | −146.424 | − | 146.424i | −0.166769 | − | 0.166769i | ||||
\(879\) | 589.495i | 0.670643i | ||||||||
\(880\) | 358.252 | − | 1268.15i | 0.407104 | − | 1.44108i | ||||
\(881\) | 1421.22 | 1.61318 | 0.806592 | − | 0.591108i | \(-0.201309\pi\) | ||||
0.806592 | + | 0.591108i | \(0.201309\pi\) | |||||||
\(882\) | −33.5853 | + | 33.5853i | −0.0380786 | + | 0.0380786i | ||||
\(883\) | −1050.05 | − | 1050.05i | −1.18919 | − | 1.18919i | −0.977292 | − | 0.211896i | \(-0.932036\pi\) |
−0.211896 | − | 0.977292i | \(-0.567964\pi\) | |||||||
\(884\) | − | 112.340i | − | 0.127081i | ||||||
\(885\) | −199.829 | − | 357.184i | −0.225795 | − | 0.403598i | ||||
\(886\) | −967.106 | −1.09154 | ||||||||
\(887\) | 798.714 | − | 798.714i | 0.900467 | − | 0.900467i | −0.0950093 | − | 0.995476i | \(-0.530288\pi\) |
0.995476 | + | 0.0950093i | \(0.0302881\pi\) | |||||||
\(888\) | −502.314 | − | 502.314i | −0.565669 | − | 0.565669i | ||||
\(889\) | 14.9278i | 0.0167916i | ||||||||
\(890\) | −1540.97 | + | 862.107i | −1.73143 | + | 0.968660i | ||||
\(891\) | 123.428 | 0.138528 | ||||||||
\(892\) | −257.032 | + | 257.032i | −0.288153 | + | 0.288153i | ||||
\(893\) | 95.2630 | + | 95.2630i | 0.106678 | + | 0.106678i | ||||
\(894\) | 182.563i | 0.204209i | ||||||||
\(895\) | 458.485 | + | 129.521i | 0.512273 | + | 0.144717i | ||||
\(896\) | −408.732 | −0.456174 | ||||||||
\(897\) | 186.549 | − | 186.549i | 0.207970 | − | 0.207970i | ||||
\(898\) | −304.093 | − | 304.093i | −0.338634 | − | 0.338634i | ||||
\(899\) | 556.995i | 0.619572i | ||||||||
\(900\) | −71.2982 | − | 43.7769i | −0.0792203 | − | 0.0486411i | ||||
\(901\) | 281.564 | 0.312501 | ||||||||
\(902\) | −451.654 | + | 451.654i | −0.500725 | + | 0.500725i | ||||
\(903\) | −192.041 | − | 192.041i | −0.212670 | − | 0.212670i | ||||
\(904\) | 373.947i | 0.413658i | ||||||||
\(905\) | 257.326 | − | 910.893i | 0.284338 | − | 1.00651i | ||||
\(906\) | 636.263 | 0.702277 | ||||||||
\(907\) | 807.370 | − | 807.370i | 0.890154 | − | 0.890154i | −0.104383 | − | 0.994537i | \(-0.533287\pi\) |
0.994537 | + | 0.104383i | \(0.0332867\pi\) | |||||||
\(908\) | −110.993 | − | 110.993i | −0.122239 | − | 0.122239i | ||||
\(909\) | − | 211.387i | − | 0.232549i | ||||||
\(910\) | 340.792 | + | 609.150i | 0.374497 | + | 0.669395i | ||||
\(911\) | −1177.41 | −1.29244 | −0.646220 | − | 0.763151i | \(-0.723651\pi\) | ||||
−0.646220 | + | 0.763151i | \(0.723651\pi\) | |||||||
\(912\) | 109.778 | − | 109.778i | 0.120371 | − | 0.120371i | ||||
\(913\) | −1335.21 | − | 1335.21i | −1.46244 | − | 1.46244i | ||||
\(914\) | − | 265.572i | − | 0.290560i | ||||||
\(915\) | 255.315 | − | 142.838i | 0.279033 | − | 0.156107i | ||||
\(916\) | 13.7910 | 0.0150557 | ||||||||
\(917\) | −135.754 | + | 135.754i | −0.148042 | + | 0.148042i | ||||
\(918\) | −35.8734 | − | 35.8734i | −0.0390778 | − | 0.0390778i | ||||
\(919\) | − | 858.202i | − | 0.933843i | −0.884299 | − | 0.466922i | \(-0.845363\pi\) | ||
0.884299 | − | 0.466922i | \(-0.154637\pi\) | |||||||
\(920\) | −204.958 | − | 57.9003i | −0.222780 | − | 0.0629351i | ||||
\(921\) | 819.948 | 0.890280 | ||||||||
\(922\) | −369.591 | + | 369.591i | −0.400857 | + | 0.400857i | ||||
\(923\) | 514.480 | + | 514.480i | 0.557399 | + | 0.557399i | ||||
\(924\) | − | 70.1077i | − | 0.0758741i | ||||||
\(925\) | 1528.55 | − | 365.568i | 1.65249 | − | 0.395209i | ||||
\(926\) | 1868.20 | 2.01750 | ||||||||
\(927\) | −182.445 | + | 182.445i | −0.196813 | + | 0.196813i | ||||
\(928\) | −618.380 | − | 618.380i | −0.666358 | − | 0.666358i | ||||
\(929\) | 874.985i | 0.941857i | 0.882171 | + | 0.470929i | \(0.156081\pi\) | ||||
−0.882171 | + | 0.470929i | \(0.843919\pi\) | |||||||
\(930\) | −58.9114 | + | 208.537i | −0.0633456 | + | 0.224233i | ||||
\(931\) | 32.6487 | 0.0350684 | ||||||||
\(932\) | 239.375 | − | 239.375i | 0.256841 | − | 0.256841i | ||||
\(933\) | 36.0766 | + | 36.0766i | 0.0386673 | + | 0.0386673i | ||||
\(934\) | − | 161.746i | − | 0.173176i | ||||||
\(935\) | 144.523 | + | 258.329i | 0.154570 | + | 0.276287i | ||||
\(936\) | −456.586 | −0.487805 | ||||||||
\(937\) | −758.907 | + | 758.907i | −0.809932 | + | 0.809932i | −0.984623 | − | 0.174691i | \(-0.944107\pi\) |
0.174691 | + | 0.984623i | \(0.444107\pi\) | |||||||
\(938\) | −377.738 | − | 377.738i | −0.402706 | − | 0.402706i | ||||
\(939\) | 918.885i | 0.978578i | ||||||||
\(940\) | 140.603 | − | 78.6611i | 0.149577 | − | 0.0836820i | ||||
\(941\) | 994.076 | 1.05640 | 0.528202 | − | 0.849119i | \(-0.322866\pi\) | ||||
0.528202 | + | 0.849119i | \(0.322866\pi\) | |||||||
\(942\) | 426.360 | − | 426.360i | 0.452611 | − | 0.452611i | ||||
\(943\) | 95.0702 | + | 95.0702i | 0.100817 | + | 0.100817i | ||||
\(944\) | − | 908.226i | − | 0.962104i | ||||||
\(945\) | 66.1497 | + | 18.6872i | 0.0699997 | + | 0.0197748i | ||||
\(946\) | 1838.31 | 1.94324 | ||||||||
\(947\) | −402.372 | + | 402.372i | −0.424891 | + | 0.424891i | −0.886884 | − | 0.461993i | \(-0.847135\pi\) |
0.461993 | + | 0.886884i | \(0.347135\pi\) | |||||||
\(948\) | −72.7314 | − | 72.7314i | −0.0767209 | − | 0.0767209i | ||||
\(949\) | 630.069i | 0.663930i | ||||||||
\(950\) | 61.3427 | + | 256.493i | 0.0645712 | + | 0.269993i | ||||
\(951\) | 1003.30 | 1.05499 | ||||||||
\(952\) | 52.6872 | − | 52.6872i | 0.0553437 | − | 0.0553437i | ||||
\(953\) | −103.317 | − | 103.317i | −0.108413 | − | 0.108413i | 0.650820 | − | 0.759232i | \(-0.274425\pi\) |
−0.759232 | + | 0.650820i | \(0.774425\pi\) | |||||||
\(954\) | 442.571i | 0.463911i | ||||||||
\(955\) | −441.476 | + | 1562.76i | −0.462279 | + | 1.63639i | ||||
\(956\) | 11.9038 | 0.0124516 | ||||||||
\(957\) | −845.648 | + | 845.648i | −0.883645 | + | 0.883645i | ||||
\(958\) | −766.089 | − | 766.089i | −0.799675 | − | 0.799675i | ||||
\(959\) | − | 253.145i | − | 0.263968i | ||||||
\(960\) | 158.917 | + | 284.057i | 0.165539 | + | 0.295893i | ||||
\(961\) | −838.606 | −0.872639 | ||||||||
\(962\) | −2345.52 | + | 2345.52i | −2.43817 | + | 2.43817i | ||||
\(963\) | −157.611 | − | 157.611i | −0.163666 | − | 0.163666i | ||||
\(964\) | 242.101i | 0.251142i | ||||||||
\(965\) | 152.598 | − | 85.3719i | 0.158133 | − | 0.0884682i | ||||
\(966\) | −67.6725 | −0.0700543 | ||||||||
\(967\) | −358.664 | + | 358.664i | −0.370904 | + | 0.370904i | −0.867806 | − | 0.496902i | \(-0.834471\pi\) |
0.496902 | + | 0.867806i | \(0.334471\pi\) | |||||||
\(968\) | −309.454 | − | 309.454i | −0.319684 | − | 0.319684i | ||||
\(969\) | 34.8730i | 0.0359886i | ||||||||
\(970\) | 1173.38 | + | 331.478i | 1.20967 | + | 0.341729i | ||||
\(971\) | −261.240 | −0.269042 | −0.134521 | − | 0.990911i | \(-0.542950\pi\) | ||||
−0.134521 | + | 0.990911i | \(0.542950\pi\) | |||||||
\(972\) | 12.2962 | − | 12.2962i | 0.0126504 | − | 0.0126504i | ||||
\(973\) | −248.805 | − | 248.805i | −0.255709 | − | 0.255709i | ||||
\(974\) | 1706.04i | 1.75158i | ||||||||
\(975\) | 528.557 | − | 860.845i | 0.542109 | − | 0.882918i | ||||
\(976\) | 649.201 | 0.665165 | ||||||||
\(977\) | 510.551 | − | 510.551i | 0.522570 | − | 0.522570i | −0.395777 | − | 0.918347i | \(-0.629525\pi\) |
0.918347 | + | 0.395777i | \(0.129525\pi\) | |||||||
\(978\) | −789.364 | − | 789.364i | −0.807121 | − | 0.807121i | ||||
\(979\) | 2141.33i | 2.18726i | ||||||||
\(980\) | 10.6144 | − | 37.5732i | 0.0108310 | − | 0.0383400i | ||||
\(981\) | 116.212 | 0.118463 | ||||||||
\(982\) | 557.027 | − | 557.027i | 0.567237 | − | 0.567237i | ||||
\(983\) | 920.586 | + | 920.586i | 0.936507 | + | 0.936507i | 0.998101 | − | 0.0615942i | \(-0.0196185\pi\) |
−0.0615942 | + | 0.998101i | \(0.519618\pi\) | |||||||
\(984\) | − | 232.688i | − | 0.236472i | ||||||
\(985\) | 31.3788 | + | 56.0881i | 0.0318567 | + | 0.0569422i | ||||
\(986\) | 491.561 | 0.498541 | ||||||||
\(987\) | −93.5979 | + | 93.5979i | −0.0948307 | + | 0.0948307i | ||||
\(988\) | −85.8275 | − | 85.8275i | −0.0868700 | − | 0.0868700i | ||||
\(989\) | − | 386.952i | − | 0.391255i | ||||||
\(990\) | −406.049 | + | 227.167i | −0.410151 | + | 0.229461i | ||||
\(991\) | 189.108 | 0.190825 | 0.0954126 | − | 0.995438i | \(-0.469583\pi\) | ||||
0.0954126 | + | 0.995438i | \(0.469583\pi\) | |||||||
\(992\) | −135.883 | + | 135.883i | −0.136978 | + | 0.136978i | ||||
\(993\) | 88.1063 | + | 88.1063i | 0.0887273 | + | 0.0887273i | ||||
\(994\) | − | 186.633i | − | 0.187759i | ||||||
\(995\) | 573.513 | + | 162.016i | 0.576395 | + | 0.162831i | ||||
\(996\) | −266.033 | −0.267101 | ||||||||
\(997\) | 67.1053 | − | 67.1053i | 0.0673072 | − | 0.0673072i | −0.672652 | − | 0.739959i | \(-0.734845\pi\) |
0.739959 | + | 0.672652i | \(0.234845\pi\) | |||||||
\(998\) | 1064.65 | + | 1064.65i | 1.06678 | + | 1.06678i | ||||
\(999\) | 326.664i | 0.326991i |
(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 | 105.3.l.a.43.2 | yes | 24 | |
3.2 | odd | 2 | 315.3.o.b.253.11 | 24 | |||
5.2 | odd | 4 | inner | 105.3.l.a.22.2 | ✓ | 24 | |
5.3 | odd | 4 | 525.3.l.e.232.11 | 24 | |||
5.4 | even | 2 | 525.3.l.e.43.11 | 24 | |||
15.2 | even | 4 | 315.3.o.b.127.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.l.a.22.2 | ✓ | 24 | 5.2 | odd | 4 | inner | |
105.3.l.a.43.2 | yes | 24 | 1.1 | even | 1 | trivial | |
315.3.o.b.127.11 | 24 | 15.2 | even | 4 | |||
315.3.o.b.253.11 | 24 | 3.2 | odd | 2 | |||
525.3.l.e.43.11 | 24 | 5.4 | even | 2 | |||
525.3.l.e.232.11 | 24 | 5.3 | odd | 4 |