Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(83,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.k (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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 83.3 | ||
Character | \(\chi\) | \(=\) | 210.83 |
Dual form | 210.3.k.b.167.3 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −2.74188 | + | 1.21742i | −0.913959 | + | 0.405806i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −3.32079 | + | 3.73796i | −0.664159 | + | 0.747592i | ||||
\(6\) | −3.95930 | − | 1.52446i | −0.659883 | − | 0.254077i | ||||
\(7\) | −6.61294 | − | 2.29543i | −0.944706 | − | 0.327919i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 6.03579 | − | 6.67602i | 0.670643 | − | 0.741780i | ||||
\(10\) | −7.05875 | + | 0.417165i | −0.705875 | + | 0.0417165i | ||||
\(11\) | − | 10.5733i | − | 0.961209i | −0.876938 | − | 0.480604i | \(-0.840417\pi\) | ||
0.876938 | − | 0.480604i | \(-0.159583\pi\) | |||||||
\(12\) | −2.43484 | − | 5.48376i | −0.202903 | − | 0.456980i | ||||
\(13\) | 14.9899 | − | 14.9899i | 1.15307 | − | 1.15307i | 0.167134 | − | 0.985934i | \(-0.446549\pi\) |
0.985934 | − | 0.167134i | \(-0.0534512\pi\) | |||||||
\(14\) | −4.31751 | − | 8.90837i | −0.308394 | − | 0.636312i | ||||
\(15\) | 4.55455 | − | 14.2918i | 0.303637 | − | 0.952788i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −15.4921 | + | 15.4921i | −0.911302 | + | 0.911302i | −0.996375 | − | 0.0850728i | \(-0.972888\pi\) |
0.0850728 | + | 0.996375i | \(0.472888\pi\) | |||||||
\(18\) | 12.7118 | − | 0.640234i | 0.706212 | − | 0.0355686i | ||||
\(19\) | −17.3342 | −0.912329 | −0.456164 | − | 0.889896i | \(-0.650777\pi\) | ||||
−0.456164 | + | 0.889896i | \(0.650777\pi\) | |||||||
\(20\) | −7.47592 | − | 6.64159i | −0.373796 | − | 0.332079i | ||||
\(21\) | 20.9264 | − | 1.75692i | 0.996494 | − | 0.0836629i | ||||
\(22\) | 10.5733 | − | 10.5733i | 0.480604 | − | 0.480604i | ||||
\(23\) | −23.1753 | + | 23.1753i | −1.00762 | + | 1.00762i | −0.00765214 | + | 0.999971i | \(0.502436\pi\) |
−0.999971 | + | 0.00765214i | \(0.997564\pi\) | |||||||
\(24\) | 3.04892 | − | 7.91859i | 0.127038 | − | 0.329941i | ||||
\(25\) | −2.94466 | − | 24.8260i | −0.117787 | − | 0.993039i | ||||
\(26\) | 29.9798 | 1.15307 | ||||||||
\(27\) | −8.42188 | + | 25.6529i | −0.311922 | + | 0.950108i | ||||
\(28\) | 4.59086 | − | 13.2259i | 0.163959 | − | 0.472353i | ||||
\(29\) | −23.7038 | −0.817373 | −0.408686 | − | 0.912675i | \(-0.634013\pi\) | ||||
−0.408686 | + | 0.912675i | \(0.634013\pi\) | |||||||
\(30\) | 18.8464 | − | 9.73727i | 0.628212 | − | 0.324576i | ||||
\(31\) | − | 33.1422i | − | 1.06910i | −0.845136 | − | 0.534551i | \(-0.820481\pi\) | ||
0.845136 | − | 0.534551i | \(-0.179519\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 12.8721 | + | 28.9907i | 0.390064 | + | 0.878505i | ||||
\(34\) | −30.9843 | −0.911302 | ||||||||
\(35\) | 30.5404 | − | 17.0962i | 0.872584 | − | 0.488464i | ||||
\(36\) | 13.3520 | + | 12.0716i | 0.370890 | + | 0.335322i | ||||
\(37\) | −17.6315 | + | 17.6315i | −0.476526 | + | 0.476526i | −0.904019 | − | 0.427492i | \(-0.859397\pi\) |
0.427492 | + | 0.904019i | \(0.359397\pi\) | |||||||
\(38\) | −17.3342 | − | 17.3342i | −0.456164 | − | 0.456164i | ||||
\(39\) | −22.8515 | + | 59.3494i | −0.585935 | + | 1.52178i | ||||
\(40\) | −0.834330 | − | 14.1175i | −0.0208583 | − | 0.352938i | ||||
\(41\) | 11.8368 | 0.288703 | 0.144352 | − | 0.989526i | \(-0.453890\pi\) | ||||
0.144352 | + | 0.989526i | \(0.453890\pi\) | |||||||
\(42\) | 22.6833 | + | 19.1695i | 0.540079 | + | 0.456416i | ||||
\(43\) | −22.8095 | − | 22.8095i | −0.530453 | − | 0.530453i | 0.390254 | − | 0.920707i | \(-0.372387\pi\) |
−0.920707 | + | 0.390254i | \(0.872387\pi\) | |||||||
\(44\) | 21.1466 | 0.480604 | ||||||||
\(45\) | 4.91109 | + | 44.7312i | 0.109135 | + | 0.994027i | ||||
\(46\) | −46.3507 | −1.00762 | ||||||||
\(47\) | −12.6291 | + | 12.6291i | −0.268704 | + | 0.268704i | −0.828578 | − | 0.559874i | \(-0.810850\pi\) |
0.559874 | + | 0.828578i | \(0.310850\pi\) | |||||||
\(48\) | 10.9675 | − | 4.86967i | 0.228490 | − | 0.101451i | ||||
\(49\) | 38.4620 | + | 30.3591i | 0.784939 | + | 0.619574i | ||||
\(50\) | 21.8813 | − | 27.7706i | 0.437626 | − | 0.555413i | ||||
\(51\) | 23.6171 | − | 61.3379i | 0.463081 | − | 1.20270i | ||||
\(52\) | 29.9798 | + | 29.9798i | 0.576534 | + | 0.576534i | ||||
\(53\) | −15.3204 | + | 15.3204i | −0.289065 | + | 0.289065i | −0.836710 | − | 0.547646i | \(-0.815524\pi\) |
0.547646 | + | 0.836710i | \(0.315524\pi\) | |||||||
\(54\) | −34.0748 | + | 17.2310i | −0.631015 | + | 0.319093i | ||||
\(55\) | 39.5225 | + | 35.1117i | 0.718592 | + | 0.638395i | ||||
\(56\) | 17.8167 | − | 8.63502i | 0.318156 | − | 0.154197i | ||||
\(57\) | 47.5284 | − | 21.1030i | 0.833831 | − | 0.370228i | ||||
\(58\) | −23.7038 | − | 23.7038i | −0.408686 | − | 0.408686i | ||||
\(59\) | 31.0849i | 0.526863i | 0.964678 | + | 0.263431i | \(0.0848542\pi\) | ||||
−0.964678 | + | 0.263431i | \(0.915146\pi\) | |||||||
\(60\) | 28.5836 | + | 9.10910i | 0.476394 | + | 0.151818i | ||||
\(61\) | 48.6492i | 0.797528i | 0.917054 | + | 0.398764i | \(0.130561\pi\) | ||||
−0.917054 | + | 0.398764i | \(0.869439\pi\) | |||||||
\(62\) | 33.1422 | − | 33.1422i | 0.534551 | − | 0.534551i | ||||
\(63\) | −55.2387 | + | 30.2934i | −0.876804 | + | 0.480848i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 6.25326 | + | 105.810i | 0.0962039 | + | 1.62784i | ||||
\(66\) | −16.1186 | + | 41.8628i | −0.244221 | + | 0.634285i | ||||
\(67\) | −77.5784 | + | 77.5784i | −1.15789 | + | 1.15789i | −0.172957 | + | 0.984929i | \(0.555332\pi\) |
−0.984929 | + | 0.172957i | \(0.944668\pi\) | |||||||
\(68\) | −30.9843 | − | 30.9843i | −0.455651 | − | 0.455651i | ||||
\(69\) | 35.3299 | − | 91.7580i | 0.512027 | − | 1.32983i | ||||
\(70\) | 47.6367 | + | 13.4442i | 0.680524 | + | 0.192060i | ||||
\(71\) | − | 60.7725i | − | 0.855951i | −0.903790 | − | 0.427976i | \(-0.859227\pi\) | ||
0.903790 | − | 0.427976i | \(-0.140773\pi\) | |||||||
\(72\) | 1.28047 | + | 25.4236i | 0.0177843 | + | 0.353106i | ||||
\(73\) | 3.52743 | − | 3.52743i | 0.0483210 | − | 0.0483210i | −0.682533 | − | 0.730854i | \(-0.739122\pi\) |
0.730854 | + | 0.682533i | \(0.239122\pi\) | |||||||
\(74\) | −35.2630 | −0.476526 | ||||||||
\(75\) | 38.2975 | + | 64.4849i | 0.510633 | + | 0.859799i | ||||
\(76\) | − | 34.6685i | − | 0.456164i | ||||||
\(77\) | −24.2703 | + | 69.9206i | −0.315198 | + | 0.908059i | ||||
\(78\) | −82.2009 | + | 36.4979i | −1.05386 | + | 0.467922i | ||||
\(79\) | − | 99.4056i | − | 1.25830i | −0.777284 | − | 0.629150i | \(-0.783403\pi\) | ||
0.777284 | − | 0.629150i | \(-0.216597\pi\) | |||||||
\(80\) | 13.2832 | − | 14.9518i | 0.166040 | − | 0.186898i | ||||
\(81\) | −8.13854 | − | 80.5901i | −0.100476 | − | 0.994940i | ||||
\(82\) | 11.8368 | + | 11.8368i | 0.144352 | + | 0.144352i | ||||
\(83\) | −16.9196 | − | 16.9196i | −0.203851 | − | 0.203851i | 0.597797 | − | 0.801648i | \(-0.296043\pi\) |
−0.801648 | + | 0.597797i | \(0.796043\pi\) | |||||||
\(84\) | 3.51384 | + | 41.8528i | 0.0418315 | + | 0.498247i | ||||
\(85\) | −6.46278 | − | 109.355i | −0.0760327 | − | 1.28653i | ||||
\(86\) | − | 45.6189i | − | 0.530453i | ||||||
\(87\) | 64.9930 | − | 28.8574i | 0.747046 | − | 0.331695i | ||||
\(88\) | 21.1466 | + | 21.1466i | 0.240302 | + | 0.240302i | ||||
\(89\) | − | 17.6839i | − | 0.198695i | −0.995053 | − | 0.0993477i | \(-0.968324\pi\) | ||
0.995053 | − | 0.0993477i | \(-0.0316756\pi\) | |||||||
\(90\) | −39.8201 | + | 49.6423i | −0.442446 | + | 0.551581i | ||||
\(91\) | −133.535 | + | 64.7190i | −1.46742 | + | 0.711198i | ||||
\(92\) | −46.3507 | − | 46.3507i | −0.503811 | − | 0.503811i | ||||
\(93\) | 40.3479 | + | 90.8718i | 0.433848 | + | 0.977116i | ||||
\(94\) | −25.2582 | −0.268704 | ||||||||
\(95\) | 57.5634 | − | 64.7947i | 0.605931 | − | 0.682049i | ||||
\(96\) | 15.8372 | + | 6.09784i | 0.164971 | + | 0.0635192i | ||||
\(97\) | −34.7968 | − | 34.7968i | −0.358730 | − | 0.358730i | 0.504615 | − | 0.863345i | \(-0.331635\pi\) |
−0.863345 | + | 0.504615i | \(0.831635\pi\) | |||||||
\(98\) | 8.10289 | + | 68.8211i | 0.0826825 | + | 0.702256i | ||||
\(99\) | −70.5875 | − | 63.8182i | −0.713006 | − | 0.644628i | ||||
\(100\) | 49.6519 | − | 5.88933i | 0.496519 | − | 0.0588933i | ||||
\(101\) | 171.092 | 1.69398 | 0.846988 | − | 0.531612i | \(-0.178413\pi\) | ||||
0.846988 | + | 0.531612i | \(0.178413\pi\) | |||||||
\(102\) | 84.9551 | − | 37.7208i | 0.832893 | − | 0.369812i | ||||
\(103\) | −35.4145 | + | 35.4145i | −0.343831 | + | 0.343831i | −0.857805 | − | 0.513975i | \(-0.828172\pi\) |
0.513975 | + | 0.857805i | \(0.328172\pi\) | |||||||
\(104\) | 59.9595i | 0.576534i | ||||||||
\(105\) | −62.9249 | + | 84.0563i | −0.599284 | + | 0.800536i | ||||
\(106\) | −30.6409 | −0.289065 | ||||||||
\(107\) | 41.0523 | + | 41.0523i | 0.383667 | + | 0.383667i | 0.872421 | − | 0.488755i | \(-0.162549\pi\) |
−0.488755 | + | 0.872421i | \(0.662549\pi\) | |||||||
\(108\) | −51.3058 | − | 16.8438i | −0.475054 | − | 0.155961i | ||||
\(109\) | 168.808i | 1.54869i | 0.632761 | + | 0.774347i | \(0.281922\pi\) | ||||
−0.632761 | + | 0.774347i | \(0.718078\pi\) | |||||||
\(110\) | 4.41081 | + | 74.6343i | 0.0400983 | + | 0.678493i | ||||
\(111\) | 26.8785 | − | 69.8082i | 0.242149 | − | 0.628903i | ||||
\(112\) | 26.4518 | + | 9.18172i | 0.236176 | + | 0.0819797i | ||||
\(113\) | 18.9763 | − | 18.9763i | 0.167932 | − | 0.167932i | −0.618138 | − | 0.786070i | \(-0.712113\pi\) |
0.786070 | + | 0.618138i | \(0.212113\pi\) | |||||||
\(114\) | 68.6314 | + | 26.4254i | 0.602030 | + | 0.231801i | ||||
\(115\) | −9.66794 | − | 163.589i | −0.0840690 | − | 1.42251i | ||||
\(116\) | − | 47.4076i | − | 0.408686i | ||||||
\(117\) | −9.59704 | − | 190.549i | −0.0820260 | − | 1.62862i | ||||
\(118\) | −31.0849 | + | 31.0849i | −0.263431 | + | 0.263431i | ||||
\(119\) | 138.010 | − | 66.8874i | 1.15975 | − | 0.562079i | ||||
\(120\) | 19.4745 | + | 37.6927i | 0.162288 | + | 0.314106i | ||||
\(121\) | 9.20544 | 0.0760780 | ||||||||
\(122\) | −48.6492 | + | 48.6492i | −0.398764 | + | 0.398764i | ||||
\(123\) | −32.4552 | + | 14.4104i | −0.263863 | + | 0.117158i | ||||
\(124\) | 66.2843 | 0.534551 | ||||||||
\(125\) | 102.577 | + | 71.4349i | 0.820617 | + | 0.571479i | ||||
\(126\) | −85.5321 | − | 24.9453i | −0.678826 | − | 0.197978i | ||||
\(127\) | 132.611 | − | 132.611i | 1.04418 | − | 1.04418i | 0.0452000 | − | 0.998978i | \(-0.485607\pi\) |
0.998978 | − | 0.0452000i | \(-0.0143925\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 90.3094 | + | 34.7721i | 0.700073 | + | 0.269551i | ||||
\(130\) | −99.5566 | + | 112.063i | −0.765820 | + | 0.862024i | ||||
\(131\) | −247.227 | −1.88723 | −0.943613 | − | 0.331051i | \(-0.892597\pi\) | ||||
−0.943613 | + | 0.331051i | \(0.892597\pi\) | |||||||
\(132\) | −57.9814 | + | 25.7442i | −0.439253 | + | 0.195032i | ||||
\(133\) | 114.630 | + | 39.7896i | 0.861882 | + | 0.299170i | ||||
\(134\) | −155.157 | −1.15789 | ||||||||
\(135\) | −67.9222 | − | 116.669i | −0.503127 | − | 0.864212i | ||||
\(136\) | − | 61.9685i | − | 0.455651i | ||||||
\(137\) | 139.005 | + | 139.005i | 1.01463 | + | 1.01463i | 0.999891 | + | 0.0147404i | \(0.00469218\pi\) |
0.0147404 | + | 0.999891i | \(0.495308\pi\) | |||||||
\(138\) | 127.088 | − | 56.4281i | 0.920926 | − | 0.408899i | ||||
\(139\) | −186.326 | −1.34047 | −0.670237 | − | 0.742147i | \(-0.733808\pi\) | ||||
−0.670237 | + | 0.742147i | \(0.733808\pi\) | |||||||
\(140\) | 34.1925 | + | 61.0809i | 0.244232 | + | 0.436292i | ||||
\(141\) | 19.2525 | − | 50.0023i | 0.136543 | − | 0.354626i | ||||
\(142\) | 60.7725 | − | 60.7725i | 0.427976 | − | 0.427976i | ||||
\(143\) | −158.492 | − | 158.492i | −1.10834 | − | 1.10834i | ||||
\(144\) | −24.1432 | + | 26.7041i | −0.167661 | + | 0.185445i | ||||
\(145\) | 78.7155 | − | 88.6039i | 0.542865 | − | 0.611061i | ||||
\(146\) | 7.05487 | 0.0483210 | ||||||||
\(147\) | −142.418 | − | 36.4166i | −0.968829 | − | 0.247732i | ||||
\(148\) | −35.2630 | − | 35.2630i | −0.238263 | − | 0.238263i | ||||
\(149\) | −253.568 | −1.70180 | −0.850899 | − | 0.525329i | \(-0.823942\pi\) | ||||
−0.850899 | + | 0.525329i | \(0.823942\pi\) | |||||||
\(150\) | −26.1874 | + | 102.782i | −0.174583 | + | 0.685216i | ||||
\(151\) | 196.889 | 1.30390 | 0.651952 | − | 0.758261i | \(-0.273951\pi\) | ||||
0.651952 | + | 0.758261i | \(0.273951\pi\) | |||||||
\(152\) | 34.6685 | − | 34.6685i | 0.228082 | − | 0.228082i | ||||
\(153\) | 9.91860 | + | 196.933i | 0.0648274 | + | 1.28714i | ||||
\(154\) | −94.1908 | + | 45.6503i | −0.611629 | + | 0.296431i | ||||
\(155\) | 123.884 | + | 110.058i | 0.799252 | + | 0.710053i | ||||
\(156\) | −118.699 | − | 45.7030i | −0.760889 | − | 0.292968i | ||||
\(157\) | −94.2693 | − | 94.2693i | −0.600442 | − | 0.600442i | 0.339988 | − | 0.940430i | \(-0.389577\pi\) |
−0.940430 | + | 0.339988i | \(0.889577\pi\) | |||||||
\(158\) | 99.4056 | − | 99.4056i | 0.629150 | − | 0.629150i | ||||
\(159\) | 23.3554 | − | 60.6581i | 0.146889 | − | 0.381498i | ||||
\(160\) | 28.2350 | − | 1.66866i | 0.176469 | − | 0.0104291i | ||||
\(161\) | 206.454 | − | 100.060i | 1.28233 | − | 0.621489i | ||||
\(162\) | 72.4516 | − | 88.7286i | 0.447232 | − | 0.547708i | ||||
\(163\) | 144.119 | + | 144.119i | 0.884164 | + | 0.884164i | 0.993955 | − | 0.109791i | \(-0.0350181\pi\) |
−0.109791 | + | 0.993955i | \(0.535018\pi\) | |||||||
\(164\) | 23.6737i | 0.144352i | ||||||||
\(165\) | −151.112 | − | 48.1566i | −0.915828 | − | 0.291858i | ||||
\(166\) | − | 33.8392i | − | 0.203851i | ||||||
\(167\) | −81.7575 | + | 81.7575i | −0.489566 | + | 0.489566i | −0.908169 | − | 0.418603i | \(-0.862520\pi\) |
0.418603 | + | 0.908169i | \(0.362520\pi\) | |||||||
\(168\) | −38.3389 | + | 45.3666i | −0.228208 | + | 0.270039i | ||||
\(169\) | − | 280.393i | − | 1.65913i | ||||||
\(170\) | 102.892 | − | 115.818i | 0.605249 | − | 0.681282i | ||||
\(171\) | −104.626 | + | 115.724i | −0.611847 | + | 0.676747i | ||||
\(172\) | 45.6189 | − | 45.6189i | 0.265226 | − | 0.265226i | ||||
\(173\) | −147.722 | − | 147.722i | −0.853885 | − | 0.853885i | 0.136724 | − | 0.990609i | \(-0.456343\pi\) |
−0.990609 | + | 0.136724i | \(0.956343\pi\) | |||||||
\(174\) | 93.8504 | + | 36.1355i | 0.539370 | + | 0.207675i | ||||
\(175\) | −37.5134 | + | 170.932i | −0.214362 | + | 0.976754i | ||||
\(176\) | 42.2932i | 0.240302i | ||||||||
\(177\) | −37.8433 | − | 85.2310i | −0.213804 | − | 0.481531i | ||||
\(178\) | 17.6839 | − | 17.6839i | 0.0993477 | − | 0.0993477i | ||||
\(179\) | −213.765 | −1.19422 | −0.597109 | − | 0.802160i | \(-0.703684\pi\) | ||||
−0.597109 | + | 0.802160i | \(0.703684\pi\) | |||||||
\(180\) | −89.4624 | + | 9.82218i | −0.497013 | + | 0.0545677i | ||||
\(181\) | − | 31.8772i | − | 0.176117i | −0.996115 | − | 0.0880587i | \(-0.971934\pi\) | ||
0.996115 | − | 0.0880587i | \(-0.0280663\pi\) | |||||||
\(182\) | −198.254 | − | 68.8165i | −1.08931 | − | 0.378113i | ||||
\(183\) | −59.2264 | − | 133.390i | −0.323642 | − | 0.728908i | ||||
\(184\) | − | 92.7013i | − | 0.503811i | ||||||
\(185\) | −7.35524 | − | 124.456i | −0.0397580 | − | 0.672736i | ||||
\(186\) | −50.5239 | + | 131.220i | −0.271634 | + | 0.705482i | ||||
\(187\) | 163.803 | + | 163.803i | 0.875951 | + | 0.875951i | ||||
\(188\) | −25.2582 | − | 25.2582i | −0.134352 | − | 0.134352i | ||||
\(189\) | 114.578 | − | 150.309i | 0.606232 | − | 0.795288i | ||||
\(190\) | 122.358 | − | 7.23124i | 0.643990 | − | 0.0380592i | ||||
\(191\) | − | 40.4552i | − | 0.211808i | −0.994376 | − | 0.105904i | \(-0.966226\pi\) | ||
0.994376 | − | 0.105904i | \(-0.0337735\pi\) | |||||||
\(192\) | 9.73934 | + | 21.9350i | 0.0507257 | + | 0.114245i | ||||
\(193\) | 17.8770 | + | 17.8770i | 0.0926271 | + | 0.0926271i | 0.751902 | − | 0.659275i | \(-0.229137\pi\) |
−0.659275 | + | 0.751902i | \(0.729137\pi\) | |||||||
\(194\) | − | 69.5936i | − | 0.358730i | ||||||
\(195\) | −145.960 | − | 282.505i | −0.748515 | − | 1.44874i | ||||
\(196\) | −60.7182 | + | 76.9240i | −0.309787 | + | 0.392469i | ||||
\(197\) | −98.2874 | − | 98.2874i | −0.498921 | − | 0.498921i | 0.412181 | − | 0.911102i | \(-0.364767\pi\) |
−0.911102 | + | 0.412181i | \(0.864767\pi\) | |||||||
\(198\) | −6.76939 | − | 134.406i | −0.0341888 | − | 0.678817i | ||||
\(199\) | 30.5172 | 0.153353 | 0.0766764 | − | 0.997056i | \(-0.475569\pi\) | ||||
0.0766764 | + | 0.997056i | \(0.475569\pi\) | |||||||
\(200\) | 55.5413 | + | 43.7626i | 0.277706 | + | 0.218813i | ||||
\(201\) | 118.265 | − | 307.156i | 0.588384 | − | 1.52814i | ||||
\(202\) | 171.092 | + | 171.092i | 0.846988 | + | 0.846988i | ||||
\(203\) | 156.752 | + | 54.4105i | 0.772177 | + | 0.268032i | ||||
\(204\) | 122.676 | + | 47.2343i | 0.601352 | + | 0.231541i | ||||
\(205\) | −39.3077 | + | 44.2456i | −0.191745 | + | 0.215832i | ||||
\(206\) | −70.8291 | −0.343831 | ||||||||
\(207\) | 14.8376 | + | 294.600i | 0.0716794 | + | 1.42319i | ||||
\(208\) | −59.9595 | + | 59.9595i | −0.288267 | + | 0.288267i | ||||
\(209\) | 183.280i | 0.876938i | ||||||||
\(210\) | −146.981 | + | 21.1314i | −0.699910 | + | 0.100626i | ||||
\(211\) | 30.5075 | 0.144585 | 0.0722926 | − | 0.997383i | \(-0.476968\pi\) | ||||
0.0722926 | + | 0.997383i | \(0.476968\pi\) | |||||||
\(212\) | −30.6409 | − | 30.6409i | −0.144532 | − | 0.144532i | ||||
\(213\) | 73.9856 | + | 166.631i | 0.347350 | + | 0.782304i | ||||
\(214\) | 82.1046i | 0.383667i | ||||||||
\(215\) | 161.006 | − | 9.51531i | 0.748867 | − | 0.0442573i | ||||
\(216\) | −34.4621 | − | 68.1496i | −0.159547 | − | 0.315507i | ||||
\(217\) | −76.0756 | + | 219.167i | −0.350579 | + | 1.00999i | ||||
\(218\) | −168.808 | + | 168.808i | −0.774347 | + | 0.774347i | ||||
\(219\) | −5.37743 | + | 13.9662i | −0.0245545 | + | 0.0637724i | ||||
\(220\) | −70.2234 | + | 79.0451i | −0.319197 | + | 0.359296i | ||||
\(221\) | 464.451i | 2.10159i | ||||||||
\(222\) | 96.6867 | − | 42.9298i | 0.435526 | − | 0.193377i | ||||
\(223\) | −70.9384 | + | 70.9384i | −0.318109 | + | 0.318109i | −0.848041 | − | 0.529931i | \(-0.822218\pi\) |
0.529931 | + | 0.848041i | \(0.322218\pi\) | |||||||
\(224\) | 17.2700 | + | 35.6335i | 0.0770984 | + | 0.159078i | ||||
\(225\) | −183.512 | − | 130.186i | −0.815609 | − | 0.578603i | ||||
\(226\) | 37.9525 | 0.167932 | ||||||||
\(227\) | −139.705 | + | 139.705i | −0.615443 | + | 0.615443i | −0.944359 | − | 0.328916i | \(-0.893317\pi\) |
0.328916 | + | 0.944359i | \(0.393317\pi\) | |||||||
\(228\) | 42.2060 | + | 95.0568i | 0.185114 | + | 0.416916i | ||||
\(229\) | 19.0520 | 0.0831966 | 0.0415983 | − | 0.999134i | \(-0.486755\pi\) | ||||
0.0415983 | + | 0.999134i | \(0.486755\pi\) | |||||||
\(230\) | 153.921 | − | 173.257i | 0.669221 | − | 0.753290i | ||||
\(231\) | −18.5764 | − | 221.261i | −0.0804175 | − | 0.957839i | ||||
\(232\) | 47.4076 | − | 47.4076i | 0.204343 | − | 0.204343i | ||||
\(233\) | 32.3878 | − | 32.3878i | 0.139003 | − | 0.139003i | −0.634181 | − | 0.773185i | \(-0.718663\pi\) |
0.773185 | + | 0.634181i | \(0.218663\pi\) | |||||||
\(234\) | 180.952 | − | 200.146i | 0.773297 | − | 0.855323i | ||||
\(235\) | −5.26842 | − | 89.1456i | −0.0224188 | − | 0.379343i | ||||
\(236\) | −62.1698 | −0.263431 | ||||||||
\(237\) | 121.018 | + | 272.558i | 0.510625 | + | 1.15003i | ||||
\(238\) | 204.897 | + | 71.1223i | 0.860912 | + | 0.298833i | ||||
\(239\) | 133.240 | 0.557489 | 0.278744 | − | 0.960365i | \(-0.410082\pi\) | ||||
0.278744 | + | 0.960365i | \(0.410082\pi\) | |||||||
\(240\) | −18.2182 | + | 57.1673i | −0.0759092 | + | 0.238197i | ||||
\(241\) | 307.045i | 1.27405i | 0.770845 | + | 0.637023i | \(0.219834\pi\) | ||||
−0.770845 | + | 0.637023i | \(0.780166\pi\) | |||||||
\(242\) | 9.20544 | + | 9.20544i | 0.0380390 | + | 0.0380390i | ||||
\(243\) | 120.427 | + | 211.060i | 0.495583 | + | 0.868561i | ||||
\(244\) | −97.2984 | −0.398764 | ||||||||
\(245\) | −241.205 | + | 42.9530i | −0.984512 | + | 0.175318i | ||||
\(246\) | −46.8656 | − | 18.0448i | −0.190510 | − | 0.0733528i | ||||
\(247\) | −259.838 | + | 259.838i | −1.05198 | + | 1.05198i | ||||
\(248\) | 66.2843 | + | 66.2843i | 0.267276 | + | 0.267276i | ||||
\(249\) | 66.9897 | + | 25.7933i | 0.269035 | + | 0.103587i | ||||
\(250\) | 31.1422 | + | 174.012i | 0.124569 | + | 0.696048i | ||||
\(251\) | 205.085 | 0.817072 | 0.408536 | − | 0.912742i | \(-0.366039\pi\) | ||||
0.408536 | + | 0.912742i | \(0.366039\pi\) | |||||||
\(252\) | −60.5868 | − | 110.477i | −0.240424 | − | 0.438402i | ||||
\(253\) | 245.040 | + | 245.040i | 0.968536 | + | 0.968536i | ||||
\(254\) | 265.221 | 1.04418 | ||||||||
\(255\) | 150.851 | + | 291.970i | 0.591573 | + | 1.14498i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 186.225 | − | 186.225i | 0.724612 | − | 0.724612i | −0.244929 | − | 0.969541i | \(-0.578765\pi\) |
0.969541 | + | 0.244929i | \(0.0787646\pi\) | |||||||
\(258\) | 55.5373 | + | 125.082i | 0.215261 | + | 0.484812i | ||||
\(259\) | 157.068 | − | 76.1241i | 0.606439 | − | 0.293915i | ||||
\(260\) | −211.620 | + | 12.5065i | −0.813922 | + | 0.0481020i | ||||
\(261\) | −143.071 | + | 158.247i | −0.548165 | + | 0.606311i | ||||
\(262\) | −247.227 | − | 247.227i | −0.943613 | − | 0.943613i | ||||
\(263\) | 203.536 | − | 203.536i | 0.773902 | − | 0.773902i | −0.204884 | − | 0.978786i | \(-0.565682\pi\) |
0.978786 | + | 0.204884i | \(0.0656817\pi\) | |||||||
\(264\) | −83.7256 | − | 32.2371i | −0.317142 | − | 0.122110i | ||||
\(265\) | −6.39115 | − | 108.143i | −0.0241175 | − | 0.408087i | ||||
\(266\) | 74.8408 | + | 154.420i | 0.281356 | + | 0.580526i | ||||
\(267\) | 21.5287 | + | 48.4871i | 0.0806318 | + | 0.181599i | ||||
\(268\) | −155.157 | − | 155.157i | −0.578943 | − | 0.578943i | ||||
\(269\) | 53.2780i | 0.198060i | 0.995084 | + | 0.0990298i | \(0.0315739\pi\) | ||||
−0.995084 | + | 0.0990298i | \(0.968426\pi\) | |||||||
\(270\) | 48.7465 | − | 184.591i | 0.180543 | − | 0.683670i | ||||
\(271\) | 312.775i | 1.15415i | 0.816691 | + | 0.577076i | \(0.195806\pi\) | ||||
−0.816691 | + | 0.577076i | \(0.804194\pi\) | |||||||
\(272\) | 61.9685 | − | 61.9685i | 0.227825 | − | 0.227825i | ||||
\(273\) | 287.348 | − | 340.020i | 1.05256 | − | 1.24549i | ||||
\(274\) | 278.009i | 1.01463i | ||||||||
\(275\) | −262.492 | + | 31.1348i | −0.954518 | + | 0.113217i | ||||
\(276\) | 183.516 | + | 70.6597i | 0.664913 | + | 0.256013i | ||||
\(277\) | 230.870 | − | 230.870i | 0.833466 | − | 0.833466i | −0.154523 | − | 0.987989i | \(-0.549384\pi\) |
0.987989 | + | 0.154523i | \(0.0493842\pi\) | |||||||
\(278\) | −186.326 | − | 186.326i | −0.670237 | − | 0.670237i | ||||
\(279\) | −221.258 | − | 200.039i | −0.793039 | − | 0.716986i | ||||
\(280\) | −26.8884 | + | 95.2734i | −0.0960299 | + | 0.340262i | ||||
\(281\) | 22.5908i | 0.0803942i | 0.999192 | + | 0.0401971i | \(0.0127986\pi\) | ||||
−0.999192 | + | 0.0401971i | \(0.987201\pi\) | |||||||
\(282\) | 69.2549 | − | 30.7498i | 0.245585 | − | 0.109042i | ||||
\(283\) | 184.657 | − | 184.657i | 0.652497 | − | 0.652497i | −0.301097 | − | 0.953594i | \(-0.597353\pi\) |
0.953594 | + | 0.301097i | \(0.0973527\pi\) | |||||||
\(284\) | 121.545 | 0.427976 | ||||||||
\(285\) | −78.9497 | + | 247.738i | −0.277017 | + | 0.869256i | ||||
\(286\) | − | 316.985i | − | 1.10834i | ||||||
\(287\) | −78.2763 | − | 27.1707i | −0.272740 | − | 0.0946713i | ||||
\(288\) | −50.8472 | + | 2.56094i | −0.176553 | + | 0.00889214i | ||||
\(289\) | − | 191.012i | − | 0.660943i | ||||||
\(290\) | 167.319 | − | 9.88840i | 0.576963 | − | 0.0340979i | ||||
\(291\) | 137.771 | + | 53.0463i | 0.473439 | + | 0.182290i | ||||
\(292\) | 7.05487 | + | 7.05487i | 0.0241605 | + | 0.0241605i | ||||
\(293\) | 50.9535 | + | 50.9535i | 0.173903 | + | 0.173903i | 0.788692 | − | 0.614789i | \(-0.210759\pi\) |
−0.614789 | + | 0.788692i | \(0.710759\pi\) | |||||||
\(294\) | −106.001 | − | 178.834i | −0.360548 | − | 0.608280i | ||||
\(295\) | −116.194 | − | 103.227i | −0.393878 | − | 0.349920i | ||||
\(296\) | − | 70.5259i | − | 0.238263i | ||||||
\(297\) | 271.236 | + | 89.0471i | 0.913252 | + | 0.299822i | ||||
\(298\) | −253.568 | − | 253.568i | −0.850899 | − | 0.850899i | ||||
\(299\) | 694.791i | 2.32372i | ||||||||
\(300\) | −128.970 | + | 76.5950i | −0.429899 | + | 0.255317i | ||||
\(301\) | 98.4801 | + | 203.195i | 0.327176 | + | 0.675067i | ||||
\(302\) | 196.889 | + | 196.889i | 0.651952 | + | 0.651952i | ||||
\(303\) | −469.112 | + | 208.290i | −1.54823 | + | 0.687426i | ||||
\(304\) | 69.3370 | 0.228082 | ||||||||
\(305\) | −181.849 | − | 161.554i | −0.596225 | − | 0.529685i | ||||
\(306\) | −187.014 | + | 206.852i | −0.611158 | + | 0.675986i | ||||
\(307\) | 69.9923 | + | 69.9923i | 0.227988 | + | 0.227988i | 0.811852 | − | 0.583864i | \(-0.198460\pi\) |
−0.583864 | + | 0.811852i | \(0.698460\pi\) | |||||||
\(308\) | −139.841 | − | 48.5405i | −0.454030 | − | 0.157599i | ||||
\(309\) | 53.9881 | − | 140.217i | 0.174719 | − | 0.453776i | ||||
\(310\) | 13.8258 | + | 233.942i | 0.0445992 | + | 0.754653i | ||||
\(311\) | −26.1121 | −0.0839618 | −0.0419809 | − | 0.999118i | \(-0.513367\pi\) | ||||
−0.0419809 | + | 0.999118i | \(0.513367\pi\) | |||||||
\(312\) | −72.9958 | − | 164.402i | −0.233961 | − | 0.526929i | ||||
\(313\) | −57.8685 | + | 57.8685i | −0.184884 | + | 0.184884i | −0.793480 | − | 0.608596i | \(-0.791733\pi\) |
0.608596 | + | 0.793480i | \(0.291733\pi\) | |||||||
\(314\) | − | 188.539i | − | 0.600442i | ||||||
\(315\) | 70.2007 | − | 307.078i | 0.222859 | − | 0.974851i | ||||
\(316\) | 198.811 | 0.629150 | ||||||||
\(317\) | −368.411 | − | 368.411i | −1.16218 | − | 1.16218i | −0.983998 | − | 0.178182i | \(-0.942978\pi\) |
−0.178182 | − | 0.983998i | \(-0.557022\pi\) | |||||||
\(318\) | 84.0135 | − | 37.3027i | 0.264193 | − | 0.117304i | ||||
\(319\) | 250.627i | 0.785666i | ||||||||
\(320\) | 29.9037 | + | 26.5663i | 0.0934490 | + | 0.0830198i | ||||
\(321\) | −162.538 | − | 62.5826i | −0.506350 | − | 0.194961i | ||||
\(322\) | 306.514 | + | 106.395i | 0.951907 | + | 0.330418i | ||||
\(323\) | 268.544 | − | 268.544i | 0.831407 | − | 0.831407i | ||||
\(324\) | 161.180 | − | 16.2771i | 0.497470 | − | 0.0502379i | ||||
\(325\) | −416.279 | − | 327.998i | −1.28086 | − | 1.00923i | ||||
\(326\) | 288.237i | 0.884164i | ||||||||
\(327\) | −205.510 | − | 462.850i | −0.628470 | − | 1.41544i | ||||
\(328\) | −23.6737 | + | 23.6737i | −0.0721759 | + | 0.0721759i | ||||
\(329\) | 112.505 | − | 54.5262i | 0.341959 | − | 0.165733i | ||||
\(330\) | −102.955 | − | 199.268i | −0.311985 | − | 0.603843i | ||||
\(331\) | 172.781 | 0.521996 | 0.260998 | − | 0.965339i | \(-0.415948\pi\) | ||||
0.260998 | + | 0.965339i | \(0.415948\pi\) | |||||||
\(332\) | 33.8392 | − | 33.8392i | 0.101925 | − | 0.101925i | ||||
\(333\) | 11.2883 | + | 224.128i | 0.0338987 | + | 0.673057i | ||||
\(334\) | −163.515 | −0.489566 | ||||||||
\(335\) | −32.3630 | − | 547.606i | −0.0966059 | − | 1.63465i | ||||
\(336\) | −83.7055 | + | 7.02769i | −0.249124 | + | 0.0209157i | ||||
\(337\) | −300.344 | + | 300.344i | −0.891227 | + | 0.891227i | −0.994639 | − | 0.103411i | \(-0.967024\pi\) |
0.103411 | + | 0.994639i | \(0.467024\pi\) | |||||||
\(338\) | 280.393 | − | 280.393i | 0.829566 | − | 0.829566i | ||||
\(339\) | −28.9286 | + | 75.1327i | −0.0853350 | + | 0.221630i | ||||
\(340\) | 218.710 | − | 12.9256i | 0.643265 | − | 0.0380163i | ||||
\(341\) | −350.422 | −1.02763 | ||||||||
\(342\) | −220.350 | + | 11.0980i | −0.644297 | + | 0.0324502i | ||||
\(343\) | −184.660 | − | 289.050i | −0.538366 | − | 0.842711i | ||||
\(344\) | 91.2379 | 0.265226 | ||||||||
\(345\) | 225.664 | + | 436.771i | 0.654099 | + | 1.26600i | ||||
\(346\) | − | 295.444i | − | 0.853885i | ||||||
\(347\) | −200.513 | − | 200.513i | −0.577846 | − | 0.577846i | 0.356463 | − | 0.934309i | \(-0.383982\pi\) |
−0.934309 | + | 0.356463i | \(0.883982\pi\) | |||||||
\(348\) | 57.7149 | + | 129.986i | 0.165847 | + | 0.373523i | ||||
\(349\) | 414.103 | 1.18654 | 0.593270 | − | 0.805003i | \(-0.297836\pi\) | ||||
0.593270 | + | 0.805003i | \(0.297836\pi\) | |||||||
\(350\) | −208.445 | + | 133.419i | −0.595558 | + | 0.381196i | ||||
\(351\) | 258.291 | + | 510.777i | 0.735872 | + | 1.45521i | ||||
\(352\) | −42.2932 | + | 42.2932i | −0.120151 | + | 0.120151i | ||||
\(353\) | −249.345 | − | 249.345i | −0.706360 | − | 0.706360i | 0.259408 | − | 0.965768i | \(-0.416473\pi\) |
−0.965768 | + | 0.259408i | \(0.916473\pi\) | |||||||
\(354\) | 47.3877 | − | 123.074i | 0.133863 | − | 0.347667i | ||||
\(355\) | 227.165 | + | 201.813i | 0.639902 | + | 0.568487i | ||||
\(356\) | 35.3678 | 0.0993477 | ||||||||
\(357\) | −296.976 | + | 351.413i | −0.831865 | + | 0.984349i | ||||
\(358\) | −213.765 | − | 213.765i | −0.597109 | − | 0.597109i | ||||
\(359\) | 267.685 | 0.745641 | 0.372821 | − | 0.927903i | \(-0.378391\pi\) | ||||
0.372821 | + | 0.927903i | \(0.378391\pi\) | |||||||
\(360\) | −99.2846 | − | 79.6402i | −0.275791 | − | 0.221223i | ||||
\(361\) | −60.5240 | −0.167657 | ||||||||
\(362\) | 31.8772 | − | 31.8772i | 0.0880587 | − | 0.0880587i | ||||
\(363\) | −25.2402 | + | 11.2069i | −0.0695322 | + | 0.0308729i | ||||
\(364\) | −129.438 | − | 267.071i | −0.355599 | − | 0.733711i | ||||
\(365\) | 1.47152 | + | 24.8993i | 0.00403157 | + | 0.0682172i | ||||
\(366\) | 74.1638 | − | 192.617i | 0.202633 | − | 0.526275i | ||||
\(367\) | −423.041 | − | 423.041i | −1.15270 | − | 1.15270i | −0.986009 | − | 0.166690i | \(-0.946692\pi\) |
−0.166690 | − | 0.986009i | \(-0.553308\pi\) | |||||||
\(368\) | 92.7013 | − | 92.7013i | 0.251906 | − | 0.251906i | ||||
\(369\) | 71.4447 | − | 79.0230i | 0.193617 | − | 0.214155i | ||||
\(370\) | 117.101 | − | 131.811i | 0.316489 | − | 0.356247i | ||||
\(371\) | 136.480 | − | 66.1461i | 0.367871 | − | 0.178291i | ||||
\(372\) | −181.744 | + | 80.6957i | −0.488558 | + | 0.216924i | ||||
\(373\) | 53.4661 | + | 53.4661i | 0.143341 | + | 0.143341i | 0.775136 | − | 0.631795i | \(-0.217682\pi\) |
−0.631795 | + | 0.775136i | \(0.717682\pi\) | |||||||
\(374\) | 327.606i | 0.875951i | ||||||||
\(375\) | −368.220 | − | 70.9866i | −0.981920 | − | 0.189298i | ||||
\(376\) | − | 50.5164i | − | 0.134352i | ||||||
\(377\) | −355.317 | + | 355.317i | −0.942486 | + | 0.942486i | ||||
\(378\) | 264.887 | − | 35.7314i | 0.700760 | − | 0.0945276i | ||||
\(379\) | 364.774i | 0.962465i | 0.876593 | + | 0.481233i | \(0.159811\pi\) | ||||
−0.876593 | + | 0.481233i | \(0.840189\pi\) | |||||||
\(380\) | 129.589 | + | 115.127i | 0.341025 | + | 0.302965i | ||||
\(381\) | −202.160 | + | 525.045i | −0.530603 | + | 1.37807i | ||||
\(382\) | 40.4552 | − | 40.4552i | 0.105904 | − | 0.105904i | ||||
\(383\) | −113.130 | − | 113.130i | −0.295378 | − | 0.295378i | 0.543823 | − | 0.839200i | \(-0.316976\pi\) |
−0.839200 | + | 0.543823i | \(0.816976\pi\) | |||||||
\(384\) | −12.1957 | + | 31.6744i | −0.0317596 | + | 0.0824853i | ||||
\(385\) | −180.764 | − | 322.913i | −0.469516 | − | 0.838735i | ||||
\(386\) | 35.7541i | 0.0926271i | ||||||||
\(387\) | −289.950 | + | 14.6034i | −0.749224 | + | 0.0377349i | ||||
\(388\) | 69.5936 | − | 69.5936i | 0.179365 | − | 0.179365i | ||||
\(389\) | 77.4189 | 0.199020 | 0.0995101 | − | 0.995037i | \(-0.468272\pi\) | ||||
0.0995101 | + | 0.995037i | \(0.468272\pi\) | |||||||
\(390\) | 136.544 | − | 428.465i | 0.350114 | − | 1.09863i | ||||
\(391\) | − | 718.071i | − | 1.83650i | ||||||
\(392\) | −137.642 | + | 16.2058i | −0.351128 | + | 0.0413413i | ||||
\(393\) | 677.865 | − | 300.978i | 1.72485 | − | 0.765847i | ||||
\(394\) | − | 196.575i | − | 0.498921i | ||||||
\(395\) | 371.574 | + | 330.106i | 0.940694 | + | 0.835710i | ||||
\(396\) | 127.636 | − | 141.175i | 0.322314 | − | 0.356503i | ||||
\(397\) | −363.425 | − | 363.425i | −0.915428 | − | 0.915428i | 0.0812649 | − | 0.996693i | \(-0.474104\pi\) |
−0.996693 | + | 0.0812649i | \(0.974104\pi\) | |||||||
\(398\) | 30.5172 | + | 30.5172i | 0.0766764 | + | 0.0766764i | ||||
\(399\) | −362.743 | + | 30.4549i | −0.909130 | + | 0.0763281i | ||||
\(400\) | 11.7787 | + | 99.3039i | 0.0294466 | + | 0.248260i | ||||
\(401\) | 257.812i | 0.642923i | 0.946923 | + | 0.321461i | \(0.104174\pi\) | ||||
−0.946923 | + | 0.321461i | \(0.895826\pi\) | |||||||
\(402\) | 425.421 | − | 188.891i | 1.05826 | − | 0.469877i | ||||
\(403\) | −496.797 | − | 496.797i | −1.23275 | − | 1.23275i | ||||
\(404\) | 342.183i | 0.846988i | ||||||||
\(405\) | 328.269 | + | 237.202i | 0.810540 | + | 0.585683i | ||||
\(406\) | 102.341 | + | 211.162i | 0.252073 | + | 0.520104i | ||||
\(407\) | 186.423 | + | 186.423i | 0.458041 | + | 0.458041i | ||||
\(408\) | 75.4416 | + | 169.910i | 0.184906 | + | 0.416446i | ||||
\(409\) | −491.252 | −1.20110 | −0.600552 | − | 0.799586i | \(-0.705052\pi\) | ||||
−0.600552 | + | 0.799586i | \(0.705052\pi\) | |||||||
\(410\) | −83.5533 | + | 4.93792i | −0.203789 | + | 0.0120437i | ||||
\(411\) | −550.360 | − | 211.907i | −1.33908 | − | 0.515588i | ||||
\(412\) | −70.8291 | − | 70.8291i | −0.171915 | − | 0.171915i | ||||
\(413\) | 71.3532 | − | 205.563i | 0.172768 | − | 0.497730i | ||||
\(414\) | −279.763 | + | 309.438i | −0.675755 | + | 0.747435i | ||||
\(415\) | 119.431 | − | 7.05827i | 0.287786 | − | 0.0170079i | ||||
\(416\) | −119.919 | −0.288267 | ||||||||
\(417\) | 510.883 | − | 226.837i | 1.22514 | − | 0.543973i | ||||
\(418\) | −183.280 | + | 183.280i | −0.438469 | + | 0.438469i | ||||
\(419\) | 400.571i | 0.956016i | 0.878356 | + | 0.478008i | \(0.158641\pi\) | ||||
−0.878356 | + | 0.478008i | \(0.841359\pi\) | |||||||
\(420\) | −168.113 | − | 125.850i | −0.400268 | − | 0.299642i | ||||
\(421\) | −281.156 | −0.667828 | −0.333914 | − | 0.942604i | \(-0.608369\pi\) | ||||
−0.333914 | + | 0.942604i | \(0.608369\pi\) | |||||||
\(422\) | 30.5075 | + | 30.5075i | 0.0722926 | + | 0.0722926i | ||||
\(423\) | 8.08558 | + | 160.539i | 0.0191148 | + | 0.379524i | ||||
\(424\) | − | 61.2817i | − | 0.144532i | ||||||
\(425\) | 430.226 | + | 338.988i | 1.01230 | + | 0.797619i | ||||
\(426\) | −92.6453 | + | 240.616i | −0.217477 | + | 0.564827i | ||||
\(427\) | 111.671 | − | 321.714i | 0.261524 | − | 0.753429i | ||||
\(428\) | −82.1046 | + | 82.1046i | −0.191833 | + | 0.191833i | ||||
\(429\) | 627.518 | + | 241.615i | 1.46275 | + | 0.563206i | ||||
\(430\) | 170.522 | + | 151.491i | 0.396562 | + | 0.352305i | ||||
\(431\) | − | 404.384i | − | 0.938246i | −0.883133 | − | 0.469123i | \(-0.844570\pi\) | ||
0.883133 | − | 0.469123i | \(-0.155430\pi\) | |||||||
\(432\) | 33.6875 | − | 102.612i | 0.0779804 | − | 0.237527i | ||||
\(433\) | 43.6114 | − | 43.6114i | 0.100719 | − | 0.100719i | −0.654952 | − | 0.755671i | \(-0.727311\pi\) |
0.755671 | + | 0.654952i | \(0.227311\pi\) | |||||||
\(434\) | −295.243 | + | 143.092i | −0.680283 | + | 0.329704i | ||||
\(435\) | −107.960 | + | 338.771i | −0.248184 | + | 0.778783i | ||||
\(436\) | −337.615 | −0.774347 | ||||||||
\(437\) | 401.727 | − | 401.727i | 0.919283 | − | 0.919283i | ||||
\(438\) | −19.3436 | + | 8.58872i | −0.0441634 | + | 0.0196090i | ||||
\(439\) | 605.567 | 1.37942 | 0.689712 | − | 0.724084i | \(-0.257737\pi\) | ||||
0.689712 | + | 0.724084i | \(0.257737\pi\) | |||||||
\(440\) | −149.269 | + | 8.82162i | −0.339247 | + | 0.0200491i | ||||
\(441\) | 434.826 | − | 73.5320i | 0.986001 | − | 0.166739i | ||||
\(442\) | −464.451 | + | 464.451i | −1.05079 | + | 1.05079i | ||||
\(443\) | −89.6580 | + | 89.6580i | −0.202388 | + | 0.202388i | −0.801023 | − | 0.598634i | \(-0.795710\pi\) |
0.598634 | + | 0.801023i | \(0.295710\pi\) | |||||||
\(444\) | 139.616 | + | 53.7570i | 0.314452 | + | 0.121074i | ||||
\(445\) | 66.1016 | + | 58.7245i | 0.148543 | + | 0.131965i | ||||
\(446\) | −141.877 | −0.318109 | ||||||||
\(447\) | 695.253 | − | 308.698i | 1.55537 | − | 0.690600i | ||||
\(448\) | −18.3634 | + | 52.9035i | −0.0409898 | + | 0.118088i | ||||
\(449\) | −335.741 | −0.747752 | −0.373876 | − | 0.927479i | \(-0.621971\pi\) | ||||
−0.373876 | + | 0.927479i | \(0.621971\pi\) | |||||||
\(450\) | −53.3265 | − | 313.698i | −0.118503 | − | 0.697106i | ||||
\(451\) | − | 125.154i | − | 0.277504i | ||||||
\(452\) | 37.9525 | + | 37.9525i | 0.0839658 | + | 0.0839658i | ||||
\(453\) | −539.847 | + | 239.697i | −1.19171 | + | 0.529132i | ||||
\(454\) | −279.411 | −0.615443 | ||||||||
\(455\) | 201.527 | − | 714.068i | 0.442916 | − | 1.56938i | ||||
\(456\) | −52.8507 | + | 137.263i | −0.115901 | + | 0.301015i | ||||
\(457\) | 429.732 | − | 429.732i | 0.940332 | − | 0.940332i | −0.0579859 | − | 0.998317i | \(-0.518468\pi\) |
0.998317 | + | 0.0579859i | \(0.0184678\pi\) | |||||||
\(458\) | 19.0520 | + | 19.0520i | 0.0415983 | + | 0.0415983i | ||||
\(459\) | −266.945 | − | 527.891i | −0.581580 | − | 1.15009i | ||||
\(460\) | 327.178 | − | 19.3359i | 0.711256 | − | 0.0420345i | ||||
\(461\) | 23.6913 | 0.0513911 | 0.0256955 | − | 0.999670i | \(-0.491820\pi\) | ||||
0.0256955 | + | 0.999670i | \(0.491820\pi\) | |||||||
\(462\) | 202.684 | − | 239.837i | 0.438711 | − | 0.519128i | ||||
\(463\) | −228.050 | − | 228.050i | −0.492548 | − | 0.492548i | 0.416560 | − | 0.909108i | \(-0.363236\pi\) |
−0.909108 | + | 0.416560i | \(0.863236\pi\) | |||||||
\(464\) | 94.8153 | 0.204343 | ||||||||
\(465\) | −473.662 | − | 150.948i | −1.01863 | − | 0.324619i | ||||
\(466\) | 64.7756 | 0.139003 | ||||||||
\(467\) | 359.835 | − | 359.835i | 0.770525 | − | 0.770525i | −0.207673 | − | 0.978198i | \(-0.566589\pi\) |
0.978198 | + | 0.207673i | \(0.0665891\pi\) | |||||||
\(468\) | 381.097 | − | 19.1941i | 0.814310 | − | 0.0410130i | ||||
\(469\) | 691.097 | − | 334.945i | 1.47355 | − | 0.714169i | ||||
\(470\) | 83.8772 | − | 94.4140i | 0.178462 | − | 0.200881i | ||||
\(471\) | 373.240 | + | 143.710i | 0.792442 | + | 0.305116i | ||||
\(472\) | −62.1698 | − | 62.1698i | −0.131716 | − | 0.131716i | ||||
\(473\) | −241.171 | + | 241.171i | −0.509876 | + | 0.509876i | ||||
\(474\) | −151.540 | + | 393.576i | −0.319704 | + | 0.830330i | ||||
\(475\) | 51.0435 | + | 430.339i | 0.107460 | + | 0.905978i | ||||
\(476\) | 133.775 | + | 276.019i | 0.281040 | + | 0.579873i | ||||
\(477\) | 9.80866 | + | 194.750i | 0.0205632 | + | 0.408282i | ||||
\(478\) | 133.240 | + | 133.240i | 0.278744 | + | 0.278744i | ||||
\(479\) | − | 470.256i | − | 0.981745i | −0.871231 | − | 0.490873i | \(-0.836678\pi\) | ||
0.871231 | − | 0.490873i | \(-0.163322\pi\) | |||||||
\(480\) | −75.3855 | + | 38.9491i | −0.157053 | + | 0.0811439i | ||||
\(481\) | 528.588i | 1.09893i | ||||||||
\(482\) | −307.045 | + | 307.045i | −0.637023 | + | 0.637023i | ||||
\(483\) | −444.258 | + | 525.693i | −0.919790 | + | 1.08839i | ||||
\(484\) | 18.4109i | 0.0380390i | ||||||||
\(485\) | 245.622 | − | 14.5160i | 0.506437 | − | 0.0299299i | ||||
\(486\) | −90.6335 | + | 331.487i | −0.186489 | + | 0.682072i | ||||
\(487\) | −246.237 | + | 246.237i | −0.505621 | + | 0.505621i | −0.913179 | − | 0.407558i | \(-0.866380\pi\) |
0.407558 | + | 0.913179i | \(0.366380\pi\) | |||||||
\(488\) | −97.2984 | − | 97.2984i | −0.199382 | − | 0.199382i | ||||
\(489\) | −570.609 | − | 219.703i | −1.16689 | − | 0.449291i | ||||
\(490\) | −284.158 | − | 198.252i | −0.579915 | − | 0.404597i | ||||
\(491\) | − | 5.09974i | − | 0.0103864i | −0.999987 | − | 0.00519322i | \(-0.998347\pi\) | ||
0.999987 | − | 0.00519322i | \(-0.00165306\pi\) | |||||||
\(492\) | −28.8208 | − | 64.9103i | −0.0585788 | − | 0.131932i | ||||
\(493\) | 367.223 | − | 367.223i | 0.744874 | − | 0.744874i | ||||
\(494\) | −519.677 | −1.05198 | ||||||||
\(495\) | 472.956 | − | 51.9264i | 0.955467 | − | 0.104902i | ||||
\(496\) | 132.569i | 0.267276i | ||||||||
\(497\) | −139.499 | + | 401.885i | −0.280682 | + | 0.808622i | ||||
\(498\) | 41.1965 | + | 92.7830i | 0.0827238 | + | 0.186311i | ||||
\(499\) | 678.365i | 1.35945i | 0.733467 | + | 0.679725i | \(0.237901\pi\) | ||||
−0.733467 | + | 0.679725i | \(0.762099\pi\) | |||||||
\(500\) | −142.870 | + | 205.154i | −0.285740 | + | 0.410308i | ||||
\(501\) | 124.636 | − | 323.702i | 0.248775 | − | 0.646112i | ||||
\(502\) | 205.085 | + | 205.085i | 0.408536 | + | 0.408536i | ||||
\(503\) | 501.769 | + | 501.769i | 0.997552 | + | 0.997552i | 0.999997 | − | 0.00244509i | \(-0.000778296\pi\) |
−0.00244509 | + | 0.999997i | \(0.500778\pi\) | |||||||
\(504\) | 49.8905 | − | 171.064i | 0.0989891 | − | 0.339413i | ||||
\(505\) | −568.160 | + | 639.533i | −1.12507 | + | 1.26640i | ||||
\(506\) | 490.079i | 0.968536i | ||||||||
\(507\) | 341.356 | + | 768.804i | 0.673285 | + | 1.51638i | ||||
\(508\) | 265.221 | + | 265.221i | 0.522089 | + | 0.522089i | ||||
\(509\) | − | 620.503i | − | 1.21906i | −0.792762 | − | 0.609531i | \(-0.791358\pi\) | ||
0.792762 | − | 0.609531i | \(-0.208642\pi\) | |||||||
\(510\) | −141.119 | + | 442.822i | −0.276705 | + | 0.868277i | ||||
\(511\) | −31.4237 | + | 15.2297i | −0.0614945 | + | 0.0298038i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 145.987 | − | 444.674i | 0.284575 | − | 0.866811i | ||||
\(514\) | 372.451 | 0.724612 | ||||||||
\(515\) | −14.7737 | − | 249.982i | −0.0286868 | − | 0.485403i | ||||
\(516\) | −69.5442 | + | 180.619i | −0.134776 | + | 0.350037i | ||||
\(517\) | 133.531 | + | 133.531i | 0.258281 | + | 0.258281i | ||||
\(518\) | 233.192 | + | 80.9437i | 0.450177 | + | 0.156262i | ||||
\(519\) | 584.876 | + | 225.197i | 1.12693 | + | 0.433905i | ||||
\(520\) | −224.126 | − | 199.113i | −0.431012 | − | 0.382910i | ||||
\(521\) | −328.476 | −0.630471 | −0.315236 | − | 0.949013i | \(-0.602084\pi\) | ||||
−0.315236 | + | 0.949013i | \(0.602084\pi\) | |||||||
\(522\) | −301.318 | + | 15.1760i | −0.577238 | + | 0.0290728i | ||||
\(523\) | 167.734 | − | 167.734i | 0.320714 | − | 0.320714i | −0.528327 | − | 0.849041i | \(-0.677180\pi\) |
0.849041 | + | 0.528327i | \(0.177180\pi\) | |||||||
\(524\) | − | 494.453i | − | 0.943613i | ||||||
\(525\) | −105.238 | − | 514.344i | −0.200454 | − | 0.979703i | ||||
\(526\) | 407.073 | 0.773902 | ||||||||
\(527\) | 513.443 | + | 513.443i | 0.974275 | + | 0.974275i | ||||
\(528\) | −51.4885 | − | 115.963i | −0.0975160 | − | 0.219626i | ||||
\(529\) | − | 545.191i | − | 1.03061i | ||||||
\(530\) | 101.752 | − | 114.534i | 0.191985 | − | 0.216102i | ||||
\(531\) | 207.523 | + | 187.622i | 0.390816 | + | 0.353337i | ||||
\(532\) | −79.5791 | + | 229.261i | −0.149585 | + | 0.430941i | ||||
\(533\) | 177.433 | − | 177.433i | 0.332895 | − | 0.332895i | ||||
\(534\) | −26.9584 | + | 70.0157i | −0.0504839 | + | 0.131116i | ||||
\(535\) | −289.778 | + | 17.1256i | −0.541641 | + | 0.0320105i | ||||
\(536\) | − | 310.313i | − | 0.578943i | ||||||
\(537\) | 586.118 | − | 260.241i | 1.09147 | − | 0.484621i | ||||
\(538\) | −53.2780 | + | 53.2780i | −0.0990298 | + | 0.0990298i | ||||
\(539\) | 320.996 | − | 406.670i | 0.595539 | − | 0.754490i | ||||
\(540\) | 233.337 | − | 135.844i | 0.432106 | − | 0.251564i | ||||
\(541\) | −850.320 | −1.57176 | −0.785878 | − | 0.618381i | \(-0.787789\pi\) | ||||
−0.785878 | + | 0.618381i | \(0.787789\pi\) | |||||||
\(542\) | −312.775 | + | 312.775i | −0.577076 | + | 0.577076i | ||||
\(543\) | 38.8079 | + | 87.4035i | 0.0714695 | + | 0.160964i | ||||
\(544\) | 123.937 | 0.227825 | ||||||||
\(545\) | −630.996 | − | 560.576i | −1.15779 | − | 1.02858i | ||||
\(546\) | 627.368 | − | 52.6721i | 1.14903 | − | 0.0964690i | ||||
\(547\) | 141.618 | − | 141.618i | 0.258899 | − | 0.258899i | −0.565707 | − | 0.824606i | \(-0.691397\pi\) |
0.824606 | + | 0.565707i | \(0.191397\pi\) | |||||||
\(548\) | −278.009 | + | 278.009i | −0.507316 | + | 0.507316i | ||||
\(549\) | 324.783 | + | 293.636i | 0.591590 | + | 0.534857i | ||||
\(550\) | −293.627 | − | 231.358i | −0.533868 | − | 0.420650i | ||||
\(551\) | 410.888 | 0.745713 | ||||||||
\(552\) | 112.856 | + | 254.176i | 0.204450 | + | 0.460463i | ||||
\(553\) | −228.179 | + | 657.364i | −0.412620 | + | 1.18872i | ||||
\(554\) | 461.740 | 0.833466 | ||||||||
\(555\) | 171.682 | + | 332.289i | 0.309338 | + | 0.598720i | ||||
\(556\) | − | 372.652i | − | 0.670237i | ||||||
\(557\) | −596.862 | − | 596.862i | −1.07157 | − | 1.07157i | −0.997234 | − | 0.0743321i | \(-0.976318\pi\) |
−0.0743321 | − | 0.997234i | \(-0.523682\pi\) | |||||||
\(558\) | −21.2188 | − | 421.297i | −0.0380264 | − | 0.755012i | ||||
\(559\) | −683.823 | −1.22330 | ||||||||
\(560\) | −122.162 | + | 68.3850i | −0.218146 | + | 0.122116i | ||||
\(561\) | −648.544 | − | 249.711i | −1.15605 | − | 0.445118i | ||||
\(562\) | −22.5908 | + | 22.5908i | −0.0401971 | + | 0.0401971i | ||||
\(563\) | −13.7370 | − | 13.7370i | −0.0243996 | − | 0.0243996i | 0.694802 | − | 0.719201i | \(-0.255492\pi\) |
−0.719201 | + | 0.694802i | \(0.755492\pi\) | |||||||
\(564\) | 100.005 | + | 38.5051i | 0.177313 | + | 0.0682714i | ||||
\(565\) | 7.91624 | + | 133.949i | 0.0140110 | + | 0.237077i | ||||
\(566\) | 369.313 | 0.652497 | ||||||||
\(567\) | −131.169 | + | 551.619i | −0.231339 | + | 0.972873i | ||||
\(568\) | 121.545 | + | 121.545i | 0.213988 | + | 0.213988i | ||||
\(569\) | −1040.51 | −1.82866 | −0.914331 | − | 0.404969i | \(-0.867282\pi\) | ||||
−0.914331 | + | 0.404969i | \(0.867282\pi\) | |||||||
\(570\) | −326.688 | + | 168.788i | −0.573136 | + | 0.296120i | ||||
\(571\) | 42.2507 | 0.0739942 | 0.0369971 | − | 0.999315i | \(-0.488221\pi\) | ||||
0.0369971 | + | 0.999315i | \(0.488221\pi\) | |||||||
\(572\) | 316.985 | − | 316.985i | 0.554169 | − | 0.554169i | ||||
\(573\) | 49.2509 | + | 110.923i | 0.0859527 | + | 0.193583i | ||||
\(574\) | −51.1057 | − | 105.447i | −0.0890343 | − | 0.183706i | ||||
\(575\) | 643.594 | + | 507.106i | 1.11929 | + | 0.881924i | ||||
\(576\) | −53.4082 | − | 48.2863i | −0.0927225 | − | 0.0838304i | ||||
\(577\) | 234.233 | + | 234.233i | 0.405950 | + | 0.405950i | 0.880324 | − | 0.474373i | \(-0.157325\pi\) |
−0.474373 | + | 0.880324i | \(0.657325\pi\) | |||||||
\(578\) | 191.012 | − | 191.012i | 0.330471 | − | 0.330471i | ||||
\(579\) | −70.7804 | − | 27.2528i | −0.122246 | − | 0.0470688i | ||||
\(580\) | 177.208 | + | 157.431i | 0.305531 | + | 0.271433i | ||||
\(581\) | 73.0506 | + | 150.726i | 0.125732 | + | 0.259425i | ||||
\(582\) | 84.7245 | + | 190.817i | 0.145575 | + | 0.327865i | ||||
\(583\) | 161.987 | + | 161.987i | 0.277851 | + | 0.277851i | ||||
\(584\) | 14.1097i | 0.0241605i | ||||||||
\(585\) | 744.132 | + | 596.899i | 1.27202 | + | 1.02034i | ||||
\(586\) | 101.907i | 0.173903i | ||||||||
\(587\) | −667.229 | + | 667.229i | −1.13668 | + | 1.13668i | −0.147635 | + | 0.989042i | \(0.547166\pi\) |
−0.989042 | + | 0.147635i | \(0.952834\pi\) | |||||||
\(588\) | 72.8333 | − | 284.836i | 0.123866 | − | 0.484414i | ||||
\(589\) | 574.494i | 0.975372i | ||||||||
\(590\) | −12.9675 | − | 219.421i | −0.0219789 | − | 0.371899i | ||||
\(591\) | 389.149 | + | 149.835i | 0.658459 | + | 0.253528i | ||||
\(592\) | 70.5259 | − | 70.5259i | 0.119132 | − | 0.119132i | ||||
\(593\) | −599.428 | − | 599.428i | −1.01084 | − | 1.01084i | −0.999941 | − | 0.0108986i | \(-0.996531\pi\) |
−0.0108986 | − | 0.999941i | \(-0.503469\pi\) | |||||||
\(594\) | 182.189 | + | 360.283i | 0.306715 | + | 0.606537i | ||||
\(595\) | −208.279 | + | 737.994i | −0.350049 | + | 1.24033i | ||||
\(596\) | − | 507.136i | − | 0.850899i | ||||||
\(597\) | −83.6745 | + | 37.1522i | −0.140158 | + | 0.0622315i | ||||
\(598\) | −694.791 | + | 694.791i | −1.16186 | + | 1.16186i | ||||
\(599\) | 303.628 | 0.506892 | 0.253446 | − | 0.967350i | \(-0.418436\pi\) | ||||
0.253446 | + | 0.967350i | \(0.418436\pi\) | |||||||
\(600\) | −205.565 | − | 52.3748i | −0.342608 | − | 0.0872913i | ||||
\(601\) | − | 34.3783i | − | 0.0572019i | −0.999591 | − | 0.0286009i | \(-0.990895\pi\) | ||
0.999591 | − | 0.0286009i | \(-0.00910520\pi\) | |||||||
\(602\) | −104.715 | + | 301.675i | −0.173945 | + | 0.501122i | ||||
\(603\) | 49.6683 | + | 986.161i | 0.0823687 | + | 1.63543i | ||||
\(604\) | 393.779i | 0.651952i | ||||||||
\(605\) | −30.5694 | + | 34.4096i | −0.0505279 | + | 0.0568753i | ||||
\(606\) | −677.402 | − | 260.822i | −1.11783 | − | 0.430400i | ||||
\(607\) | −185.983 | − | 185.983i | −0.306397 | − | 0.306397i | 0.537113 | − | 0.843510i | \(-0.319515\pi\) |
−0.843510 | + | 0.537113i | \(0.819515\pi\) | |||||||
\(608\) | 69.3370 | + | 69.3370i | 0.114041 | + | 0.114041i | ||||
\(609\) | −496.035 | + | 41.6457i | −0.814507 | + | 0.0683838i | ||||
\(610\) | −20.2947 | − | 343.403i | −0.0332701 | − | 0.562955i | ||||
\(611\) | 378.617i | 0.619668i | ||||||||
\(612\) | −393.866 | + | 19.8372i | −0.643572 | + | 0.0324137i | ||||
\(613\) | −121.390 | − | 121.390i | −0.198027 | − | 0.198027i | 0.601127 | − | 0.799154i | \(-0.294719\pi\) |
−0.799154 | + | 0.601127i | \(0.794719\pi\) | |||||||
\(614\) | 139.985i | 0.227988i | ||||||||
\(615\) | 53.9115 | − | 169.170i | 0.0876610 | − | 0.275073i | ||||
\(616\) | −91.3006 | − | 188.382i | −0.148215 | − | 0.305814i | ||||
\(617\) | −585.706 | − | 585.706i | −0.949281 | − | 0.949281i | 0.0494938 | − | 0.998774i | \(-0.484239\pi\) |
−0.998774 | + | 0.0494938i | \(0.984239\pi\) | |||||||
\(618\) | 194.205 | − | 86.2286i | 0.314247 | − | 0.139528i | ||||
\(619\) | 90.7688 | 0.146638 | 0.0733189 | − | 0.997309i | \(-0.476641\pi\) | ||||
0.0733189 | + | 0.997309i | \(0.476641\pi\) | |||||||
\(620\) | −220.117 | + | 247.768i | −0.355027 | + | 0.399626i | ||||
\(621\) | −399.335 | − | 789.694i | −0.643051 | − | 1.27165i | ||||
\(622\) | −26.1121 | − | 26.1121i | −0.0419809 | − | 0.0419809i | ||||
\(623\) | −40.5921 | + | 116.943i | −0.0651559 | + | 0.187709i | ||||
\(624\) | 91.4059 | − | 237.398i | 0.146484 | − | 0.380445i | ||||
\(625\) | −607.658 | + | 146.208i | −0.972253 | + | 0.233933i | ||||
\(626\) | −115.737 | −0.184884 | ||||||||
\(627\) | −223.128 | − | 502.532i | −0.355867 | − | 0.801486i | ||||
\(628\) | 188.539 | − | 188.539i | 0.300221 | − | 0.300221i | ||||
\(629\) | − | 546.298i | − | 0.868519i | ||||||
\(630\) | 377.279 | − | 236.877i | 0.598855 | − | 0.375996i | ||||
\(631\) | −293.524 | −0.465173 | −0.232587 | − | 0.972576i | \(-0.574719\pi\) | ||||
−0.232587 | + | 0.972576i | \(0.574719\pi\) | |||||||
\(632\) | 198.811 | + | 198.811i | 0.314575 | + | 0.314575i | ||||
\(633\) | −83.6478 | + | 37.1404i | −0.132145 | + | 0.0586735i | ||||
\(634\) | − | 736.822i | − | 1.16218i | ||||||
\(635\) | 55.3205 | + | 936.065i | 0.0871189 | + | 1.47412i | ||||
\(636\) | 121.316 | + | 46.7108i | 0.190749 | + | 0.0734446i | ||||
\(637\) | 1031.62 | − | 121.461i | 1.61950 | − | 0.190677i | ||||
\(638\) | −250.627 | + | 250.627i | −0.392833 | + | 0.392833i | ||||
\(639\) | −405.719 | − | 366.810i | −0.634928 | − | 0.574038i | ||||
\(640\) | 3.33732 | + | 56.4700i | 0.00521456 | + | 0.0882344i | ||||
\(641\) | 495.745i | 0.773393i | 0.922207 | + | 0.386697i | \(0.126384\pi\) | ||||
−0.922207 | + | 0.386697i | \(0.873616\pi\) | |||||||
\(642\) | −99.9556 | − | 225.121i | −0.155694 | − | 0.350656i | ||||
\(643\) | 195.737 | − | 195.737i | 0.304412 | − | 0.304412i | −0.538325 | − | 0.842737i | \(-0.680943\pi\) |
0.842737 | + | 0.538325i | \(0.180943\pi\) | |||||||
\(644\) | 200.119 | + | 412.909i | 0.310744 | + | 0.641163i | ||||
\(645\) | −429.876 | + | 222.102i | −0.666474 | + | 0.344344i | ||||
\(646\) | 537.089 | 0.831407 | ||||||||
\(647\) | 584.341 | − | 584.341i | 0.903154 | − | 0.903154i | −0.0925538 | − | 0.995708i | \(-0.529503\pi\) |
0.995708 | + | 0.0925538i | \(0.0295030\pi\) | |||||||
\(648\) | 177.457 | + | 144.903i | 0.273854 | + | 0.223616i | ||||
\(649\) | 328.670 | 0.506425 | ||||||||
\(650\) | −88.2804 | − | 744.277i | −0.135816 | − | 1.14504i | ||||
\(651\) | −58.2282 | − | 693.545i | −0.0894442 | − | 1.06535i | ||||
\(652\) | −288.237 | + | 288.237i | −0.442082 | + | 0.442082i | ||||
\(653\) | 25.5558 | − | 25.5558i | 0.0391360 | − | 0.0391360i | −0.687268 | − | 0.726404i | \(-0.741190\pi\) |
0.726404 | + | 0.687268i | \(0.241190\pi\) | |||||||
\(654\) | 257.341 | − | 668.360i | 0.393487 | − | 1.02196i | ||||
\(655\) | 820.988 | − | 924.122i | 1.25342 | − | 1.41087i | ||||
\(656\) | −47.3474 | −0.0721759 | ||||||||
\(657\) | −2.25838 | − | 44.8401i | −0.00343742 | − | 0.0682497i | ||||
\(658\) | 167.031 | + | 57.9784i | 0.253846 | + | 0.0881131i | ||||
\(659\) | 54.2782 | 0.0823645 | 0.0411823 | − | 0.999152i | \(-0.486888\pi\) | ||||
0.0411823 | + | 0.999152i | \(0.486888\pi\) | |||||||
\(660\) | 96.3132 | − | 302.223i | 0.145929 | − | 0.457914i | ||||
\(661\) | − | 604.587i | − | 0.914655i | −0.889298 | − | 0.457328i | \(-0.848807\pi\) | ||
0.889298 | − | 0.457328i | \(-0.151193\pi\) | |||||||
\(662\) | 172.781 | + | 172.781i | 0.260998 | + | 0.260998i | ||||
\(663\) | −565.430 | − | 1273.47i | −0.852836 | − | 1.92076i | ||||
\(664\) | 67.6784 | 0.101925 | ||||||||
\(665\) | −529.395 | + | 296.351i | −0.796083 | + | 0.445640i | ||||
\(666\) | −212.840 | + | 235.416i | −0.319579 | + | 0.353478i | ||||
\(667\) | 549.344 | − | 549.344i | 0.823604 | − | 0.823604i | ||||
\(668\) | −163.515 | − | 163.515i | −0.244783 | − | 0.244783i | ||||
\(669\) | 108.143 | − | 280.866i | 0.161648 | − | 0.419829i | ||||
\(670\) | 515.243 | − | 579.969i | 0.769020 | − | 0.865626i | ||||
\(671\) | 514.382 | 0.766591 | ||||||||
\(672\) | −90.7332 | − | 76.6778i | −0.135020 | − | 0.114104i | ||||
\(673\) | 653.084 | + | 653.084i | 0.970407 | + | 0.970407i | 0.999575 | − | 0.0291677i | \(-0.00928567\pi\) |
−0.0291677 | + | 0.999575i | \(0.509286\pi\) | |||||||
\(674\) | −600.687 | −0.891227 | ||||||||
\(675\) | 661.658 | + | 133.542i | 0.980234 | + | 0.197840i | ||||
\(676\) | 560.786 | 0.829566 | ||||||||
\(677\) | −111.338 | + | 111.338i | −0.164458 | + | 0.164458i | −0.784538 | − | 0.620080i | \(-0.787100\pi\) |
0.620080 | + | 0.784538i | \(0.287100\pi\) | |||||||
\(678\) | −104.061 | + | 46.2041i | −0.153483 | + | 0.0681476i | ||||
\(679\) | 150.236 | + | 309.983i | 0.221260 | + | 0.456529i | ||||
\(680\) | 231.636 | + | 205.785i | 0.340641 | + | 0.302625i | ||||
\(681\) | 212.975 | − | 553.135i | 0.312739 | − | 0.812240i | ||||
\(682\) | −350.422 | − | 350.422i | −0.513815 | − | 0.513815i | ||||
\(683\) | −420.406 | + | 420.406i | −0.615528 | + | 0.615528i | −0.944381 | − | 0.328853i | \(-0.893338\pi\) |
0.328853 | + | 0.944381i | \(0.393338\pi\) | |||||||
\(684\) | −231.448 | − | 209.252i | −0.338374 | − | 0.305923i | ||||
\(685\) | −981.199 | + | 57.9878i | −1.43241 | + | 0.0846538i | ||||
\(686\) | 104.390 | − | 473.710i | 0.152172 | − | 0.690539i | ||||
\(687\) | −52.2383 | + | 23.1943i | −0.0760383 | + | 0.0337617i | ||||
\(688\) | 91.2379 | + | 91.2379i | 0.132613 | + | 0.132613i | ||||
\(689\) | 459.303i | 0.666622i | ||||||||
\(690\) | −211.106 | + | 662.435i | −0.305951 | + | 0.960051i | ||||
\(691\) | 238.766i | 0.345537i | 0.984962 | + | 0.172768i | \(0.0552712\pi\) | ||||
−0.984962 | + | 0.172768i | \(0.944729\pi\) | |||||||
\(692\) | 295.444 | − | 295.444i | 0.426943 | − | 0.426943i | ||||
\(693\) | 320.301 | + | 584.055i | 0.462195 | + | 0.842792i | ||||
\(694\) | − | 401.025i | − | 0.577846i | ||||||
\(695\) | 618.750 | − | 696.479i | 0.890288 | − | 1.00213i | ||||
\(696\) | −72.2710 | + | 187.701i | −0.103838 | + | 0.269685i | ||||
\(697\) | −183.378 | + | 183.378i | −0.263096 | + | 0.263096i | ||||
\(698\) | 414.103 | + | 414.103i | 0.593270 | + | 0.593270i | ||||
\(699\) | −49.3739 | + | 128.233i | −0.0706350 | + | 0.183452i | ||||
\(700\) | −341.864 | − | 75.0268i | −0.488377 | − | 0.107181i | ||||
\(701\) | − | 1371.35i | − | 1.95628i | −0.207939 | − | 0.978142i | \(-0.566676\pi\) | ||
0.207939 | − | 0.978142i | \(-0.433324\pi\) | |||||||
\(702\) | −252.486 | + | 769.068i | −0.359667 | + | 1.09554i | ||||
\(703\) | 305.628 | − | 305.628i | 0.434749 | − | 0.434749i | ||||
\(704\) | −84.5864 | −0.120151 | ||||||||
\(705\) | 122.973 | + | 238.013i | 0.174430 | + | 0.337606i | ||||
\(706\) | − | 498.690i | − | 0.706360i | ||||||
\(707\) | −1131.42 | − | 392.729i | −1.60031 | − | 0.555487i | ||||
\(708\) | 170.462 | − | 75.6866i | 0.240765 | − | 0.106902i | ||||
\(709\) | − | 403.787i | − | 0.569516i | −0.958600 | − | 0.284758i | \(-0.908087\pi\) | ||
0.958600 | − | 0.284758i | \(-0.0919132\pi\) | |||||||
\(710\) | 25.3522 | + | 428.978i | 0.0357073 | + | 0.604195i | ||||
\(711\) | −663.634 | − | 599.991i | −0.933381 | − | 0.843870i | ||||
\(712\) | 35.3678 | + | 35.3678i | 0.0496738 | + | 0.0496738i | ||||
\(713\) | 768.081 | + | 768.081i | 1.07725 | + | 1.07725i | ||||
\(714\) | −648.388 | + | 54.4369i | −0.908107 | + | 0.0762422i | ||||
\(715\) | 1118.76 | − | 66.1175i | 1.56470 | − | 0.0924721i | ||||
\(716\) | − | 427.530i | − | 0.597109i | ||||||
\(717\) | −365.327 | + | 162.208i | −0.509522 | + | 0.226232i | ||||
\(718\) | 267.685 | + | 267.685i | 0.372821 | + | 0.372821i | ||||
\(719\) | 1058.56i | 1.47226i | 0.676840 | + | 0.736130i | \(0.263349\pi\) | ||||
−0.676840 | + | 0.736130i | \(0.736651\pi\) | |||||||
\(720\) | −19.6444 | − | 178.925i | −0.0272838 | − | 0.248507i | ||||
\(721\) | 315.486 | − | 152.903i | 0.437567 | − | 0.212070i | ||||
\(722\) | −60.5240 | − | 60.5240i | −0.0838283 | − | 0.0838283i | ||||
\(723\) | −373.802 | − | 841.880i | −0.517015 | − | 1.16443i | ||||
\(724\) | 63.7545 | 0.0880587 | ||||||||
\(725\) | 69.7998 | + | 588.470i | 0.0962756 | + | 0.811683i | ||||
\(726\) | −36.4471 | − | 14.0333i | −0.0502026 | − | 0.0193297i | ||||
\(727\) | −138.934 | − | 138.934i | −0.191106 | − | 0.191106i | 0.605068 | − | 0.796174i | \(-0.293146\pi\) |
−0.796174 | + | 0.605068i | \(0.793146\pi\) | |||||||
\(728\) | 137.633 | − | 396.509i | 0.189056 | − | 0.544655i | ||||
\(729\) | −587.144 | − | 432.092i | −0.805410 | − | 0.592718i | ||||
\(730\) | −23.4278 | + | 26.3708i | −0.0320928 | + | 0.0361244i | ||||
\(731\) | 706.735 | 0.966805 | ||||||||
\(732\) | 266.780 | − | 118.453i | 0.364454 | − | 0.161821i | ||||
\(733\) | −777.200 | + | 777.200i | −1.06030 | + | 1.06030i | −0.0622385 | + | 0.998061i | \(0.519824\pi\) |
−0.998061 | + | 0.0622385i | \(0.980176\pi\) | |||||||
\(734\) | − | 846.081i | − | 1.15270i | ||||||
\(735\) | 609.064 | − | 411.420i | 0.828658 | − | 0.559755i | ||||
\(736\) | 185.403 | 0.251906 | ||||||||
\(737\) | 820.259 | + | 820.259i | 1.11297 | + | 1.11297i | ||||
\(738\) | 150.468 | − | 7.57835i | 0.203886 | − | 0.0102688i | ||||
\(739\) | 1369.25i | 1.85285i | 0.376485 | + | 0.926423i | \(0.377133\pi\) | ||||
−0.376485 | + | 0.926423i | \(0.622867\pi\) | |||||||
\(740\) | 248.912 | − | 14.7105i | 0.336368 | − | 0.0198790i | ||||
\(741\) | 396.113 | − | 1028.78i | 0.534566 | − | 1.38836i | ||||
\(742\) | 202.626 | + | 70.3340i | 0.273081 | + | 0.0947897i | ||||
\(743\) | −903.427 | + | 903.427i | −1.21592 | + | 1.21592i | −0.246870 | + | 0.969049i | \(0.579402\pi\) |
−0.969049 | + | 0.246870i | \(0.920598\pi\) | |||||||
\(744\) | −262.439 | − | 101.048i | −0.352741 | − | 0.135817i | ||||
\(745\) | 842.047 | − | 947.827i | 1.13026 | − | 1.27225i | ||||
\(746\) | 106.932i | 0.143341i | ||||||||
\(747\) | −215.079 | + | 10.8325i | −0.287923 | + | 0.0145014i | ||||
\(748\) | −327.606 | + | 327.606i | −0.437976 | + | 0.437976i | ||||
\(749\) | −177.244 | − | 365.709i | −0.236641 | − | 0.488263i | ||||
\(750\) | −297.233 | − | 439.206i | −0.396311 | − | 0.585609i | ||||
\(751\) | 303.273 | 0.403825 | 0.201913 | − | 0.979404i | \(-0.435284\pi\) | ||||
0.201913 | + | 0.979404i | \(0.435284\pi\) | |||||||
\(752\) | 50.5164 | − | 50.5164i | 0.0671760 | − | 0.0671760i | ||||
\(753\) | −562.318 | + | 249.674i | −0.746771 | + | 0.331573i | ||||
\(754\) | −710.635 | −0.942486 | ||||||||
\(755\) | −653.829 | + | 735.964i | −0.865999 | + | 0.974787i | ||||
\(756\) | 300.619 | + | 229.156i | 0.397644 | + | 0.303116i | ||||
\(757\) | 581.912 | − | 581.912i | 0.768708 | − | 0.768708i | −0.209171 | − | 0.977879i | \(-0.567077\pi\) |
0.977879 | + | 0.209171i | \(0.0670766\pi\) | |||||||
\(758\) | −364.774 | + | 364.774i | −0.481233 | + | 0.481233i | ||||
\(759\) | −970.184 | − | 373.553i | −1.27824 | − | 0.492165i | ||||
\(760\) | 14.4625 | + | 244.716i | 0.0190296 | + | 0.321995i | ||||
\(761\) | −863.872 | −1.13518 | −0.567590 | − | 0.823311i | \(-0.692124\pi\) | ||||
−0.567590 | + | 0.823311i | \(0.692124\pi\) | |||||||
\(762\) | −727.204 | + | 322.885i | −0.954336 | + | 0.423734i | ||||
\(763\) | 387.487 | − | 1116.32i | 0.507846 | − | 1.46306i | ||||
\(764\) | 80.9105 | 0.105904 | ||||||||
\(765\) | −769.065 | − | 616.899i | −1.00531 | − | 0.806403i | ||||
\(766\) | − | 226.259i | − | 0.295378i | ||||||
\(767\) | 465.959 | + | 465.959i | 0.607508 | + | 0.607508i | ||||
\(768\) | −43.8700 | + | 19.4787i | −0.0571225 | + | 0.0253629i | ||||
\(769\) | 12.6108 | 0.0163990 | 0.00819951 | − | 0.999966i | \(-0.497390\pi\) | ||||
0.00819951 | + | 0.999966i | \(0.497390\pi\) | |||||||
\(770\) | 142.149 | − | 503.677i | 0.184610 | − | 0.654126i | ||||
\(771\) | −283.893 | + | 737.321i | −0.368214 | + | 0.956318i | ||||
\(772\) | −35.7541 | + | 35.7541i | −0.0463135 | + | 0.0463135i | ||||
\(773\) | 232.135 | + | 232.135i | 0.300304 | + | 0.300304i | 0.841133 | − | 0.540829i | \(-0.181889\pi\) |
−0.540829 | + | 0.841133i | \(0.681889\pi\) | |||||||
\(774\) | −304.553 | − | 275.346i | −0.393479 | − | 0.355744i | ||||
\(775\) | −822.787 | + | 97.5926i | −1.06166 | + | 0.125926i | ||||
\(776\) | 139.187 | 0.179365 | ||||||||
\(777\) | −337.986 | + | 399.940i | −0.434988 | + | 0.514723i | ||||
\(778\) | 77.4189 | + | 77.4189i | 0.0995101 | + | 0.0995101i | ||||
\(779\) | −205.183 | −0.263392 | ||||||||
\(780\) | 565.010 | − | 291.921i | 0.724371 | − | 0.374258i | ||||
\(781\) | −642.566 | −0.822748 | ||||||||
\(782\) | 718.071 | − | 718.071i | 0.918249 | − | 0.918249i | ||||
\(783\) | 199.631 | − | 608.072i | 0.254956 | − | 0.776592i | ||||
\(784\) | −153.848 | − | 121.436i | −0.196235 | − | 0.154893i | ||||
\(785\) | 665.424 | − | 39.3259i | 0.847674 | − | 0.0500967i | ||||
\(786\) | 978.843 | + | 376.887i | 1.24535 | + | 0.479500i | ||||
\(787\) | −241.894 | − | 241.894i | −0.307362 | − | 0.307362i | 0.536523 | − | 0.843886i | \(-0.319737\pi\) |
−0.843886 | + | 0.536523i | \(0.819737\pi\) | |||||||
\(788\) | 196.575 | − | 196.575i | 0.249461 | − | 0.249461i | ||||
\(789\) | −310.283 | + | 805.860i | −0.393261 | + | 1.02137i | ||||
\(790\) | 41.4686 | + | 701.680i | 0.0524918 | + | 0.888202i | ||||
\(791\) | −169.048 | + | 81.9302i | −0.213714 | + | 0.103578i | ||||
\(792\) | 268.811 | − | 13.5388i | 0.339408 | − | 0.0170944i | ||||
\(793\) | 729.246 | + | 729.246i | 0.919604 | + | 0.919604i | ||||
\(794\) | − | 726.850i | − | 0.915428i | ||||||
\(795\) | 149.179 | + | 288.734i | 0.187647 | + | 0.363188i | ||||
\(796\) | 61.0344i | 0.0766764i | ||||||||
\(797\) | −836.625 | + | 836.625i | −1.04972 | + | 1.04972i | −0.0510202 | + | 0.998698i | \(0.516247\pi\) |
−0.998698 | + | 0.0510202i | \(0.983753\pi\) | |||||||
\(798\) | −393.198 | − | 332.288i | −0.492729 | − | 0.416401i | ||||
\(799\) | − | 391.303i | − | 0.489741i | ||||||
\(800\) | −87.5252 | + | 111.083i | −0.109407 | + | 0.138853i | ||||
\(801\) | −118.058 | − | 106.736i | −0.147388 | − | 0.133254i | ||||
\(802\) | −257.812 | + | 257.812i | −0.321461 | + | 0.321461i | ||||
\(803\) | −37.2966 | − | 37.2966i | −0.0464466 | − | 0.0464466i | ||||
\(804\) | 614.311 | + | 236.530i | 0.764069 | + | 0.294192i | ||||
\(805\) | −311.573 | + | 1104.00i | −0.387048 | + | 1.37142i | ||||
\(806\) | − | 993.594i | − | 1.23275i | ||||||
\(807\) | −64.8616 | − | 146.082i | −0.0803737 | − | 0.181018i | ||||
\(808\) | −342.183 | + | 342.183i | −0.423494 | + | 0.423494i | ||||
\(809\) | 1379.61 | 1.70533 | 0.852667 | − | 0.522455i | \(-0.174984\pi\) | ||||
0.852667 | + | 0.522455i | \(0.174984\pi\) | |||||||
\(810\) | 91.0673 | + | 565.470i | 0.112429 | + | 0.698112i | ||||
\(811\) | 704.561i | 0.868755i | 0.900731 | + | 0.434378i | \(0.143032\pi\) | ||||
−0.900731 | + | 0.434378i | \(0.856968\pi\) | |||||||
\(812\) | −108.821 | + | 313.504i | −0.134016 | + | 0.386089i | ||||
\(813\) | −380.778 | − | 857.591i | −0.468361 | − | 1.05485i | ||||
\(814\) | 372.846i | 0.458041i | ||||||||
\(815\) | −1017.30 | + | 60.1213i | −1.24822 | + | 0.0737685i | ||||
\(816\) | −94.4686 | + | 245.352i | −0.115770 | + | 0.300676i | ||||
\(817\) | 395.385 | + | 395.385i | 0.483947 | + | 0.483947i | ||||
\(818\) | −491.252 | − | 491.252i | −0.600552 | − | 0.600552i | ||||
\(819\) | −373.926 | + | 1282.12i | −0.456565 | + | 1.56546i | ||||
\(820\) | −88.4912 | − | 78.6154i | −0.107916 | − | 0.0958724i | ||||
\(821\) | − | 1136.11i | − | 1.38381i | −0.721990 | − | 0.691903i | \(-0.756772\pi\) | ||
0.721990 | − | 0.691903i | \(-0.243228\pi\) | |||||||
\(822\) | −338.453 | − | 762.267i | −0.411744 | − | 0.927332i | ||||
\(823\) | 230.207 | + | 230.207i | 0.279717 | + | 0.279717i | 0.832996 | − | 0.553279i | \(-0.186624\pi\) |
−0.553279 | + | 0.832996i | \(0.686624\pi\) | |||||||
\(824\) | − | 141.658i | − | 0.171915i | ||||||
\(825\) | 681.818 | − | 404.931i | 0.826446 | − | 0.490825i | ||||
\(826\) | 276.916 | − | 134.209i | 0.335249 | − | 0.162481i | ||||
\(827\) | 1110.45 | + | 1110.45i | 1.34274 | + | 1.34274i | 0.893322 | + | 0.449416i | \(0.148368\pi\) |
0.449416 | + | 0.893322i | \(0.351632\pi\) | |||||||
\(828\) | −589.201 | + | 29.6753i | −0.711595 | + | 0.0358397i | ||||
\(829\) | −686.210 | −0.827756 | −0.413878 | − | 0.910332i | \(-0.635826\pi\) | ||||
−0.413878 | + | 0.910332i | \(0.635826\pi\) | |||||||
\(830\) | 126.490 | + | 112.373i | 0.152397 | + | 0.135389i | ||||
\(831\) | −351.952 | + | 914.083i | −0.423528 | + | 1.09998i | ||||
\(832\) | −119.919 | − | 119.919i | −0.144133 | − | 0.144133i | ||||
\(833\) | −1066.19 | + | 125.531i | −1.27993 | + | 0.150697i | ||||
\(834\) | 737.720 | + | 284.046i | 0.884556 | + | 0.340583i | ||||
\(835\) | −34.1064 | − | 577.106i | −0.0408460 | − | 0.691145i | ||||
\(836\) | −366.560 | −0.438469 | ||||||||
\(837\) | 850.193 | + | 279.119i | 1.01576 | + | 0.333476i | ||||
\(838\) | −400.571 | + | 400.571i | −0.478008 | + | 0.478008i | ||||
\(839\) | − | 282.137i | − | 0.336278i | −0.985763 | − | 0.168139i | \(-0.946224\pi\) | ||
0.985763 | − | 0.168139i | \(-0.0537757\pi\) | |||||||
\(840\) | −42.2628 | − | 293.962i | −0.0503129 | − | 0.349955i | ||||
\(841\) | −279.129 | −0.331902 | ||||||||
\(842\) | −281.156 | − | 281.156i | −0.333914 | − | 0.333914i | ||||
\(843\) | −27.5024 | − | 61.9412i | −0.0326245 | − | 0.0734770i | ||||
\(844\) | 61.0150i | 0.0722926i | ||||||||
\(845\) | 1048.10 | + | 931.128i | 1.24035 | + | 1.10193i | ||||
\(846\) | −152.453 | + | 168.624i | −0.180205 | + | 0.199319i | ||||
\(847\) | −60.8751 | − | 21.1305i | −0.0718714 | − | 0.0249474i | ||||
\(848\) | 61.2817 | − | 61.2817i | 0.0722662 | − | 0.0722662i | ||||
\(849\) | −281.502 | + | 731.110i | −0.331569 | + | 0.861143i | ||||
\(850\) | 91.2383 | + | 769.215i | 0.107339 | + | 0.904958i | ||||
\(851\) | − | 817.231i | − | 0.960318i | ||||||
\(852\) | −333.262 | + | 147.971i | −0.391152 | + | 0.173675i | ||||
\(853\) | 302.779 | − | 302.779i | 0.354957 | − | 0.354957i | −0.506993 | − | 0.861950i | \(-0.669243\pi\) |
0.861950 | + | 0.506993i | \(0.169243\pi\) | |||||||
\(854\) | 433.385 | − | 210.043i | 0.507477 | − | 0.245952i | ||||
\(855\) | −85.1300 | − | 775.382i | −0.0995673 | − | 0.906879i | ||||
\(856\) | −164.209 | −0.191833 | ||||||||
\(857\) | 1081.44 | − | 1081.44i | 1.26189 | − | 1.26189i | 0.311717 | − | 0.950175i | \(-0.399096\pi\) |
0.950175 | − | 0.311717i | \(-0.100904\pi\) | |||||||
\(858\) | 385.903 | + | 869.134i | 0.449770 | + | 1.01298i | ||||
\(859\) | 741.737 | 0.863489 | 0.431745 | − | 0.901996i | \(-0.357898\pi\) | ||||
0.431745 | + | 0.901996i | \(0.357898\pi\) | |||||||
\(860\) | 19.0306 | + | 322.013i | 0.0221286 | + | 0.374433i | ||||
\(861\) | 247.702 | − | 20.7964i | 0.287691 | − | 0.0241538i | ||||
\(862\) | 404.384 | − | 404.384i | 0.469123 | − | 0.469123i | ||||
\(863\) | 587.035 | − | 587.035i | 0.680226 | − | 0.680226i | −0.279825 | − | 0.960051i | \(-0.590276\pi\) |
0.960051 | + | 0.279825i | \(0.0902765\pi\) | |||||||
\(864\) | 136.299 | − | 68.9241i | 0.157754 | − | 0.0797733i | ||||
\(865\) | 1042.73 | − | 61.6245i | 1.20547 | − | 0.0712422i | ||||
\(866\) | 87.2228 | 0.100719 | ||||||||
\(867\) | 232.542 | + | 523.733i | 0.268214 | + | 0.604075i | ||||
\(868\) | −438.334 | − | 152.151i | −0.504994 | − | 0.175289i | ||||
\(869\) | −1051.04 | −1.20949 | ||||||||
\(870\) | −446.731 | + | 230.810i | −0.513484 | + | 0.265299i | ||||
\(871\) | 2325.78i | 2.67024i | ||||||||
\(872\) | −337.615 | − | 337.615i | −0.387174 | − | 0.387174i | ||||
\(873\) | −442.330 | + | 22.2781i | −0.506679 | + | 0.0255190i | ||||
\(874\) | 803.453 | 0.919283 | ||||||||
\(875\) | −514.362 | − | 707.853i | −0.587843 | − | 0.808975i | ||||
\(876\) | −27.9323 | − | 10.7549i | −0.0318862 | − | 0.0122772i | ||||
\(877\) | 173.095 | − | 173.095i | 0.197371 | − | 0.197371i | −0.601501 | − | 0.798872i | \(-0.705430\pi\) |
0.798872 | + | 0.601501i | \(0.205430\pi\) | |||||||
\(878\) | 605.567 | + | 605.567i | 0.689712 | + | 0.689712i | ||||
\(879\) | −201.740 | − | 77.6765i | −0.229511 | − | 0.0883692i | ||||
\(880\) | −158.090 | − | 140.447i | −0.179648 | − | 0.159599i | ||||
\(881\) | −253.460 | −0.287696 | −0.143848 | − | 0.989600i | \(-0.545948\pi\) | ||||
−0.143848 | + | 0.989600i | \(0.545948\pi\) | |||||||
\(882\) | 508.358 | + | 361.294i | 0.576370 | + | 0.409631i | ||||
\(883\) | −1004.53 | − | 1004.53i | −1.13764 | − | 1.13764i | −0.988873 | − | 0.148762i | \(-0.952471\pi\) |
−0.148762 | − | 0.988873i | \(-0.547529\pi\) | |||||||
\(884\) | −928.901 | −1.05079 | ||||||||
\(885\) | 444.260 | + | 141.578i | 0.501988 | + | 0.159975i | ||||
\(886\) | −179.316 | −0.202388 | ||||||||
\(887\) | 1154.22 | − | 1154.22i | 1.30126 | − | 1.30126i | 0.373718 | − | 0.927542i | \(-0.378083\pi\) |
0.927542 | − | 0.373718i | \(-0.121917\pi\) | |||||||
\(888\) | 85.8595 | + | 193.373i | 0.0966886 | + | 0.217763i | ||||
\(889\) | −1181.34 | + | 572.548i | −1.32885 | + | 0.644036i | ||||
\(890\) | 7.37710 | + | 124.826i | 0.00828888 | + | 0.140254i | ||||
\(891\) | −852.103 | + | 86.0511i | −0.956344 | + | 0.0965782i | ||||
\(892\) | −141.877 | − | 141.877i | −0.159055 | − | 0.159055i | ||||
\(893\) | 218.916 | − | 218.916i | 0.245146 | − | 0.245146i | ||||
\(894\) | 1003.95 | + | 386.554i | 1.12299 | + | 0.432387i | ||||
\(895\) | 709.870 | − | 799.045i | 0.793151 | − | 0.892788i | ||||
\(896\) | −71.2670 | + | 34.5401i | −0.0795390 | + | 0.0385492i | ||||
\(897\) | −845.851 | − | 1905.03i | −0.942977 | − | 2.12378i | ||||
\(898\) | −335.741 | − | 335.741i | −0.373876 | − | 0.373876i | ||||
\(899\) | 785.596i | 0.873855i | ||||||||
\(900\) | 260.371 | − | 367.024i | 0.289301 | − | 0.407805i | ||||
\(901\) | − | 474.692i | − | 0.526850i | ||||||
\(902\) | 125.154 | − | 125.154i | 0.138752 | − | 0.138752i | ||||
\(903\) | −517.394 | − | 437.245i | −0.572972 | − | 0.484214i | ||||
\(904\) | 75.9051i | 0.0839658i | ||||||||
\(905\) | 119.156 | + | 105.858i | 0.131664 | + | 0.116970i | ||||
\(906\) | −779.543 | − | 300.150i | −0.860423 | − | 0.331291i | ||||
\(907\) | −1224.78 | + | 1224.78i | −1.35036 | + | 1.35036i | −0.465113 | + | 0.885251i | \(0.653986\pi\) |
−0.885251 | + | 0.465113i | \(0.846014\pi\) | |||||||
\(908\) | −279.411 | − | 279.411i | −0.307721 | − | 0.307721i | ||||
\(909\) | 1032.67 | − | 1142.21i | 1.13605 | − | 1.25656i | ||||
\(910\) | 915.595 | − | 512.542i | 1.00615 | − | 0.563232i | ||||
\(911\) | 756.390i | 0.830285i | 0.909756 | + | 0.415142i | \(0.136268\pi\) | ||||
−0.909756 | + | 0.415142i | \(0.863732\pi\) | |||||||
\(912\) | −190.114 | + | 84.4121i | −0.208458 | + | 0.0925571i | ||||
\(913\) | −178.896 | + | 178.896i | −0.195943 | + | 0.195943i | ||||
\(914\) | 859.463 | 0.940332 | ||||||||
\(915\) | 695.285 | + | 221.575i | 0.759875 | + | 0.242159i | ||||
\(916\) | 38.1040i | 0.0415983i | ||||||||
\(917\) | 1634.89 | + | 567.492i | 1.78287 | + | 0.618857i | ||||
\(918\) | 260.946 | − | 794.837i | 0.284255 | − | 0.865835i | ||||
\(919\) | − | 116.689i | − | 0.126974i | −0.997983 | − | 0.0634868i | \(-0.979778\pi\) | ||
0.997983 | − | 0.0634868i | \(-0.0202221\pi\) | |||||||
\(920\) | 346.514 | + | 307.842i | 0.376645 | + | 0.334611i | ||||
\(921\) | −277.120 | − | 106.700i | −0.300891 | − | 0.115853i | ||||
\(922\) | 23.6913 | + | 23.6913i | 0.0256955 | + | 0.0256955i | ||||
\(923\) | −910.973 | − | 910.973i | −0.986970 | − | 0.986970i | ||||
\(924\) | 442.521 | − | 37.1529i | 0.478919 | − | 0.0402088i | ||||
\(925\) | 489.637 | + | 385.800i | 0.529338 | + | 0.417081i | ||||
\(926\) | − | 456.099i | − | 0.492548i | ||||||
\(927\) | 22.6736 | + | 450.183i | 0.0244591 | + | 0.485634i | ||||
\(928\) | 94.8153 | + | 94.8153i | 0.102172 | + | 0.102172i | ||||
\(929\) | 207.256i | 0.223096i | 0.993759 | + | 0.111548i | \(0.0355809\pi\) | ||||
−0.993759 | + | 0.111548i | \(0.964419\pi\) | |||||||
\(930\) | −322.714 | − | 624.610i | −0.347004 | − | 0.671623i | ||||
\(931\) | −666.710 | − | 526.252i | −0.716122 | − | 0.565255i | ||||
\(932\) | 64.7756 | + | 64.7756i | 0.0695017 | + | 0.0695017i | ||||
\(933\) | 71.5963 | − | 31.7894i | 0.0767377 | − | 0.0340722i | ||||
\(934\) | 719.670 | 0.770525 | ||||||||
\(935\) | −1156.24 | + | 68.3328i | −1.23662 | + | 0.0730833i | ||||
\(936\) | 400.291 | + | 361.903i | 0.427661 | + | 0.386649i | ||||
\(937\) | 661.552 | + | 661.552i | 0.706032 | + | 0.706032i | 0.965698 | − | 0.259667i | \(-0.0836127\pi\) |
−0.259667 | + | 0.965698i | \(0.583613\pi\) | |||||||
\(938\) | 1026.04 | + | 356.152i | 1.09386 | + | 0.379693i | ||||
\(939\) | 88.2183 | − | 229.119i | 0.0939492 | − | 0.244003i | ||||
\(940\) | 178.291 | − | 10.5368i | 0.189672 | − | 0.0112094i | ||||
\(941\) | −429.685 | −0.456626 | −0.228313 | − | 0.973588i | \(-0.573321\pi\) | ||||
−0.228313 | + | 0.973588i | \(0.573321\pi\) | |||||||
\(942\) | 229.530 | + | 516.950i | 0.243663 | + | 0.548779i | ||||
\(943\) | −274.323 | + | 274.323i | −0.290904 | + | 0.290904i | ||||
\(944\) | − | 124.340i | − | 0.131716i | ||||||
\(945\) | 181.361 | + | 927.434i | 0.191916 | + | 0.981411i | ||||
\(946\) | −482.342 | −0.509876 | ||||||||
\(947\) | −508.925 | − | 508.925i | −0.537407 | − | 0.537407i | 0.385359 | − | 0.922767i | \(-0.374077\pi\) |
−0.922767 | + | 0.385359i | \(0.874077\pi\) | |||||||
\(948\) | −545.116 | + | 242.036i | −0.575017 | + | 0.255313i | ||||
\(949\) | − | 105.752i | − | 0.111435i | ||||||
\(950\) | −379.296 | + | 481.383i | −0.399259 | + | 0.506719i | ||||
\(951\) | 1458.65 | + | 561.628i | 1.53380 | + | 0.590565i | ||||
\(952\) | −142.245 | + | 409.794i | −0.149416 | + | 0.430456i | ||||
\(953\) | −1189.34 | + | 1189.34i | −1.24799 | + | 1.24799i | −0.291390 | + | 0.956604i | \(0.594118\pi\) |
−0.956604 | + | 0.291390i | \(0.905882\pi\) | |||||||
\(954\) | −184.942 | + | 204.559i | −0.193859 | + | 0.214422i | ||||
\(955\) | 151.220 | + | 134.343i | 0.158346 | + | 0.140674i | ||||
\(956\) | 266.480i | 0.278744i | ||||||||
\(957\) | −305.118 | − | 687.190i | −0.318828 | − | 0.718067i | ||||
\(958\) | 470.256 | − | 470.256i | 0.490873 | − | 0.490873i | ||||
\(959\) | −600.154 | − | 1238.30i | −0.625812 | − | 1.29125i | ||||
\(960\) | −114.335 | − | 36.4364i | −0.119098 | − | 0.0379546i | ||||
\(961\) | −137.403 | −0.142979 | ||||||||
\(962\) | −528.588 | + | 528.588i | −0.549467 | + | 0.549467i | ||||
\(963\) | 521.849 | − | 26.2831i | 0.541900 | − | 0.0272929i | ||||
\(964\) | −614.090 | −0.637023 | ||||||||
\(965\) | −126.189 | + | 7.45767i | −0.130766 | + | 0.00772816i | ||||
\(966\) | −969.951 | + | 81.4344i | −1.00409 | + | 0.0843007i | ||||
\(967\) | 54.5754 | − | 54.5754i | 0.0564378 | − | 0.0564378i | −0.678325 | − | 0.734762i | \(-0.737294\pi\) |
0.734762 | + | 0.678325i | \(0.237294\pi\) | |||||||
\(968\) | −18.4109 | + | 18.4109i | −0.0190195 | + | 0.0190195i | ||||
\(969\) | −409.385 | + | 1063.25i | −0.422482 | + | 1.09726i | ||||
\(970\) | 260.138 | + | 231.106i | 0.268184 | + | 0.238254i | ||||
\(971\) | −726.681 | −0.748384 | −0.374192 | − | 0.927351i | \(-0.622080\pi\) | ||||
−0.374192 | + | 0.927351i | \(0.622080\pi\) | |||||||
\(972\) | −422.120 | + | 240.853i | −0.434280 | + | 0.247792i | ||||
\(973\) | 1232.16 | + | 427.698i | 1.26635 | + | 0.439567i | ||||
\(974\) | −492.475 | −0.505621 | ||||||||
\(975\) | 1540.70 | + | 392.546i | 1.58020 | + | 0.402611i | ||||
\(976\) | − | 194.597i | − | 0.199382i | ||||||
\(977\) | 569.312 | + | 569.312i | 0.582715 | + | 0.582715i | 0.935648 | − | 0.352934i | \(-0.114816\pi\) |
−0.352934 | + | 0.935648i | \(0.614816\pi\) | |||||||
\(978\) | −350.905 | − | 790.312i | −0.358799 | − | 0.808090i | ||||
\(979\) | −186.977 | −0.190988 | ||||||||
\(980\) | −85.9060 | − | 482.411i | −0.0876592 | − | 0.492256i | ||||
\(981\) | 1126.96 | + | 1018.89i | 1.14879 | + | 1.03862i | ||||
\(982\) | 5.09974 | − | 5.09974i | 0.00519322 | − | 0.00519322i | ||||
\(983\) | −451.224 | − | 451.224i | −0.459028 | − | 0.459028i | 0.439308 | − | 0.898336i | \(-0.355224\pi\) |
−0.898336 | + | 0.439308i | \(0.855224\pi\) | |||||||
\(984\) | 36.0896 | − | 93.7311i | 0.0366764 | − | 0.0952552i | ||||
\(985\) | 693.787 | − | 41.0021i | 0.704352 | − | 0.0416265i | ||||
\(986\) | 734.445 | 0.744874 | ||||||||
\(987\) | −242.093 | + | 286.469i | −0.245281 | + | 0.290243i | ||||
\(988\) | −519.677 | − | 519.677i | −0.525988 | − | 0.525988i | ||||
\(989\) | 1057.23 | 1.06899 | ||||||||
\(990\) | 524.883 | + | 421.030i | 0.530184 | + | 0.425283i | ||||
\(991\) | 532.695 | 0.537533 | 0.268766 | − | 0.963205i | \(-0.413384\pi\) | ||||
0.268766 | + | 0.963205i | \(0.413384\pi\) | |||||||
\(992\) | −132.569 | + | 132.569i | −0.133638 | + | 0.133638i | ||||
\(993\) | −473.743 | + | 210.346i | −0.477083 | + | 0.211829i | ||||
\(994\) | −541.384 | + | 262.386i | −0.544652 | + | 0.263970i | ||||
\(995\) | −101.341 | + | 114.072i | −0.101851 | + | 0.114645i | ||||
\(996\) | −51.5865 | + | 133.979i | −0.0517937 | + | 0.134518i | ||||
\(997\) | 884.526 | + | 884.526i | 0.887188 | + | 0.887188i | 0.994252 | − | 0.107064i | \(-0.0341451\pi\) |
−0.107064 | + | 0.994252i | \(0.534145\pi\) | |||||||
\(998\) | −678.365 | + | 678.365i | −0.679725 | + | 0.679725i | ||||
\(999\) | −303.809 | − | 600.789i | −0.304113 | − | 0.601390i |
(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 | 210.3.k.b.83.3 | yes | 32 | |
3.2 | odd | 2 | 210.3.k.a.83.6 | ✓ | 32 | ||
5.2 | odd | 4 | 210.3.k.a.167.11 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.b.83.14 | yes | 32 | |
15.2 | even | 4 | inner | 210.3.k.b.167.14 | yes | 32 | |
21.20 | even | 2 | 210.3.k.a.83.11 | yes | 32 | ||
35.27 | even | 4 | 210.3.k.a.167.6 | yes | 32 | ||
105.62 | odd | 4 | inner | 210.3.k.b.167.3 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.6 | ✓ | 32 | 3.2 | odd | 2 | ||
210.3.k.a.83.11 | yes | 32 | 21.20 | even | 2 | ||
210.3.k.a.167.6 | yes | 32 | 35.27 | even | 4 | ||
210.3.k.a.167.11 | yes | 32 | 5.2 | odd | 4 | ||
210.3.k.b.83.3 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.k.b.83.14 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.b.167.3 | yes | 32 | 105.62 | odd | 4 | inner | |
210.3.k.b.167.14 | yes | 32 | 15.2 | even | 4 | inner |