Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [78,3,Mod(53,78)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(78, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("78.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 78 = 2 \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 78.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.12534606201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.16845963264.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 6x^{6} + 15x^{4} + 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 53.1 | ||
Root | \(-0.444099 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 78.53 |
Dual form | 78.3.c.a.53.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(67\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | −2.93352 | + | 0.628052i | −0.977841 | + | 0.209351i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 6.81894i | 1.36379i | 0.731451 | + | 0.681894i | \(0.238844\pi\) | ||||
−0.731451 | + | 0.681894i | \(0.761156\pi\) | |||||||
\(6\) | 0.888199 | + | 4.14863i | 0.148033 | + | 0.691438i | ||||
\(7\) | −9.58440 | −1.36920 | −0.684600 | − | 0.728919i | \(-0.740023\pi\) | ||||
−0.684600 | + | 0.728919i | \(0.740023\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 8.21110 | − | 3.68481i | 0.912345 | − | 0.409423i | ||||
\(10\) | 9.64344 | 0.964344 | ||||||||
\(11\) | 15.6028i | 1.41843i | 0.704990 | + | 0.709217i | \(0.250951\pi\) | ||||
−0.704990 | + | 0.709217i | \(0.749049\pi\) | |||||||
\(12\) | 5.86704 | − | 1.25610i | 0.488920 | − | 0.104675i | ||||
\(13\) | −3.60555 | −0.277350 | ||||||||
\(14\) | 13.5544i | 0.968170i | ||||||||
\(15\) | −4.28265 | − | 20.0035i | −0.285510 | − | 1.33357i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 15.6099i | − | 0.918231i | −0.888376 | − | 0.459116i | \(-0.848166\pi\) | ||
0.888376 | − | 0.459116i | \(-0.151834\pi\) | |||||||
\(18\) | −5.21110 | − | 11.6123i | −0.289506 | − | 0.645125i | ||||
\(19\) | −24.1247 | −1.26972 | −0.634860 | − | 0.772627i | \(-0.718942\pi\) | ||||
−0.634860 | + | 0.772627i | \(0.718942\pi\) | |||||||
\(20\) | − | 13.6379i | − | 0.681894i | ||||||
\(21\) | 28.1160 | − | 6.01949i | 1.33886 | − | 0.286643i | ||||
\(22\) | 22.0656 | 1.00298 | ||||||||
\(23\) | − | 8.09698i | − | 0.352043i | −0.984386 | − | 0.176021i | \(-0.943677\pi\) | ||
0.984386 | − | 0.176021i | \(-0.0563228\pi\) | |||||||
\(24\) | −1.77640 | − | 8.29725i | −0.0740166 | − | 0.345719i | ||||
\(25\) | −21.4980 | −0.859919 | ||||||||
\(26\) | 5.09902i | 0.196116i | ||||||||
\(27\) | −21.7732 | + | 15.9665i | −0.806415 | + | 0.591350i | ||||
\(28\) | 19.1688 | 0.684600 | ||||||||
\(29\) | 33.5148i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(30\) | −28.2892 | + | 6.05658i | −0.942975 | + | 0.201886i | ||||
\(31\) | 31.1754 | 1.00566 | 0.502829 | − | 0.864386i | \(-0.332293\pi\) | ||||
0.502829 | + | 0.864386i | \(0.332293\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | −9.79934 | − | 45.7711i | −0.296950 | − | 1.38700i | ||||
\(34\) | −22.0758 | −0.649288 | ||||||||
\(35\) | − | 65.3555i | − | 1.86730i | ||||||
\(36\) | −16.4222 | + | 7.36961i | −0.456172 | + | 0.204711i | ||||
\(37\) | 40.8558 | 1.10421 | 0.552106 | − | 0.833774i | \(-0.313824\pi\) | ||||
0.552106 | + | 0.833774i | \(0.313824\pi\) | |||||||
\(38\) | 34.1175i | 0.897828i | ||||||||
\(39\) | 10.5770 | − | 2.26447i | 0.271204 | − | 0.0580634i | ||||
\(40\) | −19.2869 | −0.482172 | ||||||||
\(41\) | 60.5466i | 1.47675i | 0.674393 | + | 0.738373i | \(0.264405\pi\) | ||||
−0.674393 | + | 0.738373i | \(0.735595\pi\) | |||||||
\(42\) | −8.51285 | − | 39.7621i | −0.202687 | − | 0.946716i | ||||
\(43\) | 18.6249 | 0.433138 | 0.216569 | − | 0.976267i | \(-0.430513\pi\) | ||||
0.216569 | + | 0.976267i | \(0.430513\pi\) | |||||||
\(44\) | − | 31.2055i | − | 0.709217i | ||||||
\(45\) | 25.1265 | + | 55.9910i | 0.558366 | + | 1.24425i | ||||
\(46\) | −11.4509 | −0.248932 | ||||||||
\(47\) | 6.55340i | 0.139434i | 0.997567 | + | 0.0697170i | \(0.0222096\pi\) | ||||
−0.997567 | + | 0.0697170i | \(0.977790\pi\) | |||||||
\(48\) | −11.7341 | + | 2.51221i | −0.244460 | + | 0.0523376i | ||||
\(49\) | 42.8607 | 0.874707 | ||||||||
\(50\) | 30.4027i | 0.608055i | ||||||||
\(51\) | 9.80384 | + | 45.7921i | 0.192232 | + | 0.897884i | ||||
\(52\) | 7.21110 | 0.138675 | ||||||||
\(53\) | 39.5256i | 0.745767i | 0.927878 | + | 0.372883i | \(0.121631\pi\) | ||||
−0.927878 | + | 0.372883i | \(0.878369\pi\) | |||||||
\(54\) | 22.5800 | + | 30.7920i | 0.418148 | + | 0.570221i | ||||
\(55\) | −106.394 | −1.93444 | ||||||||
\(56\) | − | 27.1088i | − | 0.484085i | ||||||
\(57\) | 70.7703 | − | 15.1516i | 1.24158 | − | 0.265817i | ||||
\(58\) | 47.3971 | 0.817192 | ||||||||
\(59\) | − | 48.4157i | − | 0.820606i | −0.911949 | − | 0.410303i | \(-0.865423\pi\) | ||
0.911949 | − | 0.410303i | \(-0.134577\pi\) | |||||||
\(60\) | 8.56530 | + | 40.0070i | 0.142755 | + | 0.666784i | ||||
\(61\) | −33.4519 | −0.548391 | −0.274196 | − | 0.961674i | \(-0.588412\pi\) | ||||
−0.274196 | + | 0.961674i | \(0.588412\pi\) | |||||||
\(62\) | − | 44.0887i | − | 0.711107i | ||||||
\(63\) | −78.6985 | + | 35.3166i | −1.24918 | + | 0.560582i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − | 24.5860i | − | 0.378247i | ||||||
\(66\) | −64.7301 | + | 13.8584i | −0.980758 | + | 0.209975i | ||||
\(67\) | 0.352240 | 0.00525732 | 0.00262866 | − | 0.999997i | \(-0.499163\pi\) | ||||
0.00262866 | + | 0.999997i | \(0.499163\pi\) | |||||||
\(68\) | 31.2199i | 0.459116i | ||||||||
\(69\) | 5.08532 | + | 23.7527i | 0.0737003 | + | 0.344242i | ||||
\(70\) | −92.4266 | −1.32038 | ||||||||
\(71\) | 99.3891i | 1.39985i | 0.714218 | + | 0.699923i | \(0.246782\pi\) | ||||
−0.714218 | + | 0.699923i | \(0.753218\pi\) | |||||||
\(72\) | 10.4222 | + | 23.2245i | 0.144753 | + | 0.322563i | ||||
\(73\) | −94.9501 | −1.30069 | −0.650343 | − | 0.759641i | \(-0.725375\pi\) | ||||
−0.650343 | + | 0.759641i | \(0.725375\pi\) | |||||||
\(74\) | − | 57.7789i | − | 0.780796i | ||||||
\(75\) | 63.0648 | − | 13.5018i | 0.840864 | − | 0.180025i | ||||
\(76\) | 48.2494 | 0.634860 | ||||||||
\(77\) | − | 149.543i | − | 1.94212i | ||||||
\(78\) | −3.20245 | − | 14.9581i | −0.0410570 | − | 0.191770i | ||||
\(79\) | 51.4866 | 0.651729 | 0.325865 | − | 0.945416i | \(-0.394345\pi\) | ||||
0.325865 | + | 0.945416i | \(0.394345\pi\) | |||||||
\(80\) | 27.2758i | 0.340947i | ||||||||
\(81\) | 53.8444 | − | 60.5126i | 0.664746 | − | 0.747070i | ||||
\(82\) | 85.6258 | 1.04422 | ||||||||
\(83\) | 87.9015i | 1.05905i | 0.848293 | + | 0.529527i | \(0.177631\pi\) | ||||
−0.848293 | + | 0.529527i | \(0.822369\pi\) | |||||||
\(84\) | −56.2321 | + | 12.0390i | −0.669429 | + | 0.143321i | ||||
\(85\) | 106.443 | 1.25227 | ||||||||
\(86\) | − | 26.3396i | − | 0.306275i | ||||||
\(87\) | −21.0490 | − | 98.3165i | −0.241943 | − | 1.13007i | ||||
\(88\) | −44.1313 | −0.501492 | ||||||||
\(89\) | − | 108.309i | − | 1.21696i | −0.793569 | − | 0.608480i | \(-0.791780\pi\) | ||
0.793569 | − | 0.608480i | \(-0.208220\pi\) | |||||||
\(90\) | 79.1833 | − | 35.5342i | 0.879814 | − | 0.394825i | ||||
\(91\) | 34.5570 | 0.379748 | ||||||||
\(92\) | 16.1940i | 0.176021i | ||||||||
\(93\) | −91.4537 | + | 19.5798i | −0.983373 | + | 0.210535i | ||||
\(94\) | 9.26791 | 0.0985948 | ||||||||
\(95\) | − | 164.505i | − | 1.73163i | ||||||
\(96\) | 3.55280 | + | 16.5945i | 0.0370083 | + | 0.172859i | ||||
\(97\) | −82.7350 | −0.852938 | −0.426469 | − | 0.904502i | \(-0.640243\pi\) | ||||
−0.426469 | + | 0.904502i | \(0.640243\pi\) | |||||||
\(98\) | − | 60.6141i | − | 0.618511i | ||||||
\(99\) | 57.4932 | + | 128.116i | 0.580739 | + | 1.29410i | ||||
\(100\) | 42.9960 | 0.429960 | ||||||||
\(101\) | − | 43.6823i | − | 0.432498i | −0.976338 | − | 0.216249i | \(-0.930618\pi\) | ||
0.976338 | − | 0.216249i | \(-0.0693822\pi\) | |||||||
\(102\) | 64.7598 | − | 13.8647i | 0.634900 | − | 0.135929i | ||||
\(103\) | −79.9691 | −0.776399 | −0.388200 | − | 0.921575i | \(-0.626903\pi\) | ||||
−0.388200 | + | 0.921575i | \(0.626903\pi\) | |||||||
\(104\) | − | 10.1980i | − | 0.0980581i | ||||||
\(105\) | 41.0466 | + | 191.722i | 0.390920 | + | 1.82592i | ||||
\(106\) | 55.8977 | 0.527337 | ||||||||
\(107\) | − | 123.680i | − | 1.15588i | −0.816078 | − | 0.577942i | \(-0.803856\pi\) | ||
0.816078 | − | 0.577942i | \(-0.196144\pi\) | |||||||
\(108\) | 43.5464 | − | 31.9329i | 0.403207 | − | 0.295675i | ||||
\(109\) | 42.8003 | 0.392664 | 0.196332 | − | 0.980538i | \(-0.437097\pi\) | ||||
0.196332 | + | 0.980538i | \(0.437097\pi\) | |||||||
\(110\) | 150.464i | 1.36786i | ||||||||
\(111\) | −119.852 | + | 25.6596i | −1.07974 | + | 0.231167i | ||||
\(112\) | −38.3376 | −0.342300 | ||||||||
\(113\) | 84.5000i | 0.747787i | 0.927472 | + | 0.373894i | \(0.121977\pi\) | ||||
−0.927472 | + | 0.373894i | \(0.878023\pi\) | |||||||
\(114\) | −21.4275 | − | 100.084i | −0.187961 | − | 0.877933i | ||||
\(115\) | 55.2129 | 0.480112 | ||||||||
\(116\) | − | 67.0297i | − | 0.577842i | ||||||
\(117\) | −29.6056 | + | 13.2858i | −0.253039 | + | 0.113553i | ||||
\(118\) | −68.4702 | −0.580256 | ||||||||
\(119\) | 149.612i | 1.25724i | ||||||||
\(120\) | 56.5785 | − | 12.1132i | 0.471487 | − | 0.100943i | ||||
\(121\) | −122.446 | −1.01195 | ||||||||
\(122\) | 47.3081i | 0.387771i | ||||||||
\(123\) | −38.0264 | − | 177.615i | −0.309157 | − | 1.44402i | ||||
\(124\) | −62.3508 | −0.502829 | ||||||||
\(125\) | 23.8800i | 0.191040i | ||||||||
\(126\) | 49.9453 | + | 111.296i | 0.396391 | + | 0.883305i | ||||
\(127\) | −13.2028 | −0.103959 | −0.0519794 | − | 0.998648i | \(-0.516553\pi\) | ||||
−0.0519794 | + | 0.998648i | \(0.516553\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | −54.6366 | + | 11.6974i | −0.423540 | + | 0.0906776i | ||||
\(130\) | −34.7699 | −0.267461 | ||||||||
\(131\) | 164.929i | 1.25900i | 0.777000 | + | 0.629501i | \(0.216740\pi\) | ||||
−0.777000 | + | 0.629501i | \(0.783260\pi\) | |||||||
\(132\) | 19.5987 | + | 91.5421i | 0.148475 | + | 0.693501i | ||||
\(133\) | 231.221 | 1.73850 | ||||||||
\(134\) | − | 0.498143i | − | 0.00371749i | ||||||
\(135\) | −108.874 | − | 148.470i | −0.806477 | − | 1.09978i | ||||
\(136\) | 44.1516 | 0.324644 | ||||||||
\(137\) | − | 48.3810i | − | 0.353146i | −0.984288 | − | 0.176573i | \(-0.943499\pi\) | ||
0.984288 | − | 0.176573i | \(-0.0565011\pi\) | |||||||
\(138\) | 33.5914 | − | 7.19173i | 0.243416 | − | 0.0521140i | ||||
\(139\) | −40.5641 | −0.291828 | −0.145914 | − | 0.989297i | \(-0.546612\pi\) | ||||
−0.145914 | + | 0.989297i | \(0.546612\pi\) | |||||||
\(140\) | 130.711i | 0.933649i | ||||||||
\(141\) | −4.11587 | − | 19.2246i | −0.0291906 | − | 0.136344i | ||||
\(142\) | 140.557 | 0.989841 | ||||||||
\(143\) | − | 56.2566i | − | 0.393403i | ||||||
\(144\) | 32.8444 | − | 14.7392i | 0.228086 | − | 0.102356i | ||||
\(145\) | −228.536 | −1.57611 | ||||||||
\(146\) | 134.280i | 0.919724i | ||||||||
\(147\) | −125.733 | + | 26.9187i | −0.855324 | + | 0.183120i | ||||
\(148\) | −81.7117 | −0.552106 | ||||||||
\(149\) | 193.107i | 1.29602i | 0.761630 | + | 0.648012i | \(0.224399\pi\) | ||||
−0.761630 | + | 0.648012i | \(0.775601\pi\) | |||||||
\(150\) | −19.0945 | − | 89.1871i | −0.127297 | − | 0.594581i | ||||
\(151\) | 155.839 | 1.03205 | 0.516023 | − | 0.856575i | \(-0.327412\pi\) | ||||
0.516023 | + | 0.856575i | \(0.327412\pi\) | |||||||
\(152\) | − | 68.2349i | − | 0.448914i | ||||||
\(153\) | −57.5196 | − | 128.175i | −0.375945 | − | 0.837744i | ||||
\(154\) | −211.486 | −1.37329 | ||||||||
\(155\) | 212.583i | 1.37150i | ||||||||
\(156\) | −21.1539 | + | 4.52894i | −0.135602 | + | 0.0290317i | ||||
\(157\) | 64.8982 | 0.413365 | 0.206682 | − | 0.978408i | \(-0.433733\pi\) | ||||
0.206682 | + | 0.978408i | \(0.433733\pi\) | |||||||
\(158\) | − | 72.8131i | − | 0.460842i | ||||||
\(159\) | −24.8241 | − | 115.949i | −0.156127 | − | 0.729241i | ||||
\(160\) | 38.5738 | 0.241086 | ||||||||
\(161\) | 77.6047i | 0.482017i | ||||||||
\(162\) | −85.5778 | − | 76.1475i | −0.528258 | − | 0.470046i | ||||
\(163\) | 295.523 | 1.81303 | 0.906513 | − | 0.422177i | \(-0.138734\pi\) | ||||
0.906513 | + | 0.422177i | \(0.138734\pi\) | |||||||
\(164\) | − | 121.093i | − | 0.738373i | ||||||
\(165\) | 312.110 | − | 66.8212i | 1.89158 | − | 0.404977i | ||||
\(166\) | 124.311 | 0.748864 | ||||||||
\(167\) | 86.5149i | 0.518053i | 0.965870 | + | 0.259027i | \(0.0834017\pi\) | ||||
−0.965870 | + | 0.259027i | \(0.916598\pi\) | |||||||
\(168\) | 17.0257 | + | 79.5242i | 0.101343 | + | 0.473358i | ||||
\(169\) | 13.0000 | 0.0769231 | ||||||||
\(170\) | − | 150.533i | − | 0.885491i | ||||||
\(171\) | −198.090 | + | 88.8948i | −1.15842 | + | 0.519853i | ||||
\(172\) | −37.2498 | −0.216569 | ||||||||
\(173\) | 79.8623i | 0.461632i | 0.972997 | + | 0.230816i | \(0.0741395\pi\) | ||||
−0.972997 | + | 0.230816i | \(0.925861\pi\) | |||||||
\(174\) | −139.041 | + | 29.7678i | −0.799083 | + | 0.171080i | ||||
\(175\) | 206.045 | 1.17740 | ||||||||
\(176\) | 62.4111i | 0.354608i | ||||||||
\(177\) | 30.4076 | + | 142.029i | 0.171794 | + | 0.802421i | ||||
\(178\) | −153.173 | −0.860520 | ||||||||
\(179\) | − | 200.837i | − | 1.12199i | −0.827818 | − | 0.560996i | \(-0.810418\pi\) | ||
0.827818 | − | 0.560996i | \(-0.189582\pi\) | |||||||
\(180\) | −50.2530 | − | 111.982i | −0.279183 | − | 0.622123i | ||||
\(181\) | −46.9661 | −0.259481 | −0.129741 | − | 0.991548i | \(-0.541414\pi\) | ||||
−0.129741 | + | 0.991548i | \(0.541414\pi\) | |||||||
\(182\) | − | 48.8710i | − | 0.268522i | ||||||
\(183\) | 98.1317 | − | 21.0095i | 0.536239 | − | 0.114806i | ||||
\(184\) | 22.9017 | 0.124466 | ||||||||
\(185\) | 278.594i | 1.50591i | ||||||||
\(186\) | 27.6900 | + | 129.335i | 0.148871 | + | 0.695350i | ||||
\(187\) | 243.558 | 1.30245 | ||||||||
\(188\) | − | 13.1068i | − | 0.0697170i | ||||||
\(189\) | 208.683 | − | 153.029i | 1.10414 | − | 0.809676i | ||||
\(190\) | −232.645 | −1.22445 | ||||||||
\(191\) | − | 12.0342i | − | 0.0630062i | −0.999504 | − | 0.0315031i | \(-0.989971\pi\) | ||
0.999504 | − | 0.0315031i | \(-0.0100294\pi\) | |||||||
\(192\) | 23.4682 | − | 5.02441i | 0.122230 | − | 0.0261688i | ||||
\(193\) | −265.711 | −1.37674 | −0.688369 | − | 0.725360i | \(-0.741673\pi\) | ||||
−0.688369 | + | 0.725360i | \(0.741673\pi\) | |||||||
\(194\) | 117.005i | 0.603118i | ||||||||
\(195\) | 15.4413 | + | 72.1237i | 0.0791862 | + | 0.369865i | ||||
\(196\) | −85.7213 | −0.437354 | ||||||||
\(197\) | − | 324.865i | − | 1.64906i | −0.565817 | − | 0.824531i | \(-0.691439\pi\) | ||
0.565817 | − | 0.824531i | \(-0.308561\pi\) | |||||||
\(198\) | 181.183 | − | 81.3076i | 0.915067 | − | 0.410645i | ||||
\(199\) | 266.613 | 1.33976 | 0.669882 | − | 0.742468i | \(-0.266345\pi\) | ||||
0.669882 | + | 0.742468i | \(0.266345\pi\) | |||||||
\(200\) | − | 60.8055i | − | 0.304027i | ||||||
\(201\) | −1.03331 | + | 0.221225i | −0.00514082 | + | 0.00110062i | ||||
\(202\) | −61.7760 | −0.305822 | ||||||||
\(203\) | − | 321.219i | − | 1.58236i | ||||||
\(204\) | −19.6077 | − | 91.5842i | −0.0961161 | − | 0.448942i | ||||
\(205\) | −412.864 | −2.01397 | ||||||||
\(206\) | 113.093i | 0.548997i | ||||||||
\(207\) | −29.8358 | − | 66.4852i | −0.144134 | − | 0.321184i | ||||
\(208\) | −14.4222 | −0.0693375 | ||||||||
\(209\) | − | 376.412i | − | 1.80101i | ||||||
\(210\) | 271.135 | − | 58.0486i | 1.29112 | − | 0.276422i | ||||
\(211\) | −302.781 | −1.43498 | −0.717491 | − | 0.696568i | \(-0.754710\pi\) | ||||
−0.717491 | + | 0.696568i | \(0.754710\pi\) | |||||||
\(212\) | − | 79.0513i | − | 0.372883i | ||||||
\(213\) | −62.4215 | − | 291.560i | −0.293059 | − | 1.36883i | ||||
\(214\) | −174.909 | −0.817334 | ||||||||
\(215\) | 127.002i | 0.590708i | ||||||||
\(216\) | −45.1600 | − | 61.5839i | −0.209074 | − | 0.285111i | ||||
\(217\) | −298.797 | −1.37695 | ||||||||
\(218\) | − | 60.5288i | − | 0.277655i | ||||||
\(219\) | 278.538 | − | 59.6335i | 1.27186 | − | 0.272299i | ||||
\(220\) | 212.789 | 0.967222 | ||||||||
\(221\) | 56.2824i | 0.254672i | ||||||||
\(222\) | 36.2881 | + | 169.496i | 0.163460 | + | 0.763494i | ||||
\(223\) | 299.147 | 1.34147 | 0.670733 | − | 0.741699i | \(-0.265980\pi\) | ||||
0.670733 | + | 0.741699i | \(0.265980\pi\) | |||||||
\(224\) | 54.2175i | 0.242043i | ||||||||
\(225\) | −176.522 | + | 79.2159i | −0.784543 | + | 0.352071i | ||||
\(226\) | 119.501 | 0.528765 | ||||||||
\(227\) | 26.9489i | 0.118718i | 0.998237 | + | 0.0593588i | \(0.0189056\pi\) | ||||
−0.998237 | + | 0.0593588i | \(0.981094\pi\) | |||||||
\(228\) | −141.541 | + | 30.3031i | −0.620792 | + | 0.132908i | ||||
\(229\) | 268.170 | 1.17105 | 0.585523 | − | 0.810655i | \(-0.300889\pi\) | ||||
0.585523 | + | 0.810655i | \(0.300889\pi\) | |||||||
\(230\) | − | 78.0828i | − | 0.339490i | ||||||
\(231\) | 93.9208 | + | 438.688i | 0.406583 | + | 1.89908i | ||||
\(232\) | −94.7942 | −0.408596 | ||||||||
\(233\) | − | 307.370i | − | 1.31919i | −0.751623 | − | 0.659593i | \(-0.770729\pi\) | ||
0.751623 | − | 0.659593i | \(-0.229271\pi\) | |||||||
\(234\) | 18.7889 | + | 41.8686i | 0.0802944 | + | 0.178926i | ||||
\(235\) | −44.6873 | −0.190159 | ||||||||
\(236\) | 96.8314i | 0.410303i | ||||||||
\(237\) | −151.037 | + | 32.3363i | −0.637287 | + | 0.136440i | ||||
\(238\) | 211.583 | 0.889004 | ||||||||
\(239\) | 394.784i | 1.65181i | 0.563806 | + | 0.825907i | \(0.309337\pi\) | ||||
−0.563806 | + | 0.825907i | \(0.690663\pi\) | |||||||
\(240\) | −17.1306 | − | 80.0141i | −0.0713775 | − | 0.333392i | ||||
\(241\) | 4.44186 | 0.0184309 | 0.00921547 | − | 0.999958i | \(-0.497067\pi\) | ||||
0.00921547 | + | 0.999958i | \(0.497067\pi\) | |||||||
\(242\) | 173.165i | 0.715559i | ||||||||
\(243\) | −119.949 | + | 211.332i | −0.493616 | + | 0.869680i | ||||
\(244\) | 66.9037 | 0.274196 | ||||||||
\(245\) | 292.264i | 1.19292i | ||||||||
\(246\) | −251.185 | + | 53.7774i | −1.02108 | + | 0.218607i | ||||
\(247\) | 86.9828 | 0.352157 | ||||||||
\(248\) | 88.1773i | 0.355554i | ||||||||
\(249\) | −55.2067 | − | 257.861i | −0.221713 | − | 1.03559i | ||||
\(250\) | 33.7715 | 0.135086 | ||||||||
\(251\) | − | 188.722i | − | 0.751882i | −0.926644 | − | 0.375941i | \(-0.877320\pi\) | ||
0.926644 | − | 0.375941i | \(-0.122680\pi\) | |||||||
\(252\) | 157.397 | − | 70.6333i | 0.624591 | − | 0.280291i | ||||
\(253\) | 126.335 | 0.499349 | ||||||||
\(254\) | 18.6715i | 0.0735100i | ||||||||
\(255\) | −312.254 | + | 66.8519i | −1.22452 | + | 0.262164i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 288.936i | 1.12426i | 0.827047 | + | 0.562132i | \(0.190019\pi\) | ||||
−0.827047 | + | 0.562132i | \(0.809981\pi\) | |||||||
\(258\) | 16.5426 | + | 77.2678i | 0.0641187 | + | 0.299488i | ||||
\(259\) | −391.579 | −1.51189 | ||||||||
\(260\) | 49.1721i | 0.189123i | ||||||||
\(261\) | 123.496 | + | 275.194i | 0.473163 | + | 1.05438i | ||||
\(262\) | 233.245 | 0.890248 | ||||||||
\(263\) | 292.966i | 1.11394i | 0.830533 | + | 0.556969i | \(0.188036\pi\) | ||||
−0.830533 | + | 0.556969i | \(0.811964\pi\) | |||||||
\(264\) | 129.460 | − | 27.7167i | 0.490379 | − | 0.104988i | ||||
\(265\) | −269.523 | −1.01707 | ||||||||
\(266\) | − | 326.995i | − | 1.22931i | ||||||
\(267\) | 68.0239 | + | 317.728i | 0.254771 | + | 1.18999i | ||||
\(268\) | −0.704481 | −0.00262866 | ||||||||
\(269\) | − | 205.144i | − | 0.762617i | −0.924448 | − | 0.381308i | \(-0.875474\pi\) | ||
0.924448 | − | 0.381308i | \(-0.124526\pi\) | |||||||
\(270\) | −209.969 | + | 153.972i | −0.777662 | + | 0.570265i | ||||
\(271\) | 212.721 | 0.784949 | 0.392475 | − | 0.919763i | \(-0.371619\pi\) | ||||
0.392475 | + | 0.919763i | \(0.371619\pi\) | |||||||
\(272\) | − | 62.4397i | − | 0.229558i | ||||||
\(273\) | −101.374 | + | 21.7036i | −0.371333 | + | 0.0795004i | ||||
\(274\) | −68.4210 | −0.249712 | ||||||||
\(275\) | − | 335.428i | − | 1.21974i | ||||||
\(276\) | −10.1706 | − | 47.5054i | −0.0368502 | − | 0.172121i | ||||
\(277\) | −275.738 | −0.995443 | −0.497721 | − | 0.867337i | \(-0.665830\pi\) | ||||
−0.497721 | + | 0.867337i | \(0.665830\pi\) | |||||||
\(278\) | 57.3664i | 0.206354i | ||||||||
\(279\) | 255.984 | − | 114.875i | 0.917507 | − | 0.411739i | ||||
\(280\) | 184.853 | 0.660190 | ||||||||
\(281\) | − | 143.542i | − | 0.510825i | −0.966832 | − | 0.255412i | \(-0.917789\pi\) | ||
0.966832 | − | 0.255412i | \(-0.0822113\pi\) | |||||||
\(282\) | −27.1876 | + | 5.82073i | −0.0964100 | + | 0.0206409i | ||||
\(283\) | 91.9591 | 0.324944 | 0.162472 | − | 0.986713i | \(-0.448053\pi\) | ||||
0.162472 | + | 0.986713i | \(0.448053\pi\) | |||||||
\(284\) | − | 198.778i | − | 0.699923i | ||||||
\(285\) | 103.318 | + | 482.579i | 0.362518 | + | 1.69326i | ||||
\(286\) | −79.5588 | −0.278178 | ||||||||
\(287\) | − | 580.302i | − | 2.02196i | ||||||
\(288\) | −20.8444 | − | 46.4490i | −0.0723764 | − | 0.161281i | ||||
\(289\) | 45.3299 | 0.156851 | ||||||||
\(290\) | 323.198i | 1.11448i | ||||||||
\(291\) | 242.705 | − | 51.9618i | 0.834037 | − | 0.178563i | ||||
\(292\) | 189.900 | 0.650343 | ||||||||
\(293\) | 475.059i | 1.62136i | 0.585489 | + | 0.810681i | \(0.300903\pi\) | ||||
−0.585489 | + | 0.810681i | \(0.699097\pi\) | |||||||
\(294\) | 38.0688 | + | 177.813i | 0.129486 | + | 0.604806i | ||||
\(295\) | 330.144 | 1.11913 | ||||||||
\(296\) | 115.558i | 0.390398i | ||||||||
\(297\) | −249.121 | − | 339.722i | −0.838791 | − | 1.14385i | ||||
\(298\) | 273.095 | 0.916427 | ||||||||
\(299\) | 29.1941i | 0.0976391i | ||||||||
\(300\) | −126.130 | + | 27.0037i | −0.420432 | + | 0.0900123i | ||||
\(301\) | −178.509 | −0.593052 | ||||||||
\(302\) | − | 220.390i | − | 0.729767i | ||||||
\(303\) | 27.4347 | + | 128.143i | 0.0905436 | + | 0.422914i | ||||
\(304\) | −96.4988 | −0.317430 | ||||||||
\(305\) | − | 228.106i | − | 0.747889i | ||||||
\(306\) | −181.267 | + | 81.3450i | −0.592374 | + | 0.265833i | ||||
\(307\) | −455.182 | −1.48268 | −0.741338 | − | 0.671131i | \(-0.765809\pi\) | ||||
−0.741338 | + | 0.671131i | \(0.765809\pi\) | |||||||
\(308\) | 299.086i | 0.971059i | ||||||||
\(309\) | 234.591 | − | 50.2247i | 0.759195 | − | 0.162540i | ||||
\(310\) | 300.638 | 0.969800 | ||||||||
\(311\) | − | 436.493i | − | 1.40352i | −0.712416 | − | 0.701758i | \(-0.752399\pi\) | ||
0.712416 | − | 0.701758i | \(-0.247601\pi\) | |||||||
\(312\) | 6.40489 | + | 29.9162i | 0.0205285 | + | 0.0958852i | ||||
\(313\) | 191.914 | 0.613144 | 0.306572 | − | 0.951847i | \(-0.400818\pi\) | ||||
0.306572 | + | 0.951847i | \(0.400818\pi\) | |||||||
\(314\) | − | 91.7800i | − | 0.292293i | ||||||
\(315\) | −240.822 | − | 536.640i | −0.764515 | − | 1.70362i | ||||
\(316\) | −102.973 | −0.325865 | ||||||||
\(317\) | − | 239.722i | − | 0.756221i | −0.925761 | − | 0.378110i | \(-0.876574\pi\) | ||
0.925761 | − | 0.378110i | \(-0.123426\pi\) | |||||||
\(318\) | −163.977 | + | 35.1066i | −0.515651 | + | 0.110398i | ||||
\(319\) | −522.924 | −1.63926 | ||||||||
\(320\) | − | 54.5515i | − | 0.170474i | ||||||
\(321\) | 77.6772 | + | 362.817i | 0.241985 | + | 1.13027i | ||||
\(322\) | 109.750 | 0.340837 | ||||||||
\(323\) | 376.585i | 1.16590i | ||||||||
\(324\) | −107.689 | + | 121.025i | −0.332373 | + | 0.373535i | ||||
\(325\) | 77.5121 | 0.238499 | ||||||||
\(326\) | − | 417.933i | − | 1.28200i | ||||||
\(327\) | −125.556 | + | 26.8808i | −0.383962 | + | 0.0822043i | ||||
\(328\) | −171.252 | −0.522108 | ||||||||
\(329\) | − | 62.8104i | − | 0.190913i | ||||||
\(330\) | −94.4994 | − | 441.391i | −0.286362 | − | 1.33755i | ||||
\(331\) | −262.349 | −0.792594 | −0.396297 | − | 0.918122i | \(-0.629705\pi\) | ||||
−0.396297 | + | 0.918122i | \(0.629705\pi\) | |||||||
\(332\) | − | 175.803i | − | 0.529527i | ||||||
\(333\) | 335.471 | − | 150.546i | 1.00742 | − | 0.452090i | ||||
\(334\) | 122.350 | 0.366319 | ||||||||
\(335\) | 2.40191i | 0.00716987i | ||||||||
\(336\) | 112.464 | − | 24.0780i | 0.334715 | − | 0.0716607i | ||||
\(337\) | 108.189 | 0.321037 | 0.160518 | − | 0.987033i | \(-0.448683\pi\) | ||||
0.160518 | + | 0.987033i | \(0.448683\pi\) | |||||||
\(338\) | − | 18.3848i | − | 0.0543928i | ||||||
\(339\) | −53.0703 | − | 247.882i | −0.156550 | − | 0.731217i | ||||
\(340\) | −212.887 | −0.626137 | ||||||||
\(341\) | 486.422i | 1.42646i | ||||||||
\(342\) | 125.716 | + | 280.142i | 0.367591 | + | 0.819129i | ||||
\(343\) | 58.8419 | 0.171551 | ||||||||
\(344\) | 52.6792i | 0.153137i | ||||||||
\(345\) | −161.968 | + | 34.6765i | −0.469473 | + | 0.100512i | ||||
\(346\) | 112.942 | 0.326423 | ||||||||
\(347\) | 371.606i | 1.07091i | 0.844564 | + | 0.535455i | \(0.179860\pi\) | ||||
−0.844564 | + | 0.535455i | \(0.820140\pi\) | |||||||
\(348\) | 42.0981 | + | 196.633i | 0.120971 | + | 0.565037i | ||||
\(349\) | 187.750 | 0.537966 | 0.268983 | − | 0.963145i | \(-0.413312\pi\) | ||||
0.268983 | + | 0.963145i | \(0.413312\pi\) | |||||||
\(350\) | − | 291.392i | − | 0.832548i | ||||||
\(351\) | 78.5044 | − | 57.5679i | 0.223659 | − | 0.164011i | ||||
\(352\) | 88.2626 | 0.250746 | ||||||||
\(353\) | 258.521i | 0.732354i | 0.930545 | + | 0.366177i | \(0.119334\pi\) | ||||
−0.930545 | + | 0.366177i | \(0.880666\pi\) | |||||||
\(354\) | 200.859 | − | 43.0028i | 0.567398 | − | 0.121477i | ||||
\(355\) | −677.728 | −1.90909 | ||||||||
\(356\) | 216.619i | 0.608480i | ||||||||
\(357\) | −93.9639 | − | 438.890i | −0.263204 | − | 1.22938i | ||||
\(358\) | −284.026 | −0.793369 | ||||||||
\(359\) | − | 134.918i | − | 0.375816i | −0.982187 | − | 0.187908i | \(-0.939829\pi\) | ||
0.982187 | − | 0.187908i | \(-0.0601707\pi\) | |||||||
\(360\) | −158.367 | + | 71.0684i | −0.439907 | + | 0.197412i | ||||
\(361\) | 221.001 | 0.612191 | ||||||||
\(362\) | 66.4201i | 0.183481i | ||||||||
\(363\) | 359.199 | − | 76.9026i | 0.989529 | − | 0.211853i | ||||
\(364\) | −69.1141 | −0.189874 | ||||||||
\(365\) | − | 647.459i | − | 1.77386i | ||||||
\(366\) | −29.7119 | − | 138.779i | −0.0811801 | − | 0.379178i | ||||
\(367\) | 354.929 | 0.967109 | 0.483554 | − | 0.875314i | \(-0.339346\pi\) | ||||
0.483554 | + | 0.875314i | \(0.339346\pi\) | |||||||
\(368\) | − | 32.3879i | − | 0.0880107i | ||||||
\(369\) | 223.102 | + | 497.154i | 0.604613 | + | 1.34730i | ||||
\(370\) | 393.991 | 1.06484 | ||||||||
\(371\) | − | 378.829i | − | 1.02110i | ||||||
\(372\) | 182.907 | − | 39.1595i | 0.491687 | − | 0.105267i | ||||
\(373\) | 355.525 | 0.953149 | 0.476575 | − | 0.879134i | \(-0.341878\pi\) | ||||
0.476575 | + | 0.879134i | \(0.341878\pi\) | |||||||
\(374\) | − | 344.443i | − | 0.920971i | ||||||
\(375\) | −14.9979 | − | 70.0526i | −0.0399944 | − | 0.186807i | ||||
\(376\) | −18.5358 | −0.0492974 | ||||||||
\(377\) | − | 120.839i | − | 0.320529i | ||||||
\(378\) | −216.415 | − | 295.122i | −0.572528 | − | 0.780747i | ||||
\(379\) | 490.270 | 1.29359 | 0.646794 | − | 0.762665i | \(-0.276110\pi\) | ||||
0.646794 | + | 0.762665i | \(0.276110\pi\) | |||||||
\(380\) | 329.010i | 0.865815i | ||||||||
\(381\) | 38.7306 | − | 8.29202i | 0.101655 | − | 0.0217638i | ||||
\(382\) | −17.0189 | −0.0445521 | ||||||||
\(383\) | − | 102.395i | − | 0.267351i | −0.991025 | − | 0.133675i | \(-0.957322\pi\) | ||
0.991025 | − | 0.133675i | \(-0.0426780\pi\) | |||||||
\(384\) | −7.10559 | − | 33.1890i | −0.0185041 | − | 0.0864297i | ||||
\(385\) | 1019.73 | 2.64864 | ||||||||
\(386\) | 375.771i | 0.973501i | ||||||||
\(387\) | 152.931 | − | 68.6292i | 0.395171 | − | 0.177336i | ||||
\(388\) | 165.470 | 0.426469 | ||||||||
\(389\) | 365.422i | 0.939389i | 0.882829 | + | 0.469694i | \(0.155636\pi\) | ||||
−0.882829 | + | 0.469694i | \(0.844364\pi\) | |||||||
\(390\) | 101.998 | − | 21.8373i | 0.261534 | − | 0.0559931i | ||||
\(391\) | −126.393 | −0.323257 | ||||||||
\(392\) | 121.228i | 0.309256i | ||||||||
\(393\) | −103.584 | − | 483.823i | −0.263573 | − | 1.23110i | ||||
\(394\) | −459.429 | −1.16606 | ||||||||
\(395\) | 351.084i | 0.888821i | ||||||||
\(396\) | −114.986 | − | 256.232i | −0.290370 | − | 0.647050i | ||||
\(397\) | −497.163 | −1.25230 | −0.626149 | − | 0.779703i | \(-0.715370\pi\) | ||||
−0.626149 | + | 0.779703i | \(0.715370\pi\) | |||||||
\(398\) | − | 377.048i | − | 0.947356i | ||||||
\(399\) | −678.291 | + | 145.218i | −1.69998 | + | 0.363956i | ||||
\(400\) | −85.9919 | −0.214980 | ||||||||
\(401\) | − | 563.415i | − | 1.40502i | −0.711672 | − | 0.702512i | \(-0.752062\pi\) | ||
0.711672 | − | 0.702512i | \(-0.247938\pi\) | |||||||
\(402\) | 0.312860 | + | 1.46131i | 0.000778258 | + | 0.00363511i | ||||
\(403\) | −112.404 | −0.278919 | ||||||||
\(404\) | 87.3645i | 0.216249i | ||||||||
\(405\) | 412.632 | + | 367.162i | 1.01885 | + | 0.906573i | ||||
\(406\) | −454.273 | −1.11890 | ||||||||
\(407\) | 637.464i | 1.56625i | ||||||||
\(408\) | −129.520 | + | 27.7295i | −0.317450 | + | 0.0679644i | ||||
\(409\) | −734.959 | −1.79696 | −0.898482 | − | 0.439010i | \(-0.855329\pi\) | ||||
−0.898482 | + | 0.439010i | \(0.855329\pi\) | |||||||
\(410\) | 583.877i | 1.42409i | ||||||||
\(411\) | 30.3857 | + | 141.927i | 0.0739313 | + | 0.345320i | ||||
\(412\) | 159.938 | 0.388200 | ||||||||
\(413\) | 464.035i | 1.12357i | ||||||||
\(414\) | −94.0242 | + | 42.1942i | −0.227112 | + | 0.101918i | ||||
\(415\) | −599.395 | −1.44433 | ||||||||
\(416\) | 20.3961i | 0.0490290i | ||||||||
\(417\) | 118.996 | − | 25.4764i | 0.285362 | − | 0.0610944i | ||||
\(418\) | −532.327 | −1.27351 | ||||||||
\(419\) | 301.483i | 0.719529i | 0.933043 | + | 0.359765i | \(0.117143\pi\) | ||||
−0.933043 | + | 0.359765i | \(0.882857\pi\) | |||||||
\(420\) | −82.0932 | − | 383.443i | −0.195460 | − | 0.912960i | ||||
\(421\) | 50.6030 | 0.120197 | 0.0600986 | − | 0.998192i | \(-0.480858\pi\) | ||||
0.0600986 | + | 0.998192i | \(0.480858\pi\) | |||||||
\(422\) | 428.197i | 1.01469i | ||||||||
\(423\) | 24.1480 | + | 53.8107i | 0.0570875 | + | 0.127212i | ||||
\(424\) | −111.795 | −0.263668 | ||||||||
\(425\) | 335.582i | 0.789605i | ||||||||
\(426\) | −412.328 | + | 88.2773i | −0.967907 | + | 0.207224i | ||||
\(427\) | 320.616 | 0.750857 | ||||||||
\(428\) | 247.359i | 0.577942i | ||||||||
\(429\) | 35.3320 | + | 165.030i | 0.0823591 | + | 0.384685i | ||||
\(430\) | 179.608 | 0.417694 | ||||||||
\(431\) | − | 57.2102i | − | 0.132738i | −0.997795 | − | 0.0663691i | \(-0.978859\pi\) | ||
0.997795 | − | 0.0663691i | \(-0.0211415\pi\) | |||||||
\(432\) | −87.0928 | + | 63.8658i | −0.201604 | + | 0.147838i | ||||
\(433\) | 697.010 | 1.60972 | 0.804862 | − | 0.593462i | \(-0.202239\pi\) | ||||
0.804862 | + | 0.593462i | \(0.202239\pi\) | |||||||
\(434\) | 422.563i | 0.973648i | ||||||||
\(435\) | 670.415 | − | 143.532i | 1.54118 | − | 0.329959i | ||||
\(436\) | −85.6007 | −0.196332 | ||||||||
\(437\) | 195.337i | 0.446996i | ||||||||
\(438\) | −84.3346 | − | 393.912i | −0.192545 | − | 0.899343i | ||||
\(439\) | −89.8292 | −0.204622 | −0.102311 | − | 0.994752i | \(-0.532624\pi\) | ||||
−0.102311 | + | 0.994752i | \(0.532624\pi\) | |||||||
\(440\) | − | 300.929i | − | 0.683929i | ||||||
\(441\) | 351.933 | − | 157.933i | 0.798034 | − | 0.358125i | ||||
\(442\) | 79.5954 | 0.180080 | ||||||||
\(443\) | 327.588i | 0.739476i | 0.929136 | + | 0.369738i | \(0.120553\pi\) | ||||
−0.929136 | + | 0.369738i | \(0.879447\pi\) | |||||||
\(444\) | 239.703 | − | 51.3191i | 0.539872 | − | 0.115584i | ||||
\(445\) | 738.556 | 1.65968 | ||||||||
\(446\) | − | 423.058i | − | 0.948560i | ||||||
\(447\) | −121.281 | − | 566.485i | −0.271323 | − | 1.26730i | ||||
\(448\) | 76.6752 | 0.171150 | ||||||||
\(449\) | 590.940i | 1.31612i | 0.752964 | + | 0.658062i | \(0.228624\pi\) | ||||
−0.752964 | + | 0.658062i | \(0.771376\pi\) | |||||||
\(450\) | 112.028 | + | 249.640i | 0.248952 | + | 0.554756i | ||||
\(451\) | −944.694 | −2.09467 | ||||||||
\(452\) | − | 169.000i | − | 0.373894i | ||||||
\(453\) | −457.157 | + | 97.8749i | −1.00918 | + | 0.216059i | ||||
\(454\) | 38.1115 | 0.0839461 | ||||||||
\(455\) | 235.642i | 0.517895i | ||||||||
\(456\) | 42.8551 | + | 200.169i | 0.0939804 | + | 0.438966i | ||||
\(457\) | −584.524 | −1.27905 | −0.639523 | − | 0.768772i | \(-0.720868\pi\) | ||||
−0.639523 | + | 0.768772i | \(0.720868\pi\) | |||||||
\(458\) | − | 379.249i | − | 0.828055i | ||||||
\(459\) | 249.235 | + | 339.878i | 0.542996 | + | 0.740476i | ||||
\(460\) | −110.426 | −0.240056 | ||||||||
\(461\) | − | 183.062i | − | 0.397097i | −0.980091 | − | 0.198548i | \(-0.936377\pi\) | ||
0.980091 | − | 0.198548i | \(-0.0636227\pi\) | |||||||
\(462\) | 620.399 | − | 132.824i | 1.34285 | − | 0.287498i | ||||
\(463\) | −752.102 | −1.62441 | −0.812205 | − | 0.583372i | \(-0.801733\pi\) | ||||
−0.812205 | + | 0.583372i | \(0.801733\pi\) | |||||||
\(464\) | 134.059i | 0.288921i | ||||||||
\(465\) | −133.513 | − | 623.618i | −0.287125 | − | 1.34111i | ||||
\(466\) | −434.687 | −0.932806 | ||||||||
\(467\) | − | 46.3727i | − | 0.0992991i | −0.998767 | − | 0.0496495i | \(-0.984190\pi\) | ||
0.998767 | − | 0.0496495i | \(-0.0158104\pi\) | |||||||
\(468\) | 59.2111 | − | 26.5715i | 0.126519 | − | 0.0567767i | ||||
\(469\) | −3.37601 | −0.00719832 | ||||||||
\(470\) | 63.1974i | 0.134462i | ||||||||
\(471\) | −190.380 | + | 40.7594i | −0.404205 | + | 0.0865381i | ||||
\(472\) | 136.940 | 0.290128 | ||||||||
\(473\) | 290.600i | 0.614377i | ||||||||
\(474\) | 45.7304 | + | 213.599i | 0.0964776 | + | 0.450630i | ||||
\(475\) | 518.632 | 1.09186 | ||||||||
\(476\) | − | 299.224i | − | 0.628621i | ||||||
\(477\) | 145.644 | + | 324.549i | 0.305334 | + | 0.680396i | ||||
\(478\) | 558.309 | 1.16801 | ||||||||
\(479\) | − | 338.396i | − | 0.706464i | −0.935536 | − | 0.353232i | \(-0.885083\pi\) | ||
0.935536 | − | 0.353232i | \(-0.114917\pi\) | |||||||
\(480\) | −113.157 | + | 24.2263i | −0.235744 | + | 0.0504715i | ||||
\(481\) | −147.308 | −0.306253 | ||||||||
\(482\) | − | 6.28174i | − | 0.0130326i | ||||||
\(483\) | −48.7398 | − | 227.655i | −0.100910 | − | 0.471336i | ||||
\(484\) | 244.893 | 0.505977 | ||||||||
\(485\) | − | 564.165i | − | 1.16323i | ||||||
\(486\) | 298.869 | + | 169.633i | 0.614957 | + | 0.349039i | ||||
\(487\) | −104.632 | −0.214850 | −0.107425 | − | 0.994213i | \(-0.534261\pi\) | ||||
−0.107425 | + | 0.994213i | \(0.534261\pi\) | |||||||
\(488\) | − | 94.6161i | − | 0.193886i | ||||||
\(489\) | −866.924 | + | 185.604i | −1.77285 | + | 0.379558i | ||||
\(490\) | 413.324 | 0.843519 | ||||||||
\(491\) | 204.874i | 0.417259i | 0.977995 | + | 0.208630i | \(0.0669004\pi\) | ||||
−0.977995 | + | 0.208630i | \(0.933100\pi\) | |||||||
\(492\) | 76.0527 | + | 355.229i | 0.154579 | + | 0.722011i | ||||
\(493\) | 523.164 | 1.06119 | ||||||||
\(494\) | − | 123.012i | − | 0.249013i | ||||||
\(495\) | −873.615 | + | 392.043i | −1.76488 | + | 0.792005i | ||||
\(496\) | 124.702 | 0.251414 | ||||||||
\(497\) | − | 952.584i | − | 1.91667i | ||||||
\(498\) | −364.670 | + | 78.0740i | −0.732270 | + | 0.156775i | ||||
\(499\) | 398.915 | 0.799430 | 0.399715 | − | 0.916640i | \(-0.369109\pi\) | ||||
0.399715 | + | 0.916640i | \(0.369109\pi\) | |||||||
\(500\) | − | 47.7601i | − | 0.0955201i | ||||||
\(501\) | −54.3358 | − | 253.793i | −0.108455 | − | 0.506573i | ||||
\(502\) | −266.894 | −0.531661 | ||||||||
\(503\) | − | 412.934i | − | 0.820943i | −0.911873 | − | 0.410472i | \(-0.865364\pi\) | ||
0.911873 | − | 0.410472i | \(-0.134636\pi\) | |||||||
\(504\) | −99.8905 | − | 222.593i | −0.198196 | − | 0.441653i | ||||
\(505\) | 297.867 | 0.589835 | ||||||||
\(506\) | − | 178.665i | − | 0.353093i | ||||||
\(507\) | −38.1358 | + | 8.16467i | −0.0752185 | + | 0.0161039i | ||||
\(508\) | 26.4055 | 0.0519794 | ||||||||
\(509\) | − | 731.331i | − | 1.43680i | −0.695630 | − | 0.718400i | \(-0.744875\pi\) | ||
0.695630 | − | 0.718400i | \(-0.255125\pi\) | |||||||
\(510\) | 94.5428 | + | 441.593i | 0.185378 | + | 0.865869i | ||||
\(511\) | 910.039 | 1.78090 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 525.272 | − | 385.186i | 1.02392 | − | 0.750850i | ||||
\(514\) | 408.617 | 0.794975 | ||||||||
\(515\) | − | 545.305i | − | 1.05884i | ||||||
\(516\) | 109.273 | − | 23.3948i | 0.211770 | − | 0.0453388i | ||||
\(517\) | −102.251 | −0.197778 | ||||||||
\(518\) | 553.776i | 1.06907i | ||||||||
\(519\) | −50.1576 | − | 234.278i | −0.0966428 | − | 0.451402i | ||||
\(520\) | 69.5398 | 0.133730 | ||||||||
\(521\) | 802.622i | 1.54054i | 0.637717 | + | 0.770271i | \(0.279879\pi\) | ||||
−0.637717 | + | 0.770271i | \(0.720121\pi\) | |||||||
\(522\) | 389.183 | − | 174.649i | 0.745561 | − | 0.334577i | ||||
\(523\) | −832.197 | −1.59120 | −0.795599 | − | 0.605823i | \(-0.792844\pi\) | ||||
−0.795599 | + | 0.605823i | \(0.792844\pi\) | |||||||
\(524\) | − | 329.858i | − | 0.629501i | ||||||
\(525\) | −604.438 | + | 129.407i | −1.15131 | + | 0.246490i | ||||
\(526\) | 414.316 | 0.787673 | ||||||||
\(527\) | − | 486.646i | − | 0.923427i | ||||||
\(528\) | −39.1974 | − | 183.084i | −0.0742374 | − | 0.346750i | ||||
\(529\) | 463.439 | 0.876066 | ||||||||
\(530\) | 381.163i | 0.719176i | ||||||||
\(531\) | −178.403 | − | 397.546i | −0.335975 | − | 0.748675i | ||||
\(532\) | −462.441 | −0.869250 | ||||||||
\(533\) | − | 218.304i | − | 0.409575i | ||||||
\(534\) | 449.335 | − | 96.2003i | 0.841452 | − | 0.180150i | ||||
\(535\) | 843.364 | 1.57638 | ||||||||
\(536\) | 0.996287i | 0.00185874i | ||||||||
\(537\) | 126.136 | + | 589.159i | 0.234890 | + | 1.09713i | ||||
\(538\) | −290.117 | −0.539251 | ||||||||
\(539\) | 668.745i | 1.24071i | ||||||||
\(540\) | 217.749 | + | 296.940i | 0.403238 | + | 0.549890i | ||||
\(541\) | 304.987 | 0.563747 | 0.281873 | − | 0.959452i | \(-0.409044\pi\) | ||||
0.281873 | + | 0.959452i | \(0.409044\pi\) | |||||||
\(542\) | − | 300.833i | − | 0.555043i | ||||||
\(543\) | 137.776 | − | 29.4971i | 0.253731 | − | 0.0543225i | ||||
\(544\) | −88.3031 | −0.162322 | ||||||||
\(545\) | 291.853i | 0.535510i | ||||||||
\(546\) | 30.6935 | + | 143.364i | 0.0562152 | + | 0.262572i | ||||
\(547\) | 462.958 | 0.846359 | 0.423180 | − | 0.906046i | \(-0.360914\pi\) | ||||
0.423180 | + | 0.906046i | \(0.360914\pi\) | |||||||
\(548\) | 96.7620i | 0.176573i | ||||||||
\(549\) | −274.677 | + | 123.264i | −0.500322 | + | 0.224524i | ||||
\(550\) | −474.367 | −0.862485 | ||||||||
\(551\) | − | 808.535i | − | 1.46740i | ||||||
\(552\) | −67.1827 | + | 14.3835i | −0.121708 | + | 0.0260570i | ||||
\(553\) | −493.468 | −0.892348 | ||||||||
\(554\) | 389.952i | 0.703884i | ||||||||
\(555\) | −174.971 | − | 817.261i | −0.315263 | − | 1.47254i | ||||
\(556\) | 81.1283 | 0.145914 | ||||||||
\(557\) | 776.893i | 1.39478i | 0.716691 | + | 0.697391i | \(0.245656\pi\) | ||||
−0.716691 | + | 0.697391i | \(0.754344\pi\) | |||||||
\(558\) | −162.458 | − | 362.017i | −0.291144 | − | 0.648775i | ||||
\(559\) | −67.1531 | −0.120131 | ||||||||
\(560\) | − | 261.422i | − | 0.466825i | ||||||
\(561\) | −714.483 | + | 152.967i | −1.27359 | + | 0.272669i | ||||
\(562\) | −202.999 | −0.361208 | ||||||||
\(563\) | 51.4872i | 0.0914516i | 0.998954 | + | 0.0457258i | \(0.0145600\pi\) | ||||
−0.998954 | + | 0.0457258i | \(0.985440\pi\) | |||||||
\(564\) | 8.23175 | + | 38.4491i | 0.0145953 | + | 0.0681722i | ||||
\(565\) | −576.200 | −1.01982 | ||||||||
\(566\) | − | 130.050i | − | 0.229770i | ||||||
\(567\) | −516.066 | + | 579.977i | −0.910170 | + | 1.02289i | ||||
\(568\) | −281.115 | −0.494920 | ||||||||
\(569\) | − | 172.306i | − | 0.302823i | −0.988471 | − | 0.151412i | \(-0.951618\pi\) | ||
0.988471 | − | 0.151412i | \(-0.0483819\pi\) | |||||||
\(570\) | 682.469 | − | 146.113i | 1.19731 | − | 0.256339i | ||||
\(571\) | 190.675 | 0.333932 | 0.166966 | − | 0.985963i | \(-0.446603\pi\) | ||||
0.166966 | + | 0.985963i | \(0.446603\pi\) | |||||||
\(572\) | 112.513i | 0.196701i | ||||||||
\(573\) | 7.55809 | + | 35.3026i | 0.0131904 | + | 0.0616100i | ||||
\(574\) | −820.671 | −1.42974 | ||||||||
\(575\) | 174.069i | 0.302728i | ||||||||
\(576\) | −65.6888 | + | 29.4784i | −0.114043 | + | 0.0511779i | ||||
\(577\) | −279.690 | −0.484732 | −0.242366 | − | 0.970185i | \(-0.577924\pi\) | ||||
−0.242366 | + | 0.970185i | \(0.577924\pi\) | |||||||
\(578\) | − | 64.1062i | − | 0.110910i | ||||||
\(579\) | 779.468 | − | 166.880i | 1.34623 | − | 0.288221i | ||||
\(580\) | 457.071 | 0.788054 | ||||||||
\(581\) | − | 842.483i | − | 1.45006i | ||||||
\(582\) | −73.4851 | − | 343.236i | −0.126263 | − | 0.589753i | ||||
\(583\) | −616.709 | −1.05782 | ||||||||
\(584\) | − | 268.559i | − | 0.459862i | ||||||
\(585\) | −90.5948 | − | 201.879i | −0.154863 | − | 0.345092i | ||||
\(586\) | 671.835 | 1.14648 | ||||||||
\(587\) | 263.161i | 0.448315i | 0.974553 | + | 0.224157i | \(0.0719629\pi\) | ||||
−0.974553 | + | 0.224157i | \(0.928037\pi\) | |||||||
\(588\) | 251.465 | − | 53.8374i | 0.427662 | − | 0.0915602i | ||||
\(589\) | −752.097 | −1.27690 | ||||||||
\(590\) | − | 466.894i | − | 0.791346i | ||||||
\(591\) | 204.032 | + | 952.999i | 0.345232 | + | 1.61252i | ||||
\(592\) | 163.423 | 0.276053 | ||||||||
\(593\) | 316.144i | 0.533126i | 0.963817 | + | 0.266563i | \(0.0858881\pi\) | ||||
−0.963817 | + | 0.266563i | \(0.914112\pi\) | |||||||
\(594\) | −480.440 | + | 352.310i | −0.808821 | + | 0.593115i | ||||
\(595\) | −1020.19 | −1.71461 | ||||||||
\(596\) | − | 386.215i | − | 0.648012i | ||||||
\(597\) | −782.115 | + | 167.447i | −1.31008 | + | 0.280480i | ||||
\(598\) | 41.2867 | 0.0690413 | ||||||||
\(599\) | − | 159.206i | − | 0.265787i | −0.991130 | − | 0.132893i | \(-0.957573\pi\) | ||
0.991130 | − | 0.132893i | \(-0.0424268\pi\) | |||||||
\(600\) | 38.1890 | + | 178.374i | 0.0636483 | + | 0.297290i | ||||
\(601\) | 1032.53 | 1.71801 | 0.859006 | − | 0.511965i | \(-0.171082\pi\) | ||||
0.859006 | + | 0.511965i | \(0.171082\pi\) | |||||||
\(602\) | 252.449i | 0.419351i | ||||||||
\(603\) | 2.89228 | − | 1.29794i | 0.00479649 | − | 0.00215247i | ||||
\(604\) | −311.678 | −0.516023 | ||||||||
\(605\) | − | 834.955i | − | 1.38009i | ||||||
\(606\) | 181.221 | − | 38.7985i | 0.299045 | − | 0.0640240i | ||||
\(607\) | 272.955 | 0.449679 | 0.224840 | − | 0.974396i | \(-0.427814\pi\) | ||||
0.224840 | + | 0.974396i | \(0.427814\pi\) | |||||||
\(608\) | 136.470i | 0.224457i | ||||||||
\(609\) | 201.742 | + | 942.304i | 0.331268 | + | 1.54730i | ||||
\(610\) | −322.591 | −0.528838 | ||||||||
\(611\) | − | 23.6286i | − | 0.0386721i | ||||||
\(612\) | 115.039 | + | 256.350i | 0.187972 | + | 0.418872i | ||||
\(613\) | 909.866 | 1.48428 | 0.742142 | − | 0.670243i | \(-0.233810\pi\) | ||||
0.742142 | + | 0.670243i | \(0.233810\pi\) | |||||||
\(614\) | 643.724i | 1.04841i | ||||||||
\(615\) | 1211.14 | − | 259.300i | 1.96934 | − | 0.421625i | ||||
\(616\) | 422.972 | 0.686643 | ||||||||
\(617\) | 299.087i | 0.484744i | 0.970183 | + | 0.242372i | \(0.0779255\pi\) | ||||
−0.970183 | + | 0.242372i | \(0.922074\pi\) | |||||||
\(618\) | −71.0285 | − | 331.762i | −0.114933 | − | 0.536832i | ||||
\(619\) | 175.344 | 0.283269 | 0.141635 | − | 0.989919i | \(-0.454764\pi\) | ||||
0.141635 | + | 0.989919i | \(0.454764\pi\) | |||||||
\(620\) | − | 425.166i | − | 0.685752i | ||||||
\(621\) | 129.280 | + | 176.297i | 0.208181 | + | 0.283893i | ||||
\(622\) | −617.295 | −0.992435 | ||||||||
\(623\) | 1038.08i | 1.66626i | ||||||||
\(624\) | 42.3079 | − | 9.05789i | 0.0678011 | − | 0.0145158i | ||||
\(625\) | −700.286 | −1.12046 | ||||||||
\(626\) | − | 271.407i | − | 0.433558i | ||||||
\(627\) | 236.406 | + | 1104.21i | 0.377043 | + | 1.76111i | ||||
\(628\) | −129.796 | −0.206682 | ||||||||
\(629\) | − | 637.757i | − | 1.01392i | ||||||
\(630\) | −758.924 | + | 340.574i | −1.20464 | + | 0.540594i | ||||
\(631\) | 821.692 | 1.30221 | 0.651103 | − | 0.758989i | \(-0.274307\pi\) | ||||
0.651103 | + | 0.758989i | \(0.274307\pi\) | |||||||
\(632\) | 145.626i | 0.230421i | ||||||||
\(633\) | 888.215 | − | 190.162i | 1.40318 | − | 0.300414i | ||||
\(634\) | −339.018 | −0.534729 | ||||||||
\(635\) | − | 90.0290i | − | 0.141778i | ||||||
\(636\) | 49.6483 | + | 231.899i | 0.0780633 | + | 0.364621i | ||||
\(637\) | −154.536 | −0.242600 | ||||||||
\(638\) | 739.526i | 1.15913i | ||||||||
\(639\) | 366.229 | + | 816.094i | 0.573129 | + | 1.27714i | ||||
\(640\) | −77.1475 | −0.120543 | ||||||||
\(641\) | − | 774.943i | − | 1.20896i | −0.796621 | − | 0.604480i | \(-0.793381\pi\) | ||
0.796621 | − | 0.604480i | \(-0.206619\pi\) | |||||||
\(642\) | 513.101 | − | 109.852i | 0.799222 | − | 0.171109i | ||||
\(643\) | −582.871 | −0.906487 | −0.453244 | − | 0.891387i | \(-0.649733\pi\) | ||||
−0.453244 | + | 0.891387i | \(0.649733\pi\) | |||||||
\(644\) | − | 155.209i | − | 0.241008i | ||||||
\(645\) | −79.7640 | − | 372.564i | −0.123665 | − | 0.577618i | ||||
\(646\) | 532.571 | 0.824414 | ||||||||
\(647\) | − | 467.365i | − | 0.722358i | −0.932497 | − | 0.361179i | \(-0.882374\pi\) | ||
0.932497 | − | 0.361179i | \(-0.117626\pi\) | |||||||
\(648\) | 171.156 | + | 152.295i | 0.264129 | + | 0.235023i | ||||
\(649\) | 755.419 | 1.16397 | ||||||||
\(650\) | − | 109.619i | − | 0.168644i | ||||||
\(651\) | 876.529 | − | 187.660i | 1.34643 | − | 0.288264i | ||||
\(652\) | −591.047 | −0.906513 | ||||||||
\(653\) | 485.145i | 0.742948i | 0.928443 | + | 0.371474i | \(0.121147\pi\) | ||||
−0.928443 | + | 0.371474i | \(0.878853\pi\) | |||||||
\(654\) | 38.0152 | + | 177.563i | 0.0581272 | + | 0.271502i | ||||
\(655\) | −1124.64 | −1.71701 | ||||||||
\(656\) | 242.186i | 0.369186i | ||||||||
\(657\) | −779.645 | + | 349.873i | −1.18667 | + | 0.532531i | ||||
\(658\) | −88.8273 | −0.134996 | ||||||||
\(659\) | − | 545.968i | − | 0.828480i | −0.910168 | − | 0.414240i | \(-0.864047\pi\) | ||
0.910168 | − | 0.414240i | \(-0.135953\pi\) | |||||||
\(660\) | −624.221 | + | 133.642i | −0.945789 | + | 0.202488i | ||||
\(661\) | −368.850 | −0.558019 | −0.279009 | − | 0.960288i | \(-0.590006\pi\) | ||||
−0.279009 | + | 0.960288i | \(0.590006\pi\) | |||||||
\(662\) | 371.017i | 0.560449i | ||||||||
\(663\) | −35.3483 | − | 165.106i | −0.0533156 | − | 0.249028i | ||||
\(664\) | −248.623 | −0.374432 | ||||||||
\(665\) | 1576.68i | 2.37095i | ||||||||
\(666\) | −212.904 | − | 474.428i | −0.319676 | − | 0.712355i | ||||
\(667\) | 271.369 | 0.406850 | ||||||||
\(668\) | − | 173.030i | − | 0.259027i | ||||||
\(669\) | −877.554 | + | 187.880i | −1.31174 | + | 0.280837i | ||||
\(670\) | 3.39681 | 0.00506987 | ||||||||
\(671\) | − | 521.942i | − | 0.777856i | ||||||
\(672\) | −34.0514 | − | 159.048i | −0.0506717 | − | 0.236679i | ||||
\(673\) | 231.121 | 0.343418 | 0.171709 | − | 0.985148i | \(-0.445071\pi\) | ||||
0.171709 | + | 0.985148i | \(0.445071\pi\) | |||||||
\(674\) | − | 153.003i | − | 0.227007i | ||||||
\(675\) | 468.080 | − | 343.247i | 0.693452 | − | 0.508514i | ||||
\(676\) | −26.0000 | −0.0384615 | ||||||||
\(677\) | 882.725i | 1.30388i | 0.758271 | + | 0.651939i | \(0.226044\pi\) | ||||
−0.758271 | + | 0.651939i | \(0.773956\pi\) | |||||||
\(678\) | −350.559 | + | 75.0528i | −0.517048 | + | 0.110697i | ||||
\(679\) | 792.965 | 1.16784 | ||||||||
\(680\) | 301.067i | 0.442746i | ||||||||
\(681\) | −16.9253 | − | 79.0552i | −0.0248536 | − | 0.116087i | ||||
\(682\) | 687.905 | 1.00866 | ||||||||
\(683\) | 163.689i | 0.239661i | 0.992794 | + | 0.119831i | \(0.0382351\pi\) | ||||
−0.992794 | + | 0.119831i | \(0.961765\pi\) | |||||||
\(684\) | 396.181 | − | 177.790i | 0.579211 | − | 0.259926i | ||||
\(685\) | 329.907 | 0.481616 | ||||||||
\(686\) | − | 83.2151i | − | 0.121305i | ||||||
\(687\) | −786.682 | + | 168.424i | −1.14510 | + | 0.245159i | ||||
\(688\) | 74.4997 | 0.108284 | ||||||||
\(689\) | − | 142.512i | − | 0.206839i | ||||||
\(690\) | 49.0400 | + | 229.058i | 0.0710725 | + | 0.331968i | ||||
\(691\) | −940.426 | −1.36096 | −0.680482 | − | 0.732765i | \(-0.738230\pi\) | ||||
−0.680482 | + | 0.732765i | \(0.738230\pi\) | |||||||
\(692\) | − | 159.725i | − | 0.230816i | ||||||
\(693\) | −551.037 | − | 1227.91i | −0.795148 | − | 1.77188i | ||||
\(694\) | 525.530 | 0.757248 | ||||||||
\(695\) | − | 276.605i | − | 0.397992i | ||||||
\(696\) | 278.081 | − | 59.5357i | 0.399542 | − | 0.0855398i | ||||
\(697\) | 945.128 | 1.35599 | ||||||||
\(698\) | − | 265.519i | − | 0.380400i | ||||||
\(699\) | 193.044 | + | 901.678i | 0.276172 | + | 1.28995i | ||||
\(700\) | −412.090 | −0.588701 | ||||||||
\(701\) | − | 394.213i | − | 0.562357i | −0.959655 | − | 0.281179i | \(-0.909275\pi\) | ||
0.959655 | − | 0.281179i | \(-0.0907254\pi\) | |||||||
\(702\) | −81.4133 | − | 111.022i | −0.115973 | − | 0.158151i | ||||
\(703\) | −985.635 | −1.40204 | ||||||||
\(704\) | − | 124.822i | − | 0.177304i | ||||||
\(705\) | 131.091 | − | 28.0659i | 0.185945 | − | 0.0398098i | ||||
\(706\) | 365.604 | 0.517853 | ||||||||
\(707\) | 418.668i | 0.592175i | ||||||||
\(708\) | −60.8151 | − | 284.057i | −0.0858971 | − | 0.401211i | ||||
\(709\) | −433.261 | −0.611087 | −0.305544 | − | 0.952178i | \(-0.598838\pi\) | ||||
−0.305544 | + | 0.952178i | \(0.598838\pi\) | |||||||
\(710\) | 958.453i | 1.34993i | ||||||||
\(711\) | 422.762 | − | 189.718i | 0.594602 | − | 0.266833i | ||||
\(712\) | 306.345 | 0.430260 | ||||||||
\(713\) | − | 252.427i | − | 0.354035i | ||||||
\(714\) | −620.683 | + | 132.885i | −0.869305 | + | 0.186114i | ||||
\(715\) | 383.610 | 0.536518 | ||||||||
\(716\) | 401.673i | 0.560996i | ||||||||
\(717\) | −247.945 | − | 1158.11i | −0.345808 | − | 1.61521i | ||||
\(718\) | −190.803 | −0.265742 | ||||||||
\(719\) | 289.992i | 0.403326i | 0.979455 | + | 0.201663i | \(0.0646346\pi\) | ||||
−0.979455 | + | 0.201663i | \(0.935365\pi\) | |||||||
\(720\) | 100.506 | + | 223.964i | 0.139592 | + | 0.311061i | ||||
\(721\) | 766.456 | 1.06305 | ||||||||
\(722\) | − | 312.542i | − | 0.432884i | ||||||
\(723\) | −13.0303 | + | 2.78972i | −0.0180225 | + | 0.00385853i | ||||
\(724\) | 93.9322 | 0.129741 | ||||||||
\(725\) | − | 720.501i | − | 0.993795i | ||||||
\(726\) | −108.757 | − | 507.984i | −0.149803 | − | 0.699703i | ||||
\(727\) | 1161.84 | 1.59813 | 0.799067 | − | 0.601241i | \(-0.205327\pi\) | ||||
0.799067 | + | 0.601241i | \(0.205327\pi\) | |||||||
\(728\) | 97.7420i | 0.134261i | ||||||||
\(729\) | 219.145 | − | 695.282i | 0.300610 | − | 0.953747i | ||||
\(730\) | −915.646 | −1.25431 | ||||||||
\(731\) | − | 290.734i | − | 0.397721i | ||||||
\(732\) | −196.263 | + | 42.0190i | −0.268120 | + | 0.0574030i | ||||
\(733\) | 573.124 | 0.781888 | 0.390944 | − | 0.920414i | \(-0.372149\pi\) | ||||
0.390944 | + | 0.920414i | \(0.372149\pi\) | |||||||
\(734\) | − | 501.945i | − | 0.683849i | ||||||
\(735\) | −183.557 | − | 857.364i | −0.249738 | − | 1.16648i | ||||
\(736\) | −45.8035 | −0.0622330 | ||||||||
\(737\) | 5.49593i | 0.00745716i | ||||||||
\(738\) | 703.082 | − | 315.514i | 0.952686 | − | 0.427526i | ||||
\(739\) | 351.285 | 0.475352 | 0.237676 | − | 0.971344i | \(-0.423614\pi\) | ||||
0.237676 | + | 0.971344i | \(0.423614\pi\) | |||||||
\(740\) | − | 557.187i | − | 0.752956i | ||||||
\(741\) | −255.166 | + | 54.6297i | −0.344354 | + | 0.0737243i | ||||
\(742\) | −535.746 | −0.722029 | ||||||||
\(743\) | 76.8398i | 0.103418i | 0.998662 | + | 0.0517092i | \(0.0164669\pi\) | ||||
−0.998662 | + | 0.0517092i | \(0.983533\pi\) | |||||||
\(744\) | −55.3799 | − | 258.670i | −0.0744354 | − | 0.347675i | ||||
\(745\) | −1316.79 | −1.76750 | ||||||||
\(746\) | − | 502.788i | − | 0.673978i | ||||||
\(747\) | 323.900 | + | 721.768i | 0.433601 | + | 0.966222i | ||||
\(748\) | −487.116 | −0.651225 | ||||||||
\(749\) | 1185.39i | 1.58264i | ||||||||
\(750\) | −99.0693 | + | 21.2102i | −0.132092 | + | 0.0282803i | ||||
\(751\) | −74.4474 | −0.0991311 | −0.0495655 | − | 0.998771i | \(-0.515784\pi\) | ||||
−0.0495655 | + | 0.998771i | \(0.515784\pi\) | |||||||
\(752\) | 26.2136i | 0.0348585i | ||||||||
\(753\) | 118.527 | + | 553.621i | 0.157407 | + | 0.735221i | ||||
\(754\) | −170.893 | −0.226648 | ||||||||
\(755\) | 1062.66i | 1.40749i | ||||||||
\(756\) | −417.366 | + | 306.058i | −0.552071 | + | 0.404838i | ||||
\(757\) | 344.312 | 0.454838 | 0.227419 | − | 0.973797i | \(-0.426971\pi\) | ||||
0.227419 | + | 0.973797i | \(0.426971\pi\) | |||||||
\(758\) | − | 693.346i | − | 0.914704i | ||||||
\(759\) | −370.608 | + | 79.3451i | −0.488284 | + | 0.104539i | ||||
\(760\) | 465.290 | 0.612224 | ||||||||
\(761\) | − | 742.341i | − | 0.975480i | −0.872989 | − | 0.487740i | \(-0.837821\pi\) | ||
0.872989 | − | 0.487740i | \(-0.162179\pi\) | |||||||
\(762\) | −11.7267 | − | 54.7734i | −0.0153894 | − | 0.0718811i | ||||
\(763\) | −410.215 | −0.537635 | ||||||||
\(764\) | 24.0684i | 0.0315031i | ||||||||
\(765\) | 874.017 | − | 392.223i | 1.14251 | − | 0.512709i | ||||
\(766\) | −144.809 | −0.189046 | ||||||||
\(767\) | 174.565i | 0.227595i | ||||||||
\(768\) | −46.9364 | + | 10.0488i | −0.0611150 | + | 0.0130844i | ||||
\(769\) | 1264.66 | 1.64455 | 0.822275 | − | 0.569091i | \(-0.192705\pi\) | ||||
0.822275 | + | 0.569091i | \(0.192705\pi\) | |||||||
\(770\) | − | 1442.11i | − | 1.87287i | ||||||
\(771\) | −181.467 | − | 847.600i | −0.235365 | − | 1.09935i | ||||
\(772\) | 531.421 | 0.688369 | ||||||||
\(773\) | 695.508i | 0.899752i | 0.893091 | + | 0.449876i | \(0.148532\pi\) | ||||
−0.893091 | + | 0.449876i | \(0.851468\pi\) | |||||||
\(774\) | −97.0564 | − | 216.277i | −0.125396 | − | 0.279428i | ||||
\(775\) | −670.208 | −0.864785 | ||||||||
\(776\) | − | 234.010i | − | 0.301559i | ||||||
\(777\) | 1148.70 | − | 245.932i | 1.47838 | − | 0.316514i | ||||
\(778\) | 516.785 | 0.664248 | ||||||||
\(779\) | − | 1460.67i | − | 1.87505i | ||||||
\(780\) | −30.8826 | − | 144.247i | −0.0395931 | − | 0.184933i | ||||
\(781\) | −1550.74 | −1.98559 | ||||||||
\(782\) | 178.747i | 0.228577i | ||||||||
\(783\) | −535.113 | − | 729.725i | −0.683414 | − | 0.931961i | ||||
\(784\) | 171.443 | 0.218677 | ||||||||
\(785\) | 442.537i | 0.563742i | ||||||||
\(786\) | −684.229 | + | 146.490i | −0.870521 | + | 0.186374i | ||||
\(787\) | 413.104 | 0.524910 | 0.262455 | − | 0.964944i | \(-0.415468\pi\) | ||||
0.262455 | + | 0.964944i | \(0.415468\pi\) | |||||||
\(788\) | 649.730i | 0.824531i | ||||||||
\(789\) | −183.997 | − | 859.421i | −0.233203 | − | 1.08925i | ||||
\(790\) | 496.508 | 0.628491 | ||||||||
\(791\) | − | 809.881i | − | 1.02387i | ||||||
\(792\) | −362.367 | + | 162.615i | −0.457534 | + | 0.205322i | ||||
\(793\) | 120.612 | 0.152096 | ||||||||
\(794\) | 703.094i | 0.885509i | ||||||||
\(795\) | 790.652 | − | 169.274i | 0.994531 | − | 0.212924i | ||||
\(796\) | −533.226 | −0.669882 | ||||||||
\(797\) | 1085.67i | 1.36219i | 0.732194 | + | 0.681096i | \(0.238496\pi\) | ||||
−0.732194 | + | 0.681096i | \(0.761504\pi\) | |||||||
\(798\) | 205.370 | + | 959.248i | 0.257356 | + | 1.20207i | ||||
\(799\) | 102.298 | 0.128033 | ||||||||
\(800\) | 121.611i | 0.152014i | ||||||||
\(801\) | −399.099 | − | 889.340i | −0.498251 | − | 1.11029i | ||||
\(802\) | −796.789 | −0.993502 | ||||||||
\(803\) | − | 1481.48i | − | 1.84494i | ||||||
\(804\) | 2.06661 | − | 0.442450i | 0.00257041 | − | 0.000550311i | ||||
\(805\) | −529.182 | −0.657369 | ||||||||
\(806\) | 158.964i | 0.197226i | ||||||||
\(807\) | 128.841 | + | 601.794i | 0.159654 | + | 0.745718i | ||||
\(808\) | 123.552 | 0.152911 | ||||||||
\(809\) | − | 415.510i | − | 0.513609i | −0.966463 | − | 0.256805i | \(-0.917330\pi\) | ||
0.966463 | − | 0.256805i | \(-0.0826697\pi\) | |||||||
\(810\) | 519.245 | − | 583.550i | 0.641044 | − | 0.720432i | ||||
\(811\) | −720.055 | −0.887861 | −0.443930 | − | 0.896061i | \(-0.646416\pi\) | ||||
−0.443930 | + | 0.896061i | \(0.646416\pi\) | |||||||
\(812\) | 642.439i | 0.791181i | ||||||||
\(813\) | −624.023 | + | 133.600i | −0.767555 | + | 0.164330i | ||||
\(814\) | 901.511 | 1.10751 | ||||||||
\(815\) | 2015.16i | 2.47258i | ||||||||
\(816\) | 39.2154 | + | 183.168i | 0.0480581 | + | 0.224471i | ||||
\(817\) | −449.320 | −0.549964 | ||||||||
\(818\) | 1039.39i | 1.27065i | ||||||||
\(819\) | 283.751 | − | 127.336i | 0.346461 | − | 0.155477i | ||||
\(820\) | 825.727 | 1.00698 | ||||||||
\(821\) | 725.813i | 0.884059i | 0.897000 | + | 0.442030i | \(0.145741\pi\) | ||||
−0.897000 | + | 0.442030i | \(0.854259\pi\) | |||||||
\(822\) | 200.715 | − | 42.9719i | 0.244178 | − | 0.0522773i | ||||
\(823\) | 1122.02 | 1.36333 | 0.681663 | − | 0.731666i | \(-0.261257\pi\) | ||||
0.681663 | + | 0.731666i | \(0.261257\pi\) | |||||||
\(824\) | − | 226.187i | − | 0.274499i | ||||||
\(825\) | 210.666 | + | 983.986i | 0.255353 | + | 1.19271i | ||||
\(826\) | 656.245 | 0.794486 | ||||||||
\(827\) | 1451.22i | 1.75480i | 0.479758 | + | 0.877401i | \(0.340724\pi\) | ||||
−0.479758 | + | 0.877401i | \(0.659276\pi\) | |||||||
\(828\) | 59.6716 | + | 132.970i | 0.0720672 | + | 0.160592i | ||||
\(829\) | −1099.31 | −1.32607 | −0.663037 | − | 0.748587i | \(-0.730733\pi\) | ||||
−0.663037 | + | 0.748587i | \(0.730733\pi\) | |||||||
\(830\) | 847.673i | 1.02129i | ||||||||
\(831\) | 808.883 | − | 173.177i | 0.973385 | − | 0.208396i | ||||
\(832\) | 28.8444 | 0.0346688 | ||||||||
\(833\) | − | 669.052i | − | 0.803184i | ||||||
\(834\) | −36.0290 | − | 168.285i | −0.0432003 | − | 0.201781i | ||||
\(835\) | −589.940 | −0.706515 | ||||||||
\(836\) | 752.824i | 0.900507i | ||||||||
\(837\) | −678.788 | + | 497.761i | −0.810977 | + | 0.594696i | ||||
\(838\) | 426.361 | 0.508784 | ||||||||
\(839\) | 714.937i | 0.852130i | 0.904693 | + | 0.426065i | \(0.140100\pi\) | ||||
−0.904693 | + | 0.426065i | \(0.859900\pi\) | |||||||
\(840\) | −542.271 | + | 116.097i | −0.645560 | + | 0.138211i | ||||
\(841\) | −282.244 | −0.335605 | ||||||||
\(842\) | − | 71.5635i | − | 0.0849923i | ||||||
\(843\) | 90.1516 | + | 421.083i | 0.106941 | + | 0.499505i | ||||
\(844\) | 605.562 | 0.717491 | ||||||||
\(845\) | 88.6463i | 0.104907i | ||||||||
\(846\) | 76.0998 | − | 34.1505i | 0.0899524 | − | 0.0403670i | ||||
\(847\) | 1173.57 | 1.38557 | ||||||||
\(848\) | 158.103i | 0.186442i | ||||||||
\(849\) | −269.764 | + | 57.7550i | −0.317743 | + | 0.0680271i | ||||
\(850\) | 474.585 | 0.558335 | ||||||||
\(851\) | − | 330.809i | − | 0.388730i | ||||||
\(852\) | 124.843 | + | 583.120i | 0.146529 | + | 0.684413i | ||||
\(853\) | −619.594 | −0.726370 | −0.363185 | − | 0.931717i | \(-0.618311\pi\) | ||||
−0.363185 | + | 0.931717i | \(0.618311\pi\) | |||||||
\(854\) | − | 453.419i | − | 0.530936i | ||||||
\(855\) | −606.169 | − | 1350.77i | −0.708969 | − | 1.57984i | ||||
\(856\) | 349.819 | 0.408667 | ||||||||
\(857\) | − | 603.166i | − | 0.703811i | −0.936035 | − | 0.351906i | \(-0.885534\pi\) | ||
0.936035 | − | 0.351906i | \(-0.114466\pi\) | |||||||
\(858\) | 233.388 | − | 49.9670i | 0.272013 | − | 0.0582366i | ||||
\(859\) | 917.890 | 1.06856 | 0.534278 | − | 0.845309i | \(-0.320583\pi\) | ||||
0.534278 | + | 0.845309i | \(0.320583\pi\) | |||||||
\(860\) | − | 254.004i | − | 0.295354i | ||||||
\(861\) | 364.460 | + | 1702.33i | 0.423298 | + | 1.97715i | ||||
\(862\) | −80.9074 | −0.0938601 | ||||||||
\(863\) | 144.641i | 0.167602i | 0.996483 | + | 0.0838010i | \(0.0267060\pi\) | ||||
−0.996483 | + | 0.0838010i | \(0.973294\pi\) | |||||||
\(864\) | 90.3199 | + | 123.168i | 0.104537 | + | 0.142555i | ||||
\(865\) | −544.576 | −0.629568 | ||||||||
\(866\) | − | 985.721i | − | 1.13825i | ||||||
\(867\) | −132.976 | + | 28.4695i | −0.153375 | + | 0.0328368i | ||||
\(868\) | 597.595 | 0.688473 | ||||||||
\(869\) | 803.334i | 0.924435i | ||||||||
\(870\) | −202.985 | − | 948.109i | −0.233316 | − | 1.08978i | ||||
\(871\) | −1.27002 | −0.00145812 | ||||||||
\(872\) | 121.058i | 0.138828i | ||||||||
\(873\) | −679.345 | + | 304.862i | −0.778173 | + | 0.349212i | ||||
\(874\) | 276.249 | 0.316074 | ||||||||
\(875\) | − | 228.876i | − | 0.261572i | ||||||
\(876\) | −557.076 | + | 119.267i | −0.635932 | + | 0.136150i | ||||
\(877\) | −1102.64 | −1.25728 | −0.628641 | − | 0.777695i | \(-0.716389\pi\) | ||||
−0.628641 | + | 0.777695i | \(0.716389\pi\) | |||||||
\(878\) | 127.038i | 0.144690i | ||||||||
\(879\) | −298.361 | − | 1393.60i | −0.339433 | − | 1.58543i | ||||
\(880\) | −425.578 | −0.483611 | ||||||||
\(881\) | 458.046i | 0.519916i | 0.965620 | + | 0.259958i | \(0.0837088\pi\) | ||||
−0.965620 | + | 0.259958i | \(0.916291\pi\) | |||||||
\(882\) | −223.351 | − | 497.709i | −0.253233 | − | 0.564296i | ||||
\(883\) | −1578.69 | −1.78787 | −0.893935 | − | 0.448197i | \(-0.852066\pi\) | ||||
−0.893935 | + | 0.448197i | \(0.852066\pi\) | |||||||
\(884\) | − | 112.565i | − | 0.127336i | ||||||
\(885\) | −968.485 | + | 207.347i | −1.09433 | + | 0.234291i | ||||
\(886\) | 463.279 | 0.522889 | ||||||||
\(887\) | − | 1322.77i | − | 1.49128i | −0.666349 | − | 0.745640i | \(-0.732144\pi\) | ||
0.666349 | − | 0.745640i | \(-0.267856\pi\) | |||||||
\(888\) | −72.5762 | − | 338.991i | −0.0817300 | − | 0.381747i | ||||
\(889\) | 126.541 | 0.142340 | ||||||||
\(890\) | − | 1044.48i | − | 1.17357i | ||||||
\(891\) | 944.165 | + | 840.122i | 1.05967 | + | 0.942898i | ||||
\(892\) | −598.294 | −0.670733 | ||||||||
\(893\) | − | 158.099i | − | 0.177042i | ||||||
\(894\) | −801.131 | + | 171.518i | −0.896119 | + | 0.191854i | ||||
\(895\) | 1369.49 | 1.53016 | ||||||||
\(896\) | − | 108.435i | − | 0.121021i | ||||||
\(897\) | −18.3354 | − | 85.6415i | −0.0204408 | − | 0.0954755i | ||||
\(898\) | 835.715 | 0.930640 | ||||||||
\(899\) | 1044.84i | 1.16222i | ||||||||
\(900\) | 353.044 | − | 158.432i | 0.392271 | − | 0.176035i | ||||
\(901\) | 616.993 | 0.684787 | ||||||||
\(902\) | 1336.00i | 1.48115i | ||||||||
\(903\) | 523.659 | − | 112.113i | 0.579910 | − | 0.124156i | ||||
\(904\) | −239.002 | −0.264383 | ||||||||
\(905\) | − | 320.259i | − | 0.353877i | ||||||
\(906\) | 138.416 | + | 646.518i | 0.152777 | + | 0.713596i | ||||
\(907\) | 183.989 | 0.202854 | 0.101427 | − | 0.994843i | \(-0.467659\pi\) | ||||
0.101427 | + | 0.994843i | \(0.467659\pi\) | |||||||
\(908\) | − | 53.8978i | − | 0.0593588i | ||||||
\(909\) | −160.961 | − | 358.679i | −0.177074 | − | 0.394587i | ||||
\(910\) | 333.249 | 0.366207 | ||||||||
\(911\) | 662.881i | 0.727641i | 0.931469 | + | 0.363821i | \(0.118528\pi\) | ||||
−0.931469 | + | 0.363821i | \(0.881472\pi\) | |||||||
\(912\) | 283.081 | − | 60.6062i | 0.310396 | − | 0.0664542i | ||||
\(913\) | −1371.51 | −1.50220 | ||||||||
\(914\) | 826.642i | 0.904422i | ||||||||
\(915\) | 143.263 | + | 669.155i | 0.156571 | + | 0.731317i | ||||
\(916\) | −536.339 | −0.585523 | ||||||||
\(917\) | − | 1580.75i | − | 1.72382i | ||||||
\(918\) | 480.660 | − | 352.472i | 0.523595 | − | 0.383956i | ||||
\(919\) | −1062.65 | −1.15631 | −0.578153 | − | 0.815928i | \(-0.696226\pi\) | ||||
−0.578153 | + | 0.815928i | \(0.696226\pi\) | |||||||
\(920\) | 156.166i | 0.169745i | ||||||||
\(921\) | 1335.29 | − | 285.878i | 1.44982 | − | 0.310399i | ||||
\(922\) | −258.888 | −0.280790 | ||||||||
\(923\) | − | 358.352i | − | 0.388247i | ||||||
\(924\) | −187.842 | − | 877.376i | −0.203292 | − | 0.949541i | ||||
\(925\) | −878.318 | −0.949533 | ||||||||
\(926\) | 1063.63i | 1.14863i | ||||||||
\(927\) | −656.635 | + | 294.671i | −0.708344 | + | 0.317876i | ||||
\(928\) | 189.588 | 0.204298 | ||||||||
\(929\) | − | 584.511i | − | 0.629183i | −0.949227 | − | 0.314591i | \(-0.898133\pi\) | ||
0.949227 | − | 0.314591i | \(-0.101867\pi\) | |||||||
\(930\) | −881.928 | + | 188.816i | −0.948310 | + | 0.203028i | ||||
\(931\) | −1034.00 | −1.11063 | ||||||||
\(932\) | 614.741i | 0.659593i | ||||||||
\(933\) | 274.140 | + | 1280.46i | 0.293827 | + | 1.37241i | ||||
\(934\) | −65.5809 | −0.0702151 | ||||||||
\(935\) | 1660.81i | 1.77627i | ||||||||
\(936\) | −37.5778 | − | 83.7371i | −0.0401472 | − | 0.0894628i | ||||
\(937\) | −779.887 | −0.832323 | −0.416162 | − | 0.909291i | \(-0.636625\pi\) | ||||
−0.416162 | + | 0.909291i | \(0.636625\pi\) | |||||||
\(938\) | 4.77440i | 0.00508998i | ||||||||
\(939\) | −562.984 | + | 120.532i | −0.599557 | + | 0.128362i | ||||
\(940\) | 89.3746 | 0.0950793 | ||||||||
\(941\) | − | 1016.41i | − | 1.08013i | −0.841622 | − | 0.540067i | \(-0.818399\pi\) | ||
0.841622 | − | 0.540067i | \(-0.181601\pi\) | |||||||
\(942\) | 57.6426 | + | 269.239i | 0.0611917 | + | 0.285816i | ||||
\(943\) | 490.245 | 0.519878 | ||||||||
\(944\) | − | 193.663i | − | 0.205151i | ||||||
\(945\) | 1043.49 | + | 1423.00i | 1.10423 | + | 1.50582i | ||||
\(946\) | 410.971 | 0.434430 | ||||||||
\(947\) | − | 360.349i | − | 0.380516i | −0.981734 | − | 0.190258i | \(-0.939068\pi\) | ||
0.981734 | − | 0.190258i | \(-0.0609324\pi\) | |||||||
\(948\) | 302.074 | − | 64.6725i | 0.318644 | − | 0.0682199i | ||||
\(949\) | 342.347 | 0.360745 | ||||||||
\(950\) | − | 733.457i | − | 0.772060i | ||||||
\(951\) | 150.558 | + | 703.230i | 0.158315 | + | 0.739463i | ||||
\(952\) | −423.166 | −0.444502 | ||||||||
\(953\) | − | 733.168i | − | 0.769327i | −0.923057 | − | 0.384663i | \(-0.874318\pi\) | ||
0.923057 | − | 0.384663i | \(-0.125682\pi\) | |||||||
\(954\) | 458.982 | − | 205.972i | 0.481113 | − | 0.215904i | ||||
\(955\) | 82.0604 | 0.0859272 | ||||||||
\(956\) | − | 789.568i | − | 0.825907i | ||||||
\(957\) | 1534.01 | − | 328.423i | 1.60294 | − | 0.343180i | ||||
\(958\) | −478.565 | −0.499546 | ||||||||
\(959\) | 463.702i | 0.483527i | ||||||||
\(960\) | 34.2612 | + | 160.028i | 0.0356887 | + | 0.166696i | ||||
\(961\) | 10.9052 | 0.0113477 | ||||||||
\(962\) | 208.325i | 0.216554i | ||||||||
\(963\) | −455.736 | − | 1015.55i | −0.473246 | − | 1.05457i | ||||
\(964\) | −8.88372 | −0.00921547 | ||||||||
\(965\) | − | 1811.87i | − | 1.87758i | ||||||
\(966\) | −321.953 | + | 68.9284i | −0.333285 | + | 0.0713545i | ||||
\(967\) | −841.679 | −0.870402 | −0.435201 | − | 0.900333i | \(-0.643323\pi\) | ||||
−0.435201 | + | 0.900333i | \(0.643323\pi\) | |||||||
\(968\) | − | 346.331i | − | 0.357780i | ||||||
\(969\) | −236.515 | − | 1104.72i | −0.244081 | − | 1.14006i | ||||
\(970\) | −797.850 | −0.822525 | ||||||||
\(971\) | − | 536.293i | − | 0.552310i | −0.961113 | − | 0.276155i | \(-0.910940\pi\) | ||
0.961113 | − | 0.276155i | \(-0.0890604\pi\) | |||||||
\(972\) | 239.897 | − | 422.664i | 0.246808 | − | 0.434840i | ||||
\(973\) | 388.783 | 0.399571 | ||||||||
\(974\) | 147.972i | 0.151922i | ||||||||
\(975\) | −227.383 | + | 48.6816i | −0.233214 | + | 0.0499298i | ||||
\(976\) | −133.807 | −0.137098 | ||||||||
\(977\) | − | 679.462i | − | 0.695457i | −0.937595 | − | 0.347729i | \(-0.886953\pi\) | ||
0.937595 | − | 0.347729i | \(-0.113047\pi\) | |||||||
\(978\) | 262.484 | + | 1226.02i | 0.268388 | + | 1.25359i | ||||
\(979\) | 1689.93 | 1.72618 | ||||||||
\(980\) | − | 584.529i | − | 0.596458i | ||||||
\(981\) | 351.438 | − | 157.711i | 0.358245 | − | 0.160765i | ||||
\(982\) | 289.736 | 0.295047 | ||||||||
\(983\) | 462.786i | 0.470790i | 0.971900 | + | 0.235395i | \(0.0756383\pi\) | ||||
−0.971900 | + | 0.235395i | \(0.924362\pi\) | |||||||
\(984\) | 502.370 | − | 107.555i | 0.510539 | − | 0.109304i | ||||
\(985\) | 2215.24 | 2.24897 | ||||||||
\(986\) | − | 739.866i | − | 0.750371i | ||||||
\(987\) | 39.4482 | + | 184.256i | 0.0399678 | + | 0.186683i | ||||
\(988\) | −173.966 | −0.176079 | ||||||||
\(989\) | − | 150.806i | − | 0.152483i | ||||||
\(990\) | 554.432 | + | 1235.48i | 0.560032 | + | 1.24796i | ||||
\(991\) | −645.895 | −0.651760 | −0.325880 | − | 0.945411i | \(-0.605661\pi\) | ||||
−0.325880 | + | 0.945411i | \(0.605661\pi\) | |||||||
\(992\) | − | 176.355i | − | 0.177777i | ||||||
\(993\) | 769.606 | − | 164.768i | 0.775031 | − | 0.165930i | ||||
\(994\) | −1347.16 | −1.35529 | ||||||||
\(995\) | 1818.02i | 1.82715i | ||||||||
\(996\) | 110.413 | + | 515.722i | 0.110857 | + | 0.517793i | ||||
\(997\) | 761.944 | 0.764236 | 0.382118 | − | 0.924113i | \(-0.375195\pi\) | ||||
0.382118 | + | 0.924113i | \(0.375195\pi\) | |||||||
\(998\) | − | 564.151i | − | 0.565282i | ||||||
\(999\) | −889.562 | + | 652.323i | −0.890453 | + | 0.652976i |
(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 | 78.3.c.a.53.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 78.3.c.a.53.5 | yes | 8 | |
4.3 | odd | 2 | 624.3.f.b.209.7 | 8 | |||
12.11 | even | 2 | 624.3.f.b.209.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.3.c.a.53.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
78.3.c.a.53.5 | yes | 8 | 3.2 | odd | 2 | inner | |
624.3.f.b.209.7 | 8 | 4.3 | odd | 2 | |||
624.3.f.b.209.8 | 8 | 12.11 | even | 2 |