Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,3,Mod(209,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.c (of order \(2\), degree \(1\), not 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: | \(30.5177896084\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.13 | ||
Character | \(\chi\) | \(=\) | 1120.209 |
Dual form | 1120.3.c.g.209.14 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.68915i | − | 1.22972i | −0.788637 | − | 0.614859i | \(-0.789213\pi\) | ||
0.788637 | − | 0.614859i | \(-0.210787\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.693644 | − | 4.95165i | 0.138729 | − | 0.990330i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.51720 | + | 5.34742i | 0.645315 | + | 0.763917i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.60986 | −0.512207 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 10.2130i | − | 0.928458i | −0.885715 | − | 0.464229i | \(-0.846331\pi\) | ||
0.885715 | − | 0.464229i | \(-0.153669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.4358i | 1.11045i | 0.831701 | + | 0.555224i | \(0.187367\pi\) | ||||
−0.831701 | + | 0.555224i | \(0.812633\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.2674 | − | 2.55896i | −1.21783 | − | 0.170597i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16.4391 | −0.967008 | −0.483504 | − | 0.875342i | \(-0.660636\pi\) | ||||
−0.483504 | + | 0.875342i | \(0.660636\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 31.0538 | 1.63441 | 0.817206 | − | 0.576346i | \(-0.195522\pi\) | ||||
0.817206 | + | 0.576346i | \(0.195522\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 19.7275 | − | 16.6647i | 0.939403 | − | 0.793555i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 20.2273i | − | 0.879446i | −0.898133 | − | 0.439723i | \(-0.855077\pi\) | ||
0.898133 | − | 0.439723i | \(-0.144923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.0377 | − | 6.86937i | −0.961509 | − | 0.274775i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 16.1959i | − | 0.599848i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 56.8127i | − | 1.95906i | −0.201302 | − | 0.979529i | \(-0.564517\pi\) | ||
0.201302 | − | 0.979529i | \(-0.435483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 25.7499i | − | 0.830641i | −0.909675 | − | 0.415320i | \(-0.863669\pi\) | ||
0.909675 | − | 0.415320i | \(-0.136331\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −37.6775 | −1.14174 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 29.6119 | − | 18.6584i | 0.846054 | − | 0.533097i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −66.0553 | −1.78528 | −0.892640 | − | 0.450771i | \(-0.851149\pi\) | ||||
−0.892640 | + | 0.450771i | \(0.851149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 53.2560 | 1.36554 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.504264i | − | 0.0122991i | −0.999981 | − | 0.00614956i | \(-0.998043\pi\) | ||
0.999981 | − | 0.00614956i | \(-0.00195748\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −26.2293 | −0.609983 | −0.304992 | − | 0.952355i | \(-0.598654\pi\) | ||||
−0.304992 | + | 0.952355i | \(0.598654\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.19760 | + | 22.8264i | −0.0710578 | + | 0.507254i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −20.2286 | −0.430395 | −0.215197 | − | 0.976571i | \(-0.569039\pi\) | ||||
−0.215197 | + | 0.976571i | \(0.569039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.18977 | + | 48.3107i | −0.167138 | + | 0.985933i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 60.6465i | 1.18915i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 53.0620 | 1.00117 | 0.500585 | − | 0.865687i | \(-0.333118\pi\) | ||||
0.500585 | + | 0.865687i | \(0.333118\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −50.5714 | − | 7.08422i | −0.919481 | − | 0.128804i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 114.562i | − | 2.00987i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 59.3867 | 1.00655 | 0.503277 | − | 0.864125i | \(-0.332127\pi\) | ||||
0.503277 | + | 0.864125i | \(0.332127\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −69.5062 | −1.13945 | −0.569723 | − | 0.821837i | \(-0.692950\pi\) | ||||
−0.569723 | + | 0.821837i | \(0.692950\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −20.8237 | − | 24.6509i | −0.330535 | − | 0.391283i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 71.4812 | + | 10.0133i | 1.09971 | + | 0.154051i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 61.9289 | 0.924312 | 0.462156 | − | 0.886799i | \(-0.347076\pi\) | ||||
0.462156 | + | 0.886799i | \(0.347076\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −74.6215 | −1.08147 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 25.5504 | 0.359864 | 0.179932 | − | 0.983679i | \(-0.442412\pi\) | ||||
0.179932 | + | 0.983679i | \(0.442412\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34.7213 | 0.475634 | 0.237817 | − | 0.971310i | \(-0.423568\pi\) | ||||
0.237817 | + | 0.971310i | \(0.423568\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −25.3422 | + | 88.6788i | −0.337895 | + | 1.18238i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 54.6134 | − | 46.1344i | 0.709265 | − | 0.599148i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64.4865 | −0.816284 | −0.408142 | − | 0.912918i | \(-0.633823\pi\) | ||||
−0.408142 | + | 0.912918i | \(0.633823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −101.238 | −1.24985 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.27026i | 0.111690i | 0.998439 | + | 0.0558449i | \(0.0177852\pi\) | ||||
−0.998439 | + | 0.0558449i | \(0.982215\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.4029 | + | 81.4009i | −0.134152 | + | 0.957658i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −209.591 | −2.40909 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 22.0650i | − | 0.247921i | −0.992287 | − | 0.123961i | \(-0.960440\pi\) | ||
0.992287 | − | 0.123961i | \(-0.0395597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −77.1944 | + | 65.2095i | −0.848290 | + | 0.716588i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −94.9952 | −1.02145 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.5403 | − | 153.768i | 0.226740 | − | 1.61861i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −74.3644 | −0.766643 | −0.383321 | − | 0.923615i | \(-0.625220\pi\) | ||||
−0.383321 | + | 0.923615i | \(0.625220\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 47.0807i | 0.475563i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 104.960 | 1.03920 | 0.519602 | − | 0.854408i | \(-0.326080\pi\) | ||||
0.519602 | + | 0.854408i | \(0.326080\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 59.3436 | 0.576151 | 0.288076 | − | 0.957608i | \(-0.406985\pi\) | ||||
0.288076 | + | 0.957608i | \(0.406985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −68.8337 | − | 109.243i | −0.655560 | − | 1.04041i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −168.968 | −1.57914 | −0.789571 | − | 0.613660i | \(-0.789697\pi\) | ||||
−0.789571 | + | 0.613660i | \(0.789697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 40.5581i | 0.372092i | 0.982541 | + | 0.186046i | \(0.0595674\pi\) | ||||
−0.982541 | + | 0.186046i | \(0.940433\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 243.688i | 2.19539i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 145.160i | 1.28460i | 0.766453 | + | 0.642300i | \(0.222020\pi\) | ||||
−0.766453 | + | 0.642300i | \(0.777980\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −100.158 | − | 14.0305i | −0.870942 | − | 0.122005i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 66.5472i | − | 0.568779i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −74.2589 | − | 87.9070i | −0.624024 | − | 0.738714i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.6937 | 0.137965 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.86031 | −0.0151245 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −50.6883 | + | 114.262i | −0.405507 | + | 0.914092i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 131.272i | − | 1.03364i | −0.856094 | − | 0.516819i | \(-0.827116\pi\) | ||
0.856094 | − | 0.516819i | \(-0.172884\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 96.7639i | 0.750108i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −47.1382 | −0.359834 | −0.179917 | − | 0.983682i | \(-0.557583\pi\) | ||||
−0.179917 | + | 0.983682i | \(0.557583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 140.276 | + | 166.058i | 1.05471 | + | 1.24856i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −80.1965 | − | 11.2342i | −0.594048 | − | 0.0832162i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 48.2151i | − | 0.351935i | −0.984396 | − | 0.175967i | \(-0.943695\pi\) | ||
0.984396 | − | 0.175967i | \(-0.0563053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 89.2672 | 0.642210 | 0.321105 | − | 0.947044i | \(-0.395946\pi\) | ||||
0.321105 | + | 0.947044i | \(0.395946\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 74.6263i | 0.529264i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 147.434 | 1.03100 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −281.317 | − | 39.4078i | −1.94012 | − | 0.271778i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 178.226 | + | 30.2133i | 1.21242 | + | 0.205533i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 49.6284i | − | 0.333077i | −0.986035 | − | 0.166538i | \(-0.946741\pi\) | ||
0.986035 | − | 0.166538i | \(-0.0532589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 65.9244 | 0.436585 | 0.218293 | − | 0.975883i | \(-0.429951\pi\) | ||||
0.218293 | + | 0.975883i | \(0.429951\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 75.7822 | 0.495308 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −127.504 | − | 17.8612i | −0.822609 | − | 0.115234i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.29611i | 0.0209944i | 0.999945 | + | 0.0104972i | \(0.00334142\pi\) | ||||
−0.999945 | + | 0.0104972i | \(0.996659\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 195.754i | − | 1.23116i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 108.164 | − | 91.3706i | 0.671824 | − | 0.567520i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −80.8482 | −0.496001 | −0.248001 | − | 0.968760i | \(-0.579774\pi\) | ||||
−0.248001 | + | 0.968760i | \(0.579774\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −26.1348 | + | 186.566i | −0.158393 | + | 1.13070i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −185.849 | −1.11287 | −0.556434 | − | 0.830892i | \(-0.687831\pi\) | ||||
−0.556434 | + | 0.830892i | \(0.687831\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −39.3931 | −0.233095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −143.154 | −0.837157 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 203.853i | − | 1.17834i | −0.808009 | − | 0.589170i | \(-0.799455\pi\) | ||
0.808009 | − | 0.589170i | \(-0.200545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −71.8498 | − | 159.570i | −0.410570 | − | 0.911829i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 219.087i | − | 1.23778i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 252.488i | − | 1.41055i | −0.708934 | − | 0.705275i | \(-0.750824\pi\) | ||
0.708934 | − | 0.705275i | \(-0.249176\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 105.014 | 0.580186 | 0.290093 | − | 0.956998i | \(-0.406314\pi\) | ||||
0.290093 | + | 0.956998i | \(0.406314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 256.419i | 1.40120i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −45.8189 | + | 327.083i | −0.247670 | + | 1.76802i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 167.894i | 0.897827i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 86.6063 | − | 73.1602i | 0.458234 | − | 0.387091i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 91.0901 | 0.476912 | 0.238456 | − | 0.971153i | \(-0.423359\pi\) | ||||
0.238456 | + | 0.971153i | \(0.423359\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 126.767i | − | 0.656822i | −0.944535 | − | 0.328411i | \(-0.893487\pi\) | ||
0.944535 | − | 0.328411i | \(-0.106513\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 36.9407 | − | 263.705i | 0.189439 | − | 1.35233i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −315.300 | −1.60051 | −0.800253 | − | 0.599663i | \(-0.795301\pi\) | ||||
−0.800253 | + | 0.599663i | \(0.795301\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 304.652i | 1.53091i | 0.643488 | + | 0.765456i | \(0.277487\pi\) | ||||
−0.643488 | + | 0.765456i | \(0.722513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 228.465i | − | 1.13664i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 303.801 | − | 256.634i | 1.49656 | − | 1.26421i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.49694 | − | 0.349780i | −0.0121802 | − | 0.00170624i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 93.2449i | 0.450458i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 317.154i | − | 1.51748i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 119.367i | − | 0.565722i | −0.959161 | − | 0.282861i | \(-0.908716\pi\) | ||
0.959161 | − | 0.282861i | \(-0.0912836\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 94.2593i | − | 0.442532i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.1938 | + | 129.878i | −0.0846223 | + | 0.604085i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 137.695 | − | 116.317i | 0.634541 | − | 0.536025i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 128.092i | − | 0.584896i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 237.313i | − | 1.07381i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 225.950 | 1.01323 | 0.506615 | − | 0.862172i | \(-0.330896\pi\) | ||||
0.506615 | + | 0.862172i | \(0.330896\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 110.811 | + | 31.6668i | 0.492491 | + | 0.140741i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 233.683i | 1.02944i | 0.857358 | + | 0.514721i | \(0.172104\pi\) | ||||
−0.857358 | + | 0.514721i | \(0.827896\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 410.025 | 1.79050 | 0.895251 | − | 0.445562i | \(-0.146996\pi\) | ||||
0.895251 | + | 0.445562i | \(0.146996\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −170.197 | − | 201.477i | −0.736783 | − | 0.872196i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 195.365i | 0.838476i | 0.907876 | + | 0.419238i | \(0.137703\pi\) | ||||
−0.907876 | + | 0.419238i | \(0.862297\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.0314 | + | 100.165i | −0.0597081 | + | 0.426233i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 237.901i | 1.00380i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.13036 | 0.00472952 | 0.00236476 | − | 0.999997i | \(-0.499247\pi\) | ||||
0.00236476 | + | 0.999997i | \(0.499247\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 184.725i | 0.766495i | 0.923646 | + | 0.383247i | \(0.125194\pi\) | ||||
−0.923646 | + | 0.383247i | \(0.874806\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 227.719i | 0.937116i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 233.537 | + | 74.0634i | 0.953213 | + | 0.302299i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 448.288i | 1.81493i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.1994 | 0.137347 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 161.026 | 0.641537 | 0.320769 | − | 0.947158i | \(-0.396059\pi\) | ||||
0.320769 | + | 0.947158i | \(0.396059\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −206.582 | −0.816529 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 300.300 | + | 42.0671i | 1.17765 | + | 0.164969i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 280.740 | 1.09237 | 0.546186 | − | 0.837664i | \(-0.316079\pi\) | ||||
0.546186 | + | 0.837664i | \(0.316079\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −298.385 | − | 353.225i | −1.15207 | − | 1.36380i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 261.899i | 1.00344i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 114.489i | 0.435318i | 0.976025 | + | 0.217659i | \(0.0698421\pi\) | ||||
−0.976025 | + | 0.217659i | \(0.930158\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.8061 | − | 262.745i | 0.138891 | − | 0.991489i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −81.4012 | −0.304874 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 199.064 | 0.740014 | 0.370007 | − | 0.929029i | \(-0.379355\pi\) | ||||
0.370007 | + | 0.929029i | \(0.379355\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 138.300i | − | 0.510333i | −0.966897 | − | 0.255167i | \(-0.917870\pi\) | ||
0.966897 | − | 0.255167i | \(-0.0821303\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 240.568 | + | 284.782i | 0.881202 | + | 1.04316i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −70.1572 | + | 245.498i | −0.255117 | + | 0.892721i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 347.378 | 1.25407 | 0.627035 | − | 0.778991i | \(-0.284268\pi\) | ||||
0.627035 | + | 0.778991i | \(0.284268\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 118.703i | 0.425460i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −261.441 | −0.930396 | −0.465198 | − | 0.885207i | \(-0.654017\pi\) | ||||
−0.465198 | + | 0.885207i | \(0.654017\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 88.8373i | − | 0.313913i | −0.987606 | − | 0.156956i | \(-0.949832\pi\) | ||
0.987606 | − | 0.156956i | \(-0.0501682\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −567.273 | − | 79.4655i | −1.99043 | − | 0.278826i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.69651 | − | 2.27786i | 0.00939551 | − | 0.00793681i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.7547 | −0.0648952 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 274.342i | 0.942755i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 159.380i | − | 0.543960i | −0.962303 | − | 0.271980i | \(-0.912322\pi\) | ||
0.962303 | − | 0.271980i | \(-0.0876784\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.1932 | − | 294.062i | 0.139638 | − | 0.996822i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −165.409 | −0.556934 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 291.997 | 0.976579 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −118.483 | − | 140.259i | −0.393631 | − | 0.465977i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 387.212i | − | 1.27793i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −48.2126 | + | 344.171i | −0.158074 | + | 1.12843i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 190.921i | − | 0.621892i | −0.950428 | − | 0.310946i | \(-0.899354\pi\) | ||
0.950428 | − | 0.310946i | \(-0.100646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 218.928i | − | 0.708503i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 97.1437i | − | 0.312359i | −0.987729 | − | 0.156180i | \(-0.950082\pi\) | ||
0.987729 | − | 0.156180i | \(-0.0499179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −131.747 | −0.420917 | −0.210459 | − | 0.977603i | \(-0.567496\pi\) | ||||
−0.210459 | + | 0.977603i | \(0.567496\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −136.507 | + | 86.0127i | −0.433355 | + | 0.273056i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 64.5641 | 0.203672 | 0.101836 | − | 0.994801i | \(-0.467528\pi\) | ||||
0.101836 | + | 0.994801i | \(0.467528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −580.230 | −1.81890 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 623.349i | 1.94190i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −510.498 | −1.58049 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 99.1650 | − | 347.004i | 0.305123 | − | 1.06771i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 149.625 | 0.457569 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −91.3765 | − | 108.171i | −0.277740 | − | 0.328786i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 52.7603i | − | 0.159397i | −0.996819 | − | 0.0796983i | \(-0.974604\pi\) | ||
0.996819 | − | 0.0796983i | \(-0.0253957\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 304.506 | 0.914432 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 42.9566 | − | 306.650i | 0.128229 | − | 0.915374i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 251.074i | 0.745026i | 0.928027 | + | 0.372513i | \(0.121504\pi\) | ||||
−0.928027 | + | 0.372513i | \(0.878496\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 535.517 | 1.57970 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −262.984 | −0.771215 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −295.333 | + | 174.435i | −0.861028 | + | 0.508558i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −51.7608 | + | 369.500i | −0.150031 | + | 1.07101i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 555.781 | 1.60167 | 0.800837 | − | 0.598882i | \(-0.204388\pi\) | ||||
0.800837 | + | 0.598882i | \(0.204388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 202.673 | 0.580726 | 0.290363 | − | 0.956917i | \(-0.406224\pi\) | ||||
0.290363 | + | 0.956917i | \(0.406224\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 233.801 | 0.666100 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 332.885 | 0.943018 | 0.471509 | − | 0.881861i | \(-0.343710\pi\) | ||||
0.471509 | + | 0.881861i | \(0.343710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.7229 | − | 126.517i | 0.0499236 | − | 0.356385i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −324.302 | + | 273.953i | −0.908410 | + | 0.767374i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 333.845 | 0.929931 | 0.464965 | − | 0.885329i | \(-0.346067\pi\) | ||||
0.464965 | + | 0.885329i | \(0.346067\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 603.340 | 1.67130 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 61.5858i | − | 0.169658i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.0842 | − | 171.928i | 0.0659842 | − | 0.471035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 330.735 | 0.901184 | 0.450592 | − | 0.892730i | \(-0.351213\pi\) | ||||
0.450592 | + | 0.892730i | \(0.351213\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.32459i | 0.00629970i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 239.692 | + | 283.745i | 0.646070 | + | 0.764811i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −114.255 | −0.306315 | −0.153157 | − | 0.988202i | \(-0.548944\pi\) | ||||
−0.153157 | + | 0.988202i | \(0.548944\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 421.528 | + | 186.997i | 1.12408 | + | 0.498659i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 820.138 | 2.17543 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 355.076i | − | 0.936877i | −0.883496 | − | 0.468439i | \(-0.844817\pi\) | ||
0.883496 | − | 0.468439i | \(-0.155183\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −484.283 | −1.27108 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 436.582 | 1.13990 | 0.569951 | − | 0.821679i | \(-0.306962\pi\) | ||||
0.569951 | + | 0.821679i | \(0.306962\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −190.559 | − | 302.427i | −0.494959 | − | 0.785526i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 120.913 | 0.312438 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 639.735i | − | 1.64456i | −0.569080 | − | 0.822282i | \(-0.692701\pi\) | ||
0.569080 | − | 0.822282i | \(-0.307299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 332.519i | 0.850432i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 173.900i | 0.442494i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −44.7307 | + | 319.315i | −0.113242 | + | 0.808391i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 516.755i | − | 1.30165i | −0.759228 | − | 0.650825i | \(-0.774423\pi\) | ||
0.759228 | − | 0.650825i | \(-0.225577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 612.613 | − | 517.501i | 1.53537 | − | 1.29700i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −261.169 | −0.651295 | −0.325647 | − | 0.945491i | \(-0.605582\pi\) | ||||
−0.325647 | + | 0.945491i | \(0.605582\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 371.721 | 0.922383 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −70.2231 | + | 501.295i | −0.173390 | + | 1.23777i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 674.626i | 1.65756i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 94.8415i | 0.231886i | 0.993256 | + | 0.115943i | \(0.0369890\pi\) | ||||
−0.993256 | + | 0.115943i | \(0.963011\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −177.873 | −0.432781 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 268.262 | + | 317.566i | 0.649544 | + | 0.768924i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45.9031 | + | 6.43026i | 0.110610 | + | 0.0154946i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 329.320i | − | 0.789737i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 46.0965 | 0.110016 | 0.0550078 | − | 0.998486i | \(-0.482482\pi\) | ||||
0.0550078 | + | 0.998486i | \(0.482482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 710.750i | 1.68824i | 0.536153 | + | 0.844121i | \(0.319877\pi\) | ||||
−0.536153 | + | 0.844121i | \(0.680123\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 93.2508 | 0.220451 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 395.159 | + | 112.926i | 0.929787 | + | 0.265709i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −313.974 | − | 371.679i | −0.735301 | − | 0.870442i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 543.906i | − | 1.26785i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −411.504 | −0.954766 | −0.477383 | − | 0.878695i | \(-0.658415\pi\) | ||||
−0.477383 | + | 0.878695i | \(0.658415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −329.582 | −0.761159 | −0.380580 | − | 0.924748i | \(-0.624275\pi\) | ||||
−0.380580 | + | 0.924748i | \(0.624275\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −145.381 | + | 1037.82i | −0.334210 | + | 2.38579i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 628.134i | − | 1.43738i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 370.448i | − | 0.843844i | −0.906632 | − | 0.421922i | \(-0.861356\pi\) | ||
0.906632 | − | 0.421922i | \(-0.138644\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 37.7537 | − | 222.706i | 0.0856093 | − | 0.505002i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 203.437 | 0.459226 | 0.229613 | − | 0.973282i | \(-0.426254\pi\) | ||||
0.229613 | + | 0.973282i | \(0.426254\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −109.258 | − | 15.3053i | −0.245524 | − | 0.0343938i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −183.087 | −0.409590 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 274.557 | 0.611485 | 0.305742 | − | 0.952114i | \(-0.401095\pi\) | ||||
0.305742 | + | 0.952114i | \(0.401095\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.15007 | −0.0114192 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 243.205i | − | 0.536877i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 269.350 | + | 427.472i | 0.591977 | + | 0.939499i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 186.534i | 0.408170i | 0.978953 | + | 0.204085i | \(0.0654219\pi\) | ||||
−0.978953 | + | 0.204085i | \(0.934578\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 266.247i | 0.580058i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −501.181 | −1.08716 | −0.543580 | − | 0.839357i | \(-0.682932\pi\) | ||||
−0.543580 | + | 0.839357i | \(0.682932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 160.592i | 0.346850i | 0.984847 | + | 0.173425i | \(0.0554835\pi\) | ||||
−0.984847 | + | 0.173425i | \(0.944517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −65.8929 | + | 470.383i | −0.141705 | + | 1.01158i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 340.763i | 0.729686i | 0.931069 | + | 0.364843i | \(0.118877\pi\) | ||||
−0.931069 | + | 0.364843i | \(0.881123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 279.745 | + | 331.160i | 0.596472 | + | 0.706097i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.1599 | 0.0258171 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 267.881i | 0.566344i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −746.463 | − | 213.320i | −1.57150 | − | 0.449095i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −244.609 | −0.512806 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 784.653i | 1.63811i | 0.573717 | + | 0.819053i | \(0.305501\pi\) | ||||
−0.573717 | + | 0.819053i | \(0.694499\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 953.563i | − | 1.98246i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −337.080 | − | 399.032i | −0.697889 | − | 0.826154i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −51.5824 | + | 368.226i | −0.106355 | + | 0.759230i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 195.648i | − | 0.401741i | −0.979618 | − | 0.200871i | \(-0.935623\pi\) | ||
0.979618 | − | 0.200871i | \(-0.0643771\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 298.262i | 0.609942i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 153.533i | 0.312694i | 0.987702 | + | 0.156347i | \(0.0499718\pi\) | ||||
−0.987702 | + | 0.156347i | \(0.950028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 933.952i | 1.89443i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 233.127 | + | 32.6573i | 0.470964 | + | 0.0659743i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 115.416 | + | 136.629i | 0.232226 | + | 0.274907i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 636.233i | − | 1.27502i | −0.770443 | − | 0.637509i | \(-0.779965\pi\) | ||
0.770443 | − | 0.637509i | \(-0.220035\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 685.625i | 1.36851i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 48.3325 | 0.0960885 | 0.0480442 | − | 0.998845i | \(-0.484701\pi\) | ||||
0.0480442 | + | 0.998845i | \(0.484701\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 72.8046 | − | 519.724i | 0.144168 | − | 1.02916i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 145.327i | 0.286641i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −243.531 | −0.478449 | −0.239225 | − | 0.970964i | \(-0.576893\pi\) | ||||
−0.239225 | + | 0.970964i | \(0.576893\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 156.843 | + | 185.669i | 0.306934 | + | 0.363345i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 502.945i | − | 0.980399i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 41.1633 | − | 293.849i | 0.0799287 | − | 0.570580i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 206.595i | 0.399604i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −752.044 | −1.44903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 630.569i | 1.21030i | 0.796110 | + | 0.605152i | \(0.206888\pi\) | ||||
−0.796110 | + | 0.605152i | \(0.793112\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 829.843i | 1.58670i | 0.608767 | + | 0.793349i | \(0.291664\pi\) | ||||
−0.608767 | + | 0.793349i | \(0.708336\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −588.679 | + | 265.065i | −1.12129 | + | 0.504886i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 423.306i | 0.803236i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 119.858 | 0.226574 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −273.765 | −0.515564 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.27947 | 0.0136575 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −117.204 | + | 836.671i | −0.219072 | + | 1.56387i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −931.469 | −1.73458 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 493.400 | + | 83.6425i | 0.915398 | + | 0.155181i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 120.015i | − | 0.221840i | −0.993829 | − | 0.110920i | \(-0.964620\pi\) | ||
0.993829 | − | 0.110920i | \(-0.0353797\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 387.412i | − | 0.713465i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 200.829 | + | 28.1329i | 0.368494 | + | 0.0516199i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 634.970 | 1.16082 | 0.580411 | − | 0.814324i | \(-0.302892\pi\) | ||||
0.580411 | + | 0.814324i | \(0.302892\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 320.414 | 0.583632 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1764.25i | − | 3.20191i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −291.298 | − | 344.836i | −0.526760 | − | 0.623573i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1206.66 | + | 169.033i | 2.17416 | + | 0.304564i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −113.560 | −0.203877 | −0.101939 | − | 0.994791i | \(-0.532505\pi\) | ||||
−0.101939 | + | 0.994791i | \(0.532505\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 378.641i | − | 0.677355i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 619.386 | 1.10407 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 964.206i | − | 1.71262i | −0.516461 | − | 0.856311i | \(-0.672751\pi\) | ||
0.516461 | − | 0.856311i | \(-0.327249\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 718.781 | + | 100.689i | 1.27218 | + | 0.178211i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −457.312 | − | 541.362i | −0.806547 | − | 0.954782i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −761.751 | −1.33875 | −0.669377 | − | 0.742923i | \(-0.733439\pi\) | ||||
−0.669377 | + | 0.742923i | \(0.733439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 35.8939i | − | 0.0628614i | −0.999506 | − | 0.0314307i | \(-0.989994\pi\) | ||
0.999506 | − | 0.0314307i | \(-0.0100064\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 336.046i | − | 0.586467i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −138.949 | + | 486.217i | −0.241650 | + | 0.845595i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 714.079 | 1.23757 | 0.618786 | − | 0.785559i | \(-0.287625\pi\) | ||||
0.618786 | + | 0.785559i | \(0.287625\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −467.661 | −0.807705 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −49.5720 | + | 41.8756i | −0.0853218 | + | 0.0720751i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 541.925i | − | 0.929545i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −329.518 | − | 46.1600i | −0.563279 | − | 0.0789060i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 785.786i | − | 1.33865i | −0.742971 | − | 0.669323i | \(-0.766584\pi\) | ||
0.742971 | − | 0.669323i | \(-0.233416\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 799.632i | − | 1.35761i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1163.19i | 1.96817i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −618.608 | −1.04318 | −0.521592 | − | 0.853195i | \(-0.674662\pi\) | ||||
−0.521592 | + | 0.853195i | \(0.674662\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −486.794 | + | 306.728i | −0.818141 | + | 0.515509i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1123.91 | 1.88259 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 218.429 | 0.364656 | 0.182328 | − | 0.983238i | \(-0.441637\pi\) | ||||
0.182328 | + | 0.983238i | \(0.441637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 810.310i | 1.34827i | 0.738609 | + | 0.674135i | \(0.235483\pi\) | ||||
−0.738609 | + | 0.674135i | \(0.764517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −285.484 | −0.473439 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.5795 | − | 82.6616i | 0.0191397 | − | 0.136631i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −223.586 | −0.368346 | −0.184173 | − | 0.982894i | \(-0.558961\pi\) | ||||
−0.184173 | + | 0.982894i | \(0.558961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −946.764 | − | 1120.77i | −1.55462 | − | 1.84034i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 292.016i | − | 0.477931i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −416.624 | −0.679648 | −0.339824 | − | 0.940489i | \(-0.610368\pi\) | ||||
−0.339824 | + | 0.940489i | \(0.610368\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.29039 | + | 9.21160i | −0.00209820 | + | 0.0149782i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 633.821i | 1.02726i | 0.858011 | + | 0.513631i | \(0.171700\pi\) | ||||
−0.858011 | + | 0.513631i | \(0.828300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 891.451 | 1.44015 | 0.720073 | − | 0.693898i | \(-0.244108\pi\) | ||||
0.720073 | + | 0.693898i | \(0.244108\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −327.599 | −0.527534 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 117.991 | − | 99.6721i | 0.189391 | − | 0.159987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 530.624 | + | 330.248i | 0.848998 | + | 0.528397i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1170.03 | −1.86608 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1085.89 | 1.72638 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 139.865 | 0.221656 | 0.110828 | − | 0.993840i | \(-0.464650\pi\) | ||||
0.110828 | + | 0.993840i | \(0.464650\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −440.365 | −0.695679 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −650.014 | − | 91.0561i | −1.02364 | − | 0.143395i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −697.405 | − | 118.226i | −1.09483 | − | 0.185598i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −117.784 | −0.184325 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −500.317 | −0.780525 | −0.390263 | − | 0.920704i | \(-0.627616\pi\) | ||||
−0.390263 | + | 0.920704i | \(0.627616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1189.12i | 1.84933i | 0.380788 | + | 0.924663i | \(0.375653\pi\) | ||||
−0.380788 | + | 0.924663i | \(0.624347\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 479.141 | + | 67.1197i | 0.742854 | + | 0.104062i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1020.39 | 1.57711 | 0.788555 | − | 0.614964i | \(-0.210829\pi\) | ||||
0.788555 | + | 0.614964i | \(0.210829\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 606.519i | − | 0.934544i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −429.113 | − | 507.979i | −0.659159 | − | 0.780306i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 155.938 | 0.238802 | 0.119401 | − | 0.992846i | \(-0.461903\pi\) | ||||
0.119401 | + | 0.992846i | \(0.461903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.6972 | + | 233.412i | −0.0499193 | + | 0.356354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −160.060 | −0.243623 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 220.018i | − | 0.333866i | −0.985968 | − | 0.166933i | \(-0.946614\pi\) | ||
0.985968 | − | 0.166933i | \(-0.0533864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 948.923 | 1.43559 | 0.717794 | − | 0.696256i | \(-0.245152\pi\) | ||||
0.717794 | + | 0.696256i | \(0.245152\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −875.483 | −1.32049 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 919.562 | − | 579.415i | 1.38280 | − | 0.871301i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1149.17 | −1.72289 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 833.566i | − | 1.24599i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 709.870i | 1.05793i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 745.489i | − | 1.10771i | −0.832613 | − | 0.553855i | \(-0.813156\pi\) | ||
0.832613 | − | 0.553855i | \(-0.186844\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −111.256 | + | 389.312i | −0.164823 | + | 0.576759i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.12211i | 0.0119972i | 0.999982 | + | 0.00599860i | \(0.00190943\pi\) | ||||
−0.999982 | + | 0.00599860i | \(0.998091\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −335.919 | − | 397.657i | −0.494726 | − | 0.585652i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 862.094 | 1.26592 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −476.643 | −0.697867 | −0.348934 | − | 0.937147i | \(-0.613456\pi\) | ||||
−0.348934 | + | 0.937147i | \(0.613456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −238.744 | − | 33.4441i | −0.348532 | − | 0.0488235i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1512.65i | − | 2.20181i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 765.994i | 1.11175i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −85.4900 | −0.123719 | −0.0618596 | − | 0.998085i | \(-0.519703\pi\) | ||||
−0.0618596 | + | 0.998085i | \(0.519703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −251.760 | + | 212.673i | −0.363290 | + | 0.306888i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 61.9196 | − | 442.020i | 0.0890930 | − | 0.636000i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.28967i | 0.0118934i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 720.731 | 1.03109 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.5524i | − | 0.0335982i | −0.999859 | − | 0.0167991i | \(-0.994652\pi\) | ||
0.999859 | − | 0.0167991i | \(-0.00534758\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2051.27 | −2.91788 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 369.523 | + | 51.7641i | 0.524146 | + | 0.0734242i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 474.124 | + | 561.263i | 0.670614 | + | 0.793866i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 358.652i | 0.505856i | 0.967485 | + | 0.252928i | \(0.0813935\pi\) | ||||
−0.967485 | + | 0.252928i | \(0.918606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 297.274 | 0.418106 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −520.849 | −0.730504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 102.267 | − | 730.040i | 0.143030 | − | 1.02104i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 4.17005i | − | 0.00581598i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 209.881i | − | 0.291906i | −0.989292 | − | 0.145953i | \(-0.953375\pi\) | ||
0.989292 | − | 0.145953i | \(-0.0466249\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 268.067 | + | 317.335i | 0.371799 | + | 0.440132i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 681.480 | 0.942572 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −390.267 | + | 1365.65i | −0.538300 | + | 1.88365i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.50873 | −0.00207528 | −0.00103764 | − | 0.999999i | \(-0.500330\pi\) | ||||
−0.00103764 | + | 0.999999i | \(0.500330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −71.0498 | −0.0974620 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 431.187 | 0.589859 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 530.040i | − | 0.723111i | −0.932351 | − | 0.361555i | \(-0.882246\pi\) | ||
0.932351 | − | 0.361555i | \(-0.117754\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 273.231 | − | 861.555i | 0.371743 | − | 1.17218i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 632.482i | − | 0.858185i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 890.676i | − | 1.20524i | −0.798026 | − | 0.602622i | \(-0.794123\pi\) | ||
0.798026 | − | 0.602622i | \(-0.205877\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1653.80 | 2.23185 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 912.740i | − | 1.22845i | −0.789130 | − | 0.614226i | \(-0.789468\pi\) | ||
0.789130 | − | 0.614226i | \(-0.210532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −245.743 | − | 34.4245i | −0.329856 | − | 0.0462073i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 42.7346i | − | 0.0572083i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −763.263 | − | 903.543i | −1.01904 | − | 1.20633i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −910.503 | −1.21239 | −0.606194 | − | 0.795317i | \(-0.707304\pi\) | ||||
−0.606194 | + | 0.795317i | \(0.707304\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 594.049i | − | 0.788910i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.7281 | − | 326.435i | 0.0605670 | − | 0.432364i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 813.010 | 1.07399 | 0.536995 | − | 0.843585i | \(-0.319559\pi\) | ||||
0.536995 | + | 0.843585i | \(0.319559\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 762.113i | 1.00410i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1222.33i | − | 1.60622i | −0.595832 | − | 0.803109i | \(-0.703178\pi\) | ||
0.595832 | − | 0.803109i | \(-0.296822\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −216.881 | + | 183.209i | −0.284248 | + | 0.240117i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 52.5658 | − | 375.247i | 0.0687135 | − | 0.490519i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 857.296i | 1.11773i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 600.119i | 0.780388i | 0.920733 | + | 0.390194i | \(0.127592\pi\) | ||||
−0.920733 | + | 0.390194i | \(0.872408\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1035.69i | − | 1.34331i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 308.438i | 0.399015i | 0.979896 | + | 0.199507i | \(0.0639341\pi\) | ||||
−0.979896 | + | 0.199507i | \(0.936066\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −176.885 | + | 618.968i | −0.228239 | + | 0.798668i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1303.10 | + | 1100.79i | −1.67710 | + | 1.41672i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 15.6593i | − | 0.0201018i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 260.947i | − | 0.334119i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −920.133 | −1.17514 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.3212 | + | 2.28633i | 0.0207913 | + | 0.00291252i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 670.641i | − | 0.852149i | −0.904688 | − | 0.426074i | \(-0.859896\pi\) | ||
0.904688 | − | 0.426074i | \(-0.140104\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 422.366 | 0.535319 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −776.231 | + | 655.717i | −0.981328 | + | 0.828972i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1003.38i | − | 1.26530i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −969.306 | − | 135.784i | −1.21925 | − | 0.170797i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 774.242i | 0.971445i | 0.874113 | + | 0.485722i | \(0.161443\pi\) | ||||
−0.874113 | + | 0.485722i | \(0.838557\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 332.540 | 0.416195 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 101.717i | 0.126987i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 354.610i | − | 0.441607i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −377.409 | − | 598.967i | −0.468830 | − | 0.744059i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 734.377i | − | 0.910008i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1122.72 | 1.38778 | 0.693892 | − | 0.720079i | \(-0.255894\pi\) | ||||
0.693892 | + | 0.720079i | \(0.255894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −651.714 | −0.803593 | −0.401796 | − | 0.915729i | \(-0.631614\pi\) | ||||
−0.401796 | + | 0.915729i | \(0.631614\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −510.211 | −0.627566 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −56.0799 | + | 400.332i | −0.0688097 | + | 0.491205i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −814.520 | −0.996964 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 355.855 | − | 300.607i | 0.434500 | − | 0.367041i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 75.0402i | − | 0.0914009i | −0.998955 | − | 0.0457005i | \(-0.985448\pi\) | ||
0.998955 | − | 0.0457005i | \(-0.0145520\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 863.981i | − | 1.04979i | −0.851166 | − | 0.524897i | \(-0.824104\pi\) | ||
0.851166 | − | 0.524897i | \(-0.175896\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 905.681 | + | 258.821i | 1.09780 | + | 0.313722i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1535.63 | 1.85687 | 0.928434 | − | 0.371496i | \(-0.121155\pi\) | ||||
0.928434 | + | 0.371496i | \(0.121155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −129.821 | −0.156599 | −0.0782997 | − | 0.996930i | \(-0.524949\pi\) | ||||
−0.0782997 | + | 0.996930i | \(0.524949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1281.53i | − | 1.54215i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 134.633 | − | 794.187i | 0.161624 | − | 0.953406i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −128.913 | + | 920.259i | −0.154387 | + | 1.10211i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −417.042 | −0.498258 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 502.794i | − | 0.599277i | −0.954053 | − | 0.299639i | \(-0.903134\pi\) | ||
0.954053 | − | 0.299639i | \(-0.0968661\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2386.68 | −2.83791 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 964.497i | 1.14412i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27.3248 | + | 195.061i | −0.0323370 | + | 0.230841i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 75.4090 | + | 89.2685i | 0.0890307 | + | 0.105394i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −327.735 | −0.386024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1336.12i | 1.57006i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 837.144i | − | 0.981411i | −0.871326 | − | 0.490705i | \(-0.836739\pi\) | ||
0.871326 | − | 0.490705i | \(-0.163261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −99.2978 | + | 708.848i | −0.116138 | + | 0.829062i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 74.6446 | 0.0870999 | 0.0435499 | − | 0.999051i | \(-0.486133\pi\) | ||||
0.0435499 | + | 0.999051i | \(0.486133\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 985.823 | 1.14764 | 0.573820 | − | 0.818981i | \(-0.305461\pi\) | ||||
0.573820 | + | 0.818981i | \(0.305461\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.40339 | − | 9.94785i | −0.00976003 | − | 0.0115538i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1293.70i | 1.49907i | 0.661966 | + | 0.749534i | \(0.269722\pi\) | ||||
−0.661966 | + | 0.749534i | \(0.730278\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1009.41 | − | 141.401i | −1.16695 | − | 0.163470i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 69.1890i | 0.0798028i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 658.603i | 0.757886i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 893.994i | 1.02640i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 342.809 | 0.392680 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −839.974 | + | 245.091i | −0.959970 | + | 0.280103i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 92.9231 | 0.105956 | 0.0529778 | − | 0.998596i | \(-0.483129\pi\) | ||||
0.0529778 | + | 0.998596i | \(0.483129\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −587.978 | −0.668917 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 58.1276i | 0.0659792i | 0.999456 | + | 0.0329896i | \(0.0105028\pi\) | ||||
−0.999456 | + | 0.0329896i | \(0.989497\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 698.151 | 0.790658 | 0.395329 | − | 0.918540i | \(-0.370631\pi\) | ||||
0.395329 | + | 0.918540i | \(0.370631\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1084.84 | − | 151.968i | −1.22581 | − | 0.171716i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 472.357 | 0.532534 | 0.266267 | − | 0.963899i | \(-0.414210\pi\) | ||||
0.266267 | + | 0.963899i | \(0.414210\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 701.967 | − | 592.983i | 0.789614 | − | 0.667022i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1033.95i | 1.16043i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −628.174 | −0.703442 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1250.23 | − | 175.137i | −1.39691 | − | 0.195684i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1077.22i | − | 1.20092i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1462.92 | −1.62727 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −872.294 | −0.968140 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −517.437 | + | 437.102i | −0.573020 | + | 0.484055i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 72.8421 | − | 519.991i | 0.0804885 | − | 0.574576i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −497.001 | −0.547961 | −0.273981 | − | 0.961735i | \(-0.588340\pi\) | ||||
−0.273981 | + | 0.961735i | \(0.588340\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −483.849 | −0.532288 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1091.09 | 1.19769 | 0.598844 | − | 0.800865i | \(-0.295627\pi\) | ||||
0.598844 | + | 0.800865i | \(0.295627\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 94.6776 | 0.103699 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1269.70 | + | 177.864i | 1.38765 | + | 0.194387i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −212.933 | − | 252.068i | −0.232206 | − | 0.274883i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 606.413 | 0.659862 | 0.329931 | − | 0.944005i | \(-0.392974\pi\) | ||||
0.329931 | + | 0.944005i | \(0.392974\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −704.336 | −0.764752 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 368.841i | 0.399611i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1587.82 | + | 453.758i | 1.71656 | + | 0.490550i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −273.566 | −0.295108 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 718.552i | 0.773468i | 0.922191 | + | 0.386734i | \(0.126397\pi\) | ||||
−0.922191 | + | 0.386734i | \(0.873603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −254.324 | + | 1500.23i | −0.273173 | + | 1.61142i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −358.378 | −0.384114 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 831.351 | + | 116.458i | 0.889145 | + | 0.124554i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1453.79 | −1.55153 | −0.775767 | − | 0.631020i | \(-0.782637\pi\) | ||||
−0.775767 | + | 0.631020i | \(0.782637\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 486.035i | 0.517609i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1458.29 | −1.54972 | −0.774862 | − | 0.632130i | \(-0.782181\pi\) | ||||
−0.774862 | + | 0.632130i | \(0.782181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.1999 | −0.0108164 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −302.190 | − | 479.591i | −0.319777 | − | 0.507504i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −474.327 | −0.500873 | −0.250437 | − | 0.968133i | \(-0.580574\pi\) | ||||
−0.250437 | + | 0.968133i | \(0.580574\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 501.231i | 0.528167i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 238.187i | − | 0.250460i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 110.230i | − | 0.115666i | −0.998326 | − | 0.0578331i | \(-0.981581\pi\) | ||
0.998326 | − | 0.0578331i | \(-0.0184191\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63.1841 | − | 451.047i | 0.0661614 | − | 0.472300i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2140.56i | 2.23674i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 257.826 | − | 217.797i | 0.268849 | − | 0.227109i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 297.945 | 0.310036 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 778.920 | 0.808847 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −627.704 | − | 87.9309i | −0.650470 | − | 0.0911201i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1909.96i | − | 1.97514i | −0.157174 | − | 0.987571i | \(-0.550238\pi\) | ||
0.157174 | − | 0.987571i | \(-0.449762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1883.31i | 1.94356i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1347.96 | −1.38822 | −0.694111 | − | 0.719868i | \(-0.744202\pi\) | ||||
−0.694111 | + | 0.719868i | \(0.744202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 403.238 | + | 477.349i | 0.414427 | + | 0.490595i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1280.15 | − | 365.835i | −1.31298 | − | 0.375215i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1520.98i | 1.55678i | 0.627780 | + | 0.778391i | \(0.283964\pi\) | ||||
−0.627780 | + | 0.778391i | \(0.716036\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −225.351 | −0.230185 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 186.967i | − | 0.190588i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1569.64 | 1.59678 | 0.798391 | − | 0.602139i | \(-0.205685\pi\) | ||||
0.798391 | + | 0.602139i | \(0.205685\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −218.706 | + | 1561.25i | −0.222036 | + | 1.58503i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −399.058 | + | 337.102i | −0.404314 | + | 0.341542i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 530.547i | 0.536448i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1546.21 | 1.56026 | 0.780128 | − | 0.625620i | \(-0.215154\pi\) | ||||
0.780128 | + | 0.625620i | \(0.215154\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −194.641 | −0.196013 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1508.53 | + | 211.320i | 1.51611 | + | 0.212382i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1493.93i | 1.49842i | 0.662331 | + | 0.749211i | \(0.269567\pi\) | ||||
−0.662331 | + | 0.749211i | \(0.730433\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1069.83i | 1.07090i |
(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 | 1120.3.c.g.209.13 | 80 | ||
4.3 | odd | 2 | 280.3.c.g.69.6 | yes | 80 | ||
5.4 | even | 2 | inner | 1120.3.c.g.209.6 | 80 | ||
7.6 | odd | 2 | inner | 1120.3.c.g.209.24 | 80 | ||
8.3 | odd | 2 | 280.3.c.g.69.73 | yes | 80 | ||
8.5 | even | 2 | inner | 1120.3.c.g.209.2 | 80 | ||
20.19 | odd | 2 | 280.3.c.g.69.75 | yes | 80 | ||
28.27 | even | 2 | 280.3.c.g.69.5 | ✓ | 80 | ||
35.34 | odd | 2 | inner | 1120.3.c.g.209.1 | 80 | ||
40.19 | odd | 2 | 280.3.c.g.69.8 | yes | 80 | ||
40.29 | even | 2 | inner | 1120.3.c.g.209.23 | 80 | ||
56.13 | odd | 2 | inner | 1120.3.c.g.209.5 | 80 | ||
56.27 | even | 2 | 280.3.c.g.69.74 | yes | 80 | ||
140.139 | even | 2 | 280.3.c.g.69.76 | yes | 80 | ||
280.69 | odd | 2 | inner | 1120.3.c.g.209.14 | 80 | ||
280.139 | even | 2 | 280.3.c.g.69.7 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.3.c.g.69.5 | ✓ | 80 | 28.27 | even | 2 | ||
280.3.c.g.69.6 | yes | 80 | 4.3 | odd | 2 | ||
280.3.c.g.69.7 | yes | 80 | 280.139 | even | 2 | ||
280.3.c.g.69.8 | yes | 80 | 40.19 | odd | 2 | ||
280.3.c.g.69.73 | yes | 80 | 8.3 | odd | 2 | ||
280.3.c.g.69.74 | yes | 80 | 56.27 | even | 2 | ||
280.3.c.g.69.75 | yes | 80 | 20.19 | odd | 2 | ||
280.3.c.g.69.76 | yes | 80 | 140.139 | even | 2 | ||
1120.3.c.g.209.1 | 80 | 35.34 | odd | 2 | inner | ||
1120.3.c.g.209.2 | 80 | 8.5 | even | 2 | inner | ||
1120.3.c.g.209.5 | 80 | 56.13 | odd | 2 | inner | ||
1120.3.c.g.209.6 | 80 | 5.4 | even | 2 | inner | ||
1120.3.c.g.209.13 | 80 | 1.1 | even | 1 | trivial | ||
1120.3.c.g.209.14 | 80 | 280.69 | odd | 2 | inner | ||
1120.3.c.g.209.23 | 80 | 40.29 | even | 2 | inner | ||
1120.3.c.g.209.24 | 80 | 7.6 | odd | 2 | inner |