Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,4,Mod(99,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.99");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(28.9109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 185x^{10} + 12748x^{8} + 405460x^{6} + 5908496x^{4} + 33016000x^{2} + 60840000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.4 | ||
Root | \(2.20031i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.99 |
Dual form | 490.4.c.e.99.9 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | 1.20031i | 0.230999i | 0.993308 | + | 0.115500i | \(0.0368469\pi\) | ||||
−0.993308 | + | 0.115500i | \(0.963153\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −11.1276 | − | 1.08430i | −0.995286 | − | 0.0969827i | ||||
\(6\) | 2.40061 | 0.163341 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 25.5593 | 0.946639 | ||||||||
\(10\) | −2.16860 | + | 22.2553i | −0.0685772 | + | 0.703774i | ||||
\(11\) | −26.4409 | −0.724749 | −0.362374 | − | 0.932033i | \(-0.618034\pi\) | ||||
−0.362374 | + | 0.932033i | \(0.618034\pi\) | |||||||
\(12\) | − | 4.80123i | − | 0.115500i | ||||||
\(13\) | 55.0319i | 1.17408i | 0.809556 | + | 0.587042i | \(0.199708\pi\) | ||||
−0.809556 | + | 0.587042i | \(0.800292\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.30149 | − | 13.3566i | 0.0224029 | − | 0.229910i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 49.4218i | − | 0.705091i | −0.935795 | − | 0.352546i | \(-0.885316\pi\) | ||
0.935795 | − | 0.352546i | \(-0.114684\pi\) | |||||||
\(18\) | − | 51.1185i | − | 0.669375i | ||||||
\(19\) | 5.46016 | 0.0659288 | 0.0329644 | − | 0.999457i | \(-0.489505\pi\) | ||||
0.0329644 | + | 0.999457i | \(0.489505\pi\) | |||||||
\(20\) | 44.5105 | + | 4.33720i | 0.497643 | + | 0.0484914i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 52.8818i | 0.512475i | ||||||||
\(23\) | − | 1.07321i | − | 0.00972959i | −0.999988 | − | 0.00486480i | \(-0.998451\pi\) | ||
0.999988 | − | 0.00486480i | \(-0.00154852\pi\) | |||||||
\(24\) | −9.60246 | −0.0816706 | ||||||||
\(25\) | 122.649 | + | 24.1314i | 0.981189 | + | 0.193051i | ||||
\(26\) | 110.064 | 0.830203 | ||||||||
\(27\) | 63.0873i | 0.449672i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 246.181 | 1.57637 | 0.788185 | − | 0.615439i | \(-0.211021\pi\) | ||||
0.788185 | + | 0.615439i | \(0.211021\pi\) | |||||||
\(30\) | −26.7132 | − | 2.60299i | −0.162571 | − | 0.0158413i | ||||
\(31\) | −228.745 | −1.32528 | −0.662641 | − | 0.748937i | \(-0.730565\pi\) | ||||
−0.662641 | + | 0.748937i | \(0.730565\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | − | 31.7372i | − | 0.167416i | ||||||
\(34\) | −98.8437 | −0.498575 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −102.237 | −0.473320 | ||||||||
\(37\) | − | 381.237i | − | 1.69392i | −0.531658 | − | 0.846959i | \(-0.678431\pi\) | ||
0.531658 | − | 0.846959i | \(-0.321569\pi\) | |||||||
\(38\) | − | 10.9203i | − | 0.0466187i | ||||||
\(39\) | −66.0552 | −0.271213 | ||||||||
\(40\) | 8.67440 | − | 89.0211i | 0.0342886 | − | 0.351887i | ||||
\(41\) | 48.5643 | 0.184987 | 0.0924936 | − | 0.995713i | \(-0.470516\pi\) | ||||
0.0924936 | + | 0.995713i | \(0.470516\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 233.878i | − | 0.829445i | −0.909948 | − | 0.414722i | \(-0.863879\pi\) | ||
0.909948 | − | 0.414722i | \(-0.136121\pi\) | |||||||
\(44\) | 105.764 | 0.362374 | ||||||||
\(45\) | −284.414 | − | 27.7139i | −0.942177 | − | 0.0918077i | ||||
\(46\) | −2.14643 | −0.00687986 | ||||||||
\(47\) | − | 245.153i | − | 0.760836i | −0.924815 | − | 0.380418i | \(-0.875780\pi\) | ||
0.924815 | − | 0.380418i | \(-0.124220\pi\) | |||||||
\(48\) | 19.2049i | 0.0577498i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 48.2628 | − | 245.297i | 0.136508 | − | 0.693805i | ||||
\(51\) | 59.3214 | 0.162876 | ||||||||
\(52\) | − | 220.127i | − | 0.587042i | ||||||
\(53\) | − | 269.630i | − | 0.698803i | −0.936973 | − | 0.349402i | \(-0.886385\pi\) | ||
0.936973 | − | 0.349402i | \(-0.113615\pi\) | |||||||
\(54\) | 126.175 | 0.317966 | ||||||||
\(55\) | 294.225 | + | 28.6699i | 0.721332 | + | 0.0702881i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.55387i | 0.0152295i | ||||||||
\(58\) | − | 492.362i | − | 1.11466i | ||||||
\(59\) | 784.534 | 1.73115 | 0.865573 | − | 0.500783i | \(-0.166954\pi\) | ||||
0.865573 | + | 0.500783i | \(0.166954\pi\) | |||||||
\(60\) | −5.20597 | + | 53.4263i | −0.0112015 | + | 0.114955i | ||||
\(61\) | −425.992 | −0.894142 | −0.447071 | − | 0.894498i | \(-0.647533\pi\) | ||||
−0.447071 | + | 0.894498i | \(0.647533\pi\) | |||||||
\(62\) | 457.489i | 0.937116i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 59.6711 | − | 612.375i | 0.113866 | − | 1.16855i | ||||
\(66\) | −63.4744 | −0.118381 | ||||||||
\(67\) | − | 918.344i | − | 1.67453i | −0.546797 | − | 0.837265i | \(-0.684153\pi\) | ||
0.546797 | − | 0.837265i | \(-0.315847\pi\) | |||||||
\(68\) | 197.687i | 0.352546i | ||||||||
\(69\) | 1.28819 | 0.00224753 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 200.821 | 0.335676 | 0.167838 | − | 0.985815i | \(-0.446321\pi\) | ||||
0.167838 | + | 0.985815i | \(0.446321\pi\) | |||||||
\(72\) | 204.474i | 0.334688i | ||||||||
\(73\) | − | 778.434i | − | 1.24807i | −0.781398 | − | 0.624033i | \(-0.785493\pi\) | ||
0.781398 | − | 0.624033i | \(-0.214507\pi\) | |||||||
\(74\) | −762.474 | −1.19778 | ||||||||
\(75\) | −28.9651 | + | 147.216i | −0.0445947 | + | 0.226654i | ||||
\(76\) | −21.8407 | −0.0329644 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 132.110i | 0.191776i | ||||||||
\(79\) | −189.419 | −0.269764 | −0.134882 | − | 0.990862i | \(-0.543066\pi\) | ||||
−0.134882 | + | 0.990862i | \(0.543066\pi\) | |||||||
\(80\) | −178.042 | − | 17.3488i | −0.248822 | − | 0.0242457i | ||||
\(81\) | 614.376 | 0.842765 | ||||||||
\(82\) | − | 97.1287i | − | 0.130806i | ||||||
\(83\) | 611.073i | 0.808120i | 0.914732 | + | 0.404060i | \(0.132401\pi\) | ||||
−0.914732 | + | 0.404060i | \(0.867599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −53.5881 | + | 549.948i | −0.0683817 | + | 0.701768i | ||||
\(86\) | −467.757 | −0.586506 | ||||||||
\(87\) | 295.493i | 0.364140i | ||||||||
\(88\) | − | 211.527i | − | 0.256237i | ||||||
\(89\) | 292.327 | 0.348164 | 0.174082 | − | 0.984731i | \(-0.444304\pi\) | ||||
0.174082 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(90\) | −55.4278 | + | 568.828i | −0.0649178 | + | 0.666220i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.29286i | 0.00486480i | ||||||||
\(93\) | − | 274.564i | − | 0.306139i | ||||||
\(94\) | −490.307 | −0.537992 | ||||||||
\(95\) | −60.7587 | − | 5.92046i | −0.0656180 | − | 0.00639396i | ||||
\(96\) | 38.4098 | 0.0408353 | ||||||||
\(97\) | 1429.73i | 1.49657i | 0.663380 | + | 0.748283i | \(0.269121\pi\) | ||||
−0.663380 | + | 0.748283i | \(0.730879\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −675.810 | −0.686075 | ||||||||
\(100\) | −490.594 | − | 96.5256i | −0.490594 | − | 0.0965256i | ||||
\(101\) | 806.329 | 0.794384 | 0.397192 | − | 0.917736i | \(-0.369985\pi\) | ||||
0.397192 | + | 0.917736i | \(0.369985\pi\) | |||||||
\(102\) | − | 118.643i | − | 0.115170i | ||||||
\(103\) | − | 1510.14i | − | 1.44465i | −0.691554 | − | 0.722325i | \(-0.743073\pi\) | ||
0.691554 | − | 0.722325i | \(-0.256927\pi\) | |||||||
\(104\) | −440.255 | −0.415101 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −539.261 | −0.494129 | ||||||||
\(107\) | − | 621.127i | − | 0.561184i | −0.959827 | − | 0.280592i | \(-0.909469\pi\) | ||
0.959827 | − | 0.280592i | \(-0.0905307\pi\) | |||||||
\(108\) | − | 252.349i | − | 0.224836i | ||||||
\(109\) | 1542.81 | 1.35573 | 0.677863 | − | 0.735189i | \(-0.262906\pi\) | ||||
0.677863 | + | 0.735189i | \(0.262906\pi\) | |||||||
\(110\) | 57.3398 | − | 588.450i | 0.0497012 | − | 0.510059i | ||||
\(111\) | 457.602 | 0.391294 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1295.03i | − | 1.07810i | −0.842272 | − | 0.539052i | \(-0.818783\pi\) | ||
0.842272 | − | 0.539052i | \(-0.181217\pi\) | |||||||
\(114\) | 13.1077 | 0.0107689 | ||||||||
\(115\) | −1.16369 | + | 11.9423i | −0.000943602 | + | 0.00968373i | ||||
\(116\) | −984.725 | −0.788185 | ||||||||
\(117\) | 1406.57i | 1.11143i | ||||||||
\(118\) | − | 1569.07i | − | 1.22411i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 106.853 | + | 10.4119i | 0.0812856 | + | 0.00792064i | ||||
\(121\) | −631.878 | −0.474740 | ||||||||
\(122\) | 851.984i | 0.632254i | ||||||||
\(123\) | 58.2921i | 0.0427319i | ||||||||
\(124\) | 914.979 | 0.662641 | ||||||||
\(125\) | −1338.62 | − | 401.513i | −0.957841 | − | 0.287299i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 191.946i | 0.134114i | 0.997749 | + | 0.0670568i | \(0.0213609\pi\) | ||||
−0.997749 | + | 0.0670568i | \(0.978639\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 280.726 | 0.191601 | ||||||||
\(130\) | −1224.75 | − | 119.342i | −0.826289 | − | 0.0805154i | ||||
\(131\) | −1495.46 | −0.997400 | −0.498700 | − | 0.866775i | \(-0.666189\pi\) | ||||
−0.498700 | + | 0.866775i | \(0.666189\pi\) | |||||||
\(132\) | 126.949i | 0.0837082i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1836.69 | −1.18407 | ||||||||
\(135\) | 68.4055 | − | 702.012i | 0.0436104 | − | 0.447552i | ||||
\(136\) | 395.375 | 0.249287 | ||||||||
\(137\) | 1167.66i | 0.728174i | 0.931365 | + | 0.364087i | \(0.118619\pi\) | ||||
−0.931365 | + | 0.364087i | \(0.881381\pi\) | |||||||
\(138\) | − | 2.57637i | − | 0.00158924i | ||||||
\(139\) | 2084.75 | 1.27213 | 0.636066 | − | 0.771635i | \(-0.280561\pi\) | ||||
0.636066 | + | 0.771635i | \(0.280561\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 294.259 | 0.175753 | ||||||||
\(142\) | − | 401.641i | − | 0.237359i | ||||||
\(143\) | − | 1455.09i | − | 0.850916i | ||||||
\(144\) | 408.948 | 0.236660 | ||||||||
\(145\) | −2739.42 | − | 266.934i | −1.56894 | − | 0.152881i | ||||
\(146\) | −1556.87 | −0.882516 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1524.95i | 0.846959i | ||||||||
\(149\) | 1183.29 | 0.650597 | 0.325299 | − | 0.945611i | \(-0.394535\pi\) | ||||
0.325299 | + | 0.945611i | \(0.394535\pi\) | |||||||
\(150\) | 294.432 | + | 57.9302i | 0.160268 | + | 0.0315332i | ||||
\(151\) | −1485.42 | −0.800544 | −0.400272 | − | 0.916396i | \(-0.631084\pi\) | ||||
−0.400272 | + | 0.916396i | \(0.631084\pi\) | |||||||
\(152\) | 43.6813i | 0.0233094i | ||||||||
\(153\) | − | 1263.19i | − | 0.667467i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2545.39 | + | 248.028i | 1.31903 | + | 0.128530i | ||||
\(156\) | 264.221 | 0.135606 | ||||||||
\(157\) | − | 235.071i | − | 0.119495i | −0.998214 | − | 0.0597475i | \(-0.980970\pi\) | ||
0.998214 | − | 0.0597475i | \(-0.0190295\pi\) | |||||||
\(158\) | 378.839i | 0.190752i | ||||||||
\(159\) | 323.639 | 0.161423 | ||||||||
\(160\) | −34.6976 | + | 356.084i | −0.0171443 | + | 0.175943i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1228.75i | − | 0.595925i | ||||||
\(163\) | 3514.51i | 1.68882i | 0.535699 | + | 0.844409i | \(0.320048\pi\) | ||||
−0.535699 | + | 0.844409i | \(0.679952\pi\) | |||||||
\(164\) | −194.257 | −0.0924936 | ||||||||
\(165\) | −34.4127 | + | 353.160i | −0.0162365 | + | 0.166627i | ||||
\(166\) | 1222.15 | 0.571427 | ||||||||
\(167\) | − | 1675.24i | − | 0.776249i | −0.921607 | − | 0.388125i | \(-0.873123\pi\) | ||
0.921607 | − | 0.388125i | \(-0.126877\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −831.507 | −0.378474 | ||||||||
\(170\) | 1099.90 | + | 107.176i | 0.496225 | + | 0.0483532i | ||||
\(171\) | 139.558 | 0.0624108 | ||||||||
\(172\) | 935.514i | 0.414722i | ||||||||
\(173\) | 746.748i | 0.328175i | 0.986446 | + | 0.164087i | \(0.0524679\pi\) | ||||
−0.986446 | + | 0.164087i | \(0.947532\pi\) | |||||||
\(174\) | 590.986 | 0.257486 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −423.055 | −0.181187 | ||||||||
\(177\) | 941.682i | 0.399893i | ||||||||
\(178\) | − | 584.653i | − | 0.246189i | ||||||
\(179\) | 3652.52 | 1.52515 | 0.762576 | − | 0.646898i | \(-0.223934\pi\) | ||||
0.762576 | + | 0.646898i | \(0.223934\pi\) | |||||||
\(180\) | 1137.66 | + | 110.856i | 0.471088 | + | 0.0459038i | ||||
\(181\) | −767.005 | −0.314978 | −0.157489 | − | 0.987521i | \(-0.550340\pi\) | ||||
−0.157489 | + | 0.987521i | \(0.550340\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 511.321i | − | 0.206546i | ||||||
\(184\) | 8.58571 | 0.00343993 | ||||||||
\(185\) | −413.375 | + | 4242.27i | −0.164281 | + | 1.68593i | ||||
\(186\) | −549.128 | −0.216473 | ||||||||
\(187\) | 1306.76i | 0.511014i | ||||||||
\(188\) | 980.613i | 0.380418i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.8409 | + | 121.517i | −0.00452121 | + | 0.0463989i | ||||
\(191\) | 339.746 | 0.128708 | 0.0643538 | − | 0.997927i | \(-0.479501\pi\) | ||||
0.0643538 | + | 0.997927i | \(0.479501\pi\) | |||||||
\(192\) | − | 76.8197i | − | 0.0288749i | ||||||
\(193\) | − | 2244.39i | − | 0.837070i | −0.908201 | − | 0.418535i | \(-0.862544\pi\) | ||
0.908201 | − | 0.418535i | \(-0.137456\pi\) | |||||||
\(194\) | 2859.46 | 1.05823 | ||||||||
\(195\) | 735.038 | + | 71.6236i | 0.269934 | + | 0.0263029i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2130.15i | 0.770389i | 0.922835 | + | 0.385194i | \(0.125866\pi\) | ||||
−0.922835 | + | 0.385194i | \(0.874134\pi\) | |||||||
\(198\) | 1351.62i | 0.485129i | ||||||||
\(199\) | −1913.46 | −0.681615 | −0.340807 | − | 0.940133i | \(-0.610700\pi\) | ||||
−0.340807 | + | 0.940133i | \(0.610700\pi\) | |||||||
\(200\) | −193.051 | + | 981.189i | −0.0682539 | + | 0.346903i | ||||
\(201\) | 1102.29 | 0.386815 | ||||||||
\(202\) | − | 1612.66i | − | 0.561714i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −237.286 | −0.0814378 | ||||||||
\(205\) | −540.406 | − | 52.6583i | −0.184115 | − | 0.0179406i | ||||
\(206\) | −3020.29 | −1.02152 | ||||||||
\(207\) | − | 27.4306i | − | 0.00921041i | ||||||
\(208\) | 880.510i | 0.293521i | ||||||||
\(209\) | −144.372 | −0.0477818 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4018.96 | 1.31126 | 0.655632 | − | 0.755080i | \(-0.272402\pi\) | ||||
0.655632 | + | 0.755080i | \(0.272402\pi\) | |||||||
\(212\) | 1078.52i | 0.349402i | ||||||||
\(213\) | 241.046i | 0.0775410i | ||||||||
\(214\) | −1242.25 | −0.396817 | ||||||||
\(215\) | −253.594 | + | 2602.51i | −0.0804418 | + | 0.825535i | ||||
\(216\) | −504.698 | −0.158983 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 3085.61i | − | 0.958642i | ||||||
\(219\) | 934.360 | 0.288302 | ||||||||
\(220\) | −1176.90 | − | 114.680i | −0.360666 | − | 0.0351441i | ||||
\(221\) | 2719.78 | 0.827837 | ||||||||
\(222\) | − | 915.203i | − | 0.276687i | ||||||
\(223\) | − | 4659.51i | − | 1.39921i | −0.714530 | − | 0.699604i | \(-0.753360\pi\) | ||
0.714530 | − | 0.699604i | \(-0.246640\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3134.81 | + | 616.781i | 0.928832 | + | 0.182750i | ||||
\(226\) | −2590.05 | −0.762335 | ||||||||
\(227\) | 3692.30i | 1.07959i | 0.841797 | + | 0.539794i | \(0.181498\pi\) | ||||
−0.841797 | + | 0.539794i | \(0.818502\pi\) | |||||||
\(228\) | − | 26.2155i | − | 0.00761475i | ||||||
\(229\) | 1454.34 | 0.419675 | 0.209837 | − | 0.977736i | \(-0.432707\pi\) | ||||
0.209837 | + | 0.977736i | \(0.432707\pi\) | |||||||
\(230\) | 23.8847 | + | 2.32737i | 0.00684743 | + | 0.000667228i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1969.45i | 0.557331i | ||||||||
\(233\) | 6402.66i | 1.80023i | 0.435657 | + | 0.900113i | \(0.356516\pi\) | ||||
−0.435657 | + | 0.900113i | \(0.643484\pi\) | |||||||
\(234\) | 2813.15 | 0.785903 | ||||||||
\(235\) | −265.820 | + | 2727.98i | −0.0737880 | + | 0.757249i | ||||
\(236\) | −3138.14 | −0.865573 | ||||||||
\(237\) | − | 227.361i | − | 0.0623152i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1077.42 | −0.291601 | −0.145801 | − | 0.989314i | \(-0.546576\pi\) | ||||
−0.145801 | + | 0.989314i | \(0.546576\pi\) | |||||||
\(240\) | 20.8239 | − | 213.705i | 0.00560073 | − | 0.0574776i | ||||
\(241\) | 1129.47 | 0.301891 | 0.150946 | − | 0.988542i | \(-0.451768\pi\) | ||||
0.150946 | + | 0.988542i | \(0.451768\pi\) | |||||||
\(242\) | 1263.76i | 0.335692i | ||||||||
\(243\) | 2440.80i | 0.644350i | ||||||||
\(244\) | 1703.97 | 0.447071 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 116.584 | 0.0302160 | ||||||||
\(247\) | 300.483i | 0.0774060i | ||||||||
\(248\) | − | 1829.96i | − | 0.468558i | ||||||
\(249\) | −733.475 | −0.186675 | ||||||||
\(250\) | −803.026 | + | 2677.25i | −0.203151 | + | 0.677296i | ||||
\(251\) | 5190.33 | 1.30522 | 0.652610 | − | 0.757694i | \(-0.273674\pi\) | ||||
0.652610 | + | 0.757694i | \(0.273674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.3768i | 0.00705151i | ||||||||
\(254\) | 383.891 | 0.0948326 | ||||||||
\(255\) | −660.107 | − | 64.3222i | −0.162108 | − | 0.0157961i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − | 6646.83i | − | 1.61330i | −0.591030 | − | 0.806649i | \(-0.701279\pi\) | ||
0.591030 | − | 0.806649i | \(-0.298721\pi\) | |||||||
\(258\) | − | 561.452i | − | 0.135482i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −238.684 | + | 2449.50i | −0.0569330 | + | 0.584275i | ||||
\(261\) | 6292.21 | 1.49225 | ||||||||
\(262\) | 2990.93i | 0.705268i | ||||||||
\(263\) | 5975.55i | 1.40102i | 0.713643 | + | 0.700510i | \(0.247044\pi\) | ||||
−0.713643 | + | 0.700510i | \(0.752956\pi\) | |||||||
\(264\) | 253.898 | 0.0591906 | ||||||||
\(265\) | −292.360 | + | 3000.35i | −0.0677719 | + | 0.695509i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 350.882i | 0.0804255i | ||||||||
\(268\) | 3673.38i | 0.837265i | ||||||||
\(269\) | 5039.87 | 1.14233 | 0.571164 | − | 0.820836i | \(-0.306492\pi\) | ||||
0.571164 | + | 0.820836i | \(0.306492\pi\) | |||||||
\(270\) | −1404.02 | − | 136.811i | −0.316467 | − | 0.0308372i | ||||
\(271\) | −564.058 | −0.126436 | −0.0632179 | − | 0.998000i | \(-0.520136\pi\) | ||||
−0.0632179 | + | 0.998000i | \(0.520136\pi\) | |||||||
\(272\) | − | 790.749i | − | 0.176273i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2335.32 | 0.514897 | ||||||||
\(275\) | −3242.94 | − | 638.056i | −0.711115 | − | 0.139914i | ||||
\(276\) | −5.15275 | −0.00112376 | ||||||||
\(277\) | 4707.89i | 1.02119i | 0.859821 | + | 0.510596i | \(0.170575\pi\) | ||||
−0.859821 | + | 0.510596i | \(0.829425\pi\) | |||||||
\(278\) | − | 4169.50i | − | 0.899533i | ||||||
\(279\) | −5846.54 | −1.25456 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1993.69 | −0.423250 | −0.211625 | − | 0.977351i | \(-0.567876\pi\) | ||||
−0.211625 | + | 0.977351i | \(0.567876\pi\) | |||||||
\(282\) | − | 588.519i | − | 0.124276i | ||||||
\(283\) | − | 7285.39i | − | 1.53029i | −0.643859 | − | 0.765144i | \(-0.722668\pi\) | ||
0.643859 | − | 0.765144i | \(-0.277332\pi\) | |||||||
\(284\) | −803.282 | −0.167838 | ||||||||
\(285\) | 7.10637 | − | 72.9291i | 0.00147700 | − | 0.0151577i | ||||
\(286\) | −2910.19 | −0.601688 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 817.896i | − | 0.167344i | ||||||
\(289\) | 2470.48 | 0.502846 | ||||||||
\(290\) | −533.869 | + | 5478.83i | −0.108103 | + | 1.10941i | ||||
\(291\) | −1716.11 | −0.345706 | ||||||||
\(292\) | 3113.74i | 0.624033i | ||||||||
\(293\) | − | 8519.76i | − | 1.69874i | −0.527801 | − | 0.849368i | \(-0.676983\pi\) | ||
0.527801 | − | 0.849368i | \(-0.323017\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8730.01 | − | 850.670i | −1.72299 | − | 0.167891i | ||||
\(296\) | 3049.90 | 0.598891 | ||||||||
\(297\) | − | 1668.08i | − | 0.325899i | ||||||
\(298\) | − | 2366.58i | − | 0.460042i | ||||||
\(299\) | 59.0610 | 0.0114234 | ||||||||
\(300\) | 115.860 | − | 588.864i | 0.0222973 | − | 0.113327i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2970.85i | 0.566070i | ||||||||
\(303\) | 967.843i | 0.183502i | ||||||||
\(304\) | 87.3626 | 0.0164822 | ||||||||
\(305\) | 4740.28 | + | 461.903i | 0.889927 | + | 0.0867164i | ||||
\(306\) | −2526.37 | −0.471971 | ||||||||
\(307\) | − | 1738.43i | − | 0.323183i | −0.986858 | − | 0.161592i | \(-0.948337\pi\) | ||
0.986858 | − | 0.161592i | \(-0.0516627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1812.64 | 0.333713 | ||||||||
\(310\) | 496.056 | − | 5090.77i | 0.0908841 | − | 0.932699i | ||||
\(311\) | −3990.34 | −0.727562 | −0.363781 | − | 0.931485i | \(-0.618514\pi\) | ||||
−0.363781 | + | 0.931485i | \(0.618514\pi\) | |||||||
\(312\) | − | 528.441i | − | 0.0958881i | ||||||
\(313\) | 243.187i | 0.0439160i | 0.999759 | + | 0.0219580i | \(0.00699002\pi\) | ||||
−0.999759 | + | 0.0219580i | \(0.993010\pi\) | |||||||
\(314\) | −470.142 | −0.0844957 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 757.677 | 0.134882 | ||||||||
\(317\) | − | 5328.16i | − | 0.944036i | −0.881589 | − | 0.472018i | \(-0.843526\pi\) | ||
0.881589 | − | 0.472018i | \(-0.156474\pi\) | |||||||
\(318\) | − | 647.279i | − | 0.114143i | ||||||
\(319\) | −6509.26 | −1.14247 | ||||||||
\(320\) | 712.169 | + | 69.3952i | 0.124411 | + | 0.0121228i | ||||
\(321\) | 745.544 | 0.129633 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 269.851i | − | 0.0464858i | ||||||
\(324\) | −2457.50 | −0.421383 | ||||||||
\(325\) | −1328.00 | + | 6749.58i | −0.226658 | + | 1.15200i | ||||
\(326\) | 7029.01 | 1.19417 | ||||||||
\(327\) | 1851.84i | 0.313171i | ||||||||
\(328\) | 388.515i | 0.0654029i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 706.320 | + | 68.8253i | 0.117823 | + | 0.0114809i | ||||
\(331\) | −11513.2 | −1.91185 | −0.955924 | − | 0.293614i | \(-0.905142\pi\) | ||||
−0.955924 | + | 0.293614i | \(0.905142\pi\) | |||||||
\(332\) | − | 2444.29i | − | 0.404060i | ||||||
\(333\) | − | 9744.14i | − | 1.60353i | ||||||
\(334\) | −3350.47 | −0.548891 | ||||||||
\(335\) | −995.760 | + | 10219.0i | −0.162401 | + | 1.66664i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8818.86i | − | 1.42550i | −0.701418 | − | 0.712750i | \(-0.747449\pi\) | ||
0.701418 | − | 0.712750i | \(-0.252551\pi\) | |||||||
\(338\) | 1663.01i | 0.267621i | ||||||||
\(339\) | 1554.43 | 0.249041 | ||||||||
\(340\) | 214.352 | − | 2199.79i | 0.0341909 | − | 0.350884i | ||||
\(341\) | 6048.22 | 0.960496 | ||||||||
\(342\) | − | 279.115i | − | 0.0441311i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1871.03 | 0.293253 | ||||||||
\(345\) | −14.3345 | − | 1.39678i | −0.00223693 | − | 0.000217971i | ||||
\(346\) | 1493.50 | 0.232054 | ||||||||
\(347\) | − | 2160.48i | − | 0.334237i | −0.985937 | − | 0.167119i | \(-0.946554\pi\) | ||
0.985937 | − | 0.167119i | \(-0.0534463\pi\) | |||||||
\(348\) | − | 1181.97i | − | 0.182070i | ||||||
\(349\) | −1837.74 | −0.281868 | −0.140934 | − | 0.990019i | \(-0.545010\pi\) | ||||
−0.140934 | + | 0.990019i | \(0.545010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3471.81 | −0.527953 | ||||||||
\(352\) | 846.109i | 0.128119i | ||||||||
\(353\) | − | 9588.21i | − | 1.44569i | −0.691009 | − | 0.722846i | \(-0.742834\pi\) | ||
0.691009 | − | 0.722846i | \(-0.257166\pi\) | |||||||
\(354\) | 1883.36 | 0.282767 | ||||||||
\(355\) | −2234.66 | − | 217.750i | −0.334094 | − | 0.0325548i | ||||
\(356\) | −1169.31 | −0.174082 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 7305.04i | − | 1.07845i | ||||||
\(359\) | −7047.23 | −1.03604 | −0.518020 | − | 0.855368i | \(-0.673331\pi\) | ||||
−0.518020 | + | 0.855368i | \(0.673331\pi\) | |||||||
\(360\) | 221.711 | − | 2275.31i | 0.0324589 | − | 0.333110i | ||||
\(361\) | −6829.19 | −0.995653 | ||||||||
\(362\) | 1534.01i | 0.222723i | ||||||||
\(363\) | − | 758.448i | − | 0.109664i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −844.056 | + | 8662.13i | −0.121041 | + | 1.24218i | ||||
\(366\) | −1022.64 | −0.146050 | ||||||||
\(367\) | 7554.28i | 1.07447i | 0.843433 | + | 0.537234i | \(0.180531\pi\) | ||||
−0.843433 | + | 0.537234i | \(0.819469\pi\) | |||||||
\(368\) | − | 17.1714i | − | 0.00243240i | ||||||
\(369\) | 1241.27 | 0.175116 | ||||||||
\(370\) | 8484.53 | + | 826.751i | 1.19213 | + | 0.116164i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1098.26i | 0.153070i | ||||||||
\(373\) | − | 1288.31i | − | 0.178837i | −0.995994 | − | 0.0894184i | \(-0.971499\pi\) | ||
0.995994 | − | 0.0894184i | \(-0.0285008\pi\) | |||||||
\(374\) | 2613.52 | 0.361341 | ||||||||
\(375\) | 481.939 | − | 1606.76i | 0.0663660 | − | 0.221260i | ||||
\(376\) | 1961.23 | 0.268996 | ||||||||
\(377\) | 13547.8i | 1.85079i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6985.61 | −0.946773 | −0.473386 | − | 0.880855i | \(-0.656969\pi\) | ||||
−0.473386 | + | 0.880855i | \(0.656969\pi\) | |||||||
\(380\) | 243.035 | + | 23.6818i | 0.0328090 | + | 0.00319698i | ||||
\(381\) | −230.394 | −0.0309801 | ||||||||
\(382\) | − | 679.492i | − | 0.0910101i | ||||||
\(383\) | − | 5684.58i | − | 0.758403i | −0.925314 | − | 0.379202i | \(-0.876199\pi\) | ||
0.925314 | − | 0.379202i | \(-0.123801\pi\) | |||||||
\(384\) | −153.639 | −0.0204176 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4488.77 | −0.591898 | ||||||||
\(387\) | − | 5977.76i | − | 0.785185i | ||||||
\(388\) | − | 5718.91i | − | 0.748283i | ||||||
\(389\) | −2255.72 | −0.294009 | −0.147005 | − | 0.989136i | \(-0.546963\pi\) | ||||
−0.147005 | + | 0.989136i | \(0.546963\pi\) | |||||||
\(390\) | 143.247 | − | 1470.08i | 0.0185990 | − | 0.190872i | ||||
\(391\) | −53.0402 | −0.00686025 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1795.02i | − | 0.230399i | ||||||
\(394\) | 4260.29 | 0.544747 | ||||||||
\(395\) | 2107.79 | + | 205.387i | 0.268492 | + | 0.0261624i | ||||
\(396\) | 2703.24 | 0.343038 | ||||||||
\(397\) | 9949.77i | 1.25785i | 0.777468 | + | 0.628923i | \(0.216504\pi\) | ||||
−0.777468 | + | 0.628923i | \(0.783496\pi\) | |||||||
\(398\) | 3826.91i | 0.481975i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1962.38 | + | 386.102i | 0.245297 | + | 0.0482628i | ||||
\(401\) | 10864.6 | 1.35300 | 0.676501 | − | 0.736442i | \(-0.263496\pi\) | ||||
0.676501 | + | 0.736442i | \(0.263496\pi\) | |||||||
\(402\) | − | 2204.59i | − | 0.273520i | ||||||
\(403\) | − | 12588.2i | − | 1.55599i | ||||||
\(404\) | −3225.32 | −0.397192 | ||||||||
\(405\) | −6836.55 | − | 666.168i | −0.838793 | − | 0.0817337i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10080.3i | 1.22766i | ||||||||
\(408\) | 474.571i | 0.0575852i | ||||||||
\(409\) | −951.004 | −0.114973 | −0.0574867 | − | 0.998346i | \(-0.518309\pi\) | ||||
−0.0574867 | + | 0.998346i | \(0.518309\pi\) | |||||||
\(410\) | −105.317 | + | 1080.81i | −0.0126859 | + | 0.130189i | ||||
\(411\) | −1401.55 | −0.168208 | ||||||||
\(412\) | 6040.58i | 0.722325i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −54.8611 | −0.00651275 | ||||||||
\(415\) | 662.586 | − | 6799.80i | 0.0783737 | − | 0.804311i | ||||
\(416\) | 1761.02 | 0.207551 | ||||||||
\(417\) | 2502.34i | 0.293861i | ||||||||
\(418\) | 288.743i | 0.0337868i | ||||||||
\(419\) | 985.724 | 0.114930 | 0.0574651 | − | 0.998348i | \(-0.481698\pi\) | ||||
0.0574651 | + | 0.998348i | \(0.481698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3879.25 | 0.449081 | 0.224540 | − | 0.974465i | \(-0.427912\pi\) | ||||
0.224540 | + | 0.974465i | \(0.427912\pi\) | |||||||
\(422\) | − | 8037.93i | − | 0.927204i | ||||||
\(423\) | − | 6265.94i | − | 0.720237i | ||||||
\(424\) | 2157.04 | 0.247064 | ||||||||
\(425\) | 1192.62 | − | 6061.52i | 0.136119 | − | 0.691828i | ||||
\(426\) | 482.093 | 0.0548298 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2484.51i | 0.280592i | ||||||||
\(429\) | 1746.56 | 0.196561 | ||||||||
\(430\) | 5205.03 | + | 507.189i | 0.583741 | + | 0.0568810i | ||||
\(431\) | −13821.6 | −1.54470 | −0.772349 | − | 0.635199i | \(-0.780918\pi\) | ||||
−0.772349 | + | 0.635199i | \(0.780918\pi\) | |||||||
\(432\) | 1009.40i | 0.112418i | ||||||||
\(433\) | − | 520.224i | − | 0.0577375i | −0.999583 | − | 0.0288688i | \(-0.990810\pi\) | ||
0.999583 | − | 0.0288688i | \(-0.00919049\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 320.403 | − | 3288.14i | 0.0353153 | − | 0.362424i | ||||
\(436\) | −6171.23 | −0.677863 | ||||||||
\(437\) | − | 5.85992i | − | 0.000641460i | ||||||
\(438\) | − | 1868.72i | − | 0.203860i | ||||||
\(439\) | −9569.21 | −1.04035 | −0.520175 | − | 0.854060i | \(-0.674133\pi\) | ||||
−0.520175 | + | 0.854060i | \(0.674133\pi\) | |||||||
\(440\) | −229.359 | + | 2353.80i | −0.0248506 | + | 0.255029i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 5439.55i | − | 0.585369i | ||||||
\(443\) | 4313.29i | 0.462597i | 0.972883 | + | 0.231298i | \(0.0742974\pi\) | ||||
−0.972883 | + | 0.231298i | \(0.925703\pi\) | |||||||
\(444\) | −1830.41 | −0.195647 | ||||||||
\(445\) | −3252.90 | − | 316.970i | −0.346522 | − | 0.0337659i | ||||
\(446\) | −9319.01 | −0.989390 | ||||||||
\(447\) | 1420.31i | 0.150287i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4396.78 | 0.462131 | 0.231065 | − | 0.972938i | \(-0.425779\pi\) | ||||
0.231065 | + | 0.972938i | \(0.425779\pi\) | |||||||
\(450\) | 1233.56 | − | 6269.61i | 0.129224 | − | 0.656783i | ||||
\(451\) | −1284.09 | −0.134069 | ||||||||
\(452\) | 5180.10i | 0.539052i | ||||||||
\(453\) | − | 1782.97i | − | 0.184925i | ||||||
\(454\) | 7384.60 | 0.763384 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −52.4310 | −0.00538444 | ||||||||
\(457\) | − | 8466.25i | − | 0.866596i | −0.901251 | − | 0.433298i | \(-0.857350\pi\) | ||
0.901251 | − | 0.433298i | \(-0.142650\pi\) | |||||||
\(458\) | − | 2908.68i | − | 0.296755i | ||||||
\(459\) | 3117.89 | 0.317060 | ||||||||
\(460\) | 4.65474 | − | 47.7693i | 0.000471801 | − | 0.00484186i | ||||
\(461\) | 1231.15 | 0.124382 | 0.0621911 | − | 0.998064i | \(-0.480191\pi\) | ||||
0.0621911 | + | 0.998064i | \(0.480191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 9773.66i | − | 0.981038i | −0.871431 | − | 0.490519i | \(-0.836807\pi\) | ||
0.871431 | − | 0.490519i | \(-0.163193\pi\) | |||||||
\(464\) | 3938.90 | 0.394092 | ||||||||
\(465\) | −297.710 | + | 3055.25i | −0.0296902 | + | 0.304696i | ||||
\(466\) | 12805.3 | 1.27295 | ||||||||
\(467\) | − | 15981.9i | − | 1.58363i | −0.610760 | − | 0.791816i | \(-0.709136\pi\) | ||
0.610760 | − | 0.791816i | \(-0.290864\pi\) | |||||||
\(468\) | − | 5626.30i | − | 0.555717i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5455.95 | + | 531.640i | 0.535456 | + | 0.0521760i | ||||
\(471\) | 282.157 | 0.0276032 | ||||||||
\(472\) | 6276.27i | 0.612053i | ||||||||
\(473\) | 6183.96i | 0.601139i | ||||||||
\(474\) | −454.723 | −0.0440635 | ||||||||
\(475\) | 669.681 | + | 131.761i | 0.0646886 | + | 0.0127276i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6891.55i | − | 0.661515i | ||||||
\(478\) | 2154.85i | 0.206193i | ||||||||
\(479\) | −17543.5 | −1.67345 | −0.836727 | − | 0.547621i | \(-0.815534\pi\) | ||||
−0.836727 | + | 0.547621i | \(0.815534\pi\) | |||||||
\(480\) | −427.411 | − | 41.6478i | −0.0406428 | − | 0.00396032i | ||||
\(481\) | 20980.2 | 1.98880 | ||||||||
\(482\) | − | 2258.95i | − | 0.213469i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2527.51 | 0.237370 | ||||||||
\(485\) | 1550.25 | − | 15909.5i | 0.145141 | − | 1.48951i | ||||
\(486\) | 4881.59 | 0.455625 | ||||||||
\(487\) | − | 14047.2i | − | 1.30706i | −0.756901 | − | 0.653529i | \(-0.773288\pi\) | ||
0.756901 | − | 0.653529i | \(-0.226712\pi\) | |||||||
\(488\) | − | 3407.93i | − | 0.316127i | ||||||
\(489\) | −4218.49 | −0.390116 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6339.30 | 0.582665 | 0.291333 | − | 0.956622i | \(-0.405901\pi\) | ||||
0.291333 | + | 0.956622i | \(0.405901\pi\) | |||||||
\(492\) | − | 233.169i | − | 0.0213660i | ||||||
\(493\) | − | 12166.7i | − | 1.11148i | ||||||
\(494\) | 600.966 | 0.0547343 | ||||||||
\(495\) | 7520.17 | + | 732.781i | 0.682841 | + | 0.0665375i | ||||
\(496\) | −3659.91 | −0.331321 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1466.95i | 0.131999i | ||||||||
\(499\) | −18373.0 | −1.64828 | −0.824139 | − | 0.566388i | \(-0.808340\pi\) | ||||
−0.824139 | + | 0.566388i | \(0.808340\pi\) | |||||||
\(500\) | 5354.49 | + | 1606.05i | 0.478920 | + | 0.143650i | ||||
\(501\) | 2010.80 | 0.179313 | ||||||||
\(502\) | − | 10380.7i | − | 0.922930i | ||||||
\(503\) | 6870.88i | 0.609061i | 0.952503 | + | 0.304530i | \(0.0984995\pi\) | ||||
−0.952503 | + | 0.304530i | \(0.901500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8972.54 | − | 874.303i | −0.790639 | − | 0.0770415i | ||||
\(506\) | 56.7535 | 0.00498617 | ||||||||
\(507\) | − | 998.063i | − | 0.0874271i | ||||||
\(508\) | − | 767.783i | − | 0.0670568i | ||||||
\(509\) | 3520.02 | 0.306527 | 0.153264 | − | 0.988185i | \(-0.451022\pi\) | ||||
0.153264 | + | 0.988185i | \(0.451022\pi\) | |||||||
\(510\) | −128.644 | + | 1320.21i | −0.0111695 | + | 0.114628i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | 344.467i | 0.0296464i | ||||||||
\(514\) | −13293.7 | −1.14077 | ||||||||
\(515\) | −1637.45 | + | 16804.3i | −0.140106 | + | 1.43784i | ||||
\(516\) | −1122.90 | −0.0958005 | ||||||||
\(517\) | 6482.08i | 0.551415i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −896.327 | −0.0758081 | ||||||||
\(520\) | 4899.00 | + | 477.368i | 0.413145 | + | 0.0402577i | ||||
\(521\) | 9451.97 | 0.794815 | 0.397407 | − | 0.917642i | \(-0.369910\pi\) | ||||
0.397407 | + | 0.917642i | \(0.369910\pi\) | |||||||
\(522\) | − | 12584.4i | − | 1.05518i | ||||||
\(523\) | − | 2384.25i | − | 0.199343i | −0.995020 | − | 0.0996713i | \(-0.968221\pi\) | ||
0.995020 | − | 0.0996713i | \(-0.0317791\pi\) | |||||||
\(524\) | 5981.86 | 0.498700 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11951.1 | 0.990671 | ||||||||
\(527\) | 11305.0i | 0.934445i | ||||||||
\(528\) | − | 507.795i | − | 0.0418541i | ||||||
\(529\) | 12165.8 | 0.999905 | ||||||||
\(530\) | 6000.70 | + | 584.721i | 0.491799 | + | 0.0479220i | ||||
\(531\) | 20052.1 | 1.63877 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2672.59i | 0.217191i | ||||||||
\(534\) | 701.763 | 0.0568694 | ||||||||
\(535\) | −673.488 | + | 6911.68i | −0.0544251 | + | 0.558538i | ||||
\(536\) | 7346.75 | 0.592036 | ||||||||
\(537\) | 4384.15i | 0.352309i | ||||||||
\(538\) | − | 10079.7i | − | 0.807748i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −273.622 | + | 2808.05i | −0.0218052 | + | 0.223776i | ||||
\(541\) | 5638.78 | 0.448115 | 0.224057 | − | 0.974576i | \(-0.428070\pi\) | ||||
0.224057 | + | 0.974576i | \(0.428070\pi\) | |||||||
\(542\) | 1128.12i | 0.0894036i | ||||||||
\(543\) | − | 920.642i | − | 0.0727597i | ||||||
\(544\) | −1581.50 | −0.124644 | ||||||||
\(545\) | −17167.8 | − | 1672.86i | −1.34933 | − | 0.131482i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15979.0i | 1.24902i | 0.781017 | + | 0.624509i | \(0.214701\pi\) | ||||
−0.781017 | + | 0.624509i | \(0.785299\pi\) | |||||||
\(548\) | − | 4670.64i | − | 0.364087i | ||||||
\(549\) | −10888.0 | −0.846430 | ||||||||
\(550\) | −1276.11 | + | 6485.88i | −0.0989338 | + | 0.502834i | ||||
\(551\) | 1344.19 | 0.103928 | ||||||||
\(552\) | 10.3055i | 0.000794621i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9415.79 | 0.722091 | ||||||||
\(555\) | −5092.02 | − | 496.177i | −0.389449 | − | 0.0379488i | ||||
\(556\) | −8339.00 | −0.636066 | ||||||||
\(557\) | 8033.56i | 0.611118i | 0.952173 | + | 0.305559i | \(0.0988434\pi\) | ||||
−0.952173 | + | 0.305559i | \(0.901157\pi\) | |||||||
\(558\) | 11693.1i | 0.887111i | ||||||||
\(559\) | 12870.8 | 0.973838 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1568.51 | −0.118044 | ||||||||
\(562\) | 3987.37i | 0.299283i | ||||||||
\(563\) | 2495.23i | 0.186788i | 0.995629 | + | 0.0933939i | \(0.0297716\pi\) | ||||
−0.995629 | + | 0.0933939i | \(0.970228\pi\) | |||||||
\(564\) | −1177.04 | −0.0878763 | ||||||||
\(565\) | −1404.20 | + | 14410.6i | −0.104557 | + | 1.07302i | ||||
\(566\) | −14570.8 | −1.08208 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1606.56i | 0.118680i | ||||||||
\(569\) | 7234.24 | 0.532997 | 0.266498 | − | 0.963835i | \(-0.414133\pi\) | ||||
0.266498 | + | 0.963835i | \(0.414133\pi\) | |||||||
\(570\) | −145.858 | − | 14.2127i | −0.0107181 | − | 0.00104440i | ||||
\(571\) | −13910.5 | −1.01950 | −0.509750 | − | 0.860323i | \(-0.670262\pi\) | ||||
−0.509750 | + | 0.860323i | \(0.670262\pi\) | |||||||
\(572\) | 5820.37i | 0.425458i | ||||||||
\(573\) | 407.800i | 0.0297314i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.8981 | − | 131.628i | 0.00187831 | − | 0.00954656i | ||||
\(576\) | −1635.79 | −0.118330 | ||||||||
\(577\) | − | 8862.92i | − | 0.639459i | −0.947509 | − | 0.319730i | \(-0.896408\pi\) | ||
0.947509 | − | 0.319730i | \(-0.103592\pi\) | |||||||
\(578\) | − | 4940.96i | − | 0.355566i | ||||||
\(579\) | 2693.95 | 0.193362 | ||||||||
\(580\) | 10957.7 | + | 1067.74i | 0.784469 | + | 0.0764403i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3432.23i | 0.244451i | ||||||||
\(583\) | 7129.27i | 0.506457i | ||||||||
\(584\) | 6227.47 | 0.441258 | ||||||||
\(585\) | 1525.15 | − | 15651.8i | 0.107790 | − | 1.10620i | ||||
\(586\) | −17039.5 | −1.20119 | ||||||||
\(587\) | 4179.74i | 0.293895i | 0.989144 | + | 0.146948i | \(0.0469449\pi\) | ||||
−0.989144 | + | 0.146948i | \(0.953055\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1248.98 | −0.0873743 | ||||||||
\(590\) | −1701.34 | + | 17460.0i | −0.118717 | + | 1.21833i | ||||
\(591\) | −2556.83 | −0.177959 | ||||||||
\(592\) | − | 6099.79i | − | 0.423480i | ||||||
\(593\) | − | 8487.25i | − | 0.587740i | −0.955845 | − | 0.293870i | \(-0.905057\pi\) | ||
0.955845 | − | 0.293870i | \(-0.0949432\pi\) | |||||||
\(594\) | −3336.17 | −0.230446 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4733.17 | −0.325299 | ||||||||
\(597\) | − | 2296.74i | − | 0.157453i | ||||||
\(598\) | − | 118.122i | − | 0.00807753i | ||||||
\(599\) | −17356.0 | −1.18388 | −0.591941 | − | 0.805981i | \(-0.701638\pi\) | ||||
−0.591941 | + | 0.805981i | \(0.701638\pi\) | |||||||
\(600\) | −1177.73 | − | 231.721i | −0.0801342 | − | 0.0157666i | ||||
\(601\) | −5769.08 | −0.391557 | −0.195779 | − | 0.980648i | \(-0.562723\pi\) | ||||
−0.195779 | + | 0.980648i | \(0.562723\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 23472.2i | − | 1.58518i | ||||||
\(604\) | 5941.70 | 0.400272 | ||||||||
\(605\) | 7031.31 | + | 685.146i | 0.472502 | + | 0.0460415i | ||||
\(606\) | 1935.69 | 0.129756 | ||||||||
\(607\) | 20810.7i | 1.39157i | 0.718253 | + | 0.695783i | \(0.244942\pi\) | ||||
−0.718253 | + | 0.695783i | \(0.755058\pi\) | |||||||
\(608\) | − | 174.725i | − | 0.0116547i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 923.806 | − | 9480.56i | 0.0613177 | − | 0.629274i | ||||
\(611\) | 13491.2 | 0.893285 | ||||||||
\(612\) | 5052.74i | 0.333734i | ||||||||
\(613\) | 2273.33i | 0.149786i | 0.997192 | + | 0.0748929i | \(0.0238615\pi\) | ||||
−0.997192 | + | 0.0748929i | \(0.976138\pi\) | |||||||
\(614\) | −3476.85 | −0.228525 | ||||||||
\(615\) | 63.2062 | − | 648.654i | 0.00414426 | − | 0.0425305i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9970.37i | 0.650554i | 0.945619 | + | 0.325277i | \(0.105458\pi\) | ||||
−0.945619 | + | 0.325277i | \(0.894542\pi\) | |||||||
\(618\) | − | 3625.27i | − | 0.235971i | ||||||
\(619\) | 4161.01 | 0.270186 | 0.135093 | − | 0.990833i | \(-0.456867\pi\) | ||||
0.135093 | + | 0.990833i | \(0.456867\pi\) | |||||||
\(620\) | −10181.5 | − | 992.111i | −0.659517 | − | 0.0642648i | ||||
\(621\) | 67.7061 | 0.00437513 | ||||||||
\(622\) | 7980.69i | 0.514464i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1056.88 | −0.0678031 | ||||||||
\(625\) | 14460.4 | + | 5919.36i | 0.925463 | + | 0.378839i | ||||
\(626\) | 486.373 | 0.0310533 | ||||||||
\(627\) | − | 173.290i | − | 0.0110376i | ||||||
\(628\) | 940.284i | 0.0597475i | ||||||||
\(629\) | −18841.4 | −1.19437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11476.1 | −0.724018 | −0.362009 | − | 0.932175i | \(-0.617909\pi\) | ||||
−0.362009 | + | 0.932175i | \(0.617909\pi\) | |||||||
\(632\) | − | 1515.35i | − | 0.0953759i | ||||||
\(633\) | 4823.99i | 0.302901i | ||||||||
\(634\) | −10656.3 | −0.667534 | ||||||||
\(635\) | 208.127 | − | 2135.90i | 0.0130067 | − | 0.133481i | ||||
\(636\) | −1294.56 | −0.0807115 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13018.5i | 0.807849i | ||||||||
\(639\) | 5132.83 | 0.317764 | ||||||||
\(640\) | 138.790 | − | 1424.34i | 0.00857214 | − | 0.0879717i | ||||
\(641\) | 8486.13 | 0.522905 | 0.261452 | − | 0.965216i | \(-0.415799\pi\) | ||||
0.261452 | + | 0.965216i | \(0.415799\pi\) | |||||||
\(642\) | − | 1491.09i | − | 0.0916644i | ||||||
\(643\) | − | 25563.4i | − | 1.56784i | −0.620859 | − | 0.783922i | \(-0.713216\pi\) | ||
0.620859 | − | 0.783922i | \(-0.286784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3123.82 | − | 304.391i | −0.190698 | − | 0.0185820i | ||||
\(646\) | −539.703 | −0.0328705 | ||||||||
\(647\) | 19501.0i | 1.18495i | 0.805589 | + | 0.592475i | \(0.201849\pi\) | ||||
−0.805589 | + | 0.592475i | \(0.798151\pi\) | |||||||
\(648\) | 4915.01i | 0.297963i | ||||||||
\(649\) | −20743.8 | −1.25465 | ||||||||
\(650\) | 13499.2 | + | 2655.99i | 0.814586 | + | 0.160272i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 14058.0i | − | 0.844409i | ||||||
\(653\) | 32575.7i | 1.95220i | 0.217329 | + | 0.976098i | \(0.430265\pi\) | ||||
−0.217329 | + | 0.976098i | \(0.569735\pi\) | |||||||
\(654\) | 3703.68 | 0.221446 | ||||||||
\(655\) | 16641.0 | + | 1621.53i | 0.992698 | + | 0.0967306i | ||||
\(656\) | 777.030 | 0.0462468 | ||||||||
\(657\) | − | 19896.2i | − | 1.18147i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16168.7 | 0.955759 | 0.477879 | − | 0.878425i | \(-0.341406\pi\) | ||||
0.477879 | + | 0.878425i | \(0.341406\pi\) | |||||||
\(660\) | 137.651 | − | 1412.64i | 0.00811825 | − | 0.0833136i | ||||
\(661\) | 14858.4 | 0.874317 | 0.437159 | − | 0.899384i | \(-0.355985\pi\) | ||||
0.437159 | + | 0.899384i | \(0.355985\pi\) | |||||||
\(662\) | 23026.4i | 1.35188i | ||||||||
\(663\) | 3264.57i | 0.191230i | ||||||||
\(664\) | −4888.58 | −0.285714 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −19488.3 | −1.13387 | ||||||||
\(667\) | − | 264.205i | − | 0.0153374i | ||||||
\(668\) | 6700.94i | 0.388125i | ||||||||
\(669\) | 5592.84 | 0.323216 | ||||||||
\(670\) | 20438.0 | + | 1991.52i | 1.17849 | + | 0.114835i | ||||
\(671\) | 11263.6 | 0.648028 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7945.78i | 0.455108i | 0.973766 | + | 0.227554i | \(0.0730728\pi\) | ||||
−0.973766 | + | 0.227554i | \(0.926927\pi\) | |||||||
\(674\) | −17637.7 | −1.00798 | ||||||||
\(675\) | −1522.38 | + | 7737.56i | −0.0868097 | + | 0.441213i | ||||
\(676\) | 3326.03 | 0.189237 | ||||||||
\(677\) | − | 10365.2i | − | 0.588430i | −0.955739 | − | 0.294215i | \(-0.904942\pi\) | ||
0.955739 | − | 0.294215i | \(-0.0950582\pi\) | |||||||
\(678\) | − | 3108.86i | − | 0.176099i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4399.59 | − | 428.705i | −0.248112 | − | 0.0241766i | ||||
\(681\) | −4431.89 | −0.249384 | ||||||||
\(682\) | − | 12096.4i | − | 0.679173i | ||||||
\(683\) | 21394.4i | 1.19858i | 0.800531 | + | 0.599292i | \(0.204551\pi\) | ||||
−0.800531 | + | 0.599292i | \(0.795449\pi\) | |||||||
\(684\) | −558.231 | −0.0312054 | ||||||||
\(685\) | 1266.09 | − | 12993.3i | 0.0706204 | − | 0.724742i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1745.66i | 0.0969445i | ||||||||
\(688\) | − | 3742.05i | − | 0.207361i | ||||||
\(689\) | 14838.3 | 0.820454 | ||||||||
\(690\) | −2.79356 | + | 28.6689i | −0.000154129 | + | 0.00158175i | ||||
\(691\) | 22753.1 | 1.25263 | 0.626315 | − | 0.779570i | \(-0.284562\pi\) | ||||
0.626315 | + | 0.779570i | \(0.284562\pi\) | |||||||
\(692\) | − | 2986.99i | − | 0.164087i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4320.95 | −0.236342 | ||||||||
\(695\) | −23198.3 | − | 2260.50i | −1.26613 | − | 0.123375i | ||||
\(696\) | −2363.95 | −0.128743 | ||||||||
\(697\) | − | 2400.14i | − | 0.130433i | ||||||
\(698\) | 3675.47i | 0.199310i | ||||||||
\(699\) | −7685.16 | −0.415851 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11931.0 | −0.642834 | −0.321417 | − | 0.946938i | \(-0.604159\pi\) | ||||
−0.321417 | + | 0.946938i | \(0.604159\pi\) | |||||||
\(702\) | 6943.62i | 0.373319i | ||||||||
\(703\) | − | 2081.62i | − | 0.111678i | ||||||
\(704\) | 1692.22 | 0.0905936 | ||||||||
\(705\) | −3274.41 | − | 319.065i | −0.174924 | − | 0.0170450i | ||||
\(706\) | −19176.4 | −1.02226 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 3766.73i | − | 0.199947i | ||||||
\(709\) | −8551.69 | −0.452984 | −0.226492 | − | 0.974013i | \(-0.572726\pi\) | ||||
−0.226492 | + | 0.974013i | \(0.572726\pi\) | |||||||
\(710\) | −435.500 | + | 4469.32i | −0.0230197 | + | 0.236240i | ||||
\(711\) | −4841.42 | −0.255369 | ||||||||
\(712\) | 2338.61i | 0.123094i | ||||||||
\(713\) | 245.492i | 0.0128945i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1577.76 | + | 16191.7i | −0.0825241 | + | 0.846905i | ||||
\(716\) | −14610.1 | −0.762576 | ||||||||
\(717\) | − | 1293.24i | − | 0.0673597i | ||||||
\(718\) | 14094.5i | 0.732591i | ||||||||
\(719\) | −21203.9 | −1.09982 | −0.549911 | − | 0.835223i | \(-0.685338\pi\) | ||||
−0.549911 | + | 0.835223i | \(0.685338\pi\) | |||||||
\(720\) | −4550.63 | − | 443.423i | −0.235544 | − | 0.0229519i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13658.4i | 0.704033i | ||||||||
\(723\) | 1355.71i | 0.0697366i | ||||||||
\(724\) | 3068.02 | 0.157489 | ||||||||
\(725\) | 30193.8 | + | 5940.70i | 1.54672 | + | 0.304320i | ||||
\(726\) | −1516.90 | −0.0775445 | ||||||||
\(727\) | − | 25557.6i | − | 1.30382i | −0.758295 | − | 0.651911i | \(-0.773967\pi\) | ||
0.758295 | − | 0.651911i | \(-0.226033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13658.4 | 0.693921 | ||||||||
\(730\) | 17324.3 | + | 1688.11i | 0.878356 | + | 0.0855888i | ||||
\(731\) | −11558.7 | −0.584834 | ||||||||
\(732\) | 2045.28i | 0.103273i | ||||||||
\(733\) | − | 12792.4i | − | 0.644607i | −0.946636 | − | 0.322303i | \(-0.895543\pi\) | ||
0.946636 | − | 0.322303i | \(-0.104457\pi\) | |||||||
\(734\) | 15108.6 | 0.759764 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.3428 | −0.00171996 | ||||||||
\(737\) | 24281.8i | 1.21361i | ||||||||
\(738\) | − | 2482.54i | − | 0.123826i | ||||||
\(739\) | −16767.3 | −0.834636 | −0.417318 | − | 0.908760i | \(-0.637030\pi\) | ||||
−0.417318 | + | 0.908760i | \(0.637030\pi\) | |||||||
\(740\) | 1653.50 | − | 16969.1i | 0.0821404 | − | 0.842967i | ||||
\(741\) | −360.672 | −0.0178807 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17412.9i | 0.859782i | 0.902881 | + | 0.429891i | \(0.141448\pi\) | ||||
−0.902881 | + | 0.429891i | \(0.858552\pi\) | |||||||
\(744\) | 2196.51 | 0.108237 | ||||||||
\(745\) | −13167.2 | − | 1283.04i | −0.647530 | − | 0.0630967i | ||||
\(746\) | −2576.62 | −0.126457 | ||||||||
\(747\) | 15618.6i | 0.764998i | ||||||||
\(748\) | − | 5227.03i | − | 0.255507i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3213.52 | − | 963.879i | −0.156455 | − | 0.0469278i | ||||
\(751\) | −21188.3 | −1.02952 | −0.514762 | − | 0.857333i | \(-0.672120\pi\) | ||||
−0.514762 | + | 0.857333i | \(0.672120\pi\) | |||||||
\(752\) | − | 3922.45i | − | 0.190209i | ||||||
\(753\) | 6229.98i | 0.301505i | ||||||||
\(754\) | 27095.6 | 1.30871 | ||||||||
\(755\) | 16529.3 | + | 1610.65i | 0.796770 | + | 0.0776390i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 15675.9i | − | 0.752642i | −0.926489 | − | 0.376321i | \(-0.877189\pi\) | ||
0.926489 | − | 0.376321i | \(-0.122811\pi\) | |||||||
\(758\) | 13971.2i | 0.669469i | ||||||||
\(759\) | −34.0608 | −0.00162889 | ||||||||
\(760\) | 47.3636 | − | 486.070i | 0.00226061 | − | 0.0231995i | ||||
\(761\) | −11122.5 | −0.529815 | −0.264908 | − | 0.964274i | \(-0.585341\pi\) | ||||
−0.264908 | + | 0.964274i | \(0.585341\pi\) | |||||||
\(762\) | 460.787i | 0.0219063i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1358.98 | −0.0643538 | ||||||||
\(765\) | −1369.67 | + | 14056.3i | −0.0647328 | + | 0.664321i | ||||
\(766\) | −11369.2 | −0.536272 | ||||||||
\(767\) | 43174.4i | 2.03251i | ||||||||
\(768\) | 307.279i | 0.0144375i | ||||||||
\(769\) | −34411.5 | −1.61367 | −0.806833 | − | 0.590779i | \(-0.798820\pi\) | ||||
−0.806833 | + | 0.590779i | \(0.798820\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7978.24 | 0.372671 | ||||||||
\(772\) | 8977.54i | 0.418535i | ||||||||
\(773\) | 33325.4i | 1.55062i | 0.631579 | + | 0.775312i | \(0.282407\pi\) | ||||
−0.631579 | + | 0.775312i | \(0.717593\pi\) | |||||||
\(774\) | −11955.5 | −0.555210 | ||||||||
\(775\) | −28055.2 | − | 5519.93i | −1.30035 | − | 0.255847i | ||||
\(776\) | −11437.8 | −0.529116 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4511.44i | 0.207896i | ||||||||
\(779\) | 265.169 | 0.0121960 | ||||||||
\(780\) | −2940.15 | − | 286.494i | −0.134967 | − | 0.0131515i | ||||
\(781\) | −5309.88 | −0.243281 | ||||||||
\(782\) | 106.080i | 0.00485093i | ||||||||
\(783\) | 15530.9i | 0.708849i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −254.887 | + | 2615.78i | −0.0115889 | + | 0.118932i | ||||
\(786\) | −3590.03 | −0.162916 | ||||||||
\(787\) | − | 2874.46i | − | 0.130195i | −0.997879 | − | 0.0650976i | \(-0.979264\pi\) | ||
0.997879 | − | 0.0650976i | \(-0.0207359\pi\) | |||||||
\(788\) | − | 8520.58i | − | 0.385194i | ||||||
\(789\) | −7172.50 | −0.323635 | ||||||||
\(790\) | 410.775 | − | 4215.58i | 0.0184996 | − | 0.189853i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 5406.48i | − | 0.242564i | ||||||
\(793\) | − | 23443.1i | − | 1.04980i | ||||||
\(794\) | 19899.5 | 0.889431 | ||||||||
\(795\) | −3601.34 | − | 350.922i | −0.160662 | − | 0.0156553i | ||||
\(796\) | 7653.83 | 0.340807 | ||||||||
\(797\) | − | 3305.12i | − | 0.146893i | −0.997299 | − | 0.0734464i | \(-0.976600\pi\) | ||
0.997299 | − | 0.0734464i | \(-0.0233998\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12115.9 | −0.536459 | ||||||||
\(800\) | 772.205 | − | 3924.75i | 0.0341269 | − | 0.173451i | ||||
\(801\) | 7471.65 | 0.329585 | ||||||||
\(802\) | − | 21729.2i | − | 0.956716i | ||||||
\(803\) | 20582.5i | 0.904534i | ||||||||
\(804\) | −4409.18 | −0.193408 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25176.5 | −1.10025 | ||||||||
\(807\) | 6049.39i | 0.263877i | ||||||||
\(808\) | 6450.64i | 0.280857i | ||||||||
\(809\) | 26393.2 | 1.14702 | 0.573508 | − | 0.819200i | \(-0.305582\pi\) | ||||
0.573508 | + | 0.819200i | \(0.305582\pi\) | |||||||
\(810\) | −1332.34 | + | 13673.1i | −0.0577945 | + | 0.593116i | ||||
\(811\) | 35281.8 | 1.52763 | 0.763817 | − | 0.645433i | \(-0.223323\pi\) | ||||
0.763817 | + | 0.645433i | \(0.223323\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 677.043i | − | 0.0292066i | ||||||
\(814\) | 20160.5 | 0.868090 | ||||||||
\(815\) | 3810.78 | − | 39108.1i | 0.163786 | − | 1.68086i | ||||
\(816\) | 949.142 | 0.0407189 | ||||||||
\(817\) | − | 1277.01i | − | 0.0546843i | ||||||
\(818\) | 1902.01i | 0.0812985i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2161.63 | + | 210.633i | 0.0920576 | + | 0.00897029i | ||||
\(821\) | 38385.0 | 1.63172 | 0.815862 | − | 0.578246i | \(-0.196263\pi\) | ||||
0.815862 | + | 0.578246i | \(0.196263\pi\) | |||||||
\(822\) | 2803.10i | 0.118941i | ||||||||
\(823\) | − | 21575.6i | − | 0.913827i | −0.889511 | − | 0.456913i | \(-0.848955\pi\) | ||
0.889511 | − | 0.456913i | \(-0.151045\pi\) | |||||||
\(824\) | 12081.2 | 0.510761 | ||||||||
\(825\) | 765.863 | − | 3892.52i | 0.0323199 | − | 0.164267i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 31906.7i | − | 1.34160i | −0.741638 | − | 0.670800i | \(-0.765951\pi\) | ||
0.741638 | − | 0.670800i | \(-0.234049\pi\) | |||||||
\(828\) | 109.722i | 0.00460521i | ||||||||
\(829\) | 26809.9 | 1.12322 | 0.561609 | − | 0.827403i | \(-0.310183\pi\) | ||||
0.561609 | + | 0.827403i | \(0.310183\pi\) | |||||||
\(830\) | −13599.6 | − | 1325.17i | −0.568734 | − | 0.0554186i | ||||
\(831\) | −5650.92 | −0.235894 | ||||||||
\(832\) | − | 3522.04i | − | 0.146761i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5004.68 | 0.207791 | ||||||||
\(835\) | −1816.46 | + | 18641.4i | −0.0752828 | + | 0.772590i | ||||
\(836\) | 577.487 | 0.0238909 | ||||||||
\(837\) | − | 14430.9i | − | 0.595943i | ||||||
\(838\) | − | 1971.45i | − | 0.0812680i | ||||||
\(839\) | 20507.0 | 0.843838 | 0.421919 | − | 0.906633i | \(-0.361357\pi\) | ||||
0.421919 | + | 0.906633i | \(0.361357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36216.2 | 1.48494 | ||||||||
\(842\) | − | 7758.50i | − | 0.317548i | ||||||
\(843\) | − | 2393.04i | − | 0.0977705i | ||||||
\(844\) | −16075.9 | −0.655632 | ||||||||
\(845\) | 9252.70 | + | 901.603i | 0.376690 | + | 0.0367054i | ||||
\(846\) | −12531.9 | −0.509285 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 4314.09i | − | 0.174701i | ||||||
\(849\) | 8744.71 | 0.353495 | ||||||||
\(850\) | −12123.0 | − | 2385.24i | −0.489196 | − | 0.0962505i | ||||
\(851\) | −409.149 | −0.0164811 | ||||||||
\(852\) | − | 964.186i | − | 0.0387705i | ||||||
\(853\) | 36776.8i | 1.47622i | 0.674681 | + | 0.738109i | \(0.264281\pi\) | ||||
−0.674681 | + | 0.738109i | \(0.735719\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1552.95 | − | 151.322i | −0.0621166 | − | 0.00605277i | ||||
\(856\) | 4969.02 | 0.198408 | ||||||||
\(857\) | 26632.0i | 1.06153i | 0.847519 | + | 0.530765i | \(0.178095\pi\) | ||||
−0.847519 | + | 0.530765i | \(0.821905\pi\) | |||||||
\(858\) | − | 3493.12i | − | 0.138990i | ||||||
\(859\) | −2154.29 | −0.0855687 | −0.0427843 | − | 0.999084i | \(-0.513623\pi\) | ||||
−0.0427843 | + | 0.999084i | \(0.513623\pi\) | |||||||
\(860\) | 1014.38 | − | 10410.1i | 0.0402209 | − | 0.412767i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27643.3i | 1.09227i | ||||||||
\(863\) | − | 37150.8i | − | 1.46539i | −0.680559 | − | 0.732693i | \(-0.738263\pi\) | ||
0.680559 | − | 0.732693i | \(-0.261737\pi\) | |||||||
\(864\) | 2018.79 | 0.0794916 | ||||||||
\(865\) | 809.699 | − | 8309.54i | 0.0318273 | − | 0.326628i | ||||
\(866\) | −1040.45 | −0.0408266 | ||||||||
\(867\) | 2965.34i | 0.116157i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5008.42 | 0.195511 | ||||||||
\(870\) | −6576.28 | − | 640.806i | −0.256272 | − | 0.0249717i | ||||
\(871\) | 50538.2 | 1.96604 | ||||||||
\(872\) | 12342.5i | 0.479321i | ||||||||
\(873\) | 36542.8i | 1.41671i | ||||||||
\(874\) | −11.7198 | −0.000453581 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3737.44 | −0.144151 | ||||||||
\(877\) | 3945.86i | 0.151930i | 0.997111 | + | 0.0759648i | \(0.0242037\pi\) | ||||
−0.997111 | + | 0.0759648i | \(0.975796\pi\) | |||||||
\(878\) | 19138.4i | 0.735638i | ||||||||
\(879\) | 10226.3 | 0.392407 | ||||||||
\(880\) | 4707.60 | + | 458.718i | 0.180333 | + | 0.0175720i | ||||
\(881\) | 25688.1 | 0.982353 | 0.491177 | − | 0.871060i | \(-0.336567\pi\) | ||||
0.491177 | + | 0.871060i | \(0.336567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15521.1i | 0.591537i | 0.955260 | + | 0.295769i | \(0.0955757\pi\) | ||||
−0.955260 | + | 0.295769i | \(0.904424\pi\) | |||||||
\(884\) | −10879.1 | −0.413918 | ||||||||
\(885\) | 1021.07 | − | 10478.7i | 0.0387828 | − | 0.398008i | ||||
\(886\) | 8626.57 | 0.327105 | ||||||||
\(887\) | − | 31100.4i | − | 1.17728i | −0.808395 | − | 0.588641i | \(-0.799663\pi\) | ||
0.808395 | − | 0.588641i | \(-0.200337\pi\) | |||||||
\(888\) | 3660.81i | 0.138343i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −633.940 | + | 6505.81i | −0.0238761 | + | 0.245028i | ||||
\(891\) | −16244.7 | −0.610793 | ||||||||
\(892\) | 18638.0i | 0.699604i | ||||||||
\(893\) | − | 1338.58i | − | 0.0501610i | ||||||
\(894\) | 2840.63 | 0.106269 | ||||||||
\(895\) | −40643.9 | − | 3960.43i | −1.51796 | − | 0.147913i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 70.8913i | 0.00263879i | ||||||||
\(898\) | − | 8793.56i | − | 0.326776i | ||||||
\(899\) | −56312.6 | −2.08913 | ||||||||
\(900\) | −12539.2 | − | 2467.12i | −0.464416 | − | 0.0913749i | ||||
\(901\) | −13325.6 | −0.492720 | ||||||||
\(902\) | 2568.17i | 0.0948013i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10360.2 | 0.381167 | ||||||||
\(905\) | 8534.96 | + | 831.664i | 0.313493 | + | 0.0305475i | ||||
\(906\) | −3565.93 | −0.130762 | ||||||||
\(907\) | − | 15230.5i | − | 0.557577i | −0.960353 | − | 0.278788i | \(-0.910067\pi\) | ||
0.960353 | − | 0.278788i | \(-0.0899328\pi\) | |||||||
\(908\) | − | 14769.2i | − | 0.539794i | ||||||
\(909\) | 20609.2 | 0.751995 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10133.5 | 0.368537 | 0.184269 | − | 0.982876i | \(-0.441008\pi\) | ||||
0.184269 | + | 0.982876i | \(0.441008\pi\) | |||||||
\(912\) | 104.862i | 0.00380738i | ||||||||
\(913\) | − | 16157.3i | − | 0.585684i | ||||||
\(914\) | −16932.5 | −0.612776 | ||||||||
\(915\) | −554.425 | + | 5689.80i | −0.0200314 | + | 0.205572i | ||||
\(916\) | −5817.36 | −0.209837 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 6235.78i | − | 0.224195i | ||||||
\(919\) | 20113.5 | 0.721961 | 0.360981 | − | 0.932573i | \(-0.382442\pi\) | ||||
0.360981 | + | 0.932573i | \(0.382442\pi\) | |||||||
\(920\) | −95.5387 | − | 9.30949i | −0.00342371 | − | 0.000333614i | ||||
\(921\) | 2086.65 | 0.0746550 | ||||||||
\(922\) | − | 2462.29i | − | 0.0879515i | ||||||
\(923\) | 11051.5i | 0.394112i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9199.78 | − | 46758.2i | 0.327013 | − | 1.66205i | ||||
\(926\) | −19547.3 | −0.693698 | ||||||||
\(927\) | − | 38598.2i | − | 1.36756i | ||||||
\(928\) | − | 7877.80i | − | 0.278665i | ||||||
\(929\) | 34940.2 | 1.23396 | 0.616981 | − | 0.786978i | \(-0.288356\pi\) | ||||
0.616981 | + | 0.786978i | \(0.288356\pi\) | |||||||
\(930\) | 6110.49 | + | 595.419i | 0.215453 | + | 0.0209942i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 25610.7i | − | 0.900113i | ||||||
\(933\) | − | 4789.64i | − | 0.168066i | ||||||
\(934\) | −31963.9 | −1.11980 | ||||||||
\(935\) | 1416.92 | − | 14541.1i | 0.0495595 | − | 0.508605i | ||||
\(936\) | −11252.6 | −0.392951 | ||||||||
\(937\) | 6189.72i | 0.215805i | 0.994161 | + | 0.107902i | \(0.0344134\pi\) | ||||
−0.994161 | + | 0.107902i | \(0.965587\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −291.899 | −0.0101446 | ||||||||
\(940\) | 1063.28 | − | 10911.9i | 0.0368940 | − | 0.378625i | ||||
\(941\) | −57065.9 | −1.97694 | −0.988468 | − | 0.151431i | \(-0.951612\pi\) | ||||
−0.988468 | + | 0.151431i | \(0.951612\pi\) | |||||||
\(942\) | − | 564.315i | − | 0.0195184i | ||||||
\(943\) | − | 52.1199i | − | 0.00179985i | ||||||
\(944\) | 12552.5 | 0.432786 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12367.9 | 0.425069 | ||||||||
\(947\) | − | 14701.0i | − | 0.504454i | −0.967668 | − | 0.252227i | \(-0.918837\pi\) | ||
0.967668 | − | 0.252227i | \(-0.0811630\pi\) | |||||||
\(948\) | 909.446i | 0.0311576i | ||||||||
\(949\) | 42838.7 | 1.46533 | ||||||||
\(950\) | 263.523 | − | 1339.36i | 0.00899979 | − | 0.0457417i | ||||
\(951\) | 6395.43 | 0.218072 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27816.6i | 0.945507i | 0.881195 | + | 0.472754i | \(0.156740\pi\) | ||||
−0.881195 | + | 0.472754i | \(0.843260\pi\) | |||||||
\(954\) | −13783.1 | −0.467762 | ||||||||
\(955\) | −3780.57 | − | 368.387i | −0.128101 | − | 0.0124824i | ||||
\(956\) | 4309.69 | 0.145801 | ||||||||
\(957\) | − | 7813.11i | − | 0.263910i | ||||||
\(958\) | 35087.1i | 1.18331i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −83.2956 | + | 854.821i | −0.00280037 | + | 0.0287388i | ||||
\(961\) | 22533.1 | 0.756373 | ||||||||
\(962\) | − | 41960.4i | − | 1.40630i | ||||||
\(963\) | − | 15875.6i | − | 0.531238i | ||||||
\(964\) | −4517.89 | −0.150946 | ||||||||
\(965\) | −2433.59 | + | 24974.7i | −0.0811813 | + | 0.833124i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2846.67i | − | 0.0946668i | −0.998879 | − | 0.0473334i | \(-0.984928\pi\) | ||
0.998879 | − | 0.0473334i | \(-0.0150723\pi\) | |||||||
\(968\) | − | 5055.03i | − | 0.167846i | ||||||
\(969\) | 323.904 | 0.0107382 | ||||||||
\(970\) | −31819.0 | − | 3100.51i | −1.05324 | − | 0.102630i | ||||
\(971\) | 976.436 | 0.0322712 | 0.0161356 | − | 0.999870i | \(-0.494864\pi\) | ||||
0.0161356 | + | 0.999870i | \(0.494864\pi\) | |||||||
\(972\) | − | 9763.18i | − | 0.322175i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −28094.3 | −0.924230 | ||||||||
\(975\) | −8101.57 | − | 1594.00i | −0.266111 | − | 0.0523579i | ||||
\(976\) | −6815.87 | −0.223536 | ||||||||
\(977\) | − | 24202.5i | − | 0.792535i | −0.918135 | − | 0.396267i | \(-0.870305\pi\) | ||
0.918135 | − | 0.396267i | \(-0.129695\pi\) | |||||||
\(978\) | 8436.97i | 0.275853i | ||||||||
\(979\) | −7729.38 | −0.252331 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39433.0 | 1.28338 | ||||||||
\(982\) | − | 12678.6i | − | 0.412007i | ||||||
\(983\) | 47668.7i | 1.54669i | 0.633986 | + | 0.773344i | \(0.281418\pi\) | ||||
−0.633986 | + | 0.773344i | \(0.718582\pi\) | |||||||
\(984\) | −466.337 | −0.0151080 | ||||||||
\(985\) | 2309.72 | − | 23703.5i | 0.0747144 | − | 0.766757i | ||||
\(986\) | −24333.5 | −0.785938 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1201.93i | − | 0.0387030i | ||||||
\(989\) | −251.002 | −0.00807016 | ||||||||
\(990\) | 1465.56 | − | 15040.3i | 0.0470491 | − | 0.482842i | ||||
\(991\) | 25482.3 | 0.816824 | 0.408412 | − | 0.912798i | \(-0.366083\pi\) | ||||
0.408412 | + | 0.912798i | \(0.366083\pi\) | |||||||
\(992\) | 7319.83i | 0.234279i | ||||||||
\(993\) | − | 13819.4i | − | 0.441635i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21292.3 | + | 2074.76i | 0.678402 | + | 0.0661049i | ||||
\(996\) | 2933.90 | 0.0933376 | ||||||||
\(997\) | − | 34022.5i | − | 1.08075i | −0.841425 | − | 0.540373i | \(-0.818283\pi\) | ||
0.841425 | − | 0.540373i | \(-0.181717\pi\) | |||||||
\(998\) | 36746.1i | 1.16551i | ||||||||
\(999\) | 24051.2 | 0.761708 |
(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 | 490.4.c.e.99.4 | 12 | ||
5.2 | odd | 4 | 2450.4.a.cx.1.4 | 6 | |||
5.3 | odd | 4 | 2450.4.a.cw.1.3 | 6 | |||
5.4 | even | 2 | inner | 490.4.c.e.99.9 | 12 | ||
7.3 | odd | 6 | 70.4.i.a.9.9 | yes | 24 | ||
7.5 | odd | 6 | 70.4.i.a.39.4 | yes | 24 | ||
7.6 | odd | 2 | 490.4.c.f.99.3 | 12 | |||
35.3 | even | 12 | 350.4.e.o.51.3 | 12 | |||
35.12 | even | 12 | 350.4.e.n.151.4 | 12 | |||
35.13 | even | 4 | 2450.4.a.cv.1.4 | 6 | |||
35.17 | even | 12 | 350.4.e.n.51.4 | 12 | |||
35.19 | odd | 6 | 70.4.i.a.39.9 | yes | 24 | ||
35.24 | odd | 6 | 70.4.i.a.9.4 | ✓ | 24 | ||
35.27 | even | 4 | 2450.4.a.cy.1.3 | 6 | |||
35.33 | even | 12 | 350.4.e.o.151.3 | 12 | |||
35.34 | odd | 2 | 490.4.c.f.99.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.i.a.9.4 | ✓ | 24 | 35.24 | odd | 6 | ||
70.4.i.a.9.9 | yes | 24 | 7.3 | odd | 6 | ||
70.4.i.a.39.4 | yes | 24 | 7.5 | odd | 6 | ||
70.4.i.a.39.9 | yes | 24 | 35.19 | odd | 6 | ||
350.4.e.n.51.4 | 12 | 35.17 | even | 12 | |||
350.4.e.n.151.4 | 12 | 35.12 | even | 12 | |||
350.4.e.o.51.3 | 12 | 35.3 | even | 12 | |||
350.4.e.o.151.3 | 12 | 35.33 | even | 12 | |||
490.4.c.e.99.4 | 12 | 1.1 | even | 1 | trivial | ||
490.4.c.e.99.9 | 12 | 5.4 | even | 2 | inner | ||
490.4.c.f.99.3 | 12 | 7.6 | odd | 2 | |||
490.4.c.f.99.10 | 12 | 35.34 | odd | 2 | |||
2450.4.a.cv.1.4 | 6 | 35.13 | even | 4 | |||
2450.4.a.cw.1.3 | 6 | 5.3 | odd | 4 | |||
2450.4.a.cx.1.4 | 6 | 5.2 | odd | 4 | |||
2450.4.a.cy.1.3 | 6 | 35.27 | even | 4 |