Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,6,Mod(303,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("608.303");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.b (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: | \(97.5133624463\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 303.69 | ||
Character | \(\chi\) | \(=\) | 608.303 |
Dual form | 608.6.b.b.303.28 |
$q$-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 \(\left(\mathbb{Z}/608\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 14.2121i | 0.911705i | 0.890055 | + | 0.455852i | \(0.150666\pi\) | ||||
−0.890055 | + | 0.455852i | \(0.849334\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 9.24558i | − | 0.165390i | −0.996575 | − | 0.0826949i | \(-0.973647\pi\) | ||
0.996575 | − | 0.0826949i | \(-0.0263527\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 124.323i | − | 0.958975i | −0.877549 | − | 0.479488i | \(-0.840822\pi\) | ||
0.877549 | − | 0.479488i | \(-0.159178\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 41.0170 | 0.168794 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −365.060 | −0.909667 | −0.454834 | − | 0.890576i | \(-0.650301\pi\) | ||||
−0.454834 | + | 0.890576i | \(0.650301\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −366.232 | −0.601032 | −0.300516 | − | 0.953777i | \(-0.597159\pi\) | ||||
−0.300516 | + | 0.953777i | \(0.597159\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 131.399 | 0.150787 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1513.21 | 1.26992 | 0.634960 | − | 0.772545i | \(-0.281017\pi\) | ||||
0.634960 | + | 0.772545i | \(0.281017\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 794.804 | − | 1358.08i | 0.505098 | − | 0.863062i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1766.89 | 0.874303 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2261.20i | 0.891290i | 0.895210 | + | 0.445645i | \(0.147026\pi\) | ||||
−0.895210 | + | 0.445645i | \(0.852974\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3039.52 | 0.972646 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4036.47i | 1.06560i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2188.28 | −0.483178 | −0.241589 | − | 0.970379i | \(-0.577669\pi\) | ||||
−0.241589 | + | 0.970379i | \(0.577669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7701.88 | −1.43944 | −0.719719 | − | 0.694266i | \(-0.755729\pi\) | ||||
−0.719719 | + | 0.694266i | \(0.755729\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5188.26i | − | 0.829348i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1149.44 | −0.158605 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2009.12 | −0.241269 | −0.120635 | − | 0.992697i | \(-0.538493\pi\) | ||||
−0.120635 | + | 0.992697i | \(0.538493\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5204.91i | − | 0.547964i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10836.3i | − | 1.00675i | −0.864068 | − | 0.503375i | \(-0.832091\pi\) | ||
0.864068 | − | 0.503375i | \(-0.167909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6494.00 | −0.535600 | −0.267800 | − | 0.963474i | \(-0.586297\pi\) | ||||
−0.267800 | + | 0.963474i | \(0.586297\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 379.226i | − | 0.0279169i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11509.4i | − | 0.759993i | −0.924988 | − | 0.379997i | \(-0.875925\pi\) | ||
0.924988 | − | 0.379997i | \(-0.124075\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1350.71 | 0.0803660 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21505.8i | 1.15779i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31071.7 | −1.51941 | −0.759705 | − | 0.650268i | \(-0.774657\pi\) | ||||
−0.759705 | + | 0.650268i | \(0.774657\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3375.19i | 0.150450i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19301.2 | + | 11295.8i | 0.786858 | + | 0.460501i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34078.2i | 1.27452i | 0.770648 | + | 0.637261i | \(0.219932\pi\) | ||||
−0.770648 | + | 0.637261i | \(0.780068\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 54487.2i | 1.87487i | 0.348165 | + | 0.937433i | \(0.386805\pi\) | ||||
−0.348165 | + | 0.937433i | \(0.613195\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 5099.37i | − | 0.161870i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3386.03i | 0.0994047i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 40891.1i | − | 1.11286i | −0.830894 | − | 0.556431i | \(-0.812170\pi\) | ||
0.830894 | − | 0.556431i | \(-0.187830\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −32136.3 | −0.812593 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3893.87 | 0.0916719 | 0.0458359 | − | 0.998949i | \(-0.485405\pi\) | ||||
0.0458359 | + | 0.998949i | \(0.485405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −79369.5 | −1.74320 | −0.871598 | − | 0.490221i | \(-0.836916\pi\) | ||||
−0.871598 | + | 0.490221i | \(0.836916\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 43197.9i | 0.886766i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 45385.5i | 0.872349i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −18972.8 | −0.342030 | −0.171015 | − | 0.985268i | \(-0.554705\pi\) | ||||
−0.171015 | + | 0.985268i | \(0.554705\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −47399.5 | −0.802714 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 77330.3 | 1.23212 | 0.616062 | − | 0.787698i | \(-0.288727\pi\) | ||||
0.616062 | + | 0.787698i | \(0.288727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 13990.5i | − | 0.210032i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 31100.0i | − | 0.440516i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 90614.0i | − | 1.21261i | −0.795233 | − | 0.606304i | \(-0.792652\pi\) | ||
0.795233 | − | 0.606304i | \(-0.207348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 45531.2i | 0.576375i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 109460.i | − | 1.31234i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12556.2 | − | 7348.42i | −0.142742 | − | 0.0835382i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 41798.6i | 0.451058i | 0.974236 | + | 0.225529i | \(0.0724110\pi\) | ||||
−0.974236 | + | 0.225529i | \(0.927589\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14973.7 | −0.153547 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 132278.i | − | 1.29028i | −0.764063 | − | 0.645141i | \(-0.776798\pi\) | ||
0.764063 | − | 0.645141i | \(-0.223202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −94980.3 | −0.882146 | −0.441073 | − | 0.897471i | \(-0.645402\pi\) | ||||
−0.441073 | + | 0.897471i | \(0.645402\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 16335.9i | − | 0.144601i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 26503.0i | 0.223787i | 0.993720 | + | 0.111894i | \(0.0356916\pi\) | ||||
−0.993720 | + | 0.111894i | \(0.964308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −189293. | −1.52605 | −0.763026 | − | 0.646368i | \(-0.776287\pi\) | ||||
−0.763026 | + | 0.646368i | \(0.776287\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 28553.8i | − | 0.219966i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2785.22i | − | 0.0205194i | −0.999947 | − | 0.0102597i | \(-0.996734\pi\) | ||
0.999947 | − | 0.0102597i | \(-0.00326582\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20906.1 | 0.147410 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15021.7 | −0.101451 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 188127.i | − | 1.21782i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −27782.1 | −0.172505 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 154006. | 0.917859 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 56994.5i | − | 0.326256i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 256840. | 1.41304 | 0.706518 | − | 0.707695i | \(-0.250265\pi\) | ||||
0.706518 | + | 0.707695i | \(0.250265\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 92293.2i | − | 0.488310i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −243483. | −1.23963 | −0.619814 | − | 0.784749i | \(-0.712792\pi\) | ||||
−0.619814 | + | 0.784749i | \(0.712792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −168841. | − | 98812.7i | −0.827655 | − | 0.484377i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 37319.5 | 0.176239 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −179062. | −0.815082 | −0.407541 | − | 0.913187i | \(-0.633614\pi\) | ||||
−0.407541 | + | 0.913187i | \(0.633614\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 199170. | 0.874351 | 0.437176 | − | 0.899376i | \(-0.355979\pi\) | ||||
0.437176 | + | 0.899376i | \(0.355979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 163573. | 0.692890 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 133697. | 0.546740 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20231.9i | 0.0799128i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19196.4i | 0.0732701i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 54501.3i | − | 0.201114i | −0.994931 | − | 0.100557i | \(-0.967938\pi\) | ||
0.994931 | − | 0.100557i | \(-0.0320624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 121160. | 0.432432 | 0.216216 | − | 0.976346i | \(-0.430628\pi\) | ||||
0.216216 | + | 0.976346i | \(0.430628\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 62067.2 | 0.214355 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 71208.3i | 0.238068i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 471348.i | − | 1.52613i | −0.646320 | − | 0.763067i | \(-0.723693\pi\) | ||
0.646320 | − | 0.763067i | \(-0.276307\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 441593.i | − | 1.38525i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 281120. | 0.854725 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −502273. | −1.48071 | −0.740356 | − | 0.672215i | \(-0.765343\pi\) | ||||
−0.740356 | + | 0.672215i | \(0.765343\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −47968.5 | −0.137166 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −373307. | −1.03580 | −0.517898 | − | 0.855442i | \(-0.673285\pi\) | ||||
−0.517898 | + | 0.855442i | \(0.673285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −237167. | −0.638760 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 32600.5 | − | 55704.4i | 0.0852577 | − | 0.145680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −365898. | −0.929491 | −0.464745 | − | 0.885444i | \(-0.653854\pi\) | ||||
−0.464745 | + | 0.885444i | \(0.653854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 377883.i | − | 0.932744i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −484322. | −1.16199 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 156783.i | 0.365735i | 0.983138 | + | 0.182867i | \(0.0585379\pi\) | ||||
−0.983138 | + | 0.182867i | \(0.941462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 391539. | 0.888339 | 0.444169 | − | 0.895943i | \(-0.353499\pi\) | ||||
0.444169 | + | 0.895943i | \(0.353499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −774377. | −1.70932 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18575.5i | 0.0399035i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −552412. | −1.15520 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 501827. | 1.02188 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 559199.i | − | 1.10913i | −0.832140 | − | 0.554566i | \(-0.812884\pi\) | ||
0.832140 | − | 0.554566i | \(-0.187116\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 36191.3i | 0.0699377i | 0.999388 | + | 0.0349688i | \(0.0111332\pi\) | ||||
−0.999388 | + | 0.0349688i | \(0.988867\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −48122.4 | −0.0906277 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 616594.i | − | 1.13197i | −0.824417 | − | 0.565983i | \(-0.808497\pi\) | ||
0.824417 | − | 0.565983i | \(-0.191503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 155213.i | − | 0.277840i | −0.990304 | − | 0.138920i | \(-0.955637\pi\) | ||
0.990304 | − | 0.138920i | \(-0.0443631\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 581147. | 1.01460 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 272054.i | 0.463356i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −100188. | −0.166506 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 92747.5i | 0.150445i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −290151. | + | 495781.i | −0.459472 | + | 0.785099i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 339665.i | − | 0.525225i | −0.964901 | − | 0.262612i | \(-0.915416\pi\) | ||
0.964901 | − | 0.262612i | \(-0.0845840\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 55340.0i | 0.0835777i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 60040.7i | 0.0885829i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 957524.i | 1.38038i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1.12800e6i | − | 1.58928i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −554185. | −0.763263 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.08038e6 | −1.45483 | −0.727415 | − | 0.686198i | \(-0.759279\pi\) | ||||
−0.727415 | + | 0.686198i | \(0.759279\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 124672. | 0.164177 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 105829.i | − | 0.136314i | −0.997675 | − | 0.0681569i | \(-0.978288\pi\) | ||
0.997675 | − | 0.0681569i | \(-0.0217119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 285269.i | − | 0.359473i | −0.983715 | − | 0.179736i | \(-0.942475\pi\) | ||
0.983715 | − | 0.179736i | \(-0.0575245\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −645022. | −0.795325 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 981311. | 1.18418 | 0.592089 | − | 0.805873i | \(-0.298303\pi\) | ||||
0.592089 | + | 0.805873i | \(0.298303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −106411. | −0.125695 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 269643.i | − | 0.311831i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.21758e6i | − | 1.37881i | −0.724377 | − | 0.689404i | \(-0.757873\pi\) | ||
0.724377 | − | 0.689404i | \(-0.242127\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 696863.i | − | 0.772867i | −0.922317 | − | 0.386434i | \(-0.873707\pi\) | ||
0.922317 | − | 0.386434i | \(-0.126293\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 307217.i | 0.333757i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 12488.1i | − | 0.0132917i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −291083. | + | 497373.i | −0.303580 | + | 0.518728i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.09902e6i | 1.12333i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −567572. | −0.568639 | −0.284319 | − | 0.958730i | \(-0.591768\pi\) | ||||
−0.284319 | + | 0.958730i | \(0.591768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 825473.i | − | 0.810777i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 198834. | 0.191487 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 172685.i | − | 0.163088i | −0.996670 | − | 0.0815441i | \(-0.974015\pi\) | ||
0.996670 | − | 0.0815441i | \(-0.0259851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 249781.i | 0.231371i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −89756.6 | −0.0815577 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 678009.i | − | 0.604430i | −0.953240 | − | 0.302215i | \(-0.902274\pi\) | ||
0.953240 | − | 0.302215i | \(-0.0977261\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 287276.i | 0.251295i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.28781e6 | 1.10554 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.02017e6 | −0.859591 | −0.429796 | − | 0.902926i | \(-0.641414\pi\) | ||||
−0.429796 | + | 0.902926i | \(0.641414\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.30195e6i | 1.90403i | 0.306055 | + | 0.952014i | \(0.400991\pi\) | ||||
−0.306055 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −647092. | −0.525484 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.10961e6 | −0.884785 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 608040.i | 0.476138i | 0.971248 | + | 0.238069i | \(0.0765145\pi\) | ||||
−0.971248 | + | 0.238069i | \(0.923486\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −315908. | −0.242969 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 49508.2i | 0.0374034i | 0.999825 | + | 0.0187017i | \(0.00595328\pi\) | ||||
−0.999825 | + | 0.0187017i | \(0.994047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 300557. | 0.223080 | 0.111540 | − | 0.993760i | \(-0.464422\pi\) | ||||
0.111540 | + | 0.993760i | \(0.464422\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 104436. | − | 178450.i | 0.0761621 | − | 0.130138i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.34721e6 | −0.965449 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 869939. | 0.612695 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −594044. | −0.411232 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.81073e6 | −1.23221 | −0.616104 | − | 0.787664i | \(-0.711290\pi\) | ||||
−0.616104 | + | 0.787664i | \(0.711290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 315073. | 0.210793 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.47355e6i | − | 0.969337i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 828123.i | − | 0.535694i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 807355.i | 0.513628i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.87995e6 | 1.17636 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 503766. | 0.310084 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.34882e6i | 1.42234i | 0.703018 | + | 0.711172i | \(0.251835\pi\) | ||||
−0.703018 | + | 0.711172i | \(0.748165\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.34987e6i | − | 0.804256i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.13408e6i | 1.83743i | 0.394926 | + | 0.918713i | \(0.370770\pi\) | ||||
−0.394926 | + | 0.918713i | \(0.629230\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.28638e6 | −1.31913 | −0.659565 | − | 0.751648i | \(-0.729259\pi\) | ||||
−0.659565 | + | 0.751648i | \(0.729259\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −47146.6 | −0.0267716 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 96347.3 | 0.0538507 | 0.0269254 | − | 0.999637i | \(-0.491428\pi\) | ||||
0.0269254 | + | 0.999637i | \(0.491428\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 798853. | 0.439532 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −376662. | −0.204028 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.20270e6 | − | 2.05506e6i | 0.641434 | − | 1.09602i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.11317e6 | −0.584592 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.69025e6i | − | 1.39131i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.43089e6 | −0.728815 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 601438.i | 0.301731i | 0.988554 | + | 0.150866i | \(0.0482061\pi\) | ||||
−0.988554 | + | 0.150866i | \(0.951794\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −82408.1 | −0.0407249 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −378062. | −0.184056 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.82139e6i | 1.83294i | 0.400109 | + | 0.916468i | \(0.368972\pi\) | ||||
−0.400109 | + | 0.916468i | \(0.631028\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 39583.8 | 0.0187076 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.81165e6 | 1.30941 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.25743e6i | − | 1.03604i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 297119.i | 0.134395i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.55563e6 | 0.693556 | 0.346778 | − | 0.937947i | \(-0.387276\pi\) | ||||
0.346778 | + | 0.937947i | \(0.387276\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.01085e6i | − | 0.444246i | −0.975019 | − | 0.222123i | \(-0.928701\pi\) | ||
0.975019 | − | 0.222123i | \(-0.0712987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.47828e6i | − | 0.640457i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.24723e6 | 0.532731 | 0.266366 | − | 0.963872i | \(-0.414177\pi\) | ||||
0.266366 | + | 0.963872i | \(0.414177\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 36001.1i | − | 0.0151616i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.67367e6 | 1.11029 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.07100e6i | 0.438584i | 0.975659 | + | 0.219292i | \(0.0703747\pi\) | ||||
−0.975659 | + | 0.219292i | \(0.929625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.21267e6 | − | 2.15882e6i | −0.489751 | − | 0.871862i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 394842.i | − | 0.157274i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 733816.i | 0.288307i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.89160e6i | 1.12066i | 0.828270 | + | 0.560329i | \(0.189325\pi\) | ||||
−0.828270 | + | 0.560329i | \(0.810675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 444473.i | − | 0.169934i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.86294e6i | 1.45708i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.47047e6 | −0.547247 | −0.273624 | − | 0.961837i | \(-0.588222\pi\) | ||||
−0.273624 | + | 0.961837i | \(0.588222\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 810010. | 0.297449 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 801417. | 0.290406 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.89549e6i | − | 0.677833i | −0.940816 | − | 0.338917i | \(-0.889940\pi\) | ||
0.940816 | − | 0.338917i | \(-0.110060\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.65023e6i | 1.28827i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.50444e6 | 1.22073 | 0.610367 | − | 0.792119i | \(-0.291022\pi\) | ||||
0.610367 | + | 0.792119i | \(0.291022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 419615. | 0.144278 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −266364. | −0.0904063 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.31747e6i | 1.44662i | 0.690523 | + | 0.723311i | \(0.257381\pi\) | ||||
−0.690523 | + | 0.723311i | \(0.742619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.42166e6i | 1.13187i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.46041e6i | − | 1.13017i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 175415.i | 0.0565684i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 391751.i | − | 0.124748i | −0.998053 | − | 0.0623740i | \(-0.980133\pi\) | ||
0.998053 | − | 0.0623740i | \(-0.0198671\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.40433e6 | − | 2.39958e6i | 0.441609 | − | 0.754577i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.15441e6i | − | 1.60073i | −0.599514 | − | 0.800364i | \(-0.704639\pi\) | ||
0.599514 | − | 0.800364i | \(-0.295361\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.82068e6 | 0.865148 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 438235.i | 0.132761i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 733450. | 0.219475 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.89993e6i | − | 1.44838i | −0.689602 | − | 0.724189i | \(-0.742214\pi\) | ||
0.689602 | − | 0.724189i | \(-0.257786\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.54484e6i | − | 0.743114i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.23672e6 | 1.22223 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 714963.i | − | 0.203781i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.83061e6i | 0.797150i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.28386e6 | −1.19207 | −0.596033 | − | 0.802960i | \(-0.703257\pi\) | ||||
−0.596033 | + | 0.802960i | \(0.703257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.52522e6 | 0.694375 | 0.347188 | − | 0.937796i | \(-0.387137\pi\) | ||||
0.347188 | + | 0.937796i | \(0.387137\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 472083.i | − | 0.128282i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.59942e6 | 1.23518 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.77404e6 | 1.79795 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.90011e6i | 0.498465i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.42046e6 | −0.368328 | −0.184164 | − | 0.982896i | \(-0.558958\pi\) | ||||
−0.184164 | + | 0.982896i | \(0.558958\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 178506.i | − | 0.0457543i | −0.999738 | − | 0.0228772i | \(-0.992717\pi\) | ||
0.999738 | − | 0.0228772i | \(-0.00728266\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −287537. | −0.0728569 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.07089e6 | + | 1.79721e6i | 0.769238 | + | 0.450189i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.49147e6 | 1.60761 | 0.803807 | − | 0.594891i | \(-0.202805\pi\) | ||||
0.803807 | + | 0.594891i | \(0.202805\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 55402.1 | 0.0135653 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.04834e6 | 0.253800 | 0.126900 | − | 0.991915i | \(-0.459497\pi\) | ||||
0.126900 | + | 0.991915i | \(0.459497\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −837779. | −0.200553 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 774577. | 0.183356 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.14659e6i | 0.268407i | 0.990954 | + | 0.134203i | \(0.0428476\pi\) | ||||
−0.990954 | + | 0.134203i | \(0.957152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.95590e6i | 0.915808i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.72194e6i | 0.394251i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 420962. | 0.0953266 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.64223e6 | −0.815786 | −0.407893 | − | 0.913030i | \(-0.633736\pi\) | ||||
−0.407893 | + | 0.913030i | \(0.633736\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.10802e6i | 1.35322i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.78881e6i | 0.611177i | 0.952164 | + | 0.305589i | \(0.0988533\pi\) | ||||
−0.952164 | + | 0.305589i | \(0.901147\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.15763e6i | − | 0.250968i | −0.992096 | − | 0.125484i | \(-0.959952\pi\) | ||
0.992096 | − | 0.125484i | \(-0.0400483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.01202e6 | −0.217048 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.45656e6 | −1.15778 | −0.578891 | − | 0.815405i | \(-0.696514\pi\) | ||||
−0.578891 | + | 0.815405i | \(0.696514\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.08371e6 | −1.06721 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.69883e6 | 1.39138 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.37070e6 | 0.487218 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.41582e6 | − | 4.12792e6i | 0.491282 | − | 0.839454i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.27447e6 | −0.256468 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.48505e6i | 0.893157i | 0.894744 | + | 0.446579i | \(0.147358\pi\) | ||||
−0.894744 | + | 0.446579i | \(0.852642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 735805. | 0.145011 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.99529e6i | 0.779257i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 386452. | 0.0746004 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.10015e6 | −0.592326 | −0.296163 | − | 0.955137i | \(-0.595707\pi\) | ||||
−0.296163 | + | 0.955137i | \(0.595707\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.13834e6i | − | 1.34997i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.43332e6 | −0.268312 | −0.134156 | − | 0.990960i | \(-0.542832\pi\) | ||||
−0.134156 | + | 0.990960i | \(0.542832\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.31132e6 | −0.613597 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 138440.i | 0.0253951i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 484099.i | − | 0.0879111i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.39259e6 | −0.609930 | −0.304965 | − | 0.952364i | \(-0.598645\pi\) | ||||
−0.304965 | + | 0.952364i | \(0.598645\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 5.30546e6i | − | 0.944341i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.68066e6i | 1.00110i | 0.865707 | + | 0.500552i | \(0.166869\pi\) | ||||
−0.865707 | + | 0.500552i | \(0.833131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.22299e6 | −0.213400 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3.37064e6i | − | 0.582361i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.22322e6 | 0.551436 | 0.275718 | − | 0.961239i | \(-0.411084\pi\) | ||||
0.275718 | + | 0.961239i | \(0.411084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.86747e6i | 1.67168i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.48186e6 | + | 3.20820e6i | 0.919675 | + | 0.538230i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 878147.i | 0.145898i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.20164e6i | 0.691341i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 5.20017e6i | − | 0.847421i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.11994e7i | 1.80759i | 0.427962 | + | 0.903797i | \(0.359232\pi\) | ||||
−0.427962 | + | 0.903797i | \(0.640768\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.39158e6i | − | 0.382323i | −0.981559 | − | 0.191161i | \(-0.938775\pi\) | ||
0.981559 | − | 0.191161i | \(-0.0612254\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.37050e6 | 0.850387 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.16545e7 | −1.82797 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.32333e6 | 0.205603 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.39779e6i | 0.215132i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.96860e6i | 0.605089i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 245035. | 0.0370121 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.22821e6 | −0.333442 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −493091. | −0.0731063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.07981e6i | 0.746198i | 0.927792 | + | 0.373099i | \(0.121705\pi\) | ||||
−0.927792 | + | 0.373099i | \(0.878295\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.56458e6i | 0.809903i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.75013e6i | 0.252394i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.98971e6i | − | 0.713028i | −0.934290 | − | 0.356514i | \(-0.883965\pi\) | ||
0.934290 | − | 0.356514i | \(-0.116035\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.23490e6i | 0.316467i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.73925e6 | + | 2.97186e6i | −0.244053 | + | 0.417013i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.35877e6i | 0.327999i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −263996. | −0.0363802 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4.63835e6i | − | 0.633469i | −0.948514 | − | 0.316735i | \(-0.897414\pi\) | ||
0.948514 | − | 0.316735i | \(-0.102586\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.37831e6 | 0.321913 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 7.85091e6i | − | 1.05321i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.49382e7i | − | 1.98622i | −0.117175 | − | 0.993111i | \(-0.537384\pi\) | ||
0.117175 | − | 0.993111i | \(-0.462616\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25751.0 | −0.00339370 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.89286e6i | 0.769783i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.32859e7i | 1.72033i | 0.510017 | + | 0.860164i | \(0.329639\pi\) | ||||
−0.510017 | + | 0.860164i | \(0.670361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.39535e6 | 1.20593 | 0.602966 | − | 0.797767i | \(-0.293986\pi\) | ||||
0.602966 | + | 0.797767i | \(0.293986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.94738e6 | 1.01120 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.87295e6i | 0.866909i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −837200. | −0.104686 | −0.0523431 | − | 0.998629i | \(-0.516669\pi\) | ||||
−0.0523431 | + | 0.998629i | \(0.516669\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −514354. | −0.0637625 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 9.61395e6i | − | 1.18158i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.13430e7 | 1.38216 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 138885.i | 0.0167789i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.77948e6 | 0.452727 | 0.226364 | − | 0.974043i | \(-0.427316\pi\) | ||||
0.226364 | + | 0.974043i | \(0.427316\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.12149e6 | + | 1.04598e7i | −0.727057 | + | 1.24232i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.76308e6 | 1.03202 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.96912e6 | −0.697065 | −0.348532 | − | 0.937297i | \(-0.613320\pi\) | ||||
−0.348532 | + | 0.937297i | \(0.613320\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.73934e6 | −0.201415 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.20589e6 | 0.253308 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.72710e7 | −1.96675 | −0.983376 | − | 0.181581i | \(-0.941879\pi\) | ||||
−0.983376 | + | 0.181581i | \(0.941879\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.08241e6i | 0.348100i | 0.984737 | + | 0.174050i | \(0.0556854\pi\) | ||||
−0.984737 | + | 0.174050i | \(0.944315\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.67723e6i | − | 0.187845i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 256862.i | 0.0285306i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.07721e7 | −1.18667 | −0.593334 | − | 0.804957i | \(-0.702189\pi\) | ||||
−0.593334 | + | 0.804957i | \(0.702189\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.86645e6 | −0.422444 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.21513e6i | 0.456781i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.17483e6i | − | 0.341248i | −0.985336 | − | 0.170624i | \(-0.945422\pi\) | ||
0.985336 | − | 0.170624i | \(-0.0545783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1.42388e6i | − | 0.151805i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.57680e6 | 0.378253 | 0.189126 | − | 0.981953i | \(-0.439434\pi\) | ||||
0.189126 | + | 0.981953i | \(0.439434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.81270e7 | 1.90151 | 0.950757 | − | 0.309937i | \(-0.100308\pi\) | ||||
0.950757 | + | 0.309937i | \(0.100308\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.12726e6 | −0.949754 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.12654e7 | −1.16286 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.97155e6 | 0.918687 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.04608e6 | − | 4.12365e6i | −0.715779 | − | 0.418902i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.04022e6 | −0.306392 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.80712e6i | − | 0.580614i | −0.956934 | − | 0.290307i | \(-0.906243\pi\) | ||
0.956934 | − | 0.290307i | \(-0.0937574\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.82735e6 | 0.478850 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 2.37463e6i | − | 0.233702i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −494674. | −0.0483026 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 159715. | 0.0154737 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.04768e7i | 1.00712i | 0.863960 | + | 0.503560i | \(0.167977\pi\) | ||||
−0.863960 | + | 0.503560i | \(0.832023\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.09642e6 | 0.295347 | 0.147674 | − | 0.989036i | \(-0.452821\pi\) | ||||
0.147674 | + | 0.989036i | \(0.452821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −853303. | −0.0807615 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.31465e6i | − | 0.593046i | −0.955026 | − | 0.296523i | \(-0.904173\pi\) | ||
0.955026 | − | 0.296523i | \(-0.0958271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.24406e7i | − | 1.15939i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.36084e7 | −1.25850 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 9.24440e6i | − | 0.848390i | −0.905571 | − | 0.424195i | \(-0.860557\pi\) | ||
0.905571 | − | 0.424195i | \(-0.139443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.25115e6i | 0.205022i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.25550e6 | −0.294241 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.03128e6i | 0.182203i | 0.995842 | + | 0.0911015i | \(0.0290388\pi\) | ||||
−0.995842 | + | 0.0911015i | \(0.970961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.84907e6 | 0.698738 | 0.349369 | − | 0.936985i | \(-0.386396\pi\) | ||||
0.349369 | + | 0.936985i | \(0.386396\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 7.87612e6i | − | 0.695870i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −913580. | + | 1.56103e6i | −0.0801110 | + | 0.136886i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.94813e6i | − | 0.430652i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.53544e7i | − | 1.32638i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.98911e7i | − | 1.70550i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.23851e7i | 1.05405i | 0.849850 | + | 0.527025i | \(0.176693\pi\) | ||||
−0.849850 | + | 0.527025i | \(0.823307\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.22689e7i | 1.03645i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.80364e6 | −0.402808 | −0.201404 | − | 0.979508i | \(-0.564550\pi\) | ||||
−0.201404 | + | 0.979508i | \(0.564550\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.19654e6 | 0.432553 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50405e6 | 0.124278 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.17375e7i | − | 0.962769i | −0.876510 | − | 0.481384i | \(-0.840134\pi\) | ||
0.876510 | − | 0.481384i | \(-0.159866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.65553e6i | 0.134806i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.05427e6 | 0.327733 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.13794e7 | 0.913215 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.58528e7 | −1.26302 | −0.631512 | − | 0.775366i | \(-0.717565\pi\) | ||||
−0.631512 | + | 0.775366i | \(0.717565\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.86158e6i | 0.147247i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.84144e6i | − | 0.144609i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.63976e7i | − | 1.27849i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.39465e7i | 1.07962i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.17197e6i | − | 0.474382i | −0.971463 | − | 0.237191i | \(-0.923773\pi\) | ||
0.971463 | − | 0.237191i | \(-0.0762268\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.59686e6 | + | 2.72855e6i | −0.121865 | + | 0.208230i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 1.51233e6i | − | 0.114597i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.64453e7 | −1.23735 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.38638e7i | 1.03577i | 0.855449 | + | 0.517887i | \(0.173281\pi\) | ||||
−0.855449 | + | 0.517887i | \(0.826719\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −778209. | −0.0577327 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.74155e7i | − | 1.28296i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.23610e6i | − | 0.0904252i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.73044e7 | 1.25707 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.32215e7i | − | 0.953804i | −0.878956 | − | 0.476902i | \(-0.841760\pi\) | ||
0.878956 | − | 0.476902i | \(-0.158240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.18083e7i | 0.845956i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.90387e6 | 0.704627 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.65131e6 | −0.469962 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.08625e7i | 0.762242i | 0.924525 | + | 0.381121i | \(0.124462\pi\) | ||||
−0.924525 | + | 0.381121i | \(0.875538\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.58843e7 | −1.10700 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.82676e6 | −0.680169 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 5.85557e6i | − | 0.402540i | −0.979536 | − | 0.201270i | \(-0.935493\pi\) | ||
0.979536 | − | 0.201270i | \(-0.0645069\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 177482. | 0.0121181 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.49277e7i | 1.01233i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.67168e7 | −1.12601 | −0.563005 | − | 0.826453i | \(-0.690355\pi\) | ||||
−0.563005 | + | 0.826453i | \(0.690355\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.06870e6 | − | 4.13689e6i | −0.472927 | − | 0.276776i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.07962e6 | 0.337566 | 0.168783 | − | 0.985653i | \(-0.446016\pi\) | ||||
0.168783 | + | 0.985653i | \(0.446016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −503896. | −0.0332621 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.17185e6 | 0.207975 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.29494e6 | 0.214606 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.62925e6 | 0.428908 | 0.214454 | − | 0.976734i | \(-0.431203\pi\) | ||||
0.214454 | + | 0.976734i | \(0.431203\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 8.06637e6i | − | 0.518431i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.12020e6i | − | 0.0715199i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.78443e7i | − | 1.13177i | −0.824483 | − | 0.565887i | \(-0.808534\pi\) | ||
0.824483 | − | 0.565887i | \(-0.191466\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.17317e7 | 0.739190 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.27818e6 | −0.330387 | −0.165193 | − | 0.986261i | \(-0.552825\pi\) | ||||
−0.165193 | + | 0.986261i | \(0.552825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.35336e7i | 1.46345i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 573847.i | − | 0.0354522i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.24805e7i | − | 0.766028i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.13899e7 | 0.694549 | 0.347275 | − | 0.937763i | \(-0.387107\pi\) | ||||
0.347275 | + | 0.937763i | \(0.387107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.45422e6 | 0.148688 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.00043e6 | 0.120414 | 0.0602068 | − | 0.998186i | \(-0.480824\pi\) | ||||
0.0602068 | + | 0.998186i | \(0.480824\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.34100e7 | −1.40006 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.54990e6 | −0.210942 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.47166e7 | − | 8.61274e6i | −0.868888 | − | 0.508508i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.42150e6 | −0.0833909 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 8.83292e6i | − | 0.514873i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.35788e6 | −0.252407 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.23690e6i | 0.358948i | 0.983763 | + | 0.179474i | \(0.0574397\pi\) | ||||
−0.983763 | + | 0.179474i | \(0.942560\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.63591e6 | 0.551062 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −346268. | −0.0196776 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.99550e7i | − | 1.12686i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.08278e6 | −0.229107 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.80871e6 | −0.546973 | −0.273487 | − | 0.961876i | \(-0.588177\pi\) | ||||
−0.273487 | + | 0.961876i | \(0.588177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.74162e7i | − | 0.965130i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.71671e6i | − | 0.204681i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.89746e7 | 1.58573 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 2.59911e6i | − | 0.141363i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.44987e7i | − | 0.783693i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.57251e7 | −0.844738 | −0.422369 | − | 0.906424i | \(-0.638801\pi\) | ||||
−0.422369 | + | 0.906424i | \(0.638801\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.29338e6i | 0.335994i | 0.985788 | + | 0.167997i | \(0.0537299\pi\) | ||||
−0.985788 | + | 0.167997i | \(0.946270\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.27155e7 | −1.73591 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.64380e6i | 0.244895i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.16145e6 | + | 8.81938e6i | −0.270531 | + | 0.462256i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.86755e6i | 0.0972888i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.12117e7i | − | 1.09829i | −0.835726 | − | 0.549146i | \(-0.814953\pi\) | ||
0.835726 | − | 0.549146i | \(-0.185047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.52175e7i | − | 0.783146i | −0.920147 | − | 0.391573i | \(-0.871931\pi\) | ||
0.920147 | − | 0.391573i | \(-0.128069\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.57698e7i | − | 0.806662i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.76448e6i | 0.242243i | 0.992638 | + | 0.121122i | \(0.0386491\pi\) | ||||
−0.992638 | + | 0.121122i | \(0.961351\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.38161e7 | 1.20361 | 0.601804 | − | 0.798644i | \(-0.294449\pi\) | ||||
0.601804 | + | 0.798644i | \(0.294449\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.64151e6 | −0.434097 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.04391e6 | 0.102058 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.45144e6i | 0.171310i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3.10884e7i | − | 1.53386i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.66134e7 | −0.814805 | −0.407402 | − | 0.913249i | \(-0.633565\pi\) | ||||
−0.407402 | + | 0.913249i | \(0.633565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.57226e7 | −0.766539 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −703614. | −0.0341009 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.19275e6i | 0.105644i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.45397e6i | 0.165428i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.27153e6i | 0.203383i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.54302e6i | − | 0.215041i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.11169e7i | 1.46428i | 0.681155 | + | 0.732139i | \(0.261478\pi\) | ||||
−0.681155 | + | 0.732139i | \(0.738522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −515019. | − | 301410.i | −0.0240940 | − | 0.0141008i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.33524e7i | 1.08612i | 0.839692 | + | 0.543062i | \(0.182735\pi\) | ||||
−0.839692 | + | 0.543062i | \(0.817265\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.80191e6 | 0.407000 | 0.203500 | − | 0.979075i | \(-0.434768\pi\) | ||||
0.203500 | + | 0.979075i | \(0.434768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 1.91466e7i | − | 0.880204i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.16374e7 | 1.90308 | 0.951539 | − | 0.307530i | \(-0.0995023\pi\) | ||||
0.951539 | + | 0.307530i | \(0.0995023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.38294e6i | 0.153728i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.23636e7i | 0.558597i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.92623e6 | 0.311134 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.49756e7i | 0.668866i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.71445e6i | 0.0761359i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.08575e6 | −0.312871 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.62664e7 | −1.15319 | −0.576597 | − | 0.817029i | \(-0.695620\pi\) | ||||
−0.576597 | + | 0.817029i | \(0.695620\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2.57342e7i | − | 1.12341i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.51136e6 | 0.152418 | 0.0762088 | − | 0.997092i | \(-0.475718\pi\) | ||||
0.0762088 | + | 0.997092i | \(0.475718\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.99212e7 | 1.72307 | 0.861533 | − | 0.507702i | \(-0.169505\pi\) | ||||
0.861533 | + | 0.507702i | \(0.169505\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.47784e6i | 0.192181i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.51954e7 | −0.648492 | −0.324246 | − | 0.945973i | \(-0.605111\pi\) | ||||
−0.324246 | + | 0.945973i | \(0.605111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.19312e7i | − | 1.35507i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.73037e7 | 0.730203 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.56308e7 | − | 9.14775e6i | −0.655921 | − | 0.383871i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.44955e6 | 0.0604888 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.17693e7 | 0.488395 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.68539e7 | 0.695505 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.70179e7 | −1.92953 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.14742e7 | −0.468277 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 3.62000e6i | − | 0.146922i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.67286e6i | − | 0.0675215i | −0.999430 | − | 0.0337607i | \(-0.989252\pi\) | ||
0.999430 | − | 0.0337607i | \(-0.0107484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 5.42565e6i | − | 0.217792i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.59483e6 | 0.183431 | 0.0917156 | − | 0.995785i | \(-0.470765\pi\) | ||||
0.0917156 | + | 0.995785i | \(0.470765\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.82302e7 | −1.12082 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.15956e6i | 0.282705i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.02707e7i | 1.18877i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.90980e7i | − | 1.52709i | −0.645752 | − | 0.763547i | \(-0.723456\pi\) | ||
0.645752 | − | 0.763547i | \(-0.276544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.33817e7 | −1.29676 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.42606e6 | −0.0550977 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.10676e6 | −0.234670 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.89580e6 | −0.148901 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.09135e7 | 0.414881 | 0.207440 | − | 0.978248i | \(-0.433487\pi\) | ||||
0.207440 | + | 0.978248i | \(0.433487\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.07355e6 | − | 1.83438e6i | 0.0405927 | − | 0.0693608i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.45418e7 | −1.67519 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.10736e6i | 0.191059i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.77150e7 | −1.03126 | −0.515628 | − | 0.856813i | \(-0.672441\pi\) | ||||
−0.515628 | + | 0.856813i | \(0.672441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 3.24942e7i | − | 1.20266i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.89140e6 | −0.216893 | −0.108446 | − | 0.994102i | \(-0.534588\pi\) | ||||
−0.108446 | + | 0.994102i | \(0.534588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.45030e7 | 0.897306 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 4.63968e6i | − | 0.169009i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.18149e6 | 0.0428111 | 0.0214055 | − | 0.999771i | \(-0.493186\pi\) | ||||
0.0214055 | + | 0.999771i | \(0.493186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.90676e7 | 1.04772 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.36929e6i | 0.0490960i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.68084e7i | − | 0.599508i | −0.954017 | − | 0.299754i | \(-0.903095\pi\) | ||
0.954017 | − | 0.299754i | \(-0.0969046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.17012e6 | −0.183439 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.13534e7i | 0.400723i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.22616e7i | 0.781644i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.06898e7 | 1.07198 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.08707e6i | 0.0377740i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 334610. | 0.0115670 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.47806e7i | 1.54001i | 0.638037 | + | 0.770006i | \(0.279747\pi\) | ||||
−0.638037 | + | 0.770006i | \(0.720253\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.92066e7 | + | 1.70929e7i | 0.999246 | + | 0.584799i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.12614e7i | − | 1.40441i | −0.711972 | − | 0.702207i | \(-0.752198\pi\) | ||
0.711972 | − | 0.702207i | \(-0.247802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.47614e7i | − | 0.838481i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1.58204e7i | − | 0.532975i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.25883e7i | 1.76260i | 0.472560 | + | 0.881299i | \(0.343330\pi\) | ||||
−0.472560 | + | 0.881299i | \(0.656670\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.30796e7i | 1.10307i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.76425e6 | −0.257589 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.31566e7 | −0.764347 | −0.382173 | − | 0.924091i | \(-0.624824\pi\) | ||||
−0.382173 | + | 0.924091i | \(0.624824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.70076e6 | −0.187216 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2.03360e7i | − | 0.664464i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.46842e7i | − | 0.477375i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.99104e7 | −0.967472 | −0.483736 | − | 0.875214i | \(-0.660721\pi\) | ||||
−0.483736 | + | 0.875214i | \(0.660721\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.54768e6 | −0.275090 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.43503e6 | −0.0459519 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.73919e7i | 1.82858i | 0.405065 | + | 0.914288i | \(0.367249\pi\) | ||||
−0.405065 | + | 0.914288i | \(0.632751\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 8.10976e6i | − | 0.257095i |
(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 | 608.6.b.b.303.69 | 96 | ||
4.3 | odd | 2 | 152.6.b.b.75.86 | yes | 96 | ||
8.3 | odd | 2 | inner | 608.6.b.b.303.70 | 96 | ||
8.5 | even | 2 | 152.6.b.b.75.12 | yes | 96 | ||
19.18 | odd | 2 | inner | 608.6.b.b.303.27 | 96 | ||
76.75 | even | 2 | 152.6.b.b.75.11 | ✓ | 96 | ||
152.37 | odd | 2 | 152.6.b.b.75.85 | yes | 96 | ||
152.75 | even | 2 | inner | 608.6.b.b.303.28 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.6.b.b.75.11 | ✓ | 96 | 76.75 | even | 2 | ||
152.6.b.b.75.12 | yes | 96 | 8.5 | even | 2 | ||
152.6.b.b.75.85 | yes | 96 | 152.37 | odd | 2 | ||
152.6.b.b.75.86 | yes | 96 | 4.3 | odd | 2 | ||
608.6.b.b.303.27 | 96 | 19.18 | odd | 2 | inner | ||
608.6.b.b.303.28 | 96 | 152.75 | even | 2 | inner | ||
608.6.b.b.303.69 | 96 | 1.1 | even | 1 | trivial | ||
608.6.b.b.303.70 | 96 | 8.3 | odd | 2 | inner |