Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,5,Mod(91,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.91");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.d (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: | \(23.7750915093\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.10 | ||
Character | \(\chi\) | \(=\) | 230.91 |
Dual form | 230.5.d.a.91.7 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82843 | −0.707107 | ||||||||
\(3\) | 0.828614 | 0.0920682 | 0.0460341 | − | 0.998940i | \(-0.485342\pi\) | ||||
0.0460341 | + | 0.998940i | \(0.485342\pi\) | |||||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | 11.1803i | 0.447214i | ||||||||
\(6\) | −2.34367 | −0.0651021 | ||||||||
\(7\) | − | 16.9191i | − | 0.345288i | −0.984984 | − | 0.172644i | \(-0.944769\pi\) | ||
0.984984 | − | 0.172644i | \(-0.0552310\pi\) | |||||||
\(8\) | −22.6274 | −0.353553 | ||||||||
\(9\) | −80.3134 | −0.991523 | ||||||||
\(10\) | − | 31.6228i | − | 0.316228i | ||||||
\(11\) | − | 34.1074i | − | 0.281879i | −0.990018 | − | 0.140940i | \(-0.954988\pi\) | ||
0.990018 | − | 0.140940i | \(-0.0450123\pi\) | |||||||
\(12\) | 6.62891 | 0.0460341 | ||||||||
\(13\) | 274.959 | 1.62698 | 0.813489 | − | 0.581580i | \(-0.197565\pi\) | ||||
0.813489 | + | 0.581580i | \(0.197565\pi\) | |||||||
\(14\) | 47.8544i | 0.244155i | ||||||||
\(15\) | 9.26419i | 0.0411742i | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 6.91652i | 0.0239326i | 0.999928 | + | 0.0119663i | \(0.00380908\pi\) | ||||
−0.999928 | + | 0.0119663i | \(0.996191\pi\) | |||||||
\(18\) | 227.161 | 0.701113 | ||||||||
\(19\) | 302.833i | 0.838874i | 0.907784 | + | 0.419437i | \(0.137772\pi\) | ||||
−0.907784 | + | 0.419437i | \(0.862228\pi\) | |||||||
\(20\) | 89.4427i | 0.223607i | ||||||||
\(21\) | − | 14.0194i | − | 0.0317900i | ||||||
\(22\) | 96.4702i | 0.199319i | ||||||||
\(23\) | −328.833 | − | 414.379i | −0.621613 | − | 0.783324i | ||||
\(24\) | −18.7494 | −0.0325510 | ||||||||
\(25\) | −125.000 | −0.200000 | ||||||||
\(26\) | −777.702 | −1.15045 | ||||||||
\(27\) | −133.667 | −0.183356 | ||||||||
\(28\) | − | 135.353i | − | 0.172644i | ||||||
\(29\) | 266.017 | 0.316310 | 0.158155 | − | 0.987414i | \(-0.449445\pi\) | ||||
0.158155 | + | 0.987414i | \(0.449445\pi\) | |||||||
\(30\) | − | 26.2031i | − | 0.0291145i | ||||||
\(31\) | 583.049 | 0.606711 | 0.303355 | − | 0.952877i | \(-0.401893\pi\) | ||||
0.303355 | + | 0.952877i | \(0.401893\pi\) | |||||||
\(32\) | −181.019 | −0.176777 | ||||||||
\(33\) | − | 28.2618i | − | 0.0259521i | ||||||
\(34\) | − | 19.5629i | − | 0.0169229i | ||||||
\(35\) | 189.161 | 0.154417 | ||||||||
\(36\) | −642.507 | −0.495762 | ||||||||
\(37\) | 1130.86i | 0.826048i | 0.910720 | + | 0.413024i | \(0.135527\pi\) | ||||
−0.910720 | + | 0.413024i | \(0.864473\pi\) | |||||||
\(38\) | − | 856.542i | − | 0.593173i | ||||||
\(39\) | 227.835 | 0.149793 | ||||||||
\(40\) | − | 252.982i | − | 0.158114i | ||||||
\(41\) | 1769.42 | 1.05260 | 0.526299 | − | 0.850300i | \(-0.323579\pi\) | ||||
0.526299 | + | 0.850300i | \(0.323579\pi\) | |||||||
\(42\) | 39.6528i | 0.0224789i | ||||||||
\(43\) | 3303.32i | 1.78654i | 0.449519 | + | 0.893271i | \(0.351595\pi\) | ||||
−0.449519 | + | 0.893271i | \(0.648405\pi\) | |||||||
\(44\) | − | 272.859i | − | 0.140940i | ||||||
\(45\) | − | 897.931i | − | 0.443423i | ||||||
\(46\) | 930.081 | + | 1172.04i | 0.439547 | + | 0.553894i | ||||
\(47\) | 1722.09 | 0.779579 | 0.389790 | − | 0.920904i | \(-0.372548\pi\) | ||||
0.389790 | + | 0.920904i | \(0.372548\pi\) | |||||||
\(48\) | 53.0313 | 0.0230171 | ||||||||
\(49\) | 2114.74 | 0.880776 | ||||||||
\(50\) | 353.553 | 0.141421 | ||||||||
\(51\) | 5.73113i | 0.00220343i | ||||||||
\(52\) | 2199.67 | 0.813489 | ||||||||
\(53\) | 2677.50i | 0.953185i | 0.879124 | + | 0.476592i | \(0.158128\pi\) | ||||
−0.879124 | + | 0.476592i | \(0.841872\pi\) | |||||||
\(54\) | 378.066 | 0.129652 | ||||||||
\(55\) | 381.332 | 0.126060 | ||||||||
\(56\) | 382.835i | 0.122078i | ||||||||
\(57\) | 250.932i | 0.0772336i | ||||||||
\(58\) | −752.409 | −0.223665 | ||||||||
\(59\) | 1276.66 | 0.366751 | 0.183375 | − | 0.983043i | \(-0.441298\pi\) | ||||
0.183375 | + | 0.983043i | \(0.441298\pi\) | |||||||
\(60\) | 74.1135i | 0.0205871i | ||||||||
\(61\) | − | 4181.52i | − | 1.12376i | −0.827218 | − | 0.561881i | \(-0.810078\pi\) | ||
0.827218 | − | 0.561881i | \(-0.189922\pi\) | |||||||
\(62\) | −1649.11 | −0.429009 | ||||||||
\(63\) | 1358.83i | 0.342361i | ||||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | 3074.14i | 0.727607i | ||||||||
\(66\) | 79.9366i | 0.0183509i | ||||||||
\(67\) | 6231.09i | 1.38808i | 0.719936 | + | 0.694040i | \(0.244171\pi\) | ||||
−0.719936 | + | 0.694040i | \(0.755829\pi\) | |||||||
\(68\) | 55.3322i | 0.0119663i | ||||||||
\(69\) | −272.476 | − | 343.360i | −0.0572308 | − | 0.0721193i | ||||
\(70\) | −535.029 | −0.109190 | ||||||||
\(71\) | 7815.96 | 1.55048 | 0.775239 | − | 0.631668i | \(-0.217630\pi\) | ||||
0.775239 | + | 0.631668i | \(0.217630\pi\) | |||||||
\(72\) | 1817.28 | 0.350556 | ||||||||
\(73\) | 5456.59 | 1.02394 | 0.511971 | − | 0.859003i | \(-0.328916\pi\) | ||||
0.511971 | + | 0.859003i | \(0.328916\pi\) | |||||||
\(74\) | − | 3198.55i | − | 0.584104i | ||||||
\(75\) | −103.577 | −0.0184136 | ||||||||
\(76\) | 2422.67i | 0.419437i | ||||||||
\(77\) | −577.066 | −0.0973294 | ||||||||
\(78\) | −644.415 | −0.105920 | ||||||||
\(79\) | 11504.8i | 1.84342i | 0.387878 | + | 0.921711i | \(0.373208\pi\) | ||||
−0.387878 | + | 0.921711i | \(0.626792\pi\) | |||||||
\(80\) | 715.542i | 0.111803i | ||||||||
\(81\) | 6394.63 | 0.974642 | ||||||||
\(82\) | −5004.66 | −0.744299 | ||||||||
\(83\) | 2467.58i | 0.358192i | 0.983832 | + | 0.179096i | \(0.0573172\pi\) | ||||
−0.983832 | + | 0.179096i | \(0.942683\pi\) | |||||||
\(84\) | − | 112.155i | − | 0.0158950i | ||||||
\(85\) | −77.3291 | −0.0107030 | ||||||||
\(86\) | − | 9343.19i | − | 1.26328i | ||||||
\(87\) | 220.425 | 0.0291221 | ||||||||
\(88\) | 771.762i | 0.0996593i | ||||||||
\(89\) | 242.783i | 0.0306505i | 0.999883 | + | 0.0153252i | \(0.00487837\pi\) | ||||
−0.999883 | + | 0.0153252i | \(0.995122\pi\) | |||||||
\(90\) | 2539.73i | 0.313547i | ||||||||
\(91\) | − | 4652.06i | − | 0.561775i | ||||||
\(92\) | −2630.67 | − | 3315.03i | −0.310807 | − | 0.391662i | ||||
\(93\) | 483.123 | 0.0558588 | ||||||||
\(94\) | −4870.81 | −0.551246 | ||||||||
\(95\) | −3385.78 | −0.375156 | ||||||||
\(96\) | −149.995 | −0.0162755 | ||||||||
\(97\) | 13642.0i | 1.44989i | 0.688809 | + | 0.724943i | \(0.258134\pi\) | ||||
−0.688809 | + | 0.724943i | \(0.741866\pi\) | |||||||
\(98\) | −5981.40 | −0.622803 | ||||||||
\(99\) | 2739.28i | 0.279490i | ||||||||
\(100\) | −1000.00 | −0.100000 | ||||||||
\(101\) | −2916.56 | −0.285909 | −0.142954 | − | 0.989729i | \(-0.545660\pi\) | ||||
−0.142954 | + | 0.989729i | \(0.545660\pi\) | |||||||
\(102\) | − | 16.2101i | − | 0.00155806i | ||||||
\(103\) | − | 16819.4i | − | 1.58539i | −0.609621 | − | 0.792693i | \(-0.708678\pi\) | ||
0.609621 | − | 0.792693i | \(-0.291322\pi\) | |||||||
\(104\) | −6221.62 | −0.575224 | ||||||||
\(105\) | 156.742 | 0.0142169 | ||||||||
\(106\) | − | 7573.10i | − | 0.674003i | ||||||
\(107\) | − | 12039.3i | − | 1.05156i | −0.850621 | − | 0.525780i | \(-0.823774\pi\) | ||
0.850621 | − | 0.525780i | \(-0.176226\pi\) | |||||||
\(108\) | −1069.33 | −0.0916780 | ||||||||
\(109\) | − | 15109.6i | − | 1.27174i | −0.771794 | − | 0.635872i | \(-0.780641\pi\) | ||
0.771794 | − | 0.635872i | \(-0.219359\pi\) | |||||||
\(110\) | −1078.57 | −0.0891380 | ||||||||
\(111\) | 937.046i | 0.0760527i | ||||||||
\(112\) | − | 1082.82i | − | 0.0863219i | ||||||
\(113\) | − | 5430.98i | − | 0.425325i | −0.977126 | − | 0.212663i | \(-0.931787\pi\) | ||
0.977126 | − | 0.212663i | \(-0.0682135\pi\) | |||||||
\(114\) | − | 709.743i | − | 0.0546124i | ||||||
\(115\) | 4632.89 | − | 3676.47i | 0.350313 | − | 0.277994i | ||||
\(116\) | 2128.13 | 0.158155 | ||||||||
\(117\) | −22082.9 | −1.61319 | ||||||||
\(118\) | −3610.94 | −0.259332 | ||||||||
\(119\) | 117.021 | 0.00826364 | ||||||||
\(120\) | − | 209.625i | − | 0.0145573i | ||||||
\(121\) | 13477.7 | 0.920544 | ||||||||
\(122\) | 11827.1i | 0.794620i | ||||||||
\(123\) | 1466.16 | 0.0969108 | ||||||||
\(124\) | 4664.39 | 0.303355 | ||||||||
\(125\) | − | 1397.54i | − | 0.0894427i | ||||||
\(126\) | − | 3843.35i | − | 0.242086i | ||||||
\(127\) | −17536.1 | −1.08724 | −0.543621 | − | 0.839331i | \(-0.682947\pi\) | ||||
−0.543621 | + | 0.839331i | \(0.682947\pi\) | |||||||
\(128\) | −1448.15 | −0.0883883 | ||||||||
\(129\) | 2737.17i | 0.164484i | ||||||||
\(130\) | − | 8694.98i | − | 0.514496i | ||||||
\(131\) | −26126.8 | −1.52245 | −0.761226 | − | 0.648487i | \(-0.775402\pi\) | ||||
−0.761226 | + | 0.648487i | \(0.775402\pi\) | |||||||
\(132\) | − | 226.095i | − | 0.0129761i | ||||||
\(133\) | 5123.67 | 0.289653 | ||||||||
\(134\) | − | 17624.2i | − | 0.981521i | ||||||
\(135\) | − | 1494.44i | − | 0.0819993i | ||||||
\(136\) | − | 156.503i | − | 0.00846146i | ||||||
\(137\) | 17590.7i | 0.937220i | 0.883405 | + | 0.468610i | \(0.155245\pi\) | ||||
−0.883405 | + | 0.468610i | \(0.844755\pi\) | |||||||
\(138\) | 770.678 | + | 971.168i | 0.0404683 | + | 0.0509960i | ||||
\(139\) | −6189.98 | −0.320376 | −0.160188 | − | 0.987087i | \(-0.551210\pi\) | ||||
−0.160188 | + | 0.987087i | \(0.551210\pi\) | |||||||
\(140\) | 1513.29 | 0.0772087 | ||||||||
\(141\) | 1426.95 | 0.0717745 | ||||||||
\(142\) | −22106.9 | −1.09635 | ||||||||
\(143\) | − | 9378.14i | − | 0.458611i | ||||||
\(144\) | −5140.06 | −0.247881 | ||||||||
\(145\) | 2974.16i | 0.141458i | ||||||||
\(146\) | −15433.6 | −0.724036 | ||||||||
\(147\) | 1752.31 | 0.0810915 | ||||||||
\(148\) | 9046.87i | 0.413024i | ||||||||
\(149\) | − | 30482.6i | − | 1.37303i | −0.727117 | − | 0.686513i | \(-0.759140\pi\) | ||
0.727117 | − | 0.686513i | \(-0.240860\pi\) | |||||||
\(150\) | 292.959 | 0.0130204 | ||||||||
\(151\) | 6831.67 | 0.299621 | 0.149811 | − | 0.988715i | \(-0.452134\pi\) | ||||
0.149811 | + | 0.988715i | \(0.452134\pi\) | |||||||
\(152\) | − | 6852.34i | − | 0.296587i | ||||||
\(153\) | − | 555.490i | − | 0.0237297i | ||||||
\(154\) | 1632.19 | 0.0688222 | ||||||||
\(155\) | 6518.69i | 0.271329i | ||||||||
\(156\) | 1822.68 | 0.0748965 | ||||||||
\(157\) | 44251.0i | 1.79524i | 0.440766 | + | 0.897622i | \(0.354707\pi\) | ||||
−0.440766 | + | 0.897622i | \(0.645293\pi\) | |||||||
\(158\) | − | 32540.5i | − | 1.30350i | ||||||
\(159\) | 2218.61i | 0.0877580i | ||||||||
\(160\) | − | 2023.86i | − | 0.0790569i | ||||||
\(161\) | −7010.91 | + | 5563.56i | −0.270472 | + | 0.214635i | ||||
\(162\) | −18086.7 | −0.689176 | ||||||||
\(163\) | 3576.65 | 0.134618 | 0.0673088 | − | 0.997732i | \(-0.478559\pi\) | ||||
0.0673088 | + | 0.997732i | \(0.478559\pi\) | |||||||
\(164\) | 14155.3 | 0.526299 | ||||||||
\(165\) | 315.977 | 0.0116061 | ||||||||
\(166\) | − | 6979.38i | − | 0.253280i | ||||||
\(167\) | −14455.8 | −0.518332 | −0.259166 | − | 0.965833i | \(-0.583448\pi\) | ||||
−0.259166 | + | 0.965833i | \(0.583448\pi\) | |||||||
\(168\) | 317.223i | 0.0112395i | ||||||||
\(169\) | 47041.6 | 1.64706 | ||||||||
\(170\) | 218.720 | 0.00756816 | ||||||||
\(171\) | − | 24321.6i | − | 0.831763i | ||||||
\(172\) | 26426.5i | 0.893271i | ||||||||
\(173\) | −9552.18 | −0.319161 | −0.159581 | − | 0.987185i | \(-0.551014\pi\) | ||||
−0.159581 | + | 0.987185i | \(0.551014\pi\) | |||||||
\(174\) | −623.457 | −0.0205924 | ||||||||
\(175\) | 2114.89i | 0.0690575i | ||||||||
\(176\) | − | 2182.87i | − | 0.0704698i | ||||||
\(177\) | 1057.86 | 0.0337661 | ||||||||
\(178\) | − | 686.693i | − | 0.0216732i | ||||||
\(179\) | −24503.7 | −0.764761 | −0.382380 | − | 0.924005i | \(-0.624896\pi\) | ||||
−0.382380 | + | 0.924005i | \(0.624896\pi\) | |||||||
\(180\) | − | 7183.45i | − | 0.221711i | ||||||
\(181\) | − | 3317.62i | − | 0.101267i | −0.998717 | − | 0.0506337i | \(-0.983876\pi\) | ||
0.998717 | − | 0.0506337i | \(-0.0161241\pi\) | |||||||
\(182\) | 13158.0i | 0.397235i | ||||||||
\(183\) | − | 3464.87i | − | 0.103463i | ||||||
\(184\) | 7440.65 | + | 9376.32i | 0.219773 | + | 0.276947i | ||||
\(185\) | −12643.4 | −0.369420 | ||||||||
\(186\) | −1366.48 | −0.0394981 | ||||||||
\(187\) | 235.904 | 0.00674610 | ||||||||
\(188\) | 13776.7 | 0.389790 | ||||||||
\(189\) | 2261.52i | 0.0633106i | ||||||||
\(190\) | 9576.44 | 0.265275 | ||||||||
\(191\) | − | 23907.6i | − | 0.655344i | −0.944792 | − | 0.327672i | \(-0.893736\pi\) | ||
0.944792 | − | 0.327672i | \(-0.106264\pi\) | |||||||
\(192\) | 424.250 | 0.0115085 | ||||||||
\(193\) | 12502.0 | 0.335634 | 0.167817 | − | 0.985818i | \(-0.446328\pi\) | ||||
0.167817 | + | 0.985818i | \(0.446328\pi\) | |||||||
\(194\) | − | 38585.3i | − | 1.02522i | ||||||
\(195\) | 2547.27i | 0.0669895i | ||||||||
\(196\) | 16918.0 | 0.440388 | ||||||||
\(197\) | −17516.7 | −0.451357 | −0.225679 | − | 0.974202i | \(-0.572460\pi\) | ||||
−0.225679 | + | 0.974202i | \(0.572460\pi\) | |||||||
\(198\) | − | 7747.85i | − | 0.197629i | ||||||
\(199\) | − | 8686.79i | − | 0.219358i | −0.993967 | − | 0.109679i | \(-0.965018\pi\) | ||
0.993967 | − | 0.109679i | \(-0.0349823\pi\) | |||||||
\(200\) | 2828.43 | 0.0707107 | ||||||||
\(201\) | 5163.17i | 0.127798i | ||||||||
\(202\) | 8249.26 | 0.202168 | ||||||||
\(203\) | − | 4500.76i | − | 0.109218i | ||||||
\(204\) | 45.8490i | 0.00110172i | ||||||||
\(205\) | 19782.7i | 0.470736i | ||||||||
\(206\) | 47572.3i | 1.12104i | ||||||||
\(207\) | 26409.7 | + | 33280.2i | 0.616344 | + | 0.776684i | ||||
\(208\) | 17597.4 | 0.406744 | ||||||||
\(209\) | 10328.9 | 0.236461 | ||||||||
\(210\) | −443.332 | −0.0100529 | ||||||||
\(211\) | 68036.4 | 1.52819 | 0.764094 | − | 0.645105i | \(-0.223186\pi\) | ||||
0.764094 | + | 0.645105i | \(0.223186\pi\) | |||||||
\(212\) | 21420.0i | 0.476592i | ||||||||
\(213\) | 6476.41 | 0.142750 | ||||||||
\(214\) | 34052.3i | 0.743565i | ||||||||
\(215\) | −36932.2 | −0.798966 | ||||||||
\(216\) | 3024.53 | 0.0648261 | ||||||||
\(217\) | − | 9864.66i | − | 0.209490i | ||||||
\(218\) | 42736.4i | 0.899259i | ||||||||
\(219\) | 4521.40 | 0.0942725 | ||||||||
\(220\) | 3050.66 | 0.0630301 | ||||||||
\(221\) | 1901.76i | 0.0389378i | ||||||||
\(222\) | − | 2650.37i | − | 0.0537774i | ||||||
\(223\) | −1496.04 | −0.0300838 | −0.0150419 | − | 0.999887i | \(-0.504788\pi\) | ||||
−0.0150419 | + | 0.999887i | \(0.504788\pi\) | |||||||
\(224\) | 3062.68i | 0.0610388i | ||||||||
\(225\) | 10039.2 | 0.198305 | ||||||||
\(226\) | 15361.1i | 0.300750i | ||||||||
\(227\) | 16836.2i | 0.326732i | 0.986566 | + | 0.163366i | \(0.0522352\pi\) | ||||
−0.986566 | + | 0.163366i | \(0.947765\pi\) | |||||||
\(228\) | 2007.46i | 0.0386168i | ||||||||
\(229\) | − | 19026.6i | − | 0.362820i | −0.983408 | − | 0.181410i | \(-0.941934\pi\) | ||
0.983408 | − | 0.181410i | \(-0.0580661\pi\) | |||||||
\(230\) | −13103.8 | + | 10398.6i | −0.247709 | + | 0.196571i | ||||
\(231\) | −478.165 | −0.00896094 | ||||||||
\(232\) | −6019.27 | −0.111833 | ||||||||
\(233\) | 64511.4 | 1.18830 | 0.594148 | − | 0.804356i | \(-0.297489\pi\) | ||||
0.594148 | + | 0.804356i | \(0.297489\pi\) | |||||||
\(234\) | 62459.9 | 1.14070 | ||||||||
\(235\) | 19253.6i | 0.348639i | ||||||||
\(236\) | 10213.3 | 0.183375 | ||||||||
\(237\) | 9533.03i | 0.169721i | ||||||||
\(238\) | −330.986 | −0.00584327 | ||||||||
\(239\) | 5760.10 | 0.100840 | 0.0504202 | − | 0.998728i | \(-0.483944\pi\) | ||||
0.0504202 | + | 0.998728i | \(0.483944\pi\) | |||||||
\(240\) | 592.908i | 0.0102935i | ||||||||
\(241\) | − | 31647.1i | − | 0.544878i | −0.962173 | − | 0.272439i | \(-0.912170\pi\) | ||
0.962173 | − | 0.272439i | \(-0.0878303\pi\) | |||||||
\(242\) | −38120.7 | −0.650923 | ||||||||
\(243\) | 16125.7 | 0.273090 | ||||||||
\(244\) | − | 33452.2i | − | 0.561881i | ||||||
\(245\) | 23643.6i | 0.393895i | ||||||||
\(246\) | −4146.93 | −0.0685263 | ||||||||
\(247\) | 83266.9i | 1.36483i | ||||||||
\(248\) | −13192.9 | −0.214505 | ||||||||
\(249\) | 2044.67i | 0.0329781i | ||||||||
\(250\) | 3952.85i | 0.0632456i | ||||||||
\(251\) | − | 33172.4i | − | 0.526538i | −0.964722 | − | 0.263269i | \(-0.915199\pi\) | ||
0.964722 | − | 0.263269i | \(-0.0848007\pi\) | |||||||
\(252\) | 10870.6i | 0.171180i | ||||||||
\(253\) | −14133.4 | + | 11215.6i | −0.220803 | + | 0.175220i | ||||
\(254\) | 49599.7 | 0.768796 | ||||||||
\(255\) | −64.0760 | −0.000985405 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −111070. | −1.68163 | −0.840815 | − | 0.541323i | \(-0.817924\pi\) | ||||
−0.840815 | + | 0.541323i | \(0.817924\pi\) | |||||||
\(258\) | − | 7741.90i | − | 0.116308i | ||||||
\(259\) | 19133.1 | 0.285224 | ||||||||
\(260\) | 24593.1i | 0.363803i | ||||||||
\(261\) | −21364.7 | −0.313629 | ||||||||
\(262\) | 73897.8 | 1.07654 | ||||||||
\(263\) | − | 128554.i | − | 1.85855i | −0.369384 | − | 0.929277i | \(-0.620431\pi\) | ||
0.369384 | − | 0.929277i | \(-0.379569\pi\) | |||||||
\(264\) | 639.492i | 0.00917545i | ||||||||
\(265\) | −29935.3 | −0.426277 | ||||||||
\(266\) | −14491.9 | −0.204815 | ||||||||
\(267\) | 201.173i | 0.00282194i | ||||||||
\(268\) | 49848.8i | 0.694040i | ||||||||
\(269\) | 27040.9 | 0.373694 | 0.186847 | − | 0.982389i | \(-0.440173\pi\) | ||||
0.186847 | + | 0.982389i | \(0.440173\pi\) | |||||||
\(270\) | 4226.91i | 0.0579823i | ||||||||
\(271\) | 19692.1 | 0.268135 | 0.134068 | − | 0.990972i | \(-0.457196\pi\) | ||||
0.134068 | + | 0.990972i | \(0.457196\pi\) | |||||||
\(272\) | 442.658i | 0.00598315i | ||||||||
\(273\) | − | 3854.76i | − | 0.0517217i | ||||||
\(274\) | − | 49753.9i | − | 0.662714i | ||||||
\(275\) | 4263.42i | 0.0563758i | ||||||||
\(276\) | −2179.81 | − | 2746.88i | −0.0286154 | − | 0.0360596i | ||||
\(277\) | −24505.9 | −0.319382 | −0.159691 | − | 0.987167i | \(-0.551050\pi\) | ||||
−0.159691 | + | 0.987167i | \(0.551050\pi\) | |||||||
\(278\) | 17507.9 | 0.226540 | ||||||||
\(279\) | −46826.7 | −0.601568 | ||||||||
\(280\) | −4280.23 | −0.0545948 | ||||||||
\(281\) | 106703.i | 1.35133i | 0.737207 | + | 0.675667i | \(0.236144\pi\) | ||||
−0.737207 | + | 0.675667i | \(0.763856\pi\) | |||||||
\(282\) | −4036.02 | −0.0507522 | ||||||||
\(283\) | − | 34820.1i | − | 0.434767i | −0.976086 | − | 0.217383i | \(-0.930248\pi\) | ||
0.976086 | − | 0.217383i | \(-0.0697522\pi\) | |||||||
\(284\) | 62527.6 | 0.775239 | ||||||||
\(285\) | −2805.51 | −0.0345399 | ||||||||
\(286\) | 26525.4i | 0.324287i | ||||||||
\(287\) | − | 29936.9i | − | 0.363449i | ||||||
\(288\) | 14538.3 | 0.175278 | ||||||||
\(289\) | 83473.2 | 0.999427 | ||||||||
\(290\) | − | 8412.19i | − | 0.100026i | ||||||
\(291\) | 11303.9i | 0.133488i | ||||||||
\(292\) | 43652.7 | 0.511971 | ||||||||
\(293\) | 97143.9i | 1.13157i | 0.824554 | + | 0.565783i | \(0.191426\pi\) | ||||
−0.824554 | + | 0.565783i | \(0.808574\pi\) | |||||||
\(294\) | −4956.27 | −0.0573404 | ||||||||
\(295\) | 14273.5i | 0.164016i | ||||||||
\(296\) | − | 25588.4i | − | 0.292052i | ||||||
\(297\) | 4559.01i | 0.0516842i | ||||||||
\(298\) | 86217.7i | 0.970876i | ||||||||
\(299\) | −90415.8 | − | 113937.i | −1.01135 | − | 1.27445i | ||||
\(300\) | −828.614 | −0.00920682 | ||||||||
\(301\) | 55889.1 | 0.616871 | ||||||||
\(302\) | −19322.9 | −0.211864 | ||||||||
\(303\) | −2416.70 | −0.0263231 | ||||||||
\(304\) | 19381.3i | 0.209718i | ||||||||
\(305\) | 46750.8 | 0.502562 | ||||||||
\(306\) | 1571.16i | 0.0167795i | ||||||||
\(307\) | −124144. | −1.31719 | −0.658594 | − | 0.752498i | \(-0.728849\pi\) | ||||
−0.658594 | + | 0.752498i | \(0.728849\pi\) | |||||||
\(308\) | −4616.53 | −0.0486647 | ||||||||
\(309\) | − | 13936.8i | − | 0.145964i | ||||||
\(310\) | − | 18437.6i | − | 0.191859i | ||||||
\(311\) | −82226.6 | −0.850142 | −0.425071 | − | 0.905160i | \(-0.639751\pi\) | ||||
−0.425071 | + | 0.905160i | \(0.639751\pi\) | |||||||
\(312\) | −5155.32 | −0.0529598 | ||||||||
\(313\) | − | 108944.i | − | 1.11203i | −0.831173 | − | 0.556014i | \(-0.812330\pi\) | ||
0.831173 | − | 0.556014i | \(-0.187670\pi\) | |||||||
\(314\) | − | 125161.i | − | 1.26943i | ||||||
\(315\) | −15192.2 | −0.153108 | ||||||||
\(316\) | 92038.4i | 0.921711i | ||||||||
\(317\) | 107217. | 1.06695 | 0.533476 | − | 0.845815i | \(-0.320885\pi\) | ||||
0.533476 | + | 0.845815i | \(0.320885\pi\) | |||||||
\(318\) | − | 6275.18i | − | 0.0620543i | ||||||
\(319\) | − | 9073.13i | − | 0.0891612i | ||||||
\(320\) | 5724.33i | 0.0559017i | ||||||||
\(321\) | − | 9975.94i | − | 0.0968152i | ||||||
\(322\) | 19829.8 | − | 15736.1i | 0.191253 | − | 0.151770i | ||||
\(323\) | −2094.56 | −0.0200764 | ||||||||
\(324\) | 51157.0 | 0.487321 | ||||||||
\(325\) | −34369.9 | −0.325396 | ||||||||
\(326\) | −10116.3 | −0.0951890 | ||||||||
\(327\) | − | 12520.0i | − | 0.117087i | ||||||
\(328\) | −40037.3 | −0.372149 | ||||||||
\(329\) | − | 29136.2i | − | 0.269179i | ||||||
\(330\) | −893.718 | −0.00820678 | ||||||||
\(331\) | −128870. | −1.17624 | −0.588120 | − | 0.808773i | \(-0.700132\pi\) | ||||
−0.588120 | + | 0.808773i | \(0.700132\pi\) | |||||||
\(332\) | 19740.7i | 0.179096i | ||||||||
\(333\) | − | 90823.2i | − | 0.819046i | ||||||
\(334\) | 40887.1 | 0.366516 | ||||||||
\(335\) | −69665.8 | −0.620769 | ||||||||
\(336\) | − | 897.242i | − | 0.00794750i | ||||||
\(337\) | 91307.7i | 0.803984i | 0.915643 | + | 0.401992i | \(0.131682\pi\) | ||||
−0.915643 | + | 0.401992i | \(0.868318\pi\) | |||||||
\(338\) | −133054. | −1.16465 | ||||||||
\(339\) | − | 4500.18i | − | 0.0391589i | ||||||
\(340\) | −618.633 | −0.00535149 | ||||||||
\(341\) | − | 19886.3i | − | 0.171019i | ||||||
\(342\) | 68791.8i | 0.588145i | ||||||||
\(343\) | − | 76402.3i | − | 0.649409i | ||||||
\(344\) | − | 74745.5i | − | 0.631638i | ||||||
\(345\) | 3838.88 | − | 3046.37i | 0.0322527 | − | 0.0255944i | ||||
\(346\) | 27017.6 | 0.225681 | ||||||||
\(347\) | −199317. | −1.65534 | −0.827668 | − | 0.561219i | \(-0.810333\pi\) | ||||
−0.827668 | + | 0.561219i | \(0.810333\pi\) | |||||||
\(348\) | 1763.40 | 0.0145611 | ||||||||
\(349\) | 186033. | 1.52735 | 0.763674 | − | 0.645602i | \(-0.223393\pi\) | ||||
0.763674 | + | 0.645602i | \(0.223393\pi\) | |||||||
\(350\) | − | 5981.80i | − | 0.0488310i | ||||||
\(351\) | −36752.9 | −0.298316 | ||||||||
\(352\) | 6174.09i | 0.0498296i | ||||||||
\(353\) | 125942. | 1.01069 | 0.505347 | − | 0.862916i | \(-0.331365\pi\) | ||||
0.505347 | + | 0.862916i | \(0.331365\pi\) | |||||||
\(354\) | −2992.07 | −0.0238762 | ||||||||
\(355\) | 87385.0i | 0.693395i | ||||||||
\(356\) | 1942.26i | 0.0153252i | ||||||||
\(357\) | 96.9655 | 0.000760818 | ||||||||
\(358\) | 69306.9 | 0.540767 | ||||||||
\(359\) | − | 70779.3i | − | 0.549183i | −0.961561 | − | 0.274592i | \(-0.911457\pi\) | ||
0.961561 | − | 0.274592i | \(-0.0885427\pi\) | |||||||
\(360\) | 20317.9i | 0.156774i | ||||||||
\(361\) | 38612.9 | 0.296291 | ||||||||
\(362\) | 9383.64i | 0.0716068i | ||||||||
\(363\) | 11167.8 | 0.0847529 | ||||||||
\(364\) | − | 37216.5i | − | 0.280888i | ||||||
\(365\) | 61006.5i | 0.457921i | ||||||||
\(366\) | 9800.12i | 0.0731593i | ||||||||
\(367\) | 31425.9i | 0.233322i | 0.993172 | + | 0.116661i | \(0.0372191\pi\) | ||||
−0.993172 | + | 0.116661i | \(0.962781\pi\) | |||||||
\(368\) | −21045.3 | − | 26520.2i | −0.155403 | − | 0.195831i | ||||
\(369\) | −142108. | −1.04367 | ||||||||
\(370\) | 35760.9 | 0.261219 | ||||||||
\(371\) | 45300.8 | 0.329123 | ||||||||
\(372\) | 3864.98 | 0.0279294 | ||||||||
\(373\) | 173293.i | 1.24556i | 0.782399 | + | 0.622778i | \(0.213996\pi\) | ||||
−0.782399 | + | 0.622778i | \(0.786004\pi\) | |||||||
\(374\) | −667.239 | −0.00477021 | ||||||||
\(375\) | − | 1158.02i | − | 0.00823483i | ||||||
\(376\) | −38966.5 | −0.275623 | ||||||||
\(377\) | 73143.8 | 0.514630 | ||||||||
\(378\) | − | 6396.54i | − | 0.0447673i | ||||||
\(379\) | 12563.7i | 0.0874663i | 0.999043 | + | 0.0437331i | \(0.0139251\pi\) | ||||
−0.999043 | + | 0.0437331i | \(0.986075\pi\) | |||||||
\(380\) | −27086.2 | −0.187578 | ||||||||
\(381\) | −14530.7 | −0.100100 | ||||||||
\(382\) | 67620.9i | 0.463398i | ||||||||
\(383\) | − | 155679.i | − | 1.06129i | −0.847595 | − | 0.530643i | \(-0.821950\pi\) | ||
0.847595 | − | 0.530643i | \(-0.178050\pi\) | |||||||
\(384\) | −1199.96 | −0.00813776 | ||||||||
\(385\) | − | 6451.79i | − | 0.0435270i | ||||||
\(386\) | −35361.1 | −0.237329 | ||||||||
\(387\) | − | 265300.i | − | 1.77140i | ||||||
\(388\) | 109136.i | 0.724943i | ||||||||
\(389\) | 271059.i | 1.79129i | 0.444773 | + | 0.895644i | \(0.353285\pi\) | ||||
−0.444773 | + | 0.895644i | \(0.646715\pi\) | |||||||
\(390\) | − | 7204.78i | − | 0.0473687i | ||||||
\(391\) | 2866.06 | − | 2274.38i | 0.0187470 | − | 0.0148768i | ||||
\(392\) | −47851.2 | −0.311401 | ||||||||
\(393\) | −21649.0 | −0.140169 | ||||||||
\(394\) | 49544.8 | 0.319158 | ||||||||
\(395\) | −128628. | −0.824403 | ||||||||
\(396\) | 21914.2i | 0.139745i | ||||||||
\(397\) | 232055. | 1.47234 | 0.736172 | − | 0.676794i | \(-0.236631\pi\) | ||||
0.736172 | + | 0.676794i | \(0.236631\pi\) | |||||||
\(398\) | 24570.0i | 0.155109i | ||||||||
\(399\) | 4245.54 | 0.0266678 | ||||||||
\(400\) | −8000.00 | −0.0500000 | ||||||||
\(401\) | − | 313994.i | − | 1.95268i | −0.216231 | − | 0.976342i | \(-0.569377\pi\) | ||
0.216231 | − | 0.976342i | \(-0.430623\pi\) | |||||||
\(402\) | − | 14603.7i | − | 0.0903669i | ||||||
\(403\) | 160315. | 0.987105 | ||||||||
\(404\) | −23332.4 | −0.142954 | ||||||||
\(405\) | 71494.1i | 0.435873i | ||||||||
\(406\) | 12730.1i | 0.0772288i | ||||||||
\(407\) | 38570.6 | 0.232846 | ||||||||
\(408\) | − | 129.681i | − | 0.000779031i | ||||||
\(409\) | −278472. | −1.66470 | −0.832349 | − | 0.554251i | \(-0.813005\pi\) | ||||
−0.832349 | + | 0.554251i | \(0.813005\pi\) | |||||||
\(410\) | − | 55953.8i | − | 0.332860i | ||||||
\(411\) | 14575.9i | 0.0862881i | ||||||||
\(412\) | − | 134555.i | − | 0.792693i | ||||||
\(413\) | − | 21599.9i | − | 0.126635i | ||||||
\(414\) | −74698.0 | − | 94130.5i | −0.435821 | − | 0.549199i | ||||
\(415\) | −27588.4 | −0.160188 | ||||||||
\(416\) | −49772.9 | −0.287612 | ||||||||
\(417\) | −5129.11 | −0.0294964 | ||||||||
\(418\) | −29214.4 | −0.167203 | ||||||||
\(419\) | 92205.6i | 0.525206i | 0.964904 | + | 0.262603i | \(0.0845809\pi\) | ||||
−0.964904 | + | 0.262603i | \(0.915419\pi\) | |||||||
\(420\) | 1253.93 | 0.00710846 | ||||||||
\(421\) | 273540.i | 1.54332i | 0.636035 | + | 0.771660i | \(0.280573\pi\) | ||||
−0.636035 | + | 0.771660i | \(0.719427\pi\) | |||||||
\(422\) | −192436. | −1.08059 | ||||||||
\(423\) | −138307. | −0.772971 | ||||||||
\(424\) | − | 60584.8i | − | 0.337002i | ||||||
\(425\) | − | 864.566i | − | 0.00478652i | ||||||
\(426\) | −18318.1 | −0.100939 | ||||||||
\(427\) | −70747.6 | −0.388021 | ||||||||
\(428\) | − | 96314.4i | − | 0.525780i | ||||||
\(429\) | − | 7770.86i | − | 0.0422235i | ||||||
\(430\) | 104460. | 0.564954 | ||||||||
\(431\) | − | 108915.i | − | 0.586316i | −0.956064 | − | 0.293158i | \(-0.905294\pi\) | ||
0.956064 | − | 0.293158i | \(-0.0947061\pi\) | |||||||
\(432\) | −8554.66 | −0.0458390 | ||||||||
\(433\) | − | 152308.i | − | 0.812359i | −0.913793 | − | 0.406179i | \(-0.866861\pi\) | ||
0.913793 | − | 0.406179i | \(-0.133139\pi\) | |||||||
\(434\) | 27901.5i | 0.148132i | ||||||||
\(435\) | 2464.43i | 0.0130238i | ||||||||
\(436\) | − | 120877.i | − | 0.635872i | ||||||
\(437\) | 125488. | − | 99581.8i | 0.657110 | − | 0.521455i | ||||
\(438\) | −12788.5 | −0.0666607 | ||||||||
\(439\) | 130401. | 0.676632 | 0.338316 | − | 0.941033i | \(-0.390143\pi\) | ||||
0.338316 | + | 0.941033i | \(0.390143\pi\) | |||||||
\(440\) | −8628.56 | −0.0445690 | ||||||||
\(441\) | −169842. | −0.873310 | ||||||||
\(442\) | − | 5379.00i | − | 0.0275332i | ||||||
\(443\) | −253547. | −1.29197 | −0.645983 | − | 0.763352i | \(-0.723552\pi\) | ||||
−0.645983 | + | 0.763352i | \(0.723552\pi\) | |||||||
\(444\) | 7496.37i | 0.0380264i | ||||||||
\(445\) | −2714.39 | −0.0137073 | ||||||||
\(446\) | 4231.44 | 0.0212725 | ||||||||
\(447\) | − | 25258.3i | − | 0.126412i | ||||||
\(448\) | − | 8662.58i | − | 0.0431610i | ||||||
\(449\) | 102672. | 0.509282 | 0.254641 | − | 0.967036i | \(-0.418043\pi\) | ||||
0.254641 | + | 0.967036i | \(0.418043\pi\) | |||||||
\(450\) | −28395.1 | −0.140223 | ||||||||
\(451\) | − | 60350.1i | − | 0.296705i | ||||||
\(452\) | − | 43447.8i | − | 0.212663i | ||||||
\(453\) | 5660.81 | 0.0275856 | ||||||||
\(454\) | − | 47619.9i | − | 0.231035i | ||||||
\(455\) | 52011.6 | 0.251234 | ||||||||
\(456\) | − | 5677.94i | − | 0.0273062i | ||||||
\(457\) | 45739.5i | 0.219008i | 0.993986 | + | 0.109504i | \(0.0349262\pi\) | ||||
−0.993986 | + | 0.109504i | \(0.965074\pi\) | |||||||
\(458\) | 53815.5i | 0.256552i | ||||||||
\(459\) | − | 924.508i | − | 0.00438819i | ||||||
\(460\) | 37063.1 | − | 29411.8i | 0.175157 | − | 0.138997i | ||||
\(461\) | 156031. | 0.734192 | 0.367096 | − | 0.930183i | \(-0.380352\pi\) | ||||
0.367096 | + | 0.930183i | \(0.380352\pi\) | |||||||
\(462\) | 1352.45 | 0.00633634 | ||||||||
\(463\) | 234327. | 1.09310 | 0.546549 | − | 0.837427i | \(-0.315941\pi\) | ||||
0.546549 | + | 0.837427i | \(0.315941\pi\) | |||||||
\(464\) | 17025.1 | 0.0790775 | ||||||||
\(465\) | 5401.48i | 0.0249808i | ||||||||
\(466\) | −182466. | −0.840252 | ||||||||
\(467\) | 385291.i | 1.76667i | 0.468744 | + | 0.883334i | \(0.344707\pi\) | ||||
−0.468744 | + | 0.883334i | \(0.655293\pi\) | |||||||
\(468\) | −176663. | −0.806593 | ||||||||
\(469\) | 105424. | 0.479287 | ||||||||
\(470\) | − | 54457.3i | − | 0.246525i | ||||||
\(471\) | 36667.0i | 0.165285i | ||||||||
\(472\) | −28887.5 | −0.129666 | ||||||||
\(473\) | 112667. | 0.503589 | ||||||||
\(474\) | − | 26963.5i | − | 0.120011i | ||||||
\(475\) | − | 37854.2i | − | 0.167775i | ||||||
\(476\) | 936.171 | 0.00413182 | ||||||||
\(477\) | − | 215039.i | − | 0.945105i | ||||||
\(478\) | −16292.0 | −0.0713049 | ||||||||
\(479\) | − | 82157.1i | − | 0.358075i | −0.983842 | − | 0.179038i | \(-0.942702\pi\) | ||
0.983842 | − | 0.179038i | \(-0.0572984\pi\) | |||||||
\(480\) | − | 1677.00i | − | 0.00727863i | ||||||
\(481\) | 310940.i | 1.34396i | ||||||||
\(482\) | 89511.4i | 0.385287i | ||||||||
\(483\) | −5809.34 | + | 4610.05i | −0.0249019 | + | 0.0197611i | ||||
\(484\) | 107822. | 0.460272 | ||||||||
\(485\) | −152522. | −0.648408 | ||||||||
\(486\) | −45610.3 | −0.193104 | ||||||||
\(487\) | −228829. | −0.964837 | −0.482418 | − | 0.875941i | \(-0.660242\pi\) | ||||
−0.482418 | + | 0.875941i | \(0.660242\pi\) | |||||||
\(488\) | 94617.0i | 0.397310i | ||||||||
\(489\) | 2963.67 | 0.0123940 | ||||||||
\(490\) | − | 66874.1i | − | 0.278526i | ||||||
\(491\) | 225264. | 0.934390 | 0.467195 | − | 0.884154i | \(-0.345265\pi\) | ||||
0.467195 | + | 0.884154i | \(0.345265\pi\) | |||||||
\(492\) | 11729.3 | 0.0484554 | ||||||||
\(493\) | 1839.91i | 0.00757013i | ||||||||
\(494\) | − | 235514.i | − | 0.965080i | ||||||
\(495\) | −30626.1 | −0.124992 | ||||||||
\(496\) | 37315.1 | 0.151678 | ||||||||
\(497\) | − | 132239.i | − | 0.535361i | ||||||
\(498\) | − | 5783.21i | − | 0.0233190i | ||||||
\(499\) | −211941. | −0.851163 | −0.425582 | − | 0.904920i | \(-0.639930\pi\) | ||||
−0.425582 | + | 0.904920i | \(0.639930\pi\) | |||||||
\(500\) | − | 11180.3i | − | 0.0447214i | ||||||
\(501\) | −11978.3 | −0.0477220 | ||||||||
\(502\) | 93825.8i | 0.372319i | ||||||||
\(503\) | 149353.i | 0.590306i | 0.955450 | + | 0.295153i | \(0.0953706\pi\) | ||||
−0.955450 | + | 0.295153i | \(0.904629\pi\) | |||||||
\(504\) | − | 30746.8i | − | 0.121043i | ||||||
\(505\) | − | 32608.1i | − | 0.127862i | ||||||
\(506\) | 39975.2 | − | 31722.6i | 0.156131 | − | 0.123899i | ||||
\(507\) | 38979.3 | 0.151642 | ||||||||
\(508\) | −140289. | −0.543621 | ||||||||
\(509\) | −375302. | −1.44859 | −0.724295 | − | 0.689490i | \(-0.757835\pi\) | ||||
−0.724295 | + | 0.689490i | \(0.757835\pi\) | |||||||
\(510\) | 181.234 | 0.000696787 | ||||||||
\(511\) | − | 92320.5i | − | 0.353555i | ||||||
\(512\) | −11585.2 | −0.0441942 | ||||||||
\(513\) | − | 40478.7i | − | 0.153813i | ||||||
\(514\) | 314153. | 1.18909 | ||||||||
\(515\) | 188046. | 0.709006 | ||||||||
\(516\) | 21897.4i | 0.0822419i | ||||||||
\(517\) | − | 58736.0i | − | 0.219747i | ||||||
\(518\) | −54116.6 | −0.201684 | ||||||||
\(519\) | −7915.07 | −0.0293846 | ||||||||
\(520\) | − | 69559.8i | − | 0.257248i | ||||||
\(521\) | 80213.3i | 0.295509i | 0.989024 | + | 0.147755i | \(0.0472046\pi\) | ||||
−0.989024 | + | 0.147755i | \(0.952795\pi\) | |||||||
\(522\) | 60428.5 | 0.221769 | ||||||||
\(523\) | − | 61120.2i | − | 0.223451i | −0.993739 | − | 0.111725i | \(-0.964362\pi\) | ||
0.993739 | − | 0.111725i | \(-0.0356377\pi\) | |||||||
\(524\) | −209014. | −0.761226 | ||||||||
\(525\) | 1752.42i | 0.00635800i | ||||||||
\(526\) | 363606.i | 1.31420i | ||||||||
\(527\) | 4032.67i | 0.0145202i | ||||||||
\(528\) | − | 1808.76i | − | 0.00648803i | ||||||
\(529\) | −63578.2 | + | 272523.i | −0.227194 | + | 0.973850i | ||||
\(530\) | 84669.9 | 0.301424 | ||||||||
\(531\) | −102533. | −0.363642 | ||||||||
\(532\) | 40989.3 | 0.144826 | ||||||||
\(533\) | 486517. | 1.71255 | ||||||||
\(534\) | − | 569.003i | − | 0.00199541i | ||||||
\(535\) | 134603. | 0.470272 | ||||||||
\(536\) | − | 140994.i | − | 0.490761i | ||||||
\(537\) | −20304.1 | −0.0704102 | ||||||||
\(538\) | −76483.1 | −0.264241 | ||||||||
\(539\) | − | 72128.4i | − | 0.248272i | ||||||
\(540\) | − | 11955.5i | − | 0.0409997i | ||||||
\(541\) | 211761. | 0.723521 | 0.361760 | − | 0.932271i | \(-0.382176\pi\) | ||||
0.361760 | + | 0.932271i | \(0.382176\pi\) | |||||||
\(542\) | −55697.7 | −0.189600 | ||||||||
\(543\) | − | 2749.03i | − | 0.00932350i | ||||||
\(544\) | − | 1252.02i | − | 0.00423073i | ||||||
\(545\) | 168930. | 0.568741 | ||||||||
\(546\) | 10902.9i | 0.0365727i | ||||||||
\(547\) | 475518. | 1.58925 | 0.794624 | − | 0.607101i | \(-0.207668\pi\) | ||||
0.794624 | + | 0.607101i | \(0.207668\pi\) | |||||||
\(548\) | 140725.i | 0.468610i | ||||||||
\(549\) | 335832.i | 1.11424i | ||||||||
\(550\) | − | 12058.8i | − | 0.0398637i | ||||||
\(551\) | 80558.8i | 0.265344i | ||||||||
\(552\) | 6165.43 | + | 7769.35i | 0.0202342 | + | 0.0254980i | ||||
\(553\) | 194651. | 0.636511 | ||||||||
\(554\) | 69313.1 | 0.225837 | ||||||||
\(555\) | −10476.5 | −0.0340118 | ||||||||
\(556\) | −49519.9 | −0.160188 | ||||||||
\(557\) | 329137.i | 1.06088i | 0.847722 | + | 0.530441i | \(0.177974\pi\) | ||||
−0.847722 | + | 0.530441i | \(0.822026\pi\) | |||||||
\(558\) | 132446. | 0.425373 | ||||||||
\(559\) | 908277.i | 2.90666i | ||||||||
\(560\) | 12106.3 | 0.0386043 | ||||||||
\(561\) | 195.474 | 0.000621102 | ||||||||
\(562\) | − | 301801.i | − | 0.955537i | ||||||
\(563\) | − | 187233.i | − | 0.590697i | −0.955390 | − | 0.295348i | \(-0.904564\pi\) | ||
0.955390 | − | 0.295348i | \(-0.0954357\pi\) | |||||||
\(564\) | 11415.6 | 0.0358872 | ||||||||
\(565\) | 60720.1 | 0.190211 | ||||||||
\(566\) | 98486.0i | 0.307427i | ||||||||
\(567\) | − | 108191.i | − | 0.336532i | ||||||
\(568\) | −176855. | −0.548177 | ||||||||
\(569\) | 354702.i | 1.09557i | 0.836620 | + | 0.547784i | \(0.184528\pi\) | ||||
−0.836620 | + | 0.547784i | \(0.815472\pi\) | |||||||
\(570\) | 7935.17 | 0.0244234 | ||||||||
\(571\) | − | 142525.i | − | 0.437139i | −0.975821 | − | 0.218570i | \(-0.929861\pi\) | ||
0.975821 | − | 0.218570i | \(-0.0701391\pi\) | |||||||
\(572\) | − | 75025.1i | − | 0.229305i | ||||||
\(573\) | − | 19810.2i | − | 0.0603363i | ||||||
\(574\) | 84674.4i | 0.256997i | ||||||||
\(575\) | 41104.2 | + | 51797.3i | 0.124323 | + | 0.156665i | ||||
\(576\) | −41120.5 | −0.123940 | ||||||||
\(577\) | 397881. | 1.19509 | 0.597546 | − | 0.801834i | \(-0.296142\pi\) | ||||
0.597546 | + | 0.801834i | \(0.296142\pi\) | |||||||
\(578\) | −236098. | −0.706702 | ||||||||
\(579\) | 10359.4 | 0.0309012 | ||||||||
\(580\) | 23793.3i | 0.0707291i | ||||||||
\(581\) | 41749.3 | 0.123679 | ||||||||
\(582\) | − | 31972.3i | − | 0.0943905i | ||||||
\(583\) | 91322.3 | 0.268683 | ||||||||
\(584\) | −123468. | −0.362018 | ||||||||
\(585\) | − | 246894.i | − | 0.721439i | ||||||
\(586\) | − | 274764.i | − | 0.800139i | ||||||
\(587\) | 49627.5 | 0.144028 | 0.0720139 | − | 0.997404i | \(-0.477057\pi\) | ||||
0.0720139 | + | 0.997404i | \(0.477057\pi\) | |||||||
\(588\) | 14018.5 | 0.0405458 | ||||||||
\(589\) | 176567.i | 0.508954i | ||||||||
\(590\) | − | 40371.5i | − | 0.115977i | ||||||
\(591\) | −14514.6 | −0.0415557 | ||||||||
\(592\) | 72375.0i | 0.206512i | ||||||||
\(593\) | 315575. | 0.897415 | 0.448708 | − | 0.893679i | \(-0.351884\pi\) | ||||
0.448708 | + | 0.893679i | \(0.351884\pi\) | |||||||
\(594\) | − | 12894.8i | − | 0.0365463i | ||||||
\(595\) | 1308.34i | 0.00369561i | ||||||||
\(596\) | − | 243860.i | − | 0.686513i | ||||||
\(597\) | − | 7198.00i | − | 0.0201959i | ||||||
\(598\) | 255734. | + | 322263.i | 0.715133 | + | 0.901173i | ||||
\(599\) | −276969. | −0.771931 | −0.385965 | − | 0.922513i | \(-0.626132\pi\) | ||||
−0.385965 | + | 0.922513i | \(0.626132\pi\) | |||||||
\(600\) | 2343.67 | 0.00651021 | ||||||||
\(601\) | 284226. | 0.786890 | 0.393445 | − | 0.919348i | \(-0.371283\pi\) | ||||
0.393445 | + | 0.919348i | \(0.371283\pi\) | |||||||
\(602\) | −158078. | −0.436193 | ||||||||
\(603\) | − | 500440.i | − | 1.37631i | ||||||
\(604\) | 54653.3 | 0.149811 | ||||||||
\(605\) | 150685.i | 0.411680i | ||||||||
\(606\) | 6835.46 | 0.0186133 | ||||||||
\(607\) | −264420. | −0.717657 | −0.358828 | − | 0.933404i | \(-0.616824\pi\) | ||||
−0.358828 | + | 0.933404i | \(0.616824\pi\) | |||||||
\(608\) | − | 54818.7i | − | 0.148293i | ||||||
\(609\) | − | 3729.40i | − | 0.0100555i | ||||||
\(610\) | −132231. | −0.355365 | ||||||||
\(611\) | 473505. | 1.26836 | ||||||||
\(612\) | − | 4443.92i | − | 0.0118649i | ||||||
\(613\) | 321222.i | 0.854839i | 0.904053 | + | 0.427420i | \(0.140577\pi\) | ||||
−0.904053 | + | 0.427420i | \(0.859423\pi\) | |||||||
\(614\) | 351131. | 0.931393 | ||||||||
\(615\) | 16392.2i | 0.0433398i | ||||||||
\(616\) | 13057.5 | 0.0344111 | ||||||||
\(617\) | 246378.i | 0.647190i | 0.946196 | + | 0.323595i | \(0.104891\pi\) | ||||
−0.946196 | + | 0.323595i | \(0.895109\pi\) | |||||||
\(618\) | 39419.1i | 0.103212i | ||||||||
\(619\) | − | 518214.i | − | 1.35247i | −0.736685 | − | 0.676236i | \(-0.763610\pi\) | ||
0.736685 | − | 0.676236i | \(-0.236390\pi\) | |||||||
\(620\) | 52149.5i | 0.135665i | ||||||||
\(621\) | 43954.0 | + | 55388.5i | 0.113977 | + | 0.143627i | ||||
\(622\) | 232572. | 0.601141 | ||||||||
\(623\) | 4107.66 | 0.0105832 | ||||||||
\(624\) | 14581.4 | 0.0374482 | ||||||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | 308141.i | 0.786322i | ||||||||
\(627\) | 8558.63 | 0.0217705 | ||||||||
\(628\) | 354008.i | 0.897622i | ||||||||
\(629\) | −7821.62 | −0.0197695 | ||||||||
\(630\) | 42970.0 | 0.108264 | ||||||||
\(631\) | − | 173044.i | − | 0.434607i | −0.976104 | − | 0.217304i | \(-0.930274\pi\) | ||
0.976104 | − | 0.217304i | \(-0.0697262\pi\) | |||||||
\(632\) | − | 260324.i | − | 0.651748i | ||||||
\(633\) | 56376.0 | 0.140698 | ||||||||
\(634\) | −303256. | −0.754450 | ||||||||
\(635\) | − | 196060.i | − | 0.486229i | ||||||
\(636\) | 17748.9i | 0.0438790i | ||||||||
\(637\) | 581469. | 1.43300 | ||||||||
\(638\) | 25662.7i | 0.0630465i | ||||||||
\(639\) | −627726. | −1.53733 | ||||||||
\(640\) | − | 16190.9i | − | 0.0395285i | ||||||
\(641\) | − | 228416.i | − | 0.555917i | −0.960593 | − | 0.277958i | \(-0.910342\pi\) | ||
0.960593 | − | 0.277958i | \(-0.0896577\pi\) | |||||||
\(642\) | 28216.2i | 0.0684587i | ||||||||
\(643\) | 631308.i | 1.52693i | 0.645849 | + | 0.763465i | \(0.276503\pi\) | ||||
−0.645849 | + | 0.763465i | \(0.723497\pi\) | |||||||
\(644\) | −56087.3 | + | 44508.5i | −0.135236 | + | 0.107318i | ||||
\(645\) | −30602.5 | −0.0735594 | ||||||||
\(646\) | 5924.30 | 0.0141962 | ||||||||
\(647\) | 49159.1 | 0.117434 | 0.0587172 | − | 0.998275i | \(-0.481299\pi\) | ||||
0.0587172 | + | 0.998275i | \(0.481299\pi\) | |||||||
\(648\) | −144694. | −0.344588 | ||||||||
\(649\) | − | 43543.5i | − | 0.103379i | ||||||
\(650\) | 97212.8 | 0.230089 | ||||||||
\(651\) | − | 8174.00i | − | 0.0192873i | ||||||
\(652\) | 28613.2 | 0.0673088 | ||||||||
\(653\) | −473169. | −1.10966 | −0.554829 | − | 0.831964i | \(-0.687217\pi\) | ||||
−0.554829 | + | 0.831964i | \(0.687217\pi\) | |||||||
\(654\) | 35412.0i | 0.0827932i | ||||||||
\(655\) | − | 292107.i | − | 0.680861i | ||||||
\(656\) | 113243. | 0.263149 | ||||||||
\(657\) | −438237. | −1.01526 | ||||||||
\(658\) | 82409.7i | 0.190338i | ||||||||
\(659\) | 448560.i | 1.03288i | 0.856323 | + | 0.516440i | \(0.172743\pi\) | ||||
−0.856323 | + | 0.516440i | \(0.827257\pi\) | |||||||
\(660\) | 2527.82 | 0.00580307 | ||||||||
\(661\) | − | 135040.i | − | 0.309071i | −0.987987 | − | 0.154536i | \(-0.950612\pi\) | ||
0.987987 | − | 0.154536i | \(-0.0493881\pi\) | |||||||
\(662\) | 364500. | 0.831728 | ||||||||
\(663\) | 1575.83i | 0.00358494i | ||||||||
\(664\) | − | 55835.0i | − | 0.126640i | ||||||
\(665\) | 57284.3i | 0.129537i | ||||||||
\(666\) | 256887.i | 0.579153i | ||||||||
\(667\) | −87475.2 | − | 110232.i | −0.196623 | − | 0.247773i | ||||
\(668\) | −115646. | −0.259166 | ||||||||
\(669\) | −1239.64 | −0.00276977 | ||||||||
\(670\) | 197045. | 0.438950 | ||||||||
\(671\) | −142621. | −0.316765 | ||||||||
\(672\) | 2537.78i | 0.00561973i | ||||||||
\(673\) | −597311. | −1.31877 | −0.659387 | − | 0.751803i | \(-0.729184\pi\) | ||||
−0.659387 | + | 0.751803i | \(0.729184\pi\) | |||||||
\(674\) | − | 258257.i | − | 0.568502i | ||||||
\(675\) | 16708.3 | 0.0366712 | ||||||||
\(676\) | 376333. | 0.823529 | ||||||||
\(677\) | − | 735875.i | − | 1.60556i | −0.596274 | − | 0.802781i | \(-0.703353\pi\) | ||
0.596274 | − | 0.802781i | \(-0.296647\pi\) | |||||||
\(678\) | 12728.4i | 0.0276895i | ||||||||
\(679\) | 230810. | 0.500627 | ||||||||
\(680\) | 1749.76 | 0.00378408 | ||||||||
\(681\) | 13950.7i | 0.0300817i | ||||||||
\(682\) | 56246.9i | 0.120929i | ||||||||
\(683\) | −393705. | −0.843975 | −0.421988 | − | 0.906602i | \(-0.638667\pi\) | ||||
−0.421988 | + | 0.906602i | \(0.638667\pi\) | |||||||
\(684\) | − | 194573.i | − | 0.415882i | ||||||
\(685\) | −196670. | −0.419137 | ||||||||
\(686\) | 216098.i | 0.459201i | ||||||||
\(687\) | − | 15765.7i | − | 0.0334042i | ||||||
\(688\) | 211412.i | 0.446635i | ||||||||
\(689\) | 736202.i | 1.55081i | ||||||||
\(690\) | −10858.0 | + | 8616.45i | −0.0228061 | + | 0.0180980i | ||||
\(691\) | 41361.1 | 0.0866236 | 0.0433118 | − | 0.999062i | \(-0.486209\pi\) | ||||
0.0433118 | + | 0.999062i | \(0.486209\pi\) | |||||||
\(692\) | −76417.4 | −0.159581 | ||||||||
\(693\) | 46346.1 | 0.0965043 | ||||||||
\(694\) | 563754. | 1.17050 | ||||||||
\(695\) | − | 69206.1i | − | 0.143276i | ||||||
\(696\) | −4987.65 | −0.0102962 | ||||||||
\(697\) | 12238.2i | 0.0251914i | ||||||||
\(698\) | −526180. | −1.08000 | ||||||||
\(699\) | 53455.1 | 0.109404 | ||||||||
\(700\) | 16919.1i | 0.0345288i | ||||||||
\(701\) | − | 528870.i | − | 1.07625i | −0.842865 | − | 0.538124i | \(-0.819133\pi\) | ||
0.842865 | − | 0.538124i | \(-0.180867\pi\) | |||||||
\(702\) | 103953. | 0.210941 | ||||||||
\(703\) | −342462. | −0.692950 | ||||||||
\(704\) | − | 17463.0i | − | 0.0352349i | ||||||
\(705\) | 15953.8i | 0.0320985i | ||||||||
\(706\) | −356216. | −0.714668 | ||||||||
\(707\) | 49345.5i | 0.0987208i | ||||||||
\(708\) | 8462.87 | 0.0168831 | ||||||||
\(709\) | 26402.1i | 0.0525225i | 0.999655 | + | 0.0262613i | \(0.00836018\pi\) | ||||
−0.999655 | + | 0.0262613i | \(0.991640\pi\) | |||||||
\(710\) | − | 247162.i | − | 0.490304i | ||||||
\(711\) | − | 923989.i | − | 1.82780i | ||||||
\(712\) | − | 5493.54i | − | 0.0108366i | ||||||
\(713\) | −191726. | − | 241603.i | −0.377139 | − | 0.475251i | ||||
\(714\) | −274.260 | −0.000537980 | ||||||||
\(715\) | 104851. | 0.205097 | ||||||||
\(716\) | −196030. | −0.382380 | ||||||||
\(717\) | 4772.90 | 0.00928419 | ||||||||
\(718\) | 200194.i | 0.388331i | ||||||||
\(719\) | 395915. | 0.765850 | 0.382925 | − | 0.923779i | \(-0.374917\pi\) | ||||
0.382925 | + | 0.923779i | \(0.374917\pi\) | |||||||
\(720\) | − | 57467.6i | − | 0.110856i | ||||||
\(721\) | −284568. | −0.547414 | ||||||||
\(722\) | −109214. | −0.209509 | ||||||||
\(723\) | − | 26223.2i | − | 0.0501660i | ||||||
\(724\) | − | 26540.9i | − | 0.0506337i | ||||||
\(725\) | −33252.1 | −0.0632620 | ||||||||
\(726\) | −31587.3 | −0.0599293 | ||||||||
\(727\) | − | 485482.i | − | 0.918554i | −0.888293 | − | 0.459277i | \(-0.848109\pi\) | ||
0.888293 | − | 0.459277i | \(-0.151891\pi\) | |||||||
\(728\) | 105264.i | 0.198618i | ||||||||
\(729\) | −504603. | −0.949499 | ||||||||
\(730\) | − | 172552.i | − | 0.323799i | ||||||
\(731\) | −22847.5 | −0.0427566 | ||||||||
\(732\) | − | 27718.9i | − | 0.0517314i | ||||||
\(733\) | 462501.i | 0.860806i | 0.902637 | + | 0.430403i | \(0.141628\pi\) | ||||
−0.902637 | + | 0.430403i | \(0.858372\pi\) | |||||||
\(734\) | − | 88885.9i | − | 0.164984i | ||||||
\(735\) | 19591.4i | 0.0362652i | ||||||||
\(736\) | 59525.2 | + | 75010.5i | 0.109887 | + | 0.138473i | ||||
\(737\) | 212526. | 0.391271 | ||||||||
\(738\) | 401942. | 0.737990 | ||||||||
\(739\) | −1.02284e6 | −1.87291 | −0.936455 | − | 0.350787i | \(-0.885914\pi\) | ||||
−0.936455 | + | 0.350787i | \(0.885914\pi\) | |||||||
\(740\) | −101147. | −0.184710 | ||||||||
\(741\) | 68996.1i | 0.125657i | ||||||||
\(742\) | −128130. | −0.232725 | ||||||||
\(743\) | 994757.i | 1.80194i | 0.433886 | + | 0.900968i | \(0.357142\pi\) | ||||
−0.433886 | + | 0.900968i | \(0.642858\pi\) | |||||||
\(744\) | −10931.8 | −0.0197491 | ||||||||
\(745\) | 340805. | 0.614036 | ||||||||
\(746\) | − | 490146.i | − | 0.880741i | ||||||
\(747\) | − | 198180.i | − | 0.355156i | ||||||
\(748\) | 1887.24 | 0.00337305 | ||||||||
\(749\) | −203694. | −0.363090 | ||||||||
\(750\) | 3275.38i | 0.00582291i | ||||||||
\(751\) | 103292.i | 0.183142i | 0.995799 | + | 0.0915712i | \(0.0291889\pi\) | ||||
−0.995799 | + | 0.0915712i | \(0.970811\pi\) | |||||||
\(752\) | 110214. | 0.194895 | ||||||||
\(753\) | − | 27487.2i | − | 0.0484775i | ||||||
\(754\) | −206882. | −0.363898 | ||||||||
\(755\) | 76380.3i | 0.133995i | ||||||||
\(756\) | 18092.1i | 0.0316553i | ||||||||
\(757\) | − | 591075.i | − | 1.03146i | −0.856752 | − | 0.515728i | \(-0.827522\pi\) | ||
0.856752 | − | 0.515728i | \(-0.172478\pi\) | |||||||
\(758\) | − | 35535.6i | − | 0.0618480i | ||||||
\(759\) | −11711.1 | + | 9293.44i | −0.0203289 | + | 0.0161322i | ||||
\(760\) | 76611.5 | 0.132638 | ||||||||
\(761\) | 1318.58 | 0.00227686 | 0.00113843 | − | 0.999999i | \(-0.499638\pi\) | ||||
0.00113843 | + | 0.999999i | \(0.499638\pi\) | |||||||
\(762\) | 41099.0 | 0.0707817 | ||||||||
\(763\) | −255641. | −0.439118 | ||||||||
\(764\) | − | 191261.i | − | 0.327672i | ||||||
\(765\) | 6210.56 | 0.0106123 | ||||||||
\(766\) | 440327.i | 0.750443i | ||||||||
\(767\) | 351029. | 0.596696 | ||||||||
\(768\) | 3394.00 | 0.00575426 | ||||||||
\(769\) | − | 876913.i | − | 1.48287i | −0.671024 | − | 0.741436i | \(-0.734145\pi\) | ||
0.671024 | − | 0.741436i | \(-0.265855\pi\) | |||||||
\(770\) | 18248.4i | 0.0307782i | ||||||||
\(771\) | −92034.1 | −0.154825 | ||||||||
\(772\) | 100016. | 0.167817 | ||||||||
\(773\) | − | 387136.i | − | 0.647894i | −0.946075 | − | 0.323947i | \(-0.894990\pi\) | ||
0.946075 | − | 0.323947i | \(-0.105010\pi\) | |||||||
\(774\) | 750383.i | 1.25257i | ||||||||
\(775\) | −72881.1 | −0.121342 | ||||||||
\(776\) | − | 308683.i | − | 0.512612i | ||||||
\(777\) | 15854.0 | 0.0262601 | ||||||||
\(778\) | − | 766672.i | − | 1.26663i | ||||||
\(779\) | 535838.i | 0.882996i | ||||||||
\(780\) | 20378.2i | 0.0334947i | ||||||||
\(781\) | − | 266582.i | − | 0.437047i | ||||||
\(782\) | −8106.44 | + | 6432.93i | −0.0132561 | + | 0.0105195i | ||||
\(783\) | −35557.5 | −0.0579974 | ||||||||
\(784\) | 135344. | 0.220194 | ||||||||
\(785\) | −494741. | −0.802858 | ||||||||
\(786\) | 61232.7 | 0.0991148 | ||||||||
\(787\) | − | 959056.i | − | 1.54844i | −0.632916 | − | 0.774220i | \(-0.718142\pi\) | ||
0.632916 | − | 0.774220i | \(-0.281858\pi\) | |||||||
\(788\) | −140134. | −0.225679 | ||||||||
\(789\) | − | 106522.i | − | 0.171114i | ||||||
\(790\) | 363814. | 0.582941 | ||||||||
\(791\) | −91887.2 | −0.146859 | ||||||||
\(792\) | − | 61982.8i | − | 0.0988145i | ||||||
\(793\) | − | 1.14975e6i | − | 1.82834i | ||||||
\(794\) | −656350. | −1.04110 | ||||||||
\(795\) | −24804.8 | −0.0392466 | ||||||||
\(796\) | − | 69494.4i | − | 0.109679i | ||||||
\(797\) | − | 487707.i | − | 0.767790i | −0.923377 | − | 0.383895i | \(-0.874582\pi\) | ||
0.923377 | − | 0.383895i | \(-0.125418\pi\) | |||||||
\(798\) | −12008.2 | −0.0188570 | ||||||||
\(799\) | 11910.9i | 0.0186574i | ||||||||
\(800\) | 22627.4 | 0.0353553 | ||||||||
\(801\) | − | 19498.7i | − | 0.0303907i | ||||||
\(802\) | 888108.i | 1.38076i | ||||||||
\(803\) | − | 186110.i | − | 0.288628i | ||||||
\(804\) | 41305.4i | 0.0638991i | ||||||||
\(805\) | −62202.5 | − | 78384.4i | −0.0959879 | − | 0.120959i | ||||
\(806\) | −453439. | −0.697989 | ||||||||
\(807\) | 22406.4 | 0.0344053 | ||||||||
\(808\) | 65994.1 | 0.101084 | ||||||||
\(809\) | −759228. | −1.16005 | −0.580023 | − | 0.814600i | \(-0.696956\pi\) | ||||
−0.580023 | + | 0.814600i | \(0.696956\pi\) | |||||||
\(810\) | − | 202216.i | − | 0.308209i | ||||||
\(811\) | −713256. | −1.08443 | −0.542217 | − | 0.840238i | \(-0.682415\pi\) | ||||
−0.542217 | + | 0.840238i | \(0.682415\pi\) | |||||||
\(812\) | − | 36006.1i | − | 0.0546090i | ||||||
\(813\) | 16317.2 | 0.0246867 | ||||||||
\(814\) | −109094. | −0.164647 | ||||||||
\(815\) | 39988.2i | 0.0602028i | ||||||||
\(816\) | 366.792i | 0.000550858i | ||||||||
\(817\) | −1.00035e6 | −1.49868 | ||||||||
\(818\) | 787639. | 1.17712 | ||||||||
\(819\) | 373623.i | 0.557013i | ||||||||
\(820\) | 158261.i | 0.235368i | ||||||||
\(821\) | −29380.0 | −0.0435879 | −0.0217939 | − | 0.999762i | \(-0.506938\pi\) | ||||
−0.0217939 | + | 0.999762i | \(0.506938\pi\) | |||||||
\(822\) | − | 41226.8i | − | 0.0610149i | ||||||
\(823\) | −48085.4 | −0.0709927 | −0.0354964 | − | 0.999370i | \(-0.511301\pi\) | ||||
−0.0354964 | + | 0.999370i | \(0.511301\pi\) | |||||||
\(824\) | 380579.i | 0.560519i | ||||||||
\(825\) | 3532.73i | 0.00519042i | ||||||||
\(826\) | 61093.8i | 0.0895441i | ||||||||
\(827\) | 35849.1i | 0.0524165i | 0.999657 | + | 0.0262082i | \(0.00834330\pi\) | ||||
−0.999657 | + | 0.0262082i | \(0.991657\pi\) | |||||||
\(828\) | 211278. | + | 266241.i | 0.308172 | + | 0.388342i | ||||
\(829\) | −576268. | −0.838523 | −0.419262 | − | 0.907865i | \(-0.637711\pi\) | ||||
−0.419262 | + | 0.907865i | \(0.637711\pi\) | |||||||
\(830\) | 78031.8 | 0.113270 | ||||||||
\(831\) | −20305.9 | −0.0294050 | ||||||||
\(832\) | 140779. | 0.203372 | ||||||||
\(833\) | 14626.7i | 0.0210793i | ||||||||
\(834\) | 14507.3 | 0.0208571 | ||||||||
\(835\) | − | 161620.i | − | 0.231805i | ||||||
\(836\) | 82630.8 | 0.118230 | ||||||||
\(837\) | −77934.2 | −0.111244 | ||||||||
\(838\) | − | 260797.i | − | 0.371376i | ||||||
\(839\) | − | 87596.3i | − | 0.124441i | −0.998062 | − | 0.0622203i | \(-0.980182\pi\) | ||
0.998062 | − | 0.0622203i | \(-0.0198181\pi\) | |||||||
\(840\) | −3546.66 | −0.00502644 | ||||||||
\(841\) | −636516. | −0.899948 | ||||||||
\(842\) | − | 773687.i | − | 1.09129i | ||||||
\(843\) | 88415.3i | 0.124415i | ||||||||
\(844\) | 544292. | 0.764094 | ||||||||
\(845\) | 525941.i | 0.736586i | ||||||||
\(846\) | 391191. | 0.546573 | ||||||||
\(847\) | − | 228030.i | − | 0.317853i | ||||||
\(848\) | 171360.i | 0.238296i | ||||||||
\(849\) | − | 28852.4i | − | 0.0400282i | ||||||
\(850\) | 2445.36i | 0.00338458i | ||||||||
\(851\) | 468604. | − | 371864.i | 0.647063 | − | 0.513482i | ||||
\(852\) | 51811.3 | 0.0713748 | ||||||||
\(853\) | −420184. | −0.577486 | −0.288743 | − | 0.957407i | \(-0.593237\pi\) | ||||
−0.288743 | + | 0.957407i | \(0.593237\pi\) | |||||||
\(854\) | 200104. | 0.274373 | ||||||||
\(855\) | 271924. | 0.371976 | ||||||||
\(856\) | 272418.i | 0.371782i | ||||||||
\(857\) | 230966. | 0.314476 | 0.157238 | − | 0.987561i | \(-0.449741\pi\) | ||||
0.157238 | + | 0.987561i | \(0.449741\pi\) | |||||||
\(858\) | 21979.3i | 0.0298565i | ||||||||
\(859\) | −563067. | −0.763086 | −0.381543 | − | 0.924351i | \(-0.624607\pi\) | ||||
−0.381543 | + | 0.924351i | \(0.624607\pi\) | |||||||
\(860\) | −295458. | −0.399483 | ||||||||
\(861\) | − | 24806.1i | − | 0.0334621i | ||||||
\(862\) | 308057.i | 0.414588i | ||||||||
\(863\) | 126973. | 0.170486 | 0.0852432 | − | 0.996360i | \(-0.472833\pi\) | ||||
0.0852432 | + | 0.996360i | \(0.472833\pi\) | |||||||
\(864\) | 24196.2 | 0.0324131 | ||||||||
\(865\) | − | 106797.i | − | 0.142733i | ||||||
\(866\) | 430793.i | 0.574424i | ||||||||
\(867\) | 69167.0 | 0.0920155 | ||||||||
\(868\) | − | 78917.3i | − | 0.104745i | ||||||
\(869\) | 392398. | 0.519622 | ||||||||
\(870\) | − | 6970.46i | − | 0.00920922i | ||||||
\(871\) | 1.71330e6i | 2.25838i | ||||||||
\(872\) | 341891.i | 0.449629i | ||||||||
\(873\) | − | 1.09563e6i | − | 1.43759i | ||||||
\(874\) | −354933. | + | 281660.i | −0.464647 | + | 0.368724i | ||||
\(875\) | −23645.2 | −0.0308835 | ||||||||
\(876\) | 36171.2 | 0.0471363 | ||||||||
\(877\) | 189475. | 0.246351 | 0.123175 | − | 0.992385i | \(-0.460692\pi\) | ||||
0.123175 | + | 0.992385i | \(0.460692\pi\) | |||||||
\(878\) | −368830. | −0.478451 | ||||||||
\(879\) | 80494.8i | 0.104181i | ||||||||
\(880\) | 24405.2 | 0.0315150 | ||||||||
\(881\) | 1.05812e6i | 1.36328i | 0.731688 | + | 0.681640i | \(0.238733\pi\) | ||||
−0.731688 | + | 0.681640i | \(0.761267\pi\) | |||||||
\(882\) | 480387. | 0.617524 | ||||||||
\(883\) | 672501. | 0.862524 | 0.431262 | − | 0.902227i | \(-0.358068\pi\) | ||||
0.431262 | + | 0.902227i | \(0.358068\pi\) | |||||||
\(884\) | 15214.1i | 0.0194689i | ||||||||
\(885\) | 11827.2i | 0.0151007i | ||||||||
\(886\) | 717139. | 0.913558 | ||||||||
\(887\) | 868186. | 1.10348 | 0.551742 | − | 0.834015i | \(-0.313963\pi\) | ||||
0.551742 | + | 0.834015i | \(0.313963\pi\) | |||||||
\(888\) | − | 21202.9i | − | 0.0268887i | ||||||
\(889\) | 296695.i | 0.375411i | ||||||||
\(890\) | 7677.46 | 0.00969254 | ||||||||
\(891\) | − | 218104.i | − | 0.274731i | ||||||
\(892\) | −11968.3 | −0.0150419 | ||||||||
\(893\) | 521507.i | 0.653969i | ||||||||
\(894\) | 71441.2i | 0.0893869i | ||||||||
\(895\) | − | 273960.i | − | 0.342011i | ||||||
\(896\) | 24501.5i | 0.0305194i | ||||||||
\(897\) | −74919.8 | − | 94410.0i | −0.0931133 | − | 0.117336i | ||||
\(898\) | −290399. | −0.360117 | ||||||||
\(899\) | 155101. | 0.191909 | ||||||||
\(900\) | 80313.4 | 0.0991523 | ||||||||
\(901\) | −18519.0 | −0.0228122 | ||||||||
\(902\) | 170696.i | 0.209802i | ||||||||
\(903\) | 46310.5 | 0.0567942 | ||||||||
\(904\) | 122889.i | 0.150375i | ||||||||
\(905\) | 37092.1 | 0.0452881 | ||||||||
\(906\) | −16011.2 | −0.0195060 | ||||||||
\(907\) | − | 83304.6i | − | 0.101264i | −0.998717 | − | 0.0506319i | \(-0.983876\pi\) | ||
0.998717 | − | 0.0506319i | \(-0.0161235\pi\) | |||||||
\(908\) | 134690.i | 0.163366i | ||||||||
\(909\) | 234238. | 0.283485 | ||||||||
\(910\) | −147111. | −0.177649 | ||||||||
\(911\) | − | 759069.i | − | 0.914628i | −0.889305 | − | 0.457314i | \(-0.848812\pi\) | ||
0.889305 | − | 0.457314i | \(-0.151188\pi\) | |||||||
\(912\) | 16059.7i | 0.0193084i | ||||||||
\(913\) | 84162.8 | 0.100967 | ||||||||
\(914\) | − | 129371.i | − | 0.154862i | ||||||
\(915\) | 38738.4 | 0.0462700 | ||||||||
\(916\) | − | 152213.i | − | 0.181410i | ||||||
\(917\) | 442042.i | 0.525684i | ||||||||
\(918\) | 2614.90i | 0.00310292i | ||||||||
\(919\) | − | 89451.9i | − | 0.105915i | −0.998597 | − | 0.0529576i | \(-0.983135\pi\) | ||
0.998597 | − | 0.0529576i | \(-0.0168648\pi\) | |||||||
\(920\) | −104830. | + | 83189.0i | −0.123854 | + | 0.0982857i | ||||
\(921\) | −102867. | −0.121271 | ||||||||
\(922\) | −441323. | −0.519152 | ||||||||
\(923\) | 2.14907e6 | 2.52259 | ||||||||
\(924\) | −3825.32 | −0.00448047 | ||||||||
\(925\) | − | 141357.i | − | 0.165210i | ||||||
\(926\) | −662776. | −0.772938 | ||||||||
\(927\) | 1.35082e6i | 1.57195i | ||||||||
\(928\) | −48154.2 | −0.0559163 | ||||||||
\(929\) | 742708. | 0.860571 | 0.430285 | − | 0.902693i | \(-0.358413\pi\) | ||||
0.430285 | + | 0.902693i | \(0.358413\pi\) | |||||||
\(930\) | − | 15277.7i | − | 0.0176641i | ||||||
\(931\) | 640415.i | 0.738860i | ||||||||
\(932\) | 516091. | 0.594148 | ||||||||
\(933\) | −68134.1 | −0.0782711 | ||||||||
\(934\) | − | 1.08977e6i | − | 1.24922i | ||||||
\(935\) | 2637.49i | 0.00301695i | ||||||||
\(936\) | 499679. | 0.570348 | ||||||||
\(937\) | − | 534562.i | − | 0.608862i | −0.952534 | − | 0.304431i | \(-0.901534\pi\) | ||
0.952534 | − | 0.304431i | \(-0.0984663\pi\) | |||||||
\(938\) | −298185. | −0.338907 | ||||||||
\(939\) | − | 90272.7i | − | 0.102382i | ||||||
\(940\) | 154029.i | 0.174319i | ||||||||
\(941\) | 1.55592e6i | 1.75714i | 0.477611 | + | 0.878571i | \(0.341503\pi\) | ||||
−0.477611 | + | 0.878571i | \(0.658497\pi\) | |||||||
\(942\) | − | 103710.i | − | 0.116874i | ||||||
\(943\) | −581843. | − | 733208.i | −0.654308 | − | 0.824525i | ||||
\(944\) | 81706.2 | 0.0916877 | ||||||||
\(945\) | −25284.5 | −0.0283133 | ||||||||
\(946\) | −318672. | −0.356091 | ||||||||
\(947\) | 115842. | 0.129171 | 0.0645857 | − | 0.997912i | \(-0.479427\pi\) | ||||
0.0645857 | + | 0.997912i | \(0.479427\pi\) | |||||||
\(948\) | 76264.3i | 0.0848603i | ||||||||
\(949\) | 1.50034e6 | 1.66593 | ||||||||
\(950\) | 107068.i | 0.118635i | ||||||||
\(951\) | 88841.5 | 0.0982324 | ||||||||
\(952\) | −2647.89 | −0.00292164 | ||||||||
\(953\) | 158527.i | 0.174550i | 0.996184 | + | 0.0872748i | \(0.0278158\pi\) | ||||
−0.996184 | + | 0.0872748i | \(0.972184\pi\) | |||||||
\(954\) | 608222.i | 0.668290i | ||||||||
\(955\) | 267295. | 0.293079 | ||||||||
\(956\) | 46080.8 | 0.0504202 | ||||||||
\(957\) | − | 7518.13i | − | 0.00820891i | ||||||
\(958\) | 232376.i | 0.253197i | ||||||||
\(959\) | 297618. | 0.323610 | ||||||||
\(960\) | 4743.26i | 0.00514677i | ||||||||
\(961\) | −583575. | −0.631902 | ||||||||
\(962\) | − | 879472.i | − | 0.950324i | ||||||
\(963\) | 966917.i | 1.04265i | ||||||||
\(964\) | − | 253177.i | − | 0.272439i | ||||||
\(965\) | 139777.i | 0.150100i | ||||||||
\(966\) | 16431.3 | − | 13039.2i | 0.0176083 | − | 0.0139732i | ||||
\(967\) | 482715. | 0.516223 | 0.258112 | − | 0.966115i | \(-0.416900\pi\) | ||||
0.258112 | + | 0.966115i | \(0.416900\pi\) | |||||||
\(968\) | −304965. | −0.325462 | ||||||||
\(969\) | −1735.58 | −0.00184840 | ||||||||
\(970\) | 431397. | 0.458494 | ||||||||
\(971\) | 59475.4i | 0.0630810i | 0.999502 | + | 0.0315405i | \(0.0100413\pi\) | ||||
−0.999502 | + | 0.0315405i | \(0.989959\pi\) | |||||||
\(972\) | 129005. | 0.136545 | ||||||||
\(973\) | 104729.i | 0.110622i | ||||||||
\(974\) | 647227. | 0.682243 | ||||||||
\(975\) | −28479.4 | −0.0299586 | ||||||||
\(976\) | − | 267617.i | − | 0.280941i | ||||||
\(977\) | − | 935020.i | − | 0.979562i | −0.871845 | − | 0.489781i | \(-0.837077\pi\) | ||
0.871845 | − | 0.489781i | \(-0.162923\pi\) | |||||||
\(978\) | −8382.51 | −0.00876388 | ||||||||
\(979\) | 8280.67 | 0.00863973 | ||||||||
\(980\) | 189148.i | 0.196948i | ||||||||
\(981\) | 1.21350e6i | 1.26096i | ||||||||
\(982\) | −637142. | −0.660713 | ||||||||
\(983\) | 330831.i | 0.342373i | 0.985239 | + | 0.171186i | \(0.0547600\pi\) | ||||
−0.985239 | + | 0.171186i | \(0.945240\pi\) | |||||||
\(984\) | −33175.5 | −0.0342631 | ||||||||
\(985\) | − | 195843.i | − | 0.201853i | ||||||
\(986\) | − | 5204.06i | − | 0.00535289i | ||||||
\(987\) | − | 24142.7i | − | 0.0247828i | ||||||
\(988\) | 666135.i | 0.682415i | ||||||||
\(989\) | 1.36882e6 | − | 1.08624e6i | 1.39944 | − | 1.11054i | ||||
\(990\) | 86623.6 | 0.0883824 | ||||||||
\(991\) | 1.44595e6 | 1.47234 | 0.736168 | − | 0.676799i | \(-0.236634\pi\) | ||||
0.736168 | + | 0.676799i | \(0.236634\pi\) | |||||||
\(992\) | −105543. | −0.107252 | ||||||||
\(993\) | −106784. | −0.108294 | ||||||||
\(994\) | 374028.i | 0.378557i | ||||||||
\(995\) | 97121.3 | 0.0980999 | ||||||||
\(996\) | 16357.4i | 0.0164890i | ||||||||
\(997\) | 1.39234e6 | 1.40073 | 0.700365 | − | 0.713785i | \(-0.253021\pi\) | ||||
0.700365 | + | 0.713785i | \(0.253021\pi\) | |||||||
\(998\) | 599458. | 0.601863 | ||||||||
\(999\) | − | 151158.i | − | 0.151461i |
(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 | 230.5.d.a.91.10 | yes | 32 | |
23.22 | odd | 2 | inner | 230.5.d.a.91.7 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.5.d.a.91.7 | ✓ | 32 | 23.22 | odd | 2 | inner | |
230.5.d.a.91.10 | yes | 32 | 1.1 | even | 1 | trivial |