Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.9 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.32 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.85825i | − | 1.21456i | −0.794487 | − | 0.607281i | \(-0.792260\pi\) | ||
0.794487 | − | 0.607281i | \(-0.207740\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | −7.60257 | −0.475160 | ||||||||
\(5\) | −12.5087 | −0.500349 | −0.250174 | − | 0.968201i | \(-0.580488\pi\) | ||||
−0.250174 | + | 0.968201i | \(0.580488\pi\) | |||||||
\(6\) | 25.2442i | 0.701228i | ||||||||
\(7\) | 50.4755 | 1.03011 | 0.515056 | − | 0.857156i | \(-0.327771\pi\) | ||||
0.515056 | + | 0.857156i | \(0.327771\pi\) | |||||||
\(8\) | − | 40.7968i | − | 0.637450i | ||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 60.7705i | 0.607705i | ||||||||
\(11\) | − | 191.226i | − | 1.58038i | −0.612860 | − | 0.790192i | \(-0.709981\pi\) | ||
0.612860 | − | 0.790192i | \(-0.290019\pi\) | |||||||
\(12\) | 39.5041 | 0.274334 | ||||||||
\(13\) | 0.640162i | 0.00378794i | 0.999998 | + | 0.00189397i | \(0.000602869\pi\) | ||||
−0.999998 | + | 0.00189397i | \(0.999397\pi\) | |||||||
\(14\) | − | 245.222i | − | 1.25114i | ||||||
\(15\) | 64.9972 | 0.288877 | ||||||||
\(16\) | −319.842 | −1.24938 | ||||||||
\(17\) | −549.428 | −1.90113 | −0.950567 | − | 0.310520i | \(-0.899497\pi\) | ||||
−0.950567 | + | 0.310520i | \(0.899497\pi\) | |||||||
\(18\) | − | 131.173i | − | 0.404854i | ||||||
\(19\) | 524.497 | 1.45290 | 0.726450 | − | 0.687219i | \(-0.241169\pi\) | ||||
0.726450 | + | 0.687219i | \(0.241169\pi\) | |||||||
\(20\) | 95.0984 | 0.237746 | ||||||||
\(21\) | −262.278 | −0.594736 | ||||||||
\(22\) | −929.025 | −1.91947 | ||||||||
\(23\) | 543.113i | 1.02668i | 0.858186 | + | 0.513339i | \(0.171592\pi\) | ||||
−0.858186 | + | 0.513339i | \(0.828408\pi\) | |||||||
\(24\) | 211.986i | 0.368032i | ||||||||
\(25\) | −468.532 | −0.749651 | ||||||||
\(26\) | 3.11006 | 0.00460068 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | −383.743 | −0.489469 | ||||||||
\(29\) | −296.169 | −0.352163 | −0.176081 | − | 0.984376i | \(-0.556342\pi\) | ||||
−0.176081 | + | 0.984376i | \(0.556342\pi\) | |||||||
\(30\) | − | 315.773i | − | 0.350858i | ||||||
\(31\) | − | 1078.43i | − | 1.12220i | −0.827748 | − | 0.561100i | \(-0.810378\pi\) | ||
0.827748 | − | 0.561100i | \(-0.189622\pi\) | |||||||
\(32\) | 901.123i | 0.880003i | ||||||||
\(33\) | 993.642i | 0.912435i | ||||||||
\(34\) | 2669.26i | 2.30904i | ||||||||
\(35\) | −631.384 | −0.515416 | ||||||||
\(36\) | −205.269 | −0.158387 | ||||||||
\(37\) | 1168.43i | 0.853493i | 0.904371 | + | 0.426747i | \(0.140340\pi\) | ||||
−0.904371 | + | 0.426747i | \(0.859660\pi\) | |||||||
\(38\) | − | 2548.14i | − | 1.76464i | ||||||
\(39\) | − | 3.32638i | − | 0.00218697i | ||||||
\(40\) | 510.316i | 0.318947i | ||||||||
\(41\) | −1128.78 | −0.671494 | −0.335747 | − | 0.941952i | \(-0.608989\pi\) | ||||
−0.335747 | + | 0.941952i | \(0.608989\pi\) | |||||||
\(42\) | 1274.21i | 0.722343i | ||||||||
\(43\) | − | 1522.74i | − | 0.823547i | −0.911286 | − | 0.411773i | \(-0.864910\pi\) | ||
0.911286 | − | 0.411773i | \(-0.135090\pi\) | |||||||
\(44\) | 1453.81i | 0.750936i | ||||||||
\(45\) | −337.735 | −0.166783 | ||||||||
\(46\) | 2638.58 | 1.24696 | ||||||||
\(47\) | − | 103.190i | − | 0.0467135i | −0.999727 | − | 0.0233567i | \(-0.992565\pi\) | ||
0.999727 | − | 0.0233567i | \(-0.00743536\pi\) | |||||||
\(48\) | 1661.95 | 0.721332 | ||||||||
\(49\) | 146.777 | 0.0611316 | ||||||||
\(50\) | 2276.24i | 0.910498i | ||||||||
\(51\) | 2854.91 | 1.09762 | ||||||||
\(52\) | − | 4.86687i | − | 0.00179988i | ||||||
\(53\) | −2811.88 | −1.00103 | −0.500513 | − | 0.865729i | \(-0.666855\pi\) | ||||
−0.500513 | + | 0.865729i | \(0.666855\pi\) | |||||||
\(54\) | 681.593i | 0.233743i | ||||||||
\(55\) | 2392.00i | 0.790743i | ||||||||
\(56\) | − | 2059.24i | − | 0.656645i | ||||||
\(57\) | −2725.37 | −0.838832 | ||||||||
\(58\) | 1438.86i | 0.427723i | ||||||||
\(59\) | −2562.55 | − | 2355.99i | −0.736155 | − | 0.676813i | ||||
\(60\) | −494.146 | −0.137263 | ||||||||
\(61\) | 4909.65i | 1.31944i | 0.751510 | + | 0.659722i | \(0.229326\pi\) | ||||
−0.751510 | + | 0.659722i | \(0.770674\pi\) | |||||||
\(62\) | −5239.30 | −1.36298 | ||||||||
\(63\) | 1362.84 | 0.343371 | ||||||||
\(64\) | −739.596 | −0.180565 | ||||||||
\(65\) | − | 8.00760i | − | 0.00189529i | ||||||
\(66\) | 4827.36 | 1.10821 | ||||||||
\(67\) | 5854.39i | 1.30416i | 0.758149 | + | 0.652082i | \(0.226104\pi\) | ||||
−0.758149 | + | 0.652082i | \(0.773896\pi\) | |||||||
\(68\) | 4177.06 | 0.903343 | ||||||||
\(69\) | − | 2822.10i | − | 0.592753i | ||||||
\(70\) | 3067.42i | 0.626004i | ||||||||
\(71\) | 5828.87 | 1.15629 | 0.578146 | − | 0.815933i | \(-0.303776\pi\) | ||||
0.578146 | + | 0.815933i | \(0.303776\pi\) | |||||||
\(72\) | − | 1101.51i | − | 0.212483i | ||||||
\(73\) | − | 6751.02i | − | 1.26684i | −0.773806 | − | 0.633422i | \(-0.781650\pi\) | ||
0.773806 | − | 0.633422i | \(-0.218350\pi\) | |||||||
\(74\) | 5676.53 | 1.03662 | ||||||||
\(75\) | 2434.56 | 0.432811 | ||||||||
\(76\) | −3987.52 | −0.690361 | ||||||||
\(77\) | − | 9652.25i | − | 1.62797i | ||||||
\(78\) | −16.1604 | −0.00265621 | ||||||||
\(79\) | −9333.98 | −1.49559 | −0.747795 | − | 0.663929i | \(-0.768888\pi\) | ||||
−0.747795 | + | 0.663929i | \(0.768888\pi\) | |||||||
\(80\) | 4000.81 | 0.625127 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 5483.90i | 0.815571i | ||||||||
\(83\) | − | 1839.42i | − | 0.267008i | −0.991048 | − | 0.133504i | \(-0.957377\pi\) | ||
0.991048 | − | 0.133504i | \(-0.0426229\pi\) | |||||||
\(84\) | 1993.99 | 0.282595 | ||||||||
\(85\) | 6872.64 | 0.951230 | ||||||||
\(86\) | −7397.84 | −1.00025 | ||||||||
\(87\) | 1538.94 | 0.203321 | ||||||||
\(88\) | −7801.43 | −1.00742 | ||||||||
\(89\) | − | 5734.95i | − | 0.724018i | −0.932175 | − | 0.362009i | \(-0.882091\pi\) | ||
0.932175 | − | 0.362009i | \(-0.117909\pi\) | |||||||
\(90\) | 1640.80i | 0.202568i | ||||||||
\(91\) | 32.3125i | 0.00390200i | ||||||||
\(92\) | − | 4129.05i | − | 0.487837i | ||||||
\(93\) | 5603.71i | 0.647902i | ||||||||
\(94\) | −501.323 | −0.0567364 | ||||||||
\(95\) | −6560.79 | −0.726957 | ||||||||
\(96\) | − | 4682.37i | − | 0.508070i | ||||||
\(97\) | − | 15272.6i | − | 1.62319i | −0.584223 | − | 0.811593i | \(-0.698601\pi\) | ||
0.584223 | − | 0.811593i | \(-0.301399\pi\) | |||||||
\(98\) | − | 713.079i | − | 0.0742481i | ||||||
\(99\) | − | 5163.11i | − | 0.526795i | ||||||
\(100\) | 3562.04 | 0.356204 | ||||||||
\(101\) | − | 13635.2i | − | 1.33665i | −0.743868 | − | 0.668327i | \(-0.767011\pi\) | ||
0.743868 | − | 0.668327i | \(-0.232989\pi\) | |||||||
\(102\) | − | 13869.9i | − | 1.33313i | ||||||
\(103\) | − | 4773.40i | − | 0.449939i | −0.974366 | − | 0.224969i | \(-0.927772\pi\) | ||
0.974366 | − | 0.224969i | \(-0.0722282\pi\) | |||||||
\(104\) | 26.1166 | 0.00241462 | ||||||||
\(105\) | 3280.77 | 0.297575 | ||||||||
\(106\) | 13660.8i | 1.21581i | ||||||||
\(107\) | 10911.5 | 0.953051 | 0.476525 | − | 0.879161i | \(-0.341896\pi\) | ||||
0.476525 | + | 0.879161i | \(0.341896\pi\) | |||||||
\(108\) | 1066.61 | 0.0914446 | ||||||||
\(109\) | − | 1327.72i | − | 0.111752i | −0.998438 | − | 0.0558758i | \(-0.982205\pi\) | ||
0.998438 | − | 0.0558758i | \(-0.0177951\pi\) | |||||||
\(110\) | 11620.9 | 0.960406 | ||||||||
\(111\) | − | 6071.35i | − | 0.492764i | ||||||
\(112\) | −16144.2 | −1.28700 | ||||||||
\(113\) | 7206.57i | 0.564380i | 0.959359 | + | 0.282190i | \(0.0910608\pi\) | ||||
−0.959359 | + | 0.282190i | \(0.908939\pi\) | |||||||
\(114\) | 13240.5i | 1.01881i | ||||||||
\(115\) | − | 6793.65i | − | 0.513697i | ||||||
\(116\) | 2251.64 | 0.167334 | ||||||||
\(117\) | 17.2844i | 0.00126265i | ||||||||
\(118\) | −11446.0 | + | 12449.5i | −0.822031 | + | 0.894105i | ||||
\(119\) | −27732.6 | −1.95838 | ||||||||
\(120\) | − | 2651.68i | − | 0.184144i | ||||||
\(121\) | −21926.5 | −1.49761 | ||||||||
\(122\) | 23852.3 | 1.60255 | ||||||||
\(123\) | 5865.32 | 0.387687 | ||||||||
\(124\) | 8198.86i | 0.533225i | ||||||||
\(125\) | 13678.7 | 0.875436 | ||||||||
\(126\) | − | 6621.01i | − | 0.417045i | ||||||
\(127\) | 30152.5 | 1.86946 | 0.934729 | − | 0.355361i | \(-0.115642\pi\) | ||||
0.934729 | + | 0.355361i | \(0.115642\pi\) | |||||||
\(128\) | 18011.1i | 1.09931i | ||||||||
\(129\) | 7912.38i | 0.475475i | ||||||||
\(130\) | −38.9029 | −0.00230195 | ||||||||
\(131\) | − | 30591.4i | − | 1.78261i | −0.453404 | − | 0.891305i | \(-0.649790\pi\) | ||
0.453404 | − | 0.891305i | \(-0.350210\pi\) | |||||||
\(132\) | − | 7554.23i | − | 0.433553i | ||||||
\(133\) | 26474.3 | 1.49665 | ||||||||
\(134\) | 28442.1 | 1.58399 | ||||||||
\(135\) | 1754.92 | 0.0962922 | ||||||||
\(136\) | 22414.9i | 1.21188i | ||||||||
\(137\) | 28251.4 | 1.50521 | 0.752607 | − | 0.658470i | \(-0.228796\pi\) | ||||
0.752607 | + | 0.658470i | \(0.228796\pi\) | |||||||
\(138\) | −13710.4 | −0.719935 | ||||||||
\(139\) | 6125.81 | 0.317054 | 0.158527 | − | 0.987355i | \(-0.449325\pi\) | ||||
0.158527 | + | 0.987355i | \(0.449325\pi\) | |||||||
\(140\) | 4800.14 | 0.244905 | ||||||||
\(141\) | 536.191i | 0.0269700i | ||||||||
\(142\) | − | 28318.1i | − | 1.40439i | ||||||
\(143\) | 122.416 | 0.00598640 | ||||||||
\(144\) | −8635.74 | −0.416461 | ||||||||
\(145\) | 3704.69 | 0.176204 | ||||||||
\(146\) | −32798.1 | −1.53866 | ||||||||
\(147\) | −762.676 | −0.0352944 | ||||||||
\(148\) | − | 8883.08i | − | 0.405546i | ||||||
\(149\) | 35941.9i | 1.61893i | 0.587166 | + | 0.809467i | \(0.300244\pi\) | ||||
−0.587166 | + | 0.809467i | \(0.699756\pi\) | |||||||
\(150\) | − | 11827.7i | − | 0.525676i | ||||||
\(151\) | − | 3815.72i | − | 0.167349i | −0.996493 | − | 0.0836745i | \(-0.973334\pi\) | ||
0.996493 | − | 0.0836745i | \(-0.0266656\pi\) | |||||||
\(152\) | − | 21397.8i | − | 0.926152i | ||||||
\(153\) | −14834.5 | −0.633711 | ||||||||
\(154\) | −46893.0 | −1.97727 | ||||||||
\(155\) | 13489.8i | 0.561491i | ||||||||
\(156\) | 25.2890i | 0.00103916i | ||||||||
\(157\) | 14168.1i | 0.574795i | 0.957811 | + | 0.287398i | \(0.0927901\pi\) | ||||
−0.957811 | + | 0.287398i | \(0.907210\pi\) | |||||||
\(158\) | 45346.8i | 1.81649i | ||||||||
\(159\) | 14611.0 | 0.577943 | ||||||||
\(160\) | − | 11271.9i | − | 0.440308i | ||||||
\(161\) | 27413.9i | 1.05759i | ||||||||
\(162\) | − | 3541.66i | − | 0.134951i | ||||||
\(163\) | −5436.37 | −0.204613 | −0.102307 | − | 0.994753i | \(-0.532622\pi\) | ||||
−0.102307 | + | 0.994753i | \(0.532622\pi\) | |||||||
\(164\) | 8581.64 | 0.319068 | ||||||||
\(165\) | − | 12429.2i | − | 0.456536i | ||||||
\(166\) | −8936.35 | −0.324298 | ||||||||
\(167\) | 10745.5 | 0.385296 | 0.192648 | − | 0.981268i | \(-0.438293\pi\) | ||||
0.192648 | + | 0.981268i | \(0.438293\pi\) | |||||||
\(168\) | 10700.1i | 0.379114i | ||||||||
\(169\) | 28560.6 | 0.999986 | ||||||||
\(170\) | − | 33389.0i | − | 1.15533i | ||||||
\(171\) | 14161.4 | 0.484300 | ||||||||
\(172\) | 11576.7i | 0.391317i | ||||||||
\(173\) | 27249.2i | 0.910463i | 0.890373 | + | 0.455231i | \(0.150443\pi\) | ||||
−0.890373 | + | 0.455231i | \(0.849557\pi\) | |||||||
\(174\) | − | 7476.54i | − | 0.246946i | ||||||
\(175\) | −23649.4 | −0.772225 | ||||||||
\(176\) | 61162.3i | 1.97450i | ||||||||
\(177\) | 13315.4 | + | 12242.1i | 0.425019 | + | 0.390758i | ||||
\(178\) | −27861.8 | −0.879365 | ||||||||
\(179\) | − | 60313.1i | − | 1.88237i | −0.337890 | − | 0.941186i | \(-0.609713\pi\) | ||
0.337890 | − | 0.941186i | \(-0.390287\pi\) | |||||||
\(180\) | 2567.66 | 0.0792486 | ||||||||
\(181\) | −27872.8 | −0.850793 | −0.425396 | − | 0.905007i | \(-0.639865\pi\) | ||||
−0.425396 | + | 0.905007i | \(0.639865\pi\) | |||||||
\(182\) | 156.982 | 0.00473922 | ||||||||
\(183\) | − | 25511.3i | − | 0.761781i | ||||||
\(184\) | 22157.3 | 0.654456 | ||||||||
\(185\) | − | 14615.6i | − | 0.427044i | ||||||
\(186\) | 27224.2 | 0.786917 | ||||||||
\(187\) | 105065.i | 3.00452i | ||||||||
\(188\) | 784.509i | 0.0221964i | ||||||||
\(189\) | −7081.52 | −0.198245 | ||||||||
\(190\) | 31873.9i | 0.882934i | ||||||||
\(191\) | 32832.5i | 0.899989i | 0.893031 | + | 0.449995i | \(0.148574\pi\) | ||||
−0.893031 | + | 0.449995i | \(0.851426\pi\) | |||||||
\(192\) | 3843.05 | 0.104250 | ||||||||
\(193\) | −51056.4 | −1.37068 | −0.685339 | − | 0.728224i | \(-0.740346\pi\) | ||||
−0.685339 | + | 0.728224i | \(0.740346\pi\) | |||||||
\(194\) | −74197.9 | −1.97146 | ||||||||
\(195\) | 41.6087i | 0.00109425i | ||||||||
\(196\) | −1115.88 | −0.0290473 | ||||||||
\(197\) | 52427.0 | 1.35090 | 0.675449 | − | 0.737407i | \(-0.263950\pi\) | ||||
0.675449 | + | 0.737407i | \(0.263950\pi\) | |||||||
\(198\) | −25083.7 | −0.639825 | ||||||||
\(199\) | −21283.2 | −0.537440 | −0.268720 | − | 0.963218i | \(-0.586601\pi\) | ||||
−0.268720 | + | 0.963218i | \(0.586601\pi\) | |||||||
\(200\) | 19114.6i | 0.477865i | ||||||||
\(201\) | − | 30420.3i | − | 0.752959i | ||||||
\(202\) | −66243.2 | −1.62345 | ||||||||
\(203\) | −14949.3 | −0.362767 | ||||||||
\(204\) | −21704.6 | −0.521546 | ||||||||
\(205\) | 14119.6 | 0.335981 | ||||||||
\(206\) | −23190.3 | −0.546478 | ||||||||
\(207\) | 14664.0i | 0.342226i | ||||||||
\(208\) | − | 204.751i | − | 0.00473259i | ||||||
\(209\) | − | 100298.i | − | 2.29614i | ||||||
\(210\) | − | 15938.8i | − | 0.361424i | ||||||
\(211\) | − | 67797.8i | − | 1.52283i | −0.648267 | − | 0.761413i | \(-0.724506\pi\) | ||
0.648267 | − | 0.761413i | \(-0.275494\pi\) | |||||||
\(212\) | 21377.5 | 0.475648 | ||||||||
\(213\) | −30287.7 | −0.667585 | ||||||||
\(214\) | − | 53010.7i | − | 1.15754i | ||||||
\(215\) | 19047.5i | 0.412061i | ||||||||
\(216\) | 5723.63i | 0.122677i | ||||||||
\(217\) | − | 54434.5i | − | 1.15599i | ||||||
\(218\) | −6450.40 | −0.135729 | ||||||||
\(219\) | 35079.3i | 0.731413i | ||||||||
\(220\) | − | 18185.3i | − | 0.375730i | ||||||
\(221\) | − | 351.722i | − | 0.00720138i | ||||||
\(222\) | −29496.1 | −0.598493 | ||||||||
\(223\) | 45072.8 | 0.906368 | 0.453184 | − | 0.891417i | \(-0.350288\pi\) | ||||
0.453184 | + | 0.891417i | \(0.350288\pi\) | |||||||
\(224\) | 45484.6i | 0.906502i | ||||||||
\(225\) | −12650.4 | −0.249884 | ||||||||
\(226\) | 35011.3 | 0.685474 | ||||||||
\(227\) | − | 13186.6i | − | 0.255906i | −0.991780 | − | 0.127953i | \(-0.959159\pi\) | ||
0.991780 | − | 0.127953i | \(-0.0408407\pi\) | |||||||
\(228\) | 20719.8 | 0.398580 | ||||||||
\(229\) | − | 5098.55i | − | 0.0972244i | −0.998818 | − | 0.0486122i | \(-0.984520\pi\) | ||
0.998818 | − | 0.0486122i | \(-0.0154799\pi\) | |||||||
\(230\) | −33005.2 | −0.623917 | ||||||||
\(231\) | 50154.6i | 0.939911i | ||||||||
\(232\) | 12082.7i | 0.224486i | ||||||||
\(233\) | − | 45461.0i | − | 0.837390i | −0.908127 | − | 0.418695i | \(-0.862488\pi\) | ||
0.908127 | − | 0.418695i | \(-0.137512\pi\) | |||||||
\(234\) | 83.9717 | 0.00153356 | ||||||||
\(235\) | 1290.78i | 0.0233730i | ||||||||
\(236\) | 19482.0 | + | 17911.5i | 0.349792 | + | 0.321595i | ||||
\(237\) | 48500.8 | 0.863480 | ||||||||
\(238\) | 134732.i | 2.37858i | ||||||||
\(239\) | −80213.6 | −1.40427 | −0.702137 | − | 0.712041i | \(-0.747771\pi\) | ||||
−0.702137 | + | 0.712041i | \(0.747771\pi\) | |||||||
\(240\) | −20788.8 | −0.360917 | ||||||||
\(241\) | 27279.2 | 0.469676 | 0.234838 | − | 0.972035i | \(-0.424544\pi\) | ||||
0.234838 | + | 0.972035i | \(0.424544\pi\) | |||||||
\(242\) | 106525.i | 1.81894i | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | − | 37325.9i | − | 0.626947i | ||||||
\(245\) | −1835.99 | −0.0305871 | ||||||||
\(246\) | − | 28495.2i | − | 0.470870i | ||||||
\(247\) | 335.763i | 0.00550350i | ||||||||
\(248\) | −43996.7 | −0.715346 | ||||||||
\(249\) | 9557.90i | 0.154157i | ||||||||
\(250\) | − | 66454.4i | − | 1.06327i | ||||||
\(251\) | −87290.9 | −1.38555 | −0.692774 | − | 0.721155i | \(-0.743612\pi\) | ||||
−0.692774 | + | 0.721155i | \(0.743612\pi\) | |||||||
\(252\) | −10361.1 | −0.163156 | ||||||||
\(253\) | 103858. | 1.62255 | ||||||||
\(254\) | − | 146488.i | − | 2.27057i | ||||||
\(255\) | −35711.3 | −0.549193 | ||||||||
\(256\) | 75668.9 | 1.15462 | ||||||||
\(257\) | −1669.20 | −0.0252721 | −0.0126361 | − | 0.999920i | \(-0.504022\pi\) | ||||
−0.0126361 | + | 0.999920i | \(0.504022\pi\) | |||||||
\(258\) | 38440.3 | 0.577494 | ||||||||
\(259\) | 58977.2i | 0.879194i | ||||||||
\(260\) | 60.8783i | 0.000900567i | ||||||||
\(261\) | −7996.55 | −0.117388 | ||||||||
\(262\) | −148620. | −2.16509 | ||||||||
\(263\) | 99916.5 | 1.44453 | 0.722264 | − | 0.691618i | \(-0.243102\pi\) | ||||
0.722264 | + | 0.691618i | \(0.243102\pi\) | |||||||
\(264\) | 40537.4 | 0.581632 | ||||||||
\(265\) | 35173.1 | 0.500862 | ||||||||
\(266\) | − | 128618.i | − | 1.81777i | ||||||
\(267\) | 29799.7i | 0.418012i | ||||||||
\(268\) | − | 44508.4i | − | 0.619687i | ||||||
\(269\) | 24594.1i | 0.339881i | 0.985454 | + | 0.169940i | \(0.0543575\pi\) | ||||
−0.985454 | + | 0.169940i | \(0.945642\pi\) | |||||||
\(270\) | − | 8525.86i | − | 0.116953i | ||||||
\(271\) | 12306.3 | 0.167567 | 0.0837836 | − | 0.996484i | \(-0.473300\pi\) | ||||
0.0837836 | + | 0.996484i | \(0.473300\pi\) | |||||||
\(272\) | 175730. | 2.37524 | ||||||||
\(273\) | − | 167.901i | − | 0.00225282i | ||||||
\(274\) | − | 137252.i | − | 1.82818i | ||||||
\(275\) | 89595.7i | 1.18474i | ||||||||
\(276\) | 21455.2i | 0.281653i | ||||||||
\(277\) | 30853.9 | 0.402115 | 0.201058 | − | 0.979579i | \(-0.435562\pi\) | ||||
0.201058 | + | 0.979579i | \(0.435562\pi\) | |||||||
\(278\) | − | 29760.7i | − | 0.385082i | ||||||
\(279\) | − | 29117.7i | − | 0.374066i | ||||||
\(280\) | 25758.5i | 0.328552i | ||||||||
\(281\) | 6311.40 | 0.0799306 | 0.0399653 | − | 0.999201i | \(-0.487275\pi\) | ||||
0.0399653 | + | 0.999201i | \(0.487275\pi\) | |||||||
\(282\) | 2604.95 | 0.0327568 | ||||||||
\(283\) | 37474.9i | 0.467916i | 0.972247 | + | 0.233958i | \(0.0751678\pi\) | ||||
−0.972247 | + | 0.233958i | \(0.924832\pi\) | |||||||
\(284\) | −44314.3 | −0.549424 | ||||||||
\(285\) | 34090.8 | 0.419709 | ||||||||
\(286\) | − | 594.726i | − | 0.00727085i | ||||||
\(287\) | −56975.9 | −0.691715 | ||||||||
\(288\) | 24330.3i | 0.293334i | ||||||||
\(289\) | 218350. | 2.61431 | ||||||||
\(290\) | − | 17998.3i | − | 0.214011i | ||||||
\(291\) | 79358.6i | 0.937147i | ||||||||
\(292\) | 51325.0i | 0.601954i | ||||||||
\(293\) | 13284.3 | 0.154740 | 0.0773700 | − | 0.997002i | \(-0.475348\pi\) | ||||
0.0773700 | + | 0.997002i | \(0.475348\pi\) | |||||||
\(294\) | 3705.27i | 0.0428672i | ||||||||
\(295\) | 32054.3 | + | 29470.4i | 0.368334 | + | 0.338643i | ||||
\(296\) | 47668.3 | 0.544059 | ||||||||
\(297\) | 26828.3i | 0.304145i | ||||||||
\(298\) | 174615. | 1.96629 | ||||||||
\(299\) | −347.680 | −0.00388899 | ||||||||
\(300\) | −18508.9 | −0.205655 | ||||||||
\(301\) | − | 76861.0i | − | 0.848346i | ||||||
\(302\) | −18537.7 | −0.203256 | ||||||||
\(303\) | 70850.6i | 0.771717i | ||||||||
\(304\) | −167756. | −1.81523 | ||||||||
\(305\) | − | 61413.4i | − | 0.660182i | ||||||
\(306\) | 72069.9i | 0.769682i | ||||||||
\(307\) | 27275.0 | 0.289393 | 0.144697 | − | 0.989476i | \(-0.453779\pi\) | ||||
0.144697 | + | 0.989476i | \(0.453779\pi\) | |||||||
\(308\) | 73381.9i | 0.773548i | ||||||||
\(309\) | 24803.3i | 0.259772i | ||||||||
\(310\) | 65536.9 | 0.681966 | ||||||||
\(311\) | 74737.1 | 0.772708 | 0.386354 | − | 0.922351i | \(-0.373734\pi\) | ||||
0.386354 | + | 0.922351i | \(0.373734\pi\) | |||||||
\(312\) | −135.706 | −0.00139408 | ||||||||
\(313\) | − | 147610.i | − | 1.50670i | −0.657618 | − | 0.753352i | \(-0.728436\pi\) | ||
0.657618 | − | 0.753352i | \(-0.271564\pi\) | |||||||
\(314\) | 68832.3 | 0.698124 | ||||||||
\(315\) | −17047.4 | −0.171805 | ||||||||
\(316\) | 70962.2 | 0.710645 | ||||||||
\(317\) | −75632.0 | −0.752640 | −0.376320 | − | 0.926490i | \(-0.622811\pi\) | ||||
−0.376320 | + | 0.926490i | \(0.622811\pi\) | |||||||
\(318\) | − | 70983.7i | − | 0.701947i | ||||||
\(319\) | 56635.3i | 0.556552i | ||||||||
\(320\) | 9251.40 | 0.0903457 | ||||||||
\(321\) | −56697.7 | −0.550244 | ||||||||
\(322\) | 133183. | 1.28451 | ||||||||
\(323\) | −288173. | −2.76216 | ||||||||
\(324\) | −5542.27 | −0.0527956 | ||||||||
\(325\) | − | 299.936i | − | 0.00283963i | ||||||
\(326\) | 26411.2i | 0.248515i | ||||||||
\(327\) | 6899.04i | 0.0645198i | ||||||||
\(328\) | 46050.7i | 0.428044i | ||||||||
\(329\) | − | 5208.57i | − | 0.0481201i | ||||||
\(330\) | −60384.1 | −0.554491 | ||||||||
\(331\) | 43603.6 | 0.397985 | 0.198992 | − | 0.980001i | \(-0.436233\pi\) | ||||
0.198992 | + | 0.980001i | \(0.436233\pi\) | |||||||
\(332\) | 13984.3i | 0.126872i | ||||||||
\(333\) | 31547.7i | 0.284498i | ||||||||
\(334\) | − | 52204.3i | − | 0.467965i | ||||||
\(335\) | − | 73230.9i | − | 0.652537i | ||||||
\(336\) | 83887.7 | 0.743053 | ||||||||
\(337\) | − | 111943.i | − | 0.985682i | −0.870119 | − | 0.492841i | \(-0.835958\pi\) | ||
0.870119 | − | 0.492841i | \(-0.164042\pi\) | |||||||
\(338\) | − | 138754.i | − | 1.21454i | ||||||
\(339\) | − | 37446.4i | − | 0.325845i | ||||||
\(340\) | −52249.7 | −0.451987 | ||||||||
\(341\) | −206225. | −1.77351 | ||||||||
\(342\) | − | 68799.7i | − | 0.588212i | ||||||
\(343\) | −113783. | −0.967140 | ||||||||
\(344\) | −62122.9 | −0.524970 | ||||||||
\(345\) | 35300.8i | 0.296583i | ||||||||
\(346\) | 132384. | 1.10581 | ||||||||
\(347\) | 43440.9i | 0.360778i | 0.983595 | + | 0.180389i | \(0.0577357\pi\) | ||||
−0.983595 | + | 0.180389i | \(0.942264\pi\) | |||||||
\(348\) | −11699.9 | −0.0966101 | ||||||||
\(349\) | 63411.1i | 0.520612i | 0.965526 | + | 0.260306i | \(0.0838235\pi\) | ||||
−0.965526 | + | 0.260306i | \(0.916177\pi\) | |||||||
\(350\) | 114895.i | 0.937915i | ||||||||
\(351\) | − | 89.8122i | − | 0.000728989i | ||||||
\(352\) | 172318. | 1.39074 | ||||||||
\(353\) | − | 152287.i | − | 1.22212i | −0.791585 | − | 0.611059i | \(-0.790744\pi\) | ||
0.791585 | − | 0.611059i | \(-0.209256\pi\) | |||||||
\(354\) | 59475.0 | − | 64689.6i | 0.474600 | − | 0.516212i | ||||
\(355\) | −72911.7 | −0.578549 | ||||||||
\(356\) | 43600.3i | 0.344025i | ||||||||
\(357\) | 144103. | 1.13067 | ||||||||
\(358\) | −293016. | −2.28626 | ||||||||
\(359\) | 38536.4 | 0.299008 | 0.149504 | − | 0.988761i | \(-0.452232\pi\) | ||||
0.149504 | + | 0.988761i | \(0.452232\pi\) | |||||||
\(360\) | 13778.5i | 0.106316i | ||||||||
\(361\) | 144776. | 1.11092 | ||||||||
\(362\) | 135413.i | 1.03334i | ||||||||
\(363\) | 113934. | 0.864647 | ||||||||
\(364\) | − | 245.658i | − | 0.00185408i | ||||||
\(365\) | 84446.6i | 0.633864i | ||||||||
\(366\) | −123940. | −0.925230 | ||||||||
\(367\) | − | 127968.i | − | 0.950102i | −0.879958 | − | 0.475051i | \(-0.842430\pi\) | ||
0.879958 | − | 0.475051i | \(-0.157570\pi\) | |||||||
\(368\) | − | 173710.i | − | 1.28271i | ||||||
\(369\) | −30477.1 | −0.223831 | ||||||||
\(370\) | −71006.1 | −0.518672 | ||||||||
\(371\) | −141931. | −1.03117 | ||||||||
\(372\) | − | 42602.5i | − | 0.307857i | ||||||
\(373\) | −181481. | −1.30441 | −0.652203 | − | 0.758044i | \(-0.726155\pi\) | ||||
−0.652203 | + | 0.758044i | \(0.726155\pi\) | |||||||
\(374\) | 510432. | 3.64918 | ||||||||
\(375\) | −71076.5 | −0.505433 | ||||||||
\(376\) | −4209.83 | −0.0297775 | ||||||||
\(377\) | − | 189.596i | − | 0.00133397i | ||||||
\(378\) | 34403.8i | 0.240781i | ||||||||
\(379\) | −52087.4 | −0.362622 | −0.181311 | − | 0.983426i | \(-0.558034\pi\) | ||||
−0.181311 | + | 0.983426i | \(0.558034\pi\) | |||||||
\(380\) | 49878.8 | 0.345421 | ||||||||
\(381\) | −156677. | −1.07933 | ||||||||
\(382\) | 159508. | 1.09309 | ||||||||
\(383\) | −129457. | −0.882527 | −0.441263 | − | 0.897378i | \(-0.645470\pi\) | ||||
−0.441263 | + | 0.897378i | \(0.645470\pi\) | |||||||
\(384\) | − | 93588.4i | − | 0.634687i | ||||||
\(385\) | 120737.i | 0.814554i | ||||||||
\(386\) | 248045.i | 1.66477i | ||||||||
\(387\) | − | 41113.9i | − | 0.274516i | ||||||
\(388\) | 116111.i | 0.771274i | ||||||||
\(389\) | −239714. | −1.58414 | −0.792070 | − | 0.610430i | \(-0.790997\pi\) | ||||
−0.792070 | + | 0.610430i | \(0.790997\pi\) | |||||||
\(390\) | 202.145 | 0.00132903 | ||||||||
\(391\) | − | 298401.i | − | 1.95185i | ||||||
\(392\) | − | 5988.03i | − | 0.0389684i | ||||||
\(393\) | 158957.i | 1.02919i | ||||||||
\(394\) | − | 254703.i | − | 1.64075i | ||||||
\(395\) | 116756. | 0.748317 | ||||||||
\(396\) | 39252.9i | 0.250312i | ||||||||
\(397\) | 63125.7i | 0.400521i | 0.979743 | + | 0.200260i | \(0.0641788\pi\) | ||||
−0.979743 | + | 0.200260i | \(0.935821\pi\) | |||||||
\(398\) | 103399.i | 0.652755i | ||||||||
\(399\) | −137564. | −0.864092 | ||||||||
\(400\) | 149856. | 0.936601 | ||||||||
\(401\) | − | 5633.87i | − | 0.0350363i | −0.999847 | − | 0.0175181i | \(-0.994424\pi\) | ||
0.999847 | − | 0.0175181i | \(-0.00557648\pi\) | |||||||
\(402\) | −147789. | −0.914515 | ||||||||
\(403\) | 690.372 | 0.00425082 | ||||||||
\(404\) | 103663.i | 0.635125i | ||||||||
\(405\) | −9118.86 | −0.0555943 | ||||||||
\(406\) | 72627.2i | 0.440603i | ||||||||
\(407\) | 223435. | 1.34885 | ||||||||
\(408\) | − | 116471.i | − | 0.699678i | ||||||
\(409\) | − | 208211.i | − | 1.24468i | −0.782747 | − | 0.622340i | \(-0.786182\pi\) | ||
0.782747 | − | 0.622340i | \(-0.213818\pi\) | |||||||
\(410\) | − | 68596.6i | − | 0.408070i | ||||||
\(411\) | −146798. | −0.869036 | ||||||||
\(412\) | 36290.1i | 0.213793i | ||||||||
\(413\) | −129346. | − | 118920.i | −0.758322 | − | 0.697194i | ||||
\(414\) | 71241.6 | 0.415655 | ||||||||
\(415\) | 23008.8i | 0.133597i | ||||||||
\(416\) | −576.864 | −0.00333340 | ||||||||
\(417\) | −31830.6 | −0.183051 | ||||||||
\(418\) | −487271. | −2.78880 | ||||||||
\(419\) | − | 29129.4i | − | 0.165922i | −0.996553 | − | 0.0829610i | \(-0.973562\pi\) | ||
0.996553 | − | 0.0829610i | \(-0.0264377\pi\) | |||||||
\(420\) | −24942.2 | −0.141396 | ||||||||
\(421\) | − | 297451.i | − | 1.67823i | −0.543956 | − | 0.839113i | \(-0.683074\pi\) | ||
0.543956 | − | 0.839113i | \(-0.316926\pi\) | |||||||
\(422\) | −329378. | −1.84957 | ||||||||
\(423\) | − | 2786.13i | − | 0.0155712i | ||||||
\(424\) | 114716.i | 0.638105i | ||||||||
\(425\) | 257424. | 1.42519 | ||||||||
\(426\) | 147145.i | 0.810824i | ||||||||
\(427\) | 247817.i | 1.35917i | ||||||||
\(428\) | −82955.2 | −0.452852 | ||||||||
\(429\) | −636.091 | −0.00345625 | ||||||||
\(430\) | 92537.5 | 0.500473 | ||||||||
\(431\) | 340194.i | 1.83135i | 0.401917 | + | 0.915676i | \(0.368344\pi\) | ||||
−0.401917 | + | 0.915676i | \(0.631656\pi\) | |||||||
\(432\) | 44872.6 | 0.240444 | ||||||||
\(433\) | −19705.6 | −0.105103 | −0.0525514 | − | 0.998618i | \(-0.516735\pi\) | ||||
−0.0525514 | + | 0.998618i | \(0.516735\pi\) | |||||||
\(434\) | −264456. | −1.40402 | ||||||||
\(435\) | −19250.1 | −0.101731 | ||||||||
\(436\) | 10094.1i | 0.0530999i | ||||||||
\(437\) | 284861.i | 1.49166i | ||||||||
\(438\) | 170424. | 0.888347 | ||||||||
\(439\) | 29208.1 | 0.151557 | 0.0757783 | − | 0.997125i | \(-0.475856\pi\) | ||||
0.0757783 | + | 0.997125i | \(0.475856\pi\) | |||||||
\(440\) | 97585.9 | 0.504059 | ||||||||
\(441\) | 3962.98 | 0.0203772 | ||||||||
\(442\) | −1708.75 | −0.00874652 | ||||||||
\(443\) | 136923.i | 0.697698i | 0.937179 | + | 0.348849i | \(0.113427\pi\) | ||||
−0.937179 | + | 0.348849i | \(0.886573\pi\) | |||||||
\(444\) | 46157.8i | 0.234142i | ||||||||
\(445\) | 71736.9i | 0.362262i | ||||||||
\(446\) | − | 218975.i | − | 1.10084i | ||||||
\(447\) | − | 186760.i | − | 0.934692i | ||||||
\(448\) | −37331.5 | −0.186003 | ||||||||
\(449\) | 324943. | 1.61181 | 0.805906 | − | 0.592043i | \(-0.201678\pi\) | ||||
0.805906 | + | 0.592043i | \(0.201678\pi\) | |||||||
\(450\) | 61458.6i | 0.303499i | ||||||||
\(451\) | 215853.i | 1.06122i | ||||||||
\(452\) | − | 54788.4i | − | 0.268171i | ||||||
\(453\) | 19827.1i | 0.0966190i | ||||||||
\(454\) | −64063.8 | −0.310814 | ||||||||
\(455\) | − | 404.188i | − | 0.00195236i | ||||||
\(456\) | 111186.i | 0.534714i | ||||||||
\(457\) | 142683.i | 0.683189i | 0.939847 | + | 0.341595i | \(0.110967\pi\) | ||||
−0.939847 | + | 0.341595i | \(0.889033\pi\) | |||||||
\(458\) | −24770.0 | −0.118085 | ||||||||
\(459\) | 77082.6 | 0.365873 | ||||||||
\(460\) | 51649.1i | 0.244089i | ||||||||
\(461\) | 107011. | 0.503533 | 0.251767 | − | 0.967788i | \(-0.418988\pi\) | ||||
0.251767 | + | 0.967788i | \(0.418988\pi\) | |||||||
\(462\) | 243663. | 1.14158 | ||||||||
\(463\) | − | 344520.i | − | 1.60714i | −0.595213 | − | 0.803568i | \(-0.702932\pi\) | ||
0.595213 | − | 0.803568i | \(-0.297068\pi\) | |||||||
\(464\) | 94727.2 | 0.439986 | ||||||||
\(465\) | − | 70095.2i | − | 0.324177i | ||||||
\(466\) | −220861. | −1.01706 | ||||||||
\(467\) | − | 12985.4i | − | 0.0595419i | −0.999557 | − | 0.0297709i | \(-0.990522\pi\) | ||
0.999557 | − | 0.0297709i | \(-0.00947778\pi\) | |||||||
\(468\) | − | 131.405i | − | 0.000599959i | ||||||
\(469\) | 295503.i | 1.34343i | ||||||||
\(470\) | 6270.91 | 0.0283880 | ||||||||
\(471\) | − | 73619.7i | − | 0.331858i | ||||||
\(472\) | −96116.8 | + | 104544.i | −0.431435 | + | 0.469262i | ||||
\(473\) | −291188. | −1.30152 | ||||||||
\(474\) | − | 235629.i | − | 1.04875i | ||||||
\(475\) | −245744. | −1.08917 | ||||||||
\(476\) | 210839. | 0.930545 | ||||||||
\(477\) | −75920.9 | −0.333676 | ||||||||
\(478\) | 389697.i | 1.70558i | ||||||||
\(479\) | 148631. | 0.647798 | 0.323899 | − | 0.946092i | \(-0.395006\pi\) | ||||
0.323899 | + | 0.946092i | \(0.395006\pi\) | |||||||
\(480\) | 58570.5i | 0.254212i | ||||||||
\(481\) | −747.985 | −0.00323298 | ||||||||
\(482\) | − | 132529.i | − | 0.570450i | ||||||
\(483\) | − | 142447.i | − | 0.610602i | ||||||
\(484\) | 166698. | 0.711606 | ||||||||
\(485\) | 191040.i | 0.812159i | ||||||||
\(486\) | 18403.0i | 0.0779142i | ||||||||
\(487\) | 174834. | 0.737169 | 0.368584 | − | 0.929594i | \(-0.379843\pi\) | ||||
0.368584 | + | 0.929594i | \(0.379843\pi\) | |||||||
\(488\) | 200298. | 0.841079 | ||||||||
\(489\) | 28248.2 | 0.118133 | ||||||||
\(490\) | 8919.71i | 0.0371500i | ||||||||
\(491\) | −289993. | −1.20288 | −0.601442 | − | 0.798916i | \(-0.705407\pi\) | ||||
−0.601442 | + | 0.798916i | \(0.705407\pi\) | |||||||
\(492\) | −44591.5 | −0.184214 | ||||||||
\(493\) | 162723. | 0.669508 | ||||||||
\(494\) | 1631.22 | 0.00668434 | ||||||||
\(495\) | 64583.9i | 0.263581i | ||||||||
\(496\) | 344928.i | 1.40206i | ||||||||
\(497\) | 294215. | 1.19111 | ||||||||
\(498\) | 46434.6 | 0.187233 | ||||||||
\(499\) | −337039. | −1.35356 | −0.676782 | − | 0.736183i | \(-0.736626\pi\) | ||||
−0.676782 | + | 0.736183i | \(0.736626\pi\) | |||||||
\(500\) | −103993. | −0.415972 | ||||||||
\(501\) | −55835.3 | −0.222451 | ||||||||
\(502\) | 424081.i | 1.68283i | ||||||||
\(503\) | 424514.i | 1.67786i | 0.544238 | + | 0.838931i | \(0.316819\pi\) | ||||
−0.544238 | + | 0.838931i | \(0.683181\pi\) | |||||||
\(504\) | − | 55599.5i | − | 0.218882i | ||||||
\(505\) | 170559.i | 0.668793i | ||||||||
\(506\) | − | 504566.i | − | 1.97068i | ||||||
\(507\) | −148405. | −0.577342 | ||||||||
\(508\) | −229236. | −0.888292 | ||||||||
\(509\) | − | 166873.i | − | 0.644095i | −0.946724 | − | 0.322047i | \(-0.895629\pi\) | ||
0.946724 | − | 0.322047i | \(-0.104371\pi\) | |||||||
\(510\) | 173494.i | 0.667029i | ||||||||
\(511\) | − | 340761.i | − | 1.30499i | ||||||
\(512\) | − | 79440.3i | − | 0.303041i | ||||||
\(513\) | −73584.9 | −0.279611 | ||||||||
\(514\) | 8109.37i | 0.0306945i | ||||||||
\(515\) | 59709.1i | 0.225126i | ||||||||
\(516\) | − | 60154.4i | − | 0.225927i | ||||||
\(517\) | −19732.7 | −0.0738252 | ||||||||
\(518\) | 286526. | 1.06784 | ||||||||
\(519\) | − | 141591.i | − | 0.525656i | ||||||
\(520\) | −326.685 | −0.00120815 | ||||||||
\(521\) | 234510. | 0.863943 | 0.431972 | − | 0.901887i | \(-0.357818\pi\) | ||||
0.431972 | + | 0.901887i | \(0.357818\pi\) | |||||||
\(522\) | 38849.2i | 0.142574i | ||||||||
\(523\) | 133011. | 0.486277 | 0.243138 | − | 0.969992i | \(-0.421823\pi\) | ||||
0.243138 | + | 0.969992i | \(0.421823\pi\) | |||||||
\(524\) | 232573.i | 0.847026i | ||||||||
\(525\) | 122886. | 0.445844 | ||||||||
\(526\) | − | 485419.i | − | 1.75447i | ||||||
\(527\) | 592521.i | 2.13345i | ||||||||
\(528\) | − | 317808.i | − | 1.13998i | ||||||
\(529\) | −15130.5 | −0.0540683 | ||||||||
\(530\) | − | 170879.i | − | 0.608328i | ||||||
\(531\) | −69189.0 | − | 63611.6i | −0.245385 | − | 0.225604i | ||||
\(532\) | −201272. | −0.711149 | ||||||||
\(533\) | − | 722.603i | − | 0.00254358i | ||||||
\(534\) | 144774. | 0.507702 | ||||||||
\(535\) | −136489. | −0.476858 | ||||||||
\(536\) | 238840. | 0.831339 | ||||||||
\(537\) | 313396.i | 1.08679i | ||||||||
\(538\) | 119484. | 0.412806 | ||||||||
\(539\) | − | 28067.6i | − | 0.0966114i | ||||||
\(540\) | −13341.9 | −0.0457542 | ||||||||
\(541\) | − | 37399.8i | − | 0.127784i | −0.997957 | − | 0.0638918i | \(-0.979649\pi\) | ||
0.997957 | − | 0.0638918i | \(-0.0203512\pi\) | |||||||
\(542\) | − | 59787.0i | − | 0.203521i | ||||||
\(543\) | 144831. | 0.491205 | ||||||||
\(544\) | − | 495102.i | − | 1.67300i | ||||||
\(545\) | 16608.1i | 0.0559148i | ||||||||
\(546\) | −815.702 | −0.00273619 | ||||||||
\(547\) | −3623.89 | −0.0121116 | −0.00605579 | − | 0.999982i | \(-0.501928\pi\) | ||||
−0.00605579 | + | 0.999982i | \(0.501928\pi\) | |||||||
\(548\) | −214783. | −0.715218 | ||||||||
\(549\) | 132561.i | 0.439814i | ||||||||
\(550\) | 435278. | 1.43894 | ||||||||
\(551\) | −155340. | −0.511657 | ||||||||
\(552\) | −115133. | −0.377851 | ||||||||
\(553\) | −471138. | −1.54063 | ||||||||
\(554\) | − | 149896.i | − | 0.488394i | ||||||
\(555\) | 75944.8i | 0.246554i | ||||||||
\(556\) | −46571.8 | −0.150652 | ||||||||
\(557\) | 223715. | 0.721082 | 0.360541 | − | 0.932743i | \(-0.382592\pi\) | ||||
0.360541 | + | 0.932743i | \(0.382592\pi\) | |||||||
\(558\) | −141461. | −0.454327 | ||||||||
\(559\) | 974.798 | 0.00311954 | ||||||||
\(560\) | 201943. | 0.643951 | ||||||||
\(561\) | − | 545934.i | − | 1.73466i | ||||||
\(562\) | − | 30662.3i | − | 0.0970807i | ||||||
\(563\) | 74625.8i | 0.235436i | 0.993047 | + | 0.117718i | \(0.0375578\pi\) | ||||
−0.993047 | + | 0.117718i | \(0.962442\pi\) | |||||||
\(564\) | − | 4076.43i | − | 0.0128151i | ||||||
\(565\) | − | 90144.9i | − | 0.282387i | ||||||
\(566\) | 182062. | 0.568313 | ||||||||
\(567\) | 36796.6 | 0.114457 | ||||||||
\(568\) | − | 237799.i | − | 0.737079i | ||||||
\(569\) | − | 319733.i | − | 0.987558i | −0.869588 | − | 0.493779i | \(-0.835615\pi\) | ||
0.869588 | − | 0.493779i | \(-0.164385\pi\) | |||||||
\(570\) | − | 165622.i | − | 0.509762i | ||||||
\(571\) | 25255.1i | 0.0774598i | 0.999250 | + | 0.0387299i | \(0.0123312\pi\) | ||||
−0.999250 | + | 0.0387299i | \(0.987669\pi\) | |||||||
\(572\) | −930.674 | −0.00284450 | ||||||||
\(573\) | − | 170603.i | − | 0.519609i | ||||||
\(574\) | 276803.i | 0.840130i | ||||||||
\(575\) | − | 254466.i | − | 0.769650i | ||||||
\(576\) | −19969.1 | −0.0601885 | ||||||||
\(577\) | 442259. | 1.32839 | 0.664194 | − | 0.747560i | \(-0.268775\pi\) | ||||
0.664194 | + | 0.747560i | \(0.268775\pi\) | |||||||
\(578\) | − | 1.06080e6i | − | 3.17524i | ||||||
\(579\) | 265297. | 0.791362 | ||||||||
\(580\) | −28165.2 | −0.0837252 | ||||||||
\(581\) | − | 92845.6i | − | 0.275048i | ||||||
\(582\) | 385543. | 1.13822 | ||||||||
\(583\) | 537706.i | 1.58201i | ||||||||
\(584\) | −275420. | −0.807551 | ||||||||
\(585\) | − | 216.205i | − | 0.000631763i | ||||||
\(586\) | − | 64538.3i | − | 0.187941i | ||||||
\(587\) | 122543.i | 0.355641i | 0.984063 | + | 0.177821i | \(0.0569047\pi\) | ||||
−0.984063 | + | 0.177821i | \(0.943095\pi\) | |||||||
\(588\) | 5798.29 | 0.0167705 | ||||||||
\(589\) | − | 565635.i | − | 1.63044i | ||||||
\(590\) | 143174. | − | 155728.i | 0.411302 | − | 0.447365i | ||||
\(591\) | −272418. | −0.779941 | ||||||||
\(592\) | − | 373714.i | − | 1.06634i | ||||||
\(593\) | −531802. | −1.51231 | −0.756154 | − | 0.654393i | \(-0.772924\pi\) | ||||
−0.756154 | + | 0.654393i | \(0.772924\pi\) | |||||||
\(594\) | 130339. | 0.369403 | ||||||||
\(595\) | 346900. | 0.979874 | ||||||||
\(596\) | − | 273251.i | − | 0.769253i | ||||||
\(597\) | 110591. | 0.310291 | ||||||||
\(598\) | 1689.11i | 0.00472342i | ||||||||
\(599\) | 55605.2 | 0.154975 | 0.0774875 | − | 0.996993i | \(-0.475310\pi\) | ||||
0.0774875 | + | 0.996993i | \(0.475310\pi\) | |||||||
\(600\) | − | 99322.4i | − | 0.275896i | ||||||
\(601\) | − | 351895.i | − | 0.974236i | −0.873336 | − | 0.487118i | \(-0.838048\pi\) | ||
0.873336 | − | 0.487118i | \(-0.161952\pi\) | |||||||
\(602\) | −373410. | −1.03037 | ||||||||
\(603\) | 158069.i | 0.434721i | ||||||||
\(604\) | 29009.3i | 0.0795176i | ||||||||
\(605\) | 274273. | 0.749329 | ||||||||
\(606\) | 344210. | 0.937298 | ||||||||
\(607\) | 130700. | 0.354731 | 0.177365 | − | 0.984145i | \(-0.443243\pi\) | ||||
0.177365 | + | 0.984145i | \(0.443243\pi\) | |||||||
\(608\) | 472636.i | 1.27856i | ||||||||
\(609\) | 77678.7 | 0.209444 | ||||||||
\(610\) | −298362. | −0.801832 | ||||||||
\(611\) | 66.0583 | 0.000176948 | ||||||||
\(612\) | 112781. | 0.301114 | ||||||||
\(613\) | 509749.i | 1.35655i | 0.734808 | + | 0.678275i | \(0.237272\pi\) | ||||
−0.734808 | + | 0.678275i | \(0.762728\pi\) | |||||||
\(614\) | − | 132509.i | − | 0.351486i | ||||||
\(615\) | −73367.7 | −0.193979 | ||||||||
\(616\) | −393781. | −1.03775 | ||||||||
\(617\) | −77698.9 | −0.204101 | −0.102050 | − | 0.994779i | \(-0.532540\pi\) | ||||
−0.102050 | + | 0.994779i | \(0.532540\pi\) | |||||||
\(618\) | 120501. | 0.315509 | ||||||||
\(619\) | 221586. | 0.578309 | 0.289155 | − | 0.957282i | \(-0.406626\pi\) | ||||
0.289155 | + | 0.957282i | \(0.406626\pi\) | |||||||
\(620\) | − | 102557.i | − | 0.266798i | ||||||
\(621\) | − | 76196.6i | − | 0.197584i | ||||||
\(622\) | − | 363091.i | − | 0.938502i | ||||||
\(623\) | − | 289475.i | − | 0.745820i | ||||||
\(624\) | 1063.92i | 0.00273236i | ||||||||
\(625\) | 121730. | 0.311628 | ||||||||
\(626\) | −717127. | −1.82998 | ||||||||
\(627\) | 521162.i | 1.32568i | ||||||||
\(628\) | − | 107714.i | − | 0.273120i | ||||||
\(629\) | − | 641969.i | − | 1.62260i | ||||||
\(630\) | 82820.3i | 0.208668i | ||||||||
\(631\) | 2526.90 | 0.00634642 | 0.00317321 | − | 0.999995i | \(-0.498990\pi\) | ||||
0.00317321 | + | 0.999995i | \(0.498990\pi\) | |||||||
\(632\) | 380797.i | 0.953365i | ||||||||
\(633\) | 352288.i | 0.879204i | ||||||||
\(634\) | 367439.i | 0.914127i | ||||||||
\(635\) | −377169. | −0.935381 | ||||||||
\(636\) | −111081. | −0.274616 | ||||||||
\(637\) | 93.9610i | 0.000231563i | ||||||||
\(638\) | 275148. | 0.675967 | ||||||||
\(639\) | 157379. | 0.385431 | ||||||||
\(640\) | − | 225296.i | − | 0.550039i | ||||||
\(641\) | 359210. | 0.874244 | 0.437122 | − | 0.899402i | \(-0.355998\pi\) | ||||
0.437122 | + | 0.899402i | \(0.355998\pi\) | |||||||
\(642\) | 275451.i | 0.668305i | ||||||||
\(643\) | 512961. | 1.24069 | 0.620344 | − | 0.784330i | \(-0.286993\pi\) | ||||
0.620344 | + | 0.784330i | \(0.286993\pi\) | |||||||
\(644\) | − | 208416.i | − | 0.502527i | ||||||
\(645\) | − | 98973.7i | − | 0.237903i | ||||||
\(646\) | 1.40002e6i | 3.35481i | ||||||||
\(647\) | −621636. | −1.48500 | −0.742502 | − | 0.669844i | \(-0.766361\pi\) | ||||
−0.742502 | + | 0.669844i | \(0.766361\pi\) | |||||||
\(648\) | − | 29740.9i | − | 0.0708278i | ||||||
\(649\) | −450527. | + | 490028.i | −1.06962 | + | 1.16341i | ||||
\(650\) | −1457.16 | −0.00344891 | ||||||||
\(651\) | 282850.i | 0.667412i | ||||||||
\(652\) | 41330.3 | 0.0972241 | ||||||||
\(653\) | 194566. | 0.456291 | 0.228145 | − | 0.973627i | \(-0.426734\pi\) | ||||
0.228145 | + | 0.973627i | \(0.426734\pi\) | |||||||
\(654\) | 33517.2 | 0.0783633 | ||||||||
\(655\) | 382659.i | 0.891927i | ||||||||
\(656\) | 361032. | 0.838954 | ||||||||
\(657\) | − | 182277.i | − | 0.422282i | ||||||
\(658\) | −25304.5 | −0.0584449 | ||||||||
\(659\) | − | 481512.i | − | 1.10876i | −0.832265 | − | 0.554378i | \(-0.812956\pi\) | ||
0.832265 | − | 0.554378i | \(-0.187044\pi\) | |||||||
\(660\) | 94493.7i | 0.216928i | ||||||||
\(661\) | 340031. | 0.778244 | 0.389122 | − | 0.921186i | \(-0.372778\pi\) | ||||
0.389122 | + | 0.921186i | \(0.372778\pi\) | |||||||
\(662\) | − | 211837.i | − | 0.483377i | ||||||
\(663\) | 1827.60i | 0.00415772i | ||||||||
\(664\) | −75042.4 | −0.170204 | ||||||||
\(665\) | −331159. | −0.748847 | ||||||||
\(666\) | 153266. | 0.345540 | ||||||||
\(667\) | − | 160853.i | − | 0.361558i | ||||||
\(668\) | −81693.4 | −0.183077 | ||||||||
\(669\) | −234205. | −0.523292 | ||||||||
\(670\) | −355774. | −0.792546 | ||||||||
\(671\) | 938855. | 2.08523 | ||||||||
\(672\) | − | 236345.i | − | 0.523369i | ||||||
\(673\) | 413955.i | 0.913951i | 0.889479 | + | 0.456976i | \(0.151067\pi\) | ||||
−0.889479 | + | 0.456976i | \(0.848933\pi\) | |||||||
\(674\) | −543846. | −1.19717 | ||||||||
\(675\) | 65733.2 | 0.144270 | ||||||||
\(676\) | −217134. | −0.475153 | ||||||||
\(677\) | −374555. | −0.817219 | −0.408609 | − | 0.912709i | \(-0.633986\pi\) | ||||
−0.408609 | + | 0.912709i | \(0.633986\pi\) | |||||||
\(678\) | −181924. | −0.395759 | ||||||||
\(679\) | − | 770890.i | − | 1.67206i | ||||||
\(680\) | − | 280382.i | − | 0.606362i | ||||||
\(681\) | 68519.6i | 0.147748i | ||||||||
\(682\) | 1.00189e6i | 2.15403i | ||||||||
\(683\) | 648839.i | 1.39090i | 0.718576 | + | 0.695449i | \(0.244794\pi\) | ||||
−0.718576 | + | 0.695449i | \(0.755206\pi\) | |||||||
\(684\) | −107663. | −0.230120 | ||||||||
\(685\) | −353388. | −0.753132 | ||||||||
\(686\) | 552786.i | 1.17465i | ||||||||
\(687\) | 26492.8i | 0.0561326i | ||||||||
\(688\) | 487036.i | 1.02893i | ||||||||
\(689\) | − | 1800.06i | − | 0.00379183i | ||||||
\(690\) | 171500. | 0.360219 | ||||||||
\(691\) | − | 622050.i | − | 1.30277i | −0.758746 | − | 0.651387i | \(-0.774187\pi\) | ||
0.758746 | − | 0.651387i | \(-0.225813\pi\) | |||||||
\(692\) | − | 207164.i | − | 0.432616i | ||||||
\(693\) | − | 260611.i | − | 0.542658i | ||||||
\(694\) | 211047. | 0.438187 | ||||||||
\(695\) | −76626.0 | −0.158638 | ||||||||
\(696\) | − | 62783.8i | − | 0.129607i | ||||||
\(697\) | 620184. | 1.27660 | ||||||||
\(698\) | 308067. | 0.632316 | ||||||||
\(699\) | 236223.i | 0.483467i | ||||||||
\(700\) | 179796. | 0.366931 | ||||||||
\(701\) | 98359.5i | 0.200161i | 0.994979 | + | 0.100081i | \(0.0319101\pi\) | ||||
−0.994979 | + | 0.100081i | \(0.968090\pi\) | |||||||
\(702\) | −436.330 | −0.000885402 | ||||||||
\(703\) | 612839.i | 1.24004i | ||||||||
\(704\) | 141430.i | 0.285363i | ||||||||
\(705\) | − | 6707.07i | − | 0.0134944i | ||||||
\(706\) | −739847. | −1.48434 | ||||||||
\(707\) | − | 688244.i | − | 1.37690i | ||||||
\(708\) | −101231. | − | 93071.1i | −0.201952 | − | 0.185673i | ||||
\(709\) | −772872. | −1.53750 | −0.768750 | − | 0.639549i | \(-0.779121\pi\) | ||||
−0.768750 | + | 0.639549i | \(0.779121\pi\) | |||||||
\(710\) | 354223.i | 0.702684i | ||||||||
\(711\) | −252018. | −0.498530 | ||||||||
\(712\) | −233968. | −0.461526 | ||||||||
\(713\) | 585711. | 1.15214 | ||||||||
\(714\) | − | 700088.i | − | 1.37327i | ||||||
\(715\) | −1531.27 | −0.00299529 | ||||||||
\(716\) | 458534.i | 0.894428i | ||||||||
\(717\) | 416802. | 0.810758 | ||||||||
\(718\) | − | 187220.i | − | 0.363164i | ||||||
\(719\) | 273060.i | 0.528202i | 0.964495 | + | 0.264101i | \(0.0850752\pi\) | ||||
−0.964495 | + | 0.264101i | \(0.914925\pi\) | |||||||
\(720\) | 108022. | 0.208376 | ||||||||
\(721\) | − | 240940.i | − | 0.463487i | ||||||
\(722\) | − | 703358.i | − | 1.34928i | ||||||
\(723\) | −141747. | −0.271167 | ||||||||
\(724\) | 211905. | 0.404263 | ||||||||
\(725\) | 138764. | 0.263999 | ||||||||
\(726\) | − | 553518.i | − | 1.05017i | ||||||
\(727\) | 31372.5 | 0.0593581 | 0.0296791 | − | 0.999559i | \(-0.490551\pi\) | ||||
0.0296791 | + | 0.999559i | \(0.490551\pi\) | |||||||
\(728\) | 1318.25 | 0.00248733 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 410262. | 0.769867 | ||||||||
\(731\) | 836634.i | 1.56567i | ||||||||
\(732\) | 193951.i | 0.361968i | ||||||||
\(733\) | 67831.8 | 0.126248 | 0.0631241 | − | 0.998006i | \(-0.479894\pi\) | ||||
0.0631241 | + | 0.998006i | \(0.479894\pi\) | |||||||
\(734\) | −621701. | −1.15396 | ||||||||
\(735\) | 9540.10 | 0.0176595 | ||||||||
\(736\) | −489411. | −0.903480 | ||||||||
\(737\) | 1.11951e6 | 2.06108 | ||||||||
\(738\) | 148065.i | 0.271857i | ||||||||
\(739\) | − | 788958.i | − | 1.44466i | −0.691549 | − | 0.722329i | \(-0.743071\pi\) | ||
0.691549 | − | 0.722329i | \(-0.256929\pi\) | |||||||
\(740\) | 111116.i | 0.202914i | ||||||||
\(741\) | − | 1744.67i | − | 0.00317745i | ||||||
\(742\) | 689537.i | 1.25242i | ||||||||
\(743\) | 50905.9 | 0.0922127 | 0.0461064 | − | 0.998937i | \(-0.485319\pi\) | ||||
0.0461064 | + | 0.998937i | \(0.485319\pi\) | |||||||
\(744\) | 228613. | 0.413005 | ||||||||
\(745\) | − | 449588.i | − | 0.810031i | ||||||
\(746\) | 881678.i | 1.58428i | ||||||||
\(747\) | − | 49664.3i | − | 0.0890027i | ||||||
\(748\) | − | 798764.i | − | 1.42763i | ||||||
\(749\) | 550762. | 0.981749 | ||||||||
\(750\) | 345307.i | 0.613880i | ||||||||
\(751\) | 473502.i | 0.839541i | 0.907630 | + | 0.419770i | \(0.137889\pi\) | ||||
−0.907630 | + | 0.419770i | \(0.862111\pi\) | |||||||
\(752\) | 33004.5i | 0.0583630i | ||||||||
\(753\) | 453577. | 0.799947 | ||||||||
\(754\) | −921.103 | −0.00162019 | ||||||||
\(755\) | 47729.8i | 0.0837329i | ||||||||
\(756\) | 53837.7 | 0.0941983 | ||||||||
\(757\) | −5901.48 | −0.0102984 | −0.00514919 | − | 0.999987i | \(-0.501639\pi\) | ||||
−0.00514919 | + | 0.999987i | \(0.501639\pi\) | |||||||
\(758\) | 253053.i | 0.440427i | ||||||||
\(759\) | −539660. | −0.936777 | ||||||||
\(760\) | 267659.i | 0.463399i | ||||||||
\(761\) | 559827. | 0.966684 | 0.483342 | − | 0.875431i | \(-0.339423\pi\) | ||||
0.483342 | + | 0.875431i | \(0.339423\pi\) | |||||||
\(762\) | 761175.i | 1.31092i | ||||||||
\(763\) | − | 67017.4i | − | 0.115117i | ||||||
\(764\) | − | 249611.i | − | 0.427639i | ||||||
\(765\) | 185561. | 0.317077 | ||||||||
\(766\) | 628934.i | 1.07188i | ||||||||
\(767\) | 1508.21 | − | 1640.45i | 0.00256373 | − | 0.00278851i | ||||
\(768\) | −393187. | −0.666617 | ||||||||
\(769\) | 752520.i | 1.27252i | 0.771473 | + | 0.636262i | \(0.219520\pi\) | ||||
−0.771473 | + | 0.636262i | \(0.780480\pi\) | |||||||
\(770\) | 586572. | 0.989327 | ||||||||
\(771\) | 8673.40 | 0.0145909 | ||||||||
\(772\) | 388160. | 0.651292 | ||||||||
\(773\) | 293795.i | 0.491684i | 0.969310 | + | 0.245842i | \(0.0790644\pi\) | ||||
−0.969310 | + | 0.245842i | \(0.920936\pi\) | |||||||
\(774\) | −199742. | −0.333416 | ||||||||
\(775\) | 505281.i | 0.841258i | ||||||||
\(776\) | −623072. | −1.03470 | ||||||||
\(777\) | − | 306454.i | − | 0.507603i | ||||||
\(778\) | 1.16459e6i | 1.92404i | ||||||||
\(779\) | −592043. | −0.975614 | ||||||||
\(780\) | − | 316.333i | − | 0.000519942i | ||||||
\(781\) | − | 1.11463e6i | − | 1.82738i | ||||||
\(782\) | −1.44971e6 | −2.37065 | ||||||||
\(783\) | 41551.3 | 0.0677737 | ||||||||
\(784\) | −46945.5 | −0.0763768 | ||||||||
\(785\) | − | 177225.i | − | 0.287598i | ||||||
\(786\) | 772255. | 1.25002 | ||||||||
\(787\) | 642350. | 1.03710 | 0.518552 | − | 0.855046i | \(-0.326471\pi\) | ||||
0.518552 | + | 0.855046i | \(0.326471\pi\) | |||||||
\(788\) | −398579. | −0.641893 | ||||||||
\(789\) | −519181. | −0.833998 | ||||||||
\(790\) | − | 567230.i | − | 0.908877i | ||||||
\(791\) | 363755.i | 0.581375i | ||||||||
\(792\) | −210639. | −0.335805 | ||||||||
\(793\) | −3142.97 | −0.00499797 | ||||||||
\(794\) | 306680. | 0.486457 | ||||||||
\(795\) | −182765. | −0.289173 | ||||||||
\(796\) | 161807. | 0.255370 | ||||||||
\(797\) | − | 766042.i | − | 1.20597i | −0.797753 | − | 0.602984i | \(-0.793978\pi\) | ||
0.797753 | − | 0.602984i | \(-0.206022\pi\) | |||||||
\(798\) | 668321.i | 1.04949i | ||||||||
\(799\) | 56695.5i | 0.0888086i | ||||||||
\(800\) | − | 422205.i | − | 0.659695i | ||||||
\(801\) | − | 154844.i | − | 0.241339i | ||||||
\(802\) | −27370.7 | −0.0425537 | ||||||||
\(803\) | −1.29097e6 | −2.00210 | ||||||||
\(804\) | 231272.i | 0.357776i | ||||||||
\(805\) | − | 342913.i | − | 0.529166i | ||||||
\(806\) | − | 3354.00i | − | 0.00516289i | ||||||
\(807\) | − | 127795.i | − | 0.196230i | ||||||
\(808\) | −556273. | −0.852050 | ||||||||
\(809\) | − | 605837.i | − | 0.925675i | −0.886443 | − | 0.462837i | \(-0.846831\pi\) | ||
0.886443 | − | 0.462837i | \(-0.153169\pi\) | |||||||
\(810\) | 44301.7i | 0.0675227i | ||||||||
\(811\) | 98920.8i | 0.150399i | 0.997168 | + | 0.0751996i | \(0.0239594\pi\) | ||||
−0.997168 | + | 0.0751996i | \(0.976041\pi\) | |||||||
\(812\) | 113653. | 0.172372 | ||||||||
\(813\) | −63945.4 | −0.0967449 | ||||||||
\(814\) | − | 1.08550e6i | − | 1.63826i | ||||||
\(815\) | 68002.0 | 0.102378 | ||||||||
\(816\) | −913120. | −1.37135 | ||||||||
\(817\) | − | 798671.i | − | 1.19653i | ||||||
\(818\) | −1.01154e6 | −1.51174 | ||||||||
\(819\) | 872.437i | 0.00130067i | ||||||||
\(820\) | −107345. | −0.159645 | ||||||||
\(821\) | 412837.i | 0.612480i | 0.951954 | + | 0.306240i | \(0.0990710\pi\) | ||||
−0.951954 | + | 0.306240i | \(0.900929\pi\) | |||||||
\(822\) | 713183.i | 1.05550i | ||||||||
\(823\) | − | 1.01994e6i | − | 1.50583i | −0.658118 | − | 0.752915i | \(-0.728647\pi\) | ||
0.658118 | − | 0.752915i | \(-0.271353\pi\) | |||||||
\(824\) | −194739. | −0.286813 | ||||||||
\(825\) | − | 465553.i | − | 0.684008i | ||||||
\(826\) | −577741. | + | 628396.i | −0.846785 | + | 0.921029i | ||||
\(827\) | 396788. | 0.580159 | 0.290080 | − | 0.957003i | \(-0.406318\pi\) | ||||
0.290080 | + | 0.957003i | \(0.406318\pi\) | |||||||
\(828\) | − | 111484.i | − | 0.162612i | ||||||
\(829\) | 573455. | 0.834431 | 0.417216 | − | 0.908808i | \(-0.363006\pi\) | ||||
0.417216 | + | 0.908808i | \(0.363006\pi\) | |||||||
\(830\) | 111782. | 0.162262 | ||||||||
\(831\) | −160322. | −0.232161 | ||||||||
\(832\) | − | 473.461i | − | 0.000683971i | ||||||
\(833\) | −80643.4 | −0.116219 | ||||||||
\(834\) | 154641.i | 0.222327i | ||||||||
\(835\) | −134413. | −0.192782 | ||||||||
\(836\) | 762520.i | 1.09103i | ||||||||
\(837\) | 151300.i | 0.215967i | ||||||||
\(838\) | −141518. | −0.201522 | ||||||||
\(839\) | − | 1.02305e6i | − | 1.45337i | −0.686973 | − | 0.726683i | \(-0.741061\pi\) | ||
0.686973 | − | 0.726683i | \(-0.258939\pi\) | |||||||
\(840\) | − | 133845.i | − | 0.189689i | ||||||
\(841\) | −619565. | −0.875982 | ||||||||
\(842\) | −1.44509e6 | −2.03831 | ||||||||
\(843\) | −32795.0 | −0.0461480 | ||||||||
\(844\) | 515437.i | 0.723587i | ||||||||
\(845\) | −357256. | −0.500342 | ||||||||
\(846\) | −13535.7 | −0.0189121 | ||||||||
\(847\) | −1.10675e6 | −1.54271 | ||||||||
\(848\) | 899359. | 1.25067 | ||||||||
\(849\) | − | 194725.i | − | 0.270151i | ||||||
\(850\) | − | 1.25063e6i | − | 1.73098i | ||||||
\(851\) | −634590. | −0.876263 | ||||||||
\(852\) | 230264. | 0.317210 | ||||||||
\(853\) | −101559. | −0.139580 | −0.0697898 | − | 0.997562i | \(-0.522233\pi\) | ||||
−0.0697898 | + | 0.997562i | \(0.522233\pi\) | |||||||
\(854\) | 1.20396e6 | 1.65080 | ||||||||
\(855\) | −177141. | −0.242319 | ||||||||
\(856\) | − | 445154.i | − | 0.607522i | ||||||
\(857\) | 1.31133e6i | 1.78545i | 0.450598 | + | 0.892727i | \(0.351211\pi\) | ||||
−0.450598 | + | 0.892727i | \(0.648789\pi\) | |||||||
\(858\) | 3090.29i | 0.00419783i | ||||||||
\(859\) | − | 815255.i | − | 1.10486i | −0.833559 | − | 0.552430i | \(-0.813701\pi\) | ||
0.833559 | − | 0.552430i | \(-0.186299\pi\) | |||||||
\(860\) | − | 144810.i | − | 0.195795i | ||||||
\(861\) | 296055. | 0.399362 | ||||||||
\(862\) | 1.65275e6 | 2.22429 | ||||||||
\(863\) | 797750.i | 1.07114i | 0.844492 | + | 0.535569i | \(0.179903\pi\) | ||||
−0.844492 | + | 0.535569i | \(0.820097\pi\) | |||||||
\(864\) | − | 126424.i | − | 0.169357i | ||||||
\(865\) | − | 340853.i | − | 0.455549i | ||||||
\(866\) | 95734.8i | 0.127654i | ||||||||
\(867\) | −1.13458e6 | −1.50937 | ||||||||
\(868\) | 413842.i | 0.549281i | ||||||||
\(869\) | 1.78490e6i | 2.36361i | ||||||||
\(870\) | 93521.9i | 0.123559i | ||||||||
\(871\) | −3747.75 | −0.00494009 | ||||||||
\(872\) | −54166.8 | −0.0712361 | ||||||||
\(873\) | − | 412359.i | − | 0.541062i | ||||||
\(874\) | 1.38393e6 | 1.81171 | ||||||||
\(875\) | 690439. | 0.901797 | ||||||||
\(876\) | − | 266693.i | − | 0.347539i | ||||||
\(877\) | −542419. | −0.705238 | −0.352619 | − | 0.935767i | \(-0.614709\pi\) | ||||
−0.352619 | + | 0.935767i | \(0.614709\pi\) | |||||||
\(878\) | − | 141900.i | − | 0.184075i | ||||||
\(879\) | −69027.1 | −0.0893392 | ||||||||
\(880\) | − | 765062.i | − | 0.987941i | ||||||
\(881\) | 449854.i | 0.579588i | 0.957089 | + | 0.289794i | \(0.0935868\pi\) | ||||
−0.957089 | + | 0.289794i | \(0.906413\pi\) | |||||||
\(882\) | − | 19253.1i | − | 0.0247494i | ||||||
\(883\) | −469650. | −0.602355 | −0.301178 | − | 0.953568i | \(-0.597380\pi\) | ||||
−0.301178 | + | 0.953568i | \(0.597380\pi\) | |||||||
\(884\) | 2673.99i | 0.00342181i | ||||||||
\(885\) | −166559. | − | 153133.i | −0.212658 | − | 0.195515i | ||||
\(886\) | 665203. | 0.847397 | ||||||||
\(887\) | 126942.i | 0.161346i | 0.996741 | + | 0.0806729i | \(0.0257069\pi\) | ||||
−0.996741 | + | 0.0806729i | \(0.974293\pi\) | |||||||
\(888\) | −247692. | −0.314113 | ||||||||
\(889\) | 1.52196e6 | 1.92575 | ||||||||
\(890\) | 348516. | 0.439989 | ||||||||
\(891\) | − | 139404.i | − | 0.175598i | ||||||
\(892\) | −342669. | −0.430670 | ||||||||
\(893\) | − | 54122.9i | − | 0.0678700i | ||||||
\(894\) | −907325. | −1.13524 | ||||||||
\(895\) | 754439.i | 0.941842i | ||||||||
\(896\) | 909120.i | 1.13241i | ||||||||
\(897\) | 1806.60 | 0.00224531 | ||||||||
\(898\) | − | 1.57865e6i | − | 1.95765i | ||||||
\(899\) | 319398.i | 0.395197i | ||||||||
\(900\) | 96175.2 | 0.118735 | ||||||||
\(901\) | 1.54493e6 | 1.90309 | ||||||||
\(902\) | 1.04867e6 | 1.28892 | ||||||||
\(903\) | 399381.i | 0.489793i | ||||||||
\(904\) | 294005. | 0.359764 | ||||||||
\(905\) | 348653. | 0.425693 | ||||||||
\(906\) | 96324.9 | 0.117350 | ||||||||
\(907\) | 396178. | 0.481588 | 0.240794 | − | 0.970576i | \(-0.422592\pi\) | ||||
0.240794 | + | 0.970576i | \(0.422592\pi\) | |||||||
\(908\) | 100252.i | 0.121597i | ||||||||
\(909\) | − | 368150.i | − | 0.445551i | ||||||
\(910\) | −1963.64 | −0.00237126 | ||||||||
\(911\) | −1.15177e6 | −1.38780 | −0.693902 | − | 0.720070i | \(-0.744110\pi\) | ||||
−0.693902 | + | 0.720070i | \(0.744110\pi\) | |||||||
\(912\) | 871687. | 1.04802 | ||||||||
\(913\) | −351745. | −0.421975 | ||||||||
\(914\) | 693191. | 0.829776 | ||||||||
\(915\) | 319113.i | 0.381156i | ||||||||
\(916\) | 38762.0i | 0.0461972i | ||||||||
\(917\) | − | 1.54412e6i | − | 1.83629i | ||||||
\(918\) | − | 374486.i | − | 0.444376i | ||||||
\(919\) | − | 675878.i | − | 0.800271i | −0.916456 | − | 0.400136i | \(-0.868963\pi\) | ||
0.916456 | − | 0.400136i | \(-0.131037\pi\) | |||||||
\(920\) | −277159. | −0.327456 | ||||||||
\(921\) | −141725. | −0.167081 | ||||||||
\(922\) | − | 519888.i | − | 0.611572i | ||||||
\(923\) | 3731.42i | 0.00437996i | ||||||||
\(924\) | − | 381303.i | − | 0.446608i | ||||||
\(925\) | − | 547448.i | − | 0.639822i | ||||||
\(926\) | −1.67376e6 | −1.95197 | ||||||||
\(927\) | − | 128882.i | − | 0.149980i | ||||||
\(928\) | − | 266884.i | − | 0.309904i | ||||||
\(929\) | − | 729975.i | − | 0.845818i | −0.906172 | − | 0.422909i | \(-0.861009\pi\) | ||
0.906172 | − | 0.422909i | \(-0.138991\pi\) | |||||||
\(930\) | −340540. | −0.393733 | ||||||||
\(931\) | 76984.1 | 0.0888181 | ||||||||
\(932\) | 345621.i | 0.397894i | ||||||||
\(933\) | −388345. | −0.446123 | ||||||||
\(934\) | −63086.4 | −0.0723173 | ||||||||
\(935\) | − | 1.31423e6i | − | 1.50331i | ||||||
\(936\) | 705.147 | 0.000804874 | ||||||||
\(937\) | − | 487935.i | − | 0.555754i | −0.960617 | − | 0.277877i | \(-0.910369\pi\) | ||
0.960617 | − | 0.277877i | \(-0.0896308\pi\) | |||||||
\(938\) | 1.43563e6 | 1.63168 | ||||||||
\(939\) | 767005.i | 0.869896i | ||||||||
\(940\) | − | 9813.21i | − | 0.0111059i | ||||||
\(941\) | 51925.4i | 0.0586409i | 0.999570 | + | 0.0293204i | \(0.00933433\pi\) | ||||
−0.999570 | + | 0.0293204i | \(0.990666\pi\) | |||||||
\(942\) | −357663. | −0.403062 | ||||||||
\(943\) | − | 613056.i | − | 0.689409i | ||||||
\(944\) | 819613. | + | 753544.i | 0.919739 | + | 0.845599i | ||||
\(945\) | 88580.7 | 0.0991918 | ||||||||
\(946\) | 1.41466e6i | 1.58078i | ||||||||
\(947\) | 1.51811e6 | 1.69279 | 0.846393 | − | 0.532559i | \(-0.178769\pi\) | ||||
0.846393 | + | 0.532559i | \(0.178769\pi\) | |||||||
\(948\) | −368730. | −0.410291 | ||||||||
\(949\) | 4321.74 | 0.00479873 | ||||||||
\(950\) | 1.19388e6i | 1.32286i | ||||||||
\(951\) | 392995. | 0.434537 | ||||||||
\(952\) | 1.13140e6i | 1.24837i | ||||||||
\(953\) | −1.18731e6 | −1.30731 | −0.653653 | − | 0.756794i | \(-0.726764\pi\) | ||||
−0.653653 | + | 0.756794i | \(0.726764\pi\) | |||||||
\(954\) | 368842.i | 0.405270i | ||||||||
\(955\) | − | 410693.i | − | 0.450309i | ||||||
\(956\) | 609829. | 0.667256 | ||||||||
\(957\) | − | 294286.i | − | 0.321325i | ||||||
\(958\) | − | 722088.i | − | 0.786790i | ||||||
\(959\) | 1.42600e6 | 1.55054 | ||||||||
\(960\) | −48071.7 | −0.0521611 | ||||||||
\(961\) | −239498. | −0.259332 | ||||||||
\(962\) | 3633.90i | 0.00392665i | ||||||||
\(963\) | 294610. | 0.317684 | ||||||||
\(964\) | −207392. | −0.223171 | ||||||||
\(965\) | 638650. | 0.685817 | ||||||||
\(966\) | −692042. | −0.741614 | ||||||||
\(967\) | 1.72012e6i | 1.83953i | 0.392475 | + | 0.919763i | \(0.371619\pi\) | ||||
−0.392475 | + | 0.919763i | \(0.628381\pi\) | |||||||
\(968\) | 894533.i | 0.954654i | ||||||||
\(969\) | 1.49739e6 | 1.59473 | ||||||||
\(970\) | 928120. | 0.986418 | ||||||||
\(971\) | −88363.1 | −0.0937200 | −0.0468600 | − | 0.998901i | \(-0.514921\pi\) | ||||
−0.0468600 | + | 0.998901i | \(0.514921\pi\) | |||||||
\(972\) | 28798.5 | 0.0304815 | ||||||||
\(973\) | 309203. | 0.326602 | ||||||||
\(974\) | − | 849385.i | − | 0.895337i | ||||||
\(975\) | 1558.51i | 0.00163946i | ||||||||
\(976\) | − | 1.57031e6i | − | 1.64849i | ||||||
\(977\) | 205443.i | 0.215229i | 0.994193 | + | 0.107615i | \(0.0343213\pi\) | ||||
−0.994193 | + | 0.107615i | \(0.965679\pi\) | |||||||
\(978\) | − | 137237.i | − | 0.143480i | ||||||
\(979\) | −1.09667e6 | −1.14423 | ||||||||
\(980\) | 13958.3 | 0.0145338 | ||||||||
\(981\) | − | 35848.5i | − | 0.0372505i | ||||||
\(982\) | 1.40886e6i | 1.46098i | ||||||||
\(983\) | − | 1.79432e6i | − | 1.85692i | −0.371435 | − | 0.928459i | \(-0.621134\pi\) | ||
0.371435 | − | 0.928459i | \(-0.378866\pi\) | |||||||
\(984\) | − | 239287.i | − | 0.247131i | ||||||
\(985\) | −655794. | −0.675920 | ||||||||
\(986\) | − | 790550.i | − | 0.813159i | ||||||
\(987\) | 27064.5i | 0.0277822i | ||||||||
\(988\) | − | 2552.66i | − | 0.00261504i | ||||||
\(989\) | 827018. | 0.845517 | ||||||||
\(990\) | 313765. | 0.320135 | ||||||||
\(991\) | − | 660202.i | − | 0.672248i | −0.941818 | − | 0.336124i | \(-0.890884\pi\) | ||
0.941818 | − | 0.336124i | \(-0.109116\pi\) | |||||||
\(992\) | 971801. | 0.987538 | ||||||||
\(993\) | −226571. | −0.229777 | ||||||||
\(994\) | − | 1.42937e6i | − | 1.44668i | ||||||
\(995\) | 266225. | 0.268908 | ||||||||
\(996\) | − | 72664.5i | − | 0.0732494i | ||||||
\(997\) | −684976. | −0.689105 | −0.344552 | − | 0.938767i | \(-0.611969\pi\) | ||||
−0.344552 | + | 0.938767i | \(0.611969\pi\) | |||||||
\(998\) | 1.63742e6i | 1.64399i | ||||||||
\(999\) | − | 163926.i | − | 0.164255i |
(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 | 177.5.c.a.58.9 | ✓ | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.32 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.32 | yes | 40 | |
177.176 | even | 2 | 531.5.c.d.235.9 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.9 | ✓ | 40 | 1.1 | even | 1 | trivial | |
177.5.c.a.58.32 | yes | 40 | 59.58 | odd | 2 | inner | |
531.5.c.d.235.9 | 40 | 177.176 | even | 2 | |||
531.5.c.d.235.32 | 40 | 3.2 | odd | 2 |