Newspace parameters
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.7 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.34 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.77154i | − | 1.44289i | −0.692474 | − | 0.721443i | \(-0.743479\pi\) | ||
0.692474 | − | 0.721443i | \(-0.256521\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −17.3107 | −1.08192 | ||||||||
\(5\) | −34.3452 | −1.37381 | −0.686905 | − | 0.726748i | \(-0.741031\pi\) | ||||
−0.686905 | + | 0.726748i | \(0.741031\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −39.2727 | −0.801483 | −0.400741 | − | 0.916191i | \(-0.631247\pi\) | ||||
−0.400741 | + | 0.916191i | \(0.631247\pi\) | |||||||
\(8\) | 7.56484i | 0.118201i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 198.225i | 1.98225i | ||||||||
\(11\) | 56.8541i | 0.469868i | 0.972011 | + | 0.234934i | \(0.0754874\pi\) | ||||
−0.972011 | + | 0.234934i | \(0.924513\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 232.684i | 1.37683i | 0.725319 | + | 0.688413i | \(0.241692\pi\) | ||||
−0.725319 | + | 0.688413i | \(0.758308\pi\) | |||||||
\(14\) | 226.664i | 1.15645i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −233.311 | −0.911370 | ||||||||
\(17\) | 391.037 | 1.35307 | 0.676535 | − | 0.736411i | \(-0.263481\pi\) | ||||
0.676535 | + | 0.736411i | \(0.263481\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −352.390 | −0.976149 | −0.488075 | − | 0.872802i | \(-0.662301\pi\) | ||||
−0.488075 | + | 0.872802i | \(0.662301\pi\) | |||||||
\(20\) | 594.541 | 1.48635 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 328.136 | 0.677966 | ||||||||
\(23\) | − | 173.061i | − | 0.327148i | −0.986531 | − | 0.163574i | \(-0.947698\pi\) | ||
0.986531 | − | 0.163574i | \(-0.0523023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 554.595 | 0.887352 | ||||||||
\(26\) | 1342.94 | 1.98660 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 679.838 | 0.867140 | ||||||||
\(29\) | −90.7462 | −0.107903 | −0.0539514 | − | 0.998544i | \(-0.517182\pi\) | ||||
−0.0539514 | + | 0.998544i | \(0.517182\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 128.035i | − | 0.133232i | −0.997779 | − | 0.0666158i | \(-0.978780\pi\) | ||
0.997779 | − | 0.0666158i | \(-0.0212202\pi\) | |||||||
\(32\) | 1467.60i | 1.43320i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2256.89i | − | 1.95233i | ||||||
\(35\) | 1348.83 | 1.10108 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 413.192i | 0.301821i | 0.988547 | + | 0.150910i | \(0.0482204\pi\) | ||||
−0.988547 | + | 0.150910i | \(0.951780\pi\) | |||||||
\(38\) | 2033.83i | 1.40847i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 259.816i | − | 0.162385i | ||||||
\(41\) | 761.796 | 0.453180 | 0.226590 | − | 0.973990i | \(-0.427242\pi\) | ||||
0.226590 | + | 0.973990i | \(0.427242\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 874.013i | − | 0.472695i | −0.971669 | − | 0.236347i | \(-0.924050\pi\) | ||
0.971669 | − | 0.236347i | \(-0.0759504\pi\) | |||||||
\(44\) | − | 984.184i | − | 0.508360i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −998.831 | −0.472038 | ||||||||
\(47\) | 895.574i | 0.405420i | 0.979239 | + | 0.202710i | \(0.0649749\pi\) | ||||
−0.979239 | + | 0.202710i | \(0.935025\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −858.658 | −0.357625 | ||||||||
\(50\) | − | 3200.87i | − | 1.28035i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4027.92i | − | 1.48962i | ||||||
\(53\) | −3689.46 | −1.31344 | −0.656721 | − | 0.754134i | \(-0.728057\pi\) | ||||
−0.656721 | + | 0.754134i | \(0.728057\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1952.67i | − | 0.645509i | ||||||
\(56\) | − | 297.092i | − | 0.0947358i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 523.746i | 0.155691i | ||||||||
\(59\) | 1547.97 | − | 3117.88i | 0.444691 | − | 0.895684i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1498.06i | − | 0.402596i | −0.979530 | − | 0.201298i | \(-0.935484\pi\) | ||
0.979530 | − | 0.201298i | \(-0.0645159\pi\) | |||||||
\(62\) | −738.962 | −0.192238 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4737.35 | 1.15658 | ||||||||
\(65\) | − | 7991.57i | − | 1.89150i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3683.48i | 0.820558i | 0.911960 | + | 0.410279i | \(0.134569\pi\) | ||||
−0.911960 | + | 0.410279i | \(0.865431\pi\) | |||||||
\(68\) | −6769.13 | −1.46391 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 7784.82i | − | 1.58874i | ||||||
\(71\) | 9230.55 | 1.83109 | 0.915547 | − | 0.402211i | \(-0.131758\pi\) | ||||
0.915547 | + | 0.402211i | \(0.131758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4308.55i | − | 0.808510i | −0.914646 | − | 0.404255i | \(-0.867531\pi\) | ||
0.914646 | − | 0.404255i | \(-0.132469\pi\) | |||||||
\(74\) | 2384.76 | 0.435493 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6100.12 | 1.05612 | ||||||||
\(77\) | − | 2232.81i | − | 0.376591i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4707.88 | −0.754346 | −0.377173 | − | 0.926143i | \(-0.623104\pi\) | ||||
−0.377173 | + | 0.926143i | \(0.623104\pi\) | |||||||
\(80\) | 8013.11 | 1.25205 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 4396.74i | − | 0.653887i | ||||||
\(83\) | − | 398.453i | − | 0.0578390i | −0.999582 | − | 0.0289195i | \(-0.990793\pi\) | ||
0.999582 | − | 0.0289195i | \(-0.00920665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13430.3 | −1.85886 | ||||||||
\(86\) | −5044.40 | −0.682045 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −430.092 | −0.0555387 | ||||||||
\(89\) | − | 12419.6i | − | 1.56794i | −0.620802 | − | 0.783968i | \(-0.713193\pi\) | ||
0.620802 | − | 0.783968i | \(-0.286807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9138.11i | − | 1.10350i | ||||||
\(92\) | 2995.82i | 0.353948i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5168.84 | 0.584975 | ||||||||
\(95\) | 12102.9 | 1.34104 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 397.504i | − | 0.0422472i | −0.999777 | − | 0.0211236i | \(-0.993276\pi\) | ||
0.999777 | − | 0.0211236i | \(-0.00672435\pi\) | |||||||
\(98\) | 4955.78i | 0.516012i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9600.44 | −0.960044 | ||||||||
\(101\) | − | 7090.10i | − | 0.695040i | −0.937673 | − | 0.347520i | \(-0.887024\pi\) | ||
0.937673 | − | 0.347520i | \(-0.112976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6266.89i | − | 0.590714i | −0.955387 | − | 0.295357i | \(-0.904561\pi\) | ||
0.955387 | − | 0.295357i | \(-0.0954387\pi\) | |||||||
\(104\) | −1760.22 | −0.162742 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21293.9i | 1.89515i | ||||||||
\(107\) | −1508.55 | −0.131763 | −0.0658814 | − | 0.997827i | \(-0.520986\pi\) | ||||
−0.0658814 | + | 0.997827i | \(0.520986\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16261.8i | 1.36872i | 0.729144 | + | 0.684361i | \(0.239919\pi\) | ||||
−0.729144 | + | 0.684361i | \(0.760081\pi\) | |||||||
\(110\) | −11269.9 | −0.931396 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9162.73 | 0.730447 | ||||||||
\(113\) | − | 22671.8i | − | 1.77553i | −0.460293 | − | 0.887767i | \(-0.652256\pi\) | ||
0.460293 | − | 0.887767i | \(-0.347744\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5943.83i | 0.449439i | ||||||||
\(116\) | 1570.88 | 0.116742 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17995.0 | − | 8934.17i | −1.29237 | − | 0.641638i | ||||
\(119\) | −15357.1 | −1.08446 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11408.6 | 0.779224 | ||||||||
\(122\) | −8646.11 | −0.580900 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2216.39i | 0.144146i | ||||||||
\(125\) | 2418.07 | 0.154757 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7430.12 | 0.460668 | 0.230334 | − | 0.973112i | \(-0.426018\pi\) | ||||
0.230334 | + | 0.973112i | \(0.426018\pi\) | |||||||
\(128\) | − | 3860.20i | − | 0.235608i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −46123.7 | −2.72921 | ||||||||
\(131\) | 30063.5i | 1.75185i | 0.482446 | + | 0.875926i | \(0.339748\pi\) | ||||
−0.482446 | + | 0.875926i | \(0.660252\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13839.3 | 0.782367 | ||||||||
\(134\) | 21259.4 | 1.18397 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2958.14i | 0.159934i | ||||||||
\(137\) | −20907.4 | −1.11393 | −0.556967 | − | 0.830535i | \(-0.688035\pi\) | ||||
−0.556967 | + | 0.830535i | \(0.688035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22666.8 | 1.17317 | 0.586583 | − | 0.809889i | \(-0.300473\pi\) | ||||
0.586583 | + | 0.809889i | \(0.300473\pi\) | |||||||
\(140\) | −23349.2 | −1.19129 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 53274.5i | − | 2.64206i | ||||||
\(143\) | −13229.0 | −0.646927 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3116.70 | 0.148238 | ||||||||
\(146\) | −24867.0 | −1.16659 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 7152.65i | − | 0.326546i | ||||||
\(149\) | 14748.1i | 0.664299i | 0.943227 | + | 0.332150i | \(0.107774\pi\) | ||||
−0.943227 | + | 0.332150i | \(0.892226\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1352.46i | 0.0593158i | 0.999560 | + | 0.0296579i | \(0.00944179\pi\) | ||||
−0.999560 | + | 0.0296579i | \(0.990558\pi\) | |||||||
\(152\) | − | 2665.77i | − | 0.115382i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12886.8 | −0.543378 | ||||||||
\(155\) | 4397.41i | 0.183035i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 43867.4i | 1.77968i | 0.456270 | + | 0.889841i | \(0.349185\pi\) | ||||
−0.456270 | + | 0.889841i | \(0.650815\pi\) | |||||||
\(158\) | 27171.7i | 1.08844i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 50405.1i | − | 1.96895i | ||||||
\(161\) | 6796.58i | 0.262204i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24914.8 | 0.937741 | 0.468870 | − | 0.883267i | \(-0.344661\pi\) | ||||
0.468870 | + | 0.883267i | \(0.344661\pi\) | |||||||
\(164\) | −13187.2 | −0.490304 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2299.69 | −0.0834551 | ||||||||
\(167\) | 15384.8 | 0.551644 | 0.275822 | − | 0.961209i | \(-0.411050\pi\) | ||||
0.275822 | + | 0.961209i | \(0.411050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −25580.7 | −0.895651 | ||||||||
\(170\) | 77513.4i | 2.68212i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15129.8i | 0.511418i | ||||||||
\(173\) | − | 54918.5i | − | 1.83496i | −0.397784 | − | 0.917479i | \(-0.630221\pi\) | ||
0.397784 | − | 0.917479i | \(-0.369779\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21780.4 | −0.711198 | ||||||||
\(176\) | − | 13264.7i | − | 0.428224i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −71680.3 | −2.26235 | ||||||||
\(179\) | − | 50544.7i | − | 1.57750i | −0.614713 | − | 0.788751i | \(-0.710728\pi\) | ||
0.614713 | − | 0.788751i | \(-0.289272\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 34588.1 | 1.05577 | 0.527885 | − | 0.849316i | \(-0.322985\pi\) | ||||
0.527885 | + | 0.849316i | \(0.322985\pi\) | |||||||
\(182\) | −52741.0 | −1.59223 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1309.18 | 0.0386691 | ||||||||
\(185\) | − | 14191.2i | − | 0.414644i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22232.0i | 0.635765i | ||||||||
\(188\) | − | 15503.0i | − | 0.438632i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 69852.5i | − | 1.93497i | ||||||
\(191\) | 29175.3i | 0.799739i | 0.916572 | + | 0.399869i | \(0.130945\pi\) | ||||
−0.916572 | + | 0.399869i | \(0.869055\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 31941.0 | 0.857500 | 0.428750 | − | 0.903423i | \(-0.358954\pi\) | ||||
0.428750 | + | 0.903423i | \(0.358954\pi\) | |||||||
\(194\) | −2294.21 | −0.0609579 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14864.0 | 0.386922 | ||||||||
\(197\) | 4250.44 | 0.109522 | 0.0547610 | − | 0.998499i | \(-0.482560\pi\) | ||||
0.0547610 | + | 0.998499i | \(0.482560\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 28562.3 | 0.721251 | 0.360625 | − | 0.932711i | \(-0.382563\pi\) | ||||
0.360625 | + | 0.932711i | \(0.382563\pi\) | |||||||
\(200\) | 4195.43i | 0.104886i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −40920.8 | −1.00286 | ||||||||
\(203\) | 3563.84 | 0.0864822 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26164.1 | −0.622583 | ||||||||
\(206\) | −36169.6 | −0.852334 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 54287.6i | − | 1.25480i | ||||||
\(209\) | − | 20034.8i | − | 0.458662i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 26481.8i | − | 0.594816i | −0.954750 | − | 0.297408i | \(-0.903878\pi\) | ||
0.954750 | − | 0.297408i | \(-0.0961222\pi\) | |||||||
\(212\) | 63867.2 | 1.42104 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8706.68i | 0.190119i | ||||||||
\(215\) | 30018.2i | 0.649393i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5028.29i | 0.106783i | ||||||||
\(218\) | 93855.5 | 1.97491 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 33802.0i | 0.698389i | ||||||||
\(221\) | 90988.0i | 1.86294i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20499.0 | −0.412215 | −0.206108 | − | 0.978529i | \(-0.566080\pi\) | ||||
−0.206108 | + | 0.978529i | \(0.566080\pi\) | |||||||
\(224\) | − | 57636.6i | − | 1.14869i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −130851. | −2.56189 | ||||||||
\(227\) | − | 78399.4i | − | 1.52146i | −0.649067 | − | 0.760731i | \(-0.724841\pi\) | ||
0.649067 | − | 0.760731i | \(-0.275159\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 31210.2i | 0.595149i | 0.954699 | + | 0.297574i | \(0.0961776\pi\) | ||||
−0.954699 | + | 0.297574i | \(0.903822\pi\) | |||||||
\(230\) | 34305.1 | 0.648490 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 686.481i | − | 0.0127542i | ||||||
\(233\) | 91009.4i | 1.67639i | 0.545372 | + | 0.838194i | \(0.316388\pi\) | ||||
−0.545372 | + | 0.838194i | \(0.683612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 30758.7i | − | 0.556970i | ||||||
\(236\) | −26796.5 | + | 53972.7i | −0.481120 | + | 0.969058i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 88634.0i | 1.56476i | ||||||||
\(239\) | 96173.1 | 1.68367 | 0.841837 | − | 0.539732i | \(-0.181474\pi\) | ||||
0.841837 | + | 0.539732i | \(0.181474\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −69208.9 | −1.19159 | −0.595796 | − | 0.803136i | \(-0.703163\pi\) | ||||
−0.595796 | + | 0.803136i | \(0.703163\pi\) | |||||||
\(242\) | − | 65845.3i | − | 1.12433i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 25932.5i | 0.435576i | ||||||||
\(245\) | 29490.8 | 0.491309 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 81995.4i | − | 1.34399i | ||||||
\(248\) | 968.568 | 0.0157481 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 13956.0i | − | 0.223296i | ||||||
\(251\) | −94134.4 | −1.49417 | −0.747087 | − | 0.664726i | \(-0.768548\pi\) | ||||
−0.747087 | + | 0.664726i | \(0.768548\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9839.24 | 0.153717 | ||||||||
\(254\) | − | 42883.3i | − | 0.664692i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 53518.2 | 0.816623 | ||||||||
\(257\) | −11680.1 | −0.176841 | −0.0884203 | − | 0.996083i | \(-0.528182\pi\) | ||||
−0.0884203 | + | 0.996083i | \(0.528182\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 16227.2i | − | 0.241904i | ||||||
\(260\) | 138340.i | 2.04645i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 173513. | 2.52772 | ||||||||
\(263\) | 67551.5 | 0.976616 | 0.488308 | − | 0.872671i | \(-0.337614\pi\) | ||||
0.488308 | + | 0.872671i | \(0.337614\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 126715. | 1.80442 | ||||||||
\(266\) | − | 79874.1i | − | 1.12887i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 63763.7i | − | 0.887778i | ||||||
\(269\) | − | 8085.17i | − | 0.111734i | −0.998438 | − | 0.0558669i | \(-0.982208\pi\) | ||
0.998438 | − | 0.0558669i | \(-0.0177923\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3043.53 | −0.0414419 | −0.0207209 | − | 0.999785i | \(-0.506596\pi\) | ||||
−0.0207209 | + | 0.999785i | \(0.506596\pi\) | |||||||
\(272\) | −91233.1 | −1.23315 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 120668.i | 1.60728i | ||||||||
\(275\) | 31531.0i | 0.416939i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 110726. | 1.44308 | 0.721540 | − | 0.692373i | \(-0.243435\pi\) | ||||
0.721540 | + | 0.692373i | \(0.243435\pi\) | |||||||
\(278\) | − | 130822.i | − | 1.69275i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10203.7i | 0.130149i | ||||||||
\(281\) | 132826. | 1.68217 | 0.841085 | − | 0.540903i | \(-0.181917\pi\) | ||||
0.841085 | + | 0.540903i | \(0.181917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 136650.i | 1.70622i | 0.521728 | + | 0.853112i | \(0.325287\pi\) | ||||
−0.521728 | + | 0.853112i | \(0.674713\pi\) | |||||||
\(284\) | −159787. | −1.98110 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 76351.8i | 0.933442i | ||||||||
\(287\) | −29917.7 | −0.363216 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 69389.1 | 0.830798 | ||||||||
\(290\) | − | 17988.2i | − | 0.213890i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 74584.1i | 0.874743i | ||||||||
\(293\) | 138078. | 1.60838 | 0.804189 | − | 0.594374i | \(-0.202600\pi\) | ||||
0.804189 | + | 0.594374i | \(0.202600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −53165.4 | + | 107084.i | −0.610921 | + | 1.23050i | ||||
\(296\) | −3125.74 | −0.0356754 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 85119.4 | 0.958508 | ||||||||
\(299\) | 40268.6 | 0.450426 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34324.8i | 0.378857i | ||||||||
\(302\) | 7805.78 | 0.0855859 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 82216.3 | 0.889633 | ||||||||
\(305\) | 51451.2i | 0.553090i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 88705.4 | 0.941181 | 0.470591 | − | 0.882352i | \(-0.344041\pi\) | ||||
0.470591 | + | 0.882352i | \(0.344041\pi\) | |||||||
\(308\) | 38651.5i | 0.407442i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 25379.8 | 0.264098 | ||||||||
\(311\) | 120340. | 1.24420 | 0.622101 | − | 0.782937i | \(-0.286279\pi\) | ||||
0.622101 | + | 0.782937i | \(0.286279\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 153842.i | − | 1.57031i | −0.619299 | − | 0.785155i | \(-0.712583\pi\) | ||
0.619299 | − | 0.785155i | \(-0.287417\pi\) | |||||||
\(314\) | 253183. | 2.56788 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 81496.7 | 0.816142 | ||||||||
\(317\) | −13221.7 | −0.131574 | −0.0657868 | − | 0.997834i | \(-0.520956\pi\) | ||||
−0.0657868 | + | 0.997834i | \(0.520956\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5159.29i | − | 0.0507001i | ||||||
\(320\) | −162705. | −1.58892 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 39226.8 | 0.378330 | ||||||||
\(323\) | −137798. | −1.32080 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 129045.i | 1.22173i | ||||||||
\(326\) | − | 143797.i | − | 1.35305i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5762.87i | 0.0535662i | ||||||||
\(329\) | − | 35171.6i | − | 0.324938i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 56327.8 | 0.514123 | 0.257061 | − | 0.966395i | \(-0.417246\pi\) | ||||
0.257061 | + | 0.966395i | \(0.417246\pi\) | |||||||
\(332\) | 6897.50i | 0.0625771i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 88794.1i | − | 0.795960i | ||||||
\(335\) | − | 126510.i | − | 1.12729i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 115339.i | 1.01558i | 0.861481 | + | 0.507791i | \(0.169538\pi\) | ||||
−0.861481 | + | 0.507791i | \(0.830462\pi\) | |||||||
\(338\) | 147640.i | 1.29232i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 232487. | 2.01114 | ||||||||
\(341\) | 7279.34 | 0.0626013 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 128015. | 1.08811 | ||||||||
\(344\) | 6611.77 | 0.0558729 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −316964. | −2.64763 | ||||||||
\(347\) | 9584.04i | 0.0795957i | 0.999208 | + | 0.0397979i | \(0.0126714\pi\) | ||||
−0.999208 | + | 0.0397979i | \(0.987329\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 148678.i | 1.22066i | 0.792147 | + | 0.610330i | \(0.208963\pi\) | ||||
−0.792147 | + | 0.610330i | \(0.791037\pi\) | |||||||
\(350\) | 125707.i | 1.02618i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −83439.0 | −0.673416 | ||||||||
\(353\) | − | 12045.3i | − | 0.0966652i | −0.998831 | − | 0.0483326i | \(-0.984609\pi\) | ||
0.998831 | − | 0.0483326i | \(-0.0153907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −317025. | −2.51557 | ||||||||
\(356\) | 214992.i | 1.69638i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −291721. | −2.27615 | ||||||||
\(359\) | 11159.4 | 0.0865872 | 0.0432936 | − | 0.999062i | \(-0.486215\pi\) | ||||
0.0432936 | + | 0.999062i | \(0.486215\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6142.36 | −0.0471326 | ||||||||
\(362\) | − | 199627.i | − | 1.52336i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 158187.i | 1.19390i | ||||||||
\(365\) | 147978.i | 1.11074i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24075.5i | − | 0.178749i | −0.995998 | − | 0.0893744i | \(-0.971513\pi\) | ||
0.995998 | − | 0.0893744i | \(-0.0284868\pi\) | |||||||
\(368\) | 40377.1i | 0.298153i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −81905.0 | −0.598284 | ||||||||
\(371\) | 144895. | 1.05270 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −87079.2 | −0.625888 | −0.312944 | − | 0.949772i | \(-0.601315\pi\) | ||||
−0.312944 | + | 0.949772i | \(0.601315\pi\) | |||||||
\(374\) | 128313. | 0.917336 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6774.87 | −0.0479210 | ||||||||
\(377\) | − | 21115.2i | − | 0.148563i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 201608. | 1.40355 | 0.701776 | − | 0.712398i | \(-0.252391\pi\) | ||||
0.701776 | + | 0.712398i | \(0.252391\pi\) | |||||||
\(380\) | −209510. | −1.45090 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 168386. | 1.15393 | ||||||||
\(383\) | −181721. | −1.23882 | −0.619408 | − | 0.785069i | \(-0.712627\pi\) | ||||
−0.619408 | + | 0.785069i | \(0.712627\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 76686.4i | 0.517365i | ||||||||
\(386\) | − | 184349.i | − | 1.23727i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6881.08i | 0.0457081i | ||||||||
\(389\) | 133518. | 0.882350 | 0.441175 | − | 0.897421i | \(-0.354562\pi\) | ||||
0.441175 | + | 0.897421i | \(0.354562\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 67673.4i | − | 0.442654i | ||||||
\(392\) | − | 6495.61i | − | 0.0422715i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 24531.6i | − | 0.158028i | ||||||
\(395\) | 161693. | 1.03633 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27629.4i | 0.175304i | 0.996151 | + | 0.0876518i | \(0.0279363\pi\) | ||||
−0.996151 | + | 0.0876518i | \(0.972064\pi\) | |||||||
\(398\) | − | 164848.i | − | 1.04068i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −129393. | −0.808706 | ||||||||
\(401\) | − | 208735.i | − | 1.29809i | −0.760748 | − | 0.649047i | \(-0.775168\pi\) | ||
0.760748 | − | 0.649047i | \(-0.224832\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29791.8 | 0.183437 | ||||||||
\(404\) | 122735.i | 0.751977i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 20568.9i | − | 0.124784i | ||||||
\(407\) | −23491.7 | −0.141816 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 278718.i | − | 1.66616i | −0.553150 | − | 0.833082i | \(-0.686574\pi\) | ||
0.553150 | − | 0.833082i | \(-0.313426\pi\) | |||||||
\(410\) | 151007.i | 0.898316i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 108484.i | 0.639106i | ||||||||
\(413\) | −60792.9 | + | 122447.i | −0.356412 | + | 0.717875i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13685.0i | 0.0794598i | ||||||||
\(416\) | −341486. | −1.97327 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −115632. | −0.661796 | ||||||||
\(419\) | − | 15318.9i | − | 0.0872570i | −0.999048 | − | 0.0436285i | \(-0.986108\pi\) | ||
0.999048 | − | 0.0436285i | \(-0.0138918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 278756.i | − | 1.57275i | −0.617747 | − | 0.786377i | \(-0.711954\pi\) | ||
0.617747 | − | 0.786377i | \(-0.288046\pi\) | |||||||
\(422\) | −152841. | −0.858252 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 27910.2i | − | 0.155250i | ||||||
\(425\) | 216867. | 1.20065 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 58832.8i | 0.322674i | ||||||||
\(428\) | 26114.1 | 0.142557 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 173251. | 0.937000 | ||||||||
\(431\) | − | 202239.i | − | 1.08870i | −0.838857 | − | 0.544352i | \(-0.816776\pi\) | ||
0.838857 | − | 0.544352i | \(-0.183224\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −88674.2 | −0.472957 | −0.236478 | − | 0.971637i | \(-0.575993\pi\) | ||||
−0.236478 | + | 0.971637i | \(0.575993\pi\) | |||||||
\(434\) | 29021.0 | 0.154075 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 281503.i | − | 1.48085i | ||||||
\(437\) | 60985.1i | 0.319345i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −374655. | −1.94403 | −0.972013 | − | 0.234928i | \(-0.924515\pi\) | ||||
−0.972013 | + | 0.234928i | \(0.924515\pi\) | |||||||
\(440\) | 14771.6 | 0.0762997 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 525141. | 2.68801 | ||||||||
\(443\) | 19857.5i | 0.101185i | 0.998719 | + | 0.0505925i | \(0.0161110\pi\) | ||||
−0.998719 | + | 0.0505925i | \(0.983889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 426555.i | 2.15404i | ||||||||
\(446\) | 118311.i | 0.594779i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −186048. | −0.926978 | ||||||||
\(449\) | −71307.0 | −0.353703 | −0.176852 | − | 0.984238i | \(-0.556591\pi\) | ||||
−0.176852 | + | 0.984238i | \(0.556591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 43311.2i | 0.212935i | ||||||||
\(452\) | 392465.i | 1.92099i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −452486. | −2.19530 | ||||||||
\(455\) | 313850.i | 1.51600i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 134049.i | − | 0.641846i | −0.947105 | − | 0.320923i | \(-0.896007\pi\) | ||
0.947105 | − | 0.320923i | \(-0.103993\pi\) | |||||||
\(458\) | 180131. | 0.858732 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 102892.i | − | 0.486257i | ||||||
\(461\) | −281430. | −1.32425 | −0.662123 | − | 0.749395i | \(-0.730344\pi\) | ||||
−0.662123 | + | 0.749395i | \(0.730344\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 323834.i | − | 1.51064i | −0.655356 | − | 0.755320i | \(-0.727482\pi\) | ||
0.655356 | − | 0.755320i | \(-0.272518\pi\) | |||||||
\(464\) | 21172.0 | 0.0983393 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 525265. | 2.41884 | ||||||||
\(467\) | 411702.i | 1.88777i | 0.330272 | + | 0.943886i | \(0.392859\pi\) | ||||
−0.330272 | + | 0.943886i | \(0.607141\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 144660.i | − | 0.657663i | ||||||
\(470\) | −177525. | −0.803645 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23586.2 | + | 11710.1i | 0.105870 | + | 0.0525628i | ||||
\(473\) | 49691.2 | 0.222104 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −195434. | −0.866188 | ||||||||
\(476\) | 265842. | 1.17330 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 555067.i | − | 2.42935i | ||||||
\(479\) | −84811.3 | −0.369643 | −0.184822 | − | 0.982772i | \(-0.559171\pi\) | ||||
−0.184822 | + | 0.982772i | \(0.559171\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −96143.1 | −0.415554 | ||||||||
\(482\) | 399442.i | 1.71933i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −197491. | −0.843058 | ||||||||
\(485\) | 13652.4i | 0.0580396i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 249337. | 1.05131 | 0.525653 | − | 0.850699i | \(-0.323821\pi\) | ||||
0.525653 | + | 0.850699i | \(0.323821\pi\) | |||||||
\(488\) | 11332.6 | 0.0475871 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 170207.i | − | 0.708902i | ||||||
\(491\) | −50328.2 | −0.208760 | −0.104380 | − | 0.994537i | \(-0.533286\pi\) | ||||
−0.104380 | + | 0.994537i | \(0.533286\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35485.1 | −0.146000 | ||||||||
\(494\) | −473240. | −1.93922 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29872.0i | 0.121423i | ||||||||
\(497\) | −362508. | −1.46759 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23067.0 | −0.0926380 | −0.0463190 | − | 0.998927i | \(-0.514749\pi\) | ||||
−0.0463190 | + | 0.998927i | \(0.514749\pi\) | |||||||
\(500\) | −41858.5 | −0.167434 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 543301.i | 2.15592i | ||||||||
\(503\) | 410578.i | 1.62278i | 0.584505 | + | 0.811390i | \(0.301289\pi\) | ||||
−0.584505 | + | 0.811390i | \(0.698711\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 243511.i | 0.954852i | ||||||||
\(506\) | − | 56787.6i | − | 0.221795i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −128621. | −0.498406 | ||||||||
\(509\) | − | 19719.0i | − | 0.0761115i | −0.999276 | − | 0.0380557i | \(-0.987884\pi\) | ||
0.999276 | − | 0.0380557i | \(-0.0121164\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 169208.i | 0.648007i | ||||||||
\(512\) | − | 370646.i | − | 1.41390i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 67412.5i | 0.255161i | ||||||||
\(515\) | 215238.i | 0.811529i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −50917.0 | −0.190494 | ||||||||
\(518\) | −93655.8 | −0.349040 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 60455.0 | 0.223576 | ||||||||
\(521\) | −420195. | −1.54802 | −0.774008 | − | 0.633175i | \(-0.781751\pi\) | ||||
−0.774008 | + | 0.633175i | \(0.781751\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −523604. | −1.91425 | −0.957126 | − | 0.289670i | \(-0.906454\pi\) | ||||
−0.957126 | + | 0.289670i | \(0.906454\pi\) | |||||||
\(524\) | − | 520421.i | − | 1.89536i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 389877.i | − | 1.40915i | ||||||
\(527\) | − | 50066.6i | − | 0.180272i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 249891. | 0.892974 | ||||||||
\(530\) | − | 731343.i | − | 2.60357i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −239568. | −0.846458 | ||||||||
\(533\) | 177257.i | 0.623950i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 51811.6 | 0.181017 | ||||||||
\(536\) | −27865.0 | −0.0969905 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −46663.9 | −0.161219 | ||||||||
\(539\) | − | 48818.2i | − | 0.168037i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 62563.9i | − | 0.213761i | −0.994272 | − | 0.106881i | \(-0.965914\pi\) | ||
0.994272 | − | 0.106881i | \(-0.0340863\pi\) | |||||||
\(542\) | 17565.9i | 0.0597959i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 573886.i | 1.93922i | ||||||||
\(545\) | − | 558515.i | − | 1.88036i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28370.0 | 0.0948166 | 0.0474083 | − | 0.998876i | \(-0.484904\pi\) | ||||
0.0474083 | + | 0.998876i | \(0.484904\pi\) | |||||||
\(548\) | 361923. | 1.20519 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 181982. | 0.601595 | ||||||||
\(551\) | 31978.0 | 0.105329 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 184891. | 0.604596 | ||||||||
\(554\) | − | 639060.i | − | 2.08220i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −392378. | −1.26927 | ||||||||
\(557\) | 85305.1 | 0.274957 | 0.137478 | − | 0.990505i | \(-0.456100\pi\) | ||||
0.137478 | + | 0.990505i | \(0.456100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 203369. | 0.650819 | ||||||||
\(560\) | −314696. | −1.00350 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 766610.i | − | 2.42718i | ||||||
\(563\) | − | 625430.i | − | 1.97316i | −0.163282 | − | 0.986580i | \(-0.552208\pi\) | ||
0.163282 | − | 0.986580i | \(-0.447792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 778668.i | 2.43925i | ||||||||
\(566\) | 788680. | 2.46189 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 69827.6i | 0.216437i | ||||||||
\(569\) | 182688.i | 0.564269i | 0.959375 | + | 0.282134i | \(0.0910424\pi\) | ||||
−0.959375 | + | 0.282134i | \(0.908958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 366777.i | 1.12494i | 0.826817 | + | 0.562471i | \(0.190149\pi\) | ||||
−0.826817 | + | 0.562471i | \(0.809851\pi\) | |||||||
\(572\) | 229004. | 0.699923 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 172672.i | 0.524079i | ||||||||
\(575\) | − | 95979.0i | − | 0.290296i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 485860. | 1.45935 | 0.729675 | − | 0.683794i | \(-0.239671\pi\) | ||||
0.729675 | + | 0.683794i | \(0.239671\pi\) | |||||||
\(578\) | − | 400482.i | − | 1.19875i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −53952.3 | −0.160381 | ||||||||
\(581\) | 15648.3i | 0.0463570i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 209761.i | − | 0.617145i | ||||||
\(584\) | 32593.5 | 0.0955664 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 796921.i | − | 2.32071i | ||||||
\(587\) | 466181.i | 1.35294i | 0.736470 | + | 0.676470i | \(0.236491\pi\) | ||||
−0.736470 | + | 0.676470i | \(0.763509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45118.4i | 0.130054i | ||||||||
\(590\) | 618041. | + | 306846.i | 1.77547 | + | 0.881489i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 96402.1i | − | 0.275070i | ||||||
\(593\) | 263489. | 0.749294 | 0.374647 | − | 0.927167i | \(-0.377764\pi\) | ||||
0.374647 | + | 0.927167i | \(0.377764\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 527442. | 1.48984 | ||||||||
\(596\) | − | 255300.i | − | 0.718719i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 232412.i | − | 0.649914i | ||||||
\(599\) | 182847. | 0.509606 | 0.254803 | − | 0.966993i | \(-0.417989\pi\) | ||||
0.254803 | + | 0.966993i | \(0.417989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 529477.i | 1.46588i | 0.680294 | + | 0.732939i | \(0.261852\pi\) | ||||
−0.680294 | + | 0.732939i | \(0.738148\pi\) | |||||||
\(602\) | 198107. | 0.546647 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 23412.0i | − | 0.0641749i | ||||||
\(605\) | −391832. | −1.07051 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −161986. | −0.439642 | −0.219821 | − | 0.975540i | \(-0.570547\pi\) | ||||
−0.219821 | + | 0.975540i | \(0.570547\pi\) | |||||||
\(608\) | − | 517167.i | − | 1.39902i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 296953. | 0.798046 | ||||||||
\(611\) | −208385. | −0.558193 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 97048.9i | − | 0.258268i | −0.991627 | − | 0.129134i | \(-0.958780\pi\) | ||
0.991627 | − | 0.129134i | \(-0.0412197\pi\) | |||||||
\(614\) | − | 511967.i | − | 1.35802i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16890.9 | 0.0445134 | ||||||||
\(617\) | 17414.4 | 0.0457444 | 0.0228722 | − | 0.999738i | \(-0.492719\pi\) | ||||
0.0228722 | + | 0.999738i | \(0.492719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −216510. | −0.565061 | −0.282531 | − | 0.959258i | \(-0.591174\pi\) | ||||
−0.282531 | + | 0.959258i | \(0.591174\pi\) | |||||||
\(620\) | − | 76122.3i | − | 0.198029i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 694550.i | − | 1.79524i | ||||||
\(623\) | 487751.i | 1.25667i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −429671. | −1.09996 | ||||||||
\(626\) | −887904. | −2.26578 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 759376.i | − | 1.92547i | ||||||
\(629\) | 161574.i | 0.408384i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −218714. | −0.549310 | −0.274655 | − | 0.961543i | \(-0.588564\pi\) | ||||
−0.274655 | + | 0.961543i | \(0.588564\pi\) | |||||||
\(632\) | − | 35614.3i | − | 0.0891643i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 76309.6i | 0.189846i | ||||||||
\(635\) | −255189. | −0.632871 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 199796.i | − | 0.492388i | ||||||
\(638\) | −29777.1 | −0.0731544 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 132580.i | 0.323681i | ||||||||
\(641\) | 210985. | 0.513495 | 0.256747 | − | 0.966479i | \(-0.417349\pi\) | ||||
0.256747 | + | 0.966479i | \(0.417349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 192225. | 0.464932 | 0.232466 | − | 0.972605i | \(-0.425321\pi\) | ||||
0.232466 | + | 0.972605i | \(0.425321\pi\) | |||||||
\(644\) | − | 117654.i | − | 0.283683i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 795305.i | 1.90576i | ||||||||
\(647\) | 671147. | 1.60328 | 0.801639 | − | 0.597808i | \(-0.203962\pi\) | ||||
0.801639 | + | 0.597808i | \(0.203962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 177264. | + | 88008.3i | 0.420853 | + | 0.208946i | ||||
\(650\) | 744790. | 1.76282 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −431294. | −1.01456 | ||||||||
\(653\) | −330138. | −0.774227 | −0.387114 | − | 0.922032i | \(-0.626528\pi\) | ||||
−0.387114 | + | 0.922032i | \(0.626528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.03254e6i | − | 2.40671i | ||||||
\(656\) | −177735. | −0.413014 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −202994. | −0.468848 | ||||||||
\(659\) | − | 45073.9i | − | 0.103790i | −0.998653 | − | 0.0518949i | \(-0.983474\pi\) | ||
0.998653 | − | 0.0518949i | \(-0.0165261\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −304683. | −0.697341 | −0.348670 | − | 0.937245i | \(-0.613367\pi\) | ||||
−0.348670 | + | 0.937245i | \(0.613367\pi\) | |||||||
\(662\) | − | 325098.i | − | 0.741821i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3014.23 | 0.00683661 | ||||||||
\(665\) | −475314. | −1.07482 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15704.7i | 0.0353002i | ||||||||
\(668\) | −266322. | −0.596835 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −730159. | −1.62655 | ||||||||
\(671\) | 85170.7 | 0.189167 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 188450.i | 0.416070i | 0.978121 | + | 0.208035i | \(0.0667068\pi\) | ||||
−0.978121 | + | 0.208035i | \(0.933293\pi\) | |||||||
\(674\) | 665681. | 1.46537 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 442820. | 0.969022 | ||||||||
\(677\) | 254006. | 0.554199 | 0.277100 | − | 0.960841i | \(-0.410627\pi\) | ||||
0.277100 | + | 0.960841i | \(0.410627\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15611.0i | 0.0338604i | ||||||||
\(680\) | − | 101598.i | − | 0.219719i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 42013.0i | − | 0.0903265i | ||||||
\(683\) | − | 537333.i | − | 1.15187i | −0.817497 | − | 0.575933i | \(-0.804639\pi\) | ||
0.817497 | − | 0.575933i | \(-0.195361\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 718071. | 1.53033 | ||||||||
\(686\) | − | 738847.i | − | 1.57002i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 203917.i | 0.430800i | ||||||||
\(689\) | − | 858477.i | − | 1.80838i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 70666.8i | 0.147999i | 0.997258 | + | 0.0739996i | \(0.0235763\pi\) | ||||
−0.997258 | + | 0.0739996i | \(0.976424\pi\) | |||||||
\(692\) | 950678.i | 1.98528i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 55314.7 | 0.114848 | ||||||||
\(695\) | −778495. | −1.61171 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 297890. | 0.613184 | ||||||||
\(698\) | 858099. | 1.76127 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 377035. | 0.769459 | ||||||||
\(701\) | 792788.i | 1.61332i | 0.591015 | + | 0.806661i | \(0.298727\pi\) | ||||
−0.591015 | + | 0.806661i | \(0.701273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 145605.i | − | 0.294622i | ||||||
\(704\) | 269337.i | 0.543440i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −69520.3 | −0.139477 | ||||||||
\(707\) | 278447.i | 0.557063i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −867302. | −1.72535 | −0.862677 | − | 0.505756i | \(-0.831214\pi\) | ||||
−0.862677 | + | 0.505756i | \(0.831214\pi\) | |||||||
\(710\) | 1.82972e6i | 3.62969i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 93952.4 | 0.185331 | ||||||||
\(713\) | −22158.0 | −0.0435864 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 454353. | 0.888754 | ||||||||
\(716\) | 874965.i | 1.70673i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 64407.2i | − | 0.124935i | ||||||
\(719\) | 267439.i | 0.517329i | 0.965967 | + | 0.258665i | \(0.0832825\pi\) | ||||
−0.965967 | + | 0.258665i | \(0.916718\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 246117.i | 0.473448i | ||||||||
\(722\) | 35450.9i | 0.0680069i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −598745. | −1.14226 | ||||||||
\(725\) | −50327.4 | −0.0957477 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 717136. | 1.35685 | 0.678426 | − | 0.734668i | \(-0.262662\pi\) | ||||
0.678426 | + | 0.734668i | \(0.262662\pi\) | |||||||
\(728\) | 69128.4 | 0.130435 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 854062. | 1.60267 | ||||||||
\(731\) | − | 341772.i | − | 0.639589i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −443873. | −0.826134 | −0.413067 | − | 0.910701i | \(-0.635543\pi\) | ||||
−0.413067 | + | 0.910701i | \(0.635543\pi\) | |||||||
\(734\) | −138953. | −0.257914 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 253985. | 0.468870 | ||||||||
\(737\) | −209421. | −0.385554 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 177524.i | − | 0.325063i | −0.986703 | − | 0.162532i | \(-0.948034\pi\) | ||
0.986703 | − | 0.162532i | \(-0.0519659\pi\) | |||||||
\(740\) | 245660.i | 0.448611i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 836267.i | − | 1.51893i | ||||||
\(743\) | 266645. | 0.483009 | 0.241505 | − | 0.970400i | \(-0.422359\pi\) | ||||
0.241505 | + | 0.970400i | \(0.422359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 506527.i | − | 0.912621i | ||||||
\(746\) | 502581.i | 0.903085i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 384853.i | − | 0.687846i | ||||||
\(749\) | 59244.9 | 0.105606 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 438213.i | 0.776972i | 0.921455 | + | 0.388486i | \(0.127002\pi\) | ||||
−0.921455 | + | 0.388486i | \(0.872998\pi\) | |||||||
\(752\) | − | 208947.i | − | 0.369488i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −121867. | −0.214360 | ||||||||
\(755\) | − | 46450.5i | − | 0.0814886i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 999861. | 1.74481 | 0.872404 | − | 0.488785i | \(-0.162560\pi\) | ||||
0.872404 | + | 0.488785i | \(0.162560\pi\) | |||||||
\(758\) | − | 1.16359e6i | − | 2.02516i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 91556.7i | 0.158512i | ||||||||
\(761\) | 326900. | 0.564476 | 0.282238 | − | 0.959344i | \(-0.408923\pi\) | ||||
0.282238 | + | 0.959344i | \(0.408923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 638643.i | − | 1.09701i | ||||||
\(764\) | − | 505045.i | − | 0.865253i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.04881e6i | 1.78747i | ||||||||
\(767\) | 725479. | + | 360187.i | 1.23320 | + | 0.612262i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 235002.i | 0.397392i | 0.980061 | + | 0.198696i | \(0.0636707\pi\) | ||||
−0.980061 | + | 0.198696i | \(0.936329\pi\) | |||||||
\(770\) | 442599. | 0.746498 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −552922. | −0.927746 | ||||||||
\(773\) | 210457.i | 0.352213i | 0.984371 | + | 0.176106i | \(0.0563503\pi\) | ||||
−0.984371 | + | 0.176106i | \(0.943650\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 71007.9i | − | 0.118223i | ||||||
\(776\) | 3007.05 | 0.00499365 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 770606.i | − | 1.27313i | ||||||
\(779\) | −268449. | −0.442371 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 524794.i | 0.860373i | ||||||||
\(782\) | −390580. | −0.638700 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 200334. | 0.325929 | ||||||||
\(785\) | − | 1.50664e6i | − | 2.44494i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11734.5 | −0.0189459 | −0.00947293 | − | 0.999955i | \(-0.503015\pi\) | ||||
−0.00947293 | + | 0.999955i | \(0.503015\pi\) | |||||||
\(788\) | −73578.1 | −0.118494 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 933219.i | − | 1.49530i | ||||||
\(791\) | 890382.i | 1.42306i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 348574. | 0.554305 | ||||||||
\(794\) | 159464. | 0.252943 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −494433. | −0.780335 | ||||||||
\(797\) | − | 592344.i |