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 | 58.34 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.77154i | 1.44289i | 0.692474 | + | 0.721443i | \(0.256521\pi\) | ||||
−0.692474 | + | 0.721443i | \(0.743479\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | −17.3107 | −1.08192 | ||||||||
\(5\) | 34.3452 | 1.37381 | 0.686905 | − | 0.726748i | \(-0.258969\pi\) | ||||
0.686905 | + | 0.726748i | \(0.258969\pi\) | |||||||
\(6\) | − | 29.9898i | − | 0.833051i | ||||||
\(7\) | −39.2727 | −0.801483 | −0.400741 | − | 0.916191i | \(-0.631247\pi\) | ||||
−0.400741 | + | 0.916191i | \(0.631247\pi\) | |||||||
\(8\) | − | 7.56484i | − | 0.118201i | ||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 198.225i | 1.98225i | ||||||||
\(11\) | − | 56.8541i | − | 0.469868i | −0.972011 | − | 0.234934i | \(-0.924513\pi\) | ||
0.972011 | − | 0.234934i | \(-0.0754874\pi\) | |||||||
\(12\) | 89.9491 | 0.624647 | ||||||||
\(13\) | 232.684i | 1.37683i | 0.725319 | + | 0.688413i | \(0.241692\pi\) | ||||
−0.725319 | + | 0.688413i | \(0.758308\pi\) | |||||||
\(14\) | − | 226.664i | − | 1.15645i | ||||||
\(15\) | −178.463 | −0.793169 | ||||||||
\(16\) | −233.311 | −0.911370 | ||||||||
\(17\) | −391.037 | −1.35307 | −0.676535 | − | 0.736411i | \(-0.736519\pi\) | ||||
−0.676535 | + | 0.736411i | \(0.736519\pi\) | |||||||
\(18\) | 155.832i | 0.480962i | ||||||||
\(19\) | −352.390 | −0.976149 | −0.488075 | − | 0.872802i | \(-0.662301\pi\) | ||||
−0.488075 | + | 0.872802i | \(0.662301\pi\) | |||||||
\(20\) | −594.541 | −1.48635 | ||||||||
\(21\) | 204.067 | 0.462736 | ||||||||
\(22\) | 328.136 | 0.677966 | ||||||||
\(23\) | 173.061i | 0.327148i | 0.986531 | + | 0.163574i | \(0.0523023\pi\) | ||||
−0.986531 | + | 0.163574i | \(0.947698\pi\) | |||||||
\(24\) | 39.3081i | 0.0682432i | ||||||||
\(25\) | 554.595 | 0.887352 | ||||||||
\(26\) | −1342.94 | −1.98660 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | 679.838 | 0.867140 | ||||||||
\(29\) | 90.7462 | 0.107903 | 0.0539514 | − | 0.998544i | \(-0.482818\pi\) | ||||
0.0539514 | + | 0.998544i | \(0.482818\pi\) | |||||||
\(30\) | − | 1030.01i | − | 1.14445i | ||||||
\(31\) | − | 128.035i | − | 0.133232i | −0.997779 | − | 0.0666158i | \(-0.978780\pi\) | ||
0.997779 | − | 0.0666158i | \(-0.0212202\pi\) | |||||||
\(32\) | − | 1467.60i | − | 1.43320i | ||||||
\(33\) | 295.422i | 0.271279i | ||||||||
\(34\) | − | 2256.89i | − | 1.95233i | ||||||
\(35\) | −1348.83 | −1.10108 | ||||||||
\(36\) | −467.389 | −0.360640 | ||||||||
\(37\) | 413.192i | 0.301821i | 0.988547 | + | 0.150910i | \(0.0482204\pi\) | ||||
−0.988547 | + | 0.150910i | \(0.951780\pi\) | |||||||
\(38\) | − | 2033.83i | − | 1.40847i | ||||||
\(39\) | − | 1209.06i | − | 0.794911i | ||||||
\(40\) | − | 259.816i | − | 0.162385i | ||||||
\(41\) | −761.796 | −0.453180 | −0.226590 | − | 0.973990i | \(-0.572758\pi\) | ||||
−0.226590 | + | 0.973990i | \(0.572758\pi\) | |||||||
\(42\) | 1177.78i | 0.667676i | ||||||||
\(43\) | − | 874.013i | − | 0.472695i | −0.971669 | − | 0.236347i | \(-0.924050\pi\) | ||
0.971669 | − | 0.236347i | \(-0.0759504\pi\) | |||||||
\(44\) | 984.184i | 0.508360i | ||||||||
\(45\) | 927.321 | 0.457936 | ||||||||
\(46\) | −998.831 | −0.472038 | ||||||||
\(47\) | − | 895.574i | − | 0.405420i | −0.979239 | − | 0.202710i | \(-0.935025\pi\) | ||
0.979239 | − | 0.202710i | \(-0.0649749\pi\) | |||||||
\(48\) | 1212.32 | 0.526179 | ||||||||
\(49\) | −858.658 | −0.357625 | ||||||||
\(50\) | 3200.87i | 1.28035i | ||||||||
\(51\) | 2031.89 | 0.781195 | ||||||||
\(52\) | − | 4027.92i | − | 1.48962i | ||||||
\(53\) | 3689.46 | 1.31344 | 0.656721 | − | 0.754134i | \(-0.271943\pi\) | ||||
0.656721 | + | 0.754134i | \(0.271943\pi\) | |||||||
\(54\) | − | 809.725i | − | 0.277684i | ||||||
\(55\) | − | 1952.67i | − | 0.645509i | ||||||
\(56\) | 297.092i | 0.0947358i | ||||||||
\(57\) | 1831.07 | 0.563580 | ||||||||
\(58\) | 523.746i | 0.155691i | ||||||||
\(59\) | −1547.97 | + | 3117.88i | −0.444691 | + | 0.895684i | ||||
\(60\) | 3089.32 | 0.858145 | ||||||||
\(61\) | − | 1498.06i | − | 0.402596i | −0.979530 | − | 0.201298i | \(-0.935484\pi\) | ||
0.979530 | − | 0.201298i | \(-0.0645159\pi\) | |||||||
\(62\) | 738.962 | 0.192238 | ||||||||
\(63\) | −1060.36 | −0.267161 | ||||||||
\(64\) | 4737.35 | 1.15658 | ||||||||
\(65\) | 7991.57i | 1.89150i | ||||||||
\(66\) | −1705.04 | −0.391424 | ||||||||
\(67\) | 3683.48i | 0.820558i | 0.911960 | + | 0.410279i | \(0.134569\pi\) | ||||
−0.911960 | + | 0.410279i | \(0.865431\pi\) | |||||||
\(68\) | 6769.13 | 1.46391 | ||||||||
\(69\) | − | 899.253i | − | 0.188879i | ||||||
\(70\) | − | 7784.82i | − | 1.58874i | ||||||
\(71\) | −9230.55 | −1.83109 | −0.915547 | − | 0.402211i | \(-0.868242\pi\) | ||||
−0.915547 | + | 0.402211i | \(0.868242\pi\) | |||||||
\(72\) | − | 204.251i | − | 0.0394002i | ||||||
\(73\) | − | 4308.55i | − | 0.808510i | −0.914646 | − | 0.404255i | \(-0.867531\pi\) | ||
0.914646 | − | 0.404255i | \(-0.132469\pi\) | |||||||
\(74\) | −2384.76 | −0.435493 | ||||||||
\(75\) | −2881.76 | −0.512313 | ||||||||
\(76\) | 6100.12 | 1.05612 | ||||||||
\(77\) | 2232.81i | 0.376591i | ||||||||
\(78\) | 6978.14 | 1.14697 | ||||||||
\(79\) | −4707.88 | −0.754346 | −0.377173 | − | 0.926143i | \(-0.623104\pi\) | ||||
−0.377173 | + | 0.926143i | \(0.623104\pi\) | |||||||
\(80\) | −8013.11 | −1.25205 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − | 4396.74i | − | 0.653887i | ||||||
\(83\) | 398.453i | 0.0578390i | 0.999582 | + | 0.0289195i | \(0.00920665\pi\) | ||||
−0.999582 | + | 0.0289195i | \(0.990793\pi\) | |||||||
\(84\) | −3532.54 | −0.500644 | ||||||||
\(85\) | −13430.3 | −1.85886 | ||||||||
\(86\) | 5044.40 | 0.682045 | ||||||||
\(87\) | −471.531 | −0.0622977 | ||||||||
\(88\) | −430.092 | −0.0555387 | ||||||||
\(89\) | 12419.6i | 1.56794i | 0.620802 | + | 0.783968i | \(0.286807\pi\) | ||||
−0.620802 | + | 0.783968i | \(0.713193\pi\) | |||||||
\(90\) | 5352.08i | 0.660750i | ||||||||
\(91\) | − | 9138.11i | − | 1.10350i | ||||||
\(92\) | − | 2995.82i | − | 0.353948i | ||||||
\(93\) | 665.292i | 0.0769212i | ||||||||
\(94\) | 5168.84 | 0.584975 | ||||||||
\(95\) | −12102.9 | −1.34104 | ||||||||
\(96\) | 7625.87i | 0.827460i | ||||||||
\(97\) | − | 397.504i | − | 0.0422472i | −0.999777 | − | 0.0211236i | \(-0.993276\pi\) | ||
0.999777 | − | 0.0211236i | \(-0.00672435\pi\) | |||||||
\(98\) | − | 4955.78i | − | 0.516012i | ||||||
\(99\) | − | 1535.06i | − | 0.156623i | ||||||
\(100\) | −9600.44 | −0.960044 | ||||||||
\(101\) | 7090.10i | 0.695040i | 0.937673 | + | 0.347520i | \(0.112976\pi\) | ||||
−0.937673 | + | 0.347520i | \(0.887024\pi\) | |||||||
\(102\) | 11727.1i | 1.12718i | ||||||||
\(103\) | − | 6266.89i | − | 0.590714i | −0.955387 | − | 0.295357i | \(-0.904561\pi\) | ||
0.955387 | − | 0.295357i | \(-0.0954387\pi\) | |||||||
\(104\) | 1760.22 | 0.162742 | ||||||||
\(105\) | 7008.72 | 0.635712 | ||||||||
\(106\) | 21293.9i | 1.89515i | ||||||||
\(107\) | 1508.55 | 0.131763 | 0.0658814 | − | 0.997827i | \(-0.479014\pi\) | ||||
0.0658814 | + | 0.997827i | \(0.479014\pi\) | |||||||
\(108\) | 2428.63 | 0.208216 | ||||||||
\(109\) | 16261.8i | 1.36872i | 0.729144 | + | 0.684361i | \(0.239919\pi\) | ||||
−0.729144 | + | 0.684361i | \(0.760081\pi\) | |||||||
\(110\) | 11269.9 | 0.931396 | ||||||||
\(111\) | − | 2147.01i | − | 0.174256i | ||||||
\(112\) | 9162.73 | 0.730447 | ||||||||
\(113\) | 22671.8i | 1.77553i | 0.460293 | + | 0.887767i | \(0.347744\pi\) | ||||
−0.460293 | + | 0.887767i | \(0.652256\pi\) | |||||||
\(114\) | 10568.1i | 0.813182i | ||||||||
\(115\) | 5943.83i | 0.449439i | ||||||||
\(116\) | −1570.88 | −0.116742 | ||||||||
\(117\) | 6282.46i | 0.458942i | ||||||||
\(118\) | −17995.0 | − | 8934.17i | −1.29237 | − | 0.641638i | ||||
\(119\) | 15357.1 | 1.08446 | ||||||||
\(120\) | 1350.05i | 0.0937531i | ||||||||
\(121\) | 11408.6 | 0.779224 | ||||||||
\(122\) | 8646.11 | 0.580900 | ||||||||
\(123\) | 3958.41 | 0.261644 | ||||||||
\(124\) | 2216.39i | 0.144146i | ||||||||
\(125\) | −2418.07 | −0.154757 | ||||||||
\(126\) | − | 6119.93i | − | 0.385483i | ||||||
\(127\) | 7430.12 | 0.460668 | 0.230334 | − | 0.973112i | \(-0.426018\pi\) | ||||
0.230334 | + | 0.973112i | \(0.426018\pi\) | |||||||
\(128\) | 3860.20i | 0.235608i | ||||||||
\(129\) | 4541.50i | 0.272911i | ||||||||
\(130\) | −46123.7 | −2.72921 | ||||||||
\(131\) | − | 30063.5i | − | 1.75185i | −0.482446 | − | 0.875926i | \(-0.660252\pi\) | ||
0.482446 | − | 0.875926i | \(-0.339748\pi\) | |||||||
\(132\) | − | 5113.97i | − | 0.293502i | ||||||
\(133\) | 13839.3 | 0.782367 | ||||||||
\(134\) | −21259.4 | −1.18397 | ||||||||
\(135\) | −4818.50 | −0.264390 | ||||||||
\(136\) | 2958.14i | 0.159934i | ||||||||
\(137\) | 20907.4 | 1.11393 | 0.556967 | − | 0.830535i | \(-0.311965\pi\) | ||||
0.556967 | + | 0.830535i | \(0.311965\pi\) | |||||||
\(138\) | 5190.08 | 0.272531 | ||||||||
\(139\) | 22666.8 | 1.17317 | 0.586583 | − | 0.809889i | \(-0.300473\pi\) | ||||
0.586583 | + | 0.809889i | \(0.300473\pi\) | |||||||
\(140\) | 23349.2 | 1.19129 | ||||||||
\(141\) | 4653.54i | 0.234070i | ||||||||
\(142\) | − | 53274.5i | − | 2.64206i | ||||||
\(143\) | 13229.0 | 0.646927 | ||||||||
\(144\) | −6299.39 | −0.303790 | ||||||||
\(145\) | 3116.70 | 0.148238 | ||||||||
\(146\) | 24867.0 | 1.16659 | ||||||||
\(147\) | 4461.72 | 0.206475 | ||||||||
\(148\) | − | 7152.65i | − | 0.326546i | ||||||
\(149\) | − | 14748.1i | − | 0.664299i | −0.943227 | − | 0.332150i | \(-0.892226\pi\) | ||
0.943227 | − | 0.332150i | \(-0.107774\pi\) | |||||||
\(150\) | − | 16632.2i | − | 0.739209i | ||||||
\(151\) | 1352.46i | 0.0593158i | 0.999560 | + | 0.0296579i | \(0.00944179\pi\) | ||||
−0.999560 | + | 0.0296579i | \(0.990558\pi\) | |||||||
\(152\) | 2665.77i | 0.115382i | ||||||||
\(153\) | −10558.0 | −0.451023 | ||||||||
\(154\) | −12886.8 | −0.543378 | ||||||||
\(155\) | − | 4397.41i | − | 0.183035i | ||||||
\(156\) | 20929.7i | 0.860030i | ||||||||
\(157\) | 43867.4i | 1.77968i | 0.456270 | + | 0.889841i | \(0.349185\pi\) | ||||
−0.456270 | + | 0.889841i | \(0.650815\pi\) | |||||||
\(158\) | − | 27171.7i | − | 1.08844i | ||||||
\(159\) | −19171.0 | −0.758316 | ||||||||
\(160\) | − | 50405.1i | − | 1.96895i | ||||||
\(161\) | − | 6796.58i | − | 0.262204i | ||||||
\(162\) | 4207.46i | 0.160321i | ||||||||
\(163\) | 24914.8 | 0.937741 | 0.468870 | − | 0.883267i | \(-0.344661\pi\) | ||||
0.468870 | + | 0.883267i | \(0.344661\pi\) | |||||||
\(164\) | 13187.2 | 0.490304 | ||||||||
\(165\) | 10146.3i | 0.372685i | ||||||||
\(166\) | −2299.69 | −0.0834551 | ||||||||
\(167\) | −15384.8 | −0.551644 | −0.275822 | − | 0.961209i | \(-0.588950\pi\) | ||||
−0.275822 | + | 0.961209i | \(0.588950\pi\) | |||||||
\(168\) | − | 1543.73i | − | 0.0546958i | ||||||
\(169\) | −25580.7 | −0.895651 | ||||||||
\(170\) | − | 77513.4i | − | 2.68212i | ||||||
\(171\) | −9514.53 | −0.325383 | ||||||||
\(172\) | 15129.8i | 0.511418i | ||||||||
\(173\) | 54918.5i | 1.83496i | 0.397784 | + | 0.917479i | \(0.369779\pi\) | ||||
−0.397784 | + | 0.917479i | \(0.630221\pi\) | |||||||
\(174\) | − | 2721.46i | − | 0.0898884i | ||||||
\(175\) | −21780.4 | −0.711198 | ||||||||
\(176\) | 13264.7i | 0.428224i | ||||||||
\(177\) | 8043.48 | − | 16201.0i | 0.256742 | − | 0.517123i | ||||
\(178\) | −71680.3 | −2.26235 | ||||||||
\(179\) | 50544.7i | 1.57750i | 0.614713 | + | 0.788751i | \(0.289272\pi\) | ||||
−0.614713 | + | 0.788751i | \(0.710728\pi\) | |||||||
\(180\) | −16052.6 | −0.495450 | ||||||||
\(181\) | 34588.1 | 1.05577 | 0.527885 | − | 0.849316i | \(-0.322985\pi\) | ||||
0.527885 | + | 0.849316i | \(0.322985\pi\) | |||||||
\(182\) | 52741.0 | 1.59223 | ||||||||
\(183\) | 7784.14i | 0.232439i | ||||||||
\(184\) | 1309.18 | 0.0386691 | ||||||||
\(185\) | 14191.2i | 0.414644i | ||||||||
\(186\) | −3839.76 | −0.110989 | ||||||||
\(187\) | 22232.0i | 0.635765i | ||||||||
\(188\) | 15503.0i | 0.438632i | ||||||||
\(189\) | 5509.80 | 0.154245 | ||||||||
\(190\) | − | 69852.5i | − | 1.93497i | ||||||
\(191\) | − | 29175.3i | − | 0.799739i | −0.916572 | − | 0.399869i | \(-0.869055\pi\) | ||
0.916572 | − | 0.399869i | \(-0.130945\pi\) | |||||||
\(192\) | −24616.0 | −0.667751 | ||||||||
\(193\) | 31941.0 | 0.857500 | 0.428750 | − | 0.903423i | \(-0.358954\pi\) | ||||
0.428750 | + | 0.903423i | \(0.358954\pi\) | |||||||
\(194\) | 2294.21 | 0.0609579 | ||||||||
\(195\) | − | 41525.4i | − | 1.09206i | ||||||
\(196\) | 14864.0 | 0.386922 | ||||||||
\(197\) | −4250.44 | −0.109522 | −0.0547610 | − | 0.998499i | \(-0.517440\pi\) | ||||
−0.0547610 | + | 0.998499i | \(0.517440\pi\) | |||||||
\(198\) | 8859.66 | 0.225989 | ||||||||
\(199\) | 28562.3 | 0.721251 | 0.360625 | − | 0.932711i | \(-0.382563\pi\) | ||||
0.360625 | + | 0.932711i | \(0.382563\pi\) | |||||||
\(200\) | − | 4195.43i | − | 0.104886i | ||||||
\(201\) | − | 19139.9i | − | 0.473749i | ||||||
\(202\) | −40920.8 | −1.00286 | ||||||||
\(203\) | −3563.84 | −0.0864822 | ||||||||
\(204\) | −35173.4 | −0.845190 | ||||||||
\(205\) | −26164.1 | −0.622583 | ||||||||
\(206\) | 36169.6 | 0.852334 | ||||||||
\(207\) | 4672.66i | 0.109049i | ||||||||
\(208\) | − | 54287.6i | − | 1.25480i | ||||||
\(209\) | 20034.8i | 0.458662i | ||||||||
\(210\) | 40451.1i | 0.917259i | ||||||||
\(211\) | − | 26481.8i | − | 0.594816i | −0.954750 | − | 0.297408i | \(-0.903878\pi\) | ||
0.954750 | − | 0.297408i | \(-0.0961222\pi\) | |||||||
\(212\) | −63867.2 | −1.42104 | ||||||||
\(213\) | 47963.3 | 1.05718 | ||||||||
\(214\) | 8706.68i | 0.190119i | ||||||||
\(215\) | − | 30018.2i | − | 0.649393i | ||||||
\(216\) | 1061.32i | 0.0227477i | ||||||||
\(217\) | 5028.29i | 0.106783i | ||||||||
\(218\) | −93855.5 | −1.97491 | ||||||||
\(219\) | 22387.9i | 0.466793i | ||||||||
\(220\) | 33802.0i | 0.698389i | ||||||||
\(221\) | − | 90988.0i | − | 1.86294i | ||||||
\(222\) | 12391.6 | 0.251432 | ||||||||
\(223\) | −20499.0 | −0.412215 | −0.206108 | − | 0.978529i | \(-0.566080\pi\) | ||||
−0.206108 | + | 0.978529i | \(0.566080\pi\) | |||||||
\(224\) | 57636.6i | 1.14869i | ||||||||
\(225\) | 14974.1 | 0.295784 | ||||||||
\(226\) | −130851. | −2.56189 | ||||||||
\(227\) | 78399.4i | 1.52146i | 0.649067 | + | 0.760731i | \(0.275159\pi\) | ||||
−0.649067 | + | 0.760731i | \(0.724841\pi\) | |||||||
\(228\) | −31697.2 | −0.609748 | ||||||||
\(229\) | 31210.2i | 0.595149i | 0.954699 | + | 0.297574i | \(0.0961776\pi\) | ||||
−0.954699 | + | 0.297574i | \(0.903822\pi\) | |||||||
\(230\) | −34305.1 | −0.648490 | ||||||||
\(231\) | − | 11602.0i | − | 0.217425i | ||||||
\(232\) | − | 686.481i | − | 0.0127542i | ||||||
\(233\) | − | 91009.4i | − | 1.67639i | −0.545372 | − | 0.838194i | \(-0.683612\pi\) | ||
0.545372 | − | 0.838194i | \(-0.316388\pi\) | |||||||
\(234\) | −36259.5 | −0.662201 | ||||||||
\(235\) | − | 30758.7i | − | 0.556970i | ||||||
\(236\) | 26796.5 | − | 53972.7i | 0.481120 | − | 0.969058i | ||||
\(237\) | 24462.8 | 0.435522 | ||||||||
\(238\) | 88634.0i | 1.56476i | ||||||||
\(239\) | −96173.1 | −1.68367 | −0.841837 | − | 0.539732i | \(-0.818526\pi\) | ||||
−0.841837 | + | 0.539732i | \(0.818526\pi\) | |||||||
\(240\) | 41637.3 | 0.722870 | ||||||||
\(241\) | −69208.9 | −1.19159 | −0.595796 | − | 0.803136i | \(-0.703163\pi\) | ||||
−0.595796 | + | 0.803136i | \(0.703163\pi\) | |||||||
\(242\) | 65845.3i | 1.12433i | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 25932.5i | 0.435576i | ||||||||
\(245\) | −29490.8 | −0.491309 | ||||||||
\(246\) | 22846.1i | 0.377522i | ||||||||
\(247\) | − | 81995.4i | − | 1.34399i | ||||||
\(248\) | −968.568 | −0.0157481 | ||||||||
\(249\) | − | 2070.42i | − | 0.0333934i | ||||||
\(250\) | − | 13956.0i | − | 0.223296i | ||||||
\(251\) | 94134.4 | 1.49417 | 0.747087 | − | 0.664726i | \(-0.231452\pi\) | ||||
0.747087 | + | 0.664726i | \(0.231452\pi\) | |||||||
\(252\) | 18355.6 | 0.289047 | ||||||||
\(253\) | 9839.24 | 0.153717 | ||||||||
\(254\) | 42883.3i | 0.664692i | ||||||||
\(255\) | 69785.7 | 1.07321 | ||||||||
\(256\) | 53518.2 | 0.816623 | ||||||||
\(257\) | 11680.1 | 0.176841 | 0.0884203 | − | 0.996083i | \(-0.471818\pi\) | ||||
0.0884203 | + | 0.996083i | \(0.471818\pi\) | |||||||
\(258\) | −26211.5 | −0.393779 | ||||||||
\(259\) | − | 16227.2i | − | 0.241904i | ||||||
\(260\) | − | 138340.i | − | 2.04645i | ||||||
\(261\) | 2450.15 | 0.0359676 | ||||||||
\(262\) | 173513. | 2.52772 | ||||||||
\(263\) | −67551.5 | −0.976616 | −0.488308 | − | 0.872671i | \(-0.662386\pi\) | ||||
−0.488308 | + | 0.872671i | \(0.662386\pi\) | |||||||
\(264\) | 2234.82 | 0.0320653 | ||||||||
\(265\) | 126715. | 1.80442 | ||||||||
\(266\) | 79874.1i | 1.12887i | ||||||||
\(267\) | − | 64534.2i | − | 0.905248i | ||||||
\(268\) | − | 63763.7i | − | 0.887778i | ||||||
\(269\) | 8085.17i | 0.111734i | 0.998438 | + | 0.0558669i | \(0.0177923\pi\) | ||||
−0.998438 | + | 0.0558669i | \(0.982208\pi\) | |||||||
\(270\) | − | 27810.2i | − | 0.381484i | ||||||
\(271\) | −3043.53 | −0.0414419 | −0.0207209 | − | 0.999785i | \(-0.506596\pi\) | ||||
−0.0207209 | + | 0.999785i | \(0.506596\pi\) | |||||||
\(272\) | 91233.1 | 1.23315 | ||||||||
\(273\) | 47483.0i | 0.637108i | ||||||||
\(274\) | 120668.i | 1.60728i | ||||||||
\(275\) | − | 31531.0i | − | 0.416939i | ||||||
\(276\) | 15566.7i | 0.204352i | ||||||||
\(277\) | 110726. | 1.44308 | 0.721540 | − | 0.692373i | \(-0.243435\pi\) | ||||
0.721540 | + | 0.692373i | \(0.243435\pi\) | |||||||
\(278\) | 130822.i | 1.69275i | ||||||||
\(279\) | − | 3456.96i | − | 0.0444105i | ||||||
\(280\) | 10203.7i | 0.130149i | ||||||||
\(281\) | −132826. | −1.68217 | −0.841085 | − | 0.540903i | \(-0.818083\pi\) | ||||
−0.841085 | + | 0.540903i | \(0.818083\pi\) | |||||||
\(282\) | −26858.1 | −0.337736 | ||||||||
\(283\) | 136650.i | 1.70622i | 0.521728 | + | 0.853112i | \(0.325287\pi\) | ||||
−0.521728 | + | 0.853112i | \(0.674713\pi\) | |||||||
\(284\) | 159787. | 1.98110 | ||||||||
\(285\) | 62888.6 | 0.774252 | ||||||||
\(286\) | 76351.8i | 0.933442i | ||||||||
\(287\) | 29917.7 | 0.363216 | ||||||||
\(288\) | − | 39625.2i | − | 0.477734i | ||||||
\(289\) | 69389.1 | 0.830798 | ||||||||
\(290\) | 17988.2i | 0.213890i | ||||||||
\(291\) | 2065.49i | 0.0243914i | ||||||||
\(292\) | 74584.1i | 0.874743i | ||||||||
\(293\) | −138078. | −1.60838 | −0.804189 | − | 0.594374i | \(-0.797400\pi\) | ||||
−0.804189 | + | 0.594374i | \(0.797400\pi\) | |||||||
\(294\) | 25751.0i | 0.297920i | ||||||||
\(295\) | −53165.4 | + | 107084.i | −0.610921 | + | 1.23050i | ||||
\(296\) | 3125.74 | 0.0356754 | ||||||||
\(297\) | 7976.40i | 0.0904262i | ||||||||
\(298\) | 85119.4 | 0.958508 | ||||||||
\(299\) | −40268.6 | −0.450426 | ||||||||
\(300\) | 49885.3 | 0.554282 | ||||||||
\(301\) | 34324.8i | 0.378857i | ||||||||
\(302\) | −7805.78 | −0.0855859 | ||||||||
\(303\) | − | 36841.3i | − | 0.401281i | ||||||
\(304\) | 82216.3 | 0.889633 | ||||||||
\(305\) | − | 51451.2i | − | 0.553090i | ||||||
\(306\) | − | 60936.0i | − | 0.650775i | ||||||
\(307\) | 88705.4 | 0.941181 | 0.470591 | − | 0.882352i | \(-0.344041\pi\) | ||||
0.470591 | + | 0.882352i | \(0.344041\pi\) | |||||||
\(308\) | − | 38651.5i | − | 0.407442i | ||||||
\(309\) | 32563.7i | 0.341049i | ||||||||
\(310\) | 25379.8 | 0.264098 | ||||||||
\(311\) | −120340. | −1.24420 | −0.622101 | − | 0.782937i | \(-0.713721\pi\) | ||||
−0.622101 | + | 0.782937i | \(0.713721\pi\) | |||||||
\(312\) | −9146.35 | −0.0939590 | ||||||||
\(313\) | − | 153842.i | − | 1.57031i | −0.619299 | − | 0.785155i | \(-0.712583\pi\) | ||
0.619299 | − | 0.785155i | \(-0.287417\pi\) | |||||||
\(314\) | −253183. | −2.56788 | ||||||||
\(315\) | −36418.4 | −0.367028 | ||||||||
\(316\) | 81496.7 | 0.816142 | ||||||||
\(317\) | 13221.7 | 0.131574 | 0.0657868 | − | 0.997834i | \(-0.479044\pi\) | ||||
0.0657868 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(318\) | − | 110646.i | − | 1.09416i | ||||||
\(319\) | − | 5159.29i | − | 0.0507001i | ||||||
\(320\) | 162705. | 1.58892 | ||||||||
\(321\) | −7838.67 | −0.0760733 | ||||||||
\(322\) | 39226.8 | 0.378330 | ||||||||
\(323\) | 137798. | 1.32080 | ||||||||
\(324\) | −12619.5 | −0.120213 | ||||||||
\(325\) | 129045.i | 1.22173i | ||||||||
\(326\) | 143797.i | 1.35305i | ||||||||
\(327\) | − | 84498.7i | − | 0.790232i | ||||||
\(328\) | 5762.87i | 0.0535662i | ||||||||
\(329\) | 35171.6i | 0.324938i | ||||||||
\(330\) | −58560.1 | −0.537742 | ||||||||
\(331\) | 56327.8 | 0.514123 | 0.257061 | − | 0.966395i | \(-0.417246\pi\) | ||||
0.257061 | + | 0.966395i | \(0.417246\pi\) | |||||||
\(332\) | − | 6897.50i | − | 0.0625771i | ||||||
\(333\) | 11156.2i | 0.100607i | ||||||||
\(334\) | − | 88794.1i | − | 0.795960i | ||||||
\(335\) | 126510.i | 1.12729i | ||||||||
\(336\) | −47610.9 | −0.421724 | ||||||||
\(337\) | 115339.i | 1.01558i | 0.861481 | + | 0.507791i | \(0.169538\pi\) | ||||
−0.861481 | + | 0.507791i | \(0.830462\pi\) | |||||||
\(338\) | − | 147640.i | − | 1.29232i | ||||||
\(339\) | − | 117806.i | − | 1.02511i | ||||||
\(340\) | 232487. | 2.01114 | ||||||||
\(341\) | −7279.34 | −0.0626013 | ||||||||
\(342\) | − | 54913.5i | − | 0.469491i | ||||||
\(343\) | 128015. | 1.08811 | ||||||||
\(344\) | −6611.77 | −0.0558729 | ||||||||
\(345\) | − | 30885.1i | − | 0.259484i | ||||||
\(346\) | −316964. | −2.64763 | ||||||||
\(347\) | − | 9584.04i | − | 0.0795957i | −0.999208 | − | 0.0397979i | \(-0.987329\pi\) | ||
0.999208 | − | 0.0397979i | \(-0.0126714\pi\) | |||||||
\(348\) | 8162.54 | 0.0674011 | ||||||||
\(349\) | 148678.i | 1.22066i | 0.792147 | + | 0.610330i | \(0.208963\pi\) | ||||
−0.792147 | + | 0.610330i | \(0.791037\pi\) | |||||||
\(350\) | − | 125707.i | − | 1.02618i | ||||||
\(351\) | − | 32644.6i | − | 0.264970i | ||||||
\(352\) | −83439.0 | −0.673416 | ||||||||
\(353\) | 12045.3i | 0.0966652i | 0.998831 | + | 0.0483326i | \(0.0153907\pi\) | ||||
−0.998831 | + | 0.0483326i | \(0.984609\pi\) | |||||||
\(354\) | 93504.5 | + | 46423.3i | 0.746150 | + | 0.370450i | ||||
\(355\) | −317025. | −2.51557 | ||||||||
\(356\) | − | 214992.i | − | 1.69638i | ||||||
\(357\) | −79797.7 | −0.626115 | ||||||||
\(358\) | −291721. | −2.27615 | ||||||||
\(359\) | −11159.4 | −0.0865872 | −0.0432936 | − | 0.999062i | \(-0.513785\pi\) | ||||
−0.0432936 | + | 0.999062i | \(0.513785\pi\) | |||||||
\(360\) | − | 7015.04i | − | 0.0541284i | ||||||
\(361\) | −6142.36 | −0.0471326 | ||||||||
\(362\) | 199627.i | 1.52336i | ||||||||
\(363\) | −59280.9 | −0.449885 | ||||||||
\(364\) | 158187.i | 1.19390i | ||||||||
\(365\) | − | 147978.i | − | 1.11074i | ||||||
\(366\) | −44926.5 | −0.335383 | ||||||||
\(367\) | − | 24075.5i | − | 0.178749i | −0.995998 | − | 0.0893744i | \(-0.971513\pi\) | ||
0.995998 | − | 0.0893744i | \(-0.0284868\pi\) | |||||||
\(368\) | − | 40377.1i | − | 0.298153i | ||||||
\(369\) | −20568.5 | −0.151060 | ||||||||
\(370\) | −81905.0 | −0.598284 | ||||||||
\(371\) | −144895. | −1.05270 | ||||||||
\(372\) | − | 11516.7i | − | 0.0832226i | ||||||
\(373\) | −87079.2 | −0.625888 | −0.312944 | − | 0.949772i | \(-0.601315\pi\) | ||||
−0.312944 | + | 0.949772i | \(0.601315\pi\) | |||||||
\(374\) | −128313. | −0.917336 | ||||||||
\(375\) | 12564.7 | 0.0893487 | ||||||||
\(376\) | −6774.87 | −0.0479210 | ||||||||
\(377\) | 21115.2i | 0.148563i | ||||||||
\(378\) | 31800.1i | 0.222559i | ||||||||
\(379\) | 201608. | 1.40355 | 0.701776 | − | 0.712398i | \(-0.252391\pi\) | ||||
0.701776 | + | 0.712398i | \(0.252391\pi\) | |||||||
\(380\) | 209510. | 1.45090 | ||||||||
\(381\) | −38608.0 | −0.265967 | ||||||||
\(382\) | 168386. | 1.15393 | ||||||||
\(383\) | 181721. | 1.23882 | 0.619408 | − | 0.785069i | \(-0.287373\pi\) | ||||
0.619408 | + | 0.785069i | \(0.287373\pi\) | |||||||
\(384\) | − | 20058.2i | − | 0.136028i | ||||||
\(385\) | 76686.4i | 0.517365i | ||||||||
\(386\) | 184349.i | 1.23727i | ||||||||
\(387\) | − | 23598.4i | − | 0.157565i | ||||||
\(388\) | 6881.08i | 0.0457081i | ||||||||
\(389\) | −133518. | −0.882350 | −0.441175 | − | 0.897421i | \(-0.645438\pi\) | ||||
−0.441175 | + | 0.897421i | \(0.645438\pi\) | |||||||
\(390\) | 239666. | 1.57571 | ||||||||
\(391\) | − | 67673.4i | − | 0.442654i | ||||||
\(392\) | 6495.61i | 0.0422715i | ||||||||
\(393\) | 156215.i | 1.01143i | ||||||||
\(394\) | − | 24531.6i | − | 0.158028i | ||||||
\(395\) | −161693. | −1.03633 | ||||||||
\(396\) | 26573.0i | 0.169453i | ||||||||
\(397\) | 27629.4i | 0.175304i | 0.996151 | + | 0.0876518i | \(0.0279363\pi\) | ||||
−0.996151 | + | 0.0876518i | \(0.972064\pi\) | |||||||
\(398\) | 164848.i | 1.04068i | ||||||||
\(399\) | −71911.1 | −0.451700 | ||||||||
\(400\) | −129393. | −0.808706 | ||||||||
\(401\) | 208735.i | 1.29809i | 0.760748 | + | 0.649047i | \(0.224832\pi\) | ||||
−0.760748 | + | 0.649047i | \(0.775168\pi\) | |||||||
\(402\) | 110467. | 0.683566 | ||||||||
\(403\) | 29791.8 | 0.183437 | ||||||||
\(404\) | − | 122735.i | − | 0.751977i | ||||||
\(405\) | 25037.7 | 0.152645 | ||||||||
\(406\) | − | 20568.9i | − | 0.124784i | ||||||
\(407\) | 23491.7 | 0.141816 | ||||||||
\(408\) | − | 15370.9i | − | 0.0923378i | ||||||
\(409\) | − | 278718.i | − | 1.66616i | −0.553150 | − | 0.833082i | \(-0.686574\pi\) | ||
0.553150 | − | 0.833082i | \(-0.313426\pi\) | |||||||
\(410\) | − | 151007.i | − | 0.898316i | ||||||
\(411\) | −108638. | −0.643130 | ||||||||
\(412\) | 108484.i | 0.639106i | ||||||||
\(413\) | 60792.9 | − | 122447.i | 0.356412 | − | 0.717875i | ||||
\(414\) | −26968.4 | −0.157346 | ||||||||
\(415\) | 13685.0i | 0.0794598i | ||||||||
\(416\) | 341486. | 1.97327 | ||||||||
\(417\) | −117780. | −0.677328 | ||||||||
\(418\) | −115632. | −0.661796 | ||||||||
\(419\) | 15318.9i | 0.0872570i | 0.999048 | + | 0.0436285i | \(0.0138918\pi\) | ||||
−0.999048 | + | 0.0436285i | \(0.986108\pi\) | |||||||
\(420\) | −121326. | −0.687789 | ||||||||
\(421\) | − | 278756.i | − | 1.57275i | −0.617747 | − | 0.786377i | \(-0.711954\pi\) | ||
0.617747 | − | 0.786377i | \(-0.288046\pi\) | |||||||
\(422\) | 152841. | 0.858252 | ||||||||
\(423\) | − | 24180.5i | − | 0.135140i | ||||||
\(424\) | − | 27910.2i | − | 0.155250i | ||||||
\(425\) | −216867. | −1.20065 | ||||||||
\(426\) | 276822.i | 1.52539i | ||||||||
\(427\) | 58832.8i | 0.322674i | ||||||||
\(428\) | −26114.1 | −0.142557 | ||||||||
\(429\) | −68739.9 | −0.373503 | ||||||||
\(430\) | 173251. | 0.937000 | ||||||||
\(431\) | 202239.i | 1.08870i | 0.838857 | + | 0.544352i | \(0.183224\pi\) | ||||
−0.838857 | + | 0.544352i | \(0.816776\pi\) | |||||||
\(432\) | 32732.6 | 0.175393 | ||||||||
\(433\) | −88674.2 | −0.472957 | −0.236478 | − | 0.971637i | \(-0.575993\pi\) | ||||
−0.236478 | + | 0.971637i | \(0.575993\pi\) | |||||||
\(434\) | −29021.0 | −0.154075 | ||||||||
\(435\) | −16194.8 | −0.0855851 | ||||||||
\(436\) | − | 281503.i | − | 1.48085i | ||||||
\(437\) | − | 60985.1i | − | 0.319345i | ||||||
\(438\) | −129213. | −0.673530 | ||||||||
\(439\) | −374655. | −1.94403 | −0.972013 | − | 0.234928i | \(-0.924515\pi\) | ||||
−0.972013 | + | 0.234928i | \(0.924515\pi\) | |||||||
\(440\) | −14771.6 | −0.0762997 | ||||||||
\(441\) | −23183.8 | −0.119208 | ||||||||
\(442\) | 525141. | 2.68801 | ||||||||
\(443\) | − | 19857.5i | − | 0.101185i | −0.998719 | − | 0.0505925i | \(-0.983889\pi\) | ||
0.998719 | − | 0.0505925i | \(-0.0161110\pi\) | |||||||
\(444\) | 37166.3i | 0.188531i | ||||||||
\(445\) | 426555.i | 2.15404i | ||||||||
\(446\) | − | 118311.i | − | 0.594779i | ||||||
\(447\) | 76633.4i | 0.383533i | ||||||||
\(448\) | −186048. | −0.926978 | ||||||||
\(449\) | 71307.0 | 0.353703 | 0.176852 | − | 0.984238i | \(-0.443409\pi\) | ||||
0.176852 | + | 0.984238i | \(0.443409\pi\) | |||||||
\(450\) | 86423.5i | 0.426783i | ||||||||
\(451\) | 43311.2i | 0.212935i | ||||||||
\(452\) | − | 392465.i | − | 1.92099i | ||||||
\(453\) | − | 7027.59i | − | 0.0342460i | ||||||
\(454\) | −452486. | −2.19530 | ||||||||
\(455\) | − | 313850.i | − | 1.51600i | ||||||
\(456\) | − | 13851.8i | − | 0.0666156i | ||||||
\(457\) | − | 134049.i | − | 0.641846i | −0.947105 | − | 0.320923i | \(-0.896007\pi\) | ||
0.947105 | − | 0.320923i | \(-0.103993\pi\) | |||||||
\(458\) | −180131. | −0.858732 | ||||||||
\(459\) | 54861.0 | 0.260398 | ||||||||
\(460\) | − | 102892.i | − | 0.486257i | ||||||
\(461\) | 281430. | 1.32425 | 0.662123 | − | 0.749395i | \(-0.269656\pi\) | ||||
0.662123 | + | 0.749395i | \(0.269656\pi\) | |||||||
\(462\) | 66961.6 | 0.313720 | ||||||||
\(463\) | − | 323834.i | − | 1.51064i | −0.655356 | − | 0.755320i | \(-0.727482\pi\) | ||
0.655356 | − | 0.755320i | \(-0.272518\pi\) | |||||||
\(464\) | −21172.0 | −0.0983393 | ||||||||
\(465\) | 22849.6i | 0.105675i | ||||||||
\(466\) | 525265. | 2.41884 | ||||||||
\(467\) | − | 411702.i | − | 1.88777i | −0.330272 | − | 0.943886i | \(-0.607141\pi\) | ||
0.330272 | − | 0.943886i | \(-0.392859\pi\) | |||||||
\(468\) | − | 108754.i | − | 0.496538i | ||||||
\(469\) | − | 144660.i | − | 0.657663i | ||||||
\(470\) | 177525. | 0.803645 | ||||||||
\(471\) | − | 227942.i | − | 1.02750i | ||||||
\(472\) | 23586.2 | + | 11710.1i | 0.105870 | + | 0.0525628i | ||||
\(473\) | −49691.2 | −0.222104 | ||||||||
\(474\) | 141188.i | 0.628409i | ||||||||
\(475\) | −195434. | −0.866188 | ||||||||
\(476\) | −265842. | −1.17330 | ||||||||
\(477\) | 99615.4 | 0.437814 | ||||||||
\(478\) | − | 555067.i | − | 2.42935i | ||||||
\(479\) | 84811.3 | 0.369643 | 0.184822 | − | 0.982772i | \(-0.440829\pi\) | ||||
0.184822 | + | 0.982772i | \(0.440829\pi\) | |||||||
\(480\) | 261912.i | 1.13677i | ||||||||
\(481\) | −96143.1 | −0.415554 | ||||||||
\(482\) | − | 399442.i | − | 1.71933i | ||||||
\(483\) | 35316.1i | 0.151383i | ||||||||
\(484\) | −197491. | −0.843058 | ||||||||
\(485\) | − | 13652.4i | − | 0.0580396i | ||||||
\(486\) | − | 21862.6i | − | 0.0925612i | ||||||
\(487\) | 249337. | 1.05131 | 0.525653 | − | 0.850699i | \(-0.323821\pi\) | ||||
0.525653 | + | 0.850699i | \(0.323821\pi\) | |||||||
\(488\) | −11332.6 | −0.0475871 | ||||||||
\(489\) | −129461. | −0.541405 | ||||||||
\(490\) | − | 170207.i | − | 0.708902i | ||||||
\(491\) | 50328.2 | 0.208760 | 0.104380 | − | 0.994537i | \(-0.466714\pi\) | ||||
0.104380 | + | 0.994537i | \(0.466714\pi\) | |||||||
\(492\) | −68522.8 | −0.283077 | ||||||||
\(493\) | −35485.1 | −0.146000 | ||||||||
\(494\) | 473240. | 1.93922 | ||||||||
\(495\) | − | 52722.0i | − | 0.215170i | ||||||
\(496\) | 29872.0i | 0.121423i | ||||||||
\(497\) | 362508. | 1.46759 | ||||||||
\(498\) | 11949.5 | 0.0481828 | ||||||||
\(499\) | −23067.0 | −0.0926380 | −0.0463190 | − | 0.998927i | \(-0.514749\pi\) | ||||
−0.0463190 | + | 0.998927i | \(0.514749\pi\) | |||||||
\(500\) | 41858.5 | 0.167434 | ||||||||
\(501\) | 79941.8 | 0.318492 | ||||||||
\(502\) | 543301.i | 2.15592i | ||||||||
\(503\) | − | 410578.i | − | 1.62278i | −0.584505 | − | 0.811390i | \(-0.698711\pi\) | ||
0.584505 | − | 0.811390i | \(-0.301289\pi\) | |||||||
\(504\) | 8021.47i | 0.0315786i | ||||||||
\(505\) | 243511.i | 0.954852i | ||||||||
\(506\) | 56787.6i | 0.221795i | ||||||||
\(507\) | 132921. | 0.517104 | ||||||||
\(508\) | −128621. | −0.498406 | ||||||||
\(509\) | 19719.0i | 0.0761115i | 0.999276 | + | 0.0380557i | \(0.0121164\pi\) | ||||
−0.999276 | + | 0.0380557i | \(0.987884\pi\) | |||||||
\(510\) | 402771.i | 1.54852i | ||||||||
\(511\) | 169208.i | 0.648007i | ||||||||
\(512\) | 370646.i | 1.41390i | ||||||||
\(513\) | 49438.9 | 0.187860 | ||||||||
\(514\) | 67412.5i | 0.255161i | ||||||||
\(515\) | − | 215238.i | − | 0.811529i | ||||||
\(516\) | − | 78616.7i | − | 0.295267i | ||||||
\(517\) | −50917.0 | −0.190494 | ||||||||
\(518\) | 93655.8 | 0.349040 | ||||||||
\(519\) | − | 285365.i | − | 1.05941i | ||||||
\(520\) | 60455.0 | 0.223576 | ||||||||
\(521\) | 420195. | 1.54802 | 0.774008 | − | 0.633175i | \(-0.218249\pi\) | ||||
0.774008 | + | 0.633175i | \(0.218249\pi\) | |||||||
\(522\) | 14141.1i | 0.0518971i | ||||||||
\(523\) | −523604. | −1.91425 | −0.957126 | − | 0.289670i | \(-0.906454\pi\) | ||||
−0.957126 | + | 0.289670i | \(0.906454\pi\) | |||||||
\(524\) | 520421.i | 1.89536i | ||||||||
\(525\) | 113174. | 0.410610 | ||||||||
\(526\) | − | 389877.i | − | 1.40915i | ||||||
\(527\) | 50066.6i | 0.180272i | ||||||||
\(528\) | − | 68925.2i | − | 0.247235i | ||||||
\(529\) | 249891. | 0.892974 | ||||||||
\(530\) | 731343.i | 2.60357i | ||||||||
\(531\) | −41795.2 | + | 84182.7i | −0.148230 | + | 0.298561i | ||||
\(532\) | −239568. | −0.846458 | ||||||||
\(533\) | − | 177257.i | − | 0.623950i | ||||||
\(534\) | 372462. | 1.30617 | ||||||||
\(535\) | 51811.6 | 0.181017 | ||||||||
\(536\) | 27865.0 | 0.0969905 | ||||||||
\(537\) | − | 262638.i | − | 0.910771i | ||||||
\(538\) | −46663.9 | −0.161219 | ||||||||
\(539\) | 48818.2i | 0.168037i | ||||||||
\(540\) | 83411.7 | 0.286048 | ||||||||
\(541\) | − | 62563.9i | − | 0.213761i | −0.994272 | − | 0.106881i | \(-0.965914\pi\) | ||
0.994272 | − | 0.106881i | \(-0.0340863\pi\) | |||||||
\(542\) | − | 17565.9i | − | 0.0597959i | ||||||
\(543\) | −179725. | −0.609549 | ||||||||
\(544\) | 573886.i | 1.93922i | ||||||||
\(545\) | 558515.i | 1.88036i | ||||||||
\(546\) | −274050. | −0.919274 | ||||||||
\(547\) | 28370.0 | 0.0948166 | 0.0474083 | − | 0.998876i | \(-0.484904\pi\) | ||||
0.0474083 | + | 0.998876i | \(0.484904\pi\) | |||||||
\(548\) | −361923. | −1.20519 | ||||||||
\(549\) | − | 40447.6i | − | 0.134199i | ||||||
\(550\) | 181982. | 0.601595 | ||||||||
\(551\) | −31978.0 | −0.105329 | ||||||||
\(552\) | −6802.71 | −0.0223256 | ||||||||
\(553\) | 184891. | 0.604596 | ||||||||
\(554\) | 639060.i | 2.08220i | ||||||||
\(555\) | − | 73739.6i | − | 0.239395i | ||||||
\(556\) | −392378. | −1.26927 | ||||||||
\(557\) | −85305.1 | −0.274957 | −0.137478 | − | 0.990505i | \(-0.543900\pi\) | ||||
−0.137478 | + | 0.990505i | \(0.543900\pi\) | |||||||
\(558\) | 19952.0 | 0.0640793 | ||||||||
\(559\) | 203369. | 0.650819 | ||||||||
\(560\) | 314696. | 1.00350 | ||||||||
\(561\) | − | 115521.i | − | 0.367059i | ||||||
\(562\) | − | 766610.i | − | 2.42718i | ||||||
\(563\) | 625430.i | 1.97316i | 0.163282 | + | 0.986580i | \(0.447792\pi\) | ||||
−0.163282 | + | 0.986580i | \(0.552208\pi\) | |||||||
\(564\) | − | 80556.0i | − | 0.253244i | ||||||
\(565\) | 778668.i | 2.43925i | ||||||||
\(566\) | −788680. | −2.46189 | ||||||||
\(567\) | −28629.8 | −0.0890537 | ||||||||
\(568\) | 69827.6i | 0.216437i | ||||||||
\(569\) | − | 182688.i | − | 0.564269i | −0.959375 | − | 0.282134i | \(-0.908958\pi\) | ||
0.959375 | − | 0.282134i | \(-0.0910424\pi\) | |||||||
\(570\) | 362964.i | 1.11716i | ||||||||
\(571\) | 366777.i | 1.12494i | 0.826817 | + | 0.562471i | \(0.190149\pi\) | ||||
−0.826817 | + | 0.562471i | \(0.809851\pi\) | |||||||
\(572\) | −229004. | −0.699923 | ||||||||
\(573\) | 151599.i | 0.461729i | ||||||||
\(574\) | 172672.i | 0.524079i | ||||||||
\(575\) | 95979.0i | 0.290296i | ||||||||
\(576\) | 127908. | 0.385526 | ||||||||
\(577\) | 485860. | 1.45935 | 0.729675 | − | 0.683794i | \(-0.239671\pi\) | ||||
0.729675 | + | 0.683794i | \(0.239671\pi\) | |||||||
\(578\) | 400482.i | 1.19875i | ||||||||
\(579\) | −165970. | −0.495078 | ||||||||
\(580\) | −53952.3 | −0.160381 | ||||||||
\(581\) | − | 15648.3i | − | 0.0463570i | ||||||
\(582\) | −11921.1 | −0.0351940 | ||||||||
\(583\) | − | 209761.i | − | 0.617145i | ||||||
\(584\) | −32593.5 | −0.0955664 | ||||||||
\(585\) | 215773.i | 0.630499i | ||||||||
\(586\) | − | 796921.i | − | 2.32071i | ||||||
\(587\) | − | 466181.i | − | 1.35294i | −0.736470 | − | 0.676470i | \(-0.763509\pi\) | ||
0.736470 | − | 0.676470i | \(-0.236491\pi\) | |||||||
\(588\) | −77235.5 | −0.223389 | ||||||||
\(589\) | 45118.4i | 0.130054i | ||||||||
\(590\) | −618041. | − | 306846.i | −1.77547 | − | 0.881489i | ||||
\(591\) | 22085.9 | 0.0632326 | ||||||||
\(592\) | − | 96402.1i | − | 0.275070i | ||||||
\(593\) | −263489. | −0.749294 | −0.374647 | − | 0.927167i | \(-0.622236\pi\) | ||||
−0.374647 | + | 0.927167i | \(0.622236\pi\) | |||||||
\(594\) | −46036.2 | −0.130475 | ||||||||
\(595\) | 527442. | 1.48984 | ||||||||
\(596\) | 255300.i | 0.718719i | ||||||||
\(597\) | −148414. | −0.416414 | ||||||||
\(598\) | − | 232412.i | − | 0.649914i | ||||||
\(599\) | −182847. | −0.509606 | −0.254803 | − | 0.966993i | \(-0.582011\pi\) | ||||
−0.254803 | + | 0.966993i | \(0.582011\pi\) | |||||||
\(600\) | 21800.1i | 0.0605558i | ||||||||
\(601\) | 529477.i | 1.46588i | 0.680294 | + | 0.732939i | \(0.261852\pi\) | ||||
−0.680294 | + | 0.732939i | \(0.738148\pi\) | |||||||
\(602\) | −198107. | −0.546647 | ||||||||
\(603\) | 99454.1i | 0.273519i | ||||||||
\(604\) | − | 23412.0i | − | 0.0641749i | ||||||
\(605\) | 391832. | 1.07051 | ||||||||
\(606\) | 212631. | 0.579003 | ||||||||
\(607\) | −161986. | −0.439642 | −0.219821 | − | 0.975540i | \(-0.570547\pi\) | ||||
−0.219821 | + | 0.975540i | \(0.570547\pi\) | |||||||
\(608\) | 517167.i | 1.39902i | ||||||||
\(609\) | 18518.3 | 0.0499305 | ||||||||
\(610\) | 296953. | 0.798046 | ||||||||
\(611\) | 208385. | 0.558193 | ||||||||
\(612\) | 182767. | 0.487971 | ||||||||
\(613\) | − | 97048.9i | − | 0.258268i | −0.991627 | − | 0.129134i | \(-0.958780\pi\) | ||
0.991627 | − | 0.129134i | \(-0.0412197\pi\) | |||||||
\(614\) | 511967.i | 1.35802i | ||||||||
\(615\) | 135952. | 0.359448 | ||||||||
\(616\) | 16890.9 | 0.0445134 | ||||||||
\(617\) | −17414.4 | −0.0457444 | −0.0228722 | − | 0.999738i | \(-0.507281\pi\) | ||||
−0.0228722 | + | 0.999738i | \(0.507281\pi\) | |||||||
\(618\) | −187943. | −0.492095 | ||||||||
\(619\) | −216510. | −0.565061 | −0.282531 | − | 0.959258i | \(-0.591174\pi\) | ||||
−0.282531 | + | 0.959258i | \(0.591174\pi\) | |||||||
\(620\) | 76122.3i | 0.198029i | ||||||||
\(621\) | − | 24279.8i | − | 0.0629597i | ||||||
\(622\) | − | 694550.i | − | 1.79524i | ||||||
\(623\) | − | 487751.i | − | 1.25667i | ||||||
\(624\) | 282086.i | 0.724458i | ||||||||
\(625\) | −429671. | −1.09996 | ||||||||
\(626\) | 887904. | 2.26578 | ||||||||
\(627\) | − | 104104.i | − | 0.264808i | ||||||
\(628\) | − | 759376.i | − | 1.92547i | ||||||
\(629\) | − | 161574.i | − | 0.408384i | ||||||
\(630\) | − | 210190.i | − | 0.529580i | ||||||
\(631\) | −218714. | −0.549310 | −0.274655 | − | 0.961543i | \(-0.588564\pi\) | ||||
−0.274655 | + | 0.961543i | \(0.588564\pi\) | |||||||
\(632\) | 35614.3i | 0.0891643i | ||||||||
\(633\) | 137604.i | 0.343417i | ||||||||
\(634\) | 76309.6i | 0.189846i | ||||||||
\(635\) | 255189. | 0.632871 | ||||||||
\(636\) | 331864. | 0.820437 | ||||||||
\(637\) | − | 199796.i | − | 0.492388i | ||||||
\(638\) | 29777.1 | 0.0731544 | ||||||||
\(639\) | −249225. | −0.610365 | ||||||||
\(640\) | 132580.i | 0.323681i | ||||||||
\(641\) | −210985. | −0.513495 | −0.256747 | − | 0.966479i | \(-0.582651\pi\) | ||||
−0.256747 | + | 0.966479i | \(0.582651\pi\) | |||||||
\(642\) | − | 45241.2i | − | 0.109765i | ||||||
\(643\) | 192225. | 0.464932 | 0.232466 | − | 0.972605i | \(-0.425321\pi\) | ||||
0.232466 | + | 0.972605i | \(0.425321\pi\) | |||||||
\(644\) | 117654.i | 0.283683i | ||||||||
\(645\) | 155979.i | 0.374927i | ||||||||
\(646\) | 795305.i | 1.90576i | ||||||||
\(647\) | −671147. | −1.60328 | −0.801639 | − | 0.597808i | \(-0.796038\pi\) | ||||
−0.801639 | + | 0.597808i | \(0.796038\pi\) | |||||||
\(648\) | − | 5514.77i | − | 0.0131334i | ||||||
\(649\) | 177264. | + | 88008.3i | 0.420853 | + | 0.208946i | ||||
\(650\) | −744790. | −1.76282 | ||||||||
\(651\) | − | 26127.8i | − | 0.0616511i | ||||||
\(652\) | −431294. | −1.01456 | ||||||||
\(653\) | 330138. | 0.774227 | 0.387114 | − | 0.922032i | \(-0.373472\pi\) | ||||
0.387114 | + | 0.922032i | \(0.373472\pi\) | |||||||
\(654\) | 487688. | 1.14021 | ||||||||
\(655\) | − | 1.03254e6i | − | 2.40671i | ||||||
\(656\) | 177735. | 0.413014 | ||||||||
\(657\) | − | 116331.i | − | 0.269503i | ||||||
\(658\) | −202994. | −0.468848 | ||||||||
\(659\) | 45073.9i | 0.103790i | 0.998653 | + | 0.0518949i | \(0.0165261\pi\) | ||||
−0.998653 | + | 0.0518949i | \(0.983474\pi\) | |||||||
\(660\) | − | 175641.i | − | 0.403215i | ||||||
\(661\) | −304683. | −0.697341 | −0.348670 | − | 0.937245i | \(-0.613367\pi\) | ||||
−0.348670 | + | 0.937245i | \(0.613367\pi\) | |||||||
\(662\) | 325098.i | 0.741821i | ||||||||
\(663\) | 472787.i | 1.07557i | ||||||||
\(664\) | 3014.23 | 0.00683661 | ||||||||
\(665\) | 475314. | 1.07482 | ||||||||
\(666\) | −64388.4 | −0.145164 | ||||||||
\(667\) | 15704.7i | 0.0353002i | ||||||||
\(668\) | 266322. | 0.596835 | ||||||||
\(669\) | 106516. | 0.237992 | ||||||||
\(670\) | −730159. | −1.62655 | ||||||||
\(671\) | −85170.7 | −0.189167 | ||||||||
\(672\) | − | 299488.i | − | 0.663195i | ||||||
\(673\) | 188450.i | 0.416070i | 0.978121 | + | 0.208035i | \(0.0667068\pi\) | ||||
−0.978121 | + | 0.208035i | \(0.933293\pi\) | |||||||
\(674\) | −665681. | −1.46537 | ||||||||
\(675\) | −77807.5 | −0.170771 | ||||||||
\(676\) | 442820. | 0.969022 | ||||||||
\(677\) | −254006. | −0.554199 | −0.277100 | − | 0.960841i | \(-0.589373\pi\) | ||||
−0.277100 | + | 0.960841i | \(0.589373\pi\) | |||||||
\(678\) | 679923. | 1.47911 | ||||||||
\(679\) | 15611.0i | 0.0338604i | ||||||||
\(680\) | 101598.i | 0.219719i | ||||||||
\(681\) | − | 407375.i | − | 0.878417i | ||||||
\(682\) | − | 42013.0i | − | 0.0903265i | ||||||
\(683\) | 537333.i | 1.15187i | 0.817497 | + | 0.575933i | \(0.195361\pi\) | ||||
−0.817497 | + | 0.575933i | \(0.804639\pi\) | |||||||
\(684\) | 164703. | 0.352038 | ||||||||
\(685\) | 718071. | 1.53033 | ||||||||
\(686\) | 738847.i | 1.57002i | ||||||||
\(687\) | − | 162173.i | − | 0.343609i | ||||||
\(688\) | 203917.i | 0.430800i | ||||||||
\(689\) | 858477.i | 1.80838i | ||||||||
\(690\) | 178255. | 0.374406 | ||||||||
\(691\) | 70666.8i | 0.147999i | 0.997258 | + | 0.0739996i | \(0.0235763\pi\) | ||||
−0.997258 | + | 0.0739996i | \(0.976424\pi\) | |||||||
\(692\) | − | 950678.i | − | 1.98528i | ||||||
\(693\) | 60285.9i | 0.125530i | ||||||||
\(694\) | 55314.7 | 0.114848 | ||||||||
\(695\) | 778495. | 1.61171 | ||||||||
\(696\) | 3567.06i | 0.00736363i | ||||||||
\(697\) | 297890. | 0.613184 | ||||||||
\(698\) | −858099. | −1.76127 | ||||||||
\(699\) | 472899.i | 0.967863i | ||||||||
\(700\) | 377035. | 0.769459 | ||||||||
\(701\) | − | 792788.i | − | 1.61332i | −0.591015 | − | 0.806661i | \(-0.701273\pi\) | ||
0.591015 | − | 0.806661i | \(-0.298727\pi\) | |||||||
\(702\) | 188410. | 0.382322 | ||||||||
\(703\) | − | 145605.i | − | 0.294622i | ||||||
\(704\) | − | 269337.i | − | 0.543440i | ||||||
\(705\) | 159827.i | 0.321567i | ||||||||
\(706\) | −69520.3 | −0.139477 | ||||||||
\(707\) | − | 278447.i | − | 0.557063i | ||||||
\(708\) | −139238. | + | 280450.i | −0.277775 | + | 0.559486i | ||||
\(709\) | −867302. | −1.72535 | −0.862677 | − | 0.505756i | \(-0.831214\pi\) | ||||
−0.862677 | + | 0.505756i | \(0.831214\pi\) | |||||||
\(710\) | − | 1.82972e6i | − | 3.62969i | ||||||
\(711\) | −127113. | −0.251449 | ||||||||
\(712\) | 93952.4 | 0.185331 | ||||||||
\(713\) | 22158.0 | 0.0435864 | ||||||||
\(714\) | − | 460556.i | − | 0.903412i | ||||||
\(715\) | 454353. | 0.888754 | ||||||||
\(716\) | − | 874965.i | − | 1.70673i | ||||||
\(717\) | 499730. | 0.972070 | ||||||||
\(718\) | − | 64407.2i | − | 0.124935i | ||||||
\(719\) | − | 267439.i | − | 0.517329i | −0.965967 | − | 0.258665i | \(-0.916718\pi\) | ||
0.965967 | − | 0.258665i | \(-0.0832825\pi\) | |||||||
\(720\) | −216354. | −0.417349 | ||||||||
\(721\) | 246117.i | 0.473448i | ||||||||
\(722\) | − | 35450.9i | − | 0.0680069i | ||||||
\(723\) | 359620. | 0.687966 | ||||||||
\(724\) | −598745. | −1.14226 | ||||||||
\(725\) | 50327.4 | 0.0957477 | ||||||||
\(726\) | − | 342142.i | − | 0.649133i | ||||||
\(727\) | 717136. | 1.35685 | 0.678426 | − | 0.734668i | \(-0.262662\pi\) | ||||
0.678426 | + | 0.734668i | \(0.262662\pi\) | |||||||
\(728\) | −69128.4 | −0.130435 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 854062. | 1.60267 | ||||||||
\(731\) | 341772.i | 0.639589i | ||||||||
\(732\) | − | 134749.i | − | 0.251480i | ||||||
\(733\) | −443873. | −0.826134 | −0.413067 | − | 0.910701i | \(-0.635543\pi\) | ||||
−0.413067 | + | 0.910701i | \(0.635543\pi\) | |||||||
\(734\) | 138953. | 0.257914 | ||||||||
\(735\) | 153239. | 0.283657 | ||||||||
\(736\) | 253985. | 0.468870 | ||||||||
\(737\) | 209421. | 0.385554 | ||||||||
\(738\) | − | 118712.i | − | 0.217962i | ||||||
\(739\) | − | 177524.i | − | 0.325063i | −0.986703 | − | 0.162532i | \(-0.948034\pi\) | ||
0.986703 | − | 0.162532i | \(-0.0519659\pi\) | |||||||
\(740\) | − | 245660.i | − | 0.448611i | ||||||
\(741\) | 426060.i | 0.775952i | ||||||||
\(742\) | − | 836267.i | − | 1.51893i | ||||||
\(743\) | −266645. | −0.483009 | −0.241505 | − | 0.970400i | \(-0.577641\pi\) | ||||
−0.241505 | + | 0.970400i | \(0.577641\pi\) | |||||||
\(744\) | 5032.83 | 0.00909214 | ||||||||
\(745\) | − | 506527.i | − | 0.912621i | ||||||
\(746\) | − | 502581.i | − | 0.903085i | ||||||
\(747\) | 10758.2i | 0.0192797i | ||||||||
\(748\) | − | 384853.i | − | 0.687846i | ||||||
\(749\) | −59244.9 | −0.105606 | ||||||||
\(750\) | 72517.5i | 0.128920i | ||||||||
\(751\) | 438213.i | 0.776972i | 0.921455 | + | 0.388486i | \(0.127002\pi\) | ||||
−0.921455 | + | 0.388486i | \(0.872998\pi\) | |||||||
\(752\) | 208947.i | 0.369488i | ||||||||
\(753\) | −489137. | −0.862662 | ||||||||
\(754\) | −121867. | −0.214360 | ||||||||
\(755\) | 46450.5i | 0.0814886i | ||||||||
\(756\) | −95378.6 | −0.166881 | ||||||||
\(757\) | 999861. | 1.74481 | 0.872404 | − | 0.488785i | \(-0.162560\pi\) | ||||
0.872404 | + | 0.488785i | \(0.162560\pi\) | |||||||
\(758\) | 1.16359e6i | 2.02516i | ||||||||
\(759\) | −51126.2 | −0.0887483 | ||||||||
\(760\) | 91556.7i | 0.158512i | ||||||||
\(761\) | −326900. | −0.564476 | −0.282238 | − | 0.959344i | \(-0.591077\pi\) | ||||
−0.282238 | + | 0.959344i | \(0.591077\pi\) | |||||||
\(762\) | − | 222828.i | − | 0.383760i | ||||||
\(763\) | − | 638643.i | − | 1.09701i | ||||||
\(764\) | 505045.i | 0.865253i | ||||||||
\(765\) | −362617. | −0.619620 | ||||||||
\(766\) | 1.04881e6i | 1.78747i | ||||||||
\(767\) | −725479. | − | 360187.i | −1.23320 | − | 0.612262i | ||||
\(768\) | −278089. | −0.471478 | ||||||||
\(769\) | 235002.i | 0.397392i | 0.980061 | + | 0.198696i | \(0.0636707\pi\) | ||||
−0.980061 | + | 0.198696i | \(0.936329\pi\) | |||||||
\(770\) | −442599. | −0.746498 | ||||||||
\(771\) | −60691.8 | −0.102099 | ||||||||
\(772\) | −552922. | −0.927746 | ||||||||
\(773\) | − | 210457.i | − | 0.352213i | −0.984371 | − | 0.176106i | \(-0.943650\pi\) | ||
0.984371 | − | 0.176106i | \(-0.0563503\pi\) | |||||||
\(774\) | 136199. | 0.227348 | ||||||||
\(775\) | − | 71007.9i | − | 0.118223i | ||||||
\(776\) | −3007.05 | −0.00499365 | ||||||||
\(777\) | 84318.8i | 0.139663i | ||||||||
\(778\) | − | 770606.i | − | 1.27313i | ||||||
\(779\) | 268449. | 0.442371 | ||||||||
\(780\) | 718835.i | 1.18152i | ||||||||
\(781\) | 524794.i | 0.860373i | ||||||||
\(782\) | 390580. | 0.638700 | ||||||||
\(783\) | −12731.3 | −0.0207659 | ||||||||
\(784\) | 200334. | 0.325929 | ||||||||
\(785\) | 1.50664e6i | 2.44494i | ||||||||
\(786\) | −901600. | −1.45938 | ||||||||
\(787\) | −11734.5 | −0.0189459 | −0.00947293 | − | 0.999955i | \(-0.503015\pi\) | ||||
−0.00947293 | + | 0.999955i | \(0.503015\pi\) | |||||||
\(788\) | 73578.1 | 0.118494 | ||||||||
\(789\) | 351008. | 0.563849 | ||||||||
\(790\) | − | 933219.i | − | 1.49530i | ||||||
\(791\) | − | 890382.i | − | 1.42306i | ||||||
\(792\) | −11612.5 | −0.0185129 | ||||||||
\(793\) | 348574. | 0.554305 | ||||||||
\(794\) | −159464. | −0.252943 | ||||||||
\(795\) | −658432. | −1.04178 | ||||||||
\(796\) | −494433. | −0.780335 | ||||||||
\(797\) | 592344.i | 0.932518i | 0.884648 | + | 0.466259i | \(0.154399\pi\) | ||||
−0.884648 | + | 0.466259i | \(0.845601\pi\) | |||||||
\(798\) | − | 415038.i | − | 0.651751i | ||||||
\(799\) | 350203.i | 0.548562i | ||||||||
\(800\) | − | 813924.i | − | 1.27176i | ||||||
\(801\) | 335330.i | 0.522645i | ||||||||
\(802\) | −1.20472e6 | −1.87300 | ||||||||
\(803\) | −244959. | −0.379893 | ||||||||
\(804\) | 331326.i | 0.512559i | ||||||||
\(805\) | − | 233430.i | − | 0.360218i | ||||||
\(806\) | 171944.i | 0.264678i | ||||||||
\(807\) | − | 42011.8i | − | 0.0645096i | ||||||
\(808\) | 53635.5 | 0.0821542 | ||||||||
\(809\) | − | 340035.i | − | 0.519550i | −0.965669 | − | 0.259775i | \(-0.916352\pi\) | ||
0.965669 | − | 0.259775i | \(-0.0836484\pi\) | |||||||
\(810\) | 144506.i | 0.220250i | ||||||||
\(811\) | − | 10322.5i | − | 0.0156943i | −0.999969 | − | 0.00784717i | \(-0.997502\pi\) | ||
0.999969 | − | 0.00784717i | \(-0.00249786\pi\) | |||||||
\(812\) | 61692.7 | 0.0935668 | ||||||||
\(813\) | 15814.7 | 0.0239265 | ||||||||
\(814\) | 135583.i | 0.204624i | ||||||||
\(815\) | 855706. | 1.28828 | ||||||||
\(816\) | −474061. | −0.711958 | ||||||||
\(817\) | 307993.i | 0.461421i | ||||||||
\(818\) | 1.60863e6 | 2.40408 | ||||||||
\(819\) | − | 246729.i | − | 0.367834i | ||||||
\(820\) | 452918. | 0.673585 | ||||||||
\(821\) | − | 623437.i | − | 0.924924i | −0.886639 | − | 0.462462i | \(-0.846966\pi\) | ||
0.886639 | − | 0.462462i | \(-0.153034\pi\) | |||||||
\(822\) | − | 627010.i | − | 0.927963i | ||||||
\(823\) | 193091.i | 0.285077i | 0.989789 | + | 0.142538i | \(0.0455264\pi\) | ||||
−0.989789 | + | 0.142538i | \(0.954474\pi\) | |||||||
\(824\) | −47408.0 | −0.0698229 | ||||||||
\(825\) | 163840.i | 0.240720i | ||||||||
\(826\) | 706710. | + | 350869.i | 1.03581 | + | 0.514262i | ||||
\(827\) | −72588.8 | −0.106135 | −0.0530675 | − | 0.998591i | \(-0.516900\pi\) | ||||
−0.0530675 | + | 0.998591i | \(0.516900\pi\) | |||||||
\(828\) | − | 80887.0i | − | 0.117983i | ||||||
\(829\) | −941304. | −1.36969 | −0.684843 | − | 0.728691i | \(-0.740129\pi\) | ||||
−0.684843 | + | 0.728691i | \(0.740129\pi\) | |||||||
\(830\) | −78983.3 | −0.114651 | ||||||||
\(831\) | −575350. | −0.833163 | ||||||||
\(832\) | 1.10230e6i | 1.59241i | ||||||||
\(833\) | 335767. | 0.483892 | ||||||||
\(834\) | − | 679772.i | − | 0.977307i | ||||||
\(835\) | −528395. | −0.757854 | ||||||||
\(836\) | − | 346817.i | − | 0.496235i | ||||||
\(837\) | 17962.9i | 0.0256404i | ||||||||
\(838\) | −88413.8 | −0.125902 | ||||||||
\(839\) | − | 129224.i | − | 0.183578i | −0.995778 | − | 0.0917888i | \(-0.970742\pi\) | ||
0.995778 | − | 0.0917888i | \(-0.0292585\pi\) | |||||||
\(840\) | − | 53019.9i | − | 0.0751415i | ||||||
\(841\) | −699046. | −0.988357 | ||||||||
\(842\) | 1.60885e6 | 2.26930 | ||||||||
\(843\) | 690183. | 0.971201 | ||||||||
\(844\) | 458419.i | 0.643543i | ||||||||
\(845\) | −878574. | −1.23045 | ||||||||
\(846\) | 139559. | 0.194992 | ||||||||
\(847\) | −448047. | −0.624535 | ||||||||
\(848\) | −860790. | −1.19703 | ||||||||
\(849\) | − | 710053.i | − | 0.985089i | ||||||
\(850\) | − | 1.25166e6i | − | 1.73240i | ||||||
\(851\) | −71507.6 | −0.0987400 | ||||||||
\(852\) | −830279. | −1.14379 | ||||||||
\(853\) | −11458.1 | −0.0157476 | −0.00787381 | − | 0.999969i | \(-0.502506\pi\) | ||||
−0.00787381 | + | 0.999969i | \(0.502506\pi\) | |||||||
\(854\) | −339556. | −0.465581 | ||||||||
\(855\) | −326779. | −0.447014 | ||||||||
\(856\) | − | 11412.0i | − | 0.0155745i | ||||||
\(857\) | 28783.4i | 0.0391905i | 0.999808 | + | 0.0195952i | \(0.00623775\pi\) | ||||
−0.999808 | + | 0.0195952i | \(0.993762\pi\) | |||||||
\(858\) | − | 396736.i | − | 0.538923i | ||||||
\(859\) | 969548.i | 1.31396i | 0.753907 | + | 0.656982i | \(0.228167\pi\) | ||||
−0.753907 | + | 0.656982i | \(0.771833\pi\) | |||||||
\(860\) | 519636.i | 0.702591i | ||||||||
\(861\) | −155457. | −0.209703 | ||||||||
\(862\) | −1.16723e6 | −1.57088 | ||||||||
\(863\) | − | 287494.i | − | 0.386018i | −0.981197 | − | 0.193009i | \(-0.938175\pi\) | ||
0.981197 | − | 0.193009i | \(-0.0618247\pi\) | |||||||
\(864\) | 205899.i | 0.275820i | ||||||||
\(865\) | 1.88619e6i | 2.52088i | ||||||||
\(866\) | − | 511787.i | − | 0.682423i | ||||||
\(867\) | −360556. | −0.479661 | ||||||||
\(868\) | − | 87043.4i | − | 0.115530i | ||||||
\(869\) | 267662.i | 0.354443i | ||||||||
\(870\) | − | 93469.3i | − | 0.123490i | ||||||
\(871\) | −857087. | −1.12977 | ||||||||
\(872\) | 123018. | 0.161784 | ||||||||
\(873\) | − | 10732.6i | − | 0.0140824i | ||||||
\(874\) | 351978. | 0.460779 | ||||||||
\(875\) | 94964.1 | 0.124035 | ||||||||
\(876\) | − | 387550.i | − | 0.505033i | ||||||
\(877\) | 979332. | 1.27330 | 0.636650 | − | 0.771153i | \(-0.280320\pi\) | ||||
0.636650 | + | 0.771153i | \(0.280320\pi\) | |||||||
\(878\) | − | 2.16234e6i | − | 2.80501i | ||||||
\(879\) | 717473. | 0.928598 | ||||||||
\(880\) | 455578.i | 0.588298i | ||||||||
\(881\) | 389453.i | 0.501769i | 0.968017 | + | 0.250884i | \(0.0807214\pi\) | ||||
−0.968017 | + | 0.250884i | \(0.919279\pi\) | |||||||
\(882\) | − | 133806.i | − | 0.172004i | ||||||
\(883\) | −883630. | −1.13331 | −0.566655 | − | 0.823955i | \(-0.691763\pi\) | ||||
−0.566655 | + | 0.823955i | \(0.691763\pi\) | |||||||
\(884\) | 1.57507e6i | 2.01555i | ||||||||
\(885\) | 276255. | − | 556426.i | 0.352715 | − | 0.710429i | ||||
\(886\) | 114608. | 0.145999 | ||||||||
\(887\) | 283208.i | 0.359963i | 0.983670 | + | 0.179981i | \(0.0576038\pi\) | ||||
−0.983670 | + | 0.179981i | \(0.942396\pi\) | |||||||
\(888\) | −16241.8 | −0.0205972 | ||||||||
\(889\) | −291801. | −0.369218 | ||||||||
\(890\) | −2.46188e6 | −3.10804 | ||||||||
\(891\) | − | 41446.6i | − | 0.0522076i | ||||||
\(892\) | 354853. | 0.445984 | ||||||||
\(893\) | 315591.i | 0.395751i | ||||||||
\(894\) | −442293. | −0.553395 | ||||||||
\(895\) | 1.73597e6i | 2.16719i | ||||||||
\(896\) | − | 151600.i | − | 0.188836i | ||||||
\(897\) | 209242. | 0.260054 | ||||||||
\(898\) | 411551.i | 0.510354i | ||||||||
\(899\) | − | 11618.7i | − | 0.0143760i | ||||||
\(900\) | −259212. | −0.320015 | ||||||||
\(901\) | −1.44272e6 | −1.77718 | ||||||||
\(902\) | −249972. | −0.307241 | ||||||||
\(903\) | − | 178357.i | − | 0.218733i | ||||||
\(904\) | 171509. | 0.209869 | ||||||||
\(905\) | 1.18794e6 | 1.45043 | ||||||||
\(906\) | 40560.0 | 0.0494131 | ||||||||
\(907\) | 312945. | 0.380412 | 0.190206 | − | 0.981744i | \(-0.439084\pi\) | ||||
0.190206 | + | 0.981744i | \(0.439084\pi\) | |||||||
\(908\) | − | 1.35715e6i | − | 1.64610i | ||||||
\(909\) | 191433.i | 0.231680i | ||||||||
\(910\) | 1.81140e6 | 2.18742 | ||||||||
\(911\) | −150467. | −0.181303 | −0.0906514 | − | 0.995883i | \(-0.528895\pi\) | ||||
−0.0906514 | + | 0.995883i | \(0.528895\pi\) | |||||||
\(912\) | −427208. | −0.513630 | ||||||||
\(913\) | 22653.7 | 0.0271767 | ||||||||
\(914\) | 773669. | 0.926111 | ||||||||
\(915\) | 267348.i | 0.319327i | ||||||||
\(916\) | − | 540271.i | − | 0.643903i | ||||||
\(917\) | 1.18067e6i | 1.40408i | ||||||||
\(918\) | 316633.i | 0.375725i | ||||||||
\(919\) | 717926.i | 0.850059i | 0.905180 | + | 0.425029i | \(0.139736\pi\) | ||||
−0.905180 | + | 0.425029i | \(0.860264\pi\) | |||||||
\(920\) | 44964.2 | 0.0531240 | ||||||||
\(921\) | −460927. | −0.543391 | ||||||||
\(922\) | 1.62429e6i | 1.91074i | ||||||||
\(923\) | − | 2.14780e6i | − | 2.52110i | ||||||
\(924\) | 200839.i | 0.235237i | ||||||||
\(925\) | 229154.i | 0.267821i | ||||||||
\(926\) | 1.86902e6 | 2.17968 | ||||||||
\(927\) | − | 169206.i | − | 0.196905i | ||||||
\(928\) | − | 133179.i | − | 0.154647i | ||||||
\(929\) | 167906.i | 0.194551i | 0.995257 | + | 0.0972757i | \(0.0310129\pi\) | ||||
−0.995257 | + | 0.0972757i | \(0.968987\pi\) | |||||||
\(930\) | −131877. | −0.152477 | ||||||||
\(931\) | 302582. | 0.349095 | ||||||||
\(932\) | 1.57544e6i | 1.81372i | ||||||||
\(933\) | 625307. | 0.718340 | ||||||||
\(934\) | 2.37616e6 | 2.72384 | ||||||||
\(935\) | 763565.i | 0.873419i | ||||||||
\(936\) | 47525.8 | 0.0542473 | ||||||||
\(937\) | − | 1.16725e6i | − | 1.32949i | −0.747069 | − | 0.664747i | \(-0.768539\pi\) | ||
0.747069 | − | 0.664747i | \(-0.231461\pi\) | |||||||
\(938\) | 834913. | 0.948933 | ||||||||
\(939\) | 799385.i | 0.906619i | ||||||||
\(940\) | 532455.i | 0.602597i | ||||||||
\(941\) | − | 1.41681e6i | − | 1.60004i | −0.599973 | − | 0.800020i | \(-0.704822\pi\) | ||
0.599973 | − | 0.800020i | \(-0.295178\pi\) | |||||||
\(942\) | 1.31558e6 | 1.48257 | ||||||||
\(943\) | − | 131837.i | − | 0.148257i | ||||||
\(944\) | 361158. | − | 727434.i | 0.405278 | − | 0.816299i | ||||
\(945\) | 189235. | 0.211904 | ||||||||
\(946\) | − | 286795.i | − | 0.320471i | ||||||
\(947\) | −39435.9 | −0.0439735 | −0.0219868 | − | 0.999758i | \(-0.506999\pi\) | ||||
−0.0219868 | + | 0.999758i | \(0.506999\pi\) | |||||||
\(948\) | −423469. | −0.471200 | ||||||||
\(949\) | 1.00253e6 | 1.11318 | ||||||||
\(950\) | − | 1.12795e6i | − | 1.24981i | ||||||
\(951\) | −68702.0 | −0.0759641 | ||||||||
\(952\) | − | 116174.i | − | 0.128184i | ||||||
\(953\) | 1.14306e6 | 1.25858 | 0.629292 | − | 0.777169i | \(-0.283345\pi\) | ||||
0.629292 | + | 0.777169i | \(0.283345\pi\) | |||||||
\(954\) | 574935.i | 0.631716i | ||||||||
\(955\) | − | 1.00203e6i | − | 1.09869i | ||||||
\(956\) | 1.66483e6 | 1.82160 | ||||||||
\(957\) | 26808.5i | 0.0292717i | ||||||||
\(958\) | 489492.i | 0.533353i | ||||||||
\(959\) | −821090. | −0.892799 | ||||||||
\(960\) | −845441. | −0.917363 | ||||||||
\(961\) | 907128. | 0.982249 | ||||||||
\(962\) | − | 554894.i | − | 0.599598i | ||||||
\(963\) | 40730.9 | 0.0439210 | ||||||||
\(964\) | 1.19806e6 | 1.28921 | ||||||||
\(965\) | 1.09702e6 | 1.17804 | ||||||||
\(966\) | −203828. | −0.218429 | ||||||||
\(967\) | 1.11507e6i | 1.19247i | 0.802810 | + | 0.596235i | \(0.203338\pi\) | ||||
−0.802810 | + | 0.596235i | \(0.796662\pi\) | |||||||
\(968\) | − | 86304.4i | − | 0.0921048i | ||||||
\(969\) | −716017. | −0.762563 | ||||||||
\(970\) | 78795.2 | 0.0837445 | ||||||||
\(971\) | −1.58897e6 | −1.68530 | −0.842651 | − | 0.538460i | \(-0.819006\pi\) | ||||
−0.842651 | + | 0.538460i | \(0.819006\pi\) | |||||||
\(972\) | 65572.9 | 0.0694052 | ||||||||
\(973\) | −890184. | −0.940273 | ||||||||
\(974\) | 1.43906e6i | 1.51691i | ||||||||
\(975\) | − | 670539.i | − | 0.705366i | ||||||
\(976\) | 349513.i | 0.366914i | ||||||||
\(977\) | 1.26322e6i | 1.32340i | 0.749770 | + | 0.661699i | \(0.230164\pi\) | ||||
−0.749770 | + | 0.661699i | \(0.769836\pi\) | |||||||
\(978\) | − | 747191.i | − | 0.781185i | ||||||
\(979\) | 706105. | 0.736723 | ||||||||
\(980\) | 510507. | 0.531557 | ||||||||
\(981\) | 439068.i | 0.456240i | ||||||||
\(982\) | 290471.i | 0.301217i | ||||||||
\(983\) | 757024.i | 0.783435i | 0.920086 | + | 0.391717i | \(0.128119\pi\) | ||||
−0.920086 | + | 0.391717i | \(0.871881\pi\) | |||||||
\(984\) | − | 29944.7i | − | 0.0309265i | ||||||
\(985\) | −145982. | −0.150462 | ||||||||
\(986\) | − | 204804.i | − | 0.210661i | ||||||
\(987\) | − | 182757.i | − | 0.187603i | ||||||
\(988\) | 1.41940e6i | 1.45409i | ||||||||
\(989\) | 151258. | 0.154641 | ||||||||
\(990\) | 304287. | 0.310465 | ||||||||
\(991\) | 814885.i | 0.829753i | 0.909878 | + | 0.414877i | \(0.136175\pi\) | ||||
−0.909878 | + | 0.414877i | \(0.863825\pi\) | |||||||
\(992\) | −187905. | −0.190948 | ||||||||
\(993\) | −292688. | −0.296829 | ||||||||
\(994\) | 2.09223e6i | 2.11757i | ||||||||
\(995\) | 980977. | 0.990861 | ||||||||
\(996\) | 35840.5i | 0.0361289i | ||||||||
\(997\) | −472205. | −0.475051 | −0.237525 | − | 0.971381i | \(-0.576336\pi\) | ||||
−0.237525 | + | 0.971381i | \(0.576336\pi\) | |||||||
\(998\) | − | 133132.i | − | 0.133666i | ||||||
\(999\) | − | 57969.3i | − | 0.0580854i |
(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.58.34 | yes | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.7 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.7 | ✓ | 40 | |
177.176 | even | 2 | 531.5.c.d.235.34 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.7 | ✓ | 40 | 59.58 | odd | 2 | inner | |
177.5.c.a.58.34 | yes | 40 | 1.1 | even | 1 | trivial | |
531.5.c.d.235.7 | 40 | 3.2 | odd | 2 | |||
531.5.c.d.235.34 | 40 | 177.176 | even | 2 |