Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(12,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.12");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.b (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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 12.20 | ||
Character | \(\chi\) | \(=\) | 143.12 |
Dual form | 143.4.b.a.12.17 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.468651i | 0.165693i | 0.996562 | + | 0.0828467i | \(0.0264012\pi\) | ||||
−0.996562 | + | 0.0828467i | \(0.973599\pi\) | |||||||
\(3\) | −6.65460 | −1.28068 | −0.640339 | − | 0.768092i | \(-0.721206\pi\) | ||||
−0.640339 | + | 0.768092i | \(0.721206\pi\) | |||||||
\(4\) | 7.78037 | 0.972546 | ||||||||
\(5\) | 3.45502i | 0.309027i | 0.987991 | + | 0.154513i | \(0.0493809\pi\) | ||||
−0.987991 | + | 0.154513i | \(0.950619\pi\) | |||||||
\(6\) | − | 3.11869i | − | 0.212200i | ||||||
\(7\) | − | 11.5900i | − | 0.625800i | −0.949786 | − | 0.312900i | \(-0.898699\pi\) | ||
0.949786 | − | 0.312900i | \(-0.101301\pi\) | |||||||
\(8\) | 7.39549i | 0.326838i | ||||||||
\(9\) | 17.2837 | 0.640137 | ||||||||
\(10\) | −1.61920 | −0.0512036 | ||||||||
\(11\) | − | 11.0000i | − | 0.301511i | ||||||
\(12\) | −51.7752 | −1.24552 | ||||||||
\(13\) | 30.5990 | + | 35.5064i | 0.652817 | + | 0.757515i | ||||
\(14\) | 5.43166 | 0.103691 | ||||||||
\(15\) | − | 22.9918i | − | 0.395764i | ||||||
\(16\) | 58.7770 | 0.918391 | ||||||||
\(17\) | 69.5462 | 0.992202 | 0.496101 | − | 0.868265i | \(-0.334764\pi\) | ||||
0.496101 | + | 0.868265i | \(0.334764\pi\) | |||||||
\(18\) | 8.10003i | 0.106066i | ||||||||
\(19\) | 136.796i | 1.65175i | 0.563856 | + | 0.825873i | \(0.309317\pi\) | ||||
−0.563856 | + | 0.825873i | \(0.690683\pi\) | |||||||
\(20\) | 26.8813i | 0.300543i | ||||||||
\(21\) | 77.1267i | 0.801449i | ||||||||
\(22\) | 5.15517 | 0.0499584 | ||||||||
\(23\) | 13.6317 | 0.123583 | 0.0617915 | − | 0.998089i | \(-0.480319\pi\) | ||||
0.0617915 | + | 0.998089i | \(0.480319\pi\) | |||||||
\(24\) | − | 49.2140i | − | 0.418574i | ||||||
\(25\) | 113.063 | 0.904503 | ||||||||
\(26\) | −16.6401 | + | 14.3402i | −0.125515 | + | 0.108167i | ||||
\(27\) | 64.6581 | 0.460869 | ||||||||
\(28\) | − | 90.1743i | − | 0.608619i | ||||||
\(29\) | 119.298 | 0.763902 | 0.381951 | − | 0.924183i | \(-0.375252\pi\) | ||||
0.381951 | + | 0.924183i | \(0.375252\pi\) | |||||||
\(30\) | 10.7751 | 0.0655754 | ||||||||
\(31\) | 190.188i | 1.10190i | 0.834539 | + | 0.550949i | \(0.185734\pi\) | ||||
−0.834539 | + | 0.550949i | \(0.814266\pi\) | |||||||
\(32\) | 86.7099i | 0.479009i | ||||||||
\(33\) | 73.2006i | 0.386139i | ||||||||
\(34\) | 32.5930i | 0.164401i | ||||||||
\(35\) | 40.0436 | 0.193389 | ||||||||
\(36\) | 134.473 | 0.622562 | ||||||||
\(37\) | 173.788i | 0.772178i | 0.922462 | + | 0.386089i | \(0.126174\pi\) | ||||
−0.922462 | + | 0.386089i | \(0.873826\pi\) | |||||||
\(38\) | −64.1097 | −0.273683 | ||||||||
\(39\) | −203.624 | − | 236.281i | −0.836049 | − | 0.970134i | ||||
\(40\) | −25.5516 | −0.101002 | ||||||||
\(41\) | − | 390.436i | − | 1.48722i | −0.668616 | − | 0.743608i | \(-0.733113\pi\) | ||
0.668616 | − | 0.743608i | \(-0.266887\pi\) | |||||||
\(42\) | −36.1455 | −0.132795 | ||||||||
\(43\) | −443.009 | −1.57112 | −0.785561 | − | 0.618784i | \(-0.787626\pi\) | ||||
−0.785561 | + | 0.618784i | \(0.787626\pi\) | |||||||
\(44\) | − | 85.5840i | − | 0.293234i | ||||||
\(45\) | 59.7155i | 0.197819i | ||||||||
\(46\) | 6.38853i | 0.0204769i | ||||||||
\(47\) | − | 470.604i | − | 1.46052i | −0.683167 | − | 0.730262i | \(-0.739398\pi\) | ||
0.683167 | − | 0.730262i | \(-0.260602\pi\) | |||||||
\(48\) | −391.138 | −1.17616 | ||||||||
\(49\) | 208.672 | 0.608374 | ||||||||
\(50\) | 52.9871i | 0.149870i | ||||||||
\(51\) | −462.802 | −1.27069 | ||||||||
\(52\) | 238.071 | + | 276.253i | 0.634895 | + | 0.736718i | ||||
\(53\) | −395.914 | −1.02609 | −0.513047 | − | 0.858361i | \(-0.671483\pi\) | ||||
−0.513047 | + | 0.858361i | \(0.671483\pi\) | |||||||
\(54\) | 30.3021i | 0.0763629i | ||||||||
\(55\) | 38.0052 | 0.0931750 | ||||||||
\(56\) | 85.7136 | 0.204535 | ||||||||
\(57\) | − | 910.323i | − | 2.11536i | ||||||
\(58\) | 55.9094i | 0.126573i | ||||||||
\(59\) | 743.180i | 1.63990i | 0.572438 | + | 0.819948i | \(0.305998\pi\) | ||||
−0.572438 | + | 0.819948i | \(0.694002\pi\) | |||||||
\(60\) | − | 178.885i | − | 0.384898i | ||||||
\(61\) | 430.086 | 0.902735 | 0.451367 | − | 0.892338i | \(-0.350936\pi\) | ||||
0.451367 | + | 0.892338i | \(0.350936\pi\) | |||||||
\(62\) | −89.1320 | −0.182577 | ||||||||
\(63\) | − | 200.318i | − | 0.400598i | ||||||
\(64\) | 429.579 | 0.839022 | ||||||||
\(65\) | −122.675 | + | 105.720i | −0.234092 | + | 0.201738i | ||||
\(66\) | −34.3056 | −0.0639807 | ||||||||
\(67\) | − | 967.071i | − | 1.76338i | −0.471828 | − | 0.881691i | \(-0.656406\pi\) | ||
0.471828 | − | 0.881691i | \(-0.343594\pi\) | |||||||
\(68\) | 541.095 | 0.964962 | ||||||||
\(69\) | −90.7136 | −0.158270 | ||||||||
\(70\) | 18.7665i | 0.0320433i | ||||||||
\(71\) | 52.6426i | 0.0879934i | 0.999032 | + | 0.0439967i | \(0.0140091\pi\) | ||||
−0.999032 | + | 0.0439967i | \(0.985991\pi\) | |||||||
\(72\) | 127.821i | 0.209221i | ||||||||
\(73\) | 287.872i | 0.461545i | 0.973008 | + | 0.230773i | \(0.0741254\pi\) | ||||
−0.973008 | + | 0.230773i | \(0.925875\pi\) | |||||||
\(74\) | −81.4460 | −0.127945 | ||||||||
\(75\) | −752.388 | −1.15838 | ||||||||
\(76\) | 1064.32i | 1.60640i | ||||||||
\(77\) | −127.490 | −0.188686 | ||||||||
\(78\) | 110.733 | − | 95.4286i | 0.160745 | − | 0.138528i | ||||
\(79\) | 564.168 | 0.803466 | 0.401733 | − | 0.915757i | \(-0.368408\pi\) | ||||
0.401733 | + | 0.915757i | \(0.368408\pi\) | |||||||
\(80\) | 203.076i | 0.283807i | ||||||||
\(81\) | −896.934 | −1.23036 | ||||||||
\(82\) | 182.978 | 0.246422 | ||||||||
\(83\) | − | 1074.48i | − | 1.42095i | −0.703720 | − | 0.710477i | \(-0.748479\pi\) | ||
0.703720 | − | 0.710477i | \(-0.251521\pi\) | |||||||
\(84\) | 600.074i | 0.779446i | ||||||||
\(85\) | 240.284i | 0.306617i | ||||||||
\(86\) | − | 207.617i | − | 0.260325i | ||||||
\(87\) | −793.883 | −0.978313 | ||||||||
\(88\) | 81.3504 | 0.0985453 | ||||||||
\(89\) | 628.445i | 0.748483i | 0.927331 | + | 0.374242i | \(0.122097\pi\) | ||||
−0.927331 | + | 0.374242i | \(0.877903\pi\) | |||||||
\(90\) | −27.9858 | −0.0327773 | ||||||||
\(91\) | 411.518 | − | 354.641i | 0.474053 | − | 0.408533i | ||||
\(92\) | 106.060 | 0.120190 | ||||||||
\(93\) | − | 1265.63i | − | 1.41118i | ||||||
\(94\) | 220.549 | 0.241999 | ||||||||
\(95\) | −472.634 | −0.510434 | ||||||||
\(96\) | − | 577.019i | − | 0.613456i | ||||||
\(97\) | 629.130i | 0.658541i | 0.944236 | + | 0.329271i | \(0.106803\pi\) | ||||
−0.944236 | + | 0.329271i | \(0.893197\pi\) | |||||||
\(98\) | 97.7946i | 0.100804i | ||||||||
\(99\) | − | 190.121i | − | 0.193008i | ||||||
\(100\) | 879.670 | 0.879670 | ||||||||
\(101\) | 94.2837 | 0.0928869 | 0.0464435 | − | 0.998921i | \(-0.485211\pi\) | ||||
0.0464435 | + | 0.998921i | \(0.485211\pi\) | |||||||
\(102\) | − | 216.893i | − | 0.210545i | ||||||
\(103\) | −950.056 | −0.908852 | −0.454426 | − | 0.890784i | \(-0.650156\pi\) | ||||
−0.454426 | + | 0.890784i | \(0.650156\pi\) | |||||||
\(104\) | −262.587 | + | 226.294i | −0.247585 | + | 0.213365i | ||||
\(105\) | −266.474 | −0.247669 | ||||||||
\(106\) | − | 185.546i | − | 0.170017i | ||||||
\(107\) | −1209.82 | −1.09307 | −0.546533 | − | 0.837438i | \(-0.684053\pi\) | ||||
−0.546533 | + | 0.837438i | \(0.684053\pi\) | |||||||
\(108\) | 503.064 | 0.448216 | ||||||||
\(109\) | 751.273i | 0.660173i | 0.943951 | + | 0.330087i | \(0.107078\pi\) | ||||
−0.943951 | + | 0.330087i | \(0.892922\pi\) | |||||||
\(110\) | 17.8112i | 0.0154385i | ||||||||
\(111\) | − | 1156.49i | − | 0.988912i | ||||||
\(112\) | − | 681.225i | − | 0.574729i | ||||||
\(113\) | 261.719 | 0.217880 | 0.108940 | − | 0.994048i | \(-0.465254\pi\) | ||||
0.108940 | + | 0.994048i | \(0.465254\pi\) | |||||||
\(114\) | 426.624 | 0.350500 | ||||||||
\(115\) | 47.0979i | 0.0381905i | ||||||||
\(116\) | 928.185 | 0.742930 | ||||||||
\(117\) | 528.863 | + | 613.682i | 0.417892 | + | 0.484914i | ||||
\(118\) | −348.293 | −0.271720 | ||||||||
\(119\) | − | 806.040i | − | 0.620921i | ||||||
\(120\) | 170.036 | 0.129350 | ||||||||
\(121\) | −121.000 | −0.0909091 | ||||||||
\(122\) | 201.560i | 0.149577i | ||||||||
\(123\) | 2598.20i | 1.90465i | ||||||||
\(124\) | 1479.73i | 1.07165i | ||||||||
\(125\) | 822.512i | 0.588542i | ||||||||
\(126\) | 93.8792 | 0.0663764 | ||||||||
\(127\) | −655.749 | −0.458176 | −0.229088 | − | 0.973406i | \(-0.573574\pi\) | ||||
−0.229088 | + | 0.973406i | \(0.573574\pi\) | |||||||
\(128\) | 895.002i | 0.618029i | ||||||||
\(129\) | 2948.05 | 2.01210 | ||||||||
\(130\) | −49.5459 | − | 57.4920i | −0.0334266 | − | 0.0387876i | ||||
\(131\) | 924.346 | 0.616492 | 0.308246 | − | 0.951307i | \(-0.400258\pi\) | ||||
0.308246 | + | 0.951307i | \(0.400258\pi\) | |||||||
\(132\) | 569.527i | 0.375538i | ||||||||
\(133\) | 1585.46 | 1.03366 | ||||||||
\(134\) | 453.219 | 0.292181 | ||||||||
\(135\) | 223.395i | 0.142421i | ||||||||
\(136\) | 514.329i | 0.324289i | ||||||||
\(137\) | − | 1358.80i | − | 0.847376i | −0.905808 | − | 0.423688i | \(-0.860735\pi\) | ||
0.905808 | − | 0.423688i | \(-0.139265\pi\) | |||||||
\(138\) | − | 42.5131i | − | 0.0262243i | ||||||
\(139\) | 1932.17 | 1.17903 | 0.589513 | − | 0.807759i | \(-0.299320\pi\) | ||||
0.589513 | + | 0.807759i | \(0.299320\pi\) | |||||||
\(140\) | 311.554 | 0.188080 | ||||||||
\(141\) | 3131.68i | 1.87046i | ||||||||
\(142\) | −24.6710 | −0.0145799 | ||||||||
\(143\) | 390.570 | − | 336.589i | 0.228400 | − | 0.196832i | ||||
\(144\) | 1015.88 | 0.587896 | ||||||||
\(145\) | 412.179i | 0.236066i | ||||||||
\(146\) | −134.911 | −0.0764750 | ||||||||
\(147\) | −1388.63 | −0.779131 | ||||||||
\(148\) | 1352.13i | 0.750978i | ||||||||
\(149\) | 1649.22i | 0.906775i | 0.891314 | + | 0.453387i | \(0.149785\pi\) | ||||
−0.891314 | + | 0.453387i | \(0.850215\pi\) | |||||||
\(150\) | − | 352.608i | − | 0.191935i | ||||||
\(151\) | − | 2892.17i | − | 1.55868i | −0.626599 | − | 0.779342i | \(-0.715553\pi\) | ||
0.626599 | − | 0.779342i | \(-0.284447\pi\) | |||||||
\(152\) | −1011.67 | −0.539853 | ||||||||
\(153\) | 1202.02 | 0.635145 | ||||||||
\(154\) | − | 59.7483i | − | 0.0312640i | ||||||
\(155\) | −657.105 | −0.340516 | ||||||||
\(156\) | −1584.27 | − | 1838.35i | −0.813096 | − | 0.943499i | ||||
\(157\) | −1487.86 | −0.756331 | −0.378165 | − | 0.925738i | \(-0.623445\pi\) | ||||
−0.378165 | + | 0.925738i | \(0.623445\pi\) | |||||||
\(158\) | 264.398i | 0.133129i | ||||||||
\(159\) | 2634.65 | 1.31410 | ||||||||
\(160\) | −299.585 | −0.148026 | ||||||||
\(161\) | − | 157.991i | − | 0.0773383i | ||||||
\(162\) | − | 420.349i | − | 0.203863i | ||||||
\(163\) | − | 109.419i | − | 0.0525789i | −0.999654 | − | 0.0262894i | \(-0.991631\pi\) | ||
0.999654 | − | 0.0262894i | \(-0.00836915\pi\) | |||||||
\(164\) | − | 3037.73i | − | 1.44639i | ||||||
\(165\) | −252.910 | −0.119327 | ||||||||
\(166\) | 503.556 | 0.235443 | ||||||||
\(167\) | − | 813.879i | − | 0.377125i | −0.982061 | − | 0.188562i | \(-0.939617\pi\) | ||
0.982061 | − | 0.188562i | \(-0.0603828\pi\) | |||||||
\(168\) | −570.390 | −0.261944 | ||||||||
\(169\) | −324.408 | + | 2172.92i | −0.147659 | + | 0.989038i | ||||
\(170\) | −112.609 | −0.0508044 | ||||||||
\(171\) | 2364.34i | 1.05734i | ||||||||
\(172\) | −3446.77 | −1.52799 | ||||||||
\(173\) | 2890.82 | 1.27043 | 0.635216 | − | 0.772334i | \(-0.280911\pi\) | ||||
0.635216 | + | 0.772334i | \(0.280911\pi\) | |||||||
\(174\) | − | 372.054i | − | 0.162100i | ||||||
\(175\) | − | 1310.40i | − | 0.566038i | ||||||
\(176\) | − | 646.547i | − | 0.276905i | ||||||
\(177\) | − | 4945.57i | − | 2.10018i | ||||||
\(178\) | −294.521 | −0.124019 | ||||||||
\(179\) | −4254.68 | −1.77659 | −0.888295 | − | 0.459273i | \(-0.848110\pi\) | ||||
−0.888295 | + | 0.459273i | \(0.848110\pi\) | |||||||
\(180\) | 464.609i | 0.192388i | ||||||||
\(181\) | −402.638 | −0.165347 | −0.0826735 | − | 0.996577i | \(-0.526346\pi\) | ||||
−0.0826735 | + | 0.996577i | \(0.526346\pi\) | |||||||
\(182\) | 166.203 | + | 192.859i | 0.0676912 | + | 0.0785475i | ||||
\(183\) | −2862.05 | −1.15611 | ||||||||
\(184\) | 100.813i | 0.0403916i | ||||||||
\(185\) | −600.442 | −0.238624 | ||||||||
\(186\) | 593.138 | 0.233822 | ||||||||
\(187\) | − | 765.009i | − | 0.299160i | ||||||
\(188\) | − | 3661.47i | − | 1.42043i | ||||||
\(189\) | − | 749.387i | − | 0.288412i | ||||||
\(190\) | − | 221.500i | − | 0.0845754i | ||||||
\(191\) | −3850.73 | −1.45879 | −0.729395 | − | 0.684093i | \(-0.760198\pi\) | ||||
−0.729395 | + | 0.684093i | \(0.760198\pi\) | |||||||
\(192\) | −2858.68 | −1.07452 | ||||||||
\(193\) | 377.229i | 0.140692i | 0.997523 | + | 0.0703460i | \(0.0224103\pi\) | ||||
−0.997523 | + | 0.0703460i | \(0.977590\pi\) | |||||||
\(194\) | −294.843 | −0.109116 | ||||||||
\(195\) | 816.356 | − | 703.525i | 0.299797 | − | 0.258361i | ||||
\(196\) | 1623.55 | 0.591672 | ||||||||
\(197\) | − | 2482.71i | − | 0.897898i | −0.893557 | − | 0.448949i | \(-0.851798\pi\) | ||
0.893557 | − | 0.448949i | \(-0.148202\pi\) | |||||||
\(198\) | 89.1003 | 0.0319802 | ||||||||
\(199\) | −1326.65 | −0.472582 | −0.236291 | − | 0.971682i | \(-0.575932\pi\) | ||||
−0.236291 | + | 0.971682i | \(0.575932\pi\) | |||||||
\(200\) | 836.155i | 0.295625i | ||||||||
\(201\) | 6435.47i | 2.25832i | ||||||||
\(202\) | 44.1862i | 0.0153907i | ||||||||
\(203\) | − | 1382.67i | − | 0.478050i | ||||||
\(204\) | −3600.77 | −1.23581 | ||||||||
\(205\) | 1348.97 | 0.459589 | ||||||||
\(206\) | − | 445.245i | − | 0.150591i | ||||||
\(207\) | 235.606 | 0.0791101 | ||||||||
\(208\) | 1798.52 | + | 2086.96i | 0.599541 | + | 0.695695i | ||||
\(209\) | 1504.76 | 0.498020 | ||||||||
\(210\) | − | 124.884i | − | 0.0410371i | ||||||
\(211\) | 3293.99 | 1.07473 | 0.537365 | − | 0.843350i | \(-0.319420\pi\) | ||||
0.537365 | + | 0.843350i | \(0.319420\pi\) | |||||||
\(212\) | −3080.36 | −0.997923 | ||||||||
\(213\) | − | 350.316i | − | 0.112691i | ||||||
\(214\) | − | 566.985i | − | 0.181114i | ||||||
\(215\) | − | 1530.61i | − | 0.485519i | ||||||
\(216\) | 478.179i | 0.150629i | ||||||||
\(217\) | 2204.28 | 0.689568 | ||||||||
\(218\) | −352.085 | −0.109386 | ||||||||
\(219\) | − | 1915.67i | − | 0.591091i | ||||||
\(220\) | 295.695 | 0.0906170 | ||||||||
\(221\) | 2128.04 | + | 2469.34i | 0.647727 | + | 0.751609i | ||||
\(222\) | 541.991 | 0.163856 | ||||||||
\(223\) | 3935.96i | 1.18193i | 0.806696 | + | 0.590967i | \(0.201254\pi\) | ||||
−0.806696 | + | 0.590967i | \(0.798746\pi\) | |||||||
\(224\) | 1004.97 | 0.299764 | ||||||||
\(225\) | 1954.14 | 0.579005 | ||||||||
\(226\) | 122.655i | 0.0361013i | ||||||||
\(227\) | − | 319.025i | − | 0.0932795i | −0.998912 | − | 0.0466397i | \(-0.985149\pi\) | ||
0.998912 | − | 0.0466397i | \(-0.0148513\pi\) | |||||||
\(228\) | − | 7082.65i | − | 2.05728i | ||||||
\(229\) | 1181.26i | 0.340872i | 0.985369 | + | 0.170436i | \(0.0545176\pi\) | ||||
−0.985369 | + | 0.170436i | \(0.945482\pi\) | |||||||
\(230\) | −22.0725 | −0.00632790 | ||||||||
\(231\) | 848.394 | 0.241646 | ||||||||
\(232\) | 882.270i | 0.249672i | ||||||||
\(233\) | −6259.22 | −1.75989 | −0.879946 | − | 0.475073i | \(-0.842422\pi\) | ||||
−0.879946 | + | 0.475073i | \(0.842422\pi\) | |||||||
\(234\) | −287.603 | + | 247.852i | −0.0803469 | + | 0.0692420i | ||||
\(235\) | 1625.95 | 0.451341 | ||||||||
\(236\) | 5782.21i | 1.59487i | ||||||||
\(237\) | −3754.31 | −1.02898 | ||||||||
\(238\) | 377.752 | 0.102882 | ||||||||
\(239\) | − | 2469.50i | − | 0.668362i | −0.942509 | − | 0.334181i | \(-0.891540\pi\) | ||
0.942509 | − | 0.334181i | \(-0.108460\pi\) | |||||||
\(240\) | − | 1351.39i | − | 0.363466i | ||||||
\(241\) | − | 4082.66i | − | 1.09123i | −0.838035 | − | 0.545617i | \(-0.816296\pi\) | ||
0.838035 | − | 0.545617i | \(-0.183704\pi\) | |||||||
\(242\) | − | 56.7068i | − | 0.0150630i | ||||||
\(243\) | 4222.96 | 1.11483 | ||||||||
\(244\) | 3346.22 | 0.877951 | ||||||||
\(245\) | 720.968i | 0.188004i | ||||||||
\(246\) | −1217.65 | −0.315587 | ||||||||
\(247\) | −4857.14 | + | 4185.82i | −1.25122 | + | 1.07829i | ||||
\(248\) | −1406.54 | −0.360142 | ||||||||
\(249\) | 7150.22i | 1.81979i | ||||||||
\(250\) | −385.472 | −0.0975175 | ||||||||
\(251\) | −1800.08 | −0.452669 | −0.226335 | − | 0.974050i | \(-0.572674\pi\) | ||||
−0.226335 | + | 0.974050i | \(0.572674\pi\) | |||||||
\(252\) | − | 1558.54i | − | 0.389600i | ||||||
\(253\) | − | 149.949i | − | 0.0372617i | ||||||
\(254\) | − | 307.318i | − | 0.0759167i | ||||||
\(255\) | − | 1598.99i | − | 0.392678i | ||||||
\(256\) | 3017.19 | 0.736619 | ||||||||
\(257\) | 2982.53 | 0.723910 | 0.361955 | − | 0.932196i | \(-0.382109\pi\) | ||||
0.361955 | + | 0.932196i | \(0.382109\pi\) | |||||||
\(258\) | 1381.61i | 0.333392i | ||||||||
\(259\) | 2014.20 | 0.483229 | ||||||||
\(260\) | −954.459 | + | 822.541i | −0.227666 | + | 0.196199i | ||||
\(261\) | 2061.92 | 0.489002 | ||||||||
\(262\) | 433.196i | 0.102149i | ||||||||
\(263\) | 3021.93 | 0.708519 | 0.354259 | − | 0.935147i | \(-0.384733\pi\) | ||||
0.354259 | + | 0.935147i | \(0.384733\pi\) | |||||||
\(264\) | −541.354 | −0.126205 | ||||||||
\(265\) | − | 1367.89i | − | 0.317090i | ||||||
\(266\) | 743.030i | 0.171271i | ||||||||
\(267\) | − | 4182.05i | − | 0.958566i | ||||||
\(268\) | − | 7524.17i | − | 1.71497i | ||||||
\(269\) | −4105.73 | −0.930598 | −0.465299 | − | 0.885153i | \(-0.654053\pi\) | ||||
−0.465299 | + | 0.885153i | \(0.654053\pi\) | |||||||
\(270\) | −104.695 | −0.0235982 | ||||||||
\(271\) | − | 490.284i | − | 0.109899i | −0.998489 | − | 0.0549495i | \(-0.982500\pi\) | ||
0.998489 | − | 0.0549495i | \(-0.0174998\pi\) | |||||||
\(272\) | 4087.72 | 0.911230 | ||||||||
\(273\) | −2738.49 | + | 2360.00i | −0.607110 | + | 0.523200i | ||||
\(274\) | 636.806 | 0.140405 | ||||||||
\(275\) | − | 1243.69i | − | 0.272718i | ||||||
\(276\) | −705.785 | −0.153925 | ||||||||
\(277\) | 1772.57 | 0.384489 | 0.192245 | − | 0.981347i | \(-0.438423\pi\) | ||||
0.192245 | + | 0.981347i | \(0.438423\pi\) | |||||||
\(278\) | 905.515i | 0.195357i | ||||||||
\(279\) | 3287.16i | 0.705365i | ||||||||
\(280\) | 296.142i | 0.0632068i | ||||||||
\(281\) | − | 396.426i | − | 0.0841595i | −0.999114 | − | 0.0420797i | \(-0.986602\pi\) | ||
0.999114 | − | 0.0420797i | \(-0.0133984\pi\) | |||||||
\(282\) | −1467.67 | −0.309923 | ||||||||
\(283\) | 983.143 | 0.206508 | 0.103254 | − | 0.994655i | \(-0.467075\pi\) | ||||
0.103254 | + | 0.994655i | \(0.467075\pi\) | |||||||
\(284\) | 409.579i | 0.0855776i | ||||||||
\(285\) | 3145.19 | 0.653701 | ||||||||
\(286\) | 157.743 | + | 183.041i | 0.0326137 | + | 0.0378443i | ||||
\(287\) | −4525.15 | −0.930700 | ||||||||
\(288\) | 1498.67i | 0.306631i | ||||||||
\(289\) | −76.3197 | −0.0155342 | ||||||||
\(290\) | −193.168 | −0.0391146 | ||||||||
\(291\) | − | 4186.61i | − | 0.843380i | ||||||
\(292\) | 2239.75i | 0.448874i | ||||||||
\(293\) | − | 8194.68i | − | 1.63392i | −0.576695 | − | 0.816960i | \(-0.695658\pi\) | ||
0.576695 | − | 0.816960i | \(-0.304342\pi\) | |||||||
\(294\) | − | 650.784i | − | 0.129097i | ||||||
\(295\) | −2567.70 | −0.506771 | ||||||||
\(296\) | −1285.25 | −0.252377 | ||||||||
\(297\) | − | 711.239i | − | 0.138957i | ||||||
\(298\) | −772.910 | −0.150247 | ||||||||
\(299\) | 417.116 | + | 484.013i | 0.0806771 | + | 0.0936161i | ||||
\(300\) | −5853.85 | −1.12657 | ||||||||
\(301\) | 5134.47i | 0.983209i | ||||||||
\(302\) | 1355.42 | 0.258264 | ||||||||
\(303\) | −627.420 | −0.118958 | ||||||||
\(304\) | 8040.47i | 1.51695i | ||||||||
\(305\) | 1485.96i | 0.278969i | ||||||||
\(306\) | 563.327i | 0.105239i | ||||||||
\(307\) | 5224.91i | 0.971341i | 0.874142 | + | 0.485670i | \(0.161424\pi\) | ||||
−0.874142 | + | 0.485670i | \(0.838576\pi\) | |||||||
\(308\) | −991.917 | −0.183506 | ||||||||
\(309\) | 6322.24 | 1.16395 | ||||||||
\(310\) | − | 307.953i | − | 0.0564212i | ||||||
\(311\) | 5812.89 | 1.05987 | 0.529934 | − | 0.848039i | \(-0.322217\pi\) | ||||
0.529934 | + | 0.848039i | \(0.322217\pi\) | |||||||
\(312\) | 1747.41 | − | 1505.90i | 0.317076 | − | 0.273252i | ||||
\(313\) | 8225.44 | 1.48540 | 0.742699 | − | 0.669626i | \(-0.233546\pi\) | ||||
0.742699 | + | 0.669626i | \(0.233546\pi\) | |||||||
\(314\) | − | 697.286i | − | 0.125319i | ||||||
\(315\) | 692.102 | 0.123795 | ||||||||
\(316\) | 4389.43 | 0.781408 | ||||||||
\(317\) | 2807.87i | 0.497495i | 0.968568 | + | 0.248747i | \(0.0800189\pi\) | ||||
−0.968568 | + | 0.248747i | \(0.919981\pi\) | |||||||
\(318\) | 1234.73i | 0.217737i | ||||||||
\(319\) | − | 1312.28i | − | 0.230325i | ||||||
\(320\) | 1484.21i | 0.259280i | ||||||||
\(321\) | 8050.89 | 1.39987 | ||||||||
\(322\) | 74.0429 | 0.0128144 | ||||||||
\(323\) | 9513.66i | 1.63887i | ||||||||
\(324\) | −6978.47 | −1.19658 | ||||||||
\(325\) | 3459.60 | + | 4014.45i | 0.590475 | + | 0.685175i | ||||
\(326\) | 51.2794 | 0.00871197 | ||||||||
\(327\) | − | 4999.42i | − | 0.845469i | ||||||
\(328\) | 2887.47 | 0.486078 | ||||||||
\(329\) | −5454.29 | −0.913997 | ||||||||
\(330\) | − | 118.527i | − | 0.0197717i | ||||||
\(331\) | 8649.46i | 1.43631i | 0.695885 | + | 0.718153i | \(0.255012\pi\) | ||||
−0.695885 | + | 0.718153i | \(0.744988\pi\) | |||||||
\(332\) | − | 8359.83i | − | 1.38194i | ||||||
\(333\) | 3003.70i | 0.494300i | ||||||||
\(334\) | 381.425 | 0.0624870 | ||||||||
\(335\) | 3341.25 | 0.544932 | ||||||||
\(336\) | 4533.28i | 0.736043i | ||||||||
\(337\) | −714.839 | −0.115548 | −0.0577741 | − | 0.998330i | \(-0.518400\pi\) | ||||
−0.0577741 | + | 0.998330i | \(0.518400\pi\) | |||||||
\(338\) | −1018.34 | − | 152.034i | −0.163877 | − | 0.0244662i | ||||
\(339\) | −1741.64 | −0.279035 | ||||||||
\(340\) | 1869.50i | 0.298199i | ||||||||
\(341\) | 2092.07 | 0.332235 | ||||||||
\(342\) | −1108.05 | −0.175195 | ||||||||
\(343\) | − | 6393.87i | − | 1.00652i | ||||||
\(344\) | − | 3276.27i | − | 0.513502i | ||||||
\(345\) | − | 313.418i | − | 0.0489097i | ||||||
\(346\) | 1354.79i | 0.210502i | ||||||||
\(347\) | 7193.68 | 1.11290 | 0.556451 | − | 0.830880i | \(-0.312163\pi\) | ||||
0.556451 | + | 0.830880i | \(0.312163\pi\) | |||||||
\(348\) | −6176.70 | −0.951454 | ||||||||
\(349\) | − | 4972.78i | − | 0.762713i | −0.924428 | − | 0.381356i | \(-0.875457\pi\) | ||
0.924428 | − | 0.381356i | \(-0.124543\pi\) | |||||||
\(350\) | 614.119 | 0.0937887 | ||||||||
\(351\) | 1978.47 | + | 2295.78i | 0.300863 | + | 0.349115i | ||||
\(352\) | 953.809 | 0.144427 | ||||||||
\(353\) | − | 2431.78i | − | 0.366659i | −0.983051 | − | 0.183330i | \(-0.941312\pi\) | ||
0.983051 | − | 0.183330i | \(-0.0586876\pi\) | |||||||
\(354\) | 2317.75 | 0.347986 | ||||||||
\(355\) | −181.881 | −0.0271923 | ||||||||
\(356\) | 4889.53i | 0.727934i | ||||||||
\(357\) | 5363.87i | 0.795199i | ||||||||
\(358\) | − | 1993.96i | − | 0.294369i | ||||||
\(359\) | − | 4539.72i | − | 0.667402i | −0.942679 | − | 0.333701i | \(-0.891702\pi\) | ||
0.942679 | − | 0.333701i | \(-0.108298\pi\) | |||||||
\(360\) | −441.626 | −0.0646548 | ||||||||
\(361\) | −11854.2 | −1.72827 | ||||||||
\(362\) | − | 188.697i | − | 0.0273969i | ||||||
\(363\) | 805.207 | 0.116425 | ||||||||
\(364\) | 3201.76 | − | 2759.24i | 0.461039 | − | 0.397317i | ||||
\(365\) | −994.603 | −0.142630 | ||||||||
\(366\) | − | 1341.30i | − | 0.191560i | ||||||
\(367\) | −12893.9 | −1.83393 | −0.916967 | − | 0.398964i | \(-0.869370\pi\) | ||||
−0.916967 | + | 0.398964i | \(0.869370\pi\) | |||||||
\(368\) | 801.232 | 0.113498 | ||||||||
\(369\) | − | 6748.18i | − | 0.952022i | ||||||
\(370\) | − | 281.398i | − | 0.0395383i | ||||||
\(371\) | 4588.64i | 0.642130i | ||||||||
\(372\) | − | 9847.04i | − | 1.37243i | ||||||
\(373\) | 4943.47 | 0.686229 | 0.343114 | − | 0.939294i | \(-0.388518\pi\) | ||||
0.343114 | + | 0.939294i | \(0.388518\pi\) | |||||||
\(374\) | 358.522 | 0.0495689 | ||||||||
\(375\) | − | 5473.49i | − | 0.753733i | ||||||
\(376\) | 3480.35 | 0.477354 | ||||||||
\(377\) | 3650.41 | + | 4235.86i | 0.498688 | + | 0.578668i | ||||
\(378\) | 351.201 | 0.0477879 | ||||||||
\(379\) | − | 2212.86i | − | 0.299913i | −0.988693 | − | 0.149956i | \(-0.952087\pi\) | ||
0.988693 | − | 0.149956i | \(-0.0479133\pi\) | |||||||
\(380\) | −3677.26 | −0.496420 | ||||||||
\(381\) | 4363.75 | 0.586776 | ||||||||
\(382\) | − | 1804.65i | − | 0.241712i | ||||||
\(383\) | 14067.2i | 1.87677i | 0.345597 | + | 0.938383i | \(0.387676\pi\) | ||||
−0.345597 | + | 0.938383i | \(0.612324\pi\) | |||||||
\(384\) | − | 5955.88i | − | 0.791497i | ||||||
\(385\) | − | 440.480i | − | 0.0583090i | ||||||
\(386\) | −176.789 | −0.0233117 | ||||||||
\(387\) | −7656.84 | −1.00573 | ||||||||
\(388\) | 4894.86i | 0.640462i | ||||||||
\(389\) | −9822.69 | −1.28028 | −0.640141 | − | 0.768257i | \(-0.721124\pi\) | ||||
−0.640141 | + | 0.768257i | \(0.721124\pi\) | |||||||
\(390\) | 329.708 | + | 382.586i | 0.0428087 | + | 0.0496744i | ||||
\(391\) | 948.035 | 0.122619 | ||||||||
\(392\) | 1543.23i | 0.198840i | ||||||||
\(393\) | −6151.15 | −0.789529 | ||||||||
\(394\) | 1163.53 | 0.148776 | ||||||||
\(395\) | 1949.21i | 0.248292i | ||||||||
\(396\) | − | 1479.21i | − | 0.187710i | ||||||
\(397\) | 1365.99i | 0.172688i | 0.996265 | + | 0.0863441i | \(0.0275184\pi\) | ||||
−0.996265 | + | 0.0863441i | \(0.972482\pi\) | |||||||
\(398\) | − | 621.738i | − | 0.0783037i | ||||||
\(399\) | −10550.6 | −1.32379 | ||||||||
\(400\) | 6645.50 | 0.830687 | ||||||||
\(401\) | − | 13912.0i | − | 1.73250i | −0.499610 | − | 0.866250i | \(-0.666523\pi\) | ||
0.499610 | − | 0.866250i | \(-0.333477\pi\) | |||||||
\(402\) | −3015.99 | −0.374189 | ||||||||
\(403\) | −6752.90 | + | 5819.56i | −0.834704 | + | 0.719338i | ||||
\(404\) | 733.562 | 0.0903368 | ||||||||
\(405\) | − | 3098.93i | − | 0.380215i | ||||||
\(406\) | 647.989 | 0.0792097 | ||||||||
\(407\) | 1911.67 | 0.232820 | ||||||||
\(408\) | − | 3422.65i | − | 0.415310i | ||||||
\(409\) | − | 6892.66i | − | 0.833301i | −0.909067 | − | 0.416651i | \(-0.863204\pi\) | ||
0.909067 | − | 0.416651i | \(-0.136796\pi\) | |||||||
\(410\) | 632.194i | 0.0761509i | ||||||||
\(411\) | 9042.30i | 1.08522i | ||||||||
\(412\) | −7391.78 | −0.883900 | ||||||||
\(413\) | 8613.45 | 1.02625 | ||||||||
\(414\) | 110.417i | 0.0131080i | ||||||||
\(415\) | 3712.34 | 0.439113 | ||||||||
\(416\) | −3078.75 | + | 2653.23i | −0.362857 | + | 0.312705i | ||||
\(417\) | −12857.8 | −1.50995 | ||||||||
\(418\) | 705.207i | 0.0825186i | ||||||||
\(419\) | −4253.11 | −0.495890 | −0.247945 | − | 0.968774i | \(-0.579755\pi\) | ||||
−0.247945 | + | 0.968774i | \(0.579755\pi\) | |||||||
\(420\) | −2073.27 | −0.240869 | ||||||||
\(421\) | − | 16604.7i | − | 1.92224i | −0.276133 | − | 0.961119i | \(-0.589053\pi\) | ||
0.276133 | − | 0.961119i | \(-0.410947\pi\) | |||||||
\(422\) | 1543.73i | 0.178075i | ||||||||
\(423\) | − | 8133.78i | − | 0.934936i | ||||||
\(424\) | − | 2927.98i | − | 0.335366i | ||||||
\(425\) | 7863.09 | 0.897450 | ||||||||
\(426\) | 164.176 | 0.0186722 | ||||||||
\(427\) | − | 4984.68i | − | 0.564931i | ||||||
\(428\) | −9412.87 | −1.06306 | ||||||||
\(429\) | −2599.09 | + | 2239.86i | −0.292506 | + | 0.252078i | ||||
\(430\) | 717.321 | 0.0804472 | ||||||||
\(431\) | − | 12392.8i | − | 1.38501i | −0.721413 | − | 0.692505i | \(-0.756507\pi\) | ||
0.721413 | − | 0.692505i | \(-0.243493\pi\) | |||||||
\(432\) | 3800.41 | 0.423258 | ||||||||
\(433\) | −2304.50 | −0.255767 | −0.127884 | − | 0.991789i | \(-0.540818\pi\) | ||||
−0.127884 | + | 0.991789i | \(0.540818\pi\) | |||||||
\(434\) | 1033.04i | 0.114257i | ||||||||
\(435\) | − | 2742.88i | − | 0.302325i | ||||||
\(436\) | 5845.18i | 0.642049i | ||||||||
\(437\) | 1864.77i | 0.204128i | ||||||||
\(438\) | 897.781 | 0.0979398 | ||||||||
\(439\) | −8562.55 | −0.930907 | −0.465453 | − | 0.885072i | \(-0.654109\pi\) | ||||
−0.465453 | + | 0.885072i | \(0.654109\pi\) | |||||||
\(440\) | 281.068i | 0.0304531i | ||||||||
\(441\) | 3606.63 | 0.389443 | ||||||||
\(442\) | −1157.26 | + | 997.310i | −0.124537 | + | 0.107324i | ||||
\(443\) | 8542.60 | 0.916187 | 0.458094 | − | 0.888904i | \(-0.348532\pi\) | ||||
0.458094 | + | 0.888904i | \(0.348532\pi\) | |||||||
\(444\) | − | 8997.92i | − | 0.961762i | ||||||
\(445\) | −2171.29 | −0.231301 | ||||||||
\(446\) | −1844.59 | −0.195838 | ||||||||
\(447\) | − | 10974.9i | − | 1.16129i | ||||||
\(448\) | − | 4978.82i | − | 0.525060i | ||||||
\(449\) | 6995.03i | 0.735225i | 0.929979 | + | 0.367612i | \(0.119825\pi\) | ||||
−0.929979 | + | 0.367612i | \(0.880175\pi\) | |||||||
\(450\) | 915.812i | 0.0959373i | ||||||||
\(451\) | −4294.80 | −0.448412 | ||||||||
\(452\) | 2036.27 | 0.211899 | ||||||||
\(453\) | 19246.2i | 1.99617i | ||||||||
\(454\) | 149.512 | 0.0154558 | ||||||||
\(455\) | 1225.29 | + | 1421.81i | 0.126248 | + | 0.146495i | ||||
\(456\) | 6732.29 | 0.691378 | ||||||||
\(457\) | − | 5905.72i | − | 0.604503i | −0.953228 | − | 0.302252i | \(-0.902262\pi\) | ||
0.953228 | − | 0.302252i | \(-0.0977383\pi\) | |||||||
\(458\) | −553.598 | −0.0564802 | ||||||||
\(459\) | 4496.73 | 0.457275 | ||||||||
\(460\) | 366.439i | 0.0371420i | ||||||||
\(461\) | 16268.9i | 1.64364i | 0.569747 | + | 0.821820i | \(0.307041\pi\) | ||||
−0.569747 | + | 0.821820i | \(0.692959\pi\) | |||||||
\(462\) | 397.601i | 0.0400391i | ||||||||
\(463\) | − | 12086.2i | − | 1.21316i | −0.795021 | − | 0.606582i | \(-0.792540\pi\) | ||
0.795021 | − | 0.606582i | \(-0.207460\pi\) | |||||||
\(464\) | 7012.00 | 0.701561 | ||||||||
\(465\) | 4372.77 | 0.436091 | ||||||||
\(466\) | − | 2933.39i | − | 0.291602i | ||||||
\(467\) | 11438.9 | 1.13347 | 0.566736 | − | 0.823900i | \(-0.308206\pi\) | ||||
0.566736 | + | 0.823900i | \(0.308206\pi\) | |||||||
\(468\) | 4114.75 | + | 4774.67i | 0.406419 | + | 0.471601i | ||||
\(469\) | −11208.3 | −1.10352 | ||||||||
\(470\) | 762.003i | 0.0747842i | ||||||||
\(471\) | 9901.09 | 0.968616 | ||||||||
\(472\) | −5496.18 | −0.535980 | ||||||||
\(473\) | 4873.10i | 0.473711i | ||||||||
\(474\) | − | 1759.46i | − | 0.170495i | ||||||
\(475\) | 15466.6i | 1.49401i | ||||||||
\(476\) | − | 6271.28i | − | 0.603874i | ||||||
\(477\) | −6842.85 | −0.656840 | ||||||||
\(478\) | 1157.33 | 0.110743 | ||||||||
\(479\) | − | 12569.7i | − | 1.19901i | −0.800373 | − | 0.599503i | \(-0.795365\pi\) | ||
0.800373 | − | 0.599503i | \(-0.204635\pi\) | |||||||
\(480\) | 1993.62 | 0.189574 | ||||||||
\(481\) | −6170.59 | + | 5317.73i | −0.584937 | + | 0.504091i | ||||
\(482\) | 1913.34 | 0.180810 | ||||||||
\(483\) | 1051.37i | 0.0990455i | ||||||||
\(484\) | −941.424 | −0.0884132 | ||||||||
\(485\) | −2173.66 | −0.203507 | ||||||||
\(486\) | 1979.10i | 0.184720i | ||||||||
\(487\) | − | 12546.0i | − | 1.16737i | −0.811978 | − | 0.583687i | \(-0.801609\pi\) | ||
0.811978 | − | 0.583687i | \(-0.198391\pi\) | |||||||
\(488\) | 3180.69i | 0.295048i | ||||||||
\(489\) | 728.140i | 0.0673366i | ||||||||
\(490\) | −337.883 | −0.0311510 | ||||||||
\(491\) | 4510.82 | 0.414604 | 0.207302 | − | 0.978277i | \(-0.433532\pi\) | ||||
0.207302 | + | 0.978277i | \(0.433532\pi\) | |||||||
\(492\) | 20214.9i | 1.85235i | ||||||||
\(493\) | 8296.76 | 0.757945 | ||||||||
\(494\) | −1961.69 | − | 2276.30i | −0.178665 | − | 0.207319i | ||||
\(495\) | 656.871 | 0.0596448 | ||||||||
\(496\) | 11178.7i | 1.01197i | ||||||||
\(497\) | 610.127 | 0.0550663 | ||||||||
\(498\) | −3350.96 | −0.301526 | ||||||||
\(499\) | − | 10387.6i | − | 0.931889i | −0.884814 | − | 0.465944i | \(-0.845715\pi\) | ||
0.884814 | − | 0.465944i | \(-0.154285\pi\) | |||||||
\(500\) | 6399.45i | 0.572384i | ||||||||
\(501\) | 5416.04i | 0.482975i | ||||||||
\(502\) | − | 843.609i | − | 0.0750042i | ||||||
\(503\) | −16193.4 | −1.43544 | −0.717720 | − | 0.696331i | \(-0.754814\pi\) | ||||
−0.717720 | + | 0.696331i | \(0.754814\pi\) | |||||||
\(504\) | 1481.45 | 0.130930 | ||||||||
\(505\) | 325.752i | 0.0287045i | ||||||||
\(506\) | 70.2738 | 0.00617401 | ||||||||
\(507\) | 2158.80 | − | 14459.9i | 0.189104 | − | 1.26664i | ||||
\(508\) | −5101.97 | −0.445597 | ||||||||
\(509\) | − | 1633.29i | − | 0.142228i | −0.997468 | − | 0.0711142i | \(-0.977345\pi\) | ||
0.997468 | − | 0.0711142i | \(-0.0226555\pi\) | |||||||
\(510\) | 749.370 | 0.0650641 | ||||||||
\(511\) | 3336.43 | 0.288835 | ||||||||
\(512\) | 8574.03i | 0.740082i | ||||||||
\(513\) | 8844.98i | 0.761239i | ||||||||
\(514\) | 1397.77i | 0.119947i | ||||||||
\(515\) | − | 3282.46i | − | 0.280859i | ||||||
\(516\) | 22936.9 | 1.95686 | ||||||||
\(517\) | −5176.65 | −0.440365 | ||||||||
\(518\) | 943.958i | 0.0800678i | ||||||||
\(519\) | −19237.2 | −1.62702 | ||||||||
\(520\) | −781.852 | − | 907.245i | −0.0659355 | − | 0.0765102i | ||||
\(521\) | 5358.69 | 0.450611 | 0.225306 | − | 0.974288i | \(-0.427662\pi\) | ||||
0.225306 | + | 0.974288i | \(0.427662\pi\) | |||||||
\(522\) | 966.320i | 0.0810243i | ||||||||
\(523\) | −2402.72 | −0.200886 | −0.100443 | − | 0.994943i | \(-0.532026\pi\) | ||||
−0.100443 | + | 0.994943i | \(0.532026\pi\) | |||||||
\(524\) | 7191.75 | 0.599567 | ||||||||
\(525\) | 8720.16i | 0.724912i | ||||||||
\(526\) | 1416.23i | 0.117397i | ||||||||
\(527\) | 13226.9i | 1.09331i | ||||||||
\(528\) | 4302.51i | 0.354627i | ||||||||
\(529\) | −11981.2 | −0.984727 | ||||||||
\(530\) | 641.064 | 0.0525397 | ||||||||
\(531\) | 12844.9i | 1.04976i | ||||||||
\(532\) | 12335.5 | 1.00528 | ||||||||
\(533\) | 13863.0 | − | 11946.9i | 1.12659 | − | 0.970880i | ||||
\(534\) | 1959.92 | 0.158828 | ||||||||
\(535\) | − | 4179.97i | − | 0.337786i | ||||||
\(536\) | 7151.97 | 0.576339 | ||||||||
\(537\) | 28313.2 | 2.27524 | ||||||||
\(538\) | − | 1924.16i | − | 0.154194i | ||||||
\(539\) | − | 2295.40i | − | 0.183432i | ||||||
\(540\) | 1738.10i | 0.138511i | ||||||||
\(541\) | − | 6711.56i | − | 0.533368i | −0.963784 | − | 0.266684i | \(-0.914072\pi\) | ||
0.963784 | − | 0.266684i | \(-0.0859281\pi\) | |||||||
\(542\) | 229.772 | 0.0182095 | ||||||||
\(543\) | 2679.39 | 0.211756 | ||||||||
\(544\) | 6030.35i | 0.475274i | ||||||||
\(545\) | −2595.66 | −0.204011 | ||||||||
\(546\) | −1106.02 | − | 1283.40i | −0.0866907 | − | 0.100594i | ||||
\(547\) | −11094.2 | −0.867189 | −0.433595 | − | 0.901108i | \(-0.642755\pi\) | ||||
−0.433595 | + | 0.901108i | \(0.642755\pi\) | |||||||
\(548\) | − | 10572.0i | − | 0.824112i | ||||||
\(549\) | 7433.47 | 0.577874 | ||||||||
\(550\) | 582.858 | 0.0451875 | ||||||||
\(551\) | 16319.6i | 1.26177i | ||||||||
\(552\) | − | 670.872i | − | 0.0517286i | ||||||
\(553\) | − | 6538.69i | − | 0.502809i | ||||||
\(554\) | 830.719i | 0.0637073i | ||||||||
\(555\) | 3995.70 | 0.305600 | ||||||||
\(556\) | 15033.0 | 1.14666 | ||||||||
\(557\) | − | 7187.13i | − | 0.546730i | −0.961910 | − | 0.273365i | \(-0.911863\pi\) | ||
0.961910 | − | 0.273365i | \(-0.0881366\pi\) | |||||||
\(558\) | −1540.53 | −0.116874 | ||||||||
\(559\) | −13555.6 | − | 15729.7i | −1.02566 | − | 1.19015i | ||||
\(560\) | 2353.65 | 0.177607 | ||||||||
\(561\) | 5090.83i | 0.383128i | ||||||||
\(562\) | 185.786 | 0.0139447 | ||||||||
\(563\) | 1718.98 | 0.128679 | 0.0643395 | − | 0.997928i | \(-0.479506\pi\) | ||||
0.0643395 | + | 0.997928i | \(0.479506\pi\) | |||||||
\(564\) | 24365.6i | 1.81911i | ||||||||
\(565\) | 904.246i | 0.0673308i | ||||||||
\(566\) | 460.752i | 0.0342170i | ||||||||
\(567\) | 10395.4i | 0.769961i | ||||||||
\(568\) | −389.318 | −0.0287596 | ||||||||
\(569\) | −7181.26 | −0.529093 | −0.264547 | − | 0.964373i | \(-0.585222\pi\) | ||||
−0.264547 | + | 0.964373i | \(0.585222\pi\) | |||||||
\(570\) | 1474.00i | 0.108314i | ||||||||
\(571\) | −22731.5 | −1.66599 | −0.832997 | − | 0.553278i | \(-0.813377\pi\) | ||||
−0.832997 | + | 0.553278i | \(0.813377\pi\) | |||||||
\(572\) | 3038.78 | − | 2618.78i | 0.222129 | − | 0.191428i | ||||
\(573\) | 25625.0 | 1.86824 | ||||||||
\(574\) | − | 2120.72i | − | 0.154211i | ||||||
\(575\) | 1541.24 | 0.111781 | ||||||||
\(576\) | 7424.72 | 0.537089 | ||||||||
\(577\) | − | 10364.7i | − | 0.747811i | −0.927467 | − | 0.373905i | \(-0.878018\pi\) | ||
0.927467 | − | 0.373905i | \(-0.121982\pi\) | |||||||
\(578\) | − | 35.7673i | − | 0.00257392i | ||||||
\(579\) | − | 2510.31i | − | 0.180181i | ||||||
\(580\) | 3206.90i | 0.229585i | ||||||||
\(581\) | −12453.2 | −0.889234 | ||||||||
\(582\) | 1962.06 | 0.139742 | ||||||||
\(583\) | 4355.05i | 0.309379i | ||||||||
\(584\) | −2128.95 | −0.150850 | ||||||||
\(585\) | −2120.28 | + | 1827.23i | −0.149851 | + | 0.129140i | ||||
\(586\) | 3840.45 | 0.270730 | ||||||||
\(587\) | − | 13510.7i | − | 0.949991i | −0.879988 | − | 0.474996i | \(-0.842450\pi\) | ||
0.879988 | − | 0.474996i | \(-0.157550\pi\) | |||||||
\(588\) | −10804.1 | −0.757741 | ||||||||
\(589\) | −26017.0 | −1.82006 | ||||||||
\(590\) | − | 1203.36i | − | 0.0839686i | ||||||
\(591\) | 16521.5i | 1.14992i | ||||||||
\(592\) | 10214.7i | 0.709161i | ||||||||
\(593\) | − | 10472.2i | − | 0.725198i | −0.931945 | − | 0.362599i | \(-0.881889\pi\) | ||
0.931945 | − | 0.362599i | \(-0.118111\pi\) | |||||||
\(594\) | 333.323 | 0.0230243 | ||||||||
\(595\) | 2784.89 | 0.191881 | ||||||||
\(596\) | 12831.5i | 0.881880i | ||||||||
\(597\) | 8828.34 | 0.605226 | ||||||||
\(598\) | −226.833 | + | 195.482i | −0.0155116 | + | 0.0133677i | ||||
\(599\) | −11954.7 | −0.815451 | −0.407726 | − | 0.913104i | \(-0.633678\pi\) | ||||
−0.407726 | + | 0.913104i | \(0.633678\pi\) | |||||||
\(600\) | − | 5564.28i | − | 0.378601i | ||||||
\(601\) | 11581.5 | 0.786056 | 0.393028 | − | 0.919527i | \(-0.371428\pi\) | ||||
0.393028 | + | 0.919527i | \(0.371428\pi\) | |||||||
\(602\) | −2406.28 | −0.162911 | ||||||||
\(603\) | − | 16714.6i | − | 1.12881i | ||||||
\(604\) | − | 22502.1i | − | 1.51589i | ||||||
\(605\) | − | 418.058i | − | 0.0280933i | ||||||
\(606\) | − | 294.041i | − | 0.0197106i | ||||||
\(607\) | 19639.9 | 1.31328 | 0.656639 | − | 0.754205i | \(-0.271978\pi\) | ||||
0.656639 | + | 0.754205i | \(0.271978\pi\) | |||||||
\(608\) | −11861.6 | −0.791201 | ||||||||
\(609\) | 9201.09i | 0.612228i | ||||||||
\(610\) | −696.395 | −0.0462233 | ||||||||
\(611\) | 16709.5 | − | 14400.0i | 1.10637 | − | 0.953456i | ||||
\(612\) | 9352.12 | 0.617708 | ||||||||
\(613\) | − | 1278.58i | − | 0.0842435i | −0.999112 | − | 0.0421218i | \(-0.986588\pi\) | ||
0.999112 | − | 0.0421218i | \(-0.0134117\pi\) | |||||||
\(614\) | −2448.66 | −0.160945 | ||||||||
\(615\) | −8976.82 | −0.588586 | ||||||||
\(616\) | − | 942.850i | − | 0.0616696i | ||||||
\(617\) | 15522.9i | 1.01285i | 0.862283 | + | 0.506426i | \(0.169034\pi\) | ||||
−0.862283 | + | 0.506426i | \(0.830966\pi\) | |||||||
\(618\) | 2962.93i | 0.192858i | ||||||||
\(619\) | 144.033i | 0.00935247i | 0.999989 | + | 0.00467624i | \(0.00148850\pi\) | ||||
−0.999989 | + | 0.00467624i | \(0.998512\pi\) | |||||||
\(620\) | −5112.52 | −0.331167 | ||||||||
\(621\) | 881.402 | 0.0569556 | ||||||||
\(622\) | 2724.22i | 0.175613i | ||||||||
\(623\) | 7283.66 | 0.468401 | ||||||||
\(624\) | −11968.4 | − | 13887.9i | −0.767820 | − | 0.890962i | ||||
\(625\) | 11291.1 | 0.722627 | ||||||||
\(626\) | 3854.86i | 0.246120i | ||||||||
\(627\) | −10013.6 | −0.637804 | ||||||||
\(628\) | −11576.1 | −0.735566 | ||||||||
\(629\) | 12086.3i | 0.766157i | ||||||||
\(630\) | 324.355i | 0.0205121i | ||||||||
\(631\) | 2470.98i | 0.155892i | 0.996958 | + | 0.0779461i | \(0.0248362\pi\) | ||||
−0.996958 | + | 0.0779461i | \(0.975164\pi\) | |||||||
\(632\) | 4172.30i | 0.262603i | ||||||||
\(633\) | −21920.2 | −1.37638 | ||||||||
\(634\) | −1315.91 | −0.0824315 | ||||||||
\(635\) | − | 2265.63i | − | 0.141589i | ||||||
\(636\) | 20498.5 | 1.27802 | ||||||||
\(637\) | 6385.16 | + | 7409.20i | 0.397157 | + | 0.460853i | ||||
\(638\) | 615.003 | 0.0381633 | ||||||||
\(639\) | 909.859i | 0.0563278i | ||||||||
\(640\) | −3092.25 | −0.190987 | ||||||||
\(641\) | 10419.0 | 0.642004 | 0.321002 | − | 0.947079i | \(-0.395980\pi\) | ||||
0.321002 | + | 0.947079i | \(0.395980\pi\) | |||||||
\(642\) | 3773.06i | 0.231948i | ||||||||
\(643\) | − | 9261.78i | − | 0.568039i | −0.958819 | − | 0.284019i | \(-0.908332\pi\) | ||
0.958819 | − | 0.284019i | \(-0.0916680\pi\) | |||||||
\(644\) | − | 1229.23i | − | 0.0752150i | ||||||
\(645\) | 10185.6i | 0.621793i | ||||||||
\(646\) | −4458.59 | −0.271549 | ||||||||
\(647\) | −25679.8 | −1.56040 | −0.780200 | − | 0.625530i | \(-0.784883\pi\) | ||||
−0.780200 | + | 0.625530i | \(0.784883\pi\) | |||||||
\(648\) | − | 6633.27i | − | 0.402129i | ||||||
\(649\) | 8174.98 | 0.494447 | ||||||||
\(650\) | −1881.38 | + | 1621.35i | −0.113529 | + | 0.0978377i | ||||
\(651\) | −14668.6 | −0.883114 | ||||||||
\(652\) | − | 851.320i | − | 0.0511354i | ||||||
\(653\) | 5017.38 | 0.300682 | 0.150341 | − | 0.988634i | \(-0.451963\pi\) | ||||
0.150341 | + | 0.988634i | \(0.451963\pi\) | |||||||
\(654\) | 2342.99 | 0.140089 | ||||||||
\(655\) | 3193.64i | 0.190513i | ||||||||
\(656\) | − | 22948.7i | − | 1.36585i | ||||||
\(657\) | 4975.48i | 0.295452i | ||||||||
\(658\) | − | 2556.16i | − | 0.151443i | ||||||
\(659\) | 31041.0 | 1.83488 | 0.917439 | − | 0.397876i | \(-0.130253\pi\) | ||||
0.917439 | + | 0.397876i | \(0.130253\pi\) | |||||||
\(660\) | −1967.73 | −0.116051 | ||||||||
\(661\) | − | 11389.0i | − | 0.670167i | −0.942189 | − | 0.335083i | \(-0.891236\pi\) | ||
0.942189 | − | 0.335083i | \(-0.108764\pi\) | |||||||
\(662\) | −4053.58 | −0.237986 | ||||||||
\(663\) | −14161.3 | − | 16432.4i | −0.829530 | − | 0.962569i | ||||
\(664\) | 7946.29 | 0.464422 | ||||||||
\(665\) | 5477.82i | 0.319429i | ||||||||
\(666\) | −1407.69 | −0.0819021 | ||||||||
\(667\) | 1626.24 | 0.0944053 | ||||||||
\(668\) | − | 6332.27i | − | 0.366771i | ||||||
\(669\) | − | 26192.2i | − | 1.51368i | ||||||
\(670\) | 1565.88i | 0.0902916i | ||||||||
\(671\) | − | 4730.94i | − | 0.272185i | ||||||
\(672\) | −6687.64 | −0.383901 | ||||||||
\(673\) | −15036.7 | −0.861250 | −0.430625 | − | 0.902531i | \(-0.641707\pi\) | ||||
−0.430625 | + | 0.902531i | \(0.641707\pi\) | |||||||
\(674\) | − | 335.010i | − | 0.0191456i | ||||||
\(675\) | 7310.43 | 0.416857 | ||||||||
\(676\) | −2524.01 | + | 16906.1i | −0.143606 | + | 0.961885i | ||||
\(677\) | 4944.67 | 0.280708 | 0.140354 | − | 0.990101i | \(-0.455176\pi\) | ||||
0.140354 | + | 0.990101i | \(0.455176\pi\) | |||||||
\(678\) | − | 816.221i | − | 0.0462342i | ||||||
\(679\) | 7291.61 | 0.412115 | ||||||||
\(680\) | −1777.02 | −0.100214 | ||||||||
\(681\) | 2122.98i | 0.119461i | ||||||||
\(682\) | 980.452i | 0.0550491i | ||||||||
\(683\) | 22667.8i | 1.26993i | 0.772543 | + | 0.634963i | \(0.218985\pi\) | ||||
−0.772543 | + | 0.634963i | \(0.781015\pi\) | |||||||
\(684\) | 18395.4i | 1.02832i | ||||||||
\(685\) | 4694.70 | 0.261862 | ||||||||
\(686\) | 2996.50 | 0.166774 | ||||||||
\(687\) | − | 7860.80i | − | 0.436547i | ||||||
\(688\) | −26038.8 | −1.44290 | ||||||||
\(689\) | −12114.6 | − | 14057.5i | −0.669852 | − | 0.777282i | ||||
\(690\) | 146.884 | 0.00810401 | ||||||||
\(691\) | 22832.2i | 1.25699i | 0.777815 | + | 0.628493i | \(0.216328\pi\) | ||||
−0.777815 | + | 0.628493i | \(0.783672\pi\) | |||||||
\(692\) | 22491.6 | 1.23555 | ||||||||
\(693\) | −2203.49 | −0.120785 | ||||||||
\(694\) | 3371.33i | 0.184400i | ||||||||
\(695\) | 6675.70i | 0.364351i | ||||||||
\(696\) | − | 5871.16i | − | 0.319749i | ||||||
\(697\) | − | 27153.4i | − | 1.47562i | ||||||
\(698\) | 2330.50 | 0.126376 | ||||||||
\(699\) | 41652.6 | 2.25386 | ||||||||
\(700\) | − | 10195.4i | − | 0.550498i | ||||||
\(701\) | 11640.8 | 0.627200 | 0.313600 | − | 0.949555i | \(-0.398465\pi\) | ||||
0.313600 | + | 0.949555i | \(0.398465\pi\) | |||||||
\(702\) | −1075.92 | + | 927.214i | −0.0578461 | + | 0.0498510i | ||||
\(703\) | −23773.5 | −1.27544 | ||||||||
\(704\) | − | 4725.37i | − | 0.252975i | ||||||
\(705\) | −10820.0 | −0.578023 | ||||||||
\(706\) | 1139.66 | 0.0607530 | ||||||||
\(707\) | − | 1092.75i | − | 0.0581286i | ||||||
\(708\) | − | 38478.3i | − | 2.04252i | ||||||
\(709\) | 17442.6i | 0.923936i | 0.886897 | + | 0.461968i | \(0.152856\pi\) | ||||
−0.886897 | + | 0.461968i | \(0.847144\pi\) | |||||||
\(710\) | − | 85.2390i | − | 0.00450558i | ||||||
\(711\) | 9750.90 | 0.514328 | ||||||||
\(712\) | −4647.66 | −0.244632 | ||||||||
\(713\) | 2592.59i | 0.136176i | ||||||||
\(714\) | −2513.79 | −0.131759 | ||||||||
\(715\) | 1162.92 | + | 1349.43i | 0.0608263 | + | 0.0705815i | ||||
\(716\) | −33103.0 | −1.72781 | ||||||||
\(717\) | 16433.5i | 0.855957i | ||||||||
\(718\) | 2127.55 | 0.110584 | ||||||||
\(719\) | −9631.17 | −0.499558 | −0.249779 | − | 0.968303i | \(-0.580358\pi\) | ||||
−0.249779 | + | 0.968303i | \(0.580358\pi\) | |||||||
\(720\) | 3509.90i | 0.181675i | ||||||||
\(721\) | 11011.1i | 0.568760i | ||||||||
\(722\) | − | 5555.48i | − | 0.286362i | ||||||
\(723\) | 27168.5i | 1.39752i | ||||||||
\(724\) | −3132.67 | −0.160808 | ||||||||
\(725\) | 13488.2 | 0.690951 | ||||||||
\(726\) | 377.361i | 0.0192909i | ||||||||
\(727\) | −36098.8 | −1.84158 | −0.920792 | − | 0.390053i | \(-0.872457\pi\) | ||||
−0.920792 | + | 0.390053i | \(0.872457\pi\) | |||||||
\(728\) | 2622.75 | + | 3043.38i | 0.133524 | + | 0.154938i | ||||
\(729\) | −3884.93 | −0.197375 | ||||||||
\(730\) | − | 466.122i | − | 0.0236328i | ||||||
\(731\) | −30809.6 | −1.55887 | ||||||||
\(732\) | −22267.8 | −1.12437 | ||||||||
\(733\) | 12551.0i | 0.632442i | 0.948686 | + | 0.316221i | \(0.102414\pi\) | ||||
−0.948686 | + | 0.316221i | \(0.897586\pi\) | |||||||
\(734\) | − | 6042.72i | − | 0.303870i | ||||||
\(735\) | − | 4797.75i | − | 0.240772i | ||||||
\(736\) | 1182.00i | 0.0591974i | ||||||||
\(737\) | −10637.8 | −0.531680 | ||||||||
\(738\) | 3162.54 | 0.157744 | ||||||||
\(739\) | − | 38489.6i | − | 1.91592i | −0.286904 | − | 0.957959i | \(-0.592626\pi\) | ||
0.286904 | − | 0.957959i | \(-0.407374\pi\) | |||||||
\(740\) | −4671.66 | −0.232072 | ||||||||
\(741\) | 32322.3 | − | 27854.9i | 1.60241 | − | 1.38094i | ||||
\(742\) | −2150.47 | −0.106397 | ||||||||
\(743\) | − | 1045.18i | − | 0.0516068i | −0.999667 | − | 0.0258034i | \(-0.991786\pi\) | ||
0.999667 | − | 0.0258034i | \(-0.00821439\pi\) | |||||||
\(744\) | 9359.93 | 0.461225 | ||||||||
\(745\) | −5698.10 | −0.280218 | ||||||||
\(746\) | 2316.77i | 0.113704i | ||||||||
\(747\) | − | 18570.9i | − | 0.909605i | ||||||
\(748\) | − | 5952.05i | − | 0.290947i | ||||||
\(749\) | 14021.8i | 0.684041i | ||||||||
\(750\) | 2565.16 | 0.124889 | ||||||||
\(751\) | 21408.8 | 1.04024 | 0.520119 | − | 0.854094i | \(-0.325888\pi\) | ||||
0.520119 | + | 0.854094i | \(0.325888\pi\) | |||||||
\(752\) | − | 27660.7i | − | 1.34133i | ||||||
\(753\) | 11978.8 | 0.579724 | ||||||||
\(754\) | −1985.14 | + | 1710.77i | −0.0958813 | + | 0.0826293i | ||||
\(755\) | 9992.51 | 0.481675 | ||||||||
\(756\) | − | 5830.50i | − | 0.280494i | ||||||
\(757\) | −18766.9 | −0.901050 | −0.450525 | − | 0.892764i | \(-0.648763\pi\) | ||||
−0.450525 | + | 0.892764i | \(0.648763\pi\) | |||||||
\(758\) | 1037.06 | 0.0496935 | ||||||||
\(759\) | 997.850i | 0.0477202i | ||||||||
\(760\) | − | 3495.36i | − | 0.166829i | ||||||
\(761\) | − | 6430.44i | − | 0.306312i | −0.988202 | − | 0.153156i | \(-0.951056\pi\) | ||
0.988202 | − | 0.153156i | \(-0.0489437\pi\) | |||||||
\(762\) | 2045.08i | 0.0972248i | ||||||||
\(763\) | 8707.24 | 0.413137 | ||||||||
\(764\) | −29960.1 | −1.41874 | ||||||||
\(765\) | 4152.99i | 0.196277i | ||||||||
\(766\) | −6592.62 | −0.310968 | ||||||||
\(767\) | −26387.7 | + | 22740.5i | −1.24225 | + | 1.07055i | ||||
\(768\) | −20078.2 | −0.943372 | ||||||||
\(769\) | 7845.05i | 0.367880i | 0.982937 | + | 0.183940i | \(0.0588852\pi\) | ||||
−0.982937 | + | 0.183940i | \(0.941115\pi\) | |||||||
\(770\) | 206.432 | 0.00966140 | ||||||||
\(771\) | −19847.5 | −0.927096 | ||||||||
\(772\) | 2934.98i | 0.136829i | ||||||||
\(773\) | − | 9384.02i | − | 0.436636i | −0.975878 | − | 0.218318i | \(-0.929943\pi\) | ||
0.975878 | − | 0.218318i | \(-0.0700570\pi\) | |||||||
\(774\) | − | 3588.39i | − | 0.166643i | ||||||
\(775\) | 21503.2i | 0.996669i | ||||||||
\(776\) | −4652.73 | −0.215236 | ||||||||
\(777\) | −13403.7 | −0.618861 | ||||||||
\(778\) | − | 4603.42i | − | 0.212134i | ||||||
\(779\) | 53410.1 | 2.45650 | ||||||||
\(780\) | 6351.54 | − | 5473.68i | 0.291566 | − | 0.251268i | ||||
\(781\) | 579.069 | 0.0265310 | ||||||||
\(782\) | 444.298i | 0.0203172i | ||||||||
\(783\) | 7713.61 | 0.352059 | ||||||||
\(784\) | 12265.1 | 0.558725 | ||||||||
\(785\) | − | 5140.58i | − | 0.233726i | ||||||
\(786\) | − | 2882.75i | − | 0.130820i | ||||||
\(787\) | − | 9065.31i | − | 0.410602i | −0.978699 | − | 0.205301i | \(-0.934183\pi\) | ||
0.978699 | − | 0.205301i | \(-0.0658173\pi\) | |||||||
\(788\) | − | 19316.4i | − | 0.873247i | ||||||
\(789\) | −20109.8 | −0.907384 | ||||||||
\(790\) | −913.501 | −0.0411404 | ||||||||
\(791\) | − | 3033.32i | − | 0.136350i | ||||||
\(792\) | 1406.04 | 0.0630824 | ||||||||
\(793\) | 13160.2 | + | 15270.8i | 0.589321 | + | 0.683835i | ||||
\(794\) | −640.174 | −0.0286133 | ||||||||
\(795\) | 9102.77i | 0.406091i | ||||||||
\(796\) | −10321.8 | −0.459608 | ||||||||
\(797\) | 5468.59 | 0.243046 | 0.121523 | − | 0.992589i | \(-0.461222\pi\) | ||||
0.121523 | + | 0.992589i | \(0.461222\pi\) | |||||||
\(798\) | − | 4944.57i | − | 0.219343i | ||||||
\(799\) | − | 32728.7i | − | 1.44914i | ||||||
\(800\) | 9803.66i | 0.433265i | ||||||||
\(801\) | 10861.8i | 0.479132i | ||||||||
\(802\) | 6519.89 | 0.287064 | ||||||||
\(803\) | 3166.59 | 0.139161 | ||||||||
\(804\) | 50070.3i | 2.19632i | ||||||||
\(805\) | 545.864 | 0.0238996 | ||||||||
\(806\) | −2727.35 | − | 3164.76i | −0.119189 | − | 0.138305i | ||||
\(807\) | 27322.0 | 1.19180 | ||||||||
\(808\) | 697.274i | 0.0303589i | ||||||||
\(809\) | 4431.29 | 0.192578 | 0.0962892 | − | 0.995353i | \(-0.469303\pi\) | ||||
0.0962892 | + | 0.995353i | \(0.469303\pi\) | |||||||
\(810\) | 1452.32 | 0.0629990 | ||||||||
\(811\) | 24745.9i | 1.07145i | 0.844393 | + | 0.535725i | \(0.179961\pi\) | ||||
−0.844393 | + | 0.535725i | \(0.820039\pi\) | |||||||
\(812\) | − | 10757.6i | − | 0.464925i | ||||||
\(813\) | 3262.64i | 0.140745i | ||||||||
\(814\) | 895.906i | 0.0385768i | ||||||||
\(815\) | 378.045 | 0.0162483 | ||||||||
\(816\) | −27202.1 | −1.16699 | ||||||||
\(817\) | − | 60602.0i | − | 2.59510i | ||||||
\(818\) | 3230.26 | 0.138072 | ||||||||
\(819\) | 7112.56 | − | 6129.51i | 0.303459 | − | 0.261517i | ||||
\(820\) | 10495.4 | 0.446972 | ||||||||
\(821\) | 38903.8i | 1.65378i | 0.562366 | + | 0.826888i | \(0.309891\pi\) | ||||
−0.562366 | + | 0.826888i | \(0.690109\pi\) | |||||||
\(822\) | −4237.69 | −0.179813 | ||||||||
\(823\) | 42785.6 | 1.81216 | 0.906082 | − | 0.423102i | \(-0.139059\pi\) | ||||
0.906082 | + | 0.423102i | \(0.139059\pi\) | |||||||
\(824\) | − | 7026.13i | − | 0.297047i | ||||||
\(825\) | 8276.27i | 0.349264i | ||||||||
\(826\) | 4036.70i | 0.170042i | ||||||||
\(827\) | 15938.6i | 0.670179i | 0.942186 | + | 0.335090i | \(0.108767\pi\) | ||||
−0.942186 | + | 0.335090i | \(0.891233\pi\) | |||||||
\(828\) | 1833.10 | 0.0769381 | ||||||||
\(829\) | 20256.8 | 0.848670 | 0.424335 | − | 0.905505i | \(-0.360508\pi\) | ||||
0.424335 | + | 0.905505i | \(0.360508\pi\) | |||||||
\(830\) | 1739.80i | 0.0727581i | ||||||||
\(831\) | −11795.8 | −0.492407 | ||||||||
\(832\) | 13144.7 | + | 15252.8i | 0.547728 | + | 0.635572i | ||||
\(833\) | 14512.4 | 0.603630 | ||||||||
\(834\) | − | 6025.84i | − | 0.250189i | ||||||
\(835\) | 2811.97 | 0.116542 | ||||||||
\(836\) | 11707.6 | 0.484348 | ||||||||
\(837\) | 12297.2i | 0.507830i | ||||||||
\(838\) | − | 1993.23i | − | 0.0821657i | ||||||
\(839\) | 37780.0i | 1.55460i | 0.629130 | + | 0.777300i | \(0.283411\pi\) | ||||
−0.629130 | + | 0.777300i | \(0.716589\pi\) | |||||||
\(840\) | − | 1970.71i | − | 0.0809475i | ||||||
\(841\) | −10156.9 | −0.416454 | ||||||||
\(842\) | 7781.81 | 0.318502 | ||||||||
\(843\) | 2638.06i | 0.107781i | ||||||||
\(844\) | 25628.5 | 1.04522 | ||||||||
\(845\) | −7507.48 | − | 1120.84i | −0.305639 | − | 0.0456307i | ||||
\(846\) | 3811.91 | 0.154913 | ||||||||
\(847\) | 1402.39i | 0.0568909i | ||||||||
\(848\) | −23270.6 | −0.942355 | ||||||||
\(849\) | −6542.43 | −0.264471 | ||||||||
\(850\) | 3685.05i | 0.148701i | ||||||||
\(851\) | 2369.03i | 0.0954281i | ||||||||
\(852\) | − | 2725.58i | − | 0.109597i | ||||||
\(853\) | 8226.02i | 0.330192i | 0.986278 | + | 0.165096i | \(0.0527933\pi\) | ||||
−0.986278 | + | 0.165096i | \(0.947207\pi\) | |||||||
\(854\) | 2336.08 | 0.0936054 | ||||||||
\(855\) | −8168.86 | −0.326747 | ||||||||
\(856\) | − | 8947.24i | − | 0.357255i | ||||||
\(857\) | −48849.7 | −1.94711 | −0.973556 | − | 0.228447i | \(-0.926635\pi\) | ||||
−0.973556 | + | 0.228447i | \(0.926635\pi\) | |||||||
\(858\) | −1049.71 | − | 1218.07i | −0.0417677 | − | 0.0484663i | ||||
\(859\) | −5923.09 | −0.235266 | −0.117633 | − | 0.993057i | \(-0.537531\pi\) | ||||
−0.117633 | + | 0.993057i | \(0.537531\pi\) | |||||||
\(860\) | − | 11908.7i | − | 0.472189i | ||||||
\(861\) | 30113.0 | 1.19193 | ||||||||
\(862\) | 5807.90 | 0.229487 | ||||||||
\(863\) | 41950.8i | 1.65472i | 0.561672 | + | 0.827360i | \(0.310158\pi\) | ||||
−0.561672 | + | 0.827360i | \(0.689842\pi\) | |||||||
\(864\) | 5606.50i | 0.220760i | ||||||||
\(865\) | 9987.84i | 0.392598i | ||||||||
\(866\) | − | 1080.01i | − | 0.0423789i | ||||||
\(867\) | 507.877 | 0.0198944 | ||||||||
\(868\) | 17150.1 | 0.670636 | ||||||||
\(869\) | − | 6205.85i | − | 0.242254i | ||||||
\(870\) | 1285.46 | 0.0500932 | ||||||||
\(871\) | 34337.2 | − | 29591.4i | 1.33579 | − | 1.15117i | ||||
\(872\) | −5556.03 | −0.215769 | ||||||||
\(873\) | 10873.7i | 0.421557i | ||||||||
\(874\) | −873.926 | −0.0338226 | ||||||||
\(875\) | 9532.90 | 0.368310 | ||||||||
\(876\) | − | 14904.6i | − | 0.574863i | ||||||
\(877\) | 8624.62i | 0.332078i | 0.986119 | + | 0.166039i | \(0.0530978\pi\) | ||||
−0.986119 | + | 0.166039i | \(0.946902\pi\) | |||||||
\(878\) | − | 4012.85i | − | 0.154245i | ||||||
\(879\) | 54532.3i | 2.09253i | ||||||||
\(880\) | 2233.84 | 0.0855711 | ||||||||
\(881\) | 14593.9 | 0.558095 | 0.279047 | − | 0.960277i | \(-0.409981\pi\) | ||||
0.279047 | + | 0.960277i | \(0.409981\pi\) | |||||||
\(882\) | 1690.25i | 0.0645280i | ||||||||
\(883\) | 5844.68 | 0.222751 | 0.111376 | − | 0.993778i | \(-0.464474\pi\) | ||||
0.111376 | + | 0.993778i | \(0.464474\pi\) | |||||||
\(884\) | 16556.9 | + | 19212.3i | 0.629944 | + | 0.730974i | ||||
\(885\) | 17087.0 | 0.649011 | ||||||||
\(886\) | 4003.50i | 0.151806i | ||||||||
\(887\) | 49965.1 | 1.89139 | 0.945696 | − | 0.325052i | \(-0.105382\pi\) | ||||
0.945696 | + | 0.325052i | \(0.105382\pi\) | |||||||
\(888\) | 8552.81 | 0.323214 | ||||||||
\(889\) | 7600.12i | 0.286727i | ||||||||
\(890\) | − | 1017.58i | − | 0.0383251i | ||||||
\(891\) | 9866.27i | 0.370968i | ||||||||
\(892\) | 30623.2i | 1.14948i | ||||||||
\(893\) | 64376.8 | 2.41242 | ||||||||
\(894\) | 5143.41 | 0.192417 | ||||||||
\(895\) | − | 14700.0i | − | 0.549014i | ||||||
\(896\) | 10373.1 | 0.386763 | ||||||||
\(897\) | −2775.74 | − | 3220.91i | −0.103321 | − | 0.119892i | ||||
\(898\) | −3278.23 | −0.121822 | ||||||||
\(899\) | 22689.2i | 0.841742i | ||||||||
\(900\) | 15203.9 | 0.563109 | ||||||||
\(901\) | −27534.3 | −1.01809 | ||||||||
\(902\) | − | 2012.76i | − | 0.0742990i | ||||||
\(903\) | − | 34167.8i | − | 1.25917i | ||||||
\(904\) | 1935.54i | 0.0712115i | ||||||||
\(905\) | − | 1391.12i | − | 0.0510966i | ||||||
\(906\) | −9019.77 | −0.330753 | ||||||||
\(907\) | −36442.4 | −1.33412 | −0.667062 | − | 0.745002i | \(-0.732449\pi\) | ||||
−0.667062 | + | 0.745002i | \(0.732449\pi\) | |||||||
\(908\) | − | 2482.13i | − | 0.0907185i | ||||||
\(909\) | 1629.57 | 0.0594603 | ||||||||
\(910\) | −666.331 | + | 574.236i | −0.0242733 | + | 0.0209184i | ||||
\(911\) | 27482.6 | 0.999492 | 0.499746 | − | 0.866172i | \(-0.333427\pi\) | ||||
0.499746 | + | 0.866172i | \(0.333427\pi\) | |||||||
\(912\) | − | 53506.1i | − | 1.94272i | ||||||
\(913\) | −11819.3 | −0.428434 | ||||||||
\(914\) | 2767.73 | 0.100162 | ||||||||
\(915\) | − | 9888.44i | − | 0.357270i | ||||||
\(916\) | 9190.62i | 0.331514i | ||||||||
\(917\) | − | 10713.2i | − | 0.385801i | ||||||
\(918\) | 2107.40i | 0.0757675i | ||||||||
\(919\) | 21715.6 | 0.779468 | 0.389734 | − | 0.920928i | \(-0.372567\pi\) | ||||
0.389734 | + | 0.920928i | \(0.372567\pi\) | |||||||
\(920\) | −348.312 | −0.0124821 | ||||||||
\(921\) | − | 34769.7i | − | 1.24398i | ||||||
\(922\) | −7624.45 | −0.272340 | ||||||||
\(923\) | −1869.15 | + | 1610.81i | −0.0666564 | + | 0.0574436i | ||||
\(924\) | 6600.81 | 0.235012 | ||||||||
\(925\) | 19649.0i | 0.698437i | ||||||||
\(926\) | 5664.23 | 0.201013 | ||||||||
\(927\) | −16420.5 | −0.581790 | ||||||||
\(928\) | 10344.3i | 0.365916i | ||||||||
\(929\) | 12050.4i | 0.425578i | 0.977098 | + | 0.212789i | \(0.0682547\pi\) | ||||
−0.977098 | + | 0.212789i | \(0.931745\pi\) | |||||||
\(930\) | 2049.30i | 0.0722574i | ||||||||
\(931\) | 28545.6i | 1.00488i | ||||||||
\(932\) | −48699.0 | −1.71158 | ||||||||
\(933\) | −38682.4 | −1.35735 | ||||||||
\(934\) | 5360.88i | 0.187809i | ||||||||
\(935\) | 2643.12 | 0.0924485 | ||||||||
\(936\) | −4538.48 | + | 3911.20i | −0.158488 | + | 0.136583i | ||||
\(937\) | −30209.9 | −1.05327 | −0.526636 | − | 0.850091i | \(-0.676547\pi\) | ||||
−0.526636 | + | 0.850091i | \(0.676547\pi\) | |||||||
\(938\) | − | 5252.80i | − | 0.182847i | ||||||
\(939\) | −54737.0 | −1.90232 | ||||||||
\(940\) | 12650.5 | 0.438950 | ||||||||
\(941\) | − | 34124.9i | − | 1.18219i | −0.806602 | − | 0.591095i | \(-0.798696\pi\) | ||
0.806602 | − | 0.591095i | \(-0.201304\pi\) | |||||||
\(942\) | 4640.16i | 0.160493i | ||||||||
\(943\) | − | 5322.31i | − | 0.183795i | ||||||
\(944\) | 43681.9i | 1.50607i | ||||||||
\(945\) | 2589.15 | 0.0891270 | ||||||||
\(946\) | −2283.79 | −0.0784908 | ||||||||
\(947\) | − | 17470.4i | − | 0.599484i | −0.954020 | − | 0.299742i | \(-0.903099\pi\) | ||
0.954020 | − | 0.299742i | \(-0.0969005\pi\) | |||||||
\(948\) | −29209.9 | −1.00073 | ||||||||
\(949\) | −10221.3 | + | 8808.57i | −0.349628 | + | 0.301305i | ||||
\(950\) | −7248.42 | −0.247547 | ||||||||
\(951\) | − | 18685.3i | − | 0.637130i | ||||||
\(952\) | 5961.06 | 0.202940 | ||||||||
\(953\) | −27848.2 | −0.946582 | −0.473291 | − | 0.880906i | \(-0.656934\pi\) | ||||
−0.473291 | + | 0.880906i | \(0.656934\pi\) | |||||||
\(954\) | − | 3206.91i | − | 0.108834i | ||||||
\(955\) | − | 13304.3i | − | 0.450805i | ||||||
\(956\) | − | 19213.6i | − | 0.650013i | ||||||
\(957\) | 8732.71i | 0.294972i | ||||||||
\(958\) | 5890.80 | 0.198667 | ||||||||
\(959\) | −15748.5 | −0.530288 | ||||||||
\(960\) | − | 9876.80i | − | 0.332055i | ||||||
\(961\) | −6380.58 | −0.214178 | ||||||||
\(962\) | −2492.16 | − | 2891.86i | −0.0835245 | − | 0.0969201i | ||||
\(963\) | −20910.2 | −0.699712 | ||||||||
\(964\) | − | 31764.6i | − | 1.06127i | ||||||
\(965\) | −1303.33 | −0.0434775 | ||||||||
\(966\) | −492.726 | −0.0164112 | ||||||||
\(967\) | 11251.9i | 0.374184i | 0.982342 | + | 0.187092i | \(0.0599062\pi\) | ||||
−0.982342 | + | 0.187092i | \(0.940094\pi\) | |||||||
\(968\) | − | 894.854i | − | 0.0297125i | ||||||
\(969\) | − | 63309.6i | − | 2.09886i | ||||||
\(970\) | − | 1018.69i | − | 0.0337197i | ||||||
\(971\) | −8036.31 | −0.265600 | −0.132800 | − | 0.991143i | \(-0.542397\pi\) | ||||
−0.132800 | + | 0.991143i | \(0.542397\pi\) | |||||||
\(972\) | 32856.2 | 1.08422 | ||||||||
\(973\) | − | 22393.8i | − | 0.737835i | ||||||
\(974\) | 5879.68 | 0.193426 | ||||||||
\(975\) | −23022.3 | − | 26714.6i | −0.756208 | − | 0.877488i | ||||
\(976\) | 25279.1 | 0.829063 | ||||||||
\(977\) | − | 52519.0i | − | 1.71979i | −0.510474 | − | 0.859893i | \(-0.670530\pi\) | ||
0.510474 | − | 0.859893i | \(-0.329470\pi\) | |||||||
\(978\) | −341.244 | −0.0111572 | ||||||||
\(979\) | 6912.89 | 0.225676 | ||||||||
\(980\) | 5609.39i | 0.182842i | ||||||||
\(981\) | 12984.8i | 0.422601i | ||||||||
\(982\) | 2114.00i | 0.0686972i | ||||||||
\(983\) | 58820.9i | 1.90854i | 0.298943 | + | 0.954271i | \(0.403366\pi\) | ||||
−0.298943 | + | 0.954271i | \(0.596634\pi\) | |||||||
\(984\) | −19214.9 | −0.622510 | ||||||||
\(985\) | 8577.83 | 0.277474 | ||||||||
\(986\) | 3888.29i | 0.125586i | ||||||||
\(987\) | 36296.1 | 1.17054 | ||||||||
\(988\) | −37790.3 | + | 32567.2i | −1.21687 | + | 1.04868i | ||||
\(989\) | −6038.98 | −0.194164 | ||||||||
\(990\) | 307.844i | 0.00988274i | ||||||||
\(991\) | 45745.1 | 1.46634 | 0.733170 | − | 0.680046i | \(-0.238040\pi\) | ||||
0.733170 | + | 0.680046i | \(0.238040\pi\) | |||||||
\(992\) | −16491.2 | −0.527819 | ||||||||
\(993\) | − | 57558.7i | − | 1.83945i | ||||||
\(994\) | 285.937i | 0.00912412i | ||||||||
\(995\) | − | 4583.61i | − | 0.146041i | ||||||
\(996\) | 55631.3i | 1.76983i | ||||||||
\(997\) | −15148.3 | −0.481194 | −0.240597 | − | 0.970625i | \(-0.577343\pi\) | ||||
−0.240597 | + | 0.970625i | \(0.577343\pi\) | |||||||
\(998\) | 4868.16 | 0.154408 | ||||||||
\(999\) | 11236.8i | 0.355873i |
(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 | 143.4.b.a.12.20 | yes | 36 | |
13.5 | odd | 4 | 1859.4.a.k.1.10 | 18 | |||
13.8 | odd | 4 | 1859.4.a.j.1.9 | 18 | |||
13.12 | even | 2 | inner | 143.4.b.a.12.17 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.b.a.12.17 | ✓ | 36 | 13.12 | even | 2 | inner | |
143.4.b.a.12.20 | yes | 36 | 1.1 | even | 1 | trivial | |
1859.4.a.j.1.9 | 18 | 13.8 | odd | 4 | |||
1859.4.a.k.1.10 | 18 | 13.5 | odd | 4 |