Properties

Label 33.5.c.a.10.3
Level $33$
Weight $5$
Character 33.10
Analytic conductor $3.411$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 33.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.41120878177\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 102 x^{6} + 2913 x^{4} + 23292 x^{2} + 41364\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 10.3
Root \(-3.00247i\) of defining polynomial
Character \(\chi\) \(=\) 33.10
Dual form 33.5.c.a.10.6

$q$-expansion

\(f(q)\) \(=\) \(q-3.00247i q^{2} +5.19615 q^{3} +6.98517 q^{4} +8.72578 q^{5} -15.6013i q^{6} -1.45810i q^{7} -69.0123i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-3.00247i q^{2} +5.19615 q^{3} +6.98517 q^{4} +8.72578 q^{5} -15.6013i q^{6} -1.45810i q^{7} -69.0123i q^{8} +27.0000 q^{9} -26.1989i q^{10} +(-62.2476 - 103.760i) q^{11} +36.2960 q^{12} +162.221i q^{13} -4.37791 q^{14} +45.3405 q^{15} -95.4447 q^{16} +189.734i q^{17} -81.0667i q^{18} +590.443i q^{19} +60.9511 q^{20} -7.57652i q^{21} +(-311.538 + 186.897i) q^{22} -12.8557 q^{23} -358.598i q^{24} -548.861 q^{25} +487.064 q^{26} +140.296 q^{27} -10.1851i q^{28} -282.359i q^{29} -136.134i q^{30} -304.206 q^{31} -817.627i q^{32} +(-323.448 - 539.155i) q^{33} +569.671 q^{34} -12.7231i q^{35} +188.600 q^{36} +464.276 q^{37} +1772.79 q^{38} +842.925i q^{39} -602.186i q^{40} +1193.81i q^{41} -22.7483 q^{42} -1591.11i q^{43} +(-434.810 - 724.784i) q^{44} +235.596 q^{45} +38.5989i q^{46} -1825.87 q^{47} -495.945 q^{48} +2398.87 q^{49} +1647.94i q^{50} +985.887i q^{51} +1133.14i q^{52} -4023.28 q^{53} -421.235i q^{54} +(-543.159 - 905.391i) q^{55} -100.627 q^{56} +3068.03i q^{57} -847.774 q^{58} -1489.12 q^{59} +316.711 q^{60} -356.601i q^{61} +913.368i q^{62} -39.3688i q^{63} -3982.02 q^{64} +1415.51i q^{65} +(-1618.80 + 971.143i) q^{66} +8259.07 q^{67} +1325.32i q^{68} -66.8002 q^{69} -38.2007 q^{70} +7971.63 q^{71} -1863.33i q^{72} -5780.93i q^{73} -1393.98i q^{74} -2851.96 q^{75} +4124.34i q^{76} +(-151.293 + 90.7633i) q^{77} +2530.86 q^{78} -11304.5i q^{79} -832.830 q^{80} +729.000 q^{81} +3584.37 q^{82} -5449.44i q^{83} -52.9233i q^{84} +1655.58i q^{85} -4777.26 q^{86} -1467.18i q^{87} +(-7160.75 + 4295.85i) q^{88} +7332.12 q^{89} -707.371i q^{90} +236.535 q^{91} -89.7992 q^{92} -1580.70 q^{93} +5482.13i q^{94} +5152.08i q^{95} -4248.51i q^{96} -11228.1 q^{97} -7202.55i q^{98} +(-1680.69 - 2801.53i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 76q^{4} - 36q^{5} + 216q^{9} + O(q^{10}) \) \( 8q - 76q^{4} - 36q^{5} + 216q^{9} + 36q^{11} - 360q^{12} - 1140q^{14} + 108q^{15} + 1412q^{16} + 2532q^{20} - 780q^{22} + 516q^{23} - 2280q^{25} - 1524q^{26} + 2752q^{31} + 1008q^{33} - 4920q^{34} - 2052q^{36} + 5296q^{37} + 696q^{38} - 4356q^{42} - 6540q^{44} - 972q^{45} + 420q^{47} + 9936q^{48} - 6832q^{49} + 3540q^{53} + 3784q^{55} + 17964q^{56} + 21624q^{58} - 16632q^{59} - 612q^{60} - 27508q^{64} + 360q^{66} - 3656q^{67} + 9036q^{69} + 3312q^{70} - 13212q^{71} - 9288q^{75} + 23268q^{77} - 13140q^{78} - 4476q^{80} + 5832q^{81} + 17088q^{82} + 19896q^{86} - 12516q^{88} + 15528q^{89} - 19752q^{91} - 81180q^{92} - 21384q^{93} + 7624q^{97} + 972q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00247i 0.750618i −0.926900 0.375309i \(-0.877537\pi\)
0.926900 0.375309i \(-0.122463\pi\)
\(3\) 5.19615 0.577350
\(4\) 6.98517 0.436573
\(5\) 8.72578 0.349031 0.174516 0.984654i \(-0.444164\pi\)
0.174516 + 0.984654i \(0.444164\pi\)
\(6\) 15.6013i 0.433369i
\(7\) 1.45810i 0.0297572i −0.999889 0.0148786i \(-0.995264\pi\)
0.999889 0.0148786i \(-0.00473618\pi\)
\(8\) 69.0123i 1.07832i
\(9\) 27.0000 0.333333
\(10\) 26.1989i 0.261989i
\(11\) −62.2476 103.760i −0.514443 0.857525i
\(12\) 36.2960 0.252056
\(13\) 162.221i 0.959888i 0.877299 + 0.479944i \(0.159343\pi\)
−0.877299 + 0.479944i \(0.840657\pi\)
\(14\) −4.37791 −0.0223363
\(15\) 45.3405 0.201513
\(16\) −95.4447 −0.372831
\(17\) 189.734i 0.656519i 0.944588 + 0.328259i \(0.106462\pi\)
−0.944588 + 0.328259i \(0.893538\pi\)
\(18\) 81.0667i 0.250206i
\(19\) 590.443i 1.63558i 0.575520 + 0.817788i \(0.304800\pi\)
−0.575520 + 0.817788i \(0.695200\pi\)
\(20\) 60.9511 0.152378
\(21\) 7.57652i 0.0171803i
\(22\) −311.538 + 186.897i −0.643673 + 0.386150i
\(23\) −12.8557 −0.0243019 −0.0121509 0.999926i \(-0.503868\pi\)
−0.0121509 + 0.999926i \(0.503868\pi\)
\(24\) 358.598i 0.622567i
\(25\) −548.861 −0.878177
\(26\) 487.064 0.720509
\(27\) 140.296 0.192450
\(28\) 10.1851i 0.0129912i
\(29\) 282.359i 0.335742i −0.985809 0.167871i \(-0.946311\pi\)
0.985809 0.167871i \(-0.0536892\pi\)
\(30\) 136.134i 0.151259i
\(31\) −304.206 −0.316551 −0.158275 0.987395i \(-0.550593\pi\)
−0.158275 + 0.987395i \(0.550593\pi\)
\(32\) 817.627i 0.798464i
\(33\) −323.448 539.155i −0.297014 0.495092i
\(34\) 569.671 0.492795
\(35\) 12.7231i 0.0103862i
\(36\) 188.600 0.145524
\(37\) 464.276 0.339135 0.169568 0.985519i \(-0.445763\pi\)
0.169568 + 0.985519i \(0.445763\pi\)
\(38\) 1772.79 1.22769
\(39\) 842.925i 0.554191i
\(40\) 602.186i 0.376366i
\(41\) 1193.81i 0.710177i 0.934833 + 0.355089i \(0.115549\pi\)
−0.934833 + 0.355089i \(0.884451\pi\)
\(42\) −22.7483 −0.0128959
\(43\) 1591.11i 0.860525i −0.902704 0.430263i \(-0.858421\pi\)
0.902704 0.430263i \(-0.141579\pi\)
\(44\) −434.810 724.784i −0.224592 0.374372i
\(45\) 235.596 0.116344
\(46\) 38.5989i 0.0182414i
\(47\) −1825.87 −0.826561 −0.413281 0.910604i \(-0.635617\pi\)
−0.413281 + 0.910604i \(0.635617\pi\)
\(48\) −495.945 −0.215254
\(49\) 2398.87 0.999115
\(50\) 1647.94i 0.659175i
\(51\) 985.887i 0.379041i
\(52\) 1133.14i 0.419061i
\(53\) −4023.28 −1.43228 −0.716141 0.697955i \(-0.754093\pi\)
−0.716141 + 0.697955i \(0.754093\pi\)
\(54\) 421.235i 0.144456i
\(55\) −543.159 905.391i −0.179557 0.299303i
\(56\) −100.627 −0.0320877
\(57\) 3068.03i 0.944300i
\(58\) −847.774 −0.252014
\(59\) −1489.12 −0.427785 −0.213893 0.976857i \(-0.568614\pi\)
−0.213893 + 0.976857i \(0.568614\pi\)
\(60\) 316.711 0.0879753
\(61\) 356.601i 0.0958346i −0.998851 0.0479173i \(-0.984742\pi\)
0.998851 0.0479173i \(-0.0152584\pi\)
\(62\) 913.368i 0.237609i
\(63\) 39.3688i 0.00991906i
\(64\) −3982.02 −0.972172
\(65\) 1415.51i 0.335031i
\(66\) −1618.80 + 971.143i −0.371625 + 0.222944i
\(67\) 8259.07 1.83985 0.919923 0.392098i \(-0.128251\pi\)
0.919923 + 0.392098i \(0.128251\pi\)
\(68\) 1325.32i 0.286618i
\(69\) −66.8002 −0.0140307
\(70\) −38.2007 −0.00779606
\(71\) 7971.63 1.58136 0.790680 0.612230i \(-0.209727\pi\)
0.790680 + 0.612230i \(0.209727\pi\)
\(72\) 1863.33i 0.359439i
\(73\) 5780.93i 1.08481i −0.840118 0.542403i \(-0.817515\pi\)
0.840118 0.542403i \(-0.182485\pi\)
\(74\) 1393.98i 0.254561i
\(75\) −2851.96 −0.507016
\(76\) 4124.34i 0.714048i
\(77\) −151.293 + 90.7633i −0.0255175 + 0.0153084i
\(78\) 2530.86 0.415986
\(79\) 11304.5i 1.81133i −0.423998 0.905663i \(-0.639374\pi\)
0.423998 0.905663i \(-0.360626\pi\)
\(80\) −832.830 −0.130130
\(81\) 729.000 0.111111
\(82\) 3584.37 0.533071
\(83\) 5449.44i 0.791036i −0.918458 0.395518i \(-0.870565\pi\)
0.918458 0.395518i \(-0.129435\pi\)
\(84\) 52.9233i 0.00750046i
\(85\) 1655.58i 0.229146i
\(86\) −4777.26 −0.645925
\(87\) 1467.18i 0.193841i
\(88\) −7160.75 + 4295.85i −0.924684 + 0.554733i
\(89\) 7332.12 0.925656 0.462828 0.886448i \(-0.346835\pi\)
0.462828 + 0.886448i \(0.346835\pi\)
\(90\) 707.371i 0.0873297i
\(91\) 236.535 0.0285636
\(92\) −89.7992 −0.0106096
\(93\) −1580.70 −0.182761
\(94\) 5482.13i 0.620432i
\(95\) 5152.08i 0.570867i
\(96\) 4248.51i 0.460993i
\(97\) −11228.1 −1.19334 −0.596669 0.802487i \(-0.703509\pi\)
−0.596669 + 0.802487i \(0.703509\pi\)
\(98\) 7202.55i 0.749953i
\(99\) −1680.69 2801.53i −0.171481 0.285842i
\(100\) −3833.88 −0.383388
\(101\) 12735.1i 1.24842i 0.781258 + 0.624209i \(0.214578\pi\)
−0.781258 + 0.624209i \(0.785422\pi\)
\(102\) 2960.10 0.284515
\(103\) 4637.37 0.437117 0.218558 0.975824i \(-0.429865\pi\)
0.218558 + 0.975824i \(0.429865\pi\)
\(104\) 11195.2 1.03506
\(105\) 66.1111i 0.00599647i
\(106\) 12079.8i 1.07510i
\(107\) 15858.6i 1.38515i −0.721347 0.692574i \(-0.756476\pi\)
0.721347 0.692574i \(-0.243524\pi\)
\(108\) 979.992 0.0840185
\(109\) 19516.7i 1.64268i 0.570438 + 0.821341i \(0.306774\pi\)
−0.570438 + 0.821341i \(0.693226\pi\)
\(110\) −2718.41 + 1630.82i −0.224662 + 0.134778i
\(111\) 2412.45 0.195800
\(112\) 139.168i 0.0110944i
\(113\) −15343.5 −1.20162 −0.600811 0.799391i \(-0.705156\pi\)
−0.600811 + 0.799391i \(0.705156\pi\)
\(114\) 9211.67 0.708808
\(115\) −112.176 −0.00848212
\(116\) 1972.32i 0.146576i
\(117\) 4379.97i 0.319963i
\(118\) 4471.04i 0.321103i
\(119\) 276.652 0.0195362
\(120\) 3129.05i 0.217295i
\(121\) −6891.47 + 12917.7i −0.470697 + 0.882295i
\(122\) −1070.68 −0.0719351
\(123\) 6203.21i 0.410021i
\(124\) −2124.93 −0.138198
\(125\) −10242.9 −0.655543
\(126\) −118.204 −0.00744542
\(127\) 19359.4i 1.20028i −0.799893 0.600142i \(-0.795111\pi\)
0.799893 0.600142i \(-0.204889\pi\)
\(128\) 1126.14i 0.0687341i
\(129\) 8267.66i 0.496824i
\(130\) 4250.01 0.251480
\(131\) 13966.3i 0.813842i 0.913463 + 0.406921i \(0.133398\pi\)
−0.913463 + 0.406921i \(0.866602\pi\)
\(132\) −2259.34 3766.09i −0.129668 0.216144i
\(133\) 860.926 0.0486701
\(134\) 24797.6i 1.38102i
\(135\) 1224.19 0.0671711
\(136\) 13094.0 0.707936
\(137\) 10923.8 0.582010 0.291005 0.956721i \(-0.406010\pi\)
0.291005 + 0.956721i \(0.406010\pi\)
\(138\) 200.566i 0.0105317i
\(139\) 27425.4i 1.41946i −0.704474 0.709730i \(-0.748817\pi\)
0.704474 0.709730i \(-0.251183\pi\)
\(140\) 88.8729i 0.00453433i
\(141\) −9487.52 −0.477215
\(142\) 23934.6i 1.18700i
\(143\) 16832.1 10097.9i 0.823127 0.493807i
\(144\) −2577.01 −0.124277
\(145\) 2463.80i 0.117184i
\(146\) −17357.1 −0.814275
\(147\) 12464.9 0.576839
\(148\) 3243.05 0.148057
\(149\) 17646.6i 0.794856i 0.917633 + 0.397428i \(0.130097\pi\)
−0.917633 + 0.397428i \(0.869903\pi\)
\(150\) 8562.94i 0.380575i
\(151\) 19482.1i 0.854441i 0.904147 + 0.427221i \(0.140507\pi\)
−0.904147 + 0.427221i \(0.859493\pi\)
\(152\) 40747.8 1.76367
\(153\) 5122.82i 0.218840i
\(154\) 272.514 + 454.254i 0.0114907 + 0.0191539i
\(155\) −2654.43 −0.110486
\(156\) 5887.97i 0.241945i
\(157\) 20642.6 0.837462 0.418731 0.908110i \(-0.362475\pi\)
0.418731 + 0.908110i \(0.362475\pi\)
\(158\) −33941.4 −1.35961
\(159\) −20905.6 −0.826929
\(160\) 7134.43i 0.278689i
\(161\) 18.7449i 0.000723156i
\(162\) 2188.80i 0.0834020i
\(163\) 5888.63 0.221635 0.110818 0.993841i \(-0.464653\pi\)
0.110818 + 0.993841i \(0.464653\pi\)
\(164\) 8338.95i 0.310044i
\(165\) −2822.34 4704.55i −0.103667 0.172803i
\(166\) −16361.8 −0.593765
\(167\) 25996.3i 0.932135i 0.884749 + 0.466067i \(0.154330\pi\)
−0.884749 + 0.466067i \(0.845670\pi\)
\(168\) −522.873 −0.0185258
\(169\) 2245.35 0.0786159
\(170\) 4970.82 0.172001
\(171\) 15942.0i 0.545192i
\(172\) 11114.2i 0.375682i
\(173\) 22355.9i 0.746964i 0.927637 + 0.373482i \(0.121836\pi\)
−0.927637 + 0.373482i \(0.878164\pi\)
\(174\) −4405.16 −0.145500
\(175\) 800.295i 0.0261321i
\(176\) 5941.21 + 9903.39i 0.191800 + 0.319712i
\(177\) −7737.70 −0.246982
\(178\) 22014.5i 0.694814i
\(179\) 9227.98 0.288005 0.144003 0.989577i \(-0.454003\pi\)
0.144003 + 0.989577i \(0.454003\pi\)
\(180\) 1645.68 0.0507925
\(181\) −52256.0 −1.59507 −0.797534 0.603274i \(-0.793862\pi\)
−0.797534 + 0.603274i \(0.793862\pi\)
\(182\) 710.189i 0.0214403i
\(183\) 1852.95i 0.0553301i
\(184\) 887.202i 0.0262052i
\(185\) 4051.17 0.118369
\(186\) 4746.00i 0.137184i
\(187\) 19686.9 11810.5i 0.562981 0.337742i
\(188\) −12754.0 −0.360854
\(189\) 204.566i 0.00572677i
\(190\) 15469.0 0.428503
\(191\) −70655.7 −1.93678 −0.968390 0.249442i \(-0.919753\pi\)
−0.968390 + 0.249442i \(0.919753\pi\)
\(192\) −20691.2 −0.561284
\(193\) 21752.7i 0.583981i 0.956421 + 0.291991i \(0.0943176\pi\)
−0.956421 + 0.291991i \(0.905682\pi\)
\(194\) 33712.1i 0.895741i
\(195\) 7355.18i 0.193430i
\(196\) 16756.5 0.436186
\(197\) 67346.7i 1.73534i −0.497144 0.867668i \(-0.665618\pi\)
0.497144 0.867668i \(-0.334382\pi\)
\(198\) −8411.52 + 5046.21i −0.214558 + 0.128717i
\(199\) 4956.39 0.125158 0.0625791 0.998040i \(-0.480067\pi\)
0.0625791 + 0.998040i \(0.480067\pi\)
\(200\) 37878.1i 0.946954i
\(201\) 42915.4 1.06224
\(202\) 38236.8 0.937084
\(203\) −411.708 −0.00999073
\(204\) 6886.58i 0.165479i
\(205\) 10416.9i 0.247874i
\(206\) 13923.6i 0.328108i
\(207\) −347.104 −0.00810063
\(208\) 15483.1i 0.357876i
\(209\) 61264.6 36753.6i 1.40255 0.841410i
\(210\) −198.497 −0.00450106
\(211\) 5230.33i 0.117480i 0.998273 + 0.0587400i \(0.0187083\pi\)
−0.998273 + 0.0587400i \(0.981292\pi\)
\(212\) −28103.3 −0.625296
\(213\) 41421.8 0.912998
\(214\) −47614.9 −1.03972
\(215\) 13883.7i 0.300350i
\(216\) 9682.16i 0.207522i
\(217\) 443.563i 0.00941967i
\(218\) 58598.3 1.23303
\(219\) 30038.6i 0.626313i
\(220\) −3794.06 6324.31i −0.0783896 0.130668i
\(221\) −30778.8 −0.630184
\(222\) 7243.31i 0.146971i
\(223\) 70116.0 1.40996 0.704981 0.709226i \(-0.250956\pi\)
0.704981 + 0.709226i \(0.250956\pi\)
\(224\) −1192.18 −0.0237600
\(225\) −14819.2 −0.292726
\(226\) 46068.5i 0.901960i
\(227\) 69181.4i 1.34257i −0.741198 0.671287i \(-0.765742\pi\)
0.741198 0.671287i \(-0.234258\pi\)
\(228\) 21430.7i 0.412256i
\(229\) −27970.4 −0.533369 −0.266685 0.963784i \(-0.585928\pi\)
−0.266685 + 0.963784i \(0.585928\pi\)
\(230\) 336.805i 0.00636683i
\(231\) −786.143 + 471.620i −0.0147325 + 0.00883829i
\(232\) −19486.2 −0.362036
\(233\) 67591.9i 1.24504i −0.782604 0.622519i \(-0.786109\pi\)
0.782604 0.622519i \(-0.213891\pi\)
\(234\) 13150.7 0.240170
\(235\) −15932.2 −0.288496
\(236\) −10401.8 −0.186759
\(237\) 58739.8i 1.04577i
\(238\) 830.638i 0.0146642i
\(239\) 31589.5i 0.553028i 0.961010 + 0.276514i \(0.0891792\pi\)
−0.961010 + 0.276514i \(0.910821\pi\)
\(240\) −4327.51 −0.0751304
\(241\) 64415.3i 1.10906i 0.832164 + 0.554530i \(0.187102\pi\)
−0.832164 + 0.554530i \(0.812898\pi\)
\(242\) 38785.0 + 20691.4i 0.662266 + 0.353313i
\(243\) 3788.00 0.0641500
\(244\) 2490.91i 0.0418388i
\(245\) 20932.1 0.348722
\(246\) 18624.9 0.307769
\(247\) −95782.2 −1.56997
\(248\) 20993.9i 0.341342i
\(249\) 28316.1i 0.456705i
\(250\) 30753.9i 0.492062i
\(251\) 34822.1 0.552722 0.276361 0.961054i \(-0.410871\pi\)
0.276361 + 0.961054i \(0.410871\pi\)
\(252\) 274.997i 0.00433039i
\(253\) 800.237 + 1333.91i 0.0125019 + 0.0208395i
\(254\) −58126.0 −0.900955
\(255\) 8602.63i 0.132297i
\(256\) −67093.5 −1.02376
\(257\) −73746.1 −1.11654 −0.558268 0.829661i \(-0.688534\pi\)
−0.558268 + 0.829661i \(0.688534\pi\)
\(258\) −24823.4 −0.372925
\(259\) 676.962i 0.0100917i
\(260\) 9887.54i 0.146265i
\(261\) 7623.69i 0.111914i
\(262\) 41933.5 0.610884
\(263\) 103570.i 1.49734i 0.662942 + 0.748671i \(0.269308\pi\)
−0.662942 + 0.748671i \(0.730692\pi\)
\(264\) −37208.3 + 22321.9i −0.533866 + 0.320275i
\(265\) −35106.3 −0.499911
\(266\) 2584.91i 0.0365327i
\(267\) 38098.8 0.534428
\(268\) 57691.0 0.803227
\(269\) 118870. 1.64274 0.821371 0.570395i \(-0.193210\pi\)
0.821371 + 0.570395i \(0.193210\pi\)
\(270\) 3675.60i 0.0504198i
\(271\) 102742.i 1.39897i 0.714646 + 0.699486i \(0.246588\pi\)
−0.714646 + 0.699486i \(0.753412\pi\)
\(272\) 18109.1i 0.244771i
\(273\) 1229.07 0.0164912
\(274\) 32798.3i 0.436867i
\(275\) 34165.3 + 56950.1i 0.451772 + 0.753059i
\(276\) −466.611 −0.00612543
\(277\) 103336.i 1.34677i 0.739292 + 0.673385i \(0.235161\pi\)
−0.739292 + 0.673385i \(0.764839\pi\)
\(278\) −82343.9 −1.06547
\(279\) −8213.55 −0.105517
\(280\) −878.049 −0.0111996
\(281\) 37257.8i 0.471850i −0.971771 0.235925i \(-0.924188\pi\)
0.971771 0.235925i \(-0.0758120\pi\)
\(282\) 28486.0i 0.358206i
\(283\) 126640.i 1.58124i −0.612310 0.790618i \(-0.709759\pi\)
0.612310 0.790618i \(-0.290241\pi\)
\(284\) 55683.2 0.690379
\(285\) 26771.0i 0.329590i
\(286\) −30318.6 50538.0i −0.370661 0.617854i
\(287\) 1740.69 0.0211329
\(288\) 22075.9i 0.266155i
\(289\) 47522.0 0.568983
\(290\) −7397.49 −0.0879607
\(291\) −58343.0 −0.688974
\(292\) 40380.8i 0.473597i
\(293\) 1337.08i 0.0155748i 0.999970 + 0.00778741i \(0.00247883\pi\)
−0.999970 + 0.00778741i \(0.997521\pi\)
\(294\) 37425.5i 0.432986i
\(295\) −12993.7 −0.149310
\(296\) 32040.8i 0.365695i
\(297\) −8733.10 14557.2i −0.0990046 0.165031i
\(298\) 52983.4 0.596633
\(299\) 2085.46i 0.0233271i
\(300\) −19921.4 −0.221349
\(301\) −2320.00 −0.0256068
\(302\) 58494.5 0.641359
\(303\) 66173.5i 0.720774i
\(304\) 56354.7i 0.609793i
\(305\) 3111.62i 0.0334493i
\(306\) 15381.1 0.164265
\(307\) 70825.1i 0.751468i −0.926728 0.375734i \(-0.877391\pi\)
0.926728 0.375734i \(-0.122609\pi\)
\(308\) −1056.81 + 633.997i −0.0111403 + 0.00668322i
\(309\) 24096.5 0.252369
\(310\) 7969.85i 0.0829329i
\(311\) −79979.1 −0.826905 −0.413453 0.910526i \(-0.635677\pi\)
−0.413453 + 0.910526i \(0.635677\pi\)
\(312\) 58172.2 0.597594
\(313\) 45118.3 0.460537 0.230268 0.973127i \(-0.426040\pi\)
0.230268 + 0.973127i \(0.426040\pi\)
\(314\) 61978.8i 0.628614i
\(315\) 343.523i 0.00346206i
\(316\) 78963.7i 0.790776i
\(317\) −53392.1 −0.531322 −0.265661 0.964066i \(-0.585590\pi\)
−0.265661 + 0.964066i \(0.585590\pi\)
\(318\) 62768.4i 0.620707i
\(319\) −29297.7 + 17576.2i −0.287907 + 0.172720i
\(320\) −34746.2 −0.339318
\(321\) 82403.5i 0.799716i
\(322\) 56.2811 0.000542814
\(323\) −112027. −1.07379
\(324\) 5092.19 0.0485081
\(325\) 89036.7i 0.842951i
\(326\) 17680.4i 0.166363i
\(327\) 101412.i 0.948403i
\(328\) 82387.4 0.765796
\(329\) 2662.31i 0.0245961i
\(330\) −14125.3 + 8473.98i −0.129709 + 0.0778144i
\(331\) 97744.9 0.892151 0.446075 0.894995i \(-0.352821\pi\)
0.446075 + 0.894995i \(0.352821\pi\)
\(332\) 38065.3i 0.345345i
\(333\) 12535.5 0.113045
\(334\) 78053.2 0.699677
\(335\) 72066.9 0.642164
\(336\) 723.139i 0.00640536i
\(337\) 75385.5i 0.663786i 0.943317 + 0.331893i \(0.107687\pi\)
−0.943317 + 0.331893i \(0.892313\pi\)
\(338\) 6741.59i 0.0590105i
\(339\) −79727.3 −0.693757
\(340\) 11564.5i 0.100039i
\(341\) 18936.1 + 31564.5i 0.162847 + 0.271450i
\(342\) 47865.3 0.409231
\(343\) 6998.71i 0.0594880i
\(344\) −109806. −0.927919
\(345\) −582.884 −0.00489716
\(346\) 67122.9 0.560684
\(347\) 95151.0i 0.790232i 0.918631 + 0.395116i \(0.129296\pi\)
−0.918631 + 0.395116i \(0.870704\pi\)
\(348\) 10248.5i 0.0846256i
\(349\) 106717.i 0.876156i −0.898937 0.438078i \(-0.855659\pi\)
0.898937 0.438078i \(-0.144341\pi\)
\(350\) 2402.86 0.0196152
\(351\) 22759.0i 0.184730i
\(352\) −84837.3 + 50895.3i −0.684702 + 0.410764i
\(353\) 62919.0 0.504932 0.252466 0.967606i \(-0.418758\pi\)
0.252466 + 0.967606i \(0.418758\pi\)
\(354\) 23232.2i 0.185389i
\(355\) 69558.7 0.551944
\(356\) 51216.1 0.404116
\(357\) 1437.52 0.0112792
\(358\) 27706.7i 0.216182i
\(359\) 147077.i 1.14119i 0.821232 + 0.570594i \(0.193287\pi\)
−0.821232 + 0.570594i \(0.806713\pi\)
\(360\) 16259.0i 0.125455i
\(361\) −218302. −1.67511
\(362\) 156897.i 1.19729i
\(363\) −35809.1 + 67122.2i −0.271757 + 0.509393i
\(364\) 1652.24 0.0124701
\(365\) 50443.2i 0.378631i
\(366\) −5563.43 −0.0415318
\(367\) −50293.7 −0.373406 −0.186703 0.982416i \(-0.559780\pi\)
−0.186703 + 0.982416i \(0.559780\pi\)
\(368\) 1227.01 0.00906050
\(369\) 32232.8i 0.236726i
\(370\) 12163.5i 0.0888497i
\(371\) 5866.36i 0.0426207i
\(372\) −11041.4 −0.0797884
\(373\) 29786.2i 0.214090i −0.994254 0.107045i \(-0.965861\pi\)
0.994254 0.107045i \(-0.0341389\pi\)
\(374\) −35460.6 59109.3i −0.253515 0.422584i
\(375\) −53223.4 −0.378478
\(376\) 126008.i 0.891295i
\(377\) 45804.5 0.322274
\(378\) −614.204 −0.00429862
\(379\) 80930.7 0.563423 0.281712 0.959499i \(-0.409098\pi\)
0.281712 + 0.959499i \(0.409098\pi\)
\(380\) 35988.1i 0.249225i
\(381\) 100594.i 0.692985i
\(382\) 212142.i 1.45378i
\(383\) −266517. −1.81688 −0.908441 0.418012i \(-0.862727\pi\)
−0.908441 + 0.418012i \(0.862727\pi\)
\(384\) 5851.59i 0.0396836i
\(385\) −1320.15 + 791.981i −0.00890641 + 0.00534310i
\(386\) 65311.9 0.438347
\(387\) 42960.0i 0.286842i
\(388\) −78430.3 −0.520979
\(389\) 4358.49 0.0288029 0.0144015 0.999896i \(-0.495416\pi\)
0.0144015 + 0.999896i \(0.495416\pi\)
\(390\) 22083.7 0.145192
\(391\) 2439.16i 0.0159547i
\(392\) 165552.i 1.07736i
\(393\) 72571.2i 0.469872i
\(394\) −202206. −1.30257
\(395\) 98640.5i 0.632209i
\(396\) −11739.9 19569.2i −0.0748640 0.124791i
\(397\) −11014.6 −0.0698859 −0.0349429 0.999389i \(-0.511125\pi\)
−0.0349429 + 0.999389i \(0.511125\pi\)
\(398\) 14881.4i 0.0939459i
\(399\) 4473.50 0.0280997
\(400\) 52385.9 0.327412
\(401\) 244214. 1.51873 0.759366 0.650664i \(-0.225509\pi\)
0.759366 + 0.650664i \(0.225509\pi\)
\(402\) 128852.i 0.797333i
\(403\) 49348.5i 0.303853i
\(404\) 88956.8i 0.545025i
\(405\) 6361.10 0.0387813
\(406\) 1236.14i 0.00749922i
\(407\) −28900.1 48173.5i −0.174466 0.290817i
\(408\) 68038.3 0.408727
\(409\) 9069.88i 0.0542194i 0.999632 + 0.0271097i \(0.00863035\pi\)
−0.999632 + 0.0271097i \(0.991370\pi\)
\(410\) 31276.5 0.186059
\(411\) 56761.5 0.336024
\(412\) 32392.8 0.190833
\(413\) 2171.29i 0.0127297i
\(414\) 1042.17i 0.00608048i
\(415\) 47550.7i 0.276096i
\(416\) 132636. 0.766435
\(417\) 142506.i 0.819525i
\(418\) −110352. 183945.i −0.631578 1.05278i
\(419\) 317776. 1.81006 0.905029 0.425350i \(-0.139849\pi\)
0.905029 + 0.425350i \(0.139849\pi\)
\(420\) 461.797i 0.00261790i
\(421\) 89267.7 0.503651 0.251826 0.967773i \(-0.418969\pi\)
0.251826 + 0.967773i \(0.418969\pi\)
\(422\) 15703.9 0.0881826
\(423\) −49298.6 −0.275520
\(424\) 277656.i 1.54445i
\(425\) 104138.i 0.576540i
\(426\) 124368.i 0.685313i
\(427\) −519.960 −0.00285177
\(428\) 110775.i 0.604718i
\(429\) 87462.3 52470.1i 0.475233 0.285100i
\(430\) −41685.4 −0.225448
\(431\) 80855.4i 0.435266i 0.976031 + 0.217633i \(0.0698335\pi\)
−0.976031 + 0.217633i \(0.930166\pi\)
\(432\) −13390.5 −0.0717514
\(433\) 17118.8 0.0913057 0.0456529 0.998957i \(-0.485463\pi\)
0.0456529 + 0.998957i \(0.485463\pi\)
\(434\) 1331.78 0.00707057
\(435\) 12802.3i 0.0676564i
\(436\) 136327.i 0.717150i
\(437\) 7590.56i 0.0397476i
\(438\) −90190.1 −0.470122
\(439\) 32476.8i 0.168517i −0.996444 0.0842585i \(-0.973148\pi\)
0.996444 0.0842585i \(-0.0268522\pi\)
\(440\) −62483.1 + 37484.6i −0.322743 + 0.193619i
\(441\) 64769.6 0.333038
\(442\) 92412.6i 0.473028i
\(443\) 4735.01 0.0241276 0.0120638 0.999927i \(-0.496160\pi\)
0.0120638 + 0.999927i \(0.496160\pi\)
\(444\) 16851.4 0.0854809
\(445\) 63978.5 0.323083
\(446\) 210521.i 1.05834i
\(447\) 91694.4i 0.458910i
\(448\) 5806.19i 0.0289291i
\(449\) −217096. −1.07686 −0.538430 0.842670i \(-0.680982\pi\)
−0.538430 + 0.842670i \(0.680982\pi\)
\(450\) 44494.3i 0.219725i
\(451\) 123870. 74311.7i 0.608994 0.365346i
\(452\) −107177. −0.524596
\(453\) 101232.i 0.493312i
\(454\) −207715. −1.00776
\(455\) 2063.95 0.00996957
\(456\) 211732. 1.01826
\(457\) 226266.i 1.08340i 0.840573 + 0.541698i \(0.182218\pi\)
−0.840573 + 0.541698i \(0.817782\pi\)
\(458\) 83980.4i 0.400356i
\(459\) 26618.9i 0.126347i
\(460\) −783.569 −0.00370307
\(461\) 280319.i 1.31902i −0.751697 0.659509i \(-0.770764\pi\)
0.751697 0.659509i \(-0.229236\pi\)
\(462\) 1416.03 + 2360.37i 0.00663418 + 0.0110585i
\(463\) 176739. 0.824463 0.412231 0.911079i \(-0.364750\pi\)
0.412231 + 0.911079i \(0.364750\pi\)
\(464\) 26949.7i 0.125175i
\(465\) −13792.8 −0.0637892
\(466\) −202943. −0.934548
\(467\) −211683. −0.970625 −0.485312 0.874341i \(-0.661294\pi\)
−0.485312 + 0.874341i \(0.661294\pi\)
\(468\) 30594.8i 0.139687i
\(469\) 12042.6i 0.0547487i
\(470\) 47835.9i 0.216550i
\(471\) 107262. 0.483509
\(472\) 102768.i 0.461288i
\(473\) −165094. + 99042.8i −0.737921 + 0.442691i
\(474\) −176365. −0.784973
\(475\) 324071.i 1.43633i
\(476\) 1932.46 0.00852896
\(477\) −108629. −0.477428
\(478\) 94846.5 0.415112
\(479\) 80152.2i 0.349337i 0.984627 + 0.174668i \(0.0558854\pi\)
−0.984627 + 0.174668i \(0.944115\pi\)
\(480\) 37071.6i 0.160901i
\(481\) 75315.3i 0.325532i
\(482\) 193405. 0.832480
\(483\) 97.4015i 0.000417514i
\(484\) −48138.1 + 90232.2i −0.205494 + 0.385186i
\(485\) −97974.1 −0.416512
\(486\) 11373.3i 0.0481522i
\(487\) −173605. −0.731988 −0.365994 0.930617i \(-0.619271\pi\)
−0.365994 + 0.930617i \(0.619271\pi\)
\(488\) −24609.8 −0.103340
\(489\) 30598.2 0.127961
\(490\) 62847.9i 0.261757i
\(491\) 152879.i 0.634138i −0.948402 0.317069i \(-0.897301\pi\)
0.948402 0.317069i \(-0.102699\pi\)
\(492\) 43330.4i 0.179004i
\(493\) 53573.1 0.220421
\(494\) 287583.i 1.17845i
\(495\) −14665.3 24445.6i −0.0598522 0.0997676i
\(496\) 29034.8 0.118020
\(497\) 11623.5i 0.0470568i
\(498\) −85018.4 −0.342811
\(499\) 122586. 0.492312 0.246156 0.969230i \(-0.420832\pi\)
0.246156 + 0.969230i \(0.420832\pi\)
\(500\) −71548.0 −0.286192
\(501\) 135081.i 0.538168i
\(502\) 104552.i 0.414883i
\(503\) 355305.i 1.40432i 0.712020 + 0.702159i \(0.247780\pi\)
−0.712020 + 0.702159i \(0.752220\pi\)
\(504\) −2716.93 −0.0106959
\(505\) 111124.i 0.435737i
\(506\) 4005.04 2402.69i 0.0156425 0.00938418i
\(507\) 11667.2 0.0453889
\(508\) 135229.i 0.524012i
\(509\) 34844.7 0.134493 0.0672467 0.997736i \(-0.478579\pi\)
0.0672467 + 0.997736i \(0.478579\pi\)
\(510\) 25829.2 0.0993047
\(511\) −8429.19 −0.0322808
\(512\) 183428.i 0.699722i
\(513\) 82836.8i 0.314767i
\(514\) 221421.i 0.838092i
\(515\) 40464.7 0.152567
\(516\) 57751.0i 0.216900i
\(517\) 113656. + 189454.i 0.425219 + 0.708797i
\(518\) −2032.56 −0.00757501
\(519\) 116165.i 0.431260i
\(520\) 97687.3 0.361269
\(521\) 130516. 0.480825 0.240412 0.970671i \(-0.422717\pi\)
0.240412 + 0.970671i \(0.422717\pi\)
\(522\) −22889.9 −0.0840046
\(523\) 436331.i 1.59519i −0.603192 0.797596i \(-0.706105\pi\)
0.603192 0.797596i \(-0.293895\pi\)
\(524\) 97557.3i 0.355301i
\(525\) 4158.45i 0.0150874i
\(526\) 310965. 1.12393
\(527\) 57718.1i 0.207822i
\(528\) 30871.4 + 51459.5i 0.110736 + 0.184586i
\(529\) −279676. −0.999409
\(530\) 105406.i 0.375242i
\(531\) −40206.2 −0.142595
\(532\) 6013.71 0.0212481
\(533\) −193661. −0.681690
\(534\) 114391.i 0.401151i
\(535\) 138378.i 0.483460i
\(536\) 569978.i 1.98394i
\(537\) 47950.0 0.166280
\(538\) 356905.i 1.23307i
\(539\) −149324. 248908.i −0.513987 0.856765i
\(540\) 8551.20 0.0293251
\(541\) 80892.7i 0.276385i −0.990405 0.138193i \(-0.955871\pi\)
0.990405 0.138193i \(-0.0441293\pi\)
\(542\) 308480. 1.05009
\(543\) −271530. −0.920913
\(544\) 155132. 0.524206
\(545\) 170298.i 0.573347i
\(546\) 3690.25i 0.0123786i
\(547\) 231848.i 0.774870i −0.921897 0.387435i \(-0.873361\pi\)
0.921897 0.387435i \(-0.126639\pi\)
\(548\) 76304.2 0.254090
\(549\) 9628.21i 0.0319449i
\(550\) 170991. 102580.i 0.565259 0.339108i
\(551\) 166717. 0.549131
\(552\) 4610.03i 0.0151296i
\(553\) −16483.1 −0.0539000
\(554\) 310264. 1.01091
\(555\) 21050.5 0.0683402
\(556\) 191571.i 0.619698i
\(557\) 461600.i 1.48784i 0.668270 + 0.743919i \(0.267035\pi\)
−0.668270 + 0.743919i \(0.732965\pi\)
\(558\) 24660.9i 0.0792029i
\(559\) 258112. 0.826007
\(560\) 1214.35i 0.00387229i
\(561\) 102296. 61369.1i 0.325037 0.194995i
\(562\) −111865. −0.354179
\(563\) 35282.9i 0.111313i 0.998450 + 0.0556566i \(0.0177252\pi\)
−0.998450 + 0.0556566i \(0.982275\pi\)
\(564\) −66271.9 −0.208339
\(565\) −133884. −0.419404
\(566\) −380232. −1.18690
\(567\) 1062.96i 0.00330635i
\(568\) 550141.i 1.70521i
\(569\) 296349.i 0.915332i −0.889124 0.457666i \(-0.848686\pi\)
0.889124 0.457666i \(-0.151314\pi\)
\(570\) 80379.1 0.247396
\(571\) 241258.i 0.739963i 0.929039 + 0.369982i \(0.120636\pi\)
−0.929039 + 0.369982i \(0.879364\pi\)
\(572\) 117575. 70535.3i 0.359355 0.215583i
\(573\) −367138. −1.11820
\(574\) 5226.38i 0.0158627i
\(575\) 7055.99 0.0213414
\(576\) −107514. −0.324057
\(577\) −457944. −1.37550 −0.687750 0.725948i \(-0.741401\pi\)
−0.687750 + 0.725948i \(0.741401\pi\)
\(578\) 142683.i 0.427089i
\(579\) 113030.i 0.337162i
\(580\) 17210.1i 0.0511595i
\(581\) −7945.85 −0.0235390
\(582\) 175173.i 0.517156i
\(583\) 250440. + 417458.i 0.736828 + 1.22822i
\(584\) −398956. −1.16977
\(585\) 38218.6i 0.111677i
\(586\) 4014.55 0.0116907
\(587\) 481837. 1.39838 0.699188 0.714938i \(-0.253545\pi\)
0.699188 + 0.714938i \(0.253545\pi\)
\(588\) 87069.5 0.251832
\(589\) 179616.i 0.517743i
\(590\) 39013.3i 0.112075i
\(591\) 349944.i 1.00190i
\(592\) −44312.7 −0.126440
\(593\) 495129.i 1.40802i 0.710190 + 0.704010i \(0.248609\pi\)
−0.710190 + 0.704010i \(0.751391\pi\)
\(594\) −43707.5 + 26220.9i −0.123875 + 0.0743146i
\(595\) 2414.00 0.00681873
\(596\) 123264.i 0.347013i
\(597\) 25754.1 0.0722601
\(598\) −6261.55 −0.0175097
\(599\) −341737. −0.952442 −0.476221 0.879326i \(-0.657994\pi\)
−0.476221 + 0.879326i \(0.657994\pi\)
\(600\) 196821.i 0.546724i
\(601\) 404022.i 1.11855i 0.828982 + 0.559275i \(0.188920\pi\)
−0.828982 + 0.559275i \(0.811080\pi\)
\(602\) 6965.74i 0.0192209i
\(603\) 222995. 0.613282
\(604\) 136086.i 0.373026i
\(605\) −60133.5 + 112717.i −0.164288 + 0.307949i
\(606\) 198684. 0.541026
\(607\) 85001.6i 0.230701i 0.993325 + 0.115351i \(0.0367991\pi\)
−0.993325 + 0.115351i \(0.963201\pi\)
\(608\) 482762. 1.30595
\(609\) −2139.30 −0.00576815
\(610\) −9342.54 −0.0251076
\(611\) 296195.i 0.793406i
\(612\) 35783.7i 0.0955395i
\(613\) 296743.i 0.789695i 0.918747 + 0.394847i \(0.129203\pi\)
−0.918747 + 0.394847i \(0.870797\pi\)
\(614\) −212650. −0.564065
\(615\) 54127.8i 0.143110i
\(616\) 6263.79 + 10441.1i 0.0165073 + 0.0275160i
\(617\) −205712. −0.540368 −0.270184 0.962809i \(-0.587085\pi\)
−0.270184 + 0.962809i \(0.587085\pi\)
\(618\) 72349.0i 0.189433i
\(619\) −23798.6 −0.0621112 −0.0310556 0.999518i \(-0.509887\pi\)
−0.0310556 + 0.999518i \(0.509887\pi\)
\(620\) −18541.6 −0.0482353
\(621\) −1803.61 −0.00467690
\(622\) 240135.i 0.620690i
\(623\) 10691.0i 0.0275449i
\(624\) 80452.8i 0.206620i
\(625\) 253661. 0.649372
\(626\) 135466.i 0.345687i
\(627\) 318340. 190978.i 0.809761 0.485789i
\(628\) 144192. 0.365613
\(629\) 88088.9i 0.222649i
\(630\) −1031.42 −0.00259869
\(631\) −464381. −1.16631 −0.583157 0.812359i \(-0.698183\pi\)
−0.583157 + 0.812359i \(0.698183\pi\)
\(632\) −780149. −1.95318
\(633\) 27177.6i 0.0678271i
\(634\) 160308.i 0.398820i
\(635\) 168926.i 0.418937i
\(636\) −146029. −0.361015
\(637\) 389148.i 0.959038i
\(638\) 52771.9 + 87965.4i 0.129647 + 0.216108i
\(639\) 215234. 0.527120
\(640\) 9826.44i 0.0239903i
\(641\) 433460. 1.05495 0.527476 0.849570i \(-0.323138\pi\)
0.527476 + 0.849570i \(0.323138\pi\)
\(642\) −247414. −0.600281
\(643\) −228934. −0.553718 −0.276859 0.960910i \(-0.589294\pi\)
−0.276859 + 0.960910i \(0.589294\pi\)
\(644\) 130.936i 0.000315710i
\(645\) 72141.8i 0.173407i
\(646\) 336358.i 0.806003i
\(647\) −83987.4 −0.200634 −0.100317 0.994956i \(-0.531986\pi\)
−0.100317 + 0.994956i \(0.531986\pi\)
\(648\) 50310.0i 0.119813i
\(649\) 92694.1 + 154512.i 0.220071 + 0.366836i
\(650\) −267330. −0.632734
\(651\) 2304.82i 0.00543845i
\(652\) 41133.1 0.0967600
\(653\) 337789. 0.792172 0.396086 0.918213i \(-0.370368\pi\)
0.396086 + 0.918213i \(0.370368\pi\)
\(654\) 304486. 0.711888
\(655\) 121867.i 0.284056i
\(656\) 113943.i 0.264776i
\(657\) 156085.i 0.361602i
\(658\) 7993.51 0.0184623
\(659\) 586098.i 1.34958i −0.738008 0.674791i \(-0.764234\pi\)
0.738008 0.674791i \(-0.235766\pi\)
\(660\) −19714.5 32862.1i −0.0452583 0.0754410i
\(661\) −660271. −1.51119 −0.755596 0.655038i \(-0.772652\pi\)
−0.755596 + 0.655038i \(0.772652\pi\)
\(662\) 293476.i 0.669664i
\(663\) −159932. −0.363837
\(664\) −376079. −0.852987
\(665\) 7512.25 0.0169874
\(666\) 37637.3i 0.0848536i
\(667\) 3629.92i 0.00815916i
\(668\) 181589.i 0.406945i
\(669\) 364333. 0.814042
\(670\) 216379.i 0.482020i
\(671\) −37001.0 + 22197.5i −0.0821805 + 0.0493014i
\(672\) −6194.77 −0.0137179
\(673\) 362391.i 0.800105i −0.916492 0.400052i \(-0.868992\pi\)
0.916492 0.400052i \(-0.131008\pi\)
\(674\) 226343. 0.498249
\(675\) −77003.0 −0.169005
\(676\) 15684.1 0.0343216
\(677\) 92662.7i 0.202175i −0.994878 0.101088i \(-0.967768\pi\)
0.994878 0.101088i \(-0.0322322\pi\)
\(678\) 239379.i 0.520747i
\(679\) 16371.7i 0.0355104i
\(680\) 114255. 0.247092
\(681\) 359477.i 0.775135i
\(682\) 94771.5 56855.0i 0.203755 0.122236i
\(683\) 448358. 0.961132 0.480566 0.876958i \(-0.340431\pi\)
0.480566 + 0.876958i \(0.340431\pi\)
\(684\) 111357.i 0.238016i
\(685\) 95318.3 0.203140
\(686\) −21013.4 −0.0446528
\(687\) −145339. −0.307941
\(688\) 151863.i 0.320830i
\(689\) 652661.i 1.37483i
\(690\) 1750.09i 0.00367589i
\(691\) 358700. 0.751234 0.375617 0.926775i \(-0.377431\pi\)
0.375617 + 0.926775i \(0.377431\pi\)
\(692\) 156160.i 0.326104i
\(693\) −4084.92 + 2450.61i −0.00850584 + 0.00510279i
\(694\) 285688. 0.593162
\(695\) 239308.i 0.495436i
\(696\) −101253. −0.209022
\(697\) −226506. −0.466245
\(698\) −320414. −0.657659
\(699\) 351218.i 0.718823i
\(700\) 5590.19i 0.0114086i
\(701\) 159779.i 0.325150i 0.986696 + 0.162575i \(0.0519799\pi\)
−0.986696 + 0.162575i \(0.948020\pi\)
\(702\) 68333.2 0.138662
\(703\) 274128.i 0.554681i
\(704\) 247871. + 413176.i 0.500127 + 0.833661i
\(705\) −82786.0 −0.166563
\(706\) 188913.i 0.379011i
\(707\) 18569.1 0.0371494
\(708\) −54049.1 −0.107826
\(709\) 455705. 0.906550 0.453275 0.891371i \(-0.350256\pi\)
0.453275 + 0.891371i \(0.350256\pi\)
\(710\) 208848.i 0.414299i
\(711\) 305221.i 0.603775i
\(712\) 506006.i 0.998151i
\(713\) 3910.78 0.00769279
\(714\) 4316.12i 0.00846637i
\(715\) 146873. 88111.8i 0.287297 0.172354i
\(716\) 64459.0 0.125735
\(717\) 164144.i 0.319291i
\(718\) 441596. 0.856596
\(719\) 640858. 1.23966 0.619832 0.784735i \(-0.287201\pi\)
0.619832 + 0.784735i \(0.287201\pi\)
\(720\) −22486.4 −0.0433766
\(721\) 6761.76i 0.0130074i
\(722\) 655445.i 1.25737i
\(723\) 334712.i 0.640316i
\(724\) −365017. −0.696363
\(725\) 154976.i 0.294841i
\(726\) 201533. + 107516.i 0.382360 + 0.203986i
\(727\) −324283. −0.613558 −0.306779 0.951781i \(-0.599251\pi\)
−0.306779 + 0.951781i \(0.599251\pi\)
\(728\) 16323.8i 0.0308006i
\(729\) 19683.0 0.0370370
\(730\) −151454. −0.284207
\(731\) 301888. 0.564951
\(732\) 12943.2i 0.0241556i
\(733\) 633078.i 1.17828i −0.808030 0.589141i \(-0.799466\pi\)
0.808030 0.589141i \(-0.200534\pi\)
\(734\) 151005.i 0.280285i
\(735\) 108766. 0.201335
\(736\) 10511.2i 0.0194042i
\(737\) −514107. 856965.i −0.946496 1.57771i
\(738\) 96778.1 0.177690
\(739\) 218657.i 0.400382i 0.979757 + 0.200191i \(0.0641562\pi\)
−0.979757 + 0.200191i \(0.935844\pi\)
\(740\) 28298.1 0.0516766
\(741\) −497699. −0.906422
\(742\) 17613.6 0.0319919
\(743\) 740582.i 1.34152i 0.741677 + 0.670758i \(0.234031\pi\)
−0.741677 + 0.670758i \(0.765969\pi\)
\(744\) 109088.i 0.197074i
\(745\) 153980.i 0.277430i
\(746\) −89432.1 −0.160700
\(747\) 147135.i 0.263679i
\(748\) 137516. 82498.2i 0.245782 0.147449i
\(749\) −23123.4 −0.0412181
\(750\) 159802.i 0.284092i
\(751\) −1.08089e6 −1.91647 −0.958235 0.285982i \(-0.907680\pi\)
−0.958235 + 0.285982i \(0.907680\pi\)
\(752\) 174270. 0.308168
\(753\) 180941. 0.319114
\(754\) 137527.i 0.241905i
\(755\) 169997.i 0.298227i
\(756\) 1428.93i 0.00250015i
\(757\) 604976. 1.05571 0.527857 0.849333i \(-0.322996\pi\)
0.527857 + 0.849333i \(0.322996\pi\)
\(758\) 242992.i 0.422916i
\(759\) 4158.15 + 6931.22i 0.00721800 + 0.0120317i
\(760\) 355557. 0.615576
\(761\) 1.06160e6i 1.83312i 0.399901 + 0.916558i \(0.369045\pi\)
−0.399901 + 0.916558i \(0.630955\pi\)
\(762\) −302032. −0.520167
\(763\) 28457.3 0.0488816
\(764\) −493542. −0.845546
\(765\) 44700.6i 0.0763819i
\(766\) 800209.i 1.36378i
\(767\) 241567.i 0.410626i
\(768\) −348628. −0.591071
\(769\) 405621.i 0.685912i −0.939352 0.342956i \(-0.888572\pi\)
0.939352 0.342956i \(-0.111428\pi\)
\(770\) 2377.90 + 3963.72i 0.00401063 + 0.00668531i
\(771\) −383196. −0.644633
\(772\) 151946.i 0.254950i
\(773\) −279272. −0.467377 −0.233689 0.972311i \(-0.575080\pi\)
−0.233689 + 0.972311i \(0.575080\pi\)
\(774\) −128986. −0.215308
\(775\) 166966. 0.277988
\(776\) 774878.i 1.28680i
\(777\) 3517.60i 0.00582645i
\(778\) 13086.2i 0.0216200i
\(779\) −704875. −1.16155
\(780\) 51377.2i 0.0844464i
\(781\) −496215. 827141.i −0.813519 1.35605i
\(782\) −7323.52 −0.0119758
\(783\) 39613.8i 0.0646135i
\(784\) −228960. −0.372501
\(785\) 180123. 0.292301
\(786\) 217893.