Properties

Label 405.4.e.d.136.1
Level $405$
Weight $4$
Character 405.136
Analytic conductor $23.896$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.4.e.d.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-10.0000 + 17.3205i) q^{7} -21.0000 q^{8} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-10.0000 + 17.3205i) q^{7} -21.0000 q^{8} -15.0000 q^{10} +(12.0000 - 20.7846i) q^{11} +(-37.0000 - 64.0859i) q^{13} +(-30.0000 - 51.9615i) q^{14} +(35.5000 - 61.4878i) q^{16} +54.0000 q^{17} -124.000 q^{19} +(2.50000 - 4.33013i) q^{20} +(36.0000 + 62.3538i) q^{22} +(60.0000 + 103.923i) q^{23} +(-12.5000 + 21.6506i) q^{25} +222.000 q^{26} +20.0000 q^{28} +(39.0000 - 67.5500i) q^{29} +(-100.000 - 173.205i) q^{31} +(22.5000 + 38.9711i) q^{32} +(-81.0000 + 140.296i) q^{34} -100.000 q^{35} -70.0000 q^{37} +(186.000 - 322.161i) q^{38} +(-52.5000 - 90.9327i) q^{40} +(-165.000 - 285.788i) q^{41} +(-46.0000 + 79.6743i) q^{43} -24.0000 q^{44} -360.000 q^{46} +(12.0000 - 20.7846i) q^{47} +(-28.5000 - 49.3634i) q^{49} +(-37.5000 - 64.9519i) q^{50} +(-37.0000 + 64.0859i) q^{52} +450.000 q^{53} +120.000 q^{55} +(210.000 - 363.731i) q^{56} +(117.000 + 202.650i) q^{58} +(-12.0000 - 20.7846i) q^{59} +(161.000 - 278.860i) q^{61} +600.000 q^{62} +433.000 q^{64} +(185.000 - 320.429i) q^{65} +(98.0000 + 169.741i) q^{67} +(-27.0000 - 46.7654i) q^{68} +(150.000 - 259.808i) q^{70} -288.000 q^{71} -430.000 q^{73} +(105.000 - 181.865i) q^{74} +(62.0000 + 107.387i) q^{76} +(240.000 + 415.692i) q^{77} +(260.000 - 450.333i) q^{79} +355.000 q^{80} +990.000 q^{82} +(-78.0000 + 135.100i) q^{83} +(135.000 + 233.827i) q^{85} +(-138.000 - 239.023i) q^{86} +(-252.000 + 436.477i) q^{88} +1026.00 q^{89} +1480.00 q^{91} +(60.0000 - 103.923i) q^{92} +(36.0000 + 62.3538i) q^{94} +(-310.000 - 536.936i) q^{95} +(143.000 - 247.683i) q^{97} +171.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} - q^{4} + 5 q^{5} - 20 q^{7} - 42 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} - q^{4} + 5 q^{5} - 20 q^{7} - 42 q^{8} - 30 q^{10} + 24 q^{11} - 74 q^{13} - 60 q^{14} + 71 q^{16} + 108 q^{17} - 248 q^{19} + 5 q^{20} + 72 q^{22} + 120 q^{23} - 25 q^{25} + 444 q^{26} + 40 q^{28} + 78 q^{29} - 200 q^{31} + 45 q^{32} - 162 q^{34} - 200 q^{35} - 140 q^{37} + 372 q^{38} - 105 q^{40} - 330 q^{41} - 92 q^{43} - 48 q^{44} - 720 q^{46} + 24 q^{47} - 57 q^{49} - 75 q^{50} - 74 q^{52} + 900 q^{53} + 240 q^{55} + 420 q^{56} + 234 q^{58} - 24 q^{59} + 322 q^{61} + 1200 q^{62} + 866 q^{64} + 370 q^{65} + 196 q^{67} - 54 q^{68} + 300 q^{70} - 576 q^{71} - 860 q^{73} + 210 q^{74} + 124 q^{76} + 480 q^{77} + 520 q^{79} + 710 q^{80} + 1980 q^{82} - 156 q^{83} + 270 q^{85} - 276 q^{86} - 504 q^{88} + 2052 q^{89} + 2960 q^{91} + 120 q^{92} + 72 q^{94} - 620 q^{95} + 286 q^{97} + 342 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 + 2.59808i −0.530330 + 0.918559i 0.469044 + 0.883175i \(0.344599\pi\)
−0.999374 + 0.0353837i \(0.988735\pi\)
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.0625000 0.108253i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −10.0000 + 17.3205i −0.539949 + 0.935220i 0.458957 + 0.888459i \(0.348223\pi\)
−0.998906 + 0.0467610i \(0.985110\pi\)
\(8\) −21.0000 −0.928078
\(9\) 0 0
\(10\) −15.0000 −0.474342
\(11\) 12.0000 20.7846i 0.328921 0.569709i −0.653377 0.757033i \(-0.726648\pi\)
0.982298 + 0.187324i \(0.0599815\pi\)
\(12\) 0 0
\(13\) −37.0000 64.0859i −0.789381 1.36725i −0.926347 0.376672i \(-0.877068\pi\)
0.136966 0.990576i \(-0.456265\pi\)
\(14\) −30.0000 51.9615i −0.572703 0.991950i
\(15\) 0 0
\(16\) 35.5000 61.4878i 0.554688 0.960747i
\(17\) 54.0000 0.770407 0.385204 0.922832i \(-0.374131\pi\)
0.385204 + 0.922832i \(0.374131\pi\)
\(18\) 0 0
\(19\) −124.000 −1.49724 −0.748620 0.663000i \(-0.769283\pi\)
−0.748620 + 0.663000i \(0.769283\pi\)
\(20\) 2.50000 4.33013i 0.0279508 0.0484123i
\(21\) 0 0
\(22\) 36.0000 + 62.3538i 0.348874 + 0.604267i
\(23\) 60.0000 + 103.923i 0.543951 + 0.942150i 0.998672 + 0.0515165i \(0.0164055\pi\)
−0.454721 + 0.890634i \(0.650261\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 222.000 1.67453
\(27\) 0 0
\(28\) 20.0000 0.134987
\(29\) 39.0000 67.5500i 0.249728 0.432542i −0.713722 0.700429i \(-0.752992\pi\)
0.963450 + 0.267887i \(0.0863254\pi\)
\(30\) 0 0
\(31\) −100.000 173.205i −0.579372 1.00350i −0.995551 0.0942192i \(-0.969965\pi\)
0.416180 0.909282i \(-0.363369\pi\)
\(32\) 22.5000 + 38.9711i 0.124296 + 0.215287i
\(33\) 0 0
\(34\) −81.0000 + 140.296i −0.408570 + 0.707664i
\(35\) −100.000 −0.482945
\(36\) 0 0
\(37\) −70.0000 −0.311025 −0.155513 0.987834i \(-0.549703\pi\)
−0.155513 + 0.987834i \(0.549703\pi\)
\(38\) 186.000 322.161i 0.794031 1.37530i
\(39\) 0 0
\(40\) −52.5000 90.9327i −0.207524 0.359443i
\(41\) −165.000 285.788i −0.628504 1.08860i −0.987852 0.155397i \(-0.950334\pi\)
0.359348 0.933204i \(-0.382999\pi\)
\(42\) 0 0
\(43\) −46.0000 + 79.6743i −0.163138 + 0.282563i −0.935992 0.352020i \(-0.885495\pi\)
0.772854 + 0.634583i \(0.218828\pi\)
\(44\) −24.0000 −0.0822304
\(45\) 0 0
\(46\) −360.000 −1.15389
\(47\) 12.0000 20.7846i 0.0372421 0.0645053i −0.846804 0.531906i \(-0.821476\pi\)
0.884046 + 0.467401i \(0.154809\pi\)
\(48\) 0 0
\(49\) −28.5000 49.3634i −0.0830904 0.143917i
\(50\) −37.5000 64.9519i −0.106066 0.183712i
\(51\) 0 0
\(52\) −37.0000 + 64.0859i −0.0986726 + 0.170906i
\(53\) 450.000 1.16627 0.583134 0.812376i \(-0.301826\pi\)
0.583134 + 0.812376i \(0.301826\pi\)
\(54\) 0 0
\(55\) 120.000 0.294196
\(56\) 210.000 363.731i 0.501115 0.867956i
\(57\) 0 0
\(58\) 117.000 + 202.650i 0.264877 + 0.458780i
\(59\) −12.0000 20.7846i −0.0264791 0.0458631i 0.852482 0.522756i \(-0.175096\pi\)
−0.878961 + 0.476893i \(0.841763\pi\)
\(60\) 0 0
\(61\) 161.000 278.860i 0.337933 0.585318i −0.646110 0.763244i \(-0.723605\pi\)
0.984044 + 0.177926i \(0.0569388\pi\)
\(62\) 600.000 1.22903
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) 185.000 320.429i 0.353022 0.611452i
\(66\) 0 0
\(67\) 98.0000 + 169.741i 0.178696 + 0.309510i 0.941434 0.337197i \(-0.109479\pi\)
−0.762738 + 0.646707i \(0.776146\pi\)
\(68\) −27.0000 46.7654i −0.0481505 0.0833990i
\(69\) 0 0
\(70\) 150.000 259.808i 0.256120 0.443614i
\(71\) −288.000 −0.481399 −0.240699 0.970600i \(-0.577377\pi\)
−0.240699 + 0.970600i \(0.577377\pi\)
\(72\) 0 0
\(73\) −430.000 −0.689420 −0.344710 0.938709i \(-0.612023\pi\)
−0.344710 + 0.938709i \(0.612023\pi\)
\(74\) 105.000 181.865i 0.164946 0.285695i
\(75\) 0 0
\(76\) 62.0000 + 107.387i 0.0935775 + 0.162081i
\(77\) 240.000 + 415.692i 0.355202 + 0.615228i
\(78\) 0 0
\(79\) 260.000 450.333i 0.370282 0.641347i −0.619327 0.785133i \(-0.712594\pi\)
0.989609 + 0.143786i \(0.0459277\pi\)
\(80\) 355.000 0.496128
\(81\) 0 0
\(82\) 990.000 1.33326
\(83\) −78.0000 + 135.100i −0.103152 + 0.178664i −0.912982 0.408001i \(-0.866226\pi\)
0.809830 + 0.586665i \(0.199559\pi\)
\(84\) 0 0
\(85\) 135.000 + 233.827i 0.172268 + 0.298377i
\(86\) −138.000 239.023i −0.173034 0.299704i
\(87\) 0 0
\(88\) −252.000 + 436.477i −0.305265 + 0.528734i
\(89\) 1026.00 1.22198 0.610988 0.791640i \(-0.290773\pi\)
0.610988 + 0.791640i \(0.290773\pi\)
\(90\) 0 0
\(91\) 1480.00 1.70490
\(92\) 60.0000 103.923i 0.0679938 0.117769i
\(93\) 0 0
\(94\) 36.0000 + 62.3538i 0.0395012 + 0.0684182i
\(95\) −310.000 536.936i −0.334793 0.579878i
\(96\) 0 0
\(97\) 143.000 247.683i 0.149685 0.259262i −0.781426 0.623998i \(-0.785507\pi\)
0.931111 + 0.364736i \(0.118841\pi\)
\(98\) 171.000 0.176261
\(99\) 0 0
\(100\) 25.0000 0.0250000
\(101\) 867.000 1501.69i 0.854156 1.47944i −0.0232704 0.999729i \(-0.507408\pi\)
0.877426 0.479712i \(-0.159259\pi\)
\(102\) 0 0
\(103\) −226.000 391.443i −0.216198 0.374467i 0.737444 0.675408i \(-0.236032\pi\)
−0.953643 + 0.300941i \(0.902699\pi\)
\(104\) 777.000 + 1345.80i 0.732607 + 1.26891i
\(105\) 0 0
\(106\) −675.000 + 1169.13i −0.618508 + 1.07129i
\(107\) −1404.00 −1.26850 −0.634251 0.773127i \(-0.718692\pi\)
−0.634251 + 0.773127i \(0.718692\pi\)
\(108\) 0 0
\(109\) −1474.00 −1.29526 −0.647631 0.761954i \(-0.724240\pi\)
−0.647631 + 0.761954i \(0.724240\pi\)
\(110\) −180.000 + 311.769i −0.156021 + 0.270237i
\(111\) 0 0
\(112\) 710.000 + 1229.76i 0.599006 + 1.03751i
\(113\) −543.000 940.504i −0.452046 0.782966i 0.546467 0.837480i \(-0.315972\pi\)
−0.998513 + 0.0545145i \(0.982639\pi\)
\(114\) 0 0
\(115\) −300.000 + 519.615i −0.243262 + 0.421342i
\(116\) −78.0000 −0.0624321
\(117\) 0 0
\(118\) 72.0000 0.0561707
\(119\) −540.000 + 935.307i −0.415981 + 0.720500i
\(120\) 0 0
\(121\) 377.500 + 653.849i 0.283621 + 0.491247i
\(122\) 483.000 + 836.581i 0.358433 + 0.620823i
\(123\) 0 0
\(124\) −100.000 + 173.205i −0.0724215 + 0.125438i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1244.00 0.869190 0.434595 0.900626i \(-0.356891\pi\)
0.434595 + 0.900626i \(0.356891\pi\)
\(128\) −829.500 + 1436.74i −0.572798 + 0.992115i
\(129\) 0 0
\(130\) 555.000 + 961.288i 0.374436 + 0.648543i
\(131\) −1164.00 2016.11i −0.776329 1.34464i −0.934044 0.357157i \(-0.883746\pi\)
0.157715 0.987485i \(-0.449587\pi\)
\(132\) 0 0
\(133\) 1240.00 2147.74i 0.808433 1.40025i
\(134\) −588.000 −0.379071
\(135\) 0 0
\(136\) −1134.00 −0.714998
\(137\) −1059.00 + 1834.24i −0.660412 + 1.14387i 0.320095 + 0.947385i \(0.396285\pi\)
−0.980507 + 0.196482i \(0.937048\pi\)
\(138\) 0 0
\(139\) −1162.00 2012.64i −0.709062 1.22813i −0.965206 0.261492i \(-0.915785\pi\)
0.256144 0.966639i \(-0.417548\pi\)
\(140\) 50.0000 + 86.6025i 0.0301841 + 0.0522804i
\(141\) 0 0
\(142\) 432.000 748.246i 0.255300 0.442193i
\(143\) −1776.00 −1.03858
\(144\) 0 0
\(145\) 390.000 0.223364
\(146\) 645.000 1117.17i 0.365620 0.633273i
\(147\) 0 0
\(148\) 35.0000 + 60.6218i 0.0194391 + 0.0336695i
\(149\) −129.000 223.435i −0.0709268 0.122849i 0.828381 0.560165i \(-0.189262\pi\)
−0.899308 + 0.437316i \(0.855929\pi\)
\(150\) 0 0
\(151\) 404.000 699.749i 0.217729 0.377117i −0.736384 0.676563i \(-0.763468\pi\)
0.954113 + 0.299446i \(0.0968018\pi\)
\(152\) 2604.00 1.38955
\(153\) 0 0
\(154\) −1440.00 −0.753497
\(155\) 500.000 866.025i 0.259103 0.448780i
\(156\) 0 0
\(157\) −1189.00 2059.41i −0.604411 1.04687i −0.992144 0.125099i \(-0.960075\pi\)
0.387733 0.921772i \(-0.373258\pi\)
\(158\) 780.000 + 1351.00i 0.392743 + 0.680252i
\(159\) 0 0
\(160\) −112.500 + 194.856i −0.0555869 + 0.0962794i
\(161\) −2400.00 −1.17482
\(162\) 0 0
\(163\) −52.0000 −0.0249874 −0.0124937 0.999922i \(-0.503977\pi\)
−0.0124937 + 0.999922i \(0.503977\pi\)
\(164\) −165.000 + 285.788i −0.0785630 + 0.136075i
\(165\) 0 0
\(166\) −234.000 405.300i −0.109409 0.189502i
\(167\) 1860.00 + 3221.61i 0.861863 + 1.49279i 0.870129 + 0.492825i \(0.164036\pi\)
−0.00826564 + 0.999966i \(0.502631\pi\)
\(168\) 0 0
\(169\) −1639.50 + 2839.70i −0.746245 + 1.29253i
\(170\) −810.000 −0.365436
\(171\) 0 0
\(172\) 92.0000 0.0407845
\(173\) −213.000 + 368.927i −0.0936075 + 0.162133i −0.909027 0.416738i \(-0.863173\pi\)
0.815419 + 0.578871i \(0.196507\pi\)
\(174\) 0 0
\(175\) −250.000 433.013i −0.107990 0.187044i
\(176\) −852.000 1475.71i −0.364897 0.632021i
\(177\) 0 0
\(178\) −1539.00 + 2665.63i −0.648050 + 1.12246i
\(179\) −1440.00 −0.601289 −0.300644 0.953736i \(-0.597202\pi\)
−0.300644 + 0.953736i \(0.597202\pi\)
\(180\) 0 0
\(181\) −3130.00 −1.28537 −0.642683 0.766133i \(-0.722179\pi\)
−0.642683 + 0.766133i \(0.722179\pi\)
\(182\) −2220.00 + 3845.15i −0.904161 + 1.56605i
\(183\) 0 0
\(184\) −1260.00 2182.38i −0.504828 0.874389i
\(185\) −175.000 303.109i −0.0695473 0.120460i
\(186\) 0 0
\(187\) 648.000 1122.37i 0.253403 0.438908i
\(188\) −24.0000 −0.00931053
\(189\) 0 0
\(190\) 1860.00 0.710203
\(191\) −1788.00 + 3096.91i −0.677357 + 1.17322i 0.298417 + 0.954436i \(0.403541\pi\)
−0.975774 + 0.218781i \(0.929792\pi\)
\(192\) 0 0
\(193\) −1333.00 2308.82i −0.497158 0.861102i 0.502837 0.864381i \(-0.332290\pi\)
−0.999995 + 0.00327888i \(0.998956\pi\)
\(194\) 429.000 + 743.050i 0.158765 + 0.274989i
\(195\) 0 0
\(196\) −28.5000 + 49.3634i −0.0103863 + 0.0179896i
\(197\) −2718.00 −0.982992 −0.491496 0.870880i \(-0.663550\pi\)
−0.491496 + 0.870880i \(0.663550\pi\)
\(198\) 0 0
\(199\) −3832.00 −1.36504 −0.682521 0.730866i \(-0.739116\pi\)
−0.682521 + 0.730866i \(0.739116\pi\)
\(200\) 262.500 454.663i 0.0928078 0.160748i
\(201\) 0 0
\(202\) 2601.00 + 4505.06i 0.905969 + 1.56918i
\(203\) 780.000 + 1351.00i 0.269681 + 0.467101i
\(204\) 0 0
\(205\) 825.000 1428.94i 0.281076 0.486837i
\(206\) 1356.00 0.458626
\(207\) 0 0
\(208\) −5254.00 −1.75144
\(209\) −1488.00 + 2577.29i −0.492474 + 0.852990i
\(210\) 0 0
\(211\) −550.000 952.628i −0.179448 0.310813i 0.762244 0.647290i \(-0.224098\pi\)
−0.941692 + 0.336477i \(0.890765\pi\)
\(212\) −225.000 389.711i −0.0728918 0.126252i
\(213\) 0 0
\(214\) 2106.00 3647.70i 0.672725 1.16519i
\(215\) −460.000 −0.145915
\(216\) 0 0
\(217\) 4000.00 1.25133
\(218\) 2211.00 3829.56i 0.686917 1.18977i
\(219\) 0 0
\(220\) −60.0000 103.923i −0.0183873 0.0318477i
\(221\) −1998.00 3460.64i −0.608145 1.05334i
\(222\) 0 0
\(223\) −982.000 + 1700.87i −0.294886 + 0.510758i −0.974958 0.222387i \(-0.928615\pi\)
0.680072 + 0.733145i \(0.261948\pi\)
\(224\) −900.000 −0.268454
\(225\) 0 0
\(226\) 3258.00 0.958933
\(227\) −330.000 + 571.577i −0.0964884 + 0.167123i −0.910229 0.414106i \(-0.864094\pi\)
0.813740 + 0.581228i \(0.197428\pi\)
\(228\) 0 0
\(229\) 953.000 + 1650.64i 0.275004 + 0.476322i 0.970136 0.242561i \(-0.0779873\pi\)
−0.695132 + 0.718882i \(0.744654\pi\)
\(230\) −900.000 1558.85i −0.258018 0.446901i
\(231\) 0 0
\(232\) −819.000 + 1418.55i −0.231767 + 0.401433i
\(233\) −1458.00 −0.409943 −0.204972 0.978768i \(-0.565710\pi\)
−0.204972 + 0.978768i \(0.565710\pi\)
\(234\) 0 0
\(235\) 120.000 0.0333104
\(236\) −12.0000 + 20.7846i −0.00330989 + 0.00573289i
\(237\) 0 0
\(238\) −1620.00 2805.92i −0.441214 0.764206i
\(239\) −588.000 1018.45i −0.159140 0.275639i 0.775419 0.631448i \(-0.217539\pi\)
−0.934559 + 0.355808i \(0.884206\pi\)
\(240\) 0 0
\(241\) −433.000 + 749.978i −0.115734 + 0.200458i −0.918073 0.396411i \(-0.870255\pi\)
0.802339 + 0.596869i \(0.203589\pi\)
\(242\) −2265.00 −0.601652
\(243\) 0 0
\(244\) −322.000 −0.0844834
\(245\) 142.500 246.817i 0.0371591 0.0643615i
\(246\) 0 0
\(247\) 4588.00 + 7946.65i 1.18189 + 2.04710i
\(248\) 2100.00 + 3637.31i 0.537702 + 0.931327i
\(249\) 0 0
\(250\) 187.500 324.760i 0.0474342 0.0821584i
\(251\) 432.000 0.108636 0.0543179 0.998524i \(-0.482702\pi\)
0.0543179 + 0.998524i \(0.482702\pi\)
\(252\) 0 0
\(253\) 2880.00 0.715668
\(254\) −1866.00 + 3232.01i −0.460958 + 0.798402i
\(255\) 0 0
\(256\) −756.500 1310.30i −0.184692 0.319897i
\(257\) −1263.00 2187.58i −0.306552 0.530963i 0.671054 0.741409i \(-0.265842\pi\)
−0.977606 + 0.210445i \(0.932509\pi\)
\(258\) 0 0
\(259\) 700.000 1212.44i 0.167938 0.290877i
\(260\) −370.000 −0.0882555
\(261\) 0 0
\(262\) 6984.00 1.64684
\(263\) −2724.00 + 4718.11i −0.638666 + 1.10620i 0.347060 + 0.937843i \(0.387180\pi\)
−0.985726 + 0.168358i \(0.946153\pi\)
\(264\) 0 0
\(265\) 1125.00 + 1948.56i 0.260786 + 0.451694i
\(266\) 3720.00 + 6443.23i 0.857473 + 1.48519i
\(267\) 0 0
\(268\) 98.0000 169.741i 0.0223370 0.0386887i
\(269\) −2574.00 −0.583418 −0.291709 0.956507i \(-0.594224\pi\)
−0.291709 + 0.956507i \(0.594224\pi\)
\(270\) 0 0
\(271\) −3184.00 −0.713706 −0.356853 0.934161i \(-0.616150\pi\)
−0.356853 + 0.934161i \(0.616150\pi\)
\(272\) 1917.00 3320.34i 0.427335 0.740166i
\(273\) 0 0
\(274\) −3177.00 5502.73i −0.700473 1.21325i
\(275\) 300.000 + 519.615i 0.0657843 + 0.113942i
\(276\) 0 0
\(277\) −1981.00 + 3431.19i −0.429699 + 0.744261i −0.996846 0.0793553i \(-0.974714\pi\)
0.567147 + 0.823617i \(0.308047\pi\)
\(278\) 6972.00 1.50415
\(279\) 0 0
\(280\) 2100.00 0.448211
\(281\) 4143.00 7175.89i 0.879540 1.52341i 0.0276929 0.999616i \(-0.491184\pi\)
0.851847 0.523791i \(-0.175483\pi\)
\(282\) 0 0
\(283\) 1358.00 + 2352.12i 0.285246 + 0.494061i 0.972669 0.232197i \(-0.0745912\pi\)
−0.687423 + 0.726258i \(0.741258\pi\)
\(284\) 144.000 + 249.415i 0.0300874 + 0.0521129i
\(285\) 0 0
\(286\) 2664.00 4614.18i 0.550789 0.953994i
\(287\) 6600.00 1.35744
\(288\) 0 0
\(289\) −1997.00 −0.406473
\(290\) −585.000 + 1013.25i −0.118456 + 0.205173i
\(291\) 0 0
\(292\) 215.000 + 372.391i 0.0430888 + 0.0746320i
\(293\) −3009.00 5211.74i −0.599958 1.03916i −0.992827 0.119563i \(-0.961851\pi\)
0.392869 0.919595i \(-0.371483\pi\)
\(294\) 0 0
\(295\) 60.0000 103.923i 0.0118418 0.0205106i
\(296\) 1470.00 0.288655
\(297\) 0 0
\(298\) 774.000 0.150458
\(299\) 4440.00 7690.31i 0.858769 1.48743i
\(300\) 0 0
\(301\) −920.000 1593.49i −0.176172 0.305140i
\(302\) 1212.00 + 2099.25i 0.230936 + 0.399993i
\(303\) 0 0
\(304\) −4402.00 + 7624.49i −0.830500 + 1.43847i
\(305\) 1610.00 0.302257
\(306\) 0 0
\(307\) 9236.00 1.71702 0.858512 0.512793i \(-0.171389\pi\)
0.858512 + 0.512793i \(0.171389\pi\)
\(308\) 240.000 415.692i 0.0444002 0.0769034i
\(309\) 0 0
\(310\) 1500.00 + 2598.08i 0.274820 + 0.476003i
\(311\) −768.000 1330.22i −0.140030 0.242539i 0.787478 0.616343i \(-0.211387\pi\)
−0.927508 + 0.373804i \(0.878053\pi\)
\(312\) 0 0
\(313\) 3671.00 6358.36i 0.662930 1.14823i −0.316912 0.948455i \(-0.602646\pi\)
0.979842 0.199774i \(-0.0640208\pi\)
\(314\) 7134.00 1.28215
\(315\) 0 0
\(316\) −520.000 −0.0925705
\(317\) 1947.00 3372.30i 0.344967 0.597500i −0.640381 0.768057i \(-0.721224\pi\)
0.985348 + 0.170558i \(0.0545569\pi\)
\(318\) 0 0
\(319\) −936.000 1621.20i −0.164282 0.284545i
\(320\) 1082.50 + 1874.94i 0.189105 + 0.327539i
\(321\) 0 0
\(322\) 3600.00 6235.38i 0.623044 1.07914i
\(323\) −6696.00 −1.15348
\(324\) 0 0
\(325\) 1850.00 0.315752
\(326\) 78.0000 135.100i 0.0132516 0.0229524i
\(327\) 0 0
\(328\) 3465.00 + 6001.56i 0.583301 + 1.01031i
\(329\) 240.000 + 415.692i 0.0402177 + 0.0696591i
\(330\) 0 0
\(331\) −1846.00 + 3197.37i −0.306542 + 0.530946i −0.977603 0.210456i \(-0.932505\pi\)
0.671062 + 0.741402i \(0.265839\pi\)
\(332\) 156.000 0.0257880
\(333\) 0 0
\(334\) −11160.0 −1.82829
\(335\) −490.000 + 848.705i −0.0799151 + 0.138417i
\(336\) 0 0
\(337\) 4499.00 + 7792.50i 0.727229 + 1.25960i 0.958050 + 0.286601i \(0.0925255\pi\)
−0.230821 + 0.972996i \(0.574141\pi\)
\(338\) −4918.50 8519.09i −0.791512 1.37094i
\(339\) 0 0
\(340\) 135.000 233.827i 0.0215335 0.0372972i
\(341\) −4800.00 −0.762271
\(342\) 0 0
\(343\) −5720.00 −0.900440
\(344\) 966.000 1673.16i 0.151405 0.262241i
\(345\) 0 0
\(346\) −639.000 1106.78i −0.0992857 0.171968i
\(347\) −2622.00 4541.44i −0.405638 0.702585i 0.588758 0.808310i \(-0.299617\pi\)
−0.994395 + 0.105724i \(0.966284\pi\)
\(348\) 0 0
\(349\) −3151.00 + 5457.69i −0.483293 + 0.837088i −0.999816 0.0191856i \(-0.993893\pi\)
0.516523 + 0.856273i \(0.327226\pi\)
\(350\) 1500.00 0.229081
\(351\) 0 0
\(352\) 1080.00 0.163535
\(353\) −1707.00 + 2956.61i −0.257378 + 0.445792i −0.965539 0.260259i \(-0.916192\pi\)
0.708161 + 0.706051i \(0.249525\pi\)
\(354\) 0 0
\(355\) −720.000 1247.08i −0.107644 0.186445i
\(356\) −513.000 888.542i −0.0763734 0.132283i
\(357\) 0 0
\(358\) 2160.00 3741.23i 0.318881 0.552319i
\(359\) 4824.00 0.709195 0.354597 0.935019i \(-0.384618\pi\)
0.354597 + 0.935019i \(0.384618\pi\)
\(360\) 0 0
\(361\) 8517.00 1.24173
\(362\) 4695.00 8131.98i 0.681668 1.18068i
\(363\) 0 0
\(364\) −740.000 1281.72i −0.106556 0.184561i
\(365\) −1075.00 1861.95i −0.154159 0.267011i
\(366\) 0 0
\(367\) 1754.00 3038.02i 0.249477 0.432107i −0.713904 0.700244i \(-0.753075\pi\)
0.963381 + 0.268137i \(0.0864080\pi\)
\(368\) 8520.00 1.20689
\(369\) 0 0
\(370\) 1050.00 0.147532
\(371\) −4500.00 + 7794.23i −0.629726 + 1.09072i
\(372\) 0 0
\(373\) −5401.00 9354.81i −0.749740 1.29859i −0.947947 0.318428i \(-0.896845\pi\)
0.198207 0.980160i \(-0.436488\pi\)
\(374\) 1944.00 + 3367.11i 0.268775 + 0.465532i
\(375\) 0 0
\(376\) −252.000 + 436.477i −0.0345636 + 0.0598659i
\(377\) −5772.00 −0.788523
\(378\) 0 0
\(379\) 1460.00 0.197876 0.0989382 0.995094i \(-0.468455\pi\)
0.0989382 + 0.995094i \(0.468455\pi\)
\(380\) −310.000 + 536.936i −0.0418491 + 0.0724848i
\(381\) 0 0
\(382\) −5364.00 9290.72i −0.718445 1.24438i
\(383\) 2436.00 + 4219.28i 0.324997 + 0.562911i 0.981512 0.191402i \(-0.0613034\pi\)
−0.656515 + 0.754313i \(0.727970\pi\)
\(384\) 0 0
\(385\) −1200.00 + 2078.46i −0.158851 + 0.275138i
\(386\) 7998.00 1.05463
\(387\) 0 0
\(388\) −286.000 −0.0374213
\(389\) 7023.00 12164.2i 0.915373 1.58547i 0.109020 0.994040i \(-0.465229\pi\)
0.806354 0.591434i \(-0.201438\pi\)
\(390\) 0 0
\(391\) 3240.00 + 5611.84i 0.419064 + 0.725839i
\(392\) 598.500 + 1036.63i 0.0771143 + 0.133566i
\(393\) 0 0
\(394\) 4077.00 7061.57i 0.521310 0.902936i
\(395\) 2600.00 0.331190
\(396\) 0 0
\(397\) −2734.00 −0.345631 −0.172816 0.984954i \(-0.555286\pi\)
−0.172816 + 0.984954i \(0.555286\pi\)
\(398\) 5748.00 9955.83i 0.723923 1.25387i
\(399\) 0 0
\(400\) 887.500 + 1537.20i 0.110937 + 0.192149i
\(401\) 7971.00 + 13806.2i 0.992650 + 1.71932i 0.601130 + 0.799151i \(0.294717\pi\)
0.391520 + 0.920170i \(0.371949\pi\)
\(402\) 0 0
\(403\) −7400.00 + 12817.2i −0.914690 + 1.58429i
\(404\) −1734.00 −0.213539
\(405\) 0 0
\(406\) −4680.00 −0.572080
\(407\) −840.000 + 1454.92i −0.102303 + 0.177194i
\(408\) 0 0
\(409\) −4357.00 7546.55i −0.526748 0.912354i −0.999514 0.0311660i \(-0.990078\pi\)
0.472767 0.881188i \(-0.343255\pi\)
\(410\) 2475.00 + 4286.83i 0.298126 + 0.516369i
\(411\) 0 0
\(412\) −226.000 + 391.443i −0.0270248 + 0.0468083i
\(413\) 480.000 0.0571895
\(414\) 0 0
\(415\) −780.000 −0.0922619
\(416\) 1665.00 2883.86i 0.196234 0.339887i
\(417\) 0 0
\(418\) −4464.00 7731.87i −0.522348 0.904733i
\(419\) −5988.00 10371.5i −0.698169 1.20926i −0.969101 0.246666i \(-0.920665\pi\)
0.270931 0.962599i \(-0.412668\pi\)
\(420\) 0 0
\(421\) −5527.00 + 9573.04i −0.639833 + 1.10822i 0.345637 + 0.938368i \(0.387663\pi\)
−0.985469 + 0.169854i \(0.945670\pi\)
\(422\) 3300.00 0.380667
\(423\) 0 0
\(424\) −9450.00 −1.08239
\(425\) −675.000 + 1169.13i −0.0770407 + 0.133438i
\(426\) 0 0
\(427\) 3220.00 + 5577.20i 0.364934 + 0.632084i
\(428\) 702.000 + 1215.90i 0.0792814 + 0.137319i
\(429\) 0 0
\(430\) 690.000 1195.12i 0.0773832 0.134032i
\(431\) 720.000 0.0804668 0.0402334 0.999190i \(-0.487190\pi\)
0.0402334 + 0.999190i \(0.487190\pi\)
\(432\) 0 0
\(433\) −15622.0 −1.73382 −0.866912 0.498462i \(-0.833898\pi\)
−0.866912 + 0.498462i \(0.833898\pi\)
\(434\) −6000.00 + 10392.3i −0.663616 + 1.14942i
\(435\) 0 0
\(436\) 737.000 + 1276.52i 0.0809539 + 0.140216i
\(437\) −7440.00 12886.5i −0.814424 1.41062i
\(438\) 0 0
\(439\) 4940.00 8556.33i 0.537069 0.930231i −0.461991 0.886885i \(-0.652865\pi\)
0.999060 0.0433464i \(-0.0138019\pi\)
\(440\) −2520.00 −0.273037
\(441\) 0 0
\(442\) 11988.0 1.29007
\(443\) 8058.00 13956.9i 0.864215 1.49686i −0.00361002 0.999993i \(-0.501149\pi\)
0.867825 0.496870i \(-0.165518\pi\)
\(444\) 0 0
\(445\) 2565.00 + 4442.71i 0.273242 + 0.473269i
\(446\) −2946.00 5102.62i −0.312774 0.541740i
\(447\) 0 0
\(448\) −4330.00 + 7499.78i −0.456637 + 0.790918i
\(449\) 9018.00 0.947852 0.473926 0.880565i \(-0.342836\pi\)
0.473926 + 0.880565i \(0.342836\pi\)
\(450\) 0 0
\(451\) −7920.00 −0.826914
\(452\) −543.000 + 940.504i −0.0565057 + 0.0978707i
\(453\) 0 0
\(454\) −990.000 1714.73i −0.102341 0.177261i
\(455\) 3700.00 + 6408.59i 0.381228 + 0.660306i
\(456\) 0 0
\(457\) 1835.00 3178.31i 0.187829 0.325329i −0.756697 0.653765i \(-0.773188\pi\)
0.944526 + 0.328437i \(0.106522\pi\)
\(458\) −5718.00 −0.583372
\(459\) 0 0
\(460\) 600.000 0.0608155
\(461\) −8781.00 + 15209.1i −0.887141 + 1.53657i −0.0439008 + 0.999036i \(0.513979\pi\)
−0.843240 + 0.537537i \(0.819355\pi\)
\(462\) 0 0
\(463\) −586.000 1014.98i −0.0588202 0.101879i 0.835116 0.550074i \(-0.185401\pi\)
−0.893936 + 0.448195i \(0.852067\pi\)
\(464\) −2769.00 4796.05i −0.277042 0.479851i
\(465\) 0 0
\(466\) 2187.00 3788.00i 0.217405 0.376557i
\(467\) 6876.00 0.681335 0.340667 0.940184i \(-0.389347\pi\)
0.340667 + 0.940184i \(0.389347\pi\)
\(468\) 0 0
\(469\) −3920.00 −0.385946
\(470\) −180.000 + 311.769i −0.0176655 + 0.0305975i
\(471\) 0 0
\(472\) 252.000 + 436.477i 0.0245747 + 0.0425646i
\(473\) 1104.00 + 1912.18i 0.107319 + 0.185882i
\(474\) 0 0
\(475\) 1550.00 2684.68i 0.149724 0.259329i
\(476\) 1080.00 0.103995
\(477\) 0 0
\(478\) 3528.00 0.337588
\(479\) −1140.00 + 1974.54i −0.108743 + 0.188349i −0.915261 0.402861i \(-0.868016\pi\)
0.806518 + 0.591209i \(0.201349\pi\)
\(480\) 0 0
\(481\) 2590.00 + 4486.01i 0.245517 + 0.425248i
\(482\) −1299.00 2249.93i −0.122755 0.212618i
\(483\) 0 0
\(484\) 377.500 653.849i 0.0354527 0.0614058i
\(485\) 1430.00 0.133882
\(486\) 0 0
\(487\) −3076.00 −0.286215 −0.143108 0.989707i \(-0.545710\pi\)
−0.143108 + 0.989707i \(0.545710\pi\)
\(488\) −3381.00 + 5856.06i −0.313628 + 0.543220i
\(489\) 0 0
\(490\) 427.500 + 740.452i 0.0394132 + 0.0682657i
\(491\) 9456.00 + 16378.3i 0.869131 + 1.50538i 0.862886 + 0.505398i \(0.168654\pi\)
0.00624491 + 0.999981i \(0.498012\pi\)
\(492\) 0 0
\(493\) 2106.00 3647.70i 0.192392 0.333233i
\(494\) −27528.0 −2.50717
\(495\) 0 0
\(496\) −14200.0 −1.28548
\(497\) 2880.00 4988.31i 0.259931 0.450214i
\(498\) 0 0
\(499\) −4978.00 8622.15i −0.446585 0.773508i 0.551576 0.834125i \(-0.314027\pi\)
−0.998161 + 0.0606167i \(0.980693\pi\)
\(500\) 62.5000 + 108.253i 0.00559017 + 0.00968246i
\(501\) 0 0
\(502\) −648.000 + 1122.37i −0.0576129 + 0.0997884i
\(503\) −10656.0 −0.944588 −0.472294 0.881441i \(-0.656574\pi\)
−0.472294 + 0.881441i \(0.656574\pi\)
\(504\) 0 0
\(505\) 8670.00 0.763980
\(506\) −4320.00 + 7482.46i −0.379540 + 0.657383i
\(507\) 0 0
\(508\) −622.000 1077.34i −0.0543244 0.0940926i
\(509\) 1383.00 + 2395.43i 0.120433 + 0.208596i 0.919939 0.392063i \(-0.128238\pi\)
−0.799506 + 0.600659i \(0.794905\pi\)
\(510\) 0 0
\(511\) 4300.00 7447.82i 0.372252 0.644759i
\(512\) −8733.00 −0.753804
\(513\) 0 0
\(514\) 7578.00 0.650294
\(515\) 1130.00 1957.22i 0.0966869 0.167467i
\(516\) 0 0
\(517\) −288.000 498.831i −0.0244995 0.0424343i
\(518\) 2100.00 + 3637.31i 0.178125 + 0.308521i
\(519\) 0 0
\(520\) −3885.00 + 6729.02i −0.327632 + 0.567475i
\(521\) 10530.0 0.885466 0.442733 0.896654i \(-0.354009\pi\)
0.442733 + 0.896654i \(0.354009\pi\)
\(522\) 0 0
\(523\) 12692.0 1.06115 0.530576 0.847637i \(-0.321976\pi\)
0.530576 + 0.847637i \(0.321976\pi\)
\(524\) −1164.00 + 2016.11i −0.0970412 + 0.168080i
\(525\) 0 0
\(526\) −8172.00 14154.3i −0.677407 1.17330i
\(527\) −5400.00 9353.07i −0.446352 0.773105i
\(528\) 0 0
\(529\) −1116.50 + 1933.83i −0.0917646 + 0.158941i
\(530\) −6750.00 −0.553210
\(531\) 0 0
\(532\) −2480.00 −0.202108
\(533\) −12210.0 + 21148.3i −0.992259 + 1.71864i
\(534\) 0 0
\(535\) −3510.00 6079.50i −0.283646 0.491289i
\(536\) −2058.00 3564.56i −0.165843 0.287249i
\(537\) 0 0
\(538\) 3861.00 6687.45i 0.309404 0.535904i
\(539\) −1368.00 −0.109321
\(540\) 0 0
\(541\) 18110.0 1.43920 0.719602 0.694386i \(-0.244324\pi\)
0.719602 + 0.694386i \(0.244324\pi\)
\(542\) 4776.00 8272.27i 0.378500 0.655580i
\(543\) 0 0
\(544\) 1215.00 + 2104.44i 0.0957586 + 0.165859i
\(545\) −3685.00 6382.61i −0.289629 0.501653i
\(546\) 0 0
\(547\) −1810.00 + 3135.01i −0.141481 + 0.245052i −0.928054 0.372445i \(-0.878520\pi\)
0.786574 + 0.617496i \(0.211853\pi\)
\(548\) 2118.00 0.165103
\(549\) 0 0
\(550\) −1800.00 −0.139550
\(551\) −4836.00 + 8376.20i −0.373903 + 0.647619i
\(552\) 0 0
\(553\) 5200.00 + 9006.66i 0.399867 + 0.692590i
\(554\) −5943.00 10293.6i −0.455765 0.789408i
\(555\) 0 0
\(556\) −1162.00 + 2012.64i −0.0886327 + 0.153516i
\(557\) −14166.0 −1.07762 −0.538809 0.842428i \(-0.681125\pi\)
−0.538809 + 0.842428i \(0.681125\pi\)
\(558\) 0 0
\(559\) 6808.00 0.515112
\(560\) −3550.00 + 6148.78i −0.267884 + 0.463988i
\(561\) 0 0
\(562\) 12429.0 + 21527.7i 0.932893 + 1.61582i
\(563\) 6702.00 + 11608.2i 0.501697 + 0.868965i 0.999998 + 0.00196107i \(0.000624229\pi\)
−0.498301 + 0.867004i \(0.666042\pi\)
\(564\) 0 0
\(565\) 2715.00 4702.52i 0.202161 0.350153i
\(566\) −8148.00 −0.605099
\(567\) 0 0
\(568\) 6048.00 0.446775
\(569\) 9327.00 16154.8i 0.687185 1.19024i −0.285560 0.958361i \(-0.592180\pi\)
0.972745 0.231878i \(-0.0744871\pi\)
\(570\) 0 0
\(571\) 3842.00 + 6654.54i 0.281581 + 0.487712i 0.971774 0.235913i \(-0.0758079\pi\)
−0.690193 + 0.723625i \(0.742475\pi\)
\(572\) 888.000 + 1538.06i 0.0649111 + 0.112429i
\(573\) 0 0
\(574\) −9900.00 + 17147.3i −0.719892 + 1.24689i
\(575\) −3000.00 −0.217580
\(576\) 0 0
\(577\) −1726.00 −0.124531 −0.0622654 0.998060i \(-0.519833\pi\)
−0.0622654 + 0.998060i \(0.519833\pi\)
\(578\) 2995.50 5188.36i 0.215565 0.373369i
\(579\) 0 0
\(580\) −195.000 337.750i −0.0139602 0.0241798i
\(581\) −1560.00 2702.00i −0.111394 0.192939i
\(582\) 0 0
\(583\) 5400.00 9353.07i 0.383611 0.664434i
\(584\) 9030.00 0.639836
\(585\) 0 0
\(586\) 18054.0 1.27270
\(587\) −5298.00 + 9176.41i −0.372524 + 0.645231i −0.989953 0.141396i \(-0.954841\pi\)
0.617429 + 0.786627i \(0.288174\pi\)
\(588\) 0 0
\(589\) 12400.0 + 21477.4i 0.867459 + 1.50248i
\(590\) 180.000 + 311.769i 0.0125601 + 0.0217548i
\(591\) 0 0
\(592\) −2485.00 + 4304.15i −0.172522 + 0.298816i
\(593\) 2862.00 0.198193 0.0990963 0.995078i \(-0.468405\pi\)
0.0990963 + 0.995078i \(0.468405\pi\)
\(594\) 0 0
\(595\) −5400.00 −0.372065
\(596\) −129.000 + 223.435i −0.00886585 + 0.0153561i
\(597\) 0 0
\(598\) 13320.0 + 23070.9i 0.910862 + 1.57766i
\(599\) 11796.0 + 20431.3i 0.804627 + 1.39365i 0.916543 + 0.399937i \(0.130968\pi\)
−0.111916 + 0.993718i \(0.535699\pi\)
\(600\) 0 0
\(601\) 4787.00 8291.33i 0.324902 0.562746i −0.656591 0.754247i \(-0.728002\pi\)
0.981492 + 0.191501i \(0.0613355\pi\)
\(602\) 5520.00 0.373718
\(603\) 0 0
\(604\) −808.000 −0.0544322
\(605\) −1887.50 + 3269.25i −0.126839 + 0.219692i
\(606\) 0 0
\(607\) −8722.00 15106.9i −0.583221 1.01017i −0.995095 0.0989273i \(-0.968459\pi\)
0.411874 0.911241i \(-0.364874\pi\)
\(608\) −2790.00 4832.42i −0.186101 0.322336i
\(609\) 0 0
\(610\) −2415.00 + 4182.90i −0.160296 + 0.277641i
\(611\) −1776.00 −0.117593
\(612\) 0 0
\(613\) −2374.00 −0.156419 −0.0782096 0.996937i \(-0.524920\pi\)
−0.0782096 + 0.996937i \(0.524920\pi\)
\(614\) −13854.0 + 23995.8i −0.910589 + 1.57719i
\(615\) 0 0
\(616\) −5040.00 8729.54i −0.329655 0.570979i
\(617\) 6081.00 + 10532.6i 0.396778 + 0.687239i 0.993326 0.115338i \(-0.0367951\pi\)
−0.596549 + 0.802577i \(0.703462\pi\)
\(618\) 0 0
\(619\) −4402.00 + 7624.49i −0.285834 + 0.495079i −0.972811 0.231600i \(-0.925604\pi\)
0.686977 + 0.726679i \(0.258937\pi\)
\(620\) −1000.00 −0.0647758
\(621\) 0 0
\(622\) 4608.00 0.297048
\(623\) −10260.0 + 17770.8i −0.659805 + 1.14281i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 11013.0 + 19075.1i 0.703144 + 1.21788i
\(627\) 0 0
\(628\) −1189.00 + 2059.41i −0.0755514 + 0.130859i
\(629\) −3780.00 −0.239616
\(630\) 0 0
\(631\) −12688.0 −0.800478 −0.400239 0.916411i \(-0.631073\pi\)
−0.400239 + 0.916411i \(0.631073\pi\)
\(632\) −5460.00 + 9457.00i −0.343651 + 0.595220i
\(633\) 0 0
\(634\) 5841.00 + 10116.9i 0.365892 + 0.633744i
\(635\) 3110.00 + 5386.68i 0.194357 + 0.336636i
\(636\) 0 0
\(637\) −2109.00 + 3652.90i −0.131180 + 0.227210i
\(638\) 5616.00 0.348495
\(639\) 0 0
\(640\) −8295.00 −0.512326
\(641\) 4575.00 7924.13i 0.281906 0.488275i −0.689948 0.723859i \(-0.742367\pi\)
0.971854 + 0.235583i \(0.0757001\pi\)
\(642\) 0 0
\(643\) −12646.0 21903.5i −0.775598 1.34338i −0.934458 0.356074i \(-0.884115\pi\)
0.158860 0.987301i \(-0.449218\pi\)
\(644\) 1200.00 + 2078.46i 0.0734264 + 0.127178i
\(645\) 0 0
\(646\) 10044.0 17396.7i 0.611727 1.05954i
\(647\) −2736.00 −0.166249 −0.0831246 0.996539i \(-0.526490\pi\)
−0.0831246 + 0.996539i \(0.526490\pi\)
\(648\) 0 0
\(649\) −576.000 −0.0348382
\(650\) −2775.00 + 4806.44i −0.167453 + 0.290037i
\(651\) 0 0
\(652\) 26.0000 + 45.0333i 0.00156172 + 0.00270497i
\(653\) −11109.0 19241.4i −0.665741 1.15310i −0.979084 0.203457i \(-0.934782\pi\)
0.313343 0.949640i \(-0.398551\pi\)
\(654\) 0 0
\(655\) 5820.00 10080.5i 0.347185 0.601342i
\(656\) −23430.0 −1.39449
\(657\) 0 0
\(658\) −1440.00 −0.0853147
\(659\) −7260.00 + 12574.7i −0.429149 + 0.743309i −0.996798 0.0799625i \(-0.974520\pi\)
0.567648 + 0.823271i \(0.307853\pi\)
\(660\) 0 0
\(661\) 5309.00 + 9195.46i 0.312400 + 0.541092i 0.978881 0.204429i \(-0.0655339\pi\)
−0.666482 + 0.745521i \(0.732201\pi\)
\(662\) −5538.00 9592.10i −0.325137 0.563153i
\(663\) 0 0
\(664\) 1638.00 2837.10i 0.0957330 0.165814i
\(665\) 12400.0 0.723085
\(666\) 0 0
\(667\) 9360.00 0.543359
\(668\) 1860.00 3221.61i 0.107733 0.186599i
\(669\) 0 0
\(670\) −1470.00 2546.11i −0.0847628 0.146813i
\(671\) −3864.00 6692.64i −0.222307 0.385047i
\(672\) 0 0
\(673\) −685.000 + 1186.45i −0.0392345 + 0.0679561i −0.884976 0.465637i \(-0.845825\pi\)
0.845741 + 0.533593i \(0.179159\pi\)
\(674\) −26994.0 −1.54269
\(675\) 0 0
\(676\) 3279.00 0.186561
\(677\) 6879.00 11914.8i 0.390519 0.676399i −0.601999 0.798497i \(-0.705629\pi\)
0.992518 + 0.122098i \(0.0389622\pi\)
\(678\) 0 0
\(679\) 2860.00 + 4953.67i 0.161645 + 0.279977i
\(680\) −2835.00 4910.36i −0.159878 0.276917i
\(681\) 0 0
\(682\) 7200.00 12470.8i 0.404255 0.700191i
\(683\) 11988.0 0.671608 0.335804 0.941932i \(-0.390992\pi\)
0.335804 + 0.941932i \(0.390992\pi\)
\(684\) 0 0
\(685\) −10590.0 −0.590691
\(686\) 8580.00 14861.0i 0.477530 0.827107i
\(687\) 0 0
\(688\) 3266.00 + 5656.88i 0.180981 + 0.313469i
\(689\) −16650.0 28838.6i −0.920631 1.59458i
\(690\) 0 0
\(691\) −16498.0 + 28575.4i −0.908268 + 1.57317i −0.0917997 + 0.995777i \(0.529262\pi\)
−0.816469 + 0.577390i \(0.804071\pi\)
\(692\) 426.000 0.0234019
\(693\) 0 0
\(694\) 15732.0 0.860488
\(695\) 5810.00 10063.2i 0.317102 0.549237i
\(696\) 0 0
\(697\) −8910.00 15432.6i −0.484204 0.838666i
\(698\) −9453.00 16373.1i −0.512609 0.887865i
\(699\) 0 0
\(700\) −250.000 + 433.013i −0.0134987 + 0.0233805i
\(701\) −25902.0 −1.39558 −0.697792 0.716300i \(-0.745834\pi\)
−0.697792 + 0.716300i \(0.745834\pi\)
\(702\) 0 0
\(703\) 8680.00 0.465679
\(704\) 5196.00 8999.74i 0.278170 0.481804i
\(705\) 0 0
\(706\) −5121.00 8869.83i −0.272991 0.472834i
\(707\) 17340.0 + 30033.8i 0.922401 + 1.59765i
\(708\) 0 0
\(709\) 13697.0 23723.9i 0.725531 1.25666i −0.233224 0.972423i \(-0.574927\pi\)
0.958755 0.284234i \(-0.0917392\pi\)
\(710\) 4320.00 0.228347
\(711\) 0 0
\(712\) −21546.0 −1.13409
\(713\) 12000.0 20784.6i 0.630299 1.09171i
\(714\) 0 0
\(715\) −4440.00 7690.31i −0.232233 0.402239i
\(716\) 720.000 + 1247.08i 0.0375805 + 0.0650914i
\(717\) 0 0
\(718\) −7236.00 + 12533.1i −0.376107 + 0.651437i
\(719\) 34848.0 1.80753 0.903763 0.428033i \(-0.140793\pi\)
0.903763 + 0.428033i \(0.140793\pi\)
\(720\) 0 0
\(721\) 9040.00 0.466945
\(722\) −12775.5 + 22127.8i −0.658525 + 1.14060i
\(723\) 0 0
\(724\) 1565.00 + 2710.66i 0.0803353 + 0.139145i
\(725\) 975.000 + 1688.75i 0.0499456 + 0.0865084i
\(726\) 0 0
\(727\) −14014.0 + 24273.0i −0.714925 + 1.23829i 0.248063 + 0.968744i \(0.420206\pi\)
−0.962988 + 0.269543i \(0.913127\pi\)
\(728\) −31080.0 −1.58228
\(729\) 0 0
\(730\) 6450.00 0.327021
\(731\) −2484.00 + 4302.41i −0.125683 + 0.217689i
\(732\) 0 0
\(733\) −9001.00 15590.2i −0.453560 0.785589i 0.545044 0.838407i \(-0.316513\pi\)
−0.998604 + 0.0528183i \(0.983180\pi\)
\(734\) 5262.00 + 9114.05i 0.264610 + 0.458318i
\(735\) 0 0
\(736\) −2700.00 + 4676.54i −0.135222 + 0.234211i
\(737\) 4704.00 0.235107
\(738\) 0 0
\(739\) 15284.0 0.760800 0.380400 0.924822i \(-0.375786\pi\)
0.380400 + 0.924822i \(0.375786\pi\)
\(740\) −175.000 + 303.109i −0.00869342 + 0.0150574i
\(741\) 0 0
\(742\) −13500.0 23382.7i −0.667925 1.15688i
\(743\) 9384.00 + 16253.6i 0.463345 + 0.802538i 0.999125 0.0418201i \(-0.0133156\pi\)
−0.535780 + 0.844358i \(0.679982\pi\)
\(744\) 0 0
\(745\) 645.000 1117.17i 0.0317194 0.0549397i
\(746\) 32406.0 1.59044
\(747\) 0 0
\(748\) −1296.00 −0.0633509
\(749\) 14040.0 24318.0i 0.684927 1.18633i
\(750\) 0 0
\(751\) −4348.00 7530.96i −0.211266 0.365923i 0.740845 0.671676i \(-0.234425\pi\)
−0.952111 + 0.305753i \(0.901092\pi\)
\(752\) −852.000 1475.71i −0.0413155 0.0715605i
\(753\) 0 0
\(754\) 8658.00 14996.1i 0.418177 0.724305i
\(755\) 4040.00 0.194743
\(756\) 0 0
\(757\) −38662.0 −1.85627 −0.928134 0.372247i \(-0.878587\pi\)
−0.928134 + 0.372247i \(0.878587\pi\)
\(758\) −2190.00 + 3793.19i −0.104940 + 0.181761i
\(759\) 0 0
\(760\) 6510.00 + 11275.7i 0.310714 + 0.538172i
\(761\) −11937.0 20675.5i −0.568615 0.984870i −0.996703 0.0811330i \(-0.974146\pi\)
0.428088 0.903737i \(-0.359187\pi\)
\(762\) 0 0
\(763\) 14740.0 25530.4i 0.699376 1.21135i
\(764\) 3576.00 0.169339
\(765\) 0 0
\(766\) −14616.0 −0.689422
\(767\) −888.000 + 1538.06i −0.0418042 + 0.0724070i
\(768\) 0 0
\(769\) −11809.0 20453.8i −0.553763 0.959145i −0.997999 0.0632352i \(-0.979858\pi\)
0.444236 0.895910i \(-0.353475\pi\)
\(770\) −3600.00 6235.38i −0.168487 0.291828i
\(771\) 0 0
\(772\) −1333.00 + 2308.82i −0.0621447 + 0.107638i
\(773\) 11538.0 0.536860 0.268430 0.963299i \(-0.413495\pi\)
0.268430 + 0.963299i \(0.413495\pi\)
\(774\) 0 0
\(775\) 5000.00 0.231749
\(776\) −3003.00 + 5201.35i −0.138919 + 0.240615i
\(777\) 0 0
\(778\) 21069.0 + 36492.6i 0.970900 + 1.68165i
\(779\) 20460.0 + 35437.8i 0.941021 + 1.62990i
\(780\) 0 0
\(781\) −3456.00 + 5985.97i −0.158342 + 0.274257i
\(782\) −19440.0 −0.888968
\(783\) 0 0
\(784\) −4047.00 −0.184357
\(785\) 5945.00