Properties

Label 624.4.q.b.529.1
Level $624$
Weight $4$
Character 624.529
Analytic conductor $36.817$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(36.8171918436\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 624.529
Dual form 624.4.q.b.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} -9.00000 q^{5} +(1.00000 + 1.73205i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} -9.00000 q^{5} +(1.00000 + 1.73205i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(15.0000 - 25.9808i) q^{11} +(32.5000 + 33.7750i) q^{13} +(-13.5000 + 23.3827i) q^{15} +(55.5000 + 96.1288i) q^{17} +(-23.0000 - 39.8372i) q^{19} +6.00000 q^{21} +(-3.00000 + 5.19615i) q^{23} -44.0000 q^{25} -27.0000 q^{27} +(52.5000 - 90.9327i) q^{29} +100.000 q^{31} +(-45.0000 - 77.9423i) q^{33} +(-9.00000 - 15.5885i) q^{35} +(-8.50000 + 14.7224i) q^{37} +(136.500 - 33.7750i) q^{39} +(115.500 - 200.052i) q^{41} +(-257.000 - 445.137i) q^{43} +(40.5000 + 70.1481i) q^{45} +162.000 q^{47} +(169.500 - 293.583i) q^{49} +333.000 q^{51} +639.000 q^{53} +(-135.000 + 233.827i) q^{55} -138.000 q^{57} +(300.000 + 519.615i) q^{59} +(-116.500 - 201.784i) q^{61} +(9.00000 - 15.5885i) q^{63} +(-292.500 - 303.975i) q^{65} +(463.000 - 801.940i) q^{67} +(9.00000 + 15.5885i) q^{69} +(-465.000 - 805.404i) q^{71} -253.000 q^{73} +(-66.0000 + 114.315i) q^{75} +60.0000 q^{77} +1324.00 q^{79} +(-40.5000 + 70.1481i) q^{81} -810.000 q^{83} +(-499.500 - 865.159i) q^{85} +(-157.500 - 272.798i) q^{87} +(-249.000 + 431.281i) q^{89} +(-26.0000 + 90.0666i) q^{91} +(150.000 - 259.808i) q^{93} +(207.000 + 358.535i) q^{95} +(-679.000 - 1176.06i) q^{97} -270.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} - 18 q^{5} + 2 q^{7} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} - 18 q^{5} + 2 q^{7} - 9 q^{9} + 30 q^{11} + 65 q^{13} - 27 q^{15} + 111 q^{17} - 46 q^{19} + 12 q^{21} - 6 q^{23} - 88 q^{25} - 54 q^{27} + 105 q^{29} + 200 q^{31} - 90 q^{33} - 18 q^{35} - 17 q^{37} + 273 q^{39} + 231 q^{41} - 514 q^{43} + 81 q^{45} + 324 q^{47} + 339 q^{49} + 666 q^{51} + 1278 q^{53} - 270 q^{55} - 276 q^{57} + 600 q^{59} - 233 q^{61} + 18 q^{63} - 585 q^{65} + 926 q^{67} + 18 q^{69} - 930 q^{71} - 506 q^{73} - 132 q^{75} + 120 q^{77} + 2648 q^{79} - 81 q^{81} - 1620 q^{83} - 999 q^{85} - 315 q^{87} - 498 q^{89} - 52 q^{91} + 300 q^{93} + 414 q^{95} - 1358 q^{97} - 540 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) 0 0
\(5\) −9.00000 −0.804984 −0.402492 0.915423i \(-0.631856\pi\)
−0.402492 + 0.915423i \(0.631856\pi\)
\(6\) 0 0
\(7\) 1.00000 + 1.73205i 0.0539949 + 0.0935220i 0.891760 0.452510i \(-0.149471\pi\)
−0.837765 + 0.546032i \(0.816138\pi\)
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) 15.0000 25.9808i 0.411152 0.712136i −0.583864 0.811851i \(-0.698460\pi\)
0.995016 + 0.0997155i \(0.0317933\pi\)
\(12\) 0 0
\(13\) 32.5000 + 33.7750i 0.693375 + 0.720577i
\(14\) 0 0
\(15\) −13.5000 + 23.3827i −0.232379 + 0.402492i
\(16\) 0 0
\(17\) 55.5000 + 96.1288i 0.791807 + 1.37145i 0.924847 + 0.380340i \(0.124193\pi\)
−0.133039 + 0.991111i \(0.542474\pi\)
\(18\) 0 0
\(19\) −23.0000 39.8372i −0.277714 0.481014i 0.693102 0.720839i \(-0.256243\pi\)
−0.970816 + 0.239825i \(0.922910\pi\)
\(20\) 0 0
\(21\) 6.00000 0.0623480
\(22\) 0 0
\(23\) −3.00000 + 5.19615i −0.0271975 + 0.0471075i −0.879304 0.476261i \(-0.841992\pi\)
0.852106 + 0.523369i \(0.175325\pi\)
\(24\) 0 0
\(25\) −44.0000 −0.352000
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 52.5000 90.9327i 0.336173 0.582268i −0.647537 0.762034i \(-0.724201\pi\)
0.983709 + 0.179766i \(0.0575341\pi\)
\(30\) 0 0
\(31\) 100.000 0.579372 0.289686 0.957122i \(-0.406449\pi\)
0.289686 + 0.957122i \(0.406449\pi\)
\(32\) 0 0
\(33\) −45.0000 77.9423i −0.237379 0.411152i
\(34\) 0 0
\(35\) −9.00000 15.5885i −0.0434651 0.0752837i
\(36\) 0 0
\(37\) −8.50000 + 14.7224i −0.0377673 + 0.0654149i −0.884291 0.466936i \(-0.845358\pi\)
0.846524 + 0.532351i \(0.178691\pi\)
\(38\) 0 0
\(39\) 136.500 33.7750i 0.560449 0.138675i
\(40\) 0 0
\(41\) 115.500 200.052i 0.439953 0.762021i −0.557732 0.830021i \(-0.688328\pi\)
0.997685 + 0.0680000i \(0.0216618\pi\)
\(42\) 0 0
\(43\) −257.000 445.137i −0.911445 1.57867i −0.812024 0.583623i \(-0.801634\pi\)
−0.0994205 0.995046i \(-0.531699\pi\)
\(44\) 0 0
\(45\) 40.5000 + 70.1481i 0.134164 + 0.232379i
\(46\) 0 0
\(47\) 162.000 0.502769 0.251384 0.967887i \(-0.419114\pi\)
0.251384 + 0.967887i \(0.419114\pi\)
\(48\) 0 0
\(49\) 169.500 293.583i 0.494169 0.855926i
\(50\) 0 0
\(51\) 333.000 0.914301
\(52\) 0 0
\(53\) 639.000 1.65610 0.828051 0.560653i \(-0.189450\pi\)
0.828051 + 0.560653i \(0.189450\pi\)
\(54\) 0 0
\(55\) −135.000 + 233.827i −0.330971 + 0.573258i
\(56\) 0 0
\(57\) −138.000 −0.320676
\(58\) 0 0
\(59\) 300.000 + 519.615i 0.661978 + 1.14658i 0.980095 + 0.198527i \(0.0636159\pi\)
−0.318118 + 0.948051i \(0.603051\pi\)
\(60\) 0 0
\(61\) −116.500 201.784i −0.244529 0.423537i 0.717470 0.696590i \(-0.245300\pi\)
−0.961999 + 0.273052i \(0.911967\pi\)
\(62\) 0 0
\(63\) 9.00000 15.5885i 0.0179983 0.0311740i
\(64\) 0 0
\(65\) −292.500 303.975i −0.558156 0.580053i
\(66\) 0 0
\(67\) 463.000 801.940i 0.844246 1.46228i −0.0420292 0.999116i \(-0.513382\pi\)
0.886275 0.463160i \(-0.153284\pi\)
\(68\) 0 0
\(69\) 9.00000 + 15.5885i 0.0157025 + 0.0271975i
\(70\) 0 0
\(71\) −465.000 805.404i −0.777258 1.34625i −0.933516 0.358535i \(-0.883276\pi\)
0.156258 0.987716i \(-0.450057\pi\)
\(72\) 0 0
\(73\) −253.000 −0.405636 −0.202818 0.979216i \(-0.565010\pi\)
−0.202818 + 0.979216i \(0.565010\pi\)
\(74\) 0 0
\(75\) −66.0000 + 114.315i −0.101614 + 0.176000i
\(76\) 0 0
\(77\) 60.0000 0.0888004
\(78\) 0 0
\(79\) 1324.00 1.88559 0.942795 0.333373i \(-0.108187\pi\)
0.942795 + 0.333373i \(0.108187\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −810.000 −1.07119 −0.535597 0.844474i \(-0.679913\pi\)
−0.535597 + 0.844474i \(0.679913\pi\)
\(84\) 0 0
\(85\) −499.500 865.159i −0.637393 1.10400i
\(86\) 0 0
\(87\) −157.500 272.798i −0.194089 0.336173i
\(88\) 0 0
\(89\) −249.000 + 431.281i −0.296561 + 0.513659i −0.975347 0.220677i \(-0.929173\pi\)
0.678786 + 0.734336i \(0.262507\pi\)
\(90\) 0 0
\(91\) −26.0000 + 90.0666i −0.0299510 + 0.103753i
\(92\) 0 0
\(93\) 150.000 259.808i 0.167250 0.289686i
\(94\) 0 0
\(95\) 207.000 + 358.535i 0.223555 + 0.387209i
\(96\) 0 0
\(97\) −679.000 1176.06i −0.710742 1.23104i −0.964579 0.263795i \(-0.915026\pi\)
0.253837 0.967247i \(-0.418307\pi\)
\(98\) 0 0
\(99\) −270.000 −0.274101
\(100\) 0 0
\(101\) 178.500 309.171i 0.175856 0.304591i −0.764601 0.644503i \(-0.777064\pi\)
0.940457 + 0.339913i \(0.110397\pi\)
\(102\) 0 0
\(103\) −1118.00 −1.06951 −0.534756 0.845006i \(-0.679597\pi\)
−0.534756 + 0.845006i \(0.679597\pi\)
\(104\) 0 0
\(105\) −54.0000 −0.0501891
\(106\) 0 0
\(107\) 357.000 618.342i 0.322547 0.558667i −0.658466 0.752610i \(-0.728794\pi\)
0.981013 + 0.193943i \(0.0621277\pi\)
\(108\) 0 0
\(109\) 2006.00 1.76275 0.881376 0.472416i \(-0.156618\pi\)
0.881376 + 0.472416i \(0.156618\pi\)
\(110\) 0 0
\(111\) 25.5000 + 44.1673i 0.0218050 + 0.0377673i
\(112\) 0 0
\(113\) 559.500 + 969.082i 0.465782 + 0.806758i 0.999236 0.0390710i \(-0.0124399\pi\)
−0.533455 + 0.845829i \(0.679107\pi\)
\(114\) 0 0
\(115\) 27.0000 46.7654i 0.0218936 0.0379208i
\(116\) 0 0
\(117\) 117.000 405.300i 0.0924500 0.320256i
\(118\) 0 0
\(119\) −111.000 + 192.258i −0.0855072 + 0.148103i
\(120\) 0 0
\(121\) 215.500 + 373.257i 0.161908 + 0.280433i
\(122\) 0 0
\(123\) −346.500 600.156i −0.254007 0.439953i
\(124\) 0 0
\(125\) 1521.00 1.08834
\(126\) 0 0
\(127\) −302.000 + 523.079i −0.211009 + 0.365479i −0.952031 0.306003i \(-0.901008\pi\)
0.741021 + 0.671481i \(0.234342\pi\)
\(128\) 0 0
\(129\) −1542.00 −1.05245
\(130\) 0 0
\(131\) 1584.00 1.05645 0.528224 0.849105i \(-0.322858\pi\)
0.528224 + 0.849105i \(0.322858\pi\)
\(132\) 0 0
\(133\) 46.0000 79.6743i 0.0299903 0.0519447i
\(134\) 0 0
\(135\) 243.000 0.154919
\(136\) 0 0
\(137\) −358.500 620.940i −0.223567 0.387230i 0.732321 0.680959i \(-0.238437\pi\)
−0.955889 + 0.293729i \(0.905104\pi\)
\(138\) 0 0
\(139\) −410.000 710.141i −0.250185 0.433334i 0.713391 0.700766i \(-0.247158\pi\)
−0.963577 + 0.267432i \(0.913825\pi\)
\(140\) 0 0
\(141\) 243.000 420.888i 0.145137 0.251384i
\(142\) 0 0
\(143\) 1365.00 337.750i 0.798231 0.197511i
\(144\) 0 0
\(145\) −472.500 + 818.394i −0.270614 + 0.468717i
\(146\) 0 0
\(147\) −508.500 880.748i −0.285309 0.494169i
\(148\) 0 0
\(149\) 874.500 + 1514.68i 0.480818 + 0.832801i 0.999758 0.0220100i \(-0.00700656\pi\)
−0.518940 + 0.854811i \(0.673673\pi\)
\(150\) 0 0
\(151\) 370.000 0.199405 0.0997026 0.995017i \(-0.468211\pi\)
0.0997026 + 0.995017i \(0.468211\pi\)
\(152\) 0 0
\(153\) 499.500 865.159i 0.263936 0.457150i
\(154\) 0 0
\(155\) −900.000 −0.466385
\(156\) 0 0
\(157\) −2611.00 −1.32726 −0.663632 0.748059i \(-0.730986\pi\)
−0.663632 + 0.748059i \(0.730986\pi\)
\(158\) 0 0
\(159\) 958.500 1660.17i 0.478075 0.828051i
\(160\) 0 0
\(161\) −12.0000 −0.00587411
\(162\) 0 0
\(163\) −818.000 1416.82i −0.393072 0.680820i 0.599781 0.800164i \(-0.295254\pi\)
−0.992853 + 0.119344i \(0.961921\pi\)
\(164\) 0 0
\(165\) 405.000 + 701.481i 0.191086 + 0.330971i
\(166\) 0 0
\(167\) 132.000 228.631i 0.0611645 0.105940i −0.833822 0.552034i \(-0.813852\pi\)
0.894986 + 0.446094i \(0.147185\pi\)
\(168\) 0 0
\(169\) −84.5000 + 2195.37i −0.0384615 + 0.999260i
\(170\) 0 0
\(171\) −207.000 + 358.535i −0.0925713 + 0.160338i
\(172\) 0 0
\(173\) −705.000 1221.10i −0.309827 0.536637i 0.668497 0.743715i \(-0.266938\pi\)
−0.978324 + 0.207078i \(0.933605\pi\)
\(174\) 0 0
\(175\) −44.0000 76.2102i −0.0190062 0.0329197i
\(176\) 0 0
\(177\) 1800.00 0.764386
\(178\) 0 0
\(179\) −237.000 + 410.496i −0.0989621 + 0.171407i −0.911255 0.411842i \(-0.864886\pi\)
0.812293 + 0.583249i \(0.198219\pi\)
\(180\) 0 0
\(181\) 2249.00 0.923574 0.461787 0.886991i \(-0.347208\pi\)
0.461787 + 0.886991i \(0.347208\pi\)
\(182\) 0 0
\(183\) −699.000 −0.282358
\(184\) 0 0
\(185\) 76.5000 132.502i 0.0304021 0.0526580i
\(186\) 0 0
\(187\) 3330.00 1.30221
\(188\) 0 0
\(189\) −27.0000 46.7654i −0.0103913 0.0179983i
\(190\) 0 0
\(191\) 1722.00 + 2982.59i 0.652354 + 1.12991i 0.982550 + 0.185997i \(0.0595516\pi\)
−0.330197 + 0.943912i \(0.607115\pi\)
\(192\) 0 0
\(193\) 2136.50 3700.53i 0.796832 1.38015i −0.124837 0.992177i \(-0.539841\pi\)
0.921669 0.387977i \(-0.126826\pi\)
\(194\) 0 0
\(195\) −1228.50 + 303.975i −0.451152 + 0.111631i
\(196\) 0 0
\(197\) 993.000 1719.93i 0.359129 0.622029i −0.628687 0.777658i \(-0.716407\pi\)
0.987815 + 0.155630i \(0.0497406\pi\)
\(198\) 0 0
\(199\) −1193.00 2066.34i −0.424973 0.736074i 0.571445 0.820640i \(-0.306383\pi\)
−0.996418 + 0.0845661i \(0.973050\pi\)
\(200\) 0 0
\(201\) −1389.00 2405.82i −0.487425 0.844246i
\(202\) 0 0
\(203\) 210.000 0.0726065
\(204\) 0 0
\(205\) −1039.50 + 1800.47i −0.354155 + 0.613415i
\(206\) 0 0
\(207\) 54.0000 0.0181317
\(208\) 0 0
\(209\) −1380.00 −0.456730
\(210\) 0 0
\(211\) −800.000 + 1385.64i −0.261016 + 0.452092i −0.966512 0.256621i \(-0.917391\pi\)
0.705497 + 0.708713i \(0.250724\pi\)
\(212\) 0 0
\(213\) −2790.00 −0.897501
\(214\) 0 0
\(215\) 2313.00 + 4006.23i 0.733699 + 1.27080i
\(216\) 0 0
\(217\) 100.000 + 173.205i 0.0312831 + 0.0541840i
\(218\) 0 0
\(219\) −379.500 + 657.313i −0.117097 + 0.202818i
\(220\) 0 0
\(221\) −1443.00 + 4998.70i −0.439216 + 1.52149i
\(222\) 0 0
\(223\) −1916.00 + 3318.61i −0.575358 + 0.996549i 0.420645 + 0.907226i \(0.361804\pi\)
−0.996003 + 0.0893239i \(0.971529\pi\)
\(224\) 0 0
\(225\) 198.000 + 342.946i 0.0586667 + 0.101614i
\(226\) 0 0
\(227\) −699.000 1210.70i −0.204380 0.353997i 0.745555 0.666444i \(-0.232184\pi\)
−0.949935 + 0.312448i \(0.898851\pi\)
\(228\) 0 0
\(229\) 4466.00 1.28874 0.644370 0.764714i \(-0.277120\pi\)
0.644370 + 0.764714i \(0.277120\pi\)
\(230\) 0 0
\(231\) 90.0000 155.885i 0.0256345 0.0444002i
\(232\) 0 0
\(233\) −1638.00 −0.460553 −0.230277 0.973125i \(-0.573963\pi\)
−0.230277 + 0.973125i \(0.573963\pi\)
\(234\) 0 0
\(235\) −1458.00 −0.404721
\(236\) 0 0
\(237\) 1986.00 3439.85i 0.544323 0.942795i
\(238\) 0 0
\(239\) 594.000 0.160764 0.0803821 0.996764i \(-0.474386\pi\)
0.0803821 + 0.996764i \(0.474386\pi\)
\(240\) 0 0
\(241\) −1151.50 1994.46i −0.307779 0.533088i 0.670098 0.742273i \(-0.266252\pi\)
−0.977876 + 0.209185i \(0.932919\pi\)
\(242\) 0 0
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −1525.50 + 2642.24i −0.397798 + 0.689007i
\(246\) 0 0
\(247\) 598.000 2071.53i 0.154048 0.533638i
\(248\) 0 0
\(249\) −1215.00 + 2104.44i −0.309227 + 0.535597i
\(250\) 0 0
\(251\) 3162.00 + 5476.74i 0.795154 + 1.37725i 0.922741 + 0.385420i \(0.125943\pi\)
−0.127587 + 0.991827i \(0.540723\pi\)
\(252\) 0 0
\(253\) 90.0000 + 155.885i 0.0223646 + 0.0387367i
\(254\) 0 0
\(255\) −2997.00 −0.735998
\(256\) 0 0
\(257\) −3916.50 + 6783.58i −0.950601 + 1.64649i −0.206474 + 0.978452i \(0.566199\pi\)
−0.744127 + 0.668038i \(0.767134\pi\)
\(258\) 0 0
\(259\) −34.0000 −0.00815698
\(260\) 0 0
\(261\) −945.000 −0.224115
\(262\) 0 0
\(263\) −1515.00 + 2624.06i −0.355205 + 0.615233i −0.987153 0.159778i \(-0.948922\pi\)
0.631948 + 0.775011i \(0.282256\pi\)
\(264\) 0 0
\(265\) −5751.00 −1.33314
\(266\) 0 0
\(267\) 747.000 + 1293.84i 0.171220 + 0.296561i
\(268\) 0 0
\(269\) 267.000 + 462.458i 0.0605178 + 0.104820i 0.894697 0.446674i \(-0.147391\pi\)
−0.834179 + 0.551493i \(0.814058\pi\)
\(270\) 0 0
\(271\) −1844.00 + 3193.90i −0.413340 + 0.715925i −0.995253 0.0973259i \(-0.968971\pi\)
0.581913 + 0.813251i \(0.302304\pi\)
\(272\) 0 0
\(273\) 195.000 + 202.650i 0.0432305 + 0.0449265i
\(274\) 0 0
\(275\) −660.000 + 1143.15i −0.144725 + 0.250672i
\(276\) 0 0
\(277\) −932.500 1615.14i −0.202269 0.350340i 0.746990 0.664835i \(-0.231498\pi\)
−0.949259 + 0.314495i \(0.898165\pi\)
\(278\) 0 0
\(279\) −450.000 779.423i −0.0965620 0.167250i
\(280\) 0 0
\(281\) 2997.00 0.636249 0.318125 0.948049i \(-0.396947\pi\)
0.318125 + 0.948049i \(0.396947\pi\)
\(282\) 0 0
\(283\) −2057.00 + 3562.83i −0.432071 + 0.748368i −0.997051 0.0767359i \(-0.975550\pi\)
0.564981 + 0.825104i \(0.308884\pi\)
\(284\) 0 0
\(285\) 1242.00 0.258139
\(286\) 0 0
\(287\) 462.000 0.0950209
\(288\) 0 0
\(289\) −3704.00 + 6415.52i −0.753918 + 1.30582i
\(290\) 0 0
\(291\) −4074.00 −0.820695
\(292\) 0 0
\(293\) 2332.50 + 4040.01i 0.465072 + 0.805528i 0.999205 0.0398722i \(-0.0126951\pi\)
−0.534133 + 0.845401i \(0.679362\pi\)
\(294\) 0 0
\(295\) −2700.00 4676.54i −0.532882 0.922978i
\(296\) 0 0
\(297\) −405.000 + 701.481i −0.0791262 + 0.137051i
\(298\) 0 0
\(299\) −273.000 + 67.5500i −0.0528027 + 0.0130653i
\(300\) 0 0
\(301\) 514.000 890.274i 0.0984268 0.170480i
\(302\) 0 0
\(303\) −535.500 927.513i −0.101530 0.175856i
\(304\) 0 0
\(305\) 1048.50 + 1816.06i 0.196842 + 0.340941i
\(306\) 0 0
\(307\) −1502.00 −0.279230 −0.139615 0.990206i \(-0.544587\pi\)
−0.139615 + 0.990206i \(0.544587\pi\)
\(308\) 0 0
\(309\) −1677.00 + 2904.65i −0.308742 + 0.534756i
\(310\) 0 0
\(311\) −2106.00 −0.383988 −0.191994 0.981396i \(-0.561495\pi\)
−0.191994 + 0.981396i \(0.561495\pi\)
\(312\) 0 0
\(313\) −3898.00 −0.703923 −0.351962 0.936014i \(-0.614485\pi\)
−0.351962 + 0.936014i \(0.614485\pi\)
\(314\) 0 0
\(315\) −81.0000 + 140.296i −0.0144884 + 0.0250946i
\(316\) 0 0
\(317\) 9351.00 1.65680 0.828398 0.560140i \(-0.189253\pi\)
0.828398 + 0.560140i \(0.189253\pi\)
\(318\) 0 0
\(319\) −1575.00 2727.98i −0.276436 0.478801i
\(320\) 0 0
\(321\) −1071.00 1855.03i −0.186222 0.322547i
\(322\) 0 0
\(323\) 2553.00 4421.93i 0.439792 0.761742i
\(324\) 0 0
\(325\) −1430.00 1486.10i −0.244068 0.253643i
\(326\) 0 0
\(327\) 3009.00 5211.74i 0.508863 0.881376i
\(328\) 0 0
\(329\) 162.000 + 280.592i 0.0271470 + 0.0470199i
\(330\) 0 0
\(331\) −4586.00 7943.19i −0.761539 1.31902i −0.942057 0.335452i \(-0.891111\pi\)
0.180518 0.983572i \(-0.442222\pi\)
\(332\) 0 0
\(333\) 153.000 0.0251782
\(334\) 0 0
\(335\) −4167.00 + 7217.46i −0.679605 + 1.17711i
\(336\) 0 0
\(337\) −11089.0 −1.79245 −0.896226 0.443598i \(-0.853702\pi\)
−0.896226 + 0.443598i \(0.853702\pi\)
\(338\) 0 0
\(339\) 3357.00 0.537838
\(340\) 0 0
\(341\) 1500.00 2598.08i 0.238210 0.412592i
\(342\) 0 0
\(343\) 1364.00 0.214720
\(344\) 0 0
\(345\) −81.0000 140.296i −0.0126403 0.0218936i
\(346\) 0 0
\(347\) 4881.00 + 8454.14i 0.755118 + 1.30790i 0.945316 + 0.326156i \(0.105754\pi\)
−0.190198 + 0.981746i \(0.560913\pi\)
\(348\) 0 0
\(349\) 4145.00 7179.35i 0.635750 1.10115i −0.350606 0.936523i \(-0.614024\pi\)
0.986356 0.164628i \(-0.0526424\pi\)
\(350\) 0 0
\(351\) −877.500 911.925i −0.133440 0.138675i
\(352\) 0 0
\(353\) −6202.50 + 10743.0i −0.935200 + 1.61981i −0.160924 + 0.986967i \(0.551448\pi\)
−0.774276 + 0.632848i \(0.781886\pi\)
\(354\) 0 0
\(355\) 4185.00 + 7248.63i 0.625681 + 1.08371i
\(356\) 0 0
\(357\) 333.000 + 576.773i 0.0493676 + 0.0855072i
\(358\) 0 0
\(359\) 1098.00 0.161421 0.0807106 0.996738i \(-0.474281\pi\)
0.0807106 + 0.996738i \(0.474281\pi\)
\(360\) 0 0
\(361\) 2371.50 4107.56i 0.345750 0.598857i
\(362\) 0 0
\(363\) 1293.00 0.186956
\(364\) 0 0
\(365\) 2277.00 0.326530
\(366\) 0 0
\(367\) −2867.00 + 4965.79i −0.407783 + 0.706300i −0.994641 0.103390i \(-0.967031\pi\)
0.586858 + 0.809690i \(0.300365\pi\)
\(368\) 0 0
\(369\) −2079.00 −0.293302
\(370\) 0 0
\(371\) 639.000 + 1106.78i 0.0894211 + 0.154882i
\(372\) 0 0
\(373\) 4485.50 + 7769.11i 0.622655 + 1.07847i 0.988989 + 0.147987i \(0.0472794\pi\)
−0.366334 + 0.930483i \(0.619387\pi\)
\(374\) 0 0
\(375\) 2281.50 3951.67i 0.314176 0.544170i
\(376\) 0 0
\(377\) 4777.50 1182.12i 0.652663 0.161492i
\(378\) 0 0
\(379\) 3622.00 6273.49i 0.490896 0.850257i −0.509049 0.860738i \(-0.670003\pi\)
0.999945 + 0.0104805i \(0.00333611\pi\)
\(380\) 0 0
\(381\) 906.000 + 1569.24i 0.121826 + 0.211009i
\(382\) 0 0
\(383\) −3156.00 5466.35i −0.421055 0.729289i 0.574988 0.818162i \(-0.305007\pi\)
−0.996043 + 0.0888732i \(0.971673\pi\)
\(384\) 0 0
\(385\) −540.000 −0.0714830
\(386\) 0 0
\(387\) −2313.00 + 4006.23i −0.303815 + 0.526223i
\(388\) 0 0
\(389\) 3627.00 0.472741 0.236370 0.971663i \(-0.424042\pi\)
0.236370 + 0.971663i \(0.424042\pi\)
\(390\) 0 0
\(391\) −666.000 −0.0861408
\(392\) 0 0
\(393\) 2376.00 4115.35i 0.304970 0.528224i
\(394\) 0 0
\(395\) −11916.0 −1.51787
\(396\) 0 0
\(397\) 1949.00 + 3375.77i 0.246392 + 0.426763i 0.962522 0.271204i \(-0.0874217\pi\)
−0.716130 + 0.697967i \(0.754088\pi\)
\(398\) 0 0
\(399\) −138.000 239.023i −0.0173149 0.0299903i
\(400\) 0 0
\(401\) 2851.50 4938.94i 0.355105 0.615060i −0.632031 0.774943i \(-0.717778\pi\)
0.987136 + 0.159883i \(0.0511118\pi\)
\(402\) 0 0
\(403\) 3250.00 + 3377.50i 0.401722 + 0.417482i
\(404\) 0 0
\(405\) 364.500 631.333i 0.0447214 0.0774597i
\(406\) 0 0
\(407\) 255.000 + 441.673i 0.0310562 + 0.0537909i
\(408\) 0 0
\(409\) −3155.50 5465.49i −0.381490 0.660760i 0.609785 0.792567i \(-0.291256\pi\)
−0.991275 + 0.131806i \(0.957922\pi\)
\(410\) 0 0
\(411\) −2151.00 −0.258153
\(412\) 0 0
\(413\) −600.000 + 1039.23i −0.0714869 + 0.123819i
\(414\) 0 0
\(415\) 7290.00 0.862294
\(416\) 0 0
\(417\) −2460.00 −0.288889
\(418\) 0 0
\(419\) −1164.00 + 2016.11i −0.135716 + 0.235067i −0.925871 0.377840i \(-0.876667\pi\)
0.790155 + 0.612908i \(0.210000\pi\)
\(420\) 0 0
\(421\) 2045.00 0.236739 0.118370 0.992970i \(-0.462233\pi\)
0.118370 + 0.992970i \(0.462233\pi\)
\(422\) 0 0
\(423\) −729.000 1262.67i −0.0837948 0.145137i
\(424\) 0 0
\(425\) −2442.00 4229.67i −0.278716 0.482751i
\(426\) 0 0
\(427\) 233.000 403.568i 0.0264067 0.0457377i
\(428\) 0 0
\(429\) 1170.00 4053.00i 0.131674 0.456132i
\(430\) 0 0
\(431\) 2517.00 4359.57i 0.281298 0.487223i −0.690406 0.723422i \(-0.742568\pi\)
0.971705 + 0.236199i \(0.0759016\pi\)
\(432\) 0 0
\(433\) −2141.50 3709.19i −0.237676 0.411668i 0.722371 0.691506i \(-0.243052\pi\)
−0.960047 + 0.279838i \(0.909719\pi\)
\(434\) 0 0
\(435\) 1417.50 + 2455.18i 0.156239 + 0.270614i
\(436\) 0 0
\(437\) 276.000 0.0302125
\(438\) 0 0
\(439\) −653.000 + 1131.03i −0.0709931 + 0.122964i −0.899337 0.437257i \(-0.855950\pi\)
0.828344 + 0.560220i \(0.189284\pi\)
\(440\) 0 0
\(441\) −3051.00 −0.329446
\(442\) 0 0
\(443\) 5796.00 0.621617 0.310808 0.950473i \(-0.399400\pi\)
0.310808 + 0.950473i \(0.399400\pi\)
\(444\) 0 0
\(445\) 2241.00 3881.53i 0.238727 0.413488i
\(446\) 0 0
\(447\) 5247.00 0.555200
\(448\) 0 0
\(449\) −1353.00 2343.46i −0.142209 0.246314i 0.786119 0.618075i \(-0.212087\pi\)
−0.928328 + 0.371761i \(0.878754\pi\)
\(450\) 0 0
\(451\) −3465.00 6001.56i −0.361775 0.626612i
\(452\) 0 0
\(453\) 555.000 961.288i 0.0575633 0.0997026i
\(454\) 0 0
\(455\) 234.000 810.600i 0.0241101 0.0835198i
\(456\) 0 0
\(457\) 414.500 717.935i 0.0424278 0.0734871i −0.844032 0.536293i \(-0.819824\pi\)
0.886459 + 0.462806i \(0.153157\pi\)
\(458\) 0 0
\(459\) −1498.50 2595.48i −0.152383 0.263936i
\(460\) 0 0
\(461\) 2746.50 + 4757.08i 0.277478 + 0.480606i 0.970757 0.240063i \(-0.0771682\pi\)
−0.693279 + 0.720669i \(0.743835\pi\)
\(462\) 0 0
\(463\) 15346.0 1.54037 0.770183 0.637823i \(-0.220165\pi\)
0.770183 + 0.637823i \(0.220165\pi\)
\(464\) 0 0
\(465\) −1350.00 + 2338.27i −0.134634 + 0.233193i
\(466\) 0 0
\(467\) 9594.00 0.950658 0.475329 0.879808i \(-0.342329\pi\)
0.475329 + 0.879808i \(0.342329\pi\)
\(468\) 0 0
\(469\) 1852.00 0.182340
\(470\) 0 0
\(471\) −3916.50 + 6783.58i −0.383148 + 0.663632i
\(472\) 0 0
\(473\) −15420.0 −1.49897
\(474\) 0 0
\(475\) 1012.00 + 1752.84i 0.0977553 + 0.169317i
\(476\) 0 0
\(477\) −2875.50 4980.51i −0.276017 0.478075i
\(478\) 0 0
\(479\) −6420.00 + 11119.8i −0.612395 + 1.06070i 0.378440 + 0.925626i \(0.376461\pi\)
−0.990836 + 0.135074i \(0.956873\pi\)
\(480\) 0 0
\(481\) −773.500 + 191.392i −0.0733234 + 0.0181428i
\(482\) 0 0
\(483\) −18.0000 + 31.1769i −0.00169571 + 0.00293706i
\(484\) 0 0
\(485\) 6111.00 + 10584.6i 0.572137 + 0.990970i
\(486\) 0 0
\(487\) −7043.00 12198.8i −0.655336 1.13508i −0.981809 0.189869i \(-0.939194\pi\)
0.326473 0.945207i \(-0.394140\pi\)
\(488\) 0 0
\(489\) −4908.00 −0.453880
\(490\) 0 0
\(491\) 5847.00 10127.3i 0.537416 0.930832i −0.461626 0.887075i \(-0.652734\pi\)
0.999042 0.0437577i \(-0.0139329\pi\)
\(492\) 0 0
\(493\) 11655.0 1.06474
\(494\) 0 0
\(495\) 2430.00 0.220647
\(496\) 0 0
\(497\) 930.000 1610.81i 0.0839360 0.145381i
\(498\) 0 0
\(499\) 3688.00 0.330857 0.165428 0.986222i \(-0.447099\pi\)
0.165428 + 0.986222i \(0.447099\pi\)
\(500\) 0 0
\(501\) −396.000 685.892i −0.0353133 0.0611645i
\(502\) 0 0
\(503\) −2373.00 4110.16i −0.210352 0.364340i 0.741473 0.670983i \(-0.234128\pi\)
−0.951825 + 0.306643i \(0.900794\pi\)
\(504\) 0 0
\(505\) −1606.50 + 2782.54i −0.141561 + 0.245191i
\(506\) 0 0
\(507\) 5577.00 + 3512.60i 0.488527 + 0.307692i
\(508\) 0 0
\(509\) 7252.50 12561.7i 0.631555 1.09389i −0.355679 0.934608i \(-0.615750\pi\)
0.987234 0.159277i \(-0.0509163\pi\)
\(510\) 0 0
\(511\) −253.000 438.209i −0.0219023 0.0379358i
\(512\) 0 0
\(513\) 621.000 + 1075.60i 0.0534460 + 0.0925713i
\(514\) 0 0
\(515\) 10062.0 0.860941
\(516\) 0 0
\(517\) 2430.00 4208.88i 0.206714 0.358040i
\(518\) 0 0
\(519\) −4230.00 −0.357758
\(520\) 0 0
\(521\) 5085.00 0.427597 0.213798 0.976878i \(-0.431416\pi\)
0.213798 + 0.976878i \(0.431416\pi\)
\(522\) 0 0
\(523\) −5441.00 + 9424.09i −0.454911 + 0.787929i −0.998683 0.0513043i \(-0.983662\pi\)
0.543772 + 0.839233i \(0.316996\pi\)
\(524\) 0 0
\(525\) −264.000 −0.0219465
\(526\) 0 0
\(527\) 5550.00 + 9612.88i 0.458751 + 0.794580i
\(528\) 0 0
\(529\) 6065.50 + 10505.8i 0.498521 + 0.863463i
\(530\) 0 0
\(531\) 2700.00 4676.54i 0.220659 0.382193i
\(532\) 0 0
\(533\) 10510.5 2600.67i 0.854147 0.211347i
\(534\) 0 0
\(535\) −3213.00 + 5565.08i −0.259645 + 0.449718i
\(536\) 0 0
\(537\) 711.000 + 1231.49i 0.0571358 + 0.0989621i
\(538\) 0 0
\(539\) −5085.00 8807.48i −0.406357 0.703831i
\(540\) 0 0
\(541\) −4699.00 −0.373430 −0.186715 0.982414i \(-0.559784\pi\)
−0.186715 + 0.982414i \(0.559784\pi\)
\(542\) 0 0
\(543\) 3373.50 5843.07i 0.266613 0.461787i
\(544\) 0 0
\(545\) −18054.0 −1.41899
\(546\) 0 0
\(547\) −8270.00 −0.646434 −0.323217 0.946325i \(-0.604764\pi\)
−0.323217 + 0.946325i \(0.604764\pi\)
\(548\) 0 0
\(549\) −1048.50 + 1816.06i −0.0815098 + 0.141179i
\(550\) 0 0
\(551\) −4830.00 −0.373439
\(552\) 0 0
\(553\) 1324.00 + 2293.24i 0.101812 + 0.176344i
\(554\) 0 0
\(555\) −229.500 397.506i −0.0175527 0.0304021i
\(556\) 0 0
\(557\) 11392.5 19732.4i 0.866635 1.50106i 0.00122056 0.999999i \(-0.499611\pi\)
0.865414 0.501057i \(-0.167055\pi\)
\(558\) 0 0
\(559\) 6682.00 23147.1i 0.505579 1.75138i
\(560\) 0 0
\(561\) 4995.00 8651.59i 0.375916 0.651106i
\(562\) 0 0
\(563\) −5964.00 10330.0i −0.446452 0.773278i 0.551700 0.834043i \(-0.313979\pi\)
−0.998152 + 0.0607647i \(0.980646\pi\)
\(564\) 0 0
\(565\) −5035.50 8721.74i −0.374947 0.649427i
\(566\) 0 0
\(567\) −162.000 −0.0119989
\(568\) 0 0
\(569\) 3981.00 6895.29i 0.293308 0.508024i −0.681282 0.732021i \(-0.738577\pi\)
0.974590 + 0.223997i \(0.0719106\pi\)
\(570\) 0 0
\(571\) −20618.0 −1.51110 −0.755549 0.655093i \(-0.772630\pi\)
−0.755549 + 0.655093i \(0.772630\pi\)
\(572\) 0 0
\(573\) 10332.0 0.753273
\(574\) 0 0
\(575\) 132.000 228.631i 0.00957353 0.0165818i
\(576\) 0 0
\(577\) −3493.00 −0.252020 −0.126010 0.992029i \(-0.540217\pi\)
−0.126010 + 0.992029i \(0.540217\pi\)
\(578\) 0 0
\(579\) −6409.50 11101.6i −0.460051 0.796832i
\(580\) 0 0
\(581\) −810.000 1402.96i −0.0578390 0.100180i
\(582\) 0 0
\(583\) 9585.00 16601.7i 0.680909 1.17937i
\(584\) 0 0
\(585\) −1053.00 + 3647.70i −0.0744208 + 0.257801i
\(586\) 0 0
\(587\) 5208.00 9020.52i 0.366196 0.634270i −0.622771 0.782404i \(-0.713993\pi\)
0.988967 + 0.148134i \(0.0473266\pi\)
\(588\) 0 0
\(589\) −2300.00 3983.72i −0.160900 0.278686i
\(590\) 0 0
\(591\) −2979.00 5159.78i −0.207343 0.359129i
\(592\) 0 0
\(593\) 2061.00 0.142724 0.0713618 0.997450i \(-0.477266\pi\)
0.0713618 + 0.997450i \(0.477266\pi\)
\(594\) 0 0
\(595\) 999.000 1730.32i 0.0688319 0.119220i
\(596\) 0 0
\(597\) −7158.00 −0.490716
\(598\) 0 0
\(599\) −12456.0 −0.849647 −0.424823 0.905276i \(-0.639664\pi\)
−0.424823 + 0.905276i \(0.639664\pi\)
\(600\) 0 0
\(601\) 390.500 676.366i 0.0265039 0.0459061i −0.852469 0.522777i \(-0.824896\pi\)
0.878973 + 0.476871i \(0.158229\pi\)
\(602\) 0 0
\(603\) −8334.00 −0.562830
\(604\) 0 0
\(605\) −1939.50 3359.31i −0.130334 0.225745i
\(606\) 0 0
\(607\) 9652.00 + 16717.8i 0.645408 + 1.11788i 0.984207 + 0.177021i \(0.0566459\pi\)
−0.338799 + 0.940859i \(0.610021\pi\)
\(608\) 0 0
\(609\) 315.000 545.596i 0.0209597 0.0363032i
\(610\) 0 0
\(611\) 5265.00 + 5471.55i 0.348607 + 0.362283i
\(612\) 0 0
\(613\) −6020.50 + 10427.8i −0.396681 + 0.687072i −0.993314 0.115442i \(-0.963172\pi\)
0.596633 + 0.802514i \(0.296505\pi\)
\(614\) 0 0
\(615\) 3118.50 + 5401.40i 0.204472 + 0.354155i
\(616\) 0 0
\(617\) −4858.50 8415.17i −0.317011 0.549079i 0.662852 0.748751i \(-0.269346\pi\)
−0.979863 + 0.199671i \(0.936013\pi\)
\(618\) 0 0
\(619\) 21040.0 1.36619 0.683093 0.730332i \(-0.260634\pi\)
0.683093 + 0.730332i \(0.260634\pi\)
\(620\) 0 0
\(621\) 81.0000 140.296i 0.00523417 0.00906584i
\(622\) 0 0
\(623\) −996.000 −0.0640512
\(624\) 0 0
\(625\) −8189.00 −0.524096
\(626\) 0 0
\(627\) −2070.00 + 3585.35i −0.131847 + 0.228365i
\(628\) 0 0
\(629\) −1887.00 −0.119618
\(630\) 0 0
\(631\) −2534.00 4389.02i −0.159868 0.276900i 0.774953 0.632019i \(-0.217774\pi\)
−0.934821 + 0.355119i \(0.884440\pi\)
\(632\) 0 0
\(633\) 2400.00 + 4156.92i 0.150697 + 0.261016i
\(634\) 0 0
\(635\) 2718.00 4707.71i 0.169859 0.294205i
\(636\) 0 0
\(637\) 15424.5 3816.57i 0.959405 0.237391i
\(638\) 0 0
\(639\) −4185.00 + 7248.63i −0.259086 + 0.448750i
\(640\) 0 0
\(641\) −5092.50 8820.47i −0.313794 0.543506i 0.665387 0.746499i \(-0.268267\pi\)
−0.979180 + 0.202992i \(0.934933\pi\)
\(642\) 0 0
\(643\) 12964.0 + 22454.3i 0.795101 + 1.37716i 0.922775 + 0.385340i \(0.125916\pi\)
−0.127673 + 0.991816i \(0.540751\pi\)
\(644\) 0 0
\(645\) 13878.0 0.847203
\(646\) 0 0
\(647\) 11580.0 20057.1i 0.703643 1.21874i −0.263537 0.964649i \(-0.584889\pi\)
0.967179 0.254095i \(-0.0817777\pi\)
\(648\) 0 0
\(649\) 18000.0 1.08869
\(650\) 0 0
\(651\) 600.000 0.0361227
\(652\) 0 0
\(653\) −8313.00 + 14398.5i −0.498182 + 0.862876i −0.999998 0.00209801i \(-0.999332\pi\)
0.501816 + 0.864974i \(0.332666\pi\)
\(654\) 0 0
\(655\) −14256.0 −0.850424
\(656\) 0 0
\(657\) 1138.50 + 1971.94i 0.0676060 + 0.117097i
\(658\) 0 0
\(659\) −7404.00 12824.1i −0.437661 0.758052i 0.559847 0.828596i \(-0.310860\pi\)
−0.997509 + 0.0705440i \(0.977526\pi\)
\(660\) 0 0
\(661\) −2426.50 + 4202.82i −0.142784 + 0.247308i −0.928544 0.371223i \(-0.878939\pi\)
0.785760 + 0.618531i \(0.212272\pi\)
\(662\) 0 0
\(663\) 10822.5 + 11247.1i 0.633953 + 0.658824i
\(664\) 0 0
\(665\) −414.000 + 717.069i −0.0241417 + 0.0418147i
\(666\) 0 0
\(667\) 315.000 + 545.596i 0.0182861 + 0.0316725i
\(668\) 0 0
\(669\) 5748.00 + 9955.83i 0.332183 + 0.575358i
\(670\) 0 0
\(671\) −6990.00 −0.402155
\(672\) 0 0
\(673\) 8082.50 13999.3i 0.462938 0.801833i −0.536168 0.844112i \(-0.680128\pi\)
0.999106 + 0.0422789i \(0.0134618\pi\)
\(674\) 0 0
\(675\) 1188.00 0.0677424
\(676\) 0 0
\(677\) −25686.0 −1.45819 −0.729094 0.684414i \(-0.760058\pi\)
−0.729094 + 0.684414i \(0.760058\pi\)
\(678\) 0 0
\(679\) 1358.00 2352.12i 0.0767530 0.132940i
\(680\) 0 0
\(681\) −4194.00 −0.235998
\(682\) 0 0
\(683\) −9528.00 16503.0i −0.533790 0.924552i −0.999221 0.0394675i \(-0.987434\pi\)
0.465431 0.885084i \(-0.345900\pi\)
\(684\) 0 0
\(685\) 3226.50 + 5588.46i 0.179968 + 0.311714i
\(686\) 0 0
\(687\) 6699.00 11603.0i 0.372027 0.644370i
\(688\) 0 0
\(689\) 20767.5 + 21582.2i 1.14830 + 1.19335i
\(690\) 0 0
\(691\) −8195.00 + 14194.2i −0.451161 + 0.781434i −0.998458 0.0555040i \(-0.982323\pi\)
0.547297 + 0.836938i \(0.315657\pi\)
\(692\) 0 0
\(693\) −270.000 467.654i −0.0148001 0.0256345i
\(694\) 0 0
\(695\) 3690.00 + 6391.27i 0.201395 + 0.348827i
\(696\) 0 0
\(697\) 25641.0 1.39343
\(698\) 0 0
\(699\) −2457.00 + 4255.65i −0.132950 + 0.230277i
\(700\) 0 0
\(701\) −27846.0 −1.50033 −0.750163 0.661253i \(-0.770025\pi\)
−0.750163 + 0.661253i \(0.770025\pi\)
\(702\) 0 0
\(703\) 782.000 0.0419540
\(704\) 0 0
\(705\) −2187.00 + 3788.00i −0.116833 + 0.202360i
\(706\) 0 0
\(707\) 714.000 0.0379812
\(708\) 0 0
\(709\) 6141.50 + 10637.4i 0.325316 + 0.563463i 0.981576 0.191071i \(-0.0611961\pi\)
−0.656260 + 0.754534i \(0.727863\pi\)
\(710\) 0 0
\(711\) −5958.00 10319.6i −0.314265 0.544323i
\(712\) 0 0
\(713\) −300.000 + 519.615i −0.0157575 + 0.0272928i
\(714\) 0 0
\(715\) −12285.0 + 3039.75i −0.642564 + 0.158993i
\(716\) 0 0
\(717\) 891.000 1543.26i 0.0464087 0.0803821i
\(718\) 0 0
\(719\) 12756.0 + 22094.0i 0.661639 + 1.14599i 0.980185 + 0.198085i \(0.0634722\pi\)
−0.318546 + 0.947908i \(0.603194\pi\)
\(720\) 0 0
\(721\) −1118.00 1936.43i −0.0577483 0.100023i
\(722\) 0 0
\(723\) −6909.00 −0.355392
\(724\) 0 0
\(725\) −2310.00 + 4001.04i −0.118333 + 0.204958i
\(726\) 0 0
\(727\) −6110.00 −0.311702 −0.155851 0.987781i \(-0.549812\pi\)
−0.155851 + 0.987781i \(0.549812\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 28527.0 49410.2i 1.44338 2.50000i
\(732\) 0 0
\(733\) −27127.0 −1.36693 −0.683464 0.729984i \(-0.739527\pi\)
−0.683464 + 0.729984i \(0.739527\pi\)
\(734\) 0 0
\(735\) 4576.50 + 7926.73i 0.229669 + 0.397798i
\(736\) 0 0
\(737\) −13890.0 24058.2i −0.694226 1.20244i
\(738\) 0 0
\(739\) −440.000 + 762.102i −0.0219021 + 0.0379356i −0.876769 0.480912i \(-0.840306\pi\)
0.854867 + 0.518848i \(0.173639\pi\)
\(740\) 0 0
\(741\) −4485.00 4660.95i −0.222349 0.231072i
\(742\) 0 0
\(743\) −10938.0 + 18945.2i −0.540076 + 0.935439i 0.458823 + 0.888528i \(0.348271\pi\)
−0.998899 + 0.0469111i \(0.985062\pi\)
\(744\) 0 0
\(745\) −7870.50 13632.1i −0.387051 0.670392i
\(746\) 0 0
\(747\) 3645.00 + 6313.33i 0.178532 + 0.309227i
\(748\) 0 0
\(749\) 1428.00 0.0696635
\(750\) 0 0
\(751\) 5899.00 10217.4i 0.286628 0.496454i −0.686375 0.727248i \(-0.740799\pi\)
0.973003 + 0.230794i \(0.0741323\pi\)
\(752\) 0 0
\(753\) 18972.0 0.918165
\(754\) 0 0
\(755\) −3330.00 −0.160518
\(756\) 0 0
\(757\) 4037.00 6992.29i 0.193827 0.335719i −0.752688 0.658377i \(-0.771243\pi\)
0.946515 + 0.322658i \(0.104577\pi\)
\(758\) 0 0
\(759\) 540.000 0.0258245
\(760\) 0 0
\(761\) −9777.00 16934.3i −0.465724 0.806658i 0.533510 0.845794i \(-0.320873\pi\)
−0.999234 + 0.0391362i \(0.987539\pi\)
\(762\) 0 0
\(763\) 2006.00 + 3474.49i 0.0951797 + 0.164856i
\(764\) 0 0
\(765\) −4495.50 + 7786.43i −0.212464 + 0.367999i
\(766\) 0 0
\(767\) −7800.00 + 27020.0i −0.367199 + 1.27201i
\(768\) 0 0
\(769\) −7015.00 + 12150.3i −0.328956 + 0.569769i −0.982305 0.187288i \(-0.940030\pi\)
0.653349 + 0.757057i \(0.273364\pi\)
\(770\) 0 0
\(771\) 11749.5 + 20350.7i 0.548830 + 0.950601i
\(772\) 0 0
\(773\) −18021.0 31213.3i −0.838513 1.45235i −0.891138 0.453732i \(-0.850092\pi\)
0.0526253 0.998614i \(-0.483241\pi\)
\(774\) 0 0
\(775\) −4400.00 −0.203939
\(776\) 0 0
\(777\) −51.0000 + 88.3346i −0.00235472 + 0.00407849i
\(778\) 0 0
\(779\) −10626.0 −0.488724
\(780\) 0 0
\(781\) −27900.0 −1.27828
\(782\) 0 0
\(783\) −1417.50 + 2455.18i −0.0646964 + 0.112058i
\(784\) 0 0
\(785\) 23499.0 1.06843
\(786\) 0 0
\(787\) 14314.0 + 24792.6i 0.648334 + 1.12295i 0.983521 + 0.180796i \(0.0578674\pi\)
−0.335186 + 0.942152i \(0.608799\pi\)
\(788\) 0 0
\(789\) 4545.00 + 7872.17i 0.205078 + 0.355205i
\(790\) 0 0