Properties

Label 624.4.bv.h.49.3
Level $624$
Weight $4$
Character 624.49
Analytic conductor $36.817$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.bv (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(36.8171918436\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.3
Root \(-5.36472i\) of defining polynomial
Character \(\chi\) \(=\) 624.49
Dual form 624.4.bv.h.433.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 2.59808i) q^{3} +2.69631i q^{5} +(-13.1657 - 7.60123i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 + 2.59808i) q^{3} +2.69631i q^{5} +(-13.1657 - 7.60123i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-57.9240 + 33.4424i) q^{11} +(46.8650 + 0.818689i) q^{13} +(-7.00522 + 4.04447i) q^{15} +(2.08177 - 3.60573i) q^{17} +(22.5903 + 13.0425i) q^{19} -45.6074i q^{21} +(-23.6621 - 40.9839i) q^{23} +117.730 q^{25} -27.0000 q^{27} +(-128.503 - 222.575i) q^{29} -206.242i q^{31} +(-173.772 - 100.327i) q^{33} +(20.4953 - 35.4989i) q^{35} +(-152.149 + 87.8430i) q^{37} +(68.1705 + 122.987i) q^{39} +(135.501 - 78.2313i) q^{41} +(-25.9922 + 45.0199i) q^{43} +(-21.0157 - 12.1334i) q^{45} -354.222i q^{47} +(-55.9425 - 96.8953i) q^{49} +12.4906 q^{51} -10.4723 q^{53} +(-90.1712 - 156.181i) q^{55} +78.2550i q^{57} +(-385.480 - 222.557i) q^{59} +(-59.8481 + 103.660i) q^{61} +(118.491 - 68.4111i) q^{63} +(-2.20744 + 126.363i) q^{65} +(19.4057 - 11.2039i) q^{67} +(70.9863 - 122.952i) q^{69} +(246.997 + 142.604i) q^{71} -740.989i q^{73} +(176.595 + 305.871i) q^{75} +1016.81 q^{77} +547.679 q^{79} +(-40.5000 - 70.1481i) q^{81} -603.056i q^{83} +(9.72218 + 5.61310i) q^{85} +(385.510 - 667.724i) q^{87} +(-186.774 + 107.834i) q^{89} +(-610.789 - 367.011i) q^{91} +(535.833 - 309.363i) q^{93} +(-35.1666 + 60.9104i) q^{95} +(-1253.58 - 723.752i) q^{97} -601.964i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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
\(5\) 2.69631i 0.241165i 0.992703 + 0.120583i \(0.0384763\pi\)
−0.992703 + 0.120583i \(0.961524\pi\)
\(6\) 0 0
\(7\) −13.1657 7.60123i −0.710882 0.410428i 0.100505 0.994937i \(-0.467954\pi\)
−0.811388 + 0.584509i \(0.801287\pi\)
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −57.9240 + 33.4424i −1.58770 + 0.916661i −0.594018 + 0.804451i \(0.702459\pi\)
−0.993685 + 0.112209i \(0.964207\pi\)
\(12\) 0 0
\(13\) 46.8650 + 0.818689i 0.999847 + 0.0174664i
\(14\) 0 0
\(15\) −7.00522 + 4.04447i −0.120583 + 0.0696185i
\(16\) 0 0
\(17\) 2.08177 3.60573i 0.0297002 0.0514422i −0.850793 0.525501i \(-0.823878\pi\)
0.880493 + 0.474058i \(0.157211\pi\)
\(18\) 0 0
\(19\) 22.5903 + 13.0425i 0.272766 + 0.157482i 0.630144 0.776478i \(-0.282996\pi\)
−0.357378 + 0.933960i \(0.616329\pi\)
\(20\) 0 0
\(21\) 45.6074i 0.473921i
\(22\) 0 0
\(23\) −23.6621 40.9839i −0.214517 0.371554i 0.738606 0.674137i \(-0.235484\pi\)
−0.953123 + 0.302583i \(0.902151\pi\)
\(24\) 0 0
\(25\) 117.730 0.941839
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −128.503 222.575i −0.822845 1.42521i −0.903555 0.428471i \(-0.859052\pi\)
0.0807106 0.996738i \(-0.474281\pi\)
\(30\) 0 0
\(31\) 206.242i 1.19491i −0.801903 0.597455i \(-0.796179\pi\)
0.801903 0.597455i \(-0.203821\pi\)
\(32\) 0 0
\(33\) −173.772 100.327i −0.916661 0.529234i
\(34\) 0 0
\(35\) 20.4953 35.4989i 0.0989811 0.171440i
\(36\) 0 0
\(37\) −152.149 + 87.8430i −0.676029 + 0.390305i −0.798357 0.602184i \(-0.794297\pi\)
0.122328 + 0.992490i \(0.460964\pi\)
\(38\) 0 0
\(39\) 68.1705 + 122.987i 0.279898 + 0.504966i
\(40\) 0 0
\(41\) 135.501 78.2313i 0.516137 0.297992i −0.219216 0.975676i \(-0.570350\pi\)
0.735353 + 0.677684i \(0.237016\pi\)
\(42\) 0 0
\(43\) −25.9922 + 45.0199i −0.0921809 + 0.159662i −0.908429 0.418040i \(-0.862717\pi\)
0.816248 + 0.577702i \(0.196050\pi\)
\(44\) 0 0
\(45\) −21.0157 12.1334i −0.0696185 0.0401942i
\(46\) 0 0
\(47\) 354.222i 1.09933i −0.835384 0.549666i \(-0.814755\pi\)
0.835384 0.549666i \(-0.185245\pi\)
\(48\) 0 0
\(49\) −55.9425 96.8953i −0.163098 0.282494i
\(50\) 0 0
\(51\) 12.4906 0.0342948
\(52\) 0 0
\(53\) −10.4723 −0.0271412 −0.0135706 0.999908i \(-0.504320\pi\)
−0.0135706 + 0.999908i \(0.504320\pi\)
\(54\) 0 0
\(55\) −90.1712 156.181i −0.221067 0.382899i
\(56\) 0 0
\(57\) 78.2550i 0.181844i
\(58\) 0 0
\(59\) −385.480 222.557i −0.850597 0.491092i 0.0102552 0.999947i \(-0.496736\pi\)
−0.860852 + 0.508855i \(0.830069\pi\)
\(60\) 0 0
\(61\) −59.8481 + 103.660i −0.125619 + 0.217579i −0.921975 0.387250i \(-0.873425\pi\)
0.796356 + 0.604829i \(0.206758\pi\)
\(62\) 0 0
\(63\) 118.491 68.4111i 0.236961 0.136809i
\(64\) 0 0
\(65\) −2.20744 + 126.363i −0.00421230 + 0.241129i
\(66\) 0 0
\(67\) 19.4057 11.2039i 0.0353848 0.0204294i −0.482203 0.876059i \(-0.660163\pi\)
0.517588 + 0.855630i \(0.326830\pi\)
\(68\) 0 0
\(69\) 70.9863 122.952i 0.123851 0.214517i
\(70\) 0 0
\(71\) 246.997 + 142.604i 0.412861 + 0.238365i 0.692018 0.721880i \(-0.256722\pi\)
−0.279157 + 0.960245i \(0.590055\pi\)
\(72\) 0 0
\(73\) 740.989i 1.18803i −0.804454 0.594015i \(-0.797542\pi\)
0.804454 0.594015i \(-0.202458\pi\)
\(74\) 0 0
\(75\) 176.595 + 305.871i 0.271886 + 0.470920i
\(76\) 0 0
\(77\) 1016.81 1.50489
\(78\) 0 0
\(79\) 547.679 0.779983 0.389992 0.920818i \(-0.372478\pi\)
0.389992 + 0.920818i \(0.372478\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 603.056i 0.797518i −0.917056 0.398759i \(-0.869441\pi\)
0.917056 0.398759i \(-0.130559\pi\)
\(84\) 0 0
\(85\) 9.72218 + 5.61310i 0.0124061 + 0.00716266i
\(86\) 0 0
\(87\) 385.510 667.724i 0.475070 0.822845i
\(88\) 0 0
\(89\) −186.774 + 107.834i −0.222450 + 0.128431i −0.607084 0.794638i \(-0.707661\pi\)
0.384634 + 0.923069i \(0.374328\pi\)
\(90\) 0 0
\(91\) −610.789 367.011i −0.703605 0.422782i
\(92\) 0 0
\(93\) 535.833 309.363i 0.597455 0.344941i
\(94\) 0 0
\(95\) −35.1666 + 60.9104i −0.0379792 + 0.0657818i
\(96\) 0 0
\(97\) −1253.58 723.752i −1.31218 0.757586i −0.329722 0.944078i \(-0.606955\pi\)
−0.982457 + 0.186492i \(0.940288\pi\)
\(98\) 0 0
\(99\) 601.964i 0.611107i
\(100\) 0 0
\(101\) −441.725 765.090i −0.435181 0.753756i 0.562129 0.827049i \(-0.309982\pi\)
−0.997310 + 0.0732935i \(0.976649\pi\)
\(102\) 0 0
\(103\) 1251.74 1.19745 0.598726 0.800954i \(-0.295674\pi\)
0.598726 + 0.800954i \(0.295674\pi\)
\(104\) 0 0
\(105\) 122.972 0.114293
\(106\) 0 0
\(107\) −170.807 295.846i −0.154323 0.267294i 0.778490 0.627658i \(-0.215986\pi\)
−0.932812 + 0.360363i \(0.882653\pi\)
\(108\) 0 0
\(109\) 775.177i 0.681179i 0.940212 + 0.340589i \(0.110627\pi\)
−0.940212 + 0.340589i \(0.889373\pi\)
\(110\) 0 0
\(111\) −456.446 263.529i −0.390305 0.225343i
\(112\) 0 0
\(113\) −639.524 + 1107.69i −0.532402 + 0.922147i 0.466883 + 0.884319i \(0.345377\pi\)
−0.999284 + 0.0378273i \(0.987956\pi\)
\(114\) 0 0
\(115\) 110.505 63.8004i 0.0896060 0.0517340i
\(116\) 0 0
\(117\) −217.274 + 361.593i −0.171683 + 0.285720i
\(118\) 0 0
\(119\) −54.8160 + 31.6480i −0.0422267 + 0.0243796i
\(120\) 0 0
\(121\) 1571.29 2721.55i 1.18053 2.04474i
\(122\) 0 0
\(123\) 406.502 + 234.694i 0.297992 + 0.172046i
\(124\) 0 0
\(125\) 654.476i 0.468305i
\(126\) 0 0
\(127\) 556.910 + 964.597i 0.389117 + 0.673970i 0.992331 0.123609i \(-0.0394470\pi\)
−0.603214 + 0.797579i \(0.706114\pi\)
\(128\) 0 0
\(129\) −155.953 −0.106441
\(130\) 0 0
\(131\) −2100.12 −1.40068 −0.700339 0.713811i \(-0.746968\pi\)
−0.700339 + 0.713811i \(0.746968\pi\)
\(132\) 0 0
\(133\) −198.278 343.428i −0.129270 0.223902i
\(134\) 0 0
\(135\) 72.8004i 0.0464123i
\(136\) 0 0
\(137\) −1043.58 602.509i −0.650793 0.375736i 0.137967 0.990437i \(-0.455943\pi\)
−0.788760 + 0.614701i \(0.789277\pi\)
\(138\) 0 0
\(139\) 161.445 279.631i 0.0985149 0.170633i −0.812555 0.582884i \(-0.801924\pi\)
0.911070 + 0.412251i \(0.135257\pi\)
\(140\) 0 0
\(141\) 920.297 531.334i 0.549666 0.317350i
\(142\) 0 0
\(143\) −2741.99 + 1519.86i −1.60347 + 0.888789i
\(144\) 0 0
\(145\) 600.131 346.486i 0.343711 0.198442i
\(146\) 0 0
\(147\) 167.828 290.686i 0.0941645 0.163098i
\(148\) 0 0
\(149\) −977.620 564.429i −0.537515 0.310335i 0.206556 0.978435i \(-0.433774\pi\)
−0.744071 + 0.668100i \(0.767108\pi\)
\(150\) 0 0
\(151\) 2940.44i 1.58470i −0.610066 0.792350i \(-0.708857\pi\)
0.610066 0.792350i \(-0.291143\pi\)
\(152\) 0 0
\(153\) 18.7359 + 32.4516i 0.00990006 + 0.0171474i
\(154\) 0 0
\(155\) 556.093 0.288171
\(156\) 0 0
\(157\) 629.388 0.319940 0.159970 0.987122i \(-0.448860\pi\)
0.159970 + 0.987122i \(0.448860\pi\)
\(158\) 0 0
\(159\) −15.7085 27.2079i −0.00783500 0.0135706i
\(160\) 0 0
\(161\) 719.444i 0.352175i
\(162\) 0 0
\(163\) 342.004 + 197.456i 0.164343 + 0.0948832i 0.579915 0.814677i \(-0.303086\pi\)
−0.415573 + 0.909560i \(0.636419\pi\)
\(164\) 0 0
\(165\) 270.514 468.543i 0.127633 0.221067i
\(166\) 0 0
\(167\) −131.515 + 75.9299i −0.0609395 + 0.0351834i −0.530160 0.847898i \(-0.677868\pi\)
0.469221 + 0.883081i \(0.344535\pi\)
\(168\) 0 0
\(169\) 2195.66 + 76.7357i 0.999390 + 0.0349275i
\(170\) 0 0
\(171\) −203.312 + 117.382i −0.0909221 + 0.0524939i
\(172\) 0 0
\(173\) 269.407 466.626i 0.118397 0.205069i −0.800736 0.599018i \(-0.795558\pi\)
0.919132 + 0.393949i \(0.128891\pi\)
\(174\) 0 0
\(175\) −1550.00 894.892i −0.669537 0.386557i
\(176\) 0 0
\(177\) 1335.34i 0.567065i
\(178\) 0 0
\(179\) 1110.40 + 1923.27i 0.463659 + 0.803081i 0.999140 0.0414660i \(-0.0132028\pi\)
−0.535481 + 0.844548i \(0.679870\pi\)
\(180\) 0 0
\(181\) 3822.78 1.56986 0.784932 0.619582i \(-0.212698\pi\)
0.784932 + 0.619582i \(0.212698\pi\)
\(182\) 0 0
\(183\) −359.089 −0.145052
\(184\) 0 0
\(185\) −236.852 410.240i −0.0941282 0.163035i
\(186\) 0 0
\(187\) 278.478i 0.108900i
\(188\) 0 0
\(189\) 355.474 + 205.233i 0.136809 + 0.0789869i
\(190\) 0 0
\(191\) 1732.09 3000.08i 0.656178 1.13653i −0.325419 0.945570i \(-0.605505\pi\)
0.981597 0.190964i \(-0.0611612\pi\)
\(192\) 0 0
\(193\) −4068.07 + 2348.70i −1.51723 + 0.875975i −0.517438 + 0.855721i \(0.673114\pi\)
−0.999795 + 0.0202541i \(0.993552\pi\)
\(194\) 0 0
\(195\) −331.611 + 183.809i −0.121780 + 0.0675017i
\(196\) 0 0
\(197\) −2500.98 + 1443.94i −0.904506 + 0.522217i −0.878660 0.477449i \(-0.841562\pi\)
−0.0258469 + 0.999666i \(0.508228\pi\)
\(198\) 0 0
\(199\) −31.5046 + 54.5676i −0.0112226 + 0.0194382i −0.871582 0.490249i \(-0.836906\pi\)
0.860360 + 0.509688i \(0.170239\pi\)
\(200\) 0 0
\(201\) 58.2171 + 33.6117i 0.0204294 + 0.0117949i
\(202\) 0 0
\(203\) 3907.14i 1.35087i
\(204\) 0 0
\(205\) 210.936 + 365.352i 0.0718654 + 0.124474i
\(206\) 0 0
\(207\) 425.918 0.143011
\(208\) 0 0
\(209\) −1744.69 −0.577429
\(210\) 0 0
\(211\) −524.848 909.064i −0.171242 0.296600i 0.767612 0.640914i \(-0.221445\pi\)
−0.938854 + 0.344315i \(0.888111\pi\)
\(212\) 0 0
\(213\) 855.622i 0.275241i
\(214\) 0 0
\(215\) −121.388 70.0832i −0.0385050 0.0222309i
\(216\) 0 0
\(217\) −1567.69 + 2715.33i −0.490424 + 0.849440i
\(218\) 0 0
\(219\) 1925.15 1111.48i 0.594015 0.342955i
\(220\) 0 0
\(221\) 100.514 167.278i 0.0305942 0.0509156i
\(222\) 0 0
\(223\) −2003.54 + 1156.75i −0.601647 + 0.347361i −0.769689 0.638419i \(-0.779589\pi\)
0.168042 + 0.985780i \(0.446255\pi\)
\(224\) 0 0
\(225\) −529.785 + 917.614i −0.156973 + 0.271886i
\(226\) 0 0
\(227\) 3290.43 + 1899.73i 0.962085 + 0.555460i 0.896814 0.442407i \(-0.145875\pi\)
0.0652711 + 0.997868i \(0.479209\pi\)
\(228\) 0 0
\(229\) 4321.07i 1.24692i 0.781856 + 0.623459i \(0.214273\pi\)
−0.781856 + 0.623459i \(0.785727\pi\)
\(230\) 0 0
\(231\) 1525.22 + 2641.76i 0.434425 + 0.752446i
\(232\) 0 0
\(233\) −5279.77 −1.48450 −0.742251 0.670122i \(-0.766242\pi\)
−0.742251 + 0.670122i \(0.766242\pi\)
\(234\) 0 0
\(235\) 955.094 0.265121
\(236\) 0 0
\(237\) 821.518 + 1422.91i 0.225162 + 0.389992i
\(238\) 0 0
\(239\) 1547.92i 0.418939i −0.977815 0.209469i \(-0.932826\pi\)
0.977815 0.209469i \(-0.0671737\pi\)
\(240\) 0 0
\(241\) −4259.12 2459.00i −1.13840 0.657255i −0.192365 0.981323i \(-0.561616\pi\)
−0.946033 + 0.324069i \(0.894949\pi\)
\(242\) 0 0
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 261.260 150.839i 0.0681277 0.0393336i
\(246\) 0 0
\(247\) 1048.02 + 629.731i 0.269974 + 0.162222i
\(248\) 0 0
\(249\) 1566.78 904.584i 0.398759 0.230224i
\(250\) 0 0
\(251\) −577.890 + 1000.94i −0.145323 + 0.251707i −0.929493 0.368839i \(-0.879756\pi\)
0.784170 + 0.620546i \(0.213089\pi\)
\(252\) 0 0
\(253\) 2741.20 + 1582.63i 0.681178 + 0.393278i
\(254\) 0 0
\(255\) 33.6786i 0.00827073i
\(256\) 0 0
\(257\) 1175.98 + 2036.85i 0.285429 + 0.494378i 0.972713 0.232011i \(-0.0745304\pi\)
−0.687284 + 0.726389i \(0.741197\pi\)
\(258\) 0 0
\(259\) 2670.86 0.640769
\(260\) 0 0
\(261\) 2313.06 0.548563
\(262\) 0 0
\(263\) 2760.94 + 4782.09i 0.647326 + 1.12120i 0.983759 + 0.179494i \(0.0574461\pi\)
−0.336433 + 0.941707i \(0.609221\pi\)
\(264\) 0 0
\(265\) 28.2367i 0.00654553i
\(266\) 0 0
\(267\) −560.322 323.502i −0.128431 0.0741499i
\(268\) 0 0
\(269\) −1958.48 + 3392.18i −0.443905 + 0.768866i −0.997975 0.0636038i \(-0.979741\pi\)
0.554070 + 0.832470i \(0.313074\pi\)
\(270\) 0 0
\(271\) −2405.41 + 1388.76i −0.539182 + 0.311297i −0.744747 0.667347i \(-0.767430\pi\)
0.205566 + 0.978643i \(0.434097\pi\)
\(272\) 0 0
\(273\) 37.3383 2137.39i 0.00827771 0.473849i
\(274\) 0 0
\(275\) −6819.38 + 3937.17i −1.49536 + 0.863347i
\(276\) 0 0
\(277\) 3291.54 5701.12i 0.713969 1.23663i −0.249386 0.968404i \(-0.580229\pi\)
0.963356 0.268227i \(-0.0864378\pi\)
\(278\) 0 0
\(279\) 1607.50 + 928.090i 0.344941 + 0.199152i
\(280\) 0 0
\(281\) 2871.66i 0.609640i −0.952410 0.304820i \(-0.901404\pi\)
0.952410 0.304820i \(-0.0985963\pi\)
\(282\) 0 0
\(283\) −3759.02 6510.81i −0.789578 1.36759i −0.926226 0.376969i \(-0.876966\pi\)
0.136648 0.990620i \(-0.456367\pi\)
\(284\) 0 0
\(285\) −211.000 −0.0438546
\(286\) 0 0
\(287\) −2378.62 −0.489217
\(288\) 0 0
\(289\) 2447.83 + 4239.77i 0.498236 + 0.862970i
\(290\) 0 0
\(291\) 4342.51i 0.874785i
\(292\) 0 0
\(293\) 3902.80 + 2253.28i 0.778171 + 0.449278i 0.835782 0.549062i \(-0.185015\pi\)
−0.0576104 + 0.998339i \(0.518348\pi\)
\(294\) 0 0
\(295\) 600.083 1039.37i 0.118435 0.205135i
\(296\) 0 0
\(297\) 1563.95 902.945i 0.305554 0.176411i
\(298\) 0 0
\(299\) −1075.37 1940.08i −0.207994 0.375244i
\(300\) 0 0
\(301\) 684.413 395.146i 0.131060 0.0756673i
\(302\) 0 0
\(303\) 1325.18 2295.27i 0.251252 0.435181i
\(304\) 0 0
\(305\) −279.500 161.369i −0.0524725 0.0302950i
\(306\) 0 0
\(307\) 9538.89i 1.77333i 0.462409 + 0.886667i \(0.346985\pi\)
−0.462409 + 0.886667i \(0.653015\pi\)
\(308\) 0 0
\(309\) 1877.61 + 3252.12i 0.345675 + 0.598726i
\(310\) 0 0
\(311\) −7466.28 −1.36133 −0.680666 0.732594i \(-0.738309\pi\)
−0.680666 + 0.732594i \(0.738309\pi\)
\(312\) 0 0
\(313\) −1821.65 −0.328964 −0.164482 0.986380i \(-0.552595\pi\)
−0.164482 + 0.986380i \(0.552595\pi\)
\(314\) 0 0
\(315\) 184.458 + 319.490i 0.0329937 + 0.0571467i
\(316\) 0 0
\(317\) 3125.14i 0.553708i 0.960912 + 0.276854i \(0.0892918\pi\)
−0.960912 + 0.276854i \(0.910708\pi\)
\(318\) 0 0
\(319\) 14886.9 + 8594.93i 2.61287 + 1.50854i
\(320\) 0 0
\(321\) 512.420 887.538i 0.0890982 0.154323i
\(322\) 0 0
\(323\) 94.0554 54.3029i 0.0162024 0.00935448i
\(324\) 0 0
\(325\) 5517.41 + 96.3842i 0.941696 + 0.0164506i
\(326\) 0 0
\(327\) −2013.97 + 1162.77i −0.340589 + 0.196639i
\(328\) 0 0
\(329\) −2692.53 + 4663.59i −0.451197 + 0.781496i
\(330\) 0 0
\(331\) −1345.52 776.836i −0.223433 0.128999i 0.384106 0.923289i \(-0.374510\pi\)
−0.607539 + 0.794290i \(0.707843\pi\)
\(332\) 0 0
\(333\) 1581.17i 0.260204i
\(334\) 0 0
\(335\) 30.2092 + 52.3238i 0.00492688 + 0.00853360i
\(336\) 0 0
\(337\) 3190.43 0.515709 0.257855 0.966184i \(-0.416984\pi\)
0.257855 + 0.966184i \(0.416984\pi\)
\(338\) 0 0
\(339\) −3837.15 −0.614764
\(340\) 0 0
\(341\) 6897.24 + 11946.4i 1.09533 + 1.89716i
\(342\) 0 0
\(343\) 6915.37i 1.08862i
\(344\) 0 0
\(345\) 331.516 + 191.401i 0.0517340 + 0.0298687i
\(346\) 0 0
\(347\) −2859.34 + 4952.53i −0.442356 + 0.766183i −0.997864 0.0653283i \(-0.979191\pi\)
0.555508 + 0.831511i \(0.312524\pi\)
\(348\) 0 0
\(349\) 2882.53 1664.23i 0.442116 0.255256i −0.262379 0.964965i \(-0.584507\pi\)
0.704495 + 0.709709i \(0.251174\pi\)
\(350\) 0 0
\(351\) −1265.36 22.1046i −0.192421 0.00336141i
\(352\) 0 0
\(353\) −10657.7 + 6153.25i −1.60695 + 0.927774i −0.616905 + 0.787037i \(0.711614\pi\)
−0.990047 + 0.140737i \(0.955053\pi\)
\(354\) 0 0
\(355\) −384.504 + 665.981i −0.0574855 + 0.0995679i
\(356\) 0 0
\(357\) −164.448 94.9441i −0.0243796 0.0140756i
\(358\) 0 0
\(359\) 8539.97i 1.25549i 0.778418 + 0.627747i \(0.216023\pi\)
−0.778418 + 0.627747i \(0.783977\pi\)
\(360\) 0 0
\(361\) −3089.29 5350.80i −0.450399 0.780114i
\(362\) 0 0
\(363\) 9427.74 1.36316
\(364\) 0 0
\(365\) 1997.94 0.286512
\(366\) 0 0
\(367\) 1248.33 + 2162.17i 0.177553 + 0.307532i 0.941042 0.338290i \(-0.109848\pi\)
−0.763489 + 0.645821i \(0.776515\pi\)
\(368\) 0 0
\(369\) 1408.16i 0.198661i
\(370\) 0 0
\(371\) 137.876 + 79.6026i 0.0192942 + 0.0111395i
\(372\) 0 0
\(373\) 571.454 989.787i 0.0793264 0.137397i −0.823633 0.567123i \(-0.808056\pi\)
0.902960 + 0.429726i \(0.141390\pi\)
\(374\) 0 0
\(375\) −1700.38 + 981.713i −0.234152 + 0.135188i
\(376\) 0 0
\(377\) −5840.10 10536.2i −0.797826 1.43936i
\(378\) 0 0
\(379\) 10549.8 6090.91i 1.42983 0.825512i 0.432723 0.901527i \(-0.357553\pi\)
0.997107 + 0.0760146i \(0.0242196\pi\)
\(380\) 0 0
\(381\) −1670.73 + 2893.79i −0.224657 + 0.389117i
\(382\) 0 0
\(383\) −8816.66 5090.30i −1.17627 0.679118i −0.221119 0.975247i \(-0.570971\pi\)
−0.955148 + 0.296129i \(0.904304\pi\)
\(384\) 0 0
\(385\) 2741.65i 0.362928i
\(386\) 0 0
\(387\) −233.930 405.179i −0.0307270 0.0532207i
\(388\) 0 0
\(389\) −5845.83 −0.761941 −0.380971 0.924587i \(-0.624410\pi\)
−0.380971 + 0.924587i \(0.624410\pi\)
\(390\) 0 0
\(391\) −197.036 −0.0254848
\(392\) 0 0
\(393\) −3150.19 5456.28i −0.404341 0.700339i
\(394\) 0 0
\(395\) 1476.71i 0.188105i
\(396\) 0 0
\(397\) −2165.86 1250.46i −0.273807 0.158083i 0.356809 0.934177i \(-0.383865\pi\)
−0.630617 + 0.776094i \(0.717198\pi\)
\(398\) 0 0
\(399\) 594.834 1030.28i 0.0746340 0.129270i
\(400\) 0 0
\(401\) 7958.12 4594.62i 0.991046 0.572181i 0.0854594 0.996342i \(-0.472764\pi\)
0.905587 + 0.424161i \(0.139431\pi\)
\(402\) 0 0
\(403\) 168.848 9665.54i 0.0208708 1.19473i
\(404\) 0 0
\(405\) 189.141 109.201i 0.0232062 0.0133981i
\(406\) 0 0
\(407\) 5875.36 10176.4i 0.715555 1.23938i
\(408\) 0 0
\(409\) −7979.89 4607.19i −0.964744 0.556995i −0.0671140 0.997745i \(-0.521379\pi\)
−0.897630 + 0.440750i \(0.854712\pi\)
\(410\) 0 0
\(411\) 3615.05i 0.433862i
\(412\) 0 0
\(413\) 3383.42 + 5860.25i 0.403116 + 0.698218i
\(414\) 0 0
\(415\) 1626.03 0.192334
\(416\) 0 0
\(417\) 968.669 0.113755
\(418\) 0 0
\(419\) −3247.20 5624.32i −0.378607 0.655767i 0.612253 0.790662i \(-0.290263\pi\)
−0.990860 + 0.134895i \(0.956930\pi\)
\(420\) 0 0
\(421\) 3059.56i 0.354190i 0.984194 + 0.177095i \(0.0566699\pi\)
−0.984194 + 0.177095i \(0.943330\pi\)
\(422\) 0 0
\(423\) 2760.89 + 1594.00i 0.317350 + 0.183222i
\(424\) 0 0
\(425\) 245.087 424.502i 0.0279728 0.0484503i
\(426\) 0 0
\(427\) 1575.89 909.839i 0.178601 0.103115i
\(428\) 0 0
\(429\) −8061.69 4844.10i −0.907277 0.545164i
\(430\) 0 0
\(431\) −6873.69 + 3968.53i −0.768199 + 0.443520i −0.832232 0.554428i \(-0.812937\pi\)
0.0640325 + 0.997948i \(0.479604\pi\)
\(432\) 0 0
\(433\) 3647.19 6317.11i 0.404786 0.701111i −0.589510 0.807761i \(-0.700679\pi\)
0.994297 + 0.106650i \(0.0340125\pi\)
\(434\) 0 0
\(435\) 1800.39 + 1039.46i 0.198442 + 0.114570i
\(436\) 0 0
\(437\) 1234.45i 0.135130i
\(438\) 0 0
\(439\) −7607.35 13176.3i −0.827059 1.43251i −0.900335 0.435197i \(-0.856679\pi\)
0.0732765 0.997312i \(-0.476654\pi\)
\(440\) 0 0
\(441\) 1006.97 0.108732
\(442\) 0 0
\(443\) −1517.05 −0.162703 −0.0813515 0.996685i \(-0.525924\pi\)
−0.0813515 + 0.996685i \(0.525924\pi\)
\(444\) 0 0
\(445\) −290.754 503.601i −0.0309732 0.0536472i
\(446\) 0 0
\(447\) 3386.58i 0.358343i
\(448\) 0 0
\(449\) −610.761 352.623i −0.0641951 0.0370631i 0.467559 0.883962i \(-0.345134\pi\)
−0.531754 + 0.846899i \(0.678467\pi\)
\(450\) 0 0
\(451\) −5232.48 + 9062.93i −0.546315 + 0.946245i
\(452\) 0 0
\(453\) 7639.49 4410.66i 0.792350 0.457464i
\(454\) 0 0
\(455\) 989.575 1646.88i 0.101960 0.169685i
\(456\) 0 0
\(457\) −6302.69 + 3638.86i −0.645137 + 0.372470i −0.786591 0.617475i \(-0.788156\pi\)
0.141454 + 0.989945i \(0.454822\pi\)
\(458\) 0 0
\(459\) −56.2078 + 97.3547i −0.00571580 + 0.00990006i
\(460\) 0 0
\(461\) −1699.04 980.941i −0.171653 0.0991041i 0.411712 0.911314i \(-0.364931\pi\)
−0.583365 + 0.812210i \(0.698264\pi\)
\(462\) 0 0
\(463\) 10374.1i 1.04131i −0.853768 0.520653i \(-0.825689\pi\)
0.853768 0.520653i \(-0.174311\pi\)
\(464\) 0 0
\(465\) 834.140 + 1444.77i 0.0831878 + 0.144085i
\(466\) 0 0
\(467\) 8788.92 0.870883 0.435442 0.900217i \(-0.356592\pi\)
0.435442 + 0.900217i \(0.356592\pi\)
\(468\) 0 0
\(469\) −340.653 −0.0335392
\(470\) 0 0
\(471\) 944.082 + 1635.20i 0.0923588 + 0.159970i
\(472\) 0 0
\(473\) 3476.97i 0.337995i
\(474\) 0 0
\(475\) 2659.55 + 1535.49i 0.256902 + 0.148322i
\(476\) 0 0
\(477\) 47.1255 81.6237i 0.00452354 0.00783500i
\(478\) 0 0
\(479\) −9648.96 + 5570.83i −0.920401 + 0.531394i −0.883763 0.467935i \(-0.844998\pi\)
−0.0366382 + 0.999329i \(0.511665\pi\)
\(480\) 0 0
\(481\) −7202.36 + 3992.20i −0.682743 + 0.378438i
\(482\) 0 0
\(483\) −1869.17 + 1079.17i −0.176087 + 0.101664i
\(484\) 0 0
\(485\) 1951.46 3380.03i 0.182704 0.316452i
\(486\) 0 0
\(487\) −17009.1 9820.23i −1.58266 0.913752i −0.994469 0.105033i \(-0.966505\pi\)
−0.588195 0.808719i \(-0.700161\pi\)
\(488\) 0 0
\(489\) 1184.74i 0.109562i
\(490\) 0 0
\(491\) 1705.16 + 2953.42i 0.156726 + 0.271458i 0.933686 0.358092i \(-0.116573\pi\)
−0.776960 + 0.629550i \(0.783239\pi\)
\(492\) 0 0
\(493\) −1070.06 −0.0977546
\(494\) 0 0
\(495\) 1623.08 0.147378
\(496\) 0 0
\(497\) −2167.93 3754.96i −0.195664 0.338899i
\(498\) 0 0
\(499\) 5032.44i 0.451469i 0.974189 + 0.225735i \(0.0724782\pi\)
−0.974189 + 0.225735i \(0.927522\pi\)
\(500\) 0 0
\(501\) −394.544 227.790i −0.0351834 0.0203132i
\(502\) 0 0
\(503\) 8594.69 14886.4i 0.761866 1.31959i −0.180022 0.983663i \(-0.557617\pi\)
0.941888 0.335927i \(-0.109050\pi\)
\(504\) 0 0
\(505\) 2062.92 1191.03i 0.181780 0.104951i
\(506\) 0 0
\(507\) 3094.12 + 5819.59i 0.271035 + 0.509778i
\(508\) 0 0
\(509\) −805.889 + 465.280i −0.0701776 + 0.0405170i −0.534678 0.845056i \(-0.679567\pi\)
0.464501 + 0.885573i \(0.346234\pi\)
\(510\) 0 0
\(511\) −5632.43 + 9755.65i −0.487601 + 0.844549i
\(512\) 0 0
\(513\) −609.937 352.147i −0.0524939 0.0303074i
\(514\) 0 0
\(515\) 3375.08i 0.288784i
\(516\) 0 0
\(517\) 11846.1 + 20518.0i 1.00772 + 1.74541i
\(518\) 0 0
\(519\) 1616.44 0.136713
\(520\) 0 0
\(521\) −9869.60 −0.829933 −0.414966 0.909837i \(-0.636207\pi\)
−0.414966 + 0.909837i \(0.636207\pi\)
\(522\) 0 0
\(523\) −10710.3 18550.8i −0.895466 1.55099i −0.833226 0.552932i \(-0.813509\pi\)
−0.0622398 0.998061i \(-0.519824\pi\)
\(524\) 0 0
\(525\) 5369.35i 0.446358i
\(526\) 0 0
\(527\) −743.654 429.349i −0.0614688 0.0354890i
\(528\) 0 0
\(529\) 4963.71 8597.40i 0.407965 0.706616i
\(530\) 0 0
\(531\) 3469.32 2003.01i 0.283532 0.163697i
\(532\) 0 0
\(533\) 6414.28 3555.38i 0.521263 0.288931i
\(534\) 0 0
\(535\) 797.693 460.548i 0.0644622 0.0372173i
\(536\) 0 0
\(537\) −3331.19 + 5769.80i −0.267694 + 0.463659i
\(538\) 0 0
\(539\) 6480.83 + 3741.71i 0.517902 + 0.299011i
\(540\) 0 0
\(541\) 7771.50i 0.617602i −0.951127 0.308801i \(-0.900072\pi\)
0.951127 0.308801i \(-0.0999277\pi\)
\(542\) 0 0
\(543\) 5734.17 + 9931.88i 0.453180 + 0.784932i
\(544\) 0 0
\(545\) −2090.12 −0.164277
\(546\) 0 0
\(547\) 15577.5 1.21763 0.608817 0.793310i \(-0.291644\pi\)
0.608817 + 0.793310i \(0.291644\pi\)
\(548\) 0 0
\(549\) −538.633 932.940i −0.0418730 0.0725262i
\(550\) 0 0
\(551\) 6704.02i 0.518332i
\(552\) 0 0
\(553\) −7210.58 4163.03i −0.554476 0.320127i
\(554\) 0 0
\(555\) 710.556 1230.72i 0.0543449 0.0941282i
\(556\) 0 0
\(557\) 19749.3 11402.3i 1.50234 0.867377i 0.502345 0.864667i \(-0.332471\pi\)
0.999996 0.00270962i \(-0.000862500\pi\)
\(558\) 0 0
\(559\) −1254.98 + 2088.58i −0.0949556 + 0.158028i
\(560\) 0 0
\(561\) −723.506 + 417.716i −0.0544500 + 0.0314367i
\(562\) 0 0
\(563\) 1758.71 3046.17i 0.131653 0.228030i −0.792661 0.609663i \(-0.791305\pi\)
0.924314 + 0.381633i \(0.124638\pi\)
\(564\) 0 0
\(565\) −2986.67 1724.36i −0.222390 0.128397i
\(566\) 0 0
\(567\) 1231.40i 0.0912062i
\(568\) 0 0
\(569\) −3046.72 5277.08i −0.224473 0.388799i 0.731688 0.681640i \(-0.238733\pi\)
−0.956161 + 0.292841i \(0.905399\pi\)
\(570\) 0 0
\(571\) 10460.2 0.766630 0.383315 0.923618i \(-0.374782\pi\)
0.383315 + 0.923618i \(0.374782\pi\)
\(572\) 0 0
\(573\) 10392.6 0.757689
\(574\) 0 0
\(575\) −2785.74 4825.03i −0.202040 0.349944i
\(576\) 0 0
\(577\) 9648.19i 0.696117i −0.937473 0.348058i \(-0.886841\pi\)
0.937473 0.348058i \(-0.113159\pi\)
\(578\) 0 0
\(579\) −12204.2 7046.10i −0.875975 0.505744i
\(580\) 0 0
\(581\) −4583.97 + 7939.66i −0.327324 + 0.566941i
\(582\) 0 0
\(583\) 606.599 350.220i 0.0430922 0.0248793i
\(584\) 0 0
\(585\) −974.966 585.838i −0.0689058 0.0414041i
\(586\) 0 0
\(587\) −1879.91 + 1085.37i −0.132184 + 0.0763166i −0.564634 0.825341i \(-0.690983\pi\)
0.432450 + 0.901658i \(0.357649\pi\)
\(588\) 0 0
\(589\) 2689.91 4659.06i 0.188176 0.325931i
\(590\) 0 0
\(591\) −7502.95 4331.83i −0.522217 0.301502i
\(592\) 0 0
\(593\) 22885.9i 1.58484i −0.609975 0.792421i \(-0.708820\pi\)
0.609975 0.792421i \(-0.291180\pi\)
\(594\) 0 0
\(595\) −85.3330 147.801i −0.00587951 0.0101836i
\(596\) 0 0
\(597\) −189.028 −0.0129588
\(598\) 0 0
\(599\) 23978.7 1.63563 0.817815 0.575482i \(-0.195185\pi\)
0.817815 + 0.575482i \(0.195185\pi\)
\(600\) 0 0
\(601\) −6436.62 11148.6i −0.436864 0.756671i 0.560582 0.828099i \(-0.310578\pi\)
−0.997446 + 0.0714284i \(0.977244\pi\)
\(602\) 0 0
\(603\) 201.670i 0.0136196i
\(604\) 0 0
\(605\) 7338.16 + 4236.69i 0.493122 + 0.284704i
\(606\) 0 0
\(607\) −3558.57 + 6163.63i −0.237954 + 0.412148i −0.960127 0.279564i \(-0.909810\pi\)
0.722173 + 0.691712i \(0.243143\pi\)
\(608\) 0 0
\(609\) −10151.0 + 5860.71i −0.675437 + 0.389964i
\(610\) 0 0
\(611\) 289.998 16600.6i 0.0192014 1.09917i
\(612\) 0 0
\(613\) 150.079 86.6484i 0.00988850 0.00570913i −0.495048 0.868866i \(-0.664849\pi\)
0.504936 + 0.863157i \(0.331516\pi\)
\(614\) 0 0
\(615\) −632.808 + 1096.06i −0.0414915 + 0.0718654i
\(616\) 0 0
\(617\) 5285.14 + 3051.38i 0.344849 + 0.199099i 0.662414 0.749138i \(-0.269532\pi\)
−0.317565 + 0.948236i \(0.602865\pi\)
\(618\) 0 0
\(619\) 14867.8i 0.965409i −0.875783 0.482705i \(-0.839654\pi\)
0.875783 0.482705i \(-0.160346\pi\)
\(620\) 0 0
\(621\) 638.876 + 1106.57i 0.0412838 + 0.0715056i
\(622\) 0 0
\(623\) 3278.69 0.210847
\(624\) 0 0
\(625\) 12951.6 0.828900
\(626\) 0 0
\(627\) −2617.03 4532.84i −0.166689 0.288715i
\(628\) 0 0
\(629\) 731.475i 0.0463686i
\(630\) 0 0
\(631\) 14904.8 + 8605.29i 0.940334 + 0.542902i 0.890065 0.455834i \(-0.150659\pi\)
0.0502690 + 0.998736i \(0.483992\pi\)
\(632\) 0 0
\(633\) 1574.55 2727.19i 0.0988666 0.171242i
\(634\) 0 0
\(635\) −2600.86 + 1501.60i −0.162538 + 0.0938415i
\(636\) 0 0
\(637\) −2542.42 4586.80i −0.158139 0.285299i
\(638\) 0 0
\(639\) −2222.97 + 1283.43i −0.137620 + 0.0794552i
\(640\) 0 0
\(641\) −6318.01 + 10943.1i −0.389308 + 0.674301i −0.992357 0.123403i \(-0.960619\pi\)
0.603049 + 0.797704i \(0.293953\pi\)
\(642\) 0 0
\(643\) −8302.04 4793.19i −0.509177 0.293973i 0.223318 0.974746i \(-0.428311\pi\)
−0.732495 + 0.680772i \(0.761644\pi\)
\(644\) 0 0
\(645\) 420.499i 0.0256700i
\(646\) 0 0
\(647\) −2622.16 4541.72i −0.159332 0.275971i 0.775296 0.631598i \(-0.217601\pi\)
−0.934628 + 0.355627i \(0.884267\pi\)
\(648\) 0 0
\(649\) 29771.4 1.80066
\(650\) 0 0
\(651\) −9406.17 −0.566293
\(652\) 0 0
\(653\) −9434.51 16341.1i −0.565392 0.979288i −0.997013 0.0772326i \(-0.975392\pi\)
0.431621 0.902055i \(-0.357942\pi\)
\(654\) 0 0
\(655\) 5662.59i 0.337795i
\(656\) 0 0
\(657\) 5775.44 + 3334.45i 0.342955 + 0.198005i
\(658\) 0 0
\(659\) −12149.9 + 21044.2i −0.718197 + 1.24395i 0.243516 + 0.969897i \(0.421699\pi\)
−0.961713 + 0.274057i \(0.911634\pi\)
\(660\) 0 0
\(661\) −25907.2 + 14957.5i −1.52447 + 0.880151i −0.524886 + 0.851173i \(0.675892\pi\)
−0.999580 + 0.0289779i \(0.990775\pi\)
\(662\) 0 0
\(663\) 585.373 + 10.2259i 0.0342896 + 0.000599008i
\(664\) 0 0
\(665\) 925.988 534.620i 0.0539974 0.0311754i
\(666\) 0 0
\(667\) −6081.32 + 10533.2i −0.353028 + 0.611462i
\(668\) 0 0
\(669\) −6010.63 3470.24i −0.347361 0.200549i
\(670\) 0 0
\(671\) 8005.86i 0.460600i
\(672\) 0 0
\(673\) 7746.84 + 13417.9i 0.443713 + 0.768533i 0.997962 0.0638177i \(-0.0203276\pi\)
−0.554249 + 0.832351i \(0.686994\pi\)
\(674\) 0 0
\(675\) −3178.71 −0.181257
\(676\) 0 0
\(677\) 11729.7 0.665891 0.332945 0.942946i \(-0.391958\pi\)
0.332945 + 0.942946i \(0.391958\pi\)
\(678\) 0 0
\(679\) 11002.8 + 19057.4i 0.621869 + 1.07711i
\(680\) 0 0
\(681\) 11398.4i 0.641390i
\(682\) 0 0
\(683\) 1011.88 + 584.210i 0.0566889 + 0.0327294i 0.528077 0.849197i \(-0.322913\pi\)
−0.471388 + 0.881926i \(0.656247\pi\)
\(684\) 0 0
\(685\) 1624.55 2813.81i 0.0906145 0.156949i
\(686\) 0 0
\(687\) −11226.5 + 6481.61i −0.623459 + 0.359955i
\(688\) 0 0
\(689\) −490.786 8.57358i −0.0271371 0.000474060i
\(690\) 0 0
\(691\) −28572.7 + 16496.4i −1.57302 + 0.908183i −0.577222 + 0.816587i \(0.695863\pi\)
−0.995796 + 0.0915952i \(0.970803\pi\)
\(692\) 0 0
\(693\) −4575.66 + 7925.28i −0.250815 + 0.434425i
\(694\) 0 0
\(695\) 753.972 + 435.306i 0.0411508 + 0.0237584i
\(696\) 0 0
\(697\) 651.438i 0.0354017i
\(698\) 0 0
\(699\) −7919.65 13717.2i −0.428539 0.742251i
\(700\) 0 0
\(701\) 14785.8 0.796651 0.398326 0.917244i \(-0.369591\pi\)
0.398326 + 0.917244i \(0.369591\pi\)
\(702\) 0 0
\(703\) −4582.77 −0.245864
\(704\) 0 0
\(705\) 1432.64 + 2481.41i 0.0765339 + 0.132561i
\(706\) 0 0
\(707\) 13430.6i 0.714442i
\(708\) 0 0
\(709\) 10941.4 + 6317.00i 0.579565 + 0.334612i 0.760961 0.648798i \(-0.224728\pi\)
−0.181395 + 0.983410i \(0.558061\pi\)
\(710\) 0 0
\(711\) −2464.55 + 4268.73i −0.129997 + 0.225162i
\(712\) 0 0
\(713\) −8452.62 + 4880.12i −0.443973 + 0.256328i
\(714\) 0 0
\(715\) −4098.01 7393.25i −0.214345 0.386702i
\(716\) 0 0
\(717\) 4021.60 2321.87i 0.209469 0.120937i
\(718\) 0 0
\(719\) 13648.3 23639.5i 0.707920 1.22615i −0.257707 0.966223i \(-0.582967\pi\)
0.965627 0.259931i \(-0.0836998\pi\)
\(720\) 0 0
\(721\) −16480.1 9514.77i −0.851248 0.491468i
\(722\) 0 0
\(723\) 14754.0i 0.758932i
\(724\) 0 0
\(725\) −15128.7 26203.7i −0.774987 1.34232i
\(726\) 0 0
\(727\) 4658.21 0.237639 0.118819 0.992916i \(-0.462089\pi\)
0.118819 + 0.992916i \(0.462089\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 108.220 + 187.442i 0.00547558 + 0.00948399i
\(732\) 0 0
\(733\) 166.474i 0.00838864i −0.999991 0.00419432i \(-0.998665\pi\)
0.999991 0.00419432i \(-0.00133510\pi\)
\(734\) 0 0
\(735\) 783.780 + 452.516i 0.0393336 + 0.0227092i
\(736\) 0 0
\(737\) −749.370 + 1297.95i −0.0374537 + 0.0648718i
\(738\) 0 0
\(739\) 11031.5 6369.03i 0.549120 0.317035i −0.199647 0.979868i \(-0.563980\pi\)
0.748767 + 0.662833i \(0.230646\pi\)
\(740\) 0 0
\(741\) −64.0665 + 3667.42i −0.00317617 + 0.181817i
\(742\) 0 0
\(743\) 26608.2 15362.2i 1.31381 0.758527i 0.331083 0.943602i \(-0.392586\pi\)
0.982725 + 0.185074i \(0.0592526\pi\)
\(744\) 0 0
\(745\) 1521.88 2635.97i 0.0748420 0.129630i
\(746\) 0 0
\(747\) 4700.35 + 2713.75i 0.230224 + 0.132920i
\(748\) 0 0
\(749\) 5193.37i 0.253353i
\(750\) 0 0
\(751\) 19769.3 + 34241.4i 0.960575 + 1.66376i 0.721061 + 0.692872i \(0.243655\pi\)
0.239514 + 0.970893i \(0.423012\pi\)
\(752\) 0 0
\(753\) −3467.34 −0.167805
\(754\) 0 0
\(755\) 7928.35 0.382175
\(756\) 0 0
\(757\) −11517.6 19949.0i −0.552990 0.957807i −0.998057 0.0623093i \(-0.980153\pi\)
0.445067 0.895497i \(-0.353180\pi\)
\(758\) 0 0
\(759\) 9495.81i 0.454119i
\(760\) 0 0
\(761\) 28106.0 + 16227.0i 1.33882 + 0.772968i 0.986632 0.162962i \(-0.0521047\pi\)
0.352187 + 0.935930i \(0.385438\pi\)
\(762\) 0 0
\(763\) 5892.30 10205.8i 0.279575 0.484238i
\(764\) 0 0
\(765\) −87.4996 + 50.5179i −0.00413536 + 0.00238755i
\(766\) 0 0
\(767\) −17883.3 10745.7i −0.841890 0.505874i
\(768\) 0 0
\(769\) −27900.1 + 16108.1i −1.30833 + 0.755362i −0.981817 0.189831i \(-0.939206\pi\)
−0.326509 + 0.945194i \(0.605873\pi\)
\(770\) 0 0
\(771\) −3527.93 + 6110.55i −0.164793 + 0.285429i
\(772\) 0 0
\(773\) −2532.78 1462.30i −0.117849 0.0680404i 0.439917 0.898039i \(-0.355008\pi\)
−0.557766 + 0.829998i \(0.688341\pi\)
\(774\) 0 0
\(775\) 24280.9i 1.12541i
\(776\) 0 0
\(777\) 4006.29 + 6939.10i 0.184974 + 0.320384i
\(778\) 0 0
\(779\) 4081.32 0.187713
\(780\) 0 0
\(781\) −19076.1 −0.874001
\(782\) 0 0
\(783\) 3469.59 + 6009.51i 0.158357 + 0.274282i
\(784\) 0 0
\(785\) 1697.03i 0.0771586i
\(786\) 0 0
\(787\) −22089.8 12753.6i −1.00053 0.577656i −0.0921250 0.995747i \(-0.529366\pi\)
−0.908405 + 0.418091i \(0.862699\pi\)
\(788\) 0 0
\(789\) −8282.82 + 14346.3i −0.373734 + 0.647326i
\(790\) 0 0
\(791\)