Properties

Label 624.4.q.c.289.1
Level $624$
Weight $4$
Character 624.289
Analytic conductor $36.817$
Analytic rank $0$
Dimension $2$
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.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 289.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 624.289
Dual form 624.4.q.c.529.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 2.59808i) q^{3} +7.00000 q^{5} +(-5.00000 + 8.66025i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 + 2.59808i) q^{3} +7.00000 q^{5} +(-5.00000 + 8.66025i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-11.0000 - 19.0526i) q^{11} +(-45.5000 + 11.2583i) q^{13} +(10.5000 + 18.1865i) q^{15} +(-18.5000 + 32.0429i) q^{17} +(15.0000 - 25.9808i) q^{19} -30.0000 q^{21} +(-81.0000 - 140.296i) q^{23} -76.0000 q^{25} -27.0000 q^{27} +(56.5000 + 97.8609i) q^{29} -196.000 q^{31} +(33.0000 - 57.1577i) q^{33} +(-35.0000 + 60.6218i) q^{35} +(-6.50000 - 11.2583i) q^{37} +(-97.5000 - 101.325i) q^{39} +(-142.500 - 246.817i) q^{41} +(-123.000 + 213.042i) q^{43} +(-31.5000 + 54.5596i) q^{45} +462.000 q^{47} +(121.500 + 210.444i) q^{49} -111.000 q^{51} -537.000 q^{53} +(-77.0000 - 133.368i) q^{55} +90.0000 q^{57} +(288.000 - 498.831i) q^{59} +(317.500 - 549.926i) q^{61} +(-45.0000 - 77.9423i) q^{63} +(-318.500 + 78.8083i) q^{65} +(101.000 + 174.937i) q^{67} +(243.000 - 420.888i) q^{69} +(-543.000 + 940.504i) q^{71} -805.000 q^{73} +(-114.000 - 197.454i) q^{75} +220.000 q^{77} -884.000 q^{79} +(-40.5000 - 70.1481i) q^{81} -518.000 q^{83} +(-129.500 + 224.301i) q^{85} +(-169.500 + 293.583i) q^{87} +(-97.0000 - 168.009i) q^{89} +(130.000 - 450.333i) q^{91} +(-294.000 - 509.223i) q^{93} +(105.000 - 181.865i) q^{95} +(601.000 - 1040.96i) q^{97} +198.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + 14 q^{5} - 10 q^{7} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} + 14 q^{5} - 10 q^{7} - 9 q^{9} - 22 q^{11} - 91 q^{13} + 21 q^{15} - 37 q^{17} + 30 q^{19} - 60 q^{21} - 162 q^{23} - 152 q^{25} - 54 q^{27} + 113 q^{29} - 392 q^{31} + 66 q^{33} - 70 q^{35} - 13 q^{37} - 195 q^{39} - 285 q^{41} - 246 q^{43} - 63 q^{45} + 924 q^{47} + 243 q^{49} - 222 q^{51} - 1074 q^{53} - 154 q^{55} + 180 q^{57} + 576 q^{59} + 635 q^{61} - 90 q^{63} - 637 q^{65} + 202 q^{67} + 486 q^{69} - 1086 q^{71} - 1610 q^{73} - 228 q^{75} + 440 q^{77} - 1768 q^{79} - 81 q^{81} - 1036 q^{83} - 259 q^{85} - 339 q^{87} - 194 q^{89} + 260 q^{91} - 588 q^{93} + 210 q^{95} + 1202 q^{97} + 396 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) 7.00000 0.626099 0.313050 0.949737i \(-0.398649\pi\)
0.313050 + 0.949737i \(0.398649\pi\)
\(6\) 0 0
\(7\) −5.00000 + 8.66025i −0.269975 + 0.467610i −0.968855 0.247629i \(-0.920349\pi\)
0.698880 + 0.715239i \(0.253682\pi\)
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −11.0000 19.0526i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) −45.5000 + 11.2583i −0.970725 + 0.240192i
\(14\) 0 0
\(15\) 10.5000 + 18.1865i 0.180739 + 0.313050i
\(16\) 0 0
\(17\) −18.5000 + 32.0429i −0.263936 + 0.457150i −0.967284 0.253695i \(-0.918354\pi\)
0.703348 + 0.710845i \(0.251687\pi\)
\(18\) 0 0
\(19\) 15.0000 25.9808i 0.181118 0.313705i −0.761144 0.648583i \(-0.775362\pi\)
0.942261 + 0.334878i \(0.108695\pi\)
\(20\) 0 0
\(21\) −30.0000 −0.311740
\(22\) 0 0
\(23\) −81.0000 140.296i −0.734333 1.27190i −0.955015 0.296557i \(-0.904162\pi\)
0.220682 0.975346i \(-0.429172\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 56.5000 + 97.8609i 0.361786 + 0.626631i 0.988255 0.152815i \(-0.0488339\pi\)
−0.626469 + 0.779446i \(0.715501\pi\)
\(30\) 0 0
\(31\) −196.000 −1.13557 −0.567785 0.823177i \(-0.692199\pi\)
−0.567785 + 0.823177i \(0.692199\pi\)
\(32\) 0 0
\(33\) 33.0000 57.1577i 0.174078 0.301511i
\(34\) 0 0
\(35\) −35.0000 + 60.6218i −0.169031 + 0.292770i
\(36\) 0 0
\(37\) −6.50000 11.2583i −0.0288809 0.0500232i 0.851224 0.524803i \(-0.175861\pi\)
−0.880105 + 0.474780i \(0.842528\pi\)
\(38\) 0 0
\(39\) −97.5000 101.325i −0.400320 0.416025i
\(40\) 0 0
\(41\) −142.500 246.817i −0.542799 0.940156i −0.998742 0.0501465i \(-0.984031\pi\)
0.455943 0.890009i \(-0.349302\pi\)
\(42\) 0 0
\(43\) −123.000 + 213.042i −0.436217 + 0.755550i −0.997394 0.0721459i \(-0.977015\pi\)
0.561177 + 0.827696i \(0.310349\pi\)
\(44\) 0 0
\(45\) −31.5000 + 54.5596i −0.104350 + 0.180739i
\(46\) 0 0
\(47\) 462.000 1.43382 0.716911 0.697165i \(-0.245555\pi\)
0.716911 + 0.697165i \(0.245555\pi\)
\(48\) 0 0
\(49\) 121.500 + 210.444i 0.354227 + 0.613540i
\(50\) 0 0
\(51\) −111.000 −0.304767
\(52\) 0 0
\(53\) −537.000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(54\) 0 0
\(55\) −77.0000 133.368i −0.188776 0.326970i
\(56\) 0 0
\(57\) 90.0000 0.209137
\(58\) 0 0
\(59\) 288.000 498.831i 0.635498 1.10072i −0.350911 0.936409i \(-0.614128\pi\)
0.986409 0.164307i \(-0.0525387\pi\)
\(60\) 0 0
\(61\) 317.500 549.926i 0.666421 1.15428i −0.312476 0.949926i \(-0.601159\pi\)
0.978898 0.204350i \(-0.0655082\pi\)
\(62\) 0 0
\(63\) −45.0000 77.9423i −0.0899915 0.155870i
\(64\) 0 0
\(65\) −318.500 + 78.8083i −0.607770 + 0.150384i
\(66\) 0 0
\(67\) 101.000 + 174.937i 0.184166 + 0.318985i 0.943295 0.331955i \(-0.107708\pi\)
−0.759129 + 0.650940i \(0.774375\pi\)
\(68\) 0 0
\(69\) 243.000 420.888i 0.423968 0.734333i
\(70\) 0 0
\(71\) −543.000 + 940.504i −0.907637 + 1.57207i −0.0902997 + 0.995915i \(0.528783\pi\)
−0.817338 + 0.576159i \(0.804551\pi\)
\(72\) 0 0
\(73\) −805.000 −1.29066 −0.645330 0.763904i \(-0.723280\pi\)
−0.645330 + 0.763904i \(0.723280\pi\)
\(74\) 0 0
\(75\) −114.000 197.454i −0.175514 0.304000i
\(76\) 0 0
\(77\) 220.000 0.325602
\(78\) 0 0
\(79\) −884.000 −1.25896 −0.629480 0.777017i \(-0.716732\pi\)
−0.629480 + 0.777017i \(0.716732\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −518.000 −0.685035 −0.342517 0.939511i \(-0.611280\pi\)
−0.342517 + 0.939511i \(0.611280\pi\)
\(84\) 0 0
\(85\) −129.500 + 224.301i −0.165250 + 0.286221i
\(86\) 0 0
\(87\) −169.500 + 293.583i −0.208877 + 0.361786i
\(88\) 0 0
\(89\) −97.0000 168.009i −0.115528 0.200100i 0.802463 0.596702i \(-0.203523\pi\)
−0.917991 + 0.396602i \(0.870189\pi\)
\(90\) 0 0
\(91\) 130.000 450.333i 0.149755 0.518766i
\(92\) 0 0
\(93\) −294.000 509.223i −0.327811 0.567785i
\(94\) 0 0
\(95\) 105.000 181.865i 0.113398 0.196410i
\(96\) 0 0
\(97\) 601.000 1040.96i 0.629096 1.08963i −0.358638 0.933477i \(-0.616759\pi\)
0.987733 0.156149i \(-0.0499081\pi\)
\(98\) 0 0
\(99\) 198.000 0.201008
\(100\) 0 0
\(101\) 214.500 + 371.525i 0.211322 + 0.366021i 0.952129 0.305698i \(-0.0988897\pi\)
−0.740806 + 0.671719i \(0.765556\pi\)
\(102\) 0 0
\(103\) 1302.00 1.24553 0.622766 0.782408i \(-0.286009\pi\)
0.622766 + 0.782408i \(0.286009\pi\)
\(104\) 0 0
\(105\) −210.000 −0.195180
\(106\) 0 0
\(107\) −669.000 1158.74i −0.604436 1.04691i −0.992140 0.125130i \(-0.960065\pi\)
0.387704 0.921784i \(-0.373268\pi\)
\(108\) 0 0
\(109\) −1034.00 −0.908617 −0.454308 0.890844i \(-0.650114\pi\)
−0.454308 + 0.890844i \(0.650114\pi\)
\(110\) 0 0
\(111\) 19.5000 33.7750i 0.0166744 0.0288809i
\(112\) 0 0
\(113\) −538.500 + 932.709i −0.448299 + 0.776477i −0.998275 0.0587032i \(-0.981303\pi\)
0.549976 + 0.835180i \(0.314637\pi\)
\(114\) 0 0
\(115\) −567.000 982.073i −0.459765 0.796337i
\(116\) 0 0
\(117\) 117.000 405.300i 0.0924500 0.320256i
\(118\) 0 0
\(119\) −185.000 320.429i −0.142512 0.246838i
\(120\) 0 0
\(121\) 423.500 733.524i 0.318182 0.551107i
\(122\) 0 0
\(123\) 427.500 740.452i 0.313385 0.542799i
\(124\) 0 0
\(125\) −1407.00 −1.00677
\(126\) 0 0
\(127\) −494.000 855.633i −0.345161 0.597836i 0.640222 0.768190i \(-0.278842\pi\)
−0.985383 + 0.170354i \(0.945509\pi\)
\(128\) 0 0
\(129\) −738.000 −0.503700
\(130\) 0 0
\(131\) −560.000 −0.373492 −0.186746 0.982408i \(-0.559794\pi\)
−0.186746 + 0.982408i \(0.559794\pi\)
\(132\) 0 0
\(133\) 150.000 + 259.808i 0.0977944 + 0.169385i
\(134\) 0 0
\(135\) −189.000 −0.120493
\(136\) 0 0
\(137\) 259.500 449.467i 0.161829 0.280296i −0.773696 0.633557i \(-0.781594\pi\)
0.935525 + 0.353261i \(0.114927\pi\)
\(138\) 0 0
\(139\) −174.000 + 301.377i −0.106176 + 0.183903i −0.914218 0.405222i \(-0.867194\pi\)
0.808042 + 0.589125i \(0.200527\pi\)
\(140\) 0 0
\(141\) 693.000 + 1200.31i 0.413909 + 0.716911i
\(142\) 0 0
\(143\) 715.000 + 743.050i 0.418121 + 0.434524i
\(144\) 0 0
\(145\) 395.500 + 685.026i 0.226514 + 0.392333i
\(146\) 0 0
\(147\) −364.500 + 631.333i −0.204513 + 0.354227i
\(148\) 0 0
\(149\) 322.500 558.586i 0.177317 0.307122i −0.763644 0.645638i \(-0.776592\pi\)
0.940961 + 0.338516i \(0.109925\pi\)
\(150\) 0 0
\(151\) −2914.00 −1.57045 −0.785225 0.619211i \(-0.787453\pi\)
−0.785225 + 0.619211i \(0.787453\pi\)
\(152\) 0 0
\(153\) −166.500 288.386i −0.0879786 0.152383i
\(154\) 0 0
\(155\) −1372.00 −0.710979
\(156\) 0 0
\(157\) −2079.00 −1.05683 −0.528415 0.848986i \(-0.677213\pi\)
−0.528415 + 0.848986i \(0.677213\pi\)
\(158\) 0 0
\(159\) −805.500 1395.17i −0.401763 0.695874i
\(160\) 0 0
\(161\) 1620.00 0.793006
\(162\) 0 0
\(163\) 850.000 1472.24i 0.408449 0.707454i −0.586267 0.810118i \(-0.699403\pi\)
0.994716 + 0.102664i \(0.0327365\pi\)
\(164\) 0 0
\(165\) 231.000 400.104i 0.108990 0.188776i
\(166\) 0 0
\(167\) 1840.00 + 3186.97i 0.852596 + 1.47674i 0.878858 + 0.477084i \(0.158306\pi\)
−0.0262621 + 0.999655i \(0.508360\pi\)
\(168\) 0 0
\(169\) 1943.50 1024.51i 0.884615 0.466321i
\(170\) 0 0
\(171\) 135.000 + 233.827i 0.0603726 + 0.104568i
\(172\) 0 0
\(173\) −2073.00 + 3590.54i −0.911025 + 1.57794i −0.0984052 + 0.995146i \(0.531374\pi\)
−0.812619 + 0.582795i \(0.801959\pi\)
\(174\) 0 0
\(175\) 380.000 658.179i 0.164145 0.284307i
\(176\) 0 0
\(177\) 1728.00 0.733810
\(178\) 0 0
\(179\) 1837.00 + 3181.78i 0.767060 + 1.32859i 0.939150 + 0.343506i \(0.111615\pi\)
−0.172090 + 0.985081i \(0.555052\pi\)
\(180\) 0 0
\(181\) −3283.00 −1.34820 −0.674098 0.738642i \(-0.735467\pi\)
−0.674098 + 0.738642i \(0.735467\pi\)
\(182\) 0 0
\(183\) 1905.00 0.769517
\(184\) 0 0
\(185\) −45.5000 78.8083i −0.0180823 0.0313195i
\(186\) 0 0
\(187\) 814.000 0.318319
\(188\) 0 0
\(189\) 135.000 233.827i 0.0519566 0.0899915i
\(190\) 0 0
\(191\) −298.000 + 516.151i −0.112893 + 0.195536i −0.916935 0.399036i \(-0.869345\pi\)
0.804043 + 0.594572i \(0.202678\pi\)
\(192\) 0 0
\(193\) 196.500 + 340.348i 0.0732869 + 0.126937i 0.900340 0.435187i \(-0.143318\pi\)
−0.827053 + 0.562124i \(0.809984\pi\)
\(194\) 0 0
\(195\) −682.500 709.275i −0.250640 0.260473i
\(196\) 0 0
\(197\) 1761.00 + 3050.14i 0.636884 + 1.10311i 0.986113 + 0.166077i \(0.0531101\pi\)
−0.349229 + 0.937037i \(0.613557\pi\)
\(198\) 0 0
\(199\) 1009.00 1747.64i 0.359428 0.622547i −0.628438 0.777860i \(-0.716305\pi\)
0.987865 + 0.155313i \(0.0496386\pi\)
\(200\) 0 0
\(201\) −303.000 + 524.811i −0.106328 + 0.184166i
\(202\) 0 0
\(203\) −1130.00 −0.390692
\(204\) 0 0
\(205\) −997.500 1727.72i −0.339846 0.588630i
\(206\) 0 0
\(207\) 1458.00 0.489556
\(208\) 0 0
\(209\) −660.000 −0.218436
\(210\) 0 0
\(211\) 80.0000 + 138.564i 0.0261016 + 0.0452092i 0.878781 0.477225i \(-0.158357\pi\)
−0.852680 + 0.522434i \(0.825024\pi\)
\(212\) 0 0
\(213\) −3258.00 −1.04805
\(214\) 0 0
\(215\) −861.000 + 1491.30i −0.273115 + 0.473049i
\(216\) 0 0
\(217\) 980.000 1697.41i 0.306575 0.531003i
\(218\) 0 0
\(219\) −1207.50 2091.45i −0.372581 0.645330i
\(220\) 0 0
\(221\) 481.000 1666.23i 0.146405 0.507163i
\(222\) 0 0
\(223\) 2036.00 + 3526.46i 0.611393 + 1.05896i 0.991006 + 0.133818i \(0.0427239\pi\)
−0.379613 + 0.925145i \(0.623943\pi\)
\(224\) 0 0
\(225\) 342.000 592.361i 0.101333 0.175514i
\(226\) 0 0
\(227\) −2897.00 + 5017.75i −0.847051 + 1.46714i 0.0367765 + 0.999324i \(0.488291\pi\)
−0.883828 + 0.467812i \(0.845042\pi\)
\(228\) 0 0
\(229\) 6482.00 1.87049 0.935246 0.353999i \(-0.115178\pi\)
0.935246 + 0.353999i \(0.115178\pi\)
\(230\) 0 0
\(231\) 330.000 + 571.577i 0.0939931 + 0.162801i
\(232\) 0 0
\(233\) 6890.00 1.93725 0.968624 0.248530i \(-0.0799474\pi\)
0.968624 + 0.248530i \(0.0799474\pi\)
\(234\) 0 0
\(235\) 3234.00 0.897714
\(236\) 0 0
\(237\) −1326.00 2296.70i −0.363430 0.629480i
\(238\) 0 0
\(239\) −2466.00 −0.667415 −0.333708 0.942677i \(-0.608300\pi\)
−0.333708 + 0.942677i \(0.608300\pi\)
\(240\) 0 0
\(241\) 1808.50 3132.41i 0.483385 0.837247i −0.516433 0.856327i \(-0.672741\pi\)
0.999818 + 0.0190805i \(0.00607389\pi\)
\(242\) 0 0
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 850.500 + 1473.11i 0.221781 + 0.384137i
\(246\) 0 0
\(247\) −390.000 + 1351.00i −0.100466 + 0.348024i
\(248\) 0 0
\(249\) −777.000 1345.80i −0.197753 0.342517i
\(250\) 0 0
\(251\) 2430.00 4208.88i 0.611077 1.05842i −0.379983 0.924994i \(-0.624070\pi\)
0.991059 0.133422i \(-0.0425966\pi\)
\(252\) 0 0
\(253\) −1782.00 + 3086.51i −0.442820 + 0.766986i
\(254\) 0 0
\(255\) −777.000 −0.190814
\(256\) 0 0
\(257\) −282.500 489.304i −0.0685676 0.118763i 0.829703 0.558204i \(-0.188510\pi\)
−0.898271 + 0.439442i \(0.855176\pi\)
\(258\) 0 0
\(259\) 130.000 0.0311884
\(260\) 0 0
\(261\) −1017.00 −0.241190
\(262\) 0 0
\(263\) −249.000 431.281i −0.0583802 0.101118i 0.835358 0.549706i \(-0.185260\pi\)
−0.893738 + 0.448588i \(0.851927\pi\)
\(264\) 0 0
\(265\) −3759.00 −0.871372
\(266\) 0 0
\(267\) 291.000 504.027i 0.0667000 0.115528i
\(268\) 0 0
\(269\) −2773.00 + 4802.98i −0.628523 + 1.08863i 0.359325 + 0.933213i \(0.383007\pi\)
−0.987848 + 0.155422i \(0.950326\pi\)
\(270\) 0 0
\(271\) −1128.00 1953.75i −0.252845 0.437941i 0.711463 0.702724i \(-0.248033\pi\)
−0.964308 + 0.264783i \(0.914700\pi\)
\(272\) 0 0
\(273\) 1365.00 337.750i 0.302614 0.0748775i
\(274\) 0 0
\(275\) 836.000 + 1447.99i 0.183319 + 0.317518i
\(276\) 0 0
\(277\) −1154.50 + 1999.65i −0.250423 + 0.433745i −0.963642 0.267196i \(-0.913903\pi\)
0.713219 + 0.700941i \(0.247236\pi\)
\(278\) 0 0
\(279\) 882.000 1527.67i 0.189262 0.327811i
\(280\) 0 0
\(281\) 5833.00 1.23832 0.619159 0.785265i \(-0.287473\pi\)
0.619159 + 0.785265i \(0.287473\pi\)
\(282\) 0 0
\(283\) 825.000 + 1428.94i 0.173290 + 0.300148i 0.939568 0.342362i \(-0.111227\pi\)
−0.766278 + 0.642509i \(0.777893\pi\)
\(284\) 0 0
\(285\) 630.000 0.130940
\(286\) 0 0
\(287\) 2850.00 0.586168
\(288\) 0 0
\(289\) 1772.00 + 3069.19i 0.360676 + 0.624709i
\(290\) 0 0
\(291\) 3606.00 0.726417
\(292\) 0 0
\(293\) −1495.50 + 2590.28i −0.298184 + 0.516471i −0.975721 0.219019i \(-0.929714\pi\)
0.677536 + 0.735489i \(0.263048\pi\)
\(294\) 0 0
\(295\) 2016.00 3491.81i 0.397885 0.689157i
\(296\) 0 0
\(297\) 297.000 + 514.419i 0.0580259 + 0.100504i
\(298\) 0 0
\(299\) 5265.00 + 5471.55i 1.01834 + 1.05829i
\(300\) 0 0
\(301\) −1230.00 2130.42i −0.235535 0.407959i
\(302\) 0 0
\(303\) −643.500 + 1114.57i −0.122007 + 0.211322i
\(304\) 0 0
\(305\) 2222.50 3849.48i 0.417246 0.722691i
\(306\) 0 0
\(307\) 2422.00 0.450263 0.225132 0.974328i \(-0.427719\pi\)
0.225132 + 0.974328i \(0.427719\pi\)
\(308\) 0 0
\(309\) 1953.00 + 3382.70i 0.359554 + 0.622766i
\(310\) 0 0
\(311\) 3402.00 0.620288 0.310144 0.950690i \(-0.399623\pi\)
0.310144 + 0.950690i \(0.399623\pi\)
\(312\) 0 0
\(313\) 2310.00 0.417153 0.208577 0.978006i \(-0.433117\pi\)
0.208577 + 0.978006i \(0.433117\pi\)
\(314\) 0 0
\(315\) −315.000 545.596i −0.0563436 0.0975900i
\(316\) 0 0
\(317\) −257.000 −0.0455349 −0.0227674 0.999741i \(-0.507248\pi\)
−0.0227674 + 0.999741i \(0.507248\pi\)
\(318\) 0 0
\(319\) 1243.00 2152.94i 0.218165 0.377873i
\(320\) 0 0
\(321\) 2007.00 3476.23i 0.348971 0.604436i
\(322\) 0 0
\(323\) 555.000 + 961.288i 0.0956069 + 0.165596i
\(324\) 0 0
\(325\) 3458.00 855.633i 0.590201 0.146037i
\(326\) 0 0
\(327\) −1551.00 2686.41i −0.262295 0.454308i
\(328\) 0 0
\(329\) −2310.00 + 4001.04i −0.387096 + 0.670469i
\(330\) 0 0
\(331\) 514.000 890.274i 0.0853535 0.147837i −0.820188 0.572094i \(-0.806131\pi\)
0.905542 + 0.424257i \(0.139465\pi\)
\(332\) 0 0
\(333\) 117.000 0.0192539
\(334\) 0 0
\(335\) 707.000 + 1224.56i 0.115306 + 0.199716i
\(336\) 0 0
\(337\) 2487.00 0.402005 0.201002 0.979591i \(-0.435580\pi\)
0.201002 + 0.979591i \(0.435580\pi\)
\(338\) 0 0
\(339\) −3231.00 −0.517651
\(340\) 0 0
\(341\) 2156.00 + 3734.30i 0.342387 + 0.593032i
\(342\) 0 0
\(343\) −5860.00 −0.922479
\(344\) 0 0
\(345\) 1701.00 2946.22i 0.265446 0.459765i
\(346\) 0 0
\(347\) −1425.00 + 2468.17i −0.220455 + 0.381840i −0.954946 0.296779i \(-0.904088\pi\)
0.734491 + 0.678618i \(0.237421\pi\)
\(348\) 0 0
\(349\) 1009.00 + 1747.64i 0.154758 + 0.268049i 0.932971 0.359952i \(-0.117207\pi\)
−0.778213 + 0.628001i \(0.783874\pi\)
\(350\) 0 0
\(351\) 1228.50 303.975i 0.186816 0.0462250i
\(352\) 0 0
\(353\) 2643.50 + 4578.68i 0.398582 + 0.690364i 0.993551 0.113385i \(-0.0361692\pi\)
−0.594970 + 0.803748i \(0.702836\pi\)
\(354\) 0 0
\(355\) −3801.00 + 6583.53i −0.568271 + 0.984274i
\(356\) 0 0
\(357\) 555.000 961.288i 0.0822793 0.142512i
\(358\) 0 0
\(359\) 7278.00 1.06997 0.534983 0.844863i \(-0.320318\pi\)
0.534983 + 0.844863i \(0.320318\pi\)
\(360\) 0 0
\(361\) 2979.50 + 5160.65i 0.434393 + 0.752390i
\(362\) 0 0
\(363\) 2541.00 0.367405
\(364\) 0 0
\(365\) −5635.00 −0.808080
\(366\) 0 0
\(367\) −2101.00 3639.04i −0.298832 0.517592i 0.677037 0.735949i \(-0.263264\pi\)
−0.975869 + 0.218357i \(0.929930\pi\)
\(368\) 0 0
\(369\) 2565.00 0.361866
\(370\) 0 0
\(371\) 2685.00 4650.56i 0.375737 0.650795i
\(372\) 0 0
\(373\) 791.500 1370.92i 0.109872 0.190304i −0.805846 0.592125i \(-0.798289\pi\)
0.915718 + 0.401821i \(0.131623\pi\)
\(374\) 0 0
\(375\) −2110.50 3655.49i −0.290629 0.503384i
\(376\) 0 0
\(377\) −3672.50 3816.57i −0.501707 0.521389i
\(378\) 0 0
\(379\) −1026.00 1777.08i −0.139056 0.240851i 0.788084 0.615568i \(-0.211073\pi\)
−0.927139 + 0.374717i \(0.877740\pi\)
\(380\) 0 0
\(381\) 1482.00 2566.90i 0.199279 0.345161i
\(382\) 0 0
\(383\) −3436.00 + 5951.33i −0.458411 + 0.793991i −0.998877 0.0473746i \(-0.984915\pi\)
0.540466 + 0.841366i \(0.318248\pi\)
\(384\) 0 0
\(385\) 1540.00 0.203859
\(386\) 0 0
\(387\) −1107.00 1917.38i −0.145406 0.251850i
\(388\) 0 0
\(389\) −11653.0 −1.51884 −0.759422 0.650598i \(-0.774518\pi\)
−0.759422 + 0.650598i \(0.774518\pi\)
\(390\) 0 0
\(391\) 5994.00 0.775268
\(392\) 0 0
\(393\) −840.000 1454.92i −0.107818 0.186746i
\(394\) 0 0
\(395\) −6188.00 −0.788233
\(396\) 0 0
\(397\) −3067.00 + 5312.20i −0.387729 + 0.671566i −0.992144 0.125104i \(-0.960074\pi\)
0.604415 + 0.796670i \(0.293407\pi\)
\(398\) 0 0
\(399\) −450.000 + 779.423i −0.0564616 + 0.0977944i
\(400\) 0 0
\(401\) 5397.50 + 9348.74i 0.672165 + 1.16422i 0.977289 + 0.211912i \(0.0679689\pi\)
−0.305124 + 0.952313i \(0.598698\pi\)
\(402\) 0 0
\(403\) 8918.00 2206.63i 1.10233 0.272755i
\(404\) 0 0
\(405\) −283.500 491.036i −0.0347833 0.0602464i
\(406\) 0 0
\(407\) −143.000 + 247.683i −0.0174158 + 0.0301651i
\(408\) 0 0
\(409\) 4244.50 7351.69i 0.513147 0.888796i −0.486737 0.873549i \(-0.661813\pi\)
0.999884 0.0152477i \(-0.00485367\pi\)
\(410\) 0 0
\(411\) 1557.00 0.186864
\(412\) 0 0
\(413\) 2880.00 + 4988.31i 0.343137 + 0.594331i
\(414\) 0 0
\(415\) −3626.00 −0.428900
\(416\) 0 0
\(417\) −1044.00 −0.122602
\(418\) 0 0
\(419\) 748.000 + 1295.57i 0.0872129 + 0.151057i 0.906332 0.422566i \(-0.138871\pi\)
−0.819119 + 0.573623i \(0.805537\pi\)
\(420\) 0 0
\(421\) −11695.0 −1.35387 −0.676935 0.736043i \(-0.736692\pi\)
−0.676935 + 0.736043i \(0.736692\pi\)
\(422\) 0 0
\(423\) −2079.00 + 3600.93i −0.238970 + 0.413909i
\(424\) 0 0
\(425\) 1406.00 2435.26i 0.160473 0.277947i
\(426\) 0 0
\(427\) 3175.00 + 5499.26i 0.359834 + 0.623250i
\(428\) 0 0
\(429\) −858.000 + 2972.20i −0.0965609 + 0.334497i
\(430\) 0 0
\(431\) 5295.00 + 9171.21i 0.591766 + 1.02497i 0.993995 + 0.109430i \(0.0349024\pi\)
−0.402228 + 0.915539i \(0.631764\pi\)
\(432\) 0 0
\(433\) 6974.50 12080.2i 0.774072 1.34073i −0.161243 0.986915i \(-0.551550\pi\)
0.935315 0.353817i \(-0.115116\pi\)
\(434\) 0 0
\(435\) −1186.50 + 2055.08i −0.130778 + 0.226514i
\(436\) 0 0
\(437\) −4860.00 −0.532003
\(438\) 0 0
\(439\) −5363.00 9288.99i −0.583057 1.00988i −0.995115 0.0987266i \(-0.968523\pi\)
0.412058 0.911158i \(-0.364810\pi\)
\(440\) 0 0
\(441\) −2187.00 −0.236152
\(442\) 0 0
\(443\) −16228.0 −1.74044 −0.870221 0.492662i \(-0.836024\pi\)
−0.870221 + 0.492662i \(0.836024\pi\)
\(444\) 0 0
\(445\) −679.000 1176.06i −0.0723319 0.125282i
\(446\) 0 0
\(447\) 1935.00 0.204748
\(448\) 0 0
\(449\) −3769.00 + 6528.10i −0.396147 + 0.686147i −0.993247 0.116020i \(-0.962986\pi\)
0.597100 + 0.802167i \(0.296320\pi\)
\(450\) 0 0
\(451\) −3135.00 + 5429.98i −0.327320 + 0.566935i
\(452\) 0 0
\(453\) −4371.00 7570.79i −0.453350 0.785225i
\(454\) 0 0
\(455\) 910.000 3152.33i 0.0937614 0.324799i
\(456\) 0 0
\(457\) −7769.50 13457.2i −0.795278 1.37746i −0.922663 0.385608i \(-0.873992\pi\)
0.127385 0.991853i \(-0.459342\pi\)
\(458\) 0 0
\(459\) 499.500 865.159i 0.0507945 0.0879786i
\(460\) 0 0
\(461\) −2405.50 + 4166.45i −0.243027 + 0.420935i −0.961575 0.274543i \(-0.911474\pi\)
0.718548 + 0.695477i \(0.244807\pi\)
\(462\) 0 0
\(463\) −562.000 −0.0564111 −0.0282056 0.999602i \(-0.508979\pi\)
−0.0282056 + 0.999602i \(0.508979\pi\)
\(464\) 0 0
\(465\) −2058.00 3564.56i −0.205242 0.355489i
\(466\) 0 0
\(467\) −4914.00 −0.486922 −0.243461 0.969911i \(-0.578283\pi\)
−0.243461 + 0.969911i \(0.578283\pi\)
\(468\) 0 0
\(469\) −2020.00 −0.198880
\(470\) 0 0
\(471\) −3118.50 5401.40i −0.305080 0.528415i
\(472\) 0 0
\(473\) 5412.00 0.526097
\(474\) 0 0
\(475\) −1140.00 + 1974.54i −0.110120 + 0.190733i
\(476\) 0 0
\(477\) 2416.50 4185.50i 0.231958 0.401763i
\(478\) 0 0
\(479\) −1800.00 3117.69i −0.171700 0.297392i 0.767315 0.641271i \(-0.221593\pi\)
−0.939014 + 0.343878i \(0.888259\pi\)
\(480\) 0 0
\(481\) 422.500 + 439.075i 0.0400506 + 0.0416218i
\(482\) 0 0
\(483\) 2430.00 + 4208.88i 0.228921 + 0.396503i
\(484\) 0 0
\(485\) 4207.00 7286.74i 0.393876 0.682214i
\(486\) 0 0
\(487\) −8565.00 + 14835.0i −0.796955 + 1.38037i 0.124635 + 0.992203i \(0.460224\pi\)
−0.921590 + 0.388164i \(0.873109\pi\)
\(488\) 0 0
\(489\) 5100.00 0.471636
\(490\) 0 0
\(491\) −5919.00 10252.0i −0.544034 0.942295i −0.998667 0.0516158i \(-0.983563\pi\)
0.454633 0.890679i \(-0.349770\pi\)
\(492\) 0 0
\(493\) −4181.00 −0.381953
\(494\) 0 0
\(495\) 1386.00 0.125851
\(496\) 0 0
\(497\) −5430.00 9405.04i −0.490078 0.848840i
\(498\) 0 0
\(499\) −8976.00 −0.805252 −0.402626 0.915364i \(-0.631903\pi\)
−0.402626 + 0.915364i \(0.631903\pi\)
\(500\) 0 0
\(501\) −5520.00 + 9560.92i −0.492246 + 0.852596i
\(502\) 0 0
\(503\) 841.000 1456.65i 0.0745494 0.129123i −0.826341 0.563170i \(-0.809581\pi\)
0.900890 + 0.434047i \(0.142915\pi\)
\(504\) 0 0
\(505\) 1501.50 + 2600.67i 0.132309 + 0.229165i
\(506\) 0 0
\(507\) 5577.00 + 3512.60i 0.488527 + 0.307692i
\(508\) 0 0
\(509\) −7583.50 13135.0i −0.660379 1.14381i −0.980516 0.196438i \(-0.937062\pi\)
0.320138 0.947371i \(-0.396271\pi\)
\(510\) 0 0
\(511\) 4025.00 6971.50i 0.348445 0.603525i
\(512\) 0 0
\(513\) −405.000 + 701.481i −0.0348561 + 0.0603726i
\(514\) 0 0
\(515\) 9114.00 0.779827
\(516\) 0 0
\(517\) −5082.00 8802.28i −0.432314 0.748789i
\(518\) 0 0
\(519\) −12438.0 −1.05196
\(520\) 0 0
\(521\) −6783.00 −0.570381 −0.285191 0.958471i \(-0.592057\pi\)
−0.285191 + 0.958471i \(0.592057\pi\)
\(522\) 0 0
\(523\) −6959.00 12053.3i −0.581828 1.00775i −0.995263 0.0972214i \(-0.969005\pi\)
0.413435 0.910534i \(-0.364329\pi\)
\(524\) 0 0
\(525\) 2280.00 0.189538
\(526\) 0 0
\(527\) 3626.00 6280.42i 0.299717 0.519126i
\(528\) 0 0
\(529\) −7038.50 + 12191.0i −0.578491 + 1.00198i
\(530\) 0 0
\(531\) 2592.00 + 4489.48i 0.211833 + 0.366905i
\(532\) 0 0
\(533\) 9262.50 + 9625.87i 0.752727 + 0.782257i
\(534\) 0 0
\(535\) −4683.00 8111.19i −0.378437 0.655472i
\(536\) 0 0
\(537\) −5511.00 + 9545.33i −0.442863 + 0.767060i
\(538\) 0 0
\(539\) 2673.00 4629.77i 0.213607 0.369978i
\(540\) 0 0
\(541\) −1335.00 −0.106093 −0.0530463 0.998592i \(-0.516893\pi\)
−0.0530463 + 0.998592i \(0.516893\pi\)
\(542\) 0 0
\(543\) −4924.50 8529.48i −0.389191 0.674098i
\(544\) 0 0
\(545\) −7238.00 −0.568884
\(546\) 0 0
\(547\) 3806.00 0.297501 0.148750 0.988875i \(-0.452475\pi\)
0.148750 + 0.988875i \(0.452475\pi\)
\(548\) 0 0
\(549\) 2857.50 + 4949.34i 0.222140 + 0.384759i
\(550\) 0 0
\(551\) 3390.00 0.262103
\(552\) 0 0
\(553\) 4420.00 7655.66i 0.339887 0.588702i
\(554\) 0 0
\(555\) 136.500 236.425i 0.0104398 0.0180823i
\(556\) 0 0
\(557\) 952.500 + 1649.78i 0.0724573 + 0.125500i 0.899978 0.435936i \(-0.143583\pi\)
−0.827520 + 0.561436i \(0.810249\pi\)
\(558\) 0 0
\(559\) 3198.00 11078.2i 0.241970 0.838207i
\(560\) 0 0
\(561\) 1221.00 + 2114.83i 0.0918907 + 0.159159i
\(562\) 0 0
\(563\) −2400.00 + 4156.92i −0.179659 + 0.311178i −0.941764 0.336275i \(-0.890833\pi\)
0.762105 + 0.647454i \(0.224166\pi\)
\(564\) 0 0
\(565\) −3769.50 + 6528.97i −0.280680 + 0.486152i
\(566\) 0 0
\(567\) 810.000 0.0599944
\(568\) 0 0
\(569\) −7339.00 12711.5i −0.540715 0.936546i −0.998863 0.0476701i \(-0.984820\pi\)
0.458148 0.888876i \(-0.348513\pi\)
\(570\) 0 0
\(571\) 586.000 0.0429481 0.0214740 0.999769i \(-0.493164\pi\)
0.0214740 + 0.999769i \(0.493164\pi\)
\(572\) 0 0
\(573\) −1788.00 −0.130357
\(574\) 0 0
\(575\) 6156.00 + 10662.5i 0.446475 + 0.773317i
\(576\) 0 0
\(577\) 8939.00 0.644949 0.322474 0.946578i \(-0.395485\pi\)
0.322474 + 0.946578i \(0.395485\pi\)
\(578\) 0 0
\(579\) −589.500 + 1021.04i −0.0423122 + 0.0732869i
\(580\) 0 0
\(581\) 2590.00 4486.01i 0.184942 0.320329i
\(582\) 0 0
\(583\) 5907.00 + 10231.2i 0.419628 + 0.726816i
\(584\) 0 0
\(585\) 819.000 2837.10i 0.0578829 0.200512i
\(586\) 0 0
\(587\) −6896.00 11944.2i −0.484887 0.839848i 0.514963 0.857213i \(-0.327806\pi\)
−0.999849 + 0.0173645i \(0.994472\pi\)
\(588\) 0 0
\(589\) −2940.00 + 5092.23i −0.205672 + 0.356234i
\(590\) 0 0
\(591\) −5283.00 + 9150.42i −0.367705 + 0.636884i
\(592\) 0 0
\(593\) 9569.00 0.662650 0.331325 0.943517i \(-0.392504\pi\)
0.331325 + 0.943517i \(0.392504\pi\)
\(594\) 0 0
\(595\) −1295.00 2243.01i −0.0892266 0.154545i
\(596\) 0 0
\(597\) 6054.00 0.415031
\(598\) 0 0
\(599\) 5192.00 0.354156 0.177078 0.984197i \(-0.443336\pi\)
0.177078 + 0.984197i \(0.443336\pi\)
\(600\) 0 0
\(601\) 1838.50 + 3184.38i 0.124782 + 0.216129i 0.921648 0.388028i \(-0.126844\pi\)
−0.796866 + 0.604156i \(0.793510\pi\)
\(602\) 0 0
\(603\) −1818.00 −0.122777
\(604\) 0 0
\(605\) 2964.50 5134.66i 0.199213 0.345048i
\(606\) 0 0
\(607\) −5480.00 + 9491.64i −0.366435 + 0.634685i −0.989005 0.147879i \(-0.952755\pi\)
0.622570 + 0.782564i \(0.286089\pi\)
\(608\) 0 0
\(609\) −1695.00 2935.83i −0.112783 0.195346i
\(610\) 0 0
\(611\) −21021.0 + 5201.35i −1.39185 + 0.344393i
\(612\) 0 0
\(613\) 13013.5 + 22540.0i 0.857439 + 1.48513i 0.874363 + 0.485272i \(0.161279\pi\)
−0.0169241 + 0.999857i \(0.505387\pi\)
\(614\) 0 0
\(615\) 2992.50 5183.16i 0.196210 0.339846i
\(616\) 0 0
\(617\) −8840.50 + 15312.2i −0.576832 + 0.999102i 0.419008 + 0.907982i \(0.362378\pi\)
−0.995840 + 0.0911193i \(0.970956\pi\)
\(618\) 0 0
\(619\) −3192.00 −0.207265 −0.103633 0.994616i \(-0.533047\pi\)
−0.103633 + 0.994616i \(0.533047\pi\)
\(620\) 0 0
\(621\) 2187.00 + 3788.00i 0.141323 + 0.244778i
\(622\) 0 0
\(623\) 1940.00 0.124758
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 0 0
\(627\) −990.000 1714.73i −0.0630571 0.109218i
\(628\) 0 0
\(629\) 481.000 0.0304908
\(630\) 0 0
\(631\) 3790.00 6564.47i 0.239109 0.414148i −0.721350 0.692571i \(-0.756478\pi\)
0.960459 + 0.278422i \(0.0898115\pi\)
\(632\) 0 0
\(633\) −240.000 + 415.692i −0.0150697 + 0.0261016i
\(634\) 0 0
\(635\) −3458.00 5989.43i −0.216105 0.374304i
\(636\) 0 0
\(637\) −7897.50 8207.32i −0.491225 0.510496i
\(638\) 0 0
\(639\) −4887.00 8464.53i −0.302546 0.524025i
\(640\) 0 0
\(641\) 13853.5 23995.0i 0.853635 1.47854i −0.0242696 0.999705i \(-0.507726\pi\)
0.877905 0.478835i \(-0.158941\pi\)
\(642\) 0 0
\(643\) 5608.00 9713.34i 0.343947 0.595734i −0.641215 0.767361i \(-0.721569\pi\)
0.985162 + 0.171628i \(0.0549026\pi\)
\(644\) 0 0
\(645\) −5166.00 −0.315366
\(646\) 0 0
\(647\) −1268.00 2196.24i −0.0770483 0.133452i 0.824927 0.565239i \(-0.191216\pi\)
−0.901975 + 0.431788i \(0.857883\pi\)
\(648\) 0 0
\(649\) −12672.0 −0.766440
\(650\) 0 0
\(651\) 5880.00 0.354002
\(652\) 0 0
\(653\) −8865.00 15354.6i −0.531262 0.920173i −0.999334 0.0364829i \(-0.988385\pi\)
0.468072 0.883690i \(-0.344949\pi\)
\(654\) 0 0
\(655\) −3920.00 −0.233843
\(656\) 0 0
\(657\) 3622.50 6274.35i 0.215110 0.372581i
\(658\) 0 0
\(659\) 9460.00 16385.2i 0.559195 0.968554i −0.438369 0.898795i \(-0.644444\pi\)
0.997564 0.0697586i \(-0.0222229\pi\)
\(660\) 0 0
\(661\) −2620.50 4538.84i −0.154199 0.267081i 0.778568 0.627560i \(-0.215946\pi\)
−0.932767 + 0.360480i \(0.882613\pi\)
\(662\) 0 0
\(663\) 5050.50 1249.67i 0.295845 0.0732026i
\(664\) 0 0
\(665\) 1050.00 + 1818.65i 0.0612290 + 0.106052i
\(666\) 0 0
\(667\) 9153.00 15853.5i 0.531343 0.920313i
\(668\) 0 0
\(669\) −6108.00 + 10579.4i −0.352988 + 0.611393i
\(670\) 0 0
\(671\) −13970.0 −0.803735
\(672\) 0 0
\(673\) −10233.5 17724.9i −0.586140 1.01522i −0.994732 0.102508i \(-0.967313\pi\)
0.408592 0.912717i \(-0.366020\pi\)
\(674\) 0 0
\(675\) 2052.00 0.117010
\(676\) 0 0
\(677\) −70.0000 −0.00397388 −0.00198694 0.999998i \(-0.500632\pi\)
−0.00198694 + 0.999998i \(0.500632\pi\)
\(678\) 0 0
\(679\) 6010.00 + 10409.6i 0.339680 + 0.588343i
\(680\) 0 0
\(681\) −17382.0 −0.978091
\(682\) 0 0
\(683\) 3216.00 5570.28i 0.180171 0.312065i −0.761768 0.647850i \(-0.775668\pi\)
0.941939 + 0.335785i \(0.109002\pi\)
\(684\) 0 0
\(685\) 1816.50 3146.27i 0.101321 0.175493i
\(686\) 0 0
\(687\) 9723.00 + 16840.7i 0.539964 + 0.935246i
\(688\) 0 0
\(689\) 24433.5 6045.72i 1.35100 0.334287i
\(690\) 0 0
\(691\) −3333.00 5772.93i −0.183492 0.317818i 0.759575 0.650420i \(-0.225407\pi\)
−0.943067 + 0.332601i \(0.892074\pi\)
\(692\) 0 0
\(693\) −990.000 + 1714.73i −0.0542669 + 0.0939931i
\(694\) 0 0
\(695\) −1218.00 + 2109.64i −0.0664768 + 0.115141i
\(696\) 0 0
\(697\) 10545.0 0.573056
\(698\) 0 0
\(699\) 10335.0 + 17900.7i 0.559235 + 0.968624i
\(700\) 0 0
\(701\) −14054.0 −0.757221 −0.378611 0.925556i \(-0.623598\pi\)
−0.378611 + 0.925556i \(0.623598\pi\)
\(702\) 0 0
\(703\) −390.000 −0.0209234
\(704\) 0 0
\(705\) 4851.00 + 8402.18i 0.259148 + 0.448857i
\(706\) 0 0
\(707\) −4290.00 −0.228207
\(708\) 0 0
\(709\) 35.5000 61.4878i 0.00188044 0.00325701i −0.865084 0.501628i \(-0.832735\pi\)
0.866964 + 0.498371i \(0.166068\pi\)
\(710\) 0 0
\(711\) 3978.00 6890.10i 0.209827 0.363430i
\(712\) 0 0
\(713\) 15876.0 + 27498.0i 0.833886 + 1.44433i
\(714\) 0 0
\(715\) 5005.00 + 5201.35i 0.261785 + 0.272055i
\(716\) 0 0
\(717\) −3699.00 6406.86i −0.192666 0.333708i
\(718\) 0 0
\(719\) 1968.00 3408.68i 0.102078 0.176804i −0.810463 0.585790i \(-0.800784\pi\)
0.912541 + 0.408986i \(0.134118\pi\)
\(720\) 0 0
\(721\) −6510.00 + 11275.7i −0.336262 + 0.582423i
\(722\) 0 0
\(723\) 10851.0 0.558165
\(724\) 0 0
\(725\) −4294.00 7437.43i −0.219966 0.380992i
\(726\) 0 0
\(727\) −34202.0 −1.74482 −0.872409 0.488777i \(-0.837443\pi\)
−0.872409 + 0.488777i \(0.837443\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −4551.00 7882.56i −0.230267 0.398833i
\(732\) 0 0
\(733\) −27363.0 −1.37882 −0.689410 0.724371i \(-0.742130\pi\)
−0.689410 + 0.724371i \(0.742130\pi\)
\(734\) 0 0
\(735\) −2551.50 + 4419.33i −0.128046 + 0.221781i
\(736\) 0 0
\(737\) 2222.00 3848.62i 0.111056 0.192355i
\(738\) 0 0
\(739\) 10888.0 + 18858.6i 0.541978 + 0.938733i 0.998790 + 0.0491701i \(0.0156576\pi\)
−0.456813 + 0.889563i \(0.651009\pi\)
\(740\) 0 0
\(741\) −4095.00 + 1013.25i −0.203014 + 0.0502330i
\(742\) 0 0
\(743\) 1242.00 + 2151.21i 0.0613251 + 0.106218i 0.895058 0.445950i \(-0.147134\pi\)
−0.833733 + 0.552168i \(0.813801\pi\)
\(744\) 0 0
\(745\) 2257.50 3910.10i 0.111018 0.192289i
\(746\) 0 0
\(747\) 2331.00 4037.41i 0.114172 0.197753i
\(748\) 0 0
\(749\) 13380.0 0.652730
\(750\) 0 0
\(751\) 16453.0 + 28497.4i 0.799439 + 1.38467i 0.919982 + 0.391960i \(0.128203\pi\)
−0.120543 + 0.992708i \(0.538464\pi\)
\(752\) 0 0
\(753\) 14580.0 0.705611
\(754\) 0 0
\(755\) −20398.0 −0.983257
\(756\) 0 0
\(757\) 1957.00 + 3389.62i 0.0939609 + 0.162745i 0.909174 0.416415i \(-0.136714\pi\)
−0.815214 + 0.579160i \(0.803380\pi\)
\(758\) 0 0
\(759\) −10692.0 −0.511324
\(760\) 0 0
\(761\) 16519.0 28611.7i 0.786877 1.36291i −0.140995 0.990010i \(-0.545030\pi\)
0.927871 0.372900i \(-0.121637\pi\)
\(762\) 0 0
\(763\) 5170.00 8954.70i 0.245303 0.424878i
\(764\) 0 0
\(765\) −1165.50 2018.71i −0.0550833 0.0954071i
\(766\) 0 0
\(767\) −7488.00 + 25939.2i −0.352511 + 1.22113i
\(768\) 0 0
\(769\) 8793.00 + 15229.9i 0.412332 + 0.714181i 0.995144 0.0984263i \(-0.0313809\pi\)
−0.582812 + 0.812607i \(0.698048\pi\)
\(770\) 0 0
\(771\) 847.500 1467.91i 0.0395875 0.0685676i
\(772\) 0 0
\(773\) −9157.00 + 15860.4i −0.426073 + 0.737980i −0.996520 0.0833544i \(-0.973437\pi\)
0.570447 + 0.821334i \(0.306770\pi\)
\(774\) 0 0
\(775\) 14896.0 0.690426
\(776\) 0 0
\(777\) 195.000 + 337.750i 0.00900333 + 0.0155942i
\(778\) 0 0
\(779\) −8550.00 −0.393242
\(780\) 0 0
\(781\) 23892.0 1.09465
\(782\) 0 0
\(783\) −1525.50 2642.24i −0.0696257 0.120595i
\(784\) 0 0
\(785\) −14553.0 −0.661680
\(786\) 0 0
\(787\) −21034.0 + 36432.0i −0.952708 + 1.65014i −0.213180 + 0.977013i \(0.568382\pi\)
−0.739528 + 0.673125i \(0.764951\pi\)
\(788\) 0 0
\(789\) 747.000 1293.84i 0.0337058 0.0583802i
\(790\) 0 0