Properties

Label 39.4.b.a.25.3
Level $39$
Weight $4$
Character 39.25
Analytic conductor $2.301$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.30107449022\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.5054412.1
Defining polynomial: \( x^{4} + 29x^{2} + 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 25.3
Root \(1.32750i\) of defining polynomial
Character \(\chi\) \(=\) 39.25
Dual form 39.4.b.a.25.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.32750i q^{2} -3.00000 q^{3} +6.23774 q^{4} +15.4241i q^{5} -3.98251i q^{6} +7.96501i q^{7} +18.9006i q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+1.32750i q^{2} -3.00000 q^{3} +6.23774 q^{4} +15.4241i q^{5} -3.98251i q^{6} +7.96501i q^{7} +18.9006i q^{8} +9.00000 q^{9} -20.4755 q^{10} -12.7691i q^{11} -18.7132 q^{12} +(7.47548 - 46.2722i) q^{13} -10.5736 q^{14} -46.2722i q^{15} +24.8113 q^{16} +54.0000 q^{17} +11.9475i q^{18} -84.5794i q^{19} +96.2113i q^{20} -23.8950i q^{21} +16.9510 q^{22} -122.853 q^{23} -56.7019i q^{24} -112.902 q^{25} +(61.4264 + 9.92371i) q^{26} -27.0000 q^{27} +49.6837i q^{28} +140.853 q^{29} +61.4264 q^{30} -116.439i q^{31} +184.142i q^{32} +38.3072i q^{33} +71.6851i q^{34} -122.853 q^{35} +56.1397 q^{36} +433.898i q^{37} +112.279 q^{38} +(-22.4264 + 138.817i) q^{39} -291.525 q^{40} -205.823i q^{41} +31.7207 q^{42} +418.853 q^{43} -79.6501i q^{44} +138.817i q^{45} -163.087i q^{46} -485.861i q^{47} -74.4339 q^{48} +279.559 q^{49} -149.877i q^{50} -162.000 q^{51} +(46.6301 - 288.634i) q^{52} -674.559 q^{53} -35.8425i q^{54} +196.951 q^{55} -150.544 q^{56} +253.738i q^{57} +186.982i q^{58} -186.226i q^{59} -288.634i q^{60} -671.902 q^{61} +154.574 q^{62} +71.6851i q^{63} -45.9584 q^{64} +(713.706 + 115.302i) q^{65} -50.8529 q^{66} +14.0364i q^{67} +336.838 q^{68} +368.559 q^{69} -163.087i q^{70} -346.789i q^{71} +170.106i q^{72} +832.900i q^{73} -576.000 q^{74} +338.706 q^{75} -527.584i q^{76} +101.706 q^{77} +(-184.279 - 29.7711i) q^{78} -335.608 q^{79} +382.691i q^{80} +81.0000 q^{81} +273.230 q^{82} +568.797i q^{83} -149.051i q^{84} +832.900i q^{85} +556.028i q^{86} -422.559 q^{87} +241.343 q^{88} +236.671i q^{89} -184.279 q^{90} +(368.559 + 59.5423i) q^{91} -766.324 q^{92} +349.318i q^{93} +644.981 q^{94} +1304.56 q^{95} -552.426i q^{96} -1278.94i q^{97} +371.115i q^{98} -114.922i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{3} - 26 q^{4} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 12 q^{3} - 26 q^{4} + 36 q^{9} + 20 q^{10} + 78 q^{12} - 72 q^{13} - 348 q^{14} + 354 q^{16} + 216 q^{17} - 136 q^{22} + 120 q^{23} - 44 q^{25} - 60 q^{26} - 108 q^{27} - 48 q^{29} - 60 q^{30} + 120 q^{35} - 234 q^{36} - 468 q^{38} + 216 q^{39} - 1268 q^{40} + 1044 q^{42} + 1064 q^{43} - 1062 q^{48} - 716 q^{49} - 648 q^{51} + 1766 q^{52} - 864 q^{53} + 584 q^{55} + 3372 q^{56} - 2280 q^{61} + 924 q^{62} - 1050 q^{64} + 1632 q^{65} + 408 q^{66} - 1404 q^{68} - 360 q^{69} - 2304 q^{74} + 132 q^{75} - 816 q^{77} + 180 q^{78} + 288 q^{79} + 324 q^{81} - 28 q^{82} + 144 q^{87} + 2392 q^{88} + 180 q^{90} - 360 q^{91} - 8568 q^{92} + 6656 q^{94} + 3384 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32750i 0.469343i 0.972075 + 0.234671i \(0.0754014\pi\)
−0.972075 + 0.234671i \(0.924599\pi\)
\(3\) −3.00000 −0.577350
\(4\) 6.23774 0.779717
\(5\) 15.4241i 1.37957i 0.724014 + 0.689785i \(0.242295\pi\)
−0.724014 + 0.689785i \(0.757705\pi\)
\(6\) 3.98251i 0.270975i
\(7\) 7.96501i 0.430070i 0.976606 + 0.215035i \(0.0689866\pi\)
−0.976606 + 0.215035i \(0.931013\pi\)
\(8\) 18.9006i 0.835297i
\(9\) 9.00000 0.333333
\(10\) −20.4755 −0.647491
\(11\) 12.7691i 0.350002i −0.984568 0.175001i \(-0.944007\pi\)
0.984568 0.175001i \(-0.0559928\pi\)
\(12\) −18.7132 −0.450170
\(13\) 7.47548 46.2722i 0.159487 0.987200i
\(14\) −10.5736 −0.201850
\(15\) 46.2722i 0.796496i
\(16\) 24.8113 0.387677
\(17\) 54.0000 0.770407 0.385204 0.922832i \(-0.374131\pi\)
0.385204 + 0.922832i \(0.374131\pi\)
\(18\) 11.9475i 0.156448i
\(19\) 84.5794i 1.02126i −0.859802 0.510628i \(-0.829413\pi\)
0.859802 0.510628i \(-0.170587\pi\)
\(20\) 96.2113i 1.07568i
\(21\) 23.8950i 0.248301i
\(22\) 16.9510 0.164271
\(23\) −122.853 −1.11376 −0.556882 0.830591i \(-0.688003\pi\)
−0.556882 + 0.830591i \(0.688003\pi\)
\(24\) 56.7019i 0.482259i
\(25\) −112.902 −0.903215
\(26\) 61.4264 + 9.92371i 0.463335 + 0.0748538i
\(27\) −27.0000 −0.192450
\(28\) 49.6837i 0.335333i
\(29\) 140.853 0.901921 0.450961 0.892544i \(-0.351081\pi\)
0.450961 + 0.892544i \(0.351081\pi\)
\(30\) 61.4264 0.373829
\(31\) 116.439i 0.674617i −0.941394 0.337309i \(-0.890483\pi\)
0.941394 0.337309i \(-0.109517\pi\)
\(32\) 184.142i 1.01725i
\(33\) 38.3072i 0.202074i
\(34\) 71.6851i 0.361585i
\(35\) −122.853 −0.593312
\(36\) 56.1397 0.259906
\(37\) 433.898i 1.92790i 0.266081 + 0.963951i \(0.414271\pi\)
−0.266081 + 0.963951i \(0.585729\pi\)
\(38\) 112.279 0.479319
\(39\) −22.4264 + 138.817i −0.0920796 + 0.569960i
\(40\) −291.525 −1.15235
\(41\) 205.823i 0.784003i −0.919965 0.392002i \(-0.871783\pi\)
0.919965 0.392002i \(-0.128217\pi\)
\(42\) 31.7207 0.116538
\(43\) 418.853 1.48545 0.742726 0.669595i \(-0.233532\pi\)
0.742726 + 0.669595i \(0.233532\pi\)
\(44\) 79.6501i 0.272902i
\(45\) 138.817i 0.459857i
\(46\) 163.087i 0.522737i
\(47\) 485.861i 1.50787i −0.656947 0.753937i \(-0.728152\pi\)
0.656947 0.753937i \(-0.271848\pi\)
\(48\) −74.4339 −0.223825
\(49\) 279.559 0.815040
\(50\) 149.877i 0.423918i
\(51\) −162.000 −0.444795
\(52\) 46.6301 288.634i 0.124354 0.769737i
\(53\) −674.559 −1.74826 −0.874130 0.485693i \(-0.838567\pi\)
−0.874130 + 0.485693i \(0.838567\pi\)
\(54\) 35.8425i 0.0903251i
\(55\) 196.951 0.482852
\(56\) −150.544 −0.359236
\(57\) 253.738i 0.589622i
\(58\) 186.982i 0.423310i
\(59\) 186.226i 0.410925i −0.978665 0.205462i \(-0.934130\pi\)
0.978665 0.205462i \(-0.0658698\pi\)
\(60\) 288.634i 0.621041i
\(61\) −671.902 −1.41030 −0.705149 0.709059i \(-0.749120\pi\)
−0.705149 + 0.709059i \(0.749120\pi\)
\(62\) 154.574 0.316627
\(63\) 71.6851i 0.143357i
\(64\) −45.9584 −0.0897626
\(65\) 713.706 + 115.302i 1.36191 + 0.220023i
\(66\) −50.8529 −0.0948418
\(67\) 14.0364i 0.0255944i 0.999918 + 0.0127972i \(0.00407358\pi\)
−0.999918 + 0.0127972i \(0.995926\pi\)
\(68\) 336.838 0.600700
\(69\) 368.559 0.643033
\(70\) 163.087i 0.278467i
\(71\) 346.789i 0.579665i −0.957077 0.289833i \(-0.906400\pi\)
0.957077 0.289833i \(-0.0935996\pi\)
\(72\) 170.106i 0.278432i
\(73\) 832.900i 1.33539i 0.744435 + 0.667695i \(0.232719\pi\)
−0.744435 + 0.667695i \(0.767281\pi\)
\(74\) −576.000 −0.904846
\(75\) 338.706 0.521472
\(76\) 527.584i 0.796290i
\(77\) 101.706 0.150525
\(78\) −184.279 29.7711i −0.267507 0.0432169i
\(79\) −335.608 −0.477960 −0.238980 0.971025i \(-0.576813\pi\)
−0.238980 + 0.971025i \(0.576813\pi\)
\(80\) 382.691i 0.534827i
\(81\) 81.0000 0.111111
\(82\) 273.230 0.367966
\(83\) 568.797i 0.752212i 0.926577 + 0.376106i \(0.122737\pi\)
−0.926577 + 0.376106i \(0.877263\pi\)
\(84\) 149.051i 0.193605i
\(85\) 832.900i 1.06283i
\(86\) 556.028i 0.697186i
\(87\) −422.559 −0.520725
\(88\) 241.343 0.292355
\(89\) 236.671i 0.281877i 0.990018 + 0.140939i \(0.0450120\pi\)
−0.990018 + 0.140939i \(0.954988\pi\)
\(90\) −184.279 −0.215830
\(91\) 368.559 + 59.5423i 0.424565 + 0.0685904i
\(92\) −766.324 −0.868422
\(93\) 349.318i 0.389491i
\(94\) 644.981 0.707710
\(95\) 1304.56 1.40889
\(96\) 552.426i 0.587310i
\(97\) 1278.94i 1.33873i −0.742934 0.669365i \(-0.766566\pi\)
0.742934 0.669365i \(-0.233434\pi\)
\(98\) 371.115i 0.382533i
\(99\) 114.922i 0.116667i
\(100\) −704.253 −0.704253
\(101\) −632.264 −0.622898 −0.311449 0.950263i \(-0.600814\pi\)
−0.311449 + 0.950263i \(0.600814\pi\)
\(102\) 215.055i 0.208761i
\(103\) −1506.26 −1.44094 −0.720469 0.693487i \(-0.756073\pi\)
−0.720469 + 0.693487i \(0.756073\pi\)
\(104\) 874.574 + 141.291i 0.824606 + 0.133219i
\(105\) 368.559 0.342549
\(106\) 895.478i 0.820533i
\(107\) −1268.56 −1.14613 −0.573066 0.819509i \(-0.694246\pi\)
−0.573066 + 0.819509i \(0.694246\pi\)
\(108\) −168.419 −0.150057
\(109\) 347.425i 0.305296i 0.988281 + 0.152648i \(0.0487801\pi\)
−0.988281 + 0.152648i \(0.951220\pi\)
\(110\) 261.453i 0.226623i
\(111\) 1301.69i 1.11307i
\(112\) 197.622i 0.166728i
\(113\) 659.706 0.549203 0.274601 0.961558i \(-0.411454\pi\)
0.274601 + 0.961558i \(0.411454\pi\)
\(114\) −336.838 −0.276735
\(115\) 1894.89i 1.53652i
\(116\) 878.603 0.703244
\(117\) 67.2793 416.450i 0.0531622 0.329067i
\(118\) 247.215 0.192865
\(119\) 430.111i 0.331329i
\(120\) 874.574 0.665311
\(121\) 1167.95 0.877499
\(122\) 891.951i 0.661913i
\(123\) 617.469i 0.452645i
\(124\) 726.319i 0.526011i
\(125\) 186.602i 0.133521i
\(126\) −95.1621 −0.0672834
\(127\) −275.019 −0.192157 −0.0960787 0.995374i \(-0.530630\pi\)
−0.0960787 + 0.995374i \(0.530630\pi\)
\(128\) 1412.13i 0.975121i
\(129\) −1256.56 −0.857626
\(130\) −153.064 + 947.446i −0.103266 + 0.639204i
\(131\) −1183.97 −0.789648 −0.394824 0.918757i \(-0.629195\pi\)
−0.394824 + 0.918757i \(0.629195\pi\)
\(132\) 238.950i 0.157560i
\(133\) 673.676 0.439211
\(134\) −18.6334 −0.0120125
\(135\) 416.450i 0.265499i
\(136\) 1020.63i 0.643519i
\(137\) 2557.36i 1.59482i −0.603438 0.797410i \(-0.706203\pi\)
0.603438 0.797410i \(-0.293797\pi\)
\(138\) 489.262i 0.301803i
\(139\) 545.736 0.333012 0.166506 0.986040i \(-0.446751\pi\)
0.166506 + 0.986040i \(0.446751\pi\)
\(140\) −766.324 −0.462616
\(141\) 1457.58i 0.870571i
\(142\) 460.362 0.272062
\(143\) −590.853 95.4549i −0.345522 0.0558205i
\(144\) 223.302 0.129226
\(145\) 2172.52i 1.24426i
\(146\) −1105.68 −0.626756
\(147\) −838.676 −0.470563
\(148\) 2706.54i 1.50322i
\(149\) 1376.78i 0.756981i 0.925605 + 0.378491i \(0.123557\pi\)
−0.925605 + 0.378491i \(0.876443\pi\)
\(150\) 449.632i 0.244749i
\(151\) 2733.47i 1.47316i −0.676352 0.736579i \(-0.736440\pi\)
0.676352 0.736579i \(-0.263560\pi\)
\(152\) 1598.60 0.853052
\(153\) 486.000 0.256802
\(154\) 135.015i 0.0706479i
\(155\) 1795.97 0.930683
\(156\) −139.890 + 865.902i −0.0717961 + 0.444408i
\(157\) 1029.97 0.523570 0.261785 0.965126i \(-0.415689\pi\)
0.261785 + 0.965126i \(0.415689\pi\)
\(158\) 445.520i 0.224327i
\(159\) 2023.68 1.00936
\(160\) −2840.22 −1.40337
\(161\) 978.524i 0.478997i
\(162\) 107.528i 0.0521492i
\(163\) 2882.91i 1.38532i 0.721264 + 0.692660i \(0.243561\pi\)
−0.721264 + 0.692660i \(0.756439\pi\)
\(164\) 1283.87i 0.611301i
\(165\) −590.853 −0.278775
\(166\) −755.079 −0.353045
\(167\) 1153.90i 0.534679i −0.963602 0.267340i \(-0.913855\pi\)
0.963602 0.267340i \(-0.0861446\pi\)
\(168\) 451.631 0.207405
\(169\) −2085.23 691.814i −0.949128 0.314890i
\(170\) −1105.68 −0.498832
\(171\) 761.215i 0.340418i
\(172\) 2612.69 1.15823
\(173\) 1688.85 0.742203 0.371101 0.928592i \(-0.378980\pi\)
0.371101 + 0.928592i \(0.378980\pi\)
\(174\) 560.947i 0.244398i
\(175\) 899.265i 0.388446i
\(176\) 316.817i 0.135687i
\(177\) 558.678i 0.237247i
\(178\) −314.181 −0.132297
\(179\) 942.793 0.393674 0.196837 0.980436i \(-0.436933\pi\)
0.196837 + 0.980436i \(0.436933\pi\)
\(180\) 865.902i 0.358558i
\(181\) −482.030 −0.197950 −0.0989751 0.995090i \(-0.531556\pi\)
−0.0989751 + 0.995090i \(0.531556\pi\)
\(182\) −79.0425 + 489.262i −0.0321924 + 0.199267i
\(183\) 2015.71 0.814236
\(184\) 2322.00i 0.930325i
\(185\) −6692.47 −2.65968
\(186\) −463.721 −0.182805
\(187\) 689.530i 0.269644i
\(188\) 3030.67i 1.17572i
\(189\) 215.055i 0.0827670i
\(190\) 1731.80i 0.661254i
\(191\) 4223.32 1.59994 0.799971 0.600039i \(-0.204848\pi\)
0.799971 + 0.600039i \(0.204848\pi\)
\(192\) 137.875 0.0518244
\(193\) 229.092i 0.0854424i 0.999087 + 0.0427212i \(0.0136027\pi\)
−0.999087 + 0.0427212i \(0.986397\pi\)
\(194\) 1697.80 0.628323
\(195\) −2141.12 345.907i −0.786300 0.127030i
\(196\) 1743.81 0.635501
\(197\) 228.335i 0.0825798i −0.999147 0.0412899i \(-0.986853\pi\)
0.999147 0.0412899i \(-0.0131467\pi\)
\(198\) 152.559 0.0547569
\(199\) −2939.02 −1.04694 −0.523471 0.852043i \(-0.675363\pi\)
−0.523471 + 0.852043i \(0.675363\pi\)
\(200\) 2133.92i 0.754453i
\(201\) 42.1093i 0.0147769i
\(202\) 839.332i 0.292352i
\(203\) 1121.89i 0.387889i
\(204\) −1010.51 −0.346814
\(205\) 3174.63 1.08159
\(206\) 1999.57i 0.676294i
\(207\) −1105.68 −0.371255
\(208\) 185.476 1148.07i 0.0618292 0.382714i
\(209\) −1080.00 −0.357441
\(210\) 489.262i 0.160773i
\(211\) −1607.02 −0.524321 −0.262161 0.965024i \(-0.584435\pi\)
−0.262161 + 0.965024i \(0.584435\pi\)
\(212\) −4207.72 −1.36315
\(213\) 1040.37i 0.334670i
\(214\) 1684.01i 0.537929i
\(215\) 6460.42i 2.04929i
\(216\) 510.317i 0.160753i
\(217\) 927.441 0.290133
\(218\) −461.207 −0.143288
\(219\) 2498.70i 0.770988i
\(220\) 1228.53 0.376488
\(221\) 403.676 2498.70i 0.122870 0.760546i
\(222\) 1728.00 0.522413
\(223\) 130.867i 0.0392981i 0.999807 + 0.0196490i \(0.00625488\pi\)
−0.999807 + 0.0196490i \(0.993745\pi\)
\(224\) −1466.69 −0.437489
\(225\) −1016.12 −0.301072
\(226\) 875.761i 0.257764i
\(227\) 4325.19i 1.26464i 0.774708 + 0.632319i \(0.217897\pi\)
−0.774708 + 0.632319i \(0.782103\pi\)
\(228\) 1582.75i 0.459738i
\(229\) 2621.57i 0.756499i 0.925704 + 0.378250i \(0.123474\pi\)
−0.925704 + 0.378250i \(0.876526\pi\)
\(230\) 2515.47 0.721153
\(231\) −305.117 −0.0869058
\(232\) 2662.21i 0.753373i
\(233\) 4643.12 1.30550 0.652748 0.757575i \(-0.273616\pi\)
0.652748 + 0.757575i \(0.273616\pi\)
\(234\) 552.838 + 89.3134i 0.154445 + 0.0249513i
\(235\) 7493.95 2.08022
\(236\) 1161.63i 0.320405i
\(237\) 1006.82 0.275950
\(238\) −570.972 −0.155507
\(239\) 6696.69i 1.81244i 0.422809 + 0.906219i \(0.361044\pi\)
−0.422809 + 0.906219i \(0.638956\pi\)
\(240\) 1148.07i 0.308783i
\(241\) 2301.47i 0.615148i −0.951524 0.307574i \(-0.900483\pi\)
0.951524 0.307574i \(-0.0995171\pi\)
\(242\) 1550.46i 0.411848i
\(243\) −243.000 −0.0641500
\(244\) −4191.15 −1.09963
\(245\) 4311.93i 1.12440i
\(246\) −819.691 −0.212445
\(247\) −3913.68 632.272i −1.00818 0.162876i
\(248\) 2200.78 0.563506
\(249\) 1706.39i 0.434290i
\(250\) −247.714 −0.0626673
\(251\) −828.000 −0.208219 −0.104109 0.994566i \(-0.533199\pi\)
−0.104109 + 0.994566i \(0.533199\pi\)
\(252\) 447.153i 0.111778i
\(253\) 1568.72i 0.389820i
\(254\) 365.088i 0.0901877i
\(255\) 2498.70i 0.613626i
\(256\) −2242.27 −0.547429
\(257\) −884.763 −0.214747 −0.107374 0.994219i \(-0.534244\pi\)
−0.107374 + 0.994219i \(0.534244\pi\)
\(258\) 1668.08i 0.402521i
\(259\) −3456.00 −0.829133
\(260\) 4451.91 + 719.226i 1.06191 + 0.171556i
\(261\) 1267.68 0.300640
\(262\) 1571.72i 0.370616i
\(263\) −8343.94 −1.95631 −0.978155 0.207878i \(-0.933344\pi\)
−0.978155 + 0.207878i \(0.933344\pi\)
\(264\) −724.030 −0.168792
\(265\) 10404.4i 2.41185i
\(266\) 894.306i 0.206141i
\(267\) 710.013i 0.162742i
\(268\) 87.5556i 0.0199564i
\(269\) 2762.56 0.626157 0.313078 0.949727i \(-0.398640\pi\)
0.313078 + 0.949727i \(0.398640\pi\)
\(270\) 552.838 0.124610
\(271\) 3116.54i 0.698585i 0.937014 + 0.349293i \(0.113578\pi\)
−0.937014 + 0.349293i \(0.886422\pi\)
\(272\) 1339.81 0.298669
\(273\) −1105.68 178.627i −0.245123 0.0396007i
\(274\) 3394.91 0.748517
\(275\) 1441.65i 0.316127i
\(276\) 2298.97 0.501384
\(277\) 502.060 0.108902 0.0544510 0.998516i \(-0.482659\pi\)
0.0544510 + 0.998516i \(0.482659\pi\)
\(278\) 724.465i 0.156297i
\(279\) 1047.96i 0.224872i
\(280\) 2322.00i 0.495592i
\(281\) 6607.56i 1.40275i −0.712791 0.701377i \(-0.752569\pi\)
0.712791 0.701377i \(-0.247431\pi\)
\(282\) −1934.94 −0.408596
\(283\) 4368.98 0.917699 0.458850 0.888514i \(-0.348262\pi\)
0.458850 + 0.888514i \(0.348262\pi\)
\(284\) 2163.18i 0.451975i
\(285\) −3913.68 −0.813425
\(286\) 126.717 784.358i 0.0261990 0.162168i
\(287\) 1639.38 0.337176
\(288\) 1657.28i 0.339084i
\(289\) −1997.00 −0.406473
\(290\) −2884.03 −0.583986
\(291\) 3836.82i 0.772916i
\(292\) 5195.41i 1.04123i
\(293\) 5348.12i 1.06635i −0.846005 0.533175i \(-0.820999\pi\)
0.846005 0.533175i \(-0.179001\pi\)
\(294\) 1113.34i 0.220856i
\(295\) 2872.36 0.566900
\(296\) −8200.94 −1.61037
\(297\) 344.765i 0.0673579i
\(298\) −1827.68 −0.355284
\(299\) −918.384 + 5684.67i −0.177630 + 1.09951i
\(300\) 2112.76 0.406600
\(301\) 3336.17i 0.638849i
\(302\) 3628.69 0.691416
\(303\) 1896.79 0.359630
\(304\) 2098.53i 0.395917i
\(305\) 10363.5i 1.94561i
\(306\) 645.166i 0.120528i
\(307\) 4502.46i 0.837032i −0.908210 0.418516i \(-0.862550\pi\)
0.908210 0.418516i \(-0.137450\pi\)
\(308\) 634.414 0.117367
\(309\) 4518.79 0.831926
\(310\) 2384.15i 0.436809i
\(311\) 7447.20 1.35785 0.678926 0.734207i \(-0.262446\pi\)
0.678926 + 0.734207i \(0.262446\pi\)
\(312\) −2623.72 423.874i −0.476086 0.0769138i
\(313\) −6508.93 −1.17542 −0.587710 0.809072i \(-0.699970\pi\)
−0.587710 + 0.809072i \(0.699970\pi\)
\(314\) 1367.29i 0.245734i
\(315\) −1105.68 −0.197771
\(316\) −2093.43 −0.372673
\(317\) 2465.57i 0.436846i −0.975854 0.218423i \(-0.929909\pi\)
0.975854 0.218423i \(-0.0700913\pi\)
\(318\) 2686.43i 0.473735i
\(319\) 1798.56i 0.315674i
\(320\) 708.866i 0.123834i
\(321\) 3805.68 0.661720
\(322\) 1298.99 0.224814
\(323\) 4567.29i 0.786782i
\(324\) 505.257 0.0866353
\(325\) −843.996 + 5224.22i −0.144051 + 0.891654i
\(326\) −3827.07 −0.650190
\(327\) 1042.27i 0.176263i
\(328\) 3890.18 0.654876
\(329\) 3869.89 0.648491
\(330\) 784.358i 0.130841i
\(331\) 4114.84i 0.683300i 0.939827 + 0.341650i \(0.110986\pi\)
−0.939827 + 0.341650i \(0.889014\pi\)
\(332\) 3548.01i 0.586513i
\(333\) 3905.08i 0.642634i
\(334\) 1531.80 0.250948
\(335\) −216.499 −0.0353092
\(336\) 592.867i 0.0962605i
\(337\) −4798.05 −0.775568 −0.387784 0.921750i \(-0.626759\pi\)
−0.387784 + 0.921750i \(0.626759\pi\)
\(338\) 918.384 2768.15i 0.147791 0.445466i
\(339\) −1979.12 −0.317082
\(340\) 5195.41i 0.828708i
\(341\) −1486.82 −0.236117
\(342\) 1010.51 0.159773
\(343\) 4958.69i 0.780594i
\(344\) 7916.58i 1.24079i
\(345\) 5684.67i 0.887109i
\(346\) 2241.96i 0.348348i
\(347\) −3314.76 −0.512812 −0.256406 0.966569i \(-0.582538\pi\)
−0.256406 + 0.966569i \(0.582538\pi\)
\(348\) −2635.81 −0.406018
\(349\) 371.740i 0.0570166i −0.999594 0.0285083i \(-0.990924\pi\)
0.999594 0.0285083i \(-0.00907570\pi\)
\(350\) 1193.78 0.182314
\(351\) −201.838 + 1249.35i −0.0306932 + 0.189987i
\(352\) 2351.32 0.356039
\(353\) 7539.10i 1.13673i −0.822776 0.568365i \(-0.807576\pi\)
0.822776 0.568365i \(-0.192424\pi\)
\(354\) −741.646 −0.111350
\(355\) 5348.89 0.799689
\(356\) 1476.29i 0.219785i
\(357\) 1290.33i 0.191293i
\(358\) 1251.56i 0.184768i
\(359\) 12741.5i 1.87317i 0.350437 + 0.936586i \(0.386033\pi\)
−0.350437 + 0.936586i \(0.613967\pi\)
\(360\) −2623.72 −0.384117
\(361\) −294.676 −0.0429619
\(362\) 639.896i 0.0929065i
\(363\) −3503.85 −0.506624
\(364\) 2298.97 + 371.409i 0.331041 + 0.0534811i
\(365\) −12846.7 −1.84227
\(366\) 2675.85i 0.382156i
\(367\) 7187.26 1.02227 0.511134 0.859501i \(-0.329226\pi\)
0.511134 + 0.859501i \(0.329226\pi\)
\(368\) −3048.14 −0.431781
\(369\) 1852.41i 0.261334i
\(370\) 8884.26i 1.24830i
\(371\) 5372.87i 0.751874i
\(372\) 2178.96i 0.303693i
\(373\) −2087.99 −0.289845 −0.144922 0.989443i \(-0.546293\pi\)
−0.144922 + 0.989443i \(0.546293\pi\)
\(374\) 915.352 0.126555
\(375\) 559.805i 0.0770886i
\(376\) 9183.07 1.25952
\(377\) 1052.94 6517.57i 0.143844 0.890377i
\(378\) 285.486 0.0388461
\(379\) 3982.08i 0.539699i −0.962902 0.269850i \(-0.913026\pi\)
0.962902 0.269850i \(-0.0869740\pi\)
\(380\) 8137.50 1.09854
\(381\) 825.057 0.110942
\(382\) 5606.47i 0.750921i
\(383\) 8638.43i 1.15249i −0.817278 0.576244i \(-0.804518\pi\)
0.817278 0.576244i \(-0.195482\pi\)
\(384\) 4236.38i 0.562987i
\(385\) 1568.72i 0.207660i
\(386\) −304.120 −0.0401018
\(387\) 3769.68 0.495151
\(388\) 7977.70i 1.04383i
\(389\) 1275.74 0.166279 0.0831393 0.996538i \(-0.473505\pi\)
0.0831393 + 0.996538i \(0.473505\pi\)
\(390\) 459.192 2842.34i 0.0596207 0.369044i
\(391\) −6634.06 −0.858053
\(392\) 5283.83i 0.680801i
\(393\) 3551.91 0.455904
\(394\) 303.115 0.0387582
\(395\) 5176.44i 0.659379i
\(396\) 716.851i 0.0909675i
\(397\) 4622.65i 0.584394i −0.956358 0.292197i \(-0.905614\pi\)
0.956358 0.292197i \(-0.0943862\pi\)
\(398\) 3901.55i 0.491375i
\(399\) −2021.03 −0.253579
\(400\) −2801.24 −0.350155
\(401\) 138.075i 0.0171949i −0.999963 0.00859743i \(-0.997263\pi\)
0.999963 0.00859743i \(-0.00273668\pi\)
\(402\) 55.9001 0.00693544
\(403\) −5387.91 870.441i −0.665982 0.107592i
\(404\) −3943.90 −0.485684
\(405\) 1249.35i 0.153286i
\(406\) −1489.32 −0.182053
\(407\) 5540.47 0.674769
\(408\) 3061.90i 0.371536i
\(409\) 1204.64i 0.145637i 0.997345 + 0.0728186i \(0.0231994\pi\)
−0.997345 + 0.0728186i \(0.976801\pi\)
\(410\) 4214.32i 0.507635i
\(411\) 7672.09i 0.920770i
\(412\) −9395.68 −1.12352
\(413\) 1483.29 0.176726
\(414\) 1467.79i 0.174246i
\(415\) −8773.16 −1.03773
\(416\) 8520.66 + 1376.55i 1.00423 + 0.162238i
\(417\) −1637.21 −0.192265
\(418\) 1433.70i 0.167762i
\(419\) 5199.85 0.606275 0.303138 0.952947i \(-0.401966\pi\)
0.303138 + 0.952947i \(0.401966\pi\)
\(420\) 2298.97 0.267091
\(421\) 14136.5i 1.63651i 0.574854 + 0.818256i \(0.305059\pi\)
−0.574854 + 0.818256i \(0.694941\pi\)
\(422\) 2133.32i 0.246086i
\(423\) 4372.75i 0.502625i
\(424\) 12749.6i 1.46032i
\(425\) −6096.70 −0.695844
\(426\) −1381.09 −0.157075
\(427\) 5351.71i 0.606527i
\(428\) −7912.94 −0.893660
\(429\) 1772.56 + 286.365i 0.199487 + 0.0322280i
\(430\) −8576.21 −0.961818
\(431\) 2279.83i 0.254793i 0.991852 + 0.127396i \(0.0406620\pi\)
−0.991852 + 0.127396i \(0.959338\pi\)
\(432\) −669.905 −0.0746084
\(433\) 13298.7 1.47597 0.737984 0.674819i \(-0.235778\pi\)
0.737984 + 0.674819i \(0.235778\pi\)
\(434\) 1231.18i 0.136172i
\(435\) 6517.57i 0.718376i
\(436\) 2167.14i 0.238045i
\(437\) 10390.8i 1.13744i
\(438\) 3317.03 0.361858
\(439\) 10452.3 1.13635 0.568177 0.822907i \(-0.307649\pi\)
0.568177 + 0.822907i \(0.307649\pi\)
\(440\) 3722.50i 0.403325i
\(441\) 2516.03 0.271680
\(442\) 3317.03 + 535.880i 0.356957 + 0.0576679i
\(443\) 5363.50 0.575232 0.287616 0.957746i \(-0.407137\pi\)
0.287616 + 0.957746i \(0.407137\pi\)
\(444\) 8119.62i 0.867883i
\(445\) −3650.43 −0.388870
\(446\) −173.726 −0.0184443
\(447\) 4130.34i 0.437043i
\(448\) 366.059i 0.0386042i
\(449\) 9681.73i 1.01762i 0.860880 + 0.508808i \(0.169914\pi\)
−0.860880 + 0.508808i \(0.830086\pi\)
\(450\) 1348.90i 0.141306i
\(451\) −2628.17 −0.274402
\(452\) 4115.07 0.428223
\(453\) 8200.42i 0.850528i
\(454\) −5741.69 −0.593548
\(455\) −918.384 + 5684.67i −0.0946253 + 0.585718i
\(456\) −4795.81 −0.492510
\(457\) 3537.94i 0.362139i 0.983470 + 0.181070i \(0.0579560\pi\)
−0.983470 + 0.181070i \(0.942044\pi\)
\(458\) −3480.14 −0.355057
\(459\) −1458.00 −0.148265
\(460\) 11819.8i 1.19805i
\(461\) 15074.9i 1.52302i 0.648156 + 0.761508i \(0.275541\pi\)
−0.648156 + 0.761508i \(0.724459\pi\)
\(462\) 405.044i 0.0407886i
\(463\) 11070.0i 1.11116i −0.831463 0.555580i \(-0.812496\pi\)
0.831463 0.555580i \(-0.187504\pi\)
\(464\) 3494.74 0.349654
\(465\) −5387.91 −0.537330
\(466\) 6163.75i 0.612725i
\(467\) −13252.8 −1.31320 −0.656600 0.754239i \(-0.728006\pi\)
−0.656600 + 0.754239i \(0.728006\pi\)
\(468\) 419.671 2597.71i 0.0414515 0.256579i
\(469\) −111.800 −0.0110074
\(470\) 9948.23i 0.976335i
\(471\) −3089.91 −0.302284
\(472\) 3519.79 0.343244
\(473\) 5348.36i 0.519911i
\(474\) 1336.56i 0.129515i
\(475\) 9549.18i 0.922413i
\(476\) 2682.92i 0.258343i
\(477\) −6071.03 −0.582753
\(478\) −8889.86 −0.850654
\(479\) 12241.4i 1.16769i 0.811866 + 0.583843i \(0.198452\pi\)
−0.811866 + 0.583843i \(0.801548\pi\)
\(480\) 8520.66 0.810236
\(481\) 20077.4 + 3243.59i 1.90322 + 0.307474i
\(482\) 3055.20 0.288715
\(483\) 2935.57i 0.276549i
\(484\) 7285.37 0.684201
\(485\) 19726.5 1.84687
\(486\) 322.583i 0.0301084i
\(487\) 13413.3i 1.24808i 0.781392 + 0.624041i \(0.214510\pi\)
−0.781392 + 0.624041i \(0.785490\pi\)
\(488\) 12699.4i 1.17802i
\(489\) 8648.74i 0.799815i
\(490\) −5724.10 −0.527731
\(491\) 737.885 0.0678214 0.0339107 0.999425i \(-0.489204\pi\)
0.0339107 + 0.999425i \(0.489204\pi\)
\(492\) 3851.61i 0.352935i
\(493\) 7606.06 0.694847
\(494\) 839.342 5195.41i 0.0764449 0.473183i
\(495\) 1772.56 0.160951
\(496\) 2889.01i 0.261533i
\(497\) 2762.17 0.249297
\(498\) 2265.24 0.203831
\(499\) 1865.65i 0.167370i −0.996492 0.0836852i \(-0.973331\pi\)
0.996492 0.0836852i \(-0.0266690\pi\)
\(500\) 1163.97i 0.104109i
\(501\) 3461.70i 0.308697i
\(502\) 1099.17i 0.0977259i
\(503\) −16632.0 −1.47432 −0.737161 0.675717i \(-0.763834\pi\)
−0.737161 + 0.675717i \(0.763834\pi\)
\(504\) −1354.89 −0.119745
\(505\) 9752.09i 0.859331i
\(506\) −2082.47 −0.182959
\(507\) 6255.70 + 2075.44i 0.547979 + 0.181802i
\(508\) −1715.50 −0.149829
\(509\) 4128.91i 0.359549i −0.983708 0.179775i \(-0.942463\pi\)
0.983708 0.179775i \(-0.0575368\pi\)
\(510\) 3317.03 0.288001
\(511\) −6634.06 −0.574312
\(512\) 8320.40i 0.718190i
\(513\) 2283.64i 0.196541i
\(514\) 1174.52i 0.100790i
\(515\) 23232.7i 1.98788i
\(516\) −7838.08 −0.668706
\(517\) −6203.99 −0.527758
\(518\) 4587.85i 0.389147i
\(519\) −5066.56 −0.428511
\(520\) −2179.29 + 13489.5i −0.183785 + 1.13760i
\(521\) −988.234 −0.0831005 −0.0415502 0.999136i \(-0.513230\pi\)
−0.0415502 + 0.999136i \(0.513230\pi\)
\(522\) 1682.84i 0.141103i
\(523\) −9441.62 −0.789394 −0.394697 0.918811i \(-0.629150\pi\)
−0.394697 + 0.918811i \(0.629150\pi\)
\(524\) −7385.30 −0.615703
\(525\) 2697.79i 0.224269i
\(526\) 11076.6i 0.918180i
\(527\) 6287.73i 0.519730i
\(528\) 950.452i 0.0783392i
\(529\) 2925.83 0.240472
\(530\) 13811.9 1.13198
\(531\) 1676.03i 0.136975i
\(532\) 4202.21 0.342461
\(533\) −9523.88 1538.62i −0.773968 0.125038i
\(534\) 942.544 0.0763817
\(535\) 19566.3i 1.58117i
\(536\) −265.297 −0.0213789
\(537\) −2828.38 −0.227288
\(538\) 3667.30i 0.293882i
\(539\) 3569.70i 0.285265i
\(540\) 2597.71i 0.207014i
\(541\) 14001.5i 1.11270i 0.830948 + 0.556351i \(0.187799\pi\)
−0.830948 + 0.556351i \(0.812201\pi\)
\(542\) −4137.22 −0.327876
\(543\) 1446.09 0.114287
\(544\) 9943.67i 0.783697i
\(545\) −5358.70 −0.421177
\(546\) 237.127 1467.79i 0.0185863 0.115047i
\(547\) −4244.85 −0.331804 −0.165902 0.986142i \(-0.553053\pi\)
−0.165902 + 0.986142i \(0.553053\pi\)
\(548\) 15952.2i 1.24351i
\(549\) −6047.12 −0.470100
\(550\) −1913.80 −0.148372
\(551\) 11913.3i 0.921092i
\(552\) 6965.99i 0.537123i
\(553\) 2673.12i 0.205556i
\(554\) 666.485i 0.0511124i
\(555\) 20077.4 1.53556
\(556\) 3404.16 0.259655
\(557\) 11732.2i 0.892473i −0.894915 0.446236i \(-0.852764\pi\)
0.894915 0.446236i \(-0.147236\pi\)
\(558\) 1391.16 0.105542
\(559\) 3131.13 19381.2i 0.236910 1.46644i
\(560\) −3048.14 −0.230013
\(561\) 2068.59i 0.155679i
\(562\) 8771.54 0.658372
\(563\) 9941.80 0.744222 0.372111 0.928188i \(-0.378634\pi\)
0.372111 + 0.928188i \(0.378634\pi\)
\(564\) 9092.02i 0.678800i
\(565\) 10175.3i 0.757664i
\(566\) 5799.83i 0.430716i
\(567\) 645.166i 0.0477856i
\(568\) 6554.52 0.484193
\(569\) −3690.77 −0.271925 −0.135962 0.990714i \(-0.543413\pi\)
−0.135962 + 0.990714i \(0.543413\pi\)
\(570\) 5195.41i 0.381775i
\(571\) 5685.09 0.416661 0.208331 0.978058i \(-0.433197\pi\)
0.208331 + 0.978058i \(0.433197\pi\)
\(572\) −3685.59 595.423i −0.269409 0.0435242i
\(573\) −12670.0 −0.923727
\(574\) 2176.28i 0.158251i
\(575\) 13870.3 1.00597
\(576\) −413.626 −0.0299209
\(577\) 7746.50i 0.558910i −0.960159 0.279455i \(-0.909846\pi\)
0.960159 0.279455i \(-0.0901537\pi\)
\(578\) 2651.02i 0.190775i
\(579\) 687.275i 0.0493302i
\(580\) 13551.6i 0.970175i
\(581\) −4530.47 −0.323504
\(582\) −5093.39 −0.362762
\(583\) 8613.48i 0.611894i
\(584\) −15742.3 −1.11545
\(585\) 6423.35 + 1037.72i 0.453971 + 0.0733410i
\(586\) 7099.64 0.500484
\(587\) 2766.54i 0.194527i 0.995259 + 0.0972635i \(0.0310089\pi\)
−0.995259 + 0.0972635i \(0.968991\pi\)
\(588\) −5231.44 −0.366906
\(589\) −9848.38 −0.688957
\(590\) 3813.07i 0.266070i
\(591\) 685.006i 0.0476774i
\(592\) 10765.6i 0.747402i
\(593\) 1440.79i 0.0997743i −0.998755 0.0498871i \(-0.984114\pi\)
0.998755 0.0498871i \(-0.0158862\pi\)
\(594\) −457.676 −0.0316139
\(595\) −6634.06 −0.457092
\(596\) 8587.99i 0.590231i
\(597\) 8817.06 0.604452
\(598\) −7546.41 1219.16i −0.516047 0.0833696i
\(599\) 23837.5 1.62600 0.813001 0.582263i \(-0.197832\pi\)
0.813001 + 0.582263i \(0.197832\pi\)
\(600\) 6401.75i 0.435584i
\(601\) −6694.23 −0.454348 −0.227174 0.973854i \(-0.572949\pi\)
−0.227174 + 0.973854i \(0.572949\pi\)
\(602\) −4428.77 −0.299839
\(603\) 126.328i 0.00853145i
\(604\) 17050.7i 1.14865i
\(605\) 18014.6i 1.21057i
\(606\) 2518.00i 0.168790i
\(607\) 3330.50 0.222703 0.111352 0.993781i \(-0.464482\pi\)
0.111352 + 0.993781i \(0.464482\pi\)
\(608\) 15574.6 1.03887
\(609\) 3365.68i 0.223948i
\(610\) 13757.5 0.913156
\(611\) −22481.8 3632.04i −1.48857 0.240486i
\(612\) 3031.54 0.200233
\(613\) 13490.3i 0.888857i 0.895814 + 0.444428i \(0.146593\pi\)
−0.895814 + 0.444428i \(0.853407\pi\)
\(614\) 5977.02 0.392855
\(615\) −9523.88 −0.624455
\(616\) 1922.30i 0.125733i
\(617\) 7470.76i 0.487458i −0.969843 0.243729i \(-0.921629\pi\)
0.969843 0.243729i \(-0.0783707\pi\)
\(618\) 5998.71i 0.390458i
\(619\) 24806.9i 1.61078i 0.592746 + 0.805389i \(0.298044\pi\)
−0.592746 + 0.805389i \(0.701956\pi\)
\(620\) 11202.8 0.725669
\(621\) 3317.03 0.214344
\(622\) 9886.17i 0.637298i
\(623\) −1885.09 −0.121227
\(624\) −556.429 + 3444.22i −0.0356971 + 0.220960i
\(625\) −16990.9 −1.08742
\(626\) 8640.61i 0.551675i
\(627\) 3240.00 0.206369
\(628\) 6424.68 0.408237
\(629\) 23430.5i 1.48527i
\(630\) 1467.79i 0.0928222i
\(631\) 314.333i 0.0198311i 0.999951 + 0.00991554i \(0.00315627\pi\)
−0.999951 + 0.00991554i \(0.996844\pi\)
\(632\) 6343.19i 0.399238i
\(633\) 4821.06 0.302717
\(634\) 3273.05 0.205031
\(635\) 4241.91i 0.265095i
\(636\) 12623.2 0.787014
\(637\) 2089.83 12935.8i 0.129988 0.804607i
\(638\) 2387.59 0.148159
\(639\) 3121.10i 0.193222i
\(640\) −21780.7 −1.34525
\(641\) −5550.41 −0.342009 −0.171005 0.985270i \(-0.554701\pi\)
−0.171005 + 0.985270i \(0.554701\pi\)
\(642\) 5052.04i 0.310573i
\(643\) 5479.48i 0.336065i −0.985781 0.168032i \(-0.946259\pi\)
0.985781 0.168032i \(-0.0537413\pi\)
\(644\) 6103.78i 0.373482i
\(645\) 19381.2i 1.18316i
\(646\) 6063.08 0.369271
\(647\) −4724.83 −0.287098 −0.143549 0.989643i \(-0.545851\pi\)
−0.143549 + 0.989643i \(0.545851\pi\)
\(648\) 1530.95i 0.0928108i
\(649\) −2377.93 −0.143824
\(650\) −6935.16 1120.41i −0.418491 0.0676091i
\(651\) −2782.32 −0.167508
\(652\) 17982.9i 1.08016i
\(653\) 3463.91 0.207585 0.103793 0.994599i \(-0.466902\pi\)
0.103793 + 0.994599i \(0.466902\pi\)
\(654\) 1383.62 0.0827276
\(655\) 18261.6i 1.08938i
\(656\) 5106.73i 0.303940i
\(657\) 7496.10i 0.445130i
\(658\) 5137.28i 0.304365i
\(659\) −2606.35 −0.154065 −0.0770327 0.997029i \(-0.524545\pi\)
−0.0770327 + 0.997029i \(0.524545\pi\)
\(660\) −3685.59 −0.217366
\(661\) 22436.7i 1.32025i −0.751154 0.660127i \(-0.770502\pi\)
0.751154 0.660127i \(-0.229498\pi\)
\(662\) −5462.46 −0.320702
\(663\) −1211.03 + 7496.10i −0.0709388 + 0.439102i
\(664\) −10750.6 −0.628321
\(665\) 10390.8i 0.605923i
\(666\) −5184.00 −0.301615
\(667\) −17304.2 −1.00453
\(668\) 7197.73i 0.416899i
\(669\) 392.600i 0.0226888i
\(670\) 287.403i 0.0165721i
\(671\) 8579.56i 0.493607i
\(672\) 4400.08 0.252584
\(673\) 633.970 0.0363117 0.0181558 0.999835i \(-0.494221\pi\)
0.0181558 + 0.999835i \(0.494221\pi\)
\(674\) 6369.42i 0.364007i
\(675\) 3048.35 0.173824
\(676\) −13007.1 4315.35i −0.740052 0.245525i
\(677\) 24457.4 1.38844 0.694221 0.719762i \(-0.255749\pi\)
0.694221 + 0.719762i \(0.255749\pi\)
\(678\) 2627.28i 0.148820i
\(679\) 10186.8 0.575747
\(680\) −15742.3 −0.887780
\(681\) 12975.6i 0.730139i
\(682\) 1973.76i 0.110820i
\(683\) 12367.6i 0.692875i −0.938073 0.346437i \(-0.887391\pi\)
0.938073 0.346437i \(-0.112609\pi\)
\(684\) 4748.26i 0.265430i
\(685\) 39445.0 2.20017
\(686\) −6582.66 −0.366366
\(687\) 7864.71i 0.436765i
\(688\) 10392.3 0.575875
\(689\) −5042.65 + 31213.3i −0.278824 + 1.72588i
\(690\) −7546.41 −0.416358
\(691\) 1050.99i 0.0578605i −0.999581 0.0289302i \(-0.990790\pi\)
0.999581 0.0289302i \(-0.00921006\pi\)
\(692\) 10534.6 0.578709
\(693\) 915.352 0.0501751
\(694\) 4400.35i 0.240685i
\(695\) 8417.46i 0.459414i
\(696\) 7986.62i 0.434960i
\(697\) 11114.4i 0.604002i
\(698\) 493.486 0.0267603
\(699\) −13929.4 −0.753729
\(700\) 5609.38i 0.302878i
\(701\) 24294.1 1.30895 0.654476 0.756083i \(-0.272889\pi\)
0.654476 + 0.756083i \(0.272889\pi\)
\(702\) −1658.51 267.940i −0.0891689 0.0144056i
\(703\) 36698.8 1.96888
\(704\) 586.846i 0.0314170i
\(705\) −22481.8 −1.20101
\(706\) 10008.2 0.533516
\(707\) 5035.99i 0.267890i
\(708\) 3484.89i 0.184986i
\(709\) 27465.9i 1.45487i −0.686176 0.727436i \(-0.740712\pi\)
0.686176 0.727436i \(-0.259288\pi\)
\(710\) 7100.66i 0.375328i
\(711\) −3020.47 −0.159320
\(712\) −4473.23 −0.235451
\(713\) 14304.9i 0.751365i
\(714\) 1712.92 0.0897820
\(715\) 1472.30 9113.36i 0.0770084 0.476672i
\(716\) 5880.90 0.306955
\(717\) 20090.1i 1.04641i
\(718\) −16914.3 −0.879160
\(719\) −36433.5 −1.88976 −0.944882 0.327411i \(-0.893824\pi\)
−0.944882 + 0.327411i \(0.893824\pi\)
\(720\) 3444.22i 0.178276i
\(721\) 11997.4i 0.619704i
\(722\) 391.183i 0.0201639i
\(723\) 6904.40i 0.355156i
\(724\) −3006.78 −0.154345
\(725\) −15902.6 −0.814629
\(726\) 4651.37i 0.237780i
\(727\) −551.608 −0.0281403 −0.0140701 0.999901i \(-0.504479\pi\)
−0.0140701 + 0.999901i \(0.504479\pi\)
\(728\) −1125.39 + 6965.99i −0.0572934 + 0.354638i
\(729\) 729.000 0.0370370
\(730\) 17054.0i 0.864654i
\(731\) 22618.1 1.14440
\(732\) 12573.4 0.634874
\(733\) 20317.2i 1.02379i 0.859049 + 0.511893i \(0.171055\pi\)
−0.859049 + 0.511893i \(0.828945\pi\)
\(734\) 9541.10i 0.479794i
\(735\) 12935.8i 0.649175i
\(736\) 22622.4i 1.13298i
\(737\) 179.232 0.00895807
\(738\) 2459.07 0.122655
\(739\) 29931.6i 1.48992i 0.667107 + 0.744962i \(0.267532\pi\)
−0.667107 + 0.744962i \(0.732468\pi\)
\(740\) −41745.9 −2.07380
\(741\) 11741.0 + 1896.81i 0.582075 + 0.0940367i
\(742\) 7132.49 0.352887
\(743\) 24376.4i 1.20361i 0.798643 + 0.601805i \(0.205552\pi\)
−0.798643 + 0.601805i \(0.794448\pi\)
\(744\) −6602.33 −0.325340
\(745\) −21235.5 −1.04431
\(746\) 2771.81i 0.136037i
\(747\) 5119.17i 0.250737i
\(748\) 4301.11i 0.210246i
\(749\) 10104.1i 0.492917i
\(750\) 743.142 0.0361810
\(751\) −22692.2 −1.10260 −0.551298 0.834308i \(-0.685867\pi\)
−0.551298 + 0.834308i \(0.685867\pi\)
\(752\) 12054.8i 0.584567i
\(753\) 2484.00 0.120215
\(754\) 8652.09 + 1397.78i 0.417892 + 0.0675123i
\(755\) 42161.3 2.03232
\(756\) 1341.46i 0.0645349i
\(757\) −33063.5 −1.58747 −0.793734 0.608265i \(-0.791866\pi\)
−0.793734 + 0.608265i \(0.791866\pi\)
\(758\) 5286.22 0.253304
\(759\) 4706.15i 0.225062i
\(760\) 24657.0i 1.17685i
\(761\) 216.324i 0.0103045i 0.999987 + 0.00515226i \(0.00164002\pi\)
−0.999987 + 0.00515226i \(0.998360\pi\)
\(762\) 1095.27i 0.0520699i
\(763\) −2767.24 −0.131299
\(764\) 26344.0 1.24750
\(765\) 7496.10i 0.354277i
\(766\) 11467.5 0.540912
\(767\) −8617.09 1392.13i −0.405665 0.0655369i
\(768\) 6726.80 0.316058
\(769\) 19214.4i 0.901025i 0.892770 + 0.450512i \(0.148759\pi\)
−0.892770 + 0.450512i \(0.851241\pi\)
\(770\) −2082.47 −0.0974638
\(771\) 2654.29 0.123984
\(772\) 1429.01i 0.0666209i
\(773\) 33175.6i 1.54365i 0.635834 + 0.771826i \(0.280656\pi\)
−0.635834 + 0.771826i \(0.719344\pi\)
\(774\) 5004.25i 0.232395i
\(775\) 13146.2i 0.609325i
\(776\) 24172.8 1.11824
\(777\) 10368.0 0.478700
\(778\) 1693.54i 0.0780416i
\(779\) −17408.4 −0.800667
\(780\) −13355.7 2157.68i −0.613092 0.0990477i
\(781\) −4428.17 −0.202884
\(782\) 8806.72i 0.402721i
\(783\) −3803.03 −0.173575
\(784\) 6936.21 0.315972