Properties

Label 108.4.b.b.107.1
Level 108
Weight 4
Character 108.107
Analytic conductor 6.372
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + 6854 x^{2} - 888 x + 9496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{14}\cdot 3^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.1
Root \(2.61836 + 1.60260i\) of defining polynomial
Character \(\chi\) \(=\) 108.107
Dual form 108.4.b.b.107.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.72048 - 0.773954i) q^{2} +(6.80199 + 4.21105i) q^{4} +20.8488i q^{5} -13.9048i q^{7} +(-15.2455 - 16.7205i) q^{8} +O(q^{10})\) \(q+(-2.72048 - 0.773954i) q^{2} +(6.80199 + 4.21105i) q^{4} +20.8488i q^{5} -13.9048i q^{7} +(-15.2455 - 16.7205i) q^{8} +(16.1360 - 56.7186i) q^{10} -34.5116 q^{11} -31.3361 q^{13} +(-10.7617 + 37.8278i) q^{14} +(28.5341 + 57.2870i) q^{16} -34.4719i q^{17} +120.723i q^{19} +(-87.7953 + 141.813i) q^{20} +(93.8880 + 26.7104i) q^{22} -137.155 q^{23} -309.672 q^{25} +(85.2491 + 24.2527i) q^{26} +(58.5540 - 94.5806i) q^{28} +93.1005i q^{29} -111.365i q^{31} +(-33.2888 - 177.932i) q^{32} +(-26.6797 + 93.7799i) q^{34} +289.899 q^{35} -146.680 q^{37} +(93.4338 - 328.423i) q^{38} +(348.602 - 317.850i) q^{40} +8.44531i q^{41} +427.523i q^{43} +(-234.748 - 145.330i) q^{44} +(373.128 + 106.152i) q^{46} +318.826 q^{47} +149.655 q^{49} +(842.455 + 239.672i) q^{50} +(-213.148 - 131.958i) q^{52} -291.451i q^{53} -719.525i q^{55} +(-232.496 + 211.986i) q^{56} +(72.0555 - 253.278i) q^{58} -364.665 q^{59} -289.983 q^{61} +(-86.1914 + 302.966i) q^{62} +(-47.1499 + 509.824i) q^{64} -653.320i q^{65} +305.907i q^{67} +(145.163 - 234.477i) q^{68} +(-788.664 - 224.369i) q^{70} +102.802 q^{71} +442.688 q^{73} +(399.041 + 113.524i) q^{74} +(-508.369 + 821.154i) q^{76} +479.878i q^{77} +245.350i q^{79} +(-1194.37 + 594.901i) q^{80} +(6.53629 - 22.9753i) q^{82} +478.981 q^{83} +718.697 q^{85} +(330.884 - 1163.07i) q^{86} +(526.146 + 577.051i) q^{88} +1417.36i q^{89} +435.723i q^{91} +(-932.929 - 577.568i) q^{92} +(-867.360 - 246.757i) q^{94} -2516.92 q^{95} +1153.69 q^{97} +(-407.134 - 115.826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{4} + O(q^{10}) \) \( 12q + 6q^{4} + 42q^{10} - 72q^{13} + 114q^{16} + 66q^{22} - 384q^{25} - 282q^{28} - 324q^{34} - 240q^{37} + 774q^{40} + 1752q^{46} + 288q^{49} + 924q^{52} - 948q^{58} + 144q^{61} - 3066q^{64} - 3558q^{70} + 156q^{73} + 576q^{76} + 5832q^{82} - 168q^{85} + 5022q^{88} - 3444q^{94} + 516q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72048 0.773954i −0.961834 0.273634i
\(3\) 0 0
\(4\) 6.80199 + 4.21105i 0.850249 + 0.526381i
\(5\) 20.8488i 1.86477i 0.361464 + 0.932386i \(0.382277\pi\)
−0.361464 + 0.932386i \(0.617723\pi\)
\(6\) 0 0
\(7\) 13.9048i 0.750791i −0.926865 0.375395i \(-0.877507\pi\)
0.926865 0.375395i \(-0.122493\pi\)
\(8\) −15.2455 16.7205i −0.673762 0.738948i
\(9\) 0 0
\(10\) 16.1360 56.7186i 0.510266 1.79360i
\(11\) −34.5116 −0.945967 −0.472984 0.881071i \(-0.656823\pi\)
−0.472984 + 0.881071i \(0.656823\pi\)
\(12\) 0 0
\(13\) −31.3361 −0.668544 −0.334272 0.942477i \(-0.608490\pi\)
−0.334272 + 0.942477i \(0.608490\pi\)
\(14\) −10.7617 + 37.8278i −0.205442 + 0.722136i
\(15\) 0 0
\(16\) 28.5341 + 57.2870i 0.445845 + 0.895110i
\(17\) 34.4719i 0.491803i −0.969295 0.245902i \(-0.920916\pi\)
0.969295 0.245902i \(-0.0790840\pi\)
\(18\) 0 0
\(19\) 120.723i 1.45767i 0.684691 + 0.728833i \(0.259937\pi\)
−0.684691 + 0.728833i \(0.740063\pi\)
\(20\) −87.7953 + 141.813i −0.981581 + 1.58552i
\(21\) 0 0
\(22\) 93.8880 + 26.7104i 0.909863 + 0.258849i
\(23\) −137.155 −1.24343 −0.621714 0.783244i \(-0.713564\pi\)
−0.621714 + 0.783244i \(0.713564\pi\)
\(24\) 0 0
\(25\) −309.672 −2.47738
\(26\) 85.2491 + 24.2527i 0.643028 + 0.182936i
\(27\) 0 0
\(28\) 58.5540 94.5806i 0.395202 0.638359i
\(29\) 93.1005i 0.596149i 0.954543 + 0.298075i \(0.0963444\pi\)
−0.954543 + 0.298075i \(0.903656\pi\)
\(30\) 0 0
\(31\) 111.365i 0.645217i −0.946532 0.322609i \(-0.895440\pi\)
0.946532 0.322609i \(-0.104560\pi\)
\(32\) −33.2888 177.932i −0.183896 0.982946i
\(33\) 0 0
\(34\) −26.6797 + 93.7799i −0.134574 + 0.473033i
\(35\) 289.899 1.40005
\(36\) 0 0
\(37\) −146.680 −0.651733 −0.325867 0.945416i \(-0.605656\pi\)
−0.325867 + 0.945416i \(0.605656\pi\)
\(38\) 93.4338 328.423i 0.398867 1.40203i
\(39\) 0 0
\(40\) 348.602 317.850i 1.37797 1.25641i
\(41\) 8.44531i 0.0321692i 0.999871 + 0.0160846i \(0.00512011\pi\)
−0.999871 + 0.0160846i \(0.994880\pi\)
\(42\) 0 0
\(43\) 427.523i 1.51620i 0.652137 + 0.758101i \(0.273873\pi\)
−0.652137 + 0.758101i \(0.726127\pi\)
\(44\) −234.748 145.330i −0.804307 0.497939i
\(45\) 0 0
\(46\) 373.128 + 106.152i 1.19597 + 0.340245i
\(47\) 318.826 0.989481 0.494740 0.869041i \(-0.335263\pi\)
0.494740 + 0.869041i \(0.335263\pi\)
\(48\) 0 0
\(49\) 149.655 0.436313
\(50\) 842.455 + 239.672i 2.38282 + 0.677895i
\(51\) 0 0
\(52\) −213.148 131.958i −0.568428 0.351909i
\(53\) 291.451i 0.755357i −0.925937 0.377679i \(-0.876722\pi\)
0.925937 0.377679i \(-0.123278\pi\)
\(54\) 0 0
\(55\) 719.525i 1.76401i
\(56\) −232.496 + 211.986i −0.554796 + 0.505854i
\(57\) 0 0
\(58\) 72.0555 253.278i 0.163127 0.573396i
\(59\) −364.665 −0.804666 −0.402333 0.915493i \(-0.631801\pi\)
−0.402333 + 0.915493i \(0.631801\pi\)
\(60\) 0 0
\(61\) −289.983 −0.608664 −0.304332 0.952566i \(-0.598433\pi\)
−0.304332 + 0.952566i \(0.598433\pi\)
\(62\) −86.1914 + 302.966i −0.176553 + 0.620592i
\(63\) 0 0
\(64\) −47.1499 + 509.824i −0.0920897 + 0.995751i
\(65\) 653.320i 1.24668i
\(66\) 0 0
\(67\) 305.907i 0.557797i 0.960321 + 0.278899i \(0.0899694\pi\)
−0.960321 + 0.278899i \(0.910031\pi\)
\(68\) 145.163 234.477i 0.258876 0.418155i
\(69\) 0 0
\(70\) −788.664 224.369i −1.34662 0.383103i
\(71\) 102.802 0.171836 0.0859178 0.996302i \(-0.472618\pi\)
0.0859178 + 0.996302i \(0.472618\pi\)
\(72\) 0 0
\(73\) 442.688 0.709764 0.354882 0.934911i \(-0.384521\pi\)
0.354882 + 0.934911i \(0.384521\pi\)
\(74\) 399.041 + 113.524i 0.626859 + 0.178336i
\(75\) 0 0
\(76\) −508.369 + 821.154i −0.767288 + 1.23938i
\(77\) 479.878i 0.710224i
\(78\) 0 0
\(79\) 245.350i 0.349419i 0.984620 + 0.174709i \(0.0558986\pi\)
−0.984620 + 0.174709i \(0.944101\pi\)
\(80\) −1194.37 + 594.901i −1.66918 + 0.831400i
\(81\) 0 0
\(82\) 6.53629 22.9753i 0.00880259 0.0309414i
\(83\) 478.981 0.633433 0.316717 0.948520i \(-0.397420\pi\)
0.316717 + 0.948520i \(0.397420\pi\)
\(84\) 0 0
\(85\) 718.697 0.917101
\(86\) 330.884 1163.07i 0.414885 1.45833i
\(87\) 0 0
\(88\) 526.146 + 577.051i 0.637357 + 0.699021i
\(89\) 1417.36i 1.68809i 0.536273 + 0.844045i \(0.319832\pi\)
−0.536273 + 0.844045i \(0.680168\pi\)
\(90\) 0 0
\(91\) 435.723i 0.501937i
\(92\) −932.929 577.568i −1.05722 0.654518i
\(93\) 0 0
\(94\) −867.360 246.757i −0.951716 0.270756i
\(95\) −2516.92 −2.71822
\(96\) 0 0
\(97\) 1153.69 1.20762 0.603811 0.797128i \(-0.293648\pi\)
0.603811 + 0.797128i \(0.293648\pi\)
\(98\) −407.134 115.826i −0.419661 0.119390i
\(99\) 0 0
\(100\) −2106.39 1304.04i −2.10639 1.30404i
\(101\) 767.096i 0.755732i 0.925860 + 0.377866i \(0.123342\pi\)
−0.925860 + 0.377866i \(0.876658\pi\)
\(102\) 0 0
\(103\) 1202.04i 1.14991i −0.818187 0.574953i \(-0.805021\pi\)
0.818187 0.574953i \(-0.194979\pi\)
\(104\) 477.734 + 523.955i 0.450439 + 0.494019i
\(105\) 0 0
\(106\) −225.570 + 792.887i −0.206692 + 0.726528i
\(107\) 1309.28 1.18292 0.591462 0.806333i \(-0.298551\pi\)
0.591462 + 0.806333i \(0.298551\pi\)
\(108\) 0 0
\(109\) 1102.04 0.968407 0.484204 0.874955i \(-0.339109\pi\)
0.484204 + 0.874955i \(0.339109\pi\)
\(110\) −556.880 + 1957.45i −0.482694 + 1.69669i
\(111\) 0 0
\(112\) 796.567 396.762i 0.672040 0.334737i
\(113\) 69.9098i 0.0581997i 0.999577 + 0.0290998i \(0.00926407\pi\)
−0.999577 + 0.0290998i \(0.990736\pi\)
\(114\) 0 0
\(115\) 2859.52i 2.31871i
\(116\) −392.051 + 633.268i −0.313802 + 0.506875i
\(117\) 0 0
\(118\) 992.062 + 282.234i 0.773955 + 0.220184i
\(119\) −479.326 −0.369241
\(120\) 0 0
\(121\) −139.949 −0.105146
\(122\) 788.892 + 224.434i 0.585434 + 0.166551i
\(123\) 0 0
\(124\) 468.963 757.503i 0.339630 0.548595i
\(125\) 3850.19i 2.75497i
\(126\) 0 0
\(127\) 2558.29i 1.78749i 0.448574 + 0.893746i \(0.351932\pi\)
−0.448574 + 0.893746i \(0.648068\pi\)
\(128\) 522.851 1350.47i 0.361047 0.932548i
\(129\) 0 0
\(130\) −505.640 + 1777.34i −0.341135 + 1.19910i
\(131\) 86.6249 0.0577744 0.0288872 0.999583i \(-0.490804\pi\)
0.0288872 + 0.999583i \(0.490804\pi\)
\(132\) 0 0
\(133\) 1678.63 1.09440
\(134\) 236.758 832.212i 0.152632 0.536508i
\(135\) 0 0
\(136\) −576.387 + 525.540i −0.363417 + 0.331358i
\(137\) 699.734i 0.436367i −0.975908 0.218184i \(-0.929987\pi\)
0.975908 0.218184i \(-0.0700131\pi\)
\(138\) 0 0
\(139\) 789.049i 0.481484i 0.970589 + 0.240742i \(0.0773908\pi\)
−0.970589 + 0.240742i \(0.922609\pi\)
\(140\) 1971.89 + 1220.78i 1.19039 + 0.736962i
\(141\) 0 0
\(142\) −279.670 79.5639i −0.165277 0.0470201i
\(143\) 1081.46 0.632421
\(144\) 0 0
\(145\) −1941.03 −1.11168
\(146\) −1204.32 342.621i −0.682675 0.194216i
\(147\) 0 0
\(148\) −997.719 617.679i −0.554135 0.343060i
\(149\) 1593.12i 0.875930i 0.898992 + 0.437965i \(0.144301\pi\)
−0.898992 + 0.437965i \(0.855699\pi\)
\(150\) 0 0
\(151\) 1502.12i 0.809544i 0.914418 + 0.404772i \(0.132649\pi\)
−0.914418 + 0.404772i \(0.867351\pi\)
\(152\) 2018.54 1840.48i 1.07714 0.982120i
\(153\) 0 0
\(154\) 371.404 1305.50i 0.194341 0.683117i
\(155\) 2321.82 1.20318
\(156\) 0 0
\(157\) −3596.08 −1.82802 −0.914008 0.405696i \(-0.867029\pi\)
−0.914008 + 0.405696i \(0.867029\pi\)
\(158\) 189.890 667.470i 0.0956129 0.336083i
\(159\) 0 0
\(160\) 3709.67 694.031i 1.83297 0.342925i
\(161\) 1907.12i 0.933555i
\(162\) 0 0
\(163\) 3313.82i 1.59238i −0.605044 0.796192i \(-0.706844\pi\)
0.605044 0.796192i \(-0.293156\pi\)
\(164\) −35.5636 + 57.4449i −0.0169333 + 0.0273518i
\(165\) 0 0
\(166\) −1303.06 370.709i −0.609257 0.173329i
\(167\) −487.046 −0.225681 −0.112841 0.993613i \(-0.535995\pi\)
−0.112841 + 0.993613i \(0.535995\pi\)
\(168\) 0 0
\(169\) −1215.05 −0.553049
\(170\) −1955.20 556.238i −0.882099 0.250950i
\(171\) 0 0
\(172\) −1800.32 + 2908.01i −0.798101 + 1.28915i
\(173\) 1752.30i 0.770086i 0.922899 + 0.385043i \(0.125813\pi\)
−0.922899 + 0.385043i \(0.874187\pi\)
\(174\) 0 0
\(175\) 4305.94i 1.85999i
\(176\) −984.758 1977.07i −0.421755 0.846745i
\(177\) 0 0
\(178\) 1096.97 3855.90i 0.461919 1.62366i
\(179\) 2807.62 1.17236 0.586178 0.810182i \(-0.300632\pi\)
0.586178 + 0.810182i \(0.300632\pi\)
\(180\) 0 0
\(181\) −2307.37 −0.947546 −0.473773 0.880647i \(-0.657108\pi\)
−0.473773 + 0.880647i \(0.657108\pi\)
\(182\) 337.230 1185.38i 0.137347 0.482780i
\(183\) 0 0
\(184\) 2091.00 + 2293.30i 0.837775 + 0.918830i
\(185\) 3058.11i 1.21533i
\(186\) 0 0
\(187\) 1189.68i 0.465230i
\(188\) 2168.65 + 1342.59i 0.841305 + 0.520844i
\(189\) 0 0
\(190\) 6847.22 + 1947.98i 2.61447 + 0.743797i
\(191\) −3375.74 −1.27885 −0.639425 0.768854i \(-0.720827\pi\)
−0.639425 + 0.768854i \(0.720827\pi\)
\(192\) 0 0
\(193\) 561.917 0.209573 0.104787 0.994495i \(-0.466584\pi\)
0.104787 + 0.994495i \(0.466584\pi\)
\(194\) −3138.58 892.902i −1.16153 0.330446i
\(195\) 0 0
\(196\) 1017.95 + 630.206i 0.370975 + 0.229667i
\(197\) 16.7420i 0.00605491i 0.999995 + 0.00302746i \(0.000963671\pi\)
−0.999995 + 0.00302746i \(0.999036\pi\)
\(198\) 0 0
\(199\) 2760.01i 0.983176i −0.870828 0.491588i \(-0.836417\pi\)
0.870828 0.491588i \(-0.163583\pi\)
\(200\) 4721.10 + 5177.87i 1.66916 + 1.83065i
\(201\) 0 0
\(202\) 593.697 2086.87i 0.206794 0.726888i
\(203\) 1294.55 0.447583
\(204\) 0 0
\(205\) −176.075 −0.0599882
\(206\) −930.322 + 3270.11i −0.314653 + 1.10602i
\(207\) 0 0
\(208\) −894.147 1795.15i −0.298067 0.598420i
\(209\) 4166.33i 1.37890i
\(210\) 0 0
\(211\) 2766.47i 0.902615i −0.892368 0.451308i \(-0.850958\pi\)
0.892368 0.451308i \(-0.149042\pi\)
\(212\) 1227.32 1982.45i 0.397606 0.642241i
\(213\) 0 0
\(214\) −3561.86 1013.32i −1.13778 0.323688i
\(215\) −8913.34 −2.82737
\(216\) 0 0
\(217\) −1548.51 −0.484423
\(218\) −2998.08 852.930i −0.931447 0.264989i
\(219\) 0 0
\(220\) 3029.96 4894.20i 0.928544 1.49985i
\(221\) 1080.21i 0.328792i
\(222\) 0 0
\(223\) 110.636i 0.0332231i 0.999862 + 0.0166115i \(0.00528786\pi\)
−0.999862 + 0.0166115i \(0.994712\pi\)
\(224\) −2474.12 + 462.876i −0.737987 + 0.138068i
\(225\) 0 0
\(226\) 54.1070 190.188i 0.0159254 0.0559784i
\(227\) 1800.57 0.526468 0.263234 0.964732i \(-0.415211\pi\)
0.263234 + 0.964732i \(0.415211\pi\)
\(228\) 0 0
\(229\) −1491.95 −0.430528 −0.215264 0.976556i \(-0.569061\pi\)
−0.215264 + 0.976556i \(0.569061\pi\)
\(230\) −2213.14 + 7779.26i −0.634479 + 2.23022i
\(231\) 0 0
\(232\) 1556.69 1419.36i 0.440523 0.401663i
\(233\) 4545.75i 1.27812i 0.769157 + 0.639060i \(0.220676\pi\)
−0.769157 + 0.639060i \(0.779324\pi\)
\(234\) 0 0
\(235\) 6647.14i 1.84516i
\(236\) −2480.45 1535.62i −0.684166 0.423561i
\(237\) 0 0
\(238\) 1303.99 + 370.976i 0.355149 + 0.101037i
\(239\) 3305.97 0.894751 0.447376 0.894346i \(-0.352359\pi\)
0.447376 + 0.894346i \(0.352359\pi\)
\(240\) 0 0
\(241\) −2337.95 −0.624898 −0.312449 0.949934i \(-0.601149\pi\)
−0.312449 + 0.949934i \(0.601149\pi\)
\(242\) 380.729 + 108.314i 0.101133 + 0.0287715i
\(243\) 0 0
\(244\) −1972.46 1221.13i −0.517516 0.320389i
\(245\) 3120.13i 0.813624i
\(246\) 0 0
\(247\) 3782.97i 0.974514i
\(248\) −1862.08 + 1697.81i −0.476782 + 0.434723i
\(249\) 0 0
\(250\) −2979.87 + 10474.3i −0.753854 + 2.64982i
\(251\) −3625.36 −0.911675 −0.455838 0.890063i \(-0.650660\pi\)
−0.455838 + 0.890063i \(0.650660\pi\)
\(252\) 0 0
\(253\) 4733.45 1.17624
\(254\) 1980.00 6959.77i 0.489119 1.71927i
\(255\) 0 0
\(256\) −2467.61 + 3269.27i −0.602444 + 0.798161i
\(257\) 2124.02i 0.515537i 0.966207 + 0.257768i \(0.0829871\pi\)
−0.966207 + 0.257768i \(0.917013\pi\)
\(258\) 0 0
\(259\) 2039.57i 0.489315i
\(260\) 2751.16 4443.87i 0.656230 1.05999i
\(261\) 0 0
\(262\) −235.661 67.0437i −0.0555694 0.0158091i
\(263\) −4785.87 −1.12209 −0.561044 0.827786i \(-0.689600\pi\)
−0.561044 + 0.827786i \(0.689600\pi\)
\(264\) 0 0
\(265\) 6076.41 1.40857
\(266\) −4566.67 1299.18i −1.05263 0.299466i
\(267\) 0 0
\(268\) −1288.19 + 2080.77i −0.293614 + 0.474267i
\(269\) 241.884i 0.0548249i 0.999624 + 0.0274125i \(0.00872675\pi\)
−0.999624 + 0.0274125i \(0.991273\pi\)
\(270\) 0 0
\(271\) 828.799i 0.185778i 0.995676 + 0.0928892i \(0.0296102\pi\)
−0.995676 + 0.0928892i \(0.970390\pi\)
\(272\) 1974.79 983.624i 0.440218 0.219268i
\(273\) 0 0
\(274\) −541.562 + 1903.61i −0.119405 + 0.419713i
\(275\) 10687.3 2.34352
\(276\) 0 0
\(277\) −5897.19 −1.27916 −0.639581 0.768724i \(-0.720892\pi\)
−0.639581 + 0.768724i \(0.720892\pi\)
\(278\) 610.688 2146.59i 0.131751 0.463108i
\(279\) 0 0
\(280\) −4419.65 4847.26i −0.943303 1.03457i
\(281\) 3055.95i 0.648763i 0.945926 + 0.324382i \(0.105156\pi\)
−0.945926 + 0.324382i \(0.894844\pi\)
\(282\) 0 0
\(283\) 196.045i 0.0411790i 0.999788 + 0.0205895i \(0.00655430\pi\)
−0.999788 + 0.0205895i \(0.993446\pi\)
\(284\) 699.257 + 432.904i 0.146103 + 0.0904511i
\(285\) 0 0
\(286\) −2942.08 837.000i −0.608283 0.173052i
\(287\) 117.431 0.0241523
\(288\) 0 0
\(289\) 3724.69 0.758130
\(290\) 5280.53 + 1502.27i 1.06925 + 0.304194i
\(291\) 0 0
\(292\) 3011.16 + 1864.18i 0.603476 + 0.373606i
\(293\) 8748.98i 1.74444i −0.489114 0.872220i \(-0.662680\pi\)
0.489114 0.872220i \(-0.337320\pi\)
\(294\) 0 0
\(295\) 7602.82i 1.50052i
\(296\) 2236.22 + 2452.57i 0.439113 + 0.481597i
\(297\) 0 0
\(298\) 1233.00 4334.05i 0.239684 0.842499i
\(299\) 4297.91 0.831287
\(300\) 0 0
\(301\) 5944.65 1.13835
\(302\) 1162.58 4086.49i 0.221519 0.778646i
\(303\) 0 0
\(304\) −6915.84 + 3444.71i −1.30477 + 0.649894i
\(305\) 6045.79i 1.13502i
\(306\) 0 0
\(307\) 2095.99i 0.389656i −0.980837 0.194828i \(-0.937585\pi\)
0.980837 0.194828i \(-0.0624149\pi\)
\(308\) −2020.79 + 3264.13i −0.373848 + 0.603867i
\(309\) 0 0
\(310\) −6316.47 1796.99i −1.15726 0.329232i
\(311\) −3393.74 −0.618783 −0.309391 0.950935i \(-0.600125\pi\)
−0.309391 + 0.950935i \(0.600125\pi\)
\(312\) 0 0
\(313\) 3579.49 0.646405 0.323203 0.946330i \(-0.395240\pi\)
0.323203 + 0.946330i \(0.395240\pi\)
\(314\) 9783.05 + 2783.20i 1.75825 + 0.500208i
\(315\) 0 0
\(316\) −1033.18 + 1668.87i −0.183928 + 0.297093i
\(317\) 4356.56i 0.771889i −0.922522 0.385945i \(-0.873876\pi\)
0.922522 0.385945i \(-0.126124\pi\)
\(318\) 0 0
\(319\) 3213.05i 0.563937i
\(320\) −10629.2 983.019i −1.85685 0.171726i
\(321\) 0 0
\(322\) 1476.03 5188.28i 0.255453 0.897925i
\(323\) 4161.53 0.716885
\(324\) 0 0
\(325\) 9703.91 1.65623
\(326\) −2564.75 + 9015.18i −0.435731 + 1.53161i
\(327\) 0 0
\(328\) 141.210 128.753i 0.0237714 0.0216744i
\(329\) 4433.23i 0.742893i
\(330\) 0 0
\(331\) 9191.99i 1.52640i 0.646164 + 0.763198i \(0.276372\pi\)
−0.646164 + 0.763198i \(0.723628\pi\)
\(332\) 3258.02 + 2017.01i 0.538576 + 0.333427i
\(333\) 0 0
\(334\) 1325.00 + 376.951i 0.217068 + 0.0617541i
\(335\) −6377.78 −1.04017
\(336\) 0 0
\(337\) 1663.33 0.268865 0.134432 0.990923i \(-0.457079\pi\)
0.134432 + 0.990923i \(0.457079\pi\)
\(338\) 3305.51 + 940.393i 0.531941 + 0.151333i
\(339\) 0 0
\(340\) 4888.57 + 3026.47i 0.779764 + 0.482745i
\(341\) 3843.38i 0.610354i
\(342\) 0 0
\(343\) 6850.30i 1.07837i
\(344\) 7148.40 6517.80i 1.12040 1.02156i
\(345\) 0 0
\(346\) 1356.20 4767.09i 0.210722 0.740695i
\(347\) 9668.26 1.49573 0.747866 0.663850i \(-0.231078\pi\)
0.747866 + 0.663850i \(0.231078\pi\)
\(348\) 0 0
\(349\) 9928.24 1.52277 0.761384 0.648301i \(-0.224520\pi\)
0.761384 + 0.648301i \(0.224520\pi\)
\(350\) 3332.60 11714.2i 0.508957 1.78900i
\(351\) 0 0
\(352\) 1148.85 + 6140.72i 0.173960 + 0.929834i
\(353\) 4460.01i 0.672471i 0.941778 + 0.336236i \(0.109154\pi\)
−0.941778 + 0.336236i \(0.890846\pi\)
\(354\) 0 0
\(355\) 2143.29i 0.320434i
\(356\) −5968.58 + 9640.88i −0.888579 + 1.43530i
\(357\) 0 0
\(358\) −7638.08 2172.97i −1.12761 0.320797i
\(359\) −2158.32 −0.317303 −0.158652 0.987335i \(-0.550715\pi\)
−0.158652 + 0.987335i \(0.550715\pi\)
\(360\) 0 0
\(361\) −7714.95 −1.12479
\(362\) 6277.16 + 1785.80i 0.911382 + 0.259281i
\(363\) 0 0
\(364\) −1834.85 + 2963.79i −0.264210 + 0.426771i
\(365\) 9229.52i 1.32355i
\(366\) 0 0
\(367\) 1156.43i 0.164482i −0.996612 0.0822411i \(-0.973792\pi\)
0.996612 0.0822411i \(-0.0262078\pi\)
\(368\) −3913.60 7857.22i −0.554377 1.11301i
\(369\) 0 0
\(370\) −2366.84 + 8319.52i −0.332557 + 1.16895i
\(371\) −4052.59 −0.567115
\(372\) 0 0
\(373\) −6286.39 −0.872647 −0.436323 0.899790i \(-0.643720\pi\)
−0.436323 + 0.899790i \(0.643720\pi\)
\(374\) 920.758 3236.49i 0.127303 0.447474i
\(375\) 0 0
\(376\) −4860.66 5330.93i −0.666674 0.731175i
\(377\) 2917.41i 0.398552i
\(378\) 0 0
\(379\) 6921.76i 0.938119i −0.883167 0.469059i \(-0.844593\pi\)
0.883167 0.469059i \(-0.155407\pi\)
\(380\) −17120.1 10598.9i −2.31116 1.43082i
\(381\) 0 0
\(382\) 9183.63 + 2612.67i 1.23004 + 0.349937i
\(383\) 1802.67 0.240502 0.120251 0.992744i \(-0.461630\pi\)
0.120251 + 0.992744i \(0.461630\pi\)
\(384\) 0 0
\(385\) −10004.9 −1.32441
\(386\) −1528.68 434.898i −0.201575 0.0573465i
\(387\) 0 0
\(388\) 7847.37 + 4858.24i 1.02678 + 0.635669i
\(389\) 4421.02i 0.576233i −0.957595 0.288117i \(-0.906971\pi\)
0.957595 0.288117i \(-0.0930291\pi\)
\(390\) 0 0
\(391\) 4728.00i 0.611522i
\(392\) −2281.57 2502.31i −0.293971 0.322413i
\(393\) 0 0
\(394\) 12.9575 45.5462i 0.00165683 0.00582382i
\(395\) −5115.26 −0.651586
\(396\) 0 0
\(397\) −13769.8 −1.74077 −0.870383 0.492375i \(-0.836129\pi\)
−0.870383 + 0.492375i \(0.836129\pi\)
\(398\) −2136.12 + 7508.54i −0.269030 + 0.945651i
\(399\) 0 0
\(400\) −8836.21 17740.2i −1.10453 2.21752i
\(401\) 13534.1i 1.68544i 0.538350 + 0.842722i \(0.319048\pi\)
−0.538350 + 0.842722i \(0.680952\pi\)
\(402\) 0 0
\(403\) 3489.74i 0.431356i
\(404\) −3230.28 + 5217.78i −0.397803 + 0.642560i
\(405\) 0 0
\(406\) −3521.79 1001.92i −0.430501 0.122474i
\(407\) 5062.18 0.616518
\(408\) 0 0
\(409\) 7230.24 0.874114 0.437057 0.899434i \(-0.356021\pi\)
0.437057 + 0.899434i \(0.356021\pi\)
\(410\) 479.007 + 136.274i 0.0576987 + 0.0164148i
\(411\) 0 0
\(412\) 5061.84 8176.24i 0.605289 0.977705i
\(413\) 5070.61i 0.604136i
\(414\) 0 0
\(415\) 9986.16i 1.18121i
\(416\) 1043.14 + 5575.70i 0.122943 + 0.657142i
\(417\) 0 0
\(418\) −3224.55 + 11334.4i −0.377316 + 1.32628i
\(419\) −9066.85 −1.05715 −0.528574 0.848887i \(-0.677273\pi\)
−0.528574 + 0.848887i \(0.677273\pi\)
\(420\) 0 0
\(421\) 6017.63 0.696630 0.348315 0.937378i \(-0.386754\pi\)
0.348315 + 0.937378i \(0.386754\pi\)
\(422\) −2141.12 + 7526.12i −0.246986 + 0.868166i
\(423\) 0 0
\(424\) −4873.21 + 4443.32i −0.558170 + 0.508931i
\(425\) 10675.0i 1.21838i
\(426\) 0 0
\(427\) 4032.17i 0.456979i
\(428\) 8905.70 + 5513.44i 1.00578 + 0.622669i
\(429\) 0 0
\(430\) 24248.5 + 6898.52i 2.71946 + 0.773666i
\(431\) −10533.7 −1.17724 −0.588619 0.808410i \(-0.700328\pi\)
−0.588619 + 0.808410i \(0.700328\pi\)
\(432\) 0 0
\(433\) −79.2056 −0.00879071 −0.00439536 0.999990i \(-0.501399\pi\)
−0.00439536 + 0.999990i \(0.501399\pi\)
\(434\) 4212.69 + 1198.48i 0.465935 + 0.132555i
\(435\) 0 0
\(436\) 7496.07 + 4640.75i 0.823387 + 0.509751i
\(437\) 16557.7i 1.81250i
\(438\) 0 0
\(439\) 9484.31i 1.03112i 0.856854 + 0.515560i \(0.172416\pi\)
−0.856854 + 0.515560i \(0.827584\pi\)
\(440\) −12030.8 + 10969.5i −1.30352 + 1.18853i
\(441\) 0 0
\(442\) 836.036 2938.70i 0.0899687 0.316243i
\(443\) −9734.58 −1.04403 −0.522013 0.852937i \(-0.674819\pi\)
−0.522013 + 0.852937i \(0.674819\pi\)
\(444\) 0 0
\(445\) −29550.3 −3.14790
\(446\) 85.6273 300.983i 0.00909097 0.0319551i
\(447\) 0 0
\(448\) 7089.03 + 655.613i 0.747601 + 0.0691401i
\(449\) 9270.01i 0.974340i −0.873307 0.487170i \(-0.838029\pi\)
0.873307 0.487170i \(-0.161971\pi\)
\(450\) 0 0
\(451\) 291.461i 0.0304310i
\(452\) −294.394 + 475.526i −0.0306352 + 0.0494842i
\(453\) 0 0
\(454\) −4898.41 1393.56i −0.506374 0.144060i
\(455\) −9084.31 −0.935997
\(456\) 0 0
\(457\) −2542.86 −0.260285 −0.130142 0.991495i \(-0.541543\pi\)
−0.130142 + 0.991495i \(0.541543\pi\)
\(458\) 4058.81 + 1154.70i 0.414096 + 0.117807i
\(459\) 0 0
\(460\) 12041.6 19450.4i 1.22053 1.97148i
\(461\) 10664.8i 1.07746i −0.842479 0.538729i \(-0.818905\pi\)
0.842479 0.538729i \(-0.181095\pi\)
\(462\) 0 0
\(463\) 1963.48i 0.197086i −0.995133 0.0985428i \(-0.968582\pi\)
0.995133 0.0985428i \(-0.0314181\pi\)
\(464\) −5333.45 + 2656.54i −0.533619 + 0.265790i
\(465\) 0 0
\(466\) 3518.20 12366.6i 0.349737 1.22934i
\(467\) 19778.8 1.95986 0.979928 0.199350i \(-0.0638829\pi\)
0.979928 + 0.199350i \(0.0638829\pi\)
\(468\) 0 0
\(469\) 4253.58 0.418789
\(470\) 5144.59 18083.4i 0.504898 1.77473i
\(471\) 0 0
\(472\) 5559.49 + 6097.38i 0.542154 + 0.594607i
\(473\) 14754.5i 1.43428i
\(474\) 0 0
\(475\) 37384.4i 3.61119i
\(476\) −3260.37 2018.47i −0.313947 0.194362i
\(477\) 0 0
\(478\) −8993.82 2558.67i −0.860602 0.244835i
\(479\) 16062.6 1.53219 0.766095 0.642728i \(-0.222197\pi\)
0.766095 + 0.642728i \(0.222197\pi\)
\(480\) 0 0
\(481\) 4596.39 0.435712
\(482\) 6360.33 + 1809.47i 0.601048 + 0.170994i
\(483\) 0 0
\(484\) −951.933 589.333i −0.0894002 0.0553469i
\(485\) 24053.0i 2.25194i
\(486\) 0 0
\(487\) 15907.5i 1.48016i 0.672519 + 0.740080i \(0.265212\pi\)
−0.672519 + 0.740080i \(0.734788\pi\)
\(488\) 4420.93 + 4848.66i 0.410095 + 0.449771i
\(489\) 0 0
\(490\) 2414.84 8488.25i 0.222635 0.782571i
\(491\) −5924.49 −0.544538 −0.272269 0.962221i \(-0.587774\pi\)
−0.272269 + 0.962221i \(0.587774\pi\)
\(492\) 0 0
\(493\) 3209.35 0.293188
\(494\) −2927.85 + 10291.5i −0.266660 + 0.937320i
\(495\) 0 0
\(496\) 6379.77 3177.70i 0.577540 0.287667i
\(497\) 1429.44i 0.129013i
\(498\) 0 0
\(499\) 5331.33i 0.478283i −0.970985 0.239142i \(-0.923134\pi\)
0.970985 0.239142i \(-0.0768660\pi\)
\(500\) 16213.3 26188.9i 1.45016 2.34241i
\(501\) 0 0
\(502\) 9862.70 + 2805.86i 0.876880 + 0.249466i
\(503\) 2144.13 0.190064 0.0950319 0.995474i \(-0.469705\pi\)
0.0950319 + 0.995474i \(0.469705\pi\)
\(504\) 0 0
\(505\) −15993.0 −1.40927
\(506\) −12877.2 3663.47i −1.13135 0.321860i
\(507\) 0 0
\(508\) −10773.1 + 17401.5i −0.940902 + 1.51981i
\(509\) 14329.9i 1.24786i 0.781481 + 0.623929i \(0.214465\pi\)
−0.781481 + 0.623929i \(0.785535\pi\)
\(510\) 0 0
\(511\) 6155.51i 0.532884i
\(512\) 9243.34 6984.15i 0.797855 0.602849i
\(513\) 0 0
\(514\) 1643.90 5778.36i 0.141069 0.495861i
\(515\) 25061.0 2.14431
\(516\) 0 0
\(517\) −11003.2 −0.936016
\(518\) 1578.53 5548.60i 0.133893 0.470640i
\(519\) 0 0
\(520\) −10923.8 + 9960.18i −0.921234 + 0.839967i
\(521\) 10822.8i 0.910087i −0.890469 0.455043i \(-0.849624\pi\)
0.890469 0.455043i \(-0.150376\pi\)
\(522\) 0 0
\(523\) 12111.8i 1.01265i 0.862344 + 0.506323i \(0.168995\pi\)
−0.862344 + 0.506323i \(0.831005\pi\)
\(524\) 589.221 + 364.782i 0.0491226 + 0.0304114i
\(525\) 0 0
\(526\) 13019.8 + 3704.04i 1.07926 + 0.307042i
\(527\) −3838.96 −0.317320
\(528\) 0 0
\(529\) 6644.58 0.546115
\(530\) −16530.7 4702.86i −1.35481 0.385433i
\(531\) 0 0
\(532\) 11418.0 + 7068.79i 0.930514 + 0.576073i
\(533\) 264.643i 0.0215065i
\(534\) 0 0
\(535\) 27296.9i 2.20588i
\(536\) 5114.91 4663.70i 0.412184 0.375823i
\(537\) 0 0
\(538\) 187.207 658.039i 0.0150020 0.0527324i
\(539\) −5164.85 −0.412738
\(540\) 0 0
\(541\) 22063.1 1.75336 0.876681 0.481073i \(-0.159753\pi\)
0.876681 + 0.481073i \(0.159753\pi\)
\(542\) 641.453 2254.73i 0.0508353 0.178688i
\(543\) 0 0
\(544\) −6133.65 + 1147.53i −0.483416 + 0.0904409i
\(545\) 22976.2i 1.80586i
\(546\) 0 0
\(547\) 17842.7i 1.39470i 0.716731 + 0.697350i \(0.245637\pi\)
−0.716731 + 0.697350i \(0.754363\pi\)
\(548\) 2946.61 4759.58i 0.229695 0.371020i
\(549\) 0 0
\(550\) −29074.5 8271.46i −2.25407 0.641266i
\(551\) −11239.3 −0.868987
\(552\) 0 0
\(553\) 3411.56 0.262340
\(554\) 16043.2 + 4564.15i 1.23034 + 0.350022i
\(555\) 0 0
\(556\) −3322.73 + 5367.10i −0.253444 + 0.409381i
\(557\) 10942.0i 0.832365i −0.909281 0.416183i \(-0.863368\pi\)
0.909281 0.416183i \(-0.136632\pi\)
\(558\) 0 0
\(559\) 13396.9i 1.01365i
\(560\) 8272.01 + 16607.5i 0.624208 + 1.25320i
\(561\) 0 0
\(562\) 2365.16 8313.63i 0.177524 0.624002i
\(563\) −1991.56 −0.149084 −0.0745418 0.997218i \(-0.523749\pi\)
−0.0745418 + 0.997218i \(0.523749\pi\)
\(564\) 0 0
\(565\) −1457.53 −0.108529
\(566\) 151.730 533.335i 0.0112680 0.0396073i
\(567\) 0 0
\(568\) −1567.26 1718.90i −0.115776 0.126978i
\(569\) 12048.3i 0.887684i −0.896105 0.443842i \(-0.853615\pi\)
0.896105 0.443842i \(-0.146385\pi\)
\(570\) 0 0
\(571\) 24916.7i 1.82615i −0.407792 0.913075i \(-0.633701\pi\)
0.407792 0.913075i \(-0.366299\pi\)
\(572\) 7356.07 + 4554.08i 0.537715 + 0.332894i
\(573\) 0 0
\(574\) −319.468 90.8861i −0.0232305 0.00660890i
\(575\) 42473.2 3.08044
\(576\) 0 0
\(577\) −17705.3 −1.27743 −0.638717 0.769441i \(-0.720535\pi\)
−0.638717 + 0.769441i \(0.720535\pi\)
\(578\) −10132.9 2882.74i −0.729195 0.207450i
\(579\) 0 0
\(580\) −13202.9 8173.78i −0.945206 0.585169i
\(581\) 6660.15i 0.475576i
\(582\) 0 0
\(583\) 10058.5i 0.714543i
\(584\) −6749.00 7401.97i −0.478212 0.524479i
\(585\) 0 0
\(586\) −6771.31 + 23801.4i −0.477339 + 1.67786i
\(587\) −22453.6 −1.57880 −0.789402 0.613876i \(-0.789609\pi\)
−0.789402 + 0.613876i \(0.789609\pi\)
\(588\) 0 0
\(589\) 13444.3 0.940511
\(590\) −5884.24 + 20683.3i −0.410593 + 1.44325i
\(591\) 0 0
\(592\) −4185.40 8402.89i −0.290572 0.583373i
\(593\) 26839.1i 1.85860i −0.369328 0.929299i \(-0.620412\pi\)
0.369328 0.929299i \(-0.379588\pi\)
\(594\) 0 0
\(595\) 9993.36i 0.688551i
\(596\) −6708.71 + 10836.4i −0.461073 + 0.744758i
\(597\) 0 0
\(598\) −11692.4 3326.39i −0.799560 0.227468i
\(599\) −9254.44 −0.631262 −0.315631 0.948882i \(-0.602216\pi\)
−0.315631 + 0.948882i \(0.602216\pi\)
\(600\) 0 0
\(601\) 1102.45 0.0748250 0.0374125 0.999300i \(-0.488088\pi\)
0.0374125 + 0.999300i \(0.488088\pi\)
\(602\) −16172.3 4600.88i −1.09490 0.311492i
\(603\) 0 0
\(604\) −6325.52 + 10217.4i −0.426129 + 0.688313i
\(605\) 2917.77i 0.196073i
\(606\) 0 0
\(607\) 21383.2i 1.42985i −0.699202 0.714924i \(-0.746461\pi\)
0.699202 0.714924i \(-0.253539\pi\)
\(608\) 21480.4 4018.71i 1.43281 0.268060i
\(609\) 0 0
\(610\) −4679.17 + 16447.4i −0.310580 + 1.09170i
\(611\) −9990.77 −0.661511
\(612\) 0 0
\(613\) 19769.0 1.30255 0.651274 0.758843i \(-0.274235\pi\)
0.651274 + 0.758843i \(0.274235\pi\)
\(614\) −1622.20 + 5702.09i −0.106623 + 0.374784i
\(615\) 0 0
\(616\) 8023.80 7315.98i 0.524819 0.478522i
\(617\) 2702.48i 0.176333i −0.996106 0.0881667i \(-0.971899\pi\)
0.996106 0.0881667i \(-0.0281008\pi\)
\(618\) 0 0
\(619\) 6967.79i 0.452438i 0.974076 + 0.226219i \(0.0726365\pi\)
−0.974076 + 0.226219i \(0.927364\pi\)
\(620\) 15793.0 + 9777.32i 1.02300 + 0.633333i
\(621\) 0 0
\(622\) 9232.60 + 2626.60i 0.595166 + 0.169320i
\(623\) 19708.2 1.26740
\(624\) 0 0
\(625\) 41562.7 2.66001
\(626\) −9737.92 2770.36i −0.621734 0.176879i
\(627\) 0 0
\(628\) −24460.5 15143.3i −1.55427 0.962233i
\(629\) 5056.35i 0.320524i
\(630\) 0 0
\(631\) 19202.4i 1.21147i −0.795667 0.605734i \(-0.792880\pi\)
0.795667 0.605734i \(-0.207120\pi\)
\(632\) 4102.38 3740.49i 0.258202 0.235425i
\(633\) 0 0
\(634\) −3371.78 + 11851.9i −0.211215 + 0.742429i
\(635\) −53337.2 −3.33326
\(636\) 0 0
\(637\) −4689.61 −0.291694
\(638\) −2486.75 + 8741.02i −0.154313 + 0.542414i
\(639\) 0 0
\(640\) 28155.7 + 10900.8i 1.73899 + 0.673270i
\(641\) 23580.8i 1.45302i 0.687155 + 0.726511i \(0.258860\pi\)
−0.687155 + 0.726511i \(0.741140\pi\)
\(642\) 0 0
\(643\) 25167.2i 1.54354i 0.635899 + 0.771772i \(0.280629\pi\)
−0.635899 + 0.771772i \(0.719371\pi\)
\(644\) −8030.99 + 12972.2i −0.491406 + 0.793754i
\(645\) 0 0
\(646\) −11321.4 3220.84i −0.689524 0.196164i
\(647\) 2247.67 0.136577 0.0682883 0.997666i \(-0.478246\pi\)
0.0682883 + 0.997666i \(0.478246\pi\)
\(648\) 0 0
\(649\) 12585.2 0.761188
\(650\) −26399.3 7510.38i −1.59302 0.453202i
\(651\) 0 0
\(652\) 13954.7 22540.6i 0.838202 1.35392i
\(653\) 11278.6i 0.675906i 0.941163 + 0.337953i \(0.109734\pi\)
−0.941163 + 0.337953i \(0.890266\pi\)
\(654\) 0 0
\(655\) 1806.02i 0.107736i
\(656\) −483.807 + 240.979i −0.0287950 + 0.0143425i
\(657\) 0 0
\(658\) −3431.12 + 12060.5i −0.203281 + 0.714540i
\(659\) 658.636 0.0389329 0.0194665 0.999811i \(-0.493803\pi\)
0.0194665 + 0.999811i \(0.493803\pi\)
\(660\) 0 0
\(661\) 1740.41 0.102412 0.0512060 0.998688i \(-0.483694\pi\)
0.0512060 + 0.998688i \(0.483694\pi\)
\(662\) 7114.18 25006.6i 0.417674 1.46814i
\(663\) 0 0
\(664\) −7302.30 8008.79i −0.426783 0.468074i
\(665\) 34997.4i 2.04081i
\(666\) 0 0
\(667\) 12769.2i 0.741269i
\(668\) −3312.88 2050.97i −0.191885 0.118794i
\(669\) 0 0
\(670\) 17350.6 + 4936.11i 1.00047 + 0.284625i
\(671\) 10007.8 0.575776
\(672\) 0 0
\(673\) −273.146 −0.0156449 −0.00782243 0.999969i \(-0.502490\pi\)
−0.00782243 + 0.999969i \(0.502490\pi\)
\(674\) −4525.05 1287.34i −0.258603 0.0735706i
\(675\) 0 0
\(676\) −8264.75 5116.63i −0.470229 0.291115i
\(677\) 11373.1i 0.645649i 0.946459 + 0.322824i \(0.104632\pi\)
−0.946459 + 0.322824i \(0.895368\pi\)
\(678\) 0 0
\(679\) 16041.8i 0.906671i
\(680\) −10956.9 12017.0i −0.617908 0.677690i
\(681\) 0 0
\(682\) 2974.60 10455.8i 0.167014 0.587059i
\(683\) 1223.56 0.0685480 0.0342740 0.999412i \(-0.489088\pi\)
0.0342740 + 0.999412i \(0.489088\pi\)
\(684\) 0 0
\(685\) 14588.6 0.813725
\(686\) −5301.82 + 18636.1i −0.295079 + 1.03721i
\(687\) 0 0
\(688\) −24491.5 + 12199.0i −1.35717 + 0.675992i
\(689\) 9132.95i 0.504989i
\(690\) 0 0
\(691\) 9247.55i 0.509108i 0.967059 + 0.254554i \(0.0819286\pi\)
−0.967059 + 0.254554i \(0.918071\pi\)
\(692\) −7379.02 + 11919.1i −0.405359 + 0.654764i
\(693\) 0 0
\(694\) −26302.3 7482.79i −1.43865 0.409284i
\(695\) −16450.7 −0.897858
\(696\) 0 0
\(697\) 291.126 0.0158209
\(698\) −27009.5 7684.00i −1.46465 0.416682i
\(699\) 0 0
\(700\) −18132.5 + 29289.0i −0.979065 + 1.58145i
\(701\) 14448.0i 0.778447i −0.921143 0.389224i \(-0.872743\pi\)
0.921143 0.389224i \(-0.127257\pi\)
\(702\) 0 0
\(703\) 17707.6i 0.950009i
\(704\) 1627.22 17594.9i 0.0871139 0.941948i
\(705\) 0 0
\(706\) 3451.84 12133.4i 0.184011 0.646806i
\(707\) 10666.4 0.567397
\(708\) 0 0
\(709\) 7819.28 0.414188 0.207094 0.978321i \(-0.433599\pi\)
0.207094 + 0.978321i \(0.433599\pi\)
\(710\) 1658.81 5830.78i 0.0876818 0.308205i
\(711\) 0 0
\(712\) 23699.0 21608.4i 1.24741 1.13737i
\(713\) 15274.3i 0.802281i
\(714\) 0 0
\(715\) 22547.1i 1.17932i
\(716\) 19097.4 + 11823.0i 0.996794 + 0.617106i
\(717\) 0 0
\(718\) 5871.67 + 1670.44i 0.305193 + 0.0868251i
\(719\) 7251.47 0.376126 0.188063 0.982157i \(-0.439779\pi\)
0.188063 + 0.982157i \(0.439779\pi\)
\(720\) 0 0
\(721\) −16714.1 −0.863338
\(722\) 20988.3 + 5971.02i 1.08186 + 0.307781i
\(723\) 0 0
\(724\) −15694.7 9716.47i −0.805650 0.498771i
\(725\) 28830.6i 1.47689i
\(726\) 0 0
\(727\) 6605.59i 0.336985i 0.985703 + 0.168492i \(0.0538899\pi\)
−0.985703 + 0.168492i \(0.946110\pi\)
\(728\) 7285.51 6642.82i 0.370905 0.338186i
\(729\) 0 0
\(730\) 7143.23 25108.7i 0.362168 1.27303i
\(731\) 14737.5 0.745673
\(732\) 0 0
\(733\) −37147.9 −1.87188 −0.935942 0.352155i \(-0.885449\pi\)
−0.935942 + 0.352155i \(0.885449\pi\)
\(734\) −895.022 + 3146.03i −0.0450080 + 0.158205i
\(735\) 0 0
\(736\) 4565.74 + 24404.3i 0.228662 + 1.22222i
\(737\) 10557.3i 0.527658i
\(738\) 0 0
\(739\) 34209.1i 1.70285i 0.524479 + 0.851423i \(0.324260\pi\)
−0.524479 + 0.851423i \(0.675740\pi\)
\(740\) 12877.9 20801.2i 0.639729 1.03334i
\(741\) 0 0
\(742\) 11025.0 + 3136.52i 0.545471 + 0.155182i
\(743\) 15746.4 0.777494 0.388747 0.921345i \(-0.372908\pi\)
0.388747 + 0.921345i \(0.372908\pi\)
\(744\) 0 0
\(745\) −33214.6 −1.63341
\(746\) 17102.0 + 4865.38i 0.839341 + 0.238786i
\(747\) 0 0
\(748\) −5009.80 + 8092.18i −0.244888 + 0.395561i
\(749\) 18205.3i 0.888128i
\(750\) 0 0
\(751\) 27773.5i 1.34949i −0.738049 0.674747i \(-0.764253\pi\)
0.738049 0.674747i \(-0.235747\pi\)
\(752\) 9097.42 + 18264.6i 0.441155 + 0.885694i
\(753\) 0 0
\(754\) −2257.94 + 7936.73i −0.109057 + 0.383341i
\(755\) −31317.5 −1.50961
\(756\) 0 0
\(757\) −12694.0 −0.609471 −0.304736 0.952437i \(-0.598568\pi\)
−0.304736 + 0.952437i \(0.598568\pi\)
\(758\) −5357.13 + 18830.5i −0.256701 + 0.902314i
\(759\) 0 0
\(760\) 38371.7 + 42084.1i 1.83143 + 2.00862i
\(761\) 18061.4i 0.860349i −0.902746 0.430175i \(-0.858452\pi\)
0.902746 0.430175i \(-0.141548\pi\)
\(762\) 0 0
\(763\) 15323.7i 0.727071i
\(764\) −22961.8 14215.4i −1.08734 0.673162i
\(765\) 0 0
\(766\) −4904.13 1395.19i −0.231323 0.0658096i
\(767\) 11427.2 0.537955
\(768\) 0 0
\(769\) 32615.8 1.52946 0.764731 0.644350i \(-0.222872\pi\)
0.764731 + 0.644350i \(0.222872\pi\)
\(770\) 27218.1 + 7743.32i 1.27386 + 0.362403i
\(771\) 0 0
\(772\) 3822.15 + 2366.26i 0.178189 + 0.110316i
\(773\) 8518.40i 0.396359i −0.980166 0.198179i \(-0.936497\pi\)
0.980166 0.198179i \(-0.0635029\pi\)
\(774\) 0 0
\(775\) 34486.6i 1.59844i
\(776\) −17588.5 19290.2i −0.813649 0.892370i
\(777\) 0 0
\(778\) −3421.67 + 12027.3i −0.157677 + 0.554241i
\(779\) −1019.54 −0.0468919
\(780\) 0 0
\(781\) −3547.86 −0.162551
\(782\) 3659.26 12862.4i 0.167333 0.588183i
\(783\) 0 0
\(784\) 4270.28 + 8573.31i 0.194528 + 0.390548i
\(785\) 74973.9i 3.40883i
\(786\) 0 0
\(787\) 12371.2i 0.560338i 0.959951 + 0.280169i \(0.0903906\pi\)
−0.959951 + 0.280169i \(0.909609\pi\)
\(788\) −70.5014 + 113.879i −0.00318719 + 0.00514818i
\(789\) 0 0
\(790\) 13915.9 + 3958.98i 0.626718 + 0.178296i
\(791\) 972.085 0.0436958
\(792\)