Properties

Label 252.4.b.g.55.3
Level $252$
Weight $4$
Character 252.55
Analytic conductor $14.868$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 358 x^{14} - 2828 x^{13} + 52557 x^{12} - 549972 x^{11} + 4434734 x^{10} - 37785264 x^{9} + 272741368 x^{8} - 1739202044 x^{7} + 9778426658 x^{6} - 39463975388 x^{5} + 101978126949 x^{4} - 176540053420 x^{3} + 219245087130 x^{2} - 139977817400 x + 52705588025\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{26} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.3
Root \(0.929907 + 12.9280i\) of defining polynomial
Character \(\chi\) \(=\) 252.55
Dual form 252.4.b.g.55.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.69547 + 0.856992i) q^{2} +(6.53113 - 4.62000i) q^{4} -10.3049i q^{5} +(16.6272 + 8.15690i) q^{7} +(-13.6452 + 18.0502i) q^{8} +O(q^{10})\) \(q+(-2.69547 + 0.856992i) q^{2} +(6.53113 - 4.62000i) q^{4} -10.3049i q^{5} +(16.6272 + 8.15690i) q^{7} +(-13.6452 + 18.0502i) q^{8} +(8.83121 + 27.7765i) q^{10} +18.0502i q^{11} +49.0412i q^{13} +(-51.8086 - 7.73727i) q^{14} +(21.3113 - 60.3476i) q^{16} -46.6928i q^{17} +48.8465 q^{19} +(-47.6085 - 67.3025i) q^{20} +(-15.4689 - 48.6538i) q^{22} -33.7962i q^{23} +18.8094 q^{25} +(-42.0280 - 132.189i) q^{26} +(146.279 - 23.5440i) q^{28} -48.1829 q^{29} +152.751 q^{31} +(-5.72657 + 180.929i) q^{32} +(40.0153 + 125.859i) q^{34} +(84.0559 - 171.342i) q^{35} +37.6848 q^{37} +(-131.664 + 41.8611i) q^{38} +(186.005 + 140.612i) q^{40} +409.288i q^{41} -470.799i q^{43} +(83.3918 + 117.888i) q^{44} +(28.9631 + 91.0966i) q^{46} +548.980 q^{47} +(209.930 + 271.253i) q^{49} +(-50.7001 + 16.1195i) q^{50} +(226.570 + 320.295i) q^{52} +203.157 q^{53} +186.005 q^{55} +(-374.115 + 188.823i) q^{56} +(129.875 - 41.2923i) q^{58} +717.092 q^{59} +493.466i q^{61} +(-411.735 + 130.906i) q^{62} +(-139.619 - 492.596i) q^{64} +505.364 q^{65} +240.375i q^{67} +(-215.720 - 304.956i) q^{68} +(-79.7317 + 533.882i) q^{70} -995.648i q^{71} -790.766i q^{73} +(-101.578 + 32.2956i) q^{74} +(319.023 - 225.671i) q^{76} +(-147.234 + 300.125i) q^{77} +214.111i q^{79} +(-621.875 - 219.610i) q^{80} +(-350.757 - 1103.23i) q^{82} +885.204 q^{83} -481.164 q^{85} +(403.471 + 1269.03i) q^{86} +(-325.809 - 246.298i) q^{88} -67.3025i q^{89} +(-400.024 + 815.420i) q^{91} +(-156.138 - 220.727i) q^{92} +(-1479.76 + 470.472i) q^{94} -503.358i q^{95} -934.837i q^{97} +(-798.322 - 551.247i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 40 q^{4} + O(q^{10}) \) \( 16 q + 40 q^{4} - 304 q^{16} - 312 q^{22} - 1376 q^{25} - 816 q^{28} - 816 q^{37} - 2568 q^{46} - 640 q^{49} + 2336 q^{58} + 1120 q^{64} - 424 q^{70} + 5072 q^{85} - 3536 q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69547 + 0.856992i −0.952993 + 0.302992i
\(3\) 0 0
\(4\) 6.53113 4.62000i 0.816391 0.577499i
\(5\) 10.3049i 0.921697i −0.887479 0.460848i \(-0.847545\pi\)
0.887479 0.460848i \(-0.152455\pi\)
\(6\) 0 0
\(7\) 16.6272 + 8.15690i 0.897786 + 0.440431i
\(8\) −13.6452 + 18.0502i −0.603037 + 0.797713i
\(9\) 0 0
\(10\) 8.83121 + 27.7765i 0.279267 + 0.878371i
\(11\) 18.0502i 0.494758i 0.968919 + 0.247379i \(0.0795693\pi\)
−0.968919 + 0.247379i \(0.920431\pi\)
\(12\) 0 0
\(13\) 49.0412i 1.04628i 0.852248 + 0.523138i \(0.175239\pi\)
−0.852248 + 0.523138i \(0.824761\pi\)
\(14\) −51.8086 7.73727i −0.989031 0.147705i
\(15\) 0 0
\(16\) 21.3113 60.3476i 0.332989 0.942931i
\(17\) 46.6928i 0.666156i −0.942899 0.333078i \(-0.891913\pi\)
0.942899 0.333078i \(-0.108087\pi\)
\(18\) 0 0
\(19\) 48.8465 0.589798 0.294899 0.955528i \(-0.404714\pi\)
0.294899 + 0.955528i \(0.404714\pi\)
\(20\) −47.6085 67.3025i −0.532279 0.752465i
\(21\) 0 0
\(22\) −15.4689 48.6538i −0.149908 0.471501i
\(23\) 33.7962i 0.306391i −0.988196 0.153195i \(-0.951044\pi\)
0.988196 0.153195i \(-0.0489564\pi\)
\(24\) 0 0
\(25\) 18.8094 0.150475
\(26\) −42.0280 132.189i −0.317014 0.997094i
\(27\) 0 0
\(28\) 146.279 23.5440i 0.987294 0.158907i
\(29\) −48.1829 −0.308529 −0.154264 0.988030i \(-0.549301\pi\)
−0.154264 + 0.988030i \(0.549301\pi\)
\(30\) 0 0
\(31\) 152.751 0.884994 0.442497 0.896770i \(-0.354093\pi\)
0.442497 + 0.896770i \(0.354093\pi\)
\(32\) −5.72657 + 180.929i −0.0316351 + 0.999499i
\(33\) 0 0
\(34\) 40.0153 + 125.859i 0.201840 + 0.634842i
\(35\) 84.0559 171.342i 0.405944 0.827487i
\(36\) 0 0
\(37\) 37.6848 0.167442 0.0837209 0.996489i \(-0.473320\pi\)
0.0837209 + 0.996489i \(0.473320\pi\)
\(38\) −131.664 + 41.8611i −0.562073 + 0.178704i
\(39\) 0 0
\(40\) 186.005 + 140.612i 0.735250 + 0.555817i
\(41\) 409.288i 1.55903i 0.626385 + 0.779514i \(0.284534\pi\)
−0.626385 + 0.779514i \(0.715466\pi\)
\(42\) 0 0
\(43\) 470.799i 1.66968i −0.550494 0.834839i \(-0.685560\pi\)
0.550494 0.834839i \(-0.314440\pi\)
\(44\) 83.3918 + 117.888i 0.285722 + 0.403916i
\(45\) 0 0
\(46\) 28.9631 + 91.0966i 0.0928341 + 0.291988i
\(47\) 548.980 1.70377 0.851883 0.523733i \(-0.175461\pi\)
0.851883 + 0.523733i \(0.175461\pi\)
\(48\) 0 0
\(49\) 209.930 + 271.253i 0.612041 + 0.790826i
\(50\) −50.7001 + 16.1195i −0.143401 + 0.0455927i
\(51\) 0 0
\(52\) 226.570 + 320.295i 0.604224 + 0.854171i
\(53\) 203.157 0.526523 0.263262 0.964724i \(-0.415202\pi\)
0.263262 + 0.964724i \(0.415202\pi\)
\(54\) 0 0
\(55\) 186.005 0.456017
\(56\) −374.115 + 188.823i −0.892736 + 0.450580i
\(57\) 0 0
\(58\) 129.875 41.2923i 0.294026 0.0934819i
\(59\) 717.092 1.58233 0.791164 0.611604i \(-0.209475\pi\)
0.791164 + 0.611604i \(0.209475\pi\)
\(60\) 0 0
\(61\) 493.466i 1.03577i 0.855451 + 0.517884i \(0.173280\pi\)
−0.855451 + 0.517884i \(0.826720\pi\)
\(62\) −411.735 + 130.906i −0.843393 + 0.268147i
\(63\) 0 0
\(64\) −139.619 492.596i −0.272693 0.962101i
\(65\) 505.364 0.964350
\(66\) 0 0
\(67\) 240.375i 0.438305i 0.975691 + 0.219152i \(0.0703292\pi\)
−0.975691 + 0.219152i \(0.929671\pi\)
\(68\) −215.720 304.956i −0.384705 0.543844i
\(69\) 0 0
\(70\) −79.7317 + 533.882i −0.136139 + 0.911587i
\(71\) 995.648i 1.66425i −0.554589 0.832125i \(-0.687124\pi\)
0.554589 0.832125i \(-0.312876\pi\)
\(72\) 0 0
\(73\) 790.766i 1.26784i −0.773399 0.633919i \(-0.781445\pi\)
0.773399 0.633919i \(-0.218555\pi\)
\(74\) −101.578 + 32.2956i −0.159571 + 0.0507336i
\(75\) 0 0
\(76\) 319.023 225.671i 0.481506 0.340608i
\(77\) −147.234 + 300.125i −0.217907 + 0.444187i
\(78\) 0 0
\(79\) 214.111i 0.304928i 0.988309 + 0.152464i \(0.0487209\pi\)
−0.988309 + 0.152464i \(0.951279\pi\)
\(80\) −621.875 219.610i −0.869096 0.306915i
\(81\) 0 0
\(82\) −350.757 1103.23i −0.472373 1.48574i
\(83\) 885.204 1.17065 0.585324 0.810800i \(-0.300967\pi\)
0.585324 + 0.810800i \(0.300967\pi\)
\(84\) 0 0
\(85\) −481.164 −0.613994
\(86\) 403.471 + 1269.03i 0.505900 + 1.59119i
\(87\) 0 0
\(88\) −325.809 246.298i −0.394675 0.298357i
\(89\) 67.3025i 0.0801579i −0.999197 0.0400790i \(-0.987239\pi\)
0.999197 0.0400790i \(-0.0127609\pi\)
\(90\) 0 0
\(91\) −400.024 + 815.420i −0.460813 + 0.939333i
\(92\) −156.138 220.727i −0.176941 0.250135i
\(93\) 0 0
\(94\) −1479.76 + 470.472i −1.62368 + 0.516228i
\(95\) 503.358i 0.543615i
\(96\) 0 0
\(97\) 934.837i 0.978539i −0.872133 0.489269i \(-0.837263\pi\)
0.872133 0.489269i \(-0.162737\pi\)
\(98\) −798.322 551.247i −0.822885 0.568208i
\(99\) 0 0
\(100\) 122.846 86.8991i 0.122846 0.0868991i
\(101\) 643.394i 0.633862i 0.948449 + 0.316931i \(0.102652\pi\)
−0.948449 + 0.316931i \(0.897348\pi\)
\(102\) 0 0
\(103\) −834.403 −0.798215 −0.399108 0.916904i \(-0.630680\pi\)
−0.399108 + 0.916904i \(0.630680\pi\)
\(104\) −885.204 669.176i −0.834628 0.630943i
\(105\) 0 0
\(106\) −547.603 + 174.104i −0.501773 + 0.159533i
\(107\) 1511.02i 1.36520i 0.730793 + 0.682599i \(0.239150\pi\)
−0.730793 + 0.682599i \(0.760850\pi\)
\(108\) 0 0
\(109\) −1347.35 −1.18397 −0.591983 0.805950i \(-0.701655\pi\)
−0.591983 + 0.805950i \(0.701655\pi\)
\(110\) −501.371 + 159.405i −0.434581 + 0.138170i
\(111\) 0 0
\(112\) 846.597 829.579i 0.714249 0.699892i
\(113\) −1677.23 −1.39629 −0.698145 0.715956i \(-0.745991\pi\)
−0.698145 + 0.715956i \(0.745991\pi\)
\(114\) 0 0
\(115\) −348.266 −0.282400
\(116\) −314.688 + 222.605i −0.251880 + 0.178175i
\(117\) 0 0
\(118\) −1932.90 + 614.542i −1.50795 + 0.479434i
\(119\) 380.868 776.372i 0.293396 0.598066i
\(120\) 0 0
\(121\) 1005.19 0.755215
\(122\) −422.896 1330.12i −0.313830 0.987079i
\(123\) 0 0
\(124\) 997.634 705.707i 0.722502 0.511084i
\(125\) 1481.94i 1.06039i
\(126\) 0 0
\(127\) 401.212i 0.280329i 0.990128 + 0.140164i \(0.0447631\pi\)
−0.990128 + 0.140164i \(0.955237\pi\)
\(128\) 798.489 + 1208.13i 0.551384 + 0.834252i
\(129\) 0 0
\(130\) −1362.19 + 433.093i −0.919018 + 0.292191i
\(131\) −44.6445 −0.0297756 −0.0148878 0.999889i \(-0.504739\pi\)
−0.0148878 + 0.999889i \(0.504739\pi\)
\(132\) 0 0
\(133\) 812.183 + 398.436i 0.529513 + 0.259765i
\(134\) −205.999 647.923i −0.132803 0.417702i
\(135\) 0 0
\(136\) 842.813 + 637.131i 0.531402 + 0.401717i
\(137\) 1481.82 0.924089 0.462044 0.886857i \(-0.347116\pi\)
0.462044 + 0.886857i \(0.347116\pi\)
\(138\) 0 0
\(139\) −1197.16 −0.730517 −0.365259 0.930906i \(-0.619019\pi\)
−0.365259 + 0.930906i \(0.619019\pi\)
\(140\) −242.618 1507.39i −0.146464 0.909985i
\(141\) 0 0
\(142\) 853.263 + 2683.74i 0.504255 + 1.58602i
\(143\) −885.204 −0.517653
\(144\) 0 0
\(145\) 496.519i 0.284370i
\(146\) 677.680 + 2131.49i 0.384145 + 1.20824i
\(147\) 0 0
\(148\) 246.125 174.104i 0.136698 0.0966976i
\(149\) 1198.40 0.658907 0.329453 0.944172i \(-0.393136\pi\)
0.329453 + 0.944172i \(0.393136\pi\)
\(150\) 0 0
\(151\) 3058.27i 1.64820i −0.566444 0.824100i \(-0.691681\pi\)
0.566444 0.824100i \(-0.308319\pi\)
\(152\) −666.519 + 881.689i −0.355670 + 0.470490i
\(153\) 0 0
\(154\) 139.659 935.156i 0.0730783 0.489331i
\(155\) 1574.08i 0.815697i
\(156\) 0 0
\(157\) 2265.06i 1.15141i −0.817658 0.575704i \(-0.804728\pi\)
0.817658 0.575704i \(-0.195272\pi\)
\(158\) −183.491 577.129i −0.0923910 0.290595i
\(159\) 0 0
\(160\) 1864.45 + 59.0116i 0.921236 + 0.0291580i
\(161\) 275.672 561.937i 0.134944 0.275074i
\(162\) 0 0
\(163\) 1497.01i 0.719357i 0.933076 + 0.359678i \(0.117114\pi\)
−0.933076 + 0.359678i \(0.882886\pi\)
\(164\) 1890.91 + 2673.12i 0.900337 + 1.27278i
\(165\) 0 0
\(166\) −2386.04 + 758.613i −1.11562 + 0.354697i
\(167\) −672.447 −0.311590 −0.155795 0.987789i \(-0.549794\pi\)
−0.155795 + 0.987789i \(0.549794\pi\)
\(168\) 0 0
\(169\) −208.043 −0.0946940
\(170\) 1296.96 412.353i 0.585132 0.186036i
\(171\) 0 0
\(172\) −2175.09 3074.85i −0.964239 1.36311i
\(173\) 2008.77i 0.882798i 0.897311 + 0.441399i \(0.145518\pi\)
−0.897311 + 0.441399i \(0.854482\pi\)
\(174\) 0 0
\(175\) 312.748 + 153.426i 0.135094 + 0.0662738i
\(176\) 1089.29 + 384.673i 0.466522 + 0.164749i
\(177\) 0 0
\(178\) 57.6777 + 181.412i 0.0242872 + 0.0763899i
\(179\) 3724.04i 1.55502i 0.628872 + 0.777509i \(0.283517\pi\)
−0.628872 + 0.777509i \(0.716483\pi\)
\(180\) 0 0
\(181\) 2010.69i 0.825710i 0.910797 + 0.412855i \(0.135468\pi\)
−0.910797 + 0.412855i \(0.864532\pi\)
\(182\) 379.446 2540.76i 0.154541 1.03480i
\(183\) 0 0
\(184\) 610.027 + 461.155i 0.244412 + 0.184765i
\(185\) 388.338i 0.154331i
\(186\) 0 0
\(187\) 842.813 0.329586
\(188\) 3585.46 2536.28i 1.39094 0.983923i
\(189\) 0 0
\(190\) 431.374 + 1356.79i 0.164711 + 0.518061i
\(191\) 1167.67i 0.442355i 0.975234 + 0.221178i \(0.0709901\pi\)
−0.975234 + 0.221178i \(0.929010\pi\)
\(192\) 0 0
\(193\) −4481.71 −1.67150 −0.835752 0.549106i \(-0.814968\pi\)
−0.835752 + 0.549106i \(0.814968\pi\)
\(194\) 801.148 + 2519.83i 0.296490 + 0.932541i
\(195\) 0 0
\(196\) 2624.27 + 801.715i 0.956366 + 0.292170i
\(197\) −4433.60 −1.60346 −0.801728 0.597689i \(-0.796086\pi\)
−0.801728 + 0.597689i \(0.796086\pi\)
\(198\) 0 0
\(199\) 2895.34 1.03138 0.515691 0.856775i \(-0.327535\pi\)
0.515691 + 0.856775i \(0.327535\pi\)
\(200\) −256.657 + 339.512i −0.0907419 + 0.120036i
\(201\) 0 0
\(202\) −551.383 1734.25i −0.192055 0.604066i
\(203\) −801.148 393.023i −0.276993 0.135886i
\(204\) 0 0
\(205\) 4217.67 1.43695
\(206\) 2249.11 715.077i 0.760693 0.241853i
\(207\) 0 0
\(208\) 2959.52 + 1045.13i 0.986566 + 0.348398i
\(209\) 881.689i 0.291807i
\(210\) 0 0
\(211\) 2313.24i 0.754740i 0.926063 + 0.377370i \(0.123172\pi\)
−0.926063 + 0.377370i \(0.876828\pi\)
\(212\) 1326.84 938.583i 0.429849 0.304067i
\(213\) 0 0
\(214\) −1294.94 4072.92i −0.413645 1.30102i
\(215\) −4851.53 −1.53894
\(216\) 0 0
\(217\) 2539.82 + 1245.97i 0.794536 + 0.389779i
\(218\) 3631.73 1154.67i 1.12831 0.358733i
\(219\) 0 0
\(220\) 1214.82 859.343i 0.372288 0.263349i
\(221\) 2289.87 0.696984
\(222\) 0 0
\(223\) 4169.23 1.25198 0.625992 0.779830i \(-0.284694\pi\)
0.625992 + 0.779830i \(0.284694\pi\)
\(224\) −1571.03 + 2961.63i −0.468612 + 0.883404i
\(225\) 0 0
\(226\) 4520.93 1437.38i 1.33066 0.423066i
\(227\) −3461.99 −1.01225 −0.506124 0.862461i \(-0.668922\pi\)
−0.506124 + 0.862461i \(0.668922\pi\)
\(228\) 0 0
\(229\) 303.407i 0.0875533i −0.999041 0.0437766i \(-0.986061\pi\)
0.999041 0.0437766i \(-0.0139390\pi\)
\(230\) 938.740 298.461i 0.269125 0.0855649i
\(231\) 0 0
\(232\) 657.463 869.710i 0.186054 0.246117i
\(233\) −2216.24 −0.623137 −0.311569 0.950224i \(-0.600854\pi\)
−0.311569 + 0.950224i \(0.600854\pi\)
\(234\) 0 0
\(235\) 5657.18i 1.57035i
\(236\) 4683.42 3312.96i 1.29180 0.913794i
\(237\) 0 0
\(238\) −361.275 + 2419.09i −0.0983948 + 0.658850i
\(239\) 1062.67i 0.287609i 0.989606 + 0.143805i \(0.0459337\pi\)
−0.989606 + 0.143805i \(0.954066\pi\)
\(240\) 0 0
\(241\) 7334.62i 1.96043i 0.197926 + 0.980217i \(0.436579\pi\)
−0.197926 + 0.980217i \(0.563421\pi\)
\(242\) −2709.46 + 861.441i −0.719714 + 0.228824i
\(243\) 0 0
\(244\) 2279.81 + 3222.89i 0.598155 + 0.845591i
\(245\) 2795.23 2163.30i 0.728902 0.564116i
\(246\) 0 0
\(247\) 2395.49i 0.617092i
\(248\) −2084.31 + 2757.18i −0.533684 + 0.705972i
\(249\) 0 0
\(250\) 1270.01 + 3994.52i 0.321290 + 1.01054i
\(251\) −5904.85 −1.48490 −0.742451 0.669900i \(-0.766337\pi\)
−0.742451 + 0.669900i \(0.766337\pi\)
\(252\) 0 0
\(253\) 610.027 0.151589
\(254\) −343.835 1081.45i −0.0849375 0.267151i
\(255\) 0 0
\(256\) −3187.66 2572.17i −0.778237 0.627971i
\(257\) 5814.10i 1.41118i −0.708620 0.705591i \(-0.750682\pi\)
0.708620 0.705591i \(-0.249318\pi\)
\(258\) 0 0
\(259\) 626.595 + 307.391i 0.150327 + 0.0737466i
\(260\) 3300.60 2334.78i 0.787286 0.556911i
\(261\) 0 0
\(262\) 120.338 38.2600i 0.0283760 0.00902180i
\(263\) 1699.79i 0.398530i 0.979946 + 0.199265i \(0.0638555\pi\)
−0.979946 + 0.199265i \(0.936144\pi\)
\(264\) 0 0
\(265\) 2093.51i 0.485295i
\(266\) −2530.67 377.939i −0.583329 0.0871163i
\(267\) 0 0
\(268\) 1110.53 + 1569.92i 0.253121 + 0.357828i
\(269\) 5550.40i 1.25804i −0.777387 0.629022i \(-0.783455\pi\)
0.777387 0.629022i \(-0.216545\pi\)
\(270\) 0 0
\(271\) 3741.78 0.838733 0.419367 0.907817i \(-0.362252\pi\)
0.419367 + 0.907817i \(0.362252\pi\)
\(272\) −2817.79 995.083i −0.628139 0.221823i
\(273\) 0 0
\(274\) −3994.19 + 1269.91i −0.880650 + 0.279992i
\(275\) 339.512i 0.0744486i
\(276\) 0 0
\(277\) −5697.37 −1.23582 −0.617910 0.786249i \(-0.712020\pi\)
−0.617910 + 0.786249i \(0.712020\pi\)
\(278\) 3226.91 1025.96i 0.696178 0.221341i
\(279\) 0 0
\(280\) 1945.79 + 3855.21i 0.415298 + 0.822832i
\(281\) −6405.15 −1.35978 −0.679892 0.733312i \(-0.737973\pi\)
−0.679892 + 0.733312i \(0.737973\pi\)
\(282\) 0 0
\(283\) −7258.60 −1.52466 −0.762330 0.647188i \(-0.775945\pi\)
−0.762330 + 0.647188i \(0.775945\pi\)
\(284\) −4599.89 6502.71i −0.961103 1.35868i
\(285\) 0 0
\(286\) 2386.04 758.613i 0.493320 0.156845i
\(287\) −3338.52 + 6805.34i −0.686644 + 1.39967i
\(288\) 0 0
\(289\) 2732.79 0.556236
\(290\) −425.513 1338.35i −0.0861619 0.271003i
\(291\) 0 0
\(292\) −3653.34 5164.60i −0.732176 1.03505i
\(293\) 2353.32i 0.469224i 0.972089 + 0.234612i \(0.0753819\pi\)
−0.972089 + 0.234612i \(0.924618\pi\)
\(294\) 0 0
\(295\) 7389.55i 1.45843i
\(296\) −514.216 + 680.218i −0.100974 + 0.133571i
\(297\) 0 0
\(298\) −3230.27 + 1027.02i −0.627934 + 0.199644i
\(299\) 1657.41 0.320569
\(300\) 0 0
\(301\) 3840.26 7828.09i 0.735379 1.49901i
\(302\) 2620.91 + 8243.47i 0.499392 + 1.57072i
\(303\) 0 0
\(304\) 1040.98 2947.77i 0.196396 0.556139i
\(305\) 5085.11 0.954663
\(306\) 0 0
\(307\) −5602.21 −1.04148 −0.520741 0.853714i \(-0.674344\pi\)
−0.520741 + 0.853714i \(0.674344\pi\)
\(308\) 424.974 + 2640.37i 0.0786205 + 0.488471i
\(309\) 0 0
\(310\) 1348.97 + 4242.88i 0.247150 + 0.777353i
\(311\) 3081.12 0.561783 0.280891 0.959740i \(-0.409370\pi\)
0.280891 + 0.959740i \(0.409370\pi\)
\(312\) 0 0
\(313\) 5032.74i 0.908841i −0.890787 0.454420i \(-0.849846\pi\)
0.890787 0.454420i \(-0.150154\pi\)
\(314\) 1941.14 + 6105.39i 0.348868 + 1.09728i
\(315\) 0 0
\(316\) 989.190 + 1398.38i 0.176096 + 0.248941i
\(317\) −6446.37 −1.14216 −0.571079 0.820895i \(-0.693475\pi\)
−0.571079 + 0.820895i \(0.693475\pi\)
\(318\) 0 0
\(319\) 869.710i 0.152647i
\(320\) −5076.14 + 1438.75i −0.886766 + 0.251340i
\(321\) 0 0
\(322\) −261.490 + 1750.93i −0.0452555 + 0.303030i
\(323\) 2280.78i 0.392898i
\(324\) 0 0
\(325\) 922.434i 0.157438i
\(326\) −1282.93 4035.16i −0.217960 0.685542i
\(327\) 0 0
\(328\) −7387.73 5584.81i −1.24366 0.940151i
\(329\) 9128.02 + 4477.97i 1.52962 + 0.750391i
\(330\) 0 0
\(331\) 8175.39i 1.35758i 0.734331 + 0.678791i \(0.237496\pi\)
−0.734331 + 0.678791i \(0.762504\pi\)
\(332\) 5781.38 4089.64i 0.955706 0.676048i
\(333\) 0 0
\(334\) 1812.56 576.282i 0.296943 0.0944094i
\(335\) 2477.03 0.403984
\(336\) 0 0
\(337\) −5692.64 −0.920172 −0.460086 0.887874i \(-0.652181\pi\)
−0.460086 + 0.887874i \(0.652181\pi\)
\(338\) 560.773 178.291i 0.0902427 0.0286916i
\(339\) 0 0
\(340\) −3142.54 + 2222.97i −0.501259 + 0.354581i
\(341\) 2757.18i 0.437858i
\(342\) 0 0
\(343\) 1277.97 + 6222.57i 0.201177 + 0.979555i
\(344\) 8498.01 + 6424.13i 1.33192 + 1.00688i
\(345\) 0 0
\(346\) −1721.50 5414.58i −0.267481 0.841300i
\(347\) 6701.89i 1.03682i −0.855132 0.518410i \(-0.826524\pi\)
0.855132 0.518410i \(-0.173476\pi\)
\(348\) 0 0
\(349\) 3914.14i 0.600341i 0.953886 + 0.300171i \(0.0970436\pi\)
−0.953886 + 0.300171i \(0.902956\pi\)
\(350\) −974.487 145.533i −0.148824 0.0222259i
\(351\) 0 0
\(352\) −3265.80 103.366i −0.494510 0.0156517i
\(353\) 9853.62i 1.48571i 0.669453 + 0.742854i \(0.266528\pi\)
−0.669453 + 0.742854i \(0.733472\pi\)
\(354\) 0 0
\(355\) −10260.0 −1.53393
\(356\) −310.937 439.561i −0.0462911 0.0654402i
\(357\) 0 0
\(358\) −3191.48 10038.1i −0.471159 1.48192i
\(359\) 10120.4i 1.48784i −0.668270 0.743919i \(-0.732965\pi\)
0.668270 0.743919i \(-0.267035\pi\)
\(360\) 0 0
\(361\) −4473.02 −0.652138
\(362\) −1723.15 5419.76i −0.250184 0.786896i
\(363\) 0 0
\(364\) 1154.63 + 7173.73i 0.166261 + 1.03298i
\(365\) −8148.75 −1.16856
\(366\) 0 0
\(367\) 4458.69 0.634173 0.317086 0.948397i \(-0.397295\pi\)
0.317086 + 0.948397i \(0.397295\pi\)
\(368\) −2039.52 720.240i −0.288905 0.102025i
\(369\) 0 0
\(370\) 332.803 + 1046.75i 0.0467610 + 0.147076i
\(371\) 3377.94 + 1657.13i 0.472705 + 0.231897i
\(372\) 0 0
\(373\) 829.392 0.115132 0.0575661 0.998342i \(-0.481666\pi\)
0.0575661 + 0.998342i \(0.481666\pi\)
\(374\) −2271.78 + 722.284i −0.314093 + 0.0998621i
\(375\) 0 0
\(376\) −7490.92 + 9909.19i −1.02743 + 1.35912i
\(377\) 2362.95i 0.322806i
\(378\) 0 0
\(379\) 521.296i 0.0706521i 0.999376 + 0.0353261i \(0.0112470\pi\)
−0.999376 + 0.0353261i \(0.988753\pi\)
\(380\) −2325.51 3287.50i −0.313937 0.443803i
\(381\) 0 0
\(382\) −1000.69 3147.43i −0.134030 0.421562i
\(383\) 12605.6 1.68177 0.840883 0.541217i \(-0.182036\pi\)
0.840883 + 0.541217i \(0.182036\pi\)
\(384\) 0 0
\(385\) 3092.75 + 1517.23i 0.409406 + 0.200844i
\(386\) 12080.3 3840.79i 1.59293 0.506453i
\(387\) 0 0
\(388\) −4318.94 6105.54i −0.565106 0.798871i
\(389\) 11263.9 1.46812 0.734062 0.679082i \(-0.237622\pi\)
0.734062 + 0.679082i \(0.237622\pi\)
\(390\) 0 0
\(391\) −1578.04 −0.204104
\(392\) −7760.71 + 87.9778i −0.999936 + 0.0113356i
\(393\) 0 0
\(394\) 11950.6 3799.56i 1.52808 0.485835i
\(395\) 2206.39 0.281051
\(396\) 0 0
\(397\) 3304.08i 0.417701i −0.977948 0.208850i \(-0.933028\pi\)
0.977948 0.208850i \(-0.0669721\pi\)
\(398\) −7804.30 + 2481.28i −0.982900 + 0.312501i
\(399\) 0 0
\(400\) 400.852 1135.10i 0.0501064 0.141887i
\(401\) −5752.87 −0.716420 −0.358210 0.933641i \(-0.616613\pi\)
−0.358210 + 0.933641i \(0.616613\pi\)
\(402\) 0 0
\(403\) 7491.08i 0.925949i
\(404\) 2972.48 + 4202.09i 0.366055 + 0.517479i
\(405\) 0 0
\(406\) 2496.29 + 372.804i 0.305145 + 0.0455713i
\(407\) 680.218i 0.0828432i
\(408\) 0 0
\(409\) 1731.71i 0.209358i −0.994506 0.104679i \(-0.966618\pi\)
0.994506 0.104679i \(-0.0333815\pi\)
\(410\) −11368.6 + 3614.51i −1.36940 + 0.435385i
\(411\) 0 0
\(412\) −5449.59 + 3854.94i −0.651656 + 0.460969i
\(413\) 11923.3 + 5849.25i 1.42059 + 0.696907i
\(414\) 0 0
\(415\) 9121.92i 1.07898i
\(416\) −8872.97 280.838i −1.04575 0.0330991i
\(417\) 0 0
\(418\) −755.601 2376.57i −0.0884154 0.278090i
\(419\) 13882.1 1.61859 0.809293 0.587406i \(-0.199851\pi\)
0.809293 + 0.587406i \(0.199851\pi\)
\(420\) 0 0
\(421\) −3343.52 −0.387062 −0.193531 0.981094i \(-0.561994\pi\)
−0.193531 + 0.981094i \(0.561994\pi\)
\(422\) −1982.43 6235.28i −0.228681 0.719262i
\(423\) 0 0
\(424\) −2772.11 + 3667.02i −0.317513 + 0.420014i
\(425\) 878.261i 0.100240i
\(426\) 0 0
\(427\) −4025.15 + 8204.97i −0.456184 + 0.929898i
\(428\) 6980.92 + 9868.69i 0.788401 + 1.11454i
\(429\) 0 0
\(430\) 13077.2 4157.72i 1.46660 0.466287i
\(431\) 7075.93i 0.790802i 0.918509 + 0.395401i \(0.129394\pi\)
−0.918509 + 0.395401i \(0.870606\pi\)
\(432\) 0 0
\(433\) 4910.23i 0.544967i −0.962160 0.272483i \(-0.912155\pi\)
0.962160 0.272483i \(-0.0878450\pi\)
\(434\) −7913.80 1181.87i −0.875287 0.130718i
\(435\) 0 0
\(436\) −8799.69 + 6224.73i −0.966580 + 0.683740i
\(437\) 1650.83i 0.180709i
\(438\) 0 0
\(439\) 13445.2 1.46174 0.730868 0.682518i \(-0.239115\pi\)
0.730868 + 0.682518i \(0.239115\pi\)
\(440\) −2538.07 + 3357.43i −0.274995 + 0.363771i
\(441\) 0 0
\(442\) −6172.28 + 1962.40i −0.664220 + 0.211181i
\(443\) 14965.5i 1.60504i −0.596629 0.802518i \(-0.703493\pi\)
0.596629 0.802518i \(-0.296507\pi\)
\(444\) 0 0
\(445\) −693.545 −0.0738813
\(446\) −11238.0 + 3573.00i −1.19313 + 0.379342i
\(447\) 0 0
\(448\) 1696.58 9329.36i 0.178919 0.983864i
\(449\) −10908.7 −1.14658 −0.573291 0.819352i \(-0.694334\pi\)
−0.573291 + 0.819352i \(0.694334\pi\)
\(450\) 0 0
\(451\) −7387.73 −0.771341
\(452\) −10954.2 + 7748.81i −1.13992 + 0.806357i
\(453\) 0 0
\(454\) 9331.70 2966.90i 0.964666 0.306704i
\(455\) 8402.81 + 4122.21i 0.865780 + 0.424730i
\(456\) 0 0
\(457\) 4804.83 0.491817 0.245908 0.969293i \(-0.420914\pi\)
0.245908 + 0.969293i \(0.420914\pi\)
\(458\) 260.017 + 817.825i 0.0265280 + 0.0834376i
\(459\) 0 0
\(460\) −2274.57 + 1608.99i −0.230548 + 0.163086i
\(461\) 6090.11i 0.615281i −0.951503 0.307641i \(-0.900461\pi\)
0.951503 0.307641i \(-0.0995394\pi\)
\(462\) 0 0
\(463\) 4149.32i 0.416491i −0.978077 0.208246i \(-0.933225\pi\)
0.978077 0.208246i \(-0.0667753\pi\)
\(464\) −1026.84 + 2907.72i −0.102737 + 0.290921i
\(465\) 0 0
\(466\) 5973.82 1899.30i 0.593845 0.188806i
\(467\) −6598.23 −0.653810 −0.326905 0.945057i \(-0.606006\pi\)
−0.326905 + 0.945057i \(0.606006\pi\)
\(468\) 0 0
\(469\) −1960.71 + 3996.77i −0.193043 + 0.393504i
\(470\) 4848.15 + 15248.8i 0.475806 + 1.49654i
\(471\) 0 0
\(472\) −9784.84 + 12943.6i −0.954203 + 1.26224i
\(473\) 8498.01 0.826087
\(474\) 0 0
\(475\) 918.772 0.0887498
\(476\) −1099.33 6830.19i −0.105857 0.657692i
\(477\) 0 0
\(478\) −910.703 2864.41i −0.0871435 0.274090i
\(479\) 4494.37 0.428712 0.214356 0.976756i \(-0.431235\pi\)
0.214356 + 0.976756i \(0.431235\pi\)
\(480\) 0 0
\(481\) 1848.11i 0.175190i
\(482\) −6285.71 19770.3i −0.593997 1.86828i
\(483\) 0 0
\(484\) 6565.03 4643.98i 0.616550 0.436136i
\(485\) −9633.38 −0.901916
\(486\) 0 0
\(487\) 12562.5i 1.16892i −0.811424 0.584458i \(-0.801307\pi\)
0.811424 0.584458i \(-0.198693\pi\)
\(488\) −8907.15 6733.42i −0.826245 0.624606i
\(489\) 0 0
\(490\) −5680.54 + 8226.62i −0.523716 + 0.758451i
\(491\) 12172.0i 1.11877i −0.828909 0.559383i \(-0.811038\pi\)
0.828909 0.559383i \(-0.188962\pi\)
\(492\) 0 0
\(493\) 2249.79i 0.205528i
\(494\) −2052.92 6456.99i −0.186974 0.588084i
\(495\) 0 0
\(496\) 3255.31 9218.13i 0.294693 0.834488i
\(497\) 8121.40 16554.9i 0.732987 1.49414i
\(498\) 0 0
\(499\) 3482.57i 0.312427i −0.987723 0.156214i \(-0.950071\pi\)
0.987723 0.156214i \(-0.0499288\pi\)
\(500\) −6846.55 9678.73i −0.612374 0.865692i
\(501\) 0 0
\(502\) 15916.3 5060.41i 1.41510 0.449914i
\(503\) 480.623 0.0426043 0.0213021 0.999773i \(-0.493219\pi\)
0.0213021 + 0.999773i \(0.493219\pi\)
\(504\) 0 0
\(505\) 6630.10 0.584229
\(506\) −1644.31 + 522.789i −0.144464 + 0.0459304i
\(507\) 0 0
\(508\) 1853.60 + 2620.36i 0.161890 + 0.228858i
\(509\) 13977.8i 1.21720i 0.793476 + 0.608602i \(0.208269\pi\)
−0.793476 + 0.608602i \(0.791731\pi\)
\(510\) 0 0
\(511\) 6450.20 13148.3i 0.558395 1.13825i
\(512\) 10796.6 + 4201.41i 0.931925 + 0.362652i
\(513\) 0 0
\(514\) 4982.64 + 15671.7i 0.427577 + 1.34485i
\(515\) 8598.43i 0.735712i
\(516\) 0 0
\(517\) 9909.19i 0.842951i
\(518\) −1952.40 291.578i −0.165605 0.0247320i
\(519\) 0 0
\(520\) −6895.78 + 9121.92i −0.581538 + 0.769274i
\(521\) 1574.54i 0.132403i 0.997806 + 0.0662015i \(0.0210880\pi\)
−0.997806 + 0.0662015i \(0.978912\pi\)
\(522\) 0 0
\(523\) −8049.27 −0.672982 −0.336491 0.941687i \(-0.609240\pi\)
−0.336491 + 0.941687i \(0.609240\pi\)
\(524\) −291.579 + 206.257i −0.0243086 + 0.0171954i
\(525\) 0 0
\(526\) −1456.71 4581.73i −0.120752 0.379797i
\(527\) 7132.35i 0.589545i
\(528\) 0 0
\(529\) 11024.8 0.906125
\(530\) 1794.12 + 5642.99i 0.147041 + 0.462483i
\(531\) 0 0
\(532\) 7145.24 1150.04i 0.582304 0.0937231i
\(533\) −20072.0 −1.63117
\(534\) 0 0
\(535\) 15570.9 1.25830
\(536\) −4338.81 3279.95i −0.349642 0.264314i
\(537\) 0 0
\(538\) 4756.65 + 14961.0i 0.381178 + 1.19891i
\(539\) −4896.18 + 3789.28i −0.391268 + 0.302812i
\(540\) 0 0
\(541\) −4564.27 −0.362723 −0.181362 0.983416i \(-0.558050\pi\)
−0.181362 + 0.983416i \(0.558050\pi\)
\(542\) −10085.9 + 3206.67i −0.799307 + 0.254130i
\(543\) 0 0
\(544\) 8448.06 + 267.389i 0.665823 + 0.0210739i
\(545\) 13884.2i 1.09126i
\(546\) 0 0
\(547\) 3464.95i 0.270842i 0.990788 + 0.135421i \(0.0432387\pi\)
−0.990788 + 0.135421i \(0.956761\pi\)
\(548\) 9677.94 6845.99i 0.754418 0.533661i
\(549\) 0 0
\(550\) −290.959 915.146i −0.0225574 0.0709490i
\(551\) −2353.57 −0.181970
\(552\) 0 0
\(553\) −1746.48 + 3560.07i −0.134300 + 0.273760i
\(554\) 15357.1 4882.60i 1.17773 0.374444i
\(555\) 0 0
\(556\) −7818.81 + 5530.88i −0.596388 + 0.421873i
\(557\) 14056.1 1.06926 0.534629 0.845087i \(-0.320451\pi\)
0.534629 + 0.845087i \(0.320451\pi\)
\(558\) 0 0
\(559\) 23088.6 1.74695
\(560\) −8548.72 8724.08i −0.645088 0.658321i
\(561\) 0 0
\(562\) 17264.9 5489.17i 1.29586 0.412004i
\(563\) 13614.3 1.01914 0.509568 0.860430i \(-0.329805\pi\)
0.509568 + 0.860430i \(0.329805\pi\)
\(564\) 0 0
\(565\) 17283.7i 1.28696i
\(566\) 19565.3 6220.56i 1.45299 0.461961i
\(567\) 0 0
\(568\) 17971.6 + 13585.8i 1.32759 + 1.00360i
\(569\) −2692.70 −0.198390 −0.0991950 0.995068i \(-0.531627\pi\)
−0.0991950 + 0.995068i \(0.531627\pi\)
\(570\) 0 0
\(571\) 8780.97i 0.643559i 0.946815 + 0.321779i \(0.104281\pi\)
−0.946815 + 0.321779i \(0.895719\pi\)
\(572\) −5781.38 + 4089.64i −0.422608 + 0.298945i
\(573\) 0 0
\(574\) 3166.78 21204.7i 0.230276 1.54193i
\(575\) 635.684i 0.0461041i
\(576\) 0 0
\(577\) 4486.99i 0.323736i −0.986812 0.161868i \(-0.948248\pi\)
0.986812 0.161868i \(-0.0517519\pi\)
\(578\) −7366.15 + 2341.98i −0.530089 + 0.168535i
\(579\) 0 0
\(580\) 2293.91 + 3242.83i 0.164223 + 0.232157i
\(581\) 14718.5 + 7220.52i 1.05099 + 0.515589i
\(582\) 0 0
\(583\) 3667.02i 0.260502i
\(584\) 14273.5 + 10790.1i 1.01137 + 0.764553i
\(585\) 0 0
\(586\) −2016.78 6343.31i −0.142171 0.447167i
\(587\) −5983.67 −0.420737 −0.210368 0.977622i \(-0.567466\pi\)
−0.210368 + 0.977622i \(0.567466\pi\)
\(588\) 0 0
\(589\) 7461.34 0.521968
\(590\) 6332.78 + 19918.3i 0.441893 + 1.38987i
\(591\) 0 0
\(592\) 803.112 2274.19i 0.0557563 0.157886i
\(593\) 594.936i 0.0411992i −0.999788 0.0205996i \(-0.993442\pi\)
0.999788 0.0205996i \(-0.00655751\pi\)
\(594\) 0 0
\(595\) −8000.42 3924.80i −0.551236 0.270422i
\(596\) 7826.94 5536.62i 0.537926 0.380518i
\(597\) 0 0
\(598\) −4467.49 + 1420.38i −0.305500 + 0.0971301i
\(599\) 13607.8i 0.928213i −0.885779 0.464107i \(-0.846375\pi\)
0.885779 0.464107i \(-0.153625\pi\)
\(600\) 0 0
\(601\) 12594.1i 0.854779i −0.904068 0.427390i \(-0.859433\pi\)
0.904068 0.427390i \(-0.140567\pi\)
\(602\) −3642.70 + 24391.5i −0.246620 + 1.65136i
\(603\) 0 0
\(604\) −14129.2 19973.9i −0.951834 1.34558i
\(605\) 10358.4i 0.696079i
\(606\) 0 0
\(607\) 10949.8 0.732187 0.366094 0.930578i \(-0.380695\pi\)
0.366094 + 0.930578i \(0.380695\pi\)
\(608\) −279.723 + 8837.74i −0.0186583 + 0.589503i
\(609\) 0 0
\(610\) −13706.8 + 4357.90i −0.909787 + 0.289256i
\(611\) 26922.7i 1.78261i
\(612\) 0 0
\(613\) 3150.93 0.207610 0.103805 0.994598i \(-0.466898\pi\)
0.103805 + 0.994598i \(0.466898\pi\)
\(614\) 15100.6 4801.05i 0.992526 0.315562i
\(615\) 0 0
\(616\) −3408.28 6752.85i −0.222928 0.441688i
\(617\) −25804.8 −1.68373 −0.841865 0.539688i \(-0.818542\pi\)
−0.841865 + 0.539688i \(0.818542\pi\)
\(618\) 0 0
\(619\) −727.458 −0.0472359 −0.0236179 0.999721i \(-0.507519\pi\)
−0.0236179 + 0.999721i \(0.507519\pi\)
\(620\) −7272.23 10280.5i −0.471064 0.665927i
\(621\) 0 0
\(622\) −8305.08 + 2640.50i −0.535375 + 0.170216i
\(623\) 548.980 1119.06i 0.0353040 0.0719647i
\(624\) 0 0
\(625\) −12920.0 −0.826883
\(626\) 4313.02 + 13565.6i 0.275372 + 0.866119i
\(627\) 0 0
\(628\) −10464.5 14793.4i −0.664938 0.940000i
\(629\) 1759.61i 0.111542i
\(630\) 0 0
\(631\) 21044.9i 1.32771i 0.747862 + 0.663854i \(0.231080\pi\)
−0.747862 + 0.663854i \(0.768920\pi\)
\(632\) −3864.74 2921.58i −0.243245 0.183883i
\(633\) 0 0
\(634\) 17376.0 5524.49i 1.08847 0.346066i
\(635\) 4134.44 0.258378
\(636\) 0 0
\(637\) −13302.6 + 10295.2i −0.827423 + 0.640364i
\(638\) 745.334 + 2344.28i 0.0462509 + 0.145472i
\(639\) 0 0
\(640\) 12449.6 8228.34i 0.768927 0.508209i
\(641\) 22930.9 1.41297 0.706486 0.707727i \(-0.250279\pi\)
0.706486 + 0.707727i \(0.250279\pi\)
\(642\) 0 0
\(643\) −26817.0 −1.64473 −0.822364 0.568962i \(-0.807345\pi\)
−0.822364 + 0.568962i \(0.807345\pi\)
\(644\) −795.697 4943.69i −0.0486877 0.302498i
\(645\) 0 0
\(646\) 1954.61 + 6147.78i 0.119045 + 0.374429i
\(647\) −27901.0 −1.69537 −0.847683 0.530503i \(-0.822003\pi\)
−0.847683 + 0.530503i \(0.822003\pi\)
\(648\) 0 0
\(649\) 12943.6i 0.782870i
\(650\) −790.519 2486.39i −0.0477026 0.150038i
\(651\) 0 0
\(652\) 6916.19 + 9777.19i 0.415428 + 0.587276i
\(653\) 9804.28 0.587552 0.293776 0.955874i \(-0.405088\pi\)
0.293776 + 0.955874i \(0.405088\pi\)
\(654\) 0 0
\(655\) 460.057i 0.0274441i
\(656\) 24699.6 + 8722.46i 1.47005 + 0.519139i
\(657\) 0 0
\(658\) −28441.9 4247.61i −1.68508 0.251655i
\(659\) 6511.96i 0.384931i −0.981304 0.192466i \(-0.938352\pi\)
0.981304 0.192466i \(-0.0616484\pi\)
\(660\) 0 0
\(661\) 30763.5i 1.81023i −0.425165 0.905116i \(-0.639784\pi\)
0.425165 0.905116i \(-0.360216\pi\)
\(662\) −7006.24 22036.5i −0.411337 1.29377i
\(663\) 0 0
\(664\) −12078.8 + 15978.1i −0.705944 + 0.933841i
\(665\) 4105.84 8369.45i 0.239425 0.488050i
\(666\) 0 0
\(667\) 1628.40i 0.0945304i
\(668\) −4391.84 + 3106.70i −0.254379 + 0.179943i
\(669\) 0 0
\(670\) −6676.77 + 2122.80i −0.384994 + 0.122404i
\(671\) −8907.15 −0.512454
\(672\) 0 0
\(673\) −2596.57 −0.148723 −0.0743615 0.997231i \(-0.523692\pi\)
−0.0743615 + 0.997231i \(0.523692\pi\)
\(674\) 15344.3 4878.55i 0.876917 0.278805i
\(675\) 0 0
\(676\) −1358.75 + 961.156i −0.0773073 + 0.0546857i
\(677\) 15954.7i 0.905744i −0.891576 0.452872i \(-0.850399\pi\)
0.891576 0.452872i \(-0.149601\pi\)
\(678\) 0 0
\(679\) 7625.37 15543.8i 0.430979 0.878519i
\(680\) 6565.56 8685.09i 0.370261 0.489791i
\(681\) 0 0
\(682\) −2362.88 7431.89i −0.132668 0.417276i
\(683\) 17296.4i 0.969002i 0.874791 + 0.484501i \(0.160999\pi\)
−0.874791 + 0.484501i \(0.839001\pi\)
\(684\) 0 0
\(685\) 15270.0i 0.851730i
\(686\) −8777.42 15677.6i −0.488518 0.872554i
\(687\) 0 0
\(688\) −28411.6 10033.3i −1.57439 0.555985i
\(689\) 9963.06i 0.550889i
\(690\) 0 0
\(691\) −30696.5 −1.68994 −0.844970 0.534814i \(-0.820382\pi\)
−0.844970 + 0.534814i \(0.820382\pi\)
\(692\) 9280.51 + 13119.5i 0.509815 + 0.720708i
\(693\) 0 0
\(694\) 5743.47 + 18064.7i 0.314148 + 0.988081i
\(695\) 12336.6i 0.673315i
\(696\) 0 0
\(697\) 19110.8 1.03856
\(698\) −3354.39 10550.4i −0.181899 0.572121i
\(699\) 0 0
\(700\) 2751.42 442.847i 0.148563 0.0239115i
\(701\) −27695.1 −1.49219 −0.746097 0.665837i \(-0.768075\pi\)
−0.746097 + 0.665837i \(0.768075\pi\)
\(702\) 0 0
\(703\) 1840.77 0.0987569
\(704\) 8891.45 2520.14i 0.476007 0.134917i
\(705\) 0 0
\(706\) −8444.47 26560.1i −0.450158 1.41587i
\(707\) −5248.10 + 10697.9i −0.279173 + 0.569073i
\(708\) 0 0
\(709\) −10901.1 −0.577433 −0.288716 0.957415i \(-0.593228\pi\)
−0.288716 + 0.957415i \(0.593228\pi\)
\(710\) 27655.6 8792.77i 1.46183 0.464770i
\(711\) 0 0
\(712\) 1214.82 + 918.354i 0.0639430 + 0.0483382i
\(713\) 5162.39i 0.271154i
\(714\) 0 0
\(715\) 9121.92i 0.477120i
\(716\) 17205.1 + 24322.2i 0.898022 + 1.26950i
\(717\) 0 0
\(718\) 8673.10 + 27279.2i 0.450804 + 1.41790i
\(719\) −28539.3 −1.48030 −0.740150 0.672442i \(-0.765245\pi\)
−0.740150 + 0.672442i \(0.765245\pi\)
\(720\) 0 0
\(721\) −13873.8 6806.14i −0.716627 0.351559i
\(722\) 12056.9 3833.34i 0.621483 0.197593i
\(723\) 0 0
\(724\) 9289.38 + 13132.1i 0.476847 + 0.674102i
\(725\) −906.288 −0.0464258
\(726\) 0 0
\(727\) −1103.93 −0.0563169 −0.0281584 0.999603i \(-0.508964\pi\)
−0.0281584 + 0.999603i \(0.508964\pi\)
\(728\) −9260.09 18347.1i −0.471431 0.934049i
\(729\) 0 0
\(730\) 21964.7 6983.42i 1.11363 0.354066i
\(731\) −21982.9 −1.11227
\(732\) 0 0
\(733\) 12729.3i 0.641431i −0.947176 0.320716i \(-0.896077\pi\)
0.947176 0.320716i \(-0.103923\pi\)
\(734\) −12018.3 + 3821.06i −0.604362 + 0.192150i
\(735\) 0 0
\(736\) 6114.70 + 193.536i 0.306238 + 0.00969271i
\(737\) −4338.81 −0.216855
\(738\) 0 0
\(739\) 20655.8i 1.02819i 0.857732 + 0.514097i \(0.171873\pi\)
−0.857732 + 0.514097i \(0.828127\pi\)
\(740\) −1794.12 2536.28i −0.0891259 0.125994i
\(741\) 0 0
\(742\) −10525.3 1571.88i −0.520748 0.0777702i
\(743\) 30656.9i 1.51372i −0.653577 0.756860i \(-0.726732\pi\)
0.653577 0.756860i \(-0.273268\pi\)
\(744\) 0 0
\(745\) 12349.4i 0.607312i
\(746\) −2235.60 + 710.783i −0.109720 + 0.0348842i
\(747\) 0 0
\(748\) 5504.52 3893.79i 0.269071 0.190336i
\(749\) −12325.3 + 25124.2i −0.601276 + 1.22566i
\(750\) 0 0
\(751\) 18986.0i 0.922513i −0.887267 0.461257i \(-0.847399\pi\)
0.887267 0.461257i \(-0.152601\pi\)
\(752\) 11699.5 33129.6i 0.567335 1.60653i
\(753\) 0 0
\(754\) 2025.03 + 6369.25i 0.0978079 + 0.307632i
\(755\) −31515.1 −1.51914
\(756\) 0 0
\(757\) 22252.7 1.06841 0.534206 0.845354i \(-0.320611\pi\)
0.534206 + 0.845354i \(0.320611\pi\)
\(758\) −446.746 1405.14i −0.0214071 0.0673310i
\(759\) 0 0
\(760\) 9085.71 + 6868.40i 0.433649 + 0.327820i
\(761\) 21595.4i 1.02869i −0.857583 0.514346i \(-0.828035\pi\)
0.857583 0.514346i \(-0.171965\pi\)
\(762\) 0 0
\(763\) −22402.6 10990.2i −1.06295 0.521456i
\(764\) 5394.65 + 7626.23i 0.255460 + 0.361135i
\(765\) 0 0
\(766\) −33978.0 + 10802.9i −1.60271 + 0.509562i
\(767\) 35167.1i 1.65555i
\(768\) 0 0
\(769\) 37574.2i 1.76198i 0.473139 + 0.880988i \(0.343121\pi\)
−0.473139 + 0.880988i \(0.656879\pi\)
\(770\) −9636.67 1439.17i −0.451015 0.0673561i
\(771\) 0 0
\(772\) −29270.6 + 20705.5i −1.36460 + 0.965293i
\(773\) 31649.2i 1.47263i −0.676638 0.736315i \(-0.736564\pi\)
0.676638 0.736315i \(-0.263436\pi\)
\(774\) 0 0
\(775\) 2873.14 0.133169
\(776\) 16874.0 + 12756.0i 0.780593 + 0.590095i
\(777\) 0 0
\(778\) −30361.4 + 9653.04i −1.39911 + 0.444831i
\(779\) 19992.3i 0.919511i
\(780\) 0 0
\(781\) 17971.6 0.823401
\(782\) 4253.55 1352.37i 0.194510 0.0618420i
\(783\) 0 0
\(784\) 20843.4 6888.01i 0.949497 0.313776i
\(785\) −23341.1 −1.06125
\(786\) 0 0
\(787\) −13129.8 −0.594698 −0.297349 0.954769i \(-0.596103\pi\)
−0.297349 + 0.954769i \(0.596103\pi\)