Properties

Label 39.4.b.b.25.4
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: 4.0.1362828.1
Defining polynomial: \( x^{4} + 23x^{2} + 48 \) 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 25.4
Root \(4.54739i\) of defining polynomial
Character \(\chi\) \(=\) 39.25
Dual form 39.4.b.b.25.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.54739i q^{2} +3.00000 q^{3} -12.6788 q^{4} +12.9118i q^{5} +13.6422i q^{6} -16.7289i q^{7} -21.2762i q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+4.54739i q^{2} +3.00000 q^{3} -12.6788 q^{4} +12.9118i q^{5} +13.6422i q^{6} -16.7289i q^{7} -21.2762i q^{8} +9.00000 q^{9} -58.7151 q^{10} -24.9280i q^{11} -38.0363 q^{12} +(33.7151 + 32.5621i) q^{13} +76.0727 q^{14} +38.7355i q^{15} -4.67878 q^{16} +134.145 q^{17} +40.9265i q^{18} -14.9376i q^{19} -163.706i q^{20} -50.1866i q^{21} +113.358 q^{22} -72.0000 q^{23} -63.8287i q^{24} -41.7151 q^{25} +(-148.073 + 153.316i) q^{26} +27.0000 q^{27} +212.101i q^{28} -206.145 q^{29} -176.145 q^{30} -249.142i q^{31} -191.486i q^{32} -74.7841i q^{33} +610.012i q^{34} +216.000 q^{35} -114.109 q^{36} -293.955i q^{37} +67.9273 q^{38} +(101.145 + 97.6863i) q^{39} +274.715 q^{40} +250.506i q^{41} +228.218 q^{42} -432.145 q^{43} +316.057i q^{44} +116.206i q^{45} -327.412i q^{46} +159.889i q^{47} -14.0363 q^{48} +63.1454 q^{49} -189.695i q^{50} +402.436 q^{51} +(-427.467 - 412.848i) q^{52} -194.581 q^{53} +122.780i q^{54} +321.866 q^{55} -355.927 q^{56} -44.8129i q^{57} -937.424i q^{58} -232.647i q^{59} -491.118i q^{60} -185.006 q^{61} +1132.94 q^{62} -150.560i q^{63} +833.333 q^{64} +(-420.436 + 435.324i) q^{65} +340.073 q^{66} -39.4393i q^{67} -1700.80 q^{68} -216.000 q^{69} +982.237i q^{70} +920.460i q^{71} -191.486i q^{72} +549.078i q^{73} +1336.73 q^{74} -125.145 q^{75} +189.391i q^{76} -417.018 q^{77} +(-444.218 + 459.948i) q^{78} +933.140 q^{79} -60.4116i q^{80} +81.0000 q^{81} -1139.15 q^{82} -1095.38i q^{83} +636.304i q^{84} +1732.06i q^{85} -1965.13i q^{86} -618.436 q^{87} -530.375 q^{88} +532.114i q^{89} -528.436 q^{90} +(544.727 - 564.015i) q^{91} +912.872 q^{92} -747.425i q^{93} -727.079 q^{94} +192.872 q^{95} -574.459i q^{96} -362.661i q^{97} +287.147i q^{98} -224.352i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 12 q^{3} - 14 q^{4} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 12 q^{3} - 14 q^{4} + 36 q^{9} - 88 q^{10} - 42 q^{12} - 12 q^{13} + 84 q^{14} + 18 q^{16} + 96 q^{17} + 380 q^{22} - 288 q^{23} - 20 q^{25} - 372 q^{26} + 108 q^{27} - 384 q^{29} - 264 q^{30} + 864 q^{35} - 126 q^{36} + 492 q^{38} - 36 q^{39} + 952 q^{40} + 252 q^{42} - 1288 q^{43} + 54 q^{48} - 188 q^{49} + 288 q^{51} - 1306 q^{52} + 984 q^{53} - 328 q^{55} - 1644 q^{56} + 288 q^{61} + 1668 q^{62} + 1314 q^{64} - 360 q^{65} + 1140 q^{66} - 4380 q^{68} - 864 q^{69} + 3144 q^{74} - 60 q^{75} + 1416 q^{77} - 1116 q^{78} + 4320 q^{79} + 324 q^{81} - 3088 q^{82} - 1152 q^{87} + 1036 q^{88} - 792 q^{90} - 24 q^{91} + 1008 q^{92} - 1660 q^{94} - 1872 q^{95}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.54739i 1.60775i 0.594801 + 0.803873i \(0.297231\pi\)
−0.594801 + 0.803873i \(0.702769\pi\)
\(3\) 3.00000 0.577350
\(4\) −12.6788 −1.58485
\(5\) 12.9118i 1.15487i 0.816437 + 0.577434i \(0.195946\pi\)
−0.816437 + 0.577434i \(0.804054\pi\)
\(6\) 13.6422i 0.928233i
\(7\) 16.7289i 0.903273i −0.892202 0.451637i \(-0.850840\pi\)
0.892202 0.451637i \(-0.149160\pi\)
\(8\) 21.2762i 0.940286i
\(9\) 9.00000 0.333333
\(10\) −58.7151 −1.85674
\(11\) 24.9280i 0.683280i −0.939831 0.341640i \(-0.889018\pi\)
0.939831 0.341640i \(-0.110982\pi\)
\(12\) −38.0363 −0.915012
\(13\) 33.7151 + 32.5621i 0.719299 + 0.694700i
\(14\) 76.0727 1.45223
\(15\) 38.7355i 0.666764i
\(16\) −4.67878 −0.0731059
\(17\) 134.145 1.91383 0.956913 0.290376i \(-0.0937804\pi\)
0.956913 + 0.290376i \(0.0937804\pi\)
\(18\) 40.9265i 0.535915i
\(19\) 14.9376i 0.180365i −0.995925 0.0901824i \(-0.971255\pi\)
0.995925 0.0901824i \(-0.0287450\pi\)
\(20\) 163.706i 1.83029i
\(21\) 50.1866i 0.521505i
\(22\) 113.358 1.09854
\(23\) −72.0000 −0.652741 −0.326370 0.945242i \(-0.605826\pi\)
−0.326370 + 0.945242i \(0.605826\pi\)
\(24\) 63.8287i 0.542875i
\(25\) −41.7151 −0.333721
\(26\) −148.073 + 153.316i −1.11690 + 1.15645i
\(27\) 27.0000 0.192450
\(28\) 212.101i 1.43155i
\(29\) −206.145 −1.32001 −0.660004 0.751262i \(-0.729445\pi\)
−0.660004 + 0.751262i \(0.729445\pi\)
\(30\) −176.145 −1.07199
\(31\) 249.142i 1.44346i −0.692176 0.721728i \(-0.743348\pi\)
0.692176 0.721728i \(-0.256652\pi\)
\(32\) 191.486i 1.05782i
\(33\) 74.7841i 0.394492i
\(34\) 610.012i 3.07694i
\(35\) 216.000 1.04316
\(36\) −114.109 −0.528282
\(37\) 293.955i 1.30610i −0.757313 0.653052i \(-0.773488\pi\)
0.757313 0.653052i \(-0.226512\pi\)
\(38\) 67.9273 0.289981
\(39\) 101.145 + 97.6863i 0.415288 + 0.401085i
\(40\) 274.715 1.08591
\(41\) 250.506i 0.954208i 0.878847 + 0.477104i \(0.158314\pi\)
−0.878847 + 0.477104i \(0.841686\pi\)
\(42\) 228.218 0.838448
\(43\) −432.145 −1.53259 −0.766297 0.642486i \(-0.777903\pi\)
−0.766297 + 0.642486i \(0.777903\pi\)
\(44\) 316.057i 1.08290i
\(45\) 116.206i 0.384956i
\(46\) 327.412i 1.04944i
\(47\) 159.889i 0.496217i 0.968732 + 0.248109i \(0.0798090\pi\)
−0.968732 + 0.248109i \(0.920191\pi\)
\(48\) −14.0363 −0.0422077
\(49\) 63.1454 0.184097
\(50\) 189.695i 0.536539i
\(51\) 402.436 1.10495
\(52\) −427.467 412.848i −1.13998 1.10099i
\(53\) −194.581 −0.504298 −0.252149 0.967688i \(-0.581137\pi\)
−0.252149 + 0.967688i \(0.581137\pi\)
\(54\) 122.780i 0.309411i
\(55\) 321.866 0.789099
\(56\) −355.927 −0.849336
\(57\) 44.8129i 0.104134i
\(58\) 937.424i 2.12224i
\(59\) 232.647i 0.513358i −0.966497 0.256679i \(-0.917372\pi\)
0.966497 0.256679i \(-0.0826283\pi\)
\(60\) 491.118i 1.05672i
\(61\) −185.006 −0.388321 −0.194160 0.980970i \(-0.562198\pi\)
−0.194160 + 0.980970i \(0.562198\pi\)
\(62\) 1132.94 2.32071
\(63\) 150.560i 0.301091i
\(64\) 833.333 1.62760
\(65\) −420.436 + 435.324i −0.802287 + 0.830696i
\(66\) 340.073 0.634243
\(67\) 39.4393i 0.0719145i −0.999353 0.0359573i \(-0.988552\pi\)
0.999353 0.0359573i \(-0.0114480\pi\)
\(68\) −1700.80 −3.03312
\(69\) −216.000 −0.376860
\(70\) 982.237i 1.67714i
\(71\) 920.460i 1.53857i 0.638905 + 0.769286i \(0.279388\pi\)
−0.638905 + 0.769286i \(0.720612\pi\)
\(72\) 191.486i 0.313429i
\(73\) 549.078i 0.880338i 0.897915 + 0.440169i \(0.145082\pi\)
−0.897915 + 0.440169i \(0.854918\pi\)
\(74\) 1336.73 2.09988
\(75\) −125.145 −0.192674
\(76\) 189.391i 0.285851i
\(77\) −417.018 −0.617189
\(78\) −444.218 + 459.948i −0.644843 + 0.667677i
\(79\) 933.140 1.32894 0.664471 0.747314i \(-0.268657\pi\)
0.664471 + 0.747314i \(0.268657\pi\)
\(80\) 60.4116i 0.0844277i
\(81\) 81.0000 0.111111
\(82\) −1139.15 −1.53412
\(83\) 1095.38i 1.44860i −0.689484 0.724301i \(-0.742163\pi\)
0.689484 0.724301i \(-0.257837\pi\)
\(84\) 636.304i 0.826506i
\(85\) 1732.06i 2.21022i
\(86\) 1965.13i 2.46402i
\(87\) −618.436 −0.762107
\(88\) −530.375 −0.642479
\(89\) 532.114i 0.633753i 0.948467 + 0.316876i \(0.102634\pi\)
−0.948467 + 0.316876i \(0.897366\pi\)
\(90\) −528.436 −0.618912
\(91\) 544.727 564.015i 0.627504 0.649724i
\(92\) 912.872 1.03449
\(93\) 747.425i 0.833380i
\(94\) −727.079 −0.797792
\(95\) 192.872 0.208298
\(96\) 574.459i 0.610734i
\(97\) 362.661i 0.379615i −0.981821 0.189808i \(-0.939214\pi\)
0.981821 0.189808i \(-0.0607864\pi\)
\(98\) 287.147i 0.295982i
\(99\) 224.352i 0.227760i
\(100\) 528.897 0.528897
\(101\) −1490.58 −1.46850 −0.734249 0.678880i \(-0.762466\pi\)
−0.734249 + 0.678880i \(0.762466\pi\)
\(102\) 1830.03i 1.77648i
\(103\) −628.436 −0.601181 −0.300591 0.953753i \(-0.597184\pi\)
−0.300591 + 0.953753i \(0.597184\pi\)
\(104\) 692.799 717.331i 0.653217 0.676347i
\(105\) 648.000 0.602270
\(106\) 884.838i 0.810784i
\(107\) 477.454 0.431376 0.215688 0.976462i \(-0.430801\pi\)
0.215688 + 0.976462i \(0.430801\pi\)
\(108\) −342.327 −0.305004
\(109\) 378.207i 0.332345i −0.986097 0.166173i \(-0.946859\pi\)
0.986097 0.166173i \(-0.0531409\pi\)
\(110\) 1463.65i 1.26867i
\(111\) 881.864i 0.754079i
\(112\) 78.2706i 0.0660346i
\(113\) 13.2732 0.0110499 0.00552495 0.999985i \(-0.498241\pi\)
0.00552495 + 0.999985i \(0.498241\pi\)
\(114\) 203.782 0.167420
\(115\) 929.651i 0.753830i
\(116\) 2613.67 2.09201
\(117\) 303.436 + 293.059i 0.239766 + 0.231567i
\(118\) 1057.94 0.825349
\(119\) 2244.10i 1.72871i
\(120\) 824.145 0.626949
\(121\) 709.593 0.533128
\(122\) 841.294i 0.624321i
\(123\) 751.519i 0.550912i
\(124\) 3158.81i 2.28766i
\(125\) 1075.36i 0.769465i
\(126\) 684.654 0.484078
\(127\) −145.988 −0.102003 −0.0510015 0.998699i \(-0.516241\pi\)
−0.0510015 + 0.998699i \(0.516241\pi\)
\(128\) 2257.60i 1.55895i
\(129\) −1296.44 −0.884844
\(130\) −1979.59 1911.89i −1.33555 1.28987i
\(131\) 317.163 0.211532 0.105766 0.994391i \(-0.466271\pi\)
0.105766 + 0.994391i \(0.466271\pi\)
\(132\) 948.171i 0.625210i
\(133\) −249.890 −0.162919
\(134\) 179.346 0.115620
\(135\) 348.619i 0.222255i
\(136\) 2854.11i 1.79954i
\(137\) 443.149i 0.276356i −0.990407 0.138178i \(-0.955875\pi\)
0.990407 0.138178i \(-0.0441247\pi\)
\(138\) 982.237i 0.605895i
\(139\) 785.018 0.479024 0.239512 0.970893i \(-0.423013\pi\)
0.239512 + 0.970893i \(0.423013\pi\)
\(140\) −2738.62 −1.65325
\(141\) 479.667i 0.286491i
\(142\) −4185.69 −2.47363
\(143\) 811.709 840.452i 0.474675 0.491483i
\(144\) −42.1090 −0.0243686
\(145\) 2661.71i 1.52444i
\(146\) −2496.87 −1.41536
\(147\) 189.436 0.106289
\(148\) 3726.99i 2.06997i
\(149\) 135.420i 0.0744566i 0.999307 + 0.0372283i \(0.0118529\pi\)
−0.999307 + 0.0372283i \(0.988147\pi\)
\(150\) 569.085i 0.309771i
\(151\) 2373.74i 1.27929i 0.768672 + 0.639643i \(0.220918\pi\)
−0.768672 + 0.639643i \(0.779082\pi\)
\(152\) −317.817 −0.169594
\(153\) 1207.31 0.637942
\(154\) 1896.34i 0.992283i
\(155\) 3216.87 1.66700
\(156\) −1282.40 1238.54i −0.658168 0.635659i
\(157\) −1166.73 −0.593089 −0.296544 0.955019i \(-0.595834\pi\)
−0.296544 + 0.955019i \(0.595834\pi\)
\(158\) 4243.35i 2.13660i
\(159\) −583.744 −0.291157
\(160\) 2472.44 1.22165
\(161\) 1204.48i 0.589603i
\(162\) 368.339i 0.178638i
\(163\) 2309.19i 1.10963i 0.831974 + 0.554815i \(0.187211\pi\)
−0.831974 + 0.554815i \(0.812789\pi\)
\(164\) 3176.12i 1.51227i
\(165\) 965.599 0.455587
\(166\) 4981.14 2.32898
\(167\) 600.788i 0.278386i 0.990265 + 0.139193i \(0.0444508\pi\)
−0.990265 + 0.139193i \(0.955549\pi\)
\(168\) −1067.78 −0.490364
\(169\) 76.4186 + 2195.67i 0.0347831 + 0.999395i
\(170\) −7876.36 −3.55347
\(171\) 134.439i 0.0601216i
\(172\) 5479.08 2.42893
\(173\) −3430.36 −1.50755 −0.753773 0.657135i \(-0.771768\pi\)
−0.753773 + 0.657135i \(0.771768\pi\)
\(174\) 2812.27i 1.22527i
\(175\) 697.846i 0.301441i
\(176\) 116.633i 0.0499519i
\(177\) 697.942i 0.296387i
\(178\) −2419.73 −1.01891
\(179\) −978.837 −0.408725 −0.204362 0.978895i \(-0.565512\pi\)
−0.204362 + 0.978895i \(0.565512\pi\)
\(180\) 1473.36i 0.610097i
\(181\) 3839.09 1.57656 0.788279 0.615318i \(-0.210972\pi\)
0.788279 + 0.615318i \(0.210972\pi\)
\(182\) 2564.80 + 2477.09i 1.04459 + 1.00887i
\(183\) −555.018 −0.224197
\(184\) 1531.89i 0.613763i
\(185\) 3795.49 1.50838
\(186\) 3398.83 1.33986
\(187\) 3343.98i 1.30768i
\(188\) 2027.20i 0.786429i
\(189\) 451.679i 0.173835i
\(190\) 877.065i 0.334890i
\(191\) −487.709 −0.184761 −0.0923806 0.995724i \(-0.529448\pi\)
−0.0923806 + 0.995724i \(0.529448\pi\)
\(192\) 2500.00 0.939697
\(193\) 4245.61i 1.58345i −0.610878 0.791725i \(-0.709183\pi\)
0.610878 0.791725i \(-0.290817\pi\)
\(194\) 1649.16 0.610325
\(195\) −1261.31 + 1305.97i −0.463201 + 0.479603i
\(196\) −800.606 −0.291766
\(197\) 2712.71i 0.981079i −0.871419 0.490539i \(-0.836800\pi\)
0.871419 0.490539i \(-0.163200\pi\)
\(198\) 1020.22 0.366180
\(199\) −3116.90 −1.11031 −0.555153 0.831748i \(-0.687340\pi\)
−0.555153 + 0.831748i \(0.687340\pi\)
\(200\) 887.541i 0.313793i
\(201\) 118.318i 0.0415199i
\(202\) 6778.26i 2.36097i
\(203\) 3448.58i 1.19233i
\(204\) −5102.40 −1.75117
\(205\) −3234.49 −1.10198
\(206\) 2857.75i 0.966546i
\(207\) −648.000 −0.217580
\(208\) −157.746 152.351i −0.0525851 0.0507867i
\(209\) −372.366 −0.123240
\(210\) 2946.71i 0.968297i
\(211\) −1051.22 −0.342981 −0.171491 0.985186i \(-0.554858\pi\)
−0.171491 + 0.985186i \(0.554858\pi\)
\(212\) 2467.06 0.799236
\(213\) 2761.38i 0.888294i
\(214\) 2171.17i 0.693542i
\(215\) 5579.78i 1.76994i
\(216\) 574.459i 0.180958i
\(217\) −4167.85 −1.30384
\(218\) 1719.85 0.534327
\(219\) 1647.23i 0.508264i
\(220\) −4080.87 −1.25060
\(221\) 4522.73 + 4368.06i 1.37661 + 1.32953i
\(222\) 4010.18 1.21237
\(223\) 5496.12i 1.65044i 0.564814 + 0.825218i \(0.308948\pi\)
−0.564814 + 0.825218i \(0.691052\pi\)
\(224\) −3203.35 −0.955502
\(225\) −375.436 −0.111240
\(226\) 60.3585i 0.0177654i
\(227\) 921.570i 0.269457i −0.990883 0.134729i \(-0.956984\pi\)
0.990883 0.134729i \(-0.0430162\pi\)
\(228\) 568.173i 0.165036i
\(229\) 192.941i 0.0556764i −0.999612 0.0278382i \(-0.991138\pi\)
0.999612 0.0278382i \(-0.00886232\pi\)
\(230\) 4227.49 1.21197
\(231\) −1251.05 −0.356334
\(232\) 4386.00i 1.24119i
\(233\) −913.779 −0.256926 −0.128463 0.991714i \(-0.541004\pi\)
−0.128463 + 0.991714i \(0.541004\pi\)
\(234\) −1332.65 + 1379.84i −0.372301 + 0.385484i
\(235\) −2064.46 −0.573066
\(236\) 2949.68i 0.813594i
\(237\) 2799.42 0.767265
\(238\) 10204.8 2.77932
\(239\) 1976.86i 0.535032i −0.963553 0.267516i \(-0.913797\pi\)
0.963553 0.267516i \(-0.0862028\pi\)
\(240\) 181.235i 0.0487444i
\(241\) 3904.45i 1.04360i −0.853068 0.521800i \(-0.825261\pi\)
0.853068 0.521800i \(-0.174739\pi\)
\(242\) 3226.80i 0.857134i
\(243\) 243.000 0.0641500
\(244\) 2345.65 0.615429
\(245\) 815.322i 0.212608i
\(246\) −3417.45 −0.885727
\(247\) 486.401 503.624i 0.125299 0.129736i
\(248\) −5300.80 −1.35726
\(249\) 3286.15i 0.836350i
\(250\) −4890.08 −1.23710
\(251\) 942.035 0.236895 0.118448 0.992960i \(-0.462208\pi\)
0.118448 + 0.992960i \(0.462208\pi\)
\(252\) 1908.91i 0.477183i
\(253\) 1794.82i 0.446005i
\(254\) 663.866i 0.163995i
\(255\) 5196.18i 1.27607i
\(256\) −3599.54 −0.878794
\(257\) 812.616 0.197236 0.0986179 0.995125i \(-0.468558\pi\)
0.0986179 + 0.995125i \(0.468558\pi\)
\(258\) 5895.40i 1.42260i
\(259\) −4917.52 −1.17977
\(260\) 5330.62 5519.37i 1.27150 1.31653i
\(261\) −1855.31 −0.440003
\(262\) 1442.26i 0.340089i
\(263\) −2608.29 −0.611536 −0.305768 0.952106i \(-0.598913\pi\)
−0.305768 + 0.952106i \(0.598913\pi\)
\(264\) −1591.13 −0.370936
\(265\) 2512.40i 0.582398i
\(266\) 1136.35i 0.261932i
\(267\) 1596.34i 0.365897i
\(268\) 500.042i 0.113974i
\(269\) −4791.02 −1.08592 −0.542962 0.839757i \(-0.682697\pi\)
−0.542962 + 0.839757i \(0.682697\pi\)
\(270\) −1585.31 −0.357329
\(271\) 3663.62i 0.821214i 0.911812 + 0.410607i \(0.134683\pi\)
−0.911812 + 0.410607i \(0.865317\pi\)
\(272\) −627.637 −0.139912
\(273\) 1634.18 1692.05i 0.362290 0.375118i
\(274\) 2015.17 0.444311
\(275\) 1039.88i 0.228025i
\(276\) 2738.62 0.597266
\(277\) 624.326 0.135423 0.0677114 0.997705i \(-0.478430\pi\)
0.0677114 + 0.997705i \(0.478430\pi\)
\(278\) 3569.78i 0.770149i
\(279\) 2242.27i 0.481152i
\(280\) 4595.67i 0.980871i
\(281\) 5535.12i 1.17508i −0.809195 0.587540i \(-0.800096\pi\)
0.809195 0.587540i \(-0.199904\pi\)
\(282\) −2181.24 −0.460605
\(283\) −175.151 −0.0367903 −0.0183952 0.999831i \(-0.505856\pi\)
−0.0183952 + 0.999831i \(0.505856\pi\)
\(284\) 11670.3i 2.43840i
\(285\) 578.616 0.120261
\(286\) 3821.86 + 3691.16i 0.790180 + 0.763157i
\(287\) 4190.69 0.861911
\(288\) 1723.38i 0.352607i
\(289\) 13082.0 2.66273
\(290\) 12103.8 2.45091
\(291\) 1087.98i 0.219171i
\(292\) 6961.64i 1.39520i
\(293\) 7774.33i 1.55011i 0.631895 + 0.775054i \(0.282277\pi\)
−0.631895 + 0.775054i \(0.717723\pi\)
\(294\) 861.440i 0.170885i
\(295\) 3003.90 0.592861
\(296\) −6254.25 −1.22811
\(297\) 673.057i 0.131497i
\(298\) −615.808 −0.119707
\(299\) −2427.49 2344.47i −0.469516 0.453459i
\(300\) 1586.69 0.305359
\(301\) 7229.30i 1.38435i
\(302\) −10794.3 −2.05677
\(303\) −4471.74 −0.847838
\(304\) 69.8899i 0.0131857i
\(305\) 2388.76i 0.448459i
\(306\) 5490.10i 1.02565i
\(307\) 8022.85i 1.49149i −0.666230 0.745746i \(-0.732093\pi\)
0.666230 0.745746i \(-0.267907\pi\)
\(308\) 5287.27 0.978150
\(309\) −1885.31 −0.347092
\(310\) 14628.4i 2.68012i
\(311\) 9264.87 1.68927 0.844635 0.535343i \(-0.179818\pi\)
0.844635 + 0.535343i \(0.179818\pi\)
\(312\) 2078.40 2151.99i 0.377135 0.390489i
\(313\) 7423.57 1.34059 0.670296 0.742094i \(-0.266167\pi\)
0.670296 + 0.742094i \(0.266167\pi\)
\(314\) 5305.56i 0.953536i
\(315\) 1944.00 0.347721
\(316\) −11831.1 −2.10617
\(317\) 2641.04i 0.467935i 0.972244 + 0.233968i \(0.0751710\pi\)
−0.972244 + 0.233968i \(0.924829\pi\)
\(318\) 2654.51i 0.468106i
\(319\) 5138.80i 0.901936i
\(320\) 10759.8i 1.87967i
\(321\) 1432.36 0.249055
\(322\) −5477.23 −0.947932
\(323\) 2003.82i 0.345187i
\(324\) −1026.98 −0.176094
\(325\) −1406.43 1358.33i −0.240045 0.231836i
\(326\) −10500.8 −1.78400
\(327\) 1134.62i 0.191880i
\(328\) 5329.84 0.897229
\(329\) 2674.76 0.448220
\(330\) 4390.96i 0.732467i
\(331\) 10779.5i 1.79001i 0.446052 + 0.895007i \(0.352830\pi\)
−0.446052 + 0.895007i \(0.647170\pi\)
\(332\) 13888.1i 2.29581i
\(333\) 2645.59i 0.435368i
\(334\) −2732.02 −0.447573
\(335\) 509.233 0.0830518
\(336\) 234.812i 0.0381251i
\(337\) 313.465 0.0506693 0.0253346 0.999679i \(-0.491935\pi\)
0.0253346 + 0.999679i \(0.491935\pi\)
\(338\) −9984.58 + 347.505i −1.60677 + 0.0559225i
\(339\) 39.8196 0.00637966
\(340\) 21960.4i 3.50286i
\(341\) −6210.61 −0.986286
\(342\) 611.346 0.0966602
\(343\) 6794.35i 1.06956i
\(344\) 9194.43i 1.44108i
\(345\) 2788.95i 0.435224i
\(346\) 15599.2i 2.42375i
\(347\) −2849.23 −0.440792 −0.220396 0.975410i \(-0.570735\pi\)
−0.220396 + 0.975410i \(0.570735\pi\)
\(348\) 7841.01 1.20782
\(349\) 6466.94i 0.991883i −0.868356 0.495941i \(-0.834823\pi\)
0.868356 0.495941i \(-0.165177\pi\)
\(350\) −3173.38 −0.484641
\(351\) 910.308 + 879.177i 0.138429 + 0.133695i
\(352\) −4773.38 −0.722789
\(353\) 2773.10i 0.418122i −0.977903 0.209061i \(-0.932959\pi\)
0.977903 0.209061i \(-0.0670408\pi\)
\(354\) 3173.82 0.476515
\(355\) −11884.8 −1.77685
\(356\) 6746.56i 1.00440i
\(357\) 6732.30i 0.998070i
\(358\) 4451.16i 0.657126i
\(359\) 1467.11i 0.215685i 0.994168 + 0.107843i \(0.0343942\pi\)
−0.994168 + 0.107843i \(0.965606\pi\)
\(360\) 2472.44 0.361969
\(361\) 6635.87 0.967469
\(362\) 17457.8i 2.53471i
\(363\) 2128.78 0.307801
\(364\) −6906.47 + 7151.03i −0.994498 + 1.02971i
\(365\) −7089.59 −1.01667
\(366\) 2523.88i 0.360452i
\(367\) 4648.22 0.661130 0.330565 0.943783i \(-0.392761\pi\)
0.330565 + 0.943783i \(0.392761\pi\)
\(368\) 336.872 0.0477192
\(369\) 2254.56i 0.318069i
\(370\) 17259.6i 2.42509i
\(371\) 3255.12i 0.455519i
\(372\) 9476.44i 1.32078i
\(373\) 1763.72 0.244831 0.122416 0.992479i \(-0.460936\pi\)
0.122416 + 0.992479i \(0.460936\pi\)
\(374\) 15206.4 2.10242
\(375\) 3226.08i 0.444251i
\(376\) 3401.84 0.466586
\(377\) −6950.22 6712.53i −0.949481 0.917010i
\(378\) 2053.96 0.279483
\(379\) 1930.47i 0.261640i 0.991406 + 0.130820i \(0.0417611\pi\)
−0.991406 + 0.130820i \(0.958239\pi\)
\(380\) −2445.38 −0.330120
\(381\) −437.965 −0.0588914
\(382\) 2217.81i 0.297049i
\(383\) 8845.93i 1.18017i −0.807340 0.590086i \(-0.799094\pi\)
0.807340 0.590086i \(-0.200906\pi\)
\(384\) 6772.81i 0.900061i
\(385\) 5384.46i 0.712772i
\(386\) 19306.5 2.54579
\(387\) −3889.31 −0.510865
\(388\) 4598.10i 0.601632i
\(389\) 1598.08 0.208292 0.104146 0.994562i \(-0.466789\pi\)
0.104146 + 0.994562i \(0.466789\pi\)
\(390\) −5938.76 5735.66i −0.771079 0.744709i
\(391\) −9658.47 −1.24923
\(392\) 1343.50i 0.173104i
\(393\) 951.489 0.122128
\(394\) 12335.8 1.57733
\(395\) 12048.5i 1.53475i
\(396\) 2844.51i 0.360965i
\(397\) 3578.82i 0.452433i −0.974077 0.226217i \(-0.927364\pi\)
0.974077 0.226217i \(-0.0726357\pi\)
\(398\) 14173.7i 1.78509i
\(399\) −749.669 −0.0940611
\(400\) 195.176 0.0243970
\(401\) 3485.99i 0.434120i 0.976158 + 0.217060i \(0.0696467\pi\)
−0.976158 + 0.217060i \(0.930353\pi\)
\(402\) 538.038 0.0667534
\(403\) 8112.58 8399.84i 1.00277 1.03828i
\(404\) 18898.8 2.32735
\(405\) 1045.86i 0.128319i
\(406\) −15682.0 −1.91696
\(407\) −7327.71 −0.892435
\(408\) 8562.33i 1.03897i
\(409\) 14709.1i 1.77828i 0.457637 + 0.889139i \(0.348696\pi\)
−0.457637 + 0.889139i \(0.651304\pi\)
\(410\) 14708.5i 1.77171i
\(411\) 1329.45i 0.159554i
\(412\) 7967.80 0.952780
\(413\) −3891.92 −0.463702
\(414\) 2946.71i 0.349814i
\(415\) 14143.4 1.67294
\(416\) 6235.20 6455.98i 0.734869 0.760891i
\(417\) 2355.05 0.276565
\(418\) 1693.29i 0.198138i
\(419\) 3709.01 0.432451 0.216226 0.976343i \(-0.430625\pi\)
0.216226 + 0.976343i \(0.430625\pi\)
\(420\) −8215.85 −0.954506
\(421\) 794.029i 0.0919207i 0.998943 + 0.0459603i \(0.0146348\pi\)
−0.998943 + 0.0459603i \(0.985365\pi\)
\(422\) 4780.32i 0.551427i
\(423\) 1439.00i 0.165406i
\(424\) 4139.96i 0.474185i
\(425\) −5595.89 −0.638684
\(426\) −12557.1 −1.42815
\(427\) 3094.94i 0.350760i
\(428\) −6053.53 −0.683664
\(429\) 2435.13 2521.35i 0.274054 0.283758i
\(430\) 25373.5 2.84562
\(431\) 2891.52i 0.323155i 0.986860 + 0.161577i \(0.0516582\pi\)
−0.986860 + 0.161577i \(0.948342\pi\)
\(432\) −126.327 −0.0140692
\(433\) −5560.94 −0.617186 −0.308593 0.951194i \(-0.599858\pi\)
−0.308593 + 0.951194i \(0.599858\pi\)
\(434\) 18952.9i 2.09624i
\(435\) 7985.14i 0.880133i
\(436\) 4795.20i 0.526717i
\(437\) 1075.51i 0.117731i
\(438\) −7490.62 −0.817159
\(439\) −15127.2 −1.64460 −0.822302 0.569051i \(-0.807311\pi\)
−0.822302 + 0.569051i \(0.807311\pi\)
\(440\) 6848.11i 0.741979i
\(441\) 568.308 0.0613658
\(442\) −19863.3 + 20566.6i −2.13755 + 2.21324i
\(443\) 2357.89 0.252883 0.126441 0.991974i \(-0.459644\pi\)
0.126441 + 0.991974i \(0.459644\pi\)
\(444\) 11181.0i 1.19510i
\(445\) −6870.56 −0.731901
\(446\) −24993.0 −2.65348
\(447\) 406.260i 0.0429876i
\(448\) 13940.7i 1.47017i
\(449\) 7165.06i 0.753096i 0.926397 + 0.376548i \(0.122889\pi\)
−0.926397 + 0.376548i \(0.877111\pi\)
\(450\) 1707.26i 0.178846i
\(451\) 6244.63 0.651992
\(452\) −168.288 −0.0175124
\(453\) 7121.22i 0.738596i
\(454\) 4190.74 0.433219
\(455\) 7282.47 + 7033.41i 0.750346 + 0.724685i
\(456\) −953.451 −0.0979154
\(457\) 8020.96i 0.821017i 0.911857 + 0.410508i \(0.134649\pi\)
−0.911857 + 0.410508i \(0.865351\pi\)
\(458\) 877.378 0.0895135
\(459\) 3621.92 0.368316
\(460\) 11786.8i 1.19471i
\(461\) 4146.59i 0.418928i −0.977816 0.209464i \(-0.932828\pi\)
0.977816 0.209464i \(-0.0671720\pi\)
\(462\) 5689.03i 0.572895i
\(463\) 7118.21i 0.714495i −0.934010 0.357248i \(-0.883715\pi\)
0.934010 0.357248i \(-0.116285\pi\)
\(464\) 964.509 0.0965004
\(465\) 9650.62 0.962444
\(466\) 4155.31i 0.413071i
\(467\) 2128.22 0.210883 0.105441 0.994426i \(-0.466374\pi\)
0.105441 + 0.994426i \(0.466374\pi\)
\(468\) −3847.20 3715.63i −0.379993 0.366998i
\(469\) −659.774 −0.0649585
\(470\) 9387.91i 0.921344i
\(471\) −3500.18 −0.342420
\(472\) −4949.86 −0.482703
\(473\) 10772.5i 1.04719i
\(474\) 12730.1i 1.23357i
\(475\) 623.125i 0.0601915i
\(476\) 28452.4i 2.73974i
\(477\) −1751.23 −0.168099
\(478\) 8989.57 0.860196
\(479\) 3715.30i 0.354397i 0.984175 + 0.177199i \(0.0567035\pi\)
−0.984175 + 0.177199i \(0.943296\pi\)
\(480\) 7417.31 0.705317
\(481\) 9571.78 9910.71i 0.907350 0.939479i
\(482\) 17755.0 1.67784
\(483\) 3613.43i 0.340408i
\(484\) −8996.77 −0.844926
\(485\) 4682.62 0.438405
\(486\) 1105.02i 0.103137i
\(487\) 8139.28i 0.757343i −0.925531 0.378671i \(-0.876381\pi\)
0.925531 0.378671i \(-0.123619\pi\)
\(488\) 3936.23i 0.365133i
\(489\) 6927.57i 0.640645i
\(490\) −3707.59 −0.341820
\(491\) −18081.7 −1.66194 −0.830972 0.556315i \(-0.812215\pi\)
−0.830972 + 0.556315i \(0.812215\pi\)
\(492\) 9528.35i 0.873112i
\(493\) −27653.4 −2.52626
\(494\) 2290.18 + 2211.86i 0.208583 + 0.201450i
\(495\) 2896.80 0.263033
\(496\) 1165.68i 0.105525i
\(497\) 15398.3 1.38975
\(498\) 14943.4 1.34464
\(499\) 11031.5i 0.989659i 0.868990 + 0.494829i \(0.164769\pi\)
−0.868990 + 0.494829i \(0.835231\pi\)
\(500\) 13634.2i 1.21948i
\(501\) 1802.37i 0.160726i
\(502\) 4283.80i 0.380868i
\(503\) 8016.14 0.710581 0.355290 0.934756i \(-0.384382\pi\)
0.355290 + 0.934756i \(0.384382\pi\)
\(504\) −3203.35 −0.283112
\(505\) 19246.1i 1.69592i
\(506\) −8161.74 −0.717063
\(507\) 229.256 + 6587.01i 0.0200821 + 0.577001i
\(508\) 1850.95 0.161659
\(509\) 20173.9i 1.75676i 0.477959 + 0.878382i \(0.341377\pi\)
−0.477959 + 0.878382i \(0.658623\pi\)
\(510\) −23629.1 −2.05159
\(511\) 9185.44 0.795186
\(512\) 1692.30i 0.146074i
\(513\) 403.316i 0.0347112i
\(514\) 3695.29i 0.317105i
\(515\) 8114.25i 0.694285i
\(516\) 16437.2 1.40234
\(517\) 3985.72 0.339056
\(518\) 22361.9i 1.89677i
\(519\) −10291.1 −0.870382
\(520\) 9262.05 + 8945.30i 0.781092 + 0.754380i
\(521\) 9746.95 0.819619 0.409810 0.912171i \(-0.365595\pi\)
0.409810 + 0.912171i \(0.365595\pi\)
\(522\) 8436.81i 0.707413i
\(523\) −18929.3 −1.58264 −0.791320 0.611402i \(-0.790606\pi\)
−0.791320 + 0.611402i \(0.790606\pi\)
\(524\) −4021.24 −0.335245
\(525\) 2093.54i 0.174037i
\(526\) 11860.9i 0.983195i
\(527\) 33421.2i 2.76252i
\(528\) 349.898i 0.0288397i
\(529\) −6983.00 −0.573929
\(530\) 11424.9 0.936349
\(531\) 2093.83i 0.171119i
\(532\) 3168.30 0.258201
\(533\) −8157.02 + 8445.85i −0.662889 + 0.686361i
\(534\) −7259.20 −0.588270
\(535\) 6164.80i 0.498182i
\(536\) −839.120 −0.0676203
\(537\) −2936.51 −0.235977
\(538\) 21786.6i 1.74589i
\(539\) 1574.09i 0.125790i
\(540\) 4420.07i 0.352240i
\(541\) 11366.8i 0.903321i 0.892190 + 0.451661i \(0.149168\pi\)
−0.892190 + 0.451661i \(0.850832\pi\)
\(542\) −16659.9 −1.32030
\(543\) 11517.3 0.910227
\(544\) 25687.0i 2.02449i
\(545\) 4883.34 0.383815
\(546\) 7694.40 + 7431.26i 0.603095 + 0.582470i
\(547\) 17495.4 1.36755 0.683775 0.729693i \(-0.260337\pi\)
0.683775 + 0.729693i \(0.260337\pi\)
\(548\) 5618.59i 0.437983i
\(549\) −1665.05 −0.129440
\(550\) −4728.72 −0.366606
\(551\) 3079.33i 0.238083i
\(552\) 4595.67i 0.354356i
\(553\) 15610.4i 1.20040i
\(554\) 2839.05i 0.217725i
\(555\) 11386.5 0.870862
\(556\) −9953.06 −0.759180
\(557\) 11873.1i 0.903192i 0.892223 + 0.451596i \(0.149145\pi\)
−0.892223 + 0.451596i \(0.850855\pi\)
\(558\) 10196.5 0.773571
\(559\) −14569.8 14071.6i −1.10239 1.06469i
\(560\) −1010.62 −0.0762613
\(561\) 10031.9i 0.754989i
\(562\) 25170.4 1.88923
\(563\) 2829.31 0.211796 0.105898 0.994377i \(-0.466228\pi\)
0.105898 + 0.994377i \(0.466228\pi\)
\(564\) 6081.60i 0.454045i
\(565\) 171.381i 0.0127612i
\(566\) 796.481i 0.0591495i
\(567\) 1355.04i 0.100364i
\(568\) 19583.9 1.44670
\(569\) −16136.8 −1.18891 −0.594453 0.804130i \(-0.702632\pi\)
−0.594453 + 0.804130i \(0.702632\pi\)
\(570\) 2631.20i 0.193349i
\(571\) 17840.5 1.30754 0.653769 0.756695i \(-0.273187\pi\)
0.653769 + 0.756695i \(0.273187\pi\)
\(572\) −10291.5 + 10655.9i −0.752288 + 0.778926i
\(573\) −1463.13 −0.106672
\(574\) 19056.7i 1.38573i
\(575\) 3003.49 0.217833
\(576\) 7500.00 0.542534
\(577\) 8516.17i 0.614442i 0.951638 + 0.307221i \(0.0993990\pi\)
−0.951638 + 0.307221i \(0.900601\pi\)
\(578\) 59488.9i 4.28099i
\(579\) 12736.8i 0.914205i
\(580\) 33747.3i 2.41600i
\(581\) −18324.5 −1.30848
\(582\) 4947.49 0.352371
\(583\) 4850.53i 0.344577i
\(584\) 11682.3 0.827770
\(585\) −3783.92 + 3917.91i −0.267429 + 0.276899i
\(586\) −35352.9 −2.49218
\(587\) 20688.3i 1.45468i −0.686277 0.727340i \(-0.740756\pi\)
0.686277 0.727340i \(-0.259244\pi\)
\(588\) −2401.82 −0.168451
\(589\) −3721.59 −0.260349
\(590\) 13659.9i 0.953169i
\(591\) 8138.13i 0.566426i
\(592\) 1375.35i 0.0954839i
\(593\) 11435.9i 0.791933i −0.918265 0.395966i \(-0.870410\pi\)
0.918265 0.395966i \(-0.129590\pi\)
\(594\) 3060.65 0.211414
\(595\) 28975.4 1.99643
\(596\) 1716.96i 0.118002i
\(597\) −9350.69 −0.641035
\(598\) 10661.2 11038.7i 0.729047 0.754863i
\(599\) 1260.80 0.0860016 0.0430008 0.999075i \(-0.486308\pi\)
0.0430008 + 0.999075i \(0.486308\pi\)
\(600\) 2662.62i 0.181169i
\(601\) 6261.10 0.424951 0.212476 0.977166i \(-0.431847\pi\)
0.212476 + 0.977166i \(0.431847\pi\)
\(602\) −32874.5 −2.22569
\(603\) 354.954i 0.0239715i
\(604\) 30096.1i 2.02747i
\(605\) 9162.14i 0.615692i
\(606\) 20334.8i 1.36311i
\(607\) 3230.33 0.216005 0.108003 0.994151i \(-0.465555\pi\)
0.108003 + 0.994151i \(0.465555\pi\)
\(608\) −2860.35 −0.190794
\(609\) 10345.7i 0.688391i
\(610\) 10862.6 0.721009
\(611\) −5206.33 + 5390.68i −0.344722 + 0.356929i
\(612\) −15307.2 −1.01104
\(613\) 14868.5i 0.979660i 0.871818 + 0.489830i \(0.162941\pi\)
−0.871818 + 0.489830i \(0.837059\pi\)
\(614\) 36483.0 2.39794
\(615\) −9703.48 −0.636231
\(616\) 8872.57i 0.580334i
\(617\) 19952.8i 1.30190i −0.759121 0.650949i \(-0.774371\pi\)
0.759121 0.650949i \(-0.225629\pi\)
\(618\) 8573.24i 0.558036i
\(619\) 8316.48i 0.540012i −0.962859 0.270006i \(-0.912974\pi\)
0.962859 0.270006i \(-0.0870257\pi\)
\(620\) −40786.0 −2.64194
\(621\) −1944.00 −0.125620
\(622\) 42131.0i 2.71592i
\(623\) 8901.66 0.572452
\(624\) −473.237 457.053i −0.0303600 0.0293217i
\(625\) −19099.2 −1.22235
\(626\) 33757.9i 2.15533i
\(627\) −1117.10 −0.0711525
\(628\) 14792.7 0.939955
\(629\) 39432.6i 2.49965i
\(630\) 8840.13i 0.559046i
\(631\) 12605.9i 0.795299i 0.917537 + 0.397649i \(0.130174\pi\)
−0.917537 + 0.397649i \(0.869826\pi\)
\(632\) 19853.7i 1.24959i
\(633\) −3153.66 −0.198020
\(634\) −12009.8 −0.752321
\(635\) 1884.98i 0.117800i
\(636\) 7401.17 0.461439
\(637\) 2128.95 + 2056.15i 0.132421 + 0.127892i
\(638\) −23368.1 −1.45008
\(639\) 8284.14i 0.512857i
\(640\) −29149.8 −1.80038
\(641\) 9224.04 0.568374 0.284187 0.958769i \(-0.408276\pi\)
0.284187 + 0.958769i \(0.408276\pi\)
\(642\) 6513.51i 0.400417i
\(643\) 4439.16i 0.272260i 0.990691 + 0.136130i \(0.0434665\pi\)
−0.990691 + 0.136130i \(0.956533\pi\)
\(644\) 15271.3i 0.934431i
\(645\) 16739.4i 1.02188i
\(646\) 9112.13 0.554972
\(647\) 9601.15 0.583401 0.291700 0.956510i \(-0.405779\pi\)
0.291700 + 0.956510i \(0.405779\pi\)
\(648\) 1723.38i 0.104476i
\(649\) −5799.44 −0.350767
\(650\) 6176.87 6395.59i 0.372733 0.385932i
\(651\) −12503.6 −0.752770
\(652\) 29277.7i 1.75859i
\(653\) 27112.8 1.62482 0.812410 0.583087i \(-0.198155\pi\)
0.812410 + 0.583087i \(0.198155\pi\)
\(654\) 5159.56 0.308494
\(655\) 4095.15i 0.244291i
\(656\) 1172.06i 0.0697583i
\(657\) 4941.70i 0.293446i
\(658\) 12163.2i 0.720624i
\(659\) 5587.26 0.330271 0.165136 0.986271i \(-0.447194\pi\)
0.165136 + 0.986271i \(0.447194\pi\)
\(660\) −12242.6 −0.722035
\(661\) 3060.13i 0.180069i 0.995939 + 0.0900343i \(0.0286977\pi\)
−0.995939 + 0.0900343i \(0.971302\pi\)
\(662\) −49018.6 −2.87789
\(663\) 13568.2 + 13104.2i 0.794788 + 0.767607i
\(664\) −23305.6 −1.36210
\(665\) 3226.53i 0.188150i
\(666\) 12030.5 0.699961
\(667\) 14842.5 0.861623
\(668\) 7617.26i 0.441199i
\(669\) 16488.4i 0.952880i
\(670\) 2315.68i 0.133526i
\(671\) 4611.83i 0.265332i
\(672\) −9610.04 −0.551660
\(673\) −4121.55 −0.236069 −0.118034 0.993010i \(-0.537659\pi\)
−0.118034 + 0.993010i \(0.537659\pi\)
\(674\) 1425.45i 0.0814633i
\(675\) −1126.31 −0.0642246
\(676\) −968.894 27838.4i −0.0551260 1.58389i
\(677\) 22889.5 1.29943 0.649715 0.760178i \(-0.274888\pi\)
0.649715 + 0.760178i \(0.274888\pi\)
\(678\) 181.075i 0.0102569i
\(679\) −6066.91 −0.342896
\(680\) 36851.8 2.07824
\(681\) 2764.71i 0.155571i
\(682\) 28242.1i 1.58570i
\(683\) 19297.9i 1.08113i 0.841301 + 0.540566i \(0.181790\pi\)
−0.841301 + 0.540566i \(0.818210\pi\)
\(684\) 1704.52i 0.0952835i
\(685\) 5721.87 0.319155
\(686\) 30896.6 1.71959
\(687\) 578.823i 0.0321448i
\(688\) 2021.91 0.112042
\(689\) −6560.34 6335.98i −0.362742 0.350336i
\(690\) 12682.5 0.699729
\(691\) 30317.8i 1.66910i −0.550935 0.834548i \(-0.685729\pi\)
0.550935 0.834548i \(-0.314271\pi\)
\(692\) 43492.8 2.38923
\(693\) −3753.16 −0.205730
\(694\) 12956.6i 0.708682i
\(695\) 10136.0i 0.553210i
\(696\) 13158.0i 0.716599i
\(697\) 33604.3i 1.82619i
\(698\) 29407.7 1.59470
\(699\) −2741.34 −0.148336
\(700\) 8847.84i 0.477738i
\(701\) −9606.16 −0.517574 −0.258787 0.965934i \(-0.583323\pi\)
−0.258787 + 0.965934i \(0.583323\pi\)
\(702\) −3997.96 + 4139.53i −0.214948 + 0.222559i
\(703\) −4390.99 −0.235575
\(704\) 20773.4i 1.11211i
\(705\) −6193.38 −0.330860
\(706\) 12610.4 0.672235
\(707\) 24935.7i 1.32646i
\(708\) 8849.05i 0.469729i
\(709\) 23398.8i 1.23944i 0.784825 + 0.619718i \(0.212753\pi\)
−0.784825 + 0.619718i \(0.787247\pi\)
\(710\) 54044.9i 2.85672i
\(711\) 8398.26 0.442981
\(712\) 11321.4 0.595909
\(713\) 17938.2i 0.942203i
\(714\) 30614.4 1.60464
\(715\) 10851.8 + 10480.6i 0.567598 + 0.548187i
\(716\) 12410.5 0.647766
\(717\) 5930.59i 0.308901i
\(718\) −6671.51 −0.346767
\(719\) 23588.7 1.22352 0.611758 0.791045i \(-0.290463\pi\)
0.611758 + 0.791045i \(0.290463\pi\)
\(720\) 543.704i 0.0281426i
\(721\) 10513.0i 0.543031i
\(722\) 30175.9i 1.55544i
\(723\) 11713.3i 0.602522i
\(724\) −48674.9 −2.49861
\(725\) 8599.38 0.440514
\(726\) 9680.40i 0.494867i
\(727\) −15733.5 −0.802644 −0.401322 0.915937i \(-0.631449\pi\)
−0.401322 + 0.915937i \(0.631449\pi\)
\(728\) −12000.1 11589.7i −0.610926 0.590034i
\(729\) 729.000 0.0370370
\(730\) 32239.2i 1.63455i
\(731\) −57970.3 −2.93312
\(732\) 7036.94 0.355318
\(733\) 17297.1i 0.871598i −0.900044 0.435799i \(-0.856466\pi\)
0.900044 0.435799i \(-0.143534\pi\)
\(734\) 21137.3i 1.06293i
\(735\) 2445.96i 0.122749i
\(736\) 13787.0i 0.690484i
\(737\) −983.144 −0.0491378
\(738\) −10252.4 −0.511375
\(739\) 38749.2i 1.92884i −0.264377 0.964419i \(-0.585166\pi\)
0.264377 0.964419i \(-0.414834\pi\)
\(740\) −48122.2 −2.39055
\(741\) 1459.20 1510.87i 0.0723417 0.0749033i
\(742\) −14802.3 −0.732359
\(743\) 3139.76i 0.155029i −0.996991 0.0775144i \(-0.975302\pi\)
0.996991 0.0775144i \(-0.0246984\pi\)
\(744\) −15902.4 −0.783616
\(745\) −1748.52 −0.0859876
\(746\) 8020.33i 0.393626i
\(747\) 9858.45i 0.482867i
\(748\) 42397.6i 2.07247i
\(749\) 7987.25i 0.389650i
\(750\) −14670.2 −0.714242
\(751\) −40628.6 −1.97411 −0.987055 0.160380i \(-0.948728\pi\)
−0.987055 + 0.160380i \(0.948728\pi\)
\(752\) 748.086i 0.0362764i
\(753\) 2826.11 0.136772
\(754\) 30524.5 31605.4i 1.47432 1.52652i
\(755\) −30649.3 −1.47741
\(756\) 5726.74i 0.275502i
\(757\) 24004.9 1.15254 0.576271 0.817259i \(-0.304507\pi\)
0.576271 + 0.817259i \(0.304507\pi\)
\(758\) −8778.62 −0.420651
\(759\) 5384.46i 0.257501i
\(760\) 4103.60i 0.195859i
\(761\) 29540.1i 1.40713i −0.710630 0.703566i \(-0.751590\pi\)
0.710630 0.703566i \(-0.248410\pi\)
\(762\) 1991.60i 0.0946824i
\(763\) −6326.97 −0.300199
\(764\) 6183.56 0.292818
\(765\) 15588.5i 0.736739i
\(766\) 40225.9 1.89742
\(767\) 7575.49 7843.73i 0.356630 0.369258i
\(768\) −10798.6 −0.507372
\(769\) 7585.63i 0.355715i 0.984056 + 0.177857i \(0.0569166\pi\)
−0.984056 + 0.177857i \(0.943083\pi\)
\(770\) 24485.2 1.14596
\(771\) 2437.85 0.113874
\(772\) 53829.2i 2.50953i
\(773\) 3284.29i 0.152817i 0.997077 + 0.0764086i \(0.0243453\pi\)
−0.997077 + 0.0764086i \(0.975655\pi\)
\(774\) 17686.2i 0.821341i
\(775\) 10393.0i 0.481712i
\(776\) −7716.07 −0.356947
\(777\) −14752.6 −0.681140
\(778\) 7267.08i 0.334881i
\(779\) 3741.98 0.172106
\(780\) 15991.8 16558.1i 0.734103 0.760097i
\(781\) 22945.3 1.05128
\(782\) 43920.8i 2.00845i
\(783\) −5565.92 −0.254036
\(784\) −295.443 −0.0134586
\(785\) 15064.6i 0.684939i
\(786\) 4326.79i