Properties

Label 177.5.b.a.119.11
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.11
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.68

$q$-expansion

\(f(q)\) \(=\) \(q-6.25305i q^{2} +(-4.60229 - 7.73427i) q^{3} -23.1007 q^{4} -36.4421i q^{5} +(-48.3628 + 28.7783i) q^{6} +14.4138 q^{7} +44.4009i q^{8} +(-38.6379 + 71.1907i) q^{9} +O(q^{10})\) \(q-6.25305i q^{2} +(-4.60229 - 7.73427i) q^{3} -23.1007 q^{4} -36.4421i q^{5} +(-48.3628 + 28.7783i) q^{6} +14.4138 q^{7} +44.4009i q^{8} +(-38.6379 + 71.1907i) q^{9} -227.875 q^{10} +167.318i q^{11} +(106.316 + 178.667i) q^{12} -78.8759 q^{13} -90.1305i q^{14} +(-281.853 + 167.717i) q^{15} -91.9695 q^{16} -272.347i q^{17} +(445.159 + 241.605i) q^{18} -177.403 q^{19} +841.838i q^{20} +(-66.3366 - 111.481i) q^{21} +1046.25 q^{22} -272.413i q^{23} +(343.409 - 204.346i) q^{24} -703.030 q^{25} +493.215i q^{26} +(728.431 - 28.8035i) q^{27} -332.969 q^{28} +340.721i q^{29} +(1048.74 + 1762.44i) q^{30} +165.290 q^{31} +1285.51i q^{32} +(1294.08 - 770.044i) q^{33} -1703.00 q^{34} -525.271i q^{35} +(892.562 - 1644.55i) q^{36} +2330.09 q^{37} +1109.31i q^{38} +(363.009 + 610.048i) q^{39} +1618.06 q^{40} -1950.10i q^{41} +(-697.094 + 414.806i) q^{42} -2852.52 q^{43} -3865.15i q^{44} +(2594.34 + 1408.05i) q^{45} -1703.41 q^{46} -455.409i q^{47} +(423.270 + 711.317i) q^{48} -2193.24 q^{49} +4396.09i q^{50} +(-2106.41 + 1253.42i) q^{51} +1822.09 q^{52} -4275.25i q^{53} +(-180.110 - 4554.92i) q^{54} +6097.42 q^{55} +639.988i q^{56} +(816.458 + 1372.08i) q^{57} +2130.55 q^{58} +453.188i q^{59} +(6511.01 - 3874.38i) q^{60} -492.928 q^{61} -1033.56i q^{62} +(-556.921 + 1026.13i) q^{63} +6566.82 q^{64} +2874.41i q^{65} +(-4815.13 - 8091.96i) q^{66} -3713.44 q^{67} +6291.41i q^{68} +(-2106.91 + 1253.72i) q^{69} -3284.55 q^{70} +7643.39i q^{71} +(-3160.93 - 1715.56i) q^{72} -2044.92 q^{73} -14570.2i q^{74} +(3235.55 + 5437.43i) q^{75} +4098.12 q^{76} +2411.69i q^{77} +(3814.66 - 2269.92i) q^{78} -9053.34 q^{79} +3351.57i q^{80} +(-3575.22 - 5501.32i) q^{81} -12194.1 q^{82} +3263.38i q^{83} +(1532.42 + 2575.28i) q^{84} -9924.93 q^{85} +17837.0i q^{86} +(2635.23 - 1568.10i) q^{87} -7429.06 q^{88} +6547.57i q^{89} +(8804.61 - 16222.6i) q^{90} -1136.90 q^{91} +6292.92i q^{92} +(-760.710 - 1278.40i) q^{93} -2847.70 q^{94} +6464.93i q^{95} +(9942.45 - 5916.26i) q^{96} +11735.6 q^{97} +13714.5i q^{98} +(-11911.5 - 6464.81i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.25305i 1.56326i −0.623740 0.781632i \(-0.714388\pi\)
0.623740 0.781632i \(-0.285612\pi\)
\(3\) −4.60229 7.73427i −0.511365 0.859364i
\(4\) −23.1007 −1.44379
\(5\) 36.4421i 1.45769i −0.684681 0.728843i \(-0.740058\pi\)
0.684681 0.728843i \(-0.259942\pi\)
\(6\) −48.3628 + 28.7783i −1.34341 + 0.799398i
\(7\) 14.4138 0.294160 0.147080 0.989125i \(-0.453013\pi\)
0.147080 + 0.989125i \(0.453013\pi\)
\(8\) 44.4009i 0.693764i
\(9\) −38.6379 + 71.1907i −0.477012 + 0.878897i
\(10\) −227.875 −2.27875
\(11\) 167.318i 1.38279i 0.722476 + 0.691396i \(0.243004\pi\)
−0.722476 + 0.691396i \(0.756996\pi\)
\(12\) 106.316 + 178.667i 0.738305 + 1.24074i
\(13\) −78.8759 −0.466721 −0.233361 0.972390i \(-0.574972\pi\)
−0.233361 + 0.972390i \(0.574972\pi\)
\(14\) 90.1305i 0.459850i
\(15\) −281.853 + 167.717i −1.25268 + 0.745410i
\(16\) −91.9695 −0.359256
\(17\) 272.347i 0.942379i −0.882032 0.471189i \(-0.843825\pi\)
0.882032 0.471189i \(-0.156175\pi\)
\(18\) 445.159 + 241.605i 1.37395 + 0.745695i
\(19\) −177.403 −0.491420 −0.245710 0.969343i \(-0.579021\pi\)
−0.245710 + 0.969343i \(0.579021\pi\)
\(20\) 841.838i 2.10460i
\(21\) −66.3366 111.481i −0.150423 0.252790i
\(22\) 1046.25 2.16167
\(23\) 272.413i 0.514958i −0.966284 0.257479i \(-0.917108\pi\)
0.966284 0.257479i \(-0.0828918\pi\)
\(24\) 343.409 204.346i 0.596196 0.354767i
\(25\) −703.030 −1.12485
\(26\) 493.215i 0.729608i
\(27\) 728.431 28.8035i 0.999219 0.0395109i
\(28\) −332.969 −0.424706
\(29\) 340.721i 0.405138i 0.979268 + 0.202569i \(0.0649290\pi\)
−0.979268 + 0.202569i \(0.935071\pi\)
\(30\) 1048.74 + 1762.44i 1.16527 + 1.95827i
\(31\) 165.290 0.171998 0.0859988 0.996295i \(-0.472592\pi\)
0.0859988 + 0.996295i \(0.472592\pi\)
\(32\) 1285.51i 1.25538i
\(33\) 1294.08 770.044i 1.18832 0.707111i
\(34\) −1703.00 −1.47319
\(35\) 525.271i 0.428793i
\(36\) 892.562 1644.55i 0.688706 1.26894i
\(37\) 2330.09 1.70204 0.851018 0.525136i \(-0.175986\pi\)
0.851018 + 0.525136i \(0.175986\pi\)
\(38\) 1109.31i 0.768219i
\(39\) 363.009 + 610.048i 0.238665 + 0.401083i
\(40\) 1618.06 1.01129
\(41\) 1950.10i 1.16008i −0.814587 0.580042i \(-0.803036\pi\)
0.814587 0.580042i \(-0.196964\pi\)
\(42\) −697.094 + 414.806i −0.395178 + 0.235151i
\(43\) −2852.52 −1.54274 −0.771369 0.636388i \(-0.780428\pi\)
−0.771369 + 0.636388i \(0.780428\pi\)
\(44\) 3865.15i 1.99646i
\(45\) 2594.34 + 1408.05i 1.28116 + 0.695333i
\(46\) −1703.41 −0.805015
\(47\) 455.409i 0.206161i −0.994673 0.103080i \(-0.967130\pi\)
0.994673 0.103080i \(-0.0328699\pi\)
\(48\) 423.270 + 711.317i 0.183711 + 0.308731i
\(49\) −2193.24 −0.913470
\(50\) 4396.09i 1.75843i
\(51\) −2106.41 + 1253.42i −0.809846 + 0.481900i
\(52\) 1822.09 0.673848
\(53\) 4275.25i 1.52198i −0.648761 0.760992i \(-0.724713\pi\)
0.648761 0.760992i \(-0.275287\pi\)
\(54\) −180.110 4554.92i −0.0617660 1.56204i
\(55\) 6097.42 2.01568
\(56\) 639.988i 0.204078i
\(57\) 816.458 + 1372.08i 0.251295 + 0.422308i
\(58\) 2130.55 0.633337
\(59\) 453.188i 0.130189i
\(60\) 6511.01 3874.38i 1.80861 1.07622i
\(61\) −492.928 −0.132472 −0.0662359 0.997804i \(-0.521099\pi\)
−0.0662359 + 0.997804i \(0.521099\pi\)
\(62\) 1033.56i 0.268877i
\(63\) −556.921 + 1026.13i −0.140318 + 0.258536i
\(64\) 6566.82 1.60323
\(65\) 2874.41i 0.680333i
\(66\) −4815.13 8091.96i −1.10540 1.85766i
\(67\) −3713.44 −0.827231 −0.413616 0.910452i \(-0.635734\pi\)
−0.413616 + 0.910452i \(0.635734\pi\)
\(68\) 6291.41i 1.36060i
\(69\) −2106.91 + 1253.72i −0.442536 + 0.263332i
\(70\) −3284.55 −0.670316
\(71\) 7643.39i 1.51624i 0.652112 + 0.758122i \(0.273883\pi\)
−0.652112 + 0.758122i \(0.726117\pi\)
\(72\) −3160.93 1715.56i −0.609747 0.330934i
\(73\) −2044.92 −0.383735 −0.191867 0.981421i \(-0.561454\pi\)
−0.191867 + 0.981421i \(0.561454\pi\)
\(74\) 14570.2i 2.66073i
\(75\) 3235.55 + 5437.43i 0.575208 + 0.966654i
\(76\) 4098.12 0.709509
\(77\) 2411.69i 0.406762i
\(78\) 3814.66 2269.92i 0.626999 0.373096i
\(79\) −9053.34 −1.45062 −0.725312 0.688421i \(-0.758304\pi\)
−0.725312 + 0.688421i \(0.758304\pi\)
\(80\) 3351.57i 0.523682i
\(81\) −3575.22 5501.32i −0.544920 0.838488i
\(82\) −12194.1 −1.81352
\(83\) 3263.38i 0.473709i 0.971545 + 0.236854i \(0.0761164\pi\)
−0.971545 + 0.236854i \(0.923884\pi\)
\(84\) 1532.42 + 2575.28i 0.217180 + 0.364977i
\(85\) −9924.93 −1.37369
\(86\) 17837.0i 2.41171i
\(87\) 2635.23 1568.10i 0.348161 0.207173i
\(88\) −7429.06 −0.959331
\(89\) 6547.57i 0.826609i 0.910593 + 0.413304i \(0.135625\pi\)
−0.910593 + 0.413304i \(0.864375\pi\)
\(90\) 8804.61 16222.6i 1.08699 2.00278i
\(91\) −1136.90 −0.137291
\(92\) 6292.92i 0.743492i
\(93\) −760.710 1278.40i −0.0879535 0.147808i
\(94\) −2847.70 −0.322283
\(95\) 6464.93i 0.716336i
\(96\) 9942.45 5916.26i 1.07882 0.641955i
\(97\) 11735.6 1.24728 0.623639 0.781713i \(-0.285654\pi\)
0.623639 + 0.781713i \(0.285654\pi\)
\(98\) 13714.5i 1.42799i
\(99\) −11911.5 6464.81i −1.21533 0.659607i
\(100\) 16240.5 1.62405
\(101\) 15311.1i 1.50095i 0.660902 + 0.750473i \(0.270174\pi\)
−0.660902 + 0.750473i \(0.729826\pi\)
\(102\) 7837.71 + 13171.5i 0.753336 + 1.26600i
\(103\) 5975.99 0.563294 0.281647 0.959518i \(-0.409119\pi\)
0.281647 + 0.959518i \(0.409119\pi\)
\(104\) 3502.16i 0.323795i
\(105\) −4062.59 + 2417.45i −0.368489 + 0.219270i
\(106\) −26733.4 −2.37926
\(107\) 2861.36i 0.249923i −0.992162 0.124961i \(-0.960119\pi\)
0.992162 0.124961i \(-0.0398807\pi\)
\(108\) −16827.2 + 665.379i −1.44266 + 0.0570456i
\(109\) −10296.8 −0.866663 −0.433331 0.901235i \(-0.642662\pi\)
−0.433331 + 0.901235i \(0.642662\pi\)
\(110\) 38127.5i 3.15103i
\(111\) −10723.7 18021.5i −0.870362 1.46267i
\(112\) −1325.63 −0.105679
\(113\) 4167.98i 0.326414i −0.986592 0.163207i \(-0.947816\pi\)
0.986592 0.163207i \(-0.0521838\pi\)
\(114\) 8579.69 5105.35i 0.660179 0.392840i
\(115\) −9927.31 −0.750647
\(116\) 7870.89i 0.584935i
\(117\) 3047.60 5615.23i 0.222631 0.410200i
\(118\) 2833.81 0.203520
\(119\) 3925.57i 0.277210i
\(120\) −7446.80 12514.6i −0.517139 0.869066i
\(121\) −13354.2 −0.912112
\(122\) 3082.30i 0.207088i
\(123\) −15082.6 + 8974.92i −0.996933 + 0.593226i
\(124\) −3818.30 −0.248329
\(125\) 2843.59i 0.181990i
\(126\) 6416.45 + 3482.46i 0.404160 + 0.219354i
\(127\) −5496.44 −0.340780 −0.170390 0.985377i \(-0.554503\pi\)
−0.170390 + 0.985377i \(0.554503\pi\)
\(128\) 20494.6i 1.25089i
\(129\) 13128.1 + 22062.2i 0.788902 + 1.32577i
\(130\) 17973.8 1.06354
\(131\) 11680.7i 0.680653i −0.940307 0.340327i \(-0.889462\pi\)
0.940307 0.340327i \(-0.110538\pi\)
\(132\) −29894.1 + 17788.5i −1.71569 + 1.02092i
\(133\) −2557.05 −0.144556
\(134\) 23220.3i 1.29318i
\(135\) −1049.66 26545.6i −0.0575945 1.45655i
\(136\) 12092.5 0.653789
\(137\) 17084.5i 0.910250i −0.890428 0.455125i \(-0.849595\pi\)
0.890428 0.455125i \(-0.150405\pi\)
\(138\) 7839.59 + 13174.6i 0.411657 + 0.691801i
\(139\) 16865.0 0.872887 0.436443 0.899732i \(-0.356238\pi\)
0.436443 + 0.899732i \(0.356238\pi\)
\(140\) 12134.1i 0.619088i
\(141\) −3522.26 + 2095.92i −0.177167 + 0.105423i
\(142\) 47794.5 2.37029
\(143\) 13197.3i 0.645378i
\(144\) 3553.51 6547.37i 0.171369 0.315749i
\(145\) 12416.6 0.590564
\(146\) 12787.0i 0.599878i
\(147\) 10093.9 + 16963.1i 0.467117 + 0.785003i
\(148\) −53826.6 −2.45739
\(149\) 43570.1i 1.96253i −0.192662 0.981265i \(-0.561712\pi\)
0.192662 0.981265i \(-0.438288\pi\)
\(150\) 34000.5 20232.0i 1.51113 0.899202i
\(151\) 11807.7 0.517860 0.258930 0.965896i \(-0.416630\pi\)
0.258930 + 0.965896i \(0.416630\pi\)
\(152\) 7876.84i 0.340930i
\(153\) 19388.6 + 10522.9i 0.828254 + 0.449525i
\(154\) 15080.4 0.635876
\(155\) 6023.51i 0.250718i
\(156\) −8385.76 14092.5i −0.344583 0.579081i
\(157\) −39145.2 −1.58810 −0.794052 0.607850i \(-0.792032\pi\)
−0.794052 + 0.607850i \(0.792032\pi\)
\(158\) 56611.0i 2.26771i
\(159\) −33066.0 + 19675.9i −1.30794 + 0.778289i
\(160\) 46846.6 1.82994
\(161\) 3926.51i 0.151480i
\(162\) −34400.0 + 22356.0i −1.31078 + 0.851853i
\(163\) 42110.0 1.58493 0.792465 0.609917i \(-0.208797\pi\)
0.792465 + 0.609917i \(0.208797\pi\)
\(164\) 45048.6i 1.67492i
\(165\) −28062.1 47159.1i −1.03075 1.73220i
\(166\) 20406.1 0.740532
\(167\) 51642.8i 1.85173i 0.377860 + 0.925863i \(0.376660\pi\)
−0.377860 + 0.925863i \(0.623340\pi\)
\(168\) 4949.84 2945.41i 0.175377 0.104358i
\(169\) −22339.6 −0.782171
\(170\) 62061.1i 2.14744i
\(171\) 6854.47 12629.4i 0.234413 0.431908i
\(172\) 65895.2 2.22739
\(173\) 13701.7i 0.457807i −0.973449 0.228903i \(-0.926486\pi\)
0.973449 0.228903i \(-0.0735140\pi\)
\(174\) −9805.38 16478.2i −0.323867 0.544267i
\(175\) −10133.4 −0.330885
\(176\) 15388.1i 0.496776i
\(177\) 3505.08 2085.70i 0.111880 0.0665741i
\(178\) 40942.3 1.29221
\(179\) 20812.2i 0.649549i −0.945791 0.324774i \(-0.894712\pi\)
0.945791 0.324774i \(-0.105288\pi\)
\(180\) −59931.0 32526.9i −1.84972 1.00392i
\(181\) −32800.3 −1.00120 −0.500600 0.865679i \(-0.666887\pi\)
−0.500600 + 0.865679i \(0.666887\pi\)
\(182\) 7109.12i 0.214622i
\(183\) 2268.60 + 3812.44i 0.0677415 + 0.113842i
\(184\) 12095.4 0.357259
\(185\) 84913.4i 2.48104i
\(186\) −7993.87 + 4756.76i −0.231063 + 0.137495i
\(187\) 45568.6 1.30311
\(188\) 10520.3i 0.297653i
\(189\) 10499.5 415.168i 0.293930 0.0116225i
\(190\) 40425.6 1.11982
\(191\) 1293.80i 0.0354651i 0.999843 + 0.0177326i \(0.00564475\pi\)
−0.999843 + 0.0177326i \(0.994355\pi\)
\(192\) −30222.4 50789.6i −0.819835 1.37776i
\(193\) −55244.0 −1.48310 −0.741550 0.670898i \(-0.765909\pi\)
−0.741550 + 0.670898i \(0.765909\pi\)
\(194\) 73383.6i 1.94982i
\(195\) 22231.4 13228.8i 0.584653 0.347898i
\(196\) 50665.4 1.31886
\(197\) 56388.7i 1.45298i 0.687177 + 0.726490i \(0.258850\pi\)
−0.687177 + 0.726490i \(0.741150\pi\)
\(198\) −40424.8 + 74483.0i −1.03114 + 1.89988i
\(199\) 9051.91 0.228578 0.114289 0.993448i \(-0.463541\pi\)
0.114289 + 0.993448i \(0.463541\pi\)
\(200\) 31215.2i 0.780380i
\(201\) 17090.3 + 28720.8i 0.423017 + 0.710892i
\(202\) 95741.4 2.34637
\(203\) 4911.10i 0.119175i
\(204\) 48659.5 28954.9i 1.16925 0.695763i
\(205\) −71065.8 −1.69104
\(206\) 37368.2i 0.880577i
\(207\) 19393.2 + 10525.5i 0.452595 + 0.245641i
\(208\) 7254.18 0.167672
\(209\) 29682.6i 0.679531i
\(210\) 15116.4 + 25403.6i 0.342776 + 0.576045i
\(211\) −4619.34 −0.103756 −0.0518782 0.998653i \(-0.516521\pi\)
−0.0518782 + 0.998653i \(0.516521\pi\)
\(212\) 98761.2i 2.19743i
\(213\) 59116.1 35177.1i 1.30301 0.775355i
\(214\) −17892.3 −0.390695
\(215\) 103952.i 2.24883i
\(216\) 1278.90 + 32343.0i 0.0274113 + 0.693223i
\(217\) 2382.46 0.0505948
\(218\) 64386.6i 1.35482i
\(219\) 9411.31 + 15816.0i 0.196228 + 0.329768i
\(220\) −140854. −2.91022
\(221\) 21481.6i 0.439828i
\(222\) −112690. + 67056.1i −2.28654 + 1.36061i
\(223\) −8847.56 −0.177916 −0.0889578 0.996035i \(-0.528354\pi\)
−0.0889578 + 0.996035i \(0.528354\pi\)
\(224\) 18529.1i 0.369281i
\(225\) 27163.6 50049.2i 0.536566 0.988626i
\(226\) −26062.6 −0.510271
\(227\) 46243.0i 0.897417i −0.893678 0.448709i \(-0.851884\pi\)
0.893678 0.448709i \(-0.148116\pi\)
\(228\) −18860.7 31696.0i −0.362818 0.609726i
\(229\) 68889.8 1.31366 0.656832 0.754037i \(-0.271896\pi\)
0.656832 + 0.754037i \(0.271896\pi\)
\(230\) 62076.0i 1.17346i
\(231\) 18652.7 11099.3i 0.349556 0.208004i
\(232\) −15128.3 −0.281070
\(233\) 44615.8i 0.821820i 0.911676 + 0.410910i \(0.134789\pi\)
−0.911676 + 0.410910i \(0.865211\pi\)
\(234\) −35112.3 19056.8i −0.641250 0.348031i
\(235\) −16596.1 −0.300518
\(236\) 10468.9i 0.187966i
\(237\) 41666.1 + 70021.0i 0.741798 + 1.24661i
\(238\) −24546.8 −0.433352
\(239\) 2705.84i 0.0473703i 0.999719 + 0.0236852i \(0.00753992\pi\)
−0.999719 + 0.0236852i \(0.992460\pi\)
\(240\) 25921.9 15424.9i 0.450034 0.267793i
\(241\) −70711.2 −1.21746 −0.608729 0.793378i \(-0.708320\pi\)
−0.608729 + 0.793378i \(0.708320\pi\)
\(242\) 83504.7i 1.42587i
\(243\) −26094.5 + 52970.4i −0.441913 + 0.897058i
\(244\) 11387.0 0.191262
\(245\) 79926.4i 1.33155i
\(246\) 56120.6 + 94312.3i 0.927368 + 1.55847i
\(247\) 13992.8 0.229356
\(248\) 7339.01i 0.119326i
\(249\) 25239.9 15019.0i 0.407088 0.242238i
\(250\) 17781.1 0.284498
\(251\) 110496.i 1.75388i −0.480603 0.876938i \(-0.659582\pi\)
0.480603 0.876938i \(-0.340418\pi\)
\(252\) 12865.3 23704.3i 0.202590 0.373273i
\(253\) 45579.5 0.712079
\(254\) 34369.5i 0.532728i
\(255\) 45677.3 + 76762.1i 0.702458 + 1.18050i
\(256\) −23084.7 −0.352244
\(257\) 99487.8i 1.50627i −0.657864 0.753136i \(-0.728540\pi\)
0.657864 0.753136i \(-0.271460\pi\)
\(258\) 137956. 82090.8i 2.07253 1.23326i
\(259\) 33585.5 0.500671
\(260\) 66400.7i 0.982259i
\(261\) −24256.2 13164.8i −0.356075 0.193255i
\(262\) −73040.0 −1.06404
\(263\) 130318.i 1.88405i −0.335536 0.942027i \(-0.608918\pi\)
0.335536 0.942027i \(-0.391082\pi\)
\(264\) 34190.7 + 57458.4i 0.490569 + 0.824414i
\(265\) −155799. −2.21857
\(266\) 15989.4i 0.225979i
\(267\) 50640.7 30133.8i 0.710358 0.422699i
\(268\) 85783.0 1.19435
\(269\) 5034.64i 0.0695768i −0.999395 0.0347884i \(-0.988924\pi\)
0.999395 0.0347884i \(-0.0110757\pi\)
\(270\) −165991. + 6563.58i −2.27697 + 0.0900354i
\(271\) −78323.1 −1.06648 −0.533238 0.845965i \(-0.679025\pi\)
−0.533238 + 0.845965i \(0.679025\pi\)
\(272\) 25047.7i 0.338555i
\(273\) 5232.36 + 8793.13i 0.0702057 + 0.117983i
\(274\) −106830. −1.42296
\(275\) 117629.i 1.55543i
\(276\) 48671.2 28961.8i 0.638930 0.380196i
\(277\) −89690.5 −1.16893 −0.584463 0.811421i \(-0.698695\pi\)
−0.584463 + 0.811421i \(0.698695\pi\)
\(278\) 105458.i 1.36455i
\(279\) −6386.45 + 11767.1i −0.0820448 + 0.151168i
\(280\) 23322.5 0.297481
\(281\) 7922.50i 0.100334i −0.998741 0.0501672i \(-0.984025\pi\)
0.998741 0.0501672i \(-0.0159754\pi\)
\(282\) 13105.9 + 22024.9i 0.164805 + 0.276959i
\(283\) 61789.8 0.771514 0.385757 0.922600i \(-0.373940\pi\)
0.385757 + 0.922600i \(0.373940\pi\)
\(284\) 176567.i 2.18914i
\(285\) 50001.6 29753.5i 0.615593 0.366309i
\(286\) −82523.6 −1.00890
\(287\) 28108.4i 0.341250i
\(288\) −91516.0 49669.3i −1.10335 0.598829i
\(289\) 9347.88 0.111923
\(290\) 77641.7i 0.923207i
\(291\) −54010.8 90766.6i −0.637814 1.07187i
\(292\) 47239.1 0.554033
\(293\) 122115.i 1.42244i −0.702970 0.711220i \(-0.748143\pi\)
0.702970 0.711220i \(-0.251857\pi\)
\(294\) 106071. 63117.8i 1.22717 0.730226i
\(295\) 16515.1 0.189775
\(296\) 103458.i 1.18081i
\(297\) 4819.33 + 121879.i 0.0546353 + 1.38171i
\(298\) −272446. −3.06795
\(299\) 21486.8i 0.240342i
\(300\) −74743.3 125608.i −0.830481 1.39565i
\(301\) −41115.8 −0.453812
\(302\) 73834.4i 0.809552i
\(303\) 118421. 70466.2i 1.28986 0.767531i
\(304\) 16315.6 0.176546
\(305\) 17963.4i 0.193102i
\(306\) 65800.5 121238.i 0.702727 1.29478i
\(307\) 28408.8 0.301423 0.150712 0.988578i \(-0.451844\pi\)
0.150712 + 0.988578i \(0.451844\pi\)
\(308\) 55711.7i 0.587280i
\(309\) −27503.2 46219.9i −0.288049 0.484074i
\(310\) −37665.3 −0.391939
\(311\) 86931.4i 0.898786i −0.893334 0.449393i \(-0.851640\pi\)
0.893334 0.449393i \(-0.148360\pi\)
\(312\) −27086.7 + 16117.9i −0.278257 + 0.165577i
\(313\) −76544.3 −0.781311 −0.390656 0.920537i \(-0.627752\pi\)
−0.390656 + 0.920537i \(0.627752\pi\)
\(314\) 244777.i 2.48262i
\(315\) 37394.4 + 20295.4i 0.376865 + 0.204539i
\(316\) 209138. 2.09440
\(317\) 99325.7i 0.988424i 0.869341 + 0.494212i \(0.164543\pi\)
−0.869341 + 0.494212i \(0.835457\pi\)
\(318\) 123035. + 206763.i 1.21667 + 2.04465i
\(319\) −57008.7 −0.560221
\(320\) 239309.i 2.33700i
\(321\) −22130.6 + 13168.8i −0.214774 + 0.127802i
\(322\) −24552.7 −0.236803
\(323\) 48315.2i 0.463104i
\(324\) 82590.0 + 127084.i 0.786751 + 1.21060i
\(325\) 55452.1 0.524991
\(326\) 263316.i 2.47766i
\(327\) 47388.9 + 79638.4i 0.443181 + 0.744779i
\(328\) 86586.2 0.804824
\(329\) 6564.19i 0.0606442i
\(330\) −294888. + 175474.i −2.70788 + 1.61133i
\(331\) −60947.0 −0.556283 −0.278142 0.960540i \(-0.589718\pi\)
−0.278142 + 0.960540i \(0.589718\pi\)
\(332\) 75386.3i 0.683937i
\(333\) −90029.8 + 165881.i −0.811891 + 1.49592i
\(334\) 322925. 2.89474
\(335\) 135326.i 1.20584i
\(336\) 6100.95 + 10252.8i 0.0540404 + 0.0908165i
\(337\) 11894.5 0.104733 0.0523667 0.998628i \(-0.483324\pi\)
0.0523667 + 0.998628i \(0.483324\pi\)
\(338\) 139691.i 1.22274i
\(339\) −32236.3 + 19182.2i −0.280508 + 0.166917i
\(340\) 229273. 1.98333
\(341\) 27655.9i 0.237837i
\(342\) −78972.4 42861.4i −0.675185 0.366449i
\(343\) −66220.7 −0.562866
\(344\) 126655.i 1.07030i
\(345\) 45688.3 + 76780.5i 0.383855 + 0.645079i
\(346\) −85677.5 −0.715673
\(347\) 127509.i 1.05897i −0.848320 0.529484i \(-0.822385\pi\)
0.848320 0.529484i \(-0.177615\pi\)
\(348\) −60875.6 + 36224.1i −0.502672 + 0.299115i
\(349\) 103272. 0.847871 0.423936 0.905692i \(-0.360648\pi\)
0.423936 + 0.905692i \(0.360648\pi\)
\(350\) 63364.5i 0.517261i
\(351\) −57455.6 + 2271.90i −0.466357 + 0.0184406i
\(352\) −215088. −1.73592
\(353\) 50118.6i 0.402207i −0.979570 0.201103i \(-0.935547\pi\)
0.979570 0.201103i \(-0.0644527\pi\)
\(354\) −13042.0 21917.4i −0.104073 0.174897i
\(355\) 278542. 2.21021
\(356\) 151253.i 1.19345i
\(357\) −30361.4 + 18066.6i −0.238224 + 0.141756i
\(358\) −130140. −1.01542
\(359\) 177386.i 1.37636i 0.725541 + 0.688179i \(0.241590\pi\)
−0.725541 + 0.688179i \(0.758410\pi\)
\(360\) −62518.7 + 115191.i −0.482397 + 0.888820i
\(361\) −98849.3 −0.758506
\(362\) 205102.i 1.56514i
\(363\) 61460.0 + 103285.i 0.466422 + 0.783836i
\(364\) 26263.3 0.198219
\(365\) 74521.3i 0.559365i
\(366\) 23839.4 14185.6i 0.177964 0.105898i
\(367\) 236899. 1.75886 0.879428 0.476031i \(-0.157925\pi\)
0.879428 + 0.476031i \(0.157925\pi\)
\(368\) 25053.7i 0.185002i
\(369\) 138829. + 75347.8i 1.01959 + 0.553373i
\(370\) −530968. −3.87851
\(371\) 61622.8i 0.447707i
\(372\) 17572.9 + 29531.8i 0.126987 + 0.213405i
\(373\) −255567. −1.83691 −0.918454 0.395527i \(-0.870562\pi\)
−0.918454 + 0.395527i \(0.870562\pi\)
\(374\) 284943.i 2.03711i
\(375\) 21993.1 13087.0i 0.156395 0.0930631i
\(376\) 20220.6 0.143027
\(377\) 26874.7i 0.189086i
\(378\) −2596.07 65653.8i −0.0181691 0.459490i
\(379\) 31719.6 0.220826 0.110413 0.993886i \(-0.464783\pi\)
0.110413 + 0.993886i \(0.464783\pi\)
\(380\) 149344.i 1.03424i
\(381\) 25296.2 + 42510.9i 0.174263 + 0.292854i
\(382\) 8090.23 0.0554414
\(383\) 23091.9i 0.157421i −0.996898 0.0787105i \(-0.974920\pi\)
0.996898 0.0787105i \(-0.0250803\pi\)
\(384\) −158511. + 94322.0i −1.07497 + 0.639662i
\(385\) 87887.2 0.592931
\(386\) 345444.i 2.31848i
\(387\) 110216. 203073.i 0.735904 1.35591i
\(388\) −271101. −1.80081
\(389\) 227541.i 1.50370i −0.659336 0.751848i \(-0.729163\pi\)
0.659336 0.751848i \(-0.270837\pi\)
\(390\) −82720.6 139014.i −0.543857 0.913967i
\(391\) −74190.9 −0.485285
\(392\) 97381.9i 0.633733i
\(393\) −90341.6 + 53757.9i −0.584929 + 0.348062i
\(394\) 352602. 2.27139
\(395\) 329923.i 2.11455i
\(396\) 275163. + 149342.i 1.75469 + 0.952336i
\(397\) 67250.0 0.426689 0.213344 0.976977i \(-0.431564\pi\)
0.213344 + 0.976977i \(0.431564\pi\)
\(398\) 56602.1i 0.357327i
\(399\) 11768.3 + 19776.9i 0.0739210 + 0.124226i
\(400\) 64657.4 0.404108
\(401\) 273508.i 1.70091i 0.526048 + 0.850455i \(0.323673\pi\)
−0.526048 + 0.850455i \(0.676327\pi\)
\(402\) 179592. 106867.i 1.11131 0.661287i
\(403\) −13037.4 −0.0802749
\(404\) 353698.i 2.16705i
\(405\) −200480. + 130289.i −1.22225 + 0.794322i
\(406\) 30709.4 0.186303
\(407\) 389865.i 2.35356i
\(408\) −55653.0 93526.5i −0.334325 0.561842i
\(409\) −124970. −0.747069 −0.373534 0.927616i \(-0.621854\pi\)
−0.373534 + 0.927616i \(0.621854\pi\)
\(410\) 444378.i 2.64354i
\(411\) −132136. + 78627.7i −0.782236 + 0.465470i
\(412\) −138049. −0.813280
\(413\) 6532.17i 0.0382964i
\(414\) 65816.3 121267.i 0.384001 0.707525i
\(415\) 118925. 0.690519
\(416\) 101395.i 0.585911i
\(417\) −77617.8 130439.i −0.446364 0.750127i
\(418\) −185607. −1.06229
\(419\) 55609.2i 0.316751i 0.987379 + 0.158376i \(0.0506257\pi\)
−0.987379 + 0.158376i \(0.949374\pi\)
\(420\) 93848.6 55844.7i 0.532022 0.316580i
\(421\) 117171. 0.661086 0.330543 0.943791i \(-0.392768\pi\)
0.330543 + 0.943791i \(0.392768\pi\)
\(422\) 28885.0i 0.162199i
\(423\) 32420.9 + 17596.1i 0.181194 + 0.0983410i
\(424\) 189825. 1.05590
\(425\) 191468.i 1.06003i
\(426\) −219964. 369656.i −1.21208 2.03694i
\(427\) −7104.98 −0.0389679
\(428\) 66099.5i 0.360836i
\(429\) −102072. + 60737.9i −0.554614 + 0.330024i
\(430\) 650018. 3.51551
\(431\) 214459.i 1.15449i −0.816572 0.577244i \(-0.804128\pi\)
0.816572 0.577244i \(-0.195872\pi\)
\(432\) −66993.4 + 2649.04i −0.358975 + 0.0141945i
\(433\) −267726. −1.42795 −0.713977 0.700169i \(-0.753108\pi\)
−0.713977 + 0.700169i \(0.753108\pi\)
\(434\) 14897.6i 0.0790930i
\(435\) −57144.8 96033.4i −0.301994 0.507509i
\(436\) 237864. 1.25128
\(437\) 48326.7i 0.253061i
\(438\) 98898.2 58849.5i 0.515514 0.306757i
\(439\) 89658.4 0.465224 0.232612 0.972570i \(-0.425273\pi\)
0.232612 + 0.972570i \(0.425273\pi\)
\(440\) 270731.i 1.39840i
\(441\) 84742.3 156138.i 0.435736 0.802846i
\(442\) 134326. 0.687567
\(443\) 202713.i 1.03294i −0.856307 0.516468i \(-0.827247\pi\)
0.856307 0.516468i \(-0.172753\pi\)
\(444\) 247725. + 416310.i 1.25662 + 2.11179i
\(445\) 238607. 1.20494
\(446\) 55324.3i 0.278129i
\(447\) −336983. + 200522.i −1.68653 + 1.00357i
\(448\) 94653.1 0.471605
\(449\) 344509.i 1.70886i 0.519563 + 0.854432i \(0.326095\pi\)
−0.519563 + 0.854432i \(0.673905\pi\)
\(450\) −312960. 169856.i −1.54548 0.838793i
\(451\) 326286. 1.60415
\(452\) 96283.1i 0.471274i
\(453\) −54342.6 91324.2i −0.264816 0.445030i
\(454\) −289160. −1.40290
\(455\) 41431.2i 0.200127i
\(456\) −60921.6 + 36251.5i −0.292983 + 0.174340i
\(457\) −53061.8 −0.254068 −0.127034 0.991898i \(-0.540546\pi\)
−0.127034 + 0.991898i \(0.540546\pi\)
\(458\) 430772.i 2.05360i
\(459\) −7844.55 198386.i −0.0372342 0.941643i
\(460\) 229328. 1.08378
\(461\) 49500.4i 0.232920i 0.993195 + 0.116460i \(0.0371547\pi\)
−0.993195 + 0.116460i \(0.962845\pi\)
\(462\) −69404.5 116636.i −0.325165 0.546449i
\(463\) −333434. −1.55542 −0.777711 0.628622i \(-0.783619\pi\)
−0.777711 + 0.628622i \(0.783619\pi\)
\(464\) 31336.0i 0.145548i
\(465\) −46587.5 + 27721.9i −0.215458 + 0.128209i
\(466\) 278985. 1.28472
\(467\) 69025.7i 0.316502i −0.987399 0.158251i \(-0.949414\pi\)
0.987399 0.158251i \(-0.0505856\pi\)
\(468\) −70401.7 + 129716.i −0.321434 + 0.592243i
\(469\) −53524.9 −0.243338
\(470\) 103776.i 0.469788i
\(471\) 180157. + 302759.i 0.812100 + 1.36476i
\(472\) −20121.9 −0.0903204
\(473\) 477278.i 2.13328i
\(474\) 437845. 260540.i 1.94878 1.15963i
\(475\) 124719. 0.552773
\(476\) 90683.4i 0.400234i
\(477\) 304358. + 165187.i 1.33767 + 0.726004i
\(478\) 16919.8 0.0740523
\(479\) 179644.i 0.782965i 0.920186 + 0.391482i \(0.128038\pi\)
−0.920186 + 0.391482i \(0.871962\pi\)
\(480\) −215601. 362324.i −0.935769 1.57259i
\(481\) −183788. −0.794377
\(482\) 442161.i 1.90321i
\(483\) −30368.7 + 18070.9i −0.130176 + 0.0774616i
\(484\) 308492. 1.31690
\(485\) 427672.i 1.81814i
\(486\) 331227. + 163170.i 1.40234 + 0.690826i
\(487\) −174642. −0.736361 −0.368180 0.929754i \(-0.620019\pi\)
−0.368180 + 0.929754i \(0.620019\pi\)
\(488\) 21886.5i 0.0919043i
\(489\) −193802. 325690.i −0.810478 1.36203i
\(490\) 499784. 2.08157
\(491\) 13092.0i 0.0543055i −0.999631 0.0271528i \(-0.991356\pi\)
0.999631 0.0271528i \(-0.00864405\pi\)
\(492\) 348418. 207327.i 1.43936 0.856495i
\(493\) 92794.5 0.381793
\(494\) 87497.7i 0.358544i
\(495\) −235592. + 434079.i −0.961500 + 1.77157i
\(496\) −15201.6 −0.0617911
\(497\) 110171.i 0.446019i
\(498\) −93914.7 157826.i −0.378682 0.636386i
\(499\) 410282. 1.64771 0.823856 0.566800i \(-0.191819\pi\)
0.823856 + 0.566800i \(0.191819\pi\)
\(500\) 65688.8i 0.262755i
\(501\) 399419. 237675.i 1.59131 0.946908i
\(502\) −690937. −2.74177
\(503\) 179300.i 0.708670i −0.935119 0.354335i \(-0.884707\pi\)
0.935119 0.354335i \(-0.115293\pi\)
\(504\) −45561.2 24727.8i −0.179363 0.0973474i
\(505\) 557971. 2.18791
\(506\) 285011.i 1.11317i
\(507\) 102813. + 172781.i 0.399975 + 0.672170i
\(508\) 126971. 0.492015
\(509\) 3989.98i 0.0154005i 0.999970 + 0.00770025i \(0.00245109\pi\)
−0.999970 + 0.00770025i \(0.997549\pi\)
\(510\) 479997. 285623.i 1.84543 1.09813i
\(511\) −29475.2 −0.112879
\(512\) 183564.i 0.700240i
\(513\) −129226. + 5109.81i −0.491036 + 0.0194165i
\(514\) −622103. −2.35470
\(515\) 217778.i 0.821106i
\(516\) −303269. 509651.i −1.13901 1.91414i
\(517\) 76198.0 0.285077
\(518\) 210012.i 0.782681i
\(519\) −105973. + 63059.1i −0.393423 + 0.234106i
\(520\) −127626. −0.471991
\(521\) 495584.i 1.82575i −0.408238 0.912876i \(-0.633857\pi\)
0.408238 0.912876i \(-0.366143\pi\)
\(522\) −82319.9 + 151675.i −0.302109 + 0.556638i
\(523\) 311871. 1.14018 0.570088 0.821584i \(-0.306909\pi\)
0.570088 + 0.821584i \(0.306909\pi\)
\(524\) 269832.i 0.982722i
\(525\) 46636.6 + 78374.2i 0.169203 + 0.284351i
\(526\) −814886. −2.94527
\(527\) 45016.2i 0.162087i
\(528\) −119016. + 70820.6i −0.426911 + 0.254034i
\(529\) 205632. 0.734818
\(530\) 974222.i 3.46822i
\(531\) −32262.7 17510.2i −0.114423 0.0621016i
\(532\) 59069.7 0.208709
\(533\) 153816.i 0.541435i
\(534\) −188428. 316659.i −0.660790 1.11048i
\(535\) −104274. −0.364309
\(536\) 164880.i 0.573903i
\(537\) −160967. + 95783.7i −0.558199 + 0.332157i
\(538\) −31481.9 −0.108767
\(539\) 366968.i 1.26314i
\(540\) 24247.9 + 613221.i 0.0831545 + 2.10295i
\(541\) 72663.1 0.248267 0.124134 0.992266i \(-0.460385\pi\)
0.124134 + 0.992266i \(0.460385\pi\)
\(542\) 489758.i 1.66718i
\(543\) 150957. + 253687.i 0.511979 + 0.860395i
\(544\) 350104. 1.18304
\(545\) 375238.i 1.26332i
\(546\) 54983.9 32718.2i 0.184438 0.109750i
\(547\) 198926. 0.664840 0.332420 0.943131i \(-0.392135\pi\)
0.332420 + 0.943131i \(0.392135\pi\)
\(548\) 394663.i 1.31421i
\(549\) 19045.7 35091.9i 0.0631906 0.116429i
\(550\) −735543. −2.43155
\(551\) 60444.8i 0.199093i
\(552\) −55666.4 93548.9i −0.182690 0.307016i
\(553\) −130493. −0.426715
\(554\) 560839.i 1.82734i
\(555\) −656744. + 390796.i −2.13211 + 1.26871i
\(556\) −389594. −1.26027
\(557\) 589282.i 1.89939i −0.313183 0.949693i \(-0.601395\pi\)
0.313183 0.949693i \(-0.398605\pi\)
\(558\) 73580.2 + 39934.8i 0.236316 + 0.128258i
\(559\) 224995. 0.720028
\(560\) 48309.0i 0.154046i
\(561\) −209720. 352440.i −0.666366 1.11985i
\(562\) −49539.8 −0.156849
\(563\) 407823.i 1.28663i −0.765600 0.643317i \(-0.777558\pi\)
0.765600 0.643317i \(-0.222442\pi\)
\(564\) 81366.5 48417.2i 0.255792 0.152209i
\(565\) −151890. −0.475809
\(566\) 386375.i 1.20608i
\(567\) −51532.7 79295.1i −0.160294 0.246650i
\(568\) −339374. −1.05192
\(569\) 272243.i 0.840877i −0.907321 0.420439i \(-0.861876\pi\)
0.907321 0.420439i \(-0.138124\pi\)
\(570\) −186050. 312662.i −0.572638 0.962334i
\(571\) −382479. −1.17310 −0.586551 0.809913i \(-0.699515\pi\)
−0.586551 + 0.809913i \(0.699515\pi\)
\(572\) 304867.i 0.931792i
\(573\) 10006.6 5954.46i 0.0304775 0.0181356i
\(574\) −175763. −0.533464
\(575\) 191514.i 0.579250i
\(576\) −253728. + 467496.i −0.764758 + 1.40907i
\(577\) −229401. −0.689038 −0.344519 0.938779i \(-0.611958\pi\)
−0.344519 + 0.938779i \(0.611958\pi\)
\(578\) 58452.8i 0.174964i
\(579\) 254249. + 427272.i 0.758406 + 1.27452i
\(580\) −286832. −0.852652
\(581\) 47037.8i 0.139346i
\(582\) −567568. + 337732.i −1.67561 + 0.997072i
\(583\) 715326. 2.10459
\(584\) 90796.4i 0.266221i
\(585\) −204631. 111061.i −0.597943 0.324527i
\(586\) −763592. −2.22365
\(587\) 452777.i 1.31404i 0.753873 + 0.657020i \(0.228183\pi\)
−0.753873 + 0.657020i \(0.771817\pi\)
\(588\) −233176. 391860.i −0.674419 1.13338i
\(589\) −29322.8 −0.0845230
\(590\) 103270.i 0.296668i
\(591\) 436126. 259517.i 1.24864 0.743004i
\(592\) −214297. −0.611467
\(593\) 414618.i 1.17907i −0.807744 0.589534i \(-0.799312\pi\)
0.807744 0.589534i \(-0.200688\pi\)
\(594\) 762118. 30135.5i 2.15998 0.0854094i
\(595\) −143056. −0.404085
\(596\) 1.00650e6i 2.83349i
\(597\) −41659.5 70009.9i −0.116887 0.196431i
\(598\) 134358. 0.375718
\(599\) 194294.i 0.541508i 0.962649 + 0.270754i \(0.0872730\pi\)
−0.962649 + 0.270754i \(0.912727\pi\)
\(600\) −241427. + 143661.i −0.670630 + 0.399059i
\(601\) 394812. 1.09305 0.546526 0.837442i \(-0.315950\pi\)
0.546526 + 0.837442i \(0.315950\pi\)
\(602\) 257099.i 0.709427i
\(603\) 143480. 264362.i 0.394599 0.727051i
\(604\) −272767. −0.747683
\(605\) 486657.i 1.32957i
\(606\) −440629. 740490.i −1.19985 2.01639i
\(607\) −356291. −0.967002 −0.483501 0.875344i \(-0.660635\pi\)
−0.483501 + 0.875344i \(0.660635\pi\)
\(608\) 228052.i 0.616917i
\(609\) 37983.8 22602.3i 0.102415 0.0609421i
\(610\) 112326. 0.301870
\(611\) 35920.8i 0.0962196i
\(612\) −447890. 243087.i −1.19583 0.649021i
\(613\) 39079.2 0.103998 0.0519989 0.998647i \(-0.483441\pi\)
0.0519989 + 0.998647i \(0.483441\pi\)
\(614\) 177642.i 0.471204i
\(615\) 327065. + 549642.i 0.864737 + 1.45322i
\(616\) −107081. −0.282197
\(617\) 128439.i 0.337385i −0.985669 0.168692i \(-0.946046\pi\)
0.985669 0.168692i \(-0.0539544\pi\)
\(618\) −289016. + 171979.i −0.756736 + 0.450296i
\(619\) 185094. 0.483070 0.241535 0.970392i \(-0.422349\pi\)
0.241535 + 0.970392i \(0.422349\pi\)
\(620\) 139147.i 0.361985i
\(621\) −7846.43 198434.i −0.0203465 0.514556i
\(622\) −543587. −1.40504
\(623\) 94375.6i 0.243155i
\(624\) −33385.8 56105.8i −0.0857418 0.144092i
\(625\) −335767. −0.859565
\(626\) 478635.i 1.22140i
\(627\) −229573. + 136608.i −0.583965 + 0.347489i
\(628\) 904280. 2.29289
\(629\) 634594.i 1.60396i
\(630\) 126908. 233829.i 0.319749 0.589139i
\(631\) 231418. 0.581218 0.290609 0.956842i \(-0.406142\pi\)
0.290609 + 0.956842i \(0.406142\pi\)
\(632\) 401977.i 1.00639i
\(633\) 21259.5 + 35727.2i 0.0530574 + 0.0891645i
\(634\) 621089. 1.54517
\(635\) 200302.i 0.496750i
\(636\) 763846. 454527.i 1.88839 1.12369i
\(637\) 172994. 0.426336
\(638\) 356478.i 0.875773i
\(639\) −544138. 295325.i −1.33262 0.723266i
\(640\) −746867. −1.82341
\(641\) 248945.i 0.605880i 0.953010 + 0.302940i \(0.0979682\pi\)
−0.953010 + 0.302940i \(0.902032\pi\)
\(642\) 82345.3 + 138384.i 0.199788 + 0.335749i
\(643\) −90943.6 −0.219963 −0.109982 0.993934i \(-0.535079\pi\)
−0.109982 + 0.993934i \(0.535079\pi\)
\(644\) 90705.1i 0.218706i
\(645\) 803993. 478417.i 1.93256 1.14997i
\(646\) 302117. 0.723953
\(647\) 836160.i 1.99747i 0.0502618 + 0.998736i \(0.483994\pi\)
−0.0502618 + 0.998736i \(0.516006\pi\)
\(648\) 244264. 158743.i 0.581713 0.378046i
\(649\) −75826.3 −0.180024
\(650\) 346745.i 0.820698i
\(651\) −10964.8 18426.6i −0.0258724 0.0434793i
\(652\) −972770. −2.28831
\(653\) 827823.i 1.94138i −0.240327 0.970692i \(-0.577255\pi\)
0.240327 0.970692i \(-0.422745\pi\)
\(654\) 497983. 296325.i 1.16429 0.692809i
\(655\) −425669. −0.992179
\(656\) 179350.i 0.416767i
\(657\) 79011.6 145579.i 0.183046 0.337263i
\(658\) −41046.3 −0.0948029
\(659\) 655544.i 1.50949i −0.656016 0.754747i \(-0.727760\pi\)
0.656016 0.754747i \(-0.272240\pi\)
\(660\) 648253. + 1.08941e6i 1.48818 + 2.50093i
\(661\) 370337. 0.847607 0.423803 0.905754i \(-0.360695\pi\)
0.423803 + 0.905754i \(0.360695\pi\)
\(662\) 381105.i 0.869617i
\(663\) 166145. 98864.7i 0.377972 0.224913i
\(664\) −144897. −0.328642
\(665\) 93184.5i 0.210717i
\(666\) 1.03726e6 + 562961.i 2.33851 + 1.26920i
\(667\) 92816.8 0.208629
\(668\) 1.19298e6i 2.67351i
\(669\) 40719.0 + 68429.5i 0.0909798 + 0.152894i
\(670\) 846199. 1.88505
\(671\) 82475.6i 0.183181i
\(672\) 143309. 85276.1i 0.317347 0.188838i
\(673\) 585474. 1.29264 0.646320 0.763067i \(-0.276307\pi\)
0.646320 + 0.763067i \(0.276307\pi\)
\(674\) 74376.7i 0.163726i
\(675\) −512109. + 20249.7i −1.12397 + 0.0444438i
\(676\) 516060. 1.12929
\(677\) 714650.i 1.55925i −0.626246 0.779626i \(-0.715409\pi\)
0.626246 0.779626i \(-0.284591\pi\)
\(678\) 119948. + 201575.i 0.260935 + 0.438508i
\(679\) 169156. 0.366899
\(680\) 440676.i 0.953019i
\(681\) −357656. + 212824.i −0.771208 + 0.458908i
\(682\) 172934. 0.371801
\(683\) 643561.i 1.37959i 0.724007 + 0.689793i \(0.242298\pi\)
−0.724007 + 0.689793i \(0.757702\pi\)
\(684\) −158343. + 291748.i −0.338444 + 0.623585i
\(685\) −622595. −1.32686
\(686\) 414081.i 0.879908i
\(687\) −317051. 532813.i −0.671761 1.12891i
\(688\) 262345. 0.554238
\(689\) 337214.i 0.710342i
\(690\) 480113. 285691.i 1.00843 0.600066i
\(691\) 30031.3 0.0628952 0.0314476 0.999505i \(-0.489988\pi\)
0.0314476 + 0.999505i \(0.489988\pi\)
\(692\) 316519.i 0.660978i
\(693\) −171690. 93182.8i −0.357502 0.194030i
\(694\) −797323. −1.65545
\(695\) 614599.i 1.27239i
\(696\) 69624.9 + 117007.i 0.143730 + 0.241542i
\(697\) −531105. −1.09324
\(698\) 645763.i 1.32545i
\(699\) 345071. 205335.i 0.706242 0.420250i
\(700\) 234088. 0.477730
\(701\) 143951.i 0.292940i −0.989215 0.146470i \(-0.953209\pi\)
0.989215 0.146470i \(-0.0467912\pi\)
\(702\) 14206.3 + 359273.i 0.0288275 + 0.729038i
\(703\) −413364. −0.836415
\(704\) 1.09875e6i 2.21693i
\(705\) 76379.9 + 128359.i 0.153674 + 0.258254i
\(706\) −313394. −0.628755
\(707\) 220692.i 0.441518i
\(708\) −80969.6 + 48181.1i −0.161531 + 0.0961191i
\(709\) 939736. 1.86945 0.934724 0.355375i \(-0.115647\pi\)
0.934724 + 0.355375i \(0.115647\pi\)
\(710\) 1.74174e6i 3.45514i
\(711\) 349802. 644513.i 0.691964 1.27495i
\(712\) −290718. −0.573472
\(713\) 45027.0i 0.0885715i
\(714\) 112971. + 189852.i 0.221601 + 0.372407i
\(715\) −480939. −0.940758
\(716\) 480776.i 0.937814i
\(717\) 20927.7 12453.0i 0.0407083 0.0242235i
\(718\) 1.10921e6 2.15161
\(719\) 402190.i 0.777988i 0.921240 + 0.388994i \(0.127177\pi\)
−0.921240 + 0.388994i \(0.872823\pi\)
\(720\) −238600. 129498.i −0.460263 0.249803i
\(721\) 86136.9 0.165699
\(722\) 618110.i 1.18575i
\(723\) 325433. + 546900.i 0.622566 + 1.04624i
\(724\) 757710. 1.44553
\(725\) 239537.i 0.455719i
\(726\) 645848. 384313.i 1.22534 0.729141i
\(727\) −422494. −0.799377 −0.399689 0.916651i \(-0.630882\pi\)
−0.399689 + 0.916651i \(0.630882\pi\)
\(728\) 50479.6i 0.0952474i
\(729\) 529782. 41962.6i 0.996878 0.0789601i
\(730\) 465986. 0.874434
\(731\) 776877.i 1.45384i
\(732\) −52406.1 88069.9i −0.0978047 0.164364i
\(733\) −471600. −0.877741 −0.438870 0.898550i \(-0.644621\pi\)
−0.438870 + 0.898550i \(0.644621\pi\)
\(734\) 1.48134e6i 2.74956i
\(735\) 618173. 367844.i 1.14429 0.680909i
\(736\) 350188. 0.646466
\(737\) 621325.i 1.14389i
\(738\) 471154. 868104.i 0.865068 1.59389i
\(739\) 637081. 1.16656 0.583278 0.812272i \(-0.301770\pi\)
0.583278 + 0.812272i \(0.301770\pi\)
\(740\) 1.96156e6i 3.58210i
\(741\) −64398.8 108224.i −0.117285 0.197100i
\(742\) −385331. −0.699884
\(743\) 324714.i 0.588198i 0.955775 + 0.294099i \(0.0950196\pi\)
−0.955775 + 0.294099i \(0.904980\pi\)
\(744\) 56761.9 33776.2i 0.102544 0.0610190i
\(745\) −1.58779e6 −2.86075
\(746\) 1.59808e6i 2.87157i
\(747\) −232322. 126090.i −0.416341 0.225965i
\(748\) −1.05266e6 −1.88142
\(749\) 41243.3i 0.0735173i
\(750\) −81833.7 137524.i −0.145482 0.244487i
\(751\) −284150. −0.503812 −0.251906 0.967752i \(-0.581057\pi\)
−0.251906 + 0.967752i \(0.581057\pi\)
\(752\) 41883.8i 0.0740645i
\(753\) −854606. + 508534.i −1.50722 + 0.896871i
\(754\) −168049. −0.295592
\(755\) 430299.i 0.754878i
\(756\) −242545. + 9590.67i −0.424374 + 0.0167805i
\(757\) 343716. 0.599802 0.299901 0.953970i \(-0.403046\pi\)
0.299901 + 0.953970i \(0.403046\pi\)
\(758\) 198344.i 0.345209i
\(759\) −209770. 352524.i −0.364133 0.611935i
\(760\) −287049. −0.496968
\(761\) 218313.i 0.376974i 0.982076 + 0.188487i \(0.0603583\pi\)
−0.982076 + 0.188487i \(0.939642\pi\)
\(762\) 265823. 158178.i 0.457807 0.272419i
\(763\) −148417. −0.254938
\(764\) 29887.7i 0.0512043i
\(765\) 383479. 706562.i 0.655267 1.20733i
\(766\) −144395. −0.246090
\(767\) 35745.6i 0.0607619i
\(768\) 106242. + 178543.i 0.180125 + 0.302706i
\(769\) −1.07369e6 −1.81562 −0.907810 0.419382i \(-0.862247\pi\)
−0.907810 + 0.419382i \(0.862247\pi\)
\(770\) 549563.i 0.926907i
\(771\) −769466. + 457871.i −1.29444 + 0.770255i
\(772\) 1.27617e6 2.14129
\(773\) 310794.i 0.520132i 0.965591 + 0.260066i \(0.0837443\pi\)
−0.965591 + 0.260066i \(0.916256\pi\)
\(774\) −1.26983e6 689184.i −2.11964 1.15041i
\(775\) −116204. −0.193471
\(776\) 521073.i 0.865317i
\(777\) −154570. 259760.i −0.256026 0.430259i
\(778\) −1.42283e6 −2.35067
\(779\) 345953.i 0.570088i
\(780\) −513561. + 305595.i −0.844118 + 0.502293i
\(781\) −1.27887e6 −2.09665
\(782\) 463920.i 0.7