Properties

Label 177.5.b.a.119.4
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 119.4
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.75

$q$-expansion

\(f(q)\) \(=\) \(q-7.42214i q^{2} +(2.94091 - 8.50594i) q^{3} -39.0882 q^{4} +22.5647i q^{5} +(-63.1323 - 21.8278i) q^{6} +11.4871 q^{7} +171.364i q^{8} +(-63.7021 - 50.0304i) q^{9} +O(q^{10})\) \(q-7.42214i q^{2} +(2.94091 - 8.50594i) q^{3} -39.0882 q^{4} +22.5647i q^{5} +(-63.1323 - 21.8278i) q^{6} +11.4871 q^{7} +171.364i q^{8} +(-63.7021 - 50.0304i) q^{9} +167.478 q^{10} +181.567i q^{11} +(-114.955 + 332.482i) q^{12} -136.108 q^{13} -85.2592i q^{14} +(191.934 + 66.3606i) q^{15} +646.474 q^{16} +36.3548i q^{17} +(-371.333 + 472.806i) q^{18} +224.708 q^{19} -882.012i q^{20} +(33.7827 - 97.7090i) q^{21} +1347.62 q^{22} +719.829i q^{23} +(1457.61 + 503.965i) q^{24} +115.836 q^{25} +1010.22i q^{26} +(-612.898 + 394.712i) q^{27} -449.012 q^{28} -1088.37i q^{29} +(492.538 - 1424.56i) q^{30} -737.969 q^{31} -2056.40i q^{32} +(1544.40 + 533.972i) q^{33} +269.830 q^{34} +259.204i q^{35} +(2490.00 + 1955.60i) q^{36} -2150.01 q^{37} -1667.82i q^{38} +(-400.282 + 1157.73i) q^{39} -3866.76 q^{40} +1610.62i q^{41} +(-725.210 - 250.740i) q^{42} -2334.50 q^{43} -7097.12i q^{44} +(1128.92 - 1437.42i) q^{45} +5342.67 q^{46} +1691.84i q^{47} +(1901.22 - 5498.87i) q^{48} -2269.05 q^{49} -859.748i q^{50} +(309.232 + 106.916i) q^{51} +5320.23 q^{52} +124.583i q^{53} +(2929.61 + 4549.01i) q^{54} -4097.00 q^{55} +1968.48i q^{56} +(660.847 - 1911.36i) q^{57} -8078.04 q^{58} +453.188i q^{59} +(-7502.34 - 2593.92i) q^{60} +3339.38 q^{61} +5477.31i q^{62} +(-731.756 - 574.707i) q^{63} -4919.33 q^{64} -3071.24i q^{65} +(3963.21 - 11462.7i) q^{66} +2181.86 q^{67} -1421.04i q^{68} +(6122.82 + 2116.95i) q^{69} +1923.85 q^{70} +6712.50i q^{71} +(8573.39 - 10916.2i) q^{72} +7126.64 q^{73} +15957.7i q^{74} +(340.662 - 985.290i) q^{75} -8783.44 q^{76} +2085.69i q^{77} +(8592.84 + 2970.95i) q^{78} +7863.06 q^{79} +14587.5i q^{80} +(1554.92 + 6374.08i) q^{81} +11954.3 q^{82} -11056.4i q^{83} +(-1320.50 + 3819.27i) q^{84} -820.334 q^{85} +17327.0i q^{86} +(-9257.62 - 3200.80i) q^{87} -31114.0 q^{88} +3376.87i q^{89} +(-10668.7 - 8379.00i) q^{90} -1563.50 q^{91} -28136.8i q^{92} +(-2170.30 + 6277.12i) q^{93} +12557.1 q^{94} +5070.47i q^{95} +(-17491.6 - 6047.69i) q^{96} -14133.9 q^{97} +16841.2i q^{98} +(9083.87 - 11566.2i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.42214i 1.85554i −0.373159 0.927768i \(-0.621725\pi\)
0.373159 0.927768i \(-0.378275\pi\)
\(3\) 2.94091 8.50594i 0.326768 0.945105i
\(4\) −39.0882 −2.44301
\(5\) 22.5647i 0.902587i 0.892376 + 0.451293i \(0.149037\pi\)
−0.892376 + 0.451293i \(0.850963\pi\)
\(6\) −63.1323 21.8278i −1.75367 0.606329i
\(7\) 11.4871 0.234432 0.117216 0.993106i \(-0.462603\pi\)
0.117216 + 0.993106i \(0.462603\pi\)
\(8\) 171.364i 2.67756i
\(9\) −63.7021 50.0304i −0.786446 0.617659i
\(10\) 167.478 1.67478
\(11\) 181.567i 1.50055i 0.661124 + 0.750277i \(0.270080\pi\)
−0.661124 + 0.750277i \(0.729920\pi\)
\(12\) −114.955 + 332.482i −0.798297 + 2.30890i
\(13\) −136.108 −0.805375 −0.402688 0.915337i \(-0.631924\pi\)
−0.402688 + 0.915337i \(0.631924\pi\)
\(14\) 85.2592i 0.434996i
\(15\) 191.934 + 66.3606i 0.853039 + 0.294936i
\(16\) 646.474 2.52529
\(17\) 36.3548i 0.125795i 0.998020 + 0.0628976i \(0.0200341\pi\)
−0.998020 + 0.0628976i \(0.979966\pi\)
\(18\) −371.333 + 472.806i −1.14609 + 1.45928i
\(19\) 224.708 0.622461 0.311231 0.950334i \(-0.399259\pi\)
0.311231 + 0.950334i \(0.399259\pi\)
\(20\) 882.012i 2.20503i
\(21\) 33.7827 97.7090i 0.0766046 0.221562i
\(22\) 1347.62 2.78433
\(23\) 719.829i 1.36073i 0.732871 + 0.680367i \(0.238180\pi\)
−0.732871 + 0.680367i \(0.761820\pi\)
\(24\) 1457.61 + 503.965i 2.53057 + 0.874939i
\(25\) 115.836 0.185337
\(26\) 1010.22i 1.49440i
\(27\) −612.898 + 394.712i −0.840738 + 0.541443i
\(28\) −449.012 −0.572719
\(29\) 1088.37i 1.29414i −0.762431 0.647069i \(-0.775994\pi\)
0.762431 0.647069i \(-0.224006\pi\)
\(30\) 492.538 1424.56i 0.547264 1.58284i
\(31\) −737.969 −0.767917 −0.383959 0.923350i \(-0.625440\pi\)
−0.383959 + 0.923350i \(0.625440\pi\)
\(32\) 2056.40i 2.00821i
\(33\) 1544.40 + 533.972i 1.41818 + 0.490332i
\(34\) 269.830 0.233417
\(35\) 259.204i 0.211595i
\(36\) 2490.00 + 1955.60i 1.92130 + 1.50895i
\(37\) −2150.01 −1.57050 −0.785248 0.619181i \(-0.787465\pi\)
−0.785248 + 0.619181i \(0.787465\pi\)
\(38\) 1667.82i 1.15500i
\(39\) −400.282 + 1157.73i −0.263170 + 0.761164i
\(40\) −3866.76 −2.41673
\(41\) 1610.62i 0.958133i 0.877779 + 0.479067i \(0.159025\pi\)
−0.877779 + 0.479067i \(0.840975\pi\)
\(42\) −725.210 250.740i −0.411117 0.142143i
\(43\) −2334.50 −1.26257 −0.631287 0.775549i \(-0.717473\pi\)
−0.631287 + 0.775549i \(0.717473\pi\)
\(44\) 7097.12i 3.66587i
\(45\) 1128.92 1437.42i 0.557491 0.709836i
\(46\) 5342.67 2.52489
\(47\) 1691.84i 0.765885i 0.923772 + 0.382943i \(0.125089\pi\)
−0.923772 + 0.382943i \(0.874911\pi\)
\(48\) 1901.22 5498.87i 0.825183 2.38666i
\(49\) −2269.05 −0.945042
\(50\) 859.748i 0.343899i
\(51\) 309.232 + 106.916i 0.118890 + 0.0411058i
\(52\) 5320.23 1.96754
\(53\) 124.583i 0.0443513i 0.999754 + 0.0221757i \(0.00705931\pi\)
−0.999754 + 0.0221757i \(0.992941\pi\)
\(54\) 2929.61 + 4549.01i 1.00467 + 1.56002i
\(55\) −4097.00 −1.35438
\(56\) 1968.48i 0.627704i
\(57\) 660.847 1911.36i 0.203400 0.588291i
\(58\) −8078.04 −2.40132
\(59\) 453.188i 0.130189i
\(60\) −7502.34 2593.92i −2.08398 0.720532i
\(61\) 3339.38 0.897442 0.448721 0.893672i \(-0.351880\pi\)
0.448721 + 0.893672i \(0.351880\pi\)
\(62\) 5477.31i 1.42490i
\(63\) −731.756 574.707i −0.184368 0.144799i
\(64\) −4919.33 −1.20101
\(65\) 3071.24i 0.726921i
\(66\) 3963.21 11462.7i 0.909829 2.63148i
\(67\) 2181.86 0.486045 0.243023 0.970021i \(-0.421861\pi\)
0.243023 + 0.970021i \(0.421861\pi\)
\(68\) 1421.04i 0.307319i
\(69\) 6122.82 + 2116.95i 1.28604 + 0.444644i
\(70\) 1923.85 0.392622
\(71\) 6712.50i 1.33158i 0.746139 + 0.665791i \(0.231906\pi\)
−0.746139 + 0.665791i \(0.768094\pi\)
\(72\) 8573.39 10916.2i 1.65382 2.10575i
\(73\) 7126.64 1.33733 0.668666 0.743563i \(-0.266866\pi\)
0.668666 + 0.743563i \(0.266866\pi\)
\(74\) 15957.7i 2.91411i
\(75\) 340.662 985.290i 0.0605621 0.175163i
\(76\) −8783.44 −1.52068
\(77\) 2085.69i 0.351777i
\(78\) 8592.84 + 2970.95i 1.41237 + 0.488322i
\(79\) 7863.06 1.25990 0.629952 0.776634i \(-0.283074\pi\)
0.629952 + 0.776634i \(0.283074\pi\)
\(80\) 14587.5i 2.27929i
\(81\) 1554.92 + 6374.08i 0.236994 + 0.971511i
\(82\) 11954.3 1.77785
\(83\) 11056.4i 1.60493i −0.596696 0.802467i \(-0.703520\pi\)
0.596696 0.802467i \(-0.296480\pi\)
\(84\) −1320.50 + 3819.27i −0.187146 + 0.541279i
\(85\) −820.334 −0.113541
\(86\) 17327.0i 2.34275i
\(87\) −9257.62 3200.80i −1.22310 0.422883i
\(88\) −31114.0 −4.01782
\(89\) 3376.87i 0.426318i 0.977018 + 0.213159i \(0.0683753\pi\)
−0.977018 + 0.213159i \(0.931625\pi\)
\(90\) −10668.7 8379.00i −1.31713 1.03444i
\(91\) −1563.50 −0.188805
\(92\) 28136.8i 3.32429i
\(93\) −2170.30 + 6277.12i −0.250931 + 0.725762i
\(94\) 12557.1 1.42113
\(95\) 5070.47i 0.561825i
\(96\) −17491.6 6047.69i −1.89797 0.656217i
\(97\) −14133.9 −1.50217 −0.751083 0.660208i \(-0.770468\pi\)
−0.751083 + 0.660208i \(0.770468\pi\)
\(98\) 16841.2i 1.75356i
\(99\) 9083.87 11566.2i 0.926831 1.18010i
\(100\) −4527.80 −0.452780
\(101\) 2748.95i 0.269478i −0.990881 0.134739i \(-0.956980\pi\)
0.990881 0.134739i \(-0.0430197\pi\)
\(102\) 793.546 2295.16i 0.0762732 0.220604i
\(103\) −1332.88 −0.125636 −0.0628182 0.998025i \(-0.520009\pi\)
−0.0628182 + 0.998025i \(0.520009\pi\)
\(104\) 23324.0i 2.15644i
\(105\) 2204.77 + 762.294i 0.199979 + 0.0691424i
\(106\) 924.672 0.0822955
\(107\) 13219.8i 1.15467i 0.816509 + 0.577333i \(0.195906\pi\)
−0.816509 + 0.577333i \(0.804094\pi\)
\(108\) 23957.0 15428.6i 2.05393 1.32275i
\(109\) −17531.8 −1.47561 −0.737807 0.675012i \(-0.764138\pi\)
−0.737807 + 0.675012i \(0.764138\pi\)
\(110\) 30408.5i 2.51310i
\(111\) −6322.98 + 18287.9i −0.513187 + 1.48428i
\(112\) 7426.14 0.592008
\(113\) 120.154i 0.00940986i 0.999989 + 0.00470493i \(0.00149763\pi\)
−0.999989 + 0.00470493i \(0.998502\pi\)
\(114\) −14186.4 4904.90i −1.09159 0.377416i
\(115\) −16242.7 −1.22818
\(116\) 42542.4i 3.16159i
\(117\) 8670.39 + 6809.56i 0.633384 + 0.497447i
\(118\) 3363.62 0.241570
\(119\) 417.613i 0.0294904i
\(120\) −11371.8 + 32890.5i −0.789708 + 2.28406i
\(121\) −18325.6 −1.25166
\(122\) 24785.4i 1.66524i
\(123\) 13699.9 + 4736.69i 0.905536 + 0.313087i
\(124\) 28845.8 1.87603
\(125\) 16716.7i 1.06987i
\(126\) −4265.55 + 5431.19i −0.268679 + 0.342101i
\(127\) 11909.4 0.738387 0.369193 0.929353i \(-0.379634\pi\)
0.369193 + 0.929353i \(0.379634\pi\)
\(128\) 3609.50i 0.220306i
\(129\) −6865.55 + 19857.1i −0.412568 + 1.19326i
\(130\) −22795.2 −1.34883
\(131\) 13105.4i 0.763672i −0.924230 0.381836i \(-0.875292\pi\)
0.924230 0.381836i \(-0.124708\pi\)
\(132\) −60367.7 20872.0i −3.46463 1.19789i
\(133\) 2581.26 0.145925
\(134\) 16194.0i 0.901874i
\(135\) −8906.54 13829.8i −0.488699 0.758839i
\(136\) −6229.89 −0.336824
\(137\) 31042.7i 1.65393i 0.562250 + 0.826967i \(0.309936\pi\)
−0.562250 + 0.826967i \(0.690064\pi\)
\(138\) 15712.3 45444.4i 0.825052 2.38629i
\(139\) 680.779 0.0352352 0.0176176 0.999845i \(-0.494392\pi\)
0.0176176 + 0.999845i \(0.494392\pi\)
\(140\) 10131.8i 0.516929i
\(141\) 14390.7 + 4975.55i 0.723842 + 0.250266i
\(142\) 49821.1 2.47080
\(143\) 24712.8i 1.20851i
\(144\) −41181.8 32343.3i −1.98600 1.55977i
\(145\) 24558.7 1.16807
\(146\) 52894.9i 2.48147i
\(147\) −6673.05 + 19300.4i −0.308809 + 0.893163i
\(148\) 84039.9 3.83674
\(149\) 15407.1i 0.693984i −0.937868 0.346992i \(-0.887203\pi\)
0.937868 0.346992i \(-0.112797\pi\)
\(150\) −7312.96 2528.44i −0.325021 0.112375i
\(151\) −38409.0 −1.68453 −0.842265 0.539063i \(-0.818778\pi\)
−0.842265 + 0.539063i \(0.818778\pi\)
\(152\) 38506.9i 1.66667i
\(153\) 1818.84 2315.88i 0.0776985 0.0989311i
\(154\) 15480.3 0.652735
\(155\) 16652.0i 0.693112i
\(156\) 15646.3 45253.6i 0.642928 1.85953i
\(157\) 2444.86 0.0991869 0.0495935 0.998769i \(-0.484207\pi\)
0.0495935 + 0.998769i \(0.484207\pi\)
\(158\) 58360.8i 2.33780i
\(159\) 1059.69 + 366.387i 0.0419167 + 0.0144926i
\(160\) 46402.1 1.81258
\(161\) 8268.78i 0.318999i
\(162\) 47309.3 11540.8i 1.80267 0.439751i
\(163\) 6820.63 0.256714 0.128357 0.991728i \(-0.459030\pi\)
0.128357 + 0.991728i \(0.459030\pi\)
\(164\) 62956.2i 2.34073i
\(165\) −12048.9 + 34848.9i −0.442568 + 1.28003i
\(166\) −82062.1 −2.97801
\(167\) 39521.9i 1.41712i −0.705653 0.708558i \(-0.749346\pi\)
0.705653 0.708558i \(-0.250654\pi\)
\(168\) 16743.8 + 5789.12i 0.593246 + 0.205113i
\(169\) −10035.5 −0.351371
\(170\) 6088.64i 0.210679i
\(171\) −14314.4 11242.3i −0.489532 0.384469i
\(172\) 91251.3 3.08448
\(173\) 12144.2i 0.405768i 0.979203 + 0.202884i \(0.0650314\pi\)
−0.979203 + 0.202884i \(0.934969\pi\)
\(174\) −23756.8 + 68711.3i −0.784673 + 2.26950i
\(175\) 1330.62 0.0434488
\(176\) 117378.i 3.78933i
\(177\) 3854.79 + 1332.78i 0.123042 + 0.0425415i
\(178\) 25063.6 0.791048
\(179\) 30884.1i 0.963892i 0.876201 + 0.481946i \(0.160070\pi\)
−0.876201 + 0.481946i \(0.839930\pi\)
\(180\) −44127.4 + 56186.0i −1.36196 + 1.73414i
\(181\) 11872.7 0.362405 0.181202 0.983446i \(-0.442001\pi\)
0.181202 + 0.983446i \(0.442001\pi\)
\(182\) 11604.5i 0.350335i
\(183\) 9820.82 28404.6i 0.293255 0.848177i
\(184\) −123352. −3.64344
\(185\) 48514.3i 1.41751i
\(186\) 46589.7 + 16108.3i 1.34668 + 0.465610i
\(187\) −6600.83 −0.188762
\(188\) 66130.9i 1.87107i
\(189\) −7040.45 + 4534.11i −0.197095 + 0.126931i
\(190\) 37633.8 1.04249
\(191\) 33931.1i 0.930103i −0.885284 0.465052i \(-0.846036\pi\)
0.885284 0.465052i \(-0.153964\pi\)
\(192\) −14467.3 + 41843.5i −0.392450 + 1.13508i
\(193\) −4191.30 −0.112521 −0.0562606 0.998416i \(-0.517918\pi\)
−0.0562606 + 0.998416i \(0.517918\pi\)
\(194\) 104904.i 2.78732i
\(195\) −26123.8 9032.24i −0.687017 0.237534i
\(196\) 88692.8 2.30875
\(197\) 42251.1i 1.08869i 0.838860 + 0.544347i \(0.183223\pi\)
−0.838860 + 0.544347i \(0.816777\pi\)
\(198\) −85846.0 67421.8i −2.18973 1.71977i
\(199\) −51870.1 −1.30982 −0.654909 0.755708i \(-0.727293\pi\)
−0.654909 + 0.755708i \(0.727293\pi\)
\(200\) 19850.0i 0.496250i
\(201\) 6416.64 18558.8i 0.158824 0.459364i
\(202\) −20403.1 −0.500027
\(203\) 12502.3i 0.303387i
\(204\) −12087.3 4179.16i −0.290449 0.100422i
\(205\) −36343.2 −0.864798
\(206\) 9892.79i 0.233123i
\(207\) 36013.3 45854.6i 0.840470 1.07014i
\(208\) −87990.5 −2.03381
\(209\) 40799.7i 0.934037i
\(210\) 5657.86 16364.1i 0.128296 0.371069i
\(211\) −79865.5 −1.79388 −0.896942 0.442147i \(-0.854217\pi\)
−0.896942 + 0.442147i \(0.854217\pi\)
\(212\) 4869.72i 0.108351i
\(213\) 57096.2 + 19740.9i 1.25848 + 0.435118i
\(214\) 98119.0 2.14252
\(215\) 52677.2i 1.13958i
\(216\) −67639.2 105028.i −1.44974 2.25112i
\(217\) −8477.16 −0.180024
\(218\) 130123.i 2.73805i
\(219\) 20958.8 60618.8i 0.436997 1.26392i
\(220\) 160144. 3.30877
\(221\) 4948.19i 0.101312i
\(222\) 135735. + 46930.0i 2.75414 + 0.952237i
\(223\) 70159.9 1.41085 0.705423 0.708787i \(-0.250757\pi\)
0.705423 + 0.708787i \(0.250757\pi\)
\(224\) 23622.2i 0.470787i
\(225\) −7378.97 5795.30i −0.145757 0.114475i
\(226\) 891.803 0.0174603
\(227\) 46725.3i 0.906776i 0.891313 + 0.453388i \(0.149785\pi\)
−0.891313 + 0.453388i \(0.850215\pi\)
\(228\) −25831.3 + 74711.5i −0.496909 + 1.43720i
\(229\) 22705.6 0.432975 0.216487 0.976285i \(-0.430540\pi\)
0.216487 + 0.976285i \(0.430540\pi\)
\(230\) 120556.i 2.27893i
\(231\) 17740.7 + 6133.82i 0.332466 + 0.114949i
\(232\) 186507. 3.46513
\(233\) 12368.3i 0.227823i 0.993491 + 0.113911i \(0.0363380\pi\)
−0.993491 + 0.113911i \(0.963662\pi\)
\(234\) 50541.5 64352.9i 0.923031 1.17527i
\(235\) −38175.8 −0.691278
\(236\) 17714.3i 0.318053i
\(237\) 23124.5 66882.8i 0.411696 1.19074i
\(238\) 3099.58 0.0547204
\(239\) 41816.7i 0.732071i −0.930601 0.366036i \(-0.880715\pi\)
0.930601 0.366036i \(-0.119285\pi\)
\(240\) 124080. + 42900.4i 2.15417 + 0.744799i
\(241\) −43392.7 −0.747107 −0.373554 0.927609i \(-0.621861\pi\)
−0.373554 + 0.927609i \(0.621861\pi\)
\(242\) 136015.i 2.32250i
\(243\) 58790.5 + 5519.54i 0.995622 + 0.0934738i
\(244\) −130530. −2.19246
\(245\) 51200.3i 0.852982i
\(246\) 35156.4 101682.i 0.580944 1.68025i
\(247\) −30584.7 −0.501315
\(248\) 126461.i 2.05614i
\(249\) −94045.0 32515.8i −1.51683 0.524441i
\(250\) 124074. 1.98518
\(251\) 107367.i 1.70421i 0.523372 + 0.852104i \(0.324674\pi\)
−0.523372 + 0.852104i \(0.675326\pi\)
\(252\) 28603.0 + 22464.2i 0.450412 + 0.353745i
\(253\) −130697. −2.04186
\(254\) 88393.5i 1.37010i
\(255\) −2412.53 + 6977.72i −0.0371015 + 0.107308i
\(256\) −51919.1 −0.792222
\(257\) 121344.i 1.83719i −0.395202 0.918594i \(-0.629326\pi\)
0.395202 0.918594i \(-0.370674\pi\)
\(258\) 147382. + 50957.1i 2.21414 + 0.765535i
\(259\) −24697.5 −0.368174
\(260\) 120049.i 1.77588i
\(261\) −54451.6 + 69331.5i −0.799337 + 1.01777i
\(262\) −97269.9 −1.41702
\(263\) 82089.6i 1.18680i −0.804908 0.593399i \(-0.797786\pi\)
0.804908 0.593399i \(-0.202214\pi\)
\(264\) −91503.4 + 264654.i −1.31289 + 3.79726i
\(265\) −2811.17 −0.0400309
\(266\) 19158.5i 0.270768i
\(267\) 28723.4 + 9931.05i 0.402915 + 0.139307i
\(268\) −85284.8 −1.18741
\(269\) 21537.5i 0.297640i −0.988864 0.148820i \(-0.952452\pi\)
0.988864 0.148820i \(-0.0475475\pi\)
\(270\) −102647. + 66105.6i −1.40805 + 0.906798i
\(271\) −100382. −1.36684 −0.683421 0.730024i \(-0.739509\pi\)
−0.683421 + 0.730024i \(0.739509\pi\)
\(272\) 23502.4i 0.317669i
\(273\) −4598.10 + 13299.0i −0.0616955 + 0.178441i
\(274\) 230403. 3.06893
\(275\) 21031.9i 0.278108i
\(276\) −239330. 82747.7i −3.14180 1.08627i
\(277\) 34277.3 0.446732 0.223366 0.974735i \(-0.428296\pi\)
0.223366 + 0.974735i \(0.428296\pi\)
\(278\) 5052.84i 0.0653801i
\(279\) 47010.2 + 36920.9i 0.603926 + 0.474311i
\(280\) −44418.1 −0.566557
\(281\) 9887.03i 0.125214i 0.998038 + 0.0626070i \(0.0199415\pi\)
−0.998038 + 0.0626070i \(0.980059\pi\)
\(282\) 36929.2 106810.i 0.464378 1.34311i
\(283\) −10379.8 −0.129603 −0.0648015 0.997898i \(-0.520641\pi\)
−0.0648015 + 0.997898i \(0.520641\pi\)
\(284\) 262379.i 3.25307i
\(285\) 43129.2 + 14911.8i 0.530984 + 0.183586i
\(286\) −183422. −2.24243
\(287\) 18501.5i 0.224617i
\(288\) −102883. + 130997.i −1.24039 + 1.57935i
\(289\) 82199.3 0.984176
\(290\) 182278.i 2.16740i
\(291\) −41566.4 + 120222.i −0.490859 + 1.41970i
\(292\) −278567. −3.26712
\(293\) 47375.0i 0.551841i 0.961181 + 0.275920i \(0.0889826\pi\)
−0.961181 + 0.275920i \(0.911017\pi\)
\(294\) 143250. + 49528.3i 1.65730 + 0.573006i
\(295\) −10226.0 −0.117507
\(296\) 368433.i 4.20509i
\(297\) −71666.6 111282.i −0.812464 1.26157i
\(298\) −114354. −1.28771
\(299\) 97974.7i 1.09590i
\(300\) −13315.8 + 38513.2i −0.147954 + 0.427924i
\(301\) −26816.7 −0.295987
\(302\) 285077.i 3.12571i
\(303\) −23382.4 8084.41i −0.254685 0.0880568i
\(304\) 145268. 1.57189
\(305\) 75352.1i 0.810019i
\(306\) −17188.8 13499.7i −0.183570 0.144172i
\(307\) 182834. 1.93990 0.969951 0.243302i \(-0.0782307\pi\)
0.969951 + 0.243302i \(0.0782307\pi\)
\(308\) 81525.7i 0.859396i
\(309\) −3919.87 + 11337.4i −0.0410539 + 0.118740i
\(310\) −123594. −1.28609
\(311\) 87920.5i 0.909011i 0.890744 + 0.454506i \(0.150184\pi\)
−0.890744 + 0.454506i \(0.849816\pi\)
\(312\) −198393. 68593.8i −2.03806 0.704654i
\(313\) −137873. −1.40731 −0.703655 0.710542i \(-0.748450\pi\)
−0.703655 + 0.710542i \(0.748450\pi\)
\(314\) 18146.1i 0.184045i
\(315\) 12968.1 16511.8i 0.130694 0.166408i
\(316\) −307353. −3.07796
\(317\) 121818.i 1.21225i −0.795368 0.606126i \(-0.792723\pi\)
0.795368 0.606126i \(-0.207277\pi\)
\(318\) 2719.37 7865.20i 0.0268915 0.0777778i
\(319\) 197612. 1.94193
\(320\) 111003.i 1.08401i
\(321\) 112447. + 38878.1i 1.09128 + 0.377307i
\(322\) 61372.0 0.591914
\(323\) 8169.23i 0.0783026i
\(324\) −60779.0 249151.i −0.578980 2.37341i
\(325\) −15766.2 −0.149266
\(326\) 50623.7i 0.476342i
\(327\) −51559.3 + 149124.i −0.482183 + 1.39461i
\(328\) −276002. −2.56546
\(329\) 19434.4i 0.179548i
\(330\) 258653. + 89428.6i 2.37514 + 0.821200i
\(331\) 165646. 1.51190 0.755952 0.654627i \(-0.227174\pi\)
0.755952 + 0.654627i \(0.227174\pi\)
\(332\) 432174.i 3.92087i
\(333\) 136960. + 107566.i 1.23511 + 0.970031i
\(334\) −293337. −2.62951
\(335\) 49232.9i 0.438698i
\(336\) 21839.6 63166.4i 0.193449 0.559509i
\(337\) 142493. 1.25468 0.627340 0.778746i \(-0.284144\pi\)
0.627340 + 0.778746i \(0.284144\pi\)
\(338\) 74484.9i 0.651981i
\(339\) 1022.03 + 353.363i 0.00889330 + 0.00307484i
\(340\) 32065.4 0.277382
\(341\) 133991.i 1.15230i
\(342\) −83441.6 + 106244.i −0.713395 + 0.908344i
\(343\) −53645.5 −0.455979
\(344\) 400048.i 3.38061i
\(345\) −47768.3 + 138159.i −0.401330 + 1.16076i
\(346\) 90136.2 0.752917
\(347\) 230828.i 1.91703i −0.285044 0.958514i \(-0.592008\pi\)
0.285044 0.958514i \(-0.407992\pi\)
\(348\) 361863. + 125113.i 2.98804 + 1.03311i
\(349\) 37673.0 0.309299 0.154650 0.987969i \(-0.450575\pi\)
0.154650 + 0.987969i \(0.450575\pi\)
\(350\) 9876.05i 0.0806208i
\(351\) 83420.5 53723.6i 0.677109 0.436065i
\(352\) 373375. 3.01342
\(353\) 109796.i 0.881124i −0.897722 0.440562i \(-0.854779\pi\)
0.897722 0.440562i \(-0.145221\pi\)
\(354\) 9892.10 28610.8i 0.0789373 0.228309i
\(355\) −151465. −1.20187
\(356\) 131996.i 1.04150i
\(357\) 3552.19 + 1228.16i 0.0278715 + 0.00963649i
\(358\) 229226. 1.78854
\(359\) 108379.i 0.840920i −0.907311 0.420460i \(-0.861869\pi\)
0.907311 0.420460i \(-0.138131\pi\)
\(360\) 246321. + 193456.i 1.90063 + 1.49271i
\(361\) −79827.1 −0.612542
\(362\) 88121.2i 0.672455i
\(363\) −53893.9 + 155876.i −0.409003 + 1.18295i
\(364\) 61114.2 0.461254
\(365\) 160810.i 1.20706i
\(366\) −210823. 72891.5i −1.57382 0.544145i
\(367\) −189422. −1.40637 −0.703185 0.711007i \(-0.748239\pi\)
−0.703185 + 0.711007i \(0.748239\pi\)
\(368\) 465350.i 3.43625i
\(369\) 80580.0 102600.i 0.591800 0.753520i
\(370\) −360080. −2.63024
\(371\) 1431.10i 0.0103974i
\(372\) 84833.0 245361.i 0.613026 1.77305i
\(373\) −4743.01 −0.0340907 −0.0170454 0.999855i \(-0.505426\pi\)
−0.0170454 + 0.999855i \(0.505426\pi\)
\(374\) 48992.3i 0.350255i
\(375\) 142191. + 49162.3i 1.01114 + 0.349599i
\(376\) −289920. −2.05070
\(377\) 148136.i 1.04227i
\(378\) 33652.8 + 52255.2i 0.235525 + 0.365718i
\(379\) 228656. 1.59186 0.795930 0.605389i \(-0.206982\pi\)
0.795930 + 0.605389i \(0.206982\pi\)
\(380\) 198196.i 1.37255i
\(381\) 35024.6 101301.i 0.241281 0.697853i
\(382\) −251841. −1.72584
\(383\) 204491.i 1.39405i 0.717048 + 0.697023i \(0.245493\pi\)
−0.717048 + 0.697023i \(0.754507\pi\)
\(384\) 30702.2 + 10615.2i 0.208212 + 0.0719889i
\(385\) −47062.9 −0.317510
\(386\) 31108.4i 0.208787i
\(387\) 148713. + 116796.i 0.992946 + 0.779840i
\(388\) 552467. 3.66981
\(389\) 129979.i 0.858964i 0.903075 + 0.429482i \(0.141304\pi\)
−0.903075 + 0.429482i \(0.858696\pi\)
\(390\) −67038.5 + 193895.i −0.440753 + 1.27478i
\(391\) −26169.2 −0.171174
\(392\) 388832.i 2.53040i
\(393\) −111474. 38541.7i −0.721750 0.249543i
\(394\) 313594. 2.02011
\(395\) 177427.i 1.13717i
\(396\) −355072. + 452102.i −2.26426 + 2.88301i
\(397\) 173033. 1.09786 0.548930 0.835869i \(-0.315035\pi\)
0.548930 + 0.835869i \(0.315035\pi\)
\(398\) 384987.i 2.43041i
\(399\) 7591.25 21956.0i 0.0476834 0.137914i
\(400\) 74884.7 0.468029
\(401\) 97409.5i 0.605777i 0.953026 + 0.302888i \(0.0979510\pi\)
−0.953026 + 0.302888i \(0.902049\pi\)
\(402\) −137746. 47625.2i −0.852365 0.294703i
\(403\) 100444. 0.618462
\(404\) 107451.i 0.658339i
\(405\) −143829. + 35086.3i −0.876873 + 0.213908i
\(406\) −92793.6 −0.562945
\(407\) 390371.i 2.35661i
\(408\) −18321.5 + 52991.1i −0.110063 + 0.318334i
\(409\) 132708. 0.793326 0.396663 0.917964i \(-0.370168\pi\)
0.396663 + 0.917964i \(0.370168\pi\)
\(410\) 269744.i 1.60466i
\(411\) 264047. + 91293.7i 1.56314 + 0.540452i
\(412\) 52099.7 0.306931
\(413\) 5205.83i 0.0305204i
\(414\) −340339. 267296.i −1.98569 1.55952i
\(415\) 249484. 1.44859
\(416\) 279894.i 1.61736i
\(417\) 2002.11 5790.67i 0.0115137 0.0333010i
\(418\) 302821. 1.73314
\(419\) 147512.i 0.840233i 0.907470 + 0.420117i \(0.138011\pi\)
−0.907470 + 0.420117i \(0.861989\pi\)
\(420\) −86180.5 29796.7i −0.488552 0.168915i
\(421\) −51683.0 −0.291598 −0.145799 0.989314i \(-0.546575\pi\)
−0.145799 + 0.989314i \(0.546575\pi\)
\(422\) 592773.i 3.32862i
\(423\) 84643.4 107774.i 0.473056 0.602327i
\(424\) −21349.0 −0.118753
\(425\) 4211.18i 0.0233145i
\(426\) 146519. 423776.i 0.807376 2.33516i
\(427\) 38360.0 0.210389
\(428\) 516736.i 2.82086i
\(429\) −210206. 72678.1i −1.14217 0.394902i
\(430\) −390978. −2.11454
\(431\) 116826.i 0.628906i 0.949273 + 0.314453i \(0.101821\pi\)
−0.949273 + 0.314453i \(0.898179\pi\)
\(432\) −396222. + 255171.i −2.12311 + 1.36730i
\(433\) −182862. −0.975321 −0.487661 0.873033i \(-0.662150\pi\)
−0.487661 + 0.873033i \(0.662150\pi\)
\(434\) 62918.6i 0.334041i
\(435\) 72225.0 208895.i 0.381688 1.10395i
\(436\) 685284. 3.60494
\(437\) 161752.i 0.847004i
\(438\) −449921. 155559.i −2.34525 0.810863i
\(439\) −47853.4 −0.248304 −0.124152 0.992263i \(-0.539621\pi\)
−0.124152 + 0.992263i \(0.539621\pi\)
\(440\) 702077.i 3.62643i
\(441\) 144543. + 113521.i 0.743224 + 0.583714i
\(442\) −36726.2 −0.187989
\(443\) 314613.i 1.60313i 0.597906 + 0.801566i \(0.295999\pi\)
−0.597906 + 0.801566i \(0.704001\pi\)
\(444\) 247154. 714839.i 1.25372 3.62612i
\(445\) −76197.9 −0.384789
\(446\) 520737.i 2.61787i
\(447\) −131052. 45311.0i −0.655887 0.226771i
\(448\) −56509.1 −0.281554
\(449\) 324728.i 1.61075i 0.592768 + 0.805374i \(0.298035\pi\)
−0.592768 + 0.805374i \(0.701965\pi\)
\(450\) −43013.5 + 54767.7i −0.212412 + 0.270458i
\(451\) −292436. −1.43773
\(452\) 4696.62i 0.0229884i
\(453\) −112957. + 326705.i −0.550450 + 1.59206i
\(454\) 346801. 1.68255
\(455\) 35279.8i 0.170413i
\(456\) 327537. + 113245.i 1.57518 + 0.544615i
\(457\) 228122. 1.09228 0.546141 0.837693i \(-0.316096\pi\)
0.546141 + 0.837693i \(0.316096\pi\)
\(458\) 168524.i 0.803400i
\(459\) −14349.7 22281.8i −0.0681109 0.105761i
\(460\) 634897. 3.00046
\(461\) 260465.i 1.22560i −0.790238 0.612799i \(-0.790043\pi\)
0.790238 0.612799i \(-0.209957\pi\)
\(462\) 45526.0 131674.i 0.213293 0.616903i
\(463\) 39151.0 0.182634 0.0913168 0.995822i \(-0.470892\pi\)
0.0913168 + 0.995822i \(0.470892\pi\)
\(464\) 703603.i 3.26807i
\(465\) −141641. 48972.1i −0.655064 0.226487i
\(466\) 91799.1 0.422733
\(467\) 383832.i 1.75998i −0.474996 0.879988i \(-0.657550\pi\)
0.474996 0.879988i \(-0.342450\pi\)
\(468\) −338910. 266173.i −1.54736 1.21527i
\(469\) 25063.3 0.113944
\(470\) 283346.i 1.28269i
\(471\) 7190.11 20795.8i 0.0324111 0.0937420i
\(472\) −77659.9 −0.348588
\(473\) 423868.i 1.89456i
\(474\) −496413. 171634.i −2.20946 0.763916i
\(475\) 26029.2 0.115365
\(476\) 16323.7i 0.0720453i
\(477\) 6232.93 7936.19i 0.0273940 0.0348799i
\(478\) −310369. −1.35838
\(479\) 238559.i 1.03974i −0.854245 0.519871i \(-0.825980\pi\)
0.854245 0.519871i \(-0.174020\pi\)
\(480\) 136464. 394693.i 0.592293 1.71308i
\(481\) 292634. 1.26484
\(482\) 322067.i 1.38628i
\(483\) 70333.7 + 24317.7i 0.301488 + 0.104239i
\(484\) 716314. 3.05782
\(485\) 318926.i 1.35584i
\(486\) 40966.8 436351.i 0.173444 1.84741i
\(487\) 206624. 0.871210 0.435605 0.900138i \(-0.356534\pi\)
0.435605 + 0.900138i \(0.356534\pi\)
\(488\) 572249.i 2.40295i
\(489\) 20058.9 58015.9i 0.0838858 0.242622i
\(490\) −380016. −1.58274
\(491\) 356108.i 1.47713i 0.674183 + 0.738564i \(0.264496\pi\)
−0.674183 + 0.738564i \(0.735504\pi\)
\(492\) −535502. 185149.i −2.21223 0.764874i
\(493\) 39567.5 0.162796
\(494\) 227004.i 0.930207i
\(495\) 260988. + 204975.i 1.06515 + 0.836545i
\(496\) −477078. −1.93921
\(497\) 77107.5i 0.312165i
\(498\) −241337. + 698016.i −0.973118 + 2.81453i
\(499\) −234823. −0.943062 −0.471531 0.881850i \(-0.656298\pi\)
−0.471531 + 0.881850i \(0.656298\pi\)
\(500\) 653426.i 2.61370i
\(501\) −336171. 116230.i −1.33932 0.463067i
\(502\) 796892. 3.16222
\(503\) 386137.i 1.52618i −0.646294 0.763089i \(-0.723682\pi\)
0.646294 0.763089i \(-0.276318\pi\)
\(504\) 98483.8 125396.i 0.387707 0.493655i
\(505\) 62029.2 0.243228
\(506\) 970052.i 3.78873i
\(507\) −29513.5 + 85361.4i −0.114817 + 0.332082i
\(508\) −465518. −1.80389
\(509\) 47078.4i 0.181713i 0.995864 + 0.0908565i \(0.0289605\pi\)
−0.995864 + 0.0908565i \(0.971040\pi\)
\(510\) 51789.6 + 17906.1i 0.199114 + 0.0688432i
\(511\) 81864.8 0.313513
\(512\) 443103.i 1.69030i
\(513\) −137723. + 88695.1i −0.523327 + 0.337027i
\(514\) −900635. −3.40897
\(515\) 30075.9i 0.113398i
\(516\) 268362. 776178.i 1.00791 2.91516i
\(517\) −307182. −1.14925
\(518\) 183308.i 0.683160i
\(519\) 103298. + 35715.1i 0.383493 + 0.132592i
\(520\) 526299. 1.94637
\(521\) 309459.i 1.14006i 0.821624 + 0.570029i \(0.193068\pi\)
−0.821624 + 0.570029i \(0.806932\pi\)
\(522\) 514588. + 404147.i 1.88851 + 1.48320i
\(523\) 216367. 0.791019 0.395509 0.918462i \(-0.370568\pi\)
0.395509 + 0.918462i \(0.370568\pi\)
\(524\) 512265.i 1.86566i
\(525\) 3913.23 11318.2i 0.0141977 0.0410637i
\(526\) −609281. −2.20215
\(527\) 26828.7i 0.0966003i
\(528\) 998414. + 345199.i 3.58132 + 1.23823i
\(529\) −238312. −0.851598
\(530\) 20864.9i 0.0742788i
\(531\) 22673.2 28869.0i 0.0804124 0.102387i
\(532\) −100897. −0.356495
\(533\) 219219.i 0.771657i
\(534\) 73709.7 213189.i 0.258489 0.747623i
\(535\) −298300. −1.04219
\(536\) 373891.i 1.30141i
\(537\) 262698. + 90827.2i 0.910979 + 0.314969i
\(538\) −159855. −0.552282
\(539\) 411984.i 1.41809i
\(540\) 348140. + 540583.i 1.19390 + 1.85385i
\(541\) 63972.1 0.218573 0.109286 0.994010i \(-0.465143\pi\)
0.109286 + 0.994010i \(0.465143\pi\)
\(542\) 745051.i 2.53622i
\(543\) 34916.7 100989.i 0.118422 0.342511i
\(544\) 74760.1 0.252623
\(545\) 395598.i 1.33187i
\(546\) 98707.2 + 34127.8i 0.331103 + 0.114478i
\(547\) 315353. 1.05396 0.526978 0.849879i \(-0.323325\pi\)
0.526978 + 0.849879i \(0.323325\pi\)
\(548\) 1.21340e6i 4.04058i
\(549\) −212726. 167071.i −0.705790 0.554313i
\(550\) 156102. 0.516039
\(551\) 244566.i 0.805551i
\(552\) −362768. + 1.04923e6i −1.19056 + 3.44344i
\(553\) 90324.2 0.295361
\(554\) 254411.i 0.828926i
\(555\) −412660. 142676.i −1.33969 0.463196i
\(556\) −26610.4 −0.0860800
\(557\) 235733.i 0.759818i −0.925024 0.379909i \(-0.875955\pi\)
0.925024 0.379909i \(-0.124045\pi\)
\(558\) 274032. 348916.i 0.880101 1.12061i
\(559\) 317745. 1.01685
\(560\) 167568.i 0.534338i
\(561\) −19412.4 + 56146.3i −0.0616814 + 0.178400i
\(562\) 73382.9 0.232339
\(563\) 139368.i 0.439689i 0.975535 + 0.219845i \(0.0705550\pi\)
−0.975535 + 0.219845i \(0.929445\pi\)
\(564\) −562506. 194485.i −1.76835 0.611403i
\(565\) −2711.25 −0.00849321
\(566\) 77040.2i 0.240483i
\(567\) 17861.6 + 73220.1i 0.0555590 + 0.227753i
\(568\) −1.15028e6 −3.56538
\(569\) 108323.i 0.334576i 0.985908 + 0.167288i \(0.0535009\pi\)
−0.985908 + 0.167288i \(0.946499\pi\)
\(570\) 110677. 320111.i 0.340651 0.985259i
\(571\) −136058. −0.417305 −0.208652 0.977990i \(-0.566908\pi\)
−0.208652 + 0.977990i \(0.566908\pi\)
\(572\) 965978.i 2.95240i
\(573\) −288616. 99788.2i −0.879045 0.303928i
\(574\) 137320. 0.416784
\(575\) 83381.7i 0.252194i
\(576\) 313372. + 246116.i 0.944528 + 0.741814i
\(577\) −242991. −0.729860 −0.364930 0.931035i \(-0.618907\pi\)
−0.364930 + 0.931035i \(0.618907\pi\)
\(578\) 610095.i 1.82617i
\(579\) −12326.2 + 35651.0i −0.0367683 + 0.106344i
\(580\) −959956. −2.85361
\(581\) 127006.i 0.376247i
\(582\) 892304. + 308512.i 2.63431 + 0.910806i
\(583\) −22620.1 −0.0665516
\(584\) 1.22125e6i 3.58078i
\(585\) −153655. + 195645.i −0.448989 + 0.571684i
\(586\) 351624. 1.02396
\(587\) 199495.i 0.578969i 0.957183 + 0.289485i \(0.0934839\pi\)
−0.957183 + 0.289485i \(0.906516\pi\)
\(588\) 260837. 754416.i 0.754424 2.18201i
\(589\) −165828. −0.477999
\(590\) 75899.0i 0.218038i
\(591\) 359386. + 124257.i 1.02893 + 0.355750i
\(592\) −1.38993e6 −3.96596
\(593\) 218091.i 0.620196i 0.950705 + 0.310098i \(0.100362\pi\)
−0.950705 + 0.310098i \(0.899638\pi\)
\(594\) −825951. + 531920.i −2.34089 + 1.50756i
\(595\) −9423.30 −0.0266176
\(596\) 602236.i 1.69541i
\(597\) −152545. + 441204.i −0.428006 + 1.23792i
\(598\) −727182. −2.03348
\(599\) 347865.i 0.969522i −0.874647 0.484761i \(-0.838907\pi\)
0.874647 0.484761i \(-0.161093\pi\)
\(600\) 168843. + 58377.0i 0.469008 + 0.162158i
\(601\) −63259.7 −0.175137 −0.0875685 0.996158i \(-0.527910\pi\)
−0.0875685 + 0.996158i \(0.527910\pi\)
\(602\) 199038.i 0.549215i
\(603\) −138989. 109159.i −0.382248 0.300210i
\(604\) 1.50134e6 4.11533
\(605\) 413511.i 1.12973i
\(606\) −60003.6 + 173548.i −0.163393 + 0.472578i
\(607\) −407.887 −0.00110704 −0.000553518 1.00000i \(-0.500176\pi\)
−0.000553518 1.00000i \(0.500176\pi\)
\(608\) 462091.i 1.25003i
\(609\) −106344. 36768.0i −0.286733 0.0991370i
\(610\) 559274. 1.50302
\(611\) 230274.i 0.616825i
\(612\) −71095.3 + 90523.4i −0.189818 + 0.241690i
\(613\) −96854.0 −0.257749 −0.128874 0.991661i \(-0.541136\pi\)
−0.128874 + 0.991661i \(0.541136\pi\)
\(614\) 1.35702e6i 3.59955i
\(615\) −106882. + 309133.i −0.282588 + 0.817325i
\(616\) −357411. −0.941904
\(617\) 414820.i 1.08966i 0.838548 + 0.544828i \(0.183405\pi\)
−0.838548 + 0.544828i \(0.816595\pi\)
\(618\) 84147.5 + 29093.8i 0.220325 + 0.0761769i
\(619\) 285041. 0.743919 0.371960 0.928249i \(-0.378686\pi\)
0.371960 + 0.928249i \(0.378686\pi\)
\(620\) 650897.i 1.69328i
\(621\) −284125. 441181.i −0.736760 1.14402i
\(622\) 652558. 1.68670
\(623\) 38790.6i 0.0999425i
\(624\) −258772. + 748443.i −0.664582 + 1.92216i
\(625\) −304810. −0.780313
\(626\) 1.02331e6i 2.61131i
\(627\) 347040. + 119988.i 0.882762 + 0.305213i
\(628\) −95565.0 −0.242315
\(629\) 78163.2i 0.197561i
\(630\) −122553. 96250.8i −0.308776 0.242506i
\(631\) 303230. 0.761576 0.380788 0.924662i \(-0.375653\pi\)
0.380788 + 0.924662i \(0.375653\pi\)
\(632\) 1.34744e6i 3.37346i
\(633\) −234877. + 679332.i −0.586183 + 1.69541i
\(634\) −904151. −2.24938
\(635\) 268733.i 0.666458i
\(636\) −41421.5 14321.4i −0.102403 0.0354055i
\(637\) 308836. 0.761113
\(638\) 1.46671e6i 3.60331i
\(639\) 335829. 427601.i 0.822463 1.04722i
\(640\) −81447.1 −0.198845
\(641\) 595247.i 1.44871i 0.689428 + 0.724354i \(0.257862\pi\)
−0.689428 + 0.724354i \(0.742138\pi\)
\(642\) 288559. 834594.i 0.700107 2.02491i
\(643\) 222035. 0.537032 0.268516 0.963275i \(-0.413467\pi\)
0.268516 + 0.963275i \(0.413467\pi\)
\(644\) 323211.i 0.779318i
\(645\) −448069. 154919.i −1.07703 0.372379i
\(646\) 60633.2 0.145293
\(647\) 378014.i 0.903023i −0.892265 0.451512i \(-0.850885\pi\)
0.892265 0.451512i \(-0.149115\pi\)
\(648\) −1.09229e6 + 266457.i −2.60128 + 0.634566i
\(649\) −82283.9 −0.195355
\(650\) 117019.i 0.276968i
\(651\) −24930.5 + 72106.2i −0.0588261 + 0.170142i
\(652\) −266606. −0.627155
\(653\) 525594.i 1.23260i −0.787510 0.616302i \(-0.788630\pi\)
0.787510 0.616302i \(-0.211370\pi\)
\(654\) 1.10682e6 + 382680.i 2.58775 + 0.894707i
\(655\) 295718. 0.689280
\(656\) 1.04123e6i 2.41956i
\(657\) −453982. 356549.i −1.05174 0.826015i
\(658\) 144245. 0.333157
\(659\) 322632.i 0.742912i −0.928451 0.371456i \(-0.878859\pi\)
0.928451 0.371456i \(-0.121141\pi\)
\(660\) 470970. 1.36218e6i 1.08120 3.12713i
\(661\) 74391.1 0.170262 0.0851311 0.996370i \(-0.472869\pi\)
0.0851311 + 0.996370i \(0.472869\pi\)
\(662\) 1.22945e6i 2.80539i
\(663\) −42089.1 14552.2i −0.0957507 0.0331056i
\(664\) 1.89466e6 4.29730
\(665\) 58245.3i 0.131710i
\(666\) 798369. 1.01654e6i 1.79993 2.29179i
\(667\) 783440. 1.76098
\(668\) 1.54484e6i 3.46203i
\(669\) 206334. 596776.i 0.461018 1.33340i
\(670\) 365413. 0.814020
\(671\) 606322.i 1.34666i
\(672\) −200929. 69470.8i −0.444943 0.153838i
\(673\) 186945. 0.412747 0.206373 0.978473i \(-0.433834\pi\)
0.206373 + 0.978473i \(0.433834\pi\)
\(674\) 1.05760e6i 2.32810i
\(675\) −70995.3 + 45721.7i −0.155820 + 0.100349i
\(676\) 392269. 0.858403
\(677\) 286936.i 0.626048i −0.949745 0.313024i \(-0.898658\pi\)
0.949745 0.313024i \(-0.101342\pi\)
\(678\) 2622.71 7585.63i 0.00570547 0.0165018i
\(679\) −162358. −0.352155
\(680\) 140575.i 0.304013i
\(681\) 397442. + 137415.i 0.856998 + 0.296305i
\(682\) −994498. −2.13814
\(683\) 749589.i 1.60687i −0.595390 0.803437i \(-0.703002\pi\)
0.595390 0.803437i \(-0.296998\pi\)
\(684\) 559524. + 439439.i 1.19593 + 0.939261i
\(685\) −700468. −1.49282
\(686\) 398164.i 0.846086i
\(687\) 66775.2 193133.i 0.141482 0.409207i
\(688\) −1.50919e6 −3.18836
\(689\) 16956.8i 0.0357195i
\(690\) 1.02544e6 + 354543.i 2.15383 + 0.744681i
\(691\) 310447. 0.650177 0.325089 0.945684i \(-0.394606\pi\)
0.325089 + 0.945684i \(0.394606\pi\)
\(692\) 474696.i 0.991296i
\(693\) 104348. 132863.i 0.217278 0.276654i
\(694\) −1.71323e6 −3.55711
\(695\) 15361.6i 0.0318028i
\(696\) 548500. 1.58642e6i 1.13229 3.27491i
\(697\) −58553.8 −0.120529
\(698\) 279614.i 0.573916i
\(699\) 105204. + 36374.0i 0.215316 + 0.0744451i
\(700\) −52011.5 −0.106146
\(701\) 213477.i 0.434425i 0.976124 + 0.217213i \(0.0696965\pi\)
−0.976124 + 0.217213i \(0.930303\pi\)
\(702\) −398744. 619159.i −0.809133 1.25640i
\(703\) −483125. −0.977573
\(704\) 893188.i 1.80218i
\(705\) −112272. + 324721.i −0.225887 + 0.653330i
\(706\) −814921. −1.63496
\(707\) 31577.6i 0.0631743i
\(708\) −150677. 52096.0i −0.300593 0.103929i
\(709\) 136608. 0.271759 0.135879 0.990725i \(-0.456614\pi\)
0.135879 + 0.990725i \(0.456614\pi\)
\(710\) 1.12420e6i 2.23011i
\(711\) −500894. 393392.i −0.990847 0.778191i
\(712\) −578672. −1.14149
\(713\) 531211.i 1.04493i
\(714\) 9115.59 26364.9i 0.0178809 0.0517165i
\(715\) 557636. 1.09078
\(716\) 1.20720e6i 2.35480i
\(717\) −355690. 122979.i −0.691884 0.239217i
\(718\) −804401. −1.56036
\(719\) 248297.i 0.480301i 0.970736 + 0.240151i \(0.0771968\pi\)
−0.970736 + 0.240151i \(0.922803\pi\)
\(720\) 729817. 929253.i 1.40783 1.79254i
\(721\) −15310.9 −0.0294531
\(722\) 592488.i 1.13659i
\(723\) −127614. + 369096.i −0.244130 + 0.706094i
\(724\) −464084. −0.885359
\(725\) 126072.i 0.239852i
\(726\) 1.15694e6 + 400008.i 2.19501 + 0.758919i
\(727\) −867716. −1.64176 −0.820878 0.571103i \(-0.806516\pi\)
−0.820878 + 0.571103i \(0.806516\pi\)
\(728\) 267927.i 0.505537i
\(729\) 219846. 483836.i 0.413679 0.910423i
\(730\) 1.19356e6 2.23974
\(731\) 84870.3i 0.158826i
\(732\) −383878. + 1.11028e6i −0.716425 + 2.07210i
\(733\) 560656. 1.04349 0.521745 0.853101i \(-0.325281\pi\)
0.521745 + 0.853101i \(0.325281\pi\)
\(734\) 1.40592e6i 2.60957i
\(735\) −435507. 150575.i −0.806158 0.278727i
\(736\) 1.48026e6 2.73264
\(737\) 396153.i 0.729337i
\(738\) −761512. 598076.i −1.39818 1.09811i
\(739\) 246818. 0.451947 0.225974 0.974133i \(-0.427444\pi\)
0.225974 + 0.974133i \(0.427444\pi\)
\(740\) 1.89633e6i 3.46299i
\(741\) −89946.8 + 260152.i −0.163813 + 0.473795i
\(742\) 10621.8 0.0192927
\(743\) 78964.1i 0.143038i −0.997439 0.0715191i \(-0.977215\pi\)
0.997439 0.0715191i \(-0.0227847\pi\)
\(744\) −1.07567e6 371910.i −1.94327 0.671881i
\(745\) 347657. 0.626381
\(746\) 35203.3i 0.0632566i
\(747\) −553156. + 704316.i −0.991302 + 1.26219i
\(748\) 258014. 0.461149
\(749\) 151857.i 0.270690i
\(750\) 364890. 1.05536e6i 0.648693 1.87620i
\(751\) −411768. −0.730084 −0.365042 0.930991i \(-0.618945\pi\)
−0.365042 + 0.930991i \(0.618945\pi\)
\(752\) 1.09373e6i 1.93408i
\(753\) 913256. + 315756.i 1.61066 + 0.556880i
\(754\) 1.09949e6 1.93396
\(755\) 866686.i 1.52044i
\(756\) 275198. 177230.i 0.481506 0.310094i
\(757\) −1.00647e6 −1.75634 −0.878171 0.478347i \(-0.841236\pi\)
−0.878171 + 0.478347i \(0.841236\pi\)
\(758\) 1.69712e6i 2.95375i
\(759\) −384368. + 1.11170e6i −0.667212 + 1.92977i
\(760\) −868895. −1.50432
\(761\) 470668.i 0.812729i 0.913711 + 0.406364i \(0.133204\pi\)
−0.913711 + 0.406364i \(0.866796\pi\)
\(762\) −751870. 259957.i −1.29489 0.447705i
\(763\) −201390. −0.345930
\(764\) 1.32630e6i 2.27225i
\(765\) 52257.0 + 41041.6i 0.0892939 + 0.0701297i
\(766\) 1.51776e6 2.58670
\(767\) 61682.6i 0.104851i
\(768\) −152689. + 441621.i −0.258873 + 0.748733i
\(769\) −485133. −0.820367 −0.410183 0.912003i \(-0.634535\pi\)
−0.410183 + 0.912003i \(0.634535\pi\)
\(770\) 349307.i 0.589150i
\(771\) −1.03215e6 356863.i −1.73634 0.600334i
\(772\) 163830. 0.274890
\(773\) 699399.i 1.17049i 0.810858 + 0.585243i \(0.199001\pi\)
−0.810858 + 0.585243i \(0.800999\pi\)
\(774\) 866876. 1.10377e6i 1.44702 1.84245i
\(775\) −85483.0 −0.142323
\(776\) 2.42203e6i 4.02213i
\(777\) −72633.0 + 210075.i −0.120307 + 0.347963i
\(778\) 964724. 1.59384
\(779\) 361920.i 0.596401i
\(780\) 1.02113e6 + 353054.i 1.67839 + 0.580299i
\(781\) −1.21877e6 −1.99811
\(782\) 194232.i 0.317619i