Properties

Label 177.5.c.a.58.20
Level $177$
Weight $5$
Character 177.58
Analytic conductor $18.296$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.20
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.21

$q$-expansion

\(f(q)\) \(=\) \(q-0.389117i q^{2} +5.19615 q^{3} +15.8486 q^{4} -17.9988 q^{5} -2.02191i q^{6} -47.2538 q^{7} -12.3928i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-0.389117i q^{2} +5.19615 q^{3} +15.8486 q^{4} -17.9988 q^{5} -2.02191i q^{6} -47.2538 q^{7} -12.3928i q^{8} +27.0000 q^{9} +7.00365i q^{10} +197.341i q^{11} +82.3517 q^{12} +176.297i q^{13} +18.3873i q^{14} -93.5245 q^{15} +248.755 q^{16} +486.600 q^{17} -10.5062i q^{18} +56.2166 q^{19} -285.256 q^{20} -245.538 q^{21} +76.7889 q^{22} +848.854i q^{23} -64.3951i q^{24} -301.043 q^{25} +68.6003 q^{26} +140.296 q^{27} -748.906 q^{28} +275.393 q^{29} +36.3920i q^{30} -843.954i q^{31} -295.080i q^{32} +1025.42i q^{33} -189.344i q^{34} +850.512 q^{35} +427.912 q^{36} -1855.12i q^{37} -21.8749i q^{38} +916.067i q^{39} +223.056i q^{40} +1479.48 q^{41} +95.5430i q^{42} +2758.38i q^{43} +3127.58i q^{44} -485.968 q^{45} +330.304 q^{46} +1437.11i q^{47} +1292.57 q^{48} -168.080 q^{49} +117.141i q^{50} +2528.45 q^{51} +2794.06i q^{52} -1119.21 q^{53} -54.5917i q^{54} -3551.91i q^{55} +585.608i q^{56} +292.110 q^{57} -107.160i q^{58} +(-1640.41 + 3070.25i) q^{59} -1482.23 q^{60} +115.162i q^{61} -328.397 q^{62} -1275.85 q^{63} +3865.26 q^{64} -3173.14i q^{65} +399.007 q^{66} +49.5250i q^{67} +7711.92 q^{68} +4410.77i q^{69} -330.949i q^{70} -2085.72 q^{71} -334.607i q^{72} +209.953i q^{73} -721.859 q^{74} -1564.26 q^{75} +890.954 q^{76} -9325.12i q^{77} +356.457 q^{78} -6542.76 q^{79} -4477.30 q^{80} +729.000 q^{81} -575.691i q^{82} -6802.27i q^{83} -3891.43 q^{84} -8758.22 q^{85} +1073.33 q^{86} +1430.98 q^{87} +2445.62 q^{88} -9119.14i q^{89} +189.099i q^{90} -8330.70i q^{91} +13453.1i q^{92} -4385.31i q^{93} +559.206 q^{94} -1011.83 q^{95} -1533.28i q^{96} +2946.12i q^{97} +65.4030i q^{98} +5328.21i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.389117i 0.0972793i −0.998816 0.0486397i \(-0.984511\pi\)
0.998816 0.0486397i \(-0.0154886\pi\)
\(3\) 5.19615 0.577350
\(4\) 15.8486 0.990537
\(5\) −17.9988 −0.719952 −0.359976 0.932962i \(-0.617215\pi\)
−0.359976 + 0.932962i \(0.617215\pi\)
\(6\) 2.02191i 0.0561643i
\(7\) −47.2538 −0.964363 −0.482181 0.876071i \(-0.660155\pi\)
−0.482181 + 0.876071i \(0.660155\pi\)
\(8\) 12.3928i 0.193638i
\(9\) 27.0000 0.333333
\(10\) 7.00365i 0.0700365i
\(11\) 197.341i 1.63092i 0.578814 + 0.815460i \(0.303516\pi\)
−0.578814 + 0.815460i \(0.696484\pi\)
\(12\) 82.3517 0.571887
\(13\) 176.297i 1.04318i 0.853197 + 0.521589i \(0.174661\pi\)
−0.853197 + 0.521589i \(0.825339\pi\)
\(14\) 18.3873i 0.0938126i
\(15\) −93.5245 −0.415665
\(16\) 248.755 0.971700
\(17\) 486.600 1.68374 0.841868 0.539683i \(-0.181456\pi\)
0.841868 + 0.539683i \(0.181456\pi\)
\(18\) 10.5062i 0.0324264i
\(19\) 56.2166 0.155725 0.0778624 0.996964i \(-0.475191\pi\)
0.0778624 + 0.996964i \(0.475191\pi\)
\(20\) −285.256 −0.713139
\(21\) −245.538 −0.556775
\(22\) 76.7889 0.158655
\(23\) 848.854i 1.60464i 0.596895 + 0.802319i \(0.296401\pi\)
−0.596895 + 0.802319i \(0.703599\pi\)
\(24\) 64.3951i 0.111797i
\(25\) −301.043 −0.481669
\(26\) 68.6003 0.101480
\(27\) 140.296 0.192450
\(28\) −748.906 −0.955237
\(29\) 275.393 0.327459 0.163729 0.986505i \(-0.447648\pi\)
0.163729 + 0.986505i \(0.447648\pi\)
\(30\) 36.3920i 0.0404356i
\(31\) 843.954i 0.878204i −0.898437 0.439102i \(-0.855297\pi\)
0.898437 0.439102i \(-0.144703\pi\)
\(32\) 295.080i 0.288164i
\(33\) 1025.42i 0.941612i
\(34\) 189.344i 0.163793i
\(35\) 850.512 0.694295
\(36\) 427.912 0.330179
\(37\) 1855.12i 1.35509i −0.735481 0.677546i \(-0.763044\pi\)
0.735481 0.677546i \(-0.236956\pi\)
\(38\) 21.8749i 0.0151488i
\(39\) 916.067i 0.602279i
\(40\) 223.056i 0.139410i
\(41\) 1479.48 0.880118 0.440059 0.897969i \(-0.354958\pi\)
0.440059 + 0.897969i \(0.354958\pi\)
\(42\) 95.5430i 0.0541627i
\(43\) 2758.38i 1.49182i 0.666045 + 0.745912i \(0.267986\pi\)
−0.666045 + 0.745912i \(0.732014\pi\)
\(44\) 3127.58i 1.61549i
\(45\) −485.968 −0.239984
\(46\) 330.304 0.156098
\(47\) 1437.11i 0.650572i 0.945616 + 0.325286i \(0.105461\pi\)
−0.945616 + 0.325286i \(0.894539\pi\)
\(48\) 1292.57 0.561011
\(49\) −168.080 −0.0700043
\(50\) 117.141i 0.0468564i
\(51\) 2528.45 0.972106
\(52\) 2794.06i 1.03331i
\(53\) −1119.21 −0.398439 −0.199219 0.979955i \(-0.563841\pi\)
−0.199219 + 0.979955i \(0.563841\pi\)
\(54\) 54.5917i 0.0187214i
\(55\) 3551.91i 1.17418i
\(56\) 585.608i 0.186737i
\(57\) 292.110 0.0899077
\(58\) 107.160i 0.0318550i
\(59\) −1640.41 + 3070.25i −0.471247 + 0.882001i
\(60\) −1482.23 −0.411731
\(61\) 115.162i 0.0309492i 0.999880 + 0.0154746i \(0.00492592\pi\)
−0.999880 + 0.0154746i \(0.995074\pi\)
\(62\) −328.397 −0.0854311
\(63\) −1275.85 −0.321454
\(64\) 3865.26 0.943667
\(65\) 3173.14i 0.751038i
\(66\) 399.007 0.0915994
\(67\) 49.5250i 0.0110325i 0.999985 + 0.00551626i \(0.00175589\pi\)
−0.999985 + 0.00551626i \(0.998244\pi\)
\(68\) 7711.92 1.66780
\(69\) 4410.77i 0.926439i
\(70\) 330.949i 0.0675406i
\(71\) −2085.72 −0.413751 −0.206876 0.978367i \(-0.566330\pi\)
−0.206876 + 0.978367i \(0.566330\pi\)
\(72\) 334.607i 0.0645460i
\(73\) 209.953i 0.0393982i 0.999806 + 0.0196991i \(0.00627083\pi\)
−0.999806 + 0.0196991i \(0.993729\pi\)
\(74\) −721.859 −0.131822
\(75\) −1564.26 −0.278092
\(76\) 890.954 0.154251
\(77\) 9325.12i 1.57280i
\(78\) 356.457 0.0585893
\(79\) −6542.76 −1.04835 −0.524176 0.851610i \(-0.675626\pi\)
−0.524176 + 0.851610i \(0.675626\pi\)
\(80\) −4477.30 −0.699577
\(81\) 729.000 0.111111
\(82\) 575.691i 0.0856173i
\(83\) 6802.27i 0.987410i −0.869629 0.493705i \(-0.835642\pi\)
0.869629 0.493705i \(-0.164358\pi\)
\(84\) −3891.43 −0.551506
\(85\) −8758.22 −1.21221
\(86\) 1073.33 0.145124
\(87\) 1430.98 0.189058
\(88\) 2445.62 0.315808
\(89\) 9119.14i 1.15126i −0.817710 0.575630i \(-0.804757\pi\)
0.817710 0.575630i \(-0.195243\pi\)
\(90\) 189.099i 0.0233455i
\(91\) 8330.70i 1.00600i
\(92\) 13453.1i 1.58945i
\(93\) 4385.31i 0.507031i
\(94\) 559.206 0.0632872
\(95\) −1011.83 −0.112114
\(96\) 1533.28i 0.166372i
\(97\) 2946.12i 0.313117i 0.987669 + 0.156559i \(0.0500400\pi\)
−0.987669 + 0.156559i \(0.949960\pi\)
\(98\) 65.4030i 0.00680997i
\(99\) 5328.21i 0.543640i
\(100\) −4771.11 −0.477111
\(101\) 4577.99i 0.448779i 0.974500 + 0.224389i \(0.0720388\pi\)
−0.974500 + 0.224389i \(0.927961\pi\)
\(102\) 983.862i 0.0945658i
\(103\) 14158.2i 1.33455i −0.744812 0.667274i \(-0.767461\pi\)
0.744812 0.667274i \(-0.232539\pi\)
\(104\) 2184.82 0.201999
\(105\) 4419.39 0.400852
\(106\) 435.506i 0.0387598i
\(107\) 2298.00 0.200717 0.100358 0.994951i \(-0.468001\pi\)
0.100358 + 0.994951i \(0.468001\pi\)
\(108\) 2223.50 0.190629
\(109\) 18428.3i 1.55107i −0.631302 0.775537i \(-0.717479\pi\)
0.631302 0.775537i \(-0.282521\pi\)
\(110\) −1382.11 −0.114224
\(111\) 9639.49i 0.782362i
\(112\) −11754.6 −0.937071
\(113\) 15385.4i 1.20490i 0.798156 + 0.602451i \(0.205809\pi\)
−0.798156 + 0.602451i \(0.794191\pi\)
\(114\) 113.665i 0.00874616i
\(115\) 15278.4i 1.15526i
\(116\) 4364.59 0.324360
\(117\) 4760.02i 0.347726i
\(118\) 1194.69 + 638.312i 0.0858005 + 0.0458426i
\(119\) −22993.7 −1.62373
\(120\) 1159.03i 0.0804885i
\(121\) −24302.6 −1.65990
\(122\) 44.8115 0.00301072
\(123\) 7687.59 0.508136
\(124\) 13375.5i 0.869893i
\(125\) 16667.7 1.06673
\(126\) 496.456i 0.0312709i
\(127\) 28666.4 1.77732 0.888661 0.458564i \(-0.151636\pi\)
0.888661 + 0.458564i \(0.151636\pi\)
\(128\) 6225.33i 0.379964i
\(129\) 14333.0i 0.861305i
\(130\) −1234.72 −0.0730605
\(131\) 19845.6i 1.15643i 0.815883 + 0.578217i \(0.196251\pi\)
−0.815883 + 0.578217i \(0.803749\pi\)
\(132\) 16251.4i 0.932701i
\(133\) −2656.45 −0.150175
\(134\) 19.2710 0.00107324
\(135\) −2525.16 −0.138555
\(136\) 6030.35i 0.326035i
\(137\) 19165.2 1.02111 0.510555 0.859845i \(-0.329440\pi\)
0.510555 + 0.859845i \(0.329440\pi\)
\(138\) 1716.31 0.0901233
\(139\) −20252.2 −1.04820 −0.524099 0.851658i \(-0.675598\pi\)
−0.524099 + 0.851658i \(0.675598\pi\)
\(140\) 13479.4 0.687725
\(141\) 7467.46i 0.375608i
\(142\) 811.590i 0.0402495i
\(143\) −34790.7 −1.70134
\(144\) 6716.39 0.323900
\(145\) −4956.74 −0.235755
\(146\) 81.6964 0.00383263
\(147\) −873.371 −0.0404170
\(148\) 29401.0i 1.34227i
\(149\) 8521.84i 0.383849i 0.981410 + 0.191925i \(0.0614729\pi\)
−0.981410 + 0.191925i \(0.938527\pi\)
\(150\) 608.683i 0.0270526i
\(151\) 43196.8i 1.89452i −0.320473 0.947258i \(-0.603842\pi\)
0.320473 0.947258i \(-0.396158\pi\)
\(152\) 696.684i 0.0301542i
\(153\) 13138.2 0.561245
\(154\) −3628.57 −0.153001
\(155\) 15190.2i 0.632265i
\(156\) 14518.4i 0.596580i
\(157\) 7274.02i 0.295104i 0.989054 + 0.147552i \(0.0471394\pi\)
−0.989054 + 0.147552i \(0.952861\pi\)
\(158\) 2545.90i 0.101983i
\(159\) −5815.61 −0.230039
\(160\) 5311.09i 0.207465i
\(161\) 40111.6i 1.54745i
\(162\) 283.667i 0.0108088i
\(163\) −15415.8 −0.580219 −0.290109 0.956994i \(-0.593692\pi\)
−0.290109 + 0.956994i \(0.593692\pi\)
\(164\) 23447.6 0.871789
\(165\) 18456.3i 0.677916i
\(166\) −2646.88 −0.0960546
\(167\) 37730.3 1.35288 0.676438 0.736500i \(-0.263523\pi\)
0.676438 + 0.736500i \(0.263523\pi\)
\(168\) 3042.91i 0.107813i
\(169\) −2519.67 −0.0882205
\(170\) 3407.97i 0.117923i
\(171\) 1517.85 0.0519083
\(172\) 43716.4i 1.47771i
\(173\) 12104.2i 0.404430i −0.979341 0.202215i \(-0.935186\pi\)
0.979341 0.202215i \(-0.0648139\pi\)
\(174\) 556.821i 0.0183915i
\(175\) 14225.4 0.464503
\(176\) 49089.7i 1.58476i
\(177\) −8523.82 + 15953.5i −0.272074 + 0.509224i
\(178\) −3548.41 −0.111994
\(179\) 288.509i 0.00900436i 0.999990 + 0.00450218i \(0.00143309\pi\)
−0.999990 + 0.00450218i \(0.998567\pi\)
\(180\) −7701.90 −0.237713
\(181\) −12771.6 −0.389841 −0.194921 0.980819i \(-0.562445\pi\)
−0.194921 + 0.980819i \(0.562445\pi\)
\(182\) −3241.62 −0.0978632
\(183\) 598.400i 0.0178685i
\(184\) 10519.7 0.310719
\(185\) 33389.9i 0.975601i
\(186\) −1706.40 −0.0493237
\(187\) 96026.2i 2.74604i
\(188\) 22776.2i 0.644415i
\(189\) −6629.52 −0.185592
\(190\) 393.722i 0.0109064i
\(191\) 49064.3i 1.34493i −0.740130 0.672464i \(-0.765236\pi\)
0.740130 0.672464i \(-0.234764\pi\)
\(192\) 20084.5 0.544827
\(193\) 51351.0 1.37859 0.689294 0.724481i \(-0.257921\pi\)
0.689294 + 0.724481i \(0.257921\pi\)
\(194\) 1146.39 0.0304598
\(195\) 16488.1i 0.433612i
\(196\) −2663.84 −0.0693418
\(197\) −30154.4 −0.776996 −0.388498 0.921450i \(-0.627006\pi\)
−0.388498 + 0.921450i \(0.627006\pi\)
\(198\) 2073.30 0.0528849
\(199\) 67941.6 1.71565 0.857827 0.513939i \(-0.171814\pi\)
0.857827 + 0.513939i \(0.171814\pi\)
\(200\) 3730.78i 0.0932694i
\(201\) 257.339i 0.00636963i
\(202\) 1781.38 0.0436569
\(203\) −13013.4 −0.315789
\(204\) 40072.3 0.962906
\(205\) −26628.8 −0.633643
\(206\) −5509.21 −0.129824
\(207\) 22919.1i 0.534880i
\(208\) 43854.8i 1.01366i
\(209\) 11093.9i 0.253975i
\(210\) 1719.66i 0.0389946i
\(211\) 2303.99i 0.0517507i 0.999665 + 0.0258754i \(0.00823730\pi\)
−0.999665 + 0.0258754i \(0.991763\pi\)
\(212\) −17738.0 −0.394668
\(213\) −10837.7 −0.238879
\(214\) 894.193i 0.0195256i
\(215\) 49647.6i 1.07404i
\(216\) 1738.67i 0.0372657i
\(217\) 39880.0i 0.846907i
\(218\) −7170.78 −0.150888
\(219\) 1090.95i 0.0227466i
\(220\) 56292.7i 1.16307i
\(221\) 85786.1i 1.75644i
\(222\) −3750.89 −0.0761077
\(223\) 28222.6 0.567527 0.283764 0.958894i \(-0.408417\pi\)
0.283764 + 0.958894i \(0.408417\pi\)
\(224\) 13943.7i 0.277895i
\(225\) −8128.16 −0.160556
\(226\) 5986.73 0.117212
\(227\) 63511.2i 1.23253i −0.787538 0.616267i \(-0.788644\pi\)
0.787538 0.616267i \(-0.211356\pi\)
\(228\) 4629.53 0.0890569
\(229\) 36930.9i 0.704236i −0.935956 0.352118i \(-0.885462\pi\)
0.935956 0.352118i \(-0.114538\pi\)
\(230\) −5945.07 −0.112383
\(231\) 48454.7i 0.908055i
\(232\) 3412.90i 0.0634085i
\(233\) 53127.8i 0.978610i −0.872113 0.489305i \(-0.837250\pi\)
0.872113 0.489305i \(-0.162750\pi\)
\(234\) 1852.21 0.0338266
\(235\) 25866.3i 0.468381i
\(236\) −25998.2 + 48659.1i −0.466787 + 0.873655i
\(237\) −33997.2 −0.605266
\(238\) 8947.24i 0.157956i
\(239\) −24487.8 −0.428700 −0.214350 0.976757i \(-0.568763\pi\)
−0.214350 + 0.976757i \(0.568763\pi\)
\(240\) −23264.7 −0.403901
\(241\) 12746.1 0.219454 0.109727 0.993962i \(-0.465002\pi\)
0.109727 + 0.993962i \(0.465002\pi\)
\(242\) 9456.55i 0.161474i
\(243\) 3788.00 0.0641500
\(244\) 1825.16i 0.0306563i
\(245\) 3025.25 0.0503998
\(246\) 2991.38i 0.0494312i
\(247\) 9910.83i 0.162449i
\(248\) −10459.0 −0.170054
\(249\) 35345.6i 0.570082i
\(250\) 6485.68i 0.103771i
\(251\) 44798.5 0.711076 0.355538 0.934662i \(-0.384298\pi\)
0.355538 + 0.934662i \(0.384298\pi\)
\(252\) −20220.5 −0.318412
\(253\) −167514. −2.61704
\(254\) 11154.6i 0.172897i
\(255\) −45509.0 −0.699870
\(256\) 59421.8 0.906705
\(257\) 105733. 1.60083 0.800413 0.599449i \(-0.204614\pi\)
0.800413 + 0.599449i \(0.204614\pi\)
\(258\) 5577.21 0.0837871
\(259\) 87661.4i 1.30680i
\(260\) 50289.7i 0.743931i
\(261\) 7435.61 0.109153
\(262\) 7722.25 0.112497
\(263\) 9304.75 0.134522 0.0672610 0.997735i \(-0.478574\pi\)
0.0672610 + 0.997735i \(0.478574\pi\)
\(264\) 12707.8 0.182332
\(265\) 20144.5 0.286857
\(266\) 1033.67i 0.0146089i
\(267\) 47384.4i 0.664681i
\(268\) 784.901i 0.0109281i
\(269\) 6683.88i 0.0923685i 0.998933 + 0.0461842i \(0.0147061\pi\)
−0.998933 + 0.0461842i \(0.985294\pi\)
\(270\) 982.585i 0.0134785i
\(271\) −137964. −1.87856 −0.939282 0.343145i \(-0.888508\pi\)
−0.939282 + 0.343145i \(0.888508\pi\)
\(272\) 121044. 1.63609
\(273\) 43287.6i 0.580816i
\(274\) 7457.51i 0.0993329i
\(275\) 59408.2i 0.785563i
\(276\) 69904.5i 0.917671i
\(277\) 96139.5 1.25298 0.626488 0.779431i \(-0.284492\pi\)
0.626488 + 0.779431i \(0.284492\pi\)
\(278\) 7880.49i 0.101968i
\(279\) 22786.8i 0.292735i
\(280\) 10540.3i 0.134442i
\(281\) −13544.9 −0.171539 −0.0857696 0.996315i \(-0.527335\pi\)
−0.0857696 + 0.996315i \(0.527335\pi\)
\(282\) 2905.72 0.0365389
\(283\) 147321.i 1.83946i 0.392547 + 0.919732i \(0.371594\pi\)
−0.392547 + 0.919732i \(0.628406\pi\)
\(284\) −33055.7 −0.409836
\(285\) −5257.64 −0.0647293
\(286\) 13537.7i 0.165505i
\(287\) −69910.9 −0.848753
\(288\) 7967.17i 0.0960548i
\(289\) 153258. 1.83497
\(290\) 1928.76i 0.0229341i
\(291\) 15308.5i 0.180778i
\(292\) 3327.46i 0.0390254i
\(293\) 21384.4 0.249094 0.124547 0.992214i \(-0.460252\pi\)
0.124547 + 0.992214i \(0.460252\pi\)
\(294\) 339.844i 0.00393174i
\(295\) 29525.4 55260.8i 0.339275 0.634999i
\(296\) −22990.2 −0.262397
\(297\) 27686.2i 0.313871i
\(298\) 3316.00 0.0373406
\(299\) −149650. −1.67392
\(300\) −24791.4 −0.275460
\(301\) 130344.i 1.43866i
\(302\) −16808.6 −0.184297
\(303\) 23788.0i 0.259103i
\(304\) 13984.2 0.151318
\(305\) 2072.78i 0.0222820i
\(306\) 5112.30i 0.0545976i
\(307\) −89703.8 −0.951775 −0.475887 0.879506i \(-0.657873\pi\)
−0.475887 + 0.879506i \(0.657873\pi\)
\(308\) 147790.i 1.55791i
\(309\) 73568.3i 0.770502i
\(310\) 5910.76 0.0615063
\(311\) −23438.7 −0.242333 −0.121166 0.992632i \(-0.538663\pi\)
−0.121166 + 0.992632i \(0.538663\pi\)
\(312\) 11352.7 0.116624
\(313\) 48687.8i 0.496971i 0.968636 + 0.248486i \(0.0799329\pi\)
−0.968636 + 0.248486i \(0.920067\pi\)
\(314\) 2830.45 0.0287075
\(315\) 22963.8 0.231432
\(316\) −103694. −1.03843
\(317\) −126653. −1.26036 −0.630182 0.776448i \(-0.717020\pi\)
−0.630182 + 0.776448i \(0.717020\pi\)
\(318\) 2262.95i 0.0223780i
\(319\) 54346.4i 0.534059i
\(320\) −69570.1 −0.679395
\(321\) 11940.8 0.115884
\(322\) −15608.1 −0.150535
\(323\) 27355.0 0.262199
\(324\) 11553.6 0.110060
\(325\) 53073.0i 0.502466i
\(326\) 5998.57i 0.0564433i
\(327\) 95756.4i 0.895514i
\(328\) 18334.9i 0.170424i
\(329\) 67909.0i 0.627387i
\(330\) −7181.65 −0.0659472
\(331\) 177452. 1.61966 0.809831 0.586663i \(-0.199559\pi\)
0.809831 + 0.586663i \(0.199559\pi\)
\(332\) 107806.i 0.978066i
\(333\) 50088.2i 0.451697i
\(334\) 14681.5i 0.131607i
\(335\) 891.390i 0.00794289i
\(336\) −61078.8 −0.541018
\(337\) 88144.0i 0.776127i −0.921633 0.388064i \(-0.873144\pi\)
0.921633 0.388064i \(-0.126856\pi\)
\(338\) 980.446i 0.00858203i
\(339\) 79944.9i 0.695651i
\(340\) −138805. −1.20074
\(341\) 166547. 1.43228
\(342\) 590.621i 0.00504960i
\(343\) 121399. 1.03187
\(344\) 34184.2 0.288874
\(345\) 79388.7i 0.666992i
\(346\) −4709.95 −0.0393427
\(347\) 79473.9i 0.660033i −0.943975 0.330016i \(-0.892946\pi\)
0.943975 0.330016i \(-0.107054\pi\)
\(348\) 22679.1 0.187269
\(349\) 24382.5i 0.200183i 0.994978 + 0.100091i \(0.0319135\pi\)
−0.994978 + 0.100091i \(0.968086\pi\)
\(350\) 5535.36i 0.0451866i
\(351\) 24733.8i 0.200760i
\(352\) 58231.5 0.469973
\(353\) 61148.2i 0.490720i 0.969432 + 0.245360i \(0.0789062\pi\)
−0.969432 + 0.245360i \(0.921094\pi\)
\(354\) 6207.77 + 3316.77i 0.0495370 + 0.0264672i
\(355\) 37540.5 0.297881
\(356\) 144525.i 1.14037i
\(357\) −119479. −0.937462
\(358\) 112.264 0.000875939
\(359\) −241084. −1.87059 −0.935297 0.353864i \(-0.884868\pi\)
−0.935297 + 0.353864i \(0.884868\pi\)
\(360\) 6022.52i 0.0464701i
\(361\) −127161. −0.975750
\(362\) 4969.64i 0.0379235i
\(363\) −126280. −0.958343
\(364\) 132030.i 0.996482i
\(365\) 3778.91i 0.0283648i
\(366\) 232.848 0.00173824
\(367\) 237472.i 1.76311i 0.472078 + 0.881557i \(0.343504\pi\)
−0.472078 + 0.881557i \(0.656496\pi\)
\(368\) 211157.i 1.55923i
\(369\) 39945.9 0.293373
\(370\) 12992.6 0.0949058
\(371\) 52887.1 0.384239
\(372\) 69501.0i 0.502233i
\(373\) −168379. −1.21023 −0.605117 0.796137i \(-0.706874\pi\)
−0.605117 + 0.796137i \(0.706874\pi\)
\(374\) 37365.5 0.267133
\(375\) 86607.7 0.615877
\(376\) 17809.9 0.125976
\(377\) 48551.0i 0.341598i
\(378\) 2579.66i 0.0180542i
\(379\) 234352. 1.63152 0.815758 0.578394i \(-0.196320\pi\)
0.815758 + 0.578394i \(0.196320\pi\)
\(380\) −16036.1 −0.111053
\(381\) 148955. 1.02614
\(382\) −19091.8 −0.130834
\(383\) 114382. 0.779762 0.389881 0.920865i \(-0.372516\pi\)
0.389881 + 0.920865i \(0.372516\pi\)
\(384\) 32347.7i 0.219372i
\(385\) 167841.i 1.13234i
\(386\) 19981.6i 0.134108i
\(387\) 74476.3i 0.497274i
\(388\) 46691.9i 0.310154i
\(389\) −248829. −1.64438 −0.822189 0.569215i \(-0.807247\pi\)
−0.822189 + 0.569215i \(0.807247\pi\)
\(390\) −6415.81 −0.0421815
\(391\) 413052.i 2.70179i
\(392\) 2082.99i 0.0135555i
\(393\) 103121.i 0.667668i
\(394\) 11733.6i 0.0755857i
\(395\) 117762. 0.754763
\(396\) 84444.7i 0.538495i
\(397\) 178881.i 1.13497i 0.823385 + 0.567483i \(0.192083\pi\)
−0.823385 + 0.567483i \(0.807917\pi\)
\(398\) 26437.2i 0.166898i
\(399\) −13803.3 −0.0867037
\(400\) −74886.0 −0.468037
\(401\) 79311.1i 0.493225i −0.969114 0.246613i \(-0.920682\pi\)
0.969114 0.246613i \(-0.0793175\pi\)
\(402\) 100.135 0.000619633
\(403\) 148787. 0.916123
\(404\) 72554.7i 0.444532i
\(405\) −13121.1 −0.0799947
\(406\) 5063.72i 0.0307198i
\(407\) 366092. 2.21004
\(408\) 31334.6i 0.188237i
\(409\) 85968.6i 0.513917i 0.966422 + 0.256959i \(0.0827204\pi\)
−0.966422 + 0.256959i \(0.917280\pi\)
\(410\) 10361.7i 0.0616404i
\(411\) 99585.3 0.589538
\(412\) 224388.i 1.32192i
\(413\) 77515.6 145081.i 0.454453 0.850569i
\(414\) 8918.20 0.0520327
\(415\) 122433.i 0.710888i
\(416\) 52021.8 0.300607
\(417\) −105234. −0.605177
\(418\) 4316.81 0.0247065
\(419\) 282200.i 1.60742i 0.595023 + 0.803709i \(0.297143\pi\)
−0.595023 + 0.803709i \(0.702857\pi\)
\(420\) 70041.1 0.397058
\(421\) 254214.i 1.43428i −0.696928 0.717141i \(-0.745450\pi\)
0.696928 0.717141i \(-0.254550\pi\)
\(422\) 896.524 0.00503427
\(423\) 38802.1i 0.216857i
\(424\) 13870.2i 0.0771529i
\(425\) −146487. −0.811003
\(426\) 4217.15i 0.0232380i
\(427\) 5441.84i 0.0298463i
\(428\) 36420.1 0.198817
\(429\) −180778. −0.982269
\(430\) −19318.7 −0.104482
\(431\) 196721.i 1.05900i 0.848310 + 0.529500i \(0.177620\pi\)
−0.848310 + 0.529500i \(0.822380\pi\)
\(432\) 34899.4 0.187004
\(433\) 246611. 1.31533 0.657667 0.753309i \(-0.271543\pi\)
0.657667 + 0.753309i \(0.271543\pi\)
\(434\) 15518.0 0.0823866
\(435\) −25756.0 −0.136113
\(436\) 292063.i 1.53640i
\(437\) 47719.7i 0.249882i
\(438\) 424.507 0.00221277
\(439\) 73628.2 0.382046 0.191023 0.981586i \(-0.438820\pi\)
0.191023 + 0.981586i \(0.438820\pi\)
\(440\) −44018.2 −0.227367
\(441\) −4538.17 −0.0233348
\(442\) 33380.9 0.170865
\(443\) 21033.6i 0.107178i −0.998563 0.0535890i \(-0.982934\pi\)
0.998563 0.0535890i \(-0.0170661\pi\)
\(444\) 152772.i 0.774959i
\(445\) 164134.i 0.828853i
\(446\) 10981.9i 0.0552087i
\(447\) 44280.8i 0.221616i
\(448\) −182648. −0.910038
\(449\) 99536.9 0.493732 0.246866 0.969050i \(-0.420599\pi\)
0.246866 + 0.969050i \(0.420599\pi\)
\(450\) 3162.81i 0.0156188i
\(451\) 291962.i 1.43540i
\(452\) 243837.i 1.19350i
\(453\) 224457.i 1.09380i
\(454\) −24713.3 −0.119900
\(455\) 149943.i 0.724274i
\(456\) 3620.07i 0.0174096i
\(457\) 282977.i 1.35494i −0.735551 0.677469i \(-0.763077\pi\)
0.735551 0.677469i \(-0.236923\pi\)
\(458\) −14370.4 −0.0685077
\(459\) 68268.1 0.324035
\(460\) 242140.i 1.14433i
\(461\) 3519.59 0.0165611 0.00828057 0.999966i \(-0.497364\pi\)
0.00828057 + 0.999966i \(0.497364\pi\)
\(462\) −18854.6 −0.0883350
\(463\) 295702.i 1.37940i 0.724093 + 0.689702i \(0.242259\pi\)
−0.724093 + 0.689702i \(0.757741\pi\)
\(464\) 68505.4 0.318192
\(465\) 78930.4i 0.365038i
\(466\) −20672.9 −0.0951986
\(467\) 77026.5i 0.353189i 0.984284 + 0.176594i \(0.0565081\pi\)
−0.984284 + 0.176594i \(0.943492\pi\)
\(468\) 75439.6i 0.344435i
\(469\) 2340.24i 0.0106394i
\(470\) −10065.0 −0.0455638
\(471\) 37796.9i 0.170378i
\(472\) 38049.1 + 20329.3i 0.170789 + 0.0912513i
\(473\) −544342. −2.43304
\(474\) 13228.9i 0.0588799i
\(475\) −16923.6 −0.0750077
\(476\) −364417. −1.60837
\(477\) −30218.8 −0.132813
\(478\) 9528.62i 0.0417037i
\(479\) 76085.5 0.331612 0.165806 0.986158i \(-0.446977\pi\)
0.165806 + 0.986158i \(0.446977\pi\)
\(480\) 27597.3i 0.119780i
\(481\) 327052. 1.41360
\(482\) 4959.73i 0.0213483i
\(483\) 208426.i 0.893423i
\(484\) −385161. −1.64419
\(485\) 53026.7i 0.225430i
\(486\) 1473.97i 0.00624047i
\(487\) 174246. 0.734690 0.367345 0.930085i \(-0.380267\pi\)
0.367345 + 0.930085i \(0.380267\pi\)
\(488\) 1427.18 0.00599295
\(489\) −80103.0 −0.334989
\(490\) 1177.18i 0.00490285i
\(491\) 328811. 1.36390 0.681951 0.731398i \(-0.261132\pi\)
0.681951 + 0.731398i \(0.261132\pi\)
\(492\) 121838. 0.503328
\(493\) 134006. 0.551354
\(494\) 3856.48 0.0158029
\(495\) 95901.5i 0.391395i
\(496\) 209938.i 0.853351i
\(497\) 98558.2 0.399006
\(498\) −13753.6 −0.0554572
\(499\) −289611. −1.16309 −0.581546 0.813513i \(-0.697552\pi\)
−0.581546 + 0.813513i \(0.697552\pi\)
\(500\) 264159. 1.05664
\(501\) 196053. 0.781083
\(502\) 17431.9i 0.0691730i
\(503\) 453397.i 1.79202i −0.444036 0.896009i \(-0.646454\pi\)
0.444036 0.896009i \(-0.353546\pi\)
\(504\) 15811.4i 0.0622458i
\(505\) 82398.4i 0.323099i
\(506\) 65182.6i 0.254584i
\(507\) −13092.6 −0.0509341
\(508\) 454323. 1.76050
\(509\) 427793.i 1.65119i −0.564260 0.825597i \(-0.690839\pi\)
0.564260 0.825597i \(-0.309161\pi\)
\(510\) 17708.4i 0.0680829i
\(511\) 9921.08i 0.0379942i
\(512\) 122727.i 0.468167i
\(513\) 7886.98 0.0299692
\(514\) 41142.5i 0.155727i
\(515\) 254831.i 0.960811i
\(516\) 227157.i 0.853154i
\(517\) −283602. −1.06103
\(518\) 34110.6 0.127125
\(519\) 62895.1i 0.233498i
\(520\) −39324.2 −0.145430
\(521\) −142162. −0.523730 −0.261865 0.965105i \(-0.584337\pi\)
−0.261865 + 0.965105i \(0.584337\pi\)
\(522\) 2893.32i 0.0106183i
\(523\) −197294. −0.721289 −0.360645 0.932703i \(-0.617443\pi\)
−0.360645 + 0.932703i \(0.617443\pi\)
\(524\) 314524.i 1.14549i
\(525\) 73917.4 0.268181
\(526\) 3620.64i 0.0130862i
\(527\) 410668.i 1.47866i
\(528\) 255077.i 0.914964i
\(529\) −440712. −1.57487
\(530\) 7838.58i 0.0279052i
\(531\) −44291.1 + 82896.7i −0.157082 + 0.294000i
\(532\) −42101.0 −0.148754
\(533\) 260828.i 0.918120i
\(534\) −18438.1 −0.0646597
\(535\) −41361.3 −0.144506
\(536\) 613.755 0.00213632
\(537\) 1499.14i 0.00519867i
\(538\) 2600.81 0.00898554
\(539\) 33169.2i 0.114171i
\(540\) −40020.3 −0.137244
\(541\) 225666.i 0.771029i −0.922702 0.385515i \(-0.874024\pi\)
0.922702 0.385515i \(-0.125976\pi\)
\(542\) 53684.1i 0.182746i
\(543\) −66363.1 −0.225075
\(544\) 143586.i 0.485193i
\(545\) 331688.i 1.11670i
\(546\) −16844.0 −0.0565014
\(547\) 648.964 0.00216893 0.00108447 0.999999i \(-0.499655\pi\)
0.00108447 + 0.999999i \(0.499655\pi\)
\(548\) 303741. 1.01145
\(549\) 3109.38i 0.0103164i
\(550\) −23116.8 −0.0764190
\(551\) 15481.7 0.0509935
\(552\) 54662.0 0.179394
\(553\) 309170. 1.01099
\(554\) 37409.6i 0.121889i
\(555\) 173499.i 0.563264i
\(556\) −320969. −1.03828
\(557\) 179490. 0.578536 0.289268 0.957248i \(-0.406588\pi\)
0.289268 + 0.957248i \(0.406588\pi\)
\(558\) −8866.72 −0.0284770
\(559\) −486295. −1.55624
\(560\) 211569. 0.674647
\(561\) 498967.i 1.58543i
\(562\) 5270.56i 0.0166872i
\(563\) 56816.3i 0.179249i 0.995976 + 0.0896243i \(0.0285666\pi\)
−0.995976 + 0.0896243i \(0.971433\pi\)
\(564\) 118349.i 0.372053i
\(565\) 276919.i 0.867472i
\(566\) 57325.1 0.178942
\(567\) −34448.0 −0.107151
\(568\) 25848.0i 0.0801180i
\(569\) 361962.i 1.11799i −0.829170 0.558996i \(-0.811187\pi\)
0.829170 0.558996i \(-0.188813\pi\)
\(570\) 2045.84i 0.00629682i
\(571\) 496112.i 1.52163i −0.648972 0.760813i \(-0.724801\pi\)
0.648972 0.760813i \(-0.275199\pi\)
\(572\) −551383. −1.68524
\(573\) 254946.i 0.776494i
\(574\) 27203.6i 0.0825661i
\(575\) 255541.i 0.772904i
\(576\) 104362. 0.314556
\(577\) −9847.40 −0.0295781 −0.0147890 0.999891i \(-0.504708\pi\)
−0.0147890 + 0.999891i \(0.504708\pi\)
\(578\) 59635.5i 0.178504i
\(579\) 266828. 0.795929
\(580\) −78557.4 −0.233524
\(581\) 321433.i 0.952222i
\(582\) 5956.80 0.0175860
\(583\) 220867.i 0.649821i
\(584\) 2601.92 0.00762900
\(585\) 85674.7i 0.250346i
\(586\) 8321.06i 0.0242317i
\(587\) 550647.i 1.59807i 0.601282 + 0.799037i \(0.294657\pi\)
−0.601282 + 0.799037i \(0.705343\pi\)
\(588\) −13841.7 −0.0400345
\(589\) 47444.3i 0.136758i
\(590\) −21502.9 11488.9i −0.0617723 0.0330045i
\(591\) −156687. −0.448599
\(592\) 461471.i 1.31674i
\(593\) −455801. −1.29618 −0.648090 0.761563i \(-0.724432\pi\)
−0.648090 + 0.761563i \(0.724432\pi\)
\(594\) 10773.2 0.0305331
\(595\) 413859. 1.16901
\(596\) 135059.i 0.380217i
\(597\) 353035. 0.990533
\(598\) 58231.6i 0.162838i
\(599\) 556678. 1.55149 0.775747 0.631044i \(-0.217373\pi\)
0.775747 + 0.631044i \(0.217373\pi\)
\(600\) 19385.7i 0.0538491i
\(601\) 157038.i 0.434766i 0.976086 + 0.217383i \(0.0697520\pi\)
−0.976086 + 0.217383i \(0.930248\pi\)
\(602\) −50719.1 −0.139952
\(603\) 1337.17i 0.00367751i
\(604\) 684609.i 1.87659i
\(605\) 437417. 1.19505
\(606\) 9256.31 0.0252053
\(607\) −550937. −1.49529 −0.747644 0.664100i \(-0.768815\pi\)
−0.747644 + 0.664100i \(0.768815\pi\)
\(608\) 16588.4i 0.0448743i
\(609\) −67619.4 −0.182321
\(610\) −806.554 −0.00216757
\(611\) −253359. −0.678662
\(612\) 208222. 0.555934
\(613\) 582881.i 1.55117i −0.631244 0.775585i \(-0.717455\pi\)
0.631244 0.775585i \(-0.282545\pi\)
\(614\) 34905.3i 0.0925880i
\(615\) −138368. −0.365834
\(616\) −115565. −0.304554
\(617\) −498475. −1.30940 −0.654701 0.755888i \(-0.727205\pi\)
−0.654701 + 0.755888i \(0.727205\pi\)
\(618\) −28626.7 −0.0749539
\(619\) 469002. 1.22403 0.612017 0.790844i \(-0.290358\pi\)
0.612017 + 0.790844i \(0.290358\pi\)
\(620\) 240743.i 0.626282i
\(621\) 119091.i 0.308813i
\(622\) 9120.40i 0.0235740i
\(623\) 430914.i 1.11023i
\(624\) 227876.i 0.585234i
\(625\) −111846. −0.286327
\(626\) 18945.3 0.0483450
\(627\) 57645.4i 0.146632i
\(628\) 115283.i 0.292311i
\(629\) 902701.i 2.28162i
\(630\) 8935.62i 0.0225135i
\(631\) −55781.7 −0.140098 −0.0700492 0.997544i \(-0.522316\pi\)
−0.0700492 + 0.997544i \(0.522316\pi\)
\(632\) 81083.4i 0.203001i
\(633\) 11971.9i 0.0298783i
\(634\) 49282.7i 0.122607i
\(635\) −515962. −1.27959
\(636\) −92169.2 −0.227862
\(637\) 29632.1i 0.0730269i
\(638\) 21147.1 0.0519529
\(639\) −56314.5 −0.137917
\(640\) 112048.i 0.273556i
\(641\) −77645.7 −0.188974 −0.0944869 0.995526i \(-0.530121\pi\)
−0.0944869 + 0.995526i \(0.530121\pi\)
\(642\) 4646.36i 0.0112731i
\(643\) 295599. 0.714960 0.357480 0.933921i \(-0.383636\pi\)
0.357480 + 0.933921i \(0.383636\pi\)
\(644\) 635711.i 1.53281i
\(645\) 257976.i 0.620098i
\(646\) 10644.3i 0.0255066i
\(647\) −392444. −0.937496 −0.468748 0.883332i \(-0.655295\pi\)
−0.468748 + 0.883332i \(0.655295\pi\)
\(648\) 9034.38i 0.0215153i
\(649\) −605886. 323721.i −1.43847 0.768565i
\(650\) −20651.6 −0.0488796
\(651\) 207223.i 0.488962i
\(652\) −244319. −0.574728
\(653\) −225024. −0.527720 −0.263860 0.964561i \(-0.584996\pi\)
−0.263860 + 0.964561i \(0.584996\pi\)
\(654\) −37260.5 −0.0871150
\(655\) 357197.i 0.832577i
\(656\) 368028. 0.855210
\(657\) 5668.74i 0.0131327i
\(658\) −26424.6 −0.0610318
\(659\) 490926.i 1.13044i −0.824942 0.565218i \(-0.808792\pi\)
0.824942 0.565218i \(-0.191208\pi\)
\(660\) 292506.i 0.671500i
\(661\) −209902. −0.480412 −0.240206 0.970722i \(-0.577215\pi\)
−0.240206 + 0.970722i \(0.577215\pi\)
\(662\) 69049.6i 0.157560i
\(663\) 445758.i 1.01408i
\(664\) −84299.4 −0.191200
\(665\) 47812.9 0.108119
\(666\) −19490.2 −0.0439408
\(667\) 233768.i 0.525453i
\(668\) 597973. 1.34007
\(669\) 146649. 0.327662
\(670\) −346.855 −0.000772679
\(671\) −22726.2 −0.0504757
\(672\) 72453.4i 0.160443i
\(673\) 535935.i 1.18327i 0.806208 + 0.591633i \(0.201516\pi\)
−0.806208 + 0.591633i \(0.798484\pi\)
\(674\) −34298.4 −0.0755012
\(675\) −42235.2 −0.0926972
\(676\) −39933.1 −0.0873857
\(677\) 589822. 1.28690 0.643448 0.765489i \(-0.277503\pi\)
0.643448 + 0.765489i \(0.277503\pi\)
\(678\) 31107.9 0.0676725
\(679\) 139215.i 0.301959i
\(680\) 108539.i 0.234730i
\(681\) 330014.i 0.711603i
\(682\) 64806.3i 0.139331i
\(683\) 569992.i 1.22188i 0.791678 + 0.610939i \(0.209208\pi\)
−0.791678 + 0.610939i \(0.790792\pi\)
\(684\) 24055.8 0.0514170
\(685\) −344951. −0.735150
\(686\) 47238.4i 0.100380i
\(687\) 191898.i 0.406591i
\(688\) 686161.i 1.44960i
\(689\) 197314.i 0.415642i
\(690\) −30891.5 −0.0648845
\(691\) 151727.i 0.317765i 0.987297 + 0.158883i \(0.0507891\pi\)
−0.987297 + 0.158883i \(0.949211\pi\)
\(692\) 191834.i 0.400602i
\(693\) 251778.i 0.524266i
\(694\) −30924.7 −0.0642076
\(695\) 364516. 0.754652
\(696\) 17734.0i 0.0366089i
\(697\) 719914. 1.48189
\(698\) 9487.65 0.0194737
\(699\) 276060.i 0.565001i
\(700\) 225453. 0.460108
\(701\) 288172.i 0.586429i 0.956047 + 0.293214i \(0.0947250\pi\)
−0.956047 + 0.293214i \(0.905275\pi\)
\(702\) 9624.35 0.0195298
\(703\) 104289.i 0.211021i
\(704\) 762776.i 1.53905i
\(705\) 134405.i 0.270420i
\(706\) 23793.8 0.0477369
\(707\) 216328.i 0.432786i
\(708\) −135090. + 252840.i −0.269500 + 0.504405i
\(709\) −17367.9 −0.0345506 −0.0172753 0.999851i \(-0.505499\pi\)
−0.0172753 + 0.999851i \(0.505499\pi\)
\(710\) 14607.7i 0.0289777i
\(711\) −176655. −0.349450
\(712\) −113012. −0.222928
\(713\) 716394. 1.40920
\(714\) 46491.2i 0.0911957i
\(715\) 626191. 1.22488
\(716\) 4572.46i 0.00891915i
\(717\) −127242. −0.247510
\(718\) 93810.0i 0.181970i
\(719\) 524931.i 1.01542i −0.861529 0.507708i \(-0.830493\pi\)
0.861529 0.507708i \(-0.169507\pi\)
\(720\) −120887. −0.233192
\(721\) 669029.i 1.28699i
\(722\) 49480.4i 0.0949203i
\(723\) 66230.7 0.126702
\(724\) −202412. −0.386152
\(725\) −82905.1 −0.157727
\(726\) 49137.7i 0.0932269i
\(727\) 416443. 0.787928 0.393964 0.919126i \(-0.371103\pi\)
0.393964 + 0.919126i \(0.371103\pi\)
\(728\) −103241. −0.194800
\(729\) 19683.0 0.0370370
\(730\) −1470.44 −0.00275931
\(731\) 1.34223e6i 2.51184i
\(732\) 9483.79i 0.0176994i
\(733\) −22984.6 −0.0427788 −0.0213894 0.999771i \(-0.506809\pi\)
−0.0213894 + 0.999771i \(0.506809\pi\)
\(734\) 92404.5 0.171515
\(735\) 15719.6 0.0290983
\(736\) 250480. 0.462400
\(737\) −9773.32 −0.0179931
\(738\) 15543.6i 0.0285391i
\(739\) 339929.i 0.622442i 0.950337 + 0.311221i \(0.100738\pi\)
−0.950337 + 0.311221i \(0.899262\pi\)
\(740\) 529184.i 0.966369i
\(741\) 51498.2i 0.0937898i
\(742\) 20579.3i 0.0373786i
\(743\) −28658.0 −0.0519121 −0.0259560 0.999663i \(-0.508263\pi\)
−0.0259560 + 0.999663i \(0.508263\pi\)
\(744\) −54346.5 −0.0981806
\(745\) 153383.i 0.276353i
\(746\) 65519.0i 0.117731i
\(747\) 183661.i 0.329137i
\(748\) 1.52188e6i 2.72005i
\(749\) −108589. −0.193564
\(750\) 33700.6i 0.0599121i
\(751\) 398692.i 0.706899i 0.935454 + 0.353449i \(0.114991\pi\)
−0.935454 + 0.353449i \(0.885009\pi\)
\(752\) 357489.i 0.632161i
\(753\) 232780. 0.410540
\(754\) 18892.0 0.0332304
\(755\) 777492.i 1.36396i
\(756\) −105069. −0.183835
\(757\) 55848.3 0.0974581 0.0487290 0.998812i \(-0.484483\pi\)
0.0487290 + 0.998812i \(0.484483\pi\)
\(758\) 91190.6i 0.158713i
\(759\) −870428. −1.51095
\(760\) 12539.5i 0.0217096i
\(761\) −31452.4 −0.0543106 −0.0271553 0.999631i \(-0.508645\pi\)
−0.0271553 + 0.999631i \(0.508645\pi\)
\(762\) 57961.1i 0.0998220i
\(763\) 870808.i 1.49580i
\(764\) 777600.i 1.33220i
\(765\) −236472. −0.404070
\(766\) 44508.2i 0.0758547i
\(767\) −541276. 289199.i −0.920085 0.491594i
\(768\) 308765. 0.523486
\(769\) 1.10780e6i 1.87330i −0.350263 0.936651i \(-0.613908\pi\)
0.350263 0.936651i \(-0.386092\pi\)
\(770\) 65309.9 0.110153
\(771\) 549405. 0.924237
\(772\) 813842. 1.36554
\(773\) 392220.i 0.656403i −0.944608 0.328201i \(-0.893558\pi\)
0.944608 0.328201i \(-0.106442\pi\)
\(774\) 28980.0 0.0483745
\(775\) 254066.i 0.423003i
\(776\) 36510.8 0.0606314
\(777\) 455502.i 0.754481i
\(778\) 96823.6i 0.159964i
\(779\) 83171.3 0.137056
\(780\) 261313.i 0.429509i
\(781\) 411599.i 0.674795i
\(782\) 160726. 0.262828
\(783\) 38636.6 0.0630195
\(784\) −41810.8 −0.0680232
\(785\) 130924.i 0.212461i
\(786\) 40126.0 0.0649503
\(787\) 208960. 0.337376 0.168688 0.985670i \(-0.446047\pi\)
0.168688 + 0.985670i \(0.446047\pi\)
\(788\) −477905. −0.769643
\(789\) 48348.9 0.0776663