Properties

Label 177.5.c.a.58.17
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 58.17
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.24

$q$-expansion

\(f(q)\) \(=\) \(q-2.15560i q^{2} -5.19615 q^{3} +11.3534 q^{4} +30.9385 q^{5} +11.2008i q^{6} +73.3307 q^{7} -58.9629i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-2.15560i q^{2} -5.19615 q^{3} +11.3534 q^{4} +30.9385 q^{5} +11.2008i q^{6} +73.3307 q^{7} -58.9629i q^{8} +27.0000 q^{9} -66.6909i q^{10} +203.451i q^{11} -58.9940 q^{12} +115.092i q^{13} -158.071i q^{14} -160.761 q^{15} +54.5542 q^{16} -149.563 q^{17} -58.2011i q^{18} -97.5337 q^{19} +351.257 q^{20} -381.038 q^{21} +438.557 q^{22} +785.535i q^{23} +306.380i q^{24} +332.189 q^{25} +248.092 q^{26} -140.296 q^{27} +832.553 q^{28} +279.591 q^{29} +346.536i q^{30} -520.224i q^{31} -1061.00i q^{32} -1057.16i q^{33} +322.398i q^{34} +2268.74 q^{35} +306.542 q^{36} -737.478i q^{37} +210.243i q^{38} -598.036i q^{39} -1824.22i q^{40} +540.849 q^{41} +821.364i q^{42} -1171.64i q^{43} +2309.86i q^{44} +835.339 q^{45} +1693.30 q^{46} -1505.45i q^{47} -283.472 q^{48} +2976.40 q^{49} -716.067i q^{50} +777.153 q^{51} +1306.69i q^{52} -3630.24 q^{53} +302.422i q^{54} +6294.45i q^{55} -4323.79i q^{56} +506.800 q^{57} -602.686i q^{58} +(3344.70 + 964.542i) q^{59} -1825.19 q^{60} -5340.44i q^{61} -1121.39 q^{62} +1979.93 q^{63} -1414.23 q^{64} +3560.77i q^{65} -2278.81 q^{66} -1694.69i q^{67} -1698.05 q^{68} -4081.76i q^{69} -4890.49i q^{70} -9066.29 q^{71} -1592.00i q^{72} +876.744i q^{73} -1589.71 q^{74} -1726.11 q^{75} -1107.34 q^{76} +14919.2i q^{77} -1289.12 q^{78} +7895.46 q^{79} +1687.82 q^{80} +729.000 q^{81} -1165.85i q^{82} -3535.87i q^{83} -4326.07 q^{84} -4627.26 q^{85} -2525.58 q^{86} -1452.80 q^{87} +11996.0 q^{88} +11418.1i q^{89} -1800.65i q^{90} +8439.78i q^{91} +8918.49i q^{92} +2703.16i q^{93} -3245.15 q^{94} -3017.55 q^{95} +5513.14i q^{96} -15153.6i q^{97} -6415.91i q^{98} +5493.16i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.15560i 0.538899i −0.963014 0.269450i \(-0.913158\pi\)
0.963014 0.269450i \(-0.0868418\pi\)
\(3\) −5.19615 −0.577350
\(4\) 11.3534 0.709588
\(5\) 30.9385 1.23754 0.618770 0.785573i \(-0.287631\pi\)
0.618770 + 0.785573i \(0.287631\pi\)
\(6\) 11.2008i 0.311134i
\(7\) 73.3307 1.49655 0.748273 0.663391i \(-0.230883\pi\)
0.748273 + 0.663391i \(0.230883\pi\)
\(8\) 58.9629i 0.921295i
\(9\) 27.0000 0.333333
\(10\) 66.6909i 0.666909i
\(11\) 203.451i 1.68141i 0.541494 + 0.840705i \(0.317859\pi\)
−0.541494 + 0.840705i \(0.682141\pi\)
\(12\) −58.9940 −0.409681
\(13\) 115.092i 0.681018i 0.940241 + 0.340509i \(0.110599\pi\)
−0.940241 + 0.340509i \(0.889401\pi\)
\(14\) 158.071i 0.806487i
\(15\) −160.761 −0.714494
\(16\) 54.5542 0.213102
\(17\) −149.563 −0.517520 −0.258760 0.965942i \(-0.583314\pi\)
−0.258760 + 0.965942i \(0.583314\pi\)
\(18\) 58.2011i 0.179633i
\(19\) −97.5337 −0.270177 −0.135088 0.990834i \(-0.543132\pi\)
−0.135088 + 0.990834i \(0.543132\pi\)
\(20\) 351.257 0.878143
\(21\) −381.038 −0.864031
\(22\) 438.557 0.906110
\(23\) 785.535i 1.48494i 0.669878 + 0.742472i \(0.266347\pi\)
−0.669878 + 0.742472i \(0.733653\pi\)
\(24\) 306.380i 0.531910i
\(25\) 332.189 0.531503
\(26\) 248.092 0.367000
\(27\) −140.296 −0.192450
\(28\) 832.553 1.06193
\(29\) 279.591 0.332451 0.166226 0.986088i \(-0.446842\pi\)
0.166226 + 0.986088i \(0.446842\pi\)
\(30\) 346.536i 0.385040i
\(31\) 520.224i 0.541336i −0.962673 0.270668i \(-0.912755\pi\)
0.962673 0.270668i \(-0.0872445\pi\)
\(32\) 1061.00i 1.03614i
\(33\) 1057.16i 0.970762i
\(34\) 322.398i 0.278891i
\(35\) 2268.74 1.85203
\(36\) 306.542 0.236529
\(37\) 737.478i 0.538699i −0.963043 0.269349i \(-0.913191\pi\)
0.963043 0.269349i \(-0.0868086\pi\)
\(38\) 210.243i 0.145598i
\(39\) 598.036i 0.393186i
\(40\) 1824.22i 1.14014i
\(41\) 540.849 0.321743 0.160871 0.986975i \(-0.448570\pi\)
0.160871 + 0.986975i \(0.448570\pi\)
\(42\) 821.364i 0.465626i
\(43\) 1171.64i 0.633660i −0.948482 0.316830i \(-0.897382\pi\)
0.948482 0.316830i \(-0.102618\pi\)
\(44\) 2309.86i 1.19311i
\(45\) 835.339 0.412513
\(46\) 1693.30 0.800235
\(47\) 1505.45i 0.681509i −0.940152 0.340755i \(-0.889318\pi\)
0.940152 0.340755i \(-0.110682\pi\)
\(48\) −283.472 −0.123035
\(49\) 2976.40 1.23965
\(50\) 716.067i 0.286427i
\(51\) 777.153 0.298790
\(52\) 1306.69i 0.483242i
\(53\) −3630.24 −1.29236 −0.646179 0.763185i \(-0.723634\pi\)
−0.646179 + 0.763185i \(0.723634\pi\)
\(54\) 302.422i 0.103711i
\(55\) 6294.45i 2.08081i
\(56\) 4323.79i 1.37876i
\(57\) 506.800 0.155987
\(58\) 602.686i 0.179158i
\(59\) 3344.70 + 964.542i 0.960845 + 0.277088i
\(60\) −1825.19 −0.506996
\(61\) 5340.44i 1.43522i −0.696447 0.717608i \(-0.745237\pi\)
0.696447 0.717608i \(-0.254763\pi\)
\(62\) −1121.39 −0.291725
\(63\) 1979.93 0.498849
\(64\) −1414.23 −0.345270
\(65\) 3560.77i 0.842786i
\(66\) −2278.81 −0.523143
\(67\) 1694.69i 0.377520i −0.982023 0.188760i \(-0.939553\pi\)
0.982023 0.188760i \(-0.0604469\pi\)
\(68\) −1698.05 −0.367226
\(69\) 4081.76i 0.857332i
\(70\) 4890.49i 0.998059i
\(71\) −9066.29 −1.79851 −0.899255 0.437425i \(-0.855891\pi\)
−0.899255 + 0.437425i \(0.855891\pi\)
\(72\) 1592.00i 0.307098i
\(73\) 876.744i 0.164523i 0.996611 + 0.0822616i \(0.0262143\pi\)
−0.996611 + 0.0822616i \(0.973786\pi\)
\(74\) −1589.71 −0.290304
\(75\) −1726.11 −0.306864
\(76\) −1107.34 −0.191714
\(77\) 14919.2i 2.51631i
\(78\) −1289.12 −0.211888
\(79\) 7895.46 1.26509 0.632547 0.774522i \(-0.282009\pi\)
0.632547 + 0.774522i \(0.282009\pi\)
\(80\) 1687.82 0.263723
\(81\) 729.000 0.111111
\(82\) 1165.85i 0.173387i
\(83\) 3535.87i 0.513264i −0.966509 0.256632i \(-0.917387\pi\)
0.966509 0.256632i \(-0.0826128\pi\)
\(84\) −4326.07 −0.613106
\(85\) −4627.26 −0.640451
\(86\) −2525.58 −0.341479
\(87\) −1452.80 −0.191941
\(88\) 11996.0 1.54907
\(89\) 11418.1i 1.44150i 0.693195 + 0.720750i \(0.256203\pi\)
−0.693195 + 0.720750i \(0.743797\pi\)
\(90\) 1800.65i 0.222303i
\(91\) 8439.78i 1.01917i
\(92\) 8918.49i 1.05370i
\(93\) 2703.16i 0.312540i
\(94\) −3245.15 −0.367265
\(95\) −3017.55 −0.334354
\(96\) 5513.14i 0.598213i
\(97\) 15153.6i 1.61054i −0.592909 0.805269i \(-0.702021\pi\)
0.592909 0.805269i \(-0.297979\pi\)
\(98\) 6415.91i 0.668046i
\(99\) 5493.16i 0.560470i
\(100\) 3771.48 0.377148
\(101\) 10320.2i 1.01168i −0.862626 0.505842i \(-0.831182\pi\)
0.862626 0.505842i \(-0.168818\pi\)
\(102\) 1675.23i 0.161018i
\(103\) 13724.8i 1.29369i −0.762620 0.646847i \(-0.776087\pi\)
0.762620 0.646847i \(-0.223913\pi\)
\(104\) 6786.16 0.627419
\(105\) −11788.7 −1.06927
\(106\) 7825.33i 0.696451i
\(107\) −9382.60 −0.819513 −0.409756 0.912195i \(-0.634386\pi\)
−0.409756 + 0.912195i \(0.634386\pi\)
\(108\) −1592.84 −0.136560
\(109\) 15647.4i 1.31701i 0.752575 + 0.658507i \(0.228812\pi\)
−0.752575 + 0.658507i \(0.771188\pi\)
\(110\) 13568.3 1.12135
\(111\) 3832.05i 0.311018i
\(112\) 4000.50 0.318917
\(113\) 16451.0i 1.28836i −0.764875 0.644179i \(-0.777199\pi\)
0.764875 0.644179i \(-0.222801\pi\)
\(114\) 1092.46i 0.0840610i
\(115\) 24303.3i 1.83768i
\(116\) 3174.31 0.235903
\(117\) 3107.48i 0.227006i
\(118\) 2079.16 7209.82i 0.149322 0.517798i
\(119\) −10967.6 −0.774492
\(120\) 9478.94i 0.658260i
\(121\) −26751.1 −1.82714
\(122\) −11511.8 −0.773437
\(123\) −2810.34 −0.185758
\(124\) 5906.31i 0.384125i
\(125\) −9059.11 −0.579783
\(126\) 4267.93i 0.268829i
\(127\) 15007.8 0.930484 0.465242 0.885183i \(-0.345967\pi\)
0.465242 + 0.885183i \(0.345967\pi\)
\(128\) 13927.5i 0.850070i
\(129\) 6088.01i 0.365844i
\(130\) 7675.59 0.454177
\(131\) 521.489i 0.0303880i 0.999885 + 0.0151940i \(0.00483659\pi\)
−0.999885 + 0.0151940i \(0.995163\pi\)
\(132\) 12002.4i 0.688841i
\(133\) −7152.22 −0.404332
\(134\) −3653.07 −0.203445
\(135\) −4340.55 −0.238165
\(136\) 8818.68i 0.476789i
\(137\) −29732.3 −1.58411 −0.792057 0.610447i \(-0.790990\pi\)
−0.792057 + 0.610447i \(0.790990\pi\)
\(138\) −8798.63 −0.462016
\(139\) −5711.68 −0.295620 −0.147810 0.989016i \(-0.547222\pi\)
−0.147810 + 0.989016i \(0.547222\pi\)
\(140\) 25757.9 1.31418
\(141\) 7822.57i 0.393469i
\(142\) 19543.3i 0.969216i
\(143\) −23415.5 −1.14507
\(144\) 1472.96 0.0710341
\(145\) 8650.13 0.411421
\(146\) 1889.91 0.0886614
\(147\) −15465.8 −0.715711
\(148\) 8372.89i 0.382254i
\(149\) 6283.15i 0.283012i 0.989937 + 0.141506i \(0.0451944\pi\)
−0.989937 + 0.141506i \(0.954806\pi\)
\(150\) 3720.79i 0.165368i
\(151\) 39803.8i 1.74571i −0.487983 0.872853i \(-0.662267\pi\)
0.487983 0.872853i \(-0.337733\pi\)
\(152\) 5750.87i 0.248912i
\(153\) −4038.21 −0.172507
\(154\) 32159.7 1.35604
\(155\) 16094.9i 0.669924i
\(156\) 6789.74i 0.279000i
\(157\) 2933.82i 0.119024i 0.998228 + 0.0595119i \(0.0189544\pi\)
−0.998228 + 0.0595119i \(0.981046\pi\)
\(158\) 17019.4i 0.681758i
\(159\) 18863.3 0.746144
\(160\) 32825.8i 1.28226i
\(161\) 57603.8i 2.22228i
\(162\) 1571.43i 0.0598777i
\(163\) 44939.2 1.69142 0.845708 0.533645i \(-0.179178\pi\)
0.845708 + 0.533645i \(0.179178\pi\)
\(164\) 6140.48 0.228305
\(165\) 32706.9i 1.20136i
\(166\) −7621.92 −0.276597
\(167\) 5237.32 0.187791 0.0938957 0.995582i \(-0.470068\pi\)
0.0938957 + 0.995582i \(0.470068\pi\)
\(168\) 22467.1i 0.796028i
\(169\) 15314.8 0.536215
\(170\) 9974.50i 0.345138i
\(171\) −2633.41 −0.0900589
\(172\) 13302.1i 0.449637i
\(173\) 23988.2i 0.801503i 0.916187 + 0.400751i \(0.131251\pi\)
−0.916187 + 0.400751i \(0.868749\pi\)
\(174\) 3131.65i 0.103437i
\(175\) 24359.7 0.795419
\(176\) 11099.1i 0.358312i
\(177\) −17379.6 5011.91i −0.554744 0.159977i
\(178\) 24612.9 0.776824
\(179\) 48379.7i 1.50993i −0.655765 0.754965i \(-0.727654\pi\)
0.655765 0.754965i \(-0.272346\pi\)
\(180\) 9483.94 0.292714
\(181\) −9403.26 −0.287026 −0.143513 0.989648i \(-0.545840\pi\)
−0.143513 + 0.989648i \(0.545840\pi\)
\(182\) 18192.8 0.549232
\(183\) 27749.7i 0.828622i
\(184\) 46317.4 1.36807
\(185\) 22816.5i 0.666661i
\(186\) 5826.93 0.168428
\(187\) 30428.7i 0.870163i
\(188\) 17092.0i 0.483590i
\(189\) −10288.0 −0.288010
\(190\) 6504.61i 0.180183i
\(191\) 26293.8i 0.720754i 0.932807 + 0.360377i \(0.117352\pi\)
−0.932807 + 0.360377i \(0.882648\pi\)
\(192\) 7348.54 0.199342
\(193\) −35955.0 −0.965260 −0.482630 0.875824i \(-0.660318\pi\)
−0.482630 + 0.875824i \(0.660318\pi\)
\(194\) −32665.0 −0.867918
\(195\) 18502.3i 0.486583i
\(196\) 33792.2 0.879639
\(197\) 16157.0 0.416321 0.208160 0.978095i \(-0.433252\pi\)
0.208160 + 0.978095i \(0.433252\pi\)
\(198\) 11841.0 0.302037
\(199\) −8326.75 −0.210266 −0.105133 0.994458i \(-0.533527\pi\)
−0.105133 + 0.994458i \(0.533527\pi\)
\(200\) 19586.9i 0.489671i
\(201\) 8805.86i 0.217961i
\(202\) −22246.2 −0.545195
\(203\) 20502.6 0.497528
\(204\) 8823.33 0.212018
\(205\) 16733.1 0.398169
\(206\) −29585.1 −0.697171
\(207\) 21209.4i 0.494981i
\(208\) 6278.75i 0.145127i
\(209\) 19843.3i 0.454277i
\(210\) 25411.7i 0.576230i
\(211\) 75444.4i 1.69458i 0.531130 + 0.847290i \(0.321768\pi\)
−0.531130 + 0.847290i \(0.678232\pi\)
\(212\) −41215.5 −0.917042
\(213\) 47109.8 1.03837
\(214\) 20225.1i 0.441635i
\(215\) 36248.7i 0.784179i
\(216\) 8272.27i 0.177303i
\(217\) 38148.4i 0.810134i
\(218\) 33729.6 0.709738
\(219\) 4555.70i 0.0949875i
\(220\) 71463.4i 1.47652i
\(221\) 17213.5i 0.352440i
\(222\) 8260.36 0.167607
\(223\) 80926.3 1.62735 0.813673 0.581322i \(-0.197464\pi\)
0.813673 + 0.581322i \(0.197464\pi\)
\(224\) 77804.2i 1.55062i
\(225\) 8969.12 0.177168
\(226\) −35461.8 −0.694295
\(227\) 50468.1i 0.979411i 0.871888 + 0.489706i \(0.162896\pi\)
−0.871888 + 0.489706i \(0.837104\pi\)
\(228\) 5753.91 0.110686
\(229\) 88590.6i 1.68934i 0.535288 + 0.844669i \(0.320203\pi\)
−0.535288 + 0.844669i \(0.679797\pi\)
\(230\) 52388.0 0.990322
\(231\) 77522.3i 1.45279i
\(232\) 16485.5i 0.306286i
\(233\) 21367.1i 0.393580i 0.980446 + 0.196790i \(0.0630518\pi\)
−0.980446 + 0.196790i \(0.936948\pi\)
\(234\) 6698.48 0.122333
\(235\) 46576.4i 0.843394i
\(236\) 37973.7 + 10950.8i 0.681804 + 0.196618i
\(237\) −41026.0 −0.730403
\(238\) 23641.7i 0.417373i
\(239\) 27789.3 0.486498 0.243249 0.969964i \(-0.421787\pi\)
0.243249 + 0.969964i \(0.421787\pi\)
\(240\) −8770.19 −0.152260
\(241\) −114284. −1.96767 −0.983836 0.179071i \(-0.942691\pi\)
−0.983836 + 0.179071i \(0.942691\pi\)
\(242\) 57664.6i 0.984643i
\(243\) −3788.00 −0.0641500
\(244\) 60632.1i 1.01841i
\(245\) 92085.2 1.53411
\(246\) 6057.95i 0.100105i
\(247\) 11225.4i 0.183995i
\(248\) −30673.9 −0.498730
\(249\) 18372.9i 0.296333i
\(250\) 19527.8i 0.312445i
\(251\) 76189.7 1.20934 0.604671 0.796475i \(-0.293305\pi\)
0.604671 + 0.796475i \(0.293305\pi\)
\(252\) 22478.9 0.353977
\(253\) −159818. −2.49680
\(254\) 32350.7i 0.501437i
\(255\) 24043.9 0.369764
\(256\) −52649.8 −0.803373
\(257\) −9932.87 −0.150386 −0.0751932 0.997169i \(-0.523957\pi\)
−0.0751932 + 0.997169i \(0.523957\pi\)
\(258\) 13123.3 0.197153
\(259\) 54079.8i 0.806187i
\(260\) 40426.9i 0.598031i
\(261\) 7548.97 0.110817
\(262\) 1124.12 0.0163761
\(263\) 34983.1 0.505762 0.252881 0.967497i \(-0.418622\pi\)
0.252881 + 0.967497i \(0.418622\pi\)
\(264\) −62333.2 −0.894359
\(265\) −112314. −1.59934
\(266\) 15417.3i 0.217894i
\(267\) 59330.3i 0.832251i
\(268\) 19240.5i 0.267884i
\(269\) 61848.8i 0.854725i 0.904080 + 0.427363i \(0.140557\pi\)
−0.904080 + 0.427363i \(0.859443\pi\)
\(270\) 9356.47i 0.128347i
\(271\) −91570.5 −1.24686 −0.623429 0.781880i \(-0.714261\pi\)
−0.623429 + 0.781880i \(0.714261\pi\)
\(272\) −8159.30 −0.110285
\(273\) 43854.4i 0.588421i
\(274\) 64090.7i 0.853678i
\(275\) 67584.1i 0.893675i
\(276\) 46341.9i 0.608352i
\(277\) −88687.7 −1.15586 −0.577928 0.816088i \(-0.696139\pi\)
−0.577928 + 0.816088i \(0.696139\pi\)
\(278\) 12312.1i 0.159309i
\(279\) 14046.0i 0.180445i
\(280\) 133772.i 1.70627i
\(281\) −54231.2 −0.686809 −0.343405 0.939188i \(-0.611580\pi\)
−0.343405 + 0.939188i \(0.611580\pi\)
\(282\) 16862.3 0.212040
\(283\) 19900.8i 0.248483i 0.992252 + 0.124242i \(0.0396498\pi\)
−0.992252 + 0.124242i \(0.960350\pi\)
\(284\) −102933. −1.27620
\(285\) 15679.6 0.193039
\(286\) 50474.5i 0.617077i
\(287\) 39660.9 0.481503
\(288\) 28647.1i 0.345379i
\(289\) −61151.9 −0.732173
\(290\) 18646.2i 0.221715i
\(291\) 78740.2i 0.929845i
\(292\) 9954.03i 0.116744i
\(293\) 88852.6 1.03499 0.517494 0.855687i \(-0.326865\pi\)
0.517494 + 0.855687i \(0.326865\pi\)
\(294\) 33338.0i 0.385696i
\(295\) 103480. + 29841.5i 1.18908 + 0.342907i
\(296\) −43483.9 −0.496301
\(297\) 28543.3i 0.323587i
\(298\) 13543.9 0.152515
\(299\) −90408.8 −1.01127
\(300\) −19597.2 −0.217747
\(301\) 85917.0i 0.948301i
\(302\) −85801.0 −0.940760
\(303\) 53625.3i 0.584096i
\(304\) −5320.88 −0.0575753
\(305\) 165225.i 1.77614i
\(306\) 8704.74i 0.0929636i
\(307\) −5886.60 −0.0624579 −0.0312290 0.999512i \(-0.509942\pi\)
−0.0312290 + 0.999512i \(0.509942\pi\)
\(308\) 169383.i 1.78554i
\(309\) 71316.2i 0.746915i
\(310\) −34694.2 −0.361022
\(311\) −94490.4 −0.976938 −0.488469 0.872581i \(-0.662444\pi\)
−0.488469 + 0.872581i \(0.662444\pi\)
\(312\) −35261.9 −0.362240
\(313\) 90255.1i 0.921262i 0.887592 + 0.460631i \(0.152377\pi\)
−0.887592 + 0.460631i \(0.847623\pi\)
\(314\) 6324.13 0.0641418
\(315\) 61256.0 0.617345
\(316\) 89640.3 0.897696
\(317\) 159546. 1.58770 0.793849 0.608115i \(-0.208074\pi\)
0.793849 + 0.608115i \(0.208074\pi\)
\(318\) 40661.6i 0.402096i
\(319\) 56883.0i 0.558987i
\(320\) −43754.1 −0.427286
\(321\) 48753.4 0.473146
\(322\) 124171. 1.19759
\(323\) 14587.5 0.139822
\(324\) 8276.63 0.0788431
\(325\) 38232.4i 0.361963i
\(326\) 96870.9i 0.911503i
\(327\) 81306.5i 0.760378i
\(328\) 31890.1i 0.296420i
\(329\) 110396.i 1.01991i
\(330\) −70502.9 −0.647410
\(331\) 20831.2 0.190134 0.0950669 0.995471i \(-0.469694\pi\)
0.0950669 + 0.995471i \(0.469694\pi\)
\(332\) 40144.2i 0.364206i
\(333\) 19911.9i 0.179566i
\(334\) 11289.5i 0.101201i
\(335\) 52431.1i 0.467196i
\(336\) −20787.2 −0.184127
\(337\) 189217.i 1.66610i −0.553199 0.833049i \(-0.686593\pi\)
0.553199 0.833049i \(-0.313407\pi\)
\(338\) 33012.6i 0.288966i
\(339\) 85482.2i 0.743834i
\(340\) −52535.1 −0.454456
\(341\) 105840. 0.910207
\(342\) 5676.57i 0.0485326i
\(343\) 42194.2 0.358645
\(344\) −69083.1 −0.583788
\(345\) 126283.i 1.06098i
\(346\) 51708.8 0.431929
\(347\) 150636.i 1.25104i 0.780209 + 0.625519i \(0.215113\pi\)
−0.780209 + 0.625519i \(0.784887\pi\)
\(348\) −16494.2 −0.136199
\(349\) 80454.6i 0.660541i 0.943886 + 0.330271i \(0.107140\pi\)
−0.943886 + 0.330271i \(0.892860\pi\)
\(350\) 52509.7i 0.428651i
\(351\) 16147.0i 0.131062i
\(352\) 215862. 1.74217
\(353\) 93087.5i 0.747037i 0.927623 + 0.373518i \(0.121849\pi\)
−0.927623 + 0.373518i \(0.878151\pi\)
\(354\) −10803.6 + 37463.3i −0.0862112 + 0.298951i
\(355\) −280497. −2.22573
\(356\) 129635.i 1.02287i
\(357\) 56989.2 0.447153
\(358\) −104287. −0.813700
\(359\) −36181.0 −0.280732 −0.140366 0.990100i \(-0.544828\pi\)
−0.140366 + 0.990100i \(0.544828\pi\)
\(360\) 49254.0i 0.380046i
\(361\) −120808. −0.927005
\(362\) 20269.6i 0.154678i
\(363\) 139003. 1.05490
\(364\) 95820.3i 0.723194i
\(365\) 27125.1i 0.203604i
\(366\) 59817.2 0.446544
\(367\) 147497.i 1.09509i 0.836775 + 0.547547i \(0.184438\pi\)
−0.836775 + 0.547547i \(0.815562\pi\)
\(368\) 42854.2i 0.316445i
\(369\) 14602.9 0.107248
\(370\) −49183.1 −0.359263
\(371\) −266208. −1.93407
\(372\) 30690.1i 0.221775i
\(373\) 93006.2 0.668489 0.334244 0.942486i \(-0.391519\pi\)
0.334244 + 0.942486i \(0.391519\pi\)
\(374\) −65592.0 −0.468930
\(375\) 47072.5 0.334738
\(376\) −88765.9 −0.627871
\(377\) 32178.7i 0.226405i
\(378\) 22176.8i 0.155209i
\(379\) −197981. −1.37831 −0.689153 0.724615i \(-0.742017\pi\)
−0.689153 + 0.724615i \(0.742017\pi\)
\(380\) −34259.4 −0.237254
\(381\) −77982.7 −0.537215
\(382\) 56678.9 0.388414
\(383\) 130011. 0.886307 0.443153 0.896446i \(-0.353860\pi\)
0.443153 + 0.896446i \(0.353860\pi\)
\(384\) 72369.7i 0.490788i
\(385\) 461577.i 3.11403i
\(386\) 77504.4i 0.520178i
\(387\) 31634.2i 0.211220i
\(388\) 172044.i 1.14282i
\(389\) −97356.2 −0.643375 −0.321688 0.946846i \(-0.604250\pi\)
−0.321688 + 0.946846i \(0.604250\pi\)
\(390\) −39883.5 −0.262219
\(391\) 117487.i 0.768487i
\(392\) 175497.i 1.14208i
\(393\) 2709.74i 0.0175445i
\(394\) 34827.9i 0.224355i
\(395\) 244273. 1.56560
\(396\) 62366.1i 0.397703i
\(397\) 21590.6i 0.136988i −0.997652 0.0684942i \(-0.978181\pi\)
0.997652 0.0684942i \(-0.0218195\pi\)
\(398\) 17949.1i 0.113312i
\(399\) 37164.0 0.233441
\(400\) 18122.3 0.113265
\(401\) 14919.3i 0.0927809i −0.998923 0.0463905i \(-0.985228\pi\)
0.998923 0.0463905i \(-0.0147718\pi\)
\(402\) 18981.9 0.117459
\(403\) 59873.6 0.368659
\(404\) 117169.i 0.717878i
\(405\) 22554.2 0.137504
\(406\) 44195.4i 0.268118i
\(407\) 150040. 0.905773
\(408\) 45823.2i 0.275274i
\(409\) 90196.9i 0.539194i 0.962973 + 0.269597i \(0.0868905\pi\)
−0.962973 + 0.269597i \(0.913110\pi\)
\(410\) 36069.7i 0.214573i
\(411\) 154493. 0.914589
\(412\) 155823.i 0.917989i
\(413\) 245269. + 70730.5i 1.43795 + 0.414674i
\(414\) 45719.0 0.266745
\(415\) 109395.i 0.635184i
\(416\) 122113. 0.705627
\(417\) 29678.7 0.170676
\(418\) −42774.1 −0.244810
\(419\) 141820.i 0.807808i 0.914801 + 0.403904i \(0.132347\pi\)
−0.914801 + 0.403904i \(0.867653\pi\)
\(420\) −133842. −0.758742
\(421\) 328314.i 1.85236i −0.377084 0.926179i \(-0.623073\pi\)
0.377084 0.926179i \(-0.376927\pi\)
\(422\) 162628. 0.913208
\(423\) 40647.2i 0.227170i
\(424\) 214049.i 1.19064i
\(425\) −49683.3 −0.275063
\(426\) 101550.i 0.559577i
\(427\) 391618.i 2.14787i
\(428\) −106524. −0.581516
\(429\) 121671. 0.661106
\(430\) −78137.5 −0.422593
\(431\) 256724.i 1.38201i −0.722849 0.691006i \(-0.757168\pi\)
0.722849 0.691006i \(-0.242832\pi\)
\(432\) −7653.74 −0.0410116
\(433\) 63696.1 0.339733 0.169866 0.985467i \(-0.445666\pi\)
0.169866 + 0.985467i \(0.445666\pi\)
\(434\) −82232.5 −0.436580
\(435\) −44947.4 −0.237534
\(436\) 177652.i 0.934537i
\(437\) 76616.2i 0.401197i
\(438\) −9820.25 −0.0511887
\(439\) 301024. 1.56197 0.780985 0.624550i \(-0.214717\pi\)
0.780985 + 0.624550i \(0.214717\pi\)
\(440\) 371139. 1.91704
\(441\) 80362.7 0.413216
\(442\) −37105.4 −0.189930
\(443\) 214549.i 1.09325i −0.837378 0.546625i \(-0.815912\pi\)
0.837378 0.546625i \(-0.184088\pi\)
\(444\) 43506.8i 0.220694i
\(445\) 353260.i 1.78391i
\(446\) 174445.i 0.876976i
\(447\) 32648.2i 0.163397i
\(448\) −103706. −0.516713
\(449\) 20938.9 0.103863 0.0519315 0.998651i \(-0.483462\pi\)
0.0519315 + 0.998651i \(0.483462\pi\)
\(450\) 19333.8i 0.0954755i
\(451\) 110036.i 0.540981i
\(452\) 186775.i 0.914203i
\(453\) 206827.i 1.00788i
\(454\) 108789. 0.527804
\(455\) 261114.i 1.26127i
\(456\) 29882.4i 0.143710i
\(457\) 155521.i 0.744659i 0.928101 + 0.372330i \(0.121441\pi\)
−0.928101 + 0.372330i \(0.878559\pi\)
\(458\) 190966. 0.910383
\(459\) 20983.1 0.0995967
\(460\) 275925.i 1.30399i
\(461\) 424691. 1.99835 0.999175 0.0406056i \(-0.0129287\pi\)
0.999175 + 0.0406056i \(0.0129287\pi\)
\(462\) −167107. −0.782907
\(463\) 51304.1i 0.239326i 0.992815 + 0.119663i \(0.0381814\pi\)
−0.992815 + 0.119663i \(0.961819\pi\)
\(464\) 15252.9 0.0708461
\(465\) 83631.7i 0.386781i
\(466\) 46058.8 0.212100
\(467\) 18311.1i 0.0839614i 0.999118 + 0.0419807i \(0.0133668\pi\)
−0.999118 + 0.0419807i \(0.986633\pi\)
\(468\) 35280.5i 0.161081i
\(469\) 124273.i 0.564976i
\(470\) −100400. −0.454504
\(471\) 15244.6i 0.0687184i
\(472\) 56872.2 197213.i 0.255279 0.885222i
\(473\) 238370. 1.06544
\(474\) 88435.5i 0.393613i
\(475\) −32399.7 −0.143600
\(476\) −124519. −0.549570
\(477\) −98016.4 −0.430786
\(478\) 59902.4i 0.262173i
\(479\) −117396. −0.511659 −0.255830 0.966722i \(-0.582349\pi\)
−0.255830 + 0.966722i \(0.582349\pi\)
\(480\) 170568.i 0.740313i
\(481\) 84877.9 0.366863
\(482\) 246351.i 1.06038i
\(483\) 299318.i 1.28304i
\(484\) −303716. −1.29651
\(485\) 468828.i 1.99310i
\(486\) 8165.39i 0.0345704i
\(487\) 276423. 1.16551 0.582756 0.812647i \(-0.301974\pi\)
0.582756 + 0.812647i \(0.301974\pi\)
\(488\) −314888. −1.32226
\(489\) −233511. −0.976540
\(490\) 198499.i 0.826733i
\(491\) −95438.0 −0.395875 −0.197938 0.980215i \(-0.563424\pi\)
−0.197938 + 0.980215i \(0.563424\pi\)
\(492\) −31906.9 −0.131812
\(493\) −41816.6 −0.172050
\(494\) −24197.3 −0.0991548
\(495\) 169950.i 0.693603i
\(496\) 28380.4i 0.115360i
\(497\) −664838. −2.69155
\(498\) 39604.6 0.159694
\(499\) 296293. 1.18993 0.594964 0.803752i \(-0.297166\pi\)
0.594964 + 0.803752i \(0.297166\pi\)
\(500\) −102852. −0.411407
\(501\) −27213.9 −0.108421
\(502\) 164234.i 0.651713i
\(503\) 38668.3i 0.152834i 0.997076 + 0.0764169i \(0.0243480\pi\)
−0.997076 + 0.0764169i \(0.975652\pi\)
\(504\) 116742.i 0.459587i
\(505\) 319291.i 1.25200i
\(506\) 344502.i 1.34552i
\(507\) −79578.2 −0.309584
\(508\) 170389. 0.660260
\(509\) 382145.i 1.47500i −0.675347 0.737500i \(-0.736006\pi\)
0.675347 0.737500i \(-0.263994\pi\)
\(510\) 51829.0i 0.199266i
\(511\) 64292.3i 0.246217i
\(512\) 109349.i 0.417133i
\(513\) 13683.6 0.0519955
\(514\) 21411.3i 0.0810431i
\(515\) 424624.i 1.60100i
\(516\) 69119.6i 0.259598i
\(517\) 306285. 1.14590
\(518\) −116574. −0.434454
\(519\) 124646.i 0.462748i
\(520\) 209953. 0.776455
\(521\) −193927. −0.714437 −0.357218 0.934021i \(-0.616275\pi\)
−0.357218 + 0.934021i \(0.616275\pi\)
\(522\) 16272.5i 0.0597192i
\(523\) 242685. 0.887238 0.443619 0.896216i \(-0.353694\pi\)
0.443619 + 0.896216i \(0.353694\pi\)
\(524\) 5920.68i 0.0215630i
\(525\) −126577. −0.459235
\(526\) 75409.4i 0.272555i
\(527\) 77806.3i 0.280152i
\(528\) 57672.5i 0.206872i
\(529\) −337224. −1.20506
\(530\) 242104.i 0.861886i
\(531\) 90306.9 + 26042.6i 0.320282 + 0.0923625i
\(532\) −81202.0 −0.286909
\(533\) 62247.5i 0.219113i
\(534\) −127892. −0.448499
\(535\) −290283. −1.01418
\(536\) −99923.8 −0.347808
\(537\) 251388.i 0.871758i
\(538\) 133321. 0.460611
\(539\) 605550.i 2.08436i
\(540\) −49280.0 −0.168999
\(541\) 87558.4i 0.299160i 0.988750 + 0.149580i \(0.0477922\pi\)
−0.988750 + 0.149580i \(0.952208\pi\)
\(542\) 197389.i 0.671931i
\(543\) 48860.8 0.165714
\(544\) 158687.i 0.536221i
\(545\) 484108.i 1.62986i
\(546\) −94532.4 −0.317099
\(547\) −169774. −0.567411 −0.283705 0.958912i \(-0.591564\pi\)
−0.283705 + 0.958912i \(0.591564\pi\)
\(548\) −337562. −1.12407
\(549\) 144192.i 0.478405i
\(550\) 145684. 0.481600
\(551\) −27269.6 −0.0898205
\(552\) −240672. −0.789856
\(553\) 578980. 1.89327
\(554\) 191175.i 0.622890i
\(555\) 118558.i 0.384897i
\(556\) −64847.0 −0.209768
\(557\) −76223.9 −0.245686 −0.122843 0.992426i \(-0.539201\pi\)
−0.122843 + 0.992426i \(0.539201\pi\)
\(558\) −30277.6 −0.0972418
\(559\) 134846. 0.431534
\(560\) 123769. 0.394673
\(561\) 158112.i 0.502389i
\(562\) 116900.i 0.370121i
\(563\) 589979.i 1.86131i −0.365892 0.930657i \(-0.619236\pi\)
0.365892 0.930657i \(-0.380764\pi\)
\(564\) 88812.7i 0.279201i
\(565\) 508970.i 1.59439i
\(566\) 42898.0 0.133907
\(567\) 53458.1 0.166283
\(568\) 534575.i 1.65696i
\(569\) 312707.i 0.965856i 0.875660 + 0.482928i \(0.160427\pi\)
−0.875660 + 0.482928i \(0.839573\pi\)
\(570\) 33799.0i 0.104029i
\(571\) 614610.i 1.88507i 0.334110 + 0.942534i \(0.391564\pi\)
−0.334110 + 0.942534i \(0.608436\pi\)
\(572\) −265846. −0.812528
\(573\) 136627.i 0.416128i
\(574\) 85492.9i 0.259481i
\(575\) 260946.i 0.789252i
\(576\) −38184.2 −0.115090
\(577\) −170463. −0.512010 −0.256005 0.966675i \(-0.582406\pi\)
−0.256005 + 0.966675i \(0.582406\pi\)
\(578\) 131819.i 0.394568i
\(579\) 186828. 0.557293
\(580\) 98208.5 0.291940
\(581\) 259288.i 0.768123i
\(582\) 169732. 0.501093
\(583\) 738574.i 2.17298i
\(584\) 51695.4 0.151575
\(585\) 96140.8i 0.280929i
\(586\) 191530.i 0.557754i
\(587\) 315184.i 0.914721i −0.889281 0.457360i \(-0.848795\pi\)
0.889281 0.457360i \(-0.151205\pi\)
\(588\) −175590. −0.507860
\(589\) 50739.4i 0.146256i
\(590\) 64326.1 223061.i 0.184792 0.640796i
\(591\) −83954.2 −0.240363
\(592\) 40232.6i 0.114798i
\(593\) −93311.9 −0.265355 −0.132678 0.991159i \(-0.542357\pi\)
−0.132678 + 0.991159i \(0.542357\pi\)
\(594\) −61527.9 −0.174381
\(595\) −339320. −0.958464
\(596\) 71335.1i 0.200822i
\(597\) 43267.1 0.121397
\(598\) 194885.i 0.544974i
\(599\) −70659.2 −0.196932 −0.0984658 0.995140i \(-0.531393\pi\)
−0.0984658 + 0.995140i \(0.531393\pi\)
\(600\) 101776.i 0.282712i
\(601\) 624282.i 1.72835i 0.503190 + 0.864176i \(0.332159\pi\)
−0.503190 + 0.864176i \(0.667841\pi\)
\(602\) −185202. −0.511039
\(603\) 45756.6i 0.125840i
\(604\) 451909.i 1.23873i
\(605\) −827639. −2.26115
\(606\) 115594. 0.314769
\(607\) 72992.7 0.198108 0.0990540 0.995082i \(-0.468418\pi\)
0.0990540 + 0.995082i \(0.468418\pi\)
\(608\) 103484.i 0.279940i
\(609\) −106535. −0.287248
\(610\) −356158. −0.957158
\(611\) 173266. 0.464120
\(612\) −45847.4 −0.122409
\(613\) 446331.i 1.18778i −0.804546 0.593890i \(-0.797591\pi\)
0.804546 0.593890i \(-0.202409\pi\)
\(614\) 12689.1i 0.0336585i
\(615\) −86947.5 −0.229883
\(616\) 879678. 2.31826
\(617\) −676732. −1.77765 −0.888825 0.458246i \(-0.848478\pi\)
−0.888825 + 0.458246i \(0.848478\pi\)
\(618\) 153729. 0.402512
\(619\) 217204. 0.566874 0.283437 0.958991i \(-0.408525\pi\)
0.283437 + 0.958991i \(0.408525\pi\)
\(620\) 182732.i 0.475370i
\(621\) 110207.i 0.285777i
\(622\) 203683.i 0.526471i
\(623\) 837300.i 2.15727i
\(624\) 32625.4i 0.0837888i
\(625\) −487894. −1.24901
\(626\) 194554. 0.496467
\(627\) 103109.i 0.262277i
\(628\) 33308.8i 0.0844578i
\(629\) 110300.i 0.278787i
\(630\) 132043.i 0.332686i
\(631\) 74809.2 0.187887 0.0939434 0.995578i \(-0.470053\pi\)
0.0939434 + 0.995578i \(0.470053\pi\)
\(632\) 465539.i 1.16553i
\(633\) 392021.i 0.978366i
\(634\) 343917.i 0.855609i
\(635\) 464318. 1.15151
\(636\) 214162. 0.529454
\(637\) 342559.i 0.844223i
\(638\) 122617. 0.301237
\(639\) −244790. −0.599503
\(640\) 430897.i 1.05200i
\(641\) −461489. −1.12317 −0.561585 0.827419i \(-0.689808\pi\)
−0.561585 + 0.827419i \(0.689808\pi\)
\(642\) 105093.i 0.254978i
\(643\) −363629. −0.879501 −0.439751 0.898120i \(-0.644933\pi\)
−0.439751 + 0.898120i \(0.644933\pi\)
\(644\) 654000.i 1.57691i
\(645\) 188354.i 0.452746i
\(646\) 31444.7i 0.0753498i
\(647\) 641950. 1.53353 0.766766 0.641926i \(-0.221865\pi\)
0.766766 + 0.641926i \(0.221865\pi\)
\(648\) 42984.0i 0.102366i
\(649\) −196237. + 680481.i −0.465898 + 1.61557i
\(650\) 82413.6 0.195062
\(651\) 198225.i 0.467731i
\(652\) 510213. 1.20021
\(653\) 426122. 0.999327 0.499664 0.866220i \(-0.333457\pi\)
0.499664 + 0.866220i \(0.333457\pi\)
\(654\) −175264. −0.409767
\(655\) 16134.1i 0.0376064i
\(656\) 29505.6 0.0685641
\(657\) 23672.1i 0.0548411i
\(658\) −237969. −0.549628
\(659\) 468334.i 1.07841i 0.842174 + 0.539206i \(0.181276\pi\)
−0.842174 + 0.539206i \(0.818724\pi\)
\(660\) 371335.i 0.852468i
\(661\) 485472. 1.11112 0.555561 0.831476i \(-0.312504\pi\)
0.555561 + 0.831476i \(0.312504\pi\)
\(662\) 44903.8i 0.102463i
\(663\) 89444.1i 0.203481i
\(664\) −208485. −0.472868
\(665\) −221279. −0.500376
\(666\) −42922.1 −0.0967681
\(667\) 219629.i 0.493671i
\(668\) 59461.4 0.133255
\(669\) −420506. −0.939549
\(670\) −113020. −0.251772
\(671\) 1.08651e6 2.41319
\(672\) 404282.i 0.895254i
\(673\) 153856.i 0.339692i −0.985471 0.169846i \(-0.945673\pi\)
0.985471 0.169846i \(-0.0543270\pi\)
\(674\) −407876. −0.897859
\(675\) −46604.9 −0.102288
\(676\) 173875. 0.380491
\(677\) −624029. −1.36153 −0.680766 0.732501i \(-0.738353\pi\)
−0.680766 + 0.732501i \(0.738353\pi\)
\(678\) 184265. 0.400852
\(679\) 1.11122e6i 2.41024i
\(680\) 272837.i 0.590044i
\(681\) 262240.i 0.565463i
\(682\) 228148.i 0.490510i
\(683\) 717942.i 1.53903i −0.638627 0.769516i \(-0.720497\pi\)
0.638627 0.769516i \(-0.279503\pi\)
\(684\) −29898.2 −0.0639047
\(685\) −919871. −1.96040
\(686\) 90953.8i 0.193274i
\(687\) 460330.i 0.975340i
\(688\) 63917.7i 0.135034i
\(689\) 417811.i 0.880120i
\(690\) −272216. −0.571762
\(691\) 647155.i 1.35535i 0.735361 + 0.677676i \(0.237013\pi\)
−0.735361 + 0.677676i \(0.762987\pi\)
\(692\) 272347.i 0.568737i
\(693\) 402818.i 0.838769i
\(694\) 324711. 0.674184
\(695\) −176711. −0.365841
\(696\) 85661.3i 0.176834i
\(697\) −80891.2 −0.166508
\(698\) 173428. 0.355965
\(699\) 111027.i 0.227234i
\(700\) 276565. 0.564419
\(701\) 394820.i 0.803457i 0.915759 + 0.401729i \(0.131591\pi\)
−0.915759 + 0.401729i \(0.868409\pi\)
\(702\) −34806.3 −0.0706292
\(703\) 71929.0i 0.145544i
\(704\) 287725.i 0.580541i
\(705\) 242018.i 0.486934i
\(706\) 200659. 0.402578
\(707\) 756787.i 1.51403i
\(708\) −197317. 56902.2i −0.393639 0.113517i
\(709\) −404978. −0.805637 −0.402818 0.915280i \(-0.631969\pi\)
−0.402818 + 0.915280i \(0.631969\pi\)
\(710\) 604639.i 1.19944i
\(711\) 213177. 0.421698
\(712\) 673246. 1.32805
\(713\) 408654. 0.803853
\(714\) 122846.i 0.240970i
\(715\) −724441. −1.41707
\(716\) 549274.i 1.07143i
\(717\) −144397. −0.280880
\(718\) 77991.6i 0.151286i
\(719\) 54443.6i 0.105315i −0.998613 0.0526574i \(-0.983231\pi\)
0.998613 0.0526574i \(-0.0167691\pi\)
\(720\) 45571.3 0.0879075
\(721\) 1.00645e6i 1.93607i
\(722\) 260414.i 0.499562i
\(723\) 593839. 1.13604
\(724\) −106759. −0.203670
\(725\) 92877.3 0.176699
\(726\) 299634.i 0.568484i
\(727\) 611738. 1.15743 0.578717 0.815528i \(-0.303553\pi\)
0.578717 + 0.815528i \(0.303553\pi\)
\(728\) 497634. 0.938961
\(729\) 19683.0 0.0370370
\(730\) 58470.9 0.109722
\(731\) 175234.i 0.327931i
\(732\) 315054.i 0.587980i
\(733\) 523681. 0.974674 0.487337 0.873214i \(-0.337968\pi\)
0.487337 + 0.873214i \(0.337968\pi\)
\(734\) 317944. 0.590146
\(735\) −478489. −0.885721
\(736\) 833455. 1.53860
\(737\) 344785. 0.634766
\(738\) 31478.0i 0.0577956i
\(739\) 304017.i 0.556684i −0.960482 0.278342i \(-0.910215\pi\)
0.960482 0.278342i \(-0.0897848\pi\)
\(740\) 259044.i 0.473054i
\(741\) 58328.7i 0.106230i
\(742\) 573837.i 1.04227i
\(743\) 678235. 1.22858 0.614289 0.789081i \(-0.289443\pi\)
0.614289 + 0.789081i \(0.289443\pi\)
\(744\) 159386. 0.287942
\(745\) 194391.i 0.350238i
\(746\) 200484.i 0.360248i
\(747\) 95468.6i 0.171088i
\(748\) 345469.i 0.617457i
\(749\) −688033. −1.22644
\(750\) 101469.i 0.180390i
\(751\) 908208.i 1.61030i 0.593074 + 0.805148i \(0.297914\pi\)
−0.593074 + 0.805148i \(0.702086\pi\)
\(752\) 82128.8i 0.145231i
\(753\) −395894. −0.698214
\(754\) 69364.4 0.122010
\(755\) 1.23147e6i 2.16038i
\(756\) −116804. −0.204369
\(757\) −761493. −1.32885 −0.664423 0.747357i \(-0.731322\pi\)
−0.664423 + 0.747357i \(0.731322\pi\)
\(758\) 426768.i 0.742768i
\(759\) 830436. 1.44153
\(760\) 177923.i 0.308039i
\(761\) 631628. 1.09067 0.545334 0.838219i \(-0.316403\pi\)
0.545334 + 0.838219i \(0.316403\pi\)
\(762\) 168099.i 0.289505i
\(763\) 1.14744e6i 1.97097i
\(764\) 298525.i 0.511438i
\(765\) −124936. −0.213484
\(766\) 280252.i 0.477630i
\(767\) −111011. + 384948.i −0.188702 + 0.654352i
\(768\) 273577. 0.463827
\(769\) 361776.i 0.611769i −0.952069 0.305885i \(-0.901048\pi\)
0.952069 0.305885i \(-0.0989521\pi\)
\(770\) 994973. 1.67815
\(771\) 51612.7 0.0868256
\(772\) −408211. −0.684937
\(773\) 300146.i 0.502312i −0.967947 0.251156i \(-0.919189\pi\)
0.967947 0.251156i \(-0.0808108\pi\)
\(774\) −68190.6 −0.113826
\(775\) 172813.i 0.287722i
\(776\) −893498. −1.48378
\(777\) 281007.i 0.465452i
\(778\) 209861.i 0.346714i
\(779\) −52751.1 −0.0869273
\(780\) 210064.i 0.345273i
\(781\) 1.84454e6i 3.02403i
\(782\) −253255. −0.414137
\(783\) −39225.6 −0.0639803
\(784\) 162375. 0.264172
\(785\) 90767.8i 0.147297i
\(786\) −5841.10 −0.00945474
\(787\) −174818. −0.282253 −0.141126 0.989992i \(-0.545072\pi\)
−0.141126 + 0.989992i \(0.545072\pi\)
\(788\) 183437. 0.295416
\(789\) −181777. −0.292002