Properties

Label 177.5.c.a.58.10
Level $177$
Weight $5$
Character 177.58
Analytic conductor $18.296$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 58.10
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.31

$q$-expansion

\(f(q)\) \(=\) \(q-4.64719i q^{2} +5.19615 q^{3} -5.59638 q^{4} -0.691812 q^{5} -24.1475i q^{6} -76.1022 q^{7} -48.3476i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-4.64719i q^{2} +5.19615 q^{3} -5.59638 q^{4} -0.691812 q^{5} -24.1475i q^{6} -76.1022 q^{7} -48.3476i q^{8} +27.0000 q^{9} +3.21498i q^{10} -74.8765i q^{11} -29.0796 q^{12} +105.330i q^{13} +353.662i q^{14} -3.59476 q^{15} -314.223 q^{16} -141.930 q^{17} -125.474i q^{18} -170.820 q^{19} +3.87164 q^{20} -395.439 q^{21} -347.966 q^{22} -226.464i q^{23} -251.222i q^{24} -624.521 q^{25} +489.487 q^{26} +140.296 q^{27} +425.897 q^{28} -677.129 q^{29} +16.7055i q^{30} +114.554i q^{31} +686.691i q^{32} -389.070i q^{33} +659.575i q^{34} +52.6484 q^{35} -151.102 q^{36} -488.383i q^{37} +793.831i q^{38} +547.309i q^{39} +33.4475i q^{40} -1825.63 q^{41} +1837.68i q^{42} -527.862i q^{43} +419.037i q^{44} -18.6789 q^{45} -1052.42 q^{46} +1903.37i q^{47} -1632.75 q^{48} +3390.55 q^{49} +2902.27i q^{50} -737.489 q^{51} -589.465i q^{52} +4683.03 q^{53} -651.983i q^{54} +51.8005i q^{55} +3679.36i q^{56} -887.604 q^{57} +3146.75i q^{58} +(2331.20 + 2585.12i) q^{59} +20.1176 q^{60} -6414.67i q^{61} +532.355 q^{62} -2054.76 q^{63} -1836.38 q^{64} -72.8684i q^{65} -1808.08 q^{66} +1772.67i q^{67} +794.294 q^{68} -1176.74i q^{69} -244.667i q^{70} +170.581 q^{71} -1305.39i q^{72} -8999.83i q^{73} -2269.61 q^{74} -3245.11 q^{75} +955.971 q^{76} +5698.27i q^{77} +2543.45 q^{78} -204.796 q^{79} +217.383 q^{80} +729.000 q^{81} +8484.05i q^{82} -1391.38i q^{83} +2213.03 q^{84} +98.1888 q^{85} -2453.07 q^{86} -3518.47 q^{87} -3620.10 q^{88} -3001.60i q^{89} +86.8045i q^{90} -8015.83i q^{91} +1267.38i q^{92} +595.241i q^{93} +8845.32 q^{94} +118.175 q^{95} +3568.15i q^{96} -9224.90i q^{97} -15756.5i q^{98} -2021.67i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.64719i 1.16180i −0.813976 0.580899i \(-0.802701\pi\)
0.813976 0.580899i \(-0.197299\pi\)
\(3\) 5.19615 0.577350
\(4\) −5.59638 −0.349774
\(5\) −0.691812 −0.0276725 −0.0138362 0.999904i \(-0.504404\pi\)
−0.0138362 + 0.999904i \(0.504404\pi\)
\(6\) 24.1475i 0.670764i
\(7\) −76.1022 −1.55311 −0.776553 0.630051i \(-0.783034\pi\)
−0.776553 + 0.630051i \(0.783034\pi\)
\(8\) 48.3476i 0.755431i
\(9\) 27.0000 0.333333
\(10\) 3.21498i 0.0321498i
\(11\) 74.8765i 0.618814i −0.950930 0.309407i \(-0.899869\pi\)
0.950930 0.309407i \(-0.100131\pi\)
\(12\) −29.0796 −0.201942
\(13\) 105.330i 0.623253i 0.950205 + 0.311626i \(0.100874\pi\)
−0.950205 + 0.311626i \(0.899126\pi\)
\(14\) 353.662i 1.80440i
\(15\) −3.59476 −0.0159767
\(16\) −314.223 −1.22743
\(17\) −141.930 −0.491107 −0.245553 0.969383i \(-0.578970\pi\)
−0.245553 + 0.969383i \(0.578970\pi\)
\(18\) 125.474i 0.387266i
\(19\) −170.820 −0.473184 −0.236592 0.971609i \(-0.576031\pi\)
−0.236592 + 0.971609i \(0.576031\pi\)
\(20\) 3.87164 0.00967911
\(21\) −395.439 −0.896687
\(22\) −347.966 −0.718937
\(23\) 226.464i 0.428098i −0.976823 0.214049i \(-0.931335\pi\)
0.976823 0.214049i \(-0.0686653\pi\)
\(24\) 251.222i 0.436149i
\(25\) −624.521 −0.999234
\(26\) 489.487 0.724093
\(27\) 140.296 0.192450
\(28\) 425.897 0.543236
\(29\) −677.129 −0.805148 −0.402574 0.915388i \(-0.631884\pi\)
−0.402574 + 0.915388i \(0.631884\pi\)
\(30\) 16.7055i 0.0185617i
\(31\) 114.554i 0.119203i 0.998222 + 0.0596016i \(0.0189830\pi\)
−0.998222 + 0.0596016i \(0.981017\pi\)
\(32\) 686.691i 0.670596i
\(33\) 389.070i 0.357273i
\(34\) 659.575i 0.570567i
\(35\) 52.6484 0.0429783
\(36\) −151.102 −0.116591
\(37\) 488.383i 0.356745i −0.983963 0.178372i \(-0.942917\pi\)
0.983963 0.178372i \(-0.0570831\pi\)
\(38\) 793.831i 0.549744i
\(39\) 547.309i 0.359835i
\(40\) 33.4475i 0.0209047i
\(41\) −1825.63 −1.08604 −0.543019 0.839720i \(-0.682719\pi\)
−0.543019 + 0.839720i \(0.682719\pi\)
\(42\) 1837.68i 1.04177i
\(43\) 527.862i 0.285485i −0.989760 0.142742i \(-0.954408\pi\)
0.989760 0.142742i \(-0.0455921\pi\)
\(44\) 419.037i 0.216445i
\(45\) −18.6789 −0.00922416
\(46\) −1052.42 −0.497364
\(47\) 1903.37i 0.861643i 0.902437 + 0.430822i \(0.141776\pi\)
−0.902437 + 0.430822i \(0.858224\pi\)
\(48\) −1632.75 −0.708658
\(49\) 3390.55 1.41214
\(50\) 2902.27i 1.16091i
\(51\) −737.489 −0.283541
\(52\) 589.465i 0.217997i
\(53\) 4683.03 1.66715 0.833576 0.552404i \(-0.186290\pi\)
0.833576 + 0.552404i \(0.186290\pi\)
\(54\) 651.983i 0.223588i
\(55\) 51.8005i 0.0171241i
\(56\) 3679.36i 1.17327i
\(57\) −887.604 −0.273193
\(58\) 3146.75i 0.935419i
\(59\) 2331.20 + 2585.12i 0.669693 + 0.742638i
\(60\) 20.1176 0.00558823
\(61\) 6414.67i 1.72391i −0.506985 0.861955i \(-0.669240\pi\)
0.506985 0.861955i \(-0.330760\pi\)
\(62\) 532.355 0.138490
\(63\) −2054.76 −0.517702
\(64\) −1836.38 −0.448335
\(65\) 72.8684i 0.0172469i
\(66\) −1808.08 −0.415078
\(67\) 1772.67i 0.394892i 0.980314 + 0.197446i \(0.0632647\pi\)
−0.980314 + 0.197446i \(0.936735\pi\)
\(68\) 794.294 0.171776
\(69\) 1176.74i 0.247163i
\(70\) 244.667i 0.0499321i
\(71\) 170.581 0.0338387 0.0169193 0.999857i \(-0.494614\pi\)
0.0169193 + 0.999857i \(0.494614\pi\)
\(72\) 1305.39i 0.251810i
\(73\) 8999.83i 1.68884i −0.535682 0.844420i \(-0.679945\pi\)
0.535682 0.844420i \(-0.320055\pi\)
\(74\) −2269.61 −0.414465
\(75\) −3245.11 −0.576908
\(76\) 955.971 0.165507
\(77\) 5698.27i 0.961085i
\(78\) 2543.45 0.418056
\(79\) −204.796 −0.0328146 −0.0164073 0.999865i \(-0.505223\pi\)
−0.0164073 + 0.999865i \(0.505223\pi\)
\(80\) 217.383 0.0339661
\(81\) 729.000 0.111111
\(82\) 8484.05i 1.26176i
\(83\) 1391.38i 0.201971i −0.994888 0.100986i \(-0.967800\pi\)
0.994888 0.100986i \(-0.0321996\pi\)
\(84\) 2213.03 0.313637
\(85\) 98.1888 0.0135901
\(86\) −2453.07 −0.331676
\(87\) −3518.47 −0.464852
\(88\) −3620.10 −0.467472
\(89\) 3001.60i 0.378942i −0.981886 0.189471i \(-0.939323\pi\)
0.981886 0.189471i \(-0.0606773\pi\)
\(90\) 86.8045i 0.0107166i
\(91\) 8015.83i 0.967978i
\(92\) 1267.38i 0.149738i
\(93\) 595.241i 0.0688220i
\(94\) 8845.32 1.00105
\(95\) 118.175 0.0130942
\(96\) 3568.15i 0.387169i
\(97\) 9224.90i 0.980434i −0.871600 0.490217i \(-0.836918\pi\)
0.871600 0.490217i \(-0.163082\pi\)
\(98\) 15756.5i 1.64062i
\(99\) 2021.67i 0.206271i
\(100\) 3495.06 0.349506
\(101\) 15773.4i 1.54626i −0.634250 0.773128i \(-0.718691\pi\)
0.634250 0.773128i \(-0.281309\pi\)
\(102\) 3427.25i 0.329417i
\(103\) 12464.1i 1.17486i −0.809273 0.587432i \(-0.800139\pi\)
0.809273 0.587432i \(-0.199861\pi\)
\(104\) 5092.44 0.470825
\(105\) 273.569 0.0248135
\(106\) 21762.9i 1.93689i
\(107\) −5179.20 −0.452372 −0.226186 0.974084i \(-0.572626\pi\)
−0.226186 + 0.974084i \(0.572626\pi\)
\(108\) −785.150 −0.0673140
\(109\) 653.130i 0.0549727i −0.999622 0.0274863i \(-0.991250\pi\)
0.999622 0.0274863i \(-0.00875028\pi\)
\(110\) 240.727 0.0198948
\(111\) 2537.71i 0.205967i
\(112\) 23913.0 1.90633
\(113\) 12708.3i 0.995247i 0.867393 + 0.497623i \(0.165794\pi\)
−0.867393 + 0.497623i \(0.834206\pi\)
\(114\) 4124.87i 0.317395i
\(115\) 156.671i 0.0118465i
\(116\) 3789.47 0.281619
\(117\) 2843.90i 0.207751i
\(118\) 12013.6 10833.5i 0.862795 0.778048i
\(119\) 10801.2 0.762742
\(120\) 173.798i 0.0120693i
\(121\) 9034.50 0.617069
\(122\) −29810.2 −2.00283
\(123\) −9486.25 −0.627024
\(124\) 641.089i 0.0416941i
\(125\) 864.434 0.0553238
\(126\) 9548.86i 0.601465i
\(127\) −3763.18 −0.233318 −0.116659 0.993172i \(-0.537218\pi\)
−0.116659 + 0.993172i \(0.537218\pi\)
\(128\) 19521.1i 1.19147i
\(129\) 2742.85i 0.164825i
\(130\) −338.633 −0.0200375
\(131\) 1872.87i 0.109135i 0.998510 + 0.0545677i \(0.0173781\pi\)
−0.998510 + 0.0545677i \(0.982622\pi\)
\(132\) 2177.38i 0.124965i
\(133\) 12999.7 0.734906
\(134\) 8237.93 0.458784
\(135\) −97.0585 −0.00532557
\(136\) 6861.97i 0.370998i
\(137\) −7217.96 −0.384568 −0.192284 0.981339i \(-0.561590\pi\)
−0.192284 + 0.981339i \(0.561590\pi\)
\(138\) −5468.54 −0.287153
\(139\) −4580.22 −0.237059 −0.118530 0.992951i \(-0.537818\pi\)
−0.118530 + 0.992951i \(0.537818\pi\)
\(140\) −294.641 −0.0150327
\(141\) 9890.20i 0.497470i
\(142\) 792.721i 0.0393137i
\(143\) 7886.72 0.385678
\(144\) −8484.01 −0.409144
\(145\) 468.446 0.0222804
\(146\) −41823.9 −1.96209
\(147\) 17617.8 0.815300
\(148\) 2733.18i 0.124780i
\(149\) 26501.4i 1.19370i −0.802352 0.596851i \(-0.796418\pi\)
0.802352 0.596851i \(-0.203582\pi\)
\(150\) 15080.6i 0.670251i
\(151\) 28179.8i 1.23590i 0.786217 + 0.617950i \(0.212037\pi\)
−0.786217 + 0.617950i \(0.787963\pi\)
\(152\) 8258.72i 0.357458i
\(153\) −3832.11 −0.163702
\(154\) 26481.0 1.11659
\(155\) 79.2500i 0.00329865i
\(156\) 3062.95i 0.125861i
\(157\) 12508.2i 0.507452i 0.967276 + 0.253726i \(0.0816562\pi\)
−0.967276 + 0.253726i \(0.918344\pi\)
\(158\) 951.725i 0.0381239i
\(159\) 24333.7 0.962531
\(160\) 475.061i 0.0185571i
\(161\) 17234.4i 0.664882i
\(162\) 3387.80i 0.129089i
\(163\) −17112.4 −0.644075 −0.322038 0.946727i \(-0.604368\pi\)
−0.322038 + 0.946727i \(0.604368\pi\)
\(164\) 10216.9 0.379867
\(165\) 269.163i 0.00988662i
\(166\) −6466.00 −0.234650
\(167\) −5275.71 −0.189168 −0.0945841 0.995517i \(-0.530152\pi\)
−0.0945841 + 0.995517i \(0.530152\pi\)
\(168\) 19118.5i 0.677385i
\(169\) 17466.7 0.611556
\(170\) 456.302i 0.0157890i
\(171\) −4612.13 −0.157728
\(172\) 2954.11i 0.0998551i
\(173\) 19148.2i 0.639786i 0.947454 + 0.319893i \(0.103647\pi\)
−0.947454 + 0.319893i \(0.896353\pi\)
\(174\) 16351.0i 0.540064i
\(175\) 47527.5 1.55192
\(176\) 23527.9i 0.759553i
\(177\) 12113.3 + 13432.7i 0.386648 + 0.428762i
\(178\) −13949.0 −0.440254
\(179\) 59089.1i 1.84417i −0.386987 0.922085i \(-0.626484\pi\)
0.386987 0.922085i \(-0.373516\pi\)
\(180\) 104.534 0.00322637
\(181\) 21278.1 0.649494 0.324747 0.945801i \(-0.394721\pi\)
0.324747 + 0.945801i \(0.394721\pi\)
\(182\) −37251.1 −1.12459
\(183\) 33331.6i 0.995300i
\(184\) −10949.0 −0.323399
\(185\) 337.869i 0.00987201i
\(186\) 2766.20 0.0799572
\(187\) 10627.2i 0.303904i
\(188\) 10652.0i 0.301380i
\(189\) −10676.8 −0.298896
\(190\) 549.182i 0.0152128i
\(191\) 12072.7i 0.330932i −0.986215 0.165466i \(-0.947087\pi\)
0.986215 0.165466i \(-0.0529129\pi\)
\(192\) −9542.11 −0.258846
\(193\) −43480.2 −1.16728 −0.583642 0.812011i \(-0.698373\pi\)
−0.583642 + 0.812011i \(0.698373\pi\)
\(194\) −42869.9 −1.13907
\(195\) 378.635i 0.00995753i
\(196\) −18974.8 −0.493930
\(197\) 28225.1 0.727283 0.363642 0.931539i \(-0.381533\pi\)
0.363642 + 0.931539i \(0.381533\pi\)
\(198\) −9395.07 −0.239646
\(199\) −46347.4 −1.17036 −0.585180 0.810903i \(-0.698976\pi\)
−0.585180 + 0.810903i \(0.698976\pi\)
\(200\) 30194.1i 0.754853i
\(201\) 9211.06i 0.227991i
\(202\) −73301.8 −1.79644
\(203\) 51531.0 1.25048
\(204\) 4127.27 0.0991751
\(205\) 1262.99 0.0300534
\(206\) −57923.2 −1.36495
\(207\) 6114.53i 0.142699i
\(208\) 33097.0i 0.765000i
\(209\) 12790.4i 0.292813i
\(210\) 1271.33i 0.0288283i
\(211\) 49595.9i 1.11399i 0.830516 + 0.556994i \(0.188045\pi\)
−0.830516 + 0.556994i \(0.811955\pi\)
\(212\) −26208.0 −0.583126
\(213\) 886.363 0.0195368
\(214\) 24068.7i 0.525564i
\(215\) 365.181i 0.00790008i
\(216\) 6782.98i 0.145383i
\(217\) 8717.83i 0.185135i
\(218\) −3035.22 −0.0638671
\(219\) 46764.5i 0.975052i
\(220\) 289.895i 0.00598957i
\(221\) 14949.4i 0.306084i
\(222\) −11793.2 −0.239291
\(223\) 27897.9 0.560998 0.280499 0.959854i \(-0.409500\pi\)
0.280499 + 0.959854i \(0.409500\pi\)
\(224\) 52258.7i 1.04151i
\(225\) −16862.1 −0.333078
\(226\) 59057.9 1.15628
\(227\) 34726.4i 0.673919i 0.941519 + 0.336960i \(0.109399\pi\)
−0.941519 + 0.336960i \(0.890601\pi\)
\(228\) 4967.37 0.0955557
\(229\) 57357.6i 1.09376i −0.837212 0.546878i \(-0.815816\pi\)
0.837212 0.546878i \(-0.184184\pi\)
\(230\) 728.078 0.0137633
\(231\) 29609.1i 0.554883i
\(232\) 32737.6i 0.608234i
\(233\) 64148.1i 1.18160i 0.806816 + 0.590802i \(0.201189\pi\)
−0.806816 + 0.590802i \(0.798811\pi\)
\(234\) 13216.2 0.241364
\(235\) 1316.77i 0.0238438i
\(236\) −13046.3 14467.3i −0.234241 0.259755i
\(237\) −1064.15 −0.0189455
\(238\) 50195.2i 0.886151i
\(239\) −33929.5 −0.593994 −0.296997 0.954878i \(-0.595985\pi\)
−0.296997 + 0.954878i \(0.595985\pi\)
\(240\) 1129.56 0.0196103
\(241\) −35255.6 −0.607007 −0.303503 0.952830i \(-0.598156\pi\)
−0.303503 + 0.952830i \(0.598156\pi\)
\(242\) 41985.1i 0.716909i
\(243\) 3788.00 0.0641500
\(244\) 35898.9i 0.602978i
\(245\) −2345.62 −0.0390775
\(246\) 44084.4i 0.728475i
\(247\) 17992.4i 0.294913i
\(248\) 5538.42 0.0900498
\(249\) 7229.82i 0.116608i
\(250\) 4017.19i 0.0642750i
\(251\) 57278.6 0.909170 0.454585 0.890703i \(-0.349788\pi\)
0.454585 + 0.890703i \(0.349788\pi\)
\(252\) 11499.2 0.181079
\(253\) −16956.8 −0.264913
\(254\) 17488.2i 0.271068i
\(255\) 510.204 0.00784628
\(256\) 61336.0 0.935913
\(257\) −15290.7 −0.231506 −0.115753 0.993278i \(-0.536928\pi\)
−0.115753 + 0.993278i \(0.536928\pi\)
\(258\) −12746.5 −0.191493
\(259\) 37167.1i 0.554062i
\(260\) 407.799i 0.00603253i
\(261\) −18282.5 −0.268383
\(262\) 8703.60 0.126793
\(263\) 90982.9 1.31537 0.657685 0.753293i \(-0.271536\pi\)
0.657685 + 0.753293i \(0.271536\pi\)
\(264\) −18810.6 −0.269895
\(265\) −3239.78 −0.0461342
\(266\) 60412.3i 0.853812i
\(267\) 15596.8i 0.218782i
\(268\) 9920.53i 0.138123i
\(269\) 68865.4i 0.951692i 0.879529 + 0.475846i \(0.157858\pi\)
−0.879529 + 0.475846i \(0.842142\pi\)
\(270\) 451.050i 0.00618724i
\(271\) −120932. −1.64666 −0.823330 0.567563i \(-0.807886\pi\)
−0.823330 + 0.567563i \(0.807886\pi\)
\(272\) 44597.6 0.602800
\(273\) 41651.5i 0.558862i
\(274\) 33543.2i 0.446790i
\(275\) 46762.0i 0.618340i
\(276\) 6585.49i 0.0864510i
\(277\) 81260.6 1.05906 0.529530 0.848291i \(-0.322368\pi\)
0.529530 + 0.848291i \(0.322368\pi\)
\(278\) 21285.1i 0.275415i
\(279\) 3092.96i 0.0397344i
\(280\) 2545.43i 0.0324672i
\(281\) −58788.8 −0.744530 −0.372265 0.928127i \(-0.621419\pi\)
−0.372265 + 0.928127i \(0.621419\pi\)
\(282\) 45961.6 0.577959
\(283\) 74223.1i 0.926757i −0.886160 0.463379i \(-0.846637\pi\)
0.886160 0.463379i \(-0.153363\pi\)
\(284\) −954.634 −0.0118359
\(285\) 614.055 0.00755993
\(286\) 36651.1i 0.448079i
\(287\) 138934. 1.68673
\(288\) 18540.6i 0.223532i
\(289\) −63376.9 −0.758814
\(290\) 2176.96i 0.0258854i
\(291\) 47934.0i 0.566054i
\(292\) 50366.4i 0.590712i
\(293\) 105265. 1.22617 0.613083 0.790019i \(-0.289929\pi\)
0.613083 + 0.790019i \(0.289929\pi\)
\(294\) 81873.4i 0.947214i
\(295\) −1612.75 1788.42i −0.0185321 0.0205506i
\(296\) −23612.2 −0.269496
\(297\) 10504.9i 0.119091i
\(298\) −123157. −1.38684
\(299\) 23853.4 0.266813
\(300\) 18160.9 0.201787
\(301\) 40171.5i 0.443389i
\(302\) 130957. 1.43587
\(303\) 81960.7i 0.892731i
\(304\) 53675.4 0.580802
\(305\) 4437.75i 0.0477049i
\(306\) 17808.5i 0.190189i
\(307\) 3547.26 0.0376371 0.0188185 0.999823i \(-0.494010\pi\)
0.0188185 + 0.999823i \(0.494010\pi\)
\(308\) 31889.7i 0.336162i
\(309\) 64765.5i 0.678308i
\(310\) −368.290 −0.00383236
\(311\) 151291. 1.56420 0.782102 0.623150i \(-0.214147\pi\)
0.782102 + 0.623150i \(0.214147\pi\)
\(312\) 26461.1 0.271831
\(313\) 25650.3i 0.261821i 0.991394 + 0.130911i \(0.0417901\pi\)
−0.991394 + 0.130911i \(0.958210\pi\)
\(314\) 58128.0 0.589557
\(315\) 1421.51 0.0143261
\(316\) 1146.11 0.0114777
\(317\) 129307. 1.28677 0.643387 0.765541i \(-0.277529\pi\)
0.643387 + 0.765541i \(0.277529\pi\)
\(318\) 113084.i 1.11827i
\(319\) 50701.1i 0.498237i
\(320\) 1270.43 0.0124065
\(321\) −26911.9 −0.261177
\(322\) 80091.6 0.772459
\(323\) 24244.4 0.232384
\(324\) −4079.76 −0.0388637
\(325\) 65780.6i 0.622775i
\(326\) 79524.7i 0.748285i
\(327\) 3393.77i 0.0317385i
\(328\) 88264.8i 0.820427i
\(329\) 144851.i 1.33822i
\(330\) 1250.85 0.0114863
\(331\) −132570. −1.21001 −0.605004 0.796223i \(-0.706828\pi\)
−0.605004 + 0.796223i \(0.706828\pi\)
\(332\) 7786.68i 0.0706442i
\(333\) 13186.3i 0.118915i
\(334\) 24517.2i 0.219775i
\(335\) 1226.35i 0.0109276i
\(336\) 124256. 1.10062
\(337\) 182026.i 1.60277i 0.598146 + 0.801387i \(0.295904\pi\)
−0.598146 + 0.801387i \(0.704096\pi\)
\(338\) 81170.9i 0.710505i
\(339\) 66034.3i 0.574606i
\(340\) −549.502 −0.00475348
\(341\) 8577.42 0.0737646
\(342\) 21433.4i 0.183248i
\(343\) −75307.0 −0.640099
\(344\) −25520.8 −0.215664
\(345\) 814.084i 0.00683960i
\(346\) 88985.1 0.743302
\(347\) 36084.6i 0.299684i 0.988710 + 0.149842i \(0.0478765\pi\)
−0.988710 + 0.149842i \(0.952124\pi\)
\(348\) 19690.7 0.162593
\(349\) 155958.i 1.28043i −0.768194 0.640217i \(-0.778844\pi\)
0.768194 0.640217i \(-0.221156\pi\)
\(350\) 220869.i 1.80301i
\(351\) 14777.3i 0.119945i
\(352\) 51417.0 0.414975
\(353\) 106349.i 0.853464i −0.904378 0.426732i \(-0.859665\pi\)
0.904378 0.426732i \(-0.140335\pi\)
\(354\) 62424.3 56292.7i 0.498135 0.449206i
\(355\) −118.010 −0.000936400
\(356\) 16798.1i 0.132544i
\(357\) 56124.6 0.440369
\(358\) −274598. −2.14255
\(359\) −221323. −1.71726 −0.858632 0.512592i \(-0.828685\pi\)
−0.858632 + 0.512592i \(0.828685\pi\)
\(360\) 903.081i 0.00696822i
\(361\) −101142. −0.776097
\(362\) 98883.2i 0.754580i
\(363\) 46944.7 0.356265
\(364\) 44859.6i 0.338573i
\(365\) 6226.19i 0.0467344i
\(366\) −154898. −1.15634
\(367\) 231374.i 1.71784i 0.512108 + 0.858921i \(0.328865\pi\)
−0.512108 + 0.858921i \(0.671135\pi\)
\(368\) 71160.1i 0.525462i
\(369\) −49292.0 −0.362013
\(370\) 1570.14 0.0114693
\(371\) −356389. −2.58927
\(372\) 3331.19i 0.0240721i
\(373\) 129853. 0.933327 0.466663 0.884435i \(-0.345456\pi\)
0.466663 + 0.884435i \(0.345456\pi\)
\(374\) 49386.7 0.353075
\(375\) 4491.73 0.0319412
\(376\) 92023.4 0.650912
\(377\) 71321.8i 0.501810i
\(378\) 49617.3i 0.347256i
\(379\) −271372. −1.88924 −0.944618 0.328173i \(-0.893567\pi\)
−0.944618 + 0.328173i \(0.893567\pi\)
\(380\) −661.352 −0.00458000
\(381\) −19554.1 −0.134706
\(382\) −56104.4 −0.384477
\(383\) −228592. −1.55834 −0.779171 0.626811i \(-0.784360\pi\)
−0.779171 + 0.626811i \(0.784360\pi\)
\(384\) 101434.i 0.687896i
\(385\) 3942.13i 0.0265956i
\(386\) 202061.i 1.35615i
\(387\) 14252.3i 0.0951616i
\(388\) 51626.1i 0.342930i
\(389\) 19842.8 0.131131 0.0655654 0.997848i \(-0.479115\pi\)
0.0655654 + 0.997848i \(0.479115\pi\)
\(390\) −1759.59 −0.0115686
\(391\) 32142.0i 0.210242i
\(392\) 163925.i 1.06678i
\(393\) 9731.73i 0.0630093i
\(394\) 131168.i 0.844956i
\(395\) 141.680 0.000908061
\(396\) 11314.0i 0.0721483i
\(397\) 286794.i 1.81966i −0.414986 0.909828i \(-0.636213\pi\)
0.414986 0.909828i \(-0.363787\pi\)
\(398\) 215385.i 1.35972i
\(399\) 67548.7 0.424298
\(400\) 196239. 1.22649
\(401\) 227378.i 1.41403i 0.707198 + 0.707016i \(0.249959\pi\)
−0.707198 + 0.707016i \(0.750041\pi\)
\(402\) 42805.6 0.264879
\(403\) −12066.0 −0.0742937
\(404\) 88273.7i 0.540839i
\(405\) −504.331 −0.00307472
\(406\) 239475.i 1.45281i
\(407\) −36568.4 −0.220759
\(408\) 35655.8i 0.214196i
\(409\) 158393.i 0.946870i 0.880829 + 0.473435i \(0.156986\pi\)
−0.880829 + 0.473435i \(0.843014\pi\)
\(410\) 5869.37i 0.0349159i
\(411\) −37505.6 −0.222031
\(412\) 69754.0i 0.410937i
\(413\) −177410. 196734.i −1.04011 1.15340i
\(414\) −28415.4 −0.165788
\(415\) 962.573i 0.00558904i
\(416\) −72328.9 −0.417951
\(417\) −23799.5 −0.136866
\(418\) 59439.3 0.340190
\(419\) 122537.i 0.697976i −0.937127 0.348988i \(-0.886525\pi\)
0.937127 0.348988i \(-0.113475\pi\)
\(420\) −1531.00 −0.00867913
\(421\) 46500.7i 0.262359i 0.991359 + 0.131179i \(0.0418764\pi\)
−0.991359 + 0.131179i \(0.958124\pi\)
\(422\) 230481. 1.29423
\(423\) 51391.0i 0.287214i
\(424\) 226413.i 1.25942i
\(425\) 88638.3 0.490731
\(426\) 4119.10i 0.0226978i
\(427\) 488171.i 2.67742i
\(428\) 28984.8 0.158228
\(429\) 40980.6 0.222671
\(430\) 1697.07 0.00917829
\(431\) 17223.7i 0.0927198i 0.998925 + 0.0463599i \(0.0147621\pi\)
−0.998925 + 0.0463599i \(0.985238\pi\)
\(432\) −44084.2 −0.236219
\(433\) 28363.6 0.151281 0.0756407 0.997135i \(-0.475900\pi\)
0.0756407 + 0.997135i \(0.475900\pi\)
\(434\) −40513.4 −0.215090
\(435\) 2434.12 0.0128636
\(436\) 3655.17i 0.0192280i
\(437\) 38684.5i 0.202569i
\(438\) −217323. −1.13281
\(439\) −222696. −1.15554 −0.577769 0.816200i \(-0.696077\pi\)
−0.577769 + 0.816200i \(0.696077\pi\)
\(440\) 2504.43 0.0129361
\(441\) 91544.9 0.470714
\(442\) −69472.9 −0.355607
\(443\) 174192.i 0.887609i 0.896124 + 0.443804i \(0.146371\pi\)
−0.896124 + 0.443804i \(0.853629\pi\)
\(444\) 14202.0i 0.0720417i
\(445\) 2076.54i 0.0104863i
\(446\) 129647.i 0.651766i
\(447\) 137705.i 0.689184i
\(448\) 139753. 0.696312
\(449\) −24381.9 −0.120941 −0.0604706 0.998170i \(-0.519260\pi\)
−0.0604706 + 0.998170i \(0.519260\pi\)
\(450\) 78361.3i 0.386969i
\(451\) 136697.i 0.672056i
\(452\) 71120.5i 0.348111i
\(453\) 146426.i 0.713547i
\(454\) 161380. 0.782958
\(455\) 5545.44i 0.0267864i
\(456\) 42913.5i 0.206379i
\(457\) 278285.i 1.33247i 0.745741 + 0.666236i \(0.232096\pi\)
−0.745741 + 0.666236i \(0.767904\pi\)
\(458\) −266552. −1.27072
\(459\) −19912.2 −0.0945136
\(460\) 876.788i 0.00414361i
\(461\) 13805.0 0.0649581 0.0324791 0.999472i \(-0.489660\pi\)
0.0324791 + 0.999472i \(0.489660\pi\)
\(462\) 137599. 0.644661
\(463\) 129315.i 0.603234i −0.953429 0.301617i \(-0.902474\pi\)
0.953429 0.301617i \(-0.0975264\pi\)
\(464\) 212769. 0.988264
\(465\) 411.795i 0.00190447i
\(466\) 298109. 1.37279
\(467\) 294700.i 1.35128i 0.737230 + 0.675641i \(0.236133\pi\)
−0.737230 + 0.675641i \(0.763867\pi\)
\(468\) 15915.6i 0.0726658i
\(469\) 134904.i 0.613309i
\(470\) −6119.30 −0.0277017
\(471\) 64994.5i 0.292978i
\(472\) 124984. 112708.i 0.561012 0.505907i
\(473\) −39524.5 −0.176662
\(474\) 4945.31i 0.0220108i
\(475\) 106680. 0.472822
\(476\) −60447.5 −0.266787
\(477\) 126442. 0.555717
\(478\) 157677.i 0.690100i
\(479\) −144629. −0.630355 −0.315177 0.949033i \(-0.602064\pi\)
−0.315177 + 0.949033i \(0.602064\pi\)
\(480\) 2468.49i 0.0107139i
\(481\) 51441.3 0.222342
\(482\) 163839.i 0.705219i
\(483\) 89552.7i 0.383870i
\(484\) −50560.5 −0.215834
\(485\) 6381.90i 0.0271310i
\(486\) 17603.5i 0.0745294i
\(487\) −275005. −1.15953 −0.579766 0.814783i \(-0.696856\pi\)
−0.579766 + 0.814783i \(0.696856\pi\)
\(488\) −310134. −1.30230
\(489\) −88918.8 −0.371857
\(490\) 10900.6i 0.0454001i
\(491\) 32951.9 0.136684 0.0683419 0.997662i \(-0.478229\pi\)
0.0683419 + 0.997662i \(0.478229\pi\)
\(492\) 53088.6 0.219317
\(493\) 96104.9 0.395414
\(494\) −83614.0 −0.342630
\(495\) 1398.61i 0.00570804i
\(496\) 35995.5i 0.146314i
\(497\) −12981.6 −0.0525551
\(498\) −33598.3 −0.135475
\(499\) −17305.7 −0.0695005 −0.0347503 0.999396i \(-0.511064\pi\)
−0.0347503 + 0.999396i \(0.511064\pi\)
\(500\) −4837.70 −0.0193508
\(501\) −27413.4 −0.109216
\(502\) 266185.i 1.05627i
\(503\) 264972.i 1.04728i −0.851938 0.523642i \(-0.824573\pi\)
0.851938 0.523642i \(-0.175427\pi\)
\(504\) 99342.8i 0.391089i
\(505\) 10912.2i 0.0427887i
\(506\) 78801.7i 0.307776i
\(507\) 90759.4 0.353082
\(508\) 21060.2 0.0816084
\(509\) 446664.i 1.72403i −0.506882 0.862015i \(-0.669202\pi\)
0.506882 0.862015i \(-0.330798\pi\)
\(510\) 2371.02i 0.00911578i
\(511\) 684907.i 2.62295i
\(512\) 27296.9i 0.104129i
\(513\) −23965.3 −0.0910644
\(514\) 71059.0i 0.268963i
\(515\) 8622.84i 0.0325114i
\(516\) 15350.0i 0.0576514i
\(517\) 142518. 0.533197
\(518\) 172722. 0.643708
\(519\) 99496.7i 0.369381i
\(520\) −3523.01 −0.0130289
\(521\) 14595.5 0.0537703 0.0268852 0.999639i \(-0.491441\pi\)
0.0268852 + 0.999639i \(0.491441\pi\)
\(522\) 84962.2i 0.311806i
\(523\) −40396.8 −0.147687 −0.0738437 0.997270i \(-0.523527\pi\)
−0.0738437 + 0.997270i \(0.523527\pi\)
\(524\) 10481.3i 0.0381727i
\(525\) 246960. 0.896000
\(526\) 422815.i 1.52819i
\(527\) 16258.7i 0.0585415i
\(528\) 122255.i 0.438528i
\(529\) 228555. 0.816732
\(530\) 15055.9i 0.0535987i
\(531\) 62942.5 + 69798.3i 0.223231 + 0.247546i
\(532\) −72751.5 −0.257051
\(533\) 192293.i 0.676876i
\(534\) −72481.2 −0.254181
\(535\) 3583.03 0.0125182
\(536\) 85704.3 0.298314
\(537\) 307036.i 1.06473i
\(538\) 320030. 1.10567
\(539\) 253873.i 0.873853i
\(540\) 543.176 0.00186274
\(541\) 528895.i 1.80707i −0.428513 0.903536i \(-0.640962\pi\)
0.428513 0.903536i \(-0.359038\pi\)
\(542\) 561996.i 1.91309i
\(543\) 110564. 0.374985
\(544\) 97461.9i 0.329334i
\(545\) 451.843i 0.00152123i
\(546\) −193562. −0.649285
\(547\) −223190. −0.745935 −0.372967 0.927844i \(-0.621660\pi\)
−0.372967 + 0.927844i \(0.621660\pi\)
\(548\) 40394.4 0.134512
\(549\) 173196.i 0.574637i
\(550\) 217312. 0.718386
\(551\) 115667. 0.380983
\(552\) −56892.6 −0.186714
\(553\) 15585.4 0.0509645
\(554\) 377634.i 1.23041i
\(555\) 1755.62i 0.00569961i
\(556\) 25632.6 0.0829170
\(557\) 497882. 1.60478 0.802392 0.596798i \(-0.203561\pi\)
0.802392 + 0.596798i \(0.203561\pi\)
\(558\) 14373.6 0.0461633
\(559\) 55599.5 0.177929
\(560\) −16543.3 −0.0527530
\(561\) 55220.6i 0.175459i
\(562\) 273203.i 0.864993i
\(563\) 268686.i 0.847671i 0.905739 + 0.423836i \(0.139317\pi\)
−0.905739 + 0.423836i \(0.860683\pi\)
\(564\) 55349.3i 0.174002i
\(565\) 8791.76i 0.0275409i
\(566\) −344929. −1.07670
\(567\) −55478.5 −0.172567
\(568\) 8247.17i 0.0255628i
\(569\) 122187.i 0.377398i −0.982035 0.188699i \(-0.939573\pi\)
0.982035 0.188699i \(-0.0604271\pi\)
\(570\) 2853.63i 0.00878311i
\(571\) 20881.3i 0.0640449i −0.999487 0.0320224i \(-0.989805\pi\)
0.999487 0.0320224i \(-0.0101948\pi\)
\(572\) −44137.1 −0.134900
\(573\) 62731.8i 0.191064i
\(574\) 645655.i 1.95964i
\(575\) 141432.i 0.427770i
\(576\) −49582.3 −0.149445
\(577\) −309645. −0.930063 −0.465032 0.885294i \(-0.653957\pi\)
−0.465032 + 0.885294i \(0.653957\pi\)
\(578\) 294525.i 0.881588i
\(579\) −225930. −0.673932
\(580\) −2621.60 −0.00779311
\(581\) 105887.i 0.313683i
\(582\) −222758. −0.657640
\(583\) 350649.i 1.03166i
\(584\) −435120. −1.27580
\(585\) 1967.45i 0.00574898i
\(586\) 489187.i 1.42456i
\(587\) 245888.i 0.713611i −0.934179 0.356806i \(-0.883866\pi\)
0.934179 0.356806i \(-0.116134\pi\)
\(588\) −98596.0 −0.285171
\(589\) 19568.1i 0.0564050i
\(590\) −8311.12 + 7494.77i −0.0238757 + 0.0215305i
\(591\) 146662. 0.419897
\(592\) 153461.i 0.437880i
\(593\) 396294. 1.12696 0.563480 0.826130i \(-0.309462\pi\)
0.563480 + 0.826130i \(0.309462\pi\)
\(594\) −48818.2 −0.138359
\(595\) −7472.39 −0.0211070
\(596\) 148312.i 0.417526i
\(597\) −240828. −0.675708
\(598\) 110851.i 0.309983i
\(599\) −107130. −0.298579 −0.149289 0.988794i \(-0.547699\pi\)
−0.149289 + 0.988794i \(0.547699\pi\)
\(600\) 156893.i 0.435815i
\(601\) 479681.i 1.32802i −0.747725 0.664008i \(-0.768854\pi\)
0.747725 0.664008i \(-0.231146\pi\)
\(602\) 186684. 0.515128
\(603\) 47862.1i 0.131631i
\(604\) 157705.i 0.432285i
\(605\) −6250.18 −0.0170758
\(606\) −380887. −1.03717
\(607\) −182930. −0.496486 −0.248243 0.968698i \(-0.579853\pi\)
−0.248243 + 0.968698i \(0.579853\pi\)
\(608\) 117300.i 0.317316i
\(609\) 267763. 0.721965
\(610\) 20623.1 0.0554234
\(611\) −200481. −0.537021
\(612\) 21445.9 0.0572588
\(613\) 474523.i 1.26281i 0.775455 + 0.631403i \(0.217521\pi\)
−0.775455 + 0.631403i \(0.782479\pi\)
\(614\) 16484.8i 0.0437267i
\(615\) 6562.70 0.0173513
\(616\) 275498. 0.726034
\(617\) −339241. −0.891123 −0.445562 0.895251i \(-0.646996\pi\)
−0.445562 + 0.895251i \(0.646996\pi\)
\(618\) −300978. −0.788057
\(619\) 307348. 0.802137 0.401069 0.916048i \(-0.368639\pi\)
0.401069 + 0.916048i \(0.368639\pi\)
\(620\) 443.513i 0.00115378i
\(621\) 31772.0i 0.0823876i
\(622\) 703080.i 1.81729i
\(623\) 228429.i 0.588538i
\(624\) 171977.i 0.441673i
\(625\) 389728. 0.997703
\(626\) 119202. 0.304183
\(627\) 66460.7i 0.169056i
\(628\) 70000.6i 0.177493i
\(629\) 69316.2i 0.175200i
\(630\) 6606.02i 0.0166440i
\(631\) 478230. 1.20110 0.600548 0.799589i \(-0.294949\pi\)
0.600548 + 0.799589i \(0.294949\pi\)
\(632\) 9901.38i 0.0247892i
\(633\) 257708.i 0.643161i
\(634\) 600913.i 1.49497i
\(635\) 2603.41 0.00645648
\(636\) −136181. −0.336668
\(637\) 357126.i 0.880121i
\(638\) 235618. 0.578850
\(639\) 4605.68 0.0112796
\(640\) 13504.9i 0.0329710i
\(641\) 84112.5 0.204713 0.102356 0.994748i \(-0.467362\pi\)
0.102356 + 0.994748i \(0.467362\pi\)
\(642\) 125065.i 0.303435i
\(643\) 202387. 0.489508 0.244754 0.969585i \(-0.421293\pi\)
0.244754 + 0.969585i \(0.421293\pi\)
\(644\) 96450.3i 0.232558i
\(645\) 1897.54i 0.00456111i
\(646\) 112668.i 0.269983i
\(647\) 729383. 1.74240 0.871199 0.490930i \(-0.163343\pi\)
0.871199 + 0.490930i \(0.163343\pi\)
\(648\) 35245.4i 0.0839368i
\(649\) 193565. 174552.i 0.459555 0.414416i
\(650\) −305695. −0.723539
\(651\) 45299.2i 0.106888i
\(652\) 95767.6 0.225280
\(653\) −33872.3 −0.0794362 −0.0397181 0.999211i \(-0.512646\pi\)
−0.0397181 + 0.999211i \(0.512646\pi\)
\(654\) −15771.5 −0.0368737
\(655\) 1295.68i 0.00302005i
\(656\) 573654. 1.33304
\(657\) 242995.i 0.562947i
\(658\) −673149. −1.55475
\(659\) 12252.6i 0.0282134i 0.999900 + 0.0141067i \(0.00449046\pi\)
−0.999900 + 0.0141067i \(0.995510\pi\)
\(660\) 1506.34i 0.00345808i
\(661\) −193919. −0.443832 −0.221916 0.975066i \(-0.571231\pi\)
−0.221916 + 0.975066i \(0.571231\pi\)
\(662\) 616076.i 1.40578i
\(663\) 77679.5i 0.176717i
\(664\) −67269.8 −0.152575
\(665\) −8993.38 −0.0203367
\(666\) −61279.5 −0.138155
\(667\) 153345.i 0.344682i
\(668\) 29524.9 0.0661660
\(669\) 144962. 0.323892
\(670\) −5699.10 −0.0126957
\(671\) −480308. −1.06678
\(672\) 271544.i 0.601315i
\(673\) 527119.i 1.16380i −0.813260 0.581900i \(-0.802310\pi\)
0.813260 0.581900i \(-0.197690\pi\)
\(674\) 845907. 1.86210
\(675\) −87617.9 −0.192303
\(676\) −97750.0 −0.213906
\(677\) 160122. 0.349359 0.174680 0.984625i \(-0.444111\pi\)
0.174680 + 0.984625i \(0.444111\pi\)
\(678\) 306874. 0.667576
\(679\) 702036.i 1.52272i
\(680\) 4747.19i 0.0102664i
\(681\) 180444.i 0.389088i
\(682\) 39860.9i 0.0856995i
\(683\) 96946.8i 0.207822i −0.994587 0.103911i \(-0.966864\pi\)
0.994587 0.103911i \(-0.0331358\pi\)
\(684\) 25811.2 0.0551691
\(685\) 4993.47 0.0106420
\(686\) 349966.i 0.743666i
\(687\) 298039.i 0.631480i
\(688\) 165866.i 0.350413i
\(689\) 493262.i 1.03906i
\(690\) 3783.20 0.00794624
\(691\) 292122.i 0.611798i −0.952064 0.305899i \(-0.901043\pi\)
0.952064 0.305899i \(-0.0989570\pi\)
\(692\) 107160.i 0.223780i
\(693\) 153853.i 0.320362i
\(694\) 167692. 0.348172
\(695\) 3168.65 0.00656001
\(696\) 170109.i 0.351164i
\(697\) 259111. 0.533361
\(698\) −724767. −1.48761
\(699\) 333323.i 0.682200i
\(700\) −265982. −0.542820
\(701\) 761446.i 1.54954i −0.632243 0.774770i \(-0.717866\pi\)
0.632243 0.774770i \(-0.282134\pi\)
\(702\) 68673.1 0.139352
\(703\) 83425.4i 0.168806i
\(704\) 137502.i 0.277436i
\(705\) 6842.16i 0.0137662i
\(706\) −494225. −0.991552
\(707\) 1.20039e6i 2.40150i
\(708\) −67790.5 75174.4i −0.135239 0.149970i
\(709\) 9379.41 0.0186588 0.00932938 0.999956i \(-0.497030\pi\)
0.00932938 + 0.999956i \(0.497030\pi\)
\(710\) 548.414i 0.00108791i
\(711\) −5529.48 −0.0109382
\(712\) −145120. −0.286265
\(713\) 25942.4 0.0510307
\(714\) 260822.i 0.511620i
\(715\) −5456.13 −0.0106727
\(716\) 330685.i 0.645042i
\(717\) −176303. −0.342942
\(718\) 1.02853e6i 1.99511i
\(719\) 474152.i 0.917192i −0.888645 0.458596i \(-0.848353\pi\)
0.888645 0.458596i \(-0.151647\pi\)
\(720\) 5869.34 0.0113220
\(721\) 948549.i 1.82469i
\(722\) 470025.i 0.901667i
\(723\) −183193. −0.350455
\(724\) −119080. −0.227176
\(725\) 422882. 0.804531
\(726\) 218161.i 0.413908i
\(727\) −172753. −0.326857 −0.163429 0.986555i \(-0.552255\pi\)
−0.163429 + 0.986555i \(0.552255\pi\)
\(728\) −387546. −0.731241
\(729\) 19683.0 0.0370370
\(730\) 28934.3 0.0542959
\(731\) 74919.4i 0.140204i
\(732\) 186536.i 0.348130i
\(733\) 192952. 0.359122 0.179561 0.983747i \(-0.442532\pi\)
0.179561 + 0.983747i \(0.442532\pi\)
\(734\) 1.07524e6 1.99578
\(735\) −12188.2 −0.0225614
\(736\) 155511. 0.287081
\(737\) 132731. 0.244365
\(738\) 229069.i 0.420585i
\(739\) 894229.i 1.63742i −0.574208 0.818709i \(-0.694690\pi\)
0.574208 0.818709i \(-0.305310\pi\)
\(740\) 1890.85i 0.00345297i
\(741\) 93491.1i 0.170268i
\(742\) 1.65621e6i 3.00820i
\(743\) −814173. −1.47482 −0.737410 0.675445i \(-0.763952\pi\)
−0.737410 + 0.675445i \(0.763952\pi\)
\(744\) 28778.5 0.0519903
\(745\) 18334.0i 0.0330327i
\(746\) 603451.i 1.08434i
\(747\) 37567.2i 0.0673237i
\(748\) 59473.9i 0.106298i
\(749\) 394149. 0.702582
\(750\) 20873.9i 0.0371092i
\(751\) 417689.i 0.740581i 0.928916 + 0.370291i \(0.120742\pi\)
−0.928916 + 0.370291i \(0.879258\pi\)
\(752\) 598082.i 1.05761i
\(753\) 297628. 0.524910
\(754\) −331446. −0.583002
\(755\) 19495.1i 0.0342004i
\(756\) 59751.7 0.104546
\(757\) −999639. −1.74442 −0.872210 0.489131i \(-0.837314\pi\)
−0.872210 + 0.489131i \(0.837314\pi\)
\(758\) 1.26112e6i 2.19491i
\(759\) −88110.3 −0.152948
\(760\) 5713.48i 0.00989176i
\(761\) −698337. −1.20586 −0.602928 0.797795i \(-0.705999\pi\)
−0.602928 + 0.797795i \(0.705999\pi\)
\(762\) 90871.4i 0.156501i
\(763\) 49704.7i 0.0853784i
\(764\) 67563.7i 0.115751i
\(765\) 2651.10 0.00453005
\(766\) 1.06231e6i 1.81048i
\(767\) −272290. + 245545.i −0.462851 + 0.417388i
\(768\) 318711. 0.540350
\(769\) 1.02416e6i 1.73187i −0.500155 0.865936i \(-0.666724\pi\)
0.500155 0.865936i \(-0.333276\pi\)
\(770\) −18319.8 −0.0308987
\(771\) −79453.0 −0.133660
\(772\) 243332. 0.408286
\(773\) 907633.i 1.51898i −0.650521 0.759488i \(-0.725449\pi\)
0.650521 0.759488i \(-0.274551\pi\)
\(774\) −66233.0 −0.110559
\(775\) 71541.5i 0.119112i
\(776\) −446002. −0.740651
\(777\) 193126.i 0.319888i
\(778\) 92213.4i 0.152347i
\(779\) 311853. 0.513896
\(780\) 2118.99i 0.00348288i
\(781\) 12772.5i 0.0209399i
\(782\) 149370. 0.244259
\(783\) −94998.6 −0.154951
\(784\) −1.06539e6 −1.73331
\(785\) 8653.32i 0.0140425i
\(786\) 45225.2 0.0732041
\(787\) 418956. 0.676423 0.338212 0.941070i \(-0.390178\pi\)
0.338212 + 0.941070i \(0.390178\pi\)
\(788\) −157959. −0.254385
\(789\) 472761. 0.759430