Properties

Label 177.5.c.a.58.13
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 58.13
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.28

$q$-expansion

\(f(q)\) \(=\) \(q-3.44422i q^{2} +5.19615 q^{3} +4.13738 q^{4} -16.2205 q^{5} -17.8967i q^{6} +92.6602 q^{7} -69.3575i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-3.44422i q^{2} +5.19615 q^{3} +4.13738 q^{4} -16.2205 q^{5} -17.8967i q^{6} +92.6602 q^{7} -69.3575i q^{8} +27.0000 q^{9} +55.8670i q^{10} +48.6771i q^{11} +21.4985 q^{12} +216.742i q^{13} -319.142i q^{14} -84.2844 q^{15} -172.684 q^{16} +171.979 q^{17} -92.9938i q^{18} +267.365 q^{19} -67.1105 q^{20} +481.476 q^{21} +167.654 q^{22} -734.072i q^{23} -360.392i q^{24} -361.894 q^{25} +746.506 q^{26} +140.296 q^{27} +383.370 q^{28} +999.352 q^{29} +290.294i q^{30} +568.212i q^{31} -514.959i q^{32} +252.934i q^{33} -592.334i q^{34} -1503.00 q^{35} +111.709 q^{36} -1003.07i q^{37} -920.864i q^{38} +1126.22i q^{39} +1125.02i q^{40} -2301.23 q^{41} -1658.31i q^{42} -2157.18i q^{43} +201.396i q^{44} -437.954 q^{45} -2528.30 q^{46} +1199.13i q^{47} -897.293 q^{48} +6184.90 q^{49} +1246.44i q^{50} +893.631 q^{51} +896.743i q^{52} -1101.00 q^{53} -483.210i q^{54} -789.569i q^{55} -6426.67i q^{56} +1389.27 q^{57} -3441.98i q^{58} +(-1324.95 - 3218.99i) q^{59} -348.716 q^{60} -4030.40i q^{61} +1957.05 q^{62} +2501.82 q^{63} -4536.57 q^{64} -3515.67i q^{65} +871.158 q^{66} +8142.38i q^{67} +711.544 q^{68} -3814.35i q^{69} +5176.65i q^{70} -2537.07 q^{71} -1872.65i q^{72} +792.331i q^{73} -3454.80 q^{74} -1880.46 q^{75} +1106.19 q^{76} +4510.43i q^{77} +3878.96 q^{78} -3214.46 q^{79} +2801.03 q^{80} +729.000 q^{81} +7925.93i q^{82} +10537.1i q^{83} +1992.05 q^{84} -2789.60 q^{85} -7429.78 q^{86} +5192.79 q^{87} +3376.12 q^{88} +226.497i q^{89} +1508.41i q^{90} +20083.3i q^{91} -3037.13i q^{92} +2952.52i q^{93} +4130.07 q^{94} -4336.81 q^{95} -2675.80i q^{96} +7280.88i q^{97} -21302.1i q^{98} +1314.28i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.44422i 0.861054i −0.902578 0.430527i \(-0.858328\pi\)
0.902578 0.430527i \(-0.141672\pi\)
\(3\) 5.19615 0.577350
\(4\) 4.13738 0.258586
\(5\) −16.2205 −0.648821 −0.324411 0.945916i \(-0.605166\pi\)
−0.324411 + 0.945916i \(0.605166\pi\)
\(6\) 17.8967i 0.497130i
\(7\) 92.6602 1.89102 0.945512 0.325588i \(-0.105562\pi\)
0.945512 + 0.325588i \(0.105562\pi\)
\(8\) 69.3575i 1.08371i
\(9\) 27.0000 0.333333
\(10\) 55.8670i 0.558670i
\(11\) 48.6771i 0.402290i 0.979561 + 0.201145i \(0.0644663\pi\)
−0.979561 + 0.201145i \(0.935534\pi\)
\(12\) 21.4985 0.149295
\(13\) 216.742i 1.28250i 0.767334 + 0.641248i \(0.221583\pi\)
−0.767334 + 0.641248i \(0.778417\pi\)
\(14\) 319.142i 1.62827i
\(15\) −84.2844 −0.374597
\(16\) −172.684 −0.674547
\(17\) 171.979 0.595084 0.297542 0.954709i \(-0.403833\pi\)
0.297542 + 0.954709i \(0.403833\pi\)
\(18\) 92.9938i 0.287018i
\(19\) 267.365 0.740624 0.370312 0.928907i \(-0.379251\pi\)
0.370312 + 0.928907i \(0.379251\pi\)
\(20\) −67.1105 −0.167776
\(21\) 481.476 1.09178
\(22\) 167.654 0.346394
\(23\) 734.072i 1.38766i −0.720139 0.693830i \(-0.755922\pi\)
0.720139 0.693830i \(-0.244078\pi\)
\(24\) 360.392i 0.625681i
\(25\) −361.894 −0.579031
\(26\) 746.506 1.10430
\(27\) 140.296 0.192450
\(28\) 383.370 0.488993
\(29\) 999.352 1.18829 0.594145 0.804358i \(-0.297490\pi\)
0.594145 + 0.804358i \(0.297490\pi\)
\(30\) 290.294i 0.322548i
\(31\) 568.212i 0.591272i 0.955301 + 0.295636i \(0.0955315\pi\)
−0.955301 + 0.295636i \(0.904468\pi\)
\(32\) 514.959i 0.502889i
\(33\) 252.934i 0.232262i
\(34\) 592.334i 0.512400i
\(35\) −1503.00 −1.22694
\(36\) 111.709 0.0861954
\(37\) 1003.07i 0.732704i −0.930476 0.366352i \(-0.880607\pi\)
0.930476 0.366352i \(-0.119393\pi\)
\(38\) 920.864i 0.637717i
\(39\) 1126.22i 0.740449i
\(40\) 1125.02i 0.703135i
\(41\) −2301.23 −1.36897 −0.684483 0.729029i \(-0.739972\pi\)
−0.684483 + 0.729029i \(0.739972\pi\)
\(42\) 1658.31i 0.940084i
\(43\) 2157.18i 1.16667i −0.812231 0.583336i \(-0.801747\pi\)
0.812231 0.583336i \(-0.198253\pi\)
\(44\) 201.396i 0.104027i
\(45\) −437.954 −0.216274
\(46\) −2528.30 −1.19485
\(47\) 1199.13i 0.542840i 0.962461 + 0.271420i \(0.0874932\pi\)
−0.962461 + 0.271420i \(0.912507\pi\)
\(48\) −897.293 −0.389450
\(49\) 6184.90 2.57597
\(50\) 1246.44i 0.498577i
\(51\) 893.631 0.343572
\(52\) 896.743i 0.331636i
\(53\) −1101.00 −0.391956 −0.195978 0.980608i \(-0.562788\pi\)
−0.195978 + 0.980608i \(0.562788\pi\)
\(54\) 483.210i 0.165710i
\(55\) 789.569i 0.261015i
\(56\) 6426.67i 2.04932i
\(57\) 1389.27 0.427599
\(58\) 3441.98i 1.02318i
\(59\) −1324.95 3218.99i −0.380623 0.924730i
\(60\) −348.716 −0.0968657
\(61\) 4030.40i 1.08315i −0.840653 0.541574i \(-0.817828\pi\)
0.840653 0.541574i \(-0.182172\pi\)
\(62\) 1957.05 0.509117
\(63\) 2501.82 0.630341
\(64\) −4536.57 −1.10756
\(65\) 3515.67i 0.832111i
\(66\) 871.158 0.199990
\(67\) 8142.38i 1.81385i 0.421290 + 0.906926i \(0.361577\pi\)
−0.421290 + 0.906926i \(0.638423\pi\)
\(68\) 711.544 0.153881
\(69\) 3814.35i 0.801165i
\(70\) 5176.65i 1.05646i
\(71\) −2537.07 −0.503286 −0.251643 0.967820i \(-0.580971\pi\)
−0.251643 + 0.967820i \(0.580971\pi\)
\(72\) 1872.65i 0.361237i
\(73\) 792.331i 0.148683i 0.997233 + 0.0743414i \(0.0236855\pi\)
−0.997233 + 0.0743414i \(0.976315\pi\)
\(74\) −3454.80 −0.630898
\(75\) −1880.46 −0.334304
\(76\) 1106.19 0.191515
\(77\) 4510.43i 0.760740i
\(78\) 3878.96 0.637567
\(79\) −3214.46 −0.515056 −0.257528 0.966271i \(-0.582908\pi\)
−0.257528 + 0.966271i \(0.582908\pi\)
\(80\) 2801.03 0.437661
\(81\) 729.000 0.111111
\(82\) 7925.93i 1.17875i
\(83\) 10537.1i 1.52956i 0.644292 + 0.764779i \(0.277152\pi\)
−0.644292 + 0.764779i \(0.722848\pi\)
\(84\) 1992.05 0.282320
\(85\) −2789.60 −0.386103
\(86\) −7429.78 −1.00457
\(87\) 5192.79 0.686060
\(88\) 3376.12 0.435966
\(89\) 226.497i 0.0285945i 0.999898 + 0.0142972i \(0.00455111\pi\)
−0.999898 + 0.0142972i \(0.995449\pi\)
\(90\) 1508.41i 0.186223i
\(91\) 20083.3i 2.42523i
\(92\) 3037.13i 0.358829i
\(93\) 2952.52i 0.341371i
\(94\) 4130.07 0.467414
\(95\) −4336.81 −0.480533
\(96\) 2675.80i 0.290343i
\(97\) 7280.88i 0.773821i 0.922117 + 0.386911i \(0.126458\pi\)
−0.922117 + 0.386911i \(0.873542\pi\)
\(98\) 21302.1i 2.21805i
\(99\) 1314.28i 0.134097i
\(100\) −1497.29 −0.149729
\(101\) 11745.9i 1.15145i 0.817643 + 0.575725i \(0.195280\pi\)
−0.817643 + 0.575725i \(0.804720\pi\)
\(102\) 3077.86i 0.295834i
\(103\) 19029.4i 1.79370i 0.442333 + 0.896851i \(0.354151\pi\)
−0.442333 + 0.896851i \(0.645849\pi\)
\(104\) 15032.7 1.38985
\(105\) −7809.80 −0.708372
\(106\) 3792.10i 0.337495i
\(107\) 6751.89 0.589737 0.294868 0.955538i \(-0.404724\pi\)
0.294868 + 0.955538i \(0.404724\pi\)
\(108\) 580.458 0.0497649
\(109\) 22919.8i 1.92911i −0.263876 0.964556i \(-0.585001\pi\)
0.263876 0.964556i \(-0.414999\pi\)
\(110\) −2719.45 −0.224748
\(111\) 5212.12i 0.423027i
\(112\) −16000.9 −1.27558
\(113\) 1167.57i 0.0914377i −0.998954 0.0457188i \(-0.985442\pi\)
0.998954 0.0457188i \(-0.0145578\pi\)
\(114\) 4784.95i 0.368186i
\(115\) 11907.0i 0.900343i
\(116\) 4134.70 0.307276
\(117\) 5852.03i 0.427499i
\(118\) −11086.9 + 4563.41i −0.796243 + 0.327737i
\(119\) 15935.6 1.12532
\(120\) 5845.75i 0.405955i
\(121\) 12271.5 0.838163
\(122\) −13881.6 −0.932649
\(123\) −11957.5 −0.790372
\(124\) 2350.91i 0.152895i
\(125\) 16008.0 1.02451
\(126\) 8616.82i 0.542758i
\(127\) −14064.3 −0.871990 −0.435995 0.899949i \(-0.643603\pi\)
−0.435995 + 0.899949i \(0.643603\pi\)
\(128\) 7385.60i 0.450781i
\(129\) 11209.0i 0.673578i
\(130\) −12108.7 −0.716492
\(131\) 15833.5i 0.922644i 0.887233 + 0.461322i \(0.152625\pi\)
−0.887233 + 0.461322i \(0.847375\pi\)
\(132\) 1046.48i 0.0600598i
\(133\) 24774.1 1.40054
\(134\) 28044.1 1.56182
\(135\) −2275.68 −0.124866
\(136\) 11928.1i 0.644899i
\(137\) −21940.7 −1.16899 −0.584493 0.811399i \(-0.698707\pi\)
−0.584493 + 0.811399i \(0.698707\pi\)
\(138\) −13137.4 −0.689847
\(139\) −33025.6 −1.70931 −0.854655 0.519196i \(-0.826231\pi\)
−0.854655 + 0.519196i \(0.826231\pi\)
\(140\) −6218.47 −0.317269
\(141\) 6230.88i 0.313409i
\(142\) 8738.20i 0.433357i
\(143\) −10550.4 −0.515936
\(144\) −4662.47 −0.224849
\(145\) −16210.0 −0.770988
\(146\) 2728.96 0.128024
\(147\) 32137.7 1.48724
\(148\) 4150.09i 0.189467i
\(149\) 20821.5i 0.937863i 0.883235 + 0.468932i \(0.155361\pi\)
−0.883235 + 0.468932i \(0.844639\pi\)
\(150\) 6476.70i 0.287853i
\(151\) 9654.62i 0.423430i −0.977331 0.211715i \(-0.932095\pi\)
0.977331 0.211715i \(-0.0679048\pi\)
\(152\) 18543.8i 0.802622i
\(153\) 4643.44 0.198361
\(154\) 15534.9 0.655038
\(155\) 9216.71i 0.383630i
\(156\) 4659.61i 0.191470i
\(157\) 23483.9i 0.952731i 0.879247 + 0.476366i \(0.158046\pi\)
−0.879247 + 0.476366i \(0.841954\pi\)
\(158\) 11071.3i 0.443491i
\(159\) −5720.99 −0.226296
\(160\) 8352.90i 0.326285i
\(161\) 68019.2i 2.62410i
\(162\) 2510.83i 0.0956727i
\(163\) 12805.6 0.481977 0.240988 0.970528i \(-0.422528\pi\)
0.240988 + 0.970528i \(0.422528\pi\)
\(164\) −9521.06 −0.353995
\(165\) 4102.72i 0.150697i
\(166\) 36292.2 1.31703
\(167\) −29956.3 −1.07413 −0.537063 0.843542i \(-0.680466\pi\)
−0.537063 + 0.843542i \(0.680466\pi\)
\(168\) 33394.0i 1.18318i
\(169\) −18416.0 −0.644796
\(170\) 9607.98i 0.332456i
\(171\) 7218.86 0.246875
\(172\) 8925.05i 0.301685i
\(173\) 51496.1i 1.72061i −0.509781 0.860304i \(-0.670274\pi\)
0.509781 0.860304i \(-0.329726\pi\)
\(174\) 17885.1i 0.590735i
\(175\) −33533.2 −1.09496
\(176\) 8405.76i 0.271364i
\(177\) −6884.64 16726.3i −0.219753 0.533893i
\(178\) 780.104 0.0246214
\(179\) 17057.4i 0.532363i −0.963923 0.266181i \(-0.914238\pi\)
0.963923 0.266181i \(-0.0857620\pi\)
\(180\) −1811.98 −0.0559254
\(181\) 7526.56 0.229741 0.114871 0.993380i \(-0.463355\pi\)
0.114871 + 0.993380i \(0.463355\pi\)
\(182\) 69171.3 2.08825
\(183\) 20942.6i 0.625356i
\(184\) −50913.4 −1.50382
\(185\) 16270.4i 0.475394i
\(186\) 10169.1 0.293939
\(187\) 8371.46i 0.239397i
\(188\) 4961.27i 0.140371i
\(189\) 12999.9 0.363928
\(190\) 14936.9i 0.413765i
\(191\) 34367.0i 0.942053i 0.882119 + 0.471026i \(0.156116\pi\)
−0.882119 + 0.471026i \(0.843884\pi\)
\(192\) −23572.7 −0.639451
\(193\) −35591.7 −0.955507 −0.477753 0.878494i \(-0.658549\pi\)
−0.477753 + 0.878494i \(0.658549\pi\)
\(194\) 25076.9 0.666302
\(195\) 18267.9i 0.480419i
\(196\) 25589.3 0.666110
\(197\) −25127.2 −0.647458 −0.323729 0.946150i \(-0.604937\pi\)
−0.323729 + 0.946150i \(0.604937\pi\)
\(198\) 4526.67 0.115465
\(199\) 19989.2 0.504765 0.252382 0.967628i \(-0.418786\pi\)
0.252382 + 0.967628i \(0.418786\pi\)
\(200\) 25100.1i 0.627502i
\(201\) 42309.1i 1.04723i
\(202\) 40455.6 0.991460
\(203\) 92600.1 2.24709
\(204\) 3697.29 0.0888430
\(205\) 37327.2 0.888214
\(206\) 65541.3 1.54447
\(207\) 19819.9i 0.462553i
\(208\) 37427.9i 0.865104i
\(209\) 13014.6i 0.297946i
\(210\) 26898.6i 0.609947i
\(211\) 32244.7i 0.724257i −0.932128 0.362129i \(-0.882050\pi\)
0.932128 0.362129i \(-0.117950\pi\)
\(212\) −4555.27 −0.101354
\(213\) −13183.0 −0.290573
\(214\) 23255.0i 0.507795i
\(215\) 34990.5i 0.756962i
\(216\) 9730.58i 0.208560i
\(217\) 52650.6i 1.11811i
\(218\) −78940.7 −1.66107
\(219\) 4117.07i 0.0858421i
\(220\) 3266.75i 0.0674948i
\(221\) 37275.1i 0.763193i
\(222\) −17951.7 −0.364249
\(223\) −28806.5 −0.579270 −0.289635 0.957137i \(-0.593534\pi\)
−0.289635 + 0.957137i \(0.593534\pi\)
\(224\) 47716.1i 0.950975i
\(225\) −9771.14 −0.193010
\(226\) −4021.36 −0.0787328
\(227\) 57367.6i 1.11331i −0.830745 0.556654i \(-0.812085\pi\)
0.830745 0.556654i \(-0.187915\pi\)
\(228\) 5747.94 0.110571
\(229\) 8038.50i 0.153287i 0.997059 + 0.0766433i \(0.0244203\pi\)
−0.997059 + 0.0766433i \(0.975580\pi\)
\(230\) 41010.4 0.775244
\(231\) 23436.9i 0.439214i
\(232\) 69312.6i 1.28776i
\(233\) 55821.9i 1.02824i 0.857719 + 0.514118i \(0.171881\pi\)
−0.857719 + 0.514118i \(0.828119\pi\)
\(234\) 20155.7 0.368099
\(235\) 19450.6i 0.352206i
\(236\) −5481.82 13318.2i −0.0984239 0.239122i
\(237\) −16702.8 −0.297368
\(238\) 54885.8i 0.968960i
\(239\) −35079.1 −0.614120 −0.307060 0.951690i \(-0.599345\pi\)
−0.307060 + 0.951690i \(0.599345\pi\)
\(240\) 14554.6 0.252683
\(241\) 84946.1 1.46255 0.731273 0.682085i \(-0.238927\pi\)
0.731273 + 0.682085i \(0.238927\pi\)
\(242\) 42265.8i 0.721703i
\(243\) 3788.00 0.0641500
\(244\) 16675.3i 0.280087i
\(245\) −100322. −1.67134
\(246\) 41184.4i 0.680553i
\(247\) 57949.2i 0.949847i
\(248\) 39409.8 0.640768
\(249\) 54752.5i 0.883091i
\(250\) 55134.8i 0.882157i
\(251\) −62187.4 −0.987086 −0.493543 0.869721i \(-0.664298\pi\)
−0.493543 + 0.869721i \(0.664298\pi\)
\(252\) 10351.0 0.162998
\(253\) 35732.5 0.558242
\(254\) 48440.5i 0.750830i
\(255\) −14495.2 −0.222917
\(256\) −47147.6 −0.719415
\(257\) −11454.6 −0.173426 −0.0867129 0.996233i \(-0.527636\pi\)
−0.0867129 + 0.996233i \(0.527636\pi\)
\(258\) −38606.3 −0.579987
\(259\) 92944.8i 1.38556i
\(260\) 14545.7i 0.215172i
\(261\) 26982.5 0.396097
\(262\) 54533.9 0.794446
\(263\) 39389.7 0.569471 0.284735 0.958606i \(-0.408094\pi\)
0.284735 + 0.958606i \(0.408094\pi\)
\(264\) 17542.8 0.251705
\(265\) 17858.9 0.254310
\(266\) 85327.4i 1.20594i
\(267\) 1176.91i 0.0165090i
\(268\) 33688.1i 0.469037i
\(269\) 13109.8i 0.181172i 0.995889 + 0.0905861i \(0.0288740\pi\)
−0.995889 + 0.0905861i \(0.971126\pi\)
\(270\) 7837.93i 0.107516i
\(271\) 63942.9 0.870670 0.435335 0.900268i \(-0.356630\pi\)
0.435335 + 0.900268i \(0.356630\pi\)
\(272\) −29698.1 −0.401412
\(273\) 104356.i 1.40021i
\(274\) 75568.5i 1.00656i
\(275\) 17616.0i 0.232938i
\(276\) 15781.4i 0.207170i
\(277\) −26097.8 −0.340130 −0.170065 0.985433i \(-0.554398\pi\)
−0.170065 + 0.985433i \(0.554398\pi\)
\(278\) 113747.i 1.47181i
\(279\) 15341.7i 0.197091i
\(280\) 104244.i 1.32964i
\(281\) −33934.6 −0.429765 −0.214882 0.976640i \(-0.568937\pi\)
−0.214882 + 0.976640i \(0.568937\pi\)
\(282\) 21460.5 0.269862
\(283\) 50184.5i 0.626609i −0.949653 0.313305i \(-0.898564\pi\)
0.949653 0.313305i \(-0.101436\pi\)
\(284\) −10496.8 −0.130143
\(285\) −22534.7 −0.277436
\(286\) 36337.7i 0.444248i
\(287\) −213232. −2.58875
\(288\) 13903.9i 0.167630i
\(289\) −53944.1 −0.645875
\(290\) 55830.8i 0.663863i
\(291\) 37832.6i 0.446766i
\(292\) 3278.17i 0.0384473i
\(293\) −145740. −1.69764 −0.848819 0.528684i \(-0.822686\pi\)
−0.848819 + 0.528684i \(0.822686\pi\)
\(294\) 110689.i 1.28059i
\(295\) 21491.4 + 52213.7i 0.246957 + 0.599985i
\(296\) −69570.6 −0.794040
\(297\) 6829.21i 0.0774208i
\(298\) 71713.7 0.807551
\(299\) 159104. 1.77967
\(300\) −7780.17 −0.0864463
\(301\) 199884.i 2.20620i
\(302\) −33252.6 −0.364596
\(303\) 61033.7i 0.664790i
\(304\) −46169.7 −0.499586
\(305\) 65375.2i 0.702770i
\(306\) 15993.0i 0.170800i
\(307\) −37666.1 −0.399645 −0.199822 0.979832i \(-0.564037\pi\)
−0.199822 + 0.979832i \(0.564037\pi\)
\(308\) 18661.4i 0.196717i
\(309\) 98879.5i 1.03559i
\(310\) −31744.3 −0.330326
\(311\) −145763. −1.50704 −0.753522 0.657423i \(-0.771647\pi\)
−0.753522 + 0.657423i \(0.771647\pi\)
\(312\) 78112.0 0.802433
\(313\) 28891.9i 0.294908i −0.989069 0.147454i \(-0.952892\pi\)
0.989069 0.147454i \(-0.0471079\pi\)
\(314\) 80883.5 0.820353
\(315\) −40580.9 −0.408979
\(316\) −13299.5 −0.133186
\(317\) 149119. 1.48393 0.741967 0.670437i \(-0.233893\pi\)
0.741967 + 0.670437i \(0.233893\pi\)
\(318\) 19704.3i 0.194853i
\(319\) 48645.6i 0.478038i
\(320\) 73585.6 0.718610
\(321\) 35083.9 0.340485
\(322\) −234273. −2.25949
\(323\) 45981.3 0.440734
\(324\) 3016.15 0.0287318
\(325\) 78437.6i 0.742605i
\(326\) 44105.4i 0.415008i
\(327\) 119095.i 1.11377i
\(328\) 159608.i 1.48356i
\(329\) 111112.i 1.02652i
\(330\) −14130.7 −0.129758
\(331\) 20162.8 0.184033 0.0920164 0.995757i \(-0.470669\pi\)
0.0920164 + 0.995757i \(0.470669\pi\)
\(332\) 43596.1i 0.395523i
\(333\) 27083.0i 0.244235i
\(334\) 103176.i 0.924880i
\(335\) 132074.i 1.17687i
\(336\) −83143.3 −0.736459
\(337\) 56644.5i 0.498767i −0.968405 0.249384i \(-0.919772\pi\)
0.968405 0.249384i \(-0.0802280\pi\)
\(338\) 63428.7i 0.555204i
\(339\) 6066.86i 0.0527916i
\(340\) −11541.6 −0.0998410
\(341\) −27658.9 −0.237863
\(342\) 24863.3i 0.212572i
\(343\) 350617. 2.98020
\(344\) −149616. −1.26433
\(345\) 61870.8i 0.519813i
\(346\) −177364. −1.48154
\(347\) 98468.3i 0.817782i −0.912583 0.408891i \(-0.865916\pi\)
0.912583 0.408891i \(-0.134084\pi\)
\(348\) 21484.5 0.177406
\(349\) 11046.8i 0.0906953i 0.998971 + 0.0453476i \(0.0144396\pi\)
−0.998971 + 0.0453476i \(0.985560\pi\)
\(350\) 115495.i 0.942820i
\(351\) 30408.0i 0.246816i
\(352\) 25066.7 0.202307
\(353\) 82041.3i 0.658390i 0.944262 + 0.329195i \(0.106777\pi\)
−0.944262 + 0.329195i \(0.893223\pi\)
\(354\) −57609.1 + 23712.2i −0.459711 + 0.189219i
\(355\) 41152.6 0.326543
\(356\) 937.104i 0.00739414i
\(357\) 82804.0 0.649703
\(358\) −58749.5 −0.458393
\(359\) −48438.3 −0.375837 −0.187919 0.982185i \(-0.560174\pi\)
−0.187919 + 0.982185i \(0.560174\pi\)
\(360\) 30375.4i 0.234378i
\(361\) −58836.8 −0.451476
\(362\) 25923.1i 0.197820i
\(363\) 63764.8 0.483913
\(364\) 83092.3i 0.627131i
\(365\) 12852.0i 0.0964686i
\(366\) −72130.7 −0.538465
\(367\) 206944.i 1.53646i −0.640175 0.768229i \(-0.721138\pi\)
0.640175 0.768229i \(-0.278862\pi\)
\(368\) 126762.i 0.936041i
\(369\) −62133.2 −0.456322
\(370\) 56038.7 0.409340
\(371\) −102019. −0.741198
\(372\) 12215.7i 0.0882738i
\(373\) 96391.4 0.692821 0.346410 0.938083i \(-0.387401\pi\)
0.346410 + 0.938083i \(0.387401\pi\)
\(374\) 28833.1 0.206133
\(375\) 83179.8 0.591501
\(376\) 83168.8 0.588281
\(377\) 216601.i 1.52398i
\(378\) 44774.3i 0.313361i
\(379\) 222227. 1.54710 0.773549 0.633737i \(-0.218480\pi\)
0.773549 + 0.633737i \(0.218480\pi\)
\(380\) −17943.0 −0.124259
\(381\) −73080.3 −0.503443
\(382\) 118367. 0.811158
\(383\) 251261. 1.71288 0.856440 0.516246i \(-0.172671\pi\)
0.856440 + 0.516246i \(0.172671\pi\)
\(384\) 38376.7i 0.260259i
\(385\) 73161.6i 0.493585i
\(386\) 122585.i 0.822743i
\(387\) 58243.7i 0.388891i
\(388\) 30123.8i 0.200100i
\(389\) 247468. 1.63538 0.817691 0.575657i \(-0.195254\pi\)
0.817691 + 0.575657i \(0.195254\pi\)
\(390\) −62918.8 −0.413667
\(391\) 126245.i 0.825774i
\(392\) 428969.i 2.79161i
\(393\) 82273.2i 0.532689i
\(394\) 86543.4i 0.557496i
\(395\) 52140.3 0.334179
\(396\) 5437.68i 0.0346756i
\(397\) 15188.5i 0.0963684i −0.998838 0.0481842i \(-0.984657\pi\)
0.998838 0.0481842i \(-0.0153435\pi\)
\(398\) 68847.1i 0.434630i
\(399\) 128730. 0.808601
\(400\) 62493.4 0.390583
\(401\) 41102.4i 0.255611i 0.991799 + 0.127805i \(0.0407933\pi\)
−0.991799 + 0.127805i \(0.959207\pi\)
\(402\) 145722. 0.901720
\(403\) −123155. −0.758304
\(404\) 48597.4i 0.297749i
\(405\) −11824.8 −0.0720913
\(406\) 318935.i 1.93486i
\(407\) 48826.7 0.294760
\(408\) 61980.0i 0.372333i
\(409\) 119091.i 0.711925i −0.934500 0.355962i \(-0.884153\pi\)
0.934500 0.355962i \(-0.115847\pi\)
\(410\) 128563.i 0.764800i
\(411\) −114007. −0.674915
\(412\) 78731.7i 0.463826i
\(413\) −122770. 298272.i −0.719768 1.74869i
\(414\) −68264.1 −0.398283
\(415\) 170918.i 0.992411i
\(416\) 111613. 0.644953
\(417\) −171606. −0.986871
\(418\) 44825.0 0.256547
\(419\) 228690.i 1.30263i 0.758809 + 0.651313i \(0.225782\pi\)
−0.758809 + 0.651313i \(0.774218\pi\)
\(420\) −32312.1 −0.183175
\(421\) 282680.i 1.59489i −0.603390 0.797447i \(-0.706184\pi\)
0.603390 0.797447i \(-0.293816\pi\)
\(422\) −111058. −0.623624
\(423\) 32376.6i 0.180947i
\(424\) 76362.9i 0.424767i
\(425\) −62238.3 −0.344572
\(426\) 45405.0i 0.250199i
\(427\) 373457.i 2.04826i
\(428\) 27935.1 0.152498
\(429\) −54821.3 −0.297876
\(430\) 120515. 0.651785
\(431\) 270326.i 1.45524i 0.685981 + 0.727619i \(0.259373\pi\)
−0.685981 + 0.727619i \(0.740627\pi\)
\(432\) −24226.9 −0.129817
\(433\) −201414. −1.07427 −0.537136 0.843496i \(-0.680494\pi\)
−0.537136 + 0.843496i \(0.680494\pi\)
\(434\) 181340. 0.962752
\(435\) −84229.8 −0.445130
\(436\) 94827.9i 0.498842i
\(437\) 196265.i 1.02773i
\(438\) 14180.1 0.0739147
\(439\) −10876.9 −0.0564388 −0.0282194 0.999602i \(-0.508984\pi\)
−0.0282194 + 0.999602i \(0.508984\pi\)
\(440\) −54762.5 −0.282864
\(441\) 166992. 0.858657
\(442\) 128384. 0.657151
\(443\) 28282.8i 0.144117i −0.997400 0.0720584i \(-0.977043\pi\)
0.997400 0.0720584i \(-0.0229568\pi\)
\(444\) 21564.5i 0.109389i
\(445\) 3673.90i 0.0185527i
\(446\) 99215.8i 0.498782i
\(447\) 108192.i 0.541475i
\(448\) −420360. −2.09443
\(449\) 158321. 0.785320 0.392660 0.919684i \(-0.371555\pi\)
0.392660 + 0.919684i \(0.371555\pi\)
\(450\) 33653.9i 0.166192i
\(451\) 112017.i 0.550721i
\(452\) 4830.67i 0.0236445i
\(453\) 50166.9i 0.244467i
\(454\) −197586. −0.958618
\(455\) 325762.i 1.57354i
\(456\) 96356.3i 0.463394i
\(457\) 35833.3i 0.171575i 0.996313 + 0.0857876i \(0.0273406\pi\)
−0.996313 + 0.0857876i \(0.972659\pi\)
\(458\) 27686.3 0.131988
\(459\) 24128.0 0.114524
\(460\) 49263.9i 0.232816i
\(461\) 307571. 1.44725 0.723625 0.690193i \(-0.242474\pi\)
0.723625 + 0.690193i \(0.242474\pi\)
\(462\) 80721.7 0.378187
\(463\) 272379.i 1.27061i 0.772262 + 0.635304i \(0.219125\pi\)
−0.772262 + 0.635304i \(0.780875\pi\)
\(464\) −172572. −0.801558
\(465\) 47891.4i 0.221489i
\(466\) 192263. 0.885367
\(467\) 217459.i 0.997111i 0.866858 + 0.498556i \(0.166136\pi\)
−0.866858 + 0.498556i \(0.833864\pi\)
\(468\) 24212.1i 0.110545i
\(469\) 754474.i 3.43004i
\(470\) −66992.0 −0.303268
\(471\) 122026.i 0.550060i
\(472\) −223261. + 91895.2i −1.00214 + 0.412485i
\(473\) 105005. 0.469341
\(474\) 57528.2i 0.256050i
\(475\) −96757.9 −0.428844
\(476\) 65931.8 0.290992
\(477\) −29727.1 −0.130652
\(478\) 120820.i 0.528790i
\(479\) −56488.8 −0.246202 −0.123101 0.992394i \(-0.539284\pi\)
−0.123101 + 0.992394i \(0.539284\pi\)
\(480\) 43403.0i 0.188381i
\(481\) 217408. 0.939691
\(482\) 292573.i 1.25933i
\(483\) 353438.i 1.51502i
\(484\) 50772.0 0.216737
\(485\) 118100.i 0.502072i
\(486\) 13046.7i 0.0552366i
\(487\) −374783. −1.58024 −0.790118 0.612954i \(-0.789981\pi\)
−0.790118 + 0.612954i \(0.789981\pi\)
\(488\) −279538. −1.17382
\(489\) 66540.1 0.278270
\(490\) 345532.i 1.43912i
\(491\) −61744.1 −0.256114 −0.128057 0.991767i \(-0.540874\pi\)
−0.128057 + 0.991767i \(0.540874\pi\)
\(492\) −49472.9 −0.204379
\(493\) 171868. 0.707133
\(494\) 199590. 0.817870
\(495\) 21318.4i 0.0870048i
\(496\) 98121.2i 0.398841i
\(497\) −235085. −0.951726
\(498\) 188580. 0.760389
\(499\) −212124. −0.851901 −0.425950 0.904747i \(-0.640060\pi\)
−0.425950 + 0.904747i \(0.640060\pi\)
\(500\) 66231.0 0.264924
\(501\) −155657. −0.620147
\(502\) 214187.i 0.849934i
\(503\) 268106.i 1.05967i −0.848101 0.529834i \(-0.822254\pi\)
0.848101 0.529834i \(-0.177746\pi\)
\(504\) 173520.i 0.683107i
\(505\) 190525.i 0.747085i
\(506\) 123070.i 0.480676i
\(507\) −95692.4 −0.372273
\(508\) −58189.4 −0.225484
\(509\) 241532.i 0.932265i 0.884715 + 0.466133i \(0.154353\pi\)
−0.884715 + 0.466133i \(0.845647\pi\)
\(510\) 49924.5i 0.191944i
\(511\) 73417.5i 0.281163i
\(512\) 280556.i 1.07024i
\(513\) 37510.3 0.142533
\(514\) 39452.1i 0.149329i
\(515\) 308667.i 1.16379i
\(516\) 46375.9i 0.174178i
\(517\) −58370.3 −0.218379
\(518\) −320122. −1.19304
\(519\) 267581.i 0.993394i
\(520\) −243838. −0.901767
\(521\) 81137.0 0.298912 0.149456 0.988768i \(-0.452248\pi\)
0.149456 + 0.988768i \(0.452248\pi\)
\(522\) 92933.6i 0.341061i
\(523\) 507362. 1.85488 0.927438 0.373977i \(-0.122006\pi\)
0.927438 + 0.373977i \(0.122006\pi\)
\(524\) 65509.1i 0.238583i
\(525\) −174243. −0.632176
\(526\) 135667.i 0.490345i
\(527\) 97720.8i 0.351857i
\(528\) 43677.6i 0.156672i
\(529\) −259020. −0.925598
\(530\) 61509.9i 0.218974i
\(531\) −35773.6 86912.6i −0.126874 0.308243i
\(532\) 102500. 0.362160
\(533\) 498773.i 1.75569i
\(534\) 4053.54 0.0142152
\(535\) −109519. −0.382634
\(536\) 564735. 1.96569
\(537\) 88633.0i 0.307360i
\(538\) 45153.0 0.155999
\(539\) 301063.i 1.03629i
\(540\) −9415.34 −0.0322886
\(541\) 303310.i 1.03632i 0.855285 + 0.518158i \(0.173382\pi\)
−0.855285 + 0.518158i \(0.826618\pi\)
\(542\) 220233.i 0.749694i
\(543\) 39109.2 0.132641
\(544\) 88562.2i 0.299261i
\(545\) 371771.i 1.25165i
\(546\) 359425. 1.20565
\(547\) 185234. 0.619077 0.309539 0.950887i \(-0.399825\pi\)
0.309539 + 0.950887i \(0.399825\pi\)
\(548\) −90777.0 −0.302284
\(549\) 108821.i 0.361050i
\(550\) −60673.2 −0.200573
\(551\) 267192. 0.880076
\(552\) −264554. −0.868231
\(553\) −297853. −0.973983
\(554\) 89886.5i 0.292870i
\(555\) 84543.3i 0.274469i
\(556\) −136639. −0.442004
\(557\) 300545. 0.968723 0.484361 0.874868i \(-0.339052\pi\)
0.484361 + 0.874868i \(0.339052\pi\)
\(558\) 52840.2 0.169706
\(559\) 467550. 1.49625
\(560\) 259544. 0.827626
\(561\) 43499.4i 0.138216i
\(562\) 116878.i 0.370050i
\(563\) 110761.i 0.349437i −0.984618 0.174719i \(-0.944098\pi\)
0.984618 0.174719i \(-0.0559016\pi\)
\(564\) 25779.5i 0.0810432i
\(565\) 18938.6i 0.0593267i
\(566\) −172846. −0.539544
\(567\) 67549.3 0.210114
\(568\) 175965.i 0.545417i
\(569\) 85112.7i 0.262887i 0.991324 + 0.131444i \(0.0419612\pi\)
−0.991324 + 0.131444i \(0.958039\pi\)
\(570\) 77614.4i 0.238887i
\(571\) 419082.i 1.28537i −0.766132 0.642683i \(-0.777821\pi\)
0.766132 0.642683i \(-0.222179\pi\)
\(572\) −43650.9 −0.133414
\(573\) 178576.i 0.543894i
\(574\) 734418.i 2.22905i
\(575\) 265656.i 0.803497i
\(576\) −122487. −0.369187
\(577\) −210330. −0.631757 −0.315878 0.948800i \(-0.602299\pi\)
−0.315878 + 0.948800i \(0.602299\pi\)
\(578\) 185795.i 0.556133i
\(579\) −184940. −0.551662
\(580\) −67067.0 −0.199367
\(581\) 976372.i 2.89243i
\(582\) 130304. 0.384690
\(583\) 53593.7i 0.157680i
\(584\) 54954.1 0.161129
\(585\) 94923.1i 0.277370i
\(586\) 501962.i 1.46176i
\(587\) 645237.i 1.87259i −0.351213 0.936296i \(-0.614231\pi\)
0.351213 0.936296i \(-0.385769\pi\)
\(588\) 132966. 0.384579
\(589\) 151920.i 0.437910i
\(590\) 179835. 74021.0i 0.516619 0.212643i
\(591\) −130565. −0.373810
\(592\) 173215.i 0.494244i
\(593\) −386221. −1.09831 −0.549157 0.835719i \(-0.685051\pi\)
−0.549157 + 0.835719i \(0.685051\pi\)
\(594\) 23521.3 0.0666635
\(595\) −258485. −0.730131
\(596\) 86146.4i 0.242518i
\(597\) 103867. 0.291426
\(598\) 547989.i 1.53239i
\(599\) −388204. −1.08195 −0.540974 0.841039i \(-0.681944\pi\)
−0.540974 + 0.841039i \(0.681944\pi\)
\(600\) 130424.i 0.362288i
\(601\) 510006.i 1.41197i 0.708225 + 0.705987i \(0.249496\pi\)
−0.708225 + 0.705987i \(0.750504\pi\)
\(602\) −688444. −1.89966
\(603\) 219844.i 0.604617i
\(604\) 39944.8i 0.109493i
\(605\) −199051. −0.543818
\(606\) 210213. 0.572420
\(607\) −560179. −1.52037 −0.760185 0.649707i \(-0.774892\pi\)
−0.760185 + 0.649707i \(0.774892\pi\)
\(608\) 137682.i 0.372452i
\(609\) 481164. 1.29736
\(610\) 225166. 0.605123
\(611\) −259902. −0.696190
\(612\) 19211.7 0.0512935
\(613\) 306896.i 0.816715i −0.912822 0.408358i \(-0.866102\pi\)
0.912822 0.408358i \(-0.133898\pi\)
\(614\) 129730.i 0.344116i
\(615\) 193958. 0.512811
\(616\) 312832. 0.824422
\(617\) 465889. 1.22380 0.611902 0.790933i \(-0.290405\pi\)
0.611902 + 0.790933i \(0.290405\pi\)
\(618\) 340562. 0.891702
\(619\) 608265. 1.58749 0.793746 0.608250i \(-0.208128\pi\)
0.793746 + 0.608250i \(0.208128\pi\)
\(620\) 38133.0i 0.0992014i
\(621\) 102987.i 0.267055i
\(622\) 502039.i 1.29765i
\(623\) 20987.2i 0.0540728i
\(624\) 194481.i 0.499468i
\(625\) −33473.7 −0.0856927
\(626\) −99509.8 −0.253932
\(627\) 67625.7i 0.172019i
\(628\) 97161.7i 0.246363i
\(629\) 172508.i 0.436021i
\(630\) 139769.i 0.352153i
\(631\) −51223.1 −0.128649 −0.0643245 0.997929i \(-0.520489\pi\)
−0.0643245 + 0.997929i \(0.520489\pi\)
\(632\) 222947.i 0.558171i
\(633\) 167548.i 0.418150i
\(634\) 513598.i 1.27775i
\(635\) 228131. 0.565766
\(636\) −23669.9 −0.0585170
\(637\) 1.34053e6i 3.30367i
\(638\) 167546. 0.411616
\(639\) −68500.8 −0.167762
\(640\) 119798.i 0.292476i
\(641\) −194528. −0.473440 −0.236720 0.971578i \(-0.576072\pi\)
−0.236720 + 0.971578i \(0.576072\pi\)
\(642\) 120836.i 0.293176i
\(643\) −127058. −0.307312 −0.153656 0.988124i \(-0.549105\pi\)
−0.153656 + 0.988124i \(0.549105\pi\)
\(644\) 281421.i 0.678555i
\(645\) 181816.i 0.437032i
\(646\) 158370.i 0.379495i
\(647\) 298850. 0.713912 0.356956 0.934121i \(-0.383815\pi\)
0.356956 + 0.934121i \(0.383815\pi\)
\(648\) 50561.6i 0.120412i
\(649\) 156691. 64494.7i 0.372010 0.153121i
\(650\) −270156. −0.639423
\(651\) 273581.i 0.645540i
\(652\) 52981.8 0.124633
\(653\) −808235. −1.89545 −0.947723 0.319094i \(-0.896621\pi\)
−0.947723 + 0.319094i \(0.896621\pi\)
\(654\) −410188. −0.959019
\(655\) 256828.i 0.598631i
\(656\) 397386. 0.923431
\(657\) 21392.9i 0.0495609i
\(658\) 382693. 0.883891
\(659\) 205299.i 0.472732i −0.971664 0.236366i \(-0.924044\pi\)
0.971664 0.236366i \(-0.0759565\pi\)
\(660\) 16974.5i 0.0389681i
\(661\) −218321. −0.499680 −0.249840 0.968287i \(-0.580378\pi\)
−0.249840 + 0.968287i \(0.580378\pi\)
\(662\) 69445.1i 0.158462i
\(663\) 193687.i 0.440630i
\(664\) 730829. 1.65760
\(665\) −401849. −0.908699
\(666\) −93279.5 −0.210299
\(667\) 733596.i 1.64894i
\(668\) −123940. −0.277754
\(669\) −149683. −0.334441
\(670\) −454891. −1.01335
\(671\) 196188. 0.435740
\(672\) 247940.i 0.549046i
\(673\) 308870.i 0.681939i −0.940074 0.340970i \(-0.889245\pi\)
0.940074 0.340970i \(-0.110755\pi\)
\(674\) −195096. −0.429466
\(675\) −50772.4 −0.111435
\(676\) −76194.0 −0.166735
\(677\) −765077. −1.66927 −0.834637 0.550800i \(-0.814323\pi\)
−0.834637 + 0.550800i \(0.814323\pi\)
\(678\) −20895.6 −0.0454564
\(679\) 674648.i 1.46331i
\(680\) 193479.i 0.418424i
\(681\) 298091.i 0.642768i
\(682\) 95263.3i 0.204813i
\(683\) 32889.7i 0.0705047i −0.999378 0.0352523i \(-0.988777\pi\)
0.999378 0.0352523i \(-0.0112235\pi\)
\(684\) 29867.2 0.0638384
\(685\) 355890. 0.758463
\(686\) 1.20760e6i 2.56611i
\(687\) 41769.3i 0.0885000i
\(688\) 372510.i 0.786975i
\(689\) 238634.i 0.502682i
\(690\) 213096. 0.447587
\(691\) 498934.i 1.04493i −0.852661 0.522465i \(-0.825013\pi\)
0.852661 0.522465i \(-0.174987\pi\)
\(692\) 213059.i 0.444925i
\(693\) 121782.i 0.253580i
\(694\) −339146. −0.704154
\(695\) 535693. 1.10904
\(696\) 360159.i 0.743490i
\(697\) −395764. −0.814650
\(698\) 38047.5 0.0780935
\(699\) 290059.i 0.593653i
\(700\) −138739. −0.283142
\(701\) 70692.6i 0.143859i −0.997410 0.0719297i \(-0.977084\pi\)
0.997410 0.0719297i \(-0.0229157\pi\)
\(702\) 104732. 0.212522
\(703\) 268187.i 0.542658i
\(704\) 220827.i 0.445561i
\(705\) 101068.i 0.203346i
\(706\) 282568. 0.566909
\(707\) 1.08838e6i 2.17742i
\(708\) −28484.4 69203.2i −0.0568251 0.138057i
\(709\) −845715. −1.68241 −0.841204 0.540717i \(-0.818153\pi\)
−0.841204 + 0.540717i \(0.818153\pi\)
\(710\) 141738.i 0.281171i
\(711\) −86790.5 −0.171685
\(712\) 15709.3 0.0309881
\(713\) 417108. 0.820484
\(714\) 285195.i 0.559429i
\(715\) 171133. 0.334750
\(716\) 70573.0i 0.137662i
\(717\) −182277. −0.354562
\(718\) 166832.i 0.323616i
\(719\) 541985.i 1.04841i −0.851593 0.524203i \(-0.824363\pi\)
0.851593 0.524203i \(-0.175637\pi\)
\(720\) 75627.7 0.145887
\(721\) 1.76327e6i 3.39193i
\(722\) 202647.i 0.388745i
\(723\) 441393. 0.844401
\(724\) 31140.2 0.0594080
\(725\) −361660. −0.688057
\(726\) 219620.i 0.416676i
\(727\) 324956. 0.614832 0.307416 0.951575i \(-0.400536\pi\)
0.307416 + 0.951575i \(0.400536\pi\)
\(728\) 1.39293e6 2.62825
\(729\) 19683.0 0.0370370
\(730\) −44265.2 −0.0830647
\(731\) 370990.i 0.694268i
\(732\) 86647.3i 0.161708i
\(733\) −228228. −0.424777 −0.212389 0.977185i \(-0.568124\pi\)
−0.212389 + 0.977185i \(0.568124\pi\)
\(734\) −712760. −1.32297
\(735\) −521291. −0.964951
\(736\) −378016. −0.697839
\(737\) −396348. −0.729695
\(738\) 214000.i 0.392918i
\(739\) 153824.i 0.281667i 0.990033 + 0.140834i \(0.0449782\pi\)
−0.990033 + 0.140834i \(0.955022\pi\)
\(740\) 67316.7i 0.122930i
\(741\) 301113.i 0.548395i
\(742\) 351376.i 0.638212i
\(743\) 40762.4 0.0738384 0.0369192 0.999318i \(-0.488246\pi\)
0.0369192 + 0.999318i \(0.488246\pi\)
\(744\) 204779. 0.369947
\(745\) 337736.i 0.608506i
\(746\) 331993.i 0.596556i
\(747\) 284503.i 0.509853i
\(748\) 34635.9i 0.0619047i
\(749\) 625632. 1.11521
\(750\) 286489.i 0.509314i
\(751\) 947341.i 1.67968i −0.542834 0.839840i \(-0.682649\pi\)
0.542834 0.839840i \(-0.317351\pi\)
\(752\) 207071.i 0.366171i
\(753\) −323135. −0.569894
\(754\) 746022. 1.31223
\(755\) 156603.i 0.274730i
\(756\) 53785.3 0.0941067
\(757\) −384807. −0.671508 −0.335754 0.941950i \(-0.608991\pi\)
−0.335754 + 0.941950i \(0.608991\pi\)
\(758\) 765397.i 1.33213i
\(759\) 185671. 0.322301
\(760\) 300790.i 0.520758i
\(761\) 621369. 1.07295 0.536476 0.843916i \(-0.319755\pi\)
0.536476 + 0.843916i \(0.319755\pi\)
\(762\) 251704.i 0.433492i
\(763\) 2.12375e6i 3.64800i
\(764\) 142189.i 0.243602i
\(765\) −75319.1 −0.128701
\(766\) 865396.i 1.47488i
\(767\) 697689. 287172.i 1.18596 0.488148i
\(768\) −244986. −0.415354
\(769\) 140425.i 0.237460i 0.992927 + 0.118730i \(0.0378823\pi\)
−0.992927 + 0.118730i \(0.962118\pi\)
\(770\) −251984. −0.425003
\(771\) −59519.9 −0.100127
\(772\) −147256. −0.247081
\(773\) 233110.i 0.390124i 0.980791 + 0.195062i \(0.0624908\pi\)
−0.980791 + 0.195062i \(0.937509\pi\)
\(774\) −200604. −0.334856
\(775\) 205633.i 0.342365i
\(776\) 504984. 0.838598
\(777\) 482956.i 0.799954i
\(778\) 852332.i 1.40815i
\(779\) −615269. −1.01389
\(780\) 75581.4i 0.124230i
\(781\) 123497.i 0.202467i
\(782\) −434816. −0.711036
\(783\) 140205. 0.228687
\(784\) −1.06803e6 −1.73761
\(785\) 380921.i 0.618153i
\(786\) 283367. 0.458674
\(787\) 95032.6 0.153435 0.0767173 0.997053i \(-0.475556\pi\)
0.0767173 + 0.997053i \(0.475556\pi\)
\(788\) −103961. −0.167424
\(789\) 204675. 0.328784