Properties

Label 43.5.b.b.42.10
Level 43
Weight 5
Character 43.42
Analytic conductor 4.445
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.44490841261\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.10
Root \(4.43775i\) of \(x^{12} + 142 x^{10} + 7173 x^{8} + 157368 x^{6} + 1510016 x^{4} + 5098688 x^{2} + 90352\)
Character \(\chi\) \(=\) 43.42
Dual form 43.5.b.b.42.3

$q$-expansion

\(f(q)\) \(=\) \(q+4.43775i q^{2} -6.93950i q^{3} -3.69363 q^{4} +22.3554i q^{5} +30.7958 q^{6} +51.9837i q^{7} +54.6126i q^{8} +32.8434 q^{9} +O(q^{10})\) \(q+4.43775i q^{2} -6.93950i q^{3} -3.69363 q^{4} +22.3554i q^{5} +30.7958 q^{6} +51.9837i q^{7} +54.6126i q^{8} +32.8434 q^{9} -99.2077 q^{10} -25.0158 q^{11} +25.6320i q^{12} -38.7510 q^{13} -230.691 q^{14} +155.135 q^{15} -301.455 q^{16} +111.381 q^{17} +145.751i q^{18} -238.930i q^{19} -82.5727i q^{20} +360.741 q^{21} -111.014i q^{22} +823.523 q^{23} +378.984 q^{24} +125.236 q^{25} -171.967i q^{26} -790.016i q^{27} -192.009i q^{28} -424.840i q^{29} +688.452i q^{30} -1447.58 q^{31} -463.982i q^{32} +173.597i q^{33} +494.282i q^{34} -1162.12 q^{35} -121.311 q^{36} -626.677i q^{37} +1060.31 q^{38} +268.912i q^{39} -1220.89 q^{40} +580.694 q^{41} +1600.88i q^{42} +(-528.728 - 1771.79i) q^{43} +92.3990 q^{44} +734.227i q^{45} +3654.59i q^{46} -170.609 q^{47} +2091.95i q^{48} -301.309 q^{49} +555.765i q^{50} -772.930i q^{51} +143.132 q^{52} +4308.39 q^{53} +3505.89 q^{54} -559.237i q^{55} -2838.97 q^{56} -1658.05 q^{57} +1885.33 q^{58} -65.4372 q^{59} -573.013 q^{60} +3896.58i q^{61} -6423.99i q^{62} +1707.32i q^{63} -2764.25 q^{64} -866.294i q^{65} -770.379 q^{66} -5449.76 q^{67} -411.402 q^{68} -5714.84i q^{69} -5157.19i q^{70} -5845.23i q^{71} +1793.66i q^{72} +4773.87i q^{73} +2781.04 q^{74} -869.073i q^{75} +882.519i q^{76} -1300.41i q^{77} -1193.37 q^{78} +10139.3 q^{79} -6739.15i q^{80} -2822.00 q^{81} +2576.98i q^{82} +4438.95 q^{83} -1332.45 q^{84} +2489.97i q^{85} +(7862.77 - 2346.36i) q^{86} -2948.17 q^{87} -1366.18i q^{88} +9870.51i q^{89} -3258.32 q^{90} -2014.42i q^{91} -3041.79 q^{92} +10045.5i q^{93} -757.120i q^{94} +5341.37 q^{95} -3219.80 q^{96} -7761.47 q^{97} -1337.14i q^{98} -821.602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + O(q^{10}) \) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + 182q^{10} - 180q^{11} - 216q^{13} + 732q^{14} - 92q^{15} + 1076q^{16} + 678q^{17} - 2392q^{21} + 1566q^{23} - 4234q^{24} - 174q^{25} + 5710q^{31} + 936q^{35} + 4210q^{36} + 1242q^{38} - 2618q^{40} + 4878q^{41} - 1108q^{43} - 15168q^{44} - 5526q^{47} - 8544q^{49} + 24084q^{52} + 1212q^{53} - 10004q^{54} - 10152q^{56} - 7692q^{57} - 4666q^{58} + 14016q^{59} + 15848q^{60} - 15580q^{64} + 29808q^{66} - 1088q^{67} + 15186q^{68} - 7674q^{74} - 67708q^{78} + 24302q^{79} - 23660q^{81} - 7032q^{83} + 37180q^{84} - 14412q^{86} + 17850q^{87} + 4268q^{90} + 48354q^{92} + 606q^{95} + 50546q^{96} - 5842q^{97} - 25924q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.43775i 1.10944i 0.832038 + 0.554719i \(0.187174\pi\)
−0.832038 + 0.554719i \(0.812826\pi\)
\(3\) 6.93950i 0.771055i −0.922696 0.385528i \(-0.874019\pi\)
0.922696 0.385528i \(-0.125981\pi\)
\(4\) −3.69363 −0.230852
\(5\) 22.3554i 0.894216i 0.894480 + 0.447108i \(0.147546\pi\)
−0.894480 + 0.447108i \(0.852454\pi\)
\(6\) 30.7958 0.855438
\(7\) 51.9837i 1.06089i 0.847719 + 0.530446i \(0.177976\pi\)
−0.847719 + 0.530446i \(0.822024\pi\)
\(8\) 54.6126i 0.853322i
\(9\) 32.8434 0.405474
\(10\) −99.2077 −0.992077
\(11\) −25.0158 −0.206742 −0.103371 0.994643i \(-0.532963\pi\)
−0.103371 + 0.994643i \(0.532963\pi\)
\(12\) 25.6320i 0.178000i
\(13\) −38.7510 −0.229296 −0.114648 0.993406i \(-0.536574\pi\)
−0.114648 + 0.993406i \(0.536574\pi\)
\(14\) −230.691 −1.17699
\(15\) 155.135 0.689490
\(16\) −301.455 −1.17756
\(17\) 111.381 0.385402 0.192701 0.981257i \(-0.438275\pi\)
0.192701 + 0.981257i \(0.438275\pi\)
\(18\) 145.751i 0.449848i
\(19\) 238.930i 0.661856i −0.943656 0.330928i \(-0.892638\pi\)
0.943656 0.330928i \(-0.107362\pi\)
\(20\) 82.5727i 0.206432i
\(21\) 360.741 0.818007
\(22\) 111.014i 0.229367i
\(23\) 823.523 1.55675 0.778377 0.627797i \(-0.216043\pi\)
0.778377 + 0.627797i \(0.216043\pi\)
\(24\) 378.984 0.657958
\(25\) 125.236 0.200377
\(26\) 171.967i 0.254389i
\(27\) 790.016i 1.08370i
\(28\) 192.009i 0.244909i
\(29\) 424.840i 0.505160i −0.967576 0.252580i \(-0.918721\pi\)
0.967576 0.252580i \(-0.0812791\pi\)
\(30\) 688.452i 0.764946i
\(31\) −1447.58 −1.50632 −0.753162 0.657835i \(-0.771472\pi\)
−0.753162 + 0.657835i \(0.771472\pi\)
\(32\) 463.982i 0.453107i
\(33\) 173.597i 0.159409i
\(34\) 494.282i 0.427580i
\(35\) −1162.12 −0.948668
\(36\) −121.311 −0.0936045
\(37\) 626.677i 0.457763i −0.973454 0.228881i \(-0.926493\pi\)
0.973454 0.228881i \(-0.0735068\pi\)
\(38\) 1060.31 0.734287
\(39\) 268.912i 0.176800i
\(40\) −1220.89 −0.763054
\(41\) 580.694 0.345446 0.172723 0.984970i \(-0.444744\pi\)
0.172723 + 0.984970i \(0.444744\pi\)
\(42\) 1600.88i 0.907528i
\(43\) −528.728 1771.79i −0.285953 0.958244i
\(44\) 92.3990 0.0477268
\(45\) 734.227i 0.362581i
\(46\) 3654.59i 1.72712i
\(47\) −170.609 −0.0772336 −0.0386168 0.999254i \(-0.512295\pi\)
−0.0386168 + 0.999254i \(0.512295\pi\)
\(48\) 2091.95i 0.907963i
\(49\) −301.309 −0.125493
\(50\) 555.765i 0.222306i
\(51\) 772.930i 0.297167i
\(52\) 143.132 0.0529334
\(53\) 4308.39 1.53378 0.766890 0.641779i \(-0.221803\pi\)
0.766890 + 0.641779i \(0.221803\pi\)
\(54\) 3505.89 1.20230
\(55\) 559.237i 0.184872i
\(56\) −2838.97 −0.905283
\(57\) −1658.05 −0.510327
\(58\) 1885.33 0.560444
\(59\) −65.4372 −0.0187984 −0.00939919 0.999956i \(-0.502992\pi\)
−0.00939919 + 0.999956i \(0.502992\pi\)
\(60\) −573.013 −0.159170
\(61\) 3896.58i 1.04719i 0.851968 + 0.523594i \(0.175409\pi\)
−0.851968 + 0.523594i \(0.824591\pi\)
\(62\) 6423.99i 1.67117i
\(63\) 1707.32i 0.430164i
\(64\) −2764.25 −0.674865
\(65\) 866.294i 0.205040i
\(66\) −770.379 −0.176855
\(67\) −5449.76 −1.21403 −0.607013 0.794692i \(-0.707632\pi\)
−0.607013 + 0.794692i \(0.707632\pi\)
\(68\) −411.402 −0.0889709
\(69\) 5714.84i 1.20034i
\(70\) 5157.19i 1.05249i
\(71\) 5845.23i 1.15954i −0.814781 0.579769i \(-0.803143\pi\)
0.814781 0.579769i \(-0.196857\pi\)
\(72\) 1793.66i 0.346000i
\(73\) 4773.87i 0.895828i 0.894077 + 0.447914i \(0.147833\pi\)
−0.894077 + 0.447914i \(0.852167\pi\)
\(74\) 2781.04 0.507859
\(75\) 869.073i 0.154502i
\(76\) 882.519i 0.152791i
\(77\) 1300.41i 0.219331i
\(78\) −1193.37 −0.196148
\(79\) 10139.3 1.62463 0.812316 0.583217i \(-0.198206\pi\)
0.812316 + 0.583217i \(0.198206\pi\)
\(80\) 6739.15i 1.05299i
\(81\) −2822.00 −0.430117
\(82\) 2576.98i 0.383250i
\(83\) 4438.95 0.644353 0.322176 0.946680i \(-0.395586\pi\)
0.322176 + 0.946680i \(0.395586\pi\)
\(84\) −1332.45 −0.188839
\(85\) 2489.97i 0.344633i
\(86\) 7862.77 2346.36i 1.06311 0.317247i
\(87\) −2948.17 −0.389506
\(88\) 1366.18i 0.176417i
\(89\) 9870.51i 1.24612i 0.782174 + 0.623060i \(0.214111\pi\)
−0.782174 + 0.623060i \(0.785889\pi\)
\(90\) −3258.32 −0.402261
\(91\) 2014.42i 0.243258i
\(92\) −3041.79 −0.359380
\(93\) 10045.5i 1.16146i
\(94\) 757.120i 0.0856858i
\(95\) 5341.37 0.591842
\(96\) −3219.80 −0.349371
\(97\) −7761.47 −0.824899 −0.412449 0.910981i \(-0.635327\pi\)
−0.412449 + 0.910981i \(0.635327\pi\)
\(98\) 1337.14i 0.139227i
\(99\) −821.602 −0.0838284
\(100\) −462.575 −0.0462575
\(101\) −7907.71 −0.775190 −0.387595 0.921830i \(-0.626694\pi\)
−0.387595 + 0.921830i \(0.626694\pi\)
\(102\) 3430.07 0.329688
\(103\) 11579.3 1.09146 0.545728 0.837962i \(-0.316253\pi\)
0.545728 + 0.837962i \(0.316253\pi\)
\(104\) 2116.29i 0.195663i
\(105\) 8064.51i 0.731475i
\(106\) 19119.5i 1.70163i
\(107\) −6463.42 −0.564540 −0.282270 0.959335i \(-0.591087\pi\)
−0.282270 + 0.959335i \(0.591087\pi\)
\(108\) 2918.03i 0.250174i
\(109\) 3408.56 0.286892 0.143446 0.989658i \(-0.454182\pi\)
0.143446 + 0.989658i \(0.454182\pi\)
\(110\) 2481.76 0.205104
\(111\) −4348.82 −0.352960
\(112\) 15670.8i 1.24926i
\(113\) 11268.0i 0.882446i −0.897397 0.441223i \(-0.854545\pi\)
0.897397 0.441223i \(-0.145455\pi\)
\(114\) 7358.03i 0.566176i
\(115\) 18410.2i 1.39208i
\(116\) 1569.20i 0.116617i
\(117\) −1272.71 −0.0929734
\(118\) 290.394i 0.0208556i
\(119\) 5790.02i 0.408871i
\(120\) 8472.34i 0.588357i
\(121\) −14015.2 −0.957258
\(122\) −17292.1 −1.16179
\(123\) 4029.73i 0.266358i
\(124\) 5346.82 0.347738
\(125\) 16771.8i 1.07340i
\(126\) −7576.67 −0.477240
\(127\) 13207.4 0.818860 0.409430 0.912342i \(-0.365728\pi\)
0.409430 + 0.912342i \(0.365728\pi\)
\(128\) 19690.8i 1.20183i
\(129\) −12295.3 + 3669.10i −0.738859 + 0.220486i
\(130\) 3844.40 0.227479
\(131\) 29457.5i 1.71653i −0.513203 0.858267i \(-0.671541\pi\)
0.513203 0.858267i \(-0.328459\pi\)
\(132\) 641.203i 0.0368000i
\(133\) 12420.5 0.702158
\(134\) 24184.7i 1.34689i
\(135\) 17661.1 0.969060
\(136\) 6082.82i 0.328872i
\(137\) 14241.6i 0.758783i −0.925236 0.379392i \(-0.876133\pi\)
0.925236 0.379392i \(-0.123867\pi\)
\(138\) 25361.0 1.33171
\(139\) −18549.0 −0.960042 −0.480021 0.877257i \(-0.659371\pi\)
−0.480021 + 0.877257i \(0.659371\pi\)
\(140\) 4292.44 0.219002
\(141\) 1183.94i 0.0595513i
\(142\) 25939.7 1.28644
\(143\) 969.385 0.0474050
\(144\) −9900.81 −0.477469
\(145\) 9497.46 0.451722
\(146\) −21185.2 −0.993866
\(147\) 2090.94i 0.0967623i
\(148\) 2314.71i 0.105675i
\(149\) 31018.5i 1.39717i 0.715528 + 0.698584i \(0.246186\pi\)
−0.715528 + 0.698584i \(0.753814\pi\)
\(150\) 3856.73 0.171410
\(151\) 10079.5i 0.442063i −0.975267 0.221032i \(-0.929058\pi\)
0.975267 0.221032i \(-0.0709424\pi\)
\(152\) 13048.6 0.564776
\(153\) 3658.14 0.156271
\(154\) 5770.91 0.243334
\(155\) 32361.2i 1.34698i
\(156\) 993.264i 0.0408146i
\(157\) 27782.4i 1.12712i −0.826075 0.563560i \(-0.809431\pi\)
0.826075 0.563560i \(-0.190569\pi\)
\(158\) 44995.8i 1.80243i
\(159\) 29898.0i 1.18263i
\(160\) 10372.5 0.405176
\(161\) 42809.8i 1.65155i
\(162\) 12523.3i 0.477188i
\(163\) 23274.3i 0.875993i −0.898977 0.437996i \(-0.855688\pi\)
0.898977 0.437996i \(-0.144312\pi\)
\(164\) −2144.87 −0.0797469
\(165\) −3880.83 −0.142546
\(166\) 19698.9i 0.714869i
\(167\) −38477.5 −1.37967 −0.689833 0.723968i \(-0.742316\pi\)
−0.689833 + 0.723968i \(0.742316\pi\)
\(168\) 19701.0i 0.698023i
\(169\) −27059.4 −0.947423
\(170\) −11049.9 −0.382349
\(171\) 7847.26i 0.268365i
\(172\) 1952.93 + 6544.35i 0.0660129 + 0.221213i
\(173\) 26454.5 0.883909 0.441954 0.897038i \(-0.354285\pi\)
0.441954 + 0.897038i \(0.354285\pi\)
\(174\) 13083.3i 0.432133i
\(175\) 6510.22i 0.212579i
\(176\) 7541.13 0.243451
\(177\) 454.101i 0.0144946i
\(178\) −43802.9 −1.38249
\(179\) 5807.25i 0.181244i 0.995885 + 0.0906222i \(0.0288856\pi\)
−0.995885 + 0.0906222i \(0.971114\pi\)
\(180\) 2711.97i 0.0837026i
\(181\) −63912.2 −1.95086 −0.975431 0.220304i \(-0.929295\pi\)
−0.975431 + 0.220304i \(0.929295\pi\)
\(182\) 8939.50 0.269880
\(183\) 27040.3 0.807439
\(184\) 44974.7i 1.32841i
\(185\) 14009.6 0.409339
\(186\) −44579.2 −1.28857
\(187\) −2786.29 −0.0796788
\(188\) 630.167 0.0178295
\(189\) 41068.0 1.14969
\(190\) 23703.7i 0.656612i
\(191\) 58852.6i 1.61324i 0.591071 + 0.806620i \(0.298705\pi\)
−0.591071 + 0.806620i \(0.701295\pi\)
\(192\) 19182.5i 0.520358i
\(193\) −4293.94 −0.115277 −0.0576384 0.998338i \(-0.518357\pi\)
−0.0576384 + 0.998338i \(0.518357\pi\)
\(194\) 34443.5i 0.915174i
\(195\) −6011.65 −0.158097
\(196\) 1112.93 0.0289704
\(197\) 60627.5 1.56220 0.781101 0.624405i \(-0.214658\pi\)
0.781101 + 0.624405i \(0.214658\pi\)
\(198\) 3646.06i 0.0930023i
\(199\) 75910.5i 1.91688i −0.285290 0.958441i \(-0.592090\pi\)
0.285290 0.958441i \(-0.407910\pi\)
\(200\) 6839.44i 0.170986i
\(201\) 37818.6i 0.936081i
\(202\) 35092.4i 0.860025i
\(203\) 22084.8 0.535921
\(204\) 2854.92i 0.0686015i
\(205\) 12981.7i 0.308903i
\(206\) 51385.9i 1.21090i
\(207\) 27047.3 0.631223
\(208\) 11681.7 0.270009
\(209\) 5977.01i 0.136833i
\(210\) −35788.3 −0.811526
\(211\) 34858.4i 0.782964i 0.920186 + 0.391482i \(0.128038\pi\)
−0.920186 + 0.391482i \(0.871962\pi\)
\(212\) −15913.6 −0.354076
\(213\) −40563.0 −0.894068
\(214\) 28683.0i 0.626322i
\(215\) 39609.1 11819.9i 0.856877 0.255704i
\(216\) 43144.8 0.924743
\(217\) 75250.5i 1.59805i
\(218\) 15126.3i 0.318289i
\(219\) 33128.3 0.690733
\(220\) 2065.62i 0.0426781i
\(221\) −4316.13 −0.0883711
\(222\) 19299.0i 0.391587i
\(223\) 69871.4i 1.40504i −0.711662 0.702522i \(-0.752057\pi\)
0.711662 0.702522i \(-0.247943\pi\)
\(224\) 24119.5 0.480698
\(225\) 4113.16 0.0812476
\(226\) 50004.4 0.979019
\(227\) 5952.36i 0.115515i 0.998331 + 0.0577574i \(0.0183950\pi\)
−0.998331 + 0.0577574i \(0.981605\pi\)
\(228\) 6124.24 0.117810
\(229\) −31808.4 −0.606556 −0.303278 0.952902i \(-0.598081\pi\)
−0.303278 + 0.952902i \(0.598081\pi\)
\(230\) −81699.8 −1.54442
\(231\) −9024.21 −0.169116
\(232\) 23201.6 0.431064
\(233\) 55507.2i 1.02244i 0.859450 + 0.511220i \(0.170806\pi\)
−0.859450 + 0.511220i \(0.829194\pi\)
\(234\) 5647.98i 0.103148i
\(235\) 3814.03i 0.0690635i
\(236\) 241.701 0.00433965
\(237\) 70361.9i 1.25268i
\(238\) −25694.7 −0.453616
\(239\) −62886.2 −1.10093 −0.550465 0.834859i \(-0.685549\pi\)
−0.550465 + 0.834859i \(0.685549\pi\)
\(240\) −46766.3 −0.811916
\(241\) 19314.0i 0.332536i 0.986081 + 0.166268i \(0.0531717\pi\)
−0.986081 + 0.166268i \(0.946828\pi\)
\(242\) 62196.0i 1.06202i
\(243\) 44408.0i 0.752054i
\(244\) 14392.6i 0.241745i
\(245\) 6735.90i 0.112218i
\(246\) 17882.9 0.295507
\(247\) 9258.77i 0.151761i
\(248\) 79055.9i 1.28538i
\(249\) 30804.1i 0.496832i
\(250\) −74429.2 −1.19087
\(251\) −62983.5 −0.999723 −0.499862 0.866105i \(-0.666616\pi\)
−0.499862 + 0.866105i \(0.666616\pi\)
\(252\) 6306.22i 0.0993043i
\(253\) −20601.0 −0.321846
\(254\) 58611.1i 0.908474i
\(255\) 17279.2 0.265731
\(256\) 43154.7 0.658488
\(257\) 53736.0i 0.813579i 0.913522 + 0.406789i \(0.133352\pi\)
−0.913522 + 0.406789i \(0.866648\pi\)
\(258\) −16282.6 54563.7i −0.244615 0.819718i
\(259\) 32577.0 0.485637
\(260\) 3199.77i 0.0473339i
\(261\) 13953.2i 0.204829i
\(262\) 130725. 1.90439
\(263\) 133357.i 1.92798i 0.265932 + 0.963992i \(0.414320\pi\)
−0.265932 + 0.963992i \(0.585680\pi\)
\(264\) −9480.57 −0.136027
\(265\) 96315.7i 1.37153i
\(266\) 55118.9i 0.779000i
\(267\) 68496.4 0.960827
\(268\) 20129.4 0.280260
\(269\) 61320.3 0.847421 0.423711 0.905798i \(-0.360727\pi\)
0.423711 + 0.905798i \(0.360727\pi\)
\(270\) 78375.7i 1.07511i
\(271\) 66120.9 0.900326 0.450163 0.892946i \(-0.351366\pi\)
0.450163 + 0.892946i \(0.351366\pi\)
\(272\) −33576.5 −0.453834
\(273\) −13979.1 −0.187565
\(274\) 63200.7 0.841823
\(275\) −3132.86 −0.0414263
\(276\) 21108.5i 0.277102i
\(277\) 62649.4i 0.816502i 0.912870 + 0.408251i \(0.133861\pi\)
−0.912870 + 0.408251i \(0.866139\pi\)
\(278\) 82315.7i 1.06511i
\(279\) −47543.3 −0.610775
\(280\) 63466.3i 0.809519i
\(281\) 110235. 1.39606 0.698032 0.716066i \(-0.254059\pi\)
0.698032 + 0.716066i \(0.254059\pi\)
\(282\) −5254.03 −0.0660685
\(283\) −109263. −1.36427 −0.682135 0.731226i \(-0.738948\pi\)
−0.682135 + 0.731226i \(0.738948\pi\)
\(284\) 21590.1i 0.267682i
\(285\) 37066.5i 0.456343i
\(286\) 4301.89i 0.0525929i
\(287\) 30186.7i 0.366481i
\(288\) 15238.7i 0.183723i
\(289\) −71115.2 −0.851465
\(290\) 42147.4i 0.501158i
\(291\) 53860.7i 0.636042i
\(292\) 17632.9i 0.206804i
\(293\) −137382. −1.60028 −0.800139 0.599814i \(-0.795241\pi\)
−0.800139 + 0.599814i \(0.795241\pi\)
\(294\) −9279.05 −0.107352
\(295\) 1462.88i 0.0168098i
\(296\) 34224.4 0.390619
\(297\) 19762.8i 0.224046i
\(298\) −137653. −1.55007
\(299\) −31912.3 −0.356957
\(300\) 3210.04i 0.0356671i
\(301\) 92104.4 27485.2i 1.01659 0.303366i
\(302\) 44730.3 0.490442
\(303\) 54875.5i 0.597714i
\(304\) 72026.6i 0.779374i
\(305\) −87109.7 −0.936412
\(306\) 16233.9i 0.173372i
\(307\) −13056.1 −0.138528 −0.0692639 0.997598i \(-0.522065\pi\)
−0.0692639 + 0.997598i \(0.522065\pi\)
\(308\) 4803.25i 0.0506330i
\(309\) 80354.2i 0.841573i
\(310\) 143611. 1.49439
\(311\) −190885. −1.97356 −0.986781 0.162061i \(-0.948186\pi\)
−0.986781 + 0.162061i \(0.948186\pi\)
\(312\) −14686.0 −0.150867
\(313\) 31940.8i 0.326030i −0.986624 0.163015i \(-0.947878\pi\)
0.986624 0.163015i \(-0.0521219\pi\)
\(314\) 123291. 1.25047
\(315\) −38167.9 −0.384660
\(316\) −37451.0 −0.375050
\(317\) 10721.3 0.106692 0.0533459 0.998576i \(-0.483011\pi\)
0.0533459 + 0.998576i \(0.483011\pi\)
\(318\) 132680. 1.31205
\(319\) 10627.7i 0.104438i
\(320\) 61795.9i 0.603476i
\(321\) 44852.9i 0.435291i
\(322\) −189979. −1.83229
\(323\) 26612.3i 0.255081i
\(324\) 10423.4 0.0992935
\(325\) −4853.00 −0.0459456
\(326\) 103285. 0.971859
\(327\) 23653.7i 0.221209i
\(328\) 31713.2i 0.294776i
\(329\) 8868.89i 0.0819365i
\(330\) 17222.1i 0.158146i
\(331\) 49144.6i 0.448560i −0.974525 0.224280i \(-0.927997\pi\)
0.974525 0.224280i \(-0.0720030\pi\)
\(332\) −16395.8 −0.148750
\(333\) 20582.2i 0.185611i
\(334\) 170754.i 1.53065i
\(335\) 121832.i 1.08560i
\(336\) −108747. −0.963252
\(337\) 113598. 1.00025 0.500127 0.865952i \(-0.333287\pi\)
0.500127 + 0.865952i \(0.333287\pi\)
\(338\) 120083.i 1.05111i
\(339\) −78194.0 −0.680415
\(340\) 9197.05i 0.0795593i
\(341\) 36212.2 0.311420
\(342\) 34824.2 0.297734
\(343\) 109150.i 0.927758i
\(344\) 96762.2 28875.2i 0.817690 0.244010i
\(345\) 127757. 1.07337
\(346\) 117399.i 0.980642i
\(347\) 25603.4i 0.212637i −0.994332 0.106319i \(-0.966094\pi\)
0.994332 0.106319i \(-0.0339063\pi\)
\(348\) 10889.5 0.0899183
\(349\) 4308.53i 0.0353735i −0.999844 0.0176867i \(-0.994370\pi\)
0.999844 0.0176867i \(-0.00563016\pi\)
\(350\) −28890.7 −0.235843
\(351\) 30613.9i 0.248487i
\(352\) 11606.9i 0.0936762i
\(353\) 101165. 0.811856 0.405928 0.913905i \(-0.366948\pi\)
0.405928 + 0.913905i \(0.366948\pi\)
\(354\) −2015.19 −0.0160809
\(355\) 130673. 1.03688
\(356\) 36458.0i 0.287669i
\(357\) 40179.8 0.315262
\(358\) −25771.2 −0.201079
\(359\) 3103.18 0.0240779 0.0120389 0.999928i \(-0.496168\pi\)
0.0120389 + 0.999928i \(0.496168\pi\)
\(360\) −40098.0 −0.309398
\(361\) 73233.5 0.561947
\(362\) 283626.i 2.16436i
\(363\) 97258.5i 0.738099i
\(364\) 7440.53i 0.0561567i
\(365\) −106722. −0.801064
\(366\) 119998.i 0.895804i
\(367\) 158319. 1.17544 0.587722 0.809063i \(-0.300025\pi\)
0.587722 + 0.809063i \(0.300025\pi\)
\(368\) −248255. −1.83317
\(369\) 19072.0 0.140069
\(370\) 62171.2i 0.454136i
\(371\) 223966.i 1.62718i
\(372\) 37104.2i 0.268125i
\(373\) 186262.i 1.33877i −0.742914 0.669387i \(-0.766557\pi\)
0.742914 0.669387i \(-0.233443\pi\)
\(374\) 12364.8i 0.0883986i
\(375\) 116388. 0.827648
\(376\) 9317.40i 0.0659051i
\(377\) 16463.0i 0.115831i
\(378\) 182249.i 1.27551i
\(379\) 31309.9 0.217973 0.108987 0.994043i \(-0.465239\pi\)
0.108987 + 0.994043i \(0.465239\pi\)
\(380\) −19729.1 −0.136628
\(381\) 91652.6i 0.631386i
\(382\) −261173. −1.78979
\(383\) 18588.7i 0.126722i −0.997991 0.0633609i \(-0.979818\pi\)
0.997991 0.0633609i \(-0.0201819\pi\)
\(384\) −136644. −0.926676
\(385\) 29071.3 0.196129
\(386\) 19055.4i 0.127892i
\(387\) −17365.2 58191.6i −0.115947 0.388543i
\(388\) 28668.0 0.190430
\(389\) 158939.i 1.05034i −0.850997 0.525170i \(-0.824002\pi\)
0.850997 0.525170i \(-0.175998\pi\)
\(390\) 26678.2i 0.175399i
\(391\) 91725.1 0.599977
\(392\) 16455.3i 0.107086i
\(393\) −204420. −1.32354
\(394\) 269050.i 1.73317i
\(395\) 226669.i 1.45277i
\(396\) 3034.70 0.0193520
\(397\) 97945.4 0.621445 0.310723 0.950501i \(-0.399429\pi\)
0.310723 + 0.950501i \(0.399429\pi\)
\(398\) 336872. 2.12666
\(399\) 86191.8i 0.541402i
\(400\) −37752.9 −0.235956
\(401\) −252905. −1.57278 −0.786392 0.617727i \(-0.788054\pi\)
−0.786392 + 0.617727i \(0.788054\pi\)
\(402\) −167830. −1.03852
\(403\) 56095.0 0.345394
\(404\) 29208.2 0.178954
\(405\) 63086.9i 0.384618i
\(406\) 98006.6i 0.594571i
\(407\) 15676.8i 0.0946386i
\(408\) 42211.7 0.253579
\(409\) 134853.i 0.806149i 0.915167 + 0.403074i \(0.132058\pi\)
−0.915167 + 0.403074i \(0.867942\pi\)
\(410\) −57609.4 −0.342709
\(411\) −98829.6 −0.585064
\(412\) −42769.5 −0.251965
\(413\) 3401.67i 0.0199431i
\(414\) 120029.i 0.700303i
\(415\) 99234.5i 0.576191i
\(416\) 17979.7i 0.103896i
\(417\) 128720.i 0.740245i
\(418\) −26524.5 −0.151808
\(419\) 10482.5i 0.0597086i 0.999554 + 0.0298543i \(0.00950433\pi\)
−0.999554 + 0.0298543i \(0.990496\pi\)
\(420\) 29787.4i 0.168863i
\(421\) 241369.i 1.36181i −0.732371 0.680906i \(-0.761586\pi\)
0.732371 0.680906i \(-0.238414\pi\)
\(422\) −154693. −0.868650
\(423\) −5603.37 −0.0313162
\(424\) 235292.i 1.30881i
\(425\) 13948.9 0.0772258
\(426\) 180008.i 0.991913i
\(427\) −202559. −1.11095
\(428\) 23873.5 0.130325
\(429\) 6727.04i 0.0365519i
\(430\) 52453.9 + 175776.i 0.283688 + 0.950652i
\(431\) 59107.4 0.318191 0.159095 0.987263i \(-0.449142\pi\)
0.159095 + 0.987263i \(0.449142\pi\)
\(432\) 238154.i 1.27612i
\(433\) 193520.i 1.03216i −0.856539 0.516082i \(-0.827390\pi\)
0.856539 0.516082i \(-0.172610\pi\)
\(434\) 333943. 1.77293
\(435\) 65907.6i 0.348303i
\(436\) −12590.0 −0.0662296
\(437\) 196764.i 1.03035i
\(438\) 147015.i 0.766325i
\(439\) −4663.78 −0.0241997 −0.0120998 0.999927i \(-0.503852\pi\)
−0.0120998 + 0.999927i \(0.503852\pi\)
\(440\) 30541.4 0.157755
\(441\) −9896.02 −0.0508843
\(442\) 19153.9i 0.0980423i
\(443\) 102777. 0.523708 0.261854 0.965107i \(-0.415666\pi\)
0.261854 + 0.965107i \(0.415666\pi\)
\(444\) 16063.0 0.0814816
\(445\) −220659. −1.11430
\(446\) 310072. 1.55881
\(447\) 215253. 1.07729
\(448\) 143696.i 0.715960i
\(449\) 222984.i 1.10606i −0.833160 0.553032i \(-0.813471\pi\)
0.833160 0.553032i \(-0.186529\pi\)
\(450\) 18253.2i 0.0901392i
\(451\) −14526.5 −0.0714180
\(452\) 41619.7i 0.203715i
\(453\) −69946.6 −0.340855
\(454\) −26415.1 −0.128156
\(455\) 45033.2 0.217525
\(456\) 90550.6i 0.435473i
\(457\) 239772.i 1.14806i 0.818833 + 0.574032i \(0.194622\pi\)
−0.818833 + 0.574032i \(0.805378\pi\)
\(458\) 141158.i 0.672936i
\(459\) 87993.0i 0.417660i
\(460\) 68000.5i 0.321363i
\(461\) 234784. 1.10476 0.552378 0.833593i \(-0.313720\pi\)
0.552378 + 0.833593i \(0.313720\pi\)
\(462\) 40047.2i 0.187624i
\(463\) 323705.i 1.51004i 0.655704 + 0.755018i \(0.272372\pi\)
−0.655704 + 0.755018i \(0.727628\pi\)
\(464\) 128070.i 0.594856i
\(465\) −224570. −1.03860
\(466\) −246327. −1.13433
\(467\) 158850.i 0.728372i −0.931326 0.364186i \(-0.881347\pi\)
0.931326 0.364186i \(-0.118653\pi\)
\(468\) 4700.94 0.0214631
\(469\) 283299.i 1.28795i
\(470\) 16925.7 0.0766217
\(471\) −192796. −0.869072
\(472\) 3573.69i 0.0160411i
\(473\) 13226.5 + 44322.7i 0.0591185 + 0.198109i
\(474\) 312248. 1.38977
\(475\) 29922.5i 0.132621i
\(476\) 21386.2i 0.0943886i
\(477\) 141502. 0.621907
\(478\) 279073.i 1.22141i
\(479\) −50616.7 −0.220609 −0.110304 0.993898i \(-0.535183\pi\)
−0.110304 + 0.993898i \(0.535183\pi\)
\(480\) 71979.9i 0.312413i
\(481\) 24284.3i 0.104963i
\(482\) −85710.8 −0.368928
\(483\) 297079. 1.27344
\(484\) 51767.1 0.220985
\(485\) 173511.i 0.737638i
\(486\) 197072. 0.834357
\(487\) −414555. −1.74793 −0.873966 0.485987i \(-0.838460\pi\)
−0.873966 + 0.485987i \(0.838460\pi\)
\(488\) −212803. −0.893588
\(489\) −161512. −0.675439
\(490\) 29892.2 0.124499
\(491\) 162691.i 0.674841i −0.941354 0.337421i \(-0.890446\pi\)
0.941354 0.337421i \(-0.109554\pi\)
\(492\) 14884.3i 0.0614892i
\(493\) 47319.2i 0.194690i
\(494\) −41088.1 −0.168369
\(495\) 18367.2i 0.0749607i
\(496\) 436380. 1.77379
\(497\) 303857. 1.23015
\(498\) 136701. 0.551204
\(499\) 202146.i 0.811829i 0.913911 + 0.405914i \(0.133047\pi\)
−0.913911 + 0.405914i \(0.866953\pi\)
\(500\) 61949.0i 0.247796i
\(501\) 267015.i 1.06380i
\(502\) 279505.i 1.10913i
\(503\) 142571.i 0.563501i 0.959488 + 0.281751i \(0.0909151\pi\)
−0.959488 + 0.281751i \(0.909085\pi\)
\(504\) −93241.3 −0.367068
\(505\) 176780.i 0.693187i
\(506\) 91422.3i 0.357068i
\(507\) 187778.i 0.730516i
\(508\) −48783.3 −0.189035
\(509\) −132370. −0.510922 −0.255461 0.966819i \(-0.582227\pi\)
−0.255461 + 0.966819i \(0.582227\pi\)
\(510\) 76680.7i 0.294812i
\(511\) −248164. −0.950378
\(512\) 123542.i 0.471276i
\(513\) −188758. −0.717251
\(514\) −238467. −0.902615
\(515\) 258859.i 0.975998i
\(516\) 45414.5 13552.3i 0.170567 0.0508996i
\(517\) 4267.91 0.0159674
\(518\) 144569.i 0.538784i
\(519\) 183581.i 0.681542i
\(520\) 47310.6 0.174965
\(521\) 222159.i 0.818444i 0.912435 + 0.409222i \(0.134200\pi\)
−0.912435 + 0.409222i \(0.865800\pi\)
\(522\) 61920.7 0.227245
\(523\) 426785.i 1.56029i −0.625599 0.780145i \(-0.715145\pi\)
0.625599 0.780145i \(-0.284855\pi\)
\(524\) 108805.i 0.396266i
\(525\) 45177.6 0.163910
\(526\) −591804. −2.13898
\(527\) −161233. −0.580541
\(528\) 52331.6i 0.187714i
\(529\) 398349. 1.42348
\(530\) −427425. −1.52163
\(531\) −2149.18 −0.00762225
\(532\) −45876.7 −0.162095
\(533\) −22502.5 −0.0792092
\(534\) 303970.i 1.06598i
\(535\) 144492.i 0.504821i
\(536\) 297626.i 1.03595i
\(537\) 40299.4 0.139750
\(538\) 272124.i 0.940161i
\(539\) 7537.48 0.0259447
\(540\) −65233.7 −0.223710
\(541\) 225636. 0.770927 0.385463 0.922723i \(-0.374042\pi\)
0.385463 + 0.922723i \(0.374042\pi\)
\(542\) 293428.i 0.998856i
\(543\) 443519.i 1.50422i
\(544\) 51678.9i 0.174629i
\(545\) 76199.8i 0.256543i
\(546\) 62035.6i 0.208092i
\(547\) 45128.1 0.150825 0.0754124 0.997152i \(-0.475973\pi\)
0.0754124 + 0.997152i \(0.475973\pi\)
\(548\) 52603.3i 0.175167i
\(549\) 127977.i 0.424607i
\(550\) 13902.9i 0.0459599i
\(551\) −101507. −0.334343
\(552\) 312102. 1.02428
\(553\) 527080.i 1.72356i
\(554\) −278022. −0.905858
\(555\) 97219.7i 0.315623i
\(556\) 68513.1 0.221628
\(557\) 561545. 1.80998 0.904991 0.425430i \(-0.139877\pi\)
0.904991 + 0.425430i \(0.139877\pi\)
\(558\) 210985.i 0.677617i
\(559\) 20488.7 + 68658.7i 0.0655679 + 0.219721i
\(560\) 350326. 1.11711
\(561\) 19335.4i 0.0614367i
\(562\) 489194.i 1.54885i
\(563\) 140409. 0.442975 0.221487 0.975163i \(-0.428909\pi\)
0.221487 + 0.975163i \(0.428909\pi\)
\(564\) 4373.04i 0.0137476i
\(565\) 251900. 0.789098
\(566\) 484882.i 1.51357i
\(567\) 146698.i 0.456308i
\(568\) 319223. 0.989459
\(569\) −434476. −1.34197 −0.670983 0.741473i \(-0.734128\pi\)
−0.670983 + 0.741473i \(0.734128\pi\)
\(570\) 164492. 0.506284
\(571\) 63191.7i 0.193815i 0.995293 + 0.0969076i \(0.0308951\pi\)
−0.995293 + 0.0969076i \(0.969105\pi\)
\(572\) −3580.55 −0.0109435
\(573\) 408407. 1.24390
\(574\) −133961. −0.406588
\(575\) 103134. 0.311938
\(576\) −90787.2 −0.273640
\(577\) 524185.i 1.57447i 0.616656 + 0.787233i \(0.288487\pi\)
−0.616656 + 0.787233i \(0.711513\pi\)
\(578\) 315592.i 0.944647i
\(579\) 29797.8i 0.0888847i
\(580\) −35080.1 −0.104281
\(581\) 230753.i 0.683589i
\(582\) −239020. −0.705650
\(583\) −107778. −0.317096
\(584\) −260713. −0.764430
\(585\) 28452.0i 0.0831383i
\(586\) 609669.i 1.77541i
\(587\) 653761.i 1.89733i 0.316284 + 0.948665i \(0.397565\pi\)
−0.316284 + 0.948665i \(0.602435\pi\)
\(588\) 7723.15i 0.0223378i
\(589\) 345869.i 0.996969i
\(590\) 6491.88 0.0186495
\(591\) 420724.i 1.20454i
\(592\) 188915.i 0.539043i
\(593\) 73594.7i 0.209285i 0.994510 + 0.104642i \(0.0333698\pi\)
−0.994510 + 0.104642i \(0.966630\pi\)
\(594\) −87702.6 −0.248565
\(595\) −129438. −0.365619
\(596\) 114571.i 0.322539i
\(597\) −526781. −1.47802
\(598\) 141619.i 0.396022i
\(599\) −219023. −0.610430 −0.305215 0.952283i \(-0.598728\pi\)
−0.305215 + 0.952283i \(0.598728\pi\)
\(600\) 47462.3 0.131840
\(601\) 350767.i 0.971112i −0.874206 0.485556i \(-0.838617\pi\)
0.874206 0.485556i \(-0.161383\pi\)
\(602\) 121973. + 408736.i 0.336565 + 1.12785i
\(603\) −178989. −0.492256
\(604\) 37229.9i 0.102051i
\(605\) 313316.i 0.855996i
\(606\) −243524. −0.663126
\(607\) 93560.7i 0.253931i −0.991907 0.126966i \(-0.959476\pi\)
0.991907 0.126966i \(-0.0405238\pi\)
\(608\) −110859. −0.299891
\(609\) 153257.i 0.413224i
\(610\) 386571.i 1.03889i
\(611\) 6611.26 0.0177093
\(612\) −13511.8 −0.0360754
\(613\) 385616. 1.02620 0.513102 0.858327i \(-0.328496\pi\)
0.513102 + 0.858327i \(0.328496\pi\)
\(614\) 57939.8i 0.153688i
\(615\) 90086.2 0.238181
\(616\) 71018.9 0.187160
\(617\) −262907. −0.690609 −0.345304 0.938491i \(-0.612224\pi\)
−0.345304 + 0.938491i \(0.612224\pi\)
\(618\) 356592. 0.933673
\(619\) 105010. 0.274063 0.137031 0.990567i \(-0.456244\pi\)
0.137031 + 0.990567i \(0.456244\pi\)
\(620\) 119530.i 0.310953i
\(621\) 650596.i 1.68705i
\(622\) 847099.i 2.18954i
\(623\) −513106. −1.32200
\(624\) 81065.0i 0.208192i
\(625\) −296669. −0.759472
\(626\) 141745. 0.361710
\(627\) 41477.4 0.105506
\(628\) 102618.i 0.260198i
\(629\) 69800.1i 0.176423i
\(630\) 169380.i 0.426756i
\(631\) 584197.i 1.46724i −0.679561 0.733619i \(-0.737830\pi\)
0.679561 0.733619i \(-0.262170\pi\)
\(632\) 553735.i 1.38633i
\(633\) 241899. 0.603709
\(634\) 47578.7i 0.118368i
\(635\) 295257.i 0.732238i
\(636\) 110432.i 0.273012i
\(637\) 11676.0 0.0287751
\(638\) −47163.0 −0.115867
\(639\) 191977.i 0.470162i
\(640\) 440195. 1.07469
\(641\) 230667.i 0.561397i 0.959796 + 0.280699i \(0.0905661\pi\)
−0.959796 + 0.280699i \(0.909434\pi\)
\(642\) −199046. −0.482929
\(643\) 205024. 0.495886 0.247943 0.968775i \(-0.420245\pi\)
0.247943 + 0.968775i \(0.420245\pi\)
\(644\) 158124.i 0.381264i
\(645\) −82024.3 274868.i −0.197162 0.660700i
\(646\) 118099. 0.282996
\(647\) 151853.i 0.362757i 0.983413 + 0.181379i \(0.0580560\pi\)
−0.983413 + 0.181379i \(0.941944\pi\)
\(648\) 154117.i 0.367028i
\(649\) 1636.96 0.00388641
\(650\) 21536.4i 0.0509738i
\(651\) −522200. −1.23218
\(652\) 85966.5i 0.202225i
\(653\) 165779.i 0.388780i 0.980924 + 0.194390i \(0.0622727\pi\)
−0.980924 + 0.194390i \(0.937727\pi\)
\(654\) 104969. 0.245418
\(655\) 658533. 1.53495
\(656\) −175053. −0.406783
\(657\) 156790.i 0.363235i
\(658\) 39357.9 0.0909035
\(659\) 461726. 1.06320 0.531599 0.846996i \(-0.321592\pi\)
0.531599 + 0.846996i \(0.321592\pi\)
\(660\) 14334.3 0.0329071
\(661\) −206270. −0.472099 −0.236050 0.971741i \(-0.575853\pi\)
−0.236050 + 0.971741i \(0.575853\pi\)
\(662\) 218092. 0.497649
\(663\) 29951.8i 0.0681390i
\(664\) 242422.i 0.549840i
\(665\) 277665.i 0.627881i
\(666\) 91338.6 0.205924
\(667\) 349865.i 0.786410i
\(668\) 142122. 0.318499
\(669\) −484873. −1.08337
\(670\) 540659. 1.20441
\(671\) 97476.0i 0.216497i
\(672\) 167377.i 0.370645i
\(673\) 739539.i 1.63279i 0.577492 + 0.816397i \(0.304032\pi\)
−0.577492 + 0.816397i \(0.695968\pi\)
\(674\) 504119.i 1.10972i
\(675\) 98938.2i 0.217148i
\(676\) 99947.4 0.218715
\(677\) 248420.i 0.542012i −0.962578 0.271006i \(-0.912644\pi\)
0.962578 0.271006i \(-0.0873563\pi\)
\(678\) 347005.i 0.754878i
\(679\) 403470.i 0.875129i
\(680\) −135984. −0.294083
\(681\) 41306.4 0.0890682
\(682\) 160701.i 0.345501i
\(683\) 536792. 1.15071 0.575354 0.817905i \(-0.304864\pi\)
0.575354 + 0.817905i \(0.304864\pi\)
\(684\) 28984.9i 0.0619526i
\(685\) 318377. 0.678517
\(686\) −484379. −1.02929
\(687\) 220734.i 0.467688i
\(688\) 159388. + 534116.i 0.336727 + 1.12839i
\(689\) −166954. −0.351689
\(690\) 566956.i 1.19083i
\(691\) 253638.i 0.531199i −0.964083 0.265600i \(-0.914430\pi\)
0.964083 0.265600i \(-0.0855699\pi\)
\(692\) −97713.2 −0.204052
\(693\) 42709.9i 0.0889329i
\(694\) 113622. 0.235908
\(695\) 414670.i 0.858485i
\(696\) 161007.i 0.332374i
\(697\) 64678.5 0.133136
\(698\) 19120.2 0.0392447
\(699\) 385192. 0.788358
\(700\) 24046.4i 0.0490742i
\(701\) −64810.3 −0.131889 −0.0659444 0.997823i \(-0.521006\pi\)
−0.0659444 + 0.997823i \(0.521006\pi\)
\(702\) −135857. −0.275681
\(703\) −149732. −0.302973
\(704\) 69149.8 0.139523
\(705\) −26467.5 −0.0532518
\(706\) 448943.i 0.900704i
\(707\) 411072.i 0.822393i
\(708\) 1677.28i 0.00334611i
\(709\) −120036. −0.238792 −0.119396 0.992847i \(-0.538096\pi\)
−0.119396 + 0.992847i \(0.538096\pi\)
\(710\) 579892.i 1.15035i
\(711\) 333010. 0.658746
\(712\) −539054. −1.06334
\(713\) −1.19211e6 −2.34498
\(714\) 178308.i 0.349763i
\(715\) 21671.0i 0.0423903i
\(716\) 21449.9i 0.0418407i
\(717\) 436398.i 0.848877i
\(718\) 13771.2i 0.0267129i
\(719\) −332719. −0.643605 −0.321802 0.946807i \(-0.604289\pi\)
−0.321802 + 0.946807i \(0.604289\pi\)
\(720\) 221337.i 0.426961i
\(721\) 601933.i 1.15792i
\(722\) 324992.i 0.623446i
\(723\) 134030. 0.256404
\(724\) 236068. 0.450361
\(725\) 53205.1i 0.101222i
\(726\) −431609. −0.818875
\(727\) 582297.i 1.10173i 0.834594 + 0.550866i \(0.185702\pi\)
−0.834594 + 0.550866i \(0.814298\pi\)
\(728\) 110013. 0.207577
\(729\) −536751. −1.00999
\(730\) 473605.i 0.888731i
\(731\) −58890.4 197345.i −0.110207 0.369309i
\(732\) −99877.1 −0.186399
\(733\) 469633.i 0.874079i −0.899442 0.437039i \(-0.856027\pi\)
0.899442 0.437039i \(-0.143973\pi\)
\(734\) 702582.i 1.30408i
\(735\) −46743.7 −0.0865264
\(736\) 382100.i 0.705376i
\(737\) 136330. 0.250990
\(738\) 84636.6i 0.155398i
\(739\) 755334.i 1.38309i −0.722334 0.691545i \(-0.756930\pi\)
0.722334 0.691545i \(-0.243070\pi\)
\(740\) −51746.4 −0.0944967
\(741\) 64251.2 0.117016
\(742\) −993906. −1.80525
\(743\) 18481.9i 0.0334788i 0.999860 + 0.0167394i \(0.00532857\pi\)
−0.999860 + 0.0167394i \(0.994671\pi\)
\(744\) −548608. −0.991098
\(745\) −693432. −1.24937
\(746\) 826585. 1.48529
\(747\) 145790. 0.261268
\(748\) 10291.5 0.0183940
\(749\) 335993.i 0.598916i
\(750\) 516501.i 0.918224i
\(751\) 62072.3i 0.110057i 0.998485 + 0.0550286i \(0.0175250\pi\)
−0.998485 + 0.0550286i \(0.982475\pi\)
\(752\) 51431.0 0.0909471
\(753\) 437074.i 0.770842i
\(754\) −73058.5 −0.128507
\(755\) 225331. 0.395300
\(756\) −151690. −0.265408
\(757\) 452452.i 0.789551i −0.918778 0.394776i \(-0.870822\pi\)
0.918778 0.394776i \(-0.129178\pi\)
\(758\) 138946.i 0.241828i
\(759\) 142961.i 0.248161i
\(760\) 291706.i 0.505032i
\(761\) 239204.i 0.413047i 0.978442 + 0.206523i \(0.0662150\pi\)
−0.978442 + 0.206523i \(0.933785\pi\)
\(762\) 406732. 0.700484
\(763\) 177190.i 0.304361i
\(764\) 217380.i 0.372420i
\(765\) 81779.2i 0.139740i
\(766\) 82491.9 0.140590
\(767\) 2535.76 0.00431039
\(768\) 299472.i 0.507731i
\(769\) 838340. 1.41765 0.708823 0.705386i \(-0.249227\pi\)
0.708823 + 0.705386i \(0.249227\pi\)
\(770\) 129011.i 0.217593i
\(771\) 372901. 0.627314
\(772\) 15860.2 0.0266119
\(773\) 520027.i 0.870295i −0.900359 0.435148i \(-0.856696\pi\)
0.900359 0.435148i \(-0.143304\pi\)
\(774\) 258240. 77062.4i 0.431064 0.128635i
\(775\) −181288. −0.301833
\(776\) 423874.i 0.703904i
\(777\) 226068.i 0.374453i
\(778\) 705330. 1.16529
\(779\) 138745.i 0.228635i
\(780\) 22204.8 0.0364971
\(781\) 146223.i 0.239725i
\(782\) 407053.i 0.665637i
\(783\) −335630. −0.547441
\(784\) 90831.3 0.147776
\(785\) 621087. 1.00789
\(786\) 907165.i 1.46839i
\(787\) −297689. −0.480633 −0.240316 0.970695i \(-0.577251\pi\)
−0.240316 + 0.970695i \(0.577251\pi\)
\(788\) −223936. −0.360638