Properties

Label 43.5.b.b.42.9
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 42.9
Root \(3.65497i\) 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.42.4

$q$-expansion

\(f(q)\) \(=\) \(q+3.65497i q^{2} -4.18965i q^{3} +2.64117 q^{4} -45.6695i q^{5} +15.3130 q^{6} -34.3337i q^{7} +68.1330i q^{8} +63.4469 q^{9} +O(q^{10})\) \(q+3.65497i q^{2} -4.18965i q^{3} +2.64117 q^{4} -45.6695i q^{5} +15.3130 q^{6} -34.3337i q^{7} +68.1330i q^{8} +63.4469 q^{9} +166.921 q^{10} -103.099 q^{11} -11.0656i q^{12} +134.875 q^{13} +125.489 q^{14} -191.339 q^{15} -206.765 q^{16} +240.390 q^{17} +231.897i q^{18} +100.800i q^{19} -120.621i q^{20} -143.846 q^{21} -376.825i q^{22} -475.879 q^{23} +285.453 q^{24} -1460.70 q^{25} +492.966i q^{26} -605.181i q^{27} -90.6813i q^{28} +159.825i q^{29} -699.339i q^{30} +1118.26 q^{31} +334.405i q^{32} +431.949i q^{33} +878.620i q^{34} -1568.00 q^{35} +167.574 q^{36} +2451.77i q^{37} -368.423 q^{38} -565.080i q^{39} +3111.60 q^{40} +1069.81 q^{41} -525.754i q^{42} +(1742.01 + 619.833i) q^{43} -272.303 q^{44} -2897.59i q^{45} -1739.32i q^{46} -2933.56 q^{47} +866.274i q^{48} +1222.20 q^{49} -5338.84i q^{50} -1007.15i q^{51} +356.229 q^{52} -825.685 q^{53} +2211.92 q^{54} +4708.49i q^{55} +2339.26 q^{56} +422.318 q^{57} -584.155 q^{58} -1241.46 q^{59} -505.360 q^{60} +6202.15i q^{61} +4087.22i q^{62} -2178.37i q^{63} -4530.49 q^{64} -6159.69i q^{65} -1578.76 q^{66} +265.952 q^{67} +634.912 q^{68} +1993.77i q^{69} -5731.02i q^{70} +3861.16i q^{71} +4322.82i q^{72} -8274.70i q^{73} -8961.14 q^{74} +6119.84i q^{75} +266.231i q^{76} +3539.78i q^{77} +2065.35 q^{78} +4953.26 q^{79} +9442.88i q^{80} +2603.70 q^{81} +3910.14i q^{82} -13512.1 q^{83} -379.923 q^{84} -10978.5i q^{85} +(-2265.47 + 6367.01i) q^{86} +669.609 q^{87} -7024.45i q^{88} -5359.31i q^{89} +10590.6 q^{90} -4630.77i q^{91} -1256.88 q^{92} -4685.12i q^{93} -10722.1i q^{94} +4603.51 q^{95} +1401.04 q^{96} +3191.32 q^{97} +4467.09i q^{98} -6541.32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + O(q^{10}) \) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + 182q^{10} - 180q^{11} - 216q^{13} + 732q^{14} - 92q^{15} + 1076q^{16} + 678q^{17} - 2392q^{21} + 1566q^{23} - 4234q^{24} - 174q^{25} + 5710q^{31} + 936q^{35} + 4210q^{36} + 1242q^{38} - 2618q^{40} + 4878q^{41} - 1108q^{43} - 15168q^{44} - 5526q^{47} - 8544q^{49} + 24084q^{52} + 1212q^{53} - 10004q^{54} - 10152q^{56} - 7692q^{57} - 4666q^{58} + 14016q^{59} + 15848q^{60} - 15580q^{64} + 29808q^{66} - 1088q^{67} + 15186q^{68} - 7674q^{74} - 67708q^{78} + 24302q^{79} - 23660q^{81} - 7032q^{83} + 37180q^{84} - 14412q^{86} + 17850q^{87} + 4268q^{90} + 48354q^{92} + 606q^{95} + 50546q^{96} - 5842q^{97} - 25924q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.65497i 0.913743i 0.889533 + 0.456872i \(0.151030\pi\)
−0.889533 + 0.456872i \(0.848970\pi\)
\(3\) 4.18965i 0.465516i −0.972535 0.232758i \(-0.925225\pi\)
0.972535 0.232758i \(-0.0747751\pi\)
\(4\) 2.64117 0.165073
\(5\) 45.6695i 1.82678i −0.407085 0.913390i \(-0.633455\pi\)
0.407085 0.913390i \(-0.366545\pi\)
\(6\) 15.3130 0.425362
\(7\) 34.3337i 0.700688i −0.936621 0.350344i \(-0.886065\pi\)
0.936621 0.350344i \(-0.113935\pi\)
\(8\) 68.1330i 1.06458i
\(9\) 63.4469 0.783295
\(10\) 166.921 1.66921
\(11\) −103.099 −0.852059 −0.426030 0.904709i \(-0.640088\pi\)
−0.426030 + 0.904709i \(0.640088\pi\)
\(12\) 11.0656i 0.0768443i
\(13\) 134.875 0.798079 0.399039 0.916934i \(-0.369344\pi\)
0.399039 + 0.916934i \(0.369344\pi\)
\(14\) 125.489 0.640249
\(15\) −191.339 −0.850396
\(16\) −206.765 −0.807678
\(17\) 240.390 0.831800 0.415900 0.909410i \(-0.363467\pi\)
0.415900 + 0.909410i \(0.363467\pi\)
\(18\) 231.897i 0.715730i
\(19\) 100.800i 0.279225i 0.990206 + 0.139613i \(0.0445858\pi\)
−0.990206 + 0.139613i \(0.955414\pi\)
\(20\) 120.621i 0.301553i
\(21\) −143.846 −0.326182
\(22\) 376.825i 0.778564i
\(23\) −475.879 −0.899582 −0.449791 0.893134i \(-0.648502\pi\)
−0.449791 + 0.893134i \(0.648502\pi\)
\(24\) 285.453 0.495578
\(25\) −1460.70 −2.33713
\(26\) 492.966i 0.729239i
\(27\) 605.181i 0.830153i
\(28\) 90.6813i 0.115665i
\(29\) 159.825i 0.190041i 0.995475 + 0.0950207i \(0.0302917\pi\)
−0.995475 + 0.0950207i \(0.969708\pi\)
\(30\) 699.339i 0.777044i
\(31\) 1118.26 1.16364 0.581822 0.813316i \(-0.302340\pi\)
0.581822 + 0.813316i \(0.302340\pi\)
\(32\) 334.405i 0.326568i
\(33\) 431.949i 0.396648i
\(34\) 878.620i 0.760051i
\(35\) −1568.00 −1.28000
\(36\) 167.574 0.129301
\(37\) 2451.77i 1.79092i 0.445145 + 0.895459i \(0.353152\pi\)
−0.445145 + 0.895459i \(0.646848\pi\)
\(38\) −368.423 −0.255140
\(39\) 565.080i 0.371519i
\(40\) 3111.60 1.94475
\(41\) 1069.81 0.636416 0.318208 0.948021i \(-0.396919\pi\)
0.318208 + 0.948021i \(0.396919\pi\)
\(42\) 525.754i 0.298046i
\(43\) 1742.01 + 619.833i 0.942138 + 0.335226i
\(44\) −272.303 −0.140652
\(45\) 2897.59i 1.43091i
\(46\) 1739.32i 0.821987i
\(47\) −2933.56 −1.32800 −0.664002 0.747731i \(-0.731143\pi\)
−0.664002 + 0.747731i \(0.731143\pi\)
\(48\) 866.274i 0.375987i
\(49\) 1222.20 0.509036
\(50\) 5338.84i 2.13553i
\(51\) 1007.15i 0.387216i
\(52\) 356.229 0.131741
\(53\) −825.685 −0.293943 −0.146971 0.989141i \(-0.546953\pi\)
−0.146971 + 0.989141i \(0.546953\pi\)
\(54\) 2211.92 0.758546
\(55\) 4708.49i 1.55653i
\(56\) 2339.26 0.745937
\(57\) 422.318 0.129984
\(58\) −584.155 −0.173649
\(59\) −1241.46 −0.356639 −0.178320 0.983973i \(-0.557066\pi\)
−0.178320 + 0.983973i \(0.557066\pi\)
\(60\) −505.360 −0.140378
\(61\) 6202.15i 1.66680i 0.552673 + 0.833398i \(0.313608\pi\)
−0.552673 + 0.833398i \(0.686392\pi\)
\(62\) 4087.22i 1.06327i
\(63\) 2178.37i 0.548845i
\(64\) −4530.49 −1.10608
\(65\) 6159.69i 1.45791i
\(66\) −1578.76 −0.362434
\(67\) 265.952 0.0592452 0.0296226 0.999561i \(-0.490569\pi\)
0.0296226 + 0.999561i \(0.490569\pi\)
\(68\) 634.912 0.137308
\(69\) 1993.77i 0.418770i
\(70\) 5731.02i 1.16959i
\(71\) 3861.16i 0.765952i 0.923758 + 0.382976i \(0.125101\pi\)
−0.923758 + 0.382976i \(0.874899\pi\)
\(72\) 4322.82i 0.833878i
\(73\) 8274.70i 1.55277i −0.630260 0.776384i \(-0.717052\pi\)
0.630260 0.776384i \(-0.282948\pi\)
\(74\) −8961.14 −1.63644
\(75\) 6119.84i 1.08797i
\(76\) 266.231i 0.0460926i
\(77\) 3539.78i 0.597028i
\(78\) 2065.35 0.339473
\(79\) 4953.26 0.793665 0.396833 0.917891i \(-0.370109\pi\)
0.396833 + 0.917891i \(0.370109\pi\)
\(80\) 9442.88i 1.47545i
\(81\) 2603.70 0.396845
\(82\) 3910.14i 0.581520i
\(83\) −13512.1 −1.96140 −0.980700 0.195519i \(-0.937361\pi\)
−0.980700 + 0.195519i \(0.937361\pi\)
\(84\) −379.923 −0.0538439
\(85\) 10978.5i 1.51952i
\(86\) −2265.47 + 6367.01i −0.306311 + 0.860872i
\(87\) 669.609 0.0884673
\(88\) 7024.45i 0.907084i
\(89\) 5359.31i 0.676595i −0.941039 0.338298i \(-0.890149\pi\)
0.941039 0.338298i \(-0.109851\pi\)
\(90\) 10590.6 1.30748
\(91\) 4630.77i 0.559204i
\(92\) −1256.88 −0.148497
\(93\) 4685.12i 0.541695i
\(94\) 10722.1i 1.21345i
\(95\) 4603.51 0.510084
\(96\) 1401.04 0.152023
\(97\) 3191.32 0.339177 0.169588 0.985515i \(-0.445756\pi\)
0.169588 + 0.985515i \(0.445756\pi\)
\(98\) 4467.09i 0.465128i
\(99\) −6541.32 −0.667413
\(100\) −3857.97 −0.385797
\(101\) 6784.27 0.665059 0.332529 0.943093i \(-0.392098\pi\)
0.332529 + 0.943093i \(0.392098\pi\)
\(102\) 3681.11 0.353816
\(103\) −650.667 −0.0613316 −0.0306658 0.999530i \(-0.509763\pi\)
−0.0306658 + 0.999530i \(0.509763\pi\)
\(104\) 9189.46i 0.849617i
\(105\) 6569.39i 0.595863i
\(106\) 3017.86i 0.268588i
\(107\) 15902.5 1.38899 0.694495 0.719497i \(-0.255628\pi\)
0.694495 + 0.719497i \(0.255628\pi\)
\(108\) 1598.39i 0.137036i
\(109\) 17290.7 1.45533 0.727663 0.685935i \(-0.240607\pi\)
0.727663 + 0.685935i \(0.240607\pi\)
\(110\) −17209.4 −1.42226
\(111\) 10272.0 0.833701
\(112\) 7099.03i 0.565930i
\(113\) 15504.7i 1.21425i −0.794607 0.607124i \(-0.792323\pi\)
0.794607 0.607124i \(-0.207677\pi\)
\(114\) 1543.56i 0.118772i
\(115\) 21733.2i 1.64334i
\(116\) 422.125i 0.0313707i
\(117\) 8557.41 0.625131
\(118\) 4537.51i 0.325877i
\(119\) 8253.49i 0.582832i
\(120\) 13036.5i 0.905313i
\(121\) −4011.56 −0.273995
\(122\) −22668.7 −1.52302
\(123\) 4482.15i 0.296262i
\(124\) 2953.52 0.192086
\(125\) 38166.2i 2.44264i
\(126\) 7961.87 0.501504
\(127\) −24303.2 −1.50680 −0.753400 0.657562i \(-0.771588\pi\)
−0.753400 + 0.657562i \(0.771588\pi\)
\(128\) 11208.3i 0.684102i
\(129\) 2596.88 7298.42i 0.156053 0.438581i
\(130\) 22513.5 1.33216
\(131\) 6058.45i 0.353036i −0.984297 0.176518i \(-0.943517\pi\)
0.984297 0.176518i \(-0.0564834\pi\)
\(132\) 1140.85i 0.0654759i
\(133\) 3460.85 0.195650
\(134\) 972.046i 0.0541349i
\(135\) −27638.3 −1.51651
\(136\) 16378.5i 0.885516i
\(137\) 20546.4i 1.09470i −0.836905 0.547349i \(-0.815637\pi\)
0.836905 0.547349i \(-0.184363\pi\)
\(138\) −7287.16 −0.382648
\(139\) −7143.71 −0.369738 −0.184869 0.982763i \(-0.559186\pi\)
−0.184869 + 0.982763i \(0.559186\pi\)
\(140\) −4141.37 −0.211294
\(141\) 12290.6i 0.618208i
\(142\) −14112.4 −0.699883
\(143\) −13905.5 −0.680010
\(144\) −13118.6 −0.632649
\(145\) 7299.12 0.347164
\(146\) 30243.8 1.41883
\(147\) 5120.57i 0.236965i
\(148\) 6475.54i 0.295633i
\(149\) 29115.5i 1.31145i 0.754999 + 0.655726i \(0.227637\pi\)
−0.754999 + 0.655726i \(0.772363\pi\)
\(150\) −22367.8 −0.994126
\(151\) 11488.6i 0.503864i −0.967745 0.251932i \(-0.918934\pi\)
0.967745 0.251932i \(-0.0810659\pi\)
\(152\) −6867.83 −0.297257
\(153\) 15252.0 0.651544
\(154\) −12937.8 −0.545530
\(155\) 51070.5i 2.12572i
\(156\) 1492.47i 0.0613278i
\(157\) 2810.63i 0.114026i −0.998373 0.0570131i \(-0.981842\pi\)
0.998373 0.0570131i \(-0.0181577\pi\)
\(158\) 18104.0i 0.725206i
\(159\) 3459.33i 0.136835i
\(160\) 15272.1 0.596568
\(161\) 16338.7i 0.630327i
\(162\) 9516.45i 0.362614i
\(163\) 506.838i 0.0190763i −0.999955 0.00953815i \(-0.996964\pi\)
0.999955 0.00953815i \(-0.00303613\pi\)
\(164\) 2825.56 0.105055
\(165\) 19726.9 0.724588
\(166\) 49386.3i 1.79222i
\(167\) −45960.0 −1.64796 −0.823980 0.566619i \(-0.808251\pi\)
−0.823980 + 0.566619i \(0.808251\pi\)
\(168\) 9800.67i 0.347246i
\(169\) −10369.6 −0.363070
\(170\) 40126.1 1.38845
\(171\) 6395.47i 0.218716i
\(172\) 4600.95 + 1637.09i 0.155522 + 0.0553368i
\(173\) −23016.4 −0.769033 −0.384516 0.923118i \(-0.625632\pi\)
−0.384516 + 0.923118i \(0.625632\pi\)
\(174\) 2447.40i 0.0808364i
\(175\) 50151.4i 1.63760i
\(176\) 21317.4 0.688189
\(177\) 5201.28i 0.166021i
\(178\) 19588.1 0.618234
\(179\) 54490.4i 1.70065i 0.526260 + 0.850324i \(0.323594\pi\)
−0.526260 + 0.850324i \(0.676406\pi\)
\(180\) 7653.03i 0.236205i
\(181\) 24427.1 0.745616 0.372808 0.927909i \(-0.378395\pi\)
0.372808 + 0.927909i \(0.378395\pi\)
\(182\) 16925.3 0.510969
\(183\) 25984.8 0.775921
\(184\) 32423.1i 0.957675i
\(185\) 111971. 3.27161
\(186\) 17124.0 0.494970
\(187\) −24784.0 −0.708743
\(188\) −7748.04 −0.219218
\(189\) −20778.1 −0.581678
\(190\) 16825.7i 0.466086i
\(191\) 25639.4i 0.702815i −0.936223 0.351408i \(-0.885703\pi\)
0.936223 0.351408i \(-0.114297\pi\)
\(192\) 18981.2i 0.514897i
\(193\) −45243.0 −1.21461 −0.607305 0.794469i \(-0.707749\pi\)
−0.607305 + 0.794469i \(0.707749\pi\)
\(194\) 11664.2i 0.309921i
\(195\) −25806.9 −0.678683
\(196\) 3228.03 0.0840282
\(197\) −19109.6 −0.492401 −0.246200 0.969219i \(-0.579182\pi\)
−0.246200 + 0.969219i \(0.579182\pi\)
\(198\) 23908.3i 0.609845i
\(199\) 41414.6i 1.04580i −0.852395 0.522899i \(-0.824851\pi\)
0.852395 0.522899i \(-0.175149\pi\)
\(200\) 99522.2i 2.48805i
\(201\) 1114.24i 0.0275796i
\(202\) 24796.3i 0.607693i
\(203\) 5487.38 0.133160
\(204\) 2660.06i 0.0639191i
\(205\) 48857.9i 1.16259i
\(206\) 2378.17i 0.0560413i
\(207\) −30193.0 −0.704638
\(208\) −27887.6 −0.644590
\(209\) 10392.4i 0.237917i
\(210\) −24010.9 −0.544466
\(211\) 40579.3i 0.911464i 0.890117 + 0.455732i \(0.150623\pi\)
−0.890117 + 0.455732i \(0.849377\pi\)
\(212\) −2180.78 −0.0485221
\(213\) 16176.9 0.356563
\(214\) 58123.4i 1.26918i
\(215\) 28307.5 79556.9i 0.612384 1.72108i
\(216\) 41232.8 0.883762
\(217\) 38394.1i 0.815351i
\(218\) 63197.1i 1.32979i
\(219\) −34668.1 −0.722839
\(220\) 12435.9i 0.256941i
\(221\) 32422.7 0.663842
\(222\) 37544.0i 0.761789i
\(223\) 76426.0i 1.53685i 0.639940 + 0.768425i \(0.278959\pi\)
−0.639940 + 0.768425i \(0.721041\pi\)
\(224\) 11481.4 0.228822
\(225\) −92677.1 −1.83066
\(226\) 56669.4 1.10951
\(227\) 44850.6i 0.870395i 0.900335 + 0.435197i \(0.143321\pi\)
−0.900335 + 0.435197i \(0.856679\pi\)
\(228\) 1115.41 0.0214569
\(229\) −68025.3 −1.29718 −0.648589 0.761139i \(-0.724640\pi\)
−0.648589 + 0.761139i \(0.724640\pi\)
\(230\) −79434.1 −1.50159
\(231\) 14830.4 0.277926
\(232\) −10889.3 −0.202314
\(233\) 61038.6i 1.12433i −0.827026 0.562164i \(-0.809969\pi\)
0.827026 0.562164i \(-0.190031\pi\)
\(234\) 31277.1i 0.571209i
\(235\) 133974.i 2.42597i
\(236\) −3278.91 −0.0588716
\(237\) 20752.4i 0.369464i
\(238\) 30166.3 0.532559
\(239\) −18090.2 −0.316699 −0.158349 0.987383i \(-0.550617\pi\)
−0.158349 + 0.987383i \(0.550617\pi\)
\(240\) 39562.3 0.686846
\(241\) 63866.5i 1.09961i −0.835293 0.549805i \(-0.814702\pi\)
0.835293 0.549805i \(-0.185298\pi\)
\(242\) 14662.1i 0.250361i
\(243\) 59928.3i 1.01489i
\(244\) 16380.9i 0.275144i
\(245\) 55817.1i 0.929897i
\(246\) 16382.1 0.270707
\(247\) 13595.5i 0.222844i
\(248\) 76190.5i 1.23879i
\(249\) 56610.9i 0.913064i
\(250\) −139497. −2.23195
\(251\) 29813.8 0.473227 0.236613 0.971604i \(-0.423963\pi\)
0.236613 + 0.971604i \(0.423963\pi\)
\(252\) 5753.44i 0.0905997i
\(253\) 49062.7 0.766497
\(254\) 88827.5i 1.37683i
\(255\) −45996.0 −0.707359
\(256\) −31521.7 −0.480983
\(257\) 56144.1i 0.850037i 0.905185 + 0.425018i \(0.139732\pi\)
−0.905185 + 0.425018i \(0.860268\pi\)
\(258\) 26675.5 + 9491.53i 0.400750 + 0.142593i
\(259\) 84178.3 1.25487
\(260\) 16268.8i 0.240663i
\(261\) 10140.4i 0.148858i
\(262\) 22143.5 0.322584
\(263\) 7995.51i 0.115594i −0.998328 0.0577969i \(-0.981592\pi\)
0.998328 0.0577969i \(-0.0184076\pi\)
\(264\) −29430.0 −0.422262
\(265\) 37708.6i 0.536969i
\(266\) 12649.3i 0.178774i
\(267\) −22453.6 −0.314966
\(268\) 702.424 0.00977980
\(269\) 6211.47 0.0858401 0.0429200 0.999079i \(-0.486334\pi\)
0.0429200 + 0.999079i \(0.486334\pi\)
\(270\) 101017.i 1.38570i
\(271\) −15284.9 −0.208125 −0.104063 0.994571i \(-0.533184\pi\)
−0.104063 + 0.994571i \(0.533184\pi\)
\(272\) −49704.4 −0.671826
\(273\) −19401.3 −0.260319
\(274\) 75096.4 1.00027
\(275\) 150597. 1.99137
\(276\) 5265.88i 0.0691278i
\(277\) 44696.5i 0.582525i −0.956643 0.291262i \(-0.905925\pi\)
0.956643 0.291262i \(-0.0940753\pi\)
\(278\) 26110.1i 0.337846i
\(279\) 70950.2 0.911476
\(280\) 106833.i 1.36266i
\(281\) 91345.4 1.15684 0.578421 0.815739i \(-0.303669\pi\)
0.578421 + 0.815739i \(0.303669\pi\)
\(282\) −44921.8 −0.564883
\(283\) 25305.7 0.315970 0.157985 0.987442i \(-0.449500\pi\)
0.157985 + 0.987442i \(0.449500\pi\)
\(284\) 10198.0i 0.126438i
\(285\) 19287.1i 0.237452i
\(286\) 50824.4i 0.621355i
\(287\) 36730.7i 0.445929i
\(288\) 21217.0i 0.255799i
\(289\) −25733.6 −0.308109
\(290\) 26678.1i 0.317219i
\(291\) 13370.5i 0.157892i
\(292\) 21854.9i 0.256320i
\(293\) 5876.11 0.0684470 0.0342235 0.999414i \(-0.489104\pi\)
0.0342235 + 0.999414i \(0.489104\pi\)
\(294\) 18715.5 0.216525
\(295\) 56696.9i 0.651501i
\(296\) −167046. −1.90657
\(297\) 62393.7i 0.707339i
\(298\) −106417. −1.19833
\(299\) −64184.3 −0.717938
\(300\) 16163.5i 0.179595i
\(301\) 21281.2 59809.8i 0.234889 0.660145i
\(302\) 41990.5 0.460402
\(303\) 28423.7i 0.309596i
\(304\) 20842.0i 0.225524i
\(305\) 283249. 3.04487
\(306\) 55745.6i 0.595344i
\(307\) −82720.6 −0.877681 −0.438841 0.898565i \(-0.644611\pi\)
−0.438841 + 0.898565i \(0.644611\pi\)
\(308\) 9349.16i 0.0985533i
\(309\) 2726.07i 0.0285509i
\(310\) 186661. 1.94236
\(311\) 160383. 1.65820 0.829102 0.559097i \(-0.188852\pi\)
0.829102 + 0.559097i \(0.188852\pi\)
\(312\) 38500.6 0.395511
\(313\) 182768.i 1.86557i 0.360429 + 0.932787i \(0.382630\pi\)
−0.360429 + 0.932787i \(0.617370\pi\)
\(314\) 10272.8 0.104191
\(315\) −99485.0 −1.00262
\(316\) 13082.4 0.131013
\(317\) −99340.5 −0.988571 −0.494286 0.869300i \(-0.664570\pi\)
−0.494286 + 0.869300i \(0.664570\pi\)
\(318\) −12643.8 −0.125032
\(319\) 16477.8i 0.161926i
\(320\) 206905.i 2.02056i
\(321\) 66626.1i 0.646598i
\(322\) −59717.5 −0.575957
\(323\) 24231.4i 0.232260i
\(324\) 6876.82 0.0655085
\(325\) −197013. −1.86521
\(326\) 1852.48 0.0174308
\(327\) 72442.0i 0.677478i
\(328\) 72889.7i 0.677514i
\(329\) 100720.i 0.930517i
\(330\) 72101.3i 0.662088i
\(331\) 128433.i 1.17225i −0.810221 0.586124i \(-0.800653\pi\)
0.810221 0.586124i \(-0.199347\pi\)
\(332\) −35687.7 −0.323775
\(333\) 155557.i 1.40282i
\(334\) 167982.i 1.50581i
\(335\) 12145.9i 0.108228i
\(336\) 29742.4 0.263450
\(337\) −78727.5 −0.693213 −0.346606 0.938011i \(-0.612666\pi\)
−0.346606 + 0.938011i \(0.612666\pi\)
\(338\) 37900.8i 0.331753i
\(339\) −64959.4 −0.565252
\(340\) 28996.1i 0.250831i
\(341\) −115292. −0.991493
\(342\) −23375.3 −0.199850
\(343\) 124398.i 1.05736i
\(344\) −42231.1 + 118689.i −0.356874 + 1.00298i
\(345\) 91054.3 0.765001
\(346\) 84124.3i 0.702699i
\(347\) 136310.i 1.13205i −0.824387 0.566027i \(-0.808480\pi\)
0.824387 0.566027i \(-0.191520\pi\)
\(348\) 1768.55 0.0146036
\(349\) 48465.9i 0.397910i −0.980009 0.198955i \(-0.936245\pi\)
0.980009 0.198955i \(-0.0637548\pi\)
\(350\) −183302. −1.49634
\(351\) 81624.0i 0.662527i
\(352\) 34476.9i 0.278255i
\(353\) 25854.2 0.207483 0.103741 0.994604i \(-0.466919\pi\)
0.103741 + 0.994604i \(0.466919\pi\)
\(354\) −19010.5 −0.151701
\(355\) 176337. 1.39923
\(356\) 14154.9i 0.111688i
\(357\) −34579.2 −0.271318
\(358\) −199161. −1.55395
\(359\) −125163. −0.971155 −0.485577 0.874194i \(-0.661391\pi\)
−0.485577 + 0.874194i \(0.661391\pi\)
\(360\) 197421. 1.52331
\(361\) 120160. 0.922033
\(362\) 89280.5i 0.681301i
\(363\) 16807.0i 0.127549i
\(364\) 12230.7i 0.0923097i
\(365\) −377901. −2.83657
\(366\) 94973.8i 0.708993i
\(367\) 112207. 0.833082 0.416541 0.909117i \(-0.363242\pi\)
0.416541 + 0.909117i \(0.363242\pi\)
\(368\) 98395.3 0.726572
\(369\) 67876.4 0.498501
\(370\) 409251.i 2.98941i
\(371\) 28348.9i 0.205962i
\(372\) 12374.2i 0.0894194i
\(373\) 35635.8i 0.256135i −0.991765 0.128068i \(-0.959123\pi\)
0.991765 0.128068i \(-0.0408775\pi\)
\(374\) 90585.0i 0.647609i
\(375\) 159903. 1.13709
\(376\) 199872.i 1.41376i
\(377\) 21556.4i 0.151668i
\(378\) 75943.5i 0.531505i
\(379\) −205315. −1.42936 −0.714679 0.699452i \(-0.753427\pi\)
−0.714679 + 0.699452i \(0.753427\pi\)
\(380\) 12158.6 0.0842012
\(381\) 101822.i 0.701440i
\(382\) 93711.3 0.642193
\(383\) 164110.i 1.11876i 0.828912 + 0.559380i \(0.188961\pi\)
−0.828912 + 0.559380i \(0.811039\pi\)
\(384\) −46959.0 −0.318461
\(385\) 161660. 1.09064
\(386\) 165362.i 1.10984i
\(387\) 110525. + 39326.5i 0.737971 + 0.262581i
\(388\) 8428.81 0.0559890
\(389\) 190984.i 1.26211i 0.775738 + 0.631055i \(0.217378\pi\)
−0.775738 + 0.631055i \(0.782622\pi\)
\(390\) 94323.6i 0.620142i
\(391\) −114397. −0.748272
\(392\) 83271.8i 0.541908i
\(393\) −25382.8 −0.164344
\(394\) 69845.0i 0.449928i
\(395\) 226213.i 1.44985i
\(396\) −17276.7 −0.110172
\(397\) −170575. −1.08226 −0.541132 0.840938i \(-0.682004\pi\)
−0.541132 + 0.840938i \(0.682004\pi\)
\(398\) 151369. 0.955590
\(399\) 14499.8i 0.0910783i
\(400\) 302023. 1.88765
\(401\) 52348.9 0.325551 0.162775 0.986663i \(-0.447955\pi\)
0.162775 + 0.986663i \(0.447955\pi\)
\(402\) 4072.53 0.0252007
\(403\) 150826. 0.928679
\(404\) 17918.4 0.109783
\(405\) 118910.i 0.724949i
\(406\) 20056.2i 0.121674i
\(407\) 252775.i 1.52597i
\(408\) 68620.1 0.412222
\(409\) 164844.i 0.985430i −0.870191 0.492715i \(-0.836004\pi\)
0.870191 0.492715i \(-0.163996\pi\)
\(410\) 178574. 1.06231
\(411\) −86082.0 −0.509599
\(412\) −1718.52 −0.0101242
\(413\) 42624.0i 0.249893i
\(414\) 110355.i 0.643858i
\(415\) 617090.i 3.58305i
\(416\) 45103.0i 0.260627i
\(417\) 29929.6i 0.172119i
\(418\) 37984.1 0.217395
\(419\) 37268.6i 0.212283i 0.994351 + 0.106141i \(0.0338496\pi\)
−0.994351 + 0.106141i \(0.966150\pi\)
\(420\) 17350.9i 0.0983610i
\(421\) 99646.0i 0.562206i −0.959678 0.281103i \(-0.909300\pi\)
0.959678 0.281103i \(-0.0907003\pi\)
\(422\) −148316. −0.832844
\(423\) −186125. −1.04022
\(424\) 56256.4i 0.312925i
\(425\) −351139. −1.94402
\(426\) 59126.2i 0.325807i
\(427\) 212943. 1.16790
\(428\) 42001.4 0.229285
\(429\) 58259.3i 0.316556i
\(430\) 290778. + 103463.i 1.57262 + 0.559562i
\(431\) 144175. 0.776133 0.388067 0.921631i \(-0.373143\pi\)
0.388067 + 0.921631i \(0.373143\pi\)
\(432\) 125131.i 0.670496i
\(433\) 220583.i 1.17651i −0.808675 0.588256i \(-0.799815\pi\)
0.808675 0.588256i \(-0.200185\pi\)
\(434\) 140329. 0.745022
\(435\) 30580.7i 0.161610i
\(436\) 45667.8 0.240235
\(437\) 47968.8i 0.251186i
\(438\) 126711.i 0.660489i
\(439\) 68794.6 0.356965 0.178482 0.983943i \(-0.442881\pi\)
0.178482 + 0.983943i \(0.442881\pi\)
\(440\) −320803. −1.65704
\(441\) 77544.4 0.398725
\(442\) 118504.i 0.606581i
\(443\) 321595. 1.63871 0.819355 0.573286i \(-0.194332\pi\)
0.819355 + 0.573286i \(0.194332\pi\)
\(444\) 27130.2 0.137622
\(445\) −244757. −1.23599
\(446\) −279335. −1.40429
\(447\) 121984. 0.610502
\(448\) 155549.i 0.775015i
\(449\) 2687.03i 0.0133285i 0.999978 + 0.00666423i \(0.00212131\pi\)
−0.999978 + 0.00666423i \(0.997879\pi\)
\(450\) 338732.i 1.67275i
\(451\) −110297. −0.542264
\(452\) 40950.7i 0.200440i
\(453\) −48133.2 −0.234557
\(454\) −163928. −0.795318
\(455\) −211485. −1.02154
\(456\) 28773.8i 0.138378i
\(457\) 222198.i 1.06392i 0.846770 + 0.531959i \(0.178544\pi\)
−0.846770 + 0.531959i \(0.821456\pi\)
\(458\) 248631.i 1.18529i
\(459\) 145480.i 0.690521i
\(460\) 57401.0i 0.271271i
\(461\) −63915.9 −0.300751 −0.150375 0.988629i \(-0.548048\pi\)
−0.150375 + 0.988629i \(0.548048\pi\)
\(462\) 54204.8i 0.253953i
\(463\) 94323.6i 0.440006i −0.975499 0.220003i \(-0.929393\pi\)
0.975499 0.220003i \(-0.0706067\pi\)
\(464\) 33046.2i 0.153492i
\(465\) −213967. −0.989558
\(466\) 223094. 1.02735
\(467\) 288915.i 1.32476i 0.749170 + 0.662378i \(0.230453\pi\)
−0.749170 + 0.662378i \(0.769547\pi\)
\(468\) 22601.6 0.103192
\(469\) 9131.11i 0.0415124i
\(470\) −489673. −2.21672
\(471\) −11775.5 −0.0530810
\(472\) 84584.4i 0.379670i
\(473\) −179600. 63904.3i −0.802757 0.285632i
\(474\) 75849.6 0.337595
\(475\) 147240.i 0.652586i
\(476\) 21798.9i 0.0962100i
\(477\) −52387.1 −0.230244
\(478\) 66119.0i 0.289381i
\(479\) 328139. 1.43017 0.715084 0.699039i \(-0.246388\pi\)
0.715084 + 0.699039i \(0.246388\pi\)
\(480\) 63984.9i 0.277712i
\(481\) 330683.i 1.42929i
\(482\) 233430. 1.00476
\(483\) 68453.4 0.293427
\(484\) −10595.2 −0.0452292
\(485\) 145746.i 0.619602i
\(486\) 219036. 0.927349
\(487\) −225179. −0.949447 −0.474723 0.880135i \(-0.657452\pi\)
−0.474723 + 0.880135i \(0.657452\pi\)
\(488\) −422571. −1.77443
\(489\) −2123.47 −0.00888033
\(490\) 204010. 0.849687
\(491\) 119348.i 0.495053i 0.968881 + 0.247526i \(0.0796177\pi\)
−0.968881 + 0.247526i \(0.920382\pi\)
\(492\) 11838.1i 0.0489049i
\(493\) 38420.3i 0.158076i
\(494\) −49691.1 −0.203622
\(495\) 298739.i 1.21922i
\(496\) −231218. −0.939849
\(497\) 132568. 0.536693
\(498\) −206911. −0.834306
\(499\) 184960.i 0.742807i 0.928471 + 0.371404i \(0.121123\pi\)
−0.928471 + 0.371404i \(0.878877\pi\)
\(500\) 100804.i 0.403214i
\(501\) 192556.i 0.767153i
\(502\) 108968.i 0.432408i
\(503\) 340779.i 1.34691i 0.739230 + 0.673453i \(0.235190\pi\)
−0.739230 + 0.673453i \(0.764810\pi\)
\(504\) 148419. 0.584289
\(505\) 309834.i 1.21492i
\(506\) 179323.i 0.700382i
\(507\) 43445.2i 0.169015i
\(508\) −64188.9 −0.248732
\(509\) 35186.6 0.135813 0.0679066 0.997692i \(-0.478368\pi\)
0.0679066 + 0.997692i \(0.478368\pi\)
\(510\) 168114.i 0.646345i
\(511\) −284101. −1.08801
\(512\) 294544.i 1.12360i
\(513\) 61002.5 0.231800
\(514\) −205205. −0.776715
\(515\) 29715.7i 0.112039i
\(516\) 6858.81 19276.4i 0.0257602 0.0723979i
\(517\) 302448. 1.13154
\(518\) 307669.i 1.14663i
\(519\) 96430.5i 0.357997i
\(520\) 419678. 1.55206
\(521\) 167672.i 0.617712i 0.951109 + 0.308856i \(0.0999460\pi\)
−0.951109 + 0.308856i \(0.900054\pi\)
\(522\) −37062.8 −0.136018
\(523\) 388697.i 1.42105i −0.703674 0.710523i \(-0.748459\pi\)
0.703674 0.710523i \(-0.251541\pi\)
\(524\) 16001.4i 0.0582768i
\(525\) 210117. 0.762329
\(526\) 29223.4 0.105623
\(527\) 268819. 0.967918
\(528\) 89312.2i 0.320363i
\(529\) −53380.2 −0.190752
\(530\) −137824. −0.490652
\(531\) −78766.8 −0.279353
\(532\) 9140.71 0.0322966
\(533\) 144292. 0.507910
\(534\) 82067.4i 0.287798i
\(535\) 726262.i 2.53738i
\(536\) 18120.1i 0.0630711i
\(537\) 228296. 0.791679
\(538\) 22702.8i 0.0784358i
\(539\) −126007. −0.433729
\(540\) −72997.6 −0.250335
\(541\) 258688. 0.883856 0.441928 0.897050i \(-0.354295\pi\)
0.441928 + 0.897050i \(0.354295\pi\)
\(542\) 55865.9i 0.190173i
\(543\) 102341.i 0.347096i
\(544\) 80387.8i 0.271639i
\(545\) 789659.i 2.65856i
\(546\) 70911.2i 0.237865i
\(547\) −11333.8 −0.0378791 −0.0189395 0.999821i \(-0.506029\pi\)
−0.0189395 + 0.999821i \(0.506029\pi\)
\(548\) 54266.5i 0.180705i
\(549\) 393507.i 1.30559i
\(550\) 550430.i 1.81960i
\(551\) −16110.4 −0.0530644
\(552\) −135841. −0.445814
\(553\) 170064.i 0.556112i
\(554\) 163365. 0.532278
\(555\) 469119.i 1.52299i
\(556\) −18867.8 −0.0610338
\(557\) −90762.0 −0.292546 −0.146273 0.989244i \(-0.546728\pi\)
−0.146273 + 0.989244i \(0.546728\pi\)
\(558\) 259321.i 0.832855i
\(559\) 234955. + 83600.2i 0.751900 + 0.267537i
\(560\) 324209. 1.03383
\(561\) 103836.i 0.329931i
\(562\) 333865.i 1.05706i
\(563\) 198527. 0.626329 0.313165 0.949699i \(-0.398611\pi\)
0.313165 + 0.949699i \(0.398611\pi\)
\(564\) 32461.5i 0.102050i
\(565\) −708094. −2.21817
\(566\) 92491.8i 0.288716i
\(567\) 89394.7i 0.278065i
\(568\) −263073. −0.815415
\(569\) 204563. 0.631832 0.315916 0.948787i \(-0.397688\pi\)
0.315916 + 0.948787i \(0.397688\pi\)
\(570\) 70493.7 0.216970
\(571\) 103248.i 0.316670i −0.987385 0.158335i \(-0.949387\pi\)
0.987385 0.158335i \(-0.0506127\pi\)
\(572\) −36726.9 −0.112252
\(573\) −107420. −0.327172
\(574\) 134250. 0.407465
\(575\) 695119. 2.10244
\(576\) −287445. −0.866384
\(577\) 214909.i 0.645510i −0.946482 0.322755i \(-0.895391\pi\)
0.946482 0.322755i \(-0.104609\pi\)
\(578\) 94055.5i 0.281533i
\(579\) 189552.i 0.565421i
\(580\) 19278.2 0.0573075
\(581\) 463920.i 1.37433i
\(582\) 48868.8 0.144273
\(583\) 85127.5 0.250457
\(584\) 563780. 1.65304
\(585\) 390813.i 1.14198i
\(586\) 21477.0i 0.0625430i
\(587\) 508043.i 1.47443i −0.675657 0.737216i \(-0.736140\pi\)
0.675657 0.737216i \(-0.263860\pi\)
\(588\) 13524.3i 0.0391165i
\(589\) 112721.i 0.324919i
\(590\) −207226. −0.595305
\(591\) 80062.4i 0.229221i
\(592\) 506941.i 1.44648i
\(593\) 182995.i 0.520390i −0.965556 0.260195i \(-0.916213\pi\)
0.965556 0.260195i \(-0.0837869\pi\)
\(594\) −228047. −0.646327
\(595\) −376933. −1.06471
\(596\) 76899.1i 0.216486i
\(597\) −173513. −0.486836
\(598\) 234592.i 0.656011i
\(599\) −173564. −0.483733 −0.241867 0.970310i \(-0.577760\pi\)
−0.241867 + 0.970310i \(0.577760\pi\)
\(600\) −416963. −1.15823
\(601\) 370900.i 1.02685i 0.858134 + 0.513426i \(0.171624\pi\)
−0.858134 + 0.513426i \(0.828376\pi\)
\(602\) 218603. + 77782.1i 0.603203 + 0.214628i
\(603\) 16873.8 0.0464064
\(604\) 30343.4i 0.0831744i
\(605\) 183206.i 0.500529i
\(606\) 103888. 0.282891
\(607\) 274917.i 0.746147i −0.927802 0.373074i \(-0.878304\pi\)
0.927802 0.373074i \(-0.121696\pi\)
\(608\) −33708.2 −0.0911861
\(609\) 22990.2i 0.0619880i
\(610\) 1.03527e6i 2.78223i
\(611\) −395665. −1.05985
\(612\) 40283.2 0.107553
\(613\) 358829. 0.954919 0.477459 0.878654i \(-0.341558\pi\)
0.477459 + 0.878654i \(0.341558\pi\)
\(614\) 302342.i 0.801975i
\(615\) −204697. −0.541205
\(616\) −241176. −0.635583
\(617\) 275204. 0.722909 0.361455 0.932390i \(-0.382280\pi\)
0.361455 + 0.932390i \(0.382280\pi\)
\(618\) −9963.70 −0.0260882
\(619\) −303567. −0.792270 −0.396135 0.918192i \(-0.629649\pi\)
−0.396135 + 0.918192i \(0.629649\pi\)
\(620\) 134886.i 0.350900i
\(621\) 287993.i 0.746791i
\(622\) 586196.i 1.51517i
\(623\) −184005. −0.474082
\(624\) 116839.i 0.300067i
\(625\) 830093. 2.12504
\(626\) −668013. −1.70466
\(627\) −43540.6 −0.110754
\(628\) 7423.36i 0.0188227i
\(629\) 589380.i 1.48968i
\(630\) 363615.i 0.916137i
\(631\) 350000.i 0.879041i 0.898233 + 0.439520i \(0.144852\pi\)
−0.898233 + 0.439520i \(0.855148\pi\)
\(632\) 337481.i 0.844918i
\(633\) 170013. 0.424302
\(634\) 363087.i 0.903300i
\(635\) 1.10991e6i 2.75259i
\(636\) 9136.68i 0.0225878i
\(637\) 164844. 0.406251
\(638\) 60225.9 0.147959
\(639\) 244979.i 0.599966i
\(640\) −511879. −1.24970
\(641\) 404169.i 0.983665i −0.870690 0.491832i \(-0.836327\pi\)
0.870690 0.491832i \(-0.163673\pi\)
\(642\) 243516. 0.590824
\(643\) 488598. 1.18176 0.590881 0.806759i \(-0.298780\pi\)
0.590881 + 0.806759i \(0.298780\pi\)
\(644\) 43153.3i 0.104050i
\(645\) −333315. 118598.i −0.801190 0.285075i
\(646\) −88565.2 −0.212226
\(647\) 111849.i 0.267191i −0.991036 0.133595i \(-0.957348\pi\)
0.991036 0.133595i \(-0.0426523\pi\)
\(648\) 177398.i 0.422472i
\(649\) 127994. 0.303878
\(650\) 720077.i 1.70433i
\(651\) −160858. −0.379559
\(652\) 1338.65i 0.00314899i
\(653\) 92008.4i 0.215775i −0.994163 0.107887i \(-0.965591\pi\)
0.994163 0.107887i \(-0.0344086\pi\)
\(654\) 264774. 0.619041
\(655\) −276686. −0.644919
\(656\) −221201. −0.514019
\(657\) 525004.i 1.21627i
\(658\) −368129. −0.850254
\(659\) −532415. −1.22597 −0.612985 0.790095i \(-0.710031\pi\)
−0.612985 + 0.790095i \(0.710031\pi\)
\(660\) 52102.2 0.119610
\(661\) −770144. −1.76266 −0.881331 0.472499i \(-0.843352\pi\)
−0.881331 + 0.472499i \(0.843352\pi\)
\(662\) 469418. 1.07113
\(663\) 135840.i 0.309029i
\(664\) 920618.i 2.08806i
\(665\) 158055.i 0.357410i
\(666\) −568556. −1.28181
\(667\) 76057.3i 0.170958i
\(668\) −121388. −0.272034
\(669\) 320198. 0.715429
\(670\) 44392.9 0.0988926
\(671\) 639437.i 1.42021i
\(672\) 48103.0i 0.106521i
\(673\) 296438.i 0.654492i 0.944939 + 0.327246i \(0.106121\pi\)
−0.944939 + 0.327246i \(0.893879\pi\)
\(674\) 287747.i 0.633418i
\(675\) 883991.i 1.94017i
\(676\) −27388.0 −0.0599332
\(677\) 255234.i 0.556880i −0.960454 0.278440i \(-0.910183\pi\)
0.960454 0.278440i \(-0.0898174\pi\)
\(678\) 237425.i 0.516496i
\(679\) 109570.i 0.237657i
\(680\) 747998. 1.61764
\(681\) 187908. 0.405183
\(682\) 421389.i 0.905970i
\(683\) 659236. 1.41319 0.706594 0.707620i \(-0.250231\pi\)
0.706594 + 0.707620i \(0.250231\pi\)
\(684\) 16891.5i 0.0361041i
\(685\) −938343. −1.99977
\(686\) 454671. 0.966159
\(687\) 285002.i 0.603857i
\(688\) −360188. 128160.i −0.760944 0.270755i
\(689\) −111365. −0.234589
\(690\) 332801.i 0.699015i
\(691\) 428774.i 0.897993i −0.893534 0.448996i \(-0.851782\pi\)
0.893534 0.448996i \(-0.148218\pi\)
\(692\) −60790.2 −0.126947
\(693\) 224588.i 0.467649i
\(694\) 498208. 1.03441
\(695\) 326250.i 0.675430i
\(696\) 45622.5i 0.0941804i
\(697\) 257173. 0.529370
\(698\) 177141. 0.363588
\(699\) −255730. −0.523393
\(700\) 132459.i 0.270324i
\(701\) 446529. 0.908686 0.454343 0.890827i \(-0.349874\pi\)
0.454343 + 0.890827i \(0.349874\pi\)
\(702\) 298334. 0.605380
\(703\) −247139. −0.500070
\(704\) 467090. 0.942443
\(705\) 561305. 1.12933
\(706\) 94496.5i 0.189586i
\(707\) 232929.i 0.465999i
\(708\) 13737.5i 0.0274057i
\(709\) −43598.6 −0.0867321 −0.0433660 0.999059i \(-0.513808\pi\)
−0.0433660 + 0.999059i \(0.513808\pi\)
\(710\) 644509.i 1.27853i
\(711\) 314269. 0.621673
\(712\) 365146. 0.720288
\(713\) −532157. −1.04679
\(714\) 126386.i 0.247915i
\(715\) 635059.i 1.24223i
\(716\) 143919.i 0.280731i
\(717\) 75791.4i 0.147429i
\(718\) 457469.i 0.887386i
\(719\) 46047.8 0.0890741 0.0445370 0.999008i \(-0.485819\pi\)
0.0445370 + 0.999008i \(0.485819\pi\)
\(720\) 599121.i 1.15571i
\(721\) 22339.8i 0.0429743i
\(722\) 439183.i 0.842502i
\(723\) −267578. −0.511887
\(724\) 64516.2 0.123081
\(725\) 233457.i 0.444151i
\(726\) −61429.2 −0.116547
\(727\) 275601.i 0.521450i 0.965413 + 0.260725i \(0.0839615\pi\)
−0.965413 + 0.260725i \(0.916038\pi\)
\(728\) 315508. 0.595317
\(729\) −40178.7 −0.0756032
\(730\) 1.38122e6i 2.59189i
\(731\) 418763. + 149002.i 0.783670 + 0.278841i
\(732\) 68630.4 0.128084
\(733\) 324631.i 0.604201i −0.953276 0.302101i \(-0.902312\pi\)
0.953276 0.302101i \(-0.0976879\pi\)
\(734\) 410114.i 0.761223i
\(735\) −233854. −0.432882
\(736\) 159137.i 0.293775i
\(737\) −27419.4 −0.0504804
\(738\) 248086.i 0.455502i
\(739\) 359031.i 0.657421i −0.944431 0.328710i \(-0.893386\pi\)
0.944431 0.328710i \(-0.106614\pi\)
\(740\) 295735. 0.540056
\(741\) 56960.3 0.103737
\(742\) −103614. −0.188197
\(743\) 164101.i 0.297259i −0.988893 0.148629i \(-0.952514\pi\)
0.988893 0.148629i \(-0.0474862\pi\)
\(744\) 319211. 0.576677
\(745\) 1.32969e6 2.39573
\(746\) 130248. 0.234042
\(747\) −857299. −1.53635
\(748\) −65458.9 −0.116994
\(749\) 545994.i 0.973249i
\(750\) 584441.i 1.03901i
\(751\) 862173.i 1.52867i 0.644818 + 0.764336i \(0.276933\pi\)
−0.644818 + 0.764336i \(0.723067\pi\)
\(752\) 606559. 1.07260
\(753\) 124909.i 0.220295i
\(754\) −78788.1 −0.138586
\(755\) −524679. −0.920449
\(756\) −54878.6 −0.0960195
\(757\) 878771.i 1.53350i 0.641946 + 0.766750i \(0.278127\pi\)
−0.641946 + 0.766750i \(0.721873\pi\)
\(758\) 750419.i 1.30607i
\(759\) 205556.i 0.356817i
\(760\) 313651.i 0.543024i
\(761\) 452736.i 0.781763i −0.920441 0.390882i \(-0.872170\pi\)
0.920441 0.390882i \(-0.127830\pi\)
\(762\) −372156. −0.640936
\(763\) 593655.i 1.01973i
\(764\) 67718.1i 0.116016i
\(765\) 696551.i 1.19023i
\(766\) −599816. −1.02226
\(767\) −167442. −0.284626
\(768\) 132065.i 0.223905i
\(769\) 379858. 0.642346 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(770\) 590863.i 0.996564i
\(771\) 235224. 0.395706
\(772\) −119495. −0.200500
\(773\) 466697.i 0.781044i 0.920594 + 0.390522i \(0.127705\pi\)
−0.920594 + 0.390522i \(0.872295\pi\)
\(774\) −143737. + 403967.i −0.239931 + 0.674316i
\(775\) −1.63345e6 −2.71958
\(776\) 217434.i 0.361080i
\(777\) 352677.i 0.584165i
\(778\) −698041. −1.15325
\(779\) 107838.i 0.177703i
\(780\) −68160.5 −0.112032
\(781\) 398083.i 0.652636i
\(782\) 418117.i 0.683729i
\(783\) 96723.0 0.157763
\(784\) −252708. −0.411137
\(785\) −128360. −0.208301
\(786\) 92773.3i 0.150168i
\(787\) 946342. 1.52791 0.763956 0.645268i \(-0.223254\pi\)
0.763956 + 0.645268i \(0.223254\pi\)
\(788\) −50471.7 −0.0812822