Properties

Label 43.5.b.b.42.6
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 42.6
Root \(-0.133471i\) 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.42.7

$q$-expansion

\(f(q)\) \(=\) \(q-0.133471i q^{2} -14.8068i q^{3} +15.9822 q^{4} +26.0324i q^{5} -1.97628 q^{6} -87.9232i q^{7} -4.26869i q^{8} -138.241 q^{9} +O(q^{10})\) \(q-0.133471i q^{2} -14.8068i q^{3} +15.9822 q^{4} +26.0324i q^{5} -1.97628 q^{6} -87.9232i q^{7} -4.26869i q^{8} -138.241 q^{9} +3.47456 q^{10} -101.658 q^{11} -236.645i q^{12} +190.866 q^{13} -11.7352 q^{14} +385.456 q^{15} +255.145 q^{16} -227.830 q^{17} +18.4512i q^{18} +304.934i q^{19} +416.054i q^{20} -1301.86 q^{21} +13.5683i q^{22} +797.353 q^{23} -63.2056 q^{24} -52.6844 q^{25} -25.4751i q^{26} +847.562i q^{27} -1405.20i q^{28} +1084.32i q^{29} -51.4471i q^{30} +433.017 q^{31} -102.353i q^{32} +1505.23i q^{33} +30.4086i q^{34} +2288.85 q^{35} -2209.40 q^{36} -310.044i q^{37} +40.6998 q^{38} -2826.12i q^{39} +111.124 q^{40} +1339.11 q^{41} +173.760i q^{42} +(-137.757 + 1843.86i) q^{43} -1624.71 q^{44} -3598.75i q^{45} -106.423i q^{46} +1003.89 q^{47} -3777.89i q^{48} -5329.48 q^{49} +7.03183i q^{50} +3373.43i q^{51} +3050.46 q^{52} -3648.61 q^{53} +113.125 q^{54} -2646.39i q^{55} -375.317 q^{56} +4515.10 q^{57} +144.725 q^{58} -1283.47 q^{59} +6160.43 q^{60} -2277.88i q^{61} -57.7951i q^{62} +12154.6i q^{63} +4068.66 q^{64} +4968.70i q^{65} +200.904 q^{66} -4753.41 q^{67} -3641.22 q^{68} -11806.2i q^{69} -305.494i q^{70} -4258.19i q^{71} +590.109i q^{72} +3321.32i q^{73} -41.3818 q^{74} +780.087i q^{75} +4873.52i q^{76} +8938.08i q^{77} -377.205 q^{78} -227.377 q^{79} +6642.04i q^{80} +1352.14 q^{81} -178.733i q^{82} -1895.54 q^{83} -20806.6 q^{84} -5930.95i q^{85} +(246.102 + 18.3865i) q^{86} +16055.3 q^{87} +433.945i q^{88} +10806.3i q^{89} -480.328 q^{90} -16781.6i q^{91} +12743.4 q^{92} -6411.60i q^{93} -133.990i q^{94} -7938.16 q^{95} -1515.53 q^{96} +10904.7 q^{97} +711.330i q^{98} +14053.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + O(q^{10}) \) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + 182q^{10} - 180q^{11} - 216q^{13} + 732q^{14} - 92q^{15} + 1076q^{16} + 678q^{17} - 2392q^{21} + 1566q^{23} - 4234q^{24} - 174q^{25} + 5710q^{31} + 936q^{35} + 4210q^{36} + 1242q^{38} - 2618q^{40} + 4878q^{41} - 1108q^{43} - 15168q^{44} - 5526q^{47} - 8544q^{49} + 24084q^{52} + 1212q^{53} - 10004q^{54} - 10152q^{56} - 7692q^{57} - 4666q^{58} + 14016q^{59} + 15848q^{60} - 15580q^{64} + 29808q^{66} - 1088q^{67} + 15186q^{68} - 7674q^{74} - 67708q^{78} + 24302q^{79} - 23660q^{81} - 7032q^{83} + 37180q^{84} - 14412q^{86} + 17850q^{87} + 4268q^{90} + 48354q^{92} + 606q^{95} + 50546q^{96} - 5842q^{97} - 25924q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.133471i 0.0333677i −0.999861 0.0166838i \(-0.994689\pi\)
0.999861 0.0166838i \(-0.00531088\pi\)
\(3\) 14.8068i 1.64520i −0.568620 0.822600i \(-0.692523\pi\)
0.568620 0.822600i \(-0.307477\pi\)
\(4\) 15.9822 0.998887
\(5\) 26.0324i 1.04129i 0.853772 + 0.520647i \(0.174309\pi\)
−0.853772 + 0.520647i \(0.825691\pi\)
\(6\) −1.97628 −0.0548965
\(7\) 87.9232i 1.79435i −0.441675 0.897175i \(-0.645616\pi\)
0.441675 0.897175i \(-0.354384\pi\)
\(8\) 4.26869i 0.0666982i
\(9\) −138.241 −1.70668
\(10\) 3.47456 0.0347456
\(11\) −101.658 −0.840147 −0.420074 0.907490i \(-0.637996\pi\)
−0.420074 + 0.907490i \(0.637996\pi\)
\(12\) 236.645i 1.64337i
\(13\) 190.866 1.12939 0.564693 0.825301i \(-0.308994\pi\)
0.564693 + 0.825301i \(0.308994\pi\)
\(14\) −11.7352 −0.0598733
\(15\) 385.456 1.71314
\(16\) 255.145 0.996661
\(17\) −227.830 −0.788338 −0.394169 0.919038i \(-0.628968\pi\)
−0.394169 + 0.919038i \(0.628968\pi\)
\(18\) 18.4512i 0.0569481i
\(19\) 304.934i 0.844693i 0.906434 + 0.422347i \(0.138793\pi\)
−0.906434 + 0.422347i \(0.861207\pi\)
\(20\) 416.054i 1.04014i
\(21\) −1301.86 −2.95207
\(22\) 13.5683i 0.0280338i
\(23\) 797.353 1.50728 0.753641 0.657286i \(-0.228296\pi\)
0.753641 + 0.657286i \(0.228296\pi\)
\(24\) −63.2056 −0.109732
\(25\) −52.6844 −0.0842950
\(26\) 25.4751i 0.0376850i
\(27\) 847.562i 1.16264i
\(28\) 1405.20i 1.79235i
\(29\) 1084.32i 1.28932i 0.764469 + 0.644660i \(0.223001\pi\)
−0.764469 + 0.644660i \(0.776999\pi\)
\(30\) 51.4471i 0.0571635i
\(31\) 433.017 0.450590 0.225295 0.974291i \(-0.427665\pi\)
0.225295 + 0.974291i \(0.427665\pi\)
\(32\) 102.353i 0.0999545i
\(33\) 1505.23i 1.38221i
\(34\) 30.4086i 0.0263050i
\(35\) 2288.85 1.86845
\(36\) −2209.40 −1.70478
\(37\) 310.044i 0.226475i −0.993568 0.113237i \(-0.963878\pi\)
0.993568 0.113237i \(-0.0361220\pi\)
\(38\) 40.6998 0.0281855
\(39\) 2826.12i 1.85807i
\(40\) 111.124 0.0694525
\(41\) 1339.11 0.796618 0.398309 0.917251i \(-0.369597\pi\)
0.398309 + 0.917251i \(0.369597\pi\)
\(42\) 173.760i 0.0985036i
\(43\) −137.757 + 1843.86i −0.0745034 + 0.997221i
\(44\) −1624.71 −0.839212
\(45\) 3598.75i 1.77716i
\(46\) 106.423i 0.0502946i
\(47\) 1003.89 0.454456 0.227228 0.973842i \(-0.427034\pi\)
0.227228 + 0.973842i \(0.427034\pi\)
\(48\) 3777.89i 1.63971i
\(49\) −5329.48 −2.21969
\(50\) 7.03183i 0.00281273i
\(51\) 3373.43i 1.29697i
\(52\) 3050.46 1.12813
\(53\) −3648.61 −1.29890 −0.649451 0.760404i \(-0.725001\pi\)
−0.649451 + 0.760404i \(0.725001\pi\)
\(54\) 113.125 0.0387945
\(55\) 2646.39i 0.874841i
\(56\) −375.317 −0.119680
\(57\) 4515.10 1.38969
\(58\) 144.725 0.0430217
\(59\) −1283.47 −0.368708 −0.184354 0.982860i \(-0.559019\pi\)
−0.184354 + 0.982860i \(0.559019\pi\)
\(60\) 6160.43 1.71123
\(61\) 2277.88i 0.612168i −0.952005 0.306084i \(-0.900981\pi\)
0.952005 0.306084i \(-0.0990188\pi\)
\(62\) 57.7951i 0.0150351i
\(63\) 12154.6i 3.06239i
\(64\) 4068.66 0.993326
\(65\) 4968.70i 1.17602i
\(66\) 200.904 0.0461212
\(67\) −4753.41 −1.05890 −0.529451 0.848340i \(-0.677602\pi\)
−0.529451 + 0.848340i \(0.677602\pi\)
\(68\) −3641.22 −0.787460
\(69\) 11806.2i 2.47978i
\(70\) 305.494i 0.0623458i
\(71\) 4258.19i 0.844711i −0.906430 0.422356i \(-0.861203\pi\)
0.906430 0.422356i \(-0.138797\pi\)
\(72\) 590.109i 0.113833i
\(73\) 3321.32i 0.623254i 0.950204 + 0.311627i \(0.100874\pi\)
−0.950204 + 0.311627i \(0.899126\pi\)
\(74\) −41.3818 −0.00755693
\(75\) 780.087i 0.138682i
\(76\) 4873.52i 0.843753i
\(77\) 8938.08i 1.50752i
\(78\) −377.205 −0.0619994
\(79\) −227.377 −0.0364328 −0.0182164 0.999834i \(-0.505799\pi\)
−0.0182164 + 0.999834i \(0.505799\pi\)
\(80\) 6642.04i 1.03782i
\(81\) 1352.14 0.206087
\(82\) 178.733i 0.0265813i
\(83\) −1895.54 −0.275155 −0.137577 0.990491i \(-0.543932\pi\)
−0.137577 + 0.990491i \(0.543932\pi\)
\(84\) −20806.6 −2.94878
\(85\) 5930.95i 0.820892i
\(86\) 246.102 + 18.3865i 0.0332750 + 0.00248601i
\(87\) 16055.3 2.12119
\(88\) 433.945i 0.0560363i
\(89\) 10806.3i 1.36426i 0.731229 + 0.682132i \(0.238947\pi\)
−0.731229 + 0.682132i \(0.761053\pi\)
\(90\) −480.328 −0.0592998
\(91\) 16781.6i 2.02652i
\(92\) 12743.4 1.50560
\(93\) 6411.60i 0.741311i
\(94\) 133.990i 0.0151641i
\(95\) −7938.16 −0.879575
\(96\) −1515.53 −0.164445
\(97\) 10904.7 1.15897 0.579483 0.814984i \(-0.303254\pi\)
0.579483 + 0.814984i \(0.303254\pi\)
\(98\) 711.330i 0.0740660i
\(99\) 14053.3 1.43387
\(100\) −842.012 −0.0842012
\(101\) 9432.56 0.924670 0.462335 0.886705i \(-0.347012\pi\)
0.462335 + 0.886705i \(0.347012\pi\)
\(102\) 450.254 0.0432770
\(103\) −14161.0 −1.33481 −0.667406 0.744694i \(-0.732596\pi\)
−0.667406 + 0.744694i \(0.732596\pi\)
\(104\) 814.749i 0.0753281i
\(105\) 33890.5i 3.07397i
\(106\) 486.983i 0.0433413i
\(107\) −6411.74 −0.560027 −0.280013 0.959996i \(-0.590339\pi\)
−0.280013 + 0.959996i \(0.590339\pi\)
\(108\) 13545.9i 1.16134i
\(109\) −15685.0 −1.32018 −0.660088 0.751188i \(-0.729481\pi\)
−0.660088 + 0.751188i \(0.729481\pi\)
\(110\) −353.216 −0.0291914
\(111\) −4590.75 −0.372596
\(112\) 22433.2i 1.78836i
\(113\) 14798.9i 1.15897i −0.814982 0.579487i \(-0.803253\pi\)
0.814982 0.579487i \(-0.196747\pi\)
\(114\) 602.634i 0.0463707i
\(115\) 20757.0i 1.56953i
\(116\) 17329.8i 1.28789i
\(117\) −26385.6 −1.92751
\(118\) 171.306i 0.0123029i
\(119\) 20031.5i 1.41455i
\(120\) 1645.39i 0.114263i
\(121\) −4306.69 −0.294153
\(122\) −304.030 −0.0204266
\(123\) 19828.0i 1.31060i
\(124\) 6920.56 0.450088
\(125\) 14898.7i 0.953519i
\(126\) 1622.29 0.102185
\(127\) 26014.9 1.61292 0.806462 0.591286i \(-0.201379\pi\)
0.806462 + 0.591286i \(0.201379\pi\)
\(128\) 2180.70i 0.133100i
\(129\) 27301.7 + 2039.74i 1.64063 + 0.122573i
\(130\) 663.177 0.0392412
\(131\) 274.560i 0.0159991i −0.999968 0.00799954i \(-0.997454\pi\)
0.999968 0.00799954i \(-0.00254636\pi\)
\(132\) 24056.8i 1.38067i
\(133\) 26810.8 1.51568
\(134\) 634.442i 0.0353331i
\(135\) −22064.1 −1.21065
\(136\) 972.534i 0.0525808i
\(137\) 26627.9i 1.41872i −0.704849 0.709358i \(-0.748985\pi\)
0.704849 0.709358i \(-0.251015\pi\)
\(138\) −1575.79 −0.0827446
\(139\) −3210.55 −0.166169 −0.0830846 0.996542i \(-0.526477\pi\)
−0.0830846 + 0.996542i \(0.526477\pi\)
\(140\) 36580.8 1.86637
\(141\) 14864.4i 0.747671i
\(142\) −568.344 −0.0281861
\(143\) −19403.1 −0.948851
\(144\) −35271.6 −1.70099
\(145\) −28227.4 −1.34256
\(146\) 443.300 0.0207966
\(147\) 78912.6i 3.65184i
\(148\) 4955.17i 0.226222i
\(149\) 22775.1i 1.02586i 0.858431 + 0.512929i \(0.171440\pi\)
−0.858431 + 0.512929i \(0.828560\pi\)
\(150\) 104.119 0.00462751
\(151\) 3692.73i 0.161955i −0.996716 0.0809774i \(-0.974196\pi\)
0.996716 0.0809774i \(-0.0258042\pi\)
\(152\) 1301.67 0.0563396
\(153\) 31495.5 1.34544
\(154\) 1192.97 0.0503024
\(155\) 11272.5i 0.469197i
\(156\) 45167.6i 1.85600i
\(157\) 15232.3i 0.617967i 0.951067 + 0.308983i \(0.0999887\pi\)
−0.951067 + 0.308983i \(0.900011\pi\)
\(158\) 30.3482i 0.00121568i
\(159\) 54024.3i 2.13695i
\(160\) 2664.50 0.104082
\(161\) 70105.8i 2.70459i
\(162\) 180.471i 0.00687664i
\(163\) 7069.03i 0.266063i −0.991112 0.133031i \(-0.957529\pi\)
0.991112 0.133031i \(-0.0424711\pi\)
\(164\) 21402.0 0.795731
\(165\) −39184.6 −1.43929
\(166\) 252.999i 0.00918128i
\(167\) −33560.8 −1.20337 −0.601686 0.798733i \(-0.705504\pi\)
−0.601686 + 0.798733i \(0.705504\pi\)
\(168\) 5557.24i 0.196898i
\(169\) 7868.97 0.275514
\(170\) −791.608 −0.0273913
\(171\) 42154.5i 1.44162i
\(172\) −2201.66 + 29468.9i −0.0744205 + 0.996110i
\(173\) 24263.7 0.810707 0.405354 0.914160i \(-0.367148\pi\)
0.405354 + 0.914160i \(0.367148\pi\)
\(174\) 2142.91i 0.0707793i
\(175\) 4632.18i 0.151255i
\(176\) −25937.5 −0.837342
\(177\) 19004.1i 0.606599i
\(178\) 1442.33 0.0455223
\(179\) 39627.8i 1.23679i −0.785869 0.618393i \(-0.787784\pi\)
0.785869 0.618393i \(-0.212216\pi\)
\(180\) 57515.9i 1.77518i
\(181\) 33212.7 1.01379 0.506893 0.862009i \(-0.330794\pi\)
0.506893 + 0.862009i \(0.330794\pi\)
\(182\) −2239.85 −0.0676202
\(183\) −33728.1 −1.00714
\(184\) 3403.65i 0.100533i
\(185\) 8071.17 0.235827
\(186\) −855.761 −0.0247358
\(187\) 23160.7 0.662320
\(188\) 16044.4 0.453950
\(189\) 74520.4 2.08618
\(190\) 1059.51i 0.0293494i
\(191\) 24782.3i 0.679321i −0.940548 0.339661i \(-0.889688\pi\)
0.940548 0.339661i \(-0.110312\pi\)
\(192\) 60243.9i 1.63422i
\(193\) −29341.9 −0.787723 −0.393861 0.919170i \(-0.628861\pi\)
−0.393861 + 0.919170i \(0.628861\pi\)
\(194\) 1455.46i 0.0386720i
\(195\) 73570.6 1.93480
\(196\) −85176.8 −2.21722
\(197\) −39758.4 −1.02446 −0.512232 0.858847i \(-0.671181\pi\)
−0.512232 + 0.858847i \(0.671181\pi\)
\(198\) 1875.71i 0.0478448i
\(199\) 2991.17i 0.0755326i −0.999287 0.0377663i \(-0.987976\pi\)
0.999287 0.0377663i \(-0.0120242\pi\)
\(200\) 224.893i 0.00562233i
\(201\) 70382.9i 1.74211i
\(202\) 1258.97i 0.0308541i
\(203\) 95336.8 2.31349
\(204\) 53914.8i 1.29553i
\(205\) 34860.3i 0.829514i
\(206\) 1890.08i 0.0445396i
\(207\) −110227. −2.57246
\(208\) 48698.6 1.12562
\(209\) 30998.9i 0.709667i
\(210\) −4523.40 −0.102571
\(211\) 28641.7i 0.643331i 0.946853 + 0.321666i \(0.104243\pi\)
−0.946853 + 0.321666i \(0.895757\pi\)
\(212\) −58312.8 −1.29746
\(213\) −63050.2 −1.38972
\(214\) 855.781i 0.0186868i
\(215\) −48000.1 3586.14i −1.03840 0.0775801i
\(216\) 3617.98 0.0775458
\(217\) 38072.2i 0.808516i
\(218\) 2093.49i 0.0440512i
\(219\) 49178.2 1.02538
\(220\) 42295.2i 0.873867i
\(221\) −43485.0 −0.890339
\(222\) 612.732i 0.0124327i
\(223\) 35376.8i 0.711393i 0.934602 + 0.355696i \(0.115756\pi\)
−0.934602 + 0.355696i \(0.884244\pi\)
\(224\) −8999.24 −0.179353
\(225\) 7283.17 0.143865
\(226\) −1975.23 −0.0386723
\(227\) 59327.2i 1.15134i 0.817684 + 0.575668i \(0.195258\pi\)
−0.817684 + 0.575668i \(0.804742\pi\)
\(228\) 72161.2 1.38814
\(229\) −13413.3 −0.255778 −0.127889 0.991788i \(-0.540820\pi\)
−0.127889 + 0.991788i \(0.540820\pi\)
\(230\) 2770.45 0.0523715
\(231\) 132344. 2.48017
\(232\) 4628.62 0.0859954
\(233\) 39527.8i 0.728100i 0.931379 + 0.364050i \(0.118606\pi\)
−0.931379 + 0.364050i \(0.881394\pi\)
\(234\) 3521.71i 0.0643165i
\(235\) 26133.7i 0.473222i
\(236\) −20512.7 −0.368298
\(237\) 3366.73i 0.0599393i
\(238\) 2673.62 0.0472004
\(239\) −24573.9 −0.430208 −0.215104 0.976591i \(-0.569009\pi\)
−0.215104 + 0.976591i \(0.569009\pi\)
\(240\) 98347.3 1.70742
\(241\) 21288.0i 0.366522i 0.983064 + 0.183261i \(0.0586654\pi\)
−0.983064 + 0.183261i \(0.941335\pi\)
\(242\) 574.817i 0.00981520i
\(243\) 48631.8i 0.823583i
\(244\) 36405.4i 0.611486i
\(245\) 138739.i 2.31136i
\(246\) −2646.46 −0.0437316
\(247\) 58201.7i 0.953985i
\(248\) 1848.41i 0.0300536i
\(249\) 28066.9i 0.452685i
\(250\) 1988.55 0.0318167
\(251\) 3878.52 0.0615628 0.0307814 0.999526i \(-0.490200\pi\)
0.0307814 + 0.999526i \(0.490200\pi\)
\(252\) 194257.i 3.05898i
\(253\) −81057.1 −1.26634
\(254\) 3472.22i 0.0538196i
\(255\) −87818.4 −1.35053
\(256\) 64807.5 0.988885
\(257\) 33269.3i 0.503706i −0.967765 0.251853i \(-0.918960\pi\)
0.967765 0.251853i \(-0.0810400\pi\)
\(258\) 272.246 3643.98i 0.00408998 0.0547440i
\(259\) −27260.0 −0.406375
\(260\) 79410.8i 1.17472i
\(261\) 149898.i 2.20046i
\(262\) −36.6457 −0.000533852
\(263\) 40367.8i 0.583612i −0.956478 0.291806i \(-0.905744\pi\)
0.956478 0.291806i \(-0.0942561\pi\)
\(264\) 6425.34 0.0921910
\(265\) 94982.1i 1.35254i
\(266\) 3578.46i 0.0505746i
\(267\) 160007. 2.24449
\(268\) −75970.0 −1.05772
\(269\) 92958.7 1.28465 0.642326 0.766432i \(-0.277970\pi\)
0.642326 + 0.766432i \(0.277970\pi\)
\(270\) 2944.91i 0.0403965i
\(271\) −61813.2 −0.841671 −0.420835 0.907137i \(-0.638263\pi\)
−0.420835 + 0.907137i \(0.638263\pi\)
\(272\) −58129.7 −0.785706
\(273\) −248481. −3.33402
\(274\) −3554.04 −0.0473393
\(275\) 5355.78 0.0708202
\(276\) 188690.i 2.47702i
\(277\) 119892.i 1.56254i 0.624193 + 0.781270i \(0.285428\pi\)
−0.624193 + 0.781270i \(0.714572\pi\)
\(278\) 428.515i 0.00554468i
\(279\) −59860.9 −0.769015
\(280\) 9770.38i 0.124622i
\(281\) 24043.7 0.304501 0.152250 0.988342i \(-0.451348\pi\)
0.152250 + 0.988342i \(0.451348\pi\)
\(282\) −1983.97 −0.0249480
\(283\) 112052. 1.39909 0.699546 0.714588i \(-0.253386\pi\)
0.699546 + 0.714588i \(0.253386\pi\)
\(284\) 68055.2i 0.843771i
\(285\) 117539.i 1.44708i
\(286\) 2589.74i 0.0316610i
\(287\) 117739.i 1.42941i
\(288\) 14149.5i 0.170591i
\(289\) −31614.6 −0.378523
\(290\) 3767.53i 0.0447982i
\(291\) 161464.i 1.90673i
\(292\) 53082.0i 0.622560i
\(293\) 19317.9 0.225022 0.112511 0.993650i \(-0.464111\pi\)
0.112511 + 0.993650i \(0.464111\pi\)
\(294\) 10532.5 0.121853
\(295\) 33411.8i 0.383934i
\(296\) −1323.48 −0.0151055
\(297\) 86161.3i 0.976786i
\(298\) 3039.81 0.0342305
\(299\) 152188. 1.70231
\(300\) 12467.5i 0.138528i
\(301\) 162118. + 12112.0i 1.78936 + 0.133685i
\(302\) −492.872 −0.00540406
\(303\) 139666.i 1.52127i
\(304\) 77802.5i 0.841873i
\(305\) 59298.5 0.637447
\(306\) 4203.73i 0.0448944i
\(307\) 44232.3 0.469313 0.234656 0.972078i \(-0.424603\pi\)
0.234656 + 0.972078i \(0.424603\pi\)
\(308\) 142850.i 1.50584i
\(309\) 209680.i 2.19603i
\(310\) 1504.54 0.0156560
\(311\) 61470.8 0.635547 0.317774 0.948167i \(-0.397065\pi\)
0.317774 + 0.948167i \(0.397065\pi\)
\(312\) −12063.8 −0.123930
\(313\) 50511.9i 0.515590i −0.966200 0.257795i \(-0.917004\pi\)
0.966200 0.257795i \(-0.0829960\pi\)
\(314\) 2033.06 0.0206201
\(315\) −316414. −3.18885
\(316\) −3633.99 −0.0363923
\(317\) −28664.5 −0.285250 −0.142625 0.989777i \(-0.545554\pi\)
−0.142625 + 0.989777i \(0.545554\pi\)
\(318\) 7210.67 0.0713052
\(319\) 110229.i 1.08322i
\(320\) 105917.i 1.03435i
\(321\) 94937.4i 0.921356i
\(322\) −9357.07 −0.0902460
\(323\) 69473.1i 0.665904i
\(324\) 21610.1 0.205857
\(325\) −10055.7 −0.0952017
\(326\) −943.508 −0.00887791
\(327\) 232245.i 2.17195i
\(328\) 5716.26i 0.0531330i
\(329\) 88265.4i 0.815453i
\(330\) 5230.00i 0.0480257i
\(331\) 130429.i 1.19047i −0.803554 0.595233i \(-0.797060\pi\)
0.803554 0.595233i \(-0.202940\pi\)
\(332\) −30294.9 −0.274848
\(333\) 42860.9i 0.386520i
\(334\) 4479.39i 0.0401538i
\(335\) 123743.i 1.10263i
\(336\) −332164. −2.94221
\(337\) 85348.4 0.751511 0.375756 0.926719i \(-0.377383\pi\)
0.375756 + 0.926719i \(0.377383\pi\)
\(338\) 1050.28i 0.00919328i
\(339\) −219125. −1.90674
\(340\) 94789.5i 0.819978i
\(341\) −44019.6 −0.378562
\(342\) −5626.40 −0.0481037
\(343\) 257482.i 2.18856i
\(344\) 7870.87 + 588.041i 0.0665129 + 0.00496925i
\(345\) 307344. 2.58218
\(346\) 3238.49i 0.0270514i
\(347\) 145539.i 1.20871i −0.796717 0.604353i \(-0.793432\pi\)
0.796717 0.604353i \(-0.206568\pi\)
\(348\) 256599. 2.11883
\(349\) 235394.i 1.93261i 0.257391 + 0.966307i \(0.417137\pi\)
−0.257391 + 0.966307i \(0.582863\pi\)
\(350\) 618.261 0.00504702
\(351\) 161771.i 1.31307i
\(352\) 10405.0i 0.0839765i
\(353\) −228188. −1.83123 −0.915616 0.402054i \(-0.868297\pi\)
−0.915616 + 0.402054i \(0.868297\pi\)
\(354\) 2536.50 0.0202408
\(355\) 110851. 0.879593
\(356\) 172709.i 1.36274i
\(357\) 296603. 2.32723
\(358\) −5289.16 −0.0412687
\(359\) −73217.3 −0.568100 −0.284050 0.958809i \(-0.591678\pi\)
−0.284050 + 0.958809i \(0.591678\pi\)
\(360\) −15361.9 −0.118534
\(361\) 37336.1 0.286493
\(362\) 4432.92i 0.0338277i
\(363\) 63768.3i 0.483940i
\(364\) 268206.i 2.02426i
\(365\) −86461.9 −0.648992
\(366\) 4501.71i 0.0336059i
\(367\) 77952.5 0.578759 0.289380 0.957214i \(-0.406551\pi\)
0.289380 + 0.957214i \(0.406551\pi\)
\(368\) 203441. 1.50225
\(369\) −185121. −1.35958
\(370\) 1077.27i 0.00786900i
\(371\) 320798.i 2.33068i
\(372\) 102471.i 0.740485i
\(373\) 141224.i 1.01506i −0.861635 0.507529i \(-0.830559\pi\)
0.861635 0.507529i \(-0.169441\pi\)
\(374\) 3091.27i 0.0221001i
\(375\) 220603. 1.56873
\(376\) 4285.30i 0.0303114i
\(377\) 206960.i 1.45614i
\(378\) 9946.29i 0.0696110i
\(379\) −223694. −1.55731 −0.778657 0.627450i \(-0.784099\pi\)
−0.778657 + 0.627450i \(0.784099\pi\)
\(380\) −126869. −0.878595
\(381\) 385197.i 2.65358i
\(382\) −3307.71 −0.0226674
\(383\) 59491.5i 0.405562i −0.979224 0.202781i \(-0.935002\pi\)
0.979224 0.202781i \(-0.0649980\pi\)
\(384\) −32289.2 −0.218975
\(385\) −232679. −1.56977
\(386\) 3916.28i 0.0262845i
\(387\) 19043.7 254898.i 0.127154 1.70194i
\(388\) 174281. 1.15768
\(389\) 273729.i 1.80893i 0.426546 + 0.904466i \(0.359730\pi\)
−0.426546 + 0.904466i \(0.640270\pi\)
\(390\) 9819.53i 0.0645597i
\(391\) −181661. −1.18825
\(392\) 22749.9i 0.148050i
\(393\) −4065.36 −0.0263217
\(394\) 5306.59i 0.0341840i
\(395\) 5919.17i 0.0379373i
\(396\) 224603. 1.43227
\(397\) 188678. 1.19713 0.598564 0.801075i \(-0.295738\pi\)
0.598564 + 0.801075i \(0.295738\pi\)
\(398\) −399.233 −0.00252035
\(399\) 396982.i 2.49359i
\(400\) −13442.2 −0.0840136
\(401\) −27975.8 −0.173978 −0.0869889 0.996209i \(-0.527724\pi\)
−0.0869889 + 0.996209i \(0.527724\pi\)
\(402\) 9394.06 0.0581301
\(403\) 82648.4 0.508890
\(404\) 150753. 0.923641
\(405\) 35199.3i 0.214597i
\(406\) 12724.7i 0.0771959i
\(407\) 31518.4i 0.190272i
\(408\) 14400.1 0.0865059
\(409\) 22322.2i 0.133441i −0.997772 0.0667207i \(-0.978746\pi\)
0.997772 0.0667207i \(-0.0212536\pi\)
\(410\) 4652.84 0.0276790
\(411\) −394274. −2.33407
\(412\) −226324. −1.33333
\(413\) 112847.i 0.661592i
\(414\) 14712.1i 0.0858369i
\(415\) 49345.4i 0.286517i
\(416\) 19535.8i 0.112887i
\(417\) 47538.0i 0.273382i
\(418\) −4137.45 −0.0236799
\(419\) 160113.i 0.912006i −0.889978 0.456003i \(-0.849281\pi\)
0.889978 0.456003i \(-0.150719\pi\)
\(420\) 541645.i 3.07055i
\(421\) 289642.i 1.63417i −0.576517 0.817085i \(-0.695589\pi\)
0.576517 0.817085i \(-0.304411\pi\)
\(422\) 3822.84 0.0214665
\(423\) −138780. −0.775612
\(424\) 15574.8i 0.0866344i
\(425\) 12003.1 0.0664530
\(426\) 8415.35i 0.0463717i
\(427\) −200278. −1.09844
\(428\) −102474. −0.559403
\(429\) 287297.i 1.56105i
\(430\) −478.645 + 6406.61i −0.00258867 + 0.0346490i
\(431\) −6996.04 −0.0376615 −0.0188308 0.999823i \(-0.505994\pi\)
−0.0188308 + 0.999823i \(0.505994\pi\)
\(432\) 216252.i 1.15876i
\(433\) 190817.i 1.01775i 0.860841 + 0.508875i \(0.169938\pi\)
−0.860841 + 0.508875i \(0.830062\pi\)
\(434\) −5081.53 −0.0269783
\(435\) 417957.i 2.20879i
\(436\) −250681. −1.31871
\(437\) 243140.i 1.27319i
\(438\) 6563.85i 0.0342145i
\(439\) 284875. 1.47818 0.739088 0.673609i \(-0.235257\pi\)
0.739088 + 0.673609i \(0.235257\pi\)
\(440\) −11296.6 −0.0583503
\(441\) 736755. 3.78832
\(442\) 5803.98i 0.0297085i
\(443\) 278521. 1.41922 0.709610 0.704594i \(-0.248871\pi\)
0.709610 + 0.704594i \(0.248871\pi\)
\(444\) −73370.3 −0.372181
\(445\) −281314. −1.42060
\(446\) 4721.78 0.0237375
\(447\) 337226. 1.68774
\(448\) 357730.i 1.78237i
\(449\) 14484.9i 0.0718495i 0.999354 + 0.0359248i \(0.0114377\pi\)
−0.999354 + 0.0359248i \(0.988562\pi\)
\(450\) 972.090i 0.00480044i
\(451\) −136131. −0.669276
\(452\) 236519.i 1.15768i
\(453\) −54677.6 −0.266448
\(454\) 7918.45 0.0384174
\(455\) 436864. 2.11020
\(456\) 19273.6i 0.0926898i
\(457\) 352890.i 1.68969i −0.535012 0.844844i \(-0.679693\pi\)
0.535012 0.844844i \(-0.320307\pi\)
\(458\) 1790.28i 0.00853473i
\(459\) 193100.i 0.916551i
\(460\) 331742.i 1.56778i
\(461\) −183860. −0.865138 −0.432569 0.901601i \(-0.642393\pi\)
−0.432569 + 0.901601i \(0.642393\pi\)
\(462\) 17664.1i 0.0827575i
\(463\) 33276.3i 0.155229i 0.996983 + 0.0776145i \(0.0247303\pi\)
−0.996983 + 0.0776145i \(0.975270\pi\)
\(464\) 276659.i 1.28502i
\(465\) 166909. 0.771923
\(466\) 5275.81 0.0242950
\(467\) 16400.1i 0.0751992i 0.999293 + 0.0375996i \(0.0119711\pi\)
−0.999293 + 0.0375996i \(0.988029\pi\)
\(468\) −421700. −1.92536
\(469\) 417935.i 1.90004i
\(470\) 3488.09 0.0157903
\(471\) 225541. 1.01668
\(472\) 5478.75i 0.0245922i
\(473\) 14004.1 187443.i 0.0625939 0.837812i
\(474\) 449.360 0.00200004
\(475\) 16065.3i 0.0712034i
\(476\) 320147.i 1.41298i
\(477\) 504390. 2.21681
\(478\) 3279.90i 0.0143551i
\(479\) −400012. −1.74342 −0.871711 0.490020i \(-0.836989\pi\)
−0.871711 + 0.490020i \(0.836989\pi\)
\(480\) 39452.8i 0.171236i
\(481\) 59176.9i 0.255777i
\(482\) 2841.32 0.0122300
\(483\) −1.03804e6 −4.44960
\(484\) −68830.3 −0.293825
\(485\) 283876.i 1.20683i
\(486\) 6490.92 0.0274811
\(487\) 166088. 0.700293 0.350146 0.936695i \(-0.386132\pi\)
0.350146 + 0.936695i \(0.386132\pi\)
\(488\) −9723.54 −0.0408305
\(489\) −104670. −0.437727
\(490\) −18517.6 −0.0771246
\(491\) 320840.i 1.33084i 0.746470 + 0.665419i \(0.231747\pi\)
−0.746470 + 0.665419i \(0.768253\pi\)
\(492\) 316895.i 1.30914i
\(493\) 247040.i 1.01642i
\(494\) 7768.23 0.0318323
\(495\) 365841.i 1.49308i
\(496\) 110482. 0.449085
\(497\) −374393. −1.51571
\(498\) 3746.11 0.0151050
\(499\) 56730.2i 0.227831i −0.993490 0.113916i \(-0.963661\pi\)
0.993490 0.113916i \(-0.0363393\pi\)
\(500\) 238114.i 0.952457i
\(501\) 496929.i 1.97979i
\(502\) 517.669i 0.00205421i
\(503\) 331332.i 1.30957i −0.755817 0.654783i \(-0.772760\pi\)
0.755817 0.654783i \(-0.227240\pi\)
\(504\) 51884.3 0.204256
\(505\) 245552.i 0.962854i
\(506\) 10818.8i 0.0422548i
\(507\) 116514.i 0.453276i
\(508\) 415774. 1.61113
\(509\) −68886.4 −0.265887 −0.132944 0.991124i \(-0.542443\pi\)
−0.132944 + 0.991124i \(0.542443\pi\)
\(510\) 11721.2i 0.0450642i
\(511\) 292021. 1.11834
\(512\) 43541.2i 0.166096i
\(513\) −258451. −0.982072
\(514\) −4440.48 −0.0168075
\(515\) 368645.i 1.38993i
\(516\) 436341. + 32599.5i 1.63880 + 0.122437i
\(517\) −102054. −0.381810
\(518\) 3638.42i 0.0135598i
\(519\) 359267.i 1.33378i
\(520\) 21209.8 0.0784388
\(521\) 480907.i 1.77168i −0.463990 0.885841i \(-0.653582\pi\)
0.463990 0.885841i \(-0.346418\pi\)
\(522\) −20007.0 −0.0734244
\(523\) 140709.i 0.514423i 0.966355 + 0.257211i \(0.0828036\pi\)
−0.966355 + 0.257211i \(0.917196\pi\)
\(524\) 4388.07i 0.0159813i
\(525\) 68587.8 0.248844
\(526\) −5387.93 −0.0194738
\(527\) −98654.1 −0.355217
\(528\) 384051.i 1.37760i
\(529\) 355930. 1.27190
\(530\) −12677.3 −0.0451311
\(531\) 177429. 0.629268
\(532\) 428495. 1.51399
\(533\) 255592. 0.899690
\(534\) 21356.3i 0.0748934i
\(535\) 166913.i 0.583153i
\(536\) 20290.8i 0.0706269i
\(537\) −586761. −2.03476
\(538\) 12407.3i 0.0428659i
\(539\) 541784. 1.86487
\(540\) −352632. −1.20930
\(541\) −227082. −0.775869 −0.387935 0.921687i \(-0.626811\pi\)
−0.387935 + 0.921687i \(0.626811\pi\)
\(542\) 8250.25i 0.0280846i
\(543\) 491773.i 1.66788i
\(544\) 23319.2i 0.0787980i
\(545\) 408318.i 1.37469i
\(546\) 33165.0i 0.111249i
\(547\) −203039. −0.678587 −0.339294 0.940681i \(-0.610188\pi\)
−0.339294 + 0.940681i \(0.610188\pi\)
\(548\) 425572.i 1.41714i
\(549\) 314897.i 1.04478i
\(550\) 714.840i 0.00236311i
\(551\) −330646. −1.08908
\(552\) −50397.2 −0.165397
\(553\) 19991.7i 0.0653733i
\(554\) 16002.1 0.0521384
\(555\) 119508.i 0.387982i
\(556\) −51311.7 −0.165984
\(557\) −578004. −1.86303 −0.931517 0.363699i \(-0.881514\pi\)
−0.931517 + 0.363699i \(0.881514\pi\)
\(558\) 7989.68i 0.0256603i
\(559\) −26293.2 + 351931.i −0.0841432 + 1.12625i
\(560\) 583989. 1.86221
\(561\) 342935.i 1.08965i
\(562\) 3209.13i 0.0101605i
\(563\) 263355. 0.830855 0.415428 0.909626i \(-0.363632\pi\)
0.415428 + 0.909626i \(0.363632\pi\)
\(564\) 237566.i 0.746838i
\(565\) 385251. 1.20683
\(566\) 14955.6i 0.0466845i
\(567\) 118884.i 0.369792i
\(568\) −18176.9 −0.0563407
\(569\) 233303. 0.720603 0.360302 0.932836i \(-0.382674\pi\)
0.360302 + 0.932836i \(0.382674\pi\)
\(570\) 15688.0 0.0482856
\(571\) 348145.i 1.06779i −0.845549 0.533897i \(-0.820727\pi\)
0.845549 0.533897i \(-0.179273\pi\)
\(572\) −310103. −0.947795
\(573\) −366947. −1.11762
\(574\) −15714.7 −0.0476962
\(575\) −42008.0 −0.127056
\(576\) −562458. −1.69529
\(577\) 217612.i 0.653628i 0.945089 + 0.326814i \(0.105975\pi\)
−0.945089 + 0.326814i \(0.894025\pi\)
\(578\) 4219.63i 0.0126304i
\(579\) 434460.i 1.29596i
\(580\) −451135. −1.34107
\(581\) 166662.i 0.493724i
\(582\) −21550.7 −0.0636233
\(583\) 370910. 1.09127
\(584\) 14177.7 0.0415700
\(585\) 686881.i 2.00710i
\(586\) 2578.38i 0.00750848i
\(587\) 368118.i 1.06834i −0.845376 0.534172i \(-0.820624\pi\)
0.845376 0.534172i \(-0.179376\pi\)
\(588\) 1.26120e6i 3.64777i
\(589\) 132042.i 0.380610i
\(590\) −4459.51 −0.0128110
\(591\) 588696.i 1.68545i
\(592\) 79106.1i 0.225718i
\(593\) 216642.i 0.616073i 0.951374 + 0.308037i \(0.0996720\pi\)
−0.951374 + 0.308037i \(0.900328\pi\)
\(594\) −11500.0 −0.0325931
\(595\) −521468. −1.47297
\(596\) 363996.i 1.02472i
\(597\) −44289.6 −0.124266
\(598\) 20312.6i 0.0568020i
\(599\) −119963. −0.334345 −0.167173 0.985928i \(-0.553464\pi\)
−0.167173 + 0.985928i \(0.553464\pi\)
\(600\) 3329.95 0.00924986
\(601\) 128663.i 0.356207i −0.984012 0.178104i \(-0.943004\pi\)
0.984012 0.178104i \(-0.0569963\pi\)
\(602\) 1616.60 21638.0i 0.00446077 0.0597069i
\(603\) 657119. 1.80721
\(604\) 59018.0i 0.161775i
\(605\) 112113.i 0.306300i
\(606\) −18641.3 −0.0507612
\(607\) 44121.9i 0.119750i −0.998206 0.0598751i \(-0.980930\pi\)
0.998206 0.0598751i \(-0.0190703\pi\)
\(608\) 31211.1 0.0844309
\(609\) 1.41163e6i 3.80616i
\(610\) 7914.62i 0.0212701i
\(611\) 191609. 0.513256
\(612\) 503367. 1.34395
\(613\) −130644. −0.347671 −0.173836 0.984775i \(-0.555616\pi\)
−0.173836 + 0.984775i \(0.555616\pi\)
\(614\) 5903.72i 0.0156599i
\(615\) 516170. 1.36472
\(616\) 38153.9 0.100549
\(617\) −6618.63 −0.0173859 −0.00869296 0.999962i \(-0.502767\pi\)
−0.00869296 + 0.999962i \(0.502767\pi\)
\(618\) 27986.1 0.0732766
\(619\) 294513. 0.768641 0.384320 0.923200i \(-0.374436\pi\)
0.384320 + 0.923200i \(0.374436\pi\)
\(620\) 180159.i 0.468675i
\(621\) 675806.i 1.75242i
\(622\) 8204.55i 0.0212068i
\(623\) 950127. 2.44797
\(624\) 721071.i 1.85186i
\(625\) −420777. −1.07719
\(626\) −6741.86 −0.0172041
\(627\) −458995. −1.16754
\(628\) 243445.i 0.617279i
\(629\) 70637.2i 0.178539i
\(630\) 42232.0i 0.106405i
\(631\) 493017.i 1.23824i 0.785298 + 0.619118i \(0.212510\pi\)
−0.785298 + 0.619118i \(0.787490\pi\)
\(632\) 970.603i 0.00243001i
\(633\) 424093. 1.05841
\(634\) 3825.88i 0.00951815i
\(635\) 677228.i 1.67953i
\(636\) 863426.i 2.13457i
\(637\) −1.01722e6 −2.50689
\(638\) −14712.4 −0.0361445
\(639\) 588658.i 1.44165i
\(640\) 56768.9 0.138596
\(641\) 212494.i 0.517167i 0.965989 + 0.258584i \(0.0832557\pi\)
−0.965989 + 0.258584i \(0.916744\pi\)
\(642\) 12671.4 0.0307435
\(643\) 332186. 0.803451 0.401725 0.915760i \(-0.368411\pi\)
0.401725 + 0.915760i \(0.368411\pi\)
\(644\) 1.12044e6i 2.70158i
\(645\) −53099.2 + 710728.i −0.127635 + 1.70838i
\(646\) −9272.63 −0.0222197
\(647\) 672018.i 1.60536i −0.596410 0.802680i \(-0.703407\pi\)
0.596410 0.802680i \(-0.296593\pi\)
\(648\) 5771.84i 0.0137456i
\(649\) 130475. 0.309769
\(650\) 1342.14i 0.00317666i
\(651\) −563728. −1.33017
\(652\) 112978.i 0.265767i
\(653\) 471578.i 1.10593i −0.833205 0.552965i \(-0.813496\pi\)
0.833205 0.552965i \(-0.186504\pi\)
\(654\) 30997.9 0.0724731
\(655\) 7147.45 0.0166598
\(656\) 341669. 0.793958
\(657\) 459144.i 1.06370i
\(658\) −11780.9 −0.0272098
\(659\) −140481. −0.323479 −0.161739 0.986834i \(-0.551710\pi\)
−0.161739 + 0.986834i \(0.551710\pi\)
\(660\) −626256. −1.43769
\(661\) −426152. −0.975353 −0.487676 0.873024i \(-0.662155\pi\)
−0.487676 + 0.873024i \(0.662155\pi\)
\(662\) −17408.4 −0.0397231
\(663\) 643874.i 1.46479i
\(664\) 8091.47i 0.0183523i
\(665\) 697948.i 1.57827i
\(666\) 5720.67 0.0128973
\(667\) 864584.i 1.94337i
\(668\) −536376. −1.20203
\(669\) 523818. 1.17038
\(670\) −16516.0 −0.0367922
\(671\) 231564.i 0.514311i
\(672\) 133250.i 0.295072i
\(673\) 183510.i 0.405163i −0.979265 0.202582i \(-0.935067\pi\)
0.979265 0.202582i \(-0.0649332\pi\)
\(674\) 11391.5i 0.0250762i
\(675\) 44653.3i 0.0980045i
\(676\) 125763. 0.275208
\(677\) 331953.i 0.724269i −0.932126 0.362134i \(-0.882048\pi\)
0.932126 0.362134i \(-0.117952\pi\)
\(678\) 29246.8i 0.0636237i
\(679\) 958777.i 2.07959i
\(680\) −25317.4 −0.0547521
\(681\) 878446. 1.89418
\(682\) 5875.32i 0.0126317i
\(683\) −801639. −1.71845 −0.859226 0.511596i \(-0.829054\pi\)
−0.859226 + 0.511596i \(0.829054\pi\)
\(684\) 673722.i 1.44002i
\(685\) 693187. 1.47730
\(686\) 34366.3 0.0730271
\(687\) 198608.i 0.420807i
\(688\) −35148.0 + 470452.i −0.0742547 + 0.993891i
\(689\) −696398. −1.46696
\(690\) 41021.5i 0.0861615i
\(691\) 54538.3i 0.114221i 0.998368 + 0.0571105i \(0.0181887\pi\)
−0.998368 + 0.0571105i \(0.981811\pi\)
\(692\) 387786. 0.809805
\(693\) 1.23561e6i 2.57286i
\(694\) −19425.2 −0.0403317
\(695\) 83578.3i 0.173031i
\(696\) 68535.0i 0.141480i
\(697\) −305090. −0.628004
\(698\) 31418.3 0.0644869
\(699\) 585281. 1.19787
\(700\) 74032.3i 0.151086i
\(701\) −830004. −1.68906 −0.844528 0.535511i \(-0.820119\pi\)
−0.844528 + 0.535511i \(0.820119\pi\)
\(702\) 21591.7 0.0438140
\(703\) 94542.9 0.191301
\(704\) −413611. −0.834540
\(705\) 386957. 0.778546
\(706\) 30456.4i 0.0611040i
\(707\) 829341.i 1.65918i
\(708\) 303728.i 0.605923i
\(709\) 539592. 1.07343 0.536715 0.843764i \(-0.319665\pi\)
0.536715 + 0.843764i \(0.319665\pi\)
\(710\) 14795.3i 0.0293500i
\(711\) 31433.0 0.0621793
\(712\) 46128.9 0.0909940
\(713\) 345267. 0.679166
\(714\) 39587.8i 0.0776542i
\(715\) 505108.i 0.988034i
\(716\) 633339.i 1.23541i
\(717\) 363861.i 0.707779i
\(718\) 9772.37i 0.0189562i
\(719\) −707898. −1.36935 −0.684673 0.728851i \(-0.740055\pi\)
−0.684673 + 0.728851i \(0.740055\pi\)
\(720\) 918204.i 1.77123i
\(721\) 1.24508e6i 2.39512i
\(722\) 4983.28i 0.00955962i
\(723\) 315207. 0.603003
\(724\) 530811. 1.01266
\(725\) 57126.7i 0.108683i
\(726\) 8511.21 0.0161480
\(727\) 182701.i 0.345679i 0.984950 + 0.172839i \(0.0552942\pi\)
−0.984950 + 0.172839i \(0.944706\pi\)
\(728\) −71635.3 −0.135165
\(729\) 829604. 1.56105
\(730\) 11540.1i 0.0216554i
\(731\) 31385.1 420086.i 0.0587339 0.786147i
\(732\) −539048. −1.00602
\(733\) 928539.i 1.72819i −0.503326 0.864097i \(-0.667890\pi\)
0.503326 0.864097i \(-0.332110\pi\)
\(734\) 10404.4i 0.0193119i
\(735\) −2.05428e6 −3.80264
\(736\) 81611.8i 0.150660i
\(737\) 483222. 0.889634
\(738\) 24708.3i 0.0453659i
\(739\) 177700.i 0.325386i 0.986677 + 0.162693i \(0.0520180\pi\)
−0.986677 + 0.162693i \(0.947982\pi\)
\(740\) 128995. 0.235564
\(741\) 861781. 1.56950
\(742\) 42817.1 0.0777696
\(743\) 576694.i 1.04464i 0.852748 + 0.522322i \(0.174934\pi\)
−0.852748 + 0.522322i \(0.825066\pi\)
\(744\) −27369.1 −0.0494441
\(745\) −592890. −1.06822
\(746\) −18849.3 −0.0338701
\(747\) 262042. 0.469602
\(748\) 370158. 0.661583
\(749\) 563741.i 1.00488i
\(750\) 29444.0i 0.0523449i
\(751\) 478034.i 0.847576i −0.905761 0.423788i \(-0.860700\pi\)
0.905761 0.423788i \(-0.139300\pi\)
\(752\) 256138. 0.452938
\(753\) 57428.5i 0.101283i
\(754\) 27623.1 0.0485881
\(755\) 96130.6 0.168643
\(756\) 1.19100e6 2.08386
\(757\) 1.05095e6i 1.83395i −0.398939 0.916977i \(-0.630622\pi\)
0.398939 0.916977i \(-0.369378\pi\)
\(758\) 29856.6i 0.0519640i
\(759\) 1.20020e6i 2.08338i
\(760\) 33885.5i 0.0586661i
\(761\) 38638.8i 0.0667197i 0.999443 + 0.0333599i \(0.0106207\pi\)
−0.999443 + 0.0333599i \(0.989379\pi\)
\(762\) −51412.5 −0.0885440
\(763\) 1.37908e6i 2.36886i
\(764\) 396075.i 0.678565i
\(765\) 819903.i 1.40100i
\(766\) −7940.38 −0.0135327
\(767\) −244972. −0.416414
\(768\) 959592.i 1.62691i
\(769\) −582597. −0.985181 −0.492590 0.870261i \(-0.663950\pi\)
−0.492590 + 0.870261i \(0.663950\pi\)
\(770\) 31055.9i 0.0523796i
\(771\) −492612. −0.828698
\(772\) −468947. −0.786846
\(773\) 247652.i 0.414461i −0.978292 0.207230i \(-0.933555\pi\)
0.978292 0.207230i \(-0.0664450\pi\)
\(774\) −34021.4 2541.78i −0.0567898 0.00424283i
\(775\) −22813.2 −0.0379825
\(776\) 46548.8i 0.0773010i
\(777\) 403634.i 0.668568i
\(778\) 36534.9 0.0603599
\(779\) 408342.i 0.672898i
\(780\) 1.17582e6 1.93264
\(781\) 432878.i 0.709682i
\(782\) 24246.4i 0.0396491i
\(783\) −919028. −1.49901
\(784\) −1.35979e6 −2.21228
\(785\) −396532. −0.643486
\(786\) 542.606i 0.000878294i
\(787\) 840560. 1.35712 0.678561 0.734544i \(-0.262604\pi\)
0.678561 + 0.734544i \(0.262604\pi\)
\(788\) −635427. −1.02332