Properties

Label 43.3.b.b.42.1
Level 43
Weight 3
Character 43.42
Analytic conductor 1.172
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.17166513675\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} + \cdots)\)
Defining polynomial: \(x^{6} + 20 x^{4} + 121 x^{2} + 214\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.1
Root \(-3.18991i\) of defining polynomial
Character \(\chi\) \(=\) 43.42
Dual form 43.3.b.b.42.6

$q$-expansion

\(f(q)\) \(=\) \(q-3.18991i q^{2} +0.724539i q^{3} -6.17554 q^{4} -7.66434i q^{5} +2.31122 q^{6} +10.1297i q^{7} +6.93980i q^{8} +8.47504 q^{9} +O(q^{10})\) \(q-3.18991i q^{2} +0.724539i q^{3} -6.17554 q^{4} -7.66434i q^{5} +2.31122 q^{6} +10.1297i q^{7} +6.93980i q^{8} +8.47504 q^{9} -24.4486 q^{10} -2.43517 q^{11} -4.47442i q^{12} +18.1491 q^{13} +32.3129 q^{14} +5.55311 q^{15} -2.56483 q^{16} -1.13567 q^{17} -27.0346i q^{18} +12.3269i q^{19} +47.3314i q^{20} -7.33937 q^{21} +7.76798i q^{22} -24.2847 q^{23} -5.02815 q^{24} -33.7420 q^{25} -57.8939i q^{26} +12.6614i q^{27} -62.5565i q^{28} +35.5218i q^{29} -17.7139i q^{30} -12.9823 q^{31} +35.9408i q^{32} -1.76438i q^{33} +3.62270i q^{34} +77.6375 q^{35} -52.3380 q^{36} -41.5116i q^{37} +39.3216 q^{38} +13.1497i q^{39} +53.1889 q^{40} -65.0667 q^{41} +23.4120i q^{42} +(23.6064 - 35.9408i) q^{43} +15.0385 q^{44} -64.9556i q^{45} +77.4662i q^{46} +51.0402 q^{47} -1.85832i q^{48} -53.6110 q^{49} +107.634i q^{50} -0.822839i q^{51} -112.080 q^{52} +56.2026 q^{53} +40.3886 q^{54} +18.6640i q^{55} -70.2981 q^{56} -8.93130 q^{57} +113.312 q^{58} -88.8355 q^{59} -34.2935 q^{60} +65.1393i q^{61} +41.4123i q^{62} +85.8497i q^{63} +104.389 q^{64} -139.101i q^{65} -5.62821 q^{66} +45.3618 q^{67} +7.01339 q^{68} -17.5952i q^{69} -247.657i q^{70} -63.7983i q^{71} +58.8151i q^{72} -8.80247i q^{73} -132.418 q^{74} -24.4474i q^{75} -76.1251i q^{76} -24.6676i q^{77} +41.9464 q^{78} +31.8496 q^{79} +19.6577i q^{80} +67.1017 q^{81} +207.557i q^{82} -68.4740 q^{83} +45.3246 q^{84} +8.70417i q^{85} +(-114.648 - 75.3023i) q^{86} -25.7370 q^{87} -16.8996i q^{88} +5.90432i q^{89} -207.203 q^{90} +183.845i q^{91} +149.971 q^{92} -9.40616i q^{93} -162.814i q^{94} +94.4773 q^{95} -26.0405 q^{96} -100.657 q^{97} +171.015i q^{98} -20.6382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 16q^{4} + 6q^{6} - 36q^{9} + O(q^{10}) \) \( 6q - 16q^{4} + 6q^{6} - 36q^{9} - 2q^{10} + 38q^{11} + 30q^{13} + 36q^{14} + 28q^{15} - 68q^{16} - 20q^{17} + 56q^{21} - 80q^{23} + 62q^{24} - 84q^{25} - 112q^{31} + 208q^{35} - 122q^{36} + 170q^{38} + 206q^{40} - 172q^{41} + 10q^{43} - 36q^{44} + 30q^{47} - 6q^{49} - 120q^{52} - 110q^{53} - 284q^{54} - 264q^{56} + 420q^{57} + 430q^{58} - 12q^{59} - 232q^{60} + 100q^{64} - 144q^{66} - 70q^{67} - 50q^{68} - 50q^{74} + 620q^{78} + 178q^{79} + 382q^{81} + 10q^{83} + 172q^{84} - 372q^{86} - 510q^{87} - 796q^{90} + 150q^{92} - 130q^{95} + 362q^{96} - 380q^{97} - 466q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.18991i 1.59496i −0.603348 0.797478i \(-0.706167\pi\)
0.603348 0.797478i \(-0.293833\pi\)
\(3\) 0.724539i 0.241513i 0.992682 + 0.120757i \(0.0385320\pi\)
−0.992682 + 0.120757i \(0.961468\pi\)
\(4\) −6.17554 −1.54389
\(5\) 7.66434i 1.53287i −0.642324 0.766434i \(-0.722029\pi\)
0.642324 0.766434i \(-0.277971\pi\)
\(6\) 2.31122 0.385203
\(7\) 10.1297i 1.44710i 0.690271 + 0.723551i \(0.257491\pi\)
−0.690271 + 0.723551i \(0.742509\pi\)
\(8\) 6.93980i 0.867475i
\(9\) 8.47504 0.941671
\(10\) −24.4486 −2.44486
\(11\) −2.43517 −0.221379 −0.110690 0.993855i \(-0.535306\pi\)
−0.110690 + 0.993855i \(0.535306\pi\)
\(12\) 4.47442i 0.372869i
\(13\) 18.1491 1.39608 0.698041 0.716058i \(-0.254055\pi\)
0.698041 + 0.716058i \(0.254055\pi\)
\(14\) 32.3129 2.30806
\(15\) 5.55311 0.370207
\(16\) −2.56483 −0.160302
\(17\) −1.13567 −0.0668042 −0.0334021 0.999442i \(-0.510634\pi\)
−0.0334021 + 0.999442i \(0.510634\pi\)
\(18\) 27.0346i 1.50192i
\(19\) 12.3269i 0.648783i 0.945923 + 0.324391i \(0.105159\pi\)
−0.945923 + 0.324391i \(0.894841\pi\)
\(20\) 47.3314i 2.36657i
\(21\) −7.33937 −0.349494
\(22\) 7.76798i 0.353090i
\(23\) −24.2847 −1.05586 −0.527929 0.849288i \(-0.677031\pi\)
−0.527929 + 0.849288i \(0.677031\pi\)
\(24\) −5.02815 −0.209506
\(25\) −33.7420 −1.34968
\(26\) 57.8939i 2.22669i
\(27\) 12.6614i 0.468939i
\(28\) 62.5565i 2.23416i
\(29\) 35.5218i 1.22489i 0.790513 + 0.612445i \(0.209814\pi\)
−0.790513 + 0.612445i \(0.790186\pi\)
\(30\) 17.7139i 0.590465i
\(31\) −12.9823 −0.418783 −0.209391 0.977832i \(-0.567148\pi\)
−0.209391 + 0.977832i \(0.567148\pi\)
\(32\) 35.9408i 1.12315i
\(33\) 1.76438i 0.0534660i
\(34\) 3.62270i 0.106550i
\(35\) 77.6375 2.21821
\(36\) −52.3380 −1.45383
\(37\) 41.5116i 1.12193i −0.827838 0.560967i \(-0.810429\pi\)
0.827838 0.560967i \(-0.189571\pi\)
\(38\) 39.3216 1.03478
\(39\) 13.1497i 0.337172i
\(40\) 53.1889 1.32972
\(41\) −65.0667 −1.58699 −0.793496 0.608576i \(-0.791741\pi\)
−0.793496 + 0.608576i \(0.791741\pi\)
\(42\) 23.4120i 0.557427i
\(43\) 23.6064 35.9408i 0.548986 0.835832i
\(44\) 15.0385 0.341784
\(45\) 64.9556i 1.44346i
\(46\) 77.4662i 1.68405i
\(47\) 51.0402 1.08596 0.542981 0.839745i \(-0.317296\pi\)
0.542981 + 0.839745i \(0.317296\pi\)
\(48\) 1.85832i 0.0387150i
\(49\) −53.6110 −1.09410
\(50\) 107.634i 2.15268i
\(51\) 0.822839i 0.0161341i
\(52\) −112.080 −2.15539
\(53\) 56.2026 1.06043 0.530214 0.847864i \(-0.322112\pi\)
0.530214 + 0.847864i \(0.322112\pi\)
\(54\) 40.3886 0.747937
\(55\) 18.6640i 0.339345i
\(56\) −70.2981 −1.25532
\(57\) −8.93130 −0.156689
\(58\) 113.312 1.95365
\(59\) −88.8355 −1.50569 −0.752843 0.658200i \(-0.771318\pi\)
−0.752843 + 0.658200i \(0.771318\pi\)
\(60\) −34.2935 −0.571558
\(61\) 65.1393i 1.06786i 0.845529 + 0.533929i \(0.179285\pi\)
−0.845529 + 0.533929i \(0.820715\pi\)
\(62\) 41.4123i 0.667940i
\(63\) 85.8497i 1.36269i
\(64\) 104.389 1.63107
\(65\) 139.101i 2.14001i
\(66\) −5.62821 −0.0852759
\(67\) 45.3618 0.677042 0.338521 0.940959i \(-0.390073\pi\)
0.338521 + 0.940959i \(0.390073\pi\)
\(68\) 7.01339 0.103138
\(69\) 17.5952i 0.255004i
\(70\) 247.657i 3.53796i
\(71\) 63.7983i 0.898567i −0.893389 0.449284i \(-0.851679\pi\)
0.893389 0.449284i \(-0.148321\pi\)
\(72\) 58.8151i 0.816876i
\(73\) 8.80247i 0.120582i −0.998181 0.0602909i \(-0.980797\pi\)
0.998181 0.0602909i \(-0.0192028\pi\)
\(74\) −132.418 −1.78944
\(75\) 24.4474i 0.325966i
\(76\) 76.1251i 1.00165i
\(77\) 24.6676i 0.320358i
\(78\) 41.9464 0.537775
\(79\) 31.8496 0.403159 0.201580 0.979472i \(-0.435393\pi\)
0.201580 + 0.979472i \(0.435393\pi\)
\(80\) 19.6577i 0.245721i
\(81\) 67.1017 0.828417
\(82\) 207.557i 2.53118i
\(83\) −68.4740 −0.824988 −0.412494 0.910960i \(-0.635342\pi\)
−0.412494 + 0.910960i \(0.635342\pi\)
\(84\) 45.3246 0.539579
\(85\) 8.70417i 0.102402i
\(86\) −114.648 75.3023i −1.33312 0.875608i
\(87\) −25.7370 −0.295827
\(88\) 16.8996i 0.192041i
\(89\) 5.90432i 0.0663406i 0.999450 + 0.0331703i \(0.0105604\pi\)
−0.999450 + 0.0331703i \(0.989440\pi\)
\(90\) −207.203 −2.30225
\(91\) 183.845i 2.02027i
\(92\) 149.971 1.63012
\(93\) 9.40616i 0.101142i
\(94\) 162.814i 1.73206i
\(95\) 94.4773 0.994498
\(96\) −26.0405 −0.271255
\(97\) −100.657 −1.03770 −0.518849 0.854866i \(-0.673639\pi\)
−0.518849 + 0.854866i \(0.673639\pi\)
\(98\) 171.015i 1.74505i
\(99\) −20.6382 −0.208466
\(100\) 208.376 2.08376
\(101\) 13.7062 0.135705 0.0678525 0.997695i \(-0.478385\pi\)
0.0678525 + 0.997695i \(0.478385\pi\)
\(102\) −2.62478 −0.0257332
\(103\) −96.0402 −0.932429 −0.466214 0.884672i \(-0.654382\pi\)
−0.466214 + 0.884672i \(0.654382\pi\)
\(104\) 125.951i 1.21107i
\(105\) 56.2514i 0.535728i
\(106\) 179.282i 1.69134i
\(107\) −2.08036 −0.0194427 −0.00972133 0.999953i \(-0.503094\pi\)
−0.00972133 + 0.999953i \(0.503094\pi\)
\(108\) 78.1907i 0.723988i
\(109\) −53.1078 −0.487228 −0.243614 0.969872i \(-0.578333\pi\)
−0.243614 + 0.969872i \(0.578333\pi\)
\(110\) 59.5364 0.541240
\(111\) 30.0768 0.270962
\(112\) 25.9810i 0.231973i
\(113\) 28.8791i 0.255568i 0.991802 + 0.127784i \(0.0407864\pi\)
−0.991802 + 0.127784i \(0.959214\pi\)
\(114\) 28.4901i 0.249913i
\(115\) 186.126i 1.61849i
\(116\) 219.367i 1.89109i
\(117\) 153.814 1.31465
\(118\) 283.378i 2.40150i
\(119\) 11.5040i 0.0966725i
\(120\) 38.5375i 0.321146i
\(121\) −115.070 −0.950991
\(122\) 207.789 1.70319
\(123\) 47.1433i 0.383279i
\(124\) 80.1726 0.646553
\(125\) 67.0020i 0.536016i
\(126\) 273.853 2.17344
\(127\) 148.673 1.17066 0.585328 0.810797i \(-0.300966\pi\)
0.585328 + 0.810797i \(0.300966\pi\)
\(128\) 189.227i 1.47834i
\(129\) 26.0405 + 17.1037i 0.201864 + 0.132587i
\(130\) −443.719 −3.41322
\(131\) 157.214i 1.20011i −0.799960 0.600054i \(-0.795146\pi\)
0.799960 0.600054i \(-0.204854\pi\)
\(132\) 10.8960i 0.0825453i
\(133\) −124.868 −0.938854
\(134\) 144.700i 1.07985i
\(135\) 97.0409 0.718821
\(136\) 7.88133i 0.0579510i
\(137\) 121.604i 0.887618i −0.896122 0.443809i \(-0.853627\pi\)
0.896122 0.443809i \(-0.146373\pi\)
\(138\) −56.1273 −0.406719
\(139\) −27.8992 −0.200714 −0.100357 0.994952i \(-0.531998\pi\)
−0.100357 + 0.994952i \(0.531998\pi\)
\(140\) −479.454 −3.42467
\(141\) 36.9806i 0.262274i
\(142\) −203.511 −1.43318
\(143\) −44.1961 −0.309063
\(144\) −21.7370 −0.150952
\(145\) 272.251 1.87759
\(146\) −28.0791 −0.192323
\(147\) 38.8433i 0.264240i
\(148\) 256.357i 1.73214i
\(149\) 212.121i 1.42363i 0.702366 + 0.711816i \(0.252127\pi\)
−0.702366 + 0.711816i \(0.747873\pi\)
\(150\) −77.9852 −0.519901
\(151\) 108.847i 0.720842i −0.932790 0.360421i \(-0.882633\pi\)
0.932790 0.360421i \(-0.117367\pi\)
\(152\) −85.5460 −0.562802
\(153\) −9.62487 −0.0629077
\(154\) −78.6874 −0.510957
\(155\) 99.5005i 0.641938i
\(156\) 81.2066i 0.520555i
\(157\) 106.772i 0.680075i 0.940412 + 0.340038i \(0.110440\pi\)
−0.940412 + 0.340038i \(0.889560\pi\)
\(158\) 101.597i 0.643021i
\(159\) 40.7210i 0.256107i
\(160\) 275.462 1.72164
\(161\) 245.997i 1.52793i
\(162\) 214.049i 1.32129i
\(163\) 202.231i 1.24068i −0.784334 0.620339i \(-0.786995\pi\)
0.784334 0.620339i \(-0.213005\pi\)
\(164\) 401.822 2.45013
\(165\) −13.5228 −0.0819562
\(166\) 218.426i 1.31582i
\(167\) −41.0703 −0.245930 −0.122965 0.992411i \(-0.539240\pi\)
−0.122965 + 0.992411i \(0.539240\pi\)
\(168\) 50.9337i 0.303177i
\(169\) 160.389 0.949045
\(170\) 27.7656 0.163327
\(171\) 104.471i 0.610940i
\(172\) −145.782 + 221.954i −0.847571 + 1.29043i
\(173\) −24.1006 −0.139310 −0.0696549 0.997571i \(-0.522190\pi\)
−0.0696549 + 0.997571i \(0.522190\pi\)
\(174\) 82.0986i 0.471831i
\(175\) 341.797i 1.95313i
\(176\) 6.24580 0.0354875
\(177\) 64.3648i 0.363643i
\(178\) 18.8343 0.105810
\(179\) 83.0659i 0.464055i 0.972709 + 0.232028i \(0.0745360\pi\)
−0.972709 + 0.232028i \(0.925464\pi\)
\(180\) 401.136i 2.22853i
\(181\) −112.273 −0.620291 −0.310145 0.950689i \(-0.600378\pi\)
−0.310145 + 0.950689i \(0.600378\pi\)
\(182\) 586.449 3.22225
\(183\) −47.1960 −0.257902
\(184\) 168.531i 0.915930i
\(185\) −318.159 −1.71978
\(186\) −30.0048 −0.161316
\(187\) 2.76556 0.0147891
\(188\) −315.201 −1.67660
\(189\) −128.256 −0.678602
\(190\) 301.374i 1.58618i
\(191\) 43.7078i 0.228836i −0.993433 0.114418i \(-0.963500\pi\)
0.993433 0.114418i \(-0.0365004\pi\)
\(192\) 75.6336i 0.393925i
\(193\) 236.100 1.22332 0.611659 0.791122i \(-0.290503\pi\)
0.611659 + 0.791122i \(0.290503\pi\)
\(194\) 321.086i 1.65508i
\(195\) 100.784 0.516840
\(196\) 331.077 1.68917
\(197\) 350.134 1.77733 0.888665 0.458557i \(-0.151634\pi\)
0.888665 + 0.458557i \(0.151634\pi\)
\(198\) 65.8340i 0.332495i
\(199\) 353.573i 1.77675i 0.459122 + 0.888373i \(0.348164\pi\)
−0.459122 + 0.888373i \(0.651836\pi\)
\(200\) 234.163i 1.17081i
\(201\) 32.8664i 0.163514i
\(202\) 43.7216i 0.216444i
\(203\) −359.826 −1.77254
\(204\) 5.08148i 0.0249092i
\(205\) 498.693i 2.43265i
\(206\) 306.360i 1.48718i
\(207\) −205.814 −0.994272
\(208\) −46.5493 −0.223794
\(209\) 30.0180i 0.143627i
\(210\) 179.437 0.854462
\(211\) 281.519i 1.33421i −0.744962 0.667107i \(-0.767532\pi\)
0.744962 0.667107i \(-0.232468\pi\)
\(212\) −347.082 −1.63718
\(213\) 46.2243 0.217016
\(214\) 6.63618i 0.0310102i
\(215\) −275.462 180.927i −1.28122 0.841522i
\(216\) −87.8672 −0.406793
\(217\) 131.507i 0.606021i
\(218\) 169.409i 0.777107i
\(219\) 6.37774 0.0291221
\(220\) 115.260i 0.523910i
\(221\) −20.6114 −0.0932642
\(222\) 95.9423i 0.432172i
\(223\) 95.1942i 0.426880i −0.976956 0.213440i \(-0.931533\pi\)
0.976956 0.213440i \(-0.0684668\pi\)
\(224\) −364.070 −1.62531
\(225\) −285.965 −1.27096
\(226\) 92.1219 0.407619
\(227\) 106.481i 0.469079i −0.972107 0.234540i \(-0.924642\pi\)
0.972107 0.234540i \(-0.0753583\pi\)
\(228\) 55.1556 0.241911
\(229\) 170.352 0.743896 0.371948 0.928254i \(-0.378690\pi\)
0.371948 + 0.928254i \(0.378690\pi\)
\(230\) 593.727 2.58142
\(231\) 17.8726 0.0773707
\(232\) −246.514 −1.06256
\(233\) 55.4970i 0.238184i −0.992883 0.119092i \(-0.962002\pi\)
0.992883 0.119092i \(-0.0379984\pi\)
\(234\) 490.654i 2.09681i
\(235\) 391.189i 1.66463i
\(236\) 548.608 2.32461
\(237\) 23.0763i 0.0973682i
\(238\) −36.6969 −0.154188
\(239\) −20.7695 −0.0869017 −0.0434509 0.999056i \(-0.513835\pi\)
−0.0434509 + 0.999056i \(0.513835\pi\)
\(240\) −14.2428 −0.0593449
\(241\) 303.282i 1.25843i −0.777231 0.629216i \(-0.783376\pi\)
0.777231 0.629216i \(-0.216624\pi\)
\(242\) 367.063i 1.51679i
\(243\) 162.570i 0.669012i
\(244\) 402.271i 1.64865i
\(245\) 410.893i 1.67711i
\(246\) −150.383 −0.611314
\(247\) 223.721i 0.905754i
\(248\) 90.0943i 0.363283i
\(249\) 49.6121i 0.199245i
\(250\) 213.731 0.854922
\(251\) −7.25467 −0.0289031 −0.0144515 0.999896i \(-0.504600\pi\)
−0.0144515 + 0.999896i \(0.504600\pi\)
\(252\) 530.169i 2.10384i
\(253\) 59.1375 0.233745
\(254\) 474.255i 1.86715i
\(255\) −6.30651 −0.0247314
\(256\) −186.065 −0.726816
\(257\) 316.956i 1.23329i 0.787241 + 0.616645i \(0.211509\pi\)
−0.787241 + 0.616645i \(0.788491\pi\)
\(258\) 54.5595 83.0669i 0.211471 0.321965i
\(259\) 420.500 1.62355
\(260\) 859.022i 3.30393i
\(261\) 301.049i 1.15344i
\(262\) −501.499 −1.91412
\(263\) 229.845i 0.873934i 0.899478 + 0.436967i \(0.143947\pi\)
−0.899478 + 0.436967i \(0.856053\pi\)
\(264\) 12.2444 0.0463804
\(265\) 430.756i 1.62549i
\(266\) 398.317i 1.49743i
\(267\) −4.27791 −0.0160221
\(268\) −280.134 −1.04528
\(269\) 285.119 1.05992 0.529961 0.848022i \(-0.322206\pi\)
0.529961 + 0.848022i \(0.322206\pi\)
\(270\) 309.552i 1.14649i
\(271\) 78.3270 0.289030 0.144515 0.989503i \(-0.453838\pi\)
0.144515 + 0.989503i \(0.453838\pi\)
\(272\) 2.91281 0.0107088
\(273\) −133.203 −0.487922
\(274\) −387.905 −1.41571
\(275\) 82.1677 0.298791
\(276\) 108.660i 0.393696i
\(277\) 119.631i 0.431880i −0.976407 0.215940i \(-0.930718\pi\)
0.976407 0.215940i \(-0.0692815\pi\)
\(278\) 88.9960i 0.320129i
\(279\) −110.025 −0.394356
\(280\) 538.789i 1.92424i
\(281\) −150.423 −0.535314 −0.267657 0.963514i \(-0.586249\pi\)
−0.267657 + 0.963514i \(0.586249\pi\)
\(282\) 117.965 0.418315
\(283\) −261.144 −0.922771 −0.461385 0.887200i \(-0.652647\pi\)
−0.461385 + 0.887200i \(0.652647\pi\)
\(284\) 393.989i 1.38729i
\(285\) 68.4525i 0.240184i
\(286\) 140.982i 0.492943i
\(287\) 659.106i 2.29654i
\(288\) 304.600i 1.05764i
\(289\) −287.710 −0.995537
\(290\) 868.458i 2.99468i
\(291\) 72.9297i 0.250618i
\(292\) 54.3601i 0.186165i
\(293\) 358.409 1.22324 0.611619 0.791152i \(-0.290518\pi\)
0.611619 + 0.791152i \(0.290518\pi\)
\(294\) −123.907 −0.421451
\(295\) 680.865i 2.30802i
\(296\) 288.082 0.973250
\(297\) 30.8326i 0.103813i
\(298\) 676.648 2.27063
\(299\) −440.745 −1.47406
\(300\) 150.976i 0.503254i
\(301\) 364.070 + 239.126i 1.20953 + 0.794438i
\(302\) −347.213 −1.14971
\(303\) 9.93068i 0.0327745i
\(304\) 31.6163i 0.104001i
\(305\) 499.250 1.63688
\(306\) 30.7025i 0.100335i
\(307\) 509.730 1.66036 0.830180 0.557496i \(-0.188238\pi\)
0.830180 + 0.557496i \(0.188238\pi\)
\(308\) 152.336i 0.494596i
\(309\) 69.5849i 0.225194i
\(310\) 317.398 1.02386
\(311\) −27.7820 −0.0893312 −0.0446656 0.999002i \(-0.514222\pi\)
−0.0446656 + 0.999002i \(0.514222\pi\)
\(312\) −91.2563 −0.292488
\(313\) 38.5686i 0.123222i −0.998100 0.0616111i \(-0.980376\pi\)
0.998100 0.0616111i \(-0.0196239\pi\)
\(314\) 340.593 1.08469
\(315\) 657.981 2.08883
\(316\) −196.688 −0.622432
\(317\) 85.8945 0.270961 0.135480 0.990780i \(-0.456742\pi\)
0.135480 + 0.990780i \(0.456742\pi\)
\(318\) 129.896 0.408480
\(319\) 86.5017i 0.271165i
\(320\) 800.069i 2.50022i
\(321\) 1.50731i 0.00469566i
\(322\) −784.710 −2.43699
\(323\) 13.9993i 0.0433414i
\(324\) −414.390 −1.27898
\(325\) −612.387 −1.88427
\(326\) −645.098 −1.97883
\(327\) 38.4787i 0.117672i
\(328\) 451.549i 1.37668i
\(329\) 517.022i 1.57150i
\(330\) 43.1365i 0.130717i
\(331\) 363.666i 1.09869i 0.835596 + 0.549345i \(0.185123\pi\)
−0.835596 + 0.549345i \(0.814877\pi\)
\(332\) 422.864 1.27369
\(333\) 351.813i 1.05649i
\(334\) 131.011i 0.392247i
\(335\) 347.668i 1.03782i
\(336\) 18.8242 0.0560245
\(337\) 8.64293 0.0256467 0.0128233 0.999918i \(-0.495918\pi\)
0.0128233 + 0.999918i \(0.495918\pi\)
\(338\) 511.626i 1.51369i
\(339\) −20.9241 −0.0617229
\(340\) 53.7530i 0.158097i
\(341\) 31.6140 0.0927098
\(342\) 333.253 0.974423
\(343\) 46.7084i 0.136176i
\(344\) 249.422 + 163.823i 0.725063 + 0.476231i
\(345\) −134.856 −0.390887
\(346\) 76.8788i 0.222193i
\(347\) 278.736i 0.803273i −0.915799 0.401636i \(-0.868442\pi\)
0.915799 0.401636i \(-0.131558\pi\)
\(348\) 158.940 0.456723
\(349\) 169.755i 0.486403i −0.969976 0.243201i \(-0.921802\pi\)
0.969976 0.243201i \(-0.0781976\pi\)
\(350\) −1090.30 −3.11515
\(351\) 229.792i 0.654677i
\(352\) 87.5219i 0.248642i
\(353\) 26.8357 0.0760219 0.0380109 0.999277i \(-0.487898\pi\)
0.0380109 + 0.999277i \(0.487898\pi\)
\(354\) −205.318 −0.579995
\(355\) −488.971 −1.37738
\(356\) 36.4624i 0.102422i
\(357\) 8.33512 0.0233477
\(358\) 264.973 0.740148
\(359\) 169.169 0.471223 0.235611 0.971847i \(-0.424291\pi\)
0.235611 + 0.971847i \(0.424291\pi\)
\(360\) 450.779 1.25216
\(361\) 209.048 0.579081
\(362\) 358.140i 0.989336i
\(363\) 83.3727i 0.229677i
\(364\) 1135.34i 3.11907i
\(365\) −67.4651 −0.184836
\(366\) 150.551i 0.411342i
\(367\) −540.524 −1.47282 −0.736409 0.676536i \(-0.763480\pi\)
−0.736409 + 0.676536i \(0.763480\pi\)
\(368\) 62.2862 0.169256
\(369\) −551.443 −1.49442
\(370\) 1014.90i 2.74297i
\(371\) 569.316i 1.53455i
\(372\) 58.0882i 0.156151i
\(373\) 26.7152i 0.0716226i 0.999359 + 0.0358113i \(0.0114015\pi\)
−0.999359 + 0.0358113i \(0.988598\pi\)
\(374\) 8.82188i 0.0235879i
\(375\) −48.5456 −0.129455
\(376\) 354.209i 0.942044i
\(377\) 644.688i 1.71005i
\(378\) 409.125i 1.08234i
\(379\) 315.193 0.831644 0.415822 0.909446i \(-0.363494\pi\)
0.415822 + 0.909446i \(0.363494\pi\)
\(380\) −583.449 −1.53539
\(381\) 107.720i 0.282729i
\(382\) −139.424 −0.364984
\(383\) 131.099i 0.342295i 0.985245 + 0.171148i \(0.0547475\pi\)
−0.985245 + 0.171148i \(0.945252\pi\)
\(384\) 137.103 0.357038
\(385\) −189.061 −0.491066
\(386\) 753.139i 1.95114i
\(387\) 200.065 304.600i 0.516964 0.787079i
\(388\) 621.610 1.60209
\(389\) 110.050i 0.282904i 0.989945 + 0.141452i \(0.0451771\pi\)
−0.989945 + 0.141452i \(0.954823\pi\)
\(390\) 321.491i 0.824337i
\(391\) 27.5795 0.0705358
\(392\) 372.050i 0.949106i
\(393\) 113.908 0.289841
\(394\) 1116.90i 2.83476i
\(395\) 244.106i 0.617989i
\(396\) 127.452 0.321848
\(397\) 68.3215 0.172094 0.0860472 0.996291i \(-0.472576\pi\)
0.0860472 + 0.996291i \(0.472576\pi\)
\(398\) 1127.87 2.83383
\(399\) 90.4715i 0.226746i
\(400\) 86.5426 0.216356
\(401\) −675.508 −1.68456 −0.842279 0.539042i \(-0.818787\pi\)
−0.842279 + 0.539042i \(0.818787\pi\)
\(402\) 104.841 0.260798
\(403\) −235.616 −0.584655
\(404\) −84.6433 −0.209513
\(405\) 514.290i 1.26985i
\(406\) 1147.81i 2.82713i
\(407\) 101.088i 0.248373i
\(408\) 5.71034 0.0139959
\(409\) 1.76834i 0.00432356i 0.999998 + 0.00216178i \(0.000688116\pi\)
−0.999998 + 0.00216178i \(0.999312\pi\)
\(410\) 1590.79 3.87997
\(411\) 88.1066 0.214371
\(412\) 593.100 1.43956
\(413\) 899.878i 2.17888i
\(414\) 656.529i 1.58582i
\(415\) 524.808i 1.26460i
\(416\) 652.291i 1.56801i
\(417\) 20.2141i 0.0484749i
\(418\) −95.7549 −0.229079
\(419\) 444.028i 1.05973i 0.848081 + 0.529867i \(0.177758\pi\)
−0.848081 + 0.529867i \(0.822242\pi\)
\(420\) 347.383i 0.827103i
\(421\) 141.195i 0.335381i −0.985840 0.167690i \(-0.946369\pi\)
0.985840 0.167690i \(-0.0536309\pi\)
\(422\) −898.022 −2.12801
\(423\) 432.568 1.02262
\(424\) 390.035i 0.919894i
\(425\) 38.3199 0.0901645
\(426\) 147.452i 0.346131i
\(427\) −659.843 −1.54530
\(428\) 12.8474 0.0300173
\(429\) 32.0218i 0.0746429i
\(430\) −577.142 + 878.700i −1.34219 + 2.04349i
\(431\) 302.066 0.700849 0.350424 0.936591i \(-0.386037\pi\)
0.350424 + 0.936591i \(0.386037\pi\)
\(432\) 32.4742i 0.0751718i
\(433\) 380.497i 0.878747i −0.898304 0.439374i \(-0.855200\pi\)
0.898304 0.439374i \(-0.144800\pi\)
\(434\) −419.495 −0.966578
\(435\) 197.257i 0.453464i
\(436\) 327.970 0.752224
\(437\) 299.355i 0.685022i
\(438\) 20.3444i 0.0464485i
\(439\) 558.769 1.27282 0.636412 0.771350i \(-0.280418\pi\)
0.636412 + 0.771350i \(0.280418\pi\)
\(440\) −129.524 −0.294373
\(441\) −454.356 −1.03029
\(442\) 65.7485i 0.148752i
\(443\) −346.462 −0.782082 −0.391041 0.920373i \(-0.627885\pi\)
−0.391041 + 0.920373i \(0.627885\pi\)
\(444\) −185.740 −0.418334
\(445\) 45.2527 0.101691
\(446\) −303.661 −0.680855
\(447\) −153.690 −0.343826
\(448\) 1057.43i 2.36033i
\(449\) 250.699i 0.558350i −0.960240 0.279175i \(-0.909939\pi\)
0.960240 0.279175i \(-0.0900609\pi\)
\(450\) 912.204i 2.02712i
\(451\) 158.448 0.351327
\(452\) 178.344i 0.394567i
\(453\) 78.8640 0.174093
\(454\) −339.665 −0.748161
\(455\) 1409.05 3.09681
\(456\) 61.9814i 0.135924i
\(457\) 745.356i 1.63098i −0.578773 0.815488i \(-0.696468\pi\)
0.578773 0.815488i \(-0.303532\pi\)
\(458\) 543.408i 1.18648i
\(459\) 14.3791i 0.0313271i
\(460\) 1149.43i 2.49876i
\(461\) 6.73204 0.0146031 0.00730156 0.999973i \(-0.497676\pi\)
0.00730156 + 0.999973i \(0.497676\pi\)
\(462\) 57.0121i 0.123403i
\(463\) 448.198i 0.968031i −0.875059 0.484016i \(-0.839178\pi\)
0.875059 0.484016i \(-0.160822\pi\)
\(464\) 91.1074i 0.196352i
\(465\) −72.0920 −0.155037
\(466\) −177.031 −0.379894
\(467\) 506.048i 1.08361i 0.840503 + 0.541807i \(0.182260\pi\)
−0.840503 + 0.541807i \(0.817740\pi\)
\(468\) −949.886 −2.02967
\(469\) 459.502i 0.979749i
\(470\) −1247.86 −2.65502
\(471\) −77.3603 −0.164247
\(472\) 616.500i 1.30614i
\(473\) −57.4856 + 87.5219i −0.121534 + 0.185036i
\(474\) 73.6112 0.155298
\(475\) 415.934i 0.875650i
\(476\) 71.0436i 0.149251i
\(477\) 476.320 0.998574
\(478\) 66.2529i 0.138604i
\(479\) −772.714 −1.61318 −0.806591 0.591110i \(-0.798690\pi\)
−0.806591 + 0.591110i \(0.798690\pi\)
\(480\) 199.583i 0.415798i
\(481\) 753.397i 1.56631i
\(482\) −967.443 −2.00714
\(483\) 178.235 0.369016
\(484\) 710.620 1.46822
\(485\) 771.467i 1.59065i
\(486\) 518.584 1.06705
\(487\) −762.454 −1.56561 −0.782807 0.622265i \(-0.786213\pi\)
−0.782807 + 0.622265i \(0.786213\pi\)
\(488\) −452.054 −0.926340
\(489\) 146.524 0.299640
\(490\) 1310.71 2.67492
\(491\) 928.398i 1.89083i −0.325868 0.945415i \(-0.605657\pi\)
0.325868 0.945415i \(-0.394343\pi\)
\(492\) 291.136i 0.591739i
\(493\) 40.3411i 0.0818279i
\(494\) 713.651 1.44464
\(495\) 158.178i 0.319551i
\(496\) 33.2973 0.0671317
\(497\) 646.258 1.30032
\(498\) −158.258 −0.317788
\(499\) 669.978i 1.34264i 0.741167 + 0.671320i \(0.234272\pi\)
−0.741167 + 0.671320i \(0.765728\pi\)
\(500\) 413.774i 0.827548i
\(501\) 29.7570i 0.0593952i
\(502\) 23.1418i 0.0460991i
\(503\) 274.168i 0.545065i −0.962147 0.272532i \(-0.912139\pi\)
0.962147 0.272532i \(-0.0878612\pi\)
\(504\) −595.780 −1.18210
\(505\) 105.049i 0.208018i
\(506\) 188.643i 0.372813i
\(507\) 116.208i 0.229207i
\(508\) −918.139 −1.80736
\(509\) 703.988 1.38308 0.691540 0.722338i \(-0.256933\pi\)
0.691540 + 0.722338i \(0.256933\pi\)
\(510\) 20.1172i 0.0394456i
\(511\) 89.1665 0.174494
\(512\) 163.380i 0.319101i
\(513\) −156.075 −0.304239
\(514\) 1011.06 1.96704
\(515\) 736.084i 1.42929i
\(516\) −160.814 105.625i −0.311655 0.204699i
\(517\) −124.292 −0.240409
\(518\) 1341.36i 2.58950i
\(519\) 17.4618i 0.0336451i
\(520\) 965.330 1.85640
\(521\) 588.189i 1.12896i −0.825446 0.564480i \(-0.809077\pi\)
0.825446 0.564480i \(-0.190923\pi\)
\(522\) 960.320 1.83969
\(523\) 743.907i 1.42238i 0.702998 + 0.711192i \(0.251844\pi\)
−0.702998 + 0.711192i \(0.748156\pi\)
\(524\) 970.882i 1.85283i
\(525\) 247.645 0.471706
\(526\) 733.184 1.39389
\(527\) 14.7436 0.0279765
\(528\) 4.52532i 0.00857069i
\(529\) 60.7485 0.114837
\(530\) −1374.07 −2.59259
\(531\) −752.885 −1.41786
\(532\) 771.125 1.44948
\(533\) −1180.90 −2.21557
\(534\) 13.6462i 0.0255546i
\(535\) 15.9446i 0.0298030i
\(536\) 314.802i 0.587317i
\(537\) −60.1845 −0.112075
\(538\) 909.506i 1.69053i
\(539\) 130.552 0.242212
\(540\) −599.280 −1.10978
\(541\) −2.77685 −0.00513282 −0.00256641 0.999997i \(-0.500817\pi\)
−0.00256641 + 0.999997i \(0.500817\pi\)
\(542\) 249.856i 0.460990i
\(543\) 81.3459i 0.149808i
\(544\) 40.8169i 0.0750311i
\(545\) 407.036i 0.746856i
\(546\) 424.905i 0.778214i
\(547\) 700.748 1.28108 0.640538 0.767927i \(-0.278711\pi\)
0.640538 + 0.767927i \(0.278711\pi\)
\(548\) 750.968i 1.37038i
\(549\) 552.059i 1.00557i
\(550\) 262.108i 0.476559i
\(551\) −437.873 −0.794688
\(552\) 122.107 0.221209
\(553\) 322.627i 0.583412i
\(554\) −381.612 −0.688830
\(555\) 230.518i 0.415349i
\(556\) 172.293 0.309879
\(557\) −590.822 −1.06072 −0.530361 0.847772i \(-0.677944\pi\)
−0.530361 + 0.847772i \(0.677944\pi\)
\(558\) 350.971i 0.628980i
\(559\) 428.434 652.291i 0.766429 1.16689i
\(560\) −199.127 −0.355584
\(561\) 2.00375i 0.00357175i
\(562\) 479.837i 0.853803i
\(563\) −306.648 −0.544668 −0.272334 0.962203i \(-0.587795\pi\)
−0.272334 + 0.962203i \(0.587795\pi\)
\(564\) 228.375i 0.404921i
\(565\) 221.339 0.391751
\(566\) 833.027i 1.47178i
\(567\) 679.721i 1.19880i
\(568\) 442.747 0.779484
\(569\) −5.67367 −0.00997130 −0.00498565 0.999988i \(-0.501587\pi\)
−0.00498565 + 0.999988i \(0.501587\pi\)
\(570\) 218.357 0.383083
\(571\) 811.264i 1.42078i 0.703810 + 0.710389i \(0.251481\pi\)
−0.703810 + 0.710389i \(0.748519\pi\)
\(572\) 272.935 0.477159
\(573\) 31.6680 0.0552670
\(574\) −2102.49 −3.66288
\(575\) 819.417 1.42507
\(576\) 884.698 1.53593
\(577\) 976.820i 1.69293i 0.532445 + 0.846464i \(0.321273\pi\)
−0.532445 + 0.846464i \(0.678727\pi\)
\(578\) 917.771i 1.58784i
\(579\) 171.064i 0.295447i
\(580\) −1681.30 −2.89879
\(581\) 693.622i 1.19384i
\(582\) −232.639 −0.399724
\(583\) −136.863 −0.234757
\(584\) 61.0874 0.104602
\(585\) 1178.88i 2.01518i
\(586\) 1143.29i 1.95101i
\(587\) 681.557i 1.16109i −0.814230 0.580543i \(-0.802840\pi\)
0.814230 0.580543i \(-0.197160\pi\)
\(588\) 239.878i 0.407957i
\(589\) 160.031i 0.271699i
\(590\) 2171.90 3.68119
\(591\) 253.686i 0.429248i
\(592\) 106.470i 0.179848i
\(593\) 1030.13i 1.73715i 0.495561 + 0.868573i \(0.334962\pi\)
−0.495561 + 0.868573i \(0.665038\pi\)
\(594\) −98.3532 −0.165578
\(595\) −88.1708 −0.148186
\(596\) 1309.96i 2.19793i
\(597\) −256.177 −0.429107
\(598\) 1405.94i 2.35107i
\(599\) 1028.30 1.71669 0.858345 0.513073i \(-0.171493\pi\)
0.858345 + 0.513073i \(0.171493\pi\)
\(600\) 169.660 0.282767
\(601\) 655.529i 1.09073i −0.838198 0.545365i \(-0.816391\pi\)
0.838198 0.545365i \(-0.183609\pi\)
\(602\) 762.790 1161.35i 1.26709 1.92915i
\(603\) 384.443 0.637551
\(604\) 672.190i 1.11290i
\(605\) 881.935i 1.45774i
\(606\) 31.6780 0.0522739
\(607\) 1016.42i 1.67450i 0.546822 + 0.837249i \(0.315837\pi\)
−0.546822 + 0.837249i \(0.684163\pi\)
\(608\) −443.037 −0.728680
\(609\) 260.708i 0.428092i
\(610\) 1592.56i 2.61076i
\(611\) 926.332 1.51609
\(612\) 59.4388 0.0971223
\(613\) −1029.51 −1.67946 −0.839728 0.543007i \(-0.817286\pi\)
−0.839728 + 0.543007i \(0.817286\pi\)
\(614\) 1626.00i 2.64820i
\(615\) −361.322 −0.587516
\(616\) 171.188 0.277903
\(617\) 426.603 0.691415 0.345708 0.938342i \(-0.387639\pi\)
0.345708 + 0.938342i \(0.387639\pi\)
\(618\) −221.970 −0.359174
\(619\) −503.515 −0.813432 −0.406716 0.913555i \(-0.633326\pi\)
−0.406716 + 0.913555i \(0.633326\pi\)
\(620\) 614.470i 0.991080i
\(621\) 307.478i 0.495133i
\(622\) 88.6222i 0.142479i
\(623\) −59.8090 −0.0960016
\(624\) 33.7268i 0.0540493i
\(625\) −330.025 −0.528041
\(626\) −123.030 −0.196534
\(627\) 21.7492 0.0346878
\(628\) 659.374i 1.04996i
\(629\) 47.1436i 0.0749500i
\(630\) 2098.90i 3.33159i
\(631\) 299.884i 0.475252i 0.971357 + 0.237626i \(0.0763692\pi\)
−0.971357 + 0.237626i \(0.923631\pi\)
\(632\) 221.030i 0.349730i
\(633\) 203.972 0.322230
\(634\) 273.996i 0.432170i
\(635\) 1139.48i 1.79446i
\(636\) 251.474i 0.395400i
\(637\) −972.990 −1.52746
\(638\) −275.933 −0.432497
\(639\) 540.693i 0.846155i
\(640\) −1450.30 −2.26610
\(641\) 724.346i 1.13002i 0.825082 + 0.565012i \(0.191129\pi\)
−0.825082 + 0.565012i \(0.808871\pi\)
\(642\) −4.80817 −0.00748937
\(643\) 743.353 1.15607 0.578035 0.816012i \(-0.303820\pi\)
0.578035 + 0.816012i \(0.303820\pi\)
\(644\) 1519.17i 2.35896i
\(645\) 131.089 199.583i 0.203239 0.309431i
\(646\) −44.6565 −0.0691277
\(647\) 61.7177i 0.0953905i 0.998862 + 0.0476953i \(0.0151876\pi\)
−0.998862 + 0.0476953i \(0.984812\pi\)
\(648\) 465.672i 0.718630i
\(649\) 216.330 0.333328
\(650\) 1953.46i 3.00532i
\(651\) 95.2817 0.146362
\(652\) 1248.88i 1.91547i
\(653\) 422.488i 0.646996i 0.946229 + 0.323498i \(0.104859\pi\)
−0.946229 + 0.323498i \(0.895141\pi\)
\(654\) −122.744 −0.187681
\(655\) −1204.94 −1.83960
\(656\) 166.885 0.254398
\(657\) 74.6013i 0.113548i
\(658\) 1649.26 2.50647
\(659\) −620.921 −0.942217 −0.471108 0.882075i \(-0.656146\pi\)
−0.471108 + 0.882075i \(0.656146\pi\)
\(660\) 83.5105 0.126531
\(661\) 496.134 0.750581 0.375291 0.926907i \(-0.377543\pi\)
0.375291 + 0.926907i \(0.377543\pi\)
\(662\) 1160.06 1.75236
\(663\) 14.9338i 0.0225245i
\(664\) 475.196i 0.715656i
\(665\) 957.027i 1.43914i
\(666\) −1122.25 −1.68506
\(667\) 862.638i 1.29331i
\(668\) 253.631 0.379687
\(669\) 68.9719 0.103097
\(670\) −1109.03 −1.65527
\(671\) 158.625i 0.236402i
\(672\) 263.783i 0.392534i
\(673\) 453.069i 0.673209i 0.941646 + 0.336604i \(0.109278\pi\)
−0.941646 + 0.336604i \(0.890722\pi\)
\(674\) 27.5702i 0.0409053i
\(675\) 427.220i 0.632918i
\(676\) −990.487 −1.46522
\(677\) 233.751i 0.345275i 0.984985 + 0.172638i \(0.0552289\pi\)
−0.984985 + 0.172638i \(0.944771\pi\)
\(678\) 66.7459i 0.0984453i
\(679\) 1019.62i 1.50165i
\(680\) −60.4052 −0.0888312
\(681\) 77.1497 0.113289
\(682\) 100.846i 0.147868i
\(683\) 578.370 0.846808 0.423404 0.905941i \(-0.360835\pi\)
0.423404 + 0.905941i \(0.360835\pi\)
\(684\) 645.164i 0.943222i
\(685\) −932.011 −1.36060
\(686\) −148.996 −0.217195
\(687\) 123.427i 0.179660i
\(688\) −60.5463 + 92.1819i −0.0880034 + 0.133985i
\(689\) 1020.03 1.48044
\(690\) 430.178i 0.623447i
\(691\) 127.474i 0.184477i −0.995737 0.0922387i \(-0.970598\pi\)
0.995737 0.0922387i \(-0.0294023\pi\)
\(692\) 148.834 0.215078
\(693\) 209.059i 0.301672i
\(694\) −889.142 −1.28118
\(695\) 213.829i 0.307667i
\(696\) 178.609i 0.256622i
\(697\) 73.8944 0.106018
\(698\) −541.502 −0.775791
\(699\) 40.2097 0.0575247
\(700\) 2110.78i 3.01541i
\(701\) 126.686 0.180721 0.0903606 0.995909i \(-0.471198\pi\)
0.0903606 + 0.995909i \(0.471198\pi\)
\(702\) 733.016 1.04418
\(703\) 511.708 0.727892
\(704\) −254.204 −0.361085
\(705\) 283.432 0.402031
\(706\) 85.6036i 0.121252i
\(707\) 138.840i 0.196379i
\(708\) 397.488i 0.561423i
\(709\) 733.535 1.03461 0.517303 0.855803i \(-0.326936\pi\)
0.517303 + 0.855803i \(0.326936\pi\)
\(710\) 1559.78i 2.19687i
\(711\) 269.926 0.379643
\(712\) −40.9748 −0.0575488
\(713\) 315.271 0.442175
\(714\) 26.5883i 0.0372385i
\(715\) 338.734i 0.473753i
\(716\) 512.977i 0.716449i
\(717\) 15.0483i 0.0209879i
\(718\) 539.634i 0.751580i
\(719\) −885.641 −1.23177 −0.615884 0.787837i \(-0.711201\pi\)
−0.615884 + 0.787837i \(0.711201\pi\)
\(720\) 166.600i 0.231389i
\(721\) 972.859i 1.34932i
\(722\) 666.846i 0.923609i
\(723\) 219.740 0.303928
\(724\) 693.344 0.957658
\(725\) 1198.58i 1.65321i
\(726\) −265.952 −0.366324
\(727\) 244.282i 0.336014i 0.985786 + 0.168007i \(0.0537331\pi\)
−0.985786 + 0.168007i \(0.946267\pi\)
\(728\) −1275.85 −1.75253
\(729\) 486.127 0.666841
\(730\) 215.208i 0.294805i
\(731\) −26.8091 + 40.8169i −0.0366746 + 0.0558371i
\(732\) 291.461 0.398171
\(733\) 1317.81i 1.79783i −0.438120 0.898917i \(-0.644355\pi\)
0.438120 0.898917i \(-0.355645\pi\)
\(734\) 1724.23i 2.34908i
\(735\) −297.708 −0.405045
\(736\) 872.812i 1.18589i
\(737\) −110.464 −0.149883
\(738\) 1759.05i 2.38354i
\(739\) 126.907i 0.171728i −0.996307 0.0858641i \(-0.972635\pi\)
0.996307 0.0858641i \(-0.0273651\pi\)
\(740\) 1964.80 2.65514
\(741\) −162.095 −0.218751
\(742\) 1816.07 2.44753
\(743\) 483.885i 0.651259i −0.945497 0.325629i \(-0.894424\pi\)
0.945497 0.325629i \(-0.105576\pi\)
\(744\) 65.2768 0.0877377
\(745\) 1625.77 2.18224
\(746\) 85.2192 0.114235
\(747\) −580.320 −0.776867
\(748\) −17.0788 −0.0228326
\(749\) 21.0735i 0.0281355i
\(750\) 154.856i 0.206475i
\(751\) 11.4506i 0.0152471i −0.999971 0.00762354i \(-0.997573\pi\)
0.999971 0.00762354i \(-0.00242667\pi\)
\(752\) −130.909 −0.174082
\(753\) 5.25629i 0.00698047i
\(754\) 2056.50 2.72745
\(755\) −834.241 −1.10495
\(756\) 792.050 1.04768
\(757\) 995.145i 1.31459i 0.753633 + 0.657295i \(0.228299\pi\)
−0.753633 + 0.657295i \(0.771701\pi\)
\(758\) 1005.44i 1.32644i
\(759\) 42.8474i 0.0564525i
\(760\) 655.653i 0.862701i
\(761\) 1067.64i 1.40295i 0.712695 + 0.701474i \(0.247474\pi\)
−0.712695 + 0.701474i \(0.752526\pi\)
\(762\) 343.616 0.450940
\(763\) 537.967i 0.705068i
\(764\) 269.919i 0.353297i
\(765\) 73.7682i 0.0964291i
\(766\) 418.195 0.545946
\(767\) −1612.28 −2.10206
\(768\) 134.811i 0.175535i
\(769\) −361.976 −0.470710 −0.235355 0.971909i \(-0.575625\pi\)
−0.235355 + 0.971909i \(0.575625\pi\)
\(770\) 603.087i 0.783230i
\(771\) −229.647 −0.297856
\(772\) −1458.05 −1.88866
\(773\) 579.373i 0.749513i −0.927123 0.374756i \(-0.877726\pi\)
0.927123 0.374756i \(-0.122274\pi\)
\(774\) −971.646 638.190i −1.25536 0.824535i
\(775\) 438.048 0.565224
\(776\) 698.537i 0.900176i
\(777\) 304.669i 0.392109i
\(778\) 351.049 0.451220
\(779\) 802.068i 1.02961i
\(780\) −622.395 −0.797942
\(781\) 155.360i 0.198924i
\(782\) 87.9762i 0.112502i
\(783\) −449.754 −0.574399
\(784\) 137.503 0.175387
\(785\) 818.335 1.04246
\(786\) 363.356i 0.462285i
\(787\) −1046.34 −1.32954 −0.664768 0.747050i \(-0.731470\pi\)
−0.664768 + 0.747050i \(0.731470\pi\)
\(788\) −2162.27 −2.74399
\(789\) −166.531 −0.211066
\(790\) −778.676 −0.985666
\(791\) −292.537 −0.369832
\(792\) 143.225i 0.180839i
\(793\) 1182.22i 1.49082i
\(794\) 217.940i 0.274483i
\(795\) 312.100 0.392578
\(796\) 2183.50i 2.74309i