Properties

Label 43.3.b.b.42.2
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 42.2
Root \(-2.58315i\) of defining polynomial
Character \(\chi\) \(=\) 43.42
Dual form 43.3.b.b.42.5

$q$-expansion

\(f(q)\) \(=\) \(q-2.58315i q^{2} -3.59415i q^{3} -2.67267 q^{4} +7.02284i q^{5} -9.28424 q^{6} -0.845536i q^{7} -3.42869i q^{8} -3.91793 q^{9} +O(q^{10})\) \(q-2.58315i q^{2} -3.59415i q^{3} -2.67267 q^{4} +7.02284i q^{5} -9.28424 q^{6} -0.845536i q^{7} -3.42869i q^{8} -3.91793 q^{9} +18.1411 q^{10} +14.5475 q^{11} +9.60599i q^{12} -15.5505 q^{13} -2.18415 q^{14} +25.2412 q^{15} -19.5475 q^{16} +6.95691 q^{17} +10.1206i q^{18} +30.8865i q^{19} -18.7698i q^{20} -3.03899 q^{21} -37.5784i q^{22} +17.5074 q^{23} -12.3232 q^{24} -24.3203 q^{25} +40.1692i q^{26} -18.2657i q^{27} +2.25984i q^{28} +7.86076i q^{29} -65.2017i q^{30} -57.7456 q^{31} +36.7794i q^{32} -52.2860i q^{33} -17.9708i q^{34} +5.93806 q^{35} +10.4713 q^{36} +32.5310i q^{37} +79.7846 q^{38} +55.8907i q^{39} +24.0791 q^{40} -18.4425 q^{41} +7.85016i q^{42} +(22.2772 - 36.7794i) q^{43} -38.8807 q^{44} -27.5150i q^{45} -45.2242i q^{46} -25.7806 q^{47} +70.2567i q^{48} +48.2851 q^{49} +62.8230i q^{50} -25.0042i q^{51} +41.5613 q^{52} -79.9247 q^{53} -47.1832 q^{54} +102.165i q^{55} -2.89908 q^{56} +111.011 q^{57} +20.3055 q^{58} +18.4243 q^{59} -67.4613 q^{60} -76.1107i q^{61} +149.166i q^{62} +3.31275i q^{63} +16.8168 q^{64} -109.208i q^{65} -135.063 q^{66} +9.00391 q^{67} -18.5935 q^{68} -62.9242i q^{69} -15.3389i q^{70} -51.6630i q^{71} +13.4333i q^{72} -77.4556i q^{73} +84.0326 q^{74} +87.4108i q^{75} -82.5496i q^{76} -12.3004i q^{77} +144.374 q^{78} +7.04014 q^{79} -137.279i q^{80} -100.911 q^{81} +47.6397i q^{82} +83.8385 q^{83} +8.12221 q^{84} +48.8573i q^{85} +(-95.0069 - 57.5454i) q^{86} +28.2528 q^{87} -49.8789i q^{88} +91.8322i q^{89} -71.0753 q^{90} +13.1485i q^{91} -46.7915 q^{92} +207.546i q^{93} +66.5953i q^{94} -216.911 q^{95} +132.191 q^{96} -155.976 q^{97} -124.728i q^{98} -56.9961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 16q^{4} + 6q^{6} - 36q^{9} + O(q^{10}) \) \( 6q - 16q^{4} + 6q^{6} - 36q^{9} - 2q^{10} + 38q^{11} + 30q^{13} + 36q^{14} + 28q^{15} - 68q^{16} - 20q^{17} + 56q^{21} - 80q^{23} + 62q^{24} - 84q^{25} - 112q^{31} + 208q^{35} - 122q^{36} + 170q^{38} + 206q^{40} - 172q^{41} + 10q^{43} - 36q^{44} + 30q^{47} - 6q^{49} - 120q^{52} - 110q^{53} - 284q^{54} - 264q^{56} + 420q^{57} + 430q^{58} - 12q^{59} - 232q^{60} + 100q^{64} - 144q^{66} - 70q^{67} - 50q^{68} - 50q^{74} + 620q^{78} + 178q^{79} + 382q^{81} + 10q^{83} + 172q^{84} - 372q^{86} - 510q^{87} - 796q^{90} + 150q^{92} - 130q^{95} + 362q^{96} - 380q^{97} - 466q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58315i 1.29158i −0.763517 0.645788i \(-0.776529\pi\)
0.763517 0.645788i \(-0.223471\pi\)
\(3\) 3.59415i 1.19805i −0.800730 0.599025i \(-0.795555\pi\)
0.800730 0.599025i \(-0.204445\pi\)
\(4\) −2.67267 −0.668168
\(5\) 7.02284i 1.40457i 0.711897 + 0.702284i \(0.247836\pi\)
−0.711897 + 0.702284i \(0.752164\pi\)
\(6\) −9.28424 −1.54737
\(7\) 0.845536i 0.120791i −0.998175 0.0603954i \(-0.980764\pi\)
0.998175 0.0603954i \(-0.0192362\pi\)
\(8\) 3.42869i 0.428586i
\(9\) −3.91793 −0.435325
\(10\) 18.1411 1.81411
\(11\) 14.5475 1.32250 0.661251 0.750165i \(-0.270026\pi\)
0.661251 + 0.750165i \(0.270026\pi\)
\(12\) 9.60599i 0.800499i
\(13\) −15.5505 −1.19619 −0.598095 0.801425i \(-0.704075\pi\)
−0.598095 + 0.801425i \(0.704075\pi\)
\(14\) −2.18415 −0.156011
\(15\) 25.2412 1.68274
\(16\) −19.5475 −1.22172
\(17\) 6.95691 0.409230 0.204615 0.978843i \(-0.434406\pi\)
0.204615 + 0.978843i \(0.434406\pi\)
\(18\) 10.1206i 0.562256i
\(19\) 30.8865i 1.62561i 0.582539 + 0.812803i \(0.302060\pi\)
−0.582539 + 0.812803i \(0.697940\pi\)
\(20\) 18.7698i 0.938488i
\(21\) −3.03899 −0.144714
\(22\) 37.5784i 1.70811i
\(23\) 17.5074 0.761190 0.380595 0.924742i \(-0.375719\pi\)
0.380595 + 0.924742i \(0.375719\pi\)
\(24\) −12.3232 −0.513468
\(25\) −24.3203 −0.972811
\(26\) 40.1692i 1.54497i
\(27\) 18.2657i 0.676509i
\(28\) 2.25984i 0.0807086i
\(29\) 7.86076i 0.271061i 0.990773 + 0.135530i \(0.0432738\pi\)
−0.990773 + 0.135530i \(0.956726\pi\)
\(30\) 65.2017i 2.17339i
\(31\) −57.7456 −1.86276 −0.931380 0.364048i \(-0.881394\pi\)
−0.931380 + 0.364048i \(0.881394\pi\)
\(32\) 36.7794i 1.14936i
\(33\) 52.2860i 1.58442i
\(34\) 17.9708i 0.528552i
\(35\) 5.93806 0.169659
\(36\) 10.4713 0.290870
\(37\) 32.5310i 0.879217i 0.898189 + 0.439609i \(0.144883\pi\)
−0.898189 + 0.439609i \(0.855117\pi\)
\(38\) 79.7846 2.09959
\(39\) 55.8907i 1.43310i
\(40\) 24.0791 0.601978
\(41\) −18.4425 −0.449817 −0.224908 0.974380i \(-0.572208\pi\)
−0.224908 + 0.974380i \(0.572208\pi\)
\(42\) 7.85016i 0.186909i
\(43\) 22.2772 36.7794i 0.518074 0.855336i
\(44\) −38.8807 −0.883653
\(45\) 27.5150i 0.611444i
\(46\) 45.2242i 0.983135i
\(47\) −25.7806 −0.548524 −0.274262 0.961655i \(-0.588434\pi\)
−0.274262 + 0.961655i \(0.588434\pi\)
\(48\) 70.2567i 1.46368i
\(49\) 48.2851 0.985410
\(50\) 62.8230i 1.25646i
\(51\) 25.0042i 0.490278i
\(52\) 41.5613 0.799256
\(53\) −79.9247 −1.50801 −0.754006 0.656867i \(-0.771881\pi\)
−0.754006 + 0.656867i \(0.771881\pi\)
\(54\) −47.1832 −0.873763
\(55\) 102.165i 1.85754i
\(56\) −2.89908 −0.0517693
\(57\) 111.011 1.94756
\(58\) 20.3055 0.350095
\(59\) 18.4243 0.312277 0.156138 0.987735i \(-0.450095\pi\)
0.156138 + 0.987735i \(0.450095\pi\)
\(60\) −67.4613 −1.12436
\(61\) 76.1107i 1.24772i −0.781537 0.623858i \(-0.785564\pi\)
0.781537 0.623858i \(-0.214436\pi\)
\(62\) 149.166i 2.40590i
\(63\) 3.31275i 0.0525833i
\(64\) 16.8168 0.262763
\(65\) 109.208i 1.68013i
\(66\) −135.063 −2.04640
\(67\) 9.00391 0.134387 0.0671934 0.997740i \(-0.478596\pi\)
0.0671934 + 0.997740i \(0.478596\pi\)
\(68\) −18.5935 −0.273435
\(69\) 62.9242i 0.911944i
\(70\) 15.3389i 0.219127i
\(71\) 51.6630i 0.727648i −0.931468 0.363824i \(-0.881471\pi\)
0.931468 0.363824i \(-0.118529\pi\)
\(72\) 13.4333i 0.186574i
\(73\) 77.4556i 1.06104i −0.847674 0.530518i \(-0.821997\pi\)
0.847674 0.530518i \(-0.178003\pi\)
\(74\) 84.0326 1.13558
\(75\) 87.4108i 1.16548i
\(76\) 82.5496i 1.08618i
\(77\) 12.3004i 0.159746i
\(78\) 144.374 1.85095
\(79\) 7.04014 0.0891157 0.0445578 0.999007i \(-0.485812\pi\)
0.0445578 + 0.999007i \(0.485812\pi\)
\(80\) 137.279i 1.71599i
\(81\) −100.911 −1.24582
\(82\) 47.6397i 0.580972i
\(83\) 83.8385 1.01010 0.505051 0.863089i \(-0.331474\pi\)
0.505051 + 0.863089i \(0.331474\pi\)
\(84\) 8.12221 0.0966930
\(85\) 48.8573i 0.574791i
\(86\) −95.0069 57.5454i −1.10473 0.669132i
\(87\) 28.2528 0.324744
\(88\) 49.8789i 0.566805i
\(89\) 91.8322i 1.03182i 0.856642 + 0.515911i \(0.172547\pi\)
−0.856642 + 0.515911i \(0.827453\pi\)
\(90\) −71.0753 −0.789726
\(91\) 13.1485i 0.144489i
\(92\) −46.7915 −0.508603
\(93\) 207.546i 2.23168i
\(94\) 66.5953i 0.708461i
\(95\) −216.911 −2.28327
\(96\) 132.191 1.37699
\(97\) −155.976 −1.60800 −0.803998 0.594632i \(-0.797298\pi\)
−0.803998 + 0.594632i \(0.797298\pi\)
\(98\) 124.728i 1.27273i
\(99\) −56.9961 −0.575718
\(100\) 65.0001 0.650001
\(101\) 61.9489 0.613355 0.306678 0.951813i \(-0.400783\pi\)
0.306678 + 0.951813i \(0.400783\pi\)
\(102\) −64.5896 −0.633232
\(103\) −19.2194 −0.186596 −0.0932978 0.995638i \(-0.529741\pi\)
−0.0932978 + 0.995638i \(0.529741\pi\)
\(104\) 53.3177i 0.512670i
\(105\) 21.3423i 0.203260i
\(106\) 206.458i 1.94771i
\(107\) 151.561 1.41646 0.708230 0.705981i \(-0.249494\pi\)
0.708230 + 0.705981i \(0.249494\pi\)
\(108\) 48.8184i 0.452022i
\(109\) 43.6904 0.400829 0.200415 0.979711i \(-0.435771\pi\)
0.200415 + 0.979711i \(0.435771\pi\)
\(110\) 263.907 2.39916
\(111\) 116.922 1.05335
\(112\) 16.5281i 0.147573i
\(113\) 30.9047i 0.273493i −0.990606 0.136747i \(-0.956335\pi\)
0.990606 0.136747i \(-0.0436646\pi\)
\(114\) 286.758i 2.51542i
\(115\) 122.951i 1.06914i
\(116\) 21.0092i 0.181114i
\(117\) 60.9256 0.520731
\(118\) 47.5928i 0.403329i
\(119\) 5.88232i 0.0494313i
\(120\) 86.5440i 0.721200i
\(121\) 90.6301 0.749009
\(122\) −196.606 −1.61152
\(123\) 66.2851i 0.538903i
\(124\) 154.335 1.24464
\(125\) 4.77360i 0.0381888i
\(126\) 8.55733 0.0679153
\(127\) 19.3094 0.152043 0.0760214 0.997106i \(-0.475778\pi\)
0.0760214 + 0.997106i \(0.475778\pi\)
\(128\) 103.677i 0.809979i
\(129\) −132.191 80.0676i −1.02474 0.620679i
\(130\) −282.102 −2.17001
\(131\) 19.3546i 0.147745i −0.997268 0.0738725i \(-0.976464\pi\)
0.997268 0.0738725i \(-0.0235358\pi\)
\(132\) 139.743i 1.05866i
\(133\) 26.1157 0.196358
\(134\) 23.2585i 0.173571i
\(135\) 128.277 0.950203
\(136\) 23.8531i 0.175390i
\(137\) 74.8826i 0.546588i −0.961931 0.273294i \(-0.911887\pi\)
0.961931 0.273294i \(-0.0881132\pi\)
\(138\) −162.543 −1.17785
\(139\) 48.3195 0.347622 0.173811 0.984779i \(-0.444392\pi\)
0.173811 + 0.984779i \(0.444392\pi\)
\(140\) −15.8705 −0.113361
\(141\) 92.6596i 0.657160i
\(142\) −133.453 −0.939813
\(143\) −226.221 −1.58196
\(144\) 76.5857 0.531845
\(145\) −55.2048 −0.380723
\(146\) −200.080 −1.37041
\(147\) 173.544i 1.18057i
\(148\) 86.9448i 0.587465i
\(149\) 56.9508i 0.382220i 0.981569 + 0.191110i \(0.0612087\pi\)
−0.981569 + 0.191110i \(0.938791\pi\)
\(150\) 225.795 1.50530
\(151\) 133.385i 0.883346i −0.897176 0.441673i \(-0.854385\pi\)
0.897176 0.441673i \(-0.145615\pi\)
\(152\) 105.900 0.696712
\(153\) −27.2567 −0.178148
\(154\) −31.7739 −0.206324
\(155\) 405.538i 2.61637i
\(156\) 149.378i 0.957549i
\(157\) 172.766i 1.10042i 0.835026 + 0.550210i \(0.185452\pi\)
−0.835026 + 0.550210i \(0.814548\pi\)
\(158\) 18.1857i 0.115100i
\(159\) 287.261i 1.80668i
\(160\) −258.296 −1.61435
\(161\) 14.8031i 0.0919448i
\(162\) 260.669i 1.60907i
\(163\) 243.720i 1.49521i 0.664142 + 0.747607i \(0.268797\pi\)
−0.664142 + 0.747607i \(0.731203\pi\)
\(164\) 49.2907 0.300553
\(165\) 367.196 2.22543
\(166\) 216.568i 1.30462i
\(167\) 246.040 1.47330 0.736648 0.676277i \(-0.236408\pi\)
0.736648 + 0.676277i \(0.236408\pi\)
\(168\) 10.4197i 0.0620222i
\(169\) 72.8168 0.430869
\(170\) 126.206 0.742387
\(171\) 121.011i 0.707667i
\(172\) −59.5396 + 98.2994i −0.346161 + 0.571508i
\(173\) −137.397 −0.794201 −0.397100 0.917775i \(-0.629984\pi\)
−0.397100 + 0.917775i \(0.629984\pi\)
\(174\) 72.9812i 0.419432i
\(175\) 20.5637i 0.117507i
\(176\) −284.368 −1.61573
\(177\) 66.2199i 0.374123i
\(178\) 237.217 1.33268
\(179\) 131.174i 0.732816i −0.930454 0.366408i \(-0.880587\pi\)
0.930454 0.366408i \(-0.119413\pi\)
\(180\) 73.5385i 0.408547i
\(181\) 229.555 1.26826 0.634129 0.773227i \(-0.281359\pi\)
0.634129 + 0.773227i \(0.281359\pi\)
\(182\) 33.9645 0.186618
\(183\) −273.553 −1.49483
\(184\) 60.0273i 0.326235i
\(185\) −228.460 −1.23492
\(186\) 536.124 2.88239
\(187\) 101.206 0.541207
\(188\) 68.9032 0.366507
\(189\) −15.4443 −0.0817161
\(190\) 560.314i 2.94902i
\(191\) 209.496i 1.09684i −0.836204 0.548419i \(-0.815230\pi\)
0.836204 0.548419i \(-0.184770\pi\)
\(192\) 60.4422i 0.314803i
\(193\) −261.300 −1.35389 −0.676943 0.736035i \(-0.736696\pi\)
−0.676943 + 0.736035i \(0.736696\pi\)
\(194\) 402.909i 2.07685i
\(195\) −392.512 −2.01288
\(196\) −129.050 −0.658419
\(197\) 94.0645 0.477485 0.238742 0.971083i \(-0.423265\pi\)
0.238742 + 0.971083i \(0.423265\pi\)
\(198\) 147.230i 0.743584i
\(199\) 28.5992i 0.143715i 0.997415 + 0.0718573i \(0.0228926\pi\)
−0.997415 + 0.0718573i \(0.977107\pi\)
\(200\) 83.3866i 0.416933i
\(201\) 32.3614i 0.161002i
\(202\) 160.023i 0.792195i
\(203\) 6.64655 0.0327416
\(204\) 66.8280i 0.327588i
\(205\) 129.519i 0.631798i
\(206\) 49.6465i 0.241002i
\(207\) −68.5926 −0.331365
\(208\) 303.973 1.46141
\(209\) 449.322i 2.14987i
\(210\) −55.1304 −0.262526
\(211\) 22.6639i 0.107412i −0.998557 0.0537059i \(-0.982897\pi\)
0.998557 0.0537059i \(-0.0171033\pi\)
\(212\) 213.612 1.00761
\(213\) −185.685 −0.871760
\(214\) 391.506i 1.82947i
\(215\) 258.296 + 156.449i 1.20138 + 0.727670i
\(216\) −62.6275 −0.289942
\(217\) 48.8260i 0.225004i
\(218\) 112.859i 0.517701i
\(219\) −278.387 −1.27117
\(220\) 273.053i 1.24115i
\(221\) −108.183 −0.489517
\(222\) 302.026i 1.36048i
\(223\) 263.106i 1.17985i −0.807460 0.589923i \(-0.799158\pi\)
0.807460 0.589923i \(-0.200842\pi\)
\(224\) 31.0983 0.138832
\(225\) 95.2851 0.423489
\(226\) −79.8316 −0.353237
\(227\) 54.4887i 0.240038i 0.992772 + 0.120019i \(0.0382956\pi\)
−0.992772 + 0.120019i \(0.961704\pi\)
\(228\) −296.696 −1.30130
\(229\) 189.993 0.829664 0.414832 0.909898i \(-0.363840\pi\)
0.414832 + 0.909898i \(0.363840\pi\)
\(230\) 317.602 1.38088
\(231\) −44.2097 −0.191384
\(232\) 26.9521 0.116173
\(233\) 209.186i 0.897795i −0.893583 0.448898i \(-0.851817\pi\)
0.893583 0.448898i \(-0.148183\pi\)
\(234\) 157.380i 0.672564i
\(235\) 181.053i 0.770440i
\(236\) −49.2422 −0.208653
\(237\) 25.3033i 0.106765i
\(238\) −15.1949 −0.0638442
\(239\) −68.1912 −0.285319 −0.142659 0.989772i \(-0.545565\pi\)
−0.142659 + 0.989772i \(0.545565\pi\)
\(240\) −493.402 −2.05584
\(241\) 380.930i 1.58062i 0.612705 + 0.790312i \(0.290082\pi\)
−0.612705 + 0.790312i \(0.709918\pi\)
\(242\) 234.111i 0.967402i
\(243\) 198.298i 0.816043i
\(244\) 203.419i 0.833685i
\(245\) 339.098i 1.38407i
\(246\) 171.224 0.696034
\(247\) 480.300i 1.94453i
\(248\) 197.992i 0.798353i
\(249\) 301.328i 1.21015i
\(250\) 12.3309 0.0493237
\(251\) −175.752 −0.700208 −0.350104 0.936711i \(-0.613854\pi\)
−0.350104 + 0.936711i \(0.613854\pi\)
\(252\) 8.85389i 0.0351345i
\(253\) 254.689 1.00667
\(254\) 49.8792i 0.196375i
\(255\) 175.600 0.688629
\(256\) 335.082 1.30891
\(257\) 162.749i 0.633263i 0.948549 + 0.316632i \(0.102552\pi\)
−0.948549 + 0.316632i \(0.897448\pi\)
\(258\) −206.827 + 341.469i −0.801654 + 1.32352i
\(259\) 27.5062 0.106201
\(260\) 291.878i 1.12261i
\(261\) 30.7979i 0.118000i
\(262\) −49.9959 −0.190824
\(263\) 78.4612i 0.298331i −0.988812 0.149166i \(-0.952341\pi\)
0.988812 0.149166i \(-0.0476588\pi\)
\(264\) −179.272 −0.679062
\(265\) 561.298i 2.11811i
\(266\) 67.4607i 0.253612i
\(267\) 330.059 1.23618
\(268\) −24.0645 −0.0897930
\(269\) −48.1852 −0.179127 −0.0895636 0.995981i \(-0.528547\pi\)
−0.0895636 + 0.995981i \(0.528547\pi\)
\(270\) 331.360i 1.22726i
\(271\) 81.9474 0.302389 0.151194 0.988504i \(-0.451688\pi\)
0.151194 + 0.988504i \(0.451688\pi\)
\(272\) −135.990 −0.499964
\(273\) 47.2576 0.173105
\(274\) −193.433 −0.705960
\(275\) −353.799 −1.28654
\(276\) 168.176i 0.609332i
\(277\) 1.40205i 0.00506156i −0.999997 0.00253078i \(-0.999194\pi\)
0.999997 0.00253078i \(-0.000805573\pi\)
\(278\) 124.817i 0.448981i
\(279\) 226.243 0.810907
\(280\) 20.3598i 0.0727135i
\(281\) 248.005 0.882580 0.441290 0.897364i \(-0.354521\pi\)
0.441290 + 0.897364i \(0.354521\pi\)
\(282\) 239.354 0.848772
\(283\) −138.544 −0.489553 −0.244777 0.969580i \(-0.578715\pi\)
−0.244777 + 0.969580i \(0.578715\pi\)
\(284\) 138.078i 0.486191i
\(285\) 779.611i 2.73548i
\(286\) 584.362i 2.04322i
\(287\) 15.5938i 0.0543338i
\(288\) 144.099i 0.500344i
\(289\) −240.601 −0.832531
\(290\) 142.602i 0.491733i
\(291\) 560.600i 1.92646i
\(292\) 207.014i 0.708950i
\(293\) 493.442 1.68410 0.842051 0.539398i \(-0.181348\pi\)
0.842051 + 0.539398i \(0.181348\pi\)
\(294\) −448.290 −1.52480
\(295\) 129.391i 0.438614i
\(296\) 111.539 0.376820
\(297\) 265.721i 0.894684i
\(298\) 147.112 0.493666
\(299\) −272.248 −0.910527
\(300\) 233.620i 0.778735i
\(301\) −31.0983 18.8362i −0.103317 0.0625786i
\(302\) −344.554 −1.14091
\(303\) 222.654i 0.734831i
\(304\) 603.755i 1.98603i
\(305\) 534.513 1.75250
\(306\) 70.4081i 0.230092i
\(307\) 74.5297 0.242768 0.121384 0.992606i \(-0.461267\pi\)
0.121384 + 0.992606i \(0.461267\pi\)
\(308\) 32.8751i 0.106737i
\(309\) 69.0773i 0.223551i
\(310\) −1047.57 −3.37924
\(311\) 21.3831 0.0687560 0.0343780 0.999409i \(-0.489055\pi\)
0.0343780 + 0.999409i \(0.489055\pi\)
\(312\) 191.632 0.614205
\(313\) 231.173i 0.738571i 0.929316 + 0.369285i \(0.120398\pi\)
−0.929316 + 0.369285i \(0.879602\pi\)
\(314\) 446.281 1.42128
\(315\) −23.2649 −0.0738568
\(316\) −18.8160 −0.0595443
\(317\) −160.636 −0.506737 −0.253369 0.967370i \(-0.581539\pi\)
−0.253369 + 0.967370i \(0.581539\pi\)
\(318\) 742.040 2.33346
\(319\) 114.354i 0.358478i
\(320\) 118.102i 0.369068i
\(321\) 544.734i 1.69699i
\(322\) −38.2387 −0.118754
\(323\) 214.875i 0.665247i
\(324\) 269.703 0.832415
\(325\) 378.191 1.16367
\(326\) 629.565 1.93118
\(327\) 157.030i 0.480213i
\(328\) 63.2335i 0.192785i
\(329\) 21.7985i 0.0662567i
\(330\) 948.523i 2.87431i
\(331\) 409.618i 1.23752i 0.785581 + 0.618759i \(0.212364\pi\)
−0.785581 + 0.618759i \(0.787636\pi\)
\(332\) −224.073 −0.674918
\(333\) 127.454i 0.382746i
\(334\) 635.559i 1.90287i
\(335\) 63.2330i 0.188755i
\(336\) 59.4046 0.176799
\(337\) −476.795 −1.41482 −0.707411 0.706803i \(-0.750137\pi\)
−0.707411 + 0.706803i \(0.750137\pi\)
\(338\) 188.097i 0.556500i
\(339\) −111.076 −0.327659
\(340\) 130.580i 0.384057i
\(341\) −840.054 −2.46350
\(342\) −312.590 −0.914006
\(343\) 82.2580i 0.239819i
\(344\) −126.105 76.3815i −0.366585 0.222039i
\(345\) 441.906 1.28089
\(346\) 354.917i 1.02577i
\(347\) 180.778i 0.520973i −0.965477 0.260487i \(-0.916117\pi\)
0.965477 0.260487i \(-0.0838830\pi\)
\(348\) −75.5104 −0.216984
\(349\) 280.319i 0.803206i 0.915814 + 0.401603i \(0.131547\pi\)
−0.915814 + 0.401603i \(0.868453\pi\)
\(350\) 53.1191 0.151769
\(351\) 284.041i 0.809233i
\(352\) 535.049i 1.52003i
\(353\) −117.502 −0.332866 −0.166433 0.986053i \(-0.553225\pi\)
−0.166433 + 0.986053i \(0.553225\pi\)
\(354\) −171.056 −0.483209
\(355\) 362.821 1.02203
\(356\) 245.437i 0.689431i
\(357\) −21.1420 −0.0592212
\(358\) −338.843 −0.946488
\(359\) −208.289 −0.580193 −0.290096 0.956997i \(-0.593687\pi\)
−0.290096 + 0.956997i \(0.593687\pi\)
\(360\) −94.3402 −0.262056
\(361\) −592.977 −1.64260
\(362\) 592.975i 1.63805i
\(363\) 325.738i 0.897351i
\(364\) 35.1416i 0.0965428i
\(365\) 543.958 1.49030
\(366\) 706.630i 1.93068i
\(367\) −444.860 −1.21215 −0.606076 0.795407i \(-0.707257\pi\)
−0.606076 + 0.795407i \(0.707257\pi\)
\(368\) −342.226 −0.929961
\(369\) 72.2563 0.195817
\(370\) 590.148i 1.59499i
\(371\) 67.5792i 0.182154i
\(372\) 554.703i 1.49114i
\(373\) 71.8648i 0.192667i 0.995349 + 0.0963335i \(0.0307115\pi\)
−0.995349 + 0.0963335i \(0.969288\pi\)
\(374\) 261.430i 0.699010i
\(375\) 17.1570 0.0457521
\(376\) 88.3938i 0.235090i
\(377\) 122.238i 0.324240i
\(378\) 39.8951i 0.105543i
\(379\) 146.399 0.386276 0.193138 0.981172i \(-0.438133\pi\)
0.193138 + 0.981172i \(0.438133\pi\)
\(380\) 579.732 1.52561
\(381\) 69.4011i 0.182155i
\(382\) −541.160 −1.41665
\(383\) 698.948i 1.82493i −0.409155 0.912465i \(-0.634176\pi\)
0.409155 0.912465i \(-0.365824\pi\)
\(384\) 372.632 0.970396
\(385\) 86.3841 0.224374
\(386\) 674.978i 1.74865i
\(387\) −87.2804 + 144.099i −0.225531 + 0.372349i
\(388\) 416.872 1.07441
\(389\) 500.337i 1.28621i 0.765776 + 0.643107i \(0.222355\pi\)
−0.765776 + 0.643107i \(0.777645\pi\)
\(390\) 1013.92i 2.59979i
\(391\) 121.797 0.311502
\(392\) 165.554i 0.422333i
\(393\) −69.5633 −0.177006
\(394\) 242.983i 0.616708i
\(395\) 49.4418i 0.125169i
\(396\) 152.332 0.384676
\(397\) −546.245 −1.37593 −0.687966 0.725743i \(-0.741496\pi\)
−0.687966 + 0.725743i \(0.741496\pi\)
\(398\) 73.8760 0.185618
\(399\) 93.8637i 0.235247i
\(400\) 475.401 1.18850
\(401\) 393.142 0.980405 0.490203 0.871609i \(-0.336923\pi\)
0.490203 + 0.871609i \(0.336923\pi\)
\(402\) −83.5945 −0.207946
\(403\) 897.970 2.22821
\(404\) −165.569 −0.409825
\(405\) 708.683i 1.74983i
\(406\) 17.1691i 0.0422883i
\(407\) 473.246i 1.16277i
\(408\) −85.7316 −0.210126
\(409\) 788.894i 1.92884i −0.264382 0.964418i \(-0.585168\pi\)
0.264382 0.964418i \(-0.414832\pi\)
\(410\) −334.566 −0.816015
\(411\) −269.139 −0.654840
\(412\) 51.3670 0.124677
\(413\) 15.5784i 0.0377202i
\(414\) 177.185i 0.427983i
\(415\) 588.784i 1.41876i
\(416\) 571.937i 1.37485i
\(417\) 173.668i 0.416469i
\(418\) 1160.67 2.77671
\(419\) 221.714i 0.529149i −0.964365 0.264575i \(-0.914768\pi\)
0.964365 0.264575i \(-0.0852316\pi\)
\(420\) 57.0410i 0.135812i
\(421\) 253.802i 0.602855i −0.953489 0.301427i \(-0.902537\pi\)
0.953489 0.301427i \(-0.0974631\pi\)
\(422\) −58.5442 −0.138730
\(423\) 101.007 0.238786
\(424\) 274.037i 0.646313i
\(425\) −169.194 −0.398104
\(426\) 479.652i 1.12594i
\(427\) −64.3544 −0.150713
\(428\) −405.074 −0.946434
\(429\) 813.071i 1.89527i
\(430\) 404.132 667.218i 0.939841 1.55167i
\(431\) 455.340 1.05647 0.528237 0.849097i \(-0.322853\pi\)
0.528237 + 0.849097i \(0.322853\pi\)
\(432\) 357.050i 0.826504i
\(433\) 611.084i 1.41128i −0.708571 0.705640i \(-0.750660\pi\)
0.708571 0.705640i \(-0.249340\pi\)
\(434\) 126.125 0.290610
\(435\) 198.415i 0.456125i
\(436\) −116.770 −0.267821
\(437\) 540.742i 1.23740i
\(438\) 719.117i 1.64182i
\(439\) 598.936 1.36432 0.682159 0.731204i \(-0.261041\pi\)
0.682159 + 0.731204i \(0.261041\pi\)
\(440\) 350.291 0.796117
\(441\) −189.177 −0.428974
\(442\) 279.454i 0.632248i
\(443\) −379.068 −0.855683 −0.427842 0.903854i \(-0.640726\pi\)
−0.427842 + 0.903854i \(0.640726\pi\)
\(444\) −312.493 −0.703813
\(445\) −644.923 −1.44927
\(446\) −679.642 −1.52386
\(447\) 204.690 0.457919
\(448\) 14.2192i 0.0317393i
\(449\) 260.317i 0.579770i 0.957061 + 0.289885i \(0.0936171\pi\)
−0.957061 + 0.289885i \(0.906383\pi\)
\(450\) 246.136i 0.546968i
\(451\) −268.292 −0.594883
\(452\) 82.5982i 0.182739i
\(453\) −479.407 −1.05829
\(454\) 140.752 0.310027
\(455\) −92.3396 −0.202944
\(456\) 380.621i 0.834696i
\(457\) 670.232i 1.46659i 0.679910 + 0.733296i \(0.262019\pi\)
−0.679910 + 0.733296i \(0.737981\pi\)
\(458\) 490.781i 1.07157i
\(459\) 127.073i 0.276848i
\(460\) 328.609i 0.714367i
\(461\) −557.387 −1.20908 −0.604541 0.796574i \(-0.706644\pi\)
−0.604541 + 0.796574i \(0.706644\pi\)
\(462\) 114.200i 0.247187i
\(463\) 116.501i 0.251622i 0.992054 + 0.125811i \(0.0401533\pi\)
−0.992054 + 0.125811i \(0.959847\pi\)
\(464\) 153.658i 0.331160i
\(465\) −1457.56 −3.13455
\(466\) −540.360 −1.15957
\(467\) 465.465i 0.996712i −0.866972 0.498356i \(-0.833937\pi\)
0.866972 0.498356i \(-0.166063\pi\)
\(468\) −162.834 −0.347936
\(469\) 7.61313i 0.0162327i
\(470\) −467.688 −0.995081
\(471\) 620.947 1.31836
\(472\) 63.1713i 0.133837i
\(473\) 324.078 535.049i 0.685154 1.13118i
\(474\) −65.3623 −0.137895
\(475\) 751.169i 1.58141i
\(476\) 15.7215i 0.0330284i
\(477\) 313.139 0.656476
\(478\) 176.148i 0.368511i
\(479\) 24.7759 0.0517241 0.0258621 0.999666i \(-0.491767\pi\)
0.0258621 + 0.999666i \(0.491767\pi\)
\(480\) 928.355i 1.93407i
\(481\) 505.873i 1.05171i
\(482\) 984.001 2.04150
\(483\) −53.2046 −0.110155
\(484\) −242.225 −0.500464
\(485\) 1095.39i 2.25854i
\(486\) 512.235 1.05398
\(487\) 356.159 0.731333 0.365667 0.930746i \(-0.380841\pi\)
0.365667 + 0.930746i \(0.380841\pi\)
\(488\) −260.960 −0.534754
\(489\) 875.966 1.79134
\(490\) 875.942 1.78764
\(491\) 498.114i 1.01449i 0.861802 + 0.507244i \(0.169336\pi\)
−0.861802 + 0.507244i \(0.830664\pi\)
\(492\) 177.158i 0.360078i
\(493\) 54.6866i 0.110926i
\(494\) −1240.69 −2.51151
\(495\) 400.274i 0.808635i
\(496\) 1128.78 2.27577
\(497\) −43.6830 −0.0878933
\(498\) −778.376 −1.56300
\(499\) 0.670777i 0.00134424i −1.00000 0.000672122i \(-0.999786\pi\)
1.00000 0.000672122i \(-0.000213943\pi\)
\(500\) 12.7583i 0.0255165i
\(501\) 884.306i 1.76508i
\(502\) 453.995i 0.904372i
\(503\) 775.171i 1.54109i 0.637383 + 0.770547i \(0.280017\pi\)
−0.637383 + 0.770547i \(0.719983\pi\)
\(504\) 11.3584 0.0225365
\(505\) 435.057i 0.861499i
\(506\) 657.900i 1.30020i
\(507\) 261.715i 0.516203i
\(508\) −51.6078 −0.101590
\(509\) 825.181 1.62118 0.810591 0.585613i \(-0.199146\pi\)
0.810591 + 0.585613i \(0.199146\pi\)
\(510\) 453.603i 0.889417i
\(511\) −65.4915 −0.128163
\(512\) 450.857i 0.880580i
\(513\) 564.165 1.09974
\(514\) 420.404 0.817908
\(515\) 134.974i 0.262086i
\(516\) 353.303 + 213.994i 0.684696 + 0.414718i
\(517\) −375.044 −0.725424
\(518\) 71.0526i 0.137167i
\(519\) 493.825i 0.951493i
\(520\) −374.441 −0.720080
\(521\) 801.382i 1.53816i 0.639151 + 0.769081i \(0.279286\pi\)
−0.639151 + 0.769081i \(0.720714\pi\)
\(522\) −79.5556 −0.152405
\(523\) 274.667i 0.525176i −0.964908 0.262588i \(-0.915424\pi\)
0.964908 0.262588i \(-0.0845760\pi\)
\(524\) 51.7285i 0.0987185i
\(525\) 73.9090 0.140779
\(526\) −202.677 −0.385318
\(527\) −401.731 −0.762298
\(528\) 1022.06i 1.93572i
\(529\) −222.492 −0.420590
\(530\) −1449.92 −2.73569
\(531\) −72.1852 −0.135942
\(532\) −69.7986 −0.131200
\(533\) 286.789 0.538066
\(534\) 852.592i 1.59661i
\(535\) 1064.39i 1.98952i
\(536\) 30.8716i 0.0575963i
\(537\) −471.460 −0.877951
\(538\) 124.470i 0.231356i
\(539\) 702.428 1.30321
\(540\) −342.843 −0.634895
\(541\) 361.835 0.668826 0.334413 0.942427i \(-0.391462\pi\)
0.334413 + 0.942427i \(0.391462\pi\)
\(542\) 211.682i 0.390558i
\(543\) 825.055i 1.51944i
\(544\) 255.871i 0.470352i
\(545\) 306.830i 0.562992i
\(546\) 122.074i 0.223578i
\(547\) −281.855 −0.515273 −0.257637 0.966242i \(-0.582944\pi\)
−0.257637 + 0.966242i \(0.582944\pi\)
\(548\) 200.137i 0.365213i
\(549\) 298.196i 0.543163i
\(550\) 913.918i 1.66167i
\(551\) −242.791 −0.440638
\(552\) −215.747 −0.390847
\(553\) 5.95269i 0.0107644i
\(554\) −3.62171 −0.00653739
\(555\) 821.121i 1.47950i
\(556\) −129.142 −0.232270
\(557\) 227.271 0.408026 0.204013 0.978968i \(-0.434601\pi\)
0.204013 + 0.978968i \(0.434601\pi\)
\(558\) 584.420i 1.04735i
\(559\) −346.421 + 571.937i −0.619715 + 1.02314i
\(560\) −116.074 −0.207276
\(561\) 363.749i 0.648394i
\(562\) 640.635i 1.13992i
\(563\) 789.251 1.40187 0.700934 0.713226i \(-0.252767\pi\)
0.700934 + 0.713226i \(0.252767\pi\)
\(564\) 247.649i 0.439093i
\(565\) 217.039 0.384140
\(566\) 357.879i 0.632295i
\(567\) 85.3241i 0.150483i
\(568\) −177.136 −0.311860
\(569\) 581.996 1.02284 0.511420 0.859331i \(-0.329120\pi\)
0.511420 + 0.859331i \(0.329120\pi\)
\(570\) 2013.85 3.53308
\(571\) 761.473i 1.33358i 0.745246 + 0.666789i \(0.232332\pi\)
−0.745246 + 0.666789i \(0.767668\pi\)
\(572\) 604.613 1.05702
\(573\) −752.960 −1.31407
\(574\) 40.2811 0.0701762
\(575\) −425.784 −0.740494
\(576\) −65.8871 −0.114387
\(577\) 570.663i 0.989017i 0.869173 + 0.494509i \(0.164652\pi\)
−0.869173 + 0.494509i \(0.835348\pi\)
\(578\) 621.510i 1.07528i
\(579\) 939.152i 1.62202i
\(580\) 147.544 0.254387
\(581\) 70.8885i 0.122011i
\(582\) 1448.11 2.48817
\(583\) −1162.70 −1.99435
\(584\) −265.571 −0.454745
\(585\) 427.870i 0.731403i
\(586\) 1274.64i 2.17515i
\(587\) 188.120i 0.320477i −0.987078 0.160238i \(-0.948774\pi\)
0.987078 0.160238i \(-0.0512263\pi\)
\(588\) 463.826i 0.788820i
\(589\) 1783.56i 3.02811i
\(590\) 334.237 0.566503
\(591\) 338.082i 0.572051i
\(592\) 635.901i 1.07416i
\(593\) 527.123i 0.888909i −0.895801 0.444455i \(-0.853398\pi\)
0.895801 0.444455i \(-0.146602\pi\)
\(594\) −686.398 −1.15555
\(595\) 41.3106 0.0694296
\(596\) 152.211i 0.255387i
\(597\) 102.790 0.172177
\(598\) 703.257i 1.17602i
\(599\) −1156.58 −1.93085 −0.965427 0.260675i \(-0.916055\pi\)
−0.965427 + 0.260675i \(0.916055\pi\)
\(600\) 299.704 0.499507
\(601\) 119.619i 0.199033i −0.995036 0.0995166i \(-0.968270\pi\)
0.995036 0.0995166i \(-0.0317297\pi\)
\(602\) −48.6567 + 80.3317i −0.0808250 + 0.133441i
\(603\) −35.2767 −0.0585020
\(604\) 356.495i 0.590224i
\(605\) 636.481i 1.05203i
\(606\) −575.148 −0.949090
\(607\) 295.289i 0.486472i −0.969967 0.243236i \(-0.921791\pi\)
0.969967 0.243236i \(-0.0782090\pi\)
\(608\) −1135.99 −1.86840
\(609\) 23.8887i 0.0392262i
\(610\) 1380.73i 2.26349i
\(611\) 400.901 0.656139
\(612\) 72.8482 0.119033
\(613\) 846.563 1.38102 0.690508 0.723324i \(-0.257387\pi\)
0.690508 + 0.723324i \(0.257387\pi\)
\(614\) 192.522i 0.313553i
\(615\) −465.510 −0.756926
\(616\) −42.1744 −0.0684649
\(617\) 495.684 0.803377 0.401689 0.915776i \(-0.368423\pi\)
0.401689 + 0.915776i \(0.368423\pi\)
\(618\) 178.437 0.288733
\(619\) 228.258 0.368753 0.184376 0.982856i \(-0.440973\pi\)
0.184376 + 0.982856i \(0.440973\pi\)
\(620\) 1083.87i 1.74818i
\(621\) 319.785i 0.514952i
\(622\) 55.2358i 0.0888035i
\(623\) 77.6475 0.124635
\(624\) 1092.52i 1.75084i
\(625\) −641.531 −1.02645
\(626\) 597.154 0.953920
\(627\) 1614.93 2.57565
\(628\) 461.747i 0.735266i
\(629\) 226.316i 0.359802i
\(630\) 60.0968i 0.0953917i
\(631\) 702.132i 1.11273i 0.830939 + 0.556364i \(0.187804\pi\)
−0.830939 + 0.556364i \(0.812196\pi\)
\(632\) 24.1384i 0.0381937i
\(633\) −81.4574 −0.128685
\(634\) 414.946i 0.654490i
\(635\) 135.607i 0.213555i
\(636\) 767.756i 1.20716i
\(637\) −750.855 −1.17874
\(638\) 295.395 0.463001
\(639\) 202.412i 0.316764i
\(640\) −728.109 −1.13767
\(641\) 897.002i 1.39938i 0.714447 + 0.699689i \(0.246678\pi\)
−0.714447 + 0.699689i \(0.753322\pi\)
\(642\) −1407.13 −2.19179
\(643\) −1054.92 −1.64062 −0.820311 0.571918i \(-0.806200\pi\)
−0.820311 + 0.571918i \(0.806200\pi\)
\(644\) 39.5639i 0.0614346i
\(645\) 562.302 928.355i 0.871786 1.43931i
\(646\) 555.054 0.859217
\(647\) 1230.50i 1.90185i −0.309414 0.950927i \(-0.600133\pi\)
0.309414 0.950927i \(-0.399867\pi\)
\(648\) 345.993i 0.533940i
\(649\) 268.028 0.412986
\(650\) 976.926i 1.50296i
\(651\) 175.488 0.269567
\(652\) 651.383i 0.999054i
\(653\) 234.774i 0.359532i −0.983709 0.179766i \(-0.942466\pi\)
0.983709 0.179766i \(-0.0575340\pi\)
\(654\) −405.632 −0.620232
\(655\) 135.924 0.207518
\(656\) 360.505 0.549550
\(657\) 303.465i 0.461896i
\(658\) 56.3087 0.0855756
\(659\) −493.253 −0.748488 −0.374244 0.927330i \(-0.622098\pi\)
−0.374244 + 0.927330i \(0.622098\pi\)
\(660\) −981.395 −1.48696
\(661\) 429.533 0.649823 0.324911 0.945744i \(-0.394666\pi\)
0.324911 + 0.945744i \(0.394666\pi\)
\(662\) 1058.11 1.59835
\(663\) 388.827i 0.586466i
\(664\) 287.456i 0.432916i
\(665\) 183.406i 0.275799i
\(666\) −329.234 −0.494345
\(667\) 137.621i 0.206329i
\(668\) −657.585 −0.984409
\(669\) −945.642 −1.41352
\(670\) 163.341 0.243792
\(671\) 1107.22i 1.65011i
\(672\) 111.772i 0.166328i
\(673\) 349.722i 0.519647i 0.965656 + 0.259823i \(0.0836644\pi\)
−0.965656 + 0.259823i \(0.916336\pi\)
\(674\) 1231.63i 1.82735i
\(675\) 444.228i 0.658115i
\(676\) −194.616 −0.287893
\(677\) 788.649i 1.16492i 0.812861 + 0.582458i \(0.197909\pi\)
−0.812861 + 0.582458i \(0.802091\pi\)
\(678\) 286.927i 0.423196i
\(679\) 131.883i 0.194231i
\(680\) 167.516 0.246348
\(681\) 195.841 0.287578
\(682\) 2169.99i 3.18180i
\(683\) −94.5265 −0.138399 −0.0691995 0.997603i \(-0.522044\pi\)
−0.0691995 + 0.997603i \(0.522044\pi\)
\(684\) 323.423i 0.472841i
\(685\) 525.888 0.767720
\(686\) −212.485 −0.309745
\(687\) 682.864i 0.993980i
\(688\) −435.464 + 718.946i −0.632941 + 1.04498i
\(689\) 1242.87 1.80387
\(690\) 1141.51i 1.65436i
\(691\) 942.228i 1.36357i −0.731552 0.681786i \(-0.761203\pi\)
0.731552 0.681786i \(-0.238797\pi\)
\(692\) 367.217 0.530660
\(693\) 48.1922i 0.0695415i
\(694\) −466.976 −0.672877
\(695\) 339.340i 0.488259i
\(696\) 96.8699i 0.139181i
\(697\) −128.303 −0.184079
\(698\) 724.106 1.03740
\(699\) −751.847 −1.07560
\(700\) 54.9600i 0.0785142i
\(701\) 568.235 0.810607 0.405303 0.914182i \(-0.367166\pi\)
0.405303 + 0.914182i \(0.367166\pi\)
\(702\) 733.720 1.04519
\(703\) −1004.77 −1.42926
\(704\) 244.643 0.347504
\(705\) −650.733 −0.923026
\(706\) 303.524i 0.429921i
\(707\) 52.3800i 0.0740877i
\(708\) 176.984i 0.249977i
\(709\) 1211.96 1.70939 0.854696 0.519128i \(-0.173743\pi\)
0.854696 + 0.519128i \(0.173743\pi\)
\(710\) 937.222i 1.32003i
\(711\) −27.5828 −0.0387943
\(712\) 314.864 0.442225
\(713\) −1010.97 −1.41791
\(714\) 54.6129i 0.0764886i
\(715\) 1588.71i 2.22197i
\(716\) 350.585i 0.489645i
\(717\) 245.090i 0.341826i
\(718\) 538.043i 0.749363i
\(719\) 692.271 0.962825 0.481413 0.876494i \(-0.340124\pi\)
0.481413 + 0.876494i \(0.340124\pi\)
\(720\) 537.849i 0.747013i
\(721\) 16.2507i 0.0225391i
\(722\) 1531.75i 2.12154i
\(723\) 1369.12 1.89367
\(724\) −613.525 −0.847410
\(725\) 191.176i 0.263691i
\(726\) −841.431 −1.15900
\(727\) 441.195i 0.606871i 0.952852 + 0.303435i \(0.0981337\pi\)
−0.952852 + 0.303435i \(0.901866\pi\)
\(728\) 45.0820 0.0619258
\(729\) −195.486 −0.268156
\(730\) 1405.13i 1.92483i
\(731\) 154.980 255.871i 0.212012 0.350029i
\(732\) 731.119 0.998796
\(733\) 251.039i 0.342481i 0.985229 + 0.171240i \(0.0547775\pi\)
−0.985229 + 0.171240i \(0.945222\pi\)
\(734\) 1149.14i 1.56559i
\(735\) 1218.77 1.65819
\(736\) 643.911i 0.874879i
\(737\) 130.985 0.177727
\(738\) 186.649i 0.252912i
\(739\) 635.071i 0.859365i −0.902980 0.429683i \(-0.858625\pi\)
0.902980 0.429683i \(-0.141375\pi\)
\(740\) 610.600 0.825135
\(741\) −1726.27 −2.32965
\(742\) 174.567 0.235266
\(743\) 899.136i 1.21014i 0.796171 + 0.605071i \(0.206855\pi\)
−0.796171 + 0.605071i \(0.793145\pi\)
\(744\) 711.612 0.956467
\(745\) −399.956 −0.536854
\(746\) 185.638 0.248844
\(747\) −328.473 −0.439723
\(748\) −270.490 −0.361617
\(749\) 128.151i 0.171096i
\(750\) 44.3192i 0.0590923i
\(751\) 597.422i 0.795502i −0.917493 0.397751i \(-0.869791\pi\)
0.917493 0.397751i \(-0.130209\pi\)
\(752\) 503.947 0.670143
\(753\) 631.680i 0.838885i
\(754\) −315.760 −0.418780
\(755\) 936.743 1.24072
\(756\) 41.2777 0.0546001
\(757\) 392.757i 0.518834i 0.965765 + 0.259417i \(0.0835304\pi\)
−0.965765 + 0.259417i \(0.916470\pi\)
\(758\) 378.170i 0.498905i
\(759\) 915.390i 1.20605i
\(760\) 743.720i 0.978579i
\(761\) 472.103i 0.620371i −0.950676 0.310186i \(-0.899609\pi\)
0.950676 0.310186i \(-0.100391\pi\)
\(762\) −179.274 −0.235267
\(763\) 36.9418i 0.0484165i
\(764\) 559.914i 0.732872i
\(765\) 191.419i 0.250221i
\(766\) −1805.49 −2.35704
\(767\) −286.507 −0.373542
\(768\) 1204.33i 1.56814i
\(769\) −591.892 −0.769690 −0.384845 0.922981i \(-0.625745\pi\)
−0.384845 + 0.922981i \(0.625745\pi\)
\(770\) 223.143i 0.289796i
\(771\) 584.943 0.758681
\(772\) 698.369 0.904624
\(773\) 632.541i 0.818293i 0.912469 + 0.409147i \(0.134174\pi\)
−0.912469 + 0.409147i \(0.865826\pi\)
\(774\) 372.230 + 225.458i 0.480917 + 0.291290i
\(775\) 1404.39 1.81211
\(776\) 534.792i 0.689164i
\(777\) 98.8614i 0.127235i
\(778\) 1292.45 1.66124
\(779\) 569.624i 0.731225i
\(780\) 1049.05 1.34494
\(781\) 751.569i 0.962316i
\(782\) 314.621i 0.402328i
\(783\) 143.583 0.183375
\(784\) −943.853 −1.20389
\(785\) −1213.31 −1.54562
\(786\) 179.693i 0.228617i
\(787\) 26.7235 0.0339561 0.0169781 0.999856i \(-0.494595\pi\)
0.0169781 + 0.999856i \(0.494595\pi\)
\(788\) −251.404 −0.319040
\(789\) −282.001 −0.357416
\(790\) 127.716 0.161665
\(791\) −26.1311 −0.0330355
\(792\) 195.422i 0.246745i
\(793\) 1183.56i 1.49251i
\(794\) 1411.03i 1.77712i
\(795\) −2017.39 −2.53760
\(796\) 76.4363i 0.0960255i