Properties

Label 690.3.b.a.599.13
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.13
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.14

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-1.52209 - 2.58520i) q^{3} +2.00000 q^{4} +(-4.64244 + 1.85681i) q^{5} +(2.15256 + 3.65602i) q^{6} -10.7642i q^{7} -2.82843 q^{8} +(-4.36648 + 7.86981i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-1.52209 - 2.58520i) q^{3} +2.00000 q^{4} +(-4.64244 + 1.85681i) q^{5} +(2.15256 + 3.65602i) q^{6} -10.7642i q^{7} -2.82843 q^{8} +(-4.36648 + 7.86981i) q^{9} +(6.56540 - 2.62593i) q^{10} -19.8694i q^{11} +(-3.04418 - 5.17039i) q^{12} -15.8557i q^{13} +15.2228i q^{14} +(11.8664 + 9.17538i) q^{15} +4.00000 q^{16} +9.43625 q^{17} +(6.17514 - 11.1296i) q^{18} +8.14814 q^{19} +(-9.28488 + 3.71363i) q^{20} +(-27.8275 + 16.3841i) q^{21} +28.0995i q^{22} -4.79583 q^{23} +(4.30512 + 7.31204i) q^{24} +(18.1045 - 17.2403i) q^{25} +22.4233i q^{26} +(26.9912 - 0.690351i) q^{27} -21.5284i q^{28} -47.6184i q^{29} +(-16.7817 - 12.9759i) q^{30} -10.4513 q^{31} -5.65685 q^{32} +(-51.3662 + 30.2430i) q^{33} -13.3449 q^{34} +(19.9871 + 49.9720i) q^{35} +(-8.73296 + 15.7396i) q^{36} -0.317500i q^{37} -11.5232 q^{38} +(-40.9901 + 24.1338i) q^{39} +(13.1308 - 5.25186i) q^{40} -30.0257i q^{41} +(39.3540 - 23.1706i) q^{42} -13.3476i q^{43} -39.7387i q^{44} +(5.65836 - 44.6428i) q^{45} +6.78233 q^{46} +16.2940 q^{47} +(-6.08836 - 10.3408i) q^{48} -66.8675 q^{49} +(-25.6036 + 24.3814i) q^{50} +(-14.3628 - 24.3946i) q^{51} -31.7114i q^{52} -77.8949 q^{53} +(-38.1713 + 0.976304i) q^{54} +(36.8937 + 92.2423i) q^{55} +30.4457i q^{56} +(-12.4022 - 21.0645i) q^{57} +67.3426i q^{58} +15.6749i q^{59} +(23.7329 + 18.3508i) q^{60} +12.3081 q^{61} +14.7804 q^{62} +(84.7120 + 47.0016i) q^{63} +8.00000 q^{64} +(29.4410 + 73.6091i) q^{65} +(72.6428 - 42.7700i) q^{66} +42.8194i q^{67} +18.8725 q^{68} +(7.29969 + 12.3982i) q^{69} +(-28.2660 - 70.6711i) q^{70} +97.2496i q^{71} +(12.3503 - 22.2592i) q^{72} +43.7676i q^{73} +0.449013i q^{74} +(-72.1262 - 20.5624i) q^{75} +16.2963 q^{76} -213.877 q^{77} +(57.9687 - 34.1303i) q^{78} +121.730 q^{79} +(-18.5698 + 7.42725i) q^{80} +(-42.8677 - 68.7267i) q^{81} +42.4627i q^{82} -60.3906 q^{83} +(-55.6550 + 32.7681i) q^{84} +(-43.8072 + 17.5213i) q^{85} +18.8763i q^{86} +(-123.103 + 72.4795i) q^{87} +56.1990i q^{88} +5.45726i q^{89} +(-8.00214 + 63.1345i) q^{90} -170.673 q^{91} -9.59166 q^{92} +(15.9078 + 27.0187i) q^{93} -23.0432 q^{94} +(-37.8272 + 15.1296i) q^{95} +(8.61025 + 14.6241i) q^{96} -157.559i q^{97} +94.5650 q^{98} +(156.368 + 86.7592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −1.52209 2.58520i −0.507364 0.861732i
\(4\) 2.00000 0.500000
\(5\) −4.64244 + 1.85681i −0.928488 + 0.371363i
\(6\) 2.15256 + 3.65602i 0.358760 + 0.609337i
\(7\) 10.7642i 1.53774i −0.639405 0.768870i \(-0.720819\pi\)
0.639405 0.768870i \(-0.279181\pi\)
\(8\) −2.82843 −0.353553
\(9\) −4.36648 + 7.86981i −0.485164 + 0.874423i
\(10\) 6.56540 2.62593i 0.656540 0.262593i
\(11\) 19.8694i 1.80631i −0.429319 0.903153i \(-0.641246\pi\)
0.429319 0.903153i \(-0.358754\pi\)
\(12\) −3.04418 5.17039i −0.253682 0.430866i
\(13\) 15.8557i 1.21967i −0.792529 0.609834i \(-0.791236\pi\)
0.792529 0.609834i \(-0.208764\pi\)
\(14\) 15.2228i 1.08735i
\(15\) 11.8664 + 9.17538i 0.791096 + 0.611692i
\(16\) 4.00000 0.250000
\(17\) 9.43625 0.555073 0.277537 0.960715i \(-0.410482\pi\)
0.277537 + 0.960715i \(0.410482\pi\)
\(18\) 6.17514 11.1296i 0.343063 0.618310i
\(19\) 8.14814 0.428849 0.214425 0.976741i \(-0.431212\pi\)
0.214425 + 0.976741i \(0.431212\pi\)
\(20\) −9.28488 + 3.71363i −0.464244 + 0.185681i
\(21\) −27.8275 + 16.3841i −1.32512 + 0.780193i
\(22\) 28.0995i 1.27725i
\(23\) −4.79583 −0.208514
\(24\) 4.30512 + 7.31204i 0.179380 + 0.304668i
\(25\) 18.1045 17.2403i 0.724180 0.689611i
\(26\) 22.4233i 0.862436i
\(27\) 26.9912 0.690351i 0.999673 0.0255686i
\(28\) 21.5284i 0.768870i
\(29\) 47.6184i 1.64201i −0.570919 0.821007i \(-0.693413\pi\)
0.570919 0.821007i \(-0.306587\pi\)
\(30\) −16.7817 12.9759i −0.559389 0.432532i
\(31\) −10.4513 −0.337139 −0.168569 0.985690i \(-0.553915\pi\)
−0.168569 + 0.985690i \(0.553915\pi\)
\(32\) −5.65685 −0.176777
\(33\) −51.3662 + 30.2430i −1.55655 + 0.916454i
\(34\) −13.3449 −0.392496
\(35\) 19.9871 + 49.9720i 0.571059 + 1.42777i
\(36\) −8.73296 + 15.7396i −0.242582 + 0.437211i
\(37\) 0.317500i 0.00858109i −0.999991 0.00429054i \(-0.998634\pi\)
0.999991 0.00429054i \(-0.00136573\pi\)
\(38\) −11.5232 −0.303242
\(39\) −40.9901 + 24.1338i −1.05103 + 0.618815i
\(40\) 13.1308 5.25186i 0.328270 0.131296i
\(41\) 30.0257i 0.732333i −0.930549 0.366167i \(-0.880670\pi\)
0.930549 0.366167i \(-0.119330\pi\)
\(42\) 39.3540 23.1706i 0.937001 0.551680i
\(43\) 13.3476i 0.310408i −0.987882 0.155204i \(-0.950396\pi\)
0.987882 0.155204i \(-0.0496036\pi\)
\(44\) 39.7387i 0.903153i
\(45\) 5.65836 44.6428i 0.125741 0.992063i
\(46\) 6.78233 0.147442
\(47\) 16.2940 0.346681 0.173341 0.984862i \(-0.444544\pi\)
0.173341 + 0.984862i \(0.444544\pi\)
\(48\) −6.08836 10.3408i −0.126841 0.215433i
\(49\) −66.8675 −1.36464
\(50\) −25.6036 + 24.3814i −0.512072 + 0.487629i
\(51\) −14.3628 24.3946i −0.281624 0.478325i
\(52\) 31.7114i 0.609834i
\(53\) −77.8949 −1.46972 −0.734858 0.678221i \(-0.762751\pi\)
−0.734858 + 0.678221i \(0.762751\pi\)
\(54\) −38.1713 + 0.976304i −0.706876 + 0.0180797i
\(55\) 36.8937 + 92.2423i 0.670794 + 1.67713i
\(56\) 30.4457i 0.543673i
\(57\) −12.4022 21.0645i −0.217583 0.369553i
\(58\) 67.3426i 1.16108i
\(59\) 15.6749i 0.265676i 0.991138 + 0.132838i \(0.0424089\pi\)
−0.991138 + 0.132838i \(0.957591\pi\)
\(60\) 23.7329 + 18.3508i 0.395548 + 0.305846i
\(61\) 12.3081 0.201772 0.100886 0.994898i \(-0.467832\pi\)
0.100886 + 0.994898i \(0.467832\pi\)
\(62\) 14.7804 0.238393
\(63\) 84.7120 + 47.0016i 1.34463 + 0.746057i
\(64\) 8.00000 0.125000
\(65\) 29.4410 + 73.6091i 0.452939 + 1.13245i
\(66\) 72.6428 42.7700i 1.10065 0.648031i
\(67\) 42.8194i 0.639095i 0.947570 + 0.319548i \(0.103531\pi\)
−0.947570 + 0.319548i \(0.896469\pi\)
\(68\) 18.8725 0.277537
\(69\) 7.29969 + 12.3982i 0.105793 + 0.179684i
\(70\) −28.2660 70.6711i −0.403800 1.00959i
\(71\) 97.2496i 1.36971i 0.728678 + 0.684856i \(0.240135\pi\)
−0.728678 + 0.684856i \(0.759865\pi\)
\(72\) 12.3503 22.2592i 0.171532 0.309155i
\(73\) 43.7676i 0.599556i 0.954009 + 0.299778i \(0.0969127\pi\)
−0.954009 + 0.299778i \(0.903087\pi\)
\(74\) 0.449013i 0.00606774i
\(75\) −72.1262 20.5624i −0.961683 0.274165i
\(76\) 16.2963 0.214425
\(77\) −213.877 −2.77763
\(78\) 57.9687 34.1303i 0.743189 0.437568i
\(79\) 121.730 1.54089 0.770443 0.637509i \(-0.220035\pi\)
0.770443 + 0.637509i \(0.220035\pi\)
\(80\) −18.5698 + 7.42725i −0.232122 + 0.0928406i
\(81\) −42.8677 68.7267i −0.529231 0.848478i
\(82\) 42.4627i 0.517838i
\(83\) −60.3906 −0.727597 −0.363799 0.931478i \(-0.618520\pi\)
−0.363799 + 0.931478i \(0.618520\pi\)
\(84\) −55.6550 + 32.7681i −0.662560 + 0.390097i
\(85\) −43.8072 + 17.5213i −0.515379 + 0.206133i
\(86\) 18.8763i 0.219492i
\(87\) −123.103 + 72.4795i −1.41498 + 0.833098i
\(88\) 56.1990i 0.638626i
\(89\) 5.45726i 0.0613176i 0.999530 + 0.0306588i \(0.00976052\pi\)
−0.999530 + 0.0306588i \(0.990239\pi\)
\(90\) −8.00214 + 63.1345i −0.0889126 + 0.701495i
\(91\) −170.673 −1.87553
\(92\) −9.59166 −0.104257
\(93\) 15.9078 + 27.0187i 0.171052 + 0.290523i
\(94\) −23.0432 −0.245141
\(95\) −37.8272 + 15.1296i −0.398182 + 0.159259i
\(96\) 8.61025 + 14.6241i 0.0896901 + 0.152334i
\(97\) 157.559i 1.62432i −0.583432 0.812162i \(-0.698290\pi\)
0.583432 0.812162i \(-0.301710\pi\)
\(98\) 94.5650 0.964949
\(99\) 156.368 + 86.7592i 1.57948 + 0.876355i
\(100\) 36.2090 34.4806i 0.362090 0.344806i
\(101\) 125.568i 1.24325i 0.783315 + 0.621625i \(0.213527\pi\)
−0.783315 + 0.621625i \(0.786473\pi\)
\(102\) 20.3121 + 34.4991i 0.199138 + 0.338227i
\(103\) 135.773i 1.31818i 0.752062 + 0.659092i \(0.229059\pi\)
−0.752062 + 0.659092i \(0.770941\pi\)
\(104\) 44.8467i 0.431218i
\(105\) 98.7654 127.732i 0.940623 1.21650i
\(106\) 110.160 1.03925
\(107\) −26.9644 −0.252004 −0.126002 0.992030i \(-0.540215\pi\)
−0.126002 + 0.992030i \(0.540215\pi\)
\(108\) 53.9823 1.38070i 0.499837 0.0127843i
\(109\) −107.331 −0.984685 −0.492342 0.870402i \(-0.663859\pi\)
−0.492342 + 0.870402i \(0.663859\pi\)
\(110\) −52.1755 130.450i −0.474323 1.18591i
\(111\) −0.820800 + 0.483264i −0.00739460 + 0.00435373i
\(112\) 43.0567i 0.384435i
\(113\) 204.412 1.80895 0.904477 0.426522i \(-0.140261\pi\)
0.904477 + 0.426522i \(0.140261\pi\)
\(114\) 17.5394 + 29.7898i 0.153854 + 0.261314i
\(115\) 22.2644 8.90496i 0.193603 0.0774344i
\(116\) 95.2368i 0.821007i
\(117\) 124.781 + 69.2335i 1.06651 + 0.591740i
\(118\) 22.1676i 0.187861i
\(119\) 101.573i 0.853558i
\(120\) −33.5634 25.9519i −0.279695 0.216266i
\(121\) −273.792 −2.26274
\(122\) −17.4063 −0.142674
\(123\) −77.6222 + 45.7018i −0.631075 + 0.371559i
\(124\) −20.9026 −0.168569
\(125\) −52.0371 + 113.654i −0.416296 + 0.909229i
\(126\) −119.801 66.4703i −0.950800 0.527542i
\(127\) 63.8176i 0.502500i 0.967922 + 0.251250i \(0.0808417\pi\)
−0.967922 + 0.251250i \(0.919158\pi\)
\(128\) −11.3137 −0.0883883
\(129\) −34.5061 + 20.3162i −0.267489 + 0.157490i
\(130\) −41.6359 104.099i −0.320276 0.800761i
\(131\) 110.013i 0.839795i −0.907571 0.419898i \(-0.862066\pi\)
0.907571 0.419898i \(-0.137934\pi\)
\(132\) −102.732 + 60.4859i −0.778276 + 0.458227i
\(133\) 87.7080i 0.659459i
\(134\) 60.5558i 0.451909i
\(135\) −124.023 + 53.3225i −0.918689 + 0.394981i
\(136\) −26.6897 −0.196248
\(137\) −50.0168 −0.365086 −0.182543 0.983198i \(-0.558433\pi\)
−0.182543 + 0.983198i \(0.558433\pi\)
\(138\) −10.3233 17.5337i −0.0748067 0.127055i
\(139\) 264.133 1.90024 0.950120 0.311883i \(-0.100960\pi\)
0.950120 + 0.311883i \(0.100960\pi\)
\(140\) 39.9741 + 99.9441i 0.285529 + 0.713886i
\(141\) −24.8010 42.1232i −0.175893 0.298746i
\(142\) 137.532i 0.968533i
\(143\) −315.042 −2.20309
\(144\) −17.4659 + 31.4792i −0.121291 + 0.218606i
\(145\) 88.4184 + 221.065i 0.609782 + 1.52459i
\(146\) 61.8968i 0.423950i
\(147\) 101.778 + 172.866i 0.692370 + 1.17596i
\(148\) 0.635000i 0.00429054i
\(149\) 99.4139i 0.667207i −0.942713 0.333604i \(-0.891735\pi\)
0.942713 0.333604i \(-0.108265\pi\)
\(150\) 102.002 + 29.0796i 0.680012 + 0.193864i
\(151\) 44.2803 0.293247 0.146623 0.989192i \(-0.453159\pi\)
0.146623 + 0.989192i \(0.453159\pi\)
\(152\) −23.0464 −0.151621
\(153\) −41.2032 + 74.2614i −0.269302 + 0.485369i
\(154\) 302.468 1.96408
\(155\) 48.5195 19.4061i 0.313029 0.125201i
\(156\) −81.9801 + 48.2676i −0.525514 + 0.309408i
\(157\) 131.707i 0.838899i −0.907779 0.419449i \(-0.862223\pi\)
0.907779 0.419449i \(-0.137777\pi\)
\(158\) −172.152 −1.08957
\(159\) 118.563 + 201.374i 0.745680 + 1.26650i
\(160\) 26.2616 10.5037i 0.164135 0.0656482i
\(161\) 51.6232i 0.320641i
\(162\) 60.6241 + 97.1942i 0.374223 + 0.599964i
\(163\) 154.197i 0.945995i 0.881064 + 0.472998i \(0.156828\pi\)
−0.881064 + 0.472998i \(0.843172\pi\)
\(164\) 60.0513i 0.366167i
\(165\) 182.309 235.779i 1.10490 1.42896i
\(166\) 85.4052 0.514489
\(167\) −27.2956 −0.163446 −0.0817232 0.996655i \(-0.526042\pi\)
−0.0817232 + 0.996655i \(0.526042\pi\)
\(168\) 78.7081 46.3411i 0.468501 0.275840i
\(169\) −82.4028 −0.487591
\(170\) 61.9527 24.7789i 0.364428 0.145758i
\(171\) −35.5787 + 64.1243i −0.208063 + 0.374996i
\(172\) 26.6951i 0.155204i
\(173\) −229.104 −1.32430 −0.662150 0.749371i \(-0.730356\pi\)
−0.662150 + 0.749371i \(0.730356\pi\)
\(174\) 174.094 102.501i 1.00054 0.589089i
\(175\) −185.577 194.880i −1.06044 1.11360i
\(176\) 79.4775i 0.451576i
\(177\) 40.5226 23.8586i 0.228941 0.134794i
\(178\) 7.71774i 0.0433581i
\(179\) 349.348i 1.95167i −0.218518 0.975833i \(-0.570122\pi\)
0.218518 0.975833i \(-0.429878\pi\)
\(180\) 11.3167 89.2857i 0.0628707 0.496032i
\(181\) 252.087 1.39274 0.696372 0.717681i \(-0.254796\pi\)
0.696372 + 0.717681i \(0.254796\pi\)
\(182\) 241.369 1.32620
\(183\) −18.7340 31.8188i −0.102372 0.173873i
\(184\) 13.5647 0.0737210
\(185\) 0.589538 + 1.47398i 0.00318669 + 0.00796744i
\(186\) −22.4971 38.2102i −0.120952 0.205431i
\(187\) 187.492i 1.00263i
\(188\) 32.5880 0.173341
\(189\) −7.43106 290.538i −0.0393178 1.53724i
\(190\) 53.4958 21.3964i 0.281557 0.112613i
\(191\) 250.898i 1.31360i −0.754065 0.656800i \(-0.771910\pi\)
0.754065 0.656800i \(-0.228090\pi\)
\(192\) −12.1767 20.6816i −0.0634204 0.107717i
\(193\) 167.717i 0.869002i 0.900671 + 0.434501i \(0.143075\pi\)
−0.900671 + 0.434501i \(0.856925\pi\)
\(194\) 222.823i 1.14857i
\(195\) 145.482 188.151i 0.746061 0.964875i
\(196\) −133.735 −0.682322
\(197\) 127.097 0.645164 0.322582 0.946541i \(-0.395449\pi\)
0.322582 + 0.946541i \(0.395449\pi\)
\(198\) −221.138 122.696i −1.11686 0.619677i
\(199\) −275.113 −1.38248 −0.691238 0.722628i \(-0.742934\pi\)
−0.691238 + 0.722628i \(0.742934\pi\)
\(200\) −51.2072 + 48.7629i −0.256036 + 0.243814i
\(201\) 110.697 65.1750i 0.550729 0.324254i
\(202\) 177.580i 0.879111i
\(203\) −512.573 −2.52499
\(204\) −28.7256 48.7891i −0.140812 0.239162i
\(205\) 55.7520 + 139.392i 0.271961 + 0.679963i
\(206\) 192.012i 0.932097i
\(207\) 20.9409 37.7423i 0.101164 0.182330i
\(208\) 63.4228i 0.304917i
\(209\) 161.898i 0.774633i
\(210\) −139.675 + 180.641i −0.665121 + 0.860195i
\(211\) 131.348 0.622501 0.311251 0.950328i \(-0.399252\pi\)
0.311251 + 0.950328i \(0.399252\pi\)
\(212\) −155.790 −0.734858
\(213\) 251.409 148.023i 1.18033 0.694942i
\(214\) 38.1334 0.178194
\(215\) 24.7839 + 61.9653i 0.115274 + 0.288210i
\(216\) −76.3426 + 1.95261i −0.353438 + 0.00903985i
\(217\) 112.500i 0.518432i
\(218\) 151.788 0.696277
\(219\) 113.148 66.6183i 0.516657 0.304193i
\(220\) 73.7874 + 184.485i 0.335397 + 0.838567i
\(221\) 149.618i 0.677005i
\(222\) 1.16079 0.683439i 0.00522877 0.00307855i
\(223\) 113.849i 0.510534i 0.966871 + 0.255267i \(0.0821634\pi\)
−0.966871 + 0.255267i \(0.917837\pi\)
\(224\) 60.8914i 0.271837i
\(225\) 56.6248 + 217.758i 0.251666 + 0.967814i
\(226\) −289.082 −1.27912
\(227\) 421.895 1.85857 0.929284 0.369367i \(-0.120425\pi\)
0.929284 + 0.369367i \(0.120425\pi\)
\(228\) −24.8044 42.1291i −0.108791 0.184777i
\(229\) 390.869 1.70685 0.853426 0.521215i \(-0.174521\pi\)
0.853426 + 0.521215i \(0.174521\pi\)
\(230\) −31.4866 + 12.5935i −0.136898 + 0.0547544i
\(231\) 325.541 + 552.915i 1.40927 + 2.39357i
\(232\) 134.685i 0.580539i
\(233\) 196.510 0.843390 0.421695 0.906738i \(-0.361435\pi\)
0.421695 + 0.906738i \(0.361435\pi\)
\(234\) −176.467 97.9110i −0.754134 0.418423i
\(235\) −75.6440 + 30.2549i −0.321889 + 0.128744i
\(236\) 31.3497i 0.132838i
\(237\) −185.284 314.696i −0.781789 1.32783i
\(238\) 143.647i 0.603557i
\(239\) 216.164i 0.904451i 0.891904 + 0.452225i \(0.149370\pi\)
−0.891904 + 0.452225i \(0.850630\pi\)
\(240\) 47.4658 + 36.7015i 0.197774 + 0.152923i
\(241\) −338.017 −1.40256 −0.701280 0.712886i \(-0.747388\pi\)
−0.701280 + 0.712886i \(0.747388\pi\)
\(242\) 387.200 1.60000
\(243\) −112.423 + 215.430i −0.462648 + 0.886542i
\(244\) 24.6162 0.100886
\(245\) 310.428 124.160i 1.26706 0.506777i
\(246\) 109.774 64.6321i 0.446237 0.262732i
\(247\) 129.194i 0.523054i
\(248\) 29.5607 0.119197
\(249\) 91.9199 + 156.121i 0.369156 + 0.626994i
\(250\) 73.5915 160.730i 0.294366 0.642922i
\(251\) 377.506i 1.50401i −0.659159 0.752004i \(-0.729087\pi\)
0.659159 0.752004i \(-0.270913\pi\)
\(252\) 169.424 + 94.0031i 0.672317 + 0.373028i
\(253\) 95.2901i 0.376641i
\(254\) 90.2517i 0.355321i
\(255\) 111.975 + 86.5812i 0.439116 + 0.339534i
\(256\) 16.0000 0.0625000
\(257\) 371.605 1.44594 0.722968 0.690882i \(-0.242777\pi\)
0.722968 + 0.690882i \(0.242777\pi\)
\(258\) 48.7989 28.7314i 0.189143 0.111362i
\(259\) −3.41763 −0.0131955
\(260\) 58.8821 + 147.218i 0.226470 + 0.566224i
\(261\) 374.747 + 207.925i 1.43581 + 0.796647i
\(262\) 155.582i 0.593825i
\(263\) 81.0593 0.308210 0.154105 0.988054i \(-0.450751\pi\)
0.154105 + 0.988054i \(0.450751\pi\)
\(264\) 145.286 85.5400i 0.550324 0.324015i
\(265\) 361.623 144.636i 1.36461 0.545797i
\(266\) 124.038i 0.466308i
\(267\) 14.1081 8.30645i 0.0528393 0.0311103i
\(268\) 85.6388i 0.319548i
\(269\) 165.483i 0.615179i −0.951519 0.307590i \(-0.900478\pi\)
0.951519 0.307590i \(-0.0995224\pi\)
\(270\) 175.395 75.4093i 0.649611 0.279294i
\(271\) 321.114 1.18492 0.592461 0.805599i \(-0.298157\pi\)
0.592461 + 0.805599i \(0.298157\pi\)
\(272\) 37.7450 0.138768
\(273\) 259.780 + 441.224i 0.951577 + 1.61621i
\(274\) 70.7345 0.258155
\(275\) −342.553 359.725i −1.24565 1.30809i
\(276\) 14.5994 + 24.7963i 0.0528963 + 0.0898418i
\(277\) 93.4085i 0.337215i 0.985683 + 0.168607i \(0.0539270\pi\)
−0.985683 + 0.168607i \(0.946073\pi\)
\(278\) −373.541 −1.34367
\(279\) 45.6354 82.2497i 0.163568 0.294802i
\(280\) −56.5319 141.342i −0.201900 0.504794i
\(281\) 343.933i 1.22396i 0.790872 + 0.611981i \(0.209627\pi\)
−0.790872 + 0.611981i \(0.790373\pi\)
\(282\) 35.0739 + 59.5712i 0.124375 + 0.211245i
\(283\) 232.475i 0.821465i 0.911756 + 0.410733i \(0.134727\pi\)
−0.911756 + 0.410733i \(0.865273\pi\)
\(284\) 194.499i 0.684856i
\(285\) 96.6894 + 74.7623i 0.339261 + 0.262324i
\(286\) 445.537 1.55782
\(287\) −323.202 −1.12614
\(288\) 24.7005 44.5183i 0.0857658 0.154578i
\(289\) −199.957 −0.691894
\(290\) −125.043 312.634i −0.431181 1.07805i
\(291\) −407.322 + 239.820i −1.39973 + 0.824123i
\(292\) 87.5352i 0.299778i
\(293\) 19.7017 0.0672413 0.0336207 0.999435i \(-0.489296\pi\)
0.0336207 + 0.999435i \(0.489296\pi\)
\(294\) −143.936 244.469i −0.489580 0.831527i
\(295\) −29.1053 72.7696i −0.0986620 0.246677i
\(296\) 0.898026i 0.00303387i
\(297\) −13.7168 536.297i −0.0461846 1.80572i
\(298\) 140.592i 0.471787i
\(299\) 76.0412i 0.254318i
\(300\) −144.252 41.1248i −0.480841 0.137083i
\(301\) −143.676 −0.477327
\(302\) −62.6217 −0.207357
\(303\) 324.619 191.126i 1.07135 0.630780i
\(304\) 32.5926 0.107212
\(305\) −57.1396 + 22.8538i −0.187343 + 0.0749306i
\(306\) 58.2701 105.022i 0.190425 0.343208i
\(307\) 49.3669i 0.160804i 0.996763 + 0.0804021i \(0.0256204\pi\)
−0.996763 + 0.0804021i \(0.974380\pi\)
\(308\) −427.755 −1.38881
\(309\) 351.000 206.659i 1.13592 0.668799i
\(310\) −68.6170 + 27.4444i −0.221345 + 0.0885303i
\(311\) 37.9233i 0.121940i −0.998140 0.0609699i \(-0.980581\pi\)
0.998140 0.0609699i \(-0.0194194\pi\)
\(312\) 115.937 68.2607i 0.371594 0.218784i
\(313\) 105.976i 0.338582i −0.985566 0.169291i \(-0.945852\pi\)
0.985566 0.169291i \(-0.0541478\pi\)
\(314\) 186.262i 0.593191i
\(315\) −480.543 60.9076i −1.52553 0.193358i
\(316\) 243.460 0.770443
\(317\) 94.9663 0.299578 0.149789 0.988718i \(-0.452141\pi\)
0.149789 + 0.988718i \(0.452141\pi\)
\(318\) −167.674 284.785i −0.527276 0.895552i
\(319\) −946.147 −2.96598
\(320\) −37.1395 + 14.8545i −0.116061 + 0.0464203i
\(321\) 41.0423 + 69.7083i 0.127858 + 0.217160i
\(322\) 73.0062i 0.226727i
\(323\) 76.8879 0.238043
\(324\) −85.7354 137.453i −0.264615 0.424239i
\(325\) −273.357 287.059i −0.841097 0.883259i
\(326\) 218.068i 0.668920i
\(327\) 163.367 + 277.471i 0.499593 + 0.848534i
\(328\) 84.9254i 0.258919i
\(329\) 175.392i 0.533105i
\(330\) −257.824 + 333.441i −0.781284 + 1.01043i
\(331\) −47.3795 −0.143141 −0.0715703 0.997436i \(-0.522801\pi\)
−0.0715703 + 0.997436i \(0.522801\pi\)
\(332\) −120.781 −0.363799
\(333\) 2.49867 + 1.38636i 0.00750350 + 0.00416324i
\(334\) 38.6017 0.115574
\(335\) −79.5076 198.786i −0.237336 0.593392i
\(336\) −111.310 + 65.5362i −0.331280 + 0.195048i
\(337\) 554.880i 1.64653i −0.567659 0.823264i \(-0.692151\pi\)
0.567659 0.823264i \(-0.307849\pi\)
\(338\) 116.535 0.344779
\(339\) −311.133 528.445i −0.917798 1.55883i
\(340\) −87.6144 + 35.0427i −0.257689 + 0.103067i
\(341\) 207.661i 0.608976i
\(342\) 50.3159 90.6854i 0.147122 0.265162i
\(343\) 192.329i 0.560727i
\(344\) 37.7526i 0.109746i
\(345\) −56.9094 44.0036i −0.164955 0.127547i
\(346\) 324.002 0.936422
\(347\) 1.81515 0.00523097 0.00261549 0.999997i \(-0.499167\pi\)
0.00261549 + 0.999997i \(0.499167\pi\)
\(348\) −246.206 + 144.959i −0.707488 + 0.416549i
\(349\) −602.109 −1.72524 −0.862620 0.505853i \(-0.831178\pi\)
−0.862620 + 0.505853i \(0.831178\pi\)
\(350\) 262.446 + 275.602i 0.749846 + 0.787434i
\(351\) −10.9460 427.964i −0.0311852 1.21927i
\(352\) 112.398i 0.319313i
\(353\) 32.9038 0.0932120 0.0466060 0.998913i \(-0.485159\pi\)
0.0466060 + 0.998913i \(0.485159\pi\)
\(354\) −57.3076 + 33.7411i −0.161886 + 0.0953138i
\(355\) −180.574 451.475i −0.508660 1.27176i
\(356\) 10.9145i 0.0306588i
\(357\) −262.587 + 154.604i −0.735539 + 0.433064i
\(358\) 494.053i 1.38004i
\(359\) 14.4746i 0.0403193i −0.999797 0.0201597i \(-0.993583\pi\)
0.999797 0.0201597i \(-0.00641746\pi\)
\(360\) −16.0043 + 126.269i −0.0444563 + 0.350747i
\(361\) −294.608 −0.816088
\(362\) −356.505 −0.984819
\(363\) 416.736 + 707.805i 1.14803 + 1.94988i
\(364\) −341.347 −0.937766
\(365\) −81.2683 203.189i −0.222653 0.556681i
\(366\) 26.4939 + 44.9986i 0.0723878 + 0.122947i
\(367\) 501.552i 1.36663i −0.730126 0.683313i \(-0.760538\pi\)
0.730126 0.683313i \(-0.239462\pi\)
\(368\) −19.1833 −0.0521286
\(369\) 236.296 + 131.106i 0.640369 + 0.355302i
\(370\) −0.833733 2.08452i −0.00225333 0.00563383i
\(371\) 838.475i 2.26004i
\(372\) 31.8157 + 54.0373i 0.0855260 + 0.145262i
\(373\) 290.424i 0.778616i 0.921108 + 0.389308i \(0.127286\pi\)
−0.921108 + 0.389308i \(0.872714\pi\)
\(374\) 265.154i 0.708968i
\(375\) 373.022 38.4651i 0.994725 0.102574i
\(376\) −46.0864 −0.122570
\(377\) −755.022 −2.00271
\(378\) 10.5091 + 410.882i 0.0278019 + 1.08699i
\(379\) 392.815 1.03645 0.518226 0.855244i \(-0.326593\pi\)
0.518226 + 0.855244i \(0.326593\pi\)
\(380\) −75.6545 + 30.2591i −0.199091 + 0.0796293i
\(381\) 164.981 97.1361i 0.433021 0.254950i
\(382\) 354.823i 0.928856i
\(383\) −686.622 −1.79275 −0.896374 0.443299i \(-0.853808\pi\)
−0.896374 + 0.443299i \(0.853808\pi\)
\(384\) 17.2205 + 29.2482i 0.0448450 + 0.0761671i
\(385\) 992.913 397.130i 2.57899 1.03151i
\(386\) 237.188i 0.614477i
\(387\) 105.043 + 58.2819i 0.271428 + 0.150599i
\(388\) 315.119i 0.812162i
\(389\) 259.878i 0.668067i −0.942561 0.334033i \(-0.891590\pi\)
0.942561 0.334033i \(-0.108410\pi\)
\(390\) −205.743 + 266.085i −0.527545 + 0.682269i
\(391\) −45.2547 −0.115741
\(392\) 189.130 0.482474
\(393\) −284.406 + 167.450i −0.723678 + 0.426081i
\(394\) −179.743 −0.456200
\(395\) −565.124 + 226.030i −1.43069 + 0.572227i
\(396\) 312.736 + 173.518i 0.789738 + 0.438178i
\(397\) 458.235i 1.15424i −0.816658 0.577122i \(-0.804176\pi\)
0.816658 0.577122i \(-0.195824\pi\)
\(398\) 389.068 0.977558
\(399\) −226.742 + 133.500i −0.568277 + 0.334585i
\(400\) 72.4180 68.9611i 0.181045 0.172403i
\(401\) 340.506i 0.849143i 0.905394 + 0.424572i \(0.139575\pi\)
−0.905394 + 0.424572i \(0.860425\pi\)
\(402\) −156.549 + 92.1714i −0.389424 + 0.229282i
\(403\) 165.713i 0.411197i
\(404\) 251.137i 0.621625i
\(405\) 326.623 + 239.462i 0.806477 + 0.591265i
\(406\) 724.887 1.78544
\(407\) −6.30853 −0.0155001
\(408\) 40.6242 + 68.9982i 0.0995691 + 0.169113i
\(409\) −339.445 −0.829939 −0.414970 0.909835i \(-0.636208\pi\)
−0.414970 + 0.909835i \(0.636208\pi\)
\(410\) −78.8453 197.131i −0.192306 0.480806i
\(411\) 76.1302 + 129.303i 0.185232 + 0.314607i
\(412\) 271.546i 0.659092i
\(413\) 168.727 0.408540
\(414\) −29.6149 + 53.3756i −0.0715336 + 0.128927i
\(415\) 280.360 112.134i 0.675565 0.270202i
\(416\) 89.6933i 0.215609i
\(417\) −402.035 682.837i −0.964113 1.63750i
\(418\) 228.959i 0.547748i
\(419\) 680.712i 1.62461i 0.583232 + 0.812306i \(0.301788\pi\)
−0.583232 + 0.812306i \(0.698212\pi\)
\(420\) 197.531 255.465i 0.470312 0.608250i
\(421\) −318.476 −0.756475 −0.378237 0.925709i \(-0.623470\pi\)
−0.378237 + 0.925709i \(0.623470\pi\)
\(422\) −185.754 −0.440175
\(423\) −71.1475 + 128.231i −0.168197 + 0.303146i
\(424\) 220.320 0.519623
\(425\) 170.838 162.684i 0.401973 0.382785i
\(426\) −355.546 + 209.336i −0.834616 + 0.491398i
\(427\) 132.487i 0.310273i
\(428\) −53.9288 −0.126002
\(429\) 479.523 + 814.447i 1.11777 + 1.89848i
\(430\) −35.0498 87.6321i −0.0815111 0.203796i
\(431\) 442.057i 1.02565i 0.858492 + 0.512827i \(0.171402\pi\)
−0.858492 + 0.512827i \(0.828598\pi\)
\(432\) 107.965 2.76140i 0.249918 0.00639214i
\(433\) 368.341i 0.850672i −0.905036 0.425336i \(-0.860156\pi\)
0.905036 0.425336i \(-0.139844\pi\)
\(434\) 159.099i 0.366587i
\(435\) 436.917 565.061i 1.00441 1.29899i
\(436\) −214.661 −0.492342
\(437\) −39.0771 −0.0894213
\(438\) −160.015 + 94.2125i −0.365332 + 0.215097i
\(439\) −330.632 −0.753148 −0.376574 0.926387i \(-0.622898\pi\)
−0.376574 + 0.926387i \(0.622898\pi\)
\(440\) −104.351 260.901i −0.237162 0.592956i
\(441\) 291.976 526.235i 0.662077 1.19328i
\(442\) 211.592i 0.478715i
\(443\) −33.7464 −0.0761770 −0.0380885 0.999274i \(-0.512127\pi\)
−0.0380885 + 0.999274i \(0.512127\pi\)
\(444\) −1.64160 + 0.966528i −0.00369730 + 0.00217687i
\(445\) −10.1331 25.3350i −0.0227710 0.0569326i
\(446\) 161.007i 0.361002i
\(447\) −257.004 + 151.317i −0.574954 + 0.338517i
\(448\) 86.1134i 0.192217i
\(449\) 559.220i 1.24548i −0.782429 0.622739i \(-0.786020\pi\)
0.782429 0.622739i \(-0.213980\pi\)
\(450\) −80.0795 307.957i −0.177954 0.684348i
\(451\) −596.591 −1.32282
\(452\) 408.824 0.904477
\(453\) −67.3986 114.473i −0.148783 0.252700i
\(454\) −596.649 −1.31421
\(455\) 792.341 316.909i 1.74141 0.696502i
\(456\) 35.0787 + 59.5795i 0.0769271 + 0.130657i
\(457\) 492.326i 1.07730i 0.842530 + 0.538650i \(0.181065\pi\)
−0.842530 + 0.538650i \(0.818935\pi\)
\(458\) −552.772 −1.20693
\(459\) 254.695 6.51432i 0.554892 0.0141924i
\(460\) 44.5287 17.8099i 0.0968016 0.0387172i
\(461\) 289.785i 0.628601i 0.949324 + 0.314300i \(0.101770\pi\)
−0.949324 + 0.314300i \(0.898230\pi\)
\(462\) −460.384 781.940i −0.996502 1.69251i
\(463\) 887.597i 1.91706i 0.284999 + 0.958528i \(0.408007\pi\)
−0.284999 + 0.958528i \(0.591993\pi\)
\(464\) 190.474i 0.410503i
\(465\) −124.020 95.8947i −0.266709 0.206225i
\(466\) −277.907 −0.596367
\(467\) 383.155 0.820459 0.410230 0.911982i \(-0.365449\pi\)
0.410230 + 0.911982i \(0.365449\pi\)
\(468\) 249.562 + 138.467i 0.533253 + 0.295870i
\(469\) 460.916 0.982762
\(470\) 106.977 42.7869i 0.227610 0.0910360i
\(471\) −340.489 + 200.470i −0.722906 + 0.425627i
\(472\) 44.3352i 0.0939305i
\(473\) −265.208 −0.560693
\(474\) 262.031 + 445.047i 0.552809 + 0.938918i
\(475\) 147.518 140.476i 0.310564 0.295739i
\(476\) 203.147i 0.426779i
\(477\) 340.127 613.018i 0.713054 1.28515i
\(478\) 305.702i 0.639543i
\(479\) 116.267i 0.242728i 0.992608 + 0.121364i \(0.0387268\pi\)
−0.992608 + 0.121364i \(0.961273\pi\)
\(480\) −67.1267 51.9038i −0.139847 0.108133i
\(481\) −5.03418 −0.0104661
\(482\) 478.028 0.991760
\(483\) 133.456 78.5752i 0.276307 0.162682i
\(484\) −547.583 −1.13137
\(485\) 292.558 + 731.460i 0.603213 + 1.50817i
\(486\) 158.991 304.664i 0.327142 0.626880i
\(487\) 802.923i 1.64871i 0.566072 + 0.824356i \(0.308462\pi\)
−0.566072 + 0.824356i \(0.691538\pi\)
\(488\) −34.8126 −0.0713372
\(489\) 398.630 234.702i 0.815194 0.479964i
\(490\) −439.012 + 175.589i −0.895943 + 0.358346i
\(491\) 292.031i 0.594768i 0.954758 + 0.297384i \(0.0961142\pi\)
−0.954758 + 0.297384i \(0.903886\pi\)
\(492\) −155.244 + 91.4036i −0.315537 + 0.185780i
\(493\) 449.339i 0.911438i
\(494\) 182.708i 0.369855i
\(495\) −887.025 112.428i −1.79197 0.227127i
\(496\) −41.8052 −0.0842847
\(497\) 1046.81 2.10626
\(498\) −129.994 220.789i −0.261033 0.443352i
\(499\) 0.617532 0.00123754 0.000618770 1.00000i \(-0.499803\pi\)
0.000618770 1.00000i \(0.499803\pi\)
\(500\) −104.074 + 227.307i −0.208148 + 0.454614i
\(501\) 41.5463 + 70.5644i 0.0829268 + 0.140847i
\(502\) 533.874i 1.06349i
\(503\) 669.828 1.33167 0.665833 0.746101i \(-0.268076\pi\)
0.665833 + 0.746101i \(0.268076\pi\)
\(504\) −239.602 132.941i −0.475400 0.263771i
\(505\) −233.157 582.943i −0.461697 1.15434i
\(506\) 134.761i 0.266325i
\(507\) 125.425 + 213.028i 0.247386 + 0.420173i
\(508\) 127.635i 0.251250i
\(509\) 405.903i 0.797451i −0.917070 0.398726i \(-0.869453\pi\)
0.917070 0.398726i \(-0.130547\pi\)
\(510\) −158.356 122.444i −0.310502 0.240087i
\(511\) 471.122 0.921962
\(512\) −22.6274 −0.0441942
\(513\) 219.928 5.62508i 0.428709 0.0109651i
\(514\) −525.530 −1.02243
\(515\) −252.105 630.318i −0.489524 1.22392i
\(516\) −69.0121 + 40.6324i −0.133744 + 0.0787450i
\(517\) 323.752i 0.626212i
\(518\) 4.83326 0.00933061
\(519\) 348.717 + 592.279i 0.671902 + 1.14119i
\(520\) −83.2718 208.198i −0.160138 0.400381i
\(521\) 821.449i 1.57668i 0.615242 + 0.788338i \(0.289058\pi\)
−0.615242 + 0.788338i \(0.710942\pi\)
\(522\) −529.973 294.050i −1.01527 0.563314i
\(523\) 839.667i 1.60548i −0.596328 0.802741i \(-0.703374\pi\)
0.596328 0.802741i \(-0.296626\pi\)
\(524\) 220.026i 0.419898i
\(525\) −221.337 + 776.379i −0.421595 + 1.47882i
\(526\) −114.635 −0.217938
\(527\) −98.6211 −0.187137
\(528\) −205.465 + 120.972i −0.389138 + 0.229113i
\(529\) 23.0000 0.0434783
\(530\) −511.411 + 204.547i −0.964927 + 0.385937i
\(531\) −123.358 68.4440i −0.232313 0.128896i
\(532\) 175.416i 0.329729i
\(533\) −476.077 −0.893204
\(534\) −19.9519 + 11.7471i −0.0373630 + 0.0219983i
\(535\) 125.181 50.0679i 0.233983 0.0935848i
\(536\) 121.112i 0.225954i
\(537\) −903.134 + 531.740i −1.68181 + 0.990204i
\(538\) 234.029i 0.434998i
\(539\) 1328.62i 2.46496i
\(540\) −248.046 + 106.645i −0.459345 + 0.197491i
\(541\) −698.329 −1.29081 −0.645406 0.763840i \(-0.723312\pi\)
−0.645406 + 0.763840i \(0.723312\pi\)
\(542\) −454.123 −0.837866
\(543\) −383.699 651.694i −0.706628 1.20017i
\(544\) −53.3795 −0.0981240
\(545\) 498.276 199.293i 0.914268 0.365675i
\(546\) −367.385 623.985i −0.672866 1.14283i
\(547\) 294.450i 0.538299i −0.963098 0.269150i \(-0.913257\pi\)
0.963098 0.269150i \(-0.0867426\pi\)
\(548\) −100.034 −0.182543
\(549\) −53.7431 + 96.8623i −0.0978926 + 0.176434i
\(550\) 484.444 + 508.728i 0.880807 + 0.924959i
\(551\) 388.001i 0.704177i
\(552\) −20.6466 35.0673i −0.0374033 0.0635277i
\(553\) 1310.32i 2.36948i
\(554\) 132.100i 0.238447i
\(555\) 2.91319 3.76760i 0.00524898 0.00678846i
\(556\) 528.267 0.950120
\(557\) 981.172 1.76153 0.880765 0.473554i \(-0.157029\pi\)
0.880765 + 0.473554i \(0.157029\pi\)
\(558\) −64.5382 + 116.319i −0.115660 + 0.208456i
\(559\) −211.635 −0.378595
\(560\) 79.9482 + 199.888i 0.142765 + 0.356943i
\(561\) −484.704 + 285.380i −0.864000 + 0.508699i
\(562\) 486.395i 0.865472i
\(563\) 104.996 0.186494 0.0932472 0.995643i \(-0.470275\pi\)
0.0932472 + 0.995643i \(0.470275\pi\)
\(564\) −49.6019 84.2464i −0.0879467 0.149373i
\(565\) −948.970 + 379.555i −1.67959 + 0.671778i
\(566\) 328.769i 0.580864i
\(567\) −739.786 + 461.436i −1.30474 + 0.813819i
\(568\) 275.063i 0.484267i
\(569\) 756.210i 1.32902i 0.747282 + 0.664508i \(0.231359\pi\)
−0.747282 + 0.664508i \(0.768641\pi\)
\(570\) −136.739 105.730i −0.239894 0.185491i
\(571\) 526.804 0.922599 0.461300 0.887244i \(-0.347383\pi\)
0.461300 + 0.887244i \(0.347383\pi\)
\(572\) −630.085 −1.10155
\(573\) −648.620 + 381.889i −1.13197 + 0.666473i
\(574\) 457.076 0.796300
\(575\) −86.8261 + 82.6815i −0.151002 + 0.143794i
\(576\) −34.9318 + 62.9585i −0.0606456 + 0.109303i
\(577\) 752.642i 1.30440i 0.758045 + 0.652202i \(0.226155\pi\)
−0.758045 + 0.652202i \(0.773845\pi\)
\(578\) 282.782 0.489243
\(579\) 433.582 255.281i 0.748847 0.440900i
\(580\) 176.837 + 442.131i 0.304891 + 0.762295i
\(581\) 650.055i 1.11886i
\(582\) 576.041 339.156i 0.989760 0.582743i
\(583\) 1547.72i 2.65476i
\(584\) 123.794i 0.211975i
\(585\) −707.843 89.7173i −1.20999 0.153363i
\(586\) −27.8624 −0.0475468
\(587\) 317.436 0.540777 0.270388 0.962751i \(-0.412848\pi\)
0.270388 + 0.962751i \(0.412848\pi\)
\(588\) 203.557 + 345.731i 0.346185 + 0.587979i
\(589\) −85.1587 −0.144582
\(590\) 41.1611 + 102.912i 0.0697645 + 0.174427i
\(591\) −193.454 328.572i −0.327333 0.555959i
\(592\) 1.27000i 0.00214527i
\(593\) −248.326 −0.418762 −0.209381 0.977834i \(-0.567145\pi\)
−0.209381 + 0.977834i \(0.567145\pi\)
\(594\) 19.3985 + 758.439i 0.0326575 + 1.27683i
\(595\) 188.603 + 471.549i 0.316980 + 0.792519i
\(596\) 198.828i 0.333604i
\(597\) 418.746 + 711.220i 0.701418 + 1.19132i
\(598\) 107.539i 0.179830i
\(599\) 649.710i 1.08466i −0.840166 0.542329i \(-0.817543\pi\)
0.840166 0.542329i \(-0.182457\pi\)
\(600\) 204.004 + 58.1592i 0.340006 + 0.0969321i
\(601\) 354.948 0.590596 0.295298 0.955405i \(-0.404581\pi\)
0.295298 + 0.955405i \(0.404581\pi\)
\(602\) 203.188 0.337521
\(603\) −336.980 186.970i −0.558840 0.310066i
\(604\) 88.5605 0.146623
\(605\) 1271.06 508.380i 2.10093 0.840297i
\(606\) −459.080 + 270.293i −0.757558 + 0.446029i
\(607\) 692.227i 1.14041i −0.821503 0.570204i \(-0.806864\pi\)
0.821503 0.570204i \(-0.193136\pi\)
\(608\) −46.0928 −0.0758106
\(609\) 780.182 + 1325.10i 1.28109 + 2.17586i
\(610\) 80.8076 32.3202i 0.132471 0.0529839i
\(611\) 258.353i 0.422836i
\(612\) −82.4064 + 148.523i −0.134651 + 0.242684i
\(613\) 803.483i 1.31074i −0.755308 0.655370i \(-0.772513\pi\)
0.755308 0.655370i \(-0.227487\pi\)
\(614\) 69.8153i 0.113706i
\(615\) 275.497 356.298i 0.447962 0.579346i
\(616\) 604.937 0.982040
\(617\) −232.233 −0.376390 −0.188195 0.982132i \(-0.560264\pi\)
−0.188195 + 0.982132i \(0.560264\pi\)
\(618\) −496.389 + 292.260i −0.803218 + 0.472912i
\(619\) 1034.13 1.67065 0.835327 0.549754i \(-0.185278\pi\)
0.835327 + 0.549754i \(0.185278\pi\)
\(620\) 97.0391 38.8122i 0.156515 0.0626003i
\(621\) −129.445 + 3.31081i −0.208446 + 0.00533141i
\(622\) 53.6316i 0.0862245i
\(623\) 58.7429 0.0942904
\(624\) −163.960 + 96.5352i −0.262757 + 0.154704i
\(625\) 30.5454 624.253i 0.0488726 0.998805i
\(626\) 149.873i 0.239414i
\(627\) −418.539 + 246.424i −0.667526 + 0.393021i
\(628\) 263.414i 0.419449i
\(629\) 2.99601i 0.00476313i
\(630\) 679.591 + 86.1364i 1.07872 + 0.136724i
\(631\) −612.871 −0.971270 −0.485635 0.874162i \(-0.661412\pi\)
−0.485635 + 0.874162i \(0.661412\pi\)
\(632\) −344.304 −0.544785
\(633\) −199.923 339.560i −0.315835 0.536430i
\(634\) −134.303 −0.211834
\(635\) −118.497 296.269i −0.186610 0.466566i
\(636\) 237.126 + 402.747i 0.372840 + 0.633251i
\(637\) 1060.23i 1.66441i
\(638\) 1338.05 2.09726
\(639\) −765.335 424.638i −1.19771 0.664536i
\(640\) 52.5232 21.0074i 0.0820675 0.0328241i
\(641\) 475.721i 0.742154i 0.928602 + 0.371077i \(0.121011\pi\)
−0.928602 + 0.371077i \(0.878989\pi\)
\(642\) −58.0426 98.5825i −0.0904090 0.153555i
\(643\) 542.268i 0.843341i −0.906749 0.421670i \(-0.861444\pi\)
0.906749 0.421670i \(-0.138556\pi\)
\(644\) 103.246i 0.160320i
\(645\) 122.469 158.388i 0.189874 0.245563i
\(646\) −108.736 −0.168322
\(647\) 312.859 0.483554 0.241777 0.970332i \(-0.422270\pi\)
0.241777 + 0.970332i \(0.422270\pi\)
\(648\) 121.248 + 194.388i 0.187111 + 0.299982i
\(649\) 311.449 0.479891
\(650\) 386.584 + 405.963i 0.594745 + 0.624559i
\(651\) 290.834 171.235i 0.446749 0.263033i
\(652\) 308.394i 0.472998i
\(653\) 206.385 0.316057 0.158029 0.987435i \(-0.449486\pi\)
0.158029 + 0.987435i \(0.449486\pi\)
\(654\) −231.036 392.403i −0.353266 0.600004i
\(655\) 204.274 + 510.729i 0.311868 + 0.779740i
\(656\) 120.103i 0.183083i
\(657\) −344.443 191.110i −0.524266 0.290883i
\(658\) 248.041i 0.376962i
\(659\) 230.138i 0.349222i 0.984637 + 0.174611i \(0.0558669\pi\)
−0.984637 + 0.174611i \(0.944133\pi\)
\(660\) 364.618 471.557i 0.552451 0.714481i
\(661\) 529.204 0.800611 0.400305 0.916382i \(-0.368904\pi\)
0.400305 + 0.916382i \(0.368904\pi\)
\(662\) 67.0048 0.101216
\(663\) −386.792 + 227.732i −0.583397 + 0.343488i
\(664\) 170.810 0.257244
\(665\) 162.857 + 407.179i 0.244898 + 0.612300i
\(666\) −3.53365 1.96061i −0.00530578 0.00294385i
\(667\) 228.370i 0.342383i
\(668\) −54.5911 −0.0817232
\(669\) 294.322 173.289i 0.439944 0.259026i
\(670\) 112.441 + 281.126i 0.167822 + 0.419592i
\(671\) 244.554i 0.364462i
\(672\) 157.416 92.6822i 0.234250 0.137920i
\(673\) 194.311i 0.288724i −0.989525 0.144362i \(-0.953887\pi\)
0.989525 0.144362i \(-0.0461129\pi\)
\(674\) 784.719i 1.16427i
\(675\) 476.760 477.834i 0.706311 0.707902i
\(676\) −164.806 −0.243795
\(677\) 592.227 0.874782 0.437391 0.899271i \(-0.355903\pi\)
0.437391 + 0.899271i \(0.355903\pi\)
\(678\) 440.009 + 747.334i 0.648981 + 1.10226i
\(679\) −1696.00 −2.49779
\(680\) 123.905 49.5578i 0.182214 0.0728792i
\(681\) −642.162 1090.68i −0.942969 1.60159i
\(682\) 293.677i 0.430611i
\(683\) −658.091 −0.963531 −0.481765 0.876300i \(-0.660004\pi\)
−0.481765 + 0.876300i \(0.660004\pi\)
\(684\) −71.1574 + 128.249i −0.104031 + 0.187498i
\(685\) 232.200 92.8719i 0.338978 0.135579i
\(686\) 271.995i 0.396494i
\(687\) −594.938 1010.47i −0.865994 1.47085i
\(688\) 53.3902i 0.0776021i
\(689\) 1235.08i 1.79257i
\(690\) 80.4821 + 62.2305i 0.116641 + 0.0901891i
\(691\) −169.500 −0.245296 −0.122648 0.992450i \(-0.539139\pi\)
−0.122648 + 0.992450i \(0.539139\pi\)
\(692\) −458.208 −0.662150
\(693\) 933.891 1683.17i 1.34761 2.42882i
\(694\) −2.56701 −0.00369886
\(695\) −1226.22 + 490.446i −1.76435 + 0.705678i
\(696\) 348.188 205.003i 0.500269 0.294545i
\(697\) 283.330i 0.406499i
\(698\) 851.510 1.21993
\(699\) −299.106 508.017i −0.427905 0.726776i
\(700\) −371.155 389.760i −0.530221 0.556800i
\(701\) 248.155i 0.354001i −0.984211 0.177001i \(-0.943361\pi\)
0.984211 0.177001i \(-0.0566395\pi\)
\(702\) 15.4800 + 605.232i 0.0220512 + 0.862154i
\(703\) 2.58704i 0.00367999i
\(704\) 158.955i 0.225788i
\(705\) 193.352 + 149.504i 0.274258 + 0.212062i
\(706\) −46.5330 −0.0659108
\(707\) 1351.64 1.91180
\(708\) 81.0452 47.7171i 0.114471 0.0673971i
\(709\) −1199.85 −1.69231 −0.846157 0.532934i \(-0.821089\pi\)
−0.846157 + 0.532934i \(0.821089\pi\)
\(710\) 255.371 + 638.483i 0.359677 + 0.899271i
\(711\) −531.532 + 957.992i −0.747583 + 1.34739i
\(712\) 15.4355i 0.0216790i
\(713\) 50.1227 0.0702983
\(714\) 371.355 218.643i 0.520104 0.306223i
\(715\) 1462.57 584.975i 2.04555 0.818147i
\(716\) 698.696i 0.975833i
\(717\) 558.826 329.021i 0.779394 0.458885i
\(718\) 20.4702i 0.0285101i
\(719\) 1289.31i 1.79319i −0.442849 0.896596i \(-0.646032\pi\)
0.442849 0.896596i \(-0.353968\pi\)
\(720\) 22.6335 178.571i 0.0314354 0.248016i
\(721\) 1461.49 2.02703
\(722\) 416.638 0.577061
\(723\) 514.493 + 873.841i 0.711608 + 1.20863i
\(724\) 504.174 0.696372
\(725\) −820.954 862.107i −1.13235 1.18911i
\(726\) −589.353 1000.99i −0.811781 1.37877i
\(727\) 427.911i 0.588598i 0.955713 + 0.294299i \(0.0950862\pi\)
−0.955713 + 0.294299i \(0.904914\pi\)
\(728\) 482.737 0.663101
\(729\) 728.047 37.2668i 0.998692 0.0511204i
\(730\) 114.931 + 287.352i 0.157439 + 0.393633i
\(731\) 125.951i 0.172299i
\(732\) −37.4681 63.6377i −0.0511859 0.0869367i
\(733\) 339.385i 0.463008i −0.972834 0.231504i \(-0.925635\pi\)
0.972834 0.231504i \(-0.0743647\pi\)
\(734\) 709.301i 0.966351i
\(735\) −793.480 613.535i −1.07956 0.834742i
\(736\) 27.1293 0.0368605
\(737\) 850.794 1.15440
\(738\) −334.173 185.413i −0.452809 0.251236i
\(739\) −609.402 −0.824631 −0.412315 0.911041i \(-0.635280\pi\)
−0.412315 + 0.911041i \(0.635280\pi\)
\(740\) 1.17908 + 2.94795i 0.00159335 + 0.00398372i
\(741\) −333.993 + 196.646i −0.450733 + 0.265379i
\(742\) 1185.78i 1.59809i
\(743\) −441.745 −0.594543 −0.297271 0.954793i \(-0.596077\pi\)
−0.297271 + 0.954793i \(0.596077\pi\)
\(744\) −44.9941 76.4203i −0.0604760 0.102715i
\(745\) 184.593 + 461.523i 0.247776 + 0.619494i
\(746\) 410.721i 0.550565i
\(747\) 263.694 475.262i 0.353004 0.636228i
\(748\) 374.984i 0.501316i
\(749\) 290.250i 0.387516i
\(750\) −527.533 + 54.3979i −0.703377 + 0.0725305i
\(751\) −221.822 −0.295369 −0.147684 0.989035i \(-0.547182\pi\)
−0.147684 + 0.989035i \(0.547182\pi\)
\(752\) 65.1760 0.0866703
\(753\) −975.927 + 574.598i −1.29605 + 0.763079i
\(754\) 1067.76 1.41613
\(755\) −205.568 + 82.2201i −0.272276 + 0.108901i
\(756\) −14.8621 581.076i −0.0196589 0.768619i
\(757\) 422.828i 0.558557i 0.960210 + 0.279279i \(0.0900953\pi\)
−0.960210 + 0.279279i \(0.909905\pi\)
\(758\) −555.525 −0.732882
\(759\) 246.344 145.040i 0.324563 0.191094i
\(760\) 106.992 42.7929i 0.140778 0.0563064i
\(761\) 205.533i 0.270083i −0.990840 0.135041i \(-0.956883\pi\)
0.990840 0.135041i \(-0.0431167\pi\)
\(762\) −233.318 + 137.371i −0.306192 + 0.180277i
\(763\) 1155.33i 1.51419i
\(764\) 501.795i 0.656800i
\(765\) 53.3937 421.261i 0.0697957 0.550668i
\(766\) 971.031 1.26766
\(767\) 248.536 0.324036
\(768\) −24.3535 41.3631i −0.0317102 0.0538583i
\(769\) 1032.56 1.34274 0.671368 0.741124i \(-0.265707\pi\)
0.671368 + 0.741124i \(0.265707\pi\)
\(770\) −1404.19 + 561.627i −1.82362 + 0.729386i
\(771\) −565.617 960.673i −0.733615 1.24601i
\(772\) 335.435i 0.434501i
\(773\) −503.805 −0.651752 −0.325876 0.945412i \(-0.605659\pi\)
−0.325876 + 0.945412i \(0.605659\pi\)
\(774\) −148.553 82.4230i −0.191929 0.106490i
\(775\) −189.216 + 180.183i −0.244149 + 0.232495i
\(776\) 445.645i 0.574285i
\(777\) 5.20194 + 8.83524i 0.00669490 + 0.0113710i
\(778\) 367.523i 0.472395i
\(779\) 244.653i 0.314061i
\(780\) 290.964 376.301i 0.373031 0.482437i
\(781\) 1932.29 2.47412
\(782\) 63.9997 0.0818411
\(783\) −32.8734