Properties

Label 1050.3.q.a.649.3
Level $1050$
Weight $3$
Character 1050.649
Analytic conductor $28.610$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 649.3
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.a.199.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.77962 + 1.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-6.77962 + 1.74264i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(1.73205 - 3.00000i) q^{12} +21.3280 q^{13} +(-9.53553 - 2.65962i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-4.47871 - 7.75736i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(6.25736 + 3.61269i) q^{19} +(8.48528 + 8.66025i) q^{21} -8.48528i q^{22} +(-32.4377 - 18.7279i) q^{23} +(4.24264 - 2.44949i) q^{24} +(26.1213 + 15.0812i) q^{26} +5.19615 q^{27} +(-9.79796 - 10.0000i) q^{28} +33.9411 q^{29} +(38.2279 - 22.0709i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(-5.19615 + 9.00000i) q^{33} -12.6677i q^{34} -6.00000 q^{36} +(24.2232 + 13.9853i) q^{37} +(5.10911 + 8.84924i) q^{38} +(-18.4706 - 31.9920i) q^{39} +54.8313i q^{41} +(4.26858 + 16.6066i) q^{42} +1.48528i q^{43} +(6.00000 - 10.3923i) q^{44} +(-26.4853 - 45.8739i) q^{46} +(21.5020 - 37.2426i) q^{47} +6.92820 q^{48} +(42.9264 - 23.6289i) q^{49} +(-7.75736 + 13.4361i) q^{51} +(21.3280 + 36.9411i) q^{52} +(74.0069 - 42.7279i) q^{53} +(6.36396 + 3.67423i) q^{54} +(-4.92893 - 19.1757i) q^{56} -12.5147i q^{57} +(41.5692 + 24.0000i) q^{58} +(35.6985 - 20.6105i) q^{59} +(-1.02944 - 0.594346i) q^{61} +62.4259 q^{62} +(5.64191 - 20.2279i) q^{63} -8.00000 q^{64} +(-12.7279 + 7.34847i) q^{66} +(3.80789 - 2.19848i) q^{67} +(8.95743 - 15.5147i) q^{68} +64.8754i q^{69} +137.397 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-39.4635 - 68.3528i) q^{73} +(19.7782 + 34.2568i) q^{74} +14.4508i q^{76} +(29.3939 + 30.0000i) q^{77} -52.2426i q^{78} +(49.1690 - 85.1633i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-38.7716 + 67.1543i) q^{82} -110.401 q^{83} +(-6.51472 + 23.3572i) q^{84} +(-1.05025 + 1.81909i) q^{86} +(-29.3939 - 50.9117i) q^{87} +(14.6969 - 8.48528i) q^{88} +(18.0000 + 10.3923i) q^{89} +(-144.595 + 37.1670i) q^{91} -74.9117i q^{92} +(-66.2127 - 38.2279i) q^{93} +(52.6690 - 30.4085i) q^{94} +(8.48528 + 4.89898i) q^{96} -10.9867 q^{97} +(69.2820 + 1.41421i) q^{98} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} - 12 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{4} - 12 q^{9} - 24 q^{11} - 48 q^{14} - 16 q^{16} + 84 q^{19} + 192 q^{26} + 204 q^{31} - 48 q^{36} - 12 q^{39} + 48 q^{44} - 144 q^{46} + 4 q^{49} - 96 q^{51} - 96 q^{56} + 48 q^{59} - 144 q^{61} - 64 q^{64} + 624 q^{71} + 96 q^{74} + 20 q^{79} - 36 q^{81} - 120 q^{84} - 48 q^{86} + 144 q^{89} - 444 q^{91} + 48 q^{94} + 144 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) −0.866025 1.50000i −0.288675 0.500000i
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −6.77962 + 1.74264i −0.968517 + 0.248949i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −3.00000 5.19615i −0.272727 0.472377i 0.696832 0.717234i \(-0.254592\pi\)
−0.969559 + 0.244857i \(0.921259\pi\)
\(12\) 1.73205 3.00000i 0.144338 0.250000i
\(13\) 21.3280 1.64061 0.820306 0.571924i \(-0.193803\pi\)
0.820306 + 0.571924i \(0.193803\pi\)
\(14\) −9.53553 2.65962i −0.681110 0.189973i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −4.47871 7.75736i −0.263454 0.456315i 0.703704 0.710494i \(-0.251528\pi\)
−0.967157 + 0.254178i \(0.918195\pi\)
\(18\) −3.67423 + 2.12132i −0.204124 + 0.117851i
\(19\) 6.25736 + 3.61269i 0.329335 + 0.190141i 0.655546 0.755156i \(-0.272439\pi\)
−0.326211 + 0.945297i \(0.605772\pi\)
\(20\) 0 0
\(21\) 8.48528 + 8.66025i 0.404061 + 0.412393i
\(22\) 8.48528i 0.385695i
\(23\) −32.4377 18.7279i −1.41034 0.814257i −0.414916 0.909860i \(-0.636189\pi\)
−0.995420 + 0.0956024i \(0.969522\pi\)
\(24\) 4.24264 2.44949i 0.176777 0.102062i
\(25\) 0 0
\(26\) 26.1213 + 15.0812i 1.00467 + 0.580044i
\(27\) 5.19615 0.192450
\(28\) −9.79796 10.0000i −0.349927 0.357143i
\(29\) 33.9411 1.17038 0.585192 0.810895i \(-0.301019\pi\)
0.585192 + 0.810895i \(0.301019\pi\)
\(30\) 0 0
\(31\) 38.2279 22.0709i 1.23316 0.711965i 0.265472 0.964119i \(-0.414472\pi\)
0.967687 + 0.252154i \(0.0811390\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) −5.19615 + 9.00000i −0.157459 + 0.272727i
\(34\) 12.6677i 0.372580i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 24.2232 + 13.9853i 0.654682 + 0.377981i 0.790248 0.612788i \(-0.209952\pi\)
−0.135566 + 0.990768i \(0.543285\pi\)
\(38\) 5.10911 + 8.84924i 0.134450 + 0.232875i
\(39\) −18.4706 31.9920i −0.473604 0.820306i
\(40\) 0 0
\(41\) 54.8313i 1.33735i 0.743556 + 0.668674i \(0.233138\pi\)
−0.743556 + 0.668674i \(0.766862\pi\)
\(42\) 4.26858 + 16.6066i 0.101633 + 0.395395i
\(43\) 1.48528i 0.0345414i 0.999851 + 0.0172707i \(0.00549771\pi\)
−0.999851 + 0.0172707i \(0.994502\pi\)
\(44\) 6.00000 10.3923i 0.136364 0.236189i
\(45\) 0 0
\(46\) −26.4853 45.8739i −0.575767 0.997258i
\(47\) 21.5020 37.2426i 0.457490 0.792397i −0.541337 0.840806i \(-0.682082\pi\)
0.998828 + 0.0484090i \(0.0154151\pi\)
\(48\) 6.92820 0.144338
\(49\) 42.9264 23.6289i 0.876049 0.482222i
\(50\) 0 0
\(51\) −7.75736 + 13.4361i −0.152105 + 0.263454i
\(52\) 21.3280 + 36.9411i 0.410153 + 0.710406i
\(53\) 74.0069 42.7279i 1.39636 0.806187i 0.402348 0.915487i \(-0.368194\pi\)
0.994009 + 0.109299i \(0.0348607\pi\)
\(54\) 6.36396 + 3.67423i 0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −4.92893 19.1757i −0.0880166 0.342422i
\(57\) 12.5147i 0.219556i
\(58\) 41.5692 + 24.0000i 0.716711 + 0.413793i
\(59\) 35.6985 20.6105i 0.605059 0.349331i −0.165970 0.986131i \(-0.553076\pi\)
0.771029 + 0.636800i \(0.219742\pi\)
\(60\) 0 0
\(61\) −1.02944 0.594346i −0.0168760 0.00974337i 0.491538 0.870856i \(-0.336435\pi\)
−0.508414 + 0.861113i \(0.669768\pi\)
\(62\) 62.4259 1.00687
\(63\) 5.64191 20.2279i 0.0895542 0.321078i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) −12.7279 + 7.34847i −0.192847 + 0.111340i
\(67\) 3.80789 2.19848i 0.0568341 0.0328132i −0.471314 0.881966i \(-0.656220\pi\)
0.528148 + 0.849152i \(0.322887\pi\)
\(68\) 8.95743 15.5147i 0.131727 0.228158i
\(69\) 64.8754i 0.940224i
\(70\) 0 0
\(71\) 137.397 1.93517 0.967584 0.252548i \(-0.0812687\pi\)
0.967584 + 0.252548i \(0.0812687\pi\)
\(72\) −7.34847 4.24264i −0.102062 0.0589256i
\(73\) −39.4635 68.3528i −0.540596 0.936340i −0.998870 0.0475288i \(-0.984865\pi\)
0.458274 0.888811i \(-0.348468\pi\)
\(74\) 19.7782 + 34.2568i 0.267273 + 0.462930i
\(75\) 0 0
\(76\) 14.4508i 0.190141i
\(77\) 29.3939 + 30.0000i 0.381739 + 0.389610i
\(78\) 52.2426i 0.669777i
\(79\) 49.1690 85.1633i 0.622393 1.07802i −0.366646 0.930361i \(-0.619494\pi\)
0.989039 0.147656i \(-0.0471728\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) −38.7716 + 67.1543i −0.472824 + 0.818955i
\(83\) −110.401 −1.33013 −0.665067 0.746784i \(-0.731597\pi\)
−0.665067 + 0.746784i \(0.731597\pi\)
\(84\) −6.51472 + 23.3572i −0.0775562 + 0.278062i
\(85\) 0 0
\(86\) −1.05025 + 1.81909i −0.0122122 + 0.0211522i
\(87\) −29.3939 50.9117i −0.337861 0.585192i
\(88\) 14.6969 8.48528i 0.167011 0.0964237i
\(89\) 18.0000 + 10.3923i 0.202247 + 0.116767i 0.597703 0.801717i \(-0.296080\pi\)
−0.395456 + 0.918485i \(0.629413\pi\)
\(90\) 0 0
\(91\) −144.595 + 37.1670i −1.58896 + 0.408428i
\(92\) 74.9117i 0.814257i
\(93\) −66.2127 38.2279i −0.711965 0.411053i
\(94\) 52.6690 30.4085i 0.560309 0.323495i
\(95\) 0 0
\(96\) 8.48528 + 4.89898i 0.0883883 + 0.0510310i
\(97\) −10.9867 −0.113264 −0.0566322 0.998395i \(-0.518036\pi\)
−0.0566322 + 0.998395i \(0.518036\pi\)
\(98\) 69.2820 + 1.41421i 0.706960 + 0.0144308i
\(99\) 18.0000 0.181818
\(100\) 0 0
\(101\) −92.8234 + 53.5916i −0.919043 + 0.530610i −0.883330 0.468752i \(-0.844704\pi\)
−0.0357136 + 0.999362i \(0.511370\pi\)
\(102\) −19.0016 + 10.9706i −0.186290 + 0.107555i
\(103\) 52.6025 91.1102i 0.510704 0.884565i −0.489219 0.872161i \(-0.662718\pi\)
0.999923 0.0124040i \(-0.00394842\pi\)
\(104\) 60.3246i 0.580044i
\(105\) 0 0
\(106\) 120.853 1.14012
\(107\) −102.662 59.2721i −0.959460 0.553945i −0.0634534 0.997985i \(-0.520211\pi\)
−0.896007 + 0.444040i \(0.853545\pi\)
\(108\) 5.19615 + 9.00000i 0.0481125 + 0.0833333i
\(109\) 55.5294 + 96.1798i 0.509444 + 0.882384i 0.999940 + 0.0109400i \(0.00348237\pi\)
−0.490496 + 0.871444i \(0.663184\pi\)
\(110\) 0 0
\(111\) 48.4464i 0.436454i
\(112\) 7.52255 26.9706i 0.0671656 0.240809i
\(113\) 101.397i 0.897318i −0.893703 0.448659i \(-0.851902\pi\)
0.893703 0.448659i \(-0.148098\pi\)
\(114\) 8.84924 15.3273i 0.0776249 0.134450i
\(115\) 0 0
\(116\) 33.9411 + 58.7878i 0.292596 + 0.506791i
\(117\) −31.9920 + 55.4117i −0.273435 + 0.473604i
\(118\) 58.2954 0.494029
\(119\) 43.8823 + 44.7871i 0.368758 + 0.376362i
\(120\) 0 0
\(121\) 42.5000 73.6122i 0.351240 0.608365i
\(122\) −0.840532 1.45584i −0.00688961 0.0119331i
\(123\) 82.2469 47.4853i 0.668674 0.386059i
\(124\) 76.4558 + 44.1418i 0.616579 + 0.355982i
\(125\) 0 0
\(126\) 21.2132 20.7846i 0.168359 0.164957i
\(127\) 82.5736i 0.650186i 0.945682 + 0.325093i \(0.105396\pi\)
−0.945682 + 0.325093i \(0.894604\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) 2.22792 1.28629i 0.0172707 0.00997125i
\(130\) 0 0
\(131\) −52.4558 30.2854i −0.400426 0.231186i 0.286242 0.958157i \(-0.407594\pi\)
−0.686668 + 0.726971i \(0.740927\pi\)
\(132\) −20.7846 −0.157459
\(133\) −48.7181 13.5883i −0.366302 0.102168i
\(134\) 6.21825 0.0464049
\(135\) 0 0
\(136\) 21.9411 12.6677i 0.161332 0.0931450i
\(137\) 58.0492 33.5147i 0.423717 0.244633i −0.272949 0.962028i \(-0.587999\pi\)
0.696666 + 0.717395i \(0.254666\pi\)
\(138\) −45.8739 + 79.4558i −0.332419 + 0.575767i
\(139\) 91.5525i 0.658651i 0.944216 + 0.329326i \(0.106821\pi\)
−0.944216 + 0.329326i \(0.893179\pi\)
\(140\) 0 0
\(141\) −74.4853 −0.528264
\(142\) 168.276 + 97.1543i 1.18504 + 0.684185i
\(143\) −63.9839 110.823i −0.447440 0.774989i
\(144\) −6.00000 10.3923i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) 111.620i 0.764518i
\(147\) −72.6187 43.9264i −0.494005 0.298819i
\(148\) 55.9411i 0.377981i
\(149\) 40.5442 70.2245i 0.272108 0.471306i −0.697293 0.716786i \(-0.745612\pi\)
0.969402 + 0.245480i \(0.0789457\pi\)
\(150\) 0 0
\(151\) 25.6030 + 44.3457i 0.169556 + 0.293680i 0.938264 0.345920i \(-0.112433\pi\)
−0.768708 + 0.639600i \(0.779100\pi\)
\(152\) −10.2182 + 17.6985i −0.0672252 + 0.116437i
\(153\) 26.8723 0.175636
\(154\) 14.7868 + 57.5270i 0.0960182 + 0.373552i
\(155\) 0 0
\(156\) 36.9411 63.9839i 0.236802 0.410153i
\(157\) 93.5307 + 162.000i 0.595737 + 1.03185i 0.993442 + 0.114334i \(0.0364734\pi\)
−0.397705 + 0.917513i \(0.630193\pi\)
\(158\) 120.439 69.5355i 0.762273 0.440098i
\(159\) −128.184 74.0069i −0.806187 0.465452i
\(160\) 0 0
\(161\) 252.551 + 70.4409i 1.56864 + 0.437521i
\(162\) 12.7279i 0.0785674i
\(163\) 72.6951 + 41.9706i 0.445982 + 0.257488i 0.706132 0.708080i \(-0.250439\pi\)
−0.260149 + 0.965568i \(0.583772\pi\)
\(164\) −94.9706 + 54.8313i −0.579089 + 0.334337i
\(165\) 0 0
\(166\) −135.213 78.0654i −0.814537 0.470273i
\(167\) −127.620 −0.764190 −0.382095 0.924123i \(-0.624797\pi\)
−0.382095 + 0.924123i \(0.624797\pi\)
\(168\) −24.4949 + 24.0000i −0.145803 + 0.142857i
\(169\) 285.882 1.69161
\(170\) 0 0
\(171\) −18.7721 + 10.8381i −0.109778 + 0.0633805i
\(172\) −2.57258 + 1.48528i −0.0149569 + 0.00863536i
\(173\) −71.4853 + 123.816i −0.413210 + 0.715701i −0.995239 0.0974675i \(-0.968926\pi\)
0.582029 + 0.813168i \(0.302259\pi\)
\(174\) 83.1384i 0.477807i
\(175\) 0 0
\(176\) 24.0000 0.136364
\(177\) −61.8316 35.6985i −0.349331 0.201686i
\(178\) 14.6969 + 25.4558i 0.0825671 + 0.143010i
\(179\) 84.6396 + 146.600i 0.472847 + 0.818995i 0.999517 0.0310748i \(-0.00989300\pi\)
−0.526670 + 0.850070i \(0.676560\pi\)
\(180\) 0 0
\(181\) 209.969i 1.16005i 0.814600 + 0.580024i \(0.196957\pi\)
−0.814600 + 0.580024i \(0.803043\pi\)
\(182\) −203.374 56.7244i −1.11744 0.311672i
\(183\) 2.05887i 0.0112507i
\(184\) 52.9706 91.7477i 0.287883 0.498629i
\(185\) 0 0
\(186\) −54.0624 93.6389i −0.290658 0.503435i
\(187\) −26.8723 + 46.5442i −0.143702 + 0.248899i
\(188\) 86.0082 0.457490
\(189\) −35.2279 + 9.05503i −0.186391 + 0.0479102i
\(190\) 0 0
\(191\) −33.3015 + 57.6799i −0.174353 + 0.301989i −0.939937 0.341347i \(-0.889117\pi\)
0.765584 + 0.643336i \(0.222450\pi\)
\(192\) 6.92820 + 12.0000i 0.0360844 + 0.0625000i
\(193\) 8.48180 4.89697i 0.0439472 0.0253729i −0.477865 0.878433i \(-0.658589\pi\)
0.521813 + 0.853060i \(0.325256\pi\)
\(194\) −13.4558 7.76874i −0.0693600 0.0400450i
\(195\) 0 0
\(196\) 83.8528 + 50.7218i 0.427820 + 0.258785i
\(197\) 267.161i 1.35615i −0.734993 0.678075i \(-0.762815\pi\)
0.734993 0.678075i \(-0.237185\pi\)
\(198\) 22.0454 + 12.7279i 0.111340 + 0.0642824i
\(199\) 113.397 65.4698i 0.569834 0.328994i −0.187249 0.982312i \(-0.559957\pi\)
0.757083 + 0.653319i \(0.226624\pi\)
\(200\) 0 0
\(201\) −6.59545 3.80789i −0.0328132 0.0189447i
\(202\) −151.580 −0.750396
\(203\) −230.108 + 59.1472i −1.13354 + 0.291365i
\(204\) −31.0294 −0.152105
\(205\) 0 0
\(206\) 128.849 74.3911i 0.625482 0.361122i
\(207\) 97.3131 56.1838i 0.470112 0.271419i
\(208\) −42.6559 + 73.8823i −0.205077 + 0.355203i
\(209\) 43.3523i 0.207427i
\(210\) 0 0
\(211\) −23.0883 −0.109423 −0.0547116 0.998502i \(-0.517424\pi\)
−0.0547116 + 0.998502i \(0.517424\pi\)
\(212\) 148.014 + 85.4558i 0.698179 + 0.403094i
\(213\) −118.989 206.095i −0.558635 0.967584i
\(214\) −83.8234 145.186i −0.391698 0.678441i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −220.709 + 216.250i −1.01709 + 0.996543i
\(218\) 157.061i 0.720463i
\(219\) −68.3528 + 118.391i −0.312113 + 0.540596i
\(220\) 0 0
\(221\) −95.5219 165.449i −0.432226 0.748637i
\(222\) 34.2568 59.3345i 0.154310 0.267273i
\(223\) −228.631 −1.02525 −0.512625 0.858613i \(-0.671327\pi\)
−0.512625 + 0.858613i \(0.671327\pi\)
\(224\) 28.2843 27.7128i 0.126269 0.123718i
\(225\) 0 0
\(226\) 71.6985 124.185i 0.317250 0.549493i
\(227\) 32.8070 + 56.8234i 0.144524 + 0.250323i 0.929195 0.369589i \(-0.120502\pi\)
−0.784671 + 0.619912i \(0.787168\pi\)
\(228\) 21.6761 12.5147i 0.0950707 0.0548891i
\(229\) −80.9558 46.7399i −0.353519 0.204104i 0.312715 0.949847i \(-0.398761\pi\)
−0.666234 + 0.745743i \(0.732095\pi\)
\(230\) 0 0
\(231\) 19.5442 70.0716i 0.0846067 0.303340i
\(232\) 96.0000i 0.413793i
\(233\) −205.694 118.757i −0.882806 0.509688i −0.0112234 0.999937i \(-0.503573\pi\)
−0.871583 + 0.490249i \(0.836906\pi\)
\(234\) −78.3640 + 45.2435i −0.334889 + 0.193348i
\(235\) 0 0
\(236\) 71.3970 + 41.2211i 0.302530 + 0.174666i
\(237\) −170.327 −0.718678
\(238\) 22.0753 + 85.8823i 0.0927533 + 0.360850i
\(239\) −366.853 −1.53495 −0.767475 0.641079i \(-0.778487\pi\)
−0.767475 + 0.641079i \(0.778487\pi\)
\(240\) 0 0
\(241\) −364.617 + 210.512i −1.51293 + 0.873493i −0.513049 + 0.858359i \(0.671484\pi\)
−0.999885 + 0.0151343i \(0.995182\pi\)
\(242\) 104.103 60.1041i 0.430179 0.248364i
\(243\) −7.79423 + 13.5000i −0.0320750 + 0.0555556i
\(244\) 2.37738i 0.00974337i
\(245\) 0 0
\(246\) 134.309 0.545970
\(247\) 133.457 + 77.0513i 0.540311 + 0.311949i
\(248\) 62.4259 + 108.125i 0.251717 + 0.435987i
\(249\) 95.6102 + 165.602i 0.383977 + 0.665067i
\(250\) 0 0
\(251\) 146.621i 0.584148i 0.956396 + 0.292074i \(0.0943454\pi\)
−0.956396 + 0.292074i \(0.905655\pi\)
\(252\) 40.6777 10.4558i 0.161419 0.0414914i
\(253\) 224.735i 0.888281i
\(254\) −58.3883 + 101.132i −0.229875 + 0.398156i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −12.5446 + 21.7279i −0.0488118 + 0.0845444i −0.889399 0.457132i \(-0.848877\pi\)
0.840587 + 0.541676i \(0.182210\pi\)
\(258\) 3.63818 0.0141015
\(259\) −188.595 52.6025i −0.728168 0.203098i
\(260\) 0 0
\(261\) −50.9117 + 88.1816i −0.195064 + 0.337861i
\(262\) −42.8300 74.1838i −0.163473 0.283144i
\(263\) 78.5279 45.3381i 0.298585 0.172388i −0.343222 0.939254i \(-0.611518\pi\)
0.641807 + 0.766866i \(0.278185\pi\)
\(264\) −25.4558 14.6969i −0.0964237 0.0556702i
\(265\) 0 0
\(266\) −50.0589 51.0911i −0.188191 0.192072i
\(267\) 36.0000i 0.134831i
\(268\) 7.61577 + 4.39697i 0.0284171 + 0.0164066i
\(269\) 59.2355 34.1996i 0.220206 0.127136i −0.385839 0.922566i \(-0.626088\pi\)
0.606046 + 0.795430i \(0.292755\pi\)
\(270\) 0 0
\(271\) −106.971 61.7595i −0.394725 0.227895i 0.289480 0.957184i \(-0.406518\pi\)
−0.684206 + 0.729289i \(0.739851\pi\)
\(272\) 35.8297 0.131727
\(273\) 180.974 + 184.706i 0.662908 + 0.676577i
\(274\) 94.7939 0.345963
\(275\) 0 0
\(276\) −112.368 + 64.8754i −0.407129 + 0.235056i
\(277\) −236.323 + 136.441i −0.853151 + 0.492567i −0.861713 0.507396i \(-0.830608\pi\)
0.00856145 + 0.999963i \(0.497275\pi\)
\(278\) −64.7374 + 112.128i −0.232868 + 0.403340i
\(279\) 132.425i 0.474643i
\(280\) 0 0
\(281\) 133.103 0.473675 0.236837 0.971549i \(-0.423889\pi\)
0.236837 + 0.971549i \(0.423889\pi\)
\(282\) −91.2255 52.6690i −0.323495 0.186770i
\(283\) 64.3787 + 111.507i 0.227486 + 0.394018i 0.957063 0.289882i \(-0.0936159\pi\)
−0.729576 + 0.683900i \(0.760283\pi\)
\(284\) 137.397 + 237.979i 0.483792 + 0.837953i
\(285\) 0 0
\(286\) 180.974i 0.632776i
\(287\) −95.5512 371.735i −0.332931 1.29524i
\(288\) 16.9706i 0.0589256i
\(289\) 104.382 180.795i 0.361184 0.625589i
\(290\) 0 0
\(291\) 9.51472 + 16.4800i 0.0326966 + 0.0566322i
\(292\) 78.9270 136.706i 0.270298 0.468170i
\(293\) 308.984 1.05455 0.527276 0.849694i \(-0.323213\pi\)
0.527276 + 0.849694i \(0.323213\pi\)
\(294\) −57.8787 105.148i −0.196866 0.357646i
\(295\) 0 0
\(296\) −39.5563 + 68.5136i −0.133636 + 0.231465i
\(297\) −15.5885 27.0000i −0.0524864 0.0909091i
\(298\) 99.3125 57.3381i 0.333263 0.192410i
\(299\) −691.831 399.429i −2.31381 1.33588i
\(300\) 0 0
\(301\) −2.58831 10.0696i −0.00859904 0.0334539i
\(302\) 72.4163i 0.239789i
\(303\) 160.775 + 92.8234i 0.530610 + 0.306348i
\(304\) −25.0294 + 14.4508i −0.0823337 + 0.0475354i
\(305\) 0 0
\(306\) 32.9117 + 19.0016i 0.107555 + 0.0620966i
\(307\) 606.090 1.97423 0.987117 0.160003i \(-0.0511503\pi\)
0.987117 + 0.160003i \(0.0511503\pi\)
\(308\) −22.5676 + 80.9117i −0.0732716 + 0.262700i
\(309\) −182.220 −0.589710
\(310\) 0 0
\(311\) −176.044 + 101.639i −0.566057 + 0.326813i −0.755573 0.655064i \(-0.772641\pi\)
0.189516 + 0.981878i \(0.439308\pi\)
\(312\) 90.4869 52.2426i 0.290022 0.167444i
\(313\) −202.820 + 351.294i −0.647986 + 1.12234i 0.335617 + 0.941999i \(0.391055\pi\)
−0.983603 + 0.180346i \(0.942278\pi\)
\(314\) 264.545i 0.842500i
\(315\) 0 0
\(316\) 196.676 0.622393
\(317\) 22.5676 + 13.0294i 0.0711913 + 0.0411023i 0.535173 0.844742i \(-0.320246\pi\)
−0.463982 + 0.885845i \(0.653580\pi\)
\(318\) −104.662 181.279i −0.329125 0.570060i
\(319\) −101.823 176.363i −0.319196 0.552863i
\(320\) 0 0
\(321\) 205.325i 0.639640i
\(322\) 259.502 + 264.853i 0.805906 + 0.822524i
\(323\) 64.7208i 0.200374i
\(324\) 9.00000 15.5885i 0.0277778 0.0481125i
\(325\) 0 0
\(326\) 59.3553 + 102.806i 0.182072 + 0.315357i
\(327\) 96.1798 166.588i 0.294128 0.509444i
\(328\) −155.086 −0.472824
\(329\) −80.8751 + 289.961i −0.245821 + 0.881341i
\(330\) 0 0
\(331\) 54.3162 94.0785i 0.164097 0.284225i −0.772237 0.635335i \(-0.780862\pi\)
0.936334 + 0.351110i \(0.114196\pi\)
\(332\) −110.401 191.220i −0.332533 0.575965i
\(333\) −72.6697 + 41.9558i −0.218227 + 0.125994i
\(334\) −156.302 90.2407i −0.467969 0.270182i
\(335\) 0 0
\(336\) −46.9706 + 12.0734i −0.139793 + 0.0359326i
\(337\) 441.735i 1.31079i 0.755288 + 0.655393i \(0.227497\pi\)
−0.755288 + 0.655393i \(0.772503\pi\)
\(338\) 350.133 + 202.149i 1.03590 + 0.598075i
\(339\) −152.095 + 87.8124i −0.448659 + 0.259033i
\(340\) 0 0
\(341\) −229.368 132.425i −0.672632 0.388344i
\(342\) −30.6547 −0.0896336
\(343\) −249.848 + 235.000i −0.728420 + 0.685131i
\(344\) −4.20101 −0.0122122
\(345\) 0 0
\(346\) −175.103 + 101.096i −0.506077 + 0.292184i
\(347\) 29.6102 17.0955i 0.0853320 0.0492664i −0.456727 0.889607i \(-0.650978\pi\)
0.542059 + 0.840341i \(0.317645\pi\)
\(348\) 58.7878 101.823i 0.168930 0.292596i
\(349\) 221.787i 0.635493i 0.948176 + 0.317746i \(0.102926\pi\)
−0.948176 + 0.317746i \(0.897074\pi\)
\(350\) 0 0
\(351\) 110.823 0.315736
\(352\) 29.3939 + 16.9706i 0.0835053 + 0.0482118i
\(353\) −223.693 387.448i −0.633692 1.09759i −0.986791 0.162000i \(-0.948206\pi\)
0.353099 0.935586i \(-0.385128\pi\)
\(354\) −50.4853 87.4431i −0.142614 0.247014i
\(355\) 0 0
\(356\) 41.5692i 0.116767i
\(357\) 29.1776 104.610i 0.0817299 0.293026i
\(358\) 239.397i 0.668707i
\(359\) 145.882 252.675i 0.406357 0.703831i −0.588121 0.808773i \(-0.700132\pi\)
0.994478 + 0.104941i \(0.0334655\pi\)
\(360\) 0 0
\(361\) −154.397 267.423i −0.427692 0.740785i
\(362\) −148.470 + 257.158i −0.410139 + 0.710381i
\(363\) −147.224 −0.405577
\(364\) −208.971 213.280i −0.574095 0.585933i
\(365\) 0 0
\(366\) −1.45584 + 2.52160i −0.00397772 + 0.00688961i
\(367\) −209.676 363.169i −0.571324 0.989561i −0.996430 0.0844183i \(-0.973097\pi\)
0.425107 0.905143i \(-0.360237\pi\)
\(368\) 129.751 74.9117i 0.352584 0.203564i
\(369\) −142.456 82.2469i −0.386059 0.222891i
\(370\) 0 0
\(371\) −427.279 + 418.646i −1.15170 + 1.12843i
\(372\) 152.912i 0.411053i
\(373\) 27.1775 + 15.6909i 0.0728618 + 0.0420668i 0.535988 0.844225i \(-0.319939\pi\)
−0.463127 + 0.886292i \(0.653272\pi\)
\(374\) −65.8234 + 38.0031i −0.175998 + 0.101613i
\(375\) 0 0
\(376\) 105.338 + 60.8170i 0.280155 + 0.161747i
\(377\) 723.895 1.92015
\(378\) −49.5481 13.8198i −0.131080 0.0365603i
\(379\) −206.779 −0.545590 −0.272795 0.962072i \(-0.587948\pi\)
−0.272795 + 0.962072i \(0.587948\pi\)
\(380\) 0 0
\(381\) 123.860 71.5108i 0.325093 0.187692i
\(382\) −81.5717 + 47.0955i −0.213539 + 0.123287i
\(383\) −249.283 + 431.772i −0.650871 + 1.12734i 0.332041 + 0.943265i \(0.392263\pi\)
−0.982912 + 0.184076i \(0.941071\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 13.8507 0.0358827
\(387\) −3.85887 2.22792i −0.00997125 0.00575690i
\(388\) −10.9867 19.0294i −0.0283161 0.0490449i
\(389\) −324.213 561.554i −0.833453 1.44358i −0.895284 0.445496i \(-0.853027\pi\)
0.0618308 0.998087i \(-0.480306\pi\)
\(390\) 0 0
\(391\) 335.508i 0.858077i
\(392\) 66.8325 + 121.414i 0.170491 + 0.309730i
\(393\) 104.912i 0.266951i
\(394\) 188.912 327.205i 0.479471 0.830469i
\(395\) 0 0
\(396\) 18.0000 + 31.1769i 0.0454545 + 0.0787296i
\(397\) −37.8757 + 65.6026i −0.0954047 + 0.165246i −0.909777 0.415096i \(-0.863748\pi\)
0.814373 + 0.580342i \(0.197081\pi\)
\(398\) 185.176 0.465268
\(399\) 21.8087 + 84.8450i 0.0546583 + 0.212644i
\(400\) 0 0
\(401\) 282.125 488.655i 0.703553 1.21859i −0.263658 0.964616i \(-0.584929\pi\)
0.967211 0.253974i \(-0.0817377\pi\)
\(402\) −5.38517 9.32738i −0.0133959 0.0232024i
\(403\) 815.324 470.727i 2.02314 1.16806i
\(404\) −185.647 107.183i −0.459522 0.265305i
\(405\) 0 0
\(406\) −323.647 90.2706i −0.797159 0.222341i
\(407\) 167.823i 0.412342i
\(408\) −38.0031 21.9411i −0.0931450 0.0537773i
\(409\) 309.559 178.724i 0.756868 0.436978i −0.0713023 0.997455i \(-0.522716\pi\)
0.828170 + 0.560477i \(0.189382\pi\)
\(410\) 0 0
\(411\) −100.544 58.0492i −0.244633 0.141239i
\(412\) 210.410 0.510704
\(413\) −206.105 + 201.941i −0.499044 + 0.488962i
\(414\) 158.912 0.383845
\(415\) 0 0
\(416\) −104.485 + 60.3246i −0.251167 + 0.145011i
\(417\) 137.329 79.2868i 0.329326 0.190136i
\(418\) 30.6547 53.0955i 0.0733365 0.127023i
\(419\) 502.175i 1.19851i −0.800559 0.599254i \(-0.795464\pi\)
0.800559 0.599254i \(-0.204536\pi\)
\(420\) 0 0
\(421\) 33.7939 0.0802706 0.0401353 0.999194i \(-0.487221\pi\)
0.0401353 + 0.999194i \(0.487221\pi\)
\(422\) −28.2773 16.3259i −0.0670078 0.0386870i
\(423\) 64.5061 + 111.728i 0.152497 + 0.264132i
\(424\) 120.853 + 209.323i 0.285030 + 0.493687i
\(425\) 0 0
\(426\) 336.552i 0.790029i
\(427\) 8.01492 + 2.23550i 0.0187703 + 0.00523536i
\(428\) 237.088i 0.553945i
\(429\) −110.823 + 191.952i −0.258330 + 0.447440i
\(430\) 0 0
\(431\) −251.860 436.234i −0.584362 1.01214i −0.994955 0.100326i \(-0.968012\pi\)
0.410593 0.911819i \(-0.365322\pi\)
\(432\) −10.3923 + 18.0000i −0.0240563 + 0.0416667i
\(433\) 837.548 1.93429 0.967145 0.254224i \(-0.0818202\pi\)
0.967145 + 0.254224i \(0.0818202\pi\)
\(434\) −423.224 + 108.786i −0.975170 + 0.250659i
\(435\) 0 0
\(436\) −111.059 + 192.360i −0.254722 + 0.441192i
\(437\) −135.316 234.375i −0.309648 0.536326i
\(438\) −167.430 + 96.6655i −0.382259 + 0.220697i
\(439\) 164.558 + 95.0079i 0.374848 + 0.216419i 0.675575 0.737292i \(-0.263896\pi\)
−0.300726 + 0.953711i \(0.597229\pi\)
\(440\) 0 0
\(441\) −3.00000 + 146.969i −0.00680272 + 0.333264i
\(442\) 270.177i 0.611259i
\(443\) −146.753 84.7279i −0.331271 0.191259i 0.325134 0.945668i \(-0.394591\pi\)
−0.656405 + 0.754408i \(0.727924\pi\)
\(444\) 83.9117 48.4464i 0.188990 0.109114i
\(445\) 0 0
\(446\) −280.014 161.666i −0.627835 0.362481i
\(447\) −140.449 −0.314204
\(448\) 54.2369 13.9411i 0.121065 0.0311186i
\(449\) −18.1035 −0.0403195 −0.0201598 0.999797i \(-0.506417\pi\)
−0.0201598 + 0.999797i \(0.506417\pi\)
\(450\) 0 0
\(451\) 284.912 164.494i 0.631733 0.364731i
\(452\) 175.625 101.397i 0.388550 0.224330i
\(453\) 44.3457 76.8091i 0.0978935 0.169556i
\(454\) 92.7922i 0.204388i
\(455\) 0 0
\(456\) 35.3970 0.0776249
\(457\) 284.769 + 164.412i 0.623128 + 0.359763i 0.778086 0.628158i \(-0.216191\pi\)
−0.154958 + 0.987921i \(0.549524\pi\)
\(458\) −66.1002 114.489i −0.144324 0.249976i
\(459\) −23.2721 40.3084i −0.0507017 0.0878179i
\(460\) 0 0
\(461\) 794.331i 1.72306i −0.507706 0.861530i \(-0.669506\pi\)
0.507706 0.861530i \(-0.330494\pi\)
\(462\) 73.4847 72.0000i 0.159058 0.155844i
\(463\) 403.396i 0.871266i 0.900124 + 0.435633i \(0.143475\pi\)
−0.900124 + 0.435633i \(0.856525\pi\)
\(464\) −67.8823 + 117.576i −0.146298 + 0.253395i
\(465\) 0 0
\(466\) −167.948 290.895i −0.360404 0.624238i
\(467\) 1.41376 2.44870i 0.00302732 0.00524347i −0.864508 0.502619i \(-0.832370\pi\)
0.867535 + 0.497376i \(0.165703\pi\)
\(468\) −127.968 −0.273435
\(469\) −21.9848 + 21.5407i −0.0468760 + 0.0459289i
\(470\) 0 0
\(471\) 162.000 280.592i 0.343949 0.595737i
\(472\) 58.2954 + 100.971i 0.123507 + 0.213921i
\(473\) 7.71775 4.45584i 0.0163166 0.00942039i
\(474\) −208.607 120.439i −0.440098 0.254091i
\(475\) 0 0
\(476\) −33.6913 + 120.793i −0.0707801 + 0.253768i
\(477\) 256.368i 0.537458i
\(478\) −449.301 259.404i −0.939960 0.542686i
\(479\) −328.669 + 189.757i −0.686157 + 0.396153i −0.802171 0.597095i \(-0.796322\pi\)
0.116014 + 0.993248i \(0.462988\pi\)
\(480\) 0 0
\(481\) 516.632 + 298.278i 1.07408 + 0.620120i
\(482\) −595.418 −1.23531
\(483\) −113.055 439.831i −0.234067 0.910622i
\(484\) 170.000 0.351240
\(485\) 0 0
\(486\) −19.0919 + 11.0227i −0.0392837 + 0.0226805i
\(487\) 498.410 287.757i 1.02343 0.590877i 0.108333 0.994115i \(-0.465449\pi\)
0.915095 + 0.403238i \(0.132115\pi\)
\(488\) 1.68106 2.91169i 0.00344480 0.00596657i
\(489\) 145.390i 0.297322i
\(490\) 0 0
\(491\) 238.441 0.485623 0.242811 0.970074i \(-0.421930\pi\)
0.242811 + 0.970074i \(0.421930\pi\)
\(492\) 164.494 + 94.9706i 0.334337 + 0.193030i
\(493\) −152.013 263.294i −0.308342 0.534064i
\(494\) 108.967 + 188.736i 0.220581 + 0.382057i
\(495\) 0 0
\(496\) 176.567i 0.355982i
\(497\) −931.499 + 239.434i −1.87424 + 0.481758i
\(498\) 270.426i 0.543025i
\(499\) −143.287 + 248.180i −0.287148 + 0.497355i −0.973128 0.230266i \(-0.926040\pi\)
0.685980 + 0.727620i \(0.259374\pi\)
\(500\) 0 0
\(501\) 110.522 + 191.429i 0.220603 + 0.382095i
\(502\) −103.677 + 179.574i −0.206528 + 0.357716i
\(503\) 25.4374 0.0505714 0.0252857 0.999680i \(-0.491950\pi\)
0.0252857 + 0.999680i \(0.491950\pi\)
\(504\) 57.2132 + 15.9577i 0.113518 + 0.0316622i
\(505\) 0 0
\(506\) −158.912 + 275.243i −0.314055 + 0.543959i
\(507\) −247.581 428.823i −0.488326 0.845805i
\(508\) −143.022 + 82.5736i −0.281539 + 0.162546i
\(509\) 697.889 + 402.926i 1.37110 + 0.791603i 0.991066 0.133370i \(-0.0425800\pi\)
0.380031 + 0.924974i \(0.375913\pi\)
\(510\) 0 0
\(511\) 386.662 + 394.635i 0.756677 + 0.772280i
\(512\) 22.6274i 0.0441942i
\(513\) 32.5142 + 18.7721i 0.0633805 + 0.0365927i
\(514\) −30.7279 + 17.7408i −0.0597819 + 0.0345151i
\(515\) 0 0
\(516\) 4.45584 + 2.57258i 0.00863536 + 0.00498563i
\(517\) −258.025 −0.499080
\(518\) −193.786 197.782i −0.374104 0.381818i
\(519\) 247.632 0.477134
\(520\) 0 0
\(521\) −661.706 + 382.036i −1.27007 + 0.733274i −0.975001 0.222202i \(-0.928676\pi\)
−0.295068 + 0.955476i \(0.595342\pi\)
\(522\) −124.708 + 72.0000i −0.238904 + 0.137931i
\(523\) −88.3900 + 153.096i −0.169006 + 0.292726i −0.938071 0.346444i \(-0.887389\pi\)
0.769065 + 0.639171i \(0.220722\pi\)
\(524\) 121.142i 0.231186i
\(525\) 0 0
\(526\) 128.235 0.243794
\(527\) −342.424 197.698i −0.649761 0.375139i
\(528\) −20.7846 36.0000i −0.0393648 0.0681818i
\(529\) 436.970 + 756.854i 0.826030 + 1.43073i
\(530\) 0 0
\(531\) 123.663i 0.232887i
\(532\) −25.1825 97.9706i −0.0473355 0.184155i
\(533\) 1169.44i 2.19407i
\(534\) 25.4558 44.0908i 0.0476701 0.0825671i
\(535\) 0 0
\(536\) 6.21825 + 10.7703i 0.0116012 + 0.0200939i
\(537\) 146.600 253.919i 0.272998 0.472847i
\(538\) 96.7312 0.179798
\(539\) −251.558 152.166i −0.466713 0.282311i
\(540\) 0 0
\(541\) −8.58831 + 14.8754i −0.0158749 + 0.0274961i −0.873854 0.486189i \(-0.838387\pi\)
0.857979 + 0.513685i \(0.171720\pi\)
\(542\) −87.3411 151.279i −0.161146 0.279113i
\(543\) 314.953 181.838i 0.580024 0.334877i
\(544\) 43.8823 + 25.3354i 0.0806659 + 0.0465725i
\(545\) 0 0
\(546\) 91.0402 + 354.185i 0.166740 + 0.648691i
\(547\) 212.676i 0.388805i 0.980922 + 0.194402i \(0.0622767\pi\)
−0.980922 + 0.194402i \(0.937723\pi\)
\(548\) 116.098 + 67.0294i 0.211858 + 0.122316i
\(549\) 3.08831 1.78304i 0.00562534 0.00324779i
\(550\) 0 0
\(551\) 212.382 + 122.619i 0.385448 + 0.222538i
\(552\) −183.495 −0.332419
\(553\) −184.938 + 663.058i −0.334427 + 1.19902i
\(554\) −385.914 −0.696595
\(555\) 0 0
\(556\) −158.574 + 91.5525i −0.285204 + 0.164663i
\(557\) −763.528 + 440.823i −1.37079 + 0.791424i −0.991027 0.133661i \(-0.957327\pi\)
−0.379760 + 0.925085i \(0.623993\pi\)
\(558\) −93.6389 + 162.187i −0.167812 + 0.290658i
\(559\) 31.6780i 0.0566691i
\(560\) 0 0
\(561\) 93.0883 0.165933
\(562\) 163.017 + 94.1177i 0.290065 + 0.167469i
\(563\) −383.534 664.301i −0.681233 1.17993i −0.974605 0.223932i \(-0.928111\pi\)
0.293372 0.955998i \(-0.405223\pi\)
\(564\) −74.4853 129.012i −0.132066 0.228745i
\(565\) 0 0
\(566\) 182.090i 0.321714i
\(567\) 44.0908 + 45.0000i 0.0777616 + 0.0793651i
\(568\) 388.617i 0.684185i
\(569\) −14.6468 + 25.3689i −0.0257412 + 0.0445851i −0.878609 0.477542i \(-0.841528\pi\)
0.852868 + 0.522127i \(0.174861\pi\)
\(570\) 0 0
\(571\) −482.521 835.752i −0.845046 1.46366i −0.885581 0.464485i \(-0.846239\pi\)
0.0405347 0.999178i \(-0.487094\pi\)
\(572\) 127.968 221.647i 0.223720 0.387494i
\(573\) 115.360 0.201326
\(574\) 145.831 522.846i 0.254060 0.910881i
\(575\) 0 0
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) 131.568 + 227.883i 0.228021 + 0.394944i 0.957222 0.289356i \(-0.0934412\pi\)
−0.729201 + 0.684300i \(0.760108\pi\)
\(578\) 255.683 147.619i 0.442359 0.255396i
\(579\) −14.6909 8.48180i −0.0253729 0.0146491i
\(580\) 0 0
\(581\) 748.477 192.389i 1.28826 0.331135i
\(582\) 26.9117i 0.0462400i
\(583\) −444.042 256.368i −0.761649 0.439738i
\(584\) 193.331 111.620i 0.331046 0.191130i
\(585\) 0 0
\(586\) 378.426 + 218.485i 0.645779 + 0.372841i
\(587\) 436.477 0.743572 0.371786 0.928318i \(-0.378746\pi\)
0.371786 + 0.928318i \(0.378746\pi\)
\(588\) 3.46410 169.706i 0.00589133 0.288615i
\(589\) 318.941 0.541496
\(590\) 0 0
\(591\) −400.742 + 231.369i −0.678075 + 0.391487i
\(592\) −96.8929 + 55.9411i −0.163670 + 0.0944951i
\(593\) 348.490 603.603i 0.587673 1.01788i −0.406863 0.913489i \(-0.633377\pi\)
0.994536 0.104391i \(-0.0332894\pi\)
\(594\) 44.0908i 0.0742270i
\(595\) 0 0
\(596\) 162.177 0.272108
\(597\) −196.409 113.397i −0.328994 0.189945i
\(598\) −564.877 978.396i −0.944611 1.63611i
\(599\) 199.206 + 345.035i 0.332564 + 0.576018i 0.983014 0.183531i \(-0.0587528\pi\)
−0.650450 + 0.759549i \(0.725419\pi\)
\(600\) 0 0
\(601\) 36.1691i 0.0601816i −0.999547 0.0300908i \(-0.990420\pi\)
0.999547 0.0300908i \(-0.00957964\pi\)
\(602\) 3.95029 14.1630i 0.00656194 0.0235265i
\(603\) 13.1909i 0.0218755i
\(604\) −51.2061 + 88.6915i −0.0847782 + 0.146840i
\(605\) 0 0
\(606\) 131.272 + 227.370i 0.216621 + 0.375198i
\(607\) −15.7880 + 27.3457i −0.0260099 + 0.0450505i −0.878737 0.477306i \(-0.841613\pi\)
0.852727 + 0.522356i \(0.174947\pi\)
\(608\) −40.8729 −0.0672252
\(609\) 288.000 + 293.939i 0.472906 + 0.482658i
\(610\) 0 0
\(611\) 458.595 794.310i 0.750565 1.30002i
\(612\) 26.8723 + 46.5442i 0.0439090 + 0.0760525i
\(613\) 354.434 204.632i 0.578195 0.333821i −0.182220 0.983258i \(-0.558328\pi\)
0.760416 + 0.649436i \(0.224995\pi\)
\(614\) 742.305 + 428.570i 1.20897 + 0.697997i
\(615\) 0 0
\(616\) −84.8528 + 83.1384i −0.137748 + 0.134965i
\(617\) 1227.38i 1.98927i 0.103436 + 0.994636i \(0.467016\pi\)
−0.103436 + 0.994636i \(0.532984\pi\)
\(618\) −223.173 128.849i −0.361122 0.208494i
\(619\) −412.022 + 237.881i −0.665625 + 0.384299i −0.794417 0.607373i \(-0.792223\pi\)
0.128792 + 0.991672i \(0.458890\pi\)
\(620\) 0 0
\(621\) −168.551 97.3131i −0.271419 0.156704i
\(622\) −287.478 −0.462184
\(623\) −140.143 39.0883i −0.224949 0.0627421i
\(624\) 147.765 0.236802
\(625\) 0 0
\(626\) −496.805 + 286.830i −0.793618 + 0.458195i
\(627\) −65.0284 + 37.5442i −0.103714 + 0.0598790i
\(628\) −187.061 + 324.000i −0.297869 + 0.515924i
\(629\) 250.544i 0.398322i
\(630\) 0 0
\(631\) −54.9420 −0.0870713 −0.0435357 0.999052i \(-0.513862\pi\)
−0.0435357 + 0.999052i \(0.513862\pi\)
\(632\) 240.878 + 139.071i 0.381136 + 0.220049i
\(633\) 19.9951 + 34.6325i 0.0315878 + 0.0547116i
\(634\) 18.4264 + 31.9155i 0.0290637 + 0.0503399i
\(635\) 0 0
\(636\) 296.028i 0.465452i
\(637\) 915.533 503.956i 1.43726 0.791139i
\(638\) 288.000i 0.451411i
\(639\) −206.095 + 356.968i −0.322528 + 0.558635i
\(640\) 0 0
\(641\) 114.551 + 198.409i 0.178707 + 0.309530i 0.941438 0.337186i \(-0.109475\pi\)
−0.762731 + 0.646716i \(0.776142\pi\)
\(642\) −145.186 + 251.470i −0.226147 + 0.391698i
\(643\) 854.640 1.32914 0.664572 0.747224i \(-0.268614\pi\)
0.664572 + 0.747224i \(0.268614\pi\)
\(644\) 130.544 + 507.873i 0.202708 + 0.788622i
\(645\) 0 0
\(646\) 45.7645 79.2664i 0.0708429 0.122703i
\(647\) 501.505 + 868.632i 0.775124 + 1.34255i 0.934725 + 0.355372i \(0.115646\pi\)
−0.159601 + 0.987182i \(0.551021\pi\)
\(648\) 22.0454 12.7279i 0.0340207 0.0196419i
\(649\) −214.191 123.663i −0.330032 0.190544i
\(650\) 0 0
\(651\) 515.514 + 143.786i 0.791881 + 0.220869i
\(652\) 167.882i 0.257488i
\(653\) 1100.51 + 635.382i 1.68532 + 0.973020i 0.958021 + 0.286698i \(0.0925578\pi\)
0.727299 + 0.686321i \(0.240776\pi\)
\(654\) 235.591 136.019i 0.360232 0.207980i
\(655\) 0 0
\(656\) −189.941 109.663i −0.289544 0.167169i
\(657\) 236.781 0.360397
\(658\) −304.085 + 297.941i −0.462135 + 0.452798i
\(659\) 783.308 1.18863 0.594315 0.804232i \(-0.297423\pi\)
0.594315 + 0.804232i \(0.297423\pi\)
\(660\) 0 0
\(661\) 72.5589 41.8919i 0.109771 0.0633765i −0.444109 0.895973i \(-0.646480\pi\)
0.553881 + 0.832596i \(0.313146\pi\)
\(662\) 133.047 76.8148i 0.200977 0.116034i
\(663\) −165.449 + 286.566i −0.249546 + 0.432226i
\(664\) 312.262i 0.470273i
\(665\) 0 0
\(666\) −118.669 −0.178182
\(667\) −1100.97 635.647i −1.65063 0.952994i
\(668\) −127.620 221.044i −0.191047 0.330904i
\(669\) 198.000 + 342.946i 0.295964 + 0.512625i
\(670\) 0 0
\(671\) 7.13215i 0.0106291i
\(672\) −66.0641 18.4264i −0.0983097 0.0274202i
\(673\) 415.676i 0.617647i −0.951119 0.308823i \(-0.900065\pi\)
0.951119 0.308823i \(-0.0999352\pi\)
\(674\) −312.354 + 541.013i −0.463433 + 0.802690i
\(675\) 0 0
\(676\) 285.882 + 495.163i 0.422903 + 0.732489i
\(677\) −395.646 + 685.279i −0.584411 + 1.01223i 0.410538 + 0.911844i \(0.365341\pi\)
−0.994949 + 0.100386i \(0.967992\pi\)
\(678\) −248.371 −0.366329
\(679\) 74.4853 19.1458i 0.109698 0.0281970i
\(680\) 0 0
\(681\) 56.8234 98.4210i 0.0834411 0.144524i
\(682\) −187.278 324.375i −0.274601 0.475623i
\(683\) 284.195 164.080i 0.416099 0.240235i −0.277308 0.960781i \(-0.589442\pi\)
0.693407 + 0.720546i \(0.256109\pi\)
\(684\) −37.5442 21.6761i −0.0548891 0.0316902i
\(685\) 0 0
\(686\) −472.170 + 111.146i −0.688295 + 0.162020i
\(687\) 161.912i 0.235679i
\(688\) −5.14517 2.97056i −0.00747844 0.00431768i
\(689\) 1578.42 911.300i 2.29088 1.32264i
\(690\) 0 0
\(691\) 875.182 + 505.287i 1.26654 + 0.731240i 0.974333 0.225113i \(-0.0722753\pi\)
0.292212 + 0.956353i \(0.405609\pi\)
\(692\) −285.941 −0.413210
\(693\) −122.033 + 31.3675i −0.176094 + 0.0452634i
\(694\) 48.3532 0.0696733
\(695\) 0 0
\(696\) 144.000 83.1384i 0.206897 0.119452i
\(697\) 425.346 245.574i 0.610252 0.352329i
\(698\) −156.827 + 271.632i −0.224681 + 0.389158i
\(699\) 411.388i 0.588537i
\(700\) 0 0
\(701\) −0.103464 −0.000147594 −7.37972e−5 1.00000i \(-0.500023\pi\)
−7.37972e−5 1.00000i \(0.500023\pi\)
\(702\) 135.730 + 78.3640i 0.193348 + 0.111630i
\(703\) 101.049 + 175.022i 0.143740 + 0.248964i
\(704\) 24.0000 + 41.5692i 0.0340909 + 0.0590472i
\(705\) 0 0
\(706\) 632.700i 0.896175i
\(707\) 535.916 525.088i 0.758014 0.742699i
\(708\) 142.794i 0.201686i
\(709\) 602.588 1043.71i 0.849912 1.47209i −0.0313734 0.999508i \(-0.509988\pi\)
0.881286 0.472584i \(-0.156679\pi\)
\(710\) 0 0
\(711\) 147.507 + 255.490i 0.207464 + 0.359339i
\(712\) −29.3939 + 50.9117i −0.0412835 + 0.0715052i
\(713\) −1653.37 −2.31889
\(714\) 109.706 107.489i 0.153649 0.150545i
\(715\) 0 0
\(716\) −169.279 + 293.200i −0.236423 + 0.409498i
\(717\) 317.704 + 550.279i 0.443102 + 0.767475i
\(718\) 357.337 206.309i 0.497684 0.287338i
\(719\) −850.925 491.282i −1.18348 0.683285i −0.226666 0.973973i \(-0.572783\pi\)
−0.956818 + 0.290688i \(0.906116\pi\)
\(720\) 0 0
\(721\) −197.852 + 709.359i −0.274414 + 0.983855i
\(722\) 436.701i 0.604848i
\(723\) 631.536 + 364.617i 0.873493 + 0.504312i
\(724\) −363.676 + 209.969i −0.502315 + 0.290012i
\(725\) 0 0
\(726\) −180.312 104.103i −0.248364 0.143393i
\(727\) −630.440 −0.867181 −0.433590 0.901110i \(-0.642753\pi\)
−0.433590 + 0.901110i \(0.642753\pi\)
\(728\) −105.124 408.978i −0.144401 0.561783i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) 11.5219 6.65215i 0.0157618 0.00910007i
\(732\) −3.56608 + 2.05887i −0.00487169 + 0.00281267i
\(733\) 149.237 258.486i 0.203597 0.352641i −0.746088 0.665848i \(-0.768070\pi\)
0.949685 + 0.313207i \(0.101403\pi\)
\(734\) 593.053i 0.807974i
\(735\) 0 0
\(736\) 211.882 0.287883
\(737\) −22.8473 13.1909i −0.0310004 0.0178981i
\(738\) −116.315 201.463i −0.157608 0.272985i
\(739\) 172.684 + 299.097i 0.233672 + 0.404732i 0.958886 0.283792i \(-0.0915924\pi\)
−0.725214 + 0.688524i \(0.758259\pi\)
\(740\) 0 0
\(741\) 266.914i 0.360207i
\(742\) −819.336 + 210.603i −1.10423 + 0.283832i
\(743\) 683.616i 0.920076i −0.887899 0.460038i \(-0.847836\pi\)
0.887899 0.460038i \(-0.152164\pi\)
\(744\) 108.125 187.278i 0.145329 0.251717i
\(745\) 0 0
\(746\) 22.1903 + 38.4347i 0.0297457 + 0.0515211i
\(747\) 165.602 286.831i 0.221689 0.383977i
\(748\) −107.489 −0.143702
\(749\) 799.301 + 222.939i 1.06716 + 0.297648i
\(750\) 0 0
\(751\) 289.169 500.855i 0.385045 0.666918i −0.606730 0.794908i \(-0.707519\pi\)
0.991775 + 0.127990i \(0.0408525\pi\)
\(752\) 86.0082 + 148.971i 0.114373 + 0.198099i
\(753\) 219.932 126.978i 0.292074 0.168629i
\(754\) 886.587 + 511.871i 1.17584 + 0.678874i
\(755\) 0 0
\(756\) −50.9117 51.9615i −0.0673435 0.0687322i
\(757\) 1204.82i 1.59158i 0.605576 + 0.795788i \(0.292943\pi\)
−0.605576 + 0.795788i \(0.707057\pi\)
\(758\) −253.251 146.215i −0.334105 0.192895i
\(759\) 337.103 194.626i 0.444140 0.256425i
\(760\) 0 0
\(761\) −202.669 117.011i −0.266319 0.153760i 0.360894 0.932607i \(-0.382471\pi\)
−0.627214 + 0.778847i \(0.715805\pi\)
\(762\) 202.263 0.265437
\(763\) −544.075 555.294i −0.713074 0.727778i
\(764\) −133.206 −0.174353
\(765\) 0 0
\(766\) −610.617 + 352.540i −0.797151 + 0.460235i
\(767\) 761.376 439.581i 0.992668 0.573117i
\(768\) −13.8564 + 24.0000i −0.0180422 + 0.0312500i
\(769\) 1290.16i 1.67771i 0.544358 + 0.838853i \(0.316774\pi\)
−0.544358 + 0.838853i \(0.683226\pi\)
\(770\) 0 0
\(771\) 43.4558 0.0563630
\(772\) 16.9636 + 9.79394i 0.0219736 + 0.0126864i
\(773\) −199.559 345.646i −0.258161 0.447149i 0.707588 0.706625i \(-0.249783\pi\)
−0.965749 + 0.259477i \(0.916450\pi\)
\(774\) −3.15076 5.45727i −0.00407075 0.00705074i
\(775\) 0 0
\(776\) 31.0749i 0.0400450i
\(777\) 84.4247 + 328.448i 0.108655 + 0.422713i
\(778\) 917.013i 1.17868i
\(779\) −198.088 + 343.099i −0.254285 + 0.440435i
\(780\) 0 0
\(781\) −412.191 713.936i −0.527773 0.914130i
\(782\) −237.240 + 410.912i