Properties

Label 1050.3.q.a.649.2
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: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
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 649.2
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.a.199.2

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} - 12 q^{9} - 24 q^{11} - 48 q^{14} - 16 q^{16} + 84 q^{19} + 192 q^{26} + 204 q^{31} - 48 q^{36} - 12 q^{39} + 48 q^{44} - 144 q^{46} + 4 q^{49} - 96 q^{51} - 96 q^{56} + 48 q^{59} - 144 q^{61} - 64 q^{64} + 624 q^{71} + 96 q^{74} + 20 q^{79} - 36 q^{81} - 120 q^{84} - 48 q^{86} + 144 q^{89} - 444 q^{91} + 48 q^{94} + 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(-0.806197\pi\)
−0.820306 + 0.571924i \(0.806197\pi\)
\(14\) −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 0.967157 0.254178i \(-0.0818050\pi\)
−0.703704 + 0.710494i \(0.748472\pi\)
\(18\) 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 0.995420 0.0956024i \(-0.0304777\pi\)
0.414916 + 0.909860i \(0.363811\pi\)
\(24\) 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 0.135566 0.990768i \(-0.456715\pi\)
−0.790248 + 0.612788i \(0.790048\pi\)
\(38\) −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 \(-0.994502\pi\)
0.999851 0.0172707i \(-0.00549771\pi\)
\(44\) 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 −0.998828 0.0484090i \(-0.984585\pi\)
0.541337 + 0.840806i \(0.317918\pi\)
\(48\) −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 −0.994009 0.109299i \(-0.965139\pi\)
−0.402348 + 0.915487i \(0.631806\pi\)
\(54\) 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 −0.528148 0.849152i \(-0.677113\pi\)
0.471314 + 0.881966i \(0.343780\pi\)
\(68\) −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 \(0.0151346\pi\)
−0.458274 + 0.888811i \(0.651532\pi\)
\(74\) 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 \(-0.268403\pi\)
0.665067 + 0.746784i \(0.268403\pi\)
\(84\) −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 \(-0.481964\pi\)
0.0566322 + 0.998395i \(0.481964\pi\)
\(98\) −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 \(0.337282\pi\)
−0.999923 + 0.0124040i \(0.996052\pi\)
\(104\) 60.3246i 0.580044i
\(105\) 0 0
\(106\) 120.853 1.14012
\(107\) 102.662 + 59.2721i 0.959460 + 0.553945i 0.896007 0.444040i \(-0.146455\pi\)
0.0634534 + 0.997985i \(0.479789\pi\)
\(108\) −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 \(0.148098\pi\)
−0.893703 + 0.448659i \(0.851902\pi\)
\(114\) 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 \(-0.894604\pi\)
0.945682 0.325093i \(-0.105396\pi\)
\(128\) 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 −0.696666 0.717395i \(-0.745334\pi\)
0.272949 + 0.962028i \(0.412001\pi\)
\(138\) 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 \(-0.963527\pi\)
0.397705 0.917513i \(-0.369807\pi\)
\(158\) −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 0.260149 0.965568i \(-0.416228\pi\)
−0.706132 + 0.708080i \(0.749561\pi\)
\(164\) −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 \(-0.375203\pi\)
0.382095 + 0.924123i \(0.375203\pi\)
\(168\) 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 −0.582029 0.813168i \(-0.697741\pi\)
0.995239 + 0.0974675i \(0.0310742\pi\)
\(174\) 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 −0.521813 0.853060i \(-0.674744\pi\)
0.477865 + 0.878433i \(0.341411\pi\)
\(194\) −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 \(0.237185\pi\)
−0.734993 + 0.678075i \(0.762815\pi\)
\(198\) −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 \(-0.328673\pi\)
0.512625 + 0.858613i \(0.328673\pi\)
\(224\) 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 0.784671 0.619912i \(-0.212832\pi\)
−0.929195 + 0.369589i \(0.879498\pi\)
\(228\) −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 0.871583 0.490249i \(-0.163094\pi\)
0.0112234 + 0.999937i \(0.496427\pi\)
\(234\) −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 −0.840587 0.541676i \(-0.817790\pi\)
0.889399 + 0.457132i \(0.151123\pi\)
\(258\) −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 −0.641807 0.766866i \(-0.721815\pi\)
0.343222 + 0.939254i \(0.388482\pi\)
\(264\) −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 −0.00856145 0.999963i \(-0.502725\pi\)
0.861713 + 0.507396i \(0.169392\pi\)
\(278\) 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 0.729576 0.683900i \(-0.239717\pi\)
−0.957063 + 0.289882i \(0.906384\pi\)
\(284\) 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 \(-0.676787\pi\)
−0.527276 + 0.849694i \(0.676787\pi\)
\(294\) −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 \(-0.948850\pi\)
−0.987117 + 0.160003i \(0.948850\pi\)
\(308\) 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 \(-0.608945\pi\)
0.983603 0.180346i \(-0.0577219\pi\)
\(314\) 264.545i 0.842500i
\(315\) 0 0
\(316\) 196.676 0.622393
\(317\) −22.5676 13.0294i −0.0711913 0.0411023i 0.463982 0.885845i \(-0.346420\pi\)
−0.535173 + 0.844742i \(0.679754\pi\)
\(318\) 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 \(-0.772503\pi\)
0.755288 0.655393i \(-0.227497\pi\)
\(338\) −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 −0.542059 0.840341i \(-0.682355\pi\)
0.456727 + 0.889607i \(0.349022\pi\)
\(348\) −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 \(0.0517945\pi\)
−0.353099 + 0.935586i \(0.614872\pi\)
\(354\) −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 \(0.0269032\pi\)
−0.425107 + 0.905143i \(0.639763\pi\)
\(368\) −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 0.463127 0.886292i \(-0.346728\pi\)
−0.535988 + 0.844225i \(0.680061\pi\)
\(374\) −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 \(-0.607737\pi\)
0.982912 0.184076i \(-0.0589293\pi\)
\(384\) 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 −0.814373 0.580342i \(-0.802919\pi\)
0.909777 + 0.415096i \(0.136252\pi\)
\(398\) −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 \(-0.918180\pi\)
−0.967145 + 0.254224i \(0.918180\pi\)
\(434\) −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 0.656405 0.754408i \(-0.272076\pi\)
−0.325134 + 0.945668i \(0.605409\pi\)
\(444\) 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 0.154958 0.987921i \(-0.450476\pi\)
−0.778086 + 0.628158i \(0.783809\pi\)
\(458\) 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 \(-0.856525\pi\)
0.900124 0.435633i \(-0.143475\pi\)
\(464\) −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 −0.867535 0.497376i \(-0.834297\pi\)
0.864508 + 0.502619i \(0.167630\pi\)
\(468\) 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 −0.915095 0.403238i \(-0.867885\pi\)
−0.108333 + 0.994115i \(0.534551\pi\)
\(488\) −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 \(-0.508050\pi\)
−0.0252857 + 0.999680i \(0.508050\pi\)
\(504\) 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 −0.769065 0.639171i \(-0.779278\pi\)
0.938071 + 0.346444i \(0.112611\pi\)
\(524\) 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 \(-0.937723\pi\)
0.980922 0.194402i \(-0.0622767\pi\)
\(548\) −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 0.379760 0.925085i \(-0.376007\pi\)
0.991027 + 0.133661i \(0.0426732\pi\)
\(558\) 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 \(0.0718893\pi\)
−0.293372 + 0.955998i \(0.594777\pi\)
\(564\) −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 0.729201 0.684300i \(-0.239892\pi\)
−0.957222 + 0.289356i \(0.906559\pi\)
\(578\) −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 \(-0.621254\pi\)
−0.371786 + 0.928318i \(0.621254\pi\)
\(588\) −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 \(0.366623\pi\)
−0.994536 + 0.104391i \(0.966711\pi\)
\(594\) 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 −0.852727 0.522356i \(-0.825053\pi\)
0.878737 + 0.477306i \(0.158387\pi\)
\(608\) 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 −0.760416 0.649436i \(-0.775005\pi\)
0.182220 + 0.983258i \(0.441672\pi\)
\(614\) 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 \(-0.532984\pi\)
0.103436 0.994636i \(-0.467016\pi\)
\(618\) 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 \(-0.731386\pi\)
−0.664572 + 0.747224i \(0.731386\pi\)
\(644\) 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 \(-0.884354\pi\)
0.159601 0.987182i \(-0.448979\pi\)
\(648\) −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 \(-0.907442\pi\)
−0.727299 0.686321i \(-0.759224\pi\)
\(654\) 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 \(0.0999352\pi\)
−0.951119 + 0.308823i \(0.900065\pi\)
\(674\) −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 \(-0.634659\pi\)
0.994949 0.100386i \(-0.0320077\pi\)
\(678\) 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 −0.693407 0.720546i \(-0.743891\pi\)
0.277308 + 0.960781i \(0.410558\pi\)
\(684\) −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 \(-0.357247\pi\)
0.433590 + 0.901110i \(0.357247\pi\)
\(728\) 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 −0.949685 0.313207i \(-0.898597\pi\)
0.746088 + 0.665848i \(0.231930\pi\)
\(734\) 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 \(0.152164\pi\)
−0.887899 + 0.460038i \(0.847836\pi\)
\(744\) 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 \(-0.707057\pi\)
0.605576 0.795788i \(-0.292943\pi\)
\(758\) 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 0.965749 0.259477i \(-0.0835500\pi\)
−0.707588 + 0.706625i \(0.750217\pi\)
\(774\) −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
\(781\)