Properties

Label 1050.3.p.c.451.3
Level $1050$
Weight $3$
Character 1050.451
Analytic conductor $28.610$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.151613669376.6
Defining polynomial: \( x^{8} - 12x^{6} + 95x^{4} - 588x^{2} + 2401 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 451.3
Root \(1.85439 - 1.88713i\) of defining polynomial
Character \(\chi\) \(=\) 1050.451
Dual form 1050.3.p.c.901.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-3.97571 - 5.76140i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-3.97571 - 5.76140i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.64728 + 2.85317i) q^{11} +(3.00000 - 1.73205i) q^{12} +7.72850i q^{13} +(4.24500 - 8.94315i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-10.9280 - 6.30929i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(1.54304 - 0.890872i) q^{19} +(0.974040 + 12.0852i) q^{21} -4.65921 q^{22} +(3.37819 + 5.85120i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-9.46544 + 5.46488i) q^{26} -5.19615i q^{27} +(13.9547 - 1.12472i) q^{28} +39.2933 q^{29} +(9.46751 + 5.46607i) q^{31} +(2.82843 - 4.89898i) q^{32} +(4.94184 - 2.85317i) q^{33} -17.8454i q^{34} -6.00000 q^{36} +(-17.1983 - 29.7883i) q^{37} +(2.18218 + 1.25988i) q^{38} +(6.69308 - 11.5928i) q^{39} +18.8536i q^{41} +(-14.1125 + 9.73845i) q^{42} +77.4197 q^{43} +(-3.29456 - 5.70635i) q^{44} +(-4.77748 + 8.27485i) q^{46} +(11.1602 - 6.44335i) q^{47} +6.92820i q^{48} +(-17.3875 + 45.8113i) q^{49} +(10.9280 + 18.9279i) q^{51} +(-13.3862 - 7.72850i) q^{52} +(25.8440 - 44.7631i) q^{53} +(6.36396 - 3.67423i) q^{54} +(11.2450 + 16.2957i) q^{56} -3.08607 q^{57} +(27.7846 + 48.1243i) q^{58} +(97.7973 + 56.4633i) q^{59} +(-22.7184 + 13.1165i) q^{61} +15.4604i q^{62} +(9.00500 - 18.9713i) q^{63} +8.00000 q^{64} +(6.98882 + 4.03500i) q^{66} +(9.95656 - 17.2453i) q^{67} +(21.8560 - 12.6186i) q^{68} -11.7024i q^{69} +87.4319 q^{71} +(-4.24264 - 7.34847i) q^{72} +(52.7540 + 30.4575i) q^{73} +(24.3220 - 42.1270i) q^{74} +3.56349i q^{76} +(22.9874 - 1.85274i) q^{77} +18.9309 q^{78} +(17.7888 + 30.8112i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-23.0909 + 13.3315i) q^{82} +46.6773i q^{83} +(-21.9062 - 10.3981i) q^{84} +(54.7440 + 94.8194i) q^{86} +(-58.9399 - 34.0290i) q^{87} +(4.65921 - 8.06999i) q^{88} +(-47.4706 + 27.4072i) q^{89} +(44.5270 - 30.7263i) q^{91} -13.5128 q^{92} +(-9.46751 - 16.3982i) q^{93} +(15.7829 + 9.11228i) q^{94} +(-8.48528 + 4.89898i) q^{96} -45.7447i q^{97} +(-68.4020 + 11.0982i) q^{98} -9.88368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 16 q^{14} - 16 q^{16} - 24 q^{17} + 72 q^{19} + 24 q^{22} + 60 q^{23} - 72 q^{26} - 24 q^{29} + 96 q^{31} + 12 q^{33} - 48 q^{36} - 24 q^{37} - 180 q^{38} - 12 q^{39} + 12 q^{42} - 112 q^{43} - 8 q^{44} + 32 q^{46} + 84 q^{47} - 264 q^{49} + 24 q^{51} + 24 q^{52} + 44 q^{53} + 40 q^{56} - 144 q^{57} + 104 q^{58} + 312 q^{59} - 204 q^{61} + 64 q^{64} - 36 q^{66} + 120 q^{67} + 48 q^{68} - 64 q^{71} + 84 q^{73} - 16 q^{74} + 228 q^{77} + 144 q^{78} - 144 q^{79} - 36 q^{81} - 60 q^{82} + 176 q^{86} + 36 q^{87} - 24 q^{88} - 336 q^{89} - 296 q^{91} - 240 q^{92} - 96 q^{93} + 36 q^{94} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.353553 + 0.612372i
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −3.97571 5.76140i −0.567958 0.823057i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.64728 + 2.85317i −0.149753 + 0.259379i −0.931136 0.364672i \(-0.881181\pi\)
0.781383 + 0.624051i \(0.214514\pi\)
\(12\) 3.00000 1.73205i 0.250000 0.144338i
\(13\) 7.72850i 0.594500i 0.954800 + 0.297250i \(0.0960695\pi\)
−0.954800 + 0.297250i \(0.903931\pi\)
\(14\) 4.24500 8.94315i 0.303214 0.638797i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −10.9280 6.30929i −0.642824 0.371135i 0.142877 0.989740i \(-0.454365\pi\)
−0.785702 + 0.618606i \(0.787698\pi\)
\(18\) −2.12132 + 3.67423i −0.117851 + 0.204124i
\(19\) 1.54304 0.890872i 0.0812124 0.0468880i −0.458844 0.888517i \(-0.651736\pi\)
0.540056 + 0.841629i \(0.318403\pi\)
\(20\) 0 0
\(21\) 0.974040 + 12.0852i 0.0463829 + 0.575484i
\(22\) −4.65921 −0.211782
\(23\) 3.37819 + 5.85120i 0.146878 + 0.254400i 0.930072 0.367377i \(-0.119744\pi\)
−0.783194 + 0.621777i \(0.786411\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −9.46544 + 5.46488i −0.364055 + 0.210188i
\(27\) 5.19615i 0.192450i
\(28\) 13.9547 1.12472i 0.498384 0.0401687i
\(29\) 39.2933 1.35494 0.677471 0.735550i \(-0.263076\pi\)
0.677471 + 0.735550i \(0.263076\pi\)
\(30\) 0 0
\(31\) 9.46751 + 5.46607i 0.305404 + 0.176325i 0.644868 0.764294i \(-0.276912\pi\)
−0.339464 + 0.940619i \(0.610246\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) 4.94184 2.85317i 0.149753 0.0864598i
\(34\) 17.8454i 0.524864i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −17.1983 29.7883i −0.464818 0.805089i 0.534375 0.845248i \(-0.320547\pi\)
−0.999193 + 0.0401585i \(0.987214\pi\)
\(38\) 2.18218 + 1.25988i 0.0574258 + 0.0331548i
\(39\) 6.69308 11.5928i 0.171617 0.297250i
\(40\) 0 0
\(41\) 18.8536i 0.459844i 0.973209 + 0.229922i \(0.0738472\pi\)
−0.973209 + 0.229922i \(0.926153\pi\)
\(42\) −14.1125 + 9.73845i −0.336012 + 0.231868i
\(43\) 77.4197 1.80046 0.900229 0.435416i \(-0.143399\pi\)
0.900229 + 0.435416i \(0.143399\pi\)
\(44\) −3.29456 5.70635i −0.0748764 0.129690i
\(45\) 0 0
\(46\) −4.77748 + 8.27485i −0.103858 + 0.179888i
\(47\) 11.1602 6.44335i 0.237451 0.137093i −0.376553 0.926395i \(-0.622891\pi\)
0.614005 + 0.789302i \(0.289558\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −17.3875 + 45.8113i −0.354847 + 0.934924i
\(50\) 0 0
\(51\) 10.9280 + 18.9279i 0.214275 + 0.371135i
\(52\) −13.3862 7.72850i −0.257426 0.148625i
\(53\) 25.8440 44.7631i 0.487622 0.844586i −0.512276 0.858821i \(-0.671198\pi\)
0.999899 + 0.0142341i \(0.00453101\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 11.2450 + 16.2957i 0.200804 + 0.290995i
\(57\) −3.08607 −0.0541416
\(58\) 27.7846 + 48.1243i 0.479044 + 0.829729i
\(59\) 97.7973 + 56.4633i 1.65758 + 0.957005i 0.973827 + 0.227292i \(0.0729872\pi\)
0.683754 + 0.729713i \(0.260346\pi\)
\(60\) 0 0
\(61\) −22.7184 + 13.1165i −0.372432 + 0.215024i −0.674521 0.738256i \(-0.735650\pi\)
0.302088 + 0.953280i \(0.402316\pi\)
\(62\) 15.4604i 0.249361i
\(63\) 9.00500 18.9713i 0.142937 0.301132i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) 6.98882 + 4.03500i 0.105891 + 0.0611363i
\(67\) 9.95656 17.2453i 0.148605 0.257392i −0.782107 0.623144i \(-0.785855\pi\)
0.930712 + 0.365752i \(0.119188\pi\)
\(68\) 21.8560 12.6186i 0.321412 0.185567i
\(69\) 11.7024i 0.169600i
\(70\) 0 0
\(71\) 87.4319 1.23144 0.615718 0.787967i \(-0.288866\pi\)
0.615718 + 0.787967i \(0.288866\pi\)
\(72\) −4.24264 7.34847i −0.0589256 0.102062i
\(73\) 52.7540 + 30.4575i 0.722657 + 0.417226i 0.815730 0.578433i \(-0.196336\pi\)
−0.0930727 + 0.995659i \(0.529669\pi\)
\(74\) 24.3220 42.1270i 0.328676 0.569284i
\(75\) 0 0
\(76\) 3.56349i 0.0468880i
\(77\) 22.9874 1.85274i 0.298537 0.0240615i
\(78\) 18.9309 0.242704
\(79\) 17.7888 + 30.8112i 0.225175 + 0.390015i 0.956372 0.292152i \(-0.0943712\pi\)
−0.731197 + 0.682167i \(0.761038\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −23.0909 + 13.3315i −0.281596 + 0.162580i
\(83\) 46.6773i 0.562377i 0.959653 + 0.281188i \(0.0907286\pi\)
−0.959653 + 0.281188i \(0.909271\pi\)
\(84\) −21.9062 10.3981i −0.260788 0.123787i
\(85\) 0 0
\(86\) 54.7440 + 94.8194i 0.636558 + 1.10255i
\(87\) −58.9399 34.0290i −0.677471 0.391138i
\(88\) 4.65921 8.06999i 0.0529456 0.0917044i
\(89\) −47.4706 + 27.4072i −0.533378 + 0.307946i −0.742391 0.669967i \(-0.766308\pi\)
0.209013 + 0.977913i \(0.432975\pi\)
\(90\) 0 0
\(91\) 44.5270 30.7263i 0.489308 0.337651i
\(92\) −13.5128 −0.146878
\(93\) −9.46751 16.3982i −0.101801 0.176325i
\(94\) 15.7829 + 9.11228i 0.167903 + 0.0969391i
\(95\) 0 0
\(96\) −8.48528 + 4.89898i −0.0883883 + 0.0510310i
\(97\) 45.7447i 0.471595i −0.971802 0.235798i \(-0.924230\pi\)
0.971802 0.235798i \(-0.0757703\pi\)
\(98\) −68.4020 + 11.0982i −0.697979 + 0.113247i
\(99\) −9.88368 −0.0998352
\(100\) 0 0
\(101\) 79.2589 + 45.7601i 0.784741 + 0.453071i 0.838108 0.545504i \(-0.183662\pi\)
−0.0533667 + 0.998575i \(0.516995\pi\)
\(102\) −15.4545 + 26.7681i −0.151515 + 0.262432i
\(103\) −43.7414 + 25.2541i −0.424674 + 0.245186i −0.697075 0.716998i \(-0.745516\pi\)
0.272401 + 0.962184i \(0.412182\pi\)
\(104\) 21.8595i 0.210188i
\(105\) 0 0
\(106\) 73.0978 0.689602
\(107\) −46.9747 81.3626i −0.439016 0.760398i 0.558598 0.829439i \(-0.311340\pi\)
−0.997614 + 0.0690404i \(0.978006\pi\)
\(108\) 9.00000 + 5.19615i 0.0833333 + 0.0481125i
\(109\) −60.3052 + 104.452i −0.553258 + 0.958272i 0.444778 + 0.895641i \(0.353282\pi\)
−0.998037 + 0.0626310i \(0.980051\pi\)
\(110\) 0 0
\(111\) 59.5766i 0.536726i
\(112\) −12.0067 + 25.2951i −0.107202 + 0.225849i
\(113\) −10.7318 −0.0949713 −0.0474856 0.998872i \(-0.515121\pi\)
−0.0474856 + 0.998872i \(0.515121\pi\)
\(114\) −2.18218 3.77965i −0.0191419 0.0331548i
\(115\) 0 0
\(116\) −39.2933 + 68.0580i −0.338735 + 0.586707i
\(117\) −20.0792 + 11.5928i −0.171617 + 0.0990834i
\(118\) 159.702i 1.35341i
\(119\) 7.09622 + 88.0446i 0.0596321 + 0.739870i
\(120\) 0 0
\(121\) 55.0729 + 95.3891i 0.455148 + 0.788340i
\(122\) −32.1286 18.5495i −0.263349 0.152045i
\(123\) 16.3277 28.2804i 0.132746 0.229922i
\(124\) −18.9350 + 10.9321i −0.152702 + 0.0881624i
\(125\) 0 0
\(126\) 29.6025 2.38590i 0.234940 0.0189357i
\(127\) 117.281 0.923476 0.461738 0.887016i \(-0.347226\pi\)
0.461738 + 0.887016i \(0.347226\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) −116.130 67.0475i −0.900229 0.519748i
\(130\) 0 0
\(131\) 80.2758 46.3473i 0.612792 0.353796i −0.161265 0.986911i \(-0.551557\pi\)
0.774058 + 0.633115i \(0.218224\pi\)
\(132\) 11.4127i 0.0864598i
\(133\) −11.2673 5.34820i −0.0847168 0.0402120i
\(134\) 28.1614 0.210160
\(135\) 0 0
\(136\) 30.9091 + 17.8454i 0.227273 + 0.131216i
\(137\) 13.7370 23.7932i 0.100270 0.173673i −0.811526 0.584317i \(-0.801363\pi\)
0.911796 + 0.410644i \(0.134696\pi\)
\(138\) 14.3325 8.27485i 0.103858 0.0599626i
\(139\) 67.0127i 0.482106i 0.970512 + 0.241053i \(0.0774928\pi\)
−0.970512 + 0.241053i \(0.922507\pi\)
\(140\) 0 0
\(141\) −22.3204 −0.158301
\(142\) 61.8237 + 107.082i 0.435378 + 0.754097i
\(143\) −22.0507 12.7310i −0.154201 0.0890280i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 86.1469i 0.590047i
\(147\) 65.7550 53.6589i 0.447313 0.365027i
\(148\) 68.7931 0.464818
\(149\) −25.5567 44.2656i −0.171522 0.297084i 0.767430 0.641132i \(-0.221535\pi\)
−0.938952 + 0.344048i \(0.888202\pi\)
\(150\) 0 0
\(151\) 82.6090 143.083i 0.547079 0.947569i −0.451394 0.892325i \(-0.649073\pi\)
0.998473 0.0552442i \(-0.0175937\pi\)
\(152\) −4.36436 + 2.51977i −0.0287129 + 0.0165774i
\(153\) 37.8558i 0.247423i
\(154\) 18.5237 + 26.8436i 0.120284 + 0.174309i
\(155\) 0 0
\(156\) 13.3862 + 23.1855i 0.0858087 + 0.148625i
\(157\) −165.248 95.4059i −1.05253 0.607681i −0.129176 0.991622i \(-0.541233\pi\)
−0.923358 + 0.383941i \(0.874567\pi\)
\(158\) −25.1572 + 43.5736i −0.159223 + 0.275782i
\(159\) −77.5319 + 44.7631i −0.487622 + 0.281529i
\(160\) 0 0
\(161\) 20.2804 42.7258i 0.125965 0.265377i
\(162\) −12.7279 −0.0785674
\(163\) 124.101 + 214.949i 0.761356 + 1.31871i 0.942152 + 0.335186i \(0.108799\pi\)
−0.180796 + 0.983521i \(0.557867\pi\)
\(164\) −32.6554 18.8536i −0.199118 0.114961i
\(165\) 0 0
\(166\) −57.1678 + 33.0058i −0.344384 + 0.198830i
\(167\) 29.2974i 0.175433i −0.996145 0.0877167i \(-0.972043\pi\)
0.996145 0.0877167i \(-0.0279570\pi\)
\(168\) −2.75500 34.1820i −0.0163988 0.203464i
\(169\) 109.270 0.646570
\(170\) 0 0
\(171\) 4.62911 + 2.67262i 0.0270708 + 0.0156293i
\(172\) −77.4197 + 134.095i −0.450115 + 0.779622i
\(173\) 19.9982 11.5460i 0.115597 0.0667397i −0.441087 0.897464i \(-0.645407\pi\)
0.556683 + 0.830725i \(0.312074\pi\)
\(174\) 96.2485i 0.553152i
\(175\) 0 0
\(176\) 13.1782 0.0748764
\(177\) −97.7973 169.390i −0.552527 0.957005i
\(178\) −67.1336 38.7596i −0.377155 0.217751i
\(179\) 104.717 181.376i 0.585014 1.01327i −0.409860 0.912148i \(-0.634423\pi\)
0.994874 0.101125i \(-0.0322442\pi\)
\(180\) 0 0
\(181\) 243.667i 1.34622i −0.739540 0.673112i \(-0.764957\pi\)
0.739540 0.673112i \(-0.235043\pi\)
\(182\) 69.1172 + 32.8075i 0.379765 + 0.180261i
\(183\) 45.4367 0.248288
\(184\) −9.55497 16.5497i −0.0519292 0.0899440i
\(185\) 0 0
\(186\) 13.3891 23.1906i 0.0719843 0.124681i
\(187\) 36.0030 20.7863i 0.192529 0.111157i
\(188\) 25.7734i 0.137093i
\(189\) −29.9371 + 20.6584i −0.158397 + 0.109304i
\(190\) 0 0
\(191\) 118.423 + 205.114i 0.620014 + 1.07390i 0.989483 + 0.144653i \(0.0462064\pi\)
−0.369468 + 0.929243i \(0.620460\pi\)
\(192\) −12.0000 6.92820i −0.0625000 0.0360844i
\(193\) −66.4460 + 115.088i −0.344280 + 0.596310i −0.985223 0.171278i \(-0.945210\pi\)
0.640943 + 0.767589i \(0.278544\pi\)
\(194\) 56.0256 32.3464i 0.288792 0.166734i
\(195\) 0 0
\(196\) −61.9600 75.9273i −0.316122 0.387384i
\(197\) 105.779 0.536950 0.268475 0.963287i \(-0.413480\pi\)
0.268475 + 0.963287i \(0.413480\pi\)
\(198\) −6.98882 12.1050i −0.0352971 0.0611363i
\(199\) 174.541 + 100.771i 0.877091 + 0.506389i 0.869698 0.493584i \(-0.164313\pi\)
0.00739279 + 0.999973i \(0.497647\pi\)
\(200\) 0 0
\(201\) −29.8697 + 17.2453i −0.148605 + 0.0857973i
\(202\) 129.429i 0.640739i
\(203\) −156.219 226.384i −0.769550 1.11519i
\(204\) −43.7121 −0.214275
\(205\) 0 0
\(206\) −61.8597 35.7147i −0.300290 0.173372i
\(207\) −10.1346 + 17.5536i −0.0489593 + 0.0848000i
\(208\) 26.7723 15.4570i 0.128713 0.0743125i
\(209\) 5.87006i 0.0280864i
\(210\) 0 0
\(211\) 29.6045 0.140306 0.0701528 0.997536i \(-0.477651\pi\)
0.0701528 + 0.997536i \(0.477651\pi\)
\(212\) 51.6880 + 89.5262i 0.243811 + 0.422293i
\(213\) −131.148 75.7183i −0.615718 0.355485i
\(214\) 66.4323 115.064i 0.310431 0.537683i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) −6.14783 76.2777i −0.0283310 0.351510i
\(218\) −170.569 −0.782426
\(219\) −52.7540 91.3726i −0.240886 0.417226i
\(220\) 0 0
\(221\) 48.7614 84.4572i 0.220640 0.382159i
\(222\) −72.9661 + 42.1270i −0.328676 + 0.189761i
\(223\) 328.532i 1.47324i 0.676307 + 0.736620i \(0.263579\pi\)
−0.676307 + 0.736620i \(0.736421\pi\)
\(224\) −39.4700 + 3.18120i −0.176205 + 0.0142018i
\(225\) 0 0
\(226\) −7.58850 13.1437i −0.0335774 0.0581578i
\(227\) −315.628 182.228i −1.39043 0.802766i −0.397069 0.917789i \(-0.629972\pi\)
−0.993363 + 0.115023i \(0.963306\pi\)
\(228\) 3.08607 5.34523i 0.0135354 0.0234440i
\(229\) −260.716 + 150.525i −1.13850 + 0.657313i −0.946059 0.323996i \(-0.894974\pi\)
−0.192441 + 0.981309i \(0.561640\pi\)
\(230\) 0 0
\(231\) −36.0856 17.1285i −0.156215 0.0741496i
\(232\) −111.138 −0.479044
\(233\) −141.013 244.241i −0.605204 1.04824i −0.992019 0.126087i \(-0.959758\pi\)
0.386815 0.922157i \(-0.373575\pi\)
\(234\) −28.3963 16.3946i −0.121352 0.0700625i
\(235\) 0 0
\(236\) −195.595 + 112.927i −0.828790 + 0.478502i
\(237\) 61.6224i 0.260010i
\(238\) −102.814 + 70.9480i −0.431993 + 0.298101i
\(239\) 83.0347 0.347425 0.173713 0.984796i \(-0.444424\pi\)
0.173713 + 0.984796i \(0.444424\pi\)
\(240\) 0 0
\(241\) −287.369 165.912i −1.19240 0.688433i −0.233551 0.972345i \(-0.575035\pi\)
−0.958851 + 0.283911i \(0.908368\pi\)
\(242\) −77.8849 + 134.901i −0.321838 + 0.557440i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 52.4658i 0.215024i
\(245\) 0 0
\(246\) 46.1817 0.187731
\(247\) 6.88511 + 11.9254i 0.0278749 + 0.0482808i
\(248\) −26.7782 15.4604i −0.107977 0.0623403i
\(249\) 40.4237 70.0159i 0.162344 0.281188i
\(250\) 0 0
\(251\) 419.075i 1.66962i −0.550537 0.834811i \(-0.685577\pi\)
0.550537 0.834811i \(-0.314423\pi\)
\(252\) 23.8542 + 34.5684i 0.0946597 + 0.137176i
\(253\) −22.2593 −0.0879815
\(254\) 82.9305 + 143.640i 0.326498 + 0.565511i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 289.215 166.979i 1.12535 0.649722i 0.182590 0.983189i \(-0.441552\pi\)
0.942762 + 0.333467i \(0.108219\pi\)
\(258\) 189.639i 0.735034i
\(259\) −103.247 + 217.516i −0.398637 + 0.839829i
\(260\) 0 0
\(261\) 58.9399 + 102.087i 0.225824 + 0.391138i
\(262\) 113.527 + 65.5449i 0.433310 + 0.250171i
\(263\) 102.188 176.995i 0.388549 0.672986i −0.603706 0.797207i \(-0.706310\pi\)
0.992255 + 0.124221i \(0.0396432\pi\)
\(264\) −13.9776 + 8.06999i −0.0529456 + 0.0305681i
\(265\) 0 0
\(266\) −1.41702 17.5814i −0.00532715 0.0660953i
\(267\) 94.9412 0.355585
\(268\) 19.9131 + 34.4905i 0.0743027 + 0.128696i
\(269\) −120.768 69.7257i −0.448953 0.259203i 0.258435 0.966029i \(-0.416793\pi\)
−0.707388 + 0.706825i \(0.750127\pi\)
\(270\) 0 0
\(271\) −323.213 + 186.607i −1.19267 + 0.688586i −0.958910 0.283709i \(-0.908435\pi\)
−0.233756 + 0.972295i \(0.575102\pi\)
\(272\) 50.4743i 0.185567i
\(273\) −93.4002 + 7.52787i −0.342125 + 0.0275746i
\(274\) 38.8542 0.141804
\(275\) 0 0
\(276\) 20.2691 + 11.7024i 0.0734389 + 0.0424000i
\(277\) −248.752 + 430.851i −0.898022 + 1.55542i −0.0680029 + 0.997685i \(0.521663\pi\)
−0.830019 + 0.557735i \(0.811671\pi\)
\(278\) −82.0735 + 47.3852i −0.295228 + 0.170450i
\(279\) 32.7964i 0.117550i
\(280\) 0 0
\(281\) 292.779 1.04192 0.520959 0.853582i \(-0.325574\pi\)
0.520959 + 0.853582i \(0.325574\pi\)
\(282\) −15.7829 27.3368i −0.0559678 0.0969391i
\(283\) 239.686 + 138.383i 0.846949 + 0.488986i 0.859620 0.510934i \(-0.170700\pi\)
−0.0126714 + 0.999920i \(0.504034\pi\)
\(284\) −87.4319 + 151.437i −0.307859 + 0.533227i
\(285\) 0 0
\(286\) 36.0087i 0.125905i
\(287\) 108.623 74.9565i 0.378478 0.261172i
\(288\) 16.9706 0.0589256
\(289\) −64.8857 112.385i −0.224518 0.388876i
\(290\) 0 0
\(291\) −39.6161 + 68.6171i −0.136138 + 0.235798i
\(292\) −105.508 + 60.9150i −0.361329 + 0.208613i
\(293\) 375.299i 1.28088i −0.768006 0.640442i \(-0.778751\pi\)
0.768006 0.640442i \(-0.221249\pi\)
\(294\) 112.214 + 42.5905i 0.381681 + 0.144866i
\(295\) 0 0
\(296\) 48.6441 + 84.2540i 0.164338 + 0.284642i
\(297\) 14.8255 + 8.55952i 0.0499176 + 0.0288199i
\(298\) 36.1427 62.6009i 0.121284 0.210070i
\(299\) −45.2210 + 26.1084i −0.151241 + 0.0873189i
\(300\) 0 0
\(301\) −307.798 446.046i −1.02259 1.48188i
\(302\) 233.653 0.773687
\(303\) −79.2589 137.280i −0.261580 0.453071i
\(304\) −6.17214 3.56349i −0.0203031 0.0117220i
\(305\) 0 0
\(306\) 46.3636 26.7681i 0.151515 0.0874773i
\(307\) 107.784i 0.351088i 0.984472 + 0.175544i \(0.0561684\pi\)
−0.984472 + 0.175544i \(0.943832\pi\)
\(308\) −19.7783 + 41.6680i −0.0642154 + 0.135286i
\(309\) 87.4828 0.283116
\(310\) 0 0
\(311\) −499.771 288.543i −1.60698 0.927791i −0.990041 0.140780i \(-0.955039\pi\)
−0.616940 0.787010i \(-0.711628\pi\)
\(312\) −18.9309 + 32.7893i −0.0606759 + 0.105094i
\(313\) −344.050 + 198.637i −1.09920 + 0.634624i −0.936011 0.351971i \(-0.885512\pi\)
−0.163190 + 0.986595i \(0.552178\pi\)
\(314\) 269.849i 0.859390i
\(315\) 0 0
\(316\) −71.1554 −0.225175
\(317\) 40.1851 + 69.6026i 0.126767 + 0.219566i 0.922422 0.386183i \(-0.126207\pi\)
−0.795655 + 0.605749i \(0.792873\pi\)
\(318\) −109.647 63.3046i −0.344801 0.199071i
\(319\) −64.7271 + 112.111i −0.202906 + 0.351444i
\(320\) 0 0
\(321\) 162.725i 0.506932i
\(322\) 66.6686 5.37336i 0.207045 0.0166874i
\(323\) −22.4831 −0.0696071
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 0 0
\(326\) −175.505 + 303.984i −0.538360 + 0.932467i
\(327\) 180.915 104.452i 0.553258 0.319424i
\(328\) 53.3261i 0.162580i
\(329\) −81.4925 38.6816i −0.247698 0.117573i
\(330\) 0 0
\(331\) −246.021 426.121i −0.743266 1.28737i −0.951000 0.309189i \(-0.899942\pi\)
0.207734 0.978185i \(-0.433391\pi\)
\(332\) −80.8474 46.6773i −0.243516 0.140594i
\(333\) 51.5948 89.3649i 0.154939 0.268363i
\(334\) 35.8818 20.7164i 0.107431 0.0620251i
\(335\) 0 0
\(336\) 39.9162 27.5445i 0.118798 0.0819777i
\(337\) 630.123 1.86980 0.934901 0.354910i \(-0.115488\pi\)
0.934901 + 0.354910i \(0.115488\pi\)
\(338\) 77.2657 + 133.828i 0.228597 + 0.395941i
\(339\) 16.0976 + 9.29397i 0.0474856 + 0.0274159i
\(340\) 0 0
\(341\) −31.1913 + 18.0083i −0.0914701 + 0.0528103i
\(342\) 7.55930i 0.0221032i
\(343\) 333.065 81.9559i 0.971035 0.238938i
\(344\) −218.976 −0.636558
\(345\) 0 0
\(346\) 28.2817 + 16.3285i 0.0817391 + 0.0471921i
\(347\) −215.071 + 372.514i −0.619802 + 1.07353i 0.369720 + 0.929143i \(0.379454\pi\)
−0.989522 + 0.144385i \(0.953880\pi\)
\(348\) 117.880 68.0580i 0.338735 0.195569i
\(349\) 95.1819i 0.272727i −0.990659 0.136364i \(-0.956458\pi\)
0.990659 0.136364i \(-0.0435416\pi\)
\(350\) 0 0
\(351\) 40.1585 0.114412
\(352\) 9.31842 + 16.1400i 0.0264728 + 0.0458522i
\(353\) −227.710 131.469i −0.645071 0.372432i 0.141494 0.989939i \(-0.454809\pi\)
−0.786565 + 0.617507i \(0.788143\pi\)
\(354\) 138.306 239.553i 0.390696 0.676704i
\(355\) 0 0
\(356\) 109.629i 0.307946i
\(357\) 65.6045 138.212i 0.183766 0.387150i
\(358\) 296.186 0.827334
\(359\) −149.386 258.743i −0.416116 0.720734i 0.579429 0.815023i \(-0.303276\pi\)
−0.995545 + 0.0942890i \(0.969942\pi\)
\(360\) 0 0
\(361\) −178.913 + 309.886i −0.495603 + 0.858410i
\(362\) 298.429 172.298i 0.824391 0.475962i
\(363\) 190.778i 0.525560i
\(364\) 8.69244 + 107.849i 0.0238803 + 0.296289i
\(365\) 0 0
\(366\) 32.1286 + 55.6484i 0.0877831 + 0.152045i
\(367\) 114.381 + 66.0380i 0.311665 + 0.179940i 0.647671 0.761920i \(-0.275743\pi\)
−0.336006 + 0.941860i \(0.609076\pi\)
\(368\) 13.5128 23.4048i 0.0367195 0.0636000i
\(369\) −48.9831 + 28.2804i −0.132746 + 0.0766407i
\(370\) 0 0
\(371\) −360.646 + 29.0674i −0.972092 + 0.0783487i
\(372\) 37.8701 0.101801
\(373\) 5.34394 + 9.25597i 0.0143269 + 0.0248149i 0.873100 0.487541i \(-0.162106\pi\)
−0.858773 + 0.512356i \(0.828773\pi\)
\(374\) 50.9159 + 29.3963i 0.136139 + 0.0785998i
\(375\) 0 0
\(376\) −31.5659 + 18.2246i −0.0839517 + 0.0484696i
\(377\) 303.678i 0.805513i
\(378\) −46.4700 22.0577i −0.122936 0.0583536i
\(379\) 142.918 0.377092 0.188546 0.982064i \(-0.439622\pi\)
0.188546 + 0.982064i \(0.439622\pi\)
\(380\) 0 0
\(381\) −175.922 101.569i −0.461738 0.266585i
\(382\) −167.475 + 290.075i −0.438416 + 0.759359i
\(383\) 534.349 308.507i 1.39517 0.805500i 0.401286 0.915953i \(-0.368563\pi\)
0.993881 + 0.110452i \(0.0352300\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −187.938 −0.486885
\(387\) 116.130 + 201.142i 0.300076 + 0.519748i
\(388\) 79.2322 + 45.7447i 0.204207 + 0.117899i
\(389\) 346.969 600.968i 0.891951 1.54490i 0.0544171 0.998518i \(-0.482670\pi\)
0.837534 0.546386i \(-0.183997\pi\)
\(390\) 0 0
\(391\) 85.2560i 0.218046i
\(392\) 49.1793 129.574i 0.125457 0.330546i
\(393\) −160.552 −0.408528
\(394\) 74.7972 + 129.553i 0.189841 + 0.328814i
\(395\) 0 0
\(396\) 9.88368 17.1190i 0.0249588 0.0432299i
\(397\) 484.587 279.776i 1.22062 0.704726i 0.255571 0.966790i \(-0.417737\pi\)
0.965050 + 0.262065i \(0.0844033\pi\)
\(398\) 285.024i 0.716142i
\(399\) 12.2693 + 17.7801i 0.0307502 + 0.0445616i
\(400\) 0 0
\(401\) 80.6033 + 139.609i 0.201006 + 0.348152i 0.948853 0.315719i \(-0.102246\pi\)
−0.747847 + 0.663871i \(0.768912\pi\)
\(402\) −42.2421 24.3885i −0.105080 0.0606679i
\(403\) −42.2445 + 73.1697i −0.104825 + 0.181563i
\(404\) −158.518 + 91.5203i −0.392371 + 0.226535i
\(405\) 0 0
\(406\) 166.800 351.406i 0.410837 0.865532i
\(407\) 113.322 0.278431
\(408\) −30.9091 53.5361i −0.0757576 0.131216i
\(409\) 398.217 + 229.911i 0.973637 + 0.562129i 0.900343 0.435181i \(-0.143316\pi\)
0.0732937 + 0.997310i \(0.476649\pi\)
\(410\) 0 0
\(411\) −41.2111 + 23.7932i −0.100270 + 0.0578911i
\(412\) 101.016i 0.245186i
\(413\) −63.5056 787.931i −0.153767 1.90782i
\(414\) −28.6649 −0.0692389
\(415\) 0 0
\(416\) 37.8618 + 21.8595i 0.0910139 + 0.0525469i
\(417\) 58.0347 100.519i 0.139172 0.241053i
\(418\) −7.18933 + 4.15076i −0.0171994 + 0.00993005i
\(419\) 93.5818i 0.223346i 0.993745 + 0.111673i \(0.0356208\pi\)
−0.993745 + 0.111673i \(0.964379\pi\)
\(420\) 0 0
\(421\) 162.957 0.387072 0.193536 0.981093i \(-0.438004\pi\)
0.193536 + 0.981093i \(0.438004\pi\)
\(422\) 20.9335 + 36.2579i 0.0496055 + 0.0859193i
\(423\) 33.4806 + 19.3301i 0.0791504 + 0.0456975i
\(424\) −73.0978 + 126.609i −0.172400 + 0.298606i
\(425\) 0 0
\(426\) 214.164i 0.502731i
\(427\) 165.891 + 78.7425i 0.388503 + 0.184409i
\(428\) 187.899 0.439016
\(429\) 22.0507 + 38.1930i 0.0514003 + 0.0890280i
\(430\) 0 0
\(431\) 165.543 286.728i 0.384090 0.665263i −0.607553 0.794279i \(-0.707849\pi\)
0.991642 + 0.129016i \(0.0411820\pi\)
\(432\) −18.0000 + 10.3923i −0.0416667 + 0.0240563i
\(433\) 88.4130i 0.204187i 0.994775 + 0.102094i \(0.0325541\pi\)
−0.994775 + 0.102094i \(0.967446\pi\)
\(434\) 89.0735 61.4660i 0.205238 0.141627i
\(435\) 0 0
\(436\) −120.610 208.903i −0.276629 0.479136i
\(437\) 10.4253 + 6.01907i 0.0238566 + 0.0137736i
\(438\) 74.6054 129.220i 0.170332 0.295024i
\(439\) −60.4608 + 34.9070i −0.137724 + 0.0795149i −0.567279 0.823526i \(-0.692004\pi\)
0.429555 + 0.903041i \(0.358670\pi\)
\(440\) 0 0
\(441\) −145.102 + 23.5429i −0.329031 + 0.0533852i
\(442\) 137.918 0.312032
\(443\) 330.217 + 571.953i 0.745411 + 1.29109i 0.950003 + 0.312242i \(0.101080\pi\)
−0.204592 + 0.978847i \(0.565587\pi\)
\(444\) −103.190 59.5766i −0.232409 0.134182i
\(445\) 0 0
\(446\) −402.368 + 232.307i −0.902171 + 0.520869i
\(447\) 88.5311i 0.198056i
\(448\) −31.8057 46.0912i −0.0709948 0.102882i
\(449\) −560.274 −1.24783 −0.623913 0.781493i \(-0.714458\pi\)
−0.623913 + 0.781493i \(0.714458\pi\)
\(450\) 0 0
\(451\) −53.7926 31.0572i −0.119274 0.0688629i
\(452\) 10.7318 18.5879i 0.0237428 0.0411238i
\(453\) −247.827 + 143.083i −0.547079 + 0.315856i
\(454\) 515.418i 1.13528i
\(455\) 0 0
\(456\) 8.72873 0.0191419
\(457\) 91.8900 + 159.158i 0.201072 + 0.348267i 0.948874 0.315655i \(-0.102224\pi\)
−0.747802 + 0.663922i \(0.768891\pi\)
\(458\) −368.709 212.874i −0.805041 0.464790i
\(459\) −32.7840 + 56.7836i −0.0714249 + 0.123712i
\(460\) 0 0
\(461\) 28.4330i 0.0616767i 0.999524 + 0.0308384i \(0.00981771\pi\)
−0.999524 + 0.0308384i \(0.990182\pi\)
\(462\) −4.53826 56.3073i −0.00982307 0.121877i
\(463\) 269.931 0.583005 0.291503 0.956570i \(-0.405845\pi\)
0.291503 + 0.956570i \(0.405845\pi\)
\(464\) −78.5866 136.116i −0.169368 0.293353i
\(465\) 0 0
\(466\) 199.422 345.409i 0.427944 0.741221i
\(467\) −289.539 + 167.166i −0.619999 + 0.357956i −0.776868 0.629663i \(-0.783193\pi\)
0.156870 + 0.987619i \(0.449860\pi\)
\(468\) 46.3710i 0.0990834i
\(469\) −138.941 + 11.1984i −0.296250 + 0.0238772i
\(470\) 0 0
\(471\) 165.248 + 286.218i 0.350845 + 0.607681i
\(472\) −276.612 159.702i −0.586043 0.338352i
\(473\) −127.532 + 220.892i −0.269624 + 0.467002i
\(474\) 75.4717 43.5736i 0.159223 0.0919274i
\(475\) 0 0
\(476\) −159.594 75.7536i −0.335281 0.159146i
\(477\) 155.064 0.325081
\(478\) 58.7144 + 101.696i 0.122833 + 0.212754i
\(479\) 114.560 + 66.1412i 0.239165 + 0.138082i 0.614793 0.788689i \(-0.289240\pi\)
−0.375628 + 0.926771i \(0.622573\pi\)
\(480\) 0 0
\(481\) 230.219 132.917i 0.478626 0.276335i
\(482\) 469.271i 0.973592i
\(483\) −67.4222 + 46.5253i −0.139591 + 0.0963257i
\(484\) −220.292 −0.455148
\(485\) 0 0
\(486\) 19.0919 + 11.0227i 0.0392837 + 0.0226805i
\(487\) −258.635 + 447.970i −0.531079 + 0.919856i 0.468263 + 0.883589i \(0.344880\pi\)
−0.999342 + 0.0362667i \(0.988453\pi\)
\(488\) 64.2573 37.0989i 0.131675 0.0760224i
\(489\) 429.898i 0.879138i
\(490\) 0 0
\(491\) 484.805 0.987383 0.493692 0.869637i \(-0.335647\pi\)
0.493692 + 0.869637i \(0.335647\pi\)
\(492\) 32.6554 + 56.5609i 0.0663728 + 0.114961i
\(493\) −429.398 247.913i −0.870989 0.502866i
\(494\) −9.73701 + 16.8650i −0.0197105 + 0.0341397i
\(495\) 0 0
\(496\) 43.7286i 0.0881624i
\(497\) −347.604 503.730i −0.699404 1.01354i
\(498\) 114.336 0.229589
\(499\) 64.6450 + 111.968i 0.129549 + 0.224385i 0.923502 0.383594i \(-0.125314\pi\)
−0.793953 + 0.607979i \(0.791980\pi\)
\(500\) 0 0
\(501\) −25.3723 + 43.9461i −0.0506432 + 0.0877167i
\(502\) 513.260 296.331i 1.02243 0.590300i
\(503\) 160.905i 0.319890i 0.987126 + 0.159945i \(0.0511317\pi\)
−0.987126 + 0.159945i \(0.948868\pi\)
\(504\) −25.4700 + 53.6589i −0.0505357 + 0.106466i
\(505\) 0 0
\(506\) −15.7397 27.2620i −0.0311061 0.0538774i
\(507\) −163.905 94.6308i −0.323285 0.186649i
\(508\) −117.281 + 203.137i −0.230869 + 0.399877i
\(509\) −320.453 + 185.014i −0.629575 + 0.363485i −0.780587 0.625047i \(-0.785080\pi\)
0.151013 + 0.988532i \(0.451747\pi\)
\(510\) 0 0
\(511\) −34.2563 425.027i −0.0670378 0.831755i
\(512\) −22.6274 −0.0441942
\(513\) −4.62911 8.01785i −0.00902360 0.0156293i
\(514\) 409.012 + 236.143i 0.795744 + 0.459423i
\(515\) 0 0
\(516\) 232.259 134.095i 0.450115 0.259874i
\(517\) 42.4560i 0.0821200i
\(518\) −339.408 + 27.3556i −0.655228 + 0.0528101i
\(519\) −39.9964 −0.0770644
\(520\) 0 0
\(521\) 65.1395 + 37.6083i 0.125028 + 0.0721849i 0.561210 0.827674i \(-0.310336\pi\)
−0.436182 + 0.899859i \(0.643670\pi\)
\(522\) −83.3537 + 144.373i −0.159681 + 0.276576i
\(523\) −810.701 + 468.058i −1.55010 + 0.894949i −0.551965 + 0.833867i \(0.686122\pi\)
−0.998133 + 0.0610819i \(0.980545\pi\)
\(524\) 185.389i 0.353796i
\(525\) 0 0
\(526\) 289.032 0.549491
\(527\) −68.9741 119.467i −0.130881 0.226692i
\(528\) −19.7674 11.4127i −0.0374382 0.0216149i
\(529\) 241.676 418.594i 0.456854 0.791294i
\(530\) 0 0
\(531\) 338.780i 0.638003i
\(532\) 20.5307 14.1674i 0.0385915 0.0266304i
\(533\) −145.710 −0.273377
\(534\) 67.1336 + 116.279i 0.125718 + 0.217751i
\(535\) 0 0
\(536\) −28.1614 + 48.7770i −0.0525399 + 0.0910018i
\(537\) −314.152 + 181.376i −0.585014 + 0.337758i
\(538\) 197.214i 0.366569i
\(539\) −102.065 125.074i −0.189361 0.232047i
\(540\) 0 0
\(541\) 304.692 + 527.742i 0.563201 + 0.975493i 0.997215 + 0.0745867i \(0.0237638\pi\)
−0.434013 + 0.900906i \(0.642903\pi\)
\(542\) −457.092 263.902i −0.843343 0.486904i
\(543\) −211.021 + 365.500i −0.388622 + 0.673112i
\(544\) −61.8182 + 35.6907i −0.113636 + 0.0656080i
\(545\) 0 0
\(546\) −75.2637 109.068i −0.137846 0.199759i
\(547\) 491.361 0.898283 0.449141 0.893461i \(-0.351730\pi\)
0.449141 + 0.893461i \(0.351730\pi\)
\(548\) 27.4741 + 47.5865i 0.0501351 + 0.0868366i
\(549\) −68.1551 39.3494i −0.124144 0.0716746i
\(550\) 0 0
\(551\) 60.6310 35.0053i 0.110038 0.0635305i
\(552\) 33.0994i 0.0599626i
\(553\) 106.792 224.985i 0.193115 0.406844i
\(554\) −703.577 −1.27000
\(555\) 0 0
\(556\) −116.069 67.0127i −0.208758 0.120527i
\(557\) −526.110 + 911.250i −0.944543 + 1.63600i −0.187878 + 0.982192i \(0.560161\pi\)
−0.756665 + 0.653803i \(0.773172\pi\)
\(558\) −40.1673 + 23.1906i −0.0719843 + 0.0415602i
\(559\) 598.339i 1.07037i
\(560\) 0 0
\(561\) −72.0060 −0.128353
\(562\) 207.026 + 358.580i 0.368374 + 0.638042i
\(563\) 670.769 + 387.269i 1.19142 + 0.687866i 0.958628 0.284661i \(-0.0918810\pi\)
0.232791 + 0.972527i \(0.425214\pi\)
\(564\) 22.3204 38.6601i 0.0395752 0.0685463i
\(565\) 0 0
\(566\) 391.406i 0.691531i
\(567\) 62.7964 5.06126i 0.110752 0.00892639i
\(568\) −247.295 −0.435378
\(569\) −156.525 271.109i −0.275088 0.476466i 0.695070 0.718942i \(-0.255374\pi\)
−0.970157 + 0.242477i \(0.922040\pi\)
\(570\) 0 0
\(571\) −324.711 + 562.416i −0.568670 + 0.984966i 0.428027 + 0.903766i \(0.359209\pi\)
−0.996698 + 0.0812002i \(0.974125\pi\)
\(572\) 44.1015 25.4620i 0.0771005 0.0445140i
\(573\) 410.228i 0.715931i
\(574\) 168.611 + 80.0336i 0.293747 + 0.139431i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −891.822 514.893i −1.54562 0.892363i −0.998468 0.0553284i \(-0.982379\pi\)
−0.547150 0.837035i \(-0.684287\pi\)
\(578\) 91.7622 158.937i 0.158758 0.274977i
\(579\) 199.338 115.088i 0.344280 0.198770i
\(580\) 0 0
\(581\) 268.927 185.575i 0.462868 0.319406i
\(582\) −112.051 −0.192528
\(583\) 85.1445 + 147.475i 0.146046 + 0.252958i
\(584\) −149.211 86.1469i −0.255498 0.147512i
\(585\) 0 0
\(586\) 459.646 265.376i 0.784378 0.452861i
\(587\) 791.817i 1.34892i 0.738311 + 0.674461i \(0.235624\pi\)
−0.738311 + 0.674461i \(0.764376\pi\)
\(588\) 27.1850 + 167.550i 0.0462329 + 0.284949i
\(589\) 19.4783 0.0330701
\(590\) 0 0
\(591\) −158.669 91.6075i −0.268475 0.155004i
\(592\) −68.7931 + 119.153i −0.116205 + 0.201272i
\(593\) 73.1807 42.2509i 0.123408 0.0712494i −0.437025 0.899449i \(-0.643968\pi\)
0.560433 + 0.828200i \(0.310635\pi\)
\(594\) 24.2100i 0.0407575i
\(595\) 0 0
\(596\) 102.227 0.171522
\(597\) −174.541 302.314i −0.292364 0.506389i
\(598\) −63.9522 36.9228i −0.106943 0.0617438i
\(599\) 233.463 404.369i 0.389754 0.675074i −0.602662 0.797997i \(-0.705893\pi\)
0.992416 + 0.122922i \(0.0392266\pi\)
\(600\) 0 0
\(601\) 1095.93i 1.82351i 0.410733 + 0.911756i \(0.365273\pi\)
−0.410733 + 0.911756i \(0.634727\pi\)
\(602\) 328.647 692.377i 0.545925 1.15013i
\(603\) 59.7394 0.0990702
\(604\) 165.218 + 286.166i 0.273540 + 0.473785i
\(605\) 0 0
\(606\) 112.089 194.144i 0.184965 0.320369i
\(607\) 310.815 179.449i 0.512051 0.295633i −0.221625 0.975132i \(-0.571136\pi\)
0.733676 + 0.679499i \(0.237803\pi\)
\(608\) 10.0791i 0.0165774i
\(609\) 38.2733 + 474.866i 0.0628461 + 0.779747i
\(610\) 0 0
\(611\) 49.7975 + 86.2517i 0.0815016 + 0.141165i
\(612\) 65.5681 + 37.8558i 0.107137 + 0.0618558i
\(613\) −231.029 + 400.154i −0.376883 + 0.652780i −0.990607 0.136741i \(-0.956337\pi\)
0.613724 + 0.789520i \(0.289671\pi\)
\(614\) −132.008 + 76.2148i −0.214996 + 0.124128i
\(615\) 0 0
\(616\) −65.0181 + 5.24033i −0.105549 + 0.00850703i
\(617\) −219.440 −0.355656 −0.177828 0.984062i \(-0.556907\pi\)
−0.177828 + 0.984062i \(0.556907\pi\)
\(618\) 61.8597 + 107.144i 0.100097 + 0.173372i
\(619\) 832.792 + 480.813i 1.34538 + 0.776757i 0.987592 0.157044i \(-0.0501966\pi\)
0.357791 + 0.933802i \(0.383530\pi\)
\(620\) 0 0
\(621\) 30.4037 17.5536i 0.0489593 0.0282667i
\(622\) 816.123i 1.31209i
\(623\) 346.633 + 164.534i 0.556393 + 0.264100i
\(624\) −53.5446 −0.0858087
\(625\) 0 0
\(626\) −486.560 280.915i −0.777252 0.448747i
\(627\) 5.08362 8.80509i 0.00810785 0.0140432i
\(628\) 330.496 190.812i 0.526267 0.303840i
\(629\) 434.036i 0.690041i
\(630\) 0 0
\(631\) 584.721 0.926658 0.463329 0.886186i \(-0.346655\pi\)
0.463329 + 0.886186i \(0.346655\pi\)
\(632\) −50.3144 87.1472i −0.0796115 0.137891i
\(633\) −44.4067 25.6382i −0.0701528 0.0405027i
\(634\) −56.8303 + 98.4329i −0.0896376 + 0.155257i
\(635\) 0 0
\(636\) 179.052i 0.281529i
\(637\) −354.053 134.379i −0.555813 0.210957i
\(638\) −183.076 −0.286953
\(639\) 131.148 + 227.155i 0.205239 + 0.355485i
\(640\) 0 0
\(641\) −269.518 + 466.819i −0.420465 + 0.728268i −0.995985 0.0895205i \(-0.971467\pi\)
0.575520 + 0.817788i \(0.304800\pi\)
\(642\) −199.297 + 115.064i −0.310431 + 0.179228i
\(643\) 150.959i 0.234773i −0.993086 0.117386i \(-0.962548\pi\)
0.993086 0.117386i \(-0.0374516\pi\)
\(644\) 53.7228 + 77.8525i 0.0834205 + 0.120889i
\(645\) 0 0
\(646\) −15.8979 27.5360i −0.0246098 0.0426255i
\(647\) −391.111 225.808i −0.604499 0.349008i 0.166310 0.986073i \(-0.446815\pi\)
−0.770809 + 0.637066i \(0.780148\pi\)
\(648\) 12.7279 22.0454i 0.0196419 0.0340207i
\(649\) −322.199 + 186.022i −0.496454 + 0.286628i
\(650\) 0 0
\(651\) −56.8366 + 119.741i −0.0873067 + 0.183933i
\(652\) −496.404 −0.761356
\(653\) 215.848 + 373.860i 0.330548 + 0.572526i 0.982619 0.185631i \(-0.0594330\pi\)
−0.652071 + 0.758158i \(0.726100\pi\)
\(654\) 255.853 + 147.717i 0.391213 + 0.225867i
\(655\) 0 0
\(656\) 65.3108 37.7072i 0.0995592 0.0574805i
\(657\) 182.745i 0.278151i
\(658\) −10.2488 127.160i −0.0155757 0.193252i
\(659\) −195.185 −0.296184 −0.148092 0.988974i \(-0.547313\pi\)
−0.148092 + 0.988974i \(0.547313\pi\)
\(660\) 0 0
\(661\) 596.305 + 344.277i 0.902126 + 0.520843i 0.877889 0.478863i \(-0.158951\pi\)
0.0242368 + 0.999706i \(0.492284\pi\)
\(662\) 347.926 602.626i 0.525569 0.910311i
\(663\) −146.284 + 84.4572i −0.220640 + 0.127386i
\(664\) 132.023i 0.198830i
\(665\) 0 0
\(666\) 145.932 0.219118
\(667\) 132.740 + 229.913i 0.199011 + 0.344697i
\(668\) 50.7445 + 29.2974i 0.0759649 + 0.0438583i
\(669\) 284.517 492.799i 0.425288 0.736620i
\(670\) 0 0
\(671\) 86.4259i 0.128802i
\(672\) 61.9600 + 29.4102i 0.0922024 + 0.0437652i
\(673\) −200.020 −0.297206 −0.148603 0.988897i \(-0.547478\pi\)
−0.148603 + 0.988897i \(0.547478\pi\)
\(674\) 445.564 + 771.740i 0.661075 + 1.14501i
\(675\) 0 0
\(676\) −109.270 + 189.262i −0.161642 + 0.279973i
\(677\) −735.787 + 424.807i −1.08683 + 0.627484i −0.932732 0.360571i \(-0.882582\pi\)
−0.154103 + 0.988055i \(0.549249\pi\)
\(678\) 26.2873i 0.0387719i
\(679\) −263.554 + 181.868i −0.388150 + 0.267846i
\(680\) 0 0
\(681\) 315.628 + 546.684i 0.463477 + 0.802766i
\(682\) −44.1111 25.4676i −0.0646791 0.0373425i
\(683\) −224.005 + 387.988i −0.327972 + 0.568064i −0.982109 0.188311i \(-0.939699\pi\)
0.654137 + 0.756376i \(0.273032\pi\)
\(684\) −9.25821 + 5.34523i −0.0135354 + 0.00781467i
\(685\) 0 0
\(686\) 335.888 + 349.968i 0.489632 + 0.510157i
\(687\) 521.433 0.759000
\(688\) −154.839 268.190i −0.225057 0.389811i
\(689\) 345.952 + 199.735i 0.502107 + 0.289891i
\(690\) 0 0
\(691\) −337.930 + 195.104i −0.489044 + 0.282350i −0.724178 0.689613i \(-0.757781\pi\)
0.235134 + 0.971963i \(0.424447\pi\)
\(692\) 46.1839i 0.0667397i
\(693\) 39.2946 + 56.9439i 0.0567022 + 0.0821701i
\(694\) −608.313 −0.876532
\(695\) 0 0
\(696\) 166.707 + 96.2485i 0.239522 + 0.138288i
\(697\) 118.953 206.033i 0.170664 0.295599i
\(698\) 116.574 67.3038i 0.167011 0.0964237i
\(699\) 488.482i 0.698830i
\(700\) 0 0
\(701\) 989.018 1.41087 0.705434 0.708776i \(-0.250752\pi\)
0.705434 + 0.708776i \(0.250752\pi\)
\(702\) 28.3963 + 49.1839i 0.0404506 + 0.0700625i
\(703\) −53.0751 30.6429i −0.0754980 0.0435888i
\(704\) −13.1782 + 22.8254i −0.0187191 + 0.0324224i
\(705\) 0 0
\(706\) 371.849i 0.526699i
\(707\) −51.4676 638.571i −0.0727971 0.903212i
\(708\) 391.189 0.552527
\(709\) −554.927 961.161i −0.782689 1.35566i −0.930370 0.366623i \(-0.880514\pi\)
0.147680 0.989035i \(-0.452819\pi\)
\(710\) 0 0
\(711\) −53.3665 + 92.4335i −0.0750584 + 0.130005i
\(712\) 134.267 77.5192i 0.188578 0.108875i
\(713\) 73.8617i 0.103593i
\(714\) 215.664 17.3821i 0.302051 0.0243447i
\(715\) 0 0
\(716\) 209.435 + 362.752i 0.292507 + 0.506637i
\(717\) −124.552 71.9101i −0.173713 0.100293i
\(718\) 211.263 365.918i 0.294238 0.509636i
\(719\) 936.393 540.627i 1.30235 0.751915i 0.321547 0.946894i \(-0.395797\pi\)
0.980807 + 0.194979i \(0.0624638\pi\)
\(720\) 0 0
\(721\) 319.402 + 151.609i 0.442999 + 0.210276i
\(722\) −506.042 −0.700889
\(723\) 287.369 + 497.737i 0.397467 + 0.688433i
\(724\) 422.043 + 243.667i 0.582932 + 0.336556i
\(725\) 0 0
\(726\) 233.655 134.901i 0.321838 0.185813i
\(727\) 491.493i 0.676056i 0.941136 + 0.338028i \(0.109760\pi\)
−0.941136 + 0.338028i \(0.890240\pi\)
\(728\) −125.941 + 86.9070i −0.172996 + 0.119378i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −846.044 488.464i −1.15738 0.668213i
\(732\) −45.4367 + 78.6988i −0.0620721 + 0.107512i
\(733\) 40.4999 23.3826i 0.0552522 0.0318999i −0.472119 0.881535i \(-0.656511\pi\)
0.527372 + 0.849635i \(0.323178\pi\)
\(734\) 186.784i 0.254474i
\(735\) 0 0
\(736\) 38.2199 0.0519292
\(737\) 32.8025 + 56.8156i 0.0445081 + 0.0770903i
\(738\) −69.2726 39.9946i −0.0938653 0.0541932i
\(739\) 368.856 638.878i 0.499129 0.864517i −0.500870 0.865522i \(-0.666987\pi\)
0.999999 + 0.00100544i \(0.000320040\pi\)
\(740\) 0 0
\(741\) 23.8507i 0.0321872i
\(742\) −290.615 421.146i −0.391665 0.567582i
\(743\) 258.593 0.348039 0.174020 0.984742i \(-0.444324\pi\)
0.174020 + 0.984742i \(0.444324\pi\)
\(744\) 26.7782 + 46.3812i 0.0359922 + 0.0623403i
\(745\) 0 0
\(746\) −7.55747 + 13.0899i −0.0101307 + 0.0175468i
\(747\) −121.271 + 70.0159i −0.162344 + 0.0937295i
\(748\) 83.1454i 0.111157i
\(749\) −282.005 + 594.114i −0.376509 + 0.793210i
\(750\) 0 0
\(751\) −175.310 303.645i −0.233435 0.404321i 0.725382 0.688347i \(-0.241663\pi\)
−0.958817 + 0.284025i \(0.908330\pi\)
\(752\) −44.6409 25.7734i −0.0593628 0.0342731i
\(753\) −362.930 + 628.613i −0.481978 + 0.834811i
\(754\) −371.928 + 214.733i −0.493274 + 0.284792i
\(755\) 0 0
\(756\) −5.84424 72.5110i −0.00773048 0.0959140i
\(757\) −907.187 −1.19840 −0.599199 0.800600i \(-0.704514\pi\)
−0.599199 + 0.800600i \(0.704514\pi\)
\(758\) 101.058 + 175.038i 0.133322 + 0.230921i
\(759\) 33.3890 + 19.2771i 0.0439907 + 0.0253981i
\(760\) 0 0
\(761\) 1067.66 616.416i 1.40297 0.810007i 0.408277 0.912858i \(-0.366130\pi\)
0.994697 + 0.102851i \(0.0327965\pi\)
\(762\) 287.280i 0.377008i
\(763\) 841.543 67.8267i 1.10294 0.0888948i
\(764\) −473.691 −0.620014
\(765\) 0 0
\(766\) 755.684 + 436.294i 0.986532 + 0.569575i
\(767\) −436.376 + 755.826i −0.568939 + 0.985432i
\(768\) 24.0000 13.8564i 0.0312500 0.0180422i
\(769\) 685.828i 0.891844i −0.895072 0.445922i \(-0.852876\pi\)
0.895072 0.445922i \(-0.147124\pi\)
\(770\) 0 0
\(771\) −578.431 −0.750235
\(772\) −132.892 230.176i −0.172140 0.298155i
\(773\) −334.420 193.077i −0.432625 0.249776i 0.267839 0.963464i \(-0.413690\pi\)
−0.700465 + 0.713687i \(0.747024\pi\)
\(774\) −164.232 + 284.458i −0.212186 + 0.367517i
\(775\) 0 0
\(776\) 129.386i 0.166734i
\(777\) 343.245 236.859i 0.441756 0.304838i
\(778\) 981.376 1.26141
\(779\) 16.7962 + 29.0918i 0.0215612 + 0.0373451i
\(780\) 0