Properties

Label 1050.3.q.b.649.2
Level $1050$
Weight $3$
Character 1050.649
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
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: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.22986704741655040229376.1
Defining polynomial: \( x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 649.2
Root \(2.22431 + 0.596002i\) of defining polynomial
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.b.199.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(5.76140 + 3.97571i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-1.64728 - 2.85317i) q^{11} +(1.73205 - 3.00000i) q^{12} +7.72850 q^{13} +(-4.24500 - 8.94315i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(6.30929 + 10.9280i) q^{17} +(3.67423 - 2.12132i) q^{18} +(-1.54304 - 0.890872i) q^{19} +(0.974040 - 12.0852i) q^{21} +4.65921i q^{22} +(5.85120 + 3.37819i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-9.46544 - 5.46488i) q^{26} +5.19615 q^{27} +(-1.12472 + 13.9547i) q^{28} -39.2933 q^{29} +(9.46751 - 5.46607i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-2.85317 + 4.94184i) q^{33} -17.8454i q^{34} -6.00000 q^{36} +(29.7883 + 17.1983i) q^{37} +(1.25988 + 2.18218i) q^{38} +(-6.69308 - 11.5928i) q^{39} -18.8536i q^{41} +(-9.73845 + 14.1125i) q^{42} +77.4197i q^{43} +(3.29456 - 5.70635i) q^{44} +(-4.77748 - 8.27485i) q^{46} +(6.44335 - 11.1602i) q^{47} +6.92820 q^{48} +(17.3875 + 45.8113i) q^{49} +(10.9280 - 18.9279i) q^{51} +(7.72850 + 13.3862i) q^{52} +(-44.7631 + 25.8440i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(11.2450 - 16.2957i) q^{56} +3.08607i q^{57} +(48.1243 + 27.7846i) q^{58} +(-97.7973 + 56.4633i) q^{59} +(-22.7184 - 13.1165i) q^{61} -15.4604 q^{62} +(-18.9713 + 9.00500i) q^{63} -8.00000 q^{64} +(6.98882 - 4.03500i) q^{66} +(17.2453 - 9.95656i) q^{67} +(-12.6186 + 21.8560i) q^{68} -11.7024i q^{69} +87.4319 q^{71} +(7.34847 + 4.24264i) q^{72} +(30.4575 + 52.7540i) q^{73} +(-24.3220 - 42.1270i) q^{74} -3.56349i q^{76} +(1.85274 - 22.9874i) q^{77} +18.9309i q^{78} +(-17.7888 + 30.8112i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-13.3315 + 23.0909i) q^{82} +46.6773 q^{83} +(21.9062 - 10.3981i) q^{84} +(54.7440 - 94.8194i) q^{86} +(34.0290 + 58.9399i) q^{87} +(-8.06999 + 4.65921i) q^{88} +(47.4706 + 27.4072i) q^{89} +(44.5270 + 30.7263i) q^{91} +13.5128i q^{92} +(-16.3982 - 9.46751i) q^{93} +(-15.7829 + 9.11228i) q^{94} +(-8.48528 - 4.89898i) q^{96} +45.7447 q^{97} +(11.0982 - 68.4020i) q^{98} +9.88368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) 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
\(7\) 5.76140 + 3.97571i 0.823057 + 0.567958i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.64728 2.85317i −0.149753 0.259379i 0.781383 0.624051i \(-0.214514\pi\)
−0.931136 + 0.364672i \(0.881181\pi\)
\(12\) 1.73205 3.00000i 0.144338 0.250000i
\(13\) 7.72850 0.594500 0.297250 0.954800i \(-0.403931\pi\)
0.297250 + 0.954800i \(0.403931\pi\)
\(14\) −4.24500 8.94315i −0.303214 0.638797i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 6.30929 + 10.9280i 0.371135 + 0.642824i 0.989740 0.142877i \(-0.0456354\pi\)
−0.618606 + 0.785702i \(0.712302\pi\)
\(18\) 3.67423 2.12132i 0.204124 0.117851i
\(19\) −1.54304 0.890872i −0.0812124 0.0468880i 0.458844 0.888517i \(-0.348264\pi\)
−0.540056 + 0.841629i \(0.681597\pi\)
\(20\) 0 0
\(21\) 0.974040 12.0852i 0.0463829 0.575484i
\(22\) 4.65921i 0.211782i
\(23\) 5.85120 + 3.37819i 0.254400 + 0.146878i 0.621777 0.783194i \(-0.286411\pi\)
−0.367377 + 0.930072i \(0.619744\pi\)
\(24\) −4.24264 + 2.44949i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) −9.46544 5.46488i −0.364055 0.210188i
\(27\) 5.19615 0.192450
\(28\) −1.12472 + 13.9547i −0.0401687 + 0.498384i
\(29\) −39.2933 −1.35494 −0.677471 0.735550i \(-0.736924\pi\)
−0.677471 + 0.735550i \(0.736924\pi\)
\(30\) 0 0
\(31\) 9.46751 5.46607i 0.305404 0.176325i −0.339464 0.940619i \(-0.610246\pi\)
0.644868 + 0.764294i \(0.276912\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) −2.85317 + 4.94184i −0.0864598 + 0.149753i
\(34\) 17.8454i 0.524864i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 29.7883 + 17.1983i 0.805089 + 0.464818i 0.845248 0.534375i \(-0.179453\pi\)
−0.0401585 + 0.999193i \(0.512786\pi\)
\(38\) 1.25988 + 2.18218i 0.0331548 + 0.0574258i
\(39\) −6.69308 11.5928i −0.171617 0.297250i
\(40\) 0 0
\(41\) 18.8536i 0.459844i −0.973209 0.229922i \(-0.926153\pi\)
0.973209 0.229922i \(-0.0738472\pi\)
\(42\) −9.73845 + 14.1125i −0.231868 + 0.336012i
\(43\) 77.4197i 1.80046i 0.435416 + 0.900229i \(0.356601\pi\)
−0.435416 + 0.900229i \(0.643399\pi\)
\(44\) 3.29456 5.70635i 0.0748764 0.129690i
\(45\) 0 0
\(46\) −4.77748 8.27485i −0.103858 0.179888i
\(47\) 6.44335 11.1602i 0.137093 0.237451i −0.789302 0.614005i \(-0.789558\pi\)
0.926395 + 0.376553i \(0.122891\pi\)
\(48\) 6.92820 0.144338
\(49\) 17.3875 + 45.8113i 0.354847 + 0.934924i
\(50\) 0 0
\(51\) 10.9280 18.9279i 0.214275 0.371135i
\(52\) 7.72850 + 13.3862i 0.148625 + 0.257426i
\(53\) −44.7631 + 25.8440i −0.844586 + 0.487622i −0.858821 0.512276i \(-0.828802\pi\)
0.0142341 + 0.999899i \(0.495469\pi\)
\(54\) −6.36396 3.67423i −0.117851 0.0680414i
\(55\) 0 0
\(56\) 11.2450 16.2957i 0.200804 0.290995i
\(57\) 3.08607i 0.0541416i
\(58\) 48.1243 + 27.7846i 0.829729 + 0.479044i
\(59\) −97.7973 + 56.4633i −1.65758 + 0.957005i −0.683754 + 0.729713i \(0.739654\pi\)
−0.973827 + 0.227292i \(0.927013\pi\)
\(60\) 0 0
\(61\) −22.7184 13.1165i −0.372432 0.215024i 0.302088 0.953280i \(-0.402316\pi\)
−0.674521 + 0.738256i \(0.735650\pi\)
\(62\) −15.4604 −0.249361
\(63\) −18.9713 + 9.00500i −0.301132 + 0.142937i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 6.98882 4.03500i 0.105891 0.0611363i
\(67\) 17.2453 9.95656i 0.257392 0.148605i −0.365752 0.930712i \(-0.619188\pi\)
0.623144 + 0.782107i \(0.285855\pi\)
\(68\) −12.6186 + 21.8560i −0.185567 + 0.321412i
\(69\) 11.7024i 0.169600i
\(70\) 0 0
\(71\) 87.4319 1.23144 0.615718 0.787967i \(-0.288866\pi\)
0.615718 + 0.787967i \(0.288866\pi\)
\(72\) 7.34847 + 4.24264i 0.102062 + 0.0589256i
\(73\) 30.4575 + 52.7540i 0.417226 + 0.722657i 0.995659 0.0930727i \(-0.0296689\pi\)
−0.578433 + 0.815730i \(0.696336\pi\)
\(74\) −24.3220 42.1270i −0.328676 0.569284i
\(75\) 0 0
\(76\) 3.56349i 0.0468880i
\(77\) 1.85274 22.9874i 0.0240615 0.298537i
\(78\) 18.9309i 0.242704i
\(79\) −17.7888 + 30.8112i −0.225175 + 0.390015i −0.956372 0.292152i \(-0.905629\pi\)
0.731197 + 0.682167i \(0.238962\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) −13.3315 + 23.0909i −0.162580 + 0.281596i
\(83\) 46.6773 0.562377 0.281188 0.959653i \(-0.409271\pi\)
0.281188 + 0.959653i \(0.409271\pi\)
\(84\) 21.9062 10.3981i 0.260788 0.123787i
\(85\) 0 0
\(86\) 54.7440 94.8194i 0.636558 1.10255i
\(87\) 34.0290 + 58.9399i 0.391138 + 0.677471i
\(88\) −8.06999 + 4.65921i −0.0917044 + 0.0529456i
\(89\) 47.4706 + 27.4072i 0.533378 + 0.307946i 0.742391 0.669967i \(-0.233692\pi\)
−0.209013 + 0.977913i \(0.567025\pi\)
\(90\) 0 0
\(91\) 44.5270 + 30.7263i 0.489308 + 0.337651i
\(92\) 13.5128i 0.146878i
\(93\) −16.3982 9.46751i −0.176325 0.101801i
\(94\) −15.7829 + 9.11228i −0.167903 + 0.0969391i
\(95\) 0 0
\(96\) −8.48528 4.89898i −0.0883883 0.0510310i
\(97\) 45.7447 0.471595 0.235798 0.971802i \(-0.424230\pi\)
0.235798 + 0.971802i \(0.424230\pi\)
\(98\) 11.0982 68.4020i 0.113247 0.697979i
\(99\) 9.88368 0.0998352
\(100\) 0 0
\(101\) 79.2589 45.7601i 0.784741 0.453071i −0.0533667 0.998575i \(-0.516995\pi\)
0.838108 + 0.545504i \(0.183662\pi\)
\(102\) −26.7681 + 15.4545i −0.262432 + 0.151515i
\(103\) 25.2541 43.7414i 0.245186 0.424674i −0.716998 0.697075i \(-0.754484\pi\)
0.962184 + 0.272401i \(0.0878178\pi\)
\(104\) 21.8595i 0.210188i
\(105\) 0 0
\(106\) 73.0978 0.689602
\(107\) 81.3626 + 46.9747i 0.760398 + 0.439016i 0.829439 0.558598i \(-0.188660\pi\)
−0.0690404 + 0.997614i \(0.521994\pi\)
\(108\) 5.19615 + 9.00000i 0.0481125 + 0.0833333i
\(109\) 60.3052 + 104.452i 0.553258 + 0.958272i 0.998037 + 0.0626310i \(0.0199491\pi\)
−0.444778 + 0.895641i \(0.646718\pi\)
\(110\) 0 0
\(111\) 59.5766i 0.536726i
\(112\) −25.2951 + 12.0067i −0.225849 + 0.107202i
\(113\) 10.7318i 0.0949713i −0.998872 0.0474856i \(-0.984879\pi\)
0.998872 0.0474856i \(-0.0151208\pi\)
\(114\) 2.18218 3.77965i 0.0191419 0.0331548i
\(115\) 0 0
\(116\) −39.2933 68.0580i −0.338735 0.586707i
\(117\) −11.5928 + 20.0792i −0.0990834 + 0.171617i
\(118\) 159.702 1.35341
\(119\) −7.09622 + 88.0446i −0.0596321 + 0.739870i
\(120\) 0 0
\(121\) 55.0729 95.3891i 0.455148 0.788340i
\(122\) 18.5495 + 32.1286i 0.152045 + 0.263349i
\(123\) −28.2804 + 16.3277i −0.229922 + 0.132746i
\(124\) 18.9350 + 10.9321i 0.152702 + 0.0881624i
\(125\) 0 0
\(126\) 29.6025 + 2.38590i 0.234940 + 0.0189357i
\(127\) 117.281i 0.923476i −0.887016 0.461738i \(-0.847226\pi\)
0.887016 0.461738i \(-0.152774\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) 116.130 67.0475i 0.900229 0.519748i
\(130\) 0 0
\(131\) 80.2758 + 46.3473i 0.612792 + 0.353796i 0.774058 0.633115i \(-0.218224\pi\)
−0.161265 + 0.986911i \(0.551557\pi\)
\(132\) −11.4127 −0.0864598
\(133\) −5.34820 11.2673i −0.0402120 0.0847168i
\(134\) −28.1614 −0.210160
\(135\) 0 0
\(136\) 30.9091 17.8454i 0.227273 0.131216i
\(137\) 23.7932 13.7370i 0.173673 0.100270i −0.410644 0.911796i \(-0.634696\pi\)
0.584317 + 0.811526i \(0.301363\pi\)
\(138\) −8.27485 + 14.3325i −0.0599626 + 0.103858i
\(139\) 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
\(142\) −107.082 61.8237i −0.754097 0.435378i
\(143\) −12.7310 22.0507i −0.0890280 0.154201i
\(144\) −6.00000 10.3923i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) 86.1469i 0.590047i
\(147\) 53.6589 65.7550i 0.365027 0.447313i
\(148\) 68.7931i 0.464818i
\(149\) 25.5567 44.2656i 0.171522 0.297084i −0.767430 0.641132i \(-0.778465\pi\)
0.938952 + 0.344048i \(0.111798\pi\)
\(150\) 0 0
\(151\) 82.6090 + 143.083i 0.547079 + 0.947569i 0.998473 + 0.0552442i \(0.0175937\pi\)
−0.451394 + 0.892325i \(0.649073\pi\)
\(152\) −2.51977 + 4.36436i −0.0165774 + 0.0287129i
\(153\) −37.8558 −0.247423
\(154\) −18.5237 + 26.8436i −0.120284 + 0.174309i
\(155\) 0 0
\(156\) 13.3862 23.1855i 0.0858087 0.148625i
\(157\) 95.4059 + 165.248i 0.607681 + 1.05253i 0.991622 + 0.129176i \(0.0412333\pi\)
−0.383941 + 0.923358i \(0.625433\pi\)
\(158\) 43.5736 25.1572i 0.275782 0.159223i
\(159\) 77.5319 + 44.7631i 0.487622 + 0.281529i
\(160\) 0 0
\(161\) 20.2804 + 42.7258i 0.125965 + 0.265377i
\(162\) 12.7279i 0.0785674i
\(163\) 214.949 + 124.101i 1.31871 + 0.761356i 0.983521 0.180796i \(-0.0578674\pi\)
0.335186 + 0.942152i \(0.391201\pi\)
\(164\) 32.6554 18.8536i 0.199118 0.114961i
\(165\) 0 0
\(166\) −57.1678 33.0058i −0.344384 0.198830i
\(167\) 29.2974 0.175433 0.0877167 0.996145i \(-0.472043\pi\)
0.0877167 + 0.996145i \(0.472043\pi\)
\(168\) −34.1820 2.75500i −0.203464 0.0163988i
\(169\) −109.270 −0.646570
\(170\) 0 0
\(171\) 4.62911 2.67262i 0.0270708 0.0156293i
\(172\) −134.095 + 77.4197i −0.779622 + 0.450115i
\(173\) −11.5460 + 19.9982i −0.0667397 + 0.115597i −0.897464 0.441087i \(-0.854593\pi\)
0.830725 + 0.556683i \(0.187926\pi\)
\(174\) 96.2485i 0.553152i
\(175\) 0 0
\(176\) 13.1782 0.0748764
\(177\) 169.390 + 97.7973i 0.957005 + 0.552527i
\(178\) −38.7596 67.1336i −0.217751 0.377155i
\(179\) −104.717 181.376i −0.585014 1.01327i −0.994874 0.101125i \(-0.967756\pi\)
0.409860 0.912148i \(-0.365577\pi\)
\(180\) 0 0
\(181\) 243.667i 1.34622i 0.739540 + 0.673112i \(0.235043\pi\)
−0.739540 + 0.673112i \(0.764957\pi\)
\(182\) −32.8075 69.1172i −0.180261 0.379765i
\(183\) 45.4367i 0.248288i
\(184\) 9.55497 16.5497i 0.0519292 0.0899440i
\(185\) 0 0
\(186\) 13.3891 + 23.1906i 0.0719843 + 0.124681i
\(187\) 20.7863 36.0030i 0.111157 0.192529i
\(188\) 25.7734 0.137093
\(189\) 29.9371 + 20.6584i 0.158397 + 0.109304i
\(190\) 0 0
\(191\) 118.423 205.114i 0.620014 1.07390i −0.369468 0.929243i \(-0.620460\pi\)
0.989483 0.144653i \(-0.0462064\pi\)
\(192\) 6.92820 + 12.0000i 0.0360844 + 0.0625000i
\(193\) 115.088 66.4460i 0.596310 0.344280i −0.171278 0.985223i \(-0.554790\pi\)
0.767589 + 0.640943i \(0.221456\pi\)
\(194\) −56.0256 32.3464i −0.288792 0.166734i
\(195\) 0 0
\(196\) −61.9600 + 75.9273i −0.316122 + 0.387384i
\(197\) 105.779i 0.536950i −0.963287 0.268475i \(-0.913480\pi\)
0.963287 0.268475i \(-0.0865197\pi\)
\(198\) −12.1050 6.98882i −0.0611363 0.0352971i
\(199\) −174.541 + 100.771i −0.877091 + 0.506389i −0.869698 0.493584i \(-0.835687\pi\)
−0.00739279 + 0.999973i \(0.502353\pi\)
\(200\) 0 0
\(201\) −29.8697 17.2453i −0.148605 0.0857973i
\(202\) −129.429 −0.640739
\(203\) −226.384 156.219i −1.11519 0.769550i
\(204\) 43.7121 0.214275
\(205\) 0 0
\(206\) −61.8597 + 35.7147i −0.300290 + 0.173372i
\(207\) −17.5536 + 10.1346i −0.0848000 + 0.0489593i
\(208\) −15.4570 + 26.7723i −0.0743125 + 0.128713i
\(209\) 5.87006i 0.0280864i
\(210\) 0 0
\(211\) 29.6045 0.140306 0.0701528 0.997536i \(-0.477651\pi\)
0.0701528 + 0.997536i \(0.477651\pi\)
\(212\) −89.5262 51.6880i −0.422293 0.243811i
\(213\) −75.7183 131.148i −0.355485 0.615718i
\(214\) −66.4323 115.064i −0.310431 0.537683i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 76.2777 + 6.14783i 0.351510 + 0.0283310i
\(218\) 170.569i 0.782426i
\(219\) 52.7540 91.3726i 0.240886 0.417226i
\(220\) 0 0
\(221\) 48.7614 + 84.4572i 0.220640 + 0.382159i
\(222\) −42.1270 + 72.9661i −0.189761 + 0.328676i
\(223\) 328.532 1.47324 0.736620 0.676307i \(-0.236421\pi\)
0.736620 + 0.676307i \(0.236421\pi\)
\(224\) 39.4700 + 3.18120i 0.176205 + 0.0142018i
\(225\) 0 0
\(226\) −7.58850 + 13.1437i −0.0335774 + 0.0581578i
\(227\) 182.228 + 315.628i 0.802766 + 1.39043i 0.917789 + 0.397069i \(0.129972\pi\)
−0.115023 + 0.993363i \(0.536694\pi\)
\(228\) −5.34523 + 3.08607i −0.0234440 + 0.0135354i
\(229\) 260.716 + 150.525i 1.13850 + 0.657313i 0.946059 0.323996i \(-0.105026\pi\)
0.192441 + 0.981309i \(0.438360\pi\)
\(230\) 0 0
\(231\) −36.0856 + 17.1285i −0.156215 + 0.0741496i
\(232\) 111.138i 0.479044i
\(233\) −244.241 141.013i −1.04824 0.605204i −0.126087 0.992019i \(-0.540242\pi\)
−0.922157 + 0.386815i \(0.873575\pi\)
\(234\) 28.3963 16.3946i 0.121352 0.0700625i
\(235\) 0 0
\(236\) −195.595 112.927i −0.828790 0.478502i
\(237\) 61.6224 0.260010
\(238\) 70.9480 102.814i 0.298101 0.431993i
\(239\) −83.0347 −0.347425 −0.173713 0.984796i \(-0.555576\pi\)
−0.173713 + 0.984796i \(0.555576\pi\)
\(240\) 0 0
\(241\) −287.369 + 165.912i −1.19240 + 0.688433i −0.958851 0.283911i \(-0.908368\pi\)
−0.233551 + 0.972345i \(0.575035\pi\)
\(242\) −134.901 + 77.8849i −0.557440 + 0.321838i
\(243\) −7.79423 + 13.5000i −0.0320750 + 0.0555556i
\(244\) 52.4658i 0.215024i
\(245\) 0 0
\(246\) 46.1817 0.187731
\(247\) −11.9254 6.88511i −0.0482808 0.0278749i
\(248\) −15.4604 26.7782i −0.0623403 0.107977i
\(249\) −40.4237 70.0159i −0.162344 0.281188i
\(250\) 0 0
\(251\) 419.075i 1.66962i 0.550537 + 0.834811i \(0.314423\pi\)
−0.550537 + 0.834811i \(0.685577\pi\)
\(252\) −34.5684 23.8542i −0.137176 0.0946597i
\(253\) 22.2593i 0.0879815i
\(254\) −82.9305 + 143.640i −0.326498 + 0.565511i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 166.979 289.215i 0.649722 1.12535i −0.333467 0.942762i \(-0.608219\pi\)
0.983189 0.182590i \(-0.0584481\pi\)
\(258\) −189.639 −0.735034
\(259\) 103.247 + 217.516i 0.398637 + 0.839829i
\(260\) 0 0
\(261\) 58.9399 102.087i 0.225824 0.391138i
\(262\) −65.5449 113.527i −0.250171 0.433310i
\(263\) −176.995 + 102.188i −0.672986 + 0.388549i −0.797207 0.603706i \(-0.793690\pi\)
0.124221 + 0.992255i \(0.460357\pi\)
\(264\) 13.9776 + 8.06999i 0.0529456 + 0.0305681i
\(265\) 0 0
\(266\) −1.41702 + 17.5814i −0.00532715 + 0.0660953i
\(267\) 94.9412i 0.355585i
\(268\) 34.4905 + 19.9131i 0.128696 + 0.0743027i
\(269\) 120.768 69.7257i 0.448953 0.259203i −0.258435 0.966029i \(-0.583207\pi\)
0.707388 + 0.706825i \(0.249873\pi\)
\(270\) 0 0
\(271\) −323.213 186.607i −1.19267 0.688586i −0.233756 0.972295i \(-0.575102\pi\)
−0.958910 + 0.283709i \(0.908435\pi\)
\(272\) −50.4743 −0.185567
\(273\) 7.52787 93.4002i 0.0275746 0.342125i
\(274\) −38.8542 −0.141804
\(275\) 0 0
\(276\) 20.2691 11.7024i 0.0734389 0.0424000i
\(277\) −430.851 + 248.752i −1.55542 + 0.898022i −0.557735 + 0.830019i \(0.688329\pi\)
−0.997685 + 0.0680029i \(0.978337\pi\)
\(278\) 47.3852 82.0735i 0.170450 0.295228i
\(279\) 32.7964i 0.117550i
\(280\) 0 0
\(281\) 292.779 1.04192 0.520959 0.853582i \(-0.325574\pi\)
0.520959 + 0.853582i \(0.325574\pi\)
\(282\) 27.3368 + 15.7829i 0.0969391 + 0.0559678i
\(283\) 138.383 + 239.686i 0.488986 + 0.846949i 0.999920 0.0126714i \(-0.00403355\pi\)
−0.510934 + 0.859620i \(0.670700\pi\)
\(284\) 87.4319 + 151.437i 0.307859 + 0.533227i
\(285\) 0 0
\(286\) 36.0087i 0.125905i
\(287\) 74.9565 108.623i 0.261172 0.378478i
\(288\) 16.9706i 0.0589256i
\(289\) 64.8857 112.385i 0.224518 0.388876i
\(290\) 0 0
\(291\) −39.6161 68.6171i −0.136138 0.235798i
\(292\) −60.9150 + 105.508i −0.208613 + 0.361329i
\(293\) −375.299 −1.28088 −0.640442 0.768006i \(-0.721249\pi\)
−0.640442 + 0.768006i \(0.721249\pi\)
\(294\) −112.214 + 42.5905i −0.381681 + 0.144866i
\(295\) 0 0
\(296\) 48.6441 84.2540i 0.164338 0.284642i
\(297\) −8.55952 14.8255i −0.0288199 0.0499176i
\(298\) −62.6009 + 36.1427i −0.210070 + 0.121284i
\(299\) 45.2210 + 26.1084i 0.151241 + 0.0873189i
\(300\) 0 0
\(301\) −307.798 + 446.046i −1.02259 + 1.48188i
\(302\) 233.653i 0.773687i
\(303\) −137.280 79.2589i −0.453071 0.261580i
\(304\) 6.17214 3.56349i 0.0203031 0.0117220i
\(305\) 0 0
\(306\) 46.3636 + 26.7681i 0.151515 + 0.0874773i
\(307\) −107.784 −0.351088 −0.175544 0.984472i \(-0.556168\pi\)
−0.175544 + 0.984472i \(0.556168\pi\)
\(308\) 41.6680 19.7783i 0.135286 0.0642154i
\(309\) −87.4828 −0.283116
\(310\) 0 0
\(311\) −499.771 + 288.543i −1.60698 + 0.927791i −0.616940 + 0.787010i \(0.711628\pi\)
−0.990041 + 0.140780i \(0.955039\pi\)
\(312\) −32.7893 + 18.9309i −0.105094 + 0.0606759i
\(313\) 198.637 344.050i 0.634624 1.09920i −0.351971 0.936011i \(-0.614488\pi\)
0.986595 0.163190i \(-0.0521782\pi\)
\(314\) 269.849i 0.859390i
\(315\) 0 0
\(316\) −71.1554 −0.225175
\(317\) −69.6026 40.1851i −0.219566 0.126767i 0.386183 0.922422i \(-0.373793\pi\)
−0.605749 + 0.795655i \(0.707127\pi\)
\(318\) −63.3046 109.647i −0.199071 0.344801i
\(319\) 64.7271 + 112.111i 0.202906 + 0.351444i
\(320\) 0 0
\(321\) 162.725i 0.506932i
\(322\) 5.37336 66.6686i 0.0166874 0.207045i
\(323\) 22.4831i 0.0696071i
\(324\) 9.00000 15.5885i 0.0277778 0.0481125i
\(325\) 0 0
\(326\) −175.505 303.984i −0.538360 0.932467i
\(327\) 104.452 180.915i 0.319424 0.553258i
\(328\) −53.3261 −0.162580
\(329\) 81.4925 38.6816i 0.247698 0.117573i
\(330\) 0 0
\(331\) −246.021 + 426.121i −0.743266 + 1.28737i 0.207734 + 0.978185i \(0.433391\pi\)
−0.951000 + 0.309189i \(0.899942\pi\)
\(332\) 46.6773 + 80.8474i 0.140594 + 0.243516i
\(333\) −89.3649 + 51.5948i −0.268363 + 0.154939i
\(334\) −35.8818 20.7164i −0.107431 0.0620251i
\(335\) 0 0
\(336\) 39.9162 + 27.5445i 0.118798 + 0.0819777i
\(337\) 630.123i 1.86980i −0.354910 0.934901i \(-0.615488\pi\)
0.354910 0.934901i \(-0.384512\pi\)
\(338\) 133.828 + 77.2657i 0.395941 + 0.228597i
\(339\) −16.0976 + 9.29397i −0.0474856 + 0.0274159i
\(340\) 0 0
\(341\) −31.1913 18.0083i −0.0914701 0.0528103i
\(342\) −7.55930 −0.0221032
\(343\) −81.9559 + 333.065i −0.238938 + 0.971035i
\(344\) 218.976 0.636558
\(345\) 0 0
\(346\) 28.2817 16.3285i 0.0817391 0.0471921i
\(347\) −372.514 + 215.071i −1.07353 + 0.619802i −0.929143 0.369720i \(-0.879454\pi\)
−0.144385 + 0.989522i \(0.546120\pi\)
\(348\) −68.0580 + 117.880i −0.195569 + 0.338735i
\(349\) 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
\(352\) −16.1400 9.31842i −0.0458522 0.0264728i
\(353\) −131.469 227.710i −0.372432 0.645071i 0.617507 0.786565i \(-0.288143\pi\)
−0.989939 + 0.141494i \(0.954809\pi\)
\(354\) −138.306 239.553i −0.390696 0.676704i
\(355\) 0 0
\(356\) 109.629i 0.307946i
\(357\) 138.212 65.6045i 0.387150 0.183766i
\(358\) 296.186i 0.827334i
\(359\) 149.386 258.743i 0.416116 0.720734i −0.579429 0.815023i \(-0.696724\pi\)
0.995545 + 0.0942890i \(0.0300578\pi\)
\(360\) 0 0
\(361\) −178.913 309.886i −0.495603 0.858410i
\(362\) 172.298 298.429i 0.475962 0.824391i
\(363\) −190.778 −0.525560
\(364\) −8.69244 + 107.849i −0.0238803 + 0.296289i
\(365\) 0 0
\(366\) 32.1286 55.6484i 0.0877831 0.152045i
\(367\) −66.0380 114.381i −0.179940 0.311665i 0.761920 0.647671i \(-0.224257\pi\)
−0.941860 + 0.336006i \(0.890924\pi\)
\(368\) −23.4048 + 13.5128i −0.0636000 + 0.0367195i
\(369\) 48.9831 + 28.2804i 0.132746 + 0.0766407i
\(370\) 0 0
\(371\) −360.646 29.0674i −0.972092 0.0783487i
\(372\) 37.8701i 0.101801i
\(373\) 9.25597 + 5.34394i 0.0248149 + 0.0143269i 0.512356 0.858773i \(-0.328773\pi\)
−0.487541 + 0.873100i \(0.662106\pi\)
\(374\) −50.9159 + 29.3963i −0.136139 + 0.0785998i
\(375\) 0 0
\(376\) −31.5659 18.2246i −0.0839517 0.0484696i
\(377\) −303.678 −0.805513
\(378\) −22.0577 46.4700i −0.0583536 0.122936i
\(379\) −142.918 −0.377092 −0.188546 0.982064i \(-0.560378\pi\)
−0.188546 + 0.982064i \(0.560378\pi\)
\(380\) 0 0
\(381\) −175.922 + 101.569i −0.461738 + 0.266585i
\(382\) −290.075 + 167.475i −0.759359 + 0.438416i
\(383\) −308.507 + 534.349i −0.805500 + 1.39517i 0.110452 + 0.993881i \(0.464770\pi\)
−0.915953 + 0.401286i \(0.868563\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −187.938 −0.486885
\(387\) −201.142 116.130i −0.519748 0.300076i
\(388\) 45.7447 + 79.2322i 0.117899 + 0.204207i
\(389\) −346.969 600.968i −0.891951 1.54490i −0.837534 0.546386i \(-0.816003\pi\)
−0.0544171 0.998518i \(-0.517330\pi\)
\(390\) 0 0
\(391\) 85.2560i 0.218046i
\(392\) 129.574 49.1793i 0.330546 0.125457i
\(393\) 160.552i 0.408528i
\(394\) −74.7972 + 129.553i −0.189841 + 0.328814i
\(395\) 0 0
\(396\) 9.88368 + 17.1190i 0.0249588 + 0.0432299i
\(397\) 279.776 484.587i 0.704726 1.22062i −0.262065 0.965050i \(-0.584403\pi\)
0.966790 0.255571i \(-0.0822633\pi\)
\(398\) 285.024 0.716142
\(399\) −12.2693 + 17.7801i −0.0307502 + 0.0445616i
\(400\) 0 0
\(401\) 80.6033 139.609i 0.201006 0.348152i −0.747847 0.663871i \(-0.768912\pi\)
0.948853 + 0.315719i \(0.102246\pi\)
\(402\) 24.3885 + 42.2421i 0.0606679 + 0.105080i
\(403\) 73.1697 42.2445i 0.181563 0.104825i
\(404\) 158.518 + 91.5203i 0.392371 + 0.226535i
\(405\) 0 0
\(406\) 166.800 + 351.406i 0.410837 + 0.865532i
\(407\) 113.322i 0.278431i
\(408\) −53.5361 30.9091i −0.131216 0.0757576i
\(409\) −398.217 + 229.911i −0.973637 + 0.562129i −0.900343 0.435181i \(-0.856684\pi\)
−0.0732937 + 0.997310i \(0.523351\pi\)
\(410\) 0 0
\(411\) −41.2111 23.7932i −0.100270 0.0578911i
\(412\) 101.016 0.245186
\(413\) −787.931 63.5056i −1.90782 0.153767i
\(414\) 28.6649 0.0692389
\(415\) 0 0
\(416\) 37.8618 21.8595i 0.0910139 0.0525469i
\(417\) 100.519 58.0347i 0.241053 0.139172i
\(418\) 4.15076 7.18933i 0.00993005 0.0171994i
\(419\) 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 \(0.438004\pi\)
\(422\) −36.2579 20.9335i −0.0859193 0.0496055i
\(423\) 19.3301 + 33.4806i 0.0456975 + 0.0791504i
\(424\) 73.0978 + 126.609i 0.172400 + 0.298606i
\(425\) 0 0
\(426\) 214.164i 0.502731i
\(427\) −78.7425 165.891i −0.184409 0.388503i
\(428\) 187.899i 0.439016i
\(429\) −22.0507 + 38.1930i −0.0514003 + 0.0890280i
\(430\) 0 0
\(431\) 165.543 + 286.728i 0.384090 + 0.665263i 0.991642 0.129016i \(-0.0411820\pi\)
−0.607553 + 0.794279i \(0.707849\pi\)
\(432\) −10.3923 + 18.0000i −0.0240563 + 0.0416667i
\(433\) 88.4130 0.204187 0.102094 0.994775i \(-0.467446\pi\)
0.102094 + 0.994775i \(0.467446\pi\)
\(434\) −89.0735 61.4660i −0.205238 0.141627i
\(435\) 0 0
\(436\) −120.610 + 208.903i −0.276629 + 0.479136i
\(437\) −6.01907 10.4253i −0.0137736 0.0238566i
\(438\) −129.220 + 74.6054i −0.295024 + 0.170332i
\(439\) 60.4608 + 34.9070i 0.137724 + 0.0795149i 0.567279 0.823526i \(-0.307996\pi\)
−0.429555 + 0.903041i \(0.641330\pi\)
\(440\) 0 0
\(441\) −145.102 23.5429i −0.329031 0.0533852i
\(442\) 137.918i 0.312032i
\(443\) 571.953 + 330.217i 1.29109 + 0.745411i 0.978847 0.204592i \(-0.0655866\pi\)
0.312242 + 0.950003i \(0.398920\pi\)
\(444\) 103.190 59.5766i 0.232409 0.134182i
\(445\) 0 0
\(446\) −402.368 232.307i −0.902171 0.520869i
\(447\) −88.5311 −0.198056
\(448\) −46.0912 31.8057i −0.102882 0.0709948i
\(449\) 560.274 1.24783 0.623913 0.781493i \(-0.285542\pi\)
0.623913 + 0.781493i \(0.285542\pi\)
\(450\) 0 0
\(451\) −53.7926 + 31.0572i −0.119274 + 0.0688629i
\(452\) 18.5879 10.7318i 0.0411238 0.0237428i
\(453\) 143.083 247.827i 0.315856 0.547079i
\(454\) 515.418i 1.13528i
\(455\) 0 0
\(456\) 8.72873 0.0191419
\(457\) −159.158 91.8900i −0.348267 0.201072i 0.315655 0.948874i \(-0.397776\pi\)
−0.663922 + 0.747802i \(0.731109\pi\)
\(458\) −212.874 368.709i −0.464790 0.805041i
\(459\) 32.7840 + 56.7836i 0.0714249 + 0.123712i
\(460\) 0 0
\(461\) 28.4330i 0.0616767i −0.999524 0.0308384i \(-0.990182\pi\)
0.999524 0.0308384i \(-0.00981771\pi\)
\(462\) 56.3073 + 4.53826i 0.121877 + 0.00982307i
\(463\) 269.931i 0.583005i 0.956570 + 0.291503i \(0.0941552\pi\)
−0.956570 + 0.291503i \(0.905845\pi\)
\(464\) 78.5866 136.116i 0.169368 0.293353i
\(465\) 0 0
\(466\) 199.422 + 345.409i 0.427944 + 0.741221i
\(467\) −167.166 + 289.539i −0.357956 + 0.619999i −0.987619 0.156870i \(-0.949860\pi\)
0.629663 + 0.776868i \(0.283193\pi\)
\(468\) −46.3710 −0.0990834
\(469\) 138.941 + 11.1984i 0.296250 + 0.0238772i
\(470\) 0 0
\(471\) 165.248 286.218i 0.350845 0.607681i
\(472\) 159.702 + 276.612i 0.338352 + 0.586043i
\(473\) 220.892 127.532i 0.467002 0.269624i
\(474\) −75.4717 43.5736i −0.159223 0.0919274i
\(475\) 0 0
\(476\) −159.594 + 75.7536i −0.335281 + 0.159146i
\(477\) 155.064i 0.325081i
\(478\) 101.696 + 58.7144i 0.212754 + 0.122833i
\(479\) −114.560 + 66.1412i −0.239165 + 0.138082i −0.614793 0.788689i \(-0.710760\pi\)
0.375628 + 0.926771i \(0.377427\pi\)
\(480\) 0 0
\(481\) 230.219 + 132.917i 0.478626 + 0.276335i
\(482\) 469.271 0.973592
\(483\) 46.5253 67.4222i 0.0963257 0.139591i
\(484\) 220.292 0.455148
\(485\) 0 0
\(486\) 19.0919 11.0227i 0.0392837 0.0226805i
\(487\) −447.970 + 258.635i −0.919856 + 0.531079i −0.883589 0.468263i \(-0.844880\pi\)
−0.0362667 + 0.999342i \(0.511547\pi\)
\(488\) −37.0989 + 64.2573i −0.0760224 + 0.131675i
\(489\) 429.898i 0.879138i
\(490\) 0 0
\(491\) 484.805 0.987383 0.493692 0.869637i \(-0.335647\pi\)
0.493692 + 0.869637i \(0.335647\pi\)
\(492\) −56.5609 32.6554i −0.114961 0.0663728i
\(493\) −247.913 429.398i −0.502866 0.870989i
\(494\) 9.73701 + 16.8650i 0.0197105 + 0.0341397i
\(495\) 0 0
\(496\) 43.7286i 0.0881624i
\(497\) 503.730 + 347.604i 1.01354 + 0.699404i
\(498\) 114.336i 0.229589i
\(499\) −64.6450 + 111.968i −0.129549 + 0.224385i −0.923502 0.383594i \(-0.874686\pi\)
0.793953 + 0.607979i \(0.208020\pi\)
\(500\) 0 0
\(501\) −25.3723 43.9461i −0.0506432 0.0877167i
\(502\) 296.331 513.260i 0.590300 1.02243i
\(503\) 160.905 0.319890 0.159945 0.987126i \(-0.448868\pi\)
0.159945 + 0.987126i \(0.448868\pi\)
\(504\) 25.4700 + 53.6589i 0.0505357 + 0.106466i
\(505\) 0 0
\(506\) −15.7397 + 27.2620i −0.0311061 + 0.0538774i
\(507\) 94.6308 + 163.905i 0.186649 + 0.323285i
\(508\) 203.137 117.281i 0.399877 0.230869i
\(509\) 320.453 + 185.014i 0.629575 + 0.363485i 0.780587 0.625047i \(-0.214920\pi\)
−0.151013 + 0.988532i \(0.548253\pi\)
\(510\) 0 0
\(511\) −34.2563 + 425.027i −0.0670378 + 0.831755i
\(512\) 22.6274i 0.0441942i
\(513\) −8.01785 4.62911i −0.0156293 0.00902360i
\(514\) −409.012 + 236.143i −0.795744 + 0.459423i
\(515\) 0 0
\(516\) 232.259 + 134.095i 0.450115 + 0.259874i
\(517\) −42.4560 −0.0821200
\(518\) 27.3556 339.408i 0.0528101 0.655228i
\(519\) 39.9964 0.0770644
\(520\) 0 0
\(521\) 65.1395 37.6083i 0.125028 0.0721849i −0.436182 0.899859i \(-0.643670\pi\)
0.561210 + 0.827674i \(0.310336\pi\)
\(522\) −144.373 + 83.3537i −0.276576 + 0.159681i
\(523\) 468.058 810.701i 0.894949 1.55010i 0.0610819 0.998133i \(-0.480545\pi\)
0.833867 0.551965i \(-0.186122\pi\)
\(524\) 185.389i 0.353796i
\(525\) 0 0
\(526\) 289.032 0.549491
\(527\) 119.467 + 68.9741i 0.226692 + 0.130881i
\(528\) −11.4127 19.7674i −0.0216149 0.0374382i
\(529\) −241.676 418.594i −0.456854 0.791294i
\(530\) 0 0
\(531\) 338.780i 0.638003i
\(532\) 14.1674 20.5307i 0.0266304 0.0385915i
\(533\) 145.710i 0.273377i
\(534\) −67.1336 + 116.279i −0.125718 + 0.217751i
\(535\) 0 0
\(536\) −28.1614 48.7770i −0.0525399 0.0910018i
\(537\) −181.376 + 314.152i −0.337758 + 0.585014i
\(538\) −197.214 −0.366569
\(539\) 102.065 125.074i 0.189361 0.232047i
\(540\) 0 0
\(541\) 304.692 527.742i 0.563201 0.975493i −0.434013 0.900906i \(-0.642903\pi\)
0.997215 0.0745867i \(-0.0237638\pi\)
\(542\) 263.902 + 457.092i 0.486904 + 0.843343i
\(543\) 365.500 211.021i 0.673112 0.388622i
\(544\) 61.8182 + 35.6907i 0.113636 + 0.0656080i
\(545\) 0 0
\(546\) −75.2637 + 109.068i −0.137846 + 0.199759i
\(547\) 491.361i 0.898283i −0.893461 0.449141i \(-0.851730\pi\)
0.893461 0.449141i \(-0.148270\pi\)
\(548\) 47.5865 + 27.4741i 0.0868366 + 0.0501351i
\(549\) 68.1551 39.3494i 0.124144 0.0716746i
\(550\) 0 0
\(551\) 60.6310 + 35.0053i 0.110038 + 0.0635305i
\(552\) −33.0994 −0.0599626
\(553\) −224.985 + 106.792i −0.406844 + 0.193115i
\(554\) 703.577 1.27000
\(555\) 0 0
\(556\) −116.069 + 67.0127i −0.208758 + 0.120527i
\(557\) −911.250 + 526.110i −1.63600 + 0.944543i −0.653803 + 0.756665i \(0.726828\pi\)
−0.982192 + 0.187878i \(0.939839\pi\)
\(558\) 23.1906 40.1673i 0.0415602 0.0719843i
\(559\) 598.339i 1.07037i
\(560\) 0 0
\(561\) −72.0060 −0.128353
\(562\) −358.580 207.026i −0.638042 0.368374i
\(563\) 387.269 + 670.769i 0.687866 + 1.19142i 0.972527 + 0.232791i \(0.0747857\pi\)
−0.284661 + 0.958628i \(0.591881\pi\)
\(564\) −22.3204 38.6601i −0.0395752 0.0685463i
\(565\) 0 0
\(566\) 391.406i 0.691531i
\(567\) 5.06126 62.7964i 0.00892639 0.110752i
\(568\) 247.295i 0.435378i
\(569\) 156.525 271.109i 0.275088 0.476466i −0.695070 0.718942i \(-0.744626\pi\)
0.970157 + 0.242477i \(0.0779598\pi\)
\(570\) 0 0
\(571\) −324.711 562.416i −0.568670 0.984966i −0.996698 0.0812002i \(-0.974125\pi\)
0.428027 0.903766i \(-0.359209\pi\)
\(572\) 25.4620 44.1015i 0.0445140 0.0771005i
\(573\) −410.228 −0.715931
\(574\) −168.611 + 80.0336i −0.293747 + 0.139431i
\(575\) 0 0
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) 514.893 + 891.822i 0.892363 + 1.54562i 0.837035 + 0.547150i \(0.184287\pi\)
0.0553284 + 0.998468i \(0.482379\pi\)
\(578\) −158.937 + 91.7622i −0.274977 + 0.158758i
\(579\) −199.338 115.088i −0.344280 0.198770i
\(580\) 0 0
\(581\) 268.927 + 185.575i 0.462868 + 0.319406i
\(582\) 112.051i 0.192528i
\(583\) 147.475 + 85.1445i 0.252958 + 0.146046i
\(584\) 149.211 86.1469i 0.255498 0.147512i
\(585\) 0 0
\(586\) 459.646 + 265.376i 0.784378 + 0.452861i
\(587\) −791.817 −1.34892 −0.674461 0.738311i \(-0.735624\pi\)
−0.674461 + 0.738311i \(0.735624\pi\)
\(588\) 167.550 + 27.1850i 0.284949 + 0.0462329i
\(589\) −19.4783 −0.0330701
\(590\) 0 0
\(591\) −158.669 + 91.6075i −0.268475 + 0.155004i
\(592\) −119.153 + 68.7931i −0.201272 + 0.116205i
\(593\) −42.2509 + 73.1807i −0.0712494 + 0.123408i −0.899449 0.437025i \(-0.856032\pi\)
0.828200 + 0.560433i \(0.189365\pi\)
\(594\) 24.2100i 0.0407575i
\(595\) 0 0
\(596\) 102.227 0.171522
\(597\) 302.314 + 174.541i 0.506389 + 0.292364i
\(598\) −36.9228 63.9522i −0.0617438 0.106943i
\(599\) −233.463 404.369i −0.389754 0.675074i 0.602662 0.797997i \(-0.294107\pi\)
−0.992416 + 0.122922i \(0.960773\pi\)
\(600\) 0 0
\(601\) 1095.93i 1.82351i −0.410733 0.911756i \(-0.634727\pi\)
0.410733 0.911756i \(-0.365273\pi\)
\(602\) 692.377 328.647i 1.15013 0.545925i
\(603\) 59.7394i 0.0990702i
\(604\) −165.218 + 286.166i −0.273540 + 0.473785i
\(605\) 0 0
\(606\) 112.089 + 194.144i 0.184965 + 0.320369i
\(607\) 179.449 310.815i 0.295633 0.512051i −0.679499 0.733676i \(-0.737803\pi\)
0.975132 + 0.221625i \(0.0711361\pi\)
\(608\) −10.0791 −0.0165774
\(609\) −38.2733 + 474.866i −0.0628461 + 0.779747i
\(610\) 0 0
\(611\) 49.7975 86.2517i 0.0815016 0.141165i
\(612\) −37.8558 65.5681i −0.0618558 0.107137i
\(613\) 400.154 231.029i 0.652780 0.376883i −0.136741 0.990607i \(-0.543663\pi\)
0.789520 + 0.613724i \(0.210329\pi\)
\(614\) 132.008 + 76.2148i 0.214996 + 0.124128i
\(615\) 0 0
\(616\) −65.0181 5.24033i −0.105549 0.00850703i
\(617\) 219.440i 0.355656i 0.984062 + 0.177828i \(0.0569071\pi\)
−0.984062 + 0.177828i \(0.943093\pi\)
\(618\) 107.144 + 61.8597i 0.173372 + 0.100097i
\(619\) −832.792 + 480.813i −1.34538 + 0.776757i −0.987592 0.157044i \(-0.949803\pi\)
−0.357791 + 0.933802i \(0.616470\pi\)
\(620\) 0 0
\(621\) 30.4037 + 17.5536i 0.0489593 + 0.0282667i
\(622\) 816.123 1.31209
\(623\) 164.534 + 346.633i 0.264100 + 0.556393i
\(624\) 53.5446 0.0858087
\(625\) 0 0
\(626\) −486.560 + 280.915i −0.777252 + 0.448747i
\(627\) 8.80509 5.08362i 0.0140432 0.00810785i
\(628\) −190.812 + 330.496i −0.303840 + 0.526267i
\(629\) 434.036i 0.690041i
\(630\) 0 0
\(631\) 584.721 0.926658 0.463329 0.886186i \(-0.346655\pi\)
0.463329 + 0.886186i \(0.346655\pi\)
\(632\) 87.1472 + 50.3144i 0.137891 + 0.0796115i
\(633\) −25.6382 44.4067i −0.0405027 0.0701528i
\(634\) 56.8303 + 98.4329i 0.0896376 + 0.155257i
\(635\) 0 0
\(636\) 179.052i 0.281529i
\(637\) 134.379 + 354.053i 0.210957 + 0.555813i
\(638\) 183.076i 0.286953i
\(639\) −131.148 + 227.155i −0.205239 + 0.355485i
\(640\) 0 0
\(641\) −269.518 466.819i −0.420465 0.728268i 0.575520 0.817788i \(-0.304800\pi\)
−0.995985 + 0.0895205i \(0.971467\pi\)
\(642\) −115.064 + 199.297i −0.179228 + 0.310431i
\(643\) −150.959 −0.234773 −0.117386 0.993086i \(-0.537452\pi\)
−0.117386 + 0.993086i \(0.537452\pi\)
\(644\) −53.7228 + 77.8525i −0.0834205 + 0.120889i
\(645\) 0 0
\(646\) −15.8979 + 27.5360i −0.0246098 + 0.0426255i
\(647\) 225.808 + 391.111i 0.349008 + 0.604499i 0.986073 0.166310i \(-0.0531854\pi\)
−0.637066 + 0.770809i \(0.719852\pi\)
\(648\) −22.0454 + 12.7279i −0.0340207 + 0.0196419i
\(649\) 322.199 + 186.022i 0.496454 + 0.286628i
\(650\) 0 0
\(651\) −56.8366 119.741i −0.0873067 0.183933i
\(652\) 496.404i 0.761356i
\(653\) 373.860 + 215.848i 0.572526 + 0.330548i 0.758158 0.652071i \(-0.226100\pi\)
−0.185631 + 0.982619i \(0.559433\pi\)
\(654\) −255.853 + 147.717i −0.391213 + 0.225867i
\(655\) 0 0
\(656\) 65.3108 + 37.7072i 0.0995592 + 0.0574805i
\(657\) −182.745 −0.278151
\(658\) −127.160 10.2488i −0.193252 0.0155757i
\(659\) 195.185 0.296184 0.148092 0.988974i \(-0.452687\pi\)
0.148092 + 0.988974i \(0.452687\pi\)
\(660\) 0 0
\(661\) 596.305 344.277i 0.902126 0.520843i 0.0242368 0.999706i \(-0.492284\pi\)
0.877889 + 0.478863i \(0.158951\pi\)
\(662\) 602.626 347.926i 0.910311 0.525569i
\(663\) 84.4572 146.284i 0.127386 0.220640i
\(664\) 132.023i 0.198830i
\(665\) 0 0
\(666\) 145.932 0.219118
\(667\) −229.913 132.740i −0.344697 0.199011i
\(668\) 29.2974 + 50.7445i 0.0438583 + 0.0759649i
\(669\) −284.517 492.799i −0.425288 0.736620i
\(670\) 0 0
\(671\) 86.4259i 0.128802i
\(672\) −29.4102 61.9600i −0.0437652 0.0922024i
\(673\) 200.020i 0.297206i −0.988897 0.148603i \(-0.952522\pi\)
0.988897 0.148603i \(-0.0474777\pi\)
\(674\) −445.564 + 771.740i −0.661075 + 1.14501i
\(675\) 0 0
\(676\) −109.270 189.262i −0.161642 0.279973i
\(677\) −424.807 + 735.787i −0.627484 + 1.08683i 0.360571 + 0.932732i \(0.382582\pi\)
−0.988055 + 0.154103i \(0.950751\pi\)
\(678\) 26.2873 0.0387719
\(679\) 263.554 + 181.868i 0.388150 + 0.267846i
\(680\) 0 0
\(681\) 315.628 546.684i 0.463477 0.802766i
\(682\) 25.4676 + 44.1111i 0.0373425 + 0.0646791i
\(683\) 387.988 224.005i 0.568064 0.327972i −0.188311 0.982109i \(-0.560301\pi\)
0.756376 + 0.654137i \(0.226968\pi\)
\(684\) 9.25821 + 5.34523i 0.0135354 + 0.00781467i
\(685\) 0 0
\(686\) 335.888 349.968i 0.489632 0.510157i
\(687\) 521.433i 0.759000i
\(688\) −268.190 154.839i −0.389811 0.225057i
\(689\) −345.952 + 199.735i −0.502107 + 0.289891i
\(690\) 0 0
\(691\) −337.930 195.104i −0.489044 0.282350i 0.235134 0.971963i \(-0.424447\pi\)
−0.724178 + 0.689613i \(0.757781\pi\)
\(692\) −46.1839 −0.0667397
\(693\) 56.9439 + 39.2946i 0.0821701 + 0.0567022i
\(694\) 608.313 0.876532
\(695\) 0 0
\(696\) 166.707 96.2485i 0.239522 0.138288i
\(697\) 206.033 118.953i 0.295599 0.170664i
\(698\) −67.3038 + 116.574i −0.0964237 + 0.167011i
\(699\) 488.482i 0.698830i
\(700\) 0 0
\(701\) 989.018 1.41087 0.705434 0.708776i \(-0.250752\pi\)
0.705434 + 0.708776i \(0.250752\pi\)
\(702\) −49.1839 28.3963i −0.0700625 0.0404506i
\(703\) −30.6429 53.0751i −0.0435888 0.0754980i
\(704\) 13.1782 + 22.8254i 0.0187191 + 0.0324224i
\(705\) 0 0
\(706\) 371.849i 0.526699i
\(707\) 638.571 + 51.4676i 0.903212 + 0.0727971i
\(708\) 391.189i 0.552527i
\(709\) 554.927 961.161i 0.782689 1.35566i −0.147680 0.989035i \(-0.547181\pi\)
0.930370 0.366623i \(-0.119486\pi\)
\(710\) 0 0
\(711\) −53.3665 92.4335i −0.0750584 0.130005i
\(712\) 77.5192 134.267i 0.108875 0.188578i
\(713\) 73.8617 0.103593
\(714\) −215.664 17.3821i −0.302051 0.0243447i
\(715\) 0 0
\(716\) 209.435 362.752i 0.292507 0.506637i
\(717\) 71.9101 + 124.552i 0.100293 + 0.173713i
\(718\) −365.918 + 211.263i −0.509636 + 0.294238i
\(719\) −936.393 540.627i −1.30235 0.751915i −0.321547 0.946894i \(-0.604203\pi\)
−0.980807 + 0.194979i \(0.937536\pi\)
\(720\) 0 0
\(721\) 319.402 151.609i 0.442999 0.210276i
\(722\) 506.042i 0.700889i
\(723\) 497.737 + 287.369i 0.688433 + 0.397467i
\(724\) −422.043 + 243.667i −0.582932 + 0.336556i
\(725\) 0 0
\(726\) 233.655 + 134.901i 0.321838 + 0.185813i
\(727\) −491.493 −0.676056 −0.338028 0.941136i \(-0.609760\pi\)
−0.338028 + 0.941136i \(0.609760\pi\)
\(728\) 86.9070 125.941i 0.119378 0.172996i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −846.044 + 488.464i −1.15738 + 0.668213i
\(732\) −78.6988 + 45.4367i −0.107512 + 0.0620721i
\(733\) −23.3826 + 40.4999i −0.0318999 + 0.0552522i −0.881535 0.472119i \(-0.843489\pi\)
0.849635 + 0.527372i \(0.176822\pi\)
\(734\) 186.784i 0.254474i
\(735\) 0 0
\(736\) 38.2199 0.0519292
\(737\) −56.8156 32.8025i −0.0770903 0.0445081i
\(738\) −39.9946 69.2726i −0.0541932 0.0938653i
\(739\) −368.856 638.878i −0.499129 0.864517i 0.500870 0.865522i \(-0.333013\pi\)
−0.999999 + 0.00100544i \(0.999680\pi\)
\(740\) 0 0
\(741\) 23.8507i 0.0321872i
\(742\) 421.146 + 290.615i 0.567582 + 0.391665i
\(743\) 258.593i 0.348039i 0.984742 + 0.174020i \(0.0556757\pi\)
−0.984742 + 0.174020i \(0.944324\pi\)
\(744\) −26.7782 + 46.3812i −0.0359922 + 0.0623403i
\(745\) 0 0
\(746\) −7.55747 13.0899i −0.0101307 0.0175468i
\(747\) −70.0159 + 121.271i −0.0937295 + 0.162344i
\(748\) 83.1454 0.111157
\(749\) 282.005 + 594.114i 0.376509 + 0.793210i
\(750\) 0 0
\(751\) −175.310 + 303.645i −0.233435 + 0.404321i −0.958817 0.284025i \(-0.908330\pi\)
0.725382 + 0.688347i \(0.241663\pi\)
\(752\) 25.7734 + 44.6409i 0.0342731 + 0.0593628i
\(753\) 628.613 362.930i 0.834811 0.481978i
\(754\) 371.928 + 214.733i 0.493274 + 0.284792i
\(755\) 0 0
\(756\) −5.84424 + 72.5110i −0.00773048 + 0.0959140i
\(757\) 907.187i 1.19840i 0.800600 + 0.599199i \(0.204514\pi\)
−0.800600 + 0.599199i \(0.795486\pi\)
\(758\) 175.038 + 101.058i 0.230921 + 0.133322i
\(759\) −33.3890 + 19.2771i −0.0439907 + 0.0253981i
\(760\) 0 0
\(761\) 1067.66 + 616.416i 1.40297 + 0.810007i 0.994697 0.102851i \(-0.0327965\pi\)
0.408277 + 0.912858i \(0.366130\pi\)
\(762\) 287.280 0.377008
\(763\) −67.8267 + 841.543i −0.0888948 + 1.10294i
\(764\) 473.691 0.620014
\(765\) 0 0
\(766\) 755.684 436.294i 0.986532 0.569575i
\(767\) −755.826 + 436.376i −0.985432 + 0.568939i
\(768\) −13.8564 + 24.0000i −0.0180422 + 0.0312500i
\(769\) 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
\(772\) 230.176 + 132.892i 0.298155 + 0.172140i
\(773\) −193.077 334.420i −0.249776 0.432625i 0.713687 0.700465i \(-0.247024\pi\)
−0.963464 + 0.267839i \(0.913690\pi\)
\(774\) 164.232 + 284.458i 0.212186 + 0.367517i
\(775\) 0 0
\(776\) 129.386i 0.166734i
\(777\) 236.859 343.245i 0.304838 0.441756i
\(778\) 981.376i 1.26141i
\(779\) −16.7962 + 29.0918i −0.0215612 + 0.0373451i
\(780\) 0 0
\(781\) −144.025 249.458i −0.184411 0.319409i