Properties

Label 1050.2.i.s.751.1
Level 1050
Weight 2
Character 1050.751
Analytic conductor 8.384
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 751.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1050.751
Dual form 1050.2.i.s.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -7.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(0.500000 - 2.59808i) q^{21} +1.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.50000 + 6.06218i) q^{26} -1.00000 q^{27} +(-0.500000 + 2.59808i) q^{28} -8.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -4.00000 q^{34} +1.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-3.50000 - 6.06218i) q^{39} +9.00000 q^{41} +(-2.00000 - 1.73205i) q^{42} +4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-1.50000 + 2.59808i) q^{47} -1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +(2.00000 - 3.46410i) q^{51} +(3.50000 + 6.06218i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.00000 + 1.73205i) q^{56} -1.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{61} -6.00000 q^{62} +(2.50000 - 0.866025i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(6.00000 + 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{68} +1.00000 q^{69} -14.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(1.50000 + 2.59808i) q^{74} +1.00000 q^{76} +(0.500000 - 2.59808i) q^{77} -7.00000 q^{78} +(-2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} -12.0000 q^{83} +(-2.50000 + 0.866025i) q^{84} +(2.00000 - 3.46410i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(1.00000 - 1.73205i) q^{89} +(14.0000 + 12.1244i) q^{91} -1.00000 q^{92} +(3.00000 - 5.19615i) q^{93} +(1.50000 + 2.59808i) q^{94} +(-0.500000 + 0.866025i) q^{96} +16.0000 q^{97} +(6.50000 + 2.59808i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} + 2q^{6} - 4q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} + 2q^{6} - 4q^{7} - 2q^{8} - q^{9} + q^{11} + q^{12} - 14q^{13} - 5q^{14} - q^{16} - 4q^{17} + q^{18} - q^{19} + q^{21} + 2q^{22} + q^{23} - q^{24} - 7q^{26} - 2q^{27} - q^{28} - 16q^{29} - 6q^{31} + q^{32} - q^{33} - 8q^{34} + 2q^{36} - 3q^{37} + q^{38} - 7q^{39} + 18q^{41} - 4q^{42} + 8q^{43} + q^{44} - q^{46} - 3q^{47} - 2q^{48} + 2q^{49} + 4q^{51} + 7q^{52} - q^{53} - q^{54} + 4q^{56} - 2q^{57} - 8q^{58} - 12q^{59} + 4q^{61} - 12q^{62} + 5q^{63} + 2q^{64} + q^{66} + 12q^{67} - 4q^{68} + 2q^{69} - 28q^{71} + q^{72} - 14q^{73} + 3q^{74} + 2q^{76} + q^{77} - 14q^{78} - 4q^{79} - q^{81} + 9q^{82} - 24q^{83} - 5q^{84} + 4q^{86} - 8q^{87} - q^{88} + 2q^{89} + 28q^{91} - 2q^{92} + 6q^{93} + 3q^{94} - q^{96} + 32q^{97} + 13q^{98} - 2q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −7.00000 −1.94145 −0.970725 0.240192i \(-0.922790\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −2.50000 + 0.866025i −0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 0.500000 2.59808i 0.109109 0.566947i
\(22\) 1.00000 0.213201
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) −3.50000 + 6.06218i −0.686406 + 1.18889i
\(27\) −1.00000 −0.192450
\(28\) −0.500000 + 2.59808i −0.0944911 + 0.490990i
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) −3.00000 5.19615i −0.538816 0.933257i −0.998968 0.0454165i \(-0.985539\pi\)
0.460152 0.887840i \(-0.347795\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) −4.00000 −0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) −3.50000 6.06218i −0.560449 0.970725i
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) −2.00000 1.73205i −0.308607 0.267261i
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) −1.50000 + 2.59808i −0.218797 + 0.378968i −0.954441 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 2.00000 3.46410i 0.280056 0.485071i
\(52\) 3.50000 + 6.06218i 0.485363 + 0.840673i
\(53\) −0.500000 0.866025i −0.0686803 0.118958i 0.829640 0.558298i \(-0.188546\pi\)
−0.898321 + 0.439340i \(0.855212\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) −1.00000 −0.132453
\(58\) −4.00000 + 6.92820i −0.525226 + 0.909718i
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) −6.00000 −0.762001
\(63\) 2.50000 0.866025i 0.314970 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.500000 + 0.866025i 0.0615457 + 0.106600i
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −14.0000 −1.66149 −0.830747 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −7.00000 12.1244i −0.819288 1.41905i −0.906208 0.422833i \(-0.861036\pi\)
0.0869195 0.996215i \(-0.472298\pi\)
\(74\) 1.50000 + 2.59808i 0.174371 + 0.302020i
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 0.500000 2.59808i 0.0569803 0.296078i
\(78\) −7.00000 −0.792594
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −2.50000 + 0.866025i −0.272772 + 0.0944911i
\(85\) 0 0
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 1.00000 1.73205i 0.106000 0.183597i −0.808146 0.588982i \(-0.799529\pi\)
0.914146 + 0.405385i \(0.132862\pi\)
\(90\) 0 0
\(91\) 14.0000 + 12.1244i 1.46760 + 1.27098i
\(92\) −1.00000 −0.104257
\(93\) 3.00000 5.19615i 0.311086 0.538816i
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) 0 0
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 16.0000 1.62455 0.812277 0.583272i \(-0.198228\pi\)
0.812277 + 0.583272i \(0.198228\pi\)
\(98\) 6.50000 + 2.59808i 0.656599 + 0.262445i
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) −2.00000 3.46410i −0.198030 0.342997i
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) 7.00000 0.686406
\(105\) 0 0
\(106\) −1.00000 −0.0971286
\(107\) −9.00000 + 15.5885i −0.870063 + 1.50699i −0.00813215 + 0.999967i \(0.502589\pi\)
−0.861931 + 0.507026i \(0.830745\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) 2.50000 0.866025i 0.236228 0.0818317i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) −0.500000 + 0.866025i −0.0468293 + 0.0811107i
\(115\) 0 0
\(116\) 4.00000 + 6.92820i 0.371391 + 0.643268i
\(117\) 3.50000 6.06218i 0.323575 0.560449i
\(118\) −12.0000 −1.10469
\(119\) −2.00000 + 10.3923i −0.183340 + 0.952661i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) −2.00000 3.46410i −0.181071 0.313625i
\(123\) 4.50000 + 7.79423i 0.405751 + 0.702782i
\(124\) −3.00000 + 5.19615i −0.269408 + 0.466628i
\(125\) 0 0
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) −5.00000 −0.443678 −0.221839 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) 0 0
\(131\) 6.50000 11.2583i 0.567908 0.983645i −0.428865 0.903369i \(-0.641086\pi\)
0.996773 0.0802763i \(-0.0255803\pi\)
\(132\) 1.00000 0.0870388
\(133\) 2.50000 0.866025i 0.216777 0.0750939i
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) −1.00000 1.73205i −0.0854358 0.147979i 0.820141 0.572161i \(-0.193895\pi\)
−0.905577 + 0.424182i \(0.860562\pi\)
\(138\) 0.500000 0.866025i 0.0425628 0.0737210i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) −7.00000 + 12.1244i −0.587427 + 1.01745i
\(143\) −3.50000 6.06218i −0.292685 0.506945i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) −14.0000 −1.15865
\(147\) −5.50000 + 4.33013i −0.453632 + 0.357143i
\(148\) 3.00000 0.246598
\(149\) 2.00000 3.46410i 0.163846 0.283790i −0.772399 0.635138i \(-0.780943\pi\)
0.936245 + 0.351348i \(0.114277\pi\)
\(150\) 0 0
\(151\) 1.00000 + 1.73205i 0.0813788 + 0.140952i 0.903842 0.427865i \(-0.140734\pi\)
−0.822464 + 0.568818i \(0.807401\pi\)
\(152\) 0.500000 0.866025i 0.0405554 0.0702439i
\(153\) 4.00000 0.323381
\(154\) −2.00000 1.73205i −0.161165 0.139573i
\(155\) 0 0
\(156\) −3.50000 + 6.06218i −0.280224 + 0.485363i
\(157\) 7.50000 + 12.9904i 0.598565 + 1.03675i 0.993033 + 0.117836i \(0.0375956\pi\)
−0.394468 + 0.918910i \(0.629071\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) 0.500000 0.866025i 0.0396526 0.0686803i
\(160\) 0 0
\(161\) −2.50000 + 0.866025i −0.197028 + 0.0682524i
\(162\) −1.00000 −0.0785674
\(163\) 4.00000 6.92820i 0.313304 0.542659i −0.665771 0.746156i \(-0.731897\pi\)
0.979076 + 0.203497i \(0.0652307\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) 5.00000 0.386912 0.193456 0.981109i \(-0.438030\pi\)
0.193456 + 0.981109i \(0.438030\pi\)
\(168\) −0.500000 + 2.59808i −0.0385758 + 0.200446i
\(169\) 36.0000 2.76923
\(170\) 0 0
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i \(0.460934\pi\)
−0.920722 + 0.390218i \(0.872399\pi\)
\(174\) −8.00000 −0.606478
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 6.00000 10.3923i 0.450988 0.781133i
\(178\) −1.00000 1.73205i −0.0749532 0.129823i
\(179\) −6.50000 11.2583i −0.485833 0.841487i 0.514035 0.857769i \(-0.328150\pi\)
−0.999867 + 0.0162823i \(0.994817\pi\)
\(180\) 0 0
\(181\) −12.0000 −0.891953 −0.445976 0.895045i \(-0.647144\pi\)
−0.445976 + 0.895045i \(0.647144\pi\)
\(182\) 17.5000 6.06218i 1.29719 0.449359i
\(183\) 4.00000 0.295689
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 0 0
\(186\) −3.00000 5.19615i −0.219971 0.381000i
\(187\) 2.00000 3.46410i 0.146254 0.253320i
\(188\) 3.00000 0.218797
\(189\) 2.00000 + 1.73205i 0.145479 + 0.125988i
\(190\) 0 0
\(191\) 5.00000 8.66025i 0.361787 0.626634i −0.626468 0.779447i \(-0.715500\pi\)
0.988255 + 0.152813i \(0.0488333\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 13.0000 + 22.5167i 0.935760 + 1.62078i 0.773272 + 0.634074i \(0.218619\pi\)
0.162488 + 0.986710i \(0.448048\pi\)
\(194\) 8.00000 13.8564i 0.574367 0.994832i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) −0.500000 + 0.866025i −0.0355335 + 0.0615457i
\(199\) 6.00000 + 10.3923i 0.425329 + 0.736691i 0.996451 0.0841740i \(-0.0268252\pi\)
−0.571122 + 0.820865i \(0.693492\pi\)
\(200\) 0 0
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) 0 0
\(203\) 16.0000 + 13.8564i 1.12298 + 0.972529i
\(204\) −4.00000 −0.280056
\(205\) 0 0
\(206\) −8.00000 13.8564i −0.557386 0.965422i
\(207\) 0.500000 + 0.866025i 0.0347524 + 0.0601929i
\(208\) 3.50000 6.06218i 0.242681 0.420336i
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) −15.0000 −1.03264 −0.516321 0.856395i \(-0.672699\pi\)
−0.516321 + 0.856395i \(0.672699\pi\)
\(212\) −0.500000 + 0.866025i −0.0343401 + 0.0594789i
\(213\) −7.00000 12.1244i −0.479632 0.830747i
\(214\) 9.00000 + 15.5885i 0.615227 + 1.06561i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −3.00000 + 15.5885i −0.203653 + 1.05821i
\(218\) 10.0000 0.677285
\(219\) 7.00000 12.1244i 0.473016 0.819288i
\(220\) 0 0
\(221\) 14.0000 + 24.2487i 0.941742 + 1.63114i
\(222\) −1.50000 + 2.59808i −0.100673 + 0.174371i
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 0.500000 2.59808i 0.0334077 0.173591i
\(225\) 0 0
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) −10.0000 17.3205i −0.663723 1.14960i −0.979630 0.200812i \(-0.935642\pi\)
0.315906 0.948790i \(-0.397691\pi\)
\(228\) 0.500000 + 0.866025i 0.0331133 + 0.0573539i
\(229\) 11.0000 19.0526i 0.726900 1.25903i −0.231287 0.972886i \(-0.574293\pi\)
0.958187 0.286143i \(-0.0923732\pi\)
\(230\) 0 0
\(231\) 2.50000 0.866025i 0.164488 0.0569803i
\(232\) 8.00000 0.525226
\(233\) 13.0000 22.5167i 0.851658 1.47512i −0.0280525 0.999606i \(-0.508931\pi\)
0.879711 0.475509i \(-0.157736\pi\)
\(234\) −3.50000 6.06218i −0.228802 0.396297i
\(235\) 0 0
\(236\) −6.00000 + 10.3923i −0.390567 + 0.676481i
\(237\) −4.00000 −0.259828
\(238\) 8.00000 + 6.92820i 0.518563 + 0.449089i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i \(-0.239053\pi\)
−0.956456 + 0.291877i \(0.905720\pi\)
\(242\) −5.00000 8.66025i −0.321412 0.556702i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −4.00000 −0.256074
\(245\) 0 0
\(246\) 9.00000 0.573819
\(247\) 3.50000 6.06218i 0.222700 0.385727i
\(248\) 3.00000 + 5.19615i 0.190500 + 0.329956i
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) −2.00000 1.73205i −0.125988 0.109109i
\(253\) 1.00000 0.0628695
\(254\) −2.50000 + 4.33013i −0.156864 + 0.271696i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.00000 + 6.92820i −0.249513 + 0.432169i −0.963391 0.268101i \(-0.913604\pi\)
0.713878 + 0.700270i \(0.246937\pi\)
\(258\) 4.00000 0.249029
\(259\) 7.50000 2.59808i 0.466027 0.161437i
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) −6.50000 11.2583i −0.401571 0.695542i
\(263\) −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i \(-0.330877\pi\)
−0.999970 + 0.00771799i \(0.997543\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) 0 0
\(266\) 0.500000 2.59808i 0.0306570 0.159298i
\(267\) 2.00000 0.122398
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 4.00000 0.242536
\(273\) −3.50000 + 18.1865i −0.211830 + 1.10070i
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) −0.500000 0.866025i −0.0300965 0.0521286i
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) −1.50000 + 2.59808i −0.0893237 + 0.154713i
\(283\) −1.00000 1.73205i −0.0594438 0.102960i 0.834772 0.550596i \(-0.185599\pi\)
−0.894216 + 0.447636i \(0.852266\pi\)
\(284\) 7.00000 + 12.1244i 0.415374 + 0.719448i
\(285\) 0 0
\(286\) −7.00000 −0.413919
\(287\) −18.0000 15.5885i −1.06251 0.920158i
\(288\) −1.00000 −0.0589256
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 8.00000 + 13.8564i 0.468968 + 0.812277i
\(292\) −7.00000 + 12.1244i −0.409644 + 0.709524i
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 1.00000 + 6.92820i 0.0583212 + 0.404061i
\(295\) 0 0
\(296\) 1.50000 2.59808i 0.0871857 0.151010i
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) −2.00000 3.46410i −0.115857 0.200670i
\(299\) −3.50000 + 6.06218i −0.202410 + 0.350585i
\(300\) 0 0
\(301\) −8.00000 6.92820i −0.461112 0.399335i
\(302\) 2.00000 0.115087
\(303\) 0 0
\(304\) −0.500000 0.866025i −0.0286770 0.0496700i
\(305\) 0 0
\(306\) 2.00000 3.46410i 0.114332 0.198030i
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) −2.50000 + 0.866025i −0.142451 + 0.0493464i
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) −8.00000 13.8564i −0.453638 0.785725i 0.544970 0.838455i \(-0.316541\pi\)
−0.998609 + 0.0527306i \(0.983208\pi\)
\(312\) 3.50000 + 6.06218i 0.198148 + 0.343203i
\(313\) −12.0000 + 20.7846i −0.678280 + 1.17482i 0.297218 + 0.954810i \(0.403941\pi\)
−0.975499 + 0.220006i \(0.929392\pi\)
\(314\) 15.0000 0.846499
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 5.00000 8.66025i 0.280828 0.486408i −0.690761 0.723083i \(-0.742724\pi\)
0.971589 + 0.236675i \(0.0760576\pi\)
\(318\) −0.500000 0.866025i −0.0280386 0.0485643i
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) −0.500000 + 2.59808i −0.0278639 + 0.144785i
\(323\) 4.00000 0.222566
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −4.00000 6.92820i −0.221540 0.383718i
\(327\) −5.00000 + 8.66025i −0.276501 + 0.478913i
\(328\) −9.00000 −0.496942
\(329\) 7.50000 2.59808i 0.413488 0.143237i
\(330\) 0 0
\(331\) 4.50000 7.79423i 0.247342 0.428410i −0.715445 0.698669i \(-0.753776\pi\)
0.962788 + 0.270259i \(0.0871094\pi\)
\(332\) 6.00000 + 10.3923i 0.329293 + 0.570352i
\(333\) −1.50000 2.59808i −0.0821995 0.142374i
\(334\) 2.50000 4.33013i 0.136794 0.236934i
\(335\) 0 0
\(336\) 2.00000 + 1.73205i 0.109109 + 0.0944911i
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 18.0000 31.1769i 0.979071 1.69580i
\(339\) 3.00000 + 5.19615i 0.162938 + 0.282216i
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) −1.00000 −0.0540738
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 10.5000 + 18.1865i 0.564483 + 0.977714i
\(347\) −17.0000 29.4449i −0.912608 1.58068i −0.810366 0.585923i \(-0.800732\pi\)
−0.102241 0.994760i \(-0.532601\pi\)
\(348\) −4.00000 + 6.92820i −0.214423 + 0.371391i
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 0 0
\(351\) 7.00000 0.373632
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −4.00000 6.92820i −0.212899 0.368751i 0.739722 0.672913i \(-0.234957\pi\)
−0.952620 + 0.304162i \(0.901624\pi\)
\(354\) −6.00000 10.3923i −0.318896 0.552345i
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) −10.0000 + 3.46410i −0.529256 + 0.183340i
\(358\) −13.0000 −0.687071
\(359\) −18.0000 + 31.1769i −0.950004 + 1.64545i −0.204595 + 0.978847i \(0.565588\pi\)
−0.745409 + 0.666608i \(0.767746\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −6.00000 + 10.3923i −0.315353 + 0.546207i
\(363\) 10.0000 0.524864
\(364\) 3.50000 18.1865i 0.183450 0.953233i
\(365\) 0 0
\(366\) 2.00000 3.46410i 0.104542 0.181071i
\(367\) 9.50000 + 16.4545i 0.495896 + 0.858917i 0.999989 0.00473247i \(-0.00150640\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(368\) 0.500000 + 0.866025i 0.0260643 + 0.0451447i
\(369\) −4.50000 + 7.79423i −0.234261 + 0.405751i
\(370\) 0 0
\(371\) −0.500000 + 2.59808i −0.0259587 + 0.134885i
\(372\) −6.00000 −0.311086
\(373\) 13.0000 22.5167i 0.673114 1.16587i −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) −2.00000 3.46410i −0.103418 0.179124i
\(375\) 0 0
\(376\) 1.50000 2.59808i 0.0773566 0.133986i
\(377\) 56.0000 2.88415
\(378\) 2.50000 0.866025i 0.128586 0.0445435i
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 0 0
\(381\) −2.50000 4.33013i −0.128079 0.221839i
\(382\) −5.00000 8.66025i −0.255822 0.443097i
\(383\) 6.50000 11.2583i 0.332134 0.575274i −0.650796 0.759253i \(-0.725565\pi\)
0.982930 + 0.183979i \(0.0588979\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 26.0000 1.32337
\(387\) −2.00000 + 3.46410i −0.101666 + 0.176090i
\(388\) −8.00000 13.8564i −0.406138 0.703452i
\(389\) 7.00000 + 12.1244i 0.354914 + 0.614729i 0.987103 0.160085i \(-0.0511768\pi\)
−0.632189 + 0.774814i \(0.717843\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) −1.00000 6.92820i −0.0505076 0.349927i
\(393\) 13.0000 0.655763
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) 0 0
\(396\) 0.500000 + 0.866025i 0.0251259 + 0.0435194i
\(397\) 9.00000 15.5885i 0.451697 0.782362i −0.546795 0.837267i \(-0.684152\pi\)
0.998492 + 0.0549046i \(0.0174855\pi\)
\(398\) 12.0000 0.601506
\(399\) 2.00000 + 1.73205i 0.100125 + 0.0867110i
\(400\) 0 0
\(401\) 8.50000 14.7224i 0.424470 0.735203i −0.571901 0.820323i \(-0.693794\pi\)
0.996371 + 0.0851195i \(0.0271272\pi\)
\(402\) 6.00000 + 10.3923i 0.299253 + 0.518321i
\(403\) 21.0000 + 36.3731i 1.04608 + 1.81187i
\(404\) 0 0
\(405\) 0 0
\(406\) 20.0000 6.92820i 0.992583 0.343841i
\(407\) −3.00000 −0.148704
\(408\) −2.00000 + 3.46410i −0.0990148 + 0.171499i
\(409\) −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) 0 0
\(411\) 1.00000 1.73205i 0.0493264 0.0854358i
\(412\) −16.0000 −0.788263
\(413\) −6.00000 + 31.1769i −0.295241 + 1.53412i
\(414\) 1.00000 0.0491473
\(415\) 0 0
\(416\) −3.50000 6.06218i −0.171602 0.297223i
\(417\) −2.00000 3.46410i −0.0979404 0.169638i
\(418\) −0.500000 + 0.866025i −0.0244558 + 0.0423587i
\(419\) 11.0000 0.537385 0.268693 0.963226i \(-0.413408\pi\)
0.268693 + 0.963226i \(0.413408\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) −7.50000 + 12.9904i −0.365094 + 0.632362i
\(423\) −1.50000 2.59808i −0.0729325 0.126323i
\(424\) 0.500000 + 0.866025i 0.0242821 + 0.0420579i
\(425\) 0 0
\(426\) −14.0000 −0.678302
\(427\) −10.0000 + 3.46410i −0.483934 + 0.167640i
\(428\) 18.0000 0.870063
\(429\) 3.50000 6.06218i 0.168982 0.292685i
\(430\) 0 0
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −40.0000 −1.92228 −0.961139 0.276066i \(-0.910969\pi\)
−0.961139 + 0.276066i \(0.910969\pi\)
\(434\) 12.0000 + 10.3923i 0.576018 + 0.498847i
\(435\) 0 0
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) 0.500000 + 0.866025i 0.0239182 + 0.0414276i
\(438\) −7.00000 12.1244i −0.334473 0.579324i
\(439\) −8.00000 + 13.8564i −0.381819 + 0.661330i −0.991322 0.131453i \(-0.958036\pi\)
0.609503 + 0.792784i \(0.291369\pi\)
\(440\) 0 0
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 28.0000 1.33182
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) 1.50000 + 2.59808i 0.0711868 + 0.123299i
\(445\) 0 0
\(446\) 2.00000 3.46410i 0.0947027 0.164030i
\(447\) 4.00000 0.189194
\(448\) −2.00000 1.73205i −0.0944911 0.0818317i
\(449\) −25.0000 −1.17982 −0.589911 0.807468i \(-0.700837\pi\)
−0.589911 + 0.807468i \(0.700837\pi\)
\(450\) 0 0
\(451\) 4.50000 + 7.79423i 0.211897 + 0.367016i
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) −1.00000 + 1.73205i −0.0469841 + 0.0813788i
\(454\) −20.0000 −0.938647
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −11.0000 19.0526i −0.513996 0.890268i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) 0 0
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) 0.500000 2.59808i 0.0232621 0.120873i
\(463\) −33.0000 −1.53364 −0.766820 0.641862i \(-0.778162\pi\)
−0.766820 + 0.641862i \(0.778162\pi\)
\(464\) 4.00000 6.92820i 0.185695 0.321634i
\(465\) 0 0
\(466\) −13.0000 22.5167i −0.602213 1.04306i
\(467\) 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) −7.00000 −0.323575
\(469\) 6.00000 31.1769i 0.277054 1.43962i
\(470\) 0 0
\(471\) −7.50000 + 12.9904i −0.345582 + 0.598565i
\(472\) 6.00000 + 10.3923i 0.276172 + 0.478345i
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) −2.00000 + 3.46410i −0.0918630 + 0.159111i
\(475\) 0 0
\(476\) 10.0000 3.46410i 0.458349 0.158777i
\(477\) 1.00000 0.0457869
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) −13.0000 22.5167i −0.593985 1.02881i −0.993689 0.112168i \(-0.964220\pi\)
0.399704 0.916644i \(-0.369113\pi\)
\(480\) 0 0
\(481\) 10.5000 18.1865i 0.478759 0.829235i
\(482\) −7.00000 −0.318841
\(483\) −2.00000 1.73205i −0.0910032 0.0788110i
\(484\) −10.0000 −0.454545
\(485\) 0 0
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −4.00000 6.92820i −0.181257 0.313947i 0.761052 0.648691i \(-0.224683\pi\)
−0.942309 + 0.334744i \(0.891350\pi\)
\(488\) −2.00000 + 3.46410i −0.0905357 + 0.156813i
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 4.50000 7.79423i 0.202876 0.351391i
\(493\) 16.0000 + 27.7128i 0.720604 + 1.24812i
\(494\) −3.50000 6.06218i −0.157472 0.272750i
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) 28.0000 + 24.2487i 1.25597 + 1.08770i
\(498\) −12.0000 −0.537733
\(499\) −12.0000 + 20.7846i −0.537194 + 0.930447i 0.461860 + 0.886953i \(0.347182\pi\)
−0.999054 + 0.0434940i \(0.986151\pi\)
\(500\) 0 0
\(501\) 2.50000 + 4.33013i 0.111692 + 0.193456i
\(502\) −1.50000 + 2.59808i −0.0669483 + 0.115958i
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) −2.50000 + 0.866025i −0.111359 + 0.0385758i
\(505\) 0 0
\(506\) 0.500000 0.866025i 0.0222277 0.0384995i
\(507\) 18.0000 + 31.1769i 0.799408 + 1.38462i
\(508\) 2.50000 + 4.33013i 0.110920 + 0.192118i
\(509\) −15.0000 + 25.9808i −0.664863 + 1.15158i 0.314459 + 0.949271i \(0.398177\pi\)
−0.979322 + 0.202306i \(0.935156\pi\)
\(510\) 0 0
\(511\) −7.00000 + 36.3731i −0.309662 + 1.60905i
\(512\) −1.00000 −0.0441942
\(513\) 0.500000 0.866025i 0.0220755 0.0382360i
\(514\) 4.00000 + 6.92820i 0.176432 + 0.305590i
\(515\) 0 0
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) −3.00000 −0.131940
\(518\) 1.50000 7.79423i 0.0659062 0.342459i
\(519\) −21.0000 −0.921798
\(520\) 0 0
\(521\) 10.5000 + 18.1865i 0.460013 + 0.796766i 0.998961 0.0455727i \(-0.0145113\pi\)
−0.538948 + 0.842339i \(0.681178\pi\)
\(522\) −4.00000 6.92820i −0.175075 0.303239i
\(523\) −7.00000 + 12.1244i −0.306089 + 0.530161i −0.977503 0.210921i \(-0.932354\pi\)
0.671414 + 0.741082i \(0.265687\pi\)
\(524\) −13.0000 −0.567908
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) −12.0000 + 20.7846i −0.522728 + 0.905392i
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) −2.00000 1.73205i −0.0867110 0.0750939i
\(533\) −63.0000 −2.72883
\(534\) 1.00000 1.73205i 0.0432742 0.0749532i
\(535\) 0 0
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 6.50000 11.2583i 0.280496 0.485833i
\(538\) 0 0
\(539\) −5.50000 + 4.33013i −0.236902 + 0.186512i
\(540\) 0 0
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) −6.00000 10.3923i −0.257485 0.445976i
\(544\) 2.00000 3.46410i 0.0857493 0.148522i
\(545\) 0 0
\(546\) 14.0000 + 12.1244i 0.599145 + 0.518875i
\(547\) −36.0000 −1.53925 −0.769624 0.638497i \(-0.779557\pi\)
−0.769624 + 0.638497i \(0.779557\pi\)
\(548\) −1.00000 + 1.73205i −0.0427179 + 0.0739895i
\(549\) 2.00000 + 3.46410i 0.0853579 + 0.147844i
\(550\) 0 0
\(551\) 4.00000 6.92820i 0.170406 0.295151i
\(552\) −1.00000 −0.0425628
\(553\) 10.0000 3.46410i 0.425243 0.147309i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) 22.5000 + 38.9711i 0.953356 + 1.65126i 0.738087 + 0.674705i \(0.235729\pi\)
0.215268 + 0.976555i \(0.430937\pi\)
\(558\) 3.00000 5.19615i 0.127000 0.219971i
\(559\) −28.0000 −1.18427
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 1.50000 2.59808i 0.0632737 0.109593i
\(563\) 7.00000 + 12.1244i 0.295015 + 0.510981i 0.974988 0.222256i \(-0.0713421\pi\)
−0.679974 + 0.733237i \(0.738009\pi\)
\(564\) 1.50000 + 2.59808i 0.0631614 + 0.109399i
\(565\) 0 0
\(566\) −2.00000 −0.0840663
\(567\) −0.500000 + 2.59808i −0.0209980 + 0.109109i
\(568\) 14.0000 0.587427
\(569\) 18.5000 32.0429i 0.775560 1.34331i −0.158919 0.987292i \(-0.550801\pi\)
0.934479 0.356018i \(-0.115866\pi\)
\(570\) 0 0
\(571\) 4.00000 + 6.92820i 0.167395 + 0.289936i 0.937503 0.347977i \(-0.113131\pi\)
−0.770108 + 0.637913i \(0.779798\pi\)
\(572\) −3.50000 + 6.06218i −0.146342 + 0.253472i
\(573\) 10.0000 0.417756
\(574\) −22.5000 + 7.79423i −0.939132 + 0.325325i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −7.00000 12.1244i −0.291414 0.504744i 0.682730 0.730670i \(-0.260792\pi\)
−0.974144 + 0.225927i \(0.927459\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) −13.0000 + 22.5167i −0.540262 + 0.935760i
\(580\) 0 0
\(581\) 24.0000 + 20.7846i 0.995688 + 0.862291i
\(582\) 16.0000 0.663221
\(583\) 0.500000 0.866025i 0.0207079 0.0358671i
\(584\) 7.00000 + 12.1244i 0.289662 + 0.501709i
\(585\) 0 0
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 6.50000 + 2.59808i 0.268055 + 0.107143i
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) 1.50000 + 2.59808i 0.0617018 + 0.106871i
\(592\) −1.50000 2.59808i −0.0616496 0.106780i
\(593\) 6.00000 10.3923i 0.246390 0.426761i −0.716131 0.697966i \(-0.754089\pi\)
0.962522 + 0.271205i \(0.0874221\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) −4.00000 −0.163846
\(597\) −6.00000 + 10.3923i −0.245564 + 0.425329i
\(598\) 3.50000 + 6.06218i 0.143126 + 0.247901i
\(599\) −3.00000 5.19615i −0.122577 0.212309i 0.798206 0.602384i \(-0.205782\pi\)
−0.920783 + 0.390075i \(0.872449\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) −10.0000 + 3.46410i −0.407570 + 0.141186i
\(603\) −12.0000 −0.488678
\(604\) 1.00000 1.73205i 0.0406894 0.0704761i
\(605\) 0 0
\(606\) 0 0
\(607\) 12.5000 21.6506i 0.507359 0.878772i −0.492604 0.870253i \(-0.663955\pi\)
0.999964 0.00851879i \(-0.00271165\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −4.00000 + 20.7846i −0.162088 + 0.842235i
\(610\) 0 0
\(611\) 10.5000 18.1865i 0.424785 0.735748i
\(612\) −2.00000 3.46410i −0.0808452 0.140028i
\(613\) −7.50000 12.9904i −0.302922 0.524677i 0.673874 0.738846i \(-0.264629\pi\)
−0.976797 + 0.214169i \(0.931296\pi\)
\(614\) −4.00000 + 6.92820i −0.161427 + 0.279600i
\(615\) 0 0
\(616\) −0.500000 + 2.59808i −0.0201456 + 0.104679i
\(617\) −8.00000 −0.322068 −0.161034 0.986949i \(-0.551483\pi\)
−0.161034 + 0.986949i \(0.551483\pi\)
\(618\) 8.00000 13.8564i 0.321807 0.557386i
\(619\) 3.50000 + 6.06218i 0.140677 + 0.243659i 0.927752 0.373198i \(-0.121739\pi\)
−0.787075 + 0.616858i \(0.788405\pi\)
\(620\) 0 0
\(621\) −0.500000 + 0.866025i −0.0200643 + 0.0347524i
\(622\) −16.0000 −0.641542
\(623\) −5.00000 + 1.73205i −0.200321 + 0.0693932i
\(624\) 7.00000 0.280224
\(625\) 0 0
\(626\) 12.0000 + 20.7846i 0.479616 + 0.830720i
\(627\) −0.500000 0.866025i −0.0199681 0.0345857i
\(628\) 7.50000 12.9904i 0.299283 0.518373i
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 14.0000 0.557331 0.278666 0.960388i \(-0.410108\pi\)
0.278666 + 0.960388i \(0.410108\pi\)
\(632\) 2.00000 3.46410i 0.0795557 0.137795i
\(633\) −7.50000 12.9904i −0.298098 0.516321i
\(634\) −5.00000 8.66025i −0.198575 0.343943i
\(635\) 0 0
\(636\) −1.00000 −0.0396526
\(637\) −7.00000 48.4974i −0.277350 1.92154i
\(638\) −8.00000 −0.316723
\(639\) 7.00000 12.1244i 0.276916 0.479632i
\(640\) 0 0
\(641\) 11.5000 + 19.9186i 0.454223 + 0.786737i 0.998643 0.0520757i \(-0.0165837\pi\)
−0.544420 + 0.838812i \(0.683250\pi\)
\(642\) −9.00000 + 15.5885i −0.355202 + 0.615227i
\(643\) −26.0000 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(644\) 2.00000 + 1.73205i 0.0788110 + 0.0682524i
\(645\) 0 0
\(646\) 2.00000 3.46410i 0.0786889 0.136293i
\(647\) −7.50000 12.9904i −0.294855 0.510705i 0.680096 0.733123i \(-0.261938\pi\)
−0.974951 + 0.222419i \(0.928605\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 6.00000 10.3923i 0.235521 0.407934i
\(650\) 0 0
\(651\) −15.0000 + 5.19615i −0.587896 + 0.203653i
\(652\) −8.00000 −0.313304
\(653\) 14.5000 25.1147i 0.567429 0.982816i −0.429390 0.903119i \(-0.641272\pi\)
0.996819 0.0796966i \(-0.0253951\pi\)
\(654\) 5.00000 + 8.66025i 0.195515 + 0.338643i
\(655\) 0 0
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) 14.0000 0.546192
\(658\) 1.50000 7.79423i 0.0584761 0.303851i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −4.00000 6.92820i −0.155582 0.269476i 0.777689 0.628649i \(-0.216392\pi\)
−0.933271 + 0.359174i \(0.883059\pi\)
\(662\) −4.50000 7.79423i −0.174897 0.302931i
\(663\) −14.0000 + 24.2487i −0.543715 + 0.941742i
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) −3.00000 −0.116248
\(667\) −4.00000 + 6.92820i −0.154881 + 0.268261i
\(668\) −2.50000 4.33013i −0.0967279 0.167538i
\(669\) 2.00000 + 3.46410i 0.0773245 + 0.133930i
\(670\) 0 0
\(671\) 4.00000 0.154418
\(672\) 2.50000 0.866025i 0.0964396 0.0334077i
\(673\) 12.0000 0.462566 0.231283 0.972887i \(-0.425708\pi\)
0.231283 + 0.972887i \(0.425708\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −18.0000 31.1769i −0.692308 1.19911i
\(677\) 0.500000 0.866025i 0.0192166 0.0332841i −0.856257 0.516550i \(-0.827216\pi\)
0.875474 + 0.483266i \(0.160549\pi\)
\(678\) 6.00000 0.230429
\(679\) −32.0000 27.7128i −1.22805 1.06352i
\(680\) 0 0
\(681\) 10.0000 17.3205i 0.383201 0.663723i
\(682\) −3.00000 5.19615i −0.114876 0.198971i
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) −0.500000 + 0.866025i −0.0191180 + 0.0331133i
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 22.0000 0.839352
\(688\) −2.00000 + 3.46410i −0.0762493 + 0.132068i
\(689\) 3.50000 + 6.06218i 0.133339 + 0.230951i
\(690\) 0 0
\(691\) −6.00000 + 10.3923i −0.228251 + 0.395342i −0.957290 0.289130i \(-0.906634\pi\)
0.729039 + 0.684472i \(0.239967\pi\)
\(692\) 21.0000 0.798300
\(693\) 2.00000 + 1.73205i 0.0759737 + 0.0657952i
\(694\) −34.0000 −1.29062
\(695\) 0 0
\(696\) 4.00000 + 6.92820i 0.151620 + 0.262613i
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) −14.0000 + 24.2487i −0.529908 + 0.917827i
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 3.50000 6.06218i 0.132099 0.228802i
\(703\) −1.50000 2.59808i −0.0565736 0.0979883i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −8.00000 −0.301084
\(707\) 0 0
\(708\) −12.0000 −0.450988
\(709\) −2.00000 + 3.46410i −0.0751116 + 0.130097i −0.901135 0.433539i \(-0.857265\pi\)
0.826023 + 0.563636i \(0.190598\pi\)
\(710\) 0 0
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) −1.00000 + 1.73205i −0.0374766 + 0.0649113i
\(713\) −6.00000 −0.224702
\(714\) −2.00000 + 10.3923i −0.0748481 + 0.388922i
\(715\) 0 0
\(716\) −6.50000 + 11.2583i −0.242916 + 0.420744i
\(717\) −3.00000 5.19615i −0.112037 0.194054i
\(718\) 18.0000 + 31.1769i 0.671754 + 1.16351i
\(719\) −13.0000 + 22.5167i −0.484818 + 0.839730i −0.999848 0.0174426i \(-0.994448\pi\)
0.515030 + 0.857172i \(0.327781\pi\)
\(720\) 0 0
\(721\) −40.0000 + 13.8564i −1.48968 + 0.516040i
\(722\) 18.0000 0.669891
\(723\) 3.50000 6.06218i 0.130166 0.225455i
\(724\) 6.00000 + 10.3923i 0.222988 + 0.386227i
\(725\) 0 0
\(726\) 5.00000 8.66025i 0.185567 0.321412i
\(727\) −17.0000 −0.630495 −0.315248 0.949009i \(-0.602088\pi\)
−0.315248 + 0.949009i \(0.602088\pi\)
\(728\) −14.0000 12.1244i −0.518875 0.449359i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −8.00000 13.8564i −0.295891 0.512498i
\(732\) −2.00000 3.46410i −0.0739221 0.128037i
\(733\) 18.5000 32.0429i 0.683313 1.18353i −0.290651 0.956829i \(-0.593872\pi\)
0.973964 0.226704i \(-0.0727949\pi\)
\(734\) 19.0000 0.701303
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −6.00000 + 10.3923i −0.221013 + 0.382805i
\(738\) 4.50000 + 7.79423i 0.165647 + 0.286910i
\(739\) −20.5000 35.5070i −0.754105 1.30615i −0.945818 0.324697i \(-0.894738\pi\)
0.191714 0.981451i \(-0.438596\pi\)
\(740\) 0 0
\(741\) 7.00000 0.257151
\(742\) 2.00000 + 1.73205i 0.0734223 + 0.0635856i
\(743\) 9.00000 0.330178 0.165089 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) −3.00000 + 5.19615i −0.109985 + 0.190500i
\(745\) 0 0
\(746\) −13.0000 22.5167i −0.475964 0.824394i
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) −4.00000 −0.146254
\(749\) 45.0000 15.5885i 1.64426 0.569590i
\(750\) 0 0
\(751\) 13.0000 22.5167i 0.474377 0.821645i −0.525193 0.850983i \(-0.676007\pi\)
0.999570 + 0.0293387i \(0.00934013\pi\)
\(752\) −1.50000 2.59808i −0.0546994 0.0947421i
\(753\) −1.50000 2.59808i −0.0546630 0.0946792i
\(754\) 28.0000 48.4974i 1.01970 1.76617i
\(755\) 0 0
\(756\) 0.500000 2.59808i 0.0181848 0.0944911i
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0.500000 0.866025i 0.0181608 0.0314555i
\(759\) 0.500000 + 0.866025i 0.0181489 + 0.0314347i
\(760\) 0 0
\(761\) 8.50000 14.7224i 0.308125 0.533688i −0.669827 0.742517i \(-0.733632\pi\)
0.977952 + 0.208829i \(0.0669652\pi\)
\(762\) −5.00000 −0.181131
\(763\) 5.00000 25.9808i 0.181012 0.940567i
\(764\) −10.0000 −0.361787
\(765\) 0 0
\(766\) −6.50000 11.2583i −0.234855 0.406780i
\(767\) 42.0000 + 72.7461i 1.51653 + 2.62671i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −29.0000 −1.04577 −0.522883 0.852404i \(-0.675144\pi\)
−0.522883 + 0.852404i \(0.675144\pi\)
\(770\) 0 0
\(771\) −8.00000 −0.288113
\(772\) 13.0000 22.5167i 0.467880 0.810392i
\(773\) 21.5000 + 37.2391i 0.773301 + 1.33940i 0.935744 + 0.352679i \(0.114729\pi\)
−0.162443 + 0.986718i \(0.551937\pi\)
\(774\) 2.00000 + 3.46410i 0.0718885 + 0.124515i
\(775\) 0 0
\(776\) −16.0000 −0.574367
\(777\) 6.00000 + 5.19615i 0.215249 + 0.186411i
\(778\) 14.0000 0.501924
\(779\) −4.50000 + 7.79423i −0.161229 + 0.279257i
\(780\) 0 0
\(781\) −7.00000 12.1244i −0.250480 0.433844i
\(782\) −2.00000 + 3.46410i −0.0715199 + 0.123876i
\(783\) 8.00000 0.285897
\(784\) −6.50000 2.59808i −0.232143 0.0927884i
\(785\) 0 0
\(786\) 6.50000 11.2583i 0.231847 0.401571i
\(787\) −11.0000 19.0526i −0.392108 0.679150i 0.600620 0.799535i \(-0.294921\pi\)
−0.992727 + 0.120384i \(0.961587\pi\)
\(788\) −1.50000 2.59808i −0.0534353 0.0925526i
\(789\) 8.00000 13.8564i 0.284808 0.493301i
\(790\) 0 0
\(791\) −12.0000 10.3923i −0.426671 0.369508i
\(792\) 1.00000 0.0355335
\(793\) −14.0000 + 24.2487i −0.497155 + 0.861097i
\(794\) −9.00000 15.5885i −0.319398 0.553214i
\(795\) 0 0
\(796\) 6.00000 10.3923i 0.212664 0.368345i
\(797\) 6.00000 0.212531 0.106265 0.994338i \(-0.466111\pi\)
0.106265 + 0.994338i \(0.466111\pi\)
\(798\) 2.50000 0.866025i 0.0884990 0.0306570