Properties

Label 1470.2.i.i.961.1
Level $1470$
Weight $2$
Character 1470.961
Analytic conductor $11.738$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(1\)
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 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1470.961
Dual form 1470.2.i.i.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} -7.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.50000 - 6.06218i) q^{26} -1.00000 q^{27} -8.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(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} +(0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(-1.50000 + 2.59808i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(2.00000 - 3.46410i) q^{51} +(3.50000 + 6.06218i) q^{52} +(0.500000 + 0.866025i) q^{53} +(0.500000 - 0.866025i) q^{54} +1.00000 q^{55} +1.00000 q^{57} +(4.00000 - 6.92820i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-2.00000 + 3.46410i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(-3.50000 + 6.06218i) q^{65} +(-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} +(0.500000 - 0.866025i) q^{75} -1.00000 q^{76} +7.00000 q^{78} +(-2.00000 + 3.46410i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} -12.0000 q^{83} -4.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-1.00000 + 1.73205i) q^{89} -1.00000 q^{90} +1.00000 q^{92} +(-3.00000 + 5.19615i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(0.500000 - 0.866025i) q^{96} +16.0000 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} + q^{5} - 2q^{6} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} + q^{5} - 2q^{6} + 2q^{8} - q^{9} + q^{10} + q^{11} + q^{12} - 14q^{13} + 2q^{15} - q^{16} - 4q^{17} - q^{18} + q^{19} - 2q^{20} - 2q^{22} - q^{23} + q^{24} - q^{25} + 7q^{26} - 2q^{27} - 16q^{29} - q^{30} + 6q^{31} - q^{32} - q^{33} + 8q^{34} + 2q^{36} + 3q^{37} + q^{38} - 7q^{39} + q^{40} - 18q^{41} - 8q^{43} + q^{44} + q^{45} - q^{46} - 3q^{47} - 2q^{48} + 2q^{50} + 4q^{51} + 7q^{52} + q^{53} + q^{54} + 2q^{55} + 2q^{57} + 8q^{58} + 12q^{59} - q^{60} - 4q^{61} - 12q^{62} + 2q^{64} - 7q^{65} - q^{66} - 12q^{67} - 4q^{68} - 2q^{69} - 28q^{71} - q^{72} - 14q^{73} + 3q^{74} + q^{75} - 2q^{76} + 14q^{78} - 4q^{79} + q^{80} - q^{81} + 9q^{82} - 24q^{83} - 8q^{85} + 4q^{86} - 8q^{87} + q^{88} - 2q^{89} - 2q^{90} + 2q^{92} - 6q^{93} - 3q^{94} - q^{95} + q^{96} + 32q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 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 \(0.922790\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) −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 −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 3.50000 6.06218i 0.686406 1.18889i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 3.00000 + 5.19615i 0.538816 + 0.933257i 0.998968 + 0.0454165i \(0.0144615\pi\)
−0.460152 + 0.887840i \(0.652205\pi\)
\(32\) −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 −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) −3.50000 6.06218i −0.560449 0.970725i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) −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
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) 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 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) 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 \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) −0.500000 0.866025i −0.0645497 0.111803i
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.50000 + 6.06218i −0.434122 + 0.751921i
\(66\) −0.500000 0.866025i −0.0615457 0.106600i
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) −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
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 7.00000 0.792594
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −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 \(0.728845\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 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 −0.914146 0.405385i \(-0.867138\pi\)
0.808146 + 0.588982i \(0.200471\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 1.00000 0.104257
\(93\) −3.00000 + 5.19615i −0.311086 + 0.538816i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) −0.500000 0.866025i −0.0512989 0.0888523i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 16.0000 1.62455 0.812277 0.583272i \(-0.198228\pi\)
0.812277 + 0.583272i \(0.198228\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 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 \(-0.497411\pi\)
0.861931 0.507026i \(-0.169255\pi\)
\(108\) 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 \(0.674364\pi\)
\(110\) −0.500000 + 0.866025i −0.0476731 + 0.0825723i
\(111\) 3.00000 0.284747
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −0.500000 + 0.866025i −0.0468293 + 0.0811107i
\(115\) 0.500000 + 0.866025i 0.0466252 + 0.0807573i
\(116\) 4.00000 + 6.92820i 0.371391 + 0.643268i
\(117\) 3.50000 6.06218i 0.323575 0.560449i
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 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
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) −3.50000 6.06218i −0.306970 0.531688i
\(131\) −6.50000 + 11.2583i −0.567908 + 0.983645i 0.428865 + 0.903369i \(0.358914\pi\)
−0.996773 + 0.0802763i \(0.974420\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) −2.00000 3.46410i −0.171499 0.297044i
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) 0.500000 0.866025i 0.0425628 0.0737210i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 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
\(145\) −4.00000 + 6.92820i −0.332182 + 0.575356i
\(146\) 14.0000 1.15865
\(147\) 0 0
\(148\) −3.00000 −0.246598
\(149\) 2.00000 3.46410i 0.163846 0.283790i −0.772399 0.635138i \(-0.780943\pi\)
0.936245 + 0.351348i \(0.114277\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 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
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) −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
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −4.00000 + 6.92820i −0.313304 + 0.542659i −0.979076 0.203497i \(-0.934769\pi\)
0.665771 + 0.746156i \(0.268103\pi\)
\(164\) 4.50000 + 7.79423i 0.351391 + 0.608627i
\(165\) 0.500000 + 0.866025i 0.0389249 + 0.0674200i
\(166\) 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 0
\(169\) 36.0000 2.76923
\(170\) 2.00000 3.46410i 0.153393 0.265684i
\(171\) 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 \(0.994817\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 12.0000 0.891953 0.445976 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 0 0
\(183\) −4.00000 −0.295689
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) −1.50000 2.59808i −0.110282 0.191014i
\(186\) −3.00000 5.19615i −0.219971 0.381000i
\(187\) 2.00000 3.46410i 0.146254 0.253320i
\(188\) 3.00000 0.218797
\(189\) 0 0
\(190\) 1.00000 0.0725476
\(191\) 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 \(-0.781381\pi\)
−0.162488 0.986710i \(-0.551952\pi\)
\(194\) −8.00000 + 13.8564i −0.574367 + 0.994832i
\(195\) −7.00000 −0.501280
\(196\) 0 0
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 0.500000 0.866025i 0.0355335 0.0615457i
\(199\) −6.00000 10.3923i −0.425329 0.736691i 0.571122 0.820865i \(-0.306508\pi\)
−0.996451 + 0.0841740i \(0.973175\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 6.00000 10.3923i 0.423207 0.733017i
\(202\) 0 0
\(203\) 0 0
\(204\) −4.00000 −0.280056
\(205\) −4.50000 + 7.79423i −0.314294 + 0.544373i
\(206\) 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
\(215\) −2.00000 + 3.46410i −0.136399 + 0.236250i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) −10.0000 −0.677285
\(219\) 7.00000 12.1244i 0.473016 0.819288i
\(220\) −0.500000 0.866025i −0.0337100 0.0583874i
\(221\) 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 0
\(225\) 1.00000 0.0666667
\(226\) 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 \(0.425707\pi\)
−0.958187 + 0.286143i \(0.907627\pi\)
\(230\) −1.00000 −0.0659380
\(231\) 0 0
\(232\) −8.00000 −0.525226
\(233\) −13.0000 + 22.5167i −0.851658 + 1.47512i 0.0280525 + 0.999606i \(0.491069\pi\)
−0.879711 + 0.475509i \(0.842264\pi\)
\(234\) 3.50000 + 6.06218i 0.228802 + 0.396297i
\(235\) 1.50000 + 2.59808i 0.0978492 + 0.169480i
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) −4.00000 −0.259828
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) −0.500000 + 0.866025i −0.0322749 + 0.0559017i
\(241\) 3.50000 + 6.06218i 0.225455 + 0.390499i 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 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
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) −1.00000 −0.0628695
\(254\) −2.50000 + 4.33013i −0.156864 + 0.271696i
\(255\) −2.00000 3.46410i −0.125245 0.216930i
\(256\) −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
\(259\) 0 0
\(260\) 7.00000 0.434122
\(261\) 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 0.999970 0.00771799i \(-0.00245674\pi\)
−0.506669 + 0.862141i \(0.669123\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) 1.00000 0.0614295
\(266\) 0 0
\(267\) −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 \(0.833333\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 0.500000 0.866025i 0.0301511 0.0522233i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) −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
\(285\) 0.500000 0.866025i 0.0296174 0.0512989i
\(286\) 7.00000 0.413919
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) −4.00000 6.92820i −0.234888 0.406838i
\(291\) 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 \(0.584677\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) 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
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) −2.00000 −0.115087
\(303\) 0 0
\(304\) 0.500000 + 0.866025i 0.0286770 + 0.0496700i
\(305\) 2.00000 + 3.46410i 0.114520 + 0.198354i
\(306\) −2.00000 + 3.46410i −0.114332 + 0.198030i
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) −3.00000 + 5.19615i −0.170389 + 0.295122i
\(311\) 8.00000 + 13.8564i 0.453638 + 0.785725i 0.998609 0.0527306i \(-0.0167924\pi\)
−0.544970 + 0.838455i \(0.683459\pi\)
\(312\) −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 −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(318\) −0.500000 0.866025i −0.0280386 0.0485643i
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 18.0000 1.00466
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 3.50000 + 6.06218i 0.194145 + 0.336269i
\(326\) −4.00000 6.92820i −0.221540 0.383718i
\(327\) −5.00000 + 8.66025i −0.276501 + 0.478913i
\(328\) −9.00000 −0.496942
\(329\) 0 0
\(330\) −1.00000 −0.0550482
\(331\) 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
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 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
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) −1.00000 −0.0540738
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) −0.500000 + 0.866025i −0.0269191 + 0.0466252i
\(346\) −10.5000 18.1865i −0.564483 0.977714i
\(347\) 17.0000 + 29.4449i 0.912608 + 1.58068i 0.810366 + 0.585923i \(0.199268\pi\)
0.102241 + 0.994760i \(0.467399\pi\)
\(348\) −4.00000 + 6.92820i −0.214423 + 0.371391i
\(349\) 28.0000 1.49881 0.749403 0.662114i \(-0.230341\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(350\) 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
\(355\) −7.00000 + 12.1244i −0.371521 + 0.643494i
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) 13.0000 0.687071
\(359\) −18.0000 + 31.1769i −0.950004 + 1.64545i −0.204595 + 0.978847i \(0.565588\pi\)
−0.745409 + 0.666608i \(0.767746\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −6.00000 + 10.3923i −0.315353 + 0.546207i
\(363\) 10.0000 0.524864
\(364\) 0 0
\(365\) −14.0000 −0.732793
\(366\) 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
\(370\) 3.00000 0.155963
\(371\) 0 0
\(372\) 6.00000 0.311086
\(373\) −13.0000 + 22.5167i −0.673114 + 1.16587i 0.303902 + 0.952703i \(0.401711\pi\)
−0.977016 + 0.213165i \(0.931623\pi\)
\(374\) 2.00000 + 3.46410i 0.103418 + 0.179124i
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) −1.50000 + 2.59808i −0.0773566 + 0.133986i
\(377\) 56.0000 2.88415
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) −0.500000 + 0.866025i −0.0256495 + 0.0444262i
\(381\) 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 \(0.717843\pi\)
\(390\) 3.50000 6.06218i 0.177229 0.306970i
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) −13.0000 −0.655763
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) 2.00000 + 3.46410i 0.100631 + 0.174298i
\(396\) 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
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 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
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 3.00000 0.148704
\(408\) 2.00000 3.46410i 0.0990148 0.171499i
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) −4.50000 7.79423i −0.222239 0.384930i
\(411\) −1.00000 + 1.73205i −0.0493264 + 0.0854358i
\(412\) −16.0000 −0.788263
\(413\) 0 0
\(414\) 1.00000 0.0491473
\(415\) −6.00000 + 10.3923i −0.294528 + 0.510138i
\(416\) 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 \(-0.586592\pi\)
−0.268693 + 0.963226i \(0.586592\pi\)
\(420\) 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
\(425\) −2.00000 + 3.46410i −0.0970143 + 0.168034i
\(426\) 14.0000 0.678302
\(427\) 0 0
\(428\) −18.0000 −0.870063
\(429\) 3.50000 6.06218i 0.168982 0.292685i
\(430\) −2.00000 3.46410i −0.0964486 0.167054i
\(431\) 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 \(0.910969\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) 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 −0.609503 0.792784i \(-0.708631\pi\)
0.991322 + 0.131453i \(0.0419644\pi\)
\(440\) 1.00000 0.0476731
\(441\) 0 0
\(442\) −28.0000 −1.33182
\(443\) 18.0000 31.1769i 0.855206 1.48126i −0.0212481 0.999774i \(-0.506764\pi\)
0.876454 0.481486i \(-0.159903\pi\)
\(444\) −1.50000 2.59808i −0.0711868 0.123299i
\(445\) 1.00000 + 1.73205i 0.0474045 + 0.0821071i
\(446\) −2.00000 + 3.46410i −0.0947027 + 0.164030i
\(447\) 4.00000 0.189194
\(448\) 0 0
\(449\) −25.0000 −1.17982 −0.589911 0.807468i \(-0.700837\pi\)
−0.589911 + 0.807468i \(0.700837\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) −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 −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) −11.0000 19.0526i −0.513996 0.890268i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) 0.500000 0.866025i 0.0233126 0.0403786i
\(461\) 28.0000 1.30409 0.652045 0.758180i \(-0.273911\pi\)
0.652045 + 0.758180i \(0.273911\pi\)
\(462\) 0 0
\(463\) 33.0000 1.53364 0.766820 0.641862i \(-0.221838\pi\)
0.766820 + 0.641862i \(0.221838\pi\)
\(464\) 4.00000 6.92820i 0.185695 0.321634i
\(465\) 3.00000 + 5.19615i 0.139122 + 0.240966i
\(466\) −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
\(469\) 0 0
\(470\) −3.00000 −0.138380
\(471\) −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
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) −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 \(0.0357796\pi\)
−0.399704 + 0.916644i \(0.630887\pi\)
\(480\) −0.500000 0.866025i −0.0228218 0.0395285i
\(481\) −10.5000 + 18.1865i −0.478759 + 0.829235i
\(482\) −7.00000 −0.318841
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) 8.00000 13.8564i 0.363261 0.629187i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 4.00000 + 6.92820i 0.181257 + 0.313947i 0.942309 0.334744i \(-0.108650\pi\)
−0.761052 + 0.648691i \(0.775317\pi\)
\(488\) −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
\(495\) −0.500000 + 0.866025i −0.0224733 + 0.0389249i
\(496\) −6.00000 −0.269408
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −12.0000 + 20.7846i −0.537194 + 0.930447i 0.461860 + 0.886953i \(0.347182\pi\)
−0.999054 + 0.0434940i \(0.986151\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 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 \(0.714587\pi\)
\(504\) 0 0
\(505\) 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 \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) 4.00000 0.177123
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −0.500000 + 0.866025i −0.0220755 + 0.0382360i
\(514\) −4.00000 6.92820i −0.176432 0.305590i
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) −2.00000 + 3.46410i −0.0880451 + 0.152499i
\(517\) −3.00000 −0.131940
\(518\) 0 0
\(519\) −21.0000 −0.921798
\(520\) −3.50000 + 6.06218i −0.153485 + 0.265844i
\(521\) −10.5000 18.1865i −0.460013 0.796766i 0.538948 0.842339i \(-0.318822\pi\)
−0.998961 + 0.0455727i \(0.985489\pi\)
\(522\) 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
\(530\) −0.500000 + 0.866025i −0.0217186 + 0.0376177i
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 63.0000 2.72883
\(534\) 1.00000 1.73205i 0.0432742 0.0749532i
\(535\) −9.00000 15.5885i −0.389104 0.673948i
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 6.50000 11.2583i 0.280496 0.485833i
\(538\) 0 0
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) −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
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) 1.00000 1.73205i 0.0427179 0.0739895i
\(549\) −2.00000 3.46410i −0.0853579 0.147844i
\(550\) 0.500000 + 0.866025i 0.0213201 + 0.0369274i
\(551\) −4.00000 + 6.92820i −0.170406 + 0.295151i
\(552\) −1.00000 −0.0425628
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 1.50000 2.59808i 0.0636715 0.110282i
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) −22.5000 38.9711i −0.953356 1.65126i −0.738087 0.674705i \(-0.764271\pi\)
−0.215268 0.976555i \(-0.569063\pi\)
\(558\) 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
\(565\) −3.00000 + 5.19615i −0.126211 + 0.218604i
\(566\) 2.00000 0.0840663
\(567\) 0 0
\(568\) −14.0000 −0.587427
\(569\) 18.5000 32.0429i 0.775560 1.34331i −0.158919 0.987292i \(-0.550801\pi\)
0.934479 0.356018i \(-0.115866\pi\)
\(570\) 0.500000 + 0.866025i 0.0209427 + 0.0362738i
\(571\) 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
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) −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
\(580\) 8.00000 0.332182
\(581\) 0 0
\(582\) −16.0000 −0.663221
\(583\) −0.500000 + 0.866025i −0.0207079 + 0.0358671i
\(584\) −7.00000 12.1244i −0.289662 0.501709i
\(585\) −3.50000 6.06218i −0.144707 0.250640i
\(586\) 4.50000 7.79423i 0.185893 0.321977i
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) −6.00000 + 10.3923i −0.247016 + 0.427844i
\(591\) −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 \(0.872449\pi\)
\(600\) 0.500000 0.866025i 0.0204124 0.0353553i
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 1.00000 1.73205i 0.0406894 0.0704761i
\(605\) −5.00000 8.66025i −0.203279 0.352089i
\(606\) 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
\(609\) 0 0
\(610\) −4.00000 −0.161955
\(611\) 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 0.976797 0.214169i \(-0.0687045\pi\)
−0.673874 + 0.738846i \(0.735371\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) −9.00000 −0.362915
\(616\) 0 0
\(617\) 8.00000 0.322068 0.161034 0.986949i \(-0.448517\pi\)
0.161034 + 0.986949i \(0.448517\pi\)
\(618\) −8.00000 + 13.8564i −0.321807 + 0.557386i
\(619\) −3.50000 6.06218i −0.140677 0.243659i 0.787075 0.616858i \(-0.211595\pi\)
−0.927752 + 0.373198i \(0.878261\pi\)
\(620\) −3.00000 5.19615i −0.120483 0.208683i
\(621\) 0.500000 0.866025i 0.0200643 0.0347524i
\(622\) −16.0000 −0.641542
\(623\) 0 0
\(624\) 7.00000 0.280224
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −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
\(635\) 2.50000 4.33013i 0.0992095 0.171836i
\(636\) 1.00000 0.0396526
\(637\) 0 0
\(638\) 8.00000 0.316723
\(639\) 7.00000 12.1244i 0.276916 0.479632i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 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 \(0.671344\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 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
\(650\) −7.00000 −0.274563
\(651\) 0 0
\(652\) 8.00000 0.313304
\(653\) −14.5000 + 25.1147i −0.567429 + 0.982816i 0.429390 + 0.903119i \(0.358728\pi\)
−0.996819 + 0.0796966i \(0.974605\pi\)
\(654\) −5.00000 8.66025i −0.195515 0.338643i
\(655\) 6.50000 + 11.2583i 0.253976 + 0.439899i
\(656\) 4.50000 7.79423i 0.175695 0.304314i
\(657\) 14.0000 0.546192
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0.500000 0.866025i 0.0194625 0.0337100i
\(661\) 4.00000 + 6.92820i 0.155582 + 0.269476i 0.933271 0.359174i \(-0.116941\pi\)
−0.777689 + 0.628649i \(0.783608\pi\)
\(662\) 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
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) −12.0000 −0.462566 −0.231283 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(674\) 0 0
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −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
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) 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 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 0.500000 0.866025i 0.0191180 0.0331133i
\(685\) 2.00000 0.0764161
\(686\) 0 0
\(687\) −22.0000 −0.839352
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −3.50000 6.06218i −0.133339 0.230951i
\(690\) −0.500000 0.866025i −0.0190347 0.0329690i
\(691\) 6.00000 10.3923i 0.228251 0.395342i −0.729039 0.684472i \(-0.760033\pi\)
0.957290 + 0.289130i \(0.0933661\pi\)
\(692\) 21.0000 0.798300
\(693\) 0 0
\(694\) −34.0000 −1.29062
\(695\) 2.00000 3.46410i 0.0758643 0.131401i
\(696\) −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
\(705\) −1.50000 + 2.59808i −0.0564933 + 0.0978492i
\(706\) 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 \(0.190598\pi\)
\(710\) −7.00000 12.1244i −0.262705 0.455019i
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) −1.00000 + 1.73205i −0.0374766 + 0.0649113i
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) −7.00000 −0.261785
\(716\) −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 −0.515030 0.857172i \(-0.672219\pi\)
0.999848 + 0.0174426i \(0.00555244\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) −18.0000 −0.669891
\(723\) −3.50000 + 6.06218i −0.130166 + 0.225455i
\(724\) −6.00000 10.3923i −0.222988 0.386227i
\(725\) 4.00000 + 6.92820i 0.148556 + 0.257307i
\(726\) −5.00000 + 8.66025i −0.185567 + 0.321412i
\(727\) −17.0000 −0.630495 −0.315248 0.949009i \(-0.602088\pi\)
−0.315248 + 0.949009i \(0.602088\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 7.00000 12.1244i 0.259082 0.448743i
\(731\) 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 \(-0.438596\pi\)
\(740\) −1.50000 + 2.59808i −0.0551411 + 0.0955072i
\(741\) −7.00000 −0.257151
\(742\) 0 0
\(743\) −9.00000 −0.330178 −0.165089 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(744\) −3.00000 + 5.19615i −0.109985 + 0.190500i
\(745\) −2.00000 3.46410i −0.0732743 0.126915i
\(746\) −13.0000 22.5167i −0.475964 0.824394i
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) 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
\(755\) 2.00000 0.0727875
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −0.500000 + 0.866025i −0.0181608 + 0.0314555i
\(759\) −0.500000 0.866025i −0.0181489 0.0314347i
\(760\) −0.500000 0.866025i −0.0181369 0.0314140i
\(761\) −8.50000 + 14.7224i −0.308125 + 0.533688i −0.977952 0.208829i \(-0.933035\pi\)
0.669827 + 0.742517i \(0.266368\pi\)
\(762\) −5.00000 −0.181131
\(763\) 0 0
\(764\) −10.0000 −0.361787
\(765\) 2.00000 3.46410i 0.0723102 0.125245i
\(766\) 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 \(-0.324856\pi\)
0.522883 + 0.852404i \(0.324856\pi\)
\(770\) 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
\(775\) 3.00000 5.19615i 0.107763 0.186651i
\(776\) 16.0000 0.574367
\(777\) 0 0
\(778\) −14.0000 −0.501924
\(779\) −4.50000 + 7.79423i −0.161229 + 0.279257i
\(780\) 3.50000 + 6.06218i 0.125320 + 0.217061i
\(781\) −7.00000 12.1244i −0.250480 0.433844i
\(782\) −2.00000 + 3.46410i −0.0715199 + 0.123876i
\(783\) 8.00000 0.285897
\(784\) 0 0
\(785\) 15.0000 0.535373
\(786\) 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
\(790\) −4.00000 −0.142314
\(791\) 0 0
\(792\) −1.00000 −0.0355335
\(793\) 14.0000 24.2487i 0.497155 0.861097i
\(794\) 9.00000 + 15.5885i 0.319398 + 0.553214i
\(795\) 0.500000 + 0.866025i 0.0177332 + 0.0307148i
\(796\) −6.00000 + 10.3923i −0.212664 + 0.368345i
\(797\) 6.00000 0.212531