Properties

Label 882.2.l.a.227.6
Level $882$
Weight $2$
Character 882.227
Analytic conductor $7.043$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 227.6
Root \(1.40917 - 1.00709i\) of defining polynomial
Character \(\chi\) \(=\) 882.227
Dual form 882.2.l.a.509.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.167584 - 1.72392i) q^{3} -1.00000 q^{4} +(-1.17468 + 2.03460i) q^{5} +(1.72392 - 0.167584i) q^{6} -1.00000i q^{8} +(-2.94383 + 0.577806i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.167584 - 1.72392i) q^{3} -1.00000 q^{4} +(-1.17468 + 2.03460i) q^{5} +(1.72392 - 0.167584i) q^{6} -1.00000i q^{8} +(-2.94383 + 0.577806i) q^{9} +(-2.03460 - 1.17468i) q^{10} +(4.91614 - 2.83834i) q^{11} +(0.167584 + 1.72392i) q^{12} +(-1.48943 + 0.859925i) q^{13} +(3.70436 + 1.68409i) q^{15} +1.00000 q^{16} +(-0.884414 + 1.53185i) q^{17} +(-0.577806 - 2.94383i) q^{18} +(0.986680 - 0.569660i) q^{19} +(1.17468 - 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} +(3.18272 + 1.83755i) q^{23} +(-1.72392 + 0.167584i) q^{24} +(-0.259741 - 0.449885i) q^{25} +(-0.859925 - 1.48943i) q^{26} +(1.48943 + 4.97811i) q^{27} +(3.59886 + 2.07781i) q^{29} +(-1.68409 + 3.70436i) q^{30} +8.37019i q^{31} +1.00000i q^{32} +(-5.71694 - 7.99939i) q^{33} +(-1.53185 - 0.884414i) q^{34} +(2.94383 - 0.577806i) q^{36} +(4.59886 + 7.96547i) q^{37} +(0.569660 + 0.986680i) q^{38} +(1.73205 + 2.42356i) q^{39} +(2.03460 + 1.17468i) q^{40} +(-3.99709 - 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +(-4.91614 + 2.83834i) q^{44} +(2.28245 - 6.66826i) q^{45} +(-1.83755 + 3.18272i) q^{46} +11.8099 q^{47} +(-0.167584 - 1.72392i) q^{48} +(0.449885 - 0.259741i) q^{50} +(2.78901 + 1.26795i) q^{51} +(1.48943 - 0.859925i) q^{52} +(-4.97811 + 1.48943i) q^{54} +13.3365i q^{55} +(-1.14740 - 1.60550i) q^{57} +(-2.07781 + 3.59886i) q^{58} +2.22966 q^{59} +(-3.70436 - 1.68409i) q^{60} +8.99970i q^{61} -8.37019 q^{62} -1.00000 q^{64} -4.04054i q^{65} +(7.99939 - 5.71694i) q^{66} +10.8712 q^{67} +(0.884414 - 1.53185i) q^{68} +(2.63442 - 5.79472i) q^{69} +4.52106i q^{71} +(0.577806 + 2.94383i) q^{72} +(4.62660 + 2.67117i) q^{73} +(-7.96547 + 4.59886i) q^{74} +(-0.732039 + 0.523168i) q^{75} +(-0.986680 + 0.569660i) q^{76} +(-2.42356 + 1.73205i) q^{78} -13.0284 q^{79} +(-1.17468 + 2.03460i) q^{80} +(8.33228 - 3.40192i) q^{81} +(6.92317 - 3.99709i) q^{82} +(6.27298 - 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +(3.04933 + 1.76053i) q^{86} +(2.97887 - 6.55238i) q^{87} +(-2.83834 - 4.91614i) q^{88} +(-0.580529 - 1.00551i) q^{89} +(6.66826 + 2.28245i) q^{90} +(-3.18272 - 1.83755i) q^{92} +(14.4296 - 1.40271i) q^{93} +11.8099i q^{94} +2.67667i q^{95} +(1.72392 - 0.167584i) q^{96} +(3.97536 + 2.29517i) q^{97} +(-12.8323 + 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 12 q^{9} + O(q^{10}) \) \( 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.167584 1.72392i −0.0967549 0.995308i
\(4\) −1.00000 −0.500000
\(5\) −1.17468 + 2.03460i −0.525332 + 0.909902i 0.474232 + 0.880400i \(0.342726\pi\)
−0.999565 + 0.0295026i \(0.990608\pi\)
\(6\) 1.72392 0.167584i 0.703789 0.0684160i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −2.94383 + 0.577806i −0.981277 + 0.192602i
\(10\) −2.03460 1.17468i −0.643398 0.371466i
\(11\) 4.91614 2.83834i 1.48227 0.855790i 0.482475 0.875910i \(-0.339738\pi\)
0.999798 + 0.0201197i \(0.00640473\pi\)
\(12\) 0.167584 + 1.72392i 0.0483774 + 0.497654i
\(13\) −1.48943 + 0.859925i −0.413094 + 0.238500i −0.692118 0.721784i \(-0.743322\pi\)
0.279024 + 0.960284i \(0.409989\pi\)
\(14\) 0 0
\(15\) 3.70436 + 1.68409i 0.956462 + 0.434830i
\(16\) 1.00000 0.250000
\(17\) −0.884414 + 1.53185i −0.214502 + 0.371528i −0.953118 0.302598i \(-0.902146\pi\)
0.738616 + 0.674126i \(0.235480\pi\)
\(18\) −0.577806 2.94383i −0.136190 0.693868i
\(19\) 0.986680 0.569660i 0.226360 0.130689i −0.382532 0.923942i \(-0.624948\pi\)
0.608892 + 0.793253i \(0.291614\pi\)
\(20\) 1.17468 2.03460i 0.262666 0.454951i
\(21\) 0 0
\(22\) 2.83834 + 4.91614i 0.605135 + 1.04812i
\(23\) 3.18272 + 1.83755i 0.663644 + 0.383155i 0.793664 0.608356i \(-0.208171\pi\)
−0.130020 + 0.991511i \(0.541504\pi\)
\(24\) −1.72392 + 0.167584i −0.351895 + 0.0342080i
\(25\) −0.259741 0.449885i −0.0519482 0.0899769i
\(26\) −0.859925 1.48943i −0.168645 0.292102i
\(27\) 1.48943 + 4.97811i 0.286642 + 0.958038i
\(28\) 0 0
\(29\) 3.59886 + 2.07781i 0.668292 + 0.385839i 0.795429 0.606046i \(-0.207245\pi\)
−0.127137 + 0.991885i \(0.540579\pi\)
\(30\) −1.68409 + 3.70436i −0.307471 + 0.676321i
\(31\) 8.37019i 1.50333i 0.659545 + 0.751665i \(0.270749\pi\)
−0.659545 + 0.751665i \(0.729251\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −5.71694 7.99939i −0.995192 1.39252i
\(34\) −1.53185 0.884414i −0.262710 0.151676i
\(35\) 0 0
\(36\) 2.94383 0.577806i 0.490638 0.0963009i
\(37\) 4.59886 + 7.96547i 0.756049 + 1.30951i 0.944851 + 0.327500i \(0.106206\pi\)
−0.188803 + 0.982015i \(0.560461\pi\)
\(38\) 0.569660 + 0.986680i 0.0924111 + 0.160061i
\(39\) 1.73205 + 2.42356i 0.277350 + 0.388080i
\(40\) 2.03460 + 1.17468i 0.321699 + 0.185733i
\(41\) −3.99709 6.92317i −0.624241 1.08122i −0.988687 0.149993i \(-0.952075\pi\)
0.364446 0.931225i \(-0.381258\pi\)
\(42\) 0 0
\(43\) 1.76053 3.04933i 0.268478 0.465018i −0.699991 0.714152i \(-0.746813\pi\)
0.968469 + 0.249134i \(0.0801459\pi\)
\(44\) −4.91614 + 2.83834i −0.741136 + 0.427895i
\(45\) 2.28245 6.66826i 0.340248 0.994046i
\(46\) −1.83755 + 3.18272i −0.270931 + 0.469267i
\(47\) 11.8099 1.72265 0.861324 0.508055i \(-0.169635\pi\)
0.861324 + 0.508055i \(0.169635\pi\)
\(48\) −0.167584 1.72392i −0.0241887 0.248827i
\(49\) 0 0
\(50\) 0.449885 0.259741i 0.0636233 0.0367329i
\(51\) 2.78901 + 1.26795i 0.390539 + 0.177548i
\(52\) 1.48943 0.859925i 0.206547 0.119250i
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) −4.97811 + 1.48943i −0.677435 + 0.202686i
\(55\) 13.3365i 1.79830i
\(56\) 0 0
\(57\) −1.14740 1.60550i −0.151977 0.212653i
\(58\) −2.07781 + 3.59886i −0.272829 + 0.472554i
\(59\) 2.22966 0.290277 0.145139 0.989411i \(-0.453637\pi\)
0.145139 + 0.989411i \(0.453637\pi\)
\(60\) −3.70436 1.68409i −0.478231 0.217415i
\(61\) 8.99970i 1.15229i 0.817346 + 0.576146i \(0.195444\pi\)
−0.817346 + 0.576146i \(0.804556\pi\)
\(62\) −8.37019 −1.06301
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 4.04054i 0.501167i
\(66\) 7.99939 5.71694i 0.984657 0.703707i
\(67\) 10.8712 1.32813 0.664067 0.747673i \(-0.268829\pi\)
0.664067 + 0.747673i \(0.268829\pi\)
\(68\) 0.884414 1.53185i 0.107251 0.185764i
\(69\) 2.63442 5.79472i 0.317147 0.697602i
\(70\) 0 0
\(71\) 4.52106i 0.536551i 0.963342 + 0.268276i \(0.0864538\pi\)
−0.963342 + 0.268276i \(0.913546\pi\)
\(72\) 0.577806 + 2.94383i 0.0680950 + 0.346934i
\(73\) 4.62660 + 2.67117i 0.541503 + 0.312637i 0.745688 0.666295i \(-0.232121\pi\)
−0.204185 + 0.978932i \(0.565454\pi\)
\(74\) −7.96547 + 4.59886i −0.925967 + 0.534607i
\(75\) −0.732039 + 0.523168i −0.0845285 + 0.0604102i
\(76\) −0.986680 + 0.569660i −0.113180 + 0.0653445i
\(77\) 0 0
\(78\) −2.42356 + 1.73205i −0.274414 + 0.196116i
\(79\) −13.0284 −1.46581 −0.732907 0.680329i \(-0.761837\pi\)
−0.732907 + 0.680329i \(0.761837\pi\)
\(80\) −1.17468 + 2.03460i −0.131333 + 0.227476i
\(81\) 8.33228 3.40192i 0.925809 0.377992i
\(82\) 6.92317 3.99709i 0.764536 0.441405i
\(83\) 6.27298 10.8651i 0.688549 1.19260i −0.283758 0.958896i \(-0.591581\pi\)
0.972307 0.233707i \(-0.0750855\pi\)
\(84\) 0 0
\(85\) −2.07781 3.59886i −0.225370 0.390352i
\(86\) 3.04933 + 1.76053i 0.328817 + 0.189843i
\(87\) 2.97887 6.55238i 0.319368 0.702489i
\(88\) −2.83834 4.91614i −0.302568 0.524062i
\(89\) −0.580529 1.00551i −0.0615360 0.106583i 0.833616 0.552344i \(-0.186267\pi\)
−0.895152 + 0.445761i \(0.852933\pi\)
\(90\) 6.66826 + 2.28245i 0.702897 + 0.240591i
\(91\) 0 0
\(92\) −3.18272 1.83755i −0.331822 0.191577i
\(93\) 14.4296 1.40271i 1.49628 0.145454i
\(94\) 11.8099i 1.21810i
\(95\) 2.67667i 0.274621i
\(96\) 1.72392 0.167584i 0.175947 0.0171040i
\(97\) 3.97536 + 2.29517i 0.403636 + 0.233039i 0.688052 0.725662i \(-0.258466\pi\)
−0.284416 + 0.958701i \(0.591800\pi\)
\(98\) 0 0
\(99\) −12.8323 + 11.1962i −1.28969 + 1.12526i
\(100\) 0.259741 + 0.449885i 0.0259741 + 0.0449885i
\(101\) −3.31155 5.73577i −0.329511 0.570730i 0.652904 0.757441i \(-0.273551\pi\)
−0.982415 + 0.186711i \(0.940217\pi\)
\(102\) −1.26795 + 2.78901i −0.125546 + 0.276153i
\(103\) −5.07471 2.92989i −0.500026 0.288690i 0.228698 0.973497i \(-0.426553\pi\)
−0.728724 + 0.684807i \(0.759886\pi\)
\(104\) 0.859925 + 1.48943i 0.0843225 + 0.146051i
\(105\) 0 0
\(106\) 0 0
\(107\) −4.08386 + 2.35782i −0.394802 + 0.227939i −0.684239 0.729258i \(-0.739865\pi\)
0.289437 + 0.957197i \(0.406532\pi\)
\(108\) −1.48943 4.97811i −0.143321 0.479019i
\(109\) −2.11835 + 3.66908i −0.202901 + 0.351435i −0.949462 0.313882i \(-0.898370\pi\)
0.746561 + 0.665317i \(0.231704\pi\)
\(110\) −13.3365 −1.27159
\(111\) 12.9612 9.26298i 1.23022 0.879203i
\(112\) 0 0
\(113\) 5.91693 3.41614i 0.556618 0.321363i −0.195169 0.980770i \(-0.562526\pi\)
0.751787 + 0.659406i \(0.229192\pi\)
\(114\) 1.60550 1.14740i 0.150368 0.107464i
\(115\) −7.47736 + 4.31705i −0.697267 + 0.402567i
\(116\) −3.59886 2.07781i −0.334146 0.192919i
\(117\) 3.88777 3.39208i 0.359424 0.313597i
\(118\) 2.22966i 0.205257i
\(119\) 0 0
\(120\) 1.68409 3.70436i 0.153736 0.338160i
\(121\) 10.6123 18.3810i 0.964754 1.67100i
\(122\) −8.99970 −0.814794
\(123\) −11.2652 + 8.05090i −1.01575 + 0.725926i
\(124\) 8.37019i 0.751665i
\(125\) −10.5263 −0.941504
\(126\) 0 0
\(127\) −6.67667 −0.592459 −0.296229 0.955117i \(-0.595729\pi\)
−0.296229 + 0.955117i \(0.595729\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −5.55185 2.52400i −0.488813 0.222226i
\(130\) 4.04054 0.354379
\(131\) −3.73653 + 6.47185i −0.326462 + 0.565448i −0.981807 0.189881i \(-0.939190\pi\)
0.655345 + 0.755329i \(0.272523\pi\)
\(132\) 5.71694 + 7.99939i 0.497596 + 0.696258i
\(133\) 0 0
\(134\) 10.8712i 0.939133i
\(135\) −11.8781 2.81728i −1.02230 0.242473i
\(136\) 1.53185 + 0.884414i 0.131355 + 0.0758379i
\(137\) −6.91772 + 3.99395i −0.591021 + 0.341226i −0.765501 0.643435i \(-0.777509\pi\)
0.174480 + 0.984661i \(0.444175\pi\)
\(138\) 5.79472 + 2.63442i 0.493279 + 0.224256i
\(139\) −17.9792 + 10.3803i −1.52498 + 0.880446i −0.525415 + 0.850846i \(0.676090\pi\)
−0.999562 + 0.0295993i \(0.990577\pi\)
\(140\) 0 0
\(141\) −1.97915 20.3593i −0.166675 1.71457i
\(142\) −4.52106 −0.379399
\(143\) −4.88151 + 8.45502i −0.408212 + 0.707044i
\(144\) −2.94383 + 0.577806i −0.245319 + 0.0481505i
\(145\) −8.45502 + 4.88151i −0.702151 + 0.405387i
\(146\) −2.67117 + 4.62660i −0.221068 + 0.382900i
\(147\) 0 0
\(148\) −4.59886 7.96547i −0.378024 0.654757i
\(149\) 1.03726 + 0.598865i 0.0849760 + 0.0490609i 0.541886 0.840452i \(-0.317710\pi\)
−0.456910 + 0.889513i \(0.651044\pi\)
\(150\) −0.523168 0.732039i −0.0427165 0.0597707i
\(151\) −7.61229 13.1849i −0.619480 1.07297i −0.989581 0.143979i \(-0.954010\pi\)
0.370101 0.928991i \(-0.379323\pi\)
\(152\) −0.569660 0.986680i −0.0462055 0.0800303i
\(153\) 1.71845 5.02053i 0.138929 0.405886i
\(154\) 0 0
\(155\) −17.0300 9.83228i −1.36788 0.789748i
\(156\) −1.73205 2.42356i −0.138675 0.194040i
\(157\) 10.0269i 0.800237i −0.916463 0.400118i \(-0.868969\pi\)
0.916463 0.400118i \(-0.131031\pi\)
\(158\) 13.0284i 1.03649i
\(159\) 0 0
\(160\) −2.03460 1.17468i −0.160850 0.0928665i
\(161\) 0 0
\(162\) 3.40192 + 8.33228i 0.267280 + 0.654646i
\(163\) −6.00158 10.3950i −0.470080 0.814202i 0.529335 0.848413i \(-0.322442\pi\)
−0.999415 + 0.0342109i \(0.989108\pi\)
\(164\) 3.99709 + 6.92317i 0.312121 + 0.540609i
\(165\) 22.9912 2.23499i 1.78986 0.173994i
\(166\) 10.8651 + 6.27298i 0.843297 + 0.486878i
\(167\) −8.57472 14.8518i −0.663532 1.14927i −0.979681 0.200561i \(-0.935723\pi\)
0.316150 0.948709i \(-0.397610\pi\)
\(168\) 0 0
\(169\) −5.02106 + 8.69673i −0.386235 + 0.668979i
\(170\) 3.59886 2.07781i 0.276020 0.159360i
\(171\) −2.57547 + 2.24709i −0.196951 + 0.171839i
\(172\) −1.76053 + 3.04933i −0.134239 + 0.232509i
\(173\) 1.98748 0.151105 0.0755525 0.997142i \(-0.475928\pi\)
0.0755525 + 0.997142i \(0.475928\pi\)
\(174\) 6.55238 + 2.97887i 0.496735 + 0.225827i
\(175\) 0 0
\(176\) 4.91614 2.83834i 0.370568 0.213948i
\(177\) −0.373656 3.84377i −0.0280857 0.288915i
\(178\) 1.00551 0.580529i 0.0753659 0.0435125i
\(179\) 7.19773 + 4.15561i 0.537984 + 0.310605i 0.744261 0.667889i \(-0.232802\pi\)
−0.206278 + 0.978493i \(0.566135\pi\)
\(180\) −2.28245 + 6.66826i −0.170124 + 0.497023i
\(181\) 15.4541i 1.14870i 0.818611 + 0.574348i \(0.194744\pi\)
−0.818611 + 0.574348i \(0.805256\pi\)
\(182\) 0 0
\(183\) 15.5148 1.50821i 1.14689 0.111490i
\(184\) 1.83755 3.18272i 0.135466 0.234634i
\(185\) −21.6088 −1.58871
\(186\) 1.40271 + 14.4296i 0.102852 + 1.05803i
\(187\) 10.0411i 0.734275i
\(188\) −11.8099 −0.861324
\(189\) 0 0
\(190\) −2.67667 −0.194186
\(191\) 12.3381i 0.892752i −0.894845 0.446376i \(-0.852714\pi\)
0.894845 0.446376i \(-0.147286\pi\)
\(192\) 0.167584 + 1.72392i 0.0120944 + 0.124414i
\(193\) 4.39388 0.316279 0.158139 0.987417i \(-0.449451\pi\)
0.158139 + 0.987417i \(0.449451\pi\)
\(194\) −2.29517 + 3.97536i −0.164784 + 0.285414i
\(195\) −6.96559 + 0.677132i −0.498816 + 0.0484904i
\(196\) 0 0
\(197\) 10.8865i 0.775632i −0.921737 0.387816i \(-0.873230\pi\)
0.921737 0.387816i \(-0.126770\pi\)
\(198\) −11.1962 12.8323i −0.795676 0.911951i
\(199\) 23.8733 + 13.7832i 1.69233 + 0.977068i 0.952629 + 0.304135i \(0.0983674\pi\)
0.739703 + 0.672933i \(0.234966\pi\)
\(200\) −0.449885 + 0.259741i −0.0318116 + 0.0183665i
\(201\) −1.82185 18.7412i −0.128503 1.32190i
\(202\) 5.73577 3.31155i 0.403567 0.233000i
\(203\) 0 0
\(204\) −2.78901 1.26795i −0.195270 0.0887742i
\(205\) 18.7812 1.31174
\(206\) 2.92989 5.07471i 0.204135 0.353572i
\(207\) −10.4311 3.57043i −0.725015 0.248162i
\(208\) −1.48943 + 0.859925i −0.103274 + 0.0596250i
\(209\) 3.23377 5.60106i 0.223685 0.387433i
\(210\) 0 0
\(211\) 5.15561 + 8.92978i 0.354927 + 0.614751i 0.987105 0.160071i \(-0.0511724\pi\)
−0.632179 + 0.774823i \(0.717839\pi\)
\(212\) 0 0
\(213\) 7.79396 0.757659i 0.534034 0.0519139i
\(214\) −2.35782 4.08386i −0.161177 0.279167i
\(215\) 4.13611 + 7.16396i 0.282081 + 0.488578i
\(216\) 4.97811 1.48943i 0.338718 0.101343i
\(217\) 0 0
\(218\) −3.66908 2.11835i −0.248502 0.143473i
\(219\) 3.82955 8.42356i 0.258777 0.569211i
\(220\) 13.3365i 0.899149i
\(221\) 3.04212i 0.204635i
\(222\) 9.26298 + 12.9612i 0.621691 + 0.869897i
\(223\) 6.24329 + 3.60456i 0.418081 + 0.241379i 0.694256 0.719728i \(-0.255733\pi\)
−0.276175 + 0.961107i \(0.589067\pi\)
\(224\) 0 0
\(225\) 1.02458 + 1.17430i 0.0683053 + 0.0782870i
\(226\) 3.41614 + 5.91693i 0.227238 + 0.393588i
\(227\) −6.37800 11.0470i −0.423323 0.733217i 0.572939 0.819598i \(-0.305803\pi\)
−0.996262 + 0.0863812i \(0.972470\pi\)
\(228\) 1.14740 + 1.60550i 0.0759886 + 0.106327i
\(229\) 3.89208 + 2.24709i 0.257196 + 0.148492i 0.623055 0.782178i \(-0.285891\pi\)
−0.365859 + 0.930670i \(0.619225\pi\)
\(230\) −4.31705 7.47736i −0.284658 0.493042i
\(231\) 0 0
\(232\) 2.07781 3.59886i 0.136415 0.236277i
\(233\) −1.86545 + 1.07702i −0.122210 + 0.0705577i −0.559859 0.828588i \(-0.689145\pi\)
0.437649 + 0.899146i \(0.355811\pi\)
\(234\) 3.39208 + 3.88777i 0.221747 + 0.254151i
\(235\) −13.8728 + 24.0284i −0.904963 + 1.56744i
\(236\) −2.22966 −0.145139
\(237\) 2.18336 + 22.4600i 0.141825 + 1.45894i
\(238\) 0 0
\(239\) −8.78317 + 5.07096i −0.568136 + 0.328013i −0.756404 0.654104i \(-0.773046\pi\)
0.188269 + 0.982118i \(0.439712\pi\)
\(240\) 3.70436 + 1.68409i 0.239115 + 0.108708i
\(241\) 9.13490 5.27404i 0.588431 0.339731i −0.176046 0.984382i \(-0.556331\pi\)
0.764477 + 0.644651i \(0.222997\pi\)
\(242\) 18.3810 + 10.6123i 1.18158 + 0.682184i
\(243\) −7.26102 13.7941i −0.465795 0.884893i
\(244\) 8.99970i 0.576146i
\(245\) 0 0
\(246\) −8.05090 11.2652i −0.513307 0.718241i
\(247\) −0.979729 + 1.69694i −0.0623387 + 0.107974i
\(248\) 8.37019 0.531507
\(249\) −19.7819 8.99332i −1.25363 0.569929i
\(250\) 10.5263i 0.665744i
\(251\) 29.3005 1.84943 0.924714 0.380662i \(-0.124304\pi\)
0.924714 + 0.380662i \(0.124304\pi\)
\(252\) 0 0
\(253\) 20.8623 1.31160
\(254\) 6.67667i 0.418932i
\(255\) −5.85596 + 4.18509i −0.366715 + 0.262081i
\(256\) 1.00000 0.0625000
\(257\) 3.81430 6.60656i 0.237930 0.412106i −0.722190 0.691694i \(-0.756865\pi\)
0.960120 + 0.279588i \(0.0901979\pi\)
\(258\) 2.52400 5.55185i 0.157137 0.345643i
\(259\) 0 0
\(260\) 4.04054i 0.250584i
\(261\) −11.7950 4.03726i −0.730093 0.249900i
\(262\) −6.47185 3.73653i −0.399832 0.230843i
\(263\) 10.5531 6.09281i 0.650729 0.375699i −0.138006 0.990431i \(-0.544069\pi\)
0.788736 + 0.614733i \(0.210736\pi\)
\(264\) −7.99939 + 5.71694i −0.492329 + 0.351854i
\(265\) 0 0
\(266\) 0 0
\(267\) −1.63613 + 1.16930i −0.100129 + 0.0715597i
\(268\) −10.8712 −0.664067
\(269\) 1.38717 2.40264i 0.0845771 0.146492i −0.820634 0.571454i \(-0.806379\pi\)
0.905211 + 0.424963i \(0.139713\pi\)
\(270\) 2.81728 11.8781i 0.171454 0.722877i
\(271\) 2.77815 1.60396i 0.168760 0.0974338i −0.413241 0.910622i \(-0.635603\pi\)
0.582001 + 0.813188i \(0.302270\pi\)
\(272\) −0.884414 + 1.53185i −0.0536255 + 0.0928821i
\(273\) 0 0
\(274\) −3.99395 6.91772i −0.241283 0.417915i
\(275\) −2.55385 1.47446i −0.154003 0.0889135i
\(276\) −2.63442 + 5.79472i −0.158573 + 0.348801i
\(277\) −5.04054 8.73047i −0.302857 0.524563i 0.673925 0.738800i \(-0.264607\pi\)
−0.976782 + 0.214236i \(0.931274\pi\)
\(278\) −10.3803 17.9792i −0.622569 1.07832i
\(279\) −4.83634 24.6404i −0.289544 1.47518i
\(280\) 0 0
\(281\) 4.21999 + 2.43641i 0.251743 + 0.145344i 0.620562 0.784157i \(-0.286904\pi\)
−0.368819 + 0.929501i \(0.620238\pi\)
\(282\) 20.3593 1.97915i 1.21238 0.117857i
\(283\) 2.81781i 0.167502i 0.996487 + 0.0837508i \(0.0266900\pi\)
−0.996487 + 0.0837508i \(0.973310\pi\)
\(284\) 4.52106i 0.268276i
\(285\) 4.61438 0.448568i 0.273332 0.0265709i
\(286\) −8.45502 4.88151i −0.499956 0.288650i
\(287\) 0 0
\(288\) −0.577806 2.94383i −0.0340475 0.173467i
\(289\) 6.93562 + 12.0129i 0.407978 + 0.706638i
\(290\) −4.88151 8.45502i −0.286652 0.496496i
\(291\) 3.29050 7.23785i 0.192892 0.424290i
\(292\) −4.62660 2.67117i −0.270751 0.156318i
\(293\) 4.05694 + 7.02683i 0.237009 + 0.410512i 0.959855 0.280498i \(-0.0904995\pi\)
−0.722846 + 0.691010i \(0.757166\pi\)
\(294\) 0 0
\(295\) −2.61914 + 4.53648i −0.152492 + 0.264124i
\(296\) 7.96547 4.59886i 0.462983 0.267304i
\(297\) 21.4518 + 20.2456i 1.24476 + 1.17477i
\(298\) −0.598865 + 1.03726i −0.0346913 + 0.0600871i
\(299\) −6.32061 −0.365530
\(300\) 0.732039 0.523168i 0.0422643 0.0302051i
\(301\) 0 0
\(302\) 13.1849 7.61229i 0.758705 0.438038i
\(303\) −9.33307 + 6.67008i −0.536171 + 0.383186i
\(304\) 0.986680 0.569660i 0.0565900 0.0326722i
\(305\) −18.3108 10.5718i −1.04847 0.605337i
\(306\) 5.02053 + 1.71845i 0.287004 + 0.0982375i
\(307\) 10.8996i 0.622074i −0.950398 0.311037i \(-0.899324\pi\)
0.950398 0.311037i \(-0.100676\pi\)
\(308\) 0 0
\(309\) −4.20046 + 9.23943i −0.238956 + 0.525613i
\(310\) 9.83228 17.0300i 0.558436 0.967240i
\(311\) 8.23637 0.467042 0.233521 0.972352i \(-0.424975\pi\)
0.233521 + 0.972352i \(0.424975\pi\)
\(312\) 2.42356 1.73205i 0.137207 0.0980581i
\(313\) 33.8023i 1.91062i −0.295611 0.955308i \(-0.595523\pi\)
0.295611 0.955308i \(-0.404477\pi\)
\(314\) 10.0269 0.565853
\(315\) 0 0
\(316\) 13.0284 0.732907
\(317\) 6.73090i 0.378045i −0.981973 0.189022i \(-0.939468\pi\)
0.981973 0.189022i \(-0.0605319\pi\)
\(318\) 0 0
\(319\) 23.5900 1.32079
\(320\) 1.17468 2.03460i 0.0656665 0.113738i
\(321\) 4.74909 + 6.64513i 0.265068 + 0.370895i
\(322\) 0 0
\(323\) 2.01526i 0.112132i
\(324\) −8.33228 + 3.40192i −0.462905 + 0.188996i
\(325\) 0.773734 + 0.446715i 0.0429190 + 0.0247793i
\(326\) 10.3950 6.00158i 0.575728 0.332397i
\(327\) 6.68023 + 3.03699i 0.369417 + 0.167946i
\(328\) −6.92317 + 3.99709i −0.382268 + 0.220703i
\(329\) 0 0
\(330\) 2.23499 + 22.9912i 0.123032 + 1.26562i
\(331\) −32.0569 −1.76200 −0.881002 0.473112i \(-0.843131\pi\)
−0.881002 + 0.473112i \(0.843131\pi\)
\(332\) −6.27298 + 10.8651i −0.344275 + 0.596301i
\(333\) −18.1408 20.7917i −0.994108 1.13938i
\(334\) 14.8518 8.57472i 0.812657 0.469188i
\(335\) −12.7702 + 22.1187i −0.697712 + 1.20847i
\(336\) 0 0
\(337\) −12.1123 20.9791i −0.659799 1.14280i −0.980668 0.195681i \(-0.937308\pi\)
0.320869 0.947124i \(-0.396025\pi\)
\(338\) −8.69673 5.02106i −0.473040 0.273110i
\(339\) −6.88075 9.62785i −0.373711 0.522913i
\(340\) 2.07781 + 3.59886i 0.112685 + 0.195176i
\(341\) 23.7574 + 41.1490i 1.28654 + 2.22834i
\(342\) −2.24709 2.57547i −0.121509 0.139265i
\(343\) 0 0
\(344\) −3.04933 1.76053i −0.164409 0.0949214i
\(345\) 8.69536 + 12.1669i 0.468143 + 0.655045i
\(346\) 1.98748i 0.106847i
\(347\) 22.7999i 1.22396i 0.790873 + 0.611981i \(0.209627\pi\)
−0.790873 + 0.611981i \(0.790373\pi\)
\(348\) −2.97887 + 6.55238i −0.159684 + 0.351244i
\(349\) 2.46389 + 1.42253i 0.131889 + 0.0761461i 0.564493 0.825438i \(-0.309072\pi\)
−0.432604 + 0.901584i \(0.642405\pi\)
\(350\) 0 0
\(351\) −6.49921 6.13376i −0.346902 0.327396i
\(352\) 2.83834 + 4.91614i 0.151284 + 0.262031i
\(353\) 3.57212 + 6.18709i 0.190125 + 0.329306i 0.945291 0.326227i \(-0.105777\pi\)
−0.755167 + 0.655533i \(0.772444\pi\)
\(354\) 3.84377 0.373656i 0.204294 0.0198596i
\(355\) −9.19856 5.31079i −0.488209 0.281868i
\(356\) 0.580529 + 1.00551i 0.0307680 + 0.0532917i
\(357\) 0 0
\(358\) −4.15561 + 7.19773i −0.219631 + 0.380412i
\(359\) −10.0491 + 5.80186i −0.530372 + 0.306210i −0.741168 0.671320i \(-0.765728\pi\)
0.210796 + 0.977530i \(0.432394\pi\)
\(360\) −6.66826 2.28245i −0.351448 0.120296i
\(361\) −8.85097 + 15.3303i −0.465841 + 0.806860i
\(362\) −15.4541 −0.812250
\(363\) −33.4660 15.2144i −1.75651 0.798550i
\(364\) 0 0
\(365\) −10.8695 + 6.27554i −0.568938 + 0.328477i
\(366\) 1.50821 + 15.5148i 0.0788353 + 0.810971i
\(367\) 6.78525 3.91747i 0.354187 0.204490i −0.312341 0.949970i \(-0.601113\pi\)
0.666528 + 0.745480i \(0.267780\pi\)
\(368\) 3.18272 + 1.83755i 0.165911 + 0.0957887i
\(369\) 15.7670 + 18.0711i 0.820798 + 0.940744i
\(370\) 21.6088i 1.12339i
\(371\) 0 0
\(372\) −14.4296 + 1.40271i −0.748138 + 0.0727272i
\(373\) −12.8339 + 22.2289i −0.664512 + 1.15097i 0.314905 + 0.949123i \(0.398027\pi\)
−0.979417 + 0.201845i \(0.935306\pi\)
\(374\) −10.0411 −0.519211
\(375\) 1.76405 + 18.1466i 0.0910951 + 0.937087i
\(376\) 11.8099i 0.609048i
\(377\) −7.14702 −0.368091
\(378\) 0 0
\(379\) −15.1045 −0.775868 −0.387934 0.921687i \(-0.626811\pi\)
−0.387934 + 0.921687i \(0.626811\pi\)
\(380\) 2.67667i 0.137310i
\(381\) 1.11891 + 11.5101i 0.0573233 + 0.589679i
\(382\) 12.3381 0.631271
\(383\) −0.763322 + 1.32211i −0.0390040 + 0.0675568i −0.884868 0.465841i \(-0.845752\pi\)
0.845864 + 0.533398i \(0.179085\pi\)
\(384\) −1.72392 + 0.167584i −0.0879737 + 0.00855200i
\(385\) 0 0
\(386\) 4.39388i 0.223643i
\(387\) −3.42078 + 9.99395i −0.173888 + 0.508021i
\(388\) −3.97536 2.29517i −0.201818 0.116520i
\(389\) −12.8948 + 7.44483i −0.653794 + 0.377468i −0.789908 0.613225i \(-0.789872\pi\)
0.136115 + 0.990693i \(0.456538\pi\)
\(390\) −0.677132 6.96559i −0.0342879 0.352716i
\(391\) −5.62969 + 3.25030i −0.284706 + 0.164375i
\(392\) 0 0
\(393\) 11.7832 + 5.35691i 0.594382 + 0.270220i
\(394\) 10.8865 0.548454
\(395\) 15.3042 26.5077i 0.770039 1.33375i
\(396\) 12.8323 11.1962i 0.644846 0.562628i
\(397\) −24.9302 + 14.3935i −1.25121 + 0.722388i −0.971350 0.237653i \(-0.923622\pi\)
−0.279862 + 0.960040i \(0.590289\pi\)
\(398\) −13.7832 + 23.8733i −0.690892 + 1.19666i
\(399\) 0 0
\(400\) −0.259741 0.449885i −0.0129871 0.0224942i
\(401\) 33.0592 + 19.0868i 1.65090 + 0.953147i 0.976703 + 0.214595i \(0.0688431\pi\)
0.674196 + 0.738552i \(0.264490\pi\)
\(402\) 18.7412 1.82185i 0.934726 0.0908657i
\(403\) −7.19773 12.4668i −0.358544 0.621017i
\(404\) 3.31155 + 5.73577i 0.164756 + 0.285365i
\(405\) −2.86619 + 20.9491i −0.142422 + 1.04097i
\(406\) 0 0
\(407\) 45.2173 + 26.1062i 2.24134 + 1.29404i
\(408\) 1.26795 2.78901i 0.0627728 0.138076i
\(409\) 6.96694i 0.344493i −0.985054 0.172247i \(-0.944897\pi\)
0.985054 0.172247i \(-0.0551026\pi\)
\(410\) 18.7812i 0.927538i
\(411\) 8.04456 + 11.2563i 0.396809 + 0.555232i
\(412\) 5.07471 + 2.92989i 0.250013 + 0.144345i
\(413\) 0 0
\(414\) 3.57043 10.4311i 0.175477 0.512663i
\(415\) 14.7375 + 25.5261i 0.723435 + 1.25303i
\(416\) −0.859925 1.48943i −0.0421613 0.0730255i
\(417\) 20.9079 + 29.2552i 1.02386 + 1.43263i
\(418\) 5.60106 + 3.23377i 0.273957 + 0.158169i
\(419\) 17.4232 + 30.1778i 0.851177 + 1.47428i 0.880146 + 0.474702i \(0.157444\pi\)
−0.0289690 + 0.999580i \(0.509222\pi\)
\(420\) 0 0
\(421\) 2.84597 4.92936i 0.138704 0.240242i −0.788302 0.615288i \(-0.789040\pi\)
0.927006 + 0.375046i \(0.122373\pi\)
\(422\) −8.92978 + 5.15561i −0.434695 + 0.250971i
\(423\) −34.7663 + 6.82382i −1.69040 + 0.331785i
\(424\) 0 0
\(425\) 0.918875 0.0445720
\(426\) 0.757659 + 7.79396i 0.0367087 + 0.377619i
\(427\) 0 0
\(428\) 4.08386 2.35782i 0.197401 0.113969i
\(429\) 15.3939 + 6.99842i 0.743224 + 0.337887i
\(430\) −7.16396 + 4.13611i −0.345477 + 0.199461i
\(431\) −26.2350 15.1468i −1.26370 0.729595i −0.289908 0.957055i \(-0.593625\pi\)
−0.973787 + 0.227460i \(0.926958\pi\)
\(432\) 1.48943 + 4.97811i 0.0716604 + 0.239509i
\(433\) 23.6094i 1.13459i −0.823513 0.567297i \(-0.807989\pi\)
0.823513 0.567297i \(-0.192011\pi\)
\(434\) 0 0
\(435\) 9.83228 + 13.7578i 0.471422 + 0.659634i
\(436\) 2.11835 3.66908i 0.101450 0.175717i
\(437\) 4.18711 0.200297
\(438\) 8.42356 + 3.82955i 0.402493 + 0.182983i
\(439\) 25.0202i 1.19415i 0.802185 + 0.597075i \(0.203671\pi\)
−0.802185 + 0.597075i \(0.796329\pi\)
\(440\) 13.3365 0.635794
\(441\) 0 0
\(442\) 3.04212 0.144699
\(443\) 23.0300i 1.09419i 0.837071 + 0.547094i \(0.184266\pi\)
−0.837071 + 0.547094i \(0.815734\pi\)
\(444\) −12.9612 + 9.26298i −0.615110 + 0.439602i
\(445\) 2.72774 0.129307
\(446\) −3.60456 + 6.24329i −0.170681 + 0.295628i
\(447\) 0.858568 1.88853i 0.0406089 0.0893242i
\(448\) 0 0
\(449\) 15.9028i 0.750501i −0.926923 0.375251i \(-0.877557\pi\)
0.926923 0.375251i \(-0.122443\pi\)
\(450\) −1.17430 + 1.02458i −0.0553572 + 0.0482991i
\(451\) −39.3006 22.6902i −1.85059 1.06844i
\(452\) −5.91693 + 3.41614i −0.278309 + 0.160682i
\(453\) −21.4540 + 15.3326i −1.00800 + 0.720388i
\(454\) 11.0470 6.37800i 0.518462 0.299334i
\(455\) 0 0
\(456\) −1.60550 + 1.14740i −0.0751842 + 0.0537321i
\(457\) −5.66614 −0.265051 −0.132525 0.991180i \(-0.542309\pi\)
−0.132525 + 0.991180i \(0.542309\pi\)
\(458\) −2.24709 + 3.89208i −0.105000 + 0.181865i
\(459\) −8.94300 2.12112i −0.417423 0.0990056i
\(460\) 7.47736 4.31705i 0.348634 0.201284i
\(461\) 15.7292 27.2438i 0.732582 1.26887i −0.223194 0.974774i \(-0.571648\pi\)
0.955776 0.294095i \(-0.0950183\pi\)
\(462\) 0 0
\(463\) 4.55148 + 7.88340i 0.211525 + 0.366373i 0.952192 0.305500i \(-0.0988236\pi\)
−0.740667 + 0.671873i \(0.765490\pi\)
\(464\) 3.59886 + 2.07781i 0.167073 + 0.0964597i
\(465\) −14.0961 + 31.0062i −0.653693 + 1.43788i
\(466\) −1.07702 1.86545i −0.0498918 0.0864152i
\(467\) −15.1516 26.2433i −0.701132 1.21440i −0.968069 0.250682i \(-0.919345\pi\)
0.266938 0.963714i \(-0.413988\pi\)
\(468\) −3.88777 + 3.39208i −0.179712 + 0.156799i
\(469\) 0 0
\(470\) −24.0284 13.8728i −1.10835 0.639906i
\(471\) −17.2857 + 1.68036i −0.796482 + 0.0774268i
\(472\) 2.22966i 0.102628i
\(473\) 19.9879i 0.919044i
\(474\) −22.4600 + 2.18336i −1.03162 + 0.100285i
\(475\) −0.512563 0.295928i −0.0235180 0.0135781i
\(476\) 0 0
\(477\) 0 0
\(478\) −5.07096 8.78317i −0.231940 0.401733i
\(479\) 2.33143 + 4.03816i 0.106526 + 0.184508i 0.914361 0.404901i \(-0.132694\pi\)
−0.807835 + 0.589409i \(0.799361\pi\)
\(480\) −1.68409 + 3.70436i −0.0768678 + 0.169080i
\(481\) −13.6994 7.90935i −0.624639 0.360636i
\(482\) 5.27404 + 9.13490i 0.240226 + 0.416083i
\(483\) 0 0
\(484\) −10.6123 + 18.3810i −0.482377 + 0.835501i
\(485\) −9.33953 + 5.39218i −0.424086 + 0.244846i
\(486\) 13.7941 7.26102i 0.625714 0.329367i
\(487\) 9.74105 16.8720i 0.441409 0.764543i −0.556385 0.830924i \(-0.687812\pi\)
0.997794 + 0.0663816i \(0.0211455\pi\)
\(488\) 8.99970 0.407397
\(489\) −16.9145 + 12.0883i −0.764900 + 0.546652i
\(490\) 0 0
\(491\) −17.7437 + 10.2443i −0.800762 + 0.462320i −0.843737 0.536756i \(-0.819649\pi\)
0.0429758 + 0.999076i \(0.486316\pi\)
\(492\) 11.2652 8.05090i 0.507873 0.362963i
\(493\) −6.36577 + 3.67528i −0.286700 + 0.165526i
\(494\) −1.69694 0.979729i −0.0763490 0.0440801i
\(495\) −7.70592 39.2605i −0.346355 1.76463i
\(496\) 8.37019i 0.375832i
\(497\) 0 0
\(498\) 8.99332 19.7819i 0.403000 0.886449i
\(499\) 5.12598 8.87845i 0.229470 0.397454i −0.728181 0.685385i \(-0.759634\pi\)
0.957651 + 0.287931i \(0.0929673\pi\)
\(500\) 10.5263 0.470752
\(501\) −24.1665 + 17.2711i −1.07968 + 0.771616i
\(502\) 29.3005i 1.30774i
\(503\) 14.5521 0.648845 0.324422 0.945912i \(-0.394830\pi\)
0.324422 + 0.945912i \(0.394830\pi\)
\(504\) 0 0
\(505\) 15.5600 0.692412
\(506\) 20.8623i 0.927442i
\(507\) 15.8340 + 7.19849i 0.703211 + 0.319696i
\(508\) 6.67667 0.296229
\(509\) 16.6617 28.8589i 0.738517 1.27915i −0.214646 0.976692i \(-0.568860\pi\)
0.953163 0.302457i \(-0.0978068\pi\)
\(510\) −4.18509 5.85596i −0.185319 0.259306i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 4.30542 + 4.06333i 0.190089 + 0.179401i
\(514\) 6.60656 + 3.81430i 0.291403 + 0.168242i
\(515\) 11.9223 6.88335i 0.525360 0.303317i
\(516\) 5.55185 + 2.52400i 0.244406 + 0.111113i
\(517\) 58.0591 33.5204i 2.55343 1.47423i
\(518\) 0 0
\(519\) −0.333070 3.42626i −0.0146202 0.150396i
\(520\) −4.04054 −0.177189
\(521\) −3.26963 + 5.66316i −0.143245 + 0.248108i −0.928717 0.370790i \(-0.879087\pi\)
0.785472 + 0.618897i \(0.212420\pi\)
\(522\) 4.03726 11.7950i 0.176706 0.516254i
\(523\) 0.681439 0.393429i 0.0297972 0.0172034i −0.485027 0.874499i \(-0.661190\pi\)
0.514825 + 0.857296i \(0.327857\pi\)
\(524\) 3.73653 6.47185i 0.163231 0.282724i
\(525\) 0 0
\(526\) 6.09281 + 10.5531i 0.265659 + 0.460135i
\(527\) −12.8219 7.40271i −0.558530 0.322467i
\(528\) −5.71694 7.99939i −0.248798 0.348129i
\(529\) −4.74685 8.22178i −0.206385 0.357469i
\(530\) 0 0
\(531\) −6.56374 + 1.28831i −0.284842 + 0.0559079i
\(532\) 0 0
\(533\) 11.9068 + 6.87440i 0.515741 + 0.297763i
\(534\) −1.16930 1.63613i −0.0506004 0.0708022i
\(535\) 11.0787i 0.478975i
\(536\) 10.8712i 0.469566i
\(537\) 5.95773 13.1048i 0.257095 0.565512i
\(538\) 2.40264 + 1.38717i 0.103585 + 0.0598050i
\(539\) 0 0
\(540\) 11.8781 + 2.81728i 0.511152 + 0.121236i
\(541\) −2.80227 4.85367i −0.120479 0.208676i 0.799478 0.600696i \(-0.205110\pi\)
−0.919957 + 0.392020i \(0.871776\pi\)
\(542\) 1.60396 + 2.77815i 0.0688961 + 0.119332i
\(543\) 26.6417 2.58987i 1.14331 0.111142i
\(544\) −1.53185 0.884414i −0.0656775 0.0379189i
\(545\) −4.97675 8.61999i −0.213181 0.369240i
\(546\) 0 0
\(547\) −6.91456 + 11.9764i −0.295645 + 0.512073i −0.975135 0.221612i \(-0.928868\pi\)
0.679489 + 0.733685i \(0.262201\pi\)
\(548\) 6.91772 3.99395i 0.295510 0.170613i
\(549\) −5.20007 26.4936i −0.221934 1.13072i
\(550\) 1.47446 2.55385i 0.0628714 0.108896i
\(551\) 4.73457 0.201700
\(552\) −5.79472 2.63442i −0.246640 0.112128i
\(553\) 0 0
\(554\) 8.73047 5.04054i 0.370922 0.214152i
\(555\) 3.62129 + 37.2519i 0.153715 + 1.58125i
\(556\) 17.9792 10.3803i 0.762488 0.440223i
\(557\) 24.0957 + 13.9117i 1.02097 + 0.589456i 0.914384 0.404848i \(-0.132675\pi\)
0.106584 + 0.994304i \(0.466009\pi\)
\(558\) 24.6404 4.83634i 1.04311 0.204739i
\(559\) 6.05569i 0.256128i
\(560\) 0 0
\(561\) 17.3100 1.68272i 0.730830 0.0710447i
\(562\) −2.43641 + 4.21999i −0.102774 + 0.178009i
\(563\) 24.5300 1.03382 0.516909 0.856040i \(-0.327083\pi\)
0.516909 + 0.856040i \(0.327083\pi\)
\(564\) 1.97915 + 20.3593i 0.0833373 + 0.857283i
\(565\) 16.0515i 0.675291i
\(566\) −2.81781 −0.118441
\(567\) 0 0
\(568\) 4.52106 0.189699
\(569\) 27.1079i 1.13642i 0.822882 + 0.568212i \(0.192365\pi\)
−0.822882 + 0.568212i \(0.807635\pi\)
\(570\) 0.448568 + 4.61438i 0.0187885 + 0.193275i
\(571\) −29.8354 −1.24857 −0.624287 0.781195i \(-0.714610\pi\)
−0.624287 + 0.781195i \(0.714610\pi\)
\(572\) 4.88151 8.45502i 0.204106 0.353522i
\(573\) −21.2699 + 2.06767i −0.888563 + 0.0863781i
\(574\) 0 0
\(575\) 1.90915i 0.0796169i
\(576\) 2.94383 0.577806i 0.122660 0.0240752i
\(577\) −24.3930 14.0833i −1.01549 0.586296i −0.102699 0.994712i \(-0.532748\pi\)
−0.912796 + 0.408416i \(0.866081\pi\)
\(578\) −12.0129 + 6.93562i −0.499669 + 0.288484i
\(579\) −0.736346 7.57472i −0.0306015 0.314795i
\(580\) 8.45502 4.88151i 0.351076 0.202694i
\(581\) 0 0
\(582\) 7.23785 + 3.29050i 0.300018 + 0.136395i
\(583\) 0 0
\(584\) 2.67117 4.62660i 0.110534 0.191450i
\(585\) 2.33465 + 11.8947i 0.0965258 + 0.491784i
\(586\) −7.02683 + 4.05694i −0.290276 + 0.167591i
\(587\) −4.95928 + 8.58973i −0.204692 + 0.354536i −0.950034 0.312145i \(-0.898952\pi\)
0.745343 + 0.666681i \(0.232286\pi\)
\(588\) 0 0
\(589\) 4.76816 + 8.25870i 0.196469 + 0.340294i
\(590\) −4.53648 2.61914i −0.186764 0.107828i
\(591\) −18.7675 + 1.82441i −0.771992 + 0.0750461i
\(592\) 4.59886 + 7.96547i 0.189012 + 0.327379i
\(593\) −2.34936 4.06921i −0.0964766 0.167102i 0.813747 0.581219i \(-0.197424\pi\)
−0.910224 + 0.414116i \(0.864091\pi\)
\(594\) −20.2456 + 21.4518i −0.830686 + 0.880178i
\(595\) 0 0
\(596\) −1.03726 0.598865i −0.0424880 0.0245305i
\(597\) 19.7605 43.4656i 0.808743 1.77893i
\(598\) 6.32061i 0.258469i
\(599\) 14.7004i 0.600641i 0.953838 + 0.300320i \(0.0970936\pi\)
−0.953838 + 0.300320i \(0.902906\pi\)
\(600\) 0.523168 + 0.732039i 0.0213582 + 0.0298854i
\(601\) −16.2923 9.40634i −0.664575 0.383693i 0.129443 0.991587i \(-0.458681\pi\)
−0.794018 + 0.607894i \(0.792014\pi\)
\(602\) 0 0
\(603\) −32.0031 + 6.28147i −1.30327 + 0.255801i
\(604\) 7.61229 + 13.1849i 0.309740 + 0.536485i
\(605\) 24.9321 + 43.1836i 1.01363 + 1.75566i
\(606\) −6.67008 9.33307i −0.270954 0.379130i
\(607\) 10.9051 + 6.29608i 0.442625 + 0.255550i 0.704711 0.709495i \(-0.251077\pi\)
−0.262085 + 0.965045i \(0.584410\pi\)
\(608\) 0.569660 + 0.986680i 0.0231028 + 0.0400152i
\(609\) 0 0
\(610\) 10.5718 18.3108i 0.428038 0.741383i
\(611\) −17.5900 + 10.1556i −0.711617 + 0.410852i
\(612\) −1.71845 + 5.02053i −0.0694644 + 0.202943i
\(613\) 4.91009 8.50452i 0.198317 0.343494i −0.749666 0.661816i \(-0.769786\pi\)
0.947983 + 0.318322i \(0.103119\pi\)
\(614\) 10.8996 0.439873
\(615\) −3.14744 32.3774i −0.126917 1.30558i
\(616\) 0 0
\(617\) −3.25158 + 1.87730i −0.130904 + 0.0755772i −0.564022 0.825760i \(-0.690747\pi\)
0.433118 + 0.901337i \(0.357413\pi\)
\(618\) −9.23943 4.20046i −0.371664 0.168967i
\(619\) 9.56902 5.52468i 0.384611 0.222055i −0.295211 0.955432i \(-0.595390\pi\)
0.679823 + 0.733376i \(0.262057\pi\)
\(620\) 17.0300 + 9.83228i 0.683942 + 0.394874i
\(621\) −4.40706 + 18.5809i −0.176849 + 0.745624i
\(622\) 8.23637i 0.330248i
\(623\) 0 0
\(624\) 1.73205 + 2.42356i 0.0693375 + 0.0970201i
\(625\) 13.6638 23.6664i 0.546551 0.946654i
\(626\) 33.8023 1.35101
\(627\) −10.1977 4.63613i −0.407258 0.185149i
\(628\) 10.0269i 0.400118i
\(629\) −16.2692 −0.648696
\(630\) 0 0
\(631\) 19.4921 0.775969 0.387984 0.921666i \(-0.373171\pi\)
0.387984 + 0.921666i \(0.373171\pi\)
\(632\) 13.0284i 0.518243i
\(633\) 14.5303 10.3844i 0.577526 0.412742i
\(634\) 6.73090 0.267318
\(635\) 7.84294 13.5844i 0.311238 0.539080i
\(636\) 0 0
\(637\) 0 0
\(638\) 23.5900i 0.933938i
\(639\) −2.61229 13.3092i −0.103341 0.526505i
\(640\) 2.03460 + 1.17468i 0.0804248 + 0.0464333i
\(641\) 22.6669 13.0868i 0.895290 0.516896i 0.0196208 0.999807i \(-0.493754\pi\)
0.875669 + 0.482912i \(0.160421\pi\)
\(642\) −6.64513 + 4.74909i −0.262262 + 0.187432i
\(643\) −9.50955 + 5.49034i −0.375020 + 0.216518i −0.675649 0.737223i \(-0.736137\pi\)
0.300629 + 0.953741i \(0.402803\pi\)
\(644\) 0 0
\(645\) 11.6570 8.33092i 0.458993 0.328029i
\(646\) −2.01526 −0.0792894
\(647\) 16.0063 27.7237i 0.629273 1.08993i −0.358425 0.933558i \(-0.616686\pi\)
0.987698 0.156374i \(-0.0499805\pi\)
\(648\) −3.40192 8.33228i −0.133640 0.327323i
\(649\) 10.9613 6.32852i 0.430270 0.248416i
\(650\) −0.446715 + 0.773734i −0.0175216 + 0.0303483i
\(651\) 0 0
\(652\) 6.00158 + 10.3950i 0.235040 + 0.407101i
\(653\) −19.3686 11.1825i −0.757952 0.437604i 0.0706080 0.997504i \(-0.477506\pi\)
−0.828560 + 0.559900i \(0.810839\pi\)
\(654\) −3.03699 + 6.68023i −0.118756 + 0.261218i
\(655\) −8.77843 15.2047i −0.343002 0.594097i
\(656\) −3.99709 6.92317i −0.156060 0.270304i
\(657\) −15.1634 5.19020i −0.591579 0.202489i
\(658\) 0 0
\(659\) −19.2546 11.1166i −0.750053 0.433043i 0.0756603 0.997134i \(-0.475894\pi\)
−0.825713 + 0.564091i \(0.809227\pi\)
\(660\) −22.9912 + 2.23499i −0.894930 + 0.0869970i
\(661\) 10.5499i 0.410343i 0.978726 + 0.205171i \(0.0657751\pi\)
−0.978726 + 0.205171i \(0.934225\pi\)
\(662\) 32.0569i 1.24593i
\(663\) −5.24438 + 0.509811i −0.203675 + 0.0197994i
\(664\) −10.8651 6.27298i −0.421649 0.243439i
\(665\) 0 0
\(666\) 20.7917 18.1408i 0.805664 0.702941i
\(667\) 7.63613 + 13.2262i 0.295672 + 0.512119i
\(668\) 8.57472 + 14.8518i 0.331766 + 0.574635i
\(669\) 5.16772 11.3670i 0.199796 0.439475i
\(670\) −22.1187 12.7702i −0.854519 0.493357i
\(671\) 25.5442 + 44.2438i 0.986121 + 1.70801i
\(672\) 0 0
\(673\) 9.93562 17.2090i 0.382990 0.663358i −0.608498 0.793555i \(-0.708228\pi\)
0.991488 + 0.130197i \(0.0415610\pi\)
\(674\) 20.9791 12.1123i 0.808085 0.466548i
\(675\) 1.85271 1.96309i 0.0713108 0.0755595i
\(676\) 5.02106 8.69673i 0.193118 0.334490i
\(677\) −15.9290 −0.612201 −0.306100 0.951999i \(-0.599024\pi\)
−0.306100 + 0.951999i \(0.599024\pi\)
\(678\) 9.62785 6.88075i 0.369755 0.264254i
\(679\) 0 0
\(680\) −3.59886 + 2.07781i −0.138010 + 0.0796802i
\(681\) −17.9754 + 12.8465i −0.688818 + 0.492279i
\(682\) −41.1490 + 23.7574i −1.57568 + 0.909718i
\(683\) −16.4777 9.51343i −0.630503 0.364021i 0.150444 0.988619i \(-0.451930\pi\)
−0.780947 + 0.624597i \(0.785263\pi\)
\(684\) 2.57547 2.24709i 0.0984754 0.0859197i
\(685\) 18.7664i 0.717028i
\(686\) 0 0
\(687\) 3.22157 7.08623i 0.122910 0.270356i
\(688\) 1.76053 3.04933i 0.0671196 0.116254i
\(689\) 0 0
\(690\) −12.1669 + 8.69536i −0.463187 + 0.331027i
\(691\) 0.161055i 0.00612681i 0.999995 + 0.00306340i \(0.000975113\pi\)
−0.999995 + 0.00306340i \(0.999025\pi\)
\(692\) −1.98748 −0.0755525
\(693\) 0 0
\(694\) −22.7999 −0.865471
\(695\) 48.7741i 1.85011i
\(696\) −6.55238 2.97887i −0.248367 0.112914i
\(697\) 14.1403 0.535604
\(698\) −1.42253 + 2.46389i −0.0538434 + 0.0932595i
\(699\) 2.16932 + 3.03540i 0.0820511 + 0.114809i
\(700\) 0 0
\(701\) 9.98234i 0.377028i −0.982071 0.188514i \(-0.939633\pi\)
0.982071 0.188514i \(-0.0603670\pi\)
\(702\) 6.13376 6.49921i 0.231504 0.245297i
\(703\) 9.07522 + 5.23958i 0.342278 + 0.197614i
\(704\) −4.91614 + 2.83834i −0.185284 + 0.106974i
\(705\) 43.7481 + 19.8889i 1.64765 + 0.749060i
\(706\) −6.18709 + 3.57212i −0.232854 + 0.134438i
\(707\) 0 0
\(708\) 0.373656 + 3.84377i 0.0140429 + 0.144458i
\(709\) −24.3923 −0.916072 −0.458036 0.888934i \(-0.651447\pi\)
−0.458036 + 0.888934i \(0.651447\pi\)
\(710\) 5.31079 9.19856i 0.199311 0.345216i
\(711\) 38.3535 7.52790i 1.43837 0.282318i
\(712\) −1.00551 + 0.580529i −0.0376829 + 0.0217563i
\(713\) −15.3806 + 26.6400i −0.576008 + 0.997676i
\(714\) 0 0
\(715\) −11.4684 19.8639i −0.428894 0.742867i
\(716\) −7.19773 4.15561i −0.268992 0.155302i
\(717\) 10.2139 + 14.2917i 0.381444 + 0.533733i
\(718\) −5.80186 10.0491i −0.216523 0.375030i
\(719\) −8.13460 14.0895i −0.303370 0.525451i 0.673527 0.739162i \(-0.264778\pi\)
−0.976897 + 0.213711i \(0.931445\pi\)
\(720\) 2.28245 6.66826i 0.0850619 0.248512i
\(721\) 0 0
\(722\) −15.3303 8.85097i −0.570536 0.329399i
\(723\) −10.6229 14.8640i −0.395070 0.552799i
\(724\) 15.4541i 0.574348i
\(725\) 2.15877i 0.0801745i
\(726\) 15.2144 33.4660i 0.564660 1.24204i
\(727\) −20.6626 11.9296i −0.766335 0.442444i 0.0652306 0.997870i \(-0.479222\pi\)
−0.831566 + 0.555427i \(0.812555\pi\)
\(728\) 0 0
\(729\) −22.5632 + 14.8291i −0.835673 + 0.549227i
\(730\) −6.27554 10.8695i −0.232268 0.402300i
\(731\) 3.11408 + 5.39374i 0.115178 + 0.199495i
\(732\) −15.5148 + 1.50821i −0.573443 + 0.0557450i
\(733\) 10.6259 + 6.13486i 0.392476 + 0.226596i 0.683233 0.730201i \(-0.260574\pi\)
−0.290756 + 0.956797i \(0.593907\pi\)
\(734\) 3.91747 + 6.78525i 0.144596 + 0.250448i
\(735\) 0 0
\(736\) −1.83755 + 3.18272i −0.0677329 + 0.117317i
\(737\) 53.4446 30.8562i 1.96866 1.13660i
\(738\) −18.0711 + 15.7670i −0.665206 + 0.580392i
\(739\) −20.9446 + 36.2771i −0.770459 + 1.33447i 0.166853 + 0.985982i \(0.446639\pi\)
−0.937312 + 0.348492i \(0.886694\pi\)
\(740\) 21.6088 0.794354
\(741\) 3.08959 + 1.40460i 0.113499 + 0.0515992i
\(742\) 0 0
\(743\) 43.9160 25.3549i 1.61112 0.930182i 0.622011 0.783008i \(-0.286316\pi\)
0.989111 0.147173i \(-0.0470176\pi\)
\(744\) −1.40271 14.4296i −0.0514259 0.529014i
\(745\) −2.43690 + 1.40695i −0.0892813 + 0.0515466i
\(746\) −22.2289 12.8339i −0.813858 0.469881i
\(747\) −12.1887 + 35.6097i −0.445960 + 1.30289i
\(748\) 10.0411i 0.367137i
\(749\) 0 0
\(750\) −18.1466 + 1.76405i −0.662621 + 0.0644140i
\(751\) 16.3683 28.3508i 0.597289 1.03454i −0.395930 0.918281i \(-0.629578\pi\)
0.993219 0.116255i \(-0.0370890\pi\)
\(752\) 11.8099 0.430662
\(753\) −4.91030 50.5118i −0.178941 1.84075i
\(754\) 7.14702i 0.260279i
\(755\) 35.7680 1.30173
\(756\) 0 0
\(757\) −17.9255 −0.651512 −0.325756 0.945454i \(-0.605619\pi\)
−0.325756 + 0.945454i \(0.605619\pi\)
\(758\) 15.1045i 0.548622i
\(759\) −3.49619 35.9650i −0.126904 1.30545i
\(760\) 2.67667 0.0970930
\(761\) −21.8509 + 37.8469i −0.792096 + 1.37195i 0.132571 + 0.991174i \(0.457677\pi\)
−0.924667 + 0.380777i \(0.875657\pi\)
\(762\) −11.5101 + 1.11891i −0.416966 + 0.0405337i
\(763\) 0 0
\(764\) 12.3381i 0.446376i
\(765\) 8.19615 + 9.39388i 0.296333 + 0.339637i
\(766\) −1.32211 0.763322i −0.0477699 0.0275800i
\(767\) −3.32093 + 1.91734i −0.119912 + 0.0692311i
\(768\) −0.167584 1.72392i −0.00604718 0.0622068i
\(769\) 37.0864 21.4118i 1.33737 0.772131i 0.350953 0.936393i \(-0.385858\pi\)
0.986417 + 0.164262i \(0.0525242\pi\)
\(770\) 0 0
\(771\) −12.0284 5.46841i −0.433193 0.196940i
\(772\) −4.39388 −0.158139
\(773\) −10.8025 + 18.7105i −0.388540 + 0.672971i −0.992253 0.124231i \(-0.960354\pi\)
0.603714 + 0.797201i \(0.293687\pi\)
\(774\) −9.99395 3.42078i −0.359225 0.122958i
\(775\) 3.76562 2.17408i 0.135265 0.0780953i
\(776\) 2.29517 3.97536i 0.0823919 0.142707i
\(777\) 0 0
\(778\) −7.44483 12.8948i −0.266910 0.462302i
\(779\) −7.88771 4.55397i −0.282606 0.163163i
\(780\) 6.96559 0.677132i 0.249408 0.0242452i
\(781\) <