Properties

Label 882.2.l.a.509.2
Level $882$
Weight $2$
Character 882.509
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 509.2
Root \(1.40917 + 1.00709i\) of defining polynomial
Character \(\chi\) \(=\) 882.509
Dual form 882.2.l.a.227.6

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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 −0.999565 0.0295026i \(-0.990608\pi\)
0.474232 0.880400i \(-0.342726\pi\)
\(6\) 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 0.999798 0.0201197i \(-0.00640473\pi\)
0.482475 + 0.875910i \(0.339738\pi\)
\(12\) 0.167584 1.72392i 0.0483774 0.497654i
\(13\) −1.48943 0.859925i −0.413094 0.238500i 0.279024 0.960284i \(-0.409989\pi\)
−0.692118 + 0.721784i \(0.743322\pi\)
\(14\) 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 0.738616 0.674126i \(-0.235480\pi\)
−0.953118 + 0.302598i \(0.902146\pi\)
\(18\) −0.577806 + 2.94383i −0.136190 + 0.693868i
\(19\) 0.986680 + 0.569660i 0.226360 + 0.130689i 0.608892 0.793253i \(-0.291614\pi\)
−0.382532 + 0.923942i \(0.624948\pi\)
\(20\) 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 −0.130020 0.991511i \(-0.541504\pi\)
0.793664 + 0.608356i \(0.208171\pi\)
\(24\) −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 −0.127137 0.991885i \(-0.540579\pi\)
0.795429 + 0.606046i \(0.207245\pi\)
\(30\) −1.68409 3.70436i −0.307471 0.676321i
\(31\) 8.37019i 1.50333i −0.659545 0.751665i \(-0.729251\pi\)
0.659545 0.751665i \(-0.270749\pi\)
\(32\) 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 −0.188803 0.982015i \(-0.560461\pi\)
0.944851 0.327500i \(-0.106206\pi\)
\(38\) 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 0.364446 + 0.931225i \(0.381258\pi\)
−0.988687 + 0.149993i \(0.952075\pi\)
\(42\) 0 0
\(43\) 1.76053 + 3.04933i 0.268478 + 0.465018i 0.968469 0.249134i \(-0.0801459\pi\)
−0.699991 + 0.714152i \(0.746813\pi\)
\(44\) −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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −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 \(-0.804556\pi\)
0.817346 0.576146i \(-0.195444\pi\)
\(62\) −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 \(-0.913546\pi\)
0.963342 0.268276i \(-0.0864538\pi\)
\(72\) 0.577806 2.94383i 0.0680950 0.346934i
\(73\) 4.62660 2.67117i 0.541503 0.312637i −0.204185 0.978932i \(-0.565454\pi\)
0.745688 + 0.666295i \(0.232121\pi\)
\(74\) −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 0.972307 + 0.233707i \(0.0750855\pi\)
−0.283758 + 0.958896i \(0.591581\pi\)
\(84\) 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 −0.895152 0.445761i \(-0.852933\pi\)
0.833616 + 0.552344i \(0.186267\pi\)
\(90\) 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 −0.284416 0.958701i \(-0.591800\pi\)
0.688052 + 0.725662i \(0.258466\pi\)
\(98\) 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 −0.982415 0.186711i \(-0.940217\pi\)
0.652904 + 0.757441i \(0.273551\pi\)
\(102\) −1.26795 2.78901i −0.125546 0.276153i
\(103\) −5.07471 + 2.92989i −0.500026 + 0.288690i −0.728724 0.684807i \(-0.759886\pi\)
0.228698 + 0.973497i \(0.426553\pi\)
\(104\) 0.859925 1.48943i 0.0843225 0.146051i
\(105\) 0 0
\(106\) 0 0
\(107\) −4.08386 2.35782i −0.394802 0.227939i 0.289437 0.957197i \(-0.406532\pi\)
−0.684239 + 0.729258i \(0.739865\pi\)
\(108\) −1.48943 + 4.97811i −0.143321 + 0.479019i
\(109\) −2.11835 3.66908i −0.202901 0.351435i 0.746561 0.665317i \(-0.231704\pi\)
−0.949462 + 0.313882i \(0.898370\pi\)
\(110\) −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 0.751787 0.659406i \(-0.229192\pi\)
−0.195169 + 0.980770i \(0.562526\pi\)
\(114\) 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 0.655345 0.755329i \(-0.272523\pi\)
−0.981807 + 0.189881i \(0.939190\pi\)
\(132\) 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 0.174480 0.984661i \(-0.444175\pi\)
−0.765501 + 0.643435i \(0.777509\pi\)
\(138\) 5.79472 2.63442i 0.493279 0.224256i
\(139\) −17.9792 10.3803i −1.52498 0.880446i −0.999562 0.0295993i \(-0.990577\pi\)
−0.525415 0.850846i \(-0.676090\pi\)
\(140\) 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 −0.456910 0.889513i \(-0.651044\pi\)
0.541886 + 0.840452i \(0.317710\pi\)
\(150\) −0.523168 + 0.732039i −0.0427165 + 0.0597707i
\(151\) −7.61229 + 13.1849i −0.619480 + 1.07297i 0.370101 + 0.928991i \(0.379323\pi\)
−0.989581 + 0.143979i \(0.954010\pi\)
\(152\) −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 \(0.131031\pi\)
−0.916463 + 0.400118i \(0.868969\pi\)
\(158\) 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 −0.999415 0.0342109i \(-0.989108\pi\)
0.529335 + 0.848413i \(0.322442\pi\)
\(164\) 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 0.316150 + 0.948709i \(0.397610\pi\)
−0.979681 + 0.200561i \(0.935723\pi\)
\(168\) 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 −0.206278 0.978493i \(-0.566135\pi\)
0.744261 + 0.667889i \(0.232802\pi\)
\(180\) −2.28245 6.66826i −0.170124 0.497023i
\(181\) 15.4541i 1.14870i −0.818611 0.574348i \(-0.805256\pi\)
0.818611 0.574348i \(-0.194744\pi\)
\(182\) 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 \(0.147286\pi\)
−0.894845 + 0.446376i \(0.852714\pi\)
\(192\) 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 \(0.126770\pi\)
−0.921737 + 0.387816i \(0.873230\pi\)
\(198\) −11.1962 + 12.8323i −0.795676 + 0.911951i
\(199\) 23.8733 13.7832i 1.69233 0.977068i 0.739703 0.672933i \(-0.234966\pi\)
0.952629 0.304135i \(-0.0983674\pi\)
\(200\) −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 −0.632179 0.774823i \(-0.717839\pi\)
0.987105 + 0.160071i \(0.0511724\pi\)
\(212\) 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 −0.276175 0.961107i \(-0.589067\pi\)
0.694256 + 0.719728i \(0.255733\pi\)
\(224\) 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 −0.996262 0.0863812i \(-0.972470\pi\)
0.572939 + 0.819598i \(0.305803\pi\)
\(228\) 1.14740 1.60550i 0.0759886 0.106327i
\(229\) 3.89208 2.24709i 0.257196 0.148492i −0.365859 0.930670i \(-0.619225\pi\)
0.623055 + 0.782178i \(0.285891\pi\)
\(230\) −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 0.437649 0.899146i \(-0.355811\pi\)
−0.559859 + 0.828588i \(0.689145\pi\)
\(234\) 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 0.188269 0.982118i \(-0.439712\pi\)
−0.756404 + 0.654104i \(0.773046\pi\)
\(240\) 3.70436 1.68409i 0.239115 0.108708i
\(241\) 9.13490 + 5.27404i 0.588431 + 0.339731i 0.764477 0.644651i \(-0.222997\pi\)
−0.176046 + 0.984382i \(0.556331\pi\)
\(242\) 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 0.960120 0.279588i \(-0.0901979\pi\)
−0.722190 + 0.691694i \(0.756865\pi\)
\(258\) 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 0.788736 0.614733i \(-0.210736\pi\)
−0.138006 + 0.990431i \(0.544069\pi\)
\(264\) −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 0.905211 0.424963i \(-0.139713\pi\)
−0.820634 + 0.571454i \(0.806379\pi\)
\(270\) 2.81728 + 11.8781i 0.171454 + 0.722877i
\(271\) 2.77815 + 1.60396i 0.168760 + 0.0974338i 0.582001 0.813188i \(-0.302270\pi\)
−0.413241 + 0.910622i \(0.635603\pi\)
\(272\) −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 −0.976782 0.214236i \(-0.931274\pi\)
0.673925 + 0.738800i \(0.264607\pi\)
\(278\) −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 −0.368819 0.929501i \(-0.620238\pi\)
0.620562 + 0.784157i \(0.286904\pi\)
\(282\) 20.3593 + 1.97915i 1.21238 + 0.117857i
\(283\) 2.81781i 0.167502i −0.996487 0.0837508i \(-0.973310\pi\)
0.996487 0.0837508i \(-0.0266900\pi\)
\(284\) 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 −0.722846 0.691010i \(-0.757166\pi\)
0.959855 + 0.280498i \(0.0904995\pi\)
\(294\) 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 \(0.100676\pi\)
−0.950398 + 0.311037i \(0.899324\pi\)
\(308\) 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 \(0.404477\pi\)
−0.295611 + 0.955308i \(0.595523\pi\)
\(314\) 10.0269 0.565853
\(315\) 0 0
\(316\) 13.0284 0.732907
\(317\) 6.73090i 0.378045i 0.981973 + 0.189022i \(0.0605319\pi\)
−0.981973 + 0.189022i \(0.939468\pi\)
\(318\) 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 0.320869 + 0.947124i \(0.396025\pi\)
−0.980668 + 0.195681i \(0.937308\pi\)
\(338\) −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 \(-0.790373\pi\)
0.790873 0.611981i \(-0.209627\pi\)
\(348\) −2.97887 6.55238i −0.159684 0.351244i
\(349\) 2.46389 1.42253i 0.131889 0.0761461i −0.432604 0.901584i \(-0.642405\pi\)
0.564493 + 0.825438i \(0.309072\pi\)
\(350\) 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 −0.755167 0.655533i \(-0.772444\pi\)
0.945291 + 0.326227i \(0.105777\pi\)
\(354\) 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 0.210796 0.977530i \(-0.432394\pi\)
−0.741168 + 0.671320i \(0.765728\pi\)
\(360\) −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 0.666528 0.745480i \(-0.267780\pi\)
−0.312341 + 0.949970i \(0.601113\pi\)
\(368\) 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 −0.979417 0.201845i \(-0.935306\pi\)
0.314905 0.949123i \(-0.398027\pi\)
\(374\) −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 0.845864 0.533398i \(-0.179085\pi\)
−0.884868 + 0.465841i \(0.845752\pi\)
\(384\) −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 0.136115 0.990693i \(-0.456538\pi\)
−0.789908 + 0.613225i \(0.789872\pi\)
\(390\) −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 −0.279862 0.960040i \(-0.590289\pi\)
−0.971350 + 0.237653i \(0.923622\pi\)
\(398\) −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 0.674196 0.738552i \(-0.264490\pi\)
0.976703 0.214595i \(-0.0688431\pi\)
\(402\) 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 \(0.0551026\pi\)
−0.985054 + 0.172247i \(0.944897\pi\)
\(410\) 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 −0.0289690 0.999580i \(-0.509222\pi\)
0.880146 0.474702i \(-0.157444\pi\)
\(420\) 0 0
\(421\) 2.84597 + 4.92936i 0.138704 + 0.240242i 0.927006 0.375046i \(-0.122373\pi\)
−0.788302 + 0.615288i \(0.789040\pi\)
\(422\) −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 −0.973787 0.227460i \(-0.926958\pi\)
−0.289908 + 0.957055i \(0.593625\pi\)
\(432\) 1.48943 4.97811i 0.0716604 0.239509i
\(433\) 23.6094i 1.13459i 0.823513 + 0.567297i \(0.192011\pi\)
−0.823513 + 0.567297i \(0.807989\pi\)
\(434\) 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 \(-0.796329\pi\)
0.802185 0.597075i \(-0.203671\pi\)
\(440\) 13.3365 0.635794
\(441\) 0 0
\(442\) 3.04212 0.144699
\(443\) 23.0300i 1.09419i −0.837071 0.547094i \(-0.815734\pi\)
0.837071 0.547094i \(-0.184266\pi\)
\(444\) −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 \(0.122443\pi\)
−0.926923 + 0.375251i \(0.877557\pi\)
\(450\) −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 0.955776 + 0.294095i \(0.0950183\pi\)
−0.223194 + 0.974774i \(0.571648\pi\)
\(462\) 0 0
\(463\) 4.55148 7.88340i 0.211525 0.366373i −0.740667 0.671873i \(-0.765490\pi\)
0.952192 + 0.305500i \(0.0988236\pi\)
\(464\) 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 0.266938 + 0.963714i \(0.413988\pi\)
−0.968069 + 0.250682i \(0.919345\pi\)
\(468\) −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 −0.807835 0.589409i \(-0.799361\pi\)
0.914361 + 0.404901i \(0.132694\pi\)
\(480\) −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 0.997794 0.0663816i \(-0.0211455\pi\)
−0.556385 + 0.830924i \(0.687812\pi\)
\(488\) 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 0.0429758 0.999076i \(-0.486316\pi\)
−0.843737 + 0.536756i \(0.819649\pi\)
\(492\) 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 0.957651 0.287931i \(-0.0929673\pi\)
−0.728181 + 0.685385i \(0.759634\pi\)
\(500\) 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 0.953163 + 0.302457i \(0.0978068\pi\)
−0.214646 + 0.976692i \(0.568860\pi\)
\(510\) −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 0.785472 0.618897i \(-0.212420\pi\)
−0.928717 + 0.370790i \(0.879087\pi\)
\(522\) 4.03726 + 11.7950i 0.176706 + 0.516254i
\(523\) 0.681439 + 0.393429i 0.0297972 + 0.0172034i 0.514825 0.857296i \(-0.327857\pi\)
−0.485027 + 0.874499i \(0.661190\pi\)
\(524\) 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 −0.919957 0.392020i \(-0.871776\pi\)
0.799478 + 0.600696i \(0.205110\pi\)
\(542\) 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 0.679489 0.733685i \(-0.262201\pi\)
−0.975135 + 0.221612i \(0.928868\pi\)
\(548\) 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 0.106584 0.994304i \(-0.466009\pi\)
0.914384 + 0.404848i \(0.132675\pi\)
\(558\) 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 \(-0.807635\pi\)
0.822882 0.568212i \(-0.192365\pi\)
\(570\) 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 −0.912796 0.408416i \(-0.866081\pi\)
−0.102699 + 0.994712i \(0.532748\pi\)
\(578\) −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 0.745343 0.666681i \(-0.232286\pi\)
−0.950034 + 0.312145i \(0.898952\pi\)
\(588\) 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 −0.910224 0.414116i \(-0.864091\pi\)
0.813747 + 0.581219i \(0.197424\pi\)
\(594\) −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 \(-0.902906\pi\)
0.953838 0.300320i \(-0.0970936\pi\)
\(600\) 0.523168 0.732039i 0.0213582 0.0298854i
\(601\) −16.2923 + 9.40634i −0.664575 + 0.383693i −0.794018 0.607894i \(-0.792014\pi\)
0.129443 + 0.991587i \(0.458681\pi\)
\(602\) 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 −0.262085 0.965045i \(-0.584410\pi\)
0.704711 + 0.709495i \(0.251077\pi\)
\(608\) 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 0.947983 0.318322i \(-0.103119\pi\)
−0.749666 + 0.661816i \(0.769786\pi\)
\(614\) 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 0.433118 0.901337i \(-0.357413\pi\)
−0.564022 + 0.825760i \(0.690747\pi\)
\(618\) −9.23943 + 4.20046i −0.371664 + 0.168967i
\(619\) 9.56902 + 5.52468i 0.384611 + 0.222055i 0.679823 0.733376i \(-0.262057\pi\)
−0.295211 + 0.955432i \(0.595390\pi\)
\(620\) 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 0.875669 0.482912i \(-0.160421\pi\)
0.0196208 + 0.999807i \(0.493754\pi\)
\(642\) −6.64513 4.74909i −0.262262 0.187432i
\(643\) −9.50955 5.49034i −0.375020 0.216518i 0.300629 0.953741i \(-0.402803\pi\)
−0.675649 + 0.737223i \(0.736137\pi\)
\(644\) 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 0.987698 + 0.156374i \(0.0499805\pi\)
−0.358425 + 0.933558i \(0.616686\pi\)
\(648\) −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 −0.828560 0.559900i \(-0.810839\pi\)
0.0706080 + 0.997504i \(0.477506\pi\)
\(654\) −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 −0.825713 0.564091i \(-0.809227\pi\)
0.0756603 + 0.997134i \(0.475894\pi\)
\(660\) −22.9912 2.23499i −0.894930 0.0869970i
\(661\) 10.5499i 0.410343i −0.978726 0.205171i \(-0.934225\pi\)
0.978726 0.205171i \(-0.0657751\pi\)
\(662\) 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 0.991488 0.130197i \(-0.0415610\pi\)
−0.608498 + 0.793555i \(0.708228\pi\)
\(674\) 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 −0.780947 0.624597i \(-0.785263\pi\)
0.150444 + 0.988619i \(0.451930\pi\)
\(684\) 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 \(-0.999025\pi\)
0.999995 0.00306340i \(-0.000975113\pi\)
\(692\) −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 \(0.0603670\pi\)
−0.982071 + 0.188514i \(0.939633\pi\)
\(702\) 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 −0.976897 0.213711i \(-0.931445\pi\)
0.673527 + 0.739162i \(0.264778\pi\)
\(720\) 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 −0.831566 0.555427i \(-0.812555\pi\)
0.0652306 + 0.997870i \(0.479222\pi\)
\(728\) 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 −0.290756 0.956797i \(-0.593907\pi\)
0.683233 + 0.730201i \(0.260574\pi\)
\(734\) 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 −0.937312 0.348492i \(-0.886694\pi\)
0.166853 0.985982i \(-0.446639\pi\)
\(740\) 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 0.989111 + 0.147173i \(0.0470176\pi\)
0.622011 + 0.783008i \(0.286316\pi\)
\(744\) −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 0.993219 + 0.116255i \(0.0370890\pi\)
−0.395930 + 0.918281i \(0.629578\pi\)
\(752\) 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 −0.924667 0.380777i \(-0.875657\pi\)
0.132571 0.991174i \(-0.457677\pi\)
\(762\) −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 0.986417 0.164262i \(-0.0525242\pi\)
0.350953 + 0.936393i \(0.385858\pi\)
\(770\) 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 0.603714 0.797201i \(-0.293687\pi\)
−0.992253 + 0.124231i \(0.960354\pi\)
\(774\) −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
\(781\) 12.8323