Properties

Label 2646.2.t.a.1979.2
Level $2646$
Weight $2$
Character 2646.1979
Analytic conductor $21.128$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
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: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1979.2
Root \(1.40917 + 1.00709i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1979
Dual form 2646.2.t.a.2285.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -2.34936 q^{5} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -2.34936 q^{5} +1.00000i q^{8} +(2.03460 - 1.17468i) q^{10} -5.67667i q^{11} +(-1.48943 + 0.859925i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(0.884414 + 1.53185i) q^{17} +(-0.986680 - 0.569660i) q^{19} +(-1.17468 + 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} +3.67509i q^{23} +0.519482 q^{25} +(0.859925 - 1.48943i) q^{26} +(-3.59886 - 2.07781i) q^{29} +(-7.24879 - 4.18509i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.53185 - 0.884414i) q^{34} +(4.59886 - 7.96547i) q^{37} +1.13932 q^{38} -2.34936i q^{40} +(3.99709 + 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +(-4.91614 - 2.83834i) q^{44} +(-1.83755 - 3.18272i) q^{46} +(5.90494 + 10.2277i) q^{47} +(-0.449885 + 0.259741i) q^{50} +1.71985i q^{52} +13.3365i q^{55} +4.15561 q^{58} +(1.11483 - 1.93094i) q^{59} +(7.79396 - 4.49985i) q^{61} +8.37019 q^{62} -1.00000 q^{64} +(3.49921 - 2.02027i) q^{65} +(-5.43562 + 9.41477i) q^{67} +1.76883 q^{68} -4.52106i q^{71} +(-4.62660 + 2.67117i) q^{73} +9.19773i q^{74} +(-0.986680 + 0.569660i) q^{76} +(6.51422 + 11.2830i) q^{79} +(1.17468 + 2.03460i) q^{80} +(-6.92317 - 3.99709i) q^{82} +(-6.27298 + 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +3.52106i q^{86} +5.67667 q^{88} +(0.580529 - 1.00551i) q^{89} +(3.18272 + 1.83755i) q^{92} +(-10.2277 - 5.90494i) q^{94} +(2.31806 + 1.33834i) q^{95} +(3.97536 + 2.29517i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + O(q^{10}) \) \( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −2.34936 −1.05066 −0.525332 0.850897i \(-0.676059\pi\)
−0.525332 + 0.850897i \(0.676059\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.03460 1.17468i 0.643398 0.371466i
\(11\) 5.67667i 1.71158i −0.517323 0.855790i \(-0.673071\pi\)
0.517323 0.855790i \(-0.326929\pi\)
\(12\) 0 0
\(13\) −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
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.884414 + 1.53185i 0.214502 + 0.371528i 0.953118 0.302598i \(-0.0978538\pi\)
−0.738616 + 0.674126i \(0.764520\pi\)
\(18\) 0 0
\(19\) −0.986680 0.569660i −0.226360 0.130689i 0.382532 0.923942i \(-0.375052\pi\)
−0.608892 + 0.793253i \(0.708386\pi\)
\(20\) −1.17468 + 2.03460i −0.262666 + 0.454951i
\(21\) 0 0
\(22\) 2.83834 + 4.91614i 0.605135 + 1.04812i
\(23\) 3.67509i 0.766310i 0.923684 + 0.383155i \(0.125162\pi\)
−0.923684 + 0.383155i \(0.874838\pi\)
\(24\) 0 0
\(25\) 0.519482 0.103896
\(26\) 0.859925 1.48943i 0.168645 0.292102i
\(27\) 0 0
\(28\) 0 0
\(29\) −3.59886 2.07781i −0.668292 0.385839i 0.127137 0.991885i \(-0.459421\pi\)
−0.795429 + 0.606046i \(0.792755\pi\)
\(30\) 0 0
\(31\) −7.24879 4.18509i −1.30192 0.751665i −0.321188 0.947015i \(-0.604082\pi\)
−0.980734 + 0.195350i \(0.937416\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −1.53185 0.884414i −0.262710 0.151676i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.59886 7.96547i 0.756049 1.30951i −0.188803 0.982015i \(-0.560461\pi\)
0.944851 0.327500i \(-0.106206\pi\)
\(38\) 1.13932 0.184822
\(39\) 0 0
\(40\) 2.34936i 0.371466i
\(41\) 3.99709 + 6.92317i 0.624241 + 1.08122i 0.988687 + 0.149993i \(0.0479251\pi\)
−0.364446 + 0.931225i \(0.618742\pi\)
\(42\) 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
\(45\) 0 0
\(46\) −1.83755 3.18272i −0.270931 0.469267i
\(47\) 5.90494 + 10.2277i 0.861324 + 1.49186i 0.870651 + 0.491901i \(0.163698\pi\)
−0.00932669 + 0.999957i \(0.502969\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.449885 + 0.259741i −0.0636233 + 0.0367329i
\(51\) 0 0
\(52\) 1.71985i 0.238500i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0 0
\(55\) 13.3365i 1.79830i
\(56\) 0 0
\(57\) 0 0
\(58\) 4.15561 0.545658
\(59\) 1.11483 1.93094i 0.145139 0.251387i −0.784286 0.620399i \(-0.786971\pi\)
0.929425 + 0.369012i \(0.120304\pi\)
\(60\) 0 0
\(61\) 7.79396 4.49985i 0.997915 0.576146i 0.0902842 0.995916i \(-0.471222\pi\)
0.907631 + 0.419770i \(0.137889\pi\)
\(62\) 8.37019 1.06301
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.49921 2.02027i 0.434024 0.250584i
\(66\) 0 0
\(67\) −5.43562 + 9.41477i −0.664067 + 1.15020i 0.315470 + 0.948935i \(0.397838\pi\)
−0.979537 + 0.201262i \(0.935496\pi\)
\(68\) 1.76883 0.214502
\(69\) 0 0
\(70\) 0 0
\(71\) 4.52106i 0.536551i −0.963342 0.268276i \(-0.913546\pi\)
0.963342 0.268276i \(-0.0864538\pi\)
\(72\) 0 0
\(73\) −4.62660 + 2.67117i −0.541503 + 0.312637i −0.745688 0.666295i \(-0.767879\pi\)
0.204185 + 0.978932i \(0.434546\pi\)
\(74\) 9.19773i 1.06921i
\(75\) 0 0
\(76\) −0.986680 + 0.569660i −0.113180 + 0.0653445i
\(77\) 0 0
\(78\) 0 0
\(79\) 6.51422 + 11.2830i 0.732907 + 1.26943i 0.955636 + 0.294551i \(0.0951701\pi\)
−0.222729 + 0.974880i \(0.571497\pi\)
\(80\) 1.17468 + 2.03460i 0.131333 + 0.227476i
\(81\) 0 0
\(82\) −6.92317 3.99709i −0.764536 0.441405i
\(83\) −6.27298 + 10.8651i −0.688549 + 1.19260i 0.283758 + 0.958896i \(0.408419\pi\)
−0.972307 + 0.233707i \(0.924915\pi\)
\(84\) 0 0
\(85\) −2.07781 3.59886i −0.225370 0.390352i
\(86\) 3.52106i 0.379686i
\(87\) 0 0
\(88\) 5.67667 0.605135
\(89\) 0.580529 1.00551i 0.0615360 0.106583i −0.833616 0.552344i \(-0.813733\pi\)
0.895152 + 0.445761i \(0.147067\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.18272 + 1.83755i 0.331822 + 0.191577i
\(93\) 0 0
\(94\) −10.2277 5.90494i −1.05490 0.609048i
\(95\) 2.31806 + 1.33834i 0.237828 + 0.137310i
\(96\) 0 0
\(97\) 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
\(99\) 0 0
\(100\) 0.259741 0.449885i 0.0259741 0.0449885i
\(101\) −6.62310 −0.659023 −0.329511 0.944152i \(-0.606884\pi\)
−0.329511 + 0.944152i \(0.606884\pi\)
\(102\) 0 0
\(103\) 5.85977i 0.577381i 0.957423 + 0.288690i \(0.0932198\pi\)
−0.957423 + 0.288690i \(0.906780\pi\)
\(104\) −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 \(0.739865\pi\)
\(108\) 0 0
\(109\) −2.11835 3.66908i −0.202901 0.351435i 0.746561 0.665317i \(-0.231704\pi\)
−0.949462 + 0.313882i \(0.898370\pi\)
\(110\) −6.66826 11.5498i −0.635794 1.10123i
\(111\) 0 0
\(112\) 0 0
\(113\) −5.91693 + 3.41614i −0.556618 + 0.321363i −0.751787 0.659406i \(-0.770808\pi\)
0.195169 + 0.980770i \(0.437474\pi\)
\(114\) 0 0
\(115\) 8.63411i 0.805135i
\(116\) −3.59886 + 2.07781i −0.334146 + 0.192919i
\(117\) 0 0
\(118\) 2.22966i 0.205257i
\(119\) 0 0
\(120\) 0 0
\(121\) −21.2246 −1.92951
\(122\) −4.49985 + 7.79396i −0.407397 + 0.705632i
\(123\) 0 0
\(124\) −7.24879 + 4.18509i −0.650961 + 0.375832i
\(125\) 10.5263 0.941504
\(126\) 0 0
\(127\) −6.67667 −0.592459 −0.296229 0.955117i \(-0.595729\pi\)
−0.296229 + 0.955117i \(0.595729\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −2.02027 + 3.49921i −0.177189 + 0.306901i
\(131\) −7.47305 −0.652923 −0.326462 0.945210i \(-0.605856\pi\)
−0.326462 + 0.945210i \(0.605856\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 10.8712i 0.939133i
\(135\) 0 0
\(136\) −1.53185 + 0.884414i −0.131355 + 0.0758379i
\(137\) 7.98789i 0.682452i 0.939981 + 0.341226i \(0.110842\pi\)
−0.939981 + 0.341226i \(0.889158\pi\)
\(138\) 0 0
\(139\) −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
\(141\) 0 0
\(142\) 2.26053 + 3.91535i 0.189699 + 0.328569i
\(143\) 4.88151 + 8.45502i 0.408212 + 0.707044i
\(144\) 0 0
\(145\) 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
\(149\) 1.19773i 0.0981218i 0.998796 + 0.0490609i \(0.0156228\pi\)
−0.998796 + 0.0490609i \(0.984377\pi\)
\(150\) 0 0
\(151\) 15.2246 1.23896 0.619480 0.785013i \(-0.287344\pi\)
0.619480 + 0.785013i \(0.287344\pi\)
\(152\) 0.569660 0.986680i 0.0462055 0.0800303i
\(153\) 0 0
\(154\) 0 0
\(155\) 17.0300 + 9.83228i 1.36788 + 0.789748i
\(156\) 0 0
\(157\) 8.68358 + 5.01347i 0.693025 + 0.400118i 0.804744 0.593621i \(-0.202302\pi\)
−0.111719 + 0.993740i \(0.535636\pi\)
\(158\) −11.2830 6.51422i −0.897624 0.518243i
\(159\) 0 0
\(160\) −2.03460 1.17468i −0.160850 0.0928665i
\(161\) 0 0
\(162\) 0 0
\(163\) −6.00158 + 10.3950i −0.470080 + 0.814202i −0.999415 0.0342109i \(-0.989108\pi\)
0.529335 + 0.848413i \(0.322442\pi\)
\(164\) 7.99419 0.624241
\(165\) 0 0
\(166\) 12.5460i 0.973756i
\(167\) 8.57472 + 14.8518i 0.663532 + 1.14927i 0.979681 + 0.200561i \(0.0642765\pi\)
−0.316150 + 0.948709i \(0.602390\pi\)
\(168\) 0 0
\(169\) −5.02106 + 8.69673i −0.386235 + 0.668979i
\(170\) 3.59886 + 2.07781i 0.276020 + 0.159360i
\(171\) 0 0
\(172\) −1.76053 3.04933i −0.134239 0.232509i
\(173\) 0.993738 + 1.72121i 0.0755525 + 0.130861i 0.901326 0.433140i \(-0.142595\pi\)
−0.825774 + 0.564001i \(0.809261\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.91614 + 2.83834i −0.370568 + 0.213948i
\(177\) 0 0
\(178\) 1.16106i 0.0870250i
\(179\) 7.19773 4.15561i 0.537984 0.310605i −0.206278 0.978493i \(-0.566135\pi\)
0.744261 + 0.667889i \(0.232802\pi\)
\(180\) 0 0
\(181\) 15.4541i 1.14870i 0.818611 + 0.574348i \(0.194744\pi\)
−0.818611 + 0.574348i \(0.805256\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.67509 −0.270931
\(185\) −10.8044 + 18.7137i −0.794354 + 1.37586i
\(186\) 0 0
\(187\) 8.69581 5.02053i 0.635901 0.367137i
\(188\) 11.8099 0.861324
\(189\) 0 0
\(190\) −2.67667 −0.194186
\(191\) 10.6851 6.16904i 0.773146 0.446376i −0.0608498 0.998147i \(-0.519381\pi\)
0.833996 + 0.551771i \(0.186048\pi\)
\(192\) 0 0
\(193\) −2.19694 + 3.80521i −0.158139 + 0.273905i −0.934198 0.356756i \(-0.883883\pi\)
0.776058 + 0.630661i \(0.217216\pi\)
\(194\) −4.59035 −0.329568
\(195\) 0 0
\(196\) 0 0
\(197\) 10.8865i 0.775632i 0.921737 + 0.387816i \(0.126770\pi\)
−0.921737 + 0.387816i \(0.873230\pi\)
\(198\) 0 0
\(199\) −23.8733 + 13.7832i −1.69233 + 0.977068i −0.739703 + 0.672933i \(0.765034\pi\)
−0.952629 + 0.304135i \(0.901633\pi\)
\(200\) 0.519482i 0.0367329i
\(201\) 0 0
\(202\) 5.73577 3.31155i 0.403567 0.233000i
\(203\) 0 0
\(204\) 0 0
\(205\) −9.39060 16.2650i −0.655868 1.13600i
\(206\) −2.92989 5.07471i −0.204135 0.353572i
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) 4.71563 0.322354
\(215\) −4.13611 + 7.16396i −0.282081 + 0.488578i
\(216\) 0 0
\(217\) 0 0
\(218\) 3.66908 + 2.11835i 0.248502 + 0.143473i
\(219\) 0 0
\(220\) 11.5498 + 6.66826i 0.778686 + 0.449574i
\(221\) −2.63455 1.52106i −0.177219 0.102318i
\(222\) 0 0
\(223\) 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
\(225\) 0 0
\(226\) 3.41614 5.91693i 0.227238 0.393588i
\(227\) −12.7560 −0.846645 −0.423323 0.905979i \(-0.639136\pi\)
−0.423323 + 0.905979i \(0.639136\pi\)
\(228\) 0 0
\(229\) 4.49418i 0.296984i −0.988914 0.148492i \(-0.952558\pi\)
0.988914 0.148492i \(-0.0474419\pi\)
\(230\) 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 \(0.689145\pi\)
\(234\) 0 0
\(235\) −13.8728 24.0284i −0.904963 1.56744i
\(236\) −1.11483 1.93094i −0.0725693 0.125694i
\(237\) 0 0
\(238\) 0 0
\(239\) 8.78317 5.07096i 0.568136 0.328013i −0.188269 0.982118i \(-0.560288\pi\)
0.756404 + 0.654104i \(0.226954\pi\)
\(240\) 0 0
\(241\) 10.5481i 0.679461i 0.940523 + 0.339731i \(0.110336\pi\)
−0.940523 + 0.339731i \(0.889664\pi\)
\(242\) 18.3810 10.6123i 1.18158 0.682184i
\(243\) 0 0
\(244\) 8.99970i 0.576146i
\(245\) 0 0
\(246\) 0 0
\(247\) 1.95946 0.124677
\(248\) 4.18509 7.24879i 0.265754 0.460299i
\(249\) 0 0
\(250\) −9.11608 + 5.26317i −0.576551 + 0.332872i
\(251\) −29.3005 −1.84943 −0.924714 0.380662i \(-0.875696\pi\)
−0.924714 + 0.380662i \(0.875696\pi\)
\(252\) 0 0
\(253\) 20.8623 1.31160
\(254\) 5.78217 3.33834i 0.362805 0.209466i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.62860 0.475859 0.237930 0.971282i \(-0.423531\pi\)
0.237930 + 0.971282i \(0.423531\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4.04054i 0.250584i
\(261\) 0 0
\(262\) 6.47185 3.73653i 0.399832 0.230843i
\(263\) 12.1856i 0.751398i −0.926742 0.375699i \(-0.877403\pi\)
0.926742 0.375699i \(-0.122597\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 5.43562 + 9.41477i 0.332034 + 0.575099i
\(269\) −1.38717 2.40264i −0.0845771 0.146492i 0.820634 0.571454i \(-0.193621\pi\)
−0.905211 + 0.424963i \(0.860287\pi\)
\(270\) 0 0
\(271\) −2.77815 1.60396i −0.168760 0.0974338i 0.413241 0.910622i \(-0.364397\pi\)
−0.582001 + 0.813188i \(0.697730\pi\)
\(272\) 0.884414 1.53185i 0.0536255 0.0928821i
\(273\) 0 0
\(274\) −3.99395 6.91772i −0.241283 0.417915i
\(275\) 2.94893i 0.177827i
\(276\) 0 0
\(277\) 10.0811 0.605714 0.302857 0.953036i \(-0.402060\pi\)
0.302857 + 0.953036i \(0.402060\pi\)
\(278\) 10.3803 17.9792i 0.622569 1.07832i
\(279\) 0 0
\(280\) 0 0
\(281\) −4.21999 2.43641i −0.251743 0.145344i 0.368819 0.929501i \(-0.379762\pi\)
−0.620562 + 0.784157i \(0.713096\pi\)
\(282\) 0 0
\(283\) −2.44030 1.40891i −0.145061 0.0837508i 0.425713 0.904858i \(-0.360023\pi\)
−0.570774 + 0.821107i \(0.693357\pi\)
\(284\) −3.91535 2.26053i −0.232333 0.134138i
\(285\) 0 0
\(286\) −8.45502 4.88151i −0.499956 0.288650i
\(287\) 0 0
\(288\) 0 0
\(289\) 6.93562 12.0129i 0.407978 0.706638i
\(290\) −9.76302 −0.573304
\(291\) 0 0
\(292\) 5.34234i 0.312637i
\(293\) −4.05694 7.02683i −0.237009 0.410512i 0.722846 0.691010i \(-0.242834\pi\)
−0.959855 + 0.280498i \(0.909500\pi\)
\(294\) 0 0
\(295\) −2.61914 + 4.53648i −0.152492 + 0.264124i
\(296\) 7.96547 + 4.59886i 0.462983 + 0.267304i
\(297\) 0 0
\(298\) −0.598865 1.03726i −0.0346913 0.0600871i
\(299\) −3.16030 5.47381i −0.182765 0.316558i
\(300\) 0 0
\(301\) 0 0
\(302\) −13.1849 + 7.61229i −0.758705 + 0.438038i
\(303\) 0 0
\(304\) 1.13932i 0.0653445i
\(305\) −18.3108 + 10.5718i −1.04847 + 0.605337i
\(306\) 0 0
\(307\) 10.8996i 0.622074i −0.950398 0.311037i \(-0.899324\pi\)
0.950398 0.311037i \(-0.100676\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −19.6646 −1.11687
\(311\) 4.11819 7.13291i 0.233521 0.404470i −0.725321 0.688411i \(-0.758309\pi\)
0.958842 + 0.283941i \(0.0916419\pi\)
\(312\) 0 0
\(313\) −29.2736 + 16.9011i −1.65464 + 0.955308i −0.679516 + 0.733661i \(0.737810\pi\)
−0.975127 + 0.221648i \(0.928857\pi\)
\(314\) −10.0269 −0.565853
\(315\) 0 0
\(316\) 13.0284 0.732907
\(317\) 5.82913 3.36545i 0.327396 0.189022i −0.327288 0.944925i \(-0.606135\pi\)
0.654685 + 0.755902i \(0.272801\pi\)
\(318\) 0 0
\(319\) −11.7950 + 20.4296i −0.660394 + 1.14384i
\(320\) 2.34936 0.131333
\(321\) 0 0
\(322\) 0 0
\(323\) 2.01526i 0.112132i
\(324\) 0 0
\(325\) −0.773734 + 0.446715i −0.0429190 + 0.0247793i
\(326\) 12.0032i 0.664793i
\(327\) 0 0
\(328\) −6.92317 + 3.99709i −0.382268 + 0.220703i
\(329\) 0 0
\(330\) 0 0
\(331\) 16.0284 + 27.7621i 0.881002 + 1.52594i 0.850228 + 0.526415i \(0.176464\pi\)
0.0307744 + 0.999526i \(0.490203\pi\)
\(332\) 6.27298 + 10.8651i 0.344275 + 0.596301i
\(333\) 0 0
\(334\) −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 \(-0.396025\pi\)
\(338\) 10.0421i 0.546219i
\(339\) 0 0
\(340\) −4.15561 −0.225370
\(341\) −23.7574 + 41.1490i −1.28654 + 2.22834i
\(342\) 0 0
\(343\) 0 0
\(344\) 3.04933 + 1.76053i 0.164409 + 0.0949214i
\(345\) 0 0
\(346\) −1.72121 0.993738i −0.0925326 0.0534237i
\(347\) 19.7453 + 11.3999i 1.05998 + 0.611981i 0.925427 0.378926i \(-0.123706\pi\)
0.134554 + 0.990906i \(0.457040\pi\)
\(348\) 0 0
\(349\) 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
\(351\) 0 0
\(352\) 2.83834 4.91614i 0.151284 0.262031i
\(353\) 7.14424 0.380249 0.190125 0.981760i \(-0.439111\pi\)
0.190125 + 0.981760i \(0.439111\pi\)
\(354\) 0 0
\(355\) 10.6216i 0.563735i
\(356\) −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 \(0.765728\pi\)
\(360\) 0 0
\(361\) −8.85097 15.3303i −0.465841 0.806860i
\(362\) −7.72706 13.3837i −0.406125 0.703429i
\(363\) 0 0
\(364\) 0 0
\(365\) 10.8695 6.27554i 0.568938 0.328477i
\(366\) 0 0
\(367\) 7.83493i 0.408980i 0.978869 + 0.204490i \(0.0655536\pi\)
−0.978869 + 0.204490i \(0.934446\pi\)
\(368\) 3.18272 1.83755i 0.165911 0.0957887i
\(369\) 0 0
\(370\) 21.6088i 1.12339i
\(371\) 0 0
\(372\) 0 0
\(373\) 25.6677 1.32902 0.664512 0.747278i \(-0.268639\pi\)
0.664512 + 0.747278i \(0.268639\pi\)
\(374\) −5.02053 + 8.69581i −0.259605 + 0.449650i
\(375\) 0 0
\(376\) −10.2277 + 5.90494i −0.527451 + 0.304524i
\(377\) 7.14702 0.368091
\(378\) 0 0
\(379\) −15.1045 −0.775868 −0.387934 0.921687i \(-0.626811\pi\)
−0.387934 + 0.921687i \(0.626811\pi\)
\(380\) 2.31806 1.33834i 0.118914 0.0686551i
\(381\) 0 0
\(382\) −6.16904 + 10.6851i −0.315636 + 0.546697i
\(383\) −1.52664 −0.0780079 −0.0390040 0.999239i \(-0.512418\pi\)
−0.0390040 + 0.999239i \(0.512418\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4.39388i 0.223643i
\(387\) 0 0
\(388\) 3.97536 2.29517i 0.201818 0.116520i
\(389\) 14.8897i 0.754936i 0.926023 + 0.377468i \(0.123205\pi\)
−0.926023 + 0.377468i \(0.876795\pi\)
\(390\) 0 0
\(391\) −5.62969 + 3.25030i −0.284706 + 0.164375i
\(392\) 0 0
\(393\) 0 0
\(394\) −5.44325 9.42799i −0.274227 0.474975i
\(395\) −15.3042 26.5077i −0.770039 1.33375i
\(396\) 0 0
\(397\) 24.9302 + 14.3935i 1.25121 + 0.722388i 0.971350 0.237653i \(-0.0763780\pi\)
0.279862 + 0.960040i \(0.409711\pi\)
\(398\) 13.7832 23.8733i 0.690892 1.19666i
\(399\) 0 0
\(400\) −0.259741 0.449885i −0.0129871 0.0224942i
\(401\) 38.1735i 1.90629i 0.302507 + 0.953147i \(0.402176\pi\)
−0.302507 + 0.953147i \(0.597824\pi\)
\(402\) 0 0
\(403\) 14.3955 0.717089
\(404\) −3.31155 + 5.73577i −0.164756 + 0.285365i
\(405\) 0 0
\(406\) 0 0
\(407\) −45.2173 26.1062i −2.24134 1.29404i
\(408\) 0 0
\(409\) 6.03355 + 3.48347i 0.298340 + 0.172247i 0.641697 0.766958i \(-0.278231\pi\)
−0.343357 + 0.939205i \(0.611564\pi\)
\(410\) 16.2650 + 9.39060i 0.803271 + 0.463769i
\(411\) 0 0
\(412\) 5.07471 + 2.92989i 0.250013 + 0.144345i
\(413\) 0 0
\(414\) 0 0
\(415\) 14.7375 25.5261i 0.723435 1.25303i
\(416\) −1.71985 −0.0843225
\(417\) 0 0
\(418\) 6.46754i 0.316338i
\(419\) −17.4232 30.1778i −0.851177 1.47428i −0.880146 0.474702i \(-0.842556\pi\)
0.0289690 0.999580i \(-0.490778\pi\)
\(420\) 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
\(423\) 0 0
\(424\) 0 0
\(425\) 0.459437 + 0.795769i 0.0222860 + 0.0386005i
\(426\) 0 0
\(427\) 0 0
\(428\) −4.08386 + 2.35782i −0.197401 + 0.113969i
\(429\) 0 0
\(430\) 8.27223i 0.398922i
\(431\) −26.2350 + 15.1468i −1.26370 + 0.729595i −0.973787 0.227460i \(-0.926958\pi\)
−0.289908 + 0.957055i \(0.593625\pi\)
\(432\) 0 0
\(433\) 23.6094i 1.13459i −0.823513 0.567297i \(-0.807989\pi\)
0.823513 0.567297i \(-0.192011\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.23669 −0.202901
\(437\) 2.09355 3.62614i 0.100148 0.173462i
\(438\) 0 0
\(439\) 21.6681 12.5101i 1.03416 0.597075i 0.115989 0.993250i \(-0.462996\pi\)
0.918175 + 0.396175i \(0.129663\pi\)
\(440\) −13.3365 −0.635794
\(441\) 0 0
\(442\) 3.04212 0.144699
\(443\) −19.9446 + 11.5150i −0.947595 + 0.547094i −0.892333 0.451377i \(-0.850933\pi\)
−0.0552622 + 0.998472i \(0.517599\pi\)
\(444\) 0 0
\(445\) −1.36387 + 2.36229i −0.0646537 + 0.111983i
\(446\) −7.20913 −0.341362
\(447\) 0 0
\(448\) 0 0
\(449\) 15.9028i 0.750501i 0.926923 + 0.375251i \(0.122443\pi\)
−0.926923 + 0.375251i \(0.877557\pi\)
\(450\) 0 0
\(451\) 39.3006 22.6902i 1.85059 1.06844i
\(452\) 6.83228i 0.321363i
\(453\) 0 0
\(454\) 11.0470 6.37800i 0.518462 0.299334i
\(455\) 0 0
\(456\) 0 0
\(457\) 2.83307 + 4.90702i 0.132525 + 0.229541i 0.924649 0.380819i \(-0.124358\pi\)
−0.792124 + 0.610360i \(0.791025\pi\)
\(458\) 2.24709 + 3.89208i 0.105000 + 0.181865i
\(459\) 0 0
\(460\) −7.47736 4.31705i −0.348634 0.201284i
\(461\) −15.7292 + 27.2438i −0.732582 + 1.26887i 0.223194 + 0.974774i \(0.428352\pi\)
−0.955776 + 0.294095i \(0.904982\pi\)
\(462\) 0 0
\(463\) 4.55148 + 7.88340i 0.211525 + 0.366373i 0.952192 0.305500i \(-0.0988236\pi\)
−0.740667 + 0.671873i \(0.765490\pi\)
\(464\) 4.15561i 0.192919i
\(465\) 0 0
\(466\) 2.15403 0.0997837
\(467\) 15.1516 26.2433i 0.701132 1.21440i −0.266938 0.963714i \(-0.586012\pi\)
0.968069 0.250682i \(-0.0806549\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 24.0284 + 13.8728i 1.10835 + 0.639906i
\(471\) 0 0
\(472\) 1.93094 + 1.11483i 0.0888788 + 0.0513142i
\(473\) −17.3100 9.99395i −0.795916 0.459522i
\(474\) 0 0
\(475\) −0.512563 0.295928i −0.0235180 0.0135781i
\(476\) 0 0
\(477\) 0 0
\(478\) −5.07096 + 8.78317i −0.231940 + 0.401733i
\(479\) 4.66286 0.213052 0.106526 0.994310i \(-0.466027\pi\)
0.106526 + 0.994310i \(0.466027\pi\)
\(480\) 0 0
\(481\) 15.8187i 0.721271i
\(482\) −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
\(486\) 0 0
\(487\) 9.74105 + 16.8720i 0.441409 + 0.764543i 0.997794 0.0663816i \(-0.0211455\pi\)
−0.556385 + 0.830924i \(0.687812\pi\)
\(488\) 4.49985 + 7.79396i 0.203699 + 0.352816i
\(489\) 0 0
\(490\) 0 0
\(491\) 17.7437 10.2443i 0.800762 0.462320i −0.0429758 0.999076i \(-0.513684\pi\)
0.843737 + 0.536756i \(0.180351\pi\)
\(492\) 0 0
\(493\) 7.35056i 0.331053i
\(494\) −1.69694 + 0.979729i −0.0763490 + 0.0440801i
\(495\) 0 0
\(496\) 8.37019i 0.375832i
\(497\) 0 0
\(498\) 0 0
\(499\) −10.2520 −0.458941 −0.229470 0.973316i \(-0.573699\pi\)
−0.229470 + 0.973316i \(0.573699\pi\)
\(500\) 5.26317 9.11608i 0.235376 0.407683i
\(501\) 0 0
\(502\) 25.3749 14.6502i 1.13254 0.653872i
\(503\) −14.5521 −0.648845 −0.324422 0.945912i \(-0.605170\pi\)
−0.324422 + 0.945912i \(0.605170\pi\)
\(504\) 0 0
\(505\) 15.5600 0.692412
\(506\) −18.0673 + 10.4311i −0.803188 + 0.463721i
\(507\) 0 0
\(508\) −3.33834 + 5.78217i −0.148115 + 0.256542i
\(509\) 33.3234 1.47703 0.738517 0.674235i \(-0.235527\pi\)
0.738517 + 0.674235i \(0.235527\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.60656 + 3.81430i −0.291403 + 0.168242i
\(515\) 13.7667i 0.606634i
\(516\) 0 0
\(517\) 58.0591 33.5204i 2.55343 1.47423i
\(518\) 0 0
\(519\) 0 0
\(520\) 2.02027 + 3.49921i 0.0885947 + 0.153451i
\(521\) 3.26963 + 5.66316i 0.143245 + 0.248108i 0.928717 0.370790i \(-0.120913\pi\)
−0.785472 + 0.618897i \(0.787580\pi\)
\(522\) 0 0
\(523\) −0.681439 0.393429i −0.0297972 0.0172034i 0.485027 0.874499i \(-0.338810\pi\)
−0.514825 + 0.857296i \(0.672143\pi\)
\(524\) −3.73653 + 6.47185i −0.163231 + 0.282724i
\(525\) 0 0
\(526\) 6.09281 + 10.5531i 0.265659 + 0.460135i
\(527\) 14.8054i 0.644934i
\(528\) 0 0
\(529\) 9.49369 0.412769
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −11.9068 6.87440i −0.515741 0.297763i
\(534\) 0 0
\(535\) 9.59445 + 5.53936i 0.414804 + 0.239487i
\(536\) −9.41477 5.43562i −0.406656 0.234783i
\(537\) 0 0
\(538\) 2.40264 + 1.38717i 0.103585 + 0.0598050i
\(539\) 0 0
\(540\) 0 0
\(541\) −2.80227 + 4.85367i −0.120479 + 0.208676i −0.919957 0.392020i \(-0.871776\pi\)
0.799478 + 0.600696i \(0.205110\pi\)
\(542\) 3.20793 0.137792
\(543\) 0 0
\(544\) 1.76883i 0.0758379i
\(545\) 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
\(549\) 0 0
\(550\) 1.47446 + 2.55385i 0.0628714 + 0.108896i
\(551\) 2.36729 + 4.10026i 0.100850 + 0.174677i
\(552\) 0 0
\(553\) 0 0
\(554\) −8.73047 + 5.04054i −0.370922 + 0.214152i
\(555\) 0 0
\(556\) 20.7606i 0.880446i
\(557\) 24.0957 13.9117i 1.02097 0.589456i 0.106584 0.994304i \(-0.466009\pi\)
0.914384 + 0.404848i \(0.132675\pi\)
\(558\) 0 0
\(559\) 6.05569i 0.256128i
\(560\) 0 0
\(561\) 0 0
\(562\) 4.87282 0.205548
\(563\) 12.2650 21.2436i 0.516909 0.895312i −0.482898 0.875676i \(-0.660416\pi\)
0.999807 0.0196359i \(-0.00625069\pi\)
\(564\) 0 0
\(565\) 13.9010 8.02574i 0.584819 0.337645i
\(566\) 2.81781 0.118441
\(567\) 0 0
\(568\) 4.52106 0.189699
\(569\) −23.4762 + 13.5540i −0.984172 + 0.568212i −0.903527 0.428531i \(-0.859031\pi\)
−0.0806449 + 0.996743i \(0.525698\pi\)
\(570\) 0 0
\(571\) 14.9177 25.8382i 0.624287 1.08130i −0.364391 0.931246i \(-0.618723\pi\)
0.988678 0.150051i \(-0.0479438\pi\)
\(572\) 9.76302 0.408212
\(573\) 0 0
\(574\) 0 0
\(575\) 1.90915i 0.0796169i
\(576\) 0 0
\(577\) 24.3930 14.0833i 1.01549 0.586296i 0.102699 0.994712i \(-0.467252\pi\)
0.912796 + 0.408416i \(0.133919\pi\)
\(578\) 13.8712i 0.576968i
\(579\) 0 0
\(580\) 8.45502 4.88151i 0.351076 0.202694i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −2.67117 4.62660i −0.110534 0.191450i
\(585\) 0 0
\(586\) 7.02683 + 4.05694i 0.290276 + 0.167591i
\(587\) 4.95928 8.58973i 0.204692 0.354536i −0.745343 0.666681i \(-0.767714\pi\)
0.950034 + 0.312145i \(0.101048\pi\)
\(588\) 0 0
\(589\) 4.76816 + 8.25870i 0.196469 + 0.340294i
\(590\) 5.23827i 0.215656i
\(591\) 0 0
\(592\) −9.19773 −0.378024
\(593\) 2.34936 4.06921i 0.0964766 0.167102i −0.813747 0.581219i \(-0.802576\pi\)
0.910224 + 0.414116i \(0.135909\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.03726 + 0.598865i 0.0424880 + 0.0245305i
\(597\) 0 0
\(598\) 5.47381 + 3.16030i 0.223841 + 0.129234i
\(599\) 12.7309 + 7.35019i 0.520170 + 0.300320i 0.737004 0.675888i \(-0.236240\pi\)
−0.216834 + 0.976208i \(0.569573\pi\)
\(600\) 0 0
\(601\) −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
\(603\) 0 0
\(604\) 7.61229 13.1849i 0.309740 0.536485i
\(605\) 49.8641 2.02727
\(606\) 0 0
\(607\) 12.5922i 0.511100i −0.966796 0.255550i \(-0.917743\pi\)
0.966796 0.255550i \(-0.0822565\pi\)
\(608\) −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
\(612\) 0 0
\(613\) 4.91009 + 8.50452i 0.198317 + 0.343494i 0.947983 0.318322i \(-0.103119\pi\)
−0.749666 + 0.661816i \(0.769786\pi\)
\(614\) 5.44981 + 9.43935i 0.219937 + 0.380941i
\(615\) 0 0
\(616\) 0 0
\(617\) 3.25158 1.87730i 0.130904 0.0755772i −0.433118 0.901337i \(-0.642587\pi\)
0.564022 + 0.825760i \(0.309253\pi\)
\(618\) 0 0
\(619\) 11.0494i 0.444111i 0.975034 + 0.222055i \(0.0712766\pi\)
−0.975034 + 0.222055i \(0.928723\pi\)
\(620\) 17.0300 9.83228i 0.683942 0.394874i
\(621\) 0 0
\(622\) 8.23637i 0.330248i
\(623\) 0 0
\(624\) 0 0
\(625\) −27.3275 −1.09310
\(626\) 16.9011 29.2736i 0.675505 1.17001i
\(627\) 0 0
\(628\) 8.68358 5.01347i 0.346513 0.200059i
\(629\) 16.2692 0.648696
\(630\) 0 0
\(631\) 19.4921 0.775969 0.387984 0.921666i \(-0.373171\pi\)
0.387984 + 0.921666i \(0.373171\pi\)
\(632\) −11.2830 + 6.51422i −0.448812 + 0.259122i
\(633\) 0 0
\(634\) −3.36545 + 5.82913i −0.133659 + 0.231504i
\(635\) 15.6859 0.622475
\(636\) 0 0
\(637\) 0 0
\(638\) 23.5900i 0.933938i
\(639\) 0 0
\(640\) −2.03460 + 1.17468i −0.0804248 + 0.0464333i
\(641\) 26.1735i 1.03379i −0.856048 0.516896i \(-0.827087\pi\)
0.856048 0.516896i \(-0.172913\pi\)
\(642\) 0 0
\(643\) −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
\(645\) 0 0
\(646\) 1.00763 + 1.74527i 0.0396447 + 0.0686666i
\(647\) −16.0063 27.7237i −0.629273 1.08993i −0.987698 0.156374i \(-0.950019\pi\)
0.358425 0.933558i \(-0.383314\pi\)
\(648\) 0 0
\(649\) −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
\(653\) 22.3649i 0.875208i −0.899168 0.437604i \(-0.855827\pi\)
0.899168 0.437604i \(-0.144173\pi\)
\(654\) 0 0
\(655\) 17.5569 0.686004
\(656\) 3.99709 6.92317i 0.156060 0.270304i
\(657\) 0 0
\(658\) 0 0
\(659\) 19.2546 + 11.1166i 0.750053 + 0.433043i 0.825713 0.564091i \(-0.190773\pi\)
−0.0756603 + 0.997134i \(0.524106\pi\)
\(660\) 0 0
\(661\) −9.13646 5.27494i −0.355367 0.205171i 0.311679 0.950187i \(-0.399108\pi\)
−0.667047 + 0.745016i \(0.732442\pi\)
\(662\) −27.7621 16.0284i −1.07900 0.622963i
\(663\) 0 0
\(664\) −10.8651 6.27298i −0.421649 0.243439i
\(665\) 0 0
\(666\) 0 0
\(667\) 7.63613 13.2262i 0.295672 0.512119i
\(668\) 17.1494 0.663532
\(669\) 0 0
\(670\) 25.5404i 0.986713i
\(671\) −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
\(675\) 0 0
\(676\) 5.02106 + 8.69673i 0.193118 + 0.334490i
\(677\) −7.96449 13.7949i −0.306100 0.530181i 0.671405 0.741090i \(-0.265691\pi\)
−0.977506 + 0.210909i \(0.932358\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3.59886 2.07781i 0.138010 0.0796802i
\(681\) 0 0
\(682\) 47.5148i 1.81944i
\(683\) −16.4777 + 9.51343i −0.630503 + 0.364021i −0.780947 0.624597i \(-0.785263\pi\)
0.150444 + 0.988619i \(0.451930\pi\)
\(684\) 0 0
\(685\) 18.7664i 0.717028i
\(686\) 0 0
\(687\) 0 0
\(688\) −3.52106 −0.134239
\(689\) 0 0
\(690\) 0 0
\(691\) 0.139477 0.0805273i 0.00530597 0.00306340i −0.497345 0.867553i \(-0.665692\pi\)
0.502651 + 0.864490i \(0.332358\pi\)
\(692\) 1.98748 0.0755525
\(693\) 0 0
\(694\) −22.7999 −0.865471
\(695\) 42.2396 24.3870i 1.60224 0.925053i
\(696\) 0 0
\(697\) −7.07017 + 12.2459i −0.267802 + 0.463847i
\(698\) −2.84505 −0.107687
\(699\) 0 0
\(700\) 0 0
\(701\) 9.98234i 0.377028i 0.982071 + 0.188514i \(0.0603670\pi\)
−0.982071 + 0.188514i \(0.939633\pi\)
\(702\) 0 0
\(703\) −9.07522 + 5.23958i −0.342278 + 0.197614i
\(704\) 5.67667i 0.213948i
\(705\) 0 0
\(706\) −6.18709 + 3.57212i −0.232854 + 0.134438i
\(707\) 0 0
\(708\) 0 0
\(709\) 12.1962 + 21.1244i 0.458036 + 0.793342i 0.998857 0.0477959i \(-0.0152197\pi\)
−0.540821 + 0.841138i \(0.681886\pi\)
\(710\) −5.31079 9.19856i −0.199311 0.345216i
\(711\) 0 0
\(712\) 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
\(716\) 8.31122i 0.310605i
\(717\) 0 0
\(718\) 11.6037 0.433047
\(719\) 8.13460 14.0895i 0.303370 0.525451i −0.673527 0.739162i \(-0.735222\pi\)
0.976897 + 0.213711i \(0.0685550\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.3303 + 8.85097i 0.570536 + 0.329399i
\(723\) 0 0
\(724\) 13.3837 + 7.72706i 0.497400 + 0.287174i
\(725\) −1.86955 1.07938i −0.0694332 0.0400873i
\(726\) 0 0
\(727\) −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
\(729\) 0 0
\(730\) −6.27554 + 10.8695i −0.232268 + 0.402300i
\(731\) 6.22815 0.230356
\(732\) 0 0
\(733\) 12.2697i 0.453193i −0.973989 0.226596i \(-0.927240\pi\)
0.973989 0.226596i \(-0.0727598\pi\)
\(734\) −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
\(738\) 0 0
\(739\) −20.9446 36.2771i −0.770459 1.33447i −0.937312 0.348492i \(-0.886694\pi\)
0.166853 0.985982i \(-0.446639\pi\)
\(740\) 10.8044 + 18.7137i 0.397177 + 0.687931i
\(741\) 0 0
\(742\) 0 0
\(743\) −43.9160 + 25.3549i −1.61112 + 0.930182i −0.622011 + 0.783008i \(0.713684\pi\)
−0.989111 + 0.147173i \(0.952982\pi\)
\(744\) 0 0
\(745\) 2.81390i 0.103093i
\(746\) −22.2289 + 12.8339i −0.813858 + 0.469881i
\(747\) 0 0
\(748\) 10.0411i 0.367137i
\(749\) 0 0
\(750\) 0 0
\(751\) −32.7367 −1.19458 −0.597289 0.802026i \(-0.703756\pi\)
−0.597289 + 0.802026i \(0.703756\pi\)
\(752\) 5.90494 10.2277i 0.215331 0.372964i
\(753\) 0 0
\(754\) −6.18951 + 3.57351i −0.225408 + 0.130140i
\(755\) −35.7680 −1.30173
\(756\) 0 0
\(757\) −17.9255 −0.651512 −0.325756 0.945454i \(-0.605619\pi\)
−0.325756 + 0.945454i \(0.605619\pi\)
\(758\) 13.0809 7.55227i 0.475120 0.274311i
\(759\) 0 0
\(760\) −1.33834 + 2.31806i −0.0485465 + 0.0840850i
\(761\) −43.7019 −1.58419 −0.792096 0.610397i \(-0.791010\pi\)
−0.792096 + 0.610397i \(0.791010\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 12.3381i 0.446376i
\(765\) 0 0
\(766\) 1.32211 0.763322i 0.0477699 0.0275800i
\(767\) 3.83468i 0.138462i
\(768\) 0 0
\(769\) 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
\(771\) 0 0
\(772\) 2.19694 + 3.80521i 0.0790696 + 0.136953i
\(773\) 10.8025 + 18.7105i 0.388540 + 0.672971i 0.992253 0.124231i \(-0.0396462\pi\)
−0.603714 + 0.797201i \(0.706313\pi\)
\(774\) 0 0
\(775\) −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
\(779\) 9.10794i 0.326326i
\(780\) 0 0
\(781\) −25.6646 −0.918350
\(782\) 3.25030 5.62969i 0.116231 0.201317i
\(783\) 0 0
\(784\) 0 0
\(785\) −20.4008 11.7784i −0.728137 0.420390i
\(786\) 0 0
\(787\) −44.4307 25.6521i −1.58378 0.914398i −0.994300 0.106618i \(-0.965998\pi\)
−0.589484 0.807780i \(-0.700669\pi\)
\(788\) 9.42799 + 5.44325i 0.335858 + 0.193908i
\(789\) 0 0
\(790\) 26.5077 + 15.3042i 0.943102 + 0.544500i
\(791\) 0 0
\(792\) 0 0
\(793\) −7.73906 + 13.4044i −0.274822 + 0.476006i
\(794\) −28.7869 −1.02161
\(795\) 0