Properties

Label 2646.2.h.p.667.2
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.2
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.p.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} -1.00000 q^{8} +(0.880438 + 1.52496i) q^{10} -6.12476 q^{11} +(0.380438 + 0.658939i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.42107 - 5.92546i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(-0.880438 + 1.52496i) q^{20} +(-3.06238 - 5.30420i) q^{22} +0.421067 q^{23} -1.89931 q^{25} +(-0.380438 + 0.658939i) q^{26} +(-0.732287 + 1.26836i) q^{29} +(3.85185 - 6.67160i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.42107 - 5.92546i) q^{34} +(1.44282 - 2.49904i) q^{37} -1.94282 q^{38} -1.76088 q^{40} +(-3.47141 - 6.01266i) q^{41} +(4.33009 - 7.49994i) q^{43} +(3.06238 - 5.30420i) q^{44} +(0.210533 + 0.364654i) q^{46} +(-0.830095 - 1.43777i) q^{47} +(-0.949657 - 1.64485i) q^{50} -0.760877 q^{52} +(0.112725 + 0.195246i) q^{53} -10.7850 q^{55} -1.46457 q^{58} +(-0.993163 + 1.72021i) q^{59} +(-5.17511 - 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(0.669905 + 1.16031i) q^{65} +(-3.39248 + 5.87594i) q^{67} +6.84213 q^{68} -10.7850 q^{71} +(-0.153353 - 0.265616i) q^{73} +2.88564 q^{74} +(-0.971410 - 1.68253i) q^{76} +(6.72257 + 11.6438i) q^{79} +(-0.880438 - 1.52496i) q^{80} +(3.47141 - 6.01266i) q^{82} +(-1.56238 + 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +8.66019 q^{86} +6.12476 q^{88} +(1.30150 - 2.25427i) q^{89} +(-0.210533 + 0.364654i) q^{92} +(0.830095 - 1.43777i) q^{94} +(-1.71053 + 2.96273i) q^{95} +(1.81806 - 3.14897i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + O(q^{10}) \) \( 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + 5 q^{10} - 2 q^{11} + 2 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} - 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} - 2 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34} - 9 q^{37} + 6 q^{38} - 10 q^{40} - 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} + 3 q^{47} + 2 q^{50} - 4 q^{52} - 9 q^{53} - 14 q^{55} + 10 q^{58} + 4 q^{59} - 4 q^{61} + 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} + 8 q^{68} - 14 q^{71} + 25 q^{73} - 18 q^{74} + 3 q^{76} + 7 q^{79} - 5 q^{80} + 12 q^{82} + 8 q^{83} + 14 q^{85} + 36 q^{86} + 2 q^{88} - 9 q^{89} + 7 q^{92} - 3 q^{94} - 2 q^{95} + 28 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.76088 0.787488 0.393744 0.919220i \(-0.371180\pi\)
0.393744 + 0.919220i \(0.371180\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.880438 + 1.52496i 0.278419 + 0.482236i
\(11\) −6.12476 −1.84669 −0.923343 0.383977i \(-0.874554\pi\)
−0.923343 + 0.383977i \(0.874554\pi\)
\(12\) 0 0
\(13\) 0.380438 + 0.658939i 0.105515 + 0.182757i 0.913948 0.405831i \(-0.133018\pi\)
−0.808434 + 0.588587i \(0.799684\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.42107 5.92546i −0.829731 1.43714i −0.898250 0.439486i \(-0.855161\pi\)
0.0685191 0.997650i \(-0.478173\pi\)
\(18\) 0 0
\(19\) −0.971410 + 1.68253i −0.222857 + 0.385999i −0.955674 0.294426i \(-0.904872\pi\)
0.732818 + 0.680425i \(0.238205\pi\)
\(20\) −0.880438 + 1.52496i −0.196872 + 0.340992i
\(21\) 0 0
\(22\) −3.06238 5.30420i −0.652902 1.13086i
\(23\) 0.421067 0.0877985 0.0438992 0.999036i \(-0.486022\pi\)
0.0438992 + 0.999036i \(0.486022\pi\)
\(24\) 0 0
\(25\) −1.89931 −0.379863
\(26\) −0.380438 + 0.658939i −0.0746101 + 0.129228i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.732287 + 1.26836i −0.135982 + 0.235528i −0.925972 0.377592i \(-0.876752\pi\)
0.789990 + 0.613120i \(0.210086\pi\)
\(30\) 0 0
\(31\) 3.85185 6.67160i 0.691812 1.19825i −0.279431 0.960166i \(-0.590146\pi\)
0.971243 0.238088i \(-0.0765208\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.42107 5.92546i 0.586708 1.01621i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.44282 2.49904i 0.237198 0.410839i −0.722711 0.691150i \(-0.757104\pi\)
0.959909 + 0.280311i \(0.0904376\pi\)
\(38\) −1.94282 −0.315167
\(39\) 0 0
\(40\) −1.76088 −0.278419
\(41\) −3.47141 6.01266i −0.542143 0.939020i −0.998781 0.0493667i \(-0.984280\pi\)
0.456638 0.889653i \(-0.349054\pi\)
\(42\) 0 0
\(43\) 4.33009 7.49994i 0.660333 1.14373i −0.320195 0.947352i \(-0.603748\pi\)
0.980528 0.196379i \(-0.0629183\pi\)
\(44\) 3.06238 5.30420i 0.461671 0.799638i
\(45\) 0 0
\(46\) 0.210533 + 0.364654i 0.0310414 + 0.0537654i
\(47\) −0.830095 1.43777i −0.121082 0.209720i 0.799113 0.601181i \(-0.205303\pi\)
−0.920195 + 0.391461i \(0.871970\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.949657 1.64485i −0.134302 0.232617i
\(51\) 0 0
\(52\) −0.760877 −0.105515
\(53\) 0.112725 + 0.195246i 0.0154840 + 0.0268190i 0.873664 0.486531i \(-0.161738\pi\)
−0.858180 + 0.513350i \(0.828404\pi\)
\(54\) 0 0
\(55\) −10.7850 −1.45424
\(56\) 0 0
\(57\) 0 0
\(58\) −1.46457 −0.192308
\(59\) −0.993163 + 1.72021i −0.129299 + 0.223952i −0.923405 0.383827i \(-0.874606\pi\)
0.794106 + 0.607779i \(0.207939\pi\)
\(60\) 0 0
\(61\) −5.17511 8.96355i −0.662605 1.14766i −0.979929 0.199348i \(-0.936118\pi\)
0.317324 0.948317i \(-0.397216\pi\)
\(62\) 7.70370 0.978370
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.669905 + 1.16031i 0.0830915 + 0.143919i
\(66\) 0 0
\(67\) −3.39248 + 5.87594i −0.414457 + 0.717861i −0.995371 0.0961042i \(-0.969362\pi\)
0.580914 + 0.813965i \(0.302695\pi\)
\(68\) 6.84213 0.829731
\(69\) 0 0
\(70\) 0 0
\(71\) −10.7850 −1.27994 −0.639969 0.768401i \(-0.721053\pi\)
−0.639969 + 0.768401i \(0.721053\pi\)
\(72\) 0 0
\(73\) −0.153353 0.265616i −0.0179487 0.0310880i 0.856912 0.515463i \(-0.172380\pi\)
−0.874860 + 0.484375i \(0.839047\pi\)
\(74\) 2.88564 0.335449
\(75\) 0 0
\(76\) −0.971410 1.68253i −0.111428 0.193000i
\(77\) 0 0
\(78\) 0 0
\(79\) 6.72257 + 11.6438i 0.756348 + 1.31003i 0.944701 + 0.327932i \(0.106352\pi\)
−0.188353 + 0.982101i \(0.560315\pi\)
\(80\) −0.880438 1.52496i −0.0984360 0.170496i
\(81\) 0 0
\(82\) 3.47141 6.01266i 0.383353 0.663987i
\(83\) −1.56238 + 2.70612i −0.171494 + 0.297036i −0.938942 0.344075i \(-0.888193\pi\)
0.767449 + 0.641110i \(0.221526\pi\)
\(84\) 0 0
\(85\) −6.02408 10.4340i −0.653403 1.13173i
\(86\) 8.66019 0.933852
\(87\) 0 0
\(88\) 6.12476 0.652902
\(89\) 1.30150 2.25427i 0.137959 0.238952i −0.788765 0.614695i \(-0.789279\pi\)
0.926724 + 0.375743i \(0.122612\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.210533 + 0.364654i −0.0219496 + 0.0380178i
\(93\) 0 0
\(94\) 0.830095 1.43777i 0.0856178 0.148294i
\(95\) −1.71053 + 2.96273i −0.175497 + 0.303970i
\(96\) 0 0
\(97\) 1.81806 3.14897i 0.184596 0.319729i −0.758845 0.651272i \(-0.774236\pi\)
0.943440 + 0.331543i \(0.107569\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.949657 1.64485i 0.0949657 0.164485i
\(101\) −8.01040 −0.797065 −0.398532 0.917154i \(-0.630480\pi\)
−0.398532 + 0.917154i \(0.630480\pi\)
\(102\) 0 0
\(103\) 6.82846 0.672828 0.336414 0.941714i \(-0.390786\pi\)
0.336414 + 0.941714i \(0.390786\pi\)
\(104\) −0.380438 0.658939i −0.0373051 0.0646142i
\(105\) 0 0
\(106\) −0.112725 + 0.195246i −0.0109488 + 0.0189639i
\(107\) −1.77292 + 3.07078i −0.171394 + 0.296863i −0.938908 0.344170i \(-0.888160\pi\)
0.767513 + 0.641033i \(0.221494\pi\)
\(108\) 0 0
\(109\) 0.351848 + 0.609419i 0.0337010 + 0.0583718i 0.882384 0.470530i \(-0.155937\pi\)
−0.848683 + 0.528902i \(0.822604\pi\)
\(110\) −5.39248 9.34004i −0.514152 0.890538i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.25116 7.36323i −0.399916 0.692674i 0.593799 0.804613i \(-0.297627\pi\)
−0.993715 + 0.111939i \(0.964294\pi\)
\(114\) 0 0
\(115\) 0.741446 0.0691402
\(116\) −0.732287 1.26836i −0.0679911 0.117764i
\(117\) 0 0
\(118\) −1.98633 −0.182856
\(119\) 0 0
\(120\) 0 0
\(121\) 26.5127 2.41025
\(122\) 5.17511 8.96355i 0.468532 0.811521i
\(123\) 0 0
\(124\) 3.85185 + 6.67160i 0.345906 + 0.599127i
\(125\) −12.1488 −1.08663
\(126\) 0 0
\(127\) −18.9532 −1.68183 −0.840913 0.541170i \(-0.817982\pi\)
−0.840913 + 0.541170i \(0.817982\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.669905 + 1.16031i −0.0587546 + 0.101766i
\(131\) −7.29303 −0.637195 −0.318598 0.947890i \(-0.603212\pi\)
−0.318598 + 0.947890i \(0.603212\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −6.78495 −0.586131
\(135\) 0 0
\(136\) 3.42107 + 5.92546i 0.293354 + 0.508104i
\(137\) 8.18194 0.699031 0.349515 0.936931i \(-0.386346\pi\)
0.349515 + 0.936931i \(0.386346\pi\)
\(138\) 0 0
\(139\) 6.23229 + 10.7946i 0.528616 + 0.915589i 0.999443 + 0.0333640i \(0.0106220\pi\)
−0.470828 + 0.882225i \(0.656045\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.39248 9.34004i −0.452527 0.783799i
\(143\) −2.33009 4.03584i −0.194852 0.337494i
\(144\) 0 0
\(145\) −1.28947 + 2.23342i −0.107084 + 0.185476i
\(146\) 0.153353 0.265616i 0.0126916 0.0219825i
\(147\) 0 0
\(148\) 1.44282 + 2.49904i 0.118599 + 0.205420i
\(149\) −8.82846 −0.723256 −0.361628 0.932323i \(-0.617779\pi\)
−0.361628 + 0.932323i \(0.617779\pi\)
\(150\) 0 0
\(151\) −14.9863 −1.21957 −0.609785 0.792567i \(-0.708744\pi\)
−0.609785 + 0.792567i \(0.708744\pi\)
\(152\) 0.971410 1.68253i 0.0787918 0.136471i
\(153\) 0 0
\(154\) 0 0
\(155\) 6.78263 11.7479i 0.544794 0.943611i
\(156\) 0 0
\(157\) 9.49028 16.4377i 0.757407 1.31187i −0.186761 0.982405i \(-0.559799\pi\)
0.944169 0.329462i \(-0.106868\pi\)
\(158\) −6.72257 + 11.6438i −0.534819 + 0.926334i
\(159\) 0 0
\(160\) 0.880438 1.52496i 0.0696048 0.120559i
\(161\) 0 0
\(162\) 0 0
\(163\) −7.51887 + 13.0231i −0.588924 + 1.02005i 0.405450 + 0.914117i \(0.367115\pi\)
−0.994374 + 0.105929i \(0.966219\pi\)
\(164\) 6.94282 0.542143
\(165\) 0 0
\(166\) −3.12476 −0.242529
\(167\) 0.572097 + 0.990901i 0.0442702 + 0.0766782i 0.887311 0.461171i \(-0.152570\pi\)
−0.843041 + 0.537849i \(0.819237\pi\)
\(168\) 0 0
\(169\) 6.21053 10.7570i 0.477733 0.827458i
\(170\) 6.02408 10.4340i 0.462026 0.800252i
\(171\) 0 0
\(172\) 4.33009 + 7.49994i 0.330167 + 0.571865i
\(173\) −0.248838 0.431001i −0.0189188 0.0327684i 0.856411 0.516295i \(-0.172689\pi\)
−0.875330 + 0.483526i \(0.839356\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.06238 + 5.30420i 0.230836 + 0.399819i
\(177\) 0 0
\(178\) 2.60301 0.195104
\(179\) −4.41423 7.64567i −0.329935 0.571464i 0.652564 0.757734i \(-0.273694\pi\)
−0.982499 + 0.186270i \(0.940360\pi\)
\(180\) 0 0
\(181\) −1.32941 −0.0988140 −0.0494070 0.998779i \(-0.515733\pi\)
−0.0494070 + 0.998779i \(0.515733\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.421067 −0.0310414
\(185\) 2.54063 4.40050i 0.186791 0.323531i
\(186\) 0 0
\(187\) 20.9532 + 36.2920i 1.53225 + 2.65394i
\(188\) 1.66019 0.121082
\(189\) 0 0
\(190\) −3.42107 −0.248190
\(191\) −8.08414 14.0021i −0.584947 1.01316i −0.994882 0.101044i \(-0.967782\pi\)
0.409934 0.912115i \(-0.365552\pi\)
\(192\) 0 0
\(193\) 7.08414 12.2701i 0.509927 0.883220i −0.490007 0.871719i \(-0.663006\pi\)
0.999934 0.0115011i \(-0.00366101\pi\)
\(194\) 3.63611 0.261058
\(195\) 0 0
\(196\) 0 0
\(197\) −15.8421 −1.12871 −0.564353 0.825534i \(-0.690874\pi\)
−0.564353 + 0.825534i \(0.690874\pi\)
\(198\) 0 0
\(199\) 4.47141 + 7.74471i 0.316970 + 0.549008i 0.979854 0.199714i \(-0.0640013\pi\)
−0.662884 + 0.748722i \(0.730668\pi\)
\(200\) 1.89931 0.134302
\(201\) 0 0
\(202\) −4.00520 6.93721i −0.281805 0.488101i
\(203\) 0 0
\(204\) 0 0
\(205\) −6.11273 10.5876i −0.426931 0.739467i
\(206\) 3.41423 + 5.91362i 0.237881 + 0.412021i
\(207\) 0 0
\(208\) 0.380438 0.658939i 0.0263787 0.0456892i
\(209\) 5.94966 10.3051i 0.411546 0.712819i
\(210\) 0 0
\(211\) 11.3856 + 19.7205i 0.783820 + 1.35762i 0.929702 + 0.368314i \(0.120065\pi\)
−0.145882 + 0.989302i \(0.546602\pi\)
\(212\) −0.225450 −0.0154840
\(213\) 0 0
\(214\) −3.54583 −0.242388
\(215\) 7.62476 13.2065i 0.520005 0.900674i
\(216\) 0 0
\(217\) 0 0
\(218\) −0.351848 + 0.609419i −0.0238302 + 0.0412751i
\(219\) 0 0
\(220\) 5.39248 9.34004i 0.363561 0.629706i
\(221\) 2.60301 4.50855i 0.175097 0.303278i
\(222\) 0 0
\(223\) 6.44282 11.1593i 0.431443 0.747281i −0.565555 0.824711i \(-0.691338\pi\)
0.996998 + 0.0774293i \(0.0246712\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 4.25116 7.36323i 0.282783 0.489795i
\(227\) 21.9967 1.45997 0.729987 0.683461i \(-0.239526\pi\)
0.729987 + 0.683461i \(0.239526\pi\)
\(228\) 0 0
\(229\) 3.79863 0.251020 0.125510 0.992092i \(-0.459943\pi\)
0.125510 + 0.992092i \(0.459943\pi\)
\(230\) 0.370723 + 0.642111i 0.0244448 + 0.0423396i
\(231\) 0 0
\(232\) 0.732287 1.26836i 0.0480770 0.0832718i
\(233\) 3.33530 5.77690i 0.218503 0.378458i −0.735848 0.677147i \(-0.763216\pi\)
0.954350 + 0.298689i \(0.0965495\pi\)
\(234\) 0 0
\(235\) −1.46169 2.53173i −0.0953505 0.165152i
\(236\) −0.993163 1.72021i −0.0646494 0.111976i
\(237\) 0 0
\(238\) 0 0
\(239\) 7.82038 + 13.5453i 0.505858 + 0.876172i 0.999977 + 0.00677786i \(0.00215748\pi\)
−0.494119 + 0.869394i \(0.664509\pi\)
\(240\) 0 0
\(241\) −21.4120 −1.37927 −0.689635 0.724157i \(-0.742229\pi\)
−0.689635 + 0.724157i \(0.742229\pi\)
\(242\) 13.2564 + 22.9607i 0.852151 + 1.47597i
\(243\) 0 0
\(244\) 10.3502 0.662605
\(245\) 0 0
\(246\) 0 0
\(247\) −1.47825 −0.0940586
\(248\) −3.85185 + 6.67160i −0.244593 + 0.423647i
\(249\) 0 0
\(250\) −6.07442 10.5212i −0.384180 0.665419i
\(251\) −23.6030 −1.48981 −0.744904 0.667171i \(-0.767505\pi\)
−0.744904 + 0.667171i \(0.767505\pi\)
\(252\) 0 0
\(253\) −2.57893 −0.162136
\(254\) −9.47661 16.4140i −0.594616 1.02990i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 20.2599 1.26378 0.631890 0.775058i \(-0.282279\pi\)
0.631890 + 0.775058i \(0.282279\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.33981 −0.0830915
\(261\) 0 0
\(262\) −3.64652 6.31595i −0.225283 0.390201i
\(263\) 22.4887 1.38671 0.693355 0.720596i \(-0.256132\pi\)
0.693355 + 0.720596i \(0.256132\pi\)
\(264\) 0 0
\(265\) 0.198495 + 0.343803i 0.0121935 + 0.0211197i
\(266\) 0 0
\(267\) 0 0
\(268\) −3.39248 5.87594i −0.207228 0.358930i
\(269\) −12.6706 21.9461i −0.772540 1.33808i −0.936167 0.351556i \(-0.885653\pi\)
0.163627 0.986522i \(-0.447681\pi\)
\(270\) 0 0
\(271\) 6.87880 11.9144i 0.417858 0.723751i −0.577866 0.816132i \(-0.696114\pi\)
0.995724 + 0.0923810i \(0.0294478\pi\)
\(272\) −3.42107 + 5.92546i −0.207433 + 0.359284i
\(273\) 0 0
\(274\) 4.09097 + 7.08577i 0.247145 + 0.428067i
\(275\) 11.6328 0.701487
\(276\) 0 0
\(277\) −3.28263 −0.197234 −0.0986171 0.995125i \(-0.531442\pi\)
−0.0986171 + 0.995125i \(0.531442\pi\)
\(278\) −6.23229 + 10.7946i −0.373788 + 0.647419i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.634479 + 1.09895i −0.0378498 + 0.0655578i −0.884330 0.466863i \(-0.845384\pi\)
0.846480 + 0.532421i \(0.178718\pi\)
\(282\) 0 0
\(283\) −4.09617 + 7.09478i −0.243492 + 0.421741i −0.961707 0.274081i \(-0.911626\pi\)
0.718214 + 0.695822i \(0.244960\pi\)
\(284\) 5.39248 9.34004i 0.319985 0.554230i
\(285\) 0 0
\(286\) 2.33009 4.03584i 0.137781 0.238644i
\(287\) 0 0
\(288\) 0 0
\(289\) −14.9074 + 25.8204i −0.876906 + 1.51884i
\(290\) −2.57893 −0.151440
\(291\) 0 0
\(292\) 0.306707 0.0179487
\(293\) 7.72545 + 13.3809i 0.451326 + 0.781719i 0.998469 0.0553202i \(-0.0176180\pi\)
−0.547143 + 0.837039i \(0.684285\pi\)
\(294\) 0 0
\(295\) −1.74884 + 3.02908i −0.101821 + 0.176360i
\(296\) −1.44282 + 2.49904i −0.0838622 + 0.145254i
\(297\) 0 0
\(298\) −4.41423 7.64567i −0.255709 0.442902i
\(299\) 0.160190 + 0.277457i 0.00926402 + 0.0160458i
\(300\) 0 0
\(301\) 0 0
\(302\) −7.49316 12.9785i −0.431183 0.746831i
\(303\) 0 0
\(304\) 1.94282 0.111428
\(305\) −9.11273 15.7837i −0.521793 0.903772i
\(306\) 0 0
\(307\) −4.89931 −0.279619 −0.139809 0.990178i \(-0.544649\pi\)
−0.139809 + 0.990178i \(0.544649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 13.5653 0.770455
\(311\) 3.84501 6.65976i 0.218031 0.377640i −0.736175 0.676791i \(-0.763370\pi\)
0.954206 + 0.299151i \(0.0967034\pi\)
\(312\) 0 0
\(313\) −0.861564 1.49227i −0.0486985 0.0843482i 0.840649 0.541581i \(-0.182174\pi\)
−0.889347 + 0.457233i \(0.848841\pi\)
\(314\) 18.9806 1.07114
\(315\) 0 0
\(316\) −13.4451 −0.756348
\(317\) 16.6014 + 28.7544i 0.932426 + 1.61501i 0.779161 + 0.626824i \(0.215646\pi\)
0.153266 + 0.988185i \(0.451021\pi\)
\(318\) 0 0
\(319\) 4.48508 7.76839i 0.251116 0.434946i
\(320\) 1.76088 0.0984360
\(321\) 0 0
\(322\) 0 0
\(323\) 13.2930 0.739644
\(324\) 0 0
\(325\) −0.722572 1.25153i −0.0400811 0.0694224i
\(326\) −15.0377 −0.832864
\(327\) 0 0
\(328\) 3.47141 + 6.01266i 0.191677 + 0.331994i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.44445 2.50187i −0.0793944 0.137515i 0.823594 0.567179i \(-0.191965\pi\)
−0.902989 + 0.429664i \(0.858632\pi\)
\(332\) −1.56238 2.70612i −0.0857468 0.148518i
\(333\) 0 0
\(334\) −0.572097 + 0.990901i −0.0313037 + 0.0542197i
\(335\) −5.97373 + 10.3468i −0.326380 + 0.565307i
\(336\) 0 0
\(337\) −4.36156 7.55445i −0.237590 0.411517i 0.722433 0.691441i \(-0.243024\pi\)
−0.960022 + 0.279924i \(0.909691\pi\)
\(338\) 12.4211 0.675617
\(339\) 0 0
\(340\) 12.0482 0.653403
\(341\) −23.5917 + 40.8620i −1.27756 + 2.21280i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.33009 + 7.49994i −0.233463 + 0.404370i
\(345\) 0 0
\(346\) 0.248838 0.431001i 0.0133776 0.0231707i
\(347\) 4.84733 8.39583i 0.260219 0.450712i −0.706081 0.708131i \(-0.749539\pi\)
0.966300 + 0.257419i \(0.0828720\pi\)
\(348\) 0 0
\(349\) −14.1992 + 24.5937i −0.760065 + 1.31647i 0.182752 + 0.983159i \(0.441500\pi\)
−0.942817 + 0.333312i \(0.891834\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.06238 + 5.30420i −0.163225 + 0.282715i
\(353\) −4.39372 −0.233854 −0.116927 0.993141i \(-0.537304\pi\)
−0.116927 + 0.993141i \(0.537304\pi\)
\(354\) 0 0
\(355\) −18.9910 −1.00794
\(356\) 1.30150 + 2.25427i 0.0689796 + 0.119476i
\(357\) 0 0
\(358\) 4.41423 7.64567i 0.233299 0.404086i
\(359\) −16.0796 + 27.8507i −0.848650 + 1.46990i 0.0337633 + 0.999430i \(0.489251\pi\)
−0.882413 + 0.470475i \(0.844083\pi\)
\(360\) 0 0
\(361\) 7.61273 + 13.1856i 0.400670 + 0.693980i
\(362\) −0.664703 1.15130i −0.0349360 0.0605110i
\(363\) 0 0
\(364\) 0 0
\(365\) −0.270036 0.467717i −0.0141343 0.0244814i
\(366\) 0 0
\(367\) −34.6030 −1.80626 −0.903131 0.429365i \(-0.858738\pi\)
−0.903131 + 0.429365i \(0.858738\pi\)
\(368\) −0.210533 0.364654i −0.0109748 0.0190089i
\(369\) 0 0
\(370\) 5.08126 0.264162
\(371\) 0 0
\(372\) 0 0
\(373\) 10.9759 0.568312 0.284156 0.958778i \(-0.408287\pi\)
0.284156 + 0.958778i \(0.408287\pi\)
\(374\) −20.9532 + 36.2920i −1.08347 + 1.87662i
\(375\) 0 0
\(376\) 0.830095 + 1.43777i 0.0428089 + 0.0741472i
\(377\) −1.11436 −0.0573925
\(378\) 0 0
\(379\) 33.9877 1.74583 0.872916 0.487871i \(-0.162226\pi\)
0.872916 + 0.487871i \(0.162226\pi\)
\(380\) −1.71053 2.96273i −0.0877485 0.151985i
\(381\) 0 0
\(382\) 8.08414 14.0021i 0.413620 0.716411i
\(383\) −21.0241 −1.07428 −0.537140 0.843493i \(-0.680495\pi\)
−0.537140 + 0.843493i \(0.680495\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.1683 0.721146
\(387\) 0 0
\(388\) 1.81806 + 3.14897i 0.0922978 + 0.159865i
\(389\) −13.7382 −0.696553 −0.348277 0.937392i \(-0.613233\pi\)
−0.348277 + 0.937392i \(0.613233\pi\)
\(390\) 0 0
\(391\) −1.44050 2.49501i −0.0728491 0.126178i
\(392\) 0 0
\(393\) 0 0
\(394\) −7.92107 13.7197i −0.399058 0.691188i
\(395\) 11.8376 + 20.5034i 0.595615 + 1.03164i
\(396\) 0 0
\(397\) 3.57893 6.19889i 0.179622 0.311114i −0.762129 0.647425i \(-0.775846\pi\)
0.941751 + 0.336311i \(0.109179\pi\)
\(398\) −4.47141 + 7.74471i −0.224132 + 0.388207i
\(399\) 0 0
\(400\) 0.949657 + 1.64485i 0.0474828 + 0.0822427i
\(401\) 9.27936 0.463389 0.231695 0.972789i \(-0.425573\pi\)
0.231695 + 0.972789i \(0.425573\pi\)
\(402\) 0 0
\(403\) 5.86156 0.291985
\(404\) 4.00520 6.93721i 0.199266 0.345139i
\(405\) 0 0
\(406\) 0 0
\(407\) −8.83693 + 15.3060i −0.438030 + 0.758691i
\(408\) 0 0
\(409\) 7.58414 13.1361i 0.375011 0.649539i −0.615317 0.788279i \(-0.710972\pi\)
0.990329 + 0.138741i \(0.0443055\pi\)
\(410\) 6.11273 10.5876i 0.301886 0.522882i
\(411\) 0 0
\(412\) −3.41423 + 5.91362i −0.168207 + 0.291343i
\(413\) 0 0
\(414\) 0 0
\(415\) −2.75116 + 4.76515i −0.135049 + 0.233912i
\(416\) 0.760877 0.0373051
\(417\) 0 0
\(418\) 11.8993 0.582014
\(419\) −4.16827 7.21966i −0.203633 0.352703i 0.746063 0.665875i \(-0.231942\pi\)
−0.949696 + 0.313172i \(0.898608\pi\)
\(420\) 0 0
\(421\) −3.50232 + 6.06620i −0.170693 + 0.295649i −0.938662 0.344838i \(-0.887934\pi\)
0.767969 + 0.640486i \(0.221267\pi\)
\(422\) −11.3856 + 19.7205i −0.554244 + 0.959979i
\(423\) 0 0
\(424\) −0.112725 0.195246i −0.00547442 0.00948197i
\(425\) 6.49768 + 11.2543i 0.315184 + 0.545914i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.77292 3.07078i −0.0856971 0.148432i
\(429\) 0 0
\(430\) 15.2495 0.735397
\(431\) 1.72545 + 2.98857i 0.0831120 + 0.143954i 0.904585 0.426293i \(-0.140181\pi\)
−0.821473 + 0.570247i \(0.806847\pi\)
\(432\) 0 0
\(433\) −28.2599 −1.35809 −0.679043 0.734099i \(-0.737605\pi\)
−0.679043 + 0.734099i \(0.737605\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.703697 −0.0337010
\(437\) −0.409028 + 0.708458i −0.0195665 + 0.0338901i
\(438\) 0 0
\(439\) −14.4480 25.0247i −0.689566 1.19436i −0.971978 0.235071i \(-0.924468\pi\)
0.282412 0.959293i \(-0.408866\pi\)
\(440\) 10.7850 0.514152
\(441\) 0 0
\(442\) 5.20602 0.247625
\(443\) −6.88044 11.9173i −0.326899 0.566207i 0.654995 0.755633i \(-0.272671\pi\)
−0.981895 + 0.189426i \(0.939337\pi\)
\(444\) 0 0
\(445\) 2.29179 3.96950i 0.108641 0.188172i
\(446\) 12.8856 0.610153
\(447\) 0 0
\(448\) 0 0
\(449\) 20.2003 0.953309 0.476655 0.879091i \(-0.341849\pi\)
0.476655 + 0.879091i \(0.341849\pi\)
\(450\) 0 0
\(451\) 21.2616 + 36.8261i 1.00117 + 1.73407i
\(452\) 8.50232 0.399916
\(453\) 0 0
\(454\) 10.9984 + 19.0497i 0.516179 + 0.894048i
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0149 17.3463i −0.468478 0.811428i 0.530873 0.847451i \(-0.321864\pi\)
−0.999351 + 0.0360237i \(0.988531\pi\)
\(458\) 1.89931 + 3.28971i 0.0887491 + 0.153718i
\(459\) 0 0
\(460\) −0.370723 + 0.642111i −0.0172851 + 0.0299386i
\(461\) 5.97661 10.3518i 0.278359 0.482131i −0.692618 0.721304i \(-0.743543\pi\)
0.970977 + 0.239173i \(0.0768763\pi\)
\(462\) 0 0
\(463\) 6.64527 + 11.5100i 0.308832 + 0.534913i 0.978107 0.208102i \(-0.0667286\pi\)
−0.669275 + 0.743015i \(0.733395\pi\)
\(464\) 1.46457 0.0679911
\(465\) 0 0
\(466\) 6.67059 0.309009
\(467\) −5.61505 + 9.72555i −0.259833 + 0.450045i −0.966197 0.257804i \(-0.917001\pi\)
0.706364 + 0.707849i \(0.250334\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.46169 2.53173i 0.0674230 0.116780i
\(471\) 0 0
\(472\) 0.993163 1.72021i 0.0457141 0.0791791i
\(473\) −26.5208 + 45.9354i −1.21943 + 2.11211i
\(474\) 0 0
\(475\) 1.84501 3.19565i 0.0846550 0.146627i
\(476\) 0 0
\(477\) 0 0
\(478\) −7.82038 + 13.5453i −0.357696 + 0.619547i
\(479\) −32.6271 −1.49077 −0.745385 0.666634i \(-0.767734\pi\)
−0.745385 + 0.666634i \(0.767734\pi\)
\(480\) 0 0
\(481\) 2.19562 0.100111
\(482\) −10.7060 18.5434i −0.487646 0.844627i
\(483\) 0 0
\(484\) −13.2564 + 22.9607i −0.602562 + 1.04367i
\(485\) 3.20137 5.54494i 0.145367 0.251783i
\(486\) 0 0
\(487\) 1.84897 + 3.20251i 0.0837848 + 0.145120i 0.904873 0.425682i \(-0.139966\pi\)
−0.821088 + 0.570802i \(0.806632\pi\)
\(488\) 5.17511 + 8.96355i 0.234266 + 0.405761i
\(489\) 0 0
\(490\) 0 0
\(491\) 18.7804 + 32.5287i 0.847549 + 1.46800i 0.883389 + 0.468641i \(0.155256\pi\)
−0.0358393 + 0.999358i \(0.511410\pi\)
\(492\) 0 0
\(493\) 10.0208 0.451314
\(494\) −0.739123 1.28020i −0.0332547 0.0575989i
\(495\) 0 0
\(496\) −7.70370 −0.345906
\(497\) 0 0
\(498\) 0 0
\(499\) −31.7954 −1.42336 −0.711678 0.702506i \(-0.752064\pi\)
−0.711678 + 0.702506i \(0.752064\pi\)
\(500\) 6.07442 10.5212i 0.271656 0.470523i
\(501\) 0 0
\(502\) −11.8015 20.4408i −0.526727 0.912318i
\(503\) 30.8252 1.37443 0.687214 0.726455i \(-0.258834\pi\)
0.687214 + 0.726455i \(0.258834\pi\)
\(504\) 0 0
\(505\) −14.1053 −0.627679
\(506\) −1.28947 2.23342i −0.0573238 0.0992877i
\(507\) 0 0
\(508\) 9.47661 16.4140i 0.420457 0.728252i
\(509\) 8.01616 0.355310 0.177655 0.984093i \(-0.443149\pi\)
0.177655 + 0.984093i \(0.443149\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 10.1300 + 17.5456i 0.446814 + 0.773904i
\(515\) 12.0241 0.529844
\(516\) 0 0
\(517\) 5.08414 + 8.80598i 0.223600 + 0.387287i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.669905 1.16031i −0.0293773 0.0508829i
\(521\) 14.8646 + 25.7462i 0.651229 + 1.12796i 0.982825 + 0.184540i \(0.0590795\pi\)
−0.331596 + 0.943421i \(0.607587\pi\)
\(522\) 0 0
\(523\) −13.4698 + 23.3303i −0.588992 + 1.02016i 0.405373 + 0.914152i \(0.367142\pi\)
−0.994365 + 0.106013i \(0.966192\pi\)
\(524\) 3.64652 6.31595i 0.159299 0.275914i
\(525\) 0 0
\(526\) 11.2443 + 19.4757i 0.490276 + 0.849183i
\(527\) −52.7097 −2.29607
\(528\) 0 0
\(529\) −22.8227 −0.992291
\(530\) −0.198495 + 0.343803i −0.00862207 + 0.0149339i
\(531\) 0 0
\(532\) 0 0
\(533\) 2.64132 4.57489i 0.114408 0.198161i
\(534\) 0 0
\(535\) −3.12188 + 5.40726i −0.134971 + 0.233776i
\(536\) 3.39248 5.87594i 0.146533 0.253802i
\(537\) 0 0
\(538\) 12.6706 21.9461i 0.546268 0.946164i
\(539\) 0 0
\(540\) 0 0
\(541\) 7.15568 12.3940i 0.307647 0.532859i −0.670201 0.742180i \(-0.733792\pi\)
0.977847 + 0.209321i \(0.0671252\pi\)
\(542\) 13.7576 0.590940
\(543\) 0 0
\(544\) −6.84213 −0.293354
\(545\) 0.619562 + 1.07311i 0.0265391 + 0.0459671i
\(546\) 0 0
\(547\) 1.02463 1.77471i 0.0438101 0.0758813i −0.843289 0.537461i \(-0.819384\pi\)
0.887099 + 0.461579i \(0.152717\pi\)
\(548\) −4.09097 + 7.08577i −0.174758 + 0.302689i
\(549\) 0 0
\(550\) 5.81642 + 10.0743i 0.248013 + 0.429571i
\(551\) −1.42270 2.46419i −0.0606091 0.104978i
\(552\) 0 0
\(553\) 0 0
\(554\) −1.64132 2.84284i −0.0697328 0.120781i
\(555\) 0 0
\(556\) −12.4646 −0.528616
\(557\) −8.84338 15.3172i −0.374706 0.649010i 0.615577 0.788077i \(-0.288923\pi\)
−0.990283 + 0.139067i \(0.955590\pi\)
\(558\) 0 0
\(559\) 6.58934 0.278699
\(560\) 0 0
\(561\) 0 0
\(562\) −1.26896 −0.0535277
\(563\) −0.468531 + 0.811520i −0.0197462 + 0.0342015i −0.875730 0.482802i \(-0.839619\pi\)
0.855983 + 0.517003i \(0.172952\pi\)
\(564\) 0 0
\(565\) −7.48577 12.9657i −0.314929 0.545473i
\(566\) −8.19235 −0.344350
\(567\) 0 0
\(568\) 10.7850 0.452527
\(569\) 11.7632 + 20.3745i 0.493139 + 0.854142i 0.999969 0.00790437i \(-0.00251607\pi\)
−0.506830 + 0.862046i \(0.669183\pi\)
\(570\) 0 0
\(571\) 0.242002 0.419160i 0.0101275 0.0175413i −0.860917 0.508745i \(-0.830110\pi\)
0.871045 + 0.491204i \(0.163443\pi\)
\(572\) 4.66019 0.194852
\(573\) 0 0
\(574\) 0 0
\(575\) −0.799737 −0.0333514
\(576\) 0 0
\(577\) 2.23065 + 3.86360i 0.0928633 + 0.160844i 0.908715 0.417417i \(-0.137065\pi\)
−0.815852 + 0.578261i \(0.803731\pi\)
\(578\) −29.8148 −1.24013
\(579\) 0 0
\(580\) −1.28947 2.23342i −0.0535422 0.0927378i
\(581\) 0 0
\(582\) 0 0
\(583\) −0.690415 1.19583i −0.0285941 0.0495264i
\(584\) 0.153353 + 0.265616i 0.00634581 + 0.0109913i
\(585\) 0 0
\(586\) −7.72545 + 13.3809i −0.319135 + 0.552759i
\(587\) 8.31518 14.4023i 0.343204 0.594447i −0.641822 0.766854i \(-0.721821\pi\)
0.985026 + 0.172407i \(0.0551544\pi\)
\(588\) 0 0
\(589\) 7.48345 + 12.9617i 0.308350 + 0.534078i
\(590\) −3.49768 −0.143997
\(591\) 0 0
\(592\) −2.88564 −0.118599
\(593\) 20.7632 35.9629i 0.852642 1.47682i −0.0261726 0.999657i \(-0.508332\pi\)
0.878815 0.477163i \(-0.158335\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.41423 7.64567i 0.180814 0.313179i
\(597\) 0 0
\(598\) −0.160190 + 0.277457i −0.00655065 + 0.0113461i
\(599\) 7.53831 13.0567i 0.308007 0.533483i −0.669919 0.742434i \(-0.733671\pi\)
0.977926 + 0.208950i \(0.0670047\pi\)
\(600\) 0 0
\(601\) 8.05555 13.9526i 0.328593 0.569139i −0.653640 0.756805i \(-0.726759\pi\)
0.982233 + 0.187666i \(0.0600924\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 7.49316 12.9785i 0.304892 0.528089i
\(605\) 46.6856 1.89804
\(606\) 0 0
\(607\) −19.5732 −0.794451 −0.397225 0.917721i \(-0.630027\pi\)
−0.397225 + 0.917721i \(0.630027\pi\)
\(608\) 0.971410 + 1.68253i 0.0393959 + 0.0682357i
\(609\) 0 0
\(610\) 9.11273 15.7837i 0.368963 0.639063i
\(611\) 0.631600 1.09396i 0.0255518 0.0442570i
\(612\) 0 0
\(613\) −2.77579 4.80782i −0.112113 0.194186i 0.804509 0.593941i \(-0.202429\pi\)
−0.916622 + 0.399755i \(0.869095\pi\)
\(614\) −2.44966 4.24293i −0.0988601 0.171231i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.634479 1.09895i −0.0255431 0.0442420i 0.852971 0.521958i \(-0.174798\pi\)
−0.878514 + 0.477716i \(0.841465\pi\)
\(618\) 0 0
\(619\) −4.50232 −0.180964 −0.0904818 0.995898i \(-0.528841\pi\)
−0.0904818 + 0.995898i \(0.528841\pi\)
\(620\) 6.78263 + 11.7479i 0.272397 + 0.471805i
\(621\) 0 0
\(622\) 7.69002 0.308342
\(623\) 0 0
\(624\) 0 0
\(625\) −11.8960 −0.475842
\(626\) 0.861564 1.49227i 0.0344350 0.0596432i
\(627\) 0 0
\(628\) 9.49028 + 16.4377i 0.378704 + 0.655934i
\(629\) −19.7439 −0.787242
\(630\) 0 0
\(631\) −1.69905 −0.0676381 −0.0338191 0.999428i \(-0.510767\pi\)
−0.0338191 + 0.999428i \(0.510767\pi\)
\(632\) −6.72257 11.6438i −0.267410 0.463167i
\(633\) 0 0
\(634\) −16.6014 + 28.7544i −0.659325 + 1.14198i
\(635\) −33.3743 −1.32442
\(636\) 0 0
\(637\) 0 0
\(638\) 8.97017 0.355132
\(639\) 0 0
\(640\) 0.880438 + 1.52496i 0.0348024 + 0.0602795i
\(641\) 0.948577 0.0374666 0.0187333 0.999825i \(-0.494037\pi\)
0.0187333 + 0.999825i \(0.494037\pi\)
\(642\) 0 0
\(643\) 9.84897 + 17.0589i 0.388405 + 0.672738i 0.992235 0.124375i \(-0.0396927\pi\)
−0.603830 + 0.797113i \(0.706359\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.64652 + 11.5121i 0.261504 + 0.452938i
\(647\) 11.7271 + 20.3119i 0.461039 + 0.798543i 0.999013 0.0444181i \(-0.0141434\pi\)
−0.537974 + 0.842962i \(0.680810\pi\)
\(648\) 0 0
\(649\) 6.08289 10.5359i 0.238774 0.413569i
\(650\) 0.722572 1.25153i 0.0283416 0.0490891i
\(651\) 0 0
\(652\) −7.51887 13.0231i −0.294462 0.510023i
\(653\) −22.7907 −0.891869 −0.445935 0.895065i \(-0.647129\pi\)
−0.445935 + 0.895065i \(0.647129\pi\)
\(654\) 0 0
\(655\) −12.8421 −0.501784
\(656\) −3.47141 + 6.01266i −0.135536 + 0.234755i
\(657\) 0 0
\(658\) 0 0
\(659\) 13.2398 22.9320i 0.515750 0.893305i −0.484083 0.875022i \(-0.660847\pi\)
0.999833 0.0182828i \(-0.00581993\pi\)
\(660\) 0 0
\(661\) −13.3691 + 23.1559i −0.519997 + 0.900662i 0.479732 + 0.877415i \(0.340734\pi\)
−0.999730 + 0.0232469i \(0.992600\pi\)
\(662\) 1.44445 2.50187i 0.0561403 0.0972379i
\(663\) 0 0
\(664\) 1.56238 2.70612i 0.0606322 0.105018i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.308342 + 0.534063i −0.0119390 + 0.0206790i
\(668\) −1.14419 −0.0442702
\(669\) 0 0
\(670\) −11.9475 −0.461571
\(671\) 31.6963 + 54.8996i 1.22362 + 2.11938i
\(672\) 0 0
\(673\) −10.3856 + 17.9885i −0.400337 + 0.693404i −0.993766 0.111482i \(-0.964440\pi\)
0.593429 + 0.804886i \(0.297774\pi\)
\(674\) 4.36156 7.55445i 0.168001 0.290987i
\(675\) 0 0
\(676\) 6.21053 + 10.7570i 0.238867 + 0.413729i
\(677\) 10.3490 + 17.9249i 0.397743 + 0.688911i 0.993447 0.114293i \(-0.0364602\pi\)
−0.595704 + 0.803204i \(0.703127\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6.02408 + 10.4340i 0.231013 + 0.400126i
\(681\) 0 0
\(682\) −47.1833 −1.80674
\(683\) −14.2918 24.7541i −0.546860 0.947190i −0.998487 0.0549828i \(-0.982490\pi\)
0.451627 0.892207i \(-0.350844\pi\)
\(684\) 0 0
\(685\) 14.4074 0.550478
\(686\) 0 0
\(687\) 0 0
\(688\) −8.66019 −0.330167
\(689\) −0.0857699 + 0.148558i −0.00326757 + 0.00565960i
\(690\) 0 0
\(691\) −3.34897 5.80059i −0.127401 0.220665i 0.795268 0.606258i \(-0.207330\pi\)
−0.922669 + 0.385593i \(0.873997\pi\)
\(692\) 0.497677 0.0189188
\(693\) 0 0
\(694\) 9.69467 0.368005
\(695\) 10.9743 + 19.0080i 0.416278 + 0.721016i
\(696\) 0 0
\(697\) −23.7518 + 41.1394i −0.899665 + 1.55827i
\(698\) −28.3984 −1.07489
\(699\) 0 0
\(700\) 0 0
\(701\) 25.1442 0.949683 0.474842 0.880071i \(-0.342505\pi\)
0.474842 + 0.880071i \(0.342505\pi\)
\(702\) 0 0
\(703\) 2.80314 + 4.85518i 0.105722 + 0.183117i
\(704\) −6.12476 −0.230836
\(705\) 0 0
\(706\) −2.19686 3.80507i −0.0826799 0.143206i
\(707\) 0 0
\(708\) 0 0
\(709\) −4.43310 7.67836i −0.166489 0.288367i 0.770694 0.637205i \(-0.219910\pi\)
−0.937183 + 0.348838i \(0.886576\pi\)
\(710\) −9.49549 16.4467i −0.356359 0.617232i
\(711\) 0 0
\(712\) −1.30150 + 2.25427i −0.0487760 + 0.0844824i
\(713\) 1.62188 2.80919i 0.0607401 0.105205i
\(714\) 0 0
\(715\) −4.10301 7.10662i −0.153444 0.265773i
\(716\) 8.82846 0.329935
\(717\) 0 0
\(718\) −32.1592 −1.20017
\(719\) 11.8015 20.4408i 0.440122 0.762313i −0.557576 0.830126i \(-0.688269\pi\)
0.997698 + 0.0678123i \(0.0216019\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −7.61273 + 13.1856i −0.283316 + 0.490718i
\(723\) 0 0
\(724\) 0.664703 1.15130i 0.0247035 0.0427877i
\(725\) 1.39084 2.40901i 0.0516546 0.0894683i
\(726\) 0 0
\(727\) −3.25692 + 5.64115i −0.120792 + 0.209219i −0.920080 0.391730i \(-0.871877\pi\)
0.799288 + 0.600948i \(0.205210\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.270036 0.467717i 0.00999449 0.0173110i
\(731\) −59.2542 −2.19159
\(732\) 0 0
\(733\) 23.1981 0.856842 0.428421 0.903579i \(-0.359070\pi\)
0.428421 + 0.903579i \(0.359070\pi\)
\(734\) −17.3015 29.9671i −0.638610 1.10611i
\(735\) 0 0
\(736\) 0.210533 0.364654i 0.00776036 0.0134413i
\(737\) 20.7781 35.9888i 0.765372 1.32566i
\(738\) 0 0
\(739\) −7.57838 13.1261i −0.278775 0.482853i 0.692305 0.721605i \(-0.256595\pi\)
−0.971081 + 0.238752i \(0.923262\pi\)
\(740\) 2.54063 + 4.40050i 0.0933954 + 0.161765i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.21737 + 9.03675i 0.191407 + 0.331526i 0.945717 0.324992i \(-0.105362\pi\)
−0.754310 + 0.656518i \(0.772028\pi\)
\(744\) 0 0
\(745\) −15.5458 −0.569555
\(746\) 5.48796 + 9.50543i 0.200929 + 0.348018i
\(747\) 0 0
\(748\) −41.9064 −1.53225
\(749\) 0 0
\(750\) 0 0
\(751\) 40.2118 1.46735 0.733674 0.679501i \(-0.237804\pi\)
0.733674 + 0.679501i \(0.237804\pi\)
\(752\) −0.830095 + 1.43777i −0.0302704 + 0.0524300i
\(753\) 0 0
\(754\) −0.557180 0.965064i −0.0202913 0.0351456i
\(755\) −26.3891 −0.960397
\(756\) 0 0
\(757\) −21.5206 −0.782181 −0.391091 0.920352i \(-0.627902\pi\)
−0.391091 + 0.920352i \(0.627902\pi\)
\(758\) 16.9939 + 29.4342i 0.617244 + 1.06910i
\(759\) 0 0
\(760\) 1.71053 2.96273i 0.0620476 0.107470i
\(761\) −23.6627 −0.857771 −0.428886 0.903359i \(-0.641094\pi\)
−0.428886 + 0.903359i \(0.641094\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 16.1683 0.584947
\(765\) 0 0
\(766\) −10.5120 18.2074i −0.379815 0.657860i
\(767\) −1.51135 −0.0545717
\(768\) 0 0
\(769\) 5.62764 + 9.74736i 0.202938 + 0.351499i 0.949474 0.313846i \(-0.101618\pi\)
−0.746536 + 0.665345i \(0.768284\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 7.08414 + 12.2701i 0.254964 + 0.441610i
\(773\) 0.138992 + 0.240741i 0.00499919 + 0.00865886i 0.868514 0.495664i \(-0.165075\pi\)
−0.863515 + 0.504323i \(0.831742\pi\)
\(774\) 0 0
\(775\) −7.31587 + 12.6715i −0.262794 + 0.455172i
\(776\) −1.81806 + 3.14897i −0.0652644 + 0.113041i
\(777\) 0 0
\(778\) −6.86909 11.8976i −0.246269 0.426550i
\(779\) 13.4887 0.483281
\(780\) 0 0
\(781\) 66.0553 2.36364
\(782\) 1.44050 2.49501i 0.0515121 0.0892215i
\(783\) 0 0
\(784\) 0 0
\(785\) 16.7112 28.9447i 0.596449 1.03308i
\(786\) 0 0
\(787\) −14.6940 + 25.4507i −0.523784 + 0.907220i 0.475833 + 0.879536i \(0.342147\pi\)
−0.999617 + 0.0276845i \(0.991187\pi\)
\(788\) 7.92107 13.7197i 0.282176 0.488744i
\(789\) 0 0
\(790\) −11.8376 + 20.5034i −0.421164 + 0.729477i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.93762 6.82015i 0.139829 0.242191i
\(794\)