Properties

Label 672.2.h.d.575.1
Level $672$
Weight $2$
Character 672.575
Analytic conductor $5.366$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.36594701583\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 575.1
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 672.575
Dual form 672.2.h.d.575.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.292893 - 1.70711i) q^{3} -3.41421i q^{5} -1.00000i q^{7} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(0.292893 - 1.70711i) q^{3} -3.41421i q^{5} -1.00000i q^{7} +(-2.82843 - 1.00000i) q^{9} +2.00000 q^{11} +3.41421 q^{13} +(-5.82843 - 1.00000i) q^{15} -4.82843i q^{17} +6.24264i q^{19} +(-1.70711 - 0.292893i) q^{21} -4.00000 q^{23} -6.65685 q^{25} +(-2.53553 + 4.53553i) q^{27} -4.82843i q^{29} -1.17157i q^{31} +(0.585786 - 3.41421i) q^{33} -3.41421 q^{35} -0.828427 q^{37} +(1.00000 - 5.82843i) q^{39} +10.0000i q^{41} +10.4853i q^{43} +(-3.41421 + 9.65685i) q^{45} +1.65685 q^{47} -1.00000 q^{49} +(-8.24264 - 1.41421i) q^{51} -13.3137i q^{53} -6.82843i q^{55} +(10.6569 + 1.82843i) q^{57} -6.24264 q^{59} +14.2426 q^{61} +(-1.00000 + 2.82843i) q^{63} -11.6569i q^{65} -9.31371i q^{67} +(-1.17157 + 6.82843i) q^{69} -0.343146 q^{71} -3.17157 q^{73} +(-1.94975 + 11.3640i) q^{75} -2.00000i q^{77} -4.00000i q^{79} +(7.00000 + 5.65685i) q^{81} +11.4142 q^{83} -16.4853 q^{85} +(-8.24264 - 1.41421i) q^{87} -7.65685i q^{89} -3.41421i q^{91} +(-2.00000 - 0.343146i) q^{93} +21.3137 q^{95} +5.31371 q^{97} +(-5.65685 - 2.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} + O(q^{10}) \) \( 4q + 4q^{3} + 8q^{11} + 8q^{13} - 12q^{15} - 4q^{21} - 16q^{23} - 4q^{25} + 4q^{27} + 8q^{33} - 8q^{35} + 8q^{37} + 4q^{39} - 8q^{45} - 16q^{47} - 4q^{49} - 16q^{51} + 20q^{57} - 8q^{59} + 40q^{61} - 4q^{63} - 16q^{69} - 24q^{71} - 24q^{73} + 12q^{75} + 28q^{81} + 40q^{83} - 32q^{85} - 16q^{87} - 8q^{93} + 40q^{95} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.292893 1.70711i 0.169102 0.985599i
\(4\) 0 0
\(5\) 3.41421i 1.52688i −0.645877 0.763441i \(-0.723508\pi\)
0.645877 0.763441i \(-0.276492\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) −2.82843 1.00000i −0.942809 0.333333i
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 3.41421 0.946932 0.473466 0.880812i \(-0.343003\pi\)
0.473466 + 0.880812i \(0.343003\pi\)
\(14\) 0 0
\(15\) −5.82843 1.00000i −1.50489 0.258199i
\(16\) 0 0
\(17\) 4.82843i 1.17107i −0.810649 0.585533i \(-0.800885\pi\)
0.810649 0.585533i \(-0.199115\pi\)
\(18\) 0 0
\(19\) 6.24264i 1.43216i 0.698018 + 0.716080i \(0.254065\pi\)
−0.698018 + 0.716080i \(0.745935\pi\)
\(20\) 0 0
\(21\) −1.70711 0.292893i −0.372521 0.0639145i
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −6.65685 −1.33137
\(26\) 0 0
\(27\) −2.53553 + 4.53553i −0.487964 + 0.872864i
\(28\) 0 0
\(29\) 4.82843i 0.896616i −0.893879 0.448308i \(-0.852027\pi\)
0.893879 0.448308i \(-0.147973\pi\)
\(30\) 0 0
\(31\) 1.17157i 0.210421i −0.994450 0.105210i \(-0.966448\pi\)
0.994450 0.105210i \(-0.0335516\pi\)
\(32\) 0 0
\(33\) 0.585786 3.41421i 0.101972 0.594338i
\(34\) 0 0
\(35\) −3.41421 −0.577107
\(36\) 0 0
\(37\) −0.828427 −0.136193 −0.0680963 0.997679i \(-0.521693\pi\)
−0.0680963 + 0.997679i \(0.521693\pi\)
\(38\) 0 0
\(39\) 1.00000 5.82843i 0.160128 0.933295i
\(40\) 0 0
\(41\) 10.0000i 1.56174i 0.624695 + 0.780869i \(0.285223\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 10.4853i 1.59899i 0.600672 + 0.799495i \(0.294900\pi\)
−0.600672 + 0.799495i \(0.705100\pi\)
\(44\) 0 0
\(45\) −3.41421 + 9.65685i −0.508961 + 1.43956i
\(46\) 0 0
\(47\) 1.65685 0.241677 0.120839 0.992672i \(-0.461442\pi\)
0.120839 + 0.992672i \(0.461442\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −8.24264 1.41421i −1.15420 0.198030i
\(52\) 0 0
\(53\) 13.3137i 1.82878i −0.404836 0.914389i \(-0.632671\pi\)
0.404836 0.914389i \(-0.367329\pi\)
\(54\) 0 0
\(55\) 6.82843i 0.920745i
\(56\) 0 0
\(57\) 10.6569 + 1.82843i 1.41153 + 0.242181i
\(58\) 0 0
\(59\) −6.24264 −0.812723 −0.406361 0.913712i \(-0.633203\pi\)
−0.406361 + 0.913712i \(0.633203\pi\)
\(60\) 0 0
\(61\) 14.2426 1.82358 0.911792 0.410653i \(-0.134699\pi\)
0.911792 + 0.410653i \(0.134699\pi\)
\(62\) 0 0
\(63\) −1.00000 + 2.82843i −0.125988 + 0.356348i
\(64\) 0 0
\(65\) 11.6569i 1.44585i
\(66\) 0 0
\(67\) 9.31371i 1.13785i −0.822389 0.568925i \(-0.807359\pi\)
0.822389 0.568925i \(-0.192641\pi\)
\(68\) 0 0
\(69\) −1.17157 + 6.82843i −0.141041 + 0.822046i
\(70\) 0 0
\(71\) −0.343146 −0.0407239 −0.0203620 0.999793i \(-0.506482\pi\)
−0.0203620 + 0.999793i \(0.506482\pi\)
\(72\) 0 0
\(73\) −3.17157 −0.371205 −0.185602 0.982625i \(-0.559424\pi\)
−0.185602 + 0.982625i \(0.559424\pi\)
\(74\) 0 0
\(75\) −1.94975 + 11.3640i −0.225137 + 1.31220i
\(76\) 0 0
\(77\) 2.00000i 0.227921i
\(78\) 0 0
\(79\) 4.00000i 0.450035i −0.974355 0.225018i \(-0.927756\pi\)
0.974355 0.225018i \(-0.0722440\pi\)
\(80\) 0 0
\(81\) 7.00000 + 5.65685i 0.777778 + 0.628539i
\(82\) 0 0
\(83\) 11.4142 1.25287 0.626436 0.779473i \(-0.284513\pi\)
0.626436 + 0.779473i \(0.284513\pi\)
\(84\) 0 0
\(85\) −16.4853 −1.78808
\(86\) 0 0
\(87\) −8.24264 1.41421i −0.883704 0.151620i
\(88\) 0 0
\(89\) 7.65685i 0.811625i −0.913956 0.405812i \(-0.866989\pi\)
0.913956 0.405812i \(-0.133011\pi\)
\(90\) 0 0
\(91\) 3.41421i 0.357907i
\(92\) 0 0
\(93\) −2.00000 0.343146i −0.207390 0.0355826i
\(94\) 0 0
\(95\) 21.3137 2.18674
\(96\) 0 0
\(97\) 5.31371 0.539525 0.269763 0.962927i \(-0.413055\pi\)
0.269763 + 0.962927i \(0.413055\pi\)
\(98\) 0 0
\(99\) −5.65685 2.00000i −0.568535 0.201008i
\(100\) 0 0
\(101\) 18.2426i 1.81521i 0.419825 + 0.907605i \(0.362092\pi\)
−0.419825 + 0.907605i \(0.637908\pi\)
\(102\) 0 0
\(103\) 16.9706i 1.67216i −0.548608 0.836080i \(-0.684842\pi\)
0.548608 0.836080i \(-0.315158\pi\)
\(104\) 0 0
\(105\) −1.00000 + 5.82843i −0.0975900 + 0.568796i
\(106\) 0 0
\(107\) 14.4853 1.40035 0.700173 0.713974i \(-0.253106\pi\)
0.700173 + 0.713974i \(0.253106\pi\)
\(108\) 0 0
\(109\) −2.48528 −0.238047 −0.119023 0.992891i \(-0.537976\pi\)
−0.119023 + 0.992891i \(0.537976\pi\)
\(110\) 0 0
\(111\) −0.242641 + 1.41421i −0.0230304 + 0.134231i
\(112\) 0 0
\(113\) 5.31371i 0.499872i 0.968262 + 0.249936i \(0.0804095\pi\)
−0.968262 + 0.249936i \(0.919590\pi\)
\(114\) 0 0
\(115\) 13.6569i 1.27351i
\(116\) 0 0
\(117\) −9.65685 3.41421i −0.892776 0.315644i
\(118\) 0 0
\(119\) −4.82843 −0.442621
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 17.0711 + 2.92893i 1.53925 + 0.264093i
\(124\) 0 0
\(125\) 5.65685i 0.505964i
\(126\) 0 0
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 0 0
\(129\) 17.8995 + 3.07107i 1.57596 + 0.270392i
\(130\) 0 0
\(131\) 21.5563 1.88339 0.941693 0.336472i \(-0.109234\pi\)
0.941693 + 0.336472i \(0.109234\pi\)
\(132\) 0 0
\(133\) 6.24264 0.541306
\(134\) 0 0
\(135\) 15.4853 + 8.65685i 1.33276 + 0.745063i
\(136\) 0 0
\(137\) 11.3137i 0.966595i −0.875456 0.483298i \(-0.839439\pi\)
0.875456 0.483298i \(-0.160561\pi\)
\(138\) 0 0
\(139\) 1.75736i 0.149057i −0.997219 0.0745286i \(-0.976255\pi\)
0.997219 0.0745286i \(-0.0237452\pi\)
\(140\) 0 0
\(141\) 0.485281 2.82843i 0.0408681 0.238197i
\(142\) 0 0
\(143\) 6.82843 0.571022
\(144\) 0 0
\(145\) −16.4853 −1.36903
\(146\) 0 0
\(147\) −0.292893 + 1.70711i −0.0241574 + 0.140800i
\(148\) 0 0
\(149\) 7.65685i 0.627274i −0.949543 0.313637i \(-0.898453\pi\)
0.949543 0.313637i \(-0.101547\pi\)
\(150\) 0 0
\(151\) 18.0000i 1.46482i 0.680864 + 0.732410i \(0.261604\pi\)
−0.680864 + 0.732410i \(0.738396\pi\)
\(152\) 0 0
\(153\) −4.82843 + 13.6569i −0.390355 + 1.10409i
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) 2.24264 0.178982 0.0894911 0.995988i \(-0.471476\pi\)
0.0894911 + 0.995988i \(0.471476\pi\)
\(158\) 0 0
\(159\) −22.7279 3.89949i −1.80244 0.309250i
\(160\) 0 0
\(161\) 4.00000i 0.315244i
\(162\) 0 0
\(163\) 8.14214i 0.637741i −0.947798 0.318871i \(-0.896696\pi\)
0.947798 0.318871i \(-0.103304\pi\)
\(164\) 0 0
\(165\) −11.6569 2.00000i −0.907485 0.155700i
\(166\) 0 0
\(167\) −10.8284 −0.837929 −0.418964 0.908003i \(-0.637607\pi\)
−0.418964 + 0.908003i \(0.637607\pi\)
\(168\) 0 0
\(169\) −1.34315 −0.103319
\(170\) 0 0
\(171\) 6.24264 17.6569i 0.477387 1.35025i
\(172\) 0 0
\(173\) 9.55635i 0.726556i 0.931681 + 0.363278i \(0.118342\pi\)
−0.931681 + 0.363278i \(0.881658\pi\)
\(174\) 0 0
\(175\) 6.65685i 0.503211i
\(176\) 0 0
\(177\) −1.82843 + 10.6569i −0.137433 + 0.801018i
\(178\) 0 0
\(179\) 6.48528 0.484733 0.242366 0.970185i \(-0.422076\pi\)
0.242366 + 0.970185i \(0.422076\pi\)
\(180\) 0 0
\(181\) 20.3848 1.51519 0.757594 0.652726i \(-0.226375\pi\)
0.757594 + 0.652726i \(0.226375\pi\)
\(182\) 0 0
\(183\) 4.17157 24.3137i 0.308372 1.79732i
\(184\) 0 0
\(185\) 2.82843i 0.207950i
\(186\) 0 0
\(187\) 9.65685i 0.706179i
\(188\) 0 0
\(189\) 4.53553 + 2.53553i 0.329912 + 0.184433i
\(190\) 0 0
\(191\) −3.65685 −0.264601 −0.132300 0.991210i \(-0.542236\pi\)
−0.132300 + 0.991210i \(0.542236\pi\)
\(192\) 0 0
\(193\) 17.6569 1.27097 0.635484 0.772114i \(-0.280801\pi\)
0.635484 + 0.772114i \(0.280801\pi\)
\(194\) 0 0
\(195\) −19.8995 3.41421i −1.42503 0.244497i
\(196\) 0 0
\(197\) 26.0000i 1.85242i 0.377004 + 0.926212i \(0.376954\pi\)
−0.377004 + 0.926212i \(0.623046\pi\)
\(198\) 0 0
\(199\) 7.31371i 0.518455i 0.965816 + 0.259228i \(0.0834680\pi\)
−0.965816 + 0.259228i \(0.916532\pi\)
\(200\) 0 0
\(201\) −15.8995 2.72792i −1.12146 0.192413i
\(202\) 0 0
\(203\) −4.82843 −0.338889
\(204\) 0 0
\(205\) 34.1421 2.38459
\(206\) 0 0
\(207\) 11.3137 + 4.00000i 0.786357 + 0.278019i
\(208\) 0 0
\(209\) 12.4853i 0.863625i
\(210\) 0 0
\(211\) 0.343146i 0.0236231i −0.999930 0.0118116i \(-0.996240\pi\)
0.999930 0.0118116i \(-0.00375982\pi\)
\(212\) 0 0
\(213\) −0.100505 + 0.585786i −0.00688649 + 0.0401374i
\(214\) 0 0
\(215\) 35.7990 2.44147
\(216\) 0 0
\(217\) −1.17157 −0.0795315
\(218\) 0 0
\(219\) −0.928932 + 5.41421i −0.0627714 + 0.365859i
\(220\) 0 0
\(221\) 16.4853i 1.10892i
\(222\) 0 0
\(223\) 2.82843i 0.189405i 0.995506 + 0.0947027i \(0.0301901\pi\)
−0.995506 + 0.0947027i \(0.969810\pi\)
\(224\) 0 0
\(225\) 18.8284 + 6.65685i 1.25523 + 0.443790i
\(226\) 0 0
\(227\) −23.8995 −1.58627 −0.793133 0.609049i \(-0.791551\pi\)
−0.793133 + 0.609049i \(0.791551\pi\)
\(228\) 0 0
\(229\) −1.07107 −0.0707782 −0.0353891 0.999374i \(-0.511267\pi\)
−0.0353891 + 0.999374i \(0.511267\pi\)
\(230\) 0 0
\(231\) −3.41421 0.585786i −0.224639 0.0385419i
\(232\) 0 0
\(233\) 8.97056i 0.587681i −0.955854 0.293841i \(-0.905067\pi\)
0.955854 0.293841i \(-0.0949335\pi\)
\(234\) 0 0
\(235\) 5.65685i 0.369012i
\(236\) 0 0
\(237\) −6.82843 1.17157i −0.443554 0.0761018i
\(238\) 0 0
\(239\) −11.3137 −0.731823 −0.365911 0.930650i \(-0.619243\pi\)
−0.365911 + 0.930650i \(0.619243\pi\)
\(240\) 0 0
\(241\) 3.65685 0.235559 0.117779 0.993040i \(-0.462422\pi\)
0.117779 + 0.993040i \(0.462422\pi\)
\(242\) 0 0
\(243\) 11.7071 10.2929i 0.751011 0.660289i
\(244\) 0 0
\(245\) 3.41421i 0.218126i
\(246\) 0 0
\(247\) 21.3137i 1.35616i
\(248\) 0 0
\(249\) 3.34315 19.4853i 0.211863 1.23483i
\(250\) 0 0
\(251\) −20.5858 −1.29936 −0.649682 0.760206i \(-0.725098\pi\)
−0.649682 + 0.760206i \(0.725098\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) 0 0
\(255\) −4.82843 + 28.1421i −0.302368 + 1.76233i
\(256\) 0 0
\(257\) 14.4853i 0.903567i 0.892128 + 0.451784i \(0.149212\pi\)
−0.892128 + 0.451784i \(0.850788\pi\)
\(258\) 0 0
\(259\) 0.828427i 0.0514760i
\(260\) 0 0
\(261\) −4.82843 + 13.6569i −0.298872 + 0.845338i
\(262\) 0 0
\(263\) −1.31371 −0.0810067 −0.0405034 0.999179i \(-0.512896\pi\)
−0.0405034 + 0.999179i \(0.512896\pi\)
\(264\) 0 0
\(265\) −45.4558 −2.79233
\(266\) 0 0
\(267\) −13.0711 2.24264i −0.799936 0.137247i
\(268\) 0 0
\(269\) 18.7279i 1.14186i −0.820998 0.570931i \(-0.806582\pi\)
0.820998 0.570931i \(-0.193418\pi\)
\(270\) 0 0
\(271\) 12.4853i 0.758427i −0.925309 0.379213i \(-0.876195\pi\)
0.925309 0.379213i \(-0.123805\pi\)
\(272\) 0 0
\(273\) −5.82843 1.00000i −0.352752 0.0605228i
\(274\) 0 0
\(275\) −13.3137 −0.802847
\(276\) 0 0
\(277\) −1.31371 −0.0789331 −0.0394665 0.999221i \(-0.512566\pi\)
−0.0394665 + 0.999221i \(0.512566\pi\)
\(278\) 0 0
\(279\) −1.17157 + 3.31371i −0.0701402 + 0.198387i
\(280\) 0 0
\(281\) 8.97056i 0.535139i 0.963539 + 0.267569i \(0.0862205\pi\)
−0.963539 + 0.267569i \(0.913780\pi\)
\(282\) 0 0
\(283\) 10.2426i 0.608862i −0.952534 0.304431i \(-0.901534\pi\)
0.952534 0.304431i \(-0.0984663\pi\)
\(284\) 0 0
\(285\) 6.24264 36.3848i 0.369782 2.15525i
\(286\) 0 0
\(287\) 10.0000 0.590281
\(288\) 0 0
\(289\) −6.31371 −0.371395
\(290\) 0 0
\(291\) 1.55635 9.07107i 0.0912348 0.531755i
\(292\) 0 0
\(293\) 1.27208i 0.0743156i −0.999309 0.0371578i \(-0.988170\pi\)
0.999309 0.0371578i \(-0.0118304\pi\)
\(294\) 0 0
\(295\) 21.3137i 1.24093i
\(296\) 0 0
\(297\) −5.07107 + 9.07107i −0.294253 + 0.526357i
\(298\) 0 0
\(299\) −13.6569 −0.789796
\(300\) 0 0
\(301\) 10.4853 0.604362
\(302\) 0 0
\(303\) 31.1421 + 5.34315i 1.78907 + 0.306956i
\(304\) 0 0
\(305\) 48.6274i 2.78440i
\(306\) 0 0
\(307\) 9.55635i 0.545410i 0.962098 + 0.272705i \(0.0879182\pi\)
−0.962098 + 0.272705i \(0.912082\pi\)
\(308\) 0 0
\(309\) −28.9706 4.97056i −1.64808 0.282765i
\(310\) 0 0
\(311\) −19.7990 −1.12270 −0.561349 0.827579i \(-0.689717\pi\)
−0.561349 + 0.827579i \(0.689717\pi\)
\(312\) 0 0
\(313\) −8.82843 −0.499012 −0.249506 0.968373i \(-0.580268\pi\)
−0.249506 + 0.968373i \(0.580268\pi\)
\(314\) 0 0
\(315\) 9.65685 + 3.41421i 0.544102 + 0.192369i
\(316\) 0 0
\(317\) 10.0000i 0.561656i −0.959758 0.280828i \(-0.909391\pi\)
0.959758 0.280828i \(-0.0906090\pi\)
\(318\) 0 0
\(319\) 9.65685i 0.540680i
\(320\) 0 0
\(321\) 4.24264 24.7279i 0.236801 1.38018i
\(322\) 0 0
\(323\) 30.1421 1.67715
\(324\) 0 0
\(325\) −22.7279 −1.26072
\(326\) 0 0
\(327\) −0.727922 + 4.24264i −0.0402542 + 0.234619i
\(328\) 0 0
\(329\) 1.65685i 0.0913453i
\(330\) 0 0
\(331\) 4.82843i 0.265394i −0.991157 0.132697i \(-0.957636\pi\)
0.991157 0.132697i \(-0.0423638\pi\)
\(332\) 0 0
\(333\) 2.34315 + 0.828427i 0.128404 + 0.0453975i
\(334\) 0 0
\(335\) −31.7990 −1.73736
\(336\) 0 0
\(337\) 27.3137 1.48787 0.743936 0.668251i \(-0.232957\pi\)
0.743936 + 0.668251i \(0.232957\pi\)
\(338\) 0 0
\(339\) 9.07107 + 1.55635i 0.492673 + 0.0845293i
\(340\) 0 0
\(341\) 2.34315i 0.126888i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 23.3137 + 4.00000i 1.25517 + 0.215353i
\(346\) 0 0
\(347\) 0.343146 0.0184210 0.00921051 0.999958i \(-0.497068\pi\)
0.00921051 + 0.999958i \(0.497068\pi\)
\(348\) 0 0
\(349\) 14.9289 0.799127 0.399564 0.916705i \(-0.369162\pi\)
0.399564 + 0.916705i \(0.369162\pi\)
\(350\) 0 0
\(351\) −8.65685 + 15.4853i −0.462069 + 0.826543i
\(352\) 0 0
\(353\) 19.4558i 1.03553i 0.855523 + 0.517765i \(0.173236\pi\)
−0.855523 + 0.517765i \(0.826764\pi\)
\(354\) 0 0
\(355\) 1.17157i 0.0621806i
\(356\) 0 0
\(357\) −1.41421 + 8.24264i −0.0748481 + 0.436247i
\(358\) 0 0
\(359\) −26.6274 −1.40534 −0.702671 0.711515i \(-0.748009\pi\)
−0.702671 + 0.711515i \(0.748009\pi\)
\(360\) 0 0
\(361\) −19.9706 −1.05108
\(362\) 0 0
\(363\) −2.05025 + 11.9497i −0.107610 + 0.627199i
\(364\) 0 0
\(365\) 10.8284i 0.566786i
\(366\) 0 0
\(367\) 13.1716i 0.687551i −0.939052 0.343775i \(-0.888294\pi\)
0.939052 0.343775i \(-0.111706\pi\)
\(368\) 0 0
\(369\) 10.0000 28.2843i 0.520579 1.47242i
\(370\) 0 0
\(371\) −13.3137 −0.691213
\(372\) 0 0
\(373\) −22.9706 −1.18937 −0.594685 0.803959i \(-0.702723\pi\)
−0.594685 + 0.803959i \(0.702723\pi\)
\(374\) 0 0
\(375\) 9.65685 + 1.65685i 0.498678 + 0.0855596i
\(376\) 0 0
\(377\) 16.4853i 0.849035i
\(378\) 0 0
\(379\) 34.4853i 1.77139i −0.464268 0.885695i \(-0.653682\pi\)
0.464268 0.885695i \(-0.346318\pi\)
\(380\) 0 0
\(381\) 3.41421 + 0.585786i 0.174915 + 0.0300107i
\(382\) 0 0
\(383\) 5.65685 0.289052 0.144526 0.989501i \(-0.453834\pi\)
0.144526 + 0.989501i \(0.453834\pi\)
\(384\) 0 0
\(385\) −6.82843 −0.348009
\(386\) 0 0
\(387\) 10.4853 29.6569i 0.532997 1.50754i
\(388\) 0 0
\(389\) 6.48528i 0.328817i −0.986392 0.164408i \(-0.947429\pi\)
0.986392 0.164408i \(-0.0525715\pi\)
\(390\) 0 0
\(391\) 19.3137i 0.976736i
\(392\) 0 0
\(393\) 6.31371 36.7990i 0.318484 1.85626i
\(394\) 0 0
\(395\) −13.6569 −0.687151
\(396\) 0 0
\(397\) 18.2426 0.915572 0.457786 0.889062i \(-0.348643\pi\)
0.457786 + 0.889062i \(0.348643\pi\)
\(398\) 0 0
\(399\) 1.82843 10.6569i 0.0915358 0.533510i
\(400\) 0 0
\(401\) 31.6569i 1.58087i 0.612547 + 0.790434i \(0.290145\pi\)
−0.612547 + 0.790434i \(0.709855\pi\)
\(402\) 0 0
\(403\) 4.00000i 0.199254i
\(404\) 0 0
\(405\) 19.3137 23.8995i 0.959706 1.18758i
\(406\) 0 0
\(407\) −1.65685 −0.0821272
\(408\) 0 0
\(409\) 26.4853 1.30961 0.654806 0.755797i \(-0.272750\pi\)
0.654806 + 0.755797i \(0.272750\pi\)
\(410\) 0 0
\(411\) −19.3137 3.31371i −0.952675 0.163453i
\(412\) 0 0
\(413\) 6.24264i 0.307180i
\(414\) 0 0
\(415\) 38.9706i 1.91299i
\(416\) 0 0
\(417\) −3.00000 0.514719i −0.146911 0.0252059i
\(418\) 0 0
\(419\) −18.7279 −0.914919 −0.457459 0.889230i \(-0.651241\pi\)
−0.457459 + 0.889230i \(0.651241\pi\)
\(420\) 0 0
\(421\) −15.6569 −0.763068 −0.381534 0.924355i \(-0.624604\pi\)
−0.381534 + 0.924355i \(0.624604\pi\)
\(422\) 0 0
\(423\) −4.68629 1.65685i −0.227855 0.0805590i
\(424\) 0 0
\(425\) 32.1421i 1.55912i
\(426\) 0 0
\(427\) 14.2426i 0.689250i
\(428\) 0 0
\(429\) 2.00000 11.6569i 0.0965609 0.562798i
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) 14.9706 0.719439 0.359720 0.933060i \(-0.382872\pi\)
0.359720 + 0.933060i \(0.382872\pi\)
\(434\) 0 0
\(435\) −4.82843 + 28.1421i −0.231505 + 1.34931i
\(436\) 0 0
\(437\) 24.9706i 1.19450i
\(438\) 0 0
\(439\) 40.2843i 1.92266i 0.275393 + 0.961332i \(0.411192\pi\)
−0.275393 + 0.961332i \(0.588808\pi\)
\(440\) 0 0
\(441\) 2.82843 + 1.00000i 0.134687 + 0.0476190i
\(442\) 0 0
\(443\) 23.1716 1.10091 0.550457 0.834863i \(-0.314453\pi\)
0.550457 + 0.834863i \(0.314453\pi\)
\(444\) 0 0
\(445\) −26.1421 −1.23926
\(446\) 0 0
\(447\) −13.0711 2.24264i −0.618240 0.106073i
\(448\) 0 0
\(449\) 18.3431i 0.865667i −0.901474 0.432833i \(-0.857514\pi\)
0.901474 0.432833i \(-0.142486\pi\)
\(450\) 0 0
\(451\) 20.0000i 0.941763i
\(452\) 0 0
\(453\) 30.7279 + 5.27208i 1.44372 + 0.247704i
\(454\) 0 0
\(455\) −11.6569 −0.546482
\(456\) 0 0
\(457\) −24.0000 −1.12267 −0.561336 0.827588i \(-0.689713\pi\)
−0.561336 + 0.827588i \(0.689713\pi\)
\(458\) 0 0
\(459\) 21.8995 + 12.2426i 1.02218 + 0.571438i
\(460\) 0 0
\(461\) 22.0416i 1.02658i 0.858215 + 0.513291i \(0.171574\pi\)
−0.858215 + 0.513291i \(0.828426\pi\)
\(462\) 0 0
\(463\) 1.65685i 0.0770005i −0.999259 0.0385003i \(-0.987742\pi\)
0.999259 0.0385003i \(-0.0122580\pi\)
\(464\) 0 0
\(465\) −1.17157 + 6.82843i −0.0543304 + 0.316661i
\(466\) 0 0
\(467\) 18.0416 0.834867 0.417434 0.908707i \(-0.362930\pi\)
0.417434 + 0.908707i \(0.362930\pi\)
\(468\) 0 0
\(469\) −9.31371 −0.430067
\(470\) 0 0
\(471\) 0.656854 3.82843i 0.0302662 0.176405i
\(472\) 0 0
\(473\) 20.9706i 0.964228i
\(474\) 0 0
\(475\) 41.5563i 1.90674i
\(476\) 0 0
\(477\) −13.3137 + 37.6569i −0.609593 + 1.72419i
\(478\) 0 0
\(479\) −11.3137 −0.516937 −0.258468 0.966020i \(-0.583218\pi\)
−0.258468 + 0.966020i \(0.583218\pi\)
\(480\) 0 0
\(481\) −2.82843 −0.128965
\(482\) 0 0
\(483\) 6.82843 + 1.17157i 0.310704 + 0.0533084i
\(484\) 0 0
\(485\) 18.1421i 0.823792i
\(486\) 0 0
\(487\) 22.0000i 0.996915i 0.866914 + 0.498458i \(0.166100\pi\)
−0.866914 + 0.498458i \(0.833900\pi\)
\(488\) 0 0
\(489\) −13.8995 2.38478i −0.628557 0.107843i
\(490\) 0 0
\(491\) −7.17157 −0.323649 −0.161824 0.986820i \(-0.551738\pi\)
−0.161824 + 0.986820i \(0.551738\pi\)
\(492\) 0 0
\(493\) −23.3137 −1.05000
\(494\) 0 0
\(495\) −6.82843 + 19.3137i −0.306915 + 0.868087i
\(496\) 0 0
\(497\) 0.343146i 0.0153922i
\(498\) 0 0
\(499\) 36.6274i 1.63967i 0.572601 + 0.819834i \(0.305934\pi\)
−0.572601 + 0.819834i \(0.694066\pi\)
\(500\) 0 0
\(501\) −3.17157 + 18.4853i −0.141695 + 0.825861i
\(502\) 0 0
\(503\) 25.4558 1.13502 0.567510 0.823367i \(-0.307907\pi\)
0.567510 + 0.823367i \(0.307907\pi\)
\(504\) 0 0
\(505\) 62.2843 2.77161
\(506\) 0 0
\(507\) −0.393398 + 2.29289i −0.0174714 + 0.101831i
\(508\) 0 0
\(509\) 20.8701i 0.925049i 0.886606 + 0.462525i \(0.153056\pi\)
−0.886606 + 0.462525i \(0.846944\pi\)
\(510\) 0 0
\(511\) 3.17157i 0.140302i
\(512\) 0 0
\(513\) −28.3137 15.8284i −1.25008 0.698842i
\(514\) 0 0
\(515\) −57.9411 −2.55319
\(516\) 0 0
\(517\) 3.31371 0.145737
\(518\) 0 0
\(519\) 16.3137 + 2.79899i 0.716092 + 0.122862i
\(520\) 0 0
\(521\) 12.3431i 0.540763i 0.962753 + 0.270382i \(0.0871498\pi\)
−0.962753 + 0.270382i \(0.912850\pi\)
\(522\) 0 0
\(523\) 39.8995i 1.74468i 0.488897 + 0.872342i \(0.337399\pi\)
−0.488897 + 0.872342i \(0.662601\pi\)
\(524\) 0 0
\(525\) 11.3640 + 1.94975i 0.495964 + 0.0850940i
\(526\) 0 0
\(527\) −5.65685 −0.246416
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 17.6569 + 6.24264i 0.766242 + 0.270908i
\(532\) 0 0
\(533\) 34.1421i 1.47886i
\(534\) 0 0
\(535\) 49.4558i 2.13816i
\(536\) 0 0
\(537\) 1.89949 11.0711i 0.0819693 0.477752i
\(538\) 0 0
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) 12.6274 0.542895 0.271448 0.962453i \(-0.412498\pi\)
0.271448 + 0.962453i \(0.412498\pi\)
\(542\) 0 0
\(543\) 5.97056 34.7990i 0.256221 1.49337i
\(544\) 0 0
\(545\) 8.48528i 0.363470i
\(546\) 0 0
\(547\) 8.14214i 0.348133i −0.984734 0.174066i \(-0.944309\pi\)
0.984734 0.174066i \(-0.0556907\pi\)
\(548\) 0 0
\(549\) −40.2843 14.2426i −1.71929 0.607861i
\(550\) 0 0
\(551\) 30.1421 1.28410
\(552\) 0 0
\(553\) −4.00000 −0.170097
\(554\) 0 0
\(555\) 4.82843 + 0.828427i 0.204955 + 0.0351648i
\(556\) 0 0
\(557\) 6.68629i 0.283307i 0.989916 + 0.141654i \(0.0452419\pi\)
−0.989916 + 0.141654i \(0.954758\pi\)
\(558\) 0 0
\(559\) 35.7990i 1.51414i
\(560\) 0 0
\(561\) −16.4853 2.82843i −0.696009 0.119416i
\(562\) 0 0
\(563\) −7.21320 −0.304000 −0.152000 0.988380i \(-0.548571\pi\)
−0.152000 + 0.988380i \(0.548571\pi\)
\(564\) 0 0
\(565\) 18.1421 0.763245
\(566\) 0 0
\(567\) 5.65685 7.00000i 0.237566 0.293972i
\(568\) 0 0
\(569\) 1.31371i 0.0550735i 0.999621 + 0.0275368i \(0.00876633\pi\)
−0.999621 + 0.0275368i \(0.991234\pi\)
\(570\) 0 0
\(571\) 8.14214i 0.340738i 0.985380 + 0.170369i \(0.0544959\pi\)
−0.985380 + 0.170369i \(0.945504\pi\)
\(572\) 0 0
\(573\) −1.07107 + 6.24264i −0.0447445 + 0.260790i
\(574\) 0 0
\(575\) 26.6274 1.11044
\(576\) 0 0
\(577\) 29.3137 1.22035 0.610173 0.792268i \(-0.291100\pi\)
0.610173 + 0.792268i \(0.291100\pi\)
\(578\) 0 0
\(579\) 5.17157 30.1421i 0.214923 1.25266i
\(580\) 0 0
\(581\) 11.4142i 0.473541i
\(582\) 0 0
\(583\) 26.6274i 1.10279i
\(584\) 0 0
\(585\) −11.6569 + 32.9706i −0.481952 + 1.36316i
\(586\) 0 0
\(587\) 30.7279 1.26828 0.634139 0.773219i \(-0.281355\pi\)
0.634139 + 0.773219i \(0.281355\pi\)
\(588\) 0 0
\(589\) 7.31371 0.301356
\(590\) 0 0
\(591\) 44.3848 + 7.61522i 1.82575 + 0.313248i
\(592\) 0 0
\(593\) 22.4853i 0.923360i 0.887047 + 0.461680i \(0.152753\pi\)
−0.887047 + 0.461680i \(0.847247\pi\)
\(594\) 0 0
\(595\) 16.4853i 0.675831i
\(596\) 0 0
\(597\) 12.4853 + 2.14214i 0.510989 + 0.0876718i
\(598\) 0 0
\(599\) −16.6274 −0.679378 −0.339689 0.940538i \(-0.610322\pi\)
−0.339689 + 0.940538i \(0.610322\pi\)
\(600\) 0 0
\(601\) −16.1421 −0.658451 −0.329226 0.944251i \(-0.606788\pi\)
−0.329226 + 0.944251i \(0.606788\pi\)
\(602\) 0 0
\(603\) −9.31371 + 26.3431i −0.379284 + 1.07278i
\(604\) 0 0
\(605\) 23.8995i 0.971653i
\(606\) 0 0
\(607\) 2.14214i 0.0869466i 0.999055 + 0.0434733i \(0.0138423\pi\)
−0.999055 + 0.0434733i \(0.986158\pi\)
\(608\) 0 0
\(609\) −1.41421 + 8.24264i −0.0573068 + 0.334009i
\(610\) 0 0
\(611\) 5.65685 0.228852
\(612\) 0 0
\(613\) 26.7696 1.08121 0.540606 0.841276i \(-0.318195\pi\)
0.540606 + 0.841276i \(0.318195\pi\)
\(614\) 0 0
\(615\) 10.0000 58.2843i 0.403239 2.35025i
\(616\) 0 0
\(617\) 28.6274i 1.15250i 0.817275 + 0.576248i \(0.195484\pi\)
−0.817275 + 0.576248i \(0.804516\pi\)
\(618\) 0 0
\(619\) 18.2426i 0.733234i 0.930372 + 0.366617i \(0.119484\pi\)
−0.930372 + 0.366617i \(0.880516\pi\)
\(620\) 0 0
\(621\) 10.1421 18.1421i 0.406990 0.728019i
\(622\) 0 0
\(623\) −7.65685 −0.306765
\(624\) 0 0
\(625\) −13.9706 −0.558823
\(626\) 0 0
\(627\) 21.3137 + 3.65685i 0.851188 + 0.146041i
\(628\) 0 0
\(629\) 4.00000i 0.159490i
\(630\) 0 0
\(631\) 8.97056i 0.357112i −0.983930 0.178556i \(-0.942857\pi\)
0.983930 0.178556i \(-0.0571426\pi\)
\(632\) 0 0
\(633\) −0.585786 0.100505i −0.0232829 0.00399472i
\(634\) 0 0
\(635\) 6.82843 0.270978
\(636\) 0 0
\(637\) −3.41421 −0.135276
\(638\) 0 0
\(639\) 0.970563 + 0.343146i 0.0383949 + 0.0135746i
\(640\) 0 0
\(641\) 4.34315i 0.171544i −0.996315 0.0857720i \(-0.972664\pi\)
0.996315 0.0857720i \(-0.0273357\pi\)
\(642\) 0 0
\(643\) 37.7574i 1.48900i 0.667620 + 0.744502i \(0.267313\pi\)
−0.667620 + 0.744502i \(0.732687\pi\)
\(644\) 0 0
\(645\) 10.4853 61.1127i 0.412858 2.40631i
\(646\) 0 0
\(647\) 21.4558 0.843516 0.421758 0.906708i \(-0.361413\pi\)
0.421758 + 0.906708i \(0.361413\pi\)
\(648\) 0 0
\(649\) −12.4853 −0.490090
\(650\) 0 0
\(651\) −0.343146 + 2.00000i −0.0134489 + 0.0783862i
\(652\) 0 0
\(653\) 2.48528i 0.0972566i 0.998817 + 0.0486283i \(0.0154850\pi\)
−0.998817 + 0.0486283i \(0.984515\pi\)
\(654\) 0 0
\(655\) 73.5980i 2.87571i
\(656\) 0 0
\(657\) 8.97056 + 3.17157i 0.349975 + 0.123735i
\(658\) 0 0
\(659\) −14.9706 −0.583170 −0.291585 0.956545i \(-0.594183\pi\)
−0.291585 + 0.956545i \(0.594183\pi\)
\(660\) 0 0
\(661\) 40.1838 1.56297 0.781484 0.623926i \(-0.214463\pi\)
0.781484 + 0.623926i \(0.214463\pi\)
\(662\) 0 0
\(663\) −28.1421 4.82843i −1.09295 0.187521i
\(664\) 0 0
\(665\) 21.3137i 0.826510i
\(666\) 0 0
\(667\) 19.3137i 0.747830i
\(668\) 0 0
\(669\) 4.82843 + 0.828427i 0.186678 + 0.0320288i
\(670\) 0 0
\(671\) 28.4853 1.09966
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 0 0
\(675\) 16.8787 30.1924i 0.649661 1.16211i
\(676\) 0 0
\(677\) 4.87006i 0.187172i 0.995611 + 0.0935858i \(0.0298329\pi\)
−0.995611 + 0.0935858i \(0.970167\pi\)
\(678\) 0 0
\(679\) 5.31371i 0.203921i
\(680\) 0 0
\(681\) −7.00000 + 40.7990i −0.268241 + 1.56342i
\(682\) 0 0
\(683\) 29.5147 1.12935 0.564675 0.825314i \(-0.309002\pi\)
0.564675 + 0.825314i \(0.309002\pi\)
\(684\) 0 0
\(685\) −38.6274 −1.47588
\(686\) 0 0
\(687\) −0.313708 + 1.82843i −0.0119687 + 0.0697588i
\(688\) 0 0
\(689\) 45.4558i 1.73173i
\(690\) 0 0
\(691\) 22.0416i 0.838503i −0.907870 0.419252i \(-0.862293\pi\)
0.907870 0.419252i \(-0.137707\pi\)
\(692\) 0 0
\(693\) −2.00000 + 5.65685i −0.0759737 + 0.214886i
\(694\) 0 0
\(695\) −6.00000 −0.227593
\(696\) 0 0
\(697\) 48.2843 1.82890
\(698\) 0 0
\(699\) −15.3137 2.62742i −0.579218 0.0993780i
\(700\) 0 0
\(701\) 28.1421i 1.06291i −0.847085 0.531457i \(-0.821645\pi\)
0.847085 0.531457i \(-0.178355\pi\)
\(702\) 0 0
\(703\) 5.17157i 0.195050i
\(704\) 0 0
\(705\) −9.65685 1.65685i −0.363698 0.0624007i
\(706\) 0 0
\(707\) 18.2426 0.686085
\(708\) 0 0
\(709\) 5.51472 0.207110 0.103555 0.994624i \(-0.466978\pi\)
0.103555 + 0.994624i \(0.466978\pi\)
\(710\) 0 0
\(711\) −4.00000 + 11.3137i −0.150012 + 0.424297i
\(712\) 0 0
\(713\) 4.68629i 0.175503i
\(714\) 0 0
\(715\) 23.3137i 0.871883i
\(716\) 0 0
\(717\) −3.31371 + 19.3137i −0.123753 + 0.721284i
\(718\) 0 0
\(719\) −20.6863 −0.771468 −0.385734 0.922610i \(-0.626052\pi\)
−0.385734 + 0.922610i \(0.626052\pi\)
\(720\) 0 0
\(721\) −16.9706 −0.632017
\(722\) 0 0
\(723\) 1.07107 6.24264i 0.0398334 0.232166i
\(724\) 0 0
\(725\) 32.1421i 1.19373i
\(726\) 0 0
\(727\) 10.6274i 0.394149i −0.980389 0.197075i \(-0.936856\pi\)
0.980389 0.197075i \(-0.0631441\pi\)
\(728\) 0 0
\(729\) −14.1421 23.0000i −0.523783 0.851852i
\(730\) 0 0
\(731\) 50.6274 1.87252
\(732\) 0 0
\(733\) 0.384776 0.0142120 0.00710602 0.999975i \(-0.497738\pi\)
0.00710602 + 0.999975i \(0.497738\pi\)
\(734\) 0 0
\(735\) 5.82843 + 1.00000i 0.214985 + 0.0368856i
\(736\) 0 0
\(737\) 18.6274i 0.686150i
\(738\) 0 0
\(739\) 11.8579i 0.436199i −0.975927 0.218099i \(-0.930014\pi\)
0.975927 0.218099i \(-0.0699857\pi\)
\(740\) 0 0
\(741\) 36.3848 + 6.24264i 1.33663 + 0.229329i
\(742\) 0 0
\(743\) 21.9411 0.804942 0.402471 0.915433i \(-0.368151\pi\)
0.402471 + 0.915433i \(0.368151\pi\)
\(744\) 0 0
\(745\) −26.1421 −0.957774
\(746\) 0 0
\(747\) −32.2843 11.4142i −1.18122 0.417624i
\(748\) 0 0
\(749\) 14.4853i 0.529281i
\(750\) 0 0
\(751\) 30.2843i 1.10509i 0.833483 + 0.552544i \(0.186343\pi\)
−0.833483 + 0.552544i \(0.813657\pi\)
\(752\) 0 0
\(753\) −6.02944 + 35.1421i −0.219725 + 1.28065i
\(754\) 0 0
\(755\) 61.4558 2.23661
\(756\) 0 0
\(757\) −49.1127 −1.78503 −0.892516 0.451016i \(-0.851062\pi\)
−0.892516 + 0.451016i \(0.851062\pi\)
\(758\) 0 0
\(759\) −2.34315 + 13.6569i −0.0850508 + 0.495712i
\(760\) 0 0
\(761\) 1.02944i 0.0373171i −0.999826 0.0186585i \(-0.994060\pi\)
0.999826 0.0186585i \(-0.00593954\pi\)
\(762\) 0 0
\(763\) 2.48528i 0.0899732i
\(764\) 0 0
\(765\) 46.6274 + 16.4853i 1.68582 + 0.596027i
\(766\) 0 0
\(767\) −21.3137 −0.769593
\(768\) 0 0
\(769\) 8.34315 0.300862 0.150431 0.988621i \(-0.451934\pi\)
0.150431 + 0.988621i \(0.451934\pi\)
\(770\) 0 0
\(771\) 24.7279 + 4.24264i 0.890554 + 0.152795i
\(772\) 0 0
\(773\) 1.27208i 0.0457535i 0.999738 + 0.0228767i \(0.00728253\pi\)
−0.999738 + 0.0228767i \(0.992717\pi\)
\(774\) 0 0
\(775\) 7.79899i 0.280148i
\(776\) 0 0
\(777\) 1.41421 + 0.242641i 0.0507346 + 0.00870469i
\(778\) 0 0
\(779\) −62.4264 −2.23666
\(780\) 0 0
\(781\) −0.686292 −0.0245574
\(782\) 0 0
\(783\) 21.8995 + 12.2426i 0.782624 + 0.437516i
\(784\) 0 0
\(785\) 7.65685i 0.273285i
\(786\) 0 0
\(787\) 33.7574i 1.20332i 0.798752 + 0.601660i \(0.205494\pi\)
−0.798752 + 0.601660i \(0.794506\pi\)
\(788\) 0 0
\(789\) −0.384776 + 2.24264i −0.0136984 + 0.0798401i
\(790\) 0 0
\(791\) 5.31371 0.188934
\(792\) 0 0
\(793\) 48.6274 1.72681
\(794\) 0 0
\(795\) −13.3137 + 77.5980i −0.472189 + 2.75212i
\(796\) 0 0
\(797\) 12.1005i 0.428622i 0.976765 + 0.214311i \(0.0687506\pi\)
−0.976765 + 0.214311i \(0.931249\pi\)
\(798\) 0 0
\(799\) 8.00000i 0.283020i
\(800\) 0 0
\(801\) −7.65685 + 21.6569i −0.270542 + 0.765207i
\(802\) 0 0
\(803\) −6.34315 −0.223845
\(804\) 0 0
\(805\) 13.6569 0.481341
\(806\) 0 0
\(807\) −31.9706 5.48528i −1.12542 0.193091i
\(808\) 0 0
\(809\) 10.6863i