Properties

Label 216.2.f.a.107.2
Level $216$
Weight $2$
Character 216.107
Analytic conductor $1.725$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.23123460096.3
Defining polynomial: \(x^{8} + 2 x^{6} + 6 x^{4} + 8 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.2
Root \(1.08766 + 0.903873i\) of defining polynomial
Character \(\chi\) \(=\) 216.107
Dual form 216.2.f.a.107.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.08766 + 0.903873i) q^{2} +(0.366025 - 1.96622i) q^{4} -1.59245 q^{5} +1.43937i q^{7} +(1.37910 + 2.46943i) q^{8} +O(q^{10})\) \(q+(-1.08766 + 0.903873i) q^{2} +(0.366025 - 1.96622i) q^{4} -1.59245 q^{5} +1.43937i q^{7} +(1.37910 + 2.46943i) q^{8} +(1.73205 - 1.43937i) q^{10} +4.93886i q^{11} +5.37182i q^{13} +(-1.30101 - 1.56555i) q^{14} +(-3.73205 - 1.43937i) q^{16} -1.32336i q^{17} +0.267949 q^{19} +(-0.582877 + 3.13111i) q^{20} +(-4.46410 - 5.37182i) q^{22} +5.94311 q^{23} -2.46410 q^{25} +(-4.85544 - 5.84273i) q^{26} +(2.83013 + 0.526847i) q^{28} -8.70131 q^{29} +7.86488i q^{31} +(5.36023 - 1.80775i) q^{32} +(1.19615 + 1.43937i) q^{34} -2.29213i q^{35} -2.49307i q^{37} +(-0.291439 + 0.242192i) q^{38} +(-2.19615 - 3.93244i) q^{40} -9.87771i q^{41} +2.00000 q^{43} +(9.71088 + 1.80775i) q^{44} +(-6.46410 + 5.37182i) q^{46} +9.12801 q^{47} +4.92820 q^{49} +(2.68011 - 2.22724i) q^{50} +(10.5622 + 1.96622i) q^{52} +5.51641 q^{53} -7.86488i q^{55} +(-3.55443 + 1.98504i) q^{56} +(9.46410 - 7.86488i) q^{58} +4.93886i q^{59} -5.37182i q^{61} +(-7.10886 - 8.55435i) q^{62} +(-4.19615 + 6.81119i) q^{64} -8.55435i q^{65} +1.19615 q^{67} +(-2.60202 - 0.484384i) q^{68} +(2.07180 + 2.49307i) q^{70} -5.51641 q^{71} -7.92820 q^{73} +(2.25342 + 2.71162i) q^{74} +(0.0980762 - 0.526847i) q^{76} -7.10886 q^{77} -12.1830i q^{79} +(5.94311 + 2.29213i) q^{80} +(8.92820 + 10.7436i) q^{82} +7.23099i q^{83} +2.10739i q^{85} +(-2.17533 + 1.80775i) q^{86} +(-12.1962 + 6.81119i) q^{88} +15.7853i q^{89} -7.73205 q^{91} +(2.17533 - 11.6855i) q^{92} +(-9.92820 + 8.25056i) q^{94} -0.426696 q^{95} +9.39230 q^{97} +(-5.36023 + 4.45447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{4} + O(q^{10}) \) \( 8q - 4q^{4} - 16q^{16} + 16q^{19} - 8q^{22} + 8q^{25} - 12q^{28} - 32q^{34} + 24q^{40} + 16q^{43} - 24q^{46} - 16q^{49} + 36q^{52} + 48q^{58} + 8q^{64} - 32q^{67} + 72q^{70} - 8q^{73} - 20q^{76} + 16q^{82} - 56q^{88} - 48q^{91} - 24q^{94} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.08766 + 0.903873i −0.769095 + 0.639135i
\(3\) 0 0
\(4\) 0.366025 1.96622i 0.183013 0.983111i
\(5\) −1.59245 −0.712165 −0.356083 0.934454i \(-0.615888\pi\)
−0.356083 + 0.934454i \(0.615888\pi\)
\(6\) 0 0
\(7\) 1.43937i 0.544032i 0.962293 + 0.272016i \(0.0876904\pi\)
−0.962293 + 0.272016i \(0.912310\pi\)
\(8\) 1.37910 + 2.46943i 0.487586 + 0.873075i
\(9\) 0 0
\(10\) 1.73205 1.43937i 0.547723 0.455170i
\(11\) 4.93886i 1.48912i 0.667555 + 0.744561i \(0.267341\pi\)
−0.667555 + 0.744561i \(0.732659\pi\)
\(12\) 0 0
\(13\) 5.37182i 1.48987i 0.667135 + 0.744937i \(0.267520\pi\)
−0.667135 + 0.744937i \(0.732480\pi\)
\(14\) −1.30101 1.56555i −0.347710 0.418412i
\(15\) 0 0
\(16\) −3.73205 1.43937i −0.933013 0.359843i
\(17\) 1.32336i 0.320963i −0.987039 0.160481i \(-0.948695\pi\)
0.987039 0.160481i \(-0.0513046\pi\)
\(18\) 0 0
\(19\) 0.267949 0.0614718 0.0307359 0.999528i \(-0.490215\pi\)
0.0307359 + 0.999528i \(0.490215\pi\)
\(20\) −0.582877 + 3.13111i −0.130335 + 0.700137i
\(21\) 0 0
\(22\) −4.46410 5.37182i −0.951750 1.14528i
\(23\) 5.94311 1.23922 0.619612 0.784909i \(-0.287290\pi\)
0.619612 + 0.784909i \(0.287290\pi\)
\(24\) 0 0
\(25\) −2.46410 −0.492820
\(26\) −4.85544 5.84273i −0.952231 1.14585i
\(27\) 0 0
\(28\) 2.83013 + 0.526847i 0.534844 + 0.0995648i
\(29\) −8.70131 −1.61579 −0.807896 0.589324i \(-0.799394\pi\)
−0.807896 + 0.589324i \(0.799394\pi\)
\(30\) 0 0
\(31\) 7.86488i 1.41257i 0.707925 + 0.706287i \(0.249631\pi\)
−0.707925 + 0.706287i \(0.750369\pi\)
\(32\) 5.36023 1.80775i 0.947564 0.319568i
\(33\) 0 0
\(34\) 1.19615 + 1.43937i 0.205138 + 0.246851i
\(35\) 2.29213i 0.387441i
\(36\) 0 0
\(37\) 2.49307i 0.409858i −0.978777 0.204929i \(-0.934304\pi\)
0.978777 0.204929i \(-0.0656963\pi\)
\(38\) −0.291439 + 0.242192i −0.0472776 + 0.0392888i
\(39\) 0 0
\(40\) −2.19615 3.93244i −0.347242 0.621774i
\(41\) 9.87771i 1.54264i −0.636448 0.771320i \(-0.719597\pi\)
0.636448 0.771320i \(-0.280403\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 9.71088 + 1.80775i 1.46397 + 0.272528i
\(45\) 0 0
\(46\) −6.46410 + 5.37182i −0.953080 + 0.792031i
\(47\) 9.12801 1.33146 0.665728 0.746194i \(-0.268121\pi\)
0.665728 + 0.746194i \(0.268121\pi\)
\(48\) 0 0
\(49\) 4.92820 0.704029
\(50\) 2.68011 2.22724i 0.379025 0.314979i
\(51\) 0 0
\(52\) 10.5622 + 1.96622i 1.46471 + 0.272666i
\(53\) 5.51641 0.757737 0.378869 0.925450i \(-0.376313\pi\)
0.378869 + 0.925450i \(0.376313\pi\)
\(54\) 0 0
\(55\) 7.86488i 1.06050i
\(56\) −3.55443 + 1.98504i −0.474981 + 0.265263i
\(57\) 0 0
\(58\) 9.46410 7.86488i 1.24270 1.03271i
\(59\) 4.93886i 0.642984i 0.946912 + 0.321492i \(0.104184\pi\)
−0.946912 + 0.321492i \(0.895816\pi\)
\(60\) 0 0
\(61\) 5.37182i 0.687791i −0.939008 0.343895i \(-0.888253\pi\)
0.939008 0.343895i \(-0.111747\pi\)
\(62\) −7.10886 8.55435i −0.902826 1.08640i
\(63\) 0 0
\(64\) −4.19615 + 6.81119i −0.524519 + 0.851399i
\(65\) 8.55435i 1.06104i
\(66\) 0 0
\(67\) 1.19615 0.146133 0.0730666 0.997327i \(-0.476721\pi\)
0.0730666 + 0.997327i \(0.476721\pi\)
\(68\) −2.60202 0.484384i −0.315542 0.0587402i
\(69\) 0 0
\(70\) 2.07180 + 2.49307i 0.247627 + 0.297979i
\(71\) −5.51641 −0.654677 −0.327339 0.944907i \(-0.606152\pi\)
−0.327339 + 0.944907i \(0.606152\pi\)
\(72\) 0 0
\(73\) −7.92820 −0.927926 −0.463963 0.885855i \(-0.653573\pi\)
−0.463963 + 0.885855i \(0.653573\pi\)
\(74\) 2.25342 + 2.71162i 0.261955 + 0.315219i
\(75\) 0 0
\(76\) 0.0980762 0.526847i 0.0112501 0.0604335i
\(77\) −7.10886 −0.810130
\(78\) 0 0
\(79\) 12.1830i 1.37070i −0.728216 0.685348i \(-0.759650\pi\)
0.728216 0.685348i \(-0.240350\pi\)
\(80\) 5.94311 + 2.29213i 0.664459 + 0.256268i
\(81\) 0 0
\(82\) 8.92820 + 10.7436i 0.985955 + 1.18644i
\(83\) 7.23099i 0.793704i 0.917883 + 0.396852i \(0.129897\pi\)
−0.917883 + 0.396852i \(0.870103\pi\)
\(84\) 0 0
\(85\) 2.10739i 0.228578i
\(86\) −2.17533 + 1.80775i −0.234572 + 0.194934i
\(87\) 0 0
\(88\) −12.1962 + 6.81119i −1.30011 + 0.726075i
\(89\) 15.7853i 1.67324i 0.547782 + 0.836621i \(0.315472\pi\)
−0.547782 + 0.836621i \(0.684528\pi\)
\(90\) 0 0
\(91\) −7.73205 −0.810539
\(92\) 2.17533 11.6855i 0.226794 1.21829i
\(93\) 0 0
\(94\) −9.92820 + 8.25056i −1.02402 + 0.850981i
\(95\) −0.426696 −0.0437781
\(96\) 0 0
\(97\) 9.39230 0.953644 0.476822 0.879000i \(-0.341789\pi\)
0.476822 + 0.879000i \(0.341789\pi\)
\(98\) −5.36023 + 4.45447i −0.541465 + 0.449970i
\(99\) 0 0
\(100\) −0.901924 + 4.84497i −0.0901924 + 0.484497i
\(101\) −3.18490 −0.316909 −0.158455 0.987366i \(-0.550651\pi\)
−0.158455 + 0.987366i \(0.550651\pi\)
\(102\) 0 0
\(103\) 1.43937i 0.141826i −0.997483 0.0709129i \(-0.977409\pi\)
0.997483 0.0709129i \(-0.0225912\pi\)
\(104\) −13.2653 + 7.40828i −1.30077 + 0.726442i
\(105\) 0 0
\(106\) −6.00000 + 4.98614i −0.582772 + 0.484296i
\(107\) 12.1698i 1.17650i −0.808678 0.588252i \(-0.799816\pi\)
0.808678 0.588252i \(-0.200184\pi\)
\(108\) 0 0
\(109\) 13.6224i 1.30479i −0.757880 0.652394i \(-0.773765\pi\)
0.757880 0.652394i \(-0.226235\pi\)
\(110\) 7.10886 + 8.55435i 0.677803 + 0.815625i
\(111\) 0 0
\(112\) 2.07180 5.37182i 0.195766 0.507589i
\(113\) 11.2011i 1.05371i 0.849956 + 0.526854i \(0.176629\pi\)
−0.849956 + 0.526854i \(0.823371\pi\)
\(114\) 0 0
\(115\) −9.46410 −0.882532
\(116\) −3.18490 + 17.1087i −0.295711 + 1.58850i
\(117\) 0 0
\(118\) −4.46410 5.37182i −0.410954 0.494516i
\(119\) 1.90481 0.174614
\(120\) 0 0
\(121\) −13.3923 −1.21748
\(122\) 4.85544 + 5.84273i 0.439591 + 0.528976i
\(123\) 0 0
\(124\) 15.4641 + 2.87875i 1.38872 + 0.258519i
\(125\) 11.8862 1.06314
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) −1.59245 11.2011i −0.140754 0.990045i
\(129\) 0 0
\(130\) 7.73205 + 9.30426i 0.678146 + 0.816037i
\(131\) 7.23099i 0.631774i 0.948797 + 0.315887i \(0.102302\pi\)
−0.948797 + 0.315887i \(0.897698\pi\)
\(132\) 0 0
\(133\) 0.385679i 0.0334426i
\(134\) −1.30101 + 1.08117i −0.112390 + 0.0933989i
\(135\) 0 0
\(136\) 3.26795 1.82505i 0.280224 0.156497i
\(137\) 5.90763i 0.504722i −0.967633 0.252361i \(-0.918793\pi\)
0.967633 0.252361i \(-0.0812071\pi\)
\(138\) 0 0
\(139\) 7.19615 0.610370 0.305185 0.952293i \(-0.401282\pi\)
0.305185 + 0.952293i \(0.401282\pi\)
\(140\) −4.50684 0.838978i −0.380897 0.0709066i
\(141\) 0 0
\(142\) 6.00000 4.98614i 0.503509 0.418427i
\(143\) −26.5306 −2.21860
\(144\) 0 0
\(145\) 13.8564 1.15071
\(146\) 8.62322 7.16609i 0.713663 0.593070i
\(147\) 0 0
\(148\) −4.90192 0.912526i −0.402936 0.0750092i
\(149\) 3.18490 0.260917 0.130459 0.991454i \(-0.458355\pi\)
0.130459 + 0.991454i \(0.458355\pi\)
\(150\) 0 0
\(151\) 6.42551i 0.522901i 0.965217 + 0.261450i \(0.0842008\pi\)
−0.965217 + 0.261450i \(0.915799\pi\)
\(152\) 0.369529 + 0.661681i 0.0299728 + 0.0536694i
\(153\) 0 0
\(154\) 7.73205 6.42551i 0.623066 0.517782i
\(155\) 12.5244i 1.00599i
\(156\) 0 0
\(157\) 2.10739i 0.168188i −0.996458 0.0840940i \(-0.973200\pi\)
0.996458 0.0840940i \(-0.0267996\pi\)
\(158\) 11.0119 + 13.2510i 0.876059 + 1.05419i
\(159\) 0 0
\(160\) −8.53590 + 2.87875i −0.674822 + 0.227585i
\(161\) 8.55435i 0.674177i
\(162\) 0 0
\(163\) 19.1962 1.50356 0.751779 0.659415i \(-0.229196\pi\)
0.751779 + 0.659415i \(0.229196\pi\)
\(164\) −19.4218 3.61549i −1.51659 0.282323i
\(165\) 0 0
\(166\) −6.53590 7.86488i −0.507284 0.610433i
\(167\) −5.08971 −0.393854 −0.196927 0.980418i \(-0.563096\pi\)
−0.196927 + 0.980418i \(0.563096\pi\)
\(168\) 0 0
\(169\) −15.8564 −1.21972
\(170\) −1.90481 2.29213i −0.146093 0.175798i
\(171\) 0 0
\(172\) 0.732051 3.93244i 0.0558184 0.299846i
\(173\) 11.8862 0.903692 0.451846 0.892096i \(-0.350766\pi\)
0.451846 + 0.892096i \(0.350766\pi\)
\(174\) 0 0
\(175\) 3.54676i 0.268110i
\(176\) 7.10886 18.4321i 0.535851 1.38937i
\(177\) 0 0
\(178\) −14.2679 17.1691i −1.06943 1.28688i
\(179\) 9.87771i 0.738295i −0.929371 0.369147i \(-0.879650\pi\)
0.929371 0.369147i \(-0.120350\pi\)
\(180\) 0 0
\(181\) 16.1154i 1.19785i 0.800804 + 0.598926i \(0.204406\pi\)
−0.800804 + 0.598926i \(0.795594\pi\)
\(182\) 8.40987 6.98880i 0.623381 0.518044i
\(183\) 0 0
\(184\) 8.19615 + 14.6761i 0.604228 + 1.08193i
\(185\) 3.97009i 0.291887i
\(186\) 0 0
\(187\) 6.53590 0.477952
\(188\) 3.34108 17.9477i 0.243673 1.30897i
\(189\) 0 0
\(190\) 0.464102 0.385679i 0.0336695 0.0279801i
\(191\) 9.12801 0.660479 0.330240 0.943897i \(-0.392870\pi\)
0.330240 + 0.943897i \(0.392870\pi\)
\(192\) 0 0
\(193\) 15.3923 1.10796 0.553981 0.832529i \(-0.313108\pi\)
0.553981 + 0.832529i \(0.313108\pi\)
\(194\) −10.2157 + 8.48946i −0.733442 + 0.609507i
\(195\) 0 0
\(196\) 1.80385 9.68994i 0.128846 0.692138i
\(197\) 19.8485 1.41414 0.707072 0.707141i \(-0.250016\pi\)
0.707072 + 0.707141i \(0.250016\pi\)
\(198\) 0 0
\(199\) 14.2904i 1.01302i 0.862234 + 0.506510i \(0.169065\pi\)
−0.862234 + 0.506510i \(0.830935\pi\)
\(200\) −3.39825 6.08492i −0.240292 0.430269i
\(201\) 0 0
\(202\) 3.46410 2.87875i 0.243733 0.202548i
\(203\) 12.5244i 0.879043i
\(204\) 0 0
\(205\) 15.7298i 1.09861i
\(206\) 1.30101 + 1.56555i 0.0906458 + 0.109077i
\(207\) 0 0
\(208\) 7.73205 20.0479i 0.536121 1.39007i
\(209\) 1.32336i 0.0915389i
\(210\) 0 0
\(211\) −17.0526 −1.17395 −0.586973 0.809606i \(-0.699681\pi\)
−0.586973 + 0.809606i \(0.699681\pi\)
\(212\) 2.01915 10.8465i 0.138676 0.744939i
\(213\) 0 0
\(214\) 11.0000 + 13.2367i 0.751945 + 0.904842i
\(215\) −3.18490 −0.217208
\(216\) 0 0
\(217\) −11.3205 −0.768486
\(218\) 12.3129 + 14.8166i 0.833935 + 1.00350i
\(219\) 0 0
\(220\) −15.4641 2.87875i −1.04259 0.194085i
\(221\) 7.10886 0.478194
\(222\) 0 0
\(223\) 19.3799i 1.29777i 0.760885 + 0.648886i \(0.224765\pi\)
−0.760885 + 0.648886i \(0.775235\pi\)
\(224\) 2.60202 + 7.71537i 0.173855 + 0.515505i
\(225\) 0 0
\(226\) −10.1244 12.1830i −0.673462 0.810401i
\(227\) 9.87771i 0.655607i −0.944746 0.327803i \(-0.893692\pi\)
0.944746 0.327803i \(-0.106308\pi\)
\(228\) 0 0
\(229\) 15.7298i 1.03945i −0.854333 0.519726i \(-0.826034\pi\)
0.854333 0.519726i \(-0.173966\pi\)
\(230\) 10.2938 8.55435i 0.678751 0.564057i
\(231\) 0 0
\(232\) −12.0000 21.4873i −0.787839 1.41071i
\(233\) 2.64673i 0.173393i 0.996235 + 0.0866964i \(0.0276310\pi\)
−0.996235 + 0.0866964i \(0.972369\pi\)
\(234\) 0 0
\(235\) −14.5359 −0.948217
\(236\) 9.71088 + 1.80775i 0.632125 + 0.117674i
\(237\) 0 0
\(238\) −2.07180 + 1.72171i −0.134295 + 0.111602i
\(239\) −6.36980 −0.412028 −0.206014 0.978549i \(-0.566049\pi\)
−0.206014 + 0.978549i \(0.566049\pi\)
\(240\) 0 0
\(241\) 15.3923 0.991506 0.495753 0.868464i \(-0.334892\pi\)
0.495753 + 0.868464i \(0.334892\pi\)
\(242\) 14.5663 12.1049i 0.936359 0.778136i
\(243\) 0 0
\(244\) −10.5622 1.96622i −0.676174 0.125874i
\(245\) −7.84792 −0.501385
\(246\) 0 0
\(247\) 1.43937i 0.0915852i
\(248\) −19.4218 + 10.8465i −1.23328 + 0.688752i
\(249\) 0 0
\(250\) −12.9282 + 10.7436i −0.817651 + 0.679487i
\(251\) 2.64673i 0.167060i 0.996505 + 0.0835299i \(0.0266194\pi\)
−0.996505 + 0.0835299i \(0.973381\pi\)
\(252\) 0 0
\(253\) 29.3521i 1.84535i
\(254\) 0 0
\(255\) 0 0
\(256\) 11.8564 + 10.7436i 0.741025 + 0.671477i
\(257\) 9.87771i 0.616155i −0.951361 0.308077i \(-0.900314\pi\)
0.951361 0.308077i \(-0.0996856\pi\)
\(258\) 0 0
\(259\) 3.58846 0.222976
\(260\) −16.8197 3.13111i −1.04312 0.194183i
\(261\) 0 0
\(262\) −6.53590 7.86488i −0.403789 0.485894i
\(263\) −23.7724 −1.46587 −0.732935 0.680298i \(-0.761850\pi\)
−0.732935 + 0.680298i \(0.761850\pi\)
\(264\) 0 0
\(265\) −8.78461 −0.539634
\(266\) −0.348605 0.419489i −0.0213743 0.0257205i
\(267\) 0 0
\(268\) 0.437822 2.35190i 0.0267442 0.143665i
\(269\) 0.739059 0.0450612 0.0225306 0.999746i \(-0.492828\pi\)
0.0225306 + 0.999746i \(0.492828\pi\)
\(270\) 0 0
\(271\) 4.31812i 0.262307i 0.991362 + 0.131154i \(0.0418681\pi\)
−0.991362 + 0.131154i \(0.958132\pi\)
\(272\) −1.90481 + 4.93886i −0.115496 + 0.299462i
\(273\) 0 0
\(274\) 5.33975 + 6.42551i 0.322586 + 0.388179i
\(275\) 12.1698i 0.733869i
\(276\) 0 0
\(277\) 2.10739i 0.126621i 0.997994 + 0.0633104i \(0.0201658\pi\)
−0.997994 + 0.0633104i \(0.979834\pi\)
\(278\) −7.82700 + 6.50441i −0.469432 + 0.390109i
\(279\) 0 0
\(280\) 5.66025 3.16108i 0.338265 0.188911i
\(281\) 7.23099i 0.431365i 0.976464 + 0.215682i \(0.0691975\pi\)
−0.976464 + 0.215682i \(0.930802\pi\)
\(282\) 0 0
\(283\) 0.143594 0.00853575 0.00426787 0.999991i \(-0.498641\pi\)
0.00426787 + 0.999991i \(0.498641\pi\)
\(284\) −2.01915 + 10.8465i −0.119814 + 0.643620i
\(285\) 0 0
\(286\) 28.8564 23.9803i 1.70632 1.41799i
\(287\) 14.2177 0.839246
\(288\) 0 0
\(289\) 15.2487 0.896983
\(290\) −15.0711 + 12.5244i −0.885006 + 0.735460i
\(291\) 0 0
\(292\) −2.90192 + 15.5886i −0.169822 + 0.912254i
\(293\) −7.10886 −0.415304 −0.207652 0.978203i \(-0.566582\pi\)
−0.207652 + 0.978203i \(0.566582\pi\)
\(294\) 0 0
\(295\) 7.86488i 0.457911i
\(296\) 6.15645 3.43820i 0.357837 0.199841i
\(297\) 0 0
\(298\) −3.46410 + 2.87875i −0.200670 + 0.166761i
\(299\) 31.9253i 1.84629i
\(300\) 0 0
\(301\) 2.87875i 0.165928i
\(302\) −5.80785 6.98880i −0.334204 0.402160i
\(303\) 0 0
\(304\) −1.00000 0.385679i −0.0573539 0.0221202i
\(305\) 8.55435i 0.489821i
\(306\) 0 0
\(307\) 7.07180 0.403609 0.201804 0.979426i \(-0.435319\pi\)
0.201804 + 0.979426i \(0.435319\pi\)
\(308\) −2.60202 + 13.9776i −0.148264 + 0.796447i
\(309\) 0 0
\(310\) 11.3205 + 13.6224i 0.642962 + 0.773699i
\(311\) 16.9759 0.962616 0.481308 0.876551i \(-0.340162\pi\)
0.481308 + 0.876551i \(0.340162\pi\)
\(312\) 0 0
\(313\) −11.3923 −0.643931 −0.321966 0.946751i \(-0.604344\pi\)
−0.321966 + 0.946751i \(0.604344\pi\)
\(314\) 1.90481 + 2.29213i 0.107495 + 0.129352i
\(315\) 0 0
\(316\) −23.9545 4.45929i −1.34754 0.250855i
\(317\) 2.33151 0.130951 0.0654753 0.997854i \(-0.479144\pi\)
0.0654753 + 0.997854i \(0.479144\pi\)
\(318\) 0 0
\(319\) 42.9745i 2.40611i
\(320\) 6.68216 10.8465i 0.373544 0.606337i
\(321\) 0 0
\(322\) −7.73205 9.30426i −0.430890 0.518506i
\(323\) 0.354594i 0.0197301i
\(324\) 0 0
\(325\) 13.2367i 0.734240i
\(326\) −20.8790 + 17.3509i −1.15638 + 0.960977i
\(327\) 0 0
\(328\) 24.3923 13.6224i 1.34684 0.752170i
\(329\) 13.1386i 0.724355i
\(330\) 0 0
\(331\) 26.1244 1.43592 0.717962 0.696082i \(-0.245075\pi\)
0.717962 + 0.696082i \(0.245075\pi\)
\(332\) 14.2177 + 2.64673i 0.780299 + 0.145258i
\(333\) 0 0
\(334\) 5.53590 4.60046i 0.302911 0.251726i
\(335\) −1.90481 −0.104071
\(336\) 0 0
\(337\) 9.39230 0.511631 0.255816 0.966726i \(-0.417656\pi\)
0.255816 + 0.966726i \(0.417656\pi\)
\(338\) 17.2464 14.3322i 0.938083 0.779568i
\(339\) 0 0
\(340\) 4.14359 + 0.771358i 0.224718 + 0.0418328i
\(341\) −38.8435 −2.10350
\(342\) 0 0
\(343\) 17.1691i 0.927047i
\(344\) 2.75821 + 4.93886i 0.148712 + 0.266285i
\(345\) 0 0
\(346\) −12.9282 + 10.7436i −0.695025 + 0.577581i
\(347\) 19.7554i 1.06053i 0.847833 + 0.530263i \(0.177907\pi\)
−0.847833 + 0.530263i \(0.822093\pi\)
\(348\) 0 0
\(349\) 23.9803i 1.28364i −0.766856 0.641819i \(-0.778180\pi\)
0.766856 0.641819i \(-0.221820\pi\)
\(350\) 3.20583 + 3.85769i 0.171359 + 0.206202i
\(351\) 0 0
\(352\) 8.92820 + 26.4734i 0.475875 + 1.41104i
\(353\) 19.7554i 1.05148i 0.850647 + 0.525738i \(0.176211\pi\)
−0.850647 + 0.525738i \(0.823789\pi\)
\(354\) 0 0
\(355\) 8.78461 0.466239
\(356\) 31.0375 + 5.77783i 1.64498 + 0.306225i
\(357\) 0 0
\(358\) 8.92820 + 10.7436i 0.471870 + 0.567819i
\(359\) 6.79650 0.358705 0.179353 0.983785i \(-0.442600\pi\)
0.179353 + 0.983785i \(0.442600\pi\)
\(360\) 0 0
\(361\) −18.9282 −0.996221
\(362\) −14.5663 17.5282i −0.765589 0.921261i
\(363\) 0 0
\(364\) −2.83013 + 15.2029i −0.148339 + 0.796850i
\(365\) 12.6253 0.660837
\(366\) 0 0
\(367\) 16.3978i 0.855957i 0.903789 + 0.427979i \(0.140774\pi\)
−0.903789 + 0.427979i \(0.859226\pi\)
\(368\) −22.1800 8.55435i −1.15621 0.445926i
\(369\) 0 0
\(370\) −3.58846 4.31812i −0.186555 0.224488i
\(371\) 7.94018i 0.412233i
\(372\) 0 0
\(373\) 18.2228i 0.943543i −0.881721 0.471771i \(-0.843615\pi\)
0.881721 0.471771i \(-0.156385\pi\)
\(374\) −7.10886 + 5.90763i −0.367590 + 0.305476i
\(375\) 0 0
\(376\) 12.5885 + 22.5410i 0.649200 + 1.16246i
\(377\) 46.7418i 2.40733i
\(378\) 0 0
\(379\) −29.7321 −1.52723 −0.763616 0.645670i \(-0.776578\pi\)
−0.763616 + 0.645670i \(0.776578\pi\)
\(380\) −0.156182 + 0.838978i −0.00801194 + 0.0430387i
\(381\) 0 0
\(382\) −9.92820 + 8.25056i −0.507971 + 0.422136i
\(383\) −11.8862 −0.607357 −0.303679 0.952775i \(-0.598215\pi\)
−0.303679 + 0.952775i \(0.598215\pi\)
\(384\) 0 0
\(385\) 11.3205 0.576947
\(386\) −16.7417 + 13.9127i −0.852128 + 0.708138i
\(387\) 0 0
\(388\) 3.43782 18.4673i 0.174529 0.937538i
\(389\) −7.96225 −0.403702 −0.201851 0.979416i \(-0.564696\pi\)
−0.201851 + 0.979416i \(0.564696\pi\)
\(390\) 0 0
\(391\) 7.86488i 0.397744i
\(392\) 6.79650 + 12.1698i 0.343275 + 0.614670i
\(393\) 0 0
\(394\) −21.5885 + 17.9405i −1.08761 + 0.903829i
\(395\) 19.4008i 0.976162i
\(396\) 0 0
\(397\) 13.6224i 0.683688i −0.939757 0.341844i \(-0.888949\pi\)
0.939757 0.341844i \(-0.111051\pi\)
\(398\) −12.9167 15.5431i −0.647456 0.779108i
\(399\) 0 0
\(400\) 9.19615 + 3.54676i 0.459808 + 0.177338i
\(401\) 39.5109i 1.97308i −0.163527 0.986539i \(-0.552287\pi\)
0.163527 0.986539i \(-0.447713\pi\)
\(402\) 0 0
\(403\) −42.2487 −2.10456
\(404\) −1.16575 + 6.26222i −0.0579985 + 0.311557i
\(405\) 0 0
\(406\) 11.3205 + 13.6224i 0.561827 + 0.676067i
\(407\) 12.3129 0.610328
\(408\) 0 0
\(409\) −29.3923 −1.45336 −0.726678 0.686978i \(-0.758937\pi\)
−0.726678 + 0.686978i \(0.758937\pi\)
\(410\) −14.2177 17.1087i −0.702163 0.844939i
\(411\) 0 0
\(412\) −2.83013 0.526847i −0.139430 0.0259559i
\(413\) −7.10886 −0.349804
\(414\) 0 0
\(415\) 11.5150i 0.565249i
\(416\) 9.71088 + 28.7942i 0.476115 + 1.41175i
\(417\) 0 0
\(418\) −1.19615 1.43937i −0.0585057 0.0704021i
\(419\) 0.354594i 0.0173230i 0.999962 + 0.00866152i \(0.00275708\pi\)
−0.999962 + 0.00866152i \(0.997243\pi\)
\(420\) 0 0
\(421\) 13.2367i 0.645117i 0.946549 + 0.322559i \(0.104543\pi\)
−0.946549 + 0.322559i \(0.895457\pi\)
\(422\) 18.5475 15.4134i 0.902876 0.750310i
\(423\) 0 0
\(424\) 7.60770 + 13.6224i 0.369462 + 0.661561i
\(425\) 3.26090i 0.158177i
\(426\) 0 0
\(427\) 7.73205 0.374180
\(428\) −23.9286 4.45447i −1.15663 0.215315i
\(429\) 0 0
\(430\) 3.46410 2.87875i 0.167054 0.138826i
\(431\) 38.4168 1.85047 0.925237 0.379390i \(-0.123866\pi\)
0.925237 + 0.379390i \(0.123866\pi\)
\(432\) 0 0
\(433\) 11.4641 0.550930 0.275465 0.961311i \(-0.411168\pi\)
0.275465 + 0.961311i \(0.411168\pi\)
\(434\) 12.3129 10.2323i 0.591038 0.491166i
\(435\) 0 0
\(436\) −26.7846 4.98614i −1.28275 0.238793i
\(437\) 1.59245 0.0761772
\(438\) 0 0
\(439\) 35.1096i 1.67569i −0.545907 0.837846i \(-0.683815\pi\)
0.545907 0.837846i \(-0.316185\pi\)
\(440\) 19.4218 10.8465i 0.925896 0.517086i
\(441\) 0 0
\(442\) −7.73205 + 6.42551i −0.367776 + 0.305630i
\(443\) 31.5707i 1.49997i −0.661456 0.749984i \(-0.730061\pi\)
0.661456 0.749984i \(-0.269939\pi\)
\(444\) 0 0
\(445\) 25.1374i 1.19163i
\(446\) −17.5170 21.0788i −0.829452 0.998110i
\(447\) 0 0
\(448\) −9.80385 6.03983i −0.463188 0.285355i
\(449\) 23.0163i 1.08621i −0.839666 0.543104i \(-0.817249\pi\)
0.839666 0.543104i \(-0.182751\pi\)
\(450\) 0 0
\(451\) 48.7846 2.29718
\(452\) 22.0238 + 4.09988i 1.03591 + 0.192842i
\(453\) 0 0
\(454\) 8.92820 + 10.7436i 0.419021 + 0.504224i
\(455\) 12.3129 0.577238
\(456\) 0 0
\(457\) −14.3923 −0.673244 −0.336622 0.941640i \(-0.609284\pi\)
−0.336622 + 0.941640i \(0.609284\pi\)
\(458\) 14.2177 + 17.1087i 0.664350 + 0.799437i
\(459\) 0 0
\(460\) −3.46410 + 18.6085i −0.161515 + 0.867627i
\(461\) −18.9951 −0.884689 −0.442344 0.896845i \(-0.645853\pi\)
−0.442344 + 0.896845i \(0.645853\pi\)
\(462\) 0 0
\(463\) 30.7915i 1.43100i 0.698611 + 0.715502i \(0.253802\pi\)
−0.698611 + 0.715502i \(0.746198\pi\)
\(464\) 32.4737 + 12.5244i 1.50756 + 0.581432i
\(465\) 0 0
\(466\) −2.39230 2.87875i −0.110821 0.133355i
\(467\) 17.4633i 0.808105i 0.914736 + 0.404052i \(0.132399\pi\)
−0.914736 + 0.404052i \(0.867601\pi\)
\(468\) 0 0
\(469\) 1.72171i 0.0795012i
\(470\) 15.8102 13.1386i 0.729269 0.606039i
\(471\) 0 0
\(472\) −12.1962 + 6.81119i −0.561373 + 0.313510i
\(473\) 9.87771i 0.454178i
\(474\) 0 0
\(475\) −0.660254 −0.0302945
\(476\) 0.697210 3.74528i 0.0319566 0.171665i
\(477\) 0 0
\(478\) 6.92820 5.75749i 0.316889 0.263342i
\(479\) −3.18490 −0.145522 −0.0727609 0.997349i \(-0.523181\pi\)
−0.0727609 + 0.997349i \(0.523181\pi\)
\(480\) 0 0
\(481\) 13.3923 0.610637
\(482\) −16.7417 + 13.9127i −0.762561 + 0.633706i
\(483\) 0 0
\(484\) −4.90192 + 26.3322i −0.222815 + 1.19692i
\(485\) −14.9568 −0.679152
\(486\) 0 0
\(487\) 37.8850i 1.71674i −0.513035 0.858368i \(-0.671479\pi\)
0.513035 0.858368i \(-0.328521\pi\)
\(488\) 13.2653 7.40828i 0.600493 0.335357i
\(489\) 0 0
\(490\) 8.53590 7.09353i 0.385613 0.320453i
\(491\) 16.7541i 0.756102i −0.925785 0.378051i \(-0.876594\pi\)
0.925785 0.378051i \(-0.123406\pi\)
\(492\) 0 0
\(493\) 11.5150i 0.518609i
\(494\) −1.30101 1.56555i −0.0585353 0.0704376i
\(495\) 0 0
\(496\) 11.3205 29.3521i 0.508306 1.31795i
\(497\) 7.94018i 0.356166i
\(498\) 0 0
\(499\) −26.3923 −1.18148 −0.590741 0.806861i \(-0.701164\pi\)
−0.590741 + 0.806861i \(0.701164\pi\)
\(500\) 4.35066 23.3709i 0.194567 1.04518i
\(501\) 0 0
\(502\) −2.39230 2.87875i −0.106774 0.128485i
\(503\) 34.3785 1.53286 0.766432 0.642326i \(-0.222030\pi\)
0.766432 + 0.642326i \(0.222030\pi\)
\(504\) 0 0
\(505\) 5.07180 0.225692
\(506\) −26.5306 31.9253i −1.17943 1.41925i
\(507\) 0 0
\(508\) 0 0
\(509\) −22.1800 −0.983110 −0.491555 0.870847i \(-0.663571\pi\)
−0.491555 + 0.870847i \(0.663571\pi\)
\(510\) 0 0
\(511\) 11.4116i 0.504822i
\(512\) −22.6067 0.968769i −0.999083 0.0428139i
\(513\) 0 0
\(514\) 8.92820 + 10.7436i 0.393806 + 0.473881i
\(515\) 2.29213i 0.101003i
\(516\) 0 0
\(517\) 45.0819i 1.98270i
\(518\) −3.90304 + 3.24351i −0.171490 + 0.142512i
\(519\) 0 0
\(520\) 21.1244 11.7973i 0.926364 0.517347i
\(521\) 1.32336i 0.0579776i −0.999580 0.0289888i \(-0.990771\pi\)
0.999580 0.0289888i \(-0.00922871\pi\)
\(522\) 0 0
\(523\) −6.41154 −0.280357 −0.140179 0.990126i \(-0.544768\pi\)
−0.140179 + 0.990126i \(0.544768\pi\)
\(524\) 14.2177 + 2.64673i 0.621104 + 0.115623i
\(525\) 0 0
\(526\) 25.8564 21.4873i 1.12739 0.936889i
\(527\) 10.4081 0.453384
\(528\) 0 0
\(529\) 12.3205 0.535674
\(530\) 9.55470 7.94018i 0.415030 0.344899i
\(531\) 0 0
\(532\) 0.758330 + 0.141168i 0.0328778 + 0.00612042i
\(533\) 53.0613 2.29834
\(534\) 0 0
\(535\) 19.3799i 0.837865i
\(536\) 1.64962 + 2.95381i 0.0712526 + 0.127585i
\(537\) 0 0
\(538\) −0.803848 + 0.668016i −0.0346563 + 0.0288002i
\(539\) 24.3397i 1.04838i
\(540\) 0 0
\(541\) 12.4653i 0.535927i −0.963429 0.267963i \(-0.913649\pi\)
0.963429 0.267963i \(-0.0863506\pi\)
\(542\) −3.90304 4.69666i −0.167650 0.201739i
\(543\) 0 0
\(544\) −2.39230 7.09353i −0.102569 0.304132i
\(545\) 21.6930i 0.929224i
\(546\) 0 0
\(547\) −0.411543 −0.0175963 −0.00879815 0.999961i \(-0.502801\pi\)
−0.00879815 + 0.999961i \(0.502801\pi\)
\(548\) −11.6157 2.16234i −0.496198 0.0923706i
\(549\) 0 0
\(550\) 11.0000 + 13.2367i 0.469042 + 0.564415i
\(551\) −2.33151 −0.0993256
\(552\) 0 0
\(553\) 17.5359 0.745702
\(554\) −1.90481 2.29213i −0.0809278 0.0973833i
\(555\) 0 0
\(556\) 2.63397 14.1492i 0.111705 0.600061i
\(557\) −36.3977 −1.54222 −0.771110 0.636702i \(-0.780298\pi\)
−0.771110 + 0.636702i \(0.780298\pi\)
\(558\) 0 0
\(559\) 10.7436i 0.454407i
\(560\) −3.29923 + 8.55435i −0.139418 + 0.361487i
\(561\) 0 0
\(562\) −6.53590 7.86488i −0.275700 0.331760i
\(563\) 11.8153i 0.497953i 0.968509 + 0.248977i \(0.0800943\pi\)
−0.968509 + 0.248977i \(0.919906\pi\)
\(564\) 0 0
\(565\) 17.8372i 0.750415i
\(566\) −0.156182 + 0.129790i −0.00656480 + 0.00545550i
\(567\) 0 0
\(568\) −7.60770 13.6224i −0.319212 0.571582i
\(569\) 35.5408i 1.48995i −0.667094 0.744973i \(-0.732462\pi\)
0.667094 0.744973i \(-0.267538\pi\)
\(570\) 0 0
\(571\) 7.19615 0.301150 0.150575 0.988599i \(-0.451888\pi\)
0.150575 + 0.988599i \(0.451888\pi\)
\(572\) −9.71088 + 52.1651i −0.406032 + 2.18113i
\(573\) 0 0
\(574\) −15.4641 + 12.8510i −0.645459 + 0.536391i
\(575\) −14.6444 −0.610714
\(576\) 0 0
\(577\) −1.92820 −0.0802722 −0.0401361 0.999194i \(-0.512779\pi\)
−0.0401361 + 0.999194i \(0.512779\pi\)
\(578\) −16.5855 + 13.7829i −0.689865 + 0.573293i
\(579\) 0 0
\(580\) 5.07180 27.2448i 0.210595 1.13128i
\(581\) −10.4081 −0.431801
\(582\) 0 0
\(583\) 27.2448i 1.12836i
\(584\) −10.9338 19.5781i −0.452444 0.810149i
\(585\) 0 0
\(586\) 7.73205 6.42551i 0.319408 0.265435i
\(587\) 16.7541i 0.691516i −0.938324 0.345758i \(-0.887622\pi\)
0.938324 0.345758i \(-0.112378\pi\)
\(588\) 0 0
\(589\) 2.10739i 0.0868335i
\(590\) 7.10886 + 8.55435i 0.292667 + 0.352177i
\(591\) 0 0
\(592\) −3.58846 + 9.30426i −0.147485 + 0.382403i
\(593\) 1.93754i 0.0795651i −0.999208 0.0397826i \(-0.987333\pi\)
0.999208 0.0397826i \(-0.0126665\pi\)
\(594\) 0 0
\(595\) −3.03332 −0.124354
\(596\) 1.16575 6.26222i 0.0477512 0.256510i
\(597\) 0 0
\(598\) −28.8564 34.7240i −1.18003 1.41997i
\(599\) −43.5066 −1.77763 −0.888815 0.458267i \(-0.848471\pi\)
−0.888815 + 0.458267i \(0.848471\pi\)
\(600\) 0 0
\(601\) 9.60770 0.391906 0.195953 0.980613i \(-0.437220\pi\)
0.195953 + 0.980613i \(0.437220\pi\)
\(602\) −2.60202 3.13111i −0.106051 0.127615i
\(603\) 0 0
\(604\) 12.6340 + 2.35190i 0.514069 + 0.0956975i
\(605\) 21.3266 0.867049
\(606\) 0 0
\(607\) 27.1414i 1.10164i 0.834625 + 0.550818i \(0.185684\pi\)
−0.834625 + 0.550818i \(0.814316\pi\)
\(608\) 1.43627 0.484384i 0.0582484 0.0196444i
\(609\) 0 0
\(610\) −7.73205 9.30426i −0.313062 0.376718i
\(611\) 49.0340i 1.98370i
\(612\) 0 0
\(613\) 2.49307i 0.100694i 0.998732 + 0.0503470i \(0.0160327\pi\)
−0.998732 + 0.0503470i \(0.983967\pi\)
\(614\) −7.69174 + 6.39201i −0.310413 + 0.257961i
\(615\) 0 0
\(616\) −9.80385 17.5548i −0.395008 0.707304i
\(617\) 23.7255i 0.955153i 0.878590 + 0.477577i \(0.158485\pi\)
−0.878590 + 0.477577i \(0.841515\pi\)
\(618\) 0 0
\(619\) 26.8038 1.07734 0.538669 0.842518i \(-0.318927\pi\)
0.538669 + 0.842518i \(0.318927\pi\)
\(620\) −24.6258 4.58426i −0.988997 0.184108i
\(621\) 0 0
\(622\) −18.4641 + 15.3441i −0.740343 + 0.615242i
\(623\) −22.7210 −0.910298
\(624\) 0 0
\(625\) −6.60770 −0.264308
\(626\) 12.3910 10.2972i 0.495244 0.411559i
\(627\) 0 0
\(628\) −4.14359 0.771358i −0.165347 0.0307805i
\(629\) −3.29923 −0.131549
\(630\) 0 0
\(631\) 17.9405i 0.714200i 0.934066 + 0.357100i \(0.116234\pi\)
−0.934066 + 0.357100i \(0.883766\pi\)
\(632\) 30.0851 16.8016i 1.19672 0.668332i
\(633\) 0 0
\(634\) −2.53590 + 2.10739i −0.100713 + 0.0836951i
\(635\) 0 0
\(636\) 0 0
\(637\) 26.4734i 1.04891i
\(638\) 38.8435 + 46.7418i 1.53783 + 1.85053i
\(639\) 0 0
\(640\) 2.53590 + 17.8372i 0.100240 + 0.705076i
\(641\) 11.8153i 0.466674i 0.972396 + 0.233337i \(0.0749646\pi\)
−0.972396 + 0.233337i \(0.925035\pi\)
\(642\) 0 0
\(643\) 22.7846 0.898537 0.449269 0.893397i \(-0.351685\pi\)
0.449269 + 0.893397i \(0.351685\pi\)
\(644\) 16.8197 + 3.13111i 0.662791 + 0.123383i
\(645\) 0 0
\(646\) 0.320508 + 0.385679i 0.0126102 + 0.0151743i
\(647\) 1.47812 0.0581108 0.0290554 0.999578i \(-0.490750\pi\)
0.0290554 + 0.999578i \(0.490750\pi\)
\(648\) 0 0
\(649\) −24.3923 −0.957482
\(650\) 11.9643 + 14.3971i 0.469279 + 0.564700i
\(651\) 0 0
\(652\) 7.02628 37.7439i 0.275170 1.47816i
\(653\) 27.8107 1.08832 0.544159 0.838982i \(-0.316849\pi\)
0.544159 + 0.838982i \(0.316849\pi\)
\(654\) 0 0
\(655\) 11.5150i 0.449928i
\(656\) −14.2177 + 36.8641i −0.555109 + 1.43930i
\(657\) 0 0
\(658\) −11.8756 14.2904i −0.462961 0.557098i
\(659\) 22.4022i 0.872664i −0.899786 0.436332i \(-0.856277\pi\)
0.899786 0.436332i \(-0.143723\pi\)
\(660\) 0 0
\(661\) 41.2528i 1.60455i 0.596956 + 0.802274i \(0.296377\pi\)
−0.596956 + 0.802274i \(0.703623\pi\)
\(662\) −28.4145 + 23.6131i −1.10436 + 0.917750i
\(663\) 0 0
\(664\) −17.8564 + 9.97227i −0.692963 + 0.386999i
\(665\) 0.614175i 0.0238167i
\(666\) 0 0
\(667\) −51.7128 −2.00233
\(668\) −1.86296 + 10.0075i −0.0720803 + 0.387202i
\(669\) 0 0
\(670\) 2.07180 1.72171i 0.0800405 0.0665155i
\(671\) 26.5306 1.02420
\(672\) 0 0
\(673\) −13.2487 −0.510700 −0.255350 0.966849i \(-0.582191\pi\)
−0.255350 + 0.966849i \(0.582191\pi\)
\(674\) −10.2157 + 8.48946i −0.393493 + 0.327002i
\(675\) 0 0
\(676\) −5.80385 + 31.1772i −0.223225 + 1.19912i
\(677\) −12.0005 −0.461218 −0.230609 0.973046i \(-0.574072\pi\)
−0.230609 + 0.973046i \(0.574072\pi\)
\(678\) 0 0
\(679\) 13.5190i 0.518813i
\(680\) −5.20405 + 2.90631i −0.199566 + 0.111452i
\(681\) 0 0
\(682\) 42.2487 35.1096i 1.61779 1.34442i
\(683\) 34.9266i 1.33643i −0.743969 0.668214i \(-0.767059\pi\)
0.743969 0.668214i \(-0.232941\pi\)
\(684\) 0 0
\(685\) 9.40760i 0.359446i
\(686\) −15.5187 18.6743i −0.592508 0.712986i
\(687\) 0 0
\(688\) −7.46410 2.87875i −0.284566 0.109751i
\(689\) 29.6331i 1.12893i
\(690\) 0 0
\(691\) −23.8564 −0.907540 −0.453770 0.891119i \(-0.649921\pi\)
−0.453770 + 0.891119i \(0.649921\pi\)
\(692\) 4.35066 23.3709i 0.165387 0.888429i
\(693\) 0 0
\(694\) −17.8564 21.4873i −0.677820 0.815645i
\(695\) −11.4595 −0.434684
\(696\) 0 0
\(697\) −13.0718 −0.495130
\(698\) 21.6752 + 26.0825i 0.820418 + 0.987239i
\(699\) 0 0
\(700\) −6.97372 1.29821i −0.263582 0.0490676i
\(701\) −17.2883 −0.652970 −0.326485 0.945202i \(-0.605864\pi\)
−0.326485 + 0.945202i \(0.605864\pi\)
\(702\) 0 0
\(703\) 0.668016i 0.0251947i
\(704\) −33.6395 20.7242i −1.26784 0.781072i
\(705\) 0 0
\(706\) −17.8564 21.4873i −0.672035 0.808684i
\(707\) 4.58426i 0.172409i
\(708\) 0 0
\(709\) 27.6304i 1.03768i −0.854870 0.518841i \(-0.826364\pi\)
0.854870 0.518841i \(-0.173636\pi\)
\(710\) −9.55470 + 7.94018i −0.358582 + 0.297989i
\(711\) 0 0
\(712\) −38.9808 + 21.7696i −1.46087 + 0.815850i
\(713\) 46.7418i 1.75050i
\(714\) 0 0
\(715\) 42.2487 1.58001
\(716\) −19.4218 3.61549i −0.725826 0.135117i
\(717\) 0 0
\(718\) −7.39230 + 6.14317i −0.275878 + 0.229261i
\(719\) 15.0711 0.562058 0.281029 0.959699i \(-0.409324\pi\)
0.281029 + 0.959699i \(0.409324\pi\)
\(720\) 0 0
\(721\) 2.07180 0.0771577
\(722\) 20.5875 17.1087i 0.766188 0.636720i
\(723\) 0 0
\(724\) 31.6865 + 5.89866i 1.17762 + 0.219222i
\(725\) 21.4409 0.796296
\(726\) 0 0
\(727\) 19.3799i 0.718760i 0.933191 + 0.359380i \(0.117012\pi\)
−0.933191 + 0.359380i \(0.882988\pi\)
\(728\) −10.6633 19.0937i −0.395208 0.707661i
\(729\) 0 0
\(730\) −13.7321 + 11.4116i −0.508246 + 0.422364i
\(731\) 2.64673i 0.0978927i
\(732\) 0 0
\(733\) 45.0819i 1.66514i 0.553921 + 0.832569i \(0.313131\pi\)
−0.553921 + 0.832569i \(0.686869\pi\)
\(734\) −14.8215 17.8353i −0.547072 0.658312i
\(735\) 0 0
\(736\) 31.8564 10.7436i 1.17424 0.396016i
\(737\) 5.90763i 0.217610i
\(738\) 0 0
\(739\) 48.6410 1.78929 0.894644 0.446779i \(-0.147429\pi\)
0.894644 + 0.446779i \(0.147429\pi\)
\(740\) 7.80607 + 1.45315i 0.286957 + 0.0534190i
\(741\) 0 0
\(742\) −7.17691 8.63624i −0.263473 0.317046i
\(743\) −43.3085 −1.58884 −0.794418 0.607372i \(-0.792224\pi\)
−0.794418 + 0.607372i \(0.792224\pi\)
\(744\) 0 0
\(745\) −5.07180 −0.185816
\(746\) 16.4711 + 19.8203i 0.603051 + 0.725674i
\(747\) 0 0
\(748\) 2.39230 12.8510i 0.0874713 0.469880i
\(749\) 17.5170 0.640056
\(750\) 0 0
\(751\) 7.19687i 0.262617i 0.991342 + 0.131309i \(0.0419179\pi\)
−0.991342 + 0.131309i \(0.958082\pi\)
\(752\) −34.0662 13.1386i −1.24227 0.479116i
\(753\) 0 0
\(754\) 42.2487 + 50.8394i 1.53861 + 1.85146i
\(755\) 10.2323i 0.372392i
\(756\) 0 0
\(757\) 36.0600i 1.31062i −0.755359 0.655311i \(-0.772537\pi\)
0.755359 0.655311i \(-0.227463\pi\)
\(758\) 32.3385 26.8740i 1.17459 0.976108i
\(759\) 0 0
\(760\) −0.588457 1.05369i −0.0213456 0.0382215i
\(761\) 26.3722i 0.955993i −0.878362 0.477996i \(-0.841363\pi\)
0.878362 0.477996i \(-0.158637\pi\)
\(762\) 0 0
\(763\) 19.6077 0.709846
\(764\) 3.34108 17.9477i 0.120876 0.649324i
\(765\) 0 0
\(766\) 12.9282 10.7436i 0.467115 0.388183i
\(767\) −26.5306 −0.957965
\(768\) 0 0
\(769\) 17.9282 0.646508 0.323254 0.946312i \(-0.395223\pi\)
0.323254 + 0.946312i \(0.395223\pi\)
\(770\) −12.3129 + 10.2323i −0.443726 + 0.368747i
\(771\) 0 0
\(772\) 5.63397 30.2647i 0.202771 1.08925i
\(773\) 34.1805 1.22939 0.614694 0.788766i \(-0.289280\pi\)
0.614694 + 0.788766i \(0.289280\pi\)
\(774\) 0 0
\(775\) 19.3799i 0.696146i
\(776\) 12.9530 + 23.1936i 0.464984 + 0.832603i
\(777\) 0 0
\(778\) 8.66025 7.19687i 0.310485 0.258020i
\(779\) 2.64673i 0.0948288i
\(780\) 0 0
\(781\) 27.2448i 0.974894i
\(782\) 7.10886 + 8.55435i 0.254212 + 0.305903i
\(783\) 0 0
\(784\) −18.3923 7.09353i −0.656868 0.253340i
\(785\) 3.35591i 0.119778i
\(786\) 0 0
\(787\) −51.4449 −1.83381 −0.916906 0.399104i \(-0.869321\pi\)
−0.916906 + 0.399104i \(0.869321\pi\)
\(788\) 7.26504 39.0265i 0.258806 1.39026i
\(789\) 0 0
\(790\) −17.5359 21.1016i −0.623899 0.750761i
\(791\) −16.1225 −0.573251
\(792\) 0 0
\(793\) 28.8564 1.02472
\(794\) 12.3129 +