Properties

Label 2070.2.d.e.829.5
Level $2070$
Weight $2$
Character 2070.829
Analytic conductor $16.529$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2070.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.5290332184\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 690)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 829.5
Root \(-0.854638 - 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 2070.829
Dual form 2070.2.d.e.829.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(0.539189 - 2.17009i) q^{5} -4.34017i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(0.539189 - 2.17009i) q^{5} -4.34017i q^{7} -1.00000i q^{8} +(2.17009 + 0.539189i) q^{10} +1.07838 q^{11} -2.34017i q^{13} +4.34017 q^{14} +1.00000 q^{16} +0.921622i q^{17} -2.34017 q^{19} +(-0.539189 + 2.17009i) q^{20} +1.07838i q^{22} -1.00000i q^{23} +(-4.41855 - 2.34017i) q^{25} +2.34017 q^{26} +4.34017i q^{28} +10.4969 q^{29} -4.00000 q^{31} +1.00000i q^{32} -0.921622 q^{34} +(-9.41855 - 2.34017i) q^{35} -2.58145i q^{37} -2.34017i q^{38} +(-2.17009 - 0.539189i) q^{40} -0.156755 q^{41} +0.738205i q^{43} -1.07838 q^{44} +1.00000 q^{46} +6.83710i q^{47} -11.8371 q^{49} +(2.34017 - 4.41855i) q^{50} +2.34017i q^{52} +0.340173i q^{53} +(0.581449 - 2.34017i) q^{55} -4.34017 q^{56} +10.4969i q^{58} -8.83710 q^{59} -11.5753 q^{61} -4.00000i q^{62} -1.00000 q^{64} +(-5.07838 - 1.26180i) q^{65} -2.58145i q^{67} -0.921622i q^{68} +(2.34017 - 9.41855i) q^{70} -15.1773 q^{71} -4.68035i q^{73} +2.58145 q^{74} +2.34017 q^{76} -4.68035i q^{77} +11.9155 q^{79} +(0.539189 - 2.17009i) q^{80} -0.156755i q^{82} -11.4186i q^{83} +(2.00000 + 0.496928i) q^{85} -0.738205 q^{86} -1.07838i q^{88} -4.68035 q^{89} -10.1568 q^{91} +1.00000i q^{92} -6.83710 q^{94} +(-1.26180 + 5.07838i) q^{95} -9.02052i q^{97} -11.8371i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} + O(q^{10}) \) \( 6q - 6q^{4} + 2q^{10} + 4q^{14} + 6q^{16} + 8q^{19} + 2q^{25} - 8q^{26} + 28q^{29} - 24q^{31} - 12q^{34} - 28q^{35} - 2q^{40} + 12q^{41} + 6q^{46} - 14q^{49} - 8q^{50} + 32q^{55} - 4q^{56} + 4q^{59} - 28q^{61} - 6q^{64} - 24q^{65} - 8q^{70} - 12q^{71} + 44q^{74} - 8q^{76} + 8q^{79} + 12q^{85} - 20q^{86} + 16q^{89} - 48q^{91} + 16q^{94} + 8q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).

\(n\) \(461\) \(1657\) \(1891\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 0.539189 2.17009i 0.241133 0.970492i
\(6\) 0 0
\(7\) 4.34017i 1.64043i −0.572055 0.820216i \(-0.693853\pi\)
0.572055 0.820216i \(-0.306147\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.17009 + 0.539189i 0.686242 + 0.170506i
\(11\) 1.07838 0.325143 0.162572 0.986697i \(-0.448021\pi\)
0.162572 + 0.986697i \(0.448021\pi\)
\(12\) 0 0
\(13\) 2.34017i 0.649047i −0.945878 0.324524i \(-0.894796\pi\)
0.945878 0.324524i \(-0.105204\pi\)
\(14\) 4.34017 1.15996
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.921622i 0.223526i 0.993735 + 0.111763i \(0.0356498\pi\)
−0.993735 + 0.111763i \(0.964350\pi\)
\(18\) 0 0
\(19\) −2.34017 −0.536873 −0.268436 0.963297i \(-0.586507\pi\)
−0.268436 + 0.963297i \(0.586507\pi\)
\(20\) −0.539189 + 2.17009i −0.120566 + 0.485246i
\(21\) 0 0
\(22\) 1.07838i 0.229911i
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) −4.41855 2.34017i −0.883710 0.468035i
\(26\) 2.34017 0.458946
\(27\) 0 0
\(28\) 4.34017i 0.820216i
\(29\) 10.4969 1.94923 0.974615 0.223886i \(-0.0718743\pi\)
0.974615 + 0.223886i \(0.0718743\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −0.921622 −0.158057
\(35\) −9.41855 2.34017i −1.59203 0.395561i
\(36\) 0 0
\(37\) 2.58145i 0.424388i −0.977228 0.212194i \(-0.931939\pi\)
0.977228 0.212194i \(-0.0680608\pi\)
\(38\) 2.34017i 0.379626i
\(39\) 0 0
\(40\) −2.17009 0.539189i −0.343121 0.0852532i
\(41\) −0.156755 −0.0244811 −0.0122405 0.999925i \(-0.503896\pi\)
−0.0122405 + 0.999925i \(0.503896\pi\)
\(42\) 0 0
\(43\) 0.738205i 0.112575i 0.998415 + 0.0562876i \(0.0179264\pi\)
−0.998415 + 0.0562876i \(0.982074\pi\)
\(44\) −1.07838 −0.162572
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) 6.83710i 0.997294i 0.866805 + 0.498647i \(0.166170\pi\)
−0.866805 + 0.498647i \(0.833830\pi\)
\(48\) 0 0
\(49\) −11.8371 −1.69101
\(50\) 2.34017 4.41855i 0.330950 0.624877i
\(51\) 0 0
\(52\) 2.34017i 0.324524i
\(53\) 0.340173i 0.0467264i 0.999727 + 0.0233632i \(0.00743741\pi\)
−0.999727 + 0.0233632i \(0.992563\pi\)
\(54\) 0 0
\(55\) 0.581449 2.34017i 0.0784026 0.315549i
\(56\) −4.34017 −0.579980
\(57\) 0 0
\(58\) 10.4969i 1.37831i
\(59\) −8.83710 −1.15049 −0.575246 0.817980i \(-0.695094\pi\)
−0.575246 + 0.817980i \(0.695094\pi\)
\(60\) 0 0
\(61\) −11.5753 −1.48207 −0.741033 0.671469i \(-0.765664\pi\)
−0.741033 + 0.671469i \(0.765664\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −5.07838 1.26180i −0.629895 0.156506i
\(66\) 0 0
\(67\) 2.58145i 0.315374i −0.987489 0.157687i \(-0.949596\pi\)
0.987489 0.157687i \(-0.0504037\pi\)
\(68\) 0.921622i 0.111763i
\(69\) 0 0
\(70\) 2.34017 9.41855i 0.279704 1.12573i
\(71\) −15.1773 −1.80121 −0.900606 0.434637i \(-0.856877\pi\)
−0.900606 + 0.434637i \(0.856877\pi\)
\(72\) 0 0
\(73\) 4.68035i 0.547793i −0.961759 0.273897i \(-0.911687\pi\)
0.961759 0.273897i \(-0.0883126\pi\)
\(74\) 2.58145 0.300087
\(75\) 0 0
\(76\) 2.34017 0.268436
\(77\) 4.68035i 0.533375i
\(78\) 0 0
\(79\) 11.9155 1.34060 0.670298 0.742092i \(-0.266166\pi\)
0.670298 + 0.742092i \(0.266166\pi\)
\(80\) 0.539189 2.17009i 0.0602831 0.242623i
\(81\) 0 0
\(82\) 0.156755i 0.0173107i
\(83\) 11.4186i 1.25335i −0.779281 0.626674i \(-0.784416\pi\)
0.779281 0.626674i \(-0.215584\pi\)
\(84\) 0 0
\(85\) 2.00000 + 0.496928i 0.216930 + 0.0538995i
\(86\) −0.738205 −0.0796027
\(87\) 0 0
\(88\) 1.07838i 0.114955i
\(89\) −4.68035 −0.496116 −0.248058 0.968745i \(-0.579792\pi\)
−0.248058 + 0.968745i \(0.579792\pi\)
\(90\) 0 0
\(91\) −10.1568 −1.06472
\(92\) 1.00000i 0.104257i
\(93\) 0 0
\(94\) −6.83710 −0.705193
\(95\) −1.26180 + 5.07838i −0.129457 + 0.521031i
\(96\) 0 0
\(97\) 9.02052i 0.915895i −0.888979 0.457947i \(-0.848585\pi\)
0.888979 0.457947i \(-0.151415\pi\)
\(98\) 11.8371i 1.19573i
\(99\) 0 0
\(100\) 4.41855 + 2.34017i 0.441855 + 0.234017i
\(101\) −1.50307 −0.149561 −0.0747806 0.997200i \(-0.523826\pi\)
−0.0747806 + 0.997200i \(0.523826\pi\)
\(102\) 0 0
\(103\) 2.49693i 0.246030i −0.992405 0.123015i \(-0.960744\pi\)
0.992405 0.123015i \(-0.0392563\pi\)
\(104\) −2.34017 −0.229473
\(105\) 0 0
\(106\) −0.340173 −0.0330405
\(107\) 9.57531i 0.925680i 0.886442 + 0.462840i \(0.153170\pi\)
−0.886442 + 0.462840i \(0.846830\pi\)
\(108\) 0 0
\(109\) 9.78539 0.937270 0.468635 0.883392i \(-0.344746\pi\)
0.468635 + 0.883392i \(0.344746\pi\)
\(110\) 2.34017 + 0.581449i 0.223127 + 0.0554390i
\(111\) 0 0
\(112\) 4.34017i 0.410108i
\(113\) 8.92162i 0.839276i −0.907692 0.419638i \(-0.862157\pi\)
0.907692 0.419638i \(-0.137843\pi\)
\(114\) 0 0
\(115\) −2.17009 0.539189i −0.202362 0.0502796i
\(116\) −10.4969 −0.974615
\(117\) 0 0
\(118\) 8.83710i 0.813521i
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) −9.83710 −0.894282
\(122\) 11.5753i 1.04798i
\(123\) 0 0
\(124\) 4.00000 0.359211
\(125\) −7.46081 + 8.32684i −0.667315 + 0.744775i
\(126\) 0 0
\(127\) 17.1773i 1.52424i −0.647438 0.762118i \(-0.724159\pi\)
0.647438 0.762118i \(-0.275841\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 1.26180 5.07838i 0.110667 0.445403i
\(131\) 6.68035 0.583665 0.291832 0.956470i \(-0.405735\pi\)
0.291832 + 0.956470i \(0.405735\pi\)
\(132\) 0 0
\(133\) 10.1568i 0.880702i
\(134\) 2.58145 0.223003
\(135\) 0 0
\(136\) 0.921622 0.0790285
\(137\) 22.2823i 1.90371i 0.306554 + 0.951853i \(0.400824\pi\)
−0.306554 + 0.951853i \(0.599176\pi\)
\(138\) 0 0
\(139\) 10.5236 0.892599 0.446300 0.894884i \(-0.352742\pi\)
0.446300 + 0.894884i \(0.352742\pi\)
\(140\) 9.41855 + 2.34017i 0.796013 + 0.197781i
\(141\) 0 0
\(142\) 15.1773i 1.27365i
\(143\) 2.52359i 0.211033i
\(144\) 0 0
\(145\) 5.65983 22.7792i 0.470023 1.89171i
\(146\) 4.68035 0.387348
\(147\) 0 0
\(148\) 2.58145i 0.212194i
\(149\) 6.92162 0.567041 0.283521 0.958966i \(-0.408498\pi\)
0.283521 + 0.958966i \(0.408498\pi\)
\(150\) 0 0
\(151\) 6.15676 0.501030 0.250515 0.968113i \(-0.419400\pi\)
0.250515 + 0.968113i \(0.419400\pi\)
\(152\) 2.34017i 0.189813i
\(153\) 0 0
\(154\) 4.68035 0.377153
\(155\) −2.15676 + 8.68035i −0.173235 + 0.697222i
\(156\) 0 0
\(157\) 2.89496i 0.231043i −0.993305 0.115521i \(-0.963146\pi\)
0.993305 0.115521i \(-0.0368539\pi\)
\(158\) 11.9155i 0.947945i
\(159\) 0 0
\(160\) 2.17009 + 0.539189i 0.171560 + 0.0426266i
\(161\) −4.34017 −0.342054
\(162\) 0 0
\(163\) 6.52359i 0.510967i 0.966813 + 0.255484i \(0.0822347\pi\)
−0.966813 + 0.255484i \(0.917765\pi\)
\(164\) 0.156755 0.0122405
\(165\) 0 0
\(166\) 11.4186 0.886251
\(167\) 5.47641i 0.423777i 0.977294 + 0.211889i \(0.0679614\pi\)
−0.977294 + 0.211889i \(0.932039\pi\)
\(168\) 0 0
\(169\) 7.52359 0.578738
\(170\) −0.496928 + 2.00000i −0.0381127 + 0.153393i
\(171\) 0 0
\(172\) 0.738205i 0.0562876i
\(173\) 15.6742i 1.19169i 0.803100 + 0.595844i \(0.203182\pi\)
−0.803100 + 0.595844i \(0.796818\pi\)
\(174\) 0 0
\(175\) −10.1568 + 19.1773i −0.767779 + 1.44967i
\(176\) 1.07838 0.0812858
\(177\) 0 0
\(178\) 4.68035i 0.350807i
\(179\) 15.3607 1.14811 0.574056 0.818816i \(-0.305369\pi\)
0.574056 + 0.818816i \(0.305369\pi\)
\(180\) 0 0
\(181\) 21.6163 1.60673 0.803365 0.595487i \(-0.203041\pi\)
0.803365 + 0.595487i \(0.203041\pi\)
\(182\) 10.1568i 0.752869i
\(183\) 0 0
\(184\) −1.00000 −0.0737210
\(185\) −5.60197 1.39189i −0.411865 0.102334i
\(186\) 0 0
\(187\) 0.993857i 0.0726780i
\(188\) 6.83710i 0.498647i
\(189\) 0 0
\(190\) −5.07838 1.26180i −0.368424 0.0915402i
\(191\) −4.36683 −0.315973 −0.157987 0.987441i \(-0.550500\pi\)
−0.157987 + 0.987441i \(0.550500\pi\)
\(192\) 0 0
\(193\) 8.68035i 0.624825i −0.949947 0.312412i \(-0.898863\pi\)
0.949947 0.312412i \(-0.101137\pi\)
\(194\) 9.02052 0.647636
\(195\) 0 0
\(196\) 11.8371 0.845507
\(197\) 22.6803i 1.61591i −0.589246 0.807954i \(-0.700575\pi\)
0.589246 0.807954i \(-0.299425\pi\)
\(198\) 0 0
\(199\) 5.44521 0.386001 0.193000 0.981199i \(-0.438178\pi\)
0.193000 + 0.981199i \(0.438178\pi\)
\(200\) −2.34017 + 4.41855i −0.165475 + 0.312439i
\(201\) 0 0
\(202\) 1.50307i 0.105756i
\(203\) 45.5585i 3.19758i
\(204\) 0 0
\(205\) −0.0845208 + 0.340173i −0.00590319 + 0.0237587i
\(206\) 2.49693 0.173969
\(207\) 0 0
\(208\) 2.34017i 0.162262i
\(209\) −2.52359 −0.174560
\(210\) 0 0
\(211\) −22.0410 −1.51737 −0.758684 0.651459i \(-0.774157\pi\)
−0.758684 + 0.651459i \(0.774157\pi\)
\(212\) 0.340173i 0.0233632i
\(213\) 0 0
\(214\) −9.57531 −0.654554
\(215\) 1.60197 + 0.398032i 0.109253 + 0.0271455i
\(216\) 0 0
\(217\) 17.3607i 1.17852i
\(218\) 9.78539i 0.662750i
\(219\) 0 0
\(220\) −0.581449 + 2.34017i −0.0392013 + 0.157774i
\(221\) 2.15676 0.145079
\(222\) 0 0
\(223\) 21.1773i 1.41814i 0.705141 + 0.709068i \(0.250884\pi\)
−0.705141 + 0.709068i \(0.749116\pi\)
\(224\) 4.34017 0.289990
\(225\) 0 0
\(226\) 8.92162 0.593457
\(227\) 11.7854i 0.782224i −0.920343 0.391112i \(-0.872091\pi\)
0.920343 0.391112i \(-0.127909\pi\)
\(228\) 0 0
\(229\) −1.78539 −0.117982 −0.0589908 0.998259i \(-0.518788\pi\)
−0.0589908 + 0.998259i \(0.518788\pi\)
\(230\) 0.539189 2.17009i 0.0355531 0.143091i
\(231\) 0 0
\(232\) 10.4969i 0.689157i
\(233\) 18.3135i 1.19976i −0.800091 0.599879i \(-0.795215\pi\)
0.800091 0.599879i \(-0.204785\pi\)
\(234\) 0 0
\(235\) 14.8371 + 3.68649i 0.967866 + 0.240480i
\(236\) 8.83710 0.575246
\(237\) 0 0
\(238\) 4.00000i 0.259281i
\(239\) −5.33403 −0.345030 −0.172515 0.985007i \(-0.555189\pi\)
−0.172515 + 0.985007i \(0.555189\pi\)
\(240\) 0 0
\(241\) 26.1978 1.68755 0.843774 0.536698i \(-0.180329\pi\)
0.843774 + 0.536698i \(0.180329\pi\)
\(242\) 9.83710i 0.632353i
\(243\) 0 0
\(244\) 11.5753 0.741033
\(245\) −6.38243 + 25.6875i −0.407759 + 1.64112i
\(246\) 0 0
\(247\) 5.47641i 0.348456i
\(248\) 4.00000i 0.254000i
\(249\) 0 0
\(250\) −8.32684 7.46081i −0.526636 0.471863i
\(251\) −27.4329 −1.73155 −0.865775 0.500433i \(-0.833174\pi\)
−0.865775 + 0.500433i \(0.833174\pi\)
\(252\) 0 0
\(253\) 1.07838i 0.0677970i
\(254\) 17.1773 1.07780
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 10.3135i 0.643339i −0.946852 0.321670i \(-0.895756\pi\)
0.946852 0.321670i \(-0.104244\pi\)
\(258\) 0 0
\(259\) −11.2039 −0.696179
\(260\) 5.07838 + 1.26180i 0.314948 + 0.0782532i
\(261\) 0 0
\(262\) 6.68035i 0.412713i
\(263\) 20.9939i 1.29454i 0.762262 + 0.647268i \(0.224089\pi\)
−0.762262 + 0.647268i \(0.775911\pi\)
\(264\) 0 0
\(265\) 0.738205 + 0.183417i 0.0453476 + 0.0112672i
\(266\) −10.1568 −0.622751
\(267\) 0 0
\(268\) 2.58145i 0.157687i
\(269\) 25.3874 1.54789 0.773947 0.633250i \(-0.218280\pi\)
0.773947 + 0.633250i \(0.218280\pi\)
\(270\) 0 0
\(271\) −32.5646 −1.97816 −0.989080 0.147379i \(-0.952916\pi\)
−0.989080 + 0.147379i \(0.952916\pi\)
\(272\) 0.921622i 0.0558816i
\(273\) 0 0
\(274\) −22.2823 −1.34612
\(275\) −4.76487 2.52359i −0.287332 0.152178i
\(276\) 0 0
\(277\) 15.7009i 0.943374i −0.881766 0.471687i \(-0.843645\pi\)
0.881766 0.471687i \(-0.156355\pi\)
\(278\) 10.5236i 0.631163i
\(279\) 0 0
\(280\) −2.34017 + 9.41855i −0.139852 + 0.562866i
\(281\) 9.36069 0.558412 0.279206 0.960231i \(-0.409929\pi\)
0.279206 + 0.960231i \(0.409929\pi\)
\(282\) 0 0
\(283\) 17.4186i 1.03543i −0.855555 0.517713i \(-0.826784\pi\)
0.855555 0.517713i \(-0.173216\pi\)
\(284\) 15.1773 0.900606
\(285\) 0 0
\(286\) 2.52359 0.149223
\(287\) 0.680346i 0.0401596i
\(288\) 0 0
\(289\) 16.1506 0.950036
\(290\) 22.7792 + 5.65983i 1.33764 + 0.332356i
\(291\) 0 0
\(292\) 4.68035i 0.273897i
\(293\) 16.3402i 0.954603i 0.878740 + 0.477302i \(0.158385\pi\)
−0.878740 + 0.477302i \(0.841615\pi\)
\(294\) 0 0
\(295\) −4.76487 + 19.1773i −0.277421 + 1.11654i
\(296\) −2.58145 −0.150044
\(297\) 0 0
\(298\) 6.92162i 0.400959i
\(299\) −2.34017 −0.135336
\(300\) 0 0
\(301\) 3.20394 0.184672
\(302\) 6.15676i 0.354281i
\(303\) 0 0
\(304\) −2.34017 −0.134218
\(305\) −6.24128 + 25.1194i −0.357374 + 1.43833i
\(306\) 0 0
\(307\) 3.20394i 0.182858i 0.995812 + 0.0914292i \(0.0291435\pi\)
−0.995812 + 0.0914292i \(0.970856\pi\)
\(308\) 4.68035i 0.266687i
\(309\) 0 0
\(310\) −8.68035 2.15676i −0.493011 0.122495i
\(311\) −12.6537 −0.717525 −0.358762 0.933429i \(-0.616801\pi\)
−0.358762 + 0.933429i \(0.616801\pi\)
\(312\) 0 0
\(313\) 33.2183i 1.87761i 0.344449 + 0.938805i \(0.388066\pi\)
−0.344449 + 0.938805i \(0.611934\pi\)
\(314\) 2.89496 0.163372
\(315\) 0 0
\(316\) −11.9155 −0.670298
\(317\) 6.99386i 0.392814i −0.980522 0.196407i \(-0.937073\pi\)
0.980522 0.196407i \(-0.0629274\pi\)
\(318\) 0 0
\(319\) 11.3197 0.633779
\(320\) −0.539189 + 2.17009i −0.0301416 + 0.121312i
\(321\) 0 0
\(322\) 4.34017i 0.241868i
\(323\) 2.15676i 0.120005i
\(324\) 0 0
\(325\) −5.47641 + 10.3402i −0.303777 + 0.573570i
\(326\) −6.52359 −0.361308
\(327\) 0 0
\(328\) 0.156755i 0.00865537i
\(329\) 29.6742 1.63599
\(330\) 0 0
\(331\) −29.7275 −1.63397 −0.816986 0.576657i \(-0.804357\pi\)
−0.816986 + 0.576657i \(0.804357\pi\)
\(332\) 11.4186i 0.626674i
\(333\) 0 0
\(334\) −5.47641 −0.299656
\(335\) −5.60197 1.39189i −0.306068 0.0760470i
\(336\) 0 0
\(337\) 28.3402i 1.54379i −0.635751 0.771894i \(-0.719310\pi\)
0.635751 0.771894i \(-0.280690\pi\)
\(338\) 7.52359i 0.409229i
\(339\) 0 0
\(340\) −2.00000 0.496928i −0.108465 0.0269497i
\(341\) −4.31351 −0.233590
\(342\) 0 0
\(343\) 20.9939i 1.13356i
\(344\) 0.738205 0.0398013
\(345\) 0 0
\(346\) −15.6742 −0.842650
\(347\) 22.5236i 1.20913i −0.796556 0.604565i \(-0.793347\pi\)
0.796556 0.604565i \(-0.206653\pi\)
\(348\) 0 0
\(349\) −15.6742 −0.839021 −0.419510 0.907751i \(-0.637798\pi\)
−0.419510 + 0.907751i \(0.637798\pi\)
\(350\) −19.1773 10.1568i −1.02507 0.542901i
\(351\) 0 0
\(352\) 1.07838i 0.0574777i
\(353\) 26.3135i 1.40053i −0.713885 0.700263i \(-0.753066\pi\)
0.713885 0.700263i \(-0.246934\pi\)
\(354\) 0 0
\(355\) −8.18342 + 32.9360i −0.434331 + 1.74806i
\(356\) 4.68035 0.248058
\(357\) 0 0
\(358\) 15.3607i 0.811838i
\(359\) −0.796064 −0.0420146 −0.0210073 0.999779i \(-0.506687\pi\)
−0.0210073 + 0.999779i \(0.506687\pi\)
\(360\) 0 0
\(361\) −13.5236 −0.711768
\(362\) 21.6163i 1.13613i
\(363\) 0 0
\(364\) 10.1568 0.532359
\(365\) −10.1568 2.52359i −0.531629 0.132091i
\(366\) 0 0
\(367\) 13.7009i 0.715179i −0.933879 0.357590i \(-0.883599\pi\)
0.933879 0.357590i \(-0.116401\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) 0 0
\(370\) 1.39189 5.60197i 0.0723608 0.291232i
\(371\) 1.47641 0.0766514
\(372\) 0 0
\(373\) 4.25565i 0.220349i 0.993912 + 0.110175i \(0.0351410\pi\)
−0.993912 + 0.110175i \(0.964859\pi\)
\(374\) −0.993857 −0.0513911
\(375\) 0 0
\(376\) 6.83710 0.352597
\(377\) 24.5646i 1.26514i
\(378\) 0 0
\(379\) 30.6537 1.57457 0.787287 0.616587i \(-0.211485\pi\)
0.787287 + 0.616587i \(0.211485\pi\)
\(380\) 1.26180 5.07838i 0.0647287 0.260515i
\(381\) 0 0
\(382\) 4.36683i 0.223427i
\(383\) 20.8781i 1.06682i 0.845856 + 0.533412i \(0.179090\pi\)
−0.845856 + 0.533412i \(0.820910\pi\)
\(384\) 0 0
\(385\) −10.1568 2.52359i −0.517636 0.128614i
\(386\) 8.68035 0.441818
\(387\) 0 0
\(388\) 9.02052i 0.457947i
\(389\) −16.9627 −0.860041 −0.430021 0.902819i \(-0.641494\pi\)
−0.430021 + 0.902819i \(0.641494\pi\)
\(390\) 0 0
\(391\) 0.921622 0.0466084
\(392\) 11.8371i 0.597864i
\(393\) 0 0
\(394\) 22.6803 1.14262
\(395\) 6.42469 25.8576i 0.323261 1.30104i
\(396\) 0 0
\(397\) 16.4969i 0.827957i 0.910287 + 0.413979i \(0.135861\pi\)
−0.910287 + 0.413979i \(0.864139\pi\)
\(398\) 5.44521i 0.272944i
\(399\) 0 0
\(400\) −4.41855 2.34017i −0.220928 0.117009i
\(401\) 35.2039 1.75800 0.879000 0.476821i \(-0.158211\pi\)
0.879000 + 0.476821i \(0.158211\pi\)
\(402\) 0 0
\(403\) 9.36069i 0.466289i
\(404\) 1.50307 0.0747806
\(405\) 0 0
\(406\) 45.5585 2.26103
\(407\) 2.78378i 0.137987i
\(408\) 0 0
\(409\) −11.3607 −0.561750 −0.280875 0.959744i \(-0.590625\pi\)
−0.280875 + 0.959744i \(0.590625\pi\)
\(410\) −0.340173 0.0845208i −0.0167999 0.00417419i
\(411\) 0 0
\(412\) 2.49693i 0.123015i
\(413\) 38.3545i 1.88730i
\(414\) 0 0
\(415\) −24.7792 6.15676i −1.21637 0.302223i
\(416\) 2.34017 0.114736
\(417\) 0 0
\(418\) 2.52359i 0.123433i
\(419\) −18.1256 −0.885491 −0.442746 0.896647i \(-0.645996\pi\)
−0.442746 + 0.896647i \(0.645996\pi\)
\(420\) 0 0
\(421\) 2.58145 0.125812 0.0629061 0.998019i \(-0.479963\pi\)
0.0629061 + 0.998019i \(0.479963\pi\)
\(422\) 22.0410i 1.07294i
\(423\) 0 0
\(424\) 0.340173 0.0165203
\(425\) 2.15676 4.07223i 0.104618 0.197532i
\(426\) 0 0
\(427\) 50.2388i 2.43123i
\(428\) 9.57531i 0.462840i
\(429\) 0 0
\(430\) −0.398032 + 1.60197i −0.0191948 + 0.0772538i
\(431\) 33.9877 1.63713 0.818565 0.574414i \(-0.194770\pi\)
0.818565 + 0.574414i \(0.194770\pi\)
\(432\) 0 0
\(433\) 8.28685i 0.398241i −0.979975 0.199120i \(-0.936192\pi\)
0.979975 0.199120i \(-0.0638084\pi\)
\(434\) −17.3607 −0.833340
\(435\) 0 0
\(436\) −9.78539 −0.468635
\(437\) 2.34017i 0.111946i
\(438\) 0 0
\(439\) 28.9939 1.38380 0.691901 0.721993i \(-0.256774\pi\)
0.691901 + 0.721993i \(0.256774\pi\)
\(440\) −2.34017 0.581449i −0.111563 0.0277195i
\(441\) 0 0
\(442\) 2.15676i 0.102586i
\(443\) 3.20394i 0.152224i 0.997099 + 0.0761118i \(0.0242506\pi\)
−0.997099 + 0.0761118i \(0.975749\pi\)
\(444\) 0 0
\(445\) −2.52359 + 10.1568i −0.119630 + 0.481476i
\(446\) −21.1773 −1.00277
\(447\) 0 0
\(448\) 4.34017i 0.205054i
\(449\) 28.1568 1.32880 0.664400 0.747377i \(-0.268687\pi\)
0.664400 + 0.747377i \(0.268687\pi\)
\(450\) 0 0
\(451\) −0.169042 −0.00795986
\(452\) 8.92162i 0.419638i
\(453\) 0 0
\(454\) 11.7854 0.553116
\(455\) −5.47641 + 22.0410i −0.256738 + 1.03330i
\(456\) 0 0
\(457\) 23.1773i 1.08419i 0.840318 + 0.542094i \(0.182368\pi\)
−0.840318 + 0.542094i \(0.817632\pi\)
\(458\) 1.78539i 0.0834256i
\(459\) 0 0
\(460\) 2.17009 + 0.539189i 0.101181 + 0.0251398i
\(461\) 42.3279 1.97141 0.985703 0.168491i \(-0.0538896\pi\)
0.985703 + 0.168491i \(0.0538896\pi\)
\(462\) 0 0
\(463\) 34.9048i 1.62216i −0.584933 0.811082i \(-0.698879\pi\)
0.584933 0.811082i \(-0.301121\pi\)
\(464\) 10.4969 0.487308
\(465\) 0 0
\(466\) 18.3135 0.848357
\(467\) 37.7731i 1.74793i −0.485988 0.873965i \(-0.661540\pi\)
0.485988 0.873965i \(-0.338460\pi\)
\(468\) 0 0
\(469\) −11.2039 −0.517350
\(470\) −3.68649 + 14.8371i −0.170045 + 0.684384i
\(471\) 0 0
\(472\) 8.83710i 0.406761i
\(473\) 0.796064i 0.0366030i
\(474\) 0 0
\(475\) 10.3402 + 5.47641i 0.474440 + 0.251275i
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) 5.33403i 0.243973i
\(479\) −28.1978 −1.28839 −0.644195 0.764861i \(-0.722807\pi\)
−0.644195 + 0.764861i \(0.722807\pi\)
\(480\) 0 0
\(481\) −6.04104 −0.275448
\(482\) 26.1978i 1.19328i
\(483\) 0 0
\(484\) 9.83710 0.447141
\(485\) −19.5753 4.86376i −0.888869 0.220852i
\(486\) 0 0
\(487\) 38.2245i 1.73212i −0.499944 0.866058i \(-0.666646\pi\)
0.499944 0.866058i \(-0.333354\pi\)
\(488\) 11.5753i 0.523989i
\(489\) 0 0
\(490\) −25.6875 6.38243i −1.16044 0.288329i
\(491\) −11.3074 −0.510294 −0.255147 0.966902i \(-0.582124\pi\)
−0.255147 + 0.966902i \(0.582124\pi\)
\(492\) 0 0
\(493\) 9.67420i 0.435704i
\(494\) −5.47641 −0.246395
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 65.8720i 2.95476i
\(498\) 0 0
\(499\) 2.47027 0.110584 0.0552922 0.998470i \(-0.482391\pi\)
0.0552922 + 0.998470i \(0.482391\pi\)
\(500\) 7.46081 8.32684i 0.333658 0.372388i
\(501\) 0 0
\(502\) 27.4329i 1.22439i
\(503\) 20.6270i 0.919713i 0.887993 + 0.459857i \(0.152099\pi\)
−0.887993 + 0.459857i \(0.847901\pi\)
\(504\) 0 0
\(505\) −0.810439 + 3.26180i −0.0360641 + 0.145148i
\(506\) 1.07838 0.0479397
\(507\) 0 0
\(508\) 17.1773i 0.762118i
\(509\) −32.2245 −1.42832 −0.714162 0.699981i \(-0.753192\pi\)
−0.714162 + 0.699981i \(0.753192\pi\)
\(510\) 0 0
\(511\) −20.3135 −0.898617
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 10.3135 0.454909
\(515\) −5.41855 1.34632i −0.238770 0.0593258i
\(516\) 0 0
\(517\) 7.37298i 0.324263i
\(518\) 11.2039i 0.492273i
\(519\) 0 0
\(520\) −1.26180 + 5.07838i −0.0553334 + 0.222702i
\(521\) 3.51745 0.154102 0.0770511 0.997027i \(-0.475450\pi\)
0.0770511 + 0.997027i \(0.475450\pi\)
\(522\) 0 0
\(523\) 35.9421i 1.57164i −0.618455 0.785820i \(-0.712241\pi\)
0.618455 0.785820i \(-0.287759\pi\)
\(524\) −6.68035 −0.291832
\(525\) 0 0
\(526\) −20.9939 −0.915376
\(527\) 3.68649i 0.160586i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) −0.183417 + 0.738205i −0.00796715 + 0.0320656i
\(531\) 0 0
\(532\) 10.1568i 0.440351i
\(533\) 0.366835i 0.0158894i
\(534\) 0 0
\(535\) 20.7792 + 5.16290i 0.898365 + 0.223212i
\(536\) −2.58145 −0.111502
\(537\) 0 0
\(538\) 25.3874i 1.09453i
\(539\) −12.7649 −0.549822
\(540\) 0 0
\(541\) 31.7275 1.36407 0.682036 0.731318i \(-0.261095\pi\)
0.682036 + 0.731318i \(0.261095\pi\)
\(542\) 32.5646i 1.39877i
\(543\) 0 0
\(544\) −0.921622 −0.0395142
\(545\) 5.27617 21.2351i 0.226006 0.909613i
\(546\) 0 0
\(547\) 9.84324i 0.420867i 0.977608 + 0.210433i \(0.0674875\pi\)
−0.977608 + 0.210433i \(0.932512\pi\)
\(548\) 22.2823i 0.951853i
\(549\) 0 0
\(550\) 2.52359 4.76487i 0.107606 0.203175i
\(551\) −24.5646 −1.04649
\(552\) 0 0
\(553\) 51.7152i 2.19916i
\(554\) 15.7009 0.667066
\(555\) 0 0
\(556\) −10.5236 −0.446300
\(557\) 26.3279i 1.11555i 0.829993 + 0.557774i \(0.188344\pi\)
−0.829993 + 0.557774i \(0.811656\pi\)
\(558\) 0 0
\(559\) 1.72753 0.0730666
\(560\) −9.41855 2.34017i −0.398006 0.0988904i
\(561\) 0 0
\(562\) 9.36069i 0.394857i
\(563\) 30.2557i 1.27512i 0.770399 + 0.637562i \(0.220057\pi\)
−0.770399 + 0.637562i \(0.779943\pi\)
\(564\) 0 0
\(565\) −19.3607 4.81044i −0.814510 0.202377i
\(566\) 17.4186 0.732156
\(567\) 0 0
\(568\) 15.1773i 0.636824i
\(569\) 33.8720 1.41999 0.709994 0.704208i \(-0.248698\pi\)
0.709994 + 0.704208i \(0.248698\pi\)
\(570\) 0 0
\(571\) 35.1650 1.47161 0.735804 0.677194i \(-0.236804\pi\)
0.735804 + 0.677194i \(0.236804\pi\)
\(572\) 2.52359i 0.105517i
\(573\) 0 0
\(574\) −0.680346 −0.0283971
\(575\) −2.34017 + 4.41855i −0.0975920 + 0.184266i
\(576\) 0 0
\(577\) 4.00000i 0.166522i 0.996528 + 0.0832611i \(0.0265335\pi\)
−0.996528 + 0.0832611i \(0.973466\pi\)
\(578\) 16.1506i 0.671777i
\(579\) 0 0
\(580\) −5.65983 + 22.7792i −0.235012 + 0.945857i
\(581\) −49.5585 −2.05603
\(582\) 0 0
\(583\) 0.366835i 0.0151928i
\(584\) −4.68035 −0.193674
\(585\) 0 0
\(586\) −16.3402 −0.675006
\(587\) 9.30737i 0.384156i 0.981380 + 0.192078i \(0.0615227\pi\)
−0.981380 + 0.192078i \(0.938477\pi\)
\(588\) 0 0
\(589\) 9.36069 0.385701
\(590\) −19.1773 4.76487i −0.789516 0.196166i
\(591\) 0 0
\(592\) 2.58145i 0.106097i
\(593\) 33.0349i 1.35658i −0.734794 0.678290i \(-0.762721\pi\)
0.734794 0.678290i \(-0.237279\pi\)
\(594\) 0 0
\(595\) 2.15676 8.68035i 0.0884184 0.355859i
\(596\) −6.92162 −0.283521
\(597\) 0 0
\(598\) 2.34017i 0.0956968i
\(599\) 13.6475 0.557623 0.278812 0.960346i \(-0.410059\pi\)
0.278812 + 0.960346i \(0.410059\pi\)
\(600\) 0 0
\(601\) 1.68649 0.0687933 0.0343967 0.999408i \(-0.489049\pi\)
0.0343967 + 0.999408i \(0.489049\pi\)
\(602\) 3.20394i 0.130583i
\(603\) 0 0
\(604\) −6.15676 −0.250515
\(605\) −5.30406 + 21.3474i −0.215641 + 0.867894i
\(606\) 0 0
\(607\) 47.2183i 1.91653i 0.285878 + 0.958266i \(0.407715\pi\)
−0.285878 + 0.958266i \(0.592285\pi\)
\(608\) 2.34017i 0.0949065i
\(609\) 0 0
\(610\) −25.1194 6.24128i −1.01706 0.252702i
\(611\) 16.0000 0.647291
\(612\) 0 0
\(613\) 7.45959i 0.301290i −0.988588 0.150645i \(-0.951865\pi\)
0.988588 0.150645i \(-0.0481350\pi\)
\(614\) −3.20394 −0.129300
\(615\) 0 0
\(616\) −4.68035 −0.188577
\(617\) 15.8120i 0.636569i 0.947995 + 0.318285i \(0.103107\pi\)
−0.947995 + 0.318285i \(0.896893\pi\)
\(618\) 0 0
\(619\) 26.3402 1.05870 0.529350 0.848403i \(-0.322436\pi\)
0.529350 + 0.848403i \(0.322436\pi\)
\(620\) 2.15676 8.68035i 0.0866174 0.348611i
\(621\) 0 0
\(622\) 12.6537i 0.507367i
\(623\) 20.3135i 0.813844i
\(624\) 0 0
\(625\) 14.0472 + 20.6803i 0.561887 + 0.827214i
\(626\) −33.2183 −1.32767
\(627\) 0 0
\(628\) 2.89496i 0.115521i
\(629\) 2.37912 0.0948618
\(630\) 0 0
\(631\) −14.4391 −0.574810 −0.287405 0.957809i \(-0.592793\pi\)
−0.287405 + 0.957809i \(0.592793\pi\)
\(632\) 11.9155i 0.473972i
\(633\) 0 0
\(634\) 6.99386 0.277762
\(635\) −37.2762 9.26180i −1.47926 0.367543i
\(636\) 0 0
\(637\) 27.7009i 1.09755i
\(638\) 11.3197i 0.448149i
\(639\) 0 0
\(640\) −2.17009 0.539189i −0.0857802 0.0213133i
\(641\) 5.78992 0.228688 0.114344 0.993441i \(-0.463523\pi\)
0.114344 + 0.993441i \(0.463523\pi\)
\(642\) 0 0
\(643\) 23.4063i 0.923053i 0.887126 + 0.461526i \(0.152698\pi\)
−0.887126 + 0.461526i \(0.847302\pi\)
\(644\) 4.34017 0.171027
\(645\) 0 0
\(646\) 2.15676 0.0848564
\(647\) 25.9877i 1.02168i 0.859675 + 0.510841i \(0.170666\pi\)
−0.859675 + 0.510841i \(0.829334\pi\)
\(648\) 0 0
\(649\) −9.52973 −0.374075
\(650\) −10.3402 5.47641i −0.405575 0.214802i
\(651\) 0 0
\(652\) 6.52359i 0.255484i
\(653\) 0.325797i 0.0127494i 0.999980 + 0.00637471i \(0.00202915\pi\)
−0.999980 + 0.00637471i \(0.997971\pi\)
\(654\) 0 0
\(655\) 3.60197 14.4969i 0.140741 0.566442i
\(656\) −0.156755 −0.00612027
\(657\) 0 0
\(658\) 29.6742i 1.15682i
\(659\) −3.11942 −0.121515 −0.0607576 0.998153i \(-0.519352\pi\)
−0.0607576 + 0.998153i \(0.519352\pi\)
\(660\) 0 0
\(661\) 24.1399 0.938935 0.469467 0.882950i \(-0.344446\pi\)
0.469467 + 0.882950i \(0.344446\pi\)
\(662\) 29.7275i 1.15539i
\(663\) 0 0
\(664\) −11.4186 −0.443126
\(665\) 22.0410 + 5.47641i 0.854715 + 0.212366i
\(666\) 0 0
\(667\) 10.4969i 0.406443i
\(668\) 5.47641i 0.211889i
\(669\) 0 0
\(670\) 1.39189 5.60197i 0.0537734 0.216423i
\(671\) −12.4826 −0.481884
\(672\) 0 0
\(673\) 45.6742i 1.76061i −0.474407 0.880306i \(-0.657338\pi\)
0.474407 0.880306i \(-0.342662\pi\)
\(674\) 28.3402 1.09162
\(675\) 0 0
\(676\) −7.52359 −0.289369
\(677\) 9.38735i 0.360785i 0.983595 + 0.180393i \(0.0577368\pi\)
−0.983595 + 0.180393i \(0.942263\pi\)
\(678\) 0 0
\(679\) −39.1506 −1.50246
\(680\) 0.496928 2.00000i 0.0190563 0.0766965i
\(681\) 0 0
\(682\) 4.31351i 0.165173i
\(683\) 20.9939i 0.803308i −0.915792 0.401654i \(-0.868436\pi\)
0.915792 0.401654i \(-0.131564\pi\)
\(684\) 0 0
\(685\) 48.3545 + 12.0144i 1.84753 + 0.459046i
\(686\) −20.9939 −0.801549
\(687\) 0 0
\(688\) 0.738205i 0.0281438i
\(689\) 0.796064 0.0303276
\(690\) 0 0
\(691\) −44.1445 −1.67933 −0.839667 0.543101i \(-0.817250\pi\)
−0.839667 + 0.543101i \(0.817250\pi\)
\(692\) 15.6742i 0.595844i
\(693\) 0 0
\(694\) 22.5236 0.854984
\(695\) 5.67420 22.8371i 0.215235 0.866261i
\(696\) 0 0
\(697\) 0.144469i 0.00547217i
\(698\) 15.6742i 0.593277i
\(699\) 0 0
\(700\) 10.1568 19.1773i 0.383889 0.724833i
\(701\) 27.7998 1.04998 0.524991 0.851108i \(-0.324069\pi\)
0.524991 + 0.851108i \(0.324069\pi\)
\(702\) 0 0
\(703\) 6.04104i 0.227842i
\(704\) −1.07838 −0.0406429
\(705\) 0 0
\(706\) 26.3135 0.990322
\(707\) 6.52359i 0.245345i
\(708\) 0 0
\(709\) −4.30898 −0.161827 −0.0809135 0.996721i \(-0.525784\pi\)
−0.0809135 + 0.996721i \(0.525784\pi\)
\(710\) −32.9360 8.18342i −1.23607 0.307118i
\(711\) 0 0
\(712\) 4.68035i 0.175403i
\(713\) 4.00000i 0.149801i
\(714\) 0 0
\(715\) −5.47641 1.36069i −0.204806 0.0508870i
\(716\) −15.3607 −0.574056
\(717\) 0 0
\(718\) 0.796064i 0.0297088i
\(719\) 15.9733 0.595705 0.297852 0.954612i \(-0.403730\pi\)
0.297852 + 0.954612i \(0.403730\pi\)
\(720\) 0 0
\(721\) −10.8371 −0.403595
\(722\) 13.5236i 0.503296i
\(723\) 0 0
\(724\) −21.6163 −0.803365
\(725\) −46.3812 24.5646i −1.72255 0.912307i
\(726\) 0 0
\(727\) 0.340173i 0.0126163i 0.999980 + 0.00630816i \(0.00200796\pi\)
−0.999980 + 0.00630816i \(0.997992\pi\)
\(728\) 10.1568i 0.376434i
\(729\) 0 0
\(730\) 2.52359 10.1568i 0.0934023 0.375918i
\(731\) −0.680346 −0.0251635
\(732\) 0 0
\(733\) 19.2618i 0.711451i −0.934591 0.355725i \(-0.884234\pi\)
0.934591 0.355725i \(-0.115766\pi\)
\(734\) 13.7009 0.505708
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 2.78378i 0.102542i
\(738\) 0 0
\(739\) −25.5585 −0.940184 −0.470092 0.882617i \(-0.655779\pi\)
−0.470092 + 0.882617i \(0.655779\pi\)
\(740\) 5.60197 + 1.39189i 0.205932 + 0.0511668i
\(741\) 0 0
\(742\) 1.47641i 0.0542007i
\(743\) 36.8781i 1.35293i 0.736476 + 0.676464i \(0.236489\pi\)
−0.736476 + 0.676464i \(0.763511\pi\)
\(744\) 0 0
\(745\) 3.73206 15.0205i 0.136732 0.550309i
\(746\) −4.25565 −0.155810
\(747\) 0 0
\(748\) 0.993857i 0.0363390i
\(749\) 41.5585 1.51851
\(750\) 0 0
\(751\) 18.1256 0.661411 0.330706 0.943734i \(-0.392713\pi\)
0.330706 + 0.943734i \(0.392713\pi\)
\(752\) 6.83710i 0.249323i
\(753\) 0 0
\(754\) 24.5646 0.894591
\(755\) 3.31965 13.3607i 0.120815 0.486245i
\(756\) 0 0
\(757\) 17.4186i 0.633088i 0.948578 + 0.316544i \(0.102522\pi\)
−0.948578 + 0.316544i \(0.897478\pi\)
\(758\) 30.6537i 1.11339i
\(759\) 0 0
\(760\) 5.07838 + 1.26180i 0.184212 + 0.0457701i
\(761\) 23.4140 0.848757 0.424379 0.905485i \(-0.360493\pi\)
0.424379 + 0.905485i \(0.360493\pi\)
\(762\) 0 0
\(763\) 42.4703i 1.53753i
\(764\) 4.36683 0.157987
\(765\) 0 0
\(766\) −20.8781 −0.754358
\(767\) 20.6803i 0.746724i
\(768\) 0 0
\(769\) 29.7152 1.07156 0.535779 0.844358i \(-0.320018\pi\)
0.535779 + 0.844358i \(0.320018\pi\)
\(770\) 2.52359 10.1568i 0.0909439 0.366024i
\(771\) 0 0
\(772\) 8.68035i 0.312412i
\(773\) 15.3463i 0.551969i −0.961162 0.275984i \(-0.910996\pi\)
0.961162 0.275984i \(-0.0890038\pi\)
\(774\) 0 0
\(775\) 17.6742 + 9.36069i 0.634876 + 0.336246i
\(776\) −9.02052 −0.323818
\(777\) 0 0
\(778\) 16.9627i 0.608141i
\(779\) 0.366835 0.0131432
\(780\) 0 0
\(781\) −16.3668 −0.585651
\(782\) 0.921622i 0.0329571i
\(783\) 0 0
\(784\) −11.8371 −0.422754
\(785\) −6.28231 1.56093i −0.224225 0.0557120i
\(786\) 0 0
\(787\) 22.8950i 0.816117i 0.912956 + 0.408059i \(0.133794\pi\)
−0.912956 + 0.408059i \(0.866206\pi\)
\(788\) 22.6803i 0.807954i
\(789\) 0 0
\(790\) 25.8576 + 6.42469i 0.919973 + 0.228580i
\(791\) −38.7214 −1.37677
\(792\) 0 0
\(793\) 27.0882i 0.961931i
\(794\) −16.4969 −0.585454
\(795\) 0 0
\(796\) −5.44521 −0.193000
\(797\) 7.60650i 0.269436i −0.990884 0.134718i \(-0.956987\pi\)
0.990884 0.134718i \(-0.0430129\pi\)