Properties

Label 690.2.d.c.139.5
Level $690$
Weight $2$
Character 690.139
Analytic conductor $5.510$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.5
Root \(-0.854638 + 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 690.139
Dual form 690.2.d.c.139.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.539189 - 2.17009i) q^{5} -1.00000 q^{6} +4.34017i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-0.539189 - 2.17009i) q^{5} -1.00000 q^{6} +4.34017i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(2.17009 - 0.539189i) q^{10} -1.07838 q^{11} -1.00000i q^{12} +2.34017i q^{13} -4.34017 q^{14} +(2.17009 - 0.539189i) q^{15} +1.00000 q^{16} +0.921622i q^{17} -1.00000i q^{18} -2.34017 q^{19} +(0.539189 + 2.17009i) q^{20} -4.34017 q^{21} -1.07838i q^{22} -1.00000i q^{23} +1.00000 q^{24} +(-4.41855 + 2.34017i) q^{25} -2.34017 q^{26} -1.00000i q^{27} -4.34017i q^{28} -10.4969 q^{29} +(0.539189 + 2.17009i) q^{30} -4.00000 q^{31} +1.00000i q^{32} -1.07838i q^{33} -0.921622 q^{34} +(9.41855 - 2.34017i) q^{35} +1.00000 q^{36} +2.58145i q^{37} -2.34017i q^{38} -2.34017 q^{39} +(-2.17009 + 0.539189i) q^{40} +0.156755 q^{41} -4.34017i q^{42} -0.738205i q^{43} +1.07838 q^{44} +(0.539189 + 2.17009i) q^{45} +1.00000 q^{46} +6.83710i q^{47} +1.00000i q^{48} -11.8371 q^{49} +(-2.34017 - 4.41855i) q^{50} -0.921622 q^{51} -2.34017i q^{52} +0.340173i q^{53} +1.00000 q^{54} +(0.581449 + 2.34017i) q^{55} +4.34017 q^{56} -2.34017i q^{57} -10.4969i q^{58} +8.83710 q^{59} +(-2.17009 + 0.539189i) q^{60} -11.5753 q^{61} -4.00000i q^{62} -4.34017i q^{63} -1.00000 q^{64} +(5.07838 - 1.26180i) q^{65} +1.07838 q^{66} +2.58145i q^{67} -0.921622i q^{68} +1.00000 q^{69} +(2.34017 + 9.41855i) q^{70} +15.1773 q^{71} +1.00000i q^{72} +4.68035i q^{73} -2.58145 q^{74} +(-2.34017 - 4.41855i) q^{75} +2.34017 q^{76} -4.68035i q^{77} -2.34017i q^{78} +11.9155 q^{79} +(-0.539189 - 2.17009i) q^{80} +1.00000 q^{81} +0.156755i q^{82} -11.4186i q^{83} +4.34017 q^{84} +(2.00000 - 0.496928i) q^{85} +0.738205 q^{86} -10.4969i q^{87} +1.07838i q^{88} +4.68035 q^{89} +(-2.17009 + 0.539189i) q^{90} -10.1568 q^{91} +1.00000i q^{92} -4.00000i q^{93} -6.83710 q^{94} +(1.26180 + 5.07838i) q^{95} -1.00000 q^{96} +9.02052i q^{97} -11.8371i q^{98} +1.07838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + 2q^{10} - 4q^{14} + 2q^{15} + 6q^{16} + 8q^{19} - 4q^{21} + 6q^{24} + 2q^{25} + 8q^{26} - 28q^{29} - 24q^{31} - 12q^{34} + 28q^{35} + 6q^{36} + 8q^{39} - 2q^{40} - 12q^{41} + 6q^{46} - 14q^{49} + 8q^{50} - 12q^{51} + 6q^{54} + 32q^{55} + 4q^{56} - 4q^{59} - 2q^{60} - 28q^{61} - 6q^{64} + 24q^{65} + 6q^{69} - 8q^{70} + 12q^{71} - 44q^{74} + 8q^{75} - 8q^{76} + 8q^{79} + 6q^{81} + 4q^{84} + 12q^{85} + 20q^{86} - 16q^{89} - 2q^{90} - 48q^{91} + 16q^{94} - 8q^{95} - 6q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) −0.539189 2.17009i −0.241133 0.970492i
\(6\) −1.00000 −0.408248
\(7\) 4.34017i 1.64043i 0.572055 + 0.820216i \(0.306147\pi\)
−0.572055 + 0.820216i \(0.693853\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 2.17009 0.539189i 0.686242 0.170506i
\(11\) −1.07838 −0.325143 −0.162572 0.986697i \(-0.551979\pi\)
−0.162572 + 0.986697i \(0.551979\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.34017i 0.649047i 0.945878 + 0.324524i \(0.105204\pi\)
−0.945878 + 0.324524i \(0.894796\pi\)
\(14\) −4.34017 −1.15996
\(15\) 2.17009 0.539189i 0.560314 0.139218i
\(16\) 1.00000 0.250000
\(17\) 0.921622i 0.223526i 0.993735 + 0.111763i \(0.0356498\pi\)
−0.993735 + 0.111763i \(0.964350\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −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
\(21\) −4.34017 −0.947103
\(22\) 1.07838i 0.229911i
\(23\) 1.00000i 0.208514i
\(24\) 1.00000 0.204124
\(25\) −4.41855 + 2.34017i −0.883710 + 0.468035i
\(26\) −2.34017 −0.458946
\(27\) 1.00000i 0.192450i
\(28\) 4.34017i 0.820216i
\(29\) −10.4969 −1.94923 −0.974615 0.223886i \(-0.928126\pi\)
−0.974615 + 0.223886i \(0.928126\pi\)
\(30\) 0.539189 + 2.17009i 0.0984420 + 0.396202i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.07838i 0.187721i
\(34\) −0.921622 −0.158057
\(35\) 9.41855 2.34017i 1.59203 0.395561i
\(36\) 1.00000 0.166667
\(37\) 2.58145i 0.424388i 0.977228 + 0.212194i \(0.0680608\pi\)
−0.977228 + 0.212194i \(0.931939\pi\)
\(38\) 2.34017i 0.379626i
\(39\) −2.34017 −0.374728
\(40\) −2.17009 + 0.539189i −0.343121 + 0.0852532i
\(41\) 0.156755 0.0244811 0.0122405 0.999925i \(-0.496104\pi\)
0.0122405 + 0.999925i \(0.496104\pi\)
\(42\) 4.34017i 0.669703i
\(43\) 0.738205i 0.112575i −0.998415 0.0562876i \(-0.982074\pi\)
0.998415 0.0562876i \(-0.0179264\pi\)
\(44\) 1.07838 0.162572
\(45\) 0.539189 + 2.17009i 0.0803775 + 0.323497i
\(46\) 1.00000 0.147442
\(47\) 6.83710i 0.997294i 0.866805 + 0.498647i \(0.166170\pi\)
−0.866805 + 0.498647i \(0.833830\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −11.8371 −1.69101
\(50\) −2.34017 4.41855i −0.330950 0.624877i
\(51\) −0.921622 −0.129053
\(52\) 2.34017i 0.324524i
\(53\) 0.340173i 0.0467264i 0.999727 + 0.0233632i \(0.00743741\pi\)
−0.999727 + 0.0233632i \(0.992563\pi\)
\(54\) 1.00000 0.136083
\(55\) 0.581449 + 2.34017i 0.0784026 + 0.315549i
\(56\) 4.34017 0.579980
\(57\) 2.34017i 0.309963i
\(58\) 10.4969i 1.37831i
\(59\) 8.83710 1.15049 0.575246 0.817980i \(-0.304906\pi\)
0.575246 + 0.817980i \(0.304906\pi\)
\(60\) −2.17009 + 0.539189i −0.280157 + 0.0696090i
\(61\) −11.5753 −1.48207 −0.741033 0.671469i \(-0.765664\pi\)
−0.741033 + 0.671469i \(0.765664\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 4.34017i 0.546810i
\(64\) −1.00000 −0.125000
\(65\) 5.07838 1.26180i 0.629895 0.156506i
\(66\) 1.07838 0.132739
\(67\) 2.58145i 0.315374i 0.987489 + 0.157687i \(0.0504037\pi\)
−0.987489 + 0.157687i \(0.949596\pi\)
\(68\) 0.921622i 0.111763i
\(69\) 1.00000 0.120386
\(70\) 2.34017 + 9.41855i 0.279704 + 1.12573i
\(71\) 15.1773 1.80121 0.900606 0.434637i \(-0.143123\pi\)
0.900606 + 0.434637i \(0.143123\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 4.68035i 0.547793i 0.961759 + 0.273897i \(0.0883126\pi\)
−0.961759 + 0.273897i \(0.911687\pi\)
\(74\) −2.58145 −0.300087
\(75\) −2.34017 4.41855i −0.270220 0.510210i
\(76\) 2.34017 0.268436
\(77\) 4.68035i 0.533375i
\(78\) 2.34017i 0.264972i
\(79\) 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
\(81\) 1.00000 0.111111
\(82\) 0.156755i 0.0173107i
\(83\) 11.4186i 1.25335i −0.779281 0.626674i \(-0.784416\pi\)
0.779281 0.626674i \(-0.215584\pi\)
\(84\) 4.34017 0.473552
\(85\) 2.00000 0.496928i 0.216930 0.0538995i
\(86\) 0.738205 0.0796027
\(87\) 10.4969i 1.12539i
\(88\) 1.07838i 0.114955i
\(89\) 4.68035 0.496116 0.248058 0.968745i \(-0.420208\pi\)
0.248058 + 0.968745i \(0.420208\pi\)
\(90\) −2.17009 + 0.539189i −0.228747 + 0.0568355i
\(91\) −10.1568 −1.06472
\(92\) 1.00000i 0.104257i
\(93\) 4.00000i 0.414781i
\(94\) −6.83710 −0.705193
\(95\) 1.26180 + 5.07838i 0.129457 + 0.521031i
\(96\) −1.00000 −0.102062
\(97\) 9.02052i 0.915895i 0.888979 + 0.457947i \(0.151415\pi\)
−0.888979 + 0.457947i \(0.848585\pi\)
\(98\) 11.8371i 1.19573i
\(99\) 1.07838 0.108381
\(100\) 4.41855 2.34017i 0.441855 0.234017i
\(101\) 1.50307 0.149561 0.0747806 0.997200i \(-0.476174\pi\)
0.0747806 + 0.997200i \(0.476174\pi\)
\(102\) 0.921622i 0.0912542i
\(103\) 2.49693i 0.246030i 0.992405 + 0.123015i \(0.0392563\pi\)
−0.992405 + 0.123015i \(0.960744\pi\)
\(104\) 2.34017 0.229473
\(105\) 2.34017 + 9.41855i 0.228377 + 0.919156i
\(106\) −0.340173 −0.0330405
\(107\) 9.57531i 0.925680i 0.886442 + 0.462840i \(0.153170\pi\)
−0.886442 + 0.462840i \(0.846830\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 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
\(111\) −2.58145 −0.245020
\(112\) 4.34017i 0.410108i
\(113\) 8.92162i 0.839276i −0.907692 0.419638i \(-0.862157\pi\)
0.907692 0.419638i \(-0.137843\pi\)
\(114\) 2.34017 0.219177
\(115\) −2.17009 + 0.539189i −0.202362 + 0.0502796i
\(116\) 10.4969 0.974615
\(117\) 2.34017i 0.216349i
\(118\) 8.83710i 0.813521i
\(119\) −4.00000 −0.366679
\(120\) −0.539189 2.17009i −0.0492210 0.198101i
\(121\) −9.83710 −0.894282
\(122\) 11.5753i 1.04798i
\(123\) 0.156755i 0.0141342i
\(124\) 4.00000 0.359211
\(125\) 7.46081 + 8.32684i 0.667315 + 0.744775i
\(126\) 4.34017 0.386653
\(127\) 17.1773i 1.52424i 0.647438 + 0.762118i \(0.275841\pi\)
−0.647438 + 0.762118i \(0.724159\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.738205 0.0649953
\(130\) 1.26180 + 5.07838i 0.110667 + 0.445403i
\(131\) −6.68035 −0.583665 −0.291832 0.956470i \(-0.594265\pi\)
−0.291832 + 0.956470i \(0.594265\pi\)
\(132\) 1.07838i 0.0938607i
\(133\) 10.1568i 0.880702i
\(134\) −2.58145 −0.223003
\(135\) −2.17009 + 0.539189i −0.186771 + 0.0464060i
\(136\) 0.921622 0.0790285
\(137\) 22.2823i 1.90371i 0.306554 + 0.951853i \(0.400824\pi\)
−0.306554 + 0.951853i \(0.599176\pi\)
\(138\) 1.00000i 0.0851257i
\(139\) 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
\(141\) −6.83710 −0.575788
\(142\) 15.1773i 1.27365i
\(143\) 2.52359i 0.211033i
\(144\) −1.00000 −0.0833333
\(145\) 5.65983 + 22.7792i 0.470023 + 1.89171i
\(146\) −4.68035 −0.387348
\(147\) 11.8371i 0.976308i
\(148\) 2.58145i 0.212194i
\(149\) −6.92162 −0.567041 −0.283521 0.958966i \(-0.591502\pi\)
−0.283521 + 0.958966i \(0.591502\pi\)
\(150\) 4.41855 2.34017i 0.360773 0.191074i
\(151\) 6.15676 0.501030 0.250515 0.968113i \(-0.419400\pi\)
0.250515 + 0.968113i \(0.419400\pi\)
\(152\) 2.34017i 0.189813i
\(153\) 0.921622i 0.0745087i
\(154\) 4.68035 0.377153
\(155\) 2.15676 + 8.68035i 0.173235 + 0.697222i
\(156\) 2.34017 0.187364
\(157\) 2.89496i 0.231043i 0.993305 + 0.115521i \(0.0368539\pi\)
−0.993305 + 0.115521i \(0.963146\pi\)
\(158\) 11.9155i 0.947945i
\(159\) −0.340173 −0.0269775
\(160\) 2.17009 0.539189i 0.171560 0.0426266i
\(161\) 4.34017 0.342054
\(162\) 1.00000i 0.0785674i
\(163\) 6.52359i 0.510967i −0.966813 0.255484i \(-0.917765\pi\)
0.966813 0.255484i \(-0.0822347\pi\)
\(164\) −0.156755 −0.0122405
\(165\) −2.34017 + 0.581449i −0.182182 + 0.0452658i
\(166\) 11.4186 0.886251
\(167\) 5.47641i 0.423777i 0.977294 + 0.211889i \(0.0679614\pi\)
−0.977294 + 0.211889i \(0.932039\pi\)
\(168\) 4.34017i 0.334852i
\(169\) 7.52359 0.578738
\(170\) 0.496928 + 2.00000i 0.0381127 + 0.153393i
\(171\) 2.34017 0.178958
\(172\) 0.738205i 0.0562876i
\(173\) 15.6742i 1.19169i 0.803100 + 0.595844i \(0.203182\pi\)
−0.803100 + 0.595844i \(0.796818\pi\)
\(174\) 10.4969 0.795770
\(175\) −10.1568 19.1773i −0.767779 1.44967i
\(176\) −1.07838 −0.0812858
\(177\) 8.83710i 0.664237i
\(178\) 4.68035i 0.350807i
\(179\) −15.3607 −1.14811 −0.574056 0.818816i \(-0.694631\pi\)
−0.574056 + 0.818816i \(0.694631\pi\)
\(180\) −0.539189 2.17009i −0.0401888 0.161749i
\(181\) 21.6163 1.60673 0.803365 0.595487i \(-0.203041\pi\)
0.803365 + 0.595487i \(0.203041\pi\)
\(182\) 10.1568i 0.752869i
\(183\) 11.5753i 0.855671i
\(184\) −1.00000 −0.0737210
\(185\) 5.60197 1.39189i 0.411865 0.102334i
\(186\) 4.00000 0.293294
\(187\) 0.993857i 0.0726780i
\(188\) 6.83710i 0.498647i
\(189\) 4.34017 0.315701
\(190\) −5.07838 + 1.26180i −0.368424 + 0.0915402i
\(191\) 4.36683 0.315973 0.157987 0.987441i \(-0.449500\pi\)
0.157987 + 0.987441i \(0.449500\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 8.68035i 0.624825i 0.949947 + 0.312412i \(0.101137\pi\)
−0.949947 + 0.312412i \(0.898863\pi\)
\(194\) −9.02052 −0.647636
\(195\) 1.26180 + 5.07838i 0.0903590 + 0.363670i
\(196\) 11.8371 0.845507
\(197\) 22.6803i 1.61591i −0.589246 0.807954i \(-0.700575\pi\)
0.589246 0.807954i \(-0.299425\pi\)
\(198\) 1.07838i 0.0766370i
\(199\) 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
\(201\) −2.58145 −0.182081
\(202\) 1.50307i 0.105756i
\(203\) 45.5585i 3.19758i
\(204\) 0.921622 0.0645265
\(205\) −0.0845208 0.340173i −0.00590319 0.0237587i
\(206\) −2.49693 −0.173969
\(207\) 1.00000i 0.0695048i
\(208\) 2.34017i 0.162262i
\(209\) 2.52359 0.174560
\(210\) −9.41855 + 2.34017i −0.649942 + 0.161487i
\(211\) −22.0410 −1.51737 −0.758684 0.651459i \(-0.774157\pi\)
−0.758684 + 0.651459i \(0.774157\pi\)
\(212\) 0.340173i 0.0233632i
\(213\) 15.1773i 1.03993i
\(214\) −9.57531 −0.654554
\(215\) −1.60197 + 0.398032i −0.109253 + 0.0271455i
\(216\) −1.00000 −0.0680414
\(217\) 17.3607i 1.17852i
\(218\) 9.78539i 0.662750i
\(219\) −4.68035 −0.316268
\(220\) −0.581449 2.34017i −0.0392013 0.157774i
\(221\) −2.15676 −0.145079
\(222\) 2.58145i 0.173256i
\(223\) 21.1773i 1.41814i −0.705141 0.709068i \(-0.749116\pi\)
0.705141 0.709068i \(-0.250884\pi\)
\(224\) −4.34017 −0.289990
\(225\) 4.41855 2.34017i 0.294570 0.156012i
\(226\) 8.92162 0.593457
\(227\) 11.7854i 0.782224i −0.920343 0.391112i \(-0.872091\pi\)
0.920343 0.391112i \(-0.127909\pi\)
\(228\) 2.34017i 0.154982i
\(229\) −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
\(231\) 4.68035 0.307944
\(232\) 10.4969i 0.689157i
\(233\) 18.3135i 1.19976i −0.800091 0.599879i \(-0.795215\pi\)
0.800091 0.599879i \(-0.204785\pi\)
\(234\) 2.34017 0.152982
\(235\) 14.8371 3.68649i 0.967866 0.240480i
\(236\) −8.83710 −0.575246
\(237\) 11.9155i 0.773994i
\(238\) 4.00000i 0.259281i
\(239\) 5.33403 0.345030 0.172515 0.985007i \(-0.444811\pi\)
0.172515 + 0.985007i \(0.444811\pi\)
\(240\) 2.17009 0.539189i 0.140078 0.0348045i
\(241\) 26.1978 1.68755 0.843774 0.536698i \(-0.180329\pi\)
0.843774 + 0.536698i \(0.180329\pi\)
\(242\) 9.83710i 0.632353i
\(243\) 1.00000i 0.0641500i
\(244\) 11.5753 0.741033
\(245\) 6.38243 + 25.6875i 0.407759 + 1.64112i
\(246\) −0.156755 −0.00999437
\(247\) 5.47641i 0.348456i
\(248\) 4.00000i 0.254000i
\(249\) 11.4186 0.723621
\(250\) −8.32684 + 7.46081i −0.526636 + 0.471863i
\(251\) 27.4329 1.73155 0.865775 0.500433i \(-0.166826\pi\)
0.865775 + 0.500433i \(0.166826\pi\)
\(252\) 4.34017i 0.273405i
\(253\) 1.07838i 0.0677970i
\(254\) −17.1773 −1.07780
\(255\) 0.496928 + 2.00000i 0.0311189 + 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 10.3135i 0.643339i −0.946852 0.321670i \(-0.895756\pi\)
0.946852 0.321670i \(-0.104244\pi\)
\(258\) 0.738205i 0.0459586i
\(259\) −11.2039 −0.696179
\(260\) −5.07838 + 1.26180i −0.314948 + 0.0782532i
\(261\) 10.4969 0.649744
\(262\) 6.68035i 0.412713i
\(263\) 20.9939i 1.29454i 0.762262 + 0.647268i \(0.224089\pi\)
−0.762262 + 0.647268i \(0.775911\pi\)
\(264\) −1.07838 −0.0663696
\(265\) 0.738205 0.183417i 0.0453476 0.0112672i
\(266\) 10.1568 0.622751
\(267\) 4.68035i 0.286433i
\(268\) 2.58145i 0.157687i
\(269\) −25.3874 −1.54789 −0.773947 0.633250i \(-0.781720\pi\)
−0.773947 + 0.633250i \(0.781720\pi\)
\(270\) −0.539189 2.17009i −0.0328140 0.132067i
\(271\) −32.5646 −1.97816 −0.989080 0.147379i \(-0.952916\pi\)
−0.989080 + 0.147379i \(0.952916\pi\)
\(272\) 0.921622i 0.0558816i
\(273\) 10.1568i 0.614715i
\(274\) −22.2823 −1.34612
\(275\) 4.76487 2.52359i 0.287332 0.152178i
\(276\) −1.00000 −0.0601929
\(277\) 15.7009i 0.943374i 0.881766 + 0.471687i \(0.156355\pi\)
−0.881766 + 0.471687i \(0.843645\pi\)
\(278\) 10.5236i 0.631163i
\(279\) 4.00000 0.239474
\(280\) −2.34017 9.41855i −0.139852 0.562866i
\(281\) −9.36069 −0.558412 −0.279206 0.960231i \(-0.590071\pi\)
−0.279206 + 0.960231i \(0.590071\pi\)
\(282\) 6.83710i 0.407143i
\(283\) 17.4186i 1.03543i 0.855555 + 0.517713i \(0.173216\pi\)
−0.855555 + 0.517713i \(0.826784\pi\)
\(284\) −15.1773 −0.900606
\(285\) −5.07838 + 1.26180i −0.300817 + 0.0747423i
\(286\) 2.52359 0.149223
\(287\) 0.680346i 0.0401596i
\(288\) 1.00000i 0.0589256i
\(289\) 16.1506 0.950036
\(290\) −22.7792 + 5.65983i −1.33764 + 0.332356i
\(291\) −9.02052 −0.528792
\(292\) 4.68035i 0.273897i
\(293\) 16.3402i 0.954603i 0.878740 + 0.477302i \(0.158385\pi\)
−0.878740 + 0.477302i \(0.841615\pi\)
\(294\) 11.8371 0.690354
\(295\) −4.76487 19.1773i −0.277421 1.11654i
\(296\) 2.58145 0.150044
\(297\) 1.07838i 0.0625738i
\(298\) 6.92162i 0.400959i
\(299\) 2.34017 0.135336
\(300\) 2.34017 + 4.41855i 0.135110 + 0.255105i
\(301\) 3.20394 0.184672
\(302\) 6.15676i 0.354281i
\(303\) 1.50307i 0.0863492i
\(304\) −2.34017 −0.134218
\(305\) 6.24128 + 25.1194i 0.357374 + 1.43833i
\(306\) 0.921622 0.0526856
\(307\) 3.20394i 0.182858i −0.995812 0.0914292i \(-0.970856\pi\)
0.995812 0.0914292i \(-0.0291435\pi\)
\(308\) 4.68035i 0.266687i
\(309\) −2.49693 −0.142045
\(310\) −8.68035 + 2.15676i −0.493011 + 0.122495i
\(311\) 12.6537 0.717525 0.358762 0.933429i \(-0.383199\pi\)
0.358762 + 0.933429i \(0.383199\pi\)
\(312\) 2.34017i 0.132486i
\(313\) 33.2183i 1.87761i −0.344449 0.938805i \(-0.611934\pi\)
0.344449 0.938805i \(-0.388066\pi\)
\(314\) −2.89496 −0.163372
\(315\) −9.41855 + 2.34017i −0.530675 + 0.131854i
\(316\) −11.9155 −0.670298
\(317\) 6.99386i 0.392814i −0.980522 0.196407i \(-0.937073\pi\)
0.980522 0.196407i \(-0.0629274\pi\)
\(318\) 0.340173i 0.0190760i
\(319\) 11.3197 0.633779
\(320\) 0.539189 + 2.17009i 0.0301416 + 0.121312i
\(321\) −9.57531 −0.534441
\(322\) 4.34017i 0.241868i
\(323\) 2.15676i 0.120005i
\(324\) −1.00000 −0.0555556
\(325\) −5.47641 10.3402i −0.303777 0.573570i
\(326\) 6.52359 0.361308
\(327\) 9.78539i 0.541133i
\(328\) 0.156755i 0.00865537i
\(329\) −29.6742 −1.63599
\(330\) −0.581449 2.34017i −0.0320077 0.128822i
\(331\) −29.7275 −1.63397 −0.816986 0.576657i \(-0.804357\pi\)
−0.816986 + 0.576657i \(0.804357\pi\)
\(332\) 11.4186i 0.626674i
\(333\) 2.58145i 0.141463i
\(334\) −5.47641 −0.299656
\(335\) 5.60197 1.39189i 0.306068 0.0760470i
\(336\) −4.34017 −0.236776
\(337\) 28.3402i 1.54379i 0.635751 + 0.771894i \(0.280690\pi\)
−0.635751 + 0.771894i \(0.719310\pi\)
\(338\) 7.52359i 0.409229i
\(339\) 8.92162 0.484556
\(340\) −2.00000 + 0.496928i −0.108465 + 0.0269497i
\(341\) 4.31351 0.233590
\(342\) 2.34017i 0.126542i
\(343\) 20.9939i 1.13356i
\(344\) −0.738205 −0.0398013
\(345\) −0.539189 2.17009i −0.0290290 0.116834i
\(346\) −15.6742 −0.842650
\(347\) 22.5236i 1.20913i −0.796556 0.604565i \(-0.793347\pi\)
0.796556 0.604565i \(-0.206653\pi\)
\(348\) 10.4969i 0.562694i
\(349\) −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
\(351\) 2.34017 0.124909
\(352\) 1.07838i 0.0574777i
\(353\) 26.3135i 1.40053i −0.713885 0.700263i \(-0.753066\pi\)
0.713885 0.700263i \(-0.246934\pi\)
\(354\) −8.83710 −0.469687
\(355\) −8.18342 32.9360i −0.434331 1.74806i
\(356\) −4.68035 −0.248058
\(357\) 4.00000i 0.211702i
\(358\) 15.3607i 0.811838i
\(359\) 0.796064 0.0420146 0.0210073 0.999779i \(-0.493313\pi\)
0.0210073 + 0.999779i \(0.493313\pi\)
\(360\) 2.17009 0.539189i 0.114374 0.0284177i
\(361\) −13.5236 −0.711768
\(362\) 21.6163i 1.13613i
\(363\) 9.83710i 0.516314i
\(364\) 10.1568 0.532359
\(365\) 10.1568 2.52359i 0.531629 0.132091i
\(366\) 11.5753 0.605051
\(367\) 13.7009i 0.715179i 0.933879 + 0.357590i \(0.116401\pi\)
−0.933879 + 0.357590i \(0.883599\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) −0.156755 −0.00816036
\(370\) 1.39189 + 5.60197i 0.0723608 + 0.291232i
\(371\) −1.47641 −0.0766514
\(372\) 4.00000i 0.207390i
\(373\) 4.25565i 0.220349i −0.993912 0.110175i \(-0.964859\pi\)
0.993912 0.110175i \(-0.0351410\pi\)
\(374\) 0.993857 0.0513911
\(375\) −8.32684 + 7.46081i −0.429996 + 0.385275i
\(376\) 6.83710 0.352597
\(377\) 24.5646i 1.26514i
\(378\) 4.34017i 0.223234i
\(379\) 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
\(381\) −17.1773 −0.880018
\(382\) 4.36683i 0.223427i
\(383\) 20.8781i 1.06682i 0.845856 + 0.533412i \(0.179090\pi\)
−0.845856 + 0.533412i \(0.820910\pi\)
\(384\) 1.00000 0.0510310
\(385\) −10.1568 + 2.52359i −0.517636 + 0.128614i
\(386\) −8.68035 −0.441818
\(387\) 0.738205i 0.0375251i
\(388\) 9.02052i 0.457947i
\(389\) 16.9627 0.860041 0.430021 0.902819i \(-0.358506\pi\)
0.430021 + 0.902819i \(0.358506\pi\)
\(390\) −5.07838 + 1.26180i −0.257154 + 0.0638935i
\(391\) 0.921622 0.0466084
\(392\) 11.8371i 0.597864i
\(393\) 6.68035i 0.336979i
\(394\) 22.6803 1.14262
\(395\) −6.42469 25.8576i −0.323261 1.30104i
\(396\) −1.07838 −0.0541905
\(397\) 16.4969i 0.827957i −0.910287 0.413979i \(-0.864139\pi\)
0.910287 0.413979i \(-0.135861\pi\)
\(398\) 5.44521i 0.272944i
\(399\) 10.1568 0.508474
\(400\) −4.41855 + 2.34017i −0.220928 + 0.117009i
\(401\) −35.2039 −1.75800 −0.879000 0.476821i \(-0.841789\pi\)
−0.879000 + 0.476821i \(0.841789\pi\)
\(402\) 2.58145i 0.128751i
\(403\) 9.36069i 0.466289i
\(404\) −1.50307 −0.0747806
\(405\) −0.539189 2.17009i −0.0267925 0.107832i
\(406\) 45.5585 2.26103
\(407\) 2.78378i 0.137987i
\(408\) 0.921622i 0.0456271i
\(409\) −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
\(411\) −22.2823 −1.09911
\(412\) 2.49693i 0.123015i
\(413\) 38.3545i 1.88730i
\(414\) −1.00000 −0.0491473
\(415\) −24.7792 + 6.15676i −1.21637 + 0.302223i
\(416\) −2.34017 −0.114736
\(417\) 10.5236i 0.515342i
\(418\) 2.52359i 0.123433i
\(419\) 18.1256 0.885491 0.442746 0.896647i \(-0.354004\pi\)
0.442746 + 0.896647i \(0.354004\pi\)
\(420\) −2.34017 9.41855i −0.114189 0.459578i
\(421\) 2.58145 0.125812 0.0629061 0.998019i \(-0.479963\pi\)
0.0629061 + 0.998019i \(0.479963\pi\)
\(422\) 22.0410i 1.07294i
\(423\) 6.83710i 0.332431i
\(424\) 0.340173 0.0165203
\(425\) −2.15676 4.07223i −0.104618 0.197532i
\(426\) −15.1773 −0.735341
\(427\) 50.2388i 2.43123i
\(428\) 9.57531i 0.462840i
\(429\) 2.52359 0.121840
\(430\) −0.398032 1.60197i −0.0191948 0.0772538i
\(431\) −33.9877 −1.63713 −0.818565 0.574414i \(-0.805230\pi\)
−0.818565 + 0.574414i \(0.805230\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 8.28685i 0.398241i 0.979975 + 0.199120i \(0.0638084\pi\)
−0.979975 + 0.199120i \(0.936192\pi\)
\(434\) 17.3607 0.833340
\(435\) −22.7792 + 5.65983i −1.09218 + 0.271368i
\(436\) −9.78539 −0.468635
\(437\) 2.34017i 0.111946i
\(438\) 4.68035i 0.223636i
\(439\) 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
\(441\) 11.8371 0.563671
\(442\) 2.15676i 0.102586i
\(443\) 3.20394i 0.152224i 0.997099 + 0.0761118i \(0.0242506\pi\)
−0.997099 + 0.0761118i \(0.975749\pi\)
\(444\) 2.58145 0.122510
\(445\) −2.52359 10.1568i −0.119630 0.481476i
\(446\) 21.1773 1.00277
\(447\) 6.92162i 0.327381i
\(448\) 4.34017i 0.205054i
\(449\) −28.1568 −1.32880 −0.664400 0.747377i \(-0.731313\pi\)
−0.664400 + 0.747377i \(0.731313\pi\)
\(450\) 2.34017 + 4.41855i 0.110317 + 0.208292i
\(451\) −0.169042 −0.00795986
\(452\) 8.92162i 0.419638i
\(453\) 6.15676i 0.289270i
\(454\) 11.7854 0.553116
\(455\) 5.47641 + 22.0410i 0.256738 + 1.03330i
\(456\) −2.34017 −0.109589
\(457\) 23.1773i 1.08419i −0.840318 0.542094i \(-0.817632\pi\)
0.840318 0.542094i \(-0.182368\pi\)
\(458\) 1.78539i 0.0834256i
\(459\) 0.921622 0.0430176
\(460\) 2.17009 0.539189i 0.101181 0.0251398i
\(461\) −42.3279 −1.97141 −0.985703 0.168491i \(-0.946110\pi\)
−0.985703 + 0.168491i \(0.946110\pi\)
\(462\) 4.68035i 0.217749i
\(463\) 34.9048i 1.62216i 0.584933 + 0.811082i \(0.301121\pi\)
−0.584933 + 0.811082i \(0.698879\pi\)
\(464\) −10.4969 −0.487308
\(465\) −8.68035 + 2.15676i −0.402541 + 0.100017i
\(466\) 18.3135 0.848357
\(467\) 37.7731i 1.74793i −0.485988 0.873965i \(-0.661540\pi\)
0.485988 0.873965i \(-0.338460\pi\)
\(468\) 2.34017i 0.108175i
\(469\) −11.2039 −0.517350
\(470\) 3.68649 + 14.8371i 0.170045 + 0.684384i
\(471\) −2.89496 −0.133393
\(472\) 8.83710i 0.406761i
\(473\) 0.796064i 0.0366030i
\(474\) −11.9155 −0.547296
\(475\) 10.3402 5.47641i 0.474440 0.251275i
\(476\) 4.00000 0.183340
\(477\) 0.340173i 0.0155755i
\(478\) 5.33403i 0.243973i
\(479\) 28.1978 1.28839 0.644195 0.764861i \(-0.277193\pi\)
0.644195 + 0.764861i \(0.277193\pi\)
\(480\) 0.539189 + 2.17009i 0.0246105 + 0.0990504i
\(481\) −6.04104 −0.275448
\(482\) 26.1978i 1.19328i
\(483\) 4.34017i 0.197485i
\(484\) 9.83710 0.447141
\(485\) 19.5753 4.86376i 0.888869 0.220852i
\(486\) −1.00000 −0.0453609
\(487\) 38.2245i 1.73212i 0.499944 + 0.866058i \(0.333354\pi\)
−0.499944 + 0.866058i \(0.666646\pi\)
\(488\) 11.5753i 0.523989i
\(489\) 6.52359 0.295007
\(490\) −25.6875 + 6.38243i −1.16044 + 0.288329i
\(491\) 11.3074 0.510294 0.255147 0.966902i \(-0.417876\pi\)
0.255147 + 0.966902i \(0.417876\pi\)
\(492\) 0.156755i 0.00706708i
\(493\) 9.67420i 0.435704i
\(494\) 5.47641 0.246395
\(495\) −0.581449 2.34017i −0.0261342 0.105183i
\(496\) −4.00000 −0.179605
\(497\) 65.8720i 2.95476i
\(498\) 11.4186i 0.511677i
\(499\) 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
\(501\) −5.47641 −0.244668
\(502\) 27.4329i 1.22439i
\(503\) 20.6270i 0.919713i 0.887993 + 0.459857i \(0.152099\pi\)
−0.887993 + 0.459857i \(0.847901\pi\)
\(504\) −4.34017 −0.193327
\(505\) −0.810439 3.26180i −0.0360641 0.145148i
\(506\) −1.07838 −0.0479397
\(507\) 7.52359i 0.334134i
\(508\) 17.1773i 0.762118i
\(509\) 32.2245 1.42832 0.714162 0.699981i \(-0.246808\pi\)
0.714162 + 0.699981i \(0.246808\pi\)
\(510\) −2.00000 + 0.496928i −0.0885615 + 0.0220044i
\(511\) −20.3135 −0.898617
\(512\) 1.00000i 0.0441942i
\(513\) 2.34017i 0.103321i
\(514\) 10.3135 0.454909
\(515\) 5.41855 1.34632i 0.238770 0.0593258i
\(516\) −0.738205 −0.0324977
\(517\) 7.37298i 0.324263i
\(518\) 11.2039i 0.492273i
\(519\) −15.6742 −0.688021
\(520\) −1.26180 5.07838i −0.0553334 0.222702i
\(521\) −3.51745 −0.154102 −0.0770511 0.997027i \(-0.524550\pi\)
−0.0770511 + 0.997027i \(0.524550\pi\)
\(522\) 10.4969i 0.459438i
\(523\) 35.9421i 1.57164i 0.618455 + 0.785820i \(0.287759\pi\)
−0.618455 + 0.785820i \(0.712241\pi\)
\(524\) 6.68035 0.291832
\(525\) 19.1773 10.1568i 0.836965 0.443277i
\(526\) −20.9939 −0.915376
\(527\) 3.68649i 0.160586i
\(528\) 1.07838i 0.0469304i
\(529\) −1.00000 −0.0434783
\(530\) 0.183417 + 0.738205i 0.00796715 + 0.0320656i
\(531\) −8.83710 −0.383498
\(532\) 10.1568i 0.440351i
\(533\) 0.366835i 0.0158894i
\(534\) −4.68035 −0.202538
\(535\) 20.7792 5.16290i 0.898365 0.223212i
\(536\) 2.58145 0.111502
\(537\) 15.3607i 0.662863i
\(538\) 25.3874i 1.09453i
\(539\) 12.7649 0.549822
\(540\) 2.17009 0.539189i 0.0933857 0.0232030i
\(541\) 31.7275 1.36407 0.682036 0.731318i \(-0.261095\pi\)
0.682036 + 0.731318i \(0.261095\pi\)
\(542\) 32.5646i 1.39877i
\(543\) 21.6163i 0.927646i
\(544\) −0.921622 −0.0395142
\(545\) −5.27617 21.2351i −0.226006 0.909613i
\(546\) 10.1568 0.434669
\(547\) 9.84324i 0.420867i −0.977608 0.210433i \(-0.932512\pi\)
0.977608 0.210433i \(-0.0674875\pi\)
\(548\) 22.2823i 0.951853i
\(549\) 11.5753 0.494022
\(550\) 2.52359 + 4.76487i 0.107606 + 0.203175i
\(551\) 24.5646 1.04649
\(552\) 1.00000i 0.0425628i
\(553\) 51.7152i 2.19916i
\(554\) −15.7009 −0.667066
\(555\) 1.39189 + 5.60197i 0.0590824 + 0.237790i
\(556\) −10.5236 −0.446300
\(557\) 26.3279i 1.11555i 0.829993 + 0.557774i \(0.188344\pi\)
−0.829993 + 0.557774i \(0.811656\pi\)
\(558\) 4.00000i 0.169334i
\(559\) 1.72753 0.0730666
\(560\) 9.41855 2.34017i 0.398006 0.0988904i
\(561\) 0.993857 0.0419607
\(562\) 9.36069i 0.394857i
\(563\) 30.2557i 1.27512i 0.770399 + 0.637562i \(0.220057\pi\)
−0.770399 + 0.637562i \(0.779943\pi\)
\(564\) 6.83710 0.287894
\(565\) −19.3607 + 4.81044i −0.814510 + 0.202377i
\(566\) −17.4186 −0.732156
\(567\) 4.34017i 0.182270i
\(568\) 15.1773i 0.636824i
\(569\) −33.8720 −1.41999 −0.709994 0.704208i \(-0.751302\pi\)
−0.709994 + 0.704208i \(0.751302\pi\)
\(570\) −1.26180 5.07838i −0.0528508 0.212710i
\(571\) 35.1650 1.47161 0.735804 0.677194i \(-0.236804\pi\)
0.735804 + 0.677194i \(0.236804\pi\)
\(572\) 2.52359i 0.105517i
\(573\) 4.36683i 0.182427i
\(574\) −0.680346 −0.0283971
\(575\) 2.34017 + 4.41855i 0.0975920 + 0.184266i
\(576\) 1.00000 0.0416667
\(577\) 4.00000i 0.166522i −0.996528 0.0832611i \(-0.973466\pi\)
0.996528 0.0832611i \(-0.0265335\pi\)
\(578\) 16.1506i 0.671777i
\(579\) −8.68035 −0.360743
\(580\) −5.65983 22.7792i −0.235012 0.945857i
\(581\) 49.5585 2.05603
\(582\) 9.02052i 0.373913i
\(583\) 0.366835i 0.0151928i
\(584\) 4.68035 0.193674
\(585\) −5.07838 + 1.26180i −0.209965 + 0.0521688i
\(586\) −16.3402 −0.675006
\(587\) 9.30737i 0.384156i 0.981380 + 0.192078i \(0.0615227\pi\)
−0.981380 + 0.192078i \(0.938477\pi\)
\(588\) 11.8371i 0.488154i
\(589\) 9.36069 0.385701
\(590\) 19.1773 4.76487i 0.789516 0.196166i
\(591\) 22.6803 0.932945
\(592\) 2.58145i 0.106097i
\(593\) 33.0349i 1.35658i −0.734794 0.678290i \(-0.762721\pi\)
0.734794 0.678290i \(-0.237279\pi\)
\(594\) −1.07838 −0.0442464
\(595\) 2.15676 + 8.68035i 0.0884184 + 0.355859i
\(596\) 6.92162 0.283521
\(597\) 5.44521i 0.222858i
\(598\) 2.34017i 0.0956968i
\(599\) −13.6475 −0.557623 −0.278812 0.960346i \(-0.589941\pi\)
−0.278812 + 0.960346i \(0.589941\pi\)
\(600\) −4.41855 + 2.34017i −0.180387 + 0.0955372i
\(601\) 1.68649 0.0687933 0.0343967 0.999408i \(-0.489049\pi\)
0.0343967 + 0.999408i \(0.489049\pi\)
\(602\) 3.20394i 0.130583i
\(603\) 2.58145i 0.105125i
\(604\) −6.15676 −0.250515
\(605\) 5.30406 + 21.3474i 0.215641 + 0.867894i
\(606\) −1.50307 −0.0610581
\(607\) 47.2183i 1.91653i −0.285878 0.958266i \(-0.592285\pi\)
0.285878 0.958266i \(-0.407715\pi\)
\(608\) 2.34017i 0.0949065i
\(609\) 45.5585 1.84612
\(610\) −25.1194 + 6.24128i −1.01706 + 0.252702i
\(611\) −16.0000 −0.647291
\(612\) 0.921622i 0.0372544i
\(613\) 7.45959i 0.301290i 0.988588 + 0.150645i \(0.0481350\pi\)
−0.988588 + 0.150645i \(0.951865\pi\)
\(614\) 3.20394 0.129300
\(615\) 0.340173 0.0845208i 0.0137171 0.00340821i
\(616\) −4.68035 −0.188577
\(617\) 15.8120i 0.636569i 0.947995 + 0.318285i \(0.103107\pi\)
−0.947995 + 0.318285i \(0.896893\pi\)
\(618\) 2.49693i 0.100441i
\(619\) 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
\(621\) −1.00000 −0.0401286
\(622\) 12.6537i 0.507367i
\(623\) 20.3135i 0.813844i
\(624\) −2.34017 −0.0936819
\(625\) 14.0472 20.6803i 0.561887 0.827214i
\(626\) 33.2183 1.32767
\(627\) 2.52359i 0.100782i
\(628\) 2.89496i 0.115521i
\(629\) −2.37912 −0.0948618
\(630\) −2.34017 9.41855i −0.0932347 0.375244i
\(631\) −14.4391 −0.574810 −0.287405 0.957809i \(-0.592793\pi\)
−0.287405 + 0.957809i \(0.592793\pi\)
\(632\) 11.9155i 0.473972i
\(633\) 22.0410i 0.876053i
\(634\) 6.99386 0.277762
\(635\) 37.2762 9.26180i 1.47926 0.367543i
\(636\) 0.340173 0.0134887
\(637\) 27.7009i 1.09755i
\(638\) 11.3197i 0.448149i
\(639\) −15.1773 −0.600404
\(640\) −2.17009 + 0.539189i −0.0857802 + 0.0213133i
\(641\) −5.78992 −0.228688 −0.114344 0.993441i \(-0.536477\pi\)
−0.114344 + 0.993441i \(0.536477\pi\)
\(642\) 9.57531i 0.377907i
\(643\) 23.4063i 0.923053i −0.887126 0.461526i \(-0.847302\pi\)
0.887126 0.461526i \(-0.152698\pi\)
\(644\) −4.34017 −0.171027
\(645\) −0.398032 1.60197i −0.0156725 0.0630774i
\(646\) 2.15676 0.0848564
\(647\) 25.9877i 1.02168i 0.859675 + 0.510841i \(0.170666\pi\)
−0.859675 + 0.510841i \(0.829334\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −9.52973 −0.374075
\(650\) 10.3402 5.47641i 0.405575 0.214802i
\(651\) 17.3607 0.680419
\(652\) 6.52359i 0.255484i
\(653\) 0.325797i 0.0127494i 0.999980 + 0.00637471i \(0.00202915\pi\)
−0.999980 + 0.00637471i \(0.997971\pi\)
\(654\) −9.78539 −0.382639
\(655\) 3.60197 + 14.4969i 0.140741 + 0.566442i
\(656\) 0.156755 0.00612027
\(657\) 4.68035i 0.182598i
\(658\) 29.6742i 1.15682i
\(659\) 3.11942 0.121515 0.0607576 0.998153i \(-0.480648\pi\)
0.0607576 + 0.998153i \(0.480648\pi\)
\(660\) 2.34017 0.581449i 0.0910911 0.0226329i
\(661\) 24.1399 0.938935 0.469467 0.882950i \(-0.344446\pi\)
0.469467 + 0.882950i \(0.344446\pi\)
\(662\) 29.7275i 1.15539i
\(663\) 2.15676i 0.0837614i
\(664\) −11.4186 −0.443126
\(665\) −22.0410 + 5.47641i −0.854715 + 0.212366i
\(666\) 2.58145 0.100029
\(667\) 10.4969i 0.406443i
\(668\) 5.47641i 0.211889i
\(669\) 21.1773 0.818761
\(670\) 1.39189 + 5.60197i 0.0537734 + 0.216423i
\(671\) 12.4826 0.481884
\(672\) 4.34017i 0.167426i
\(673\) 45.6742i 1.76061i 0.474407 + 0.880306i \(0.342662\pi\)
−0.474407 + 0.880306i \(0.657338\pi\)
\(674\) −28.3402 −1.09162
\(675\) 2.34017 + 4.41855i 0.0900733 + 0.170070i
\(676\) −7.52359 −0.289369
\(677\) 9.38735i 0.360785i 0.983595 + 0.180393i \(0.0577368\pi\)
−0.983595 + 0.180393i \(0.942263\pi\)
\(678\) 8.92162i 0.342633i
\(679\) −39.1506 −1.50246
\(680\) −0.496928 2.00000i −0.0190563 0.0766965i
\(681\) 11.7854 0.451617
\(682\) 4.31351i 0.165173i
\(683\) 20.9939i 0.803308i −0.915792 0.401654i \(-0.868436\pi\)
0.915792 0.401654i \(-0.131564\pi\)
\(684\) −2.34017 −0.0894788
\(685\) 48.3545 12.0144i 1.84753 0.459046i
\(686\) 20.9939 0.801549
\(687\) 1.78539i 0.0681167i
\(688\) 0.738205i 0.0281438i
\(689\) −0.796064 −0.0303276
\(690\) 2.17009 0.539189i 0.0826138 0.0205266i
\(691\) −44.1445 −1.67933 −0.839667 0.543101i \(-0.817250\pi\)
−0.839667 + 0.543101i \(0.817250\pi\)
\(692\) 15.6742i 0.595844i
\(693\) 4.68035i 0.177792i
\(694\) 22.5236 0.854984
\(695\) −5.67420 22.8371i −0.215235 0.866261i
\(696\) −10.4969 −0.397885
\(697\) 0.144469i 0.00547217i
\(698\) 15.6742i 0.593277i
\(699\) 18.3135 0.692681
\(700\) 10.1568 + 19.1773i 0.383889 + 0.724833i
\(701\) −27.7998 −1.04998 −0.524991 0.851108i \(-0.675931\pi\)
−0.524991 + 0.851108i \(0.675931\pi\)
\(702\) 2.34017i 0.0883241i
\(703\) 6.04104i 0.227842i
\(704\) 1.07838 0.0406429
\(705\) 3.68649 + 14.8371i 0.138841 + 0.558798i
\(706\) 26.3135 0.990322
\(707\) 6.52359i 0.245345i
\(708\) 8.83710i 0.332119i
\(709\) −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
\(711\) −11.9155 −0.446865
\(712\) 4.68035i 0.175403i
\(713\) 4.00000i 0.149801i
\(714\) 4.00000 0.149696
\(715\) −5.47641 + 1.36069i −0.204806 + 0.0508870i
\(716\) 15.3607 0.574056
\(717\) 5.33403i 0.199203i
\(718\) 0.796064i 0.0297088i
\(719\) −15.9733 −0.595705 −0.297852 0.954612i \(-0.596270\pi\)
−0.297852 + 0.954612i \(0.596270\pi\)
\(720\) 0.539189 + 2.17009i 0.0200944 + 0.0808743i
\(721\) −10.8371 −0.403595
\(722\) 13.5236i 0.503296i
\(723\) 26.1978i 0.974306i
\(724\) −21.6163 −0.803365
\(725\) 46.3812 24.5646i 1.72255 0.912307i
\(726\) 9.83710 0.365089
\(727\) 0.340173i 0.0126163i −0.999980 0.00630816i \(-0.997992\pi\)
0.999980 0.00630816i \(-0.00200796\pi\)
\(728\) 10.1568i 0.376434i
\(729\) −1.00000 −0.0370370
\(730\) 2.52359 + 10.1568i 0.0934023 + 0.375918i
\(731\) 0.680346 0.0251635
\(732\) 11.5753i 0.427836i
\(733\) 19.2618i 0.711451i 0.934591 + 0.355725i \(0.115766\pi\)
−0.934591 + 0.355725i \(0.884234\pi\)
\(734\) −13.7009 −0.505708
\(735\) −25.6875 + 6.38243i −0.947499 + 0.235420i
\(736\) 1.00000 0.0368605
\(737\) 2.78378i 0.102542i
\(738\) 0.156755i 0.00577025i
\(739\) −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
\(741\) 5.47641 0.201181
\(742\) 1.47641i 0.0542007i
\(743\) 36.8781i 1.35293i 0.736476 + 0.676464i \(0.236489\pi\)
−0.736476 + 0.676464i \(0.763511\pi\)
\(744\) −4.00000 −0.146647
\(745\) 3.73206 + 15.0205i 0.136732 + 0.550309i
\(746\) 4.25565 0.155810
\(747\) 11.4186i 0.417783i
\(748\) 0.993857i 0.0363390i
\(749\) −41.5585 −1.51851
\(750\) −7.46081 8.32684i −0.272430 0.304053i
\(751\) 18.1256 0.661411 0.330706 0.943734i \(-0.392713\pi\)
0.330706 + 0.943734i \(0.392713\pi\)
\(752\) 6.83710i 0.249323i
\(753\) 27.4329i 0.999711i
\(754\) 24.5646 0.894591
\(755\) −3.31965 13.3607i −0.120815 0.486245i
\(756\) −4.34017 −0.157851
\(757\) 17.4186i 0.633088i −0.948578 0.316544i \(-0.897478\pi\)
0.948578 0.316544i \(-0.102522\pi\)
\(758\) 30.6537i 1.11339i
\(759\) −1.07838 −0.0391426
\(760\) 5.07838 1.26180i 0.184212 0.0457701i
\(761\) −23.4140 −0.848757 −0.424379 0.905485i \(-0.639507\pi\)
−0.424379 + 0.905485i \(0.639507\pi\)
\(762\) 17.1773i 0.622267i
\(763\) 42.4703i 1.53753i
\(764\) −4.36683 −0.157987
\(765\) −2.00000 + 0.496928i −0.0723102 + 0.0179665i
\(766\) −20.8781 −0.754358
\(767\) 20.6803i 0.746724i
\(768\) 1.00000i 0.0360844i
\(769\) 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
\(771\) 10.3135 0.371432
\(772\) 8.68035i 0.312412i
\(773\) 15.3463i 0.551969i −0.961162 0.275984i \(-0.910996\pi\)
0.961162 0.275984i \(-0.0890038\pi\)
\(774\) −0.738205 −0.0265342
\(775\) 17.6742 9.36069i 0.634876 0.336246i
\(776\) 9.02052 0.323818
\(777\) 11.2039i 0.401939i
\(778\) 16.9627i 0.608141i
\(779\) −0.366835 −0.0131432
\(780\) −1.26180 5.07838i −0.0451795 0.181835i
\(781\) −16.3668 −0.585651
\(782\) 0.921622i 0.0329571i
\(783\) 10.4969i 0.375130i
\(784\) −11.8371 −0.422754
\(785\) 6.28231 1.56093i 0.224225 0.0557120i
\(786\) 6.68035 0.238280
\(787\) 22.8950i 0.816117i −0.912956 0.408059i \(-0.866206\pi\)
0.912956 0.408059i \(-0.133794\pi\)
\(788\) 22.6803i