Properties

Label 804.2.e.a.535.8
Level 804
Weight 2
Character 804.535
Analytic conductor 6.420
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(34\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 535.8
Character \(\chi\) = 804.535
Dual form 804.2.e.a.535.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.956986 + 1.04124i) q^{2} -1.00000 q^{3} +(-0.168355 - 1.99290i) q^{4} -1.36325i q^{5} +(0.956986 - 1.04124i) q^{6} -1.56640 q^{7} +(2.23620 + 1.73188i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.956986 + 1.04124i) q^{2} -1.00000 q^{3} +(-0.168355 - 1.99290i) q^{4} -1.36325i q^{5} +(0.956986 - 1.04124i) q^{6} -1.56640 q^{7} +(2.23620 + 1.73188i) q^{8} +1.00000 q^{9} +(1.41947 + 1.30461i) q^{10} -0.528628 q^{11} +(0.168355 + 1.99290i) q^{12} +2.52074i q^{13} +(1.49903 - 1.63100i) q^{14} +1.36325i q^{15} +(-3.94331 + 0.671030i) q^{16} +5.97533 q^{17} +(-0.956986 + 1.04124i) q^{18} -2.51124i q^{19} +(-2.71682 + 0.229510i) q^{20} +1.56640 q^{21} +(0.505890 - 0.550428i) q^{22} -2.87303i q^{23} +(-2.23620 - 1.73188i) q^{24} +3.14155 q^{25} +(-2.62470 - 2.41232i) q^{26} -1.00000 q^{27} +(0.263712 + 3.12169i) q^{28} -7.65326 q^{29} +(-1.41947 - 1.30461i) q^{30} -8.15854 q^{31} +(3.07499 - 4.74810i) q^{32} +0.528628 q^{33} +(-5.71831 + 6.22174i) q^{34} +2.13540i q^{35} +(-0.168355 - 1.99290i) q^{36} -7.80230 q^{37} +(2.61480 + 2.40322i) q^{38} -2.52074i q^{39} +(2.36098 - 3.04849i) q^{40} -11.2829i q^{41} +(-1.49903 + 1.63100i) q^{42} -3.82695 q^{43} +(0.0889972 + 1.05350i) q^{44} -1.36325i q^{45} +(2.99151 + 2.74945i) q^{46} -3.73630i q^{47} +(3.94331 - 0.671030i) q^{48} -4.54638 q^{49} +(-3.00642 + 3.27111i) q^{50} -5.97533 q^{51} +(5.02360 - 0.424380i) q^{52} -11.2351i q^{53} +(0.956986 - 1.04124i) q^{54} +0.720652i q^{55} +(-3.50279 - 2.71282i) q^{56} +2.51124i q^{57} +(7.32406 - 7.96886i) q^{58} -8.44668i q^{59} +(2.71682 - 0.229510i) q^{60} +2.04476i q^{61} +(7.80761 - 8.49498i) q^{62} -1.56640 q^{63} +(2.00117 + 7.74566i) q^{64} +3.43640 q^{65} +(-0.505890 + 0.550428i) q^{66} +(7.97595 + 1.83962i) q^{67} +(-1.00598 - 11.9082i) q^{68} +2.87303i q^{69} +(-2.22346 - 2.04354i) q^{70} +4.62331i q^{71} +(2.23620 + 1.73188i) q^{72} -12.1580 q^{73} +(7.46669 - 8.12405i) q^{74} -3.14155 q^{75} +(-5.00465 + 0.422780i) q^{76} +0.828045 q^{77} +(2.62470 + 2.41232i) q^{78} +2.66595 q^{79} +(0.914781 + 5.37572i) q^{80} +1.00000 q^{81} +(11.7481 + 10.7975i) q^{82} +11.3473i q^{83} +(-0.263712 - 3.12169i) q^{84} -8.14586i q^{85} +(3.66234 - 3.98477i) q^{86} +7.65326 q^{87} +(-1.18212 - 0.915522i) q^{88} +2.96297 q^{89} +(1.41947 + 1.30461i) q^{90} -3.94850i q^{91} +(-5.72567 + 0.483690i) q^{92} +8.15854 q^{93} +(3.89038 + 3.57559i) q^{94} -3.42344 q^{95} +(-3.07499 + 4.74810i) q^{96} -13.7074i q^{97} +(4.35083 - 4.73387i) q^{98} -0.528628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{3} + 2q^{4} - 4q^{7} + 6q^{8} + 34q^{9} + O(q^{10}) \) \( 34q - 34q^{3} + 2q^{4} - 4q^{7} + 6q^{8} + 34q^{9} - 6q^{10} - 2q^{12} - 4q^{14} + 2q^{16} + 12q^{20} + 4q^{21} - 8q^{22} - 6q^{24} - 34q^{25} + 10q^{26} - 34q^{27} + 8q^{28} - 16q^{29} + 6q^{30} + 4q^{31} + 2q^{36} + 12q^{37} - 26q^{38} - 18q^{40} + 4q^{42} + 4q^{43} - 26q^{44} + 4q^{46} - 2q^{48} + 46q^{49} + 18q^{50} - 32q^{52} + 14q^{56} - 4q^{58} - 12q^{60} - 2q^{62} - 4q^{63} + 26q^{64} + 8q^{66} + 18q^{67} - 34q^{68} - 56q^{70} + 6q^{72} + 12q^{73} - 22q^{74} + 34q^{75} - 32q^{76} - 8q^{77} - 10q^{78} + 12q^{79} + 2q^{80} + 34q^{81} + 26q^{82} - 8q^{84} + 6q^{86} + 16q^{87} - 28q^{88} - 6q^{90} - 46q^{92} - 4q^{93} - 32q^{94} + 40q^{95} + 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.956986 + 1.04124i −0.676691 + 0.736267i
\(3\) −1.00000 −0.577350
\(4\) −0.168355 1.99290i −0.0841775 0.996451i
\(5\) 1.36325i 0.609663i −0.952406 0.304832i \(-0.901400\pi\)
0.952406 0.304832i \(-0.0986002\pi\)
\(6\) 0.956986 1.04124i 0.390688 0.425084i
\(7\) −1.56640 −0.592044 −0.296022 0.955181i \(-0.595660\pi\)
−0.296022 + 0.955181i \(0.595660\pi\)
\(8\) 2.23620 + 1.73188i 0.790616 + 0.612313i
\(9\) 1.00000 0.333333
\(10\) 1.41947 + 1.30461i 0.448875 + 0.412554i
\(11\) −0.528628 −0.159387 −0.0796937 0.996819i \(-0.525394\pi\)
−0.0796937 + 0.996819i \(0.525394\pi\)
\(12\) 0.168355 + 1.99290i 0.0485999 + 0.575301i
\(13\) 2.52074i 0.699129i 0.936912 + 0.349564i \(0.113670\pi\)
−0.936912 + 0.349564i \(0.886330\pi\)
\(14\) 1.49903 1.63100i 0.400631 0.435903i
\(15\) 1.36325i 0.351989i
\(16\) −3.94331 + 0.671030i −0.985828 + 0.167757i
\(17\) 5.97533 1.44923 0.724615 0.689154i \(-0.242018\pi\)
0.724615 + 0.689154i \(0.242018\pi\)
\(18\) −0.956986 + 1.04124i −0.225564 + 0.245422i
\(19\) 2.51124i 0.576118i −0.957613 0.288059i \(-0.906990\pi\)
0.957613 0.288059i \(-0.0930099\pi\)
\(20\) −2.71682 + 0.229510i −0.607499 + 0.0513199i
\(21\) 1.56640 0.341817
\(22\) 0.505890 0.550428i 0.107856 0.117352i
\(23\) 2.87303i 0.599069i −0.954085 0.299534i \(-0.903169\pi\)
0.954085 0.299534i \(-0.0968314\pi\)
\(24\) −2.23620 1.73188i −0.456462 0.353519i
\(25\) 3.14155 0.628311
\(26\) −2.62470 2.41232i −0.514745 0.473094i
\(27\) −1.00000 −0.192450
\(28\) 0.263712 + 3.12169i 0.0498368 + 0.589943i
\(29\) −7.65326 −1.42117 −0.710587 0.703609i \(-0.751570\pi\)
−0.710587 + 0.703609i \(0.751570\pi\)
\(30\) −1.41947 1.30461i −0.259158 0.238188i
\(31\) −8.15854 −1.46532 −0.732658 0.680597i \(-0.761721\pi\)
−0.732658 + 0.680597i \(0.761721\pi\)
\(32\) 3.07499 4.74810i 0.543587 0.839353i
\(33\) 0.528628 0.0920224
\(34\) −5.71831 + 6.22174i −0.980682 + 1.06702i
\(35\) 2.13540i 0.360948i
\(36\) −0.168355 1.99290i −0.0280592 0.332150i
\(37\) −7.80230 −1.28269 −0.641345 0.767253i \(-0.721623\pi\)
−0.641345 + 0.767253i \(0.721623\pi\)
\(38\) 2.61480 + 2.40322i 0.424177 + 0.389854i
\(39\) 2.52074i 0.403642i
\(40\) 2.36098 3.04849i 0.373304 0.482009i
\(41\) 11.2829i 1.76209i −0.473037 0.881043i \(-0.656842\pi\)
0.473037 0.881043i \(-0.343158\pi\)
\(42\) −1.49903 + 1.63100i −0.231305 + 0.251668i
\(43\) −3.82695 −0.583605 −0.291802 0.956479i \(-0.594255\pi\)
−0.291802 + 0.956479i \(0.594255\pi\)
\(44\) 0.0889972 + 1.05350i 0.0134168 + 0.158822i
\(45\) 1.36325i 0.203221i
\(46\) 2.99151 + 2.74945i 0.441075 + 0.405385i
\(47\) 3.73630i 0.544995i −0.962156 0.272498i \(-0.912150\pi\)
0.962156 0.272498i \(-0.0878497\pi\)
\(48\) 3.94331 0.671030i 0.569168 0.0968548i
\(49\) −4.54638 −0.649483
\(50\) −3.00642 + 3.27111i −0.425172 + 0.462604i
\(51\) −5.97533 −0.836713
\(52\) 5.02360 0.424380i 0.696647 0.0588509i
\(53\) 11.2351i 1.54326i −0.636075 0.771628i \(-0.719443\pi\)
0.636075 0.771628i \(-0.280557\pi\)
\(54\) 0.956986 1.04124i 0.130229 0.141695i
\(55\) 0.720652i 0.0971727i
\(56\) −3.50279 2.71282i −0.468080 0.362516i
\(57\) 2.51124i 0.332622i
\(58\) 7.32406 7.96886i 0.961696 1.04636i
\(59\) 8.44668i 1.09966i −0.835275 0.549832i \(-0.814692\pi\)
0.835275 0.549832i \(-0.185308\pi\)
\(60\) 2.71682 0.229510i 0.350740 0.0296296i
\(61\) 2.04476i 0.261805i 0.991395 + 0.130902i \(0.0417875\pi\)
−0.991395 + 0.130902i \(0.958213\pi\)
\(62\) 7.80761 8.49498i 0.991567 1.07886i
\(63\) −1.56640 −0.197348
\(64\) 2.00117 + 7.74566i 0.250147 + 0.968208i
\(65\) 3.43640 0.426233
\(66\) −0.505890 + 0.550428i −0.0622707 + 0.0677530i
\(67\) 7.97595 + 1.83962i 0.974418 + 0.224745i
\(68\) −1.00598 11.9082i −0.121993 1.44409i
\(69\) 2.87303i 0.345873i
\(70\) −2.22346 2.04354i −0.265754 0.244250i
\(71\) 4.62331i 0.548686i 0.961632 + 0.274343i \(0.0884604\pi\)
−0.961632 + 0.274343i \(0.911540\pi\)
\(72\) 2.23620 + 1.73188i 0.263539 + 0.204104i
\(73\) −12.1580 −1.42299 −0.711493 0.702694i \(-0.751981\pi\)
−0.711493 + 0.702694i \(0.751981\pi\)
\(74\) 7.46669 8.12405i 0.867985 0.944402i
\(75\) −3.14155 −0.362755
\(76\) −5.00465 + 0.422780i −0.574073 + 0.0484962i
\(77\) 0.828045 0.0943644
\(78\) 2.62470 + 2.41232i 0.297188 + 0.273141i
\(79\) 2.66595 0.299942 0.149971 0.988690i \(-0.452082\pi\)
0.149971 + 0.988690i \(0.452082\pi\)
\(80\) 0.914781 + 5.37572i 0.102276 + 0.601023i
\(81\) 1.00000 0.111111
\(82\) 11.7481 + 10.7975i 1.29737 + 1.19239i
\(83\) 11.3473i 1.24553i 0.782411 + 0.622763i \(0.213990\pi\)
−0.782411 + 0.622763i \(0.786010\pi\)
\(84\) −0.263712 3.12169i −0.0287733 0.340604i
\(85\) 8.14586i 0.883542i
\(86\) 3.66234 3.98477i 0.394920 0.429689i
\(87\) 7.65326 0.820515
\(88\) −1.18212 0.915522i −0.126014 0.0975949i
\(89\) 2.96297 0.314075 0.157037 0.987593i \(-0.449806\pi\)
0.157037 + 0.987593i \(0.449806\pi\)
\(90\) 1.41947 + 1.30461i 0.149625 + 0.137518i
\(91\) 3.94850i 0.413915i
\(92\) −5.72567 + 0.483690i −0.596943 + 0.0504281i
\(93\) 8.15854 0.846001
\(94\) 3.89038 + 3.57559i 0.401262 + 0.368793i
\(95\) −3.42344 −0.351238
\(96\) −3.07499 + 4.74810i −0.313840 + 0.484600i
\(97\) 13.7074i 1.39177i −0.718152 0.695886i \(-0.755012\pi\)
0.718152 0.695886i \(-0.244988\pi\)
\(98\) 4.35083 4.73387i 0.439500 0.478193i
\(99\) −0.528628 −0.0531291
\(100\) −0.528896 6.26081i −0.0528896 0.626081i
\(101\) 0.747709i 0.0743998i −0.999308 0.0371999i \(-0.988156\pi\)
0.999308 0.0371999i \(-0.0118438\pi\)
\(102\) 5.71831 6.22174i 0.566197 0.616044i
\(103\) 6.33839i 0.624540i −0.949993 0.312270i \(-0.898911\pi\)
0.949993 0.312270i \(-0.101089\pi\)
\(104\) −4.36563 + 5.63689i −0.428085 + 0.552742i
\(105\) 2.13540i 0.208393i
\(106\) 11.6984 + 10.7518i 1.13625 + 1.04431i
\(107\) 3.47954i 0.336380i 0.985755 + 0.168190i \(0.0537923\pi\)
−0.985755 + 0.168190i \(0.946208\pi\)
\(108\) 0.168355 + 1.99290i 0.0162000 + 0.191767i
\(109\) 14.6802i 1.40611i 0.711135 + 0.703055i \(0.248181\pi\)
−0.711135 + 0.703055i \(0.751819\pi\)
\(110\) −0.750370 0.689654i −0.0715450 0.0657559i
\(111\) 7.80230 0.740562
\(112\) 6.17681 1.05110i 0.583654 0.0993199i
\(113\) 13.5436i 1.27407i −0.770834 0.637036i \(-0.780160\pi\)
0.770834 0.637036i \(-0.219840\pi\)
\(114\) −2.61480 2.40322i −0.244898 0.225082i
\(115\) −3.91666 −0.365230
\(116\) 1.28846 + 15.2522i 0.119631 + 1.41613i
\(117\) 2.52074i 0.233043i
\(118\) 8.79501 + 8.08335i 0.809646 + 0.744133i
\(119\) −9.35977 −0.858009
\(120\) −2.36098 + 3.04849i −0.215527 + 0.278288i
\(121\) −10.7206 −0.974596
\(122\) −2.12909 1.95681i −0.192758 0.177161i
\(123\) 11.2829i 1.01734i
\(124\) 1.37353 + 16.2592i 0.123347 + 1.46012i
\(125\) 11.0990i 0.992721i
\(126\) 1.49903 1.63100i 0.133544 0.145301i
\(127\) 11.8234i 1.04916i −0.851362 0.524578i \(-0.824223\pi\)
0.851362 0.524578i \(-0.175777\pi\)
\(128\) −9.98018 5.32879i −0.882131 0.471003i
\(129\) 3.82695 0.336944
\(130\) −3.28859 + 3.57811i −0.288428 + 0.313821i
\(131\) 4.47623i 0.391090i −0.980695 0.195545i \(-0.937352\pi\)
0.980695 0.195545i \(-0.0626476\pi\)
\(132\) −0.0889972 1.05350i −0.00774621 0.0916958i
\(133\) 3.93361i 0.341087i
\(134\) −9.54836 + 6.54438i −0.824852 + 0.565348i
\(135\) 1.36325i 0.117330i
\(136\) 13.3620 + 10.3486i 1.14578 + 0.887382i
\(137\) 3.72743i 0.318455i −0.987242 0.159228i \(-0.949100\pi\)
0.987242 0.159228i \(-0.0509004\pi\)
\(138\) −2.99151 2.74945i −0.254655 0.234049i
\(139\) −9.91407 −0.840900 −0.420450 0.907316i \(-0.638128\pi\)
−0.420450 + 0.907316i \(0.638128\pi\)
\(140\) 4.25563 0.359505i 0.359667 0.0303837i
\(141\) 3.73630i 0.314653i
\(142\) −4.81397 4.42445i −0.403979 0.371291i
\(143\) 1.33254i 0.111432i
\(144\) −3.94331 + 0.671030i −0.328609 + 0.0559192i
\(145\) 10.4333i 0.866437i
\(146\) 11.6350 12.6594i 0.962922 1.04770i
\(147\) 4.54638 0.374979
\(148\) 1.31356 + 15.5492i 0.107974 + 1.27814i
\(149\) −3.92269 −0.321359 −0.160680 0.987007i \(-0.551369\pi\)
−0.160680 + 0.987007i \(0.551369\pi\)
\(150\) 3.00642 3.27111i 0.245473 0.267085i
\(151\) 23.1961i 1.88767i 0.330412 + 0.943837i \(0.392812\pi\)
−0.330412 + 0.943837i \(0.607188\pi\)
\(152\) 4.34917 5.61563i 0.352764 0.455488i
\(153\) 5.97533 0.483077
\(154\) −0.792427 + 0.862192i −0.0638556 + 0.0694774i
\(155\) 11.1221i 0.893349i
\(156\) −5.02360 + 0.424380i −0.402210 + 0.0339776i
\(157\) −1.72814 −0.137921 −0.0689604 0.997619i \(-0.521968\pi\)
−0.0689604 + 0.997619i \(0.521968\pi\)
\(158\) −2.55127 + 2.77589i −0.202968 + 0.220838i
\(159\) 11.2351i 0.890999i
\(160\) −6.47283 4.19198i −0.511722 0.331405i
\(161\) 4.50033i 0.354675i
\(162\) −0.956986 + 1.04124i −0.0751879 + 0.0818074i
\(163\) 19.0214i 1.48987i −0.667136 0.744936i \(-0.732480\pi\)
0.667136 0.744936i \(-0.267520\pi\)
\(164\) −22.4856 + 1.89952i −1.75583 + 0.148328i
\(165\) 0.720652i 0.0561027i
\(166\) −11.8152 10.8592i −0.917039 0.842836i
\(167\) 8.38078i 0.648524i 0.945967 + 0.324262i \(0.105116\pi\)
−0.945967 + 0.324262i \(0.894884\pi\)
\(168\) 3.50279 + 2.71282i 0.270246 + 0.209299i
\(169\) 6.64585 0.511219
\(170\) 8.48178 + 7.79547i 0.650523 + 0.597886i
\(171\) 2.51124i 0.192039i
\(172\) 0.644287 + 7.62674i 0.0491264 + 0.581534i
\(173\) −4.16884 −0.316951 −0.158476 0.987363i \(-0.550658\pi\)
−0.158476 + 0.987363i \(0.550658\pi\)
\(174\) −7.32406 + 7.96886i −0.555235 + 0.604118i
\(175\) −4.92094 −0.371988
\(176\) 2.08455 0.354725i 0.157129 0.0267384i
\(177\) 8.44668i 0.634891i
\(178\) −2.83553 + 3.08516i −0.212532 + 0.231243i
\(179\) −16.2271 −1.21287 −0.606436 0.795132i \(-0.707401\pi\)
−0.606436 + 0.795132i \(0.707401\pi\)
\(180\) −2.71682 + 0.229510i −0.202500 + 0.0171066i
\(181\) −5.93853 −0.441407 −0.220704 0.975341i \(-0.570835\pi\)
−0.220704 + 0.975341i \(0.570835\pi\)
\(182\) 4.11133 + 3.77866i 0.304752 + 0.280093i
\(183\) 2.04476i 0.151153i
\(184\) 4.97575 6.42468i 0.366817 0.473633i
\(185\) 10.6365i 0.782009i
\(186\) −7.80761 + 8.49498i −0.572481 + 0.622882i
\(187\) −3.15873 −0.230989
\(188\) −7.44607 + 0.629025i −0.543061 + 0.0458763i
\(189\) 1.56640 0.113939
\(190\) 3.27619 3.56462i 0.237680 0.258605i
\(191\) 14.8390 1.07371 0.536855 0.843675i \(-0.319612\pi\)
0.536855 + 0.843675i \(0.319612\pi\)
\(192\) −2.00117 7.74566i −0.144422 0.558995i
\(193\) 11.3774 0.818967 0.409483 0.912318i \(-0.365709\pi\)
0.409483 + 0.912318i \(0.365709\pi\)
\(194\) 14.2726 + 13.1178i 1.02472 + 0.941800i
\(195\) −3.43640 −0.246086
\(196\) 0.765407 + 9.06050i 0.0546719 + 0.647178i
\(197\) 14.0886i 1.00377i 0.864933 + 0.501887i \(0.167361\pi\)
−0.864933 + 0.501887i \(0.832639\pi\)
\(198\) 0.505890 0.550428i 0.0359520 0.0391172i
\(199\) 10.3476i 0.733523i 0.930315 + 0.366762i \(0.119534\pi\)
−0.930315 + 0.366762i \(0.880466\pi\)
\(200\) 7.02514 + 5.44080i 0.496752 + 0.384723i
\(201\) −7.97595 1.83962i −0.562580 0.129757i
\(202\) 0.778543 + 0.715547i 0.0547781 + 0.0503457i
\(203\) 11.9881 0.841398
\(204\) 1.00598 + 11.9082i 0.0704325 + 0.833744i
\(205\) −15.3813 −1.07428
\(206\) 6.59977 + 6.06575i 0.459828 + 0.422621i
\(207\) 2.87303i 0.199690i
\(208\) −1.69150 9.94009i −0.117284 0.689221i
\(209\) 1.32751i 0.0918260i
\(210\) 2.22346 + 2.04354i 0.153433 + 0.141018i
\(211\) 11.9542i 0.822960i −0.911419 0.411480i \(-0.865012\pi\)
0.911419 0.411480i \(-0.134988\pi\)
\(212\) −22.3904 + 1.89148i −1.53778 + 0.129907i
\(213\) 4.62331i 0.316784i
\(214\) −3.62304 3.32988i −0.247666 0.227626i
\(215\) 5.21709i 0.355802i
\(216\) −2.23620 1.73188i −0.152154 0.117840i
\(217\) 12.7795 0.867532
\(218\) −15.2856 14.0488i −1.03527 0.951503i
\(219\) 12.1580 0.821561
\(220\) 1.43619 0.121325i 0.0968278 0.00817975i
\(221\) 15.0623i 1.01320i
\(222\) −7.46669 + 8.12405i −0.501132 + 0.545251i
\(223\) 20.0207i 1.34069i −0.742052 0.670343i \(-0.766147\pi\)
0.742052 0.670343i \(-0.233853\pi\)
\(224\) −4.81668 + 7.43743i −0.321828 + 0.496934i
\(225\) 3.14155 0.209437
\(226\) 14.1021 + 12.9610i 0.938057 + 0.862153i
\(227\) 26.1910i 1.73836i 0.494496 + 0.869180i \(0.335352\pi\)
−0.494496 + 0.869180i \(0.664648\pi\)
\(228\) 5.00465 0.422780i 0.331441 0.0279993i
\(229\) 2.35904i 0.155890i 0.996958 + 0.0779448i \(0.0248358\pi\)
−0.996958 + 0.0779448i \(0.975164\pi\)
\(230\) 3.74819 4.07818i 0.247148 0.268907i
\(231\) −0.828045 −0.0544813
\(232\) −17.1142 13.2545i −1.12360 0.870203i
\(233\) 8.87262i 0.581264i −0.956835 0.290632i \(-0.906134\pi\)
0.956835 0.290632i \(-0.0938656\pi\)
\(234\) −2.62470 2.41232i −0.171582 0.157698i
\(235\) −5.09350 −0.332263
\(236\) −16.8334 + 1.42204i −1.09576 + 0.0925670i
\(237\) −2.66595 −0.173172
\(238\) 8.95717 9.74575i 0.580607 0.631723i
\(239\) −1.14012 −0.0737480 −0.0368740 0.999320i \(-0.511740\pi\)
−0.0368740 + 0.999320i \(0.511740\pi\)
\(240\) −0.914781 5.37572i −0.0590488 0.347001i
\(241\) −5.93089 −0.382042 −0.191021 0.981586i \(-0.561180\pi\)
−0.191021 + 0.981586i \(0.561180\pi\)
\(242\) 10.2594 11.1627i 0.659500 0.717562i
\(243\) −1.00000 −0.0641500
\(244\) 4.07501 0.344246i 0.260876 0.0220381i
\(245\) 6.19785i 0.395966i
\(246\) −11.7481 10.7975i −0.749034 0.688426i
\(247\) 6.33020 0.402781
\(248\) −18.2441 14.1296i −1.15850 0.897232i
\(249\) 11.3473i 0.719104i
\(250\) 11.5567 + 10.6216i 0.730908 + 0.671766i
\(251\) 10.4883 0.662016 0.331008 0.943628i \(-0.392611\pi\)
0.331008 + 0.943628i \(0.392611\pi\)
\(252\) 0.263712 + 3.12169i 0.0166123 + 0.196648i
\(253\) 1.51877i 0.0954841i
\(254\) 12.3110 + 11.3148i 0.772459 + 0.709955i
\(255\) 8.14586i 0.510113i
\(256\) 15.0994 5.29216i 0.943715 0.330760i
\(257\) 31.3242 1.95395 0.976974 0.213357i \(-0.0684397\pi\)
0.976974 + 0.213357i \(0.0684397\pi\)
\(258\) −3.66234 + 3.98477i −0.228007 + 0.248081i
\(259\) 12.2215 0.759410
\(260\) −0.578535 6.84841i −0.0358792 0.424720i
\(261\) −7.65326 −0.473725
\(262\) 4.66083 + 4.28369i 0.287947 + 0.264647i
\(263\) 6.28457i 0.387523i −0.981049 0.193762i \(-0.937931\pi\)
0.981049 0.193762i \(-0.0620689\pi\)
\(264\) 1.18212 + 0.915522i 0.0727543 + 0.0563465i
\(265\) −15.3162 −0.940866
\(266\) −4.09583 3.76441i −0.251131 0.230811i
\(267\) −2.96297 −0.181331
\(268\) 2.32339 16.2050i 0.141923 0.989878i
\(269\) −15.0340 −0.916638 −0.458319 0.888788i \(-0.651548\pi\)
−0.458319 + 0.888788i \(0.651548\pi\)
\(270\) −1.41947 1.30461i −0.0863860 0.0793960i
\(271\) 18.8437 1.14468 0.572338 0.820018i \(-0.306037\pi\)
0.572338 + 0.820018i \(0.306037\pi\)
\(272\) −23.5626 + 4.00962i −1.42869 + 0.243119i
\(273\) 3.94850i 0.238974i
\(274\) 3.88114 + 3.56709i 0.234468 + 0.215496i
\(275\) −1.66071 −0.100145
\(276\) 5.72567 0.483690i 0.344645 0.0291147i
\(277\) 6.93613 0.416752 0.208376 0.978049i \(-0.433182\pi\)
0.208376 + 0.978049i \(0.433182\pi\)
\(278\) 9.48763 10.3229i 0.569030 0.619127i
\(279\) −8.15854 −0.488439
\(280\) −3.69825 + 4.77517i −0.221013 + 0.285371i
\(281\) 14.3372i 0.855284i −0.903948 0.427642i \(-0.859344\pi\)
0.903948 0.427642i \(-0.140656\pi\)
\(282\) −3.89038 3.57559i −0.231669 0.212923i
\(283\) 15.1828i 0.902524i −0.892392 0.451262i \(-0.850974\pi\)
0.892392 0.451262i \(-0.149026\pi\)
\(284\) 9.21381 0.778358i 0.546739 0.0461870i
\(285\) 3.42344 0.202787
\(286\) 1.38749 + 1.27522i 0.0820439 + 0.0754053i
\(287\) 17.6735i 1.04323i
\(288\) 3.07499 4.74810i 0.181196 0.279784i
\(289\) 18.7046 1.10027
\(290\) −10.8635 9.98451i −0.637929 0.586311i
\(291\) 13.7074i 0.803540i
\(292\) 2.04686 + 24.2297i 0.119783 + 1.41793i
\(293\) 18.5571 1.08412 0.542060 0.840340i \(-0.317645\pi\)
0.542060 + 0.840340i \(0.317645\pi\)
\(294\) −4.35083 + 4.73387i −0.253745 + 0.276085i
\(295\) −11.5149 −0.670425
\(296\) −17.4475 13.5127i −1.01412 0.785407i
\(297\) 0.528628 0.0306741
\(298\) 3.75396 4.08445i 0.217461 0.236606i
\(299\) 7.24219 0.418826
\(300\) 0.528896 + 6.26081i 0.0305358 + 0.361468i
\(301\) 5.99455 0.345520
\(302\) −24.1527 22.1984i −1.38983 1.27737i
\(303\) 0.747709i 0.0429547i
\(304\) 1.68512 + 9.90261i 0.0966481 + 0.567953i
\(305\) 2.78752 0.159613
\(306\) −5.71831 + 6.22174i −0.326894 + 0.355673i
\(307\) 9.16937i 0.523324i 0.965160 + 0.261662i \(0.0842705\pi\)
−0.965160 + 0.261662i \(0.915729\pi\)
\(308\) −0.139405 1.65021i −0.00794336 0.0940295i
\(309\) 6.33839i 0.360578i
\(310\) −11.5808 10.6437i −0.657744 0.604522i
\(311\) −0.305968 −0.0173499 −0.00867493 0.999962i \(-0.502761\pi\)
−0.00867493 + 0.999962i \(0.502761\pi\)
\(312\) 4.36563 5.63689i 0.247155 0.319126i
\(313\) 4.08597i 0.230952i −0.993310 0.115476i \(-0.963161\pi\)
0.993310 0.115476i \(-0.0368394\pi\)
\(314\) 1.65381 1.79941i 0.0933298 0.101546i
\(315\) 2.13540i 0.120316i
\(316\) −0.448825 5.31297i −0.0252484 0.298878i
\(317\) −12.1082 −0.680064 −0.340032 0.940414i \(-0.610438\pi\)
−0.340032 + 0.940414i \(0.610438\pi\)
\(318\) −11.6984 10.7518i −0.656013 0.602931i
\(319\) 4.04573 0.226517
\(320\) 10.5593 2.72810i 0.590281 0.152505i
\(321\) 3.47954i 0.194209i
\(322\) −4.68591 4.30675i −0.261136 0.240006i
\(323\) 15.0055i 0.834928i
\(324\) −0.168355 1.99290i −0.00935306 0.110717i
\(325\) 7.91906i 0.439270i
\(326\) 19.8058 + 18.2032i 1.09694 + 1.00818i
\(327\) 14.6802i 0.811818i
\(328\) 19.5406 25.2307i 1.07895 1.39313i
\(329\) 5.85255i 0.322661i
\(330\) 0.750370 + 0.689654i 0.0413065 + 0.0379642i
\(331\) −34.6082 −1.90224 −0.951120 0.308821i \(-0.900065\pi\)
−0.951120 + 0.308821i \(0.900065\pi\)
\(332\) 22.6140 1.91037i 1.24110 0.104845i
\(333\) −7.80230 −0.427563
\(334\) −8.72639 8.02029i −0.477487 0.438851i
\(335\) 2.50786 10.8732i 0.137019 0.594067i
\(336\) −6.17681 + 1.05110i −0.336973 + 0.0573424i
\(337\) 14.8377i 0.808261i 0.914701 + 0.404130i \(0.132426\pi\)
−0.914701 + 0.404130i \(0.867574\pi\)
\(338\) −6.35998 + 6.91991i −0.345937 + 0.376393i
\(339\) 13.5436i 0.735586i
\(340\) −16.2339 + 1.37140i −0.880407 + 0.0743744i
\(341\) 4.31283 0.233553
\(342\) 2.61480 + 2.40322i 0.141392 + 0.129951i
\(343\) 18.0863 0.976567
\(344\) −8.55783 6.62783i −0.461407 0.357349i
\(345\) 3.91666 0.210866
\(346\) 3.98953 4.34076i 0.214478 0.233361i
\(347\) 20.5055 1.10079 0.550396 0.834904i \(-0.314477\pi\)
0.550396 + 0.834904i \(0.314477\pi\)
\(348\) −1.28846 15.2522i −0.0690689 0.817603i
\(349\) −13.8409 −0.740885 −0.370443 0.928855i \(-0.620794\pi\)
−0.370443 + 0.928855i \(0.620794\pi\)
\(350\) 4.70927 5.12387i 0.251721 0.273882i
\(351\) 2.52074i 0.134547i
\(352\) −1.62553 + 2.50998i −0.0866410 + 0.133782i
\(353\) 34.4969i 1.83608i 0.396483 + 0.918042i \(0.370231\pi\)
−0.396483 + 0.918042i \(0.629769\pi\)
\(354\) −8.79501 8.08335i −0.467449 0.429625i
\(355\) 6.30272 0.334514
\(356\) −0.498832 5.90492i −0.0264380 0.312960i
\(357\) 9.35977 0.495372
\(358\) 15.5291 16.8963i 0.820740 0.892998i
\(359\) 19.8390i 1.04706i −0.852007 0.523531i \(-0.824614\pi\)
0.852007 0.523531i \(-0.175386\pi\)
\(360\) 2.36098 3.04849i 0.124435 0.160670i
\(361\) 12.6937 0.668088
\(362\) 5.68309 6.18342i 0.298696 0.324993i
\(363\) 10.7206 0.562683
\(364\) −7.86897 + 0.664750i −0.412446 + 0.0348424i
\(365\) 16.5744i 0.867542i
\(366\) 2.12909 + 1.95681i 0.111289 + 0.102284i
\(367\) 30.4913 1.59163 0.795815 0.605540i \(-0.207043\pi\)
0.795815 + 0.605540i \(0.207043\pi\)
\(368\) 1.92789 + 11.3293i 0.100498 + 0.590579i
\(369\) 11.2829i 0.587362i
\(370\) −11.0751 10.1790i −0.575767 0.529179i
\(371\) 17.5986i 0.913675i
\(372\) −1.37353 16.2592i −0.0712142 0.842998i
\(373\) 13.4697i 0.697436i −0.937228 0.348718i \(-0.886617\pi\)
0.937228 0.348718i \(-0.113383\pi\)
\(374\) 3.02286 3.28899i 0.156308 0.170070i
\(375\) 11.0990i 0.573148i
\(376\) 6.47083 8.35511i 0.333707 0.430882i
\(377\) 19.2919i 0.993584i
\(378\) −1.49903 + 1.63100i −0.0771015 + 0.0838895i
\(379\) −0.700479 −0.0359812 −0.0179906 0.999838i \(-0.505727\pi\)
−0.0179906 + 0.999838i \(0.505727\pi\)
\(380\) 0.576354 + 6.82259i 0.0295663 + 0.349991i
\(381\) 11.8234i 0.605730i
\(382\) −14.2007 + 15.4509i −0.726570 + 0.790537i
\(383\) 20.8295 1.06434 0.532170 0.846638i \(-0.321377\pi\)
0.532170 + 0.846638i \(0.321377\pi\)
\(384\) 9.98018 + 5.32879i 0.509299 + 0.271934i
\(385\) 1.12883i 0.0575305i
\(386\) −10.8881 + 11.8466i −0.554188 + 0.602978i
\(387\) −3.82695 −0.194535
\(388\) −27.3174 + 2.30770i −1.38683 + 0.117156i
\(389\) −13.9967 −0.709661 −0.354830 0.934931i \(-0.615461\pi\)
−0.354830 + 0.934931i \(0.615461\pi\)
\(390\) 3.28859 3.57811i 0.166524 0.181185i
\(391\) 17.1673i 0.868189i
\(392\) −10.1666 7.87380i −0.513492 0.397687i
\(393\) 4.47623i 0.225796i
\(394\) −14.6696 13.4826i −0.739046 0.679245i
\(395\) 3.63435i 0.182864i
\(396\) 0.0889972 + 1.05350i 0.00447228 + 0.0529406i
\(397\) −0.391387 −0.0196431 −0.00982157 0.999952i \(-0.503126\pi\)
−0.00982157 + 0.999952i \(0.503126\pi\)
\(398\) −10.7743 9.90253i −0.540069 0.496369i
\(399\) 3.93361i 0.196927i
\(400\) −12.3881 + 2.10808i −0.619407 + 0.105404i
\(401\) 13.7484i 0.686561i 0.939233 + 0.343281i \(0.111538\pi\)
−0.939233 + 0.343281i \(0.888462\pi\)
\(402\) 9.54836 6.54438i 0.476229 0.326404i
\(403\) 20.5656i 1.02444i
\(404\) −1.49011 + 0.125881i −0.0741357 + 0.00626279i
\(405\) 1.36325i 0.0677404i
\(406\) −11.4724 + 12.4824i −0.569367 + 0.619493i
\(407\) 4.12452 0.204445
\(408\) −13.3620 10.3486i −0.661519 0.512330i
\(409\) 19.5659i 0.967469i 0.875215 + 0.483735i \(0.160720\pi\)
−0.875215 + 0.483735i \(0.839280\pi\)
\(410\) 14.7197 16.0156i 0.726955 0.790956i
\(411\) 3.72743i 0.183860i
\(412\) −12.6318 + 1.06710i −0.622323 + 0.0525722i
\(413\) 13.2309i 0.651050i
\(414\) 2.99151 + 2.74945i 0.147025 + 0.135128i
\(415\) 15.4692 0.759351
\(416\) 11.9687 + 7.75127i 0.586816 + 0.380038i
\(417\) 9.91407 0.485494
\(418\) −1.38226 1.27041i −0.0676084 0.0621378i
\(419\) 30.3583i 1.48310i −0.670896 0.741551i \(-0.734090\pi\)
0.670896 0.741551i \(-0.265910\pi\)
\(420\) −4.25563 + 0.359505i −0.207654 + 0.0175420i
\(421\) −8.09140 −0.394351 −0.197175 0.980368i \(-0.563177\pi\)
−0.197175 + 0.980368i \(0.563177\pi\)
\(422\) 12.4472 + 11.4400i 0.605918 + 0.556890i
\(423\) 3.73630i 0.181665i
\(424\) 19.4578 25.1238i 0.944954 1.22012i
\(425\) 18.7718 0.910567
\(426\) 4.81397 + 4.42445i 0.233238 + 0.214365i
\(427\) 3.20292i 0.155000i
\(428\) 6.93439 0.585799i 0.335186 0.0283156i
\(429\) 1.33254i 0.0643355i
\(430\) −5.43223 4.99268i −0.261965 0.240768i
\(431\) 21.3247i 1.02717i −0.858037 0.513587i \(-0.828316\pi\)
0.858037 0.513587i \(-0.171684\pi\)
\(432\) 3.94331 0.671030i 0.189723 0.0322849i
\(433\) 10.3106i 0.495494i 0.968825 + 0.247747i \(0.0796901\pi\)
−0.968825 + 0.247747i \(0.920310\pi\)
\(434\) −12.2299 + 13.3066i −0.587052 + 0.638735i
\(435\) 10.4333i 0.500238i
\(436\) 29.2562 2.47149i 1.40112 0.118363i
\(437\) −7.21488 −0.345134
\(438\) −11.6350 + 12.6594i −0.555943 + 0.604888i
\(439\) 35.7951i 1.70840i −0.519941 0.854202i \(-0.674046\pi\)
0.519941 0.854202i \(-0.325954\pi\)
\(440\) −1.24808 + 1.61152i −0.0595000 + 0.0768262i
\(441\) −4.54638 −0.216494
\(442\) −15.6834 14.4144i −0.745984 0.685623i
\(443\) −9.33817 −0.443670 −0.221835 0.975084i \(-0.571205\pi\)
−0.221835 + 0.975084i \(0.571205\pi\)
\(444\) −1.31356 15.5492i −0.0623386 0.737933i
\(445\) 4.03927i 0.191480i
\(446\) 20.8463 + 19.1595i 0.987102 + 0.907230i
\(447\) 3.92269 0.185537
\(448\) −3.13464 12.1328i −0.148098 0.573222i
\(449\) −6.33662 −0.299044 −0.149522 0.988758i \(-0.547773\pi\)
−0.149522 + 0.988758i \(0.547773\pi\)
\(450\) −3.00642 + 3.27111i −0.141724 + 0.154201i
\(451\) 5.96444i 0.280854i
\(452\) −26.9910 + 2.28013i −1.26955 + 0.107248i
\(453\) 23.1961i 1.08985i
\(454\) −27.2711 25.0644i −1.27990 1.17633i
\(455\) −5.38279 −0.252349
\(456\) −4.34917 + 5.61563i −0.203669 + 0.262976i
\(457\) 2.11160 0.0987765 0.0493883 0.998780i \(-0.484273\pi\)
0.0493883 + 0.998780i \(0.484273\pi\)
\(458\) −2.45632 2.25757i −0.114776 0.105489i
\(459\) −5.97533 −0.278904
\(460\) 0.659389 + 7.80552i 0.0307442 + 0.363934i
\(461\) 16.4701 0.767087 0.383544 0.923523i \(-0.374704\pi\)
0.383544 + 0.923523i \(0.374704\pi\)
\(462\) 0.792427 0.862192i 0.0368670 0.0401128i
\(463\) −3.43056 −0.159432 −0.0797158 0.996818i \(-0.525401\pi\)
−0.0797158 + 0.996818i \(0.525401\pi\)
\(464\) 30.1792 5.13556i 1.40103 0.238413i
\(465\) 11.1221i 0.515776i
\(466\) 9.23851 + 8.49097i 0.427966 + 0.393337i
\(467\) 3.69099i 0.170798i −0.996347 0.0853992i \(-0.972783\pi\)
0.996347 0.0853992i \(-0.0272166\pi\)
\(468\) 5.02360 0.424380i 0.232216 0.0196170i
\(469\) −12.4935 2.88158i −0.576898 0.133059i
\(470\) 4.87441 5.30355i 0.224840 0.244635i
\(471\) 1.72814 0.0796286
\(472\) 14.6286 18.8885i 0.673338 0.869412i
\(473\) 2.02304 0.0930193
\(474\) 2.55127 2.77589i 0.117184 0.127501i
\(475\) 7.88920i 0.361981i
\(476\) 1.57576 + 18.6531i 0.0722250 + 0.854963i
\(477\) 11.2351i 0.514418i
\(478\) 1.09108 1.18713i 0.0499047 0.0542982i
\(479\) 21.8923i 1.00028i 0.865943 + 0.500142i \(0.166719\pi\)
−0.865943 + 0.500142i \(0.833281\pi\)
\(480\) 6.47283 + 4.19198i 0.295443 + 0.191337i
\(481\) 19.6676i 0.896766i
\(482\) 5.67578 6.17547i 0.258525 0.281285i
\(483\) 4.50033i 0.204772i
\(484\) 1.80486 + 21.3650i 0.0820390 + 0.971137i
\(485\) −18.6865 −0.848512
\(486\) 0.956986 1.04124i 0.0434098 0.0472315i
\(487\) −11.7289 −0.531488 −0.265744 0.964044i \(-0.585618\pi\)
−0.265744 + 0.964044i \(0.585618\pi\)
\(488\) −3.54129 + 4.57250i −0.160306 + 0.206987i
\(489\) 19.0214i 0.860178i
\(490\) −6.45344 5.93126i −0.291537 0.267947i
\(491\) 8.85707i 0.399714i −0.979825 0.199857i \(-0.935952\pi\)
0.979825 0.199857i \(-0.0640478\pi\)
\(492\) 22.4856 1.89952i 1.01373 0.0856372i
\(493\) −45.7307 −2.05961
\(494\) −6.05791 + 6.59124i −0.272558 + 0.296554i
\(495\) 0.720652i 0.0323909i
\(496\) 32.1717 5.47462i 1.44455 0.245818i
\(497\) 7.24197i 0.324847i
\(498\) 11.8152 + 10.8592i 0.529453 + 0.486612i
\(499\) −21.7924 −0.975561 −0.487781 0.872966i \(-0.662193\pi\)
−0.487781 + 0.872966i \(0.662193\pi\)
\(500\) −22.1191 + 1.86857i −0.989198 + 0.0835648i
\(501\) 8.38078i 0.374426i
\(502\) −10.0372 + 10.9208i −0.447981 + 0.487421i
\(503\) −11.4232 −0.509334 −0.254667 0.967029i \(-0.581966\pi\)
−0.254667 + 0.967029i \(0.581966\pi\)
\(504\) −3.50279 2.71282i −0.156027 0.120839i
\(505\) −1.01931 −0.0453588
\(506\) −1.58140 1.45344i −0.0703017 0.0646132i
\(507\) −6.64585 −0.295152
\(508\) −23.5628 + 1.99053i −1.04543 + 0.0883153i
\(509\) −2.75233 −0.121995 −0.0609974 0.998138i \(-0.519428\pi\)
−0.0609974 + 0.998138i \(0.519428\pi\)
\(510\) −8.48178 7.79547i −0.375580 0.345189i
\(511\) 19.0443 0.842470
\(512\) −8.93955 + 20.7866i −0.395076 + 0.918648i
\(513\) 2.51124i 0.110874i
\(514\) −29.9768 + 32.6159i −1.32222 + 1.43863i
\(515\) −8.64079 −0.380759
\(516\) −0.644287 7.62674i −0.0283631 0.335749i
\(517\) 1.97511i 0.0868654i
\(518\) −11.6958 + 12.7255i −0.513886 + 0.559128i
\(519\) 4.16884 0.182992
\(520\) 7.68448 + 5.95144i 0.336987 + 0.260988i
\(521\) 23.2054i 1.01665i 0.861166 + 0.508324i \(0.169735\pi\)
−0.861166 + 0.508324i \(0.830265\pi\)
\(522\) 7.32406 7.96886i 0.320565 0.348788i
\(523\) 3.30778i 0.144639i −0.997382 0.0723196i \(-0.976960\pi\)
0.997382 0.0723196i \(-0.0230402\pi\)
\(524\) −8.92069 + 0.753596i −0.389702 + 0.0329210i
\(525\) 4.92094 0.214767
\(526\) 6.54374 + 6.01425i 0.285321 + 0.262234i
\(527\) −48.7499 −2.12358
\(528\) −2.08455 + 0.354725i −0.0907183 + 0.0154374i
\(529\) 14.7457 0.641116
\(530\) 14.6574 15.9478i 0.636676 0.692728i
\(531\) 8.44668i 0.366555i
\(532\) 7.83930 0.662243i 0.339877 0.0287119i
\(533\) 28.4412 1.23192
\(534\) 2.83553 3.08516i 0.122705 0.133508i
\(535\) 4.74348 0.205079
\(536\) 14.6498 + 17.9272i 0.632776 + 0.774335i
\(537\) 16.2271 0.700252
\(538\) 14.3873 15.6540i 0.620281 0.674890i
\(539\) 2.40335 0.103519
\(540\) 2.71682 0.229510i 0.116913 0.00987653i
\(541\) 12.1689i 0.523183i −0.965179 0.261592i \(-0.915753\pi\)
0.965179 0.261592i \(-0.0842474\pi\)
\(542\) −18.0332 + 19.6208i −0.774592 + 0.842787i
\(543\) 5.93853 0.254847
\(544\) 18.3741 28.3714i 0.787783 1.21642i
\(545\) 20.0128 0.857254
\(546\) −4.11133 3.77866i −0.175949 0.161712i
\(547\) −15.3448 −0.656096 −0.328048 0.944661i \(-0.606391\pi\)
−0.328048 + 0.944661i \(0.606391\pi\)
\(548\) −7.42839 + 0.627531i −0.317325 + 0.0268068i
\(549\) 2.04476i 0.0872683i
\(550\) 1.58928 1.72920i 0.0677671 0.0737333i
\(551\) 19.2192i 0.818764i
\(552\) −4.97575 + 6.42468i −0.211782 + 0.273452i
\(553\) −4.17594 −0.177579
\(554\) −6.63778 + 7.22216i −0.282012 + 0.306840i
\(555\) 10.6365i 0.451493i
\(556\) 1.66908 + 19.7578i 0.0707849 + 0.837916i
\(557\) −22.2115 −0.941132 −0.470566 0.882365i \(-0.655950\pi\)
−0.470566 + 0.882365i \(0.655950\pi\)
\(558\) 7.80761 8.49498i 0.330522 0.359621i
\(559\) 9.64677i 0.408015i
\(560\) −1.43291 8.42053i −0.0605517 0.355832i
\(561\) 3.15873 0.133362
\(562\) 14.9284 + 13.7205i 0.629718 + 0.578764i
\(563\) 46.6259 1.96505 0.982523 0.186143i \(-0.0595987\pi\)
0.982523 + 0.186143i \(0.0595987\pi\)
\(564\) 7.44607 0.629025i 0.313536 0.0264867i
\(565\) −18.4633 −0.776755
\(566\) 15.8089 + 14.5297i 0.664498 + 0.610730i
\(567\) −1.56640 −0.0657827
\(568\) −8.00703 + 10.3386i −0.335967 + 0.433800i
\(569\) 13.3971 0.561637 0.280819 0.959761i \(-0.409394\pi\)
0.280819 + 0.959761i \(0.409394\pi\)
\(570\) −3.27619 + 3.56462i −0.137224 + 0.149306i
\(571\) 22.6544i 0.948059i 0.880509 + 0.474029i \(0.157201\pi\)
−0.880509 + 0.474029i \(0.842799\pi\)
\(572\) −2.65562 + 0.224339i −0.111037 + 0.00938010i
\(573\) −14.8390 −0.619907
\(574\) −18.4023 16.9133i −0.768098 0.705947i
\(575\) 9.02579i 0.376401i
\(576\) 2.00117 + 7.74566i 0.0833822 + 0.322736i
\(577\) 28.6399i 1.19229i 0.802875 + 0.596147i \(0.203302\pi\)
−0.802875 + 0.596147i \(0.796698\pi\)
\(578\) −17.9000 + 19.4759i −0.744542 + 0.810091i
\(579\) −11.3774 −0.472831
\(580\) 20.7925 1.75650i 0.863362 0.0729345i
\(581\) 17.7744i 0.737406i
\(582\) −14.2726 13.1178i −0.591620 0.543749i
\(583\) 5.93917i 0.245975i
\(584\) −27.1877 21.0562i −1.12503 0.871312i
\(585\) 3.43640 0.142078
\(586\) −17.7589 + 19.3224i −0.733614 + 0.798201i
\(587\) 46.9051 1.93598 0.967990 0.250988i \(-0.0807556\pi\)
0.967990 + 0.250988i \(0.0807556\pi\)
\(588\) −0.765407 9.06050i −0.0315648 0.373649i
\(589\) 20.4880i 0.844195i
\(590\) 11.0196 11.9898i 0.453671 0.493611i
\(591\) 14.0886i 0.579529i
\(592\) 30.7669 5.23558i 1.26451 0.215181i
\(593\) 32.0451i 1.31594i 0.753046 + 0.657968i \(0.228584\pi\)
−0.753046 + 0.657968i \(0.771416\pi\)
\(594\) −0.505890 + 0.550428i −0.0207569 + 0.0225843i
\(595\) 12.7597i 0.523096i
\(596\) 0.660404 + 7.81753i 0.0270512 + 0.320218i
\(597\) 10.3476i 0.423500i
\(598\) −6.93067 + 7.54084i −0.283416 + 0.308368i
\(599\) −30.2463 −1.23583 −0.617915 0.786245i \(-0.712022\pi\)
−0.617915 + 0.786245i \(0.712022\pi\)
\(600\) −7.02514 5.44080i −0.286800 0.222120i
\(601\) 14.4069 0.587670 0.293835 0.955856i \(-0.405068\pi\)
0.293835 + 0.955856i \(0.405068\pi\)
\(602\) −5.73670 + 6.24175i −0.233810 + 0.254395i
\(603\) 7.97595 + 1.83962i 0.324806 + 0.0749151i
\(604\) 46.2276 3.90518i 1.88097 0.158900i
\(605\) 14.6148i 0.594175i
\(606\) −0.778543 0.715547i −0.0316262 0.0290671i
\(607\) 28.9051i 1.17322i 0.809869 + 0.586611i \(0.199538\pi\)
−0.809869 + 0.586611i \(0.800462\pi\)
\(608\) −11.9236 7.72205i −0.483566 0.313170i
\(609\) −11.9881 −0.485781
\(610\) −2.66762 + 2.90247i −0.108009 + 0.117518i
\(611\) 9.41825 0.381022
\(612\) −1.00598 11.9082i −0.0406642 0.481362i
\(613\) 13.7771 0.556450 0.278225 0.960516i \(-0.410254\pi\)
0.278225 + 0.960516i \(0.410254\pi\)
\(614\) −9.54750 8.77496i −0.385306 0.354129i
\(615\) 15.3813 0.620235
\(616\) 1.85167 + 1.43407i 0.0746060 + 0.0577805i
\(617\) 27.5346 1.10850 0.554251 0.832349i \(-0.313005\pi\)
0.554251 + 0.832349i \(0.313005\pi\)
\(618\) −6.59977 6.06575i −0.265482 0.244000i
\(619\) 23.0359i 0.925891i 0.886387 + 0.462945i \(0.153207\pi\)
−0.886387 + 0.462945i \(0.846793\pi\)
\(620\) 22.1653 1.87246i 0.890179 0.0751999i
\(621\) 2.87303i 0.115291i
\(622\) 0.292807 0.318586i 0.0117405 0.0127741i
\(623\) −4.64121 −0.185946
\(624\) 1.69150 + 9.94009i 0.0677140 + 0.397922i
\(625\) 0.577128 0.0230851
\(626\) 4.25447 + 3.91021i 0.170043 + 0.156284i
\(627\) 1.32751i 0.0530157i
\(628\) 0.290941 + 3.44402i 0.0116098 + 0.137431i
\(629\) −46.6213 −1.85891
\(630\) −2.22346 2.04354i −0.0885846 0.0814167i
\(631\) −48.1322 −1.91611 −0.958055 0.286583i \(-0.907481\pi\)
−0.958055 + 0.286583i \(0.907481\pi\)
\(632\) 5.96159 + 4.61710i 0.237139 + 0.183659i
\(633\) 11.9542i 0.475136i
\(634\) 11.5874 12.6075i 0.460193 0.500708i
\(635\) −16.1182 −0.639632
\(636\) 22.3904 1.89148i 0.887836 0.0750020i
\(637\) 11.4603i 0.454073i
\(638\) −3.87170 + 4.21257i −0.153282 + 0.166777i
\(639\) 4.62331i 0.182895i
\(640\) −7.26447 + 13.6055i −0.287153 + 0.537803i
\(641\) 40.2935i 1.59150i −0.605628 0.795748i \(-0.707078\pi\)
0.605628 0.795748i \(-0.292922\pi\)
\(642\) 3.62304 + 3.32988i 0.142990 + 0.131420i
\(643\) 0.501719i 0.0197859i 0.999951 + 0.00989294i \(0.00314907\pi\)
−0.999951 + 0.00989294i \(0.996851\pi\)
\(644\) 8.96871 0.757653i 0.353417 0.0298557i
\(645\) 5.21709i 0.205423i
\(646\) 15.6243 + 14.3600i 0.614729 + 0.564988i
\(647\) −33.5887 −1.32051 −0.660253 0.751043i \(-0.729551\pi\)
−0.660253 + 0.751043i \(0.729551\pi\)
\(648\) 2.23620 + 1.73188i 0.0878462 + 0.0680347i
\(649\) 4.46515i 0.175273i
\(650\) −8.24562 7.57843i −0.323420 0.297250i
\(651\) −12.7795 −0.500870
\(652\) −37.9078 + 3.20235i −1.48458 + 0.125414i
\(653\) 16.6382i 0.651104i −0.945524 0.325552i \(-0.894450\pi\)
0.945524 0.325552i \(-0.105550\pi\)
\(654\) 15.2856 + 14.0488i 0.597715 + 0.549350i
\(655\) −6.10222 −0.238433
\(656\) 7.57113 + 44.4918i 0.295603 + 1.73711i
\(657\) −12.1580 −0.474328
\(658\) −6.09390 5.60080i −0.237565 0.218342i
\(659\) 19.4030i 0.755835i −0.925839 0.377917i \(-0.876640\pi\)
0.925839 0.377917i \(-0.123360\pi\)
\(660\) −1.43619 + 0.121325i −0.0559035 + 0.00472258i
\(661\) 12.7137i 0.494505i −0.968951 0.247252i \(-0.920472\pi\)
0.968951 0.247252i \(-0.0795277\pi\)
\(662\) 33.1196 36.0354i 1.28723 1.40056i
\(663\) 15.0623i 0.584971i
\(664\) −19.6521 + 25.3748i −0.762651 + 0.984732i
\(665\) 5.36249 0.207948
\(666\) 7.46669 8.12405i 0.289328 0.314801i
\(667\) 21.9881i 0.851381i
\(668\) 16.7021 1.41095i 0.646223 0.0545912i
\(669\) 20.0207i 0.774045i
\(670\) 8.92161 + 13.0168i 0.344672 + 0.502882i
\(671\) 1.08092i 0.0417284i
\(672\) 4.81668 7.43743i 0.185807 0.286905i
\(673\) 49.2662i 1.89907i −0.313660 0.949535i \(-0.601555\pi\)
0.313660 0.949535i \(-0.398445\pi\)
\(674\) −15.4496 14.1995i −0.595096 0.546943i
\(675\) −3.14155 −0.120918
\(676\) −1.11886 13.2445i −0.0430331 0.509404i
\(677\) 5.46737i 0.210128i 0.994465 + 0.105064i \(0.0335048\pi\)
−0.994465 + 0.105064i \(0.966495\pi\)
\(678\) −14.1021 12.9610i −0.541587 0.497765i
\(679\) 21.4712i 0.823991i
\(680\) 14.1077 18.2158i 0.541004 0.698543i
\(681\) 26.1910i 1.00364i
\(682\) −4.12732 + 4.49069i −0.158043 + 0.171957i
\(683\) −27.5247 −1.05320 −0.526601 0.850112i \(-0.676534\pi\)
−0.526601 + 0.850112i \(0.676534\pi\)
\(684\) −5.00465 + 0.422780i −0.191358 + 0.0161654i
\(685\) −5.08141 −0.194151
\(686\) −17.3083 + 18.8321i −0.660835 + 0.719014i
\(687\) 2.35904i 0.0900029i
\(688\) 15.0909 2.56800i 0.575334 0.0979041i
\(689\) 28.3207 1.07893
\(690\) −3.74819 + 4.07818i −0.142691 + 0.155254i
\(691\) 42.9779i 1.63496i 0.575960 + 0.817478i \(0.304628\pi\)
−0.575960 + 0.817478i \(0.695372\pi\)
\(692\) 0.701846 + 8.30810i 0.0266802 + 0.315826i
\(693\) 0.828045 0.0314548
\(694\) −19.6235 + 21.3511i −0.744896 + 0.810476i
\(695\) 13.5153i 0.512666i
\(696\) 17.1142 + 13.2545i 0.648712 + 0.502412i
\(697\) 67.4188i 2.55367i
\(698\) 13.2455 14.4117i 0.501351 0.545489i
\(699\) 8.87262i 0.335593i
\(700\) 0.828464 + 9.80694i 0.0313130 + 0.370668i
\(701\) 21.8416i 0.824947i 0.910970 + 0.412473i \(0.135335\pi\)
−0.910970 + 0.412473i \(0.864665\pi\)
\(702\) 2.62470 + 2.41232i 0.0990628 + 0.0910471i
\(703\) 19.5934i 0.738981i
\(704\) −1.05788 4.09458i −0.0398702 0.154320i
\(705\) 5.09350 0.191832
\(706\) −35.9195 33.0130i −1.35185 1.24246i
\(707\) 1.17121i 0.0440480i
\(708\) 16.8334 1.42204i 0.632638 0.0534436i
\(709\) 25.6113 0.961854 0.480927 0.876761i \(-0.340300\pi\)
0.480927 + 0.876761i \(0.340300\pi\)
\(710\) −6.03162 + 6.56264i −0.226363 + 0.246291i
\(711\) 2.66595 0.0999808
\(712\) 6.62580 + 5.13152i 0.248312 + 0.192312i
\(713\) 23.4397i 0.877825i
\(714\) −8.95717 + 9.74575i −0.335214 + 0.364726i
\(715\) −1.81658 −0.0679362
\(716\) 2.73192 + 32.3391i 0.102097 + 1.20857i
\(717\) 1.14012 0.0425785
\(718\) 20.6571 + 18.9856i 0.770917 + 0.708538i
\(719\) 22.2369i 0.829296i 0.909982 + 0.414648i \(0.136095\pi\)
−0.909982 + 0.414648i \(0.863905\pi\)
\(720\) 0.914781 + 5.37572i 0.0340919 + 0.200341i
\(721\) 9.92846i 0.369755i
\(722\) −12.1477 + 13.2171i −0.452089 + 0.491891i
\(723\) 5.93089 0.220572
\(724\) 0.999781 + 11.8349i 0.0371566 + 0.439841i
\(725\) −24.0431 −0.892939
\(726\) −10.2594 + 11.1627i −0.380763 + 0.414285i
\(727\) 44.1322 1.63677 0.818387 0.574668i \(-0.194869\pi\)
0.818387 + 0.574668i \(0.194869\pi\)
\(728\) 6.83833 8.82963i 0.253446 0.327248i
\(729\) 1.00000 0.0370370
\(730\) −17.2579 15.8614i −0.638742 0.587058i
\(731\) −22.8673 −0.845778
\(732\) −4.07501 + 0.344246i −0.150617 + 0.0127237i
\(733\) 25.1028i 0.927194i −0.886046 0.463597i \(-0.846559\pi\)
0.886046 0.463597i \(-0.153441\pi\)
\(734\) −29.1797 + 31.7487i −1.07704 + 1.17186i
\(735\) 6.19785i 0.228611i
\(736\) −13.6414 8.83456i −0.502830 0.325646i
\(737\) −4.21631 0.972474i −0.155310 0.0358216i
\(738\) 11.7481 + 10.7975i 0.432455 + 0.397463i
\(739\) 26.6506 0.980358 0.490179 0.871622i \(-0.336931\pi\)
0.490179 + 0.871622i \(0.336931\pi\)
\(740\) 21.1974 1.79070i 0.779234 0.0658276i
\(741\) −6.33020 −0.232546
\(742\) −18.3244 16.8416i −0.672709 0.618276i
\(743\) 24.2167i 0.888424i 0.895922 + 0.444212i \(0.146516\pi\)
−0.895922 + 0.444212i \(0.853484\pi\)
\(744\) 18.2441 + 14.1296i 0.668862 + 0.518017i
\(745\) 5.34760i 0.195921i
\(746\) 14.0252 + 12.8903i 0.513499 + 0.471949i
\(747\) 11.3473i 0.415175i
\(748\) 0.531788 + 6.29503i 0.0194441 + 0.230169i
\(749\) 5.45037i 0.199152i
\(750\) −11.5567 10.6216i −0.421990 0.387844i
\(751\) 51.6938i 1.88633i 0.332321 + 0.943166i \(0.392168\pi\)
−0.332321 + 0.943166i \(0.607832\pi\)
\(752\) 2.50717 + 14.7334i 0.0914270 + 0.537272i
\(753\) −10.4883 −0.382215
\(754\) 20.0875 + 18.4621i 0.731543 + 0.672349i
\(755\) 31.6221 1.15085
\(756\) −0.263712 3.12169i −0.00959110 0.113535i
\(757\) 49.1422i 1.78610i 0.449953 + 0.893052i \(0.351441\pi\)
−0.449953 + 0.893052i \(0.648559\pi\)
\(758\) 0.670349 0.729366i 0.0243482 0.0264918i
\(759\) 1.51877i 0.0551277i
\(760\) −7.65550 5.92900i −0.277694 0.215067i
\(761\) −42.2284 −1.53078 −0.765389 0.643567i \(-0.777454\pi\)
−0.765389 + 0.643567i \(0.777454\pi\)
\(762\) −12.3110 11.3148i −0.445979 0.409893i
\(763\) 22.9951i 0.832480i
\(764\) −2.49821 29.5726i −0.0903822 1.06990i
\(765\) 8.14586i 0.294514i
\(766\) −19.9336 + 21.6885i −0.720229 + 0.783638i
\(767\) 21.2919 0.768807
\(768\) −15.0994 + 5.29216i −0.544854 + 0.190964i
\(769\) 25.7365i 0.928081i −0.885814 0.464040i \(-0.846399\pi\)
0.885814 0.464040i \(-0.153601\pi\)
\(770\) 1.17538 + 1.08028i 0.0423578 + 0.0389304i
\(771\) −31.3242 −1.12811