Properties

Label 252.2.b.d.55.1
Level $252$
Weight $2$
Character 252.55
Analytic conductor $2.012$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.2312.1
Defining polynomial: \(x^{4} - x^{3} - 2 x + 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.1
Root \(-0.780776 - 1.17915i\) of defining polynomial
Character \(\chi\) \(=\) 252.55
Dual form 252.2.b.d.55.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.780776 - 1.17915i) q^{2} +(-0.780776 + 1.84130i) q^{4} +1.69614i q^{5} +(-2.56155 - 0.662153i) q^{7} +(2.78078 - 0.516994i) q^{8} +O(q^{10})\) \(q+(-0.780776 - 1.17915i) q^{2} +(-0.780776 + 1.84130i) q^{4} +1.69614i q^{5} +(-2.56155 - 0.662153i) q^{7} +(2.78078 - 0.516994i) q^{8} +(2.00000 - 1.32431i) q^{10} +3.02045i q^{11} +6.04090i q^{13} +(1.21922 + 3.53744i) q^{14} +(-2.78078 - 2.87529i) q^{16} +4.34475i q^{17} +1.12311 q^{19} +(-3.12311 - 1.32431i) q^{20} +(3.56155 - 2.35829i) q^{22} -3.02045i q^{23} +2.12311 q^{25} +(7.12311 - 4.71659i) q^{26} +(3.21922 - 4.19960i) q^{28} +2.00000 q^{29} +(-1.21922 + 5.52390i) q^{32} +(5.12311 - 3.39228i) q^{34} +(1.12311 - 4.34475i) q^{35} -7.12311 q^{37} +(-0.876894 - 1.32431i) q^{38} +(0.876894 + 4.71659i) q^{40} -7.73704i q^{41} +8.10887i q^{43} +(-5.56155 - 2.35829i) q^{44} +(-3.56155 + 2.35829i) q^{46} -10.2462 q^{47} +(6.12311 + 3.39228i) q^{49} +(-1.65767 - 2.50345i) q^{50} +(-11.1231 - 4.71659i) q^{52} +4.24621 q^{53} -5.12311 q^{55} +(-7.46543 - 0.516994i) q^{56} +(-1.56155 - 2.35829i) q^{58} +4.00000 q^{59} -9.43318i q^{61} +(7.46543 - 2.87529i) q^{64} -10.2462 q^{65} -2.06798i q^{67} +(-8.00000 - 3.39228i) q^{68} +(-6.00000 + 2.06798i) q^{70} +12.4536i q^{71} -3.39228i q^{73} +(5.56155 + 8.39919i) q^{74} +(-0.876894 + 2.06798i) q^{76} +(2.00000 - 7.73704i) q^{77} -4.71659i q^{79} +(4.87689 - 4.71659i) q^{80} +(-9.12311 + 6.04090i) q^{82} +6.24621 q^{83} -7.36932 q^{85} +(9.56155 - 6.33122i) q^{86} +(1.56155 + 8.39919i) q^{88} +7.73704i q^{89} +(4.00000 - 15.4741i) q^{91} +(5.56155 + 2.35829i) q^{92} +(8.00000 + 12.0818i) q^{94} +1.90495i q^{95} -8.68951i q^{97} +(-0.780776 - 9.86866i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} + q^{4} - 2q^{7} + 7q^{8} + O(q^{10}) \) \( 4q + q^{2} + q^{4} - 2q^{7} + 7q^{8} + 8q^{10} + 9q^{14} - 7q^{16} - 12q^{19} + 4q^{20} + 6q^{22} - 8q^{25} + 12q^{26} + 17q^{28} + 8q^{29} - 9q^{32} + 4q^{34} - 12q^{35} - 12q^{37} - 20q^{38} + 20q^{40} - 14q^{44} - 6q^{46} - 8q^{47} + 8q^{49} - 19q^{50} - 28q^{52} - 16q^{53} - 4q^{55} - q^{56} + 2q^{58} + 16q^{59} + q^{64} - 8q^{65} - 32q^{68} - 24q^{70} + 14q^{74} - 20q^{76} + 8q^{77} + 36q^{80} - 20q^{82} - 8q^{83} + 20q^{85} + 30q^{86} - 2q^{88} + 16q^{91} + 14q^{92} + 32q^{94} + q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.780776 1.17915i −0.552092 0.833783i
\(3\) 0 0
\(4\) −0.780776 + 1.84130i −0.390388 + 0.920650i
\(5\) 1.69614i 0.758537i 0.925287 + 0.379269i \(0.123824\pi\)
−0.925287 + 0.379269i \(0.876176\pi\)
\(6\) 0 0
\(7\) −2.56155 0.662153i −0.968176 0.250270i
\(8\) 2.78078 0.516994i 0.983153 0.182785i
\(9\) 0 0
\(10\) 2.00000 1.32431i 0.632456 0.418783i
\(11\) 3.02045i 0.910699i 0.890313 + 0.455350i \(0.150486\pi\)
−0.890313 + 0.455350i \(0.849514\pi\)
\(12\) 0 0
\(13\) 6.04090i 1.67544i 0.546098 + 0.837722i \(0.316113\pi\)
−0.546098 + 0.837722i \(0.683887\pi\)
\(14\) 1.21922 + 3.53744i 0.325851 + 0.945421i
\(15\) 0 0
\(16\) −2.78078 2.87529i −0.695194 0.718822i
\(17\) 4.34475i 1.05376i 0.849940 + 0.526879i \(0.176638\pi\)
−0.849940 + 0.526879i \(0.823362\pi\)
\(18\) 0 0
\(19\) 1.12311 0.257658 0.128829 0.991667i \(-0.458878\pi\)
0.128829 + 0.991667i \(0.458878\pi\)
\(20\) −3.12311 1.32431i −0.698348 0.296124i
\(21\) 0 0
\(22\) 3.56155 2.35829i 0.759326 0.502790i
\(23\) 3.02045i 0.629807i −0.949124 0.314903i \(-0.898028\pi\)
0.949124 0.314903i \(-0.101972\pi\)
\(24\) 0 0
\(25\) 2.12311 0.424621
\(26\) 7.12311 4.71659i 1.39696 0.924999i
\(27\) 0 0
\(28\) 3.21922 4.19960i 0.608376 0.793649i
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.21922 + 5.52390i −0.215530 + 0.976497i
\(33\) 0 0
\(34\) 5.12311 3.39228i 0.878605 0.581772i
\(35\) 1.12311 4.34475i 0.189839 0.734398i
\(36\) 0 0
\(37\) −7.12311 −1.17103 −0.585516 0.810661i \(-0.699108\pi\)
−0.585516 + 0.810661i \(0.699108\pi\)
\(38\) −0.876894 1.32431i −0.142251 0.214831i
\(39\) 0 0
\(40\) 0.876894 + 4.71659i 0.138649 + 0.745758i
\(41\) 7.73704i 1.20832i −0.796862 0.604161i \(-0.793508\pi\)
0.796862 0.604161i \(-0.206492\pi\)
\(42\) 0 0
\(43\) 8.10887i 1.23659i 0.785946 + 0.618296i \(0.212177\pi\)
−0.785946 + 0.618296i \(0.787823\pi\)
\(44\) −5.56155 2.35829i −0.838436 0.355526i
\(45\) 0 0
\(46\) −3.56155 + 2.35829i −0.525122 + 0.347712i
\(47\) −10.2462 −1.49456 −0.747282 0.664507i \(-0.768641\pi\)
−0.747282 + 0.664507i \(0.768641\pi\)
\(48\) 0 0
\(49\) 6.12311 + 3.39228i 0.874729 + 0.484612i
\(50\) −1.65767 2.50345i −0.234430 0.354042i
\(51\) 0 0
\(52\) −11.1231 4.71659i −1.54250 0.654073i
\(53\) 4.24621 0.583262 0.291631 0.956531i \(-0.405802\pi\)
0.291631 + 0.956531i \(0.405802\pi\)
\(54\) 0 0
\(55\) −5.12311 −0.690799
\(56\) −7.46543 0.516994i −0.997611 0.0690862i
\(57\) 0 0
\(58\) −1.56155 2.35829i −0.205042 0.309659i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 9.43318i 1.20779i −0.797062 0.603897i \(-0.793614\pi\)
0.797062 0.603897i \(-0.206386\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.46543 2.87529i 0.933179 0.359411i
\(65\) −10.2462 −1.27089
\(66\) 0 0
\(67\) 2.06798i 0.252643i −0.991989 0.126322i \(-0.959683\pi\)
0.991989 0.126322i \(-0.0403172\pi\)
\(68\) −8.00000 3.39228i −0.970143 0.411375i
\(69\) 0 0
\(70\) −6.00000 + 2.06798i −0.717137 + 0.247170i
\(71\) 12.4536i 1.47797i 0.673720 + 0.738987i \(0.264695\pi\)
−0.673720 + 0.738987i \(0.735305\pi\)
\(72\) 0 0
\(73\) 3.39228i 0.397037i −0.980097 0.198518i \(-0.936387\pi\)
0.980097 0.198518i \(-0.0636129\pi\)
\(74\) 5.56155 + 8.39919i 0.646517 + 0.976386i
\(75\) 0 0
\(76\) −0.876894 + 2.06798i −0.100587 + 0.237213i
\(77\) 2.00000 7.73704i 0.227921 0.881717i
\(78\) 0 0
\(79\) 4.71659i 0.530658i −0.964158 0.265329i \(-0.914519\pi\)
0.964158 0.265329i \(-0.0854805\pi\)
\(80\) 4.87689 4.71659i 0.545253 0.527331i
\(81\) 0 0
\(82\) −9.12311 + 6.04090i −1.00748 + 0.667105i
\(83\) 6.24621 0.685611 0.342805 0.939406i \(-0.388623\pi\)
0.342805 + 0.939406i \(0.388623\pi\)
\(84\) 0 0
\(85\) −7.36932 −0.799315
\(86\) 9.56155 6.33122i 1.03105 0.682712i
\(87\) 0 0
\(88\) 1.56155 + 8.39919i 0.166462 + 0.895357i
\(89\) 7.73704i 0.820124i 0.912058 + 0.410062i \(0.134493\pi\)
−0.912058 + 0.410062i \(0.865507\pi\)
\(90\) 0 0
\(91\) 4.00000 15.4741i 0.419314 1.62212i
\(92\) 5.56155 + 2.35829i 0.579832 + 0.245869i
\(93\) 0 0
\(94\) 8.00000 + 12.0818i 0.825137 + 1.24614i
\(95\) 1.90495i 0.195443i
\(96\) 0 0
\(97\) 8.68951i 0.882286i −0.897437 0.441143i \(-0.854573\pi\)
0.897437 0.441143i \(-0.145427\pi\)
\(98\) −0.780776 9.86866i −0.0788703 0.996885i
\(99\) 0 0
\(100\) −1.65767 + 3.90928i −0.165767 + 0.390928i
\(101\) 6.99337i 0.695866i −0.937519 0.347933i \(-0.886884\pi\)
0.937519 0.347933i \(-0.113116\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 3.12311 + 16.7984i 0.306246 + 1.64722i
\(105\) 0 0
\(106\) −3.31534 5.00691i −0.322014 0.486314i
\(107\) 5.66906i 0.548049i −0.961723 0.274024i \(-0.911645\pi\)
0.961723 0.274024i \(-0.0883549\pi\)
\(108\) 0 0
\(109\) 8.24621 0.789844 0.394922 0.918715i \(-0.370772\pi\)
0.394922 + 0.918715i \(0.370772\pi\)
\(110\) 4.00000 + 6.04090i 0.381385 + 0.575977i
\(111\) 0 0
\(112\) 5.21922 + 9.20650i 0.493170 + 0.869933i
\(113\) −12.2462 −1.15203 −0.576013 0.817440i \(-0.695392\pi\)
−0.576013 + 0.817440i \(0.695392\pi\)
\(114\) 0 0
\(115\) 5.12311 0.477732
\(116\) −1.56155 + 3.68260i −0.144987 + 0.341921i
\(117\) 0 0
\(118\) −3.12311 4.71659i −0.287505 0.434197i
\(119\) 2.87689 11.1293i 0.263724 1.02022i
\(120\) 0 0
\(121\) 1.87689 0.170627
\(122\) −11.1231 + 7.36520i −1.00704 + 0.666814i
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0818i 1.08063i
\(126\) 0 0
\(127\) 19.4470i 1.72564i 0.505510 + 0.862821i \(0.331304\pi\)
−0.505510 + 0.862821i \(0.668696\pi\)
\(128\) −9.21922 6.55789i −0.814872 0.579641i
\(129\) 0 0
\(130\) 8.00000 + 12.0818i 0.701646 + 1.05964i
\(131\) 22.2462 1.94366 0.971830 0.235682i \(-0.0757323\pi\)
0.971830 + 0.235682i \(0.0757323\pi\)
\(132\) 0 0
\(133\) −2.87689 0.743668i −0.249458 0.0644842i
\(134\) −2.43845 + 1.61463i −0.210650 + 0.139482i
\(135\) 0 0
\(136\) 2.24621 + 12.0818i 0.192611 + 1.03601i
\(137\) 16.2462 1.38801 0.694004 0.719971i \(-0.255845\pi\)
0.694004 + 0.719971i \(0.255845\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 7.12311 + 5.46026i 0.602012 + 0.461476i
\(141\) 0 0
\(142\) 14.6847 9.72350i 1.23231 0.815978i
\(143\) −18.2462 −1.52582
\(144\) 0 0
\(145\) 3.39228i 0.281714i
\(146\) −4.00000 + 2.64861i −0.331042 + 0.219201i
\(147\) 0 0
\(148\) 5.56155 13.1158i 0.457157 1.07811i
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) 8.10887i 0.659891i −0.944000 0.329945i \(-0.892970\pi\)
0.944000 0.329945i \(-0.107030\pi\)
\(152\) 3.12311 0.580639i 0.253317 0.0470960i
\(153\) 0 0
\(154\) −10.6847 + 3.68260i −0.860994 + 0.296752i
\(155\) 0 0
\(156\) 0 0
\(157\) 4.13595i 0.330085i 0.986286 + 0.165042i \(0.0527761\pi\)
−0.986286 + 0.165042i \(0.947224\pi\)
\(158\) −5.56155 + 3.68260i −0.442453 + 0.292972i
\(159\) 0 0
\(160\) −9.36932 2.06798i −0.740710 0.163488i
\(161\) −2.00000 + 7.73704i −0.157622 + 0.609764i
\(162\) 0 0
\(163\) 11.5012i 0.900840i 0.892817 + 0.450420i \(0.148726\pi\)
−0.892817 + 0.450420i \(0.851274\pi\)
\(164\) 14.2462 + 6.04090i 1.11244 + 0.471715i
\(165\) 0 0
\(166\) −4.87689 7.36520i −0.378520 0.571651i
\(167\) −2.24621 −0.173817 −0.0869085 0.996216i \(-0.527699\pi\)
−0.0869085 + 0.996216i \(0.527699\pi\)
\(168\) 0 0
\(169\) −23.4924 −1.80711
\(170\) 5.75379 + 8.68951i 0.441295 + 0.666455i
\(171\) 0 0
\(172\) −14.9309 6.33122i −1.13847 0.482751i
\(173\) 8.48071i 0.644776i −0.946608 0.322388i \(-0.895514\pi\)
0.946608 0.322388i \(-0.104486\pi\)
\(174\) 0 0
\(175\) −5.43845 1.40582i −0.411108 0.106270i
\(176\) 8.68466 8.39919i 0.654631 0.633113i
\(177\) 0 0
\(178\) 9.12311 6.04090i 0.683806 0.452784i
\(179\) 2.27678i 0.170175i −0.996374 0.0850873i \(-0.972883\pi\)
0.996374 0.0850873i \(-0.0271169\pi\)
\(180\) 0 0
\(181\) 6.04090i 0.449016i −0.974472 0.224508i \(-0.927922\pi\)
0.974472 0.224508i \(-0.0720775\pi\)
\(182\) −21.3693 + 7.36520i −1.58400 + 0.545945i
\(183\) 0 0
\(184\) −1.56155 8.39919i −0.115119 0.619197i
\(185\) 12.0818i 0.888271i
\(186\) 0 0
\(187\) −13.1231 −0.959657
\(188\) 8.00000 18.8664i 0.583460 1.37597i
\(189\) 0 0
\(190\) 2.24621 1.48734i 0.162957 0.107903i
\(191\) 9.06134i 0.655656i 0.944737 + 0.327828i \(0.106317\pi\)
−0.944737 + 0.327828i \(0.893683\pi\)
\(192\) 0 0
\(193\) 9.36932 0.674418 0.337209 0.941430i \(-0.390517\pi\)
0.337209 + 0.941430i \(0.390517\pi\)
\(194\) −10.2462 + 6.78456i −0.735635 + 0.487103i
\(195\) 0 0
\(196\) −11.0270 + 8.62586i −0.787642 + 0.616133i
\(197\) −0.246211 −0.0175418 −0.00877091 0.999962i \(-0.502792\pi\)
−0.00877091 + 0.999962i \(0.502792\pi\)
\(198\) 0 0
\(199\) −5.12311 −0.363167 −0.181584 0.983375i \(-0.558122\pi\)
−0.181584 + 0.983375i \(0.558122\pi\)
\(200\) 5.90388 1.09763i 0.417468 0.0776143i
\(201\) 0 0
\(202\) −8.24621 + 5.46026i −0.580201 + 0.384182i
\(203\) −5.12311 1.32431i −0.359572 0.0929481i
\(204\) 0 0
\(205\) 13.1231 0.916557
\(206\) −6.24621 9.43318i −0.435194 0.657241i
\(207\) 0 0
\(208\) 17.3693 16.7984i 1.20435 1.16476i
\(209\) 3.39228i 0.234649i
\(210\) 0 0
\(211\) 3.97292i 0.273507i −0.990605 0.136754i \(-0.956333\pi\)
0.990605 0.136754i \(-0.0436668\pi\)
\(212\) −3.31534 + 7.81855i −0.227699 + 0.536980i
\(213\) 0 0
\(214\) −6.68466 + 4.42627i −0.456954 + 0.302574i
\(215\) −13.7538 −0.938001
\(216\) 0 0
\(217\) 0 0
\(218\) −6.43845 9.72350i −0.436067 0.658558i
\(219\) 0 0
\(220\) 4.00000 9.43318i 0.269680 0.635985i
\(221\) −26.2462 −1.76551
\(222\) 0 0
\(223\) −18.8769 −1.26409 −0.632045 0.774932i \(-0.717784\pi\)
−0.632045 + 0.774932i \(0.717784\pi\)
\(224\) 6.78078 13.3425i 0.453060 0.891480i
\(225\) 0 0
\(226\) 9.56155 + 14.4401i 0.636025 + 0.960540i
\(227\) 16.4924 1.09464 0.547320 0.836923i \(-0.315648\pi\)
0.547320 + 0.836923i \(0.315648\pi\)
\(228\) 0 0
\(229\) 18.1227i 1.19758i 0.800906 + 0.598790i \(0.204352\pi\)
−0.800906 + 0.598790i \(0.795648\pi\)
\(230\) −4.00000 6.04090i −0.263752 0.398325i
\(231\) 0 0
\(232\) 5.56155 1.03399i 0.365134 0.0678846i
\(233\) 10.4924 0.687381 0.343691 0.939083i \(-0.388323\pi\)
0.343691 + 0.939083i \(0.388323\pi\)
\(234\) 0 0
\(235\) 17.3790i 1.13368i
\(236\) −3.12311 + 7.36520i −0.203297 + 0.479434i
\(237\) 0 0
\(238\) −15.3693 + 5.29723i −0.996245 + 0.343368i
\(239\) 2.27678i 0.147273i 0.997285 + 0.0736363i \(0.0234604\pi\)
−0.997285 + 0.0736363i \(0.976540\pi\)
\(240\) 0 0
\(241\) 1.90495i 0.122708i 0.998116 + 0.0613542i \(0.0195419\pi\)
−0.998116 + 0.0613542i \(0.980458\pi\)
\(242\) −1.46543 2.21313i −0.0942017 0.142266i
\(243\) 0 0
\(244\) 17.3693 + 7.36520i 1.11196 + 0.471509i
\(245\) −5.75379 + 10.3857i −0.367596 + 0.663515i
\(246\) 0 0
\(247\) 6.78456i 0.431691i
\(248\) 0 0
\(249\) 0 0
\(250\) 14.2462 9.43318i 0.901010 0.596607i
\(251\) −22.2462 −1.40417 −0.702084 0.712094i \(-0.747747\pi\)
−0.702084 + 0.712094i \(0.747747\pi\)
\(252\) 0 0
\(253\) 9.12311 0.573565
\(254\) 22.9309 15.1838i 1.43881 0.952713i
\(255\) 0 0
\(256\) −0.534565 + 15.9911i −0.0334103 + 0.999442i
\(257\) 19.8188i 1.23626i −0.786074 0.618132i \(-0.787890\pi\)
0.786074 0.618132i \(-0.212110\pi\)
\(258\) 0 0
\(259\) 18.2462 + 4.71659i 1.13376 + 0.293075i
\(260\) 8.00000 18.8664i 0.496139 1.17004i
\(261\) 0 0
\(262\) −17.3693 26.2316i −1.07308 1.62059i
\(263\) 4.92539i 0.303713i −0.988403 0.151856i \(-0.951475\pi\)
0.988403 0.151856i \(-0.0485251\pi\)
\(264\) 0 0
\(265\) 7.20217i 0.442426i
\(266\) 1.36932 + 3.97292i 0.0839582 + 0.243595i
\(267\) 0 0
\(268\) 3.80776 + 1.61463i 0.232596 + 0.0986290i
\(269\) 22.4674i 1.36986i 0.728607 + 0.684932i \(0.240168\pi\)
−0.728607 + 0.684932i \(0.759832\pi\)
\(270\) 0 0
\(271\) −4.49242 −0.272895 −0.136448 0.990647i \(-0.543569\pi\)
−0.136448 + 0.990647i \(0.543569\pi\)
\(272\) 12.4924 12.0818i 0.757464 0.732566i
\(273\) 0 0
\(274\) −12.6847 19.1567i −0.766308 1.15730i
\(275\) 6.41273i 0.386702i
\(276\) 0 0
\(277\) 3.12311 0.187649 0.0938246 0.995589i \(-0.470091\pi\)
0.0938246 + 0.995589i \(0.470091\pi\)
\(278\) −9.36932 14.1498i −0.561934 0.848647i
\(279\) 0 0
\(280\) 0.876894 12.6624i 0.0524045 0.756725i
\(281\) 0.246211 0.0146877 0.00734387 0.999973i \(-0.497662\pi\)
0.00734387 + 0.999973i \(0.497662\pi\)
\(282\) 0 0
\(283\) −17.1231 −1.01786 −0.508931 0.860807i \(-0.669959\pi\)
−0.508931 + 0.860807i \(0.669959\pi\)
\(284\) −22.9309 9.72350i −1.36070 0.576983i
\(285\) 0 0
\(286\) 14.2462 + 21.5150i 0.842396 + 1.27221i
\(287\) −5.12311 + 19.8188i −0.302407 + 1.16987i
\(288\) 0 0
\(289\) −1.87689 −0.110406
\(290\) 4.00000 2.64861i 0.234888 0.155532i
\(291\) 0 0
\(292\) 6.24621 + 2.64861i 0.365532 + 0.154998i
\(293\) 6.99337i 0.408557i −0.978913 0.204278i \(-0.934515\pi\)
0.978913 0.204278i \(-0.0654848\pi\)
\(294\) 0 0
\(295\) 6.78456i 0.395013i
\(296\) −19.8078 + 3.68260i −1.15130 + 0.214047i
\(297\) 0 0
\(298\) −7.80776 11.7915i −0.452292 0.683062i
\(299\) 18.2462 1.05521
\(300\) 0 0
\(301\) 5.36932 20.7713i 0.309482 1.19724i
\(302\) −9.56155 + 6.33122i −0.550206 + 0.364320i
\(303\) 0 0
\(304\) −3.12311 3.22925i −0.179122 0.185210i
\(305\) 16.0000 0.916157
\(306\) 0 0
\(307\) 21.6155 1.23366 0.616832 0.787095i \(-0.288416\pi\)
0.616832 + 0.787095i \(0.288416\pi\)
\(308\) 12.6847 + 9.72350i 0.722775 + 0.554048i
\(309\) 0 0
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) 25.6509i 1.44988i 0.688814 + 0.724938i \(0.258132\pi\)
−0.688814 + 0.724938i \(0.741868\pi\)
\(314\) 4.87689 3.22925i 0.275219 0.182237i
\(315\) 0 0
\(316\) 8.68466 + 3.68260i 0.488550 + 0.207163i
\(317\) −18.4924 −1.03864 −0.519319 0.854580i \(-0.673814\pi\)
−0.519319 + 0.854580i \(0.673814\pi\)
\(318\) 0 0
\(319\) 6.04090i 0.338225i
\(320\) 4.87689 + 12.6624i 0.272627 + 0.707851i
\(321\) 0 0
\(322\) 10.6847 3.68260i 0.595433 0.205223i
\(323\) 4.87962i 0.271509i
\(324\) 0 0
\(325\) 12.8255i 0.711429i
\(326\) 13.5616 8.97983i 0.751105 0.497347i
\(327\) 0 0
\(328\) −4.00000 21.5150i −0.220863 1.18797i
\(329\) 26.2462 + 6.78456i 1.44700 + 0.374045i
\(330\) 0 0
\(331\) 5.46026i 0.300123i −0.988677 0.150061i \(-0.952053\pi\)
0.988677 0.150061i \(-0.0479472\pi\)
\(332\) −4.87689 + 11.5012i −0.267654 + 0.631208i
\(333\) 0 0
\(334\) 1.75379 + 2.64861i 0.0959631 + 0.144926i
\(335\) 3.50758 0.191639
\(336\) 0 0
\(337\) −8.24621 −0.449200 −0.224600 0.974451i \(-0.572108\pi\)
−0.224600 + 0.974451i \(0.572108\pi\)
\(338\) 18.3423 + 27.7010i 0.997691 + 1.50674i
\(339\) 0 0
\(340\) 5.75379 13.5691i 0.312043 0.735889i
\(341\) 0 0
\(342\) 0 0
\(343\) −13.4384 12.7439i −0.725608 0.688108i
\(344\) 4.19224 + 22.5490i 0.226030 + 1.21576i
\(345\) 0 0
\(346\) −10.0000 + 6.62153i −0.537603 + 0.355976i
\(347\) 34.7123i 1.86345i −0.363162 0.931726i \(-0.618303\pi\)
0.363162 0.931726i \(-0.381697\pi\)
\(348\) 0 0
\(349\) 4.13595i 0.221392i 0.993854 + 0.110696i \(0.0353080\pi\)
−0.993854 + 0.110696i \(0.964692\pi\)
\(350\) 2.58854 + 7.51036i 0.138363 + 0.401446i
\(351\) 0 0
\(352\) −16.6847 3.68260i −0.889295 0.196283i
\(353\) 6.24970i 0.332638i 0.986072 + 0.166319i \(0.0531881\pi\)
−0.986072 + 0.166319i \(0.946812\pi\)
\(354\) 0 0
\(355\) −21.1231 −1.12110
\(356\) −14.2462 6.04090i −0.755048 0.320167i
\(357\) 0 0
\(358\) −2.68466 + 1.77766i −0.141889 + 0.0939520i
\(359\) 1.11550i 0.0588740i −0.999567 0.0294370i \(-0.990629\pi\)
0.999567 0.0294370i \(-0.00937144\pi\)
\(360\) 0 0
\(361\) −17.7386 −0.933612
\(362\) −7.12311 + 4.71659i −0.374382 + 0.247898i
\(363\) 0 0
\(364\) 25.3693 + 19.4470i 1.32971 + 1.01930i
\(365\) 5.75379 0.301167
\(366\) 0 0
\(367\) 8.63068 0.450518 0.225259 0.974299i \(-0.427677\pi\)
0.225259 + 0.974299i \(0.427677\pi\)
\(368\) −8.68466 + 8.39919i −0.452719 + 0.437838i
\(369\) 0 0
\(370\) −14.2462 + 9.43318i −0.740625 + 0.490408i
\(371\) −10.8769 2.81164i −0.564700 0.145973i
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 10.2462 + 15.4741i 0.529819 + 0.800145i
\(375\) 0 0
\(376\) −28.4924 + 5.29723i −1.46938 + 0.273184i
\(377\) 12.0818i 0.622244i
\(378\) 0 0
\(379\) 18.7033i 0.960725i 0.877070 + 0.480363i \(0.159495\pi\)
−0.877070 + 0.480363i \(0.840505\pi\)
\(380\) −3.50758 1.48734i −0.179935 0.0762988i
\(381\) 0 0
\(382\) 10.6847 7.07488i 0.546675 0.361983i
\(383\) −26.2462 −1.34112 −0.670559 0.741856i \(-0.733946\pi\)
−0.670559 + 0.741856i \(0.733946\pi\)
\(384\) 0 0
\(385\) 13.1231 + 3.39228i 0.668815 + 0.172887i
\(386\) −7.31534 11.0478i −0.372341 0.562318i
\(387\) 0 0
\(388\) 16.0000 + 6.78456i 0.812277 + 0.344434i
\(389\) −0.246211 −0.0124834 −0.00624170 0.999981i \(-0.501987\pi\)
−0.00624170 + 0.999981i \(0.501987\pi\)
\(390\) 0 0
\(391\) 13.1231 0.663664
\(392\) 18.7808 + 6.26757i 0.948572 + 0.316560i
\(393\) 0 0
\(394\) 0.192236 + 0.290319i 0.00968471 + 0.0146261i
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) 16.2177i 0.813945i −0.913440 0.406973i \(-0.866584\pi\)
0.913440 0.406973i \(-0.133416\pi\)
\(398\) 4.00000 + 6.04090i 0.200502 + 0.302803i
\(399\) 0 0
\(400\) −5.90388 6.10454i −0.295194 0.305227i
\(401\) 8.24621 0.411796 0.205898 0.978573i \(-0.433988\pi\)
0.205898 + 0.978573i \(0.433988\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 12.8769 + 5.46026i 0.640649 + 0.271658i
\(405\) 0 0
\(406\) 2.43845 + 7.07488i 0.121018 + 0.351121i
\(407\) 21.5150i 1.06646i
\(408\) 0 0
\(409\) 27.5559i 1.36255i −0.732028 0.681275i \(-0.761426\pi\)
0.732028 0.681275i \(-0.238574\pi\)
\(410\) −10.2462 15.4741i −0.506024 0.764210i
\(411\) 0 0
\(412\) −6.24621 + 14.7304i −0.307729 + 0.725715i
\(413\) −10.2462 2.64861i −0.504183 0.130330i
\(414\) 0 0
\(415\) 10.5945i 0.520061i
\(416\) −33.3693 7.36520i −1.63607 0.361109i
\(417\) 0 0
\(418\) 4.00000 2.64861i 0.195646 0.129548i
\(419\) 16.4924 0.805708 0.402854 0.915264i \(-0.368018\pi\)
0.402854 + 0.915264i \(0.368018\pi\)
\(420\) 0 0
\(421\) 19.1231 0.932003 0.466002 0.884784i \(-0.345694\pi\)
0.466002 + 0.884784i \(0.345694\pi\)
\(422\) −4.68466 + 3.10196i −0.228046 + 0.151001i
\(423\) 0 0
\(424\) 11.8078 2.19526i 0.573436 0.106611i
\(425\) 9.22437i 0.447448i
\(426\) 0 0
\(427\) −6.24621 + 24.1636i −0.302275 + 1.16936i
\(428\) 10.4384 + 4.42627i 0.504561 + 0.213952i
\(429\) 0 0
\(430\) 10.7386 + 16.2177i 0.517863 + 0.782089i
\(431\) 15.1022i 0.727449i −0.931507 0.363725i \(-0.881505\pi\)
0.931507 0.363725i \(-0.118495\pi\)
\(432\) 0 0
\(433\) 6.78456i 0.326045i 0.986622 + 0.163023i \(0.0521244\pi\)
−0.986622 + 0.163023i \(0.947876\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −6.43845 + 15.1838i −0.308346 + 0.727170i
\(437\) 3.39228i 0.162275i
\(438\) 0 0
\(439\) 31.3693 1.49718 0.748588 0.663036i \(-0.230732\pi\)
0.748588 + 0.663036i \(0.230732\pi\)
\(440\) −14.2462 + 2.64861i −0.679161 + 0.126268i
\(441\) 0 0
\(442\) 20.4924 + 30.9481i 0.974725 + 1.47205i
\(443\) 35.8735i 1.70440i 0.523213 + 0.852202i \(0.324733\pi\)
−0.523213 + 0.852202i \(0.675267\pi\)
\(444\) 0 0
\(445\) −13.1231 −0.622095
\(446\) 14.7386 + 22.2586i 0.697895 + 1.05398i
\(447\) 0 0
\(448\) −21.0270 + 2.42194i −0.993432 + 0.114426i
\(449\) −28.2462 −1.33302 −0.666511 0.745496i \(-0.732213\pi\)
−0.666511 + 0.745496i \(0.732213\pi\)
\(450\) 0 0
\(451\) 23.3693 1.10042
\(452\) 9.56155 22.5490i 0.449738 1.06061i
\(453\) 0 0
\(454\) −12.8769 19.4470i −0.604343 0.912693i
\(455\) 26.2462 + 6.78456i 1.23044 + 0.318065i
\(456\) 0 0
\(457\) −16.2462 −0.759966 −0.379983 0.924994i \(-0.624070\pi\)
−0.379983 + 0.924994i \(0.624070\pi\)
\(458\) 21.3693 14.1498i 0.998523 0.661175i
\(459\) 0 0
\(460\) −4.00000 + 9.43318i −0.186501 + 0.439824i
\(461\) 17.1702i 0.799697i −0.916581 0.399848i \(-0.869063\pi\)
0.916581 0.399848i \(-0.130937\pi\)
\(462\) 0 0
\(463\) 39.4746i 1.83454i −0.398264 0.917271i \(-0.630387\pi\)
0.398264 0.917271i \(-0.369613\pi\)
\(464\) −5.56155 5.75058i −0.258189 0.266964i
\(465\) 0 0
\(466\) −8.19224 12.3721i −0.379498 0.573127i
\(467\) 17.7538 0.821547 0.410774 0.911737i \(-0.365259\pi\)
0.410774 + 0.911737i \(0.365259\pi\)
\(468\) 0 0
\(469\) −1.36932 + 5.29723i −0.0632292 + 0.244603i
\(470\) −20.4924 + 13.5691i −0.945245 + 0.625897i
\(471\) 0 0
\(472\) 11.1231 2.06798i 0.511982 0.0951863i
\(473\) −24.4924 −1.12616
\(474\) 0 0
\(475\) 2.38447 0.109407
\(476\) 18.2462 + 13.9867i 0.836314 + 0.641081i
\(477\) 0 0
\(478\) 2.68466 1.77766i 0.122793 0.0813081i
\(479\) −20.4924 −0.936323 −0.468161 0.883643i \(-0.655083\pi\)
−0.468161 + 0.883643i \(0.655083\pi\)
\(480\) 0 0
\(481\) 43.0299i 1.96200i
\(482\) 2.24621 1.48734i 0.102312 0.0677463i
\(483\) 0 0
\(484\) −1.46543 + 3.45593i −0.0666107 + 0.157088i
\(485\) 14.7386 0.669247
\(486\) 0 0
\(487\) 32.2725i 1.46240i −0.682161 0.731202i \(-0.738960\pi\)
0.682161 0.731202i \(-0.261040\pi\)
\(488\) −4.87689 26.2316i −0.220767 1.18745i
\(489\) 0 0
\(490\) 16.7386 1.32431i 0.756174 0.0598261i
\(491\) 11.7100i 0.528463i 0.964459 + 0.264231i \(0.0851183\pi\)
−0.964459 + 0.264231i \(0.914882\pi\)
\(492\) 0 0
\(493\) 8.68951i 0.391356i
\(494\) 8.00000 5.29723i 0.359937 0.238334i
\(495\) 0 0
\(496\) 0 0
\(497\) 8.24621 31.9006i 0.369893 1.43094i
\(498\) 0 0
\(499\) 17.5420i 0.785290i −0.919690 0.392645i \(-0.871560\pi\)
0.919690 0.392645i \(-0.128440\pi\)
\(500\) −22.2462 9.43318i −0.994881 0.421865i
\(501\) 0 0
\(502\) 17.3693 + 26.2316i 0.775231 + 1.17077i
\(503\) 22.7386 1.01387 0.506933 0.861986i \(-0.330779\pi\)
0.506933 + 0.861986i \(0.330779\pi\)
\(504\) 0 0
\(505\) 11.8617 0.527840
\(506\) −7.12311 10.7575i −0.316661 0.478229i
\(507\) 0 0
\(508\) −35.8078 15.1838i −1.58871 0.673670i
\(509\) 1.69614i 0.0751801i −0.999293 0.0375901i \(-0.988032\pi\)
0.999293 0.0375901i \(-0.0119681\pi\)
\(510\) 0 0
\(511\) −2.24621 + 8.68951i −0.0993665 + 0.384401i
\(512\) 19.2732 11.8551i 0.851763 0.523927i
\(513\) 0 0
\(514\) −23.3693 + 15.4741i −1.03078 + 0.682532i
\(515\) 13.5691i 0.597927i
\(516\) 0 0
\(517\) 30.9481i 1.36110i
\(518\) −8.68466 25.1976i −0.381582 1.10712i
\(519\) 0 0
\(520\) −28.4924 + 5.29723i −1.24948 + 0.232299i
\(521\) 33.8056i 1.48105i −0.672030 0.740524i \(-0.734577\pi\)
0.672030 0.740524i \(-0.265423\pi\)
\(522\) 0 0
\(523\) 0.492423 0.0215321 0.0107661 0.999942i \(-0.496573\pi\)
0.0107661 + 0.999942i \(0.496573\pi\)
\(524\) −17.3693 + 40.9620i −0.758782 + 1.78943i
\(525\) 0 0
\(526\) −5.80776 + 3.84563i −0.253231 + 0.167677i
\(527\) 0 0
\(528\) 0 0
\(529\) 13.8769 0.603343
\(530\) 8.49242 5.62329i 0.368887 0.244260i
\(531\) 0 0
\(532\) 3.61553 4.71659i 0.156753 0.204490i
\(533\) 46.7386 2.02447
\(534\) 0 0
\(535\) 9.61553 0.415716
\(536\) −1.06913 5.75058i −0.0461794 0.248387i
\(537\) 0 0
\(538\) 26.4924 17.5420i 1.14217 0.756291i
\(539\) −10.2462 + 18.4945i −0.441336 + 0.796615i
\(540\) 0 0
\(541\) 11.1231 0.478220 0.239110 0.970993i \(-0.423144\pi\)
0.239110 + 0.970993i \(0.423144\pi\)
\(542\) 3.50758 + 5.29723i 0.150663 + 0.227535i
\(543\) 0 0
\(544\) −24.0000 5.29723i −1.02899 0.227117i
\(545\) 13.9867i 0.599126i
\(546\) 0 0
\(547\) 33.0161i 1.41167i −0.708378 0.705834i \(-0.750573\pi\)
0.708378 0.705834i \(-0.249427\pi\)
\(548\) −12.6847 + 29.9142i −0.541862 + 1.27787i
\(549\) 0 0
\(550\) 7.56155 5.00691i 0.322426 0.213495i
\(551\) 2.24621 0.0956918
\(552\) 0 0
\(553\) −3.12311 + 12.0818i −0.132808 + 0.513770i
\(554\) −2.43845 3.68260i −0.103600 0.156459i
\(555\) 0 0
\(556\) −9.36932 + 22.0956i −0.397348 + 0.937063i
\(557\) −14.0000 −0.593199 −0.296600 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 0 0
\(559\) −48.9848 −2.07184
\(560\) −15.6155 + 8.85254i −0.659877 + 0.374088i
\(561\) 0 0
\(562\) −0.192236 0.290319i −0.00810898 0.0122464i
\(563\) −14.2462 −0.600406 −0.300203 0.953875i \(-0.597054\pi\)
−0.300203 + 0.953875i \(0.597054\pi\)
\(564\) 0 0
\(565\) 20.7713i 0.873855i
\(566\) 13.3693 + 20.1907i 0.561954 + 0.848677i
\(567\) 0 0
\(568\) 6.43845 + 34.6307i 0.270151 + 1.45307i
\(569\) −34.9848 −1.46664 −0.733320 0.679883i \(-0.762031\pi\)
−0.733320 + 0.679883i \(0.762031\pi\)
\(570\) 0 0
\(571\) 40.9620i 1.71420i 0.515146 + 0.857102i \(0.327738\pi\)
−0.515146 + 0.857102i \(0.672262\pi\)
\(572\) 14.2462 33.5968i 0.595664 1.40475i
\(573\) 0 0
\(574\) 27.3693 9.43318i 1.14237 0.393733i
\(575\) 6.41273i 0.267429i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 1.46543 + 2.21313i 0.0609541 + 0.0920543i
\(579\) 0 0
\(580\) −6.24621 2.64861i −0.259360 0.109978i
\(581\) −16.0000 4.13595i −0.663792 0.171588i
\(582\) 0 0
\(583\) 12.8255i 0.531176i
\(584\) −1.75379 9.43318i −0.0725723 0.390348i
\(585\) 0 0
\(586\) −8.24621 + 5.46026i −0.340648 + 0.225561i
\(587\) −38.2462 −1.57859 −0.789295 0.614014i \(-0.789554\pi\)
−0.789295 + 0.614014i \(0.789554\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 8.00000 5.29723i 0.329355 0.218083i
\(591\) 0 0
\(592\) 19.8078 + 20.4810i 0.814094 + 0.841763i
\(593\) 21.7238i 0.892088i 0.895011 + 0.446044i \(0.147168\pi\)
−0.895011 + 0.446044i \(0.852832\pi\)
\(594\) 0 0
\(595\) 18.8769 + 4.87962i 0.773877 + 0.200045i
\(596\) −7.80776 + 18.4130i −0.319818 + 0.754226i
\(597\) 0 0
\(598\) −14.2462 21.5150i −0.582571 0.879813i
\(599\) 19.2382i 0.786051i 0.919528 + 0.393026i \(0.128572\pi\)
−0.919528 + 0.393026i \(0.871428\pi\)
\(600\) 0 0
\(601\) 5.29723i 0.216078i −0.994147 0.108039i \(-0.965543\pi\)
0.994147 0.108039i \(-0.0344572\pi\)
\(602\) −28.6847 + 9.88653i −1.16910 + 0.402945i
\(603\) 0 0
\(604\) 14.9309 + 6.33122i 0.607528 + 0.257613i
\(605\) 3.18348i 0.129427i
\(606\) 0 0
\(607\) 33.6155 1.36441 0.682206 0.731160i \(-0.261021\pi\)
0.682206 + 0.731160i \(0.261021\pi\)
\(608\) −1.36932 + 6.20393i −0.0555331 + 0.251602i
\(609\) 0 0
\(610\) −12.4924 18.8664i −0.505803 0.763876i
\(611\) 61.8963i 2.50406i
\(612\) 0 0
\(613\) −40.7386 −1.64542 −0.822709 0.568463i \(-0.807538\pi\)
−0.822709 + 0.568463i \(0.807538\pi\)
\(614\) −16.8769 25.4879i −0.681096 1.02861i
\(615\) 0 0
\(616\) 1.56155 22.5490i 0.0629168 0.908523i
\(617\) −15.7538 −0.634224 −0.317112 0.948388i \(-0.602713\pi\)
−0.317112 + 0.948388i \(0.602713\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −6.24621 9.43318i −0.250450 0.378236i
\(623\) 5.12311 19.8188i 0.205253 0.794025i
\(624\) 0 0
\(625\) −9.87689 −0.395076
\(626\) 30.2462 20.0276i 1.20888 0.800465i
\(627\) 0 0
\(628\) −7.61553 3.22925i −0.303893 0.128861i
\(629\) 30.9481i 1.23398i
\(630\) 0 0
\(631\) 17.9597i 0.714963i 0.933920 + 0.357481i \(0.116364\pi\)
−0.933920 + 0.357481i \(0.883636\pi\)
\(632\) −2.43845 13.1158i −0.0969962 0.521718i
\(633\) 0 0
\(634\) 14.4384 + 21.8053i 0.573424 + 0.865999i
\(635\) −32.9848 −1.30896
\(636\) 0 0
\(637\) −20.4924 + 36.9890i −0.811939 + 1.46556i
\(638\) 7.12311 4.71659i 0.282006 0.186732i
\(639\) 0 0
\(640\) 11.1231 15.6371i 0.439679 0.618111i
\(641\) 9.50758 0.375527 0.187763 0.982214i \(-0.439876\pi\)
0.187763 + 0.982214i \(0.439876\pi\)
\(642\) 0 0
\(643\) −29.6155 −1.16792 −0.583961 0.811782i \(-0.698498\pi\)
−0.583961 + 0.811782i \(0.698498\pi\)
\(644\) −12.6847 9.72350i −0.499846 0.383159i
\(645\) 0 0
\(646\) 5.75379 3.80989i 0.226380 0.149898i
\(647\) 32.9848 1.29677 0.648384 0.761313i \(-0.275445\pi\)
0.648384 + 0.761313i \(0.275445\pi\)
\(648\) 0 0
\(649\) 12.0818i 0.474252i
\(650\) 15.1231 10.0138i 0.593177 0.392774i
\(651\) 0 0
\(652\) −21.1771 8.97983i −0.829358 0.351677i
\(653\) 32.7386 1.28116 0.640581 0.767891i \(-0.278694\pi\)
0.640581 + 0.767891i \(0.278694\pi\)
\(654\) 0 0
\(655\) 37.7327i 1.47434i
\(656\) −22.2462 + 21.5150i −0.868569 + 0.840018i
\(657\) 0 0
\(658\) −12.4924 36.2454i −0.487005 1.41299i
\(659\) 38.1045i 1.48434i −0.670210 0.742171i \(-0.733796\pi\)
0.670210 0.742171i \(-0.266204\pi\)
\(660\) 0 0
\(661\) 2.64861i 0.103019i 0.998673 + 0.0515096i \(0.0164033\pi\)
−0.998673 + 0.0515096i \(0.983597\pi\)
\(662\) −6.43845 + 4.26324i −0.250237 + 0.165696i
\(663\) 0 0
\(664\) 17.3693 3.22925i 0.674060 0.125319i
\(665\) 1.26137 4.87962i 0.0489137 0.189223i
\(666\) 0 0
\(667\) 6.04090i 0.233904i
\(668\) 1.75379 4.13595i 0.0678561 0.160025i
\(669\) 0 0
\(670\) −2.73863 4.13595i −0.105803 0.159786i
\(671\) 28.4924 1.09994
\(672\) 0 0
\(673\) 29.8617 1.15109 0.575543 0.817772i \(-0.304791\pi\)
0.575543 + 0.817772i \(0.304791\pi\)
\(674\) 6.43845 + 9.72350i 0.248000 + 0.374535i
\(675\) 0 0
\(676\) 18.3423 43.2566i 0.705474 1.66372i
\(677\) 32.6443i 1.25462i 0.778769 + 0.627311i \(0.215844\pi\)
−0.778769 + 0.627311i \(0.784156\pi\)
\(678\) 0 0
\(679\) −5.75379 + 22.2586i −0.220810 + 0.854208i
\(680\) −20.4924 + 3.80989i −0.785849 + 0.146103i
\(681\) 0 0
\(682\) 0 0
\(683\) 29.0890i 1.11306i 0.830828 + 0.556529i \(0.187867\pi\)
−0.830828 + 0.556529i \(0.812133\pi\)
\(684\) 0 0
\(685\) 27.5559i 1.05286i
\(686\) −4.53457 + 25.7961i −0.173131 + 0.984899i
\(687\) 0 0
\(688\) 23.3153 22.5490i 0.888889 0.859671i
\(689\) 25.6509i 0.977222i
\(690\) 0 0
\(691\) −12.0000 −0.456502 −0.228251 0.973602i \(-0.573301\pi\)
−0.228251 + 0.973602i \(0.573301\pi\)
\(692\) 15.6155 + 6.62153i 0.593613 + 0.251713i
\(693\) 0 0
\(694\) −40.9309 + 27.1025i −1.55371 + 1.02880i
\(695\) 20.3537i 0.772060i
\(696\) 0 0
\(697\) 33.6155 1.27328
\(698\) 4.87689 3.22925i 0.184593 0.122229i
\(699\) 0 0
\(700\) 6.83475 8.91618i 0.258329 0.337000i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 0 0
\(703\) −8.00000 −0.301726
\(704\) 8.68466 + 22.5490i 0.327315 + 0.849846i
\(705\) 0 0
\(706\) 7.36932 4.87962i 0.277348 0.183647i
\(707\) −4.63068 + 17.9139i −0.174155 + 0.673721i
\(708\) 0 0
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 16.4924 + 24.9073i 0.618950 + 0.934752i
\(711\) 0 0
\(712\) 4.00000 + 21.5150i 0.149906 + 0.806308i
\(713\) 0 0
\(714\) 0 0
\(715\) 30.9481i 1.15740i
\(716\) 4.19224 + 1.77766i 0.156671 + 0.0664341i
\(717\) 0 0
\(718\) −1.31534 + 0.870958i −0.0490881 + 0.0325039i
\(719\) −4.49242 −0.167539 −0.0837695 0.996485i \(-0.526696\pi\)
−0.0837695 + 0.996485i \(0.526696\pi\)
\(720\) 0 0
\(721\) −20.4924 5.29723i −0.763178 0.197279i
\(722\) 13.8499 + 20.9165i 0.515440 + 0.778430i
\(723\) 0 0
\(724\) 11.1231 + 4.71659i 0.413387 + 0.175291i
\(725\) 4.24621 0.157700
\(726\) 0 0
\(727\) 32.9848 1.22334 0.611670 0.791113i \(-0.290498\pi\)
0.611670 + 0.791113i \(0.290498\pi\)
\(728\) 3.12311 45.0979i 0.115750 1.67144i
\(729\) 0 0
\(730\) −4.49242 6.78456i −0.166272 0.251108i
\(731\) −35.2311 −1.30307
\(732\) 0 0
\(733\) 16.6354i 0.614441i 0.951638 + 0.307220i \(0.0993989\pi\)
−0.951638 + 0.307220i \(0.900601\pi\)
\(734\) −6.73863 10.1768i −0.248728 0.375634i
\(735\) 0 0
\(736\) 16.6847 + 3.68260i 0.615005 + 0.135742i
\(737\) 6.24621 0.230082
\(738\) 0 0
\(739\) 5.87787i 0.216221i −0.994139 0.108110i \(-0.965520\pi\)
0.994139 0.108110i \(-0.0344800\pi\)
\(740\) 22.2462 + 9.43318i 0.817787 + 0.346771i
\(741\) 0 0
\(742\) 5.17708 + 15.0207i 0.190057 + 0.551428i
\(743\) 13.6149i 0.499482i −0.968313 0.249741i \(-0.919654\pi\)
0.968313 0.249741i \(-0.0803455\pi\)
\(744\) 0 0
\(745\) 16.9614i 0.621418i
\(746\) 7.80776 + 11.7915i 0.285863 + 0.431716i
\(747\) 0 0
\(748\) 10.2462 24.1636i 0.374639 0.883508i
\(749\) −3.75379 + 14.5216i −0.137160 + 0.530608i
\(750\) 0 0
\(751\) 30.7851i 1.12336i −0.827353 0.561682i \(-0.810154\pi\)
0.827353 0.561682i \(-0.189846\pi\)
\(752\) 28.4924 + 29.4608i 1.03901 + 1.07433i
\(753\) 0 0
\(754\) 14.2462 9.43318i 0.518816 0.343536i
\(755\) 13.7538 0.500552
\(756\) 0 0
\(757\) 30.9848 1.12616 0.563082 0.826401i \(-0.309616\pi\)
0.563082 + 0.826401i \(0.309616\pi\)
\(758\) 22.0540 14.6031i 0.801036 0.530409i
\(759\) 0 0
\(760\) 0.984845 + 5.29723i 0.0357241 + 0.192151i
\(761\) 33.8056i 1.22545i 0.790296 + 0.612725i \(0.209927\pi\)
−0.790296 + 0.612725i \(0.790073\pi\)
\(762\) 0 0
\(763\) −21.1231 5.46026i −0.764708 0.197675i
\(764\) −16.6847 7.07488i −0.603630 0.255960i
\(765\) 0 0
\(766\) 20.4924 + 30.9481i 0.740421 + 1.11820i
\(767\) 24.1636i 0.872496i
\(768\) 0 0
\(769\) 44.5173i 1.60533i 0.596427 + 0.802667i \(0.296586\pi\)
−0.596427 + 0.802667i \(0.703414\pi\)
\(770\) −6.24621 18.1227i −0.225098 0.653096i
\(771\) 0 0
\(772\) −7.31534 + 17.2517i −0.263285 + 0.620903i
\(773\) 1.69614i 0.0610060i 0.999535 + 0.0305030i \(0.00971091\pi\)
−0.999535 + 0.0305030i \(0.990289\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −4.49242 24.1636i −0.161269 0.867422i
\(777\) 0 0
\(778\) 0.192236 + 0.290319i 0.00689199 + 0.0104085i
\(779\) 8.68951i 0.311334i
\(780\) 0 0
\(781\) −37.6155 −1.34599
\(782\) −10.2462 15.4741i −0.366404 0.553352i
\(783\) 0 0
\(784\) −7.27320 27.0389i −0.259757 0.965674i
\(785\) −7.01515 −0.250382
\(786\) 0 0
\(787\) −20.9848 −0.748029 −0.374014 0.927423i \(-0.622019\pi\)
−0.374014 + 0.927423i \(0.622019\pi\)
\(788\) 0.192236 0.453349i 0.00684812 0.0161499i
\(789\) 0 0
\(790\) −6.24621 9.43318i −0.222230 0.335617i
\(791\) 31.3693 + 8.10887i 1.11536 + 0.288318i