Properties

Label 1386.2.ba.a.1187.4
Level $1386$
Weight $2$
Character 1386.1187
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1187.4
Character \(\chi\) \(=\) 1386.1187
Dual form 1386.2.ba.a.989.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.87061 + 1.08000i) q^{5} +(2.63666 + 0.219149i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.87061 + 1.08000i) q^{5} +(2.63666 + 0.219149i) q^{7} +1.00000 q^{8} +(1.87061 + 1.08000i) q^{10} +(-2.19270 - 2.48839i) q^{11} -3.53956i q^{13} +(-1.12854 - 2.39299i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.82953 + 6.63294i) q^{17} +(1.66946 - 0.963864i) q^{19} -2.15999i q^{20} +(-1.05866 + 3.14313i) q^{22} +(7.21952 - 4.16819i) q^{23} +(-0.167211 + 0.289618i) q^{25} +(-3.06535 + 1.76978i) q^{26} +(-1.50812 + 2.17384i) q^{28} -4.79594 q^{29} +(2.97154 - 5.14685i) q^{31} +(-0.500000 + 0.866025i) q^{32} +7.65906 q^{34} +(-5.16884 + 2.43764i) q^{35} +(-1.55673 - 2.69634i) q^{37} +(-1.66946 - 0.963864i) q^{38} +(-1.87061 + 1.08000i) q^{40} +9.00600 q^{41} +2.48924i q^{43} +(3.25136 - 0.654737i) q^{44} +(-7.21952 - 4.16819i) q^{46} +(7.34212 - 4.23898i) q^{47} +(6.90395 + 1.15564i) q^{49} +0.334422 q^{50} +(3.06535 + 1.76978i) q^{52} +(-4.83344 - 2.79059i) q^{53} +(6.78914 + 2.28670i) q^{55} +(2.63666 + 0.219149i) q^{56} +(2.39797 + 4.15341i) q^{58} +(-3.95479 - 2.28330i) q^{59} +(9.71354 - 5.60811i) q^{61} -5.94307 q^{62} +1.00000 q^{64} +(3.82272 + 6.62114i) q^{65} +(1.46173 - 2.53179i) q^{67} +(-3.82953 - 6.63294i) q^{68} +(4.69548 + 3.25753i) q^{70} -14.9539i q^{71} +(0.486281 + 0.280755i) q^{73} +(-1.55673 + 2.69634i) q^{74} +1.92773i q^{76} +(-5.23607 - 7.04156i) q^{77} +(6.63288 - 3.82950i) q^{79} +(1.87061 + 1.08000i) q^{80} +(-4.50300 - 7.79943i) q^{82} +8.45117 q^{83} -16.5435i q^{85} +(2.15574 - 1.24462i) q^{86} +(-2.19270 - 2.48839i) q^{88} +(-0.609275 + 0.351765i) q^{89} +(0.775692 - 9.33262i) q^{91} +8.33638i q^{92} +(-7.34212 - 4.23898i) q^{94} +(-2.08194 + 3.60603i) q^{95} -1.23783 q^{97} +(-2.45116 - 6.55682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.87061 + 1.08000i −0.836562 + 0.482990i −0.856094 0.516820i \(-0.827116\pi\)
0.0195319 + 0.999809i \(0.493782\pi\)
\(6\) 0 0
\(7\) 2.63666 + 0.219149i 0.996564 + 0.0828306i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.87061 + 1.08000i 0.591539 + 0.341525i
\(11\) −2.19270 2.48839i −0.661123 0.750277i
\(12\) 0 0
\(13\) 3.53956i 0.981698i −0.871245 0.490849i \(-0.836687\pi\)
0.871245 0.490849i \(-0.163313\pi\)
\(14\) −1.12854 2.39299i −0.301615 0.639553i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.82953 + 6.63294i −0.928798 + 1.60873i −0.143461 + 0.989656i \(0.545823\pi\)
−0.785336 + 0.619069i \(0.787510\pi\)
\(18\) 0 0
\(19\) 1.66946 0.963864i 0.383001 0.221126i −0.296122 0.955150i \(-0.595694\pi\)
0.679123 + 0.734024i \(0.262360\pi\)
\(20\) 2.15999i 0.482990i
\(21\) 0 0
\(22\) −1.05866 + 3.14313i −0.225707 + 0.670117i
\(23\) 7.21952 4.16819i 1.50537 0.869128i 0.505394 0.862889i \(-0.331347\pi\)
0.999981 0.00623916i \(-0.00198600\pi\)
\(24\) 0 0
\(25\) −0.167211 + 0.289618i −0.0334422 + 0.0579236i
\(26\) −3.06535 + 1.76978i −0.601165 + 0.347083i
\(27\) 0 0
\(28\) −1.50812 + 2.17384i −0.285008 + 0.410817i
\(29\) −4.79594 −0.890584 −0.445292 0.895385i \(-0.646900\pi\)
−0.445292 + 0.895385i \(0.646900\pi\)
\(30\) 0 0
\(31\) 2.97154 5.14685i 0.533704 0.924402i −0.465521 0.885037i \(-0.654133\pi\)
0.999225 0.0393651i \(-0.0125335\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 7.65906 1.31352
\(35\) −5.16884 + 2.43764i −0.873694 + 0.412037i
\(36\) 0 0
\(37\) −1.55673 2.69634i −0.255926 0.443276i 0.709221 0.704986i \(-0.249047\pi\)
−0.965147 + 0.261710i \(0.915714\pi\)
\(38\) −1.66946 0.963864i −0.270822 0.156359i
\(39\) 0 0
\(40\) −1.87061 + 1.08000i −0.295769 + 0.170763i
\(41\) 9.00600 1.40650 0.703251 0.710942i \(-0.251731\pi\)
0.703251 + 0.710942i \(0.251731\pi\)
\(42\) 0 0
\(43\) 2.48924i 0.379605i 0.981822 + 0.189803i \(0.0607848\pi\)
−0.981822 + 0.189803i \(0.939215\pi\)
\(44\) 3.25136 0.654737i 0.490160 0.0987053i
\(45\) 0 0
\(46\) −7.21952 4.16819i −1.06446 0.614566i
\(47\) 7.34212 4.23898i 1.07096 0.618318i 0.142515 0.989793i \(-0.454481\pi\)
0.928443 + 0.371474i \(0.121148\pi\)
\(48\) 0 0
\(49\) 6.90395 + 1.15564i 0.986278 + 0.165092i
\(50\) 0.334422 0.0472945
\(51\) 0 0
\(52\) 3.06535 + 1.76978i 0.425088 + 0.245424i
\(53\) −4.83344 2.79059i −0.663923 0.383316i 0.129847 0.991534i \(-0.458551\pi\)
−0.793770 + 0.608218i \(0.791885\pi\)
\(54\) 0 0
\(55\) 6.78914 + 2.28670i 0.915447 + 0.308338i
\(56\) 2.63666 + 0.219149i 0.352338 + 0.0292850i
\(57\) 0 0
\(58\) 2.39797 + 4.15341i 0.314869 + 0.545369i
\(59\) −3.95479 2.28330i −0.514870 0.297260i 0.219963 0.975508i \(-0.429406\pi\)
−0.734833 + 0.678248i \(0.762740\pi\)
\(60\) 0 0
\(61\) 9.71354 5.60811i 1.24369 0.718045i 0.273847 0.961773i \(-0.411704\pi\)
0.969844 + 0.243728i \(0.0783704\pi\)
\(62\) −5.94307 −0.754771
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.82272 + 6.62114i 0.474150 + 0.821252i
\(66\) 0 0
\(67\) 1.46173 2.53179i 0.178578 0.309307i −0.762815 0.646616i \(-0.776183\pi\)
0.941394 + 0.337309i \(0.109517\pi\)
\(68\) −3.82953 6.63294i −0.464399 0.804363i
\(69\) 0 0
\(70\) 4.69548 + 3.25753i 0.561217 + 0.389349i
\(71\) 14.9539i 1.77470i −0.461093 0.887352i \(-0.652542\pi\)
0.461093 0.887352i \(-0.347458\pi\)
\(72\) 0 0
\(73\) 0.486281 + 0.280755i 0.0569149 + 0.0328598i 0.528187 0.849128i \(-0.322872\pi\)
−0.471273 + 0.881988i \(0.656205\pi\)
\(74\) −1.55673 + 2.69634i −0.180967 + 0.313444i
\(75\) 0 0
\(76\) 1.92773i 0.221126i
\(77\) −5.23607 7.04156i −0.596705 0.802460i
\(78\) 0 0
\(79\) 6.63288 3.82950i 0.746258 0.430852i −0.0780826 0.996947i \(-0.524880\pi\)
0.824340 + 0.566095i \(0.191546\pi\)
\(80\) 1.87061 + 1.08000i 0.209141 + 0.120747i
\(81\) 0 0
\(82\) −4.50300 7.79943i −0.497273 0.861303i
\(83\) 8.45117 0.927637 0.463818 0.885930i \(-0.346479\pi\)
0.463818 + 0.885930i \(0.346479\pi\)
\(84\) 0 0
\(85\) 16.5435i 1.79440i
\(86\) 2.15574 1.24462i 0.232460 0.134211i
\(87\) 0 0
\(88\) −2.19270 2.48839i −0.233742 0.265263i
\(89\) −0.609275 + 0.351765i −0.0645830 + 0.0372870i −0.531944 0.846780i \(-0.678538\pi\)
0.467361 + 0.884067i \(0.345205\pi\)
\(90\) 0 0
\(91\) 0.775692 9.33262i 0.0813146 0.978324i
\(92\) 8.33638i 0.869128i
\(93\) 0 0
\(94\) −7.34212 4.23898i −0.757282 0.437217i
\(95\) −2.08194 + 3.60603i −0.213603 + 0.369971i
\(96\) 0 0
\(97\) −1.23783 −0.125682 −0.0628412 0.998024i \(-0.520016\pi\)
−0.0628412 + 0.998024i \(0.520016\pi\)
\(98\) −2.45116 6.55682i −0.247604 0.662338i
\(99\) 0 0
\(100\) −0.167211 0.289618i −0.0167211 0.0289618i
\(101\) 1.57357 2.72549i 0.156576 0.271197i −0.777056 0.629431i \(-0.783288\pi\)
0.933632 + 0.358235i \(0.116621\pi\)
\(102\) 0 0
\(103\) −0.118651 0.205510i −0.0116911 0.0202495i 0.860121 0.510091i \(-0.170388\pi\)
−0.871812 + 0.489841i \(0.837055\pi\)
\(104\) 3.53956i 0.347083i
\(105\) 0 0
\(106\) 5.58117i 0.542091i
\(107\) −5.40857 9.36792i −0.522866 0.905631i −0.999646 0.0266081i \(-0.991529\pi\)
0.476780 0.879023i \(-0.341804\pi\)
\(108\) 0 0
\(109\) −3.77972 2.18222i −0.362032 0.209019i 0.307940 0.951406i \(-0.400360\pi\)
−0.669972 + 0.742387i \(0.733694\pi\)
\(110\) −1.41423 7.02291i −0.134841 0.669609i
\(111\) 0 0
\(112\) −1.12854 2.39299i −0.106637 0.226116i
\(113\) 17.7468i 1.66948i −0.550648 0.834738i \(-0.685619\pi\)
0.550648 0.834738i \(-0.314381\pi\)
\(114\) 0 0
\(115\) −9.00327 + 15.5941i −0.839560 + 1.45416i
\(116\) 2.39797 4.15341i 0.222646 0.385634i
\(117\) 0 0
\(118\) 4.56660i 0.420389i
\(119\) −11.5508 + 16.6496i −1.05886 + 1.52626i
\(120\) 0 0
\(121\) −1.38416 + 10.9126i −0.125832 + 0.992052i
\(122\) −9.71354 5.60811i −0.879422 0.507735i
\(123\) 0 0
\(124\) 2.97154 + 5.14685i 0.266852 + 0.462201i
\(125\) 11.5223i 1.03059i
\(126\) 0 0
\(127\) 12.6515i 1.12264i 0.827598 + 0.561322i \(0.189707\pi\)
−0.827598 + 0.561322i \(0.810293\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 3.82272 6.62114i 0.335275 0.580713i
\(131\) −1.52954 2.64924i −0.133637 0.231466i 0.791439 0.611248i \(-0.209332\pi\)
−0.925076 + 0.379782i \(0.875999\pi\)
\(132\) 0 0
\(133\) 4.61303 2.17552i 0.400001 0.188642i
\(134\) −2.92346 −0.252548
\(135\) 0 0
\(136\) −3.82953 + 6.63294i −0.328380 + 0.568770i
\(137\) 6.20778 + 3.58406i 0.530366 + 0.306207i 0.741166 0.671322i \(-0.234273\pi\)
−0.210799 + 0.977529i \(0.567607\pi\)
\(138\) 0 0
\(139\) 2.77438i 0.235320i 0.993054 + 0.117660i \(0.0375393\pi\)
−0.993054 + 0.117660i \(0.962461\pi\)
\(140\) 0.473361 5.69517i 0.0400063 0.481330i
\(141\) 0 0
\(142\) −12.9505 + 7.47696i −1.08678 + 0.627453i
\(143\) −8.80781 + 7.76119i −0.736546 + 0.649023i
\(144\) 0 0
\(145\) 8.97134 5.17960i 0.745029 0.430143i
\(146\) 0.561509i 0.0464708i
\(147\) 0 0
\(148\) 3.11347 0.255926
\(149\) 11.7155 + 20.2918i 0.959770 + 1.66237i 0.723054 + 0.690792i \(0.242738\pi\)
0.236716 + 0.971579i \(0.423929\pi\)
\(150\) 0 0
\(151\) −7.98285 4.60890i −0.649635 0.375067i 0.138681 0.990337i \(-0.455714\pi\)
−0.788317 + 0.615270i \(0.789047\pi\)
\(152\) 1.66946 0.963864i 0.135411 0.0781797i
\(153\) 0 0
\(154\) −3.48014 + 8.05535i −0.280437 + 0.649118i
\(155\) 12.8370i 1.03109i
\(156\) 0 0
\(157\) −11.5804 + 20.0579i −0.924218 + 1.60079i −0.131403 + 0.991329i \(0.541948\pi\)
−0.792814 + 0.609463i \(0.791385\pi\)
\(158\) −6.63288 3.82950i −0.527684 0.304658i
\(159\) 0 0
\(160\) 2.15999i 0.170763i
\(161\) 19.9489 9.40795i 1.57219 0.741450i
\(162\) 0 0
\(163\) −9.30376 16.1146i −0.728727 1.26219i −0.957422 0.288693i \(-0.906779\pi\)
0.228695 0.973498i \(-0.426554\pi\)
\(164\) −4.50300 + 7.79943i −0.351625 + 0.609033i
\(165\) 0 0
\(166\) −4.22559 7.31893i −0.327969 0.568059i
\(167\) 21.3908 1.65527 0.827636 0.561265i \(-0.189685\pi\)
0.827636 + 0.561265i \(0.189685\pi\)
\(168\) 0 0
\(169\) 0.471500 0.0362692
\(170\) −14.3271 + 8.27177i −1.09884 + 0.634416i
\(171\) 0 0
\(172\) −2.15574 1.24462i −0.164374 0.0949013i
\(173\) 0.430083 + 0.744926i 0.0326986 + 0.0566356i 0.881912 0.471415i \(-0.156257\pi\)
−0.849213 + 0.528050i \(0.822923\pi\)
\(174\) 0 0
\(175\) −0.504349 + 0.726981i −0.0381252 + 0.0549546i
\(176\) −1.05866 + 3.14313i −0.0797994 + 0.236922i
\(177\) 0 0
\(178\) 0.609275 + 0.351765i 0.0456671 + 0.0263659i
\(179\) 9.01762 + 5.20633i 0.674009 + 0.389139i 0.797594 0.603195i \(-0.206106\pi\)
−0.123585 + 0.992334i \(0.539439\pi\)
\(180\) 0 0
\(181\) −7.02598 −0.522237 −0.261118 0.965307i \(-0.584091\pi\)
−0.261118 + 0.965307i \(0.584091\pi\)
\(182\) −8.47013 + 3.99454i −0.627848 + 0.296095i
\(183\) 0 0
\(184\) 7.21952 4.16819i 0.532230 0.307283i
\(185\) 5.82409 + 3.36254i 0.428196 + 0.247219i
\(186\) 0 0
\(187\) 24.9023 5.01467i 1.82104 0.366709i
\(188\) 8.47795i 0.618318i
\(189\) 0 0
\(190\) 4.16388 0.302080
\(191\) −4.03039 + 2.32695i −0.291629 + 0.168372i −0.638676 0.769476i \(-0.720518\pi\)
0.347047 + 0.937848i \(0.387184\pi\)
\(192\) 0 0
\(193\) −13.5837 7.84257i −0.977778 0.564521i −0.0761796 0.997094i \(-0.524272\pi\)
−0.901599 + 0.432574i \(0.857606\pi\)
\(194\) 0.618915 + 1.07199i 0.0444355 + 0.0769645i
\(195\) 0 0
\(196\) −4.45279 + 5.40117i −0.318056 + 0.385798i
\(197\) −6.39141 −0.455369 −0.227684 0.973735i \(-0.573115\pi\)
−0.227684 + 0.973735i \(0.573115\pi\)
\(198\) 0 0
\(199\) 12.8469 22.2515i 0.910694 1.57737i 0.0976086 0.995225i \(-0.468881\pi\)
0.813086 0.582144i \(-0.197786\pi\)
\(200\) −0.167211 + 0.289618i −0.0118236 + 0.0204791i
\(201\) 0 0
\(202\) −3.14713 −0.221431
\(203\) −12.6453 1.05103i −0.887524 0.0737676i
\(204\) 0 0
\(205\) −16.8467 + 9.72646i −1.17663 + 0.679326i
\(206\) −0.118651 + 0.205510i −0.00826683 + 0.0143186i
\(207\) 0 0
\(208\) −3.06535 + 1.76978i −0.212544 + 0.122712i
\(209\) −6.05909 2.04081i −0.419116 0.141166i
\(210\) 0 0
\(211\) 16.6604i 1.14695i 0.819224 + 0.573474i \(0.194405\pi\)
−0.819224 + 0.573474i \(0.805595\pi\)
\(212\) 4.83344 2.79059i 0.331962 0.191658i
\(213\) 0 0
\(214\) −5.40857 + 9.36792i −0.369722 + 0.640378i
\(215\) −2.68837 4.65639i −0.183345 0.317563i
\(216\) 0 0
\(217\) 8.96286 12.9193i 0.608438 0.877018i
\(218\) 4.36445i 0.295598i
\(219\) 0 0
\(220\) −5.37491 + 4.73621i −0.362376 + 0.319316i
\(221\) 23.4777 + 13.5549i 1.57928 + 0.911799i
\(222\) 0 0
\(223\) 9.81557 0.657299 0.328650 0.944452i \(-0.393406\pi\)
0.328650 + 0.944452i \(0.393406\pi\)
\(224\) −1.50812 + 2.17384i −0.100765 + 0.145246i
\(225\) 0 0
\(226\) −15.3691 + 8.87338i −1.02234 + 0.590249i
\(227\) 5.08719 8.81128i 0.337649 0.584825i −0.646341 0.763049i \(-0.723702\pi\)
0.983990 + 0.178224i \(0.0570350\pi\)
\(228\) 0 0
\(229\) −13.3669 23.1522i −0.883310 1.52994i −0.847639 0.530574i \(-0.821976\pi\)
−0.0356712 0.999364i \(-0.511357\pi\)
\(230\) 18.0065 1.18732
\(231\) 0 0
\(232\) −4.79594 −0.314869
\(233\) −2.09943 3.63631i −0.137538 0.238223i 0.789026 0.614360i \(-0.210586\pi\)
−0.926564 + 0.376137i \(0.877252\pi\)
\(234\) 0 0
\(235\) −9.15617 + 15.8589i −0.597283 + 1.03452i
\(236\) 3.95479 2.28330i 0.257435 0.148630i
\(237\) 0 0
\(238\) 20.1943 + 1.67848i 1.30900 + 0.108800i
\(239\) −19.4583 −1.25865 −0.629326 0.777141i \(-0.716669\pi\)
−0.629326 + 0.777141i \(0.716669\pi\)
\(240\) 0 0
\(241\) −4.53621 2.61898i −0.292203 0.168704i 0.346732 0.937964i \(-0.387291\pi\)
−0.638935 + 0.769261i \(0.720625\pi\)
\(242\) 10.1426 4.25757i 0.651993 0.273687i
\(243\) 0 0
\(244\) 11.2162i 0.718045i
\(245\) −14.1627 + 5.29449i −0.904821 + 0.338252i
\(246\) 0 0
\(247\) −3.41166 5.90916i −0.217079 0.375991i
\(248\) 2.97154 5.14685i 0.188693 0.326825i
\(249\) 0 0
\(250\) −9.97863 + 5.76116i −0.631104 + 0.364368i
\(251\) 17.2995i 1.09193i 0.837807 + 0.545967i \(0.183838\pi\)
−0.837807 + 0.545967i \(0.816162\pi\)
\(252\) 0 0
\(253\) −26.2023 8.82539i −1.64732 0.554848i
\(254\) 10.9566 6.32577i 0.687476 0.396914i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −22.9253 + 13.2359i −1.43004 + 0.825635i −0.997123 0.0757980i \(-0.975850\pi\)
−0.432919 + 0.901433i \(0.642516\pi\)
\(258\) 0 0
\(259\) −3.51368 7.45050i −0.218329 0.462951i
\(260\) −7.64544 −0.474150
\(261\) 0 0
\(262\) −1.52954 + 2.64924i −0.0944954 + 0.163671i
\(263\) −6.30039 + 10.9126i −0.388499 + 0.672900i −0.992248 0.124275i \(-0.960340\pi\)
0.603749 + 0.797175i \(0.293673\pi\)
\(264\) 0 0
\(265\) 12.0553 0.740551
\(266\) −4.19057 2.90724i −0.256940 0.178254i
\(267\) 0 0
\(268\) 1.46173 + 2.53179i 0.0892892 + 0.154653i
\(269\) 16.2413 + 9.37693i 0.990251 + 0.571722i 0.905349 0.424668i \(-0.139609\pi\)
0.0849016 + 0.996389i \(0.472942\pi\)
\(270\) 0 0
\(271\) −3.87768 + 2.23878i −0.235552 + 0.135996i −0.613131 0.789981i \(-0.710090\pi\)
0.377579 + 0.925978i \(0.376757\pi\)
\(272\) 7.65906 0.464399
\(273\) 0 0
\(274\) 7.16812i 0.433042i
\(275\) 1.08733 0.218959i 0.0655682 0.0132037i
\(276\) 0 0
\(277\) 8.09768 + 4.67520i 0.486543 + 0.280905i 0.723139 0.690703i \(-0.242699\pi\)
−0.236596 + 0.971608i \(0.576032\pi\)
\(278\) 2.40268 1.38719i 0.144103 0.0831981i
\(279\) 0 0
\(280\) −5.16884 + 2.43764i −0.308897 + 0.145677i
\(281\) 23.8976 1.42561 0.712807 0.701361i \(-0.247424\pi\)
0.712807 + 0.701361i \(0.247424\pi\)
\(282\) 0 0
\(283\) 15.6461 + 9.03326i 0.930063 + 0.536972i 0.886831 0.462093i \(-0.152901\pi\)
0.0432312 + 0.999065i \(0.486235\pi\)
\(284\) 12.9505 + 7.47696i 0.768469 + 0.443676i
\(285\) 0 0
\(286\) 11.1253 + 3.74719i 0.657852 + 0.221576i
\(287\) 23.7458 + 1.97366i 1.40167 + 0.116501i
\(288\) 0 0
\(289\) −20.8306 36.0797i −1.22533 2.12234i
\(290\) −8.97134 5.17960i −0.526815 0.304157i
\(291\) 0 0
\(292\) −0.486281 + 0.280755i −0.0284574 + 0.0164299i
\(293\) 16.3262 0.953785 0.476893 0.878962i \(-0.341763\pi\)
0.476893 + 0.878962i \(0.341763\pi\)
\(294\) 0 0
\(295\) 9.86383 0.574294
\(296\) −1.55673 2.69634i −0.0904834 0.156722i
\(297\) 0 0
\(298\) 11.7155 20.2918i 0.678660 1.17547i
\(299\) −14.7536 25.5539i −0.853221 1.47782i
\(300\) 0 0
\(301\) −0.545514 + 6.56327i −0.0314429 + 0.378301i
\(302\) 9.21781i 0.530425i
\(303\) 0 0
\(304\) −1.66946 0.963864i −0.0957502 0.0552814i
\(305\) −12.1135 + 20.9812i −0.693617 + 1.20138i
\(306\) 0 0
\(307\) 6.91177i 0.394476i 0.980356 + 0.197238i \(0.0631971\pi\)
−0.980356 + 0.197238i \(0.936803\pi\)
\(308\) 8.71621 1.01379i 0.496652 0.0577659i
\(309\) 0 0
\(310\) 11.1172 6.41850i 0.631413 0.364546i
\(311\) 0.717875 + 0.414465i 0.0407069 + 0.0235022i 0.520215 0.854035i \(-0.325852\pi\)
−0.479508 + 0.877537i \(0.659185\pi\)
\(312\) 0 0
\(313\) 8.66175 + 15.0026i 0.489591 + 0.847996i 0.999928 0.0119780i \(-0.00381282\pi\)
−0.510337 + 0.859974i \(0.670479\pi\)
\(314\) 23.1608 1.30704
\(315\) 0 0
\(316\) 7.65899i 0.430852i
\(317\) 24.1286 13.9306i 1.35520 0.782423i 0.366224 0.930527i \(-0.380650\pi\)
0.988972 + 0.148104i \(0.0473170\pi\)
\(318\) 0 0
\(319\) 10.5160 + 11.9342i 0.588786 + 0.668185i
\(320\) −1.87061 + 1.08000i −0.104570 + 0.0603737i
\(321\) 0 0
\(322\) −18.1220 12.5723i −1.00990 0.700624i
\(323\) 14.7646i 0.821524i
\(324\) 0 0
\(325\) 1.02512 + 0.591854i 0.0568635 + 0.0328302i
\(326\) −9.30376 + 16.1146i −0.515288 + 0.892504i
\(327\) 0 0
\(328\) 9.00600 0.497273
\(329\) 20.2876 9.56772i 1.11849 0.527485i
\(330\) 0 0
\(331\) 2.76388 + 4.78718i 0.151916 + 0.263127i 0.931932 0.362633i \(-0.118122\pi\)
−0.780015 + 0.625760i \(0.784789\pi\)
\(332\) −4.22559 + 7.31893i −0.231909 + 0.401679i
\(333\) 0 0
\(334\) −10.6954 18.5250i −0.585227 1.01364i
\(335\) 6.31465i 0.345006i
\(336\) 0 0
\(337\) 23.7409i 1.29325i −0.762809 0.646624i \(-0.776180\pi\)
0.762809 0.646624i \(-0.223820\pi\)
\(338\) −0.235750 0.408331i −0.0128231 0.0222103i
\(339\) 0 0
\(340\) 14.3271 + 8.27177i 0.776997 + 0.448600i
\(341\) −19.3230 + 3.89115i −1.04640 + 0.210718i
\(342\) 0 0
\(343\) 17.9501 + 4.56003i 0.969214 + 0.246219i
\(344\) 2.48924i 0.134211i
\(345\) 0 0
\(346\) 0.430083 0.744926i 0.0231214 0.0400475i
\(347\) −10.1900 + 17.6496i −0.547027 + 0.947478i 0.451450 + 0.892297i \(0.350907\pi\)
−0.998476 + 0.0551813i \(0.982426\pi\)
\(348\) 0 0
\(349\) 11.3460i 0.607338i 0.952778 + 0.303669i \(0.0982118\pi\)
−0.952778 + 0.303669i \(0.901788\pi\)
\(350\) 0.881758 + 0.0732884i 0.0471319 + 0.00391743i
\(351\) 0 0
\(352\) 3.25136 0.654737i 0.173298 0.0348976i
\(353\) 8.88905 + 5.13209i 0.473116 + 0.273154i 0.717543 0.696514i \(-0.245267\pi\)
−0.244427 + 0.969668i \(0.578600\pi\)
\(354\) 0 0
\(355\) 16.1502 + 27.9730i 0.857163 + 1.48465i
\(356\) 0.703530i 0.0372870i
\(357\) 0 0
\(358\) 10.4127i 0.550326i
\(359\) 8.12523 + 14.0733i 0.428833 + 0.742761i 0.996770 0.0803116i \(-0.0255915\pi\)
−0.567937 + 0.823072i \(0.692258\pi\)
\(360\) 0 0
\(361\) −7.64193 + 13.2362i −0.402207 + 0.696643i
\(362\) 3.51299 + 6.08468i 0.184639 + 0.319803i
\(363\) 0 0
\(364\) 7.69444 + 5.33808i 0.403298 + 0.279791i
\(365\) −1.21286 −0.0634838
\(366\) 0 0
\(367\) −18.3681 + 31.8145i −0.958808 + 1.66070i −0.233407 + 0.972379i \(0.574987\pi\)
−0.725402 + 0.688326i \(0.758346\pi\)
\(368\) −7.21952 4.16819i −0.376344 0.217282i
\(369\) 0 0
\(370\) 6.72508i 0.349620i
\(371\) −12.1326 8.41707i −0.629892 0.436992i
\(372\) 0 0
\(373\) −0.721045 + 0.416295i −0.0373343 + 0.0215550i −0.518551 0.855047i \(-0.673528\pi\)
0.481217 + 0.876602i \(0.340195\pi\)
\(374\) −16.7940 19.0587i −0.868397 0.985503i
\(375\) 0 0
\(376\) 7.34212 4.23898i 0.378641 0.218609i
\(377\) 16.9755i 0.874284i
\(378\) 0 0
\(379\) −35.9823 −1.84829 −0.924143 0.382047i \(-0.875219\pi\)
−0.924143 + 0.382047i \(0.875219\pi\)
\(380\) −2.08194 3.60603i −0.106801 0.184985i
\(381\) 0 0
\(382\) 4.03039 + 2.32695i 0.206213 + 0.119057i
\(383\) 1.51172 0.872794i 0.0772454 0.0445977i −0.460880 0.887463i \(-0.652466\pi\)
0.538125 + 0.842865i \(0.319133\pi\)
\(384\) 0 0
\(385\) 17.3995 + 7.51708i 0.886761 + 0.383106i
\(386\) 15.6851i 0.798353i
\(387\) 0 0
\(388\) 0.618915 1.07199i 0.0314206 0.0544221i
\(389\) −19.9922 11.5425i −1.01364 0.585228i −0.101388 0.994847i \(-0.532328\pi\)
−0.912257 + 0.409619i \(0.865662\pi\)
\(390\) 0 0
\(391\) 63.8489i 3.22898i
\(392\) 6.90395 + 1.15564i 0.348702 + 0.0583688i
\(393\) 0 0
\(394\) 3.19570 + 5.53512i 0.160997 + 0.278855i
\(395\) −8.27169 + 14.3270i −0.416194 + 0.720869i
\(396\) 0 0
\(397\) −3.99083 6.91231i −0.200294 0.346919i 0.748329 0.663327i \(-0.230856\pi\)
−0.948623 + 0.316408i \(0.897523\pi\)
\(398\) −25.6938 −1.28792
\(399\) 0 0
\(400\) 0.334422 0.0167211
\(401\) −8.88905 + 5.13209i −0.443898 + 0.256285i −0.705250 0.708959i \(-0.749165\pi\)
0.261352 + 0.965244i \(0.415832\pi\)
\(402\) 0 0
\(403\) −18.2176 10.5179i −0.907483 0.523936i
\(404\) 1.57357 + 2.72549i 0.0782878 + 0.135598i
\(405\) 0 0
\(406\) 5.41242 + 11.4766i 0.268614 + 0.569576i
\(407\) −3.29610 + 9.78603i −0.163382 + 0.485075i
\(408\) 0 0
\(409\) −6.14427 3.54740i −0.303815 0.175407i 0.340341 0.940302i \(-0.389458\pi\)
−0.644155 + 0.764895i \(0.722791\pi\)
\(410\) 16.8467 + 9.72646i 0.832001 + 0.480356i
\(411\) 0 0
\(412\) 0.237303 0.0116911
\(413\) −9.92705 6.88697i −0.488478 0.338886i
\(414\) 0 0
\(415\) −15.8089 + 9.12725i −0.776026 + 0.448039i
\(416\) 3.06535 + 1.76978i 0.150291 + 0.0867707i
\(417\) 0 0
\(418\) 1.26216 + 6.26773i 0.0617340 + 0.306565i
\(419\) 20.6094i 1.00684i −0.864043 0.503418i \(-0.832076\pi\)
0.864043 0.503418i \(-0.167924\pi\)
\(420\) 0 0
\(421\) 0.107995 0.00526337 0.00263169 0.999997i \(-0.499162\pi\)
0.00263169 + 0.999997i \(0.499162\pi\)
\(422\) 14.4283 8.33019i 0.702359 0.405507i
\(423\) 0 0
\(424\) −4.83344 2.79059i −0.234732 0.135523i
\(425\) −1.28068 2.21820i −0.0621221 0.107599i
\(426\) 0 0
\(427\) 26.8403 12.6580i 1.29889 0.612562i
\(428\) 10.8171 0.522866
\(429\) 0 0
\(430\) −2.68837 + 4.65639i −0.129645 + 0.224551i
\(431\) −20.2561 + 35.0846i −0.975702 + 1.68997i −0.298105 + 0.954533i \(0.596354\pi\)
−0.677598 + 0.735433i \(0.736979\pi\)
\(432\) 0 0
\(433\) −3.27124 −0.157206 −0.0786028 0.996906i \(-0.525046\pi\)
−0.0786028 + 0.996906i \(0.525046\pi\)
\(434\) −15.6699 1.30242i −0.752177 0.0625181i
\(435\) 0 0
\(436\) 3.77972 2.18222i 0.181016 0.104510i
\(437\) 8.03514 13.9173i 0.384373 0.665753i
\(438\) 0 0
\(439\) −5.95716 + 3.43937i −0.284320 + 0.164152i −0.635377 0.772202i \(-0.719155\pi\)
0.351058 + 0.936354i \(0.385822\pi\)
\(440\) 6.78914 + 2.28670i 0.323659 + 0.109014i
\(441\) 0 0
\(442\) 27.1097i 1.28948i
\(443\) −5.64003 + 3.25627i −0.267966 + 0.154710i −0.627963 0.778243i \(-0.716111\pi\)
0.359997 + 0.932953i \(0.382778\pi\)
\(444\) 0 0
\(445\) 0.759811 1.31603i 0.0360185 0.0623858i
\(446\) −4.90779 8.50054i −0.232390 0.402512i
\(447\) 0 0
\(448\) 2.63666 + 0.219149i 0.124570 + 0.0103538i
\(449\) 13.3141i 0.628331i −0.949368 0.314165i \(-0.898275\pi\)
0.949368 0.314165i \(-0.101725\pi\)
\(450\) 0 0
\(451\) −19.7474 22.4104i −0.929871 1.05527i
\(452\) 15.3691 + 8.87338i 0.722904 + 0.417369i
\(453\) 0 0
\(454\) −10.1744 −0.477508
\(455\) 8.62819 + 18.2954i 0.404496 + 0.857704i
\(456\) 0 0
\(457\) 22.5222 13.0032i 1.05354 0.608263i 0.129904 0.991527i \(-0.458533\pi\)
0.923639 + 0.383264i \(0.125200\pi\)
\(458\) −13.3669 + 23.1522i −0.624594 + 1.08183i
\(459\) 0 0
\(460\) −9.00327 15.5941i −0.419780 0.727080i
\(461\) 15.8542 0.738404 0.369202 0.929349i \(-0.379631\pi\)
0.369202 + 0.929349i \(0.379631\pi\)
\(462\) 0 0
\(463\) −27.6377 −1.28443 −0.642216 0.766524i \(-0.721985\pi\)
−0.642216 + 0.766524i \(0.721985\pi\)
\(464\) 2.39797 + 4.15341i 0.111323 + 0.192817i
\(465\) 0 0
\(466\) −2.09943 + 3.63631i −0.0972540 + 0.168449i
\(467\) 3.49877 2.02001i 0.161904 0.0934751i −0.416859 0.908971i \(-0.636869\pi\)
0.578763 + 0.815496i \(0.303536\pi\)
\(468\) 0 0
\(469\) 4.40892 6.35512i 0.203585 0.293452i
\(470\) 18.3123 0.844685
\(471\) 0 0
\(472\) −3.95479 2.28330i −0.182034 0.105097i
\(473\) 6.19419 5.45814i 0.284809 0.250966i
\(474\) 0 0
\(475\) 0.644675i 0.0295797i
\(476\) −8.64357 18.3281i −0.396177 0.840065i
\(477\) 0 0
\(478\) 9.72914 + 16.8514i 0.445001 + 0.770764i
\(479\) −3.06163 + 5.30290i −0.139890 + 0.242296i −0.927455 0.373936i \(-0.878008\pi\)
0.787565 + 0.616231i \(0.211341\pi\)
\(480\) 0 0
\(481\) −9.54388 + 5.51016i −0.435163 + 0.251242i
\(482\) 5.23797i 0.238583i
\(483\) 0 0
\(484\) −8.75848 6.65500i −0.398113 0.302500i
\(485\) 2.31550 1.33685i 0.105141 0.0607033i
\(486\) 0 0
\(487\) 3.06196 5.30347i 0.138751 0.240323i −0.788273 0.615325i \(-0.789025\pi\)
0.927024 + 0.375002i \(0.122358\pi\)
\(488\) 9.71354 5.60811i 0.439711 0.253867i
\(489\) 0 0
\(490\) 11.6665 + 9.61800i 0.527039 + 0.434497i
\(491\) −20.9024 −0.943311 −0.471656 0.881783i \(-0.656343\pi\)
−0.471656 + 0.881783i \(0.656343\pi\)
\(492\) 0 0
\(493\) 18.3662 31.8112i 0.827173 1.43270i
\(494\) −3.41166 + 5.90916i −0.153498 + 0.265866i
\(495\) 0 0
\(496\) −5.94307 −0.266852
\(497\) 3.27714 39.4284i 0.147000 1.76861i
\(498\) 0 0
\(499\) 13.3081 + 23.0503i 0.595753 + 1.03188i 0.993440 + 0.114354i \(0.0364798\pi\)
−0.397687 + 0.917521i \(0.630187\pi\)
\(500\) 9.97863 + 5.76116i 0.446258 + 0.257647i
\(501\) 0 0
\(502\) 14.9818 8.64975i 0.668670 0.386057i
\(503\) 15.2781 0.681215 0.340607 0.940206i \(-0.389367\pi\)
0.340607 + 0.940206i \(0.389367\pi\)
\(504\) 0 0
\(505\) 6.79779i 0.302497i
\(506\) 5.45814 + 27.1046i 0.242644 + 1.20494i
\(507\) 0 0
\(508\) −10.9566 6.32577i −0.486119 0.280661i
\(509\) −13.3048 + 7.68152i −0.589724 + 0.340478i −0.764989 0.644044i \(-0.777255\pi\)
0.175264 + 0.984521i \(0.443922\pi\)
\(510\) 0 0
\(511\) 1.22063 + 0.846822i 0.0539975 + 0.0374612i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 22.9253 + 13.2359i 1.01119 + 0.583812i
\(515\) 0.443901 + 0.256286i 0.0195606 + 0.0112933i
\(516\) 0 0
\(517\) −26.6473 8.97526i −1.17195 0.394732i
\(518\) −4.69548 + 6.76818i −0.206308 + 0.297377i
\(519\) 0 0
\(520\) 3.82272 + 6.62114i 0.167637 + 0.290356i
\(521\) −15.9036 9.18197i −0.696751 0.402269i 0.109385 0.993999i \(-0.465112\pi\)
−0.806136 + 0.591730i \(0.798445\pi\)
\(522\) 0 0
\(523\) −33.5412 + 19.3650i −1.46666 + 0.846774i −0.999304 0.0372968i \(-0.988125\pi\)
−0.467352 + 0.884071i \(0.654792\pi\)
\(524\) 3.05908 0.133637
\(525\) 0 0
\(526\) 12.6008 0.549420
\(527\) 22.7592 + 39.4201i 0.991406 + 1.71716i
\(528\) 0 0
\(529\) 23.2477 40.2661i 1.01077 1.75070i
\(530\) −6.02765 10.4402i −0.261824 0.453493i
\(531\) 0 0
\(532\) −0.422460 + 5.08276i −0.0183160 + 0.220366i
\(533\) 31.8773i 1.38076i
\(534\) 0 0
\(535\) 20.2347 + 11.6825i 0.874820 + 0.505078i
\(536\) 1.46173 2.53179i 0.0631370 0.109357i
\(537\) 0 0
\(538\) 18.7539i 0.808536i
\(539\) −12.2626 19.7137i −0.528187 0.849128i
\(540\) 0 0
\(541\) −25.5849 + 14.7714i −1.09998 + 0.635073i −0.936215 0.351426i \(-0.885697\pi\)
−0.163763 + 0.986500i \(0.552363\pi\)
\(542\) 3.87768 + 2.23878i 0.166561 + 0.0961638i
\(543\) 0 0
\(544\) −3.82953 6.63294i −0.164190 0.284385i
\(545\) 9.42718 0.403816
\(546\) 0 0
\(547\) 8.96112i 0.383150i 0.981478 + 0.191575i \(0.0613595\pi\)
−0.981478 + 0.191575i \(0.938640\pi\)
\(548\) −6.20778 + 3.58406i −0.265183 + 0.153104i
\(549\) 0 0
\(550\) −0.733287 0.832173i −0.0312675 0.0354840i
\(551\) −8.00664 + 4.62264i −0.341094 + 0.196931i
\(552\) 0 0
\(553\) 18.3279 8.64349i 0.779381 0.367558i
\(554\) 9.35040i 0.397260i
\(555\) 0 0
\(556\) −2.40268 1.38719i −0.101896 0.0588299i
\(557\) 11.1860 19.3748i 0.473968 0.820936i −0.525588 0.850739i \(-0.676155\pi\)
0.999556 + 0.0298032i \(0.00948806\pi\)
\(558\) 0 0
\(559\) 8.81081 0.372658
\(560\) 4.69548 + 3.25753i 0.198420 + 0.137656i
\(561\) 0 0
\(562\) −11.9488 20.6960i −0.504030 0.873006i
\(563\) 12.3032 21.3098i 0.518518 0.898100i −0.481250 0.876583i \(-0.659817\pi\)
0.999768 0.0215165i \(-0.00684945\pi\)
\(564\) 0 0
\(565\) 19.1665 + 33.1973i 0.806339 + 1.39662i
\(566\) 18.0665i 0.759393i
\(567\) 0 0
\(568\) 14.9539i 0.627453i
\(569\) −20.0433 34.7160i −0.840258 1.45537i −0.889677 0.456591i \(-0.849070\pi\)
0.0494186 0.998778i \(-0.484263\pi\)
\(570\) 0 0
\(571\) −10.6799 6.16602i −0.446938 0.258040i 0.259598 0.965717i \(-0.416410\pi\)
−0.706536 + 0.707677i \(0.749743\pi\)
\(572\) −2.31748 11.5084i −0.0968988 0.481189i
\(573\) 0 0
\(574\) −10.1636 21.5513i −0.424222 0.899533i
\(575\) 2.78787i 0.116262i
\(576\) 0 0
\(577\) −8.58087 + 14.8625i −0.357226 + 0.618734i −0.987496 0.157642i \(-0.949611\pi\)
0.630270 + 0.776376i \(0.282944\pi\)
\(578\) −20.8306 + 36.0797i −0.866440 + 1.50072i
\(579\) 0 0
\(580\) 10.3592i 0.430143i
\(581\) 22.2829 + 1.85207i 0.924449 + 0.0768367i
\(582\) 0 0
\(583\) 3.65420 + 18.1464i 0.151341 + 0.751546i
\(584\) 0.486281 + 0.280755i 0.0201225 + 0.0116177i
\(585\) 0 0
\(586\) −8.16309 14.1389i −0.337214 0.584072i
\(587\) 27.7349i 1.14474i −0.819995 0.572371i \(-0.806024\pi\)
0.819995 0.572371i \(-0.193976\pi\)
\(588\) 0 0
\(589\) 11.4566i 0.472062i
\(590\) −4.93191 8.54232i −0.203044 0.351682i
\(591\) 0 0
\(592\) −1.55673 + 2.69634i −0.0639814 + 0.110819i
\(593\) −10.2740 17.7950i −0.421901 0.730753i 0.574225 0.818698i \(-0.305304\pi\)
−0.996125 + 0.0879443i \(0.971970\pi\)
\(594\) 0 0
\(595\) 3.62550 43.6197i 0.148631 1.78823i
\(596\) −23.4310 −0.959770
\(597\) 0 0
\(598\) −14.7536 + 25.5539i −0.603319 + 1.04498i
\(599\) −26.0773 15.0557i −1.06549 0.615161i −0.138544 0.990356i \(-0.544242\pi\)
−0.926946 + 0.375195i \(0.877576\pi\)
\(600\) 0 0
\(601\) 17.8081i 0.726406i 0.931710 + 0.363203i \(0.118317\pi\)
−0.931710 + 0.363203i \(0.881683\pi\)
\(602\) 5.95672 2.80921i 0.242778 0.114495i
\(603\) 0 0
\(604\) 7.98285 4.60890i 0.324818 0.187534i
\(605\) −9.19632 21.9080i −0.373884 0.890689i
\(606\) 0 0
\(607\) 4.13802 2.38909i 0.167957 0.0969700i −0.413665 0.910429i \(-0.635752\pi\)
0.581622 + 0.813459i \(0.302418\pi\)
\(608\) 1.92773i 0.0781797i
\(609\) 0 0
\(610\) 24.2270 0.980922
\(611\) −15.0041 25.9879i −0.607002 1.05136i
\(612\) 0 0
\(613\) −31.0386 17.9202i −1.25364 0.723788i −0.281808 0.959471i \(-0.590934\pi\)
−0.971830 + 0.235683i \(0.924267\pi\)
\(614\) 5.98577 3.45589i 0.241566 0.139468i
\(615\) 0 0
\(616\) −5.23607 7.04156i −0.210967 0.283713i
\(617\) 26.4982i 1.06678i 0.845871 + 0.533388i \(0.179081\pi\)
−0.845871 + 0.533388i \(0.820919\pi\)
\(618\) 0 0
\(619\) 10.4961 18.1798i 0.421874 0.730707i −0.574249 0.818681i \(-0.694706\pi\)
0.996123 + 0.0879736i \(0.0280391\pi\)
\(620\) −11.1172 6.41850i −0.446476 0.257773i
\(621\) 0 0
\(622\) 0.828930i 0.0332371i
\(623\) −1.68354 + 0.793963i −0.0674496 + 0.0318094i
\(624\) 0 0
\(625\) 11.6080 + 20.1057i 0.464321 + 0.804228i
\(626\) 8.66175 15.0026i 0.346193 0.599624i
\(627\) 0 0
\(628\) −11.5804 20.0579i −0.462109 0.800396i
\(629\) 23.8463 0.950813
\(630\) 0 0
\(631\) −3.84169 −0.152935 −0.0764676 0.997072i \(-0.524364\pi\)
−0.0764676 + 0.997072i \(0.524364\pi\)
\(632\) 6.63288 3.82950i 0.263842 0.152329i
\(633\) 0 0
\(634\) −24.1286 13.9306i −0.958268 0.553256i
\(635\) −13.6636 23.6661i −0.542225 0.939161i
\(636\) 0 0
\(637\) 4.09047 24.4370i 0.162070 0.968227i
\(638\) 5.07727 15.0742i 0.201011 0.596795i
\(639\) 0 0
\(640\) 1.87061 + 1.08000i 0.0739424 + 0.0426906i
\(641\) 22.0788 + 12.7472i 0.872061 + 0.503485i 0.868033 0.496507i \(-0.165384\pi\)
0.00402867 + 0.999992i \(0.498718\pi\)
\(642\) 0 0
\(643\) 47.8391 1.88659 0.943296 0.331953i \(-0.107708\pi\)
0.943296 + 0.331953i \(0.107708\pi\)
\(644\) −1.82691 + 21.9802i −0.0719904 + 0.866141i
\(645\) 0 0
\(646\) 12.7865 7.38230i 0.503079 0.290453i
\(647\) 40.1193 + 23.1629i 1.57725 + 0.910628i 0.995241 + 0.0974487i \(0.0310682\pi\)
0.582013 + 0.813179i \(0.302265\pi\)
\(648\) 0 0
\(649\) 2.98992 + 14.8476i 0.117365 + 0.582821i
\(650\) 1.18371i 0.0464289i
\(651\) 0 0
\(652\) 18.6075 0.728727
\(653\) 19.4171 11.2105i 0.759850 0.438699i −0.0693921 0.997589i \(-0.522106\pi\)
0.829242 + 0.558890i \(0.188773\pi\)
\(654\) 0 0
\(655\) 5.72235 + 3.30380i 0.223591 + 0.129090i
\(656\) −4.50300 7.79943i −0.175813 0.304517i
\(657\) 0 0
\(658\) −18.4297 12.7858i −0.718465 0.498441i
\(659\) −34.8470 −1.35745 −0.678724 0.734394i \(-0.737467\pi\)
−0.678724 + 0.734394i \(0.737467\pi\)
\(660\) 0 0
\(661\) 14.7306 25.5141i 0.572953 0.992383i −0.423308 0.905986i \(-0.639131\pi\)
0.996261 0.0863973i \(-0.0275354\pi\)
\(662\) 2.76388 4.78718i 0.107421 0.186059i
\(663\) 0 0
\(664\) 8.45117 0.327969
\(665\) −6.27963 + 9.05161i −0.243514 + 0.351007i
\(666\) 0 0
\(667\) −34.6244 + 19.9904i −1.34066 + 0.774032i
\(668\) −10.6954 + 18.5250i −0.413818 + 0.716754i
\(669\) 0 0
\(670\) 5.46865 3.15732i 0.211272 0.121978i
\(671\) −35.2540 11.8742i −1.36097 0.458397i
\(672\) 0 0
\(673\) 18.7674i 0.723430i −0.932289 0.361715i \(-0.882191\pi\)
0.932289 0.361715i \(-0.117809\pi\)
\(674\) −20.5602 + 11.8704i −0.791949 + 0.457232i
\(675\) 0 0
\(676\) −0.235750 + 0.408331i −0.00906730 + 0.0157050i
\(677\) 19.4967 + 33.7692i 0.749317 + 1.29786i 0.948150 + 0.317822i \(0.102951\pi\)
−0.198833 + 0.980033i \(0.563715\pi\)
\(678\) 0 0
\(679\) −3.26373 0.271269i −0.125251 0.0104104i
\(680\) 16.5435i 0.634416i
\(681\) 0 0
\(682\) 13.0314 + 14.7887i 0.498997 + 0.566288i
\(683\) −9.14108 5.27760i −0.349774 0.201942i 0.314812 0.949154i \(-0.398059\pi\)
−0.664586 + 0.747212i \(0.731392\pi\)
\(684\) 0 0
\(685\) −15.4831 −0.591579
\(686\) −5.02595 17.8253i −0.191891 0.680572i
\(687\) 0 0
\(688\) 2.15574 1.24462i 0.0821869 0.0474506i
\(689\) −9.87745 + 17.1082i −0.376301 + 0.651772i
\(690\) 0 0
\(691\) −5.97059 10.3414i −0.227132 0.393404i 0.729825 0.683634i \(-0.239602\pi\)
−0.956957 + 0.290230i \(0.906268\pi\)
\(692\) −0.860166 −0.0326986
\(693\) 0 0
\(694\) 20.3800 0.773612
\(695\) −2.99632 5.18978i −0.113657 0.196860i
\(696\) 0 0
\(697\) −34.4888 + 59.7363i −1.30636 + 2.26267i
\(698\) 9.82594 5.67301i 0.371917 0.214727i
\(699\) 0 0
\(700\) −0.377409 0.800269i −0.0142647 0.0302473i
\(701\) −42.9751 −1.62315 −0.811573 0.584251i \(-0.801388\pi\)
−0.811573 + 0.584251i \(0.801388\pi\)
\(702\) 0 0
\(703\) −5.19782 3.00096i −0.196039 0.113183i
\(704\) −2.19270 2.48839i −0.0826404 0.0937847i
\(705\) 0 0
\(706\) 10.2642i 0.386298i
\(707\) 4.74625 6.84136i 0.178501 0.257296i
\(708\) 0 0
\(709\) 12.1613 + 21.0640i 0.456726 + 0.791073i 0.998786 0.0492669i \(-0.0156885\pi\)
−0.542059 + 0.840340i \(0.682355\pi\)
\(710\) 16.1502 27.9730i 0.606106 1.04981i
\(711\) 0 0
\(712\) −0.609275 + 0.351765i −0.0228335 + 0.0131830i
\(713\) 49.5437i 1.85543i
\(714\) 0 0
\(715\) 8.09391 24.0306i 0.302695 0.898692i
\(716\) −9.01762 + 5.20633i −0.337004 + 0.194570i
\(717\) 0 0
\(718\) 8.12523 14.0733i 0.303231 0.525211i
\(719\) −9.25091 + 5.34101i −0.345001 + 0.199186i −0.662481 0.749079i \(-0.730497\pi\)
0.317480 + 0.948265i \(0.397163\pi\)
\(720\) 0 0
\(721\) −0.267806 0.567862i −0.00997360 0.0211483i
\(722\) 15.2839 0.568807
\(723\) 0 0
\(724\) 3.51299 6.08468i 0.130559 0.226135i
\(725\) 0.801935 1.38899i 0.0297831 0.0515859i
\(726\) 0 0
\(727\) 31.0522 1.15166 0.575832 0.817568i \(-0.304678\pi\)
0.575832 + 0.817568i \(0.304678\pi\)
\(728\) 0.775692 9.33262i 0.0287491 0.345890i
\(729\) 0 0
\(730\) 0.606428 + 1.05036i 0.0224449 + 0.0388757i
\(731\) −16.5110 9.53261i −0.610680 0.352576i
\(732\) 0 0
\(733\) 23.6044 13.6280i 0.871848 0.503362i 0.00388629 0.999992i \(-0.498763\pi\)
0.867962 + 0.496631i \(0.165430\pi\)
\(734\) 36.7363 1.35596
\(735\) 0 0
\(736\) 8.33638i 0.307283i
\(737\) −9.50520 + 1.91409i −0.350128 + 0.0705066i
\(738\) 0 0
\(739\) 30.9864 + 17.8900i 1.13985 + 0.658095i 0.946394 0.323013i \(-0.104696\pi\)
0.193460 + 0.981108i \(0.438029\pi\)
\(740\) −5.82409 + 3.36254i −0.214098 + 0.123609i
\(741\) 0 0
\(742\) −1.22311 + 14.7156i −0.0449017 + 0.540228i
\(743\) −13.7096 −0.502957 −0.251478 0.967863i \(-0.580917\pi\)
−0.251478 + 0.967863i \(0.580917\pi\)
\(744\) 0 0
\(745\) −43.8302 25.3054i −1.60582 0.927118i
\(746\) 0.721045 + 0.416295i 0.0263993 + 0.0152417i
\(747\) 0 0
\(748\) −8.10834 + 24.0734i −0.296470 + 0.880211i
\(749\) −12.2076 25.8853i −0.446056 0.945828i
\(750\) 0 0
\(751\) 2.74195 + 4.74920i 0.100055 + 0.173301i 0.911707 0.410840i \(-0.134765\pi\)
−0.811652 + 0.584141i \(0.801431\pi\)
\(752\) −7.34212 4.23898i −0.267740 0.154580i
\(753\) 0 0
\(754\) 14.7012 8.48777i 0.535388 0.309106i
\(755\) 19.9104 0.724614
\(756\) 0 0
\(757\) 39.5786 1.43851 0.719254 0.694747i \(-0.244484\pi\)
0.719254 + 0.694747i \(0.244484\pi\)
\(758\) 17.9911 + 31.1616i 0.653468 + 1.13184i
\(759\) 0 0
\(760\) −2.08194 + 3.60603i −0.0755200 + 0.130804i
\(761\) 12.9323 + 22.3994i 0.468794 + 0.811976i 0.999364 0.0356657i \(-0.0113552\pi\)
−0.530569 + 0.847642i \(0.678022\pi\)
\(762\) 0 0
\(763\) −9.48761 6.58210i −0.343474 0.238288i
\(764\) 4.65390i 0.168372i
\(765\) 0 0
\(766\) −1.51172 0.872794i −0.0546208 0.0315353i
\(767\) −8.08188 + 13.9982i −0.291820 + 0.505447i
\(768\) 0 0
\(769\) 30.4651i 1.09860i −0.835626 0.549299i \(-0.814895\pi\)
0.835626 0.549299i \(-0.185105\pi\)
\(770\) −2.18977 18.8270i −0.0789140 0.678476i
\(771\) 0 0
\(772\) 13.5837 7.84257i 0.488889 0.282260i
\(773\) −34.2466 19.7723i −1.23177 0.711160i −0.264367 0.964422i \(-0.585163\pi\)
−0.967398 + 0.253262i \(0.918497\pi\)
\(774\) 0 0
\(775\) 0.993748 + 1.72122i 0.0356965 + 0.0618281i
\(776\) −1.23783 −0.0444355
\(777\) 0 0
\(778\) 23.0850i 0.827637i
\(779\) 15.0352 8.68057i 0.538691 0.311014i
\(780\) 0 0
\(781\) −37.2112 + 32.7894i −1.33152 + 1.17330i
\(782\) 55.2948 31.9244i 1.97734 1.14162i
\(783\) 0 0
\(784\) −2.45116 6.55682i −0.0875413 0.234172i
\(785\) 50.0273i 1.78555i
\(786\) 0 0
\(787\) −26.6490 15.3858i −0.949933 0.548444i −0.0568731 0.998381i \(-0.518113\pi\)
−0.893060 + 0.449937i \(0.851446\pi\)
\(788\) 3.19570 5.53512i 0.113842 0.197181i
\(789\) 0 0
\(790\) 16.5434 0.588587