Properties

Label 1386.2.ba.a.989.13
Level $1386$
Weight $2$
Character 1386.989
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 989.13
Character \(\chi\) \(=\) 1386.989
Dual form 1386.2.ba.a.1187.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.87061 + 1.08000i) q^{5} +(-2.63666 + 0.219149i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.87061 + 1.08000i) q^{5} +(-2.63666 + 0.219149i) q^{7} +1.00000 q^{8} +(-1.87061 + 1.08000i) q^{10} +(3.25136 - 0.654737i) q^{11} -3.53956i q^{13} +(1.12854 - 2.39299i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.82953 - 6.63294i) q^{17} +(-1.66946 - 0.963864i) q^{19} -2.15999i q^{20} +(-1.05866 + 3.14313i) q^{22} +(-7.21952 - 4.16819i) q^{23} +(-0.167211 - 0.289618i) q^{25} +(3.06535 + 1.76978i) q^{26} +(1.50812 + 2.17384i) q^{28} -4.79594 q^{29} +(2.97154 + 5.14685i) q^{31} +(-0.500000 - 0.866025i) q^{32} +7.65906 q^{34} +(-5.16884 - 2.43764i) q^{35} +(-1.55673 + 2.69634i) q^{37} +(1.66946 - 0.963864i) q^{38} +(1.87061 + 1.08000i) q^{40} +9.00600 q^{41} +2.48924i q^{43} +(-2.19270 - 2.48839i) q^{44} +(7.21952 - 4.16819i) q^{46} +(-7.34212 - 4.23898i) q^{47} +(6.90395 - 1.15564i) q^{49} +0.334422 q^{50} +(-3.06535 + 1.76978i) q^{52} +(4.83344 - 2.79059i) q^{53} +(6.78914 + 2.28670i) q^{55} +(-2.63666 + 0.219149i) q^{56} +(2.39797 - 4.15341i) q^{58} +(3.95479 - 2.28330i) q^{59} +(-9.71354 - 5.60811i) q^{61} -5.94307 q^{62} +1.00000 q^{64} +(3.82272 - 6.62114i) q^{65} +(1.46173 + 2.53179i) q^{67} +(-3.82953 + 6.63294i) q^{68} +(4.69548 - 3.25753i) q^{70} -14.9539i q^{71} +(-0.486281 + 0.280755i) q^{73} +(-1.55673 - 2.69634i) q^{74} +1.92773i q^{76} +(-8.42924 + 2.43885i) q^{77} +(-6.63288 - 3.82950i) q^{79} +(-1.87061 + 1.08000i) q^{80} +(-4.50300 + 7.79943i) q^{82} +8.45117 q^{83} -16.5435i q^{85} +(-2.15574 - 1.24462i) q^{86} +(3.25136 - 0.654737i) q^{88} +(0.609275 + 0.351765i) q^{89} +(0.775692 + 9.33262i) q^{91} +8.33638i q^{92} +(7.34212 - 4.23898i) q^{94} +(-2.08194 - 3.60603i) q^{95} -1.23783 q^{97} +(-2.45116 + 6.55682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

Character values

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

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

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 \(-0.172884\pi\)
−0.0195319 + 0.999809i \(0.506218\pi\)
\(6\) 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
\(11\) 3.25136 0.654737i 0.980321 0.197411i
\(12\) 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 −0.785336 0.619069i \(-0.787510\pi\)
−0.143461 0.989656i \(-0.545823\pi\)
\(18\) 0 0
\(19\) −1.66946 0.963864i −0.383001 0.221126i 0.296122 0.955150i \(-0.404306\pi\)
−0.679123 + 0.734024i \(0.737640\pi\)
\(20\) 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 −0.999981 0.00623916i \(-0.998014\pi\)
−0.505394 0.862889i \(-0.668653\pi\)
\(24\) 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 0.999225 + 0.0393651i \(0.0125335\pi\)
−0.465521 + 0.885037i \(0.654133\pi\)
\(32\) −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 −0.965147 0.261710i \(-0.915714\pi\)
0.709221 + 0.704986i \(0.249047\pi\)
\(38\) 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 \(0.939215\pi\)
\(44\) −2.19270 2.48839i −0.330562 0.375139i
\(45\) 0 0
\(46\) 7.21952 4.16819i 1.06446 0.614566i
\(47\) −7.34212 4.23898i −1.07096 0.618318i −0.142515 0.989793i \(-0.545519\pi\)
−0.928443 + 0.371474i \(0.878852\pi\)
\(48\) 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 \(-0.541449\pi\)
0.793770 + 0.608218i \(0.208115\pi\)
\(54\) 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 \(-0.570594\pi\)
0.734833 + 0.678248i \(0.237260\pi\)
\(60\) 0 0
\(61\) −9.71354 5.60811i −1.24369 0.718045i −0.273847 0.961773i \(-0.588296\pi\)
−0.969844 + 0.243728i \(0.921630\pi\)
\(62\) −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 0.941394 0.337309i \(-0.109517\pi\)
−0.762815 + 0.646616i \(0.776183\pi\)
\(68\) −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 \(-0.677128\pi\)
0.471273 + 0.881988i \(0.343795\pi\)
\(74\) −1.55673 2.69634i −0.180967 0.313444i
\(75\) 0 0
\(76\) 1.92773i 0.221126i
\(77\) −8.42924 + 2.43885i −0.960600 + 0.277933i
\(78\) 0 0
\(79\) −6.63288 3.82950i −0.746258 0.430852i 0.0780826 0.996947i \(-0.475120\pi\)
−0.824340 + 0.566095i \(0.808454\pi\)
\(80\) −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
\(88\) 3.25136 0.654737i 0.346596 0.0697952i
\(89\) 0.609275 + 0.351765i 0.0645830 + 0.0372870i 0.531944 0.846780i \(-0.321462\pi\)
−0.467361 + 0.884067i \(0.654795\pi\)
\(90\) 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 0.933632 0.358235i \(-0.116621\pi\)
−0.777056 + 0.629431i \(0.783288\pi\)
\(102\) 0 0
\(103\) −0.118651 + 0.205510i −0.0116911 + 0.0202495i −0.871812 0.489841i \(-0.837055\pi\)
0.860121 + 0.510091i \(0.170388\pi\)
\(104\) 3.53956i 0.347083i
\(105\) 0 0
\(106\) 5.58117i 0.542091i
\(107\) −5.40857 + 9.36792i −0.522866 + 0.905631i 0.476780 + 0.879023i \(0.341804\pi\)
−0.999646 + 0.0266081i \(0.991529\pi\)
\(108\) 0 0
\(109\) 3.77972 2.18222i 0.362032 0.209019i −0.307940 0.951406i \(-0.599640\pi\)
0.669972 + 0.742387i \(0.266306\pi\)
\(110\) −5.37491 + 4.73621i −0.512477 + 0.451580i
\(111\) 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
\(121\) 10.1426 4.25757i 0.922058 0.387052i
\(122\) 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 −0.925076 0.379782i \(-0.875999\pi\)
0.791439 + 0.611248i \(0.209332\pi\)
\(132\) 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 \(-0.765727\pi\)
0.210799 + 0.977529i \(0.432393\pi\)
\(138\) 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
\(143\) −2.31748 11.5084i −0.193798 0.962379i
\(144\) 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 0.236716 0.971579i \(-0.423929\pi\)
0.723054 0.690792i \(-0.242738\pi\)
\(150\) 0 0
\(151\) 7.98285 4.60890i 0.649635 0.375067i −0.138681 0.990337i \(-0.544286\pi\)
0.788317 + 0.615270i \(0.210953\pi\)
\(152\) −1.66946 0.963864i −0.135411 0.0781797i
\(153\) 0 0
\(154\) 2.10251 8.51936i 0.169425 0.686509i
\(155\) 12.8370i 1.03109i
\(156\) 0 0
\(157\) −11.5804 20.0579i −0.924218 1.60079i −0.792814 0.609463i \(-0.791385\pi\)
−0.131403 0.991329i \(-0.541948\pi\)
\(158\) 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 0.228695 + 0.973498i \(0.426554\pi\)
−0.957422 + 0.288693i \(0.906779\pi\)
\(164\) −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 −0.849213 0.528050i \(-0.822923\pi\)
0.881912 + 0.471415i \(0.156257\pi\)
\(174\) 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 \(-0.793894\pi\)
0.123585 + 0.992334i \(0.460561\pi\)
\(180\) 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
\(187\) −16.7940 19.0587i −1.22810 1.39371i
\(188\) 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 \(-0.279482\pi\)
−0.347047 + 0.937848i \(0.612816\pi\)
\(192\) 0 0
\(193\) 13.5837 7.84257i 0.977778 0.564521i 0.0761796 0.997094i \(-0.475728\pi\)
0.901599 + 0.432574i \(0.142394\pi\)
\(194\) 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 0.813086 + 0.582144i \(0.197786\pi\)
0.0976086 + 0.995225i \(0.468881\pi\)
\(200\) −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
\(220\) −1.41423 7.02291i −0.0953473 0.473485i
\(221\) −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 0.983990 0.178224i \(-0.0570350\pi\)
−0.646341 + 0.763049i \(0.723702\pi\)
\(228\) 0 0
\(229\) −13.3669 + 23.1522i −0.883310 + 1.52994i −0.0356712 + 0.999364i \(0.511357\pi\)
−0.847639 + 0.530574i \(0.821976\pi\)
\(230\) 18.0065 1.18732
\(231\) 0 0
\(232\) −4.79594 −0.314869
\(233\) −2.09943 + 3.63631i −0.137538 + 0.238223i −0.926564 0.376137i \(-0.877252\pi\)
0.789026 + 0.614360i \(0.210586\pi\)
\(234\) 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 \(-0.612709\pi\)
0.638935 + 0.769261i \(0.279375\pi\)
\(242\) −1.38416 + 10.9126i −0.0889770 + 0.701486i
\(243\) 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 \(-0.0241504\pi\)
0.432919 + 0.901433i \(0.357484\pi\)
\(258\) 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 0.603749 0.797175i \(-0.293673\pi\)
−0.992248 + 0.124275i \(0.960340\pi\)
\(264\) 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 \(-0.860391\pi\)
−0.0849016 + 0.996389i \(0.527058\pi\)
\(270\) 0 0
\(271\) 3.87768 + 2.23878i 0.235552 + 0.135996i 0.613131 0.789981i \(-0.289910\pi\)
−0.377579 + 0.925978i \(0.623243\pi\)
\(272\) 7.65906 0.464399
\(273\) 0 0
\(274\) 7.16812i 0.433042i
\(275\) −0.733287 0.832173i −0.0442189 0.0501819i
\(276\) 0 0
\(277\) −8.09768 + 4.67520i −0.486543 + 0.280905i −0.723139 0.690703i \(-0.757301\pi\)
0.236596 + 0.971608i \(0.423968\pi\)
\(278\) −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 \(-0.847099\pi\)
−0.0432312 + 0.999065i \(0.513765\pi\)
\(284\) −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 \(0.936803\pi\)
\(308\) 6.32672 + 6.08051i 0.360499 + 0.346469i
\(309\) 0 0
\(310\) −11.1172 6.41850i −0.631413 0.364546i
\(311\) −0.717875 + 0.414465i −0.0407069 + 0.0235022i −0.520215 0.854035i \(-0.674148\pi\)
0.479508 + 0.877537i \(0.340815\pi\)
\(312\) 0 0
\(313\) 8.66175 15.0026i 0.489591 0.847996i −0.510337 0.859974i \(-0.670479\pi\)
0.999928 + 0.0119780i \(0.00381282\pi\)
\(314\) 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 \(-0.619350\pi\)
−0.988972 + 0.148104i \(0.952683\pi\)
\(318\) 0 0
\(319\) −15.5933 + 3.14008i −0.873058 + 0.175811i
\(320\) 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 −0.780015 0.625760i \(-0.784789\pi\)
0.931932 + 0.362633i \(0.118122\pi\)
\(332\) −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
\(341\) 13.0314 + 14.7887i 0.705688 + 0.800852i
\(342\) 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 −0.998476 0.0551813i \(-0.982426\pi\)
0.451450 0.892297i \(-0.350907\pi\)
\(348\) 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
\(352\) −2.19270 2.48839i −0.116871 0.132632i
\(353\) −8.88905 + 5.13209i −0.473116 + 0.273154i −0.717543 0.696514i \(-0.754733\pi\)
0.244427 + 0.969668i \(0.421400\pi\)
\(354\) 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 −0.567937 0.823072i \(-0.692258\pi\)
0.996770 + 0.0803116i \(0.0255915\pi\)
\(360\) 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 −0.725402 0.688326i \(-0.758346\pi\)
−0.233407 0.972379i \(-0.574987\pi\)
\(368\) 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 \(-0.326472\pi\)
−0.481217 + 0.876602i \(0.659805\pi\)
\(374\) 24.9023 5.01467i 1.28767 0.259303i
\(375\) 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 \(-0.347534\pi\)
−0.538125 + 0.842865i \(0.680867\pi\)
\(384\) 0 0
\(385\) −18.4018 4.54141i −0.937841 0.231452i
\(386\) 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 \(-0.467672\pi\)
0.912257 + 0.409619i \(0.134338\pi\)
\(390\) 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 −0.948623 0.316408i \(-0.897523\pi\)
0.748329 + 0.663327i \(0.230856\pi\)
\(398\) −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 \(-0.250835\pi\)
−0.261352 + 0.965244i \(0.584168\pi\)
\(402\) 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 \(-0.610542\pi\)
0.644155 + 0.764895i \(0.277209\pi\)
\(410\) −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
\(418\) 4.79694 4.22692i 0.234626 0.206746i
\(419\) 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 −0.677598 0.735433i \(-0.736979\pi\)
−0.298105 0.954533i \(-0.596354\pi\)
\(432\) 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 \(-0.280845\pi\)
−0.351058 + 0.936354i \(0.614178\pi\)
\(440\) 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 \(-0.283889\pi\)
−0.359997 + 0.932953i \(0.617222\pi\)
\(444\) 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
\(451\) 29.2817 5.89657i 1.37882 0.277658i
\(452\) −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 \(-0.541467\pi\)
−0.923639 + 0.383264i \(0.874800\pi\)
\(458\) −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 \(-0.363131\pi\)
−0.578763 + 0.815496i \(0.696464\pi\)
\(468\) 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
\(473\) 1.62980 + 8.09340i 0.0749381 + 0.372135i
\(474\) 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 0.787565 0.616231i \(-0.211341\pi\)
−0.927455 + 0.373936i \(0.878008\pi\)
\(480\) 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 0.927024 0.375002i \(-0.122358\pi\)
−0.788273 + 0.615325i \(0.789025\pi\)
\(488\) −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 −0.397687 0.917521i \(-0.630187\pi\)
0.993440 0.114354i \(-0.0364798\pi\)
\(500\) −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
\(506\) 20.7442 18.2792i 0.922191 0.812608i
\(507\) 0 0
\(508\) 10.9566 6.32577i 0.486119 0.280661i
\(509\) 13.3048 + 7.68152i 0.589724 + 0.340478i 0.764989 0.644044i \(-0.222745\pi\)
−0.175264 + 0.984521i \(0.556078\pi\)
\(510\) 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 \(-0.534888\pi\)
0.806136 + 0.591730i \(0.201555\pi\)
\(522\) 0 0
\(523\) 33.5412 + 19.3650i 1.46666 + 0.846774i 0.999304 0.0372968i \(-0.0118747\pi\)
0.467352 + 0.884071i \(0.345208\pi\)
\(524\) 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
\(539\) 21.6906 8.27768i 0.934278 0.356545i
\(540\) 0 0
\(541\) 25.5849 + 14.7714i 1.09998 + 0.635073i 0.936215 0.351426i \(-0.114303\pi\)
0.163763 + 0.986500i \(0.447637\pi\)
\(542\) −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
\(550\) 1.08733 0.218959i 0.0463637 0.00933643i
\(551\) 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 0.999556 0.0298032i \(-0.00948806\pi\)
−0.525588 + 0.850739i \(0.676155\pi\)
\(558\) 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 0.999768 + 0.0215165i \(0.00684945\pi\)
−0.481250 + 0.876583i \(0.659817\pi\)
\(564\) 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 0.0494186 + 0.998778i \(0.484263\pi\)
−0.889677 + 0.456591i \(0.849070\pi\)
\(570\) 0 0
\(571\) 10.6799 6.16602i 0.446938 0.258040i −0.259598 0.965717i \(-0.583590\pi\)
0.706536 + 0.707677i \(0.250257\pi\)
\(572\) −8.80781 + 7.76119i −0.368273 + 0.324512i
\(573\) 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 0.630270 0.776376i \(-0.282944\pi\)
−0.987496 + 0.157642i \(0.949611\pi\)
\(578\) −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
\(583\) 13.8881 12.2378i 0.575187 0.506839i
\(584\) −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 −0.996125 0.0879443i \(-0.971970\pi\)
0.574225 + 0.818698i \(0.305304\pi\)
\(594\) 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 \(-0.455758\pi\)
0.926946 + 0.375195i \(0.122424\pi\)
\(600\) 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
\(605\) 23.5711 + 2.98977i 0.958301 + 0.121552i
\(606\) 0 0
\(607\) −4.13802 2.38909i −0.167957 0.0969700i 0.413665 0.910429i \(-0.364248\pi\)
−0.581622 + 0.813459i \(0.697582\pi\)
\(608\) 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 \(-0.409066\pi\)
0.971830 + 0.235683i \(0.0757325\pi\)
\(614\) −5.98577 3.45589i −0.241566 0.139468i
\(615\) 0 0
\(616\) −8.42924 + 2.43885i −0.339624 + 0.0982641i
\(617\) 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 0.996123 0.0879736i \(-0.0280391\pi\)
−0.574249 + 0.818681i \(0.694706\pi\)
\(620\) 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 \(-0.834616\pi\)
−0.00402867 + 0.999992i \(0.501282\pi\)
\(642\) 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 −0.582013 + 0.813179i \(0.697735\pi\)
−0.995241 + 0.0974487i \(0.968932\pi\)
\(648\) 0 0
\(649\) 11.3635 10.0132i 0.446055 0.393051i
\(650\) 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 \(-0.477894\pi\)
−0.829242 + 0.558890i \(0.811227\pi\)
\(654\) 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 0.996261 + 0.0863973i \(0.0275354\pi\)
−0.423308 + 0.905986i \(0.639131\pi\)
\(662\) 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 −0.198833 0.980033i \(-0.563715\pi\)
0.948150 0.317822i \(-0.102951\pi\)
\(678\) 0 0
\(679\) 3.26373 0.271269i 0.125251 0.0104104i
\(680\) 16.5435i 0.634416i
\(681\) 0 0
\(682\) −19.3230 + 3.89115i −0.739918 + 0.149000i
\(683\) 9.14108 5.27760i 0.349774 0.201942i −0.314812 0.949154i \(-0.601941\pi\)
0.664586 + 0.747212i \(0.268608\pi\)
\(684\) 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 −0.956957 0.290230i \(-0.906268\pi\)
0.729825 + 0.683634i \(0.239602\pi\)
\(692\) −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
\(704\) 3.25136 0.654737i 0.122540 0.0246763i
\(705\) 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 −0.542059 0.840340i \(-0.682355\pi\)
0.998786 + 0.0492669i \(0.0156885\pi\)
\(710\) 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 \(-0.269503\pi\)
−0.317480 + 0.948265i \(0.602837\pi\)
\(720\) 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 \(-0.501237\pi\)
−0.867962 + 0.496631i \(0.834570\pi\)
\(734\) 36.7363 1.35596
\(735\) 0 0
\(736\) 8.33638i 0.307283i
\(737\) 6.41025 + 7.27469i 0.236125 + 0.267967i
\(738\) 0 0
\(739\) −30.9864 + 17.8900i −1.13985 + 0.658095i −0.946394 0.323013i \(-0.895304\pi\)
−0.193460 + 0.981108i \(0.561971\pi\)
\(740\) 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 −0.811652 0.584141i \(-0.801431\pi\)
0.911707 + 0.410840i \(0.134765\pi\)
\(752\) 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 −0.530569 0.847642i \(-0.678022\pi\)
0.999364 + 0.0356657i \(0.0113552\pi\)
\(762\) 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 \(-0.185105\pi\)
\(770\) 13.1339 13.6657i 0.473312 0.492477i
\(771\) 0 0
\(772\) −13.5837 7.84257i −0.488889 0.282260i
\(773\) 34.2466 19.7723i 1.23177 0.711160i 0.264367 0.964422i \(-0.414837\pi\)
0.967398 + 0.253262i \(0.0815035\pi\)
\(774\) 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
\(781\) −9.79089 48.6205i −0.350346 1.73978i
\(782\) −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 \(-0.481887\pi\)
0.893060 + 0.449937i \(0.148554\pi\)
\(788\) 3.19570 + 5.53512i 0.113842 + 0.197181i
\(789\) 0 0
\(790\) 16.5434 0.588587