Properties

Label 668.2.e.a.9.6
Level $668$
Weight $2$
Character 668.9
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\), degree \(82\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(1148\)
Relative dimension: \(14\) over \(\Q(\zeta_{83})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label 9.6
Character \(\chi\) \(=\) 668.9
Dual form 668.2.e.a.297.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0387535 - 0.290817i) q^{3} +(-1.08122 - 0.478126i) q^{5} +(-0.661531 + 1.42256i) q^{7} +(2.81224 - 0.763053i) q^{9} +O(q^{10})\) \(q+(-0.0387535 - 0.290817i) q^{3} +(-1.08122 - 0.478126i) q^{5} +(-0.661531 + 1.42256i) q^{7} +(2.81224 - 0.763053i) q^{9} +(-1.52518 + 1.95553i) q^{11} +(1.57161 - 3.07008i) q^{13} +(-0.0971461 + 0.332967i) q^{15} +(5.30559 + 0.402408i) q^{17} +(0.514102 - 0.773362i) q^{19} +(0.439342 + 0.137255i) q^{21} +(7.30313 + 2.90431i) q^{23} +(-2.42392 - 2.66487i) q^{25} +(-0.671561 - 1.59984i) q^{27} +(0.705224 - 0.280454i) q^{29} +(4.90024 - 1.13240i) q^{31} +(0.627807 + 0.367764i) q^{33} +(1.39542 - 1.22181i) q^{35} +(-0.523913 - 0.142155i) q^{37} +(-0.953739 - 0.338075i) q^{39} +(6.73144 - 3.28665i) q^{41} +(-0.649411 + 6.84241i) q^{43} +(-3.40549 - 0.519575i) q^{45} +(-0.232797 - 12.2994i) q^{47} +(2.92473 + 3.47070i) q^{49} +(-0.0885833 - 1.55855i) q^{51} +(-0.808450 - 4.70046i) q^{53} +(2.58404 - 1.38513i) q^{55} +(-0.244830 - 0.119539i) q^{57} +(8.03690 - 0.609566i) q^{59} +(-8.00247 + 8.15537i) q^{61} +(-0.774895 + 4.50536i) q^{63} +(-3.16715 + 2.56802i) q^{65} +(2.08121 - 0.920329i) q^{67} +(0.561602 - 2.23643i) q^{69} +(-3.99676 + 0.455799i) q^{71} +(-5.25963 + 3.94438i) q^{73} +(-0.681055 + 0.808192i) q^{75} +(-1.77290 - 3.46330i) q^{77} +(-3.52765 + 9.38398i) q^{79} +(7.10364 - 4.16126i) q^{81} +(-6.17495 + 8.56709i) q^{83} +(-5.54413 - 2.97183i) q^{85} +(-0.108891 - 0.194223i) q^{87} +(-3.78095 - 12.9592i) q^{89} +(3.32771 + 4.26666i) q^{91} +(-0.519222 - 1.38119i) q^{93} +(-0.925624 + 0.590372i) q^{95} +(11.7691 + 2.71971i) q^{97} +(-2.79700 + 6.66320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{11}{83}\right)\) \(1\)

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 0
\(3\) −0.0387535 0.290817i −0.0223744 0.167903i 0.976489 0.215567i \(-0.0691599\pi\)
−0.998863 + 0.0476633i \(0.984823\pi\)
\(4\) 0 0
\(5\) −1.08122 0.478126i −0.483538 0.213824i 0.148274 0.988946i \(-0.452628\pi\)
−0.631812 + 0.775122i \(0.717688\pi\)
\(6\) 0 0
\(7\) −0.661531 + 1.42256i −0.250035 + 0.537677i −0.990999 0.133867i \(-0.957260\pi\)
0.740964 + 0.671545i \(0.234369\pi\)
\(8\) 0 0
\(9\) 2.81224 0.763053i 0.937414 0.254351i
\(10\) 0 0
\(11\) −1.52518 + 1.95553i −0.459858 + 0.589613i −0.961274 0.275593i \(-0.911126\pi\)
0.501416 + 0.865206i \(0.332813\pi\)
\(12\) 0 0
\(13\) 1.57161 3.07008i 0.435887 0.851488i −0.563787 0.825921i \(-0.690656\pi\)
0.999673 0.0255673i \(-0.00813923\pi\)
\(14\) 0 0
\(15\) −0.0971461 + 0.332967i −0.0250830 + 0.0859718i
\(16\) 0 0
\(17\) 5.30559 + 0.402408i 1.28680 + 0.0975983i 0.701176 0.712988i \(-0.252659\pi\)
0.585619 + 0.810586i \(0.300851\pi\)
\(18\) 0 0
\(19\) 0.514102 0.773362i 0.117943 0.177421i −0.769072 0.639163i \(-0.779281\pi\)
0.887015 + 0.461741i \(0.152775\pi\)
\(20\) 0 0
\(21\) 0.439342 + 0.137255i 0.0958722 + 0.0299516i
\(22\) 0 0
\(23\) 7.30313 + 2.90431i 1.52281 + 0.605591i 0.973226 0.229849i \(-0.0738232\pi\)
0.549582 + 0.835440i \(0.314787\pi\)
\(24\) 0 0
\(25\) −2.42392 2.66487i −0.484785 0.532974i
\(26\) 0 0
\(27\) −0.671561 1.59984i −0.129242 0.307889i
\(28\) 0 0
\(29\) 0.705224 0.280454i 0.130957 0.0520790i −0.303135 0.952948i \(-0.598033\pi\)
0.434092 + 0.900869i \(0.357069\pi\)
\(30\) 0 0
\(31\) 4.90024 1.13240i 0.880109 0.203384i 0.239172 0.970977i \(-0.423124\pi\)
0.640937 + 0.767593i \(0.278546\pi\)
\(32\) 0 0
\(33\) 0.627807 + 0.367764i 0.109287 + 0.0640195i
\(34\) 0 0
\(35\) 1.39542 1.22181i 0.235870 0.206523i
\(36\) 0 0
\(37\) −0.523913 0.142155i −0.0861308 0.0233701i 0.218538 0.975828i \(-0.429871\pi\)
−0.304669 + 0.952458i \(0.598546\pi\)
\(38\) 0 0
\(39\) −0.953739 0.338075i −0.152720 0.0541354i
\(40\) 0 0
\(41\) 6.73144 3.28665i 1.05127 0.513288i 0.169780 0.985482i \(-0.445694\pi\)
0.881495 + 0.472194i \(0.156538\pi\)
\(42\) 0 0
\(43\) −0.649411 + 6.84241i −0.0990343 + 1.04346i 0.798346 + 0.602199i \(0.205709\pi\)
−0.897380 + 0.441258i \(0.854532\pi\)
\(44\) 0 0
\(45\) −3.40549 0.519575i −0.507661 0.0774537i
\(46\) 0 0
\(47\) −0.232797 12.2994i −0.0339570 1.79405i −0.458550 0.888669i \(-0.651631\pi\)
0.424593 0.905384i \(-0.360417\pi\)
\(48\) 0 0
\(49\) 2.92473 + 3.47070i 0.417818 + 0.495815i
\(50\) 0 0
\(51\) −0.0885833 1.55855i −0.0124041 0.218241i
\(52\) 0 0
\(53\) −0.808450 4.70046i −0.111049 0.645658i −0.986680 0.162676i \(-0.947987\pi\)
0.875630 0.482982i \(-0.160446\pi\)
\(54\) 0 0
\(55\) 2.58404 1.38513i 0.348432 0.186771i
\(56\) 0 0
\(57\) −0.244830 0.119539i −0.0324286 0.0158334i
\(58\) 0 0
\(59\) 8.03690 0.609566i 1.04631 0.0793588i 0.458774 0.888553i \(-0.348289\pi\)
0.587541 + 0.809194i \(0.300096\pi\)
\(60\) 0 0
\(61\) −8.00247 + 8.15537i −1.02461 + 1.04419i −0.0256024 + 0.999672i \(0.508150\pi\)
−0.999009 + 0.0445158i \(0.985826\pi\)
\(62\) 0 0
\(63\) −0.774895 + 4.50536i −0.0976276 + 0.567623i
\(64\) 0 0
\(65\) −3.16715 + 2.56802i −0.392836 + 0.318523i
\(66\) 0 0
\(67\) 2.08121 0.920329i 0.254260 0.112436i −0.273374 0.961908i \(-0.588140\pi\)
0.527634 + 0.849472i \(0.323079\pi\)
\(68\) 0 0
\(69\) 0.561602 2.23643i 0.0676090 0.269234i
\(70\) 0 0
\(71\) −3.99676 + 0.455799i −0.474328 + 0.0540934i −0.347196 0.937792i \(-0.612866\pi\)
−0.127132 + 0.991886i \(0.540577\pi\)
\(72\) 0 0
\(73\) −5.25963 + 3.94438i −0.615594 + 0.461655i −0.861582 0.507618i \(-0.830526\pi\)
0.245988 + 0.969273i \(0.420887\pi\)
\(74\) 0 0
\(75\) −0.681055 + 0.808192i −0.0786414 + 0.0933220i
\(76\) 0 0
\(77\) −1.77290 3.46330i −0.202041 0.394679i
\(78\) 0 0
\(79\) −3.52765 + 9.38398i −0.396892 + 1.05578i 0.574543 + 0.818474i \(0.305180\pi\)
−0.971435 + 0.237305i \(0.923736\pi\)
\(80\) 0 0
\(81\) 7.10364 4.16126i 0.789293 0.462362i
\(82\) 0 0
\(83\) −6.17495 + 8.56709i −0.677788 + 0.940360i −0.999980 0.00631424i \(-0.997990\pi\)
0.322192 + 0.946674i \(0.395580\pi\)
\(84\) 0 0
\(85\) −5.54413 2.97183i −0.601345 0.322341i
\(86\) 0 0
\(87\) −0.108891 0.194223i −0.0116743 0.0208229i
\(88\) 0 0
\(89\) −3.78095 12.9592i −0.400780 1.37367i −0.871070 0.491158i \(-0.836574\pi\)
0.470290 0.882512i \(-0.344149\pi\)
\(90\) 0 0
\(91\) 3.32771 + 4.26666i 0.348839 + 0.447268i
\(92\) 0 0
\(93\) −0.519222 1.38119i −0.0538408 0.143223i
\(94\) 0 0
\(95\) −0.925624 + 0.590372i −0.0949670 + 0.0605708i
\(96\) 0 0
\(97\) 11.7691 + 2.71971i 1.19497 + 0.276145i 0.775335 0.631550i \(-0.217581\pi\)
0.419632 + 0.907694i \(0.362159\pi\)
\(98\) 0 0
\(99\) −2.79700 + 6.66320i −0.281109 + 0.669677i
\(100\) 0 0
\(101\) −0.296888 3.12811i −0.0295415 0.311259i −0.998057 0.0623059i \(-0.980155\pi\)
0.968516 0.248953i \(-0.0800864\pi\)
\(102\) 0 0
\(103\) −9.72112 + 6.73092i −0.957851 + 0.663217i −0.941629 0.336651i \(-0.890706\pi\)
−0.0162211 + 0.999868i \(0.505164\pi\)
\(104\) 0 0
\(105\) −0.409401 0.358464i −0.0399534 0.0349825i
\(106\) 0 0
\(107\) 11.9990 + 8.30810i 1.15998 + 0.803174i 0.983461 0.181122i \(-0.0579729\pi\)
0.176523 + 0.984297i \(0.443515\pi\)
\(108\) 0 0
\(109\) −12.4546 7.94368i −1.19294 0.760866i −0.216418 0.976301i \(-0.569438\pi\)
−0.976518 + 0.215434i \(0.930883\pi\)
\(110\) 0 0
\(111\) −0.0210376 + 0.157872i −0.00199680 + 0.0149846i
\(112\) 0 0
\(113\) 5.16835 8.45192i 0.486197 0.795090i −0.511750 0.859135i \(-0.671003\pi\)
0.997947 + 0.0640449i \(0.0204001\pi\)
\(114\) 0 0
\(115\) −6.50769 6.63203i −0.606845 0.618440i
\(116\) 0 0
\(117\) 2.07711 9.83304i 0.192029 0.909065i
\(118\) 0 0
\(119\) −4.08226 + 7.28132i −0.374220 + 0.667478i
\(120\) 0 0
\(121\) 1.18118 + 4.70372i 0.107380 + 0.427611i
\(122\) 0 0
\(123\) −1.21668 1.83025i −0.109704 0.165028i
\(124\) 0 0
\(125\) 3.21580 + 9.64807i 0.287630 + 0.862949i
\(126\) 0 0
\(127\) −1.81226 0.206673i −0.160812 0.0183393i 0.0325302 0.999471i \(-0.489643\pi\)
−0.193342 + 0.981131i \(0.561933\pi\)
\(128\) 0 0
\(129\) 2.01506 0.0763074i 0.177416 0.00671850i
\(130\) 0 0
\(131\) −0.150962 + 2.65605i −0.0131896 + 0.232060i 0.985029 + 0.172391i \(0.0551492\pi\)
−0.998218 + 0.0596693i \(0.980995\pi\)
\(132\) 0 0
\(133\) 0.760060 + 1.24294i 0.0659056 + 0.107777i
\(134\) 0 0
\(135\) −0.0388180 + 2.05087i −0.00334092 + 0.176511i
\(136\) 0 0
\(137\) −14.7482 + 5.22784i −1.26002 + 0.446645i −0.878512 0.477720i \(-0.841463\pi\)
−0.381510 + 0.924365i \(0.624596\pi\)
\(138\) 0 0
\(139\) −5.24139 4.95195i −0.444569 0.420019i 0.431568 0.902080i \(-0.357960\pi\)
−0.876137 + 0.482061i \(0.839888\pi\)
\(140\) 0 0
\(141\) −3.56786 + 0.544347i −0.300468 + 0.0458423i
\(142\) 0 0
\(143\) 3.60664 + 7.75575i 0.301602 + 0.648568i
\(144\) 0 0
\(145\) −0.896596 0.0339529i −0.0744583 0.00281963i
\(146\) 0 0
\(147\) 0.895997 0.985063i 0.0739006 0.0812466i
\(148\) 0 0
\(149\) −9.82438 7.96589i −0.804845 0.652591i 0.136273 0.990671i \(-0.456488\pi\)
−0.941117 + 0.338080i \(0.890223\pi\)
\(150\) 0 0
\(151\) −11.5218 8.64059i −0.937632 0.703162i 0.0173429 0.999850i \(-0.494479\pi\)
−0.954974 + 0.296688i \(0.904118\pi\)
\(152\) 0 0
\(153\) 15.2277 2.91678i 1.23108 0.235808i
\(154\) 0 0
\(155\) −5.83968 1.11856i −0.469054 0.0898450i
\(156\) 0 0
\(157\) −1.45063 6.86726i −0.115773 0.548067i −0.997136 0.0756282i \(-0.975904\pi\)
0.881363 0.472439i \(-0.156626\pi\)
\(158\) 0 0
\(159\) −1.33565 + 0.417271i −0.105924 + 0.0330917i
\(160\) 0 0
\(161\) −8.96280 + 8.46785i −0.706368 + 0.667360i
\(162\) 0 0
\(163\) −5.18031 + 15.5420i −0.405754 + 1.21735i 0.524811 + 0.851219i \(0.324136\pi\)
−0.930565 + 0.366128i \(0.880683\pi\)
\(164\) 0 0
\(165\) −0.502961 0.697806i −0.0391555 0.0543241i
\(166\) 0 0
\(167\) −9.79664 + 8.42768i −0.758087 + 0.652153i
\(168\) 0 0
\(169\) 0.645897 + 0.896114i 0.0496844 + 0.0689318i
\(170\) 0 0
\(171\) 0.855662 2.56717i 0.0654341 0.196316i
\(172\) 0 0
\(173\) 5.60127 5.29195i 0.425856 0.402339i −0.443698 0.896176i \(-0.646334\pi\)
0.869555 + 0.493837i \(0.164406\pi\)
\(174\) 0 0
\(175\) 5.39444 1.68528i 0.407781 0.127395i
\(176\) 0 0
\(177\) −0.488730 2.31365i −0.0367352 0.173904i
\(178\) 0 0
\(179\) −12.3176 2.35937i −0.920659 0.176348i −0.294148 0.955760i \(-0.595036\pi\)
−0.626511 + 0.779412i \(0.715518\pi\)
\(180\) 0 0
\(181\) −20.2160 + 3.87227i −1.50264 + 0.287824i −0.872484 0.488642i \(-0.837492\pi\)
−0.630159 + 0.776466i \(0.717010\pi\)
\(182\) 0 0
\(183\) 2.68185 + 2.01121i 0.198248 + 0.148673i
\(184\) 0 0
\(185\) 0.498499 + 0.404198i 0.0366504 + 0.0297172i
\(186\) 0 0
\(187\) −8.87889 + 9.76148i −0.649289 + 0.713830i
\(188\) 0 0
\(189\) 2.72013 + 0.103007i 0.197860 + 0.00749268i
\(190\) 0 0
\(191\) −4.83847 10.4047i −0.350099 0.752856i 0.649875 0.760041i \(-0.274821\pi\)
−0.999974 + 0.00718499i \(0.997713\pi\)
\(192\) 0 0
\(193\) −0.975189 + 0.148784i −0.0701956 + 0.0107097i −0.185827 0.982582i \(-0.559496\pi\)
0.115631 + 0.993292i \(0.463111\pi\)
\(194\) 0 0
\(195\) 0.869562 + 0.821542i 0.0622706 + 0.0588318i
\(196\) 0 0
\(197\) 11.3167 4.01147i 0.806281 0.285805i 0.101140 0.994872i \(-0.467751\pi\)
0.705141 + 0.709067i \(0.250884\pi\)
\(198\) 0 0
\(199\) −0.210627 + 11.1281i −0.0149310 + 0.788849i 0.911268 + 0.411814i \(0.135105\pi\)
−0.926199 + 0.377035i \(0.876944\pi\)
\(200\) 0 0
\(201\) −0.348302 0.569586i −0.0245673 0.0401755i
\(202\) 0 0
\(203\) −0.0675649 + 1.18875i −0.00474213 + 0.0834340i
\(204\) 0 0
\(205\) −8.84962 + 0.335123i −0.618085 + 0.0234060i
\(206\) 0 0
\(207\) 22.7543 + 2.59495i 1.58153 + 0.180361i
\(208\) 0 0
\(209\) 0.728233 + 2.18485i 0.0503729 + 0.151130i
\(210\) 0 0
\(211\) −8.50596 12.7955i −0.585574 0.880878i 0.413993 0.910280i \(-0.364134\pi\)
−0.999568 + 0.0294020i \(0.990640\pi\)
\(212\) 0 0
\(213\) 0.287443 + 1.14466i 0.0196953 + 0.0784310i
\(214\) 0 0
\(215\) 3.97369 7.08767i 0.271004 0.483375i
\(216\) 0 0
\(217\) −1.63076 + 7.72000i −0.110703 + 0.524068i
\(218\) 0 0
\(219\) 1.35092 + 1.37673i 0.0912869 + 0.0930311i
\(220\) 0 0
\(221\) 9.57376 15.6562i 0.644001 1.05315i
\(222\) 0 0
\(223\) 2.10496 15.7962i 0.140958 1.05779i −0.767865 0.640612i \(-0.778681\pi\)
0.908824 0.417181i \(-0.136982\pi\)
\(224\) 0 0
\(225\) −8.85010 5.64468i −0.590006 0.376312i
\(226\) 0 0
\(227\) 23.2731 + 16.1143i 1.54469 + 1.06955i 0.967479 + 0.252951i \(0.0814011\pi\)
0.577211 + 0.816595i \(0.304141\pi\)
\(228\) 0 0
\(229\) 21.7396 + 19.0348i 1.43659 + 1.25786i 0.914268 + 0.405110i \(0.132767\pi\)
0.522326 + 0.852746i \(0.325064\pi\)
\(230\) 0 0
\(231\) −0.938480 + 0.649805i −0.0617474 + 0.0427540i
\(232\) 0 0
\(233\) −0.238496 2.51287i −0.0156244 0.164624i 0.984305 0.176473i \(-0.0564690\pi\)
−0.999930 + 0.0118498i \(0.996228\pi\)
\(234\) 0 0
\(235\) −5.62896 + 13.4097i −0.367193 + 0.874753i
\(236\) 0 0
\(237\) 2.86573 + 0.662241i 0.186149 + 0.0430172i
\(238\) 0 0
\(239\) 1.91779 1.22319i 0.124052 0.0791213i −0.474260 0.880385i \(-0.657284\pi\)
0.598312 + 0.801264i \(0.295839\pi\)
\(240\) 0 0
\(241\) −6.16860 16.4092i −0.397354 1.05701i −0.971246 0.238078i \(-0.923483\pi\)
0.573892 0.818931i \(-0.305433\pi\)
\(242\) 0 0
\(243\) −4.68666 6.00906i −0.300649 0.385482i
\(244\) 0 0
\(245\) −1.50285 5.15099i −0.0960133 0.329085i
\(246\) 0 0
\(247\) −1.56632 2.79376i −0.0996624 0.177763i
\(248\) 0 0
\(249\) 2.73076 + 1.46378i 0.173055 + 0.0927631i
\(250\) 0 0
\(251\) −9.47076 + 13.1397i −0.597789 + 0.829370i −0.996132 0.0878669i \(-0.971995\pi\)
0.398343 + 0.917236i \(0.369585\pi\)
\(252\) 0 0
\(253\) −16.8180 + 9.85187i −1.05734 + 0.619382i
\(254\) 0 0
\(255\) −0.649406 + 1.72750i −0.0406674 + 0.108180i
\(256\) 0 0
\(257\) 12.9482 + 25.2939i 0.807689 + 1.57779i 0.816160 + 0.577825i \(0.196099\pi\)
−0.00847155 + 0.999964i \(0.502697\pi\)
\(258\) 0 0
\(259\) 0.548809 0.651258i 0.0341013 0.0404672i
\(260\) 0 0
\(261\) 1.76926 1.32683i 0.109514 0.0821285i
\(262\) 0 0
\(263\) 13.7733 1.57074i 0.849298 0.0968557i 0.322212 0.946668i \(-0.395574\pi\)
0.527086 + 0.849812i \(0.323285\pi\)
\(264\) 0 0
\(265\) −1.37330 + 5.46879i −0.0843610 + 0.335945i
\(266\) 0 0
\(267\) −3.62223 + 1.60178i −0.221677 + 0.0980273i
\(268\) 0 0
\(269\) 3.10007 2.51362i 0.189014 0.153258i −0.530624 0.847607i \(-0.678042\pi\)
0.719639 + 0.694349i \(0.244308\pi\)
\(270\) 0 0
\(271\) 2.55941 14.8809i 0.155473 0.903947i −0.798042 0.602602i \(-0.794131\pi\)
0.953515 0.301345i \(-0.0974357\pi\)
\(272\) 0 0
\(273\) 1.11186 1.13310i 0.0672928 0.0685785i
\(274\) 0 0
\(275\) 8.90814 0.675646i 0.537181 0.0407430i
\(276\) 0 0
\(277\) −13.9240 6.79845i −0.836613 0.408479i −0.0299934 0.999550i \(-0.509549\pi\)
−0.806619 + 0.591071i \(0.798705\pi\)
\(278\) 0 0
\(279\) 12.9166 6.92371i 0.773295 0.414512i
\(280\) 0 0
\(281\) −4.15417 24.1530i −0.247817 1.44085i −0.796409 0.604758i \(-0.793270\pi\)
0.548592 0.836090i \(-0.315164\pi\)
\(282\) 0 0
\(283\) −0.465963 8.19825i −0.0276986 0.487335i −0.982047 0.188638i \(-0.939593\pi\)
0.954348 0.298697i \(-0.0965519\pi\)
\(284\) 0 0
\(285\) 0.207561 + 0.246308i 0.0122949 + 0.0145900i
\(286\) 0 0
\(287\) 0.222400 + 11.7501i 0.0131279 + 0.693587i
\(288\) 0 0
\(289\) 11.1819 + 1.70601i 0.657757 + 0.100354i
\(290\) 0 0
\(291\) 0.334846 3.52805i 0.0196290 0.206818i
\(292\) 0 0
\(293\) 5.35528 2.61473i 0.312859 0.152754i −0.275621 0.961266i \(-0.588883\pi\)
0.588480 + 0.808512i \(0.299727\pi\)
\(294\) 0 0
\(295\) −8.98113 3.18357i −0.522901 0.185355i
\(296\) 0 0
\(297\) 4.15278 + 1.12678i 0.240969 + 0.0653827i
\(298\) 0 0
\(299\) 20.3942 17.8568i 1.17942 1.03268i
\(300\) 0 0
\(301\) −9.30413 5.45029i −0.536281 0.314150i
\(302\) 0 0
\(303\) −0.898203 + 0.207566i −0.0516004 + 0.0119243i
\(304\) 0 0
\(305\) 12.5517 4.99158i 0.718711 0.285817i
\(306\) 0 0
\(307\) −5.05314 12.0379i −0.288398 0.687041i 0.711480 0.702707i \(-0.248025\pi\)
−0.999877 + 0.0156653i \(0.995013\pi\)
\(308\) 0 0
\(309\) 2.33420 + 2.56622i 0.132788 + 0.145987i
\(310\) 0 0
\(311\) −12.2474 4.87055i −0.694486 0.276183i −0.00448272 0.999990i \(-0.501427\pi\)
−0.690003 + 0.723807i \(0.742391\pi\)
\(312\) 0 0
\(313\) 25.7486 + 8.04414i 1.45539 + 0.454682i 0.920669 0.390344i \(-0.127644\pi\)
0.534725 + 0.845026i \(0.320415\pi\)
\(314\) 0 0
\(315\) 2.99197 4.50081i 0.168578 0.253592i
\(316\) 0 0
\(317\) 7.73712 + 0.586830i 0.434560 + 0.0329596i 0.291091 0.956695i \(-0.405982\pi\)
0.143469 + 0.989655i \(0.454174\pi\)
\(318\) 0 0
\(319\) −0.527157 + 1.80682i −0.0295151 + 0.101163i
\(320\) 0 0
\(321\) 1.95114 3.81147i 0.108902 0.212736i
\(322\) 0 0
\(323\) 3.03882 3.89627i 0.169085 0.216794i
\(324\) 0 0
\(325\) −11.9908 + 3.25351i −0.665132 + 0.180472i
\(326\) 0 0
\(327\) −1.82750 + 3.92987i −0.101061 + 0.217322i
\(328\) 0 0
\(329\) 17.6506 + 7.80527i 0.973112 + 0.430318i
\(330\) 0 0
\(331\) −2.17672 16.3347i −0.119643 0.897837i −0.943578 0.331152i \(-0.892563\pi\)
0.823934 0.566686i \(-0.191775\pi\)
\(332\) 0 0
\(333\) −1.58184 −0.0866844
\(334\) 0 0
\(335\) −2.69028 −0.146986
\(336\) 0 0
\(337\) 3.77217 + 28.3074i 0.205483 + 1.54200i 0.725725 + 0.687985i \(0.241504\pi\)
−0.520242 + 0.854019i \(0.674158\pi\)
\(338\) 0 0
\(339\) −2.65826 1.17550i −0.144377 0.0638446i
\(340\) 0 0
\(341\) −5.25931 + 11.3096i −0.284807 + 0.612452i
\(342\) 0 0
\(343\) −17.4708 + 4.74041i −0.943336 + 0.255958i
\(344\) 0 0
\(345\) −1.67651 + 2.14956i −0.0902604 + 0.115729i
\(346\) 0 0
\(347\) 9.72301 18.9935i 0.521958 1.01963i −0.468713 0.883351i \(-0.655282\pi\)
0.990671 0.136275i \(-0.0435132\pi\)
\(348\) 0 0
\(349\) −1.98459 + 6.80215i −0.106232 + 0.364111i −0.995671 0.0929433i \(-0.970372\pi\)
0.889439 + 0.457054i \(0.151095\pi\)
\(350\) 0 0
\(351\) −5.96708 0.452579i −0.318499 0.0241569i
\(352\) 0 0
\(353\) 4.52715 6.81019i 0.240956 0.362470i −0.692344 0.721568i \(-0.743422\pi\)
0.933300 + 0.359098i \(0.116916\pi\)
\(354\) 0 0
\(355\) 4.53932 + 1.41813i 0.240922 + 0.0752668i
\(356\) 0 0
\(357\) 2.27574 + 0.905016i 0.120445 + 0.0478985i
\(358\) 0 0
\(359\) 8.87690 + 9.75930i 0.468505 + 0.515076i 0.927734 0.373242i \(-0.121754\pi\)
−0.459229 + 0.888318i \(0.651874\pi\)
\(360\) 0 0
\(361\) 7.02017 + 16.7239i 0.369482 + 0.880207i
\(362\) 0 0
\(363\) 1.32215 0.525792i 0.0693947 0.0275969i
\(364\) 0 0
\(365\) 7.57275 1.74998i 0.396376 0.0915983i
\(366\) 0 0
\(367\) 5.45278 + 3.19420i 0.284633 + 0.166736i 0.640847 0.767669i \(-0.278583\pi\)
−0.356214 + 0.934404i \(0.615933\pi\)
\(368\) 0 0
\(369\) 16.4226 14.3793i 0.854924 0.748556i
\(370\) 0 0
\(371\) 7.22150 + 1.95943i 0.374922 + 0.101729i
\(372\) 0 0
\(373\) 20.0244 + 7.09813i 1.03682 + 0.367527i 0.797440 0.603398i \(-0.206187\pi\)
0.239385 + 0.970925i \(0.423054\pi\)
\(374\) 0 0
\(375\) 2.68120 1.30911i 0.138457 0.0676019i
\(376\) 0 0
\(377\) 0.247322 2.60586i 0.0127377 0.134209i
\(378\) 0 0
\(379\) 17.2331 + 2.62925i 0.885206 + 0.135055i 0.577466 0.816415i \(-0.304042\pi\)
0.307740 + 0.951470i \(0.400427\pi\)
\(380\) 0 0
\(381\) 0.0101271 + 0.535045i 0.000518825 + 0.0274112i
\(382\) 0 0
\(383\) 8.70213 + 10.3266i 0.444658 + 0.527666i 0.940065 0.340995i \(-0.110764\pi\)
−0.495407 + 0.868661i \(0.664981\pi\)
\(384\) 0 0
\(385\) 0.261010 + 4.59226i 0.0133023 + 0.234043i
\(386\) 0 0
\(387\) 3.39482 + 19.7380i 0.172568 + 1.00334i
\(388\) 0 0
\(389\) −26.3902 + 14.1460i −1.33803 + 0.717231i −0.976579 0.215159i \(-0.930973\pi\)
−0.361456 + 0.932389i \(0.617720\pi\)
\(390\) 0 0
\(391\) 37.5787 + 18.3479i 1.90044 + 0.927895i
\(392\) 0 0
\(393\) 0.778276 0.0590291i 0.0392588 0.00297762i
\(394\) 0 0
\(395\) 8.30090 8.45951i 0.417664 0.425644i
\(396\) 0 0
\(397\) 4.43279 25.7729i 0.222475 1.29351i −0.632387 0.774652i \(-0.717925\pi\)
0.854862 0.518855i \(-0.173641\pi\)
\(398\) 0 0
\(399\) 0.332015 0.269207i 0.0166215 0.0134772i
\(400\) 0 0
\(401\) 8.24562 3.64628i 0.411767 0.182087i −0.188166 0.982137i \(-0.560254\pi\)
0.599933 + 0.800051i \(0.295194\pi\)
\(402\) 0 0
\(403\) 4.22473 16.8238i 0.210449 0.838055i
\(404\) 0 0
\(405\) −9.67022 + 1.10281i −0.480517 + 0.0547992i
\(406\) 0 0
\(407\) 1.07705 0.807715i 0.0533873 0.0400369i
\(408\) 0 0
\(409\) −12.2890 + 14.5831i −0.607652 + 0.721086i −0.978186 0.207733i \(-0.933392\pi\)
0.370534 + 0.928819i \(0.379175\pi\)
\(410\) 0 0
\(411\) 2.09189 + 4.08643i 0.103185 + 0.201569i
\(412\) 0 0
\(413\) −4.44951 + 11.8362i −0.218946 + 0.582422i
\(414\) 0 0
\(415\) 10.7726 6.31053i 0.528808 0.309772i
\(416\) 0 0
\(417\) −1.23699 + 1.71619i −0.0605757 + 0.0840424i
\(418\) 0 0
\(419\) −3.36845 1.80560i −0.164560 0.0882094i 0.388096 0.921619i \(-0.373133\pi\)
−0.552656 + 0.833409i \(0.686386\pi\)
\(420\) 0 0
\(421\) −12.7997 22.8302i −0.623821 1.11268i −0.983724 0.179687i \(-0.942491\pi\)
0.359903 0.932990i \(-0.382810\pi\)
\(422\) 0 0
\(423\) −10.0398 34.4113i −0.488151 1.67313i
\(424\) 0 0
\(425\) −11.7880 15.1141i −0.571802 0.733143i
\(426\) 0 0
\(427\) −6.30762 16.7790i −0.305247 0.811994i
\(428\) 0 0
\(429\) 2.11573 1.34944i 0.102149 0.0651514i
\(430\) 0 0
\(431\) −28.1126 6.49654i −1.35414 0.312927i −0.515160 0.857094i \(-0.672268\pi\)
−0.838977 + 0.544167i \(0.816846\pi\)
\(432\) 0 0
\(433\) 1.19288 2.84177i 0.0573264 0.136567i −0.890864 0.454271i \(-0.849900\pi\)
0.948190 + 0.317704i \(0.102912\pi\)
\(434\) 0 0
\(435\) 0.0248722 + 0.262062i 0.00119253 + 0.0125649i
\(436\) 0 0
\(437\) 6.00064 4.15485i 0.287050 0.198754i
\(438\) 0 0
\(439\) 28.3578 + 24.8296i 1.35344 + 1.18505i 0.964591 + 0.263751i \(0.0849597\pi\)
0.388852 + 0.921300i \(0.372872\pi\)
\(440\) 0 0
\(441\) 10.8734 + 7.52874i 0.517779 + 0.358511i
\(442\) 0 0
\(443\) −9.25699 5.90420i −0.439813 0.280517i 0.299223 0.954183i \(-0.403273\pi\)
−0.739036 + 0.673666i \(0.764718\pi\)
\(444\) 0 0
\(445\) −2.10807 + 15.8195i −0.0999320 + 0.749918i
\(446\) 0 0
\(447\) −1.93589 + 3.16581i −0.0915645 + 0.149737i
\(448\) 0 0
\(449\) −7.23565 7.37390i −0.341471 0.347996i 0.521497 0.853253i \(-0.325374\pi\)
−0.862969 + 0.505257i \(0.831398\pi\)
\(450\) 0 0
\(451\) −3.83951 + 18.1762i −0.180796 + 0.855885i
\(452\) 0 0
\(453\) −2.06632 + 3.68559i −0.0970844 + 0.173164i
\(454\) 0 0
\(455\) −1.55799 6.20428i −0.0730398 0.290861i
\(456\) 0 0
\(457\) −5.92741 8.91658i −0.277272 0.417100i 0.667609 0.744512i \(-0.267318\pi\)
−0.944882 + 0.327411i \(0.893824\pi\)
\(458\) 0 0
\(459\) −2.91924 8.75834i −0.136259 0.408804i
\(460\) 0 0
\(461\) −34.2345 3.90418i −1.59446 0.181836i −0.729609 0.683864i \(-0.760298\pi\)
−0.864851 + 0.502029i \(0.832587\pi\)
\(462\) 0 0
\(463\) −36.9238 + 1.39825i −1.71600 + 0.0649824i −0.877397 0.479766i \(-0.840722\pi\)
−0.838600 + 0.544748i \(0.816625\pi\)
\(464\) 0 0
\(465\) −0.0989887 + 1.74163i −0.00459049 + 0.0807661i
\(466\) 0 0
\(467\) 14.1226 + 23.0950i 0.653516 + 1.06871i 0.991817 + 0.127671i \(0.0407503\pi\)
−0.338301 + 0.941038i \(0.609852\pi\)
\(468\) 0 0
\(469\) −0.0675612 + 3.56947i −0.00311969 + 0.164823i
\(470\) 0 0
\(471\) −1.94090 + 0.687998i −0.0894320 + 0.0317013i
\(472\) 0 0
\(473\) −12.3900 11.7058i −0.569695 0.538234i
\(474\) 0 0
\(475\) −3.30706 + 0.504556i −0.151738 + 0.0231506i
\(476\) 0 0
\(477\) −5.86026 12.6019i −0.268323 0.577003i
\(478\) 0 0
\(479\) −7.30589 0.276664i −0.333814 0.0126411i −0.129597 0.991567i \(-0.541368\pi\)
−0.204217 + 0.978926i \(0.565465\pi\)
\(480\) 0 0
\(481\) −1.25982 + 1.38505i −0.0574426 + 0.0631526i
\(482\) 0 0
\(483\) 2.80994 + 2.27838i 0.127857 + 0.103670i
\(484\) 0 0
\(485\) −11.4246 8.56771i −0.518765 0.389040i
\(486\) 0 0
\(487\) −10.7237 + 2.05408i −0.485939 + 0.0930791i −0.425247 0.905077i \(-0.639813\pi\)
−0.0606920 + 0.998157i \(0.519331\pi\)
\(488\) 0 0
\(489\) 4.72065 + 0.904216i 0.213475 + 0.0408901i
\(490\) 0 0
\(491\) 4.18092 + 19.7924i 0.188682 + 0.893220i 0.964872 + 0.262720i \(0.0846197\pi\)
−0.776190 + 0.630499i \(0.782850\pi\)
\(492\) 0 0
\(493\) 3.85449 1.20419i 0.173597 0.0542338i
\(494\) 0 0
\(495\) 6.21002 5.86709i 0.279120 0.263706i
\(496\) 0 0
\(497\) 1.99558 5.98716i 0.0895139 0.268561i
\(498\) 0 0
\(499\) −16.5613 22.9771i −0.741387 1.02860i −0.998070 0.0621003i \(-0.980220\pi\)
0.256683 0.966496i \(-0.417370\pi\)
\(500\) 0 0
\(501\) 2.83057 + 2.52243i 0.126460 + 0.112694i
\(502\) 0 0
\(503\) −0.232796 0.322980i −0.0103799 0.0144010i 0.806014 0.591896i \(-0.201621\pi\)
−0.816394 + 0.577495i \(0.804030\pi\)
\(504\) 0 0
\(505\) −1.17463 + 3.52414i −0.0522703 + 0.156822i
\(506\) 0 0
\(507\) 0.235575 0.222566i 0.0104622 0.00988448i
\(508\) 0 0
\(509\) 14.9790 4.67962i 0.663935 0.207421i 0.0523851 0.998627i \(-0.483318\pi\)
0.611549 + 0.791206i \(0.290547\pi\)
\(510\) 0 0
\(511\) −2.13170 10.0915i −0.0943011 0.446420i
\(512\) 0 0
\(513\) −1.58251 0.303121i −0.0698694 0.0133831i
\(514\) 0 0
\(515\) 13.7289 2.62971i 0.604969 0.115879i
\(516\) 0 0
\(517\) 24.4069 + 18.3035i 1.07341 + 0.804988i
\(518\) 0 0
\(519\) −1.75606 1.42386i −0.0770824 0.0625007i
\(520\) 0 0
\(521\) 3.02147 3.32181i 0.132373 0.145531i −0.669985 0.742375i \(-0.733699\pi\)
0.802357 + 0.596844i \(0.203579\pi\)
\(522\) 0 0
\(523\) 1.77142 + 0.0670813i 0.0774589 + 0.00293326i 0.0765425 0.997066i \(-0.475612\pi\)
0.000916395 1.00000i \(0.499708\pi\)
\(524\) 0 0
\(525\) −0.699163 1.50349i −0.0305140 0.0656175i
\(526\) 0 0
\(527\) 26.4544 4.03613i 1.15237 0.175817i
\(528\) 0 0
\(529\) 28.1822 + 26.6259i 1.22531 + 1.15765i
\(530\) 0 0
\(531\) 22.1366 7.84683i 0.960645 0.340523i
\(532\) 0 0
\(533\) 0.488925 25.8314i 0.0211777 1.11888i
\(534\) 0 0
\(535\) −9.00123 14.7199i −0.389157 0.636398i
\(536\) 0 0
\(537\) −0.208796 + 3.67360i −0.00901020 + 0.158527i
\(538\) 0 0
\(539\) −11.2478 + 0.425937i −0.484476 + 0.0183464i
\(540\) 0 0
\(541\) 6.87453 + 0.783986i 0.295559 + 0.0337062i 0.259827 0.965655i \(-0.416335\pi\)
0.0357322 + 0.999361i \(0.488624\pi\)
\(542\) 0 0
\(543\) 1.90956 + 5.72910i 0.0819472 + 0.245859i
\(544\) 0 0
\(545\) 9.66815 + 14.5438i 0.414138 + 0.622987i
\(546\) 0 0
\(547\) −1.06569 4.24383i −0.0455656 0.181453i 0.942852 0.333212i \(-0.108133\pi\)
−0.988417 + 0.151759i \(0.951506\pi\)
\(548\) 0 0
\(549\) −16.2819 + 29.0412i −0.694894 + 1.23945i
\(550\) 0 0
\(551\) 0.145665 0.689576i 0.00620553 0.0293769i
\(552\) 0 0
\(553\) −11.0156 11.2261i −0.468432 0.477382i
\(554\) 0 0
\(555\) 0.0982291 0.160636i 0.00416959 0.00681863i
\(556\) 0 0
\(557\) −4.21395 + 31.6226i −0.178551 + 1.33989i 0.641288 + 0.767300i \(0.278400\pi\)
−0.819839 + 0.572594i \(0.805937\pi\)
\(558\) 0 0
\(559\) 19.9861 + 12.7474i 0.845324 + 0.539156i
\(560\) 0 0
\(561\) 3.18290 + 2.20384i 0.134382 + 0.0930463i
\(562\) 0 0
\(563\) −3.30506 2.89385i −0.139292 0.121961i 0.586278 0.810110i \(-0.300592\pi\)
−0.725570 + 0.688148i \(0.758424\pi\)
\(564\) 0 0
\(565\) −9.62922 + 6.66729i −0.405104 + 0.280495i
\(566\) 0 0
\(567\) 1.22036 + 12.8581i 0.0512504 + 0.539991i
\(568\) 0 0
\(569\) −7.94024 + 18.9158i −0.332872 + 0.792991i 0.666020 + 0.745934i \(0.267996\pi\)
−0.998892 + 0.0470576i \(0.985016\pi\)
\(570\) 0 0
\(571\) −44.9720 10.3926i −1.88202 0.434915i −0.882637 0.470056i \(-0.844234\pi\)
−0.999382 + 0.0351407i \(0.988812\pi\)
\(572\) 0 0
\(573\) −2.83835 + 1.81033i −0.118574 + 0.0756276i
\(574\) 0 0
\(575\) −9.96262 26.5017i −0.415470 1.10520i
\(576\) 0 0
\(577\) 10.8035 + 13.8519i 0.449757 + 0.576661i 0.958801 0.284079i \(-0.0916878\pi\)
−0.509044 + 0.860740i \(0.670001\pi\)
\(578\) 0 0
\(579\) 0.0810610 + 0.277836i 0.00336878 + 0.0115465i
\(580\) 0 0
\(581\) −8.10228 14.4516i −0.336139 0.599554i
\(582\) 0 0
\(583\) 10.4249 + 5.58809i 0.431755 + 0.231435i
\(584\) 0 0
\(585\) −6.94725 + 9.63858i −0.287234 + 0.398506i
\(586\) 0 0
\(587\) −6.82577 + 3.99849i −0.281730 + 0.165035i −0.639537 0.768760i \(-0.720874\pi\)
0.357807 + 0.933795i \(0.383525\pi\)
\(588\) 0 0
\(589\) 1.64347 4.37183i 0.0677181 0.180138i
\(590\) 0 0
\(591\) −1.60517 3.13563i −0.0660277 0.128983i
\(592\) 0 0
\(593\) −5.75298 + 6.82692i −0.236246 + 0.280348i −0.869857 0.493304i \(-0.835789\pi\)
0.633611 + 0.773652i \(0.281572\pi\)
\(594\) 0 0
\(595\) 7.89522 5.92089i 0.323673 0.242733i
\(596\) 0 0
\(597\) 3.24440 0.369998i 0.132785 0.0151430i
\(598\) 0 0
\(599\) 3.96986 15.8089i 0.162204 0.645934i −0.833433 0.552621i \(-0.813628\pi\)
0.995637 0.0933129i \(-0.0297457\pi\)
\(600\) 0 0
\(601\) −39.3184 + 17.3869i −1.60383 + 0.709228i −0.996371 0.0851206i \(-0.972872\pi\)
−0.607462 + 0.794349i \(0.707812\pi\)
\(602\) 0 0
\(603\) 5.15060 4.17626i 0.209749 0.170070i
\(604\) 0 0
\(605\) 0.971854 5.65052i 0.0395115 0.229726i
\(606\) 0 0
\(607\) −20.8847 + 21.2838i −0.847684 + 0.863881i −0.992076 0.125640i \(-0.959902\pi\)
0.144392 + 0.989521i \(0.453878\pi\)
\(608\) 0 0
\(609\) 0.348328 0.0264193i 0.0141150 0.00107056i
\(610\) 0 0
\(611\) −38.1261 18.6152i −1.54242 0.753090i
\(612\) 0 0
\(613\) −32.3697 + 17.3512i −1.30740 + 0.700809i −0.970584 0.240761i \(-0.922603\pi\)
−0.336815 + 0.941571i \(0.609350\pi\)
\(614\) 0 0
\(615\) 0.440414 + 2.56064i 0.0177592 + 0.103255i
\(616\) 0 0
\(617\) −0.154406 2.71666i −0.00621616 0.109368i 0.993782 0.111344i \(-0.0355156\pi\)
−0.999998 + 0.00197587i \(0.999371\pi\)
\(618\) 0 0
\(619\) −12.3874 14.6998i −0.497890 0.590834i 0.456379 0.889786i \(-0.349146\pi\)
−0.954268 + 0.298951i \(0.903363\pi\)
\(620\) 0 0
\(621\) −0.258063 13.6343i −0.0103557 0.547124i
\(622\) 0 0
\(623\) 20.9364 + 3.19426i 0.838800 + 0.127975i
\(624\) 0 0
\(625\) −0.565844 + 5.96192i −0.0226338 + 0.238477i
\(626\) 0 0
\(627\) 0.607172 0.296454i 0.0242481 0.0118392i
\(628\) 0 0
\(629\) −2.72247 0.965043i −0.108552 0.0384788i
\(630\) 0 0
\(631\) −25.1091 6.81293i −0.999579 0.271218i −0.275773 0.961223i \(-0.588934\pi\)
−0.723805 + 0.690004i \(0.757609\pi\)
\(632\) 0 0
\(633\) −3.39151 + 2.96955i −0.134801 + 0.118029i
\(634\) 0 0
\(635\) 1.86064 + 1.08995i 0.0738371 + 0.0432532i
\(636\) 0 0
\(637\) 15.2519 3.52455i 0.604302 0.139648i
\(638\) 0 0
\(639\) −10.8921 + 4.33156i −0.430883 + 0.171354i
\(640\) 0 0
\(641\) 10.4844 + 24.9766i 0.414107 + 0.986516i 0.986084 + 0.166246i \(0.0531646\pi\)
−0.571977 + 0.820270i \(0.693823\pi\)
\(642\) 0 0
\(643\) −17.5217 19.2635i −0.690990 0.759677i 0.289300 0.957238i \(-0.406577\pi\)
−0.980291 + 0.197561i \(0.936698\pi\)
\(644\) 0 0
\(645\) −2.21521 0.880946i −0.0872239 0.0346872i
\(646\) 0 0
\(647\) −11.2656 3.51949i −0.442896 0.138366i 0.0686138 0.997643i \(-0.478142\pi\)
−0.511509 + 0.859278i \(0.670913\pi\)
\(648\) 0 0
\(649\) −11.0657 + 16.6461i −0.434365 + 0.653415i
\(650\) 0 0
\(651\) 2.30831 + 0.175076i 0.0904697 + 0.00686176i
\(652\) 0 0
\(653\) −1.13985 + 3.90682i −0.0446057 + 0.152886i −0.979231 0.202749i \(-0.935012\pi\)
0.934625 + 0.355635i \(0.115735\pi\)
\(654\) 0 0
\(655\) 1.43315 2.79960i 0.0559978 0.109390i
\(656\) 0 0
\(657\) −11.7816 + 15.1059i −0.459644 + 0.589338i
\(658\) 0 0
\(659\) −9.47888 + 2.57193i −0.369245 + 0.100188i −0.441651 0.897187i \(-0.645607\pi\)
0.0724060 + 0.997375i \(0.476932\pi\)
\(660\) 0 0
\(661\) −10.3604 + 22.2790i −0.402972 + 0.866554i 0.595050 + 0.803689i \(0.297132\pi\)
−0.998022 + 0.0628650i \(0.979976\pi\)
\(662\) 0 0
\(663\) −4.92411 2.17748i −0.191236 0.0845664i
\(664\) 0 0
\(665\) −0.227511 1.70730i −0.00882248 0.0662064i
\(666\) 0 0
\(667\) 5.96487 0.230961
\(668\) 0 0
\(669\) −4.67538 −0.180761
\(670\) 0 0
\(671\) −3.74285 28.0874i −0.144491 1.08430i
\(672\) 0 0
\(673\) −14.6331 6.47089i −0.564065 0.249435i 0.102687 0.994714i \(-0.467256\pi\)
−0.666753 + 0.745279i \(0.732316\pi\)
\(674\) 0 0
\(675\) −2.63555 + 5.66751i −0.101443 + 0.218143i
\(676\) 0 0
\(677\) 2.80459 0.760977i 0.107789 0.0292467i −0.207561 0.978222i \(-0.566553\pi\)
0.315350 + 0.948975i \(0.397878\pi\)
\(678\) 0 0
\(679\) −11.6545 + 14.9430i −0.447260 + 0.573461i
\(680\) 0 0
\(681\) 3.78441 7.39271i 0.145019 0.283289i
\(682\) 0 0
\(683\) −3.42351 + 11.7341i −0.130997 + 0.448991i −0.998856 0.0478194i \(-0.984773\pi\)
0.867859 + 0.496811i \(0.165496\pi\)
\(684\) 0 0
\(685\) 18.4456 + 1.39903i 0.704772 + 0.0534541i
\(686\) 0 0
\(687\) 4.69317 7.05992i 0.179056 0.269353i
\(688\) 0 0
\(689\) −15.7014 4.90529i −0.598175 0.186877i
\(690\) 0 0
\(691\) −26.7306 10.6302i −1.01688 0.404393i −0.199134 0.979972i \(-0.563813\pi\)
−0.817746 + 0.575579i \(0.804777\pi\)
\(692\) 0 0
\(693\) −7.62850 8.38680i −0.289783 0.318588i
\(694\) 0 0
\(695\) 3.29946 + 7.86021i 0.125156 + 0.298155i
\(696\) 0 0
\(697\) 37.0369 14.7288i 1.40287 0.557895i
\(698\) 0 0
\(699\) −0.721544 + 0.166741i −0.0272913 + 0.00630674i
\(700\) 0 0
\(701\) −16.7806 9.82997i −0.633796 0.371273i 0.153232 0.988190i \(-0.451032\pi\)
−0.787028 + 0.616918i \(0.788381\pi\)
\(702\) 0 0
\(703\) −0.379282 + 0.332093i −0.0143049 + 0.0125251i
\(704\) 0 0
\(705\) 4.11792 + 1.11733i 0.155090 + 0.0420809i
\(706\) 0 0
\(707\) 4.64633 + 1.64700i 0.174743 + 0.0619418i
\(708\) 0 0
\(709\) −22.0329 + 10.7577i −0.827464 + 0.404012i −0.803212 0.595694i \(-0.796877\pi\)
−0.0242526 + 0.999706i \(0.507721\pi\)
\(710\) 0 0
\(711\) −2.76014 + 29.0818i −0.103514 + 1.09065i
\(712\) 0 0
\(713\) 39.0759 + 5.96180i 1.46341 + 0.223271i
\(714\) 0 0
\(715\) −0.191359 10.1101i −0.00715644 0.378097i
\(716\) 0 0
\(717\) −0.430045 0.510324i −0.0160603 0.0190584i
\(718\) 0 0
\(719\) 0.458211 + 8.06186i 0.0170884 + 0.300657i 0.995550 + 0.0942300i \(0.0300389\pi\)
−0.978462 + 0.206427i \(0.933817\pi\)
\(720\) 0 0
\(721\) −3.14432 18.2816i −0.117101 0.680842i
\(722\) 0 0
\(723\) −4.53302 + 2.42985i −0.168585 + 0.0903670i
\(724\) 0 0
\(725\) −2.45678 1.19953i −0.0912426 0.0445495i
\(726\) 0 0
\(727\) 19.6141 1.48765i 0.727445 0.0551738i 0.293305 0.956019i \(-0.405245\pi\)
0.434140 + 0.900845i \(0.357052\pi\)
\(728\) 0 0
\(729\) 15.7323 16.0329i 0.582677 0.593810i
\(730\) 0 0
\(731\) −6.19895 + 36.0417i −0.229277 + 1.33305i
\(732\) 0 0
\(733\) −13.1171 + 10.6357i −0.484490 + 0.392839i −0.840644 0.541589i \(-0.817823\pi\)
0.356153 + 0.934427i \(0.384088\pi\)
\(734\) 0 0
\(735\) −1.43976 + 0.636673i −0.0531062 + 0.0234840i
\(736\) 0 0
\(737\) −1.37449 + 5.47352i −0.0506299 + 0.201620i
\(738\) 0 0
\(739\) 46.1363 5.26148i 1.69715 0.193547i 0.789638 0.613573i \(-0.210268\pi\)
0.907512 + 0.420027i \(0.137979\pi\)
\(740\) 0 0
\(741\) −0.751774 + 0.563780i −0.0276171 + 0.0207110i
\(742\) 0 0
\(743\) −21.1796 + 25.1334i −0.777005 + 0.922053i −0.998590 0.0530877i \(-0.983094\pi\)
0.221585 + 0.975141i \(0.428877\pi\)
\(744\) 0 0
\(745\) 6.81364 + 13.3102i 0.249633 + 0.487648i
\(746\) 0 0
\(747\) −10.8283 + 28.8045i −0.396187 + 1.05390i
\(748\) 0 0
\(749\) −19.7565 + 11.5732i −0.721885 + 0.422875i
\(750\) 0 0
\(751\) 16.9242 23.4805i 0.617572 0.856816i −0.380105 0.924943i \(-0.624112\pi\)
0.997677 + 0.0681276i \(0.0217025\pi\)
\(752\) 0 0
\(753\) 4.18827 + 2.24505i 0.152629 + 0.0818142i
\(754\) 0 0
\(755\) 8.32635 + 14.8513i 0.303027 + 0.540494i
\(756\) 0 0
\(757\) −11.8844 40.7338i −0.431947 1.48049i −0.827192 0.561919i \(-0.810063\pi\)
0.395245 0.918576i \(-0.370660\pi\)
\(758\) 0 0
\(759\) 3.51685 + 4.50918i 0.127654 + 0.163673i
\(760\) 0 0
\(761\) 12.8942 + 34.3000i 0.467414 + 1.24337i 0.933481 + 0.358626i \(0.116755\pi\)
−0.466068 + 0.884749i \(0.654330\pi\)
\(762\) 0 0
\(763\) 19.5395 12.4625i 0.707376 0.451171i
\(764\) 0 0
\(765\) −17.8591 4.12705i −0.645697 0.149214i
\(766\) 0 0
\(767\) 10.7595 25.6319i 0.388501 0.925516i
\(768\) 0 0
\(769\) 0.0230929 + 0.243314i 0.000832750 + 0.00877413i 0.995933 0.0900971i \(-0.0287178\pi\)
−0.995100 + 0.0988713i \(0.968477\pi\)
\(770\) 0 0
\(771\) 6.85411 4.74580i 0.246845 0.170916i
\(772\) 0 0
\(773\) −8.48903 7.43285i −0.305329 0.267341i 0.492384 0.870378i \(-0.336126\pi\)
−0.797713 + 0.603037i \(0.793957\pi\)
\(774\) 0 0
\(775\) −14.8955 10.3137i −0.535062 0.370478i
\(776\) 0 0
\(777\) −0.210665 0.134364i −0.00755758 0.00482030i
\(778\) 0 0
\(779\) 0.918878 6.89552i 0.0329222 0.247058i
\(780\) 0 0
\(781\) 5.20444 8.51094i 0.186230 0.304545i
\(782\) 0 0
\(783\) −0.922282 0.939904i −0.0329597 0.0335894i
\(784\) 0 0
\(785\) −1.71496 + 8.11863i −0.0612097 + 0.289766i
\(786\) 0 0
\(787\) 5.80745 10.3584i 0.207013 0.369239i −0.748997 0.662574i \(-0.769464\pi\)
0.956010 + 0.293335i \(0.0947653\pi\)
\(788\) 0 0
\(789\) −0.990561 3.94464i −0.0352649 0.140433i
\(790\) 0 0
\(791\) 8.60434 + 12.9435i 0.305935 + 0.460217i
\(792\) 0 0
\(793\) 12.4609 + 37.3853i 0.442499 + 1.32759i
\(794\) 0 0
\(795\) 1.64364 + 0.187444i 0.0582939 + 0.00664795i
\(796\) 0