Properties

Label 668.2.e.a.21.5
Level $668$
Weight $2$
Character 668.21
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 21.5
Character \(\chi\) \(=\) 668.21
Dual form 668.2.e.a.509.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.69992 - 0.259356i) q^{3} +(-0.724427 - 0.859660i) q^{5} +(-2.54038 + 3.52451i) q^{7} +(-0.0410528 - 0.0128253i) q^{9} +O(q^{10})\) \(q+(-1.69992 - 0.259356i) q^{3} +(-0.724427 - 0.859660i) q^{5} +(-2.54038 + 3.52451i) q^{7} +(-0.0410528 - 0.0128253i) q^{9} +(3.97566 - 3.75611i) q^{11} +(0.411828 - 3.09047i) q^{13} +(1.00851 + 1.64924i) q^{15} +(-3.90237 + 5.87032i) q^{17} +(4.29909 + 0.993475i) q^{19} +(5.23254 - 5.33251i) q^{21} +(1.11800 + 5.29258i) q^{23} +(0.633303 - 3.68213i) q^{25} +(4.70218 + 2.29586i) q^{27} +(0.0318815 - 0.150927i) q^{29} +(9.99434 - 1.91437i) q^{31} +(-7.73247 + 5.35398i) q^{33} +(4.87020 - 0.369385i) q^{35} +(4.21572 - 1.31704i) q^{37} +(-1.50161 + 5.14674i) q^{39} +(8.59220 - 3.41695i) q^{41} +(-0.170641 - 0.0604876i) q^{43} +(0.0187143 + 0.0445825i) q^{45} +(0.0288402 - 0.114848i) q^{47} +(-3.75518 - 11.2663i) q^{49} +(8.15621 - 8.96697i) q^{51} +(0.180465 + 0.135337i) q^{53} +(-6.10906 - 0.696690i) q^{55} +(-7.05044 - 2.80382i) q^{57} +(0.557327 + 0.838386i) q^{59} +(-0.548065 - 0.702708i) q^{61} +(0.149493 - 0.112109i) q^{63} +(-2.95510 + 1.88479i) q^{65} +(1.41050 - 1.67380i) q^{67} +(-0.527839 - 9.28692i) q^{69} +(0.759892 + 8.00647i) q^{71} +(-0.447602 + 0.798365i) q^{73} +(-2.03154 + 6.09506i) q^{75} +(3.13877 + 23.5542i) q^{77} +(5.29749 + 0.200609i) q^{79} +(-7.29180 - 5.04886i) q^{81} +(2.99997 - 0.813991i) q^{83} +(7.87346 - 0.897906i) q^{85} +(-0.0933398 + 0.248295i) q^{87} +(-6.10917 + 9.99046i) q^{89} +(9.84619 + 9.30246i) q^{91} +(-17.4861 + 0.662173i) q^{93} +(-2.26032 - 4.41545i) q^{95} +(17.0247 + 3.26100i) q^{97} +(-0.211385 + 0.103210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{23}{83}\right)\) \(1\)

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
\(3\) −1.69992 0.259356i −0.981449 0.149739i −0.359795 0.933031i \(-0.617153\pi\)
−0.621654 + 0.783292i \(0.713539\pi\)
\(4\) 0 0
\(5\) −0.724427 0.859660i −0.323973 0.384452i 0.578150 0.815931i \(-0.303775\pi\)
−0.902123 + 0.431479i \(0.857992\pi\)
\(6\) 0 0
\(7\) −2.54038 + 3.52451i −0.960172 + 1.33214i −0.0169925 + 0.999856i \(0.505409\pi\)
−0.943180 + 0.332283i \(0.892181\pi\)
\(8\) 0 0
\(9\) −0.0410528 0.0128253i −0.0136843 0.00427512i
\(10\) 0 0
\(11\) 3.97566 3.75611i 1.19871 1.13251i 0.210789 0.977532i \(-0.432397\pi\)
0.987918 0.154979i \(-0.0495310\pi\)
\(12\) 0 0
\(13\) 0.411828 3.09047i 0.114221 0.857143i −0.836690 0.547677i \(-0.815512\pi\)
0.950910 0.309466i \(-0.100150\pi\)
\(14\) 0 0
\(15\) 1.00851 + 1.64924i 0.260396 + 0.425831i
\(16\) 0 0
\(17\) −3.90237 + 5.87032i −0.946463 + 1.42376i −0.0410853 + 0.999156i \(0.513082\pi\)
−0.905378 + 0.424607i \(0.860412\pi\)
\(18\) 0 0
\(19\) 4.29909 + 0.993475i 0.986278 + 0.227919i 0.687326 0.726349i \(-0.258784\pi\)
0.298952 + 0.954268i \(0.403363\pi\)
\(20\) 0 0
\(21\) 5.23254 5.33251i 1.14183 1.16365i
\(22\) 0 0
\(23\) 1.11800 + 5.29258i 0.233118 + 1.10358i 0.924527 + 0.381116i \(0.124460\pi\)
−0.691409 + 0.722463i \(0.743010\pi\)
\(24\) 0 0
\(25\) 0.633303 3.68213i 0.126661 0.736425i
\(26\) 0 0
\(27\) 4.70218 + 2.29586i 0.904935 + 0.441838i
\(28\) 0 0
\(29\) 0.0318815 0.150927i 0.00592025 0.0280264i −0.975349 0.220669i \(-0.929176\pi\)
0.981269 + 0.192643i \(0.0617059\pi\)
\(30\) 0 0
\(31\) 9.99434 1.91437i 1.79504 0.343830i 0.821124 0.570750i \(-0.193348\pi\)
0.973913 + 0.226920i \(0.0728657\pi\)
\(32\) 0 0
\(33\) −7.73247 + 5.35398i −1.34605 + 0.932008i
\(34\) 0 0
\(35\) 4.87020 0.369385i 0.823213 0.0624374i
\(36\) 0 0
\(37\) 4.21572 1.31704i 0.693059 0.216520i 0.0686776 0.997639i \(-0.478122\pi\)
0.624382 + 0.781119i \(0.285351\pi\)
\(38\) 0 0
\(39\) −1.50161 + 5.14674i −0.240450 + 0.824139i
\(40\) 0 0
\(41\) 8.59220 3.41695i 1.34188 0.533638i 0.415280 0.909694i \(-0.363684\pi\)
0.926597 + 0.376056i \(0.122720\pi\)
\(42\) 0 0
\(43\) −0.170641 0.0604876i −0.0260224 0.00922427i 0.321061 0.947058i \(-0.395961\pi\)
−0.347084 + 0.937834i \(0.612828\pi\)
\(44\) 0 0
\(45\) 0.0187143 + 0.0445825i 0.00278976 + 0.00664596i
\(46\) 0 0
\(47\) 0.0288402 0.114848i 0.00420677 0.0167523i −0.967748 0.251921i \(-0.918938\pi\)
0.971955 + 0.235169i \(0.0755642\pi\)
\(48\) 0 0
\(49\) −3.75518 11.2663i −0.536454 1.60947i
\(50\) 0 0
\(51\) 8.15621 8.96697i 1.14210 1.25563i
\(52\) 0 0
\(53\) 0.180465 + 0.135337i 0.0247887 + 0.0185899i 0.612288 0.790634i \(-0.290249\pi\)
−0.587500 + 0.809224i \(0.699888\pi\)
\(54\) 0 0
\(55\) −6.10906 0.696690i −0.823745 0.0939416i
\(56\) 0 0
\(57\) −7.05044 2.80382i −0.933853 0.371375i
\(58\) 0 0
\(59\) 0.557327 + 0.838386i 0.0725579 + 0.109149i 0.867270 0.497837i \(-0.165872\pi\)
−0.794713 + 0.606986i \(0.792378\pi\)
\(60\) 0 0
\(61\) −0.548065 0.702708i −0.0701725 0.0899726i 0.752158 0.658983i \(-0.229013\pi\)
−0.822330 + 0.569010i \(0.807326\pi\)
\(62\) 0 0
\(63\) 0.149493 0.112109i 0.0188343 0.0141245i
\(64\) 0 0
\(65\) −2.95510 + 1.88479i −0.366535 + 0.233779i
\(66\) 0 0
\(67\) 1.41050 1.67380i 0.172319 0.204488i −0.671665 0.740855i \(-0.734421\pi\)
0.843985 + 0.536367i \(0.180204\pi\)
\(68\) 0 0
\(69\) −0.527839 9.28692i −0.0635444 1.11801i
\(70\) 0 0
\(71\) 0.759892 + 8.00647i 0.0901826 + 0.950194i 0.919937 + 0.392065i \(0.128239\pi\)
−0.829755 + 0.558128i \(0.811520\pi\)
\(72\) 0 0
\(73\) −0.447602 + 0.798365i −0.0523879 + 0.0934415i −0.897207 0.441611i \(-0.854407\pi\)
0.844819 + 0.535053i \(0.179708\pi\)
\(74\) 0 0
\(75\) −2.03154 + 6.09506i −0.234583 + 0.703797i
\(76\) 0 0
\(77\) 3.13877 + 23.5542i 0.357696 + 2.68425i
\(78\) 0 0
\(79\) 5.29749 + 0.200609i 0.596014 + 0.0225702i 0.334127 0.942528i \(-0.391559\pi\)
0.261888 + 0.965098i \(0.415655\pi\)
\(80\) 0 0
\(81\) −7.29180 5.04886i −0.810200 0.560984i
\(82\) 0 0
\(83\) 2.99997 0.813991i 0.329290 0.0893471i −0.0933808 0.995630i \(-0.529767\pi\)
0.422671 + 0.906283i \(0.361093\pi\)
\(84\) 0 0
\(85\) 7.87346 0.897906i 0.853997 0.0973916i
\(86\) 0 0
\(87\) −0.0933398 + 0.248295i −0.0100071 + 0.0266200i
\(88\) 0 0
\(89\) −6.10917 + 9.99046i −0.647570 + 1.05899i 0.345150 + 0.938547i \(0.387828\pi\)
−0.992721 + 0.120439i \(0.961570\pi\)
\(90\) 0 0
\(91\) 9.84619 + 9.30246i 1.03216 + 0.975163i
\(92\) 0 0
\(93\) −17.4861 + 0.662173i −1.81322 + 0.0686642i
\(94\) 0 0
\(95\) −2.26032 4.41545i −0.231904 0.453016i
\(96\) 0 0
\(97\) 17.0247 + 3.26100i 1.72860 + 0.331104i 0.953650 0.300920i \(-0.0972936\pi\)
0.774949 + 0.632024i \(0.217776\pi\)
\(98\) 0 0
\(99\) −0.211385 + 0.103210i −0.0212450 + 0.0103730i
\(100\) 0 0
\(101\) −5.24763 + 1.86015i −0.522159 + 0.185092i −0.582111 0.813110i \(-0.697773\pi\)
0.0599514 + 0.998201i \(0.480905\pi\)
\(102\) 0 0
\(103\) −0.253172 + 13.3759i −0.0249458 + 1.31797i 0.739447 + 0.673215i \(0.235087\pi\)
−0.764393 + 0.644751i \(0.776961\pi\)
\(104\) 0 0
\(105\) −8.37474 0.635190i −0.817291 0.0619882i
\(106\) 0 0
\(107\) −0.362987 19.1777i −0.0350913 1.85398i −0.392152 0.919900i \(-0.628269\pi\)
0.357061 0.934081i \(-0.383779\pi\)
\(108\) 0 0
\(109\) −5.98037 + 11.6824i −0.572816 + 1.11897i 0.405931 + 0.913904i \(0.366947\pi\)
−0.978747 + 0.205071i \(0.934258\pi\)
\(110\) 0 0
\(111\) −7.50796 + 1.14549i −0.712624 + 0.108725i
\(112\) 0 0
\(113\) −9.13471 7.99819i −0.859321 0.752407i 0.111104 0.993809i \(-0.464561\pi\)
−0.970425 + 0.241402i \(0.922393\pi\)
\(114\) 0 0
\(115\) 3.73992 4.79518i 0.348749 0.447153i
\(116\) 0 0
\(117\) −0.0565431 + 0.121591i −0.00522741 + 0.0112411i
\(118\) 0 0
\(119\) −10.7765 28.6668i −0.987880 2.62788i
\(120\) 0 0
\(121\) 1.07329 18.8838i 0.0975722 1.71671i
\(122\) 0 0
\(123\) −15.4923 + 3.58010i −1.39689 + 0.322807i
\(124\) 0 0
\(125\) −8.47423 + 4.96414i −0.757958 + 0.444006i
\(126\) 0 0
\(127\) −0.0565232 + 0.595546i −0.00501562 + 0.0528462i −0.997683 0.0680287i \(-0.978329\pi\)
0.992668 + 0.120875i \(0.0385700\pi\)
\(128\) 0 0
\(129\) 0.274387 + 0.147081i 0.0241585 + 0.0129497i
\(130\) 0 0
\(131\) −2.50237 2.75111i −0.218633 0.240366i 0.620614 0.784116i \(-0.286883\pi\)
−0.839247 + 0.543750i \(0.817004\pi\)
\(132\) 0 0
\(133\) −14.4228 + 12.6284i −1.25062 + 1.09502i
\(134\) 0 0
\(135\) −1.43273 5.70546i −0.123310 0.491048i
\(136\) 0 0
\(137\) −4.07494 13.9668i −0.348145 1.19326i −0.926126 0.377214i \(-0.876882\pi\)
0.577981 0.816050i \(-0.303841\pi\)
\(138\) 0 0
\(139\) −12.7574 + 5.64142i −1.08207 + 0.478499i −0.867106 0.498124i \(-0.834023\pi\)
−0.214961 + 0.976623i \(0.568962\pi\)
\(140\) 0 0
\(141\) −0.0788125 + 0.187753i −0.00663721 + 0.0158116i
\(142\) 0 0
\(143\) −9.97088 13.8335i −0.833807 1.15682i
\(144\) 0 0
\(145\) −0.152842 + 0.0819281i −0.0126928 + 0.00680376i
\(146\) 0 0
\(147\) 3.46151 + 20.1258i 0.285500 + 1.65995i
\(148\) 0 0
\(149\) 14.0286 + 8.94759i 1.14927 + 0.733016i 0.968132 0.250442i \(-0.0805760\pi\)
0.181139 + 0.983458i \(0.442022\pi\)
\(150\) 0 0
\(151\) 2.42211 + 4.32019i 0.197108 + 0.351572i 0.952922 0.303214i \(-0.0980599\pi\)
−0.755814 + 0.654786i \(0.772759\pi\)
\(152\) 0 0
\(153\) 0.235492 0.190944i 0.0190384 0.0154369i
\(154\) 0 0
\(155\) −8.88587 7.20492i −0.713730 0.578713i
\(156\) 0 0
\(157\) −4.93351 10.6091i −0.393737 0.846695i −0.998726 0.0504609i \(-0.983931\pi\)
0.604989 0.796234i \(-0.293177\pi\)
\(158\) 0 0
\(159\) −0.271675 0.276866i −0.0215452 0.0219569i
\(160\) 0 0
\(161\) −21.4939 9.50477i −1.69395 0.749081i
\(162\) 0 0
\(163\) 18.5886 + 10.8891i 1.45597 + 0.852899i 0.999325 0.0367480i \(-0.0116999\pi\)
0.456650 + 0.889647i \(0.349049\pi\)
\(164\) 0 0
\(165\) 10.2042 + 2.76874i 0.794397 + 0.215546i
\(166\) 0 0
\(167\) −3.88125 + 12.3262i −0.300340 + 0.953832i
\(168\) 0 0
\(169\) 3.16494 + 0.858752i 0.243457 + 0.0660578i
\(170\) 0 0
\(171\) −0.163748 0.0959222i −0.0125221 0.00733535i
\(172\) 0 0
\(173\) 5.91298 + 2.61477i 0.449556 + 0.198797i 0.616803 0.787118i \(-0.288428\pi\)
−0.167247 + 0.985915i \(0.553488\pi\)
\(174\) 0 0
\(175\) 11.3688 + 11.5861i 0.859404 + 0.875824i
\(176\) 0 0
\(177\) −0.729971 1.56973i −0.0548680 0.117989i
\(178\) 0 0
\(179\) 5.95683 + 4.82997i 0.445234 + 0.361009i 0.826007 0.563660i \(-0.190607\pi\)
−0.380773 + 0.924669i \(0.624342\pi\)
\(180\) 0 0
\(181\) 11.2305 9.10601i 0.834756 0.676844i −0.113783 0.993506i \(-0.536297\pi\)
0.948539 + 0.316661i \(0.102562\pi\)
\(182\) 0 0
\(183\) 0.749414 + 1.33669i 0.0553983 + 0.0988111i
\(184\) 0 0
\(185\) −4.18618 2.66999i −0.307774 0.196301i
\(186\) 0 0
\(187\) 6.53510 + 37.9961i 0.477894 + 2.77855i
\(188\) 0 0
\(189\) −20.0371 + 10.7405i −1.45748 + 0.781258i
\(190\) 0 0
\(191\) −3.81289 5.28999i −0.275891 0.382770i 0.650392 0.759599i \(-0.274605\pi\)
−0.926283 + 0.376829i \(0.877014\pi\)
\(192\) 0 0
\(193\) 8.10430 19.3066i 0.583360 1.38972i −0.314423 0.949283i \(-0.601811\pi\)
0.897783 0.440439i \(-0.145177\pi\)
\(194\) 0 0
\(195\) 5.51226 2.43757i 0.394741 0.174558i
\(196\) 0 0
\(197\) −6.79435 23.2876i −0.484077 1.65917i −0.725095 0.688649i \(-0.758204\pi\)
0.241017 0.970521i \(-0.422519\pi\)
\(198\) 0 0
\(199\) −2.13212 8.49061i −0.151142 0.601883i −0.997588 0.0694088i \(-0.977889\pi\)
0.846446 0.532475i \(-0.178738\pi\)
\(200\) 0 0
\(201\) −2.83184 + 2.47951i −0.199743 + 0.174891i
\(202\) 0 0
\(203\) 0.450952 + 0.495778i 0.0316506 + 0.0347968i
\(204\) 0 0
\(205\) −9.16184 4.91105i −0.639890 0.343002i
\(206\) 0 0
\(207\) 0.0219824 0.231614i 0.00152788 0.0160983i
\(208\) 0 0
\(209\) 20.8233 12.1981i 1.44038 0.843763i
\(210\) 0 0
\(211\) −21.9127 + 5.06379i −1.50853 + 0.348606i −0.896791 0.442454i \(-0.854108\pi\)
−0.611739 + 0.791060i \(0.709530\pi\)
\(212\) 0 0
\(213\) 0.784772 13.8074i 0.0537717 0.946070i
\(214\) 0 0
\(215\) 0.0716178 + 0.190512i 0.00488429 + 0.0129928i
\(216\) 0 0
\(217\) −18.6422 + 40.0883i −1.26552 + 2.72137i
\(218\) 0 0
\(219\) 0.967948 1.24107i 0.0654079 0.0838636i
\(220\) 0 0
\(221\) 16.5350 + 14.4777i 1.11226 + 0.973877i
\(222\) 0 0
\(223\) 25.6470 3.91295i 1.71745 0.262031i 0.784006 0.620753i \(-0.213173\pi\)
0.933444 + 0.358723i \(0.116788\pi\)
\(224\) 0 0
\(225\) −0.0732234 + 0.143039i −0.00488156 + 0.00953594i
\(226\) 0 0
\(227\) 0.502403 + 26.5435i 0.0333457 + 1.76176i 0.489638 + 0.871926i \(0.337129\pi\)
−0.456293 + 0.889830i \(0.650823\pi\)
\(228\) 0 0
\(229\) 19.3624 + 1.46856i 1.27950 + 0.0970451i 0.697762 0.716330i \(-0.254179\pi\)
0.581740 + 0.813375i \(0.302372\pi\)
\(230\) 0 0
\(231\) 0.773270 40.8543i 0.0508774 2.68801i
\(232\) 0 0
\(233\) 6.76873 2.39934i 0.443434 0.157186i −0.103012 0.994680i \(-0.532848\pi\)
0.546446 + 0.837494i \(0.315980\pi\)
\(234\) 0 0
\(235\) −0.119623 + 0.0584063i −0.00780335 + 0.00381001i
\(236\) 0 0
\(237\) −8.95328 1.71495i −0.581578 0.111398i
\(238\) 0 0
\(239\) 1.59414 + 3.11409i 0.103116 + 0.201434i 0.935988 0.352033i \(-0.114509\pi\)
−0.832871 + 0.553467i \(0.813305\pi\)
\(240\) 0 0
\(241\) 17.2838 0.654514i 1.11335 0.0421610i 0.525248 0.850949i \(-0.323972\pi\)
0.588100 + 0.808788i \(0.299876\pi\)
\(242\) 0 0
\(243\) −0.324872 0.306932i −0.0208406 0.0196897i
\(244\) 0 0
\(245\) −6.96486 + 11.3898i −0.444969 + 0.727668i
\(246\) 0 0
\(247\) 4.84079 12.8771i 0.308012 0.819349i
\(248\) 0 0
\(249\) −5.31082 + 0.605658i −0.336560 + 0.0383820i
\(250\) 0 0
\(251\) −3.56203 + 0.966496i −0.224834 + 0.0610047i −0.372499 0.928033i \(-0.621499\pi\)
0.147665 + 0.989037i \(0.452824\pi\)
\(252\) 0 0
\(253\) 24.3243 + 16.8422i 1.52926 + 1.05886i
\(254\) 0 0
\(255\) −13.6171 0.515662i −0.852738 0.0322920i
\(256\) 0 0
\(257\) 2.08825 + 15.6708i 0.130261 + 0.977517i 0.927492 + 0.373842i \(0.121960\pi\)
−0.797231 + 0.603674i \(0.793703\pi\)
\(258\) 0 0
\(259\) −6.06760 + 18.2041i −0.377022 + 1.13115i
\(260\) 0 0
\(261\) −0.00324451 + 0.00578707i −0.000200830 + 0.000358211i
\(262\) 0 0
\(263\) −2.44048 25.7137i −0.150487 1.58558i −0.677372 0.735640i \(-0.736881\pi\)
0.526886 0.849936i \(-0.323360\pi\)
\(264\) 0 0
\(265\) −0.0143899 0.253180i −0.000883968 0.0155527i
\(266\) 0 0
\(267\) 12.9762 15.3985i 0.794129 0.942375i
\(268\) 0 0
\(269\) 8.26750 5.27309i 0.504078 0.321506i −0.261114 0.965308i \(-0.584090\pi\)
0.765192 + 0.643802i \(0.222644\pi\)
\(270\) 0 0
\(271\) −11.7338 + 8.79958i −0.712778 + 0.534536i −0.893536 0.448991i \(-0.851783\pi\)
0.180758 + 0.983528i \(0.442145\pi\)
\(272\) 0 0
\(273\) −14.3251 18.3671i −0.866994 1.11163i
\(274\) 0 0
\(275\) −11.3127 17.0176i −0.682180 1.02620i
\(276\) 0 0
\(277\) −2.26907 0.902366i −0.136335 0.0542179i 0.300368 0.953823i \(-0.402890\pi\)
−0.436704 + 0.899605i \(0.643854\pi\)
\(278\) 0 0
\(279\) −0.434848 0.0495910i −0.0260337 0.00296893i
\(280\) 0 0
\(281\) 3.68087 + 2.76041i 0.219582 + 0.164672i 0.704081 0.710120i \(-0.251359\pi\)
−0.484499 + 0.874792i \(0.660998\pi\)
\(282\) 0 0
\(283\) 20.1125 22.1117i 1.19556 1.31441i 0.258184 0.966096i \(-0.416876\pi\)
0.937379 0.348310i \(-0.113244\pi\)
\(284\) 0 0
\(285\) 2.69719 + 8.09214i 0.159768 + 0.479337i
\(286\) 0 0
\(287\) −9.78437 + 38.9636i −0.577553 + 2.29995i
\(288\) 0 0
\(289\) −12.6523 30.1413i −0.744256 1.77302i
\(290\) 0 0
\(291\) −28.0949 9.95890i −1.64695 0.583801i
\(292\) 0 0
\(293\) 3.39053 1.34835i 0.198077 0.0787713i −0.268388 0.963311i \(-0.586491\pi\)
0.466465 + 0.884539i \(0.345527\pi\)
\(294\) 0 0
\(295\) 0.316985 1.08646i 0.0184556 0.0632562i
\(296\) 0 0
\(297\) 27.3178 8.53438i 1.58514 0.495215i
\(298\) 0 0
\(299\) 16.8170 1.27550i 0.972552 0.0737641i
\(300\) 0 0
\(301\) 0.646680 0.447763i 0.0372740 0.0258086i
\(302\) 0 0
\(303\) 9.40300 1.80110i 0.540188 0.103470i
\(304\) 0 0
\(305\) −0.207058 + 0.980210i −0.0118561 + 0.0561267i
\(306\) 0 0
\(307\) 0.897746 + 0.438327i 0.0512371 + 0.0250167i 0.464189 0.885736i \(-0.346346\pi\)
−0.412952 + 0.910753i \(0.635502\pi\)
\(308\) 0 0
\(309\) 3.89949 22.6723i 0.221834 1.28978i
\(310\) 0 0
\(311\) 4.77983 + 22.6277i 0.271039 + 1.28310i 0.874235 + 0.485503i \(0.161364\pi\)
−0.603196 + 0.797593i \(0.706106\pi\)
\(312\) 0 0
\(313\) 8.25408 8.41178i 0.466548 0.475462i −0.439739 0.898126i \(-0.644929\pi\)
0.906287 + 0.422664i \(0.138905\pi\)
\(314\) 0 0
\(315\) −0.204672 0.0472977i −0.0115320 0.00266492i
\(316\) 0 0
\(317\) −4.14208 + 6.23091i −0.232642 + 0.349963i −0.930512 0.366262i \(-0.880637\pi\)
0.697870 + 0.716225i \(0.254131\pi\)
\(318\) 0 0
\(319\) −0.440148 0.719784i −0.0246436 0.0403002i
\(320\) 0 0
\(321\) −4.35681 + 32.6947i −0.243174 + 1.82484i
\(322\) 0 0
\(323\) −22.6086 + 21.3601i −1.25798 + 1.18851i
\(324\) 0 0
\(325\) −11.1187 3.47361i −0.616754 0.192681i
\(326\) 0 0
\(327\) 13.1961 18.3081i 0.729744 1.01244i
\(328\) 0 0
\(329\) 0.331518 + 0.393405i 0.0182772 + 0.0216891i
\(330\) 0 0
\(331\) 17.0057 + 2.59455i 0.934718 + 0.142610i 0.600263 0.799802i \(-0.295062\pi\)
0.334454 + 0.942412i \(0.391448\pi\)
\(332\) 0 0
\(333\) −0.189958 −0.0104096
\(334\) 0 0
\(335\) −2.46070 −0.134443
\(336\) 0 0
\(337\) −24.1738 3.68819i −1.31683 0.200909i −0.545914 0.837841i \(-0.683817\pi\)
−0.770919 + 0.636933i \(0.780203\pi\)
\(338\) 0 0
\(339\) 13.4539 + 15.9654i 0.730715 + 0.867123i
\(340\) 0 0
\(341\) 32.5435 45.1507i 1.76233 2.44505i
\(342\) 0 0
\(343\) 20.2191 + 6.31669i 1.09173 + 0.341069i
\(344\) 0 0
\(345\) −7.60121 + 7.18145i −0.409236 + 0.386636i
\(346\) 0 0
\(347\) 1.62901 12.2245i 0.0874496 0.656246i −0.891629 0.452766i \(-0.850437\pi\)
0.979079 0.203480i \(-0.0652253\pi\)
\(348\) 0 0
\(349\) 12.4654 + 20.3850i 0.667259 + 1.09118i 0.989501 + 0.144527i \(0.0461661\pi\)
−0.322241 + 0.946658i \(0.604436\pi\)
\(350\) 0 0
\(351\) 9.03177 13.5865i 0.482080 0.725192i
\(352\) 0 0
\(353\) −3.91764 0.905325i −0.208515 0.0481856i 0.119606 0.992821i \(-0.461837\pi\)
−0.328121 + 0.944636i \(0.606415\pi\)
\(354\) 0 0
\(355\) 6.33236 6.45335i 0.336087 0.342508i
\(356\) 0 0
\(357\) 10.8843 + 51.5261i 0.576057 + 2.72705i
\(358\) 0 0
\(359\) −0.743703 + 4.32401i −0.0392512 + 0.228213i −0.998527 0.0542586i \(-0.982720\pi\)
0.959276 + 0.282471i \(0.0911542\pi\)
\(360\) 0 0
\(361\) 0.421578 + 0.205837i 0.0221883 + 0.0108335i
\(362\) 0 0
\(363\) −6.72214 + 31.8225i −0.352821 + 1.67025i
\(364\) 0 0
\(365\) 1.01058 0.193571i 0.0528960 0.0101320i
\(366\) 0 0
\(367\) −24.7729 + 17.1528i −1.29313 + 0.895368i −0.998190 0.0601460i \(-0.980843\pi\)
−0.294945 + 0.955514i \(0.595301\pi\)
\(368\) 0 0
\(369\) −0.396557 + 0.0300773i −0.0206439 + 0.00156576i
\(370\) 0 0
\(371\) −0.935444 + 0.292243i −0.0485658 + 0.0151725i
\(372\) 0 0
\(373\) −6.93563 + 23.7718i −0.359113 + 1.23086i 0.557194 + 0.830382i \(0.311878\pi\)
−0.916308 + 0.400475i \(0.868845\pi\)
\(374\) 0 0
\(375\) 15.6930 6.24079i 0.810382 0.322273i
\(376\) 0 0
\(377\) −0.453306 0.160685i −0.0233464 0.00827569i
\(378\) 0 0
\(379\) −8.26649 19.6930i −0.424621 1.01156i −0.983269 0.182158i \(-0.941692\pi\)
0.558648 0.829405i \(-0.311320\pi\)
\(380\) 0 0
\(381\) 0.250543 0.997721i 0.0128357 0.0511148i
\(382\) 0 0
\(383\) −0.851737 2.55539i −0.0435217 0.130574i 0.924680 0.380745i \(-0.124332\pi\)
−0.968202 + 0.250171i \(0.919513\pi\)
\(384\) 0 0
\(385\) 17.9748 19.7616i 0.916080 1.00714i
\(386\) 0 0
\(387\) 0.00622949 + 0.00467171i 0.000316663 + 0.000237476i
\(388\) 0 0
\(389\) 4.74278 + 0.540877i 0.240469 + 0.0274236i 0.232709 0.972546i \(-0.425241\pi\)
0.00775940 + 0.999970i \(0.497530\pi\)
\(390\) 0 0
\(391\) −35.4320 14.0906i −1.79187 0.712592i
\(392\) 0 0
\(393\) 3.54031 + 5.32568i 0.178585 + 0.268645i
\(394\) 0 0
\(395\) −3.66519 4.69937i −0.184416 0.236451i
\(396\) 0 0
\(397\) −9.11239 + 6.83369i −0.457338 + 0.342973i −0.803605 0.595163i \(-0.797088\pi\)
0.346267 + 0.938136i \(0.387449\pi\)
\(398\) 0 0
\(399\) 27.7929 17.7265i 1.39138 0.887437i
\(400\) 0 0
\(401\) −19.3822 + 23.0004i −0.967901 + 1.14859i 0.0209657 + 0.999780i \(0.493326\pi\)
−0.988867 + 0.148805i \(0.952457\pi\)
\(402\) 0 0
\(403\) −1.80034 31.6756i −0.0896815 1.57788i
\(404\) 0 0
\(405\) 0.942074 + 9.92600i 0.0468120 + 0.493227i
\(406\) 0 0
\(407\) 11.8133 21.0708i 0.585564 1.04444i
\(408\) 0 0
\(409\) 3.26876 9.80698i 0.161630 0.484924i −0.836368 0.548168i \(-0.815325\pi\)
0.997998 + 0.0632442i \(0.0201447\pi\)
\(410\) 0 0
\(411\) 3.30469 + 24.7993i 0.163008 + 1.22326i
\(412\) 0 0
\(413\) −4.37072 0.165513i −0.215069 0.00814436i
\(414\) 0 0
\(415\) −2.87302 1.98928i −0.141031 0.0976500i
\(416\) 0 0
\(417\) 23.1496 6.28126i 1.13364 0.307594i
\(418\) 0 0
\(419\) −8.64432 + 0.985817i −0.422303 + 0.0481603i −0.321871 0.946784i \(-0.604312\pi\)
−0.100432 + 0.994944i \(0.532022\pi\)
\(420\) 0 0
\(421\) 1.38513 3.68461i 0.0675072 0.179577i −0.897975 0.440047i \(-0.854962\pi\)
0.965482 + 0.260470i \(0.0838775\pi\)
\(422\) 0 0
\(423\) −0.00265694 + 0.00434495i −0.000129185 + 0.000211259i
\(424\) 0 0
\(425\) 19.1439 + 18.0867i 0.928615 + 0.877334i
\(426\) 0 0
\(427\) 3.86899 0.146513i 0.187234 0.00709028i
\(428\) 0 0
\(429\) 13.3619 + 26.1019i 0.645117 + 1.26021i
\(430\) 0 0
\(431\) −14.0396 2.68921i −0.676262 0.129535i −0.161507 0.986872i \(-0.551635\pi\)
−0.514755 + 0.857337i \(0.672117\pi\)
\(432\) 0 0
\(433\) −11.3423 + 5.53791i −0.545075 + 0.266135i −0.690621 0.723217i \(-0.742663\pi\)
0.145546 + 0.989352i \(0.453506\pi\)
\(434\) 0 0
\(435\) 0.281067 0.0996308i 0.0134761 0.00477693i
\(436\) 0 0
\(437\) −0.451686 + 23.8640i −0.0216071 + 1.14157i
\(438\) 0 0
\(439\) 25.1248 + 1.90561i 1.19914 + 0.0909500i 0.660000 0.751266i \(-0.270556\pi\)
0.539141 + 0.842216i \(0.318749\pi\)
\(440\) 0 0
\(441\) 0.00966581 + 0.510675i 0.000460277 + 0.0243179i
\(442\) 0 0
\(443\) 4.18149 8.16838i 0.198669 0.388091i −0.769404 0.638763i \(-0.779447\pi\)
0.968072 + 0.250671i \(0.0806513\pi\)
\(444\) 0 0
\(445\) 13.0140 1.98555i 0.616925 0.0941240i
\(446\) 0 0
\(447\) −21.5269 18.8486i −1.01819 0.891508i
\(448\) 0 0
\(449\) −1.45182 + 1.86147i −0.0685155 + 0.0878481i −0.821562 0.570120i \(-0.806897\pi\)
0.753046 + 0.657968i \(0.228584\pi\)
\(450\) 0 0
\(451\) 21.3252 45.8579i 1.00417 2.15937i
\(452\) 0 0
\(453\) −2.99692 7.97215i −0.140808 0.374565i
\(454\) 0 0
\(455\) 0.864109 15.2033i 0.0405101 0.712743i
\(456\) 0 0
\(457\) −6.23312 + 1.44041i −0.291573 + 0.0673795i −0.368408 0.929664i \(-0.620097\pi\)
0.0768347 + 0.997044i \(0.475519\pi\)
\(458\) 0 0
\(459\) −31.8271 + 18.6440i −1.48556 + 0.870229i
\(460\) 0 0
\(461\) 1.77021 18.6515i 0.0824470 0.868689i −0.854554 0.519362i \(-0.826169\pi\)
0.937001 0.349326i \(-0.113590\pi\)
\(462\) 0 0
\(463\) 24.8760 + 13.3344i 1.15609 + 0.619700i 0.934683 0.355482i \(-0.115683\pi\)
0.221403 + 0.975182i \(0.428936\pi\)
\(464\) 0 0
\(465\) 13.2366 + 14.5524i 0.613834 + 0.674851i
\(466\) 0 0
\(467\) 3.72059 3.25768i 0.172168 0.150748i −0.568342 0.822792i \(-0.692415\pi\)
0.740511 + 0.672045i \(0.234584\pi\)
\(468\) 0 0
\(469\) 2.31614 + 9.22339i 0.106949 + 0.425897i
\(470\) 0 0
\(471\) 5.63505 + 19.3141i 0.259649 + 0.889945i
\(472\) 0 0
\(473\) −0.905607 + 0.400467i −0.0416399 + 0.0184135i
\(474\) 0 0
\(475\) 6.38072 15.2006i 0.292768 0.697452i
\(476\) 0 0
\(477\) −0.00567284 0.00787047i −0.000259741 0.000360364i
\(478\) 0 0
\(479\) −8.28183 + 4.43933i −0.378406 + 0.202838i −0.650628 0.759396i \(-0.725494\pi\)
0.272222 + 0.962234i \(0.412241\pi\)
\(480\) 0 0
\(481\) −2.33412 13.5709i −0.106427 0.618782i
\(482\) 0 0
\(483\) 34.0727 + 21.7319i 1.55036 + 0.988836i
\(484\) 0 0
\(485\) −9.52981 16.9978i −0.432726 0.771832i
\(486\) 0 0
\(487\) 11.2279 9.10388i 0.508783 0.412536i −0.340684 0.940178i \(-0.610659\pi\)
0.849467 + 0.527642i \(0.176924\pi\)
\(488\) 0 0
\(489\) −28.7750 23.3316i −1.30125 1.05509i
\(490\) 0 0
\(491\) 8.72505 + 18.7624i 0.393756 + 0.846735i 0.998725 + 0.0504863i \(0.0160771\pi\)
−0.604969 + 0.796249i \(0.706814\pi\)
\(492\) 0 0
\(493\) 0.761576 + 0.776127i 0.0342996 + 0.0349550i
\(494\) 0 0
\(495\) 0.241858 + 0.106952i 0.0108707 + 0.00480713i
\(496\) 0 0
\(497\) −30.1493 17.6612i −1.35238 0.792214i
\(498\) 0 0
\(499\) 8.02173 + 2.17656i 0.359102 + 0.0974362i 0.436844 0.899537i \(-0.356096\pi\)
−0.0777417 + 0.996974i \(0.524771\pi\)
\(500\) 0 0
\(501\) 9.79469 19.9470i 0.437595 0.891165i
\(502\) 0 0
\(503\) −3.03912 0.824612i −0.135508 0.0367676i 0.193465 0.981107i \(-0.438028\pi\)
−0.328972 + 0.944340i \(0.606702\pi\)
\(504\) 0 0
\(505\) 5.40062 + 3.16364i 0.240325 + 0.140780i
\(506\) 0 0
\(507\) −5.15742 2.28065i −0.229049 0.101287i
\(508\) 0 0
\(509\) 9.31439 + 9.49236i 0.412853 + 0.420741i 0.888487 0.458902i \(-0.151757\pi\)
−0.475634 + 0.879643i \(0.657781\pi\)
\(510\) 0 0
\(511\) −1.67676 3.60572i −0.0741757 0.159508i
\(512\) 0 0
\(513\) 17.9342 + 14.5416i 0.791815 + 0.642026i
\(514\) 0 0
\(515\) 11.6821 9.47221i 0.514776 0.417396i
\(516\) 0 0
\(517\) −0.316724 0.564924i −0.0139295 0.0248453i
\(518\) 0 0
\(519\) −9.37344 5.97847i −0.411448 0.262426i
\(520\) 0 0
\(521\) −6.06561 35.2665i −0.265739 1.54505i −0.744810 0.667276i \(-0.767460\pi\)
0.479071 0.877776i \(-0.340974\pi\)
\(522\) 0 0
\(523\) 20.5508 11.0159i 0.898624 0.481692i 0.0428733 0.999081i \(-0.486349\pi\)
0.855751 + 0.517389i \(0.173096\pi\)
\(524\) 0 0
\(525\) −16.3212 22.6440i −0.712316 0.988263i
\(526\) 0 0
\(527\) −27.7637 + 66.1406i −1.20940 + 2.88113i
\(528\) 0 0
\(529\) −5.72640 + 2.53226i −0.248974 + 0.110098i
\(530\) 0 0
\(531\) −0.0121272 0.0415660i −0.000526277 0.00180381i
\(532\) 0 0
\(533\) −7.02148 27.9612i −0.304134 1.21113i
\(534\) 0 0
\(535\) −16.2234 + 14.2049i −0.701398 + 0.614132i
\(536\) 0 0
\(537\) −8.87345 9.75550i −0.382918 0.420981i
\(538\) 0 0
\(539\) −57.2469 30.6862i −2.46580 1.32175i
\(540\) 0 0
\(541\) −2.86426 + 30.1787i −0.123144 + 1.29749i 0.693548 + 0.720411i \(0.256047\pi\)
−0.816692 + 0.577074i \(0.804194\pi\)
\(542\) 0 0
\(543\) −21.4526 + 12.5668i −0.920620 + 0.539292i
\(544\) 0 0
\(545\) 14.3753 3.32198i 0.615769 0.142298i
\(546\) 0 0
\(547\) 0.132164 2.32532i 0.00565091 0.0994234i −0.994325 0.106387i \(-0.966072\pi\)
0.999976 + 0.00696320i \(0.00221647\pi\)
\(548\) 0 0
\(549\) 0.0134871 + 0.0358772i 0.000575615 + 0.00153120i
\(550\) 0 0
\(551\) 0.287003 0.617174i 0.0122268 0.0262925i
\(552\) 0 0
\(553\) −14.1647 + 18.1614i −0.602343 + 0.772302i
\(554\) 0 0
\(555\) 6.42369 + 5.62447i 0.272671 + 0.238746i
\(556\) 0 0
\(557\) 11.2179 1.71151i 0.475317 0.0725190i 0.0912578 0.995827i \(-0.470911\pi\)
0.384060 + 0.923308i \(0.374526\pi\)
\(558\) 0 0
\(559\) −0.257210 + 0.502450i −0.0108788 + 0.0212514i
\(560\) 0 0
\(561\) −1.25462 66.2853i −0.0529699 2.79857i
\(562\) 0 0
\(563\) −46.3977 3.51908i −1.95543 0.148311i −0.962860 0.270001i \(-0.912976\pi\)
−0.992568 + 0.121690i \(0.961169\pi\)
\(564\) 0 0
\(565\) −0.258301 + 13.6469i −0.0108668 + 0.574127i
\(566\) 0 0
\(567\) 36.3187 12.8740i 1.52524 0.540657i
\(568\) 0 0
\(569\) −8.46771 + 4.13439i −0.354985 + 0.173323i −0.607598 0.794245i \(-0.707867\pi\)
0.252613 + 0.967567i \(0.418710\pi\)
\(570\) 0 0
\(571\) −22.8941 4.38525i −0.958088 0.183517i −0.314815 0.949153i \(-0.601942\pi\)
−0.643274 + 0.765636i \(0.722424\pi\)
\(572\) 0 0
\(573\) 5.10962 + 9.98144i 0.213457 + 0.416981i
\(574\) 0 0
\(575\) 20.1960 0.764793i 0.842230 0.0318941i
\(576\) 0 0
\(577\) −2.97414 2.80990i −0.123815 0.116978i 0.622349 0.782740i \(-0.286179\pi\)
−0.746164 + 0.665763i \(0.768106\pi\)
\(578\) 0 0
\(579\) −18.7839 + 30.7178i −0.780634 + 1.27659i
\(580\) 0 0
\(581\) −4.75215 + 12.6413i −0.197152 + 0.524448i
\(582\) 0 0
\(583\) 1.22581 0.139794i 0.0507677 0.00578966i
\(584\) 0 0
\(585\) 0.145488 0.0394756i 0.00601519 0.00163212i
\(586\) 0 0
\(587\) 35.9399 + 24.8849i 1.48340 + 1.02711i 0.987304 + 0.158839i \(0.0507751\pi\)
0.496094 + 0.868269i \(0.334767\pi\)
\(588\) 0 0
\(589\) 44.8684 + 1.69910i 1.84877 + 0.0700104i
\(590\) 0 0
\(591\) 5.51007 + 41.3491i 0.226654 + 1.70088i
\(592\) 0 0
\(593\) −6.44363 + 19.3323i −0.264608 + 0.793881i 0.729352 + 0.684139i \(0.239822\pi\)
−0.993960 + 0.109742i \(0.964998\pi\)
\(594\) 0 0
\(595\) −16.8369 + 30.0311i −0.690245 + 1.23115i
\(596\) 0 0
\(597\) 1.42235 + 14.9863i 0.0582128 + 0.613350i
\(598\) 0 0
\(599\) −0.0653149 1.14916i −0.00266869 0.0469536i 0.996778 0.0802064i \(-0.0255579\pi\)
−0.999447 + 0.0332528i \(0.989413\pi\)
\(600\) 0 0
\(601\) 10.3476 12.2793i 0.422087 0.500881i −0.511474 0.859299i \(-0.670900\pi\)
0.933561 + 0.358418i \(0.116684\pi\)
\(602\) 0 0
\(603\) −0.0793718 + 0.0506241i −0.00323227 + 0.00206157i
\(604\) 0 0
\(605\) −17.0112 + 12.7572i −0.691602 + 0.518656i
\(606\) 0 0
\(607\) 26.1737 + 33.5589i 1.06236 + 1.36212i 0.928592 + 0.371103i \(0.121020\pi\)
0.133766 + 0.991013i \(0.457293\pi\)
\(608\) 0 0
\(609\) −0.637998 0.959739i −0.0258530 0.0388906i
\(610\) 0 0
\(611\) −0.343058 0.136427i −0.0138786 0.00551927i
\(612\) 0 0
\(613\) −42.3561 4.83038i −1.71075 0.195097i −0.797730 0.603015i \(-0.793966\pi\)
−0.913019 + 0.407918i \(0.866255\pi\)
\(614\) 0 0
\(615\) 14.3007 + 10.7246i 0.576659 + 0.432456i
\(616\) 0 0
\(617\) 29.1406 32.0373i 1.17316 1.28977i 0.224136 0.974558i \(-0.428044\pi\)
0.949020 0.315215i \(-0.102077\pi\)
\(618\) 0 0
\(619\) −12.4233 37.2724i −0.499333 1.49810i −0.831846 0.555006i \(-0.812716\pi\)
0.332514 0.943098i \(-0.392103\pi\)
\(620\) 0 0
\(621\) −6.89398 + 27.4534i −0.276646 + 1.10167i
\(622\) 0 0
\(623\) −19.6919 46.9113i −0.788938 1.87946i
\(624\) 0 0
\(625\) −7.20104 2.55258i −0.288042 0.102103i
\(626\) 0 0
\(627\) −38.5616 + 15.3352i −1.54000 + 0.612429i
\(628\) 0 0
\(629\) −8.71984 + 29.8872i −0.347683 + 1.19168i
\(630\) 0 0
\(631\) −34.1169 + 10.6585i −1.35817 + 0.424308i −0.888639 0.458607i \(-0.848348\pi\)
−0.469532 + 0.882915i \(0.655577\pi\)
\(632\) 0 0
\(633\) 38.5631 2.92485i 1.53274 0.116253i
\(634\) 0 0
\(635\) 0.552915 0.382839i 0.0219417 0.0151925i
\(636\) 0 0
\(637\) −36.3648 + 6.96548i −1.44082 + 0.275982i
\(638\) 0 0
\(639\) 0.0714901 0.338434i 0.00282811 0.0133882i
\(640\) 0 0
\(641\) −14.2526 6.95889i −0.562944 0.274859i 0.135198 0.990819i \(-0.456833\pi\)
−0.698142 + 0.715959i \(0.745990\pi\)
\(642\) 0 0
\(643\) −0.478272 + 2.78075i −0.0188612 + 0.109662i −0.993433 0.114411i \(-0.963502\pi\)
0.974572 + 0.224073i \(0.0719356\pi\)
\(644\) 0 0
\(645\) −0.0723341 0.342429i −0.00284815 0.0134831i
\(646\) 0 0
\(647\) −25.5993 + 26.0884i −1.00641 + 1.02564i −0.00674061 + 0.999977i \(0.502146\pi\)
−0.999671 + 0.0256631i \(0.991830\pi\)
\(648\) 0 0
\(649\) 5.36482 + 1.23975i 0.210588 + 0.0486646i
\(650\) 0 0
\(651\) 42.0874 63.3120i 1.64954 2.48139i
\(652\) 0 0
\(653\) 1.28593 + 2.10291i 0.0503224 + 0.0822934i 0.877303 0.479938i \(-0.159341\pi\)
−0.826980 + 0.562231i \(0.809943\pi\)
\(654\) 0 0
\(655\) −0.552240 + 4.14417i −0.0215778 + 0.161926i
\(656\) 0 0
\(657\) 0.0286146 0.0270344i 0.00111636 0.00105471i
\(658\) 0 0
\(659\) −42.2943 13.2132i −1.64755 0.514714i −0.673145 0.739511i \(-0.735057\pi\)
−0.974406 + 0.224797i \(0.927828\pi\)
\(660\) 0 0
\(661\) 24.8920 34.5351i 0.968188 1.34326i 0.0291027 0.999576i \(-0.490735\pi\)
0.939086 0.343683i \(-0.111675\pi\)
\(662\) 0 0
\(663\) −24.3532 28.8994i −0.945801 1.12236i
\(664\) 0 0
\(665\) 21.3044 + 3.25040i 0.826148 + 0.126045i
\(666\) 0 0
\(667\) 0.834436 0.0323095
\(668\) 0 0
\(669\) −44.6127 −1.72483
\(670\) 0 0
\(671\) −4.81837 0.735137i −0.186011 0.0283796i
\(672\) 0 0
\(673\) −1.57957 1.87443i −0.0608878 0.0722541i 0.733393 0.679805i \(-0.237935\pi\)
−0.794281 + 0.607550i \(0.792152\pi\)
\(674\) 0 0
\(675\) 11.4315 15.8600i 0.440000 0.610453i
\(676\) 0 0
\(677\) −25.5706 7.98854i −0.982757 0.307024i −0.235730 0.971818i \(-0.575748\pi\)
−0.747027 + 0.664794i \(0.768519\pi\)
\(678\) 0 0
\(679\) −54.7426 + 51.7196i −2.10083 + 1.98482i
\(680\) 0 0
\(681\) 6.03018 45.2521i 0.231077 1.73407i
\(682\) 0 0
\(683\) −17.6330 28.8357i −0.674709 1.10337i −0.988110 0.153747i \(-0.950866\pi\)
0.313401 0.949621i \(-0.398532\pi\)
\(684\) 0 0
\(685\) −9.05472 + 13.6210i −0.345963 + 0.520431i
\(686\) 0 0
\(687\) −32.5336 7.51818i −1.24123 0.286836i
\(688\) 0 0
\(689\) 0.492575 0.501986i 0.0187656 0.0191241i
\(690\) 0 0
\(691\) 2.49949 + 11.8326i 0.0950852 + 0.450133i 0.999714 + 0.0239314i \(0.00761831\pi\)
−0.904628 + 0.426201i \(0.859852\pi\)
\(692\) 0 0
\(693\) 0.173236 1.00722i 0.00658068 0.0382611i
\(694\) 0 0
\(695\) 14.0915 + 6.88022i 0.534521 + 0.260981i
\(696\) 0 0
\(697\) −13.4713 + 63.7732i −0.510263 + 2.41558i
\(698\) 0 0
\(699\) −12.1286 + 2.32317i −0.458745 + 0.0878702i
\(700\) 0 0
\(701\) −35.3826 + 24.4990i −1.33638 + 0.925314i −0.999866 0.0163632i \(-0.994791\pi\)
−0.336517 + 0.941677i \(0.609249\pi\)
\(702\) 0 0
\(703\) 19.4322 1.47385i 0.732898 0.0555874i
\(704\) 0 0
\(705\) 0.218498 0.0682611i 0.00822909 0.00257086i
\(706\) 0 0
\(707\) 6.77487 23.2208i 0.254795 0.873308i
\(708\) 0 0
\(709\) 20.8149 8.27769i 0.781721 0.310875i 0.0556101 0.998453i \(-0.482290\pi\)
0.726111 + 0.687577i \(0.241326\pi\)
\(710\) 0 0
\(711\) −0.214904 0.0761777i −0.00805952 0.00285689i
\(712\) 0 0
\(713\) 21.3056 + 50.7556i 0.797899 + 1.90081i
\(714\) 0 0
\(715\) −4.66898 + 18.5930i −0.174610 + 0.695337i
\(716\) 0 0
\(717\) −1.90225 5.70715i −0.0710408 0.213138i
\(718\) 0 0
\(719\) 2.45184 2.69557i 0.0914383 0.100528i −0.692330 0.721581i \(-0.743416\pi\)
0.783768 + 0.621054i \(0.213295\pi\)
\(720\) 0 0
\(721\) −46.5003 34.8721i −1.73176 1.29871i
\(722\) 0 0
\(723\) −29.5509 3.37004i −1.09901 0.125333i
\(724\) 0 0
\(725\) −0.535541 0.212974i −0.0198895 0.00790966i
\(726\) 0 0
\(727\) −0.559928 0.842298i −0.0207666 0.0312391i 0.822252 0.569124i \(-0.192718\pi\)
−0.843018 + 0.537885i \(0.819224\pi\)
\(728\) 0 0
\(729\) 16.8361 + 21.5867i 0.623561 + 0.799507i
\(730\) 0 0
\(731\) 1.02098 0.765670i 0.0377624 0.0283193i
\(732\) 0 0
\(733\) 13.2342 8.44089i 0.488816 0.311771i −0.270245 0.962792i \(-0.587105\pi\)
0.759060 + 0.651020i \(0.225659\pi\)
\(734\) 0 0
\(735\) 14.7937 17.5554i 0.545674 0.647539i
\(736\) 0 0
\(737\) −0.679340 11.9525i −0.0250238 0.440274i
\(738\) 0 0
\(739\) −4.18215 44.0645i −0.153843 1.62094i −0.655033 0.755601i \(-0.727345\pi\)
0.501190 0.865337i \(-0.332896\pi\)
\(740\) 0 0
\(741\) −11.5687 + 20.6345i −0.424987 + 0.758027i
\(742\) 0 0
\(743\) −9.19392 + 27.5837i −0.337292 + 1.01195i 0.633852 + 0.773455i \(0.281473\pi\)
−0.971144 + 0.238494i \(0.923346\pi\)
\(744\) 0 0
\(745\) −2.47082 18.5417i −0.0905239 0.679317i
\(746\) 0 0
\(747\) −0.133597 0.00505913i −0.00488805 0.000185104i
\(748\) 0 0
\(749\) 68.5142 + 47.4393i 2.50345 + 1.73340i
\(750\) 0 0
\(751\) −41.5790 + 11.2818i −1.51724 + 0.411677i −0.920495 0.390754i \(-0.872214\pi\)
−0.596745 + 0.802431i \(0.703540\pi\)
\(752\) 0 0
\(753\) 6.30583 0.719131i 0.229797 0.0262066i
\(754\) 0 0
\(755\) 1.95925 5.21185i 0.0713046 0.189679i
\(756\) 0 0
\(757\) −0.255296 + 0.417492i −0.00927890 + 0.0151740i −0.857740 0.514084i \(-0.828132\pi\)
0.848461 + 0.529258i \(0.177530\pi\)
\(758\) 0 0
\(759\) −36.9812 34.9390i −1.34233 1.26821i
\(760\) 0 0
\(761\) −31.8648 + 1.20667i −1.15510 + 0.0437419i −0.608430 0.793608i \(-0.708200\pi\)
−0.546667 + 0.837350i \(0.684104\pi\)
\(762\) 0 0
\(763\) −25.9824 50.7557i −0.940626 1.83748i
\(764\) 0 0
\(765\) −0.334743 0.0641184i −0.0121027 0.00231820i
\(766\) 0 0
\(767\) 2.82053 1.37713i 0.101844 0.0497254i
\(768\) 0 0
\(769\) −15.4122 + 5.46321i −0.555778 + 0.197008i −0.597142 0.802136i \(-0.703697\pi\)
0.0413642 + 0.999144i \(0.486830\pi\)
\(770\) 0 0
\(771\) 0.514462 27.1807i 0.0185279 0.978888i
\(772\) 0 0
\(773\) 22.3872 + 1.69798i 0.805211 + 0.0610720i 0.471796 0.881708i \(-0.343606\pi\)
0.333416 + 0.942780i \(0.391799\pi\)
\(774\) 0 0
\(775\) −0.719488 38.0128i −0.0258448 1.36546i
\(776\) 0 0
\(777\) 15.0358 29.3718i 0.539405 1.05371i
\(778\) 0 0
\(779\) 40.3333 6.15363i 1.44509 0.220477i
\(780\) 0 0
\(781\) 33.0943 + 28.9768i 1.18421 + 1.03687i
\(782\) 0 0
\(783\) 0.496419 0.636490i 0.0177406 0.0227463i
\(784\) 0 0
\(785\) −5.54622 + 11.9266i −0.197953 + 0.425679i
\(786\) 0 0
\(787\) −5.94201 15.8064i −0.211810 0.563439i 0.786739 0.617285i \(-0.211768\pi\)
−0.998549 + 0.0538464i \(0.982852\pi\)
\(788\) 0 0
\(789\) −2.52039 + 44.3442i −0.0897281 + 1.57870i
\(790\) 0 0
\(791\) 51.3953 11.8769i 1.82741 0.422295i
\(792\) 0 0
\(793\) −2.39741 + 1.40438i −0.0851345 + 0.0498712i
\(794\) 0 0
\(795\) −0.0412020 + 0.434117i −0.00146128 + 0.0153966i
\(796\) 0