Properties

Label 441.2.g.h.79.10
Level $441$
Weight $2$
Character 441.79
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.10
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.h.67.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.863305 + 1.49529i) q^{2} +(0.615283 - 1.61908i) q^{3} +(-0.490592 + 0.849731i) q^{4} +3.51231 q^{5} +(2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(-2.24285 - 1.99239i) q^{9} +O(q^{10})\) \(q+(0.863305 + 1.49529i) q^{2} +(0.615283 - 1.61908i) q^{3} +(-0.490592 + 0.849731i) q^{4} +3.51231 q^{5} +(2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(-2.24285 - 1.99239i) q^{9} +(3.03220 + 5.25192i) q^{10} -6.09064 q^{11} +(1.07393 + 1.31713i) q^{12} +(0.560139 + 0.970190i) q^{13} +(2.16106 - 5.68672i) q^{15} +(2.49982 + 4.32982i) q^{16} +(-0.601978 - 1.04266i) q^{17} +(1.04293 - 5.07375i) q^{18} +(1.10269 - 1.90991i) q^{19} +(-1.72311 + 2.98452i) q^{20} +(-5.25808 - 9.10727i) q^{22} -1.27339 q^{23} +(1.08234 - 2.84812i) q^{24} +7.33633 q^{25} +(-0.967143 + 1.67514i) q^{26} +(-4.60583 + 2.40548i) q^{27} +(-3.10262 + 5.37390i) q^{29} +(10.3689 - 1.67796i) q^{30} +(0.0942019 - 0.163162i) q^{31} +(-2.55712 + 4.42907i) q^{32} +(-3.74747 + 9.86125i) q^{33} +(1.03938 - 1.80026i) q^{34} +(2.79332 - 0.928373i) q^{36} +(-1.78835 + 3.09752i) q^{37} +3.80782 q^{38} +(1.91546 - 0.309971i) q^{39} +6.17850 q^{40} +(1.68320 + 2.91538i) q^{41} +(-1.90276 + 3.29567i) q^{43} +(2.98802 - 5.17540i) q^{44} +(-7.87760 - 6.99788i) q^{45} +(-1.09932 - 1.90408i) q^{46} +(2.86035 + 4.95427i) q^{47} +(8.54843 - 1.38336i) q^{48} +(6.33349 + 10.9699i) q^{50} +(-2.05853 + 0.333123i) q^{51} -1.09920 q^{52} +(4.16913 + 7.22115i) q^{53} +(-7.57313 - 4.81037i) q^{54} -21.3922 q^{55} +(-2.41384 - 2.96047i) q^{57} -10.7140 q^{58} +(5.63427 - 9.75883i) q^{59} +(3.77198 + 4.62618i) q^{60} +(-6.00109 - 10.3942i) q^{61} +0.325300 q^{62} +1.16898 q^{64} +(1.96738 + 3.40761i) q^{65} +(-17.9806 + 2.90972i) q^{66} +(3.95652 - 6.85289i) q^{67} +1.18130 q^{68} +(-0.783494 + 2.06172i) q^{69} -12.2052 q^{71} +(-3.94540 - 3.50480i) q^{72} +(2.65737 + 4.60269i) q^{73} -6.17557 q^{74} +(4.51392 - 11.8781i) q^{75} +(1.08194 + 1.87397i) q^{76} +(2.11712 + 2.59657i) q^{78} +(-4.60855 - 7.98225i) q^{79} +(8.78016 + 15.2077i) q^{80} +(1.06079 + 8.93727i) q^{81} +(-2.90623 + 5.03373i) q^{82} +(0.624950 - 1.08245i) q^{83} +(-2.11433 - 3.66213i) q^{85} -6.57064 q^{86} +(6.79179 + 8.32986i) q^{87} -10.7140 q^{88} +(-2.77066 + 4.79892i) q^{89} +(3.66308 - 17.8206i) q^{90} +(0.624715 - 1.08204i) q^{92} +(-0.206213 - 0.252912i) q^{93} +(-4.93871 + 8.55409i) q^{94} +(3.87298 - 6.70820i) q^{95} +(5.59767 + 6.86532i) q^{96} +(8.24277 - 14.2769i) q^{97} +(13.6604 + 12.1349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} - 40q^{11} + 4q^{15} - 12q^{16} + 28q^{18} - 64q^{23} + 24q^{25} + 16q^{29} + 84q^{30} + 48q^{32} - 4q^{36} - 12q^{37} - 40q^{39} + 56q^{44} + 24q^{46} - 4q^{50} - 8q^{51} + 32q^{53} - 12q^{57} + 56q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} - 168q^{72} - 136q^{74} - 60q^{78} + 12q^{79} - 40q^{81} + 12q^{85} - 152q^{86} + 16q^{92} + 112q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.863305 + 1.49529i 0.610449 + 1.05733i 0.991165 + 0.132637i \(0.0423443\pi\)
−0.380716 + 0.924692i \(0.624322\pi\)
\(3\) 0.615283 1.61908i 0.355234 0.934778i
\(4\) −0.490592 + 0.849731i −0.245296 + 0.424865i
\(5\) 3.51231 1.57075 0.785377 0.619018i \(-0.212469\pi\)
0.785377 + 0.619018i \(0.212469\pi\)
\(6\) 2.95217 0.477737i 1.20522 0.195035i
\(7\) 0 0
\(8\) 1.75910 0.621935
\(9\) −2.24285 1.99239i −0.747618 0.664129i
\(10\) 3.03220 + 5.25192i 0.958865 + 1.66080i
\(11\) −6.09064 −1.83640 −0.918199 0.396120i \(-0.870356\pi\)
−0.918199 + 0.396120i \(0.870356\pi\)
\(12\) 1.07393 + 1.31713i 0.310017 + 0.380224i
\(13\) 0.560139 + 0.970190i 0.155355 + 0.269082i 0.933188 0.359388i \(-0.117015\pi\)
−0.777833 + 0.628471i \(0.783681\pi\)
\(14\) 0 0
\(15\) 2.16106 5.68672i 0.557984 1.46831i
\(16\) 2.49982 + 4.32982i 0.624956 + 1.08246i
\(17\) −0.601978 1.04266i −0.146001 0.252881i 0.783745 0.621083i \(-0.213307\pi\)
−0.929746 + 0.368202i \(0.879974\pi\)
\(18\) 1.04293 5.07375i 0.245820 1.19589i
\(19\) 1.10269 1.90991i 0.252974 0.438163i −0.711370 0.702818i \(-0.751925\pi\)
0.964343 + 0.264655i \(0.0852581\pi\)
\(20\) −1.72311 + 2.98452i −0.385300 + 0.667359i
\(21\) 0 0
\(22\) −5.25808 9.10727i −1.12103 1.94168i
\(23\) −1.27339 −0.265520 −0.132760 0.991148i \(-0.542384\pi\)
−0.132760 + 0.991148i \(0.542384\pi\)
\(24\) 1.08234 2.84812i 0.220932 0.581371i
\(25\) 7.33633 1.46727
\(26\) −0.967143 + 1.67514i −0.189672 + 0.328522i
\(27\) −4.60583 + 2.40548i −0.886392 + 0.462936i
\(28\) 0 0
\(29\) −3.10262 + 5.37390i −0.576142 + 0.997907i 0.419774 + 0.907628i \(0.362109\pi\)
−0.995917 + 0.0902789i \(0.971224\pi\)
\(30\) 10.3689 1.67796i 1.89310 0.306352i
\(31\) 0.0942019 0.163162i 0.0169192 0.0293048i −0.857442 0.514581i \(-0.827948\pi\)
0.874361 + 0.485276i \(0.161281\pi\)
\(32\) −2.55712 + 4.42907i −0.452040 + 0.782956i
\(33\) −3.74747 + 9.86125i −0.652350 + 1.71662i
\(34\) 1.03938 1.80026i 0.178252 0.308742i
\(35\) 0 0
\(36\) 2.79332 0.928373i 0.465553 0.154729i
\(37\) −1.78835 + 3.09752i −0.294003 + 0.509228i −0.974753 0.223288i \(-0.928321\pi\)
0.680749 + 0.732516i \(0.261654\pi\)
\(38\) 3.80782 0.617710
\(39\) 1.91546 0.309971i 0.306719 0.0496350i
\(40\) 6.17850 0.976907
\(41\) 1.68320 + 2.91538i 0.262871 + 0.455307i 0.967004 0.254762i \(-0.0819972\pi\)
−0.704132 + 0.710069i \(0.748664\pi\)
\(42\) 0 0
\(43\) −1.90276 + 3.29567i −0.290168 + 0.502585i −0.973849 0.227195i \(-0.927044\pi\)
0.683681 + 0.729781i \(0.260378\pi\)
\(44\) 2.98802 5.17540i 0.450461 0.780221i
\(45\) −7.87760 6.99788i −1.17432 1.04318i
\(46\) −1.09932 1.90408i −0.162086 0.280742i
\(47\) 2.86035 + 4.95427i 0.417225 + 0.722654i 0.995659 0.0930746i \(-0.0296695\pi\)
−0.578434 + 0.815729i \(0.696336\pi\)
\(48\) 8.54843 1.38336i 1.23386 0.199670i
\(49\) 0 0
\(50\) 6.33349 + 10.9699i 0.895691 + 1.55138i
\(51\) −2.05853 + 0.333123i −0.288252 + 0.0466466i
\(52\) −1.09920 −0.152432
\(53\) 4.16913 + 7.22115i 0.572675 + 0.991901i 0.996290 + 0.0860593i \(0.0274275\pi\)
−0.423615 + 0.905842i \(0.639239\pi\)
\(54\) −7.57313 4.81037i −1.03057 0.654609i
\(55\) −21.3922 −2.88453
\(56\) 0 0
\(57\) −2.41384 2.96047i −0.319720 0.392124i
\(58\) −10.7140 −1.40682
\(59\) 5.63427 9.75883i 0.733519 1.27049i −0.221851 0.975081i \(-0.571210\pi\)
0.955370 0.295411i \(-0.0954567\pi\)
\(60\) 3.77198 + 4.62618i 0.486960 + 0.597238i
\(61\) −6.00109 10.3942i −0.768361 1.33084i −0.938451 0.345411i \(-0.887739\pi\)
0.170091 0.985428i \(-0.445594\pi\)
\(62\) 0.325300 0.0413131
\(63\) 0 0
\(64\) 1.16898 0.146123
\(65\) 1.96738 + 3.40761i 0.244024 + 0.422662i
\(66\) −17.9806 + 2.90972i −2.21326 + 0.358162i
\(67\) 3.95652 6.85289i 0.483366 0.837214i −0.516452 0.856316i \(-0.672748\pi\)
0.999818 + 0.0191025i \(0.00608088\pi\)
\(68\) 1.18130 0.143254
\(69\) −0.783494 + 2.06172i −0.0943217 + 0.248202i
\(70\) 0 0
\(71\) −12.2052 −1.44850 −0.724248 0.689540i \(-0.757813\pi\)
−0.724248 + 0.689540i \(0.757813\pi\)
\(72\) −3.94540 3.50480i −0.464970 0.413045i
\(73\) 2.65737 + 4.60269i 0.311021 + 0.538704i 0.978584 0.205849i \(-0.0659957\pi\)
−0.667563 + 0.744554i \(0.732662\pi\)
\(74\) −6.17557 −0.717896
\(75\) 4.51392 11.8781i 0.521222 1.37157i
\(76\) 1.08194 + 1.87397i 0.124107 + 0.214959i
\(77\) 0 0
\(78\) 2.11712 + 2.59657i 0.239717 + 0.294003i
\(79\) −4.60855 7.98225i −0.518503 0.898073i −0.999769 0.0214988i \(-0.993156\pi\)
0.481266 0.876575i \(-0.340177\pi\)
\(80\) 8.78016 + 15.2077i 0.981651 + 1.70027i
\(81\) 1.06079 + 8.93727i 0.117866 + 0.993030i
\(82\) −2.90623 + 5.03373i −0.320939 + 0.555883i
\(83\) 0.624950 1.08245i 0.0685972 0.118814i −0.829687 0.558229i \(-0.811481\pi\)
0.898284 + 0.439415i \(0.144814\pi\)
\(84\) 0 0
\(85\) −2.11433 3.66213i −0.229332 0.397214i
\(86\) −6.57064 −0.708531
\(87\) 6.79179 + 8.32986i 0.728156 + 0.893055i
\(88\) −10.7140 −1.14212
\(89\) −2.77066 + 4.79892i −0.293689 + 0.508684i −0.974679 0.223608i \(-0.928216\pi\)
0.680990 + 0.732293i \(0.261550\pi\)
\(90\) 3.66308 17.8206i 0.386122 1.87846i
\(91\) 0 0
\(92\) 0.624715 1.08204i 0.0651310 0.112810i
\(93\) −0.206213 0.252912i −0.0213832 0.0262257i
\(94\) −4.93871 + 8.55409i −0.509389 + 0.882287i
\(95\) 3.87298 6.70820i 0.397359 0.688246i
\(96\) 5.59767 + 6.86532i 0.571310 + 0.700689i
\(97\) 8.24277 14.2769i 0.836926 1.44960i −0.0555261 0.998457i \(-0.517684\pi\)
0.892452 0.451142i \(-0.148983\pi\)
\(98\) 0 0
\(99\) 13.6604 + 12.1349i 1.37292 + 1.21960i
\(100\) −3.59915 + 6.23391i −0.359915 + 0.623391i
\(101\) −12.9638 −1.28995 −0.644975 0.764203i \(-0.723132\pi\)
−0.644975 + 0.764203i \(0.723132\pi\)
\(102\) −2.27526 2.79051i −0.225284 0.276302i
\(103\) 2.70182 0.266218 0.133109 0.991101i \(-0.457504\pi\)
0.133109 + 0.991101i \(0.457504\pi\)
\(104\) 0.985340 + 1.70666i 0.0966205 + 0.167352i
\(105\) 0 0
\(106\) −7.19847 + 12.4681i −0.699177 + 1.21101i
\(107\) 0.0892402 0.154569i 0.00862718 0.0149427i −0.861680 0.507453i \(-0.830587\pi\)
0.870307 + 0.492510i \(0.163921\pi\)
\(108\) 0.215569 5.09382i 0.0207431 0.490153i
\(109\) −4.67927 8.10473i −0.448192 0.776292i 0.550076 0.835115i \(-0.314599\pi\)
−0.998268 + 0.0588226i \(0.981265\pi\)
\(110\) −18.4680 31.9876i −1.76086 3.04989i
\(111\) 3.91479 + 4.80134i 0.371575 + 0.455723i
\(112\) 0 0
\(113\) 4.21019 + 7.29226i 0.396061 + 0.685998i 0.993236 0.116113i \(-0.0370434\pi\)
−0.597175 + 0.802111i \(0.703710\pi\)
\(114\) 2.34289 6.16517i 0.219431 0.577422i
\(115\) −4.47254 −0.417067
\(116\) −3.04424 5.27278i −0.282651 0.489565i
\(117\) 0.676682 3.29201i 0.0625593 0.304346i
\(118\) 19.4564 1.79110
\(119\) 0 0
\(120\) 3.80152 10.0035i 0.347030 0.913190i
\(121\) 26.0959 2.37235
\(122\) 10.3615 17.9467i 0.938090 1.62482i
\(123\) 5.75589 0.931450i 0.518991 0.0839861i
\(124\) 0.0924294 + 0.160092i 0.00830040 + 0.0143767i
\(125\) 8.20593 0.733960
\(126\) 0 0
\(127\) −9.92438 −0.880647 −0.440323 0.897839i \(-0.645136\pi\)
−0.440323 + 0.897839i \(0.645136\pi\)
\(128\) 6.12343 + 10.6061i 0.541240 + 0.937455i
\(129\) 4.16523 + 5.10849i 0.366728 + 0.449778i
\(130\) −3.39691 + 5.88361i −0.297928 + 0.516027i
\(131\) −15.2467 −1.33211 −0.666055 0.745902i \(-0.732019\pi\)
−0.666055 + 0.745902i \(0.732019\pi\)
\(132\) −6.54093 8.02219i −0.569314 0.698242i
\(133\) 0 0
\(134\) 13.6627 1.18028
\(135\) −16.1771 + 8.44881i −1.39230 + 0.727158i
\(136\) −1.05894 1.83413i −0.0908032 0.157276i
\(137\) 6.14700 0.525174 0.262587 0.964908i \(-0.415424\pi\)
0.262587 + 0.964908i \(0.415424\pi\)
\(138\) −3.75926 + 0.608345i −0.320010 + 0.0517858i
\(139\) 0.438687 + 0.759829i 0.0372090 + 0.0644478i 0.884030 0.467430i \(-0.154820\pi\)
−0.846821 + 0.531878i \(0.821487\pi\)
\(140\) 0 0
\(141\) 9.78129 1.58286i 0.823733 0.133301i
\(142\) −10.5368 18.2504i −0.884233 1.53154i
\(143\) −3.41161 5.90908i −0.285293 0.494142i
\(144\) 3.01994 14.6918i 0.251661 1.22431i
\(145\) −10.8974 + 18.8748i −0.904977 + 1.56747i
\(146\) −4.58824 + 7.94706i −0.379725 + 0.657703i
\(147\) 0 0
\(148\) −1.75470 3.03923i −0.144236 0.249823i
\(149\) 5.77553 0.473150 0.236575 0.971613i \(-0.423975\pi\)
0.236575 + 0.971613i \(0.423975\pi\)
\(150\) 21.6581 3.50484i 1.76838 0.286169i
\(151\) −2.02643 −0.164908 −0.0824541 0.996595i \(-0.526276\pi\)
−0.0824541 + 0.996595i \(0.526276\pi\)
\(152\) 1.93973 3.35972i 0.157333 0.272509i
\(153\) −0.727226 + 3.53790i −0.0587927 + 0.286022i
\(154\) 0 0
\(155\) 0.330866 0.573077i 0.0265758 0.0460307i
\(156\) −0.676319 + 1.77969i −0.0541488 + 0.142490i
\(157\) 1.52378 2.63927i 0.121611 0.210636i −0.798792 0.601607i \(-0.794527\pi\)
0.920403 + 0.390971i \(0.127861\pi\)
\(158\) 7.95718 13.7822i 0.633039 1.09646i
\(159\) 14.2568 2.30712i 1.13064 0.182967i
\(160\) −8.98141 + 15.5563i −0.710043 + 1.22983i
\(161\) 0 0
\(162\) −12.4480 + 9.30178i −0.978008 + 0.730817i
\(163\) 2.69445 4.66693i 0.211046 0.365542i −0.740996 0.671509i \(-0.765646\pi\)
0.952042 + 0.305967i \(0.0989797\pi\)
\(164\) −3.30306 −0.257925
\(165\) −13.1623 + 34.6358i −1.02468 + 2.69639i
\(166\) 2.15809 0.167500
\(167\) −8.30480 14.3843i −0.642645 1.11309i −0.984840 0.173464i \(-0.944504\pi\)
0.342196 0.939629i \(-0.388829\pi\)
\(168\) 0 0
\(169\) 5.87249 10.1714i 0.451730 0.782419i
\(170\) 3.65063 6.32308i 0.279991 0.484958i
\(171\) −6.27844 + 2.08667i −0.480125 + 0.159572i
\(172\) −1.86696 3.23366i −0.142354 0.246564i
\(173\) 8.82516 + 15.2856i 0.670965 + 1.16214i 0.977631 + 0.210328i \(0.0674531\pi\)
−0.306666 + 0.951817i \(0.599214\pi\)
\(174\) −6.59216 + 17.3469i −0.499750 + 1.31507i
\(175\) 0 0
\(176\) −15.2255 26.3714i −1.14767 1.98782i
\(177\) −12.3337 15.1268i −0.927057 1.13700i
\(178\) −9.56769 −0.717128
\(179\) −1.31422 2.27630i −0.0982294 0.170138i 0.812722 0.582651i \(-0.197985\pi\)
−0.910952 + 0.412513i \(0.864651\pi\)
\(180\) 9.81100 3.26073i 0.731269 0.243041i
\(181\) 3.97391 0.295378 0.147689 0.989034i \(-0.452816\pi\)
0.147689 + 0.989034i \(0.452816\pi\)
\(182\) 0 0
\(183\) −20.5214 + 3.32089i −1.51699 + 0.245487i
\(184\) −2.24002 −0.165136
\(185\) −6.28125 + 10.8794i −0.461806 + 0.799872i
\(186\) 0.200151 0.526687i 0.0146758 0.0386186i
\(187\) 3.66643 + 6.35045i 0.268116 + 0.464391i
\(188\) −5.61306 −0.409374
\(189\) 0 0
\(190\) 13.3743 0.970270
\(191\) 9.10295 + 15.7668i 0.658666 + 1.14084i 0.980961 + 0.194204i \(0.0622125\pi\)
−0.322295 + 0.946639i \(0.604454\pi\)
\(192\) 0.719254 1.89268i 0.0519077 0.136592i
\(193\) 0.101193 0.175271i 0.00728401 0.0126163i −0.862360 0.506295i \(-0.831015\pi\)
0.869644 + 0.493679i \(0.164348\pi\)
\(194\) 28.4641 2.04360
\(195\) 6.72770 1.08871i 0.481780 0.0779644i
\(196\) 0 0
\(197\) −1.63136 −0.116229 −0.0581147 0.998310i \(-0.518509\pi\)
−0.0581147 + 0.998310i \(0.518509\pi\)
\(198\) −6.35208 + 30.9024i −0.451423 + 2.19614i
\(199\) −3.14605 5.44912i −0.223018 0.386278i 0.732705 0.680546i \(-0.238257\pi\)
−0.955723 + 0.294268i \(0.904924\pi\)
\(200\) 12.9053 0.912544
\(201\) −8.66101 10.6224i −0.610901 0.749246i
\(202\) −11.1918 19.3847i −0.787449 1.36390i
\(203\) 0 0
\(204\) 0.726835 1.91263i 0.0508886 0.133911i
\(205\) 5.91192 + 10.2397i 0.412906 + 0.715174i
\(206\) 2.33249 + 4.04000i 0.162512 + 0.281480i
\(207\) 2.85603 + 2.53708i 0.198508 + 0.176340i
\(208\) −2.80050 + 4.85061i −0.194180 + 0.336329i
\(209\) −6.71607 + 11.6326i −0.464560 + 0.804642i
\(210\) 0 0
\(211\) 8.14368 + 14.1053i 0.560634 + 0.971046i 0.997441 + 0.0714912i \(0.0227758\pi\)
−0.436807 + 0.899555i \(0.643891\pi\)
\(212\) −8.18138 −0.561899
\(213\) −7.50967 + 19.7613i −0.514554 + 1.35402i
\(214\) 0.308166 0.0210658
\(215\) −6.68308 + 11.5754i −0.455782 + 0.789438i
\(216\) −8.10210 + 4.23148i −0.551278 + 0.287916i
\(217\) 0 0
\(218\) 8.07927 13.9937i 0.547197 0.947773i
\(219\) 9.08717 1.47054i 0.614054 0.0993696i
\(220\) 10.4949 18.1776i 0.707563 1.22554i
\(221\) 0.674383 1.16807i 0.0453639 0.0785726i
\(222\) −3.79972 + 9.99876i −0.255021 + 0.671073i
\(223\) −9.98472 + 17.2940i −0.668626 + 1.15809i 0.309662 + 0.950847i \(0.399784\pi\)
−0.978288 + 0.207248i \(0.933549\pi\)
\(224\) 0 0
\(225\) −16.4543 14.6168i −1.09695 0.974454i
\(226\) −7.26936 + 12.5909i −0.483551 + 0.837534i
\(227\) 3.61283 0.239792 0.119896 0.992786i \(-0.461744\pi\)
0.119896 + 0.992786i \(0.461744\pi\)
\(228\) 3.69981 0.598725i 0.245026 0.0396515i
\(229\) 13.7147 0.906290 0.453145 0.891437i \(-0.350302\pi\)
0.453145 + 0.891437i \(0.350302\pi\)
\(230\) −3.86117 6.68774i −0.254598 0.440976i
\(231\) 0 0
\(232\) −5.45781 + 9.45321i −0.358323 + 0.620634i
\(233\) 12.6271 21.8707i 0.827227 1.43280i −0.0729776 0.997334i \(-0.523250\pi\)
0.900205 0.435466i \(-0.143417\pi\)
\(234\) 5.50669 1.83017i 0.359983 0.119642i
\(235\) 10.0464 + 17.4009i 0.655357 + 1.13511i
\(236\) 5.52825 + 9.57521i 0.359859 + 0.623293i
\(237\) −15.7595 + 2.55029i −1.02369 + 0.165659i
\(238\) 0 0
\(239\) −4.49495 7.78549i −0.290754 0.503601i 0.683234 0.730200i \(-0.260573\pi\)
−0.973988 + 0.226598i \(0.927240\pi\)
\(240\) 30.0248 4.85877i 1.93809 0.313633i
\(241\) 9.25724 0.596311 0.298156 0.954517i \(-0.403629\pi\)
0.298156 + 0.954517i \(0.403629\pi\)
\(242\) 22.5287 + 39.0209i 1.44820 + 2.50836i
\(243\) 15.1229 + 3.78144i 0.970132 + 0.242579i
\(244\) 11.7763 0.753903
\(245\) 0 0
\(246\) 6.36188 + 7.80259i 0.405619 + 0.497475i
\(247\) 2.47063 0.157203
\(248\) 0.165710 0.287019i 0.0105226 0.0182257i
\(249\) −1.36805 1.67786i −0.0866965 0.106330i
\(250\) 7.08422 + 12.2702i 0.448045 + 0.776037i
\(251\) 20.6517 1.30353 0.651763 0.758422i \(-0.274030\pi\)
0.651763 + 0.758422i \(0.274030\pi\)
\(252\) 0 0
\(253\) 7.75576 0.487600
\(254\) −8.56777 14.8398i −0.537590 0.931133i
\(255\) −7.23021 + 1.17003i −0.452773 + 0.0732703i
\(256\) −9.40380 + 16.2879i −0.587738 + 1.01799i
\(257\) −2.44579 −0.152564 −0.0762819 0.997086i \(-0.524305\pi\)
−0.0762819 + 0.997086i \(0.524305\pi\)
\(258\) −4.04280 + 10.6384i −0.251694 + 0.662318i
\(259\) 0 0
\(260\) −3.86073 −0.239432
\(261\) 17.6656 5.87125i 1.09347 0.363421i
\(262\) −13.1626 22.7982i −0.813186 1.40848i
\(263\) −24.5628 −1.51460 −0.757302 0.653065i \(-0.773483\pi\)
−0.757302 + 0.653065i \(0.773483\pi\)
\(264\) −6.59216 + 17.3469i −0.405719 + 1.06763i
\(265\) 14.6433 + 25.3629i 0.899531 + 1.55803i
\(266\) 0 0
\(267\) 6.06510 + 7.43861i 0.371178 + 0.455236i
\(268\) 3.88207 + 6.72395i 0.237135 + 0.410730i
\(269\) 14.7851 + 25.6086i 0.901466 + 1.56139i 0.825592 + 0.564268i \(0.190842\pi\)
0.0758746 + 0.997117i \(0.475825\pi\)
\(270\) −26.5992 16.8955i −1.61877 1.02823i
\(271\) 12.3958 21.4701i 0.752989 1.30421i −0.193380 0.981124i \(-0.561945\pi\)
0.946368 0.323090i \(-0.104722\pi\)
\(272\) 3.00968 5.21291i 0.182488 0.316079i
\(273\) 0 0
\(274\) 5.30674 + 9.19154i 0.320592 + 0.555281i
\(275\) −44.6830 −2.69448
\(276\) −1.36753 1.67722i −0.0823157 0.100957i
\(277\) 1.87850 0.112868 0.0564340 0.998406i \(-0.482027\pi\)
0.0564340 + 0.998406i \(0.482027\pi\)
\(278\) −0.757442 + 1.31193i −0.0454284 + 0.0786842i
\(279\) −0.536364 + 0.178263i −0.0321113 + 0.0106723i
\(280\) 0 0
\(281\) 6.03965 10.4610i 0.360295 0.624049i −0.627714 0.778444i \(-0.716009\pi\)
0.988009 + 0.154395i \(0.0493427\pi\)
\(282\) 10.8111 + 13.2594i 0.643790 + 0.789583i
\(283\) 13.9859 24.2244i 0.831378 1.43999i −0.0655680 0.997848i \(-0.520886\pi\)
0.896946 0.442140i \(-0.145781\pi\)
\(284\) 5.98779 10.3712i 0.355310 0.615415i
\(285\) −8.47814 10.3981i −0.502202 0.615931i
\(286\) 5.89052 10.2027i 0.348314 0.603297i
\(287\) 0 0
\(288\) 14.5597 4.83897i 0.857937 0.285139i
\(289\) 7.77524 13.4671i 0.457367 0.792183i
\(290\) −37.6310 −2.20977
\(291\) −18.0438 22.1300i −1.05775 1.29729i
\(292\) −5.21473 −0.305169
\(293\) −4.41163 7.64117i −0.257730 0.446402i 0.707903 0.706309i \(-0.249641\pi\)
−0.965634 + 0.259908i \(0.916308\pi\)
\(294\) 0 0
\(295\) 19.7893 34.2761i 1.15218 1.99563i
\(296\) −3.14589 + 5.44883i −0.182851 + 0.316707i
\(297\) 28.0524 14.6509i 1.62777 0.850134i
\(298\) 4.98604 + 8.63608i 0.288834 + 0.500275i
\(299\) −0.713276 1.23543i −0.0412498 0.0714467i
\(300\) 7.87871 + 9.66293i 0.454878 + 0.557889i
\(301\) 0 0
\(302\) −1.74942 3.03009i −0.100668 0.174362i
\(303\) −7.97643 + 20.9895i −0.458234 + 1.20582i
\(304\) 11.0261 0.632389
\(305\) −21.0777 36.5076i −1.20691 2.09042i
\(306\) −5.91800 + 1.96687i −0.338309 + 0.112439i
\(307\) 1.05532 0.0602304 0.0301152 0.999546i \(-0.490413\pi\)
0.0301152 + 0.999546i \(0.490413\pi\)
\(308\) 0 0
\(309\) 1.66238 4.37446i 0.0945696 0.248855i
\(310\) 1.14255 0.0648927
\(311\) −1.53608 + 2.66056i −0.0871029 + 0.150867i −0.906285 0.422666i \(-0.861094\pi\)
0.819182 + 0.573533i \(0.194428\pi\)
\(312\) 3.36948 0.545269i 0.190759 0.0308698i
\(313\) −14.0810 24.3891i −0.795907 1.37855i −0.922262 0.386566i \(-0.873661\pi\)
0.126355 0.991985i \(-0.459672\pi\)
\(314\) 5.26196 0.296949
\(315\) 0 0
\(316\) 9.04368 0.508747
\(317\) −6.42324 11.1254i −0.360765 0.624863i 0.627322 0.778760i \(-0.284151\pi\)
−0.988087 + 0.153897i \(0.950818\pi\)
\(318\) 15.7578 + 19.3263i 0.883654 + 1.08377i
\(319\) 18.8969 32.7305i 1.05803 1.83255i
\(320\) 4.10582 0.229523
\(321\) −0.195351 0.239591i −0.0109034 0.0133726i
\(322\) 0 0
\(323\) −2.65517 −0.147738
\(324\) −8.11468 3.48317i −0.450816 0.193509i
\(325\) 4.10937 + 7.11763i 0.227947 + 0.394815i
\(326\) 9.30454 0.515331
\(327\) −16.0013 + 2.58942i −0.884873 + 0.143195i
\(328\) 2.96091 + 5.12845i 0.163489 + 0.283171i
\(329\) 0 0
\(330\) −63.1535 + 10.2199i −3.47649 + 0.562585i
\(331\) 10.7780 + 18.6681i 0.592413 + 1.02609i 0.993906 + 0.110228i \(0.0351581\pi\)
−0.401493 + 0.915862i \(0.631509\pi\)
\(332\) 0.613191 + 1.06208i 0.0336532 + 0.0582891i
\(333\) 10.1825 3.38419i 0.557995 0.185452i
\(334\) 14.3392 24.8361i 0.784604 1.35897i
\(335\) 13.8965 24.0695i 0.759248 1.31506i
\(336\) 0 0
\(337\) 6.30340 + 10.9178i 0.343368 + 0.594731i 0.985056 0.172235i \(-0.0550989\pi\)
−0.641688 + 0.766966i \(0.721766\pi\)
\(338\) 20.2790 1.10303
\(339\) 14.3972 2.32984i 0.781950 0.126540i
\(340\) 4.14910 0.225017
\(341\) −0.573750 + 0.993764i −0.0310703 + 0.0538153i
\(342\) −8.54039 7.58665i −0.461811 0.410239i
\(343\) 0 0
\(344\) −3.34714 + 5.79741i −0.180466 + 0.312575i
\(345\) −2.75188 + 7.24141i −0.148156 + 0.389864i
\(346\) −15.2376 + 26.3923i −0.819179 + 1.41886i
\(347\) −11.5683 + 20.0369i −0.621020 + 1.07564i 0.368276 + 0.929716i \(0.379948\pi\)
−0.989296 + 0.145922i \(0.953385\pi\)
\(348\) −10.4101 + 1.68463i −0.558042 + 0.0903055i
\(349\) 8.24346 14.2781i 0.441262 0.764289i −0.556521 0.830833i \(-0.687864\pi\)
0.997783 + 0.0665448i \(0.0211975\pi\)
\(350\) 0 0
\(351\) −4.91368 3.12112i −0.262273 0.166593i
\(352\) 15.5745 26.9759i 0.830124 1.43782i
\(353\) −24.4875 −1.30334 −0.651669 0.758503i \(-0.725931\pi\)
−0.651669 + 0.758503i \(0.725931\pi\)
\(354\) 11.9712 31.5015i 0.636260 1.67428i
\(355\) −42.8686 −2.27523
\(356\) −2.71852 4.70862i −0.144081 0.249556i
\(357\) 0 0
\(358\) 2.26915 3.93028i 0.119928 0.207722i
\(359\) −10.2389 + 17.7342i −0.540386 + 0.935977i 0.458495 + 0.888697i \(0.348389\pi\)
−0.998882 + 0.0472797i \(0.984945\pi\)
\(360\) −13.8575 12.3100i −0.730353 0.648792i
\(361\) 7.06816 + 12.2424i 0.372009 + 0.644338i
\(362\) 3.43070 + 5.94214i 0.180313 + 0.312312i
\(363\) 16.0564 42.2514i 0.842740 2.21762i
\(364\) 0 0
\(365\) 9.33349 + 16.1661i 0.488537 + 0.846172i
\(366\) −22.6819 27.8185i −1.18560 1.45410i
\(367\) 22.2539 1.16164 0.580821 0.814031i \(-0.302732\pi\)
0.580821 + 0.814031i \(0.302732\pi\)
\(368\) −3.18325 5.51355i −0.165938 0.287414i
\(369\) 2.03341 9.89237i 0.105855 0.514976i
\(370\) −21.6905 −1.12764
\(371\) 0 0
\(372\) 0.316073 0.0511487i 0.0163876 0.00265194i
\(373\) −32.5369 −1.68469 −0.842347 0.538935i \(-0.818827\pi\)
−0.842347 + 0.538935i \(0.818827\pi\)
\(374\) −6.33050 + 10.9647i −0.327342 + 0.566974i
\(375\) 5.04896 13.2861i 0.260727 0.686090i
\(376\) 5.03163 + 8.71504i 0.259487 + 0.449444i
\(377\) −6.95160 −0.358026
\(378\) 0 0
\(379\) 1.54440 0.0793306 0.0396653 0.999213i \(-0.487371\pi\)
0.0396653 + 0.999213i \(0.487371\pi\)
\(380\) 3.80011 + 6.58198i 0.194941 + 0.337648i
\(381\) −6.10630 + 16.0684i −0.312835 + 0.823209i
\(382\) −15.7173 + 27.2231i −0.804165 + 1.39285i
\(383\) 31.6294 1.61619 0.808093 0.589055i \(-0.200500\pi\)
0.808093 + 0.589055i \(0.200500\pi\)
\(384\) 20.9398 3.38859i 1.06858 0.172923i
\(385\) 0 0
\(386\) 0.349441 0.0177861
\(387\) 10.8339 3.60068i 0.550716 0.183033i
\(388\) 8.08767 + 14.0083i 0.410589 + 0.711162i
\(389\) −5.24626 −0.265996 −0.132998 0.991116i \(-0.542460\pi\)
−0.132998 + 0.991116i \(0.542460\pi\)
\(390\) 7.43600 + 9.11996i 0.376536 + 0.461807i
\(391\) 0.766552 + 1.32771i 0.0387662 + 0.0671451i
\(392\) 0 0
\(393\) −9.38103 + 24.6857i −0.473210 + 1.24523i
\(394\) −1.40836 2.43935i −0.0709521 0.122893i
\(395\) −16.1867 28.0362i −0.814440 1.41065i
\(396\) −17.0131 + 5.65438i −0.854940 + 0.284143i
\(397\) −0.0138175 + 0.0239325i −0.000693478 + 0.00120114i −0.866372 0.499399i \(-0.833554\pi\)
0.865678 + 0.500600i \(0.166887\pi\)
\(398\) 5.43201 9.40851i 0.272282 0.471606i
\(399\) 0 0
\(400\) 18.3395 + 31.7650i 0.916977 + 1.58825i
\(401\) 12.1377 0.606127 0.303064 0.952970i \(-0.401991\pi\)
0.303064 + 0.952970i \(0.401991\pi\)
\(402\) 8.40644 22.1211i 0.419275 1.10330i
\(403\) 0.211065 0.0105139
\(404\) 6.35996 11.0158i 0.316420 0.548055i
\(405\) 3.72583 + 31.3905i 0.185138 + 1.55980i
\(406\) 0 0
\(407\) 10.8922 18.8659i 0.539907 0.935146i
\(408\) −3.62116 + 0.585997i −0.179274 + 0.0290112i
\(409\) −15.6726 + 27.1458i −0.774963 + 1.34227i 0.159853 + 0.987141i \(0.448898\pi\)
−0.934816 + 0.355134i \(0.884435\pi\)
\(410\) −10.2076 + 17.6800i −0.504116 + 0.873155i
\(411\) 3.78214 9.95250i 0.186559 0.490921i
\(412\) −1.32549 + 2.29582i −0.0653022 + 0.113107i
\(413\) 0 0
\(414\) −1.32805 + 6.46086i −0.0652701 + 0.317534i
\(415\) 2.19502 3.80189i 0.107749 0.186627i
\(416\) −5.72938 −0.280906
\(417\) 1.50014 0.242761i 0.0734623 0.0118881i
\(418\) −23.1921 −1.13436
\(419\) 7.44319 + 12.8920i 0.363623 + 0.629814i 0.988554 0.150866i \(-0.0482061\pi\)
−0.624931 + 0.780680i \(0.714873\pi\)
\(420\) 0 0
\(421\) −4.54213 + 7.86721i −0.221370 + 0.383424i −0.955224 0.295883i \(-0.904386\pi\)
0.733854 + 0.679307i \(0.237720\pi\)
\(422\) −14.0610 + 24.3543i −0.684477 + 1.18555i
\(423\) 3.45547 16.8106i 0.168011 0.817360i
\(424\) 7.33392 + 12.7027i 0.356166 + 0.616898i
\(425\) −4.41631 7.64927i −0.214223 0.371044i
\(426\) −36.0320 + 5.83089i −1.74575 + 0.282508i
\(427\) 0 0
\(428\) 0.0875611 + 0.151660i 0.00423243 + 0.00733078i
\(429\) −11.6664 + 1.88792i −0.563258 + 0.0911496i
\(430\) −23.0781 −1.11293
\(431\) 8.31776 + 14.4068i 0.400652 + 0.693950i 0.993805 0.111140i \(-0.0354502\pi\)
−0.593152 + 0.805090i \(0.702117\pi\)
\(432\) −21.9291 13.9291i −1.05506 0.670165i
\(433\) 19.7423 0.948756 0.474378 0.880321i \(-0.342673\pi\)
0.474378 + 0.880321i \(0.342673\pi\)
\(434\) 0 0
\(435\) 23.8549 + 29.2571i 1.14375 + 1.40277i
\(436\) 9.18244 0.439759
\(437\) −1.40415 + 2.43206i −0.0671696 + 0.116341i
\(438\) 10.0439 + 12.3184i 0.479915 + 0.588597i
\(439\) 3.36757 + 5.83280i 0.160725 + 0.278384i 0.935129 0.354307i \(-0.115283\pi\)
−0.774404 + 0.632692i \(0.781950\pi\)
\(440\) −37.6310 −1.79399
\(441\) 0 0
\(442\) 2.32879 0.110769
\(443\) −14.3202 24.8033i −0.680372 1.17844i −0.974867 0.222786i \(-0.928485\pi\)
0.294496 0.955653i \(-0.404848\pi\)
\(444\) −6.00041 + 0.971019i −0.284767 + 0.0460825i
\(445\) −9.73141 + 16.8553i −0.461313 + 0.799017i
\(446\) −34.4794 −1.63265
\(447\) 3.55358 9.35105i 0.168079 0.442290i
\(448\) 0 0
\(449\) −6.66872 −0.314716 −0.157358 0.987542i \(-0.550298\pi\)
−0.157358 + 0.987542i \(0.550298\pi\)
\(450\) 7.65124 37.2227i 0.360683 1.75470i
\(451\) −10.2518 17.7566i −0.482736 0.836124i
\(452\) −8.26194 −0.388609
\(453\) −1.24683 + 3.28095i −0.0585810 + 0.154153i
\(454\) 3.11898 + 5.40223i 0.146381 + 0.253539i
\(455\) 0 0
\(456\) −4.24617 5.20776i −0.198845 0.243876i
\(457\) 14.3287 + 24.8180i 0.670266 + 1.16093i 0.977829 + 0.209407i \(0.0671533\pi\)
−0.307563 + 0.951528i \(0.599513\pi\)
\(458\) 11.8399 + 20.5074i 0.553244 + 0.958246i
\(459\) 5.28070 + 3.35425i 0.246482 + 0.156563i
\(460\) 2.19419 3.80045i 0.102305 0.177197i
\(461\) −10.0087 + 17.3355i −0.466150 + 0.807395i −0.999253 0.0386554i \(-0.987693\pi\)
0.533103 + 0.846050i \(0.321026\pi\)
\(462\) 0 0
\(463\) −4.95789 8.58731i −0.230413 0.399086i 0.727517 0.686090i \(-0.240674\pi\)
−0.957930 + 0.287003i \(0.907341\pi\)
\(464\) −31.0240 −1.44025
\(465\) −0.724283 0.888304i −0.0335878 0.0411941i
\(466\) 43.6041 2.01992
\(467\) 8.04035 13.9263i 0.372063 0.644432i −0.617820 0.786320i \(-0.711984\pi\)
0.989883 + 0.141888i \(0.0453172\pi\)
\(468\) 2.46535 + 2.19003i 0.113961 + 0.101234i
\(469\) 0 0
\(470\) −17.3463 + 30.0446i −0.800124 + 1.38586i
\(471\) −3.33563 4.09102i −0.153698 0.188504i
\(472\) 9.91123 17.1667i 0.456201 0.790164i
\(473\) 11.5890 20.0728i 0.532863 0.922946i
\(474\) −17.4187 21.3633i −0.800066 0.981249i
\(475\) 8.08967 14.0117i 0.371180 0.642902i
\(476\) 0 0
\(477\) 5.03657 24.5025i 0.230609 1.12189i
\(478\) 7.76103 13.4425i 0.354981 0.614846i
\(479\) 8.20255 0.374784 0.187392 0.982285i \(-0.439997\pi\)
0.187392 + 0.982285i \(0.439997\pi\)
\(480\) 19.6608 + 24.1131i 0.897387 + 1.10061i
\(481\) −4.00690 −0.182699
\(482\) 7.99183 + 13.8423i 0.364018 + 0.630497i
\(483\) 0 0
\(484\) −12.8024 + 22.1745i −0.581929 + 1.00793i
\(485\) 28.9512 50.1449i 1.31460 2.27696i
\(486\) 7.40130 + 25.8776i 0.335730 + 1.17383i
\(487\) −1.36840 2.37014i −0.0620081 0.107401i 0.833355 0.552738i \(-0.186417\pi\)
−0.895363 + 0.445337i \(0.853084\pi\)
\(488\) −10.5565 18.2844i −0.477871 0.827696i
\(489\) −5.89829 7.23402i −0.266730 0.327134i
\(490\) 0 0
\(491\) 9.85482 + 17.0690i 0.444742 + 0.770315i 0.998034 0.0626719i \(-0.0199622\pi\)
−0.553293 + 0.832987i \(0.686629\pi\)
\(492\) −2.03231 + 5.34792i −0.0916237 + 0.241103i
\(493\) 7.47084 0.336470
\(494\) 2.13291 + 3.69431i 0.0959642 + 0.166215i
\(495\) 47.9796 + 42.6216i 2.15652 + 1.91570i
\(496\) 0.941952 0.0422949
\(497\) 0 0
\(498\) 1.32784 3.49413i 0.0595018 0.156576i
\(499\) −33.0960 −1.48158 −0.740789 0.671737i \(-0.765548\pi\)
−0.740789 + 0.671737i \(0.765548\pi\)
\(500\) −4.02576 + 6.97283i −0.180038 + 0.311834i
\(501\) −28.3992 + 4.59572i −1.26878 + 0.205322i
\(502\) 17.8288 + 30.8803i 0.795737 + 1.37826i
\(503\) −12.1860 −0.543346 −0.271673 0.962390i \(-0.587577\pi\)
−0.271673 + 0.962390i \(0.587577\pi\)
\(504\) 0 0
\(505\) −45.5331 −2.02619
\(506\) 6.69559 + 11.5971i 0.297655 + 0.515554i
\(507\) −12.8552 15.7664i −0.570918 0.700208i
\(508\) 4.86882 8.43305i 0.216019 0.374156i
\(509\) −13.6393 −0.604551 −0.302276 0.953221i \(-0.597746\pi\)
−0.302276 + 0.953221i \(0.597746\pi\)
\(510\) −7.99142 9.80116i −0.353866 0.434002i
\(511\) 0 0
\(512\) −7.97968 −0.352656
\(513\) −0.484527 + 11.4492i −0.0213924 + 0.505495i
\(514\) −2.11146 3.65715i −0.0931325 0.161310i
\(515\) 9.48962 0.418163
\(516\) −6.38427 + 1.03314i −0.281052 + 0.0454814i
\(517\) −17.4214 30.1747i −0.766190 1.32708i
\(518\) 0 0
\(519\) 30.1787 4.88368i 1.32470 0.214370i
\(520\) 3.46082 + 5.99432i 0.151767 + 0.262868i
\(521\) −17.7745 30.7863i −0.778714 1.34877i −0.932683 0.360697i \(-0.882539\pi\)
0.153969 0.988076i \(-0.450794\pi\)
\(522\) 24.0300 + 21.3465i 1.05177 + 0.934311i
\(523\) 13.3593 23.1391i 0.584163 1.01180i −0.410816 0.911718i \(-0.634756\pi\)
0.994979 0.100082i \(-0.0319105\pi\)
\(524\) 7.47991 12.9556i 0.326761 0.565967i
\(525\) 0 0
\(526\) −21.2052 36.7284i −0.924589 1.60143i
\(527\) −0.226830 −0.00988086
\(528\) −52.0654 + 8.42552i −2.26586 + 0.366674i
\(529\) −21.3785 −0.929499
\(530\) −25.2833 + 43.7919i −1.09824 + 1.90220i
\(531\) −32.0802 + 10.6620i −1.39216 + 0.462692i
\(532\) 0 0
\(533\) −1.88565 + 3.26604i −0.0816766 + 0.141468i
\(534\) −5.88683 + 15.4909i −0.254748 + 0.670356i
\(535\) 0.313440 0.542893i 0.0135512 0.0234713i
\(536\) 6.95990 12.0549i 0.300622 0.520693i
\(537\) −4.49413 + 0.727265i −0.193936 + 0.0313838i
\(538\) −25.5282 + 44.2161i −1.10060 + 1.90629i
\(539\) 0 0
\(540\) 0.757146 17.8911i 0.0325824 0.769910i
\(541\) −18.7927 + 32.5500i −0.807963 + 1.39943i 0.106309 + 0.994333i \(0.466097\pi\)
−0.914272 + 0.405100i \(0.867237\pi\)
\(542\) 42.8053 1.83864
\(543\) 2.44508 6.43408i 0.104928 0.276113i
\(544\) 6.15733 0.263993
\(545\) −16.4350 28.4663i −0.704000 1.21936i
\(546\) 0 0
\(547\) −9.13381 + 15.8202i −0.390533 + 0.676424i −0.992520 0.122082i \(-0.961043\pi\)
0.601986 + 0.798506i \(0.294376\pi\)
\(548\) −3.01567 + 5.22329i −0.128823 + 0.223128i
\(549\) −7.24968 + 35.2691i −0.309409 + 1.50525i
\(550\) −38.5750 66.8139i −1.64485 2.84896i
\(551\) 6.84243 + 11.8514i 0.291498 + 0.504889i
\(552\) −1.37824 + 3.62677i −0.0586619 + 0.154366i
\(553\) 0 0
\(554\) 1.62172 + 2.80890i 0.0689002 + 0.119339i
\(555\) 13.7500 + 16.8638i 0.583653 + 0.715828i
\(556\) −0.860866 −0.0365089
\(557\) 1.94636 + 3.37119i 0.0824698 + 0.142842i 0.904310 0.426876i \(-0.140386\pi\)
−0.821840 + 0.569718i \(0.807053\pi\)
\(558\) −0.729600 0.648123i −0.0308864 0.0274372i
\(559\) −4.26324 −0.180316
\(560\) 0 0
\(561\) 12.5378 2.02893i 0.529346 0.0856617i
\(562\) 20.8562 0.879767
\(563\) −1.66428 + 2.88261i −0.0701409 + 0.121488i −0.898963 0.438025i \(-0.855678\pi\)
0.828822 + 0.559512i \(0.189012\pi\)
\(564\) −3.45362 + 9.08800i −0.145424 + 0.382674i
\(565\) 14.7875 + 25.6127i 0.622115 + 1.07753i
\(566\) 48.2965 2.03006
\(567\) 0 0
\(568\) −21.4702 −0.900870
\(569\) 18.3122 + 31.7177i 0.767688 + 1.32967i 0.938814 + 0.344425i \(0.111926\pi\)
−0.171126 + 0.985249i \(0.554741\pi\)
\(570\) 8.22895 21.6540i 0.344673 0.906987i
\(571\) 11.2912 19.5569i 0.472522 0.818432i −0.526984 0.849875i \(-0.676677\pi\)
0.999506 + 0.0314435i \(0.0100104\pi\)
\(572\) 6.69483 0.279925
\(573\) 31.1286 5.03740i 1.30042 0.210441i
\(574\) 0 0
\(575\) −9.34201 −0.389589
\(576\) −2.62185 2.32906i −0.109244 0.0970442i
\(577\) −11.2725 19.5245i −0.469279 0.812815i 0.530104 0.847932i \(-0.322153\pi\)
−0.999383 + 0.0351177i \(0.988819\pi\)
\(578\) 26.8496 1.11680
\(579\) −0.221516 0.271680i −0.00920588 0.0112906i
\(580\) −10.6923 18.5197i −0.443975 0.768987i
\(581\) 0 0
\(582\) 17.5135 46.0857i 0.725957 1.91031i
\(583\) −25.3927 43.9814i −1.05166 1.82152i
\(584\) 4.67457 + 8.09659i 0.193435 + 0.335039i
\(585\) 2.37672 11.5626i 0.0982652 0.478053i
\(586\) 7.61717 13.1933i 0.314662 0.545011i
\(587\) −12.1198 + 20.9921i −0.500237 + 0.866436i 0.499763 + 0.866162i \(0.333421\pi\)
−1.00000 0.000273884i \(0.999913\pi\)
\(588\) 0 0
\(589\) −0.207750 0.359834i −0.00856020 0.0148267i
\(590\) 68.3368 2.81338
\(591\) −1.00375 + 2.64130i −0.0412886 + 0.108649i
\(592\) −17.8822 −0.734956
\(593\) 22.8663 39.6056i 0.939007 1.62641i 0.171680 0.985153i \(-0.445081\pi\)
0.767328 0.641255i \(-0.221586\pi\)
\(594\) 46.1252 + 29.2983i 1.89254 + 1.20212i
\(595\) 0 0
\(596\) −2.83343 + 4.90764i −0.116062 + 0.201025i
\(597\) −10.7583 + 1.74097i −0.440308 + 0.0712530i
\(598\) 1.23155 2.13311i 0.0503618 0.0872292i
\(599\) 15.0834 26.1252i 0.616290 1.06745i −0.373866 0.927483i \(-0.621968\pi\)
0.990157 0.139963i \(-0.0446985\pi\)
\(600\) 7.94042 20.8948i 0.324166 0.853026i
\(601\) 7.36933 12.7641i 0.300601 0.520657i −0.675671 0.737203i \(-0.736146\pi\)
0.976272 + 0.216547i \(0.0694794\pi\)
\(602\) 0 0
\(603\) −22.5275 + 7.48712i −0.917391 + 0.304899i
\(604\) 0.994149 1.72192i 0.0404513 0.0700638i
\(605\) 91.6569 3.72638
\(606\) −38.2715 + 6.19331i −1.55467 + 0.251586i
\(607\) −6.07836 −0.246713 −0.123356 0.992362i \(-0.539366\pi\)
−0.123356 + 0.992362i \(0.539366\pi\)
\(608\) 5.63941 + 9.76774i 0.228708 + 0.396134i
\(609\) 0 0
\(610\) 36.3930 63.0345i 1.47351 2.55219i
\(611\) −3.20439 + 5.55016i −0.129636 + 0.224535i
\(612\) −2.64949 2.35361i −0.107099 0.0951391i
\(613\) −5.88668 10.1960i −0.237761 0.411814i 0.722311 0.691569i \(-0.243080\pi\)
−0.960071 + 0.279755i \(0.909747\pi\)
\(614\) 0.911065 + 1.57801i 0.0367676 + 0.0636833i
\(615\) 20.2165 3.27154i 0.815207 0.131921i
\(616\) 0 0
\(617\) −16.0319 27.7680i −0.645418 1.11790i −0.984205 0.177034i \(-0.943350\pi\)
0.338786 0.940863i \(-0.389984\pi\)
\(618\) 7.97623 1.29076i 0.320851 0.0519219i
\(619\) −12.5518 −0.504498 −0.252249 0.967662i \(-0.581170\pi\)
−0.252249 + 0.967662i \(0.581170\pi\)
\(620\) 0.324641 + 0.562294i 0.0130379 + 0.0225823i
\(621\) 5.86501 3.06312i 0.235355 0.122919i
\(622\) −5.30441 −0.212688
\(623\) 0 0
\(624\) 6.13043 + 7.51873i 0.245414 + 0.300990i
\(625\) −7.85989 −0.314396
\(626\) 24.3125 42.1104i 0.971721 1.68307i
\(627\) 14.7018 + 18.0312i 0.587134 + 0.720096i
\(628\) 1.49511 + 2.58961i 0.0596614 + 0.103337i
\(629\) 4.30619 0.171699
\(630\) 0 0
\(631\) 33.4642 1.33219 0.666095 0.745867i \(-0.267964\pi\)
0.666095 + 0.745867i \(0.267964\pi\)
\(632\) −8.10690 14.0416i −0.322475 0.558543i
\(633\) 27.8482 4.50656i 1.10687 0.179120i
\(634\) 11.0904 19.2092i 0.440457 0.762894i
\(635\) −34.8575 −1.38328
\(636\) −5.03386 + 13.2463i −0.199606 + 0.525251i
\(637\) 0 0
\(638\) 65.2553 2.58348
\(639\) 27.3746 + 24.3176i 1.08292 + 0.961988i
\(640\) 21.5074 + 37.2519i 0.850155 + 1.47251i
\(641\) −18.9837 −0.749809 −0.374905 0.927063i \(-0.622325\pi\)
−0.374905 + 0.927063i \(0.622325\pi\)
\(642\) 0.189609 0.498947i 0.00748329 0.0196918i
\(643\) 4.81347 + 8.33718i 0.189825 + 0.328786i 0.945192 0.326516i \(-0.105875\pi\)
−0.755367 + 0.655302i \(0.772541\pi\)
\(644\) 0 0
\(645\) 14.6296 + 17.9426i 0.576039 + 0.706490i
\(646\) −2.29222 3.97025i −0.0901864 0.156207i
\(647\) 3.90607 + 6.76551i 0.153564 + 0.265980i 0.932535 0.361079i \(-0.117592\pi\)
−0.778972 + 0.627059i \(0.784258\pi\)
\(648\) 1.86604 + 15.7215i 0.0733048 + 0.617600i
\(649\) −34.3163 + 59.4375i −1.34703 + 2.33313i
\(650\) −7.09528 + 12.2894i −0.278300 + 0.482029i
\(651\) 0 0
\(652\) 2.64376 + 4.57912i 0.103537 + 0.179332i
\(653\) 31.7429 1.24219 0.621097 0.783734i \(-0.286687\pi\)
0.621097 + 0.783734i \(0.286687\pi\)
\(654\) −17.6859 21.6911i −0.691574 0.848189i
\(655\) −53.5512 −2.09242
\(656\) −8.41540 + 14.5759i −0.328566 + 0.569093i
\(657\) 3.21026 15.6177i 0.125244 0.609303i
\(658\) 0 0
\(659\) 3.10685 5.38122i 0.121026 0.209623i −0.799147 0.601136i \(-0.794715\pi\)
0.920172 + 0.391513i \(0.128048\pi\)
\(660\) −22.9738 28.1764i −0.894253 1.09677i
\(661\) −13.7631 + 23.8384i −0.535324 + 0.927208i 0.463824 + 0.885927i \(0.346477\pi\)
−0.999148 + 0.0412802i \(0.986856\pi\)
\(662\) −18.6094 + 32.2325i −0.723276 + 1.25275i
\(663\) −1.47626 1.81057i −0.0573331 0.0703168i
\(664\) 1.09935 1.90413i 0.0426630 0.0738945i
\(665\) 0 0
\(666\) 13.8509 + 12.3041i 0.536712 + 0.476775i
\(667\) 3.95084 6.84306i 0.152977 0.264964i
\(668\) 16.2971 0.630553
\(669\) 21.8570 + 26.8068i 0.845042 + 1.03641i
\(670\) 47.9878 1.85393
\(671\) 36.5505 + 63.3073i 1.41102 + 2.44395i
\(672\) 0 0
\(673\) −8.10894 + 14.0451i −0.312577 + 0.541399i −0.978919 0.204247i \(-0.934526\pi\)
0.666343 + 0.745646i \(0.267859\pi\)
\(674\) −10.8835 + 18.8508i −0.419217 + 0.726106i
\(675\) −33.7899 + 17.6474i −1.30057 + 0.679250i
\(676\) 5.76199 + 9.98006i 0.221615 + 0.383849i
\(677\) 10.2545 + 17.7613i 0.394112 + 0.682623i 0.992987 0.118220i \(-0.0377188\pi\)
−0.598875 + 0.800842i \(0.704385\pi\)
\(678\) 15.9130 + 19.5167i 0.611135 + 0.749532i
\(679\) 0 0
\(680\) −3.71932 6.44205i −0.142629 0.247041i
\(681\) 2.22291 5.84947i 0.0851822 0.224152i
\(682\) −1.98128 −0.0758673
\(683\) 0.0561542 + 0.0972618i 0.00214868 + 0.00372162i 0.867098 0.498138i \(-0.165983\pi\)
−0.864949 + 0.501860i \(0.832649\pi\)
\(684\) 1.30705 6.35869i 0.0499762 0.243131i
\(685\) 21.5902 0.824918
\(686\) 0 0
\(687\) 8.43839 22.2052i 0.321945 0.847179i
\(688\) −19.0262 −0.725368
\(689\) −4.67059 + 8.08970i −0.177935 + 0.308193i
\(690\) −13.2037 + 2.13670i −0.502657 + 0.0813427i
\(691\) −9.43351 16.3393i −0.358868 0.621577i 0.628904 0.777483i \(-0.283504\pi\)
−0.987772 + 0.155906i \(0.950170\pi\)
\(692\) −17.3182 −0.658340
\(693\) 0 0
\(694\) −39.9480 −1.51640
\(695\) 1.54081 + 2.66876i 0.0584461 + 0.101232i
\(696\) 11.9474 + 14.6530i 0.452866 + 0.555422i
\(697\) 2.02650 3.51000i 0.0767590 0.132951i
\(698\) 28.4665 1.07747
\(699\) −27.6413 33.9010i −1.04549 1.28225i
\(700\) 0 0
\(701\) −3.16006 −0.119354 −0.0596770 0.998218i \(-0.519007\pi\)
−0.0596770 + 0.998218i \(0.519007\pi\)
\(702\) 0.424968 10.0419i 0.0160394 0.379005i
\(703\) 3.94398 + 6.83118i 0.148750 + 0.257643i
\(704\) −7.11984 −0.268339
\(705\) 34.3549 5.55951i 1.29388 0.209383i
\(706\) −21.1402 36.6159i −0.795622 1.37806i
\(707\) 0 0
\(708\) 18.9045 3.05923i 0.710475 0.114973i
\(709\) 10.7606 + 18.6378i 0.404121 + 0.699959i 0.994219 0.107373i \(-0.0342440\pi\)
−0.590097 + 0.807332i \(0.700911\pi\)
\(710\) −37.0087 64.1009i −1.38891 2.40567i
\(711\) −5.56741 + 27.0850i −0.208794 + 1.01577i
\(712\) −4.87385 + 8.44176i −0.182655 + 0.316368i
\(713\) −0.119956 + 0.207769i −0.00449237 + 0.00778102i
\(714\) 0 0
\(715\) −11.9826 20.7545i −0.448125 0.776175i
\(716\) 2.57898 0.0963812
\(717\) −15.3710 + 2.48742i −0.574041 + 0.0928945i
\(718\) −35.3570 −1.31951
\(719\) 9.41508 16.3074i 0.351123 0.608163i −0.635323 0.772246i \(-0.719133\pi\)
0.986447 + 0.164083i \(0.0524665\pi\)
\(720\) 10.6070 51.6021i 0.395298 1.92310i
\(721\) 0 0
\(722\) −12.2040 + 21.1379i −0.454185 + 0.786671i
\(723\) 5.69582 14.9882i 0.211830 0.557419i
\(724\) −1.94957 + 3.37675i −0.0724551 + 0.125496i
\(725\) −22.7618 + 39.4247i −0.845354 + 1.46420i
\(726\) 77.0396 12.4670i 2.85921 0.462693i
\(727\) −19.5426 + 33.8489i −0.724797 + 1.25538i 0.234261 + 0.972174i \(0.424733\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(728\) 0 0
\(729\) 15.4273 22.1585i 0.571381 0.820685i
\(730\) −16.1153 + 27.9125i −0.596454 + 1.03309i
\(731\) 4.58167 0.169459
\(732\) 7.24578 19.0669i 0.267812 0.704732i
\(733\) 18.5985 0.686951 0.343475 0.939162i \(-0.388396\pi\)
0.343475 + 0.939162i \(0.388396\pi\)
\(734\) 19.2119 + 33.2759i 0.709123 + 1.22824i
\(735\) 0 0
\(736\) 3.25621 5.63993i 0.120026 0.207890i
\(737\) −24.0977 + 41.7385i −0.887651 + 1.53746i
\(738\) 16.5474 5.49960i 0.609118 0.202443i
\(739\) −2.75068 4.76432i −0.101185 0.175258i 0.810988 0.585063i \(-0.198930\pi\)
−0.912173 + 0.409805i \(0.865597\pi\)
\(740\) −6.16306 10.6747i −0.226559 0.392411i
\(741\) 1.52014 4.00016i 0.0558436 0.146949i
\(742\) 0 0
\(743\) 10.2326 + 17.7234i 0.375399 + 0.650210i 0.990387 0.138327i \(-0.0441725\pi\)
−0.614988 + 0.788537i \(0.710839\pi\)
\(744\) −0.362748 0.444896i −0.0132990 0.0163107i
\(745\) 20.2855 0.743201
\(746\) −28.0892 48.6520i −1.02842 1.78128i
\(747\) −3.55832 + 1.18262i −0.130192 + 0.0432700i
\(748\) −7.19489 −0.263071
\(749\) 0 0
\(750\) 24.2253 3.92027i 0.884583 0.143148i
\(751\) 38.0460 1.38832 0.694159 0.719822i \(-0.255777\pi\)
0.694159 + 0.719822i \(0.255777\pi\)
\(752\) −14.3007 + 24.7696i −0.521494 + 0.903254i
\(753\) 12.7067 33.4369i 0.463057 1.21851i
\(754\) −6.00135 10.3946i −0.218556 0.378551i
\(755\) −7.11744 −0.259030
\(756\) 0 0
\(757\) −51.0780 −1.85646 −0.928230 0.372006i \(-0.878670\pi\)
−0.928230 + 0.372006i \(0.878670\pi\)
\(758\) 1.33329 + 2.30933i 0.0484273 + 0.0838786i
\(759\) 4.77198 12.5572i 0.173212 0.455798i
\(760\) 6.81295 11.8004i 0.247132 0.428045i
\(761\) −40.0749 −1.45271 −0.726357 0.687317i \(-0.758788\pi\)
−0.726357 + 0.687317i \(0.758788\pi\)
\(762\) −29.2985 + 4.74124i −1.06137 + 0.171757i
\(763\) 0 0
\(764\) −17.8633 −0.646273
\(765\) −2.55424 + 12.4262i −0.0923489 + 0.449270i
\(766\) 27.3058 + 47.2951i 0.986599 + 1.70884i
\(767\) 12.6239 0.455822
\(768\) 20.5854 + 25.2472i 0.742812 + 0.911029i
\(769\) 22.4828 + 38.9414i 0.810751 + 1.40426i 0.912339 + 0.409436i \(0.134274\pi\)
−0.101587 + 0.994827i \(0.532392\pi\)
\(770\) 0 0
\(771\) −1.50485 + 3.95993i −0.0541958 + 0.142613i
\(772\) 0.0992886 + 0.171973i 0.00357348 + 0.00618944i
\(773\) 12.1781 + 21.0930i 0.438014 + 0.758663i 0.997536 0.0701524i \(-0.0223485\pi\)
−0.559522 + 0.828816i \(0.689015\pi\)
\(774\) 14.7370 + 13.0913i 0.529710 + 0.470556i
\(775\) 0.691096 1.19701i 0.0248249 0.0429980i
\(776\) 14.4998 25.1145i 0.520514 0.901556i
\(777\) 0 0
\(778\) −4.52913 7.84468i −0.162377 0.281245i
\(779\) 7.42416 0.265998
\(780\) −2.37544 + 6.25084i −0.0850545 + 0.223816i
\(781\) 74.3377 2.66001
\(782\) −1.32354 + 2.29243i −0.0473296 + 0.0819773i
\(783\) 1.36331 32.2145i 0.0487207 1.15125i