Properties

Label 441.2.g.h.67.9
Level $441$
Weight $2$
Character 441.67
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

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 67.9
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.h.79.9

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

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 −0.380716 0.924692i \(-0.624322\pi\)
0.991165 0.132637i \(-0.0423443\pi\)
\(3\) −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 \(-0.787531\pi\)
−0.785377 + 0.619018i \(0.787531\pi\)
\(6\) −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 \(-0.882985\pi\)
0.777833 + 0.628471i \(0.216319\pi\)
\(14\) 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 \(-0.786693\pi\)
0.929746 + 0.368202i \(0.120026\pi\)
\(18\) 1.04293 + 5.07375i 0.245820 + 1.19589i
\(19\) −1.10269 1.90991i −0.252974 0.438163i 0.711370 0.702818i \(-0.248075\pi\)
−0.964343 + 0.264655i \(0.914742\pi\)
\(20\) 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 −0.995917 0.0902789i \(-0.971224\pi\)
0.419774 0.907628i \(-0.362109\pi\)
\(30\) 10.3689 + 1.67796i 1.89310 + 0.306352i
\(31\) −0.0942019 0.163162i −0.0169192 0.0293048i 0.857442 0.514581i \(-0.172052\pi\)
−0.874361 + 0.485276i \(0.838719\pi\)
\(32\) −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 0.680749 0.732516i \(-0.261654\pi\)
−0.974753 + 0.223288i \(0.928321\pi\)
\(38\) −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 \(-0.918003\pi\)
0.704132 + 0.710069i \(0.251336\pi\)
\(42\) 0 0
\(43\) −1.90276 3.29567i −0.290168 0.502585i 0.683681 0.729781i \(-0.260378\pi\)
−0.973849 + 0.227195i \(0.927044\pi\)
\(44\) 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 \(-0.970331\pi\)
0.578434 + 0.815729i \(0.303664\pi\)
\(48\) −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 −0.423615 0.905842i \(-0.639239\pi\)
0.996290 0.0860593i \(-0.0274275\pi\)
\(54\) 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 −0.955370 0.295411i \(-0.904543\pi\)
0.221851 0.975081i \(-0.428790\pi\)
\(60\) 3.77198 4.62618i 0.486960 0.597238i
\(61\) 6.00109 10.3942i 0.768361 1.33084i −0.170091 0.985428i \(-0.554406\pi\)
0.938451 0.345411i \(-0.112261\pi\)
\(62\) −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 0.999818 0.0191025i \(-0.00608088\pi\)
−0.516452 + 0.856316i \(0.672748\pi\)
\(68\) −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 \(-0.934004\pi\)
0.667563 + 0.744554i \(0.267338\pi\)
\(74\) −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 0.481266 + 0.876575i \(0.340177\pi\)
−0.999769 + 0.0214988i \(0.993156\pi\)
\(80\) −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 \(-0.188519\pi\)
−0.898284 + 0.439415i \(0.855186\pi\)
\(84\) 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 \(-0.0717837\pi\)
−0.680990 + 0.732293i \(0.738450\pi\)
\(90\) −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 −0.892452 0.451142i \(-0.851017\pi\)
0.0555261 0.998457i \(-0.482316\pi\)
\(98\) 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 \(-0.276868\pi\)
0.644975 + 0.764203i \(0.276868\pi\)
\(102\) −2.27526 + 2.79051i −0.225284 + 0.276302i
\(103\) −2.70182 −0.266218 −0.133109 0.991101i \(-0.542496\pi\)
−0.133109 + 0.991101i \(0.542496\pi\)
\(104\) −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 0.870307 0.492510i \(-0.163921\pi\)
−0.861680 + 0.507453i \(0.830587\pi\)
\(108\) −0.215569 5.09382i −0.0207431 0.490153i
\(109\) −4.67927 + 8.10473i −0.448192 + 0.776292i −0.998268 0.0588226i \(-0.981265\pi\)
0.550076 + 0.835115i \(0.314599\pi\)
\(110\) 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 −0.597175 0.802111i \(-0.703710\pi\)
0.993236 + 0.116113i \(0.0370434\pi\)
\(114\) 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 \(-0.267981\pi\)
0.666055 + 0.745902i \(0.267981\pi\)
\(132\) 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 \(-0.845180\pi\)
0.846821 + 0.531878i \(0.178513\pi\)
\(140\) 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 \(-0.205473\pi\)
−0.920403 + 0.390971i \(0.872139\pi\)
\(158\) 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 0.952042 0.305967i \(-0.0989797\pi\)
−0.740996 + 0.671509i \(0.765646\pi\)
\(164\) 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 −0.342196 0.939629i \(-0.611171\pi\)
0.984840 0.173464i \(-0.0554961\pi\)
\(168\) 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 0.306666 + 0.951817i \(0.400786\pi\)
−0.977631 + 0.210328i \(0.932547\pi\)
\(174\) 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 −0.910952 0.412513i \(-0.864651\pi\)
0.812722 + 0.582651i \(0.197985\pi\)
\(180\) −9.81100 3.26073i −0.731269 0.243041i
\(181\) −3.97391 −0.295378 −0.147689 0.989034i \(-0.547184\pi\)
−0.147689 + 0.989034i \(0.547184\pi\)
\(182\) 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 −0.322295 0.946639i \(-0.604454\pi\)
0.980961 0.194204i \(-0.0622125\pi\)
\(192\) −0.719254 1.89268i −0.0519077 0.136592i
\(193\) 0.101193 + 0.175271i 0.00728401 + 0.0126163i 0.869644 0.493679i \(-0.164348\pi\)
−0.862360 + 0.506295i \(0.831015\pi\)
\(194\) −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 \(-0.761743\pi\)
0.955723 + 0.294268i \(0.0950759\pi\)
\(200\) 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 −0.436807 0.899555i \(-0.643891\pi\)
0.997441 0.0714912i \(-0.0227758\pi\)
\(212\) −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 0.978288 + 0.207248i \(0.0664507\pi\)
−0.309662 + 0.950847i \(0.600216\pi\)
\(224\) 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 \(-0.538256\pi\)
−0.119896 + 0.992786i \(0.538256\pi\)
\(228\) 3.69981 + 0.598725i 0.245026 + 0.0396515i
\(229\) −13.7147 −0.906290 −0.453145 0.891437i \(-0.649698\pi\)
−0.453145 + 0.891437i \(0.649698\pi\)
\(230\) 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 0.900205 + 0.435466i \(0.143417\pi\)
−0.0729776 + 0.997334i \(0.523250\pi\)
\(234\) −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 −0.973988 0.226598i \(-0.927240\pi\)
0.683234 + 0.730200i \(0.260573\pi\)
\(240\) 30.0248 + 4.85877i 1.93809 + 0.313633i
\(241\) −9.25724 −0.596311 −0.298156 0.954517i \(-0.596371\pi\)
−0.298156 + 0.954517i \(0.596371\pi\)
\(242\) 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 \(-0.725970\pi\)
−0.651763 + 0.758422i \(0.725970\pi\)
\(252\) 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 \(-0.475695\pi\)
0.0762819 + 0.997086i \(0.475695\pi\)
\(258\) 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 −0.0758746 + 0.997117i \(0.524175\pi\)
−0.825592 + 0.564268i \(0.809158\pi\)
\(270\) −26.5992 + 16.8955i −1.61877 + 1.02823i
\(271\) −12.3958 21.4701i −0.752989 1.30421i −0.946368 0.323090i \(-0.895278\pi\)
0.193380 0.981124i \(-0.438055\pi\)
\(272\) −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 0.988009 0.154395i \(-0.0493427\pi\)
−0.627714 + 0.778444i \(0.716009\pi\)
\(282\) 10.8111 13.2594i 0.643790 0.789583i
\(283\) −13.9859 24.2244i −0.831378 1.43999i −0.896946 0.442140i \(-0.854219\pi\)
0.0655680 0.997848i \(-0.479114\pi\)
\(284\) 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 \(-0.750359\pi\)
0.965634 + 0.259908i \(0.0836921\pi\)
\(294\) 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 \(-0.509587\pi\)
−0.0301152 + 0.999546i \(0.509587\pi\)
\(308\) 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 \(-0.138906\pi\)
−0.819182 + 0.573533i \(0.805572\pi\)
\(312\) 3.36948 + 0.545269i 0.190759 + 0.0308698i
\(313\) 14.0810 24.3891i 0.795907 1.37855i −0.126355 0.991985i \(-0.540328\pi\)
0.922262 0.386566i \(-0.126339\pi\)
\(314\) −5.26196 −0.296949
\(315\) 0 0
\(316\) 9.04368 0.508747
\(317\) −6.42324 + 11.1254i −0.360765 + 0.624863i −0.988087 0.153897i \(-0.950818\pi\)
0.627322 + 0.778760i \(0.284151\pi\)
\(318\) −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 −0.401493 0.915862i \(-0.631509\pi\)
0.993906 0.110228i \(-0.0351581\pi\)
\(332\) −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 −0.641688 0.766966i \(-0.721766\pi\)
0.985056 + 0.172235i \(0.0550989\pi\)
\(338\) 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 −0.989296 0.145922i \(-0.953385\pi\)
0.368276 0.929716i \(-0.379948\pi\)
\(348\) 10.4101 + 1.68463i 0.558042 + 0.0903055i
\(349\) −8.24346 14.2781i −0.441262 0.764289i 0.556521 0.830833i \(-0.312136\pi\)
−0.997783 + 0.0665448i \(0.978802\pi\)
\(350\) 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 \(-0.274069\pi\)
0.651669 + 0.758503i \(0.274069\pi\)
\(354\) 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 −0.998882 0.0472797i \(-0.984945\pi\)
0.458495 0.888697i \(-0.348389\pi\)
\(360\) 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 \(-0.697268\pi\)
−0.580821 + 0.814031i \(0.697268\pi\)
\(368\) −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 \(-0.799500\pi\)
−0.808093 + 0.589055i \(0.799500\pi\)
\(384\) −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 \(-0.166446\pi\)
−0.865678 + 0.500600i \(0.833113\pi\)
\(398\) −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 0.934816 + 0.355134i \(0.115565\pi\)
−0.159853 + 0.987141i \(0.551102\pi\)
\(410\) −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 \(-0.951794\pi\)
0.624931 + 0.780680i \(0.285127\pi\)
\(420\) 0 0
\(421\) −4.54213 7.86721i −0.221370 0.383424i 0.733854 0.679307i \(-0.237720\pi\)
−0.955224 + 0.295883i \(0.904386\pi\)
\(422\) −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 −0.593152 0.805090i \(-0.702117\pi\)
0.993805 + 0.111140i \(0.0354502\pi\)
\(432\) 21.9291 13.9291i 1.05506 0.670165i
\(433\) −19.7423 −0.948756 −0.474378 0.880321i \(-0.657327\pi\)
−0.474378 + 0.880321i \(0.657327\pi\)
\(434\) 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 \(-0.884717\pi\)
0.774404 + 0.632692i \(0.218050\pi\)
\(440\) 37.6310 1.79399
\(441\) 0 0
\(442\) 2.32879 0.110769
\(443\) −14.3202 + 24.8033i −0.680372 + 1.17844i 0.294496 + 0.955653i \(0.404848\pi\)
−0.974867 + 0.222786i \(0.928485\pi\)
\(444\) 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 −0.307563 0.951528i \(-0.599513\pi\)
0.977829 0.209407i \(-0.0671533\pi\)
\(458\) −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 \(-0.0123075\pi\)
−0.533103 + 0.846050i \(0.678974\pi\)
\(462\) 0 0
\(463\) −4.95789 + 8.58731i −0.230413 + 0.399086i −0.957930 0.287003i \(-0.907341\pi\)
0.727517 + 0.686090i \(0.240674\pi\)
\(464\) −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 \(-0.288016\pi\)
−0.989883 + 0.141888i \(0.954683\pi\)
\(468\) −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 \(-0.560003\pi\)
−0.187392 + 0.982285i \(0.560003\pi\)
\(480\) 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 −0.895363 0.445337i \(-0.853084\pi\)
0.833355 + 0.552738i \(0.186417\pi\)
\(488\) 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 −0.553293 0.832987i \(-0.686629\pi\)
0.998034 + 0.0626719i \(0.0199622\pi\)
\(492\) −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 \(-0.412423\pi\)
0.271673 + 0.962390i \(0.412423\pi\)
\(504\) 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 \(-0.402254\pi\)
0.302276 + 0.953221i \(0.402254\pi\)
\(510\) 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 −0.153969 0.988076i \(-0.549206\pi\)
0.932683 0.360697i \(-0.117461\pi\)
\(522\) 24.0300 21.3465i 1.05177 0.934311i
\(523\) −13.3593 23.1391i −0.584163 1.01180i −0.994979 0.100082i \(-0.968089\pi\)
0.410816 0.911718i \(-0.365244\pi\)
\(524\) −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 −0.914272 0.405100i \(-0.867237\pi\)
0.106309 0.994333i \(-0.466097\pi\)
\(542\) −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 0.601986 0.798506i \(-0.294376\pi\)
−0.992520 + 0.122082i \(0.961043\pi\)
\(548\) −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 −0.821840 0.569718i \(-0.807053\pi\)
0.904310 + 0.426876i \(0.140386\pi\)
\(558\) 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 \(-0.144322\pi\)
−0.828822 + 0.559512i \(0.810988\pi\)
\(564\) −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 −0.171126 0.985249i \(-0.554741\pi\)
0.938814 0.344425i \(-0.111926\pi\)
\(570\) −8.22895 21.6540i −0.344673 0.906987i
\(571\) 11.2912 + 19.5569i 0.472522 + 0.818432i 0.999506 0.0314435i \(-0.0100104\pi\)
−0.526984 + 0.849875i \(0.676677\pi\)
\(572\) −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 \(-0.677847\pi\)
0.999383 + 0.0351177i \(0.0111806\pi\)
\(578\) 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 1.00000 0.000273884i \(8.71801e-5\pi\)
−0.499763 + 0.866162i \(0.666579\pi\)
\(588\) 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 −0.767328 0.641255i \(-0.778414\pi\)
−0.171680 0.985153i \(-0.554919\pi\)
\(594\) −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 0.990157 + 0.139963i \(0.0446985\pi\)
−0.373866 + 0.927483i \(0.621968\pi\)
\(600\) −7.94042 20.8948i −0.324166 0.853026i
\(601\) −7.36933 12.7641i −0.300601 0.520657i 0.675671 0.737203i \(-0.263854\pi\)
−0.976272 + 0.216547i \(0.930521\pi\)
\(602\) 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 \(-0.460634\pi\)
0.123356 + 0.992362i \(0.460634\pi\)
\(608\) −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 −0.960071 0.279755i \(-0.909747\pi\)
0.722311 + 0.691569i \(0.243080\pi\)
\(614\) −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 0.338786 + 0.940863i \(0.389984\pi\)
−0.984205 + 0.177034i \(0.943350\pi\)
\(618\) 7.97623 + 1.29076i 0.320851 + 0.0519219i
\(619\) 12.5518 0.504498 0.252249 0.967662i \(-0.418830\pi\)
0.252249 + 0.967662i \(0.418830\pi\)
\(620\) 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 \(-0.894125\pi\)
0.755367 + 0.655302i \(0.227459\pi\)
\(644\) 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 \(-0.882408\pi\)
0.778972 + 0.627059i \(0.215742\pi\)
\(648\) 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 0.920172 0.391513i \(-0.128048\pi\)
−0.799147 + 0.601136i \(0.794715\pi\)
\(660\) −22.9738 + 28.1764i −0.894253 + 1.09677i
\(661\) 13.7631 + 23.8384i 0.535324 + 0.927208i 0.999148 + 0.0412802i \(0.0131436\pi\)
−0.463824 + 0.885927i \(0.653523\pi\)
\(662\) −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 0.666343 0.745646i \(-0.267859\pi\)
−0.978919 + 0.204247i \(0.934526\pi\)
\(674\) −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 \(-0.962281\pi\)
0.598875 + 0.800842i \(0.295615\pi\)
\(678\) −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 −0.864949 0.501860i \(-0.832649\pi\)
0.867098 + 0.498138i \(0.165983\pi\)
\(684\) −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 \(-0.716496\pi\)
0.987772 + 0.155906i \(0.0498296\pi\)
\(692\) 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 −0.590097 0.807332i \(-0.700911\pi\)
0.994219 + 0.107373i \(0.0342440\pi\)
\(710\) 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 \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947533\pi\)
\(720\) −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 0.959058 + 0.283211i \(0.0913996\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(728\) 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 \(-0.611604\pi\)
−0.343475 + 0.939162i \(0.611604\pi\)
\(734\) −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 −0.912173 0.409805i \(-0.865597\pi\)
0.810988 + 0.585063i \(0.198930\pi\)
\(740\) 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 −0.614988 0.788537i \(-0.710839\pi\)
0.990387 + 0.138327i \(0.0441725\pi\)
\(744\) −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 \(-0.241212\pi\)
0.726357 + 0.687317i \(0.241212\pi\)
\(762\) 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 0.101587 + 0.994827i \(0.467608\pi\)
−0.912339 + 0.409436i \(0.865726\pi\)
\(770\) 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 \(-0.977651\pi\)
0.559522 + 0.828816i \(0.310985\pi\)
\(774\) 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