Properties

Label 637.2.e.n.79.5
Level $637$
Weight $2$
Character 637.79
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + 43 x^{2} + 6 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.5
Root \(1.17550 - 2.03602i\) of defining polynomial
Character \(\chi\) \(=\) 637.79
Dual form 637.2.e.n.508.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.588093 - 1.01861i) q^{2} +(-1.67550 - 2.90205i) q^{3} +(0.308293 + 0.533979i) q^{4} +(-1.57431 + 2.72679i) q^{5} -3.94140 q^{6} +3.07759 q^{8} +(-4.11459 + 7.12667i) q^{9} +O(q^{10})\) \(q+(0.588093 - 1.01861i) q^{2} +(-1.67550 - 2.90205i) q^{3} +(0.308293 + 0.533979i) q^{4} +(-1.57431 + 2.72679i) q^{5} -3.94140 q^{6} +3.07759 q^{8} +(-4.11459 + 7.12667i) q^{9} +(1.85168 + 3.20721i) q^{10} +(0.386695 + 0.669775i) q^{11} +(1.03309 - 1.78936i) q^{12} +1.00000 q^{13} +10.5510 q^{15} +(1.19333 - 2.06690i) q^{16} +(2.87670 + 4.98259i) q^{17} +(4.83952 + 8.38230i) q^{18} +(0.611490 - 1.05913i) q^{19} -1.94140 q^{20} +0.909650 q^{22} +(1.49591 - 2.59099i) q^{23} +(-5.15650 - 8.93132i) q^{24} +(-2.45692 - 4.25550i) q^{25} +(0.588093 - 1.01861i) q^{26} +17.5229 q^{27} -2.46882 q^{29} +(6.20499 - 10.7474i) q^{30} +(3.06743 + 5.31295i) q^{31} +(1.67402 + 2.89949i) q^{32} +(1.29581 - 2.24441i) q^{33} +6.76707 q^{34} -5.07399 q^{36} +(-2.49966 + 4.32954i) q^{37} +(-0.719226 - 1.24574i) q^{38} +(-1.67550 - 2.90205i) q^{39} +(-4.84509 + 8.39194i) q^{40} -2.55981 q^{41} -2.73150 q^{43} +(-0.238430 + 0.412974i) q^{44} +(-12.9553 - 22.4392i) q^{45} +(-1.75947 - 3.04749i) q^{46} +(-2.68585 + 4.65202i) q^{47} -7.99766 q^{48} -5.77958 q^{50} +(9.63981 - 16.6966i) q^{51} +(0.308293 + 0.533979i) q^{52} +(4.89508 + 8.47852i) q^{53} +(10.3051 - 17.8490i) q^{54} -2.43511 q^{55} -4.09820 q^{57} +(-1.45190 + 2.51476i) q^{58} +(-1.25228 - 2.16902i) q^{59} +(3.25281 + 5.63402i) q^{60} +(5.45835 - 9.45414i) q^{61} +7.21575 q^{62} +8.71122 q^{64} +(-1.57431 + 2.72679i) q^{65} +(-1.52412 - 2.63985i) q^{66} +(-2.16259 - 3.74571i) q^{67} +(-1.77373 + 3.07219i) q^{68} -10.0256 q^{69} +10.6649 q^{71} +(-12.6630 + 21.9330i) q^{72} +(2.58725 + 4.48125i) q^{73} +(2.94007 + 5.09235i) q^{74} +(-8.23312 + 14.2602i) q^{75} +0.754072 q^{76} -3.94140 q^{78} +(0.271019 - 0.469419i) q^{79} +(3.75733 + 6.50789i) q^{80} +(-17.0159 - 29.4724i) q^{81} +(-1.50540 + 2.60744i) q^{82} +15.2259 q^{83} -18.1153 q^{85} +(-1.60638 + 2.78233i) q^{86} +(4.13650 + 7.16464i) q^{87} +(1.19009 + 2.06129i) q^{88} +(-4.61604 + 7.99522i) q^{89} -30.4757 q^{90} +1.84471 q^{92} +(10.2790 - 17.8037i) q^{93} +(3.15905 + 5.47164i) q^{94} +(1.92535 + 3.33481i) q^{95} +(5.60963 - 9.71617i) q^{96} -1.26291 q^{97} -6.36436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 8q^{3} - 4q^{4} - 6q^{5} + 8q^{6} - 6q^{9} + O(q^{10}) \) \( 12q - 8q^{3} - 4q^{4} - 6q^{5} + 8q^{6} - 6q^{9} - 4q^{10} - 4q^{11} + 4q^{12} + 12q^{13} + 24q^{15} - 16q^{17} + 4q^{18} - 2q^{19} + 32q^{20} - 24q^{22} + 6q^{23} - 12q^{24} + 4q^{25} + 40q^{27} - 12q^{29} - 6q^{31} + 20q^{32} - 4q^{33} - 48q^{36} - 8q^{38} - 8q^{39} - 4q^{40} - 16q^{41} + 4q^{43} + 4q^{44} - 14q^{45} - 8q^{46} - 30q^{47} - 16q^{48} + 16q^{50} + 4q^{51} - 4q^{52} + 14q^{53} + 48q^{54} - 16q^{55} + 8q^{57} + 8q^{58} - 24q^{59} - 12q^{60} + 56q^{62} - 40q^{64} - 6q^{65} + 4q^{66} - 16q^{67} - 28q^{68} - 40q^{69} + 16q^{71} - 28q^{72} + 6q^{73} + 12q^{74} - 12q^{75} - 32q^{76} + 8q^{78} + 22q^{79} + 28q^{80} - 46q^{81} + 40q^{82} + 100q^{83} - 16q^{85} + 16q^{86} + 16q^{87} + 44q^{88} - 26q^{89} - 80q^{90} + 40q^{92} - 16q^{93} + 32q^{94} + 6q^{95} + 20q^{96} - 28q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.588093 1.01861i 0.415845 0.720264i −0.579672 0.814850i \(-0.696819\pi\)
0.995517 + 0.0945858i \(0.0301527\pi\)
\(3\) −1.67550 2.90205i −0.967349 1.67550i −0.703166 0.711025i \(-0.748231\pi\)
−0.264183 0.964473i \(-0.585102\pi\)
\(4\) 0.308293 + 0.533979i 0.154146 + 0.266989i
\(5\) −1.57431 + 2.72679i −0.704054 + 1.21946i 0.262978 + 0.964802i \(0.415295\pi\)
−0.967032 + 0.254655i \(0.918038\pi\)
\(6\) −3.94140 −1.60907
\(7\) 0 0
\(8\) 3.07759 1.08809
\(9\) −4.11459 + 7.12667i −1.37153 + 2.37556i
\(10\) 1.85168 + 3.20721i 0.585554 + 1.01421i
\(11\) 0.386695 + 0.669775i 0.116593 + 0.201945i 0.918415 0.395618i \(-0.129469\pi\)
−0.801823 + 0.597562i \(0.796136\pi\)
\(12\) 1.03309 1.78936i 0.298227 0.516544i
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 10.5510 2.72426
\(16\) 1.19333 2.06690i 0.298331 0.516725i
\(17\) 2.87670 + 4.98259i 0.697702 + 1.20846i 0.969261 + 0.246034i \(0.0791274\pi\)
−0.271559 + 0.962422i \(0.587539\pi\)
\(18\) 4.83952 + 8.38230i 1.14069 + 1.97573i
\(19\) 0.611490 1.05913i 0.140285 0.242981i −0.787319 0.616546i \(-0.788531\pi\)
0.927604 + 0.373565i \(0.121865\pi\)
\(20\) −1.94140 −0.434109
\(21\) 0 0
\(22\) 0.909650 0.193938
\(23\) 1.49591 2.59099i 0.311919 0.540259i −0.666859 0.745184i \(-0.732362\pi\)
0.978778 + 0.204925i \(0.0656950\pi\)
\(24\) −5.15650 8.93132i −1.05257 1.82310i
\(25\) −2.45692 4.25550i −0.491383 0.851101i
\(26\) 0.588093 1.01861i 0.115335 0.199765i
\(27\) 17.5229 3.37229
\(28\) 0 0
\(29\) −2.46882 −0.458449 −0.229224 0.973374i \(-0.573619\pi\)
−0.229224 + 0.973374i \(0.573619\pi\)
\(30\) 6.20499 10.7474i 1.13287 1.96219i
\(31\) 3.06743 + 5.31295i 0.550927 + 0.954234i 0.998208 + 0.0598404i \(0.0190592\pi\)
−0.447281 + 0.894394i \(0.647607\pi\)
\(32\) 1.67402 + 2.89949i 0.295928 + 0.512562i
\(33\) 1.29581 2.24441i 0.225572 0.390702i
\(34\) 6.76707 1.16054
\(35\) 0 0
\(36\) −5.07399 −0.845665
\(37\) −2.49966 + 4.32954i −0.410942 + 0.711773i −0.994993 0.0999443i \(-0.968134\pi\)
0.584051 + 0.811717i \(0.301467\pi\)
\(38\) −0.719226 1.24574i −0.116674 0.202085i
\(39\) −1.67550 2.90205i −0.268294 0.464700i
\(40\) −4.84509 + 8.39194i −0.766076 + 1.32688i
\(41\) −2.55981 −0.399774 −0.199887 0.979819i \(-0.564058\pi\)
−0.199887 + 0.979819i \(0.564058\pi\)
\(42\) 0 0
\(43\) −2.73150 −0.416550 −0.208275 0.978070i \(-0.566785\pi\)
−0.208275 + 0.978070i \(0.566785\pi\)
\(44\) −0.238430 + 0.412974i −0.0359447 + 0.0622581i
\(45\) −12.9553 22.4392i −1.93126 3.34504i
\(46\) −1.75947 3.04749i −0.259420 0.449328i
\(47\) −2.68585 + 4.65202i −0.391771 + 0.678567i −0.992683 0.120748i \(-0.961471\pi\)
0.600912 + 0.799315i \(0.294804\pi\)
\(48\) −7.99766 −1.15436
\(49\) 0 0
\(50\) −5.77958 −0.817357
\(51\) 9.63981 16.6966i 1.34984 2.33800i
\(52\) 0.308293 + 0.533979i 0.0427525 + 0.0740495i
\(53\) 4.89508 + 8.47852i 0.672390 + 1.16461i 0.977224 + 0.212209i \(0.0680657\pi\)
−0.304834 + 0.952406i \(0.598601\pi\)
\(54\) 10.3051 17.8490i 1.40235 2.42894i
\(55\) −2.43511 −0.328351
\(56\) 0 0
\(57\) −4.09820 −0.542820
\(58\) −1.45190 + 2.51476i −0.190643 + 0.330204i
\(59\) −1.25228 2.16902i −0.163033 0.282382i 0.772922 0.634501i \(-0.218794\pi\)
−0.935955 + 0.352119i \(0.885461\pi\)
\(60\) 3.25281 + 5.63402i 0.419935 + 0.727349i
\(61\) 5.45835 9.45414i 0.698870 1.21048i −0.269988 0.962864i \(-0.587020\pi\)
0.968858 0.247615i \(-0.0796469\pi\)
\(62\) 7.21575 0.916401
\(63\) 0 0
\(64\) 8.71122 1.08890
\(65\) −1.57431 + 2.72679i −0.195269 + 0.338216i
\(66\) −1.52412 2.63985i −0.187606 0.324943i
\(67\) −2.16259 3.74571i −0.264202 0.457612i 0.703152 0.711039i \(-0.251775\pi\)
−0.967354 + 0.253428i \(0.918442\pi\)
\(68\) −1.77373 + 3.07219i −0.215097 + 0.372558i
\(69\) −10.0256 −1.20694
\(70\) 0 0
\(71\) 10.6649 1.26570 0.632848 0.774276i \(-0.281886\pi\)
0.632848 + 0.774276i \(0.281886\pi\)
\(72\) −12.6630 + 21.9330i −1.49235 + 2.58483i
\(73\) 2.58725 + 4.48125i 0.302815 + 0.524491i 0.976772 0.214279i \(-0.0687403\pi\)
−0.673958 + 0.738770i \(0.735407\pi\)
\(74\) 2.94007 + 5.09235i 0.341776 + 0.591974i
\(75\) −8.23312 + 14.2602i −0.950679 + 1.64662i
\(76\) 0.754072 0.0864979
\(77\) 0 0
\(78\) −3.94140 −0.446275
\(79\) 0.271019 0.469419i 0.0304920 0.0528138i −0.850377 0.526174i \(-0.823626\pi\)
0.880869 + 0.473361i \(0.156959\pi\)
\(80\) 3.75733 + 6.50789i 0.420083 + 0.727605i
\(81\) −17.0159 29.4724i −1.89066 3.27471i
\(82\) −1.50540 + 2.60744i −0.166244 + 0.287943i
\(83\) 15.2259 1.67125 0.835627 0.549297i \(-0.185104\pi\)
0.835627 + 0.549297i \(0.185104\pi\)
\(84\) 0 0
\(85\) −18.1153 −1.96488
\(86\) −1.60638 + 2.78233i −0.173220 + 0.300026i
\(87\) 4.13650 + 7.16464i 0.443480 + 0.768130i
\(88\) 1.19009 + 2.06129i 0.126864 + 0.219735i
\(89\) −4.61604 + 7.99522i −0.489299 + 0.847492i −0.999924 0.0123122i \(-0.996081\pi\)
0.510625 + 0.859804i \(0.329414\pi\)
\(90\) −30.4757 −3.21242
\(91\) 0 0
\(92\) 1.84471 0.192325
\(93\) 10.2790 17.8037i 1.06588 1.84616i
\(94\) 3.15905 + 5.47164i 0.325832 + 0.564357i
\(95\) 1.92535 + 3.33481i 0.197537 + 0.342144i
\(96\) 5.60963 9.71617i 0.572531 0.991652i
\(97\) −1.26291 −0.128229 −0.0641145 0.997943i \(-0.520422\pi\)
−0.0641145 + 0.997943i \(0.520422\pi\)
\(98\) 0 0
\(99\) −6.36436 −0.639642
\(100\) 1.51490 2.62388i 0.151490 0.262388i
\(101\) −0.302724 0.524333i −0.0301221 0.0521731i 0.850571 0.525860i \(-0.176256\pi\)
−0.880693 + 0.473687i \(0.842923\pi\)
\(102\) −11.3382 19.6384i −1.12265 1.94449i
\(103\) −3.82402 + 6.62340i −0.376792 + 0.652623i −0.990593 0.136838i \(-0.956306\pi\)
0.613802 + 0.789460i \(0.289639\pi\)
\(104\) 3.07759 0.301783
\(105\) 0 0
\(106\) 11.5150 1.11844
\(107\) −2.41482 + 4.18260i −0.233450 + 0.404347i −0.958821 0.284011i \(-0.908335\pi\)
0.725371 + 0.688358i \(0.241668\pi\)
\(108\) 5.40220 + 9.35688i 0.519827 + 0.900366i
\(109\) −3.61546 6.26216i −0.346298 0.599806i 0.639291 0.768965i \(-0.279228\pi\)
−0.985589 + 0.169159i \(0.945895\pi\)
\(110\) −1.43207 + 2.48042i −0.136543 + 0.236499i
\(111\) 16.7527 1.59010
\(112\) 0 0
\(113\) −9.19375 −0.864875 −0.432438 0.901664i \(-0.642346\pi\)
−0.432438 + 0.901664i \(0.642346\pi\)
\(114\) −2.41012 + 4.17446i −0.225729 + 0.390974i
\(115\) 4.71006 + 8.15806i 0.439215 + 0.760743i
\(116\) −0.761120 1.31830i −0.0706682 0.122401i
\(117\) −4.11459 + 7.12667i −0.380394 + 0.658861i
\(118\) −2.94583 −0.271186
\(119\) 0 0
\(120\) 32.4718 2.96425
\(121\) 5.20093 9.00828i 0.472812 0.818935i
\(122\) −6.42004 11.1198i −0.581243 1.00674i
\(123\) 4.28895 + 7.42868i 0.386722 + 0.669821i
\(124\) −1.89133 + 3.27589i −0.169847 + 0.294183i
\(125\) −0.271305 −0.0242663
\(126\) 0 0
\(127\) −11.2118 −0.994888 −0.497444 0.867496i \(-0.665728\pi\)
−0.497444 + 0.867496i \(0.665728\pi\)
\(128\) 1.77497 3.07434i 0.156887 0.271736i
\(129\) 4.57663 + 7.92695i 0.402949 + 0.697929i
\(130\) 1.85168 + 3.20721i 0.162403 + 0.281291i
\(131\) −7.86899 + 13.6295i −0.687517 + 1.19081i 0.285122 + 0.958491i \(0.407966\pi\)
−0.972639 + 0.232323i \(0.925368\pi\)
\(132\) 1.59796 0.139084
\(133\) 0 0
\(134\) −5.08721 −0.439468
\(135\) −27.5866 + 47.7814i −2.37427 + 4.11236i
\(136\) 8.85331 + 15.3344i 0.759165 + 1.31491i
\(137\) 9.31050 + 16.1263i 0.795449 + 1.37776i 0.922553 + 0.385869i \(0.126098\pi\)
−0.127104 + 0.991889i \(0.540568\pi\)
\(138\) −5.89597 + 10.2121i −0.501899 + 0.869314i
\(139\) −11.9137 −1.01050 −0.505252 0.862972i \(-0.668601\pi\)
−0.505252 + 0.862972i \(0.668601\pi\)
\(140\) 0 0
\(141\) 18.0005 1.51592
\(142\) 6.27198 10.8634i 0.526333 0.911635i
\(143\) 0.386695 + 0.669775i 0.0323370 + 0.0560094i
\(144\) 9.82008 + 17.0089i 0.818340 + 1.41741i
\(145\) 3.88669 6.73195i 0.322772 0.559058i
\(146\) 6.08618 0.503696
\(147\) 0 0
\(148\) −3.08251 −0.253381
\(149\) −5.68767 + 9.85133i −0.465952 + 0.807053i −0.999244 0.0388786i \(-0.987621\pi\)
0.533292 + 0.845931i \(0.320955\pi\)
\(150\) 9.68368 + 16.7726i 0.790669 + 1.36948i
\(151\) 1.84625 + 3.19780i 0.150246 + 0.260234i 0.931318 0.364208i \(-0.118660\pi\)
−0.781072 + 0.624441i \(0.785327\pi\)
\(152\) 1.88192 3.25957i 0.152644 0.264386i
\(153\) −47.3457 −3.82767
\(154\) 0 0
\(155\) −19.3164 −1.55153
\(156\) 1.03309 1.78936i 0.0827132 0.143264i
\(157\) −0.560324 0.970509i −0.0447187 0.0774550i 0.842800 0.538227i \(-0.180906\pi\)
−0.887518 + 0.460772i \(0.847572\pi\)
\(158\) −0.318769 0.552124i −0.0253599 0.0439246i
\(159\) 16.4034 28.4115i 1.30087 2.25318i
\(160\) −10.5417 −0.833396
\(161\) 0 0
\(162\) −40.0277 −3.14488
\(163\) 10.1717 17.6180i 0.796712 1.37995i −0.125034 0.992152i \(-0.539904\pi\)
0.921746 0.387794i \(-0.126763\pi\)
\(164\) −0.789170 1.36688i −0.0616238 0.106736i
\(165\) 4.08003 + 7.06681i 0.317630 + 0.550151i
\(166\) 8.95422 15.5092i 0.694982 1.20374i
\(167\) 13.0063 1.00646 0.503228 0.864154i \(-0.332146\pi\)
0.503228 + 0.864154i \(0.332146\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −10.6535 + 18.4524i −0.817085 + 1.41523i
\(171\) 5.03206 + 8.71578i 0.384811 + 0.666512i
\(172\) −0.842102 1.45856i −0.0642097 0.111214i
\(173\) 12.9555 22.4396i 0.984989 1.70605i 0.343004 0.939334i \(-0.388555\pi\)
0.641985 0.766717i \(-0.278111\pi\)
\(174\) 9.73060 0.737675
\(175\) 0 0
\(176\) 1.84581 0.139133
\(177\) −4.19639 + 7.26836i −0.315420 + 0.546324i
\(178\) 5.42933 + 9.40387i 0.406945 + 0.704850i
\(179\) −4.82081 8.34989i −0.360325 0.624100i 0.627690 0.778464i \(-0.284001\pi\)
−0.988014 + 0.154363i \(0.950667\pi\)
\(180\) 7.98804 13.8357i 0.595394 1.03125i
\(181\) −2.92683 −0.217550 −0.108775 0.994066i \(-0.534693\pi\)
−0.108775 + 0.994066i \(0.534693\pi\)
\(182\) 0 0
\(183\) −36.5818 −2.70421
\(184\) 4.60380 7.97402i 0.339397 0.587852i
\(185\) −7.87050 13.6321i −0.578651 1.00225i
\(186\) −12.0900 20.9404i −0.886480 1.53543i
\(187\) −2.22481 + 3.85348i −0.162694 + 0.281795i
\(188\) −3.31211 −0.241560
\(189\) 0 0
\(190\) 4.52914 0.328579
\(191\) 8.06822 13.9746i 0.583796 1.01116i −0.411229 0.911532i \(-0.634900\pi\)
0.995024 0.0996315i \(-0.0317664\pi\)
\(192\) −14.5956 25.2804i −1.05335 1.82445i
\(193\) 0.0431908 + 0.0748087i 0.00310894 + 0.00538485i 0.867576 0.497305i \(-0.165677\pi\)
−0.864467 + 0.502690i \(0.832344\pi\)
\(194\) −0.742709 + 1.28641i −0.0533234 + 0.0923588i
\(195\) 10.5510 0.755575
\(196\) 0 0
\(197\) 15.0589 1.07290 0.536451 0.843932i \(-0.319765\pi\)
0.536451 + 0.843932i \(0.319765\pi\)
\(198\) −3.74284 + 6.48278i −0.265992 + 0.460711i
\(199\) −7.72332 13.3772i −0.547492 0.948284i −0.998446 0.0557363i \(-0.982249\pi\)
0.450954 0.892547i \(-0.351084\pi\)
\(200\) −7.56139 13.0967i −0.534671 0.926077i
\(201\) −7.24682 + 12.5519i −0.511152 + 0.885340i
\(202\) −0.712119 −0.0501045
\(203\) 0 0
\(204\) 11.8875 0.832294
\(205\) 4.02993 6.98005i 0.281463 0.487508i
\(206\) 4.49776 + 7.79035i 0.313374 + 0.542779i
\(207\) 12.3101 + 21.3217i 0.855611 + 1.48196i
\(208\) 1.19333 2.06690i 0.0827422 0.143314i
\(209\) 0.945840 0.0654251
\(210\) 0 0
\(211\) −25.0561 −1.72493 −0.862466 0.506115i \(-0.831081\pi\)
−0.862466 + 0.506115i \(0.831081\pi\)
\(212\) −3.01823 + 5.22773i −0.207293 + 0.359042i
\(213\) −17.8691 30.9502i −1.22437 2.12067i
\(214\) 2.84028 + 4.91952i 0.194158 + 0.336291i
\(215\) 4.30024 7.44823i 0.293274 0.507965i
\(216\) 53.9285 3.66937
\(217\) 0 0
\(218\) −8.50491 −0.576025
\(219\) 8.66987 15.0167i 0.585855 1.01473i
\(220\) −0.750728 1.30030i −0.0506141 0.0876661i
\(221\) 2.87670 + 4.98259i 0.193508 + 0.335165i
\(222\) 9.85216 17.0644i 0.661234 1.14529i
\(223\) −20.6640 −1.38376 −0.691881 0.722012i \(-0.743218\pi\)
−0.691881 + 0.722012i \(0.743218\pi\)
\(224\) 0 0
\(225\) 40.4368 2.69579
\(226\) −5.40678 + 9.36482i −0.359654 + 0.622939i
\(227\) −0.491189 0.850764i −0.0326013 0.0564672i 0.849264 0.527968i \(-0.177046\pi\)
−0.881866 + 0.471501i \(0.843713\pi\)
\(228\) −1.26345 2.18835i −0.0836737 0.144927i
\(229\) 7.13712 12.3619i 0.471634 0.816895i −0.527839 0.849344i \(-0.676998\pi\)
0.999473 + 0.0324498i \(0.0103309\pi\)
\(230\) 11.0798 0.730581
\(231\) 0 0
\(232\) −7.59802 −0.498835
\(233\) −0.697671 + 1.20840i −0.0457060 + 0.0791651i −0.887973 0.459895i \(-0.847887\pi\)
0.842267 + 0.539060i \(0.181220\pi\)
\(234\) 4.83952 + 8.38230i 0.316369 + 0.547968i
\(235\) −8.45672 14.6475i −0.551655 0.955495i
\(236\) 0.772139 1.33738i 0.0502620 0.0870563i
\(237\) −1.81637 −0.117986
\(238\) 0 0
\(239\) 2.54875 0.164865 0.0824326 0.996597i \(-0.473731\pi\)
0.0824326 + 0.996597i \(0.473731\pi\)
\(240\) 12.5908 21.8079i 0.812733 1.40770i
\(241\) −14.8373 25.6990i −0.955755 1.65542i −0.732631 0.680626i \(-0.761708\pi\)
−0.223124 0.974790i \(-0.571625\pi\)
\(242\) −6.11727 10.5954i −0.393233 0.681099i
\(243\) −30.7358 + 53.2359i −1.97170 + 3.41509i
\(244\) 6.73108 0.430913
\(245\) 0 0
\(246\) 10.0892 0.643264
\(247\) 0.611490 1.05913i 0.0389082 0.0673909i
\(248\) 9.44031 + 16.3511i 0.599460 + 1.03830i
\(249\) −25.5109 44.1861i −1.61669 2.80018i
\(250\) −0.159553 + 0.276353i −0.0100910 + 0.0174781i
\(251\) 18.0858 1.14157 0.570784 0.821100i \(-0.306639\pi\)
0.570784 + 0.821100i \(0.306639\pi\)
\(252\) 0 0
\(253\) 2.31384 0.145470
\(254\) −6.59359 + 11.4204i −0.413719 + 0.716582i
\(255\) 30.3521 + 52.5714i 1.90072 + 3.29215i
\(256\) 6.62352 + 11.4723i 0.413970 + 0.717017i
\(257\) −7.37014 + 12.7655i −0.459737 + 0.796287i −0.998947 0.0458839i \(-0.985390\pi\)
0.539210 + 0.842171i \(0.318723\pi\)
\(258\) 10.7659 0.670257
\(259\) 0 0
\(260\) −1.94140 −0.120400
\(261\) 10.1582 17.5945i 0.628776 1.08907i
\(262\) 9.25540 + 16.0308i 0.571800 + 0.990387i
\(263\) 4.07961 + 7.06609i 0.251560 + 0.435714i 0.963955 0.266064i \(-0.0857232\pi\)
−0.712396 + 0.701778i \(0.752390\pi\)
\(264\) 3.98798 6.90739i 0.245443 0.425120i
\(265\) −30.8255 −1.89360
\(266\) 0 0
\(267\) 30.9367 1.89329
\(268\) 1.33342 2.30955i 0.0814516 0.141078i
\(269\) −0.221291 0.383288i −0.0134924 0.0233695i 0.859200 0.511639i \(-0.170962\pi\)
−0.872693 + 0.488270i \(0.837628\pi\)
\(270\) 32.4470 + 56.1998i 1.97466 + 3.42021i
\(271\) 10.5416 18.2585i 0.640354 1.10913i −0.345000 0.938603i \(-0.612121\pi\)
0.985354 0.170523i \(-0.0545457\pi\)
\(272\) 13.7314 0.832586
\(273\) 0 0
\(274\) 21.9018 1.32313
\(275\) 1.90015 3.29116i 0.114584 0.198465i
\(276\) −3.09081 5.35345i −0.186045 0.322240i
\(277\) −1.79710 3.11267i −0.107977 0.187022i 0.806973 0.590588i \(-0.201104\pi\)
−0.914951 + 0.403565i \(0.867771\pi\)
\(278\) −7.00635 + 12.1354i −0.420213 + 0.727831i
\(279\) −50.4849 −3.02245
\(280\) 0 0
\(281\) −9.01252 −0.537642 −0.268821 0.963190i \(-0.586634\pi\)
−0.268821 + 0.963190i \(0.586634\pi\)
\(282\) 10.5860 18.3355i 0.630386 1.09186i
\(283\) −13.8706 24.0245i −0.824520 1.42811i −0.902286 0.431139i \(-0.858112\pi\)
0.0777659 0.996972i \(-0.475221\pi\)
\(284\) 3.28792 + 5.69485i 0.195102 + 0.337927i
\(285\) 6.45185 11.1749i 0.382174 0.661945i
\(286\) 0.909650 0.0537887
\(287\) 0 0
\(288\) −27.5516 −1.62349
\(289\) −8.05080 + 13.9444i −0.473576 + 0.820258i
\(290\) −4.57148 7.91803i −0.268446 0.464963i
\(291\) 2.11600 + 3.66502i 0.124042 + 0.214848i
\(292\) −1.59526 + 2.76307i −0.0933556 + 0.161697i
\(293\) 12.7409 0.744333 0.372167 0.928166i \(-0.378615\pi\)
0.372167 + 0.928166i \(0.378615\pi\)
\(294\) 0 0
\(295\) 7.88593 0.459137
\(296\) −7.69295 + 13.3246i −0.447143 + 0.774475i
\(297\) 6.77603 + 11.7364i 0.393185 + 0.681017i
\(298\) 6.68976 + 11.5870i 0.387527 + 0.671217i
\(299\) 1.49591 2.59099i 0.0865107 0.149841i
\(300\) −10.1528 −0.586175
\(301\) 0 0
\(302\) 4.34307 0.249916
\(303\) −1.01443 + 1.75704i −0.0582773 + 0.100939i
\(304\) −1.45941 2.52778i −0.0837031 0.144978i
\(305\) 17.1863 + 29.7675i 0.984085 + 1.70448i
\(306\) −27.8437 + 48.2267i −1.59172 + 2.75694i
\(307\) 10.1384 0.578626 0.289313 0.957235i \(-0.406573\pi\)
0.289313 + 0.957235i \(0.406573\pi\)
\(308\) 0 0
\(309\) 25.6286 1.45796
\(310\) −11.3598 + 19.6758i −0.645195 + 1.11751i
\(311\) −10.3006 17.8412i −0.584096 1.01168i −0.994987 0.0999994i \(-0.968116\pi\)
0.410892 0.911684i \(-0.365217\pi\)
\(312\) −5.15650 8.93132i −0.291929 0.505636i
\(313\) −8.27280 + 14.3289i −0.467606 + 0.809918i −0.999315 0.0370095i \(-0.988217\pi\)
0.531709 + 0.846927i \(0.321550\pi\)
\(314\) −1.31809 −0.0743841
\(315\) 0 0
\(316\) 0.334213 0.0188010
\(317\) 10.6170 18.3892i 0.596310 1.03284i −0.397050 0.917797i \(-0.629966\pi\)
0.993361 0.115043i \(-0.0367006\pi\)
\(318\) −19.2934 33.4172i −1.08192 1.87394i
\(319\) −0.954680 1.65355i −0.0534518 0.0925813i
\(320\) −13.7142 + 23.7537i −0.766646 + 1.32787i
\(321\) 16.1841 0.903310
\(322\) 0 0
\(323\) 7.03629 0.391510
\(324\) 10.4918 18.1723i 0.582875 1.00957i
\(325\) −2.45692 4.25550i −0.136285 0.236053i
\(326\) −11.9639 20.7220i −0.662617 1.14769i
\(327\) −12.1154 + 20.9845i −0.669982 + 1.16044i
\(328\) −7.87804 −0.434992
\(329\) 0 0
\(330\) 9.59774 0.528338
\(331\) −8.12074 + 14.0655i −0.446356 + 0.773111i −0.998146 0.0608720i \(-0.980612\pi\)
0.551789 + 0.833983i \(0.313945\pi\)
\(332\) 4.69402 + 8.13028i 0.257618 + 0.446207i
\(333\) −20.5702 35.6286i −1.12724 1.95243i
\(334\) 7.64890 13.2483i 0.418529 0.724914i
\(335\) 13.6184 0.744050
\(336\) 0 0
\(337\) 6.42141 0.349797 0.174898 0.984586i \(-0.444040\pi\)
0.174898 + 0.984586i \(0.444040\pi\)
\(338\) 0.588093 1.01861i 0.0319881 0.0554049i
\(339\) 15.4041 + 26.6807i 0.836636 + 1.44910i
\(340\) −5.58481 9.67318i −0.302879 0.524602i
\(341\) −2.37232 + 4.10898i −0.128468 + 0.222514i
\(342\) 11.8373 0.640086
\(343\) 0 0
\(344\) −8.40645 −0.453245
\(345\) 15.7834 27.3376i 0.849749 1.47181i
\(346\) −15.2381 26.3932i −0.819205 1.41890i
\(347\) −7.24046 12.5408i −0.388688 0.673228i 0.603585 0.797298i \(-0.293738\pi\)
−0.992273 + 0.124071i \(0.960405\pi\)
\(348\) −2.55051 + 4.41761i −0.136722 + 0.236809i
\(349\) 1.74500 0.0934079 0.0467040 0.998909i \(-0.485128\pi\)
0.0467040 + 0.998909i \(0.485128\pi\)
\(350\) 0 0
\(351\) 17.5229 0.935306
\(352\) −1.29467 + 2.24243i −0.0690061 + 0.119522i
\(353\) −7.97900 13.8200i −0.424679 0.735566i 0.571711 0.820455i \(-0.306280\pi\)
−0.996390 + 0.0848891i \(0.972946\pi\)
\(354\) 4.93574 + 8.54895i 0.262332 + 0.454372i
\(355\) −16.7899 + 29.0810i −0.891118 + 1.54346i
\(356\) −5.69237 −0.301695
\(357\) 0 0
\(358\) −11.3404 −0.599356
\(359\) −4.40700 + 7.63315i −0.232593 + 0.402862i −0.958570 0.284856i \(-0.908054\pi\)
0.725978 + 0.687718i \(0.241388\pi\)
\(360\) −39.8711 69.0588i −2.10139 3.63972i
\(361\) 8.75216 + 15.1592i 0.460640 + 0.797852i
\(362\) −1.72125 + 2.98129i −0.0904670 + 0.156693i
\(363\) −34.8566 −1.82950
\(364\) 0 0
\(365\) −16.2926 −0.852792
\(366\) −21.5135 + 37.2625i −1.12453 + 1.94774i
\(367\) 9.85399 + 17.0676i 0.514374 + 0.890922i 0.999861 + 0.0166783i \(0.00530910\pi\)
−0.485487 + 0.874244i \(0.661358\pi\)
\(368\) −3.57022 6.18379i −0.186110 0.322353i
\(369\) 10.5325 18.2429i 0.548302 0.949687i
\(370\) −18.5144 −0.962515
\(371\) 0 0
\(372\) 12.6757 0.657205
\(373\) 0.182896 0.316785i 0.00947000 0.0164025i −0.861252 0.508179i \(-0.830319\pi\)
0.870722 + 0.491776i \(0.163652\pi\)
\(374\) 2.61679 + 4.53241i 0.135311 + 0.234366i
\(375\) 0.454571 + 0.787341i 0.0234740 + 0.0406581i
\(376\) −8.26594 + 14.3170i −0.426283 + 0.738344i
\(377\) −2.46882 −0.127151
\(378\) 0 0
\(379\) 7.39215 0.379709 0.189855 0.981812i \(-0.439198\pi\)
0.189855 + 0.981812i \(0.439198\pi\)
\(380\) −1.18714 + 2.05619i −0.0608992 + 0.105481i
\(381\) 18.7854 + 32.5372i 0.962404 + 1.66693i
\(382\) −9.48973 16.4367i −0.485537 0.840974i
\(383\) 1.67682 2.90433i 0.0856814 0.148405i −0.820000 0.572364i \(-0.806027\pi\)
0.905681 + 0.423959i \(0.139360\pi\)
\(384\) −11.8958 −0.607057
\(385\) 0 0
\(386\) 0.101601 0.00517135
\(387\) 11.2390 19.4665i 0.571311 0.989539i
\(388\) −0.389346 0.674367i −0.0197660 0.0342358i
\(389\) 1.29672 + 2.24598i 0.0657462 + 0.113876i 0.897025 0.441980i \(-0.145724\pi\)
−0.831279 + 0.555856i \(0.812391\pi\)
\(390\) 6.20499 10.7474i 0.314202 0.544213i
\(391\) 17.2131 0.870506
\(392\) 0 0
\(393\) 52.7379 2.66027
\(394\) 8.85603 15.3391i 0.446160 0.772773i
\(395\) 0.853338 + 1.47802i 0.0429361 + 0.0743675i
\(396\) −1.96209 3.39843i −0.0985985 0.170778i
\(397\) 16.7457 29.0044i 0.840441 1.45569i −0.0490806 0.998795i \(-0.515629\pi\)
0.889522 0.456892i \(-0.151038\pi\)
\(398\) −18.1681 −0.910686
\(399\) 0 0
\(400\) −11.7276 −0.586380
\(401\) −19.7578 + 34.2215i −0.986657 + 1.70894i −0.352330 + 0.935876i \(0.614611\pi\)
−0.634327 + 0.773065i \(0.718723\pi\)
\(402\) 8.52362 + 14.7633i 0.425119 + 0.736328i
\(403\) 3.06743 + 5.31295i 0.152800 + 0.264657i
\(404\) 0.186655 0.323296i 0.00928644 0.0160846i
\(405\) 107.153 5.32449
\(406\) 0 0
\(407\) −3.86643 −0.191652
\(408\) 29.6674 51.3854i 1.46876 2.54396i
\(409\) 5.48996 + 9.50889i 0.271461 + 0.470184i 0.969236 0.246133i \(-0.0791599\pi\)
−0.697775 + 0.716317i \(0.745827\pi\)
\(410\) −4.73995 8.20984i −0.234090 0.405455i
\(411\) 31.1994 54.0390i 1.53895 2.66555i
\(412\) −4.71567 −0.232324
\(413\) 0 0
\(414\) 28.9580 1.42321
\(415\) −23.9702 + 41.5177i −1.17665 + 2.03802i
\(416\) 1.67402 + 2.89949i 0.0820755 + 0.142159i
\(417\) 19.9613 + 34.5741i 0.977511 + 1.69310i
\(418\) 0.556242 0.963439i 0.0272067 0.0471234i
\(419\) 31.5621 1.54191 0.770954 0.636891i \(-0.219780\pi\)
0.770954 + 0.636891i \(0.219780\pi\)
\(420\) 0 0
\(421\) −17.7055 −0.862914 −0.431457 0.902134i \(-0.642000\pi\)
−0.431457 + 0.902134i \(0.642000\pi\)
\(422\) −14.7353 + 25.5223i −0.717304 + 1.24241i
\(423\) −22.1023 38.2823i −1.07465 1.86135i
\(424\) 15.0650 + 26.0934i 0.731623 + 1.26721i
\(425\) 14.1356 24.4836i 0.685678 1.18763i
\(426\) −42.0348 −2.03659
\(427\) 0 0
\(428\) −2.97789 −0.143942
\(429\) 1.29581 2.24441i 0.0625624 0.108361i
\(430\) −5.05788 8.76050i −0.243913 0.422469i
\(431\) 10.7408 + 18.6036i 0.517367 + 0.896106i 0.999797 + 0.0201713i \(0.00642116\pi\)
−0.482429 + 0.875935i \(0.660246\pi\)
\(432\) 20.9106 36.2182i 1.00606 1.74255i
\(433\) 34.7200 1.66854 0.834269 0.551358i \(-0.185890\pi\)
0.834269 + 0.551358i \(0.185890\pi\)
\(434\) 0 0
\(435\) −26.0486 −1.24893
\(436\) 2.22924 3.86116i 0.106761 0.184916i
\(437\) −1.82947 3.16873i −0.0875153 0.151581i
\(438\) −10.1974 17.6624i −0.487250 0.843941i
\(439\) −0.364253 + 0.630904i −0.0173848 + 0.0301114i −0.874587 0.484869i \(-0.838867\pi\)
0.857202 + 0.514980i \(0.172201\pi\)
\(440\) −7.49428 −0.357276
\(441\) 0 0
\(442\) 6.76707 0.321877
\(443\) −0.418645 + 0.725115i −0.0198904 + 0.0344513i −0.875799 0.482675i \(-0.839665\pi\)
0.855909 + 0.517127i \(0.172998\pi\)
\(444\) 5.16474 + 8.94560i 0.245108 + 0.424539i
\(445\) −14.5342 25.1739i −0.688986 1.19336i
\(446\) −12.1523 + 21.0485i −0.575430 + 0.996674i
\(447\) 38.1187 1.80295
\(448\) 0 0
\(449\) 26.4312 1.24737 0.623683 0.781677i \(-0.285635\pi\)
0.623683 + 0.781677i \(0.285635\pi\)
\(450\) 23.7806 41.1892i 1.12103 1.94168i
\(451\) −0.989863 1.71449i −0.0466108 0.0807324i
\(452\) −2.83437 4.90927i −0.133317 0.230912i
\(453\) 6.18678 10.7158i 0.290680 0.503473i
\(454\) −1.15546 −0.0542284
\(455\) 0 0
\(456\) −12.6126 −0.590639
\(457\) 1.20237 2.08257i 0.0562447 0.0974186i −0.836532 0.547918i \(-0.815421\pi\)
0.892777 + 0.450499i \(0.148754\pi\)
\(458\) −8.39459 14.5399i −0.392253 0.679403i
\(459\) 50.4082 + 87.3096i 2.35286 + 4.07526i
\(460\) −2.90415 + 5.03014i −0.135407 + 0.234532i
\(461\) −22.2702 −1.03722 −0.518612 0.855010i \(-0.673551\pi\)
−0.518612 + 0.855010i \(0.673551\pi\)
\(462\) 0 0
\(463\) 32.3085 1.50151 0.750753 0.660583i \(-0.229691\pi\)
0.750753 + 0.660583i \(0.229691\pi\)
\(464\) −2.94611 + 5.10281i −0.136770 + 0.236892i
\(465\) 32.3646 + 56.0571i 1.50087 + 2.59958i
\(466\) 0.820592 + 1.42131i 0.0380132 + 0.0658407i
\(467\) 6.43720 11.1496i 0.297878 0.515940i −0.677772 0.735272i \(-0.737054\pi\)
0.975650 + 0.219332i \(0.0703878\pi\)
\(468\) −5.07399 −0.234545
\(469\) 0 0
\(470\) −19.8934 −0.917612
\(471\) −1.87764 + 3.25217i −0.0865172 + 0.149852i
\(472\) −3.85401 6.67535i −0.177395 0.307258i
\(473\) −1.05626 1.82949i −0.0485668 0.0841201i
\(474\) −1.06819 + 1.85017i −0.0490638 + 0.0849809i
\(475\) −6.00952 −0.275736
\(476\) 0 0
\(477\) −80.5649 −3.68881
\(478\) 1.49891 2.59618i 0.0685583 0.118747i
\(479\) −5.27093 9.12952i −0.240835 0.417138i 0.720117 0.693852i \(-0.244088\pi\)
−0.960952 + 0.276714i \(0.910755\pi\)
\(480\) 17.6626 + 30.5926i 0.806185 + 1.39635i
\(481\) −2.49966 + 4.32954i −0.113975 + 0.197410i
\(482\) −34.9029 −1.58978
\(483\) 0 0
\(484\) 6.41364 0.291529
\(485\) 1.98821 3.44369i 0.0902802 0.156370i
\(486\) 36.1510 + 62.6154i 1.63984 + 2.84029i
\(487\) −19.1208 33.1182i −0.866446 1.50073i −0.865604 0.500728i \(-0.833066\pi\)
−0.000841391 1.00000i \(-0.500268\pi\)
\(488\) 16.7986 29.0960i 0.760436 1.31711i
\(489\) −68.1709 −3.08280
\(490\) 0 0
\(491\) −15.4291 −0.696306 −0.348153 0.937438i \(-0.613191\pi\)
−0.348153 + 0.937438i \(0.613191\pi\)
\(492\) −2.64450 + 4.58042i −0.119223 + 0.206501i
\(493\) −7.10206 12.3011i −0.319861 0.554015i
\(494\) −0.719226 1.24574i −0.0323595 0.0560483i
\(495\) 10.0195 17.3543i 0.450342 0.780016i
\(496\) 14.6418 0.657436
\(497\) 0 0
\(498\) −60.0111 −2.68916
\(499\) 19.4106 33.6202i 0.868938 1.50505i 0.00585522 0.999983i \(-0.498136\pi\)
0.863083 0.505062i \(-0.168530\pi\)
\(500\) −0.0836414 0.144871i −0.00374056 0.00647884i
\(501\) −21.7920 37.7448i −0.973594 1.68631i
\(502\) 10.6362 18.4224i 0.474715 0.822230i
\(503\) −27.0935 −1.20804 −0.604020 0.796969i \(-0.706435\pi\)
−0.604020 + 0.796969i \(0.706435\pi\)
\(504\) 0 0
\(505\) 1.90633 0.0848304
\(506\) 1.36075 2.35690i 0.0604929 0.104777i
\(507\) −1.67550 2.90205i −0.0744115 0.128884i
\(508\) −3.45652 5.98687i −0.153358 0.265624i
\(509\) 7.88464 13.6566i 0.349480 0.605318i −0.636677 0.771131i \(-0.719691\pi\)
0.986157 + 0.165813i \(0.0530248\pi\)
\(510\) 71.3995 3.16162
\(511\) 0 0
\(512\) 22.6809 1.00236
\(513\) 10.7151 18.5591i 0.473083 0.819404i
\(514\) 8.66866 + 15.0146i 0.382358 + 0.662264i
\(515\) −12.0404 20.8546i −0.530563 0.918963i
\(516\) −2.82188 + 4.88764i −0.124226 + 0.215166i
\(517\) −4.15441 −0.182711
\(518\) 0 0
\(519\) −86.8277 −3.81131
\(520\) −4.84509 + 8.39194i −0.212471 + 0.368011i
\(521\) −3.65369 6.32837i −0.160071 0.277251i 0.774823 0.632178i \(-0.217839\pi\)
−0.934894 + 0.354927i \(0.884506\pi\)
\(522\) −11.9479 20.6944i −0.522946 0.905769i
\(523\) −7.04128 + 12.1959i −0.307894 + 0.533288i −0.977901 0.209066i \(-0.932958\pi\)
0.670008 + 0.742354i \(0.266291\pi\)
\(524\) −9.70381 −0.423913
\(525\) 0 0
\(526\) 9.59677 0.418439
\(527\) −17.6482 + 30.5675i −0.768766 + 1.33154i
\(528\) −3.09265 5.35663i −0.134590 0.233117i
\(529\) 7.02451 + 12.1668i 0.305413 + 0.528991i
\(530\) −18.1283 + 31.3991i −0.787442 + 1.36389i
\(531\) 20.6105 0.894419
\(532\) 0 0
\(533\) −2.55981 −0.110877
\(534\) 18.1936 31.5123i 0.787316 1.36367i
\(535\) −7.60337 13.1694i −0.328723 0.569364i
\(536\) −6.65556 11.5278i −0.287477 0.497924i
\(537\) −16.1545 + 27.9805i −0.697119 + 1.20745i
\(538\) −0.520559 −0.0224429
\(539\) 0 0
\(540\) −34.0190 −1.46394
\(541\) 19.5875 33.9265i 0.842132 1.45862i −0.0459559 0.998943i \(-0.514633\pi\)
0.888088 0.459673i \(-0.152033\pi\)
\(542\) −12.3988 21.4754i −0.532576 0.922448i
\(543\) 4.90390 + 8.49381i 0.210447 + 0.364504i
\(544\) −9.63130 + 16.6819i −0.412939 + 0.715231i
\(545\) 22.7674 0.975250
\(546\) 0 0
\(547\) 38.7917 1.65862 0.829308 0.558792i \(-0.188735\pi\)
0.829308 + 0.558792i \(0.188735\pi\)
\(548\) −5.74072 + 9.94321i −0.245231 + 0.424753i
\(549\) 44.9177 + 77.7998i 1.91704 + 3.32041i
\(550\) −2.23494 3.87102i −0.0952980 0.165061i
\(551\) −1.50966 + 2.61481i −0.0643136 + 0.111394i
\(552\) −30.8546 −1.31326
\(553\) 0 0
\(554\) −4.22746 −0.179607
\(555\) −26.3740 + 45.6811i −1.11951 + 1.93906i
\(556\) −3.67290 6.36165i −0.155766 0.269794i
\(557\) 13.7347 + 23.7891i 0.581956 + 1.00798i 0.995247 + 0.0973791i \(0.0310459\pi\)
−0.413291 + 0.910599i \(0.635621\pi\)
\(558\) −29.6898 + 51.4243i −1.25687 + 2.17696i
\(559\) −2.73150 −0.115530
\(560\) 0 0
\(561\) 14.9107 0.629528
\(562\) −5.30020 + 9.18022i −0.223576 + 0.387244i
\(563\) −7.06050 12.2291i −0.297565 0.515397i 0.678014 0.735049i \(-0.262841\pi\)
−0.975578 + 0.219652i \(0.929508\pi\)
\(564\) 5.54943 + 9.61189i 0.233673 + 0.404734i
\(565\) 14.4738 25.0694i 0.608919 1.05468i
\(566\) −32.6288 −1.37149
\(567\) 0 0
\(568\) 32.8223 1.37720
\(569\) 4.14324 7.17631i 0.173694 0.300846i −0.766015 0.642823i \(-0.777763\pi\)
0.939708 + 0.341977i \(0.111096\pi\)
\(570\) −7.58857 13.1438i −0.317850 0.550533i
\(571\) 11.7637 + 20.3753i 0.492295 + 0.852681i 0.999961 0.00887373i \(-0.00282463\pi\)
−0.507665 + 0.861554i \(0.669491\pi\)
\(572\) −0.238430 + 0.412974i −0.00996928 + 0.0172673i
\(573\) −54.0731 −2.25894
\(574\) 0 0
\(575\) −14.7013 −0.613087
\(576\) −35.8431 + 62.0820i −1.49346 + 2.58675i
\(577\) 8.88658 + 15.3920i 0.369953 + 0.640777i 0.989558 0.144137i \(-0.0460405\pi\)
−0.619605 + 0.784914i \(0.712707\pi\)
\(578\) 9.46924 + 16.4012i 0.393869 + 0.682200i
\(579\) 0.144732 0.250684i 0.00601487 0.0104181i
\(580\) 4.79296 0.199017
\(581\) 0 0
\(582\) 4.97763 0.206329
\(583\) −3.78580 + 6.55720i −0.156792 + 0.271571i
\(584\) 7.96250 + 13.7915i 0.329491 + 0.570695i
\(585\) −12.9553 22.4392i −0.535635 0.927747i
\(586\) 7.49286 12.9780i 0.309527 0.536117i
\(587\) −6.64096 −0.274102 −0.137051 0.990564i \(-0.543762\pi\)
−0.137051 + 0.990564i \(0.543762\pi\)
\(588\) 0 0
\(589\) 7.50282 0.309148
\(590\) 4.63766 8.03266i 0.190929 0.330700i
\(591\) −25.2311 43.7016i −1.03787 1.79764i
\(592\) 5.96583 + 10.3331i 0.245194 + 0.424688i
\(593\) −17.0252 + 29.4885i −0.699141 + 1.21095i 0.269624 + 0.962966i \(0.413101\pi\)
−0.968765 + 0.247982i \(0.920233\pi\)
\(594\) 15.9398 0.654016
\(595\) 0 0
\(596\) −7.01387 −0.287299
\(597\) −25.8808 + 44.8269i −1.05923 + 1.83464i
\(598\) −1.75947 3.04749i −0.0719500 0.124621i
\(599\) −4.69221 8.12714i −0.191718 0.332066i 0.754101 0.656758i \(-0.228073\pi\)
−0.945820 + 0.324692i \(0.894739\pi\)
\(600\) −25.3382 + 43.8870i −1.03443 + 1.79168i
\(601\) 8.80294 0.359079 0.179540 0.983751i \(-0.442539\pi\)
0.179540 + 0.983751i \(0.442539\pi\)
\(602\) 0 0
\(603\) 35.5926 1.44944
\(604\) −1.13837 + 1.97172i −0.0463197 + 0.0802281i
\(605\) 16.3758 + 28.3637i 0.665770 + 1.15315i
\(606\) 1.19315 + 2.06660i 0.0484686 + 0.0839500i
\(607\) −8.88598 + 15.3910i −0.360671 + 0.624700i −0.988071 0.153997i \(-0.950786\pi\)
0.627401 + 0.778697i \(0.284119\pi\)
\(608\) 4.09458 0.166057
\(609\) 0 0
\(610\) 40.4286 1.63691
\(611\) −2.68585 + 4.65202i −0.108658 + 0.188201i
\(612\) −14.5963 25.2816i −0.590022 1.02195i
\(613\) −5.30405 9.18688i −0.214228 0.371055i 0.738805 0.673919i \(-0.235390\pi\)
−0.953034 + 0.302865i \(0.902057\pi\)
\(614\) 5.96230 10.3270i 0.240619 0.416764i
\(615\) −27.0086 −1.08909
\(616\) 0 0
\(617\) 49.3483 1.98669 0.993344 0.115188i \(-0.0367469\pi\)
0.993344 + 0.115188i \(0.0367469\pi\)
\(618\) 15.0720 26.1054i 0.606284 1.05011i
\(619\) −3.71101 6.42767i −0.149158 0.258350i 0.781758 0.623582i \(-0.214323\pi\)
−0.930917 + 0.365232i \(0.880990\pi\)
\(620\) −5.95510 10.3145i −0.239163 0.414242i
\(621\) 26.2127 45.4018i 1.05188 1.82191i
\(622\) −24.2309 −0.971573
\(623\) 0 0
\(624\) −7.99766 −0.320163
\(625\) 12.7117 22.0173i 0.508468 0.880693i
\(626\) 9.73036 + 16.8535i 0.388903 + 0.673600i
\(627\) −1.58475 2.74487i −0.0632889 0.109620i
\(628\) 0.345487 0.598402i 0.0137864 0.0238788i
\(629\) −28.7631 −1.14686
\(630\) 0 0
\(631\) 35.5184 1.41396 0.706982 0.707231i \(-0.250056\pi\)
0.706982 + 0.707231i \(0.250056\pi\)
\(632\) 0.834087 1.44468i 0.0331782 0.0574663i
\(633\) 41.9814 + 72.7139i 1.66861 + 2.89012i
\(634\) −12.4876 21.6291i −0.495945 0.859002i
\(635\) 17.6509 30.5722i 0.700454 1.21322i
\(636\) 20.2282 0.802099
\(637\) 0 0
\(638\) −2.24576 −0.0889106
\(639\) −43.8818 + 76.0056i −1.73594 + 3.00673i
\(640\) 5.58872 + 9.67994i 0.220913 + 0.382633i
\(641\) −18.5777 32.1775i −0.733775 1.27093i −0.955259 0.295771i \(-0.904424\pi\)
0.221484 0.975164i \(-0.428910\pi\)
\(642\) 9.51778 16.4853i 0.375637 0.650622i
\(643\) 39.7694 1.56835 0.784176 0.620538i \(-0.213086\pi\)
0.784176 + 0.620538i \(0.213086\pi\)
\(644\) 0 0
\(645\) −28.8201 −1.13479
\(646\) 4.13799 7.16722i 0.162807 0.281990i
\(647\) −11.4877 19.8973i −0.451628 0.782243i 0.546859 0.837224i \(-0.315823\pi\)
−0.998487 + 0.0549819i \(0.982490\pi\)
\(648\) −52.3680 90.7040i −2.05721 3.56319i
\(649\) 0.968502 1.67749i 0.0380170 0.0658474i
\(650\) −5.77958 −0.226694
\(651\) 0 0
\(652\) 12.5435 0.491241
\(653\) −9.08783 + 15.7406i −0.355634 + 0.615976i −0.987226 0.159324i \(-0.949068\pi\)
0.631592 + 0.775301i \(0.282402\pi\)
\(654\) 14.2500 + 24.6816i 0.557217 + 0.965129i
\(655\) −24.7765 42.9141i −0.968097 1.67679i
\(656\) −3.05468 + 5.29086i −0.119265 + 0.206574i
\(657\) −42.5819 −1.66128
\(658\) 0 0
\(659\) 14.1044 0.549431 0.274716 0.961526i \(-0.411416\pi\)
0.274716 + 0.961526i \(0.411416\pi\)
\(660\) −2.51569 + 4.35730i −0.0979229 + 0.169607i
\(661\) 6.42783 + 11.1333i 0.250013 + 0.433036i 0.963529 0.267603i \(-0.0862316\pi\)
−0.713516 + 0.700639i \(0.752898\pi\)
\(662\) 9.55150 + 16.5437i 0.371230 + 0.642989i
\(663\) 9.63981 16.6966i 0.374379 0.648444i
\(664\) 46.8590 1.81848
\(665\) 0 0
\(666\) −48.3887 −1.87502
\(667\) −3.69313 + 6.39670i −0.142999 + 0.247681i
\(668\) 4.00974 + 6.94507i 0.155141 + 0.268713i
\(669\) 34.6224 + 59.9678i 1.33858 + 2.31849i
\(670\) 8.00886 13.8718i 0.309409 0.535913i
\(671\) 8.44287 0.325933
\(672\) 0 0
\(673\) −45.6138 −1.75828 −0.879141 0.476561i \(-0.841883\pi\)
−0.879141 + 0.476561i \(0.841883\pi\)
\(674\) 3.77639 6.54090i 0.145461 0.251946i
\(675\) −43.0524 74.5690i −1.65709 2.87016i
\(676\) 0.308293 + 0.533979i 0.0118574 + 0.0205376i
\(677\) −5.12346 + 8.87409i −0.196910 + 0.341059i −0.947525 0.319681i \(-0.896424\pi\)
0.750615 + 0.660740i \(0.229757\pi\)
\(678\) 36.2362 1.39164
\(679\) 0 0
\(680\) −55.7515 −2.13797
\(681\) −1.64597 + 2.85091i −0.0630738 + 0.109247i
\(682\) 2.79029 + 4.83293i 0.106846 + 0.185062i
\(683\) −1.45020 2.51182i −0.0554904 0.0961122i 0.836946 0.547286i \(-0.184339\pi\)
−0.892436 + 0.451173i \(0.851006\pi\)
\(684\) −3.10269 + 5.37402i −0.118634 + 0.205481i
\(685\) −58.6305 −2.24016
\(686\) 0 0
\(687\) −47.8329 −1.82494
\(688\) −3.25957 + 5.64574i −0.124270 + 0.215242i
\(689\) 4.89508 + 8.47852i 0.186488 + 0.323006i
\(690\) −18.5642 32.1541i −0.706727 1.22409i
\(691\) −3.45735 + 5.98831i −0.131524 + 0.227806i −0.924264 0.381753i \(-0.875320\pi\)
0.792740 + 0.609560i \(0.208654\pi\)
\(692\) 15.9764 0.607330
\(693\) 0 0
\(694\) −17.0323 −0.646536
\(695\) 18.7558 32.4861i 0.711450 1.23227i
\(696\) 12.7305 + 22.0498i 0.482547 + 0.835797i
\(697\) −7.36379 12.7545i −0.278923 0.483110i
\(698\) 1.02622 1.77747i 0.0388432 0.0672784i
\(699\) 4.67579 0.176855
\(700\) 0 0
\(701\) −26.0973 −0.985682 −0.492841 0.870119i \(-0.664042\pi\)
−0.492841 + 0.870119i \(0.664042\pi\)
\(702\) 10.3051 17.8490i 0.388942 0.673667i
\(703\) 3.05704 + 5.29494i 0.115298 + 0.199703i
\(704\) 3.36858 + 5.83456i 0.126958 + 0.219898i
\(705\) −28.3384 + 49.0836i −1.06729 + 1.84860i
\(706\) −18.7696 −0.706402
\(707\) 0 0
\(708\) −5.17487 −0.194483
\(709\) 1.69236 2.93126i 0.0635580 0.110086i −0.832495 0.554032i \(-0.813089\pi\)
0.896053 + 0.443946i \(0.146422\pi\)
\(710\) 19.7481 + 34.2047i 0.741133 + 1.28368i
\(711\) 2.23026 + 3.86293i 0.0836414 + 0.144871i
\(712\) −14.2063 + 24.6060i −0.532403 + 0.922150i
\(713\) 18.3544 0.687378
\(714\) 0 0
\(715\) −2.43511 −0.0910681
\(716\) 2.97244 5.14842i 0.111085 0.192406i
\(717\) −4.27043 7.39661i −0.159482 0.276231i
\(718\) 5.18346 + 8.97801i 0.193445 + 0.335056i
\(719\) 1.20787 2.09209i 0.0450459 0.0780218i −0.842623 0.538503i \(-0.818990\pi\)
0.887669 + 0.460482i \(0.152323\pi\)
\(720\) −61.8395 −2.30462
\(721\) 0 0
\(722\) 20.5883 0.766219
\(723\) −49.7198 + 86.1171i −1.84910 + 3.20273i
\(724\) −0.902322 1.56287i −0.0335345 0.0580835i
\(725\) 6.06569 + 10.5061i 0.225274 + 0.390186i
\(726\) −20.4989 + 35.5052i −0.760787 + 1.31772i
\(727\) 17.0150 0.631050 0.315525 0.948917i \(-0.397819\pi\)
0.315525 + 0.948917i \(0.397819\pi\)
\(728\) 0 0
\(729\) 103.896 3.84799
\(730\) −9.58155 + 16.5957i −0.354629 + 0.614235i
\(731\) −7.85771 13.6100i −0.290628 0.503382i
\(732\) −11.2779 19.5339i −0.416844 0.721995i
\(733\) −2.09226 + 3.62391i −0.0772795 + 0.133852i −0.902075 0.431579i \(-0.857957\pi\)
0.824796 + 0.565431i \(0.191290\pi\)
\(734\) 23.1803 0.855599
\(735\) 0 0
\(736\) 10.0167 0.369221
\(737\) 1.67252 2.89689i 0.0616082 0.106708i
\(738\) −12.3882 21.4571i −0.456017 0.789845i
\(739\) 14.0397 + 24.3175i 0.516458 + 0.894532i 0.999817 + 0.0191099i \(0.00608325\pi\)
−0.483359 + 0.875422i \(0.660583\pi\)
\(740\) 4.85284 8.40536i 0.178394 0.308987i
\(741\) −4.09820 −0.150551
\(742\) 0 0
\(743\) −26.5210 −0.972961 −0.486481 0.873691i \(-0.661720\pi\)
−0.486481 + 0.873691i \(0.661720\pi\)
\(744\) 31.6344 54.7925i 1.15977 2.00879i
\(745\) −17.9083 31.0181i −0.656111 1.13642i
\(746\) −0.215120 0.372599i −0.00787610 0.0136418i
\(747\) −62.6481 + 108.510i −2.29217 + 3.97016i
\(748\) −2.74357 −0.100315
\(749\) 0 0
\(750\) 1.06932 0.0390461
\(751\) 11.8581 20.5389i 0.432709 0.749474i −0.564396 0.825504i \(-0.690891\pi\)
0.997106 + 0.0760297i \(0.0242244\pi\)
\(752\) 6.41018 + 11.1028i 0.233755 + 0.404876i
\(753\) −30.3028 52.4860i −1.10429 1.91269i
\(754\) −1.45190 + 2.51476i −0.0528750 + 0.0915821i
\(755\) −11.6263 −0.423125
\(756\) 0 0
\(757\) −52.3661 −1.90328 −0.951639 0.307219i \(-0.900602\pi\)
−0.951639 + 0.307219i \(0.900602\pi\)
\(758\) 4.34727 7.52970i 0.157900 0.273491i
\(759\) −3.87684 6.71488i −0.140720 0.243735i
\(760\) 5.92545 + 10.2632i 0.214939 + 0.372285i
\(761\) −11.9347 + 20.6716i −0.432634 + 0.749344i −0.997099 0.0761129i \(-0.975749\pi\)
0.564465 + 0.825457i \(0.309082\pi\)
\(762\) 44.1902 1.60084
\(763\) 0 0
\(764\) 9.94949 0.359960
\(765\) 74.5369 129.102i 2.69489 4.66768i
\(766\) −1.97225 3.41604i −0.0712603 0.123426i
\(767\) −1.25228 2.16902i −0.0452173 0.0783186i
\(768\) 22.1954 38.4436i 0.800907 1.38721i
\(769\) 41.7599 1.50590 0.752950 0.658077i \(-0.228630\pi\)
0.752950 + 0.658077i \(0.228630\pi\)
\(770\) 0 0
\(771\) 49.3946 1.77890
\(772\) −0.0266308 + 0.0461260i −0.000958465 + 0.00166011i
\(773\) −1.48589 2.57364i −0.0534438 0.0925674i 0.838066 0.545569i \(-0.183686\pi\)
−0.891510 + 0.453002i \(0.850353\pi\)
\(774\) −13.2192 22.8963i −0.475153 0.822989i
\(775\) 15.0729 26.1070i 0.541433 0.937789i
\(776\) −3.88672 −0.139525
\(777\) 0 0
\(778\) 3.05037 0.109361
\(779\) −1.56530 + 2.71117i −0.0560825 + 0.0971378i
\(780\) 3.25281 + 5.63402i 0.116469 + 0.201730i
\(781\) 4.12408 + 7.14311i 0.147571 + 0.255601i
\(782\) 10.1229 17.5334i 0.361995 0.626994i
\(783\) −43.2610 −1.54602