Properties

Label 637.2.e.n.508.5
Level $637$
Weight $2$
Character 637.508
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 508.5
Root \(1.17550 + 2.03602i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.n.79.5

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9} + O(q^{10}) \) \( 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} + 12 q^{13} + 24 q^{15} - 16 q^{17} + 4 q^{18} - 2 q^{19} + 32 q^{20} - 24 q^{22} + 6 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{27} - 12 q^{29} - 6 q^{31} + 20 q^{32} - 4 q^{33} - 48 q^{36} - 8 q^{38} - 8 q^{39} - 4 q^{40} - 16 q^{41} + 4 q^{43} + 4 q^{44} - 14 q^{45} - 8 q^{46} - 30 q^{47} - 16 q^{48} + 16 q^{50} + 4 q^{51} - 4 q^{52} + 14 q^{53} + 48 q^{54} - 16 q^{55} + 8 q^{57} + 8 q^{58} - 24 q^{59} - 12 q^{60} + 56 q^{62} - 40 q^{64} - 6 q^{65} + 4 q^{66} - 16 q^{67} - 28 q^{68} - 40 q^{69} + 16 q^{71} - 28 q^{72} + 6 q^{73} + 12 q^{74} - 12 q^{75} - 32 q^{76} + 8 q^{78} + 22 q^{79} + 28 q^{80} - 46 q^{81} + 40 q^{82} + 100 q^{83} - 16 q^{85} + 16 q^{86} + 16 q^{87} + 44 q^{88} - 26 q^{89} - 80 q^{90} + 40 q^{92} - 16 q^{93} + 32 q^{94} + 6 q^{95} + 20 q^{96} - 28 q^{97} + 24 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.588093 + 1.01861i 0.415845 + 0.720264i 0.995517 0.0945858i \(-0.0301527\pi\)
−0.579672 + 0.814850i \(0.696819\pi\)
\(3\) −1.67550 + 2.90205i −0.967349 + 1.67550i −0.264183 + 0.964473i \(0.585102\pi\)
−0.703166 + 0.711025i \(0.748231\pi\)
\(4\) 0.308293 0.533979i 0.154146 0.266989i
\(5\) −1.57431 2.72679i −0.704054 1.21946i −0.967032 0.254655i \(-0.918038\pi\)
0.262978 0.964802i \(-0.415295\pi\)
\(6\) −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 −0.801823 0.597562i \(-0.796136\pi\)
0.918415 + 0.395618i \(0.129469\pi\)
\(12\) 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 −0.271559 0.962422i \(-0.587539\pi\)
0.969261 0.246034i \(-0.0791274\pi\)
\(18\) 4.83952 8.38230i 1.14069 1.97573i
\(19\) 0.611490 + 1.05913i 0.140285 + 0.242981i 0.927604 0.373565i \(-0.121865\pi\)
−0.787319 + 0.616546i \(0.788531\pi\)
\(20\) −1.94140 −0.434109
\(21\) 0 0
\(22\) 0.909650 0.193938
\(23\) 1.49591 + 2.59099i 0.311919 + 0.540259i 0.978778 0.204925i \(-0.0656950\pi\)
−0.666859 + 0.745184i \(0.732362\pi\)
\(24\) −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 −0.447281 0.894394i \(-0.647607\pi\)
0.998208 0.0598404i \(-0.0190592\pi\)
\(32\) 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 0.584051 0.811717i \(-0.301467\pi\)
−0.994993 + 0.0999443i \(0.968134\pi\)
\(38\) −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 0.600912 0.799315i \(-0.294804\pi\)
−0.992683 + 0.120748i \(0.961471\pi\)
\(48\) −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 −0.304834 0.952406i \(-0.598601\pi\)
0.977224 0.212209i \(-0.0680657\pi\)
\(54\) 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 −0.935955 0.352119i \(-0.885461\pi\)
0.772922 + 0.634501i \(0.218794\pi\)
\(60\) 3.25281 5.63402i 0.419935 0.727349i
\(61\) 5.45835 + 9.45414i 0.698870 + 1.21048i 0.968858 + 0.247615i \(0.0796469\pi\)
−0.269988 + 0.962864i \(0.587020\pi\)
\(62\) 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 −0.967354 0.253428i \(-0.918442\pi\)
0.703152 + 0.711039i \(0.251775\pi\)
\(68\) −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 −0.673958 0.738770i \(-0.735407\pi\)
0.976772 + 0.214279i \(0.0687403\pi\)
\(74\) 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 0.880869 0.473361i \(-0.156959\pi\)
−0.850377 + 0.526174i \(0.823626\pi\)
\(80\) 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 0.510625 0.859804i \(-0.329414\pi\)
−0.999924 + 0.0123122i \(0.996081\pi\)
\(90\) −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 −0.880693 0.473687i \(-0.842923\pi\)
0.850571 + 0.525860i \(0.176256\pi\)
\(102\) −11.3382 + 19.6384i −1.12265 + 1.94449i
\(103\) −3.82402 6.62340i −0.376792 0.652623i 0.613802 0.789460i \(-0.289639\pi\)
−0.990593 + 0.136838i \(0.956306\pi\)
\(104\) 3.07759 0.301783
\(105\) 0 0
\(106\) 11.5150 1.11844
\(107\) −2.41482 4.18260i −0.233450 0.404347i 0.725371 0.688358i \(-0.241668\pi\)
−0.958821 + 0.284011i \(0.908335\pi\)
\(108\) 5.40220 9.35688i 0.519827 0.900366i
\(109\) −3.61546 + 6.26216i −0.346298 + 0.599806i −0.985589 0.169159i \(-0.945895\pi\)
0.639291 + 0.768965i \(0.279228\pi\)
\(110\) −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 −0.972639 0.232323i \(-0.925368\pi\)
0.285122 0.958491i \(-0.407966\pi\)
\(132\) 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 −0.127104 0.991889i \(-0.540568\pi\)
0.922553 0.385869i \(-0.126098\pi\)
\(138\) −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 0.533292 0.845931i \(-0.320955\pi\)
−0.999244 + 0.0388786i \(0.987621\pi\)
\(150\) 9.68368 16.7726i 0.790669 1.36948i
\(151\) 1.84625 3.19780i 0.150246 0.260234i −0.781072 0.624441i \(-0.785327\pi\)
0.931318 + 0.364208i \(0.118660\pi\)
\(152\) 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 −0.887518 0.460772i \(-0.847572\pi\)
0.842800 + 0.538227i \(0.180906\pi\)
\(158\) −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 0.921746 + 0.387794i \(0.126763\pi\)
−0.125034 + 0.992152i \(0.539904\pi\)
\(164\) −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 0.641985 + 0.766717i \(0.278111\pi\)
0.343004 + 0.939334i \(0.388555\pi\)
\(174\) 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 −0.988014 0.154363i \(-0.950667\pi\)
0.627690 + 0.778464i \(0.284001\pi\)
\(180\) 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 0.995024 + 0.0996315i \(0.0317664\pi\)
−0.411229 + 0.911532i \(0.634900\pi\)
\(192\) −14.5956 + 25.2804i −1.05335 + 1.82445i
\(193\) 0.0431908 0.0748087i 0.00310894 0.00538485i −0.864467 0.502690i \(-0.832344\pi\)
0.867576 + 0.497305i \(0.165677\pi\)
\(194\) −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 0.450954 + 0.892547i \(0.351084\pi\)
−0.998446 + 0.0557363i \(0.982249\pi\)
\(200\) −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 −0.881866 0.471501i \(-0.843713\pi\)
0.849264 + 0.527968i \(0.177046\pi\)
\(228\) −1.26345 + 2.18835i −0.0836737 + 0.144927i
\(229\) 7.13712 + 12.3619i 0.471634 + 0.816895i 0.999473 0.0324498i \(-0.0103309\pi\)
−0.527839 + 0.849344i \(0.676998\pi\)
\(230\) 11.0798 0.730581
\(231\) 0 0
\(232\) −7.59802 −0.498835
\(233\) −0.697671 1.20840i −0.0457060 0.0791651i 0.842267 0.539060i \(-0.181220\pi\)
−0.887973 + 0.459895i \(0.847887\pi\)
\(234\) 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 −0.223124 + 0.974790i \(0.571625\pi\)
−0.732631 + 0.680626i \(0.761708\pi\)
\(242\) −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 0.539210 0.842171i \(-0.318723\pi\)
−0.998947 + 0.0458839i \(0.985390\pi\)
\(258\) 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 −0.712396 0.701778i \(-0.752390\pi\)
0.963955 + 0.266064i \(0.0857232\pi\)
\(264\) 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 −0.872693 0.488270i \(-0.837628\pi\)
0.859200 + 0.511639i \(0.170962\pi\)
\(270\) 32.4470 56.1998i 1.97466 3.42021i
\(271\) 10.5416 + 18.2585i 0.640354 + 1.10913i 0.985354 + 0.170523i \(0.0545457\pi\)
−0.345000 + 0.938603i \(0.612121\pi\)
\(272\) 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 −0.914951 0.403565i \(-0.867771\pi\)
0.806973 + 0.590588i \(0.201104\pi\)
\(278\) −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 0.0777659 + 0.996972i \(0.475221\pi\)
−0.902286 + 0.431139i \(0.858112\pi\)
\(284\) 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 0.410892 + 0.911684i \(0.365217\pi\)
−0.994987 + 0.0999994i \(0.968116\pi\)
\(312\) −5.15650 + 8.93132i −0.291929 + 0.505636i
\(313\) −8.27280 14.3289i −0.467606 0.809918i 0.531709 0.846927i \(-0.321550\pi\)
−0.999315 + 0.0370095i \(0.988217\pi\)
\(314\) −1.31809 −0.0743841
\(315\) 0 0
\(316\) 0.334213 0.0188010
\(317\) 10.6170 + 18.3892i 0.596310 + 1.03284i 0.993361 + 0.115043i \(0.0367006\pi\)
−0.397050 + 0.917797i \(0.629966\pi\)
\(318\) −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 0.551789 0.833983i \(-0.313945\pi\)
−0.998146 + 0.0608720i \(0.980612\pi\)
\(332\) 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 −0.992273 0.124071i \(-0.960405\pi\)
0.603585 + 0.797298i \(0.293738\pi\)
\(348\) −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 −0.996390 0.0848891i \(-0.972946\pi\)
0.571711 + 0.820455i \(0.306280\pi\)
\(354\) 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 0.725978 0.687718i \(-0.241388\pi\)
−0.958570 + 0.284856i \(0.908054\pi\)
\(360\) −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 −0.485487 0.874244i \(-0.661358\pi\)
0.999861 0.0166783i \(-0.00530910\pi\)
\(368\) −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 0.870722 0.491776i \(-0.163652\pi\)
−0.861252 + 0.508179i \(0.830319\pi\)
\(374\) 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 0.905681 0.423959i \(-0.139360\pi\)
−0.820000 + 0.572364i \(0.806027\pi\)
\(384\) −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 −0.831279 0.555856i \(-0.812391\pi\)
0.897025 + 0.441980i \(0.145724\pi\)
\(390\) 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 0.889522 + 0.456892i \(0.151038\pi\)
−0.0490806 + 0.998795i \(0.515629\pi\)
\(398\) −18.1681 −0.910686
\(399\) 0 0
\(400\) −11.7276 −0.586380
\(401\) −19.7578 34.2215i −0.986657 1.70894i −0.634327 0.773065i \(-0.718723\pi\)
−0.352330 0.935876i \(-0.614611\pi\)
\(402\) 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 −0.697775 0.716317i \(-0.745827\pi\)
0.969236 + 0.246133i \(0.0791599\pi\)
\(410\) −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 −0.482429 0.875935i \(-0.660246\pi\)
0.999797 0.0201713i \(-0.00642116\pi\)
\(432\) 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 0.857202 0.514980i \(-0.172201\pi\)
−0.874587 + 0.484869i \(0.838867\pi\)
\(440\) −7.49428 −0.357276
\(441\) 0 0
\(442\) 6.76707 0.321877
\(443\) −0.418645 0.725115i −0.0198904 0.0344513i 0.855909 0.517127i \(-0.172998\pi\)
−0.875799 + 0.482675i \(0.839665\pi\)
\(444\) 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 0.892777 0.450499i \(-0.148754\pi\)
−0.836532 + 0.547918i \(0.815421\pi\)
\(458\) −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 0.975650 0.219332i \(-0.0703878\pi\)
−0.677772 + 0.735272i \(0.737054\pi\)
\(468\) −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 −0.960952 0.276714i \(-0.910755\pi\)
0.720117 + 0.693852i \(0.244088\pi\)
\(480\) 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 −0.000841391 1.00000i \(0.500268\pi\)
−0.865604 + 0.500728i \(0.833066\pi\)
\(488\) 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 0.863083 + 0.505062i \(0.168530\pi\)
0.00585522 + 0.999983i \(0.498136\pi\)
\(500\) −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 0.986157 0.165813i \(-0.0530248\pi\)
−0.636677 + 0.771131i \(0.719691\pi\)
\(510\) 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 −0.934894 0.354927i \(-0.884506\pi\)
0.774823 + 0.632178i \(0.217839\pi\)
\(522\) −11.9479 + 20.6944i −0.522946 + 0.905769i
\(523\) −7.04128 12.1959i −0.307894 0.533288i 0.670008 0.742354i \(-0.266291\pi\)
−0.977901 + 0.209066i \(0.932958\pi\)
\(524\) −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 0.888088 + 0.459673i \(0.152033\pi\)
−0.0459559 + 0.998943i \(0.514633\pi\)
\(542\) −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 −0.413291 0.910599i \(-0.635621\pi\)
0.995247 0.0973791i \(-0.0310459\pi\)
\(558\) −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 −0.975578 0.219652i \(-0.929508\pi\)
0.678014 + 0.735049i \(0.262841\pi\)
\(564\) 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 0.939708 0.341977i \(-0.111096\pi\)
−0.766015 + 0.642823i \(0.777763\pi\)
\(570\) −7.58857 + 13.1438i −0.317850 + 0.550533i
\(571\) 11.7637 20.3753i 0.492295 0.852681i −0.507665 0.861554i \(-0.669491\pi\)
0.999961 + 0.00887373i \(0.00282463\pi\)
\(572\) −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 −0.619605 0.784914i \(-0.712707\pi\)
0.989558 + 0.144137i \(0.0460405\pi\)
\(578\) 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 −0.968765 0.247982i \(-0.920233\pi\)
0.269624 0.962966i \(-0.413101\pi\)
\(594\) 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 −0.945820 0.324692i \(-0.894739\pi\)
0.754101 + 0.656758i \(0.228073\pi\)
\(600\) −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 0.627401 0.778697i \(-0.284119\pi\)
−0.988071 + 0.153997i \(0.950786\pi\)
\(608\) 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 −0.953034 0.302865i \(-0.902057\pi\)
0.738805 + 0.673919i \(0.235390\pi\)
\(614\) 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 −0.930917 0.365232i \(-0.880990\pi\)
0.781758 + 0.623582i \(0.214323\pi\)
\(620\) −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 0.221484 + 0.975164i \(0.428910\pi\)
−0.955259 + 0.295771i \(0.904424\pi\)
\(642\) 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 −0.998487 0.0549819i \(-0.982490\pi\)
0.546859 + 0.837224i \(0.315823\pi\)
\(648\) −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 0.631592 0.775301i \(-0.282402\pi\)
−0.987226 + 0.159324i \(0.949068\pi\)
\(654\) 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 −0.713516 0.700639i \(-0.752898\pi\)
0.963529 + 0.267603i \(0.0862316\pi\)
\(662\) 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 0.750615 0.660740i \(-0.229757\pi\)
−0.947525 + 0.319681i \(0.896424\pi\)
\(678\) 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 −0.892436 0.451173i \(-0.851006\pi\)
0.836946 + 0.547286i \(0.184339\pi\)
\(684\) −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 0.792740 0.609560i \(-0.208654\pi\)
−0.924264 + 0.381753i \(0.875320\pi\)
\(692\) 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 0.896053 0.443946i \(-0.146422\pi\)
−0.832495 + 0.554032i \(0.813089\pi\)
\(710\) 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 0.887669 0.460482i \(-0.152323\pi\)
−0.842623 + 0.538503i \(0.818990\pi\)
\(720\) −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 0.824796 0.565431i \(-0.191290\pi\)
−0.902075 + 0.431579i \(0.857957\pi\)
\(734\) 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 −0.483359 0.875422i \(-0.660583\pi\)
0.999817 0.0191099i \(-0.00608325\pi\)
\(740\) 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 0.997106 0.0760297i \(-0.0242244\pi\)
−0.564396 + 0.825504i \(0.690891\pi\)
\(752\) 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 0.564465 0.825457i \(-0.309082\pi\)
−0.997099 + 0.0761129i \(0.975749\pi\)
\(762\) 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 −0.891510 0.453002i \(-0.850353\pi\)
0.838066 + 0.545569i \(0.183686\pi\)
\(774\) −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