Properties

Label 637.2.e.o.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.o.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 \(-0.414898\pi\)
0.703166 0.711025i \(-0.251769\pi\)
\(4\) 0.308293 0.533979i 0.154146 0.266989i
\(5\) 1.57431 + 2.72679i 0.704054 + 1.21946i 0.967032 + 0.254655i \(0.0819619\pi\)
−0.262978 + 0.964802i \(0.584705\pi\)
\(6\) 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 \(0.412461\pi\)
−0.969261 + 0.246034i \(0.920873\pi\)
\(18\) 4.83952 8.38230i 1.14069 1.97573i
\(19\) −0.611490 1.05913i −0.140285 0.242981i 0.787319 0.616546i \(-0.211469\pi\)
−0.927604 + 0.373565i \(0.878135\pi\)
\(20\) 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 \(0.352393\pi\)
−0.998208 + 0.0598404i \(0.980941\pi\)
\(32\) 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 \(-0.435942\pi\)
0.199887 + 0.979819i \(0.435942\pi\)
\(42\) 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 \(-0.0385293\pi\)
−0.600912 + 0.799315i \(0.705196\pi\)
\(48\) 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 −0.772922 0.634501i \(-0.781206\pi\)
0.935955 + 0.352119i \(0.114539\pi\)
\(60\) 3.25281 5.63402i 0.419935 0.727349i
\(61\) −5.45835 9.45414i −0.698870 1.21048i −0.968858 0.247615i \(-0.920353\pi\)
0.269988 0.962864i \(-0.412980\pi\)
\(62\) −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 −0.976772 0.214279i \(-0.931260\pi\)
0.673958 + 0.738770i \(0.264593\pi\)
\(74\) 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 \(-0.814896\pi\)
−0.835627 + 0.549297i \(0.814896\pi\)
\(84\) 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 \(-0.00391918\pi\)
−0.510625 + 0.859804i \(0.670586\pi\)
\(90\) 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 \(-0.479578\pi\)
0.0641145 + 0.997943i \(0.479578\pi\)
\(98\) 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 \(-0.823744\pi\)
0.880693 + 0.473687i \(0.157077\pi\)
\(102\) −11.3382 + 19.6384i −1.12265 + 1.94449i
\(103\) 3.82402 + 6.62340i 0.376792 + 0.652623i 0.990593 0.136838i \(-0.0436939\pi\)
−0.613802 + 0.789460i \(0.710361\pi\)
\(104\) −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 \(0.0746325\pi\)
−0.285122 + 0.958491i \(0.592034\pi\)
\(132\) −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 \(-0.331399\pi\)
0.505252 + 0.862972i \(0.331399\pi\)
\(140\) 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 −0.842800 0.538227i \(-0.819094\pi\)
0.887518 + 0.460772i \(0.152428\pi\)
\(158\) −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 \(-0.667854\pi\)
−0.503228 + 0.864154i \(0.667854\pi\)
\(168\) 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 \(-0.721889\pi\)
−0.343004 0.939334i \(-0.611445\pi\)
\(174\) −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 \(-0.465307\pi\)
0.108775 + 0.994066i \(0.465307\pi\)
\(182\) 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 \(-0.648916\pi\)
0.998446 0.0557363i \(-0.0177506\pi\)
\(200\) −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 \(-0.256782\pi\)
0.691881 + 0.722012i \(0.256782\pi\)
\(224\) 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 \(-0.822954\pi\)
0.881866 + 0.471501i \(0.156287\pi\)
\(228\) −1.26345 + 2.18835i −0.0836737 + 0.144927i
\(229\) −7.13712 12.3619i −0.471634 0.816895i 0.527839 0.849344i \(-0.323002\pi\)
−0.999473 + 0.0324498i \(0.989669\pi\)
\(230\) −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 \(-0.428375\pi\)
0.732631 0.680626i \(-0.238292\pi\)
\(242\) −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 \(-0.693361\pi\)
−0.570784 + 0.821100i \(0.693361\pi\)
\(252\) 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 \(-0.0146104\pi\)
−0.539210 + 0.842171i \(0.681277\pi\)
\(258\) −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 −0.859200 0.511639i \(-0.829038\pi\)
0.872693 + 0.488270i \(0.162372\pi\)
\(270\) 32.4470 56.1998i 1.97466 3.42021i
\(271\) −10.5416 18.2585i −0.640354 1.10913i −0.985354 0.170523i \(-0.945454\pi\)
0.345000 0.938603i \(-0.387879\pi\)
\(272\) −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 \(-0.524779\pi\)
0.902286 0.431139i \(-0.141888\pi\)
\(284\) 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 \(-0.621385\pi\)
−0.372167 + 0.928166i \(0.621385\pi\)
\(294\) 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 \(-0.593427\pi\)
−0.289313 + 0.957235i \(0.593427\pi\)
\(308\) 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 \(-0.634783\pi\)
0.994987 0.0999994i \(-0.0318841\pi\)
\(312\) −5.15650 + 8.93132i −0.291929 + 0.505636i
\(313\) 8.27280 + 14.3289i 0.467606 + 0.809918i 0.999315 0.0370095i \(-0.0117832\pi\)
−0.531709 + 0.846927i \(0.678450\pi\)
\(314\) 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 \(-0.514872\pi\)
−0.0467040 + 0.998909i \(0.514872\pi\)
\(350\) 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 \(-0.693720\pi\)
0.996390 + 0.0848891i \(0.0270536\pi\)
\(354\) 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 \(0.338642\pi\)
−0.999861 + 0.0166783i \(0.994691\pi\)
\(368\) −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 0.820000 0.572364i \(-0.193973\pi\)
−0.905681 + 0.423959i \(0.860640\pi\)
\(384\) 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 \(-0.848962\pi\)
0.0490806 0.998795i \(-0.484371\pi\)
\(398\) 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 −0.969236 0.246133i \(-0.920840\pi\)
0.697775 + 0.716317i \(0.254173\pi\)
\(410\) −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 \(-0.780220\pi\)
−0.770954 + 0.636891i \(0.780220\pi\)
\(420\) 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 \(-0.814110\pi\)
−0.834269 + 0.551358i \(0.814110\pi\)
\(434\) 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 \(-0.161133\pi\)
−0.857202 + 0.514980i \(0.827799\pi\)
\(440\) 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 \(-0.326449\pi\)
0.518612 + 0.855010i \(0.326449\pi\)
\(462\) 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 \(-0.262946\pi\)
−0.975650 + 0.219332i \(0.929612\pi\)
\(468\) 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 \(-0.755912\pi\)
0.960952 + 0.276714i \(0.0892454\pi\)
\(480\) 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 \(-0.293565\pi\)
0.604020 + 0.796969i \(0.293565\pi\)
\(504\) 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 \(-0.280309\pi\)
−0.986157 + 0.165813i \(0.946975\pi\)
\(510\) −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 \(-0.782161\pi\)
0.934894 + 0.354927i \(0.115494\pi\)
\(522\) −11.9479 + 20.6944i −0.522946 + 0.905769i
\(523\) 7.04128 + 12.1959i 0.307894 + 0.533288i 0.977901 0.209066i \(-0.0670425\pi\)
−0.670008 + 0.742354i \(0.733709\pi\)
\(524\) 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 −0.678014 0.735049i \(-0.737159\pi\)
0.975578 + 0.219652i \(0.0704923\pi\)
\(564\) 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 −0.989558 0.144137i \(-0.953960\pi\)
0.619605 + 0.784914i \(0.287293\pi\)
\(578\) 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 \(-0.456238\pi\)
0.137051 + 0.990564i \(0.456238\pi\)
\(588\) 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 \(0.0797674\pi\)
−0.269624 + 0.962966i \(0.586899\pi\)
\(594\) −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 \(-0.557461\pi\)
−0.179540 + 0.983751i \(0.557461\pi\)
\(602\) 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 \(-0.0492145\pi\)
−0.627401 + 0.778697i \(0.715881\pi\)
\(608\) −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 −0.781758 0.623582i \(-0.785677\pi\)
0.930917 + 0.365232i \(0.119010\pi\)
\(620\) −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 \(-0.786914\pi\)
−0.784176 + 0.620538i \(0.786914\pi\)
\(644\) 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 \(-0.684177\pi\)
0.998487 + 0.0549819i \(0.0175101\pi\)
\(648\) −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 −0.963529 0.267603i \(-0.913768\pi\)
0.713516 + 0.700639i \(0.247102\pi\)
\(662\) 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 \(-0.103576\pi\)
−0.750615 + 0.660740i \(0.770243\pi\)
\(678\) −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 0.924264 0.381753i \(-0.124680\pi\)
−0.792740 + 0.609560i \(0.791346\pi\)
\(692\) −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 0.842623 0.538503i \(-0.181010\pi\)
−0.887669 + 0.460482i \(0.847677\pi\)
\(720\) 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 \(-0.602181\pi\)
−0.315525 + 0.948917i \(0.602181\pi\)
\(728\) 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 \(-0.142043\pi\)
−0.824796 + 0.565431i \(0.808710\pi\)
\(734\) −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 0.997099 0.0761129i \(-0.0242509\pi\)
−0.564465 + 0.825457i \(0.690918\pi\)
\(762\) −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 \(-0.771370\pi\)
−0.752950 + 0.658077i \(0.771370\pi\)
\(770\) 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 \(-0.816314\pi\)
0.891510 + 0.453002i \(0.149647\pi\)
\(774\) −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
\(784\) 0 0
\(785\)