Properties

Label 637.2.e.o.79.6
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 79.6
Root \(-0.833726 + 1.44406i\) of defining polynomial
Character \(\chi\) \(=\) 637.79
Dual form 637.2.e.o.508.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22392 - 2.11990i) q^{2} +(-0.333726 - 0.578030i) q^{3} +(-1.99598 - 3.45713i) q^{4} +(0.455143 - 0.788331i) q^{5} -1.63382 q^{6} -4.87599 q^{8} +(1.27725 - 2.21227i) q^{9} +O(q^{10})\) \(q+(1.22392 - 2.11990i) q^{2} +(-0.333726 - 0.578030i) q^{3} +(-1.99598 - 3.45713i) q^{4} +(0.455143 - 0.788331i) q^{5} -1.63382 q^{6} -4.87599 q^{8} +(1.27725 - 2.21227i) q^{9} +(-1.11412 - 1.92971i) q^{10} +(-1.83918 - 3.18556i) q^{11} +(-1.33222 + 2.30747i) q^{12} -1.00000 q^{13} -0.607572 q^{15} +(-1.97589 + 3.42234i) q^{16} +(3.59265 + 6.22266i) q^{17} +(-3.12652 - 5.41529i) q^{18} +(-0.989010 + 1.71302i) q^{19} -3.63382 q^{20} -9.00407 q^{22} +(0.298350 - 0.516758i) q^{23} +(1.62724 + 2.81847i) q^{24} +(2.08569 + 3.61252i) q^{25} +(-1.22392 + 2.11990i) q^{26} -3.70737 q^{27} -3.64900 q^{29} +(-0.743621 + 1.28799i) q^{30} +(-3.54416 - 6.13867i) q^{31} +(-0.0393239 - 0.0681110i) q^{32} +(-1.22757 + 2.12621i) q^{33} +17.5885 q^{34} -10.1975 q^{36} +(-0.355426 + 0.615615i) q^{37} +(2.42094 + 4.19320i) q^{38} +(0.333726 + 0.578030i) q^{39} +(-2.21927 + 3.84390i) q^{40} -5.27529 q^{41} +11.0790 q^{43} +(-7.34193 + 12.7166i) q^{44} +(-1.16267 - 2.01380i) q^{45} +(-0.730315 - 1.26494i) q^{46} +(6.05674 - 10.4906i) q^{47} +2.63762 q^{48} +10.2109 q^{50} +(2.39792 - 4.15332i) q^{51} +(1.99598 + 3.45713i) q^{52} +(5.72422 + 9.91463i) q^{53} +(-4.53753 + 7.85923i) q^{54} -3.34837 q^{55} +1.32023 q^{57} +(-4.46610 + 7.73550i) q^{58} +(4.79493 + 8.30506i) q^{59} +(1.21270 + 2.10046i) q^{60} +(3.49268 - 6.04950i) q^{61} -17.3511 q^{62} -8.09606 q^{64} +(-0.455143 + 0.788331i) q^{65} +(3.00489 + 5.20462i) q^{66} +(-0.614197 - 1.06382i) q^{67} +(14.3417 - 24.8406i) q^{68} -0.398269 q^{69} +11.3635 q^{71} +(-6.22788 + 10.7870i) q^{72} +(3.26709 + 5.65877i) q^{73} +(0.870027 + 1.50693i) q^{74} +(1.39210 - 2.41118i) q^{75} +7.89616 q^{76} +1.63382 q^{78} +(5.76021 - 9.97697i) q^{79} +(1.79862 + 3.11531i) q^{80} +(-2.59452 - 4.49384i) q^{81} +(-6.45655 + 11.1831i) q^{82} -7.16403 q^{83} +6.54069 q^{85} +(13.5599 - 23.4864i) q^{86} +(1.21777 + 2.10923i) q^{87} +(8.96784 + 15.5328i) q^{88} +(6.42451 - 11.1276i) q^{89} -5.69206 q^{90} -2.38200 q^{92} +(-2.36556 + 4.09727i) q^{93} +(-14.8260 - 25.6793i) q^{94} +(0.900282 + 1.55933i) q^{95} +(-0.0262468 + 0.0454608i) q^{96} -9.09062 q^{97} -9.39642 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22392 2.11990i 0.865444 1.49899i −0.00116093 0.999999i \(-0.500370\pi\)
0.866605 0.498994i \(-0.166297\pi\)
\(3\) −0.333726 0.578030i −0.192677 0.333726i 0.753460 0.657494i \(-0.228384\pi\)
−0.946136 + 0.323768i \(0.895050\pi\)
\(4\) −1.99598 3.45713i −0.997988 1.72857i
\(5\) 0.455143 0.788331i 0.203546 0.352552i −0.746122 0.665809i \(-0.768087\pi\)
0.949669 + 0.313256i \(0.101420\pi\)
\(6\) −1.63382 −0.667004
\(7\) 0 0
\(8\) −4.87599 −1.72392
\(9\) 1.27725 2.21227i 0.425751 0.737423i
\(10\) −1.11412 1.92971i −0.352316 0.610229i
\(11\) −1.83918 3.18556i −0.554534 0.960482i −0.997940 0.0641605i \(-0.979563\pi\)
0.443405 0.896321i \(-0.353770\pi\)
\(12\) −1.33222 + 2.30747i −0.384578 + 0.666109i
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −0.607572 −0.156874
\(16\) −1.97589 + 3.42234i −0.493972 + 0.855584i
\(17\) 3.59265 + 6.22266i 0.871347 + 1.50922i 0.860604 + 0.509275i \(0.170086\pi\)
0.0107428 + 0.999942i \(0.496580\pi\)
\(18\) −3.12652 5.41529i −0.736928 1.27640i
\(19\) −0.989010 + 1.71302i −0.226894 + 0.392993i −0.956886 0.290463i \(-0.906191\pi\)
0.729992 + 0.683456i \(0.239524\pi\)
\(20\) −3.63382 −0.812547
\(21\) 0 0
\(22\) −9.00407 −1.91967
\(23\) 0.298350 0.516758i 0.0622103 0.107751i −0.833243 0.552907i \(-0.813518\pi\)
0.895453 + 0.445156i \(0.146852\pi\)
\(24\) 1.62724 + 2.81847i 0.332160 + 0.575318i
\(25\) 2.08569 + 3.61252i 0.417138 + 0.722504i
\(26\) −1.22392 + 2.11990i −0.240031 + 0.415746i
\(27\) −3.70737 −0.713483
\(28\) 0 0
\(29\) −3.64900 −0.677602 −0.338801 0.940858i \(-0.610021\pi\)
−0.338801 + 0.940858i \(0.610021\pi\)
\(30\) −0.743621 + 1.28799i −0.135766 + 0.235154i
\(31\) −3.54416 6.13867i −0.636551 1.10254i −0.986184 0.165652i \(-0.947027\pi\)
0.349634 0.936887i \(-0.386306\pi\)
\(32\) −0.0393239 0.0681110i −0.00695155 0.0120404i
\(33\) −1.22757 + 2.12621i −0.213692 + 0.370125i
\(34\) 17.5885 3.01641
\(35\) 0 0
\(36\) −10.1975 −1.69958
\(37\) −0.355426 + 0.615615i −0.0584316 + 0.101207i −0.893762 0.448542i \(-0.851943\pi\)
0.835330 + 0.549749i \(0.185277\pi\)
\(38\) 2.42094 + 4.19320i 0.392729 + 0.680227i
\(39\) 0.333726 + 0.578030i 0.0534389 + 0.0925589i
\(40\) −2.21927 + 3.84390i −0.350898 + 0.607773i
\(41\) −5.27529 −0.823863 −0.411931 0.911215i \(-0.635146\pi\)
−0.411931 + 0.911215i \(0.635146\pi\)
\(42\) 0 0
\(43\) 11.0790 1.68954 0.844768 0.535132i \(-0.179738\pi\)
0.844768 + 0.535132i \(0.179738\pi\)
\(44\) −7.34193 + 12.7166i −1.10684 + 1.91710i
\(45\) −1.16267 2.01380i −0.173320 0.300199i
\(46\) −0.730315 1.26494i −0.107679 0.186506i
\(47\) 6.05674 10.4906i 0.883467 1.53021i 0.0360062 0.999352i \(-0.488536\pi\)
0.847461 0.530858i \(-0.178130\pi\)
\(48\) 2.63762 0.380707
\(49\) 0 0
\(50\) 10.2109 1.44404
\(51\) 2.39792 4.15332i 0.335776 0.581582i
\(52\) 1.99598 + 3.45713i 0.276792 + 0.479418i
\(53\) 5.72422 + 9.91463i 0.786282 + 1.36188i 0.928230 + 0.372006i \(0.121330\pi\)
−0.141949 + 0.989874i \(0.545337\pi\)
\(54\) −4.53753 + 7.85923i −0.617480 + 1.06951i
\(55\) −3.34837 −0.451494
\(56\) 0 0
\(57\) 1.32023 0.174869
\(58\) −4.46610 + 7.73550i −0.586427 + 1.01572i
\(59\) 4.79493 + 8.30506i 0.624247 + 1.08123i 0.988686 + 0.150000i \(0.0479273\pi\)
−0.364439 + 0.931227i \(0.618739\pi\)
\(60\) 1.21270 + 2.10046i 0.156559 + 0.271168i
\(61\) 3.49268 6.04950i 0.447192 0.774559i −0.551010 0.834499i \(-0.685757\pi\)
0.998202 + 0.0599392i \(0.0190907\pi\)
\(62\) −17.3511 −2.20360
\(63\) 0 0
\(64\) −8.09606 −1.01201
\(65\) −0.455143 + 0.788331i −0.0564536 + 0.0977804i
\(66\) 3.00489 + 5.20462i 0.369877 + 0.640645i
\(67\) −0.614197 1.06382i −0.0750360 0.129966i 0.826066 0.563574i \(-0.190574\pi\)
−0.901102 + 0.433607i \(0.857241\pi\)
\(68\) 14.3417 24.8406i 1.73919 3.01236i
\(69\) −0.398269 −0.0479459
\(70\) 0 0
\(71\) 11.3635 1.34859 0.674297 0.738460i \(-0.264447\pi\)
0.674297 + 0.738460i \(0.264447\pi\)
\(72\) −6.22788 + 10.7870i −0.733963 + 1.27126i
\(73\) 3.26709 + 5.65877i 0.382384 + 0.662309i 0.991403 0.130847i \(-0.0417697\pi\)
−0.609018 + 0.793156i \(0.708436\pi\)
\(74\) 0.870027 + 1.50693i 0.101139 + 0.175177i
\(75\) 1.39210 2.41118i 0.160745 0.278419i
\(76\) 7.89616 0.905752
\(77\) 0 0
\(78\) 1.63382 0.184994
\(79\) 5.76021 9.97697i 0.648074 1.12250i −0.335508 0.942037i \(-0.608908\pi\)
0.983582 0.180460i \(-0.0577586\pi\)
\(80\) 1.79862 + 3.11531i 0.201092 + 0.348302i
\(81\) −2.59452 4.49384i −0.288280 0.499315i
\(82\) −6.45655 + 11.1831i −0.713007 + 1.23496i
\(83\) −7.16403 −0.786355 −0.393177 0.919463i \(-0.628624\pi\)
−0.393177 + 0.919463i \(0.628624\pi\)
\(84\) 0 0
\(85\) 6.54069 0.709437
\(86\) 13.5599 23.4864i 1.46220 2.53260i
\(87\) 1.21777 + 2.10923i 0.130558 + 0.226133i
\(88\) 8.96784 + 15.5328i 0.955975 + 1.65580i
\(89\) 6.42451 11.1276i 0.680997 1.17952i −0.293680 0.955904i \(-0.594880\pi\)
0.974677 0.223617i \(-0.0717866\pi\)
\(90\) −5.69206 −0.599996
\(91\) 0 0
\(92\) −2.38200 −0.248341
\(93\) −2.36556 + 4.09727i −0.245297 + 0.424867i
\(94\) −14.8260 25.6793i −1.52918 2.64862i
\(95\) 0.900282 + 1.55933i 0.0923670 + 0.159984i
\(96\) −0.0262468 + 0.0454608i −0.00267880 + 0.00463982i
\(97\) −9.09062 −0.923012 −0.461506 0.887137i \(-0.652691\pi\)
−0.461506 + 0.887137i \(0.652691\pi\)
\(98\) 0 0
\(99\) −9.39642 −0.944375
\(100\) 8.32597 14.4210i 0.832597 1.44210i
\(101\) −2.90322 5.02853i −0.288882 0.500358i 0.684661 0.728861i \(-0.259950\pi\)
−0.973543 + 0.228504i \(0.926617\pi\)
\(102\) −5.86975 10.1667i −0.581192 1.00665i
\(103\) 6.43411 11.1442i 0.633971 1.09807i −0.352761 0.935714i \(-0.614757\pi\)
0.986732 0.162357i \(-0.0519096\pi\)
\(104\) 4.87599 0.478130
\(105\) 0 0
\(106\) 28.0240 2.72193
\(107\) −2.22874 + 3.86029i −0.215460 + 0.373188i −0.953415 0.301662i \(-0.902458\pi\)
0.737955 + 0.674850i \(0.235792\pi\)
\(108\) 7.39981 + 12.8168i 0.712047 + 1.23330i
\(109\) −0.439448 0.761146i −0.0420915 0.0729046i 0.844212 0.536009i \(-0.180069\pi\)
−0.886304 + 0.463105i \(0.846735\pi\)
\(110\) −4.09814 + 7.09819i −0.390743 + 0.676786i
\(111\) 0.474459 0.0450336
\(112\) 0 0
\(113\) −5.36723 −0.504906 −0.252453 0.967609i \(-0.581237\pi\)
−0.252453 + 0.967609i \(0.581237\pi\)
\(114\) 1.61586 2.79876i 0.151339 0.262128i
\(115\) −0.271584 0.470397i −0.0253253 0.0438648i
\(116\) 7.28332 + 12.6151i 0.676239 + 1.17128i
\(117\) −1.27725 + 2.21227i −0.118082 + 0.204524i
\(118\) 23.4745 2.16100
\(119\) 0 0
\(120\) 2.96252 0.270439
\(121\) −1.26519 + 2.19137i −0.115017 + 0.199215i
\(122\) −8.54955 14.8083i −0.774040 1.34068i
\(123\) 1.76050 + 3.04928i 0.158739 + 0.274944i
\(124\) −14.1481 + 24.5053i −1.27054 + 2.20064i
\(125\) 8.34858 0.746720
\(126\) 0 0
\(127\) 6.61029 0.586568 0.293284 0.956025i \(-0.405252\pi\)
0.293284 + 0.956025i \(0.405252\pi\)
\(128\) −9.83031 + 17.0266i −0.868885 + 1.50495i
\(129\) −3.69736 6.40401i −0.325534 0.563842i
\(130\) 1.11412 + 1.92971i 0.0977148 + 0.169247i
\(131\) −9.98324 + 17.2915i −0.872240 + 1.51076i −0.0125654 + 0.999921i \(0.504000\pi\)
−0.859674 + 0.510843i \(0.829334\pi\)
\(132\) 9.80076 0.853047
\(133\) 0 0
\(134\) −3.00692 −0.259758
\(135\) −1.68738 + 2.92263i −0.145227 + 0.251540i
\(136\) −17.5178 30.3416i −1.50213 2.60177i
\(137\) −2.87726 4.98355i −0.245821 0.425774i 0.716541 0.697545i \(-0.245724\pi\)
−0.962362 + 0.271771i \(0.912391\pi\)
\(138\) −0.487450 + 0.844288i −0.0414945 + 0.0718706i
\(139\) 1.55138 0.131586 0.0657931 0.997833i \(-0.479042\pi\)
0.0657931 + 0.997833i \(0.479042\pi\)
\(140\) 0 0
\(141\) −8.08517 −0.680894
\(142\) 13.9080 24.0894i 1.16713 2.02153i
\(143\) 1.83918 + 3.18556i 0.153800 + 0.266390i
\(144\) 5.04742 + 8.74239i 0.420618 + 0.728532i
\(145\) −1.66082 + 2.87662i −0.137923 + 0.238890i
\(146\) 15.9947 1.32373
\(147\) 0 0
\(148\) 2.83768 0.233256
\(149\) −7.46683 + 12.9329i −0.611707 + 1.05951i 0.379246 + 0.925296i \(0.376183\pi\)
−0.990953 + 0.134211i \(0.957150\pi\)
\(150\) −3.40764 5.90220i −0.278233 0.481913i
\(151\) 3.95051 + 6.84248i 0.321488 + 0.556833i 0.980795 0.195040i \(-0.0624838\pi\)
−0.659307 + 0.751873i \(0.729150\pi\)
\(152\) 4.82240 8.35265i 0.391149 0.677489i
\(153\) 18.3549 1.48391
\(154\) 0 0
\(155\) −6.45241 −0.518270
\(156\) 1.33222 2.30747i 0.106663 0.184745i
\(157\) 6.24740 + 10.8208i 0.498597 + 0.863595i 0.999999 0.00161951i \(-0.000515506\pi\)
−0.501402 + 0.865215i \(0.667182\pi\)
\(158\) −14.1001 24.4221i −1.12174 1.94292i
\(159\) 3.82064 6.61754i 0.302996 0.524805i
\(160\) −0.0715920 −0.00565985
\(161\) 0 0
\(162\) −12.7020 −0.997961
\(163\) −3.50714 + 6.07454i −0.274700 + 0.475795i −0.970059 0.242868i \(-0.921912\pi\)
0.695359 + 0.718662i \(0.255245\pi\)
\(164\) 10.5294 + 18.2374i 0.822205 + 1.42410i
\(165\) 1.11744 + 1.93546i 0.0869923 + 0.150675i
\(166\) −8.76823 + 15.1870i −0.680546 + 1.17874i
\(167\) −4.82764 −0.373574 −0.186787 0.982400i \(-0.559807\pi\)
−0.186787 + 0.982400i \(0.559807\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 8.00530 13.8656i 0.613979 1.06344i
\(171\) 2.52643 + 4.37591i 0.193201 + 0.334634i
\(172\) −22.1135 38.3017i −1.68614 2.92047i
\(173\) −11.1062 + 19.2365i −0.844388 + 1.46252i 0.0417636 + 0.999128i \(0.486702\pi\)
−0.886152 + 0.463395i \(0.846631\pi\)
\(174\) 5.96180 0.451963
\(175\) 0 0
\(176\) 14.5361 1.09570
\(177\) 3.20038 5.54323i 0.240556 0.416654i
\(178\) −15.7262 27.2386i −1.17873 2.04162i
\(179\) −2.28753 3.96211i −0.170978 0.296142i 0.767784 0.640709i \(-0.221359\pi\)
−0.938762 + 0.344566i \(0.888026\pi\)
\(180\) −4.64131 + 8.03899i −0.345943 + 0.599191i
\(181\) 7.23332 0.537649 0.268824 0.963189i \(-0.413365\pi\)
0.268824 + 0.963189i \(0.413365\pi\)
\(182\) 0 0
\(183\) −4.66239 −0.344654
\(184\) −1.45475 + 2.51971i −0.107246 + 0.185755i
\(185\) 0.323539 + 0.560386i 0.0237871 + 0.0412004i
\(186\) 5.79052 + 10.0295i 0.424582 + 0.735397i
\(187\) 13.2151 22.8892i 0.966384 1.67383i
\(188\) −48.3565 −3.52676
\(189\) 0 0
\(190\) 4.40751 0.319754
\(191\) −0.986209 + 1.70816i −0.0713596 + 0.123598i −0.899497 0.436926i \(-0.856067\pi\)
0.828138 + 0.560525i \(0.189400\pi\)
\(192\) 2.70187 + 4.67977i 0.194990 + 0.337733i
\(193\) 12.6036 + 21.8301i 0.907230 + 1.57137i 0.817896 + 0.575366i \(0.195140\pi\)
0.0893339 + 0.996002i \(0.471526\pi\)
\(194\) −11.1262 + 19.2712i −0.798816 + 1.38359i
\(195\) 0.607572 0.0435091
\(196\) 0 0
\(197\) −3.04497 −0.216945 −0.108473 0.994099i \(-0.534596\pi\)
−0.108473 + 0.994099i \(0.534596\pi\)
\(198\) −11.5005 + 19.9194i −0.817304 + 1.41561i
\(199\) 2.02846 + 3.51339i 0.143794 + 0.249058i 0.928922 0.370275i \(-0.120737\pi\)
−0.785129 + 0.619333i \(0.787403\pi\)
\(200\) −10.1698 17.6146i −0.719114 1.24554i
\(201\) −0.409946 + 0.710048i −0.0289154 + 0.0500829i
\(202\) −14.2133 −1.00004
\(203\) 0 0
\(204\) −19.1448 −1.34040
\(205\) −2.40101 + 4.15868i −0.167694 + 0.290455i
\(206\) −15.7497 27.2793i −1.09733 1.90064i
\(207\) −0.762138 1.32006i −0.0529722 0.0917506i
\(208\) 1.97589 3.42234i 0.137003 0.237296i
\(209\) 7.27588 0.503283
\(210\) 0 0
\(211\) 16.4116 1.12982 0.564910 0.825152i \(-0.308911\pi\)
0.564910 + 0.825152i \(0.308911\pi\)
\(212\) 22.8508 39.5787i 1.56940 2.71828i
\(213\) −3.79228 6.56842i −0.259843 0.450061i
\(214\) 5.45561 + 9.44939i 0.372938 + 0.645947i
\(215\) 5.04255 8.73394i 0.343899 0.595650i
\(216\) 18.0771 1.22999
\(217\) 0 0
\(218\) −2.15140 −0.145711
\(219\) 2.18063 3.77696i 0.147353 0.255223i
\(220\) 6.68326 + 11.5757i 0.450585 + 0.780436i
\(221\) −3.59265 6.22266i −0.241668 0.418581i
\(222\) 0.580701 1.00580i 0.0389741 0.0675051i
\(223\) 16.1205 1.07951 0.539755 0.841822i \(-0.318517\pi\)
0.539755 + 0.841822i \(0.318517\pi\)
\(224\) 0 0
\(225\) 10.6558 0.710388
\(226\) −6.56907 + 11.3780i −0.436968 + 0.756851i
\(227\) −4.33902 7.51540i −0.287991 0.498815i 0.685339 0.728224i \(-0.259654\pi\)
−0.973330 + 0.229409i \(0.926321\pi\)
\(228\) −2.63515 4.56422i −0.174517 0.302273i
\(229\) −10.3796 + 17.9780i −0.685902 + 1.18802i 0.287250 + 0.957856i \(0.407259\pi\)
−0.973152 + 0.230162i \(0.926074\pi\)
\(230\) −1.32959 −0.0876707
\(231\) 0 0
\(232\) 17.7925 1.16813
\(233\) 4.92234 8.52574i 0.322473 0.558540i −0.658525 0.752559i \(-0.728819\pi\)
0.980998 + 0.194019i \(0.0621525\pi\)
\(234\) 3.12652 + 5.41529i 0.204387 + 0.354009i
\(235\) −5.51337 9.54944i −0.359653 0.622937i
\(236\) 19.1411 33.1534i 1.24598 2.15810i
\(237\) −7.68932 −0.499475
\(238\) 0 0
\(239\) 1.13539 0.0734424 0.0367212 0.999326i \(-0.488309\pi\)
0.0367212 + 0.999326i \(0.488309\pi\)
\(240\) 1.20049 2.07932i 0.0774915 0.134219i
\(241\) −10.9104 18.8974i −0.702802 1.21729i −0.967479 0.252951i \(-0.918599\pi\)
0.264677 0.964337i \(-0.414735\pi\)
\(242\) 3.09698 + 5.36413i 0.199081 + 0.344819i
\(243\) −7.29276 + 12.6314i −0.467831 + 0.810307i
\(244\) −27.8852 −1.78517
\(245\) 0 0
\(246\) 8.61888 0.549519
\(247\) 0.989010 1.71302i 0.0629292 0.108997i
\(248\) 17.2813 + 29.9321i 1.09736 + 1.90069i
\(249\) 2.39082 + 4.14103i 0.151512 + 0.262427i
\(250\) 10.2180 17.6981i 0.646244 1.11933i
\(251\) −9.44377 −0.596086 −0.298043 0.954552i \(-0.596334\pi\)
−0.298043 + 0.954552i \(0.596334\pi\)
\(252\) 0 0
\(253\) −2.19488 −0.137991
\(254\) 8.09048 14.0131i 0.507642 0.879262i
\(255\) −2.18280 3.78071i −0.136692 0.236758i
\(256\) 15.9670 + 27.6557i 0.997939 + 1.72848i
\(257\) −1.81376 + 3.14153i −0.113139 + 0.195963i −0.917034 0.398808i \(-0.869424\pi\)
0.803895 + 0.594771i \(0.202757\pi\)
\(258\) −18.1011 −1.12693
\(259\) 0 0
\(260\) 3.63382 0.225360
\(261\) −4.66070 + 8.07257i −0.288490 + 0.499680i
\(262\) 24.4374 + 42.3269i 1.50975 + 2.61496i
\(263\) −3.29792 5.71217i −0.203359 0.352227i 0.746250 0.665666i \(-0.231852\pi\)
−0.949608 + 0.313439i \(0.898519\pi\)
\(264\) 5.98560 10.3674i 0.368388 0.638067i
\(265\) 10.4214 0.640179
\(266\) 0 0
\(267\) −8.57610 −0.524849
\(268\) −2.45184 + 4.24672i −0.149770 + 0.259409i
\(269\) 11.7657 + 20.3787i 0.717365 + 1.24251i 0.962040 + 0.272908i \(0.0879853\pi\)
−0.244675 + 0.969605i \(0.578681\pi\)
\(270\) 4.13045 + 7.15415i 0.251371 + 0.435388i
\(271\) 1.34883 2.33625i 0.0819358 0.141917i −0.822146 0.569277i \(-0.807223\pi\)
0.904081 + 0.427360i \(0.140556\pi\)
\(272\) −28.3947 −1.72168
\(273\) 0 0
\(274\) −14.0862 −0.850976
\(275\) 7.67193 13.2882i 0.462635 0.801307i
\(276\) 0.794934 + 1.37687i 0.0478494 + 0.0828776i
\(277\) 12.3775 + 21.4384i 0.743690 + 1.28811i 0.950804 + 0.309792i \(0.100259\pi\)
−0.207115 + 0.978317i \(0.566407\pi\)
\(278\) 1.89877 3.28876i 0.113881 0.197247i
\(279\) −18.1072 −1.08405
\(280\) 0 0
\(281\) −4.05377 −0.241828 −0.120914 0.992663i \(-0.538582\pi\)
−0.120914 + 0.992663i \(0.538582\pi\)
\(282\) −9.89562 + 17.1397i −0.589276 + 1.02066i
\(283\) 6.46186 + 11.1923i 0.384118 + 0.665311i 0.991646 0.128987i \(-0.0411724\pi\)
−0.607529 + 0.794298i \(0.707839\pi\)
\(284\) −22.6812 39.2850i −1.34588 2.33113i
\(285\) 0.600895 1.04078i 0.0355939 0.0616505i
\(286\) 9.00407 0.532422
\(287\) 0 0
\(288\) −0.200906 −0.0118385
\(289\) −17.3143 + 29.9893i −1.01849 + 1.76408i
\(290\) 4.06543 + 7.04152i 0.238730 + 0.413492i
\(291\) 3.03377 + 5.25465i 0.177843 + 0.308033i
\(292\) 13.0421 22.5895i 0.763230 1.32195i
\(293\) 23.5553 1.37611 0.688057 0.725656i \(-0.258464\pi\)
0.688057 + 0.725656i \(0.258464\pi\)
\(294\) 0 0
\(295\) 8.72952 0.508252
\(296\) 1.73305 3.00173i 0.100732 0.174472i
\(297\) 6.81852 + 11.8100i 0.395651 + 0.685287i
\(298\) 18.2777 + 31.6578i 1.05880 + 1.83389i
\(299\) −0.298350 + 0.516758i −0.0172540 + 0.0298849i
\(300\) −11.1144 −0.641688
\(301\) 0 0
\(302\) 19.3405 1.11292
\(303\) −1.93776 + 3.35630i −0.111321 + 0.192814i
\(304\) −3.90834 6.76945i −0.224159 0.388255i
\(305\) −3.17934 5.50678i −0.182049 0.315317i
\(306\) 22.4650 38.9106i 1.28424 2.22437i
\(307\) −19.9551 −1.13890 −0.569450 0.822026i \(-0.692844\pi\)
−0.569450 + 0.822026i \(0.692844\pi\)
\(308\) 0 0
\(309\) −8.58891 −0.488606
\(310\) −7.89725 + 13.6784i −0.448534 + 0.776883i
\(311\) 3.24035 + 5.61245i 0.183743 + 0.318253i 0.943152 0.332361i \(-0.107845\pi\)
−0.759409 + 0.650613i \(0.774512\pi\)
\(312\) −1.62724 2.81847i −0.0921245 0.159564i
\(313\) 8.05771 13.9564i 0.455449 0.788860i −0.543265 0.839561i \(-0.682812\pi\)
0.998714 + 0.0507010i \(0.0161455\pi\)
\(314\) 30.5854 1.72603
\(315\) 0 0
\(316\) −45.9889 −2.58708
\(317\) −7.26517 + 12.5836i −0.408053 + 0.706768i −0.994672 0.103095i \(-0.967125\pi\)
0.586619 + 0.809863i \(0.300459\pi\)
\(318\) −9.35233 16.1987i −0.524453 0.908379i
\(319\) 6.71118 + 11.6241i 0.375754 + 0.650825i
\(320\) −3.68487 + 6.38238i −0.205990 + 0.356786i
\(321\) 2.97515 0.166057
\(322\) 0 0
\(323\) −14.2127 −0.790815
\(324\) −10.3572 + 17.9392i −0.575400 + 0.996622i
\(325\) −2.08569 3.61252i −0.115693 0.200387i
\(326\) 8.58493 + 14.8695i 0.475475 + 0.823547i
\(327\) −0.293310 + 0.508028i −0.0162201 + 0.0280940i
\(328\) 25.7223 1.42028
\(329\) 0 0
\(330\) 5.47062 0.301148
\(331\) −10.5473 + 18.2684i −0.579730 + 1.00412i 0.415780 + 0.909465i \(0.363509\pi\)
−0.995510 + 0.0946563i \(0.969825\pi\)
\(332\) 14.2992 + 24.7670i 0.784773 + 1.35927i
\(333\) 0.907938 + 1.57259i 0.0497547 + 0.0861776i
\(334\) −5.90866 + 10.2341i −0.323308 + 0.559985i
\(335\) −1.11819 −0.0610932
\(336\) 0 0
\(337\) −32.8693 −1.79050 −0.895251 0.445562i \(-0.853004\pi\)
−0.895251 + 0.445562i \(0.853004\pi\)
\(338\) 1.22392 2.11990i 0.0665726 0.115307i
\(339\) 1.79118 + 3.10242i 0.0972836 + 0.168500i
\(340\) −13.0551 22.6120i −0.708010 1.22631i
\(341\) −13.0367 + 22.5803i −0.705979 + 1.22279i
\(342\) 12.3686 0.668820
\(343\) 0 0
\(344\) −54.0213 −2.91263
\(345\) −0.181269 + 0.313967i −0.00975921 + 0.0169034i
\(346\) 27.1862 + 47.0880i 1.46154 + 2.53146i
\(347\) −7.95802 13.7837i −0.427209 0.739948i 0.569415 0.822050i \(-0.307170\pi\)
−0.996624 + 0.0821026i \(0.973836\pi\)
\(348\) 4.86126 8.41995i 0.260591 0.451357i
\(349\) 29.6245 1.58576 0.792882 0.609375i \(-0.208580\pi\)
0.792882 + 0.609375i \(0.208580\pi\)
\(350\) 0 0
\(351\) 3.70737 0.197885
\(352\) −0.144648 + 0.250537i −0.00770975 + 0.0133537i
\(353\) −14.3539 24.8617i −0.763980 1.32325i −0.940784 0.339006i \(-0.889909\pi\)
0.176804 0.984246i \(-0.443424\pi\)
\(354\) −7.83405 13.5690i −0.416375 0.721182i
\(355\) 5.17200 8.95817i 0.274501 0.475450i
\(356\) −51.2927 −2.71851
\(357\) 0 0
\(358\) −11.1990 −0.591887
\(359\) −13.6466 + 23.6365i −0.720238 + 1.24749i 0.240666 + 0.970608i \(0.422634\pi\)
−0.960904 + 0.276881i \(0.910699\pi\)
\(360\) 5.66915 + 9.81926i 0.298791 + 0.517521i
\(361\) 7.54372 + 13.0661i 0.397038 + 0.687690i
\(362\) 8.85303 15.3339i 0.465305 0.805932i
\(363\) 1.68890 0.0886443
\(364\) 0 0
\(365\) 5.94798 0.311332
\(366\) −5.70641 + 9.88379i −0.298279 + 0.516634i
\(367\) −4.99163 8.64575i −0.260561 0.451305i 0.705830 0.708381i \(-0.250574\pi\)
−0.966391 + 0.257076i \(0.917241\pi\)
\(368\) 1.17901 + 2.04211i 0.0614603 + 0.106452i
\(369\) −6.73789 + 11.6704i −0.350761 + 0.607535i
\(370\) 1.58395 0.0823455
\(371\) 0 0
\(372\) 18.8864 0.979214
\(373\) −2.34304 + 4.05827i −0.121318 + 0.210129i −0.920288 0.391242i \(-0.872045\pi\)
0.798970 + 0.601371i \(0.205379\pi\)
\(374\) −32.3485 56.0293i −1.67270 2.89721i
\(375\) −2.78614 4.82573i −0.143875 0.249200i
\(376\) −29.5326 + 51.1520i −1.52303 + 2.63796i
\(377\) 3.64900 0.187933
\(378\) 0 0
\(379\) −2.45019 −0.125858 −0.0629288 0.998018i \(-0.520044\pi\)
−0.0629288 + 0.998018i \(0.520044\pi\)
\(380\) 3.59388 6.22479i 0.184362 0.319325i
\(381\) −2.20602 3.82094i −0.113018 0.195753i
\(382\) 2.41409 + 4.18132i 0.123515 + 0.213935i
\(383\) −5.38356 + 9.32461i −0.275087 + 0.476465i −0.970157 0.242477i \(-0.922040\pi\)
0.695070 + 0.718942i \(0.255373\pi\)
\(384\) 13.1225 0.669656
\(385\) 0 0
\(386\) 61.7035 3.14063
\(387\) 14.1507 24.5098i 0.719322 1.24590i
\(388\) 18.1447 + 31.4275i 0.921155 + 1.59549i
\(389\) −7.01860 12.1566i −0.355857 0.616362i 0.631407 0.775451i \(-0.282478\pi\)
−0.987264 + 0.159089i \(0.949144\pi\)
\(390\) 0.743621 1.28799i 0.0376547 0.0652199i
\(391\) 4.28748 0.216827
\(392\) 0 0
\(393\) 13.3267 0.672241
\(394\) −3.72681 + 6.45503i −0.187754 + 0.325200i
\(395\) −5.24344 9.08190i −0.263826 0.456960i
\(396\) 18.7550 + 32.4846i 0.942475 + 1.63241i
\(397\) 13.2303 22.9155i 0.664007 1.15009i −0.315546 0.948910i \(-0.602188\pi\)
0.979553 0.201184i \(-0.0644790\pi\)
\(398\) 9.93070 0.497781
\(399\) 0 0
\(400\) −16.4843 −0.824217
\(401\) 9.50779 16.4680i 0.474796 0.822371i −0.524787 0.851234i \(-0.675855\pi\)
0.999583 + 0.0288621i \(0.00918838\pi\)
\(402\) 1.00349 + 1.73809i 0.0500493 + 0.0866880i
\(403\) 3.54416 + 6.13867i 0.176547 + 0.305789i
\(404\) −11.5895 + 20.0737i −0.576601 + 0.998701i
\(405\) −4.72351 −0.234713
\(406\) 0 0
\(407\) 2.61477 0.129609
\(408\) −11.6923 + 20.2516i −0.578853 + 1.00260i
\(409\) 6.38796 + 11.0643i 0.315864 + 0.547093i 0.979621 0.200856i \(-0.0643723\pi\)
−0.663757 + 0.747949i \(0.731039\pi\)
\(410\) 5.87731 + 10.1798i 0.290260 + 0.502745i
\(411\) −1.92043 + 3.32628i −0.0947278 + 0.164073i
\(412\) −51.3693 −2.53078
\(413\) 0 0
\(414\) −3.73119 −0.183378
\(415\) −3.26066 + 5.64763i −0.160060 + 0.277231i
\(416\) 0.0393239 + 0.0681110i 0.00192801 + 0.00333942i
\(417\) −0.517735 0.896744i −0.0253536 0.0439137i
\(418\) 8.90512 15.4241i 0.435564 0.754418i
\(419\) −12.9811 −0.634170 −0.317085 0.948397i \(-0.602704\pi\)
−0.317085 + 0.948397i \(0.602704\pi\)
\(420\) 0 0
\(421\) −11.6737 −0.568943 −0.284472 0.958684i \(-0.591818\pi\)
−0.284472 + 0.958684i \(0.591818\pi\)
\(422\) 20.0865 34.7909i 0.977797 1.69359i
\(423\) −15.4720 26.7983i −0.752275 1.30298i
\(424\) −27.9112 48.3437i −1.35549 2.34778i
\(425\) −14.9863 + 25.9571i −0.726944 + 1.25910i
\(426\) −18.5658 −0.899517
\(427\) 0 0
\(428\) 17.7940 0.860107
\(429\) 1.22757 2.12621i 0.0592674 0.102654i
\(430\) −12.3434 21.3794i −0.595250 1.03100i
\(431\) 0.233842 + 0.405026i 0.0112638 + 0.0195094i 0.871602 0.490214i \(-0.163081\pi\)
−0.860339 + 0.509723i \(0.829748\pi\)
\(432\) 7.32533 12.6879i 0.352440 0.610445i
\(433\) 9.27593 0.445773 0.222886 0.974844i \(-0.428452\pi\)
0.222886 + 0.974844i \(0.428452\pi\)
\(434\) 0 0
\(435\) 2.21703 0.106298
\(436\) −1.75426 + 3.03846i −0.0840136 + 0.145516i
\(437\) 0.590143 + 1.02216i 0.0282303 + 0.0488964i
\(438\) −5.33784 9.24541i −0.255052 0.441763i
\(439\) −17.8539 + 30.9238i −0.852119 + 1.47591i 0.0271736 + 0.999631i \(0.491349\pi\)
−0.879292 + 0.476282i \(0.841984\pi\)
\(440\) 16.3266 0.778340
\(441\) 0 0
\(442\) −17.5885 −0.836601
\(443\) 18.1729 31.4764i 0.863421 1.49549i −0.00518509 0.999987i \(-0.501650\pi\)
0.868606 0.495503i \(-0.165016\pi\)
\(444\) −0.947008 1.64027i −0.0449430 0.0778436i
\(445\) −5.84814 10.1293i −0.277229 0.480174i
\(446\) 19.7303 34.1738i 0.934255 1.61818i
\(447\) 9.96750 0.471447
\(448\) 0 0
\(449\) −40.4910 −1.91089 −0.955444 0.295171i \(-0.904623\pi\)
−0.955444 + 0.295171i \(0.904623\pi\)
\(450\) 13.0419 22.5892i 0.614801 1.06487i
\(451\) 9.70223 + 16.8048i 0.456860 + 0.791305i
\(452\) 10.7129 + 18.5552i 0.503890 + 0.872764i
\(453\) 2.63677 4.56702i 0.123886 0.214578i
\(454\) −21.2425 −0.996960
\(455\) 0 0
\(456\) −6.43744 −0.301461
\(457\) −2.50994 + 4.34734i −0.117410 + 0.203360i −0.918741 0.394862i \(-0.870793\pi\)
0.801331 + 0.598222i \(0.204126\pi\)
\(458\) 25.4076 + 44.0073i 1.18722 + 2.05633i
\(459\) −13.3193 23.0697i −0.621691 1.07680i
\(460\) −1.08415 + 1.87780i −0.0505488 + 0.0875530i
\(461\) 17.3627 0.808661 0.404331 0.914613i \(-0.367505\pi\)
0.404331 + 0.914613i \(0.367505\pi\)
\(462\) 0 0
\(463\) 35.4306 1.64660 0.823301 0.567606i \(-0.192130\pi\)
0.823301 + 0.567606i \(0.192130\pi\)
\(464\) 7.21001 12.4881i 0.334716 0.579746i
\(465\) 2.15334 + 3.72969i 0.0998585 + 0.172960i
\(466\) −12.0491 20.8697i −0.558165 0.966770i
\(467\) 17.7479 30.7403i 0.821275 1.42249i −0.0834584 0.996511i \(-0.526597\pi\)
0.904733 0.425978i \(-0.140070\pi\)
\(468\) 10.1975 0.471378
\(469\) 0 0
\(470\) −26.9918 −1.24504
\(471\) 4.16984 7.22237i 0.192136 0.332789i
\(472\) −23.3800 40.4954i −1.07615 1.86395i
\(473\) −20.3764 35.2929i −0.936906 1.62277i
\(474\) −9.41114 + 16.3006i −0.432268 + 0.748710i
\(475\) −8.25107 −0.378585
\(476\) 0 0
\(477\) 29.2451 1.33904
\(478\) 1.38963 2.40691i 0.0635603 0.110090i
\(479\) −12.0135 20.8080i −0.548911 0.950742i −0.998349 0.0574308i \(-0.981709\pi\)
0.449438 0.893311i \(-0.351624\pi\)
\(480\) 0.0238921 + 0.0413823i 0.00109052 + 0.00188884i
\(481\) 0.355426 0.615615i 0.0162060 0.0280696i
\(482\) −53.4140 −2.43294
\(483\) 0 0
\(484\) 10.1011 0.459142
\(485\) −4.13753 + 7.16642i −0.187876 + 0.325410i
\(486\) 17.8516 + 30.9198i 0.809763 + 1.40255i
\(487\) −10.4038 18.0199i −0.471440 0.816558i 0.528026 0.849228i \(-0.322932\pi\)
−0.999466 + 0.0326699i \(0.989599\pi\)
\(488\) −17.0303 + 29.4973i −0.770925 + 1.33528i
\(489\) 4.68169 0.211713
\(490\) 0 0
\(491\) −36.2195 −1.63456 −0.817281 0.576240i \(-0.804519\pi\)
−0.817281 + 0.576240i \(0.804519\pi\)
\(492\) 7.02784 12.1726i 0.316839 0.548782i
\(493\) −13.1096 22.7065i −0.590427 1.02265i
\(494\) −2.42094 4.19320i −0.108923 0.188661i
\(495\) −4.27671 + 7.40749i −0.192224 + 0.332942i
\(496\) 28.0115 1.25775
\(497\) 0 0
\(498\) 11.7047 0.524502
\(499\) 20.0914 34.7994i 0.899416 1.55783i 0.0711731 0.997464i \(-0.477326\pi\)
0.828243 0.560370i \(-0.189341\pi\)
\(500\) −16.6636 28.8621i −0.745217 1.29075i
\(501\) 1.61111 + 2.79052i 0.0719790 + 0.124671i
\(502\) −11.5585 + 20.0198i −0.515879 + 0.893529i
\(503\) −38.5636 −1.71946 −0.859732 0.510745i \(-0.829370\pi\)
−0.859732 + 0.510745i \(0.829370\pi\)
\(504\) 0 0
\(505\) −5.28553 −0.235203
\(506\) −2.68637 + 4.65292i −0.119424 + 0.206848i
\(507\) −0.333726 0.578030i −0.0148213 0.0256712i
\(508\) −13.1940 22.8526i −0.585388 1.01392i
\(509\) 2.16989 3.75835i 0.0961785 0.166586i −0.813921 0.580975i \(-0.802671\pi\)
0.910100 + 0.414389i \(0.136005\pi\)
\(510\) −10.6863 −0.473197
\(511\) 0 0
\(512\) 38.8484 1.71687
\(513\) 3.66662 6.35078i 0.161885 0.280394i
\(514\) 4.43981 + 7.68998i 0.195832 + 0.339190i
\(515\) −5.85688 10.1444i −0.258085 0.447016i
\(516\) −14.7597 + 25.5645i −0.649758 + 1.12541i
\(517\) −44.5578 −1.95965
\(518\) 0 0
\(519\) 14.8257 0.650776
\(520\) 2.21927 3.84390i 0.0973216 0.168566i
\(521\) 6.89219 + 11.9376i 0.301952 + 0.522997i 0.976578 0.215163i \(-0.0690283\pi\)
−0.674626 + 0.738160i \(0.735695\pi\)
\(522\) 11.4087 + 19.7604i 0.499344 + 0.864890i
\(523\) −14.7417 + 25.5334i −0.644609 + 1.11650i 0.339782 + 0.940504i \(0.389647\pi\)
−0.984392 + 0.175992i \(0.943687\pi\)
\(524\) 79.7052 3.48194
\(525\) 0 0
\(526\) −16.1456 −0.703982
\(527\) 25.4659 44.1083i 1.10931 1.92139i
\(528\) −4.85106 8.40228i −0.211115 0.365662i
\(529\) 11.3220 + 19.6102i 0.492260 + 0.852619i
\(530\) 12.7549 22.0922i 0.554039 0.959624i
\(531\) 24.4974 1.06310
\(532\) 0 0
\(533\) 5.27529 0.228498
\(534\) −10.4965 + 18.1804i −0.454227 + 0.786745i
\(535\) 2.02879 + 3.51397i 0.0877122 + 0.151922i
\(536\) 2.99482 + 5.18717i 0.129356 + 0.224052i
\(537\) −1.52681 + 2.64452i −0.0658869 + 0.114119i
\(538\) 57.6011 2.48336
\(539\) 0 0
\(540\) 13.4719 0.579738
\(541\) −11.6260 + 20.1368i −0.499840 + 0.865747i −1.00000 0.000185310i \(-0.999941\pi\)
0.500160 + 0.865933i \(0.333274\pi\)
\(542\) −3.30174 5.71878i −0.141822 0.245643i
\(543\) −2.41395 4.18108i −0.103592 0.179427i
\(544\) 0.282554 0.489399i 0.0121144 0.0209828i
\(545\) −0.800047 −0.0342703
\(546\) 0 0
\(547\) 1.18365 0.0506093 0.0253046 0.999680i \(-0.491944\pi\)
0.0253046 + 0.999680i \(0.491944\pi\)
\(548\) −11.4859 + 19.8941i −0.490652 + 0.849834i
\(549\) −8.92209 15.4535i −0.380785 0.659540i
\(550\) −18.7797 32.5274i −0.800769 1.38697i
\(551\) 3.60890 6.25079i 0.153744 0.266293i
\(552\) 1.94195 0.0826550
\(553\) 0 0
\(554\) 60.5962 2.57449
\(555\) 0.215947 0.374031i 0.00916642 0.0158767i
\(556\) −3.09651 5.36332i −0.131321 0.227455i
\(557\) 3.21412 + 5.56702i 0.136187 + 0.235882i 0.926050 0.377401i \(-0.123182\pi\)
−0.789864 + 0.613283i \(0.789849\pi\)
\(558\) −22.1618 + 38.3854i −0.938184 + 1.62498i
\(559\) −11.0790 −0.468593
\(560\) 0 0
\(561\) −17.6409 −0.744798
\(562\) −4.96150 + 8.59357i −0.209288 + 0.362498i
\(563\) 5.72813 + 9.92141i 0.241412 + 0.418138i 0.961117 0.276142i \(-0.0890562\pi\)
−0.719705 + 0.694280i \(0.755723\pi\)
\(564\) 16.1378 + 27.9515i 0.679524 + 1.17697i
\(565\) −2.44286 + 4.23115i −0.102772 + 0.178006i
\(566\) 31.6353 1.32973
\(567\) 0 0
\(568\) −55.4081 −2.32487
\(569\) −19.1668 + 33.1978i −0.803512 + 1.39172i 0.113779 + 0.993506i \(0.463705\pi\)
−0.917291 + 0.398218i \(0.869629\pi\)
\(570\) −1.47090 2.54767i −0.0616092 0.106710i
\(571\) −3.12928 5.42008i −0.130956 0.226823i 0.793089 0.609106i \(-0.208471\pi\)
−0.924046 + 0.382282i \(0.875138\pi\)
\(572\) 7.34193 12.7166i 0.306981 0.531707i
\(573\) 1.31649 0.0549973
\(574\) 0 0
\(575\) 2.48906 0.103801
\(576\) −10.3407 + 17.9107i −0.430864 + 0.746278i
\(577\) 0.0225966 + 0.0391384i 0.000940708 + 0.00162935i 0.866495 0.499185i \(-0.166367\pi\)
−0.865555 + 0.500814i \(0.833034\pi\)
\(578\) 42.3828 + 73.4092i 1.76289 + 3.05342i
\(579\) 8.41232 14.5706i 0.349604 0.605532i
\(580\) 13.2598 0.550583
\(581\) 0 0
\(582\) 14.8524 0.615653
\(583\) 21.0558 36.4696i 0.872041 1.51042i
\(584\) −15.9303 27.5921i −0.659201 1.14177i
\(585\) 1.16267 + 2.01380i 0.0480704 + 0.0832603i
\(586\) 28.8299 49.9348i 1.19095 2.06279i
\(587\) −2.71409 −0.112023 −0.0560113 0.998430i \(-0.517838\pi\)
−0.0560113 + 0.998430i \(0.517838\pi\)
\(588\) 0 0
\(589\) 14.0209 0.577719
\(590\) 10.6843 18.5057i 0.439864 0.761867i
\(591\) 1.01619 + 1.76009i 0.0418003 + 0.0724003i
\(592\) −1.40456 2.43277i −0.0577271 0.0999863i
\(593\) 3.39307 5.87698i 0.139337 0.241339i −0.787909 0.615792i \(-0.788836\pi\)
0.927246 + 0.374453i \(0.122170\pi\)
\(594\) 33.3814 1.36965
\(595\) 0 0
\(596\) 59.6145 2.44190
\(597\) 1.35390 2.34502i 0.0554113 0.0959752i
\(598\) 0.730315 + 1.26494i 0.0298648 + 0.0517274i
\(599\) 13.4169 + 23.2387i 0.548198 + 0.949507i 0.998398 + 0.0565794i \(0.0180194\pi\)
−0.450200 + 0.892928i \(0.648647\pi\)
\(600\) −6.78785 + 11.7569i −0.277113 + 0.479974i
\(601\) −12.3356 −0.503178 −0.251589 0.967834i \(-0.580953\pi\)
−0.251589 + 0.967834i \(0.580953\pi\)
\(602\) 0 0
\(603\) −3.13794 −0.127787
\(604\) 15.7702 27.3148i 0.641682 1.11143i
\(605\) 1.15168 + 1.99477i 0.0468225 + 0.0810990i
\(606\) 4.74334 + 8.21571i 0.192685 + 0.333740i
\(607\) −8.72982 + 15.1205i −0.354332 + 0.613722i −0.987003 0.160699i \(-0.948625\pi\)
0.632671 + 0.774421i \(0.281958\pi\)
\(608\) 0.155567 0.00630907
\(609\) 0 0
\(610\) −15.5651 −0.630211
\(611\) −6.05674 + 10.4906i −0.245030 + 0.424404i
\(612\) −36.6360 63.4554i −1.48092 2.56503i
\(613\) −0.525132 0.909556i −0.0212099 0.0367366i 0.855226 0.518256i \(-0.173418\pi\)
−0.876436 + 0.481519i \(0.840085\pi\)
\(614\) −24.4236 + 42.3028i −0.985654 + 1.70720i
\(615\) 3.20512 0.129243
\(616\) 0 0
\(617\) 10.5872 0.426223 0.213111 0.977028i \(-0.431640\pi\)
0.213111 + 0.977028i \(0.431640\pi\)
\(618\) −10.5122 + 18.2076i −0.422861 + 0.732417i
\(619\) 0.619027 + 1.07219i 0.0248808 + 0.0430948i 0.878198 0.478298i \(-0.158746\pi\)
−0.853317 + 0.521393i \(0.825413\pi\)
\(620\) 12.8789 + 22.3068i 0.517227 + 0.895864i
\(621\) −1.10609 + 1.91581i −0.0443860 + 0.0768788i
\(622\) 15.8637 0.636078
\(623\) 0 0
\(624\) −2.63762 −0.105589
\(625\) −6.62865 + 11.4812i −0.265146 + 0.459246i
\(626\) −19.7240 34.1630i −0.788331 1.36543i
\(627\) −2.42815 4.20568i −0.0969709 0.167959i
\(628\) 24.9393 43.1962i 0.995187 1.72371i
\(629\) −5.10769 −0.203657
\(630\) 0 0
\(631\) −21.2658 −0.846577 −0.423289 0.905995i \(-0.639124\pi\)
−0.423289 + 0.905995i \(0.639124\pi\)
\(632\) −28.0867 + 48.6476i −1.11723 + 1.93510i
\(633\) −5.47697 9.48640i −0.217690 0.377050i
\(634\) 17.7840 + 30.8028i 0.706294 + 1.22334i
\(635\) 3.00863 5.21109i 0.119394 0.206796i
\(636\) −30.5036 −1.20955
\(637\) 0 0
\(638\) 32.8559 1.30078
\(639\) 14.5140 25.1390i 0.574166 0.994484i
\(640\) 8.94840 + 15.4991i 0.353717 + 0.612655i
\(641\) −5.52532 9.57013i −0.218237 0.377998i 0.736032 0.676947i \(-0.236697\pi\)
−0.954269 + 0.298949i \(0.903364\pi\)
\(642\) 3.64135 6.30701i 0.143713 0.248918i
\(643\) −6.50321 −0.256461 −0.128231 0.991744i \(-0.540930\pi\)
−0.128231 + 0.991744i \(0.540930\pi\)
\(644\) 0 0
\(645\) −6.73131 −0.265045
\(646\) −17.3952 + 30.1294i −0.684407 + 1.18543i
\(647\) −0.446970 0.774175i −0.0175722 0.0304360i 0.857106 0.515141i \(-0.172260\pi\)
−0.874678 + 0.484705i \(0.838927\pi\)
\(648\) 12.6509 + 21.9119i 0.496972 + 0.860781i
\(649\) 17.6375 30.5491i 0.692333 1.19916i
\(650\) −10.2109 −0.400504
\(651\) 0 0
\(652\) 28.0006 1.09659
\(653\) 19.2739 33.3833i 0.754244 1.30639i −0.191505 0.981492i \(-0.561337\pi\)
0.945749 0.324898i \(-0.105330\pi\)
\(654\) 0.717979 + 1.24358i 0.0280752 + 0.0486276i
\(655\) 9.08761 + 15.7402i 0.355082 + 0.615020i
\(656\) 10.4234 18.0538i 0.406965 0.704884i
\(657\) 16.6916 0.651203
\(658\) 0 0
\(659\) −10.8013 −0.420759 −0.210380 0.977620i \(-0.567470\pi\)
−0.210380 + 0.977620i \(0.567470\pi\)
\(660\) 4.46075 7.72625i 0.173634 0.300744i
\(661\) 20.3169 + 35.1900i 0.790237 + 1.36873i 0.925820 + 0.377965i \(0.123376\pi\)
−0.135583 + 0.990766i \(0.543291\pi\)
\(662\) 25.8181 + 44.7182i 1.00345 + 1.73802i
\(663\) −2.39792 + 4.15332i −0.0931276 + 0.161302i
\(664\) 34.9318 1.35562
\(665\) 0 0
\(666\) 4.44498 0.172240
\(667\) −1.08868 + 1.88565i −0.0421538 + 0.0730126i
\(668\) 9.63586 + 16.6898i 0.372822 + 0.645747i
\(669\) −5.37983 9.31814i −0.207996 0.360260i
\(670\) −1.36858 + 2.37045i −0.0528728 + 0.0915783i
\(671\) −25.6947 −0.991934
\(672\) 0 0
\(673\) 32.3136 1.24560 0.622799 0.782382i \(-0.285995\pi\)
0.622799 + 0.782382i \(0.285995\pi\)
\(674\) −40.2294 + 69.6794i −1.54958 + 2.68395i
\(675\) −7.73241 13.3929i −0.297621 0.515494i
\(676\) −1.99598 3.45713i −0.0767683 0.132967i
\(677\) −12.6079 + 21.8376i −0.484562 + 0.839285i −0.999843 0.0177358i \(-0.994354\pi\)
0.515281 + 0.857021i \(0.327688\pi\)
\(678\) 8.76908 0.336774
\(679\) 0 0
\(680\) −31.8923 −1.22302
\(681\) −2.89608 + 5.01617i −0.110978 + 0.192220i
\(682\) 31.9119 + 55.2731i 1.22197 + 2.11651i
\(683\) 3.14365 + 5.44497i 0.120289 + 0.208346i 0.919881 0.392197i \(-0.128285\pi\)
−0.799593 + 0.600542i \(0.794951\pi\)
\(684\) 10.0854 17.4684i 0.385625 0.667922i
\(685\) −5.23826 −0.200143
\(686\) 0 0
\(687\) 13.8557 0.528629
\(688\) −21.8909 + 37.9162i −0.834583 + 1.44554i
\(689\) −5.72422 9.91463i −0.218075 0.377717i
\(690\) 0.443719 + 0.768544i 0.0168921 + 0.0292580i
\(691\) 8.57653 14.8550i 0.326267 0.565110i −0.655501 0.755194i \(-0.727543\pi\)
0.981768 + 0.190084i \(0.0608759\pi\)
\(692\) 88.6707 3.37076
\(693\) 0 0
\(694\) −38.9600 −1.47890
\(695\) 0.706100 1.22300i 0.0267839 0.0463910i
\(696\) −5.93781 10.2846i −0.225072 0.389837i
\(697\) −18.9523 32.8264i −0.717870 1.24339i
\(698\) 36.2581 62.8009i 1.37239 2.37705i
\(699\) −6.57085 −0.248532
\(700\) 0 0
\(701\) −23.6620 −0.893702 −0.446851 0.894609i \(-0.647455\pi\)
−0.446851 + 0.894609i \(0.647455\pi\)
\(702\) 4.53753 7.85923i 0.171258 0.296628i
\(703\) −0.703039 1.21770i −0.0265156 0.0459264i
\(704\) 14.8901 + 25.7905i 0.561193 + 0.972015i
\(705\) −3.67991 + 6.37379i −0.138593 + 0.240051i
\(706\) −70.2722 −2.64473
\(707\) 0 0
\(708\) −25.5516 −0.960286
\(709\) 10.7515 18.6222i 0.403782 0.699370i −0.590397 0.807113i \(-0.701029\pi\)
0.994179 + 0.107742i \(0.0343622\pi\)
\(710\) −12.6603 21.9282i −0.475131 0.822951i
\(711\) −14.7145 25.4863i −0.551837 0.955810i
\(712\) −31.3259 + 54.2580i −1.17399 + 2.03340i
\(713\) −4.22961 −0.158400
\(714\) 0 0
\(715\) 3.34837 0.125222
\(716\) −9.13170 + 15.8166i −0.341268 + 0.591093i
\(717\) −0.378909 0.656290i −0.0141506 0.0245096i
\(718\) 33.4047 + 57.8586i 1.24665 + 2.15927i
\(719\) −6.43464 + 11.1451i −0.239971 + 0.415643i −0.960706 0.277569i \(-0.910471\pi\)
0.720734 + 0.693211i \(0.243805\pi\)
\(720\) 9.18919 0.342461
\(721\) 0 0
\(722\) 36.9317 1.37446
\(723\) −7.28217 + 12.6131i −0.270827 + 0.469086i
\(724\) −14.4375 25.0065i −0.536567 0.929361i
\(725\) −7.61068 13.1821i −0.282654 0.489570i
\(726\) 2.06708 3.58030i 0.0767167 0.132877i
\(727\) 16.4329 0.609463 0.304732 0.952438i \(-0.401433\pi\)
0.304732 + 0.952438i \(0.401433\pi\)
\(728\) 0 0
\(729\) −5.83198 −0.215999
\(730\) 7.27987 12.6091i 0.269440 0.466684i
\(731\) 39.8031 + 68.9411i 1.47217 + 2.54988i
\(732\) 9.30602 + 16.1185i 0.343960 + 0.595757i
\(733\) 10.8611 18.8120i 0.401164 0.694836i −0.592703 0.805421i \(-0.701939\pi\)
0.993867 + 0.110585i \(0.0352724\pi\)
\(734\) −24.4375 −0.902004
\(735\) 0 0
\(736\) −0.0469292 −0.00172983
\(737\) −2.25924 + 3.91312i −0.0832201 + 0.144142i
\(738\) 16.4933 + 28.5673i 0.607128 + 1.05158i
\(739\) −0.790007 1.36833i −0.0290609 0.0503349i 0.851129 0.524956i \(-0.175918\pi\)
−0.880190 + 0.474621i \(0.842585\pi\)
\(740\) 1.29155 2.23703i 0.0474784 0.0822350i
\(741\) −1.32023 −0.0485000
\(742\) 0 0
\(743\) 45.9718 1.68654 0.843271 0.537489i \(-0.180627\pi\)
0.843271 + 0.537489i \(0.180627\pi\)
\(744\) 11.5344 19.9782i 0.422873 0.732438i
\(745\) 6.79696 + 11.7727i 0.249021 + 0.431317i
\(746\) 5.73541 + 9.93402i 0.209988 + 0.363710i
\(747\) −9.15029 + 15.8488i −0.334792 + 0.579876i
\(748\) −105.508 −3.85776
\(749\) 0 0
\(750\) −13.6401 −0.498065
\(751\) 3.21143 5.56236i 0.117187 0.202973i −0.801465 0.598042i \(-0.795946\pi\)
0.918652 + 0.395068i \(0.129279\pi\)
\(752\) 23.9349 + 41.4564i 0.872815 + 1.51176i
\(753\) 3.15163 + 5.45878i 0.114852 + 0.198929i
\(754\) 4.46610 7.73550i 0.162646 0.281710i
\(755\) 7.19219 0.261750
\(756\) 0 0
\(757\) −6.10016 −0.221714 −0.110857 0.993836i \(-0.535360\pi\)
−0.110857 + 0.993836i \(0.535360\pi\)
\(758\) −2.99884 + 5.19414i −0.108923 + 0.188660i
\(759\) 0.732489 + 1.26871i 0.0265877 + 0.0460512i
\(760\) −4.38977 7.60330i −0.159234 0.275801i
\(761\) 9.19742 15.9304i 0.333406 0.577476i −0.649771 0.760130i \(-0.725135\pi\)
0.983177 + 0.182653i \(0.0584686\pi\)
\(762\) −10.8000 −0.391243
\(763\) 0 0
\(764\) 7.87380 0.284864
\(765\) 8.35412 14.4698i 0.302044 0.523155i
\(766\) 13.1781 + 22.8252i 0.476146 + 0.824708i
\(767\) −4.79493 8.30506i −0.173135 0.299878i
\(768\) 10.6572 18.4588i 0.384559 0.666076i
\(769\) 24.1850 0.872133 0.436066 0.899914i \(-0.356371\pi\)
0.436066 + 0.899914i \(0.356371\pi\)
\(770\) 0 0
\(771\) 2.42120 0.0871973
\(772\) 50.3131 87.1449i 1.81081 3.13641i
\(773\) −5.38005 9.31852i −0.193507 0.335164i 0.752903 0.658131i \(-0.228653\pi\)
−0.946410 + 0.322967i \(0.895320\pi\)
\(774\) −34.6388 59.9962i −1.24507 2.15652i
\(775\) 14.7841 25.6067i 0.531059 0.919821i
\(776\) 44.3258 1.59120
\(777\) 0 0
\(778\) −34.3609 −1.23190
\(779\) 5.21732 9.03666i 0.186930 0.323772i
\(780\) −1.21270 2.10046i −0.0434216 0.0752084i
\(781\) −20.8995 36.1989i −0.747842 1.29530i
\(782\) 5.24754 9.08901i 0.187652 0.325022i
\(783\) 13.5282 0.483458
\(784\) 0 0
\(785\) 11.3738 0.405950