Properties

Label 637.2.e.n.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: \( x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + 43 x^{2} + 6 x + 1 \) Copy content Toggle raw display
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.n.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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} + 12 q^{13} + 24 q^{15} - 16 q^{17} + 4 q^{18} - 2 q^{19} + 32 q^{20} - 24 q^{22} + 6 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{27} - 12 q^{29} - 6 q^{31} + 20 q^{32} - 4 q^{33} - 48 q^{36} - 8 q^{38} - 8 q^{39} - 4 q^{40} - 16 q^{41} + 4 q^{43} + 4 q^{44} - 14 q^{45} - 8 q^{46} - 30 q^{47} - 16 q^{48} + 16 q^{50} + 4 q^{51} - 4 q^{52} + 14 q^{53} + 48 q^{54} - 16 q^{55} + 8 q^{57} + 8 q^{58} - 24 q^{59} - 12 q^{60} + 56 q^{62} - 40 q^{64} - 6 q^{65} + 4 q^{66} - 16 q^{67} - 28 q^{68} - 40 q^{69} + 16 q^{71} - 28 q^{72} + 6 q^{73} + 12 q^{74} - 12 q^{75} - 32 q^{76} + 8 q^{78} + 22 q^{79} + 28 q^{80} - 46 q^{81} + 40 q^{82} + 100 q^{83} - 16 q^{85} + 16 q^{86} + 16 q^{87} + 44 q^{88} - 26 q^{89} - 80 q^{90} + 40 q^{92} - 16 q^{93} + 32 q^{94} + 6 q^{95} + 20 q^{96} - 28 q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 0.946136 0.323768i \(-0.104950\pi\)
−0.753460 + 0.657494i \(0.771616\pi\)
\(4\) −1.99598 3.45713i −0.997988 1.72857i
\(5\) −0.455143 + 0.788331i −0.203546 + 0.352552i −0.949669 0.313256i \(-0.898580\pi\)
0.746122 + 0.665809i \(0.231913\pi\)
\(6\) 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 \(-0.829914\pi\)
−0.0107428 0.999942i \(-0.503420\pi\)
\(18\) −3.12652 5.41529i −0.736928 1.27640i
\(19\) 0.989010 1.71302i 0.226894 0.392993i −0.729992 0.683456i \(-0.760476\pi\)
0.956886 + 0.290463i \(0.0938094\pi\)
\(20\) 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 \(0.0529727\pi\)
−0.349634 + 0.936887i \(0.613694\pi\)
\(32\) −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 \(-0.364854\pi\)
0.411931 + 0.911215i \(0.364854\pi\)
\(42\) 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 \(0.511464\pi\)
−0.847461 + 0.530858i \(0.821870\pi\)
\(48\) −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 \(-0.952073\pi\)
0.364439 0.931227i \(-0.381261\pi\)
\(60\) 1.21270 + 2.10046i 0.156559 + 0.271168i
\(61\) −3.49268 + 6.04950i −0.447192 + 0.774559i −0.998202 0.0599392i \(-0.980909\pi\)
0.551010 + 0.834499i \(0.314243\pi\)
\(62\) 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 0.609018 0.793156i \(-0.291564\pi\)
−0.991403 + 0.130847i \(0.958230\pi\)
\(74\) 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 \(-0.371376\pi\)
0.393177 + 0.919463i \(0.371376\pi\)
\(84\) 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 \(0.405120\pi\)
−0.974677 + 0.223617i \(0.928213\pi\)
\(90\) 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 \(-0.347309\pi\)
0.461506 + 0.887137i \(0.347309\pi\)
\(98\) 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 0.973543 0.228504i \(-0.0733833\pi\)
−0.684661 + 0.728861i \(0.740050\pi\)
\(102\) −5.86975 10.1667i −0.581192 1.00665i
\(103\) −6.43411 + 11.1442i −0.633971 + 1.09807i 0.352761 + 0.935714i \(0.385243\pi\)
−0.986732 + 0.162357i \(0.948090\pi\)
\(104\) −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 \(-0.496000\pi\)
0.859674 0.510843i \(-0.170666\pi\)
\(132\) −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 \(-0.520958\pi\)
−0.0657931 + 0.997833i \(0.520958\pi\)
\(140\) 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 0.501402 0.865215i \(-0.332818\pi\)
−0.999999 + 0.00161951i \(0.999484\pi\)
\(158\) −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 \(-0.440193\pi\)
0.186787 + 0.982400i \(0.440193\pi\)
\(168\) 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 \(-0.513298\pi\)
0.886152 0.463395i \(-0.153369\pi\)
\(174\) −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 \(-0.586635\pi\)
−0.268824 + 0.963189i \(0.586635\pi\)
\(182\) 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 0.785129 0.619333i \(-0.212597\pi\)
−0.928922 + 0.370275i \(0.879263\pi\)
\(200\) −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 \(-0.681483\pi\)
−0.539755 + 0.841822i \(0.681483\pi\)
\(224\) 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 0.973330 0.229409i \(-0.0736794\pi\)
−0.685339 + 0.728224i \(0.740346\pi\)
\(228\) −2.63515 4.56422i −0.174517 0.302273i
\(229\) 10.3796 17.9780i 0.685902 1.18802i −0.287250 0.957856i \(-0.592741\pi\)
0.973152 0.230162i \(-0.0739256\pi\)
\(230\) 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 \(0.0814012\pi\)
−0.264677 + 0.964337i \(0.585265\pi\)
\(242\) 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 \(-0.403666\pi\)
0.298043 + 0.954552i \(0.403666\pi\)
\(252\) 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 −0.803895 0.594771i \(-0.797243\pi\)
0.917034 + 0.398808i \(0.130576\pi\)
\(258\) 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 \(-0.912015\pi\)
0.244675 0.969605i \(-0.421319\pi\)
\(270\) 4.13045 + 7.15415i 0.251371 + 0.435388i
\(271\) −1.34883 + 2.33625i −0.0819358 + 0.141917i −0.904081 0.427360i \(-0.859444\pi\)
0.822146 + 0.569277i \(0.192777\pi\)
\(272\) 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 0.607529 0.794298i \(-0.292161\pi\)
−0.991646 + 0.128987i \(0.958828\pi\)
\(284\) −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 \(-0.741536\pi\)
−0.688057 + 0.725656i \(0.741536\pi\)
\(294\) 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 \(-0.307156\pi\)
0.569450 + 0.822026i \(0.307156\pi\)
\(308\) 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 0.759409 0.650613i \(-0.225488\pi\)
−0.943152 + 0.332361i \(0.892155\pi\)
\(312\) −1.62724 2.81847i −0.0921245 0.159564i
\(313\) −8.05771 + 13.9564i −0.455449 + 0.788860i −0.998714 0.0507010i \(-0.983854\pi\)
0.543265 + 0.839561i \(0.317188\pi\)
\(314\) −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 \(-0.791420\pi\)
−0.792882 + 0.609375i \(0.791420\pi\)
\(350\) 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 \(0.110091\pi\)
−0.176804 + 0.984246i \(0.556576\pi\)
\(354\) −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 0.966391 0.257076i \(-0.0827592\pi\)
−0.705830 + 0.708381i \(0.749426\pi\)
\(368\) 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 −0.695070 0.718942i \(-0.744627\pi\)
0.970157 + 0.242477i \(0.0779599\pi\)
\(384\) −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 \(0.397812\pi\)
−0.979553 + 0.201184i \(0.935521\pi\)
\(398\) −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 0.663757 0.747949i \(-0.268961\pi\)
−0.979621 + 0.200856i \(0.935628\pi\)
\(410\) 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 \(-0.397296\pi\)
0.317085 + 0.948397i \(0.397296\pi\)
\(420\) 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 \(-0.571548\pi\)
−0.222886 + 0.974844i \(0.571548\pi\)
\(434\) 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 \(-0.508651\pi\)
0.879292 0.476282i \(-0.158016\pi\)
\(440\) −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 \(-0.632495\pi\)
−0.404331 + 0.914613i \(0.632495\pi\)
\(462\) 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 \(0.473403\pi\)
−0.904733 + 0.425978i \(0.859930\pi\)
\(468\) −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 \(0.0182909\pi\)
−0.449438 + 0.893311i \(0.648376\pi\)
\(480\) 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 \(-0.170630\pi\)
0.859732 + 0.510745i \(0.170630\pi\)
\(504\) 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 −0.910100 0.414389i \(-0.863995\pi\)
0.813921 + 0.580975i \(0.197329\pi\)
\(510\) 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 0.674626 0.738160i \(-0.264305\pi\)
−0.976578 + 0.215163i \(0.930972\pi\)
\(522\) 11.4087 + 19.7604i 0.499344 + 0.864890i
\(523\) 14.7417 25.5334i 0.644609 1.11650i −0.339782 0.940504i \(-0.610353\pi\)
0.984392 0.175992i \(-0.0563132\pi\)
\(524\) −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 0.719705 0.694280i \(-0.244277\pi\)
−0.961117 + 0.276142i \(0.910944\pi\)
\(564\) 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 0.865555 0.500814i \(-0.166966\pi\)
−0.866495 + 0.499185i \(0.833633\pi\)
\(578\) 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 \(-0.482162\pi\)
0.0560113 + 0.998430i \(0.482162\pi\)
\(588\) 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 −0.927246 0.374453i \(-0.877830\pi\)
0.787909 + 0.615792i \(0.211164\pi\)
\(594\) −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 \(-0.419047\pi\)
0.251589 + 0.967834i \(0.419047\pi\)
\(602\) 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 −0.632671 0.774421i \(-0.718042\pi\)
0.987003 + 0.160699i \(0.0513748\pi\)
\(608\) −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 0.853317 0.521393i \(-0.174587\pi\)
−0.878198 + 0.478298i \(0.841254\pi\)
\(620\) 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 \(-0.459070\pi\)
0.128231 + 0.991744i \(0.459070\pi\)
\(644\) 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 0.874678 0.484705i \(-0.161073\pi\)
−0.857106 + 0.515141i \(0.827740\pi\)
\(648\) 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 \(-0.876624\pi\)
0.135583 0.990766i \(-0.456709\pi\)
\(662\) 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 −0.515281 0.857021i \(-0.672312\pi\)
0.999843 + 0.0177358i \(0.00564578\pi\)
\(678\) −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 −0.981768 0.190084i \(-0.939124\pi\)
0.655501 + 0.755194i \(0.272457\pi\)
\(692\) −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 −0.720734 0.693211i \(-0.756195\pi\)
0.960706 + 0.277569i \(0.0895286\pi\)
\(720\) −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 \(-0.598567\pi\)
−0.304732 + 0.952438i \(0.598567\pi\)
\(728\) 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 −0.993867 0.110585i \(-0.964728\pi\)
0.592703 + 0.805421i \(0.298061\pi\)
\(734\) 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 −0.983177 0.182653i \(-0.941531\pi\)
0.649771 + 0.760130i \(0.274865\pi\)
\(762\) 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 \(-0.643629\pi\)
−0.436066 + 0.899914i \(0.643629\pi\)
\(770\) 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 0.946410 0.322967i \(-0.104680\pi\)
−0.752903 + 0.658131i \(0.771347\pi\)
\(774\) −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