Properties

Label 261.3.s.a.73.2
Level $261$
Weight $3$
Character 261.73
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 73.2
Character \(\chi\) \(=\) 261.73
Dual form 261.3.s.a.118.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.415096 + 0.0467701i) q^{2} +(-3.72959 + 0.851255i) q^{4} +(-0.738700 - 0.589093i) q^{5} +(-0.577468 + 2.53005i) q^{7} +(3.08546 - 1.07965i) q^{8} +O(q^{10})\) \(q+(-0.415096 + 0.0467701i) q^{2} +(-3.72959 + 0.851255i) q^{4} +(-0.738700 - 0.589093i) q^{5} +(-0.577468 + 2.53005i) q^{7} +(3.08546 - 1.07965i) q^{8} +(0.334184 + 0.209981i) q^{10} +(8.65125 + 3.02720i) q^{11} +(-4.51239 - 9.37008i) q^{13} +(0.121374 - 1.07722i) q^{14} +(12.5564 - 6.04684i) q^{16} +(-21.4949 - 21.4949i) q^{17} +(14.2589 - 22.6929i) q^{19} +(3.25652 + 1.56826i) q^{20} +(-3.73269 - 0.851961i) q^{22} +(2.27710 + 2.85539i) q^{23} +(-5.36438 - 23.5029i) q^{25} +(2.31132 + 3.67844i) q^{26} -9.92764i q^{28} +(24.3191 - 15.7981i) q^{29} +(21.7090 - 2.44602i) q^{31} +(-16.0007 + 10.0539i) q^{32} +(9.92777 + 7.91713i) q^{34} +(1.91701 - 1.52877i) q^{35} +(-46.0478 + 16.1128i) q^{37} +(-4.85746 + 10.0866i) q^{38} +(-2.91524 - 1.02009i) q^{40} +(25.3355 - 25.3355i) q^{41} +(2.78030 - 24.6759i) q^{43} +(-34.8426 - 3.92581i) q^{44} +(-1.07876 - 1.07876i) q^{46} +(-7.49184 + 21.4104i) q^{47} +(38.0798 + 18.3383i) q^{49} +(3.32597 + 9.50507i) q^{50} +(24.8057 + 31.1054i) q^{52} +(18.6271 - 23.3576i) q^{53} +(-4.60737 - 7.33259i) q^{55} +(0.949813 + 8.42982i) q^{56} +(-9.35591 + 7.69514i) q^{58} -18.2577 q^{59} +(-78.8333 + 49.5342i) q^{61} +(-8.89694 + 2.03067i) q^{62} +(-37.4125 + 29.8355i) q^{64} +(-2.18655 + 9.57990i) q^{65} +(24.5454 - 50.9691i) q^{67} +(98.4648 + 61.8696i) q^{68} +(-0.724244 + 0.724244i) q^{70} +(-56.1438 - 116.584i) q^{71} +(47.2614 + 5.32509i) q^{73} +(18.3607 - 8.84204i) q^{74} +(-33.8624 + 96.7732i) q^{76} +(-12.6548 + 20.1400i) q^{77} +(-13.7375 - 39.2594i) q^{79} +(-12.8375 - 2.93009i) q^{80} +(-9.33174 + 11.7016i) q^{82} +(29.4538 + 129.046i) q^{83} +(3.21577 + 28.5408i) q^{85} +10.3729i q^{86} +29.9614 q^{88} +(-32.3276 + 3.64244i) q^{89} +(26.3125 - 6.00567i) q^{91} +(-10.9233 - 8.71105i) q^{92} +(2.10847 - 9.23779i) q^{94} +(-23.9012 + 8.36341i) q^{95} +(-36.1089 - 22.6888i) q^{97} +(-16.6645 - 5.83115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{27}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.415096 + 0.0467701i −0.207548 + 0.0233851i −0.215126 0.976586i \(-0.569016\pi\)
0.00757815 + 0.999971i \(0.497588\pi\)
\(3\) 0 0
\(4\) −3.72959 + 0.851255i −0.932398 + 0.212814i
\(5\) −0.738700 0.589093i −0.147740 0.117819i 0.546831 0.837243i \(-0.315834\pi\)
−0.694571 + 0.719425i \(0.744406\pi\)
\(6\) 0 0
\(7\) −0.577468 + 2.53005i −0.0824954 + 0.361436i −0.999280 0.0379466i \(-0.987918\pi\)
0.916784 + 0.399383i \(0.130775\pi\)
\(8\) 3.08546 1.07965i 0.385682 0.134956i
\(9\) 0 0
\(10\) 0.334184 + 0.209981i 0.0334184 + 0.0209981i
\(11\) 8.65125 + 3.02720i 0.786477 + 0.275200i 0.693489 0.720467i \(-0.256072\pi\)
0.0929879 + 0.995667i \(0.470358\pi\)
\(12\) 0 0
\(13\) −4.51239 9.37008i −0.347107 0.720775i 0.652198 0.758049i \(-0.273847\pi\)
−0.999305 + 0.0372733i \(0.988133\pi\)
\(14\) 0.121374 1.07722i 0.00866957 0.0769445i
\(15\) 0 0
\(16\) 12.5564 6.04684i 0.784774 0.377927i
\(17\) −21.4949 21.4949i −1.26441 1.26441i −0.948936 0.315469i \(-0.897838\pi\)
−0.315469 0.948936i \(-0.602162\pi\)
\(18\) 0 0
\(19\) 14.2589 22.6929i 0.750467 1.19436i −0.225030 0.974352i \(-0.572248\pi\)
0.975498 0.220010i \(-0.0706090\pi\)
\(20\) 3.25652 + 1.56826i 0.162826 + 0.0784128i
\(21\) 0 0
\(22\) −3.73269 0.851961i −0.169668 0.0387255i
\(23\) 2.27710 + 2.85539i 0.0990042 + 0.124147i 0.828866 0.559448i \(-0.188987\pi\)
−0.729861 + 0.683595i \(0.760415\pi\)
\(24\) 0 0
\(25\) −5.36438 23.5029i −0.214575 0.940115i
\(26\) 2.31132 + 3.67844i 0.0888969 + 0.141479i
\(27\) 0 0
\(28\) 9.92764i 0.354558i
\(29\) 24.3191 15.7981i 0.838591 0.544761i
\(30\) 0 0
\(31\) 21.7090 2.44602i 0.700291 0.0789039i 0.245362 0.969431i \(-0.421093\pi\)
0.454929 + 0.890528i \(0.349665\pi\)
\(32\) −16.0007 + 10.0539i −0.500022 + 0.314185i
\(33\) 0 0
\(34\) 9.92777 + 7.91713i 0.291993 + 0.232857i
\(35\) 1.91701 1.52877i 0.0547718 0.0436790i
\(36\) 0 0
\(37\) −46.0478 + 16.1128i −1.24454 + 0.435482i −0.870608 0.491976i \(-0.836275\pi\)
−0.373927 + 0.927458i \(0.621989\pi\)
\(38\) −4.85746 + 10.0866i −0.127828 + 0.265437i
\(39\) 0 0
\(40\) −2.91524 1.02009i −0.0728810 0.0255021i
\(41\) 25.3355 25.3355i 0.617940 0.617940i −0.327063 0.945003i \(-0.606059\pi\)
0.945003 + 0.327063i \(0.106059\pi\)
\(42\) 0 0
\(43\) 2.78030 24.6759i 0.0646582 0.573857i −0.919057 0.394124i \(-0.871048\pi\)
0.983715 0.179733i \(-0.0575234\pi\)
\(44\) −34.8426 3.92581i −0.791877 0.0892231i
\(45\) 0 0
\(46\) −1.07876 1.07876i −0.0234513 0.0234513i
\(47\) −7.49184 + 21.4104i −0.159401 + 0.455541i −0.995690 0.0927479i \(-0.970435\pi\)
0.836289 + 0.548289i \(0.184721\pi\)
\(48\) 0 0
\(49\) 38.0798 + 18.3383i 0.777138 + 0.374250i
\(50\) 3.32597 + 9.50507i 0.0665193 + 0.190101i
\(51\) 0 0
\(52\) 24.8057 + 31.1054i 0.477033 + 0.598181i
\(53\) 18.6271 23.3576i 0.351454 0.440709i −0.574409 0.818568i \(-0.694768\pi\)
0.925863 + 0.377859i \(0.123340\pi\)
\(54\) 0 0
\(55\) −4.60737 7.33259i −0.0837704 0.133320i
\(56\) 0.949813 + 8.42982i 0.0169609 + 0.150533i
\(57\) 0 0
\(58\) −9.35591 + 7.69514i −0.161309 + 0.132675i
\(59\) −18.2577 −0.309453 −0.154726 0.987957i \(-0.549450\pi\)
−0.154726 + 0.987957i \(0.549450\pi\)
\(60\) 0 0
\(61\) −78.8333 + 49.5342i −1.29235 + 0.812037i −0.989987 0.141156i \(-0.954918\pi\)
−0.302362 + 0.953193i \(0.597775\pi\)
\(62\) −8.89694 + 2.03067i −0.143499 + 0.0327527i
\(63\) 0 0
\(64\) −37.4125 + 29.8355i −0.584570 + 0.466179i
\(65\) −2.18655 + 9.57990i −0.0336392 + 0.147383i
\(66\) 0 0
\(67\) 24.5454 50.9691i 0.366349 0.760732i −0.633567 0.773688i \(-0.718410\pi\)
0.999916 + 0.0129558i \(0.00412406\pi\)
\(68\) 98.4648 + 61.8696i 1.44801 + 0.909846i
\(69\) 0 0
\(70\) −0.724244 + 0.724244i −0.0103463 + 0.0103463i
\(71\) −56.1438 116.584i −0.790758 1.64203i −0.766436 0.642321i \(-0.777972\pi\)
−0.0243218 0.999704i \(-0.507743\pi\)
\(72\) 0 0
\(73\) 47.2614 + 5.32509i 0.647417 + 0.0729464i 0.429566 0.903036i \(-0.358667\pi\)
0.217851 + 0.975982i \(0.430095\pi\)
\(74\) 18.3607 8.84204i 0.248117 0.119487i
\(75\) 0 0
\(76\) −33.8624 + 96.7732i −0.445558 + 1.27333i
\(77\) −12.6548 + 20.1400i −0.164348 + 0.261558i
\(78\) 0 0
\(79\) −13.7375 39.2594i −0.173892 0.496954i 0.823644 0.567107i \(-0.191937\pi\)
−0.997536 + 0.0701522i \(0.977652\pi\)
\(80\) −12.8375 2.93009i −0.160469 0.0366261i
\(81\) 0 0
\(82\) −9.33174 + 11.7016i −0.113802 + 0.142703i
\(83\) 29.4538 + 129.046i 0.354865 + 1.55477i 0.765786 + 0.643095i \(0.222350\pi\)
−0.410921 + 0.911671i \(0.634793\pi\)
\(84\) 0 0
\(85\) 3.21577 + 28.5408i 0.0378326 + 0.335774i
\(86\) 10.3729i 0.120615i
\(87\) 0 0
\(88\) 29.9614 0.340470
\(89\) −32.3276 + 3.64244i −0.363231 + 0.0409263i −0.291694 0.956512i \(-0.594219\pi\)
−0.0715370 + 0.997438i \(0.522790\pi\)
\(90\) 0 0
\(91\) 26.3125 6.00567i 0.289149 0.0659963i
\(92\) −10.9233 8.71105i −0.118732 0.0946853i
\(93\) 0 0
\(94\) 2.10847 9.23779i 0.0224305 0.0982744i
\(95\) −23.9012 + 8.36341i −0.251592 + 0.0880359i
\(96\) 0 0
\(97\) −36.1089 22.6888i −0.372257 0.233905i 0.332890 0.942966i \(-0.391976\pi\)
−0.705147 + 0.709061i \(0.749119\pi\)
\(98\) −16.6645 5.83115i −0.170046 0.0595015i
\(99\) 0 0
\(100\) 40.0139 + 83.0897i 0.400139 + 0.830897i
\(101\) −10.9637 + 97.3053i −0.108551 + 0.963419i 0.814873 + 0.579639i \(0.196806\pi\)
−0.923425 + 0.383780i \(0.874622\pi\)
\(102\) 0 0
\(103\) −66.1244 + 31.8438i −0.641985 + 0.309164i −0.726405 0.687267i \(-0.758810\pi\)
0.0844205 + 0.996430i \(0.473096\pi\)
\(104\) −24.0392 24.0392i −0.231146 0.231146i
\(105\) 0 0
\(106\) −6.63959 + 10.5668i −0.0626376 + 0.0996872i
\(107\) −55.3820 26.6706i −0.517589 0.249258i 0.156805 0.987630i \(-0.449881\pi\)
−0.674394 + 0.738372i \(0.735595\pi\)
\(108\) 0 0
\(109\) 154.567 + 35.2790i 1.41805 + 0.323660i 0.861755 0.507325i \(-0.169366\pi\)
0.556294 + 0.830985i \(0.312223\pi\)
\(110\) 2.25545 + 2.82824i 0.0205041 + 0.0257113i
\(111\) 0 0
\(112\) 8.04790 + 35.2602i 0.0718562 + 0.314823i
\(113\) 46.5316 + 74.0546i 0.411784 + 0.655351i 0.986642 0.162902i \(-0.0520856\pi\)
−0.574858 + 0.818253i \(0.694943\pi\)
\(114\) 0 0
\(115\) 3.45070i 0.0300061i
\(116\) −77.2523 + 79.6222i −0.665968 + 0.686398i
\(117\) 0 0
\(118\) 7.57871 0.853915i 0.0642263 0.00723657i
\(119\) 66.7958 41.9706i 0.561309 0.352694i
\(120\) 0 0
\(121\) −28.9215 23.0641i −0.239020 0.190612i
\(122\) 30.4067 24.2485i 0.249235 0.198759i
\(123\) 0 0
\(124\) −78.8837 + 27.6026i −0.636159 + 0.222602i
\(125\) −20.1314 + 41.8033i −0.161051 + 0.334426i
\(126\) 0 0
\(127\) −171.713 60.0851i −1.35207 0.473111i −0.445546 0.895259i \(-0.646990\pi\)
−0.906527 + 0.422148i \(0.861276\pi\)
\(128\) 67.5837 67.5837i 0.527998 0.527998i
\(129\) 0 0
\(130\) 0.459576 4.07885i 0.00353520 0.0313757i
\(131\) 72.7489 + 8.19683i 0.555335 + 0.0625712i 0.385172 0.922845i \(-0.374142\pi\)
0.170163 + 0.985416i \(0.445571\pi\)
\(132\) 0 0
\(133\) 49.1801 + 49.1801i 0.369775 + 0.369775i
\(134\) −7.80488 + 22.3051i −0.0582454 + 0.166456i
\(135\) 0 0
\(136\) −89.5284 43.1146i −0.658297 0.317019i
\(137\) −65.2470 186.465i −0.476255 1.36106i −0.892188 0.451664i \(-0.850831\pi\)
0.415933 0.909395i \(-0.363455\pi\)
\(138\) 0 0
\(139\) −38.5551 48.3466i −0.277375 0.347817i 0.623557 0.781778i \(-0.285687\pi\)
−0.900932 + 0.433961i \(0.857116\pi\)
\(140\) −5.84830 + 7.33354i −0.0417736 + 0.0523824i
\(141\) 0 0
\(142\) 28.7577 + 45.7677i 0.202519 + 0.322308i
\(143\) −10.6727 94.7228i −0.0746343 0.662397i
\(144\) 0 0
\(145\) −27.2711 2.65621i −0.188076 0.0183187i
\(146\) −19.8671 −0.136076
\(147\) 0 0
\(148\) 158.023 99.2927i 1.06773 0.670897i
\(149\) 29.6561 6.76882i 0.199034 0.0454283i −0.121841 0.992550i \(-0.538880\pi\)
0.320876 + 0.947121i \(0.396023\pi\)
\(150\) 0 0
\(151\) 110.649 88.2399i 0.732777 0.584370i −0.184399 0.982851i \(-0.559034\pi\)
0.917177 + 0.398481i \(0.130463\pi\)
\(152\) 19.4948 85.4124i 0.128255 0.561924i
\(153\) 0 0
\(154\) 4.31101 8.95191i 0.0279936 0.0581293i
\(155\) −17.4774 10.9818i −0.112757 0.0708501i
\(156\) 0 0
\(157\) 19.5784 19.5784i 0.124703 0.124703i −0.642001 0.766704i \(-0.721895\pi\)
0.766704 + 0.642001i \(0.221895\pi\)
\(158\) 7.53854 + 15.6539i 0.0477123 + 0.0990755i
\(159\) 0 0
\(160\) 17.7424 + 1.99909i 0.110890 + 0.0124943i
\(161\) −8.53923 + 4.11228i −0.0530387 + 0.0255421i
\(162\) 0 0
\(163\) 34.1257 97.5257i 0.209360 0.598317i −0.790541 0.612410i \(-0.790200\pi\)
0.999901 + 0.0140927i \(0.00448600\pi\)
\(164\) −72.9242 + 116.058i −0.444660 + 0.707672i
\(165\) 0 0
\(166\) −18.2617 52.1888i −0.110010 0.314390i
\(167\) 262.410 + 59.8934i 1.57132 + 0.358643i 0.917414 0.397934i \(-0.130273\pi\)
0.653904 + 0.756577i \(0.273130\pi\)
\(168\) 0 0
\(169\) 37.9331 47.5666i 0.224456 0.281459i
\(170\) −2.66971 11.6968i −0.0157042 0.0688045i
\(171\) 0 0
\(172\) 10.6361 + 94.3977i 0.0618376 + 0.548824i
\(173\) 126.379i 0.730512i −0.930907 0.365256i \(-0.880981\pi\)
0.930907 0.365256i \(-0.119019\pi\)
\(174\) 0 0
\(175\) 62.5612 0.357493
\(176\) 126.933 14.3020i 0.721213 0.0812612i
\(177\) 0 0
\(178\) 13.2487 3.02393i 0.0744309 0.0169884i
\(179\) −220.984 176.229i −1.23455 0.984520i −0.999923 0.0124338i \(-0.996042\pi\)
−0.234626 0.972086i \(-0.575386\pi\)
\(180\) 0 0
\(181\) 51.3580 225.014i 0.283746 1.24317i −0.609204 0.793014i \(-0.708511\pi\)
0.892949 0.450157i \(-0.148632\pi\)
\(182\) −10.6414 + 3.72357i −0.0584690 + 0.0204592i
\(183\) 0 0
\(184\) 10.1087 + 6.35171i 0.0549386 + 0.0345202i
\(185\) 43.5075 + 15.2239i 0.235175 + 0.0822914i
\(186\) 0 0
\(187\) −120.888 251.027i −0.646461 1.34239i
\(188\) 9.71575 86.2297i 0.0516795 0.458669i
\(189\) 0 0
\(190\) 9.53017 4.58949i 0.0501588 0.0241552i
\(191\) −68.5806 68.5806i −0.359061 0.359061i 0.504406 0.863467i \(-0.331711\pi\)
−0.863467 + 0.504406i \(0.831711\pi\)
\(192\) 0 0
\(193\) −16.7176 + 26.6059i −0.0866198 + 0.137855i −0.887224 0.461339i \(-0.847369\pi\)
0.800604 + 0.599194i \(0.204512\pi\)
\(194\) 16.0499 + 7.72920i 0.0827312 + 0.0398413i
\(195\) 0 0
\(196\) −157.633 35.9786i −0.804248 0.183564i
\(197\) 63.4701 + 79.5889i 0.322183 + 0.404005i 0.916377 0.400317i \(-0.131100\pi\)
−0.594194 + 0.804322i \(0.702529\pi\)
\(198\) 0 0
\(199\) 34.8200 + 152.557i 0.174975 + 0.766616i 0.983902 + 0.178707i \(0.0571915\pi\)
−0.808927 + 0.587909i \(0.799951\pi\)
\(200\) −41.9264 66.7254i −0.209632 0.333627i
\(201\) 0 0
\(202\) 40.9039i 0.202494i
\(203\) 25.9264 + 70.6516i 0.127716 + 0.348037i
\(204\) 0 0
\(205\) −33.6403 + 3.79036i −0.164099 + 0.0184895i
\(206\) 25.9587 16.3109i 0.126013 0.0791792i
\(207\) 0 0
\(208\) −113.319 90.3686i −0.544801 0.434465i
\(209\) 192.053 153.157i 0.918914 0.732810i
\(210\) 0 0
\(211\) −19.1966 + 6.71718i −0.0909791 + 0.0318350i −0.375385 0.926869i \(-0.622489\pi\)
0.284406 + 0.958704i \(0.408204\pi\)
\(212\) −49.5881 + 102.971i −0.233906 + 0.485711i
\(213\) 0 0
\(214\) 24.2363 + 8.48064i 0.113254 + 0.0396291i
\(215\) −16.5902 + 16.5902i −0.0771637 + 0.0771637i
\(216\) 0 0
\(217\) −6.34771 + 56.3375i −0.0292521 + 0.259620i
\(218\) −65.8104 7.41505i −0.301882 0.0340140i
\(219\) 0 0
\(220\) 23.4255 + 23.4255i 0.106480 + 0.106480i
\(221\) −104.415 + 298.402i −0.472468 + 1.35024i
\(222\) 0 0
\(223\) 228.933 + 110.248i 1.02661 + 0.494387i 0.869884 0.493256i \(-0.164193\pi\)
0.156721 + 0.987643i \(0.449908\pi\)
\(224\) −16.1970 46.2884i −0.0723081 0.206645i
\(225\) 0 0
\(226\) −22.7787 28.5635i −0.100791 0.126387i
\(227\) −261.380 + 327.760i −1.15145 + 1.44388i −0.275617 + 0.961268i \(0.588882\pi\)
−0.875836 + 0.482609i \(0.839689\pi\)
\(228\) 0 0
\(229\) 140.386 + 223.424i 0.613041 + 0.975649i 0.998596 + 0.0529641i \(0.0168669\pi\)
−0.385556 + 0.922685i \(0.625990\pi\)
\(230\) 0.161390 + 1.43237i 0.000701694 + 0.00622771i
\(231\) 0 0
\(232\) 57.9793 75.0004i 0.249911 0.323277i
\(233\) −233.305 −1.00131 −0.500654 0.865648i \(-0.666907\pi\)
−0.500654 + 0.865648i \(0.666907\pi\)
\(234\) 0 0
\(235\) 18.1470 11.4025i 0.0772211 0.0485212i
\(236\) 68.0938 15.5420i 0.288533 0.0658558i
\(237\) 0 0
\(238\) −25.7637 + 20.5459i −0.108251 + 0.0863272i
\(239\) −37.0417 + 162.290i −0.154986 + 0.679038i 0.836406 + 0.548111i \(0.184653\pi\)
−0.991392 + 0.130928i \(0.958204\pi\)
\(240\) 0 0
\(241\) −119.624 + 248.401i −0.496363 + 1.03071i 0.490841 + 0.871249i \(0.336689\pi\)
−0.987204 + 0.159460i \(0.949025\pi\)
\(242\) 13.0839 + 8.22116i 0.0540657 + 0.0339717i
\(243\) 0 0
\(244\) 251.850 251.850i 1.03217 1.03217i
\(245\) −17.3266 35.9790i −0.0707207 0.146853i
\(246\) 0 0
\(247\) −276.976 31.2077i −1.12136 0.126347i
\(248\) 64.3414 30.9852i 0.259441 0.124940i
\(249\) 0 0
\(250\) 6.40133 18.2940i 0.0256053 0.0731758i
\(251\) 222.330 353.836i 0.885777 1.40971i −0.0262849 0.999654i \(-0.508368\pi\)
0.912062 0.410052i \(-0.134489\pi\)
\(252\) 0 0
\(253\) 11.0559 + 31.5959i 0.0436992 + 0.124885i
\(254\) 74.0878 + 16.9100i 0.291684 + 0.0665750i
\(255\) 0 0
\(256\) 94.4490 118.435i 0.368941 0.462638i
\(257\) −2.48412 10.8836i −0.00966583 0.0423487i 0.969865 0.243643i \(-0.0783425\pi\)
−0.979531 + 0.201294i \(0.935485\pi\)
\(258\) 0 0
\(259\) −14.1752 125.808i −0.0547303 0.485745i
\(260\) 37.5904i 0.144579i
\(261\) 0 0
\(262\) −30.5812 −0.116722
\(263\) 325.997 36.7310i 1.23953 0.139662i 0.532246 0.846590i \(-0.321348\pi\)
0.707285 + 0.706928i \(0.249920\pi\)
\(264\) 0 0
\(265\) −27.5196 + 6.28117i −0.103848 + 0.0237025i
\(266\) −22.7146 18.1143i −0.0853934 0.0680990i
\(267\) 0 0
\(268\) −48.1567 + 210.988i −0.179689 + 0.787270i
\(269\) −292.071 + 102.200i −1.08577 + 0.379926i −0.813066 0.582172i \(-0.802203\pi\)
−0.272702 + 0.962099i \(0.587917\pi\)
\(270\) 0 0
\(271\) 16.8213 + 10.5695i 0.0620712 + 0.0390019i 0.562710 0.826654i \(-0.309759\pi\)
−0.500639 + 0.865656i \(0.666902\pi\)
\(272\) −399.874 139.922i −1.47013 0.514419i
\(273\) 0 0
\(274\) 35.8048 + 74.3494i 0.130674 + 0.271348i
\(275\) 24.7394 219.568i 0.0899615 0.798430i
\(276\) 0 0
\(277\) −278.671 + 134.201i −1.00603 + 0.484480i −0.862981 0.505236i \(-0.831406\pi\)
−0.143051 + 0.989715i \(0.545691\pi\)
\(278\) 18.2653 + 18.2653i 0.0657024 + 0.0657024i
\(279\) 0 0
\(280\) 4.26433 6.78663i 0.0152297 0.0242380i
\(281\) 275.413 + 132.632i 0.980118 + 0.472000i 0.854146 0.520034i \(-0.174081\pi\)
0.125972 + 0.992034i \(0.459795\pi\)
\(282\) 0 0
\(283\) −104.652 23.8861i −0.369794 0.0844032i 0.0335853 0.999436i \(-0.489307\pi\)
−0.403380 + 0.915033i \(0.632165\pi\)
\(284\) 308.636 + 387.017i 1.08675 + 1.36274i
\(285\) 0 0
\(286\) 8.86040 + 38.8199i 0.0309804 + 0.135734i
\(287\) 49.4697 + 78.7306i 0.172368 + 0.274323i
\(288\) 0 0
\(289\) 635.060i 2.19744i
\(290\) 11.4444 0.172888i 0.0394633 0.000596165i
\(291\) 0 0
\(292\) −180.799 + 20.3712i −0.619175 + 0.0697642i
\(293\) 230.684 144.948i 0.787318 0.494705i −0.0773772 0.997002i \(-0.524655\pi\)
0.864695 + 0.502297i \(0.167512\pi\)
\(294\) 0 0
\(295\) 13.4870 + 10.7555i 0.0457185 + 0.0364593i
\(296\) −124.682 + 99.4308i −0.421224 + 0.335915i
\(297\) 0 0
\(298\) −11.9936 + 4.19673i −0.0402469 + 0.0140830i
\(299\) 16.4801 34.2212i 0.0551173 0.114452i
\(300\) 0 0
\(301\) 60.8257 + 21.2838i 0.202079 + 0.0707104i
\(302\) −41.8032 + 41.8032i −0.138421 + 0.138421i
\(303\) 0 0
\(304\) 41.8199 371.162i 0.137565 1.22093i
\(305\) 87.4144 + 9.84924i 0.286605 + 0.0322926i
\(306\) 0 0
\(307\) −134.403 134.403i −0.437796 0.437796i 0.453473 0.891270i \(-0.350185\pi\)
−0.891270 + 0.453473i \(0.850185\pi\)
\(308\) 30.0530 85.8865i 0.0975746 0.278852i
\(309\) 0 0
\(310\) 7.76842 + 3.74108i 0.0250594 + 0.0120680i
\(311\) −60.8757 173.973i −0.195742 0.559398i 0.803619 0.595144i \(-0.202905\pi\)
−0.999361 + 0.0357461i \(0.988619\pi\)
\(312\) 0 0
\(313\) 263.236 + 330.088i 0.841010 + 1.05459i 0.997756 + 0.0669540i \(0.0213281\pi\)
−0.156746 + 0.987639i \(0.550101\pi\)
\(314\) −7.21125 + 9.04262i −0.0229658 + 0.0287981i
\(315\) 0 0
\(316\) 84.6549 + 134.728i 0.267895 + 0.426353i
\(317\) 45.6880 + 405.492i 0.144126 + 1.27915i 0.832592 + 0.553886i \(0.186856\pi\)
−0.688466 + 0.725268i \(0.741716\pi\)
\(318\) 0 0
\(319\) 258.215 63.0541i 0.809451 0.197662i
\(320\) 45.2125 0.141289
\(321\) 0 0
\(322\) 3.35227 2.10637i 0.0104108 0.00654153i
\(323\) −794.274 + 181.288i −2.45905 + 0.561263i
\(324\) 0 0
\(325\) −196.018 + 156.319i −0.603131 + 0.480981i
\(326\) −9.60417 + 42.0786i −0.0294607 + 0.129076i
\(327\) 0 0
\(328\) 50.8182 105.525i 0.154934 0.321723i
\(329\) −49.8432 31.3186i −0.151499 0.0951932i
\(330\) 0 0
\(331\) 53.9759 53.9759i 0.163069 0.163069i −0.620856 0.783925i \(-0.713215\pi\)
0.783925 + 0.620856i \(0.213215\pi\)
\(332\) −219.702 456.215i −0.661752 1.37414i
\(333\) 0 0
\(334\) −111.727 12.5886i −0.334511 0.0376904i
\(335\) −48.1572 + 23.1913i −0.143753 + 0.0692277i
\(336\) 0 0
\(337\) −100.512 + 287.246i −0.298255 + 0.852363i 0.693063 + 0.720877i \(0.256261\pi\)
−0.991318 + 0.131486i \(0.958025\pi\)
\(338\) −13.5212 + 21.5189i −0.0400035 + 0.0636652i
\(339\) 0 0
\(340\) −36.2890 103.708i −0.106732 0.305024i
\(341\) 195.215 + 44.5565i 0.572478 + 0.130664i
\(342\) 0 0
\(343\) −147.670 + 185.172i −0.430525 + 0.539861i
\(344\) −18.0627 79.1380i −0.0525080 0.230052i
\(345\) 0 0
\(346\) 5.91075 + 52.4593i 0.0170831 + 0.151617i
\(347\) 3.76060i 0.0108375i −0.999985 0.00541873i \(-0.998275\pi\)
0.999985 0.00541873i \(-0.00172484\pi\)
\(348\) 0 0
\(349\) 227.541 0.651979 0.325989 0.945373i \(-0.394303\pi\)
0.325989 + 0.945373i \(0.394303\pi\)
\(350\) −25.9689 + 2.92600i −0.0741970 + 0.00835999i
\(351\) 0 0
\(352\) −168.861 + 38.5415i −0.479720 + 0.109493i
\(353\) 317.199 + 252.957i 0.898579 + 0.716593i 0.959548 0.281547i \(-0.0908474\pi\)
−0.0609682 + 0.998140i \(0.519419\pi\)
\(354\) 0 0
\(355\) −27.2053 + 119.194i −0.0766347 + 0.335759i
\(356\) 117.468 41.1039i 0.329967 0.115460i
\(357\) 0 0
\(358\) 99.9720 + 62.8166i 0.279251 + 0.175465i
\(359\) 237.999 + 83.2794i 0.662949 + 0.231976i 0.640717 0.767777i \(-0.278637\pi\)
0.0222319 + 0.999753i \(0.492923\pi\)
\(360\) 0 0
\(361\) −155.019 321.900i −0.429415 0.891690i
\(362\) −10.7946 + 95.8045i −0.0298193 + 0.264653i
\(363\) 0 0
\(364\) −93.0227 + 44.7974i −0.255557 + 0.123070i
\(365\) −31.7750 31.7750i −0.0870549 0.0870549i
\(366\) 0 0
\(367\) −246.647 + 392.537i −0.672063 + 1.06958i 0.320429 + 0.947273i \(0.396173\pi\)
−0.992492 + 0.122310i \(0.960970\pi\)
\(368\) 45.8582 + 22.0841i 0.124615 + 0.0600112i
\(369\) 0 0
\(370\) −18.7718 4.28454i −0.0507346 0.0115799i
\(371\) 48.3394 + 60.6157i 0.130295 + 0.163385i
\(372\) 0 0
\(373\) −55.7998 244.475i −0.149597 0.655429i −0.992997 0.118142i \(-0.962306\pi\)
0.843399 0.537287i \(-0.180551\pi\)
\(374\) 61.9209 + 98.5465i 0.165564 + 0.263493i
\(375\) 0 0
\(376\) 74.1495i 0.197206i
\(377\) −257.767 156.585i −0.683731 0.415345i
\(378\) 0 0
\(379\) 487.332 54.9091i 1.28584 0.144879i 0.557545 0.830147i \(-0.311743\pi\)
0.728291 + 0.685268i \(0.240315\pi\)
\(380\) 82.0226 51.5382i 0.215849 0.135627i
\(381\) 0 0
\(382\) 31.6751 + 25.2600i 0.0829190 + 0.0661257i
\(383\) −172.689 + 137.715i −0.450886 + 0.359570i −0.822450 0.568838i \(-0.807393\pi\)
0.371564 + 0.928407i \(0.378822\pi\)
\(384\) 0 0
\(385\) 21.2124 7.42255i 0.0550972 0.0192794i
\(386\) 5.69506 11.8259i 0.0147540 0.0306371i
\(387\) 0 0
\(388\) 153.986 + 53.8819i 0.396870 + 0.138871i
\(389\) 291.445 291.445i 0.749217 0.749217i −0.225115 0.974332i \(-0.572276\pi\)
0.974332 + 0.225115i \(0.0722759\pi\)
\(390\) 0 0
\(391\) 12.4303 110.322i 0.0317911 0.282154i
\(392\) 137.292 + 15.4691i 0.350236 + 0.0394621i
\(393\) 0 0
\(394\) −30.0686 30.0686i −0.0763162 0.0763162i
\(395\) −12.9796 + 37.0935i −0.0328597 + 0.0939077i
\(396\) 0 0
\(397\) −65.4912 31.5389i −0.164965 0.0794430i 0.349579 0.936907i \(-0.386325\pi\)
−0.514544 + 0.857464i \(0.672039\pi\)
\(398\) −21.5888 61.6972i −0.0542431 0.155018i
\(399\) 0 0
\(400\) −209.475 262.674i −0.523688 0.656684i
\(401\) −324.268 + 406.619i −0.808649 + 1.01401i 0.190826 + 0.981624i \(0.438883\pi\)
−0.999475 + 0.0323898i \(0.989688\pi\)
\(402\) 0 0
\(403\) −120.879 192.378i −0.299948 0.477365i
\(404\) −41.9416 372.242i −0.103816 0.921392i
\(405\) 0 0
\(406\) −14.0663 28.1146i −0.0346462 0.0692479i
\(407\) −447.148 −1.09864
\(408\) 0 0
\(409\) 250.417 157.347i 0.612266 0.384712i −0.189909 0.981802i \(-0.560819\pi\)
0.802174 + 0.597090i \(0.203676\pi\)
\(410\) 13.7867 3.14673i 0.0336261 0.00767494i
\(411\) 0 0
\(412\) 219.510 175.053i 0.532791 0.424887i
\(413\) 10.5432 46.1929i 0.0255284 0.111847i
\(414\) 0 0
\(415\) 54.2624 112.677i 0.130753 0.271511i
\(416\) 166.407 + 104.561i 0.400018 + 0.251348i
\(417\) 0 0
\(418\) −72.5574 + 72.5574i −0.173582 + 0.173582i
\(419\) −59.7192 124.008i −0.142528 0.295962i 0.817469 0.575972i \(-0.195376\pi\)
−0.959997 + 0.280010i \(0.909662\pi\)
\(420\) 0 0
\(421\) 432.517 + 48.7330i 1.02736 + 0.115755i 0.609523 0.792768i \(-0.291361\pi\)
0.417833 + 0.908524i \(0.362790\pi\)
\(422\) 7.65428 3.68611i 0.0181381 0.00873485i
\(423\) 0 0
\(424\) 32.2550 92.1795i 0.0760731 0.217404i
\(425\) −389.885 + 620.498i −0.917376 + 1.46000i
\(426\) 0 0
\(427\) −79.8005 228.057i −0.186886 0.534091i
\(428\) 229.256 + 52.3262i 0.535645 + 0.122257i
\(429\) 0 0
\(430\) 6.11061 7.66246i 0.0142107 0.0178197i
\(431\) −38.3560 168.049i −0.0889930 0.389904i 0.910741 0.412979i \(-0.135512\pi\)
−0.999734 + 0.0230748i \(0.992654\pi\)
\(432\) 0 0
\(433\) 5.55493 + 49.3014i 0.0128289 + 0.113860i 0.998495 0.0548506i \(-0.0174682\pi\)
−0.985666 + 0.168711i \(0.946040\pi\)
\(434\) 23.6824i 0.0545677i
\(435\) 0 0
\(436\) −606.505 −1.39107
\(437\) 97.2658 10.9592i 0.222576 0.0250783i
\(438\) 0 0
\(439\) 190.067 43.3816i 0.432955 0.0988191i −0.000488576 1.00000i \(-0.500156\pi\)
0.433443 + 0.901181i \(0.357298\pi\)
\(440\) −22.1324 17.6500i −0.0503010 0.0401137i
\(441\) 0 0
\(442\) 29.3862 128.749i 0.0664845 0.291288i
\(443\) 228.033 79.7920i 0.514746 0.180117i −0.0603905 0.998175i \(-0.519235\pi\)
0.575137 + 0.818057i \(0.304949\pi\)
\(444\) 0 0
\(445\) 26.0261 + 16.3533i 0.0584856 + 0.0367490i
\(446\) −100.186 35.0565i −0.224631 0.0786019i
\(447\) 0 0
\(448\) −53.8807 111.884i −0.120269 0.249742i
\(449\) 55.8565 495.740i 0.124402 1.10410i −0.764059 0.645147i \(-0.776796\pi\)
0.888461 0.458952i \(-0.151775\pi\)
\(450\) 0 0
\(451\) 295.880 142.488i 0.656053 0.315938i
\(452\) −236.583 236.583i −0.523415 0.523415i
\(453\) 0 0
\(454\) 93.1685 148.277i 0.205217 0.326601i
\(455\) −22.9750 11.0642i −0.0504944 0.0243168i
\(456\) 0 0
\(457\) 204.659 + 46.7120i 0.447831 + 0.102215i 0.440488 0.897759i \(-0.354805\pi\)
0.00734312 + 0.999973i \(0.497663\pi\)
\(458\) −68.7234 86.1764i −0.150051 0.188158i
\(459\) 0 0
\(460\) 2.93743 + 12.8697i 0.00638571 + 0.0279776i
\(461\) 129.473 + 206.054i 0.280852 + 0.446973i 0.957124 0.289679i \(-0.0935486\pi\)
−0.676272 + 0.736652i \(0.736406\pi\)
\(462\) 0 0
\(463\) 710.071i 1.53363i −0.641868 0.766815i \(-0.721840\pi\)
0.641868 0.766815i \(-0.278160\pi\)
\(464\) 209.832 345.421i 0.452225 0.744441i
\(465\) 0 0
\(466\) 96.8439 10.9117i 0.207820 0.0234156i
\(467\) 676.037 424.782i 1.44762 0.909598i 0.447735 0.894166i \(-0.352231\pi\)
0.999881 0.0154315i \(-0.00491219\pi\)
\(468\) 0 0
\(469\) 114.780 + 91.5341i 0.244734 + 0.195169i
\(470\) −6.99944 + 5.58187i −0.0148924 + 0.0118763i
\(471\) 0 0
\(472\) −56.3333 + 19.7119i −0.119350 + 0.0417625i
\(473\) 98.7519 205.061i 0.208778 0.433532i
\(474\) 0 0
\(475\) −609.838 213.391i −1.28387 0.449245i
\(476\) −213.393 + 213.393i −0.448306 + 0.448306i
\(477\) 0 0
\(478\) 7.78553 69.0985i 0.0162877 0.144558i
\(479\) 483.953 + 54.5284i 1.01034 + 0.113838i 0.601587 0.798807i \(-0.294535\pi\)
0.408753 + 0.912645i \(0.365964\pi\)
\(480\) 0 0
\(481\) 358.764 + 358.764i 0.745872 + 0.745872i
\(482\) 38.0376 108.705i 0.0789161 0.225529i
\(483\) 0 0
\(484\) 127.499 + 61.4001i 0.263427 + 0.126860i
\(485\) 13.3079 + 38.0317i 0.0274389 + 0.0784159i
\(486\) 0 0
\(487\) −72.6889 91.1490i −0.149259 0.187164i 0.701581 0.712589i \(-0.252478\pi\)
−0.850840 + 0.525425i \(0.823906\pi\)
\(488\) −189.757 + 237.948i −0.388847 + 0.487598i
\(489\) 0 0
\(490\) 8.87495 + 14.1244i 0.0181121 + 0.0288253i
\(491\) −75.7150 671.989i −0.154206 1.36861i −0.797650 0.603120i \(-0.793924\pi\)
0.643445 0.765493i \(-0.277505\pi\)
\(492\) 0 0
\(493\) −862.315 183.159i −1.74912 0.371520i
\(494\) 116.431 0.235691
\(495\) 0 0
\(496\) 257.796 161.984i 0.519751 0.326581i
\(497\) 327.384 74.7233i 0.658721 0.150349i
\(498\) 0 0
\(499\) −611.573 + 487.713i −1.22560 + 0.977381i −0.225602 + 0.974220i \(0.572435\pi\)
−0.999995 + 0.00316117i \(0.998994\pi\)
\(500\) 39.4967 173.046i 0.0789934 0.346093i
\(501\) 0 0
\(502\) −75.7395 + 157.275i −0.150875 + 0.313296i
\(503\) 418.298 + 262.834i 0.831606 + 0.522533i 0.879266 0.476331i \(-0.158033\pi\)
−0.0476598 + 0.998864i \(0.515176\pi\)
\(504\) 0 0
\(505\) 65.4208 65.4208i 0.129546 0.129546i
\(506\) −6.06701 12.5983i −0.0119901 0.0248978i
\(507\) 0 0
\(508\) 691.569 + 77.9211i 1.36136 + 0.153388i
\(509\) −658.293 + 317.017i −1.29331 + 0.622823i −0.948775 0.315952i \(-0.897676\pi\)
−0.344531 + 0.938775i \(0.611962\pi\)
\(510\) 0 0
\(511\) −40.7647 + 116.499i −0.0797744 + 0.227982i
\(512\) −237.068 + 377.292i −0.463023 + 0.736898i
\(513\) 0 0
\(514\) 1.54018 + 4.40157i 0.00299645 + 0.00856337i
\(515\) 67.6051 + 15.4304i 0.131272 + 0.0299620i
\(516\) 0 0
\(517\) −129.627 + 162.548i −0.250730 + 0.314406i
\(518\) 11.7681 + 51.5595i 0.0227184 + 0.0995356i
\(519\) 0 0
\(520\) 3.59641 + 31.9190i 0.00691618 + 0.0613828i
\(521\) 412.503i 0.791753i 0.918304 + 0.395876i \(0.129559\pi\)
−0.918304 + 0.395876i \(0.870441\pi\)
\(522\) 0 0
\(523\) −54.7428 −0.104671 −0.0523354 0.998630i \(-0.516666\pi\)
−0.0523354 + 0.998630i \(0.516666\pi\)
\(524\) −278.301 + 31.3570i −0.531110 + 0.0598417i
\(525\) 0 0
\(526\) −133.602 + 30.4938i −0.253996 + 0.0579730i
\(527\) −519.210 414.056i −0.985219 0.785686i
\(528\) 0 0
\(529\) 114.745 502.733i 0.216910 0.950346i
\(530\) 11.1295 3.89439i 0.0209991 0.00734790i
\(531\) 0 0
\(532\) −225.287 141.557i −0.423471 0.266084i
\(533\) −351.720 123.072i −0.659887 0.230904i
\(534\) 0 0
\(535\) 25.1992 + 52.3267i 0.0471013 + 0.0978069i
\(536\) 20.7051 183.763i 0.0386290 0.342842i
\(537\) 0 0
\(538\) 116.458 56.0832i 0.216465 0.104244i
\(539\) 273.924 + 273.924i 0.508208 + 0.508208i
\(540\) 0 0
\(541\) −6.00071 + 9.55008i −0.0110919 + 0.0176526i −0.852224 0.523177i \(-0.824747\pi\)
0.841132 + 0.540829i \(0.181890\pi\)
\(542\) −7.47680 3.60064i −0.0137948 0.00664324i
\(543\) 0 0
\(544\) 560.041 + 127.826i 1.02949 + 0.234974i
\(545\) −93.3962 117.115i −0.171369 0.214890i
\(546\) 0 0
\(547\) −11.9903 52.5331i −0.0219202 0.0960385i 0.962785 0.270270i \(-0.0871130\pi\)
−0.984705 + 0.174232i \(0.944256\pi\)
\(548\) 402.074 + 639.897i 0.733712 + 1.16770i
\(549\) 0 0
\(550\) 92.2991i 0.167817i
\(551\) −11.7400 777.134i −0.0213068 1.41041i
\(552\) 0 0
\(553\) 107.261 12.0854i 0.193962 0.0218543i
\(554\) 109.399 68.7398i 0.197471 0.124079i
\(555\) 0 0
\(556\) 184.950 + 147.493i 0.332644 + 0.265275i
\(557\) −543.971 + 433.802i −0.976608 + 0.778819i −0.975233 0.221180i \(-0.929009\pi\)
−0.00137506 + 0.999999i \(0.500438\pi\)
\(558\) 0 0
\(559\) −243.761 + 85.2955i −0.436066 + 0.152586i
\(560\) 14.8265 30.7876i 0.0264760 0.0549779i
\(561\) 0 0
\(562\) −120.526 42.1740i −0.214460 0.0750426i
\(563\) 319.915 319.915i 0.568233 0.568233i −0.363400 0.931633i \(-0.618384\pi\)
0.931633 + 0.363400i \(0.118384\pi\)
\(564\) 0 0
\(565\) 9.25221 82.1156i 0.0163756 0.145337i
\(566\) 44.5578 + 5.02045i 0.0787239 + 0.00887006i
\(567\) 0 0
\(568\) −299.099 299.099i −0.526582 0.526582i
\(569\) −173.583 + 496.072i −0.305067 + 0.871832i 0.684660 + 0.728863i \(0.259951\pi\)
−0.989727 + 0.142969i \(0.954335\pi\)
\(570\) 0 0
\(571\) 619.219 + 298.200i 1.08445 + 0.522242i 0.888736 0.458419i \(-0.151584\pi\)
0.195711 + 0.980662i \(0.437299\pi\)
\(572\) 120.438 + 344.192i 0.210556 + 0.601735i
\(573\) 0 0
\(574\) −24.2170 30.3671i −0.0421898 0.0529044i
\(575\) 54.8946 68.8357i 0.0954689 0.119714i
\(576\) 0 0
\(577\) −30.2263 48.1049i −0.0523853 0.0833707i 0.819505 0.573072i \(-0.194249\pi\)
−0.871890 + 0.489702i \(0.837106\pi\)
\(578\) −29.7019 263.611i −0.0513873 0.456075i
\(579\) 0 0
\(580\) 103.971 13.3081i 0.179261 0.0229449i
\(581\) −343.501 −0.591223
\(582\) 0 0
\(583\) 231.855 145.684i 0.397694 0.249888i
\(584\) 151.572 34.5954i 0.259542 0.0592387i
\(585\) 0 0
\(586\) −88.9769 + 70.9567i −0.151838 + 0.121087i
\(587\) 71.8016 314.583i 0.122320 0.535917i −0.876221 0.481910i \(-0.839943\pi\)
0.998541 0.0540076i \(-0.0171995\pi\)
\(588\) 0 0
\(589\) 254.039 527.518i 0.431306 0.895616i
\(590\) −6.10142 3.83378i −0.0103414 0.00649793i
\(591\) 0 0
\(592\) −480.762 + 480.762i −0.812099 + 0.812099i
\(593\) −209.288 434.591i −0.352931 0.732869i 0.646621 0.762812i \(-0.276182\pi\)
−0.999552 + 0.0299430i \(0.990467\pi\)
\(594\) 0 0
\(595\) −74.0666 8.34530i −0.124482 0.0140257i
\(596\) −104.843 + 50.4899i −0.175912 + 0.0847146i
\(597\) 0 0
\(598\) −5.24029 + 14.9759i −0.00876302 + 0.0250433i
\(599\) −452.046 + 719.427i −0.754668 + 1.20105i 0.219586 + 0.975593i \(0.429529\pi\)
−0.974254 + 0.225454i \(0.927613\pi\)
\(600\) 0 0
\(601\) 241.988 + 691.562i 0.402642 + 1.15069i 0.949584 + 0.313514i \(0.101506\pi\)
−0.546941 + 0.837171i \(0.684208\pi\)
\(602\) −26.2440 5.99001i −0.0435946 0.00995019i
\(603\) 0 0
\(604\) −337.563 + 423.290i −0.558878 + 0.700811i
\(605\) 7.77737 + 34.0749i 0.0128552 + 0.0563221i
\(606\) 0 0
\(607\) −27.7513 246.300i −0.0457188 0.405766i −0.995640 0.0932767i \(-0.970266\pi\)
0.949921 0.312489i \(-0.101163\pi\)
\(608\) 506.460i 0.832993i
\(609\) 0 0
\(610\) −36.7461 −0.0602395
\(611\) 234.424 26.4132i 0.383672 0.0432295i
\(612\) 0 0
\(613\) 1.19680 0.273162i 0.00195236 0.000445614i −0.221545 0.975150i \(-0.571110\pi\)
0.223497 + 0.974705i \(0.428253\pi\)
\(614\) 62.0765 + 49.5043i 0.101102 + 0.0806260i
\(615\) 0 0
\(616\) −17.3017 + 75.8038i −0.0280872 + 0.123058i
\(617\) 285.233 99.8075i 0.462291 0.161762i −0.0890772 0.996025i \(-0.528392\pi\)
0.551368 + 0.834262i \(0.314106\pi\)
\(618\) 0 0
\(619\) −272.432 171.181i −0.440117 0.276544i 0.293691 0.955900i \(-0.405116\pi\)
−0.733808 + 0.679356i \(0.762259\pi\)
\(620\) 74.5319 + 26.0798i 0.120213 + 0.0420642i
\(621\) 0 0
\(622\) 33.4060 + 69.3683i 0.0537074 + 0.111525i
\(623\) 9.45256 83.8938i 0.0151727 0.134661i
\(624\) 0 0
\(625\) −503.501 + 242.473i −0.805601 + 0.387957i
\(626\) −124.707 124.707i −0.199212 0.199212i
\(627\) 0 0
\(628\) −56.3533 + 89.6858i −0.0897346 + 0.142812i
\(629\) 1336.14 + 643.449i 2.12422 + 1.02297i
\(630\) 0 0
\(631\) 680.376 + 155.291i 1.07825 + 0.246103i 0.724527 0.689247i \(-0.242058\pi\)
0.353723 + 0.935350i \(0.384916\pi\)
\(632\) −84.7726 106.301i −0.134134 0.168199i
\(633\) 0 0
\(634\) −37.9298 166.181i −0.0598262 0.262116i
\(635\) 91.4488 + 145.540i 0.144014 + 0.229197i
\(636\) 0 0
\(637\) 439.560i 0.690047i
\(638\) −104.235 + 38.2503i −0.163378 + 0.0599534i
\(639\) 0 0
\(640\) −89.7372 + 10.1110i −0.140214 + 0.0157984i
\(641\) 989.853 621.966i 1.54423 0.970306i 0.553748 0.832684i \(-0.313197\pi\)
0.990485 0.137621i \(-0.0439457\pi\)
\(642\) 0 0
\(643\) −234.086 186.677i −0.364052 0.290322i 0.424330 0.905508i \(-0.360510\pi\)
−0.788382 + 0.615186i \(0.789081\pi\)
\(644\) 28.3473 22.6062i 0.0440175 0.0351028i
\(645\) 0 0
\(646\) 321.221 112.400i 0.497247 0.173994i
\(647\) −493.455 + 1024.67i −0.762681 + 1.58372i 0.0484269 + 0.998827i \(0.484579\pi\)
−0.811108 + 0.584897i \(0.801135\pi\)
\(648\) 0 0
\(649\) −157.952 55.2698i −0.243377 0.0851614i
\(650\) 74.0552 74.0552i 0.113931 0.113931i
\(651\) 0 0
\(652\) −44.2558 + 392.781i −0.0678770 + 0.602425i
\(653\) −609.259 68.6470i −0.933015 0.105126i −0.367648 0.929965i \(-0.619837\pi\)
−0.565367 + 0.824839i \(0.691265\pi\)
\(654\) 0 0
\(655\) −48.9109 48.9109i −0.0746731 0.0746731i
\(656\) 164.923 471.322i 0.251407 0.718479i
\(657\) 0 0
\(658\) 22.1545 + 10.6691i 0.0336695 + 0.0162144i
\(659\) −176.059 503.147i −0.267161 0.763501i −0.996820 0.0796900i \(-0.974607\pi\)
0.729659 0.683811i \(-0.239679\pi\)
\(660\) 0 0
\(661\) 620.208 + 777.717i 0.938288 + 1.17658i 0.984098 + 0.177626i \(0.0568417\pi\)
−0.0458100 + 0.998950i \(0.514587\pi\)
\(662\) −19.8808 + 24.9297i −0.0300314 + 0.0376581i
\(663\) 0 0
\(664\) 230.202 + 366.365i 0.346690 + 0.551754i
\(665\) −7.35765 65.3010i −0.0110641 0.0981970i
\(666\) 0 0
\(667\) 100.487 + 33.4669i 0.150655 + 0.0501752i
\(668\) −1029.67 −1.54142
\(669\) 0 0
\(670\) 18.9052 11.8789i 0.0282168 0.0177298i
\(671\) −831.957 + 189.889i −1.23988 + 0.282994i
\(672\) 0 0
\(673\) 314.226 250.587i 0.466903 0.372343i −0.361594 0.932336i \(-0.617767\pi\)
0.828498 + 0.559992i \(0.189196\pi\)
\(674\) 28.2876 123.936i 0.0419697 0.183881i
\(675\) 0 0
\(676\) −100.984 + 209.695i −0.149384 + 0.310199i
\(677\) −424.331 266.625i −0.626781 0.393833i 0.180858 0.983509i \(-0.442112\pi\)
−0.807640 + 0.589676i \(0.799255\pi\)
\(678\) 0 0
\(679\) 78.2555 78.2555i 0.115251 0.115251i
\(680\) 40.7361 + 84.5893i 0.0599060 + 0.124396i
\(681\) 0 0
\(682\) −83.1169 9.36503i −0.121872 0.0137317i
\(683\) 344.482 165.894i 0.504366 0.242890i −0.164358 0.986401i \(-0.552555\pi\)
0.668724 + 0.743511i \(0.266841\pi\)
\(684\) 0 0
\(685\) −61.6474 + 176.178i −0.0899963 + 0.257195i
\(686\) 52.6368 83.7709i 0.0767300 0.122115i
\(687\) 0 0
\(688\) −114.300 326.652i −0.166134 0.474784i
\(689\) −302.915 69.1384i −0.439645 0.100346i
\(690\) 0 0
\(691\) −495.980 + 621.939i −0.717771 + 0.900056i −0.998209 0.0598158i \(-0.980949\pi\)
0.280439 + 0.959872i \(0.409520\pi\)
\(692\) 107.580 + 471.341i 0.155463 + 0.681129i
\(693\) 0 0
\(694\) 0.175884 + 1.56101i 0.000253435 + 0.00224930i
\(695\) 58.4262i 0.0840664i
\(696\) 0 0
\(697\) −1089.17 −1.56265
\(698\) −94.4513 + 10.6421i −0.135317 + 0.0152466i
\(699\) 0 0
\(700\) −233.328 + 53.2556i −0.333326 + 0.0760794i
\(701\) 825.456 + 658.279i 1.17754 + 0.939057i 0.998993 0.0448739i \(-0.0142886\pi\)
0.178548 + 0.983931i \(0.442860\pi\)
\(702\) 0 0
\(703\) −290.944 + 1274.71i −0.413860 + 1.81324i
\(704\) −413.983 + 144.859i −0.588044 + 0.205765i
\(705\) 0 0
\(706\) −143.499 90.1663i −0.203256 0.127714i
\(707\) −239.856 83.9294i −0.339259 0.118712i
\(708\) 0 0
\(709\) 313.200 + 650.367i 0.441749 + 0.917301i 0.996364 + 0.0851945i \(0.0271512\pi\)
−0.554615 + 0.832107i \(0.687135\pi\)
\(710\) 5.71810 50.7495i 0.00805366 0.0714782i
\(711\) 0 0
\(712\) −95.8127 + 46.1410i −0.134568 + 0.0648048i
\(713\) 56.4179 + 56.4179i 0.0791275 + 0.0791275i
\(714\) 0 0
\(715\) −47.9167 + 76.2589i −0.0670163 + 0.106656i
\(716\) 974.197 + 469.149i 1.36061 + 0.655236i
\(717\) 0 0
\(718\) −102.687 23.4377i −0.143019 0.0326431i
\(719\) 684.608 + 858.472i 0.952167 + 1.19398i 0.980924 + 0.194394i \(0.0622739\pi\)
−0.0287562 + 0.999586i \(0.509155\pi\)
\(720\) 0 0
\(721\) −42.3818 185.687i −0.0587820 0.257541i
\(722\) 79.4031 + 126.369i 0.109977 + 0.175027i
\(723\) 0 0
\(724\) 882.929i 1.21952i
\(725\) −501.757 486.823i −0.692079 0.671480i
\(726\) 0 0
\(727\) 31.1294 3.50744i 0.0428190 0.00482454i −0.0905290 0.995894i \(-0.528856\pi\)
0.133348 + 0.991069i \(0.457427\pi\)
\(728\) 74.7022 46.9385i 0.102613 0.0644759i
\(729\) 0 0
\(730\) 14.6758 + 11.7036i 0.0201039 + 0.0160323i
\(731\) −590.167 + 470.643i −0.807342 + 0.643834i
\(732\) 0 0
\(733\) 143.446 50.1941i 0.195698 0.0684776i −0.230651 0.973037i \(-0.574085\pi\)
0.426348 + 0.904559i \(0.359800\pi\)
\(734\) 84.0234 174.476i 0.114473 0.237706i
\(735\) 0 0
\(736\) −65.1430 22.7945i −0.0885095 0.0309708i
\(737\) 366.642 366.642i 0.497479 0.497479i
\(738\) 0 0
\(739\) 125.579 1114.55i 0.169931 1.50818i −0.562191 0.827008i \(-0.690041\pi\)
0.732122 0.681174i \(-0.238530\pi\)
\(740\) −175.225 19.7431i −0.236790 0.0266798i
\(741\) 0 0
\(742\) −22.9005 22.9005i −0.0308632 0.0308632i
\(743\) 63.5004 181.474i 0.0854649 0.244245i −0.893217 0.449625i \(-0.851558\pi\)
0.978682 + 0.205381i \(0.0658432\pi\)
\(744\) 0 0
\(745\) −25.8944 12.4701i −0.0347576 0.0167384i
\(746\) 34.5965 + 98.8710i 0.0463759 + 0.132535i
\(747\) 0 0
\(748\) 664.552 + 833.322i 0.888439 + 1.11407i
\(749\) 99.4592 124.718i 0.132789 0.166513i
\(750\) 0 0
\(751\) −192.970 307.110i −0.256950 0.408934i 0.693191 0.720754i \(-0.256204\pi\)
−0.950141 + 0.311820i \(0.899061\pi\)
\(752\) 35.3950 + 314.140i 0.0470679 + 0.417739i
\(753\) 0 0
\(754\) 114.322 + 52.9422i 0.151620 + 0.0702151i
\(755\) −133.718 −0.177110
\(756\) 0 0
\(757\) −145.660 + 91.5245i −0.192418 + 0.120904i −0.624796 0.780788i \(-0.714818\pi\)
0.432377 + 0.901693i \(0.357675\pi\)
\(758\) −199.722 + 45.5852i −0.263485 + 0.0601387i
\(759\) 0 0
\(760\) −64.7167 + 51.6098i −0.0851536 + 0.0679077i
\(761\) 64.7556 283.713i 0.0850928 0.372816i −0.914395 0.404824i \(-0.867333\pi\)
0.999488 + 0.0320077i \(0.0101901\pi\)
\(762\) 0 0
\(763\) −178.515 + 370.691i −0.233965 + 0.485833i
\(764\) 314.157 + 197.398i 0.411201 + 0.258374i
\(765\) 0 0
\(766\) 65.2418 65.2418i 0.0851721 0.0851721i
\(767\) 82.3859 + 171.076i 0.107413 + 0.223046i
\(768\) 0 0
\(769\) −609.620 68.6876i −0.792743 0.0893207i −0.293700 0.955898i \(-0.594887\pi\)
−0.499043 + 0.866577i \(0.666315\pi\)
\(770\) −8.45805 + 4.07318i −0.0109845 + 0.00528985i
\(771\) 0 0
\(772\) 39.7015 113.460i 0.0514268 0.146969i
\(773\) 70.0120 111.423i 0.0905718 0.144144i −0.798365 0.602173i \(-0.794302\pi\)
0.888937 + 0.458029i \(0.151444\pi\)
\(774\) 0 0
\(775\) −173.944 497.103i −0.224444 0.641424i
\(776\) −135.908 31.0202i −0.175140 0.0399745i
\(777\) 0 0
\(778\) −107.347 + 134.609i −0.137978 + 0.173019i
\(779\) −213.680 936.192i −0.274300 1.20179i
\(780\) 0 0
\(781\) −132.791 1178.55i −0.170027 1.50903i
\(782\) 46.3757i 0.0593040i
\(783\) 0 0
\(784\) 589.033 0.751318
\(785\) −25.9961 + 2.92906i −0.0331160 + 0.00373128i
\(786\) 0 0
\(787\) −729.969 + 166.611i −0.927534 + 0.211704i −0.659499