Properties

Label 819.2.fm.e.496.6
Level $819$
Weight $2$
Character 819.496
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 496.6
Character \(\chi\) \(=\) 819.496
Dual form 819.2.fm.e.748.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.38083 + 0.369991i) q^{2} +(0.0377371 + 0.0217876i) q^{4} +(-0.512287 - 0.512287i) q^{5} +(-2.41005 - 1.09162i) q^{7} +(-1.97762 - 1.97762i) q^{8} +O(q^{10})\) \(q+(1.38083 + 0.369991i) q^{2} +(0.0377371 + 0.0217876i) q^{4} +(-0.512287 - 0.512287i) q^{5} +(-2.41005 - 1.09162i) q^{7} +(-1.97762 - 1.97762i) q^{8} +(-0.517838 - 0.896921i) q^{10} +(-1.38992 + 5.18727i) q^{11} +(-0.0545462 - 3.60514i) q^{13} +(-2.92397 - 2.39904i) q^{14} +(-2.04263 - 3.53793i) q^{16} +(1.31681 - 2.28077i) q^{17} +(-5.26328 + 1.41029i) q^{19} +(-0.00817077 - 0.0304937i) q^{20} +(-3.83849 + 6.64846i) q^{22} +(-5.51236 + 3.18256i) q^{23} -4.47512i q^{25} +(1.25855 - 4.99825i) q^{26} +(-0.0671647 - 0.0937039i) q^{28} +(-0.300703 - 0.520832i) q^{29} +(-6.22737 - 6.22737i) q^{31} +(-0.0637871 - 0.238057i) q^{32} +(2.66215 - 2.66215i) q^{34} +(0.675414 + 1.79386i) q^{35} +(0.172749 - 0.644708i) q^{37} -7.78948 q^{38} +2.02622i q^{40} +(2.11401 - 7.88960i) q^{41} +(4.10340 + 2.36910i) q^{43} +(-0.165470 + 0.165470i) q^{44} +(-8.78913 + 2.35504i) q^{46} +(-4.25821 + 4.25821i) q^{47} +(4.61671 + 5.26174i) q^{49} +(1.65576 - 6.17937i) q^{50} +(0.0764887 - 0.137236i) q^{52} -0.282101 q^{53} +(3.36941 - 1.94533i) q^{55} +(2.60736 + 6.92500i) q^{56} +(-0.222515 - 0.830436i) q^{58} +(1.21690 + 4.54153i) q^{59} +(13.0884 + 7.55656i) q^{61} +(-6.29485 - 10.9030i) q^{62} +7.81819i q^{64} +(-1.81892 + 1.87481i) q^{65} +(4.48192 + 1.20093i) q^{67} +(0.0993850 - 0.0573799i) q^{68} +(0.268916 + 2.72691i) q^{70} +(-4.11194 - 15.3460i) q^{71} +(3.04327 - 3.04327i) q^{73} +(0.477073 - 0.826314i) q^{74} +(-0.229348 - 0.0614536i) q^{76} +(9.01234 - 10.9843i) q^{77} +4.77147 q^{79} +(-0.766026 + 2.85885i) q^{80} +(5.83817 - 10.1120i) q^{82} +(-2.42351 - 2.42351i) q^{83} +(-1.84299 + 0.493829i) q^{85} +(4.78954 + 4.78954i) q^{86} +(13.0072 - 7.50971i) q^{88} +(5.75969 + 1.54330i) q^{89} +(-3.80400 + 8.74812i) q^{91} -0.277361 q^{92} +(-7.45535 + 4.30435i) q^{94} +(3.41879 + 1.97384i) q^{95} +(-15.7347 + 4.21610i) q^{97} +(4.42808 + 8.97370i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38083 + 0.369991i 0.976392 + 0.261623i 0.711524 0.702661i \(-0.248005\pi\)
0.264867 + 0.964285i \(0.414672\pi\)
\(3\) 0 0
\(4\) 0.0377371 + 0.0217876i 0.0188686 + 0.0108938i
\(5\) −0.512287 0.512287i −0.229102 0.229102i 0.583216 0.812317i \(-0.301794\pi\)
−0.812317 + 0.583216i \(0.801794\pi\)
\(6\) 0 0
\(7\) −2.41005 1.09162i −0.910915 0.412595i
\(8\) −1.97762 1.97762i −0.699195 0.699195i
\(9\) 0 0
\(10\) −0.517838 0.896921i −0.163755 0.283631i
\(11\) −1.38992 + 5.18727i −0.419078 + 1.56402i 0.357447 + 0.933933i \(0.383647\pi\)
−0.776525 + 0.630086i \(0.783019\pi\)
\(12\) 0 0
\(13\) −0.0545462 3.60514i −0.0151284 0.999886i
\(14\) −2.92397 2.39904i −0.781465 0.641171i
\(15\) 0 0
\(16\) −2.04263 3.53793i −0.510656 0.884483i
\(17\) 1.31681 2.28077i 0.319372 0.553169i −0.660985 0.750399i \(-0.729861\pi\)
0.980357 + 0.197230i \(0.0631946\pi\)
\(18\) 0 0
\(19\) −5.26328 + 1.41029i −1.20748 + 0.323543i −0.805773 0.592225i \(-0.798250\pi\)
−0.401707 + 0.915768i \(0.631583\pi\)
\(20\) −0.00817077 0.0304937i −0.00182704 0.00681861i
\(21\) 0 0
\(22\) −3.83849 + 6.64846i −0.818368 + 1.41746i
\(23\) −5.51236 + 3.18256i −1.14941 + 0.663610i −0.948742 0.316051i \(-0.897643\pi\)
−0.200663 + 0.979660i \(0.564310\pi\)
\(24\) 0 0
\(25\) 4.47512i 0.895025i
\(26\) 1.25855 4.99825i 0.246822 0.980238i
\(27\) 0 0
\(28\) −0.0671647 0.0937039i −0.0126929 0.0177084i
\(29\) −0.300703 0.520832i −0.0558391 0.0967161i 0.836755 0.547578i \(-0.184450\pi\)
−0.892594 + 0.450862i \(0.851117\pi\)
\(30\) 0 0
\(31\) −6.22737 6.22737i −1.11847 1.11847i −0.991966 0.126503i \(-0.959625\pi\)
−0.126503 0.991966i \(-0.540375\pi\)
\(32\) −0.0637871 0.238057i −0.0112761 0.0420829i
\(33\) 0 0
\(34\) 2.66215 2.66215i 0.456554 0.456554i
\(35\) 0.675414 + 1.79386i 0.114166 + 0.303218i
\(36\) 0 0
\(37\) 0.172749 0.644708i 0.0283998 0.105989i −0.950271 0.311424i \(-0.899194\pi\)
0.978671 + 0.205435i \(0.0658608\pi\)
\(38\) −7.78948 −1.26362
\(39\) 0 0
\(40\) 2.02622i 0.320374i
\(41\) 2.11401 7.88960i 0.330153 1.23215i −0.578876 0.815416i \(-0.696508\pi\)
0.909029 0.416733i \(-0.136825\pi\)
\(42\) 0 0
\(43\) 4.10340 + 2.36910i 0.625762 + 0.361284i 0.779109 0.626888i \(-0.215672\pi\)
−0.153347 + 0.988172i \(0.549005\pi\)
\(44\) −0.165470 + 0.165470i −0.0249455 + 0.0249455i
\(45\) 0 0
\(46\) −8.78913 + 2.35504i −1.29589 + 0.347232i
\(47\) −4.25821 + 4.25821i −0.621123 + 0.621123i −0.945819 0.324695i \(-0.894738\pi\)
0.324695 + 0.945819i \(0.394738\pi\)
\(48\) 0 0
\(49\) 4.61671 + 5.26174i 0.659530 + 0.751678i
\(50\) 1.65576 6.17937i 0.234159 0.873895i
\(51\) 0 0
\(52\) 0.0764887 0.137236i 0.0106071 0.0190312i
\(53\) −0.282101 −0.0387495 −0.0193748 0.999812i \(-0.506168\pi\)
−0.0193748 + 0.999812i \(0.506168\pi\)
\(54\) 0 0
\(55\) 3.36941 1.94533i 0.454331 0.262308i
\(56\) 2.60736 + 6.92500i 0.348423 + 0.925392i
\(57\) 0 0
\(58\) −0.222515 0.830436i −0.0292176 0.109042i
\(59\) 1.21690 + 4.54153i 0.158427 + 0.591257i 0.998787 + 0.0492295i \(0.0156766\pi\)
−0.840361 + 0.542028i \(0.817657\pi\)
\(60\) 0 0
\(61\) 13.0884 + 7.55656i 1.67579 + 0.967519i 0.964295 + 0.264829i \(0.0853156\pi\)
0.711497 + 0.702690i \(0.248018\pi\)
\(62\) −6.29485 10.9030i −0.799446 1.38468i
\(63\) 0 0
\(64\) 7.81819i 0.977273i
\(65\) −1.81892 + 1.87481i −0.225610 + 0.232541i
\(66\) 0 0
\(67\) 4.48192 + 1.20093i 0.547553 + 0.146716i 0.521982 0.852957i \(-0.325193\pi\)
0.0255714 + 0.999673i \(0.491859\pi\)
\(68\) 0.0993850 0.0573799i 0.0120522 0.00695834i
\(69\) 0 0
\(70\) 0.268916 + 2.72691i 0.0321416 + 0.325928i
\(71\) −4.11194 15.3460i −0.487998 1.82123i −0.566165 0.824292i \(-0.691573\pi\)
0.0781668 0.996940i \(-0.475093\pi\)
\(72\) 0 0
\(73\) 3.04327 3.04327i 0.356188 0.356188i −0.506218 0.862406i \(-0.668957\pi\)
0.862406 + 0.506218i \(0.168957\pi\)
\(74\) 0.477073 0.826314i 0.0554586 0.0960571i
\(75\) 0 0
\(76\) −0.229348 0.0614536i −0.0263080 0.00704922i
\(77\) 9.01234 10.9843i 1.02705 1.25178i
\(78\) 0 0
\(79\) 4.77147 0.536832 0.268416 0.963303i \(-0.413500\pi\)
0.268416 + 0.963303i \(0.413500\pi\)
\(80\) −0.766026 + 2.85885i −0.0856443 + 0.319629i
\(81\) 0 0
\(82\) 5.83817 10.1120i 0.644718 1.11668i
\(83\) −2.42351 2.42351i −0.266015 0.266015i 0.561477 0.827492i \(-0.310233\pi\)
−0.827492 + 0.561477i \(0.810233\pi\)
\(84\) 0 0
\(85\) −1.84299 + 0.493829i −0.199901 + 0.0535632i
\(86\) 4.78954 + 4.78954i 0.516469 + 0.516469i
\(87\) 0 0
\(88\) 13.0072 7.50971i 1.38657 0.800538i
\(89\) 5.75969 + 1.54330i 0.610526 + 0.163590i 0.550817 0.834626i \(-0.314316\pi\)
0.0597085 + 0.998216i \(0.480983\pi\)
\(90\) 0 0
\(91\) −3.80400 + 8.74812i −0.398767 + 0.917052i
\(92\) −0.277361 −0.0289169
\(93\) 0 0
\(94\) −7.45535 + 4.30435i −0.768960 + 0.443959i
\(95\) 3.41879 + 1.97384i 0.350760 + 0.202511i
\(96\) 0 0
\(97\) −15.7347 + 4.21610i −1.59762 + 0.428080i −0.944322 0.329022i \(-0.893281\pi\)
−0.653296 + 0.757103i \(0.726614\pi\)
\(98\) 4.42808 + 8.97370i 0.447304 + 0.906481i
\(99\) 0 0
\(100\) 0.0975020 0.168878i 0.00975020 0.0168878i
\(101\) −8.39661 14.5434i −0.835494 1.44712i −0.893627 0.448810i \(-0.851848\pi\)
0.0581328 0.998309i \(-0.481485\pi\)
\(102\) 0 0
\(103\) 0.962454 0.0948334 0.0474167 0.998875i \(-0.484901\pi\)
0.0474167 + 0.998875i \(0.484901\pi\)
\(104\) −7.02173 + 7.23748i −0.688538 + 0.709693i
\(105\) 0 0
\(106\) −0.389532 0.104375i −0.0378347 0.0101378i
\(107\) 5.96703 + 10.3352i 0.576854 + 0.999141i 0.995837 + 0.0911468i \(0.0290533\pi\)
−0.418983 + 0.907994i \(0.637613\pi\)
\(108\) 0 0
\(109\) 3.42240 3.42240i 0.327807 0.327807i −0.523945 0.851752i \(-0.675540\pi\)
0.851752 + 0.523945i \(0.175540\pi\)
\(110\) 5.37233 1.43951i 0.512231 0.137252i
\(111\) 0 0
\(112\) 1.06075 + 10.7564i 0.100231 + 1.01638i
\(113\) −6.78443 + 11.7510i −0.638226 + 1.10544i 0.347596 + 0.937644i \(0.386998\pi\)
−0.985822 + 0.167795i \(0.946335\pi\)
\(114\) 0 0
\(115\) 4.45429 + 1.19352i 0.415365 + 0.111297i
\(116\) 0.0262063i 0.00243319i
\(117\) 0 0
\(118\) 6.72131i 0.618747i
\(119\) −5.66332 + 4.05933i −0.519156 + 0.372118i
\(120\) 0 0
\(121\) −15.4496 8.91981i −1.40451 0.810892i
\(122\) 15.2769 + 15.2769i 1.38310 + 1.38310i
\(123\) 0 0
\(124\) −0.0993241 0.370682i −0.00891956 0.0332883i
\(125\) −4.85398 + 4.85398i −0.434153 + 0.434153i
\(126\) 0 0
\(127\) 11.3554 6.55606i 1.00763 0.581757i 0.0971344 0.995271i \(-0.469032\pi\)
0.910497 + 0.413515i \(0.135699\pi\)
\(128\) −3.02024 + 11.2717i −0.266954 + 0.996285i
\(129\) 0 0
\(130\) −3.20528 + 1.91580i −0.281122 + 0.168027i
\(131\) 6.96325i 0.608382i −0.952611 0.304191i \(-0.901614\pi\)
0.952611 0.304191i \(-0.0983861\pi\)
\(132\) 0 0
\(133\) 14.2243 + 2.34665i 1.23340 + 0.203480i
\(134\) 5.74442 + 3.31654i 0.496242 + 0.286506i
\(135\) 0 0
\(136\) −7.11466 + 1.90637i −0.610077 + 0.163470i
\(137\) 0.989826 0.265223i 0.0845665 0.0226595i −0.216288 0.976330i \(-0.569395\pi\)
0.300854 + 0.953670i \(0.402728\pi\)
\(138\) 0 0
\(139\) −13.5680 7.83346i −1.15082 0.664426i −0.201732 0.979441i \(-0.564657\pi\)
−0.949087 + 0.315015i \(0.897990\pi\)
\(140\) −0.0135957 + 0.0824109i −0.00114905 + 0.00696499i
\(141\) 0 0
\(142\) 22.7115i 1.90591i
\(143\) 18.7766 + 4.72792i 1.57018 + 0.395369i
\(144\) 0 0
\(145\) −0.112770 + 0.420862i −0.00936500 + 0.0349507i
\(146\) 5.32821 3.07624i 0.440966 0.254592i
\(147\) 0 0
\(148\) 0.0205657 0.0205657i 0.00169049 0.00169049i
\(149\) −3.05630 11.4063i −0.250382 0.934438i −0.970602 0.240692i \(-0.922626\pi\)
0.720220 0.693746i \(-0.244041\pi\)
\(150\) 0 0
\(151\) −8.50103 8.50103i −0.691804 0.691804i 0.270825 0.962629i \(-0.412704\pi\)
−0.962629 + 0.270825i \(0.912704\pi\)
\(152\) 13.1978 + 7.61976i 1.07048 + 0.618044i
\(153\) 0 0
\(154\) 16.5086 11.8329i 1.33030 0.953526i
\(155\) 6.38040i 0.512486i
\(156\) 0 0
\(157\) 0.627679i 0.0500942i −0.999686 0.0250471i \(-0.992026\pi\)
0.999686 0.0250471i \(-0.00797357\pi\)
\(158\) 6.58857 + 1.76540i 0.524158 + 0.140448i
\(159\) 0 0
\(160\) −0.0892761 + 0.154631i −0.00705789 + 0.0122246i
\(161\) 16.7592 1.65272i 1.32081 0.130252i
\(162\) 0 0
\(163\) 12.2260 3.27594i 0.957613 0.256592i 0.254023 0.967198i \(-0.418246\pi\)
0.703590 + 0.710607i \(0.251579\pi\)
\(164\) 0.251672 0.251672i 0.0196523 0.0196523i
\(165\) 0 0
\(166\) −2.44977 4.24312i −0.190139 0.329330i
\(167\) −14.4241 3.86492i −1.11617 0.299076i −0.346837 0.937926i \(-0.612744\pi\)
−0.769332 + 0.638849i \(0.779411\pi\)
\(168\) 0 0
\(169\) −12.9940 + 0.393293i −0.999542 + 0.0302533i
\(170\) −2.72757 −0.209195
\(171\) 0 0
\(172\) 0.103234 + 0.178806i 0.00787150 + 0.0136338i
\(173\) −6.31043 + 10.9300i −0.479773 + 0.830991i −0.999731 0.0232010i \(-0.992614\pi\)
0.519958 + 0.854192i \(0.325948\pi\)
\(174\) 0 0
\(175\) −4.88515 + 10.7853i −0.369283 + 0.815291i
\(176\) 21.1913 5.67819i 1.59735 0.428010i
\(177\) 0 0
\(178\) 7.38212 + 4.26207i 0.553313 + 0.319456i
\(179\) 9.45522 5.45897i 0.706716 0.408023i −0.103128 0.994668i \(-0.532885\pi\)
0.809844 + 0.586645i \(0.199552\pi\)
\(180\) 0 0
\(181\) −5.94105 −0.441595 −0.220797 0.975320i \(-0.570866\pi\)
−0.220797 + 0.975320i \(0.570866\pi\)
\(182\) −8.48939 + 10.6722i −0.629275 + 0.791075i
\(183\) 0 0
\(184\) 17.1953 + 4.60746i 1.26765 + 0.339666i
\(185\) −0.418773 + 0.241779i −0.0307888 + 0.0177759i
\(186\) 0 0
\(187\) 10.0007 + 10.0007i 0.731326 + 0.731326i
\(188\) −0.253469 + 0.0679167i −0.0184861 + 0.00495333i
\(189\) 0 0
\(190\) 3.99045 + 3.99045i 0.289498 + 0.289498i
\(191\) 0.805155 1.39457i 0.0582590 0.100907i −0.835425 0.549604i \(-0.814778\pi\)
0.893684 + 0.448697i \(0.148112\pi\)
\(192\) 0 0
\(193\) −6.36607 + 23.7585i −0.458240 + 1.71017i 0.220144 + 0.975467i \(0.429347\pi\)
−0.678384 + 0.734707i \(0.737319\pi\)
\(194\) −23.2868 −1.67190
\(195\) 0 0
\(196\) 0.0595811 + 0.299150i 0.00425579 + 0.0213679i
\(197\) 4.77159 + 1.27854i 0.339962 + 0.0910925i 0.424761 0.905306i \(-0.360358\pi\)
−0.0847991 + 0.996398i \(0.527025\pi\)
\(198\) 0 0
\(199\) −2.30866 + 3.99871i −0.163656 + 0.283461i −0.936177 0.351528i \(-0.885662\pi\)
0.772521 + 0.634989i \(0.218995\pi\)
\(200\) −8.85011 + 8.85011i −0.625797 + 0.625797i
\(201\) 0 0
\(202\) −6.21335 23.1885i −0.437170 1.63154i
\(203\) 0.156156 + 1.58349i 0.0109600 + 0.111139i
\(204\) 0 0
\(205\) −5.12472 + 2.95876i −0.357926 + 0.206649i
\(206\) 1.32898 + 0.356100i 0.0925946 + 0.0248106i
\(207\) 0 0
\(208\) −12.6433 + 7.55693i −0.876656 + 0.523979i
\(209\) 29.2623i 2.02411i
\(210\) 0 0
\(211\) −3.39083 5.87308i −0.233434 0.404320i 0.725382 0.688346i \(-0.241663\pi\)
−0.958816 + 0.284026i \(0.908330\pi\)
\(212\) −0.0106457 0.00614629i −0.000731149 0.000422129i
\(213\) 0 0
\(214\) 4.41550 + 16.4789i 0.301837 + 1.12647i
\(215\) −0.888460 3.31578i −0.0605924 0.226134i
\(216\) 0 0
\(217\) 8.21035 + 21.8062i 0.557355 + 1.48030i
\(218\) 5.99200 3.45948i 0.405830 0.234306i
\(219\) 0 0
\(220\) 0.169536 0.0114301
\(221\) −8.29434 4.62286i −0.557937 0.310967i
\(222\) 0 0
\(223\) 5.00651 18.6845i 0.335260 1.25121i −0.568326 0.822803i \(-0.692409\pi\)
0.903587 0.428406i \(-0.140925\pi\)
\(224\) −0.106138 + 0.643361i −0.00709165 + 0.0429864i
\(225\) 0 0
\(226\) −13.7159 + 13.7159i −0.912367 + 0.912367i
\(227\) −11.5655 + 3.09897i −0.767631 + 0.205686i −0.621324 0.783553i \(-0.713405\pi\)
−0.146306 + 0.989239i \(0.546738\pi\)
\(228\) 0 0
\(229\) −0.755536 + 0.755536i −0.0499272 + 0.0499272i −0.731630 0.681702i \(-0.761240\pi\)
0.681702 + 0.731630i \(0.261240\pi\)
\(230\) 5.70901 + 3.29610i 0.376441 + 0.217338i
\(231\) 0 0
\(232\) −0.435333 + 1.62469i −0.0285810 + 0.106666i
\(233\) 16.2619i 1.06535i −0.846318 0.532677i \(-0.821186\pi\)
0.846318 0.532677i \(-0.178814\pi\)
\(234\) 0 0
\(235\) 4.36285 0.284601
\(236\) −0.0530266 + 0.197898i −0.00345173 + 0.0128820i
\(237\) 0 0
\(238\) −9.32198 + 3.50985i −0.604254 + 0.227510i
\(239\) −15.1795 + 15.1795i −0.981878 + 0.981878i −0.999839 0.0179604i \(-0.994283\pi\)
0.0179604 + 0.999839i \(0.494283\pi\)
\(240\) 0 0
\(241\) −3.31373 12.3670i −0.213456 0.796630i −0.986704 0.162526i \(-0.948036\pi\)
0.773248 0.634104i \(-0.218631\pi\)
\(242\) −18.0329 18.0329i −1.15920 1.15920i
\(243\) 0 0
\(244\) 0.329278 + 0.570326i 0.0210799 + 0.0365114i
\(245\) 0.330441 5.06061i 0.0211111 0.323310i
\(246\) 0 0
\(247\) 5.37139 + 18.8979i 0.341773 + 1.20245i
\(248\) 24.6308i 1.56406i
\(249\) 0 0
\(250\) −8.49844 + 4.90658i −0.537489 + 0.310319i
\(251\) 3.61972 6.26954i 0.228475 0.395730i −0.728881 0.684640i \(-0.759959\pi\)
0.957356 + 0.288910i \(0.0932928\pi\)
\(252\) 0 0
\(253\) −8.84703 33.0176i −0.556208 2.07580i
\(254\) 18.1056 4.85137i 1.13604 0.304402i
\(255\) 0 0
\(256\) −0.522655 + 0.905265i −0.0326659 + 0.0565790i
\(257\) 1.90293 + 3.29597i 0.118701 + 0.205597i 0.919253 0.393667i \(-0.128794\pi\)
−0.800552 + 0.599263i \(0.795460\pi\)
\(258\) 0 0
\(259\) −1.12011 + 1.36520i −0.0696005 + 0.0848296i
\(260\) −0.109488 + 0.0311201i −0.00679019 + 0.00192999i
\(261\) 0 0
\(262\) 2.57634 9.61504i 0.159167 0.594019i
\(263\) −2.01647 3.49263i −0.124341 0.215365i 0.797134 0.603802i \(-0.206348\pi\)
−0.921475 + 0.388437i \(0.873015\pi\)
\(264\) 0 0
\(265\) 0.144517 + 0.144517i 0.00887759 + 0.00887759i
\(266\) 18.7731 + 8.50318i 1.15105 + 0.521363i
\(267\) 0 0
\(268\) 0.142970 + 0.142970i 0.00873325 + 0.00873325i
\(269\) −6.03395 3.48370i −0.367897 0.212405i 0.304643 0.952467i \(-0.401463\pi\)
−0.672539 + 0.740062i \(0.734796\pi\)
\(270\) 0 0
\(271\) 8.12317 + 2.17660i 0.493447 + 0.132219i 0.496957 0.867775i \(-0.334451\pi\)
−0.00350987 + 0.999994i \(0.501117\pi\)
\(272\) −10.7590 −0.652358
\(273\) 0 0
\(274\) 1.46491 0.0884983
\(275\) 23.2137 + 6.22008i 1.39984 + 0.375085i
\(276\) 0 0
\(277\) −8.34222 4.81638i −0.501236 0.289388i 0.227988 0.973664i \(-0.426785\pi\)
−0.729224 + 0.684275i \(0.760119\pi\)
\(278\) −15.8367 15.8367i −0.949821 0.949821i
\(279\) 0 0
\(280\) 2.21187 4.88330i 0.132185 0.291833i
\(281\) 9.81783 + 9.81783i 0.585683 + 0.585683i 0.936459 0.350777i \(-0.114082\pi\)
−0.350777 + 0.936459i \(0.614082\pi\)
\(282\) 0 0
\(283\) 0.916453 + 1.58734i 0.0544775 + 0.0943578i 0.891978 0.452079i \(-0.149317\pi\)
−0.837501 + 0.546436i \(0.815984\pi\)
\(284\) 0.179178 0.668703i 0.0106323 0.0396802i
\(285\) 0 0
\(286\) 24.1780 + 13.4756i 1.42967 + 0.796831i
\(287\) −13.7074 + 16.7067i −0.809120 + 0.986163i
\(288\) 0 0
\(289\) 5.03204 + 8.71576i 0.296003 + 0.512692i
\(290\) −0.311430 + 0.539413i −0.0182878 + 0.0316754i
\(291\) 0 0
\(292\) 0.181150 0.0485389i 0.0106010 0.00284052i
\(293\) −7.17194 26.7660i −0.418989 1.56369i −0.776709 0.629860i \(-0.783112\pi\)
0.357719 0.933829i \(-0.383554\pi\)
\(294\) 0 0
\(295\) 1.70317 2.94997i 0.0991622 0.171754i
\(296\) −1.61662 + 0.933357i −0.0939642 + 0.0542503i
\(297\) 0 0
\(298\) 16.8809i 0.977883i
\(299\) 11.7742 + 19.6992i 0.680922 + 1.13923i
\(300\) 0 0
\(301\) −7.30324 10.1890i −0.420952 0.587285i
\(302\) −8.59314 14.8838i −0.494480 0.856464i
\(303\) 0 0
\(304\) 15.7404 + 15.7404i 0.902776 + 0.902776i
\(305\) −2.83386 10.5761i −0.162267 0.605587i
\(306\) 0 0
\(307\) 16.7091 16.7091i 0.953641 0.953641i −0.0453311 0.998972i \(-0.514434\pi\)
0.998972 + 0.0453311i \(0.0144343\pi\)
\(308\) 0.579421 0.218160i 0.0330156 0.0124308i
\(309\) 0 0
\(310\) −2.36069 + 8.81023i −0.134078 + 0.500387i
\(311\) 1.88740 0.107025 0.0535124 0.998567i \(-0.482958\pi\)
0.0535124 + 0.998567i \(0.482958\pi\)
\(312\) 0 0
\(313\) 4.73972i 0.267905i −0.990988 0.133953i \(-0.957233\pi\)
0.990988 0.133953i \(-0.0427670\pi\)
\(314\) 0.232236 0.866715i 0.0131058 0.0489116i
\(315\) 0 0
\(316\) 0.180062 + 0.103959i 0.0101293 + 0.00584813i
\(317\) −12.0340 + 12.0340i −0.675897 + 0.675897i −0.959069 0.283172i \(-0.908613\pi\)
0.283172 + 0.959069i \(0.408613\pi\)
\(318\) 0 0
\(319\) 3.11965 0.835908i 0.174667 0.0468019i
\(320\) 4.00516 4.00516i 0.223895 0.223895i
\(321\) 0 0
\(322\) 23.7531 + 3.91865i 1.32371 + 0.218378i
\(323\) −3.71416 + 13.8614i −0.206662 + 0.771271i
\(324\) 0 0
\(325\) −16.1334 + 0.244101i −0.894922 + 0.0135403i
\(326\) 18.0940 1.00214
\(327\) 0 0
\(328\) −19.7834 + 11.4219i −1.09235 + 0.630671i
\(329\) 14.9109 5.61414i 0.822063 0.309518i
\(330\) 0 0
\(331\) −4.49452 16.7738i −0.247041 0.921969i −0.972347 0.233542i \(-0.924968\pi\)
0.725306 0.688427i \(-0.241698\pi\)
\(332\) −0.0386540 0.144259i −0.00212141 0.00791722i
\(333\) 0 0
\(334\) −18.4872 10.6736i −1.01157 0.584032i
\(335\) −1.68081 2.91125i −0.0918324 0.159058i
\(336\) 0 0
\(337\) 10.9597i 0.597011i 0.954408 + 0.298506i \(0.0964882\pi\)
−0.954408 + 0.298506i \(0.903512\pi\)
\(338\) −18.0880 4.26462i −0.983860 0.231965i
\(339\) 0 0
\(340\) −0.0803086 0.0215186i −0.00435535 0.00116701i
\(341\) 40.9586 23.6475i 2.21803 1.28058i
\(342\) 0 0
\(343\) −5.38268 17.7208i −0.290637 0.956833i
\(344\) −3.42979 12.8002i −0.184922 0.690138i
\(345\) 0 0
\(346\) −12.7576 + 12.7576i −0.685853 + 0.685853i
\(347\) 1.04935 1.81754i 0.0563323 0.0975704i −0.836484 0.547991i \(-0.815393\pi\)
0.892816 + 0.450421i \(0.148726\pi\)
\(348\) 0 0
\(349\) −4.33364 1.16119i −0.231974 0.0621573i 0.140959 0.990015i \(-0.454981\pi\)
−0.372933 + 0.927858i \(0.621648\pi\)
\(350\) −10.7360 + 13.0851i −0.573864 + 0.699430i
\(351\) 0 0
\(352\) 1.32352 0.0705440
\(353\) −3.60851 + 13.4671i −0.192061 + 0.716783i 0.800946 + 0.598736i \(0.204330\pi\)
−0.993008 + 0.118047i \(0.962337\pi\)
\(354\) 0 0
\(355\) −5.75505 + 9.96804i −0.305446 + 0.529049i
\(356\) 0.183729 + 0.183729i 0.00973764 + 0.00973764i
\(357\) 0 0
\(358\) 15.0758 4.03954i 0.796780 0.213497i
\(359\) −14.5777 14.5777i −0.769383 0.769383i 0.208615 0.977998i \(-0.433104\pi\)
−0.977998 + 0.208615i \(0.933104\pi\)
\(360\) 0 0
\(361\) 9.25874 5.34554i 0.487302 0.281344i
\(362\) −8.20356 2.19814i −0.431169 0.115531i
\(363\) 0 0
\(364\) −0.334152 + 0.247249i −0.0175143 + 0.0129594i
\(365\) −3.11805 −0.163206
\(366\) 0 0
\(367\) 6.13097 3.53972i 0.320034 0.184772i −0.331374 0.943500i \(-0.607512\pi\)
0.651408 + 0.758728i \(0.274179\pi\)
\(368\) 22.5194 + 13.0016i 1.17390 + 0.677753i
\(369\) 0 0
\(370\) −0.667708 + 0.178912i −0.0347125 + 0.00930119i
\(371\) 0.679878 + 0.307948i 0.0352975 + 0.0159879i
\(372\) 0 0
\(373\) −8.61866 + 14.9280i −0.446257 + 0.772941i −0.998139 0.0609820i \(-0.980577\pi\)
0.551881 + 0.833923i \(0.313910\pi\)
\(374\) 10.1091 + 17.5094i 0.522728 + 0.905392i
\(375\) 0 0
\(376\) 16.8423 0.868573
\(377\) −1.86127 + 1.11248i −0.0958603 + 0.0572959i
\(378\) 0 0
\(379\) 4.36936 + 1.17077i 0.224439 + 0.0601382i 0.369286 0.929316i \(-0.379602\pi\)
−0.144847 + 0.989454i \(0.546269\pi\)
\(380\) 0.0860102 + 0.148974i 0.00441223 + 0.00764220i
\(381\) 0 0
\(382\) 1.62776 1.62776i 0.0832833 0.0832833i
\(383\) −27.6971 + 7.42141i −1.41525 + 0.379216i −0.883798 0.467870i \(-0.845022\pi\)
−0.531456 + 0.847086i \(0.678355\pi\)
\(384\) 0 0
\(385\) −10.2440 + 1.01022i −0.522084 + 0.0514855i
\(386\) −17.5809 + 30.4510i −0.894843 + 1.54991i
\(387\) 0 0
\(388\) −0.685642 0.183717i −0.0348082 0.00932682i
\(389\) 6.44786i 0.326919i 0.986550 + 0.163460i \(0.0522654\pi\)
−0.986550 + 0.163460i \(0.947735\pi\)
\(390\) 0 0
\(391\) 16.7633i 0.847754i
\(392\) 1.27563 19.5359i 0.0644290 0.986710i
\(393\) 0 0
\(394\) 6.11569 + 3.53089i 0.308104 + 0.177884i
\(395\) −2.44436 2.44436i −0.122989 0.122989i
\(396\) 0 0
\(397\) 7.70578 + 28.7583i 0.386742 + 1.44334i 0.835403 + 0.549638i \(0.185234\pi\)
−0.448661 + 0.893702i \(0.648099\pi\)
\(398\) −4.66734 + 4.66734i −0.233953 + 0.233953i
\(399\) 0 0
\(400\) −15.8327 + 9.14100i −0.791634 + 0.457050i
\(401\) 5.89581 22.0035i 0.294423 1.09880i −0.647252 0.762276i \(-0.724082\pi\)
0.941675 0.336524i \(-0.109251\pi\)
\(402\) 0 0
\(403\) −22.1109 + 22.7902i −1.10142 + 1.13526i
\(404\) 0.731767i 0.0364068i
\(405\) 0 0
\(406\) −0.370252 + 2.24430i −0.0183753 + 0.111383i
\(407\) 3.10417 + 1.79219i 0.153868 + 0.0888356i
\(408\) 0 0
\(409\) −2.36322 + 0.633222i −0.116854 + 0.0313108i −0.316772 0.948502i \(-0.602599\pi\)
0.199918 + 0.979813i \(0.435932\pi\)
\(410\) −8.17107 + 2.18943i −0.403540 + 0.108128i
\(411\) 0 0
\(412\) 0.0363203 + 0.0209695i 0.00178937 + 0.00103309i
\(413\) 2.02485 12.2737i 0.0996365 0.603951i
\(414\) 0 0
\(415\) 2.48306i 0.121889i
\(416\) −0.854748 + 0.242946i −0.0419075 + 0.0119114i
\(417\) 0 0
\(418\) 10.8268 40.4061i 0.529555 1.97633i
\(419\) −16.9152 + 9.76598i −0.826361 + 0.477100i −0.852605 0.522556i \(-0.824979\pi\)
0.0262443 + 0.999656i \(0.491645\pi\)
\(420\) 0 0
\(421\) 14.8560 14.8560i 0.724035 0.724035i −0.245389 0.969425i \(-0.578916\pi\)
0.969425 + 0.245389i \(0.0789158\pi\)
\(422\) −2.50915 9.36428i −0.122144 0.455846i
\(423\) 0 0
\(424\) 0.557889 + 0.557889i 0.0270935 + 0.0270935i
\(425\) −10.2067 5.89287i −0.495100 0.285846i
\(426\) 0 0
\(427\) −23.2947 32.4993i −1.12731 1.57275i
\(428\) 0.520028i 0.0251365i
\(429\) 0 0
\(430\) 4.90723i 0.236648i
\(431\) −13.8720 3.71698i −0.668188 0.179041i −0.0912498 0.995828i \(-0.529086\pi\)
−0.576939 + 0.816788i \(0.695753\pi\)
\(432\) 0 0
\(433\) 18.2103 31.5412i 0.875131 1.51577i 0.0185084 0.999829i \(-0.494108\pi\)
0.856623 0.515943i \(-0.172558\pi\)
\(434\) 3.26894 + 33.1484i 0.156914 + 1.59117i
\(435\) 0 0
\(436\) 0.203717 0.0545859i 0.00975630 0.00261419i
\(437\) 24.5248 24.5248i 1.17318 1.17318i
\(438\) 0 0
\(439\) −16.0130 27.7354i −0.764259 1.32374i −0.940637 0.339414i \(-0.889771\pi\)
0.176378 0.984323i \(-0.443562\pi\)
\(440\) −10.5106 2.81629i −0.501071 0.134262i
\(441\) 0 0
\(442\) −9.74262 9.45220i −0.463409 0.449595i
\(443\) −13.4249 −0.637834 −0.318917 0.947783i \(-0.603319\pi\)
−0.318917 + 0.947783i \(0.603319\pi\)
\(444\) 0 0
\(445\) −2.16000 3.74123i −0.102394 0.177351i
\(446\) 13.8262 23.9477i 0.654691 1.13396i
\(447\) 0 0
\(448\) 8.53452 18.8422i 0.403218 0.890213i
\(449\) −18.5886 + 4.98079i −0.877248 + 0.235058i −0.669220 0.743065i \(-0.733371\pi\)
−0.208029 + 0.978123i \(0.566705\pi\)
\(450\) 0 0
\(451\) 37.9872 + 21.9319i 1.78875 + 1.03273i
\(452\) −0.512050 + 0.295632i −0.0240848 + 0.0139054i
\(453\) 0 0
\(454\) −17.1166 −0.803320
\(455\) 6.43029 2.53281i 0.301457 0.118740i
\(456\) 0 0
\(457\) 24.5036 + 6.56571i 1.14623 + 0.307131i 0.781453 0.623964i \(-0.214479\pi\)
0.364776 + 0.931095i \(0.381146\pi\)
\(458\) −1.32281 + 0.763722i −0.0618107 + 0.0356864i
\(459\) 0 0
\(460\) 0.142088 + 0.142088i 0.00662490 + 0.00662490i
\(461\) 23.2002 6.21648i 1.08054 0.289530i 0.325724 0.945465i \(-0.394392\pi\)
0.754818 + 0.655935i \(0.227725\pi\)
\(462\) 0 0
\(463\) 1.96489 + 1.96489i 0.0913160 + 0.0913160i 0.751289 0.659973i \(-0.229432\pi\)
−0.659973 + 0.751289i \(0.729432\pi\)
\(464\) −1.22845 + 2.12773i −0.0570292 + 0.0987774i
\(465\) 0 0
\(466\) 6.01678 22.4549i 0.278722 1.04020i
\(467\) −1.05748 −0.0489341 −0.0244671 0.999701i \(-0.507789\pi\)
−0.0244671 + 0.999701i \(0.507789\pi\)
\(468\) 0 0
\(469\) −9.49070 7.78687i −0.438240 0.359564i
\(470\) 6.02434 + 1.61422i 0.277882 + 0.0744582i
\(471\) 0 0
\(472\) 6.57487 11.3880i 0.302633 0.524176i
\(473\) −17.9926 + 17.9926i −0.827299 + 0.827299i
\(474\) 0 0
\(475\) 6.31123 + 23.5538i 0.289579 + 1.08072i
\(476\) −0.302160 + 0.0297977i −0.0138495 + 0.00136577i
\(477\) 0 0
\(478\) −26.5765 + 15.3439i −1.21558 + 0.701816i
\(479\) 4.87277 + 1.30565i 0.222643 + 0.0596569i 0.368416 0.929661i \(-0.379900\pi\)
−0.145773 + 0.989318i \(0.546567\pi\)
\(480\) 0 0
\(481\) −2.33369 0.587618i −0.106407 0.0267931i
\(482\) 18.3028i 0.833668i
\(483\) 0 0
\(484\) −0.388682 0.673217i −0.0176674 0.0306008i
\(485\) 10.2205 + 5.90083i 0.464091 + 0.267943i
\(486\) 0 0
\(487\) 0.725342 + 2.70701i 0.0328684 + 0.122666i 0.980411 0.196964i \(-0.0631081\pi\)
−0.947542 + 0.319630i \(0.896441\pi\)
\(488\) −10.9398 40.8279i −0.495221 1.84819i
\(489\) 0 0
\(490\) 2.32866 6.86556i 0.105198 0.310154i
\(491\) 10.7778 6.22255i 0.486394 0.280820i −0.236683 0.971587i \(-0.576060\pi\)
0.723077 + 0.690767i \(0.242727\pi\)
\(492\) 0 0
\(493\) −1.58387 −0.0713338
\(494\) 0.424886 + 28.0821i 0.0191165 + 1.26348i
\(495\) 0 0
\(496\) −9.31182 + 34.7522i −0.418113 + 1.56042i
\(497\) −6.84204 + 41.4733i −0.306907 + 1.86033i
\(498\) 0 0
\(499\) −6.23994 + 6.23994i −0.279338 + 0.279338i −0.832845 0.553507i \(-0.813289\pi\)
0.553507 + 0.832845i \(0.313289\pi\)
\(500\) −0.288932 + 0.0774191i −0.0129214 + 0.00346229i
\(501\) 0 0
\(502\) 7.31788 7.31788i 0.326613 0.326613i
\(503\) 13.6723 + 7.89370i 0.609617 + 0.351963i 0.772816 0.634631i \(-0.218848\pi\)
−0.163198 + 0.986593i \(0.552181\pi\)
\(504\) 0 0
\(505\) −3.14890 + 11.7519i −0.140124 + 0.522951i
\(506\) 48.8649i 2.17231i
\(507\) 0 0
\(508\) 0.571362 0.0253501
\(509\) −6.32401 + 23.6015i −0.280307 + 1.04612i 0.671894 + 0.740647i \(0.265481\pi\)
−0.952201 + 0.305472i \(0.901186\pi\)
\(510\) 0 0
\(511\) −10.6565 + 4.01233i −0.471418 + 0.177495i
\(512\) 15.4462 15.4462i 0.682634 0.682634i
\(513\) 0 0
\(514\) 1.40813 + 5.25523i 0.0621101 + 0.231798i
\(515\) −0.493053 0.493053i −0.0217265 0.0217265i
\(516\) 0 0
\(517\) −16.1699 28.0070i −0.711150 1.23175i
\(518\) −2.05180 + 1.47068i −0.0901507 + 0.0646179i
\(519\) 0 0
\(520\) 7.30481 0.110523i 0.320337 0.00484674i
\(521\) 2.98806i 0.130909i 0.997856 + 0.0654547i \(0.0208498\pi\)
−0.997856 + 0.0654547i \(0.979150\pi\)
\(522\) 0 0
\(523\) −23.5900 + 13.6197i −1.03152 + 0.595547i −0.917419 0.397922i \(-0.869731\pi\)
−0.114099 + 0.993469i \(0.536398\pi\)
\(524\) 0.151712 0.262773i 0.00662757 0.0114793i
\(525\) 0 0
\(526\) −1.49215 5.56879i −0.0650610 0.242811i
\(527\) −22.4035 + 6.00299i −0.975910 + 0.261494i
\(528\) 0 0
\(529\) 8.75738 15.1682i 0.380756 0.659488i
\(530\) 0.146083 + 0.253022i 0.00634542 + 0.0109906i
\(531\) 0 0
\(532\) 0.485657 + 0.398468i 0.0210559 + 0.0172758i
\(533\) −28.5584 7.19096i −1.23700 0.311475i
\(534\) 0 0
\(535\) 2.23776 8.35142i 0.0967466 0.361063i
\(536\) −6.48856 11.2385i −0.280263 0.485430i
\(537\) 0 0
\(538\) −7.04290 7.04290i −0.303641 0.303641i
\(539\) −33.7110 + 16.6347i −1.45203 + 0.716507i
\(540\) 0 0
\(541\) −5.00068 5.00068i −0.214996 0.214996i 0.591390 0.806386i \(-0.298579\pi\)
−0.806386 + 0.591390i \(0.798579\pi\)
\(542\) 10.4114 + 6.01100i 0.447206 + 0.258195i
\(543\) 0 0
\(544\) −0.626949 0.167990i −0.0268802 0.00720253i
\(545\) −3.50650 −0.150202
\(546\) 0 0
\(547\) −23.2544 −0.994288 −0.497144 0.867668i \(-0.665618\pi\)
−0.497144 + 0.867668i \(0.665618\pi\)
\(548\) 0.0431318 + 0.0115571i 0.00184250 + 0.000493696i
\(549\) 0 0
\(550\) 29.7527 + 17.1777i 1.26866 + 0.732460i
\(551\) 2.31721 + 2.31721i 0.0987164 + 0.0987164i
\(552\) 0 0
\(553\) −11.4995 5.20865i −0.489008 0.221494i
\(554\) −9.73714 9.73714i −0.413691 0.413691i
\(555\) 0 0
\(556\) −0.341344 0.591225i −0.0144762 0.0250735i
\(557\) 4.49356 16.7702i 0.190398 0.710576i −0.803012 0.595963i \(-0.796770\pi\)
0.993410 0.114613i \(-0.0365629\pi\)
\(558\) 0 0
\(559\) 8.31710 14.9225i 0.351776 0.631156i
\(560\) 4.96695 6.05376i 0.209892 0.255818i
\(561\) 0 0
\(562\) 9.92421 + 17.1892i 0.418627 + 0.725084i
\(563\) 9.17267 15.8875i 0.386582 0.669579i −0.605405 0.795917i \(-0.706989\pi\)
0.991987 + 0.126338i \(0.0403223\pi\)
\(564\) 0 0
\(565\) 9.49545 2.54430i 0.399477 0.107039i
\(566\) 0.678159 + 2.53093i 0.0285052 + 0.106383i
\(567\) 0 0
\(568\) −22.2167 + 38.4804i −0.932191 + 1.61460i
\(569\) 12.1394 7.00867i 0.508909 0.293819i −0.223476 0.974709i \(-0.571740\pi\)
0.732385 + 0.680891i \(0.238407\pi\)
\(570\) 0 0
\(571\) 10.4239i 0.436226i 0.975924 + 0.218113i \(0.0699901\pi\)
−0.975924 + 0.218113i \(0.930010\pi\)
\(572\) 0.605567 + 0.587515i 0.0253200 + 0.0245652i
\(573\) 0 0
\(574\) −25.1088 + 17.9974i −1.04802 + 0.751196i
\(575\) 14.2424 + 24.6685i 0.593947 + 1.02875i
\(576\) 0 0
\(577\) 11.2444 + 11.2444i 0.468111 + 0.468111i 0.901302 0.433191i \(-0.142612\pi\)
−0.433191 + 0.901302i \(0.642612\pi\)
\(578\) 3.72363 + 13.8968i 0.154882 + 0.578029i
\(579\) 0 0
\(580\) −0.0134252 + 0.0134252i −0.000557449 + 0.000557449i
\(581\) 3.19522 + 8.48634i 0.132560 + 0.352073i
\(582\) 0 0
\(583\) 0.392099 1.46333i 0.0162391 0.0606051i
\(584\) −12.0369 −0.498090
\(585\) 0 0
\(586\) 39.6128i 1.63639i
\(587\) 10.3083 38.4710i 0.425468 1.58787i −0.337432 0.941350i \(-0.609558\pi\)
0.762900 0.646517i \(-0.223775\pi\)
\(588\) 0 0
\(589\) 41.5588 + 23.9940i 1.71240 + 0.988656i
\(590\) 3.44324 3.44324i 0.141756 0.141756i
\(591\) 0 0
\(592\) −2.63379 + 0.705723i −0.108248 + 0.0290050i
\(593\) −23.4934 + 23.4934i −0.964759 + 0.964759i −0.999400 0.0346408i \(-0.988971\pi\)
0.0346408 + 0.999400i \(0.488971\pi\)
\(594\) 0 0
\(595\) 4.98079 + 0.821703i 0.204192 + 0.0336865i
\(596\) 0.133179 0.497029i 0.00545521 0.0203591i
\(597\) 0 0
\(598\) 8.96966 + 31.5576i 0.366797 + 1.29048i
\(599\) 45.3452 1.85276 0.926378 0.376594i \(-0.122905\pi\)
0.926378 + 0.376594i \(0.122905\pi\)
\(600\) 0 0
\(601\) 24.8361 14.3392i 1.01309 0.584906i 0.100993 0.994887i \(-0.467798\pi\)
0.912094 + 0.409981i \(0.134465\pi\)
\(602\) −6.31466 16.7714i −0.257366 0.683552i
\(603\) 0 0
\(604\) −0.135588 0.506021i −0.00551700 0.0205897i
\(605\) 3.34511 + 12.4841i 0.135998 + 0.507552i
\(606\) 0 0
\(607\) −8.50843 4.91234i −0.345347 0.199386i 0.317287 0.948329i \(-0.397228\pi\)
−0.662634 + 0.748944i \(0.730561\pi\)
\(608\) 0.671459 + 1.16300i 0.0272313 + 0.0471659i
\(609\) 0 0
\(610\) 15.6523i 0.633743i
\(611\) 15.5837 + 15.1192i 0.630449 + 0.611656i
\(612\) 0 0
\(613\) −24.7029 6.61912i −0.997741 0.267344i −0.277242 0.960800i \(-0.589420\pi\)
−0.720499 + 0.693456i \(0.756087\pi\)
\(614\) 29.2547 16.8902i 1.18062 0.681632i
\(615\) 0 0
\(616\) −39.5458 + 3.89983i −1.59335 + 0.157129i
\(617\) −1.62469 6.06341i −0.0654074 0.244104i 0.925480 0.378796i \(-0.123662\pi\)
−0.990887 + 0.134693i \(0.956995\pi\)
\(618\) 0 0
\(619\) −28.4665 + 28.4665i −1.14416 + 1.14416i −0.156484 + 0.987680i \(0.550016\pi\)
−0.987680 + 0.156484i \(0.949984\pi\)
\(620\) −0.139013 + 0.240778i −0.00558291 + 0.00966989i
\(621\) 0 0
\(622\) 2.60617 + 0.698322i 0.104498 + 0.0280002i
\(623\) −12.1964 10.0069i −0.488640 0.400916i
\(624\) 0 0
\(625\) −17.4024 −0.696094
\(626\) 1.75366 6.54474i 0.0700902 0.261580i
\(627\) 0 0
\(628\) 0.0136756 0.0236868i 0.000545715 0.000945206i
\(629\) −1.24296 1.24296i −0.0495599 0.0495599i
\(630\) 0 0
\(631\) 12.2380 3.27917i 0.487188 0.130542i −0.00685968 0.999976i \(-0.502184\pi\)
0.494048 + 0.869435i \(0.335517\pi\)
\(632\) −9.43616 9.43616i −0.375350 0.375350i
\(633\) 0 0
\(634\) −21.0693 + 12.1644i −0.836771 + 0.483110i
\(635\) −9.17583 2.45866i −0.364132 0.0975688i
\(636\) 0 0
\(637\) 18.7175 16.9309i 0.741614 0.670827i
\(638\) 4.61697 0.182788
\(639\) 0 0
\(640\) 7.32156 4.22710i 0.289410 0.167091i
\(641\) −24.0436 13.8816i −0.949666 0.548290i −0.0566885 0.998392i \(-0.518054\pi\)
−0.892977 + 0.450102i \(0.851388\pi\)
\(642\) 0 0
\(643\) −17.1125 + 4.58528i −0.674851 + 0.180826i −0.579939 0.814660i \(-0.696924\pi\)
−0.0949121 + 0.995486i \(0.530257\pi\)
\(644\) 0.668454 + 0.302774i 0.0263408 + 0.0119310i
\(645\) 0 0
\(646\) −10.2572 + 17.7660i −0.403565 + 0.698995i
\(647\) 3.33450 + 5.77553i 0.131093 + 0.227059i 0.924098 0.382155i \(-0.124818\pi\)
−0.793005 + 0.609215i \(0.791485\pi\)
\(648\) 0 0
\(649\) −25.2495 −0.991131
\(650\) −22.3678 5.63217i −0.877337 0.220912i
\(651\) 0 0
\(652\) 0.532748 + 0.142749i 0.0208640 + 0.00559050i
\(653\) 0.491840 + 0.851891i 0.0192472 + 0.0333371i 0.875489 0.483239i \(-0.160540\pi\)
−0.856241 + 0.516576i \(0.827206\pi\)
\(654\) 0 0
\(655\) −3.56718 + 3.56718i −0.139381 + 0.139381i
\(656\) −32.2310 + 8.63627i −1.25841 + 0.337190i
\(657\) 0 0
\(658\) 22.6665 2.23527i 0.883632 0.0871398i
\(659\) 10.5833 18.3308i 0.412267 0.714067i −0.582871 0.812565i \(-0.698071\pi\)
0.995137 + 0.0984983i \(0.0314039\pi\)
\(660\) 0 0
\(661\) 16.8983 + 4.52790i 0.657270 + 0.176115i 0.572013 0.820244i \(-0.306163\pi\)
0.0852561 + 0.996359i \(0.472829\pi\)
\(662\) 24.8246i 0.964835i
\(663\) 0 0
\(664\) 9.58557i 0.371992i
\(665\) −6.08477 8.48908i −0.235957 0.329193i
\(666\) 0 0
\(667\) 3.31516 + 1.91401i 0.128364 + 0.0741107i
\(668\) −0.460116 0.460116i −0.0178024 0.0178024i
\(669\) 0 0
\(670\) −1.24377 4.64181i −0.0480510 0.179329i
\(671\) −57.3897 + 57.3897i −2.21551 + 2.21551i
\(672\) 0 0
\(673\) 21.4934 12.4092i 0.828511 0.478341i −0.0248316 0.999692i \(-0.507905\pi\)
0.853343 + 0.521351i \(0.174572\pi\)
\(674\) −4.05498 + 15.1334i −0.156192 + 0.582917i
\(675\) 0 0
\(676\) −0.498927 0.268267i −0.0191895 0.0103180i
\(677\) 18.0191i 0.692531i 0.938137 + 0.346266i \(0.112550\pi\)
−0.938137 + 0.346266i \(0.887450\pi\)
\(678\) 0 0
\(679\) 42.5239 + 7.01536i 1.63192 + 0.269225i
\(680\) 4.62135 + 2.66814i 0.177221 + 0.102318i
\(681\) 0 0
\(682\) 65.3061 17.4987i 2.50070 0.670060i
\(683\) 31.7978 8.52018i 1.21671 0.326016i 0.407317 0.913287i \(-0.366464\pi\)
0.809390 + 0.587271i \(0.199798\pi\)
\(684\) 0 0
\(685\) −0.642945 0.371205i −0.0245657 0.0141830i
\(686\) −0.876001 26.4609i −0.0334459 1.01028i
\(687\) 0 0
\(688\) 19.3567i 0.737968i
\(689\) 0.0153875 + 1.01701i 0.000586218 + 0.0387451i
\(690\) 0 0
\(691\) 4.58957 17.1285i 0.174595 0.651599i −0.822025 0.569452i \(-0.807156\pi\)
0.996620 0.0821472i \(-0.0261778\pi\)
\(692\) −0.476275 + 0.274977i −0.0181053 + 0.0104531i
\(693\) 0 0
\(694\) 2.12145 2.12145i 0.0805291 0.0805291i
\(695\) 2.93771 + 10.9637i 0.111434 + 0.415876i
\(696\) 0 0
\(697\) −15.2107 15.2107i −0.576145 0.576145i
\(698\) −5.55437 3.20682i −0.210236 0.121380i
\(699\) 0 0
\(700\) −0.419337 + 0.300570i −0.0158494 + 0.0113605i
\(701\) 41.2421i 1.55769i −0.627214 0.778847i \(-0.715805\pi\)
0.627214 0.778847i \(-0.284195\pi\)
\(702\) 0 0
\(703\) 3.63691i 0.137169i
\(704\) −40.5550 10.8667i −1.52848 0.409554i
\(705\) 0 0
\(706\) −9.96545 + 17.2607i −0.375054 + 0.649613i
\(707\) 4.36040 + 44.2162i 0.163990 + 1.66292i
\(708\) 0 0
\(709\) −23.1654 + 6.20716i −0.869996 + 0.233115i −0.666086 0.745875i \(-0.732032\pi\)
−0.203910 + 0.978990i \(0.565365\pi\)
\(710\) −11.6348 + 11.6348i −0.436647 + 0.436647i
\(711\) 0 0
\(712\) −8.33842 14.4426i −0.312495 0.541258i
\(713\) 54.1465 + 14.5085i 2.02780 + 0.543348i
\(714\) 0 0
\(715\) −7.19697 12.0411i −0.269151 0.450311i
\(716\) 0.475751 0.0177796
\(717\) 0 0
\(718\) −14.7357 25.5229i −0.549930 0.952507i
\(719\) 10.7383 18.5992i 0.400469 0.693633i −0.593313 0.804972i \(-0.702180\pi\)
0.993783 + 0.111338i \(0.0355137\pi\)
\(720\) 0 0
\(721\) −2.31957 1.05064i −0.0863851 0.0391278i
\(722\) 14.7625 3.95561i 0.549404 0.147212i
\(723\) 0 0
\(724\) −0.224198 0.129441i −0.00833226 0.00481063i
\(725\) −2.33079 + 1.34568i −0.0865633 + 0.0499774i
\(726\) 0 0
\(727\) −16.2550 −0.602863 −0.301431 0.953488i \(-0.597464\pi\)
−0.301431 + 0.953488i \(0.597464\pi\)
\(728\) 24.8234 9.77761i 0.920015 0.362382i
\(729\) 0 0
\(730\) −4.30549 1.15365i −0.159353 0.0426986i
\(731\) 10.8068 6.23928i 0.399702 0.230768i
\(732\) 0 0
\(733\) 37.7313 + 37.7313i 1.39364 + 1.39364i 0.817001 + 0.576637i \(0.195635\pi\)
0.576637 + 0.817001i \(0.304365\pi\)
\(734\) 9.77547 2.61933i 0.360819 0.0966812i
\(735\) 0 0
\(736\) 1.10925 + 1.10925i 0.0408874 + 0.0408874i
\(737\) −12.4591 + 21.5797i −0.458935 + 0.794899i
\(738\) 0 0
\(739\) −11.5735 + 43.1929i −0.425738 + 1.58888i 0.336567 + 0.941660i \(0.390734\pi\)
−0.762305 + 0.647218i \(0.775932\pi\)
\(740\) −0.0210711 −0.000774587
\(741\) 0 0
\(742\) 0.824856 + 0.676772i 0.0302814 + 0.0248451i
\(743\) 43.8408 + 11.7471i 1.60836 + 0.430959i 0.947554 0.319596i \(-0.103547\pi\)
0.660808 + 0.750555i \(0.270214\pi\)
\(744\) 0 0
\(745\) −4.27758 + 7.40899i −0.156718 + 0.271444i
\(746\) −17.4241 + 17.4241i −0.637941 + 0.637941i
\(747\) 0 0
\(748\) 0.159508 + 0.595290i 0.00583217 + 0.0217660i
\(749\) −3.09870 31.4221i −0.113224 1.14814i
\(750\) 0 0
\(751\) 27.9904 16.1603i 1.02138 0.589696i 0.106880 0.994272i \(-0.465914\pi\)
0.914505 + 0.404575i \(0.132581\pi\)
\(752\) 23.7632 + 6.36732i 0.866554 + 0.232192i
\(753\) 0 0
\(754\) −2.98170 + 0.847494i −0.108587 + 0.0308639i
\(755\) 8.70994i 0.316987i
\(756\) 0 0
\(757\) −14.5363 25.1776i −0.528331 0.915097i −0.999454 0.0330294i \(-0.989484\pi\)
0.471123 0.882068i \(-0.343849\pi\)
\(758\) 5.60015 + 3.23325i 0.203407 + 0.117437i
\(759\) 0 0
\(760\) −2.85756 10.6646i −0.103655 0.386845i
\(761\) 7.58218 + 28.2971i 0.274854 + 1.02577i 0.955939 + 0.293564i \(0.0948414\pi\)
−0.681086 + 0.732204i \(0.738492\pi\)
\(762\) 0 0
\(763\) −11.9841 + 4.51219i −0.433855 + 0.163352i
\(764\) 0.0607685 0.0350847i 0.00219853 0.00126932i
\(765\) 0 0
\(766\) −40.9907 −1.48105
\(767\) 16.3065 4.63482i 0.588793 0.167354i
\(768\) 0 0
\(769\) −13.2029 + 49.2739i −0.476109 + 1.77686i 0.141027 + 0.990006i \(0.454960\pi\)
−0.617136 + 0.786857i \(0.711707\pi\)
\(770\) −14.5190 2.39526i −0.523228 0.0863193i
\(771\) 0 0
\(772\) −0.757877 + 0.757877i −0.0272766 + 0.0272766i
\(773\) −7.92985 + 2.12480i −0.285217 + 0.0764236i −0.398591 0.917129i \(-0.630501\pi\)
0.113374 + 0.993552i \(0.463834\pi\)
\(774\) 0 0
\(775\) −27.8683 + 27.8683i −1.00106 + 1.00106i
\(776\) 39.4552 + 22.7795i 1.41636 + 0.817735i
\(777\) 0 0
\(778\) −2.38565 + 8.90337i −0.0855298 + 0.319201i
\(779\) 44.5066i 1.59461i
\(780\) 0 0
\(781\) 85.3190 3.05295
\(782\) −6.20226 + 23.1471i −0.221792 + 0.827740i
\(783\) 0 0
\(784\) 9.18548 27.0814i 0.328053 0.967193i
\(785\) −0.321552 + 0.321552i −0.0114767 + 0.0114767i
\(786\) 0 0
\(787\) 0.450270 + 1.68043i 0.0160504 + 0.0599009i 0.973487 0.228744i \(-0.0734619\pi\)
−0.957436 + 0.288645i \(0.906795\pi\)
\(788\) 0.152210