Properties

Label 819.2.fm.e.748.6
Level $819$
Weight $2$
Character 819.748
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 748.6
Character \(\chi\) \(=\) 819.748
Dual form 819.2.fm.e.496.6

$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(-1\)

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 0.264867 0.964285i \(-0.414672\pi\)
0.711524 + 0.702661i \(0.248005\pi\)
\(3\) 0 0
\(4\) 0.0377371 0.0217876i 0.0188686 0.0108938i
\(5\) −0.512287 + 0.512287i −0.229102 + 0.229102i −0.812317 0.583216i \(-0.801794\pi\)
0.583216 + 0.812317i \(0.301794\pi\)
\(6\) 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 −0.776525 0.630086i \(-0.783019\pi\)
0.357447 0.933933i \(-0.383647\pi\)
\(12\) 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 0.980357 0.197230i \(-0.0631946\pi\)
−0.660985 + 0.750399i \(0.729861\pi\)
\(18\) 0 0
\(19\) −5.26328 1.41029i −1.20748 0.323543i −0.401707 0.915768i \(-0.631583\pi\)
−0.805773 + 0.592225i \(0.798250\pi\)
\(20\) −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 −0.200663 0.979660i \(-0.564310\pi\)
−0.948742 + 0.316051i \(0.897643\pi\)
\(24\) 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 −0.892594 0.450862i \(-0.851117\pi\)
0.836755 + 0.547578i \(0.184450\pi\)
\(30\) 0 0
\(31\) −6.22737 + 6.22737i −1.11847 + 1.11847i −0.126503 + 0.991966i \(0.540375\pi\)
−0.991966 + 0.126503i \(0.959625\pi\)
\(32\) −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 0.978671 0.205435i \(-0.0658608\pi\)
−0.950271 + 0.311424i \(0.899194\pi\)
\(38\) −7.78948 −1.26362
\(39\) 0 0
\(40\) 2.02622i 0.320374i
\(41\) 2.11401 + 7.88960i 0.330153 + 1.23215i 0.909029 + 0.416733i \(0.136825\pi\)
−0.578876 + 0.815416i \(0.696508\pi\)
\(42\) 0 0
\(43\) 4.10340 2.36910i 0.625762 0.361284i −0.153347 0.988172i \(-0.549005\pi\)
0.779109 + 0.626888i \(0.215672\pi\)
\(44\) −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 0.324695 0.945819i \(-0.394738\pi\)
−0.945819 + 0.324695i \(0.894738\pi\)
\(48\) 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 −0.840361 0.542028i \(-0.817657\pi\)
0.998787 0.0492295i \(-0.0156766\pi\)
\(60\) 0 0
\(61\) 13.0884 7.55656i 1.67579 0.967519i 0.711497 0.702690i \(-0.248018\pi\)
0.964295 0.264829i \(-0.0853156\pi\)
\(62\) −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 0.0255714 0.999673i \(-0.491859\pi\)
0.521982 + 0.852957i \(0.325193\pi\)
\(68\) 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 0.0781668 + 0.996940i \(0.475093\pi\)
−0.566165 + 0.824292i \(0.691573\pi\)
\(72\) 0 0
\(73\) 3.04327 + 3.04327i 0.356188 + 0.356188i 0.862406 0.506218i \(-0.168957\pi\)
−0.506218 + 0.862406i \(0.668957\pi\)
\(74\) 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 −0.827492 0.561477i \(-0.810233\pi\)
0.561477 + 0.827492i \(0.310233\pi\)
\(84\) 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 0.0597085 0.998216i \(-0.480983\pi\)
0.550817 + 0.834626i \(0.314316\pi\)
\(90\) 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 −0.653296 0.757103i \(-0.726614\pi\)
−0.944322 + 0.329022i \(0.893281\pi\)
\(98\) 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 0.0581328 + 0.998309i \(0.481485\pi\)
−0.893627 + 0.448810i \(0.851848\pi\)
\(102\) 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 −0.418983 0.907994i \(-0.637613\pi\)
0.995837 0.0911468i \(-0.0290533\pi\)
\(108\) 0 0
\(109\) 3.42240 + 3.42240i 0.327807 + 0.327807i 0.851752 0.523945i \(-0.175540\pi\)
−0.523945 + 0.851752i \(0.675540\pi\)
\(110\) 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 −0.985822 0.167795i \(-0.946335\pi\)
0.347596 0.937644i \(-0.386998\pi\)
\(114\) 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 0.910497 0.413515i \(-0.135699\pi\)
0.0971344 + 0.995271i \(0.469032\pi\)
\(128\) −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 \(0.0983861\pi\)
−0.952611 + 0.304191i \(0.901614\pi\)
\(132\) 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 0.300854 0.953670i \(-0.402728\pi\)
−0.216288 + 0.976330i \(0.569395\pi\)
\(138\) 0 0
\(139\) −13.5680 + 7.83346i −1.15082 + 0.664426i −0.949087 0.315015i \(-0.897990\pi\)
−0.201732 + 0.979441i \(0.564657\pi\)
\(140\) −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 0.720220 + 0.693746i \(0.244041\pi\)
−0.970602 + 0.240692i \(0.922626\pi\)
\(150\) 0 0
\(151\) −8.50103 + 8.50103i −0.691804 + 0.691804i −0.962629 0.270825i \(-0.912704\pi\)
0.270825 + 0.962629i \(0.412704\pi\)
\(152\) 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 \(0.00797357\pi\)
−0.999686 + 0.0250471i \(0.992026\pi\)
\(158\) 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 0.703590 0.710607i \(-0.251579\pi\)
0.254023 + 0.967198i \(0.418246\pi\)
\(164\) 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 −0.769332 0.638849i \(-0.779411\pi\)
−0.346837 + 0.937926i \(0.612744\pi\)
\(168\) 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 0.519958 0.854192i \(-0.325948\pi\)
−0.999731 + 0.0232010i \(0.992614\pi\)
\(174\) 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 0.809844 0.586645i \(-0.199552\pi\)
−0.103128 + 0.994668i \(0.532885\pi\)
\(180\) 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 0.893684 0.448697i \(-0.148112\pi\)
−0.835425 + 0.549604i \(0.814778\pi\)
\(192\) 0 0
\(193\) −6.36607 23.7585i −0.458240 1.71017i −0.678384 0.734707i \(-0.737319\pi\)
0.220144 0.975467i \(-0.429347\pi\)
\(194\) −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 −0.0847991 0.996398i \(-0.527025\pi\)
0.424761 + 0.905306i \(0.360358\pi\)
\(198\) 0 0
\(199\) −2.30866 3.99871i −0.163656 0.283461i 0.772521 0.634989i \(-0.218995\pi\)
−0.936177 + 0.351528i \(0.885662\pi\)
\(200\) −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 −0.958816 0.284026i \(-0.908330\pi\)
0.725382 + 0.688346i \(0.241663\pi\)
\(212\) −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 0.903587 + 0.428406i \(0.140925\pi\)
−0.568326 + 0.822803i \(0.692409\pi\)
\(224\) −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 −0.146306 0.989239i \(-0.546738\pi\)
−0.621324 + 0.783553i \(0.713405\pi\)
\(228\) 0 0
\(229\) −0.755536 0.755536i −0.0499272 0.0499272i 0.681702 0.731630i \(-0.261240\pi\)
−0.731630 + 0.681702i \(0.761240\pi\)
\(230\) 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 \(0.178814\pi\)
−0.846318 + 0.532677i \(0.821186\pi\)
\(234\) 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 0.0179604 0.999839i \(-0.494283\pi\)
−0.999839 + 0.0179604i \(0.994283\pi\)
\(240\) 0 0
\(241\) −3.31373 + 12.3670i −0.213456 + 0.796630i 0.773248 + 0.634104i \(0.218631\pi\)
−0.986704 + 0.162526i \(0.948036\pi\)
\(242\) −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 0.957356 0.288910i \(-0.0932928\pi\)
−0.728881 + 0.684640i \(0.759959\pi\)
\(252\) 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 −0.800552 0.599263i \(-0.795460\pi\)
0.919253 + 0.393667i \(0.128794\pi\)
\(258\) 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 −0.921475 0.388437i \(-0.873015\pi\)
0.797134 + 0.603802i \(0.206348\pi\)
\(264\) 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 −0.672539 0.740062i \(-0.734796\pi\)
0.304643 + 0.952467i \(0.401463\pi\)
\(270\) 0 0
\(271\) 8.12317 2.17660i 0.493447 0.132219i −0.00350987 0.999994i \(-0.501117\pi\)
0.496957 + 0.867775i \(0.334451\pi\)
\(272\) −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 −0.729224 0.684275i \(-0.760119\pi\)
0.227988 + 0.973664i \(0.426785\pi\)
\(278\) −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 −0.350777 0.936459i \(-0.614082\pi\)
0.936459 + 0.350777i \(0.114082\pi\)
\(282\) 0 0
\(283\) 0.916453 1.58734i 0.0544775 0.0943578i −0.837501 0.546436i \(-0.815984\pi\)
0.891978 + 0.452079i \(0.149317\pi\)
\(284\) 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 0.357719 + 0.933829i \(0.383554\pi\)
−0.776709 + 0.629860i \(0.783112\pi\)
\(294\) 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 0.998972 0.0453311i \(-0.0144343\pi\)
−0.0453311 + 0.998972i \(0.514434\pi\)
\(308\) 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 \(0.0427670\pi\)
−0.990988 + 0.133953i \(0.957233\pi\)
\(314\) 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 0.283172 0.959069i \(-0.408613\pi\)
−0.959069 + 0.283172i \(0.908613\pi\)
\(318\) 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 0.725306 + 0.688427i \(0.241698\pi\)
−0.972347 + 0.233542i \(0.924968\pi\)
\(332\) −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 \(-0.903512\pi\)
0.954408 0.298506i \(-0.0964882\pi\)
\(338\) −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 0.892816 0.450421i \(-0.148726\pi\)
−0.836484 + 0.547991i \(0.815393\pi\)
\(348\) 0 0
\(349\) −4.33364 + 1.16119i −0.231974 + 0.0621573i −0.372933 0.927858i \(-0.621648\pi\)
0.140959 + 0.990015i \(0.454981\pi\)
\(350\) −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 −0.993008 0.118047i \(-0.962337\pi\)
0.800946 0.598736i \(-0.204330\pi\)
\(354\) 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 −0.977998 0.208615i \(-0.933104\pi\)
0.208615 + 0.977998i \(0.433104\pi\)
\(360\) 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 0.651408 0.758728i \(-0.274179\pi\)
−0.331374 + 0.943500i \(0.607512\pi\)
\(368\) 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 0.551881 0.833923i \(-0.313910\pi\)
−0.998139 + 0.0609820i \(0.980577\pi\)
\(374\) 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 −0.144847 0.989454i \(-0.546269\pi\)
0.369286 + 0.929316i \(0.379602\pi\)
\(380\) 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 −0.531456 0.847086i \(-0.678355\pi\)
−0.883798 + 0.467870i \(0.845022\pi\)
\(384\) 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 \(-0.947735\pi\)
0.986550 0.163460i \(-0.0522654\pi\)
\(390\) 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 −0.448661 0.893702i \(-0.648099\pi\)
0.835403 0.549638i \(-0.185234\pi\)
\(398\) −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 0.941675 + 0.336524i \(0.109251\pi\)
−0.647252 + 0.762276i \(0.724082\pi\)
\(402\) 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 0.199918 0.979813i \(-0.435932\pi\)
−0.316772 + 0.948502i \(0.602599\pi\)
\(410\) −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 0.0262443 0.999656i \(-0.491645\pi\)
−0.852605 + 0.522556i \(0.824979\pi\)
\(420\) 0 0
\(421\) 14.8560 + 14.8560i 0.724035 + 0.724035i 0.969425 0.245389i \(-0.0789158\pi\)
−0.245389 + 0.969425i \(0.578916\pi\)
\(422\) −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 −0.576939 0.816788i \(-0.695753\pi\)
−0.0912498 + 0.995828i \(0.529086\pi\)
\(432\) 0 0
\(433\) 18.2103 + 31.5412i 0.875131 + 1.51577i 0.856623 + 0.515943i \(0.172558\pi\)
0.0185084 + 0.999829i \(0.494108\pi\)
\(434\) 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 0.176378 + 0.984323i \(0.443562\pi\)
−0.940637 + 0.339414i \(0.889771\pi\)
\(440\) −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 −0.208029 0.978123i \(-0.566705\pi\)
−0.669220 + 0.743065i \(0.733371\pi\)
\(450\) 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 0.364776 0.931095i \(-0.381146\pi\)
0.781453 + 0.623964i \(0.214479\pi\)
\(458\) −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 0.754818 0.655935i \(-0.227725\pi\)
0.325724 + 0.945465i \(0.394392\pi\)
\(462\) 0 0
\(463\) 1.96489 1.96489i 0.0913160 0.0913160i −0.659973 0.751289i \(-0.729432\pi\)
0.751289 + 0.659973i \(0.229432\pi\)
\(464\) −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 −0.145773 0.989318i \(-0.546567\pi\)
0.368416 + 0.929661i \(0.379900\pi\)
\(480\) 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 −0.947542 0.319630i \(-0.896441\pi\)
0.980411 + 0.196964i \(0.0631081\pi\)
\(488\) −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 0.723077 0.690767i \(-0.242727\pi\)
−0.236683 + 0.971587i \(0.576060\pi\)
\(492\) 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 0.553507 0.832845i \(-0.313289\pi\)
−0.832845 + 0.553507i \(0.813289\pi\)
\(500\) −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 −0.163198 0.986593i \(-0.552181\pi\)
0.772816 + 0.634631i \(0.218848\pi\)
\(504\) 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 −0.952201 0.305472i \(-0.901186\pi\)
0.671894 0.740647i \(-0.265481\pi\)
\(510\) 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 \(-0.979150\pi\)
0.997856 0.0654547i \(-0.0208498\pi\)
\(522\) 0 0
\(523\) −23.5900 13.6197i −1.03152 0.595547i −0.114099 0.993469i \(-0.536398\pi\)
−0.917419 + 0.397922i \(0.869731\pi\)
\(524\) 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 −0.806386 0.591390i \(-0.798579\pi\)
0.591390 + 0.806386i \(0.298579\pi\)
\(542\) 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 0.993410 + 0.114613i \(0.0365629\pi\)
−0.803012 + 0.595963i \(0.796770\pi\)
\(558\) 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 0.991987 0.126338i \(-0.0403223\pi\)
−0.605405 + 0.795917i \(0.706989\pi\)
\(564\) 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 0.732385 0.680891i \(-0.238407\pi\)
−0.223476 + 0.974709i \(0.571740\pi\)
\(570\) 0 0
\(571\) 10.4239i 0.436226i −0.975924 0.218113i \(-0.930010\pi\)
0.975924 0.218113i \(-0.0699901\pi\)
\(572\) 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 −0.433191 0.901302i \(-0.642612\pi\)
0.901302 + 0.433191i \(0.142612\pi\)
\(578\) 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 0.762900 + 0.646517i \(0.223775\pi\)
−0.337432 + 0.941350i \(0.609558\pi\)
\(588\) 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 0.0346408 0.999400i \(-0.488971\pi\)
−0.999400 + 0.0346408i \(0.988971\pi\)
\(594\) 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 0.912094 0.409981i \(-0.134465\pi\)
0.100993 + 0.994887i \(0.467798\pi\)
\(602\) −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 −0.662634 0.748944i \(-0.730561\pi\)
0.317287 + 0.948329i \(0.397228\pi\)
\(608\) 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 −0.720499 0.693456i \(-0.756087\pi\)
−0.277242 + 0.960800i \(0.589420\pi\)
\(614\) 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 −0.990887 0.134693i \(-0.956995\pi\)
0.925480 + 0.378796i \(0.123662\pi\)
\(618\) 0 0
\(619\) −28.4665 28.4665i −1.14416 1.14416i −0.987680 0.156484i \(-0.949984\pi\)
−0.156484 0.987680i \(-0.550016\pi\)
\(620\) −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 0.494048 0.869435i \(-0.335517\pi\)
−0.00685968 + 0.999976i \(0.502184\pi\)
\(632\) −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 −0.892977 0.450102i \(-0.851388\pi\)
−0.0566885 + 0.998392i \(0.518054\pi\)
\(642\) 0 0
\(643\) −17.1125 4.58528i −0.674851 0.180826i −0.0949121 0.995486i \(-0.530257\pi\)
−0.579939 + 0.814660i \(0.696924\pi\)
\(644\) 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 −0.793005 0.609215i \(-0.791485\pi\)
0.924098 + 0.382155i \(0.124818\pi\)
\(648\) 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 −0.856241 0.516576i \(-0.827206\pi\)
0.875489 + 0.483239i \(0.160540\pi\)
\(654\) 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 0.995137 0.0984983i \(-0.0314039\pi\)
−0.582871 + 0.812565i \(0.698071\pi\)
\(660\) 0 0
\(661\) 16.8983 4.52790i 0.657270 0.176115i 0.0852561 0.996359i \(-0.472829\pi\)
0.572013 + 0.820244i \(0.306163\pi\)
\(662\) 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 0.853343 0.521351i \(-0.174572\pi\)
−0.0248316 + 0.999692i \(0.507905\pi\)
\(674\) −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 \(-0.887450\pi\)
0.938137 0.346266i \(-0.112550\pi\)
\(678\) 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 0.809390 0.587271i \(-0.199798\pi\)
0.407317 + 0.913287i \(0.366464\pi\)
\(684\) 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 0.996620 + 0.0821472i \(0.0261778\pi\)
−0.822025 + 0.569452i \(0.807156\pi\)
\(692\) −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 \(0.284195\pi\)
−0.627214 + 0.778847i \(0.715805\pi\)
\(702\) 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 −0.203910 0.978990i \(-0.565365\pi\)
−0.666086 + 0.745875i \(0.732032\pi\)
\(710\) −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 0.993783 0.111338i \(-0.0355137\pi\)
−0.593313 + 0.804972i \(0.702180\pi\)
\(720\) 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 0.576637 0.817001i \(-0.304365\pi\)
0.817001 0.576637i \(-0.195635\pi\)
\(734\) 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 −0.762305 0.647218i \(-0.775932\pi\)
0.336567 0.941660i \(-0.390734\pi\)
\(740\) −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 0.660808 0.750555i \(-0.270214\pi\)
0.947554 + 0.319596i \(0.103547\pi\)
\(744\) 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 0.914505 0.404575i \(-0.132581\pi\)
0.106880 + 0.994272i \(0.465914\pi\)
\(752\) 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 0.471123 + 0.882068i \(0.343849\pi\)
−0.999454 + 0.0330294i \(0.989484\pi\)
\(758\) 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 −0.681086 0.732204i \(-0.738492\pi\)
0.955939 0.293564i \(-0.0948414\pi\)
\(762\) 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 −0.617136 0.786857i \(-0.711707\pi\)
0.141027 0.990006i \(-0.454960\pi\)
\(770\) −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 0.113374 0.993552i \(-0.463834\pi\)
−0.398591 + 0.917129i \(0.630501\pi\)
\(774\) 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 −0.957436 0.288645i \(-0.906795\pi\)
0.973487 + 0.228744i \(0.0734619\pi\)