Properties

Label 576.2.bd.a.181.2
Level $576$
Weight $2$
Character 576.181
Analytic conductor $4.599$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 181.2
Character \(\chi\) \(=\) 576.181
Dual form 576.2.bd.a.541.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.468362 - 1.33441i) q^{2} +(-1.56127 + 1.24997i) q^{4} +(-0.914126 - 1.36809i) q^{5} +(2.65574 + 1.10004i) q^{7} +(2.39921 + 1.49793i) q^{8} +O(q^{10})\) \(q+(-0.468362 - 1.33441i) q^{2} +(-1.56127 + 1.24997i) q^{4} +(-0.914126 - 1.36809i) q^{5} +(2.65574 + 1.10004i) q^{7} +(2.39921 + 1.49793i) q^{8} +(-1.39744 + 1.86057i) q^{10} +(-0.246413 + 1.23880i) q^{11} +(0.319413 - 0.478036i) q^{13} +(0.224055 - 4.05906i) q^{14} +(0.875149 - 3.90309i) q^{16} +(3.38390 - 3.38390i) q^{17} +(4.19561 + 2.80342i) q^{19} +(3.13727 + 0.993326i) q^{20} +(1.76847 - 0.251393i) q^{22} +(-0.178010 - 0.429755i) q^{23} +(0.877384 - 2.11819i) q^{25} +(-0.787494 - 0.202333i) q^{26} +(-5.52137 + 1.60213i) q^{28} +(1.02242 + 5.14005i) q^{29} -10.0065i q^{31} +(-5.61819 + 0.660257i) q^{32} +(-6.10038 - 2.93060i) q^{34} +(-0.922728 - 4.63887i) q^{35} +(0.447703 - 0.299146i) q^{37} +(1.77583 - 6.91166i) q^{38} +(-0.143878 - 4.65162i) q^{40} +(-2.44115 - 5.89346i) q^{41} +(3.80641 + 0.757142i) q^{43} +(-1.16375 - 2.24212i) q^{44} +(-0.490094 + 0.438819i) q^{46} +(5.99084 - 5.99084i) q^{47} +(0.893127 + 0.893127i) q^{49} +(-3.23746 - 0.178704i) q^{50} +(0.0988389 + 1.14560i) q^{52} +(-0.810472 + 4.07452i) q^{53} +(1.92004 - 0.795307i) q^{55} +(4.72389 + 6.61736i) q^{56} +(6.38004 - 3.77172i) q^{58} +(1.03615 + 1.55070i) q^{59} +(-6.47490 + 1.28794i) q^{61} +(-13.3528 + 4.68668i) q^{62} +(3.51240 + 7.18770i) q^{64} -0.945978 q^{65} +(6.01983 - 1.19742i) q^{67} +(-1.05342 + 9.51296i) q^{68} +(-5.75795 + 3.40396i) q^{70} +(4.20400 + 1.74136i) q^{71} +(-0.911379 + 0.377506i) q^{73} +(-0.608868 - 0.457308i) q^{74} +(-10.0547 + 0.867487i) q^{76} +(-2.01715 + 3.01887i) q^{77} +(0.152459 + 0.152459i) q^{79} +(-6.13976 + 2.37064i) q^{80} +(-6.72092 + 6.01776i) q^{82} +(5.16472 + 3.45096i) q^{83} +(-7.72277 - 1.53615i) q^{85} +(-0.772445 - 5.43391i) q^{86} +(-2.44684 + 2.60303i) q^{88} +(-1.48745 + 3.59102i) q^{89} +(1.37414 - 0.918171i) q^{91} +(0.815104 + 0.448458i) q^{92} +(-10.8001 - 5.18832i) q^{94} -8.30263i q^{95} +13.7742i q^{97} +(0.773486 - 1.61010i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} + O(q^{10}) \) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} - 8q^{10} + 8q^{11} - 8q^{13} + 8q^{14} - 8q^{16} + 8q^{17} - 8q^{19} + 8q^{20} + 8q^{23} - 8q^{25} - 32q^{26} + 32q^{28} + 8q^{29} - 32q^{32} + 32q^{34} + 8q^{35} - 8q^{37} - 32q^{38} + 32q^{40} + 8q^{41} - 8q^{43} - 8q^{46} + 8q^{47} - 8q^{49} + 32q^{50} - 56q^{52} + 8q^{53} + 56q^{55} + 64q^{56} - 80q^{58} - 56q^{59} - 8q^{61} + 40q^{62} - 104q^{64} + 16q^{65} + 72q^{67} + 56q^{68} - 104q^{70} - 56q^{71} - 8q^{73} + 64q^{74} - 72q^{76} + 8q^{77} + 24q^{79} - 32q^{80} + 72q^{82} + 8q^{83} - 8q^{85} - 96q^{86} + 72q^{88} + 8q^{89} - 8q^{91} - 144q^{92} + 88q^{94} - 128q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{16}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.468362 1.33441i −0.331182 0.943567i
\(3\) 0 0
\(4\) −1.56127 + 1.24997i −0.780637 + 0.624985i
\(5\) −0.914126 1.36809i −0.408810 0.611827i 0.568744 0.822515i \(-0.307430\pi\)
−0.977553 + 0.210688i \(0.932430\pi\)
\(6\) 0 0
\(7\) 2.65574 + 1.10004i 1.00378 + 0.415778i 0.823181 0.567779i \(-0.192197\pi\)
0.180596 + 0.983557i \(0.442197\pi\)
\(8\) 2.39921 + 1.49793i 0.848248 + 0.529599i
\(9\) 0 0
\(10\) −1.39744 + 1.86057i −0.441909 + 0.588365i
\(11\) −0.246413 + 1.23880i −0.0742963 + 0.373513i −0.999989 0.00476447i \(-0.998483\pi\)
0.925692 + 0.378277i \(0.123483\pi\)
\(12\) 0 0
\(13\) 0.319413 0.478036i 0.0885893 0.132583i −0.784528 0.620093i \(-0.787095\pi\)
0.873117 + 0.487510i \(0.162095\pi\)
\(14\) 0.224055 4.05906i 0.0598813 1.08483i
\(15\) 0 0
\(16\) 0.875149 3.90309i 0.218787 0.975773i
\(17\) 3.38390 3.38390i 0.820715 0.820715i −0.165495 0.986211i \(-0.552922\pi\)
0.986211 + 0.165495i \(0.0529223\pi\)
\(18\) 0 0
\(19\) 4.19561 + 2.80342i 0.962539 + 0.643148i 0.934313 0.356453i \(-0.116014\pi\)
0.0282261 + 0.999602i \(0.491014\pi\)
\(20\) 3.13727 + 0.993326i 0.701514 + 0.222115i
\(21\) 0 0
\(22\) 1.76847 0.251393i 0.377040 0.0535972i
\(23\) −0.178010 0.429755i −0.0371177 0.0896101i 0.904234 0.427038i \(-0.140443\pi\)
−0.941351 + 0.337428i \(0.890443\pi\)
\(24\) 0 0
\(25\) 0.877384 2.11819i 0.175477 0.423638i
\(26\) −0.787494 0.202333i −0.154440 0.0396807i
\(27\) 0 0
\(28\) −5.52137 + 1.60213i −1.04344 + 0.302774i
\(29\) 1.02242 + 5.14005i 0.189858 + 0.954483i 0.951773 + 0.306805i \(0.0992598\pi\)
−0.761914 + 0.647678i \(0.775740\pi\)
\(30\) 0 0
\(31\) 10.0065i 1.79722i −0.438743 0.898612i \(-0.644576\pi\)
0.438743 0.898612i \(-0.355424\pi\)
\(32\) −5.61819 + 0.660257i −0.993165 + 0.116718i
\(33\) 0 0
\(34\) −6.10038 2.93060i −1.04621 0.502593i
\(35\) −0.922728 4.63887i −0.155969 0.784111i
\(36\) 0 0
\(37\) 0.447703 0.299146i 0.0736019 0.0491792i −0.518225 0.855244i \(-0.673407\pi\)
0.591827 + 0.806065i \(0.298407\pi\)
\(38\) 1.77583 6.91166i 0.288077 1.12122i
\(39\) 0 0
\(40\) −0.143878 4.65162i −0.0227491 0.735486i
\(41\) −2.44115 5.89346i −0.381244 0.920404i −0.991726 0.128374i \(-0.959024\pi\)
0.610482 0.792030i \(-0.290976\pi\)
\(42\) 0 0
\(43\) 3.80641 + 0.757142i 0.580472 + 0.115463i 0.476589 0.879126i \(-0.341873\pi\)
0.103883 + 0.994589i \(0.466873\pi\)
\(44\) −1.16375 2.24212i −0.175441 0.338012i
\(45\) 0 0
\(46\) −0.490094 + 0.438819i −0.0722604 + 0.0647003i
\(47\) 5.99084 5.99084i 0.873854 0.873854i −0.119036 0.992890i \(-0.537980\pi\)
0.992890 + 0.119036i \(0.0379804\pi\)
\(48\) 0 0
\(49\) 0.893127 + 0.893127i 0.127590 + 0.127590i
\(50\) −3.23746 0.178704i −0.457846 0.0252726i
\(51\) 0 0
\(52\) 0.0988389 + 1.14560i 0.0137065 + 0.158866i
\(53\) −0.810472 + 4.07452i −0.111327 + 0.559678i 0.884353 + 0.466820i \(0.154600\pi\)
−0.995679 + 0.0928581i \(0.970400\pi\)
\(54\) 0 0
\(55\) 1.92004 0.795307i 0.258898 0.107239i
\(56\) 4.72389 + 6.61736i 0.631256 + 0.884282i
\(57\) 0 0
\(58\) 6.38004 3.77172i 0.837740 0.495252i
\(59\) 1.03615 + 1.55070i 0.134895 + 0.201884i 0.892767 0.450519i \(-0.148761\pi\)
−0.757872 + 0.652403i \(0.773761\pi\)
\(60\) 0 0
\(61\) −6.47490 + 1.28794i −0.829026 + 0.164903i −0.591323 0.806435i \(-0.701394\pi\)
−0.237702 + 0.971338i \(0.576394\pi\)
\(62\) −13.3528 + 4.68668i −1.69580 + 0.595209i
\(63\) 0 0
\(64\) 3.51240 + 7.18770i 0.439050 + 0.898463i
\(65\) −0.945978 −0.117334
\(66\) 0 0
\(67\) 6.01983 1.19742i 0.735439 0.146288i 0.186860 0.982387i \(-0.440169\pi\)
0.548579 + 0.836099i \(0.315169\pi\)
\(68\) −1.05342 + 9.51296i −0.127746 + 1.15362i
\(69\) 0 0
\(70\) −5.75795 + 3.40396i −0.688207 + 0.406851i
\(71\) 4.20400 + 1.74136i 0.498924 + 0.206661i 0.617931 0.786232i \(-0.287971\pi\)
−0.119007 + 0.992893i \(0.537971\pi\)
\(72\) 0 0
\(73\) −0.911379 + 0.377506i −0.106669 + 0.0441837i −0.435380 0.900247i \(-0.643386\pi\)
0.328711 + 0.944431i \(0.393386\pi\)
\(74\) −0.608868 0.457308i −0.0707795 0.0531610i
\(75\) 0 0
\(76\) −10.0547 + 0.867487i −1.15335 + 0.0995076i
\(77\) −2.01715 + 3.01887i −0.229875 + 0.344033i
\(78\) 0 0
\(79\) 0.152459 + 0.152459i 0.0171530 + 0.0171530i 0.715631 0.698478i \(-0.246139\pi\)
−0.698478 + 0.715631i \(0.746139\pi\)
\(80\) −6.13976 + 2.37064i −0.686446 + 0.265045i
\(81\) 0 0
\(82\) −6.72092 + 6.01776i −0.742201 + 0.664550i
\(83\) 5.16472 + 3.45096i 0.566902 + 0.378792i 0.805741 0.592267i \(-0.201767\pi\)
−0.238840 + 0.971059i \(0.576767\pi\)
\(84\) 0 0
\(85\) −7.72277 1.53615i −0.837652 0.166619i
\(86\) −0.772445 5.43391i −0.0832949 0.585954i
\(87\) 0 0
\(88\) −2.44684 + 2.60303i −0.260834 + 0.277484i
\(89\) −1.48745 + 3.59102i −0.157669 + 0.380648i −0.982898 0.184151i \(-0.941046\pi\)
0.825228 + 0.564799i \(0.191046\pi\)
\(90\) 0 0
\(91\) 1.37414 0.918171i 0.144049 0.0962505i
\(92\) 0.815104 + 0.448458i 0.0849805 + 0.0467549i
\(93\) 0 0
\(94\) −10.8001 5.18832i −1.11394 0.535135i
\(95\) 8.30263i 0.851832i
\(96\) 0 0
\(97\) 13.7742i 1.39856i 0.714849 + 0.699279i \(0.246495\pi\)
−0.714849 + 0.699279i \(0.753505\pi\)
\(98\) 0.773486 1.61010i 0.0781339 0.162645i
\(99\) 0 0
\(100\) 1.27784 + 4.40378i 0.127784 + 0.440378i
\(101\) −3.34129 + 2.23258i −0.332470 + 0.222150i −0.710589 0.703608i \(-0.751571\pi\)
0.378118 + 0.925757i \(0.376571\pi\)
\(102\) 0 0
\(103\) 3.02140 7.29430i 0.297707 0.718728i −0.702270 0.711911i \(-0.747830\pi\)
0.999977 0.00681740i \(-0.00217006\pi\)
\(104\) 1.48240 0.668448i 0.145362 0.0655467i
\(105\) 0 0
\(106\) 5.81665 0.826852i 0.564963 0.0803110i
\(107\) 5.40913 + 1.07594i 0.522920 + 0.104015i 0.449490 0.893285i \(-0.351606\pi\)
0.0734296 + 0.997300i \(0.476606\pi\)
\(108\) 0 0
\(109\) −3.62995 2.42545i −0.347686 0.232316i 0.369448 0.929251i \(-0.379547\pi\)
−0.717134 + 0.696935i \(0.754547\pi\)
\(110\) −1.96054 2.18962i −0.186930 0.208772i
\(111\) 0 0
\(112\) 6.61775 9.40290i 0.625318 0.888491i
\(113\) 11.6929 + 11.6929i 1.09998 + 1.09998i 0.994412 + 0.105567i \(0.0336656\pi\)
0.105567 + 0.994412i \(0.466334\pi\)
\(114\) 0 0
\(115\) −0.425218 + 0.636384i −0.0396518 + 0.0593431i
\(116\) −8.02118 6.74702i −0.744748 0.626445i
\(117\) 0 0
\(118\) 1.58397 2.10893i 0.145816 0.194142i
\(119\) 12.7092 5.26432i 1.16505 0.482580i
\(120\) 0 0
\(121\) 8.68876 + 3.59900i 0.789888 + 0.327182i
\(122\) 4.75123 + 8.03691i 0.430156 + 0.727628i
\(123\) 0 0
\(124\) 12.5079 + 15.6229i 1.12324 + 1.40298i
\(125\) −11.7687 + 2.34095i −1.05263 + 0.209381i
\(126\) 0 0
\(127\) −21.9517 −1.94790 −0.973949 0.226767i \(-0.927185\pi\)
−0.973949 + 0.226767i \(0.927185\pi\)
\(128\) 7.94623 8.05341i 0.702354 0.711828i
\(129\) 0 0
\(130\) 0.443060 + 1.26232i 0.0388590 + 0.110713i
\(131\) 7.05871 1.40406i 0.616722 0.122674i 0.123164 0.992386i \(-0.460696\pi\)
0.493558 + 0.869713i \(0.335696\pi\)
\(132\) 0 0
\(133\) 8.05858 + 12.0605i 0.698768 + 1.04578i
\(134\) −4.41730 7.47207i −0.381597 0.645488i
\(135\) 0 0
\(136\) 13.1875 3.04982i 1.13082 0.261520i
\(137\) −10.2318 + 4.23815i −0.874161 + 0.362089i −0.774229 0.632905i \(-0.781862\pi\)
−0.0999315 + 0.994994i \(0.531862\pi\)
\(138\) 0 0
\(139\) −0.752410 + 3.78262i −0.0638186 + 0.320838i −0.999486 0.0320443i \(-0.989798\pi\)
0.935668 + 0.352882i \(0.114798\pi\)
\(140\) 7.23907 + 6.08916i 0.611813 + 0.514628i
\(141\) 0 0
\(142\) 0.354676 6.42543i 0.0297638 0.539210i
\(143\) 0.513484 + 0.513484i 0.0429397 + 0.0429397i
\(144\) 0 0
\(145\) 6.09741 6.09741i 0.506362 0.506362i
\(146\) 0.930601 + 1.03934i 0.0770171 + 0.0860163i
\(147\) 0 0
\(148\) −0.325064 + 1.02666i −0.0267201 + 0.0843912i
\(149\) −21.8201 4.34028i −1.78757 0.355569i −0.813455 0.581628i \(-0.802416\pi\)
−0.974114 + 0.226059i \(0.927416\pi\)
\(150\) 0 0
\(151\) 2.99065 + 7.22006i 0.243375 + 0.587560i 0.997614 0.0690406i \(-0.0219938\pi\)
−0.754239 + 0.656600i \(0.771994\pi\)
\(152\) 5.86681 + 13.0107i 0.475861 + 1.05531i
\(153\) 0 0
\(154\) 4.97316 + 1.27776i 0.400748 + 0.102965i
\(155\) −13.6898 + 9.14722i −1.09959 + 0.734723i
\(156\) 0 0
\(157\) −4.09955 20.6098i −0.327180 1.64484i −0.697970 0.716127i \(-0.745913\pi\)
0.370790 0.928717i \(-0.379087\pi\)
\(158\) 0.132036 0.274849i 0.0105042 0.0218658i
\(159\) 0 0
\(160\) 6.03902 + 7.08261i 0.477427 + 0.559930i
\(161\) 1.33714i 0.105381i
\(162\) 0 0
\(163\) 3.99966 + 20.1077i 0.313278 + 1.57495i 0.741293 + 0.671182i \(0.234213\pi\)
−0.428015 + 0.903772i \(0.640787\pi\)
\(164\) 11.1780 + 6.14994i 0.872851 + 0.480229i
\(165\) 0 0
\(166\) 2.18601 8.50812i 0.169667 0.660359i
\(167\) −5.57052 + 13.4484i −0.431060 + 1.04067i 0.547886 + 0.836553i \(0.315433\pi\)
−0.978946 + 0.204118i \(0.934567\pi\)
\(168\) 0 0
\(169\) 4.84839 + 11.7051i 0.372953 + 0.900389i
\(170\) 1.56720 + 11.0248i 0.120199 + 0.845562i
\(171\) 0 0
\(172\) −6.88925 + 3.57579i −0.525301 + 0.272652i
\(173\) 15.4616 + 10.3311i 1.17552 + 0.785459i 0.980727 0.195384i \(-0.0625954\pi\)
0.194796 + 0.980844i \(0.437595\pi\)
\(174\) 0 0
\(175\) 4.66021 4.66021i 0.352279 0.352279i
\(176\) 4.61951 + 2.04591i 0.348208 + 0.154216i
\(177\) 0 0
\(178\) 5.48854 + 0.302961i 0.411384 + 0.0227079i
\(179\) 5.99376 8.97030i 0.447995 0.670472i −0.536896 0.843648i \(-0.680403\pi\)
0.984891 + 0.173177i \(0.0554032\pi\)
\(180\) 0 0
\(181\) 0.698076 3.50946i 0.0518876 0.260856i −0.946130 0.323786i \(-0.895044\pi\)
0.998018 + 0.0629294i \(0.0200443\pi\)
\(182\) −1.86881 1.40362i −0.138525 0.104043i
\(183\) 0 0
\(184\) 0.216660 1.29772i 0.0159724 0.0956691i
\(185\) −0.818514 0.339039i −0.0601783 0.0249267i
\(186\) 0 0
\(187\) 3.35814 + 5.02581i 0.245572 + 0.367524i
\(188\) −1.86497 + 16.8417i −0.136017 + 1.22831i
\(189\) 0 0
\(190\) −11.0791 + 3.88864i −0.803761 + 0.282112i
\(191\) 0.722126 0.0522512 0.0261256 0.999659i \(-0.491683\pi\)
0.0261256 + 0.999659i \(0.491683\pi\)
\(192\) 0 0
\(193\) −5.30778 −0.382063 −0.191031 0.981584i \(-0.561183\pi\)
−0.191031 + 0.981584i \(0.561183\pi\)
\(194\) 18.3804 6.45131i 1.31963 0.463177i
\(195\) 0 0
\(196\) −2.51080 0.278034i −0.179343 0.0198595i
\(197\) −8.28629 12.4013i −0.590373 0.883556i 0.409209 0.912441i \(-0.365805\pi\)
−0.999583 + 0.0288843i \(0.990805\pi\)
\(198\) 0 0
\(199\) −0.443861 0.183853i −0.0314644 0.0130330i 0.366896 0.930262i \(-0.380421\pi\)
−0.398360 + 0.917229i \(0.630421\pi\)
\(200\) 5.27793 3.76772i 0.373206 0.266418i
\(201\) 0 0
\(202\) 4.54409 + 3.41297i 0.319721 + 0.240136i
\(203\) −2.93900 + 14.7753i −0.206277 + 1.03703i
\(204\) 0 0
\(205\) −5.83124 + 8.72707i −0.407272 + 0.609525i
\(206\) −11.1487 0.615393i −0.776764 0.0428765i
\(207\) 0 0
\(208\) −1.58628 1.66505i −0.109989 0.115451i
\(209\) −4.50673 + 4.50673i −0.311737 + 0.311737i
\(210\) 0 0
\(211\) −12.2014 8.15273i −0.839980 0.561257i 0.0594948 0.998229i \(-0.481051\pi\)
−0.899475 + 0.436972i \(0.856051\pi\)
\(212\) −3.82766 7.37450i −0.262884 0.506483i
\(213\) 0 0
\(214\) −1.09769 7.72190i −0.0750365 0.527858i
\(215\) −2.44370 5.89962i −0.166659 0.402351i
\(216\) 0 0
\(217\) 11.0076 26.5748i 0.747246 1.80401i
\(218\) −1.53641 + 5.97982i −0.104059 + 0.405004i
\(219\) 0 0
\(220\) −2.00360 + 3.64168i −0.135083 + 0.245522i
\(221\) −0.536762 2.69848i −0.0361065 0.181520i
\(222\) 0 0
\(223\) 20.5439i 1.37572i −0.725843 0.687860i \(-0.758550\pi\)
0.725843 0.687860i \(-0.241450\pi\)
\(224\) −15.6468 4.42679i −1.04544 0.295777i
\(225\) 0 0
\(226\) 10.1266 21.0796i 0.673610 1.40220i
\(227\) −3.83215 19.2655i −0.254348 1.27870i −0.870931 0.491406i \(-0.836483\pi\)
0.616582 0.787290i \(-0.288517\pi\)
\(228\) 0 0
\(229\) −18.1422 + 12.1223i −1.19887 + 0.801061i −0.984447 0.175680i \(-0.943788\pi\)
−0.214425 + 0.976740i \(0.568788\pi\)
\(230\) 1.04835 + 0.269355i 0.0691261 + 0.0177607i
\(231\) 0 0
\(232\) −5.24644 + 13.8636i −0.344446 + 0.910187i
\(233\) 1.49754 + 3.61539i 0.0981074 + 0.236852i 0.965312 0.261100i \(-0.0840854\pi\)
−0.867204 + 0.497953i \(0.834085\pi\)
\(234\) 0 0
\(235\) −13.6724 2.71960i −0.891887 0.177407i
\(236\) −3.55604 1.12592i −0.231478 0.0732910i
\(237\) 0 0
\(238\) −12.9772 14.4936i −0.841190 0.939481i
\(239\) −4.87803 + 4.87803i −0.315534 + 0.315534i −0.847049 0.531515i \(-0.821623\pi\)
0.531515 + 0.847049i \(0.321623\pi\)
\(240\) 0 0
\(241\) 1.70539 + 1.70539i 0.109854 + 0.109854i 0.759897 0.650043i \(-0.225249\pi\)
−0.650043 + 0.759897i \(0.725249\pi\)
\(242\) 0.733039 13.2800i 0.0471215 0.853669i
\(243\) 0 0
\(244\) 8.49920 10.1042i 0.544106 0.646858i
\(245\) 0.405444 2.03831i 0.0259029 0.130223i
\(246\) 0 0
\(247\) 2.68027 1.11020i 0.170541 0.0706405i
\(248\) 14.9891 24.0077i 0.951808 1.52449i
\(249\) 0 0
\(250\) 8.63581 + 14.6079i 0.546177 + 0.923882i
\(251\) 0.380597 + 0.569604i 0.0240231 + 0.0359531i 0.843287 0.537464i \(-0.180618\pi\)
−0.819264 + 0.573417i \(0.805618\pi\)
\(252\) 0 0
\(253\) 0.576245 0.114622i 0.0362282 0.00720625i
\(254\) 10.2813 + 29.2925i 0.645109 + 1.83797i
\(255\) 0 0
\(256\) −14.4682 6.83157i −0.904264 0.426973i
\(257\) −24.3404 −1.51831 −0.759156 0.650908i \(-0.774388\pi\)
−0.759156 + 0.650908i \(0.774388\pi\)
\(258\) 0 0
\(259\) 1.51806 0.301960i 0.0943275 0.0187629i
\(260\) 1.47693 1.18244i 0.0915953 0.0733321i
\(261\) 0 0
\(262\) −5.17963 8.76157i −0.319998 0.541291i
\(263\) −9.60085 3.97680i −0.592014 0.245220i 0.0665030 0.997786i \(-0.478816\pi\)
−0.658517 + 0.752566i \(0.728816\pi\)
\(264\) 0 0
\(265\) 6.31516 2.61583i 0.387937 0.160689i
\(266\) 12.3193 16.4021i 0.755344 1.00568i
\(267\) 0 0
\(268\) −7.90186 + 9.39411i −0.482683 + 0.573836i
\(269\) 17.3303 25.9367i 1.05665 1.58139i 0.271136 0.962541i \(-0.412601\pi\)
0.785513 0.618845i \(-0.212399\pi\)
\(270\) 0 0
\(271\) 11.8443 + 11.8443i 0.719491 + 0.719491i 0.968501 0.249010i \(-0.0801053\pi\)
−0.249010 + 0.968501i \(0.580105\pi\)
\(272\) −10.2462 16.1691i −0.621269 0.980394i
\(273\) 0 0
\(274\) 10.4476 + 11.6684i 0.631162 + 0.704912i
\(275\) 2.40782 + 1.60885i 0.145197 + 0.0970176i
\(276\) 0 0
\(277\) −25.5130 5.07485i −1.53293 0.304918i −0.644741 0.764401i \(-0.723035\pi\)
−0.888187 + 0.459483i \(0.848035\pi\)
\(278\) 5.39995 0.767617i 0.323867 0.0460386i
\(279\) 0 0
\(280\) 4.73489 12.5118i 0.282964 0.747722i
\(281\) 9.37710 22.6383i 0.559391 1.35049i −0.350858 0.936429i \(-0.614110\pi\)
0.910249 0.414061i \(-0.135890\pi\)
\(282\) 0 0
\(283\) −19.3155 + 12.9062i −1.14819 + 0.767195i −0.975979 0.217865i \(-0.930091\pi\)
−0.172210 + 0.985060i \(0.555091\pi\)
\(284\) −8.74024 + 2.53615i −0.518638 + 0.150493i
\(285\) 0 0
\(286\) 0.444699 0.925692i 0.0262956 0.0547373i
\(287\) 18.3369i 1.08239i
\(288\) 0 0
\(289\) 5.90150i 0.347147i
\(290\) −10.9922 5.28061i −0.645484 0.310088i
\(291\) 0 0
\(292\) 0.951041 1.72859i 0.0556555 0.101158i
\(293\) −23.5455 + 15.7326i −1.37554 + 0.919109i −0.999970 0.00768446i \(-0.997554\pi\)
−0.375573 + 0.926793i \(0.622554\pi\)
\(294\) 0 0
\(295\) 1.17433 2.83507i 0.0683719 0.165064i
\(296\) 1.52223 0.0470838i 0.0884779 0.00273669i
\(297\) 0 0
\(298\) 4.42800 + 31.1496i 0.256507 + 1.80445i
\(299\) −0.262297 0.0521741i −0.0151690 0.00301731i
\(300\) 0 0
\(301\) 9.27596 + 6.19800i 0.534657 + 0.357247i
\(302\) 8.23377 7.37234i 0.473800 0.424230i
\(303\) 0 0
\(304\) 14.6138 13.9224i 0.838158 0.798507i
\(305\) 7.68088 + 7.68088i 0.439806 + 0.439806i
\(306\) 0 0
\(307\) −6.01712 + 9.00525i −0.343415 + 0.513957i −0.962469 0.271392i \(-0.912516\pi\)
0.619054 + 0.785348i \(0.287516\pi\)
\(308\) −0.624184 7.23466i −0.0355662 0.412233i
\(309\) 0 0
\(310\) 18.6179 + 13.9835i 1.05742 + 0.794210i
\(311\) 6.91332 2.86359i 0.392018 0.162379i −0.177963 0.984037i \(-0.556951\pi\)
0.569981 + 0.821658i \(0.306951\pi\)
\(312\) 0 0
\(313\) −20.9463 8.67625i −1.18396 0.490411i −0.298174 0.954511i \(-0.596378\pi\)
−0.885783 + 0.464101i \(0.846378\pi\)
\(314\) −25.5818 + 15.1233i −1.44366 + 0.853459i
\(315\) 0 0
\(316\) −0.428600 0.0474611i −0.0241106 0.00266989i
\(317\) 12.9479 2.57551i 0.727229 0.144655i 0.182427 0.983219i \(-0.441605\pi\)
0.544802 + 0.838565i \(0.316605\pi\)
\(318\) 0 0
\(319\) −6.61944 −0.370617
\(320\) 6.62262 11.3757i 0.370216 0.635923i
\(321\) 0 0
\(322\) −1.78428 + 0.626265i −0.0994343 + 0.0349004i
\(323\) 23.6840 4.71104i 1.31781 0.262129i
\(324\) 0 0
\(325\) −0.732323 1.09600i −0.0406220 0.0607951i
\(326\) 24.9585 14.7548i 1.38232 0.817195i
\(327\) 0 0
\(328\) 2.97117 17.7963i 0.164056 0.982637i
\(329\) 22.5003 9.31994i 1.24048 0.513825i
\(330\) 0 0
\(331\) 0.994900 5.00170i 0.0546846 0.274918i −0.943763 0.330624i \(-0.892741\pi\)
0.998447 + 0.0557056i \(0.0177408\pi\)
\(332\) −12.3771 + 1.06786i −0.679283 + 0.0586064i
\(333\) 0 0
\(334\) 20.5547 + 1.13459i 1.12470 + 0.0620822i
\(335\) −7.14106 7.14106i −0.390158 0.390158i
\(336\) 0 0
\(337\) −9.51763 + 9.51763i −0.518459 + 0.518459i −0.917105 0.398646i \(-0.869480\pi\)
0.398646 + 0.917105i \(0.369480\pi\)
\(338\) 13.3485 11.9519i 0.726061 0.650099i
\(339\) 0 0
\(340\) 13.9775 7.25487i 0.758036 0.393451i
\(341\) 12.3961 + 2.46574i 0.671286 + 0.133527i
\(342\) 0 0
\(343\) −6.31088 15.2358i −0.340755 0.822656i
\(344\) 7.99822 + 7.51829i 0.431235 + 0.405359i
\(345\) 0 0
\(346\) 6.54425 25.4707i 0.351821 1.36931i
\(347\) −24.8873 + 16.6292i −1.33602 + 0.892701i −0.998812 0.0487284i \(-0.984483\pi\)
−0.337210 + 0.941430i \(0.609483\pi\)
\(348\) 0 0
\(349\) 2.77238 + 13.9377i 0.148402 + 0.746067i 0.981276 + 0.192605i \(0.0616936\pi\)
−0.832874 + 0.553462i \(0.813306\pi\)
\(350\) −8.40128 4.03594i −0.449067 0.215730i
\(351\) 0 0
\(352\) 0.566468 7.12252i 0.0301928 0.379632i
\(353\) 22.9803i 1.22312i 0.791199 + 0.611558i \(0.209457\pi\)
−0.791199 + 0.611558i \(0.790543\pi\)
\(354\) 0 0
\(355\) −1.46066 7.34326i −0.0775240 0.389740i
\(356\) −2.16635 7.46584i −0.114817 0.395689i
\(357\) 0 0
\(358\) −14.7773 3.79676i −0.781003 0.200665i
\(359\) −2.63107 + 6.35196i −0.138862 + 0.335244i −0.977978 0.208710i \(-0.933073\pi\)
0.839115 + 0.543954i \(0.183073\pi\)
\(360\) 0 0
\(361\) 2.47302 + 5.97039i 0.130159 + 0.314231i
\(362\) −5.01000 + 0.712185i −0.263320 + 0.0374316i
\(363\) 0 0
\(364\) −0.997722 + 3.15115i −0.0522948 + 0.165165i
\(365\) 1.34958 + 0.901757i 0.0706400 + 0.0472001i
\(366\) 0 0
\(367\) −2.41091 + 2.41091i −0.125848 + 0.125848i −0.767226 0.641377i \(-0.778363\pi\)
0.641377 + 0.767226i \(0.278363\pi\)
\(368\) −1.83316 + 0.318691i −0.0955600 + 0.0166129i
\(369\) 0 0
\(370\) −0.0690550 + 1.25102i −0.00359000 + 0.0650375i
\(371\) −6.63456 + 9.92931i −0.344449 + 0.515504i
\(372\) 0 0
\(373\) 2.78301 13.9911i 0.144099 0.724433i −0.839400 0.543515i \(-0.817093\pi\)
0.983498 0.180918i \(-0.0579068\pi\)
\(374\) 5.13364 6.83502i 0.265454 0.353431i
\(375\) 0 0
\(376\) 23.3471 5.39940i 1.20404 0.278453i
\(377\) 2.78370 + 1.15305i 0.143368 + 0.0593849i
\(378\) 0 0
\(379\) 14.2902 + 21.3867i 0.734036 + 1.09856i 0.991223 + 0.132201i \(0.0422044\pi\)
−0.257187 + 0.966362i \(0.582796\pi\)
\(380\) 10.3780 + 12.9627i 0.532382 + 0.664972i
\(381\) 0 0
\(382\) −0.338217 0.963608i −0.0173047 0.0493025i
\(383\) −21.5847 −1.10293 −0.551463 0.834199i \(-0.685930\pi\)
−0.551463 + 0.834199i \(0.685930\pi\)
\(384\) 0 0
\(385\) 5.97401 0.304464
\(386\) 2.48597 + 7.08273i 0.126532 + 0.360502i
\(387\) 0 0
\(388\) −17.2173 21.5053i −0.874077 1.09177i
\(389\) −3.94394 5.90253i −0.199966 0.299270i 0.717911 0.696135i \(-0.245098\pi\)
−0.917877 + 0.396864i \(0.870098\pi\)
\(390\) 0 0
\(391\) −2.05662 0.851878i −0.104007 0.0430813i
\(392\) 0.804954 + 3.48064i 0.0406563 + 0.175799i
\(393\) 0 0
\(394\) −12.6674 + 16.8656i −0.638173 + 0.849675i
\(395\) 0.0692105 0.347944i 0.00348236 0.0175070i
\(396\) 0 0
\(397\) −7.40790 + 11.0867i −0.371792 + 0.556426i −0.969439 0.245334i \(-0.921102\pi\)
0.597647 + 0.801759i \(0.296102\pi\)
\(398\) −0.0374469 + 0.678400i −0.00187704 + 0.0340051i
\(399\) 0 0
\(400\) −7.49965 5.27824i −0.374983 0.263912i
\(401\) 8.50260 8.50260i 0.424600 0.424600i −0.462184 0.886784i \(-0.652934\pi\)
0.886784 + 0.462184i \(0.152934\pi\)
\(402\) 0 0
\(403\) −4.78347 3.19622i −0.238282 0.159215i
\(404\) 2.42601 7.66217i 0.120698 0.381207i
\(405\) 0 0
\(406\) 21.0928 2.99840i 1.04682 0.148808i
\(407\) 0.260262 + 0.628329i 0.0129007 + 0.0311451i
\(408\) 0 0
\(409\) 10.8420 26.1750i 0.536104 1.29427i −0.391320 0.920255i \(-0.627981\pi\)
0.927423 0.374014i \(-0.122019\pi\)
\(410\) 14.3766 + 3.69381i 0.710009 + 0.182424i
\(411\) 0 0
\(412\) 4.40043 + 15.1650i 0.216793 + 0.747128i
\(413\) 1.04590 + 5.25807i 0.0514651 + 0.258733i
\(414\) 0 0
\(415\) 10.2204i 0.501699i
\(416\) −1.47890 + 2.89659i −0.0725089 + 0.142017i
\(417\) 0 0
\(418\) 8.12459 + 3.90302i 0.397387 + 0.190903i
\(419\) 4.06419 + 20.4320i 0.198549 + 0.998171i 0.943581 + 0.331142i \(0.107434\pi\)
−0.745032 + 0.667028i \(0.767566\pi\)
\(420\) 0 0
\(421\) −18.4939 + 12.3572i −0.901337 + 0.602254i −0.917553 0.397614i \(-0.869838\pi\)
0.0162157 + 0.999869i \(0.494838\pi\)
\(422\) −5.16436 + 20.1001i −0.251397 + 0.978456i
\(423\) 0 0
\(424\) −8.04784 + 8.56158i −0.390838 + 0.415787i
\(425\) −4.19876 10.1367i −0.203670 0.491703i
\(426\) 0 0
\(427\) −18.6125 3.70225i −0.900720 0.179164i
\(428\) −9.79002 + 5.08141i −0.473219 + 0.245619i
\(429\) 0 0
\(430\) −6.72795 + 6.02405i −0.324450 + 0.290505i
\(431\) −9.16945 + 9.16945i −0.441677 + 0.441677i −0.892575 0.450898i \(-0.851104\pi\)
0.450898 + 0.892575i \(0.351104\pi\)
\(432\) 0 0
\(433\) 9.06306 + 9.06306i 0.435543 + 0.435543i 0.890509 0.454966i \(-0.150349\pi\)
−0.454966 + 0.890509i \(0.650349\pi\)
\(434\) −40.6171 2.24201i −1.94968 0.107620i
\(435\) 0 0
\(436\) 8.69909 0.750530i 0.416611 0.0359439i
\(437\) 0.457921 2.30212i 0.0219053 0.110125i
\(438\) 0 0
\(439\) 37.3964 15.4901i 1.78483 0.739301i 0.793395 0.608707i \(-0.208312\pi\)
0.991436 0.130594i \(-0.0416884\pi\)
\(440\) 5.79789 + 0.967984i 0.276404 + 0.0461468i
\(441\) 0 0
\(442\) −3.34947 + 1.98013i −0.159318 + 0.0941850i
\(443\) 0.953921 + 1.42764i 0.0453222 + 0.0678294i 0.853439 0.521193i \(-0.174513\pi\)
−0.808117 + 0.589023i \(0.799513\pi\)
\(444\) 0 0
\(445\) 6.27255 1.24769i 0.297347 0.0591460i
\(446\) −27.4139 + 9.62198i −1.29808 + 0.455614i
\(447\) 0 0
\(448\) 1.42123 + 22.9525i 0.0671470 + 1.08440i
\(449\) 24.6119 1.16151 0.580754 0.814079i \(-0.302758\pi\)
0.580754 + 0.814079i \(0.302758\pi\)
\(450\) 0 0
\(451\) 7.90236 1.57188i 0.372108 0.0740168i
\(452\) −32.8717 3.64005i −1.54615 0.171214i
\(453\) 0 0
\(454\) −23.9131 + 14.1369i −1.12230 + 0.663476i
\(455\) −2.51227 1.04062i −0.117777 0.0487849i
\(456\) 0 0
\(457\) 0.962960 0.398871i 0.0450454 0.0186584i −0.360047 0.932934i \(-0.617239\pi\)
0.405092 + 0.914276i \(0.367239\pi\)
\(458\) 24.6731 + 18.5315i 1.15290 + 0.865919i
\(459\) 0 0
\(460\) −0.131579 1.52508i −0.00613491 0.0711072i
\(461\) 7.72794 11.5657i 0.359926 0.538667i −0.606676 0.794949i \(-0.707498\pi\)
0.966602 + 0.256282i \(0.0824975\pi\)
\(462\) 0 0
\(463\) 8.29596 + 8.29596i 0.385546 + 0.385546i 0.873095 0.487549i \(-0.162109\pi\)
−0.487549 + 0.873095i \(0.662109\pi\)
\(464\) 20.9568 + 0.507716i 0.972896 + 0.0235701i
\(465\) 0 0
\(466\) 4.12300 3.69164i 0.190994 0.171012i
\(467\) 0.240041 + 0.160391i 0.0111078 + 0.00742199i 0.561112 0.827740i \(-0.310374\pi\)
−0.550004 + 0.835162i \(0.685374\pi\)
\(468\) 0 0
\(469\) 17.3043 + 3.44205i 0.799040 + 0.158939i
\(470\) 2.77457 + 19.5182i 0.127981 + 0.900309i
\(471\) 0 0
\(472\) 0.163083 + 5.27253i 0.00750651 + 0.242688i
\(473\) −1.87590 + 4.52882i −0.0862539 + 0.208235i
\(474\) 0 0
\(475\) 9.61934 6.42743i 0.441365 0.294911i
\(476\) −13.2623 + 24.1052i −0.607876 + 1.10486i
\(477\) 0 0
\(478\) 8.79395 + 4.22458i 0.402226 + 0.193228i
\(479\) 27.3994i 1.25191i 0.779860 + 0.625954i \(0.215290\pi\)
−0.779860 + 0.625954i \(0.784710\pi\)
\(480\) 0 0
\(481\) 0.309569i 0.0141151i
\(482\) 1.47694 3.07443i 0.0672730 0.140036i
\(483\) 0 0
\(484\) −18.0642 + 5.24167i −0.821099 + 0.238258i
\(485\) 18.8443 12.5913i 0.855675 0.571744i
\(486\) 0 0
\(487\) −11.7477 + 28.3614i −0.532338 + 1.28518i 0.397633 + 0.917544i \(0.369832\pi\)
−0.929971 + 0.367633i \(0.880168\pi\)
\(488\) −17.4639 6.60893i −0.790552 0.299172i
\(489\) 0 0
\(490\) −2.90982 + 0.413639i −0.131452 + 0.0186863i
\(491\) −1.43618 0.285675i −0.0648141 0.0128923i 0.162577 0.986696i \(-0.448019\pi\)
−0.227391 + 0.973804i \(0.573019\pi\)
\(492\) 0 0
\(493\) 20.8531 + 13.9336i 0.939178 + 0.627539i
\(494\) −2.73680 3.05658i −0.123134 0.137522i
\(495\) 0 0
\(496\) −39.0564 8.75720i −1.75368 0.393210i
\(497\) 9.24919 + 9.24919i 0.414883 + 0.414883i
\(498\) 0 0
\(499\) 8.33594 12.4756i 0.373168 0.558485i −0.596592 0.802544i \(-0.703479\pi\)
0.969760 + 0.244059i \(0.0784791\pi\)
\(500\) 15.4481 18.3654i 0.690861 0.821328i
\(501\) 0 0
\(502\) 0.581825 0.774652i 0.0259681 0.0345744i
\(503\) 9.56425 3.96164i 0.426449 0.176641i −0.159128 0.987258i \(-0.550868\pi\)
0.585577 + 0.810617i \(0.300868\pi\)
\(504\) 0 0
\(505\) 6.10871 + 2.53031i 0.271834 + 0.112597i
\(506\) −0.422844 0.715260i −0.0187977 0.0317972i
\(507\) 0 0
\(508\) 34.2726 27.4390i 1.52060 1.21741i
\(509\) 1.27790 0.254190i 0.0566419 0.0112668i −0.166688 0.986010i \(-0.553307\pi\)
0.223330 + 0.974743i \(0.428307\pi\)
\(510\) 0 0
\(511\) −2.83566 −0.125442
\(512\) −2.33971 + 22.5061i −0.103402 + 0.994640i
\(513\) 0 0
\(514\) 11.4001 + 32.4800i 0.502838 + 1.43263i
\(515\) −12.7412 + 2.53437i −0.561443 + 0.111678i
\(516\) 0 0
\(517\) 5.94524 + 8.89768i 0.261471 + 0.391320i
\(518\) −1.11394 1.88428i −0.0489436 0.0827904i
\(519\) 0 0
\(520\) −2.26960 1.41701i −0.0995284 0.0621400i
\(521\) 30.4733 12.6225i 1.33506 0.553001i 0.402967 0.915215i \(-0.367979\pi\)
0.932095 + 0.362214i \(0.117979\pi\)
\(522\) 0 0
\(523\) 0.709853 3.56867i 0.0310397 0.156047i −0.962157 0.272496i \(-0.912151\pi\)
0.993197 + 0.116448i \(0.0371510\pi\)
\(524\) −9.26554 + 11.0153i −0.404767 + 0.481206i
\(525\) 0 0
\(526\) −0.809988 + 14.6740i −0.0353172 + 0.639817i
\(527\) −33.8610 33.8610i −1.47501 1.47501i
\(528\) 0 0
\(529\) 16.1105 16.1105i 0.700455 0.700455i
\(530\) −6.44835 7.20183i −0.280099 0.312827i
\(531\) 0 0
\(532\) −27.6569 8.75678i −1.19908 0.379655i
\(533\) −3.59702 0.715492i −0.155804 0.0309914i
\(534\) 0 0
\(535\) −3.47264 8.38370i −0.150135 0.362459i
\(536\) 16.2365 + 6.14444i 0.701309 + 0.265399i
\(537\) 0 0
\(538\) −42.7269 10.9779i −1.84209 0.473292i
\(539\) −1.32649 + 0.886330i −0.0571358 + 0.0381769i
\(540\) 0 0
\(541\) 0.728776 + 3.66380i 0.0313325 + 0.157519i 0.993284 0.115701i \(-0.0369113\pi\)
−0.961952 + 0.273220i \(0.911911\pi\)
\(542\) 10.2577 21.3525i 0.440605 0.917170i
\(543\) 0 0
\(544\) −16.7771 + 21.2456i −0.719314 + 0.910898i
\(545\) 7.18326i 0.307697i
\(546\) 0 0
\(547\) 2.21811 + 11.1512i 0.0948394 + 0.476790i 0.998791 + 0.0491555i \(0.0156530\pi\)
−0.903952 + 0.427635i \(0.859347\pi\)
\(548\) 10.6771 19.4063i 0.456102 0.828998i
\(549\) 0 0
\(550\) 1.01913 3.96653i 0.0434559 0.169134i
\(551\) −10.1200 + 24.4319i −0.431128 + 1.04083i
\(552\) 0 0
\(553\) 0.237181 + 0.572605i 0.0100859 + 0.0243496i
\(554\) 5.17742 + 36.4215i 0.219968 + 1.54740i
\(555\) 0 0
\(556\) −3.55344 6.84619i −0.150700 0.290343i
\(557\) 15.2399 + 10.1830i 0.645734 + 0.431466i 0.834841 0.550491i \(-0.185559\pi\)
−0.189107 + 0.981956i \(0.560559\pi\)
\(558\) 0 0
\(559\) 1.57776 1.57776i 0.0667321 0.0667321i
\(560\) −18.9134 0.458211i −0.799239 0.0193630i
\(561\) 0 0
\(562\) −34.6006 1.90991i −1.45954 0.0805648i
\(563\) −2.21898 + 3.32093i −0.0935187 + 0.139961i −0.875279 0.483619i \(-0.839322\pi\)
0.781760 + 0.623579i \(0.214322\pi\)
\(564\) 0 0
\(565\) 5.30813 26.6858i 0.223315 1.12268i
\(566\) 26.2688 + 19.7300i 1.10416 + 0.829312i
\(567\) 0 0
\(568\) 7.47785 + 10.4752i 0.313764 + 0.439529i
\(569\) −27.7449 11.4923i −1.16313 0.481783i −0.284213 0.958761i \(-0.591732\pi\)
−0.878915 + 0.476978i \(0.841732\pi\)
\(570\) 0 0
\(571\) 17.3752 + 26.0038i 0.727128 + 1.08822i 0.992280 + 0.124017i \(0.0395777\pi\)
−0.265152 + 0.964207i \(0.585422\pi\)
\(572\) −1.44353 0.159849i −0.0603569 0.00668363i
\(573\) 0 0
\(574\) −24.4688 + 8.58831i −1.02131 + 0.358469i
\(575\) −1.06649 −0.0444756
\(576\) 0 0
\(577\) −4.61192 −0.191997 −0.0959984 0.995381i \(-0.530604\pi\)
−0.0959984 + 0.995381i \(0.530604\pi\)
\(578\) −7.87499 + 2.76404i −0.327557 + 0.114969i
\(579\) 0 0
\(580\) −1.89814 + 17.1413i −0.0788161 + 0.711753i
\(581\) 9.91996 + 14.8463i 0.411549 + 0.615927i
\(582\) 0 0
\(583\) −4.84781 2.00803i −0.200776 0.0831640i
\(584\) −2.75207 0.459470i −0.113881 0.0190130i
\(585\) 0 0
\(586\) 32.0215 + 24.0507i 1.32280 + 0.993524i
\(587\) 4.06182 20.4202i 0.167649 0.842831i −0.801810 0.597579i \(-0.796129\pi\)
0.969459 0.245252i \(-0.0788706\pi\)
\(588\) 0 0
\(589\) 28.0525 41.9835i 1.15588 1.72990i
\(590\) −4.33314 0.239185i −0.178393 0.00984707i
\(591\) 0 0
\(592\) −0.775785 2.00922i −0.0318846 0.0825785i
\(593\) 3.69463 3.69463i 0.151720 0.151720i −0.627166 0.778886i \(-0.715785\pi\)
0.778886 + 0.627166i \(0.215785\pi\)
\(594\) 0 0
\(595\) −18.8199 12.5750i −0.771539 0.515526i
\(596\) 39.4923 20.4981i 1.61767 0.839633i
\(597\) 0 0
\(598\) 0.0532287 + 0.374447i 0.00217668 + 0.0153123i
\(599\) 4.44136 + 10.7224i 0.181469 + 0.438105i 0.988270 0.152719i \(-0.0488028\pi\)
−0.806801 + 0.590824i \(0.798803\pi\)
\(600\) 0 0
\(601\) −4.16840 + 10.0634i −0.170033 + 0.410495i −0.985809 0.167873i \(-0.946310\pi\)
0.815776 + 0.578368i \(0.196310\pi\)
\(602\) 3.92613 15.2808i 0.160017 0.622799i
\(603\) 0 0
\(604\) −13.6941 7.53427i −0.557204 0.306565i
\(605\) −3.01888 15.1769i −0.122735 0.617030i
\(606\) 0 0
\(607\) 29.1457i 1.18299i 0.806310 + 0.591493i \(0.201461\pi\)
−0.806310 + 0.591493i \(0.798539\pi\)
\(608\) −25.4227 12.9800i −1.03103 0.526407i
\(609\) 0 0
\(610\) 6.65197 13.8468i 0.269330 0.560642i
\(611\) −0.950281 4.77739i −0.0384443 0.193272i
\(612\) 0 0
\(613\) −5.29850 + 3.54035i −0.214005 + 0.142993i −0.657953 0.753059i \(-0.728577\pi\)
0.443948 + 0.896052i \(0.353577\pi\)
\(614\) 14.8348 + 3.81155i 0.598686 + 0.153822i
\(615\) 0 0
\(616\) −9.36163 + 4.22136i −0.377191 + 0.170083i
\(617\) −3.88763 9.38556i −0.156510 0.377849i 0.826102 0.563521i \(-0.190554\pi\)
−0.982612 + 0.185673i \(0.940554\pi\)
\(618\) 0 0
\(619\) −3.09719 0.616070i −0.124487 0.0247620i 0.132454 0.991189i \(-0.457714\pi\)
−0.256940 + 0.966427i \(0.582714\pi\)
\(620\) 9.93975 31.3931i 0.399190 1.26078i
\(621\) 0 0
\(622\) −7.05913 7.88397i −0.283045 0.316118i
\(623\) −7.90057 + 7.90057i −0.316530 + 0.316530i
\(624\) 0 0
\(625\) 5.85477 + 5.85477i 0.234191 + 0.234191i
\(626\) −1.76716 + 32.0145i −0.0706301 + 1.27956i
\(627\) 0 0
\(628\) 32.1622 + 27.0533i 1.28341 + 1.07954i
\(629\) 0.502703 2.52726i 0.0200441 0.100768i
\(630\) 0 0
\(631\) −29.9605 + 12.4100i −1.19271 + 0.494036i −0.888636 0.458613i \(-0.848347\pi\)
−0.304073 + 0.952649i \(0.598347\pi\)
\(632\) 0.137408 + 0.594155i 0.00546579 + 0.0236342i
\(633\) 0 0
\(634\) −9.50110 16.0715i −0.377337 0.638282i
\(635\) 20.0666 + 30.0318i 0.796319 + 1.19178i
\(636\) 0 0
\(637\) 0.712223 0.141670i 0.0282193 0.00561317i
\(638\) 3.10029 + 8.83301i 0.122742 + 0.349702i
\(639\) 0 0
\(640\) −18.2816 3.50930i −0.722644 0.138717i
\(641\) −27.6811 −1.09334 −0.546668 0.837349i \(-0.684104\pi\)
−0.546668 + 0.837349i \(0.684104\pi\)
\(642\) 0 0
\(643\) 42.4514 8.44410i 1.67412 0.333003i 0.735386 0.677649i \(-0.237001\pi\)
0.938733 + 0.344646i \(0.112001\pi\)
\(644\) 1.67138 + 2.08764i 0.0658617 + 0.0822645i
\(645\) 0 0
\(646\) −17.3791 29.3976i −0.683772 1.15663i
\(647\) 35.3075 + 14.6248i 1.38808 + 0.574962i 0.946630 0.322324i \(-0.104464\pi\)
0.441451 + 0.897285i \(0.354464\pi\)
\(648\) 0 0
\(649\) −2.17633 + 0.901466i −0.0854285 + 0.0353856i
\(650\) −1.11951 + 1.49054i −0.0439109 + 0.0584638i
\(651\) 0 0
\(652\) −31.3785 26.3941i −1.22888 1.03367i
\(653\) −13.3150 + 19.9272i −0.521055 + 0.779813i −0.994908 0.100791i \(-0.967863\pi\)
0.473853 + 0.880604i \(0.342863\pi\)
\(654\) 0 0
\(655\) −8.37343 8.37343i −0.327177 0.327177i
\(656\) −25.1391 + 4.37037i −0.981516 + 0.170634i
\(657\) 0 0
\(658\) −22.9749 25.6594i −0.895654 1.00031i
\(659\) −17.2984 11.5584i −0.673852 0.450253i 0.170988 0.985273i \(-0.445304\pi\)
−0.844839 + 0.535020i \(0.820304\pi\)
\(660\) 0 0
\(661\) 14.9381 + 2.97137i 0.581025 + 0.115573i 0.476848 0.878986i \(-0.341779\pi\)
0.104177 + 0.994559i \(0.466779\pi\)
\(662\) −7.14027 + 1.01501i −0.277514 + 0.0394494i
\(663\) 0 0
\(664\) 7.22194 + 16.0160i 0.280266 + 0.621540i
\(665\) 9.13327 22.0497i 0.354173 0.855049i
\(666\) 0 0
\(667\) 2.02696 1.35437i 0.0784842 0.0524415i
\(668\) −8.11303 27.9597i −0.313902 1.08179i
\(669\) 0 0
\(670\) −6.18446 + 12.8737i −0.238927 + 0.497353i
\(671\) 8.33848i 0.321903i
\(672\) 0 0
\(673\) 33.8371i 1.30432i 0.758080 + 0.652162i \(0.226138\pi\)
−0.758080 + 0.652162i \(0.773862\pi\)
\(674\) 17.1581 + 8.24268i 0.660905 + 0.317496i
\(675\) 0 0
\(676\) −22.2006 12.2144i −0.853870 0.469786i
\(677\) −28.0419 + 18.7370i −1.07774 + 0.720121i −0.961970 0.273155i \(-0.911933\pi\)
−0.115768 + 0.993276i \(0.536933\pi\)
\(678\) 0 0
\(679\) −15.1522 + 36.5807i −0.581489 + 1.40384i
\(680\) −16.2275 15.2537i −0.622295 0.584954i
\(681\) 0 0
\(682\) −2.51557 17.6963i −0.0963263 0.677625i
\(683\) −14.0115 2.78707i −0.536137 0.106644i −0.0804066 0.996762i \(-0.525622\pi\)
−0.455730 + 0.890118i \(0.650622\pi\)
\(684\) 0 0
\(685\) 15.1513 + 10.1238i 0.578901 + 0.386809i
\(686\) −17.3750 + 15.5571i −0.663379 + 0.593975i
\(687\) 0 0
\(688\) 6.28637 14.1942i 0.239666 0.541147i
\(689\) 1.68889 + 1.68889i 0.0643415 + 0.0643415i
\(690\) 0 0
\(691\) 10.9236 16.3483i 0.415552 0.621918i −0.563357 0.826214i \(-0.690490\pi\)
0.978909 + 0.204296i \(0.0654904\pi\)
\(692\) −37.0533 + 3.19685i −1.40856 + 0.121526i
\(693\) 0 0
\(694\) 33.8463 + 25.4213i 1.28479 + 0.964979i
\(695\) 5.86275 2.42843i 0.222387 0.0921156i
\(696\) 0 0
\(697\) −28.2035 11.6823i −1.06828 0.442497i
\(698\) 17.3000 10.2274i 0.654816 0.387111i
\(699\) 0 0
\(700\) −1.45074 + 13.1010i −0.0548328 + 0.495171i
\(701\) −11.0341 + 2.19482i −0.416753 + 0.0828974i −0.399013 0.916945i \(-0.630647\pi\)
−0.0177402 + 0.999843i \(0.505647\pi\)
\(702\) 0 0
\(703\) 2.71702 0.102474
\(704\) −9.76964 + 2.58002i −0.368207 + 0.0972383i
\(705\) 0 0
\(706\) 30.6650 10.7631i 1.15409 0.405075i
\(707\) −11.3295 + 2.25358i −0.426091 + 0.0847548i
\(708\) 0 0
\(709\) −23.4418 35.0831i −0.880374 1.31757i −0.947476 0.319827i \(-0.896375\pi\)
0.0671017 0.997746i \(-0.478625\pi\)
\(710\) −9.11476 + 5.38842i −0.342071 + 0.202224i
\(711\) 0 0
\(712\) −8.94781 + 6.38751i −0.335333 + 0.239382i
\(713\) −4.30035 + 1.78127i −0.161050 + 0.0667089i
\(714\) 0 0
\(715\) 0.233101 1.17188i 0.00871749 0.0438258i
\(716\) 1.85470 + 21.4971i 0.0693135 + 0.803385i
\(717\) 0 0
\(718\) 9.70838 + 0.535892i 0.362314 + 0.0199993i
\(719\) 9.10621 + 9.10621i 0.339604 + 0.339604i 0.856218 0.516614i \(-0.172808\pi\)
−0.516614 + 0.856218i \(0.672808\pi\)
\(720\) 0 0
\(721\) 16.0481 16.0481i 0.597663 0.597663i
\(722\) 6.80865 6.09631i 0.253392 0.226881i
\(723\) 0 0
\(724\) 3.29684 + 6.35181i 0.122526 + 0.236063i
\(725\) 11.7847 + 2.34411i 0.437671 + 0.0870582i
\(726\) 0 0
\(727\) 8.28934 + 20.0122i 0.307435 + 0.742213i 0.999787 + 0.0206529i \(0.00657449\pi\)
−0.692352 + 0.721560i \(0.743426\pi\)
\(728\) 4.67221 0.144515i 0.173163 0.00535607i
\(729\) 0 0
\(730\) 0.571219 2.22323i 0.0211418 0.0822854i
\(731\) 15.4426 10.3184i 0.571165 0.381640i
\(732\) 0 0
\(733\) −1.86746 9.38837i −0.0689763 0.346767i 0.930850 0.365401i \(-0.119068\pi\)
−0.999826 + 0.0186340i \(0.994068\pi\)
\(734\) 4.34630 + 2.08795i 0.160425 + 0.0770676i
\(735\) 0 0
\(736\) 1.28384 + 2.29691i 0.0473232 + 0.0846653i
\(737\) 7.75244i 0.285565i
\(738\) 0 0
\(739\) −3.72209 18.7122i −0.136919 0.688340i −0.986875 0.161486i \(-0.948371\pi\)
0.849956 0.526854i \(-0.176629\pi\)
\(740\) 1.70171 0.493784i 0.0625562 0.0181519i
\(741\) 0 0
\(742\) 16.3571 + 4.20267i 0.600488 + 0.154285i
\(743\) 2.74886 6.63633i 0.100846 0.243463i −0.865402 0.501079i \(-0.832937\pi\)
0.966248 + 0.257615i \(0.0829368\pi\)
\(744\) 0 0
\(745\) 14.0084 + 33.8193i 0.513228 + 1.23904i
\(746\) −19.9733 + 2.83926i −0.731274 + 0.103953i
\(747\) 0 0
\(748\) −11.5251 3.64909i −0.421399 0.133424i
\(749\) 13.1817 + 8.80771i 0.481648 + 0.321827i
\(750\) 0 0
\(751\) −1.88191 + 1.88191i −0.0686719 + 0.0686719i −0.740609 0.671937i \(-0.765463\pi\)
0.671937 + 0.740609i \(0.265463\pi\)
\(752\) −18.1399 28.6257i −0.661494 1.04387i
\(753\) 0 0
\(754\) 0.234850 4.25462i 0.00855275 0.154944i
\(755\) 7.14383 10.6915i 0.259991 0.389104i
\(756\) 0 0
\(757\) 7.70412 38.7312i 0.280011 1.40771i −0.543023 0.839718i \(-0.682720\pi\)
0.823034 0.567992i \(-0.192280\pi\)
\(758\) 21.8456 29.0856i 0.793468 1.05644i
\(759\) 0 0
\(760\) 12.4368 19.9197i 0.451130 0.722565i
\(761\) 7.53878 + 3.12266i 0.273280 + 0.113196i 0.515115 0.857121i \(-0.327749\pi\)
−0.241835 + 0.970317i \(0.577749\pi\)
\(762\) 0 0
\(763\) −6.97211 10.4345i −0.252407 0.377754i
\(764\) −1.12744 + 0.902636i −0.0407892 + 0.0326562i
\(765\) 0 0
\(766\) 10.1095 + 28.8027i 0.365270 + 1.04068i
\(767\) 1.07225 0.0387167
\(768\) 0 0
\(769\) 3.77877 0.136266 0.0681330 0.997676i \(-0.478296\pi\)
0.0681330 + 0.997676i \(0.478296\pi\)
\(770\) −2.79800 7.97175i −0.100833 0.287282i
\(771\) 0 0
\(772\) 8.28690 6.63457i 0.298252 0.238783i
\(773\) 2.84091 + 4.25173i 0.102181 + 0.152924i 0.879037 0.476754i \(-0.158187\pi\)
−0.776856 + 0.629678i \(0.783187\pi\)
\(774\) 0 0
\(775\) −21.1957 8.77956i −0.761373 0.315371i
\(776\) −20.6328 + 33.0472i −0.740675 + 1.18632i
\(777\) 0 0
\(778\) −6.02917 + 8.02734i −0.216156 + 0.287794i
\(779\) 6.27971 31.5702i 0.224994 1.13112i
\(780\) 0 0
\(781\) −3.19312 + 4.77884i −0.114259 + 0.171000i
\(782\) −0.173509 + 3.14335i −0.00620467 + 0.112406i
\(783\) 0 0
\(784\) 4.26758 2.70434i 0.152413 0.0965835i
\(785\) −24.4485 + 24.4485i −0.872605 + 0.872605i
\(786\) 0 0
\(787\) −25.7884 17.2312i −0.919257 0.614228i 0.00333965 0.999994i \(-0.498937\pi\)
−0.922596 + 0.385767i \(0.873937\pi\)
\(788\) 28.4384 + 9.00422i