Properties

Label 1323.2.o.e.440.1
Level $1323$
Weight $2$
Character 1323.440
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 440.1
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.23278 - 1.28910i) q^{2} +(2.32354 + 4.02449i) q^{4} +(1.16595 + 2.01948i) q^{5} -6.82470i q^{8} +O(q^{10})\) \(q+(-2.23278 - 1.28910i) q^{2} +(2.32354 + 4.02449i) q^{4} +(1.16595 + 2.01948i) q^{5} -6.82470i q^{8} -6.01207i q^{10} +(3.78114 + 2.18304i) q^{11} +(1.14392 - 0.660445i) q^{13} +(-4.15061 + 7.18908i) q^{16} +5.78655 q^{17} -0.675357i q^{19} +(-5.41825 + 9.38468i) q^{20} +(-5.62830 - 9.74851i) q^{22} +(4.81799 - 2.78167i) q^{23} +(-0.218858 + 0.379074i) q^{25} -3.40551 q^{26} +(-3.86926 - 2.23392i) q^{29} +(-3.47965 + 2.00898i) q^{31} +(6.71411 - 3.87639i) q^{32} +(-12.9201 - 7.45942i) q^{34} +3.01658 q^{37} +(-0.870601 + 1.50792i) q^{38} +(13.7823 - 7.95723i) q^{40} +(-3.29501 - 5.70713i) q^{41} +(3.89217 - 6.74143i) q^{43} +20.2896i q^{44} -14.3434 q^{46} +(0.246705 - 0.427306i) q^{47} +(0.977326 - 0.564259i) q^{50} +(5.31591 + 3.06914i) q^{52} +4.14566i q^{53} +10.1812i q^{55} +(5.75947 + 9.97570i) q^{58} +(2.15699 + 3.73602i) q^{59} +(-1.77661 - 1.02572i) q^{61} +10.3591 q^{62} -3.38572 q^{64} +(2.66751 + 1.54009i) q^{65} +(2.41218 + 4.17802i) q^{67} +(13.4453 + 23.2879i) q^{68} +1.17135i q^{71} +15.1153i q^{73} +(-6.73536 - 3.88866i) q^{74} +(2.71797 - 1.56922i) q^{76} +(5.30428 - 9.18728i) q^{79} -19.3576 q^{80} +16.9904i q^{82} +(-5.32432 + 9.22199i) q^{83} +(6.74680 + 11.6858i) q^{85} +(-17.3807 + 10.0348i) q^{86} +(14.8986 - 25.8051i) q^{88} +3.32535 q^{89} +(22.3896 + 12.9266i) q^{92} +(-1.10168 + 0.636053i) q^{94} +(1.36387 - 0.787429i) q^{95} +(12.7531 + 7.36299i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23278 1.28910i −1.57882 0.911529i −0.995025 0.0996245i \(-0.968236\pi\)
−0.583790 0.811905i \(-0.698431\pi\)
\(3\) 0 0
\(4\) 2.32354 + 4.02449i 1.16177 + 2.01225i
\(5\) 1.16595 + 2.01948i 0.521427 + 0.903138i 0.999689 + 0.0249208i \(0.00793335\pi\)
−0.478263 + 0.878217i \(0.658733\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 6.82470i 2.41290i
\(9\) 0 0
\(10\) 6.01207i 1.90118i
\(11\) 3.78114 + 2.18304i 1.14006 + 0.658212i 0.946444 0.322867i \(-0.104647\pi\)
0.193612 + 0.981078i \(0.437980\pi\)
\(12\) 0 0
\(13\) 1.14392 0.660445i 0.317267 0.183174i −0.332906 0.942960i \(-0.608029\pi\)
0.650174 + 0.759785i \(0.274696\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.15061 + 7.18908i −1.03765 + 1.79727i
\(17\) 5.78655 1.40344 0.701722 0.712451i \(-0.252415\pi\)
0.701722 + 0.712451i \(0.252415\pi\)
\(18\) 0 0
\(19\) 0.675357i 0.154937i −0.996995 0.0774687i \(-0.975316\pi\)
0.996995 0.0774687i \(-0.0246838\pi\)
\(20\) −5.41825 + 9.38468i −1.21156 + 2.09848i
\(21\) 0 0
\(22\) −5.62830 9.74851i −1.19996 2.07839i
\(23\) 4.81799 2.78167i 1.00462 0.580018i 0.0950080 0.995477i \(-0.469712\pi\)
0.909612 + 0.415459i \(0.136379\pi\)
\(24\) 0 0
\(25\) −0.218858 + 0.379074i −0.0437717 + 0.0758147i
\(26\) −3.40551 −0.667875
\(27\) 0 0
\(28\) 0 0
\(29\) −3.86926 2.23392i −0.718503 0.414828i 0.0956983 0.995410i \(-0.469492\pi\)
−0.814202 + 0.580582i \(0.802825\pi\)
\(30\) 0 0
\(31\) −3.47965 + 2.00898i −0.624964 + 0.360823i −0.778799 0.627273i \(-0.784171\pi\)
0.153835 + 0.988097i \(0.450838\pi\)
\(32\) 6.71411 3.87639i 1.18690 0.685256i
\(33\) 0 0
\(34\) −12.9201 7.45942i −2.21578 1.27928i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.01658 0.495923 0.247961 0.968770i \(-0.420239\pi\)
0.247961 + 0.968770i \(0.420239\pi\)
\(38\) −0.870601 + 1.50792i −0.141230 + 0.244618i
\(39\) 0 0
\(40\) 13.7823 7.95723i 2.17918 1.25815i
\(41\) −3.29501 5.70713i −0.514594 0.891303i −0.999857 0.0169348i \(-0.994609\pi\)
0.485262 0.874369i \(-0.338724\pi\)
\(42\) 0 0
\(43\) 3.89217 6.74143i 0.593550 1.02806i −0.400200 0.916428i \(-0.631059\pi\)
0.993750 0.111631i \(-0.0356074\pi\)
\(44\) 20.2896i 3.05877i
\(45\) 0 0
\(46\) −14.3434 −2.11481
\(47\) 0.246705 0.427306i 0.0359856 0.0623289i −0.847472 0.530841i \(-0.821876\pi\)
0.883457 + 0.468512i \(0.155210\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.977326 0.564259i 0.138215 0.0797983i
\(51\) 0 0
\(52\) 5.31591 + 3.06914i 0.737184 + 0.425614i
\(53\) 4.14566i 0.569451i 0.958609 + 0.284725i \(0.0919024\pi\)
−0.958609 + 0.284725i \(0.908098\pi\)
\(54\) 0 0
\(55\) 10.1812i 1.37284i
\(56\) 0 0
\(57\) 0 0
\(58\) 5.75947 + 9.97570i 0.756256 + 1.30987i
\(59\) 2.15699 + 3.73602i 0.280816 + 0.486388i 0.971586 0.236687i \(-0.0760615\pi\)
−0.690770 + 0.723075i \(0.742728\pi\)
\(60\) 0 0
\(61\) −1.77661 1.02572i −0.227471 0.131330i 0.381934 0.924190i \(-0.375258\pi\)
−0.609405 + 0.792859i \(0.708592\pi\)
\(62\) 10.3591 1.31560
\(63\) 0 0
\(64\) −3.38572 −0.423215
\(65\) 2.66751 + 1.54009i 0.330863 + 0.191024i
\(66\) 0 0
\(67\) 2.41218 + 4.17802i 0.294695 + 0.510427i 0.974914 0.222582i \(-0.0714486\pi\)
−0.680219 + 0.733009i \(0.738115\pi\)
\(68\) 13.4453 + 23.2879i 1.63048 + 2.82408i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.17135i 0.139014i 0.997581 + 0.0695068i \(0.0221426\pi\)
−0.997581 + 0.0695068i \(0.977857\pi\)
\(72\) 0 0
\(73\) 15.1153i 1.76911i 0.466432 + 0.884557i \(0.345539\pi\)
−0.466432 + 0.884557i \(0.654461\pi\)
\(74\) −6.73536 3.88866i −0.782970 0.452048i
\(75\) 0 0
\(76\) 2.71797 1.56922i 0.311772 0.180002i
\(77\) 0 0
\(78\) 0 0
\(79\) 5.30428 9.18728i 0.596778 1.03365i −0.396515 0.918028i \(-0.629781\pi\)
0.993293 0.115622i \(-0.0368861\pi\)
\(80\) −19.3576 −2.16424
\(81\) 0 0
\(82\) 16.9904i 1.87627i
\(83\) −5.32432 + 9.22199i −0.584420 + 1.01225i 0.410527 + 0.911848i \(0.365345\pi\)
−0.994947 + 0.100397i \(0.967989\pi\)
\(84\) 0 0
\(85\) 6.74680 + 11.6858i 0.731793 + 1.26750i
\(86\) −17.3807 + 10.0348i −1.87421 + 1.08208i
\(87\) 0 0
\(88\) 14.8986 25.8051i 1.58820 2.75084i
\(89\) 3.32535 0.352486 0.176243 0.984347i \(-0.443605\pi\)
0.176243 + 0.984347i \(0.443605\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 22.3896 + 12.9266i 2.33428 + 1.34770i
\(93\) 0 0
\(94\) −1.10168 + 0.636053i −0.113629 + 0.0656039i
\(95\) 1.36387 0.787429i 0.139930 0.0807886i
\(96\) 0 0
\(97\) 12.7531 + 7.36299i 1.29488 + 0.747598i 0.979515 0.201373i \(-0.0645403\pi\)
0.315363 + 0.948971i \(0.397874\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.03411 −0.203411
\(101\) −0.832092 + 1.44123i −0.0827963 + 0.143407i −0.904450 0.426580i \(-0.859718\pi\)
0.821654 + 0.569987i \(0.193052\pi\)
\(102\) 0 0
\(103\) −1.40783 + 0.812812i −0.138718 + 0.0800887i −0.567753 0.823199i \(-0.692187\pi\)
0.429035 + 0.903288i \(0.358854\pi\)
\(104\) −4.50734 7.80694i −0.441981 0.765533i
\(105\) 0 0
\(106\) 5.34416 9.25636i 0.519071 0.899057i
\(107\) 18.3130i 1.77039i −0.465221 0.885194i \(-0.654025\pi\)
0.465221 0.885194i \(-0.345975\pi\)
\(108\) 0 0
\(109\) −15.9736 −1.52999 −0.764995 0.644036i \(-0.777259\pi\)
−0.764995 + 0.644036i \(0.777259\pi\)
\(110\) 13.1246 22.7325i 1.25138 2.16746i
\(111\) 0 0
\(112\) 0 0
\(113\) 5.07612 2.93070i 0.477521 0.275697i −0.241862 0.970311i \(-0.577758\pi\)
0.719383 + 0.694614i \(0.244425\pi\)
\(114\) 0 0
\(115\) 11.2350 + 6.48654i 1.04767 + 0.604873i
\(116\) 20.7624i 1.92774i
\(117\) 0 0
\(118\) 11.1223i 1.02389i
\(119\) 0 0
\(120\) 0 0
\(121\) 4.03134 + 6.98248i 0.366485 + 0.634771i
\(122\) 2.64451 + 4.58043i 0.239423 + 0.414693i
\(123\) 0 0
\(124\) −16.1702 9.33589i −1.45213 0.838388i
\(125\) 10.6387 0.951559
\(126\) 0 0
\(127\) −16.5710 −1.47044 −0.735218 0.677831i \(-0.762920\pi\)
−0.735218 + 0.677831i \(0.762920\pi\)
\(128\) −5.86864 3.38826i −0.518719 0.299483i
\(129\) 0 0
\(130\) −3.97064 6.87735i −0.348248 0.603183i
\(131\) −3.55989 6.16591i −0.311029 0.538718i 0.667556 0.744559i \(-0.267340\pi\)
−0.978585 + 0.205841i \(0.934007\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.4382i 1.07449i
\(135\) 0 0
\(136\) 39.4914i 3.38636i
\(137\) 0.716584 + 0.413720i 0.0612219 + 0.0353465i 0.530298 0.847811i \(-0.322080\pi\)
−0.469077 + 0.883157i \(0.655413\pi\)
\(138\) 0 0
\(139\) 12.0735 6.97062i 1.02406 0.591241i 0.108782 0.994066i \(-0.465305\pi\)
0.915277 + 0.402825i \(0.131972\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.50998 2.61537i 0.126715 0.219477i
\(143\) 5.76711 0.482270
\(144\) 0 0
\(145\) 10.4185i 0.865210i
\(146\) 19.4851 33.7492i 1.61260 2.79310i
\(147\) 0 0
\(148\) 7.00915 + 12.1402i 0.576149 + 0.997919i
\(149\) 9.46916 5.46702i 0.775744 0.447876i −0.0591761 0.998248i \(-0.518847\pi\)
0.834920 + 0.550372i \(0.185514\pi\)
\(150\) 0 0
\(151\) 6.97277 12.0772i 0.567436 0.982828i −0.429383 0.903123i \(-0.641269\pi\)
0.996818 0.0797050i \(-0.0253978\pi\)
\(152\) −4.60911 −0.373848
\(153\) 0 0
\(154\) 0 0
\(155\) −8.11417 4.68472i −0.651746 0.376286i
\(156\) 0 0
\(157\) 13.6641 7.88894i 1.09051 0.629606i 0.156798 0.987631i \(-0.449883\pi\)
0.933712 + 0.358024i \(0.116550\pi\)
\(158\) −23.6866 + 13.6755i −1.88440 + 1.08796i
\(159\) 0 0
\(160\) 15.6566 + 9.03932i 1.23776 + 0.714621i
\(161\) 0 0
\(162\) 0 0
\(163\) −6.76552 −0.529916 −0.264958 0.964260i \(-0.585358\pi\)
−0.264958 + 0.964260i \(0.585358\pi\)
\(164\) 15.3122 26.5215i 1.19568 2.07098i
\(165\) 0 0
\(166\) 23.7761 13.7271i 1.84538 1.06543i
\(167\) 9.54631 + 16.5347i 0.738716 + 1.27949i 0.953074 + 0.302738i \(0.0979008\pi\)
−0.214358 + 0.976755i \(0.568766\pi\)
\(168\) 0 0
\(169\) −5.62763 + 9.74733i −0.432894 + 0.749795i
\(170\) 34.7891i 2.66820i
\(171\) 0 0
\(172\) 36.1745 2.75828
\(173\) −10.9246 + 18.9219i −0.830579 + 1.43860i 0.0670016 + 0.997753i \(0.478657\pi\)
−0.897580 + 0.440851i \(0.854677\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −31.3881 + 18.1219i −2.36597 + 1.36599i
\(177\) 0 0
\(178\) −7.42478 4.28670i −0.556511 0.321302i
\(179\) 17.1896i 1.28481i 0.766364 + 0.642406i \(0.222064\pi\)
−0.766364 + 0.642406i \(0.777936\pi\)
\(180\) 0 0
\(181\) 16.6462i 1.23730i 0.785666 + 0.618650i \(0.212320\pi\)
−0.785666 + 0.618650i \(0.787680\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −18.9840 32.8813i −1.39952 2.42404i
\(185\) 3.51717 + 6.09191i 0.258587 + 0.447886i
\(186\) 0 0
\(187\) 21.8797 + 12.6323i 1.60000 + 0.923763i
\(188\) 2.29292 0.167228
\(189\) 0 0
\(190\) −4.06029 −0.294565
\(191\) −0.826254 0.477038i −0.0597857 0.0345173i 0.469809 0.882768i \(-0.344323\pi\)
−0.529595 + 0.848251i \(0.677656\pi\)
\(192\) 0 0
\(193\) 0.847203 + 1.46740i 0.0609830 + 0.105626i 0.894905 0.446257i \(-0.147243\pi\)
−0.833922 + 0.551882i \(0.813910\pi\)
\(194\) −18.9832 32.8799i −1.36292 2.36064i
\(195\) 0 0
\(196\) 0 0
\(197\) 12.7486i 0.908301i −0.890925 0.454150i \(-0.849943\pi\)
0.890925 0.454150i \(-0.150057\pi\)
\(198\) 0 0
\(199\) 4.35807i 0.308935i 0.987998 + 0.154468i \(0.0493662\pi\)
−0.987998 + 0.154468i \(0.950634\pi\)
\(200\) 2.58706 + 1.49364i 0.182933 + 0.105616i
\(201\) 0 0
\(202\) 3.71576 2.14530i 0.261440 0.150942i
\(203\) 0 0
\(204\) 0 0
\(205\) 7.68361 13.3084i 0.536646 0.929499i
\(206\) 4.19117 0.292013
\(207\) 0 0
\(208\) 10.9650i 0.760287i
\(209\) 1.47433 2.55362i 0.101982 0.176637i
\(210\) 0 0
\(211\) −2.24368 3.88617i −0.154461 0.267535i 0.778401 0.627767i \(-0.216031\pi\)
−0.932863 + 0.360232i \(0.882698\pi\)
\(212\) −16.6842 + 9.63263i −1.14588 + 0.661571i
\(213\) 0 0
\(214\) −23.6073 + 40.8890i −1.61376 + 2.79512i
\(215\) 18.1522 1.23797
\(216\) 0 0
\(217\) 0 0
\(218\) 35.6655 + 20.5915i 2.41557 + 1.39463i
\(219\) 0 0
\(220\) −40.9743 + 23.6565i −2.76249 + 1.59492i
\(221\) 6.61937 3.82170i 0.445267 0.257075i
\(222\) 0 0
\(223\) −18.0005 10.3926i −1.20540 0.695939i −0.243650 0.969863i \(-0.578345\pi\)
−0.961751 + 0.273924i \(0.911678\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −15.1118 −1.00522
\(227\) 14.1579 24.5223i 0.939696 1.62760i 0.173657 0.984806i \(-0.444442\pi\)
0.766039 0.642795i \(-0.222225\pi\)
\(228\) 0 0
\(229\) −18.8670 + 10.8929i −1.24677 + 0.719821i −0.970463 0.241250i \(-0.922443\pi\)
−0.276303 + 0.961071i \(0.589109\pi\)
\(230\) −16.7236 28.9661i −1.10272 1.90997i
\(231\) 0 0
\(232\) −15.2458 + 26.4065i −1.00094 + 1.73367i
\(233\) 15.2335i 0.997978i 0.866608 + 0.498989i \(0.166295\pi\)
−0.866608 + 0.498989i \(0.833705\pi\)
\(234\) 0 0
\(235\) 1.15058 0.0750554
\(236\) −10.0237 + 17.3616i −0.652489 + 1.13014i
\(237\) 0 0
\(238\) 0 0
\(239\) 4.95125 2.85861i 0.320270 0.184908i −0.331243 0.943545i \(-0.607468\pi\)
0.651513 + 0.758638i \(0.274135\pi\)
\(240\) 0 0
\(241\) 3.87212 + 2.23557i 0.249425 + 0.144006i 0.619501 0.784996i \(-0.287335\pi\)
−0.370076 + 0.929002i \(0.620668\pi\)
\(242\) 20.7871i 1.33625i
\(243\) 0 0
\(244\) 9.53325i 0.610304i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.446036 0.772557i −0.0283806 0.0491566i
\(248\) 13.7107 + 23.7476i 0.870629 + 1.50797i
\(249\) 0 0
\(250\) −23.7540 13.7144i −1.50234 0.867374i
\(251\) −11.6265 −0.733861 −0.366931 0.930248i \(-0.619591\pi\)
−0.366931 + 0.930248i \(0.619591\pi\)
\(252\) 0 0
\(253\) 24.2900 1.52710
\(254\) 36.9993 + 21.3616i 2.32155 + 1.34034i
\(255\) 0 0
\(256\) 12.1213 + 20.9947i 0.757582 + 1.31217i
\(257\) 1.05140 + 1.82108i 0.0655846 + 0.113596i 0.896953 0.442126i \(-0.145775\pi\)
−0.831369 + 0.555721i \(0.812442\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 14.3138i 0.887705i
\(261\) 0 0
\(262\) 18.3562i 1.13405i
\(263\) 1.90773 + 1.10143i 0.117636 + 0.0679170i 0.557663 0.830067i \(-0.311698\pi\)
−0.440028 + 0.897984i \(0.645031\pi\)
\(264\) 0 0
\(265\) −8.37207 + 4.83362i −0.514292 + 0.296927i
\(266\) 0 0
\(267\) 0 0
\(268\) −11.2096 + 19.4156i −0.684737 + 1.18600i
\(269\) −27.8623 −1.69880 −0.849398 0.527753i \(-0.823035\pi\)
−0.849398 + 0.527753i \(0.823035\pi\)
\(270\) 0 0
\(271\) 11.4804i 0.697382i 0.937238 + 0.348691i \(0.113374\pi\)
−0.937238 + 0.348691i \(0.886626\pi\)
\(272\) −24.0177 + 41.5999i −1.45629 + 2.52237i
\(273\) 0 0
\(274\) −1.06665 1.84749i −0.0644387 0.111611i
\(275\) −1.65507 + 0.955553i −0.0998043 + 0.0576220i
\(276\) 0 0
\(277\) 5.10000 8.83346i 0.306429 0.530751i −0.671149 0.741322i \(-0.734199\pi\)
0.977579 + 0.210571i \(0.0675323\pi\)
\(278\) −35.9432 −2.15573
\(279\) 0 0
\(280\) 0 0
\(281\) −9.45116 5.45663i −0.563809 0.325515i 0.190864 0.981617i \(-0.438871\pi\)
−0.754673 + 0.656101i \(0.772204\pi\)
\(282\) 0 0
\(283\) −10.2766 + 5.93322i −0.610882 + 0.352693i −0.773311 0.634027i \(-0.781401\pi\)
0.162428 + 0.986720i \(0.448067\pi\)
\(284\) −4.71409 + 2.72168i −0.279730 + 0.161502i
\(285\) 0 0
\(286\) −12.8767 7.43437i −0.761415 0.439603i
\(287\) 0 0
\(288\) 0 0
\(289\) 16.4841 0.969655
\(290\) −13.4305 + 23.2622i −0.788664 + 1.36601i
\(291\) 0 0
\(292\) −60.8315 + 35.1211i −3.55989 + 2.05531i
\(293\) 9.55012 + 16.5413i 0.557924 + 0.966353i 0.997670 + 0.0682302i \(0.0217352\pi\)
−0.439746 + 0.898122i \(0.644931\pi\)
\(294\) 0 0
\(295\) −5.02987 + 8.71199i −0.292850 + 0.507232i
\(296\) 20.5872i 1.19661i
\(297\) 0 0
\(298\) −28.1901 −1.63301
\(299\) 3.67427 6.36403i 0.212489 0.368041i
\(300\) 0 0
\(301\) 0 0
\(302\) −31.1373 + 17.9772i −1.79175 + 1.03447i
\(303\) 0 0
\(304\) 4.85519 + 2.80315i 0.278464 + 0.160771i
\(305\) 4.78375i 0.273917i
\(306\) 0 0
\(307\) 2.35488i 0.134400i 0.997740 + 0.0672001i \(0.0214066\pi\)
−0.997740 + 0.0672001i \(0.978593\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 12.0781 + 20.9199i 0.685991 + 1.18817i
\(311\) 3.92483 + 6.79801i 0.222557 + 0.385480i 0.955584 0.294720i \(-0.0952263\pi\)
−0.733027 + 0.680200i \(0.761893\pi\)
\(312\) 0 0
\(313\) 26.0268 + 15.0266i 1.47112 + 0.849352i 0.999474 0.0324349i \(-0.0103262\pi\)
0.471647 + 0.881787i \(0.343660\pi\)
\(314\) −40.6785 −2.29562
\(315\) 0 0
\(316\) 49.2989 2.77328
\(317\) 9.61906 + 5.55356i 0.540260 + 0.311919i 0.745184 0.666859i \(-0.232361\pi\)
−0.204924 + 0.978778i \(0.565695\pi\)
\(318\) 0 0
\(319\) −9.75347 16.8935i −0.546089 0.945854i
\(320\) −3.94757 6.83739i −0.220676 0.382222i
\(321\) 0 0
\(322\) 0 0
\(323\) 3.90798i 0.217446i
\(324\) 0 0
\(325\) 0.578175i 0.0320714i
\(326\) 15.1059 + 8.72141i 0.836640 + 0.483034i
\(327\) 0 0
\(328\) −38.9494 + 22.4875i −2.15062 + 1.24166i
\(329\) 0 0
\(330\) 0 0
\(331\) 8.63362 14.9539i 0.474547 0.821939i −0.525028 0.851085i \(-0.675945\pi\)
0.999575 + 0.0291457i \(0.00927866\pi\)
\(332\) −49.4851 −2.71585
\(333\) 0 0
\(334\) 49.2245i 2.69345i
\(335\) −5.62495 + 9.74270i −0.307324 + 0.532300i
\(336\) 0 0
\(337\) −3.82962 6.63309i −0.208612 0.361327i 0.742665 0.669663i \(-0.233561\pi\)
−0.951278 + 0.308336i \(0.900228\pi\)
\(338\) 25.1305 14.5091i 1.36692 0.789192i
\(339\) 0 0
\(340\) −31.3530 + 54.3049i −1.70035 + 2.94510i
\(341\) −17.5427 −0.949992
\(342\) 0 0
\(343\) 0 0
\(344\) −46.0082 26.5629i −2.48060 1.43217i
\(345\) 0 0
\(346\) 48.7843 28.1656i 2.62266 1.51419i
\(347\) 11.4014 6.58262i 0.612061 0.353374i −0.161711 0.986838i \(-0.551701\pi\)
0.773772 + 0.633465i \(0.218368\pi\)
\(348\) 0 0
\(349\) 1.05185 + 0.607283i 0.0563040 + 0.0325071i 0.527888 0.849314i \(-0.322984\pi\)
−0.471584 + 0.881821i \(0.656318\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 33.8493 1.80417
\(353\) −13.4114 + 23.2292i −0.713816 + 1.23637i 0.249598 + 0.968349i \(0.419701\pi\)
−0.963414 + 0.268016i \(0.913632\pi\)
\(354\) 0 0
\(355\) −2.36551 + 1.36573i −0.125548 + 0.0724854i
\(356\) 7.72659 + 13.3829i 0.409509 + 0.709290i
\(357\) 0 0
\(358\) 22.1591 38.3807i 1.17114 2.02848i
\(359\) 7.45024i 0.393208i 0.980483 + 0.196604i \(0.0629914\pi\)
−0.980483 + 0.196604i \(0.937009\pi\)
\(360\) 0 0
\(361\) 18.5439 0.975994
\(362\) 21.4585 37.1673i 1.12784 1.95347i
\(363\) 0 0
\(364\) 0 0
\(365\) −30.5250 + 17.6236i −1.59775 + 0.922463i
\(366\) 0 0
\(367\) −30.3000 17.4937i −1.58165 0.913166i −0.994619 0.103601i \(-0.966963\pi\)
−0.587031 0.809565i \(-0.699703\pi\)
\(368\) 46.1825i 2.40743i
\(369\) 0 0
\(370\) 18.1359i 0.942840i
\(371\) 0 0
\(372\) 0 0
\(373\) 15.0495 + 26.0665i 0.779233 + 1.34967i 0.932384 + 0.361469i \(0.117725\pi\)
−0.153151 + 0.988203i \(0.548942\pi\)
\(374\) −32.5684 56.4102i −1.68407 2.91690i
\(375\) 0 0
\(376\) −2.91623 1.68369i −0.150393 0.0868295i
\(377\) −5.90152 −0.303944
\(378\) 0 0
\(379\) −27.0996 −1.39201 −0.696006 0.718036i \(-0.745041\pi\)
−0.696006 + 0.718036i \(0.745041\pi\)
\(380\) 6.33801 + 3.65925i 0.325133 + 0.187716i
\(381\) 0 0
\(382\) 1.22990 + 2.13024i 0.0629270 + 0.108993i
\(383\) 1.83015 + 3.16992i 0.0935164 + 0.161975i 0.908988 0.416821i \(-0.136856\pi\)
−0.815472 + 0.578796i \(0.803523\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4.36851i 0.222351i
\(387\) 0 0
\(388\) 68.4329i 3.47415i
\(389\) −10.5387 6.08449i −0.534331 0.308496i 0.208447 0.978034i \(-0.433159\pi\)
−0.742778 + 0.669537i \(0.766492\pi\)
\(390\) 0 0
\(391\) 27.8795 16.0962i 1.40993 0.814022i
\(392\) 0 0
\(393\) 0 0
\(394\) −16.4342 + 28.4649i −0.827943 + 1.43404i
\(395\) 24.7380 1.24470
\(396\) 0 0
\(397\) 26.7741i 1.34375i −0.740663 0.671876i \(-0.765489\pi\)
0.740663 0.671876i \(-0.234511\pi\)
\(398\) 5.61797 9.73061i 0.281603 0.487752i
\(399\) 0 0
\(400\) −1.81679 3.14678i −0.0908397 0.157339i
\(401\) −6.69428 + 3.86494i −0.334296 + 0.193006i −0.657747 0.753239i \(-0.728490\pi\)
0.323451 + 0.946245i \(0.395157\pi\)
\(402\) 0 0
\(403\) −2.65364 + 4.59624i −0.132187 + 0.228955i
\(404\) −7.73361 −0.384761
\(405\) 0 0
\(406\) 0 0
\(407\) 11.4061 + 6.58532i 0.565380 + 0.326422i
\(408\) 0 0
\(409\) 7.84660 4.53024i 0.387989 0.224006i −0.293299 0.956021i \(-0.594753\pi\)
0.681289 + 0.732015i \(0.261420\pi\)
\(410\) −34.3116 + 19.8098i −1.69453 + 0.978338i
\(411\) 0 0
\(412\) −6.54231 3.77720i −0.322316 0.186090i
\(413\) 0 0
\(414\) 0 0
\(415\) −24.8315 −1.21893
\(416\) 5.12029 8.86860i 0.251043 0.434819i
\(417\) 0 0
\(418\) −6.58372 + 3.80111i −0.322020 + 0.185919i
\(419\) −3.30466 5.72384i −0.161443 0.279628i 0.773943 0.633255i \(-0.218282\pi\)
−0.935386 + 0.353627i \(0.884948\pi\)
\(420\) 0 0
\(421\) 6.39209 11.0714i 0.311531 0.539588i −0.667163 0.744912i \(-0.732491\pi\)
0.978694 + 0.205324i \(0.0658248\pi\)
\(422\) 11.5693i 0.563184i
\(423\) 0 0
\(424\) 28.2929 1.37403
\(425\) −1.26643 + 2.19353i −0.0614311 + 0.106402i
\(426\) 0 0
\(427\) 0 0
\(428\) 73.7007 42.5511i 3.56246 2.05679i
\(429\) 0 0
\(430\) −40.5299 23.4000i −1.95453 1.12845i
\(431\) 21.9112i 1.05542i 0.849424 + 0.527712i \(0.176950\pi\)
−0.849424 + 0.527712i \(0.823050\pi\)
\(432\) 0 0
\(433\) 8.21181i 0.394635i 0.980340 + 0.197317i \(0.0632229\pi\)
−0.980340 + 0.197317i \(0.936777\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −37.1153 64.2855i −1.77750 3.07872i
\(437\) −1.87862 3.25386i −0.0898665 0.155653i
\(438\) 0 0
\(439\) −32.7996 18.9368i −1.56544 0.903806i −0.996690 0.0812949i \(-0.974094\pi\)
−0.568749 0.822511i \(-0.692572\pi\)
\(440\) 69.4838 3.31251
\(441\) 0 0
\(442\) −19.7061 −0.937326
\(443\) −17.7210 10.2312i −0.841950 0.486100i 0.0159769 0.999872i \(-0.494914\pi\)
−0.857926 + 0.513773i \(0.828248\pi\)
\(444\) 0 0
\(445\) 3.87718 + 6.71547i 0.183796 + 0.318344i
\(446\) 26.7941 + 46.4087i 1.26874 + 2.19752i
\(447\) 0 0
\(448\) 0 0
\(449\) 35.7054i 1.68504i 0.538665 + 0.842520i \(0.318929\pi\)
−0.538665 + 0.842520i \(0.681071\pi\)
\(450\) 0 0
\(451\) 28.7726i 1.35485i
\(452\) 23.5892 + 13.6192i 1.10954 + 0.640594i
\(453\) 0 0
\(454\) −63.2232 + 36.5019i −2.96721 + 1.71312i
\(455\) 0 0
\(456\) 0 0
\(457\) 0.127090 0.220126i 0.00594501 0.0102971i −0.863038 0.505140i \(-0.831441\pi\)
0.868983 + 0.494843i \(0.164774\pi\)
\(458\) 56.1678 2.62455
\(459\) 0 0
\(460\) 60.2870i 2.81090i
\(461\) −12.2175 + 21.1613i −0.569025 + 0.985581i 0.427637 + 0.903950i \(0.359346\pi\)
−0.996663 + 0.0816304i \(0.973987\pi\)
\(462\) 0 0
\(463\) 0.409986 + 0.710116i 0.0190536 + 0.0330019i 0.875395 0.483408i \(-0.160601\pi\)
−0.856341 + 0.516410i \(0.827268\pi\)
\(464\) 32.1196 18.5443i 1.49112 0.860896i
\(465\) 0 0
\(466\) 19.6374 34.0130i 0.909686 1.57562i
\(467\) −1.81925 −0.0841848 −0.0420924 0.999114i \(-0.513402\pi\)
−0.0420924 + 0.999114i \(0.513402\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2.56899 1.48321i −0.118499 0.0684152i
\(471\) 0 0
\(472\) 25.4972 14.7208i 1.17360 0.677581i
\(473\) 29.4336 16.9935i 1.35336 0.781363i
\(474\) 0 0
\(475\) 0.256010 + 0.147807i 0.0117465 + 0.00678187i
\(476\) 0 0
\(477\) 0 0
\(478\) −14.7401 −0.674196
\(479\) −0.681074 + 1.17965i −0.0311191 + 0.0538998i −0.881166 0.472808i \(-0.843240\pi\)
0.850046 + 0.526708i \(0.176574\pi\)
\(480\) 0 0
\(481\) 3.45074 1.99228i 0.157340 0.0908403i
\(482\) −5.76373 9.98308i −0.262531 0.454717i
\(483\) 0 0
\(484\) −18.7340 + 32.4482i −0.851544 + 1.47492i
\(485\) 34.3394i 1.55927i
\(486\) 0 0
\(487\) 31.6121 1.43248 0.716241 0.697853i \(-0.245861\pi\)
0.716241 + 0.697853i \(0.245861\pi\)
\(488\) −7.00026 + 12.1248i −0.316887 + 0.548864i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.97415 1.13977i 0.0890919 0.0514373i −0.454792 0.890598i \(-0.650286\pi\)
0.543884 + 0.839160i \(0.316953\pi\)
\(492\) 0 0
\(493\) −22.3897 12.9267i −1.00838 0.582188i
\(494\) 2.29993i 0.103479i
\(495\) 0 0
\(496\) 33.3540i 1.49764i
\(497\) 0 0
\(498\) 0 0
\(499\) −13.5195 23.4164i −0.605215 1.04826i −0.992017 0.126101i \(-0.959754\pi\)
0.386802 0.922163i \(-0.373580\pi\)
\(500\) 24.7196 + 42.8156i 1.10549 + 1.91477i
\(501\) 0 0
\(502\) 25.9595 + 14.9877i 1.15863 + 0.668936i
\(503\) −0.276948 −0.0123485 −0.00617426 0.999981i \(-0.501965\pi\)
−0.00617426 + 0.999981i \(0.501965\pi\)
\(504\) 0 0
\(505\) −3.88070 −0.172689
\(506\) −54.2342 31.3121i −2.41100 1.39199i
\(507\) 0 0
\(508\) −38.5033 66.6897i −1.70831 2.95888i
\(509\) −9.21476 15.9604i −0.408437 0.707434i 0.586278 0.810110i \(-0.300593\pi\)
−0.994715 + 0.102676i \(0.967259\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 48.9492i 2.16327i
\(513\) 0 0
\(514\) 5.42143i 0.239129i
\(515\) −3.28291 1.89539i −0.144662 0.0835208i
\(516\) 0 0
\(517\) 1.86565 1.07713i 0.0820512 0.0473723i
\(518\) 0 0
\(519\) 0 0
\(520\) 10.5106 18.2049i 0.460921 0.798339i
\(521\) −23.2527 −1.01872 −0.509360 0.860554i \(-0.670118\pi\)
−0.509360 + 0.860554i \(0.670118\pi\)
\(522\) 0 0
\(523\) 13.3052i 0.581798i −0.956754 0.290899i \(-0.906046\pi\)
0.956754 0.290899i \(-0.0939543\pi\)
\(524\) 16.5431 28.6535i 0.722689 1.25173i
\(525\) 0 0
\(526\) −2.83970 4.91850i −0.123817 0.214457i
\(527\) −20.1352 + 11.6251i −0.877102 + 0.506395i
\(528\) 0 0
\(529\) 3.97534 6.88549i 0.172841 0.299369i
\(530\) 24.9240 1.08263
\(531\) 0 0
\(532\) 0 0
\(533\) −7.53848 4.35235i −0.326528 0.188521i
\(534\) 0 0
\(535\) 36.9828 21.3520i 1.59890 0.923128i
\(536\) 28.5138 16.4624i 1.23161 0.711069i
\(537\) 0 0
\(538\) 62.2105 + 35.9172i 2.68208 + 1.54850i
\(539\) 0 0
\(540\) 0 0
\(541\) −30.1692 −1.29707 −0.648537 0.761183i \(-0.724619\pi\)
−0.648537 + 0.761183i \(0.724619\pi\)
\(542\) 14.7993 25.6331i 0.635684 1.10104i
\(543\) 0 0
\(544\) 38.8515 22.4309i 1.66574 0.961718i
\(545\) −18.6243 32.2582i −0.797778 1.38179i
\(546\) 0 0
\(547\) −0.572061 + 0.990840i −0.0244596 + 0.0423652i −0.877996 0.478668i \(-0.841120\pi\)
0.853537 + 0.521033i \(0.174453\pi\)
\(548\) 3.84518i 0.164258i
\(549\) 0 0
\(550\) 4.92720 0.210097
\(551\) −1.50869 + 2.61313i −0.0642724 + 0.111323i
\(552\) 0 0
\(553\) 0 0
\(554\) −22.7744 + 13.1488i −0.967591 + 0.558639i
\(555\) 0 0
\(556\) 56.1065 + 32.3931i 2.37944 + 1.37377i
\(557\) 9.64623i 0.408724i −0.978895 0.204362i \(-0.934488\pi\)
0.978895 0.204362i \(-0.0655120\pi\)
\(558\) 0 0
\(559\) 10.2822i 0.434893i
\(560\) 0 0
\(561\) 0 0
\(562\) 14.0683 + 24.3669i 0.593434 + 1.02786i
\(563\) 1.54395 + 2.67420i 0.0650698 + 0.112704i 0.896725 0.442588i \(-0.145940\pi\)
−0.831655 + 0.555292i \(0.812606\pi\)
\(564\) 0 0
\(565\) 11.8370 + 6.83407i 0.497985 + 0.287512i
\(566\) 30.5940 1.28596
\(567\) 0 0
\(568\) 7.99411 0.335425
\(569\) −7.30588 4.21805i −0.306278 0.176830i 0.338982 0.940793i \(-0.389918\pi\)
−0.645260 + 0.763963i \(0.723251\pi\)
\(570\) 0 0
\(571\) 17.0208 + 29.4808i 0.712297 + 1.23373i 0.963993 + 0.265928i \(0.0856782\pi\)
−0.251696 + 0.967806i \(0.580988\pi\)
\(572\) 13.4001 + 23.2097i 0.560288 + 0.970447i
\(573\) 0 0
\(574\) 0 0
\(575\) 2.43516i 0.101553i
\(576\) 0 0
\(577\) 18.1052i 0.753730i 0.926268 + 0.376865i \(0.122998\pi\)
−0.926268 + 0.376865i \(0.877002\pi\)
\(578\) −36.8055 21.2497i −1.53091 0.883869i
\(579\) 0 0
\(580\) 41.9292 24.2078i 1.74102 1.00518i
\(581\) 0 0
\(582\) 0 0
\(583\) −9.05015 + 15.6753i −0.374819 + 0.649206i
\(584\) 103.157 4.26869
\(585\) 0 0
\(586\) 49.2441i 2.03426i
\(587\) 4.04900 7.01308i 0.167120 0.289461i −0.770286 0.637699i \(-0.779887\pi\)
0.937406 + 0.348238i \(0.113220\pi\)
\(588\) 0 0
\(589\) 1.35678 + 2.35001i 0.0559050 + 0.0968304i
\(590\) 22.4612 12.9680i 0.924713 0.533883i
\(591\) 0 0
\(592\) −12.5207 + 21.6864i −0.514596 + 0.891306i
\(593\) 6.66433 0.273671 0.136836 0.990594i \(-0.456307\pi\)
0.136836 + 0.990594i \(0.456307\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 44.0040 + 25.4057i 1.80247 + 1.04066i
\(597\) 0 0
\(598\) −16.4077 + 9.47299i −0.670961 + 0.387380i
\(599\) 3.10562 1.79303i 0.126892 0.0732614i −0.435210 0.900329i \(-0.643326\pi\)
0.562103 + 0.827068i \(0.309993\pi\)
\(600\) 0 0
\(601\) −4.86949 2.81140i −0.198631 0.114679i 0.397386 0.917652i \(-0.369917\pi\)
−0.596017 + 0.802972i \(0.703251\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 64.8061 2.63692
\(605\) −9.40064 + 16.2824i −0.382190 + 0.661973i
\(606\) 0 0
\(607\) 1.93239 1.11566i 0.0784332 0.0452834i −0.460270 0.887779i \(-0.652248\pi\)
0.538704 + 0.842495i \(0.318914\pi\)
\(608\) −2.61795 4.53442i −0.106172 0.183895i
\(609\) 0 0
\(610\) −6.16672 + 10.6811i −0.249683 + 0.432464i
\(611\) 0.651740i 0.0263666i
\(612\) 0 0
\(613\) −6.82038 −0.275473 −0.137736 0.990469i \(-0.543983\pi\)
−0.137736 + 0.990469i \(0.543983\pi\)
\(614\) 3.03567 5.25793i 0.122510 0.212193i
\(615\) 0 0
\(616\) 0 0
\(617\) 2.35139 1.35757i 0.0946632 0.0546538i −0.451921 0.892058i \(-0.649261\pi\)
0.546584 + 0.837404i \(0.315928\pi\)
\(618\) 0 0
\(619\) −23.1886 13.3880i −0.932029 0.538107i −0.0445762 0.999006i \(-0.514194\pi\)
−0.887453 + 0.460899i \(0.847527\pi\)
\(620\) 43.5406i 1.74863i
\(621\) 0 0
\(622\) 20.2380i 0.811469i
\(623\) 0 0
\(624\) 0 0
\(625\) 13.4985 + 23.3801i 0.539940 + 0.935203i
\(626\) −38.7414 67.1021i −1.54842 2.68194i
\(627\) 0 0
\(628\) 63.4980 + 36.6606i 2.53385 + 1.46292i
\(629\) 17.4556 0.696000
\(630\) 0 0
\(631\) −11.1620 −0.444354 −0.222177 0.975006i \(-0.571316\pi\)
−0.222177 + 0.975006i \(0.571316\pi\)
\(632\) −62.7004 36.2001i −2.49409 1.43996i
\(633\) 0 0
\(634\) −14.3182 24.7998i −0.568647 0.984926i
\(635\) −19.3208 33.4647i −0.766724 1.32801i
\(636\) 0 0
\(637\) 0 0
\(638\) 50.2927i 1.99111i
\(639\) 0 0
\(640\) 15.8021i 0.624633i
\(641\) −38.6251 22.3002i −1.52560 0.880805i −0.999539 0.0303565i \(-0.990336\pi\)
−0.526059 0.850448i \(-0.676331\pi\)
\(642\) 0 0
\(643\) 23.6268 13.6410i 0.931751 0.537947i 0.0443860 0.999014i \(-0.485867\pi\)
0.887365 + 0.461068i \(0.152534\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −5.03777 + 8.72568i −0.198208 + 0.343307i
\(647\) −44.9350 −1.76658 −0.883288 0.468831i \(-0.844675\pi\)
−0.883288 + 0.468831i \(0.844675\pi\)
\(648\) 0 0
\(649\) 18.8352i 0.739347i
\(650\) 0.745324 1.29094i 0.0292340 0.0506348i
\(651\) 0 0
\(652\) −15.7200 27.2278i −0.615642 1.06632i
\(653\) 24.0549 13.8881i 0.941343 0.543484i 0.0509617 0.998701i \(-0.483771\pi\)
0.890381 + 0.455216i \(0.150438\pi\)
\(654\) 0 0
\(655\) 8.30128 14.3782i 0.324358 0.561804i
\(656\) 54.7053 2.13588
\(657\) 0 0
\(658\) 0 0
\(659\) −0.801975 0.463021i −0.0312405 0.0180367i 0.484298 0.874903i \(-0.339075\pi\)
−0.515539 + 0.856866i \(0.672408\pi\)
\(660\) 0 0
\(661\) −28.3028 + 16.3406i −1.10085 + 0.635577i −0.936445 0.350815i \(-0.885905\pi\)
−0.164408 + 0.986392i \(0.552571\pi\)
\(662\) −38.5540 + 22.2592i −1.49844 + 0.865126i
\(663\) 0 0
\(664\) 62.9373 + 36.3369i 2.44244 + 1.41014i
\(665\) 0 0
\(666\) 0 0
\(667\) −24.8561 −0.962430
\(668\) −44.3625 + 76.8382i −1.71644 + 2.97296i
\(669\) 0 0
\(670\) 25.1186 14.5022i 0.970415 0.560269i
\(671\) −4.47839 7.75681i −0.172886 0.299448i
\(672\) 0 0
\(673\) −15.6947 + 27.1840i −0.604987 + 1.04787i 0.387067 + 0.922052i \(0.373488\pi\)
−0.992054 + 0.125816i \(0.959845\pi\)
\(674\) 19.7470i 0.760625i
\(675\) 0 0
\(676\) −52.3041 −2.01170
\(677\) 10.7882 18.6858i 0.414626 0.718153i −0.580763 0.814072i \(-0.697246\pi\)
0.995389 + 0.0959196i \(0.0305792\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 79.7521 46.0449i 3.05835 1.76574i
\(681\) 0 0
\(682\) 39.1691 + 22.6143i 1.49986 + 0.865946i
\(683\) 36.2593i 1.38742i −0.720253 0.693711i \(-0.755974\pi\)
0.720253 0.693711i \(-0.244026\pi\)
\(684\) 0 0
\(685\) 1.92950i 0.0737224i
\(686\) 0 0
\(687\) 0 0
\(688\) 32.3098 + 55.9622i 1.23180 + 2.13354i
\(689\) 2.73798 + 4.74232i 0.104309 + 0.180668i
\(690\) 0 0
\(691\) 6.16389 + 3.55872i 0.234485 + 0.135380i 0.612640 0.790362i \(-0.290108\pi\)
−0.378154 + 0.925743i \(0.623441\pi\)
\(692\) −101.535 −3.85977
\(693\) 0 0
\(694\) −33.9426 −1.28844
\(695\) 28.1540 + 16.2547i 1.06794 + 0.616577i
\(696\) 0 0
\(697\) −19.0667 33.0246i −0.722204 1.25089i
\(698\) −1.56569 2.71186i −0.0592624 0.102645i
\(699\) 0 0
\(700\) 0 0
\(701\) 29.4609i 1.11272i 0.830940 + 0.556362i \(0.187803\pi\)
−0.830940 + 0.556362i \(0.812197\pi\)
\(702\) 0 0
\(703\) 2.03727i 0.0768370i
\(704\) −12.8019 7.39117i −0.482489 0.278565i
\(705\) 0 0
\(706\) 59.8894 34.5772i 2.25397 1.30133i
\(707\) 0 0
\(708\) 0 0
\(709\) 19.0361 32.9715i 0.714916 1.23827i −0.248076 0.968740i \(-0.579798\pi\)
0.962992 0.269530i \(-0.0868683\pi\)
\(710\) 7.04224 0.264290
\(711\) 0 0
\(712\) 22.6945i 0.850513i
\(713\) −11.1766 + 19.3585i −0.418568 + 0.724980i
\(714\) 0 0
\(715\) 6.72414 + 11.6466i 0.251469 + 0.435556i
\(716\) −69.1795 + 39.9408i −2.58536 + 1.49266i
\(717\) 0 0
\(718\) 9.60408 16.6348i 0.358421 0.620803i
\(719\) 38.2114 1.42505 0.712523 0.701649i \(-0.247553\pi\)
0.712523 + 0.701649i \(0.247553\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −41.4045 23.9049i −1.54091 0.889647i
\(723\) 0 0
\(724\) −66.9924 + 38.6781i −2.48975 + 1.43746i
\(725\) 1.69364 0.977823i 0.0629002 0.0363154i
\(726\) 0 0
\(727\) −17.7563 10.2516i −0.658546 0.380212i 0.133177 0.991092i \(-0.457482\pi\)
−0.791723 + 0.610881i \(0.790816\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 90.8743 3.36341
\(731\) 22.5222 39.0096i 0.833014 1.44282i
\(732\) 0 0
\(733\) −0.900627 + 0.519977i −0.0332654 + 0.0192058i −0.516540 0.856263i \(-0.672780\pi\)
0.483275 + 0.875469i \(0.339447\pi\)
\(734\) 45.1023 + 78.1194i 1.66475 + 2.88344i
\(735\) 0 0
\(736\) 21.5657 37.3528i 0.794921 1.37684i
\(737\) 21.0636i 0.775887i
\(738\) 0 0
\(739\) 24.1609 0.888774 0.444387 0.895835i \(-0.353422\pi\)
0.444387 + 0.895835i \(0.353422\pi\)
\(740\) −16.3446 + 28.3096i −0.600839 + 1.04068i
\(741\) 0 0
\(742\) 0 0
\(743\) 13.1637 7.60008i 0.482930 0.278820i −0.238707 0.971092i \(-0.576723\pi\)
0.721637 + 0.692272i \(0.243390\pi\)
\(744\) 0 0
\(745\) 22.0810 + 12.7485i 0.808987 + 0.467069i
\(746\) 77.6010i 2.84118i
\(747\) 0 0
\(748\) 117.406i 4.29281i
\(749\) 0 0
\(750\) 0 0
\(751\) −1.52037 2.63336i −0.0554791 0.0960926i 0.836952 0.547276i \(-0.184335\pi\)
−0.892431 + 0.451184i \(0.851002\pi\)
\(752\) 2.04795 + 3.54716i 0.0746812 + 0.129352i
\(753\) 0 0
\(754\) 13.1768 + 7.60763i 0.479871 + 0.277053i
\(755\) 32.5195 1.18350
\(756\) 0 0
\(757\) 43.3700 1.57631 0.788155 0.615477i \(-0.211036\pi\)
0.788155 + 0.615477i \(0.211036\pi\)
\(758\) 60.5075 + 34.9340i 2.19773 + 1.26886i
\(759\) 0 0
\(760\) −5.37397 9.30799i −0.194934 0.337636i
\(761\) 14.6319 + 25.3432i 0.530406 + 0.918690i 0.999371 + 0.0354731i \(0.0112938\pi\)
−0.468965 + 0.883217i \(0.655373\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4.43367i 0.160405i
\(765\) 0 0
\(766\) 9.43698i 0.340972i
\(767\) 4.93487 + 2.84915i 0.178188 + 0.102877i
\(768\) 0 0
\(769\) −29.6496 + 17.1182i −1.06919 + 0.617299i −0.927961 0.372678i \(-0.878440\pi\)
−0.141232 + 0.989977i \(0.545106\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.93702 + 6.81912i −0.141697 + 0.245426i
\(773\) −33.9854 −1.22237 −0.611185 0.791488i \(-0.709307\pi\)
−0.611185 + 0.791488i \(0.709307\pi\)
\(774\) 0 0
\(775\) 1.75873i 0.0631753i
\(776\) 50.2502 87.0359i 1.80388 3.12441i
\(777\) 0 0
\(778\) 15.6870 + 27.1707i 0.562406 + 0.974117i
\(779\) −3.85435 + 2.22531i −0.138096 + 0.0797299i
\(780\) 0 0
\(781\) −2.55710 + 4.42904i −0.0915004 + 0.158483i
\(782\) −82.9985 −2.96802
\(783\) 0 0
\(784\) 0 0
\(785\) 31.8631 + 18.3962i 1.13724 + 0.656587i
\(786\) 0 0
\(787\) 23.8225 13.7539i 0.849180 0.490274i −0.0111939 0.999937i \(-0.503563\pi\)
0.860374 + 0.509663i \(0.170230\pi\)
\(788\) 51.3067 29.6219i 1.82773 1.05524i
\(789\) 0 0
\(790\) −55.2346 31.8897i −1.96516 1.13458i
\(791\) 0 0
\(792\) 0 0
\(793\) −2.70974 −0.0962255
\(794\) −34.5144 + 59.7807i −1.22487 + 2.12154i
\(795\) 0 0
\(796\) −17.5390 + 10.1262i −0.621654 + 0.358912i