Properties

Label 804.2.ba.b.41.9
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.9
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.709719 - 1.57997i) q^{3} +(0.569745 - 3.96266i) q^{5} +(0.363865 + 3.81057i) q^{7} +(-1.99260 + 2.24267i) q^{9} +O(q^{10})\) \(q+(-0.709719 - 1.57997i) q^{3} +(0.569745 - 3.96266i) q^{5} +(0.363865 + 3.81057i) q^{7} +(-1.99260 + 2.24267i) q^{9} +(-4.23450 + 1.69524i) q^{11} +(-3.77004 - 3.95391i) q^{13} +(-6.66524 + 1.91220i) q^{15} +(6.20169 - 2.14643i) q^{17} +(-6.82859 - 0.652051i) q^{19} +(5.76233 - 3.27933i) q^{21} +(0.473873 - 0.0225734i) q^{23} +(-10.5806 - 3.10675i) q^{25} +(4.95752 + 1.55658i) q^{27} +(-7.56004 + 4.36479i) q^{29} +(-0.649047 + 0.680701i) q^{31} +(5.68373 + 5.48724i) q^{33} +(15.3073 + 0.729177i) q^{35} +(-0.455768 + 0.789413i) q^{37} +(-3.57138 + 8.76271i) q^{39} +(0.877682 + 0.169159i) q^{41} +(0.287793 + 0.249374i) q^{43} +(7.75166 + 9.17375i) q^{45} +(1.32173 - 2.56380i) q^{47} +(-7.51452 + 1.44831i) q^{49} +(-7.79274 - 8.27512i) q^{51} +(2.31995 + 2.67736i) q^{53} +(4.30508 + 17.7458i) q^{55} +(3.81616 + 11.2517i) q^{57} +(-2.25065 - 7.66500i) q^{59} +(0.666695 - 1.66532i) q^{61} +(-9.27086 - 6.77690i) q^{63} +(-17.8160 + 12.6867i) q^{65} +(-2.35801 + 7.83835i) q^{67} +(-0.371982 - 0.732684i) q^{69} +(-0.304090 - 0.105247i) q^{71} +(-3.59390 - 1.43878i) q^{73} +(2.60070 + 18.9220i) q^{75} +(-8.00061 - 15.5190i) q^{77} +(1.01436 - 0.246082i) q^{79} +(-1.05910 - 8.93747i) q^{81} +(7.37794 - 9.38182i) q^{83} +(-4.97218 - 25.7981i) q^{85} +(12.2617 + 8.84685i) q^{87} +(1.27636 - 1.98605i) q^{89} +(13.6948 - 15.8047i) q^{91} +(1.53613 + 0.542368i) q^{93} +(-6.47442 + 26.6879i) q^{95} +(-13.0824 - 7.55312i) q^{97} +(4.63581 - 12.8745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.709719 1.57997i −0.409756 0.912195i
\(4\) 0 0
\(5\) 0.569745 3.96266i 0.254798 1.77216i −0.313749 0.949506i \(-0.601585\pi\)
0.568547 0.822651i \(-0.307506\pi\)
\(6\) 0 0
\(7\) 0.363865 + 3.81057i 0.137528 + 1.44026i 0.756062 + 0.654501i \(0.227121\pi\)
−0.618533 + 0.785758i \(0.712273\pi\)
\(8\) 0 0
\(9\) −1.99260 + 2.24267i −0.664200 + 0.747555i
\(10\) 0 0
\(11\) −4.23450 + 1.69524i −1.27675 + 0.511134i −0.908224 0.418484i \(-0.862562\pi\)
−0.368526 + 0.929617i \(0.620137\pi\)
\(12\) 0 0
\(13\) −3.77004 3.95391i −1.04562 1.09662i −0.995197 0.0978884i \(-0.968791\pi\)
−0.0504242 0.998728i \(-0.516057\pi\)
\(14\) 0 0
\(15\) −6.66524 + 1.91220i −1.72096 + 0.493727i
\(16\) 0 0
\(17\) 6.20169 2.14643i 1.50413 0.520585i 0.554022 0.832502i \(-0.313092\pi\)
0.950109 + 0.311917i \(0.100971\pi\)
\(18\) 0 0
\(19\) −6.82859 0.652051i −1.56659 0.149591i −0.724630 0.689138i \(-0.757990\pi\)
−0.841956 + 0.539547i \(0.818596\pi\)
\(20\) 0 0
\(21\) 5.76233 3.27933i 1.25744 0.715607i
\(22\) 0 0
\(23\) 0.473873 0.0225734i 0.0988094 0.00470687i 0.00188104 0.999998i \(-0.499401\pi\)
0.0969284 + 0.995291i \(0.469098\pi\)
\(24\) 0 0
\(25\) −10.5806 3.10675i −2.11613 0.621351i
\(26\) 0 0
\(27\) 4.95752 + 1.55658i 0.954076 + 0.299564i
\(28\) 0 0
\(29\) −7.56004 + 4.36479i −1.40386 + 0.810521i −0.994787 0.101978i \(-0.967483\pi\)
−0.409077 + 0.912500i \(0.634149\pi\)
\(30\) 0 0
\(31\) −0.649047 + 0.680701i −0.116572 + 0.122258i −0.779434 0.626484i \(-0.784493\pi\)
0.662862 + 0.748742i \(0.269342\pi\)
\(32\) 0 0
\(33\) 5.68373 + 5.48724i 0.989410 + 0.955205i
\(34\) 0 0
\(35\) 15.3073 + 0.729177i 2.58741 + 0.123253i
\(36\) 0 0
\(37\) −0.455768 + 0.789413i −0.0749278 + 0.129779i −0.901055 0.433705i \(-0.857206\pi\)
0.826127 + 0.563484i \(0.190539\pi\)
\(38\) 0 0
\(39\) −3.57138 + 8.76271i −0.571878 + 1.40316i
\(40\) 0 0
\(41\) 0.877682 + 0.169159i 0.137071 + 0.0264182i 0.257325 0.966325i \(-0.417159\pi\)
−0.120254 + 0.992743i \(0.538371\pi\)
\(42\) 0 0
\(43\) 0.287793 + 0.249374i 0.0438880 + 0.0380292i 0.676529 0.736416i \(-0.263483\pi\)
−0.632641 + 0.774446i \(0.718029\pi\)
\(44\) 0 0
\(45\) 7.75166 + 9.17375i 1.15555 + 1.36754i
\(46\) 0 0
\(47\) 1.32173 2.56380i 0.192794 0.373969i −0.772548 0.634957i \(-0.781018\pi\)
0.965342 + 0.260988i \(0.0840483\pi\)
\(48\) 0 0
\(49\) −7.51452 + 1.44831i −1.07350 + 0.206901i
\(50\) 0 0
\(51\) −7.79274 8.27512i −1.09120 1.15875i
\(52\) 0 0
\(53\) 2.31995 + 2.67736i 0.318669 + 0.367764i 0.892373 0.451299i \(-0.149039\pi\)
−0.573703 + 0.819063i \(0.694494\pi\)
\(54\) 0 0
\(55\) 4.30508 + 17.7458i 0.580496 + 2.39284i
\(56\) 0 0
\(57\) 3.81616 + 11.2517i 0.505462 + 1.49033i
\(58\) 0 0
\(59\) −2.25065 7.66500i −0.293009 0.997898i −0.966063 0.258305i \(-0.916836\pi\)
0.673054 0.739593i \(-0.264982\pi\)
\(60\) 0 0
\(61\) 0.666695 1.66532i 0.0853616 0.213223i −0.879545 0.475815i \(-0.842153\pi\)
0.964907 + 0.262592i \(0.0845774\pi\)
\(62\) 0 0
\(63\) −9.27086 6.77690i −1.16802 0.853810i
\(64\) 0 0
\(65\) −17.8160 + 12.6867i −2.20980 + 1.57359i
\(66\) 0 0
\(67\) −2.35801 + 7.83835i −0.288077 + 0.957607i
\(68\) 0 0
\(69\) −0.371982 0.732684i −0.0447814 0.0882048i
\(70\) 0 0
\(71\) −0.304090 0.105247i −0.0360889 0.0124905i 0.308964 0.951074i \(-0.400018\pi\)
−0.345053 + 0.938583i \(0.612139\pi\)
\(72\) 0 0
\(73\) −3.59390 1.43878i −0.420634 0.168396i 0.151683 0.988429i \(-0.451531\pi\)
−0.572316 + 0.820033i \(0.693955\pi\)
\(74\) 0 0
\(75\) 2.60070 + 18.9220i 0.300303 + 2.18492i
\(76\) 0 0
\(77\) −8.00061 15.5190i −0.911754 1.76856i
\(78\) 0 0
\(79\) 1.01436 0.246082i 0.114125 0.0276864i −0.178290 0.983978i \(-0.557056\pi\)
0.292415 + 0.956292i \(0.405541\pi\)
\(80\) 0 0
\(81\) −1.05910 8.93747i −0.117678 0.993052i
\(82\) 0 0
\(83\) 7.37794 9.38182i 0.809835 1.02979i −0.189022 0.981973i \(-0.560532\pi\)
0.998856 0.0478154i \(-0.0152259\pi\)
\(84\) 0 0
\(85\) −4.97218 25.7981i −0.539309 2.79820i
\(86\) 0 0
\(87\) 12.2617 + 8.84685i 1.31460 + 0.948482i
\(88\) 0 0
\(89\) 1.27636 1.98605i 0.135294 0.210521i −0.766995 0.641653i \(-0.778249\pi\)
0.902289 + 0.431131i \(0.141885\pi\)
\(90\) 0 0
\(91\) 13.6948 15.8047i 1.43561 1.65678i
\(92\) 0 0
\(93\) 1.53613 + 0.542368i 0.159289 + 0.0562409i
\(94\) 0 0
\(95\) −6.47442 + 26.6879i −0.664261 + 2.73812i
\(96\) 0 0
\(97\) −13.0824 7.55312i −1.32831 0.766903i −0.343275 0.939235i \(-0.611536\pi\)
−0.985039 + 0.172332i \(0.944870\pi\)
\(98\) 0 0
\(99\) 4.63581 12.8745i 0.465917 1.29394i
\(100\) 0 0
\(101\) 8.64998 12.1472i 0.860705 1.20869i −0.115816 0.993271i \(-0.536948\pi\)
0.976521 0.215421i \(-0.0691123\pi\)
\(102\) 0 0
\(103\) −2.77344 2.64447i −0.273275 0.260568i 0.541031 0.841002i \(-0.318034\pi\)
−0.814307 + 0.580435i \(0.802883\pi\)
\(104\) 0 0
\(105\) −9.71180 24.7026i −0.947775 2.41072i
\(106\) 0 0
\(107\) −9.27796 + 1.33397i −0.896935 + 0.128960i −0.575337 0.817917i \(-0.695129\pi\)
−0.321598 + 0.946876i \(0.604220\pi\)
\(108\) 0 0
\(109\) −1.85530 + 6.31856i −0.177705 + 0.605208i 0.821673 + 0.569959i \(0.193041\pi\)
−0.999379 + 0.0352495i \(0.988777\pi\)
\(110\) 0 0
\(111\) 1.57071 + 0.159838i 0.149086 + 0.0151711i
\(112\) 0 0
\(113\) −1.89021 + 1.48648i −0.177816 + 0.139836i −0.703100 0.711091i \(-0.748201\pi\)
0.525284 + 0.850927i \(0.323959\pi\)
\(114\) 0 0
\(115\) 0.180536 1.89066i 0.0168351 0.176305i
\(116\) 0 0
\(117\) 16.3795 0.576394i 1.51428 0.0532876i
\(118\) 0 0
\(119\) 10.4357 + 22.8510i 0.956637 + 2.09474i
\(120\) 0 0
\(121\) 7.09610 6.76612i 0.645100 0.615102i
\(122\) 0 0
\(123\) −0.355641 1.50676i −0.0320670 0.135860i
\(124\) 0 0
\(125\) −10.0239 + 21.9493i −0.896564 + 1.96320i
\(126\) 0 0
\(127\) −9.16081 + 0.874751i −0.812890 + 0.0776216i −0.493217 0.869906i \(-0.664179\pi\)
−0.319673 + 0.947528i \(0.603573\pi\)
\(128\) 0 0
\(129\) 0.189751 0.631689i 0.0167067 0.0556171i
\(130\) 0 0
\(131\) −6.10471 9.49911i −0.533371 0.829941i 0.465098 0.885259i \(-0.346019\pi\)
−0.998469 + 0.0553182i \(0.982383\pi\)
\(132\) 0 0
\(133\) 26.2581i 2.27686i
\(134\) 0 0
\(135\) 8.99273 18.7581i 0.773971 1.61444i
\(136\) 0 0
\(137\) 6.28180 4.03707i 0.536690 0.344910i −0.244053 0.969762i \(-0.578477\pi\)
0.780743 + 0.624852i \(0.214841\pi\)
\(138\) 0 0
\(139\) 17.1347 + 2.46360i 1.45335 + 0.208960i 0.823305 0.567600i \(-0.192128\pi\)
0.630044 + 0.776560i \(0.283037\pi\)
\(140\) 0 0
\(141\) −4.98878 0.268716i −0.420131 0.0226300i
\(142\) 0 0
\(143\) 22.6671 + 10.3517i 1.89552 + 0.865653i
\(144\) 0 0
\(145\) 12.9889 + 32.4447i 1.07867 + 2.69439i
\(146\) 0 0
\(147\) 7.62147 + 10.8448i 0.628608 + 0.894465i
\(148\) 0 0
\(149\) 6.30772 2.88064i 0.516749 0.235991i −0.139930 0.990161i \(-0.544688\pi\)
0.656679 + 0.754170i \(0.271961\pi\)
\(150\) 0 0
\(151\) −3.12993 9.04333i −0.254710 0.735936i −0.997772 0.0667138i \(-0.978749\pi\)
0.743062 0.669222i \(-0.233373\pi\)
\(152\) 0 0
\(153\) −7.54377 + 18.1853i −0.609878 + 1.47019i
\(154\) 0 0
\(155\) 2.32760 + 2.95978i 0.186957 + 0.237735i
\(156\) 0 0
\(157\) 0.0258516 + 0.542692i 0.00206318 + 0.0433116i 0.999664 0.0259150i \(-0.00824991\pi\)
−0.997601 + 0.0692265i \(0.977947\pi\)
\(158\) 0 0
\(159\) 2.58364 5.56562i 0.204896 0.441382i
\(160\) 0 0
\(161\) 0.258443 + 1.79751i 0.0203682 + 0.141664i
\(162\) 0 0
\(163\) 1.36123 + 2.35772i 0.106620 + 0.184671i 0.914399 0.404815i \(-0.132664\pi\)
−0.807779 + 0.589485i \(0.799331\pi\)
\(164\) 0 0
\(165\) 24.9823 19.3964i 1.94487 1.51001i
\(166\) 0 0
\(167\) −13.3168 9.48282i −1.03048 0.733803i −0.0659645 0.997822i \(-0.521012\pi\)
−0.964517 + 0.264019i \(0.914952\pi\)
\(168\) 0 0
\(169\) −0.801593 + 16.8275i −0.0616610 + 1.29442i
\(170\) 0 0
\(171\) 15.0690 14.0150i 1.15235 1.07175i
\(172\) 0 0
\(173\) −13.3200 3.23140i −1.01270 0.245679i −0.305123 0.952313i \(-0.598698\pi\)
−0.707579 + 0.706634i \(0.750213\pi\)
\(174\) 0 0
\(175\) 7.98857 41.4486i 0.603879 3.13322i
\(176\) 0 0
\(177\) −10.5131 + 8.99594i −0.790215 + 0.676176i
\(178\) 0 0
\(179\) 3.78598 + 2.43310i 0.282977 + 0.181858i 0.674428 0.738341i \(-0.264390\pi\)
−0.391451 + 0.920199i \(0.628027\pi\)
\(180\) 0 0
\(181\) 2.98907 + 1.54097i 0.222176 + 0.114540i 0.565722 0.824596i \(-0.308598\pi\)
−0.343546 + 0.939136i \(0.611628\pi\)
\(182\) 0 0
\(183\) −3.10432 + 0.128554i −0.229478 + 0.00950300i
\(184\) 0 0
\(185\) 2.86851 + 2.25582i 0.210897 + 0.165851i
\(186\) 0 0
\(187\) −22.6224 + 19.6024i −1.65431 + 1.43347i
\(188\) 0 0
\(189\) −4.12759 + 19.4574i −0.300238 + 1.41532i
\(190\) 0 0
\(191\) −7.89943 + 4.07244i −0.571583 + 0.294671i −0.719685 0.694301i \(-0.755714\pi\)
0.148102 + 0.988972i \(0.452683\pi\)
\(192\) 0 0
\(193\) 2.52896 0.742570i 0.182039 0.0534514i −0.189443 0.981892i \(-0.560668\pi\)
0.371481 + 0.928440i \(0.378850\pi\)
\(194\) 0 0
\(195\) 32.6889 + 19.1447i 2.34090 + 1.37098i
\(196\) 0 0
\(197\) 4.11304 11.8839i 0.293042 0.846690i −0.698349 0.715757i \(-0.746082\pi\)
0.991391 0.130933i \(-0.0417971\pi\)
\(198\) 0 0
\(199\) −5.40198 7.58602i −0.382936 0.537759i 0.577452 0.816425i \(-0.304047\pi\)
−0.960388 + 0.278666i \(0.910108\pi\)
\(200\) 0 0
\(201\) 14.0579 1.83745i 0.991566 0.129604i
\(202\) 0 0
\(203\) −19.3832 27.2198i −1.36043 1.91046i
\(204\) 0 0
\(205\) 1.17038 3.38158i 0.0817426 0.236180i
\(206\) 0 0
\(207\) −0.893615 + 1.10772i −0.0621105 + 0.0769918i
\(208\) 0 0
\(209\) 30.0211 8.81498i 2.07660 0.609745i
\(210\) 0 0
\(211\) −8.13656 + 4.19469i −0.560144 + 0.288774i −0.714956 0.699170i \(-0.753553\pi\)
0.154812 + 0.987944i \(0.450523\pi\)
\(212\) 0 0
\(213\) 0.0495321 + 0.555148i 0.00339388 + 0.0380381i
\(214\) 0 0
\(215\) 1.15215 0.998347i 0.0785763 0.0680867i
\(216\) 0 0
\(217\) −2.83002 2.22555i −0.192114 0.151080i
\(218\) 0 0
\(219\) 0.277430 + 6.69937i 0.0187470 + 0.452702i
\(220\) 0 0
\(221\) −31.8674 16.4288i −2.14363 1.10512i
\(222\) 0 0
\(223\) 20.3495 + 13.0778i 1.36270 + 0.875755i 0.998456 0.0555480i \(-0.0176906\pi\)
0.364245 + 0.931303i \(0.381327\pi\)
\(224\) 0 0
\(225\) 28.0504 17.5383i 1.87002 1.16922i
\(226\) 0 0
\(227\) 3.78530 19.6400i 0.251239 1.30355i −0.608799 0.793324i \(-0.708348\pi\)
0.860038 0.510229i \(-0.170439\pi\)
\(228\) 0 0
\(229\) −6.67849 1.62018i −0.441327 0.107065i 0.00893740 0.999960i \(-0.497155\pi\)
−0.450264 + 0.892895i \(0.648670\pi\)
\(230\) 0 0
\(231\) −18.8414 + 23.6548i −1.23967 + 1.55637i
\(232\) 0 0
\(233\) 1.02952 21.6122i 0.0674458 1.41586i −0.670954 0.741499i \(-0.734115\pi\)
0.738400 0.674363i \(-0.235582\pi\)
\(234\) 0 0
\(235\) −9.40643 6.69829i −0.613608 0.436948i
\(236\) 0 0
\(237\) −1.10872 1.42802i −0.0720188 0.0927595i
\(238\) 0 0
\(239\) −13.4972 23.3778i −0.873059 1.51218i −0.858816 0.512284i \(-0.828800\pi\)
−0.0142427 0.999899i \(-0.504534\pi\)
\(240\) 0 0
\(241\) 0.119122 + 0.828514i 0.00767334 + 0.0533692i 0.993298 0.115578i \(-0.0368722\pi\)
−0.985625 + 0.168948i \(0.945963\pi\)
\(242\) 0 0
\(243\) −13.3693 + 8.01643i −0.857638 + 0.514254i
\(244\) 0 0
\(245\) 1.45779 + 30.6027i 0.0931345 + 1.95513i
\(246\) 0 0
\(247\) 23.1659 + 29.4579i 1.47401 + 1.87436i
\(248\) 0 0
\(249\) −20.0592 4.99847i −1.27120 0.316765i
\(250\) 0 0
\(251\) 2.83602 + 8.19414i 0.179008 + 0.517210i 0.998432 0.0559781i \(-0.0178277\pi\)
−0.819424 + 0.573188i \(0.805706\pi\)
\(252\) 0 0
\(253\) −1.96835 + 0.898916i −0.123749 + 0.0565143i
\(254\) 0 0
\(255\) −37.2314 + 26.1653i −2.33152 + 1.63854i
\(256\) 0 0
\(257\) 3.09708 + 7.73614i 0.193191 + 0.482567i 0.993060 0.117607i \(-0.0375223\pi\)
−0.799870 + 0.600174i \(0.795098\pi\)
\(258\) 0 0
\(259\) −3.17395 1.44949i −0.197220 0.0900672i
\(260\) 0 0
\(261\) 5.27536 25.6519i 0.326537 1.58781i
\(262\) 0 0
\(263\) 2.25468 + 0.324173i 0.139029 + 0.0199894i 0.211478 0.977383i \(-0.432172\pi\)
−0.0724488 + 0.997372i \(0.523081\pi\)
\(264\) 0 0
\(265\) 11.9313 7.66776i 0.732932 0.471027i
\(266\) 0 0
\(267\) −4.04376 0.607067i −0.247474 0.0371519i
\(268\) 0 0
\(269\) 18.6624i 1.13787i 0.822383 + 0.568934i \(0.192644\pi\)
−0.822383 + 0.568934i \(0.807356\pi\)
\(270\) 0 0
\(271\) −7.96322 12.3910i −0.483731 0.752700i 0.510509 0.859872i \(-0.329457\pi\)
−0.994240 + 0.107172i \(0.965820\pi\)
\(272\) 0 0
\(273\) −34.6904 10.4205i −2.09956 0.630679i
\(274\) 0 0
\(275\) 50.0704 4.78114i 3.01936 0.288314i
\(276\) 0 0
\(277\) 3.23729 7.08868i 0.194510 0.425918i −0.787097 0.616829i \(-0.788417\pi\)
0.981607 + 0.190911i \(0.0611443\pi\)
\(278\) 0 0
\(279\) −0.233294 2.81196i −0.0139670 0.168348i
\(280\) 0 0
\(281\) 19.8167 18.8951i 1.18216 1.12719i 0.192873 0.981224i \(-0.438220\pi\)
0.989290 0.145966i \(-0.0466289\pi\)
\(282\) 0 0
\(283\) 6.67726 + 14.6212i 0.396922 + 0.869138i 0.997573 + 0.0696269i \(0.0221809\pi\)
−0.600651 + 0.799511i \(0.705092\pi\)
\(284\) 0 0
\(285\) 46.7611 8.71153i 2.76989 0.516027i
\(286\) 0 0
\(287\) −0.325235 + 3.40602i −0.0191980 + 0.201051i
\(288\) 0 0
\(289\) 20.4909 16.1143i 1.20535 0.947898i
\(290\) 0 0
\(291\) −2.64887 + 26.0303i −0.155280 + 1.52592i
\(292\) 0 0
\(293\) −0.694325 + 2.36465i −0.0405629 + 0.138145i −0.977285 0.211929i \(-0.932025\pi\)
0.936722 + 0.350074i \(0.113844\pi\)
\(294\) 0 0
\(295\) −31.6561 + 4.55146i −1.84309 + 0.264996i
\(296\) 0 0
\(297\) −23.6314 + 1.81284i −1.37123 + 0.105192i
\(298\) 0 0
\(299\) −1.87578 1.78855i −0.108479 0.103434i
\(300\) 0 0
\(301\) −0.845539 + 1.18739i −0.0487361 + 0.0684402i
\(302\) 0 0
\(303\) −25.3312 5.04560i −1.45524 0.289862i
\(304\) 0 0
\(305\) −6.21927 3.59070i −0.356114 0.205603i
\(306\) 0 0
\(307\) 5.41852 22.3354i 0.309251 1.27475i −0.578975 0.815345i \(-0.696547\pi\)
0.888227 0.459406i \(-0.151938\pi\)
\(308\) 0 0
\(309\) −2.20982 + 6.25878i −0.125712 + 0.356050i
\(310\) 0 0
\(311\) −9.33597 + 10.7743i −0.529394 + 0.610953i −0.955958 0.293504i \(-0.905179\pi\)
0.426564 + 0.904458i \(0.359724\pi\)
\(312\) 0 0
\(313\) −7.74371 + 12.0494i −0.437700 + 0.681075i −0.988098 0.153828i \(-0.950840\pi\)
0.550398 + 0.834903i \(0.314476\pi\)
\(314\) 0 0
\(315\) −32.1366 + 32.8762i −1.81069 + 1.85236i
\(316\) 0 0
\(317\) −0.497571 2.58165i −0.0279464 0.145000i 0.965275 0.261235i \(-0.0841296\pi\)
−0.993222 + 0.116235i \(0.962917\pi\)
\(318\) 0 0
\(319\) 24.6136 31.2988i 1.37810 1.75240i
\(320\) 0 0
\(321\) 8.69237 + 13.7121i 0.485161 + 0.765337i
\(322\) 0 0
\(323\) −43.7484 + 10.6132i −2.43423 + 0.590537i
\(324\) 0 0
\(325\) 27.6056 + 53.5474i 1.53128 + 2.97028i
\(326\) 0 0
\(327\) 11.2999 1.55309i 0.624884 0.0858860i
\(328\) 0 0
\(329\) 10.2505 + 4.10367i 0.565127 + 0.226243i
\(330\) 0 0
\(331\) 12.2573 + 4.24230i 0.673723 + 0.233178i 0.642444 0.766333i \(-0.277921\pi\)
0.0312795 + 0.999511i \(0.490042\pi\)
\(332\) 0 0
\(333\) −0.862227 2.59512i −0.0472498 0.142212i
\(334\) 0 0
\(335\) 29.7173 + 13.8099i 1.62363 + 0.754513i
\(336\) 0 0
\(337\) −17.1383 + 12.2041i −0.933581 + 0.664800i −0.942160 0.335163i \(-0.891209\pi\)
0.00857916 + 0.999963i \(0.497269\pi\)
\(338\) 0 0
\(339\) 3.69010 + 1.93149i 0.200419 + 0.104904i
\(340\) 0 0
\(341\) 1.59444 3.98272i 0.0863438 0.215676i
\(342\) 0 0
\(343\) −0.704029 2.39770i −0.0380140 0.129464i
\(344\) 0 0
\(345\) −3.11532 + 1.05660i −0.167723 + 0.0568852i
\(346\) 0 0
\(347\) 5.98733 + 24.6801i 0.321417 + 1.32490i 0.871749 + 0.489952i \(0.162986\pi\)
−0.550332 + 0.834946i \(0.685499\pi\)
\(348\) 0 0
\(349\) −16.2936 18.8039i −0.872179 1.00655i −0.999891 0.0147371i \(-0.995309\pi\)
0.127712 0.991811i \(-0.459237\pi\)
\(350\) 0 0
\(351\) −12.5355 25.4700i −0.669095 1.35949i
\(352\) 0 0
\(353\) −18.3506 + 3.53680i −0.976706 + 0.188245i −0.652539 0.757755i \(-0.726296\pi\)
−0.324167 + 0.946000i \(0.605084\pi\)
\(354\) 0 0
\(355\) −0.590311 + 1.14504i −0.0313304 + 0.0607726i
\(356\) 0 0
\(357\) 28.6974 32.7058i 1.51883 1.73097i
\(358\) 0 0
\(359\) −15.0463 13.0377i −0.794113 0.688103i 0.160143 0.987094i \(-0.448805\pi\)
−0.954256 + 0.298991i \(0.903350\pi\)
\(360\) 0 0
\(361\) 27.5478 + 5.30941i 1.44989 + 0.279443i
\(362\) 0 0
\(363\) −15.7265 6.40957i −0.825426 0.336415i
\(364\) 0 0
\(365\) −7.74900 + 13.4217i −0.405601 + 0.702522i
\(366\) 0 0
\(367\) −19.1788 0.913599i −1.00113 0.0476895i −0.459387 0.888236i \(-0.651931\pi\)
−0.541739 + 0.840547i \(0.682234\pi\)
\(368\) 0 0
\(369\) −2.12824 + 1.63128i −0.110792 + 0.0849210i
\(370\) 0 0
\(371\) −9.35813 + 9.81452i −0.485850 + 0.509544i
\(372\) 0 0
\(373\) −21.7588 + 12.5624i −1.12663 + 0.650458i −0.943084 0.332554i \(-0.892090\pi\)
−0.183542 + 0.983012i \(0.558756\pi\)
\(374\) 0 0
\(375\) 41.7933 + 0.259631i 2.15820 + 0.0134073i
\(376\) 0 0
\(377\) 45.7596 + 13.4362i 2.35674 + 0.692002i
\(378\) 0 0
\(379\) 12.2492 0.583500i 0.629198 0.0299724i 0.269439 0.963018i \(-0.413162\pi\)
0.359759 + 0.933045i \(0.382859\pi\)
\(380\) 0 0
\(381\) 7.88367 + 13.8530i 0.403893 + 0.709708i
\(382\) 0 0
\(383\) −1.23833 0.118247i −0.0632759 0.00604212i 0.0633701 0.997990i \(-0.479815\pi\)
−0.126646 + 0.991948i \(0.540421\pi\)
\(384\) 0 0
\(385\) −66.0549 + 22.8618i −3.36647 + 1.16515i
\(386\) 0 0
\(387\) −1.13272 + 0.148521i −0.0575793 + 0.00754975i
\(388\) 0 0
\(389\) 23.8600 + 25.0237i 1.20975 + 1.26875i 0.953241 + 0.302210i \(0.0977243\pi\)
0.256510 + 0.966541i \(0.417427\pi\)
\(390\) 0 0
\(391\) 2.89037 1.15713i 0.146172 0.0585185i
\(392\) 0 0
\(393\) −10.6757 + 16.3869i −0.538516 + 0.826612i
\(394\) 0 0
\(395\) −0.397212 4.15979i −0.0199859 0.209302i
\(396\) 0 0
\(397\) 2.89713 20.1500i 0.145403 1.01130i −0.778219 0.627993i \(-0.783877\pi\)
0.923622 0.383306i \(-0.125214\pi\)
\(398\) 0 0
\(399\) −41.4869 + 18.6358i −2.07694 + 0.932959i
\(400\) 0 0
\(401\) 33.0777 1.65182 0.825912 0.563799i \(-0.190661\pi\)
0.825912 + 0.563799i \(0.190661\pi\)
\(402\) 0 0
\(403\) 5.13836 0.255960
\(404\) 0 0
\(405\) −36.0196 0.895227i −1.78983 0.0444842i
\(406\) 0 0
\(407\) 0.591706 4.11541i 0.0293298 0.203993i
\(408\) 0 0
\(409\) 3.30888 + 34.6522i 0.163614 + 1.71344i 0.588753 + 0.808313i \(0.299619\pi\)
−0.425139 + 0.905128i \(0.639775\pi\)
\(410\) 0 0
\(411\) −10.8367 7.05986i −0.534537 0.348237i
\(412\) 0 0
\(413\) 28.3891 11.3653i 1.39693 0.559248i
\(414\) 0 0
\(415\) −32.9734 34.5816i −1.61860 1.69754i
\(416\) 0 0
\(417\) −8.26842 28.8208i −0.404906 1.41136i
\(418\) 0 0
\(419\) −19.5218 + 6.75657i −0.953703 + 0.330080i −0.759226 0.650827i \(-0.774422\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(420\) 0 0
\(421\) 17.7061 + 1.69072i 0.862941 + 0.0824009i 0.517134 0.855905i \(-0.326999\pi\)
0.345807 + 0.938306i \(0.387605\pi\)
\(422\) 0 0
\(423\) 3.11607 + 8.07283i 0.151508 + 0.392514i
\(424\) 0 0
\(425\) −72.2862 + 3.44342i −3.50640 + 0.167030i
\(426\) 0 0
\(427\) 6.58841 + 1.93453i 0.318836 + 0.0936186i
\(428\) 0 0
\(429\) 0.268122 43.1600i 0.0129451 2.08379i
\(430\) 0 0
\(431\) −13.2824 + 7.66862i −0.639793 + 0.369384i −0.784535 0.620085i \(-0.787098\pi\)
0.144742 + 0.989469i \(0.453765\pi\)
\(432\) 0 0
\(433\) 27.6278 28.9752i 1.32771 1.39246i 0.466230 0.884664i \(-0.345612\pi\)
0.861478 0.507796i \(-0.169539\pi\)
\(434\) 0 0
\(435\) 42.0431 43.5487i 2.01581 2.08800i
\(436\) 0 0
\(437\) −3.25061 0.154845i −0.155498 0.00740726i
\(438\) 0 0
\(439\) 0.819748 1.41985i 0.0391245 0.0677655i −0.845800 0.533500i \(-0.820876\pi\)
0.884925 + 0.465734i \(0.154210\pi\)
\(440\) 0 0
\(441\) 11.7254 19.7385i 0.558351 0.939926i
\(442\) 0 0
\(443\) 16.7254 + 3.22355i 0.794646 + 0.153155i 0.570389 0.821375i \(-0.306792\pi\)
0.224257 + 0.974530i \(0.428005\pi\)
\(444\) 0 0
\(445\) −7.14286 6.18932i −0.338604 0.293402i
\(446\) 0 0
\(447\) −9.02803 7.92156i −0.427011 0.374677i
\(448\) 0 0
\(449\) −0.467197 + 0.906237i −0.0220484 + 0.0427679i −0.899602 0.436710i \(-0.856144\pi\)
0.877554 + 0.479478i \(0.159174\pi\)
\(450\) 0 0
\(451\) −4.00331 + 0.771575i −0.188509 + 0.0363320i
\(452\) 0 0
\(453\) −12.0668 + 11.3634i −0.566948 + 0.533900i
\(454\) 0 0
\(455\) −54.8261 63.2727i −2.57029 2.96627i
\(456\) 0 0
\(457\) 1.17246 + 4.83294i 0.0548453 + 0.226075i 0.992638 0.121121i \(-0.0386489\pi\)
−0.937792 + 0.347196i \(0.887134\pi\)
\(458\) 0 0
\(459\) 34.0861 0.987523i 1.59100 0.0460936i
\(460\) 0 0
\(461\) −11.2355 38.2645i −0.523288 1.78215i −0.617464 0.786599i \(-0.711840\pi\)
0.0941766 0.995556i \(-0.469978\pi\)
\(462\) 0 0
\(463\) −10.8258 + 27.0415i −0.503118 + 1.25673i 0.431834 + 0.901953i \(0.357866\pi\)
−0.934952 + 0.354774i \(0.884558\pi\)
\(464\) 0 0
\(465\) 3.02442 5.77814i 0.140254 0.267955i
\(466\) 0 0
\(467\) −23.3011 + 16.5926i −1.07825 + 0.767815i −0.973957 0.226732i \(-0.927196\pi\)
−0.104288 + 0.994547i \(0.533256\pi\)
\(468\) 0 0
\(469\) −30.7266 6.13325i −1.41882 0.283207i
\(470\) 0 0
\(471\) 0.839089 0.426004i 0.0386632 0.0196292i
\(472\) 0 0
\(473\) −1.64141 0.568097i −0.0754721 0.0261211i
\(474\) 0 0
\(475\) 70.2250 + 28.1139i 3.22214 + 1.28995i
\(476\) 0 0
\(477\) −10.6272 0.132043i −0.486584 0.00604582i
\(478\) 0 0
\(479\) 5.00608 + 9.71045i 0.228734 + 0.443682i 0.975073 0.221884i \(-0.0712206\pi\)
−0.746339 + 0.665566i \(0.768190\pi\)
\(480\) 0 0
\(481\) 4.83953 1.17406i 0.220664 0.0535324i
\(482\) 0 0
\(483\) 2.65659 1.68406i 0.120879 0.0766274i
\(484\) 0 0
\(485\) −37.3841 + 47.5377i −1.69752 + 2.15858i
\(486\) 0 0
\(487\) 2.04050 + 10.5871i 0.0924641 + 0.479749i 0.998411 + 0.0563572i \(0.0179486\pi\)
−0.905947 + 0.423392i \(0.860839\pi\)
\(488\) 0 0
\(489\) 2.75903 3.82402i 0.124768 0.172928i
\(490\) 0 0
\(491\) 18.0872 28.1443i 0.816265 1.27013i −0.143591 0.989637i \(-0.545865\pi\)
0.959855 0.280495i \(-0.0904987\pi\)
\(492\) 0 0
\(493\) −37.5163 + 43.2962i −1.68965 + 1.94996i
\(494\) 0 0
\(495\) −48.3761 25.7053i −2.17434 1.15537i
\(496\) 0 0
\(497\) 0.290402 1.19705i 0.0130263 0.0536951i
\(498\) 0 0
\(499\) 15.0922 + 8.71346i 0.675618 + 0.390068i 0.798202 0.602390i \(-0.205785\pi\)
−0.122584 + 0.992458i \(0.539118\pi\)
\(500\) 0 0
\(501\) −5.53141 + 27.7702i −0.247125 + 1.24068i
\(502\) 0 0
\(503\) 8.60875 12.0893i 0.383845 0.539035i −0.576774 0.816904i \(-0.695689\pi\)
0.960619 + 0.277869i \(0.0896280\pi\)
\(504\) 0 0
\(505\) −43.2070 41.1978i −1.92269 1.83328i
\(506\) 0 0
\(507\) 27.1558 10.6763i 1.20603 0.474151i
\(508\) 0 0
\(509\) −30.5372 + 4.39058i −1.35354 + 0.194609i −0.780621 0.625005i \(-0.785097\pi\)
−0.572916 + 0.819614i \(0.694188\pi\)
\(510\) 0 0
\(511\) 4.17487 14.2183i 0.184685 0.628981i
\(512\) 0 0
\(513\) −32.8379 13.8618i −1.44983 0.612014i
\(514\) 0 0
\(515\) −12.0593 + 9.48354i −0.531397 + 0.417895i
\(516\) 0 0
\(517\) −1.25062 + 13.0971i −0.0550021 + 0.576009i
\(518\) 0 0
\(519\) 4.34796 + 23.3386i 0.190854 + 1.02445i
\(520\) 0 0
\(521\) 0.431533 + 0.944926i 0.0189058 + 0.0413980i 0.918849 0.394608i \(-0.129120\pi\)
−0.899944 + 0.436006i \(0.856392\pi\)
\(522\) 0 0
\(523\) −17.2682 + 16.4652i −0.755086 + 0.719973i −0.966286 0.257470i \(-0.917111\pi\)
0.211200 + 0.977443i \(0.432263\pi\)
\(524\) 0 0
\(525\) −71.1572 + 16.7952i −3.10555 + 0.733002i
\(526\) 0 0
\(527\) −2.56412 + 5.61463i −0.111695 + 0.244577i
\(528\) 0 0
\(529\) −22.6718 + 2.16490i −0.985731 + 0.0941259i
\(530\) 0 0
\(531\) 21.6747 + 10.2258i 0.940600 + 0.443763i
\(532\) 0 0
\(533\) −2.64006 4.10801i −0.114354 0.177938i
\(534\) 0 0
\(535\) 37.5255i 1.62237i
\(536\) 0 0
\(537\) 1.15724 7.70854i 0.0499387 0.332648i
\(538\) 0 0
\(539\) 29.3650 18.8718i 1.26484 0.812864i
\(540\) 0 0
\(541\) 44.8532 + 6.44892i 1.92839 + 0.277261i 0.996369 0.0851428i \(-0.0271346\pi\)
0.932021 + 0.362403i \(0.118044\pi\)
\(542\) 0 0
\(543\) 0.313289 5.81629i 0.0134445 0.249601i
\(544\) 0 0
\(545\) 23.9813 + 10.9519i 1.02724 + 0.469127i
\(546\) 0 0
\(547\) 13.0376 + 32.5664i 0.557448 + 1.39244i 0.892847 + 0.450361i \(0.148705\pi\)
−0.335399 + 0.942076i \(0.608871\pi\)
\(548\) 0 0
\(549\) 2.40631 + 4.81350i 0.102699 + 0.205435i
\(550\) 0 0
\(551\) 54.4705 24.8758i 2.32052 1.05975i
\(552\) 0 0
\(553\) 1.30680 + 3.77576i 0.0555710 + 0.160562i
\(554\) 0 0
\(555\) 1.52829 6.13315i 0.0648723 0.260338i
\(556\) 0 0
\(557\) 12.5450 + 15.9522i 0.531547 + 0.675917i 0.975466 0.220150i \(-0.0706547\pi\)
−0.443919 + 0.896067i \(0.646412\pi\)
\(558\) 0 0
\(559\) −0.0989901 2.07806i −0.00418683 0.0878925i
\(560\) 0 0
\(561\) 47.0267 + 21.8304i 1.98547 + 0.921682i
\(562\) 0 0
\(563\) 5.67121 + 39.4441i 0.239013 + 1.66237i 0.656979 + 0.753909i \(0.271834\pi\)
−0.417966 + 0.908463i \(0.637257\pi\)
\(564\) 0 0
\(565\) 4.81347 + 8.33718i 0.202504 + 0.350748i
\(566\) 0 0
\(567\) 33.6714 7.28780i 1.41407 0.306059i
\(568\) 0 0
\(569\) 15.4182 + 10.9793i 0.646366 + 0.460275i 0.855633 0.517583i \(-0.173168\pi\)
−0.209267 + 0.977859i \(0.567108\pi\)
\(570\) 0 0
\(571\) −0.213972 + 4.49182i −0.00895444 + 0.187977i 0.989958 + 0.141359i \(0.0451473\pi\)
−0.998913 + 0.0466176i \(0.985156\pi\)
\(572\) 0 0
\(573\) 12.0407 + 9.59056i 0.503007 + 0.400651i
\(574\) 0 0
\(575\) −5.08401 1.23337i −0.212018 0.0514350i
\(576\) 0 0
\(577\) −1.10764 + 5.74698i −0.0461116 + 0.239250i −0.997671 0.0682166i \(-0.978269\pi\)
0.951559 + 0.307467i \(0.0994812\pi\)
\(578\) 0 0
\(579\) −2.96809 3.46866i −0.123350 0.144153i
\(580\) 0 0
\(581\) 38.4346 + 24.7004i 1.59454 + 1.02475i
\(582\) 0 0
\(583\) −14.3626 7.40443i −0.594838 0.306660i
\(584\) 0 0
\(585\) 7.04807 65.2347i 0.291402 2.69712i
\(586\) 0 0
\(587\) 7.45216 + 5.86044i 0.307584 + 0.241886i 0.760004 0.649918i \(-0.225197\pi\)
−0.452420 + 0.891805i \(0.649439\pi\)
\(588\) 0 0
\(589\) 4.87593 4.22502i 0.200909 0.174089i
\(590\) 0 0
\(591\) −21.6952 + 1.93572i −0.892422 + 0.0796248i
\(592\) 0 0
\(593\) 24.9153 12.8447i 1.02315 0.527470i 0.136854 0.990591i \(-0.456301\pi\)
0.886295 + 0.463121i \(0.153271\pi\)
\(594\) 0 0
\(595\) 96.4963 28.3339i 3.95596 1.16158i
\(596\) 0 0
\(597\) −8.15179 + 13.9189i −0.333630 + 0.569663i
\(598\) 0 0
\(599\) −5.73363 + 16.5662i −0.234270 + 0.676879i 0.765183 + 0.643813i \(0.222648\pi\)
−0.999453 + 0.0330660i \(0.989473\pi\)
\(600\) 0 0
\(601\) 12.0619 + 16.9386i 0.492016 + 0.690939i 0.983697 0.179836i \(-0.0575567\pi\)
−0.491681 + 0.870775i \(0.663617\pi\)
\(602\) 0 0
\(603\) −12.8802 20.9069i −0.524524 0.851396i
\(604\) 0 0
\(605\) −22.7689 31.9744i −0.925687 1.29994i
\(606\) 0 0
\(607\) 10.1742 29.3965i 0.412959 1.19317i −0.526402 0.850236i \(-0.676459\pi\)
0.939361 0.342931i \(-0.111420\pi\)
\(608\) 0 0
\(609\) −29.2499 + 49.9432i −1.18527 + 2.02380i
\(610\) 0 0
\(611\) −15.1200 + 4.43964i −0.611690 + 0.179608i
\(612\) 0 0
\(613\) −42.3253 + 21.8202i −1.70950 + 0.881309i −0.729072 + 0.684437i \(0.760048\pi\)
−0.980429 + 0.196873i \(0.936921\pi\)
\(614\) 0 0
\(615\) −6.17343 + 0.550813i −0.248937 + 0.0222109i
\(616\) 0 0
\(617\) 15.9181 13.7931i 0.640839 0.555290i −0.272671 0.962107i \(-0.587907\pi\)
0.913509 + 0.406818i \(0.133362\pi\)
\(618\) 0 0
\(619\) 0.0630314 + 0.0495684i 0.00253345 + 0.00199232i 0.619425 0.785056i \(-0.287366\pi\)
−0.616891 + 0.787048i \(0.711608\pi\)
\(620\) 0 0
\(621\) 2.38438 + 0.625715i 0.0956817 + 0.0251091i
\(622\) 0 0
\(623\) 8.03241 + 4.14100i 0.321812 + 0.165905i
\(624\) 0 0
\(625\) 34.8826 + 22.4177i 1.39531 + 0.896708i
\(626\) 0 0
\(627\) −35.2339 41.1762i −1.40711 1.64442i
\(628\) 0 0
\(629\) −1.13212 + 5.87397i −0.0451404 + 0.234211i
\(630\) 0 0
\(631\) −26.7125 6.48038i −1.06341 0.257980i −0.334362 0.942445i \(-0.608521\pi\)
−0.729046 + 0.684465i \(0.760036\pi\)
\(632\) 0 0
\(633\) 12.4021 + 9.87846i 0.492941 + 0.392633i
\(634\) 0 0
\(635\) −1.75298 + 36.7996i −0.0695649 + 1.46035i
\(636\) 0 0
\(637\) 34.0565 + 24.2515i 1.34937 + 0.960881i
\(638\) 0 0
\(639\) 0.841963 0.472258i 0.0333075 0.0186822i
\(640\) 0 0
\(641\) 18.5552 + 32.1386i 0.732888 + 1.26940i 0.955644 + 0.294525i \(0.0951613\pi\)
−0.222756 + 0.974874i \(0.571505\pi\)
\(642\) 0 0
\(643\) −5.39724 37.5386i −0.212846 1.48038i −0.763589 0.645703i \(-0.776565\pi\)
0.550743 0.834675i \(-0.314345\pi\)
\(644\) 0 0
\(645\) −2.39506 1.11182i −0.0943055 0.0437779i
\(646\) 0 0
\(647\) −1.07522 22.5717i −0.0422714 0.887385i −0.916051 0.401063i \(-0.868641\pi\)
0.873779 0.486323i \(-0.161662\pi\)
\(648\) 0 0
\(649\) 22.5244 + 28.6421i 0.884159 + 1.12430i
\(650\) 0 0
\(651\) −1.50779 + 6.05086i −0.0590948 + 0.237152i
\(652\) 0 0
\(653\) 13.9877 + 40.4147i 0.547380 + 1.58155i 0.791088 + 0.611702i \(0.209515\pi\)
−0.243708 + 0.969849i \(0.578364\pi\)
\(654\) 0 0
\(655\) −41.1199 + 18.7788i −1.60669 + 0.733750i
\(656\) 0 0
\(657\) 10.3879 5.19300i 0.405270 0.202598i
\(658\) 0 0
\(659\) −0.755882 1.88810i −0.0294450 0.0735500i 0.912917 0.408146i \(-0.133824\pi\)
−0.942362 + 0.334596i \(0.891400\pi\)
\(660\) 0 0
\(661\) 14.3871 + 6.57039i 0.559595 + 0.255558i 0.675072 0.737752i \(-0.264112\pi\)
−0.115477 + 0.993310i \(0.536840\pi\)
\(662\) 0 0
\(663\) −3.34008 + 62.0093i −0.129718 + 2.40824i
\(664\) 0 0
\(665\) −104.052 14.9604i −4.03496 0.580139i
\(666\) 0 0
\(667\) −3.48397 + 2.23901i −0.134900 + 0.0866950i
\(668\) 0 0
\(669\) 6.22013 41.4331i 0.240484 1.60190i
\(670\) 0 0
\(671\) 8.18202i 0.315864i
\(672\) 0 0
\(673\) 24.7710 + 38.5444i 0.954850 + 1.48578i 0.872172 + 0.489200i \(0.162711\pi\)
0.0826789 + 0.996576i \(0.473652\pi\)
\(674\) 0 0
\(675\) −47.6178 31.8714i −1.83281 1.22673i
\(676\) 0 0
\(677\) −45.8487 + 4.37802i −1.76211 + 0.168261i −0.925301 0.379234i \(-0.876188\pi\)
−0.836809 + 0.547495i \(0.815582\pi\)
\(678\) 0 0
\(679\) 24.0214 52.5996i 0.921858 2.01859i
\(680\) 0 0
\(681\) −33.7171 + 7.95823i −1.29204 + 0.304960i
\(682\) 0 0
\(683\) 11.3455 10.8179i 0.434122 0.413934i −0.441250 0.897384i \(-0.645465\pi\)
0.875372 + 0.483450i \(0.160616\pi\)
\(684\) 0 0
\(685\) −12.4185 27.1928i −0.474487 1.03898i
\(686\) 0 0
\(687\) 2.18001 + 11.7017i 0.0831725 + 0.446447i
\(688\) 0 0
\(689\) 1.83974 19.2666i 0.0700885 0.734000i
\(690\) 0 0
\(691\) 12.4877 9.82041i 0.475053 0.373586i −0.351735 0.936100i \(-0.614408\pi\)
0.826788 + 0.562514i \(0.190166\pi\)
\(692\) 0 0
\(693\) 50.7460 + 12.9805i 1.92768 + 0.493088i
\(694\) 0 0
\(695\) 19.5249 66.4955i 0.740620 2.52232i
\(696\) 0 0
\(697\) 5.80620 0.834806i 0.219926 0.0316205i
\(698\) 0 0
\(699\) −34.8772 + 13.7120i −1.31918 + 0.518634i
\(700\) 0 0
\(701\) −11.8887 11.3358i −0.449030 0.428149i 0.431520 0.902104i \(-0.357978\pi\)
−0.880549 + 0.473955i \(0.842826\pi\)
\(702\) 0 0
\(703\) 3.62699 5.09339i 0.136795 0.192101i
\(704\) 0 0
\(705\) −3.90716 + 19.6158i −0.147152 + 0.738772i
\(706\) 0 0
\(707\) 49.4351 + 28.5414i 1.85920 + 1.07341i
\(708\) 0 0
\(709\) 7.93887 32.7245i 0.298151 1.22899i −0.603793 0.797141i \(-0.706345\pi\)
0.901944 0.431853i \(-0.142140\pi\)
\(710\) 0 0
\(711\) −1.46934 + 2.76522i −0.0551046 + 0.103704i
\(712\) 0 0
\(713\) −0.292200 + 0.337217i −0.0109430 + 0.0126289i
\(714\) 0 0
\(715\) 53.9348 83.9241i 2.01705 3.13858i
\(716\) 0 0
\(717\) −27.3569 + 37.9167i −1.02166 + 1.41603i
\(718\) 0 0
\(719\) −9.26034 48.0472i −0.345353 1.79186i −0.574539 0.818477i \(-0.694819\pi\)
0.229187 0.973382i \(-0.426393\pi\)
\(720\) 0 0
\(721\) 9.06778 11.5306i 0.337702 0.429423i
\(722\) 0 0
\(723\) 1.22448 0.776221i 0.0455390 0.0288680i
\(724\) 0 0
\(725\) 93.5503 22.6951i 3.47437 0.842873i
\(726\) 0 0
\(727\) 2.88289 + 5.59202i 0.106920 + 0.207397i 0.936226 0.351399i \(-0.114294\pi\)
−0.829305 + 0.558796i \(0.811264\pi\)
\(728\) 0 0
\(729\) 22.1541 + 15.4336i 0.820522 + 0.571614i
\(730\) 0 0
\(731\) 2.32007 + 0.928815i 0.0858108 + 0.0343535i
\(732\) 0 0
\(733\) −3.72505 1.28925i −0.137588 0.0476196i 0.257406 0.966303i \(-0.417132\pi\)
−0.394994 + 0.918684i \(0.629253\pi\)
\(734\) 0 0
\(735\) 47.3167 24.0226i 1.74530 0.886085i
\(736\) 0 0
\(737\) −3.30289 37.1889i −0.121664 1.36987i
\(738\) 0 0
\(739\) −9.69527 + 6.90397i −0.356646 + 0.253967i −0.744310 0.667834i \(-0.767222\pi\)
0.387664 + 0.921801i \(0.373282\pi\)
\(740\) 0 0
\(741\) 30.1012 57.5082i 1.10580 2.11262i
\(742\) 0 0
\(743\) 12.4358 31.0630i 0.456224 1.13959i −0.504827 0.863220i \(-0.668444\pi\)
0.961051 0.276371i \(-0.0891320\pi\)
\(744\) 0 0
\(745\) −7.82122 26.6366i −0.286547 0.975890i
\(746\) 0 0
\(747\) 6.33900 + 35.2405i 0.231932 + 1.28938i
\(748\) 0 0
\(749\) −8.45911 34.8689i −0.309089 1.27408i
\(750\) 0 0
\(751\) 12.8772 + 14.8611i 0.469897 + 0.542290i 0.940383 0.340118i \(-0.110467\pi\)
−0.470486 + 0.882407i \(0.655921\pi\)
\(752\) 0 0
\(753\) 10.9337 10.2964i 0.398447 0.375220i
\(754\) 0 0
\(755\) −37.6190 + 7.25046i −1.36909 + 0.263871i
\(756\) 0 0
\(757\) 4.60302 8.92862i 0.167300 0.324516i −0.790250 0.612785i \(-0.790049\pi\)
0.957550 + 0.288269i \(0.0930796\pi\)
\(758\) 0 0
\(759\) 2.81723 + 2.47195i 0.102259 + 0.0897263i
\(760\) 0 0
\(761\) −29.0122 25.1392i −1.05169 0.911295i −0.0554962 0.998459i \(-0.517674\pi\)
−0.996194 + 0.0871642i \(0.972220\pi\)
\(762\) 0 0
\(763\) −24.7524 4.77063i −0.896096 0.172708i
\(764\) 0 0
\(765\) 67.7642 + 40.2544i 2.45002 + 1.45540i
\(766\) 0 0
\(767\) −21.8217 + 37.7962i −0.787934 + 1.36474i
\(768\) 0 0
\(769\) 15.2605 + 0.726948i 0.550308 + 0.0262144i 0.320895 0.947115i \(-0.396016\pi\)
0.229413 + 0.973329i \(0.426319\pi\)
\(770\) 0 0
\(771\) 10.0248 10.3838i 0.361034 0.373962i
\(772\) 0 0
\(773\) 7.80493 8.18557i 0.280724 0.294415i −0.568243 0.822861i \(-0.692377\pi\)
0.848967 + 0.528446i \(0.177225\pi\)