Properties

Label 804.2.ba.b.41.7
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 41.7
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.14236 - 1.30193i) q^{3} +(-0.569745 + 3.96266i) q^{5} +(0.363865 + 3.81057i) q^{7} +(-0.390019 + 2.97454i) q^{9} +O(q^{10})\) \(q+(-1.14236 - 1.30193i) q^{3} +(-0.569745 + 3.96266i) q^{5} +(0.363865 + 3.81057i) q^{7} +(-0.390019 + 2.97454i) q^{9} +(4.23450 - 1.69524i) q^{11} +(-3.77004 - 3.95391i) q^{13} +(5.80995 - 3.78503i) q^{15} +(-6.20169 + 2.14643i) q^{17} +(-6.82859 - 0.652051i) q^{19} +(4.54541 - 4.82677i) q^{21} +(-0.473873 + 0.0225734i) q^{23} +(-10.5806 - 3.10675i) q^{25} +(4.31817 - 2.89023i) q^{27} +(7.56004 - 4.36479i) q^{29} +(-0.649047 + 0.680701i) q^{31} +(-7.04441 - 3.57643i) q^{33} +(-15.3073 - 0.729177i) q^{35} +(-0.455768 + 0.789413i) q^{37} +(-0.840938 + 9.42510i) q^{39} +(-0.877682 - 0.169159i) q^{41} +(0.287793 + 0.249374i) q^{43} +(-11.5649 - 3.24024i) q^{45} +(-1.32173 + 2.56380i) q^{47} +(-7.51452 + 1.44831i) q^{49} +(9.87907 + 5.62214i) q^{51} +(-2.31995 - 2.67736i) q^{53} +(4.30508 + 17.7458i) q^{55} +(6.95180 + 9.63519i) q^{57} +(2.25065 + 7.66500i) q^{59} +(0.666695 - 1.66532i) q^{61} +(-11.4766 - 0.403862i) q^{63} +(17.8160 - 12.6867i) q^{65} +(-2.35801 + 7.83835i) q^{67} +(0.570724 + 0.591161i) q^{69} +(0.304090 + 0.105247i) q^{71} +(-3.59390 - 1.43878i) q^{73} +(8.04215 + 17.3242i) q^{75} +(8.00061 + 15.5190i) q^{77} +(1.01436 - 0.246082i) q^{79} +(-8.69577 - 2.32025i) q^{81} +(-7.37794 + 9.38182i) q^{83} +(-4.97218 - 25.7981i) q^{85} +(-14.3189 - 4.85644i) q^{87} +(-1.27636 + 1.98605i) q^{89} +(13.6948 - 15.8047i) q^{91} +(1.62767 + 0.0674039i) q^{93} +(6.47442 - 26.6879i) q^{95} +(-13.0824 - 7.55312i) q^{97} +(3.39102 + 13.2569i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

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
\(3\) −1.14236 1.30193i −0.659543 0.751667i
\(4\) 0 0
\(5\) −0.569745 + 3.96266i −0.254798 + 1.77216i 0.313749 + 0.949506i \(0.398415\pi\)
−0.568547 + 0.822651i \(0.692494\pi\)
\(6\) 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
\(9\) −0.390019 + 2.97454i −0.130006 + 0.991513i
\(10\) 0 0
\(11\) 4.23450 1.69524i 1.27675 0.511134i 0.368526 0.929617i \(-0.379863\pi\)
0.908224 + 0.418484i \(0.137438\pi\)
\(12\) 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
\(15\) 5.80995 3.78503i 1.50012 0.977291i
\(16\) 0 0
\(17\) −6.20169 + 2.14643i −1.50413 + 0.520585i −0.950109 0.311917i \(-0.899029\pi\)
−0.554022 + 0.832502i \(0.686908\pi\)
\(18\) 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
\(21\) 4.54541 4.82677i 0.991889 1.05329i
\(22\) 0 0
\(23\) −0.473873 + 0.0225734i −0.0988094 + 0.00470687i −0.0969284 0.995291i \(-0.530902\pi\)
−0.00188104 + 0.999998i \(0.500599\pi\)
\(24\) 0 0
\(25\) −10.5806 3.10675i −2.11613 0.621351i
\(26\) 0 0
\(27\) 4.31817 2.89023i 0.831032 0.556224i
\(28\) 0 0
\(29\) 7.56004 4.36479i 1.40386 0.810521i 0.409077 0.912500i \(-0.365851\pi\)
0.994787 + 0.101978i \(0.0325173\pi\)
\(30\) 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
\(33\) −7.04441 3.57643i −1.22627 0.622576i
\(34\) 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
\(39\) −0.840938 + 9.42510i −0.134658 + 1.50922i
\(40\) 0 0
\(41\) −0.877682 0.169159i −0.137071 0.0264182i 0.120254 0.992743i \(-0.461629\pi\)
−0.257325 + 0.966325i \(0.582841\pi\)
\(42\) 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
\(45\) −11.5649 3.24024i −1.72399 0.483027i
\(46\) 0 0
\(47\) −1.32173 + 2.56380i −0.192794 + 0.373969i −0.965342 0.260988i \(-0.915952\pi\)
0.772548 + 0.634957i \(0.218982\pi\)
\(48\) 0 0
\(49\) −7.51452 + 1.44831i −1.07350 + 0.206901i
\(50\) 0 0
\(51\) 9.87907 + 5.62214i 1.38335 + 0.787258i
\(52\) 0 0
\(53\) −2.31995 2.67736i −0.318669 0.367764i 0.573703 0.819063i \(-0.305506\pi\)
−0.892373 + 0.451299i \(0.850961\pi\)
\(54\) 0 0
\(55\) 4.30508 + 17.7458i 0.580496 + 2.39284i
\(56\) 0 0
\(57\) 6.95180 + 9.63519i 0.920788 + 1.27621i
\(58\) 0 0
\(59\) 2.25065 + 7.66500i 0.293009 + 0.997898i 0.966063 + 0.258305i \(0.0831639\pi\)
−0.673054 + 0.739593i \(0.735018\pi\)
\(60\) 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
\(63\) −11.4766 0.403862i −1.44592 0.0508818i
\(64\) 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
\(69\) 0.570724 + 0.591161i 0.0687071 + 0.0711674i
\(70\) 0 0
\(71\) 0.304090 + 0.105247i 0.0360889 + 0.0124905i 0.345053 0.938583i \(-0.387861\pi\)
−0.308964 + 0.951074i \(0.599982\pi\)
\(72\) 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
\(75\) 8.04215 + 17.3242i 0.928627 + 2.00043i
\(76\) 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
\(81\) −8.69577 2.32025i −0.966197 0.257806i
\(82\) 0 0
\(83\) −7.37794 + 9.38182i −0.809835 + 1.02979i 0.189022 + 0.981973i \(0.439468\pi\)
−0.998856 + 0.0478154i \(0.984774\pi\)
\(84\) 0 0
\(85\) −4.97218 25.7981i −0.539309 2.79820i
\(86\) 0 0
\(87\) −14.3189 4.85644i −1.53515 0.520665i
\(88\) 0 0
\(89\) −1.27636 + 1.98605i −0.135294 + 0.210521i −0.902289 0.431131i \(-0.858115\pi\)
0.766995 + 0.641653i \(0.221751\pi\)
\(90\) 0 0
\(91\) 13.6948 15.8047i 1.43561 1.65678i
\(92\) 0 0
\(93\) 1.62767 + 0.0674039i 0.168781 + 0.00698946i
\(94\) 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
\(99\) 3.39102 + 13.2569i 0.340810 + 1.33237i
\(100\) 0 0
\(101\) −8.64998 + 12.1472i −0.860705 + 1.20869i 0.115816 + 0.993271i \(0.463052\pi\)
−0.976521 + 0.215421i \(0.930888\pi\)
\(102\) 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
\(105\) 16.5371 + 20.7620i 1.61386 + 2.02616i
\(106\) 0 0
\(107\) 9.27796 1.33397i 0.896935 0.128960i 0.321598 0.946876i \(-0.395780\pi\)
0.575337 + 0.817917i \(0.304871\pi\)
\(108\) 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
\(111\) 1.54841 0.308420i 0.146968 0.0292739i
\(112\) 0 0
\(113\) 1.89021 1.48648i 0.177816 0.139836i −0.525284 0.850927i \(-0.676041\pi\)
0.703100 + 0.711091i \(0.251799\pi\)
\(114\) 0 0
\(115\) 0.180536 1.89066i 0.0168351 0.176305i
\(116\) 0 0
\(117\) 13.2314 9.67204i 1.22325 0.894181i
\(118\) 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
\(123\) 0.782397 + 1.33592i 0.0705464 + 0.120456i
\(124\) 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
\(129\) −0.00409737 0.659561i −0.000360753 0.0580711i
\(130\) 0 0
\(131\) 6.10471 + 9.49911i 0.533371 + 0.829941i 0.998469 0.0553182i \(-0.0176173\pi\)
−0.465098 + 0.885259i \(0.653981\pi\)
\(132\) 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 −0.780743 0.624852i \(-0.785159\pi\)
0.244053 + 0.969762i \(0.421523\pi\)
\(138\) 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
\(141\) 4.84777 1.20799i 0.408256 0.101731i
\(142\) 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
\(147\) 10.4699 + 8.12886i 0.863542 + 0.670457i
\(148\) 0 0
\(149\) −6.30772 + 2.88064i −0.516749 + 0.235991i −0.656679 0.754170i \(-0.728039\pi\)
0.139930 + 0.990161i \(0.455312\pi\)
\(150\) 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
\(153\) −3.96586 19.2843i −0.320620 1.55905i
\(154\) 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
\(159\) −0.835506 + 6.07892i −0.0662600 + 0.482090i
\(160\) 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
\(165\) 18.1857 25.8770i 1.41575 2.01452i
\(166\) 0 0
\(167\) 13.3168 + 9.48282i 1.03048 + 0.733803i 0.964517 0.264019i \(-0.0850482\pi\)
0.0659645 + 0.997822i \(0.478988\pi\)
\(168\) 0 0
\(169\) −0.801593 + 16.8275i −0.0616610 + 1.29442i
\(170\) 0 0
\(171\) 4.60283 20.0576i 0.351987 1.53384i
\(172\) 0 0
\(173\) 13.3200 + 3.23140i 1.01270 + 0.245679i 0.707579 0.706634i \(-0.249787\pi\)
0.305123 + 0.952313i \(0.401302\pi\)
\(174\) 0 0
\(175\) 7.98857 41.4486i 0.603879 3.13322i
\(176\) 0 0
\(177\) 7.40820 11.6864i 0.556835 0.878402i
\(178\) 0 0
\(179\) −3.78598 2.43310i −0.282977 0.181858i 0.391451 0.920199i \(-0.371973\pi\)
−0.674428 + 0.738341i \(0.735610\pi\)
\(180\) 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
\(183\) −2.92973 + 1.03442i −0.216572 + 0.0764662i
\(184\) 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
\(189\) 12.5846 + 15.4030i 0.915397 + 1.12041i
\(190\) 0 0
\(191\) 7.89943 4.07244i 0.571583 0.294671i −0.148102 0.988972i \(-0.547317\pi\)
0.719685 + 0.694301i \(0.244286\pi\)
\(192\) 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
\(195\) −36.8694 8.70226i −2.64027 0.623182i
\(196\) 0 0
\(197\) −4.11304 + 11.8839i −0.293042 + 0.846690i 0.698349 + 0.715757i \(0.253918\pi\)
−0.991391 + 0.130933i \(0.958203\pi\)
\(198\) 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
\(201\) 12.8987 5.88429i 0.909801 0.415046i
\(202\) 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
\(207\) 0.117674 1.41836i 0.00817892 0.0985828i
\(208\) 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
\(213\) −0.210358 0.516132i −0.0144135 0.0353648i
\(214\) 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
\(219\) 2.23235 + 6.32259i 0.150848 + 0.427241i
\(220\) 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
\(225\) 13.3678 30.2608i 0.891187 2.01739i
\(226\) 0 0
\(227\) −3.78530 + 19.6400i −0.251239 + 1.30355i 0.608799 + 0.793324i \(0.291652\pi\)
−0.860038 + 0.510229i \(0.829561\pi\)
\(228\) 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
\(231\) 11.0650 28.1445i 0.728024 1.85177i
\(232\) 0 0
\(233\) −1.02952 + 21.6122i −0.0674458 + 1.41586i 0.670954 + 0.741499i \(0.265885\pi\)
−0.738400 + 0.674363i \(0.764418\pi\)
\(234\) 0 0
\(235\) −9.40643 6.69829i −0.613608 0.436948i
\(236\) 0 0
\(237\) −1.47915 1.03951i −0.0960813 0.0675236i
\(238\) 0 0
\(239\) 13.4972 + 23.3778i 0.873059 + 1.51218i 0.858816 + 0.512284i \(0.171200\pi\)
0.0142427 + 0.999899i \(0.495466\pi\)
\(240\) 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
\(243\) 6.91292 + 13.9718i 0.443464 + 0.896292i
\(244\) 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
\(249\) 20.6427 1.11190i 1.30818 0.0704638i
\(250\) 0 0
\(251\) −2.83602 8.19414i −0.179008 0.517210i 0.819424 0.573188i \(-0.194294\pi\)
−0.998432 + 0.0559781i \(0.982172\pi\)
\(252\) 0 0
\(253\) −1.96835 + 0.898916i −0.123749 + 0.0565143i
\(254\) 0 0
\(255\) −27.9072 + 35.9442i −1.74762 + 2.25091i
\(256\) 0 0
\(257\) −3.09708 7.73614i −0.193191 0.482567i 0.799870 0.600174i \(-0.204902\pi\)
−0.993060 + 0.117607i \(0.962478\pi\)
\(258\) 0 0
\(259\) −3.17395 1.44949i −0.197220 0.0900672i
\(260\) 0 0
\(261\) 10.0347 + 24.1900i 0.621131 + 1.49732i
\(262\) 0 0
\(263\) −2.25468 0.324173i −0.139029 0.0199894i 0.0724488 0.997372i \(-0.476919\pi\)
−0.211478 + 0.977383i \(0.567828\pi\)
\(264\) 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 \(-0.807356\pi\)
0.822383 0.568934i \(-0.192644\pi\)
\(270\) 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
\(273\) −36.2210 + 0.225015i −2.19219 + 0.0136185i
\(274\) 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
\(279\) −1.77163 2.19610i −0.106065 0.131477i
\(280\) 0 0
\(281\) −19.8167 + 18.8951i −1.18216 + 1.12719i −0.192873 + 0.981224i \(0.561780\pi\)
−0.989290 + 0.145966i \(0.953371\pi\)
\(282\) 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
\(285\) −42.1418 + 22.0580i −2.49626 + 1.30661i
\(286\) 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
\(291\) 5.11122 + 25.6607i 0.299625 + 1.50426i
\(292\) 0 0
\(293\) 0.694325 2.36465i 0.0405629 0.138145i −0.936722 0.350074i \(-0.886156\pi\)
0.977285 + 0.211929i \(0.0679747\pi\)
\(294\) 0 0
\(295\) −31.6561 + 4.55146i −1.84309 + 0.264996i
\(296\) 0 0
\(297\) 13.3857 19.5590i 0.776716 1.13493i
\(298\) 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
\(303\) 25.6962 2.61487i 1.47621 0.150220i
\(304\) 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
\(309\) −0.274630 + 6.63176i −0.0156232 + 0.377268i
\(310\) 0 0
\(311\) 9.33597 10.7743i 0.529394 0.610953i −0.426564 0.904458i \(-0.640276\pi\)
0.955958 + 0.293504i \(0.0948215\pi\)
\(312\) 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
\(315\) 8.13910 45.2478i 0.458586 2.54942i
\(316\) 0 0
\(317\) 0.497571 + 2.58165i 0.0279464 + 0.145000i 0.993222 0.116235i \(-0.0370825\pi\)
−0.965275 + 0.261235i \(0.915870\pi\)
\(318\) 0 0
\(319\) 24.6136 31.2988i 1.37810 1.75240i
\(320\) 0 0
\(321\) −12.3355 10.5553i −0.688502 0.589142i
\(322\) 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
\(327\) 10.3457 4.80262i 0.572119 0.265586i
\(328\) 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
\(333\) −2.17038 1.66359i −0.118936 0.0911639i
\(334\) 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
\(339\) −4.09458 0.762817i −0.222387 0.0414305i
\(340\) 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
\(345\) −2.66774 + 1.92478i −0.143626 + 0.103626i
\(346\) 0 0
\(347\) −5.98733 24.6801i −0.321417 1.32490i −0.871749 0.489952i \(-0.837014\pi\)
0.550332 0.834946i \(-0.314501\pi\)
\(348\) 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
\(351\) −27.7074 6.17737i −1.47891 0.329724i
\(352\) 0 0
\(353\) 18.3506 3.53680i 0.976706 0.188245i 0.324167 0.946000i \(-0.394916\pi\)
0.652539 + 0.757755i \(0.273704\pi\)
\(354\) 0 0
\(355\) −0.590311 + 1.14504i −0.0313304 + 0.0607726i
\(356\) 0 0
\(357\) −17.8289 + 39.6905i −0.943606 + 2.10065i
\(358\) 0 0
\(359\) 15.0463 + 13.0377i 0.794113 + 0.688103i 0.954256 0.298991i \(-0.0966500\pi\)
−0.160143 + 0.987094i \(0.551195\pi\)
\(360\) 0 0
\(361\) 27.5478 + 5.30941i 1.44989 + 0.279443i
\(362\) 0 0
\(363\) −16.9153 1.50924i −0.887823 0.0792144i
\(364\) 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
\(369\) 0.845483 2.54472i 0.0440141 0.132473i
\(370\) 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
\(375\) −40.0272 + 12.0236i −2.06700 + 0.620898i
\(376\) 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
\(381\) 11.6038 + 10.9274i 0.594481 + 0.559828i
\(382\) 0 0
\(383\) 1.23833 + 0.118247i 0.0632759 + 0.00604212i 0.126646 0.991948i \(-0.459579\pi\)
−0.0633701 + 0.997990i \(0.520185\pi\)
\(384\) 0 0
\(385\) −66.0549 + 22.8618i −3.36647 + 1.16515i
\(386\) 0 0
\(387\) −0.854018 + 0.758791i −0.0434122 + 0.0385715i
\(388\) 0 0
\(389\) −23.8600 25.0237i −1.20975 1.26875i −0.953241 0.302210i \(-0.902276\pi\)
−0.256510 0.966541i \(-0.582573\pi\)
\(390\) 0 0
\(391\) 2.89037 1.15713i 0.146172 0.0585185i
\(392\) 0 0
\(393\) 5.39335 18.7993i 0.272058 0.948299i
\(394\) 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
\(399\) −34.1860 + 29.9962i −1.71144 + 1.50169i
\(400\) 0 0
\(401\) −33.0777 −1.65182 −0.825912 0.563799i \(-0.809339\pi\)
−0.825912 + 0.563799i \(0.809339\pi\)
\(402\) 0 0
\(403\) 5.13836 0.255960
\(404\) 0 0
\(405\) 14.1488 33.1365i 0.703057 1.64656i
\(406\) 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
\(411\) 12.4320 + 3.56664i 0.613228 + 0.175929i
\(412\) 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
\(417\) −16.3666 25.1225i −0.801478 1.23025i
\(418\) 0 0
\(419\) 19.5218 6.75657i 0.953703 0.330080i 0.194477 0.980907i \(-0.437699\pi\)
0.759226 + 0.650827i \(0.225578\pi\)
\(420\) 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
\(423\) −7.11063 4.93147i −0.345731 0.239776i
\(424\) 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
\(429\) 12.4169 + 41.3362i 0.599491 + 1.99573i
\(430\) 0 0
\(431\) 13.2824 7.66862i 0.639793 0.369384i −0.144742 0.989469i \(-0.546235\pi\)
0.784535 + 0.620085i \(0.212902\pi\)
\(432\) 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
\(435\) 27.4026 53.9742i 1.31385 2.58786i
\(436\) 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
\(441\) −1.37724 22.9171i −0.0655827 1.09129i
\(442\) 0 0
\(443\) −16.7254 3.22355i −0.794646 0.153155i −0.224257 0.974530i \(-0.571995\pi\)
−0.570389 + 0.821375i \(0.693208\pi\)
\(444\) 0 0
\(445\) −7.14286 6.18932i −0.338604 0.293402i
\(446\) 0 0
\(447\) 10.9561 + 4.92145i 0.518205 + 0.232777i
\(448\) 0 0
\(449\) 0.467197 0.906237i 0.0220484 0.0427679i −0.877554 0.479478i \(-0.840826\pi\)
0.899602 + 0.436710i \(0.143856\pi\)
\(450\) 0 0
\(451\) −4.00331 + 0.771575i −0.188509 + 0.0363320i
\(452\) 0 0
\(453\) −8.19824 + 14.4057i −0.385187 + 0.676839i
\(454\) 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
\(459\) −20.5763 + 27.1929i −0.960420 + 1.26926i
\(460\) 0 0
\(461\) 11.2355 + 38.2645i 0.523288 + 1.78215i 0.617464 + 0.786599i \(0.288160\pi\)
−0.0941766 + 0.995556i \(0.530022\pi\)
\(462\) 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
\(465\) −1.19446 + 6.41150i −0.0553915 + 0.297326i
\(466\) 0 0
\(467\) 23.3011 16.5926i 1.07825 0.767815i 0.104288 0.994547i \(-0.466744\pi\)
0.973957 + 0.226732i \(0.0728042\pi\)
\(468\) 0 0
\(469\) −30.7266 6.13325i −1.41882 0.283207i
\(470\) 0 0
\(471\) 0.677013 0.653608i 0.0311951 0.0301167i
\(472\) 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
\(477\) 8.86875 5.85656i 0.406072 0.268153i
\(478\) 0 0
\(479\) −5.00608 9.71045i −0.228734 0.443682i 0.746339 0.665566i \(-0.231810\pi\)
−0.975073 + 0.221884i \(0.928779\pi\)
\(480\) 0 0
\(481\) 4.83953 1.17406i 0.220664 0.0535324i
\(482\) 0 0
\(483\) −2.04499 + 2.38988i −0.0930503 + 0.108743i
\(484\) 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
\(489\) 1.51456 4.46559i 0.0684906 0.201941i
\(490\) 0 0
\(491\) −18.0872 + 28.1443i −0.816265 + 1.27013i 0.143591 + 0.989637i \(0.454135\pi\)
−0.959855 + 0.280495i \(0.909501\pi\)
\(492\) 0 0
\(493\) −37.5163 + 43.2962i −1.68965 + 1.94996i
\(494\) 0 0
\(495\) −54.4645 + 5.88444i −2.44800 + 0.264486i
\(496\) 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
\(501\) −2.86663 28.1702i −0.128072 1.25855i
\(502\) 0 0
\(503\) −8.60875 + 12.0893i −0.383845 + 0.539035i −0.960619 0.277869i \(-0.910372\pi\)
0.576774 + 0.816904i \(0.304311\pi\)
\(504\) 0 0
\(505\) −43.2070 41.1978i −1.92269 1.83328i
\(506\) 0 0
\(507\) 22.8239 18.1795i 1.01364 0.807380i
\(508\) 0 0
\(509\) 30.5372 4.39058i 1.35354 0.194609i 0.572916 0.819614i \(-0.305812\pi\)
0.780621 + 0.625005i \(0.214903\pi\)
\(510\) 0 0
\(511\) 4.17487 14.2183i 0.184685 0.628981i
\(512\) 0 0
\(513\) −31.3716 + 16.9205i −1.38509 + 0.747058i
\(514\) 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
\(519\) −11.0092 21.0331i −0.483252 0.923251i
\(520\) 0 0
\(521\) −0.431533 0.944926i −0.0189058 0.0413980i 0.899944 0.436006i \(-0.143608\pi\)
−0.918849 + 0.394608i \(0.870880\pi\)
\(522\) 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
\(525\) −63.0889 + 36.9488i −2.75342 + 1.61258i
\(526\) 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
\(531\) −23.6776 + 3.70514i −1.02752 + 0.160790i
\(532\) 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
\(543\) −1.40837 5.65190i −0.0604389 0.242546i
\(544\) 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
\(549\) 4.69355 + 2.63262i 0.200316 + 0.112357i
\(550\) 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
\(555\) 0.339966 + 6.31154i 0.0144307 + 0.267910i
\(556\) 0 0
\(557\) −12.5450 15.9522i −0.531547 0.675917i 0.443919 0.896067i \(-0.353588\pi\)
−0.975466 + 0.220150i \(0.929345\pi\)
\(558\) 0 0
\(559\) −0.0989901 2.07806i −0.00418683 0.0878925i
\(560\) 0 0
\(561\) 51.3638 + 7.05961i 2.16858 + 0.298057i
\(562\) 0 0
\(563\) −5.67121 39.4441i −0.239013 1.66237i −0.656979 0.753909i \(-0.728166\pi\)
0.417966 0.908463i \(-0.362743\pi\)
\(564\) 0 0
\(565\) 4.81347 + 8.33718i 0.202504 + 0.350748i
\(566\) 0 0
\(567\) 5.67739 33.9801i 0.238428 1.42703i
\(568\) 0 0
\(569\) −15.4182 10.9793i −0.646366 0.460275i 0.209267 0.977859i \(-0.432892\pi\)
−0.855633 + 0.517583i \(0.826832\pi\)
\(570\) 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
\(573\) −14.3260 5.63227i −0.598478 0.235291i
\(574\) 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
\(579\) −3.85576 2.44423i −0.160240 0.101579i
\(580\) 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
\(585\) 30.7885 + 57.9423i 1.27295 + 2.39562i
\(586\) 0 0
\(587\) −7.45216 5.86044i −0.307584 0.241886i 0.452420 0.891805i \(-0.350561\pi\)
−0.760004 + 0.649918i \(0.774803\pi\)
\(588\) 0 0
\(589\) 4.87593 4.22502i 0.200909 0.174089i
\(590\) 0 0
\(591\) 20.1705 8.22079i 0.829703 0.338158i
\(592\) 0 0
\(593\) −24.9153 + 12.8447i −1.02315 + 0.527470i −0.886295 0.463121i \(-0.846729\pi\)
−0.136854 + 0.990591i \(0.543699\pi\)
\(594\) 0 0
\(595\) 96.4963 28.3339i 3.95596 1.16158i
\(596\) 0 0
\(597\) −3.70542 + 15.6990i −0.151653 + 0.642516i
\(598\) 0 0
\(599\) 5.73363 16.5662i 0.234270 0.676879i −0.765183 0.643813i \(-0.777352\pi\)
0.999453 0.0330660i \(-0.0105271\pi\)
\(600\) 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
\(603\) −22.3958 10.0711i −0.912029 0.410127i
\(604\) 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
\(609\) 13.2956 56.3303i 0.538765 2.28262i
\(610\) 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
\(615\) −5.73956 + 2.33925i −0.231441 + 0.0943275i
\(616\) 0 0
\(617\) −15.9181 + 13.7931i −0.640839 + 0.555290i −0.913509 0.406818i \(-0.866638\pi\)
0.272671 + 0.962107i \(0.412093\pi\)
\(618\) 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
\(621\) −1.98102 + 1.46708i −0.0794958 + 0.0588718i
\(622\) 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
\(627\) 45.7714 + 29.0153i 1.82793 + 1.15876i
\(628\) 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
\(633\) 14.7561 + 5.80134i 0.586501 + 0.230583i
\(634\) 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
\(639\) −0.431661 + 0.863480i −0.0170762 + 0.0341587i
\(640\) 0 0
\(641\) −18.5552 32.1386i −0.732888 1.26940i −0.955644 0.294525i \(-0.904839\pi\)
0.222756 0.974874i \(-0.428495\pi\)
\(642\) 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
\(645\) 2.61595 + 0.359545i 0.103003 + 0.0141571i
\(646\) 0 0
\(647\) 1.07522 + 22.5717i 0.0422714 + 0.887385i 0.916051 + 0.401063i \(0.131359\pi\)
−0.873779 + 0.486323i \(0.838338\pi\)
\(648\) 0 0
\(649\) 22.5244 + 28.6421i 0.884159 + 1.12430i
\(650\) 0 0
\(651\) 0.335404 + 6.22687i 0.0131455 + 0.244050i
\(652\) 0 0
\(653\) −13.9877 40.4147i −0.547380 1.58155i −0.791088 0.611702i \(-0.790485\pi\)
0.243708 0.969849i \(-0.421636\pi\)
\(654\) 0 0
\(655\) −41.1199 + 18.7788i −1.60669 + 0.733750i
\(656\) 0 0
\(657\) 5.68139 10.1290i 0.221652 0.395171i
\(658\) 0 0
\(659\) 0.755882 + 1.88810i 0.0294450 + 0.0735500i 0.942362 0.334596i \(-0.108600\pi\)
−0.912917 + 0.408146i \(0.866176\pi\)
\(660\) 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
\(663\) −15.0151 60.2566i −0.583137 2.34017i
\(664\) 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
\(675\) −54.6682 + 17.1649i −2.10418 + 0.660678i
\(676\) 0 0
\(677\) 45.8487 4.37802i 1.76211 0.168261i 0.836809 0.547495i \(-0.184418\pi\)
0.925301 + 0.379234i \(0.123812\pi\)
\(678\) 0 0
\(679\) 24.0214 52.5996i 0.921858 2.01859i
\(680\) 0 0
\(681\) 29.8940 17.5078i 1.14554 0.670901i
\(682\) 0 0
\(683\) −11.3455 + 10.8179i −0.434122 + 0.413934i −0.875372 0.483450i \(-0.839384\pi\)
0.441250 + 0.897384i \(0.354535\pi\)
\(684\) 0 0
\(685\) −12.4185 27.1928i −0.474487 1.03898i
\(686\) 0 0
\(687\) 5.51989 + 10.5457i 0.210597 + 0.402345i
\(688\) 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
\(693\) −49.2823 + 17.7454i −1.87208 + 0.674093i
\(694\) 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
\(699\) 29.3135 23.3486i 1.10874 0.883125i
\(700\) 0 0
\(701\) 11.8887 + 11.3358i 0.449030 + 0.428149i 0.880549 0.473955i \(-0.157174\pi\)
−0.431520 + 0.902104i \(0.642022\pi\)
\(702\) 0 0
\(703\) 3.62699 5.09339i 0.136795 0.192101i
\(704\) 0 0
\(705\) 2.02488 + 19.8983i 0.0762613 + 0.749415i
\(706\) 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
\(711\) 0.336360 + 3.11325i 0.0126145 + 0.116756i
\(712\) 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
\(717\) 15.0175 44.2782i 0.560838 1.65360i
\(718\) 0 0
\(719\) 9.26034 + 48.0472i 0.345353 + 1.79186i 0.574539 + 0.818477i \(0.305181\pi\)
−0.229187 + 0.973382i \(0.573607\pi\)
\(720\) 0 0
\(721\) 9.06778 11.5306i 0.337702 0.429423i
\(722\) 0 0
\(723\) 0.942582 1.10155i 0.0350550 0.0409671i
\(724\) 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
\(729\) 10.2932 24.9610i 0.381229 0.924480i
\(730\) 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
\(735\) −38.1771 + 36.8573i −1.40818 + 1.35950i
\(736\) 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
\(741\) 11.8881 63.8118i 0.436719 2.34419i
\(742\) 0 0
\(743\) −12.4358 + 31.0630i −0.456224 + 1.13959i 0.504827 + 0.863220i \(0.331556\pi\)
−0.961051 + 0.276371i \(0.910868\pi\)
\(744\) 0 0
\(745\) −7.82122 26.6366i −0.286547 0.975890i
\(746\) 0 0
\(747\) −25.0291 25.6051i −0.915765 0.936840i
\(748\) 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
\(753\) −7.42840 + 13.0530i −0.270706 + 0.475677i
\(754\) 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
\(759\) 3.41889 + 1.53576i 0.124098 + 0.0557445i
\(760\) 0 0
\(761\) 29.0122 + 25.1392i 1.05169 + 0.911295i 0.996194 0.0871642i \(-0.0277805\pi\)
0.0554962 + 0.998459i \(0.482326\pi\)
\(762\) 0 0
\(763\) −24.7524 4.77063i −0.896096 0.172708i
\(764\) 0 0
\(765\) 78.6768 4.72820i 2.84457 0.170948i
\(766\) 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
\(771\) −6.53388 + 12.8696i −0.235312 + 0.463489i
\(772\) 0 0
\(773\) −7.80493 + 8.18557i −0.280724 + 0.294415i −0.848967 0.528446i \(-0.822775\pi\)
0.568243 + 0.822861i \(0.307623\pi\)
\(774\)