Properties

Label 405.2.r.a.368.7
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 368.7
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.160295 - 0.0140240i) q^{2} +(-1.94412 - 0.342800i) q^{4} +(0.476055 + 2.18480i) q^{5} +(-2.37204 - 1.66092i) q^{7} +(0.617675 + 0.165506i) q^{8} +O(q^{10})\) \(q+(-0.160295 - 0.0140240i) q^{2} +(-1.94412 - 0.342800i) q^{4} +(0.476055 + 2.18480i) q^{5} +(-2.37204 - 1.66092i) q^{7} +(0.617675 + 0.165506i) q^{8} +(-0.0456696 - 0.356890i) q^{10} +(1.48958 - 4.09258i) q^{11} +(-0.412163 - 4.71104i) q^{13} +(0.356933 + 0.299503i) q^{14} +(3.61342 + 1.31518i) q^{16} +(5.66739 - 1.51857i) q^{17} +(0.695229 - 0.401391i) q^{19} +(-0.176555 - 4.41071i) q^{20} +(-0.296167 + 0.635132i) q^{22} +(-1.52888 - 2.18347i) q^{23} +(-4.54674 + 2.08017i) q^{25} +0.760939i q^{26} +(4.04215 + 4.04215i) q^{28} +(-2.06994 + 1.73689i) q^{29} +(1.27517 - 7.23183i) q^{31} +(-1.71987 - 0.801990i) q^{32} +(-0.929752 + 0.163940i) q^{34} +(2.49956 - 5.97312i) q^{35} +(-0.841448 - 3.14033i) q^{37} +(-0.117071 + 0.0545912i) q^{38} +(-0.0675500 + 1.42829i) q^{40} +(-2.88706 + 3.44066i) q^{41} +(-2.90471 - 6.22917i) q^{43} +(-4.29885 + 7.44583i) q^{44} +(0.214452 + 0.371442i) q^{46} +(-3.17114 + 4.52886i) q^{47} +(0.473765 + 1.30166i) q^{49} +(0.757994 - 0.269679i) q^{50} +(-0.813654 + 9.30011i) q^{52} +(1.70331 - 1.70331i) q^{53} +(9.65061 + 1.30614i) q^{55} +(-1.19026 - 1.41849i) q^{56} +(0.356161 - 0.249386i) q^{58} +(4.31439 - 1.57031i) q^{59} +(2.10123 + 11.9167i) q^{61} +(-0.305823 + 1.14135i) q^{62} +(-6.39585 - 3.69265i) q^{64} +(10.0965 - 3.14321i) q^{65} +(-6.65253 + 0.582021i) q^{67} +(-11.5386 + 1.00950i) q^{68} +(-0.484435 + 0.922410i) q^{70} +(5.61473 + 3.24167i) q^{71} +(2.49666 - 9.31768i) q^{73} +(0.0908402 + 0.515180i) q^{74} +(-1.48920 + 0.542026i) q^{76} +(-10.3308 + 7.23368i) q^{77} +(-0.322504 - 0.384345i) q^{79} +(-1.15322 + 8.52072i) q^{80} +(0.511034 - 0.511034i) q^{82} +(0.780495 - 8.92110i) q^{83} +(6.01577 + 11.6592i) q^{85} +(0.378253 + 1.03924i) q^{86} +(1.59742 - 2.28135i) q^{88} +(6.84734 + 11.8599i) q^{89} +(-6.84699 + 11.8593i) q^{91} +(2.22384 + 4.76903i) q^{92} +(0.571832 - 0.681483i) q^{94} +(1.20793 + 1.32786i) q^{95} +(6.60652 - 3.08067i) q^{97} +(-0.0576878 - 0.215294i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.160295 0.0140240i −0.113346 0.00991648i 0.0303416 0.999540i \(-0.490340\pi\)
−0.143688 + 0.989623i \(0.545896\pi\)
\(3\) 0 0
\(4\) −1.94412 0.342800i −0.972059 0.171400i
\(5\) 0.476055 + 2.18480i 0.212898 + 0.977074i
\(6\) 0 0
\(7\) −2.37204 1.66092i −0.896545 0.627768i 0.0317971 0.999494i \(-0.489877\pi\)
−0.928342 + 0.371727i \(0.878766\pi\)
\(8\) 0.617675 + 0.165506i 0.218381 + 0.0585151i
\(9\) 0 0
\(10\) −0.0456696 0.356890i −0.0144420 0.112859i
\(11\) 1.48958 4.09258i 0.449125 1.23396i −0.484210 0.874952i \(-0.660893\pi\)
0.933335 0.359008i \(-0.116885\pi\)
\(12\) 0 0
\(13\) −0.412163 4.71104i −0.114313 1.30661i −0.809219 0.587507i \(-0.800109\pi\)
0.694905 0.719101i \(-0.255446\pi\)
\(14\) 0.356933 + 0.299503i 0.0953945 + 0.0800455i
\(15\) 0 0
\(16\) 3.61342 + 1.31518i 0.903355 + 0.328794i
\(17\) 5.66739 1.51857i 1.37454 0.368308i 0.505407 0.862881i \(-0.331342\pi\)
0.869136 + 0.494573i \(0.164676\pi\)
\(18\) 0 0
\(19\) 0.695229 0.401391i 0.159497 0.0920854i −0.418127 0.908388i \(-0.637313\pi\)
0.577624 + 0.816303i \(0.303980\pi\)
\(20\) −0.176555 4.41071i −0.0394789 0.986265i
\(21\) 0 0
\(22\) −0.296167 + 0.635132i −0.0631430 + 0.135411i
\(23\) −1.52888 2.18347i −0.318794 0.455286i 0.627488 0.778626i \(-0.284083\pi\)
−0.946283 + 0.323340i \(0.895194\pi\)
\(24\) 0 0
\(25\) −4.54674 + 2.08017i −0.909349 + 0.416035i
\(26\) 0.760939i 0.149232i
\(27\) 0 0
\(28\) 4.04215 + 4.04215i 0.763895 + 0.763895i
\(29\) −2.06994 + 1.73689i −0.384379 + 0.322532i −0.814419 0.580278i \(-0.802944\pi\)
0.430040 + 0.902810i \(0.358500\pi\)
\(30\) 0 0
\(31\) 1.27517 7.23183i 0.229027 1.29887i −0.625809 0.779976i \(-0.715231\pi\)
0.854836 0.518899i \(-0.173658\pi\)
\(32\) −1.71987 0.801990i −0.304034 0.141773i
\(33\) 0 0
\(34\) −0.929752 + 0.163940i −0.159451 + 0.0281155i
\(35\) 2.49956 5.97312i 0.422503 1.00964i
\(36\) 0 0
\(37\) −0.841448 3.14033i −0.138333 0.516266i −0.999962 0.00872734i \(-0.997222\pi\)
0.861629 0.507539i \(-0.169445\pi\)
\(38\) −0.117071 + 0.0545912i −0.0189914 + 0.00885586i
\(39\) 0 0
\(40\) −0.0675500 + 1.42829i −0.0106806 + 0.225832i
\(41\) −2.88706 + 3.44066i −0.450883 + 0.537341i −0.942826 0.333286i \(-0.891842\pi\)
0.491943 + 0.870628i \(0.336287\pi\)
\(42\) 0 0
\(43\) −2.90471 6.22917i −0.442964 0.949940i −0.993361 0.115037i \(-0.963301\pi\)
0.550397 0.834903i \(-0.314476\pi\)
\(44\) −4.29885 + 7.44583i −0.648076 + 1.12250i
\(45\) 0 0
\(46\) 0.214452 + 0.371442i 0.0316192 + 0.0547661i
\(47\) −3.17114 + 4.52886i −0.462558 + 0.660602i −0.980887 0.194580i \(-0.937666\pi\)
0.518328 + 0.855182i \(0.326555\pi\)
\(48\) 0 0
\(49\) 0.473765 + 1.30166i 0.0676807 + 0.185951i
\(50\) 0.757994 0.269679i 0.107197 0.0381383i
\(51\) 0 0
\(52\) −0.813654 + 9.30011i −0.112834 + 1.28969i
\(53\) 1.70331 1.70331i 0.233968 0.233968i −0.580379 0.814347i \(-0.697095\pi\)
0.814347 + 0.580379i \(0.197095\pi\)
\(54\) 0 0
\(55\) 9.65061 + 1.30614i 1.30129 + 0.176120i
\(56\) −1.19026 1.41849i −0.159055 0.189554i
\(57\) 0 0
\(58\) 0.356161 0.249386i 0.0467662 0.0327460i
\(59\) 4.31439 1.57031i 0.561686 0.204437i −0.0455453 0.998962i \(-0.514503\pi\)
0.607231 + 0.794525i \(0.292280\pi\)
\(60\) 0 0
\(61\) 2.10123 + 11.9167i 0.269035 + 1.52577i 0.757294 + 0.653074i \(0.226521\pi\)
−0.488259 + 0.872699i \(0.662368\pi\)
\(62\) −0.305823 + 1.14135i −0.0388395 + 0.144951i
\(63\) 0 0
\(64\) −6.39585 3.69265i −0.799482 0.461581i
\(65\) 10.0965 3.14321i 1.25232 0.389867i
\(66\) 0 0
\(67\) −6.65253 + 0.582021i −0.812736 + 0.0711052i −0.485943 0.873991i \(-0.661524\pi\)
−0.326793 + 0.945096i \(0.605968\pi\)
\(68\) −11.5386 + 1.00950i −1.39926 + 0.122420i
\(69\) 0 0
\(70\) −0.484435 + 0.922410i −0.0579011 + 0.110249i
\(71\) 5.61473 + 3.24167i 0.666346 + 0.384715i 0.794691 0.607014i \(-0.207633\pi\)
−0.128345 + 0.991730i \(0.540966\pi\)
\(72\) 0 0
\(73\) 2.49666 9.31768i 0.292212 1.09055i −0.651194 0.758912i \(-0.725731\pi\)
0.943406 0.331640i \(-0.107602\pi\)
\(74\) 0.0908402 + 0.515180i 0.0105600 + 0.0598885i
\(75\) 0 0
\(76\) −1.48920 + 0.542026i −0.170823 + 0.0621747i
\(77\) −10.3308 + 7.23368i −1.17730 + 0.824355i
\(78\) 0 0
\(79\) −0.322504 0.384345i −0.0362845 0.0432422i 0.747597 0.664153i \(-0.231208\pi\)
−0.783882 + 0.620910i \(0.786763\pi\)
\(80\) −1.15322 + 8.52072i −0.128934 + 0.952645i
\(81\) 0 0
\(82\) 0.511034 0.511034i 0.0564343 0.0564343i
\(83\) 0.780495 8.92110i 0.0856704 0.979218i −0.824740 0.565512i \(-0.808679\pi\)
0.910411 0.413706i \(-0.135766\pi\)
\(84\) 0 0
\(85\) 6.01577 + 11.6592i 0.652502 + 1.26462i
\(86\) 0.378253 + 1.03924i 0.0407881 + 0.112064i
\(87\) 0 0
\(88\) 1.59742 2.28135i 0.170286 0.243193i
\(89\) 6.84734 + 11.8599i 0.725816 + 1.25715i 0.958637 + 0.284631i \(0.0918711\pi\)
−0.232821 + 0.972520i \(0.574796\pi\)
\(90\) 0 0
\(91\) −6.84699 + 11.8593i −0.717759 + 1.24320i
\(92\) 2.22384 + 4.76903i 0.231851 + 0.497206i
\(93\) 0 0
\(94\) 0.571832 0.681483i 0.0589800 0.0702896i
\(95\) 1.20793 + 1.32786i 0.123931 + 0.136235i
\(96\) 0 0
\(97\) 6.60652 3.08067i 0.670790 0.312795i −0.0572192 0.998362i \(-0.518223\pi\)
0.728010 + 0.685567i \(0.240446\pi\)
\(98\) −0.0576878 0.215294i −0.00582735 0.0217480i
\(99\) 0 0
\(100\) 9.55249 2.48548i 0.955249 0.248548i
\(101\) −5.17835 + 0.913082i −0.515265 + 0.0908551i −0.425233 0.905084i \(-0.639808\pi\)
−0.0900315 + 0.995939i \(0.528697\pi\)
\(102\) 0 0
\(103\) −3.40559 1.58805i −0.335562 0.156475i 0.247532 0.968880i \(-0.420380\pi\)
−0.583094 + 0.812404i \(0.698158\pi\)
\(104\) 0.525121 2.97811i 0.0514924 0.292028i
\(105\) 0 0
\(106\) −0.296920 + 0.249146i −0.0288395 + 0.0241992i
\(107\) −5.69179 5.69179i −0.550246 0.550246i 0.376266 0.926512i \(-0.377208\pi\)
−0.926512 + 0.376266i \(0.877208\pi\)
\(108\) 0 0
\(109\) 12.1610i 1.16481i 0.812899 + 0.582405i \(0.197888\pi\)
−0.812899 + 0.582405i \(0.802112\pi\)
\(110\) −1.52863 0.344709i −0.145749 0.0328667i
\(111\) 0 0
\(112\) −6.38676 9.12124i −0.603492 0.861876i
\(113\) 1.72075 3.69017i 0.161875 0.347142i −0.808594 0.588366i \(-0.799771\pi\)
0.970469 + 0.241225i \(0.0775490\pi\)
\(114\) 0 0
\(115\) 4.04263 4.37977i 0.376977 0.408415i
\(116\) 4.61962 2.66714i 0.428921 0.247638i
\(117\) 0 0
\(118\) −0.713599 + 0.191208i −0.0656921 + 0.0176021i
\(119\) −15.9655 5.81095i −1.46355 0.532689i
\(120\) 0 0
\(121\) −6.10389 5.12177i −0.554899 0.465616i
\(122\) −0.169698 1.93965i −0.0153637 0.175608i
\(123\) 0 0
\(124\) −4.95815 + 13.6224i −0.445255 + 1.22333i
\(125\) −6.70927 8.94347i −0.600096 0.799928i
\(126\) 0 0
\(127\) 0.748856 + 0.200655i 0.0664502 + 0.0178053i 0.291891 0.956452i \(-0.405716\pi\)
−0.225441 + 0.974257i \(0.572382\pi\)
\(128\) 4.08240 + 2.85853i 0.360837 + 0.252661i
\(129\) 0 0
\(130\) −1.66250 + 0.362249i −0.145811 + 0.0317713i
\(131\) 7.46979 + 1.31713i 0.652639 + 0.115078i 0.490158 0.871634i \(-0.336939\pi\)
0.162481 + 0.986712i \(0.448050\pi\)
\(132\) 0 0
\(133\) −2.31579 0.202605i −0.200804 0.0175681i
\(134\) 1.07453 0.0928254
\(135\) 0 0
\(136\) 3.75194 0.321726
\(137\) −9.86611 0.863173i −0.842919 0.0737459i −0.342488 0.939522i \(-0.611270\pi\)
−0.500431 + 0.865776i \(0.666825\pi\)
\(138\) 0 0
\(139\) 14.8464 + 2.61782i 1.25926 + 0.222041i 0.763150 0.646222i \(-0.223652\pi\)
0.496105 + 0.868262i \(0.334763\pi\)
\(140\) −6.90703 + 10.7556i −0.583750 + 0.909014i
\(141\) 0 0
\(142\) −0.854554 0.598365i −0.0717126 0.0502137i
\(143\) −19.8943 5.33066i −1.66364 0.445772i
\(144\) 0 0
\(145\) −4.78017 3.69557i −0.396972 0.306900i
\(146\) −0.530875 + 1.45857i −0.0439355 + 0.120712i
\(147\) 0 0
\(148\) 0.559369 + 6.39361i 0.0459798 + 0.525552i
\(149\) 11.3083 + 9.48879i 0.926412 + 0.777352i 0.975170 0.221459i \(-0.0710818\pi\)
−0.0487579 + 0.998811i \(0.515526\pi\)
\(150\) 0 0
\(151\) −2.23835 0.814693i −0.182154 0.0662987i 0.249333 0.968418i \(-0.419789\pi\)
−0.431487 + 0.902119i \(0.642011\pi\)
\(152\) 0.495858 0.132865i 0.0402194 0.0107768i
\(153\) 0 0
\(154\) 1.75742 1.01465i 0.141617 0.0817626i
\(155\) 16.4072 0.656758i 1.31786 0.0527521i
\(156\) 0 0
\(157\) 3.31405 7.10700i 0.264490 0.567200i −0.728548 0.684995i \(-0.759805\pi\)
0.993038 + 0.117794i \(0.0375824\pi\)
\(158\) 0.0463058 + 0.0661316i 0.00368389 + 0.00526114i
\(159\) 0 0
\(160\) 0.933438 4.13938i 0.0737947 0.327247i
\(161\) 7.71863i 0.608313i
\(162\) 0 0
\(163\) 10.1968 + 10.1968i 0.798677 + 0.798677i 0.982887 0.184210i \(-0.0589726\pi\)
−0.184210 + 0.982887i \(0.558973\pi\)
\(164\) 6.79225 5.69937i 0.530385 0.445046i
\(165\) 0 0
\(166\) −0.250219 + 1.41906i −0.0194208 + 0.110141i
\(167\) 5.88244 + 2.74303i 0.455197 + 0.212262i 0.636673 0.771133i \(-0.280310\pi\)
−0.181477 + 0.983395i \(0.558088\pi\)
\(168\) 0 0
\(169\) −9.22155 + 1.62601i −0.709350 + 0.125078i
\(170\) −0.800791 1.95328i −0.0614178 0.149810i
\(171\) 0 0
\(172\) 3.51174 + 13.1060i 0.267767 + 0.999321i
\(173\) −10.5085 + 4.90021i −0.798949 + 0.372556i −0.778825 0.627242i \(-0.784184\pi\)
−0.0201240 + 0.999797i \(0.506406\pi\)
\(174\) 0 0
\(175\) 14.2400 + 2.61752i 1.07645 + 0.197866i
\(176\) 10.7649 12.8292i 0.811438 0.967034i
\(177\) 0 0
\(178\) −0.931272 1.99712i −0.0698018 0.149690i
\(179\) 3.42048 5.92444i 0.255658 0.442813i −0.709416 0.704790i \(-0.751041\pi\)
0.965074 + 0.261977i \(0.0843744\pi\)
\(180\) 0 0
\(181\) −8.12103 14.0660i −0.603631 1.04552i −0.992266 0.124128i \(-0.960387\pi\)
0.388635 0.921392i \(-0.372947\pi\)
\(182\) 1.26386 1.80497i 0.0936832 0.133794i
\(183\) 0 0
\(184\) −0.582977 1.60172i −0.0429776 0.118080i
\(185\) 6.46042 3.33337i 0.474980 0.245074i
\(186\) 0 0
\(187\) 2.22713 25.4563i 0.162864 1.86155i
\(188\) 7.71757 7.71757i 0.562861 0.562861i
\(189\) 0 0
\(190\) −0.175003 0.229789i −0.0126961 0.0166707i
\(191\) 13.1571 + 15.6801i 0.952017 + 1.13457i 0.990802 + 0.135322i \(0.0432069\pi\)
−0.0387846 + 0.999248i \(0.512349\pi\)
\(192\) 0 0
\(193\) −6.37883 + 4.46650i −0.459158 + 0.321506i −0.780168 0.625570i \(-0.784867\pi\)
0.321010 + 0.947076i \(0.395978\pi\)
\(194\) −1.10220 + 0.401167i −0.0791332 + 0.0288021i
\(195\) 0 0
\(196\) −0.474846 2.69298i −0.0339176 0.192356i
\(197\) 1.37044 5.11454i 0.0976395 0.364396i −0.899767 0.436371i \(-0.856264\pi\)
0.997406 + 0.0719752i \(0.0229303\pi\)
\(198\) 0 0
\(199\) −24.0896 13.9081i −1.70766 0.985920i −0.937440 0.348148i \(-0.886811\pi\)
−0.770225 0.637773i \(-0.779856\pi\)
\(200\) −3.15269 + 0.532361i −0.222929 + 0.0376436i
\(201\) 0 0
\(202\) 0.842870 0.0737416i 0.0593041 0.00518844i
\(203\) 7.79481 0.681958i 0.547088 0.0478640i
\(204\) 0 0
\(205\) −8.89158 4.66972i −0.621015 0.326147i
\(206\) 0.523629 + 0.302317i 0.0364829 + 0.0210634i
\(207\) 0 0
\(208\) 4.70654 17.5651i 0.326340 1.21792i
\(209\) −0.607127 3.44319i −0.0419958 0.238170i
\(210\) 0 0
\(211\) 8.85421 3.22267i 0.609549 0.221858i −0.0187568 0.999824i \(-0.505971\pi\)
0.628306 + 0.777966i \(0.283749\pi\)
\(212\) −3.89534 + 2.72754i −0.267533 + 0.187328i
\(213\) 0 0
\(214\) 0.832546 + 0.992189i 0.0569116 + 0.0678247i
\(215\) 12.2267 9.31165i 0.833855 0.635049i
\(216\) 0 0
\(217\) −15.0362 + 15.0362i −1.02072 + 1.02072i
\(218\) 0.170546 1.94935i 0.0115508 0.132026i
\(219\) 0 0
\(220\) −18.3142 5.84753i −1.23474 0.394240i
\(221\) −9.48994 26.0734i −0.638363 1.75389i
\(222\) 0 0
\(223\) 5.95553 8.50538i 0.398812 0.569562i −0.568650 0.822580i \(-0.692534\pi\)
0.967462 + 0.253017i \(0.0814230\pi\)
\(224\) 2.74756 + 4.75892i 0.183579 + 0.317969i
\(225\) 0 0
\(226\) −0.327580 + 0.567385i −0.0217903 + 0.0377419i
\(227\) 6.37560 + 13.6725i 0.423164 + 0.907477i 0.996129 + 0.0878980i \(0.0280150\pi\)
−0.572966 + 0.819579i \(0.694207\pi\)
\(228\) 0 0
\(229\) 0.604581 0.720511i 0.0399518 0.0476127i −0.745699 0.666284i \(-0.767884\pi\)
0.785650 + 0.618671i \(0.212329\pi\)
\(230\) −0.709437 + 0.645362i −0.0467789 + 0.0425539i
\(231\) 0 0
\(232\) −1.56602 + 0.730246i −0.102814 + 0.0479430i
\(233\) 1.45382 + 5.42572i 0.0952427 + 0.355451i 0.997056 0.0766749i \(-0.0244304\pi\)
−0.901813 + 0.432126i \(0.857764\pi\)
\(234\) 0 0
\(235\) −11.4043 4.77234i −0.743935 0.311313i
\(236\) −8.92598 + 1.57389i −0.581032 + 0.102452i
\(237\) 0 0
\(238\) 2.47770 + 1.15537i 0.160605 + 0.0748914i
\(239\) 2.69221 15.2683i 0.174144 0.987622i −0.764982 0.644051i \(-0.777252\pi\)
0.939127 0.343571i \(-0.111637\pi\)
\(240\) 0 0
\(241\) 14.6302 12.2762i 0.942414 0.790779i −0.0355896 0.999366i \(-0.511331\pi\)
0.978004 + 0.208587i \(0.0668865\pi\)
\(242\) 0.906597 + 0.906597i 0.0582783 + 0.0582783i
\(243\) 0 0
\(244\) 23.8877i 1.52925i
\(245\) −2.61833 + 1.65475i −0.167279 + 0.105718i
\(246\) 0 0
\(247\) −2.17752 3.10982i −0.138552 0.197873i
\(248\) 1.98455 4.25587i 0.126019 0.270248i
\(249\) 0 0
\(250\) 0.950042 + 1.52769i 0.0600859 + 0.0966194i
\(251\) 10.8992 6.29267i 0.687953 0.397190i −0.114892 0.993378i \(-0.536652\pi\)
0.802845 + 0.596188i \(0.203319\pi\)
\(252\) 0 0
\(253\) −11.2134 + 3.00463i −0.704983 + 0.188900i
\(254\) −0.117224 0.0426661i −0.00735529 0.00267711i
\(255\) 0 0
\(256\) 10.7006 + 8.97889i 0.668789 + 0.561181i
\(257\) −2.58192 29.5115i −0.161056 1.84088i −0.461576 0.887100i \(-0.652716\pi\)
0.300521 0.953775i \(-0.402840\pi\)
\(258\) 0 0
\(259\) −3.21988 + 8.84654i −0.200073 + 0.549697i
\(260\) −20.7063 + 2.64969i −1.28415 + 0.164327i
\(261\) 0 0
\(262\) −1.17890 0.315886i −0.0728328 0.0195155i
\(263\) −0.484194 0.339036i −0.0298567 0.0209059i 0.558553 0.829469i \(-0.311357\pi\)
−0.588410 + 0.808563i \(0.700246\pi\)
\(264\) 0 0
\(265\) 4.53228 + 2.91054i 0.278416 + 0.178793i
\(266\) 0.368368 + 0.0649533i 0.0225861 + 0.00398254i
\(267\) 0 0
\(268\) 13.1328 + 1.14897i 0.802215 + 0.0701847i
\(269\) −29.5187 −1.79979 −0.899894 0.436108i \(-0.856357\pi\)
−0.899894 + 0.436108i \(0.856357\pi\)
\(270\) 0 0
\(271\) −9.45815 −0.574542 −0.287271 0.957849i \(-0.592748\pi\)
−0.287271 + 0.957849i \(0.592748\pi\)
\(272\) 22.4758 + 1.96638i 1.36280 + 0.119229i
\(273\) 0 0
\(274\) 1.56939 + 0.276725i 0.0948101 + 0.0167176i
\(275\) 1.74055 + 21.7065i 0.104959 + 1.30895i
\(276\) 0 0
\(277\) 16.7047 + 11.6968i 1.00369 + 0.702792i 0.955178 0.296031i \(-0.0956631\pi\)
0.0485123 + 0.998823i \(0.484552\pi\)
\(278\) −2.34310 0.627831i −0.140530 0.0376548i
\(279\) 0 0
\(280\) 2.53250 3.27576i 0.151346 0.195764i
\(281\) −7.06656 + 19.4152i −0.421555 + 1.15821i 0.529261 + 0.848459i \(0.322469\pi\)
−0.950816 + 0.309755i \(0.899753\pi\)
\(282\) 0 0
\(283\) 1.12399 + 12.8473i 0.0668145 + 0.763693i 0.953514 + 0.301348i \(0.0974364\pi\)
−0.886700 + 0.462345i \(0.847008\pi\)
\(284\) −9.80446 8.22692i −0.581787 0.488178i
\(285\) 0 0
\(286\) 3.11420 + 1.13348i 0.184147 + 0.0670239i
\(287\) 12.5629 3.36621i 0.741563 0.198701i
\(288\) 0 0
\(289\) 15.0908 8.71266i 0.887692 0.512509i
\(290\) 0.714413 + 0.659420i 0.0419518 + 0.0387225i
\(291\) 0 0
\(292\) −8.04791 + 17.2588i −0.470968 + 1.01000i
\(293\) 19.3518 + 27.6373i 1.13055 + 1.61459i 0.704153 + 0.710048i \(0.251327\pi\)
0.426392 + 0.904538i \(0.359784\pi\)
\(294\) 0 0
\(295\) 5.48471 + 8.67854i 0.319332 + 0.505284i
\(296\) 2.07897i 0.120837i
\(297\) 0 0
\(298\) −1.67960 1.67960i −0.0972964 0.0972964i
\(299\) −9.65629 + 8.10259i −0.558438 + 0.468585i
\(300\) 0 0
\(301\) −3.45606 + 19.6003i −0.199204 + 1.12974i
\(302\) 0.347372 + 0.161982i 0.0199890 + 0.00932102i
\(303\) 0 0
\(304\) 3.04006 0.536044i 0.174359 0.0307442i
\(305\) −25.0353 + 10.2638i −1.43352 + 0.587702i
\(306\) 0 0
\(307\) 2.60886 + 9.73639i 0.148895 + 0.555685i 0.999551 + 0.0299620i \(0.00953863\pi\)
−0.850656 + 0.525723i \(0.823795\pi\)
\(308\) 22.5639 10.5217i 1.28570 0.599532i
\(309\) 0 0
\(310\) −2.63921 0.124819i −0.149897 0.00708927i
\(311\) −16.5976 + 19.7803i −0.941166 + 1.12164i 0.0512465 + 0.998686i \(0.483681\pi\)
−0.992413 + 0.122952i \(0.960764\pi\)
\(312\) 0 0
\(313\) 2.37968 + 5.10324i 0.134508 + 0.288452i 0.962012 0.273007i \(-0.0880181\pi\)
−0.827505 + 0.561459i \(0.810240\pi\)
\(314\) −0.630895 + 1.09274i −0.0356035 + 0.0616670i
\(315\) 0 0
\(316\) 0.495232 + 0.857767i 0.0278590 + 0.0482532i
\(317\) 1.06328 1.51852i 0.0597197 0.0852886i −0.788181 0.615443i \(-0.788977\pi\)
0.847901 + 0.530154i \(0.177866\pi\)
\(318\) 0 0
\(319\) 4.02502 + 11.0586i 0.225358 + 0.619165i
\(320\) 5.02294 15.7316i 0.280791 0.879423i
\(321\) 0 0
\(322\) 0.108246 1.23726i 0.00603233 0.0689498i
\(323\) 3.33059 3.33059i 0.185319 0.185319i
\(324\) 0 0
\(325\) 11.6738 + 20.5625i 0.647545 + 1.14060i
\(326\) −1.49150 1.77750i −0.0826067 0.0984469i
\(327\) 0 0
\(328\) −2.35271 + 1.64739i −0.129907 + 0.0909618i
\(329\) 15.0441 5.47561i 0.829409 0.301880i
\(330\) 0 0
\(331\) −3.34434 18.9667i −0.183822 1.04251i −0.927460 0.373923i \(-0.878012\pi\)
0.743638 0.668583i \(-0.233099\pi\)
\(332\) −4.57553 + 17.0761i −0.251115 + 0.937173i
\(333\) 0 0
\(334\) −0.904459 0.522190i −0.0494898 0.0285730i
\(335\) −4.43857 14.2574i −0.242505 0.778965i
\(336\) 0 0
\(337\) 3.43672 0.300674i 0.187210 0.0163788i 0.00683487 0.999977i \(-0.497824\pi\)
0.180375 + 0.983598i \(0.442269\pi\)
\(338\) 1.50097 0.131318i 0.0816423 0.00714277i
\(339\) 0 0
\(340\) −7.69858 24.7291i −0.417514 1.34112i
\(341\) −27.6974 15.9911i −1.49990 0.865966i
\(342\) 0 0
\(343\) −4.20811 + 15.7049i −0.227217 + 0.847984i
\(344\) −0.763205 4.32835i −0.0411493 0.233369i
\(345\) 0 0
\(346\) 1.75319 0.638109i 0.0942520 0.0343049i
\(347\) −7.09044 + 4.96478i −0.380635 + 0.266523i −0.748198 0.663475i \(-0.769081\pi\)
0.367564 + 0.929998i \(0.380192\pi\)
\(348\) 0 0
\(349\) 6.93929 + 8.26992i 0.371452 + 0.442679i 0.919097 0.394032i \(-0.128920\pi\)
−0.547645 + 0.836711i \(0.684476\pi\)
\(350\) −2.24590 0.619278i −0.120049 0.0331018i
\(351\) 0 0
\(352\) −5.84410 + 5.84410i −0.311491 + 0.311491i
\(353\) −2.33150 + 26.6492i −0.124093 + 1.41839i 0.637555 + 0.770405i \(0.279946\pi\)
−0.761649 + 0.647990i \(0.775610\pi\)
\(354\) 0 0
\(355\) −4.40949 + 13.8103i −0.234031 + 0.732975i
\(356\) −9.24644 25.4044i −0.490060 1.34643i
\(357\) 0 0
\(358\) −0.631371 + 0.901691i −0.0333690 + 0.0476559i
\(359\) 6.82588 + 11.8228i 0.360256 + 0.623982i 0.988003 0.154436i \(-0.0493560\pi\)
−0.627747 + 0.778418i \(0.716023\pi\)
\(360\) 0 0
\(361\) −9.17777 + 15.8964i −0.483041 + 0.836651i
\(362\) 1.10450 + 2.36861i 0.0580513 + 0.124491i
\(363\) 0 0
\(364\) 17.3767 20.7088i 0.910788 1.08544i
\(365\) 21.5459 + 1.01900i 1.12776 + 0.0533367i
\(366\) 0 0
\(367\) 11.8122 5.50814i 0.616594 0.287523i −0.0891181 0.996021i \(-0.528405\pi\)
0.705712 + 0.708498i \(0.250627\pi\)
\(368\) −2.65285 9.90056i −0.138289 0.516103i
\(369\) 0 0
\(370\) −1.08232 + 0.443722i −0.0562673 + 0.0230680i
\(371\) −6.86938 + 1.21126i −0.356640 + 0.0628853i
\(372\) 0 0
\(373\) −1.71551 0.799956i −0.0888258 0.0414201i 0.377698 0.925929i \(-0.376716\pi\)
−0.466523 + 0.884509i \(0.654494\pi\)
\(374\) −0.713999 + 4.04929i −0.0369200 + 0.209384i
\(375\) 0 0
\(376\) −2.70829 + 2.27252i −0.139669 + 0.117196i
\(377\) 9.03572 + 9.03572i 0.465363 + 0.465363i
\(378\) 0 0
\(379\) 8.64900i 0.444270i −0.975016 0.222135i \(-0.928698\pi\)
0.975016 0.222135i \(-0.0713025\pi\)
\(380\) −1.89316 2.99559i −0.0971173 0.153670i
\(381\) 0 0
\(382\) −1.88913 2.69796i −0.0966563 0.138040i
\(383\) −7.21777 + 15.4786i −0.368811 + 0.790917i 0.631074 + 0.775723i \(0.282614\pi\)
−0.999885 + 0.0151943i \(0.995163\pi\)
\(384\) 0 0
\(385\) −20.7222 19.1271i −1.05610 0.974806i
\(386\) 1.08513 0.626503i 0.0552319 0.0318881i
\(387\) 0 0
\(388\) −13.8999 + 3.72447i −0.705661 + 0.189081i
\(389\) 0.823821 + 0.299846i 0.0417694 + 0.0152028i 0.362820 0.931859i \(-0.381814\pi\)
−0.321051 + 0.947062i \(0.604036\pi\)
\(390\) 0 0
\(391\) −11.9805 10.0529i −0.605882 0.508395i
\(392\) 0.0772012 + 0.882413i 0.00389925 + 0.0445686i
\(393\) 0 0
\(394\) −0.291401 + 0.800617i −0.0146806 + 0.0403345i
\(395\) 0.686190 0.887578i 0.0345260 0.0446589i
\(396\) 0 0
\(397\) 2.23467 + 0.598779i 0.112155 + 0.0300519i 0.314460 0.949271i \(-0.398177\pi\)
−0.202305 + 0.979323i \(0.564843\pi\)
\(398\) 3.66640 + 2.56724i 0.183780 + 0.128684i
\(399\) 0 0
\(400\) −19.1651 + 1.53677i −0.958255 + 0.0768385i
\(401\) −6.34251 1.11835i −0.316730 0.0558480i 0.0130235 0.999915i \(-0.495854\pi\)
−0.329753 + 0.944067i \(0.606965\pi\)
\(402\) 0 0
\(403\) −34.5950 3.02667i −1.72330 0.150769i
\(404\) 10.3803 0.516440
\(405\) 0 0
\(406\) −1.25904 −0.0624849
\(407\) −14.1054 1.23407i −0.699181 0.0611704i
\(408\) 0 0
\(409\) 27.7142 + 4.88676i 1.37038 + 0.241635i 0.809916 0.586546i \(-0.199513\pi\)
0.560462 + 0.828180i \(0.310624\pi\)
\(410\) 1.35979 + 0.873230i 0.0671553 + 0.0431257i
\(411\) 0 0
\(412\) 6.07648 + 4.25479i 0.299367 + 0.209619i
\(413\) −12.8420 3.44101i −0.631915 0.169321i
\(414\) 0 0
\(415\) 19.8624 2.54170i 0.975008 0.124767i
\(416\) −3.06934 + 8.43295i −0.150487 + 0.413459i
\(417\) 0 0
\(418\) 0.0490322 + 0.560441i 0.00239824 + 0.0274121i
\(419\) 28.5256 + 23.9358i 1.39357 + 1.16934i 0.963872 + 0.266365i \(0.0858226\pi\)
0.429693 + 0.902975i \(0.358622\pi\)
\(420\) 0 0
\(421\) 27.5767 + 10.0371i 1.34400 + 0.489178i 0.911071 0.412249i \(-0.135256\pi\)
0.432933 + 0.901426i \(0.357479\pi\)
\(422\) −1.46448 + 0.392407i −0.0712900 + 0.0191021i
\(423\) 0 0
\(424\) 1.33400 0.770186i 0.0647849 0.0374036i
\(425\) −22.6093 + 18.6937i −1.09671 + 0.906778i
\(426\) 0 0
\(427\) 14.8084 31.7567i 0.716629 1.53682i
\(428\) 9.11436 + 13.0167i 0.440559 + 0.629184i
\(429\) 0 0
\(430\) −2.09047 + 1.32115i −0.100812 + 0.0637113i
\(431\) 0.480686i 0.0231538i −0.999933 0.0115769i \(-0.996315\pi\)
0.999933 0.0115769i \(-0.00368513\pi\)
\(432\) 0 0
\(433\) −5.55599 5.55599i −0.267004 0.267004i 0.560888 0.827892i \(-0.310460\pi\)
−0.827892 + 0.560888i \(0.810460\pi\)
\(434\) 2.62110 2.19937i 0.125817 0.105573i
\(435\) 0 0
\(436\) 4.16878 23.6423i 0.199648 1.13226i
\(437\) −1.93935 0.904335i −0.0927718 0.0432602i
\(438\) 0 0
\(439\) −12.2268 + 2.15591i −0.583551 + 0.102896i −0.457627 0.889144i \(-0.651301\pi\)
−0.125924 + 0.992040i \(0.540190\pi\)
\(440\) 5.74477 + 2.40400i 0.273871 + 0.114606i
\(441\) 0 0
\(442\) 1.15554 + 4.31253i 0.0549634 + 0.205126i
\(443\) 16.1231 7.51833i 0.766033 0.357207i −7.21597e−6 1.00000i \(-0.500002\pi\)
0.766040 + 0.642793i \(0.222225\pi\)
\(444\) 0 0
\(445\) −22.6519 + 20.6061i −1.07380 + 0.976822i
\(446\) −1.07392 + 1.27985i −0.0508517 + 0.0606028i
\(447\) 0 0
\(448\) 9.03801 + 19.3821i 0.427006 + 0.915717i
\(449\) −1.91039 + 3.30889i −0.0901568 + 0.156156i −0.907577 0.419886i \(-0.862070\pi\)
0.817420 + 0.576042i \(0.195403\pi\)
\(450\) 0 0
\(451\) 9.78070 + 16.9407i 0.460555 + 0.797705i
\(452\) −4.61034 + 6.58425i −0.216852 + 0.309697i
\(453\) 0 0
\(454\) −0.830236 2.28105i −0.0389649 0.107055i
\(455\) −29.1699 9.31364i −1.36750 0.436630i
\(456\) 0 0
\(457\) −1.92516 + 22.0047i −0.0900553 + 1.02934i 0.807920 + 0.589292i \(0.200593\pi\)
−0.897976 + 0.440045i \(0.854962\pi\)
\(458\) −0.107016 + 0.107016i −0.00500053 + 0.00500053i
\(459\) 0 0
\(460\) −9.36073 + 7.12897i −0.436446 + 0.332390i
\(461\) −4.15610 4.95304i −0.193569 0.230686i 0.660527 0.750803i \(-0.270333\pi\)
−0.854095 + 0.520116i \(0.825889\pi\)
\(462\) 0 0
\(463\) 0.251426 0.176051i 0.0116848 0.00818177i −0.567719 0.823222i \(-0.692174\pi\)
0.579404 + 0.815040i \(0.303285\pi\)
\(464\) −9.76390 + 3.55377i −0.453278 + 0.164980i
\(465\) 0 0
\(466\) −0.156950 0.890106i −0.00727056 0.0412334i
\(467\) 11.0784 41.3450i 0.512645 1.91322i 0.122489 0.992470i \(-0.460912\pi\)
0.390156 0.920749i \(-0.372421\pi\)
\(468\) 0 0
\(469\) 16.7467 + 9.66873i 0.773292 + 0.446460i
\(470\) 1.76113 + 0.924918i 0.0812349 + 0.0426633i
\(471\) 0 0
\(472\) 2.92479 0.255886i 0.134624 0.0117781i
\(473\) −29.8202 + 2.60893i −1.37113 + 0.119959i
\(474\) 0 0
\(475\) −2.32607 + 3.27122i −0.106727 + 0.150094i
\(476\) 29.0467 + 16.7701i 1.33135 + 0.768658i
\(477\) 0 0
\(478\) −0.645671 + 2.40968i −0.0295323 + 0.110216i
\(479\) −7.22789 40.9914i −0.330251 1.87295i −0.469863 0.882740i \(-0.655697\pi\)
0.139612 0.990206i \(-0.455415\pi\)
\(480\) 0 0
\(481\) −14.4474 + 5.25842i −0.658745 + 0.239763i
\(482\) −2.51732 + 1.76264i −0.114661 + 0.0802862i
\(483\) 0 0
\(484\) 10.1109 + 12.0497i 0.459588 + 0.547716i
\(485\) 9.87573 + 12.9674i 0.448434 + 0.588819i
\(486\) 0 0
\(487\) 16.8595 16.8595i 0.763975 0.763975i −0.213064 0.977038i \(-0.568344\pi\)
0.977038 + 0.213064i \(0.0683442\pi\)
\(488\) −0.674397 + 7.70840i −0.0305285 + 0.348943i
\(489\) 0 0
\(490\) 0.442913 0.228528i 0.0200088 0.0103239i
\(491\) 5.41828 + 14.8866i 0.244524 + 0.671823i 0.999864 + 0.0164907i \(0.00524938\pi\)
−0.755340 + 0.655333i \(0.772528\pi\)
\(492\) 0 0
\(493\) −9.09358 + 12.9870i −0.409554 + 0.584904i
\(494\) 0.305434 + 0.529027i 0.0137421 + 0.0238020i
\(495\) 0 0
\(496\) 14.1189 24.4546i 0.633955 1.09804i
\(497\) −7.93420 17.0150i −0.355898 0.763225i
\(498\) 0 0
\(499\) −0.350248 + 0.417409i −0.0156792 + 0.0186858i −0.773827 0.633397i \(-0.781660\pi\)
0.758148 + 0.652083i \(0.226105\pi\)
\(500\) 9.97779 + 19.6871i 0.446220 + 0.880434i
\(501\) 0 0
\(502\) −1.83534 + 0.855835i −0.0819154 + 0.0381978i
\(503\) 5.01841 + 18.7290i 0.223760 + 0.835083i 0.982898 + 0.184153i \(0.0589542\pi\)
−0.759138 + 0.650930i \(0.774379\pi\)
\(504\) 0 0
\(505\) −4.46008 10.8790i −0.198471 0.484109i
\(506\) 1.83960 0.324371i 0.0817801 0.0144200i
\(507\) 0 0
\(508\) −1.38708 0.646805i −0.0615417 0.0286974i
\(509\) 4.57685 25.9566i 0.202865 1.15051i −0.697898 0.716197i \(-0.745881\pi\)
0.900764 0.434310i \(-0.143008\pi\)
\(510\) 0 0
\(511\) −21.3981 + 17.9551i −0.946595 + 0.794287i
\(512\) −8.63735 8.63735i −0.381720 0.381720i
\(513\) 0 0
\(514\) 4.76676i 0.210253i
\(515\) 1.84834 8.19654i 0.0814474 0.361183i
\(516\) 0 0
\(517\) 13.8111 + 19.7242i 0.607410 + 0.867471i
\(518\) 0.640195 1.37290i 0.0281286 0.0603219i
\(519\) 0 0
\(520\) 6.75658 0.270457i 0.296295 0.0118603i
\(521\) 6.99745 4.03998i 0.306564 0.176995i −0.338824 0.940850i \(-0.610029\pi\)
0.645388 + 0.763855i \(0.276696\pi\)
\(522\) 0 0
\(523\) 34.5655 9.26181i 1.51145 0.404991i 0.594530 0.804073i \(-0.297338\pi\)
0.916915 + 0.399083i \(0.130671\pi\)
\(524\) −14.0706 5.12130i −0.614679 0.223725i
\(525\) 0 0
\(526\) 0.0728594 + 0.0611363i 0.00317682 + 0.00266567i
\(527\) −3.75519 42.9220i −0.163579 1.86971i
\(528\) 0 0
\(529\) 5.43640 14.9364i 0.236365 0.649408i
\(530\) −0.685685 0.530106i −0.0297843 0.0230263i
\(531\) 0 0
\(532\) 4.43271 + 1.18774i 0.192182 + 0.0514951i
\(533\) 17.3991 + 12.1830i 0.753637 + 0.527702i
\(534\) 0 0
\(535\) 9.72584 15.1451i 0.420485 0.654778i
\(536\) −4.20543 0.741531i −0.181647 0.0320293i
\(537\) 0 0
\(538\) 4.73172 + 0.413971i 0.203999 + 0.0178476i
\(539\) 6.03285 0.259853
\(540\) 0 0
\(541\) −6.99126 −0.300578 −0.150289 0.988642i \(-0.548020\pi\)
−0.150289 + 0.988642i \(0.548020\pi\)
\(542\) 1.51610 + 0.132641i 0.0651220 + 0.00569743i
\(543\) 0 0
\(544\) −10.9651 1.93344i −0.470123 0.0828954i
\(545\) −26.5693 + 5.78929i −1.13811 + 0.247986i
\(546\) 0 0
\(547\) −9.60101 6.72270i −0.410509 0.287442i 0.350024 0.936741i \(-0.386174\pi\)
−0.760533 + 0.649299i \(0.775062\pi\)
\(548\) 18.8850 + 5.06022i 0.806727 + 0.216162i
\(549\) 0 0
\(550\) 0.0254097 3.50386i 0.00108347 0.149405i
\(551\) −0.741915 + 2.03839i −0.0316066 + 0.0868385i
\(552\) 0 0
\(553\) 0.126625 + 1.44733i 0.00538465 + 0.0615469i
\(554\) −2.51366 2.10921i −0.106795 0.0896117i
\(555\) 0 0
\(556\) −27.9658 10.1787i −1.18601 0.431673i
\(557\) 11.5536 3.09577i 0.489541 0.131172i −0.00560082 0.999984i \(-0.501783\pi\)
0.495142 + 0.868812i \(0.335116\pi\)
\(558\) 0 0
\(559\) −28.1487 + 16.2516i −1.19056 + 0.687371i
\(560\) 16.8877 18.2960i 0.713635 0.773149i
\(561\) 0 0
\(562\) 1.40502 3.01306i 0.0592670 0.127098i
\(563\) −4.83500 6.90509i −0.203771 0.291015i 0.704240 0.709962i \(-0.251288\pi\)
−0.908010 + 0.418947i \(0.862399\pi\)
\(564\) 0 0
\(565\) 8.88147 + 2.00279i 0.373646 + 0.0842579i
\(566\) 2.07513i 0.0872241i
\(567\) 0 0
\(568\) 2.93157 + 2.93157i 0.123006 + 0.123006i
\(569\) 9.07677 7.61631i 0.380518 0.319292i −0.432388 0.901688i \(-0.642329\pi\)
0.812906 + 0.582395i \(0.197884\pi\)
\(570\) 0 0
\(571\) 5.84395 33.1427i 0.244562 1.38698i −0.576946 0.816782i \(-0.695756\pi\)
0.821508 0.570197i \(-0.193133\pi\)
\(572\) 36.8495 + 17.1832i 1.54075 + 0.718465i
\(573\) 0 0
\(574\) −2.06098 + 0.363406i −0.0860235 + 0.0151683i
\(575\) 11.4935 + 6.74735i 0.479310 + 0.281384i
\(576\) 0 0
\(577\) −7.63587 28.4975i −0.317886 1.18637i −0.921273 0.388917i \(-0.872849\pi\)
0.603387 0.797448i \(-0.293817\pi\)
\(578\) −2.54117 + 1.18497i −0.105699 + 0.0492881i
\(579\) 0 0
\(580\) 8.02637 + 8.82327i 0.333277 + 0.366366i
\(581\) −16.6686 + 19.8648i −0.691529 + 0.824132i
\(582\) 0 0
\(583\) −4.43373 9.50816i −0.183626 0.393788i
\(584\) 3.08426 5.34209i 0.127627 0.221057i
\(585\) 0 0
\(586\) −2.71442 4.70152i −0.112132 0.194218i
\(587\) −13.0366 + 18.6182i −0.538077 + 0.768453i −0.992488 0.122338i \(-0.960961\pi\)
0.454412 + 0.890792i \(0.349850\pi\)
\(588\) 0 0
\(589\) −2.01626 5.53962i −0.0830784 0.228256i
\(590\) −0.757465 1.46805i −0.0311843 0.0604386i
\(591\) 0 0
\(592\) 1.08958 12.4540i 0.0447815 0.511855i
\(593\) −9.57575 + 9.57575i −0.393229 + 0.393229i −0.875837 0.482608i \(-0.839690\pi\)
0.482608 + 0.875837i \(0.339690\pi\)
\(594\) 0 0
\(595\) 5.09536 37.6477i 0.208889 1.54341i
\(596\) −18.7319 22.3238i −0.767288 0.914419i
\(597\) 0 0
\(598\) 1.66149 1.16339i 0.0679433 0.0475744i
\(599\) −13.5529 + 4.93284i −0.553755 + 0.201550i −0.603714 0.797201i \(-0.706313\pi\)
0.0499591 + 0.998751i \(0.484091\pi\)
\(600\) 0 0
\(601\) 4.30406 + 24.4095i 0.175566 + 0.995686i 0.937488 + 0.348017i \(0.113145\pi\)
−0.761922 + 0.647669i \(0.775744\pi\)
\(602\) 0.828865 3.09337i 0.0337820 0.126076i
\(603\) 0 0
\(604\) 4.07234 + 2.35117i 0.165701 + 0.0956676i
\(605\) 8.28429 15.7741i 0.336804 0.641307i
\(606\) 0 0
\(607\) −27.7738 + 2.42989i −1.12730 + 0.0986264i −0.635516 0.772088i \(-0.719212\pi\)
−0.491789 + 0.870714i \(0.663657\pi\)
\(608\) −1.51762 + 0.132774i −0.0615476 + 0.00538471i
\(609\) 0 0
\(610\) 4.15698 1.29414i 0.168311 0.0523981i
\(611\) 22.6427 + 13.0728i 0.916025 + 0.528867i
\(612\) 0 0
\(613\) −8.68995 + 32.4313i −0.350984 + 1.30989i 0.534480 + 0.845181i \(0.320507\pi\)
−0.885464 + 0.464708i \(0.846159\pi\)
\(614\) −0.281645 1.59729i −0.0113662 0.0644612i
\(615\) 0 0
\(616\) −7.57828 + 2.75827i −0.305337 + 0.111134i
\(617\) −23.2671 + 16.2918i −0.936700 + 0.655884i −0.938928 0.344113i \(-0.888180\pi\)
0.00222854 + 0.999998i \(0.499291\pi\)
\(618\) 0 0
\(619\) −16.2376 19.3513i −0.652646 0.777793i 0.333665 0.942692i \(-0.391715\pi\)
−0.986310 + 0.164899i \(0.947270\pi\)
\(620\) −32.1226 4.34757i −1.29008 0.174603i
\(621\) 0 0
\(622\) 2.93792 2.93792i 0.117800 0.117800i
\(623\) 3.45624 39.5050i 0.138471 1.58274i
\(624\) 0 0
\(625\) 16.3458 18.9160i 0.653830 0.756641i
\(626\) −0.309884 0.851399i −0.0123854 0.0340287i
\(627\) 0 0
\(628\) −8.87918 + 12.6808i −0.354318 + 0.506018i
\(629\) −9.53762 16.5196i −0.380290 0.658681i
\(630\) 0 0
\(631\) 2.76033 4.78103i 0.109887 0.190330i −0.805837 0.592137i \(-0.798284\pi\)
0.915724 + 0.401807i \(0.131618\pi\)
\(632\) −0.135591 0.290777i −0.00539354 0.0115665i
\(633\) 0 0
\(634\) −0.191734 + 0.228500i −0.00761475 + 0.00907490i
\(635\) −0.0818961 + 1.73163i −0.00324995 + 0.0687175i
\(636\) 0 0
\(637\) 5.93690 2.76842i 0.235229 0.109689i
\(638\) −0.490105 1.82910i −0.0194034 0.0724146i
\(639\) 0 0
\(640\) −4.30188 + 10.2801i −0.170047 + 0.406355i
\(641\) 45.0144 7.93726i 1.77796 0.313503i 0.814264 0.580494i \(-0.197141\pi\)
0.963699 + 0.266991i \(0.0860295\pi\)
\(642\) 0 0
\(643\) 14.3424 + 6.68798i 0.565610 + 0.263748i 0.684321 0.729181i \(-0.260099\pi\)
−0.118711 + 0.992929i \(0.537876\pi\)
\(644\) 2.64595 15.0059i 0.104265 0.591316i
\(645\) 0 0
\(646\) −0.580587 + 0.487170i −0.0228429 + 0.0191675i
\(647\) 8.27160 + 8.27160i 0.325190 + 0.325190i 0.850754 0.525564i \(-0.176146\pi\)
−0.525564 + 0.850754i \(0.676146\pi\)
\(648\) 0 0
\(649\) 19.9961i 0.784915i
\(650\) −1.58288 3.45979i −0.0620858 0.135704i
\(651\) 0 0
\(652\) −16.3284 23.3193i −0.639468 0.913255i
\(653\) 20.8882 44.7948i 0.817417 1.75296i 0.178100 0.984012i \(-0.443005\pi\)
0.639316 0.768944i \(-0.279217\pi\)
\(654\) 0 0
\(655\) 0.678369 + 16.9471i 0.0265061 + 0.662177i
\(656\) −14.9572 + 8.63557i −0.583982 + 0.337162i
\(657\) 0 0
\(658\) −2.48829 + 0.666736i −0.0970037 + 0.0259921i
\(659\) 25.0705 + 9.12491i 0.976607 + 0.355456i 0.780520 0.625130i \(-0.214954\pi\)
0.196087 + 0.980586i \(0.437176\pi\)
\(660\) 0 0
\(661\) −33.2465 27.8971i −1.29314 1.08507i −0.991287 0.131716i \(-0.957951\pi\)
−0.301851 0.953355i \(-0.597604\pi\)
\(662\) 0.270093 + 3.08718i 0.0104975 + 0.119987i
\(663\) 0 0
\(664\) 1.95858 5.38117i 0.0760078 0.208830i
\(665\) −0.659789 5.15599i −0.0255855 0.199941i
\(666\) 0 0
\(667\) 6.95716 + 1.86416i 0.269382 + 0.0721808i
\(668\) −10.4958 7.34927i −0.406096 0.284352i
\(669\) 0 0
\(670\) 0.511536 + 2.34764i 0.0197624 + 0.0906974i
\(671\) 51.8999 + 9.15135i 2.00357 + 0.353284i
\(672\) 0 0
\(673\) 9.97924 + 0.873070i 0.384671 + 0.0336544i 0.277852 0.960624i \(-0.410378\pi\)
0.106820 + 0.994278i \(0.465933\pi\)
\(674\) −0.555107 −0.0213819
\(675\) 0 0
\(676\) 18.4852 0.710968
\(677\) 35.9148 + 3.14213i 1.38032 + 0.120762i 0.753009 0.658010i \(-0.228602\pi\)
0.627307 + 0.778772i \(0.284157\pi\)
\(678\) 0 0
\(679\) −20.7876 3.66542i −0.797756 0.140666i
\(680\) 1.78613 + 8.19725i 0.0684949 + 0.314350i
\(681\) 0 0
\(682\) 4.21550 + 2.95173i 0.161420 + 0.113027i
\(683\) 40.8281 + 10.9399i 1.56224 + 0.418602i 0.933373 0.358908i \(-0.116851\pi\)
0.628871 + 0.777510i \(0.283517\pi\)
\(684\) 0 0
\(685\) −2.81095 21.9664i −0.107401 0.839295i
\(686\) 0.894787 2.45841i 0.0341631 0.0938624i
\(687\) 0 0
\(688\) −2.30347 26.3288i −0.0878191 1.00378i
\(689\) −8.72642 7.32234i −0.332450 0.278959i
\(690\) 0 0
\(691\) −5.10153 1.85681i −0.194071 0.0706362i 0.243156 0.969987i \(-0.421817\pi\)
−0.437227 + 0.899351i \(0.644040\pi\)
\(692\) 22.1096 5.92425i 0.840481 0.225206i
\(693\) 0 0
\(694\) 1.20619 0.696395i 0.0457864 0.0264348i
\(695\) 1.34827 + 33.6827i 0.0511430 + 1.27766i
\(696\) 0 0
\(697\) −11.1372 + 23.8838i −0.421851 + 0.904663i
\(698\) −0.996358 1.42295i −0.0377127 0.0538593i
\(699\) 0 0
\(700\) −26.7870 9.97025i −1.01245 0.376840i
\(701\) 8.37641i 0.316373i −0.987409 0.158186i \(-0.949435\pi\)
0.987409 0.158186i \(-0.0505647\pi\)
\(702\) 0 0
\(703\) −1.84550 1.84550i −0.0696043 0.0696043i
\(704\) −24.6396 + 20.6751i −0.928639 + 0.779221i
\(705\) 0 0
\(706\) 0.747459 4.23905i 0.0281310 0.159539i
\(707\) 13.7998 + 6.43494i 0.518994 + 0.242011i
\(708\) 0 0
\(709\) 27.2222 4.80001i 1.02235 0.180268i 0.362752 0.931886i \(-0.381837\pi\)
0.659599 + 0.751617i \(0.270726\pi\)
\(710\) 0.900497 2.15189i 0.0337950 0.0807590i
\(711\) 0 0
\(712\) 2.26655 + 8.45886i 0.0849424 + 0.317009i
\(713\) −17.7401 + 8.27234i −0.664372 + 0.309802i
\(714\) 0 0
\(715\) 2.17567 46.0028i 0.0813655 1.72041i
\(716\) −8.68071 + 10.3453i −0.324413 + 0.386621i
\(717\) 0 0
\(718\) −0.928354 1.99086i −0.0346459 0.0742983i
\(719\) −13.4438 + 23.2854i −0.501371 + 0.868400i 0.498628 + 0.866816i \(0.333837\pi\)
−0.999999 + 0.00158362i \(0.999496\pi\)
\(720\) 0 0
\(721\) 5.44055 + 9.42331i 0.202617 + 0.350942i
\(722\) 1.69408 2.41940i 0.0630473 0.0900409i
\(723\) 0 0
\(724\) 10.9664 + 30.1299i 0.407563 + 1.11977i
\(725\) 5.79847 12.2030i 0.215350 0.453209i
\(726\) 0 0
\(727\) −1.67023 + 19.0908i −0.0619455 + 0.708040i 0.900195 + 0.435487i \(0.143424\pi\)
−0.962141 + 0.272553i \(0.912132\pi\)
\(728\) −6.19200 + 6.19200i −0.229491 + 0.229491i
\(729\) 0 0
\(730\) −3.43941 0.465500i −0.127298 0.0172289i
\(731\) −25.9216 30.8921i −0.958743 1.14259i
\(732\) 0 0
\(733\) −28.9707 + 20.2855i −1.07006 + 0.749261i −0.969357 0.245656i \(-0.920997\pi\)
−0.100699 + 0.994917i \(0.532108\pi\)
\(734\) −1.97069 + 0.717274i −0.0727397 + 0.0264751i
\(735\) 0 0
\(736\) 0.878364 + 4.98145i 0.0323769 + 0.183619i
\(737\) −7.52749 + 28.0930i −0.277279 + 1.03482i
\(738\) 0 0
\(739\) 16.8271 + 9.71511i 0.618993 + 0.357376i 0.776477 0.630146i \(-0.217005\pi\)
−0.157484 + 0.987522i \(0.550338\pi\)
\(740\) −13.7025 + 4.26582i −0.503714 + 0.156815i
\(741\) 0 0
\(742\) 1.11812 0.0978225i 0.0410473 0.00359118i
\(743\) −31.1397 + 2.72437i −1.14240 + 0.0999474i −0.642608 0.766195i \(-0.722147\pi\)
−0.499796 + 0.866143i \(0.666592\pi\)
\(744\) 0 0
\(745\) −15.3478 + 29.2236i −0.562299 + 1.07067i
\(746\) 0.263770 + 0.152288i 0.00965730 + 0.00557564i
\(747\) 0 0
\(748\) −13.0562 + 48.7265i −0.477383 + 1.78162i
\(749\) 4.04754 + 22.9547i 0.147894 + 0.838747i
\(750\) 0 0
\(751\) 21.6560 7.88215i 0.790240 0.287624i 0.0848041 0.996398i \(-0.472974\pi\)
0.705436 + 0.708774i \(0.250751\pi\)
\(752\) −17.4149 + 12.1941i −0.635057 + 0.444672i
\(753\) 0 0
\(754\) −1.32167 1.57510i −0.0481322 0.0573618i
\(755\) 0.714367 5.27819i 0.0259985 0.192093i
\(756\) 0 0
\(757\) 10.7861 10.7861i 0.392029 0.392029i −0.483381 0.875410i \(-0.660592\pi\)
0.875410 + 0.483381i \(0.160592\pi\)
\(758\) −0.121294 + 1.38640i −0.00440559 + 0.0503561i
\(759\) 0 0
\(760\) 0.526340 + 1.02010i 0.0190923 + 0.0370030i
\(761\) −3.19211 8.77024i −0.115714 0.317921i 0.868293 0.496051i \(-0.165217\pi\)
−0.984007 + 0.178131i \(0.942995\pi\)
\(762\) 0 0
\(763\) 20.1984 28.8462i 0.731229 1.04430i
\(764\) −20.2039 34.9942i −0.730951 1.26604i
\(765\) 0 0
\(766\) 1.37405 2.37992i 0.0496463 0.0859899i
\(767\) −9.17603 19.6781i −0.331327 0.710533i
\(768\) 0 0
\(769\) −7.77292 + 9.26340i −0.280299 + 0.334047i −0.887764 0.460300i \(-0.847742\pi\)
0.607465 + 0.794346i \(0.292186\pi\)
\(770\) 3.05343 + 3.35659i 0.110038 + 0.120963i
\(771\) 0 0
\(772\) 13.9323 6.49674i 0.501435 0.233823i
\(773\) 0.479004 + 1.78767i 0.0172286 + 0.0642980i 0.974005 0.226527i \(-0.0727370\pi\)
−0.956776 + 0.290825i \(0.906070\pi\)
\(774\) 0 0
\(775\) 9.24561 + 35.5338i 0.332112 + 1.27641i
\(776\) 4.59055 0.809438i 0.164791 0.0290571i
\(777\) 0 0
\(778\) −0.127850 0.0596173i −0.00458363 0.00213738i
\(779\) −0.626118 + 3.55089i −0.0224330 + 0.127224i
\(780\) 0 0
\(781\) 21.6304 18.1500i 0.773996 0.649459i
\(782\) 1.77944 + 1.77944i 0.0636327 + 0.0636327i
\(783\) 0 0
\(784\) 5.32653i 0.190233i
\(785\) 17.1051 + 3.85723i 0.610506 + 0.137670i
\(786\) 0 0