Properties

Label 405.2.r.a.197.7
Level $405$
Weight $2$
Character 405.197
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 197.7
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.7

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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 −0.143688 0.989623i \(-0.545896\pi\)
0.0303416 + 0.999540i \(0.490340\pi\)
\(3\) 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 −0.928342 0.371727i \(-0.878766\pi\)
0.0317971 + 0.999494i \(0.489877\pi\)
\(8\) 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 0.933335 + 0.359008i \(0.116885\pi\)
−0.484210 + 0.874952i \(0.660893\pi\)
\(12\) 0 0
\(13\) −0.412163 + 4.71104i −0.114313 + 1.30661i 0.694905 + 0.719101i \(0.255446\pi\)
−0.809219 + 0.587507i \(0.800109\pi\)
\(14\) 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 0.869136 0.494573i \(-0.164676\pi\)
0.505407 + 0.862881i \(0.331342\pi\)
\(18\) 0 0
\(19\) 0.695229 + 0.401391i 0.159497 + 0.0920854i 0.577624 0.816303i \(-0.303980\pi\)
−0.418127 + 0.908388i \(0.637313\pi\)
\(20\) −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 −0.946283 0.323340i \(-0.895194\pi\)
0.627488 + 0.778626i \(0.284083\pi\)
\(24\) 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 0.430040 0.902810i \(-0.358500\pi\)
−0.814419 + 0.580278i \(0.802944\pi\)
\(30\) 0 0
\(31\) 1.27517 + 7.23183i 0.229027 + 1.29887i 0.854836 + 0.518899i \(0.173658\pi\)
−0.625809 + 0.779976i \(0.715231\pi\)
\(32\) −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 0.861629 + 0.507539i \(0.169445\pi\)
−0.999962 + 0.00872734i \(0.997222\pi\)
\(38\) −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 0.491943 0.870628i \(-0.336287\pi\)
−0.942826 + 0.333286i \(0.891842\pi\)
\(42\) 0 0
\(43\) −2.90471 + 6.22917i −0.442964 + 0.949940i 0.550397 + 0.834903i \(0.314476\pi\)
−0.993361 + 0.115037i \(0.963301\pi\)
\(44\) −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 0.518328 0.855182i \(-0.326555\pi\)
−0.980887 + 0.194580i \(0.937666\pi\)
\(48\) 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 0.814347 0.580379i \(-0.197095\pi\)
−0.580379 + 0.814347i \(0.697095\pi\)
\(54\) 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 0.607231 0.794525i \(-0.292280\pi\)
−0.0455453 + 0.998962i \(0.514503\pi\)
\(60\) 0 0
\(61\) 2.10123 11.9167i 0.269035 1.52577i −0.488259 0.872699i \(-0.662368\pi\)
0.757294 0.653074i \(-0.226521\pi\)
\(62\) −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 −0.326793 0.945096i \(-0.605968\pi\)
−0.485943 + 0.873991i \(0.661524\pi\)
\(68\) −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 −0.128345 0.991730i \(-0.540966\pi\)
0.794691 + 0.607014i \(0.207633\pi\)
\(72\) 0 0
\(73\) 2.49666 + 9.31768i 0.292212 + 1.09055i 0.943406 + 0.331640i \(0.107602\pi\)
−0.651194 + 0.758912i \(0.725731\pi\)
\(74\) 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 −0.783882 0.620910i \(-0.786763\pi\)
0.747597 + 0.664153i \(0.231208\pi\)
\(80\) −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 0.910411 + 0.413706i \(0.135766\pi\)
−0.824740 + 0.565512i \(0.808679\pi\)
\(84\) 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 −0.232821 0.972520i \(-0.574796\pi\)
0.958637 0.284631i \(-0.0918711\pi\)
\(90\) 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 0.728010 0.685567i \(-0.240446\pi\)
−0.0572192 + 0.998362i \(0.518223\pi\)
\(98\) −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 −0.0900315 0.995939i \(-0.528697\pi\)
−0.425233 + 0.905084i \(0.639808\pi\)
\(102\) 0 0
\(103\) −3.40559 + 1.58805i −0.335562 + 0.156475i −0.583094 0.812404i \(-0.698158\pi\)
0.247532 + 0.968880i \(0.420380\pi\)
\(104\) 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 −0.926512 0.376266i \(-0.877208\pi\)
0.376266 + 0.926512i \(0.377208\pi\)
\(108\) 0 0
\(109\) 12.1610i 1.16481i −0.812899 0.582405i \(-0.802112\pi\)
0.812899 0.582405i \(-0.197888\pi\)
\(110\) −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 0.970469 0.241225i \(-0.0775490\pi\)
−0.808594 + 0.588366i \(0.799771\pi\)
\(114\) 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 −0.225441 0.974257i \(-0.572382\pi\)
0.291891 + 0.956452i \(0.405716\pi\)
\(128\) 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 0.162481 0.986712i \(-0.448050\pi\)
0.490158 + 0.871634i \(0.336939\pi\)
\(132\) 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 −0.500431 0.865776i \(-0.666825\pi\)
−0.342488 + 0.939522i \(0.611270\pi\)
\(138\) 0 0
\(139\) 14.8464 2.61782i 1.25926 0.222041i 0.496105 0.868262i \(-0.334763\pi\)
0.763150 + 0.646222i \(0.223652\pi\)
\(140\) −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 −0.0487579 0.998811i \(-0.515526\pi\)
0.975170 + 0.221459i \(0.0710818\pi\)
\(150\) 0 0
\(151\) −2.23835 + 0.814693i −0.182154 + 0.0662987i −0.431487 0.902119i \(-0.642011\pi\)
0.249333 + 0.968418i \(0.419789\pi\)
\(152\) 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 0.993038 0.117794i \(-0.0375824\pi\)
−0.728548 + 0.684995i \(0.759805\pi\)
\(158\) 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 −0.184210 0.982887i \(-0.558973\pi\)
0.982887 + 0.184210i \(0.0589726\pi\)
\(164\) 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 −0.181477 0.983395i \(-0.558088\pi\)
0.636673 + 0.771133i \(0.280310\pi\)
\(168\) 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 −0.0201240 0.999797i \(-0.506406\pi\)
−0.778825 + 0.627242i \(0.784184\pi\)
\(174\) 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 0.965074 0.261977i \(-0.0843744\pi\)
−0.709416 + 0.704790i \(0.751041\pi\)
\(180\) 0 0
\(181\) −8.12103 + 14.0660i −0.603631 + 1.04552i 0.388635 + 0.921392i \(0.372947\pi\)
−0.992266 + 0.124128i \(0.960387\pi\)
\(182\) 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 −0.0387846 0.999248i \(-0.512349\pi\)
0.990802 0.135322i \(-0.0432069\pi\)
\(192\) 0 0
\(193\) −6.37883 4.46650i −0.459158 0.321506i 0.321010 0.947076i \(-0.395978\pi\)
−0.780168 + 0.625570i \(0.784867\pi\)
\(194\) −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 0.997406 0.0719752i \(-0.0229303\pi\)
−0.899767 + 0.436371i \(0.856264\pi\)
\(198\) 0 0
\(199\) −24.0896 + 13.9081i −1.70766 + 0.985920i −0.770225 + 0.637773i \(0.779856\pi\)
−0.937440 + 0.348148i \(0.886811\pi\)
\(200\) −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 0.628306 0.777966i \(-0.283749\pi\)
−0.0187568 + 0.999824i \(0.505971\pi\)
\(212\) −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 0.967462 0.253017i \(-0.0814230\pi\)
−0.568650 + 0.822580i \(0.692534\pi\)
\(224\) 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 −0.572966 0.819579i \(-0.694207\pi\)
0.996129 0.0878980i \(-0.0280150\pi\)
\(228\) 0 0
\(229\) 0.604581 + 0.720511i 0.0399518 + 0.0476127i 0.785650 0.618671i \(-0.212329\pi\)
−0.745699 + 0.666284i \(0.767884\pi\)
\(230\) −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 −0.901813 0.432126i \(-0.857764\pi\)
0.997056 + 0.0766749i \(0.0244304\pi\)
\(234\) 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 0.939127 + 0.343571i \(0.111637\pi\)
−0.764982 + 0.644051i \(0.777252\pi\)
\(240\) 0 0
\(241\) 14.6302 + 12.2762i 0.942414 + 0.790779i 0.978004 0.208587i \(-0.0668865\pi\)
−0.0355896 + 0.999366i \(0.511331\pi\)
\(242\) 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 0.802845 0.596188i \(-0.203319\pi\)
−0.114892 + 0.993378i \(0.536652\pi\)
\(252\) 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 0.300521 + 0.953775i \(0.402840\pi\)
−0.461576 + 0.887100i \(0.652716\pi\)
\(258\) 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 −0.588410 0.808563i \(-0.700246\pi\)
0.558553 + 0.829469i \(0.311357\pi\)
\(264\) 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 0.0485123 0.998823i \(-0.484552\pi\)
0.955178 + 0.296031i \(0.0956631\pi\)
\(278\) −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 −0.950816 0.309755i \(-0.899753\pi\)
0.529261 0.848459i \(-0.322469\pi\)
\(282\) 0 0
\(283\) 1.12399 12.8473i 0.0668145 0.763693i −0.886700 0.462345i \(-0.847008\pi\)
0.953514 0.301348i \(-0.0974364\pi\)
\(284\) −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 0.426392 0.904538i \(-0.359784\pi\)
0.704153 0.710048i \(-0.251327\pi\)
\(294\) 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 −0.850656 0.525723i \(-0.823795\pi\)
0.999551 0.0299620i \(-0.00953863\pi\)
\(308\) 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 −0.992413 0.122952i \(-0.960764\pi\)
0.0512465 0.998686i \(-0.483681\pi\)
\(312\) 0 0
\(313\) 2.37968 5.10324i 0.134508 0.288452i −0.827505 0.561459i \(-0.810240\pi\)
0.962012 + 0.273007i \(0.0880181\pi\)
\(314\) −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 0.847901 0.530154i \(-0.177866\pi\)
−0.788181 + 0.615443i \(0.788977\pi\)
\(318\) 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 0.743638 + 0.668583i \(0.233099\pi\)
−0.927460 + 0.373923i \(0.878012\pi\)
\(332\) −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 0.180375 0.983598i \(-0.442269\pi\)
0.00683487 + 0.999977i \(0.497824\pi\)
\(338\) 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 0.367564 0.929998i \(-0.380192\pi\)
−0.748198 + 0.663475i \(0.769081\pi\)
\(348\) 0 0
\(349\) 6.93929 8.26992i 0.371452 0.442679i −0.547645 0.836711i \(-0.684476\pi\)
0.919097 + 0.394032i \(0.128920\pi\)
\(350\) −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 −0.761649 0.647990i \(-0.775610\pi\)
0.637555 0.770405i \(-0.279946\pi\)
\(354\) 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 −0.627747 0.778418i \(-0.716023\pi\)
0.988003 + 0.154436i \(0.0493560\pi\)
\(360\) 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 0.705712 0.708498i \(-0.250627\pi\)
−0.0891181 + 0.996021i \(0.528405\pi\)
\(368\) −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 −0.466523 0.884509i \(-0.654494\pi\)
0.377698 + 0.925929i \(0.376716\pi\)
\(374\) −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 \(0.0713025\pi\)
−0.975016 + 0.222135i \(0.928698\pi\)
\(380\) −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 −0.999885 0.0151943i \(-0.995163\pi\)
0.631074 0.775723i \(-0.282614\pi\)
\(384\) 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 −0.321051 0.947062i \(-0.604036\pi\)
0.362820 + 0.931859i \(0.381814\pi\)
\(390\) 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 −0.202305 0.979323i \(-0.564843\pi\)
0.314460 + 0.949271i \(0.398177\pi\)
\(398\) 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 −0.329753 0.944067i \(-0.606965\pi\)
0.0130235 + 0.999915i \(0.495854\pi\)
\(402\) 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 0.560462 0.828180i \(-0.310624\pi\)
0.809916 + 0.586546i \(0.199513\pi\)
\(410\) 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 0.429693 0.902975i \(-0.358622\pi\)
0.963872 0.266365i \(-0.0858226\pi\)
\(420\) 0 0
\(421\) 27.5767 10.0371i 1.34400 0.489178i 0.432933 0.901426i \(-0.357479\pi\)
0.911071 + 0.412249i \(0.135256\pi\)
\(422\) −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 \(0.00368513\pi\)
−0.999933 + 0.0115769i \(0.996315\pi\)
\(432\) 0 0
\(433\) −5.55599 + 5.55599i −0.267004 + 0.267004i −0.827892 0.560888i \(-0.810460\pi\)
0.560888 + 0.827892i \(0.310460\pi\)
\(434\) 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 −0.125924 0.992040i \(-0.540190\pi\)
−0.457627 + 0.889144i \(0.651301\pi\)
\(440\) 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 0.766040 0.642793i \(-0.222225\pi\)
−7.21597e−6 1.00000i \(0.500002\pi\)
\(444\) 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 0.817420 0.576042i \(-0.195403\pi\)
−0.907577 + 0.419886i \(0.862070\pi\)
\(450\) 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 −0.897976 0.440045i \(-0.854962\pi\)
0.807920 0.589292i \(-0.200593\pi\)
\(458\) −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 −0.854095 0.520116i \(-0.825889\pi\)
0.660527 + 0.750803i \(0.270333\pi\)
\(462\) 0 0
\(463\) 0.251426 + 0.176051i 0.0116848 + 0.00818177i 0.579404 0.815040i \(-0.303285\pi\)
−0.567719 + 0.823222i \(0.692174\pi\)
\(464\) −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 0.390156 + 0.920749i \(0.372421\pi\)
0.122489 + 0.992470i \(0.460912\pi\)
\(468\) 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 0.139612 + 0.990206i \(0.455415\pi\)
−0.469863 + 0.882740i \(0.655697\pi\)
\(480\) 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 0.977038 0.213064i \(-0.0683442\pi\)
−0.213064 + 0.977038i \(0.568344\pi\)
\(488\) −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 −0.755340 0.655333i \(-0.772528\pi\)
0.999864 0.0164907i \(-0.00524938\pi\)
\(492\) 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 0.758148 0.652083i \(-0.226105\pi\)
−0.773827 + 0.633397i \(0.781660\pi\)
\(500\) 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 −0.759138 0.650930i \(-0.774379\pi\)
0.982898 0.184153i \(-0.0589542\pi\)
\(504\) 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 0.900764 + 0.434310i \(0.143008\pi\)
−0.697898 + 0.716197i \(0.745881\pi\)
\(510\) 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 0.645388 0.763855i \(-0.276696\pi\)
−0.338824 + 0.940850i \(0.610029\pi\)
\(522\) 0 0
\(523\) 34.5655 + 9.26181i 1.51145 + 0.404991i 0.916915 0.399083i \(-0.130671\pi\)
0.594530 + 0.804073i \(0.297338\pi\)
\(524\) −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 −0.760533 0.649299i \(-0.775062\pi\)
0.350024 + 0.936741i \(0.386174\pi\)
\(548\) 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 0.495142 0.868812i \(-0.335116\pi\)
−0.00560082 + 0.999984i \(0.501783\pi\)
\(558\) 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 −0.908010 0.418947i \(-0.862399\pi\)
0.704240 + 0.709962i \(0.251288\pi\)
\(564\) 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 0.812906 0.582395i \(-0.197884\pi\)
−0.432388 + 0.901688i \(0.642329\pi\)
\(570\) 0 0
\(571\) 5.84395 + 33.1427i 0.244562 + 1.38698i 0.821508 + 0.570197i \(0.193133\pi\)
−0.576946 + 0.816782i \(0.695756\pi\)
\(572\) 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 0.603387 + 0.797448i \(0.293817\pi\)
−0.921273 + 0.388917i \(0.872849\pi\)
\(578\) −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 0.454412 0.890792i \(-0.349850\pi\)
−0.992488 + 0.122338i \(0.960961\pi\)
\(588\) 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 0.482608 0.875837i \(-0.339690\pi\)
−0.875837 + 0.482608i \(0.839690\pi\)
\(594\) 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 0.0499591 0.998751i \(-0.484091\pi\)
−0.603714 + 0.797201i \(0.706313\pi\)
\(600\) 0 0
\(601\) 4.30406 24.4095i 0.175566 0.995686i −0.761922 0.647669i \(-0.775744\pi\)
0.937488 0.348017i \(-0.113145\pi\)
\(602\) 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 −0.491789 0.870714i \(-0.663657\pi\)
−0.635516 + 0.772088i \(0.719212\pi\)
\(608\) −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 −0.885464 0.464708i \(-0.846159\pi\)
0.534480 0.845181i \(-0.320507\pi\)
\(614\) −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 0.00222854 0.999998i \(-0.499291\pi\)
−0.938928 + 0.344113i \(0.888180\pi\)
\(618\) 0 0
\(619\) −16.2376 + 19.3513i −0.652646 + 0.777793i −0.986310 0.164899i \(-0.947270\pi\)
0.333665 + 0.942692i \(0.391715\pi\)
\(620\) −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 0.915724 0.401807i \(-0.131618\pi\)
−0.805837 + 0.592137i \(0.798284\pi\)
\(632\) −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 0.963699 0.266991i \(-0.0860295\pi\)
0.814264 + 0.580494i \(0.197141\pi\)
\(642\) 0 0
\(643\) 14.3424 6.68798i 0.565610 0.263748i −0.118711 0.992929i \(-0.537876\pi\)
0.684321 + 0.729181i \(0.260099\pi\)
\(644\) 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 −0.525564 0.850754i \(-0.676146\pi\)
0.850754 + 0.525564i \(0.176146\pi\)
\(648\) 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 0.639316 + 0.768944i \(0.279217\pi\)
0.178100 + 0.984012i \(0.443005\pi\)
\(654\) 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 0.196087 0.980586i \(-0.437176\pi\)
0.780520 + 0.625130i \(0.214954\pi\)
\(660\) 0 0
\(661\) −33.2465 + 27.8971i −1.29314 + 1.08507i −0.301851 + 0.953355i \(0.597604\pi\)
−0.991287 + 0.131716i \(0.957951\pi\)
\(662\) 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 0.106820 0.994278i \(-0.465933\pi\)
0.277852 + 0.960624i \(0.410378\pi\)
\(674\) −0.555107 −0.0213819
\(675\) 0 0
\(676\) 18.4852 0.710968
\(677\) 35.9148 3.14213i 1.38032 0.120762i 0.627307 0.778772i \(-0.284157\pi\)
0.753009 + 0.658010i \(0.228602\pi\)
\(678\) 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 0.628871 0.777510i \(-0.283517\pi\)
0.933373 + 0.358908i \(0.116851\pi\)
\(684\) 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 −0.437227 0.899351i \(-0.644040\pi\)
0.243156 + 0.969987i \(0.421817\pi\)
\(692\) 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 \(0.0505647\pi\)
−0.987409 + 0.158186i \(0.949435\pi\)
\(702\) 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 0.659599 0.751617i \(-0.270726\pi\)
0.362752 + 0.931886i \(0.381837\pi\)
\(710\) 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 −0.999999 0.00158362i \(-0.999496\pi\)
0.498628 0.866816i \(-0.333837\pi\)
\(720\) 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 −0.962141 0.272553i \(-0.912132\pi\)
0.900195 0.435487i \(-0.143424\pi\)
\(728\) −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 −0.100699 0.994917i \(-0.532108\pi\)
−0.969357 + 0.245656i \(0.920997\pi\)
\(734\) −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 −0.157484 0.987522i \(-0.550338\pi\)
0.776477 + 0.630146i \(0.217005\pi\)
\(740\) −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 −0.499796 0.866143i \(-0.666592\pi\)
−0.642608 + 0.766195i \(0.722147\pi\)
\(744\) 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 0.705436 0.708774i \(-0.250751\pi\)
0.0848041 + 0.996398i \(0.472974\pi\)
\(752\) −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 0.875410 0.483381i \(-0.160592\pi\)
−0.483381 + 0.875410i \(0.660592\pi\)
\(758\) −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 −0.984007 0.178131i \(-0.942995\pi\)
0.868293 + 0.496051i \(0.165217\pi\)
\(762\) 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 0.607465 0.794346i \(-0.292186\pi\)
−0.887764 + 0.460300i \(0.847742\pi\)
\(770\) 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 −0.956776 0.290825i \(-0.906070\pi\)
0.974005 + 0.226527i \(0.0727370\pi\)
\(774\) 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