Properties

Label 570.2.k.a.77.12
Level $570$
Weight $2$
Character 570.77
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.12
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.966096 - 1.43759i) q^{3} -1.00000i q^{4} +(1.74702 + 1.39568i) q^{5} +(-1.69966 - 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.13332 + 2.77770i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.966096 - 1.43759i) q^{3} -1.00000i q^{4} +(1.74702 + 1.39568i) q^{5} +(-1.69966 - 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.13332 + 2.77770i) q^{9} +(2.22222 - 0.248430i) q^{10} -4.73487i q^{11} +(-1.43759 + 0.966096i) q^{12} +(3.07524 - 3.07524i) q^{13} +0.524733 q^{14} +(0.318631 - 3.85985i) q^{15} -1.00000 q^{16} +(2.77446 - 2.77446i) q^{17} +(1.16275 + 2.76550i) q^{18} +1.00000i q^{19} +(1.39568 - 1.74702i) q^{20} +(0.174943 - 0.891868i) q^{21} +(-3.34806 - 3.34806i) q^{22} +(-5.62880 - 5.62880i) q^{23} +(-0.333395 + 1.69966i) q^{24} +(1.10414 + 4.87656i) q^{25} -4.34904i q^{26} +(5.08807 - 1.05428i) q^{27} +(0.371042 - 0.371042i) q^{28} -4.06253 q^{29} +(-2.50402 - 2.95464i) q^{30} +3.53345 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.80679 + 4.57434i) q^{33} -3.92368i q^{34} +(0.130360 + 1.16607i) q^{35} +(2.77770 + 1.13332i) q^{36} +(2.20796 + 2.20796i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-7.39190 - 1.44995i) q^{39} +(-0.248430 - 2.22222i) q^{40} +6.41083i q^{41} +(-0.506942 - 0.754350i) q^{42} +(-6.80047 + 6.80047i) q^{43} -4.73487 q^{44} +(-5.85671 + 3.27093i) q^{45} -7.96032 q^{46} +(5.86781 - 5.86781i) q^{47} +(0.966096 + 1.43759i) q^{48} -6.72466i q^{49} +(4.22899 + 2.66751i) q^{50} +(-6.66893 - 1.30814i) q^{51} +(-3.07524 - 3.07524i) q^{52} +(6.65823 + 6.65823i) q^{53} +(2.85232 - 4.34330i) q^{54} +(6.60838 - 8.27189i) q^{55} -0.524733i q^{56} +(1.43759 - 0.966096i) q^{57} +(-2.87264 + 2.87264i) q^{58} -6.00225 q^{59} +(-3.85985 - 0.318631i) q^{60} -3.00545 q^{61} +(2.49852 - 2.49852i) q^{62} +(-1.45115 + 0.610134i) q^{63} +1.00000i q^{64} +(9.66455 - 1.08043i) q^{65} +(-1.57858 + 8.04767i) q^{66} +(4.01127 + 4.01127i) q^{67} +(-2.77446 - 2.77446i) q^{68} +(-2.65393 + 13.5299i) q^{69} +(0.916717 + 0.732361i) q^{70} +3.67498i q^{71} +(2.76550 - 1.16275i) q^{72} +(7.51659 - 7.51659i) q^{73} +3.12253 q^{74} +(5.94379 - 6.29852i) q^{75} +1.00000 q^{76} +(1.75684 - 1.75684i) q^{77} +(-6.25213 + 4.20159i) q^{78} -7.93390i q^{79} +(-1.74702 - 1.39568i) q^{80} +(-6.43119 - 6.29602i) q^{81} +(4.53314 + 4.53314i) q^{82} +(7.74087 + 7.74087i) q^{83} +(-0.891868 - 0.174943i) q^{84} +(8.71931 - 0.974762i) q^{85} +9.61732i q^{86} +(3.92480 + 5.84025i) q^{87} +(-3.34806 + 3.34806i) q^{88} -7.13257 q^{89} +(-1.82842 + 6.45421i) q^{90} +2.28209 q^{91} +(-5.62880 + 5.62880i) q^{92} +(-3.41365 - 5.07964i) q^{93} -8.29833i q^{94} +(-1.39568 + 1.74702i) q^{95} +(1.69966 + 0.333395i) q^{96} +(5.01544 + 5.01544i) q^{97} +(-4.75505 - 4.75505i) q^{98} +(13.1520 + 5.36611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} - 32q^{21} - 4q^{22} + 32q^{25} + 28q^{27} - 12q^{28} - 8q^{30} + 8q^{31} + 36q^{33} + 4q^{36} - 32q^{37} - 8q^{40} + 12q^{42} - 24q^{43} - 28q^{45} - 16q^{46} - 4q^{48} - 40q^{51} - 8q^{52} - 4q^{55} + 4q^{57} - 4q^{58} - 24q^{60} + 200q^{61} + 28q^{63} + 12q^{70} - 68q^{73} - 36q^{75} + 36q^{76} + 24q^{78} - 92q^{81} + 24q^{82} + 24q^{85} + 28q^{87} - 4q^{88} - 68q^{90} + 64q^{91} + 16q^{93} - 4q^{96} - 148q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −0.966096 1.43759i −0.557776 0.829992i
\(4\) 1.00000i 0.500000i
\(5\) 1.74702 + 1.39568i 0.781290 + 0.624169i
\(6\) −1.69966 0.333395i −0.693884 0.136108i
\(7\) 0.371042 + 0.371042i 0.140241 + 0.140241i 0.773742 0.633501i \(-0.218383\pi\)
−0.633501 + 0.773742i \(0.718383\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −1.13332 + 2.77770i −0.377772 + 0.925899i
\(10\) 2.22222 0.248430i 0.702729 0.0785605i
\(11\) 4.73487i 1.42762i −0.700341 0.713808i \(-0.746969\pi\)
0.700341 0.713808i \(-0.253031\pi\)
\(12\) −1.43759 + 0.966096i −0.414996 + 0.278888i
\(13\) 3.07524 3.07524i 0.852917 0.852917i −0.137574 0.990491i \(-0.543931\pi\)
0.990491 + 0.137574i \(0.0439305\pi\)
\(14\) 0.524733 0.140241
\(15\) 0.318631 3.85985i 0.0822703 0.996610i
\(16\) −1.00000 −0.250000
\(17\) 2.77446 2.77446i 0.672906 0.672906i −0.285479 0.958385i \(-0.592153\pi\)
0.958385 + 0.285479i \(0.0921526\pi\)
\(18\) 1.16275 + 2.76550i 0.274063 + 0.651835i
\(19\) 1.00000i 0.229416i
\(20\) 1.39568 1.74702i 0.312084 0.390645i
\(21\) 0.174943 0.891868i 0.0381758 0.194622i
\(22\) −3.34806 3.34806i −0.713808 0.713808i
\(23\) −5.62880 5.62880i −1.17369 1.17369i −0.981324 0.192362i \(-0.938385\pi\)
−0.192362 0.981324i \(-0.561615\pi\)
\(24\) −0.333395 + 1.69966i −0.0680540 + 0.346942i
\(25\) 1.10414 + 4.87656i 0.220827 + 0.975313i
\(26\) 4.34904i 0.852917i
\(27\) 5.08807 1.05428i 0.979200 0.202896i
\(28\) 0.371042 0.371042i 0.0701204 0.0701204i
\(29\) −4.06253 −0.754393 −0.377197 0.926133i \(-0.623112\pi\)
−0.377197 + 0.926133i \(0.623112\pi\)
\(30\) −2.50402 2.95464i −0.457170 0.539440i
\(31\) 3.53345 0.634625 0.317313 0.948321i \(-0.397220\pi\)
0.317313 + 0.948321i \(0.397220\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −6.80679 + 4.57434i −1.18491 + 0.796290i
\(34\) 3.92368i 0.672906i
\(35\) 0.130360 + 1.16607i 0.0220348 + 0.197103i
\(36\) 2.77770 + 1.13332i 0.462949 + 0.188886i
\(37\) 2.20796 + 2.20796i 0.362987 + 0.362987i 0.864911 0.501925i \(-0.167375\pi\)
−0.501925 + 0.864911i \(0.667375\pi\)
\(38\) 0.707107 + 0.707107i 0.114708 + 0.114708i
\(39\) −7.39190 1.44995i −1.18365 0.232178i
\(40\) −0.248430 2.22222i −0.0392803 0.351365i
\(41\) 6.41083i 1.00120i 0.865678 + 0.500601i \(0.166888\pi\)
−0.865678 + 0.500601i \(0.833112\pi\)
\(42\) −0.506942 0.754350i −0.0782229 0.116399i
\(43\) −6.80047 + 6.80047i −1.03706 + 1.03706i −0.0377764 + 0.999286i \(0.512027\pi\)
−0.999286 + 0.0377764i \(0.987973\pi\)
\(44\) −4.73487 −0.713808
\(45\) −5.85671 + 3.27093i −0.873066 + 0.487601i
\(46\) −7.96032 −1.17369
\(47\) 5.86781 5.86781i 0.855908 0.855908i −0.134945 0.990853i \(-0.543086\pi\)
0.990853 + 0.134945i \(0.0430859\pi\)
\(48\) 0.966096 + 1.43759i 0.139444 + 0.207498i
\(49\) 6.72466i 0.960665i
\(50\) 4.22899 + 2.66751i 0.598070 + 0.377243i
\(51\) −6.66893 1.30814i −0.933837 0.183176i
\(52\) −3.07524 3.07524i −0.426459 0.426459i
\(53\) 6.65823 + 6.65823i 0.914579 + 0.914579i 0.996628 0.0820496i \(-0.0261466\pi\)
−0.0820496 + 0.996628i \(0.526147\pi\)
\(54\) 2.85232 4.34330i 0.388152 0.591048i
\(55\) 6.60838 8.27189i 0.891073 1.11538i
\(56\) 0.524733i 0.0701204i
\(57\) 1.43759 0.966096i 0.190413 0.127963i
\(58\) −2.87264 + 2.87264i −0.377197 + 0.377197i
\(59\) −6.00225 −0.781426 −0.390713 0.920513i \(-0.627772\pi\)
−0.390713 + 0.920513i \(0.627772\pi\)
\(60\) −3.85985 0.318631i −0.498305 0.0411351i
\(61\) −3.00545 −0.384809 −0.192404 0.981316i \(-0.561628\pi\)
−0.192404 + 0.981316i \(0.561628\pi\)
\(62\) 2.49852 2.49852i 0.317313 0.317313i
\(63\) −1.45115 + 0.610134i −0.182828 + 0.0768696i
\(64\) 1.00000i 0.125000i
\(65\) 9.66455 1.08043i 1.19874 0.134011i
\(66\) −1.57858 + 8.04767i −0.194310 + 0.990600i
\(67\) 4.01127 + 4.01127i 0.490055 + 0.490055i 0.908323 0.418269i \(-0.137363\pi\)
−0.418269 + 0.908323i \(0.637363\pi\)
\(68\) −2.77446 2.77446i −0.336453 0.336453i
\(69\) −2.65393 + 13.5299i −0.319496 + 1.62880i
\(70\) 0.916717 + 0.732361i 0.109569 + 0.0875339i
\(71\) 3.67498i 0.436140i 0.975933 + 0.218070i \(0.0699762\pi\)
−0.975933 + 0.218070i \(0.930024\pi\)
\(72\) 2.76550 1.16275i 0.325918 0.137032i
\(73\) 7.51659 7.51659i 0.879750 0.879750i −0.113758 0.993508i \(-0.536289\pi\)
0.993508 + 0.113758i \(0.0362890\pi\)
\(74\) 3.12253 0.362987
\(75\) 5.94379 6.29852i 0.686330 0.727291i
\(76\) 1.00000 0.114708
\(77\) 1.75684 1.75684i 0.200210 0.200210i
\(78\) −6.25213 + 4.20159i −0.707914 + 0.475737i
\(79\) 7.93390i 0.892633i −0.894875 0.446317i \(-0.852735\pi\)
0.894875 0.446317i \(-0.147265\pi\)
\(80\) −1.74702 1.39568i −0.195322 0.156042i
\(81\) −6.43119 6.29602i −0.714576 0.699558i
\(82\) 4.53314 + 4.53314i 0.500601 + 0.500601i
\(83\) 7.74087 + 7.74087i 0.849671 + 0.849671i 0.990092 0.140421i \(-0.0448455\pi\)
−0.140421 + 0.990092i \(0.544846\pi\)
\(84\) −0.891868 0.174943i −0.0973108 0.0190879i
\(85\) 8.71931 0.974762i 0.945742 0.105728i
\(86\) 9.61732i 1.03706i
\(87\) 3.92480 + 5.84025i 0.420782 + 0.626140i
\(88\) −3.34806 + 3.34806i −0.356904 + 0.356904i
\(89\) −7.13257 −0.756051 −0.378026 0.925795i \(-0.623397\pi\)
−0.378026 + 0.925795i \(0.623397\pi\)
\(90\) −1.82842 + 6.45421i −0.192733 + 0.680334i
\(91\) 2.28209 0.239228
\(92\) −5.62880 + 5.62880i −0.586843 + 0.586843i
\(93\) −3.41365 5.07964i −0.353979 0.526734i
\(94\) 8.29833i 0.855908i
\(95\) −1.39568 + 1.74702i −0.143194 + 0.179240i
\(96\) 1.69966 + 0.333395i 0.173471 + 0.0340270i
\(97\) 5.01544 + 5.01544i 0.509241 + 0.509241i 0.914293 0.405053i \(-0.132747\pi\)
−0.405053 + 0.914293i \(0.632747\pi\)
\(98\) −4.75505 4.75505i −0.480333 0.480333i
\(99\) 13.1520 + 5.36611i 1.32183 + 0.539314i
\(100\) 4.87656 1.10414i 0.487656 0.110414i
\(101\) 14.1063i 1.40363i 0.712361 + 0.701813i \(0.247626\pi\)
−0.712361 + 0.701813i \(0.752374\pi\)
\(102\) −5.64064 + 3.79066i −0.558507 + 0.375331i
\(103\) −5.16485 + 5.16485i −0.508907 + 0.508907i −0.914191 0.405284i \(-0.867173\pi\)
0.405284 + 0.914191i \(0.367173\pi\)
\(104\) −4.34904 −0.426459
\(105\) 1.55039 1.31394i 0.151303 0.128228i
\(106\) 9.41616 0.914579
\(107\) 5.85663 5.85663i 0.566182 0.566182i −0.364875 0.931057i \(-0.618888\pi\)
0.931057 + 0.364875i \(0.118888\pi\)
\(108\) −1.05428 5.08807i −0.101448 0.489600i
\(109\) 10.5464i 1.01016i 0.863073 + 0.505079i \(0.168537\pi\)
−0.863073 + 0.505079i \(0.831463\pi\)
\(110\) −1.17628 10.5219i −0.112154 1.00323i
\(111\) 1.04104 5.30724i 0.0988107 0.503741i
\(112\) −0.371042 0.371042i −0.0350602 0.0350602i
\(113\) 11.6877 + 11.6877i 1.09948 + 1.09948i 0.994471 + 0.105011i \(0.0334878\pi\)
0.105011 + 0.994471i \(0.466512\pi\)
\(114\) 0.333395 1.69966i 0.0312253 0.159188i
\(115\) −1.97758 17.6896i −0.184411 1.64957i
\(116\) 4.06253i 0.377197i
\(117\) 5.05685 + 12.0273i 0.467506 + 1.11192i
\(118\) −4.24423 + 4.24423i −0.390713 + 0.390713i
\(119\) 2.05889 0.188738
\(120\) −2.95464 + 2.50402i −0.269720 + 0.228585i
\(121\) −11.4190 −1.03809
\(122\) −2.12517 + 2.12517i −0.192404 + 0.192404i
\(123\) 9.21612 6.19347i 0.830990 0.558447i
\(124\) 3.53345i 0.317313i
\(125\) −4.87720 + 10.0605i −0.436230 + 0.899835i
\(126\) −0.594689 + 1.45755i −0.0529791 + 0.129849i
\(127\) 11.5688 + 11.5688i 1.02656 + 1.02656i 0.999637 + 0.0269261i \(0.00857187\pi\)
0.0269261 + 0.999637i \(0.491428\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 16.3462 + 3.20637i 1.43920 + 0.282305i
\(130\) 6.06989 7.59785i 0.532364 0.666376i
\(131\) 12.1137i 1.05838i 0.848505 + 0.529188i \(0.177503\pi\)
−0.848505 + 0.529188i \(0.822497\pi\)
\(132\) 4.57434 + 6.80679i 0.398145 + 0.592455i
\(133\) −0.371042 + 0.371042i −0.0321734 + 0.0321734i
\(134\) 5.67279 0.490055
\(135\) 10.3604 + 5.25950i 0.891680 + 0.452666i
\(136\) −3.92368 −0.336453
\(137\) 1.08854 1.08854i 0.0930002 0.0930002i −0.659076 0.752076i \(-0.729052\pi\)
0.752076 + 0.659076i \(0.229052\pi\)
\(138\) 7.69044 + 11.4437i 0.654653 + 0.974149i
\(139\) 6.34474i 0.538154i −0.963119 0.269077i \(-0.913281\pi\)
0.963119 0.269077i \(-0.0867185\pi\)
\(140\) 1.16607 0.130360i 0.0985513 0.0110174i
\(141\) −14.1044 2.76662i −1.18780 0.232992i
\(142\) 2.59861 + 2.59861i 0.218070 + 0.218070i
\(143\) −14.5608 14.5608i −1.21764 1.21764i
\(144\) 1.13332 2.77770i 0.0944431 0.231475i
\(145\) −7.09731 5.67001i −0.589400 0.470869i
\(146\) 10.6301i 0.879750i
\(147\) −9.66728 + 6.49666i −0.797344 + 0.535836i
\(148\) 2.20796 2.20796i 0.181493 0.181493i
\(149\) −19.2260 −1.57506 −0.787529 0.616278i \(-0.788640\pi\)
−0.787529 + 0.616278i \(0.788640\pi\)
\(150\) −0.250834 8.65662i −0.0204805 0.706810i
\(151\) 5.62170 0.457487 0.228744 0.973487i \(-0.426538\pi\)
0.228744 + 0.973487i \(0.426538\pi\)
\(152\) 0.707107 0.707107i 0.0573539 0.0573539i
\(153\) 4.56227 + 10.8510i 0.368838 + 0.877248i
\(154\) 2.48454i 0.200210i
\(155\) 6.17299 + 4.93157i 0.495826 + 0.396113i
\(156\) −1.44995 + 7.39190i −0.116089 + 0.591825i
\(157\) −10.3090 10.3090i −0.822747 0.822747i 0.163754 0.986501i \(-0.447640\pi\)
−0.986501 + 0.163754i \(0.947640\pi\)
\(158\) −5.61011 5.61011i −0.446317 0.446317i
\(159\) 3.13930 16.0043i 0.248963 1.26922i
\(160\) −2.22222 + 0.248430i −0.175682 + 0.0196401i
\(161\) 4.17704i 0.329197i
\(162\) −8.99949 + 0.0955769i −0.707067 + 0.00750923i
\(163\) 15.8628 15.8628i 1.24247 1.24247i 0.283497 0.958973i \(-0.408505\pi\)
0.958973 0.283497i \(-0.0914947\pi\)
\(164\) 6.41083 0.500601
\(165\) −18.2759 1.50868i −1.42278 0.117450i
\(166\) 10.9472 0.849671
\(167\) −16.9172 + 16.9172i −1.30910 + 1.30910i −0.387027 + 0.922068i \(0.626498\pi\)
−0.922068 + 0.387027i \(0.873502\pi\)
\(168\) −0.754350 + 0.506942i −0.0581993 + 0.0391115i
\(169\) 5.91417i 0.454936i
\(170\) 5.47622 6.85474i 0.420007 0.525735i
\(171\) −2.77770 1.13332i −0.212416 0.0866669i
\(172\) 6.80047 + 6.80047i 0.518531 + 0.518531i
\(173\) −6.04290 6.04290i −0.459433 0.459433i 0.439036 0.898469i \(-0.355320\pi\)
−0.898469 + 0.439036i \(0.855320\pi\)
\(174\) 6.90493 + 1.35443i 0.523461 + 0.102679i
\(175\) −1.39973 + 2.21909i −0.105810 + 0.167748i
\(176\) 4.73487i 0.356904i
\(177\) 5.79875 + 8.62876i 0.435861 + 0.648577i
\(178\) −5.04349 + 5.04349i −0.378026 + 0.378026i
\(179\) −7.72862 −0.577664 −0.288832 0.957380i \(-0.593267\pi\)
−0.288832 + 0.957380i \(0.593267\pi\)
\(180\) 3.27093 + 5.85671i 0.243801 + 0.436533i
\(181\) −15.5179 −1.15343 −0.576717 0.816944i \(-0.695666\pi\)
−0.576717 + 0.816944i \(0.695666\pi\)
\(182\) 1.61368 1.61368i 0.119614 0.119614i
\(183\) 2.90355 + 4.32060i 0.214637 + 0.319388i
\(184\) 7.96032i 0.586843i
\(185\) 0.775731 + 6.93896i 0.0570328 + 0.510163i
\(186\) −6.00566 1.17803i −0.440356 0.0863776i
\(187\) −13.1367 13.1367i −0.960652 0.960652i
\(188\) −5.86781 5.86781i −0.427954 0.427954i
\(189\) 2.27907 + 1.49671i 0.165778 + 0.108870i
\(190\) 0.248430 + 2.22222i 0.0180230 + 0.161217i
\(191\) 13.5080i 0.977402i 0.872451 + 0.488701i \(0.162529\pi\)
−0.872451 + 0.488701i \(0.837471\pi\)
\(192\) 1.43759 0.966096i 0.103749 0.0697220i
\(193\) −2.95772 + 2.95772i −0.212901 + 0.212901i −0.805499 0.592597i \(-0.798103\pi\)
0.592597 + 0.805499i \(0.298103\pi\)
\(194\) 7.09290 0.509241
\(195\) −10.8901 12.8498i −0.779856 0.920196i
\(196\) −6.72466 −0.480333
\(197\) 14.5718 14.5718i 1.03820 1.03820i 0.0389574 0.999241i \(-0.487596\pi\)
0.999241 0.0389574i \(-0.0124037\pi\)
\(198\) 13.0943 5.50547i 0.930571 0.391257i
\(199\) 5.90849i 0.418842i −0.977826 0.209421i \(-0.932842\pi\)
0.977826 0.209421i \(-0.0671578\pi\)
\(200\) 2.66751 4.22899i 0.188621 0.299035i
\(201\) 1.89128 9.64183i 0.133401 0.680082i
\(202\) 9.97464 + 9.97464i 0.701813 + 0.701813i
\(203\) −1.50737 1.50737i −0.105797 0.105797i
\(204\) −1.30814 + 6.66893i −0.0915879 + 0.466919i
\(205\) −8.94748 + 11.1998i −0.624919 + 0.782229i
\(206\) 7.30419i 0.508907i
\(207\) 22.0143 9.25588i 1.53010 0.643328i
\(208\) −3.07524 + 3.07524i −0.213229 + 0.213229i
\(209\) 4.73487 0.327518
\(210\) 0.167196 2.02539i 0.0115376 0.139765i
\(211\) −6.45326 −0.444261 −0.222130 0.975017i \(-0.571301\pi\)
−0.222130 + 0.975017i \(0.571301\pi\)
\(212\) 6.65823 6.65823i 0.457289 0.457289i
\(213\) 5.28311 3.55039i 0.361993 0.243268i
\(214\) 8.28252i 0.566182i
\(215\) −21.3719 + 2.38923i −1.45755 + 0.162944i
\(216\) −4.34330 2.85232i −0.295524 0.194076i
\(217\) 1.31106 + 1.31106i 0.0890004 + 0.0890004i
\(218\) 7.45740 + 7.45740i 0.505079 + 0.505079i
\(219\) −18.0675 3.54401i −1.22089 0.239482i
\(220\) −8.27189 6.60838i −0.557691 0.445537i
\(221\) 17.0643i 1.14787i
\(222\) −3.01666 4.48891i −0.202465 0.301276i
\(223\) −12.4934 + 12.4934i −0.836618 + 0.836618i −0.988412 0.151794i \(-0.951495\pi\)
0.151794 + 0.988412i \(0.451495\pi\)
\(224\) −0.524733 −0.0350602
\(225\) −14.7969 2.45974i −0.986463 0.163983i
\(226\) 16.5288 1.09948
\(227\) 3.12326 3.12326i 0.207298 0.207298i −0.595820 0.803118i \(-0.703173\pi\)
0.803118 + 0.595820i \(0.203173\pi\)
\(228\) −0.966096 1.43759i −0.0639813 0.0952066i
\(229\) 4.46088i 0.294783i 0.989078 + 0.147392i \(0.0470878\pi\)
−0.989078 + 0.147392i \(0.952912\pi\)
\(230\) −13.9068 11.1101i −0.916989 0.732578i
\(231\) −4.22288 0.828333i −0.277845 0.0545003i
\(232\) 2.87264 + 2.87264i 0.188598 + 0.188598i
\(233\) −2.29263 2.29263i −0.150195 0.150195i 0.628010 0.778205i \(-0.283870\pi\)
−0.778205 + 0.628010i \(0.783870\pi\)
\(234\) 12.0803 + 4.92884i 0.789715 + 0.322209i
\(235\) 18.4408 2.06156i 1.20294 0.134481i
\(236\) 6.00225i 0.390713i
\(237\) −11.4057 + 7.66491i −0.740878 + 0.497889i
\(238\) 1.45585 1.45585i 0.0943689 0.0943689i
\(239\) 4.10728 0.265678 0.132839 0.991138i \(-0.457591\pi\)
0.132839 + 0.991138i \(0.457591\pi\)
\(240\) −0.318631 + 3.85985i −0.0205676 + 0.249153i
\(241\) 25.0963 1.61659 0.808297 0.588776i \(-0.200390\pi\)
0.808297 + 0.588776i \(0.200390\pi\)
\(242\) −8.07443 + 8.07443i −0.519044 + 0.519044i
\(243\) −2.83794 + 15.3280i −0.182054 + 0.983289i
\(244\) 3.00545i 0.192404i
\(245\) 9.38549 11.7481i 0.599617 0.750558i
\(246\) 2.13734 10.8962i 0.136272 0.694718i
\(247\) 3.07524 + 3.07524i 0.195673 + 0.195673i
\(248\) −2.49852 2.49852i −0.158656 0.158656i
\(249\) 3.64976 18.6066i 0.231294 1.17915i
\(250\) 3.66512 + 10.5625i 0.231803 + 0.668033i
\(251\) 21.3779i 1.34936i 0.738110 + 0.674681i \(0.235719\pi\)
−0.738110 + 0.674681i \(0.764281\pi\)
\(252\) 0.610134 + 1.45115i 0.0384348 + 0.0914139i
\(253\) −26.6516 + 26.6516i −1.67557 + 1.67557i
\(254\) 16.3607 1.02656
\(255\) −9.82499 11.5931i −0.615265 0.725985i
\(256\) 1.00000 0.0625000
\(257\) 7.08612 7.08612i 0.442020 0.442020i −0.450670 0.892690i \(-0.648815\pi\)
0.892690 + 0.450670i \(0.148815\pi\)
\(258\) 13.8257 9.29126i 0.860753 0.578448i
\(259\) 1.63849i 0.101811i
\(260\) −1.08043 9.66455i −0.0670056 0.599370i
\(261\) 4.60414 11.2845i 0.284989 0.698492i
\(262\) 8.56565 + 8.56565i 0.529188 + 0.529188i
\(263\) −10.3710 10.3710i −0.639500 0.639500i 0.310932 0.950432i \(-0.399359\pi\)
−0.950432 + 0.310932i \(0.899359\pi\)
\(264\) 8.04767 + 1.57858i 0.495300 + 0.0971549i
\(265\) 2.33926 + 20.9248i 0.143700 + 1.28540i
\(266\) 0.524733i 0.0321734i
\(267\) 6.89075 + 10.2537i 0.421707 + 0.627516i
\(268\) 4.01127 4.01127i 0.245027 0.245027i
\(269\) 13.9150 0.848410 0.424205 0.905566i \(-0.360554\pi\)
0.424205 + 0.905566i \(0.360554\pi\)
\(270\) 11.0449 3.60687i 0.672173 0.219507i
\(271\) 9.79499 0.595003 0.297502 0.954721i \(-0.403847\pi\)
0.297502 + 0.954721i \(0.403847\pi\)
\(272\) −2.77446 + 2.77446i −0.168227 + 0.168227i
\(273\) −2.20471 3.28070i −0.133435 0.198557i
\(274\) 1.53943i 0.0930002i
\(275\) 23.0899 5.22793i 1.39237 0.315256i
\(276\) 13.5299 + 2.65393i 0.814401 + 0.159748i
\(277\) −4.58635 4.58635i −0.275567 0.275567i 0.555770 0.831336i \(-0.312424\pi\)
−0.831336 + 0.555770i \(0.812424\pi\)
\(278\) −4.48641 4.48641i −0.269077 0.269077i
\(279\) −4.00451 + 9.81484i −0.239744 + 0.587599i
\(280\) 0.732361 0.916717i 0.0437669 0.0547843i
\(281\) 12.1098i 0.722412i −0.932486 0.361206i \(-0.882365\pi\)
0.932486 0.361206i \(-0.117635\pi\)
\(282\) −11.9296 + 8.01699i −0.710396 + 0.477405i
\(283\) −1.32735 + 1.32735i −0.0789029 + 0.0789029i −0.745457 0.666554i \(-0.767769\pi\)
0.666554 + 0.745457i \(0.267769\pi\)
\(284\) 3.67498 0.218070
\(285\) 3.85985 + 0.318631i 0.228638 + 0.0188741i
\(286\) −20.5921 −1.21764
\(287\) −2.37869 + 2.37869i −0.140409 + 0.140409i
\(288\) −1.16275 2.76550i −0.0685158 0.162959i
\(289\) 1.60471i 0.0943944i
\(290\) −9.02786 + 1.00926i −0.530134 + 0.0592655i
\(291\) 2.36474 12.0555i 0.138623 0.706708i
\(292\) −7.51659 7.51659i −0.439875 0.439875i
\(293\) 12.6506 + 12.6506i 0.739057 + 0.739057i 0.972395 0.233339i \(-0.0749651\pi\)
−0.233339 + 0.972395i \(0.574965\pi\)
\(294\) −2.24197 + 11.4296i −0.130754 + 0.666590i
\(295\) −10.4860 8.37724i −0.610520 0.487742i
\(296\) 3.12253i 0.181493i
\(297\) −4.99187 24.0914i −0.289657 1.39792i
\(298\) −13.5949 + 13.5949i −0.787529 + 0.787529i
\(299\) −34.6198 −2.00211
\(300\) −6.29852 5.94379i −0.363645 0.343165i
\(301\) −5.04653 −0.290877
\(302\) 3.97514 3.97514i 0.228744 0.228744i
\(303\) 20.2790 13.6280i 1.16500 0.782909i
\(304\) 1.00000i 0.0573539i
\(305\) −5.25057 4.19466i −0.300647 0.240185i
\(306\) 10.8988 + 4.44678i 0.623043 + 0.254205i
\(307\) −16.4288 16.4288i −0.937644 0.937644i 0.0605232 0.998167i \(-0.480723\pi\)
−0.998167 + 0.0605232i \(0.980723\pi\)
\(308\) −1.75684 1.75684i −0.100105 0.100105i
\(309\) 12.4147 + 2.43518i 0.706245 + 0.138533i
\(310\) 7.85211 0.877815i 0.445970 0.0498565i
\(311\) 6.49385i 0.368232i −0.982904 0.184116i \(-0.941058\pi\)
0.982904 0.184116i \(-0.0589423\pi\)
\(312\) 4.20159 + 6.25213i 0.237868 + 0.353957i
\(313\) −15.5616 + 15.5616i −0.879591 + 0.879591i −0.993492 0.113901i \(-0.963665\pi\)
0.113901 + 0.993492i \(0.463665\pi\)
\(314\) −14.5791 −0.822747
\(315\) −3.38674 0.959433i −0.190821 0.0540579i
\(316\) −7.93390 −0.446317
\(317\) −21.8274 + 21.8274i −1.22595 + 1.22595i −0.260466 + 0.965483i \(0.583876\pi\)
−0.965483 + 0.260466i \(0.916124\pi\)
\(318\) −9.09692 13.5366i −0.510130 0.759093i
\(319\) 19.2355i 1.07698i
\(320\) −1.39568 + 1.74702i −0.0780211 + 0.0976612i
\(321\) −14.0775 2.76135i −0.785728 0.154124i
\(322\) −2.95362 2.95362i −0.164599 0.164599i
\(323\) 2.77446 + 2.77446i 0.154375 + 0.154375i
\(324\) −6.29602 + 6.43119i −0.349779 + 0.357288i
\(325\) 18.3921 + 11.6011i 1.02021 + 0.643514i
\(326\) 22.4334i 1.24247i
\(327\) 15.1613 10.1888i 0.838422 0.563442i
\(328\) 4.53314 4.53314i 0.250301 0.250301i
\(329\) 4.35441 0.240066
\(330\) −13.9898 + 11.8562i −0.770113 + 0.652663i
\(331\) −10.9575 −0.602276 −0.301138 0.953581i \(-0.597367\pi\)
−0.301138 + 0.953581i \(0.597367\pi\)
\(332\) 7.74087 7.74087i 0.424836 0.424836i
\(333\) −8.63536 + 3.63072i −0.473215 + 0.198962i
\(334\) 23.9246i 1.30910i
\(335\) 1.40929 + 12.6062i 0.0769979 + 0.688752i
\(336\) −0.174943 + 0.891868i −0.00954394 + 0.0486554i
\(337\) −9.98105 9.98105i −0.543702 0.543702i 0.380910 0.924612i \(-0.375611\pi\)
−0.924612 + 0.380910i \(0.875611\pi\)
\(338\) −4.18195 4.18195i −0.227468 0.227468i
\(339\) 5.51063 28.0934i 0.299296 1.52583i
\(340\) −0.974762 8.71931i −0.0528639 0.472871i
\(341\) 16.7304i 0.906002i
\(342\) −2.76550 + 1.16275i −0.149541 + 0.0628744i
\(343\) 5.09243 5.09243i 0.274965 0.274965i
\(344\) 9.61732 0.518531
\(345\) −23.5199 + 19.9328i −1.26627 + 1.07315i
\(346\) −8.54595 −0.459433
\(347\) 6.53710 6.53710i 0.350930 0.350930i −0.509526 0.860456i \(-0.670179\pi\)
0.860456 + 0.509526i \(0.170179\pi\)
\(348\) 5.84025 3.92480i 0.313070 0.210391i
\(349\) 16.6692i 0.892280i −0.894963 0.446140i \(-0.852798\pi\)
0.894963 0.446140i \(-0.147202\pi\)
\(350\) 0.579376 + 2.55889i 0.0309690 + 0.136779i
\(351\) 12.4049 18.8892i 0.662123 1.00823i
\(352\) 3.34806 + 3.34806i 0.178452 + 0.178452i
\(353\) −18.7729 18.7729i −0.999178 0.999178i 0.000821466 1.00000i \(-0.499739\pi\)
−1.00000 0.000821466i \(0.999739\pi\)
\(354\) 10.2018 + 2.00112i 0.542219 + 0.106358i
\(355\) −5.12911 + 6.42026i −0.272225 + 0.340752i
\(356\) 7.13257i 0.378026i
\(357\) −1.98908 2.95983i −0.105273 0.156651i
\(358\) −5.46496 + 5.46496i −0.288832 + 0.288832i
\(359\) 31.0918 1.64096 0.820480 0.571675i \(-0.193706\pi\)
0.820480 + 0.571675i \(0.193706\pi\)
\(360\) 6.45421 + 1.82842i 0.340167 + 0.0963663i
\(361\) −1.00000 −0.0526316
\(362\) −10.9728 + 10.9728i −0.576717 + 0.576717i
\(363\) 11.0318 + 16.4158i 0.579020 + 0.861604i
\(364\) 2.28209i 0.119614i
\(365\) 23.6224 2.64083i 1.23645 0.138227i
\(366\) 5.10825 + 1.00200i 0.267012 + 0.0523755i
\(367\) −0.761107 0.761107i −0.0397295 0.0397295i 0.686963 0.726692i \(-0.258943\pi\)
−0.726692 + 0.686963i \(0.758943\pi\)
\(368\) 5.62880 + 5.62880i 0.293421 + 0.293421i
\(369\) −17.8073 7.26550i −0.927012 0.378227i
\(370\) 5.45511 + 4.35806i 0.283598 + 0.226565i
\(371\) 4.94097i 0.256522i
\(372\) −5.07964 + 3.41365i −0.263367 + 0.176989i
\(373\) 8.01035 8.01035i 0.414760 0.414760i −0.468633 0.883393i \(-0.655253\pi\)
0.883393 + 0.468633i \(0.155253\pi\)
\(374\) −18.5781 −0.960652
\(375\) 19.1746 2.70798i 0.990174 0.139839i
\(376\) −8.29833 −0.427954
\(377\) −12.4932 + 12.4932i −0.643435 + 0.643435i
\(378\) 2.66988 0.553214i 0.137324 0.0284543i
\(379\) 15.0607i 0.773616i −0.922160 0.386808i \(-0.873578\pi\)
0.922160 0.386808i \(-0.126422\pi\)
\(380\) 1.74702 + 1.39568i 0.0896201 + 0.0715970i
\(381\) 5.45459 27.8077i 0.279447 1.42463i
\(382\) 9.55157 + 9.55157i 0.488701 + 0.488701i
\(383\) 21.4822 + 21.4822i 1.09769 + 1.09769i 0.994680 + 0.103010i \(0.0328474\pi\)
0.103010 + 0.994680i \(0.467153\pi\)
\(384\) 0.333395 1.69966i 0.0170135 0.0867355i
\(385\) 5.52121 0.617235i 0.281387 0.0314572i
\(386\) 4.18285i 0.212901i
\(387\) −11.1826 26.5967i −0.568441 1.35199i
\(388\) 5.01544 5.01544i 0.254620 0.254620i
\(389\) −11.7608 −0.596296 −0.298148 0.954520i \(-0.596369\pi\)
−0.298148 + 0.954520i \(0.596369\pi\)
\(390\) −16.7867 1.38574i −0.850026 0.0701697i
\(391\) −31.2338 −1.57956
\(392\) −4.75505 + 4.75505i −0.240166 + 0.240166i
\(393\) 17.4144 11.7030i 0.878443 0.590336i
\(394\) 20.6076i 1.03820i
\(395\) 11.0732 13.8607i 0.557154 0.697405i
\(396\) 5.36611 13.1520i 0.269657 0.660914i
\(397\) 6.27425 + 6.27425i 0.314895 + 0.314895i 0.846803 0.531907i \(-0.178524\pi\)
−0.531907 + 0.846803i \(0.678524\pi\)
\(398\) −4.17793 4.17793i −0.209421 0.209421i
\(399\) 0.891868 + 0.174943i 0.0446493 + 0.00875812i
\(400\) −1.10414 4.87656i −0.0552068 0.243828i
\(401\) 28.8320i 1.43980i −0.694076 0.719901i \(-0.744187\pi\)
0.694076 0.719901i \(-0.255813\pi\)
\(402\) −5.48046 8.15514i −0.273341 0.406741i
\(403\) 10.8662 10.8662i 0.541283 0.541283i
\(404\) 14.1063 0.701813
\(405\) −2.44814 19.9751i −0.121649 0.992573i
\(406\) −2.13174 −0.105797
\(407\) 10.4544 10.4544i 0.518206 0.518206i
\(408\) 3.79066 + 5.64064i 0.187665 + 0.279253i
\(409\) 18.6400i 0.921687i 0.887482 + 0.460843i \(0.152453\pi\)
−0.887482 + 0.460843i \(0.847547\pi\)
\(410\) 1.59264 + 14.2463i 0.0786550 + 0.703574i
\(411\) −2.61650 0.513237i −0.129063 0.0253161i
\(412\) 5.16485 + 5.16485i 0.254454 + 0.254454i
\(413\) −2.22709 2.22709i −0.109588 0.109588i
\(414\) 9.02157 22.1114i 0.443386 1.08671i
\(415\) 2.71963 + 24.3272i 0.133501 + 1.19418i
\(416\) 4.34904i 0.213229i
\(417\) −9.12112 + 6.12962i −0.446663 + 0.300169i
\(418\) 3.34806 3.34806i 0.163759 0.163759i
\(419\) −33.3598 −1.62974 −0.814868 0.579647i \(-0.803190\pi\)
−0.814868 + 0.579647i \(0.803190\pi\)
\(420\) −1.31394 1.55039i −0.0641139 0.0756515i
\(421\) −14.3797 −0.700824 −0.350412 0.936596i \(-0.613959\pi\)
−0.350412 + 0.936596i \(0.613959\pi\)
\(422\) −4.56315 + 4.56315i −0.222130 + 0.222130i
\(423\) 9.64890 + 22.9491i 0.469145 + 1.11582i
\(424\) 9.41616i 0.457289i
\(425\) 16.5932 + 10.4665i 0.804890 + 0.507698i
\(426\) 1.22522 6.24623i 0.0593622 0.302631i
\(427\) −1.11515 1.11515i −0.0539658 0.0539658i
\(428\) −5.85663 5.85663i −0.283091 0.283091i
\(429\) −6.86532 + 34.9997i −0.331461 + 1.68980i
\(430\) −13.4227 + 16.8016i −0.647302 + 0.810246i
\(431\) 13.4317i 0.646980i 0.946232 + 0.323490i \(0.104856\pi\)
−0.946232 + 0.323490i \(0.895144\pi\)
\(432\) −5.08807 + 1.05428i −0.244800 + 0.0507240i
\(433\) 4.59824 4.59824i 0.220977 0.220977i −0.587933 0.808910i \(-0.700058\pi\)
0.808910 + 0.587933i \(0.200058\pi\)
\(434\) 1.85411 0.0890004
\(435\) −1.29445 + 15.6808i −0.0620641 + 0.751836i
\(436\) 10.5464 0.505079
\(437\) 5.62880 5.62880i 0.269262 0.269262i
\(438\) −15.2816 + 10.2697i −0.730185 + 0.490703i
\(439\) 8.50450i 0.405898i −0.979189 0.202949i \(-0.934948\pi\)
0.979189 0.202949i \(-0.0650525\pi\)
\(440\) −10.5219 + 1.17628i −0.501614 + 0.0560771i
\(441\) 18.6790 + 7.62117i 0.889478 + 0.362913i
\(442\) −12.0663 12.0663i −0.573933 0.573933i
\(443\) −21.4192 21.4192i −1.01766 1.01766i −0.999841 0.0178169i \(-0.994328\pi\)
−0.0178169 0.999841i \(-0.505672\pi\)
\(444\) −5.30724 1.04104i −0.251871 0.0494054i
\(445\) −12.4607 9.95481i −0.590695 0.471903i
\(446\) 17.6683i 0.836618i
\(447\) 18.5742 + 27.6391i 0.878529 + 1.30728i
\(448\) −0.371042 + 0.371042i −0.0175301 + 0.0175301i
\(449\) 33.6163 1.58645 0.793226 0.608927i \(-0.208400\pi\)
0.793226 + 0.608927i \(0.208400\pi\)
\(450\) −12.2023 + 8.72372i −0.575223 + 0.411240i
\(451\) 30.3544 1.42933
\(452\) 11.6877 11.6877i 0.549741 0.549741i
\(453\) −5.43110 8.08168i −0.255175 0.379710i
\(454\) 4.41695i 0.207298i
\(455\) 3.98684 + 3.18507i 0.186906 + 0.149318i
\(456\) −1.69966 0.333395i −0.0795939 0.0156127i
\(457\) −14.7287 14.7287i −0.688978 0.688978i 0.273028 0.962006i \(-0.411975\pi\)
−0.962006 + 0.273028i \(0.911975\pi\)
\(458\) 3.15432 + 3.15432i 0.147392 + 0.147392i
\(459\) 11.1916 17.0417i 0.522380 0.795440i
\(460\) −17.6896 + 1.97758i −0.824783 + 0.0922054i
\(461\) 1.22359i 0.0569885i −0.999594 0.0284942i \(-0.990929\pi\)
0.999594 0.0284942i \(-0.00907123\pi\)
\(462\) −3.57174 + 2.40030i −0.166173 + 0.111672i
\(463\) 12.9428 12.9428i 0.601501 0.601501i −0.339209 0.940711i \(-0.610160\pi\)
0.940711 + 0.339209i \(0.110160\pi\)
\(464\) 4.06253 0.188598
\(465\) 1.12587 13.6386i 0.0522108 0.632474i
\(466\) −3.24227 −0.150195
\(467\) 8.23017 8.23017i 0.380847 0.380847i −0.490560 0.871407i \(-0.663208\pi\)
0.871407 + 0.490560i \(0.163208\pi\)
\(468\) 12.0273 5.05685i 0.555962 0.233753i
\(469\) 2.97670i 0.137451i
\(470\) 11.5818 14.4973i 0.534231 0.668712i
\(471\) −4.86060 + 24.7796i −0.223965 + 1.14178i
\(472\) 4.24423 + 4.24423i 0.195357 + 0.195357i
\(473\) 32.1993 + 32.1993i 1.48053 + 1.48053i
\(474\) −2.64512 + 13.4849i −0.121494 + 0.619384i
\(475\) −4.87656 + 1.10414i −0.223752 + 0.0506612i
\(476\) 2.05889i 0.0943689i
\(477\) −26.0404 + 10.9487i −1.19231 + 0.501304i
\(478\) 2.90428 2.90428i 0.132839 0.132839i
\(479\) −23.7395 −1.08469 −0.542344 0.840157i \(-0.682463\pi\)
−0.542344 + 0.840157i \(0.682463\pi\)
\(480\) 2.50402 + 2.95464i 0.114292 + 0.134860i
\(481\) 13.5800 0.619195
\(482\) 17.7457 17.7457i 0.808297 0.808297i
\(483\) −6.00487 + 4.03543i −0.273231 + 0.183618i
\(484\) 11.4190i 0.519044i
\(485\) 1.76209 + 15.7620i 0.0800125 + 0.715717i
\(486\) 8.83177 + 12.8452i 0.400617 + 0.582671i
\(487\) 27.2107 + 27.2107i 1.23303 + 1.23303i 0.962793 + 0.270239i \(0.0871028\pi\)
0.270239 + 0.962793i \(0.412897\pi\)
\(488\) 2.12517 + 2.12517i 0.0962021 + 0.0962021i
\(489\) −38.1292 7.47918i −1.72426 0.338220i
\(490\) −1.67061 14.9437i −0.0754704 0.675087i
\(491\) 40.4871i 1.82716i 0.406662 + 0.913579i \(0.366693\pi\)
−0.406662 + 0.913579i \(0.633307\pi\)
\(492\) −6.19347 9.21612i −0.279223 0.415495i
\(493\) −11.2713 + 11.2713i −0.507636 + 0.507636i
\(494\) 4.34904 0.195673
\(495\) 15.4874 + 27.7307i 0.696108 + 1.24640i
\(496\) −3.53345 −0.158656
\(497\) −1.36357 + 1.36357i −0.0611646 + 0.0611646i
\(498\) −10.5761 15.7376i −0.473926 0.705220i
\(499\) 5.75646i 0.257695i 0.991664 + 0.128847i \(0.0411277\pi\)
−0.991664 + 0.128847i \(0.958872\pi\)
\(500\) 10.0605 + 4.87720i 0.449918 + 0.218115i
\(501\) 40.6637 + 7.97634i 1.81672 + 0.356357i
\(502\) 15.1165 + 15.1165i 0.674681 + 0.674681i
\(503\) −25.9616 25.9616i −1.15757 1.15757i −0.984997 0.172573i \(-0.944792\pi\)
−0.172573 0.984997i \(-0.555208\pi\)
\(504\) 1.45755 + 0.594689i 0.0649244 + 0.0264895i
\(505\) −19.6879 + 24.6439i −0.876100 + 1.09664i
\(506\) 37.6911i 1.67557i
\(507\) −8.50213 + 5.71365i −0.377593 + 0.253752i
\(508\) 11.5688 11.5688i 0.513282 0.513282i
\(509\) 5.27569 0.233841 0.116920 0.993141i \(-0.462698\pi\)
0.116920 + 0.993141i \(0.462698\pi\)
\(510\) −15.1448 1.25021i −0.670625 0.0553602i
\(511\) 5.57794 0.246754
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 1.05428 + 5.08807i 0.0465475 + 0.224644i
\(514\) 10.0213i 0.442020i
\(515\) −16.2316 + 1.81458i −0.715248 + 0.0799601i
\(516\) 3.20637 16.3462i 0.141152 0.719601i
\(517\) −27.7833 27.7833i −1.22191 1.22191i
\(518\) 1.15859 + 1.15859i 0.0509055 + 0.0509055i
\(519\) −2.84918 + 14.5252i −0.125065 + 0.637586i
\(520\) −7.59785 6.06989i −0.333188 0.266182i
\(521\) 1.12070i 0.0490988i 0.999699 + 0.0245494i \(0.00781510\pi\)
−0.999699 + 0.0245494i \(0.992185\pi\)
\(522\) −4.72371 11.2349i −0.206751 0.491740i
\(523\) −3.66564 + 3.66564i −0.160287 + 0.160287i −0.782694 0.622407i \(-0.786155\pi\)
0.622407 + 0.782694i \(0.286155\pi\)
\(524\) 12.1137 0.529188
\(525\) 4.54241 0.131621i 0.198247 0.00574440i
\(526\) −14.6667 −0.639500
\(527\) 9.80341 9.80341i 0.427043 0.427043i
\(528\) 6.80679 4.57434i 0.296227 0.199072i
\(529\) 40.3668i 1.75508i
\(530\) 16.4502 + 13.1420i 0.714551 + 0.570851i
\(531\) 6.80245 16.6724i 0.295201 0.723521i
\(532\) 0.371042 + 0.371042i 0.0160867 + 0.0160867i
\(533\) 19.7148 + 19.7148i 0.853943 + 0.853943i
\(534\) 12.1230 + 2.37796i 0.524612 + 0.102905i
\(535\) 18.4056 2.05763i 0.795745 0.0889591i
\(536\) 5.67279i 0.245027i
\(537\) 7.46659 + 11.1106i 0.322207 + 0.479456i
\(538\) 9.83936 9.83936i 0.424205 0.424205i
\(539\) −31.8403 −1.37146
\(540\) 5.25950 10.3604i 0.226333 0.445840i
\(541\) 35.1833 1.51265 0.756324 0.654197i \(-0.226993\pi\)
0.756324 + 0.654197i \(0.226993\pi\)
\(542\) 6.92611 6.92611i 0.297502 0.297502i
\(543\) 14.9917 + 22.3083i 0.643357 + 0.957340i
\(544\) 3.92368i 0.168227i
\(545\) −14.7194 + 18.4247i −0.630509 + 0.789226i
\(546\) −3.87877 0.760836i −0.165996 0.0325608i
\(547\) −11.8492 11.8492i −0.506635 0.506635i 0.406857 0.913492i \(-0.366625\pi\)
−0.913492 + 0.406857i \(0.866625\pi\)
\(548\) −1.08854 1.08854i −0.0465001 0.0465001i
\(549\) 3.40613 8.34823i 0.145370 0.356294i
\(550\) 12.6303 20.0237i 0.538558 0.853814i
\(551\) 4.06253i 0.173070i
\(552\) 11.4437 7.69044i 0.487075 0.327327i
\(553\) 2.94381 2.94381i 0.125184 0.125184i
\(554\) −6.48607 −0.275567
\(555\) 9.22593 7.81888i 0.391619 0.331893i
\(556\) −6.34474 −0.269077
\(557\) −10.8257 + 10.8257i −0.458701 + 0.458701i −0.898229 0.439528i \(-0.855146\pi\)
0.439528 + 0.898229i \(0.355146\pi\)
\(558\) 4.10852 + 9.77176i 0.173927 + 0.413671i
\(559\) 41.8261i 1.76906i
\(560\) −0.130360 1.16607i −0.00550869 0.0492756i
\(561\) −6.19385 + 31.5765i −0.261505 + 1.33316i
\(562\) −8.56294 8.56294i −0.361206 0.361206i
\(563\) −15.9790 15.9790i −0.673433 0.673433i 0.285073 0.958506i \(-0.407982\pi\)
−0.958506 + 0.285073i \(0.907982\pi\)
\(564\) −2.76662 + 14.1044i −0.116496 + 0.593900i
\(565\) 4.10626 + 36.7308i 0.172752 + 1.54528i
\(566\) 1.87716i 0.0789029i
\(567\) −0.0501524 4.72233i −0.00210620 0.198319i
\(568\) 2.59861 2.59861i 0.109035 0.109035i
\(569\) 18.1067 0.759073 0.379536 0.925177i \(-0.376084\pi\)
0.379536 + 0.925177i \(0.376084\pi\)
\(570\) 2.95464 2.50402i 0.123756 0.104882i
\(571\) −19.9248 −0.833826 −0.416913 0.908946i \(-0.636888\pi\)
−0.416913 + 0.908946i \(0.636888\pi\)
\(572\) −14.5608 + 14.5608i −0.608819 + 0.608819i
\(573\) 19.4189 13.0500i 0.811235 0.545171i
\(574\) 3.36397i 0.140409i
\(575\) 21.2342 33.6642i 0.885529 1.40389i
\(576\) −2.77770 1.13332i −0.115737 0.0472215i
\(577\) −9.32107 9.32107i −0.388041 0.388041i 0.485947 0.873988i \(-0.338475\pi\)
−0.873988 + 0.485947i \(0.838475\pi\)
\(578\) 1.13470 + 1.13470i 0.0471972 + 0.0471972i
\(579\) 7.10943 + 1.39454i 0.295458 + 0.0579552i
\(580\) −5.67001 + 7.09731i −0.235434 + 0.294700i
\(581\) 5.74438i 0.238317i
\(582\) −6.85243 10.1967i −0.284042 0.422666i
\(583\) 31.5258 31.5258i 1.30567 1.30567i
\(584\) −10.6301 −0.439875
\(585\) −7.95188 + 28.0696i −0.328770 + 1.16054i
\(586\) 17.8907 0.739057
\(587\) 29.1721 29.1721i 1.20406 1.20406i 0.231141 0.972920i \(-0.425754\pi\)
0.972920 0.231141i \(-0.0742458\pi\)
\(588\) 6.49666 + 9.66728i 0.267918 + 0.398672i
\(589\) 3.53345i 0.145593i
\(590\) −13.3383 + 1.49114i −0.549131 + 0.0613893i
\(591\) −35.0260 6.87049i −1.44078 0.282614i
\(592\) −2.20796 2.20796i −0.0907467 0.0907467i
\(593\) −3.55825 3.55825i −0.146120 0.146120i 0.630262 0.776382i \(-0.282947\pi\)
−0.776382 + 0.630262i \(0.782947\pi\)
\(594\) −20.5649 13.5054i −0.843790 0.554132i
\(595\) 3.59691 + 2.87355i 0.147459 + 0.117804i
\(596\) 19.2260i 0.787529i
\(597\) −8.49397 + 5.70817i −0.347635 + 0.233620i
\(598\) −24.4799 + 24.4799i −1.00106 + 1.00106i
\(599\) −30.7070 −1.25466 −0.627328 0.778755i \(-0.715851\pi\)
−0.627328 + 0.778755i \(0.715851\pi\)
\(600\) −8.65662 + 0.250834i −0.353405 + 0.0102403i
\(601\) 40.1017 1.63578 0.817891 0.575373i \(-0.195143\pi\)
0.817891 + 0.575373i \(0.195143\pi\)
\(602\) −3.56843 + 3.56843i −0.145438 + 0.145438i
\(603\) −15.6881 + 6.59605i −0.638870 + 0.268612i
\(604\) 5.62170i 0.228744i
\(605\) −19.9491 15.9373i −0.811047 0.647942i
\(606\) 4.70296 23.9759i 0.191045 0.973954i
\(607\) −19.8610 19.8610i −0.806134 0.806134i 0.177912 0.984046i \(-0.443066\pi\)
−0.984046 + 0.177912i \(0.943066\pi\)
\(608\) −0.707107 0.707107i −0.0286770 0.0286770i
\(609\) −0.710713 + 3.62324i −0.0287995 + 0.146821i
\(610\) −6.67879 + 0.746645i −0.270416 + 0.0302308i
\(611\) 36.0898i 1.46004i
\(612\) 10.8510 4.56227i 0.438624 0.184419i
\(613\) 22.6569 22.6569i 0.915102 0.915102i −0.0815658 0.996668i \(-0.525992\pi\)
0.996668 + 0.0815658i \(0.0259921\pi\)
\(614\) −23.2339 −0.937644
\(615\) 24.7449 + 2.04269i 0.997809 + 0.0823692i
\(616\) −2.48454 −0.100105
\(617\) 15.5110 15.5110i 0.624451 0.624451i −0.322215 0.946666i \(-0.604427\pi\)
0.946666 + 0.322215i \(0.104427\pi\)
\(618\) 10.5004 7.05655i 0.422389 0.283856i
\(619\) 15.5862i 0.626463i 0.949677 + 0.313232i \(0.101412\pi\)
−0.949677 + 0.313232i \(0.898588\pi\)
\(620\) 4.93157 6.17299i 0.198057 0.247913i
\(621\) −34.5741 22.7054i −1.38741 0.911137i
\(622\) −4.59184 4.59184i −0.184116 0.184116i
\(623\) −2.64649 2.64649i −0.106029 0.106029i
\(624\) 7.39190 + 1.44995i 0.295913 + 0.0580444i
\(625\) −22.5618 + 10.7688i −0.902471 + 0.430751i
\(626\) 22.0074i 0.879591i
\(627\) −4.57434 6.80679i −0.182681 0.271837i
\(628\) −10.3090 + 10.3090i −0.411374 + 0.411374i
\(629\) 12.2518 0.488512
\(630\) −3.07321 + 1.71636i −0.122440 + 0.0683816i
\(631\) 25.8671 1.02975 0.514876 0.857264i \(-0.327838\pi\)
0.514876 + 0.857264i \(0.327838\pi\)
\(632\) −5.61011 + 5.61011i −0.223158 + 0.223158i
\(633\) 6.23447 + 9.27713i 0.247798 + 0.368733i
\(634\) 30.8686i 1.22595i
\(635\) 4.06450 + 36.3572i 0.161295 + 1.44279i
\(636\) −16.0043 3.13930i −0.634611 0.124481i
\(637\) −20.6799 20.6799i −0.819368 0.819368i
\(638\) 13.6016 + 13.6016i 0.538492 + 0.538492i
\(639\) −10.2080 4.16492i −0.403822 0.164762i
\(640\) 0.248430 + 2.22222i 0.00982007 + 0.0878411i
\(641\) 1.67735i 0.0662515i −0.999451 0.0331258i \(-0.989454\pi\)
0.999451 0.0331258i \(-0.0105462\pi\)
\(642\) −11.9069 + 8.00171i −0.469926 + 0.315802i
\(643\) −23.1508 + 23.1508i −0.912978 + 0.912978i −0.996505 0.0835277i \(-0.973381\pi\)
0.0835277 + 0.996505i \(0.473381\pi\)
\(644\) −4.17704 −0.164599
\(645\) 24.0820 + 28.4157i 0.948228 + 1.11887i
\(646\) 3.92368 0.154375
\(647\) −1.87972 + 1.87972i −0.0738993 + 0.0738993i −0.743090 0.669191i \(-0.766641\pi\)
0.669191 + 0.743090i \(0.266641\pi\)
\(648\) 0.0955769 + 8.99949i 0.00375462 + 0.353533i
\(649\) 28.4198i 1.11558i
\(650\) 21.2084 4.80193i 0.831861 0.188347i
\(651\) 0.618153 3.15137i 0.0242273 0.123512i
\(652\) −15.8628 15.8628i −0.621235 0.621235i
\(653\) 4.68423 + 4.68423i 0.183308 + 0.183308i 0.792796 0.609488i \(-0.208625\pi\)
−0.609488 + 0.792796i \(0.708625\pi\)
\(654\) 3.51610 17.9252i 0.137490 0.700932i
\(655\) −16.9068 + 21.1628i −0.660605 + 0.826898i
\(656\) 6.41083i 0.250301i
\(657\) 12.3601 + 29.3975i 0.482214 + 1.14690i
\(658\) 3.07903 3.07903i 0.120033 0.120033i
\(659\) −29.9598 −1.16707 −0.583533 0.812089i \(-0.698330\pi\)
−0.583533 + 0.812089i \(0.698330\pi\)
\(660\) −1.50868 + 18.2759i −0.0587252 + 0.711388i
\(661\) 25.1252 0.977257 0.488629 0.872492i \(-0.337497\pi\)
0.488629 + 0.872492i \(0.337497\pi\)
\(662\) −7.74809 + 7.74809i −0.301138 + 0.301138i
\(663\) −24.5314 + 16.4857i −0.952720 + 0.640252i
\(664\) 10.9472i 0.424836i
\(665\) −1.16607 + 0.130360i −0.0452184 + 0.00505513i
\(666\) −3.53882 + 8.67343i −0.137126 + 0.336089i
\(667\) 22.8672 + 22.8672i 0.885421 + 0.885421i
\(668\) 16.9172 + 16.9172i 0.654548 + 0.654548i
\(669\) 30.0301 + 5.89052i 1.16103 + 0.227741i
\(670\) 9.91047 + 7.91742i 0.382875 + 0.305877i
\(671\) 14.2304i 0.549359i
\(672\) 0.506942 + 0.754350i 0.0195557 + 0.0290997i
\(673\) 31.2587 31.2587i 1.20493 1.20493i 0.232285 0.972648i \(-0.425380\pi\)
0.972648 0.232285i \(-0.0746201\pi\)
\(674\) −14.1153 −0.543702
\(675\) 10.7592 + 23.6483i 0.414121 + 0.910222i
\(676\) −5.91417 −0.227468
\(677\) −23.6302 + 23.6302i −0.908182 + 0.908182i −0.996125 0.0879438i \(-0.971970\pi\)
0.0879438 + 0.996125i \(0.471970\pi\)
\(678\) −15.9684 23.7617i −0.613265 0.912561i
\(679\) 3.72188i 0.142833i
\(680\) −6.85474 5.47622i −0.262867 0.210003i
\(681\) −7.50733 1.47259i −0.287681 0.0564298i
\(682\) −11.8302 11.8302i −0.453001 0.453001i
\(683\) 18.9685 + 18.9685i 0.725809 + 0.725809i 0.969782 0.243973i \(-0.0784507\pi\)
−0.243973 + 0.969782i \(0.578451\pi\)
\(684\) −1.13332 + 2.77770i −0.0433335 + 0.106208i
\(685\) 3.42095 0.382440i 0.130708 0.0146123i
\(686\) 7.20178i 0.274965i
\(687\) 6.41291 4.30964i 0.244668 0.164423i
\(688\) 6.80047 6.80047i 0.259266 0.259266i
\(689\) 40.9513 1.56012
\(690\) −2.53641 + 30.7257i −0.0965594 + 1.16971i
\(691\) 4.36817 0.166173 0.0830866 0.996542i \(-0.473522\pi\)
0.0830866 + 0.996542i \(0.473522\pi\)
\(692\) −6.04290 + 6.04290i −0.229717 + 0.229717i
\(693\) 2.88890 + 6.87101i 0.109740 + 0.261008i
\(694\) 9.24486i 0.350930i
\(695\) 8.85524 11.0844i 0.335899 0.420454i
\(696\) 1.35443 6.90493i 0.0513395 0.261731i
\(697\) 17.7866 + 17.7866i 0.673716 + 0.673716i
\(698\) −11.7869 11.7869i −0.446140 0.446140i
\(699\) −1.08096 + 5.51077i −0.0408856 + 0.208436i
\(700\) 2.21909 + 1.39973i 0.0838738 + 0.0529048i
\(701\) 20.9191i 0.790102i 0.918659 + 0.395051i \(0.129273\pi\)
−0.918659 + 0.395051i \(0.870727\pi\)
\(702\) −4.58510 22.1282i −0.173053 0.835177i
\(703\) −2.20796 + 2.20796i −0.0832748 + 0.0832748i
\(704\) 4.73487 0.178452
\(705\) −20.7792 24.5185i −0.782590 0.923422i
\(706\) −26.5488 −0.999178
\(707\) −5.23402 + 5.23402i −0.196846 + 0.196846i
\(708\) 8.62876 5.79875i 0.324289 0.217930i
\(709\) 46.0079i 1.72786i −0.503610 0.863931i \(-0.667995\pi\)
0.503610 0.863931i \(-0.332005\pi\)
\(710\) 0.912977 + 8.16664i 0.0342634 + 0.306488i
\(711\) 22.0380 + 8.99162i 0.826488 + 0.337212i
\(712\) 5.04349 + 5.04349i 0.189013 + 0.189013i
\(713\) −19.8891 19.8891i −0.744851 0.744851i
\(714\) −3.49941 0.686422i −0.130962 0.0256887i
\(715\) −5.11571 45.7604i −0.191317 1.71134i
\(716\) 7.72862i 0.288832i
\(717\) −3.96803 5.90457i −0.148189 0.220510i
\(718\) 21.9852 21.9852i 0.820480 0.820480i
\(719\) 25.7542 0.960468 0.480234 0.877140i \(-0.340552\pi\)
0.480234 + 0.877140i \(0.340552\pi\)
\(720\) 5.85671 3.27093i 0.218267 0.121900i
\(721\) −3.83275 −0.142739
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) −24.2454 36.0781i −0.901697 1.34176i
\(724\) 15.5179i 0.576717i
\(725\) −4.48559 19.8112i −0.166590 0.735770i
\(726\) 19.4084 + 3.80703i 0.720312 + 0.141292i
\(727\) −11.1708 11.1708i −0.414302 0.414302i 0.468932 0.883234i \(-0.344639\pi\)
−0.883234 + 0.468932i \(0.844639\pi\)
\(728\) −1.61368 1.61368i −0.0598069 0.0598069i
\(729\) 24.7770 10.7285i 0.917667 0.397351i
\(730\) 14.8362 18.5709i 0.549112 0.687340i
\(731\) 37.7353i 1.39569i
\(732\) 4.32060 2.90355i 0.159694 0.107318i
\(733\) 9.70478 9.70478i 0.358454 0.358454i −0.504789 0.863243i \(-0.668430\pi\)
0.863243 + 0.504789i \(0.168430\pi\)
\(734\) −1.07637 −0.0397295
\(735\) −25.9562 2.14269i −0.957408 0.0790342i
\(736\) 7.96032 0.293421
\(737\) 18.9928 18.9928i 0.699610 0.699610i
\(738\) −17.7292 + 7.45420i −0.652619 + 0.274393i
\(739\) 31.4666i 1.15752i 0.815499 + 0.578759i \(0.196463\pi\)
−0.815499 + 0.578759i \(0.803537\pi\)
\(740\) 6.93896 0.775731i 0.255081 0.0285164i
\(741\) 1.44995 7.39190i 0.0532652 0.271548i
\(742\) 3.49379 + 3.49379i 0.128261 + 0.128261i
\(743\) −0.387245 0.387245i −0.0142066 0.0142066i 0.699968 0.714174i \(-0.253198\pi\)
−0.714174 + 0.699968i \(0.753198\pi\)
\(744\) −1.17803 + 6.00566i −0.0431888 + 0.220178i
\(745\) −33.5882 26.8334i −1.23058 0.983101i
\(746\) 11.3284i 0.414760i
\(747\) −30.2747 + 12.7289i −1.10769 + 0.465727i
\(748\) −13.1367 + 13.1367i −0.480326 + 0.480326i
\(749\) 4.34611 0.158803
\(750\) 11.6437 15.4733i 0.425167 0.565007i
\(751\) 8.65270 0.315742 0.157871 0.987460i \(-0.449537\pi\)
0.157871 + 0.987460i \(0.449537\pi\)
\(752\) −5.86781 + 5.86781i −0.213977 + 0.213977i
\(753\) 30.7326 20.6531i 1.11996 0.752641i
\(754\) 17.6681i 0.643435i
\(755\) 9.82120 + 7.84611i 0.357430 + 0.285549i
\(756\) 1.49671 2.27907i 0.0544348 0.0828890i
\(757\) −2.24043 2.24043i −0.0814299 0.0814299i 0.665219 0.746649i \(-0.268338\pi\)
−0.746649 + 0.665219i \(0.768338\pi\)
\(758\) −10.6495 10.6495i −0.386808 0.386808i
\(759\) 64.0621 + 12.5660i 2.32531 + 0.456117i
\(760\) 2.22222 0.248430i 0.0806086 0.00901151i
\(761\) 9.75042i 0.353452i −0.984260 0.176726i \(-0.943449\pi\)
0.984260 0.176726i \(-0.0565507\pi\)
\(762\) −15.8060 23.5200i −0.572592 0.852039i
\(763\) −3.91314 + 3.91314i −0.141665 + 0.141665i
\(764\) 13.5080 0.488701
\(765\) −7.17415 + 25.3243i −0.259382 + 0.915602i
\(766\) 30.3805 1.09769
\(767\) −18.4583 + 18.4583i −0.666492 + 0.666492i
\(768\) −0.966096 1.43759i −0.0348610 0.0518745i
\(769\) 49.3395i 1.77923i −0.456714 0.889614i \(-0.650974\pi\)
0.456714 0.889614i \(-0.349026\pi\)
\(770\) 3.46763 4.34053i 0.124965 0.156422i
\(771\) −17.0328 3.34105i −0.613421 0.120325i
\(772\) 2.95772 + 2.95772i 0.106451 + 0.106451i
\(773\) −22.1512 22.1512i −0.796725 0.796725i 0.185853 0.982578i \(-0.440495\pi\)
−0.982578 + 0.185853i \(0.940495\pi\)
\(774\) −26.7140 10.8995i −0.960215 0.391774i
\(775\) 3.90140 + 17.2311i 0.140143 + 0.618958i
\(776\) 7.09290i 0.254620i
\(777\) 2.35548 1.58294i 0.0845023 0.0567877i