Properties

Label 570.2.k.a.77.7
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 77.7
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.43759 + 0.966096i) q^{3} -1.00000i q^{4} +(-1.74702 - 1.39568i) q^{5} +(-1.69966 + 0.333395i) q^{6} +(0.371042 + 0.371042i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.13332 + 2.77770i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.43759 + 0.966096i) 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} +(0.966096 - 1.43759i) q^{12} +(3.07524 - 3.07524i) q^{13} -0.524733 q^{14} +(-1.16313 - 3.69420i) q^{15} -1.00000 q^{16} +(-2.77446 + 2.77446i) q^{17} +(-2.76550 - 1.16275i) 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} +(-1.05428 + 5.08807i) q^{27} +(0.371042 - 0.371042i) q^{28} +4.06253 q^{29} +(3.43465 + 1.78974i) q^{30} +3.53345 q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.57434 + 6.80679i) 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} +(-0.754350 - 0.506942i) q^{42} +(-6.80047 + 6.80047i) q^{43} +4.73487 q^{44} +(1.89686 - 6.43443i) q^{45} -7.96032 q^{46} +(-5.86781 + 5.86781i) q^{47} +(-1.43759 - 0.966096i) 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} +(-0.966096 + 1.43759i) q^{57} +(-2.87264 + 2.87264i) q^{58} +6.00225 q^{59} +(-3.69420 + 1.16313i) q^{60} -3.00545 q^{61} +(-2.49852 + 2.49852i) q^{62} +(-0.610134 + 1.45115i) 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} +(-1.16275 + 2.76550i) q^{72} +(7.51659 - 7.51659i) q^{73} -3.12253 q^{74} +(-3.12394 + 8.07719i) q^{75} +1.00000 q^{76} +(-1.75684 + 1.75684i) q^{77} +(-4.20159 + 6.25213i) 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} +(5.84025 + 3.92480i) q^{87} +(-3.34806 + 3.34806i) q^{88} +7.13257 q^{89} +(3.20855 + 5.89111i) q^{90} +2.28209 q^{91} +(5.62880 - 5.62880i) q^{92} +(5.07964 + 3.41365i) 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
\(3\) 1.43759 + 0.966096i 0.829992 + 0.557776i
\(4\) 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 \(0.253031\pi\)
−0.700341 + 0.713808i \(0.746969\pi\)
\(12\) 0.966096 1.43759i 0.278888 0.414996i
\(13\) 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
\(15\) −1.16313 3.69420i −0.300318 0.953839i
\(16\) −1.00000 −0.250000
\(17\) −2.77446 + 2.77446i −0.672906 + 0.672906i −0.958385 0.285479i \(-0.907847\pi\)
0.285479 + 0.958385i \(0.407847\pi\)
\(18\) −2.76550 1.16275i −0.651835 0.274063i
\(19\) 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 \(0.0616146\pi\)
0.192362 + 0.981324i \(0.438385\pi\)
\(24\) 0.333395 + 1.69966i 0.0680540 + 0.346942i
\(25\) 1.10414 + 4.87656i 0.220827 + 0.975313i
\(26\) 4.34904i 0.852917i
\(27\) −1.05428 + 5.08807i −0.202896 + 0.979200i
\(28\) 0.371042 0.371042i 0.0701204 0.0701204i
\(29\) 4.06253 0.754393 0.377197 0.926133i \(-0.376888\pi\)
0.377197 + 0.926133i \(0.376888\pi\)
\(30\) 3.43465 + 1.78974i 0.627078 + 0.326761i
\(31\) 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
\(33\) −4.57434 + 6.80679i −0.796290 + 1.18491i
\(34\) 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 \(-0.833112\pi\)
0.865678 0.500601i \(-0.166888\pi\)
\(42\) −0.754350 0.506942i −0.116399 0.0782229i
\(43\) −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
\(45\) 1.89686 6.43443i 0.282767 0.959189i
\(46\) −7.96032 −1.17369
\(47\) −5.86781 + 5.86781i −0.855908 + 0.855908i −0.990853 0.134945i \(-0.956914\pi\)
0.134945 + 0.990853i \(0.456914\pi\)
\(48\) −1.43759 0.966096i −0.207498 0.139444i
\(49\) 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 0.0820496 0.996628i \(-0.473853\pi\)
−0.996628 + 0.0820496i \(0.973853\pi\)
\(54\) −2.85232 4.34330i −0.388152 0.591048i
\(55\) 6.60838 8.27189i 0.891073 1.11538i
\(56\) 0.524733i 0.0701204i
\(57\) −0.966096 + 1.43759i −0.127963 + 0.190413i
\(58\) −2.87264 + 2.87264i −0.377197 + 0.377197i
\(59\) 6.00225 0.781426 0.390713 0.920513i \(-0.372228\pi\)
0.390713 + 0.920513i \(0.372228\pi\)
\(60\) −3.69420 + 1.16313i −0.476920 + 0.150159i
\(61\) −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
\(63\) −0.610134 + 1.45115i −0.0768696 + 0.182828i
\(64\) 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 \(-0.930024\pi\)
0.975933 0.218070i \(-0.0699762\pi\)
\(72\) −1.16275 + 2.76550i −0.137032 + 0.325918i
\(73\) 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
\(75\) −3.12394 + 8.07719i −0.360721 + 0.932674i
\(76\) 1.00000 0.114708
\(77\) −1.75684 + 1.75684i −0.200210 + 0.200210i
\(78\) −4.20159 + 6.25213i −0.475737 + 0.707914i
\(79\) 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 0.140421 0.990092i \(-0.455154\pi\)
−0.990092 + 0.140421i \(0.955154\pi\)
\(84\) 0.891868 0.174943i 0.0973108 0.0190879i
\(85\) 8.71931 0.974762i 0.945742 0.105728i
\(86\) 9.61732i 1.03706i
\(87\) 5.84025 + 3.92480i 0.626140 + 0.420782i
\(88\) −3.34806 + 3.34806i −0.356904 + 0.356904i
\(89\) 7.13257 0.756051 0.378026 0.925795i \(-0.376603\pi\)
0.378026 + 0.925795i \(0.376603\pi\)
\(90\) 3.20855 + 5.89111i 0.338211 + 0.620978i
\(91\) 2.28209 0.239228
\(92\) 5.62880 5.62880i 0.586843 0.586843i
\(93\) 5.07964 + 3.41365i 0.526734 + 0.353979i
\(94\) 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 \(-0.752374\pi\)
0.712361 0.701813i \(-0.247626\pi\)
\(102\) 3.79066 5.64064i 0.375331 0.558507i
\(103\) −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
\(105\) 0.939137 1.80227i 0.0916503 0.175884i
\(106\) 9.41616 0.914579
\(107\) −5.85663 + 5.85663i −0.566182 + 0.566182i −0.931057 0.364875i \(-0.881112\pi\)
0.364875 + 0.931057i \(0.381112\pi\)
\(108\) 5.08807 + 1.05428i 0.489600 + 0.101448i
\(109\) 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 \(-0.966512\pi\)
−0.105011 0.994471i \(-0.533488\pi\)
\(114\) −0.333395 1.69966i −0.0312253 0.159188i
\(115\) −1.97758 17.6896i −0.184411 1.64957i
\(116\) 4.06253i 0.377197i
\(117\) 12.0273 + 5.05685i 1.11192 + 0.467506i
\(118\) −4.24423 + 4.24423i −0.390713 + 0.390713i
\(119\) −2.05889 −0.188738
\(120\) 1.78974 3.43465i 0.163380 0.313539i
\(121\) −11.4190 −1.03809
\(122\) 2.12517 2.12517i 0.192404 0.192404i
\(123\) 6.19347 9.21612i 0.558447 0.830990i
\(124\) 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 \(-0.822497\pi\)
0.848505 0.529188i \(-0.177503\pi\)
\(132\) 6.80679 + 4.57434i 0.592455 + 0.398145i
\(133\) −0.371042 + 0.371042i −0.0321734 + 0.0321734i
\(134\) −5.67279 −0.490055
\(135\) 8.94318 7.41751i 0.769707 0.638398i
\(136\) −3.92368 −0.336453
\(137\) −1.08854 + 1.08854i −0.0930002 + 0.0930002i −0.752076 0.659076i \(-0.770948\pi\)
0.659076 + 0.752076i \(0.270948\pi\)
\(138\) −11.4437 7.69044i −0.974149 0.654653i
\(139\) 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
\(147\) 6.49666 9.66728i 0.535836 0.797344i
\(148\) 2.20796 2.20796i 0.181493 0.181493i
\(149\) 19.2260 1.57506 0.787529 0.616278i \(-0.211360\pi\)
0.787529 + 0.616278i \(0.211360\pi\)
\(150\) −3.50248 7.92039i −0.285976 0.646697i
\(151\) 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
\(153\) −10.8510 4.56227i −0.877248 0.368838i
\(154\) 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
\(162\) 0.0955769 8.99949i 0.00750923 0.707067i
\(163\) 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
\(165\) 17.4916 5.50725i 1.36172 0.428738i
\(166\) 10.9472 0.849671
\(167\) 16.9172 16.9172i 1.30910 1.30910i 0.387027 0.922068i \(-0.373502\pi\)
0.922068 0.387027i \(-0.126498\pi\)
\(168\) −0.506942 + 0.754350i −0.0391115 + 0.0581993i
\(169\) 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 0.898469 0.439036i \(-0.144680\pi\)
−0.439036 + 0.898469i \(0.644680\pi\)
\(174\) −6.90493 + 1.35443i −0.523461 + 0.102679i
\(175\) −1.39973 + 2.21909i −0.105810 + 0.167748i
\(176\) 4.73487i 0.356904i
\(177\) 8.62876 + 5.79875i 0.648577 + 0.435861i
\(178\) −5.04349 + 5.04349i −0.378026 + 0.378026i
\(179\) 7.72862 0.577664 0.288832 0.957380i \(-0.406733\pi\)
0.288832 + 0.957380i \(0.406733\pi\)
\(180\) −6.43443 1.89686i −0.479594 0.141384i
\(181\) −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
\(183\) −4.32060 2.90355i −0.319388 0.214637i
\(184\) 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 \(-0.837471\pi\)
0.872451 0.488701i \(-0.162529\pi\)
\(192\) −0.966096 + 1.43759i −0.0697220 + 0.103749i
\(193\) −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
\(195\) −14.9374 7.78366i −1.06969 0.557400i
\(196\) −6.72466 −0.480333
\(197\) −14.5718 + 14.5718i −1.03820 + 1.03820i −0.0389574 + 0.999241i \(0.512404\pi\)
−0.999241 + 0.0389574i \(0.987596\pi\)
\(198\) 5.50547 13.0943i 0.391257 0.930571i
\(199\) 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
\(207\) −9.25588 + 22.0143i −0.643328 + 1.53010i
\(208\) −3.07524 + 3.07524i −0.213229 + 0.213229i
\(209\) −4.73487 −0.327518
\(210\) 0.610330 + 1.93847i 0.0421168 + 0.133767i
\(211\) −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
\(213\) 3.55039 5.28311i 0.243268 0.361993i
\(214\) 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
\(222\) −4.48891 3.01666i −0.301276 0.202465i
\(223\) −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
\(225\) −12.2943 + 8.59365i −0.819618 + 0.572910i
\(226\) 16.5288 1.09948
\(227\) −3.12326 + 3.12326i −0.207298 + 0.207298i −0.803118 0.595820i \(-0.796827\pi\)
0.595820 + 0.803118i \(0.296827\pi\)
\(228\) 1.43759 + 0.966096i 0.0952066 + 0.0639813i
\(229\) 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 0.778205 0.628010i \(-0.216130\pi\)
−0.628010 + 0.778205i \(0.716130\pi\)
\(234\) −12.0803 + 4.92884i −0.789715 + 0.322209i
\(235\) 18.4408 2.06156i 1.20294 0.134481i
\(236\) 6.00225i 0.390713i
\(237\) 7.66491 11.4057i 0.497889 0.740878i
\(238\) 1.45585 1.45585i 0.0943689 0.0943689i
\(239\) −4.10728 −0.265678 −0.132839 0.991138i \(-0.542409\pi\)
−0.132839 + 0.991138i \(0.542409\pi\)
\(240\) 1.16313 + 3.69420i 0.0750794 + 0.238460i
\(241\) 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
\(243\) −15.3280 + 2.83794i −0.983289 + 0.182054i
\(244\) 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 \(-0.764281\pi\)
0.738110 0.674681i \(-0.235719\pi\)
\(252\) 1.45115 + 0.610134i 0.0914139 + 0.0384348i
\(253\) −26.6516 + 26.6516i −1.67557 + 1.67557i
\(254\) −16.3607 −1.02656
\(255\) 13.4765 + 7.02238i 0.843930 + 0.439759i
\(256\) 1.00000 0.0625000
\(257\) −7.08612 + 7.08612i −0.442020 + 0.442020i −0.892690 0.450670i \(-0.851185\pi\)
0.450670 + 0.892690i \(0.351185\pi\)
\(258\) 9.29126 13.8257i 0.578448 0.860753i
\(259\) 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 0.950432 0.310932i \(-0.100641\pi\)
−0.310932 + 0.950432i \(0.600641\pi\)
\(264\) −8.04767 + 1.57858i −0.495300 + 0.0971549i
\(265\) 2.33926 + 20.9248i 0.143700 + 1.28540i
\(266\) 0.524733i 0.0321734i
\(267\) 10.2537 + 6.89075i 0.627516 + 0.421707i
\(268\) 4.01127 4.01127i 0.245027 0.245027i
\(269\) −13.9150 −0.848410 −0.424205 0.905566i \(-0.639446\pi\)
−0.424205 + 0.905566i \(0.639446\pi\)
\(270\) −1.07881 + 11.5688i −0.0656544 + 0.704052i
\(271\) 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
\(273\) 3.28070 + 2.20471i 0.198557 + 0.133435i
\(274\) 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 \(0.117635\pi\)
−0.932486 + 0.361206i \(0.882365\pi\)
\(282\) 8.01699 11.9296i 0.477405 0.710396i
\(283\) −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
\(285\) 3.69420 1.16313i 0.218826 0.0688976i
\(286\) −20.5921 −1.21764
\(287\) 2.37869 2.37869i 0.140409 0.140409i
\(288\) 2.76550 + 1.16275i 0.162959 + 0.0685158i
\(289\) 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 0.233339 0.972395i \(-0.425035\pi\)
−0.972395 + 0.233339i \(0.925035\pi\)
\(294\) 2.24197 + 11.4296i 0.130754 + 0.666590i
\(295\) −10.4860 8.37724i −0.610520 0.487742i
\(296\) 3.12253i 0.181493i
\(297\) −24.0914 4.99187i −1.39792 0.289657i
\(298\) −13.5949 + 13.5949i −0.787529 + 0.787529i
\(299\) 34.6198 2.00211
\(300\) 8.07719 + 3.12394i 0.466337 + 0.180361i
\(301\) −5.04653 −0.290877
\(302\) −3.97514 + 3.97514i −0.228744 + 0.228744i
\(303\) 13.6280 20.2790i 0.782909 1.16500i
\(304\) 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 \(0.0589423\pi\)
−0.982904 + 0.184116i \(0.941058\pi\)
\(312\) 6.25213 + 4.20159i 0.353957 + 0.237868i
\(313\) −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
\(315\) 3.09126 1.68363i 0.174173 0.0948619i
\(316\) −7.93390 −0.446317
\(317\) 21.8274 21.8274i 1.22595 1.22595i 0.260466 0.965483i \(-0.416124\pi\)
0.965483 0.260466i \(-0.0838762\pi\)
\(318\) 13.5366 + 9.09692i 0.759093 + 0.510130i
\(319\) 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
\(327\) −10.1888 + 15.1613i −0.563442 + 0.838422i
\(328\) 4.53314 4.53314i 0.250301 0.250301i
\(329\) −4.35441 −0.240066
\(330\) −8.47419 + 16.2626i −0.466489 + 0.895227i
\(331\) −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
\(333\) −3.63072 + 8.63536i −0.198962 + 0.473215i
\(334\) 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
\(342\) 1.16275 2.76550i 0.0628744 0.149541i
\(343\) 5.09243 5.09243i 0.274965 0.274965i
\(344\) −9.61732 −0.518531
\(345\) 14.2469 27.3409i 0.767029 1.47199i
\(346\) −8.54595 −0.459433
\(347\) −6.53710 + 6.53710i −0.350930 + 0.350930i −0.860456 0.509526i \(-0.829821\pi\)
0.509526 + 0.860456i \(0.329821\pi\)
\(348\) 3.92480 5.84025i 0.210391 0.313070i
\(349\) 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 1.00000 0.000821466i \(-0.000261481\pi\)
−0.000821466 1.00000i \(0.500261\pi\)
\(354\) −10.2018 + 2.00112i −0.542219 + 0.106358i
\(355\) −5.12911 + 6.42026i −0.272225 + 0.340752i
\(356\) 7.13257i 0.378026i
\(357\) −2.95983 1.98908i −0.156651 0.105273i
\(358\) −5.46496 + 5.46496i −0.288832 + 0.288832i
\(359\) −31.0918 −1.64096 −0.820480 0.571675i \(-0.806294\pi\)
−0.820480 + 0.571675i \(0.806294\pi\)
\(360\) 5.89111 3.20855i 0.310489 0.169105i
\(361\) −1.00000 −0.0526316
\(362\) 10.9728 10.9728i 0.576717 0.576717i
\(363\) −16.4158 11.0318i −0.861604 0.579020i
\(364\) 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
\(372\) 3.41365 5.07964i 0.176989 0.263367i
\(373\) 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
\(375\) 16.7308 9.75096i 0.863973 0.503537i
\(376\) −8.29833 −0.427954
\(377\) 12.4932 12.4932i 0.643435 0.643435i
\(378\) 0.553214 2.66988i 0.0284543 0.137324i
\(379\) 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 \(-0.967153\pi\)
−0.103010 0.994680i \(-0.532847\pi\)
\(384\) −0.333395 1.69966i −0.0170135 0.0867355i
\(385\) 5.52121 0.617235i 0.281387 0.0314572i
\(386\) 4.18285i 0.212901i
\(387\) −26.5967 11.1826i −1.35199 0.568441i
\(388\) 5.01544 5.01544i 0.254620 0.254620i
\(389\) 11.7608 0.596296 0.298148 0.954520i \(-0.403631\pi\)
0.298148 + 0.954520i \(0.403631\pi\)
\(390\) 16.0662 5.05848i 0.813546 0.256146i
\(391\) −31.2338 −1.57956
\(392\) 4.75505 4.75505i 0.240166 0.240166i
\(393\) 11.7030 17.4144i 0.590336 0.878443i
\(394\) 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 \(0.255813\pi\)
−0.694076 + 0.719901i \(0.744187\pi\)
\(402\) −8.15514 5.48046i −0.406741 0.273341i
\(403\) 10.8662 10.8662i 0.541283 0.541283i
\(404\) −14.1063 −0.701813
\(405\) 20.0226 2.02335i 0.994933 0.100541i
\(406\) −2.13174 −0.105797
\(407\) −10.4544 + 10.4544i −0.518206 + 0.518206i
\(408\) −5.64064 3.79066i −0.279253 0.187665i
\(409\) 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
\(417\) 6.12962 9.12112i 0.300169 0.446663i
\(418\) 3.34806 3.34806i 0.163759 0.163759i
\(419\) 33.3598 1.62974 0.814868 0.579647i \(-0.196810\pi\)
0.814868 + 0.579647i \(0.196810\pi\)
\(420\) −1.80227 0.939137i −0.0879420 0.0458252i
\(421\) −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
\(423\) −22.9491 9.64890i −1.11582 0.469145i
\(424\) 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 \(-0.895144\pi\)
0.946232 0.323490i \(-0.104856\pi\)
\(432\) 1.05428 5.08807i 0.0507240 0.244800i
\(433\) 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
\(435\) −4.72524 15.0078i −0.226558 0.719570i
\(436\) 10.5464 0.505079
\(437\) −5.62880 + 5.62880i −0.269262 + 0.269262i
\(438\) −10.2697 + 15.2816i −0.490703 + 0.730185i
\(439\) 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 \(0.00567159\pi\)
0.0178169 + 0.999841i \(0.494328\pi\)
\(444\) 5.30724 1.04104i 0.251871 0.0494054i
\(445\) −12.4607 9.95481i −0.590695 0.471903i
\(446\) 17.6683i 0.836618i
\(447\) 27.6391 + 18.5742i 1.30728 + 0.878529i
\(448\) −0.371042 + 0.371042i −0.0175301 + 0.0175301i
\(449\) −33.6163 −1.58645 −0.793226 0.608927i \(-0.791600\pi\)
−0.793226 + 0.608927i \(0.791600\pi\)
\(450\) 2.61674 14.7700i 0.123354 0.696264i
\(451\) 30.3544 1.42933
\(452\) −11.6877 + 11.6877i −0.549741 + 0.549741i
\(453\) 8.08168 + 5.43110i 0.379710 + 0.255175i
\(454\) 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 \(0.00907123\pi\)
−0.999594 + 0.0284942i \(0.990929\pi\)
\(462\) 2.40030 3.57174i 0.111672 0.166173i
\(463\) 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
\(465\) −4.10984 13.0533i −0.190589 0.605331i
\(466\) −3.24227 −0.150195
\(467\) −8.23017 + 8.23017i −0.380847 + 0.380847i −0.871407 0.490560i \(-0.836792\pi\)
0.490560 + 0.871407i \(0.336792\pi\)
\(468\) 5.05685 12.0273i 0.233753 0.555962i
\(469\) 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
\(477\) 10.9487 26.0404i 0.501304 1.19231i
\(478\) 2.90428 2.90428i 0.132839 0.132839i
\(479\) 23.7395 1.08469 0.542344 0.840157i \(-0.317537\pi\)
0.542344 + 0.840157i \(0.317537\pi\)
\(480\) −3.43465 1.78974i −0.156770 0.0816902i
\(481\) 13.5800 0.619195
\(482\) −17.7457 + 17.7457i −0.808297 + 0.808297i
\(483\) −4.03543 + 6.00487i −0.183618 + 0.273231i
\(484\) 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 \(-0.633307\pi\)
0.406662 0.913579i \(-0.366693\pi\)
\(492\) −9.21612 6.19347i −0.415495 0.279223i
\(493\) −11.2713 + 11.2713i −0.507636 + 0.507636i
\(494\) −4.34904 −0.195673
\(495\) 30.4662 + 8.98138i 1.36935 + 0.403683i
\(496\) −3.53345 −0.158656
\(497\) 1.36357 1.36357i 0.0611646 0.0611646i
\(498\) 15.7376 + 10.5761i 0.705220 + 0.473926i
\(499\) 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 \(0.0552081\pi\)
0.172573 + 0.984997i \(0.444792\pi\)
\(504\) −1.45755 + 0.594689i −0.0649244 + 0.0264895i
\(505\) −19.6879 + 24.6439i −0.876100 + 1.09664i
\(506\) 37.6911i 1.67557i
\(507\) 5.71365 8.50213i 0.253752 0.377593i
\(508\) 11.5688 11.5688i 0.513282 0.513282i
\(509\) −5.27569 −0.233841 −0.116920 0.993141i \(-0.537302\pi\)
−0.116920 + 0.993141i \(0.537302\pi\)
\(510\) −14.4949 + 4.56374i −0.641844 + 0.202086i
\(511\) 5.57794 0.246754
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −5.08807 1.05428i −0.224644 0.0465475i
\(514\) 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 \(-0.992185\pi\)
0.999699 0.0245494i \(-0.00781510\pi\)
\(522\) −11.2349 4.72371i −0.491740 0.206751i
\(523\) −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
\(525\) −4.15609 + 1.83787i −0.181387 + 0.0802110i
\(526\) −14.6667 −0.639500
\(527\) −9.80341 + 9.80341i −0.427043 + 0.427043i
\(528\) 4.57434 6.80679i 0.199072 0.296227i
\(529\) 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
\(537\) 11.1106 + 7.46659i 0.479456 + 0.322207i
\(538\) 9.83936 9.83936i 0.424205 0.424205i
\(539\) 31.8403 1.37146
\(540\) −7.41751 8.94318i −0.319199 0.384853i
\(541\) 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
\(543\) −22.3083 14.9917i −0.957340 0.643357i
\(544\) 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
\(552\) −7.69044 + 11.4437i −0.327327 + 0.487075i
\(553\) 2.94381 2.94381i 0.125184 0.125184i
\(554\) 6.48607 0.275567
\(555\) 5.58852 10.7248i 0.237220 0.455242i
\(556\) −6.34474 −0.269077
\(557\) 10.8257 10.8257i 0.458701 0.458701i −0.439528 0.898229i \(-0.644854\pi\)
0.898229 + 0.439528i \(0.144854\pi\)
\(558\) −9.77176 4.10852i −0.413671 0.173927i
\(559\) 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 0.958506 0.285073i \(-0.0920179\pi\)
−0.285073 + 0.958506i \(0.592018\pi\)
\(564\) 2.76662 + 14.1044i 0.116496 + 0.593900i
\(565\) 4.10626 + 36.7308i 0.172752 + 1.54528i
\(566\) 1.87716i 0.0789029i
\(567\) −4.72233 0.0501524i −0.198319 0.00210620i
\(568\) 2.59861 2.59861i 0.109035 0.109035i
\(569\) −18.1067 −0.759073 −0.379536 0.925177i \(-0.623916\pi\)
−0.379536 + 0.925177i \(0.623916\pi\)
\(570\) −1.78974 + 3.43465i −0.0749640 + 0.143862i
\(571\) −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
\(573\) 13.0500 19.4189i 0.545171 0.811235i
\(574\) 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
\(582\) −10.1967 6.85243i −0.422666 0.284042i
\(583\) 31.5258 31.5258i 1.30567 1.30567i
\(584\) 10.6301 0.439875
\(585\) −13.9541 25.6207i −0.576932 1.05929i
\(586\) 17.8907 0.739057
\(587\) −29.1721 + 29.1721i −1.20406 + 1.20406i −0.231141 + 0.972920i \(0.574246\pi\)
−0.972920 + 0.231141i \(0.925754\pi\)
\(588\) −9.66728 6.49666i −0.398672 0.267918i
\(589\) 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 0.776382 0.630262i \(-0.217053\pi\)
−0.630262 + 0.776382i \(0.717053\pi\)
\(594\) 20.5649 13.5054i 0.843790 0.554132i
\(595\) 3.59691 + 2.87355i 0.147459 + 0.117804i
\(596\) 19.2260i 0.787529i
\(597\) 5.70817 8.49397i 0.233620 0.347635i
\(598\) −24.4799 + 24.4799i −1.00106 + 1.00106i
\(599\) 30.7070 1.25466 0.627328 0.778755i \(-0.284149\pi\)
0.627328 + 0.778755i \(0.284149\pi\)
\(600\) −7.92039 + 3.50248i −0.323349 + 0.142988i
\(601\) 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
\(603\) −6.59605 + 15.6881i −0.268612 + 0.638870i
\(604\) 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
\(612\) −4.56227 + 10.8510i −0.184419 + 0.438624i
\(613\) 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
\(615\) −23.6829 + 7.45660i −0.954986 + 0.300679i
\(616\) −2.48454 −0.100105
\(617\) −15.5110 + 15.5110i −0.624451 + 0.624451i −0.946666 0.322215i \(-0.895573\pi\)
0.322215 + 0.946666i \(0.395573\pi\)
\(618\) 7.05655 10.5004i 0.283856 0.422389i
\(619\) 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
\(627\) −6.80679 4.57434i −0.271837 0.182681i
\(628\) −10.3090 + 10.3090i −0.411374 + 0.411374i
\(629\) −12.2518 −0.488512
\(630\) −0.995345 + 3.37636i −0.0396555 + 0.134517i
\(631\) 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
\(633\) −9.27713 6.23447i −0.368733 0.247798i
\(634\) 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 \(0.0105462\pi\)
−0.999451 + 0.0331258i \(0.989454\pi\)
\(642\) 8.00171 11.9069i 0.315802 0.469926i
\(643\) −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
\(645\) 33.0321 + 17.2125i 1.30064 + 0.677743i
\(646\) 3.92368 0.154375
\(647\) 1.87972 1.87972i 0.0738993 0.0738993i −0.669191 0.743090i \(-0.733359\pi\)
0.743090 + 0.669191i \(0.233359\pi\)
\(648\) −8.99949 0.0955769i −0.353533 0.00375462i
\(649\) 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 0.609488 0.792796i \(-0.291375\pi\)
−0.792796 + 0.609488i \(0.791375\pi\)
\(654\) −3.51610 17.9252i −0.137490 0.700932i
\(655\) −16.9068 + 21.1628i −0.660605 + 0.826898i
\(656\) 6.41083i 0.250301i
\(657\) 29.3975 + 12.3601i 1.14690 + 0.482214i
\(658\) 3.07903 3.07903i 0.120033 0.120033i
\(659\) 29.9598 1.16707 0.583533 0.812089i \(-0.301670\pi\)
0.583533 + 0.812089i \(0.301670\pi\)
\(660\) −5.50725 17.4916i −0.214369 0.680858i
\(661\) 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
\(663\) −16.4857 + 24.5314i −0.640252 + 0.952720i
\(664\) 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
\(672\) 0.754350 + 0.506942i 0.0290997 + 0.0195557i
\(673\) 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
\(675\) −25.9764 + 0.476668i −0.999832 + 0.0183470i
\(676\) −5.91417 −0.227468
\(677\) 23.6302 23.6302i 0.908182 0.908182i −0.0879438 0.996125i \(-0.528030\pi\)
0.996125 + 0.0879438i \(0.0280296\pi\)
\(678\) 23.7617 + 15.9684i 0.912561 + 0.613265i
\(679\) 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 0.243973 0.969782i \(-0.421549\pi\)
−0.969782 + 0.243973i \(0.921549\pi\)
\(684\) 1.13332 + 2.77770i 0.0433335 + 0.106208i
\(685\) 3.42095 0.382440i 0.130708 0.0146123i
\(686\) 7.20178i 0.274965i
\(687\) −4.30964 + 6.41291i −0.164423 + 0.244668i
\(688\) 6.80047 6.80047i 0.259266 0.259266i
\(689\) −40.9513 −1.56012
\(690\) 9.25886 + 29.4071i 0.352479 + 1.11951i
\(691\) 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
\(693\) −6.87101 2.88890i −0.261008 0.109740i
\(694\) 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 \(-0.870727\pi\)
0.918659 0.395051i \(-0.129273\pi\)
\(702\) −22.1282 4.58510i −0.835177 0.173053i
\(703\) −2.20796 + 2.20796i −0.0832748 + 0.0832748i
\(704\) −4.73487 −0.178452
\(705\) 28.5019 + 14.8519i 1.07344 + 0.559354i
\(706\) −26.5488 −0.999178
\(707\) 5.23402 5.23402i 0.196846 0.196846i
\(708\) 5.79875 8.62876i 0.217930 0.324289i
\(709\) 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
\(717\) −5.90457 3.96803i −0.220510 0.148189i
\(718\) 21.9852 21.9852i 0.820480 0.820480i
\(719\) −25.7542 −0.960468 −0.480234 0.877140i \(-0.659448\pi\)
−0.480234 + 0.877140i \(0.659448\pi\)
\(720\) −1.89686 + 6.43443i −0.0706918 + 0.239797i
\(721\) −3.83275 −0.142739
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) 36.0781 + 24.2454i 1.34176 + 0.901697i
\(724\) 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
\(732\) −2.90355 + 4.32060i −0.107318 + 0.159694i
\(733\) 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
\(735\) −24.8422 + 7.82162i −0.916320 + 0.288505i
\(736\) 7.96032 0.293421
\(737\) −18.9928 + 18.9928i −0.699610 + 0.699610i
\(738\) −7.45420 + 17.7292i −0.274393 + 0.652619i
\(739\) 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 0.714174 0.699968i \(-0.246802\pi\)
−0.699968 + 0.714174i \(0.746802\pi\)
\(744\) 1.17803 + 6.00566i 0.0431888 + 0.220178i
\(745\) −33.5882 26.8334i −1.23058 0.983101i
\(746\) 11.3284i 0.414760i
\(747\) 12.7289 30.2747i 0.465727 1.10769i
\(748\) −13.1367 + 13.1367i −0.480326 + 0.480326i
\(749\) −4.34611 −0.158803
\(750\) −4.93547 + 18.7254i −0.180218 + 0.683755i
\(751\) 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
\(753\) 20.6531 30.7326i 0.752641 1.11996i
\(754\) 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 \(0.0565507\pi\)
−0.984260 + 0.176726i \(0.943449\pi\)
\(762\) −23.5200 15.8060i −0.852039 0.572592i
\(763\) −3.91314 + 3.91314i −0.141665 + 0.141665i
\(764\) −13.5080 −0.488701
\(765\) 12.5893 + 23.1149i 0.455168 + 0.835720i
\(766\) 30.3805 1.09769
\(767\) 18.4583 18.4583i 0.666492 0.666492i
\(768\) 1.43759 + 0.966096i 0.0518745 + 0.0348610i
\(769\) 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 0.982578 0.185853i \(-0.0595048\pi\)
−0.185853 + 0.982578i \(0.559505\pi\)
\(774\) 26.7140 10.8995i 0.960215 0.391774i
\(775\) 3.90140 + 17.2311i 0.140143 + 0.618958i
\(776\) 7.09290i 0.254620i
\(777\) −1.58294 + 2.35548i −0.0567877 + 0.0845023i
\(778\) −8.31614 + 8.31614i