Properties

Label 570.2.k.a.77.15
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 77.15
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.867616 + 1.49908i) q^{3} -1.00000i q^{4} +(0.850241 + 2.06811i) q^{5} +(1.67351 + 0.446512i) q^{6} +(0.811234 + 0.811234i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.49448 + 2.60125i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.867616 + 1.49908i) q^{3} -1.00000i q^{4} +(0.850241 + 2.06811i) q^{5} +(1.67351 + 0.446512i) q^{6} +(0.811234 + 0.811234i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.49448 + 2.60125i) q^{9} +(2.06359 + 0.861165i) q^{10} -1.25204i q^{11} +(1.49908 - 0.867616i) q^{12} +(3.40609 - 3.40609i) q^{13} +1.14726 q^{14} +(-2.36258 + 3.06891i) q^{15} -1.00000 q^{16} +(-3.04078 + 3.04078i) q^{17} +(0.782605 + 2.89612i) q^{18} +1.00000i q^{19} +(2.06811 - 0.850241i) q^{20} +(-0.512265 + 1.91995i) q^{21} +(-0.885325 - 0.885325i) q^{22} +(5.51574 + 5.51574i) q^{23} +(0.446512 - 1.67351i) q^{24} +(-3.55418 + 3.51679i) q^{25} -4.81693i q^{26} +(-5.19613 + 0.0165399i) q^{27} +(0.811234 - 0.811234i) q^{28} +5.49893 q^{29} +(0.499447 + 3.84064i) q^{30} -5.80986 q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.87691 - 1.08629i) q^{33} +4.30032i q^{34} +(-0.987979 + 2.36747i) q^{35} +(2.60125 + 1.49448i) q^{36} +(-7.08962 - 7.08962i) q^{37} +(0.707107 + 0.707107i) q^{38} +(8.06117 + 2.15082i) q^{39} +(0.861165 - 2.06359i) q^{40} +0.259187i q^{41} +(0.995380 + 1.71983i) q^{42} +(5.60388 - 5.60388i) q^{43} -1.25204 q^{44} +(-6.65036 - 0.879067i) q^{45} +7.80043 q^{46} +(6.12099 - 6.12099i) q^{47} +(-0.867616 - 1.49908i) q^{48} -5.68380i q^{49} +(-0.0264390 + 4.99993i) q^{50} +(-7.19661 - 1.92015i) q^{51} +(-3.40609 - 3.40609i) q^{52} +(-0.465266 - 0.465266i) q^{53} +(-3.66252 + 3.68591i) q^{54} +(2.58936 - 1.06454i) q^{55} -1.14726i q^{56} +(-1.49908 + 0.867616i) q^{57} +(3.88833 - 3.88833i) q^{58} -9.08034 q^{59} +(3.06891 + 2.36258i) q^{60} +6.32624 q^{61} +(-4.10819 + 4.10819i) q^{62} +(-3.32260 + 0.897850i) q^{63} +1.00000i q^{64} +(9.94016 + 4.14817i) q^{65} +(0.559051 - 2.09530i) q^{66} +(-2.40925 - 2.40925i) q^{67} +(3.04078 + 3.04078i) q^{68} +(-3.48299 + 13.0541i) q^{69} +(0.975447 + 2.37266i) q^{70} +0.747767i q^{71} +(2.89612 - 0.782605i) q^{72} +(5.45994 - 5.45994i) q^{73} -10.0262 q^{74} +(-8.35561 - 2.27678i) q^{75} +1.00000 q^{76} +(1.01570 - 1.01570i) q^{77} +(7.22097 - 4.17925i) q^{78} +4.84381i q^{79} +(-0.850241 - 2.06811i) q^{80} +(-4.53304 - 7.77506i) q^{81} +(0.183273 + 0.183273i) q^{82} +(-4.22891 - 4.22891i) q^{83} +(1.91995 + 0.512265i) q^{84} +(-8.87408 - 3.70328i) q^{85} -7.92509i q^{86} +(4.77097 + 8.24334i) q^{87} +(-0.885325 + 0.885325i) q^{88} +12.7982 q^{89} +(-5.32411 + 4.08092i) q^{90} +5.52627 q^{91} +(5.51574 - 5.51574i) q^{92} +(-5.04073 - 8.70945i) q^{93} -8.65639i q^{94} +(-2.06811 + 0.850241i) q^{95} +(-1.67351 - 0.446512i) q^{96} +(-12.5537 - 12.5537i) q^{97} +(-4.01905 - 4.01905i) q^{98} +(3.25687 + 1.87115i) 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
\(3\) 0.867616 + 1.49908i 0.500919 + 0.865494i
\(4\) 1.00000i 0.500000i
\(5\) 0.850241 + 2.06811i 0.380239 + 0.924888i
\(6\) 1.67351 + 0.446512i 0.683207 + 0.182288i
\(7\) 0.811234 + 0.811234i 0.306618 + 0.306618i 0.843596 0.536978i \(-0.180434\pi\)
−0.536978 + 0.843596i \(0.680434\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −1.49448 + 2.60125i −0.498161 + 0.867084i
\(10\) 2.06359 + 0.861165i 0.652564 + 0.272324i
\(11\) 1.25204i 0.377504i −0.982025 0.188752i \(-0.939556\pi\)
0.982025 0.188752i \(-0.0604442\pi\)
\(12\) 1.49908 0.867616i 0.432747 0.250459i
\(13\) 3.40609 3.40609i 0.944678 0.944678i −0.0538698 0.998548i \(-0.517156\pi\)
0.998548 + 0.0538698i \(0.0171556\pi\)
\(14\) 1.14726 0.306618
\(15\) −2.36258 + 3.06891i −0.610016 + 0.792389i
\(16\) −1.00000 −0.250000
\(17\) −3.04078 + 3.04078i −0.737498 + 0.737498i −0.972093 0.234595i \(-0.924624\pi\)
0.234595 + 0.972093i \(0.424624\pi\)
\(18\) 0.782605 + 2.89612i 0.184462 + 0.682623i
\(19\) 1.00000i 0.229416i
\(20\) 2.06811 0.850241i 0.462444 0.190120i
\(21\) −0.512265 + 1.91995i −0.111785 + 0.418966i
\(22\) −0.885325 0.885325i −0.188752 0.188752i
\(23\) 5.51574 + 5.51574i 1.15011 + 1.15011i 0.986530 + 0.163581i \(0.0523045\pi\)
0.163581 + 0.986530i \(0.447696\pi\)
\(24\) 0.446512 1.67351i 0.0911439 0.341603i
\(25\) −3.55418 + 3.51679i −0.710836 + 0.703358i
\(26\) 4.81693i 0.944678i
\(27\) −5.19613 + 0.0165399i −0.999995 + 0.00318310i
\(28\) 0.811234 0.811234i 0.153309 0.153309i
\(29\) 5.49893 1.02113 0.510563 0.859840i \(-0.329437\pi\)
0.510563 + 0.859840i \(0.329437\pi\)
\(30\) 0.499447 + 3.84064i 0.0911862 + 0.701203i
\(31\) −5.80986 −1.04348 −0.521741 0.853104i \(-0.674717\pi\)
−0.521741 + 0.853104i \(0.674717\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 1.87691 1.08629i 0.326728 0.189099i
\(34\) 4.30032i 0.737498i
\(35\) −0.987979 + 2.36747i −0.166999 + 0.400175i
\(36\) 2.60125 + 1.49448i 0.433542 + 0.249081i
\(37\) −7.08962 7.08962i −1.16553 1.16553i −0.983247 0.182280i \(-0.941652\pi\)
−0.182280 0.983247i \(-0.558348\pi\)
\(38\) 0.707107 + 0.707107i 0.114708 + 0.114708i
\(39\) 8.06117 + 2.15082i 1.29082 + 0.344407i
\(40\) 0.861165 2.06359i 0.136162 0.326282i
\(41\) 0.259187i 0.0404782i 0.999795 + 0.0202391i \(0.00644274\pi\)
−0.999795 + 0.0202391i \(0.993557\pi\)
\(42\) 0.995380 + 1.71983i 0.153591 + 0.265376i
\(43\) 5.60388 5.60388i 0.854584 0.854584i −0.136109 0.990694i \(-0.543460\pi\)
0.990694 + 0.136109i \(0.0434599\pi\)
\(44\) −1.25204 −0.188752
\(45\) −6.65036 0.879067i −0.991377 0.131044i
\(46\) 7.80043 1.15011
\(47\) 6.12099 6.12099i 0.892838 0.892838i −0.101951 0.994789i \(-0.532509\pi\)
0.994789 + 0.101951i \(0.0325086\pi\)
\(48\) −0.867616 1.49908i −0.125230 0.216374i
\(49\) 5.68380i 0.811971i
\(50\) −0.0264390 + 4.99993i −0.00373904 + 0.707097i
\(51\) −7.19661 1.92015i −1.00773 0.268874i
\(52\) −3.40609 3.40609i −0.472339 0.472339i
\(53\) −0.465266 0.465266i −0.0639091 0.0639091i 0.674430 0.738339i \(-0.264390\pi\)
−0.738339 + 0.674430i \(0.764390\pi\)
\(54\) −3.66252 + 3.68591i −0.498406 + 0.501589i
\(55\) 2.58936 1.06454i 0.349149 0.143542i
\(56\) 1.14726i 0.153309i
\(57\) −1.49908 + 0.867616i −0.198558 + 0.114919i
\(58\) 3.88833 3.88833i 0.510563 0.510563i
\(59\) −9.08034 −1.18216 −0.591080 0.806613i \(-0.701298\pi\)
−0.591080 + 0.806613i \(0.701298\pi\)
\(60\) 3.06891 + 2.36258i 0.396194 + 0.305008i
\(61\) 6.32624 0.809992 0.404996 0.914318i \(-0.367273\pi\)
0.404996 + 0.914318i \(0.367273\pi\)
\(62\) −4.10819 + 4.10819i −0.521741 + 0.521741i
\(63\) −3.32260 + 0.897850i −0.418609 + 0.113118i
\(64\) 1.00000i 0.125000i
\(65\) 9.94016 + 4.14817i 1.23293 + 0.514518i
\(66\) 0.559051 2.09530i 0.0688144 0.257913i
\(67\) −2.40925 2.40925i −0.294336 0.294336i 0.544454 0.838791i \(-0.316737\pi\)
−0.838791 + 0.544454i \(0.816737\pi\)
\(68\) 3.04078 + 3.04078i 0.368749 + 0.368749i
\(69\) −3.48299 + 13.0541i −0.419303 + 1.57153i
\(70\) 0.975447 + 2.37266i 0.116588 + 0.283587i
\(71\) 0.747767i 0.0887437i 0.999015 + 0.0443718i \(0.0141286\pi\)
−0.999015 + 0.0443718i \(0.985871\pi\)
\(72\) 2.89612 0.782605i 0.341311 0.0922308i
\(73\) 5.45994 5.45994i 0.639038 0.639038i −0.311280 0.950318i \(-0.600758\pi\)
0.950318 + 0.311280i \(0.100758\pi\)
\(74\) −10.0262 −1.16553
\(75\) −8.35561 2.27678i −0.964823 0.262899i
\(76\) 1.00000 0.114708
\(77\) 1.01570 1.01570i 0.115749 0.115749i
\(78\) 7.22097 4.17925i 0.817614 0.473207i
\(79\) 4.84381i 0.544971i 0.962160 + 0.272485i \(0.0878457\pi\)
−0.962160 + 0.272485i \(0.912154\pi\)
\(80\) −0.850241 2.06811i −0.0950599 0.231222i
\(81\) −4.53304 7.77506i −0.503671 0.863896i
\(82\) 0.183273 + 0.183273i 0.0202391 + 0.0202391i
\(83\) −4.22891 4.22891i −0.464183 0.464183i 0.435841 0.900024i \(-0.356451\pi\)
−0.900024 + 0.435841i \(0.856451\pi\)
\(84\) 1.91995 + 0.512265i 0.209483 + 0.0558927i
\(85\) −8.87408 3.70328i −0.962530 0.401678i
\(86\) 7.92509i 0.854584i
\(87\) 4.77097 + 8.24334i 0.511501 + 0.883779i
\(88\) −0.885325 + 0.885325i −0.0943760 + 0.0943760i
\(89\) 12.7982 1.35660 0.678302 0.734784i \(-0.262716\pi\)
0.678302 + 0.734784i \(0.262716\pi\)
\(90\) −5.32411 + 4.08092i −0.561210 + 0.430167i
\(91\) 5.52627 0.579310
\(92\) 5.51574 5.51574i 0.575055 0.575055i
\(93\) −5.04073 8.70945i −0.522699 0.903128i
\(94\) 8.65639i 0.892838i
\(95\) −2.06811 + 0.850241i −0.212184 + 0.0872329i
\(96\) −1.67351 0.446512i −0.170802 0.0455720i
\(97\) −12.5537 12.5537i −1.27463 1.27463i −0.943629 0.331005i \(-0.892612\pi\)
−0.331005 0.943629i \(-0.607388\pi\)
\(98\) −4.01905 4.01905i −0.405986 0.405986i
\(99\) 3.25687 + 1.87115i 0.327328 + 0.188058i
\(100\) 3.51679 + 3.55418i 0.351679 + 0.355418i
\(101\) 3.55522i 0.353758i −0.984233 0.176879i \(-0.943400\pi\)
0.984233 0.176879i \(-0.0566001\pi\)
\(102\) −6.44652 + 3.73103i −0.638301 + 0.369427i
\(103\) −8.68610 + 8.68610i −0.855867 + 0.855867i −0.990848 0.134981i \(-0.956903\pi\)
0.134981 + 0.990848i \(0.456903\pi\)
\(104\) −4.81693 −0.472339
\(105\) −4.40621 + 0.572995i −0.430002 + 0.0559186i
\(106\) −0.657985 −0.0639091
\(107\) 5.27680 5.27680i 0.510128 0.510128i −0.404438 0.914566i \(-0.632533\pi\)
0.914566 + 0.404438i \(0.132533\pi\)
\(108\) 0.0165399 + 5.19613i 0.00159155 + 0.499997i
\(109\) 19.4996i 1.86773i −0.357632 0.933863i \(-0.616416\pi\)
0.357632 0.933863i \(-0.383584\pi\)
\(110\) 1.07821 2.58369i 0.102804 0.246345i
\(111\) 4.47684 16.7790i 0.424923 1.59259i
\(112\) −0.811234 0.811234i −0.0766544 0.0766544i
\(113\) −3.30686 3.30686i −0.311083 0.311083i 0.534246 0.845329i \(-0.320596\pi\)
−0.845329 + 0.534246i \(0.820596\pi\)
\(114\) −0.446512 + 1.67351i −0.0418197 + 0.156738i
\(115\) −6.71746 + 16.0969i −0.626406 + 1.50104i
\(116\) 5.49893i 0.510563i
\(117\) 3.76975 + 13.9504i 0.348514 + 1.28972i
\(118\) −6.42077 + 6.42077i −0.591080 + 0.591080i
\(119\) −4.93358 −0.452260
\(120\) 3.84064 0.499447i 0.350601 0.0455931i
\(121\) 9.43240 0.857491
\(122\) 4.47333 4.47333i 0.404996 0.404996i
\(123\) −0.388542 + 0.224875i −0.0350336 + 0.0202763i
\(124\) 5.80986i 0.521741i
\(125\) −10.2950 4.36032i −0.920815 0.389999i
\(126\) −1.71456 + 2.98431i −0.152745 + 0.265864i
\(127\) −5.40945 5.40945i −0.480011 0.480011i 0.425124 0.905135i \(-0.360231\pi\)
−0.905135 + 0.425124i \(0.860231\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 13.2627 + 3.53865i 1.16772 + 0.311561i
\(130\) 9.96196 4.09555i 0.873722 0.359204i
\(131\) 21.4587i 1.87485i 0.348185 + 0.937426i \(0.386798\pi\)
−0.348185 + 0.937426i \(0.613202\pi\)
\(132\) −1.08629 1.87691i −0.0945494 0.163364i
\(133\) −0.811234 + 0.811234i −0.0703429 + 0.0703429i
\(134\) −3.40719 −0.294336
\(135\) −4.45217 10.7321i −0.383182 0.923673i
\(136\) 4.30032 0.368749
\(137\) −13.6290 + 13.6290i −1.16440 + 1.16440i −0.180902 + 0.983501i \(0.557902\pi\)
−0.983501 + 0.180902i \(0.942098\pi\)
\(138\) 6.76778 + 11.6935i 0.576112 + 0.995414i
\(139\) 10.5758i 0.897030i 0.893775 + 0.448515i \(0.148047\pi\)
−0.893775 + 0.448515i \(0.851953\pi\)
\(140\) 2.36747 + 0.987979i 0.200088 + 0.0834995i
\(141\) 14.4865 + 3.86518i 1.21999 + 0.325507i
\(142\) 0.528751 + 0.528751i 0.0443718 + 0.0443718i
\(143\) −4.26455 4.26455i −0.356620 0.356620i
\(144\) 1.49448 2.60125i 0.124540 0.216771i
\(145\) 4.67542 + 11.3724i 0.388273 + 0.944428i
\(146\) 7.72152i 0.639038i
\(147\) 8.52047 4.93136i 0.702756 0.406731i
\(148\) −7.08962 + 7.08962i −0.582763 + 0.582763i
\(149\) −0.688172 −0.0563772 −0.0281886 0.999603i \(-0.508974\pi\)
−0.0281886 + 0.999603i \(0.508974\pi\)
\(150\) −7.51824 + 4.29839i −0.613861 + 0.350962i
\(151\) −7.78234 −0.633318 −0.316659 0.948539i \(-0.602561\pi\)
−0.316659 + 0.948539i \(0.602561\pi\)
\(152\) 0.707107 0.707107i 0.0573539 0.0573539i
\(153\) −3.36545 12.4543i −0.272080 1.00687i
\(154\) 1.43641i 0.115749i
\(155\) −4.93978 12.0154i −0.396773 0.965104i
\(156\) 2.15082 8.06117i 0.172203 0.645410i
\(157\) 4.92864 + 4.92864i 0.393348 + 0.393348i 0.875879 0.482531i \(-0.160282\pi\)
−0.482531 + 0.875879i \(0.660282\pi\)
\(158\) 3.42509 + 3.42509i 0.272485 + 0.272485i
\(159\) 0.293798 1.10114i 0.0232997 0.0873263i
\(160\) −2.06359 0.861165i −0.163141 0.0680811i
\(161\) 8.94911i 0.705289i
\(162\) −8.70314 2.29245i −0.683783 0.180112i
\(163\) −0.293352 + 0.293352i −0.0229771 + 0.0229771i −0.718502 0.695525i \(-0.755172\pi\)
0.695525 + 0.718502i \(0.255172\pi\)
\(164\) 0.259187 0.0202391
\(165\) 3.84239 + 2.95805i 0.299130 + 0.230284i
\(166\) −5.98058 −0.464183
\(167\) −4.29057 + 4.29057i −0.332015 + 0.332015i −0.853351 0.521337i \(-0.825434\pi\)
0.521337 + 0.853351i \(0.325434\pi\)
\(168\) 1.71983 0.995380i 0.132688 0.0767953i
\(169\) 10.2028i 0.784834i
\(170\) −8.89354 + 3.65631i −0.682104 + 0.280426i
\(171\) −2.60125 1.49448i −0.198923 0.114286i
\(172\) −5.60388 5.60388i −0.427292 0.427292i
\(173\) −3.16382 3.16382i −0.240541 0.240541i 0.576533 0.817074i \(-0.304405\pi\)
−0.817074 + 0.576533i \(0.804405\pi\)
\(174\) 9.20251 + 2.45534i 0.697640 + 0.186139i
\(175\) −5.73621 0.0303324i −0.433617 0.00229291i
\(176\) 1.25204i 0.0943760i
\(177\) −7.87825 13.6122i −0.592166 1.02315i
\(178\) 9.04967 9.04967i 0.678302 0.678302i
\(179\) 3.82605 0.285973 0.142986 0.989725i \(-0.454330\pi\)
0.142986 + 0.989725i \(0.454330\pi\)
\(180\) −0.879067 + 6.65036i −0.0655218 + 0.495688i
\(181\) 11.7262 0.871603 0.435801 0.900043i \(-0.356465\pi\)
0.435801 + 0.900043i \(0.356465\pi\)
\(182\) 3.90766 3.90766i 0.289655 0.289655i
\(183\) 5.48875 + 9.48354i 0.405740 + 0.701044i
\(184\) 7.80043i 0.575055i
\(185\) 8.63425 20.6900i 0.634803 1.52116i
\(186\) −9.72284 2.59417i −0.712913 0.190214i
\(187\) 3.80718 + 3.80718i 0.278409 + 0.278409i
\(188\) −6.12099 6.12099i −0.446419 0.446419i
\(189\) −4.22869 4.20186i −0.307592 0.305640i
\(190\) −0.861165 + 2.06359i −0.0624755 + 0.149708i
\(191\) 11.0228i 0.797579i −0.917042 0.398790i \(-0.869430\pi\)
0.917042 0.398790i \(-0.130570\pi\)
\(192\) −1.49908 + 0.867616i −0.108187 + 0.0626148i
\(193\) 6.75179 6.75179i 0.486004 0.486004i −0.421039 0.907043i \(-0.638334\pi\)
0.907043 + 0.421039i \(0.138334\pi\)
\(194\) −17.7536 −1.27463
\(195\) 2.40580 + 18.5001i 0.172283 + 1.32482i
\(196\) −5.68380 −0.405986
\(197\) −7.05740 + 7.05740i −0.502819 + 0.502819i −0.912313 0.409494i \(-0.865705\pi\)
0.409494 + 0.912313i \(0.365705\pi\)
\(198\) 3.62606 0.979852i 0.257693 0.0696350i
\(199\) 23.7718i 1.68514i 0.538588 + 0.842569i \(0.318958\pi\)
−0.538588 + 0.842569i \(0.681042\pi\)
\(200\) 4.99993 + 0.0264390i 0.353548 + 0.00186952i
\(201\) 1.52135 5.70196i 0.107308 0.402185i
\(202\) −2.51392 2.51392i −0.176879 0.176879i
\(203\) 4.46092 + 4.46092i 0.313096 + 0.313096i
\(204\) −1.92015 + 7.19661i −0.134437 + 0.503864i
\(205\) −0.536027 + 0.220371i −0.0374378 + 0.0153914i
\(206\) 12.2840i 0.855867i
\(207\) −22.5910 + 6.10465i −1.57018 + 0.424303i
\(208\) −3.40609 + 3.40609i −0.236170 + 0.236170i
\(209\) 1.25204 0.0866054
\(210\) −2.71049 + 3.52083i −0.187042 + 0.242960i
\(211\) 16.9279 1.16536 0.582682 0.812700i \(-0.302003\pi\)
0.582682 + 0.812700i \(0.302003\pi\)
\(212\) −0.465266 + 0.465266i −0.0319546 + 0.0319546i
\(213\) −1.12096 + 0.648775i −0.0768071 + 0.0444534i
\(214\) 7.46253i 0.510128i
\(215\) 16.3541 + 6.82481i 1.11534 + 0.465448i
\(216\) 3.68591 + 3.66252i 0.250795 + 0.249203i
\(217\) −4.71316 4.71316i −0.319950 0.319950i
\(218\) −13.7883 13.7883i −0.933863 0.933863i
\(219\) 12.9220 + 3.44776i 0.873190 + 0.232978i
\(220\) −1.06454 2.58936i −0.0717710 0.174574i
\(221\) 20.7143i 1.39340i
\(222\) −8.69893 15.0301i −0.583834 1.00876i
\(223\) −13.0760 + 13.0760i −0.875634 + 0.875634i −0.993079 0.117446i \(-0.962529\pi\)
0.117446 + 0.993079i \(0.462529\pi\)
\(224\) −1.14726 −0.0766544
\(225\) −3.83640 14.5011i −0.255760 0.966740i
\(226\) −4.67660 −0.311083
\(227\) −18.5524 + 18.5524i −1.23136 + 1.23136i −0.267923 + 0.963440i \(0.586337\pi\)
−0.963440 + 0.267923i \(0.913663\pi\)
\(228\) 0.867616 + 1.49908i 0.0574593 + 0.0992790i
\(229\) 2.63822i 0.174338i 0.996194 + 0.0871692i \(0.0277821\pi\)
−0.996194 + 0.0871692i \(0.972218\pi\)
\(230\) 6.63225 + 16.1322i 0.437317 + 1.06372i
\(231\) 2.40385 + 0.641376i 0.158162 + 0.0421994i
\(232\) −3.88833 3.88833i −0.255282 0.255282i
\(233\) −13.3570 13.3570i −0.875046 0.875046i 0.117971 0.993017i \(-0.462361\pi\)
−0.993017 + 0.117971i \(0.962361\pi\)
\(234\) 12.5301 + 7.19883i 0.819116 + 0.470602i
\(235\) 17.8632 + 7.45458i 1.16527 + 0.486283i
\(236\) 9.08034i 0.591080i
\(237\) −7.26126 + 4.20257i −0.471669 + 0.272986i
\(238\) −3.48857 + 3.48857i −0.226130 + 0.226130i
\(239\) 0.359134 0.0232304 0.0116152 0.999933i \(-0.496303\pi\)
0.0116152 + 0.999933i \(0.496303\pi\)
\(240\) 2.36258 3.06891i 0.152504 0.198097i
\(241\) 5.42354 0.349361 0.174681 0.984625i \(-0.444111\pi\)
0.174681 + 0.984625i \(0.444111\pi\)
\(242\) 6.66971 6.66971i 0.428745 0.428745i
\(243\) 7.72250 13.5412i 0.495399 0.868666i
\(244\) 6.32624i 0.404996i
\(245\) 11.7547 4.83260i 0.750982 0.308743i
\(246\) −0.115730 + 0.433751i −0.00737868 + 0.0276549i
\(247\) 3.40609 + 3.40609i 0.216724 + 0.216724i
\(248\) 4.10819 + 4.10819i 0.260870 + 0.260870i
\(249\) 2.67040 10.0085i 0.169230 0.634265i
\(250\) −10.3629 + 4.19647i −0.655407 + 0.265408i
\(251\) 13.3902i 0.845179i 0.906321 + 0.422590i \(0.138879\pi\)
−0.906321 + 0.422590i \(0.861121\pi\)
\(252\) 0.897850 + 3.32260i 0.0565592 + 0.209304i
\(253\) 6.90592 6.90592i 0.434171 0.434171i
\(254\) −7.65012 −0.480011
\(255\) −2.14778 16.5160i −0.134499 1.03427i
\(256\) 1.00000 0.0625000
\(257\) 16.2263 16.2263i 1.01217 1.01217i 0.0122435 0.999925i \(-0.496103\pi\)
0.999925 0.0122435i \(-0.00389731\pi\)
\(258\) 11.8803 6.87594i 0.739638 0.428077i
\(259\) 11.5027i 0.714742i
\(260\) 4.14817 9.94016i 0.257259 0.616463i
\(261\) −8.21807 + 14.3041i −0.508686 + 0.885403i
\(262\) 15.1736 + 15.1736i 0.937426 + 0.937426i
\(263\) −3.46688 3.46688i −0.213777 0.213777i 0.592093 0.805870i \(-0.298302\pi\)
−0.805870 + 0.592093i \(0.798302\pi\)
\(264\) −2.09530 0.559051i −0.128957 0.0344072i
\(265\) 0.566634 1.35781i 0.0348080 0.0834096i
\(266\) 1.14726i 0.0703429i
\(267\) 11.1039 + 19.1855i 0.679548 + 1.17413i
\(268\) −2.40925 + 2.40925i −0.147168 + 0.147168i
\(269\) 4.91421 0.299625 0.149812 0.988714i \(-0.452133\pi\)
0.149812 + 0.988714i \(0.452133\pi\)
\(270\) −10.7369 4.44059i −0.653427 0.270246i
\(271\) 6.09935 0.370509 0.185255 0.982691i \(-0.440689\pi\)
0.185255 + 0.982691i \(0.440689\pi\)
\(272\) 3.04078 3.04078i 0.184375 0.184375i
\(273\) 4.79468 + 8.28432i 0.290187 + 0.501390i
\(274\) 19.2743i 1.16440i
\(275\) 4.40316 + 4.44997i 0.265520 + 0.268343i
\(276\) 13.0541 + 3.48299i 0.785763 + 0.209651i
\(277\) −11.4817 11.4817i −0.689866 0.689866i 0.272336 0.962202i \(-0.412204\pi\)
−0.962202 + 0.272336i \(0.912204\pi\)
\(278\) 7.47824 + 7.47824i 0.448515 + 0.448515i
\(279\) 8.68274 15.1129i 0.519822 0.904787i
\(280\) 2.37266 0.975447i 0.141794 0.0582941i
\(281\) 19.8457i 1.18389i 0.805977 + 0.591947i \(0.201641\pi\)
−0.805977 + 0.591947i \(0.798359\pi\)
\(282\) 12.9766 7.51042i 0.772746 0.447239i
\(283\) 13.5529 13.5529i 0.805635 0.805635i −0.178335 0.983970i \(-0.557071\pi\)
0.983970 + 0.178335i \(0.0570711\pi\)
\(284\) 0.747767 0.0443718
\(285\) −3.06891 2.36258i −0.181786 0.139947i
\(286\) −6.03099 −0.356620
\(287\) −0.210261 + 0.210261i −0.0124113 + 0.0124113i
\(288\) −0.782605 2.89612i −0.0461154 0.170656i
\(289\) 1.49273i 0.0878079i
\(290\) 11.3475 + 4.73549i 0.666350 + 0.278078i
\(291\) 7.92720 29.7108i 0.464701 1.74168i
\(292\) −5.45994 5.45994i −0.319519 0.319519i
\(293\) −4.72321 4.72321i −0.275933 0.275933i 0.555550 0.831483i \(-0.312508\pi\)
−0.831483 + 0.555550i \(0.812508\pi\)
\(294\) 2.53789 9.51188i 0.148013 0.554744i
\(295\) −7.72048 18.7792i −0.449504 1.09336i
\(296\) 10.0262i 0.582763i
\(297\) 0.0207086 + 6.50575i 0.00120163 + 0.377502i
\(298\) −0.486611 + 0.486611i −0.0281886 + 0.0281886i
\(299\) 37.5741 2.17297
\(300\) −2.27678 + 8.35561i −0.131450 + 0.482412i
\(301\) 9.09213 0.524062
\(302\) −5.50294 + 5.50294i −0.316659 + 0.316659i
\(303\) 5.32956 3.08457i 0.306175 0.177204i
\(304\) 1.00000i 0.0573539i
\(305\) 5.37883 + 13.0834i 0.307991 + 0.749152i
\(306\) −11.1862 6.42675i −0.639473 0.367393i
\(307\) 10.8953 + 10.8953i 0.621830 + 0.621830i 0.945999 0.324169i \(-0.105085\pi\)
−0.324169 + 0.945999i \(0.605085\pi\)
\(308\) −1.01570 1.01570i −0.0578747 0.0578747i
\(309\) −20.5574 5.48496i −1.16947 0.312028i
\(310\) −11.9892 5.00325i −0.680938 0.284165i
\(311\) 18.6727i 1.05883i 0.848363 + 0.529415i \(0.177588\pi\)
−0.848363 + 0.529415i \(0.822412\pi\)
\(312\) −4.17925 7.22097i −0.236603 0.408807i
\(313\) −5.71317 + 5.71317i −0.322928 + 0.322928i −0.849889 0.526961i \(-0.823331\pi\)
0.526961 + 0.849889i \(0.323331\pi\)
\(314\) 6.97014 0.393348
\(315\) −4.68187 6.10813i −0.263793 0.344154i
\(316\) 4.84381 0.272485
\(317\) 11.0822 11.0822i 0.622438 0.622438i −0.323716 0.946154i \(-0.604932\pi\)
0.946154 + 0.323716i \(0.104932\pi\)
\(318\) −0.570878 0.986372i −0.0320133 0.0553130i
\(319\) 6.88488i 0.385479i
\(320\) −2.06811 + 0.850241i −0.115611 + 0.0475299i
\(321\) 12.4886 + 3.33211i 0.697045 + 0.185980i
\(322\) 6.32798 + 6.32798i 0.352644 + 0.352644i
\(323\) −3.04078 3.04078i −0.169194 0.169194i
\(324\) −7.77506 + 4.53304i −0.431948 + 0.251836i
\(325\) −0.127355 + 24.0843i −0.00706438 + 1.33596i
\(326\) 0.414863i 0.0229771i
\(327\) 29.2315 16.9182i 1.61651 0.935578i
\(328\) 0.183273 0.183273i 0.0101195 0.0101195i
\(329\) 9.93112 0.547520
\(330\) 4.80864 0.625327i 0.264707 0.0344231i
\(331\) 20.0068 1.09967 0.549837 0.835272i \(-0.314690\pi\)
0.549837 + 0.835272i \(0.314690\pi\)
\(332\) −4.22891 + 4.22891i −0.232091 + 0.232091i
\(333\) 29.0372 7.84658i 1.59123 0.429990i
\(334\) 6.06779i 0.332015i
\(335\) 2.93415 7.03103i 0.160310 0.384146i
\(336\) 0.512265 1.91995i 0.0279464 0.104742i
\(337\) 8.69484 + 8.69484i 0.473638 + 0.473638i 0.903090 0.429452i \(-0.141293\pi\)
−0.429452 + 0.903090i \(0.641293\pi\)
\(338\) −7.21450 7.21450i −0.392417 0.392417i
\(339\) 2.08816 7.82632i 0.113413 0.425068i
\(340\) −3.70328 + 8.87408i −0.200839 + 0.481265i
\(341\) 7.27417i 0.393919i
\(342\) −2.89612 + 0.782605i −0.156604 + 0.0423184i
\(343\) 10.2895 10.2895i 0.555583 0.555583i
\(344\) −7.92509 −0.427292
\(345\) −29.9587 + 3.89590i −1.61292 + 0.209748i
\(346\) −4.47431 −0.240541
\(347\) −5.08826 + 5.08826i −0.273152 + 0.273152i −0.830368 0.557216i \(-0.811870\pi\)
0.557216 + 0.830368i \(0.311870\pi\)
\(348\) 8.24334 4.77097i 0.441890 0.255751i
\(349\) 21.6797i 1.16049i 0.814442 + 0.580244i \(0.197043\pi\)
−0.814442 + 0.580244i \(0.802957\pi\)
\(350\) −4.07756 + 4.03467i −0.217955 + 0.215662i
\(351\) −17.6421 + 17.7548i −0.941666 + 0.947680i
\(352\) 0.885325 + 0.885325i 0.0471880 + 0.0471880i
\(353\) −7.11922 7.11922i −0.378918 0.378918i 0.491794 0.870712i \(-0.336341\pi\)
−0.870712 + 0.491794i \(0.836341\pi\)
\(354\) −15.1960 4.05448i −0.807659 0.215493i
\(355\) −1.54647 + 0.635783i −0.0820780 + 0.0337438i
\(356\) 12.7982i 0.678302i
\(357\) −4.28045 7.39583i −0.226546 0.391429i
\(358\) 2.70543 2.70543i 0.142986 0.142986i
\(359\) −24.6824 −1.30269 −0.651343 0.758783i \(-0.725794\pi\)
−0.651343 + 0.758783i \(0.725794\pi\)
\(360\) 4.08092 + 5.32411i 0.215083 + 0.280605i
\(361\) −1.00000 −0.0526316
\(362\) 8.29169 8.29169i 0.435801 0.435801i
\(363\) 8.18370 + 14.1399i 0.429533 + 0.742153i
\(364\) 5.52627i 0.289655i
\(365\) 15.9340 + 6.64951i 0.834026 + 0.348051i
\(366\) 10.5870 + 2.82474i 0.553392 + 0.147652i
\(367\) −1.59834 1.59834i −0.0834327 0.0834327i 0.664159 0.747591i \(-0.268790\pi\)
−0.747591 + 0.664159i \(0.768790\pi\)
\(368\) −5.51574 5.51574i −0.287528 0.287528i
\(369\) −0.674210 0.387350i −0.0350980 0.0201647i
\(370\) −8.52472 20.7354i −0.443179 1.07798i
\(371\) 0.754879i 0.0391914i
\(372\) −8.70945 + 5.04073i −0.451564 + 0.261350i
\(373\) −20.6849 + 20.6849i −1.07102 + 1.07102i −0.0737477 + 0.997277i \(0.523496\pi\)
−0.997277 + 0.0737477i \(0.976504\pi\)
\(374\) 5.38417 0.278409
\(375\) −2.39566 19.2162i −0.123711 0.992318i
\(376\) −8.65639 −0.446419
\(377\) 18.7298 18.7298i 0.964636 0.964636i
\(378\) −5.96130 + 0.0189755i −0.306616 + 0.000975995i
\(379\) 19.2862i 0.990668i 0.868703 + 0.495334i \(0.164954\pi\)
−0.868703 + 0.495334i \(0.835046\pi\)
\(380\) 0.850241 + 2.06811i 0.0436165 + 0.106092i
\(381\) 3.41587 12.8025i 0.175001 0.655894i
\(382\) −7.79427 7.79427i −0.398790 0.398790i
\(383\) 22.7437 + 22.7437i 1.16215 + 1.16215i 0.984004 + 0.178146i \(0.0570100\pi\)
0.178146 + 0.984004i \(0.442990\pi\)
\(384\) −0.446512 + 1.67351i −0.0227860 + 0.0854008i
\(385\) 2.96416 + 1.23699i 0.151068 + 0.0630428i
\(386\) 9.54847i 0.486004i
\(387\) 6.20221 + 22.9520i 0.315276 + 1.16672i
\(388\) −12.5537 + 12.5537i −0.637317 + 0.637317i
\(389\) −20.2169 −1.02504 −0.512519 0.858676i \(-0.671287\pi\)
−0.512519 + 0.858676i \(0.671287\pi\)
\(390\) 14.7827 + 11.3804i 0.748552 + 0.576269i
\(391\) −33.5443 −1.69641
\(392\) −4.01905 + 4.01905i −0.202993 + 0.202993i
\(393\) −32.1683 + 18.6179i −1.62267 + 0.939148i
\(394\) 9.98068i 0.502819i
\(395\) −10.0175 + 4.11841i −0.504037 + 0.207219i
\(396\) 1.87115 3.25687i 0.0940289 0.163664i
\(397\) 0.250592 + 0.250592i 0.0125768 + 0.0125768i 0.713367 0.700790i \(-0.247169\pi\)
−0.700790 + 0.713367i \(0.747169\pi\)
\(398\) 16.8092 + 16.8092i 0.842569 + 0.842569i
\(399\) −1.91995 0.512265i −0.0961175 0.0256453i
\(400\) 3.55418 3.51679i 0.177709 0.175839i
\(401\) 21.6861i 1.08295i −0.840716 0.541476i \(-0.817866\pi\)
0.840716 0.541476i \(-0.182134\pi\)
\(402\) −2.95613 5.10765i −0.147439 0.254746i
\(403\) −19.7889 + 19.7889i −0.985754 + 0.985754i
\(404\) −3.55522 −0.176879
\(405\) 12.2255 15.9855i 0.607491 0.794326i
\(406\) 6.30870 0.313096
\(407\) −8.87649 + 8.87649i −0.439991 + 0.439991i
\(408\) 3.73103 + 6.44652i 0.184713 + 0.319150i
\(409\) 5.94808i 0.294114i −0.989128 0.147057i \(-0.953020\pi\)
0.989128 0.147057i \(-0.0469800\pi\)
\(410\) −0.223203 + 0.534855i −0.0110232 + 0.0264146i
\(411\) −32.2557 8.60622i −1.59106 0.424513i
\(412\) 8.68610 + 8.68610i 0.427933 + 0.427933i
\(413\) −7.36628 7.36628i −0.362471 0.362471i
\(414\) −11.6576 + 20.2909i −0.572940 + 0.997243i
\(415\) 5.15026 12.3414i 0.252817 0.605818i
\(416\) 4.81693i 0.236170i
\(417\) −15.8540 + 9.17576i −0.776375 + 0.449339i
\(418\) 0.885325 0.885325i 0.0433027 0.0433027i
\(419\) 35.8879 1.75324 0.876620 0.481184i \(-0.159793\pi\)
0.876620 + 0.481184i \(0.159793\pi\)
\(420\) 0.572995 + 4.40621i 0.0279593 + 0.215001i
\(421\) −13.5450 −0.660145 −0.330073 0.943956i \(-0.607073\pi\)
−0.330073 + 0.943956i \(0.607073\pi\)
\(422\) 11.9698 11.9698i 0.582682 0.582682i
\(423\) 6.77453 + 25.0700i 0.329389 + 1.21894i
\(424\) 0.657985i 0.0319546i
\(425\) 0.113696 21.5013i 0.00551507 1.04297i
\(426\) −0.333887 + 1.25139i −0.0161769 + 0.0606302i
\(427\) 5.13206 + 5.13206i 0.248358 + 0.248358i
\(428\) −5.27680 5.27680i −0.255064 0.255064i
\(429\) 2.69291 10.0929i 0.130015 0.487290i
\(430\) 16.3900 6.73824i 0.790395 0.324947i
\(431\) 0.445342i 0.0214514i −0.999942 0.0107257i \(-0.996586\pi\)
0.999942 0.0107257i \(-0.00341416\pi\)
\(432\) 5.19613 0.0165399i 0.249999 0.000795775i
\(433\) 20.9273 20.9273i 1.00570 1.00570i 0.00571854 0.999984i \(-0.498180\pi\)
0.999984 0.00571854i \(-0.00182028\pi\)
\(434\) −6.66541 −0.319950
\(435\) −12.9917 + 16.8757i −0.622904 + 0.809129i
\(436\) −19.4996 −0.933863
\(437\) −5.51574 + 5.51574i −0.263854 + 0.263854i
\(438\) 11.5752 6.69932i 0.553084 0.320106i
\(439\) 0.487999i 0.0232909i −0.999932 0.0116455i \(-0.996293\pi\)
0.999932 0.0116455i \(-0.00370695\pi\)
\(440\) −2.58369 1.07821i −0.123173 0.0514018i
\(441\) 14.7850 + 8.49434i 0.704048 + 0.404492i
\(442\) 14.6473 + 14.6473i 0.696699 + 0.696699i
\(443\) 5.91639 + 5.91639i 0.281096 + 0.281096i 0.833546 0.552450i \(-0.186307\pi\)
−0.552450 + 0.833546i \(0.686307\pi\)
\(444\) −16.7790 4.47684i −0.796295 0.212461i
\(445\) 10.8815 + 26.4681i 0.515834 + 1.25471i
\(446\) 18.4923i 0.875634i
\(447\) −0.597069 1.03162i −0.0282404 0.0487942i
\(448\) −0.811234 + 0.811234i −0.0383272 + 0.0383272i
\(449\) −16.3599 −0.772074 −0.386037 0.922483i \(-0.626156\pi\)
−0.386037 + 0.922483i \(0.626156\pi\)
\(450\) −12.9666 7.54109i −0.611250 0.355490i
\(451\) 0.324512 0.0152807
\(452\) −3.30686 + 3.30686i −0.155541 + 0.155541i
\(453\) −6.75209 11.6664i −0.317241 0.548133i
\(454\) 26.2370i 1.23136i
\(455\) 4.69866 + 11.4289i 0.220277 + 0.535797i
\(456\) 1.67351 + 0.446512i 0.0783692 + 0.0209099i
\(457\) −22.9810 22.9810i −1.07501 1.07501i −0.996949 0.0780586i \(-0.975128\pi\)
−0.0780586 0.996949i \(-0.524872\pi\)
\(458\) 1.86550 + 1.86550i 0.0871692 + 0.0871692i
\(459\) 15.7500 15.8506i 0.735147 0.739842i
\(460\) 16.0969 + 6.71746i 0.750521 + 0.313203i
\(461\) 16.8678i 0.785612i 0.919621 + 0.392806i \(0.128496\pi\)
−0.919621 + 0.392806i \(0.871504\pi\)
\(462\) 2.15330 1.24626i 0.100180 0.0579811i
\(463\) −17.7793 + 17.7793i −0.826272 + 0.826272i −0.986999 0.160727i \(-0.948616\pi\)
0.160727 + 0.986999i \(0.448616\pi\)
\(464\) −5.49893 −0.255282
\(465\) 13.7263 17.8299i 0.636541 0.826843i
\(466\) −18.8897 −0.875046
\(467\) 12.4366 12.4366i 0.575497 0.575497i −0.358162 0.933659i \(-0.616596\pi\)
0.933659 + 0.358162i \(0.116596\pi\)
\(468\) 13.9504 3.76975i 0.644859 0.174257i
\(469\) 3.90893i 0.180497i
\(470\) 17.9024 7.36002i 0.825775 0.339492i
\(471\) −3.11225 + 11.6646i −0.143405 + 0.537476i
\(472\) 6.42077 + 6.42077i 0.295540 + 0.295540i
\(473\) −7.01628 7.01628i −0.322609 0.322609i
\(474\) −2.16282 + 8.10615i −0.0993416 + 0.372328i
\(475\) −3.51679 3.55418i −0.161361 0.163077i
\(476\) 4.93358i 0.226130i
\(477\) 1.90561 0.514942i 0.0872517 0.0235776i
\(478\) 0.253946 0.253946i 0.0116152 0.0116152i
\(479\) −37.6990 −1.72251 −0.861256 0.508172i \(-0.830321\pi\)
−0.861256 + 0.508172i \(0.830321\pi\)
\(480\) −0.499447 3.84064i −0.0227965 0.175301i
\(481\) −48.2957 −2.20210
\(482\) 3.83502 3.83502i 0.174681 0.174681i
\(483\) −13.4154 + 7.76440i −0.610423 + 0.353292i
\(484\) 9.43240i 0.428745i
\(485\) 15.2888 36.6361i 0.694228 1.66356i
\(486\) −4.11441 15.0357i −0.186634 0.682032i
\(487\) 1.14616 + 1.14616i 0.0519376 + 0.0519376i 0.732599 0.680661i \(-0.238307\pi\)
−0.680661 + 0.732599i \(0.738307\pi\)
\(488\) −4.47333 4.47333i −0.202498 0.202498i
\(489\) −0.694276 0.185241i −0.0313963 0.00837691i
\(490\) 4.89469 11.7290i 0.221119 0.529863i
\(491\) 11.1351i 0.502519i 0.967920 + 0.251260i \(0.0808448\pi\)
−0.967920 + 0.251260i \(0.919155\pi\)
\(492\) 0.224875 + 0.388542i 0.0101381 + 0.0175168i
\(493\) −16.7211 + 16.7211i −0.753079 + 0.753079i
\(494\) 4.81693 0.216724
\(495\) −1.10063 + 8.32651i −0.0494695 + 0.374249i
\(496\) 5.80986 0.260870
\(497\) −0.606615 + 0.606615i −0.0272104 + 0.0272104i
\(498\) −5.18885 8.96537i −0.232518 0.401748i
\(499\) 2.14480i 0.0960142i 0.998847 + 0.0480071i \(0.0152870\pi\)
−0.998847 + 0.0480071i \(0.984713\pi\)
\(500\) −4.36032 + 10.2950i −0.195000 + 0.460408i
\(501\) −10.1545 2.70934i −0.453669 0.121044i
\(502\) 9.46827 + 9.46827i 0.422590 + 0.422590i
\(503\) −22.0328 22.0328i −0.982393 0.982393i 0.0174544 0.999848i \(-0.494444\pi\)
−0.999848 + 0.0174544i \(0.994444\pi\)
\(504\) 2.98431 + 1.71456i 0.132932 + 0.0763725i
\(505\) 7.35260 3.02280i 0.327186 0.134513i
\(506\) 9.76645i 0.434171i
\(507\) 15.2949 8.85215i 0.679269 0.393138i
\(508\) −5.40945 + 5.40945i −0.240006 + 0.240006i
\(509\) −44.4681 −1.97101 −0.985507 0.169634i \(-0.945741\pi\)
−0.985507 + 0.169634i \(0.945741\pi\)
\(510\) −13.1973 10.1599i −0.584385 0.449886i
\(511\) 8.85858 0.391881
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −0.0165399 5.19613i −0.000730253 0.229415i
\(514\) 22.9474i 1.01217i
\(515\) −25.3491 10.5785i −1.11702 0.466147i
\(516\) 3.53865 13.2627i 0.155780 0.583858i
\(517\) −7.66372 7.66372i −0.337050 0.337050i
\(518\) −8.13363 8.13363i −0.357371 0.357371i
\(519\) 1.99784 7.48780i 0.0876953 0.328678i
\(520\) −4.09555 9.96196i −0.179602 0.436861i
\(521\) 24.7771i 1.08551i −0.839892 0.542753i \(-0.817382\pi\)
0.839892 0.542753i \(-0.182618\pi\)
\(522\) 4.30349 + 15.9256i 0.188359 + 0.697044i
\(523\) −15.2015 + 15.2015i −0.664717 + 0.664717i −0.956488 0.291771i \(-0.905755\pi\)
0.291771 + 0.956488i \(0.405755\pi\)
\(524\) 21.4587 0.937426
\(525\) −4.93136 8.62536i −0.215222 0.376442i
\(526\) −4.90290 −0.213777
\(527\) 17.6665 17.6665i 0.769566 0.769566i
\(528\) −1.87691 + 1.08629i −0.0816819 + 0.0472747i
\(529\) 37.8467i 1.64551i
\(530\) −0.559446 1.36079i −0.0243008 0.0591088i
\(531\) 13.5704 23.6203i 0.588906 1.02503i
\(532\) 0.811234 + 0.811234i 0.0351715 + 0.0351715i
\(533\) 0.882812 + 0.882812i 0.0382388 + 0.0382388i
\(534\) 21.4178 + 5.71454i 0.926840 + 0.247292i
\(535\) 15.3996 + 6.42647i 0.665782 + 0.277840i
\(536\) 3.40719i 0.147168i
\(537\) 3.31955 + 5.73556i 0.143249 + 0.247508i
\(538\) 3.47487 3.47487i 0.149812 0.149812i
\(539\) −7.11634 −0.306522
\(540\) −10.7321 + 4.45217i −0.461837 + 0.191591i
\(541\) 30.5234 1.31231 0.656153 0.754628i \(-0.272183\pi\)
0.656153 + 0.754628i \(0.272183\pi\)
\(542\) 4.31289 4.31289i 0.185255 0.185255i
\(543\) 10.1739 + 17.5785i 0.436602 + 0.754367i
\(544\) 4.30032i 0.184375i
\(545\) 40.3274 16.5794i 1.72744 0.710183i
\(546\) 9.24825 + 2.46755i 0.395788 + 0.105601i
\(547\) 2.58026 + 2.58026i 0.110324 + 0.110324i 0.760114 0.649790i \(-0.225143\pi\)
−0.649790 + 0.760114i \(0.725143\pi\)
\(548\) 13.6290 + 13.6290i 0.582202 + 0.582202i
\(549\) −9.45446 + 16.4562i −0.403507 + 0.702332i
\(550\) 6.26011 + 0.0331027i 0.266932 + 0.00141150i
\(551\) 5.49893i 0.234263i
\(552\) 11.6935 6.76778i 0.497707 0.288056i
\(553\) −3.92946 + 3.92946i −0.167098 + 0.167098i
\(554\) −16.2375 −0.689866
\(555\) 38.5072 5.00758i 1.63454 0.212560i
\(556\) 10.5758 0.448515
\(557\) 23.0216 23.0216i 0.975455 0.975455i −0.0242514 0.999706i \(-0.507720\pi\)
0.999706 + 0.0242514i \(0.00772021\pi\)
\(558\) −4.54682 16.8261i −0.192482 0.712304i
\(559\) 38.1746i 1.61461i
\(560\) 0.987979 2.36747i 0.0417497 0.100044i
\(561\) −2.40410 + 9.01044i −0.101501 + 0.380421i
\(562\) 14.0330 + 14.0330i 0.591947 + 0.591947i
\(563\) −29.0925 29.0925i −1.22610 1.22610i −0.965426 0.260676i \(-0.916055\pi\)
−0.260676 0.965426i \(-0.583945\pi\)
\(564\) 3.86518 14.4865i 0.162754 0.609993i
\(565\) 4.02732 9.65057i 0.169431 0.406003i
\(566\) 19.1667i 0.805635i
\(567\) 2.63004 9.98475i 0.110451 0.419320i
\(568\) 0.528751 0.528751i 0.0221859 0.0221859i
\(569\) −31.9886 −1.34103 −0.670515 0.741896i \(-0.733927\pi\)
−0.670515 + 0.741896i \(0.733927\pi\)
\(570\) −3.84064 + 0.499447i −0.160867 + 0.0209195i
\(571\) −19.7915 −0.828248 −0.414124 0.910220i \(-0.635912\pi\)
−0.414124 + 0.910220i \(0.635912\pi\)
\(572\) −4.26455 + 4.26455i −0.178310 + 0.178310i
\(573\) 16.5240 9.56353i 0.690300 0.399522i
\(574\) 0.297354i 0.0124113i
\(575\) −39.0016 0.206236i −1.62648 0.00860062i
\(576\) −2.60125 1.49448i −0.108386 0.0622701i
\(577\) 21.8776 + 21.8776i 0.910777 + 0.910777i 0.996333 0.0855565i \(-0.0272668\pi\)
−0.0855565 + 0.996333i \(0.527267\pi\)
\(578\) −1.05552 1.05552i −0.0439040 0.0439040i
\(579\) 15.9794 + 4.26351i 0.664082 + 0.177185i
\(580\) 11.3724 4.67542i 0.472214 0.194136i
\(581\) 6.86127i 0.284653i
\(582\) −15.4033 26.6141i −0.638488 1.10319i
\(583\) −0.582531 + 0.582531i −0.0241260 + 0.0241260i
\(584\) −7.72152 −0.319519
\(585\) −25.6459 + 19.6575i −1.06033 + 0.812738i
\(586\) −6.67963 −0.275933
\(587\) −19.3270 + 19.3270i −0.797710 + 0.797710i −0.982734 0.185024i \(-0.940764\pi\)
0.185024 + 0.982734i \(0.440764\pi\)
\(588\) −4.93136 8.52047i −0.203366 0.351378i
\(589\) 5.80986i 0.239391i
\(590\) −18.7381 7.81967i −0.771434 0.321931i
\(591\) −16.7027 4.45649i −0.687059 0.183316i
\(592\) 7.08962 + 7.08962i 0.291382 + 0.291382i
\(593\) 4.82260 + 4.82260i 0.198040 + 0.198040i 0.799159 0.601119i \(-0.205278\pi\)
−0.601119 + 0.799159i \(0.705278\pi\)
\(594\) 4.61491 + 4.58562i 0.189352 + 0.188150i
\(595\) −4.19473 10.2032i −0.171967 0.418290i
\(596\) 0.688172i 0.0281886i
\(597\) −35.6358 + 20.6248i −1.45848 + 0.844117i
\(598\) 26.5689 26.5689i 1.08648 1.08648i
\(599\) −12.4755 −0.509735 −0.254868 0.966976i \(-0.582032\pi\)
−0.254868 + 0.966976i \(0.582032\pi\)
\(600\) 4.29839 + 7.51824i 0.175481 + 0.306931i
\(601\) 33.9363 1.38429 0.692145 0.721758i \(-0.256666\pi\)
0.692145 + 0.721758i \(0.256666\pi\)
\(602\) 6.42911 6.42911i 0.262031 0.262031i
\(603\) 9.86764 2.66648i 0.401841 0.108588i
\(604\) 7.78234i 0.316659i
\(605\) 8.01981 + 19.5073i 0.326052 + 0.793083i
\(606\) 1.58745 5.94969i 0.0644858 0.241690i
\(607\) 9.17452 + 9.17452i 0.372382 + 0.372382i 0.868344 0.495962i \(-0.165185\pi\)
−0.495962 + 0.868344i \(0.665185\pi\)
\(608\) −0.707107 0.707107i −0.0286770 0.0286770i
\(609\) −2.81691 + 10.5577i −0.114147 + 0.427818i
\(610\) 13.0548 + 5.44794i 0.528571 + 0.220581i
\(611\) 41.6972i 1.68689i
\(612\) −12.4543 + 3.36545i −0.503433 + 0.136040i
\(613\) −9.18173 + 9.18173i −0.370847 + 0.370847i −0.867786 0.496939i \(-0.834457\pi\)
0.496939 + 0.867786i \(0.334457\pi\)
\(614\) 15.4083 0.621830
\(615\) −0.795420 0.612350i −0.0320744 0.0246924i
\(616\) −1.43641 −0.0578747
\(617\) 22.1031 22.1031i 0.889839 0.889839i −0.104668 0.994507i \(-0.533378\pi\)
0.994507 + 0.104668i \(0.0333780\pi\)
\(618\) −18.4147 + 10.6578i −0.740748 + 0.428720i
\(619\) 45.0921i 1.81240i −0.422844 0.906202i \(-0.638968\pi\)
0.422844 0.906202i \(-0.361032\pi\)
\(620\) −12.0154 + 4.93978i −0.482552 + 0.198386i
\(621\) −28.7517 28.5692i −1.15377 1.14644i
\(622\) 13.2036 + 13.2036i 0.529415 + 0.529415i
\(623\) 10.3823 + 10.3823i 0.415959 + 0.415959i
\(624\) −8.06117 2.15082i −0.322705 0.0861017i
\(625\) 0.264386 24.9986i 0.0105755 0.999944i
\(626\) 8.07965i 0.322928i
\(627\) 1.08629 + 1.87691i 0.0433822 + 0.0749565i
\(628\) 4.92864 4.92864i 0.196674 0.196674i
\(629\) 43.1160 1.71915
\(630\) −7.62968 1.00852i −0.303974 0.0401803i
\(631\) −10.9260 −0.434958 −0.217479 0.976065i \(-0.569783\pi\)
−0.217479 + 0.976065i \(0.569783\pi\)
\(632\) 3.42509 3.42509i 0.136243 0.136243i
\(633\) 14.6869 + 25.3763i 0.583752 + 1.00862i
\(634\) 15.6726i 0.622438i
\(635\) 6.58802 15.7867i 0.261438 0.626476i
\(636\) −1.10114 0.293798i −0.0436631 0.0116499i
\(637\) −19.3595 19.3595i −0.767051 0.767051i
\(638\) −4.86835 4.86835i −0.192740 0.192740i
\(639\) −1.94513 1.11753i −0.0769483 0.0442086i
\(640\) −0.861165 + 2.06359i −0.0340405 + 0.0815705i
\(641\) 26.0023i 1.02703i 0.858081 + 0.513515i \(0.171657\pi\)
−0.858081 + 0.513515i \(0.828343\pi\)
\(642\) 11.1869 6.47461i 0.441513 0.255533i
\(643\) 9.72854 9.72854i 0.383656 0.383656i −0.488761 0.872418i \(-0.662551\pi\)
0.872418 + 0.488761i \(0.162551\pi\)
\(644\) 8.94911 0.352644
\(645\) 3.95816 + 30.4375i 0.155853 + 1.19847i
\(646\) −4.30032 −0.169194
\(647\) −27.1481 + 27.1481i −1.06730 + 1.06730i −0.0697360 + 0.997565i \(0.522216\pi\)
−0.997565 + 0.0697360i \(0.977784\pi\)
\(648\) −2.29245 + 8.70314i −0.0900561 + 0.341892i
\(649\) 11.3689i 0.446270i
\(650\) 16.9401 + 17.1202i 0.664447 + 0.671511i
\(651\) 2.97619 11.1546i 0.116646 0.437184i
\(652\) 0.293352 + 0.293352i 0.0114886 + 0.0114886i
\(653\) 14.8598 + 14.8598i 0.581507 + 0.581507i 0.935317 0.353810i \(-0.115114\pi\)
−0.353810 + 0.935317i \(0.615114\pi\)
\(654\) 8.70682 32.6328i 0.340464 1.27604i
\(655\) −44.3789 + 18.2450i −1.73403 + 0.712893i
\(656\) 0.259187i 0.0101195i
\(657\) 6.04290 + 22.3625i 0.235756 + 0.872444i
\(658\) 7.02236 7.02236i 0.273760 0.273760i
\(659\) −3.67408 −0.143122 −0.0715609 0.997436i \(-0.522798\pi\)
−0.0715609 + 0.997436i \(0.522798\pi\)
\(660\) 2.95805 3.84239i 0.115142 0.149565i
\(661\) 5.30895 0.206494 0.103247 0.994656i \(-0.467077\pi\)
0.103247 + 0.994656i \(0.467077\pi\)
\(662\) 14.1470 14.1470i 0.549837 0.549837i
\(663\) −31.0525 + 17.9721i −1.20598 + 0.697979i
\(664\) 5.98058i 0.232091i
\(665\) −2.36747 0.987979i −0.0918065 0.0383122i
\(666\) 14.9840 26.0808i 0.580620 1.01061i
\(667\) 30.3307 + 30.3307i 1.17441 + 1.17441i
\(668\) 4.29057 + 4.29057i 0.166007 + 0.166007i
\(669\) −30.9469 8.25702i −1.19648 0.319235i
\(670\) −2.89693 7.04645i −0.111918 0.272228i
\(671\) 7.92070i 0.305775i
\(672\) −0.995380 1.71983i −0.0383976 0.0663440i
\(673\) 25.8750 25.8750i 0.997409 0.997409i −0.00258791 0.999997i \(-0.500824\pi\)
0.999997 + 0.00258791i \(0.000823758\pi\)
\(674\) 12.2964 0.473638
\(675\) 18.4098 18.3325i 0.708593 0.705617i
\(676\) −10.2028 −0.392417
\(677\) −19.1276 + 19.1276i −0.735134 + 0.735134i −0.971632 0.236498i \(-0.924000\pi\)
0.236498 + 0.971632i \(0.424000\pi\)
\(678\) −4.05749 7.01060i −0.155827 0.269240i
\(679\) 20.3680i 0.781651i
\(680\) 3.65631 + 8.89354i 0.140213 + 0.341052i
\(681\) −43.9078 11.7151i −1.68255 0.448925i
\(682\) 5.14362 + 5.14362i 0.196959 + 0.196959i
\(683\) 3.97993 + 3.97993i 0.152288 + 0.152288i 0.779139 0.626851i \(-0.215657\pi\)
−0.626851 + 0.779139i \(0.715657\pi\)
\(684\) −1.49448 + 2.60125i −0.0571430 + 0.0994614i
\(685\) −39.7742 16.5984i −1.51970 0.634191i
\(686\) 14.5516i 0.555583i
\(687\) −3.95490 + 2.28896i −0.150889 + 0.0873293i
\(688\) −5.60388 + 5.60388i −0.213646 + 0.213646i
\(689\) −3.16947 −0.120747
\(690\) −18.4292 + 23.9388i −0.701586 + 0.911335i
\(691\) −15.6719 −0.596186 −0.298093 0.954537i \(-0.596351\pi\)
−0.298093 + 0.954537i \(0.596351\pi\)
\(692\) −3.16382 + 3.16382i −0.120270 + 0.120270i
\(693\) 1.12414 + 4.16003i 0.0427027 + 0.158026i
\(694\) 7.19589i 0.273152i
\(695\) −21.8720 + 8.99201i −0.829653 + 0.341086i
\(696\) 2.45534 9.20251i 0.0930695 0.348820i
\(697\) −0.788131 0.788131i −0.0298526 0.0298526i
\(698\) 15.3299 + 15.3299i 0.580244 + 0.580244i
\(699\) 8.43446 31.6120i 0.319021 1.19567i
\(700\) −0.0303324 + 5.73621i −0.00114646 + 0.216808i
\(701\) 43.9609i 1.66038i 0.557480 + 0.830191i \(0.311768\pi\)
−0.557480 + 0.830191i \(0.688232\pi\)
\(702\) 0.0796715 + 25.0294i 0.00300701 + 0.944673i
\(703\) 7.08962 7.08962i 0.267390 0.267390i
\(704\) 1.25204 0.0471880
\(705\) 4.32341 + 33.2461i 0.162829 + 1.25212i
\(706\) −10.0681 −0.378918
\(707\) 2.88412 2.88412i 0.108468 0.108468i
\(708\) −13.6122 + 7.87825i −0.511576 + 0.296083i
\(709\) 25.0308i 0.940050i −0.882653 0.470025i \(-0.844245\pi\)
0.882653 0.470025i \(-0.155755\pi\)
\(710\) −0.643951 + 1.54308i −0.0241671 + 0.0579109i
\(711\) −12.6000 7.23899i −0.472536 0.271483i
\(712\) −9.04967 9.04967i −0.339151 0.339151i
\(713\) −32.0457 32.0457i −1.20012 1.20012i
\(714\) −8.25638 2.20290i −0.308987 0.0824416i
\(715\) 5.19368 12.4455i 0.194233 0.465434i
\(716\) 3.82605i 0.142986i
\(717\) 0.311590 + 0.538370i 0.0116366 + 0.0201058i
\(718\) −17.4531 + 17.4531i −0.651343 + 0.651343i
\(719\) 22.3343 0.832930 0.416465 0.909152i \(-0.363269\pi\)
0.416465 + 0.909152i \(0.363269\pi\)
\(720\) 6.65036 + 0.879067i 0.247844 + 0.0327609i
\(721\) −14.0929 −0.524848
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) 4.70555 + 8.13033i 0.175001 + 0.302370i
\(724\) 11.7262i 0.435801i
\(725\) −19.5442 + 19.3386i −0.725853 + 0.718217i
\(726\) 15.7852 + 4.21168i 0.585843 + 0.156310i
\(727\) −27.5404 27.5404i −1.02142 1.02142i −0.999766 0.0216511i \(-0.993108\pi\)
−0.0216511 0.999766i \(-0.506892\pi\)
\(728\) −3.90766 3.90766i −0.144828 0.144828i
\(729\) 26.9995 0.171887i 0.999980 0.00636617i
\(730\) 15.9690 6.56516i 0.591038 0.242987i
\(731\) 34.0804i 1.26051i
\(732\) 9.48354 5.48875i 0.350522 0.202870i
\(733\) −28.9159 + 28.9159i −1.06803 + 1.06803i −0.0705243 + 0.997510i \(0.522467\pi\)
−0.997510 + 0.0705243i \(0.977533\pi\)
\(734\) −2.26039 −0.0834327
\(735\) 17.4431 + 13.4284i 0.643397 + 0.495316i
\(736\) −7.80043 −0.287528
\(737\) −3.01647 + 3.01647i −0.111113 + 0.111113i
\(738\) −0.750637 + 0.202841i −0.0276313 + 0.00746667i
\(739\) 20.1578i 0.741515i 0.928730 + 0.370758i \(0.120902\pi\)
−0.928730 + 0.370758i \(0.879098\pi\)
\(740\) −20.6900 8.63425i −0.760581 0.317401i
\(741\) −2.15082 + 8.06117i −0.0790123 + 0.296135i
\(742\) −0.533780 0.533780i −0.0195957 0.0195957i
\(743\) 26.7472 + 26.7472i 0.981260 + 0.981260i 0.999828 0.0185673i \(-0.00591049\pi\)
−0.0185673 + 0.999828i \(0.505910\pi\)
\(744\) −2.59417 + 9.72284i −0.0951070 + 0.356457i
\(745\) −0.585112 1.42322i −0.0214369 0.0521426i
\(746\) 29.2529i 1.07102i
\(747\) 17.3205 4.68043i 0.633724 0.171248i
\(748\) 3.80718 3.80718i 0.139204 0.139204i
\(749\) 8.56145 0.312828
\(750\) −15.2819 11.8939i −0.558015 0.434304i
\(751\) −30.8503 −1.12574 −0.562871 0.826545i \(-0.690303\pi\)
−0.562871 + 0.826545i \(0.690303\pi\)
\(752\) −6.12099 + 6.12099i −0.223210 + 0.223210i
\(753\) −20.0729 + 11.6175i −0.731498 + 0.423366i
\(754\) 26.4880i 0.964636i
\(755\) −6.61687 16.0948i −0.240812 0.585748i
\(756\) −4.20186 + 4.22869i −0.152820 + 0.153796i
\(757\) 25.2568 + 25.2568i 0.917975 + 0.917975i 0.996882 0.0789067i \(-0.0251429\pi\)
−0.0789067 + 0.996882i \(0.525143\pi\)
\(758\) 13.6374 + 13.6374i 0.495334 + 0.495334i
\(759\) 16.3442 + 4.36084i 0.593258 + 0.158288i
\(760\) 2.06359 + 0.861165i 0.0748542 + 0.0312377i
\(761\) 7.51765i 0.272514i 0.990673 + 0.136257i \(0.0435074\pi\)
−0.990673 + 0.136257i \(0.956493\pi\)
\(762\) −6.63737 11.4681i −0.240447 0.415447i
\(763\) 15.8188 15.8188i 0.572678 0.572678i
\(764\) −11.0228 −0.398790
\(765\) 22.8954 17.5492i 0.827783 0.634494i
\(766\) 32.1645 1.16215
\(767\) −30.9284 + 30.9284i −1.11676 + 1.11676i
\(768\) 0.867616 + 1.49908i 0.0313074 + 0.0540934i
\(769\) 45.1162i 1.62693i 0.581611 + 0.813467i \(0.302422\pi\)
−0.581611 + 0.813467i \(0.697578\pi\)
\(770\) 2.97066 1.22130i 0.107055 0.0440125i
\(771\) 38.4027 + 10.2463i 1.38304 + 0.369012i
\(772\) −6.75179 6.75179i −0.243002 0.243002i
\(773\) 25.7371 + 25.7371i 0.925698 + 0.925698i 0.997424 0.0717268i \(-0.0228510\pi\)
−0.0717268 + 0.997424i \(0.522851\pi\)
\(774\) 20.6152 + 11.8439i 0.740997 + 0.425721i
\(775\) 20.6493 20.4321i 0.741744 0.733941i
\(776\) 17.7536i 0.637317i
\(777\) 17.2435 9.97992i 0.618606 0.358028i