Properties

Label 570.2.k.a.77.1
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 77.1
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.49908 - 0.867616i) q^{3} -1.00000i q^{4} +(-0.850241 - 2.06811i) q^{5} +(1.67351 - 0.446512i) q^{6} +(0.811234 + 0.811234i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.49448 + 2.60125i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.49908 - 0.867616i) 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} +(-0.867616 + 1.49908i) q^{12} +(3.40609 - 3.40609i) q^{13} -1.14726 q^{14} +(-0.519749 + 3.83795i) q^{15} -1.00000 q^{16} +(3.04078 - 3.04078i) q^{17} +(-2.89612 - 0.782605i) 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} +(0.0165399 - 5.19613i) q^{27} +(0.811234 - 0.811234i) q^{28} -5.49893 q^{29} +(-2.34632 - 3.08136i) q^{30} -5.80986 q^{31} +(0.707107 - 0.707107i) q^{32} +(1.08629 - 1.87691i) 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} +(1.71983 + 0.995380i) q^{42} +(5.60388 - 5.60388i) q^{43} +1.25204 q^{44} +(4.10901 - 5.30245i) q^{45} +7.80043 q^{46} +(-6.12099 + 6.12099i) q^{47} +(1.49908 + 0.867616i) 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} +(0.867616 - 1.49908i) q^{57} +(3.88833 - 3.88833i) q^{58} +9.08034 q^{59} +(3.83795 + 0.519749i) q^{60} +6.32624 q^{61} +(4.10819 - 4.10819i) q^{62} +(-0.897850 + 3.32260i) 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} +(-0.782605 + 2.89612i) q^{72} +(5.45994 - 5.45994i) q^{73} +10.0262 q^{74} +(8.37922 - 2.18828i) q^{75} +1.00000 q^{76} +(-1.01570 + 1.01570i) q^{77} +(4.17925 - 7.22097i) 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} +(8.24334 + 4.77097i) q^{87} +(-0.885325 + 0.885325i) q^{88} -12.7982 q^{89} +(0.843889 + 6.65491i) q^{90} +5.52627 q^{91} +(-5.51574 + 5.51574i) q^{92} +(8.70945 + 5.04073i) 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
\(3\) −1.49908 0.867616i −0.865494 0.500919i
\(4\) 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 \(0.0604442\pi\)
−0.982025 + 0.188752i \(0.939556\pi\)
\(12\) −0.867616 + 1.49908i −0.250459 + 0.432747i
\(13\) 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
\(15\) −0.519749 + 3.83795i −0.134199 + 0.990954i
\(16\) −1.00000 −0.250000
\(17\) 3.04078 3.04078i 0.737498 0.737498i −0.234595 0.972093i \(-0.575376\pi\)
0.972093 + 0.234595i \(0.0753763\pi\)
\(18\) −2.89612 0.782605i −0.682623 0.184462i
\(19\) 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 \(-0.947696\pi\)
−0.163581 0.986530i \(-0.552304\pi\)
\(24\) −0.446512 1.67351i −0.0911439 0.341603i
\(25\) −3.55418 + 3.51679i −0.710836 + 0.703358i
\(26\) 4.81693i 0.944678i
\(27\) 0.0165399 5.19613i 0.00318310 0.999995i
\(28\) 0.811234 0.811234i 0.153309 0.153309i
\(29\) −5.49893 −1.02113 −0.510563 0.859840i \(-0.670563\pi\)
−0.510563 + 0.859840i \(0.670563\pi\)
\(30\) −2.34632 3.08136i −0.428378 0.562577i
\(31\) −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
\(33\) 1.08629 1.87691i 0.189099 0.326728i
\(34\) 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 \(-0.993557\pi\)
0.999795 0.0202391i \(-0.00644274\pi\)
\(42\) 1.71983 + 0.995380i 0.265376 + 0.153591i
\(43\) 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
\(45\) 4.10901 5.30245i 0.612536 0.790443i
\(46\) 7.80043 1.15011
\(47\) −6.12099 + 6.12099i −0.892838 + 0.892838i −0.994789 0.101951i \(-0.967491\pi\)
0.101951 + 0.994789i \(0.467491\pi\)
\(48\) 1.49908 + 0.867616i 0.216374 + 0.125230i
\(49\) 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 0.738339 0.674430i \(-0.235610\pi\)
−0.674430 + 0.738339i \(0.735610\pi\)
\(54\) 3.66252 + 3.68591i 0.498406 + 0.501589i
\(55\) 2.58936 1.06454i 0.349149 0.143542i
\(56\) 1.14726i 0.153309i
\(57\) 0.867616 1.49908i 0.114919 0.198558i
\(58\) 3.88833 3.88833i 0.510563 0.510563i
\(59\) 9.08034 1.18216 0.591080 0.806613i \(-0.298702\pi\)
0.591080 + 0.806613i \(0.298702\pi\)
\(60\) 3.83795 + 0.519749i 0.495477 + 0.0670993i
\(61\) 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
\(63\) −0.897850 + 3.32260i −0.113118 + 0.418609i
\(64\) 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 \(-0.985871\pi\)
0.999015 0.0443718i \(-0.0141286\pi\)
\(72\) −0.782605 + 2.89612i −0.0922308 + 0.341311i
\(73\) 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
\(75\) 8.37922 2.18828i 0.967550 0.252681i
\(76\) 1.00000 0.114708
\(77\) −1.01570 + 1.01570i −0.115749 + 0.115749i
\(78\) 4.17925 7.22097i 0.473207 0.817614i
\(79\) 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 0.900024 0.435841i \(-0.143549\pi\)
−0.435841 + 0.900024i \(0.643549\pi\)
\(84\) −1.91995 + 0.512265i −0.209483 + 0.0558927i
\(85\) −8.87408 3.70328i −0.962530 0.401678i
\(86\) 7.92509i 0.854584i
\(87\) 8.24334 + 4.77097i 0.883779 + 0.511501i
\(88\) −0.885325 + 0.885325i −0.0943760 + 0.0943760i
\(89\) −12.7982 −1.35660 −0.678302 0.734784i \(-0.737284\pi\)
−0.678302 + 0.734784i \(0.737284\pi\)
\(90\) 0.843889 + 6.65491i 0.0889537 + 0.701489i
\(91\) 5.52627 0.579310
\(92\) −5.51574 + 5.51574i −0.575055 + 0.575055i
\(93\) 8.70945 + 5.04073i 0.903128 + 0.522699i
\(94\) 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 \(0.0566001\pi\)
−0.984233 + 0.176879i \(0.943400\pi\)
\(102\) 3.73103 6.44652i 0.369427 0.638301i
\(103\) −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
\(105\) −3.53511 + 2.69184i −0.344992 + 0.262697i
\(106\) −0.657985 −0.0639091
\(107\) −5.27680 + 5.27680i −0.510128 + 0.510128i −0.914566 0.404438i \(-0.867467\pi\)
0.404438 + 0.914566i \(0.367467\pi\)
\(108\) −5.19613 0.0165399i −0.499997 0.00159155i
\(109\) 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 0.845329 0.534246i \(-0.179404\pi\)
−0.534246 + 0.845329i \(0.679404\pi\)
\(114\) 0.446512 + 1.67351i 0.0418197 + 0.156738i
\(115\) −6.71746 + 16.0969i −0.626406 + 1.50104i
\(116\) 5.49893i 0.510563i
\(117\) 13.9504 + 3.76975i 1.28972 + 0.348514i
\(118\) −6.42077 + 6.42077i −0.591080 + 0.591080i
\(119\) 4.93358 0.452260
\(120\) −3.08136 + 2.34632i −0.281288 + 0.214189i
\(121\) 9.43240 0.857491
\(122\) −4.47333 + 4.47333i −0.404996 + 0.404996i
\(123\) −0.224875 + 0.388542i −0.0202763 + 0.0350336i
\(124\) 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 \(-0.613202\pi\)
0.348185 0.937426i \(-0.386798\pi\)
\(132\) −1.87691 1.08629i −0.163364 0.0945494i
\(133\) −0.811234 + 0.811234i −0.0703429 + 0.0703429i
\(134\) 3.40719 0.294336
\(135\) −10.7602 + 4.38375i −0.926094 + 0.377294i
\(136\) 4.30032 0.368749
\(137\) 13.6290 13.6290i 1.16440 1.16440i 0.180902 0.983501i \(-0.442098\pi\)
0.983501 0.180902i \(-0.0579018\pi\)
\(138\) −11.6935 6.76778i −0.995414 0.576112i
\(139\) 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
\(147\) −4.93136 + 8.52047i −0.406731 + 0.702756i
\(148\) −7.08962 + 7.08962i −0.582763 + 0.582763i
\(149\) 0.688172 0.0563772 0.0281886 0.999603i \(-0.491026\pi\)
0.0281886 + 0.999603i \(0.491026\pi\)
\(150\) −4.37766 + 7.47236i −0.357434 + 0.610115i
\(151\) −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
\(153\) 12.4543 + 3.36545i 1.00687 + 0.272080i
\(154\) 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
\(162\) −2.29245 8.70314i −0.180112 0.683783i
\(163\) −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
\(165\) −4.80526 0.650746i −0.374089 0.0506605i
\(166\) −5.98058 −0.464183
\(167\) 4.29057 4.29057i 0.332015 0.332015i −0.521337 0.853351i \(-0.674566\pi\)
0.853351 + 0.521337i \(0.174566\pi\)
\(168\) 0.995380 1.71983i 0.0767953 0.132688i
\(169\) 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 0.817074 0.576533i \(-0.195595\pi\)
−0.576533 + 0.817074i \(0.695595\pi\)
\(174\) −9.20251 + 2.45534i −0.697640 + 0.186139i
\(175\) −5.73621 0.0303324i −0.433617 0.00229291i
\(176\) 1.25204i 0.0943760i
\(177\) −13.6122 7.87825i −1.02315 0.592166i
\(178\) 9.04967 9.04967i 0.678302 0.678302i
\(179\) −3.82605 −0.285973 −0.142986 0.989725i \(-0.545670\pi\)
−0.142986 + 0.989725i \(0.545670\pi\)
\(180\) −5.30245 4.10901i −0.395221 0.306268i
\(181\) 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
\(183\) −9.48354 5.48875i −0.701044 0.405740i
\(184\) 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 \(0.130570\pi\)
−0.917042 + 0.398790i \(0.869430\pi\)
\(192\) 0.867616 1.49908i 0.0626148 0.108187i
\(193\) 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
\(195\) 11.3021 + 14.8427i 0.809359 + 1.06291i
\(196\) −5.68380 −0.405986
\(197\) 7.05740 7.05740i 0.502819 0.502819i −0.409494 0.912313i \(-0.634295\pi\)
0.912313 + 0.409494i \(0.134295\pi\)
\(198\) 0.979852 3.62606i 0.0696350 0.257693i
\(199\) 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
\(207\) 6.10465 22.5910i 0.424303 1.57018i
\(208\) −3.40609 + 3.40609i −0.236170 + 0.236170i
\(209\) −1.25204 −0.0866054
\(210\) 0.596286 4.40312i 0.0411477 0.303844i
\(211\) 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
\(213\) −0.648775 + 1.12096i −0.0444534 + 0.0768071i
\(214\) 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
\(222\) −15.0301 8.69893i −1.00876 0.583834i
\(223\) −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
\(225\) −14.4597 3.98954i −0.963982 0.265969i
\(226\) −4.67660 −0.311083
\(227\) 18.5524 18.5524i 1.23136 1.23136i 0.267923 0.963440i \(-0.413663\pi\)
0.963440 0.267923i \(-0.0863373\pi\)
\(228\) −1.49908 0.867616i −0.0992790 0.0574593i
\(229\) 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 0.993017 0.117971i \(-0.0376389\pi\)
−0.117971 + 0.993017i \(0.537639\pi\)
\(234\) −12.5301 + 7.19883i −0.819116 + 0.470602i
\(235\) 17.8632 + 7.45458i 1.16527 + 0.486283i
\(236\) 9.08034i 0.591080i
\(237\) 4.20257 7.26126i 0.272986 0.471669i
\(238\) −3.48857 + 3.48857i −0.226130 + 0.226130i
\(239\) −0.359134 −0.0232304 −0.0116152 0.999933i \(-0.503697\pi\)
−0.0116152 + 0.999933i \(0.503697\pi\)
\(240\) 0.519749 3.83795i 0.0335496 0.247739i
\(241\) 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
\(243\) 13.5412 7.72250i 0.868666 0.495399i
\(244\) 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 \(-0.861121\pi\)
0.906321 0.422590i \(-0.138879\pi\)
\(252\) 3.32260 + 0.897850i 0.209304 + 0.0565592i
\(253\) 6.90592 6.90592i 0.434171 0.434171i
\(254\) 7.65012 0.480011
\(255\) 10.0899 + 13.2508i 0.631856 + 0.829799i
\(256\) 1.00000 0.0625000
\(257\) −16.2263 + 16.2263i −1.01217 + 1.01217i −0.0122435 + 0.999925i \(0.503897\pi\)
−0.999925 + 0.0122435i \(0.996103\pi\)
\(258\) 6.87594 11.8803i 0.428077 0.739638i
\(259\) 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 0.805870 0.592093i \(-0.201698\pi\)
−0.592093 + 0.805870i \(0.701698\pi\)
\(264\) 2.09530 0.559051i 0.128957 0.0344072i
\(265\) 0.566634 1.35781i 0.0348080 0.0834096i
\(266\) 1.14726i 0.0703429i
\(267\) 19.1855 + 11.1039i 1.17413 + 0.679548i
\(268\) −2.40925 + 2.40925i −0.147168 + 0.147168i
\(269\) −4.91421 −0.299625 −0.149812 0.988714i \(-0.547867\pi\)
−0.149812 + 0.988714i \(0.547867\pi\)
\(270\) 4.50885 10.7084i 0.274400 0.651694i
\(271\) 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
\(273\) −8.28432 4.79468i −0.501390 0.290187i
\(274\) 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 \(-0.798359\pi\)
0.805977 0.591947i \(-0.201641\pi\)
\(282\) −7.51042 + 12.9766i −0.447239 + 0.772746i
\(283\) 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
\(285\) −3.83795 0.519749i −0.227341 0.0307873i
\(286\) −6.03099 −0.356620
\(287\) 0.210261 0.210261i 0.0124113 0.0124113i
\(288\) 2.89612 + 0.782605i 0.170656 + 0.0461154i
\(289\) 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 0.831483 0.555550i \(-0.187492\pi\)
−0.555550 + 0.831483i \(0.687492\pi\)
\(294\) −2.53789 9.51188i −0.148013 0.554744i
\(295\) −7.72048 18.7792i −0.449504 1.09336i
\(296\) 10.0262i 0.582763i
\(297\) 6.50575 + 0.0207086i 0.377502 + 0.00120163i
\(298\) −0.486611 + 0.486611i −0.0281886 + 0.0281886i
\(299\) −37.5741 −2.17297
\(300\) −2.18828 8.37922i −0.126341 0.483775i
\(301\) 9.09213 0.524062
\(302\) 5.50294 5.50294i 0.316659 0.316659i
\(303\) 3.08457 5.32956i 0.177204 0.306175i
\(304\) 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 \(-0.822412\pi\)
0.848363 0.529415i \(-0.177588\pi\)
\(312\) −7.22097 4.17925i −0.408807 0.236603i
\(313\) −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
\(315\) 7.63490 0.968159i 0.430178 0.0545496i
\(316\) 4.84381 0.272485
\(317\) −11.0822 + 11.0822i −0.622438 + 0.622438i −0.946154 0.323716i \(-0.895068\pi\)
0.323716 + 0.946154i \(0.395068\pi\)
\(318\) 0.986372 + 0.570878i 0.0553130 + 0.0320133i
\(319\) 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
\(327\) −16.9182 + 29.2315i −0.935578 + 1.61651i
\(328\) 0.183273 0.183273i 0.0101195 0.0101195i
\(329\) −9.93112 −0.547520
\(330\) 3.85798 2.93769i 0.212375 0.161714i
\(331\) 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
\(333\) 7.84658 29.0372i 0.429990 1.59123i
\(334\) 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
\(342\) 0.782605 2.89612i 0.0423184 0.156604i
\(343\) 10.2895 10.2895i 0.555583 0.555583i
\(344\) 7.92509 0.427292
\(345\) 24.0359 18.3023i 1.29405 0.985364i
\(346\) −4.47431 −0.240541
\(347\) 5.08826 5.08826i 0.273152 0.273152i −0.557216 0.830368i \(-0.688130\pi\)
0.830368 + 0.557216i \(0.188130\pi\)
\(348\) 4.77097 8.24334i 0.255751 0.441890i
\(349\) 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 0.870712 0.491794i \(-0.163659\pi\)
−0.491794 + 0.870712i \(0.663659\pi\)
\(354\) 15.1960 4.05448i 0.807659 0.215493i
\(355\) −1.54647 + 0.635783i −0.0820780 + 0.0337438i
\(356\) 12.7982i 0.678302i
\(357\) −7.39583 4.28045i −0.391429 0.226546i
\(358\) 2.70543 2.70543i 0.142986 0.142986i
\(359\) 24.6824 1.30269 0.651343 0.758783i \(-0.274206\pi\)
0.651343 + 0.758783i \(0.274206\pi\)
\(360\) 6.65491 0.843889i 0.350745 0.0444768i
\(361\) −1.00000 −0.0526316
\(362\) −8.29169 + 8.29169i −0.435801 + 0.435801i
\(363\) −14.1399 8.18370i −0.742153 0.429533i
\(364\) 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
\(372\) 5.04073 8.70945i 0.261350 0.451564i
\(373\) −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
\(375\) −11.6500 15.4686i −0.601602 0.798796i
\(376\) −8.65639 −0.446419
\(377\) −18.7298 + 18.7298i −0.964636 + 0.964636i
\(378\) −0.0189755 + 5.96130i −0.000975995 + 0.306616i
\(379\) 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 \(-0.942990\pi\)
−0.178146 0.984004i \(-0.557010\pi\)
\(384\) 0.446512 + 1.67351i 0.0227860 + 0.0854008i
\(385\) 2.96416 + 1.23699i 0.151068 + 0.0630428i
\(386\) 9.54847i 0.486004i
\(387\) 22.9520 + 6.20221i 1.16672 + 0.315276i
\(388\) −12.5537 + 12.5537i −0.637317 + 0.637317i
\(389\) 20.2169 1.02504 0.512519 0.858676i \(-0.328713\pi\)
0.512519 + 0.858676i \(0.328713\pi\)
\(390\) −18.4871 2.50359i −0.936133 0.126774i
\(391\) −33.5443 −1.69641
\(392\) 4.01905 4.01905i 0.202993 0.202993i
\(393\) −18.6179 + 32.1683i −0.939148 + 1.62267i
\(394\) 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 \(0.182134\pi\)
−0.840716 + 0.541476i \(0.817866\pi\)
\(402\) −5.10765 2.95613i −0.254746 0.147439i
\(403\) −19.7889 + 19.7889i −0.985754 + 0.985754i
\(404\) 3.55522 0.176879
\(405\) 19.9339 + 2.76416i 0.990522 + 0.137352i
\(406\) 6.30870 0.313096
\(407\) 8.87649 8.87649i 0.439991 0.439991i
\(408\) −6.44652 3.73103i −0.319150 0.184713i
\(409\) 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
\(417\) 9.17576 15.8540i 0.449339 0.776375i
\(418\) 0.885325 0.885325i 0.0433027 0.0433027i
\(419\) −35.8879 −1.75324 −0.876620 0.481184i \(-0.840207\pi\)
−0.876620 + 0.481184i \(0.840207\pi\)
\(420\) 2.69184 + 3.53511i 0.131348 + 0.172496i
\(421\) −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
\(423\) −25.0700 6.77453i −1.21894 0.329389i
\(424\) 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 \(0.00341416\pi\)
−0.999942 + 0.0107257i \(0.996586\pi\)
\(432\) −0.0165399 + 5.19613i −0.000795775 + 0.249999i
\(433\) 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
\(435\) 2.85806 21.1046i 0.137034 1.01189i
\(436\) −19.4996 −0.933863
\(437\) 5.51574 5.51574i 0.263854 0.263854i
\(438\) 6.69932 11.5752i 0.320106 0.553084i
\(439\) 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 0.552450 0.833546i \(-0.313693\pi\)
−0.833546 + 0.552450i \(0.813693\pi\)
\(444\) 16.7790 4.47684i 0.796295 0.212461i
\(445\) 10.8815 + 26.4681i 0.515834 + 1.25471i
\(446\) 18.4923i 0.875634i
\(447\) −1.03162 0.597069i −0.0487942 0.0282404i
\(448\) −0.811234 + 0.811234i −0.0383272 + 0.0383272i
\(449\) 16.3599 0.772074 0.386037 0.922483i \(-0.373844\pi\)
0.386037 + 0.922483i \(0.373844\pi\)
\(450\) 13.0456 7.40354i 0.614975 0.349006i
\(451\) 0.324512 0.0152807
\(452\) 3.30686 3.30686i 0.155541 0.155541i
\(453\) 11.6664 + 6.75209i 0.548133 + 0.317241i
\(454\) 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 \(-0.871504\pi\)
0.919621 0.392806i \(-0.128496\pi\)
\(462\) −1.24626 + 2.15330i −0.0579811 + 0.100180i
\(463\) −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
\(465\) 3.01967 22.2980i 0.140034 1.03404i
\(466\) −18.8897 −0.875046
\(467\) −12.4366 + 12.4366i −0.575497 + 0.575497i −0.933659 0.358162i \(-0.883404\pi\)
0.358162 + 0.933659i \(0.383404\pi\)
\(468\) 3.76975 13.9504i 0.174257 0.644859i
\(469\) 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
\(477\) −0.514942 + 1.90561i −0.0235776 + 0.0872517i
\(478\) 0.253946 0.253946i 0.0116152 0.0116152i
\(479\) 37.6990 1.72251 0.861256 0.508172i \(-0.169679\pi\)
0.861256 + 0.508172i \(0.169679\pi\)
\(480\) 2.34632 + 3.08136i 0.107094 + 0.140644i
\(481\) −48.2957 −2.20210
\(482\) −3.83502 + 3.83502i −0.174681 + 0.174681i
\(483\) −7.76440 + 13.4154i −0.353292 + 0.610423i
\(484\) 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 \(-0.919155\pi\)
0.967920 0.251260i \(-0.0808448\pi\)
\(492\) 0.388542 + 0.224875i 0.0175168 + 0.0101381i
\(493\) −16.7211 + 16.7211i −0.753079 + 0.753079i
\(494\) −4.81693 −0.216724
\(495\) 6.63888 + 5.14465i 0.298395 + 0.231235i
\(496\) 5.80986 0.260870
\(497\) 0.606615 0.606615i 0.0272104 0.0272104i
\(498\) 8.96537 + 5.18885i 0.401748 + 0.232518i
\(499\) 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 0.999848 0.0174544i \(-0.00555619\pi\)
−0.0174544 + 0.999848i \(0.505556\pi\)
\(504\) −2.98431 + 1.71456i −0.132932 + 0.0763725i
\(505\) 7.35260 3.02280i 0.327186 0.134513i
\(506\) 9.76645i 0.434171i
\(507\) −8.85215 + 15.2949i −0.393138 + 0.679269i
\(508\) −5.40945 + 5.40945i −0.240006 + 0.240006i
\(509\) 44.4681 1.97101 0.985507 0.169634i \(-0.0542586\pi\)
0.985507 + 0.169634i \(0.0542586\pi\)
\(510\) −16.5044 2.23508i −0.730827 0.0989712i
\(511\) 8.85858 0.391881
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 5.19613 + 0.0165399i 0.229415 + 0.000730253i
\(514\) 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 \(0.182618\pi\)
−0.839892 + 0.542753i \(0.817382\pi\)
\(522\) 15.9256 + 4.30349i 0.697044 + 0.188359i
\(523\) −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
\(525\) 8.57273 + 5.02230i 0.374144 + 0.219191i
\(526\) −4.90290 −0.213777
\(527\) −17.6665 + 17.6665i −0.769566 + 0.769566i
\(528\) −1.08629 + 1.87691i −0.0472747 + 0.0816819i
\(529\) 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
\(537\) 5.73556 + 3.31955i 0.247508 + 0.143249i
\(538\) 3.47487 3.47487i 0.149812 0.149812i
\(539\) 7.11634 0.306522
\(540\) 4.38375 + 10.7602i 0.188647 + 0.463047i
\(541\) 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
\(543\) −17.5785 10.1739i −0.754367 0.436602i
\(544\) 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
\(552\) −6.76778 + 11.6935i −0.288056 + 0.497707i
\(553\) −3.92946 + 3.92946i −0.167098 + 0.167098i
\(554\) 16.2375 0.689866
\(555\) 30.8944 23.5248i 1.31140 0.998572i
\(556\) 10.5758 0.448515
\(557\) −23.0216 + 23.0216i −0.975455 + 0.975455i −0.999706 0.0242514i \(-0.992280\pi\)
0.0242514 + 0.999706i \(0.492280\pi\)
\(558\) 16.8261 + 4.54682i 0.712304 + 0.192482i
\(559\) 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 \(0.0839453\pi\)
0.260676 + 0.965426i \(0.416055\pi\)
\(564\) −3.86518 14.4865i −0.162754 0.609993i
\(565\) 4.02732 9.65057i 0.169431 0.406003i
\(566\) 19.1667i 0.805635i
\(567\) −9.98475 + 2.63004i −0.419320 + 0.110451i
\(568\) 0.528751 0.528751i 0.0221859 0.0221859i
\(569\) 31.9886 1.34103 0.670515 0.741896i \(-0.266073\pi\)
0.670515 + 0.741896i \(0.266073\pi\)
\(570\) 3.08136 2.34632i 0.129064 0.0982766i
\(571\) −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
\(573\) 9.56353 16.5240i 0.399522 0.690300i
\(574\) 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
\(582\) −26.6141 15.4033i −1.10319 0.638488i
\(583\) −0.582531 + 0.582531i −0.0241260 + 0.0241260i
\(584\) 7.72152 0.319519
\(585\) −4.06496 32.0563i −0.168065 1.32536i
\(586\) −6.67963 −0.275933
\(587\) 19.3270 19.3270i 0.797710 0.797710i −0.185024 0.982734i \(-0.559236\pi\)
0.982734 + 0.185024i \(0.0592363\pi\)
\(588\) 8.52047 + 4.93136i 0.351378 + 0.203366i
\(589\) 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 0.601119 0.799159i \(-0.294722\pi\)
−0.799159 + 0.601119i \(0.794722\pi\)
\(594\) −4.61491 + 4.58562i −0.189352 + 0.188150i
\(595\) −4.19473 10.2032i −0.171967 0.418290i
\(596\) 0.688172i 0.0281886i
\(597\) 20.6248 35.6358i 0.844117 1.45848i
\(598\) 26.5689 26.5689i 1.08648 1.08648i
\(599\) 12.4755 0.509735 0.254868 0.966976i \(-0.417968\pi\)
0.254868 + 0.966976i \(0.417968\pi\)
\(600\) 7.47236 + 4.37766i 0.305058 + 0.178717i
\(601\) 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
\(603\) 2.66648 9.86764i 0.108588 0.401841i
\(604\) 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
\(612\) 3.36545 12.4543i 0.136040 0.503433i
\(613\) −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
\(615\) 0.994746 + 0.134712i 0.0401120 + 0.00543211i
\(616\) −1.43641 −0.0578747
\(617\) −22.1031 + 22.1031i −0.889839 + 0.889839i −0.994507 0.104668i \(-0.966622\pi\)
0.104668 + 0.994507i \(0.466622\pi\)
\(618\) −10.6578 + 18.4147i −0.428720 + 0.740748i
\(619\) 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
\(627\) 1.87691 + 1.08629i 0.0749565 + 0.0433822i
\(628\) 4.92864 4.92864i 0.196674 0.196674i
\(629\) −43.1160 −1.71915
\(630\) −4.71410 + 6.08328i −0.187814 + 0.242364i
\(631\) −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
\(633\) −25.3763 14.6869i −1.00862 0.583752i
\(634\) 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 \(-0.828343\pi\)
0.858081 0.513515i \(-0.171657\pi\)
\(642\) −6.47461 + 11.1869i −0.255533 + 0.441513i
\(643\) 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
\(645\) 18.5948 + 24.4200i 0.732170 + 0.961538i
\(646\) −4.30032 −0.169194
\(647\) 27.1481 27.1481i 1.06730 1.06730i 0.0697360 0.997565i \(-0.477784\pi\)
0.997565 0.0697360i \(-0.0222157\pi\)
\(648\) −8.70314 + 2.29245i −0.341892 + 0.0900561i
\(649\) 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 0.353810 0.935317i \(-0.384886\pi\)
−0.935317 + 0.353810i \(0.884886\pi\)
\(654\) −8.70682 32.6328i −0.340464 1.27604i
\(655\) −44.3789 + 18.2450i −1.73403 + 0.712893i
\(656\) 0.259187i 0.0101195i
\(657\) 22.3625 + 6.04290i 0.872444 + 0.235756i
\(658\) 7.02236 7.02236i 0.273760 0.273760i
\(659\) 3.67408 0.143122 0.0715609 0.997436i \(-0.477202\pi\)
0.0715609 + 0.997436i \(0.477202\pi\)
\(660\) −0.650746 + 4.80526i −0.0253302 + 0.187045i
\(661\) 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
\(663\) −17.9721 + 31.0525i −0.697979 + 1.20598i
\(664\) 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
\(672\) −1.71983 0.995380i −0.0663440 0.0383976i
\(673\) 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
\(675\) 18.2149 + 18.5261i 0.701092 + 0.713071i
\(676\) −10.2028 −0.392417
\(677\) 19.1276 19.1276i 0.735134 0.735134i −0.236498 0.971632i \(-0.576000\pi\)
0.971632 + 0.236498i \(0.0759996\pi\)
\(678\) 7.01060 + 4.05749i 0.269240 + 0.155827i
\(679\) 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 0.626851 0.779139i \(-0.284343\pi\)
−0.779139 + 0.626851i \(0.784343\pi\)
\(684\) 1.49448 + 2.60125i 0.0571430 + 0.0994614i
\(685\) −39.7742 16.5984i −1.51970 0.634191i
\(686\) 14.5516i 0.555583i
\(687\) 2.28896 3.95490i 0.0873293 0.150889i
\(688\) −5.60388 + 5.60388i −0.213646 + 0.213646i
\(689\) 3.16947 0.120747
\(690\) −4.05426 + 29.9377i −0.154343 + 1.13971i
\(691\) −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
\(693\) −4.16003 1.12414i −0.158026 0.0427027i
\(694\) 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 \(-0.688232\pi\)
0.557480 0.830191i \(-0.311768\pi\)
\(702\) 25.0294 + 0.0796715i 0.944673 + 0.00300701i
\(703\) 7.08962 7.08962i 0.267390 0.267390i
\(704\) −1.25204 −0.0471880
\(705\) −20.3107 26.6734i −0.764944 1.00458i
\(706\) −10.0681 −0.378918
\(707\) −2.88412 + 2.88412i −0.108468 + 0.108468i
\(708\) −7.87825 + 13.6122i −0.296083 + 0.511576i
\(709\) 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
\(717\) 0.538370 + 0.311590i 0.0201058 + 0.0116366i
\(718\) −17.4531 + 17.4531i −0.651343 + 0.651343i
\(719\) −22.3343 −0.832930 −0.416465 0.909152i \(-0.636731\pi\)
−0.416465 + 0.909152i \(0.636731\pi\)
\(720\) −4.10901 + 5.30245i −0.153134 + 0.197611i
\(721\) −14.0929 −0.524848
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) −8.13033 4.70555i −0.302370 0.175001i
\(724\) 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
\(732\) −5.48875 + 9.48354i −0.202870 + 0.350522i
\(733\) −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
\(735\) 21.8141 + 2.95415i 0.804626 + 0.108965i
\(736\) −7.80043 −0.287528
\(737\) 3.01647 3.01647i 0.111113 0.111113i
\(738\) −0.202841 + 0.750637i −0.00746667 + 0.0276313i
\(739\) 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 0.0185673 0.999828i \(-0.494090\pi\)
−0.999828 + 0.0185673i \(0.994090\pi\)
\(744\) 2.59417 + 9.72284i 0.0951070 + 0.356457i
\(745\) −0.585112 1.42322i −0.0214369 0.0521426i
\(746\) 29.2529i 1.07102i
\(747\) −4.68043 + 17.3205i −0.171248 + 0.633724i
\(748\) 3.80718 3.80718i 0.139204 0.139204i
\(749\) −8.56145 −0.312828
\(750\) 19.1757 + 2.70018i 0.700199 + 0.0985966i
\(751\) −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
\(753\) −11.6175 + 20.0729i −0.423366 + 0.731498i
\(754\) 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 \(-0.956493\pi\)
0.990673 0.136257i \(-0.0435074\pi\)
\(762\) −11.4681 6.63737i −0.415447 0.240447i
\(763\) 15.8188 15.8188i 0.572678 0.572678i
\(764\) 11.0228 0.398790
\(765\) −3.62899 28.6182i −0.131206 1.03469i
\(766\) 32.1645 1.16215
\(767\) 30.9284 30.9284i 1.11676 1.11676i
\(768\) −1.49908 0.867616i −0.0540934 0.0313074i
\(769\) 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 0.0717268 0.997424i \(-0.477149\pi\)
−0.997424 + 0.0717268i \(0.977149\pi\)
\(774\) −20.6152 + 11.8439i −0.740997 + 0.425721i
\(775\) 20.6493 20.4321i 0.741744 0.733941i
\(776\) 17.7536i 0.637317i
\(777\) −9.97992 + 17.2435i −0.358028 + 0.618606i
\(778\)