Properties

Label 570.2.k.b.77.4
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 77.4
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.0916341 - 1.72963i) q^{3} -1.00000i q^{4} +(-2.17182 - 0.532166i) q^{5} +(1.28782 + 1.15823i) q^{6} +(1.32508 + 1.32508i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98321 + 0.316985i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.0916341 - 1.72963i) q^{3} -1.00000i q^{4} +(-2.17182 - 0.532166i) q^{5} +(1.28782 + 1.15823i) q^{6} +(1.32508 + 1.32508i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98321 + 0.316985i) q^{9} +(1.91201 - 1.15941i) q^{10} +4.14708i q^{11} +(-1.72963 + 0.0916341i) q^{12} +(-3.92411 + 3.92411i) q^{13} -1.87395 q^{14} +(-0.721435 + 3.80520i) q^{15} -1.00000 q^{16} +(5.01690 - 5.01690i) q^{17} +(1.88530 - 2.33359i) q^{18} -1.00000i q^{19} +(-0.532166 + 2.17182i) q^{20} +(2.17047 - 2.41332i) q^{21} +(-2.93243 - 2.93243i) q^{22} +(5.46874 + 5.46874i) q^{23} +(1.15823 - 1.28782i) q^{24} +(4.43360 + 2.31154i) q^{25} -5.54954i q^{26} +(0.821629 + 5.13078i) q^{27} +(1.32508 - 1.32508i) q^{28} +0.0964393 q^{29} +(-2.18055 - 3.20081i) q^{30} +0.0111704 q^{31} +(0.707107 - 0.707107i) q^{32} +(7.17289 - 0.380013i) q^{33} +7.09497i q^{34} +(-2.17267 - 3.58300i) q^{35} +(0.316985 + 2.98321i) q^{36} +(1.55524 + 1.55524i) q^{37} +(0.707107 + 0.707107i) q^{38} +(7.14683 + 6.42767i) q^{39} +(-1.15941 - 1.91201i) q^{40} +8.45893i q^{41} +(0.171717 + 3.24123i) q^{42} +(0.130534 - 0.130534i) q^{43} +4.14708 q^{44} +(6.64767 + 0.899127i) q^{45} -7.73397 q^{46} +(-1.71433 + 1.71433i) q^{47} +(0.0916341 + 1.72963i) q^{48} -3.48832i q^{49} +(-4.76953 + 1.50052i) q^{50} +(-9.13708 - 8.21764i) q^{51} +(3.92411 + 3.92411i) q^{52} +(8.88222 + 8.88222i) q^{53} +(-4.20899 - 3.04703i) q^{54} +(2.20693 - 9.00670i) q^{55} +1.87395i q^{56} +(-1.72963 + 0.0916341i) q^{57} +(-0.0681929 + 0.0681929i) q^{58} -6.40826 q^{59} +(3.80520 + 0.721435i) q^{60} -10.2484 q^{61} +(-0.00789865 + 0.00789865i) q^{62} +(-4.37302 - 3.53296i) q^{63} +1.00000i q^{64} +(10.6107 - 6.43419i) q^{65} +(-4.80329 + 5.34071i) q^{66} +(4.77624 + 4.77624i) q^{67} +(-5.01690 - 5.01690i) q^{68} +(8.95775 - 9.95999i) q^{69} +(4.06987 + 0.997251i) q^{70} -9.47461i q^{71} +(-2.33359 - 1.88530i) q^{72} +(-4.04666 + 4.04666i) q^{73} -2.19944 q^{74} +(3.59182 - 7.88028i) q^{75} -1.00000 q^{76} +(-5.49521 + 5.49521i) q^{77} +(-9.59862 + 0.508527i) q^{78} +12.4743i q^{79} +(2.17182 + 0.532166i) q^{80} +(8.79904 - 1.89126i) q^{81} +(-5.98137 - 5.98137i) q^{82} +(1.43685 + 1.43685i) q^{83} +(-2.41332 - 2.17047i) q^{84} +(-13.5656 + 8.22598i) q^{85} +0.184604i q^{86} +(-0.00883712 - 0.166804i) q^{87} +(-2.93243 + 2.93243i) q^{88} -17.0881 q^{89} +(-5.33639 + 4.06484i) q^{90} -10.3995 q^{91} +(5.46874 - 5.46874i) q^{92} +(-0.00102359 - 0.0193206i) q^{93} -2.42443i q^{94} +(-0.532166 + 2.17182i) q^{95} +(-1.28782 - 1.15823i) q^{96} +(3.48454 + 3.48454i) q^{97} +(2.46662 + 2.46662i) q^{98} +(-1.31456 - 12.3716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} + 16q^{21} - 4q^{22} + 16q^{25} - 44q^{27} + 20q^{28} + 32q^{30} - 24q^{31} - 4q^{33} + 4q^{36} - 8q^{40} + 12q^{42} - 8q^{43} + 28q^{45} - 16q^{46} - 4q^{48} + 40q^{51} - 8q^{52} - 36q^{55} - 4q^{57} + 44q^{58} + 16q^{60} - 120q^{61} - 12q^{63} + 80q^{67} - 36q^{70} + 44q^{73} + 4q^{75} - 36q^{76} - 64q^{78} + 36q^{81} + 8q^{82} - 24q^{85} - 28q^{87} - 4q^{88} + 44q^{90} - 72q^{93} - 4q^{96} + 92q^{97} + O(q^{100}) \)

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
\(3\) −0.0916341 1.72963i −0.0529049 0.998600i
\(4\) 1.00000i 0.500000i
\(5\) −2.17182 0.532166i −0.971267 0.237992i
\(6\) 1.28782 + 1.15823i 0.525752 + 0.472847i
\(7\) 1.32508 + 1.32508i 0.500833 + 0.500833i 0.911697 0.410863i \(-0.134773\pi\)
−0.410863 + 0.911697i \(0.634773\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.98321 + 0.316985i −0.994402 + 0.105662i
\(10\) 1.91201 1.15941i 0.604630 0.366638i
\(11\) 4.14708i 1.25039i 0.780468 + 0.625195i \(0.214981\pi\)
−0.780468 + 0.625195i \(0.785019\pi\)
\(12\) −1.72963 + 0.0916341i −0.499300 + 0.0264525i
\(13\) −3.92411 + 3.92411i −1.08835 + 1.08835i −0.0926554 + 0.995698i \(0.529536\pi\)
−0.995698 + 0.0926554i \(0.970464\pi\)
\(14\) −1.87395 −0.500833
\(15\) −0.721435 + 3.80520i −0.186274 + 0.982498i
\(16\) −1.00000 −0.250000
\(17\) 5.01690 5.01690i 1.21678 1.21678i 0.248024 0.968754i \(-0.420219\pi\)
0.968754 0.248024i \(-0.0797813\pi\)
\(18\) 1.88530 2.33359i 0.444370 0.550032i
\(19\) 1.00000i 0.229416i
\(20\) −0.532166 + 2.17182i −0.118996 + 0.485634i
\(21\) 2.17047 2.41332i 0.473635 0.526629i
\(22\) −2.93243 2.93243i −0.625195 0.625195i
\(23\) 5.46874 + 5.46874i 1.14031 + 1.14031i 0.988393 + 0.151918i \(0.0485449\pi\)
0.151918 + 0.988393i \(0.451455\pi\)
\(24\) 1.15823 1.28782i 0.236424 0.262876i
\(25\) 4.43360 + 2.31154i 0.886720 + 0.462307i
\(26\) 5.54954i 1.08835i
\(27\) 0.821629 + 5.13078i 0.158123 + 0.987419i
\(28\) 1.32508 1.32508i 0.250417 0.250417i
\(29\) 0.0964393 0.0179083 0.00895416 0.999960i \(-0.497150\pi\)
0.00895416 + 0.999960i \(0.497150\pi\)
\(30\) −2.18055 3.20081i −0.398112 0.584386i
\(31\) 0.0111704 0.00200626 0.00100313 0.999999i \(-0.499681\pi\)
0.00100313 + 0.999999i \(0.499681\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 7.17289 0.380013i 1.24864 0.0661519i
\(34\) 7.09497i 1.21678i
\(35\) −2.17267 3.58300i −0.367249 0.605637i
\(36\) 0.316985 + 2.98321i 0.0528309 + 0.497201i
\(37\) 1.55524 + 1.55524i 0.255679 + 0.255679i 0.823294 0.567615i \(-0.192134\pi\)
−0.567615 + 0.823294i \(0.692134\pi\)
\(38\) 0.707107 + 0.707107i 0.114708 + 0.114708i
\(39\) 7.14683 + 6.42767i 1.14441 + 1.02925i
\(40\) −1.15941 1.91201i −0.183319 0.302315i
\(41\) 8.45893i 1.32106i 0.750798 + 0.660532i \(0.229669\pi\)
−0.750798 + 0.660532i \(0.770331\pi\)
\(42\) 0.171717 + 3.24123i 0.0264966 + 0.500132i
\(43\) 0.130534 0.130534i 0.0199063 0.0199063i −0.697084 0.716990i \(-0.745519\pi\)
0.716990 + 0.697084i \(0.245519\pi\)
\(44\) 4.14708 0.625195
\(45\) 6.64767 + 0.899127i 0.990977 + 0.134034i
\(46\) −7.73397 −1.14031
\(47\) −1.71433 + 1.71433i −0.250061 + 0.250061i −0.820996 0.570934i \(-0.806581\pi\)
0.570934 + 0.820996i \(0.306581\pi\)
\(48\) 0.0916341 + 1.72963i 0.0132262 + 0.249650i
\(49\) 3.48832i 0.498332i
\(50\) −4.76953 + 1.50052i −0.674514 + 0.212206i
\(51\) −9.13708 8.21764i −1.27945 1.15070i
\(52\) 3.92411 + 3.92411i 0.544177 + 0.544177i
\(53\) 8.88222 + 8.88222i 1.22007 + 1.22007i 0.967608 + 0.252459i \(0.0812392\pi\)
0.252459 + 0.967608i \(0.418761\pi\)
\(54\) −4.20899 3.04703i −0.572771 0.414648i
\(55\) 2.20693 9.00670i 0.297583 1.21446i
\(56\) 1.87395i 0.250417i
\(57\) −1.72963 + 0.0916341i −0.229094 + 0.0121372i
\(58\) −0.0681929 + 0.0681929i −0.00895416 + 0.00895416i
\(59\) −6.40826 −0.834284 −0.417142 0.908841i \(-0.636968\pi\)
−0.417142 + 0.908841i \(0.636968\pi\)
\(60\) 3.80520 + 0.721435i 0.491249 + 0.0931369i
\(61\) −10.2484 −1.31218 −0.656090 0.754683i \(-0.727791\pi\)
−0.656090 + 0.754683i \(0.727791\pi\)
\(62\) −0.00789865 + 0.00789865i −0.00100313 + 0.00100313i
\(63\) −4.37302 3.53296i −0.550949 0.445111i
\(64\) 1.00000i 0.125000i
\(65\) 10.6107 6.43419i 1.31610 0.798063i
\(66\) −4.80329 + 5.34071i −0.591244 + 0.657396i
\(67\) 4.77624 + 4.77624i 0.583511 + 0.583511i 0.935866 0.352355i \(-0.114619\pi\)
−0.352355 + 0.935866i \(0.614619\pi\)
\(68\) −5.01690 5.01690i −0.608389 0.608389i
\(69\) 8.95775 9.95999i 1.07839 1.19904i
\(70\) 4.06987 + 0.997251i 0.486443 + 0.119194i
\(71\) 9.47461i 1.12443i −0.826991 0.562215i \(-0.809949\pi\)
0.826991 0.562215i \(-0.190051\pi\)
\(72\) −2.33359 1.88530i −0.275016 0.222185i
\(73\) −4.04666 + 4.04666i −0.473626 + 0.473626i −0.903086 0.429460i \(-0.858704\pi\)
0.429460 + 0.903086i \(0.358704\pi\)
\(74\) −2.19944 −0.255679
\(75\) 3.59182 7.88028i 0.414748 0.909936i
\(76\) −1.00000 −0.114708
\(77\) −5.49521 + 5.49521i −0.626238 + 0.626238i
\(78\) −9.59862 + 0.508527i −1.08683 + 0.0575793i
\(79\) 12.4743i 1.40347i 0.712438 + 0.701735i \(0.247591\pi\)
−0.712438 + 0.701735i \(0.752409\pi\)
\(80\) 2.17182 + 0.532166i 0.242817 + 0.0594980i
\(81\) 8.79904 1.89126i 0.977671 0.210140i
\(82\) −5.98137 5.98137i −0.660532 0.660532i
\(83\) 1.43685 + 1.43685i 0.157715 + 0.157715i 0.781553 0.623838i \(-0.214428\pi\)
−0.623838 + 0.781553i \(0.714428\pi\)
\(84\) −2.41332 2.17047i −0.263314 0.236818i
\(85\) −13.5656 + 8.22598i −1.47140 + 0.892233i
\(86\) 0.184604i 0.0199063i
\(87\) −0.00883712 0.166804i −0.000947439 0.0178832i
\(88\) −2.93243 + 2.93243i −0.312598 + 0.312598i
\(89\) −17.0881 −1.81134 −0.905668 0.423988i \(-0.860630\pi\)
−0.905668 + 0.423988i \(0.860630\pi\)
\(90\) −5.33639 + 4.06484i −0.562505 + 0.428471i
\(91\) −10.3995 −1.09017
\(92\) 5.46874 5.46874i 0.570155 0.570155i
\(93\) −0.00102359 0.0193206i −0.000106141 0.00200345i
\(94\) 2.42443i 0.250061i
\(95\) −0.532166 + 2.17182i −0.0545991 + 0.222824i
\(96\) −1.28782 1.15823i −0.131438 0.118212i
\(97\) 3.48454 + 3.48454i 0.353801 + 0.353801i 0.861522 0.507721i \(-0.169512\pi\)
−0.507721 + 0.861522i \(0.669512\pi\)
\(98\) 2.46662 + 2.46662i 0.249166 + 0.249166i
\(99\) −1.31456 12.3716i −0.132118 1.24339i
\(100\) 2.31154 4.43360i 0.231154 0.443360i
\(101\) 16.2835i 1.62027i 0.586244 + 0.810135i \(0.300606\pi\)
−0.586244 + 0.810135i \(0.699394\pi\)
\(102\) 12.2716 0.650141i 1.21507 0.0643736i
\(103\) 2.44289 2.44289i 0.240705 0.240705i −0.576437 0.817142i \(-0.695557\pi\)
0.817142 + 0.576437i \(0.195557\pi\)
\(104\) −5.54954 −0.544177
\(105\) −5.99815 + 4.08623i −0.585360 + 0.398776i
\(106\) −12.5614 −1.22007
\(107\) 1.32951 1.32951i 0.128529 0.128529i −0.639916 0.768445i \(-0.721031\pi\)
0.768445 + 0.639916i \(0.221031\pi\)
\(108\) 5.13078 0.821629i 0.493710 0.0790613i
\(109\) 8.51296i 0.815394i 0.913117 + 0.407697i \(0.133668\pi\)
−0.913117 + 0.407697i \(0.866332\pi\)
\(110\) 4.80816 + 7.92924i 0.458440 + 0.756023i
\(111\) 2.54746 2.83249i 0.241795 0.268848i
\(112\) −1.32508 1.32508i −0.125208 0.125208i
\(113\) −1.46934 1.46934i −0.138224 0.138224i 0.634609 0.772833i \(-0.281161\pi\)
−0.772833 + 0.634609i \(0.781161\pi\)
\(114\) 1.15823 1.28782i 0.108479 0.120616i
\(115\) −8.96684 14.7874i −0.836162 1.37893i
\(116\) 0.0964393i 0.00895416i
\(117\) 10.4626 12.9503i 0.967264 1.19726i
\(118\) 4.53132 4.53132i 0.417142 0.417142i
\(119\) 13.2956 1.21881
\(120\) −3.20081 + 2.18055i −0.292193 + 0.199056i
\(121\) −6.19825 −0.563477
\(122\) 7.24675 7.24675i 0.656090 0.656090i
\(123\) 14.6308 0.775126i 1.31921 0.0698908i
\(124\) 0.0111704i 0.00100313i
\(125\) −8.39885 7.37965i −0.751216 0.660056i
\(126\) 5.59037 0.594013i 0.498030 0.0529189i
\(127\) −0.469960 0.469960i −0.0417022 0.0417022i 0.685948 0.727650i \(-0.259388\pi\)
−0.727650 + 0.685948i \(0.759388\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −0.237737 0.213814i −0.0209316 0.0188253i
\(130\) −2.95328 + 12.0526i −0.259019 + 1.05708i
\(131\) 17.7953i 1.55478i −0.629018 0.777391i \(-0.716543\pi\)
0.629018 0.777391i \(-0.283457\pi\)
\(132\) −0.380013 7.17289i −0.0330759 0.624320i
\(133\) 1.32508 1.32508i 0.114899 0.114899i
\(134\) −6.75463 −0.583511
\(135\) 0.945999 11.5804i 0.0814186 0.996680i
\(136\) 7.09497 0.608389
\(137\) 9.30953 9.30953i 0.795367 0.795367i −0.186994 0.982361i \(-0.559875\pi\)
0.982361 + 0.186994i \(0.0598746\pi\)
\(138\) 0.708695 + 13.3769i 0.0603281 + 1.13871i
\(139\) 12.4068i 1.05233i −0.850383 0.526165i \(-0.823630\pi\)
0.850383 0.526165i \(-0.176370\pi\)
\(140\) −3.58300 + 2.17267i −0.302819 + 0.183624i
\(141\) 3.12225 + 2.80806i 0.262941 + 0.236482i
\(142\) 6.69956 + 6.69956i 0.562215 + 0.562215i
\(143\) −16.2736 16.2736i −1.36087 1.36087i
\(144\) 2.98321 0.316985i 0.248601 0.0264154i
\(145\) −0.209449 0.0513217i −0.0173938 0.00426204i
\(146\) 5.72284i 0.473626i
\(147\) −6.03349 + 0.319649i −0.497634 + 0.0263642i
\(148\) 1.55524 1.55524i 0.127840 0.127840i
\(149\) 10.8534 0.889142 0.444571 0.895744i \(-0.353356\pi\)
0.444571 + 0.895744i \(0.353356\pi\)
\(150\) 3.03240 + 8.11200i 0.247594 + 0.662342i
\(151\) 1.21233 0.0986577 0.0493288 0.998783i \(-0.484292\pi\)
0.0493288 + 0.998783i \(0.484292\pi\)
\(152\) 0.707107 0.707107i 0.0573539 0.0573539i
\(153\) −13.3762 + 16.5567i −1.08140 + 1.33853i
\(154\) 7.77140i 0.626238i
\(155\) −0.0242600 0.00594450i −0.00194861 0.000477474i
\(156\) 6.42767 7.14683i 0.514625 0.572204i
\(157\) 10.0557 + 10.0557i 0.802530 + 0.802530i 0.983490 0.180960i \(-0.0579204\pi\)
−0.180960 + 0.983490i \(0.557920\pi\)
\(158\) −8.82067 8.82067i −0.701735 0.701735i
\(159\) 14.5490 16.1768i 1.15381 1.28291i
\(160\) −1.91201 + 1.15941i −0.151157 + 0.0916594i
\(161\) 14.4930i 1.14221i
\(162\) −4.88454 + 7.55919i −0.383765 + 0.593906i
\(163\) −8.60942 + 8.60942i −0.674342 + 0.674342i −0.958714 0.284372i \(-0.908215\pi\)
0.284372 + 0.958714i \(0.408215\pi\)
\(164\) 8.45893 0.660532
\(165\) −15.7804 2.99185i −1.22851 0.232915i
\(166\) −2.03202 −0.157715
\(167\) −2.30123 + 2.30123i −0.178074 + 0.178074i −0.790516 0.612441i \(-0.790188\pi\)
0.612441 + 0.790516i \(0.290188\pi\)
\(168\) 3.24123 0.171717i 0.250066 0.0132483i
\(169\) 17.7974i 1.36903i
\(170\) 3.77570 15.4090i 0.289583 1.18182i
\(171\) 0.316985 + 2.98321i 0.0242405 + 0.228131i
\(172\) −0.130534 0.130534i −0.00995316 0.00995316i
\(173\) −7.70257 7.70257i −0.585616 0.585616i 0.350825 0.936441i \(-0.385901\pi\)
−0.936441 + 0.350825i \(0.885901\pi\)
\(174\) 0.124197 + 0.111699i 0.00941534 + 0.00846790i
\(175\) 2.81190 + 8.93785i 0.212560 + 0.675638i
\(176\) 4.14708i 0.312598i
\(177\) 0.587215 + 11.0839i 0.0441378 + 0.833116i
\(178\) 12.0831 12.0831i 0.905668 0.905668i
\(179\) −9.05937 −0.677129 −0.338565 0.940943i \(-0.609941\pi\)
−0.338565 + 0.940943i \(0.609941\pi\)
\(180\) 0.899127 6.64767i 0.0670170 0.495488i
\(181\) −17.9179 −1.33183 −0.665915 0.746028i \(-0.731959\pi\)
−0.665915 + 0.746028i \(0.731959\pi\)
\(182\) 7.35358 7.35358i 0.545084 0.545084i
\(183\) 0.939107 + 17.7260i 0.0694208 + 1.31034i
\(184\) 7.73397i 0.570155i
\(185\) −2.55005 4.20534i −0.187483 0.309183i
\(186\) 0.0143855 + 0.0129379i 0.00105480 + 0.000948654i
\(187\) 20.8055 + 20.8055i 1.52145 + 1.52145i
\(188\) 1.71433 + 1.71433i 0.125031 + 0.125031i
\(189\) −5.70998 + 7.88743i −0.415340 + 0.573726i
\(190\) −1.15941 1.91201i −0.0841124 0.138712i
\(191\) 8.41348i 0.608778i −0.952548 0.304389i \(-0.901548\pi\)
0.952548 0.304389i \(-0.0984522\pi\)
\(192\) 1.72963 0.0916341i 0.124825 0.00661312i
\(193\) 0.408503 0.408503i 0.0294047 0.0294047i −0.692252 0.721656i \(-0.743381\pi\)
0.721656 + 0.692252i \(0.243381\pi\)
\(194\) −4.92788 −0.353801
\(195\) −12.1010 17.7630i −0.866573 1.27204i
\(196\) −3.48832 −0.249166
\(197\) 3.06602 3.06602i 0.218445 0.218445i −0.589398 0.807843i \(-0.700635\pi\)
0.807843 + 0.589398i \(0.200635\pi\)
\(198\) 9.67757 + 7.81850i 0.687755 + 0.555636i
\(199\) 21.9659i 1.55712i −0.627570 0.778560i \(-0.715950\pi\)
0.627570 0.778560i \(-0.284050\pi\)
\(200\) 1.50052 + 4.76953i 0.106103 + 0.337257i
\(201\) 7.82344 8.69878i 0.551823 0.613564i
\(202\) −11.5142 11.5142i −0.810135 0.810135i
\(203\) 0.127790 + 0.127790i 0.00896909 + 0.00896909i
\(204\) −8.21764 + 9.13708i −0.575350 + 0.639724i
\(205\) 4.50156 18.3713i 0.314402 1.28311i
\(206\) 3.45477i 0.240705i
\(207\) −18.0479 14.5809i −1.25441 1.01344i
\(208\) 3.92411 3.92411i 0.272088 0.272088i
\(209\) 4.14708 0.286859
\(210\) 1.35193 7.13074i 0.0932921 0.492068i
\(211\) 10.9572 0.754327 0.377163 0.926147i \(-0.376899\pi\)
0.377163 + 0.926147i \(0.376899\pi\)
\(212\) 8.88222 8.88222i 0.610033 0.610033i
\(213\) −16.3875 + 0.868197i −1.12285 + 0.0594879i
\(214\) 1.88021i 0.128529i
\(215\) −0.352963 + 0.214031i −0.0240719 + 0.0145968i
\(216\) −3.04703 + 4.20899i −0.207324 + 0.286386i
\(217\) 0.0148017 + 0.0148017i 0.00100480 + 0.00100480i
\(218\) −6.01957 6.01957i −0.407697 0.407697i
\(219\) 7.37001 + 6.62839i 0.498019 + 0.447905i
\(220\) −9.00670 2.20693i −0.607232 0.148791i
\(221\) 39.3738i 2.64857i
\(222\) 0.201543 + 3.80420i 0.0135267 + 0.255321i
\(223\) −3.81435 + 3.81435i −0.255428 + 0.255428i −0.823191 0.567764i \(-0.807809\pi\)
0.567764 + 0.823191i \(0.307809\pi\)
\(224\) 1.87395 0.125208
\(225\) −13.9591 5.49041i −0.930604 0.366027i
\(226\) 2.07797 0.138224
\(227\) −8.48460 + 8.48460i −0.563143 + 0.563143i −0.930199 0.367056i \(-0.880366\pi\)
0.367056 + 0.930199i \(0.380366\pi\)
\(228\) 0.0916341 + 1.72963i 0.00606861 + 0.114547i
\(229\) 13.8975i 0.918372i 0.888340 + 0.459186i \(0.151859\pi\)
−0.888340 + 0.459186i \(0.848141\pi\)
\(230\) 16.7968 + 4.11575i 1.10755 + 0.271385i
\(231\) 10.0082 + 9.00111i 0.658492 + 0.592229i
\(232\) 0.0681929 + 0.0681929i 0.00447708 + 0.00447708i
\(233\) 21.1265 + 21.1265i 1.38404 + 1.38404i 0.837300 + 0.546744i \(0.184133\pi\)
0.546744 + 0.837300i \(0.315867\pi\)
\(234\) 1.75912 + 16.5554i 0.114997 + 1.08226i
\(235\) 4.63553 2.81091i 0.302389 0.183364i
\(236\) 6.40826i 0.417142i
\(237\) 21.5759 1.14307i 1.40150 0.0742505i
\(238\) −9.40141 + 9.40141i −0.609403 + 0.609403i
\(239\) −3.09410 −0.200141 −0.100070 0.994980i \(-0.531907\pi\)
−0.100070 + 0.994980i \(0.531907\pi\)
\(240\) 0.721435 3.80520i 0.0465684 0.245624i
\(241\) 6.62578 0.426804 0.213402 0.976964i \(-0.431546\pi\)
0.213402 + 0.976964i \(0.431546\pi\)
\(242\) 4.38282 4.38282i 0.281738 0.281738i
\(243\) −4.07747 15.0457i −0.261570 0.965185i
\(244\) 10.2484i 0.656090i
\(245\) −1.85637 + 7.57600i −0.118599 + 0.484013i
\(246\) −9.79743 + 10.8936i −0.624661 + 0.694552i
\(247\) 3.92411 + 3.92411i 0.249685 + 0.249685i
\(248\) 0.00789865 + 0.00789865i 0.000501565 + 0.000501565i
\(249\) 2.35355 2.61688i 0.149150 0.165838i
\(250\) 11.1571 0.720684i 0.705636 0.0455800i
\(251\) 21.3523i 1.34775i 0.738847 + 0.673874i \(0.235371\pi\)
−0.738847 + 0.673874i \(0.764629\pi\)
\(252\) −3.53296 + 4.37302i −0.222555 + 0.275474i
\(253\) −22.6793 + 22.6793i −1.42583 + 1.42583i
\(254\) 0.664624 0.0417022
\(255\) 15.4709 + 22.7097i 0.968828 + 1.42214i
\(256\) 1.00000 0.0625000
\(257\) 2.86047 2.86047i 0.178431 0.178431i −0.612240 0.790672i \(-0.709732\pi\)
0.790672 + 0.612240i \(0.209732\pi\)
\(258\) 0.319295 0.0169160i 0.0198784 0.00105314i
\(259\) 4.12163i 0.256106i
\(260\) −6.43419 10.6107i −0.399031 0.658051i
\(261\) −0.287698 + 0.0305698i −0.0178081 + 0.00189222i
\(262\) 12.5832 + 12.5832i 0.777391 + 0.777391i
\(263\) −19.5180 19.5180i −1.20353 1.20353i −0.973085 0.230446i \(-0.925982\pi\)
−0.230446 0.973085i \(-0.574018\pi\)
\(264\) 5.34071 + 4.80329i 0.328698 + 0.295622i
\(265\) −14.5638 24.0174i −0.894644 1.47538i
\(266\) 1.87395i 0.114899i
\(267\) 1.56585 + 29.5560i 0.0958286 + 1.80880i
\(268\) 4.77624 4.77624i 0.291756 0.291756i
\(269\) −9.59340 −0.584920 −0.292460 0.956278i \(-0.594474\pi\)
−0.292460 + 0.956278i \(0.594474\pi\)
\(270\) 7.51964 + 8.85748i 0.457631 + 0.539049i
\(271\) 30.4023 1.84681 0.923405 0.383828i \(-0.125394\pi\)
0.923405 + 0.383828i \(0.125394\pi\)
\(272\) −5.01690 + 5.01690i −0.304195 + 0.304195i
\(273\) 0.952952 + 17.9873i 0.0576753 + 1.08864i
\(274\) 13.1657i 0.795367i
\(275\) −9.58612 + 18.3865i −0.578065 + 1.10875i
\(276\) −9.95999 8.95775i −0.599521 0.539193i
\(277\) −8.02745 8.02745i −0.482323 0.482323i 0.423550 0.905873i \(-0.360784\pi\)
−0.905873 + 0.423550i \(0.860784\pi\)
\(278\) 8.77292 + 8.77292i 0.526165 + 0.526165i
\(279\) −0.0333235 + 0.00354084i −0.00199503 + 0.000211985i
\(280\) 0.997251 4.06987i 0.0595972 0.243222i
\(281\) 13.4543i 0.802618i 0.915943 + 0.401309i \(0.131445\pi\)
−0.915943 + 0.401309i \(0.868555\pi\)
\(282\) −4.19336 + 0.222161i −0.249711 + 0.0132295i
\(283\) 13.5068 13.5068i 0.802894 0.802894i −0.180653 0.983547i \(-0.557821\pi\)
0.983547 + 0.180653i \(0.0578209\pi\)
\(284\) −9.47461 −0.562215
\(285\) 3.80520 + 0.721435i 0.225400 + 0.0427341i
\(286\) 23.0144 1.36087
\(287\) −11.2088 + 11.2088i −0.661633 + 0.661633i
\(288\) −1.88530 + 2.33359i −0.111093 + 0.137508i
\(289\) 33.3387i 1.96110i
\(290\) 0.184392 0.111813i 0.0108279 0.00656586i
\(291\) 5.70764 6.34625i 0.334588 0.372024i
\(292\) 4.04666 + 4.04666i 0.236813 + 0.236813i
\(293\) −1.92348 1.92348i −0.112371 0.112371i 0.648686 0.761056i \(-0.275319\pi\)
−0.761056 + 0.648686i \(0.775319\pi\)
\(294\) 4.04030 4.49235i 0.235635 0.261999i
\(295\) 13.9176 + 3.41026i 0.810313 + 0.198553i
\(296\) 2.19944i 0.127840i
\(297\) −21.2777 + 3.40736i −1.23466 + 0.197715i
\(298\) −7.67448 + 7.67448i −0.444571 + 0.444571i
\(299\) −42.9199 −2.48212
\(300\) −7.88028 3.59182i −0.454968 0.207374i
\(301\) 0.345937 0.0199395
\(302\) −0.857244 + 0.857244i −0.0493288 + 0.0493288i
\(303\) 28.1644 1.49212i 1.61800 0.0857203i
\(304\) 1.00000i 0.0573539i
\(305\) 22.2578 + 5.45388i 1.27448 + 0.312288i
\(306\) −2.24900 21.1658i −0.128567 1.20997i
\(307\) −17.6649 17.6649i −1.00819 1.00819i −0.999966 0.00822043i \(-0.997383\pi\)
−0.00822043 0.999966i \(-0.502617\pi\)
\(308\) 5.49521 + 5.49521i 0.313119 + 0.313119i
\(309\) −4.44913 4.00143i −0.253102 0.227633i
\(310\) 0.0213578 0.0129510i 0.00121304 0.000735570i
\(311\) 9.64561i 0.546952i 0.961879 + 0.273476i \(0.0881735\pi\)
−0.961879 + 0.273476i \(0.911827\pi\)
\(312\) 0.508527 + 9.59862i 0.0287896 + 0.543415i
\(313\) 10.1110 10.1110i 0.571508 0.571508i −0.361042 0.932550i \(-0.617579\pi\)
0.932550 + 0.361042i \(0.117579\pi\)
\(314\) −14.2209 −0.802530
\(315\) 7.61729 + 10.0001i 0.429186 + 0.563443i
\(316\) 12.4743 0.701735
\(317\) −9.56745 + 9.56745i −0.537361 + 0.537361i −0.922753 0.385392i \(-0.874066\pi\)
0.385392 + 0.922753i \(0.374066\pi\)
\(318\) 1.15105 + 21.7264i 0.0645475 + 1.21836i
\(319\) 0.399941i 0.0223924i
\(320\) 0.532166 2.17182i 0.0297490 0.121408i
\(321\) −2.42138 2.17773i −0.135148 0.121549i
\(322\) −10.2481 10.2481i −0.571106 0.571106i
\(323\) −5.01690 5.01690i −0.279148 0.279148i
\(324\) −1.89126 8.79904i −0.105070 0.488836i
\(325\) −26.4687 + 8.32721i −1.46822 + 0.461911i
\(326\) 12.1756i 0.674342i
\(327\) 14.7242 0.780077i 0.814252 0.0431384i
\(328\) −5.98137 + 5.98137i −0.330266 + 0.330266i
\(329\) −4.54326 −0.250478
\(330\) 13.2740 9.04291i 0.730711 0.497796i
\(331\) −10.8642 −0.597152 −0.298576 0.954386i \(-0.596512\pi\)
−0.298576 + 0.954386i \(0.596512\pi\)
\(332\) 1.43685 1.43685i 0.0788575 0.0788575i
\(333\) −5.13258 4.14660i −0.281264 0.227233i
\(334\) 3.25443i 0.178074i
\(335\) −7.83138 12.9149i −0.427874 0.705616i
\(336\) −2.17047 + 2.41332i −0.118409 + 0.131657i
\(337\) 2.83368 + 2.83368i 0.154361 + 0.154361i 0.780062 0.625702i \(-0.215187\pi\)
−0.625702 + 0.780062i \(0.715187\pi\)
\(338\) 12.5846 + 12.5846i 0.684514 + 0.684514i
\(339\) −2.40677 + 2.67606i −0.130718 + 0.145343i
\(340\) 8.22598 + 13.5656i 0.446117 + 0.735700i
\(341\) 0.0463244i 0.00250861i
\(342\) −2.33359 1.88530i −0.126186 0.101946i
\(343\) 13.8979 13.8979i 0.750415 0.750415i
\(344\) 0.184604 0.00995316
\(345\) −24.7550 + 16.8643i −1.33276 + 0.907943i
\(346\) 10.8931 0.585616
\(347\) 12.2836 12.2836i 0.659418 0.659418i −0.295825 0.955242i \(-0.595594\pi\)
0.955242 + 0.295825i \(0.0955944\pi\)
\(348\) −0.166804 + 0.00883712i −0.00894162 + 0.000473719i
\(349\) 25.9576i 1.38948i 0.719261 + 0.694740i \(0.244480\pi\)
−0.719261 + 0.694740i \(0.755520\pi\)
\(350\) −8.30833 4.33170i −0.444099 0.231539i
\(351\) −23.3579 16.9096i −1.24675 0.902568i
\(352\) 2.93243 + 2.93243i 0.156299 + 0.156299i
\(353\) −11.5702 11.5702i −0.615818 0.615818i 0.328638 0.944456i \(-0.393410\pi\)
−0.944456 + 0.328638i \(0.893410\pi\)
\(354\) −8.25271 7.42227i −0.438627 0.394489i
\(355\) −5.04207 + 20.5771i −0.267605 + 1.09212i
\(356\) 17.0881i 0.905668i
\(357\) −1.21833 22.9964i −0.0644809 1.21710i
\(358\) 6.40594 6.40594i 0.338565 0.338565i
\(359\) 31.0266 1.63752 0.818760 0.574136i \(-0.194662\pi\)
0.818760 + 0.574136i \(0.194662\pi\)
\(360\) 4.06484 + 5.33639i 0.214236 + 0.281253i
\(361\) −1.00000 −0.0526316
\(362\) 12.6699 12.6699i 0.665915 0.665915i
\(363\) 0.567970 + 10.7206i 0.0298107 + 0.562688i
\(364\) 10.3995i 0.545084i
\(365\) 10.9421 6.63512i 0.572736 0.347298i
\(366\) −13.1982 11.8701i −0.689881 0.620460i
\(367\) 13.0593 + 13.0593i 0.681690 + 0.681690i 0.960381 0.278691i \(-0.0899004\pi\)
−0.278691 + 0.960381i \(0.589900\pi\)
\(368\) −5.46874 5.46874i −0.285078 0.285078i
\(369\) −2.68136 25.2347i −0.139586 1.31367i
\(370\) 4.77678 + 1.17047i 0.248333 + 0.0608496i
\(371\) 23.5393i 1.22210i
\(372\) −0.0193206 + 0.00102359i −0.00100172 + 5.30705e-5i
\(373\) 21.2626 21.2626i 1.10093 1.10093i 0.106636 0.994298i \(-0.465992\pi\)
0.994298 0.106636i \(-0.0340080\pi\)
\(374\) −29.4234 −1.52145
\(375\) −11.9944 + 15.2031i −0.619389 + 0.785084i
\(376\) −2.42443 −0.125031
\(377\) −0.378439 + 0.378439i −0.0194906 + 0.0194906i
\(378\) −1.53969 9.61481i −0.0791931 0.494533i
\(379\) 27.4201i 1.40848i −0.709963 0.704239i \(-0.751288\pi\)
0.709963 0.704239i \(-0.248712\pi\)
\(380\) 2.17182 + 0.532166i 0.111412 + 0.0272995i
\(381\) −0.769791 + 0.855919i −0.0394376 + 0.0438501i
\(382\) 5.94923 + 5.94923i 0.304389 + 0.304389i
\(383\) 1.51688 + 1.51688i 0.0775089 + 0.0775089i 0.744798 0.667290i \(-0.232546\pi\)
−0.667290 + 0.744798i \(0.732546\pi\)
\(384\) −1.15823 + 1.28782i −0.0591059 + 0.0657190i
\(385\) 14.8590 9.01024i 0.757283 0.459204i
\(386\) 0.577710i 0.0294047i
\(387\) −0.348034 + 0.430789i −0.0176916 + 0.0218982i
\(388\) 3.48454 3.48454i 0.176901 0.176901i
\(389\) 27.2165 1.37993 0.689966 0.723841i \(-0.257625\pi\)
0.689966 + 0.723841i \(0.257625\pi\)
\(390\) 21.1171 + 4.00363i 1.06931 + 0.202732i
\(391\) 54.8723 2.77501
\(392\) 2.46662 2.46662i 0.124583 0.124583i
\(393\) −30.7792 + 1.63066i −1.55260 + 0.0822557i
\(394\) 4.33601i 0.218445i
\(395\) 6.63841 27.0919i 0.334014 1.36314i
\(396\) −12.3716 + 1.31456i −0.621696 + 0.0660592i
\(397\) 11.0403 + 11.0403i 0.554095 + 0.554095i 0.927620 0.373525i \(-0.121851\pi\)
−0.373525 + 0.927620i \(0.621851\pi\)
\(398\) 15.5322 + 15.5322i 0.778560 + 0.778560i
\(399\) −2.41332 2.17047i −0.120817 0.108659i
\(400\) −4.43360 2.31154i −0.221680 0.115577i
\(401\) 9.33422i 0.466129i 0.972461 + 0.233064i \(0.0748753\pi\)
−0.972461 + 0.233064i \(0.925125\pi\)
\(402\) 0.618954 + 11.6830i 0.0308706 + 0.582694i
\(403\) −0.0438339 + 0.0438339i −0.00218352 + 0.00218352i
\(404\) 16.2835 0.810135
\(405\) −20.1164 0.575067i −0.999592 0.0285753i
\(406\) −0.180722 −0.00896909
\(407\) −6.44969 + 6.44969i −0.319699 + 0.319699i
\(408\) −0.650141 12.2716i −0.0321868 0.607537i
\(409\) 15.1973i 0.751460i 0.926729 + 0.375730i \(0.122608\pi\)
−0.926729 + 0.375730i \(0.877392\pi\)
\(410\) 9.80737 + 16.1735i 0.484352 + 0.798754i
\(411\) −16.9551 15.2489i −0.836332 0.752174i
\(412\) −2.44289 2.44289i −0.120353 0.120353i
\(413\) −8.49146 8.49146i −0.417837 0.417837i
\(414\) 23.0720 2.45155i 1.13393 0.120487i
\(415\) −2.35594 3.88523i −0.115648 0.190718i
\(416\) 5.54954i 0.272088i
\(417\) −21.4591 + 1.13688i −1.05086 + 0.0556734i
\(418\) −2.93243 + 2.93243i −0.143430 + 0.143430i
\(419\) 3.37395 0.164828 0.0824142 0.996598i \(-0.473737\pi\)
0.0824142 + 0.996598i \(0.473737\pi\)
\(420\) 4.08623 + 5.99815i 0.199388 + 0.292680i
\(421\) 16.8556 0.821493 0.410746 0.911750i \(-0.365268\pi\)
0.410746 + 0.911750i \(0.365268\pi\)
\(422\) −7.74793 + 7.74793i −0.377163 + 0.377163i
\(423\) 4.57079 5.65763i 0.222240 0.275083i
\(424\) 12.5614i 0.610033i
\(425\) 33.8397 10.6462i 1.64147 0.516415i
\(426\) 10.9738 12.2016i 0.531683 0.591171i
\(427\) −13.5800 13.5800i −0.657183 0.657183i
\(428\) −1.32951 1.32951i −0.0642643 0.0642643i
\(429\) −26.6560 + 29.6385i −1.28696 + 1.43096i
\(430\) 0.0982398 0.400926i 0.00473754 0.0193344i
\(431\) 16.6210i 0.800607i −0.916383 0.400303i \(-0.868905\pi\)
0.916383 0.400303i \(-0.131095\pi\)
\(432\) −0.821629 5.13078i −0.0395306 0.246855i
\(433\) 10.6960 10.6960i 0.514019 0.514019i −0.401737 0.915755i \(-0.631593\pi\)
0.915755 + 0.401737i \(0.131593\pi\)
\(434\) −0.0209327 −0.00100480
\(435\) −0.0695747 + 0.366970i −0.00333585 + 0.0175949i
\(436\) 8.51296 0.407697
\(437\) 5.46874 5.46874i 0.261605 0.261605i
\(438\) −9.89837 + 0.524407i −0.472962 + 0.0250571i
\(439\) 18.1152i 0.864593i 0.901731 + 0.432297i \(0.142297\pi\)
−0.901731 + 0.432297i \(0.857703\pi\)
\(440\) 7.92924 4.80816i 0.378012 0.229220i
\(441\) 1.10575 + 10.4064i 0.0526546 + 0.495542i
\(442\) −27.8415 27.8415i −1.32428 1.32428i
\(443\) −15.6435 15.6435i −0.743247 0.743247i 0.229955 0.973201i \(-0.426142\pi\)
−0.973201 + 0.229955i \(0.926142\pi\)
\(444\) −2.83249 2.54746i −0.134424 0.120897i
\(445\) 37.1123 + 9.09371i 1.75929 + 0.431083i
\(446\) 5.39430i 0.255428i
\(447\) −0.994537 18.7722i −0.0470400 0.887897i
\(448\) −1.32508 + 1.32508i −0.0626042 + 0.0626042i
\(449\) 4.48299 0.211565 0.105783 0.994389i \(-0.466265\pi\)
0.105783 + 0.994389i \(0.466265\pi\)
\(450\) 13.7529 5.98824i 0.648316 0.282288i
\(451\) −35.0798 −1.65185
\(452\) −1.46934 + 1.46934i −0.0691122 + 0.0691122i
\(453\) −0.111090 2.09687i −0.00521948 0.0985195i
\(454\) 11.9990i 0.563143i
\(455\) 22.5859 + 5.53428i 1.05884 + 0.259451i
\(456\) −1.28782 1.15823i −0.0603079 0.0542393i
\(457\) −6.38576 6.38576i −0.298713 0.298713i 0.541797 0.840510i \(-0.317744\pi\)
−0.840510 + 0.541797i \(0.817744\pi\)
\(458\) −9.82700 9.82700i −0.459186 0.459186i
\(459\) 29.8627 + 21.6186i 1.39387 + 1.00907i
\(460\) −14.7874 + 8.96684i −0.689466 + 0.418081i
\(461\) 9.14050i 0.425716i 0.977083 + 0.212858i \(0.0682771\pi\)
−0.977083 + 0.212858i \(0.931723\pi\)
\(462\) −13.4416 + 0.712125i −0.625360 + 0.0331311i
\(463\) −11.7522 + 11.7522i −0.546170 + 0.546170i −0.925331 0.379161i \(-0.876213\pi\)
0.379161 + 0.925331i \(0.376213\pi\)
\(464\) −0.0964393 −0.00447708
\(465\) −0.00805871 + 0.0425055i −0.000373714 + 0.00197115i
\(466\) −29.8774 −1.38404
\(467\) 10.8294 10.8294i 0.501124 0.501124i −0.410663 0.911787i \(-0.634703\pi\)
0.911787 + 0.410663i \(0.134703\pi\)
\(468\) −12.9503 10.4626i −0.598629 0.483632i
\(469\) 12.6578i 0.584484i
\(470\) −1.29020 + 5.26543i −0.0595126 + 0.242876i
\(471\) 16.4711 18.3140i 0.758949 0.843864i
\(472\) −4.53132 4.53132i −0.208571 0.208571i
\(473\) 0.541336 + 0.541336i 0.0248907 + 0.0248907i
\(474\) −14.4482 + 16.0647i −0.663627 + 0.737877i
\(475\) 2.31154 4.43360i 0.106061 0.203427i
\(476\) 13.2956i 0.609403i
\(477\) −29.3130 23.6820i −1.34215 1.08432i
\(478\) 2.18786 2.18786i 0.100070 0.100070i
\(479\) 16.6381 0.760216 0.380108 0.924942i \(-0.375887\pi\)
0.380108 + 0.924942i \(0.375887\pi\)
\(480\) 2.18055 + 3.20081i 0.0995280 + 0.146096i
\(481\) −12.2059 −0.556539
\(482\) −4.68513 + 4.68513i −0.213402 + 0.213402i
\(483\) 25.0675 1.32806i 1.14061 0.0604287i
\(484\) 6.19825i 0.281738i
\(485\) −5.71343 9.42214i −0.259434 0.427837i
\(486\) 13.5222 + 7.75574i 0.613377 + 0.351807i
\(487\) 6.95016 + 6.95016i 0.314942 + 0.314942i 0.846820 0.531879i \(-0.178514\pi\)
−0.531879 + 0.846820i \(0.678514\pi\)
\(488\) −7.24675 7.24675i −0.328045 0.328045i
\(489\) 15.6800 + 14.1022i 0.709073 + 0.637721i
\(490\) −4.04439 6.66969i −0.182707 0.301306i
\(491\) 3.80980i 0.171934i 0.996298 + 0.0859670i \(0.0273980\pi\)
−0.996298 + 0.0859670i \(0.972602\pi\)
\(492\) −0.775126 14.6308i −0.0349454 0.659607i
\(493\) 0.483827 0.483827i 0.0217905 0.0217905i
\(494\) −5.54954 −0.249685
\(495\) −3.72875 + 27.5684i −0.167595 + 1.23911i
\(496\) −0.0111704 −0.000501565
\(497\) 12.5546 12.5546i 0.563152 0.563152i
\(498\) 0.186202 + 3.51463i 0.00834390 + 0.157494i
\(499\) 12.0717i 0.540405i −0.962804 0.270202i \(-0.912909\pi\)
0.962804 0.270202i \(-0.0870906\pi\)
\(500\) −7.37965 + 8.39885i −0.330028 + 0.375608i
\(501\) 4.19113 + 3.76939i 0.187246 + 0.168404i
\(502\) −15.0984 15.0984i −0.673874 0.673874i
\(503\) −8.43285 8.43285i −0.376002 0.376002i 0.493655 0.869658i \(-0.335660\pi\)
−0.869658 + 0.493655i \(0.835660\pi\)
\(504\) −0.594013 5.59037i −0.0264595 0.249015i
\(505\) 8.66553 35.3648i 0.385611 1.57371i
\(506\) 32.0733i 1.42583i
\(507\) −30.7828 + 1.63084i −1.36711 + 0.0724283i
\(508\) −0.469960 + 0.469960i −0.0208511 + 0.0208511i
\(509\) 14.4418 0.640120 0.320060 0.947397i \(-0.396297\pi\)
0.320060 + 0.947397i \(0.396297\pi\)
\(510\) −26.9978 5.11856i −1.19548 0.226654i
\(511\) −10.7243 −0.474415
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 5.13078 0.821629i 0.226530 0.0362758i
\(514\) 4.04532i 0.178431i
\(515\) −6.60554 + 4.00549i −0.291075 + 0.176503i
\(516\) −0.213814 + 0.237737i −0.00941265 + 0.0104658i
\(517\) −7.10947 7.10947i −0.312674 0.312674i
\(518\) −2.91443 2.91443i −0.128053 0.128053i
\(519\) −12.6167 + 14.0284i −0.553814 + 0.615778i
\(520\) 12.0526 + 2.95328i 0.528541 + 0.129510i
\(521\) 36.0409i 1.57898i −0.613762 0.789491i \(-0.710345\pi\)
0.613762 0.789491i \(-0.289655\pi\)
\(522\) 0.181817 0.225049i 0.00795792 0.00985015i
\(523\) 21.2547 21.2547i 0.929403 0.929403i −0.0682644 0.997667i \(-0.521746\pi\)
0.997667 + 0.0682644i \(0.0217461\pi\)
\(524\) −17.7953 −0.777391
\(525\) 15.2015 5.68255i 0.663446 0.248007i
\(526\) 27.6026 1.20353
\(527\) 0.0560407 0.0560407i 0.00244117 0.00244117i
\(528\) −7.17289 + 0.380013i −0.312160 + 0.0165380i
\(529\) 36.8142i 1.60062i
\(530\) 27.2810 + 6.68473i 1.18501 + 0.290366i
\(531\) 19.1172 2.03132i 0.829614 0.0881519i
\(532\) −1.32508 1.32508i −0.0574495 0.0574495i
\(533\) −33.1938 33.1938i −1.43778 1.43778i
\(534\) −22.0065 19.7920i −0.952314 0.856485i
\(535\) −3.59497 + 2.17993i −0.155424 + 0.0942468i
\(536\) 6.75463i 0.291756i
\(537\) 0.830147 + 15.6693i 0.0358235 + 0.676181i
\(538\) 6.78356 6.78356i 0.292460 0.292460i
\(539\) 14.4663 0.623109
\(540\) −11.5804 0.945999i −0.498340 0.0407093i
\(541\) −10.6163 −0.456431 −0.228216 0.973611i \(-0.573289\pi\)
−0.228216 + 0.973611i \(0.573289\pi\)
\(542\) −21.4977 + 21.4977i −0.923405 + 0.923405i
\(543\) 1.64189 + 30.9913i 0.0704604 + 1.32996i
\(544\) 7.09497i 0.304195i
\(545\) 4.53031 18.4886i 0.194057 0.791965i
\(546\) −13.3928 12.0451i −0.573158 0.515483i
\(547\) 13.8661 + 13.8661i 0.592872 + 0.592872i 0.938406 0.345534i \(-0.112302\pi\)
−0.345534 + 0.938406i \(0.612302\pi\)
\(548\) −9.30953 9.30953i −0.397683 0.397683i
\(549\) 30.5732 3.24861i 1.30483 0.138647i
\(550\) −6.22279 19.7796i −0.265341 0.843406i
\(551\) 0.0964393i 0.00410845i
\(552\) 13.3769 0.708695i 0.569357 0.0301640i
\(553\) −16.5295 + 16.5295i −0.702905 + 0.702905i
\(554\) 11.3525 0.482323
\(555\) −7.03999 + 4.79598i −0.298831 + 0.203578i
\(556\) −12.4068 −0.526165
\(557\) −0.548599 + 0.548599i −0.0232449 + 0.0232449i −0.718634 0.695389i \(-0.755232\pi\)
0.695389 + 0.718634i \(0.255232\pi\)
\(558\) 0.0210596 0.0260671i 0.000891522 0.00110351i
\(559\) 1.02446i 0.0433302i
\(560\) 2.17267 + 3.58300i 0.0918122 + 0.151409i
\(561\) 34.0792 37.8922i 1.43883 1.59981i
\(562\) −9.51365 9.51365i −0.401309 0.401309i
\(563\) −1.13682 1.13682i −0.0479114 0.0479114i 0.682745 0.730657i \(-0.260786\pi\)
−0.730657 + 0.682745i \(0.760786\pi\)
\(564\) 2.80806 3.12225i 0.118241 0.131470i
\(565\) 2.40922 + 3.97309i 0.101356 + 0.167149i
\(566\) 19.1015i 0.802894i
\(567\) 14.1655 + 9.15336i 0.594896 + 0.384405i
\(568\) 6.69956 6.69956i 0.281107 0.281107i
\(569\) 25.5607 1.07156 0.535781 0.844357i \(-0.320017\pi\)
0.535781 + 0.844357i \(0.320017\pi\)
\(570\) −3.20081 + 2.18055i −0.134067 + 0.0913332i
\(571\) −28.9943 −1.21337 −0.606686 0.794942i \(-0.707501\pi\)
−0.606686 + 0.794942i \(0.707501\pi\)
\(572\) −16.2736 + 16.2736i −0.680434 + 0.680434i
\(573\) −14.5522 + 0.770961i −0.607925 + 0.0322074i
\(574\) 15.8516i 0.661633i
\(575\) 11.6050 + 36.8874i 0.483962 + 1.53831i
\(576\) −0.316985 2.98321i −0.0132077 0.124300i
\(577\) −28.4272 28.4272i −1.18344 1.18344i −0.978847 0.204594i \(-0.934413\pi\)
−0.204594 0.978847i \(-0.565587\pi\)
\(578\) 23.5740 + 23.5740i 0.980549 + 0.980549i
\(579\) −0.743990 0.669124i −0.0309192 0.0278079i
\(580\) −0.0513217 + 0.209449i −0.00213102 + 0.00869688i
\(581\) 3.80789i 0.157978i
\(582\) 0.451562 + 8.52339i 0.0187178 + 0.353306i
\(583\) −36.8352 + 36.8352i −1.52556 + 1.52556i
\(584\) −5.72284 −0.236813
\(585\) −29.6145 + 22.5580i −1.22441 + 0.932657i
\(586\) 2.72021 0.112371
\(587\) −23.4065 + 23.4065i −0.966088 + 0.966088i −0.999444 0.0333555i \(-0.989381\pi\)
0.0333555 + 0.999444i \(0.489381\pi\)
\(588\) 0.319649 + 6.03349i 0.0131821 + 0.248817i
\(589\) 0.0111704i 0.000460267i
\(590\) −12.2526 + 7.42980i −0.504433 + 0.305880i
\(591\) −5.58402 5.02211i −0.229696 0.206582i
\(592\) −1.55524 1.55524i −0.0639198 0.0639198i
\(593\) 17.7918 + 17.7918i 0.730620 + 0.730620i 0.970743 0.240122i \(-0.0771876\pi\)
−0.240122 + 0.970743i \(0.577188\pi\)
\(594\) 12.6363 17.4550i 0.518473 0.716188i
\(595\) −28.8757 7.07547i −1.18379 0.290066i
\(596\) 10.8534i 0.444571i
\(597\) −37.9927 + 2.01282i −1.55494 + 0.0823794i
\(598\) 30.3490 30.3490i 1.24106 1.24106i
\(599\) −30.4391 −1.24371 −0.621854 0.783134i \(-0.713620\pi\)
−0.621854 + 0.783134i \(0.713620\pi\)
\(600\) 8.11200 3.03240i 0.331171 0.123797i
\(601\) 1.09778 0.0447792 0.0223896 0.999749i \(-0.492873\pi\)
0.0223896 + 0.999749i \(0.492873\pi\)
\(602\) −0.244615 + 0.244615i −0.00996975 + 0.00996975i
\(603\) −15.7625 12.7345i −0.641899 0.518590i
\(604\) 1.21233i 0.0493288i
\(605\) 13.4615 + 3.29850i 0.547287 + 0.134103i
\(606\) −18.8601 + 20.9703i −0.766140 + 0.851860i
\(607\) −8.70025 8.70025i −0.353132 0.353132i 0.508141 0.861274i \(-0.330333\pi\)
−0.861274 + 0.508141i \(0.830333\pi\)
\(608\) −0.707107 0.707107i −0.0286770 0.0286770i
\(609\) 0.209319 0.232738i 0.00848202 0.00943104i
\(610\) −19.5951 + 11.8822i −0.793382 + 0.481094i
\(611\) 13.4545i 0.544310i
\(612\) 16.5567 + 13.3762i 0.669267 + 0.540700i
\(613\) 4.40309 4.40309i 0.177839 0.177839i −0.612574 0.790413i \(-0.709866\pi\)
0.790413 + 0.612574i \(0.209866\pi\)
\(614\) 24.9819 1.00819
\(615\) −32.1879 6.10257i −1.29794 0.246079i
\(616\) −7.77140 −0.313119
\(617\) 8.04047 8.04047i 0.323697 0.323697i −0.526486 0.850183i \(-0.676491\pi\)
0.850183 + 0.526486i \(0.176491\pi\)
\(618\) 5.97545 0.316574i 0.240368 0.0127345i
\(619\) 23.1721i 0.931366i −0.884952 0.465683i \(-0.845809\pi\)
0.884952 0.465683i \(-0.154191\pi\)
\(620\) −0.00594450 + 0.0242600i −0.000238737 + 0.000974307i
\(621\) −23.5656 + 32.5522i −0.945656 + 1.30627i
\(622\) −6.82047 6.82047i −0.273476 0.273476i
\(623\) −22.6431 22.6431i −0.907178 0.907178i
\(624\) −7.14683 6.42767i −0.286102 0.257313i
\(625\) 14.3136 + 20.4969i 0.572544 + 0.819874i
\(626\) 14.2991i 0.571508i
\(627\) −0.380013 7.17289i −0.0151763 0.286458i
\(628\) 10.0557 10.0557i 0.401265 0.401265i
\(629\) 15.6049 0.622210
\(630\) −12.4574 1.68492i −0.496314 0.0671287i
\(631\) −16.4094 −0.653249 −0.326625 0.945154i \(-0.605911\pi\)
−0.326625 + 0.945154i \(0.605911\pi\)
\(632\) −8.82067 + 8.82067i −0.350867 + 0.350867i
\(633\) −1.00406 18.9519i −0.0399076 0.753271i
\(634\) 13.5304i 0.537361i
\(635\) 0.770572 + 1.27077i 0.0305792 + 0.0504288i
\(636\) −16.1768 14.5490i −0.641453 0.576905i
\(637\) 13.6886 + 13.6886i 0.542361 + 0.542361i
\(638\) −0.282801 0.282801i −0.0111962 0.0111962i
\(639\) 3.00331 + 28.2647i 0.118809 + 1.11813i
\(640\) 1.15941 + 1.91201i 0.0458297 + 0.0755787i
\(641\) 28.1764i 1.11290i −0.830881 0.556450i \(-0.812163\pi\)
0.830881 0.556450i \(-0.187837\pi\)
\(642\) 3.25206 0.172291i 0.128349 0.00679980i
\(643\) 4.86470 4.86470i 0.191845 0.191845i −0.604648 0.796493i \(-0.706686\pi\)
0.796493 + 0.604648i \(0.206686\pi\)
\(644\) 14.4930 0.571106
\(645\) 0.402537 + 0.590882i 0.0158499 + 0.0232659i
\(646\) 7.09497 0.279148
\(647\) 7.02609 7.02609i 0.276224 0.276224i −0.555376 0.831600i \(-0.687425\pi\)
0.831600 + 0.555376i \(0.187425\pi\)
\(648\) 7.55919 + 4.88454i 0.296953 + 0.191883i
\(649\) 26.5755i 1.04318i
\(650\) 12.8280 24.6044i 0.503154 0.965065i
\(651\) 0.0242450 0.0269577i 0.000950236 0.00105655i
\(652\) 8.60942 + 8.60942i 0.337171 + 0.337171i
\(653\) 26.3564 + 26.3564i 1.03141 + 1.03141i 0.999491 + 0.0319150i \(0.0101606\pi\)
0.0319150 + 0.999491i \(0.489839\pi\)
\(654\) −9.86001 + 10.9632i −0.385557 + 0.428695i
\(655\) −9.47005 + 38.6482i −0.370026 + 1.51011i
\(656\) 8.45893i 0.330266i
\(657\) 10.7893 13.3547i 0.420930 0.521018i
\(658\) 3.21257 3.21257i 0.125239 0.125239i
\(659\) −11.1631 −0.434853 −0.217426 0.976077i \(-0.569766\pi\)
−0.217426 + 0.976077i \(0.569766\pi\)
\(660\) −2.99185 + 15.7804i −0.116458 + 0.614253i
\(661\) 39.9360 1.55333 0.776665 0.629914i \(-0.216910\pi\)
0.776665 + 0.629914i \(0.216910\pi\)
\(662\) 7.68217 7.68217i 0.298576 0.298576i
\(663\) 68.1019 3.60798i 2.64486 0.140122i
\(664\) 2.03202i 0.0788575i
\(665\) −3.58300 + 2.17267i −0.138943 + 0.0842526i
\(666\) 6.56137 0.697189i 0.254248 0.0270155i
\(667\) 0.527401 + 0.527401i 0.0204211 + 0.0204211i
\(668\) 2.30123 + 2.30123i 0.0890372 + 0.0890372i
\(669\) 6.94691 + 6.24787i 0.268583 + 0.241556i
\(670\) 14.6698 + 3.59458i 0.566745 + 0.138871i
\(671\) 42.5011i 1.64074i
\(672\) −0.171717 3.24123i −0.00662414 0.125033i
\(673\) −27.5847 + 27.5847i −1.06331 + 1.06331i −0.0654567 + 0.997855i \(0.520850\pi\)
−0.997855 + 0.0654567i \(0.979150\pi\)
\(674\) −4.00743 −0.154361
\(675\) −8.21722 + 24.6471i −0.316281 + 0.948666i
\(676\) −17.7974 −0.684514
\(677\) 18.4404 18.4404i 0.708721 0.708721i −0.257545 0.966266i \(-0.582914\pi\)
0.966266 + 0.257545i \(0.0829135\pi\)
\(678\) −0.190413 3.59410i −0.00731275 0.138031i
\(679\) 9.23459i 0.354391i
\(680\) −15.4090 3.77570i −0.590908 0.144792i
\(681\) 15.4527 + 13.8977i 0.592147 + 0.532561i
\(682\) −0.0327563 0.0327563i −0.00125430 0.00125430i
\(683\) −6.88800 6.88800i −0.263562 0.263562i 0.562937 0.826500i \(-0.309671\pi\)
−0.826500 + 0.562937i \(0.809671\pi\)
\(684\) 2.98321 0.316985i 0.114066 0.0121202i
\(685\) −25.1728 + 15.2644i −0.961804 + 0.583223i
\(686\) 19.6546i 0.750415i
\(687\) 24.0374 1.27348i 0.917085 0.0485864i
\(688\) −0.130534 + 0.130534i −0.00497658 + 0.00497658i
\(689\) −69.7097 −2.65573
\(690\) 5.57956 29.4293i 0.212410 1.12035i
\(691\) −6.70656 −0.255129 −0.127565 0.991830i \(-0.540716\pi\)
−0.127565 + 0.991830i \(0.540716\pi\)
\(692\) −7.70257 + 7.70257i −0.292808 + 0.292808i
\(693\) 14.6515 18.1353i 0.556563 0.688901i
\(694\) 17.3716i 0.659418i
\(695\) −6.60247 + 26.9453i −0.250446 + 1.02209i
\(696\) 0.111699 0.124197i 0.00423395 0.00470767i
\(697\) 42.4377 + 42.4377i 1.60744 + 1.60744i
\(698\) −18.3548 18.3548i −0.694740 0.694740i
\(699\) 34.6050 38.4769i 1.30888 1.45533i
\(700\) 8.93785 2.81190i 0.337819 0.106280i
\(701\) 8.68700i 0.328104i −0.986452 0.164052i \(-0.947544\pi\)
0.986452 0.164052i \(-0.0524564\pi\)
\(702\) 28.4735 4.55966i 1.07466 0.172093i
\(703\) 1.55524 1.55524i 0.0586569 0.0586569i
\(704\) −4.14708 −0.156299
\(705\) −5.28660 7.76016i −0.199105 0.292265i
\(706\) 16.3627 0.615818
\(707\) −21.5770 + 21.5770i −0.811485 + 0.811485i
\(708\) 11.0839 0.587215i 0.416558 0.0220689i
\(709\) 20.6106i 0.774049i 0.922070 + 0.387024i \(0.126497\pi\)
−0.922070 + 0.387024i \(0.873503\pi\)
\(710\) −10.9850 18.1155i −0.412258 0.679863i
\(711\) −3.95417 37.2134i −0.148293 1.39561i
\(712\) −12.0831 12.0831i −0.452834 0.452834i
\(713\) 0.0610879 + 0.0610879i 0.00228776 + 0.00228776i
\(714\) 17.1224 + 15.3994i 0.640790 + 0.576309i
\(715\) 26.6831 + 44.0036i 0.997890 + 1.64564i
\(716\) 9.05937i 0.338565i
\(717\) 0.283525 + 5.35164i 0.0105884 + 0.199861i
\(718\) −21.9391 + 21.9391i −0.818760 + 0.818760i
\(719\) 39.9182 1.48870 0.744350 0.667790i \(-0.232760\pi\)
0.744350 + 0.667790i \(0.232760\pi\)
\(720\) −6.64767 0.899127i −0.247744 0.0335085i
\(721\) 6.47405 0.241106
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) −0.607147 11.4601i −0.0225800 0.426206i
\(724\) 17.9179i 0.665915i
\(725\) 0.427573 + 0.222923i 0.0158797 + 0.00827915i
\(726\) −7.98226 7.17902i −0.296249 0.266439i
\(727\) −4.40463 4.40463i −0.163359 0.163359i 0.620694 0.784053i \(-0.286851\pi\)
−0.784053 + 0.620694i \(0.786851\pi\)
\(728\) −7.35358 7.35358i −0.272542 0.272542i
\(729\) −25.6499 + 8.43120i −0.949995 + 0.312267i
\(730\) −3.04550 + 12.4290i −0.112719 + 0.460017i
\(731\) 1.30976i 0.0484431i
\(732\) 17.7260 0.939107i 0.655171 0.0347104i
\(733\) −13.9718 + 13.9718i −0.516061 + 0.516061i −0.916377 0.400316i \(-0.868900\pi\)
0.400316 + 0.916377i \(0.368900\pi\)
\(734\) −18.4687 −0.681690
\(735\) 13.2738 + 2.51660i 0.489610 + 0.0928261i
\(736\) 7.73397 0.285078
\(737\) −19.8074 + 19.8074i −0.729617 + 0.729617i
\(738\) 19.7397 + 15.9477i 0.726627 + 0.587041i
\(739\) 38.9043i 1.43112i −0.698553 0.715558i \(-0.746172\pi\)
0.698553 0.715558i \(-0.253828\pi\)
\(740\) −4.20534 + 2.55005i −0.154591 + 0.0937417i
\(741\) 6.42767 7.14683i 0.236126 0.262545i
\(742\) −16.6448 16.6448i −0.611050 0.611050i
\(743\) 31.6523 + 31.6523i 1.16121 + 1.16121i 0.984211 + 0.177000i \(0.0566393\pi\)
0.177000 + 0.984211i \(0.443361\pi\)
\(744\) 0.0129379 0.0143855i 0.000474327 0.000527398i
\(745\) −23.5715 5.77579i −0.863594 0.211609i
\(746\) 30.0698i 1.10093i
\(747\) −4.74189 3.83097i −0.173497 0.140168i
\(748\) 20.8055 20.8055i 0.760724 0.760724i
\(749\) 3.52342 0.128743
\(750\) −2.26888 19.2315i −0.0828479 0.702237i
\(751\) −35.5821 −1.29841 −0.649205 0.760613i \(-0.724898\pi\)
−0.649205 + 0.760613i \(0.724898\pi\)
\(752\) 1.71433 1.71433i 0.0625153 0.0625153i
\(753\) 36.9315 1.95660i 1.34586 0.0713025i
\(754\) 0.535193i 0.0194906i
\(755\) −2.63295 0.645159i −0.0958230 0.0234797i
\(756\) 7.88743 + 5.70998i 0.286863 + 0.207670i
\(757\) −11.1640 11.1640i −0.405762 0.405762i 0.474496 0.880258i \(-0.342630\pi\)
−0.880258 + 0.474496i \(0.842630\pi\)
\(758\) 19.3890 + 19.3890i 0.704239 + 0.704239i
\(759\) 41.3049 + 37.1485i 1.49927 + 1.34840i
\(760\) −1.91201 + 1.15941i −0.0693558 + 0.0420562i
\(761\) 9.30941i 0.337466i 0.985662 + 0.168733i \(0.0539675\pi\)
−0.985662 + 0.168733i \(0.946032\pi\)
\(762\) −0.0609022 1.14955i −0.00220625 0.0416438i
\(763\) −11.2804 + 11.2804i −0.408377 + 0.408377i
\(764\) −8.41348 −0.304389
\(765\) 37.8616 28.8399i 1.36889 1.04271i
\(766\) −2.14519 −0.0775089
\(767\) 25.1467 25.1467i 0.907996 0.907996i
\(768\) −0.0916341 1.72963i −0.00330656 0.0624125i
\(769\) 36.9866i 1.33377i 0.745161 + 0.666885i \(0.232373\pi\)
−0.745161 + 0.666885i \(0.767627\pi\)
\(770\) −4.13568 + 16.8781i −0.149039 + 0.608244i
\(771\) −5.20966 4.68542i −0.187621 0.168741i
\(772\) −0.408503 0.408503i −0.0147023 0.0147023i
\(773\) 32.3504 + 32.3504i 1.16356 + 1.16356i 0.983690 + 0.179873i \(0.0575687\pi\)
0.179873 + 0.983690i \(0.442431\pi\)
\(774\) −0.0585166 0.550711i −0.00210334 0.0197949i
\(775\) 0.0495250 + 0.0258207i 0.00177899 + 0.000927509i
\(776\) 4.92788i 0.176901i
\(777\) 7.12887 0.377682i 0.255747 0.0135492i