Properties

Label 570.2.k.b.77.16
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 77.16
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.11099 + 1.32879i) q^{3} -1.00000i q^{4} +(1.28568 - 1.82949i) q^{5} +(1.72519 + 0.154007i) q^{6} +(1.30605 + 1.30605i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.531382 + 2.95256i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(1.11099 + 1.32879i) q^{3} -1.00000i q^{4} +(1.28568 - 1.82949i) q^{5} +(1.72519 + 0.154007i) q^{6} +(1.30605 + 1.30605i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.531382 + 2.95256i) q^{9} +(-0.384532 - 2.20276i) q^{10} +5.15114i q^{11} +(1.32879 - 1.11099i) q^{12} +(0.342145 - 0.342145i) q^{13} +1.84704 q^{14} +(3.85939 - 0.324151i) q^{15} -1.00000 q^{16} +(4.25002 - 4.25002i) q^{17} +(1.71203 + 2.46352i) q^{18} -1.00000i q^{19} +(-1.82949 - 1.28568i) q^{20} +(-0.284456 + 3.18649i) q^{21} +(3.64241 + 3.64241i) q^{22} +(-3.32373 - 3.32373i) q^{23} +(0.154007 - 1.72519i) q^{24} +(-1.69406 - 4.70427i) q^{25} -0.483866i q^{26} +(-4.51371 + 2.57419i) q^{27} +(1.30605 - 1.30605i) q^{28} +8.73926 q^{29} +(2.49979 - 2.95821i) q^{30} -10.0988 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-6.84480 + 5.72289i) q^{33} -6.01044i q^{34} +(4.06858 - 0.710245i) q^{35} +(2.95256 + 0.531382i) q^{36} +(0.317424 + 0.317424i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(0.834762 + 0.0745186i) q^{39} +(-2.20276 + 0.384532i) q^{40} -8.89223i q^{41} +(2.05205 + 2.45433i) q^{42} +(-8.84777 + 8.84777i) q^{43} +5.15114 q^{44} +(4.71850 + 4.76821i) q^{45} -4.70047 q^{46} +(2.14509 - 2.14509i) q^{47} +(-1.11099 - 1.32879i) q^{48} -3.58845i q^{49} +(-4.52430 - 2.12854i) q^{50} +(10.3691 + 0.925647i) q^{51} +(-0.342145 - 0.342145i) q^{52} +(8.17583 + 8.17583i) q^{53} +(-1.37145 + 5.01190i) q^{54} +(9.42396 + 6.62272i) q^{55} -1.84704i q^{56} +(1.32879 - 1.11099i) q^{57} +(6.17959 - 6.17959i) q^{58} -1.27397 q^{59} +(-0.324151 - 3.85939i) q^{60} -6.26456 q^{61} +(-7.14093 + 7.14093i) q^{62} +(-4.55022 + 3.16219i) q^{63} +1.00000i q^{64} +(-0.186062 - 1.06584i) q^{65} +(-0.793310 + 8.88670i) q^{66} +(-1.50061 - 1.50061i) q^{67} +(-4.25002 - 4.25002i) q^{68} +(0.723903 - 8.10920i) q^{69} +(2.37470 - 3.37914i) q^{70} +11.7068i q^{71} +(2.46352 - 1.71203i) q^{72} +(-2.73639 + 2.73639i) q^{73} +0.448905 q^{74} +(4.36891 - 7.47747i) q^{75} -1.00000 q^{76} +(-6.72767 + 6.72767i) q^{77} +(0.642958 - 0.537573i) q^{78} -5.23062i q^{79} +(-1.28568 + 1.82949i) q^{80} +(-8.43527 - 3.13788i) q^{81} +(-6.28776 - 6.28776i) q^{82} +(-9.88555 - 9.88555i) q^{83} +(3.18649 + 0.284456i) q^{84} +(-2.31120 - 13.2395i) q^{85} +12.5126i q^{86} +(9.70927 + 11.6127i) q^{87} +(3.64241 - 3.64241i) q^{88} -16.2880 q^{89} +(6.70811 + 0.0351501i) q^{90} +0.893720 q^{91} +(-3.32373 + 3.32373i) q^{92} +(-11.2197 - 13.4192i) q^{93} -3.03362i q^{94} +(-1.82949 - 1.28568i) q^{95} +(-1.72519 - 0.154007i) q^{96} +(4.02586 + 4.02586i) q^{97} +(-2.53742 - 2.53742i) q^{98} +(-15.2091 - 2.73722i) 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
\(3\) 1.11099 + 1.32879i 0.641433 + 0.767179i
\(4\) 1.00000i 0.500000i
\(5\) 1.28568 1.82949i 0.574973 0.818172i
\(6\) 1.72519 + 0.154007i 0.704306 + 0.0628729i
\(7\) 1.30605 + 1.30605i 0.493642 + 0.493642i 0.909452 0.415810i \(-0.136502\pi\)
−0.415810 + 0.909452i \(0.636502\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) −0.531382 + 2.95256i −0.177127 + 0.984188i
\(10\) −0.384532 2.20276i −0.121600 0.696573i
\(11\) 5.15114i 1.55313i 0.630038 + 0.776564i \(0.283039\pi\)
−0.630038 + 0.776564i \(0.716961\pi\)
\(12\) 1.32879 1.11099i 0.383589 0.320717i
\(13\) 0.342145 0.342145i 0.0948940 0.0948940i −0.658066 0.752960i \(-0.728625\pi\)
0.752960 + 0.658066i \(0.228625\pi\)
\(14\) 1.84704 0.493642
\(15\) 3.85939 0.324151i 0.996491 0.0836954i
\(16\) −1.00000 −0.250000
\(17\) 4.25002 4.25002i 1.03078 1.03078i 0.0312704 0.999511i \(-0.490045\pi\)
0.999511 0.0312704i \(-0.00995530\pi\)
\(18\) 1.71203 + 2.46352i 0.403530 + 0.580658i
\(19\) 1.00000i 0.229416i
\(20\) −1.82949 1.28568i −0.409086 0.287487i
\(21\) −0.284456 + 3.18649i −0.0620734 + 0.695350i
\(22\) 3.64241 + 3.64241i 0.776564 + 0.776564i
\(23\) −3.32373 3.32373i −0.693046 0.693046i 0.269855 0.962901i \(-0.413024\pi\)
−0.962901 + 0.269855i \(0.913024\pi\)
\(24\) 0.154007 1.72519i 0.0314365 0.352153i
\(25\) −1.69406 4.70427i −0.338812 0.940854i
\(26\) 0.483866i 0.0948940i
\(27\) −4.51371 + 2.57419i −0.868664 + 0.495402i
\(28\) 1.30605 1.30605i 0.246821 0.246821i
\(29\) 8.73926 1.62284 0.811420 0.584463i \(-0.198695\pi\)
0.811420 + 0.584463i \(0.198695\pi\)
\(30\) 2.49979 2.95821i 0.456398 0.540093i
\(31\) −10.0988 −1.81380 −0.906899 0.421348i \(-0.861557\pi\)
−0.906899 + 0.421348i \(0.861557\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −6.84480 + 5.72289i −1.19153 + 0.996228i
\(34\) 6.01044i 1.03078i
\(35\) 4.06858 0.710245i 0.687715 0.120053i
\(36\) 2.95256 + 0.531382i 0.492094 + 0.0885636i
\(37\) 0.317424 + 0.317424i 0.0521842 + 0.0521842i 0.732717 0.680533i \(-0.238252\pi\)
−0.680533 + 0.732717i \(0.738252\pi\)
\(38\) −0.707107 0.707107i −0.114708 0.114708i
\(39\) 0.834762 + 0.0745186i 0.133669 + 0.0119325i
\(40\) −2.20276 + 0.384532i −0.348286 + 0.0607998i
\(41\) 8.89223i 1.38873i −0.719622 0.694366i \(-0.755685\pi\)
0.719622 0.694366i \(-0.244315\pi\)
\(42\) 2.05205 + 2.45433i 0.316638 + 0.378712i
\(43\) −8.84777 + 8.84777i −1.34927 + 1.34927i −0.462820 + 0.886452i \(0.653162\pi\)
−0.886452 + 0.462820i \(0.846838\pi\)
\(44\) 5.15114 0.776564
\(45\) 4.71850 + 4.76821i 0.703392 + 0.710802i
\(46\) −4.70047 −0.693046
\(47\) 2.14509 2.14509i 0.312894 0.312894i −0.533136 0.846030i \(-0.678986\pi\)
0.846030 + 0.533136i \(0.178986\pi\)
\(48\) −1.11099 1.32879i −0.160358 0.191795i
\(49\) 3.58845i 0.512636i
\(50\) −4.52430 2.12854i −0.639833 0.301021i
\(51\) 10.3691 + 0.925647i 1.45197 + 0.129617i
\(52\) −0.342145 0.342145i −0.0474470 0.0474470i
\(53\) 8.17583 + 8.17583i 1.12304 + 1.12304i 0.991283 + 0.131754i \(0.0420607\pi\)
0.131754 + 0.991283i \(0.457939\pi\)
\(54\) −1.37145 + 5.01190i −0.186631 + 0.682033i
\(55\) 9.42396 + 6.62272i 1.27073 + 0.893007i
\(56\) 1.84704i 0.246821i
\(57\) 1.32879 1.11099i 0.176003 0.147155i
\(58\) 6.17959 6.17959i 0.811420 0.811420i
\(59\) −1.27397 −0.165856 −0.0829282 0.996556i \(-0.526427\pi\)
−0.0829282 + 0.996556i \(0.526427\pi\)
\(60\) −0.324151 3.85939i −0.0418477 0.498246i
\(61\) −6.26456 −0.802094 −0.401047 0.916057i \(-0.631354\pi\)
−0.401047 + 0.916057i \(0.631354\pi\)
\(62\) −7.14093 + 7.14093i −0.906899 + 0.906899i
\(63\) −4.55022 + 3.16219i −0.573274 + 0.398399i
\(64\) 1.00000i 0.125000i
\(65\) −0.186062 1.06584i −0.0230781 0.132201i
\(66\) −0.793310 + 8.88670i −0.0976498 + 1.09388i
\(67\) −1.50061 1.50061i −0.183328 0.183328i 0.609476 0.792804i \(-0.291380\pi\)
−0.792804 + 0.609476i \(0.791380\pi\)
\(68\) −4.25002 4.25002i −0.515391 0.515391i
\(69\) 0.723903 8.10920i 0.0871477 0.976233i
\(70\) 2.37470 3.37914i 0.283831 0.403884i
\(71\) 11.7068i 1.38935i 0.719325 + 0.694674i \(0.244451\pi\)
−0.719325 + 0.694674i \(0.755549\pi\)
\(72\) 2.46352 1.71203i 0.290329 0.201765i
\(73\) −2.73639 + 2.73639i −0.320270 + 0.320270i −0.848871 0.528601i \(-0.822717\pi\)
0.528601 + 0.848871i \(0.322717\pi\)
\(74\) 0.448905 0.0521842
\(75\) 4.36891 7.47747i 0.504478 0.863424i
\(76\) −1.00000 −0.114708
\(77\) −6.72767 + 6.72767i −0.766689 + 0.766689i
\(78\) 0.642958 0.537573i 0.0728007 0.0608682i
\(79\) 5.23062i 0.588491i −0.955730 0.294246i \(-0.904932\pi\)
0.955730 0.294246i \(-0.0950683\pi\)
\(80\) −1.28568 + 1.82949i −0.143743 + 0.204543i
\(81\) −8.43527 3.13788i −0.937252 0.348653i
\(82\) −6.28776 6.28776i −0.694366 0.694366i
\(83\) −9.88555 9.88555i −1.08508 1.08508i −0.996027 0.0890537i \(-0.971616\pi\)
−0.0890537 0.996027i \(-0.528384\pi\)
\(84\) 3.18649 + 0.284456i 0.347675 + 0.0310367i
\(85\) −2.31120 13.2395i −0.250685 1.43603i
\(86\) 12.5126i 1.34927i
\(87\) 9.70927 + 11.6127i 1.04094 + 1.24501i
\(88\) 3.64241 3.64241i 0.388282 0.388282i
\(89\) −16.2880 −1.72653 −0.863264 0.504753i \(-0.831584\pi\)
−0.863264 + 0.504753i \(0.831584\pi\)
\(90\) 6.70811 + 0.0351501i 0.707097 + 0.00370514i
\(91\) 0.893720 0.0936873
\(92\) −3.32373 + 3.32373i −0.346523 + 0.346523i
\(93\) −11.2197 13.4192i −1.16343 1.39151i
\(94\) 3.03362i 0.312894i
\(95\) −1.82949 1.28568i −0.187702 0.131908i
\(96\) −1.72519 0.154007i −0.176077 0.0157182i
\(97\) 4.02586 + 4.02586i 0.408765 + 0.408765i 0.881308 0.472543i \(-0.156664\pi\)
−0.472543 + 0.881308i \(0.656664\pi\)
\(98\) −2.53742 2.53742i −0.256318 0.256318i
\(99\) −15.2091 2.73722i −1.52857 0.275101i
\(100\) −4.70427 + 1.69406i −0.470427 + 0.169406i
\(101\) 3.68192i 0.366365i 0.983079 + 0.183183i \(0.0586400\pi\)
−0.983079 + 0.183183i \(0.941360\pi\)
\(102\) 7.98663 6.67756i 0.790794 0.661177i
\(103\) −5.58428 + 5.58428i −0.550235 + 0.550235i −0.926509 0.376273i \(-0.877205\pi\)
0.376273 + 0.926509i \(0.377205\pi\)
\(104\) −0.483866 −0.0474470
\(105\) 5.46393 + 4.61722i 0.533225 + 0.450594i
\(106\) 11.5624 1.12304
\(107\) 2.07440 2.07440i 0.200540 0.200540i −0.599691 0.800231i \(-0.704710\pi\)
0.800231 + 0.599691i \(0.204710\pi\)
\(108\) 2.57419 + 4.51371i 0.247701 + 0.434332i
\(109\) 4.47191i 0.428331i −0.976797 0.214165i \(-0.931297\pi\)
0.976797 0.214165i \(-0.0687032\pi\)
\(110\) 11.3467 1.98078i 1.08187 0.188860i
\(111\) −0.0691344 + 0.774447i −0.00656195 + 0.0735073i
\(112\) −1.30605 1.30605i −0.123410 0.123410i
\(113\) 6.24110 + 6.24110i 0.587114 + 0.587114i 0.936849 0.349735i \(-0.113728\pi\)
−0.349735 + 0.936849i \(0.613728\pi\)
\(114\) 0.154007 1.72519i 0.0144240 0.161579i
\(115\) −10.3540 + 1.80748i −0.965514 + 0.168548i
\(116\) 8.73926i 0.811420i
\(117\) 0.828396 + 1.19202i 0.0765852 + 0.110202i
\(118\) −0.900830 + 0.900830i −0.0829282 + 0.0829282i
\(119\) 11.1015 1.01767
\(120\) −2.95821 2.49979i −0.270047 0.228199i
\(121\) −15.5343 −1.41221
\(122\) −4.42971 + 4.42971i −0.401047 + 0.401047i
\(123\) 11.8159 9.87922i 1.06541 0.890779i
\(124\) 10.0988i 0.906899i
\(125\) −10.7844 2.94892i −0.964588 0.263760i
\(126\) −0.981482 + 5.45350i −0.0874374 + 0.485836i
\(127\) 1.82261 + 1.82261i 0.161730 + 0.161730i 0.783333 0.621603i \(-0.213518\pi\)
−0.621603 + 0.783333i \(0.713518\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −21.5867 1.92703i −1.90060 0.169665i
\(130\) −0.885228 0.622097i −0.0776397 0.0545615i
\(131\) 11.4188i 0.997666i −0.866698 0.498833i \(-0.833762\pi\)
0.866698 0.498833i \(-0.166238\pi\)
\(132\) 5.72289 + 6.84480i 0.498114 + 0.595764i
\(133\) 1.30605 1.30605i 0.113249 0.113249i
\(134\) −2.12218 −0.183328
\(135\) −1.09373 + 11.5674i −0.0941337 + 0.995560i
\(136\) −6.01044 −0.515391
\(137\) 11.0007 11.0007i 0.939857 0.939857i −0.0584339 0.998291i \(-0.518611\pi\)
0.998291 + 0.0584339i \(0.0186107\pi\)
\(138\) −5.22220 6.24595i −0.444543 0.531690i
\(139\) 1.23352i 0.104626i −0.998631 0.0523128i \(-0.983341\pi\)
0.998631 0.0523128i \(-0.0166593\pi\)
\(140\) −0.710245 4.06858i −0.0600266 0.343857i
\(141\) 5.23357 + 0.467198i 0.440746 + 0.0393452i
\(142\) 8.27799 + 8.27799i 0.694674 + 0.694674i
\(143\) 1.76244 + 1.76244i 0.147383 + 0.147383i
\(144\) 0.531382 2.95256i 0.0442818 0.246047i
\(145\) 11.2359 15.9884i 0.933090 1.32776i
\(146\) 3.86983i 0.320270i
\(147\) 4.76831 3.98675i 0.393283 0.328821i
\(148\) 0.317424 0.317424i 0.0260921 0.0260921i
\(149\) 0.607952 0.0498053 0.0249027 0.999690i \(-0.492072\pi\)
0.0249027 + 0.999690i \(0.492072\pi\)
\(150\) −2.19808 8.37666i −0.179473 0.683951i
\(151\) 2.49294 0.202873 0.101436 0.994842i \(-0.467656\pi\)
0.101436 + 0.994842i \(0.467656\pi\)
\(152\) −0.707107 + 0.707107i −0.0573539 + 0.0573539i
\(153\) 10.2901 + 14.8068i 0.831903 + 1.19706i
\(154\) 9.51436i 0.766689i
\(155\) −12.9838 + 18.4756i −1.04288 + 1.48400i
\(156\) 0.0745186 0.834762i 0.00596627 0.0668344i
\(157\) 0.0444358 + 0.0444358i 0.00354636 + 0.00354636i 0.708878 0.705331i \(-0.249202\pi\)
−0.705331 + 0.708878i \(0.749202\pi\)
\(158\) −3.69861 3.69861i −0.294246 0.294246i
\(159\) −1.78068 + 19.9473i −0.141217 + 1.58192i
\(160\) 0.384532 + 2.20276i 0.0303999 + 0.174143i
\(161\) 8.68195i 0.684233i
\(162\) −8.18345 + 3.74582i −0.642952 + 0.294300i
\(163\) 8.99735 8.99735i 0.704727 0.704727i −0.260694 0.965421i \(-0.583952\pi\)
0.965421 + 0.260694i \(0.0839515\pi\)
\(164\) −8.89223 −0.694366
\(165\) 1.66975 + 19.8803i 0.129990 + 1.54768i
\(166\) −13.9803 −1.08508
\(167\) −1.17503 + 1.17503i −0.0909264 + 0.0909264i −0.751107 0.660181i \(-0.770480\pi\)
0.660181 + 0.751107i \(0.270480\pi\)
\(168\) 2.45433 2.05205i 0.189356 0.158319i
\(169\) 12.7659i 0.981990i
\(170\) −10.9960 7.72749i −0.843357 0.592672i
\(171\) 2.95256 + 0.531382i 0.225788 + 0.0406358i
\(172\) 8.84777 + 8.84777i 0.674636 + 0.674636i
\(173\) 13.5995 + 13.5995i 1.03395 + 1.03395i 0.999403 + 0.0345455i \(0.0109984\pi\)
0.0345455 + 0.999403i \(0.489002\pi\)
\(174\) 15.0769 + 1.34590i 1.14298 + 0.102033i
\(175\) 3.93150 8.35656i 0.297193 0.631697i
\(176\) 5.15114i 0.388282i
\(177\) −1.41537 1.69284i −0.106386 0.127241i
\(178\) −11.5174 + 11.5174i −0.863264 + 0.863264i
\(179\) −17.9786 −1.34378 −0.671892 0.740649i \(-0.734518\pi\)
−0.671892 + 0.740649i \(0.734518\pi\)
\(180\) 4.76821 4.71850i 0.355401 0.351696i
\(181\) 4.58187 0.340568 0.170284 0.985395i \(-0.445531\pi\)
0.170284 + 0.985395i \(0.445531\pi\)
\(182\) 0.631955 0.631955i 0.0468437 0.0468437i
\(183\) −6.95989 8.32430i −0.514490 0.615350i
\(184\) 4.70047i 0.346523i
\(185\) 0.988829 0.172618i 0.0727002 0.0126911i
\(186\) −17.4223 1.55528i −1.27747 0.114039i
\(187\) 21.8925 + 21.8925i 1.60094 + 1.60094i
\(188\) −2.14509 2.14509i −0.156447 0.156447i
\(189\) −9.25717 2.53312i −0.673360 0.184257i
\(190\) −2.20276 + 0.384532i −0.159805 + 0.0278969i
\(191\) 12.3225i 0.891626i −0.895126 0.445813i \(-0.852915\pi\)
0.895126 0.445813i \(-0.147085\pi\)
\(192\) −1.32879 + 1.11099i −0.0958974 + 0.0801791i
\(193\) −11.8604 + 11.8604i −0.853728 + 0.853728i −0.990590 0.136862i \(-0.956298\pi\)
0.136862 + 0.990590i \(0.456298\pi\)
\(194\) 5.69343 0.408765
\(195\) 1.20957 1.43138i 0.0866189 0.102503i
\(196\) −3.58845 −0.256318
\(197\) 3.56808 3.56808i 0.254215 0.254215i −0.568481 0.822696i \(-0.692469\pi\)
0.822696 + 0.568481i \(0.192469\pi\)
\(198\) −12.6900 + 8.81894i −0.901836 + 0.626735i
\(199\) 3.23189i 0.229102i −0.993417 0.114551i \(-0.963457\pi\)
0.993417 0.114551i \(-0.0365430\pi\)
\(200\) −2.12854 + 4.52430i −0.150511 + 0.319916i
\(201\) 0.326830 3.66116i 0.0230528 0.258239i
\(202\) 2.60351 + 2.60351i 0.183183 + 0.183183i
\(203\) 11.4139 + 11.4139i 0.801102 + 0.801102i
\(204\) 0.925647 10.3691i 0.0648083 0.725986i
\(205\) −16.2682 11.4326i −1.13622 0.798484i
\(206\) 7.89736i 0.550235i
\(207\) 11.5797 8.04736i 0.804845 0.559330i
\(208\) −0.342145 + 0.342145i −0.0237235 + 0.0237235i
\(209\) 5.15114 0.356312
\(210\) 7.12845 0.598720i 0.491910 0.0413156i
\(211\) 13.2442 0.911766 0.455883 0.890040i \(-0.349324\pi\)
0.455883 + 0.890040i \(0.349324\pi\)
\(212\) 8.17583 8.17583i 0.561518 0.561518i
\(213\) −15.5560 + 13.0062i −1.06588 + 0.891173i
\(214\) 2.93365i 0.200540i
\(215\) 4.81150 + 27.5623i 0.328142 + 1.87973i
\(216\) 5.01190 + 1.37145i 0.341017 + 0.0933153i
\(217\) −13.1896 13.1896i −0.895366 0.895366i
\(218\) −3.16212 3.16212i −0.214165 0.214165i
\(219\) −6.67620 0.595980i −0.451136 0.0402726i
\(220\) 6.62272 9.42396i 0.446504 0.635363i
\(221\) 2.90825i 0.195630i
\(222\) 0.498731 + 0.596502i 0.0334727 + 0.0400346i
\(223\) 3.93298 3.93298i 0.263372 0.263372i −0.563050 0.826423i \(-0.690372\pi\)
0.826423 + 0.563050i \(0.190372\pi\)
\(224\) −1.84704 −0.123410
\(225\) 14.7899 2.50205i 0.985990 0.166804i
\(226\) 8.82625 0.587114
\(227\) −4.90875 + 4.90875i −0.325805 + 0.325805i −0.850989 0.525184i \(-0.823997\pi\)
0.525184 + 0.850989i \(0.323997\pi\)
\(228\) −1.11099 1.32879i −0.0735774 0.0880015i
\(229\) 0.309162i 0.0204300i 0.999948 + 0.0102150i \(0.00325159\pi\)
−0.999948 + 0.0102150i \(0.996748\pi\)
\(230\) −6.04329 + 8.59945i −0.398483 + 0.567031i
\(231\) −16.4141 1.46527i −1.07997 0.0964080i
\(232\) −6.17959 6.17959i −0.405710 0.405710i
\(233\) −1.09776 1.09776i −0.0719169 0.0719169i 0.670233 0.742150i \(-0.266194\pi\)
−0.742150 + 0.670233i \(0.766194\pi\)
\(234\) 1.42865 + 0.257118i 0.0933935 + 0.0168083i
\(235\) −1.16652 6.68233i −0.0760956 0.435907i
\(236\) 1.27397i 0.0829282i
\(237\) 6.95041 5.81119i 0.451478 0.377478i
\(238\) 7.84995 7.84995i 0.508837 0.508837i
\(239\) 24.4016 1.57841 0.789205 0.614130i \(-0.210493\pi\)
0.789205 + 0.614130i \(0.210493\pi\)
\(240\) −3.85939 + 0.324151i −0.249123 + 0.0209239i
\(241\) −15.4813 −0.997235 −0.498618 0.866822i \(-0.666159\pi\)
−0.498618 + 0.866822i \(0.666159\pi\)
\(242\) −10.9844 + 10.9844i −0.706104 + 0.706104i
\(243\) −5.20195 14.6949i −0.333705 0.942677i
\(244\) 6.26456i 0.401047i
\(245\) −6.56503 4.61359i −0.419424 0.294752i
\(246\) 1.36946 15.3408i 0.0873137 0.978093i
\(247\) −0.342145 0.342145i −0.0217702 0.0217702i
\(248\) 7.14093 + 7.14093i 0.453449 + 0.453449i
\(249\) 2.15306 24.1187i 0.136444 1.52846i
\(250\) −9.71094 + 5.54054i −0.614174 + 0.350414i
\(251\) 10.3840i 0.655435i −0.944776 0.327718i \(-0.893721\pi\)
0.944776 0.327718i \(-0.106279\pi\)
\(252\) 3.16219 + 4.55022i 0.199199 + 0.286637i
\(253\) 17.1210 17.1210i 1.07639 1.07639i
\(254\) 2.57755 0.161730
\(255\) 15.0249 17.7802i 0.940893 1.11344i
\(256\) 1.00000 0.0625000
\(257\) −10.1303 + 10.1303i −0.631914 + 0.631914i −0.948548 0.316634i \(-0.897447\pi\)
0.316634 + 0.948548i \(0.397447\pi\)
\(258\) −16.6267 + 13.9015i −1.03513 + 0.865468i
\(259\) 0.829145i 0.0515206i
\(260\) −1.06584 + 0.186062i −0.0661006 + 0.0115391i
\(261\) −4.64388 + 25.8032i −0.287449 + 1.59718i
\(262\) −8.07432 8.07432i −0.498833 0.498833i
\(263\) 18.8740 + 18.8740i 1.16382 + 1.16382i 0.983632 + 0.180189i \(0.0576710\pi\)
0.180189 + 0.983632i \(0.442329\pi\)
\(264\) 8.88670 + 0.793310i 0.546939 + 0.0488249i
\(265\) 25.4691 4.44609i 1.56455 0.273121i
\(266\) 1.84704i 0.113249i
\(267\) −18.0959 21.6434i −1.10745 1.32456i
\(268\) −1.50061 + 1.50061i −0.0916642 + 0.0916642i
\(269\) 6.51981 0.397520 0.198760 0.980048i \(-0.436309\pi\)
0.198760 + 0.980048i \(0.436309\pi\)
\(270\) 7.40597 + 8.95274i 0.450713 + 0.544847i
\(271\) 14.4070 0.875160 0.437580 0.899179i \(-0.355836\pi\)
0.437580 + 0.899179i \(0.355836\pi\)
\(272\) −4.25002 + 4.25002i −0.257695 + 0.257695i
\(273\) 0.992918 + 1.18757i 0.0600941 + 0.0718749i
\(274\) 15.5574i 0.939857i
\(275\) 24.2324 8.72634i 1.46127 0.526218i
\(276\) −8.10920 0.723903i −0.488117 0.0435739i
\(277\) 13.9724 + 13.9724i 0.839520 + 0.839520i 0.988796 0.149276i \(-0.0476942\pi\)
−0.149276 + 0.988796i \(0.547694\pi\)
\(278\) −0.872229 0.872229i −0.0523128 0.0523128i
\(279\) 5.36632 29.8173i 0.321273 1.78512i
\(280\) −3.37914 2.37470i −0.201942 0.141915i
\(281\) 24.2309i 1.44549i −0.691113 0.722747i \(-0.742879\pi\)
0.691113 0.722747i \(-0.257121\pi\)
\(282\) 4.03105 3.37034i 0.240046 0.200701i
\(283\) 9.26434 9.26434i 0.550708 0.550708i −0.375937 0.926645i \(-0.622679\pi\)
0.926645 + 0.375937i \(0.122679\pi\)
\(284\) 11.7068 0.694674
\(285\) −0.324151 3.85939i −0.0192011 0.228611i
\(286\) 2.49247 0.147383
\(287\) 11.6137 11.6137i 0.685537 0.685537i
\(288\) −1.71203 2.46352i −0.100883 0.145164i
\(289\) 19.1253i 1.12502i
\(290\) −3.36052 19.2505i −0.197337 1.13043i
\(291\) −0.876826 + 9.82225i −0.0514005 + 0.575791i
\(292\) 2.73639 + 2.73639i 0.160135 + 0.160135i
\(293\) 9.00595 + 9.00595i 0.526133 + 0.526133i 0.919417 0.393284i \(-0.128661\pi\)
−0.393284 + 0.919417i \(0.628661\pi\)
\(294\) 0.552645 6.19076i 0.0322309 0.361052i
\(295\) −1.63791 + 2.33071i −0.0953629 + 0.135699i
\(296\) 0.448905i 0.0260921i
\(297\) −13.2600 23.2508i −0.769424 1.34915i
\(298\) 0.429887 0.429887i 0.0249027 0.0249027i
\(299\) −2.27440 −0.131532
\(300\) −7.47747 4.36891i −0.431712 0.252239i
\(301\) −23.1113 −1.33211
\(302\) 1.76278 1.76278i 0.101436 0.101436i
\(303\) −4.89252 + 4.09060i −0.281068 + 0.234999i
\(304\) 1.00000i 0.0573539i
\(305\) −8.05421 + 11.4609i −0.461183 + 0.656251i
\(306\) 17.7462 + 3.19384i 1.01448 + 0.182579i
\(307\) 4.39219 + 4.39219i 0.250675 + 0.250675i 0.821247 0.570572i \(-0.193279\pi\)
−0.570572 + 0.821247i \(0.693279\pi\)
\(308\) 6.72767 + 6.72767i 0.383345 + 0.383345i
\(309\) −13.6245 1.21625i −0.775068 0.0691898i
\(310\) 3.88331 + 22.2452i 0.220557 + 1.26344i
\(311\) 16.1534i 0.915975i −0.888959 0.457988i \(-0.848570\pi\)
0.888959 0.457988i \(-0.151430\pi\)
\(312\) −0.537573 0.642958i −0.0304341 0.0364003i
\(313\) −0.493189 + 0.493189i −0.0278767 + 0.0278767i −0.720908 0.693031i \(-0.756275\pi\)
0.693031 + 0.720908i \(0.256275\pi\)
\(314\) 0.0628417 0.00354636
\(315\) −0.0649235 + 12.3901i −0.00365803 + 0.698105i
\(316\) −5.23062 −0.294246
\(317\) −16.9755 + 16.9755i −0.953441 + 0.953441i −0.998963 0.0455227i \(-0.985505\pi\)
0.0455227 + 0.998963i \(0.485505\pi\)
\(318\) 12.8457 + 15.3640i 0.720352 + 0.861570i
\(319\) 45.0172i 2.52048i
\(320\) 1.82949 + 1.28568i 0.102272 + 0.0718716i
\(321\) 5.06110 + 0.451801i 0.282483 + 0.0252171i
\(322\) −6.13906 6.13906i −0.342117 0.342117i
\(323\) −4.25002 4.25002i −0.236477 0.236477i
\(324\) −3.13788 + 8.43527i −0.174326 + 0.468626i
\(325\) −2.18916 1.02993i −0.121433 0.0571302i
\(326\) 12.7242i 0.704727i
\(327\) 5.94224 4.96826i 0.328607 0.274746i
\(328\) −6.28776 + 6.28776i −0.347183 + 0.347183i
\(329\) 5.60322 0.308915
\(330\) 15.2382 + 12.8768i 0.838834 + 0.708845i
\(331\) 14.7118 0.808635 0.404318 0.914619i \(-0.367509\pi\)
0.404318 + 0.914619i \(0.367509\pi\)
\(332\) −9.88555 + 9.88555i −0.542540 + 0.542540i
\(333\) −1.10589 + 0.768541i −0.0606023 + 0.0421158i
\(334\) 1.66174i 0.0909264i
\(335\) −4.67464 + 0.816045i −0.255403 + 0.0445853i
\(336\) 0.284456 3.18649i 0.0155184 0.173837i
\(337\) 13.8928 + 13.8928i 0.756787 + 0.756787i 0.975736 0.218949i \(-0.0702629\pi\)
−0.218949 + 0.975736i \(0.570263\pi\)
\(338\) 9.02684 + 9.02684i 0.490995 + 0.490995i
\(339\) −1.35930 + 15.2270i −0.0738271 + 0.827015i
\(340\) −13.2395 + 2.31120i −0.718014 + 0.125343i
\(341\) 52.0204i 2.81706i
\(342\) 2.46352 1.71203i 0.133212 0.0925762i
\(343\) 13.8291 13.8291i 0.746700 0.746700i
\(344\) 12.5126 0.674636
\(345\) −13.9050 11.7502i −0.748619 0.632610i
\(346\) 19.2326 1.03395
\(347\) 21.0082 21.0082i 1.12778 1.12778i 0.137245 0.990537i \(-0.456175\pi\)
0.990537 0.137245i \(-0.0438246\pi\)
\(348\) 11.6127 9.70927i 0.622504 0.520472i
\(349\) 18.0913i 0.968404i −0.874956 0.484202i \(-0.839110\pi\)
0.874956 0.484202i \(-0.160890\pi\)
\(350\) −3.12899 8.68897i −0.167252 0.464445i
\(351\) −0.663598 + 2.42509i −0.0354202 + 0.129442i
\(352\) −3.64241 3.64241i −0.194141 0.194141i
\(353\) 8.95609 + 8.95609i 0.476685 + 0.476685i 0.904070 0.427385i \(-0.140565\pi\)
−0.427385 + 0.904070i \(0.640565\pi\)
\(354\) −2.19783 0.196199i −0.116814 0.0104279i
\(355\) 21.4175 + 15.0512i 1.13673 + 0.798837i
\(356\) 16.2880i 0.863264i
\(357\) 12.3337 + 14.7516i 0.652769 + 0.780738i
\(358\) −12.7128 + 12.7128i −0.671892 + 0.671892i
\(359\) −13.9018 −0.733708 −0.366854 0.930278i \(-0.619565\pi\)
−0.366854 + 0.930278i \(0.619565\pi\)
\(360\) 0.0351501 6.70811i 0.00185257 0.353549i
\(361\) −1.00000 −0.0526316
\(362\) 3.23987 3.23987i 0.170284 0.170284i
\(363\) −17.2585 20.6419i −0.905837 1.08342i
\(364\) 0.893720i 0.0468437i
\(365\) 1.48807 + 8.52430i 0.0778893 + 0.446182i
\(366\) −10.8076 0.964784i −0.564920 0.0504300i
\(367\) 2.43869 + 2.43869i 0.127299 + 0.127299i 0.767886 0.640587i \(-0.221309\pi\)
−0.640587 + 0.767886i \(0.721309\pi\)
\(368\) 3.32373 + 3.32373i 0.173262 + 0.173262i
\(369\) 26.2549 + 4.72517i 1.36677 + 0.245982i
\(370\) 0.577148 0.821267i 0.0300045 0.0426957i
\(371\) 21.3561i 1.10876i
\(372\) −13.4192 + 11.2197i −0.695754 + 0.581715i
\(373\) −21.0831 + 21.0831i −1.09164 + 1.09164i −0.0962879 + 0.995354i \(0.530697\pi\)
−0.995354 + 0.0962879i \(0.969303\pi\)
\(374\) 30.9606 1.60094
\(375\) −8.06294 17.6065i −0.416368 0.909196i
\(376\) −3.03362 −0.156447
\(377\) 2.99010 2.99010i 0.153998 0.153998i
\(378\) −8.33699 + 4.75462i −0.428809 + 0.244551i
\(379\) 2.25390i 0.115775i 0.998323 + 0.0578874i \(0.0184364\pi\)
−0.998323 + 0.0578874i \(0.981564\pi\)
\(380\) −1.28568 + 1.82949i −0.0659539 + 0.0938508i
\(381\) −0.396960 + 4.44677i −0.0203369 + 0.227815i
\(382\) −8.71334 8.71334i −0.445813 0.445813i
\(383\) 4.29081 + 4.29081i 0.219250 + 0.219250i 0.808182 0.588932i \(-0.200452\pi\)
−0.588932 + 0.808182i \(0.700452\pi\)
\(384\) −0.154007 + 1.72519i −0.00785912 + 0.0880383i
\(385\) 3.65857 + 20.9578i 0.186458 + 1.06811i
\(386\) 16.7731i 0.853728i
\(387\) −21.4221 30.8252i −1.08894 1.56693i
\(388\) 4.02586 4.02586i 0.204382 0.204382i
\(389\) −21.0267 −1.06609 −0.533047 0.846086i \(-0.678953\pi\)
−0.533047 + 0.846086i \(0.678953\pi\)
\(390\) −0.156846 1.86743i −0.00794220 0.0945611i
\(391\) −28.2519 −1.42876
\(392\) −2.53742 + 2.53742i −0.128159 + 0.128159i
\(393\) 15.1732 12.6862i 0.765389 0.639936i
\(394\) 5.04603i 0.254215i
\(395\) −9.56937 6.72490i −0.481487 0.338367i
\(396\) −2.73722 + 15.2091i −0.137551 + 0.764285i
\(397\) 7.05671 + 7.05671i 0.354166 + 0.354166i 0.861657 0.507491i \(-0.169427\pi\)
−0.507491 + 0.861657i \(0.669427\pi\)
\(398\) −2.28529 2.28529i −0.114551 0.114551i
\(399\) 3.18649 + 0.284456i 0.159524 + 0.0142406i
\(400\) 1.69406 + 4.70427i 0.0847029 + 0.235214i
\(401\) 3.58548i 0.179050i 0.995985 + 0.0895252i \(0.0285350\pi\)
−0.995985 + 0.0895252i \(0.971465\pi\)
\(402\) −2.35773 2.81994i −0.117593 0.140646i
\(403\) −3.45526 + 3.45526i −0.172119 + 0.172119i
\(404\) 3.68192 0.183183
\(405\) −16.5858 + 11.3979i −0.824153 + 0.566367i
\(406\) 16.1418 0.801102
\(407\) −1.63510 + 1.63510i −0.0810487 + 0.0810487i
\(408\) −6.67756 7.98663i −0.330589 0.395397i
\(409\) 16.2138i 0.801720i 0.916139 + 0.400860i \(0.131289\pi\)
−0.916139 + 0.400860i \(0.868711\pi\)
\(410\) −19.5874 + 3.41934i −0.967354 + 0.168869i
\(411\) 26.8395 + 2.39594i 1.32389 + 0.118183i
\(412\) 5.58428 + 5.58428i 0.275118 + 0.275118i
\(413\) −1.66387 1.66387i −0.0818736 0.0818736i
\(414\) 2.49774 13.8784i 0.122757 0.682088i
\(415\) −30.7952 + 5.37586i −1.51168 + 0.263891i
\(416\) 0.483866i 0.0237235i
\(417\) 1.63909 1.37043i 0.0802666 0.0671104i
\(418\) 3.64241 3.64241i 0.178156 0.178156i
\(419\) 7.46153 0.364520 0.182260 0.983250i \(-0.441659\pi\)
0.182260 + 0.983250i \(0.441659\pi\)
\(420\) 4.61722 5.46393i 0.225297 0.266613i
\(421\) 3.53068 0.172075 0.0860374 0.996292i \(-0.472580\pi\)
0.0860374 + 0.996292i \(0.472580\pi\)
\(422\) 9.36503 9.36503i 0.455883 0.455883i
\(423\) 5.19366 + 7.47339i 0.252525 + 0.363369i
\(424\) 11.5624i 0.561518i
\(425\) −27.1930 12.7935i −1.31906 0.620574i
\(426\) −1.80293 + 20.1965i −0.0873523 + 0.978526i
\(427\) −8.18185 8.18185i −0.395947 0.395947i
\(428\) −2.07440 2.07440i −0.100270 0.100270i
\(429\) −0.383856 + 4.29998i −0.0185328 + 0.207605i
\(430\) 22.8917 + 16.0872i 1.10394 + 0.775795i
\(431\) 36.0994i 1.73885i 0.494067 + 0.869424i \(0.335510\pi\)
−0.494067 + 0.869424i \(0.664490\pi\)
\(432\) 4.51371 2.57419i 0.217166 0.123851i
\(433\) 8.42713 8.42713i 0.404982 0.404982i −0.475003 0.879984i \(-0.657553\pi\)
0.879984 + 0.475003i \(0.157553\pi\)
\(434\) −18.6529 −0.895366
\(435\) 33.7283 2.83284i 1.61715 0.135824i
\(436\) −4.47191 −0.214165
\(437\) −3.32373 + 3.32373i −0.158996 + 0.158996i
\(438\) −5.14221 + 4.29936i −0.245704 + 0.205432i
\(439\) 6.71446i 0.320464i 0.987079 + 0.160232i \(0.0512242\pi\)
−0.987079 + 0.160232i \(0.948776\pi\)
\(440\) −1.98078 11.3467i −0.0944299 0.540933i
\(441\) 10.5951 + 1.90684i 0.504530 + 0.0908017i
\(442\) −2.05644 2.05644i −0.0978150 0.0978150i
\(443\) 15.5862 + 15.5862i 0.740522 + 0.740522i 0.972678 0.232157i \(-0.0745782\pi\)
−0.232157 + 0.972678i \(0.574578\pi\)
\(444\) 0.774447 + 0.0691344i 0.0367536 + 0.00328097i
\(445\) −20.9412 + 29.7988i −0.992707 + 1.41260i
\(446\) 5.56208i 0.263372i
\(447\) 0.675431 + 0.807842i 0.0319468 + 0.0382096i
\(448\) −1.30605 + 1.30605i −0.0617052 + 0.0617052i
\(449\) 21.1036 0.995941 0.497971 0.867194i \(-0.334079\pi\)
0.497971 + 0.867194i \(0.334079\pi\)
\(450\) 8.68879 12.2272i 0.409593 0.576397i
\(451\) 45.8052 2.15688
\(452\) 6.24110 6.24110i 0.293557 0.293557i
\(453\) 2.76964 + 3.31260i 0.130129 + 0.155640i
\(454\) 6.94202i 0.325805i
\(455\) 1.14904 1.63505i 0.0538677 0.0766524i
\(456\) −1.72519 0.154007i −0.0807894 0.00721202i
\(457\) −3.24691 3.24691i −0.151884 0.151884i 0.627075 0.778959i \(-0.284252\pi\)
−0.778959 + 0.627075i \(0.784252\pi\)
\(458\) 0.218610 + 0.218610i 0.0102150 + 0.0102150i
\(459\) −8.24301 + 30.1237i −0.384751 + 1.40605i
\(460\) 1.80748 + 10.3540i 0.0842741 + 0.482757i
\(461\) 31.5064i 1.46740i −0.679473 0.733700i \(-0.737792\pi\)
0.679473 0.733700i \(-0.262208\pi\)
\(462\) −12.6426 + 10.5704i −0.588188 + 0.491780i
\(463\) −8.81741 + 8.81741i −0.409780 + 0.409780i −0.881662 0.471882i \(-0.843575\pi\)
0.471882 + 0.881662i \(0.343575\pi\)
\(464\) −8.73926 −0.405710
\(465\) −38.9752 + 3.27354i −1.80743 + 0.151807i
\(466\) −1.55247 −0.0719169
\(467\) 4.04048 4.04048i 0.186971 0.186971i −0.607414 0.794385i \(-0.707793\pi\)
0.794385 + 0.607414i \(0.207793\pi\)
\(468\) 1.19202 0.828396i 0.0551009 0.0382926i
\(469\) 3.91975i 0.180997i
\(470\) −5.54998 3.90026i −0.256001 0.179906i
\(471\) −0.00967804 + 0.108414i −0.000445941 + 0.00499545i
\(472\) 0.900830 + 0.900830i 0.0414641 + 0.0414641i
\(473\) −45.5761 45.5761i −2.09559 2.09559i
\(474\) 0.805551 9.02382i 0.0370002 0.414478i
\(475\) −4.70427 + 1.69406i −0.215847 + 0.0777287i
\(476\) 11.1015i 0.508837i
\(477\) −28.4841 + 19.7952i −1.30420 + 0.906358i
\(478\) 17.2546 17.2546i 0.789205 0.789205i
\(479\) −25.6778 −1.17325 −0.586624 0.809859i \(-0.699543\pi\)
−0.586624 + 0.809859i \(0.699543\pi\)
\(480\) −2.49979 + 2.95821i −0.114099 + 0.135023i
\(481\) 0.217210 0.00990393
\(482\) −10.9469 + 10.9469i −0.498618 + 0.498618i
\(483\) 11.5365 9.64560i 0.524929 0.438890i
\(484\) 15.5343i 0.706104i
\(485\) 12.5412 2.18930i 0.569469 0.0994112i
\(486\) −14.0692 6.71252i −0.638191 0.304486i
\(487\) −10.1276 10.1276i −0.458925 0.458925i 0.439377 0.898303i \(-0.355199\pi\)
−0.898303 + 0.439377i \(0.855199\pi\)
\(488\) 4.42971 + 4.42971i 0.200524 + 0.200524i
\(489\) 21.9516 + 1.95961i 0.992687 + 0.0886165i
\(490\) −7.90448 + 1.37987i −0.357088 + 0.0623363i
\(491\) 19.2496i 0.868723i 0.900739 + 0.434361i \(0.143026\pi\)
−0.900739 + 0.434361i \(0.856974\pi\)
\(492\) −9.87922 11.8159i −0.445390 0.532703i
\(493\) 37.1420 37.1420i 1.67279 1.67279i
\(494\) −0.483866 −0.0217702
\(495\) −24.5617 + 24.3057i −1.10397 + 1.09246i
\(496\) 10.0988 0.453449
\(497\) −15.2898 + 15.2898i −0.685840 + 0.685840i
\(498\) −15.5320 18.5769i −0.696007 0.832451i
\(499\) 19.5782i 0.876439i −0.898868 0.438220i \(-0.855609\pi\)
0.898868 0.438220i \(-0.144391\pi\)
\(500\) −2.94892 + 10.7844i −0.131880 + 0.482294i
\(501\) −2.86682 0.255919i −0.128080 0.0114336i
\(502\) −7.34263 7.34263i −0.327718 0.327718i
\(503\) −18.0640 18.0640i −0.805434 0.805434i 0.178505 0.983939i \(-0.442874\pi\)
−0.983939 + 0.178505i \(0.942874\pi\)
\(504\) 5.45350 + 0.981482i 0.242918 + 0.0437187i
\(505\) 6.73604 + 4.73377i 0.299750 + 0.210650i
\(506\) 24.2128i 1.07639i
\(507\) −16.9632 + 14.1828i −0.753362 + 0.629881i
\(508\) 1.82261 1.82261i 0.0808651 0.0808651i
\(509\) 24.2848 1.07640 0.538202 0.842816i \(-0.319104\pi\)
0.538202 + 0.842816i \(0.319104\pi\)
\(510\) −1.94829 23.1966i −0.0862717 1.02716i
\(511\) −7.14773 −0.316197
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 2.57419 + 4.51371i 0.113653 + 0.199285i
\(514\) 14.3265i 0.631914i
\(515\) 3.03678 + 17.3960i 0.133817 + 0.766558i
\(516\) −1.92703 + 21.5867i −0.0848327 + 0.950301i
\(517\) 11.0497 + 11.0497i 0.485965 + 0.485965i
\(518\) 0.586294 + 0.586294i 0.0257603 + 0.0257603i
\(519\) −2.96194 + 33.1798i −0.130015 + 1.45643i
\(520\) −0.622097 + 0.885228i −0.0272808 + 0.0388198i
\(521\) 19.1374i 0.838425i −0.907888 0.419213i \(-0.862306\pi\)
0.907888 0.419213i \(-0.137694\pi\)
\(522\) 14.9619 + 21.5294i 0.654865 + 0.942315i
\(523\) −3.69849 + 3.69849i −0.161724 + 0.161724i −0.783330 0.621606i \(-0.786480\pi\)
0.621606 + 0.783330i \(0.286480\pi\)
\(524\) −11.4188 −0.498833
\(525\) 15.4720 4.05995i 0.675254 0.177191i
\(526\) 26.6919 1.16382
\(527\) −42.9201 + 42.9201i −1.86963 + 1.86963i
\(528\) 6.84480 5.72289i 0.297882 0.249057i
\(529\) 0.905600i 0.0393739i
\(530\) 14.8655 21.1532i 0.645716 0.918837i
\(531\) 0.676962 3.76147i 0.0293777 0.163234i
\(532\) −1.30605 1.30605i −0.0566246 0.0566246i
\(533\) −3.04243 3.04243i −0.131782 0.131782i
\(534\) −28.0999 2.50846i −1.21600 0.108552i
\(535\) −1.12808 6.46211i −0.0487711 0.279381i
\(536\) 2.12218i 0.0916642i
\(537\) −19.9741 23.8899i −0.861948 1.03092i
\(538\) 4.61020 4.61020i 0.198760 0.198760i
\(539\) 18.4846 0.796189
\(540\) 11.5674 + 1.09373i 0.497780 + 0.0470668i
\(541\) −15.7000 −0.674995 −0.337498 0.941326i \(-0.609581\pi\)
−0.337498 + 0.941326i \(0.609581\pi\)
\(542\) 10.1873 10.1873i 0.437580 0.437580i
\(543\) 5.09044 + 6.08836i 0.218452 + 0.261277i
\(544\) 6.01044i 0.257695i
\(545\) −8.18130 5.74944i −0.350449 0.246279i
\(546\) 1.54184 + 0.137639i 0.0659845 + 0.00589040i
\(547\) 6.76457 + 6.76457i 0.289232 + 0.289232i 0.836777 0.547545i \(-0.184437\pi\)
−0.547545 + 0.836777i \(0.684437\pi\)
\(548\) −11.0007 11.0007i −0.469929 0.469929i
\(549\) 3.32887 18.4965i 0.142073 0.789412i
\(550\) 10.9644 23.3053i 0.467525 0.993743i
\(551\) 8.73926i 0.372305i
\(552\) −6.24595 + 5.22220i −0.265845 + 0.222271i
\(553\) 6.83147 6.83147i 0.290504 0.290504i
\(554\) 19.7600 0.839520
\(555\) 1.32796 + 1.12217i 0.0563687 + 0.0476335i
\(556\) −1.23352 −0.0523128
\(557\) −7.92409 + 7.92409i −0.335754 + 0.335754i −0.854767 0.519012i \(-0.826300\pi\)
0.519012 + 0.854767i \(0.326300\pi\)
\(558\) −17.2895 24.8786i −0.731922 1.05320i
\(559\) 6.05445i 0.256076i
\(560\) −4.06858 + 0.710245i −0.171929 + 0.0300133i
\(561\) −4.76814 + 53.4130i −0.201311 + 2.25510i
\(562\) −17.1338 17.1338i −0.722747 0.722747i
\(563\) 2.50755 + 2.50755i 0.105681 + 0.105681i 0.757970 0.652289i \(-0.226191\pi\)
−0.652289 + 0.757970i \(0.726191\pi\)
\(564\) 0.467198 5.23357i 0.0196726 0.220373i
\(565\) 19.4421 3.39397i 0.817935 0.142786i
\(566\) 13.1018i 0.550708i
\(567\) −6.91868 15.1151i −0.290557 0.634776i
\(568\) 8.27799 8.27799i 0.347337 0.347337i
\(569\) −19.7316 −0.827190 −0.413595 0.910461i \(-0.635727\pi\)
−0.413595 + 0.910461i \(0.635727\pi\)
\(570\) −2.95821 2.49979i −0.123906 0.104705i
\(571\) 11.2502 0.470807 0.235403 0.971898i \(-0.424359\pi\)
0.235403 + 0.971898i \(0.424359\pi\)
\(572\) 1.76244 1.76244i 0.0736913 0.0736913i
\(573\) 16.3741 13.6903i 0.684037 0.571919i
\(574\) 16.4243i 0.685537i
\(575\) −10.0051 + 21.2663i −0.417243 + 0.886868i
\(576\) −2.95256 0.531382i −0.123023 0.0221409i
\(577\) 22.9715 + 22.9715i 0.956315 + 0.956315i 0.999085 0.0427697i \(-0.0136182\pi\)
−0.0427697 + 0.999085i \(0.513618\pi\)
\(578\) −13.5237 13.5237i −0.562510 0.562510i
\(579\) −28.9368 2.58317i −1.20257 0.107353i
\(580\) −15.9884 11.2359i −0.663881 0.466545i
\(581\) 25.8221i 1.07128i
\(582\) 6.32537 + 7.56539i 0.262195 + 0.313596i
\(583\) −42.1149 + 42.1149i −1.74422 + 1.74422i
\(584\) 3.86983 0.160135
\(585\) 3.24583 + 0.0170079i 0.134199 + 0.000703192i
\(586\) 12.7363 0.526133
\(587\) 20.3746 20.3746i 0.840951 0.840951i −0.148032 0.988983i \(-0.547294\pi\)
0.988983 + 0.148032i \(0.0472939\pi\)
\(588\) −3.98675 4.76831i −0.164411 0.196642i
\(589\) 10.0988i 0.416114i
\(590\) 0.489880 + 2.80624i 0.0201681 + 0.115531i
\(591\) 8.70536 + 0.777122i 0.358091 + 0.0319665i
\(592\) −0.317424 0.317424i −0.0130460 0.0130460i
\(593\) −7.81504 7.81504i −0.320925 0.320925i 0.528197 0.849122i \(-0.322868\pi\)
−0.849122 + 0.528197i \(0.822868\pi\)
\(594\) −25.8170 7.06453i −1.05928 0.289861i
\(595\) 14.2730 20.3101i 0.585135 0.832632i
\(596\) 0.607952i 0.0249027i
\(597\) 4.29451 3.59061i 0.175762 0.146954i
\(598\) −1.60824 + 1.60824i −0.0657659 + 0.0657659i
\(599\) −6.25932 −0.255749 −0.127874 0.991790i \(-0.540815\pi\)
−0.127874 + 0.991790i \(0.540815\pi\)
\(600\) −8.37666 + 2.19808i −0.341976 + 0.0897364i
\(601\) −13.5081 −0.551009 −0.275504 0.961300i \(-0.588845\pi\)
−0.275504 + 0.961300i \(0.588845\pi\)
\(602\) −16.3422 + 16.3422i −0.666057 + 0.666057i
\(603\) 5.22803 3.63324i 0.212902 0.147957i
\(604\) 2.49294i 0.101436i
\(605\) −19.9721 + 28.4198i −0.811982 + 1.15543i
\(606\) −0.567041 + 6.35202i −0.0230345 + 0.258033i
\(607\) −19.7516 19.7516i −0.801691 0.801691i 0.181669 0.983360i \(-0.441850\pi\)
−0.983360 + 0.181669i \(0.941850\pi\)
\(608\) 0.707107 + 0.707107i 0.0286770 + 0.0286770i
\(609\) −2.48594 + 27.8476i −0.100735 + 1.12844i
\(610\) 2.40892 + 13.7993i 0.0975343 + 0.558717i
\(611\) 1.46787i 0.0593836i
\(612\) 14.8068 10.2901i 0.598531 0.415952i
\(613\) −8.37167 + 8.37167i −0.338129 + 0.338129i −0.855663 0.517534i \(-0.826850\pi\)
0.517534 + 0.855663i \(0.326850\pi\)
\(614\) 6.21149 0.250675
\(615\) −2.88243 34.3186i −0.116231 1.38386i
\(616\) 9.51436 0.383345
\(617\) 18.8481 18.8481i 0.758795 0.758795i −0.217308 0.976103i \(-0.569728\pi\)
0.976103 + 0.217308i \(0.0697277\pi\)
\(618\) −10.4940 + 8.77393i −0.422129 + 0.352939i
\(619\) 19.7510i 0.793860i −0.917849 0.396930i \(-0.870076\pi\)
0.917849 0.396930i \(-0.129924\pi\)
\(620\) 18.4756 + 12.9838i 0.741999 + 0.521442i
\(621\) 23.5583 + 6.44645i 0.945361 + 0.258687i
\(622\) −11.4222 11.4222i −0.457988 0.457988i
\(623\) −21.2730 21.2730i −0.852286 0.852286i
\(624\) −0.834762 0.0745186i −0.0334172 0.00298313i
\(625\) −19.2603 + 15.9386i −0.770413 + 0.637545i
\(626\) 0.697474i 0.0278767i
\(627\) 5.72289 + 6.84480i 0.228550 + 0.273355i
\(628\) 0.0444358 0.0444358i 0.00177318 0.00177318i
\(629\) 2.69812 0.107581
\(630\) 8.71524 + 8.80706i 0.347224 + 0.350882i
\(631\) 16.2630 0.647418 0.323709 0.946157i \(-0.395070\pi\)
0.323709 + 0.946157i \(0.395070\pi\)
\(632\) −3.69861 + 3.69861i −0.147123 + 0.147123i
\(633\) 14.7142 + 17.5987i 0.584837 + 0.699487i
\(634\) 24.0070i 0.953441i
\(635\) 5.67772 0.991151i 0.225314 0.0393326i
\(636\) 19.9473 + 1.78068i 0.790961 + 0.0706086i
\(637\) −1.22777 1.22777i −0.0486460 0.0486460i
\(638\) 31.8320 + 31.8320i 1.26024 + 1.26024i
\(639\) −34.5652 6.22080i −1.36738 0.246091i
\(640\) 2.20276 0.384532i 0.0870716 0.0151999i
\(641\) 16.4351i 0.649146i 0.945861 + 0.324573i \(0.105221\pi\)
−0.945861 + 0.324573i \(0.894779\pi\)
\(642\) 3.89821 3.25926i 0.153850 0.128633i
\(643\) 16.1113 16.1113i 0.635369 0.635369i −0.314041 0.949409i \(-0.601683\pi\)
0.949409 + 0.314041i \(0.101683\pi\)
\(644\) −8.68195 −0.342117
\(645\) −31.2790 + 37.0151i −1.23161 + 1.45747i
\(646\) −6.01044 −0.236477
\(647\) −33.8022 + 33.8022i −1.32890 + 1.32890i −0.422570 + 0.906330i \(0.638872\pi\)
−0.906330 + 0.422570i \(0.861128\pi\)
\(648\) 3.74582 + 8.18345i 0.147150 + 0.321476i
\(649\) 6.56239i 0.257596i
\(650\) −2.27624 + 0.819698i −0.0892814 + 0.0321512i
\(651\) 2.87267 32.1797i 0.112589 1.26122i
\(652\) −8.99735 8.99735i −0.352363 0.352363i
\(653\) 6.58374 + 6.58374i 0.257642 + 0.257642i 0.824094 0.566453i \(-0.191685\pi\)
−0.566453 + 0.824094i \(0.691685\pi\)
\(654\) 0.688703 7.71489i 0.0269304 0.301676i
\(655\) −20.8906 14.6809i −0.816263 0.573631i
\(656\) 8.89223i 0.347183i
\(657\) −6.62529 9.53342i −0.258477 0.371934i
\(658\) 3.96207 3.96207i 0.154458 0.154458i
\(659\) −0.843524 −0.0328590 −0.0164295 0.999865i \(-0.505230\pi\)
−0.0164295 + 0.999865i \(0.505230\pi\)
\(660\) 19.8803 1.66975i 0.773840 0.0649949i
\(661\) 20.3317 0.790813 0.395406 0.918506i \(-0.370604\pi\)
0.395406 + 0.918506i \(0.370604\pi\)
\(662\) 10.4028 10.4028i 0.404318 0.404318i
\(663\) 3.86446 3.23105i 0.150083 0.125484i
\(664\) 13.9803i 0.542540i
\(665\) −0.710245 4.06858i −0.0275421 0.157773i
\(666\) −0.238540 + 1.32542i −0.00924324 + 0.0513590i
\(667\) −29.0470 29.0470i −1.12470 1.12470i
\(668\) 1.17503 + 1.17503i 0.0454632 + 0.0454632i
\(669\) 9.59564 + 0.856597i 0.370989 + 0.0331180i
\(670\) −2.72844 + 3.88250i −0.105409 + 0.149994i
\(671\) 32.2696i 1.24576i
\(672\) −2.05205 2.45433i −0.0791595 0.0946779i
\(673\) −23.9996 + 23.9996i −0.925115 + 0.925115i −0.997385 0.0722701i \(-0.976976\pi\)
0.0722701 + 0.997385i \(0.476976\pi\)
\(674\) 19.6473 0.756787
\(675\) 19.7562 + 16.8729i 0.760415 + 0.649438i
\(676\) 12.7659 0.490995
\(677\) 18.9600 18.9600i 0.728691 0.728691i −0.241668 0.970359i \(-0.577695\pi\)
0.970359 + 0.241668i \(0.0776946\pi\)
\(678\) 9.80592 + 11.7283i 0.376594 + 0.450421i
\(679\) 10.5160i 0.403567i
\(680\) −7.72749 + 10.9960i −0.296336 + 0.421678i
\(681\) −11.9763 1.06912i −0.458933 0.0409686i
\(682\) −36.7840 36.7840i −1.40853 1.40853i
\(683\) −6.99901 6.99901i −0.267810 0.267810i 0.560407 0.828217i \(-0.310645\pi\)
−0.828217 + 0.560407i \(0.810645\pi\)
\(684\) 0.531382 2.95256i 0.0203179 0.112894i
\(685\) −5.98231 34.2692i −0.228572 1.30936i
\(686\) 19.5573i 0.746700i
\(687\) −0.410812 + 0.343477i −0.0156735 + 0.0131045i
\(688\) 8.84777 8.84777i 0.337318 0.337318i
\(689\) 5.59464 0.213139
\(690\) −18.1410 + 1.52366i −0.690615 + 0.0580048i
\(691\) −44.2770 −1.68438 −0.842189 0.539183i \(-0.818733\pi\)
−0.842189 + 0.539183i \(0.818733\pi\)
\(692\) 13.5995 13.5995i 0.516974 0.516974i
\(693\) −16.2889 23.4388i −0.618765 0.890368i
\(694\) 29.7101i 1.12778i
\(695\) −2.25671 1.58591i −0.0856018 0.0601570i
\(696\) 1.34590 15.0769i 0.0510164 0.571488i
\(697\) −37.7922 37.7922i −1.43148 1.43148i
\(698\) −12.7925 12.7925i −0.484202 0.484202i
\(699\) 0.239091 2.67831i 0.00904325 0.101303i
\(700\) −8.35656 3.93150i −0.315848 0.148597i
\(701\) 47.5139i 1.79458i 0.441445 + 0.897288i \(0.354466\pi\)
−0.441445 + 0.897288i \(0.645534\pi\)
\(702\) 1.24556 + 2.18403i 0.0470107 + 0.0824310i
\(703\) 0.317424 0.317424i 0.0119719 0.0119719i
\(704\) −5.15114 −0.194141
\(705\) 7.58343 8.97410i 0.285609 0.337984i
\(706\) 12.6658 0.476685
\(707\) −4.80879 + 4.80879i −0.180853 + 0.180853i
\(708\) −1.69284 + 1.41537i −0.0636207 + 0.0531929i
\(709\) 34.9010i 1.31073i 0.755311 + 0.655367i \(0.227486\pi\)
−0.755311 + 0.655367i \(0.772514\pi\)
\(710\) 25.7873 4.50165i 0.967781 0.168944i
\(711\) 15.4437 + 2.77946i 0.579186 + 0.104238i
\(712\) 11.5174 + 11.5174i 0.431632 + 0.431632i
\(713\) 33.5657 + 33.5657i 1.25705 + 1.25705i
\(714\) 19.1522 + 1.70971i 0.716754 + 0.0639841i
\(715\) 5.49029 0.958432i 0.205325 0.0358433i
\(716\) 17.9786i 0.671892i
\(717\) 27.1101 + 32.4247i 1.01244 + 1.21092i
\(718\) −9.83005 + 9.83005i −0.366854 + 0.366854i
\(719\) −31.1460 −1.16155 −0.580775 0.814064i \(-0.697250\pi\)
−0.580775 + 0.814064i \(0.697250\pi\)
\(720\) −4.71850 4.76821i −0.175848 0.177701i
\(721\) −14.5867 −0.543238
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) −17.1996 20.5714i −0.639660 0.765058i
\(724\) 4.58187i 0.170284i
\(725\) −14.8048 41.1119i −0.549837 1.52686i
\(726\) −26.7996 2.39238i −0.994627 0.0887897i
\(727\) 18.0500 + 18.0500i 0.669439 + 0.669439i 0.957586 0.288147i \(-0.0930393\pi\)
−0.288147 + 0.957586i \(0.593039\pi\)
\(728\) −0.631955 0.631955i −0.0234218 0.0234218i
\(729\) 13.7471 23.2383i 0.509153 0.860676i
\(730\) 7.07982 + 4.97536i 0.262036 + 0.184146i
\(731\) 75.2064i 2.78161i
\(732\) −8.32430 + 6.95989i −0.307675 + 0.257245i
\(733\) −9.66033 + 9.66033i −0.356812 + 0.356812i −0.862637 0.505824i \(-0.831188\pi\)
0.505824 + 0.862637i \(0.331188\pi\)
\(734\) 3.44883 0.127299
\(735\) −1.16320 13.8492i −0.0429053 0.510837i
\(736\) 4.70047 0.173262
\(737\) 7.72984 7.72984i 0.284732 0.284732i
\(738\) 21.9062 15.2238i 0.806378 0.560396i
\(739\) 5.67646i 0.208812i −0.994535 0.104406i \(-0.966706\pi\)
0.994535 0.104406i \(-0.0332941\pi\)
\(740\) −0.172618 0.988829i −0.00634557 0.0363501i
\(741\) 0.0745186 0.834762i 0.00273751 0.0306657i
\(742\) 15.1011 + 15.1011i 0.554378 + 0.554378i
\(743\) 31.4477 + 31.4477i 1.15370 + 1.15370i 0.985804 + 0.167901i \(0.0536988\pi\)
0.167901 + 0.985804i \(0.446301\pi\)
\(744\) −1.55528 + 17.4223i −0.0570194 + 0.638734i
\(745\) 0.781631 1.11224i 0.0286367 0.0407494i
\(746\) 29.8160i 1.09164i
\(747\) 34.4407 23.9347i 1.26012 0.875726i
\(748\) 21.8925 21.8925i 0.800468 0.800468i
\(749\) 5.41856 0.197990
\(750\) −18.1510 6.74832i −0.662782 0.246414i
\(751\) 35.7096 1.30306 0.651532 0.758622i \(-0.274127\pi\)
0.651532 + 0.758622i \(0.274127\pi\)
\(752\) −2.14509 + 2.14509i −0.0782235 + 0.0782235i
\(753\) 13.7983 11.5366i 0.502836 0.420418i
\(754\) 4.22864i 0.153998i
\(755\) 3.20512 4.56081i 0.116646 0.165985i
\(756\) −2.53312 + 9.25717i −0.0921286 + 0.336680i
\(757\) −16.5848 16.5848i −0.602785 0.602785i 0.338266 0.941051i \(-0.390160\pi\)
−0.941051 + 0.338266i \(0.890160\pi\)
\(758\) 1.59375 + 1.59375i 0.0578874 + 0.0578874i
\(759\) 41.7717 + 3.72893i 1.51622 + 0.135352i
\(760\) 0.384532 + 2.20276i 0.0139484 + 0.0799024i
\(761\) 34.9067i 1.26537i 0.774411 + 0.632683i \(0.218047\pi\)
−0.774411 + 0.632683i \(0.781953\pi\)
\(762\) 2.86365 + 3.42504i 0.103739 + 0.124076i
\(763\) 5.84055 5.84055i 0.211442 0.211442i
\(764\) −12.3225 −0.445813
\(765\) 40.3187 + 0.211267i 1.45772 + 0.00763838i
\(766\) 6.06812 0.219250
\(767\) −0.435882 + 0.435882i −0.0157388 + 0.0157388i
\(768\) 1.11099 + 1.32879i 0.0400896 + 0.0479487i
\(769\) 37.8613i 1.36531i 0.730739 + 0.682657i \(0.239176\pi\)
−0.730739 + 0.682657i \(0.760824\pi\)
\(770\) 17.4064 + 12.2324i 0.627284 + 0.440826i
\(771\) −24.7159 2.20637i −0.890121 0.0794605i
\(772\) 11.8604 + 11.8604i 0.426864 + 0.426864i
\(773\) 12.9141 + 12.9141i 0.464488 + 0.464488i 0.900123 0.435635i \(-0.143476\pi\)
−0.435635 + 0.900123i \(0.643476\pi\)
\(774\) −36.9444 6.64899i −1.32794 0.238993i
\(775\) 17.1080 + 47.5075i 0.614536 + 1.70652i
\(776\) 5.69343i 0.204382i
\(777\) −1.10176 + 0.921176i −0.0395255 + 0.0330470i