Properties

Label 570.2.k.b.77.3
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 77.3
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.32879 - 1.11099i) q^{3} -1.00000i q^{4} +(-1.28568 + 1.82949i) q^{5} +(1.72519 - 0.154007i) q^{6} +(1.30605 + 1.30605i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.531382 + 2.95256i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.32879 - 1.11099i) 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} +(-1.11099 + 1.32879i) q^{12} +(0.342145 - 0.342145i) q^{13} -1.84704 q^{14} +(3.74095 - 1.00263i) q^{15} -1.00000 q^{16} +(-4.25002 + 4.25002i) q^{17} +(-2.46352 - 1.71203i) 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} +(2.57419 - 4.51371i) q^{27} +(1.30605 - 1.30605i) q^{28} -8.73926 q^{29} +(-1.93629 + 3.35422i) q^{30} -10.0988 q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.72289 + 6.84480i) 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} +(2.45433 + 2.05205i) q^{42} +(-8.84777 + 8.84777i) q^{43} -5.15114 q^{44} +(-6.08487 - 2.82389i) q^{45} -4.70047 q^{46} +(-2.14509 + 2.14509i) q^{47} +(1.32879 + 1.11099i) 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} +(-1.11099 + 1.32879i) q^{57} +(6.17959 - 6.17959i) q^{58} +1.27397 q^{59} +(-1.00263 - 3.74095i) q^{60} -6.26456 q^{61} +(7.14093 - 7.14093i) q^{62} +(-3.16219 + 4.55022i) 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} +(-1.71203 + 2.46352i) q^{72} +(-2.73639 + 2.73639i) q^{73} -0.448905 q^{74} +(-2.97537 + 8.13309i) q^{75} -1.00000 q^{76} +(6.72767 - 6.72767i) q^{77} +(0.537573 - 0.642958i) 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} +(11.6127 + 9.70927i) q^{87} +(3.64241 - 3.64241i) q^{88} +16.2880 q^{89} +(6.29945 - 2.30586i) q^{90} +0.893720 q^{91} +(3.32373 - 3.32373i) q^{92} +(13.4192 + 11.2197i) 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
\(3\) −1.32879 1.11099i −0.767179 0.641433i
\(4\) 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 \(-0.716961\pi\)
0.630038 0.776564i \(-0.283039\pi\)
\(12\) −1.11099 + 1.32879i −0.320717 + 0.383589i
\(13\) 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
\(15\) 3.74095 1.00263i 0.965910 0.258878i
\(16\) −1.00000 −0.250000
\(17\) −4.25002 + 4.25002i −1.03078 + 1.03078i −0.0312704 + 0.999511i \(0.509955\pi\)
−0.999511 + 0.0312704i \(0.990045\pi\)
\(18\) −2.46352 1.71203i −0.580658 0.403530i
\(19\) 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 0.962901 0.269855i \(-0.0869757\pi\)
−0.269855 + 0.962901i \(0.586976\pi\)
\(24\) −0.154007 1.72519i −0.0314365 0.352153i
\(25\) −1.69406 4.70427i −0.338812 0.940854i
\(26\) 0.483866i 0.0948940i
\(27\) 2.57419 4.51371i 0.495402 0.868664i
\(28\) 1.30605 1.30605i 0.246821 0.246821i
\(29\) −8.73926 −1.62284 −0.811420 0.584463i \(-0.801305\pi\)
−0.811420 + 0.584463i \(0.801305\pi\)
\(30\) −1.93629 + 3.35422i −0.353516 + 0.612394i
\(31\) −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
\(33\) −5.72289 + 6.84480i −0.996228 + 1.19153i
\(34\) 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 \(0.244315\pi\)
−0.719622 + 0.694366i \(0.755685\pi\)
\(42\) 2.45433 + 2.05205i 0.378712 + 0.316638i
\(43\) −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
\(45\) −6.08487 2.82389i −0.907079 0.420961i
\(46\) −4.70047 −0.693046
\(47\) −2.14509 + 2.14509i −0.312894 + 0.312894i −0.846030 0.533136i \(-0.821014\pi\)
0.533136 + 0.846030i \(0.321014\pi\)
\(48\) 1.32879 + 1.11099i 0.191795 + 0.160358i
\(49\) 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 \(-0.957939\pi\)
−0.131754 0.991283i \(-0.542061\pi\)
\(54\) 1.37145 + 5.01190i 0.186631 + 0.682033i
\(55\) 9.42396 + 6.62272i 1.27073 + 0.893007i
\(56\) 1.84704i 0.246821i
\(57\) −1.11099 + 1.32879i −0.147155 + 0.176003i
\(58\) 6.17959 6.17959i 0.811420 0.811420i
\(59\) 1.27397 0.165856 0.0829282 0.996556i \(-0.473573\pi\)
0.0829282 + 0.996556i \(0.473573\pi\)
\(60\) −1.00263 3.74095i −0.129439 0.482955i
\(61\) −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
\(63\) −3.16219 + 4.55022i −0.398399 + 0.573274i
\(64\) 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 \(-0.755549\pi\)
0.719325 0.694674i \(-0.244451\pi\)
\(72\) −1.71203 + 2.46352i −0.201765 + 0.290329i
\(73\) −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
\(75\) −2.97537 + 8.13309i −0.343566 + 0.939129i
\(76\) −1.00000 −0.114708
\(77\) 6.72767 6.72767i 0.766689 0.766689i
\(78\) 0.537573 0.642958i 0.0608682 0.0728007i
\(79\) 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 \(0.0283843\pi\)
0.0890537 + 0.996027i \(0.471616\pi\)
\(84\) −3.18649 + 0.284456i −0.347675 + 0.0310367i
\(85\) −2.31120 13.2395i −0.250685 1.43603i
\(86\) 12.5126i 1.34927i
\(87\) 11.6127 + 9.70927i 1.24501 + 1.04094i
\(88\) 3.64241 3.64241i 0.388282 0.388282i
\(89\) 16.2880 1.72653 0.863264 0.504753i \(-0.168416\pi\)
0.863264 + 0.504753i \(0.168416\pi\)
\(90\) 6.29945 2.30586i 0.664020 0.243059i
\(91\) 0.893720 0.0936873
\(92\) 3.32373 3.32373i 0.346523 0.346523i
\(93\) 13.4192 + 11.2197i 1.39151 + 1.16343i
\(94\) 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 \(-0.941360\pi\)
0.983079 0.183183i \(-0.0586400\pi\)
\(102\) −6.67756 + 7.98663i −0.661177 + 0.790794i
\(103\) −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
\(105\) 6.19537 + 3.57640i 0.604606 + 0.349021i
\(106\) 11.5624 1.12304
\(107\) −2.07440 + 2.07440i −0.200540 + 0.200540i −0.800231 0.599691i \(-0.795290\pi\)
0.599691 + 0.800231i \(0.295290\pi\)
\(108\) −4.51371 2.57419i −0.434332 0.247701i
\(109\) 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 0.349735 0.936849i \(-0.386272\pi\)
−0.936849 + 0.349735i \(0.886272\pi\)
\(114\) −0.154007 1.72519i −0.0144240 0.161579i
\(115\) −10.3540 + 1.80748i −0.965514 + 0.168548i
\(116\) 8.73926i 0.811420i
\(117\) 1.19202 + 0.828396i 0.110202 + 0.0765852i
\(118\) −0.900830 + 0.900830i −0.0829282 + 0.0829282i
\(119\) −11.1015 −1.01767
\(120\) 3.35422 + 1.93629i 0.306197 + 0.176758i
\(121\) −15.5343 −1.41221
\(122\) 4.42971 4.42971i 0.401047 0.401047i
\(123\) 9.87922 11.8159i 0.890779 1.06541i
\(124\) 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 \(0.166238\pi\)
−0.866698 + 0.498833i \(0.833762\pi\)
\(132\) 6.84480 + 5.72289i 0.595764 + 0.498114i
\(133\) 1.30605 1.30605i 0.113249 0.113249i
\(134\) 2.12218 0.183328
\(135\) 4.94820 + 10.5126i 0.425873 + 0.904783i
\(136\) −6.01044 −0.515391
\(137\) −11.0007 + 11.0007i −0.939857 + 0.939857i −0.998291 0.0584339i \(-0.981389\pi\)
0.0584339 + 0.998291i \(0.481389\pi\)
\(138\) 6.24595 + 5.22220i 0.531690 + 0.444543i
\(139\) 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
\(147\) −3.98675 + 4.76831i −0.328821 + 0.393283i
\(148\) 0.317424 0.317424i 0.0260921 0.0260921i
\(149\) −0.607952 −0.0498053 −0.0249027 0.999690i \(-0.507928\pi\)
−0.0249027 + 0.999690i \(0.507928\pi\)
\(150\) −3.64706 7.85487i −0.297781 0.641347i
\(151\) 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
\(153\) −14.8068 10.2901i −1.19706 0.831903i
\(154\) 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
\(162\) 3.74582 8.18345i 0.294300 0.642952i
\(163\) 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
\(165\) −5.16469 19.2702i −0.402070 1.50018i
\(166\) −13.9803 −1.08508
\(167\) 1.17503 1.17503i 0.0909264 0.0909264i −0.660181 0.751107i \(-0.729520\pi\)
0.751107 + 0.660181i \(0.229520\pi\)
\(168\) 2.05205 2.45433i 0.158319 0.189356i
\(169\) 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 \(-0.989002\pi\)
−0.0345455 0.999403i \(-0.510998\pi\)
\(174\) −15.0769 + 1.34590i −1.14298 + 0.102033i
\(175\) 3.93150 8.35656i 0.297193 0.631697i
\(176\) 5.15114i 0.388282i
\(177\) −1.69284 1.41537i −0.127241 0.106386i
\(178\) −11.5174 + 11.5174i −0.863264 + 0.863264i
\(179\) 17.9786 1.34378 0.671892 0.740649i \(-0.265482\pi\)
0.671892 + 0.740649i \(0.265482\pi\)
\(180\) −2.82389 + 6.08487i −0.210481 + 0.453539i
\(181\) 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
\(183\) 8.32430 + 6.95989i 0.615350 + 0.514490i
\(184\) 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 \(0.147085\pi\)
−0.895126 + 0.445813i \(0.852915\pi\)
\(192\) 1.11099 1.32879i 0.0801791 0.0958974i
\(193\) −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
\(195\) 0.936905 1.62299i 0.0670931 0.116225i
\(196\) −3.58845 −0.256318
\(197\) −3.56808 + 3.56808i −0.254215 + 0.254215i −0.822696 0.568481i \(-0.807531\pi\)
0.568481 + 0.822696i \(0.307531\pi\)
\(198\) −8.81894 + 12.6900i −0.626735 + 0.901836i
\(199\) 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
\(207\) −8.04736 + 11.5797i −0.559330 + 0.804845i
\(208\) −0.342145 + 0.342145i −0.0237235 + 0.0237235i
\(209\) −5.15114 −0.356312
\(210\) −6.90969 + 1.85189i −0.476814 + 0.127793i
\(211\) 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
\(213\) −13.0062 + 15.5560i −0.891173 + 1.06588i
\(214\) 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
\(222\) 0.596502 + 0.498731i 0.0400346 + 0.0334727i
\(223\) 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
\(225\) 12.9895 7.50158i 0.865965 0.500105i
\(226\) 8.82625 0.587114
\(227\) 4.90875 4.90875i 0.325805 0.325805i −0.525184 0.850989i \(-0.676003\pi\)
0.850989 + 0.525184i \(0.176003\pi\)
\(228\) 1.32879 + 1.11099i 0.0880015 + 0.0735774i
\(229\) 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 0.742150 0.670233i \(-0.233806\pi\)
−0.670233 + 0.742150i \(0.733806\pi\)
\(234\) −1.42865 + 0.257118i −0.0933935 + 0.0168083i
\(235\) −1.16652 6.68233i −0.0760956 0.435907i
\(236\) 1.27397i 0.0829282i
\(237\) −5.81119 + 6.95041i −0.377478 + 0.451478i
\(238\) 7.84995 7.84995i 0.508837 0.508837i
\(239\) −24.4016 −1.57841 −0.789205 0.614130i \(-0.789507\pi\)
−0.789205 + 0.614130i \(0.789507\pi\)
\(240\) −3.74095 + 1.00263i −0.241478 + 0.0647194i
\(241\) −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
\(243\) 14.6949 + 5.20195i 0.942677 + 0.333705i
\(244\) 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 \(0.106279\pi\)
−0.944776 + 0.327718i \(0.893721\pi\)
\(252\) 4.55022 + 3.16219i 0.286637 + 0.199199i
\(253\) 17.1210 17.1210i 1.07639 1.07639i
\(254\) −2.57755 −0.161730
\(255\) −11.6379 + 20.1603i −0.728796 + 1.26249i
\(256\) 1.00000 0.0625000
\(257\) 10.1303 10.1303i 0.631914 0.631914i −0.316634 0.948548i \(-0.602553\pi\)
0.948548 + 0.316634i \(0.102553\pi\)
\(258\) −13.9015 + 16.6267i −0.865468 + 1.03513i
\(259\) 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 \(-0.942329\pi\)
−0.180189 0.983632i \(-0.557671\pi\)
\(264\) −8.88670 + 0.793310i −0.546939 + 0.0488249i
\(265\) 25.4691 4.44609i 1.56455 0.273121i
\(266\) 1.84704i 0.113249i
\(267\) −21.6434 18.0959i −1.32456 1.10745i
\(268\) −1.50061 + 1.50061i −0.0916642 + 0.0916642i
\(269\) −6.51981 −0.397520 −0.198760 0.980048i \(-0.563691\pi\)
−0.198760 + 0.980048i \(0.563691\pi\)
\(270\) −10.9325 3.93464i −0.665328 0.239455i
\(271\) 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
\(273\) −1.18757 0.992918i −0.0718749 0.0600941i
\(274\) 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 \(0.257121\pi\)
−0.691113 + 0.722747i \(0.742879\pi\)
\(282\) −3.37034 + 4.03105i −0.200701 + 0.240046i
\(283\) 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
\(285\) −1.00263 3.74095i −0.0593906 0.221595i
\(286\) 2.49247 0.147383
\(287\) −11.6137 + 11.6137i −0.685537 + 0.685537i
\(288\) 2.46352 + 1.71203i 0.145164 + 0.100883i
\(289\) 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 0.393284 0.919417i \(-0.371339\pi\)
−0.919417 + 0.393284i \(0.871339\pi\)
\(294\) −0.552645 6.19076i −0.0322309 0.361052i
\(295\) −1.63791 + 2.33071i −0.0953629 + 0.135699i
\(296\) 0.448905i 0.0260921i
\(297\) −23.2508 13.2600i −1.34915 0.769424i
\(298\) 0.429887 0.429887i 0.0249027 0.0249027i
\(299\) 2.27440 0.131532
\(300\) 8.13309 + 2.97537i 0.469564 + 0.171783i
\(301\) −23.1113 −1.33211
\(302\) −1.76278 + 1.76278i −0.101436 + 0.101436i
\(303\) −4.09060 + 4.89252i −0.234999 + 0.281068i
\(304\) 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 \(0.151430\pi\)
−0.888959 + 0.457988i \(0.848570\pi\)
\(312\) −0.642958 0.537573i −0.0364003 0.0304341i
\(313\) −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
\(315\) −4.25901 11.6353i −0.239968 0.655576i
\(316\) −5.23062 −0.294246
\(317\) 16.9755 16.9755i 0.953441 0.953441i −0.0455227 0.998963i \(-0.514495\pi\)
0.998963 + 0.0455227i \(0.0144953\pi\)
\(318\) −15.3640 12.8457i −0.861570 0.720352i
\(319\) 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
\(327\) −4.96826 + 5.94224i −0.274746 + 0.328607i
\(328\) −6.28776 + 6.28776i −0.347183 + 0.347183i
\(329\) −5.60322 −0.308915
\(330\) 17.2781 + 9.97410i 0.951126 + 0.549056i
\(331\) 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
\(333\) −0.768541 + 1.10589i −0.0421158 + 0.0606023i
\(334\) 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
\(342\) −1.71203 + 2.46352i −0.0925762 + 0.133212i
\(343\) 13.8291 13.8291i 0.746700 0.746700i
\(344\) −12.5126 −0.674636
\(345\) 15.7664 + 9.10146i 0.848835 + 0.490006i
\(346\) 19.2326 1.03395
\(347\) −21.0082 + 21.0082i −1.12778 + 1.12778i −0.137245 + 0.990537i \(0.543825\pi\)
−0.990537 + 0.137245i \(0.956175\pi\)
\(348\) 9.70927 11.6127i 0.520472 0.622504i
\(349\) 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 0.427385 0.904070i \(-0.359435\pi\)
−0.904070 + 0.427385i \(0.859435\pi\)
\(354\) 2.19783 0.196199i 0.116814 0.0104279i
\(355\) 21.4175 + 15.0512i 1.13673 + 0.798837i
\(356\) 16.2880i 0.863264i
\(357\) 14.7516 + 12.3337i 0.780738 + 0.652769i
\(358\) −12.7128 + 12.7128i −0.671892 + 0.671892i
\(359\) 13.9018 0.733708 0.366854 0.930278i \(-0.380435\pi\)
0.366854 + 0.930278i \(0.380435\pi\)
\(360\) −2.30586 6.29945i −0.121529 0.332010i
\(361\) −1.00000 −0.0526316
\(362\) −3.23987 + 3.23987i −0.170284 + 0.170284i
\(363\) 20.6419 + 17.2585i 1.08342 + 0.905837i
\(364\) 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
\(372\) 11.2197 13.4192i 0.581715 0.695754i
\(373\) −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
\(375\) −11.0540 15.8999i −0.570828 0.821070i
\(376\) −3.03362 −0.156447
\(377\) −2.99010 + 2.99010i −0.153998 + 0.153998i
\(378\) −4.75462 + 8.33699i −0.244551 + 0.428809i
\(379\) 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 0.588932 0.808182i \(-0.299548\pi\)
−0.808182 + 0.588932i \(0.799548\pi\)
\(384\) 0.154007 + 1.72519i 0.00785912 + 0.0880383i
\(385\) 3.65857 + 20.9578i 0.186458 + 1.06811i
\(386\) 16.7731i 0.853728i
\(387\) −30.8252 21.4221i −1.56693 1.08894i
\(388\) 4.02586 4.02586i 0.204382 0.204382i
\(389\) 21.0267 1.06609 0.533047 0.846086i \(-0.321047\pi\)
0.533047 + 0.846086i \(0.321047\pi\)
\(390\) 0.485139 + 1.81012i 0.0245660 + 0.0916591i
\(391\) −28.2519 −1.42876
\(392\) 2.53742 2.53742i 0.128159 0.128159i
\(393\) 12.6862 15.1732i 0.639936 0.765389i
\(394\) 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 \(-0.971465\pi\)
0.995985 0.0895252i \(-0.0285350\pi\)
\(402\) −2.81994 2.35773i −0.140646 0.117593i
\(403\) −3.45526 + 3.45526i −0.172119 + 0.172119i
\(404\) −3.68192 −0.183183
\(405\) 5.10434 19.4665i 0.253637 0.967300i
\(406\) 16.1418 0.801102
\(407\) 1.63510 1.63510i 0.0810487 0.0810487i
\(408\) 7.98663 + 6.67756i 0.395397 + 0.330589i
\(409\) 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
\(417\) −1.37043 + 1.63909i −0.0671104 + 0.0802666i
\(418\) 3.64241 3.64241i 0.178156 0.178156i
\(419\) −7.46153 −0.364520 −0.182260 0.983250i \(-0.558341\pi\)
−0.182260 + 0.983250i \(0.558341\pi\)
\(420\) 3.57640 6.19537i 0.174510 0.302303i
\(421\) 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
\(423\) −7.47339 5.19366i −0.363369 0.252525i
\(424\) 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 \(-0.664490\pi\)
0.494067 0.869424i \(-0.335510\pi\)
\(432\) −2.57419 + 4.51371i −0.123851 + 0.217166i
\(433\) 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
\(435\) −32.6932 + 8.76224i −1.56752 + 0.420117i
\(436\) −4.47191 −0.214165
\(437\) 3.32373 3.32373i 0.158996 0.158996i
\(438\) −4.29936 + 5.14221i −0.205432 + 0.245704i
\(439\) 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 0.232157 0.972678i \(-0.425422\pi\)
−0.972678 + 0.232157i \(0.925422\pi\)
\(444\) −0.774447 + 0.0691344i −0.0367536 + 0.00328097i
\(445\) −20.9412 + 29.7988i −0.992707 + 1.41260i
\(446\) 5.56208i 0.263372i
\(447\) 0.807842 + 0.675431i 0.0382096 + 0.0319468i
\(448\) −1.30605 + 1.30605i −0.0617052 + 0.0617052i
\(449\) −21.1036 −0.995941 −0.497971 0.867194i \(-0.665921\pi\)
−0.497971 + 0.867194i \(0.665921\pi\)
\(450\) −3.88052 + 14.4894i −0.182930 + 0.683035i
\(451\) 45.8052 2.15688
\(452\) −6.24110 + 6.24110i −0.293557 + 0.293557i
\(453\) −3.31260 2.76964i −0.155640 0.130129i
\(454\) 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 \(0.262208\pi\)
−0.679473 + 0.733700i \(0.737792\pi\)
\(462\) 10.5704 12.6426i 0.491780 0.588188i
\(463\) −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
\(465\) −37.7791 + 10.1254i −1.75197 + 0.469552i
\(466\) −1.55247 −0.0719169
\(467\) −4.04048 + 4.04048i −0.186971 + 0.186971i −0.794385 0.607414i \(-0.792207\pi\)
0.607414 + 0.794385i \(0.292207\pi\)
\(468\) 0.828396 1.19202i 0.0382926 0.0551009i
\(469\) 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
\(477\) 19.7952 28.4841i 0.906358 1.30420i
\(478\) 17.2546 17.2546i 0.789205 0.789205i
\(479\) 25.6778 1.17325 0.586624 0.809859i \(-0.300457\pi\)
0.586624 + 0.809859i \(0.300457\pi\)
\(480\) 1.93629 3.35422i 0.0883790 0.153098i
\(481\) 0.217210 0.00990393
\(482\) 10.9469 10.9469i 0.498618 0.498618i
\(483\) 9.64560 11.5365i 0.438890 0.524929i
\(484\) 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 \(-0.856974\pi\)
0.900739 0.434361i \(-0.143026\pi\)
\(492\) −11.8159 9.87922i −0.532703 0.445390i
\(493\) 37.1420 37.1420i 1.67279 1.67279i
\(494\) 0.483866 0.0217702
\(495\) −14.5463 + 31.3440i −0.653807 + 1.40881i
\(496\) 10.0988 0.453449
\(497\) 15.2898 15.2898i 0.685840 0.685840i
\(498\) 18.5769 + 15.5320i 0.832451 + 0.696007i
\(499\) 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 0.983939 0.178505i \(-0.0571262\pi\)
−0.178505 + 0.983939i \(0.557126\pi\)
\(504\) −5.45350 + 0.981482i −0.242918 + 0.0437187i
\(505\) 6.73604 + 4.73377i 0.299750 + 0.210650i
\(506\) 24.2128i 1.07639i
\(507\) 14.1828 16.9632i 0.629881 0.753362i
\(508\) 1.82261 1.82261i 0.0808651 0.0808651i
\(509\) −24.2848 −1.07640 −0.538202 0.842816i \(-0.680896\pi\)
−0.538202 + 0.842816i \(0.680896\pi\)
\(510\) −6.02624 22.4848i −0.266846 0.995642i
\(511\) −7.14773 −0.316197
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −4.51371 2.57419i −0.199285 0.113653i
\(514\) 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 \(0.137694\pi\)
−0.907888 + 0.419213i \(0.862306\pi\)
\(522\) 21.5294 + 14.9619i 0.942315 + 0.654865i
\(523\) −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
\(525\) −14.5082 + 6.73627i −0.633192 + 0.293995i
\(526\) 26.6919 1.16382
\(527\) 42.9201 42.9201i 1.86963 1.86963i
\(528\) 5.72289 6.84480i 0.249057 0.297882i
\(529\) 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
\(537\) −23.8899 19.9741i −1.03092 0.861948i
\(538\) 4.61020 4.61020i 0.198760 0.198760i
\(539\) −18.4846 −0.796189
\(540\) 10.5126 4.94820i 0.452391 0.212937i
\(541\) −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
\(543\) −6.08836 5.09044i −0.261277 0.218452i
\(544\) 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
\(552\) 5.22220 6.24595i 0.222271 0.265845i
\(553\) 6.83147 6.83147i 0.290504 0.290504i
\(554\) −19.7600 −0.839520
\(555\) 1.50573 + 0.869210i 0.0639146 + 0.0368959i
\(556\) −1.23352 −0.0523128
\(557\) 7.92409 7.92409i 0.335754 0.335754i −0.519012 0.854767i \(-0.673700\pi\)
0.854767 + 0.519012i \(0.173700\pi\)
\(558\) 24.8786 + 17.2895i 1.05320 + 0.731922i
\(559\) 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 0.652289 0.757970i \(-0.273809\pi\)
−0.757970 + 0.652289i \(0.773809\pi\)
\(564\) −0.467198 5.23357i −0.0196726 0.220373i
\(565\) 19.4421 3.39397i 0.817935 0.142786i
\(566\) 13.1018i 0.550708i
\(567\) −15.1151 6.91868i −0.634776 0.290557i
\(568\) 8.27799 8.27799i 0.347337 0.347337i
\(569\) 19.7316 0.827190 0.413595 0.910461i \(-0.364273\pi\)
0.413595 + 0.910461i \(0.364273\pi\)
\(570\) 3.35422 + 1.93629i 0.140493 + 0.0811022i
\(571\) 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
\(573\) 13.6903 16.3741i 0.571919 0.684037i
\(574\) 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
\(582\) 7.56539 + 6.32537i 0.313596 + 0.262195i
\(583\) −42.1149 + 42.1149i −1.74422 + 1.74422i
\(584\) −3.86983 −0.160135
\(585\) −3.04809 + 1.11573i −0.126023 + 0.0461297i
\(586\) 12.7363 0.526133
\(587\) −20.3746 + 20.3746i −0.840951 + 0.840951i −0.988983 0.148032i \(-0.952706\pi\)
0.148032 + 0.988983i \(0.452706\pi\)
\(588\) 4.76831 + 3.98675i 0.196642 + 0.164411i
\(589\) 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 0.849122 0.528197i \(-0.177132\pi\)
−0.528197 + 0.849122i \(0.677132\pi\)
\(594\) 25.8170 7.06453i 1.05928 0.289861i
\(595\) 14.2730 20.3101i 0.585135 0.832632i
\(596\) 0.607952i 0.0249027i
\(597\) −3.59061 + 4.29451i −0.146954 + 0.175762i
\(598\) −1.60824 + 1.60824i −0.0657659 + 0.0657659i
\(599\) 6.25932 0.255749 0.127874 0.991790i \(-0.459185\pi\)
0.127874 + 0.991790i \(0.459185\pi\)
\(600\) −7.85487 + 3.64706i −0.320674 + 0.148891i
\(601\) −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
\(603\) 3.63324 5.22803i 0.147957 0.212902i
\(604\) 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
\(612\) −10.2901 + 14.8068i −0.415952 + 0.598531i
\(613\) −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
\(615\) 8.91561 + 33.2654i 0.359512 + 1.34139i
\(616\) 9.51436 0.383345
\(617\) −18.8481 + 18.8481i −0.758795 + 0.758795i −0.976103 0.217308i \(-0.930272\pi\)
0.217308 + 0.976103i \(0.430272\pi\)
\(618\) −8.77393 + 10.4940i −0.352939 + 0.422129i
\(619\) 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
\(627\) 6.84480 + 5.72289i 0.273355 + 0.228550i
\(628\) 0.0444358 0.0444358i 0.00177318 0.00177318i
\(629\) −2.69812 −0.107581
\(630\) 11.2390 + 5.21584i 0.447772 + 0.207804i
\(631\) 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
\(633\) −17.5987 14.7142i −0.699487 0.584837i
\(634\) 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 \(-0.894779\pi\)
0.945861 0.324573i \(-0.105221\pi\)
\(642\) −3.25926 + 3.89821i −0.128633 + 0.153850i
\(643\) 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
\(645\) −24.2281 + 41.9701i −0.953979 + 1.65257i
\(646\) −6.01044 −0.236477
\(647\) 33.8022 33.8022i 1.32890 1.32890i 0.422570 0.906330i \(-0.361128\pi\)
0.906330 0.422570i \(-0.138872\pi\)
\(648\) −8.18345 3.74582i −0.321476 0.147150i
\(649\) 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 0.566453 0.824094i \(-0.308315\pi\)
−0.824094 + 0.566453i \(0.808315\pi\)
\(654\) −0.688703 7.71489i −0.0269304 0.301676i
\(655\) −20.8906 14.6809i −0.816263 0.573631i
\(656\) 8.89223i 0.347183i
\(657\) −9.53342 6.62529i −0.371934 0.258477i
\(658\) 3.96207 3.96207i 0.154458 0.154458i
\(659\) 0.843524 0.0328590 0.0164295 0.999865i \(-0.494770\pi\)
0.0164295 + 0.999865i \(0.494770\pi\)
\(660\) −19.2702 + 5.16469i −0.750091 + 0.201035i
\(661\) 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
\(663\) 3.23105 3.86446i 0.125484 0.150083i
\(664\) 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
\(672\) −2.45433 2.05205i −0.0946779 0.0791595i
\(673\) −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
\(675\) −25.5945 4.46318i −0.985134 0.171788i
\(676\) 12.7659 0.490995
\(677\) −18.9600 + 18.9600i −0.728691 + 0.728691i −0.970359 0.241668i \(-0.922305\pi\)
0.241668 + 0.970359i \(0.422305\pi\)
\(678\) −11.7283 9.80592i −0.450421 0.376594i
\(679\) 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 0.828217 0.560407i \(-0.189355\pi\)
−0.560407 + 0.828217i \(0.689355\pi\)
\(684\) −0.531382 2.95256i −0.0203179 0.112894i
\(685\) −5.98231 34.2692i −0.228572 1.30936i
\(686\) 19.5573i 0.746700i
\(687\) 0.343477 0.410812i 0.0131045 0.0156735i
\(688\) 8.84777 8.84777i 0.337318 0.337318i
\(689\) −5.59464 −0.213139
\(690\) −17.5842 + 4.71283i −0.669420 + 0.179414i
\(691\) −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
\(693\) 23.4388 + 16.2889i 0.890368 + 0.618765i
\(694\) 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 \(-0.645534\pi\)
0.441445 0.897288i \(-0.354466\pi\)
\(702\) 2.18403 + 1.24556i 0.0824310 + 0.0470107i
\(703\) 0.317424 0.317424i 0.0119719 0.0119719i
\(704\) 5.15114 0.194141
\(705\) −5.87396 + 10.1754i −0.221226 + 0.383229i
\(706\) 12.6658 0.476685
\(707\) 4.80879 4.80879i 0.180853 0.180853i
\(708\) −1.41537 + 1.69284i −0.0531929 + 0.0636207i
\(709\) 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
\(717\) 32.4247 + 27.1101i 1.21092 + 1.01244i
\(718\) −9.83005 + 9.83005i −0.366854 + 0.366854i
\(719\) 31.1460 1.16155 0.580775 0.814064i \(-0.302750\pi\)
0.580775 + 0.814064i \(0.302750\pi\)
\(720\) 6.08487 + 2.82389i 0.226770 + 0.105240i
\(721\) −14.5867 −0.543238
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) 20.5714 + 17.1996i 0.765058 + 0.639660i
\(724\) 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
\(732\) 6.95989 8.32430i 0.257245 0.307675i
\(733\) −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
\(735\) −3.59788 13.4242i −0.132710 0.495160i
\(736\) 4.70047 0.173262
\(737\) −7.72984 + 7.72984i −0.284732 + 0.284732i
\(738\) 15.2238 21.9062i 0.560396 0.806378i
\(739\) 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 \(-0.946301\pi\)
−0.167901 0.985804i \(-0.553699\pi\)
\(744\) 1.55528 + 17.4223i 0.0570194 + 0.638734i
\(745\) 0.781631 1.11224i 0.0286367 0.0407494i
\(746\) 29.8160i 1.09164i
\(747\) −23.9347 + 34.4407i −0.875726 + 1.26012i
\(748\) 21.8925 21.8925i 0.800468 0.800468i
\(749\) −5.41856 −0.197990
\(750\) 19.0593 + 3.42658i 0.695949 + 0.125121i
\(751\) 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
\(753\) 11.5366 13.7983i 0.420418 0.502836i
\(754\) 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 \(-0.781953\pi\)
0.774411 0.632683i \(-0.218047\pi\)
\(762\) 3.42504 + 2.86365i 0.124076 + 0.103739i
\(763\) 5.84055 5.84055i 0.211442 0.211442i
\(764\) 12.3225 0.445813
\(765\) 37.8624 13.8592i 1.36892 0.501081i
\(766\) 6.06812 0.219250
\(767\) 0.435882 0.435882i 0.0157388 0.0157388i
\(768\) −1.32879 1.11099i −0.0479487 0.0400896i
\(769\) 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 0.435635 0.900123i \(-0.356524\pi\)
−0.900123 + 0.435635i \(0.856524\pi\)
\(774\) 36.9444 6.64899i 1.32794 0.238993i
\(775\) 17.1080 + 47.5075i 0.614536 + 1.70652i
\(776\) 5.69343i 0.204382i
\(777\) 0.921176 1.10176i 0.0330470 0.0395255i
\(778\)