Properties

Label 552.2.n.b.91.24
Level $552$
Weight $2$
Character 552.91
Analytic conductor $4.408$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.n (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.40774219157\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.24
Character \(\chi\) \(=\) 552.91
Dual form 552.2.n.b.91.22

$q$-expansion

\(f(q)\) \(=\) \(q+(1.38507 + 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 + 0.791193i) q^{4} +2.80468 q^{5} +(-1.38507 - 0.285614i) q^{6} -0.415199 q^{7} +(2.31819 + 1.62049i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(1.38507 + 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 + 0.791193i) q^{4} +2.80468 q^{5} +(-1.38507 - 0.285614i) q^{6} -0.415199 q^{7} +(2.31819 + 1.62049i) q^{8} +1.00000 q^{9} +(3.88469 + 0.801057i) q^{10} -5.54747i q^{11} +(-1.83685 - 0.791193i) q^{12} +3.19024i q^{13} +(-0.575080 - 0.118587i) q^{14} -2.80468 q^{15} +(2.74803 + 2.90660i) q^{16} -2.01349i q^{17} +(1.38507 + 0.285614i) q^{18} +2.50622i q^{19} +(5.15178 + 2.21904i) q^{20} +0.415199 q^{21} +(1.58444 - 7.68365i) q^{22} +(-2.87533 + 3.83829i) q^{23} +(-2.31819 - 1.62049i) q^{24} +2.86624 q^{25} +(-0.911179 + 4.41871i) q^{26} -1.00000 q^{27} +(-0.762658 - 0.328502i) q^{28} +4.69915i q^{29} +(-3.88469 - 0.801057i) q^{30} -8.16330i q^{31} +(2.97605 + 4.81073i) q^{32} +5.54747i q^{33} +(0.575080 - 2.78882i) q^{34} -1.16450 q^{35} +(1.83685 + 0.791193i) q^{36} +3.59504 q^{37} +(-0.715812 + 3.47129i) q^{38} -3.19024i q^{39} +(6.50179 + 4.54496i) q^{40} +2.52410 q^{41} +(0.575080 + 0.118587i) q^{42} +1.80649i q^{43} +(4.38912 - 10.1899i) q^{44} +2.80468 q^{45} +(-5.07881 + 4.49507i) q^{46} -3.58339i q^{47} +(-2.74803 - 2.90660i) q^{48} -6.82761 q^{49} +(3.96995 + 0.818639i) q^{50} +2.01349i q^{51} +(-2.52410 + 5.85999i) q^{52} -0.270501 q^{53} +(-1.38507 - 0.285614i) q^{54} -15.5589i q^{55} +(-0.962511 - 0.672826i) q^{56} -2.50622i q^{57} +(-1.34214 + 6.50865i) q^{58} -0.657857 q^{59} +(-5.15178 - 2.21904i) q^{60} -11.8024 q^{61} +(2.33155 - 11.3068i) q^{62} -0.415199 q^{63} +(2.74803 + 7.51321i) q^{64} +8.94761i q^{65} +(-1.58444 + 7.68365i) q^{66} +5.41363i q^{67} +(1.59306 - 3.69847i) q^{68} +(2.87533 - 3.83829i) q^{69} +(-1.61292 - 0.332598i) q^{70} -6.09004i q^{71} +(2.31819 + 1.62049i) q^{72} -2.82330 q^{73} +(4.97938 + 1.02679i) q^{74} -2.86624 q^{75} +(-1.98290 + 4.60355i) q^{76} +2.30330i q^{77} +(0.911179 - 4.41871i) q^{78} -15.0378 q^{79} +(7.70734 + 8.15210i) q^{80} +1.00000 q^{81} +(3.49606 + 0.720918i) q^{82} +11.1848i q^{83} +(0.762658 + 0.328502i) q^{84} -5.64719i q^{85} +(-0.515959 + 2.50212i) q^{86} -4.69915i q^{87} +(8.98962 - 12.8601i) q^{88} -4.02672i q^{89} +(3.88469 + 0.801057i) q^{90} -1.32459i q^{91} +(-8.31837 + 4.77542i) q^{92} +8.16330i q^{93} +(1.02347 - 4.96325i) q^{94} +7.02915i q^{95} +(-2.97605 - 4.81073i) q^{96} -14.5135i q^{97} +(-9.45673 - 1.95006i) q^{98} -5.54747i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{3} + 4q^{4} + 24q^{9} + O(q^{10}) \) \( 24q - 24q^{3} + 4q^{4} + 24q^{9} - 4q^{12} + 4q^{16} + 24q^{25} - 24q^{27} + 4q^{36} - 44q^{46} - 4q^{48} + 56q^{49} - 40q^{50} - 48q^{58} - 40q^{62} + 4q^{64} + 32q^{73} - 24q^{75} + 24q^{81} - 40q^{82} + 40q^{92} - 48q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38507 + 0.285614i 0.979394 + 0.201960i
\(3\) −1.00000 −0.577350
\(4\) 1.83685 + 0.791193i 0.918424 + 0.395596i
\(5\) 2.80468 1.25429 0.627146 0.778902i \(-0.284223\pi\)
0.627146 + 0.778902i \(0.284223\pi\)
\(6\) −1.38507 0.285614i −0.565453 0.116602i
\(7\) −0.415199 −0.156930 −0.0784652 0.996917i \(-0.525002\pi\)
−0.0784652 + 0.996917i \(0.525002\pi\)
\(8\) 2.31819 + 1.62049i 0.819605 + 0.572930i
\(9\) 1.00000 0.333333
\(10\) 3.88469 + 0.801057i 1.22845 + 0.253317i
\(11\) 5.54747i 1.67263i −0.548253 0.836313i \(-0.684707\pi\)
0.548253 0.836313i \(-0.315293\pi\)
\(12\) −1.83685 0.791193i −0.530253 0.228398i
\(13\) 3.19024i 0.884814i 0.896814 + 0.442407i \(0.145875\pi\)
−0.896814 + 0.442407i \(0.854125\pi\)
\(14\) −0.575080 0.118587i −0.153697 0.0316937i
\(15\) −2.80468 −0.724166
\(16\) 2.74803 + 2.90660i 0.687007 + 0.726651i
\(17\) 2.01349i 0.488342i −0.969732 0.244171i \(-0.921484\pi\)
0.969732 0.244171i \(-0.0785158\pi\)
\(18\) 1.38507 + 0.285614i 0.326465 + 0.0673199i
\(19\) 2.50622i 0.574966i 0.957786 + 0.287483i \(0.0928185\pi\)
−0.957786 + 0.287483i \(0.907182\pi\)
\(20\) 5.15178 + 2.21904i 1.15197 + 0.496193i
\(21\) 0.415199 0.0906038
\(22\) 1.58444 7.68365i 0.337803 1.63816i
\(23\) −2.87533 + 3.83829i −0.599548 + 0.800339i
\(24\) −2.31819 1.62049i −0.473199 0.330781i
\(25\) 2.86624 0.573248
\(26\) −0.911179 + 4.41871i −0.178697 + 0.866581i
\(27\) −1.00000 −0.192450
\(28\) −0.762658 0.328502i −0.144129 0.0620811i
\(29\) 4.69915i 0.872609i 0.899799 + 0.436305i \(0.143713\pi\)
−0.899799 + 0.436305i \(0.856287\pi\)
\(30\) −3.88469 0.801057i −0.709243 0.146252i
\(31\) 8.16330i 1.46617i −0.680136 0.733086i \(-0.738079\pi\)
0.680136 0.733086i \(-0.261921\pi\)
\(32\) 2.97605 + 4.81073i 0.526096 + 0.850425i
\(33\) 5.54747i 0.965691i
\(34\) 0.575080 2.78882i 0.0986255 0.478279i
\(35\) −1.16450 −0.196837
\(36\) 1.83685 + 0.791193i 0.306141 + 0.131865i
\(37\) 3.59504 0.591020 0.295510 0.955340i \(-0.404510\pi\)
0.295510 + 0.955340i \(0.404510\pi\)
\(38\) −0.715812 + 3.47129i −0.116120 + 0.563118i
\(39\) 3.19024i 0.510848i
\(40\) 6.50179 + 4.54496i 1.02802 + 0.718621i
\(41\) 2.52410 0.394198 0.197099 0.980384i \(-0.436848\pi\)
0.197099 + 0.980384i \(0.436848\pi\)
\(42\) 0.575080 + 0.118587i 0.0887368 + 0.0182983i
\(43\) 1.80649i 0.275487i 0.990468 + 0.137743i \(0.0439849\pi\)
−0.990468 + 0.137743i \(0.956015\pi\)
\(44\) 4.38912 10.1899i 0.661685 1.53618i
\(45\) 2.80468 0.418097
\(46\) −5.07881 + 4.49507i −0.748830 + 0.662763i
\(47\) 3.58339i 0.522690i −0.965245 0.261345i \(-0.915834\pi\)
0.965245 0.261345i \(-0.0841661\pi\)
\(48\) −2.74803 2.90660i −0.396644 0.419532i
\(49\) −6.82761 −0.975373
\(50\) 3.96995 + 0.818639i 0.561436 + 0.115773i
\(51\) 2.01349i 0.281944i
\(52\) −2.52410 + 5.85999i −0.350029 + 0.812635i
\(53\) −0.270501 −0.0371562 −0.0185781 0.999827i \(-0.505914\pi\)
−0.0185781 + 0.999827i \(0.505914\pi\)
\(54\) −1.38507 0.285614i −0.188484 0.0388672i
\(55\) 15.5589i 2.09796i
\(56\) −0.962511 0.672826i −0.128621 0.0899101i
\(57\) 2.50622i 0.331957i
\(58\) −1.34214 + 6.50865i −0.176232 + 0.854628i
\(59\) −0.657857 −0.0856456 −0.0428228 0.999083i \(-0.513635\pi\)
−0.0428228 + 0.999083i \(0.513635\pi\)
\(60\) −5.15178 2.21904i −0.665092 0.286477i
\(61\) −11.8024 −1.51114 −0.755572 0.655065i \(-0.772641\pi\)
−0.755572 + 0.655065i \(0.772641\pi\)
\(62\) 2.33155 11.3068i 0.296108 1.43596i
\(63\) −0.415199 −0.0523102
\(64\) 2.74803 + 7.51321i 0.343503 + 0.939151i
\(65\) 8.94761i 1.10981i
\(66\) −1.58444 + 7.68365i −0.195031 + 0.945791i
\(67\) 5.41363i 0.661380i 0.943739 + 0.330690i \(0.107281\pi\)
−0.943739 + 0.330690i \(0.892719\pi\)
\(68\) 1.59306 3.69847i 0.193186 0.448505i
\(69\) 2.87533 3.83829i 0.346149 0.462076i
\(70\) −1.61292 0.332598i −0.192781 0.0397531i
\(71\) 6.09004i 0.722755i −0.932420 0.361377i \(-0.882307\pi\)
0.932420 0.361377i \(-0.117693\pi\)
\(72\) 2.31819 + 1.62049i 0.273202 + 0.190977i
\(73\) −2.82330 −0.330442 −0.165221 0.986257i \(-0.552834\pi\)
−0.165221 + 0.986257i \(0.552834\pi\)
\(74\) 4.97938 + 1.02679i 0.578841 + 0.119362i
\(75\) −2.86624 −0.330965
\(76\) −1.98290 + 4.60355i −0.227455 + 0.528063i
\(77\) 2.30330i 0.262486i
\(78\) 0.911179 4.41871i 0.103171 0.500321i
\(79\) −15.0378 −1.69188 −0.845942 0.533276i \(-0.820961\pi\)
−0.845942 + 0.533276i \(0.820961\pi\)
\(80\) 7.70734 + 8.15210i 0.861707 + 0.911432i
\(81\) 1.00000 0.111111
\(82\) 3.49606 + 0.720918i 0.386075 + 0.0796121i
\(83\) 11.1848i 1.22769i 0.789428 + 0.613844i \(0.210377\pi\)
−0.789428 + 0.613844i \(0.789623\pi\)
\(84\) 0.762658 + 0.328502i 0.0832128 + 0.0358426i
\(85\) 5.64719i 0.612523i
\(86\) −0.515959 + 2.50212i −0.0556373 + 0.269810i
\(87\) 4.69915i 0.503801i
\(88\) 8.98962 12.8601i 0.958296 1.37089i
\(89\) 4.02672i 0.426831i −0.976962 0.213416i \(-0.931541\pi\)
0.976962 0.213416i \(-0.0684588\pi\)
\(90\) 3.88469 + 0.801057i 0.409482 + 0.0844389i
\(91\) 1.32459i 0.138854i
\(92\) −8.31837 + 4.77542i −0.867251 + 0.497872i
\(93\) 8.16330i 0.846494i
\(94\) 1.02347 4.96325i 0.105562 0.511920i
\(95\) 7.02915i 0.721175i
\(96\) −2.97605 4.81073i −0.303742 0.490993i
\(97\) 14.5135i 1.47362i −0.676100 0.736810i \(-0.736331\pi\)
0.676100 0.736810i \(-0.263669\pi\)
\(98\) −9.45673 1.95006i −0.955274 0.196986i
\(99\) 5.54747i 0.557542i
\(100\) 5.26485 + 2.26775i 0.526485 + 0.226775i
\(101\) 7.00245i 0.696770i −0.937352 0.348385i \(-0.886730\pi\)
0.937352 0.348385i \(-0.113270\pi\)
\(102\) −0.575080 + 2.78882i −0.0569415 + 0.276135i
\(103\) −18.4881 −1.82169 −0.910845 0.412750i \(-0.864568\pi\)
−0.910845 + 0.412750i \(0.864568\pi\)
\(104\) −5.16975 + 7.39559i −0.506936 + 0.725198i
\(105\) 1.16450 0.113644
\(106\) −0.374663 0.0772590i −0.0363905 0.00750405i
\(107\) 2.34324i 0.226530i 0.993565 + 0.113265i \(0.0361308\pi\)
−0.993565 + 0.113265i \(0.963869\pi\)
\(108\) −1.83685 0.791193i −0.176751 0.0761326i
\(109\) 9.34569 0.895155 0.447578 0.894245i \(-0.352287\pi\)
0.447578 + 0.894245i \(0.352287\pi\)
\(110\) 4.44384 21.5502i 0.423704 2.05473i
\(111\) −3.59504 −0.341226
\(112\) −1.14098 1.20682i −0.107812 0.114034i
\(113\) 18.5203i 1.74225i −0.491064 0.871123i \(-0.663392\pi\)
0.491064 0.871123i \(-0.336608\pi\)
\(114\) 0.715812 3.47129i 0.0670419 0.325116i
\(115\) −8.06438 + 10.7652i −0.752008 + 1.00386i
\(116\) −3.71793 + 8.63162i −0.345201 + 0.801426i
\(117\) 3.19024i 0.294938i
\(118\) −0.911179 0.187893i −0.0838808 0.0172970i
\(119\) 0.835997i 0.0766357i
\(120\) −6.50179 4.54496i −0.593530 0.414896i
\(121\) −19.7744 −1.79768
\(122\) −16.3472 3.37094i −1.48001 0.305190i
\(123\) −2.52410 −0.227590
\(124\) 6.45874 14.9947i 0.580012 1.34657i
\(125\) −5.98452 −0.535272
\(126\) −0.575080 0.118587i −0.0512322 0.0105646i
\(127\) 5.31443i 0.471580i −0.971804 0.235790i \(-0.924232\pi\)
0.971804 0.235790i \(-0.0757677\pi\)
\(128\) 1.66034 + 11.1912i 0.146754 + 0.989173i
\(129\) 1.80649i 0.159052i
\(130\) −2.55557 + 12.3931i −0.224138 + 1.08695i
\(131\) 1.82236 0.159220 0.0796101 0.996826i \(-0.474632\pi\)
0.0796101 + 0.996826i \(0.474632\pi\)
\(132\) −4.38912 + 10.1899i −0.382024 + 0.886914i
\(133\) 1.04058i 0.0902297i
\(134\) −1.54621 + 7.49827i −0.133572 + 0.647751i
\(135\) −2.80468 −0.241389
\(136\) 3.26283 4.66765i 0.279786 0.400247i
\(137\) 18.7457i 1.60155i 0.598962 + 0.800777i \(0.295580\pi\)
−0.598962 + 0.800777i \(0.704420\pi\)
\(138\) 5.07881 4.49507i 0.432337 0.382646i
\(139\) −7.64330 −0.648296 −0.324148 0.946006i \(-0.605078\pi\)
−0.324148 + 0.946006i \(0.605078\pi\)
\(140\) −2.13901 0.921345i −0.180780 0.0778679i
\(141\) 3.58339i 0.301775i
\(142\) 1.73940 8.43515i 0.145967 0.707862i
\(143\) 17.6978 1.47996
\(144\) 2.74803 + 2.90660i 0.229002 + 0.242217i
\(145\) 13.1796i 1.09451i
\(146\) −3.91047 0.806375i −0.323633 0.0667360i
\(147\) 6.82761 0.563132
\(148\) 6.60354 + 2.84437i 0.542807 + 0.233805i
\(149\) 10.0586 0.824032 0.412016 0.911177i \(-0.364825\pi\)
0.412016 + 0.911177i \(0.364825\pi\)
\(150\) −3.96995 0.818639i −0.324145 0.0668416i
\(151\) 16.6249i 1.35292i −0.736480 0.676459i \(-0.763514\pi\)
0.736480 0.676459i \(-0.236486\pi\)
\(152\) −4.06130 + 5.80990i −0.329415 + 0.471245i
\(153\) 2.01349i 0.162781i
\(154\) −0.657857 + 3.19024i −0.0530116 + 0.257077i
\(155\) 22.8954i 1.83901i
\(156\) 2.52410 5.85999i 0.202089 0.469175i
\(157\) 6.29506 0.502401 0.251200 0.967935i \(-0.419175\pi\)
0.251200 + 0.967935i \(0.419175\pi\)
\(158\) −20.8284 4.29501i −1.65702 0.341692i
\(159\) 0.270501 0.0214521
\(160\) 8.34687 + 13.4926i 0.659878 + 1.06668i
\(161\) 1.19383 1.59365i 0.0940873 0.125598i
\(162\) 1.38507 + 0.285614i 0.108822 + 0.0224400i
\(163\) 18.3381 1.43635 0.718175 0.695862i \(-0.244978\pi\)
0.718175 + 0.695862i \(0.244978\pi\)
\(164\) 4.63638 + 1.99705i 0.362041 + 0.155943i
\(165\) 15.5589i 1.21126i
\(166\) −3.19453 + 15.4917i −0.247944 + 1.20239i
\(167\) 19.7559i 1.52876i 0.644766 + 0.764380i \(0.276955\pi\)
−0.644766 + 0.764380i \(0.723045\pi\)
\(168\) 0.962511 + 0.672826i 0.0742593 + 0.0519096i
\(169\) 2.82236 0.217104
\(170\) 1.61292 7.82176i 0.123705 0.599902i
\(171\) 2.50622i 0.191655i
\(172\) −1.42928 + 3.31825i −0.108982 + 0.253014i
\(173\) 11.3869i 0.865731i 0.901459 + 0.432865i \(0.142497\pi\)
−0.901459 + 0.432865i \(0.857503\pi\)
\(174\) 1.34214 6.50865i 0.101748 0.493420i
\(175\) −1.19006 −0.0899601
\(176\) 16.1243 15.2446i 1.21541 1.14911i
\(177\) 0.657857 0.0494475
\(178\) 1.15009 5.57729i 0.0862028 0.418036i
\(179\) 19.1156 1.42877 0.714385 0.699753i \(-0.246707\pi\)
0.714385 + 0.699753i \(0.246707\pi\)
\(180\) 5.15178 + 2.21904i 0.383991 + 0.165398i
\(181\) −5.60596 −0.416688 −0.208344 0.978056i \(-0.566807\pi\)
−0.208344 + 0.978056i \(0.566807\pi\)
\(182\) 0.378321 1.83465i 0.0280430 0.135993i
\(183\) 11.8024 0.872460
\(184\) −12.8855 + 4.23845i −0.949930 + 0.312463i
\(185\) 10.0829 0.741312
\(186\) −2.33155 + 11.3068i −0.170958 + 0.829051i
\(187\) −11.1698 −0.816813
\(188\) 2.83515 6.58214i 0.206774 0.480052i
\(189\) 0.415199 0.0302013
\(190\) −2.00763 + 9.73587i −0.145648 + 0.706315i
\(191\) 25.0291 1.81104 0.905522 0.424298i \(-0.139479\pi\)
0.905522 + 0.424298i \(0.139479\pi\)
\(192\) −2.74803 7.51321i −0.198322 0.542219i
\(193\) 24.6407 1.77367 0.886837 0.462082i \(-0.152898\pi\)
0.886837 + 0.462082i \(0.152898\pi\)
\(194\) 4.14525 20.1022i 0.297612 1.44325i
\(195\) 8.94761i 0.640752i
\(196\) −12.5413 5.40196i −0.895806 0.385854i
\(197\) 2.39584i 0.170697i −0.996351 0.0853483i \(-0.972800\pi\)
0.996351 0.0853483i \(-0.0272003\pi\)
\(198\) 1.58444 7.68365i 0.112601 0.546053i
\(199\) 3.76352 0.266789 0.133395 0.991063i \(-0.457412\pi\)
0.133395 + 0.991063i \(0.457412\pi\)
\(200\) 6.64449 + 4.64471i 0.469837 + 0.328431i
\(201\) 5.41363i 0.381848i
\(202\) 2.00000 9.69890i 0.140720 0.682412i
\(203\) 1.95108i 0.136939i
\(204\) −1.59306 + 3.69847i −0.111536 + 0.258945i
\(205\) 7.07929 0.494439
\(206\) −25.6074 5.28047i −1.78415 0.367908i
\(207\) −2.87533 + 3.83829i −0.199849 + 0.266780i
\(208\) −9.27277 + 8.76687i −0.642951 + 0.607873i
\(209\) 13.9032 0.961703
\(210\) 1.61292 + 0.332598i 0.111302 + 0.0229515i
\(211\) −17.0238 −1.17197 −0.585983 0.810323i \(-0.699292\pi\)
−0.585983 + 0.810323i \(0.699292\pi\)
\(212\) −0.496869 0.214018i −0.0341251 0.0146988i
\(213\) 6.09004i 0.417283i
\(214\) −0.669263 + 3.24556i −0.0457499 + 0.221862i
\(215\) 5.06662i 0.345541i
\(216\) −2.31819 1.62049i −0.157733 0.110260i
\(217\) 3.38939i 0.230087i
\(218\) 12.9445 + 2.66926i 0.876709 + 0.180785i
\(219\) 2.82330 0.190781
\(220\) 12.3101 28.5793i 0.829946 1.92682i
\(221\) 6.42351 0.432092
\(222\) −4.97938 1.02679i −0.334194 0.0689139i
\(223\) 15.8920i 1.06421i 0.846678 + 0.532105i \(0.178599\pi\)
−0.846678 + 0.532105i \(0.821401\pi\)
\(224\) −1.23565 1.99741i −0.0825605 0.133458i
\(225\) 2.86624 0.191083
\(226\) 5.28967 25.6520i 0.351864 1.70635i
\(227\) 0.778468i 0.0516687i −0.999666 0.0258344i \(-0.991776\pi\)
0.999666 0.0258344i \(-0.00822425\pi\)
\(228\) 1.98290 4.60355i 0.131321 0.304877i
\(229\) −18.3034 −1.20952 −0.604761 0.796407i \(-0.706731\pi\)
−0.604761 + 0.796407i \(0.706731\pi\)
\(230\) −14.2444 + 12.6073i −0.939251 + 0.831298i
\(231\) 2.30330i 0.151546i
\(232\) −7.61492 + 10.8935i −0.499944 + 0.715195i
\(233\) 10.1288 0.663558 0.331779 0.943357i \(-0.392351\pi\)
0.331779 + 0.943357i \(0.392351\pi\)
\(234\) −0.911179 + 4.41871i −0.0595656 + 0.288860i
\(235\) 10.0503i 0.655606i
\(236\) −1.20838 0.520491i −0.0786590 0.0338811i
\(237\) 15.0378 0.976809
\(238\) −0.238773 + 1.15792i −0.0154773 + 0.0750566i
\(239\) 22.8436i 1.47763i 0.673910 + 0.738813i \(0.264613\pi\)
−0.673910 + 0.738813i \(0.735387\pi\)
\(240\) −7.70734 8.15210i −0.497507 0.526216i
\(241\) 26.9055i 1.73314i 0.499059 + 0.866568i \(0.333679\pi\)
−0.499059 + 0.866568i \(0.666321\pi\)
\(242\) −27.3890 5.64786i −1.76063 0.363058i
\(243\) −1.00000 −0.0641500
\(244\) −21.6793 9.33799i −1.38787 0.597803i
\(245\) −19.1493 −1.22340
\(246\) −3.49606 0.720918i −0.222900 0.0459641i
\(247\) −7.99544 −0.508738
\(248\) 13.2285 18.9241i 0.840013 1.20168i
\(249\) 11.1848i 0.708806i
\(250\) −8.28899 1.70926i −0.524242 0.108103i
\(251\) 25.7950i 1.62817i 0.580747 + 0.814084i \(0.302761\pi\)
−0.580747 + 0.814084i \(0.697239\pi\)
\(252\) −0.762658 0.328502i −0.0480429 0.0206937i
\(253\) 21.2928 + 15.9508i 1.33867 + 1.00282i
\(254\) 1.51788 7.36087i 0.0952402 0.461862i
\(255\) 5.64719i 0.353641i
\(256\) −0.896688 + 15.9749i −0.0560430 + 0.998428i
\(257\) −24.9514 −1.55642 −0.778212 0.628002i \(-0.783873\pi\)
−0.778212 + 0.628002i \(0.783873\pi\)
\(258\) 0.515959 2.50212i 0.0321222 0.155775i
\(259\) −1.49265 −0.0927491
\(260\) −7.07929 + 16.4354i −0.439039 + 1.01928i
\(261\) 4.69915i 0.290870i
\(262\) 2.52410 + 0.520491i 0.155939 + 0.0321561i
\(263\) −4.92026 −0.303396 −0.151698 0.988427i \(-0.548474\pi\)
−0.151698 + 0.988427i \(0.548474\pi\)
\(264\) −8.98962 + 12.8601i −0.553273 + 0.791484i
\(265\) −0.758669 −0.0466047
\(266\) 0.297204 1.44128i 0.0182228 0.0883704i
\(267\) 4.02672i 0.246431i
\(268\) −4.28322 + 9.94402i −0.261640 + 0.607428i
\(269\) 8.77633i 0.535102i −0.963544 0.267551i \(-0.913786\pi\)
0.963544 0.267551i \(-0.0862144\pi\)
\(270\) −3.88469 0.801057i −0.236414 0.0487508i
\(271\) 7.39559i 0.449250i −0.974445 0.224625i \(-0.927884\pi\)
0.974445 0.224625i \(-0.0721158\pi\)
\(272\) 5.85241 5.53312i 0.354854 0.335494i
\(273\) 1.32459i 0.0801675i
\(274\) −5.35405 + 25.9642i −0.323450 + 1.56855i
\(275\) 15.9004i 0.958829i
\(276\) 8.31837 4.77542i 0.500707 0.287447i
\(277\) 8.71879i 0.523861i −0.965087 0.261931i \(-0.915641\pi\)
0.965087 0.261931i \(-0.0843592\pi\)
\(278\) −10.5865 2.18304i −0.634938 0.130930i
\(279\) 8.16330i 0.488724i
\(280\) −2.69954 1.88706i −0.161328 0.112773i
\(281\) 5.18858i 0.309525i −0.987952 0.154762i \(-0.950539\pi\)
0.987952 0.154762i \(-0.0494612\pi\)
\(282\) −1.02347 + 4.96325i −0.0609465 + 0.295557i
\(283\) 26.9752i 1.60351i −0.597653 0.801755i \(-0.703900\pi\)
0.597653 0.801755i \(-0.296100\pi\)
\(284\) 4.81840 11.1865i 0.285919 0.663796i
\(285\) 7.02915i 0.416371i
\(286\) 24.5127 + 5.05474i 1.44947 + 0.298893i
\(287\) −1.04800 −0.0618616
\(288\) 2.97605 + 4.81073i 0.175365 + 0.283475i
\(289\) 12.9459 0.761522
\(290\) −3.76429 + 18.2547i −0.221046 + 1.07195i
\(291\) 14.5135i 0.850795i
\(292\) −5.18597 2.23377i −0.303486 0.130722i
\(293\) 22.7008 1.32619 0.663096 0.748534i \(-0.269242\pi\)
0.663096 + 0.748534i \(0.269242\pi\)
\(294\) 9.45673 + 1.95006i 0.551528 + 0.113730i
\(295\) −1.84508 −0.107425
\(296\) 8.33398 + 5.82572i 0.484403 + 0.338613i
\(297\) 5.54747i 0.321897i
\(298\) 13.9319 + 2.87288i 0.807051 + 0.166421i
\(299\) −12.2451 9.17300i −0.708151 0.530488i
\(300\) −5.26485 2.26775i −0.303966 0.130929i
\(301\) 0.750052i 0.0432323i
\(302\) 4.74832 23.0267i 0.273235 1.32504i
\(303\) 7.00245i 0.402280i
\(304\) −7.28458 + 6.88716i −0.417800 + 0.395006i
\(305\) −33.1020 −1.89542
\(306\) 0.575080 2.78882i 0.0328752 0.159426i
\(307\) 4.84075 0.276276 0.138138 0.990413i \(-0.455888\pi\)
0.138138 + 0.990413i \(0.455888\pi\)
\(308\) −1.82236 + 4.23082i −0.103838 + 0.241073i
\(309\) 18.4881 1.05175
\(310\) 6.53927 31.7118i 0.371405 1.80111i
\(311\) 9.16116i 0.519482i 0.965678 + 0.259741i \(0.0836372\pi\)
−0.965678 + 0.259741i \(0.916363\pi\)
\(312\) 5.16975 7.39559i 0.292680 0.418693i
\(313\) 17.8518i 1.00904i −0.863399 0.504522i \(-0.831669\pi\)
0.863399 0.504522i \(-0.168331\pi\)
\(314\) 8.71912 + 1.79796i 0.492048 + 0.101465i
\(315\) −1.16450 −0.0656122
\(316\) −27.6221 11.8978i −1.55387 0.669303i
\(317\) 31.8091i 1.78658i −0.449485 0.893288i \(-0.648393\pi\)
0.449485 0.893288i \(-0.351607\pi\)
\(318\) 0.374663 + 0.0772590i 0.0210101 + 0.00433247i
\(319\) 26.0684 1.45955
\(320\) 7.70734 + 21.0722i 0.430854 + 1.17797i
\(321\) 2.34324i 0.130787i
\(322\) 2.10872 1.86635i 0.117514 0.104008i
\(323\) 5.04624 0.280780
\(324\) 1.83685 + 0.791193i 0.102047 + 0.0439552i
\(325\) 9.14400i 0.507218i
\(326\) 25.3996 + 5.23762i 1.40675 + 0.290085i
\(327\) −9.34569 −0.516818
\(328\) 5.85134 + 4.09027i 0.323086 + 0.225847i
\(329\) 1.48782i 0.0820260i
\(330\) −4.44384 + 21.5502i −0.244625 + 1.18630i
\(331\) −3.34810 −0.184028 −0.0920140 0.995758i \(-0.529330\pi\)
−0.0920140 + 0.995758i \(0.529330\pi\)
\(332\) −8.84930 + 20.5447i −0.485669 + 1.12754i
\(333\) 3.59504 0.197007
\(334\) −5.64258 + 27.3634i −0.308748 + 1.49726i
\(335\) 15.1835i 0.829564i
\(336\) 1.14098 + 1.20682i 0.0622455 + 0.0658374i
\(337\) 14.8251i 0.807574i −0.914853 0.403787i \(-0.867694\pi\)
0.914853 0.403787i \(-0.132306\pi\)
\(338\) 3.90917 + 0.806106i 0.212631 + 0.0438464i
\(339\) 18.5203i 1.00589i
\(340\) 4.46801 10.3730i 0.242312 0.562557i
\(341\) −45.2856 −2.45235
\(342\) −0.715812 + 3.47129i −0.0387067 + 0.187706i
\(343\) 5.74121 0.309996
\(344\) −2.92739 + 4.18779i −0.157835 + 0.225790i
\(345\) 8.06438 10.7652i 0.434172 0.579578i
\(346\) −3.25227 + 15.7717i −0.174843 + 0.847891i
\(347\) 32.8500 1.76348 0.881740 0.471736i \(-0.156372\pi\)
0.881740 + 0.471736i \(0.156372\pi\)
\(348\) 3.71793 8.63162i 0.199302 0.462703i
\(349\) 16.1566i 0.864844i 0.901671 + 0.432422i \(0.142341\pi\)
−0.901671 + 0.432422i \(0.857659\pi\)
\(350\) −1.64832 0.339898i −0.0881063 0.0181683i
\(351\) 3.19024i 0.170283i
\(352\) 26.6874 16.5095i 1.42244 0.879961i
\(353\) 1.52645 0.0812448 0.0406224 0.999175i \(-0.487066\pi\)
0.0406224 + 0.999175i \(0.487066\pi\)
\(354\) 0.911179 + 0.187893i 0.0484286 + 0.00998642i
\(355\) 17.0806i 0.906546i
\(356\) 3.18591 7.39647i 0.168853 0.392012i
\(357\) 0.835997i 0.0442457i
\(358\) 26.4765 + 5.45970i 1.39933 + 0.288554i
\(359\) −30.2471 −1.59638 −0.798190 0.602405i \(-0.794209\pi\)
−0.798190 + 0.602405i \(0.794209\pi\)
\(360\) 6.50179 + 4.54496i 0.342674 + 0.239540i
\(361\) 12.7189 0.669414
\(362\) −7.76466 1.60114i −0.408101 0.0841542i
\(363\) 19.7744 1.03789
\(364\) 1.04800 2.43306i 0.0549302 0.127527i
\(365\) −7.91846 −0.414471
\(366\) 16.3472 + 3.37094i 0.854481 + 0.176202i
\(367\) 1.47265 0.0768718 0.0384359 0.999261i \(-0.487762\pi\)
0.0384359 + 0.999261i \(0.487762\pi\)
\(368\) −19.0579 + 2.19029i −0.993460 + 0.114177i
\(369\) 2.52410 0.131399
\(370\) 13.9656 + 2.87983i 0.726036 + 0.149715i
\(371\) 0.112312 0.00583093
\(372\) −6.45874 + 14.9947i −0.334870 + 0.777441i
\(373\) 12.4114 0.642639 0.321320 0.946971i \(-0.395874\pi\)
0.321320 + 0.946971i \(0.395874\pi\)
\(374\) −15.4709 3.19024i −0.799982 0.164963i
\(375\) 5.98452 0.309039
\(376\) 5.80684 8.30697i 0.299465 0.428399i
\(377\) −14.9914 −0.772097
\(378\) 0.575080 + 0.118587i 0.0295789 + 0.00609945i
\(379\) 27.0869i 1.39136i 0.718352 + 0.695679i \(0.244897\pi\)
−0.718352 + 0.695679i \(0.755103\pi\)
\(380\) −5.56141 + 12.9115i −0.285294 + 0.662345i
\(381\) 5.31443i 0.272267i
\(382\) 34.6672 + 7.14868i 1.77373 + 0.365758i
\(383\) 30.4292 1.55486 0.777430 0.628970i \(-0.216523\pi\)
0.777430 + 0.628970i \(0.216523\pi\)
\(384\) −1.66034 11.1912i −0.0847286 0.571099i
\(385\) 6.46003i 0.329234i
\(386\) 34.1291 + 7.03773i 1.73713 + 0.358211i
\(387\) 1.80649i 0.0918290i
\(388\) 11.4830 26.6590i 0.582959 1.35341i
\(389\) −16.9108 −0.857413 −0.428706 0.903444i \(-0.641030\pi\)
−0.428706 + 0.903444i \(0.641030\pi\)
\(390\) 2.55557 12.3931i 0.129406 0.627548i
\(391\) 7.72835 + 5.78944i 0.390839 + 0.292784i
\(392\) −15.8277 11.0641i −0.799420 0.558820i
\(393\) −1.82236 −0.0919258
\(394\) 0.684287 3.31841i 0.0344739 0.167179i
\(395\) −42.1762 −2.12212
\(396\) 4.38912 10.1899i 0.220562 0.512060i
\(397\) 24.9043i 1.24991i 0.780661 + 0.624955i \(0.214883\pi\)
−0.780661 + 0.624955i \(0.785117\pi\)
\(398\) 5.21275 + 1.07492i 0.261292 + 0.0538807i
\(399\) 1.04058i 0.0520941i
\(400\) 7.87651 + 8.33102i 0.393825 + 0.416551i
\(401\) 9.00074i 0.449476i −0.974419 0.224738i \(-0.927847\pi\)
0.974419 0.224738i \(-0.0721526\pi\)
\(402\) 1.54621 7.49827i 0.0771179 0.373979i
\(403\) 26.0429 1.29729
\(404\) 5.54029 12.8624i 0.275640 0.639930i
\(405\) 2.80468 0.139366
\(406\) 0.557257 2.70239i 0.0276562 0.134117i
\(407\) 19.9434i 0.988555i
\(408\) −3.26283 + 4.66765i −0.161534 + 0.231083i
\(409\) −3.97216 −0.196411 −0.0982053 0.995166i \(-0.531310\pi\)
−0.0982053 + 0.995166i \(0.531310\pi\)
\(410\) 9.80532 + 2.02195i 0.484250 + 0.0998568i
\(411\) 18.7457i 0.924658i
\(412\) −33.9599 14.6277i −1.67308 0.720654i
\(413\) 0.273141 0.0134404
\(414\) −5.07881 + 4.49507i −0.249610 + 0.220921i
\(415\) 31.3697i 1.53988i
\(416\) −15.3474 + 9.49431i −0.752468 + 0.465497i
\(417\) 7.64330 0.374294
\(418\) 19.2569 + 3.97095i 0.941886 + 0.194225i
\(419\) 19.3554i 0.945572i 0.881177 + 0.472786i \(0.156752\pi\)
−0.881177 + 0.472786i \(0.843248\pi\)
\(420\) 2.13901 + 0.921345i 0.104373 + 0.0449570i
\(421\) −14.5334 −0.708316 −0.354158 0.935186i \(-0.615232\pi\)
−0.354158 + 0.935186i \(0.615232\pi\)
\(422\) −23.5792 4.86224i −1.14782 0.236690i
\(423\) 3.58339i 0.174230i
\(424\) −0.627073 0.438344i −0.0304534 0.0212879i
\(425\) 5.77113i 0.279941i
\(426\) −1.73940 + 8.43515i −0.0842744 + 0.408684i
\(427\) 4.90035 0.237145
\(428\) −1.85396 + 4.30418i −0.0896143 + 0.208050i
\(429\) −17.6978 −0.854456
\(430\) −1.44710 + 7.01764i −0.0697854 + 0.338421i
\(431\) 11.2407 0.541443 0.270722 0.962658i \(-0.412738\pi\)
0.270722 + 0.962658i \(0.412738\pi\)
\(432\) −2.74803 2.90660i −0.132215 0.139844i
\(433\) 5.81482i 0.279442i −0.990191 0.139721i \(-0.955379\pi\)
0.990191 0.139721i \(-0.0446206\pi\)
\(434\) −0.968059 + 4.69455i −0.0464683 + 0.225346i
\(435\) 13.1796i 0.631914i
\(436\) 17.1666 + 7.39425i 0.822132 + 0.354120i
\(437\) −9.61960 7.20621i −0.460168 0.344720i
\(438\) 3.91047 + 0.806375i 0.186850 + 0.0385301i
\(439\) 41.2559i 1.96904i −0.175278 0.984519i \(-0.556082\pi\)
0.175278 0.984519i \(-0.443918\pi\)
\(440\) 25.2130 36.0685i 1.20198 1.71950i
\(441\) −6.82761 −0.325124
\(442\) 8.89702 + 1.83465i 0.423188 + 0.0872652i
\(443\) −1.67570 −0.0796148 −0.0398074 0.999207i \(-0.512674\pi\)
−0.0398074 + 0.999207i \(0.512674\pi\)
\(444\) −6.60354 2.84437i −0.313390 0.134988i
\(445\) 11.2937i 0.535371i
\(446\) −4.53900 + 22.0116i −0.214928 + 1.04228i
\(447\) −10.0586 −0.475755
\(448\) −1.14098 3.11948i −0.0539062 0.147381i
\(449\) −17.2494 −0.814049 −0.407024 0.913417i \(-0.633434\pi\)
−0.407024 + 0.913417i \(0.633434\pi\)
\(450\) 3.96995 + 0.818639i 0.187145 + 0.0385910i
\(451\) 14.0024i 0.659345i
\(452\) 14.6532 34.0191i 0.689227 1.60012i
\(453\) 16.6249i 0.781108i
\(454\) 0.222342 1.07823i 0.0104350 0.0506040i
\(455\) 3.71504i 0.174164i
\(456\) 4.06130 5.80990i 0.190188 0.272073i
\(457\) 22.5158i 1.05325i 0.850099 + 0.526623i \(0.176542\pi\)
−0.850099 + 0.526623i \(0.823458\pi\)
\(458\) −25.3515 5.22771i −1.18460 0.244275i
\(459\) 2.01349i 0.0939815i
\(460\) −23.3304 + 13.3935i −1.08779 + 0.624477i
\(461\) 34.5037i 1.60700i −0.595308 0.803498i \(-0.702970\pi\)
0.595308 0.803498i \(-0.297030\pi\)
\(462\) 0.657857 3.19024i 0.0306063 0.148423i
\(463\) 28.5673i 1.32763i 0.747895 + 0.663817i \(0.231064\pi\)
−0.747895 + 0.663817i \(0.768936\pi\)
\(464\) −13.6586 + 12.9134i −0.634082 + 0.599489i
\(465\) 22.8954i 1.06175i
\(466\) 14.0291 + 2.89292i 0.649884 + 0.134012i
\(467\) 4.59322i 0.212549i 0.994337 + 0.106274i \(0.0338922\pi\)
−0.994337 + 0.106274i \(0.966108\pi\)
\(468\) −2.52410 + 5.85999i −0.116676 + 0.270878i
\(469\) 2.24773i 0.103791i
\(470\) 2.87050 13.9203i 0.132406 0.642097i
\(471\) −6.29506 −0.290061
\(472\) −1.52504 1.06605i −0.0701956 0.0490689i
\(473\) 10.0214 0.460786
\(474\) 20.8284 + 4.29501i 0.956681 + 0.197276i
\(475\) 7.18342i 0.329598i
\(476\) −0.661435 + 1.53560i −0.0303168 + 0.0703841i
\(477\) −0.270501 −0.0123854
\(478\) −6.52445 + 31.6400i −0.298421 + 1.44718i
\(479\) 6.78356 0.309949 0.154974 0.987918i \(-0.450470\pi\)
0.154974 + 0.987918i \(0.450470\pi\)
\(480\) −8.34687 13.4926i −0.380981 0.615849i
\(481\) 11.4690i 0.522943i
\(482\) −7.68460 + 37.2661i −0.350024 + 1.69742i
\(483\) −1.19383 + 1.59365i −0.0543213 + 0.0725138i
\(484\) −36.3226 15.6454i −1.65103 0.711154i
\(485\) 40.7057i 1.84835i
\(486\) −1.38507 0.285614i −0.0628281 0.0129557i
\(487\) 2.73804i 0.124073i 0.998074 + 0.0620363i \(0.0197595\pi\)
−0.998074 + 0.0620363i \(0.980241\pi\)
\(488\) −27.3603 19.1257i −1.23854 0.865779i
\(489\) −18.3381 −0.829277
\(490\) −26.5231 5.46931i −1.19819 0.247078i
\(491\) 26.6421 1.20234 0.601170 0.799121i \(-0.294701\pi\)
0.601170 + 0.799121i \(0.294701\pi\)
\(492\) −4.63638 1.99705i −0.209024 0.0900338i
\(493\) 9.46166 0.426132
\(494\) −11.0743 2.28361i −0.498255 0.102745i
\(495\) 15.5589i 0.699320i
\(496\) 23.7275 22.4330i 1.06539 1.00727i
\(497\) 2.52858i 0.113422i
\(498\) 3.19453 15.4917i 0.143150 0.694200i
\(499\) 13.3190 0.596240 0.298120 0.954528i \(-0.403640\pi\)
0.298120 + 0.954528i \(0.403640\pi\)
\(500\) −10.9927 4.73491i −0.491607 0.211752i
\(501\) 19.7559i 0.882630i
\(502\) −7.36744 + 35.7280i −0.328825 + 1.59462i
\(503\) 26.7050 1.19072 0.595359 0.803460i \(-0.297010\pi\)
0.595359 + 0.803460i \(0.297010\pi\)
\(504\) −0.962511 0.672826i −0.0428736 0.0299700i
\(505\) 19.6396i 0.873953i
\(506\) 24.9363 + 28.1745i 1.10855 + 1.25251i
\(507\) −2.82236 −0.125345
\(508\) 4.20474 9.76181i 0.186555 0.433110i
\(509\) 28.4096i 1.25923i −0.776906 0.629617i \(-0.783212\pi\)
0.776906 0.629617i \(-0.216788\pi\)
\(510\) −1.61292 + 7.82176i −0.0714212 + 0.346353i
\(511\) 1.17223 0.0518564
\(512\) −5.80462 + 21.8702i −0.256531 + 0.966536i
\(513\) 2.50622i 0.110652i
\(514\) −34.5594 7.12647i −1.52435 0.314335i
\(515\) −51.8533 −2.28493
\(516\) 1.42928 3.31825i 0.0629206 0.146078i
\(517\) −19.8787 −0.874265
\(518\) −2.06743 0.426324i −0.0908379 0.0187316i
\(519\) 11.3869i 0.499830i
\(520\) −14.4995 + 20.7423i −0.635846 + 0.909609i
\(521\) 24.7986i 1.08645i 0.839588 + 0.543224i \(0.182797\pi\)
−0.839588 + 0.543224i \(0.817203\pi\)
\(522\) −1.34214 + 6.50865i −0.0587440 + 0.284876i
\(523\) 26.1728i 1.14446i 0.820094 + 0.572229i \(0.193921\pi\)
−0.820094 + 0.572229i \(0.806079\pi\)
\(524\) 3.34740 + 1.44184i 0.146232 + 0.0629869i
\(525\) 1.19006 0.0519385
\(526\) −6.81492 1.40530i −0.297144 0.0612739i
\(527\) −16.4367 −0.715993
\(528\) −16.1243 + 15.2446i −0.701720 + 0.663436i
\(529\) −6.46496 22.0727i −0.281085 0.959683i
\(530\) −1.05081 0.216687i −0.0456443 0.00941227i
\(531\) −0.657857 −0.0285485
\(532\) 0.823299 1.91139i 0.0356945 0.0828691i
\(533\) 8.05248i 0.348792i
\(534\) −1.15009 + 5.57729i −0.0497692 + 0.241353i
\(535\) 6.57204i 0.284134i
\(536\) −8.77273 + 12.5498i −0.378924 + 0.542070i
\(537\) −19.1156 −0.824900
\(538\) 2.50664 12.1558i 0.108069 0.524076i
\(539\) 37.8760i 1.63143i
\(540\) −5.15178 2.21904i −0.221697 0.0954925i
\(541\) 21.3299i 0.917046i −0.888683 0.458523i \(-0.848379\pi\)
0.888683 0.458523i \(-0.151621\pi\)
\(542\) 2.11229 10.2434i 0.0907305 0.439993i
\(543\) 5.60596 0.240575
\(544\) 9.68634 5.99223i 0.415298 0.256915i
\(545\) 26.2117 1.12279
\(546\) −0.378321 + 1.83465i −0.0161906 + 0.0785156i
\(547\) −6.09639 −0.260663 −0.130331 0.991470i \(-0.541604\pi\)
−0.130331 + 0.991470i \(0.541604\pi\)
\(548\) −14.8315 + 34.4331i −0.633569 + 1.47091i
\(549\) −11.8024 −0.503715
\(550\) 4.54138 22.0232i 0.193645 0.939071i
\(551\) −11.7771 −0.501721
\(552\) 12.8855 4.23845i 0.548442 0.180401i
\(553\) 6.24367 0.265508
\(554\) 2.49021 12.0762i 0.105799 0.513067i
\(555\) −10.0829 −0.427997
\(556\) −14.0396 6.04733i −0.595411 0.256464i
\(557\) −21.1916 −0.897915 −0.448958 0.893553i \(-0.648205\pi\)
−0.448958 + 0.893553i \(0.648205\pi\)
\(558\) 2.33155 11.3068i 0.0987026 0.478653i
\(559\) −5.76313 −0.243755
\(560\) −3.20008 3.38474i −0.135228 0.143031i
\(561\) 11.1698 0.471587
\(562\) 1.48193 7.18656i 0.0625116 0.303147i
\(563\) 14.2901i 0.602254i −0.953584 0.301127i \(-0.902637\pi\)
0.953584 0.301127i \(-0.0973628\pi\)
\(564\) −2.83515 + 6.58214i −0.119381 + 0.277158i
\(565\) 51.9436i 2.18529i
\(566\) 7.70451 37.3626i 0.323845 1.57047i
\(567\) −0.415199 −0.0174367
\(568\) 9.86885 14.1179i 0.414088 0.592373i
\(569\) 31.9346i 1.33877i 0.742917 + 0.669384i \(0.233442\pi\)
−0.742917 + 0.669384i \(0.766558\pi\)
\(570\) 2.00763 9.73587i 0.0840902 0.407791i
\(571\) 25.5699i 1.07007i 0.844831 + 0.535034i \(0.179701\pi\)
−0.844831 + 0.535034i \(0.820299\pi\)
\(572\) 32.5081 + 14.0024i 1.35923 + 0.585468i
\(573\) −25.0291 −1.04561
\(574\) −1.45156 0.299324i −0.0605869 0.0124936i
\(575\) −8.24138 + 11.0015i −0.343689 + 0.458793i
\(576\) 2.74803 + 7.51321i 0.114501 + 0.313050i
\(577\) 25.3417 1.05499 0.527494 0.849558i \(-0.323132\pi\)
0.527494 + 0.849558i \(0.323132\pi\)
\(578\) 17.9310 + 3.69753i 0.745830 + 0.153797i
\(579\) −24.6407 −1.02403
\(580\) −10.4276 + 24.2089i −0.432983 + 1.00522i
\(581\) 4.64390i 0.192662i
\(582\) −4.14525 + 20.1022i −0.171826 + 0.833263i
\(583\) 1.50060i 0.0621483i
\(584\) −6.54495 4.57513i −0.270832 0.189320i
\(585\) 8.94761i 0.369938i
\(586\) 31.4422 + 6.48366i 1.29886 + 0.267838i
\(587\) 11.6750 0.481878 0.240939 0.970540i \(-0.422545\pi\)
0.240939 + 0.970540i \(0.422545\pi\)
\(588\) 12.5413 + 5.40196i 0.517194 + 0.222773i
\(589\) 20.4590 0.842999
\(590\) −2.55557 0.526981i −0.105211 0.0216955i
\(591\) 2.39584i 0.0985518i
\(592\) 9.87926 + 10.4493i 0.406035 + 0.429465i
\(593\) −39.6476 −1.62813 −0.814065 0.580774i \(-0.802750\pi\)
−0.814065 + 0.580774i \(0.802750\pi\)
\(594\) −1.58444 + 7.68365i −0.0650102 + 0.315264i
\(595\) 2.34471i 0.0961236i
\(596\) 18.4761 + 7.95828i 0.756811 + 0.325984i
\(597\) −3.76352 −0.154031
\(598\) −14.3404 16.2026i −0.586421 0.662575i
\(599\) 20.5586i 0.840003i −0.907523 0.420002i \(-0.862030\pi\)
0.907523 0.420002i \(-0.137970\pi\)
\(600\) −6.64449 4.64471i −0.271260 0.189620i
\(601\) −35.6416 −1.45385 −0.726926 0.686716i \(-0.759052\pi\)
−0.726926 + 0.686716i \(0.759052\pi\)
\(602\) 0.214226 1.03888i 0.00873118 0.0423414i
\(603\) 5.41363i 0.220460i
\(604\) 13.1535 30.5375i 0.535210 1.24255i
\(605\) −55.4610 −2.25481
\(606\) −2.00000 + 9.69890i −0.0812444 + 0.393991i
\(607\) 23.1724i 0.940539i 0.882523 + 0.470269i \(0.155843\pi\)
−0.882523 + 0.470269i \(0.844157\pi\)
\(608\) −12.0567 + 7.45863i −0.488966 + 0.302487i
\(609\) 1.95108i 0.0790618i
\(610\) −45.8487 9.45441i −1.85636 0.382798i
\(611\) 11.4319 0.462484
\(612\) 1.59306 3.69847i 0.0643955 0.149502i
\(613\) 24.7805 1.00087 0.500437 0.865773i \(-0.333173\pi\)
0.500437 + 0.865773i \(0.333173\pi\)
\(614\) 6.70479 + 1.38259i 0.270583 + 0.0557967i
\(615\) −7.07929 −0.285464
\(616\) −3.73248 + 5.33950i −0.150386 + 0.215135i
\(617\) 17.9944i 0.724428i 0.932095 + 0.362214i \(0.117979\pi\)
−0.932095 + 0.362214i \(0.882021\pi\)
\(618\) 25.6074 + 5.28047i 1.03008 + 0.212412i
\(619\) 45.4728i 1.82771i −0.406043 0.913854i \(-0.633092\pi\)
0.406043 0.913854i \(-0.366908\pi\)
\(620\) 18.1147 42.0555i 0.727504 1.68899i
\(621\) 2.87533 3.83829i 0.115383 0.154025i
\(622\) −2.61656 + 12.6889i −0.104914 + 0.508777i
\(623\) 1.67189i 0.0669828i
\(624\) 9.27277 8.76687i 0.371208 0.350956i
\(625\) −31.1159 −1.24463
\(626\) 5.09873 24.7260i 0.203786 0.988251i
\(627\) −13.9032 −0.555239
\(628\) 11.5631 + 4.98061i 0.461417 + 0.198748i
\(629\) 7.23855i 0.288620i
\(630\) −1.61292 0.332598i −0.0642602 0.0132510i
\(631\) −38.7133 −1.54115 −0.770576 0.637349i \(-0.780031\pi\)
−0.770576 + 0.637349i \(0.780031\pi\)
\(632\) −34.8605 24.3686i −1.38668 0.969330i
\(633\) 17.0238 0.676635
\(634\) 9.08513 44.0579i 0.360817 1.74976i
\(635\) 14.9053i 0.591499i
\(636\) 0.496869 + 0.214018i 0.0197022 + 0.00848638i
\(637\) 21.7817i 0.863023i
\(638\) 36.1066 + 7.44550i 1.42947 + 0.294770i
\(639\) 6.09004i 0.240918i
\(640\) 4.65671 + 31.3878i 0.184073 + 1.24071i
\(641\) 16.6975i 0.659512i −0.944066 0.329756i \(-0.893033\pi\)
0.944066 0.329756i \(-0.106967\pi\)
\(642\) 0.669263 3.24556i 0.0264137 0.128092i
\(643\) 4.54910i 0.179399i −0.995969 0.0896994i \(-0.971409\pi\)
0.995969 0.0896994i \(-0.0285906\pi\)
\(644\) 3.45378 1.98275i 0.136098 0.0781313i
\(645\) 5.06662i 0.199498i
\(646\) 6.98940 + 1.44128i 0.274994 + 0.0567063i
\(647\) 24.8216i 0.975838i −0.872889 0.487919i \(-0.837756\pi\)
0.872889 0.487919i \(-0.162244\pi\)
\(648\) 2.31819 + 1.62049i 0.0910672 + 0.0636588i
\(649\) 3.64944i 0.143253i
\(650\) −2.61166 + 12.6651i −0.102438 + 0.496766i
\(651\) 3.38939i 0.132841i
\(652\) 33.6843 + 14.5090i 1.31918 + 0.568215i
\(653\) 20.1907i 0.790122i 0.918655 + 0.395061i \(0.129277\pi\)
−0.918655 + 0.395061i \(0.870723\pi\)
\(654\) −12.9445 2.66926i −0.506168 0.104376i
\(655\) 5.11113 0.199708
\(656\) 6.93629 + 7.33655i 0.270817 + 0.286444i
\(657\) −2.82330 −0.110147
\(658\) −0.424942 + 2.06073i −0.0165660 + 0.0803358i
\(659\) 33.2939i 1.29695i −0.761237 0.648474i \(-0.775408\pi\)
0.761237 0.648474i \(-0.224592\pi\)
\(660\) −12.3101 + 28.5793i −0.479169 + 1.11245i
\(661\) −32.2531 −1.25450 −0.627251 0.778818i \(-0.715820\pi\)
−0.627251 + 0.778818i \(0.715820\pi\)
\(662\) −4.63735 0.956264i −0.180236 0.0371663i
\(663\) −6.42351 −0.249468
\(664\) −18.1248 + 25.9284i −0.703378 + 1.00622i
\(665\) 2.91849i 0.113174i
\(666\) 4.97938 + 1.02679i 0.192947 + 0.0397874i
\(667\) −18.0367 13.5116i −0.698383 0.523171i
\(668\) −15.6308 + 36.2887i −0.604772 + 1.40405i
\(669\) 15.8920i 0.614422i
\(670\) −4.33663 + 21.0302i −0.167539 + 0.812469i
\(671\) 65.4735i 2.52758i
\(672\) 1.23565 + 1.99741i 0.0476663 + 0.0770518i
\(673\) −39.3450 −1.51664 −0.758319 0.651884i \(-0.773979\pi\)
−0.758319 + 0.651884i \(0.773979\pi\)
\(674\) 4.23426 20.5338i 0.163098 0.790933i
\(675\) −2.86624 −0.110322
\(676\) 5.18424 + 2.23303i 0.199394 + 0.0858857i
\(677\) 15.4597 0.594165 0.297083 0.954852i \(-0.403986\pi\)
0.297083 + 0.954852i \(0.403986\pi\)
\(678\) −5.28967 + 25.6520i −0.203149 + 0.985159i
\(679\) 6.02598i 0.231256i
\(680\) 9.15121 13.0913i 0.350933 0.502027i
\(681\) 0.778468i 0.0298310i
\(682\) −62.7239 12.9342i −2.40182 0.495277i
\(683\) 10.8401 0.414783 0.207392 0.978258i \(-0.433503\pi\)
0.207392 + 0.978258i \(0.433503\pi\)
\(684\) −1.98290 + 4.60355i −0.0758182 + 0.176021i
\(685\) 52.5758i 2.00882i
\(686\) 7.95199 + 1.63977i 0.303608 + 0.0626068i
\(687\) 18.3034 0.698318
\(688\) −5.25074 + 4.96428i −0.200183 + 0.189261i
\(689\) 0.862963i 0.0328763i
\(690\) 14.2444 12.6073i 0.542277 0.479950i
\(691\) −31.6585 −1.20435 −0.602173 0.798366i \(-0.705698\pi\)
−0.602173 + 0.798366i \(0.705698\pi\)
\(692\) −9.00924 + 20.9160i −0.342480 + 0.795108i
\(693\) 2.30330i 0.0874953i
\(694\) 45.4996 + 9.38243i 1.72714 + 0.356152i
\(695\) −21.4370 −0.813153
\(696\) 7.61492 10.8935i 0.288643 0.412918i
\(697\) 5.08223i 0.192503i
\(698\) −4.61456 + 22.3781i −0.174664 + 0.847022i
\(699\) −10.1288 −0.383105
\(700\) −2.18596 0.941567i −0.0826215 0.0355879i
\(701\) 25.0600 0.946504 0.473252 0.880927i \(-0.343080\pi\)
0.473252 + 0.880927i \(0.343080\pi\)
\(702\) 0.911179 4.41871i 0.0343902 0.166774i
\(703\) 9.00995i 0.339817i
\(704\) 41.6793 15.2446i 1.57085 0.574553i
\(705\) 10.0503i 0.378514i
\(706\) 2.11424 + 0.435976i 0.0795706 + 0.0164082i
\(707\) 2.90741i 0.109344i
\(708\) 1.20838 + 0.520491i 0.0454138 + 0.0195613i
\(709\) 1.51261 0.0568072 0.0284036 0.999597i \(-0.490958\pi\)
0.0284036 + 0.999597i \(0.490958\pi\)
\(710\) 4.87847 23.6579i 0.183086 0.887865i
\(711\) −15.0378 −0.563961
\(712\) 6.52525 9.33470i 0.244544 0.349833i
\(713\) 31.3331 + 23.4722i 1.17343 + 0.879040i
\(714\) 0.238773 1.15792i 0.00893585 0.0433339i
\(715\) 49.6366 1.85630
\(716\) 35.1125 + 15.1241i 1.31222 + 0.565216i
\(717\) 22.8436i 0.853108i
\(718\) −41.8944 8.63900i −1.56349 0.322405i
\(719\) 14.5869i 0.543999i −0.962297 0.272000i \(-0.912315\pi\)
0.962297 0.272000i \(-0.0876850\pi\)
\(720\) 7.70734 + 8.15210i 0.287236 + 0.303811i
\(721\) 7.67625 0.285878
\(722\) 17.6165 + 3.63269i 0.655620 + 0.135195i
\(723\) 26.9055i 1.00063i
\(724\) −10.2973 4.43540i −0.382696 0.164840i
\(725\) 13.4689i 0.500222i
\(726\) 27.3890 + 5.64786i 1.01650 + 0.209612i
\(727\) 21.7360 0.806142 0.403071 0.915169i \(-0.367943\pi\)
0.403071 + 0.915169i \(0.367943\pi\)
\(728\) 2.14648 3.07064i 0.0795537 0.113806i
\(729\) 1.00000 0.0370370
\(730\) −10.9676 2.26162i −0.405930 0.0837065i
\(731\) 3.63734 0.134532
\(732\) 21.6793 + 9.33799i 0.801288 + 0.345142i
\(733\) −8.74545 −0.323021 −0.161510 0.986871i \(-0.551637\pi\)
−0.161510 + 0.986871i \(0.551637\pi\)
\(734\) 2.03973 + 0.420610i 0.0752877 + 0.0155250i
\(735\) 19.1493 0.706332
\(736\) −27.0221 2.40950i −0.996048 0.0888152i
\(737\) 30.0319 1.10624
\(738\) 3.49606 + 0.720918i 0.128692 + 0.0265374i
\(739\) −7.34669 −0.270253 −0.135126 0.990828i \(-0.543144\pi\)
−0.135126 + 0.990828i \(0.543144\pi\)
\(740\) 18.5208 + 7.97754i 0.680839 + 0.293260i
\(741\) 7.99544 0.293720
\(742\) 0.155560 + 0.0320778i 0.00571078 + 0.00117761i
\(743\) 28.2818 1.03756 0.518779 0.854908i \(-0.326387\pi\)
0.518779 + 0.854908i \(0.326387\pi\)
\(744\) −13.2285 + 18.9241i −0.484982 + 0.693791i
\(745\) 28.2111 1.03358
\(746\) 17.1907 + 3.54488i 0.629397 + 0.129787i
\(747\) 11.1848i 0.409229i
\(748\) −20.5171 8.83743i −0.750181 0.323128i
\(749\) 0.972911i 0.0355494i
\(750\) 8.28899 + 1.70926i 0.302671 + 0.0624135i
\(751\) 45.1818 1.64871 0.824353 0.566076i \(-0.191539\pi\)
0.824353 + 0.566076i \(0.191539\pi\)
\(752\) 10.4155 9.84724i 0.379813 0.359092i
\(753\) 25.7950i 0.940024i
\(754\) −20.7642 4.28176i −0.756187 0.155933i
\(755\) 46.6277i 1.69695i
\(756\) 0.762658 + 0.328502i 0.0277376 + 0.0119475i
\(757\) 11.8830 0.431894 0.215947 0.976405i \(-0.430716\pi\)
0.215947 + 0.976405i \(0.430716\pi\)
\(758\) −7.73640 + 37.5173i −0.280999 + 1.36269i
\(759\) −21.2928 15.9508i −0.772880 0.578978i
\(760\) −11.3907 + 16.2949i −0.413183 + 0.591079i
\(761\) 29.0606 1.05345 0.526723 0.850037i \(-0.323421\pi\)
0.526723 + 0.850037i \(0.323421\pi\)
\(762\) −1.51788 + 7.36087i −0.0549869 + 0.266656i
\(763\) −3.88032 −0.140477
\(764\) 45.9747 + 19.8029i 1.66331 + 0.716443i
\(765\) 5.64719i 0.204174i
\(766\) 42.1466 + 8.69101i 1.52282 + 0.314019i
\(767\) 2.09872i 0.0757804i
\(768\) 0.896688 15.9749i 0.0323564 0.576443i
\(769\) 0.831518i 0.0299853i −0.999888 0.0149927i \(-0.995228\pi\)
0.999888 0.0149927i \(-0.00477249\pi\)
\(770\) −1.84508 + 8.94761i −0.0664920 + 0.322450i
\(771\) 24.9514 0.898602
\(772\) 45.2612 + 19.4955i 1.62899 + 0.701659i
\(773\) 35.9982 1.29477 0.647383 0.762165i \(-0.275864\pi\)
0.647383 + 0.762165i \(0.275864\pi\)
\(774\) −0.515959 + 2.50212i −0.0185458 + 0.0899367i
\(775\) 23.3980i 0.840480i
\(776\) 23.5189 33.6450i 0.844280 1.20779i
\(777\) 1.49265 0.0535487
\(778\) −23.4227 4.82997i −0.839745 0.173163i
\(779\) 6.32594i 0.226650i
\(780\) 7.07929 16.4354i 0.253479 0.588482i
\(781\) −33.7843 −1.20890
\(782\) 9.05077 + 10.2261i