Properties

Label 804.2.c.b.671.9
Level 804
Weight 2
Character 804.671
Analytic conductor 6.420
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(128\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 671.9
Character \(\chi\) = 804.671
Dual form 804.2.c.b.671.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.38271 - 0.296856i) q^{2} +(-1.71448 + 0.246081i) q^{3} +(1.82375 + 0.820930i) q^{4} -2.85244i q^{5} +(2.44367 + 0.168697i) q^{6} -2.12311i q^{7} +(-2.27802 - 1.67650i) q^{8} +(2.87889 - 0.843802i) q^{9} +O(q^{10})\) \(q+(-1.38271 - 0.296856i) q^{2} +(-1.71448 + 0.246081i) q^{3} +(1.82375 + 0.820930i) q^{4} -2.85244i q^{5} +(2.44367 + 0.168697i) q^{6} -2.12311i q^{7} +(-2.27802 - 1.67650i) q^{8} +(2.87889 - 0.843802i) q^{9} +(-0.846765 + 3.94409i) q^{10} +5.05538 q^{11} +(-3.32880 - 0.958677i) q^{12} +1.45615 q^{13} +(-0.630258 + 2.93564i) q^{14} +(0.701931 + 4.89046i) q^{15} +(2.65215 + 2.99435i) q^{16} -0.803856i q^{17} +(-4.23114 + 0.312114i) q^{18} -3.66618i q^{19} +(2.34165 - 5.20215i) q^{20} +(0.522456 + 3.64003i) q^{21} +(-6.99011 - 1.50072i) q^{22} +2.52796 q^{23} +(4.31817 + 2.31375i) q^{24} -3.13642 q^{25} +(-2.01342 - 0.432266i) q^{26} +(-4.72816 + 2.15512i) q^{27} +(1.74292 - 3.87203i) q^{28} +8.38116i q^{29} +(0.481197 - 6.97044i) q^{30} +2.39032i q^{31} +(-2.77825 - 4.92761i) q^{32} +(-8.66735 + 1.24403i) q^{33} +(-0.238630 + 1.11150i) q^{34} -6.05605 q^{35} +(5.94308 + 0.824479i) q^{36} +1.53809 q^{37} +(-1.08833 + 5.06925i) q^{38} +(-2.49654 + 0.358330i) q^{39} +(-4.78211 + 6.49791i) q^{40} -0.167196i q^{41} +(0.358161 - 5.18819i) q^{42} -11.3226i q^{43} +(9.21977 + 4.15011i) q^{44} +(-2.40690 - 8.21186i) q^{45} +(-3.49542 - 0.750439i) q^{46} +10.3130 q^{47} +(-5.28391 - 4.48110i) q^{48} +2.49241 q^{49} +(4.33675 + 0.931067i) q^{50} +(0.197814 + 1.37820i) q^{51} +(2.65565 + 1.19539i) q^{52} -11.2890i q^{53} +(7.17741 - 1.57632i) q^{54} -14.4202i q^{55} +(-3.55939 + 4.83648i) q^{56} +(0.902176 + 6.28559i) q^{57} +(2.48800 - 11.5887i) q^{58} +4.56971 q^{59} +(-2.73457 + 9.49522i) q^{60} -7.45650 q^{61} +(0.709581 - 3.30511i) q^{62} +(-1.79148 - 6.11219i) q^{63} +(2.37872 + 7.63817i) q^{64} -4.15357i q^{65} +(12.3537 + 0.852826i) q^{66} +1.00000i q^{67} +(0.659909 - 1.46603i) q^{68} +(-4.33413 + 0.622081i) q^{69} +(8.37373 + 1.79777i) q^{70} -15.5562 q^{71} +(-7.97279 - 2.90425i) q^{72} +0.104759 q^{73} +(-2.12672 - 0.456590i) q^{74} +(5.37734 - 0.771814i) q^{75} +(3.00968 - 6.68621i) q^{76} -10.7331i q^{77} +(3.55835 + 0.245647i) q^{78} -6.42169i q^{79} +(8.54120 - 7.56510i) q^{80} +(7.57600 - 4.85842i) q^{81} +(-0.0496331 + 0.231183i) q^{82} -11.4145 q^{83} +(-2.03538 + 7.06741i) q^{84} -2.29295 q^{85} +(-3.36119 + 15.6558i) q^{86} +(-2.06244 - 14.3693i) q^{87} +(-11.5162 - 8.47533i) q^{88} +6.70211i q^{89} +(0.890287 + 12.0691i) q^{90} -3.09156i q^{91} +(4.61037 + 2.07527i) q^{92} +(-0.588211 - 4.09815i) q^{93} +(-14.2599 - 3.06149i) q^{94} -10.4576 q^{95} +(5.97585 + 7.76461i) q^{96} -11.1470 q^{97} +(-3.44627 - 0.739887i) q^{98} +(14.5539 - 4.26574i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} - 4q^{10} + 4q^{12} - 8q^{13} - 4q^{16} + 18q^{18} - 8q^{21} - 8q^{22} - 24q^{24} - 136q^{25} + 14q^{30} - 32q^{33} + 34q^{36} - 48q^{37} + 16q^{40} - 28q^{42} - 16q^{45} - 28q^{46} - 22q^{48} - 152q^{49} + 8q^{52} - 16q^{54} - 32q^{57} - 20q^{58} - 14q^{60} + 8q^{61} + 16q^{64} + 14q^{66} + 56q^{69} - 4q^{70} - 8q^{72} - 48q^{73} - 36q^{76} + 40q^{78} + 44q^{81} + 60q^{82} + 46q^{84} + 64q^{85} - 28q^{88} - 14q^{90} + 32q^{93} - 8q^{96} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38271 0.296856i −0.977721 0.209909i
\(3\) −1.71448 + 0.246081i −0.989856 + 0.142075i
\(4\) 1.82375 + 0.820930i 0.911876 + 0.410465i
\(5\) 2.85244i 1.27565i −0.770181 0.637825i \(-0.779834\pi\)
0.770181 0.637825i \(-0.220166\pi\)
\(6\) 2.44367 + 0.168697i 0.997626 + 0.0688701i
\(7\) 2.12311i 0.802460i −0.915977 0.401230i \(-0.868583\pi\)
0.915977 0.401230i \(-0.131417\pi\)
\(8\) −2.27802 1.67650i −0.805400 0.592731i
\(9\) 2.87889 0.843802i 0.959629 0.281267i
\(10\) −0.846765 + 3.94409i −0.267771 + 1.24723i
\(11\) 5.05538 1.52425 0.762127 0.647427i \(-0.224155\pi\)
0.762127 + 0.647427i \(0.224155\pi\)
\(12\) −3.32880 0.958677i −0.960943 0.276746i
\(13\) 1.45615 0.403862 0.201931 0.979400i \(-0.435278\pi\)
0.201931 + 0.979400i \(0.435278\pi\)
\(14\) −0.630258 + 2.93564i −0.168444 + 0.784582i
\(15\) 0.701931 + 4.89046i 0.181238 + 1.26271i
\(16\) 2.65215 + 2.99435i 0.663037 + 0.748586i
\(17\) 0.803856i 0.194964i −0.995237 0.0974818i \(-0.968921\pi\)
0.995237 0.0974818i \(-0.0310788\pi\)
\(18\) −4.23114 + 0.312114i −0.997290 + 0.0735660i
\(19\) 3.66618i 0.841079i −0.907274 0.420540i \(-0.861841\pi\)
0.907274 0.420540i \(-0.138159\pi\)
\(20\) 2.34165 5.20215i 0.523610 1.16324i
\(21\) 0.522456 + 3.64003i 0.114009 + 0.794320i
\(22\) −6.99011 1.50072i −1.49030 0.319955i
\(23\) 2.52796 0.527115 0.263558 0.964644i \(-0.415104\pi\)
0.263558 + 0.964644i \(0.415104\pi\)
\(24\) 4.31817 + 2.31375i 0.881443 + 0.472291i
\(25\) −3.13642 −0.627285
\(26\) −2.01342 0.432266i −0.394865 0.0847744i
\(27\) −4.72816 + 2.15512i −0.909934 + 0.414753i
\(28\) 1.74292 3.87203i 0.329382 0.731744i
\(29\) 8.38116i 1.55634i 0.628052 + 0.778171i \(0.283852\pi\)
−0.628052 + 0.778171i \(0.716148\pi\)
\(30\) 0.481197 6.97044i 0.0878542 1.27262i
\(31\) 2.39032i 0.429314i 0.976690 + 0.214657i \(0.0688633\pi\)
−0.976690 + 0.214657i \(0.931137\pi\)
\(32\) −2.77825 4.92761i −0.491130 0.871086i
\(33\) −8.66735 + 1.24403i −1.50879 + 0.216558i
\(34\) −0.238630 + 1.11150i −0.0409246 + 0.190620i
\(35\) −6.05605 −1.02366
\(36\) 5.94308 + 0.824479i 0.990514 + 0.137413i
\(37\) 1.53809 0.252860 0.126430 0.991976i \(-0.459648\pi\)
0.126430 + 0.991976i \(0.459648\pi\)
\(38\) −1.08833 + 5.06925i −0.176550 + 0.822341i
\(39\) −2.49654 + 0.358330i −0.399766 + 0.0573787i
\(40\) −4.78211 + 6.49791i −0.756118 + 1.02741i
\(41\) 0.167196i 0.0261116i −0.999915 0.0130558i \(-0.995844\pi\)
0.999915 0.0130558i \(-0.00415591\pi\)
\(42\) 0.358161 5.18819i 0.0552655 0.800554i
\(43\) 11.3226i 1.72668i −0.504621 0.863341i \(-0.668368\pi\)
0.504621 0.863341i \(-0.331632\pi\)
\(44\) 9.21977 + 4.15011i 1.38993 + 0.625653i
\(45\) −2.40690 8.21186i −0.358799 1.22415i
\(46\) −3.49542 0.750439i −0.515371 0.110646i
\(47\) 10.3130 1.50431 0.752155 0.658986i \(-0.229014\pi\)
0.752155 + 0.658986i \(0.229014\pi\)
\(48\) −5.28391 4.48110i −0.762667 0.646792i
\(49\) 2.49241 0.356058
\(50\) 4.33675 + 0.931067i 0.613310 + 0.131673i
\(51\) 0.197814 + 1.37820i 0.0276994 + 0.192986i
\(52\) 2.65565 + 1.19539i 0.368273 + 0.165771i
\(53\) 11.2890i 1.55066i −0.631554 0.775332i \(-0.717583\pi\)
0.631554 0.775332i \(-0.282417\pi\)
\(54\) 7.17741 1.57632i 0.976722 0.214510i
\(55\) 14.4202i 1.94442i
\(56\) −3.55939 + 4.83648i −0.475643 + 0.646301i
\(57\) 0.902176 + 6.28559i 0.119496 + 0.832547i
\(58\) 2.48800 11.5887i 0.326690 1.52167i
\(59\) 4.56971 0.594926 0.297463 0.954733i \(-0.403860\pi\)
0.297463 + 0.954733i \(0.403860\pi\)
\(60\) −2.73457 + 9.49522i −0.353032 + 1.22583i
\(61\) −7.45650 −0.954707 −0.477353 0.878711i \(-0.658404\pi\)
−0.477353 + 0.878711i \(0.658404\pi\)
\(62\) 0.709581 3.30511i 0.0901168 0.419749i
\(63\) −1.79148 6.11219i −0.225706 0.770064i
\(64\) 2.37872 + 7.63817i 0.297340 + 0.954772i
\(65\) 4.15357i 0.515187i
\(66\) 12.3537 + 0.852826i 1.52064 + 0.104976i
\(67\) 1.00000i 0.122169i
\(68\) 0.659909 1.46603i 0.0800257 0.177783i
\(69\) −4.33413 + 0.622081i −0.521768 + 0.0748898i
\(70\) 8.37373 + 1.79777i 1.00085 + 0.214875i
\(71\) −15.5562 −1.84619 −0.923094 0.384576i \(-0.874348\pi\)
−0.923094 + 0.384576i \(0.874348\pi\)
\(72\) −7.97279 2.90425i −0.939602 0.342269i
\(73\) 0.104759 0.0122611 0.00613056 0.999981i \(-0.498049\pi\)
0.00613056 + 0.999981i \(0.498049\pi\)
\(74\) −2.12672 0.456590i −0.247226 0.0530775i
\(75\) 5.37734 0.771814i 0.620922 0.0891214i
\(76\) 3.00968 6.68621i 0.345233 0.766960i
\(77\) 10.7331i 1.22315i
\(78\) 3.55835 + 0.245647i 0.402904 + 0.0278141i
\(79\) 6.42169i 0.722496i −0.932470 0.361248i \(-0.882351\pi\)
0.932470 0.361248i \(-0.117649\pi\)
\(80\) 8.54120 7.56510i 0.954935 0.845804i
\(81\) 7.57600 4.85842i 0.841777 0.539825i
\(82\) −0.0496331 + 0.231183i −0.00548106 + 0.0255299i
\(83\) −11.4145 −1.25290 −0.626452 0.779460i \(-0.715494\pi\)
−0.626452 + 0.779460i \(0.715494\pi\)
\(84\) −2.03538 + 7.06741i −0.222078 + 0.771118i
\(85\) −2.29295 −0.248706
\(86\) −3.36119 + 15.6558i −0.362446 + 1.68821i
\(87\) −2.06244 14.3693i −0.221117 1.54055i
\(88\) −11.5162 8.47533i −1.22764 0.903473i
\(89\) 6.70211i 0.710422i 0.934786 + 0.355211i \(0.115591\pi\)
−0.934786 + 0.355211i \(0.884409\pi\)
\(90\) 0.890287 + 12.0691i 0.0938445 + 1.27219i
\(91\) 3.09156i 0.324083i
\(92\) 4.61037 + 2.07527i 0.480664 + 0.216362i
\(93\) −0.588211 4.09815i −0.0609947 0.424959i
\(94\) −14.2599 3.06149i −1.47080 0.315768i
\(95\) −10.4576 −1.07292
\(96\) 5.97585 + 7.76461i 0.609908 + 0.792472i
\(97\) −11.1470 −1.13181 −0.565904 0.824471i \(-0.691473\pi\)
−0.565904 + 0.824471i \(0.691473\pi\)
\(98\) −3.44627 0.739887i −0.348126 0.0747398i
\(99\) 14.5539 4.26574i 1.46272 0.428723i
\(100\) −5.72006 2.57478i −0.572006 0.257478i
\(101\) 7.50257i 0.746533i −0.927724 0.373267i \(-0.878238\pi\)
0.927724 0.373267i \(-0.121762\pi\)
\(102\) 0.135608 1.96436i 0.0134272 0.194501i
\(103\) 10.6120i 1.04563i −0.852445 0.522817i \(-0.824881\pi\)
0.852445 0.522817i \(-0.175119\pi\)
\(104\) −3.31713 2.44123i −0.325271 0.239382i
\(105\) 10.3830 1.49028i 1.01327 0.145436i
\(106\) −3.35121 + 15.6094i −0.325498 + 1.51612i
\(107\) 8.88638 0.859079 0.429539 0.903048i \(-0.358676\pi\)
0.429539 + 0.903048i \(0.358676\pi\)
\(108\) −10.3922 + 0.0489252i −0.999989 + 0.00470783i
\(109\) 3.23863 0.310205 0.155102 0.987898i \(-0.450429\pi\)
0.155102 + 0.987898i \(0.450429\pi\)
\(110\) −4.28072 + 19.9389i −0.408151 + 1.90110i
\(111\) −2.63702 + 0.378493i −0.250295 + 0.0359250i
\(112\) 6.35732 5.63080i 0.600710 0.532061i
\(113\) 11.6367i 1.09469i 0.836908 + 0.547344i \(0.184361\pi\)
−0.836908 + 0.547344i \(0.815639\pi\)
\(114\) 0.618472 8.95895i 0.0579252 0.839082i
\(115\) 7.21085i 0.672415i
\(116\) −6.88034 + 15.2852i −0.638824 + 1.41919i
\(117\) 4.19208 1.22870i 0.387558 0.113593i
\(118\) −6.31857 1.35655i −0.581671 0.124880i
\(119\) −1.70667 −0.156451
\(120\) 6.59982 12.3173i 0.602479 1.12441i
\(121\) 14.5569 1.32335
\(122\) 10.3101 + 2.21351i 0.933437 + 0.200402i
\(123\) 0.0411437 + 0.286654i 0.00370980 + 0.0258467i
\(124\) −1.96228 + 4.35935i −0.176218 + 0.391481i
\(125\) 5.31574i 0.475454i
\(126\) 0.662652 + 8.98318i 0.0590338 + 0.800285i
\(127\) 8.64258i 0.766905i 0.923561 + 0.383453i \(0.125265\pi\)
−0.923561 + 0.383453i \(0.874735\pi\)
\(128\) −1.02163 11.2675i −0.0903001 0.995915i
\(129\) 2.78628 + 19.4124i 0.245318 + 1.70917i
\(130\) −1.23301 + 5.74317i −0.108142 + 0.503710i
\(131\) 1.46011 0.127570 0.0637851 0.997964i \(-0.479683\pi\)
0.0637851 + 0.997964i \(0.479683\pi\)
\(132\) −16.8284 4.84648i −1.46472 0.421832i
\(133\) −7.78370 −0.674932
\(134\) 0.296856 1.38271i 0.0256445 0.119448i
\(135\) 6.14736 + 13.4868i 0.529080 + 1.16076i
\(136\) −1.34766 + 1.83120i −0.115561 + 0.157024i
\(137\) 15.1807i 1.29697i 0.761226 + 0.648486i \(0.224598\pi\)
−0.761226 + 0.648486i \(0.775402\pi\)
\(138\) 6.17750 + 0.426458i 0.525864 + 0.0363025i
\(139\) 6.98434i 0.592404i −0.955125 0.296202i \(-0.904280\pi\)
0.955125 0.296202i \(-0.0957201\pi\)
\(140\) −11.0447 4.97159i −0.933450 0.420176i
\(141\) −17.6815 + 2.53784i −1.48905 + 0.213725i
\(142\) 21.5097 + 4.61797i 1.80506 + 0.387531i
\(143\) 7.36138 0.615589
\(144\) 10.1619 + 6.38250i 0.846823 + 0.531875i
\(145\) 23.9068 1.98535
\(146\) −0.144851 0.0310984i −0.0119880 0.00257372i
\(147\) −4.27319 + 0.613334i −0.352446 + 0.0505869i
\(148\) 2.80509 + 1.26266i 0.230577 + 0.103790i
\(149\) 22.7781i 1.86606i −0.359802 0.933029i \(-0.617156\pi\)
0.359802 0.933029i \(-0.382844\pi\)
\(150\) −7.66440 0.529104i −0.625796 0.0432012i
\(151\) 18.4108i 1.49825i 0.662427 + 0.749126i \(0.269526\pi\)
−0.662427 + 0.749126i \(0.730474\pi\)
\(152\) −6.14634 + 8.35162i −0.498534 + 0.677406i
\(153\) −0.678295 2.31421i −0.0548369 0.187093i
\(154\) −3.18619 + 14.8408i −0.256751 + 1.19590i
\(155\) 6.81824 0.547654
\(156\) −4.84723 1.39598i −0.388089 0.111767i
\(157\) −20.6893 −1.65119 −0.825595 0.564264i \(-0.809160\pi\)
−0.825595 + 0.564264i \(0.809160\pi\)
\(158\) −1.90632 + 8.87931i −0.151658 + 0.706400i
\(159\) 2.77801 + 19.3548i 0.220310 + 1.53493i
\(160\) −14.0557 + 7.92481i −1.11120 + 0.626511i
\(161\) 5.36712i 0.422989i
\(162\) −11.9176 + 4.46879i −0.936338 + 0.351101i
\(163\) 19.3440i 1.51514i 0.652755 + 0.757569i \(0.273613\pi\)
−0.652755 + 0.757569i \(0.726387\pi\)
\(164\) 0.137256 0.304924i 0.0107179 0.0238106i
\(165\) 3.54853 + 24.7231i 0.276253 + 1.92469i
\(166\) 15.7829 + 3.38847i 1.22499 + 0.262996i
\(167\) −11.2352 −0.869403 −0.434702 0.900575i \(-0.643146\pi\)
−0.434702 + 0.900575i \(0.643146\pi\)
\(168\) 4.91233 9.16794i 0.378995 0.707322i
\(169\) −10.8796 −0.836895
\(170\) 3.17048 + 0.680677i 0.243165 + 0.0522055i
\(171\) −3.09353 10.5545i −0.236568 0.807124i
\(172\) 9.29507 20.6496i 0.708742 1.57452i
\(173\) 2.96270i 0.225250i −0.993638 0.112625i \(-0.964074\pi\)
0.993638 0.112625i \(-0.0359259\pi\)
\(174\) −1.41387 + 20.4808i −0.107185 + 1.55265i
\(175\) 6.65897i 0.503371i
\(176\) 13.4076 + 15.1376i 1.01064 + 1.14104i
\(177\) −7.83468 + 1.12452i −0.588891 + 0.0845240i
\(178\) 1.98956 9.26705i 0.149124 0.694594i
\(179\) 23.1507 1.73036 0.865182 0.501457i \(-0.167203\pi\)
0.865182 + 0.501457i \(0.167203\pi\)
\(180\) 2.35178 16.9523i 0.175291 1.26355i
\(181\) 5.97889 0.444408 0.222204 0.975000i \(-0.428675\pi\)
0.222204 + 0.975000i \(0.428675\pi\)
\(182\) −0.917748 + 4.27472i −0.0680280 + 0.316863i
\(183\) 12.7840 1.83490i 0.945022 0.135640i
\(184\) −5.75872 4.23811i −0.424539 0.312438i
\(185\) 4.38730i 0.322561i
\(186\) −0.403239 + 5.84116i −0.0295669 + 0.428294i
\(187\) 4.06380i 0.297174i
\(188\) 18.8084 + 8.46627i 1.37175 + 0.617467i
\(189\) 4.57556 + 10.0384i 0.332823 + 0.730185i
\(190\) 14.4597 + 3.10439i 1.04902 + 0.225216i
\(191\) 12.2895 0.889238 0.444619 0.895720i \(-0.353339\pi\)
0.444619 + 0.895720i \(0.353339\pi\)
\(192\) −5.95787 12.5101i −0.429972 0.902842i
\(193\) −2.14293 −0.154252 −0.0771259 0.997021i \(-0.524574\pi\)
−0.0771259 + 0.997021i \(0.524574\pi\)
\(194\) 15.4131 + 3.30906i 1.10659 + 0.237577i
\(195\) 1.02211 + 7.12122i 0.0731952 + 0.509961i
\(196\) 4.54554 + 2.04609i 0.324681 + 0.146149i
\(197\) 13.7192i 0.977452i 0.872437 + 0.488726i \(0.162538\pi\)
−0.872437 + 0.488726i \(0.837462\pi\)
\(198\) −21.3900 + 1.57786i −1.52012 + 0.112133i
\(199\) 9.05671i 0.642013i 0.947077 + 0.321006i \(0.104021\pi\)
−0.947077 + 0.321006i \(0.895979\pi\)
\(200\) 7.14483 + 5.25821i 0.505216 + 0.371811i
\(201\) −0.246081 1.71448i −0.0173572 0.120930i
\(202\) −2.22718 + 10.3738i −0.156704 + 0.729901i
\(203\) 17.7941 1.24890
\(204\) −0.770638 + 2.67588i −0.0539555 + 0.187349i
\(205\) −0.476917 −0.0333093
\(206\) −3.15025 + 14.6733i −0.219488 + 1.02234i
\(207\) 7.27770 2.13309i 0.505835 0.148260i
\(208\) 3.86192 + 4.36021i 0.267776 + 0.302326i
\(209\) 18.5339i 1.28202i
\(210\) −14.7990 1.02163i −1.02123 0.0704995i
\(211\) 11.8674i 0.816987i −0.912761 0.408494i \(-0.866054\pi\)
0.912761 0.408494i \(-0.133946\pi\)
\(212\) 9.26748 20.5884i 0.636493 1.41401i
\(213\) 26.6709 3.82809i 1.82746 0.262297i
\(214\) −12.2873 2.63798i −0.839939 0.180328i
\(215\) −32.2971 −2.20264
\(216\) 14.3839 + 3.01734i 0.978698 + 0.205304i
\(217\) 5.07491 0.344507
\(218\) −4.47808 0.961408i −0.303294 0.0651147i
\(219\) −0.179607 + 0.0257792i −0.0121367 + 0.00174200i
\(220\) 11.8380 26.2988i 0.798115 1.77307i
\(221\) 1.17053i 0.0787385i
\(222\) 3.75858 + 0.259470i 0.252259 + 0.0174145i
\(223\) 3.55716i 0.238205i 0.992882 + 0.119102i \(0.0380017\pi\)
−0.992882 + 0.119102i \(0.961998\pi\)
\(224\) −10.4618 + 5.89853i −0.699012 + 0.394112i
\(225\) −9.02942 + 2.64652i −0.601961 + 0.176435i
\(226\) 3.45442 16.0901i 0.229785 1.07030i
\(227\) −7.87327 −0.522567 −0.261284 0.965262i \(-0.584146\pi\)
−0.261284 + 0.965262i \(0.584146\pi\)
\(228\) −3.51468 + 12.2040i −0.232766 + 0.808229i
\(229\) −9.51932 −0.629054 −0.314527 0.949248i \(-0.601846\pi\)
−0.314527 + 0.949248i \(0.601846\pi\)
\(230\) −2.14058 + 9.97048i −0.141146 + 0.657434i
\(231\) 2.64122 + 18.4017i 0.173779 + 1.21075i
\(232\) 14.0510 19.0924i 0.922492 1.25348i
\(233\) 21.2749i 1.39376i 0.717186 + 0.696882i \(0.245430\pi\)
−0.717186 + 0.696882i \(0.754570\pi\)
\(234\) −6.16117 + 0.454484i −0.402768 + 0.0297105i
\(235\) 29.4173i 1.91897i
\(236\) 8.33402 + 3.75141i 0.542499 + 0.244196i
\(237\) 1.58025 + 11.0099i 0.102649 + 0.715167i
\(238\) 2.35983 + 0.506637i 0.152965 + 0.0328404i
\(239\) −2.42407 −0.156800 −0.0783999 0.996922i \(-0.524981\pi\)
−0.0783999 + 0.996922i \(0.524981\pi\)
\(240\) −12.7821 + 15.0720i −0.825080 + 0.972896i
\(241\) −7.40619 −0.477075 −0.238537 0.971133i \(-0.576668\pi\)
−0.238537 + 0.971133i \(0.576668\pi\)
\(242\) −20.1279 4.32130i −1.29387 0.277784i
\(243\) −11.7933 + 10.1940i −0.756543 + 0.653944i
\(244\) −13.5988 6.12126i −0.870575 0.391874i
\(245\) 7.10945i 0.454206i
\(246\) 0.0282054 0.408572i 0.00179831 0.0260496i
\(247\) 5.33850i 0.339680i
\(248\) 4.00736 5.44518i 0.254468 0.345769i
\(249\) 19.5699 2.80889i 1.24020 0.178006i
\(250\) −1.57801 + 7.35011i −0.0998021 + 0.464862i
\(251\) −3.61478 −0.228163 −0.114081 0.993471i \(-0.536392\pi\)
−0.114081 + 0.993471i \(0.536392\pi\)
\(252\) 1.75046 12.6178i 0.110269 0.794848i
\(253\) 12.7798 0.803458
\(254\) 2.56560 11.9502i 0.160980 0.749819i
\(255\) 3.93122 0.564252i 0.246183 0.0353348i
\(256\) −1.93221 + 15.8829i −0.120763 + 0.992681i
\(257\) 6.59715i 0.411519i 0.978603 + 0.205759i \(0.0659664\pi\)
−0.978603 + 0.205759i \(0.934034\pi\)
\(258\) 1.91009 27.6688i 0.118917 1.72258i
\(259\) 3.26552i 0.202910i
\(260\) 3.40979 7.57509i 0.211466 0.469787i
\(261\) 7.07204 + 24.1284i 0.437748 + 1.49351i
\(262\) −2.01890 0.433442i −0.124728 0.0267781i
\(263\) −23.6376 −1.45756 −0.728780 0.684748i \(-0.759912\pi\)
−0.728780 + 0.684748i \(0.759912\pi\)
\(264\) 21.8300 + 11.6969i 1.34354 + 0.719892i
\(265\) −32.2012 −1.97811
\(266\) 10.7626 + 2.31064i 0.659895 + 0.141674i
\(267\) −1.64926 11.4906i −0.100933 0.703215i
\(268\) −0.820930 + 1.82375i −0.0501463 + 0.111403i
\(269\) 18.1628i 1.10741i −0.832714 0.553704i \(-0.813214\pi\)
0.832714 0.553704i \(-0.186786\pi\)
\(270\) −4.49635 20.4731i −0.273639 1.24596i
\(271\) 14.8714i 0.903373i 0.892177 + 0.451687i \(0.149178\pi\)
−0.892177 + 0.451687i \(0.850822\pi\)
\(272\) 2.40702 2.13195i 0.145947 0.129268i
\(273\) 0.760773 + 5.30042i 0.0460441 + 0.320796i
\(274\) 4.50648 20.9904i 0.272246 1.26808i
\(275\) −15.8558 −0.956142
\(276\) −8.41507 2.42349i −0.506528 0.145877i
\(277\) −1.90014 −0.114168 −0.0570842 0.998369i \(-0.518180\pi\)
−0.0570842 + 0.998369i \(0.518180\pi\)
\(278\) −2.07334 + 9.65729i −0.124351 + 0.579206i
\(279\) 2.01695 + 6.88146i 0.120752 + 0.411982i
\(280\) 13.7958 + 10.1529i 0.824455 + 0.606754i
\(281\) 16.5030i 0.984487i 0.870458 + 0.492243i \(0.163823\pi\)
−0.870458 + 0.492243i \(0.836177\pi\)
\(282\) 25.2017 + 1.73977i 1.50074 + 0.103602i
\(283\) 1.11291i 0.0661559i −0.999453 0.0330780i \(-0.989469\pi\)
0.999453 0.0330780i \(-0.0105310\pi\)
\(284\) −28.3708 12.7706i −1.68349 0.757795i
\(285\) 17.9293 2.57341i 1.06204 0.152435i
\(286\) −10.1786 2.18527i −0.601875 0.129218i
\(287\) −0.354975 −0.0209535
\(288\) −12.1562 11.8417i −0.716311 0.697781i
\(289\) 16.3538 0.961989
\(290\) −33.0560 7.09687i −1.94112 0.416743i
\(291\) 19.1114 2.74307i 1.12033 0.160802i
\(292\) 0.191055 + 0.0859998i 0.0111806 + 0.00503276i
\(293\) 27.9266i 1.63149i −0.578411 0.815745i \(-0.696327\pi\)
0.578411 0.815745i \(-0.303673\pi\)
\(294\) 6.09063 + 0.420461i 0.355213 + 0.0245218i
\(295\) 13.0348i 0.758917i
\(296\) −3.50379 2.57860i −0.203653 0.149878i
\(297\) −23.9026 + 10.8950i −1.38697 + 0.632190i
\(298\) −6.76183 + 31.4955i −0.391702 + 1.82448i
\(299\) 3.68107 0.212882
\(300\) 10.4405 + 3.00682i 0.602785 + 0.173599i
\(301\) −24.0391 −1.38559
\(302\) 5.46537 25.4568i 0.314497 1.46487i
\(303\) 1.84624 + 12.8630i 0.106064 + 0.738960i
\(304\) 10.9778 9.72325i 0.629620 0.557667i
\(305\) 21.2692i 1.21787i
\(306\) 0.250895 + 3.40123i 0.0143427 + 0.194435i
\(307\) 28.0248i 1.59946i 0.600358 + 0.799731i \(0.295025\pi\)
−0.600358 + 0.799731i \(0.704975\pi\)
\(308\) 8.81114 19.5746i 0.502061 1.11536i
\(309\) 2.61142 + 18.1941i 0.148558 + 1.03503i
\(310\) −9.42763 2.02404i −0.535453 0.114958i
\(311\) 18.7867 1.06529 0.532647 0.846338i \(-0.321197\pi\)
0.532647 + 0.846338i \(0.321197\pi\)
\(312\) 6.28789 + 3.36915i 0.355982 + 0.190741i
\(313\) 23.2463 1.31396 0.656980 0.753908i \(-0.271833\pi\)
0.656980 + 0.753908i \(0.271833\pi\)
\(314\) 28.6073 + 6.14176i 1.61440 + 0.346599i
\(315\) −17.4347 + 5.11010i −0.982333 + 0.287922i
\(316\) 5.27175 11.7116i 0.296559 0.658827i
\(317\) 10.0106i 0.562254i −0.959671 0.281127i \(-0.909292\pi\)
0.959671 0.281127i \(-0.0907082\pi\)
\(318\) 1.90442 27.5866i 0.106794 1.54698i
\(319\) 42.3700i 2.37226i
\(320\) 21.7874 6.78515i 1.21796 0.379302i
\(321\) −15.2355 + 2.18677i −0.850364 + 0.122053i
\(322\) −1.59326 + 7.42116i −0.0887891 + 0.413565i
\(323\) −2.94708 −0.163980
\(324\) 17.8052 2.64120i 0.989176 0.146733i
\(325\) −4.56709 −0.253337
\(326\) 5.74238 26.7471i 0.318041 1.48138i
\(327\) −5.55257 + 0.796965i −0.307058 + 0.0440723i
\(328\) −0.280303 + 0.380875i −0.0154772 + 0.0210303i
\(329\) 21.8957i 1.20715i
\(330\) 2.43264 35.2382i 0.133912 1.93980i
\(331\) 8.21433i 0.451500i −0.974185 0.225750i \(-0.927517\pi\)
0.974185 0.225750i \(-0.0724833\pi\)
\(332\) −20.8172 9.37050i −1.14249 0.514273i
\(333\) 4.42798 1.29784i 0.242652 0.0711212i
\(334\) 15.5349 + 3.33523i 0.850034 + 0.182496i
\(335\) 2.85244 0.155846
\(336\) −9.51387 + 11.2183i −0.519024 + 0.612009i
\(337\) −4.38801 −0.239030 −0.119515 0.992832i \(-0.538134\pi\)
−0.119515 + 0.992832i \(0.538134\pi\)
\(338\) 15.0433 + 3.22969i 0.818250 + 0.175672i
\(339\) −2.86357 19.9509i −0.155528 1.08358i
\(340\) −4.18178 1.88235i −0.226789 0.102085i
\(341\) 12.0840i 0.654384i
\(342\) 1.14427 + 15.5121i 0.0618748 + 0.838800i
\(343\) 20.1534i 1.08818i
\(344\) −18.9823 + 25.7931i −1.02346 + 1.39067i
\(345\) 1.77445 + 12.3629i 0.0955332 + 0.665594i
\(346\) −0.879496 + 4.09655i −0.0472820 + 0.220232i
\(347\) 32.4290 1.74088 0.870441 0.492273i \(-0.163834\pi\)
0.870441 + 0.492273i \(0.163834\pi\)
\(348\) 8.03483 27.8992i 0.430712 1.49556i
\(349\) −9.03367 −0.483562 −0.241781 0.970331i \(-0.577731\pi\)
−0.241781 + 0.970331i \(0.577731\pi\)
\(350\) 1.97676 9.20740i 0.105662 0.492156i
\(351\) −6.88489 + 3.13817i −0.367488 + 0.167503i
\(352\) −14.0451 24.9109i −0.748608 1.32776i
\(353\) 37.0762i 1.97337i −0.162653 0.986683i \(-0.552005\pi\)
0.162653 0.986683i \(-0.447995\pi\)
\(354\) 11.1669 + 0.770895i 0.593513 + 0.0409726i
\(355\) 44.3733i 2.35509i
\(356\) −5.50196 + 12.2230i −0.291603 + 0.647817i
\(357\) 2.92606 0.419980i 0.154863 0.0222277i
\(358\) −32.0106 6.87243i −1.69181 0.363219i
\(359\) −6.59057 −0.347837 −0.173918 0.984760i \(-0.555643\pi\)
−0.173918 + 0.984760i \(0.555643\pi\)
\(360\) −8.28421 + 22.7419i −0.436616 + 1.19860i
\(361\) 5.55913 0.292586
\(362\) −8.26705 1.77487i −0.434507 0.0932852i
\(363\) −24.9575 + 3.58217i −1.30993 + 0.188015i
\(364\) 2.53795 5.63824i 0.133025 0.295524i
\(365\) 0.298819i 0.0156409i
\(366\) −18.2213 1.25789i −0.952440 0.0657508i
\(367\) 10.1782i 0.531298i −0.964070 0.265649i \(-0.914414\pi\)
0.964070 0.265649i \(-0.0855862\pi\)
\(368\) 6.70451 + 7.56957i 0.349497 + 0.394591i
\(369\) −0.141080 0.481338i −0.00734434 0.0250575i
\(370\) −1.30240 + 6.06635i −0.0677084 + 0.315374i
\(371\) −23.9678 −1.24435
\(372\) 2.29154 7.95690i 0.118811 0.412546i
\(373\) 1.30447 0.0675429 0.0337715 0.999430i \(-0.489248\pi\)
0.0337715 + 0.999430i \(0.489248\pi\)
\(374\) −1.20636 + 5.61904i −0.0623796 + 0.290554i
\(375\) 1.30810 + 9.11373i 0.0675501 + 0.470631i
\(376\) −23.4933 17.2898i −1.21157 0.891652i
\(377\) 12.2042i 0.628548i
\(378\) −3.34669 15.2384i −0.172135 0.783780i
\(379\) 16.4614i 0.845567i 0.906231 + 0.422783i \(0.138947\pi\)
−0.906231 + 0.422783i \(0.861053\pi\)
\(380\) −19.0720 8.58492i −0.978374 0.440397i
\(381\) −2.12677 14.8175i −0.108958 0.759126i
\(382\) −16.9928 3.64822i −0.869427 0.186659i
\(383\) −34.5749 −1.76669 −0.883347 0.468719i \(-0.844716\pi\)
−0.883347 + 0.468719i \(0.844716\pi\)
\(384\) 4.52428 + 19.0665i 0.230878 + 0.972983i
\(385\) −30.6156 −1.56032
\(386\) 2.96305 + 0.636143i 0.150815 + 0.0323788i
\(387\) −9.55404 32.5965i −0.485659 1.65698i
\(388\) −20.3294 9.15092i −1.03207 0.464568i
\(389\) 19.6800i 0.997815i −0.866655 0.498908i \(-0.833735\pi\)
0.866655 0.498908i \(-0.166265\pi\)
\(390\) 0.700694 10.1500i 0.0354810 0.513964i
\(391\) 2.03211i 0.102768i
\(392\) −5.67775 4.17851i −0.286769 0.211047i
\(393\) −2.50333 + 0.359304i −0.126276 + 0.0181245i
\(394\) 4.07262 18.9696i 0.205176 0.955675i
\(395\) −18.3175 −0.921653
\(396\) 30.0445 + 4.16806i 1.50980 + 0.209453i
\(397\) 35.8383 1.79867 0.899337 0.437256i \(-0.144050\pi\)
0.899337 + 0.437256i \(0.144050\pi\)
\(398\) 2.68854 12.5228i 0.134764 0.627709i
\(399\) 13.3450 1.91542i 0.668086 0.0958909i
\(400\) −8.31827 9.39154i −0.415913 0.469577i
\(401\) 4.40721i 0.220086i −0.993927 0.110043i \(-0.964901\pi\)
0.993927 0.110043i \(-0.0350988\pi\)
\(402\) −0.168697 + 2.44367i −0.00841382 + 0.121879i
\(403\) 3.48065i 0.173384i
\(404\) 6.15908 13.6828i 0.306426 0.680746i
\(405\) −13.8584 21.6101i −0.688628 1.07381i
\(406\) −24.6040 5.28229i −1.22108 0.262156i
\(407\) 7.77561 0.385423
\(408\) 1.85992 3.47119i 0.0920796 0.171849i
\(409\) 36.5773 1.80863 0.904316 0.426864i \(-0.140382\pi\)
0.904316 + 0.426864i \(0.140382\pi\)
\(410\) 0.659436 + 0.141576i 0.0325672 + 0.00699192i
\(411\) −3.73567 26.0270i −0.184267 1.28382i
\(412\) 8.71173 19.3537i 0.429196 0.953490i
\(413\) 9.70200i 0.477404i
\(414\) −10.6961 + 0.789011i −0.525687 + 0.0387778i
\(415\) 32.5592i 1.59827i
\(416\) −4.04554 7.17532i −0.198349 0.351799i
\(417\) 1.71871 + 11.9745i 0.0841657 + 0.586395i
\(418\) −5.50191 + 25.6270i −0.269107 + 1.25346i
\(419\) −4.31729 −0.210914 −0.105457 0.994424i \(-0.533630\pi\)
−0.105457 + 0.994424i \(0.533630\pi\)
\(420\) 20.1594 + 5.80579i 0.983677 + 0.283294i
\(421\) 1.17156 0.0570982 0.0285491 0.999592i \(-0.490911\pi\)
0.0285491 + 0.999592i \(0.490911\pi\)
\(422\) −3.52292 + 16.4092i −0.171493 + 0.798786i
\(423\) 29.6901 8.70215i 1.44358 0.423113i
\(424\) −18.9260 + 25.7165i −0.919127 + 1.24891i
\(425\) 2.52123i 0.122298i
\(426\) −38.0144 2.62429i −1.84180 0.127147i
\(427\) 15.8310i 0.766114i
\(428\) 16.2066 + 7.29509i 0.783374 + 0.352622i
\(429\) −12.6209 + 1.81149i −0.609345 + 0.0874597i
\(430\) 44.6574 + 9.58759i 2.15357 + 0.462355i
\(431\) 20.4106 0.983144 0.491572 0.870837i \(-0.336423\pi\)
0.491572 + 0.870837i \(0.336423\pi\)
\(432\) −18.9929 8.44203i −0.913799 0.406167i
\(433\) 9.00788 0.432891 0.216445 0.976295i \(-0.430554\pi\)
0.216445 + 0.976295i \(0.430554\pi\)
\(434\) −7.01710 1.50652i −0.336832 0.0723151i
\(435\) −40.9877 + 5.88300i −1.96521 + 0.282068i
\(436\) 5.90646 + 2.65869i 0.282868 + 0.127328i
\(437\) 9.26794i 0.443346i
\(438\) 0.255997 + 0.0176725i 0.0122320 + 0.000844425i
\(439\) 21.3555i 1.01924i −0.860399 0.509621i \(-0.829786\pi\)
0.860399 0.509621i \(-0.170214\pi\)
\(440\) −24.1754 + 32.8494i −1.15252 + 1.56603i
\(441\) 7.17536 2.10310i 0.341684 0.100148i
\(442\) −0.347480 + 1.61850i −0.0165279 + 0.0769843i
\(443\) 13.0837 0.621625 0.310812 0.950471i \(-0.399399\pi\)
0.310812 + 0.950471i \(0.399399\pi\)
\(444\) −5.11999 1.47453i −0.242984 0.0699780i
\(445\) 19.1174 0.906250
\(446\) 1.05596 4.91850i 0.0500013 0.232898i
\(447\) 5.60526 + 39.0527i 0.265120 + 1.84713i
\(448\) 16.2167 5.05028i 0.766166 0.238603i
\(449\) 28.1175i 1.32695i 0.748199 + 0.663474i \(0.230919\pi\)
−0.748199 + 0.663474i \(0.769081\pi\)
\(450\) 13.2707 0.978922i 0.625585 0.0461468i
\(451\) 0.845239i 0.0398008i
\(452\) −9.55290 + 21.2224i −0.449331 + 0.998220i
\(453\) −4.53055 31.5650i −0.212864 1.48305i
\(454\) 10.8864 + 2.33723i 0.510925 + 0.109692i
\(455\) −8.81849 −0.413417
\(456\) 8.48260 15.8312i 0.397234 0.741363i
\(457\) 27.2212 1.27336 0.636678 0.771130i \(-0.280308\pi\)
0.636678 + 0.771130i \(0.280308\pi\)
\(458\) 13.1624 + 2.82587i 0.615040 + 0.132044i
\(459\) 1.73241 + 3.80076i 0.0808618 + 0.177404i
\(460\) 5.91960 13.1508i 0.276003 0.613159i
\(461\) 18.3120i 0.852877i −0.904517 0.426438i \(-0.859768\pi\)
0.904517 0.426438i \(-0.140232\pi\)
\(462\) 1.81064 26.2283i 0.0842387 1.22025i
\(463\) 10.0274i 0.466012i 0.972475 + 0.233006i \(0.0748562\pi\)
−0.972475 + 0.233006i \(0.925144\pi\)
\(464\) −25.0961 + 22.2281i −1.16506 + 1.03191i
\(465\) −11.6897 + 1.67784i −0.542099 + 0.0778079i
\(466\) 6.31558 29.4169i 0.292563 1.36271i
\(467\) 13.3284 0.616765 0.308383 0.951262i \(-0.400212\pi\)
0.308383 + 0.951262i \(0.400212\pi\)
\(468\) 8.65400 + 1.20056i 0.400031 + 0.0554960i
\(469\) 2.12311 0.0980361
\(470\) −8.73271 + 40.6755i −0.402810 + 1.87622i
\(471\) 35.4715 5.09125i 1.63444 0.234592i
\(472\) −10.4099 7.66111i −0.479153 0.352631i
\(473\) 57.2401i 2.63190i
\(474\) 1.08332 15.6925i 0.0497584 0.720781i
\(475\) 11.4987i 0.527596i
\(476\) −3.11255 1.40106i −0.142664 0.0642174i
\(477\) −9.52568 32.4998i −0.436151 1.48806i
\(478\) 3.35177 + 0.719599i 0.153306 + 0.0329137i
\(479\) 7.57165 0.345958 0.172979 0.984926i \(-0.444661\pi\)
0.172979 + 0.984926i \(0.444661\pi\)
\(480\) 22.1481 17.0458i 1.01092 0.778029i
\(481\) 2.23968 0.102121
\(482\) 10.2406 + 2.19857i 0.466446 + 0.100142i
\(483\) 1.32075 + 9.20183i 0.0600960 + 0.418698i
\(484\) 26.5481 + 11.9502i 1.20673 + 0.543190i
\(485\) 31.7962i 1.44379i
\(486\) 19.3329 10.5944i 0.876957 0.480570i
\(487\) 27.0871i 1.22743i 0.789527 + 0.613716i \(0.210326\pi\)
−0.789527 + 0.613716i \(0.789674\pi\)
\(488\) 16.9860 + 12.5008i 0.768921 + 0.565884i
\(489\) −4.76019 33.1649i −0.215263 1.49977i
\(490\) −2.11048 + 9.83028i −0.0953419 + 0.444087i
\(491\) −5.08156 −0.229328 −0.114664 0.993404i \(-0.536579\pi\)
−0.114664 + 0.993404i \(0.536579\pi\)
\(492\) −0.160287 + 0.556563i −0.00722630 + 0.0250918i
\(493\) 6.73724 0.303430
\(494\) −1.58477 + 7.38157i −0.0713020 + 0.332113i
\(495\) −12.1678 41.5141i −0.546901 1.86592i
\(496\) −7.15744 + 6.33948i −0.321378 + 0.284651i
\(497\) 33.0276i 1.48149i
\(498\) −27.8933 1.92559i −1.24993 0.0862877i
\(499\) 15.9343i 0.713318i 0.934235 + 0.356659i \(0.116084\pi\)
−0.934235 + 0.356659i \(0.883916\pi\)
\(500\) 4.36385 9.69460i 0.195157 0.433556i
\(501\) 19.2625 2.76476i 0.860584 0.123520i
\(502\) 4.99818 + 1.07307i 0.223080 + 0.0478934i
\(503\) 39.2197 1.74872 0.874359 0.485280i \(-0.161282\pi\)
0.874359 + 0.485280i \(0.161282\pi\)
\(504\) −6.16605 + 16.9271i −0.274658 + 0.753993i
\(505\) −21.4006 −0.952316
\(506\) −17.6707 3.79376i −0.785557 0.168653i
\(507\) 18.6529 2.67727i 0.828406 0.118902i
\(508\) −7.09495 + 15.7619i −0.314788 + 0.699323i
\(509\) 7.49202i 0.332078i −0.986119 0.166039i \(-0.946902\pi\)
0.986119 0.166039i \(-0.0530978\pi\)
\(510\) −5.60323 0.386813i −0.248115 0.0171284i
\(511\) 0.222415i 0.00983905i
\(512\) 7.38662 21.3878i 0.326445 0.945216i
\(513\) 7.90106 + 17.3343i 0.348840 + 0.765327i
\(514\) 1.95840 9.12192i 0.0863815 0.402351i
\(515\) −30.2702 −1.33386
\(516\) −10.8547 + 37.6908i −0.477853 + 1.65924i
\(517\) 52.1363 2.29295
\(518\) −0.969391 + 4.51526i −0.0425926 + 0.198389i
\(519\) 0.729064 + 5.07950i 0.0320024 + 0.222965i
\(520\) −6.96345 + 9.46191i −0.305368 + 0.414932i
\(521\) 6.35296i 0.278328i −0.990269 0.139164i \(-0.955558\pi\)
0.990269 0.139164i \(-0.0444416\pi\)
\(522\) −2.61588 35.4619i −0.114494 1.55213i
\(523\) 11.5021i 0.502952i 0.967864 + 0.251476i \(0.0809159\pi\)
−0.967864 + 0.251476i \(0.919084\pi\)
\(524\) 2.66287 + 1.19865i 0.116328 + 0.0523631i
\(525\) −1.63865 11.4167i −0.0715163 0.498265i
\(526\) 32.6839 + 7.01698i 1.42509 + 0.305955i
\(527\) 1.92147 0.0837006
\(528\) −26.7122 22.6537i −1.16250 0.985875i
\(529\) −16.6094 −0.722150
\(530\) 44.5248 + 9.55913i 1.93404 + 0.415222i
\(531\) 13.1557 3.85593i 0.570908 0.167333i
\(532\) −14.1955 6.38987i −0.615455 0.277036i
\(533\) 0.243462i 0.0105455i
\(534\) −1.13062 + 16.3778i −0.0489268 + 0.708735i
\(535\) 25.3479i 1.09588i
\(536\) 1.67650 2.27802i 0.0724136 0.0983953i
\(537\) −39.6914 + 5.69694i −1.71281 + 0.245841i
\(538\) −5.39175 + 25.1139i −0.232455 + 1.08274i
\(539\) 12.6001 0.542723
\(540\) 0.139556 + 29.6431i 0.00600555 + 1.27564i
\(541\) −23.7717 −1.02202 −0.511012 0.859573i \(-0.670729\pi\)
−0.511012 + 0.859573i \(0.670729\pi\)
\(542\) 4.41467 20.5628i 0.189626 0.883247i
\(543\) −10.2507 + 1.47129i −0.439900 + 0.0631391i
\(544\) −3.96109 + 2.23331i −0.169830 + 0.0957526i
\(545\) 9.23801i 0.395713i
\(546\) 0.521536 7.55476i 0.0223197 0.323314i
\(547\) 6.10422i 0.260998i −0.991448 0.130499i \(-0.958342\pi\)
0.991448 0.130499i \(-0.0416579\pi\)
\(548\) −12.4623 + 27.6858i −0.532362 + 1.18268i
\(549\) −21.4664 + 6.29181i −0.916165 + 0.268528i
\(550\) 21.9239 + 4.70690i 0.934840 + 0.200703i
\(551\) 30.7268 1.30901
\(552\) 10.9161 + 5.84904i 0.464622 + 0.248952i
\(553\) −13.6339 −0.579774
\(554\) 2.62734 + 0.564069i 0.111625 + 0.0239650i
\(555\) 1.07963 + 7.52194i 0.0458278 + 0.319289i
\(556\) 5.73365 12.7377i 0.243161 0.540199i
\(557\) 21.7496i 0.921561i 0.887514 + 0.460781i \(0.152430\pi\)
−0.887514 + 0.460781i \(0.847570\pi\)
\(558\) −0.746052 10.1138i −0.0315829 0.428150i
\(559\) 16.4874i 0.697342i
\(560\) −16.0615 18.1339i −0.678724 0.766297i
\(561\) 1.00002 + 6.96730i 0.0422210 + 0.294160i
\(562\) 4.89902 22.8188i 0.206653 0.962553i
\(563\) −32.0628 −1.35128 −0.675642 0.737230i \(-0.736134\pi\)
−0.675642 + 0.737230i \(0.736134\pi\)
\(564\) −34.3301 9.88687i −1.44556 0.416312i
\(565\) 33.1930 1.39644
\(566\) −0.330376 + 1.53883i −0.0138867 + 0.0646820i
\(567\) −10.3150 16.0847i −0.433188 0.675493i
\(568\) 35.4374 + 26.0800i 1.48692 + 1.09429i
\(569\) 17.3619i 0.727850i 0.931428 + 0.363925i \(0.118564\pi\)
−0.931428 + 0.363925i \(0.881436\pi\)
\(570\) −25.5549 1.76416i −1.07038 0.0738924i
\(571\) 8.49419i 0.355471i −0.984078 0.177735i \(-0.943123\pi\)
0.984078 0.177735i \(-0.0568771\pi\)
\(572\) 13.4253 + 6.04317i 0.561341 + 0.252678i
\(573\) −21.0701 + 3.02421i −0.880218 + 0.126338i
\(574\) 0.490826 + 0.105377i 0.0204867 + 0.00439833i
\(575\) −7.92874 −0.330651
\(576\) 13.2932 + 19.9823i 0.553882 + 0.832595i
\(577\) −26.2794 −1.09402 −0.547012 0.837125i \(-0.684235\pi\)
−0.547012 + 0.837125i \(0.684235\pi\)
\(578\) −22.6125 4.85473i −0.940557 0.201930i
\(579\) 3.67402 0.527335i 0.152687 0.0219153i
\(580\) 43.6000 + 19.6258i 1.81039 + 0.814916i
\(581\) 24.2342i 1.00541i
\(582\) −27.2397 1.88047i −1.12912 0.0779478i
\(583\) 57.0702i 2.36361i
\(584\) −0.238643 0.175628i −0.00987511 0.00726755i
\(585\) −3.50479 11.9577i −0.144905 0.494389i
\(586\) −8.29019 + 38.6143i −0.342464 + 1.59514i
\(587\) −22.2560 −0.918602 −0.459301 0.888281i \(-0.651900\pi\)
−0.459301 + 0.888281i \(0.651900\pi\)
\(588\) −8.29674 2.38942i −0.342152 0.0985378i
\(589\) 8.76333 0.361087
\(590\) −3.86947 + 18.0233i −0.159304 + 0.742009i
\(591\) −3.37603 23.5213i −0.138871 0.967536i
\(592\) 4.07923 + 4.60556i 0.167655 + 0.189287i
\(593\) 24.8234i 1.01937i −0.860360 0.509687i \(-0.829761\pi\)
0.860360 0.509687i \(-0.170239\pi\)
\(594\) 36.2845 7.96888i 1.48877 0.326967i
\(595\) 4.86819i 0.199576i
\(596\) 18.6992 41.5417i 0.765951 1.70161i
\(597\) −2.22868 15.5275i −0.0912139 0.635500i
\(598\) −5.08984 1.09275i −0.208139 0.0446858i
\(599\) −44.5649 −1.82087 −0.910436 0.413649i \(-0.864254\pi\)
−0.910436 + 0.413649i \(0.864254\pi\)
\(600\) −13.5436 7.25689i −0.552916 0.296261i
\(601\) 25.2111 1.02838 0.514190 0.857676i \(-0.328093\pi\)
0.514190 + 0.857676i \(0.328093\pi\)
\(602\) 33.2391 + 7.13617i 1.35472 + 0.290848i
\(603\) 0.843802 + 2.87889i 0.0343623 + 0.117237i
\(604\) −15.1140 + 33.5768i −0.614980 + 1.36622i
\(605\) 41.5226i 1.68814i
\(606\) 1.26566 18.3338i 0.0514138 0.744761i
\(607\) 5.55928i 0.225644i −0.993615 0.112822i \(-0.964011\pi\)
0.993615 0.112822i \(-0.0359890\pi\)
\(608\) −18.0655 + 10.1856i −0.732652 + 0.413080i
\(609\) −30.5077 + 4.37879i −1.23623 + 0.177438i
\(610\) 6.31390 29.4091i 0.255642 1.19074i
\(611\) 15.0173 0.607535
\(612\) 0.662762 4.77738i 0.0267906 0.193114i
\(613\) 7.97048 0.321925 0.160962 0.986961i \(-0.448540\pi\)
0.160962 + 0.986961i \(0.448540\pi\)
\(614\) 8.31935 38.7501i 0.335742 1.56383i
\(615\) 0.817665 0.117360i 0.0329714 0.00473241i
\(616\) −17.9940 + 24.4502i −0.725001 + 0.985128i
\(617\) 42.4971i 1.71087i 0.517911 + 0.855435i \(0.326710\pi\)
−0.517911 + 0.855435i \(0.673290\pi\)
\(618\) 1.79021 25.9323i 0.0720130 1.04315i
\(619\) 22.5315i 0.905619i 0.891607 + 0.452810i \(0.149578\pi\)
−0.891607 + 0.452810i \(0.850422\pi\)
\(620\) 12.4348 + 5.59730i 0.499393 + 0.224793i
\(621\) −11.9526 + 5.44805i −0.479640 + 0.218623i
\(622\) −25.9764 5.57693i −1.04156 0.223615i
\(623\) 14.2293 0.570085
\(624\) −7.69415 6.52515i −0.308012 0.261215i
\(625\) −30.8450 −1.23380
\(626\) −32.1429 6.90082i −1.28469 0.275812i
\(627\) 4.56085 + 31.7761i 0.182143 + 1.26901i
\(628\) −37.7322 16.9845i −1.50568 0.677755i
\(629\) 1.23640i 0.0492985i
\(630\) 25.6240 1.89018i 1.02088 0.0753065i
\(631\) 21.5848i 0.859278i −0.903001 0.429639i \(-0.858641\pi\)
0.903001 0.429639i \(-0.141359\pi\)
\(632\) −10.7659 + 14.6287i −0.428246 + 0.581899i
\(633\) 2.92035 + 20.3465i 0.116073 + 0.808700i
\(634\) −2.97172 + 13.8418i −0.118022 + 0.549728i
\(635\) 24.6525 0.978303
\(636\) −10.8225 + 37.5789i −0.429141 + 1.49010i
\(637\) 3.62931 0.143799
\(638\) 12.5778 58.5852i 0.497959 2.31941i
\(639\) −44.7847 + 13.1264i −1.77166 + 0.519272i
\(640\) −32.1399 + 2.91414i −1.27044 + 0.115191i
\(641\) 5.43407i 0.214633i −0.994225 0.107316i \(-0.965774\pi\)
0.994225 0.107316i \(-0.0342258\pi\)
\(642\) 21.7154 + 1.49910i 0.857039 + 0.0591648i
\(643\) 26.2544i 1.03537i 0.855570 + 0.517687i \(0.173207\pi\)
−0.855570 + 0.517687i \(0.826793\pi\)
\(644\) 4.40603 9.78831i 0.173622 0.385713i
\(645\) 55.3728 7.94770i 2.18030 0.312940i
\(646\) 4.07495 + 0.874859i 0.160327 + 0.0344209i
\(647\) 19.5905 0.770181 0.385090 0.922879i \(-0.374170\pi\)
0.385090 + 0.922879i \(0.374170\pi\)
\(648\) −25.4034 1.63357i −0.997939 0.0641727i
\(649\) 23.1016 0.906818
\(650\) 6.31495 + 1.35577i 0.247693 + 0.0531777i
\(651\) −8.70083 + 1.24884i −0.341012 + 0.0489458i
\(652\) −15.8801 + 35.2787i −0.621911 + 1.38162i
\(653\) 37.5923i 1.47110i 0.677470 + 0.735550i \(0.263076\pi\)
−0.677470 + 0.735550i \(0.736924\pi\)
\(654\) 7.91416 + 0.546346i 0.309468 + 0.0213638i
\(655\) 4.16487i 0.162735i
\(656\) 0.500642 0.443429i 0.0195468 0.0173130i
\(657\) 0.301590 0.0883959i 0.0117661 0.00344865i
\(658\) −6.49987 + 30.2753i −0.253391 + 1.18025i
\(659\) 13.5327 0.527157 0.263579 0.964638i \(-0.415097\pi\)
0.263579 + 0.964638i \(0.415097\pi\)
\(660\) −13.8243 + 48.0020i −0.538110 + 1.86847i
\(661\) 1.18561 0.0461147 0.0230573 0.999734i \(-0.492660\pi\)
0.0230573 + 0.999734i \(0.492660\pi\)
\(662\) −2.43847 + 11.3580i −0.0947739 + 0.441441i
\(663\) 0.288046 + 2.00685i 0.0111868 + 0.0779398i
\(664\) 26.0024 + 19.1364i 1.00909 + 0.742636i
\(665\) 22.2025i 0.860978i
\(666\) −6.50786 + 0.480058i −0.252175 + 0.0186019i
\(667\) 21.1872i 0.820372i
\(668\) −20.4902 9.22328i −0.792788 0.356859i
\(669\) −0.875348 6.09868i −0.0338429 0.235788i
\(670\) −3.94409 0.846765i −0.152373 0.0327134i
\(671\) −37.6954 −1.45522
\(672\) 16.4851 12.6874i 0.635927 0.489426i
\(673\) 28.8260 1.11116 0.555581 0.831463i \(-0.312496\pi\)
0.555581 + 0.831463i \(0.312496\pi\)
\(674\) 6.06733 + 1.30261i 0.233705 + 0.0501746i
\(675\) 14.8295 6.75937i 0.570788 0.260168i
\(676\) −19.8418 8.93142i −0.763145 0.343516i
\(677\) 2.13643i 0.0821098i −0.999157 0.0410549i \(-0.986928\pi\)
0.999157 0.0410549i \(-0.0130719\pi\)
\(678\) −1.96307 + 28.4363i −0.0753912 + 1.09209i
\(679\) 23.6663i 0.908231i
\(680\) 5.22338 + 3.84413i 0.200308 + 0.147416i
\(681\) 13.4986 1.93746i 0.517266 0.0742436i
\(682\) 3.58720 16.7086i 0.137361 0.639805i
\(683\) 27.8685 1.06636 0.533179 0.846003i \(-0.320997\pi\)
0.533179 + 0.846003i \(0.320997\pi\)
\(684\) 3.02269 21.7884i 0.115575 0.833101i
\(685\) 43.3020 1.65448
\(686\) −5.98267 + 27.8663i −0.228419 + 1.06394i
\(687\) 16.3207 2.34252i 0.622673 0.0893728i
\(688\) 33.9038 30.0293i 1.29257 1.14485i
\(689\) 16.4384i 0.626255i
\(690\) 1.21645 17.6210i 0.0463093 0.670818i
\(691\) 0.711215i 0.0270559i 0.999908 + 0.0135280i \(0.00430621\pi\)
−0.999908 + 0.0135280i \(0.995694\pi\)
\(692\) 2.43217 5.40324i 0.0924572 0.205400i
\(693\) −9.05663 30.8995i −0.344033 1.17377i
\(694\) −44.8398 9.62676i −1.70210 0.365427i
\(695\) −19.9224 −0.755701
\(696\) −19.3919 + 36.1913i −0.735047 + 1.37183i
\(697\) −0.134401 −0.00509082
\(698\) 12.4909 + 2.68170i 0.472788 + 0.101504i
\(699\) −5.23534 36.4754i −0.198019 1.37963i
\(700\) −5.46655 + 12.1443i −0.206616 + 0.459012i
\(701\) 6.63817i 0.250720i 0.992111 + 0.125360i \(0.0400086\pi\)
−0.992111 + 0.125360i \(0.959991\pi\)
\(702\) 10.4514 2.29535i 0.394461 0.0866324i
\(703\) 5.63890i 0.212675i
\(704\) 12.0253 + 38.6139i 0.453221 + 1.45532i
\(705\) 7.23904 + 50.4354i 0.272638 + 1.89951i
\(706\) −11.0063 + 51.2655i −0.414227 + 1.92940i
\(707\) −15.9288 −0.599063
\(708\) −15.2117 4.38088i −0.571690 0.164644i
\(709\) 7.64531 0.287126 0.143563 0.989641i \(-0.454144\pi\)
0.143563 + 0.989641i \(0.454144\pi\)
\(710\) 13.1725 61.3552i 0.494355 2.30262i
\(711\) −5.41863 18.4873i −0.203214 0.693329i
\(712\) 11.2361 15.2675i 0.421089 0.572174i
\(713\) 6.04262i 0.226298i
\(714\) −4.17055 0.287910i −0.156079 0.0107748i
\(715\) 20.9979i 0.785277i
\(716\) 42.2212 + 19.0051i 1.57788 + 0.710254i
\(717\) 4.15601 0.596516i 0.155209 0.0222773i
\(718\) 9.11282 + 1.95645i 0.340088 + 0.0730141i
\(719\) −34.9849 −1.30472 −0.652359 0.757910i \(-0.726220\pi\)
−0.652359 + 0.757910i \(0.726220\pi\)
\(720\) 18.2057 28.9862i 0.678487 1.08025i
\(721\) −22.5305 −0.839080
\(722\) −7.68664 1.65026i −0.286067 0.0614164i
\(723\) 12.6978 1.82252i 0.472235 0.0677803i
\(724\) 10.9040 + 4.90825i 0.405245 + 0.182414i
\(725\) 26.2869i 0.976270i
\(726\) 35.5723 + 2.45570i 1.32021 + 0.0911394i
\(727\) 25.8783i 0.959773i 0.877330 + 0.479887i \(0.159322\pi\)
−0.877330 + 0.479887i \(0.840678\pi\)
\(728\) −5.18299 + 7.04262i −0.192094 + 0.261017i
\(729\) 17.7109 20.3795i 0.655960 0.754796i
\(730\) −0.0887063 + 0.413179i −0.00328317 + 0.0152924i
\(731\) −9.10175 −0.336640
\(732\) 24.8212 + 7.14838i 0.917419 + 0.264212i
\(733\) −28.6885 −1.05964 −0.529818 0.848112i \(-0.677740\pi\)
−0.529818 + 0.848112i \(0.677740\pi\)
\(734\) −3.02146 + 14.0735i −0.111524 + 0.519461i
\(735\) 1.74950 + 12.1890i 0.0645312 + 0.449598i
\(736\) −7.02330 12.4568i −0.258882 0.459163i
\(737\) 5.05538i 0.186217i
\(738\) 0.0521842 + 0.707430i 0.00192093 + 0.0260409i
\(739\) 32.7425i 1.20445i −0.798326 0.602226i \(-0.794281\pi\)
0.798326 0.602226i \(-0.205719\pi\)
\(740\) 3.60167 8.00135i 0.132400 0.294136i
\(741\) 1.31370 + 9.15275i 0.0482600 + 0.336235i
\(742\) 33.1404 + 7.11498i 1.21662 + 0.261199i
\(743\) −12.8638 −0.471927 −0.235963 0.971762i \(-0.575825\pi\)
−0.235963 + 0.971762i \(0.575825\pi\)
\(744\) −5.53059 + 10.3218i −0.202761 + 0.378415i
\(745\) −64.9733 −2.38044
\(746\) −1.80370 0.387240i −0.0660381 0.0141779i
\(747\) −32.8611 + 9.63158i −1.20232 + 0.352401i
\(748\) 3.33609 7.41136i 0.121980 0.270986i
\(749\) 18.8668i 0.689376i
\(750\) 0.896748 12.9899i 0.0327446 0.474325i
\(751\) 22.4339i 0.818623i −0.912395 0.409312i \(-0.865769\pi\)
0.912395 0.409312i \(-0.134231\pi\)
\(752\) 27.3517 + 30.8808i 0.997414 + 1.12611i
\(753\) 6.19747 0.889528i 0.225848 0.0324162i
\(754\) 3.62289 16.8748i 0.131938 0.614545i
\(755\) 52.5158 1.91125
\(756\) 0.103874 + 22.0638i 0.00377785 + 0.802451i
\(757\) −16.4339 −0.597301 −0.298651 0.954363i \(-0.596537\pi\)
−0.298651 + 0.954363i \(0.596537\pi\)
\(758\) 4.88668 22.7613i 0.177492 0.826728i
\(759\) −21.9107 + 3.14486i −0.795307 + 0.114151i
\(760\) 23.8225 + 17.5321i 0.864133 + 0.635955i
\(761\) 43.7728i 1.58676i 0.608724 + 0.793382i \(0.291682\pi\)
−0.608724 + 0.793382i \(0.708318\pi\)
\(762\) −1.45797 + 21.1197i −0.0528169 + 0.765084i
\(763\) 6.87597i 0.248927i