Properties

Label 546.2.p.c.239.5
Level $546$
Weight $2$
Character 546.239
Analytic conductor $4.360$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + 23328 x^{6} - 34020 x^{5} + 40824 x^{4} - 43740 x^{3} + 52488 x^{2} - 78732 x + 59049\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 239.5
Root \(0.813276 - 1.52924i\) of defining polynomial
Character \(\chi\) \(=\) 546.239
Dual form 546.2.p.c.281.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.65641 - 0.506265i) q^{3} +1.00000i q^{4} +(-0.645532 - 0.645532i) q^{5} +(-1.52924 - 0.813276i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.48739 - 1.67717i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(1.65641 - 0.506265i) q^{3} +1.00000i q^{4} +(-0.645532 - 0.645532i) q^{5} +(-1.52924 - 0.813276i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.48739 - 1.67717i) q^{9} +0.912921i q^{10} +(-0.346115 + 0.346115i) q^{11} +(0.506265 + 1.65641i) q^{12} +(0.964947 - 3.47403i) q^{13} -1.00000i q^{14} +(-1.39608 - 0.742456i) q^{15} -1.00000 q^{16} +3.74401 q^{17} +(-2.94479 - 0.572916i) q^{18} +(-0.564337 + 0.564337i) q^{19} +(0.645532 - 0.645532i) q^{20} +(1.52924 + 0.813276i) q^{21} +0.489480 q^{22} +2.93468 q^{23} +(0.813276 - 1.52924i) q^{24} -4.16658i q^{25} +(-3.13883 + 1.77419i) q^{26} +(3.27105 - 4.03735i) q^{27} +(-0.707107 + 0.707107i) q^{28} -4.18850i q^{29} +(0.462180 + 1.51217i) q^{30} +(-1.21118 + 1.21118i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.398082 + 0.748534i) q^{33} +(-2.64741 - 2.64741i) q^{34} -0.912921i q^{35} +(1.67717 + 2.48739i) q^{36} +(2.17001 + 2.17001i) q^{37} +0.798093 q^{38} +(-0.160431 - 6.24294i) q^{39} -0.912921 q^{40} +(2.35038 + 2.35038i) q^{41} +(-0.506265 - 1.65641i) q^{42} -2.44891i q^{43} +(-0.346115 - 0.346115i) q^{44} +(-2.68836 - 0.523027i) q^{45} +(-2.07513 - 2.07513i) q^{46} +(-7.22377 + 7.22377i) q^{47} +(-1.65641 + 0.506265i) q^{48} +1.00000i q^{49} +(-2.94621 + 2.94621i) q^{50} +(6.20161 - 1.89546i) q^{51} +(3.47403 + 0.964947i) q^{52} +5.03273i q^{53} +(-5.16782 + 0.541858i) q^{54} +0.446857 q^{55} +1.00000 q^{56} +(-0.649069 + 1.22048i) q^{57} +(-2.96172 + 2.96172i) q^{58} +(2.23605 - 2.23605i) q^{59} +(0.742456 - 1.39608i) q^{60} -4.58319 q^{61} +1.71287 q^{62} +(2.94479 + 0.572916i) q^{63} -1.00000i q^{64} +(-2.86550 + 1.61969i) q^{65} +(0.810780 - 0.247807i) q^{66} +(1.55654 - 1.55654i) q^{67} +3.74401i q^{68} +(4.86103 - 1.48572i) q^{69} +(-0.645532 + 0.645532i) q^{70} +(-1.98965 - 1.98965i) q^{71} +(0.572916 - 2.94479i) q^{72} +(-2.94861 - 2.94861i) q^{73} -3.06885i q^{74} +(-2.10939 - 6.90156i) q^{75} +(-0.564337 - 0.564337i) q^{76} -0.489480 q^{77} +(-4.30098 + 4.52787i) q^{78} -5.80866 q^{79} +(0.645532 + 0.645532i) q^{80} +(3.37423 - 8.34353i) q^{81} -3.32394i q^{82} +(1.45281 + 1.45281i) q^{83} +(-0.813276 + 1.52924i) q^{84} +(-2.41688 - 2.41688i) q^{85} +(-1.73164 + 1.73164i) q^{86} +(-2.12049 - 6.93788i) q^{87} +0.489480i q^{88} +(-12.0210 + 12.0210i) q^{89} +(1.53112 + 2.27079i) q^{90} +(3.13883 - 1.77419i) q^{91} +2.93468i q^{92} +(-1.39303 + 2.61939i) q^{93} +10.2160 q^{94} +0.728595 q^{95} +(1.52924 + 0.813276i) q^{96} +(6.69250 - 6.69250i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-0.280431 + 1.44142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} + O(q^{10}) \) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} - 16q^{11} - 8q^{12} + 4q^{13} - 4q^{15} - 20q^{16} + 12q^{17} - 8q^{18} + 12q^{19} + 4q^{20} + 4q^{21} - 12q^{22} - 4q^{23} + 4q^{24} + 24q^{27} + 12q^{30} - 8q^{31} - 48q^{33} - 4q^{34} + 32q^{37} - 4q^{38} - 16q^{39} - 4q^{40} + 8q^{41} + 8q^{42} - 16q^{44} + 16q^{45} - 8q^{46} + 32q^{50} - 8q^{51} - 8q^{52} + 28q^{54} + 28q^{55} + 20q^{56} + 36q^{57} - 4q^{58} + 20q^{59} - 4q^{60} - 4q^{61} + 48q^{62} + 8q^{63} + 52q^{65} - 36q^{67} + 68q^{69} - 4q^{70} - 28q^{71} - 16q^{72} - 24q^{73} - 76q^{75} + 12q^{76} + 12q^{77} + 40q^{78} - 64q^{79} + 4q^{80} + 32q^{81} - 24q^{83} - 4q^{84} + 24q^{85} + 4q^{86} + 4q^{87} - 4q^{89} - 8q^{90} - 32q^{93} - 40q^{94} - 76q^{95} + 4q^{96} + 32q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 1.65641 0.506265i 0.956329 0.292292i
\(4\) 1.00000i 0.500000i
\(5\) −0.645532 0.645532i −0.288691 0.288691i 0.547872 0.836562i \(-0.315438\pi\)
−0.836562 + 0.547872i \(0.815438\pi\)
\(6\) −1.52924 0.813276i −0.624311 0.332018i
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 2.48739 1.67717i 0.829130 0.559055i
\(10\) 0.912921i 0.288691i
\(11\) −0.346115 + 0.346115i −0.104358 + 0.104358i −0.757358 0.653000i \(-0.773510\pi\)
0.653000 + 0.757358i \(0.273510\pi\)
\(12\) 0.506265 + 1.65641i 0.146146 + 0.478165i
\(13\) 0.964947 3.47403i 0.267628 0.963522i
\(14\) 1.00000i 0.267261i
\(15\) −1.39608 0.742456i −0.360466 0.191701i
\(16\) −1.00000 −0.250000
\(17\) 3.74401 0.908055 0.454028 0.890988i \(-0.349987\pi\)
0.454028 + 0.890988i \(0.349987\pi\)
\(18\) −2.94479 0.572916i −0.694093 0.135038i
\(19\) −0.564337 + 0.564337i −0.129468 + 0.129468i −0.768871 0.639404i \(-0.779181\pi\)
0.639404 + 0.768871i \(0.279181\pi\)
\(20\) 0.645532 0.645532i 0.144345 0.144345i
\(21\) 1.52924 + 0.813276i 0.333708 + 0.177471i
\(22\) 0.489480 0.104358
\(23\) 2.93468 0.611922 0.305961 0.952044i \(-0.401022\pi\)
0.305961 + 0.952044i \(0.401022\pi\)
\(24\) 0.813276 1.52924i 0.166009 0.312155i
\(25\) 4.16658i 0.833315i
\(26\) −3.13883 + 1.77419i −0.615575 + 0.347947i
\(27\) 3.27105 4.03735i 0.629514 0.776989i
\(28\) −0.707107 + 0.707107i −0.133631 + 0.133631i
\(29\) 4.18850i 0.777785i −0.921283 0.388893i \(-0.872858\pi\)
0.921283 0.388893i \(-0.127142\pi\)
\(30\) 0.462180 + 1.51217i 0.0843821 + 0.276083i
\(31\) −1.21118 + 1.21118i −0.217534 + 0.217534i −0.807459 0.589924i \(-0.799158\pi\)
0.589924 + 0.807459i \(0.299158\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −0.398082 + 0.748534i −0.0692973 + 0.130303i
\(34\) −2.64741 2.64741i −0.454028 0.454028i
\(35\) 0.912921i 0.154312i
\(36\) 1.67717 + 2.48739i 0.279528 + 0.414565i
\(37\) 2.17001 + 2.17001i 0.356747 + 0.356747i 0.862612 0.505866i \(-0.168827\pi\)
−0.505866 + 0.862612i \(0.668827\pi\)
\(38\) 0.798093 0.129468
\(39\) −0.160431 6.24294i −0.0256896 0.999670i
\(40\) −0.912921 −0.144345
\(41\) 2.35038 + 2.35038i 0.367068 + 0.367068i 0.866407 0.499339i \(-0.166424\pi\)
−0.499339 + 0.866407i \(0.666424\pi\)
\(42\) −0.506265 1.65641i −0.0781184 0.255590i
\(43\) 2.44891i 0.373455i −0.982412 0.186727i \(-0.940212\pi\)
0.982412 0.186727i \(-0.0597881\pi\)
\(44\) −0.346115 0.346115i −0.0521788 0.0521788i
\(45\) −2.68836 0.523027i −0.400757 0.0779683i
\(46\) −2.07513 2.07513i −0.305961 0.305961i
\(47\) −7.22377 + 7.22377i −1.05370 + 1.05370i −0.0552213 + 0.998474i \(0.517586\pi\)
−0.998474 + 0.0552213i \(0.982414\pi\)
\(48\) −1.65641 + 0.506265i −0.239082 + 0.0730731i
\(49\) 1.00000i 0.142857i
\(50\) −2.94621 + 2.94621i −0.416658 + 0.416658i
\(51\) 6.20161 1.89546i 0.868400 0.265418i
\(52\) 3.47403 + 0.964947i 0.481761 + 0.133814i
\(53\) 5.03273i 0.691298i 0.938364 + 0.345649i \(0.112341\pi\)
−0.938364 + 0.345649i \(0.887659\pi\)
\(54\) −5.16782 + 0.541858i −0.703252 + 0.0737376i
\(55\) 0.446857 0.0602542
\(56\) 1.00000 0.133631
\(57\) −0.649069 + 1.22048i −0.0859713 + 0.161656i
\(58\) −2.96172 + 2.96172i −0.388893 + 0.388893i
\(59\) 2.23605 2.23605i 0.291109 0.291109i −0.546409 0.837518i \(-0.684006\pi\)
0.837518 + 0.546409i \(0.184006\pi\)
\(60\) 0.742456 1.39608i 0.0958507 0.180233i
\(61\) −4.58319 −0.586818 −0.293409 0.955987i \(-0.594790\pi\)
−0.293409 + 0.955987i \(0.594790\pi\)
\(62\) 1.71287 0.217534
\(63\) 2.94479 + 0.572916i 0.371008 + 0.0721806i
\(64\) 1.00000i 0.125000i
\(65\) −2.86550 + 1.61969i −0.355422 + 0.200898i
\(66\) 0.810780 0.247807i 0.0998002 0.0305029i
\(67\) 1.55654 1.55654i 0.190162 0.190162i −0.605604 0.795766i \(-0.707069\pi\)
0.795766 + 0.605604i \(0.207069\pi\)
\(68\) 3.74401i 0.454028i
\(69\) 4.86103 1.48572i 0.585199 0.178860i
\(70\) −0.645532 + 0.645532i −0.0771559 + 0.0771559i
\(71\) −1.98965 1.98965i −0.236128 0.236128i 0.579117 0.815245i \(-0.303398\pi\)
−0.815245 + 0.579117i \(0.803398\pi\)
\(72\) 0.572916 2.94479i 0.0675188 0.347046i
\(73\) −2.94861 2.94861i −0.345108 0.345108i 0.513175 0.858284i \(-0.328469\pi\)
−0.858284 + 0.513175i \(0.828469\pi\)
\(74\) 3.06885i 0.356747i
\(75\) −2.10939 6.90156i −0.243572 0.796923i
\(76\) −0.564337 0.564337i −0.0647339 0.0647339i
\(77\) −0.489480 −0.0557815
\(78\) −4.30098 + 4.52787i −0.486990 + 0.512680i
\(79\) −5.80866 −0.653525 −0.326762 0.945106i \(-0.605958\pi\)
−0.326762 + 0.945106i \(0.605958\pi\)
\(80\) 0.645532 + 0.645532i 0.0721727 + 0.0721727i
\(81\) 3.37423 8.34353i 0.374915 0.927059i
\(82\) 3.32394i 0.367068i
\(83\) 1.45281 + 1.45281i 0.159467 + 0.159467i 0.782330 0.622864i \(-0.214031\pi\)
−0.622864 + 0.782330i \(0.714031\pi\)
\(84\) −0.813276 + 1.52924i −0.0887356 + 0.166854i
\(85\) −2.41688 2.41688i −0.262147 0.262147i
\(86\) −1.73164 + 1.73164i −0.186727 + 0.186727i
\(87\) −2.12049 6.93788i −0.227341 0.743819i
\(88\) 0.489480i 0.0521788i
\(89\) −12.0210 + 12.0210i −1.27423 + 1.27423i −0.330380 + 0.943848i \(0.607177\pi\)
−0.943848 + 0.330380i \(0.892823\pi\)
\(90\) 1.53112 + 2.27079i 0.161394 + 0.239362i
\(91\) 3.13883 1.77419i 0.329039 0.185986i
\(92\) 2.93468i 0.305961i
\(93\) −1.39303 + 2.61939i −0.144451 + 0.271618i
\(94\) 10.2160 1.05370
\(95\) 0.728595 0.0747523
\(96\) 1.52924 + 0.813276i 0.156078 + 0.0830046i
\(97\) 6.69250 6.69250i 0.679520 0.679520i −0.280371 0.959892i \(-0.590458\pi\)
0.959892 + 0.280371i \(0.0904576\pi\)
\(98\) 0.707107 0.707107i 0.0714286 0.0714286i
\(99\) −0.280431 + 1.44142i −0.0281844 + 0.144868i
\(100\) 4.16658 0.416658
\(101\) 13.4516 1.33848 0.669241 0.743045i \(-0.266619\pi\)
0.669241 + 0.743045i \(0.266619\pi\)
\(102\) −5.72550 3.04491i −0.566909 0.301491i
\(103\) 6.61463i 0.651759i 0.945411 + 0.325879i \(0.105660\pi\)
−0.945411 + 0.325879i \(0.894340\pi\)
\(104\) −1.77419 3.13883i −0.173974 0.307788i
\(105\) −0.462180 1.51217i −0.0451041 0.147573i
\(106\) 3.55868 3.55868i 0.345649 0.345649i
\(107\) 0.232092i 0.0224372i −0.999937 0.0112186i \(-0.996429\pi\)
0.999937 0.0112186i \(-0.00357107\pi\)
\(108\) 4.03735 + 3.27105i 0.388495 + 0.314757i
\(109\) −8.15828 + 8.15828i −0.781422 + 0.781422i −0.980071 0.198649i \(-0.936345\pi\)
0.198649 + 0.980071i \(0.436345\pi\)
\(110\) −0.315975 0.315975i −0.0301271 0.0301271i
\(111\) 4.69302 + 2.49582i 0.445441 + 0.236893i
\(112\) −0.707107 0.707107i −0.0668153 0.0668153i
\(113\) 9.58107i 0.901311i 0.892698 + 0.450656i \(0.148810\pi\)
−0.892698 + 0.450656i \(0.851190\pi\)
\(114\) 1.32197 0.404047i 0.123814 0.0378424i
\(115\) −1.89443 1.89443i −0.176656 0.176656i
\(116\) 4.18850 0.388893
\(117\) −3.42632 10.2596i −0.316764 0.948505i
\(118\) −3.16225 −0.291109
\(119\) 2.64741 + 2.64741i 0.242688 + 0.242688i
\(120\) −1.51217 + 0.462180i −0.138042 + 0.0421911i
\(121\) 10.7604i 0.978219i
\(122\) 3.24081 + 3.24081i 0.293409 + 0.293409i
\(123\) 5.08311 + 2.70328i 0.458329 + 0.243747i
\(124\) −1.21118 1.21118i −0.108767 0.108767i
\(125\) −5.91732 + 5.91732i −0.529261 + 0.529261i
\(126\) −1.67717 2.48739i −0.149414 0.221594i
\(127\) 16.8593i 1.49602i 0.663686 + 0.748012i \(0.268991\pi\)
−0.663686 + 0.748012i \(0.731009\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −1.23980 4.05640i −0.109158 0.357146i
\(130\) 3.17151 + 0.880920i 0.278160 + 0.0772618i
\(131\) 21.4186i 1.87135i 0.352862 + 0.935676i \(0.385209\pi\)
−0.352862 + 0.935676i \(0.614791\pi\)
\(132\) −0.748534 0.398082i −0.0651515 0.0346486i
\(133\) −0.798093 −0.0692034
\(134\) −2.20128 −0.190162
\(135\) −4.71781 + 0.494674i −0.406045 + 0.0425747i
\(136\) 2.64741 2.64741i 0.227014 0.227014i
\(137\) 4.89961 4.89961i 0.418602 0.418602i −0.466120 0.884722i \(-0.654348\pi\)
0.884722 + 0.466120i \(0.154348\pi\)
\(138\) −4.48783 2.38670i −0.382030 0.203169i
\(139\) 4.43061 0.375799 0.187900 0.982188i \(-0.439832\pi\)
0.187900 + 0.982188i \(0.439832\pi\)
\(140\) 0.912921 0.0771559
\(141\) −8.30839 + 15.6227i −0.699692 + 1.31567i
\(142\) 2.81379i 0.236128i
\(143\) 0.868431 + 1.53640i 0.0726218 + 0.128480i
\(144\) −2.48739 + 1.67717i −0.207283 + 0.139764i
\(145\) −2.70381 + 2.70381i −0.224540 + 0.224540i
\(146\) 4.16996i 0.345108i
\(147\) 0.506265 + 1.65641i 0.0417560 + 0.136618i
\(148\) −2.17001 + 2.17001i −0.178373 + 0.178373i
\(149\) −7.00938 7.00938i −0.574231 0.574231i 0.359077 0.933308i \(-0.383091\pi\)
−0.933308 + 0.359077i \(0.883091\pi\)
\(150\) −3.38857 + 6.37171i −0.276676 + 0.520248i
\(151\) 6.30515 + 6.30515i 0.513105 + 0.513105i 0.915477 0.402371i \(-0.131814\pi\)
−0.402371 + 0.915477i \(0.631814\pi\)
\(152\) 0.798093i 0.0647339i
\(153\) 9.31281 6.27932i 0.752896 0.507653i
\(154\) 0.346115 + 0.346115i 0.0278907 + 0.0278907i
\(155\) 1.56371 0.125600
\(156\) 6.24294 0.160431i 0.499835 0.0128448i
\(157\) −19.2209 −1.53400 −0.766998 0.641649i \(-0.778250\pi\)
−0.766998 + 0.641649i \(0.778250\pi\)
\(158\) 4.10734 + 4.10734i 0.326762 + 0.326762i
\(159\) 2.54789 + 8.33626i 0.202061 + 0.661109i
\(160\) 0.912921i 0.0721727i
\(161\) 2.07513 + 2.07513i 0.163543 + 0.163543i
\(162\) −8.28571 + 3.51383i −0.650987 + 0.276072i
\(163\) 9.47285 + 9.47285i 0.741971 + 0.741971i 0.972957 0.230986i \(-0.0741953\pi\)
−0.230986 + 0.972957i \(0.574195\pi\)
\(164\) −2.35038 + 2.35038i −0.183534 + 0.183534i
\(165\) 0.740178 0.226228i 0.0576228 0.0176118i
\(166\) 2.05459i 0.159467i
\(167\) −17.0105 + 17.0105i −1.31631 + 1.31631i −0.399636 + 0.916674i \(0.630863\pi\)
−0.916674 + 0.399636i \(0.869137\pi\)
\(168\) 1.65641 0.506265i 0.127795 0.0390592i
\(169\) −11.1378 6.70451i −0.856750 0.515731i
\(170\) 3.41798i 0.262147i
\(171\) −0.457240 + 2.35021i −0.0349660 + 0.179725i
\(172\) 2.44891 0.186727
\(173\) −0.945226 −0.0718642 −0.0359321 0.999354i \(-0.511440\pi\)
−0.0359321 + 0.999354i \(0.511440\pi\)
\(174\) −3.40641 + 6.40524i −0.258239 + 0.485580i
\(175\) 2.94621 2.94621i 0.222713 0.222713i
\(176\) 0.346115 0.346115i 0.0260894 0.0260894i
\(177\) 2.57178 4.83585i 0.193307 0.363485i
\(178\) 17.0003 1.27423
\(179\) 18.1644 1.35767 0.678834 0.734292i \(-0.262485\pi\)
0.678834 + 0.734292i \(0.262485\pi\)
\(180\) 0.523027 2.68836i 0.0389841 0.200378i
\(181\) 18.4772i 1.37340i −0.726940 0.686701i \(-0.759058\pi\)
0.726940 0.686701i \(-0.240942\pi\)
\(182\) −3.47403 0.964947i −0.257512 0.0715266i
\(183\) −7.59165 + 2.32031i −0.561191 + 0.171522i
\(184\) 2.07513 2.07513i 0.152981 0.152981i
\(185\) 2.80162i 0.205979i
\(186\) 2.83721 0.867164i 0.208034 0.0635836i
\(187\) −1.29586 + 1.29586i −0.0947625 + 0.0947625i
\(188\) −7.22377 7.22377i −0.526848 0.526848i
\(189\) 5.16782 0.541858i 0.375904 0.0394144i
\(190\) −0.515195 0.515195i −0.0373762 0.0373762i
\(191\) 14.1792i 1.02597i −0.858398 0.512984i \(-0.828540\pi\)
0.858398 0.512984i \(-0.171460\pi\)
\(192\) −0.506265 1.65641i −0.0365365 0.119541i
\(193\) 3.37846 + 3.37846i 0.243187 + 0.243187i 0.818167 0.574980i \(-0.194990\pi\)
−0.574980 + 0.818167i \(0.694990\pi\)
\(194\) −9.46462 −0.679520
\(195\) −3.92645 + 4.13358i −0.281179 + 0.296012i
\(196\) −1.00000 −0.0714286
\(197\) 1.50781 + 1.50781i 0.107427 + 0.107427i 0.758777 0.651350i \(-0.225797\pi\)
−0.651350 + 0.758777i \(0.725797\pi\)
\(198\) 1.21753 0.820940i 0.0865260 0.0583416i
\(199\) 11.1999i 0.793937i 0.917832 + 0.396968i \(0.129938\pi\)
−0.917832 + 0.396968i \(0.870062\pi\)
\(200\) −2.94621 2.94621i −0.208329 0.208329i
\(201\) 1.79025 3.36629i 0.126274 0.237440i
\(202\) −9.51170 9.51170i −0.669241 0.669241i
\(203\) 2.96172 2.96172i 0.207872 0.207872i
\(204\) 1.89546 + 6.20161i 0.132709 + 0.434200i
\(205\) 3.03449i 0.211938i
\(206\) 4.67725 4.67725i 0.325879 0.325879i
\(207\) 7.29969 4.92194i 0.507364 0.342098i
\(208\) −0.964947 + 3.47403i −0.0669070 + 0.240881i
\(209\) 0.390651i 0.0270219i
\(210\) −0.742456 + 1.39608i −0.0512343 + 0.0963385i
\(211\) 16.7046 1.14999 0.574997 0.818156i \(-0.305003\pi\)
0.574997 + 0.818156i \(0.305003\pi\)
\(212\) −5.03273 −0.345649
\(213\) −4.30297 2.28839i −0.294834 0.156798i
\(214\) −0.164114 + 0.164114i −0.0112186 + 0.0112186i
\(215\) −1.58085 + 1.58085i −0.107813 + 0.107813i
\(216\) −0.541858 5.16782i −0.0368688 0.351626i
\(217\) −1.71287 −0.116277
\(218\) 11.5376 0.781422
\(219\) −6.37688 3.39133i −0.430910 0.229165i
\(220\) 0.446857i 0.0301271i
\(221\) 3.61277 13.0068i 0.243021 0.874932i
\(222\) −1.55365 5.08328i −0.104274 0.341167i
\(223\) −16.2269 + 16.2269i −1.08663 + 1.08663i −0.0907580 + 0.995873i \(0.528929\pi\)
−0.995873 + 0.0907580i \(0.971071\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) −6.98804 10.3639i −0.465869 0.690927i
\(226\) 6.77484 6.77484i 0.450656 0.450656i
\(227\) −18.5844 18.5844i −1.23349 1.23349i −0.962616 0.270871i \(-0.912688\pi\)
−0.270871 0.962616i \(-0.587312\pi\)
\(228\) −1.22048 0.649069i −0.0808281 0.0429857i
\(229\) −10.3015 10.3015i −0.680741 0.680741i 0.279426 0.960167i \(-0.409856\pi\)
−0.960167 + 0.279426i \(0.909856\pi\)
\(230\) 2.67913i 0.176656i
\(231\) −0.810780 + 0.247807i −0.0533454 + 0.0163045i
\(232\) −2.96172 2.96172i −0.194446 0.194446i
\(233\) 29.5763 1.93761 0.968803 0.247830i \(-0.0797176\pi\)
0.968803 + 0.247830i \(0.0797176\pi\)
\(234\) −4.83189 + 9.67744i −0.315871 + 0.632634i
\(235\) 9.32636 0.608384
\(236\) 2.23605 + 2.23605i 0.145555 + 0.145555i
\(237\) −9.62152 + 2.94072i −0.624985 + 0.191020i
\(238\) 3.74401i 0.242688i
\(239\) −4.42519 4.42519i −0.286242 0.286242i 0.549350 0.835592i \(-0.314875\pi\)
−0.835592 + 0.549350i \(0.814875\pi\)
\(240\) 1.39608 + 0.742456i 0.0901164 + 0.0479253i
\(241\) −11.6682 11.6682i −0.751615 0.751615i 0.223165 0.974781i \(-0.428361\pi\)
−0.974781 + 0.223165i \(0.928361\pi\)
\(242\) 7.60876 7.60876i 0.489109 0.489109i
\(243\) 1.36507 15.5286i 0.0875694 0.996158i
\(244\) 4.58319i 0.293409i
\(245\) 0.645532 0.645532i 0.0412416 0.0412416i
\(246\) −1.68280 5.50581i −0.107291 0.351038i
\(247\) 1.41597 + 2.50508i 0.0900958 + 0.159394i
\(248\) 1.71287i 0.108767i
\(249\) 3.14196 + 1.67094i 0.199114 + 0.105892i
\(250\) 8.36836 0.529261
\(251\) −14.2635 −0.900304 −0.450152 0.892952i \(-0.648630\pi\)
−0.450152 + 0.892952i \(0.648630\pi\)
\(252\) −0.572916 + 2.94479i −0.0360903 + 0.185504i
\(253\) −1.01574 + 1.01574i −0.0638587 + 0.0638587i
\(254\) 11.9213 11.9213i 0.748012 0.748012i
\(255\) −5.22692 2.77976i −0.327323 0.174075i
\(256\) 1.00000 0.0625000
\(257\) −14.5921 −0.910229 −0.455114 0.890433i \(-0.650402\pi\)
−0.455114 + 0.890433i \(0.650402\pi\)
\(258\) −1.99164 + 3.74497i −0.123994 + 0.233152i
\(259\) 3.06885i 0.190689i
\(260\) −1.61969 2.86550i −0.100449 0.177711i
\(261\) −7.02481 10.4184i −0.434825 0.644886i
\(262\) 15.1452 15.1452i 0.935676 0.935676i
\(263\) 26.6102i 1.64086i −0.571749 0.820429i \(-0.693735\pi\)
0.571749 0.820429i \(-0.306265\pi\)
\(264\) 0.247807 + 0.810780i 0.0152515 + 0.0499001i
\(265\) 3.24879 3.24879i 0.199571 0.199571i
\(266\) 0.564337 + 0.564337i 0.0346017 + 0.0346017i
\(267\) −13.8259 + 25.9976i −0.846134 + 1.59103i
\(268\) 1.55654 + 1.55654i 0.0950808 + 0.0950808i
\(269\) 27.5224i 1.67807i −0.544078 0.839035i \(-0.683120\pi\)
0.544078 0.839035i \(-0.316880\pi\)
\(270\) 3.68578 + 2.98621i 0.224310 + 0.181735i
\(271\) 11.2423 + 11.2423i 0.682924 + 0.682924i 0.960658 0.277734i \(-0.0895834\pi\)
−0.277734 + 0.960658i \(0.589583\pi\)
\(272\) −3.74401 −0.227014
\(273\) 4.30098 4.52787i 0.260307 0.274039i
\(274\) −6.92909 −0.418602
\(275\) 1.44211 + 1.44211i 0.0869627 + 0.0869627i
\(276\) 1.48572 + 4.86103i 0.0894301 + 0.292600i
\(277\) 24.6439i 1.48071i 0.672216 + 0.740355i \(0.265343\pi\)
−0.672216 + 0.740355i \(0.734657\pi\)
\(278\) −3.13291 3.13291i −0.187900 0.187900i
\(279\) −0.981329 + 5.04402i −0.0587506 + 0.301978i
\(280\) −0.645532 0.645532i −0.0385779 0.0385779i
\(281\) 23.3880 23.3880i 1.39521 1.39521i 0.582087 0.813126i \(-0.302236\pi\)
0.813126 0.582087i \(-0.197764\pi\)
\(282\) 16.9218 5.17198i 1.00768 0.307987i
\(283\) 9.52921i 0.566453i 0.959053 + 0.283226i \(0.0914048\pi\)
−0.959053 + 0.283226i \(0.908595\pi\)
\(284\) 1.98965 1.98965i 0.118064 0.118064i
\(285\) 1.20685 0.368862i 0.0714878 0.0218495i
\(286\) 0.472323 1.70047i 0.0279290 0.100551i
\(287\) 3.32394i 0.196206i
\(288\) 2.94479 + 0.572916i 0.173523 + 0.0337594i
\(289\) −2.98240 −0.175435
\(290\) 3.82377 0.224540
\(291\) 7.69735 14.4737i 0.451227 0.848464i
\(292\) 2.94861 2.94861i 0.172554 0.172554i
\(293\) 6.68662 6.68662i 0.390636 0.390636i −0.484278 0.874914i \(-0.660918\pi\)
0.874914 + 0.484278i \(0.160918\pi\)
\(294\) 0.813276 1.52924i 0.0474312 0.0891872i
\(295\) −2.88689 −0.168081
\(296\) 3.06885 0.178373
\(297\) 0.265229 + 2.52955i 0.0153901 + 0.146779i
\(298\) 9.91276i 0.574231i
\(299\) 2.83181 10.1952i 0.163768 0.589601i
\(300\) 6.90156 2.10939i 0.398462 0.121786i
\(301\) 1.73164 1.73164i 0.0998100 0.0998100i
\(302\) 8.91682i 0.513105i
\(303\) 22.2813 6.81006i 1.28003 0.391228i
\(304\) 0.564337 0.564337i 0.0323669 0.0323669i
\(305\) 2.95860 + 2.95860i 0.169409 + 0.169409i
\(306\) −11.0253 2.14500i −0.630275 0.122622i
\(307\) 17.6200 + 17.6200i 1.00563 + 1.00563i 0.999984 + 0.00564240i \(0.00179604\pi\)
0.00564240 + 0.999984i \(0.498204\pi\)
\(308\) 0.489480i 0.0278907i
\(309\) 3.34876 + 10.9565i 0.190504 + 0.623296i
\(310\) −1.10571 1.10571i −0.0628001 0.0628001i
\(311\) 4.11610 0.233403 0.116701 0.993167i \(-0.462768\pi\)
0.116701 + 0.993167i \(0.462768\pi\)
\(312\) −4.52787 4.30098i −0.256340 0.243495i
\(313\) −15.1426 −0.855910 −0.427955 0.903800i \(-0.640766\pi\)
−0.427955 + 0.903800i \(0.640766\pi\)
\(314\) 13.5912 + 13.5912i 0.766998 + 0.766998i
\(315\) −1.53112 2.27079i −0.0862688 0.127945i
\(316\) 5.80866i 0.326762i
\(317\) −15.8113 15.8113i −0.888053 0.888053i 0.106283 0.994336i \(-0.466105\pi\)
−0.994336 + 0.106283i \(0.966105\pi\)
\(318\) 4.09299 7.69626i 0.229524 0.431585i
\(319\) 1.44970 + 1.44970i 0.0811678 + 0.0811678i
\(320\) −0.645532 + 0.645532i −0.0360864 + 0.0360864i
\(321\) −0.117500 0.384440i −0.00655823 0.0214574i
\(322\) 2.93468i 0.163543i
\(323\) −2.11288 + 2.11288i −0.117564 + 0.117564i
\(324\) 8.34353 + 3.37423i 0.463530 + 0.187457i
\(325\) −14.4748 4.02052i −0.802918 0.223019i
\(326\) 13.3966i 0.741971i
\(327\) −9.38321 + 17.6437i −0.518893 + 0.975700i
\(328\) 3.32394 0.183534
\(329\) −10.2160 −0.563224
\(330\) −0.683352 0.363418i −0.0376173 0.0200055i
\(331\) 11.5195 11.5195i 0.633169 0.633169i −0.315693 0.948861i \(-0.602237\pi\)
0.948861 + 0.315693i \(0.102237\pi\)
\(332\) −1.45281 + 1.45281i −0.0797334 + 0.0797334i
\(333\) 9.03711 + 1.75819i 0.495231 + 0.0963484i
\(334\) 24.0564 1.31631
\(335\) −2.00959 −0.109796
\(336\) −1.52924 0.813276i −0.0834270 0.0443678i
\(337\) 29.3517i 1.59889i −0.600740 0.799444i \(-0.705127\pi\)
0.600740 0.799444i \(-0.294873\pi\)
\(338\) 3.13478 + 12.6164i 0.170510 + 0.686241i
\(339\) 4.85056 + 15.8702i 0.263446 + 0.861950i
\(340\) 2.41688 2.41688i 0.131074 0.131074i
\(341\) 0.838414i 0.0454027i
\(342\) 1.98517 1.33853i 0.107346 0.0723796i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) −1.73164 1.73164i −0.0933637 0.0933637i
\(345\) −4.09704 2.17887i −0.220577 0.117306i
\(346\) 0.668376 + 0.668376i 0.0359321 + 0.0359321i
\(347\) 11.4483i 0.614575i −0.951617 0.307287i \(-0.900579\pi\)
0.951617 0.307287i \(-0.0994212\pi\)
\(348\) 6.93788 2.12049i 0.371909 0.113670i
\(349\) −3.56656 3.56656i −0.190914 0.190914i 0.605177 0.796091i \(-0.293102\pi\)
−0.796091 + 0.605177i \(0.793102\pi\)
\(350\) −4.16658 −0.222713
\(351\) −10.8695 15.2596i −0.580171 0.814495i
\(352\) −0.489480 −0.0260894
\(353\) 3.64816 + 3.64816i 0.194172 + 0.194172i 0.797496 0.603324i \(-0.206157\pi\)
−0.603324 + 0.797496i \(0.706157\pi\)
\(354\) −5.23799 + 1.60094i −0.278396 + 0.0850889i
\(355\) 2.56877i 0.136336i
\(356\) −12.0210 12.0210i −0.637114 0.637114i
\(357\) 5.72550 + 3.04491i 0.303025 + 0.161154i
\(358\) −12.8441 12.8441i −0.678834 0.678834i
\(359\) −0.169016 + 0.169016i −0.00892035 + 0.00892035i −0.711553 0.702633i \(-0.752008\pi\)
0.702633 + 0.711553i \(0.252008\pi\)
\(360\) −2.27079 + 1.53112i −0.119681 + 0.0806971i
\(361\) 18.3630i 0.966476i
\(362\) −13.0654 + 13.0654i −0.686701 + 0.686701i
\(363\) 5.44762 + 17.8237i 0.285926 + 0.935499i
\(364\) 1.77419 + 3.13883i 0.0929928 + 0.164519i
\(365\) 3.80684i 0.199259i
\(366\) 7.00881 + 3.72740i 0.366357 + 0.194834i
\(367\) −19.5827 −1.02221 −0.511104 0.859519i \(-0.670763\pi\)
−0.511104 + 0.859519i \(0.670763\pi\)
\(368\) −2.93468 −0.152981
\(369\) 9.78830 + 1.90434i 0.509558 + 0.0991359i
\(370\) −1.98104 + 1.98104i −0.102989 + 0.102989i
\(371\) −3.55868 + 3.55868i −0.184757 + 0.184757i
\(372\) −2.61939 1.39303i −0.135809 0.0722254i
\(373\) −26.8148 −1.38842 −0.694210 0.719773i \(-0.744246\pi\)
−0.694210 + 0.719773i \(0.744246\pi\)
\(374\) 1.83262 0.0947625
\(375\) −6.80578 + 12.7972i −0.351449 + 0.660847i
\(376\) 10.2160i 0.526848i
\(377\) −14.5510 4.04168i −0.749414 0.208157i
\(378\) −4.03735 3.27105i −0.207659 0.168245i
\(379\) 0.249109 0.249109i 0.0127959 0.0127959i −0.700680 0.713476i \(-0.747120\pi\)
0.713476 + 0.700680i \(0.247120\pi\)
\(380\) 0.728595i 0.0373762i
\(381\) 8.53529 + 27.9260i 0.437276 + 1.43069i
\(382\) −10.0262 + 10.0262i −0.512984 + 0.512984i
\(383\) −2.01331 2.01331i −0.102875 0.102875i 0.653796 0.756671i \(-0.273176\pi\)
−0.756671 + 0.653796i \(0.773176\pi\)
\(384\) −0.813276 + 1.52924i −0.0415023 + 0.0780388i
\(385\) 0.315975 + 0.315975i 0.0161036 + 0.0161036i
\(386\) 4.77786i 0.243187i
\(387\) −4.10722 6.09139i −0.208782 0.309643i
\(388\) 6.69250 + 6.69250i 0.339760 + 0.339760i
\(389\) −6.62477 −0.335889 −0.167945 0.985796i \(-0.553713\pi\)
−0.167945 + 0.985796i \(0.553713\pi\)
\(390\) 5.69931 0.146461i 0.288596 0.00741635i
\(391\) 10.9875 0.555659
\(392\) 0.707107 + 0.707107i 0.0357143 + 0.0357143i
\(393\) 10.8435 + 35.4780i 0.546981 + 1.78963i
\(394\) 2.13237i 0.107427i
\(395\) 3.74968 + 3.74968i 0.188667 + 0.188667i
\(396\) −1.44142 0.280431i −0.0724338 0.0140922i
\(397\) −16.9697 16.9697i −0.851684 0.851684i 0.138657 0.990341i \(-0.455722\pi\)
−0.990341 + 0.138657i \(0.955722\pi\)
\(398\) 7.91950 7.91950i 0.396968 0.396968i
\(399\) −1.32197 + 0.404047i −0.0661812 + 0.0202276i
\(400\) 4.16658i 0.208329i
\(401\) −19.1843 + 19.1843i −0.958019 + 0.958019i −0.999154 0.0411346i \(-0.986903\pi\)
0.0411346 + 0.999154i \(0.486903\pi\)
\(402\) −3.64622 + 1.11443i −0.181857 + 0.0555828i
\(403\) 3.03895 + 5.37640i 0.151381 + 0.267817i
\(404\) 13.4516i 0.669241i
\(405\) −7.56420 + 3.20785i −0.375868 + 0.159399i
\(406\) −4.18850 −0.207872
\(407\) −1.50214 −0.0744584
\(408\) 3.04491 5.72550i 0.150746 0.283454i
\(409\) 6.18510 6.18510i 0.305834 0.305834i −0.537457 0.843291i \(-0.680615\pi\)
0.843291 + 0.537457i \(0.180615\pi\)
\(410\) −2.14571 + 2.14571i −0.105969 + 0.105969i
\(411\) 5.63526 10.5963i 0.277967 0.522675i
\(412\) −6.61463 −0.325879
\(413\) 3.16225 0.155604
\(414\) −8.64200 1.68132i −0.424731 0.0826325i
\(415\) 1.87567i 0.0920732i
\(416\) 3.13883 1.77419i 0.153894 0.0869868i
\(417\) 7.33891 2.24306i 0.359388 0.109843i
\(418\) −0.276232 + 0.276232i −0.0135109 + 0.0135109i
\(419\) 21.7419i 1.06216i 0.847321 + 0.531080i \(0.178214\pi\)
−0.847321 + 0.531080i \(0.821786\pi\)
\(420\) 1.51217 0.462180i 0.0737864 0.0225521i
\(421\) 20.0060 20.0060i 0.975035 0.975035i −0.0246608 0.999696i \(-0.507851\pi\)
0.999696 + 0.0246608i \(0.00785059\pi\)
\(422\) −11.8119 11.8119i −0.574997 0.574997i
\(423\) −5.85289 + 30.0838i −0.284577 + 1.46272i
\(424\) 3.55868 + 3.55868i 0.172825 + 0.172825i
\(425\) 15.5997i 0.756696i
\(426\) 1.42452 + 4.66079i 0.0690184 + 0.225816i
\(427\) −3.24081 3.24081i −0.156834 0.156834i
\(428\) 0.232092 0.0112186
\(429\) 2.21630 + 2.10525i 0.107004 + 0.101642i
\(430\) 2.23566 0.107813
\(431\) 19.5706 + 19.5706i 0.942682 + 0.942682i 0.998444 0.0557616i \(-0.0177587\pi\)
−0.0557616 + 0.998444i \(0.517759\pi\)
\(432\) −3.27105 + 4.03735i −0.157378 + 0.194247i
\(433\) 1.51276i 0.0726985i 0.999339 + 0.0363493i \(0.0115729\pi\)
−0.999339 + 0.0363493i \(0.988427\pi\)
\(434\) 1.21118 + 1.21118i 0.0581385 + 0.0581385i
\(435\) −3.10978 + 5.84747i −0.149102 + 0.280365i
\(436\) −8.15828 8.15828i −0.390711 0.390711i
\(437\) −1.65615 + 1.65615i −0.0792242 + 0.0792242i
\(438\) 2.11111 + 6.90717i 0.100873 + 0.330037i
\(439\) 3.57755i 0.170747i −0.996349 0.0853737i \(-0.972792\pi\)
0.996349 0.0853737i \(-0.0272084\pi\)
\(440\) 0.315975 0.315975i 0.0150635 0.0150635i
\(441\) 1.67717 + 2.48739i 0.0798650 + 0.118447i
\(442\) −11.7518 + 6.64258i −0.558976 + 0.315955i
\(443\) 2.53190i 0.120294i 0.998190 + 0.0601472i \(0.0191570\pi\)
−0.998190 + 0.0601472i \(0.980843\pi\)
\(444\) −2.49582 + 4.69302i −0.118446 + 0.222721i
\(445\) 15.5199 0.735716
\(446\) 22.9482 1.08663
\(447\) −15.1590 8.06181i −0.716997 0.381310i
\(448\) 0.707107 0.707107i 0.0334077 0.0334077i
\(449\) 12.5933 12.5933i 0.594314 0.594314i −0.344480 0.938794i \(-0.611945\pi\)
0.938794 + 0.344480i \(0.111945\pi\)
\(450\) −2.38710 + 12.2697i −0.112529 + 0.578398i
\(451\) −1.62700 −0.0766126
\(452\) −9.58107 −0.450656
\(453\) 13.6360 + 7.25183i 0.640674 + 0.340721i
\(454\) 26.2822i 1.23349i
\(455\) −3.17151 0.880920i −0.148683 0.0412982i
\(456\) 0.404047 + 1.32197i 0.0189212 + 0.0619069i
\(457\) 2.80065 2.80065i 0.131009 0.131009i −0.638562 0.769571i \(-0.720470\pi\)
0.769571 + 0.638562i \(0.220470\pi\)
\(458\) 14.5685i 0.680741i
\(459\) 12.2468 15.1159i 0.571634 0.705549i
\(460\) 1.89443 1.89443i 0.0883282 0.0883282i
\(461\) 1.30086 + 1.30086i 0.0605872 + 0.0605872i 0.736751 0.676164i \(-0.236359\pi\)
−0.676164 + 0.736751i \(0.736359\pi\)
\(462\) 0.748534 + 0.398082i 0.0348250 + 0.0185205i
\(463\) 8.21976 + 8.21976i 0.382005 + 0.382005i 0.871824 0.489819i \(-0.162937\pi\)
−0.489819 + 0.871824i \(0.662937\pi\)
\(464\) 4.18850i 0.194446i
\(465\) 2.59015 0.791652i 0.120115 0.0367120i
\(466\) −20.9136 20.9136i −0.968803 0.968803i
\(467\) −32.5141 −1.50457 −0.752286 0.658837i \(-0.771049\pi\)
−0.752286 + 0.658837i \(0.771049\pi\)
\(468\) 10.2596 3.42632i 0.474252 0.158382i
\(469\) 2.20128 0.101646
\(470\) −6.59473 6.59473i −0.304192 0.304192i
\(471\) −31.8377 + 9.73088i −1.46701 + 0.448375i
\(472\) 3.16225i 0.145555i
\(473\) 0.847603 + 0.847603i 0.0389728 + 0.0389728i
\(474\) 8.88285 + 4.72404i 0.408003 + 0.216982i
\(475\) 2.35135 + 2.35135i 0.107887 + 0.107887i
\(476\) −2.64741 + 2.64741i −0.121344 + 0.121344i
\(477\) 8.44072 + 12.5184i 0.386474 + 0.573176i
\(478\) 6.25816i 0.286242i
\(479\) 22.3153 22.3153i 1.01961 1.01961i 0.0198079 0.999804i \(-0.493695\pi\)
0.999804 0.0198079i \(-0.00630546\pi\)
\(480\) −0.462180 1.51217i −0.0210955 0.0690209i
\(481\) 9.63260 5.44472i 0.439209 0.248258i
\(482\) 16.5013i 0.751615i
\(483\) 4.48783 + 2.38670i 0.204203 + 0.108599i
\(484\) −10.7604 −0.489109
\(485\) −8.64045 −0.392343
\(486\) −11.9456 + 10.0151i −0.541864 + 0.454295i
\(487\) −7.39827 + 7.39827i −0.335247 + 0.335247i −0.854575 0.519328i \(-0.826182\pi\)
0.519328 + 0.854575i \(0.326182\pi\)
\(488\) −3.24081 + 3.24081i −0.146704 + 0.146704i
\(489\) 20.4867 + 10.8952i 0.926440 + 0.492696i
\(490\) −0.912921 −0.0412416
\(491\) 22.4035 1.01106 0.505528 0.862810i \(-0.331298\pi\)
0.505528 + 0.862810i \(0.331298\pi\)
\(492\) −2.70328 + 5.08311i −0.121873 + 0.229164i
\(493\) 15.6818i 0.706272i
\(494\) 0.770117 2.77260i 0.0346492 0.124745i
\(495\) 1.11151 0.749453i 0.0499586 0.0336854i
\(496\) 1.21118 1.21118i 0.0543836 0.0543836i
\(497\) 2.81379i 0.126216i
\(498\) −1.04017 3.40324i −0.0466109 0.152503i
\(499\) 25.8150 25.8150i 1.15564 1.15564i 0.170232 0.985404i \(-0.445548\pi\)
0.985404 0.170232i \(-0.0544517\pi\)
\(500\) −5.91732 5.91732i −0.264631 0.264631i
\(501\) −19.5645 + 36.7881i −0.874078 + 1.64357i
\(502\) 10.0858 + 10.0858i 0.450152 + 0.450152i
\(503\) 2.80539i 0.125086i −0.998042 0.0625430i \(-0.980079\pi\)
0.998042 0.0625430i \(-0.0199211\pi\)
\(504\) 2.48739 1.67717i 0.110797 0.0747069i
\(505\) −8.68343 8.68343i −0.386408 0.386408i
\(506\) 1.43647 0.0638587
\(507\) −21.8430 5.46676i −0.970080 0.242787i
\(508\) −16.8593 −0.748012
\(509\) 14.7980 + 14.7980i 0.655912 + 0.655912i 0.954410 0.298499i \(-0.0964858\pi\)
−0.298499 + 0.954410i \(0.596486\pi\)
\(510\) 1.73041 + 5.66158i 0.0766236 + 0.250699i
\(511\) 4.16996i 0.184468i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0.432453 + 4.12440i 0.0190933 + 0.182097i
\(514\) 10.3182 + 10.3182i 0.455114 + 0.455114i
\(515\) 4.26996 4.26996i 0.188157 0.188157i
\(516\) 4.05640 1.23980i 0.178573 0.0545790i
\(517\) 5.00051i 0.219922i
\(518\) 2.17001 2.17001i 0.0953446 0.0953446i
\(519\) −1.56568 + 0.478535i −0.0687258 + 0.0210054i
\(520\) −0.880920 + 3.17151i −0.0386309 + 0.139080i
\(521\) 41.1077i 1.80096i 0.434896 + 0.900481i \(0.356785\pi\)
−0.434896 + 0.900481i \(0.643215\pi\)
\(522\) −2.39966 + 12.3342i −0.105030 + 0.539855i
\(523\) −10.5444 −0.461074 −0.230537 0.973064i \(-0.574048\pi\)
−0.230537 + 0.973064i \(0.574048\pi\)
\(524\) −21.4186 −0.935676
\(525\) 3.38857 6.37171i 0.147890 0.278084i
\(526\) −18.8163 + 18.8163i −0.820429 + 0.820429i
\(527\) −4.53467 + 4.53467i −0.197533 + 0.197533i
\(528\) 0.398082 0.748534i 0.0173243 0.0325758i
\(529\) −14.3877 −0.625551
\(530\) −4.59448 −0.199571
\(531\) 1.81171 9.31216i 0.0786214 0.404113i
\(532\) 0.798093i 0.0346017i
\(533\) 10.4333 5.89730i 0.451916 0.255440i
\(534\) 28.1595 8.60667i 1.21858 0.372447i
\(535\) −0.149823 + 0.149823i −0.00647742 + 0.00647742i
\(536\) 2.20128i 0.0950808i
\(537\) 30.0876 9.19598i 1.29838 0.396836i
\(538\) −19.4613 + 19.4613i −0.839035 + 0.839035i
\(539\) −0.346115 0.346115i −0.0149082 0.0149082i
\(540\) −0.494674 4.71781i −0.0212874 0.203022i
\(541\) 9.48820 + 9.48820i 0.407930 + 0.407930i 0.881016 0.473086i \(-0.156860\pi\)
−0.473086 + 0.881016i \(0.656860\pi\)
\(542\) 15.8991i 0.682924i
\(543\) −9.35438 30.6059i −0.401435 1.31342i
\(544\) 2.64741 + 2.64741i 0.113507 + 0.113507i
\(545\) 10.5329 0.451179
\(546\) −6.24294 + 0.160431i −0.267173 + 0.00686583i
\(547\) 34.3778 1.46989 0.734945 0.678127i \(-0.237208\pi\)
0.734945 + 0.678127i \(0.237208\pi\)
\(548\) 4.89961 + 4.89961i 0.209301 + 0.209301i
\(549\) −11.4002 + 7.68677i −0.486549 + 0.328064i
\(550\) 2.03946i 0.0869627i
\(551\) 2.36373 + 2.36373i 0.100698 + 0.100698i
\(552\) 2.38670 4.48783i 0.101585 0.191015i
\(553\) −4.10734 4.10734i −0.174662 0.174662i
\(554\) 17.4259 17.4259i 0.740355 0.740355i
\(555\) −1.41836 4.64063i −0.0602061 0.196984i
\(556\) 4.43061i 0.187900i
\(557\) −23.0785 + 23.0785i −0.977867 + 0.977867i −0.999760 0.0218937i \(-0.993030\pi\)
0.0218937 + 0.999760i \(0.493030\pi\)
\(558\) 4.26057 2.87276i 0.180364 0.121614i
\(559\) −8.50757 2.36307i −0.359832 0.0999470i
\(560\) 0.912921i 0.0385779i
\(561\) −1.49042 + 2.80252i −0.0629258 + 0.118322i
\(562\) −33.0757 −1.39521
\(563\) 19.8382 0.836082 0.418041 0.908428i \(-0.362717\pi\)
0.418041 + 0.908428i \(0.362717\pi\)
\(564\) −15.6227 8.30839i −0.657833 0.349846i
\(565\) 6.18489 6.18489i 0.260200 0.260200i
\(566\) 6.73817 6.73817i 0.283226 0.283226i
\(567\) 8.28571 3.51383i 0.347967 0.147567i
\(568\) −2.81379 −0.118064
\(569\) 6.55300 0.274716 0.137358 0.990521i \(-0.456139\pi\)
0.137358 + 0.990521i \(0.456139\pi\)
\(570\) −1.11420 0.592549i −0.0466687 0.0248191i
\(571\) 30.9170i 1.29384i −0.762559 0.646919i \(-0.776057\pi\)
0.762559 0.646919i \(-0.223943\pi\)
\(572\) −1.53640 + 0.868431i −0.0642399 + 0.0363109i
\(573\) −7.17841 23.4865i −0.299882 0.981163i
\(574\) 2.35038 2.35038i 0.0981030 0.0981030i
\(575\) 12.2276i 0.509924i
\(576\) −1.67717 2.48739i −0.0698819 0.103641i
\(577\) 10.8612 10.8612i 0.452158 0.452158i −0.443912 0.896070i \(-0.646410\pi\)
0.896070 + 0.443912i \(0.146410\pi\)
\(578\) 2.10888 + 2.10888i 0.0877177 + 0.0877177i
\(579\) 7.30651 + 3.88572i 0.303648 + 0.161485i
\(580\) −2.70381 2.70381i −0.112270 0.112270i
\(581\) 2.05459i 0.0852386i
\(582\) −15.6773 + 4.79161i −0.649845 + 0.198619i
\(583\) −1.74190 1.74190i −0.0721422 0.0721422i
\(584\) −4.16996 −0.172554
\(585\) −4.41113 + 8.83473i −0.182378 + 0.365271i
\(586\) −9.45631 −0.390636
\(587\) −4.36741 4.36741i −0.180262 0.180262i 0.611208 0.791470i \(-0.290684\pi\)
−0.791470 + 0.611208i \(0.790684\pi\)
\(588\) −1.65641 + 0.506265i −0.0683092 + 0.0208780i
\(589\) 1.36703i 0.0563273i
\(590\) 2.04134 + 2.04134i 0.0840405 + 0.0840405i
\(591\) 3.26091 + 1.73421i 0.134136 + 0.0713357i
\(592\) −2.17001 2.17001i −0.0891867 0.0891867i
\(593\) 6.15560 6.15560i 0.252780 0.252780i −0.569329 0.822109i \(-0.692797\pi\)
0.822109 + 0.569329i \(0.192797\pi\)
\(594\) 1.60112 1.97621i 0.0656945 0.0810847i
\(595\) 3.41798i 0.140124i
\(596\) 7.00938 7.00938i 0.287115 0.287115i
\(597\) 5.67010 + 18.5516i 0.232062 + 0.759265i
\(598\) −9.21145 + 5.20667i −0.376684 + 0.212917i
\(599\) 31.1615i 1.27323i 0.771184 + 0.636613i \(0.219665\pi\)
−0.771184 + 0.636613i \(0.780335\pi\)
\(600\) −6.37171 3.38857i −0.260124 0.138338i
\(601\) 10.3915 0.423878 0.211939 0.977283i \(-0.432022\pi\)
0.211939 + 0.977283i \(0.432022\pi\)
\(602\) −2.44891 −0.0998100
\(603\) 1.26115 6.48230i 0.0513579 0.263980i
\(604\) −6.30515 + 6.30515i −0.256553 + 0.256553i
\(605\) 6.94619 6.94619i 0.282403 0.282403i
\(606\) −20.5707 10.9398i −0.835629 0.444401i
\(607\) −19.5779 −0.794643 −0.397322 0.917679i \(-0.630060\pi\)
−0.397322 + 0.917679i \(0.630060\pi\)
\(608\) −0.798093 −0.0323669
\(609\) 3.40641 6.40524i 0.138035 0.259553i
\(610\) 4.18409i 0.169409i
\(611\) 18.1250 + 32.0661i 0.733260 + 1.29726i
\(612\) 6.27932 + 9.31281i 0.253827 + 0.376448i
\(613\) 6.71448 6.71448i 0.271195 0.271195i −0.558386 0.829581i \(-0.688579\pi\)
0.829581 + 0.558386i \(0.188579\pi\)
\(614\) 24.9184i 1.00563i
\(615\) −1.53626 5.02637i −0.0619479 0.202683i
\(616\) −0.346115 + 0.346115i −0.0139454 + 0.0139454i
\(617\) −10.3723 10.3723i −0.417575 0.417575i 0.466792 0.884367i \(-0.345410\pi\)
−0.884367 + 0.466792i \(0.845410\pi\)
\(618\) 5.37952 10.1154i 0.216396 0.406900i
\(619\) −17.7776 17.7776i −0.714542 0.714542i 0.252940 0.967482i \(-0.418602\pi\)
−0.967482 + 0.252940i \(0.918602\pi\)
\(620\) 1.56371i 0.0628001i
\(621\) 9.59948 11.8483i 0.385214 0.475457i
\(622\) −2.91052 2.91052i −0.116701 0.116701i
\(623\) −17.0003 −0.681104
\(624\) 0.160431 + 6.24294i 0.00642240 + 0.249917i
\(625\) −13.1932 −0.527729
\(626\) 10.7074 + 10.7074i 0.427955 + 0.427955i
\(627\) −0.197773 0.647078i −0.00789829 0.0258418i
\(628\) 19.2209i 0.766998i
\(629\) 8.12452 + 8.12452i 0.323946 + 0.323946i
\(630\) −0.523027 + 2.68836i −0.0208379 + 0.107107i
\(631\) 33.4192 + 33.4192i 1.33040 + 1.33040i 0.905011 + 0.425388i \(0.139862\pi\)
0.425388 + 0.905011i \(0.360138\pi\)
\(632\) −4.10734 + 4.10734i −0.163381 + 0.163381i
\(633\) 27.6697 8.45697i 1.09977 0.336134i
\(634\) 22.3606i 0.888053i
\(635\) 10.8832 10.8832i 0.431888 0.431888i
\(636\) −8.33626 + 2.54789i −0.330554 + 0.101031i
\(637\) 3.47403 + 0.964947i 0.137646 + 0.0382326i
\(638\) 2.05019i 0.0811678i
\(639\) −8.28601 1.61206i −0.327789 0.0637723i
\(640\) 0.912921 0.0360864
\(641\) −33.1552 −1.30955 −0.654775 0.755823i \(-0.727237\pi\)
−0.654775 + 0.755823i \(0.727237\pi\)
\(642\) −0.188755 + 0.354926i −0.00744957 + 0.0140078i
\(643\) 12.7533 12.7533i 0.502941 0.502941i −0.409410 0.912351i \(-0.634265\pi\)
0.912351 + 0.409410i \(0.134265\pi\)
\(644\) −2.07513 + 2.07513i −0.0817716 + 0.0817716i
\(645\) −1.81821 + 3.41886i −0.0715918 + 0.134618i
\(646\) 2.98807 0.117564
\(647\) −25.5626 −1.00497 −0.502484 0.864586i \(-0.667580\pi\)
−0.502484 + 0.864586i \(0.667580\pi\)
\(648\) −3.51383 8.28571i −0.138036 0.325493i
\(649\) 1.54786i 0.0607589i
\(650\) 7.39229 + 13.0782i 0.289950 + 0.512968i
\(651\) −2.83721 + 0.867164i −0.111199 + 0.0339868i
\(652\) −9.47285 + 9.47285i −0.370985 + 0.370985i
\(653\) 37.4482i 1.46546i 0.680520 + 0.732730i \(0.261754\pi\)
−0.680520 + 0.732730i \(0.738246\pi\)
\(654\) 19.1109 5.84106i 0.747296 0.228404i
\(655\) 13.8264 13.8264i 0.540242 0.540242i
\(656\) −2.35038 2.35038i −0.0917670 0.0917670i
\(657\) −12.2796 2.38904i −0.479075 0.0932052i
\(658\) 7.22377 + 7.22377i 0.281612 + 0.281612i
\(659\) 9.60599i 0.374196i −0.982341 0.187098i \(-0.940092\pi\)
0.982341 0.187098i \(-0.0599082\pi\)
\(660\) 0.226228 + 0.740178i 0.00880591 + 0.0288114i
\(661\) 6.14906 + 6.14906i 0.239171 + 0.239171i 0.816507 0.577336i \(-0.195908\pi\)
−0.577336 + 0.816507i \(0.695908\pi\)
\(662\) −16.2910 −0.633169
\(663\) −0.600657 23.3736i −0.0233276 0.907756i
\(664\) 2.05459 0.0797334
\(665\) 0.515195 + 0.515195i 0.0199784 + 0.0199784i
\(666\) −5.14697 7.63343i −0.199441 0.295790i
\(667\) 12.2919i 0.475944i
\(668\) −17.0105 17.0105i −0.658155 0.658155i
\(669\) −18.6632 + 35.0934i −0.721563 + 1.35679i
\(670\) 1.42100 + 1.42100i 0.0548979 + 0.0548979i
\(671\) 1.58631 1.58631i 0.0612389 0.0612389i
\(672\) 0.506265 + 1.65641i 0.0195296 + 0.0638974i
\(673\) 6.96650i 0.268539i 0.990945 + 0.134269i \(0.0428688\pi\)
−0.990945 + 0.134269i \(0.957131\pi\)
\(674\) −20.7548 + 20.7548i −0.799444 + 0.799444i
\(675\) −16.8219 13.6291i −0.647477 0.524584i
\(676\) 6.70451 11.1378i 0.257866 0.428375i
\(677\) 5.13417i 0.197322i 0.995121 + 0.0986611i \(0.0314560\pi\)
−0.995121 + 0.0986611i \(0.968544\pi\)
\(678\) 7.79205 14.6518i 0.299252 0.562698i
\(679\) 9.46462 0.363219
\(680\) −3.41798 −0.131074
\(681\) −40.1919 21.3747i −1.54016 0.819081i
\(682\) −0.592848 + 0.592848i −0.0227013 + 0.0227013i
\(683\) −15.1739 + 15.1739i −0.580615 + 0.580615i −0.935072 0.354457i \(-0.884666\pi\)
0.354457 + 0.935072i \(0.384666\pi\)
\(684\) −2.35021 0.457240i −0.0898626 0.0174830i
\(685\) −6.32571 −0.241693
\(686\) 1.00000 0.0381802
\(687\) −22.2788 11.8482i −0.849988 0.452037i
\(688\) 2.44891i 0.0933637i
\(689\) 17.4838 + 4.85631i 0.666081 + 0.185011i
\(690\) 1.35635 + 4.43773i 0.0516353 + 0.168942i
\(691\) −19.4188 + 19.4188i −0.738725 + 0.738725i −0.972331 0.233607i \(-0.924947\pi\)
0.233607 + 0.972331i \(0.424947\pi\)
\(692\) 0.945226i 0.0359321i
\(693\) −1.21753 + 0.820940i −0.0462501 + 0.0311849i
\(694\) −8.09514 + 8.09514i −0.307287 + 0.307287i
\(695\) −2.86010 2.86010i −0.108490 0.108490i
\(696\) −6.40524 3.40641i −0.242790 0.129120i
\(697\) 8.79985 + 8.79985i 0.333318 + 0.333318i
\(698\) 5.04388i 0.190914i
\(699\) 48.9905 14.9734i 1.85299 0.566348i
\(700\) 2.94621 + 2.94621i 0.111356 + 0.111356i
\(701\) 24.6973 0.932803 0.466402 0.884573i \(-0.345550\pi\)
0.466402 + 0.884573i \(0.345550\pi\)
\(702\) −3.10424 + 18.4760i −0.117162 + 0.697333i
\(703\) −2.44923 −0.0923744
\(704\) 0.346115 + 0.346115i 0.0130447 + 0.0130447i
\(705\) 15.4483 4.72161i 0.581816 0.177826i
\(706\) 5.15928i 0.194172i
\(707\) 9.51170 + 9.51170i 0.357724 + 0.357724i
\(708\) 4.83585 + 2.57178i 0.181743 + 0.0966536i
\(709\) 15.9540 + 15.9540i 0.599167 + 0.599167i 0.940091 0.340924i \(-0.110740\pi\)
−0.340924 + 0.940091i \(0.610740\pi\)
\(710\) 1.81639 1.81639i 0.0681680 0.0681680i
\(711\) −14.4484 + 9.74208i −0.541857 + 0.365357i
\(712\) 17.0003i 0.637114i
\(713\) −3.55442 + 3.55442i −0.133114 + 0.133114i
\(714\) −1.89546 6.20161i −0.0709358 0.232090i
\(715\) 0.431193 1.55239i 0.0161257 0.0580562i
\(716\) 18.1644i 0.678834i
\(717\) −9.57025 5.08961i −0.357407 0.190075i
\(718\) 0.239025 0.00892035
\(719\) 10.8293 0.403865 0.201933 0.979399i \(-0.435278\pi\)
0.201933 + 0.979399i \(0.435278\pi\)
\(720\) 2.68836 + 0.523027i 0.100189 + 0.0194921i
\(721\) −4.67725 + 4.67725i −0.174190 + 0.174190i
\(722\) 12.9846 12.9846i 0.483238 0.483238i
\(723\) −25.2345 13.4201i −0.938483 0.499100i
\(724\) 18.4772 0.686701
\(725\) −17.4517 −0.648140
\(726\) 8.75118 16.4553i 0.324787 0.610713i
\(727\) 33.1488i 1.22942i 0.788753 + 0.614710i \(0.210727\pi\)
−0.788753 + 0.614710i \(0.789273\pi\)
\(728\) 0.964947 3.47403i 0.0357633 0.128756i
\(729\) −5.60046 26.4128i −0.207424 0.978251i
\(730\) 2.69185 2.69185i 0.0996297 0.0996297i
\(731\) 9.16873i 0.339118i
\(732\) −2.32031 7.59165i −0.0857612 0.280595i
\(733\) 16.6460 16.6460i 0.614835 0.614835i −0.329367 0.944202i \(-0.606835\pi\)
0.944202 + 0.329367i \(0.106835\pi\)
\(734\) 13.8470 + 13.8470i 0.511104 + 0.511104i
\(735\) 0.742456 1.39608i 0.0273859 0.0514951i
\(736\) 2.07513 + 2.07513i 0.0764903 + 0.0764903i
\(737\) 1.07748i 0.0396896i
\(738\) −5.57480 8.26794i −0.205211 0.304347i
\(739\) −31.1450 31.1450i −1.14569 1.14569i −0.987392 0.158294i \(-0.949401\pi\)
−0.158294 0.987392i \(-0.550599\pi\)
\(740\) 2.80162 0.102989
\(741\) 3.61366 + 3.43258i 0.132751 + 0.126099i
\(742\) 5.03273 0.184757
\(743\) 20.0711 + 20.0711i 0.736339 + 0.736339i 0.971867 0.235529i \(-0.0756822\pi\)
−0.235529 + 0.971867i \(0.575682\pi\)
\(744\) 0.867164 + 2.83721i 0.0317918 + 0.104017i
\(745\) 9.04956i 0.331550i
\(746\) 18.9610 + 18.9610i 0.694210 + 0.694210i
\(747\) 6.05032 + 1.17711i 0.221369 + 0.0430680i
\(748\) −1.29586 1.29586i −0.0473812 0.0473812i
\(749\) 0.164114 0.164114i 0.00599660 0.00599660i
\(750\) 13.8614 4.23661i 0.506148 0.154699i
\(751\) 5.53789i 0.202080i −0.994882 0.101040i \(-0.967783\pi\)
0.994882 0.101040i \(-0.0322171\pi\)
\(752\) 7.22377 7.22377i 0.263424 0.263424i
\(753\) −23.6262 + 7.22111i −0.860987 + 0.263152i
\(754\) 7.43119 + 13.1470i 0.270628 + 0.478785i
\(755\) 8.14035i 0.296258i
\(756\) 0.541858 + 5.16782i 0.0197072 + 0.187952i
\(757\) 37.7422 1.37176 0.685882 0.727713i \(-0.259417\pi\)
0.685882 + 0.727713i \(0.259417\pi\)
\(758\) −0.352294 −0.0127959
\(759\) −1.16824 + 2.19671i −0.0424045 + 0.0797354i
\(760\) 0.515195 0.515195i 0.0186881 0.0186881i
\(761\) 13.0324 13.0324i 0.472423 0.472423i −0.430275 0.902698i \(-0.641583\pi\)
0.902698 + 0.430275i \(0.141583\pi\)
\(762\) 13.7113 25.7820i 0.496707 0.933983i
\(763\) −11.5376 −0.417687
\(764\) 14.1792 0.512984
\(765\) −10.0652 1.95822i −0.363909 0.0707995i
\(766\) 2.84725i 0.102875i
\(767\) −5.61044 9.92578i −0.202581 0.358399i
\(768\) 1.65641 0.506265i 0.0597706 0.0182683i
\(769\) −8.01862 + 8.01862i −0.289159 + 0.289159i −0.836748 0.547589i \(-0.815546\pi\)
0.547589 + 0.836748i \(0.315546\pi\)
\(770\) 0.446857i 0.0161036i
\(771\) −24.1705 + 7.38746i −0.870478 + 0.266053i
\(772\) −3.37846 + 3.37846i −0.121593 + 0.121593i
\(773\) −27.9230 27.9230i −1.00432 1.00432i −0.999991 0.00433086i \(-0.998621\pi\)
−0.00433086 0.999991i \(-0.501379\pi\)
\(774\) −1.40302 + 7.21151i −0.0504304 + 0.259212i
\(775\) 5.04647 + 5.04647i 0.181275 + 0.181275i
\(776\) 9.46462i