Properties

Label 546.2.p.c.281.1
Level $546$
Weight $2$
Character 546.281
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 281.1
Root \(0.0557032 - 1.73115i\) of defining polynomial
Character \(\chi\) \(=\) 546.281
Dual form 546.2.p.c.239.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.18472 - 1.26350i) q^{3} -1.00000i q^{4} +(2.80148 - 2.80148i) q^{5} +(1.73115 + 0.0557032i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.192862 + 2.99379i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.18472 - 1.26350i) q^{3} -1.00000i q^{4} +(2.80148 - 2.80148i) q^{5} +(1.73115 + 0.0557032i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.192862 + 2.99379i) q^{9} +3.96189i q^{10} +(3.20912 + 3.20912i) q^{11} +(-1.26350 + 1.18472i) q^{12} +(3.52656 - 0.750597i) q^{13} +1.00000i q^{14} +(-6.85864 - 0.220690i) q^{15} -1.00000 q^{16} +3.46154 q^{17} +(-1.98056 - 2.25331i) q^{18} +(-1.81073 - 1.81073i) q^{19} +(-2.80148 - 2.80148i) q^{20} +(-1.73115 - 0.0557032i) q^{21} -4.53838 q^{22} -0.728379 q^{23} +(0.0557032 - 1.73115i) q^{24} -10.6966i q^{25} +(-1.96290 + 3.02440i) q^{26} +(4.01115 - 3.30314i) q^{27} +(-0.707107 - 0.707107i) q^{28} +6.96800i q^{29} +(5.00584 - 4.69374i) q^{30} +(-7.26840 - 7.26840i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.252802 - 7.85664i) q^{33} +(-2.44768 + 2.44768i) q^{34} -3.96189i q^{35} +(2.99379 + 0.192862i) q^{36} +(-1.56147 + 1.56147i) q^{37} +2.56075 q^{38} +(-5.12637 - 3.56655i) q^{39} +3.96189 q^{40} +(3.59240 - 3.59240i) q^{41} +(1.26350 - 1.18472i) q^{42} +7.44129i q^{43} +(3.20912 - 3.20912i) q^{44} +(7.84675 + 8.92735i) q^{45} +(0.515041 - 0.515041i) q^{46} +(7.17522 + 7.17522i) q^{47} +(1.18472 + 1.26350i) q^{48} -1.00000i q^{49} +(7.56361 + 7.56361i) q^{50} +(-4.10096 - 4.37365i) q^{51} +(-0.750597 - 3.52656i) q^{52} -11.8689i q^{53} +(-0.500638 + 5.17198i) q^{54} +17.9806 q^{55} +1.00000 q^{56} +(-0.142642 + 4.43306i) q^{57} +(-4.92712 - 4.92712i) q^{58} +(-7.33162 - 7.33162i) q^{59} +(-0.220690 + 6.85864i) q^{60} -0.300726 q^{61} +10.2791 q^{62} +(1.98056 + 2.25331i) q^{63} +1.00000i q^{64} +(7.77679 - 11.9824i) q^{65} +(5.37672 + 5.73424i) q^{66} +(-3.02964 - 3.02964i) q^{67} -3.46154i q^{68} +(0.862927 + 0.920306i) q^{69} +(2.80148 + 2.80148i) q^{70} +(-3.36041 + 3.36041i) q^{71} +(-2.25331 + 1.98056i) q^{72} +(-6.89498 + 6.89498i) q^{73} -2.20825i q^{74} +(-13.5151 + 12.6725i) q^{75} +(-1.81073 + 1.81073i) q^{76} +4.53838 q^{77} +(6.14683 - 1.10296i) q^{78} -5.87555 q^{79} +(-2.80148 + 2.80148i) q^{80} +(-8.92561 - 1.15478i) q^{81} +5.08041i q^{82} +(-7.55138 + 7.55138i) q^{83} +(-0.0557032 + 1.73115i) q^{84} +(9.69742 - 9.69742i) q^{85} +(-5.26178 - 5.26178i) q^{86} +(8.80407 - 8.25516i) q^{87} +4.53838i q^{88} +(0.819132 + 0.819132i) q^{89} +(-11.8611 - 0.764097i) q^{90} +(1.96290 - 3.02440i) q^{91} +0.728379i q^{92} +(-0.572577 + 17.7947i) q^{93} -10.1473 q^{94} -10.1454 q^{95} +(-1.73115 - 0.0557032i) q^{96} +(1.37504 + 1.37504i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-10.2264 + 8.98852i) 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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.18472 1.26350i −0.684000 0.729482i
\(4\) 1.00000i 0.500000i
\(5\) 2.80148 2.80148i 1.25286 1.25286i 0.298426 0.954433i \(-0.403538\pi\)
0.954433 0.298426i \(-0.0964617\pi\)
\(6\) 1.73115 + 0.0557032i 0.706741 + 0.0227407i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −0.192862 + 2.99379i −0.0642873 + 0.997931i
\(10\) 3.96189i 1.25286i
\(11\) 3.20912 + 3.20912i 0.967586 + 0.967586i 0.999491 0.0319052i \(-0.0101575\pi\)
−0.0319052 + 0.999491i \(0.510157\pi\)
\(12\) −1.26350 + 1.18472i −0.364741 + 0.342000i
\(13\) 3.52656 0.750597i 0.978091 0.208178i
\(14\) 1.00000i 0.267261i
\(15\) −6.85864 0.220690i −1.77089 0.0569819i
\(16\) −1.00000 −0.250000
\(17\) 3.46154 0.839546 0.419773 0.907629i \(-0.362110\pi\)
0.419773 + 0.907629i \(0.362110\pi\)
\(18\) −1.98056 2.25331i −0.466822 0.531109i
\(19\) −1.81073 1.81073i −0.415409 0.415409i 0.468209 0.883618i \(-0.344899\pi\)
−0.883618 + 0.468209i \(0.844899\pi\)
\(20\) −2.80148 2.80148i −0.626430 0.626430i
\(21\) −1.73115 0.0557032i −0.377769 0.0121554i
\(22\) −4.53838 −0.967586
\(23\) −0.728379 −0.151877 −0.0759387 0.997112i \(-0.524195\pi\)
−0.0759387 + 0.997112i \(0.524195\pi\)
\(24\) 0.0557032 1.73115i 0.0113704 0.353371i
\(25\) 10.6966i 2.13931i
\(26\) −1.96290 + 3.02440i −0.384956 + 0.593134i
\(27\) 4.01115 3.30314i 0.771945 0.635689i
\(28\) −0.707107 0.707107i −0.133631 0.133631i
\(29\) 6.96800i 1.29393i 0.762521 + 0.646963i \(0.223961\pi\)
−0.762521 + 0.646963i \(0.776039\pi\)
\(30\) 5.00584 4.69374i 0.913938 0.856956i
\(31\) −7.26840 7.26840i −1.30544 1.30544i −0.924668 0.380775i \(-0.875657\pi\)
−0.380775 0.924668i \(-0.624343\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0.252802 7.85664i 0.0440072 1.36766i
\(34\) −2.44768 + 2.44768i −0.419773 + 0.419773i
\(35\) 3.96189i 0.669681i
\(36\) 2.99379 + 0.192862i 0.498966 + 0.0321436i
\(37\) −1.56147 + 1.56147i −0.256703 + 0.256703i −0.823712 0.567009i \(-0.808101\pi\)
0.567009 + 0.823712i \(0.308101\pi\)
\(38\) 2.56075 0.415409
\(39\) −5.12637 3.56655i −0.820877 0.571106i
\(40\) 3.96189 0.626430
\(41\) 3.59240 3.59240i 0.561038 0.561038i −0.368564 0.929602i \(-0.620151\pi\)
0.929602 + 0.368564i \(0.120151\pi\)
\(42\) 1.26350 1.18472i 0.194962 0.182807i
\(43\) 7.44129i 1.13479i 0.823447 + 0.567393i \(0.192048\pi\)
−0.823447 + 0.567393i \(0.807952\pi\)
\(44\) 3.20912 3.20912i 0.483793 0.483793i
\(45\) 7.84675 + 8.92735i 1.16972 + 1.33081i
\(46\) 0.515041 0.515041i 0.0759387 0.0759387i
\(47\) 7.17522 + 7.17522i 1.04661 + 1.04661i 0.998859 + 0.0477542i \(0.0152064\pi\)
0.0477542 + 0.998859i \(0.484794\pi\)
\(48\) 1.18472 + 1.26350i 0.171000 + 0.182370i
\(49\) 1.00000i 0.142857i
\(50\) 7.56361 + 7.56361i 1.06966 + 1.06966i
\(51\) −4.10096 4.37365i −0.574250 0.612434i
\(52\) −0.750597 3.52656i −0.104089 0.489045i
\(53\) 11.8689i 1.63031i −0.579240 0.815157i \(-0.696651\pi\)
0.579240 0.815157i \(-0.303349\pi\)
\(54\) −0.500638 + 5.17198i −0.0681282 + 0.703817i
\(55\) 17.9806 2.42450
\(56\) 1.00000 0.133631
\(57\) −0.142642 + 4.43306i −0.0188934 + 0.587173i
\(58\) −4.92712 4.92712i −0.646963 0.646963i
\(59\) −7.33162 7.33162i −0.954495 0.954495i 0.0445134 0.999009i \(-0.485826\pi\)
−0.999009 + 0.0445134i \(0.985826\pi\)
\(60\) −0.220690 + 6.85864i −0.0284910 + 0.885447i
\(61\) −0.300726 −0.0385040 −0.0192520 0.999815i \(-0.506128\pi\)
−0.0192520 + 0.999815i \(0.506128\pi\)
\(62\) 10.2791 1.30544
\(63\) 1.98056 + 2.25331i 0.249527 + 0.283890i
\(64\) 1.00000i 0.125000i
\(65\) 7.77679 11.9824i 0.964592 1.48623i
\(66\) 5.37672 + 5.73424i 0.661829 + 0.705836i
\(67\) −3.02964 3.02964i −0.370130 0.370130i 0.497395 0.867524i \(-0.334290\pi\)
−0.867524 + 0.497395i \(0.834290\pi\)
\(68\) 3.46154i 0.419773i
\(69\) 0.862927 + 0.920306i 0.103884 + 0.110792i
\(70\) 2.80148 + 2.80148i 0.334841 + 0.334841i
\(71\) −3.36041 + 3.36041i −0.398807 + 0.398807i −0.877812 0.479005i \(-0.840998\pi\)
0.479005 + 0.877812i \(0.340998\pi\)
\(72\) −2.25331 + 1.98056i −0.265555 + 0.233411i
\(73\) −6.89498 + 6.89498i −0.806996 + 0.806996i −0.984178 0.177182i \(-0.943302\pi\)
0.177182 + 0.984178i \(0.443302\pi\)
\(74\) 2.20825i 0.256703i
\(75\) −13.5151 + 12.6725i −1.56059 + 1.46329i
\(76\) −1.81073 + 1.81073i −0.207704 + 0.207704i
\(77\) 4.53838 0.517196
\(78\) 6.14683 1.10296i 0.695991 0.124885i
\(79\) −5.87555 −0.661051 −0.330525 0.943797i \(-0.607226\pi\)
−0.330525 + 0.943797i \(0.607226\pi\)
\(80\) −2.80148 + 2.80148i −0.313215 + 0.313215i
\(81\) −8.92561 1.15478i −0.991734 0.128309i
\(82\) 5.08041i 0.561038i
\(83\) −7.55138 + 7.55138i −0.828872 + 0.828872i −0.987361 0.158489i \(-0.949338\pi\)
0.158489 + 0.987361i \(0.449338\pi\)
\(84\) −0.0557032 + 1.73115i −0.00607772 + 0.188884i
\(85\) 9.69742 9.69742i 1.05183 1.05183i
\(86\) −5.26178 5.26178i −0.567393 0.567393i
\(87\) 8.80407 8.25516i 0.943895 0.885046i
\(88\) 4.53838i 0.483793i
\(89\) 0.819132 + 0.819132i 0.0868278 + 0.0868278i 0.749187 0.662359i \(-0.230445\pi\)
−0.662359 + 0.749187i \(0.730445\pi\)
\(90\) −11.8611 0.764097i −1.25027 0.0805429i
\(91\) 1.96290 3.02440i 0.205768 0.317044i
\(92\) 0.728379i 0.0759387i
\(93\) −0.572577 + 17.7947i −0.0593735 + 1.84522i
\(94\) −10.1473 −1.04661
\(95\) −10.1454 −1.04090
\(96\) −1.73115 0.0557032i −0.176685 0.00568519i
\(97\) 1.37504 + 1.37504i 0.139614 + 0.139614i 0.773460 0.633846i \(-0.218525\pi\)
−0.633846 + 0.773460i \(0.718525\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) −10.2264 + 8.98852i −1.02779 + 0.903381i
\(100\) −10.6966 −1.06966
\(101\) 1.04374 0.103856 0.0519282 0.998651i \(-0.483463\pi\)
0.0519282 + 0.998651i \(0.483463\pi\)
\(102\) 5.99246 + 0.192819i 0.593342 + 0.0190919i
\(103\) 8.39105i 0.826795i −0.910551 0.413398i \(-0.864342\pi\)
0.910551 0.413398i \(-0.135658\pi\)
\(104\) 3.02440 + 1.96290i 0.296567 + 0.192478i
\(105\) −5.00584 + 4.69374i −0.488520 + 0.458062i
\(106\) 8.39255 + 8.39255i 0.815157 + 0.815157i
\(107\) 14.3199i 1.38435i 0.721728 + 0.692176i \(0.243348\pi\)
−0.721728 + 0.692176i \(0.756652\pi\)
\(108\) −3.30314 4.01115i −0.317844 0.385973i
\(109\) −0.311497 0.311497i −0.0298360 0.0298360i 0.692031 0.721867i \(-0.256716\pi\)
−0.721867 + 0.692031i \(0.756716\pi\)
\(110\) −12.7142 + 12.7142i −1.21225 + 1.21225i
\(111\) 3.82282 + 0.123006i 0.362846 + 0.0116753i
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) 4.65219i 0.437641i −0.975765 0.218821i \(-0.929779\pi\)
0.975765 0.218821i \(-0.0702209\pi\)
\(114\) −3.03378 3.23551i −0.284140 0.303033i
\(115\) −2.04054 + 2.04054i −0.190281 + 0.190281i
\(116\) 6.96800 0.646963
\(117\) 1.56699 + 10.7025i 0.144869 + 0.989451i
\(118\) 10.3685 0.954495
\(119\) 2.44768 2.44768i 0.224378 0.224378i
\(120\) −4.69374 5.00584i −0.428478 0.456969i
\(121\) 9.59688i 0.872444i
\(122\) 0.212645 0.212645i 0.0192520 0.0192520i
\(123\) −8.79498 0.282995i −0.793017 0.0255168i
\(124\) −7.26840 + 7.26840i −0.652721 + 0.652721i
\(125\) −15.9588 15.9588i −1.42740 1.42740i
\(126\) −2.99379 0.192862i −0.266708 0.0171815i
\(127\) 8.51785i 0.755837i 0.925839 + 0.377918i \(0.123360\pi\)
−0.925839 + 0.377918i \(0.876640\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 9.40206 8.81586i 0.827805 0.776194i
\(130\) 2.97378 + 13.9718i 0.260818 + 1.22541i
\(131\) 1.65007i 0.144167i 0.997399 + 0.0720837i \(0.0229649\pi\)
−0.997399 + 0.0720837i \(0.977035\pi\)
\(132\) −7.85664 0.252802i −0.683832 0.0220036i
\(133\) −2.56075 −0.222045
\(134\) 4.28456 0.370130
\(135\) 1.98347 20.4908i 0.170710 1.76357i
\(136\) 2.44768 + 2.44768i 0.209887 + 0.209887i
\(137\) 9.11987 + 9.11987i 0.779163 + 0.779163i 0.979689 0.200525i \(-0.0642648\pi\)
−0.200525 + 0.979689i \(0.564265\pi\)
\(138\) −1.26094 0.0405730i −0.107338 0.00345381i
\(139\) −19.2565 −1.63331 −0.816656 0.577125i \(-0.804175\pi\)
−0.816656 + 0.577125i \(0.804175\pi\)
\(140\) −3.96189 −0.334841
\(141\) 0.565237 17.5665i 0.0476015 1.47937i
\(142\) 4.75234i 0.398807i
\(143\) 13.7259 + 8.90839i 1.14782 + 0.744957i
\(144\) 0.192862 2.99379i 0.0160718 0.249483i
\(145\) 19.5207 + 19.5207i 1.62111 + 1.62111i
\(146\) 9.75097i 0.806996i
\(147\) −1.26350 + 1.18472i −0.104212 + 0.0977143i
\(148\) 1.56147 + 1.56147i 0.128352 + 0.128352i
\(149\) 15.7466 15.7466i 1.29001 1.29001i 0.355233 0.934778i \(-0.384401\pi\)
0.934778 0.355233i \(-0.115599\pi\)
\(150\) 0.595833 18.5174i 0.0486495 1.51194i
\(151\) 13.5912 13.5912i 1.10604 1.10604i 0.112374 0.993666i \(-0.464155\pi\)
0.993666 0.112374i \(-0.0358454\pi\)
\(152\) 2.56075i 0.207704i
\(153\) −0.667599 + 10.3631i −0.0539721 + 0.837810i
\(154\) −3.20912 + 3.20912i −0.258598 + 0.258598i
\(155\) −40.7245 −3.27107
\(156\) −3.56655 + 5.12637i −0.285553 + 0.410438i
\(157\) 1.54786 0.123533 0.0617665 0.998091i \(-0.480327\pi\)
0.0617665 + 0.998091i \(0.480327\pi\)
\(158\) 4.15464 4.15464i 0.330525 0.330525i
\(159\) −14.9963 + 14.0613i −1.18928 + 1.11514i
\(160\) 3.96189i 0.313215i
\(161\) −0.515041 + 0.515041i −0.0405910 + 0.0405910i
\(162\) 7.12791 5.49481i 0.560021 0.431713i
\(163\) 0.281966 0.281966i 0.0220853 0.0220853i −0.695978 0.718063i \(-0.745029\pi\)
0.718063 + 0.695978i \(0.245029\pi\)
\(164\) −3.59240 3.59240i −0.280519 0.280519i
\(165\) −21.3020 22.7184i −1.65836 1.76863i
\(166\) 10.6793i 0.828872i
\(167\) 13.9826 + 13.9826i 1.08201 + 1.08201i 0.996322 + 0.0856865i \(0.0273083\pi\)
0.0856865 + 0.996322i \(0.472692\pi\)
\(168\) −1.18472 1.26350i −0.0914034 0.0974811i
\(169\) 11.8732 5.29404i 0.913324 0.407234i
\(170\) 13.7142i 1.05183i
\(171\) 5.77016 5.07172i 0.441255 0.387844i
\(172\) 7.44129 0.567393
\(173\) −4.63785 −0.352609 −0.176304 0.984336i \(-0.556414\pi\)
−0.176304 + 0.984336i \(0.556414\pi\)
\(174\) −0.388140 + 12.0627i −0.0294248 + 0.914471i
\(175\) −7.56361 7.56361i −0.571755 0.571755i
\(176\) −3.20912 3.20912i −0.241896 0.241896i
\(177\) −0.577557 + 17.9494i −0.0434119 + 1.34916i
\(178\) −1.15843 −0.0868278
\(179\) −7.59068 −0.567354 −0.283677 0.958920i \(-0.591554\pi\)
−0.283677 + 0.958920i \(0.591554\pi\)
\(180\) 8.92735 7.84675i 0.665405 0.584862i
\(181\) 17.9019i 1.33064i 0.746558 + 0.665320i \(0.231705\pi\)
−0.746558 + 0.665320i \(0.768295\pi\)
\(182\) 0.750597 + 3.52656i 0.0556379 + 0.261406i
\(183\) 0.356277 + 0.379967i 0.0263367 + 0.0280879i
\(184\) −0.515041 0.515041i −0.0379694 0.0379694i
\(185\) 8.74882i 0.643226i
\(186\) −12.1779 12.9876i −0.892923 0.952297i
\(187\) 11.1085 + 11.1085i 0.812333 + 0.812333i
\(188\) 7.17522 7.17522i 0.523307 0.523307i
\(189\) 0.500638 5.17198i 0.0364160 0.376206i
\(190\) 7.17389 7.17389i 0.520449 0.520449i
\(191\) 9.21892i 0.667058i 0.942740 + 0.333529i \(0.108239\pi\)
−0.942740 + 0.333529i \(0.891761\pi\)
\(192\) 1.26350 1.18472i 0.0911852 0.0855000i
\(193\) −0.100044 + 0.100044i −0.00720135 + 0.00720135i −0.710698 0.703497i \(-0.751621\pi\)
0.703497 + 0.710698i \(0.251621\pi\)
\(194\) −1.94460 −0.139614
\(195\) −24.3530 + 4.36980i −1.74396 + 0.312928i
\(196\) −1.00000 −0.0714286
\(197\) −8.24868 + 8.24868i −0.587694 + 0.587694i −0.937006 0.349312i \(-0.886415\pi\)
0.349312 + 0.937006i \(0.386415\pi\)
\(198\) 0.875280 13.5870i 0.0622034 0.965584i
\(199\) 7.57896i 0.537258i 0.963244 + 0.268629i \(0.0865706\pi\)
−0.963244 + 0.268629i \(0.913429\pi\)
\(200\) 7.56361 7.56361i 0.534828 0.534828i
\(201\) −0.238664 + 7.41724i −0.0168341 + 0.523172i
\(202\) −0.738039 + 0.738039i −0.0519282 + 0.0519282i
\(203\) 4.92712 + 4.92712i 0.345816 + 0.345816i
\(204\) −4.37365 + 4.10096i −0.306217 + 0.287125i
\(205\) 20.1280i 1.40580i
\(206\) 5.93337 + 5.93337i 0.413398 + 0.413398i
\(207\) 0.140476 2.18062i 0.00976379 0.151563i
\(208\) −3.52656 + 0.750597i −0.244523 + 0.0520445i
\(209\) 11.6217i 0.803887i
\(210\) 0.220690 6.85864i 0.0152291 0.473291i
\(211\) 11.7943 0.811951 0.405976 0.913884i \(-0.366932\pi\)
0.405976 + 0.913884i \(0.366932\pi\)
\(212\) −11.8689 −0.815157
\(213\) 8.22703 + 0.264720i 0.563707 + 0.0181383i
\(214\) −10.1257 10.1257i −0.692176 0.692176i
\(215\) 20.8466 + 20.8466i 1.42173 + 1.42173i
\(216\) 5.17198 + 0.500638i 0.351909 + 0.0340641i
\(217\) −10.2791 −0.697789
\(218\) 0.440523 0.0298360
\(219\) 16.8804 + 0.543161i 1.14067 + 0.0367034i
\(220\) 17.9806i 1.21225i
\(221\) 12.2073 2.59822i 0.821153 0.174775i
\(222\) −2.79012 + 2.61616i −0.187260 + 0.175585i
\(223\) 5.27800 + 5.27800i 0.353441 + 0.353441i 0.861388 0.507947i \(-0.169595\pi\)
−0.507947 + 0.861388i \(0.669595\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 32.0233 + 2.06296i 2.13489 + 0.137531i
\(226\) 3.28959 + 3.28959i 0.218821 + 0.218821i
\(227\) 12.0460 12.0460i 0.799522 0.799522i −0.183498 0.983020i \(-0.558742\pi\)
0.983020 + 0.183498i \(0.0587420\pi\)
\(228\) 4.43306 + 0.142642i 0.293587 + 0.00944671i
\(229\) −12.4724 + 12.4724i −0.824200 + 0.824200i −0.986707 0.162507i \(-0.948042\pi\)
0.162507 + 0.986707i \(0.448042\pi\)
\(230\) 2.88575i 0.190281i
\(231\) −5.37672 5.73424i −0.353762 0.377285i
\(232\) −4.92712 + 4.92712i −0.323481 + 0.323481i
\(233\) −17.2708 −1.13144 −0.565722 0.824596i \(-0.691403\pi\)
−0.565722 + 0.824596i \(0.691403\pi\)
\(234\) −8.67588 6.45981i −0.567160 0.422291i
\(235\) 40.2024 2.62252
\(236\) −7.33162 + 7.33162i −0.477248 + 0.477248i
\(237\) 6.96090 + 7.42375i 0.452159 + 0.482224i
\(238\) 3.46154i 0.224378i
\(239\) 3.19200 3.19200i 0.206473 0.206473i −0.596293 0.802767i \(-0.703360\pi\)
0.802767 + 0.596293i \(0.203360\pi\)
\(240\) 6.85864 + 0.220690i 0.442723 + 0.0142455i
\(241\) −9.64002 + 9.64002i −0.620968 + 0.620968i −0.945779 0.324811i \(-0.894699\pi\)
0.324811 + 0.945779i \(0.394699\pi\)
\(242\) −6.78602 6.78602i −0.436222 0.436222i
\(243\) 9.11532 + 12.6456i 0.584748 + 0.811215i
\(244\) 0.300726i 0.0192520i
\(245\) −2.80148 2.80148i −0.178980 0.178980i
\(246\) 6.41910 6.01888i 0.409267 0.383750i
\(247\) −7.74475 5.02650i −0.492787 0.319829i
\(248\) 10.2791i 0.652721i
\(249\) 18.4875 + 0.594870i 1.17160 + 0.0376983i
\(250\) 22.5691 1.42740
\(251\) −10.4429 −0.659151 −0.329576 0.944129i \(-0.606906\pi\)
−0.329576 + 0.944129i \(0.606906\pi\)
\(252\) 2.25331 1.98056i 0.141945 0.124763i
\(253\) −2.33745 2.33745i −0.146954 0.146954i
\(254\) −6.02303 6.02303i −0.377918 0.377918i
\(255\) −23.7415 0.763927i −1.48675 0.0478389i
\(256\) 1.00000 0.0625000
\(257\) −24.8464 −1.54987 −0.774937 0.632039i \(-0.782218\pi\)
−0.774937 + 0.632039i \(0.782218\pi\)
\(258\) −0.414504 + 12.8820i −0.0258059 + 0.801999i
\(259\) 2.20825i 0.137214i
\(260\) −11.9824 7.77679i −0.743114 0.482296i
\(261\) −20.8608 1.34386i −1.29125 0.0831830i
\(262\) −1.16678 1.16678i −0.0720837 0.0720837i
\(263\) 13.4778i 0.831079i 0.909575 + 0.415540i \(0.136407\pi\)
−0.909575 + 0.415540i \(0.863593\pi\)
\(264\) 5.73424 5.37672i 0.352918 0.330914i
\(265\) −33.2504 33.2504i −2.04255 2.04255i
\(266\) 1.81073 1.81073i 0.111023 0.111023i
\(267\) 0.0645281 2.00542i 0.00394906 0.122729i
\(268\) −3.02964 + 3.02964i −0.185065 + 0.185065i
\(269\) 0.0472472i 0.00288071i −0.999999 0.00144036i \(-0.999542\pi\)
0.999999 0.00144036i \(-0.000458480\pi\)
\(270\) 13.0867 + 15.8917i 0.796429 + 0.967139i
\(271\) 9.20531 9.20531i 0.559183 0.559183i −0.369892 0.929075i \(-0.620605\pi\)
0.929075 + 0.369892i \(0.120605\pi\)
\(272\) −3.46154 −0.209887
\(273\) −6.14683 + 1.10296i −0.372023 + 0.0667541i
\(274\) −12.8974 −0.779163
\(275\) 34.3265 34.3265i 2.06997 2.06997i
\(276\) 0.920306 0.862927i 0.0553959 0.0519421i
\(277\) 7.05593i 0.423950i 0.977275 + 0.211975i \(0.0679895\pi\)
−0.977275 + 0.211975i \(0.932010\pi\)
\(278\) 13.6164 13.6164i 0.816656 0.816656i
\(279\) 23.1619 20.3583i 1.38667 1.21882i
\(280\) 2.80148 2.80148i 0.167420 0.167420i
\(281\) 10.2852 + 10.2852i 0.613563 + 0.613563i 0.943873 0.330309i \(-0.107153\pi\)
−0.330309 + 0.943873i \(0.607153\pi\)
\(282\) 12.0217 + 12.8211i 0.715884 + 0.763485i
\(283\) 1.95168i 0.116015i −0.998316 0.0580076i \(-0.981525\pi\)
0.998316 0.0580076i \(-0.0184748\pi\)
\(284\) 3.36041 + 3.36041i 0.199404 + 0.199404i
\(285\) 12.0195 + 12.8187i 0.711974 + 0.759316i
\(286\) −16.0049 + 3.40649i −0.946387 + 0.201430i
\(287\) 5.08041i 0.299887i
\(288\) 1.98056 + 2.25331i 0.116706 + 0.132777i
\(289\) −5.01775 −0.295162
\(290\) −27.6065 −1.62111
\(291\) 0.108320 3.36640i 0.00634984 0.197342i
\(292\) 6.89498 + 6.89498i 0.403498 + 0.403498i
\(293\) 17.6386 + 17.6386i 1.03046 + 1.03046i 0.999521 + 0.0309390i \(0.00984977\pi\)
0.0309390 + 0.999521i \(0.490150\pi\)
\(294\) 0.0557032 1.73115i 0.00324868 0.100963i
\(295\) −41.0787 −2.39170
\(296\) −2.20825 −0.128352
\(297\) 23.4724 + 2.27208i 1.36201 + 0.131840i
\(298\) 22.2690i 1.29001i
\(299\) −2.56867 + 0.546718i −0.148550 + 0.0316175i
\(300\) 12.6725 + 13.5151i 0.731645 + 0.780294i
\(301\) 5.26178 + 5.26178i 0.303284 + 0.303284i
\(302\) 19.2209i 1.10604i
\(303\) −1.23655 1.31877i −0.0710378 0.0757614i
\(304\) 1.81073 + 1.81073i 0.103852 + 0.103852i
\(305\) −0.842476 + 0.842476i −0.0482401 + 0.0482401i
\(306\) −6.85578 7.79991i −0.391919 0.445891i
\(307\) 20.4024 20.4024i 1.16443 1.16443i 0.180931 0.983496i \(-0.442089\pi\)
0.983496 0.180931i \(-0.0579110\pi\)
\(308\) 4.53838i 0.258598i
\(309\) −10.6021 + 9.94108i −0.603132 + 0.565528i
\(310\) 28.7966 28.7966i 1.63554 1.63554i
\(311\) 21.1901 1.20158 0.600790 0.799407i \(-0.294853\pi\)
0.600790 + 0.799407i \(0.294853\pi\)
\(312\) −1.10296 6.14683i −0.0624427 0.347996i
\(313\) 25.8039 1.45852 0.729262 0.684235i \(-0.239864\pi\)
0.729262 + 0.684235i \(0.239864\pi\)
\(314\) −1.09450 + 1.09450i −0.0617665 + 0.0617665i
\(315\) 11.8611 + 0.764097i 0.668296 + 0.0430520i
\(316\) 5.87555i 0.330525i
\(317\) 14.4728 14.4728i 0.812873 0.812873i −0.172190 0.985064i \(-0.555084\pi\)
0.985064 + 0.172190i \(0.0550844\pi\)
\(318\) 0.661134 20.5468i 0.0370746 1.15221i
\(319\) −22.3612 + 22.3612i −1.25198 + 1.25198i
\(320\) 2.80148 + 2.80148i 0.156607 + 0.156607i
\(321\) 18.0931 16.9651i 1.00986 0.946898i
\(322\) 0.728379i 0.0405910i
\(323\) −6.26790 6.26790i −0.348755 0.348755i
\(324\) −1.15478 + 8.92561i −0.0641543 + 0.495867i
\(325\) −8.02880 37.7220i −0.445358 2.09244i
\(326\) 0.398760i 0.0220853i
\(327\) −0.0245385 + 0.762613i −0.00135698 + 0.0421726i
\(328\) 5.08041 0.280519
\(329\) 10.1473 0.559438
\(330\) 31.1271 + 1.00157i 1.71349 + 0.0551349i
\(331\) 0.263725 + 0.263725i 0.0144956 + 0.0144956i 0.714317 0.699822i \(-0.246737\pi\)
−0.699822 + 0.714317i \(0.746737\pi\)
\(332\) 7.55138 + 7.55138i 0.414436 + 0.414436i
\(333\) −4.37356 4.97585i −0.239670 0.272675i
\(334\) −19.7744 −1.08201
\(335\) −16.9750 −0.927441
\(336\) 1.73115 + 0.0557032i 0.0944422 + 0.00303886i
\(337\) 5.07335i 0.276363i −0.990407 0.138181i \(-0.955874\pi\)
0.990407 0.138181i \(-0.0441257\pi\)
\(338\) −4.65217 + 12.1391i −0.253045 + 0.660279i
\(339\) −5.87804 + 5.51156i −0.319251 + 0.299347i
\(340\) −9.69742 9.69742i −0.525917 0.525917i
\(341\) 46.6503i 2.52626i
\(342\) −0.493871 + 7.66637i −0.0267055 + 0.414550i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) −5.26178 + 5.26178i −0.283696 + 0.283696i
\(345\) 4.99569 + 0.160746i 0.268959 + 0.00865427i
\(346\) 3.27945 3.27945i 0.176304 0.176304i
\(347\) 5.56263i 0.298618i −0.988791 0.149309i \(-0.952295\pi\)
0.988791 0.149309i \(-0.0477049\pi\)
\(348\) −8.25516 8.80407i −0.442523 0.471948i
\(349\) −13.8464 + 13.8464i −0.741180 + 0.741180i −0.972805 0.231625i \(-0.925596\pi\)
0.231625 + 0.972805i \(0.425596\pi\)
\(350\) 10.6966 0.571755
\(351\) 11.6662 14.6595i 0.622696 0.782464i
\(352\) 4.53838 0.241896
\(353\) −25.3196 + 25.3196i −1.34762 + 1.34762i −0.459389 + 0.888235i \(0.651932\pi\)
−0.888235 + 0.459389i \(0.848068\pi\)
\(354\) −12.2838 13.1006i −0.652875 0.696287i
\(355\) 18.8282i 0.999298i
\(356\) 0.819132 0.819132i 0.0434139 0.0434139i
\(357\) −5.99246 0.192819i −0.317155 0.0102051i
\(358\) 5.36742 5.36742i 0.283677 0.283677i
\(359\) 2.81055 + 2.81055i 0.148335 + 0.148335i 0.777374 0.629039i \(-0.216551\pi\)
−0.629039 + 0.777374i \(0.716551\pi\)
\(360\) −0.764097 + 11.8611i −0.0402714 + 0.625134i
\(361\) 12.4425i 0.654871i
\(362\) −12.6586 12.6586i −0.665320 0.665320i
\(363\) 12.1257 11.3697i 0.636432 0.596752i
\(364\) −3.02440 1.96290i −0.158522 0.102884i
\(365\) 38.6323i 2.02211i
\(366\) −0.520603 0.0167514i −0.0272123 0.000875609i
\(367\) −11.1457 −0.581803 −0.290902 0.956753i \(-0.593955\pi\)
−0.290902 + 0.956753i \(0.593955\pi\)
\(368\) 0.728379 0.0379694
\(369\) 10.0621 + 11.4477i 0.523810 + 0.595945i
\(370\) −6.18635 6.18635i −0.321613 0.321613i
\(371\) −8.39255 8.39255i −0.435720 0.435720i
\(372\) 17.7947 + 0.572577i 0.922610 + 0.0296867i
\(373\) 15.2818 0.791262 0.395631 0.918409i \(-0.370526\pi\)
0.395631 + 0.918409i \(0.370526\pi\)
\(374\) −15.7098 −0.812333
\(375\) −1.25717 + 39.0707i −0.0649201 + 2.01760i
\(376\) 10.1473i 0.523307i
\(377\) 5.23016 + 24.5731i 0.269367 + 1.26558i
\(378\) 3.30314 + 4.01115i 0.169895 + 0.206311i
\(379\) −13.4151 13.4151i −0.689088 0.689088i 0.272943 0.962030i \(-0.412003\pi\)
−0.962030 + 0.272943i \(0.912003\pi\)
\(380\) 10.1454i 0.520449i
\(381\) 10.7623 10.0913i 0.551369 0.516992i
\(382\) −6.51876 6.51876i −0.333529 0.333529i
\(383\) 1.21551 1.21551i 0.0621098 0.0621098i −0.675370 0.737479i \(-0.736016\pi\)
0.737479 + 0.675370i \(0.236016\pi\)
\(384\) −0.0557032 + 1.73115i −0.00284259 + 0.0883426i
\(385\) 12.7142 12.7142i 0.647974 0.647974i
\(386\) 0.141484i 0.00720135i
\(387\) −22.2777 1.43514i −1.13244 0.0729523i
\(388\) 1.37504 1.37504i 0.0698069 0.0698069i
\(389\) −27.2012 −1.37915 −0.689577 0.724212i \(-0.742204\pi\)
−0.689577 + 0.724212i \(0.742204\pi\)
\(390\) 14.1303 20.3101i 0.715515 1.02844i
\(391\) −2.52131 −0.127508
\(392\) 0.707107 0.707107i 0.0357143 0.0357143i
\(393\) 2.08486 1.95488i 0.105167 0.0986105i
\(394\) 11.6654i 0.587694i
\(395\) −16.4602 + 16.4602i −0.828203 + 0.828203i
\(396\) 8.98852 + 10.2264i 0.451690 + 0.513894i
\(397\) 13.1240 13.1240i 0.658677 0.658677i −0.296390 0.955067i \(-0.595783\pi\)
0.955067 + 0.296390i \(0.0957829\pi\)
\(398\) −5.35913 5.35913i −0.268629 0.268629i
\(399\) 3.03378 + 3.23551i 0.151879 + 0.161978i
\(400\) 10.6966i 0.534828i
\(401\) 0.204321 + 0.204321i 0.0102033 + 0.0102033i 0.712190 0.701987i \(-0.247703\pi\)
−0.701987 + 0.712190i \(0.747703\pi\)
\(402\) −5.07602 5.41354i −0.253169 0.270003i
\(403\) −31.0881 20.1768i −1.54861 1.00508i
\(404\) 1.04374i 0.0519282i
\(405\) −28.2400 + 21.7698i −1.40326 + 1.08175i
\(406\) −6.96800 −0.345816
\(407\) −10.0219 −0.496765
\(408\) 0.192819 5.99246i 0.00954596 0.296671i
\(409\) 3.12131 + 3.12131i 0.154339 + 0.154339i 0.780053 0.625714i \(-0.215192\pi\)
−0.625714 + 0.780053i \(0.715192\pi\)
\(410\) 14.2327 + 14.2327i 0.702901 + 0.702901i
\(411\) 0.718430 22.3275i 0.0354375 1.10133i
\(412\) −8.39105 −0.413398
\(413\) −10.3685 −0.510199
\(414\) 1.44260 + 1.64126i 0.0708997 + 0.0806635i
\(415\) 42.3101i 2.07692i
\(416\) 1.96290 3.02440i 0.0962391 0.148284i
\(417\) 22.8136 + 24.3305i 1.11719 + 1.19147i
\(418\) 8.21776 + 8.21776i 0.401944 + 0.401944i
\(419\) 10.6945i 0.522459i −0.965277 0.261229i \(-0.915872\pi\)
0.965277 0.261229i \(-0.0841279\pi\)
\(420\) 4.69374 + 5.00584i 0.229031 + 0.244260i
\(421\) −9.86237 9.86237i −0.480663 0.480663i 0.424681 0.905343i \(-0.360386\pi\)
−0.905343 + 0.424681i \(0.860386\pi\)
\(422\) −8.33981 + 8.33981i −0.405976 + 0.405976i
\(423\) −22.8650 + 20.0973i −1.11173 + 0.977164i
\(424\) 8.39255 8.39255i 0.407578 0.407578i
\(425\) 37.0265i 1.79605i
\(426\) −6.00457 + 5.63020i −0.290923 + 0.272784i
\(427\) −0.212645 + 0.212645i −0.0102906 + 0.0102906i
\(428\) 14.3199 0.692176
\(429\) −5.00564 27.8966i −0.241675 1.34686i
\(430\) −29.4815 −1.42173
\(431\) −12.4189 + 12.4189i −0.598196 + 0.598196i −0.939832 0.341636i \(-0.889019\pi\)
0.341636 + 0.939832i \(0.389019\pi\)
\(432\) −4.01115 + 3.30314i −0.192986 + 0.158922i
\(433\) 29.3877i 1.41228i −0.708070 0.706142i \(-0.750434\pi\)
0.708070 0.706142i \(-0.249566\pi\)
\(434\) 7.26840 7.26840i 0.348894 0.348894i
\(435\) 1.53777 47.7910i 0.0737304 2.29141i
\(436\) −0.311497 + 0.311497i −0.0149180 + 0.0149180i
\(437\) 1.31889 + 1.31889i 0.0630912 + 0.0630912i
\(438\) −12.3204 + 11.5522i −0.588689 + 0.551986i
\(439\) 35.4420i 1.69155i −0.533537 0.845776i \(-0.679138\pi\)
0.533537 0.845776i \(-0.320862\pi\)
\(440\) 12.7142 + 12.7142i 0.606124 + 0.606124i
\(441\) 2.99379 + 0.192862i 0.142562 + 0.00918390i
\(442\) −6.79466 + 10.4691i −0.323189 + 0.497964i
\(443\) 10.2171i 0.485431i −0.970097 0.242716i \(-0.921962\pi\)
0.970097 0.242716i \(-0.0780382\pi\)
\(444\) 0.123006 3.82282i 0.00583763 0.181423i
\(445\) 4.58956 0.217566
\(446\) −7.46422 −0.353441
\(447\) −38.5512 1.24046i −1.82341 0.0586716i
\(448\) 0.707107 + 0.707107i 0.0334077 + 0.0334077i
\(449\) 10.2744 + 10.2744i 0.484877 + 0.484877i 0.906685 0.421808i \(-0.138604\pi\)
−0.421808 + 0.906685i \(0.638604\pi\)
\(450\) −24.1026 + 21.1852i −1.13621 + 0.998678i
\(451\) 23.0568 1.08570
\(452\) −4.65219 −0.218821
\(453\) −33.2744 1.07067i −1.56337 0.0503043i
\(454\) 17.0356i 0.799522i
\(455\) −2.97378 13.9718i −0.139413 0.655009i
\(456\) −3.23551 + 3.03378i −0.151517 + 0.142070i
\(457\) 20.4058 + 20.4058i 0.954543 + 0.954543i 0.999011 0.0444681i \(-0.0141593\pi\)
−0.0444681 + 0.999011i \(0.514159\pi\)
\(458\) 17.6387i 0.824200i
\(459\) 13.8847 11.4339i 0.648084 0.533690i
\(460\) 2.04054 + 2.04054i 0.0951405 + 0.0951405i
\(461\) −9.03208 + 9.03208i −0.420666 + 0.420666i −0.885433 0.464767i \(-0.846138\pi\)
0.464767 + 0.885433i \(0.346138\pi\)
\(462\) 7.85664 + 0.252802i 0.365524 + 0.0117614i
\(463\) −1.89548 + 1.89548i −0.0880905 + 0.0880905i −0.749779 0.661688i \(-0.769840\pi\)
0.661688 + 0.749779i \(0.269840\pi\)
\(464\) 6.96800i 0.323481i
\(465\) 48.2473 + 51.4554i 2.23741 + 2.38619i
\(466\) 12.2123 12.2123i 0.565722 0.565722i
\(467\) −3.05929 −0.141567 −0.0707834 0.997492i \(-0.522550\pi\)
−0.0707834 + 0.997492i \(0.522550\pi\)
\(468\) 10.7025 1.56699i 0.494725 0.0724343i
\(469\) −4.28456 −0.197843
\(470\) −28.4274 + 28.4274i −1.31126 + 1.31126i
\(471\) −1.83379 1.95572i −0.0844966 0.0901150i
\(472\) 10.3685i 0.477248i
\(473\) −23.8800 + 23.8800i −1.09800 + 1.09800i
\(474\) −10.1715 0.327287i −0.467192 0.0150328i
\(475\) −19.3685 + 19.3685i −0.888689 + 0.888689i
\(476\) −2.44768 2.44768i −0.112189 0.112189i
\(477\) 35.5329 + 2.28905i 1.62694 + 0.104808i
\(478\) 4.51417i 0.206473i
\(479\) −13.5200 13.5200i −0.617747 0.617747i 0.327206 0.944953i \(-0.393893\pi\)
−0.944953 + 0.327206i \(0.893893\pi\)
\(480\) −5.00584 + 4.69374i −0.228484 + 0.214239i
\(481\) −4.33457 + 6.67863i −0.197639 + 0.304519i
\(482\) 13.6330i 0.620968i
\(483\) 1.26094 + 0.0405730i 0.0573746 + 0.00184614i
\(484\) 9.59688 0.436222
\(485\) 7.70427 0.349833
\(486\) −15.3873 2.49628i −0.697981 0.113234i
\(487\) 12.0429 + 12.0429i 0.545716 + 0.545716i 0.925199 0.379483i \(-0.123898\pi\)
−0.379483 + 0.925199i \(0.623898\pi\)
\(488\) −0.212645 0.212645i −0.00962599 0.00962599i
\(489\) −0.690315 0.0222122i −0.0312171 0.00100447i
\(490\) 3.96189 0.178980
\(491\) −22.3159 −1.00710 −0.503551 0.863965i \(-0.667973\pi\)
−0.503551 + 0.863965i \(0.667973\pi\)
\(492\) −0.282995 + 8.79498i −0.0127584 + 0.396508i
\(493\) 24.1200i 1.08631i
\(494\) 9.03064 1.92209i 0.406308 0.0864790i
\(495\) −3.46776 + 53.8301i −0.155864 + 2.41948i
\(496\) 7.26840 + 7.26840i 0.326361 + 0.326361i
\(497\) 4.75234i 0.213171i
\(498\) −13.4932 + 12.6520i −0.604647 + 0.566949i
\(499\) 27.8917 + 27.8917i 1.24860 + 1.24860i 0.956337 + 0.292267i \(0.0944097\pi\)
0.292267 + 0.956337i \(0.405590\pi\)
\(500\) −15.9588 + 15.9588i −0.713698 + 0.713698i
\(501\) 1.10150 34.2326i 0.0492114 1.52940i
\(502\) 7.38426 7.38426i 0.329576 0.329576i
\(503\) 18.1161i 0.807758i −0.914813 0.403879i \(-0.867662\pi\)
0.914813 0.403879i \(-0.132338\pi\)
\(504\) −0.192862 + 2.99379i −0.00859075 + 0.133354i
\(505\) 2.92403 2.92403i 0.130117 0.130117i
\(506\) 3.30566 0.146954
\(507\) −20.7555 8.72982i −0.921784 0.387705i
\(508\) 8.51785 0.377918
\(509\) −7.75052 + 7.75052i −0.343536 + 0.343536i −0.857695 0.514159i \(-0.828104\pi\)
0.514159 + 0.857695i \(0.328104\pi\)
\(510\) 17.3279 16.2476i 0.767293 0.719454i
\(511\) 9.75097i 0.431358i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −13.2442 1.28201i −0.584744 0.0566021i
\(514\) 17.5690 17.5690i 0.774937 0.774937i
\(515\) −23.5074 23.5074i −1.03586 1.03586i
\(516\) −8.81586 9.40206i −0.388097 0.413903i
\(517\) 46.0523i 2.02538i
\(518\) −1.56147 1.56147i −0.0686069 0.0686069i
\(519\) 5.49456 + 5.85992i 0.241185 + 0.257222i
\(520\) 13.9718 2.97378i 0.612705 0.130409i
\(521\) 2.45446i 0.107532i −0.998554 0.0537659i \(-0.982878\pi\)
0.998554 0.0537659i \(-0.0171225\pi\)
\(522\) 15.7010 13.8005i 0.687216 0.604033i
\(523\) −29.1475 −1.27453 −0.637265 0.770645i \(-0.719934\pi\)
−0.637265 + 0.770645i \(0.719934\pi\)
\(524\) 1.65007 0.0720837
\(525\) −0.595833 + 18.5174i −0.0260043 + 0.808166i
\(526\) −9.53027 9.53027i −0.415540 0.415540i
\(527\) −25.1598 25.1598i −1.09598 1.09598i
\(528\) −0.252802 + 7.85664i −0.0110018 + 0.341916i
\(529\) −22.4695 −0.976933
\(530\) 47.0231 2.04255
\(531\) 23.3633 20.5354i 1.01388 0.891159i
\(532\) 2.56075i 0.111023i
\(533\) 9.97235 15.3652i 0.431950 0.665542i
\(534\) 1.37242 + 1.46367i 0.0593902 + 0.0633393i
\(535\) 40.1168 + 40.1168i 1.73440 + 1.73440i
\(536\) 4.28456i 0.185065i
\(537\) 8.99286 + 9.59082i 0.388070 + 0.413875i
\(538\) 0.0334088 + 0.0334088i 0.00144036 + 0.00144036i
\(539\) 3.20912 3.20912i 0.138227 0.138227i
\(540\) −20.4908 1.98347i −0.881784 0.0853550i
\(541\) −22.0191 + 22.0191i −0.946673 + 0.946673i −0.998648 0.0519752i \(-0.983448\pi\)
0.0519752 + 0.998648i \(0.483448\pi\)
\(542\) 13.0183i 0.559183i
\(543\) 22.6191 21.2088i 0.970678 0.910158i
\(544\) 2.44768 2.44768i 0.104943 0.104943i
\(545\) −1.74530 −0.0747605
\(546\) 3.56655 5.12637i 0.152634 0.219388i
\(547\) 12.6981 0.542930 0.271465 0.962448i \(-0.412492\pi\)
0.271465 + 0.962448i \(0.412492\pi\)
\(548\) 9.11987 9.11987i 0.389582 0.389582i
\(549\) 0.0579985 0.900311i 0.00247532 0.0384243i
\(550\) 48.5450i 2.06997i
\(551\) 12.6171 12.6171i 0.537508 0.537508i
\(552\) −0.0405730 + 1.26094i −0.00172690 + 0.0536690i
\(553\) −4.15464 + 4.15464i −0.176673 + 0.176673i
\(554\) −4.98930 4.98930i −0.211975 0.211975i
\(555\) 11.0541 10.3649i 0.469222 0.439967i
\(556\) 19.2565i 0.816656i
\(557\) 10.0740 + 10.0740i 0.426849 + 0.426849i 0.887554 0.460705i \(-0.152403\pi\)
−0.460705 + 0.887554i \(0.652403\pi\)
\(558\) −1.98244 + 30.7734i −0.0839234 + 1.30274i
\(559\) 5.58540 + 26.2421i 0.236237 + 1.10992i
\(560\) 3.96189i 0.167420i
\(561\) 0.875085 27.1960i 0.0369461 1.14822i
\(562\) −14.5455 −0.613563
\(563\) −10.5842 −0.446073 −0.223036 0.974810i \(-0.571597\pi\)
−0.223036 + 0.974810i \(0.571597\pi\)
\(564\) −17.5665 0.565237i −0.739685 0.0238008i
\(565\) −13.0330 13.0330i −0.548303 0.548303i
\(566\) 1.38004 + 1.38004i 0.0580076 + 0.0580076i
\(567\) −7.12791 + 5.49481i −0.299344 + 0.230760i
\(568\) −4.75234 −0.199404
\(569\) −22.5816 −0.946669 −0.473334 0.880883i \(-0.656950\pi\)
−0.473334 + 0.880883i \(0.656950\pi\)
\(570\) −17.5633 0.565132i −0.735645 0.0236708i
\(571\) 6.83794i 0.286159i −0.989711 0.143079i \(-0.954300\pi\)
0.989711 0.143079i \(-0.0457004\pi\)
\(572\) 8.90839 13.7259i 0.372478 0.573908i
\(573\) 11.6481 10.9219i 0.486606 0.456268i
\(574\) 3.59240 + 3.59240i 0.149944 + 0.149944i
\(575\) 7.79114i 0.324913i
\(576\) −2.99379 0.192862i −0.124741 0.00803591i
\(577\) 20.7633 + 20.7633i 0.864388 + 0.864388i 0.991844 0.127456i \(-0.0406812\pi\)
−0.127456 + 0.991844i \(0.540681\pi\)
\(578\) 3.54809 3.54809i 0.147581 0.147581i
\(579\) 0.244931 + 0.00788112i 0.0101790 + 0.000327528i
\(580\) 19.5207 19.5207i 0.810553 0.810553i
\(581\) 10.6793i 0.443051i
\(582\) 2.30381 + 2.45699i 0.0954959 + 0.101846i
\(583\) 38.0886 38.0886i 1.57747 1.57747i
\(584\) −9.75097 −0.403498
\(585\) 34.3729 + 25.5931i 1.42114 + 1.05814i
\(586\) −24.9448 −1.03046
\(587\) 18.8625 18.8625i 0.778540 0.778540i −0.201042 0.979583i \(-0.564433\pi\)
0.979583 + 0.201042i \(0.0644328\pi\)
\(588\) 1.18472 + 1.26350i 0.0488572 + 0.0521058i
\(589\) 26.3222i 1.08459i
\(590\) 29.0471 29.0471i 1.19585 1.19585i
\(591\) 20.1946 + 0.649800i 0.830695 + 0.0267292i
\(592\) 1.56147 1.56147i 0.0641758 0.0641758i
\(593\) 10.7560 + 10.7560i 0.441694 + 0.441694i 0.892581 0.450887i \(-0.148892\pi\)
−0.450887 + 0.892581i \(0.648892\pi\)
\(594\) −18.2041 + 14.9909i −0.746923 + 0.615084i
\(595\) 13.7142i 0.562229i
\(596\) −15.7466 15.7466i −0.645006 0.645006i
\(597\) 9.57601 8.97897i 0.391920 0.367485i
\(598\) 1.42973 2.20291i 0.0584662 0.0900837i
\(599\) 6.53963i 0.267202i −0.991035 0.133601i \(-0.957346\pi\)
0.991035 0.133601i \(-0.0426541\pi\)
\(600\) −18.5174 0.595833i −0.755970 0.0243248i
\(601\) −15.8483 −0.646465 −0.323232 0.946320i \(-0.604770\pi\)
−0.323232 + 0.946320i \(0.604770\pi\)
\(602\) −7.44129 −0.303284
\(603\) 9.65443 8.48583i 0.393159 0.345570i
\(604\) −13.5912 13.5912i −0.553020 0.553020i
\(605\) 26.8855 + 26.8855i 1.09305 + 1.09305i
\(606\) 1.80688 + 0.0581399i 0.0733996 + 0.00236177i
\(607\) 33.8692 1.37471 0.687354 0.726323i \(-0.258772\pi\)
0.687354 + 0.726323i \(0.258772\pi\)
\(608\) −2.56075 −0.103852
\(609\) 0.388140 12.0627i 0.0157282 0.488805i
\(610\) 1.19144i 0.0482401i
\(611\) 30.6895 + 19.9181i 1.24156 + 0.805801i
\(612\) 10.3631 + 0.667599i 0.418905 + 0.0269861i
\(613\) −31.6180 31.6180i −1.27704 1.27704i −0.942316 0.334724i \(-0.891357\pi\)
−0.334724 0.942316i \(-0.608643\pi\)
\(614\) 28.8534i 1.16443i
\(615\) −25.4318 + 23.8461i −1.02551 + 0.961570i
\(616\) 3.20912 + 3.20912i 0.129299 + 0.129299i
\(617\) 1.92767 1.92767i 0.0776053 0.0776053i −0.667239 0.744844i \(-0.732524\pi\)
0.744844 + 0.667239i \(0.232524\pi\)
\(618\) 0.467409 14.5262i 0.0188019 0.584330i
\(619\) 3.42808 3.42808i 0.137786 0.137786i −0.634850 0.772636i \(-0.718938\pi\)
0.772636 + 0.634850i \(0.218938\pi\)
\(620\) 40.7245i 1.63554i
\(621\) −2.92163 + 2.40593i −0.117241 + 0.0965468i
\(622\) −14.9836 + 14.9836i −0.600790 + 0.600790i
\(623\) 1.15843 0.0464114
\(624\) 5.12637 + 3.56655i 0.205219 + 0.142776i
\(625\) −35.9336 −1.43734
\(626\) −18.2461 + 18.2461i −0.729262 + 0.729262i
\(627\) −14.6840 + 13.7685i −0.586421 + 0.549859i
\(628\) 1.54786i 0.0617665i
\(629\) −5.40507 + 5.40507i −0.215514 + 0.215514i
\(630\) −8.92735 + 7.84675i −0.355674 + 0.312622i
\(631\) −16.8098 + 16.8098i −0.669188 + 0.669188i −0.957528 0.288340i \(-0.906897\pi\)
0.288340 + 0.957528i \(0.406897\pi\)
\(632\) −4.15464 4.15464i −0.165263 0.165263i
\(633\) −13.9730 14.9021i −0.555375 0.592304i
\(634\) 20.4676i 0.812873i
\(635\) 23.8626 + 23.8626i 0.946957 + 0.946957i
\(636\) 14.0613 + 14.9963i 0.557568 + 0.594642i
\(637\) −0.750597 3.52656i −0.0297397 0.139727i
\(638\) 31.6234i 1.25198i
\(639\) −9.41228 10.7085i −0.372344 0.423620i
\(640\) −3.96189 −0.156607
\(641\) −37.3693 −1.47600 −0.738000 0.674801i \(-0.764229\pi\)
−0.738000 + 0.674801i \(0.764229\pi\)
\(642\) −0.797662 + 24.7899i −0.0314812 + 0.978379i
\(643\) −23.3585 23.3585i −0.921171 0.921171i 0.0759411 0.997112i \(-0.475804\pi\)
−0.997112 + 0.0759411i \(0.975804\pi\)
\(644\) 0.515041 + 0.515041i 0.0202955 + 0.0202955i
\(645\) 1.64222 51.0371i 0.0646622 2.00958i
\(646\) 8.86414 0.348755
\(647\) 12.8059 0.503453 0.251727 0.967798i \(-0.419002\pi\)
0.251727 + 0.967798i \(0.419002\pi\)
\(648\) −5.49481 7.12791i −0.215856 0.280011i
\(649\) 47.0561i 1.84711i
\(650\) 32.3507 + 20.9963i 1.26890 + 0.823542i
\(651\) 12.1779 + 12.9876i 0.477288 + 0.509024i
\(652\) −0.281966 0.281966i −0.0110426 0.0110426i
\(653\) 15.8484i 0.620194i 0.950705 + 0.310097i \(0.100362\pi\)
−0.950705 + 0.310097i \(0.899638\pi\)
\(654\) −0.521898 0.556600i −0.0204078 0.0217648i
\(655\) 4.62264 + 4.62264i 0.180621 + 0.180621i
\(656\) −3.59240 + 3.59240i −0.140259 + 0.140259i
\(657\) −19.3124 21.9719i −0.753447 0.857207i
\(658\) −7.17522 + 7.17522i −0.279719 + 0.279719i
\(659\) 14.8247i 0.577488i 0.957406 + 0.288744i \(0.0932377\pi\)
−0.957406 + 0.288744i \(0.906762\pi\)
\(660\) −22.7184 + 21.3020i −0.884313 + 0.829178i
\(661\) 0.547620 0.547620i 0.0212999 0.0212999i −0.696377 0.717677i \(-0.745206\pi\)
0.717677 + 0.696377i \(0.245206\pi\)
\(662\) −0.372963 −0.0144956
\(663\) −17.7451 12.3458i −0.689164 0.479470i
\(664\) −10.6793 −0.414436
\(665\) −7.17389 + 7.17389i −0.278192 + 0.278192i
\(666\) 6.61103 + 0.425886i 0.256172 + 0.0165028i
\(667\) 5.07535i 0.196518i
\(668\) 13.9826 13.9826i 0.541004 0.541004i
\(669\) 0.415781 12.9217i 0.0160750 0.499583i
\(670\) 12.0031 12.0031i 0.463720 0.463720i
\(671\) −0.965064 0.965064i −0.0372559 0.0372559i
\(672\) −1.26350 + 1.18472i −0.0487406 + 0.0457017i
\(673\) 17.2387i 0.664502i −0.943191 0.332251i \(-0.892192\pi\)
0.943191 0.332251i \(-0.107808\pi\)
\(674\) 3.58740 + 3.58740i 0.138181 + 0.138181i
\(675\) −35.3322 42.9055i −1.35994 1.65143i
\(676\) −5.29404 11.8732i −0.203617 0.456662i
\(677\) 16.5049i 0.634333i −0.948370 0.317167i \(-0.897269\pi\)
0.948370 0.317167i \(-0.102731\pi\)
\(678\) 0.259142 8.05366i 0.00995229 0.309299i
\(679\) 1.94460 0.0746267
\(680\) 13.7142 0.525917
\(681\) −29.4913 0.948940i −1.13011 0.0363635i
\(682\) 32.9867 + 32.9867i 1.26313 + 1.26313i
\(683\) 9.73430 + 9.73430i 0.372473 + 0.372473i 0.868377 0.495904i \(-0.165163\pi\)
−0.495904 + 0.868377i \(0.665163\pi\)
\(684\) −5.07172 5.77016i −0.193922 0.220628i
\(685\) 51.0983 1.95236
\(686\) 1.00000 0.0381802
\(687\) 30.5352 + 0.982530i 1.16499 + 0.0374859i
\(688\) 7.44129i 0.283696i
\(689\) −8.90873 41.8562i −0.339396 1.59460i
\(690\) −3.64615 + 3.41882i −0.138807 + 0.130152i
\(691\) −27.4763 27.4763i −1.04525 1.04525i −0.998927 0.0463224i \(-0.985250\pi\)
−0.0463224 0.998927i \(-0.514750\pi\)
\(692\) 4.63785i 0.176304i
\(693\) −0.875280 + 13.5870i −0.0332491 + 0.516126i
\(694\) 3.93338 + 3.93338i 0.149309 + 0.149309i
\(695\) −53.9466 + 53.9466i −2.04631 + 2.04631i
\(696\) 12.0627 + 0.388140i 0.457235 + 0.0147124i
\(697\) 12.4352 12.4352i 0.471017 0.471017i
\(698\) 19.5818i 0.741180i
\(699\) 20.4611 + 21.8216i 0.773908 + 0.825368i
\(700\) −7.56361 + 7.56361i −0.285878 + 0.285878i
\(701\) −13.3217 −0.503153 −0.251576 0.967837i \(-0.580949\pi\)
−0.251576 + 0.967837i \(0.580949\pi\)
\(702\) 2.11654 + 18.6151i 0.0798837 + 0.702580i
\(703\) 5.65477 0.213274
\(704\) −3.20912 + 3.20912i −0.120948 + 0.120948i
\(705\) −47.6288 50.7958i −1.79380 1.91308i
\(706\) 35.8073i 1.34762i
\(707\) 0.738039 0.738039i 0.0277568 0.0277568i
\(708\) 17.9494 + 0.577557i 0.674581 + 0.0217059i
\(709\) −18.7138 + 18.7138i −0.702813 + 0.702813i −0.965013 0.262200i \(-0.915552\pi\)
0.262200 + 0.965013i \(0.415552\pi\)
\(710\) −13.3136 13.3136i −0.499649 0.499649i
\(711\) 1.13317 17.5902i 0.0424971 0.659683i
\(712\) 1.15843i 0.0434139i
\(713\) 5.29415 + 5.29415i 0.198267 + 0.198267i
\(714\) 4.37365 4.10096i 0.163680 0.153475i
\(715\) 63.4094 13.4961i 2.37138 0.504727i
\(716\) 7.59068i 0.283677i
\(717\) −7.81472 0.251454i −0.291846 0.00939071i
\(718\) −3.97472 −0.148335
\(719\) 31.8959 1.18952 0.594759 0.803904i \(-0.297247\pi\)
0.594759 + 0.803904i \(0.297247\pi\)
\(720\) −7.84675 8.92735i −0.292431 0.332703i
\(721\) −5.93337 5.93337i −0.220970 0.220970i
\(722\) 8.79821 + 8.79821i 0.327435 + 0.327435i
\(723\) 23.6009 + 0.759405i 0.877727 + 0.0282426i
\(724\) 17.9019 0.665320
\(725\) 74.5337 2.76811
\(726\) −0.534577 + 16.6137i −0.0198400 + 0.616592i
\(727\) 14.0190i 0.519935i 0.965617 + 0.259967i \(0.0837118\pi\)
−0.965617 + 0.259967i \(0.916288\pi\)
\(728\) 3.52656 0.750597i 0.130703 0.0278190i
\(729\) 5.17857 26.4987i 0.191799 0.981434i
\(730\) −27.3171 27.3171i −1.01105 1.01105i
\(731\) 25.7583i 0.952705i
\(732\) 0.379967 0.356277i 0.0140440 0.0131684i
\(733\) −24.3910 24.3910i −0.900902 0.900902i 0.0946120 0.995514i \(-0.469839\pi\)
−0.995514 + 0.0946120i \(0.969839\pi\)
\(734\) 7.88123 7.88123i 0.290902 0.290902i
\(735\) −0.220690 + 6.85864i −0.00814027 + 0.252985i
\(736\) −0.515041 + 0.515041i −0.0189847 + 0.0189847i
\(737\) 19.4450i 0.716265i
\(738\) −15.2097 0.979818i −0.559877 0.0360676i
\(739\) 24.7933 24.7933i 0.912037 0.912037i −0.0843950 0.996432i \(-0.526896\pi\)
0.996432 + 0.0843950i \(0.0268957\pi\)
\(740\) 8.74882 0.321613
\(741\) 2.82440 + 15.7405i 0.103757 + 0.578242i
\(742\) 11.8689 0.435720
\(743\) 26.9802 26.9802i 0.989806 0.989806i −0.0101427 0.999949i \(-0.503229\pi\)
0.999949 + 0.0101427i \(0.00322858\pi\)
\(744\) −12.9876 + 12.1779i −0.476148 + 0.446462i
\(745\) 88.2275i 3.23240i
\(746\) −10.8059 + 10.8059i −0.395631 + 0.395631i
\(747\) −21.1509 24.0637i −0.773871 0.880443i
\(748\) 11.1085 11.1085i 0.406166 0.406166i
\(749\) 10.1257 + 10.1257i 0.369984 + 0.369984i
\(750\) −26.7382 28.5161i −0.976340 1.04126i
\(751\) 31.4776i 1.14864i 0.818633 + 0.574318i \(0.194733\pi\)
−0.818633 + 0.574318i \(0.805267\pi\)
\(752\) −7.17522 7.17522i −0.261653 0.261653i
\(753\) 12.3720 + 13.1946i 0.450860 + 0.480839i
\(754\) −21.0741 13.6775i −0.767472 0.498105i
\(755\) 76.1511i 2.77142i
\(756\) −5.17198 0.500638i −0.188103 0.0182080i
\(757\) −40.9867 −1.48969 −0.744843 0.667240i \(-0.767476\pi\)
−0.744843 + 0.667240i \(0.767476\pi\)
\(758\) 18.9718 0.689088
\(759\) −0.184136 + 5.72261i −0.00668371 + 0.207717i
\(760\) −7.17389 7.17389i −0.260224 0.260224i
\(761\) 14.0359 + 14.0359i 0.508801 + 0.508801i 0.914158 0.405357i \(-0.132853\pi\)
−0.405357 + 0.914158i \(0.632853\pi\)
\(762\) −0.474472 + 14.7457i −0.0171883 + 0.534181i
\(763\) −0.440523 −0.0159480
\(764\) 9.21892 0.333529
\(765\) 27.1618 + 30.9024i 0.982038 + 1.11728i
\(766\) 1.71899i 0.0621098i
\(767\) −31.3585 20.3523i −1.13229 0.734878i
\(768\) −1.18472 1.26350i −0.0427500 0.0455926i
\(769\) −0.689254 0.689254i −0.0248551 0.0248551i 0.694570 0.719425i \(-0.255595\pi\)
−0.719425 + 0.694570i \(0.755595\pi\)
\(770\) 17.9806i 0.647974i
\(771\) 29.4361 + 31.3934i 1.06011 + 1.13060i
\(772\) 0.100044 + 0.100044i 0.00360067 + 0.00360067i
\(773\) 2.82339 2.82339i 0.101550 0.101550i −0.654506 0.756057i \(-0.727123\pi\)
0.756057 + 0.654506i \(0.227123\pi\)
\(774\) 16.7675 14.7379i 0.602695 0.529743i
\(775\) −77.7468 + 77.7468i −2.79275 + 2.79275i
\(776\) 1.94460i