Properties

Label 546.2.p.c.239.7
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 239.7
Root \(1.72893 + 0.103975i\) of defining polynomial
Character \(\chi\) \(=\) 546.239
Dual form 546.2.p.c.281.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.14901 - 1.29606i) q^{3} +1.00000i q^{4} +(0.237140 + 0.237140i) q^{5} +(0.103975 - 1.72893i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.359531 + 2.97838i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.14901 - 1.29606i) q^{3} +1.00000i q^{4} +(0.237140 + 0.237140i) q^{5} +(0.103975 - 1.72893i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.359531 + 2.97838i) q^{9} +0.335367i q^{10} +(2.55493 - 2.55493i) q^{11} +(1.29606 - 1.14901i) q^{12} +(3.37961 - 1.25628i) q^{13} -1.00000i q^{14} +(0.0348698 - 0.579825i) q^{15} -1.00000 q^{16} +5.26383 q^{17} +(-2.36026 + 1.85180i) q^{18} +(0.906991 - 0.906991i) q^{19} +(-0.237140 + 0.237140i) q^{20} +(-0.103975 + 1.72893i) q^{21} +3.61322 q^{22} -1.48838 q^{23} +(1.72893 + 0.103975i) q^{24} -4.88753i q^{25} +(3.27807 + 1.50142i) q^{26} +(4.27326 - 2.95623i) q^{27} +(0.707107 - 0.707107i) q^{28} +7.36454i q^{29} +(0.434655 - 0.385342i) q^{30} +(7.20598 - 7.20598i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-6.24699 - 0.375685i) q^{33} +(3.72209 + 3.72209i) q^{34} -0.335367i q^{35} +(-2.97838 - 0.359531i) q^{36} +(-2.83332 - 2.83332i) q^{37} +1.28268 q^{38} +(-5.51143 - 2.93668i) q^{39} -0.335367 q^{40} +(1.32329 + 1.32329i) q^{41} +(-1.29606 + 1.14901i) q^{42} -2.75805i q^{43} +(2.55493 + 2.55493i) q^{44} +(-0.791553 + 0.621034i) q^{45} +(-1.05244 - 1.05244i) q^{46} +(-2.27264 + 2.27264i) q^{47} +(1.14901 + 1.29606i) q^{48} +1.00000i q^{49} +(3.45600 - 3.45600i) q^{50} +(-6.04822 - 6.82223i) q^{51} +(1.25628 + 3.37961i) q^{52} +8.80608i q^{53} +(5.11202 + 0.931280i) q^{54} +1.21175 q^{55} +1.00000 q^{56} +(-2.21766 - 0.133367i) q^{57} +(-5.20752 + 5.20752i) q^{58} +(-0.785394 + 0.785394i) q^{59} +(0.579825 + 0.0348698i) q^{60} +8.74912 q^{61} +10.1908 q^{62} +(2.36026 - 1.85180i) q^{63} -1.00000i q^{64} +(1.09936 + 0.503526i) q^{65} +(-4.15164 - 4.68294i) q^{66} +(-9.68048 + 9.68048i) q^{67} +5.26383i q^{68} +(1.71017 + 1.92903i) q^{69} +(0.237140 - 0.237140i) q^{70} +(4.94294 + 4.94294i) q^{71} +(-1.85180 - 2.36026i) q^{72} +(-4.00560 - 4.00560i) q^{73} -4.00692i q^{74} +(-6.33452 + 5.61584i) q^{75} +(0.906991 + 0.906991i) q^{76} -3.61322 q^{77} +(-1.82063 - 5.97372i) q^{78} -8.50862 q^{79} +(-0.237140 - 0.237140i) q^{80} +(-8.74148 - 2.14164i) q^{81} +1.87142i q^{82} +(-3.05668 - 3.05668i) q^{83} +(-1.72893 - 0.103975i) q^{84} +(1.24827 + 1.24827i) q^{85} +(1.95023 - 1.95023i) q^{86} +(9.54487 - 8.46196i) q^{87} +3.61322i q^{88} +(1.62293 - 1.62293i) q^{89} +(-0.998850 - 0.120575i) q^{90} +(-3.27807 - 1.50142i) q^{91} -1.48838i q^{92} +(-17.6191 - 1.05959i) q^{93} -3.21400 q^{94} +0.430168 q^{95} +(-0.103975 + 1.72893i) q^{96} +(-4.86305 + 4.86305i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(6.69097 + 8.52813i) 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
\(3\) −1.14901 1.29606i −0.663384 0.748279i
\(4\) 1.00000i 0.500000i
\(5\) 0.237140 + 0.237140i 0.106052 + 0.106052i 0.758142 0.652090i \(-0.226107\pi\)
−0.652090 + 0.758142i \(0.726107\pi\)
\(6\) 0.103975 1.72893i 0.0424477 0.705832i
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −0.359531 + 2.97838i −0.119844 + 0.992793i
\(10\) 0.335367i 0.106052i
\(11\) 2.55493 2.55493i 0.770341 0.770341i −0.207825 0.978166i \(-0.566639\pi\)
0.978166 + 0.207825i \(0.0666386\pi\)
\(12\) 1.29606 1.14901i 0.374140 0.331692i
\(13\) 3.37961 1.25628i 0.937335 0.348430i
\(14\) 1.00000i 0.267261i
\(15\) 0.0348698 0.579825i 0.00900335 0.149710i
\(16\) −1.00000 −0.250000
\(17\) 5.26383 1.27667 0.638334 0.769760i \(-0.279624\pi\)
0.638334 + 0.769760i \(0.279624\pi\)
\(18\) −2.36026 + 1.85180i −0.556318 + 0.436475i
\(19\) 0.906991 0.906991i 0.208078 0.208078i −0.595372 0.803450i \(-0.702995\pi\)
0.803450 + 0.595372i \(0.202995\pi\)
\(20\) −0.237140 + 0.237140i −0.0530262 + 0.0530262i
\(21\) −0.103975 + 1.72893i −0.0226892 + 0.377283i
\(22\) 3.61322 0.770341
\(23\) −1.48838 −0.310349 −0.155175 0.987887i \(-0.549594\pi\)
−0.155175 + 0.987887i \(0.549594\pi\)
\(24\) 1.72893 + 0.103975i 0.352916 + 0.0212238i
\(25\) 4.88753i 0.977506i
\(26\) 3.27807 + 1.50142i 0.642882 + 0.294452i
\(27\) 4.27326 2.95623i 0.822389 0.568926i
\(28\) 0.707107 0.707107i 0.133631 0.133631i
\(29\) 7.36454i 1.36756i 0.729688 + 0.683780i \(0.239665\pi\)
−0.729688 + 0.683780i \(0.760335\pi\)
\(30\) 0.434655 0.385342i 0.0793568 0.0703534i
\(31\) 7.20598 7.20598i 1.29423 1.29423i 0.362089 0.932143i \(-0.382064\pi\)
0.932143 0.362089i \(-0.117936\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −6.24699 0.375685i −1.08746 0.0653983i
\(34\) 3.72209 + 3.72209i 0.638334 + 0.638334i
\(35\) 0.335367i 0.0566874i
\(36\) −2.97838 0.359531i −0.496396 0.0599218i
\(37\) −2.83332 2.83332i −0.465795 0.465795i 0.434754 0.900549i \(-0.356835\pi\)
−0.900549 + 0.434754i \(0.856835\pi\)
\(38\) 1.28268 0.208078
\(39\) −5.51143 2.93668i −0.882536 0.470245i
\(40\) −0.335367 −0.0530262
\(41\) 1.32329 + 1.32329i 0.206664 + 0.206664i 0.802848 0.596184i \(-0.203317\pi\)
−0.596184 + 0.802848i \(0.703317\pi\)
\(42\) −1.29606 + 1.14901i −0.199986 + 0.177297i
\(43\) 2.75805i 0.420598i −0.977637 0.210299i \(-0.932556\pi\)
0.977637 0.210299i \(-0.0674437\pi\)
\(44\) 2.55493 + 2.55493i 0.385170 + 0.385170i
\(45\) −0.791553 + 0.621034i −0.117998 + 0.0925783i
\(46\) −1.05244 1.05244i −0.155175 0.155175i
\(47\) −2.27264 + 2.27264i −0.331499 + 0.331499i −0.853156 0.521657i \(-0.825314\pi\)
0.521657 + 0.853156i \(0.325314\pi\)
\(48\) 1.14901 + 1.29606i 0.165846 + 0.187070i
\(49\) 1.00000i 0.142857i
\(50\) 3.45600 3.45600i 0.488753 0.488753i
\(51\) −6.04822 6.82223i −0.846920 0.955304i
\(52\) 1.25628 + 3.37961i 0.174215 + 0.468667i
\(53\) 8.80608i 1.20961i 0.796374 + 0.604804i \(0.206749\pi\)
−0.796374 + 0.604804i \(0.793251\pi\)
\(54\) 5.11202 + 0.931280i 0.695657 + 0.126731i
\(55\) 1.21175 0.163393
\(56\) 1.00000 0.133631
\(57\) −2.21766 0.133367i −0.293736 0.0176648i
\(58\) −5.20752 + 5.20752i −0.683780 + 0.683780i
\(59\) −0.785394 + 0.785394i −0.102250 + 0.102250i −0.756381 0.654131i \(-0.773034\pi\)
0.654131 + 0.756381i \(0.273034\pi\)
\(60\) 0.579825 + 0.0348698i 0.0748551 + 0.00450167i
\(61\) 8.74912 1.12021 0.560105 0.828422i \(-0.310761\pi\)
0.560105 + 0.828422i \(0.310761\pi\)
\(62\) 10.1908 1.29423
\(63\) 2.36026 1.85180i 0.297365 0.233305i
\(64\) 1.00000i 0.125000i
\(65\) 1.09936 + 0.503526i 0.136358 + 0.0624547i
\(66\) −4.15164 4.68294i −0.511032 0.576430i
\(67\) −9.68048 + 9.68048i −1.18266 + 1.18266i −0.203606 + 0.979053i \(0.565266\pi\)
−0.979053 + 0.203606i \(0.934734\pi\)
\(68\) 5.26383i 0.638334i
\(69\) 1.71017 + 1.92903i 0.205881 + 0.232228i
\(70\) 0.237140 0.237140i 0.0283437 0.0283437i
\(71\) 4.94294 + 4.94294i 0.586619 + 0.586619i 0.936714 0.350095i \(-0.113851\pi\)
−0.350095 + 0.936714i \(0.613851\pi\)
\(72\) −1.85180 2.36026i −0.218237 0.278159i
\(73\) −4.00560 4.00560i −0.468821 0.468821i 0.432712 0.901532i \(-0.357557\pi\)
−0.901532 + 0.432712i \(0.857557\pi\)
\(74\) 4.00692i 0.465795i
\(75\) −6.33452 + 5.61584i −0.731447 + 0.648462i
\(76\) 0.906991 + 0.906991i 0.104039 + 0.104039i
\(77\) −3.61322 −0.411764
\(78\) −1.82063 5.97372i −0.206145 0.676390i
\(79\) −8.50862 −0.957294 −0.478647 0.878007i \(-0.658873\pi\)
−0.478647 + 0.878007i \(0.658873\pi\)
\(80\) −0.237140 0.237140i −0.0265131 0.0265131i
\(81\) −8.74148 2.14164i −0.971275 0.237960i
\(82\) 1.87142i 0.206664i
\(83\) −3.05668 3.05668i −0.335515 0.335515i 0.519162 0.854676i \(-0.326244\pi\)
−0.854676 + 0.519162i \(0.826244\pi\)
\(84\) −1.72893 0.103975i −0.188641 0.0113446i
\(85\) 1.24827 + 1.24827i 0.135394 + 0.135394i
\(86\) 1.95023 1.95023i 0.210299 0.210299i
\(87\) 9.54487 8.46196i 1.02332 0.907218i
\(88\) 3.61322i 0.385170i
\(89\) 1.62293 1.62293i 0.172030 0.172030i −0.615840 0.787871i \(-0.711183\pi\)
0.787871 + 0.615840i \(0.211183\pi\)
\(90\) −0.998850 0.120575i −0.105288 0.0127097i
\(91\) −3.27807 1.50142i −0.343635 0.157391i
\(92\) 1.48838i 0.155175i
\(93\) −17.6191 1.05959i −1.82702 0.109874i
\(94\) −3.21400 −0.331499
\(95\) 0.430168 0.0441343
\(96\) −0.103975 + 1.72893i −0.0106119 + 0.176458i
\(97\) −4.86305 + 4.86305i −0.493768 + 0.493768i −0.909491 0.415723i \(-0.863529\pi\)
0.415723 + 0.909491i \(0.363529\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) 6.69097 + 8.52813i 0.672468 + 0.857109i
\(100\) 4.88753 0.488753
\(101\) −18.5302 −1.84382 −0.921911 0.387402i \(-0.873373\pi\)
−0.921911 + 0.387402i \(0.873373\pi\)
\(102\) 0.547308 9.10078i 0.0541915 0.901112i
\(103\) 5.76073i 0.567622i −0.958880 0.283811i \(-0.908401\pi\)
0.958880 0.283811i \(-0.0915988\pi\)
\(104\) −1.50142 + 3.27807i −0.147226 + 0.321441i
\(105\) −0.434655 + 0.385342i −0.0424180 + 0.0376055i
\(106\) −6.22684 + 6.22684i −0.604804 + 0.604804i
\(107\) 18.3125i 1.77034i −0.465270 0.885169i \(-0.654043\pi\)
0.465270 0.885169i \(-0.345957\pi\)
\(108\) 2.95623 + 4.27326i 0.284463 + 0.411194i
\(109\) −6.72226 + 6.72226i −0.643876 + 0.643876i −0.951506 0.307630i \(-0.900464\pi\)
0.307630 + 0.951506i \(0.400464\pi\)
\(110\) 0.856839 + 0.856839i 0.0816964 + 0.0816964i
\(111\) −0.416620 + 6.92768i −0.0395439 + 0.657546i
\(112\) 0.707107 + 0.707107i 0.0668153 + 0.0668153i
\(113\) 15.8812i 1.49398i 0.664835 + 0.746990i \(0.268502\pi\)
−0.664835 + 0.746990i \(0.731498\pi\)
\(114\) −1.47382 1.66243i −0.138036 0.155700i
\(115\) −0.352955 0.352955i −0.0329132 0.0329132i
\(116\) −7.36454 −0.683780
\(117\) 2.52661 + 10.5174i 0.233585 + 0.972336i
\(118\) −1.11071 −0.102250
\(119\) −3.72209 3.72209i −0.341204 0.341204i
\(120\) 0.385342 + 0.434655i 0.0351767 + 0.0396784i
\(121\) 2.05534i 0.186849i
\(122\) 6.18656 + 6.18656i 0.560105 + 0.560105i
\(123\) 0.194581 3.23555i 0.0175448 0.291739i
\(124\) 7.20598 + 7.20598i 0.647116 + 0.647116i
\(125\) 2.34473 2.34473i 0.209719 0.209719i
\(126\) 2.97838 + 0.359531i 0.265335 + 0.0320295i
\(127\) 8.38087i 0.743682i −0.928297 0.371841i \(-0.878727\pi\)
0.928297 0.371841i \(-0.121273\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −3.57459 + 3.16903i −0.314725 + 0.279018i
\(130\) 0.421316 + 1.13341i 0.0369518 + 0.0994066i
\(131\) 14.5927i 1.27497i 0.770464 + 0.637484i \(0.220025\pi\)
−0.770464 + 0.637484i \(0.779975\pi\)
\(132\) 0.375685 6.24699i 0.0326992 0.543731i
\(133\) −1.28268 −0.111222
\(134\) −13.6903 −1.18266
\(135\) 1.71440 + 0.312321i 0.147552 + 0.0268803i
\(136\) −3.72209 + 3.72209i −0.319167 + 0.319167i
\(137\) 11.5852 11.5852i 0.989790 0.989790i −0.0101587 0.999948i \(-0.503234\pi\)
0.999948 + 0.0101587i \(0.00323368\pi\)
\(138\) −0.154755 + 2.57330i −0.0131736 + 0.219054i
\(139\) 11.9801 1.01614 0.508070 0.861316i \(-0.330359\pi\)
0.508070 + 0.861316i \(0.330359\pi\)
\(140\) 0.335367 0.0283437
\(141\) 5.55677 + 0.334176i 0.467965 + 0.0281427i
\(142\) 6.99038i 0.586619i
\(143\) 5.42495 11.8444i 0.453657 0.990477i
\(144\) 0.359531 2.97838i 0.0299609 0.248198i
\(145\) −1.74643 + 1.74643i −0.145033 + 0.145033i
\(146\) 5.66478i 0.468821i
\(147\) 1.29606 1.14901i 0.106897 0.0947691i
\(148\) 2.83332 2.83332i 0.232898 0.232898i
\(149\) 2.17899 + 2.17899i 0.178510 + 0.178510i 0.790706 0.612196i \(-0.209714\pi\)
−0.612196 + 0.790706i \(0.709714\pi\)
\(150\) −8.45018 0.508181i −0.689954 0.0414928i
\(151\) 9.34711 + 9.34711i 0.760657 + 0.760657i 0.976441 0.215784i \(-0.0692307\pi\)
−0.215784 + 0.976441i \(0.569231\pi\)
\(152\) 1.28268i 0.104039i
\(153\) −1.89251 + 15.6777i −0.153000 + 1.26747i
\(154\) −2.55493 2.55493i −0.205882 0.205882i
\(155\) 3.41766 0.274513
\(156\) 2.93668 5.51143i 0.235123 0.441268i
\(157\) −17.6346 −1.40740 −0.703698 0.710499i \(-0.748469\pi\)
−0.703698 + 0.710499i \(0.748469\pi\)
\(158\) −6.01650 6.01650i −0.478647 0.478647i
\(159\) 11.4132 10.1183i 0.905125 0.802435i
\(160\) 0.335367i 0.0265131i
\(161\) 1.05244 + 1.05244i 0.0829443 + 0.0829443i
\(162\) −4.66679 7.69552i −0.366658 0.604617i
\(163\) −2.26457 2.26457i −0.177375 0.177375i 0.612836 0.790210i \(-0.290029\pi\)
−0.790210 + 0.612836i \(0.790029\pi\)
\(164\) −1.32329 + 1.32329i −0.103332 + 0.103332i
\(165\) −1.39232 1.57050i −0.108392 0.122263i
\(166\) 4.32280i 0.335515i
\(167\) 12.4482 12.4482i 0.963272 0.963272i −0.0360774 0.999349i \(-0.511486\pi\)
0.999349 + 0.0360774i \(0.0114863\pi\)
\(168\) −1.14901 1.29606i −0.0886484 0.0999930i
\(169\) 9.84351 8.49149i 0.757193 0.653192i
\(170\) 1.76532i 0.135394i
\(171\) 2.37527 + 3.02745i 0.181641 + 0.231515i
\(172\) 2.75805 0.210299
\(173\) −12.8517 −0.977096 −0.488548 0.872537i \(-0.662473\pi\)
−0.488548 + 0.872537i \(0.662473\pi\)
\(174\) 12.7328 + 0.765729i 0.965267 + 0.0580497i
\(175\) −3.45600 + 3.45600i −0.261249 + 0.261249i
\(176\) −2.55493 + 2.55493i −0.192585 + 0.192585i
\(177\) 1.92034 + 0.115487i 0.144342 + 0.00868051i
\(178\) 2.29517 0.172030
\(179\) −13.7258 −1.02592 −0.512959 0.858413i \(-0.671451\pi\)
−0.512959 + 0.858413i \(0.671451\pi\)
\(180\) −0.621034 0.791553i −0.0462892 0.0589989i
\(181\) 17.7979i 1.32291i −0.749986 0.661454i \(-0.769940\pi\)
0.749986 0.661454i \(-0.230060\pi\)
\(182\) −1.25628 3.37961i −0.0931219 0.250513i
\(183\) −10.0529 11.3394i −0.743129 0.838230i
\(184\) 1.05244 1.05244i 0.0775873 0.0775873i
\(185\) 1.34379i 0.0987974i
\(186\) −11.7094 13.2079i −0.858573 0.968447i
\(187\) 13.4487 13.4487i 0.983469 0.983469i
\(188\) −2.27264 2.27264i −0.165749 0.165749i
\(189\) −5.11202 0.931280i −0.371845 0.0677406i
\(190\) 0.304175 + 0.304175i 0.0220672 + 0.0220672i
\(191\) 0.449102i 0.0324959i −0.999868 0.0162479i \(-0.994828\pi\)
0.999868 0.0162479i \(-0.00517211\pi\)
\(192\) −1.29606 + 1.14901i −0.0935349 + 0.0829230i
\(193\) −5.53933 5.53933i −0.398730 0.398730i 0.479055 0.877785i \(-0.340979\pi\)
−0.877785 + 0.479055i \(0.840979\pi\)
\(194\) −6.87739 −0.493768
\(195\) −0.610578 2.00339i −0.0437244 0.143466i
\(196\) −1.00000 −0.0714286
\(197\) 15.8126 + 15.8126i 1.12660 + 1.12660i 0.990726 + 0.135878i \(0.0433855\pi\)
0.135878 + 0.990726i \(0.456614\pi\)
\(198\) −1.29906 + 10.7615i −0.0923204 + 0.764789i
\(199\) 26.3160i 1.86549i 0.360531 + 0.932747i \(0.382595\pi\)
−0.360531 + 0.932747i \(0.617405\pi\)
\(200\) 3.45600 + 3.45600i 0.244376 + 0.244376i
\(201\) 23.6695 + 1.42345i 1.66952 + 0.100402i
\(202\) −13.1028 13.1028i −0.921911 0.921911i
\(203\) 5.20752 5.20752i 0.365496 0.365496i
\(204\) 6.82223 6.04822i 0.477652 0.423460i
\(205\) 0.627612i 0.0438343i
\(206\) 4.07345 4.07345i 0.283811 0.283811i
\(207\) 0.535119 4.43296i 0.0371933 0.308112i
\(208\) −3.37961 + 1.25628i −0.234334 + 0.0871076i
\(209\) 4.63460i 0.320582i
\(210\) −0.579825 0.0348698i −0.0400117 0.00240625i
\(211\) −11.4416 −0.787669 −0.393835 0.919181i \(-0.628852\pi\)
−0.393835 + 0.919181i \(0.628852\pi\)
\(212\) −8.80608 −0.604804
\(213\) 0.726825 12.0859i 0.0498012 0.828109i
\(214\) 12.9489 12.9489i 0.885169 0.885169i
\(215\) 0.654044 0.654044i 0.0446054 0.0446054i
\(216\) −0.931280 + 5.11202i −0.0633656 + 0.347829i
\(217\) −10.1908 −0.691796
\(218\) −9.50671 −0.643876
\(219\) −0.588996 + 9.79399i −0.0398007 + 0.661817i
\(220\) 1.21175i 0.0816964i
\(221\) 17.7897 6.61287i 1.19666 0.444829i
\(222\) −5.19320 + 4.60401i −0.348545 + 0.309001i
\(223\) −9.06520 + 9.06520i −0.607051 + 0.607051i −0.942174 0.335124i \(-0.891222\pi\)
0.335124 + 0.942174i \(0.391222\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 14.5569 + 1.75722i 0.970461 + 0.117148i
\(226\) −11.2297 + 11.2297i −0.746990 + 0.746990i
\(227\) 1.95892 + 1.95892i 0.130018 + 0.130018i 0.769121 0.639103i \(-0.220694\pi\)
−0.639103 + 0.769121i \(0.720694\pi\)
\(228\) 0.133367 2.21766i 0.00883242 0.146868i
\(229\) 19.6908 + 19.6908i 1.30120 + 1.30120i 0.927581 + 0.373622i \(0.121884\pi\)
0.373622 + 0.927581i \(0.378116\pi\)
\(230\) 0.499154i 0.0329132i
\(231\) 4.15164 + 4.68294i 0.273158 + 0.308115i
\(232\) −5.20752 5.20752i −0.341890 0.341890i
\(233\) 8.08237 0.529494 0.264747 0.964318i \(-0.414712\pi\)
0.264747 + 0.964318i \(0.414712\pi\)
\(234\) −5.65036 + 9.22353i −0.369375 + 0.602961i
\(235\) −1.07787 −0.0703125
\(236\) −0.785394 0.785394i −0.0511248 0.0511248i
\(237\) 9.77652 + 11.0277i 0.635053 + 0.716323i
\(238\) 5.26383i 0.341204i
\(239\) 17.1098 + 17.1098i 1.10674 + 1.10674i 0.993576 + 0.113167i \(0.0360994\pi\)
0.113167 + 0.993576i \(0.463901\pi\)
\(240\) −0.0348698 + 0.579825i −0.00225084 + 0.0374275i
\(241\) −1.64646 1.64646i −0.106058 0.106058i 0.652087 0.758144i \(-0.273894\pi\)
−0.758144 + 0.652087i \(0.773894\pi\)
\(242\) 1.45335 1.45335i 0.0934247 0.0934247i
\(243\) 7.26840 + 13.7902i 0.466268 + 0.884644i
\(244\) 8.74912i 0.560105i
\(245\) −0.237140 + 0.237140i −0.0151503 + 0.0151503i
\(246\) 2.42547 2.15029i 0.154642 0.137097i
\(247\) 1.92584 4.20471i 0.122538 0.267539i
\(248\) 10.1908i 0.647116i
\(249\) −0.449464 + 7.47381i −0.0284836 + 0.473633i
\(250\) 3.31595 0.209719
\(251\) −5.59492 −0.353148 −0.176574 0.984287i \(-0.556501\pi\)
−0.176574 + 0.984287i \(0.556501\pi\)
\(252\) 1.85180 + 2.36026i 0.116653 + 0.148682i
\(253\) −3.80271 + 3.80271i −0.239074 + 0.239074i
\(254\) 5.92617 5.92617i 0.371841 0.371841i
\(255\) 0.183549 3.05210i 0.0114943 0.191130i
\(256\) 1.00000 0.0625000
\(257\) 9.37697 0.584920 0.292460 0.956278i \(-0.405526\pi\)
0.292460 + 0.956278i \(0.405526\pi\)
\(258\) −4.76846 0.286768i −0.296871 0.0178534i
\(259\) 4.00692i 0.248978i
\(260\) −0.503526 + 1.09936i −0.0312274 + 0.0681792i
\(261\) −21.9344 2.64778i −1.35770 0.163893i
\(262\) −10.3186 + 10.3186i −0.637484 + 0.637484i
\(263\) 7.28774i 0.449382i −0.974430 0.224691i \(-0.927863\pi\)
0.974430 0.224691i \(-0.0721372\pi\)
\(264\) 4.68294 4.15164i 0.288215 0.255516i
\(265\) −2.08828 + 2.08828i −0.128282 + 0.128282i
\(266\) −0.906991 0.906991i −0.0556112 0.0556112i
\(267\) −3.96818 0.238641i −0.242849 0.0146046i
\(268\) −9.68048 9.68048i −0.591330 0.591330i
\(269\) 16.4964i 1.00580i 0.864344 + 0.502901i \(0.167734\pi\)
−0.864344 + 0.502901i \(0.832266\pi\)
\(270\) 0.991421 + 1.43311i 0.0603360 + 0.0872162i
\(271\) −2.57036 2.57036i −0.156138 0.156138i 0.624715 0.780853i \(-0.285215\pi\)
−0.780853 + 0.624715i \(0.785215\pi\)
\(272\) −5.26383 −0.319167
\(273\) 1.82063 + 5.97372i 0.110189 + 0.361546i
\(274\) 16.3839 0.989790
\(275\) −12.4873 12.4873i −0.753012 0.753012i
\(276\) −1.92903 + 1.71017i −0.116114 + 0.102940i
\(277\) 7.42795i 0.446302i −0.974784 0.223151i \(-0.928366\pi\)
0.974784 0.223151i \(-0.0716344\pi\)
\(278\) 8.47121 + 8.47121i 0.508070 + 0.508070i
\(279\) 18.8714 + 24.0529i 1.12980 + 1.44001i
\(280\) 0.237140 + 0.237140i 0.0141718 + 0.0141718i
\(281\) −9.42247 + 9.42247i −0.562097 + 0.562097i −0.929903 0.367805i \(-0.880109\pi\)
0.367805 + 0.929903i \(0.380109\pi\)
\(282\) 3.69293 + 4.16553i 0.219911 + 0.248054i
\(283\) 21.5878i 1.28326i −0.767014 0.641631i \(-0.778258\pi\)
0.767014 0.641631i \(-0.221742\pi\)
\(284\) −4.94294 + 4.94294i −0.293310 + 0.293310i
\(285\) −0.494269 0.557523i −0.0292780 0.0330248i
\(286\) 12.2113 4.53922i 0.722067 0.268410i
\(287\) 1.87142i 0.110466i
\(288\) 2.36026 1.85180i 0.139080 0.109119i
\(289\) 10.7079 0.629879
\(290\) −2.46982 −0.145033
\(291\) 11.8905 + 0.715078i 0.697034 + 0.0419186i
\(292\) 4.00560 4.00560i 0.234410 0.234410i
\(293\) −3.94771 + 3.94771i −0.230628 + 0.230628i −0.812955 0.582327i \(-0.802142\pi\)
0.582327 + 0.812955i \(0.302142\pi\)
\(294\) 1.72893 + 0.103975i 0.100833 + 0.00606395i
\(295\) −0.372497 −0.0216876
\(296\) 4.00692 0.232898
\(297\) 3.36492 18.4708i 0.195252 1.07179i
\(298\) 3.08156i 0.178510i
\(299\) −5.03015 + 1.86983i −0.290901 + 0.108135i
\(300\) −5.61584 6.33452i −0.324231 0.365724i
\(301\) −1.95023 + 1.95023i −0.112410 + 0.112410i
\(302\) 13.2188i 0.760657i
\(303\) 21.2915 + 24.0162i 1.22316 + 1.37969i
\(304\) −0.906991 + 0.906991i −0.0520195 + 0.0520195i
\(305\) 2.07477 + 2.07477i 0.118801 + 0.118801i
\(306\) −12.4240 + 9.74759i −0.710233 + 0.557233i
\(307\) −11.8118 11.8118i −0.674136 0.674136i 0.284531 0.958667i \(-0.408162\pi\)
−0.958667 + 0.284531i \(0.908162\pi\)
\(308\) 3.61322i 0.205882i
\(309\) −7.46624 + 6.61917i −0.424740 + 0.376551i
\(310\) 2.41665 + 2.41665i 0.137256 + 0.137256i
\(311\) −20.8401 −1.18174 −0.590868 0.806769i \(-0.701214\pi\)
−0.590868 + 0.806769i \(0.701214\pi\)
\(312\) 5.97372 1.82063i 0.338195 0.103073i
\(313\) 9.67697 0.546975 0.273487 0.961876i \(-0.411823\pi\)
0.273487 + 0.961876i \(0.411823\pi\)
\(314\) −12.4696 12.4696i −0.703698 0.703698i
\(315\) 0.998850 + 0.120575i 0.0562788 + 0.00679362i
\(316\) 8.50862i 0.478647i
\(317\) −14.4793 14.4793i −0.813239 0.813239i 0.171879 0.985118i \(-0.445016\pi\)
−0.985118 + 0.171879i \(0.945016\pi\)
\(318\) 15.2251 + 0.915613i 0.853780 + 0.0513450i
\(319\) 18.8159 + 18.8159i 1.05349 + 1.05349i
\(320\) 0.237140 0.237140i 0.0132565 0.0132565i
\(321\) −23.7341 + 21.0414i −1.32471 + 1.17441i
\(322\) 1.48838i 0.0829443i
\(323\) 4.77425 4.77425i 0.265646 0.265646i
\(324\) 2.14164 8.74148i 0.118980 0.485638i
\(325\) −6.14012 16.5179i −0.340593 0.916250i
\(326\) 3.20259i 0.177375i
\(327\) 16.4364 + 0.988462i 0.908936 + 0.0546620i
\(328\) −1.87142 −0.103332
\(329\) 3.21400 0.177194
\(330\) 0.125992 2.09503i 0.00693565 0.115328i
\(331\) 23.9019 23.9019i 1.31377 1.31377i 0.395149 0.918617i \(-0.370693\pi\)
0.918617 0.395149i \(-0.129307\pi\)
\(332\) 3.05668 3.05668i 0.167757 0.167757i
\(333\) 9.45737 7.42004i 0.518261 0.406616i
\(334\) 17.6044 0.963272
\(335\) −4.59126 −0.250848
\(336\) 0.103975 1.72893i 0.00567231 0.0943207i
\(337\) 19.1386i 1.04254i 0.853390 + 0.521272i \(0.174542\pi\)
−0.853390 + 0.521272i \(0.825458\pi\)
\(338\) 12.9648 + 0.956020i 0.705192 + 0.0520006i
\(339\) 20.5830 18.2478i 1.11791 0.991083i
\(340\) −1.24827 + 1.24827i −0.0676968 + 0.0676968i
\(341\) 36.8216i 1.99400i
\(342\) −0.461162 + 3.82030i −0.0249368 + 0.206578i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) 1.95023 + 1.95023i 0.105149 + 0.105149i
\(345\) −0.0518996 + 0.863001i −0.00279418 + 0.0464624i
\(346\) −9.08752 9.08752i −0.488548 0.488548i
\(347\) 22.2918i 1.19669i 0.801240 + 0.598343i \(0.204174\pi\)
−0.801240 + 0.598343i \(0.795826\pi\)
\(348\) 8.46196 + 9.54487i 0.453609 + 0.511659i
\(349\) −11.5388 11.5388i −0.617658 0.617658i 0.327272 0.944930i \(-0.393871\pi\)
−0.944930 + 0.327272i \(0.893871\pi\)
\(350\) −4.88753 −0.261249
\(351\) 10.7281 15.3593i 0.572622 0.819819i
\(352\) −3.61322 −0.192585
\(353\) −10.9867 10.9867i −0.584765 0.584765i 0.351444 0.936209i \(-0.385691\pi\)
−0.936209 + 0.351444i \(0.885691\pi\)
\(354\) 1.27623 + 1.43955i 0.0678307 + 0.0765112i
\(355\) 2.34434i 0.124425i
\(356\) 1.62293 + 1.62293i 0.0860152 + 0.0860152i
\(357\) −0.547308 + 9.10078i −0.0289666 + 0.481665i
\(358\) −9.70564 9.70564i −0.512959 0.512959i
\(359\) −12.3937 + 12.3937i −0.654116 + 0.654116i −0.953982 0.299865i \(-0.903058\pi\)
0.299865 + 0.953982i \(0.403058\pi\)
\(360\) 0.120575 0.998850i 0.00635485 0.0526440i
\(361\) 17.3547i 0.913407i
\(362\) 12.5850 12.5850i 0.661454 0.661454i
\(363\) −2.66384 + 2.36162i −0.139816 + 0.123953i
\(364\) 1.50142 3.27807i 0.0786957 0.171818i
\(365\) 1.89978i 0.0994390i
\(366\) 0.909691 15.1266i 0.0475503 0.790679i
\(367\) −19.3712 −1.01117 −0.505583 0.862778i \(-0.668723\pi\)
−0.505583 + 0.862778i \(0.668723\pi\)
\(368\) 1.48838 0.0775873
\(369\) −4.41703 + 3.46550i −0.229941 + 0.180407i
\(370\) 0.950203 0.950203i 0.0493987 0.0493987i
\(371\) 6.22684 6.22684i 0.323281 0.323281i
\(372\) 1.05959 17.6191i 0.0549372 0.913510i
\(373\) 26.6583 1.38031 0.690157 0.723659i \(-0.257541\pi\)
0.690157 + 0.723659i \(0.257541\pi\)
\(374\) 19.0194 0.983469
\(375\) −5.73304 0.344776i −0.296053 0.0178042i
\(376\) 3.21400i 0.165749i
\(377\) 9.25195 + 24.8893i 0.476499 + 1.28186i
\(378\) −2.95623 4.27326i −0.152052 0.219793i
\(379\) −7.17262 + 7.17262i −0.368433 + 0.368433i −0.866905 0.498473i \(-0.833894\pi\)
0.498473 + 0.866905i \(0.333894\pi\)
\(380\) 0.430168i 0.0220672i
\(381\) −10.8621 + 9.62974i −0.556482 + 0.493346i
\(382\) 0.317563 0.317563i 0.0162479 0.0162479i
\(383\) 1.75953 + 1.75953i 0.0899076 + 0.0899076i 0.750630 0.660723i \(-0.229750\pi\)
−0.660723 + 0.750630i \(0.729750\pi\)
\(384\) −1.72893 0.103975i −0.0882289 0.00530596i
\(385\) −0.856839 0.856839i −0.0436686 0.0436686i
\(386\) 7.83380i 0.398730i
\(387\) 8.21450 + 0.991602i 0.417567 + 0.0504060i
\(388\) −4.86305 4.86305i −0.246884 0.246884i
\(389\) −23.3995 −1.18640 −0.593200 0.805055i \(-0.702136\pi\)
−0.593200 + 0.805055i \(0.702136\pi\)
\(390\) 0.984865 1.84835i 0.0498706 0.0935950i
\(391\) −7.83459 −0.396212
\(392\) −0.707107 0.707107i −0.0357143 0.0357143i
\(393\) 18.9130 16.7672i 0.954032 0.845793i
\(394\) 22.3624i 1.12660i
\(395\) −2.01774 2.01774i −0.101523 0.101523i
\(396\) −8.52813 + 6.69097i −0.428555 + 0.336234i
\(397\) 12.7022 + 12.7022i 0.637506 + 0.637506i 0.949940 0.312434i \(-0.101144\pi\)
−0.312434 + 0.949940i \(0.601144\pi\)
\(398\) −18.6082 + 18.6082i −0.932747 + 0.932747i
\(399\) 1.47382 + 1.66243i 0.0737831 + 0.0832254i
\(400\) 4.88753i 0.244376i
\(401\) −4.63460 + 4.63460i −0.231441 + 0.231441i −0.813294 0.581853i \(-0.802328\pi\)
0.581853 + 0.813294i \(0.302328\pi\)
\(402\) 15.7303 + 17.7434i 0.784557 + 0.884959i
\(403\) 15.3006 33.4062i 0.762179 1.66408i
\(404\) 18.5302i 0.921911i
\(405\) −1.56509 2.58082i −0.0777698 0.128242i
\(406\) 7.36454 0.365496
\(407\) −14.4779 −0.717642
\(408\) 9.10078 + 0.547308i 0.450556 + 0.0270958i
\(409\) 20.9632 20.9632i 1.03656 1.03656i 0.0372568 0.999306i \(-0.488138\pi\)
0.999306 0.0372568i \(-0.0118619\pi\)
\(410\) −0.443789 + 0.443789i −0.0219172 + 0.0219172i
\(411\) −28.3266 1.70352i −1.39725 0.0840285i
\(412\) 5.76073 0.283811
\(413\) 1.11071 0.0546547
\(414\) 3.51297 2.75619i 0.172653 0.135459i
\(415\) 1.44973i 0.0711642i
\(416\) −3.27807 1.50142i −0.160721 0.0736131i
\(417\) −13.7653 15.5269i −0.674091 0.760356i
\(418\) 3.27716 3.27716i 0.160291 0.160291i
\(419\) 2.30031i 0.112377i −0.998420 0.0561886i \(-0.982105\pi\)
0.998420 0.0561886i \(-0.0178948\pi\)
\(420\) −0.385342 0.434655i −0.0188027 0.0212090i
\(421\) −5.27352 + 5.27352i −0.257016 + 0.257016i −0.823839 0.566823i \(-0.808172\pi\)
0.566823 + 0.823839i \(0.308172\pi\)
\(422\) −8.09040 8.09040i −0.393835 0.393835i
\(423\) −5.95170 7.58587i −0.289382 0.368838i
\(424\) −6.22684 6.22684i −0.302402 0.302402i
\(425\) 25.7271i 1.24795i
\(426\) 9.05993 8.03204i 0.438955 0.389154i
\(427\) −6.18656 6.18656i −0.299389 0.299389i
\(428\) 18.3125 0.885169
\(429\) −21.5843 + 6.57832i −1.04210 + 0.317604i
\(430\) 0.924957 0.0446054
\(431\) 4.81808 + 4.81808i 0.232079 + 0.232079i 0.813560 0.581481i \(-0.197527\pi\)
−0.581481 + 0.813560i \(0.697527\pi\)
\(432\) −4.27326 + 2.95623i −0.205597 + 0.142232i
\(433\) 4.81966i 0.231618i 0.993272 + 0.115809i \(0.0369460\pi\)
−0.993272 + 0.115809i \(0.963054\pi\)
\(434\) −7.20598 7.20598i −0.345898 0.345898i
\(435\) 4.27014 + 0.256800i 0.204738 + 0.0123126i
\(436\) −6.72226 6.72226i −0.321938 0.321938i
\(437\) −1.34995 + 1.34995i −0.0645768 + 0.0645768i
\(438\) −7.34188 + 6.50891i −0.350809 + 0.311008i
\(439\) 13.0143i 0.621137i 0.950551 + 0.310569i \(0.100519\pi\)
−0.950551 + 0.310569i \(0.899481\pi\)
\(440\) −0.856839 + 0.856839i −0.0408482 + 0.0408482i
\(441\) −2.97838 0.359531i −0.141828 0.0171205i
\(442\) 17.2552 + 7.90321i 0.820747 + 0.375918i
\(443\) 23.1864i 1.10162i −0.834631 0.550810i \(-0.814319\pi\)
0.834631 0.550810i \(-0.185681\pi\)
\(444\) −6.92768 0.416620i −0.328773 0.0197719i
\(445\) 0.769725 0.0364884
\(446\) −12.8201 −0.607051
\(447\) 0.320406 5.32779i 0.0151547 0.251996i
\(448\) −0.707107 + 0.707107i −0.0334077 + 0.0334077i
\(449\) 7.31378 7.31378i 0.345159 0.345159i −0.513144 0.858303i \(-0.671519\pi\)
0.858303 + 0.513144i \(0.171519\pi\)
\(450\) 9.05075 + 11.5358i 0.426656 + 0.543804i
\(451\) 6.76184 0.318403
\(452\) −15.8812 −0.746990
\(453\) 1.37443 22.8544i 0.0645762 1.07379i
\(454\) 2.77033i 0.130018i
\(455\) −0.421316 1.13341i −0.0197516 0.0531350i
\(456\) 1.66243 1.47382i 0.0778502 0.0690178i
\(457\) 7.58631 7.58631i 0.354873 0.354873i −0.507046 0.861919i \(-0.669263\pi\)
0.861919 + 0.507046i \(0.169263\pi\)
\(458\) 27.8470i 1.30120i
\(459\) 22.4937 15.5611i 1.04992 0.726329i
\(460\) 0.352955 0.352955i 0.0164566 0.0164566i
\(461\) −9.45526 9.45526i −0.440375 0.440375i 0.451763 0.892138i \(-0.350795\pi\)
−0.892138 + 0.451763i \(0.850795\pi\)
\(462\) −0.375685 + 6.24699i −0.0174784 + 0.290636i
\(463\) 24.1674 + 24.1674i 1.12315 + 1.12315i 0.991264 + 0.131890i \(0.0421046\pi\)
0.131890 + 0.991264i \(0.457895\pi\)
\(464\) 7.36454i 0.341890i
\(465\) −3.92694 4.42948i −0.182107 0.205412i
\(466\) 5.71510 + 5.71510i 0.264747 + 0.264747i
\(467\) −23.9765 −1.10950 −0.554750 0.832017i \(-0.687186\pi\)
−0.554750 + 0.832017i \(0.687186\pi\)
\(468\) −10.5174 + 2.52661i −0.486168 + 0.116793i
\(469\) 13.6903 0.632158
\(470\) −0.762169 0.762169i −0.0351562 0.0351562i
\(471\) 20.2624 + 22.8555i 0.933644 + 1.05313i
\(472\) 1.11071i 0.0511248i
\(473\) −7.04661 7.04661i −0.324004 0.324004i
\(474\) −0.884684 + 14.7108i −0.0406349 + 0.675688i
\(475\) −4.43294 4.43294i −0.203397 0.203397i
\(476\) 3.72209 3.72209i 0.170602 0.170602i
\(477\) −26.2278 3.16606i −1.20089 0.144964i
\(478\) 24.1969i 1.10674i
\(479\) 13.3006 13.3006i 0.607720 0.607720i −0.334630 0.942350i \(-0.608611\pi\)
0.942350 + 0.334630i \(0.108611\pi\)
\(480\) −0.434655 + 0.385342i −0.0198392 + 0.0175884i
\(481\) −13.1350 6.01607i −0.598903 0.274309i
\(482\) 2.32844i 0.106058i
\(483\) 0.154755 2.57330i 0.00704158 0.117089i
\(484\) 2.05534 0.0934247
\(485\) −2.30645 −0.104731
\(486\) −4.61163 + 14.8907i −0.209188 + 0.675456i
\(487\) −12.0715 + 12.0715i −0.547013 + 0.547013i −0.925576 0.378563i \(-0.876418\pi\)
0.378563 + 0.925576i \(0.376418\pi\)
\(488\) −6.18656 + 6.18656i −0.280052 + 0.280052i
\(489\) −0.332989 + 5.53704i −0.0150583 + 0.250393i
\(490\) −0.335367 −0.0151503
\(491\) −28.9991 −1.30871 −0.654356 0.756187i \(-0.727060\pi\)
−0.654356 + 0.756187i \(0.727060\pi\)
\(492\) 3.23555 + 0.194581i 0.145870 + 0.00877239i
\(493\) 38.7657i 1.74592i
\(494\) 4.33495 1.61141i 0.195039 0.0725007i
\(495\) −0.435663 + 3.60906i −0.0195816 + 0.162215i
\(496\) −7.20598 + 7.20598i −0.323558 + 0.323558i
\(497\) 6.99038i 0.313561i
\(498\) −5.60260 + 4.96696i −0.251059 + 0.222575i
\(499\) −16.4961 + 16.4961i −0.738468 + 0.738468i −0.972281 0.233814i \(-0.924879\pi\)
0.233814 + 0.972281i \(0.424879\pi\)
\(500\) 2.34473 + 2.34473i 0.104860 + 0.104860i
\(501\) −30.4368 1.83042i −1.35982 0.0817773i
\(502\) −3.95620 3.95620i −0.176574 0.176574i
\(503\) 3.30047i 0.147161i 0.997289 + 0.0735804i \(0.0234425\pi\)
−0.997289 + 0.0735804i \(0.976557\pi\)
\(504\) −0.359531 + 2.97838i −0.0160148 + 0.132668i
\(505\) −4.39425 4.39425i −0.195542 0.195542i
\(506\) −5.37785 −0.239074
\(507\) −22.3158 3.00090i −0.991079 0.133275i
\(508\) 8.38087 0.371841
\(509\) 4.74000 + 4.74000i 0.210097 + 0.210097i 0.804309 0.594212i \(-0.202536\pi\)
−0.594212 + 0.804309i \(0.702536\pi\)
\(510\) 2.28795 2.02837i 0.101312 0.0898179i
\(511\) 5.66478i 0.250595i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 1.19453 6.55708i 0.0527399 0.289502i
\(514\) 6.63052 + 6.63052i 0.292460 + 0.292460i
\(515\) 1.36610 1.36610i 0.0601976 0.0601976i
\(516\) −3.16903 3.57459i −0.139509 0.157362i
\(517\) 11.6129i 0.510734i
\(518\) −2.83332 + 2.83332i −0.124489 + 0.124489i
\(519\) 14.7668 + 16.6565i 0.648190 + 0.731140i
\(520\) −1.13341 + 0.421316i −0.0497033 + 0.0184759i
\(521\) 23.6757i 1.03725i 0.855001 + 0.518627i \(0.173557\pi\)
−0.855001 + 0.518627i \(0.826443\pi\)
\(522\) −13.6377 17.3822i −0.596905 0.760799i
\(523\) −39.0606 −1.70800 −0.854000 0.520272i \(-0.825830\pi\)
−0.854000 + 0.520272i \(0.825830\pi\)
\(524\) −14.5927 −0.637484
\(525\) 8.45018 + 0.508181i 0.368796 + 0.0221789i
\(526\) 5.15321 5.15321i 0.224691 0.224691i
\(527\) 37.9311 37.9311i 1.65230 1.65230i
\(528\) 6.24699 + 0.375685i 0.271865 + 0.0163496i
\(529\) −20.7847 −0.903683
\(530\) −2.95327 −0.128282
\(531\) −2.05683 2.62157i −0.0892586 0.113767i
\(532\) 1.28268i 0.0556112i
\(533\) 6.13464 + 2.80978i 0.265721 + 0.121705i
\(534\) −2.63719 2.97467i −0.114122 0.128727i
\(535\) 4.34264 4.34264i 0.187749 0.187749i
\(536\) 13.6903i 0.591330i
\(537\) 15.7712 + 17.7895i 0.680577 + 0.767673i
\(538\) −11.6647 + 11.6647i −0.502901 + 0.502901i
\(539\) 2.55493 + 2.55493i 0.110049 + 0.110049i
\(540\) −0.312321 + 1.71440i −0.0134401 + 0.0737761i
\(541\) −19.3541 19.3541i −0.832100 0.832100i 0.155704 0.987804i \(-0.450235\pi\)
−0.987804 + 0.155704i \(0.950235\pi\)
\(542\) 3.63504i 0.156138i
\(543\) −23.0671 + 20.4500i −0.989904 + 0.877595i
\(544\) −3.72209 3.72209i −0.159583 0.159583i
\(545\) −3.18824 −0.136569
\(546\) −2.93668 + 5.51143i −0.125678 + 0.235868i
\(547\) −17.0333 −0.728292 −0.364146 0.931342i \(-0.618639\pi\)
−0.364146 + 0.931342i \(0.618639\pi\)
\(548\) 11.5852 + 11.5852i 0.494895 + 0.494895i
\(549\) −3.14558 + 26.0582i −0.134250 + 1.11214i
\(550\) 17.6597i 0.753012i
\(551\) 6.67957 + 6.67957i 0.284559 + 0.284559i
\(552\) −2.57330 0.154755i −0.109527 0.00658680i
\(553\) 6.01650 + 6.01650i 0.255848 + 0.255848i
\(554\) 5.25236 5.25236i 0.223151 0.223151i
\(555\) −1.74163 + 1.54403i −0.0739280 + 0.0655406i
\(556\) 11.9801i 0.508070i
\(557\) −17.6970 + 17.6970i −0.749846 + 0.749846i −0.974450 0.224604i \(-0.927891\pi\)
0.224604 + 0.974450i \(0.427891\pi\)
\(558\) −3.66391 + 30.3521i −0.155106 + 1.28490i
\(559\) −3.46489 9.32111i −0.146549 0.394241i
\(560\) 0.335367i 0.0141718i
\(561\) −32.8831 1.97754i −1.38833 0.0834919i
\(562\) −13.3254 −0.562097
\(563\) 1.91330 0.0806362 0.0403181 0.999187i \(-0.487163\pi\)
0.0403181 + 0.999187i \(0.487163\pi\)
\(564\) −0.334176 + 5.55677i −0.0140714 + 0.233982i
\(565\) −3.76608 + 3.76608i −0.158440 + 0.158440i
\(566\) 15.2649 15.2649i 0.641631 0.641631i
\(567\) 4.66679 + 7.69552i 0.195987 + 0.323182i
\(568\) −6.99038 −0.293310
\(569\) −16.3399 −0.685003 −0.342501 0.939517i \(-0.611274\pi\)
−0.342501 + 0.939517i \(0.611274\pi\)
\(570\) 0.0447268 0.743729i 0.00187340 0.0311514i
\(571\) 42.0194i 1.75846i 0.476400 + 0.879229i \(0.341941\pi\)
−0.476400 + 0.879229i \(0.658059\pi\)
\(572\) 11.8444 + 5.42495i 0.495238 + 0.226829i
\(573\) −0.582062 + 0.516025i −0.0243160 + 0.0215572i
\(574\) 1.32329 1.32329i 0.0552332 0.0552332i
\(575\) 7.27451i 0.303368i
\(576\) 2.97838 + 0.359531i 0.124099 + 0.0149804i
\(577\) 24.8112 24.8112i 1.03290 1.03290i 0.0334650 0.999440i \(-0.489346\pi\)
0.999440 0.0334650i \(-0.0106542\pi\)
\(578\) 7.57166 + 7.57166i 0.314940 + 0.314940i
\(579\) −0.814520 + 13.5441i −0.0338503 + 0.562872i
\(580\) −1.74643 1.74643i −0.0725165 0.0725165i
\(581\) 4.32280i 0.179340i
\(582\) 7.90223 + 8.91350i 0.327558 + 0.369476i
\(583\) 22.4989 + 22.4989i 0.931810 + 0.931810i
\(584\) 5.66478 0.234410
\(585\) −1.89494 + 3.09327i −0.0783463 + 0.127891i
\(586\) −5.58290 −0.230628
\(587\) −9.34332 9.34332i −0.385640 0.385640i 0.487489 0.873129i \(-0.337913\pi\)
−0.873129 + 0.487489i \(0.837913\pi\)
\(588\) 1.14901 + 1.29606i 0.0473846 + 0.0534485i
\(589\) 13.0715i 0.538603i
\(590\) −0.263395 0.263395i −0.0108438 0.0108438i
\(591\) 2.32514 38.6630i 0.0956434 1.59038i
\(592\) 2.83332 + 2.83332i 0.116449 + 0.116449i
\(593\) 8.89198 8.89198i 0.365150 0.365150i −0.500555 0.865705i \(-0.666871\pi\)
0.865705 + 0.500555i \(0.166871\pi\)
\(594\) 15.4402 10.6815i 0.633519 0.438267i
\(595\) 1.76532i 0.0723709i
\(596\) −2.17899 + 2.17899i −0.0892550 + 0.0892550i
\(597\) 34.1071 30.2375i 1.39591 1.23754i
\(598\) −4.87902 2.23468i −0.199518 0.0913830i
\(599\) 39.8265i 1.62727i 0.581379 + 0.813633i \(0.302513\pi\)
−0.581379 + 0.813633i \(0.697487\pi\)
\(600\) 0.508181 8.45018i 0.0207464 0.344977i
\(601\) 40.3328 1.64521 0.822605 0.568613i \(-0.192520\pi\)
0.822605 + 0.568613i \(0.192520\pi\)
\(602\) −2.75805 −0.112410
\(603\) −25.3517 32.3126i −1.03240 1.31587i
\(604\) −9.34711 + 9.34711i −0.380329 + 0.380329i
\(605\) 0.487405 0.487405i 0.0198158 0.0198158i
\(606\) −1.92668 + 32.0373i −0.0782659 + 1.30143i
\(607\) −29.9002 −1.21361 −0.606805 0.794851i \(-0.707549\pi\)
−0.606805 + 0.794851i \(0.707549\pi\)
\(608\) −1.28268 −0.0520195
\(609\) −12.7328 0.765729i −0.515957 0.0310289i
\(610\) 2.93417i 0.118801i
\(611\) −4.82556 + 10.5357i −0.195221 + 0.426230i
\(612\) −15.6777 1.89251i −0.633733 0.0765002i
\(613\) 0.240034 0.240034i 0.00969490 0.00969490i −0.702243 0.711938i \(-0.747818\pi\)
0.711938 + 0.702243i \(0.247818\pi\)
\(614\) 16.7044i 0.674136i
\(615\) 0.813421 0.721135i 0.0328003 0.0290790i
\(616\) 2.55493 2.55493i 0.102941 0.102941i
\(617\) −25.7734 25.7734i −1.03760 1.03760i −0.999265 0.0383316i \(-0.987796\pi\)
−0.0383316 0.999265i \(-0.512204\pi\)
\(618\) −9.95989 0.598973i −0.400645 0.0240942i
\(619\) −26.3806 26.3806i −1.06033 1.06033i −0.998059 0.0622679i \(-0.980167\pi\)
−0.0622679 0.998059i \(-0.519833\pi\)
\(620\) 3.41766i 0.137256i
\(621\) −6.36024 + 4.40000i −0.255227 + 0.176566i
\(622\) −14.7362 14.7362i −0.590868 0.590868i
\(623\) −2.29517 −0.0919541
\(624\) 5.51143 + 2.93668i 0.220634 + 0.117561i
\(625\) −23.3256 −0.933023
\(626\) 6.84265 + 6.84265i 0.273487 + 0.273487i
\(627\) −6.00671 + 5.32522i −0.239885 + 0.212669i
\(628\) 17.6346i 0.703698i
\(629\) −14.9141 14.9141i −0.594666 0.594666i
\(630\) 0.621034 + 0.791553i 0.0247426 + 0.0315362i
\(631\) −4.98978 4.98978i −0.198640 0.198640i 0.600777 0.799417i \(-0.294858\pi\)
−0.799417 + 0.600777i \(0.794858\pi\)
\(632\) 6.01650 6.01650i 0.239324 0.239324i
\(633\) 13.1465 + 14.8289i 0.522527 + 0.589396i
\(634\) 20.4768i 0.813239i
\(635\) 1.98744 1.98744i 0.0788692 0.0788692i
\(636\) 10.1183 + 11.4132i 0.401217 + 0.452562i
\(637\) 1.25628 + 3.37961i 0.0497757 + 0.133905i
\(638\) 26.6097i 1.05349i
\(639\) −16.4991 + 12.9448i −0.652694 + 0.512089i
\(640\) 0.335367 0.0132565
\(641\) 6.77888 0.267750 0.133875 0.990998i \(-0.457258\pi\)
0.133875 + 0.990998i \(0.457258\pi\)
\(642\) −31.6610 1.90405i −1.24956 0.0751467i
\(643\) −11.9887 + 11.9887i −0.472790 + 0.472790i −0.902816 0.430026i \(-0.858504\pi\)
0.430026 + 0.902816i \(0.358504\pi\)
\(644\) −1.05244 + 1.05244i −0.0414721 + 0.0414721i
\(645\) −1.59918 0.0961725i −0.0629678 0.00378679i
\(646\) 6.75181 0.265646
\(647\) −4.90621 −0.192883 −0.0964415 0.995339i \(-0.530746\pi\)
−0.0964415 + 0.995339i \(0.530746\pi\)
\(648\) 7.69552 4.66679i 0.302309 0.183329i
\(649\) 4.01325i 0.157534i
\(650\) 7.33822 16.0217i 0.287829 0.628421i
\(651\) 11.7094 + 13.2079i 0.458927 + 0.517657i
\(652\) 2.26457 2.26457i 0.0886874 0.0886874i
\(653\) 16.9184i 0.662069i 0.943619 + 0.331035i \(0.107398\pi\)
−0.943619 + 0.331035i \(0.892602\pi\)
\(654\) 10.9234 + 12.3212i 0.427137 + 0.481799i
\(655\) −3.46051 + 3.46051i −0.135213 + 0.135213i
\(656\) −1.32329 1.32329i −0.0516659 0.0516659i
\(657\) 13.3703 10.4901i 0.521627 0.409256i
\(658\) 2.27264 + 2.27264i 0.0885968 + 0.0885968i
\(659\) 42.8877i 1.67067i 0.549744 + 0.835333i \(0.314725\pi\)
−0.549744 + 0.835333i \(0.685275\pi\)
\(660\) 1.57050 1.39232i 0.0611317 0.0541961i
\(661\) 23.1466 + 23.1466i 0.900299 + 0.900299i 0.995462 0.0951631i \(-0.0303373\pi\)
−0.0951631 + 0.995462i \(0.530337\pi\)
\(662\) 33.8024 1.31377
\(663\) −29.0113 15.4582i −1.12670 0.600346i
\(664\) 4.32280 0.167757
\(665\) −0.304175 0.304175i −0.0117954 0.0117954i
\(666\) 11.9341 + 1.44061i 0.462438 + 0.0558226i
\(667\) 10.9612i 0.424421i
\(668\) 12.4482 + 12.4482i 0.481636 + 0.481636i
\(669\) 22.1651 + 1.33297i 0.856951 + 0.0515357i
\(670\) −3.24651 3.24651i −0.125424 0.125424i
\(671\) 22.3534 22.3534i 0.862943 0.862943i
\(672\) 1.29606 1.14901i 0.0499965 0.0443242i
\(673\) 29.7951i 1.14852i −0.818674 0.574259i \(-0.805290\pi\)
0.818674 0.574259i \(-0.194710\pi\)
\(674\) −13.5330 + 13.5330i −0.521272 + 0.521272i
\(675\) −14.4486 20.8857i −0.556129 0.803890i
\(676\) 8.49149 + 9.84351i 0.326596 + 0.378596i
\(677\) 21.9759i 0.844602i −0.906456 0.422301i \(-0.861222\pi\)
0.906456 0.422301i \(-0.138778\pi\)
\(678\) 27.4575 + 1.65125i 1.05450 + 0.0634160i
\(679\) 6.87739 0.263930
\(680\) −1.76532 −0.0676968
\(681\) 0.288045 4.78970i 0.0110379 0.183542i
\(682\) 26.0368 26.0368i 0.997000 0.997000i
\(683\) −5.21995 + 5.21995i −0.199736 + 0.199736i −0.799887 0.600151i \(-0.795107\pi\)
0.600151 + 0.799887i \(0.295107\pi\)
\(684\) −3.02745 + 2.37527i −0.115758 + 0.0908207i
\(685\) 5.49463 0.209939
\(686\) 1.00000 0.0381802
\(687\) 2.89539 48.1454i 0.110466 1.83686i
\(688\) 2.75805i 0.105149i
\(689\) 11.0629 + 29.7611i 0.421464 + 1.13381i
\(690\) −0.646932 + 0.573535i −0.0246283 + 0.0218341i
\(691\) −16.8889 + 16.8889i −0.642485 + 0.642485i −0.951166 0.308681i \(-0.900112\pi\)
0.308681 + 0.951166i \(0.400112\pi\)
\(692\) 12.8517i 0.488548i
\(693\) 1.29906 10.7615i 0.0493473 0.408797i
\(694\) −15.7627 + 15.7627i −0.598343 + 0.598343i
\(695\) 2.84097 + 2.84097i 0.107764 + 0.107764i
\(696\) −0.765729 + 12.7328i −0.0290249 + 0.482634i
\(697\) 6.96559 + 6.96559i 0.263841 + 0.263841i
\(698\) 16.3183i 0.617658i
\(699\) −9.28676 10.4752i −0.351258 0.396209i
\(700\) −3.45600 3.45600i −0.130625 0.130625i
\(701\) 37.1491 1.40310 0.701550 0.712620i \(-0.252491\pi\)
0.701550 + 0.712620i \(0.252491\pi\)
\(702\) 18.4466 3.27478i 0.696221 0.123599i
\(703\) −5.13960 −0.193844
\(704\) −2.55493 2.55493i −0.0962926 0.0962926i
\(705\) 1.23849 + 1.39698i 0.0466442 + 0.0526134i
\(706\) 15.5376i 0.584765i
\(707\) 13.1028 + 13.1028i 0.492782 + 0.492782i
\(708\) −0.115487 + 1.92034i −0.00434025 + 0.0721709i
\(709\) 17.2343 + 17.2343i 0.647249 + 0.647249i 0.952327 0.305078i \(-0.0986826\pi\)
−0.305078 + 0.952327i \(0.598683\pi\)
\(710\) −1.65770 + 1.65770i −0.0622124 + 0.0622124i
\(711\) 3.05911 25.3419i 0.114726 0.950395i
\(712\) 2.29517i 0.0860152i
\(713\) −10.7253 + 10.7253i −0.401664 + 0.401664i
\(714\) −6.82223 + 6.04822i −0.255316 + 0.226349i
\(715\) 4.09525 1.52231i 0.153154 0.0569310i
\(716\) 13.7258i 0.512959i
\(717\) 2.51588 41.8348i 0.0939573 1.56235i
\(718\) −17.5274 −0.654116
\(719\) −2.42778 −0.0905411 −0.0452705 0.998975i \(-0.514415\pi\)
−0.0452705 + 0.998975i \(0.514415\pi\)
\(720\) 0.791553 0.621034i 0.0294994 0.0231446i
\(721\) −4.07345 + 4.07345i −0.151703 + 0.151703i
\(722\) −12.2717 + 12.2717i −0.456704 + 0.456704i
\(723\) −0.242100 + 4.02570i −0.00900379 + 0.149718i
\(724\) 17.7979 0.661454
\(725\) 35.9944 1.33680
\(726\) −3.55354 0.213705i −0.131884 0.00793132i
\(727\) 2.06159i 0.0764603i 0.999269 + 0.0382301i \(0.0121720\pi\)
−0.999269 + 0.0382301i \(0.987828\pi\)
\(728\) 3.37961 1.25628i 0.125257 0.0465609i
\(729\) 9.52144 25.2654i 0.352646 0.935757i
\(730\) 1.34335 1.34335i 0.0497195 0.0497195i
\(731\) 14.5179i 0.536964i
\(732\) 11.3394 10.0529i 0.419115 0.371565i
\(733\) 16.8266 16.8266i 0.621505 0.621505i −0.324412 0.945916i \(-0.605166\pi\)
0.945916 + 0.324412i \(0.105166\pi\)
\(734\) −13.6975 13.6975i −0.505583 0.505583i
\(735\) 0.579825 + 0.0348698i 0.0213872 + 0.00128619i
\(736\) 1.05244 + 1.05244i 0.0387936 + 0.0387936i
\(737\) 49.4659i 1.82210i
\(738\) −5.57379 0.672833i −0.205174 0.0247673i
\(739\) −29.5329 29.5329i −1.08638 1.08638i −0.995898 0.0904869i \(-0.971158\pi\)
−0.0904869 0.995898i \(-0.528842\pi\)
\(740\) 1.34379 0.0493987
\(741\) −7.66236 + 2.33528i −0.281484 + 0.0857886i
\(742\) 8.80608 0.323281
\(743\) 21.2462 + 21.2462i 0.779446 + 0.779446i 0.979737 0.200290i \(-0.0641886\pi\)
−0.200290 + 0.979737i \(0.564189\pi\)
\(744\) 13.2079 11.7094i 0.484224 0.429287i
\(745\) 1.03345i 0.0378628i
\(746\) 18.8503 + 18.8503i 0.690157 + 0.690157i
\(747\) 10.2029 8.00499i 0.373306 0.292887i
\(748\) 13.4487 + 13.4487i 0.491734 + 0.491734i
\(749\) −12.9489 + 12.9489i −0.473143 + 0.473143i
\(750\) −3.81008 4.29766i −0.139124 0.156928i
\(751\) 22.6437i 0.826281i −0.910667 0.413140i \(-0.864432\pi\)
0.910667 0.413140i \(-0.135568\pi\)
\(752\) 2.27264 2.27264i 0.0828747 0.0828747i
\(753\) 6.42864 + 7.25133i 0.234273 + 0.264253i
\(754\) −11.0572 + 24.1415i −0.402681 + 0.879181i
\(755\) 4.43315i 0.161339i
\(756\) 0.931280 5.11202i 0.0338703 0.185922i
\(757\) 28.9363 1.05171 0.525853 0.850575i \(-0.323746\pi\)
0.525853 + 0.850575i \(0.323746\pi\)
\(758\) −10.1436 −0.368433
\(759\) 9.29791 + 0.559162i 0.337493 + 0.0202963i
\(760\) −0.304175 + 0.304175i −0.0110336 + 0.0110336i
\(761\) 34.0212 34.0212i 1.23327 1.23327i 0.270567 0.962701i \(-0.412789\pi\)
0.962701 0.270567i \(-0.0872113\pi\)
\(762\) −14.4899 0.871402i −0.524914 0.0315675i
\(763\) 9.50671 0.344166
\(764\) 0.449102 0.0162479
\(765\) −4.16660 + 3.26902i −0.150644 + 0.118192i
\(766\) 2.48835i 0.0899076i
\(767\) −1.66765 + 3.64100i −0.0602152 + 0.131469i
\(768\) −1.14901 1.29606i −0.0414615 0.0467675i
\(769\) 14.2161 14.2161i 0.512647 0.512647i −0.402690 0.915337i \(-0.631925\pi\)
0.915337 + 0.402690i \(0.131925\pi\)
\(770\) 1.21175i 0.0436686i
\(771\) −10.7743 12.1531i −0.388026 0.437683i
\(772\) 5.53933 5.53933i 0.199365 0.199365i
\(773\) −29.6369 29.6369i −1.06596 1.06596i −0.997665 0.0682992i \(-0.978243\pi\)
−0.0682992 0.997665i \(-0.521757\pi\)
\(774\) 5.10736 + 6.50970i 0.183580 + 0.233986i
\(775\) −35.2194 35.2194i −1.26512 1.26512i
\(776\) 6.87739i