Properties

Label 546.2.l.l.211.2
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
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.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.2
Root \(-0.780776 + 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.l.295.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.56155 q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.56155 q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.780776 - 1.35234i) q^{10} +(1.28078 + 2.21837i) q^{11} -1.00000 q^{12} +(-0.500000 + 3.57071i) q^{13} +1.00000 q^{14} +(0.780776 + 1.35234i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0615528 + 0.106613i) q^{17} +1.00000 q^{18} +(1.28078 - 2.21837i) q^{19} +(-0.780776 + 1.35234i) q^{20} -1.00000 q^{21} +(1.28078 - 2.21837i) q^{22} +(0.561553 + 0.972638i) q^{23} +(0.500000 + 0.866025i) q^{24} -2.56155 q^{25} +(3.34233 - 1.35234i) q^{26} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(3.06155 + 5.30277i) q^{29} +(0.780776 - 1.35234i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(-1.28078 + 2.21837i) q^{33} +0.123106 q^{34} +(-0.780776 + 1.35234i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.21922 + 2.11176i) q^{37} -2.56155 q^{38} +(-3.34233 + 1.35234i) q^{39} +1.56155 q^{40} +(5.62311 + 9.73950i) q^{41} +(0.500000 + 0.866025i) q^{42} +(4.00000 - 6.92820i) q^{43} -2.56155 q^{44} +(-0.780776 + 1.35234i) q^{45} +(0.561553 - 0.972638i) q^{46} -0.315342 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.28078 + 2.21837i) q^{50} -0.123106 q^{51} +(-2.84233 - 2.21837i) q^{52} +7.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(2.00000 + 3.46410i) q^{55} +(-0.500000 + 0.866025i) q^{56} +2.56155 q^{57} +(3.06155 - 5.30277i) q^{58} +(-2.56155 + 4.43674i) q^{59} -1.56155 q^{60} +(5.62311 - 9.73950i) q^{61} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-0.780776 + 5.57586i) q^{65} +2.56155 q^{66} +(-4.56155 - 7.90084i) q^{67} +(-0.0615528 - 0.106613i) q^{68} +(-0.561553 + 0.972638i) q^{69} +1.56155 q^{70} +(5.68466 - 9.84612i) q^{71} +(-0.500000 + 0.866025i) q^{72} -2.43845 q^{73} +(1.21922 - 2.11176i) q^{74} +(-1.28078 - 2.21837i) q^{75} +(1.28078 + 2.21837i) q^{76} -2.56155 q^{77} +(2.84233 + 2.21837i) q^{78} -6.56155 q^{79} +(-0.780776 - 1.35234i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.62311 - 9.73950i) q^{82} -5.12311 q^{83} +(0.500000 - 0.866025i) q^{84} +(-0.0961180 + 0.166481i) q^{85} -8.00000 q^{86} +(-3.06155 + 5.30277i) q^{87} +(1.28078 + 2.21837i) q^{88} +(-1.71922 - 2.97778i) q^{89} +1.56155 q^{90} +(-2.84233 - 2.21837i) q^{91} -1.12311 q^{92} +(0.157671 + 0.273094i) q^{94} +(2.00000 - 3.46410i) q^{95} -1.00000 q^{96} +(0.438447 - 0.759413i) q^{97} +(-0.500000 + 0.866025i) q^{98} -2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 2q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 2q^{7} + 4q^{8} - 2q^{9} + q^{10} + q^{11} - 4q^{12} - 2q^{13} + 4q^{14} - q^{15} - 2q^{16} + 8q^{17} + 4q^{18} + q^{19} + q^{20} - 4q^{21} + q^{22} - 6q^{23} + 2q^{24} - 2q^{25} + q^{26} - 4q^{27} - 2q^{28} + 4q^{29} - q^{30} - 2q^{32} - q^{33} - 16q^{34} + q^{35} - 2q^{36} + 9q^{37} - 2q^{38} - q^{39} - 2q^{40} + 6q^{41} + 2q^{42} + 16q^{43} - 2q^{44} + q^{45} - 6q^{46} - 26q^{47} + 2q^{48} - 2q^{49} + q^{50} + 16q^{51} + q^{52} + 28q^{53} + 2q^{54} + 8q^{55} - 2q^{56} + 2q^{57} + 4q^{58} - 2q^{59} + 2q^{60} + 6q^{61} - 2q^{63} + 4q^{64} + q^{65} + 2q^{66} - 10q^{67} + 8q^{68} + 6q^{69} - 2q^{70} - 2q^{71} - 2q^{72} - 18q^{73} + 9q^{74} - q^{75} + q^{76} - 2q^{77} - q^{78} - 18q^{79} + q^{80} - 2q^{81} + 6q^{82} - 4q^{83} + 2q^{84} - 21q^{85} - 32q^{86} - 4q^{87} + q^{88} - 11q^{89} - 2q^{90} + q^{91} + 12q^{92} + 13q^{94} + 8q^{95} - 4q^{96} + 10q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.56155 0.698348 0.349174 0.937058i \(-0.386462\pi\)
0.349174 + 0.937058i \(0.386462\pi\)
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.780776 1.35234i −0.246903 0.427649i
\(11\) 1.28078 + 2.21837i 0.386169 + 0.668864i 0.991931 0.126782i \(-0.0404650\pi\)
−0.605762 + 0.795646i \(0.707132\pi\)
\(12\) −1.00000 −0.288675
\(13\) −0.500000 + 3.57071i −0.138675 + 0.990338i
\(14\) 1.00000 0.267261
\(15\) 0.780776 + 1.35234i 0.201596 + 0.349174i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.0615528 + 0.106613i −0.0149287 + 0.0258574i −0.873393 0.487016i \(-0.838085\pi\)
0.858465 + 0.512873i \(0.171419\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.28078 2.21837i 0.293830 0.508929i −0.680882 0.732393i \(-0.738403\pi\)
0.974712 + 0.223464i \(0.0717366\pi\)
\(20\) −0.780776 + 1.35234i −0.174587 + 0.302393i
\(21\) −1.00000 −0.218218
\(22\) 1.28078 2.21837i 0.273062 0.472958i
\(23\) 0.561553 + 0.972638i 0.117092 + 0.202809i 0.918614 0.395156i \(-0.129309\pi\)
−0.801522 + 0.597965i \(0.795976\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −2.56155 −0.512311
\(26\) 3.34233 1.35234i 0.655485 0.265217i
\(27\) −1.00000 −0.192450
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) 3.06155 + 5.30277i 0.568516 + 0.984699i 0.996713 + 0.0810133i \(0.0258156\pi\)
−0.428197 + 0.903685i \(0.640851\pi\)
\(30\) 0.780776 1.35234i 0.142550 0.246903i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.28078 + 2.21837i −0.222955 + 0.386169i
\(34\) 0.123106 0.0211124
\(35\) −0.780776 + 1.35234i −0.131975 + 0.228588i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 1.21922 + 2.11176i 0.200439 + 0.347171i 0.948670 0.316268i \(-0.102430\pi\)
−0.748231 + 0.663438i \(0.769096\pi\)
\(38\) −2.56155 −0.415539
\(39\) −3.34233 + 1.35234i −0.535201 + 0.216548i
\(40\) 1.56155 0.246903
\(41\) 5.62311 + 9.73950i 0.878182 + 1.52106i 0.853335 + 0.521364i \(0.174577\pi\)
0.0248471 + 0.999691i \(0.492090\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i \(-0.624505\pi\)
0.991241 0.132068i \(-0.0421616\pi\)
\(44\) −2.56155 −0.386169
\(45\) −0.780776 + 1.35234i −0.116391 + 0.201596i
\(46\) 0.561553 0.972638i 0.0827964 0.143408i
\(47\) −0.315342 −0.0459973 −0.0229986 0.999735i \(-0.507321\pi\)
−0.0229986 + 0.999735i \(0.507321\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 1.28078 + 2.21837i 0.181129 + 0.313725i
\(51\) −0.123106 −0.0172382
\(52\) −2.84233 2.21837i −0.394160 0.307633i
\(53\) 7.00000 0.961524 0.480762 0.876851i \(-0.340360\pi\)
0.480762 + 0.876851i \(0.340360\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 2.00000 + 3.46410i 0.269680 + 0.467099i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 2.56155 0.339286
\(58\) 3.06155 5.30277i 0.402002 0.696287i
\(59\) −2.56155 + 4.43674i −0.333486 + 0.577614i −0.983193 0.182570i \(-0.941558\pi\)
0.649707 + 0.760185i \(0.274892\pi\)
\(60\) −1.56155 −0.201596
\(61\) 5.62311 9.73950i 0.719965 1.24702i −0.241048 0.970513i \(-0.577491\pi\)
0.961013 0.276503i \(-0.0891755\pi\)
\(62\) 0 0
\(63\) −0.500000 0.866025i −0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) −0.780776 + 5.57586i −0.0968434 + 0.691600i
\(66\) 2.56155 0.315305
\(67\) −4.56155 7.90084i −0.557282 0.965241i −0.997722 0.0674592i \(-0.978511\pi\)
0.440440 0.897782i \(-0.354823\pi\)
\(68\) −0.0615528 0.106613i −0.00746437 0.0129287i
\(69\) −0.561553 + 0.972638i −0.0676030 + 0.117092i
\(70\) 1.56155 0.186641
\(71\) 5.68466 9.84612i 0.674645 1.16852i −0.301928 0.953331i \(-0.597630\pi\)
0.976573 0.215188i \(-0.0690365\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −2.43845 −0.285399 −0.142699 0.989766i \(-0.545578\pi\)
−0.142699 + 0.989766i \(0.545578\pi\)
\(74\) 1.21922 2.11176i 0.141732 0.245487i
\(75\) −1.28078 2.21837i −0.147891 0.256155i
\(76\) 1.28078 + 2.21837i 0.146915 + 0.254464i
\(77\) −2.56155 −0.291916
\(78\) 2.84233 + 2.21837i 0.321830 + 0.251181i
\(79\) −6.56155 −0.738232 −0.369116 0.929383i \(-0.620340\pi\)
−0.369116 + 0.929383i \(0.620340\pi\)
\(80\) −0.780776 1.35234i −0.0872935 0.151197i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.62311 9.73950i 0.620968 1.07555i
\(83\) −5.12311 −0.562334 −0.281167 0.959659i \(-0.590721\pi\)
−0.281167 + 0.959659i \(0.590721\pi\)
\(84\) 0.500000 0.866025i 0.0545545 0.0944911i
\(85\) −0.0961180 + 0.166481i −0.0104255 + 0.0180574i
\(86\) −8.00000 −0.862662
\(87\) −3.06155 + 5.30277i −0.328233 + 0.568516i
\(88\) 1.28078 + 2.21837i 0.136531 + 0.236479i
\(89\) −1.71922 2.97778i −0.182237 0.315644i 0.760405 0.649449i \(-0.225001\pi\)
−0.942642 + 0.333805i \(0.891667\pi\)
\(90\) 1.56155 0.164602
\(91\) −2.84233 2.21837i −0.297957 0.232548i
\(92\) −1.12311 −0.117092
\(93\) 0 0
\(94\) 0.157671 + 0.273094i 0.0162625 + 0.0281675i
\(95\) 2.00000 3.46410i 0.205196 0.355409i
\(96\) −1.00000 −0.102062
\(97\) 0.438447 0.759413i 0.0445176 0.0771067i −0.842908 0.538058i \(-0.819158\pi\)
0.887426 + 0.460951i \(0.152492\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) −2.56155 −0.257446
\(100\) 1.28078 2.21837i 0.128078 0.221837i
\(101\) 2.90388 + 5.02967i 0.288947 + 0.500471i 0.973559 0.228437i \(-0.0733615\pi\)
−0.684612 + 0.728908i \(0.740028\pi\)
\(102\) 0.0615528 + 0.106613i 0.00609464 + 0.0105562i
\(103\) 6.24621 0.615457 0.307729 0.951474i \(-0.400431\pi\)
0.307729 + 0.951474i \(0.400431\pi\)
\(104\) −0.500000 + 3.57071i −0.0490290 + 0.350137i
\(105\) −1.56155 −0.152392
\(106\) −3.50000 6.06218i −0.339950 0.588811i
\(107\) −6.96543 12.0645i −0.673374 1.16632i −0.976941 0.213508i \(-0.931511\pi\)
0.303567 0.952810i \(-0.401822\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −12.2462 −1.17297 −0.586487 0.809959i \(-0.699490\pi\)
−0.586487 + 0.809959i \(0.699490\pi\)
\(110\) 2.00000 3.46410i 0.190693 0.330289i
\(111\) −1.21922 + 2.11176i −0.115724 + 0.200439i
\(112\) 1.00000 0.0944911
\(113\) −0.780776 + 1.35234i −0.0734493 + 0.127218i −0.900411 0.435041i \(-0.856734\pi\)
0.826962 + 0.562258i \(0.190067\pi\)
\(114\) −1.28078 2.21837i −0.119956 0.207769i
\(115\) 0.876894 + 1.51883i 0.0817708 + 0.141631i
\(116\) −6.12311 −0.568516
\(117\) −2.84233 2.21837i −0.262773 0.205088i
\(118\) 5.12311 0.471620
\(119\) −0.0615528 0.106613i −0.00564254 0.00977316i
\(120\) 0.780776 + 1.35234i 0.0712748 + 0.123452i
\(121\) 2.21922 3.84381i 0.201748 0.349437i
\(122\) −11.2462 −1.01818
\(123\) −5.62311 + 9.73950i −0.507018 + 0.878182i
\(124\) 0 0
\(125\) −11.8078 −1.05612
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) −6.24621 10.8188i −0.554262 0.960009i −0.997961 0.0638334i \(-0.979667\pi\)
0.443699 0.896176i \(-0.353666\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 8.00000 0.704361
\(130\) 5.21922 2.11176i 0.457756 0.185213i
\(131\) 14.2462 1.24470 0.622349 0.782740i \(-0.286179\pi\)
0.622349 + 0.782740i \(0.286179\pi\)
\(132\) −1.28078 2.21837i −0.111477 0.193084i
\(133\) 1.28078 + 2.21837i 0.111057 + 0.192357i
\(134\) −4.56155 + 7.90084i −0.394058 + 0.682529i
\(135\) −1.56155 −0.134397
\(136\) −0.0615528 + 0.106613i −0.00527811 + 0.00914195i
\(137\) −6.21922 + 10.7720i −0.531344 + 0.920315i 0.467987 + 0.883736i \(0.344980\pi\)
−0.999331 + 0.0365795i \(0.988354\pi\)
\(138\) 1.12311 0.0956051
\(139\) 2.71922 4.70983i 0.230642 0.399483i −0.727356 0.686261i \(-0.759251\pi\)
0.957997 + 0.286778i \(0.0925842\pi\)
\(140\) −0.780776 1.35234i −0.0659877 0.114294i
\(141\) −0.157671 0.273094i −0.0132783 0.0229986i
\(142\) −11.3693 −0.954092
\(143\) −8.56155 + 3.46410i −0.715953 + 0.289683i
\(144\) 1.00000 0.0833333
\(145\) 4.78078 + 8.28055i 0.397022 + 0.687662i
\(146\) 1.21922 + 2.11176i 0.100904 + 0.174770i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) −2.43845 −0.200439
\(149\) 7.78078 13.4767i 0.637426 1.10405i −0.348570 0.937283i \(-0.613332\pi\)
0.985996 0.166771i \(-0.0533342\pi\)
\(150\) −1.28078 + 2.21837i −0.104575 + 0.181129i
\(151\) −21.9309 −1.78471 −0.892354 0.451335i \(-0.850948\pi\)
−0.892354 + 0.451335i \(0.850948\pi\)
\(152\) 1.28078 2.21837i 0.103885 0.179934i
\(153\) −0.0615528 0.106613i −0.00497625 0.00861912i
\(154\) 1.28078 + 2.21837i 0.103208 + 0.178761i
\(155\) 0 0
\(156\) 0.500000 3.57071i 0.0400320 0.285886i
\(157\) −1.31534 −0.104976 −0.0524878 0.998622i \(-0.516715\pi\)
−0.0524878 + 0.998622i \(0.516715\pi\)
\(158\) 3.28078 + 5.68247i 0.261005 + 0.452073i
\(159\) 3.50000 + 6.06218i 0.277568 + 0.480762i
\(160\) −0.780776 + 1.35234i −0.0617258 + 0.106912i
\(161\) −1.12311 −0.0885131
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −12.2462 + 21.2111i −0.959197 + 1.66138i −0.234741 + 0.972058i \(0.575424\pi\)
−0.724457 + 0.689320i \(0.757909\pi\)
\(164\) −11.2462 −0.878182
\(165\) −2.00000 + 3.46410i −0.155700 + 0.269680i
\(166\) 2.56155 + 4.43674i 0.198815 + 0.344358i
\(167\) −6.24621 10.8188i −0.483346 0.837180i 0.516471 0.856305i \(-0.327245\pi\)
−0.999817 + 0.0191244i \(0.993912\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −12.5000 3.57071i −0.961538 0.274670i
\(170\) 0.192236 0.0147438
\(171\) 1.28078 + 2.21837i 0.0979434 + 0.169643i
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) 6.12311 0.464191
\(175\) 1.28078 2.21837i 0.0968176 0.167693i
\(176\) 1.28078 2.21837i 0.0965422 0.167216i
\(177\) −5.12311 −0.385076
\(178\) −1.71922 + 2.97778i −0.128861 + 0.223194i
\(179\) 0.876894 + 1.51883i 0.0655422 + 0.113522i 0.896934 0.442164i \(-0.145789\pi\)
−0.831392 + 0.555686i \(0.812456\pi\)
\(180\) −0.780776 1.35234i −0.0581956 0.100798i
\(181\) 13.2462 0.984583 0.492292 0.870430i \(-0.336159\pi\)
0.492292 + 0.870430i \(0.336159\pi\)
\(182\) −0.500000 + 3.57071i −0.0370625 + 0.264679i
\(183\) 11.2462 0.831344
\(184\) 0.561553 + 0.972638i 0.0413982 + 0.0717038i
\(185\) 1.90388 + 3.29762i 0.139976 + 0.242446i
\(186\) 0 0
\(187\) −0.315342 −0.0230601
\(188\) 0.157671 0.273094i 0.0114993 0.0199174i
\(189\) 0.500000 0.866025i 0.0363696 0.0629941i
\(190\) −4.00000 −0.290191
\(191\) 2.56155 4.43674i 0.185347 0.321031i −0.758346 0.651852i \(-0.773992\pi\)
0.943694 + 0.330821i \(0.107326\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −0.0615528 0.106613i −0.00443067 0.00767414i 0.863802 0.503832i \(-0.168077\pi\)
−0.868232 + 0.496158i \(0.834744\pi\)
\(194\) −0.876894 −0.0629573
\(195\) −5.21922 + 2.11176i −0.373756 + 0.151226i
\(196\) 1.00000 0.0714286
\(197\) −6.28078 10.8786i −0.447487 0.775070i 0.550735 0.834680i \(-0.314348\pi\)
−0.998222 + 0.0596103i \(0.981014\pi\)
\(198\) 1.28078 + 2.21837i 0.0910208 + 0.157653i
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) −2.56155 −0.181129
\(201\) 4.56155 7.90084i 0.321747 0.557282i
\(202\) 2.90388 5.02967i 0.204316 0.353886i
\(203\) −6.12311 −0.429758
\(204\) 0.0615528 0.106613i 0.00430956 0.00746437i
\(205\) 8.78078 + 15.2088i 0.613276 + 1.06223i
\(206\) −3.12311 5.40938i −0.217597 0.376889i
\(207\) −1.12311 −0.0780612
\(208\) 3.34233 1.35234i 0.231749 0.0937682i
\(209\) 6.56155 0.453872
\(210\) 0.780776 + 1.35234i 0.0538787 + 0.0933206i
\(211\) −2.56155 4.43674i −0.176345 0.305438i 0.764281 0.644883i \(-0.223094\pi\)
−0.940626 + 0.339445i \(0.889761\pi\)
\(212\) −3.50000 + 6.06218i −0.240381 + 0.416352i
\(213\) 11.3693 0.779013
\(214\) −6.96543 + 12.0645i −0.476147 + 0.824711i
\(215\) 6.24621 10.8188i 0.425988 0.737833i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 6.12311 + 10.6055i 0.414709 + 0.718297i
\(219\) −1.21922 2.11176i −0.0823875 0.142699i
\(220\) −4.00000 −0.269680
\(221\) −0.349907 0.273094i −0.0235373 0.0183703i
\(222\) 2.43845 0.163658
\(223\) −4.87689 8.44703i −0.326581 0.565655i 0.655250 0.755412i \(-0.272563\pi\)
−0.981831 + 0.189757i \(0.939230\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) 1.28078 2.21837i 0.0853851 0.147891i
\(226\) 1.56155 0.103873
\(227\) 5.43845 9.41967i 0.360962 0.625205i −0.627157 0.778893i \(-0.715782\pi\)
0.988119 + 0.153688i \(0.0491149\pi\)
\(228\) −1.28078 + 2.21837i −0.0848215 + 0.146915i
\(229\) 17.0540 1.12696 0.563479 0.826130i \(-0.309462\pi\)
0.563479 + 0.826130i \(0.309462\pi\)
\(230\) 0.876894 1.51883i 0.0578207 0.100148i
\(231\) −1.28078 2.21837i −0.0842689 0.145958i
\(232\) 3.06155 + 5.30277i 0.201001 + 0.348144i
\(233\) 1.36932 0.0897069 0.0448535 0.998994i \(-0.485718\pi\)
0.0448535 + 0.998994i \(0.485718\pi\)
\(234\) −0.500000 + 3.57071i −0.0326860 + 0.233425i
\(235\) −0.492423 −0.0321221
\(236\) −2.56155 4.43674i −0.166743 0.288807i
\(237\) −3.28078 5.68247i −0.213109 0.369116i
\(238\) −0.0615528 + 0.106613i −0.00398988 + 0.00691067i
\(239\) 19.3693 1.25290 0.626448 0.779463i \(-0.284508\pi\)
0.626448 + 0.779463i \(0.284508\pi\)
\(240\) 0.780776 1.35234i 0.0503989 0.0872935i
\(241\) 0.0961180 0.166481i 0.00619150 0.0107240i −0.862913 0.505352i \(-0.831363\pi\)
0.869105 + 0.494628i \(0.164696\pi\)
\(242\) −4.43845 −0.285314
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 5.62311 + 9.73950i 0.359982 + 0.623508i
\(245\) −0.780776 1.35234i −0.0498820 0.0863981i
\(246\) 11.2462 0.717032
\(247\) 7.28078 + 5.68247i 0.463265 + 0.361567i
\(248\) 0 0
\(249\) −2.56155 4.43674i −0.162332 0.281167i
\(250\) 5.90388 + 10.2258i 0.373394 + 0.646738i
\(251\) 6.80776 11.7914i 0.429702 0.744266i −0.567144 0.823618i \(-0.691952\pi\)
0.996847 + 0.0793522i \(0.0252852\pi\)
\(252\) 1.00000 0.0629941
\(253\) −1.43845 + 2.49146i −0.0904344 + 0.156637i
\(254\) −6.24621 + 10.8188i −0.391922 + 0.678829i
\(255\) −0.192236 −0.0120383
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 12.1847 + 21.1044i 0.760058 + 1.31646i 0.942820 + 0.333302i \(0.108163\pi\)
−0.182762 + 0.983157i \(0.558504\pi\)
\(258\) −4.00000 6.92820i −0.249029 0.431331i
\(259\) −2.43845 −0.151518
\(260\) −4.43845 3.46410i −0.275261 0.214834i
\(261\) −6.12311 −0.379011
\(262\) −7.12311 12.3376i −0.440067 0.762218i
\(263\) −2.56155 4.43674i −0.157952 0.273581i 0.776178 0.630514i \(-0.217156\pi\)
−0.934130 + 0.356933i \(0.883822\pi\)
\(264\) −1.28078 + 2.21837i −0.0788263 + 0.136531i
\(265\) 10.9309 0.671478
\(266\) 1.28078 2.21837i 0.0785294 0.136017i
\(267\) 1.71922 2.97778i 0.105215 0.182237i
\(268\) 9.12311 0.557282
\(269\) −13.5616 + 23.4893i −0.826862 + 1.43217i 0.0736251 + 0.997286i \(0.476543\pi\)
−0.900488 + 0.434882i \(0.856790\pi\)
\(270\) 0.780776 + 1.35234i 0.0475165 + 0.0823011i
\(271\) 11.3693 + 19.6922i 0.690637 + 1.19622i 0.971630 + 0.236508i \(0.0760030\pi\)
−0.280993 + 0.959710i \(0.590664\pi\)
\(272\) 0.123106 0.00746437
\(273\) 0.500000 3.57071i 0.0302614 0.216109i
\(274\) 12.4384 0.751434
\(275\) −3.28078 5.68247i −0.197838 0.342666i
\(276\) −0.561553 0.972638i −0.0338015 0.0585459i
\(277\) 9.78078 16.9408i 0.587670 1.01787i −0.406867 0.913487i \(-0.633379\pi\)
0.994537 0.104387i \(-0.0332879\pi\)
\(278\) −5.43845 −0.326176
\(279\) 0 0
\(280\) −0.780776 + 1.35234i −0.0466603 + 0.0808180i
\(281\) 12.9309 0.771391 0.385696 0.922626i \(-0.373962\pi\)
0.385696 + 0.922626i \(0.373962\pi\)
\(282\) −0.157671 + 0.273094i −0.00938916 + 0.0162625i
\(283\) 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i \(0.0359589\pi\)
−0.399188 + 0.916869i \(0.630708\pi\)
\(284\) 5.68466 + 9.84612i 0.337322 + 0.584260i
\(285\) 4.00000 0.236940
\(286\) 7.28078 + 5.68247i 0.430521 + 0.336012i
\(287\) −11.2462 −0.663843
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 8.49242 + 14.7093i 0.499554 + 0.865253i
\(290\) 4.78078 8.28055i 0.280737 0.486251i
\(291\) 0.876894 0.0514045
\(292\) 1.21922 2.11176i 0.0713497 0.123581i
\(293\) 3.46543 6.00231i 0.202453 0.350659i −0.746865 0.664975i \(-0.768442\pi\)
0.949318 + 0.314317i \(0.101775\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −4.00000 + 6.92820i −0.232889 + 0.403376i
\(296\) 1.21922 + 2.11176i 0.0708659 + 0.122743i
\(297\) −1.28078 2.21837i −0.0743182 0.128723i
\(298\) −15.5616 −0.901457
\(299\) −3.75379 + 1.51883i −0.217087 + 0.0878360i
\(300\) 2.56155 0.147891
\(301\) 4.00000 + 6.92820i 0.230556 + 0.399335i
\(302\) 10.9654 + 18.9927i 0.630990 + 1.09291i
\(303\) −2.90388 + 5.02967i −0.166824 + 0.288947i
\(304\) −2.56155 −0.146915
\(305\) 8.78078 15.2088i 0.502786 0.870851i
\(306\) −0.0615528 + 0.106613i −0.00351874 + 0.00609464i
\(307\) −9.93087 −0.566785 −0.283392 0.959004i \(-0.591460\pi\)
−0.283392 + 0.959004i \(0.591460\pi\)
\(308\) 1.28078 2.21837i 0.0729790 0.126403i
\(309\) 3.12311 + 5.40938i 0.177667 + 0.307729i
\(310\) 0 0
\(311\) 21.9309 1.24359 0.621793 0.783182i \(-0.286405\pi\)
0.621793 + 0.783182i \(0.286405\pi\)
\(312\) −3.34233 + 1.35234i −0.189222 + 0.0765614i
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 0.657671 + 1.13912i 0.0371145 + 0.0642842i
\(315\) −0.780776 1.35234i −0.0439918 0.0761960i
\(316\) 3.28078 5.68247i 0.184558 0.319664i
\(317\) 12.4384 0.698613 0.349306 0.937009i \(-0.386417\pi\)
0.349306 + 0.937009i \(0.386417\pi\)
\(318\) 3.50000 6.06218i 0.196270 0.339950i
\(319\) −7.84233 + 13.5833i −0.439086 + 0.760520i
\(320\) 1.56155 0.0872935
\(321\) 6.96543 12.0645i 0.388773 0.673374i
\(322\) 0.561553 + 0.972638i 0.0312941 + 0.0542030i
\(323\) 0.157671 + 0.273094i 0.00877304 + 0.0151953i
\(324\) 1.00000 0.0555556
\(325\) 1.28078 9.14657i 0.0710447 0.507361i
\(326\) 24.4924 1.35651
\(327\) −6.12311 10.6055i −0.338609 0.586487i
\(328\) 5.62311 + 9.73950i 0.310484 + 0.537774i
\(329\) 0.157671 0.273094i 0.00869267 0.0150561i
\(330\) 4.00000 0.220193
\(331\) −9.68466 + 16.7743i −0.532317 + 0.922000i 0.466971 + 0.884273i \(0.345345\pi\)
−0.999288 + 0.0377275i \(0.987988\pi\)
\(332\) 2.56155 4.43674i 0.140583 0.243498i
\(333\) −2.43845 −0.133626
\(334\) −6.24621 + 10.8188i −0.341777 + 0.591976i
\(335\) −7.12311 12.3376i −0.389177 0.674074i
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) −13.4924 −0.734979 −0.367490 0.930028i \(-0.619783\pi\)
−0.367490 + 0.930028i \(0.619783\pi\)
\(338\) 3.15767 + 12.6107i 0.171755 + 0.685930i
\(339\) −1.56155 −0.0848119
\(340\) −0.0961180 0.166481i −0.00521273 0.00902871i
\(341\) 0 0
\(342\) 1.28078 2.21837i 0.0692565 0.119956i
\(343\) 1.00000 0.0539949
\(344\) 4.00000 6.92820i 0.215666 0.373544i
\(345\) −0.876894 + 1.51883i −0.0472104 + 0.0817708i
\(346\) −18.0000 −0.967686
\(347\) −7.52699 + 13.0371i −0.404070 + 0.699870i −0.994213 0.107429i \(-0.965738\pi\)
0.590143 + 0.807299i \(0.299071\pi\)
\(348\) −3.06155 5.30277i −0.164116 0.284258i
\(349\) 9.00000 + 15.5885i 0.481759 + 0.834431i 0.999781 0.0209364i \(-0.00666475\pi\)
−0.518022 + 0.855367i \(0.673331\pi\)
\(350\) −2.56155 −0.136921
\(351\) 0.500000 3.57071i 0.0266880 0.190591i
\(352\) −2.56155 −0.136531
\(353\) 16.9039 + 29.2784i 0.899703 + 1.55833i 0.827874 + 0.560914i \(0.189550\pi\)
0.0718288 + 0.997417i \(0.477116\pi\)
\(354\) 2.56155 + 4.43674i 0.136145 + 0.235810i
\(355\) 8.87689 15.3752i 0.471137 0.816033i
\(356\) 3.43845 0.182237
\(357\) 0.0615528 0.106613i 0.00325772 0.00564254i
\(358\) 0.876894 1.51883i 0.0463453 0.0802724i
\(359\) −1.75379 −0.0925614 −0.0462807 0.998928i \(-0.514737\pi\)
−0.0462807 + 0.998928i \(0.514737\pi\)
\(360\) −0.780776 + 1.35234i −0.0411505 + 0.0712748i
\(361\) 6.21922 + 10.7720i 0.327328 + 0.566948i
\(362\) −6.62311 11.4716i −0.348103 0.602932i
\(363\) 4.43845 0.232958
\(364\) 3.34233 1.35234i 0.175186 0.0708821i
\(365\) −3.80776 −0.199307
\(366\) −5.62311 9.73950i −0.293924 0.509092i
\(367\) −6.80776 11.7914i −0.355362 0.615506i 0.631818 0.775117i \(-0.282309\pi\)
−0.987180 + 0.159611i \(0.948976\pi\)
\(368\) 0.561553 0.972638i 0.0292730 0.0507023i
\(369\) −11.2462 −0.585454
\(370\) 1.90388 3.29762i 0.0989781 0.171435i
\(371\) −3.50000 + 6.06218i −0.181711 + 0.314733i
\(372\) 0 0
\(373\) 1.53457 2.65794i 0.0794568 0.137623i −0.823559 0.567231i \(-0.808015\pi\)
0.903016 + 0.429608i \(0.141348\pi\)
\(374\) 0.157671 + 0.273094i 0.00815296 + 0.0141213i
\(375\) −5.90388 10.2258i −0.304875 0.528059i
\(376\) −0.315342 −0.0162625
\(377\) −20.4654 + 8.28055i −1.05402 + 0.426470i
\(378\) −1.00000 −0.0514344
\(379\) −18.8078 32.5760i −0.966090 1.67332i −0.706658 0.707556i \(-0.749798\pi\)
−0.259432 0.965761i \(-0.583535\pi\)
\(380\) 2.00000 + 3.46410i 0.102598 + 0.177705i
\(381\) 6.24621 10.8188i 0.320003 0.554262i
\(382\) −5.12311 −0.262121
\(383\) 6.40388 11.0918i 0.327223 0.566767i −0.654737 0.755857i \(-0.727220\pi\)
0.981960 + 0.189090i \(0.0605538\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) −4.00000 −0.203859
\(386\) −0.0615528 + 0.106613i −0.00313296 + 0.00542644i
\(387\) 4.00000 + 6.92820i 0.203331 + 0.352180i
\(388\) 0.438447 + 0.759413i 0.0222588 + 0.0385533i
\(389\) −5.31534 −0.269499 −0.134749 0.990880i \(-0.543023\pi\)
−0.134749 + 0.990880i \(0.543023\pi\)
\(390\) 4.43845 + 3.46410i 0.224750 + 0.175412i
\(391\) −0.138261 −0.00699214
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 7.12311 + 12.3376i 0.359313 + 0.622349i
\(394\) −6.28078 + 10.8786i −0.316421 + 0.548057i
\(395\) −10.2462 −0.515543
\(396\) 1.28078 2.21837i 0.0643614 0.111477i
\(397\) −13.9654 + 24.1888i −0.700905 + 1.21400i 0.267244 + 0.963629i \(0.413887\pi\)
−0.968149 + 0.250374i \(0.919446\pi\)
\(398\) −16.0000 −0.802008
\(399\) −1.28078 + 2.21837i −0.0641190 + 0.111057i
\(400\) 1.28078 + 2.21837i 0.0640388 + 0.110918i
\(401\) 0.903882 + 1.56557i 0.0451377 + 0.0781808i 0.887712 0.460400i \(-0.152294\pi\)
−0.842574 + 0.538581i \(0.818961\pi\)
\(402\) −9.12311 −0.455019
\(403\) 0 0
\(404\) −5.80776 −0.288947
\(405\) −0.780776 1.35234i −0.0387971 0.0671985i
\(406\) 3.06155 + 5.30277i 0.151942 + 0.263172i
\(407\) −3.12311 + 5.40938i −0.154807 + 0.268133i
\(408\) −0.123106 −0.00609464
\(409\) 5.78078 10.0126i 0.285841 0.495091i −0.686972 0.726684i \(-0.741060\pi\)
0.972813 + 0.231593i \(0.0743937\pi\)
\(410\) 8.78078 15.2088i 0.433652 0.751107i
\(411\) −12.4384 −0.613543
\(412\) −3.12311 + 5.40938i −0.153864 + 0.266501i
\(413\) −2.56155 4.43674i −0.126046 0.218318i
\(414\) 0.561553 + 0.972638i 0.0275988 + 0.0478025i
\(415\) −8.00000 −0.392705
\(416\) −2.84233 2.21837i −0.139357 0.108765i
\(417\) 5.43845 0.266322
\(418\) −3.28078 5.68247i −0.160468 0.277939i
\(419\) −11.6847 20.2384i −0.570833 0.988712i −0.996481 0.0838227i \(-0.973287\pi\)
0.425648 0.904889i \(-0.360046\pi\)
\(420\) 0.780776 1.35234i 0.0380980 0.0659877i
\(421\) −22.3002 −1.08684 −0.543422 0.839459i \(-0.682872\pi\)
−0.543422 + 0.839459i \(0.682872\pi\)
\(422\) −2.56155 + 4.43674i −0.124694 + 0.215977i
\(423\) 0.157671 0.273094i 0.00766622 0.0132783i
\(424\) 7.00000 0.339950
\(425\) 0.157671 0.273094i 0.00764816 0.0132470i
\(426\) −5.68466 9.84612i −0.275423 0.477046i
\(427\) 5.62311 + 9.73950i 0.272121 + 0.471328i
\(428\) 13.9309 0.673374
\(429\) −7.28078 5.68247i −0.351519 0.274352i
\(430\) −12.4924 −0.602438
\(431\) −9.68466 16.7743i −0.466494 0.807991i 0.532774 0.846258i \(-0.321150\pi\)
−0.999268 + 0.0382670i \(0.987816\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 10.6577 18.4596i 0.512175 0.887113i −0.487725 0.872997i \(-0.662173\pi\)
0.999900 0.0141160i \(-0.00449340\pi\)
\(434\) 0 0
\(435\) −4.78078 + 8.28055i −0.229221 + 0.397022i
\(436\) 6.12311 10.6055i 0.293244 0.507913i
\(437\) 2.87689 0.137621
\(438\) −1.21922 + 2.11176i −0.0582568 + 0.100904i
\(439\) 13.1231 + 22.7299i 0.626332 + 1.08484i 0.988282 + 0.152641i \(0.0487777\pi\)
−0.361950 + 0.932197i \(0.617889\pi\)
\(440\) 2.00000 + 3.46410i 0.0953463 + 0.165145i
\(441\) 1.00000 0.0476190
\(442\) −0.0615528 + 0.439575i −0.00292777 + 0.0209085i
\(443\) −27.0540 −1.28537 −0.642687 0.766129i \(-0.722180\pi\)
−0.642687 + 0.766129i \(0.722180\pi\)
\(444\) −1.21922 2.11176i −0.0578618 0.100220i
\(445\) −2.68466 4.64996i −0.127265 0.220429i
\(446\) −4.87689 + 8.44703i −0.230928 + 0.399978i
\(447\) 15.5616 0.736036
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) 3.31534 5.74234i 0.156461 0.270998i −0.777129 0.629341i \(-0.783325\pi\)
0.933590 + 0.358343i \(0.116658\pi\)
\(450\) −2.56155 −0.120753
\(451\) −14.4039 + 24.9483i −0.678252 + 1.17477i
\(452\) −0.780776 1.35234i −0.0367246 0.0636089i
\(453\) −10.9654 18.9927i −0.515201 0.892354i
\(454\) −10.8769 −0.510478
\(455\) −4.43845 3.46410i −0.208078 0.162400i
\(456\) 2.56155 0.119956
\(457\) −14.4654 25.0549i −0.676665 1.17202i −0.975979 0.217863i \(-0.930091\pi\)
0.299315 0.954154i \(-0.403242\pi\)
\(458\) −8.52699 14.7692i −0.398440 0.690118i
\(459\) 0.0615528 0.106613i 0.00287304 0.00497625i
\(460\) −1.75379 −0.0817708
\(461\) −3.02699 + 5.24290i −0.140981 + 0.244186i −0.927866 0.372913i \(-0.878359\pi\)
0.786885 + 0.617099i \(0.211692\pi\)
\(462\) −1.28078 + 2.21837i −0.0595871 + 0.103208i
\(463\) 12.3153 0.572342 0.286171 0.958178i \(-0.407617\pi\)
0.286171 + 0.958178i \(0.407617\pi\)
\(464\) 3.06155 5.30277i 0.142129 0.246175i
\(465\) 0 0
\(466\) −0.684658 1.18586i −0.0317162 0.0549341i
\(467\) −36.9848 −1.71145 −0.855727 0.517427i \(-0.826890\pi\)
−0.855727 + 0.517427i \(0.826890\pi\)
\(468\) 3.34233 1.35234i 0.154499 0.0625121i
\(469\) 9.12311 0.421266
\(470\) 0.246211 + 0.426450i 0.0113569 + 0.0196707i
\(471\) −0.657671 1.13912i −0.0303039 0.0524878i
\(472\) −2.56155 + 4.43674i −0.117905 + 0.204217i
\(473\) 20.4924 0.942243
\(474\) −3.28078 + 5.68247i −0.150691 + 0.261005i
\(475\) −3.28078 + 5.68247i −0.150532 + 0.260730i
\(476\) 0.123106 0.00564254
\(477\) −3.50000 + 6.06218i −0.160254 + 0.277568i
\(478\) −9.68466 16.7743i −0.442966 0.767240i
\(479\) 0.965435 + 1.67218i 0.0441118 + 0.0764040i 0.887238 0.461311i \(-0.152621\pi\)
−0.843126 + 0.537715i \(0.819288\pi\)
\(480\) −1.56155 −0.0712748
\(481\) −8.15009 + 3.29762i −0.371612 + 0.150359i
\(482\) −0.192236 −0.00875611
\(483\) −0.561553 0.972638i −0.0255515 0.0442566i
\(484\) 2.21922 + 3.84381i 0.100874 + 0.174719i
\(485\) 0.684658 1.18586i 0.0310887 0.0538473i
\(486\) −1.00000 −0.0453609
\(487\) −11.8423 + 20.5115i −0.536627 + 0.929466i 0.462456 + 0.886642i \(0.346968\pi\)
−0.999083 + 0.0428230i \(0.986365\pi\)
\(488\) 5.62311 9.73950i 0.254546 0.440887i
\(489\) −24.4924 −1.10759
\(490\) −0.780776 + 1.35234i −0.0352719 + 0.0610927i
\(491\) 8.24621 + 14.2829i 0.372146 + 0.644576i 0.989895 0.141799i \(-0.0452886\pi\)
−0.617749 + 0.786375i \(0.711955\pi\)
\(492\) −5.62311 9.73950i −0.253509 0.439091i
\(493\) −0.753789 −0.0339489
\(494\) 1.28078 9.14657i 0.0576249 0.411524i
\(495\) −4.00000 −0.179787
\(496\) 0 0
\(497\) 5.68466 + 9.84612i 0.254992 + 0.441659i
\(498\) −2.56155 + 4.43674i −0.114786 + 0.198815i
\(499\) 30.2462 1.35401 0.677003 0.735980i \(-0.263278\pi\)
0.677003 + 0.735980i \(0.263278\pi\)
\(500\) 5.90388 10.2258i 0.264030 0.457313i
\(501\) 6.24621 10.8188i 0.279060 0.483346i
\(502\) −13.6155 −0.607691
\(503\) 14.2462 24.6752i 0.635207 1.10021i −0.351264 0.936276i \(-0.614248\pi\)
0.986471 0.163935i \(-0.0524186\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) 4.53457 + 7.85410i 0.201786 + 0.349503i
\(506\) 2.87689 0.127894
\(507\) −3.15767 12.6107i −0.140237 0.560060i
\(508\) 12.4924 0.554262
\(509\) 20.9039 + 36.2066i 0.926548 + 1.60483i 0.789052 + 0.614326i \(0.210572\pi\)
0.137496 + 0.990502i \(0.456094\pi\)
\(510\) 0.0961180 + 0.166481i 0.00425618 + 0.00737191i
\(511\) 1.21922 2.11176i 0.0539353 0.0934186i
\(512\) 1.00000 0.0441942
\(513\) −1.28078 + 2.21837i −0.0565477 + 0.0979434i
\(514\) 12.1847 21.1044i 0.537442 0.930877i
\(515\) 9.75379 0.429803
\(516\) −4.00000 + 6.92820i −0.176090 + 0.304997i
\(517\) −0.403882 0.699544i −0.0177627 0.0307659i
\(518\) 1.21922 + 2.11176i 0.0535696 + 0.0927853i
\(519\) 18.0000 0.790112
\(520\) −0.780776 + 5.57586i −0.0342393 + 0.244518i
\(521\) 25.8769 1.13369 0.566844 0.823825i \(-0.308164\pi\)
0.566844 + 0.823825i \(0.308164\pi\)
\(522\) 3.06155 + 5.30277i 0.134001 + 0.232096i
\(523\) 8.40388 + 14.5560i 0.367476 + 0.636487i 0.989170 0.146773i \(-0.0468886\pi\)
−0.621694 + 0.783260i \(0.713555\pi\)
\(524\) −7.12311 + 12.3376i −0.311174 + 0.538970i
\(525\) 2.56155 0.111795
\(526\) −2.56155 + 4.43674i −0.111689 + 0.193451i
\(527\) 0 0
\(528\) 2.56155 0.111477
\(529\) 10.8693 18.8262i 0.472579 0.818531i
\(530\) −5.46543 9.46641i −0.237403 0.411195i
\(531\) −2.56155 4.43674i −0.111162 0.192538i
\(532\) −2.56155 −0.111057
\(533\) −37.5885 + 15.2088i −1.62814 + 0.658764i
\(534\) −3.43845 −0.148796
\(535\) −10.8769 18.8393i −0.470249 0.814495i
\(536\) −4.56155 7.90084i −0.197029 0.341264i
\(537\) −0.876894 + 1.51883i −0.0378408 + 0.0655422i
\(538\) 27.1231 1.16936
\(539\) 1.28078 2.21837i 0.0551669 0.0955520i
\(540\) 0.780776 1.35234i 0.0335993 0.0581956i
\(541\) 19.1771 0.824487 0.412244 0.911074i \(-0.364745\pi\)
0.412244 + 0.911074i \(0.364745\pi\)
\(542\) 11.3693 19.6922i 0.488354 0.845854i
\(543\) 6.62311 + 11.4716i 0.284225 + 0.492292i
\(544\) −0.0615528 0.106613i −0.00263906 0.00457098i
\(545\) −19.1231 −0.819144
\(546\) −3.34233 + 1.35234i −0.143038 + 0.0578750i
\(547\) −33.6155 −1.43730 −0.718648 0.695374i \(-0.755239\pi\)
−0.718648 + 0.695374i \(0.755239\pi\)
\(548\) −6.21922 10.7720i −0.265672 0.460158i
\(549\) 5.62311 + 9.73950i 0.239988 + 0.415672i
\(550\) −3.28078 + 5.68247i −0.139893 + 0.242301i
\(551\) 15.6847 0.668189
\(552\) −0.561553 + 0.972638i −0.0239013 + 0.0413982i
\(553\) 3.28078 5.68247i 0.139513 0.241643i
\(554\) −19.5616 −0.831091
\(555\) −1.90388 + 3.29762i −0.0808153 + 0.139976i
\(556\) 2.71922 + 4.70983i 0.115321 + 0.199741i
\(557\) −6.06155 10.4989i −0.256836 0.444853i 0.708556 0.705654i \(-0.249347\pi\)
−0.965393 + 0.260801i \(0.916013\pi\)
\(558\) 0 0
\(559\) 22.7386 + 17.7470i 0.961742 + 0.750616i
\(560\) 1.56155 0.0659877
\(561\) −0.157671 0.273094i −0.00665687 0.0115300i
\(562\) −6.46543 11.1985i −0.272728 0.472379i
\(563\) 2.87689 4.98293i 0.121247 0.210005i −0.799013 0.601314i \(-0.794644\pi\)
0.920260 + 0.391309i \(0.127977\pi\)
\(564\) 0.315342 0.0132783
\(565\) −1.21922 + 2.11176i −0.0512931 + 0.0888423i
\(566\) 10.0000 17.3205i 0.420331 0.728035i
\(567\) 1.00000 0.0419961
\(568\) 5.68466 9.84612i 0.238523 0.413134i
\(569\) 11.0000 + 19.0526i 0.461144 + 0.798725i 0.999018 0.0443003i \(-0.0141058\pi\)
−0.537874 + 0.843025i \(0.680772\pi\)
\(570\) −2.00000 3.46410i −0.0837708 0.145095i
\(571\) −21.1231 −0.883974 −0.441987 0.897021i \(-0.645726\pi\)
−0.441987 + 0.897021i \(0.645726\pi\)
\(572\) 1.28078 9.14657i 0.0535520 0.382437i
\(573\) 5.12311 0.214021
\(574\) 5.62311 + 9.73950i 0.234704 + 0.406519i
\(575\) −1.43845 2.49146i −0.0599874 0.103901i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −35.5616 −1.48045 −0.740223 0.672361i \(-0.765280\pi\)
−0.740223 + 0.672361i \(0.765280\pi\)
\(578\) 8.49242 14.7093i 0.353238 0.611827i
\(579\) 0.0615528 0.106613i 0.00255805 0.00443067i
\(580\) −9.56155 −0.397022
\(581\) 2.56155 4.43674i 0.106271 0.184067i
\(582\) −0.438447 0.759413i −0.0181742 0.0314787i
\(583\) 8.96543 + 15.5286i 0.371310 + 0.643128i
\(584\) −2.43845 −0.100904
\(585\) −4.43845 3.46410i −0.183507 0.143223i
\(586\) −6.93087 −0.286312
\(587\) −1.12311 1.94528i −0.0463555 0.0802901i 0.841917 0.539608i \(-0.181427\pi\)
−0.888272 + 0.459317i \(0.848094\pi\)
\(588\) 0.500000 + 0.866025i 0.0206197 + 0.0357143i
\(589\) 0 0
\(590\) 8.00000 0.329355
\(591\) 6.28078 10.8786i 0.258357 0.447487i
\(592\) 1.21922 2.11176i 0.0501098 0.0867927i
\(593\) −33.9848 −1.39559 −0.697795 0.716297i \(-0.745835\pi\)
−0.697795 + 0.716297i \(0.745835\pi\)
\(594\) −1.28078 + 2.21837i −0.0525509 + 0.0910208i
\(595\) −0.0961180 0.166481i −0.00394045 0.00682506i
\(596\) 7.78078 + 13.4767i 0.318713 + 0.552027i
\(597\) 16.0000 0.654836
\(598\) 3.19224 + 2.49146i 0.130540 + 0.101884i
\(599\) 23.8617 0.974964 0.487482 0.873133i \(-0.337915\pi\)
0.487482 + 0.873133i \(0.337915\pi\)
\(600\) −1.28078 2.21837i −0.0522875 0.0905646i
\(601\) −14.1501 24.5087i −0.577194 0.999730i −0.995799 0.0915616i \(-0.970814\pi\)
0.418605 0.908168i \(-0.362519\pi\)
\(602\) 4.00000 6.92820i 0.163028 0.282372i
\(603\) 9.12311 0.371522
\(604\) 10.9654 18.9927i 0.446177 0.772802i
\(605\) 3.46543 6.00231i 0.140890 0.244029i
\(606\) 5.80776 0.235924
\(607\) 24.4924 42.4221i 0.994117 1.72186i 0.403256 0.915087i \(-0.367878\pi\)
0.590861 0.806774i \(-0.298788\pi\)
\(608\) 1.28078 + 2.21837i 0.0519423 + 0.0899668i
\(609\) −3.06155 5.30277i −0.124060 0.214879i
\(610\) −17.5616 −0.711046
\(611\) 0.157671 1.12599i 0.00637868 0.0455529i
\(612\) 0.123106 0.00497625
\(613\) −10.7808 18.6729i −0.435431 0.754189i 0.561899 0.827206i \(-0.310071\pi\)
−0.997331 + 0.0730162i \(0.976738\pi\)
\(614\) 4.96543 + 8.60039i 0.200389 + 0.347083i
\(615\) −8.78078 + 15.2088i −0.354075 + 0.613276i
\(616\) −2.56155 −0.103208
\(617\) −11.5885 + 20.0719i −0.466537 + 0.808066i −0.999269 0.0382179i \(-0.987832\pi\)
0.532732 + 0.846284i \(0.321165\pi\)
\(618\) 3.12311 5.40938i 0.125630 0.217597i
\(619\) 2.06913 0.0831654 0.0415827 0.999135i \(-0.486760\pi\)
0.0415827 + 0.999135i \(0.486760\pi\)
\(620\) 0 0
\(621\) −0.561553 0.972638i −0.0225343 0.0390306i
\(622\) −10.9654 18.9927i −0.439674 0.761537i
\(623\) 3.43845 0.137758
\(624\) 2.84233 + 2.21837i 0.113784 + 0.0888059i
\(625\) −5.63068 −0.225227
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) 3.28078 + 5.68247i 0.131022 + 0.226936i
\(628\) 0.657671 1.13912i 0.0262439 0.0454558i
\(629\) −0.300187 −0.0119692
\(630\) −0.780776 + 1.35234i −0.0311069 + 0.0538787i
\(631\) 5.03457 8.72012i 0.200423 0.347143i −0.748242 0.663426i \(-0.769102\pi\)
0.948665 + 0.316283i \(0.102435\pi\)
\(632\) −6.56155 −0.261005
\(633\) 2.56155 4.43674i 0.101813 0.176345i
\(634\) −6.21922 10.7720i −0.246997 0.427811i
\(635\) −9.75379 16.8941i −0.387067 0.670420i
\(636\) −7.00000 −0.277568
\(637\) 3.34233 1.35234i 0.132428 0.0535818i
\(638\) 15.6847 0.620962
\(639\) 5.68466 + 9.84612i 0.224882 + 0.389506i
\(640\) −0.780776 1.35234i −0.0308629 0.0534561i
\(641\) −4.21922 + 7.30791i −0.166649 + 0.288645i −0.937240 0.348686i \(-0.886628\pi\)
0.770590 + 0.637331i \(0.219961\pi\)
\(642\) −13.9309 −0.549808
\(643\) −23.8423 + 41.2961i −0.940250 + 1.62856i −0.175256 + 0.984523i \(0.556075\pi\)
−0.764994 + 0.644037i \(0.777258\pi\)
\(644\) 0.561553 0.972638i 0.0221283 0.0383273i
\(645\) 12.4924 0.491889
\(646\) 0.157671 0.273094i 0.00620347 0.0107447i
\(647\) 4.47301 + 7.74748i 0.175852 + 0.304585i 0.940456 0.339916i \(-0.110399\pi\)
−0.764604 + 0.644501i \(0.777065\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −13.1231 −0.515127
\(650\) −8.56155 + 3.46410i −0.335812 + 0.135873i
\(651\) 0 0
\(652\) −12.2462 21.2111i −0.479599 0.830689i
\(653\) −10.2808 17.8068i −0.402318 0.696835i 0.591687 0.806168i \(-0.298462\pi\)
−0.994005 + 0.109333i \(0.965129\pi\)
\(654\) −6.12311 + 10.6055i −0.239432 + 0.414709i
\(655\) 22.2462 0.869231
\(656\) 5.62311 9.73950i 0.219545 0.380264i
\(657\) 1.21922 2.11176i 0.0475664 0.0823875i
\(658\) −0.315342 −0.0122933
\(659\) −1.03457 + 1.79192i −0.0403009 + 0.0698033i −0.885472 0.464692i \(-0.846165\pi\)
0.845171 + 0.534495i \(0.179498\pi\)
\(660\) −2.00000 3.46410i −0.0778499 0.134840i
\(661\) 10.0270 + 17.3673i 0.390005 + 0.675508i 0.992450 0.122653i \(-0.0391401\pi\)
−0.602445 + 0.798160i \(0.705807\pi\)
\(662\) 19.3693 0.752810
\(663\) 0.0615528 0.439575i 0.00239051 0.0170717i
\(664\) −5.12311 −0.198815
\(665\) 2.00000 + 3.46410i 0.0775567 + 0.134332i
\(666\) 1.21922 + 2.11176i 0.0472440 + 0.0818289i
\(667\) −3.43845 + 5.95557i −0.133137 + 0.230600i
\(668\) 12.4924 0.483346
\(669\) 4.87689 8.44703i 0.188552 0.326581i
\(670\) −7.12311 + 12.3376i −0.275190 + 0.476642i
\(671\) 28.8078 1.11211
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) 1.37689 + 2.38485i 0.0530754 + 0.0919293i 0.891342 0.453331i \(-0.149764\pi\)
−0.838267 + 0.545260i \(0.816431\pi\)
\(674\) 6.74621 + 11.6848i 0.259854 + 0.450081i
\(675\) 2.56155 0.0985942
\(676\) 9.34233 9.03996i 0.359320 0.347691i
\(677\) −24.7386 −0.950783 −0.475391 0.879774i \(-0.657694\pi\)
−0.475391 + 0.879774i \(0.657694\pi\)
\(678\) 0.780776 + 1.35234i 0.0299855 + 0.0519365i
\(679\) 0.438447 + 0.759413i 0.0168261 + 0.0291436i
\(680\) −0.0961180 + 0.166481i −0.00368596 + 0.00638426i
\(681\) 10.8769 0.416803
\(682\) 0 0
\(683\) −20.2462 + 35.0675i −0.774700 + 1.34182i 0.160263 + 0.987074i \(0.448766\pi\)
−0.934963 + 0.354745i \(0.884568\pi\)
\(684\) −2.56155 −0.0979434
\(685\) −9.71165 + 16.8211i −0.371063 + 0.642700i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 8.52699 + 14.7692i 0.325325 + 0.563479i
\(688\) −8.00000 −0.304997
\(689\) −3.50000 + 24.9950i −0.133339 + 0.952234i
\(690\) 1.75379 0.0667656
\(691\) 16.4924 + 28.5657i 0.627401 + 1.08669i 0.988071 + 0.153997i \(0.0492148\pi\)
−0.360670 + 0.932694i \(0.617452\pi\)
\(692\) 9.00000 + 15.5885i 0.342129 + 0.592584i
\(693\) 1.28078 2.21837i 0.0486527 0.0842689i
\(694\) 15.0540 0.571441
\(695\) 4.24621 7.35465i 0.161068 0.278978i
\(696\) −3.06155 + 5.30277i −0.116048 + 0.201001i
\(697\) −1.38447 −0.0524406
\(698\) 9.00000 15.5885i 0.340655 0.590032i
\(699\) 0.684658 + 1.18586i 0.0258962 + 0.0448535i
\(700\) 1.28078 + 2.21837i 0.0484088 + 0.0838465i
\(701\) −39.3002 −1.48435 −0.742174 0.670207i \(-0.766205\pi\)
−0.742174 + 0.670207i \(0.766205\pi\)
\(702\) −3.34233 + 1.35234i −0.126148 + 0.0510410i
\(703\) 6.24621 0.235580
\(704\) 1.28078 + 2.21837i 0.0482711 + 0.0836080i
\(705\) −0.246211 0.426450i −0.00927285 0.0160611i
\(706\) 16.9039 29.2784i 0.636186 1.10191i
\(707\) −5.80776 −0.218423
\(708\) 2.56155 4.43674i 0.0962690 0.166743i
\(709\) 19.1501 33.1689i 0.719197 1.24569i −0.242122 0.970246i \(-0.577843\pi\)
0.961318 0.275440i \(-0.0888234\pi\)
\(710\) −17.7538 −0.666288
\(711\) 3.28078 5.68247i 0.123039 0.213109i
\(712\) −1.71922 2.97778i −0.0644306 0.111597i
\(713\) 0 0
\(714\) −0.123106 −0.00460711
\(715\) −13.3693 + 5.40938i −0.499984 + 0.202299i
\(716\) −1.75379 −0.0655422
\(717\) 9.68466 + 16.7743i 0.361680 + 0.626448i
\(718\) 0.876894 + 1.51883i 0.0327254 + 0.0566821i
\(719\) −0.403882 + 0.699544i −0.0150623 + 0.0260886i −0.873458 0.486899i \(-0.838128\pi\)
0.858396 + 0.512988i \(0.171461\pi\)
\(720\) 1.56155 0.0581956
\(721\) −3.12311 + 5.40938i −0.116311 + 0.201456i
\(722\) 6.21922 10.7720i 0.231456 0.400893i
\(723\) 0.192236 0.00714933
\(724\) −6.62311 + 11.4716i −0.246146 + 0.426337i
\(725\) −7.84233 13.5833i −0.291257 0.504472i
\(726\) −2.21922 3.84381i −0.0823631 0.142657i
\(727\) 40.0000 1.48352 0.741759 0.670667i \(-0.233992\pi\)
0.741759 + 0.670667i \(0.233992\pi\)
\(728\) −2.84233 2.21837i −0.105344 0.0822183i
\(729\) 1.00000 0.0370370
\(730\) 1.90388 + 3.29762i 0.0704658 + 0.122050i
\(731\) 0.492423 + 0.852901i 0.0182129 + 0.0315457i
\(732\) −5.62311 + 9.73950i −0.207836 + 0.359982i
\(733\) −28.8617 −1.06603 −0.533016 0.846105i \(-0.678942\pi\)
−0.533016 + 0.846105i \(0.678942\pi\)
\(734\) −6.80776 + 11.7914i −0.251279 + 0.435228i
\(735\) 0.780776 1.35234i 0.0287994 0.0498820i
\(736\) −1.12311 −0.0413982
\(737\) 11.6847 20.2384i 0.430410 0.745492i
\(738\) 5.62311 + 9.73950i 0.206989 + 0.358516i
\(739\) −7.68466 13.3102i −0.282685 0.489624i 0.689360 0.724419i \(-0.257892\pi\)
−0.972045 + 0.234794i \(0.924558\pi\)
\(740\) −3.80776 −0.139976
\(741\) −1.28078 + 9.14657i −0.0470505 + 0.336008i
\(742\) 7.00000 0.256978
\(743\) 2.24621 + 3.89055i 0.0824055 + 0.142731i 0.904283 0.426934i \(-0.140406\pi\)
−0.821877 + 0.569665i \(0.807073\pi\)
\(744\) 0 0
\(745\) 12.1501 21.0446i 0.445145 0.771014i
\(746\) −3.06913 −0.112369
\(747\) 2.56155 4.43674i 0.0937223 0.162332i
\(748\) 0.157671 0.273094i 0.00576501 0.00998530i
\(749\) 13.9309 0.509023
\(750\) −5.90388 + 10.2258i −0.215579 + 0.373394i
\(751\) 20.4039 + 35.3406i 0.744548 + 1.28960i 0.950406 + 0.311013i \(0.100668\pi\)
−0.205857 + 0.978582i \(0.565998\pi\)
\(752\) 0.157671 + 0.273094i 0.00574966 + 0.00995871i
\(753\) 13.6155 0.496177
\(754\) 17.4039 + 13.5833i 0.633812 + 0.494675i
\(755\) −34.2462 −1.24635
\(756\) 0.500000 + 0.866025i 0.0181848 + 0.0314970i
\(757\) −26.3693 45.6730i −0.958409 1.66001i −0.726366 0.687308i \(-0.758792\pi\)
−0.232043 0.972706i \(-0.574541\pi\)
\(758\) −18.8078 + 32.5760i −0.683129 + 1.18321i
\(759\) −2.87689 −0.104425
\(760\) 2.00000 3.46410i 0.0725476 0.125656i
\(761\) −25.4924 + 44.1542i −0.924100 + 1.60059i −0.131097 + 0.991370i \(0.541850\pi\)
−0.793003 + 0.609218i \(0.791483\pi\)
\(762\) −12.4924 −0.452553
\(763\) 6.12311 10.6055i 0.221671 0.383946i
\(764\) 2.56155 + 4.43674i 0.0926737 + 0.160516i
\(765\) −0.0961180 0.166481i −0.00347515 0.00601914i
\(766\) −12.8078 −0.462763
\(767\) −14.5616 11.3649i −0.525787 0.410364i
\(768\) −1.00000 −0.0360844
\(769\) −2.43845 4.22351i −0.0879327 0.152304i 0.818704 0.574215i \(-0.194693\pi\)
−0.906637 + 0.421911i \(0.861359\pi\)
\(770\) 2.00000 + 3.46410i 0.0720750 + 0.124838i
\(771\) −12.1847 + 21.1044i −0.438820 + 0.760058i
\(772\) 0.123106 0.00443067
\(773\) −10.3693 + 17.9602i −0.372958 + 0.645983i −0.990019 0.140933i \(-0.954990\pi\)
0.617061 + 0.786915i \(0.288323\pi\)
\(774\) 4.00000 6.92820i 0.143777 0.249029i
\(775\) 0 0
\(776\) 0.438447 0.759413i 0.0157393 0.0272613i
\(777\) −1.21922 2.11176i −0.0437394 0.0757589i
\(778\) 2.65767 + 4.60322i 0.0952821 + 0.165033i
\(779\) 28.8078