Properties

Label 546.2.l.l.295.2
Level $546$
Weight $2$
Character 546.295
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 295.2
Root \(-0.780776 - 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 546.295
Dual form 546.2.l.l.211.2

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} + q^{19} + q^{20} - 4 q^{21} + q^{22} - 6 q^{23} + 2 q^{24} - 2 q^{25} + q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{29} - q^{30} - 2 q^{32} - q^{33} - 16 q^{34} + q^{35} - 2 q^{36} + 9 q^{37} - 2 q^{38} - q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 16 q^{43} - 2 q^{44} + q^{45} - 6 q^{46} - 26 q^{47} + 2 q^{48} - 2 q^{49} + q^{50} + 16 q^{51} + q^{52} + 28 q^{53} + 2 q^{54} + 8 q^{55} - 2 q^{56} + 2 q^{57} + 4 q^{58} - 2 q^{59} + 2 q^{60} + 6 q^{61} - 2 q^{63} + 4 q^{64} + q^{65} + 2 q^{66} - 10 q^{67} + 8 q^{68} + 6 q^{69} - 2 q^{70} - 2 q^{71} - 2 q^{72} - 18 q^{73} + 9 q^{74} - q^{75} + q^{76} - 2 q^{77} - q^{78} - 18 q^{79} + q^{80} - 2 q^{81} + 6 q^{82} - 4 q^{83} + 2 q^{84} - 21 q^{85} - 32 q^{86} - 4 q^{87} + q^{88} - 11 q^{89} - 2 q^{90} + q^{91} + 12 q^{92} + 13 q^{94} + 8 q^{95} - 4 q^{96} + 10 q^{97} - 2 q^{98} - 2 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.605762 0.795646i \(-0.707132\pi\)
0.991931 + 0.126782i \(0.0404650\pi\)
\(12\) −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 0.858465 0.512873i \(-0.171419\pi\)
−0.873393 + 0.487016i \(0.838085\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.28078 + 2.21837i 0.293830 + 0.508929i 0.974712 0.223464i \(-0.0717366\pi\)
−0.680882 + 0.732393i \(0.738403\pi\)
\(20\) −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 −0.801522 0.597965i \(-0.795976\pi\)
0.918614 + 0.395156i \(0.129309\pi\)
\(24\) 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 −0.428197 0.903685i \(-0.640851\pi\)
0.996713 0.0810133i \(-0.0258156\pi\)
\(30\) 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 −0.748231 0.663438i \(-0.769096\pi\)
0.948670 + 0.316268i \(0.102430\pi\)
\(38\) −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 0.0248471 0.999691i \(-0.492090\pi\)
0.853335 0.521364i \(-0.174577\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −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 0.649707 0.760185i \(-0.274892\pi\)
−0.983193 + 0.182570i \(0.941558\pi\)
\(60\) −1.56155 −0.201596
\(61\) 5.62311 + 9.73950i 0.719965 + 1.24702i 0.961013 + 0.276503i \(0.0891755\pi\)
−0.241048 + 0.970513i \(0.577491\pi\)
\(62\) 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 0.440440 + 0.897782i \(0.354823\pi\)
−0.997722 + 0.0674592i \(0.978511\pi\)
\(68\) −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 0.976573 + 0.215188i \(0.0690365\pi\)
−0.301928 + 0.953331i \(0.597630\pi\)
\(72\) −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 −0.942642 0.333805i \(-0.891667\pi\)
0.760405 + 0.649449i \(0.225001\pi\)
\(90\) 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 0.887426 0.460951i \(-0.152492\pi\)
−0.842908 + 0.538058i \(0.819158\pi\)
\(98\) −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 −0.684612 0.728908i \(-0.740028\pi\)
0.973559 + 0.228437i \(0.0733615\pi\)
\(102\) 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 0.303567 + 0.952810i \(0.401822\pi\)
−0.976941 + 0.213508i \(0.931511\pi\)
\(108\) 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 0.826962 0.562258i \(-0.190067\pi\)
−0.900411 + 0.435041i \(0.856734\pi\)
\(114\) −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 0.443699 + 0.896176i \(0.353666\pi\)
−0.997961 + 0.0638334i \(0.979667\pi\)
\(128\) −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 −0.999331 0.0365795i \(-0.988354\pi\)
0.467987 0.883736i \(-0.344980\pi\)
\(138\) 1.12311 0.0956051
\(139\) 2.71922 + 4.70983i 0.230642 + 0.399483i 0.957997 0.286778i \(-0.0925842\pi\)
−0.727356 + 0.686261i \(0.759251\pi\)
\(140\) −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 0.985996 + 0.166771i \(0.0533342\pi\)
−0.348570 + 0.937283i \(0.613332\pi\)
\(150\) −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 −0.724457 0.689320i \(-0.757909\pi\)
−0.234741 0.972058i \(-0.575424\pi\)
\(164\) −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 −0.999817 0.0191244i \(-0.993912\pi\)
0.516471 + 0.856305i \(0.327245\pi\)
\(168\) −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 0.973670 + 0.227964i \(0.0732068\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(174\) 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 −0.831392 0.555686i \(-0.812456\pi\)
0.896934 + 0.442164i \(0.145789\pi\)
\(180\) −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 0.943694 0.330821i \(-0.107326\pi\)
−0.758346 + 0.651852i \(0.773992\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −0.0615528 + 0.106613i −0.00443067 + 0.00767414i −0.868232 0.496158i \(-0.834744\pi\)
0.863802 + 0.503832i \(0.168077\pi\)
\(194\) −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 −0.998222 0.0596103i \(-0.981014\pi\)
0.550735 + 0.834680i \(0.314348\pi\)
\(198\) 1.28078 2.21837i 0.0910208 0.157653i
\(199\) 8.00000 + 13.8564i 0.567105 + 0.982255i 0.996850 + 0.0793045i \(0.0252700\pi\)
−0.429745 + 0.902950i \(0.641397\pi\)
\(200\) −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 −0.940626 0.339445i \(-0.889761\pi\)
0.764281 + 0.644883i \(0.223094\pi\)
\(212\) −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 −0.981831 0.189757i \(-0.939230\pi\)
0.655250 + 0.755412i \(0.272563\pi\)
\(224\) −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 0.988119 0.153688i \(-0.0491149\pi\)
−0.627157 + 0.778893i \(0.715782\pi\)
\(228\) −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 0.869105 0.494628i \(-0.164696\pi\)
−0.862913 + 0.505352i \(0.831363\pi\)
\(242\) −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 0.996847 0.0793522i \(-0.0252852\pi\)
−0.567144 + 0.823618i \(0.691952\pi\)
\(252\) 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 −0.182762 0.983157i \(-0.558504\pi\)
0.942820 0.333302i \(-0.108163\pi\)
\(258\) −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 −0.934130 0.356933i \(-0.883822\pi\)
0.776178 + 0.630514i \(0.217156\pi\)
\(264\) −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 −0.900488 0.434882i \(-0.856790\pi\)
0.0736251 0.997286i \(-0.476543\pi\)
\(270\) 0.780776 1.35234i 0.0475165 0.0823011i
\(271\) 11.3693 19.6922i 0.690637 1.19622i −0.280993 0.959710i \(-0.590664\pi\)
0.971630 0.236508i \(-0.0760030\pi\)
\(272\) 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 0.994537 + 0.104387i \(0.0332879\pi\)
−0.406867 + 0.913487i \(0.633379\pi\)
\(278\) −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 −0.399188 0.916869i \(-0.630708\pi\)
0.993626 0.112728i \(-0.0359589\pi\)
\(284\) 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 0.949318 0.314317i \(-0.101775\pi\)
−0.746865 + 0.664975i \(0.768442\pi\)
\(294\) −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 −0.999288 0.0377275i \(-0.987988\pi\)
0.466971 0.884273i \(-0.345345\pi\)
\(332\) 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 0.590143 0.807299i \(-0.299071\pi\)
−0.994213 + 0.107429i \(0.965738\pi\)
\(348\) −3.06155 + 5.30277i −0.164116 + 0.284258i
\(349\) 9.00000 15.5885i 0.481759 0.834431i −0.518022 0.855367i \(-0.673331\pi\)
0.999781 + 0.0209364i \(0.00666475\pi\)
\(350\) −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 0.0718288 0.997417i \(-0.477116\pi\)
0.827874 0.560914i \(-0.189550\pi\)
\(354\) 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 −0.987180 0.159611i \(-0.948976\pi\)
0.631818 + 0.775117i \(0.282309\pi\)
\(368\) 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 0.903016 0.429608i \(-0.141348\pi\)
−0.823559 + 0.567231i \(0.808015\pi\)
\(374\) 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 −0.259432 + 0.965761i \(0.583535\pi\)
−0.706658 + 0.707556i \(0.749798\pi\)
\(380\) 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 0.981960 0.189090i \(-0.0605538\pi\)
−0.654737 + 0.755857i \(0.727220\pi\)
\(384\) 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 −0.968149 0.250374i \(-0.919446\pi\)
0.267244 0.963629i \(-0.413887\pi\)
\(398\) −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 −0.842574 0.538581i \(-0.818961\pi\)
0.887712 + 0.460400i \(0.152294\pi\)
\(402\) −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 0.972813 0.231593i \(-0.0743937\pi\)
−0.686972 + 0.726684i \(0.741060\pi\)
\(410\) 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 0.425648 + 0.904889i \(0.360046\pi\)
−0.996481 + 0.0838227i \(0.973287\pi\)
\(420\) 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 −0.999268 0.0382670i \(-0.987816\pi\)
0.532774 + 0.846258i \(0.321150\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 10.6577 + 18.4596i 0.512175 + 0.887113i 0.999900 + 0.0141160i \(0.00449340\pi\)
−0.487725 + 0.872997i \(0.662173\pi\)
\(434\) 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 −0.361950 0.932197i \(-0.617889\pi\)
0.988282 0.152641i \(-0.0487777\pi\)
\(440\) 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 0.933590 0.358343i \(-0.116658\pi\)
−0.777129 + 0.629341i \(0.783325\pi\)
\(450\) −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 0.299315 + 0.954154i \(0.403242\pi\)
−0.975979 + 0.217863i \(0.930091\pi\)
\(458\) −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 0.786885 0.617099i \(-0.211692\pi\)
−0.927866 + 0.372913i \(0.878359\pi\)
\(462\) −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 −0.843126 0.537715i \(-0.819288\pi\)
0.887238 + 0.461311i \(0.152621\pi\)
\(480\) −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 −0.999083 0.0428230i \(-0.986365\pi\)
0.462456 0.886642i \(-0.346968\pi\)
\(488\) 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 −0.617749 0.786375i \(-0.711955\pi\)
0.989895 + 0.141799i \(0.0452886\pi\)
\(492\) −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 0.986471 + 0.163935i \(0.0524186\pi\)
−0.351264 + 0.936276i \(0.614248\pi\)
\(504\) −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 0.137496 0.990502i \(-0.456094\pi\)
0.789052 0.614326i \(-0.210572\pi\)
\(510\) 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 −0.621694 0.783260i \(-0.713555\pi\)
0.989170 + 0.146773i \(0.0468886\pi\)
\(524\) −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 −0.965393 0.260801i \(-0.916013\pi\)
0.708556 + 0.705654i \(0.249347\pi\)
\(558\) 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 0.920260 0.391309i \(-0.127977\pi\)
−0.799013 + 0.601314i \(0.794644\pi\)
\(564\) 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 −0.537874 0.843025i \(-0.680772\pi\)
0.999018 + 0.0443003i \(0.0141058\pi\)
\(570\) −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 −0.888272 0.459317i \(-0.848094\pi\)
0.841917 + 0.539608i \(0.181427\pi\)
\(588\) 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 0.418605 + 0.908168i \(0.362519\pi\)
−0.995799 + 0.0915616i \(0.970814\pi\)
\(602\) 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 0.590861 + 0.806774i \(0.298788\pi\)
0.403256 + 0.915087i \(0.367878\pi\)
\(608\) 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 −0.997331 0.0730162i \(-0.976738\pi\)
0.561899 + 0.827206i \(0.310071\pi\)
\(614\) 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 0.532732 0.846284i \(-0.321165\pi\)
−0.999269 + 0.0382179i \(0.987832\pi\)
\(618\) 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 0.948665 0.316283i \(-0.102435\pi\)
−0.748242 + 0.663426i \(0.769102\pi\)
\(632\) −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 0.770590 0.637331i \(-0.219961\pi\)
−0.937240 + 0.348686i \(0.886628\pi\)
\(642\) −13.9309 −0.549808
\(643\) −23.8423 41.2961i −0.940250 1.62856i −0.764994 0.644037i \(-0.777258\pi\)
−0.175256 0.984523i \(-0.556075\pi\)
\(644\) 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 −0.764604 0.644501i \(-0.777065\pi\)
0.940456 + 0.339916i \(0.110399\pi\)
\(648\) −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 −0.994005 0.109333i \(-0.965129\pi\)
0.591687 + 0.806168i \(0.298462\pi\)
\(654\) −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 0.845171 0.534495i \(-0.179498\pi\)
−0.885472 + 0.464692i \(0.846165\pi\)
\(660\) −2.00000 + 3.46410i −0.0778499 + 0.134840i
\(661\) 10.0270 17.3673i 0.390005 0.675508i −0.602445 0.798160i \(-0.705807\pi\)
0.992450 + 0.122653i \(0.0391401\pi\)
\(662\) 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 −0.838267 0.545260i \(-0.816431\pi\)
0.891342 + 0.453331i \(0.149764\pi\)
\(674\) 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 −0.934963 0.354745i \(-0.884568\pi\)
0.160263 0.987074i \(-0.448766\pi\)
\(684\) −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 −0.360670 0.932694i \(-0.617452\pi\)
0.988071 0.153997i \(-0.0492148\pi\)
\(692\) 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 0.961318 + 0.275440i \(0.0888234\pi\)
−0.242122 + 0.970246i \(0.577843\pi\)
\(710\) −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 0.858396 0.512988i \(-0.171461\pi\)
−0.873458 + 0.486899i \(0.838128\pi\)
\(720\) 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 −0.972045 0.234794i \(-0.924558\pi\)
0.689360 + 0.724419i \(0.257892\pi\)
\(740\) −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 −0.821877 0.569665i \(-0.807073\pi\)
0.904283 + 0.426934i \(0.140406\pi\)
\(744\) 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 −0.205857 0.978582i \(-0.565998\pi\)
0.950406 0.311013i \(-0.100668\pi\)
\(752\) 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 −0.232043 + 0.972706i \(0.574541\pi\)
−0.726366 + 0.687308i \(0.758792\pi\)
\(758\) −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 −0.793003 0.609218i \(-0.791483\pi\)
−0.131097 0.991370i \(-0.541850\pi\)
\(762\) −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 −0.906637 0.421911i \(-0.861359\pi\)
0.818704 + 0.574215i \(0.194693\pi\)
\(770\) 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 0.617061 0.786915i \(-0.288323\pi\)
−0.990019 + 0.140933i \(0.954990\pi\)
\(774\) 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