Properties

Label 1110.2.x.d.751.6
Level $1110$
Weight $2$
Character 1110.751
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.6
Root \(1.95985i\) of defining polynomial
Character \(\chi\) \(=\) 1110.751
Dual form 1110.2.x.d.841.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-0.979923 + 1.69728i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +(-0.979923 + 1.69728i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +2.45634 q^{11} +(0.500000 + 0.866025i) q^{12} +(1.23082 + 0.710611i) q^{13} +1.95985i q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.831252 + 0.479923i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(3.95806 + 2.28518i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-0.979923 - 1.69728i) q^{21} +(2.12726 - 1.22817i) q^{22} -3.15327i q^{23} +(0.866025 + 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +1.42122 q^{26} +1.00000 q^{27} +(0.979923 + 1.69728i) q^{28} +8.68349i q^{29} +(-0.500000 + 0.866025i) q^{30} +6.99935i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.22817 + 2.12726i) q^{33} +(-0.479923 + 0.831252i) q^{34} +(-1.69728 + 0.979923i) q^{35} -1.00000 q^{36} +(5.73867 - 2.01686i) q^{37} +4.57037 q^{38} +(-1.23082 + 0.710611i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-4.88647 + 8.46362i) q^{41} +(-1.69728 - 0.979923i) q^{42} -3.84608i q^{43} +(1.22817 - 2.12726i) q^{44} -1.00000i q^{45} +(-1.57664 - 2.73082i) q^{46} +13.5293 q^{47} +1.00000 q^{48} +(1.57950 + 2.73577i) q^{49} +(0.866025 + 0.500000i) q^{50} -0.959847i q^{51} +(1.23082 - 0.710611i) q^{52} +(-5.33799 - 9.24568i) q^{53} +(0.866025 - 0.500000i) q^{54} +(2.12726 + 1.22817i) q^{55} +(1.69728 + 0.979923i) q^{56} +(-3.95806 + 2.28518i) q^{57} +(4.34174 + 7.52012i) q^{58} +(6.41533 - 3.70389i) q^{59} +1.00000i q^{60} +(-7.96035 - 4.59591i) q^{61} +(3.49967 + 6.06161i) q^{62} +1.95985 q^{63} -1.00000 q^{64} +(0.710611 + 1.23082i) q^{65} +2.45634i q^{66} +(-4.23409 + 7.33365i) q^{67} +0.959847i q^{68} +(2.73082 + 1.57664i) q^{69} +(-0.979923 + 1.69728i) q^{70} +(-1.35088 + 2.33979i) q^{71} +(-0.866025 + 0.500000i) q^{72} -3.05026 q^{73} +(3.96140 - 4.61598i) q^{74} -1.00000 q^{75} +(3.95806 - 2.28518i) q^{76} +(-2.40703 + 4.16910i) q^{77} +(-0.710611 + 1.23082i) q^{78} +(3.52786 + 2.03681i) q^{79} -1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +9.77295i q^{82} +(-2.77834 - 4.81222i) q^{83} -1.95985 q^{84} -0.959847 q^{85} +(-1.92304 - 3.33080i) q^{86} +(-7.52012 - 4.34174i) q^{87} -2.45634i q^{88} +(2.26457 - 1.30745i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-2.41221 + 1.39269i) q^{91} +(-2.73082 - 1.57664i) q^{92} +(-6.06161 - 3.49967i) q^{93} +(11.7167 - 6.76466i) q^{94} +(2.28518 + 3.95806i) q^{95} +(0.866025 - 0.500000i) q^{96} -1.53772i q^{97} +(2.73577 + 1.57950i) q^{98} +(-1.22817 - 2.12726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) 1.00000i 0.408248i
\(7\) −0.979923 + 1.69728i −0.370376 + 0.641510i −0.989623 0.143686i \(-0.954105\pi\)
0.619247 + 0.785196i \(0.287438\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 0.316228
\(11\) 2.45634 0.740616 0.370308 0.928909i \(-0.379252\pi\)
0.370308 + 0.928909i \(0.379252\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 1.23082 + 0.710611i 0.341367 + 0.197088i 0.660876 0.750495i \(-0.270185\pi\)
−0.319510 + 0.947583i \(0.603518\pi\)
\(14\) 1.95985i 0.523791i
\(15\) −0.866025 + 0.500000i −0.223607 + 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.831252 + 0.479923i −0.201608 + 0.116399i −0.597405 0.801939i \(-0.703802\pi\)
0.395797 + 0.918338i \(0.370468\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) 3.95806 + 2.28518i 0.908040 + 0.524257i 0.879800 0.475344i \(-0.157676\pi\)
0.0282402 + 0.999601i \(0.491010\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) −0.979923 1.69728i −0.213837 0.370376i
\(22\) 2.12726 1.22817i 0.453533 0.261847i
\(23\) 3.15327i 0.657503i −0.944416 0.328752i \(-0.893372\pi\)
0.944416 0.328752i \(-0.106628\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 1.42122 0.278725
\(27\) 1.00000 0.192450
\(28\) 0.979923 + 1.69728i 0.185188 + 0.320755i
\(29\) 8.68349i 1.61248i 0.591586 + 0.806242i \(0.298502\pi\)
−0.591586 + 0.806242i \(0.701498\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 6.99935i 1.25712i 0.777761 + 0.628560i \(0.216355\pi\)
−0.777761 + 0.628560i \(0.783645\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −1.22817 + 2.12726i −0.213797 + 0.370308i
\(34\) −0.479923 + 0.831252i −0.0823062 + 0.142558i
\(35\) −1.69728 + 0.979923i −0.286892 + 0.165637i
\(36\) −1.00000 −0.166667
\(37\) 5.73867 2.01686i 0.943431 0.331570i
\(38\) 4.57037 0.741412
\(39\) −1.23082 + 0.710611i −0.197088 + 0.113789i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) −4.88647 + 8.46362i −0.763139 + 1.32180i 0.178086 + 0.984015i \(0.443009\pi\)
−0.941225 + 0.337780i \(0.890324\pi\)
\(42\) −1.69728 0.979923i −0.261896 0.151205i
\(43\) 3.84608i 0.586521i −0.956033 0.293261i \(-0.905260\pi\)
0.956033 0.293261i \(-0.0947403\pi\)
\(44\) 1.22817 2.12726i 0.185154 0.320696i
\(45\) 1.00000i 0.149071i
\(46\) −1.57664 2.73082i −0.232462 0.402637i
\(47\) 13.5293 1.97345 0.986726 0.162391i \(-0.0519207\pi\)
0.986726 + 0.162391i \(0.0519207\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.57950 + 2.73577i 0.225643 + 0.390825i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 0.959847i 0.134405i
\(52\) 1.23082 0.710611i 0.170683 0.0985441i
\(53\) −5.33799 9.24568i −0.733230 1.26999i −0.955496 0.295005i \(-0.904679\pi\)
0.222266 0.974986i \(-0.428655\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 2.12726 + 1.22817i 0.286839 + 0.165607i
\(56\) 1.69728 + 0.979923i 0.226808 + 0.130948i
\(57\) −3.95806 + 2.28518i −0.524257 + 0.302680i
\(58\) 4.34174 + 7.52012i 0.570099 + 0.987440i
\(59\) 6.41533 3.70389i 0.835205 0.482206i −0.0204265 0.999791i \(-0.506502\pi\)
0.855631 + 0.517586i \(0.173169\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −7.96035 4.59591i −1.01922 0.588446i −0.105340 0.994436i \(-0.533593\pi\)
−0.913877 + 0.405991i \(0.866927\pi\)
\(62\) 3.49967 + 6.06161i 0.444459 + 0.769826i
\(63\) 1.95985 0.246917
\(64\) −1.00000 −0.125000
\(65\) 0.710611 + 1.23082i 0.0881405 + 0.152664i
\(66\) 2.45634i 0.302355i
\(67\) −4.23409 + 7.33365i −0.517276 + 0.895948i 0.482523 + 0.875883i \(0.339721\pi\)
−0.999799 + 0.0200647i \(0.993613\pi\)
\(68\) 0.959847i 0.116399i
\(69\) 2.73082 + 1.57664i 0.328752 + 0.189805i
\(70\) −0.979923 + 1.69728i −0.117123 + 0.202863i
\(71\) −1.35088 + 2.33979i −0.160319 + 0.277681i −0.934983 0.354692i \(-0.884586\pi\)
0.774664 + 0.632373i \(0.217919\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) −3.05026 −0.357006 −0.178503 0.983939i \(-0.557125\pi\)
−0.178503 + 0.983939i \(0.557125\pi\)
\(74\) 3.96140 4.61598i 0.460503 0.536597i
\(75\) −1.00000 −0.115470
\(76\) 3.95806 2.28518i 0.454020 0.262129i
\(77\) −2.40703 + 4.16910i −0.274306 + 0.475113i
\(78\) −0.710611 + 1.23082i −0.0804609 + 0.139362i
\(79\) 3.52786 + 2.03681i 0.396915 + 0.229159i 0.685152 0.728400i \(-0.259736\pi\)
−0.288237 + 0.957559i \(0.593069\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 9.77295i 1.07924i
\(83\) −2.77834 4.81222i −0.304962 0.528210i 0.672291 0.740287i \(-0.265311\pi\)
−0.977253 + 0.212077i \(0.931977\pi\)
\(84\) −1.95985 −0.213837
\(85\) −0.959847 −0.104110
\(86\) −1.92304 3.33080i −0.207367 0.359169i
\(87\) −7.52012 4.34174i −0.806242 0.465484i
\(88\) 2.45634i 0.261847i
\(89\) 2.26457 1.30745i 0.240044 0.138590i −0.375153 0.926963i \(-0.622410\pi\)
0.615197 + 0.788373i \(0.289076\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) −2.41221 + 1.39269i −0.252868 + 0.145994i
\(92\) −2.73082 1.57664i −0.284707 0.164376i
\(93\) −6.06161 3.49967i −0.628560 0.362899i
\(94\) 11.7167 6.76466i 1.20849 0.697721i
\(95\) 2.28518 + 3.95806i 0.234455 + 0.406088i
\(96\) 0.866025 0.500000i 0.0883883 0.0510310i
\(97\) 1.53772i 0.156132i −0.996948 0.0780659i \(-0.975126\pi\)
0.996948 0.0780659i \(-0.0248744\pi\)
\(98\) 2.73577 + 1.57950i 0.276355 + 0.159554i
\(99\) −1.22817 2.12726i −0.123436 0.213797i
\(100\) 1.00000 0.100000
\(101\) 5.16988 0.514422 0.257211 0.966355i \(-0.417196\pi\)
0.257211 + 0.966355i \(0.417196\pi\)
\(102\) −0.479923 0.831252i −0.0475195 0.0823062i
\(103\) 10.6296i 1.04737i −0.851912 0.523685i \(-0.824557\pi\)
0.851912 0.523685i \(-0.175443\pi\)
\(104\) 0.710611 1.23082i 0.0696812 0.120691i
\(105\) 1.95985i 0.191261i
\(106\) −9.24568 5.33799i −0.898020 0.518472i
\(107\) 4.87448 8.44284i 0.471234 0.816201i −0.528225 0.849105i \(-0.677142\pi\)
0.999459 + 0.0329039i \(0.0104755\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −12.8257 + 7.40492i −1.22848 + 0.709263i −0.966712 0.255868i \(-0.917639\pi\)
−0.261767 + 0.965131i \(0.584305\pi\)
\(110\) 2.45634 0.234203
\(111\) −1.12268 + 5.97826i −0.106560 + 0.567431i
\(112\) 1.95985 0.185188
\(113\) 15.2963 8.83130i 1.43895 0.830779i 0.441174 0.897422i \(-0.354562\pi\)
0.997777 + 0.0666430i \(0.0212289\pi\)
\(114\) −2.28518 + 3.95806i −0.214027 + 0.370706i
\(115\) 1.57664 2.73082i 0.147022 0.254650i
\(116\) 7.52012 + 4.34174i 0.698226 + 0.403121i
\(117\) 1.42122i 0.131392i
\(118\) 3.70389 6.41533i 0.340971 0.590579i
\(119\) 1.88115i 0.172445i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) −4.96637 −0.451489
\(122\) −9.19181 −0.832188
\(123\) −4.88647 8.46362i −0.440598 0.763139i
\(124\) 6.06161 + 3.49967i 0.544349 + 0.314280i
\(125\) 1.00000i 0.0894427i
\(126\) 1.69728 0.979923i 0.151205 0.0872985i
\(127\) 1.59045 + 2.75473i 0.141129 + 0.244443i 0.927922 0.372774i \(-0.121593\pi\)
−0.786793 + 0.617217i \(0.788260\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 3.33080 + 1.92304i 0.293261 + 0.169314i
\(130\) 1.23082 + 0.710611i 0.107950 + 0.0623247i
\(131\) 16.7556 9.67385i 1.46394 0.845208i 0.464753 0.885440i \(-0.346143\pi\)
0.999190 + 0.0402323i \(0.0128098\pi\)
\(132\) 1.22817 + 2.12726i 0.106899 + 0.185154i
\(133\) −7.75718 + 4.47861i −0.672633 + 0.388345i
\(134\) 8.46817i 0.731539i
\(135\) 0.866025 + 0.500000i 0.0745356 + 0.0430331i
\(136\) 0.479923 + 0.831252i 0.0411531 + 0.0712792i
\(137\) −12.5602 −1.07309 −0.536543 0.843873i \(-0.680270\pi\)
−0.536543 + 0.843873i \(0.680270\pi\)
\(138\) 3.15327 0.268424
\(139\) −6.81393 11.8021i −0.577950 1.00104i −0.995714 0.0924830i \(-0.970520\pi\)
0.417764 0.908555i \(-0.362814\pi\)
\(140\) 1.95985i 0.165637i
\(141\) −6.76466 + 11.7167i −0.569687 + 0.986726i
\(142\) 2.70175i 0.226726i
\(143\) 3.02331 + 1.74551i 0.252822 + 0.145967i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −4.34174 + 7.52012i −0.360562 + 0.624512i
\(146\) −2.64160 + 1.52513i −0.218621 + 0.126221i
\(147\) −3.15900 −0.260550
\(148\) 1.12268 5.97826i 0.0922838 0.491410i
\(149\) −13.4425 −1.10125 −0.550625 0.834753i \(-0.685610\pi\)
−0.550625 + 0.834753i \(0.685610\pi\)
\(150\) −0.866025 + 0.500000i −0.0707107 + 0.0408248i
\(151\) 5.96442 10.3307i 0.485378 0.840699i −0.514481 0.857502i \(-0.672015\pi\)
0.999859 + 0.0168028i \(0.00534874\pi\)
\(152\) 2.28518 3.95806i 0.185353 0.321041i
\(153\) 0.831252 + 0.479923i 0.0672027 + 0.0387995i
\(154\) 4.81406i 0.387928i
\(155\) −3.49967 + 6.06161i −0.281101 + 0.486881i
\(156\) 1.42122i 0.113789i
\(157\) 11.8965 + 20.6054i 0.949445 + 1.64449i 0.746596 + 0.665277i \(0.231687\pi\)
0.202849 + 0.979210i \(0.434980\pi\)
\(158\) 4.07362 0.324080
\(159\) 10.6760 0.846661
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 5.35198 + 3.08997i 0.421795 + 0.243523i
\(162\) 1.00000i 0.0785674i
\(163\) −9.71043 + 5.60632i −0.760580 + 0.439121i −0.829504 0.558501i \(-0.811377\pi\)
0.0689241 + 0.997622i \(0.478043\pi\)
\(164\) 4.88647 + 8.46362i 0.381569 + 0.660898i
\(165\) −2.12726 + 1.22817i −0.165607 + 0.0956131i
\(166\) −4.81222 2.77834i −0.373501 0.215641i
\(167\) −9.73668 5.62147i −0.753447 0.435003i 0.0734911 0.997296i \(-0.476586\pi\)
−0.826938 + 0.562293i \(0.809919\pi\)
\(168\) −1.69728 + 0.979923i −0.130948 + 0.0756027i
\(169\) −5.49006 9.50907i −0.422313 0.731467i
\(170\) −0.831252 + 0.479923i −0.0637541 + 0.0368084i
\(171\) 4.57037i 0.349505i
\(172\) −3.33080 1.92304i −0.253971 0.146630i
\(173\) −9.08041 15.7277i −0.690371 1.19576i −0.971716 0.236151i \(-0.924114\pi\)
0.281346 0.959607i \(-0.409219\pi\)
\(174\) −8.68349 −0.658294
\(175\) −1.95985 −0.148150
\(176\) −1.22817 2.12726i −0.0925770 0.160348i
\(177\) 7.40779i 0.556803i
\(178\) 1.30745 2.26457i 0.0979977 0.169737i
\(179\) 19.5613i 1.46208i −0.682336 0.731039i \(-0.739036\pi\)
0.682336 0.731039i \(-0.260964\pi\)
\(180\) −0.866025 0.500000i −0.0645497 0.0372678i
\(181\) −2.38223 + 4.12613i −0.177069 + 0.306693i −0.940875 0.338753i \(-0.889995\pi\)
0.763806 + 0.645446i \(0.223328\pi\)
\(182\) −1.39269 + 2.41221i −0.103233 + 0.178805i
\(183\) 7.96035 4.59591i 0.588446 0.339739i
\(184\) −3.15327 −0.232462
\(185\) 5.97826 + 1.12268i 0.439530 + 0.0825412i
\(186\) −6.99935 −0.513217
\(187\) −2.04184 + 1.17886i −0.149314 + 0.0862066i
\(188\) 6.76466 11.7167i 0.493363 0.854530i
\(189\) −0.979923 + 1.69728i −0.0712789 + 0.123459i
\(190\) 3.95806 + 2.28518i 0.287148 + 0.165785i
\(191\) 2.01489i 0.145792i −0.997340 0.0728960i \(-0.976776\pi\)
0.997340 0.0728960i \(-0.0232241\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 10.7992i 0.777341i −0.921377 0.388671i \(-0.872934\pi\)
0.921377 0.388671i \(-0.127066\pi\)
\(194\) −0.768860 1.33170i −0.0552009 0.0956108i
\(195\) −1.42122 −0.101776
\(196\) 3.15900 0.225643
\(197\) −7.10275 12.3023i −0.506050 0.876505i −0.999975 0.00700028i \(-0.997772\pi\)
0.493925 0.869504i \(-0.335562\pi\)
\(198\) −2.12726 1.22817i −0.151178 0.0872824i
\(199\) 24.0509i 1.70492i 0.522792 + 0.852460i \(0.324891\pi\)
−0.522792 + 0.852460i \(0.675109\pi\)
\(200\) 0.866025 0.500000i 0.0612372 0.0353553i
\(201\) −4.23409 7.33365i −0.298649 0.517276i
\(202\) 4.47725 2.58494i 0.315018 0.181876i
\(203\) −14.7383 8.50915i −1.03443 0.597226i
\(204\) −0.831252 0.479923i −0.0581993 0.0336014i
\(205\) −8.46362 + 4.88647i −0.591125 + 0.341286i
\(206\) −5.31482 9.20554i −0.370301 0.641381i
\(207\) −2.73082 + 1.57664i −0.189805 + 0.109584i
\(208\) 1.42122i 0.0985441i
\(209\) 9.72235 + 5.61320i 0.672509 + 0.388273i
\(210\) −0.979923 1.69728i −0.0676211 0.117123i
\(211\) −8.79370 −0.605383 −0.302692 0.953089i \(-0.597885\pi\)
−0.302692 + 0.953089i \(0.597885\pi\)
\(212\) −10.6760 −0.733230
\(213\) −1.35088 2.33979i −0.0925605 0.160319i
\(214\) 9.74896i 0.666425i
\(215\) 1.92304 3.33080i 0.131150 0.227159i
\(216\) 1.00000i 0.0680414i
\(217\) −11.8798 6.85883i −0.806456 0.465607i
\(218\) −7.40492 + 12.8257i −0.501524 + 0.868666i
\(219\) 1.52513 2.64160i 0.103059 0.178503i
\(220\) 2.12726 1.22817i 0.143420 0.0828033i
\(221\) −1.36416 −0.0917631
\(222\) 2.01686 + 5.73867i 0.135363 + 0.385154i
\(223\) −13.3323 −0.892794 −0.446397 0.894835i \(-0.647293\pi\)
−0.446397 + 0.894835i \(0.647293\pi\)
\(224\) 1.69728 0.979923i 0.113404 0.0654739i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 8.83130 15.2963i 0.587449 1.01749i
\(227\) −0.418906 0.241856i −0.0278038 0.0160525i 0.486034 0.873940i \(-0.338443\pi\)
−0.513837 + 0.857888i \(0.671777\pi\)
\(228\) 4.57037i 0.302680i
\(229\) −5.29548 + 9.17204i −0.349935 + 0.606106i −0.986238 0.165334i \(-0.947130\pi\)
0.636302 + 0.771440i \(0.280463\pi\)
\(230\) 3.15327i 0.207921i
\(231\) −2.40703 4.16910i −0.158371 0.274306i
\(232\) 8.68349 0.570099
\(233\) 1.71544 0.112382 0.0561912 0.998420i \(-0.482104\pi\)
0.0561912 + 0.998420i \(0.482104\pi\)
\(234\) −0.710611 1.23082i −0.0464541 0.0804609i
\(235\) 11.7167 + 6.76466i 0.764315 + 0.441277i
\(236\) 7.40779i 0.482206i
\(237\) −3.52786 + 2.03681i −0.229159 + 0.132305i
\(238\) −0.940576 1.62913i −0.0609685 0.105601i
\(239\) 0.476446 0.275076i 0.0308187 0.0177932i −0.484511 0.874785i \(-0.661003\pi\)
0.515330 + 0.856992i \(0.327669\pi\)
\(240\) 0.866025 + 0.500000i 0.0559017 + 0.0322749i
\(241\) −20.2817 11.7097i −1.30646 0.754286i −0.324957 0.945729i \(-0.605350\pi\)
−0.981504 + 0.191443i \(0.938683\pi\)
\(242\) −4.30101 + 2.48319i −0.276479 + 0.159625i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −7.96035 + 4.59591i −0.509609 + 0.294223i
\(245\) 3.15900i 0.201821i
\(246\) −8.46362 4.88647i −0.539621 0.311550i
\(247\) 3.24776 + 5.62528i 0.206650 + 0.357928i
\(248\) 6.99935 0.444459
\(249\) 5.55668 0.352140
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 0.166006i 0.0104782i 0.999986 + 0.00523910i \(0.00166767\pi\)
−0.999986 + 0.00523910i \(0.998332\pi\)
\(252\) 0.979923 1.69728i 0.0617294 0.106918i
\(253\) 7.74553i 0.486957i
\(254\) 2.75473 + 1.59045i 0.172847 + 0.0997934i
\(255\) 0.479923 0.831252i 0.0300540 0.0520550i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.31676 + 3.64698i −0.394029 + 0.227493i −0.683904 0.729572i \(-0.739719\pi\)
0.289876 + 0.957064i \(0.406386\pi\)
\(258\) 3.84608 0.239446
\(259\) −2.20028 + 11.7165i −0.136719 + 0.728026i
\(260\) 1.42122 0.0881405
\(261\) 7.52012 4.34174i 0.465484 0.268747i
\(262\) 9.67385 16.7556i 0.597652 1.03516i
\(263\) 9.39514 16.2729i 0.579329 1.00343i −0.416227 0.909261i \(-0.636648\pi\)
0.995556 0.0941669i \(-0.0300187\pi\)
\(264\) 2.12726 + 1.22817i 0.130924 + 0.0755888i
\(265\) 10.6760i 0.655821i
\(266\) −4.47861 + 7.75718i −0.274601 + 0.475623i
\(267\) 2.61490i 0.160030i
\(268\) 4.23409 + 7.33365i 0.258638 + 0.447974i
\(269\) 28.7529 1.75310 0.876548 0.481314i \(-0.159840\pi\)
0.876548 + 0.481314i \(0.159840\pi\)
\(270\) 1.00000 0.0608581
\(271\) −8.47039 14.6711i −0.514540 0.891209i −0.999858 0.0168711i \(-0.994630\pi\)
0.485318 0.874338i \(-0.338704\pi\)
\(272\) 0.831252 + 0.479923i 0.0504020 + 0.0290996i
\(273\) 2.78538i 0.168579i
\(274\) −10.8774 + 6.28008i −0.657129 + 0.379393i
\(275\) 1.22817 + 2.12726i 0.0740616 + 0.128278i
\(276\) 2.73082 1.57664i 0.164376 0.0949024i
\(277\) −3.99658 2.30743i −0.240131 0.138640i 0.375106 0.926982i \(-0.377606\pi\)
−0.615237 + 0.788342i \(0.710940\pi\)
\(278\) −11.8021 6.81393i −0.707841 0.408672i
\(279\) 6.06161 3.49967i 0.362899 0.209520i
\(280\) 0.979923 + 1.69728i 0.0585616 + 0.101432i
\(281\) 15.5544 8.98032i 0.927896 0.535721i 0.0417507 0.999128i \(-0.486706\pi\)
0.886146 + 0.463407i \(0.153373\pi\)
\(282\) 13.5293i 0.805659i
\(283\) −3.55264 2.05112i −0.211183 0.121926i 0.390678 0.920527i \(-0.372241\pi\)
−0.601861 + 0.798601i \(0.705574\pi\)
\(284\) 1.35088 + 2.33979i 0.0801597 + 0.138841i
\(285\) −4.57037 −0.270725
\(286\) 3.49101 0.206428
\(287\) −9.57674 16.5874i −0.565297 0.979123i
\(288\) 1.00000i 0.0589256i
\(289\) −8.03935 + 13.9246i −0.472903 + 0.819092i
\(290\) 8.68349i 0.509912i
\(291\) 1.33170 + 0.768860i 0.0780659 + 0.0450713i
\(292\) −1.52513 + 2.64160i −0.0892515 + 0.154588i
\(293\) 5.98605 10.3681i 0.349709 0.605713i −0.636489 0.771286i \(-0.719614\pi\)
0.986198 + 0.165573i \(0.0529472\pi\)
\(294\) −2.73577 + 1.57950i −0.159554 + 0.0921183i
\(295\) 7.40779 0.431298
\(296\) −2.01686 5.73867i −0.117228 0.333553i
\(297\) 2.45634 0.142532
\(298\) −11.6415 + 6.72123i −0.674375 + 0.389350i
\(299\) 2.24075 3.88110i 0.129586 0.224450i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) 6.52786 + 3.76886i 0.376259 + 0.217233i
\(302\) 11.9288i 0.686428i
\(303\) −2.58494 + 4.47725i −0.148501 + 0.257211i
\(304\) 4.57037i 0.262129i
\(305\) −4.59591 7.96035i −0.263161 0.455808i
\(306\) 0.959847 0.0548708
\(307\) 14.1554 0.807892 0.403946 0.914783i \(-0.367638\pi\)
0.403946 + 0.914783i \(0.367638\pi\)
\(308\) 2.40703 + 4.16910i 0.137153 + 0.237556i
\(309\) 9.20554 + 5.31482i 0.523685 + 0.302350i
\(310\) 6.99935i 0.397536i
\(311\) 2.16085 1.24756i 0.122530 0.0707429i −0.437482 0.899227i \(-0.644130\pi\)
0.560012 + 0.828484i \(0.310796\pi\)
\(312\) 0.710611 + 1.23082i 0.0402305 + 0.0696812i
\(313\) −9.00030 + 5.19632i −0.508727 + 0.293714i −0.732310 0.680971i \(-0.761558\pi\)
0.223583 + 0.974685i \(0.428225\pi\)
\(314\) 20.6054 + 11.8965i 1.16283 + 0.671359i
\(315\) 1.69728 + 0.979923i 0.0956307 + 0.0552124i
\(316\) 3.52786 2.03681i 0.198457 0.114579i
\(317\) 15.1018 + 26.1571i 0.848201 + 1.46913i 0.882812 + 0.469727i \(0.155647\pi\)
−0.0346109 + 0.999401i \(0.511019\pi\)
\(318\) 9.24568 5.33799i 0.518472 0.299340i
\(319\) 21.3296i 1.19423i
\(320\) −0.866025 0.500000i −0.0484123 0.0279508i
\(321\) 4.87448 + 8.44284i 0.272067 + 0.471234i
\(322\) 6.17993 0.344394
\(323\) −4.38685 −0.244091
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 1.42122i 0.0788353i
\(326\) −5.60632 + 9.71043i −0.310505 + 0.537811i
\(327\) 14.8098i 0.818986i
\(328\) 8.46362 + 4.88647i 0.467325 + 0.269810i
\(329\) −13.2577 + 22.9630i −0.730920 + 1.26599i
\(330\) −1.22817 + 2.12726i −0.0676086 + 0.117102i
\(331\) 11.8460 6.83928i 0.651114 0.375921i −0.137769 0.990464i \(-0.543993\pi\)
0.788883 + 0.614544i \(0.210660\pi\)
\(332\) −5.55668 −0.304962
\(333\) −4.61598 3.96140i −0.252954 0.217083i
\(334\) −11.2429 −0.615187
\(335\) −7.33365 + 4.23409i −0.400680 + 0.231333i
\(336\) −0.979923 + 1.69728i −0.0534592 + 0.0925941i
\(337\) −1.71735 + 2.97454i −0.0935501 + 0.162034i −0.909003 0.416791i \(-0.863155\pi\)
0.815452 + 0.578824i \(0.196488\pi\)
\(338\) −9.50907 5.49006i −0.517225 0.298620i
\(339\) 17.6626i 0.959301i
\(340\) −0.479923 + 0.831252i −0.0260275 + 0.0450810i
\(341\) 17.1928i 0.931043i
\(342\) −2.28518 3.95806i −0.123569 0.214027i
\(343\) −19.9101 −1.07504
\(344\) −3.84608 −0.207367
\(345\) 1.57664 + 2.73082i 0.0848833 + 0.147022i
\(346\) −15.7277 9.08041i −0.845528 0.488166i
\(347\) 12.1793i 0.653819i 0.945056 + 0.326909i \(0.106007\pi\)
−0.945056 + 0.326909i \(0.893993\pi\)
\(348\) −7.52012 + 4.34174i −0.403121 + 0.232742i
\(349\) −12.4499 21.5639i −0.666428 1.15429i −0.978896 0.204359i \(-0.934489\pi\)
0.312468 0.949928i \(-0.398844\pi\)
\(350\) −1.69728 + 0.979923i −0.0907233 + 0.0523791i
\(351\) 1.23082 + 0.710611i 0.0656961 + 0.0379296i
\(352\) −2.12726 1.22817i −0.113383 0.0654618i
\(353\) −20.3650 + 11.7577i −1.08392 + 0.625801i −0.931951 0.362584i \(-0.881895\pi\)
−0.151969 + 0.988385i \(0.548561\pi\)
\(354\) 3.70389 + 6.41533i 0.196860 + 0.340971i
\(355\) −2.33979 + 1.35088i −0.124183 + 0.0716971i
\(356\) 2.61490i 0.138590i
\(357\) 1.62913 + 0.940576i 0.0862225 + 0.0497806i
\(358\) −9.78063 16.9405i −0.516922 0.895336i
\(359\) 1.98677 0.104858 0.0524289 0.998625i \(-0.483304\pi\)
0.0524289 + 0.998625i \(0.483304\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 0.944137 + 1.63529i 0.0496914 + 0.0860681i
\(362\) 4.76445i 0.250414i
\(363\) 2.48319 4.30101i 0.130334 0.225744i
\(364\) 2.78538i 0.145994i
\(365\) −2.64160 1.52513i −0.138268 0.0798290i
\(366\) 4.59591 7.96035i 0.240232 0.416094i
\(367\) 8.86266 15.3506i 0.462627 0.801293i −0.536464 0.843923i \(-0.680240\pi\)
0.999091 + 0.0426298i \(0.0135736\pi\)
\(368\) −2.73082 + 1.57664i −0.142354 + 0.0821879i
\(369\) 9.77295 0.508759
\(370\) 5.73867 2.01686i 0.298339 0.104852i
\(371\) 20.9233 1.08628
\(372\) −6.06161 + 3.49967i −0.314280 + 0.181450i
\(373\) −7.30423 + 12.6513i −0.378199 + 0.655059i −0.990800 0.135333i \(-0.956790\pi\)
0.612602 + 0.790392i \(0.290123\pi\)
\(374\) −1.17886 + 2.04184i −0.0609572 + 0.105581i
\(375\) −0.866025 0.500000i −0.0447214 0.0258199i
\(376\) 13.5293i 0.697721i
\(377\) −6.17059 + 10.6878i −0.317801 + 0.550448i
\(378\) 1.95985i 0.100804i
\(379\) −0.713939 1.23658i −0.0366726 0.0635188i 0.847107 0.531423i \(-0.178343\pi\)
−0.883779 + 0.467904i \(0.845009\pi\)
\(380\) 4.57037 0.234455
\(381\) −3.18089 −0.162962
\(382\) −1.00744 1.74494i −0.0515453 0.0892790i
\(383\) 6.66805 + 3.84980i 0.340721 + 0.196716i 0.660591 0.750746i \(-0.270306\pi\)
−0.319870 + 0.947462i \(0.603639\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −4.16910 + 2.40703i −0.212477 + 0.122674i
\(386\) −5.39958 9.35235i −0.274832 0.476022i
\(387\) −3.33080 + 1.92304i −0.169314 + 0.0977535i
\(388\) −1.33170 0.768860i −0.0676070 0.0390329i
\(389\) −7.69776 4.44430i −0.390292 0.225335i 0.291995 0.956420i \(-0.405681\pi\)
−0.682287 + 0.731085i \(0.739014\pi\)
\(390\) −1.23082 + 0.710611i −0.0623247 + 0.0359832i
\(391\) 1.51333 + 2.62116i 0.0765324 + 0.132558i
\(392\) 2.73577 1.57950i 0.138177 0.0797768i
\(393\) 19.3477i 0.975962i
\(394\) −12.3023 7.10275i −0.619782 0.357832i
\(395\) 2.03681 + 3.52786i 0.102483 + 0.177506i
\(396\) −2.45634 −0.123436
\(397\) 24.6140 1.23534 0.617670 0.786437i \(-0.288077\pi\)
0.617670 + 0.786437i \(0.288077\pi\)
\(398\) 12.0254 + 20.8287i 0.602781 + 1.04405i
\(399\) 8.95722i 0.448422i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 4.32734i 0.216097i 0.994146 + 0.108049i \(0.0344602\pi\)
−0.994146 + 0.108049i \(0.965540\pi\)
\(402\) −7.33365 4.23409i −0.365769 0.211177i
\(403\) −4.97382 + 8.61491i −0.247764 + 0.429139i
\(404\) 2.58494 4.47725i 0.128606 0.222751i
\(405\) −0.866025 + 0.500000i −0.0430331 + 0.0248452i
\(406\) −17.0183 −0.844604
\(407\) 14.0961 4.95410i 0.698720 0.245566i
\(408\) −0.959847 −0.0475195
\(409\) 25.9709 14.9943i 1.28418 0.741422i 0.306571 0.951848i \(-0.400818\pi\)
0.977610 + 0.210426i \(0.0674850\pi\)
\(410\) −4.88647 + 8.46362i −0.241326 + 0.417988i
\(411\) 6.28008 10.8774i 0.309773 0.536543i
\(412\) −9.20554 5.31482i −0.453525 0.261843i
\(413\) 14.5181i 0.714390i
\(414\) −1.57664 + 2.73082i −0.0774875 + 0.134212i
\(415\) 5.55668i 0.272767i
\(416\) −0.710611 1.23082i −0.0348406 0.0603457i
\(417\) 13.6279 0.667359
\(418\) 11.2264 0.549101
\(419\) 18.9838 + 32.8809i 0.927420 + 1.60634i 0.787622 + 0.616159i \(0.211312\pi\)
0.139798 + 0.990180i \(0.455355\pi\)
\(420\) −1.69728 0.979923i −0.0828186 0.0478154i
\(421\) 28.8277i 1.40498i 0.711695 + 0.702488i \(0.247928\pi\)
−0.711695 + 0.702488i \(0.752072\pi\)
\(422\) −7.61557 + 4.39685i −0.370720 + 0.214035i
\(423\) −6.76466 11.7167i −0.328909 0.569687i
\(424\) −9.24568 + 5.33799i −0.449010 + 0.259236i
\(425\) −0.831252 0.479923i −0.0403216 0.0232797i
\(426\) −2.33979 1.35088i −0.113363 0.0654502i
\(427\) 15.6011 9.00727i 0.754988 0.435893i
\(428\) −4.87448 8.44284i −0.235617 0.408100i
\(429\) −3.02331 + 1.74551i −0.145967 + 0.0842738i
\(430\) 3.84608i 0.185474i
\(431\) 12.0063 + 6.93184i 0.578323 + 0.333895i 0.760467 0.649377i \(-0.224970\pi\)
−0.182144 + 0.983272i \(0.558304\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 1.13995 0.0547826 0.0273913 0.999625i \(-0.491280\pi\)
0.0273913 + 0.999625i \(0.491280\pi\)
\(434\) −13.7177 −0.658468
\(435\) −4.34174 7.52012i −0.208171 0.360562i
\(436\) 14.8098i 0.709263i
\(437\) 7.20581 12.4808i 0.344701 0.597039i
\(438\) 3.05026i 0.145747i
\(439\) 23.2357 + 13.4152i 1.10898 + 0.640271i 0.938565 0.345101i \(-0.112155\pi\)
0.170416 + 0.985372i \(0.445489\pi\)
\(440\) 1.22817 2.12726i 0.0585508 0.101413i
\(441\) 1.57950 2.73577i 0.0752143 0.130275i
\(442\) −1.18139 + 0.682078i −0.0561932 + 0.0324431i
\(443\) 20.6441 0.980830 0.490415 0.871489i \(-0.336845\pi\)
0.490415 + 0.871489i \(0.336845\pi\)
\(444\) 4.61598 + 3.96140i 0.219065 + 0.188000i
\(445\) 2.61490 0.123958
\(446\) −11.5461 + 6.66613i −0.546722 + 0.315650i
\(447\) 6.72123 11.6415i 0.317903 0.550625i
\(448\) 0.979923 1.69728i 0.0462970 0.0801888i
\(449\) −8.94501 5.16440i −0.422141 0.243723i 0.273852 0.961772i \(-0.411702\pi\)
−0.695993 + 0.718049i \(0.745036\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −12.0029 + 20.7896i −0.565193 + 0.978942i
\(452\) 17.6626i 0.830779i
\(453\) 5.96442 + 10.3307i 0.280233 + 0.485378i
\(454\) −0.483711 −0.0227017
\(455\) −2.78538 −0.130581
\(456\) 2.28518 + 3.95806i 0.107014 + 0.185353i
\(457\) −12.4941 7.21346i −0.584448 0.337431i 0.178451 0.983949i \(-0.442891\pi\)
−0.762899 + 0.646518i \(0.776225\pi\)
\(458\) 10.5910i 0.494883i
\(459\) −0.831252 + 0.479923i −0.0387995 + 0.0224009i
\(460\) −1.57664 2.73082i −0.0735111 0.127325i
\(461\) 22.3966 12.9307i 1.04311 0.602241i 0.122399 0.992481i \(-0.460941\pi\)
0.920713 + 0.390240i \(0.127608\pi\)
\(462\) −4.16910 2.40703i −0.193964 0.111985i
\(463\) −14.2261 8.21342i −0.661141 0.381710i 0.131571 0.991307i \(-0.457998\pi\)
−0.792712 + 0.609597i \(0.791331\pi\)
\(464\) 7.52012 4.34174i 0.349113 0.201560i
\(465\) −3.49967 6.06161i −0.162294 0.281101i
\(466\) 1.48562 0.857721i 0.0688199 0.0397332i
\(467\) 36.9384i 1.70931i −0.519200 0.854653i \(-0.673770\pi\)
0.519200 0.854653i \(-0.326230\pi\)
\(468\) −1.23082 0.710611i −0.0568945 0.0328480i
\(469\) −8.29816 14.3728i −0.383173 0.663676i
\(470\) 13.5293 0.624061
\(471\) −23.7930 −1.09632
\(472\) −3.70389 6.41533i −0.170486 0.295290i
\(473\) 9.44729i 0.434387i
\(474\) −2.03681 + 3.52786i −0.0935537 + 0.162040i
\(475\) 4.57037i 0.209703i
\(476\) −1.62913 0.940576i −0.0746709 0.0431112i
\(477\) −5.33799 + 9.24568i −0.244410 + 0.423331i
\(478\) 0.275076 0.476446i 0.0125817 0.0217921i
\(479\) −16.4828 + 9.51634i −0.753117 + 0.434813i −0.826819 0.562468i \(-0.809852\pi\)
0.0737018 + 0.997280i \(0.476519\pi\)
\(480\) 1.00000 0.0456435
\(481\) 8.49644 + 1.59558i 0.387404 + 0.0727522i
\(482\) −23.4193 −1.06672
\(483\) −5.35198 + 3.08997i −0.243523 + 0.140598i
\(484\) −2.48319 + 4.30101i −0.112872 + 0.195500i
\(485\) 0.768860 1.33170i 0.0349121 0.0604696i
\(486\) −0.866025 0.500000i −0.0392837 0.0226805i
\(487\) 9.27395i 0.420243i 0.977675 + 0.210121i \(0.0673859\pi\)
−0.977675 + 0.210121i \(0.932614\pi\)
\(488\) −4.59591 + 7.96035i −0.208047 + 0.360348i
\(489\) 11.2126i 0.507053i
\(490\) 1.57950 + 2.73577i 0.0713546 + 0.123590i
\(491\) 30.1195 1.35928 0.679638 0.733548i \(-0.262137\pi\)
0.679638 + 0.733548i \(0.262137\pi\)
\(492\) −9.77295 −0.440598
\(493\) −4.16741 7.21817i −0.187691 0.325090i
\(494\) 5.62528 + 3.24776i 0.253093 + 0.146123i
\(495\) 2.45634i 0.110404i
\(496\) 6.06161 3.49967i 0.272175 0.157140i
\(497\) −2.64751 4.58562i −0.118757 0.205693i
\(498\) 4.81222 2.77834i 0.215641 0.124500i
\(499\) −9.72002 5.61186i −0.435128 0.251221i 0.266401 0.963862i \(-0.414166\pi\)
−0.701529 + 0.712641i \(0.747499\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) 9.73668 5.62147i 0.435003 0.251149i
\(502\) 0.0830030 + 0.143765i 0.00370460 + 0.00641656i
\(503\) −10.2927 + 5.94248i −0.458928 + 0.264962i −0.711593 0.702592i \(-0.752026\pi\)
0.252666 + 0.967554i \(0.418693\pi\)
\(504\) 1.95985i 0.0872985i
\(505\) 4.47725 + 2.58494i 0.199235 + 0.115028i
\(506\) −3.87276 6.70782i −0.172165 0.298199i
\(507\) 10.9801 0.487644
\(508\) 3.18089 0.141129
\(509\) 11.5878 + 20.0707i 0.513621 + 0.889618i 0.999875 + 0.0158008i \(0.00502976\pi\)
−0.486254 + 0.873818i \(0.661637\pi\)
\(510\) 0.959847i 0.0425027i
\(511\) 2.98902 5.17714i 0.132227 0.229023i
\(512\) 1.00000i 0.0441942i
\(513\) 3.95806 + 2.28518i 0.174752 + 0.100893i
\(514\) −3.64698 + 6.31676i −0.160862 + 0.278620i
\(515\) 5.31482 9.20554i 0.234199 0.405645i
\(516\) 3.33080 1.92304i 0.146630 0.0846570i
\(517\) 33.2326 1.46157
\(518\) 3.95274 + 11.2469i 0.173673 + 0.494161i
\(519\) 18.1608 0.797172
\(520\) 1.23082 0.710611i 0.0539748 0.0311624i
\(521\) 11.8446 20.5154i 0.518920 0.898795i −0.480839 0.876809i \(-0.659668\pi\)
0.999758 0.0219860i \(-0.00699891\pi\)
\(522\) 4.34174 7.52012i 0.190033 0.329147i
\(523\) 10.7377 + 6.19940i 0.469525 + 0.271081i 0.716041 0.698058i \(-0.245952\pi\)
−0.246516 + 0.969139i \(0.579286\pi\)
\(524\) 19.3477i 0.845208i
\(525\) 0.979923 1.69728i 0.0427674 0.0740752i
\(526\) 18.7903i 0.819295i
\(527\) −3.35915 5.81822i −0.146327 0.253446i
\(528\) 2.45634 0.106899
\(529\) 13.0569 0.567690
\(530\) −5.33799 9.24568i −0.231868 0.401607i
\(531\) −6.41533 3.70389i −0.278402 0.160735i
\(532\) 8.95722i 0.388345i
\(533\) −12.0287 + 6.94477i −0.521020 + 0.300811i
\(534\) 1.30745 + 2.26457i 0.0565790 + 0.0979977i
\(535\) 8.44284 4.87448i 0.365016 0.210742i
\(536\) 7.33365 + 4.23409i 0.316766 + 0.182885i
\(537\) 16.9405 + 9.78063i 0.731039 + 0.422065i
\(538\) 24.9008 14.3765i 1.07355 0.619813i
\(539\) 3.87980 + 6.72000i 0.167115 + 0.289451i
\(540\) 0.866025 0.500000i 0.0372678 0.0215166i
\(541\) 13.1696i 0.566207i −0.959089 0.283103i \(-0.908636\pi\)
0.959089 0.283103i \(-0.0913639\pi\)
\(542\) −14.6711 8.47039i −0.630180 0.363834i
\(543\) −2.38223 4.12613i −0.102231 0.177069i
\(544\) 0.959847 0.0411531
\(545\) −14.8098 −0.634384
\(546\) −1.39269 2.41221i −0.0596016 0.103233i
\(547\) 15.3546i 0.656514i 0.944589 + 0.328257i \(0.106461\pi\)
−0.944589 + 0.328257i \(0.893539\pi\)
\(548\) −6.28008 + 10.8774i −0.268272 + 0.464660i
\(549\) 9.19181i 0.392297i
\(550\) 2.12726 + 1.22817i 0.0907065 + 0.0523694i
\(551\) −19.8434 + 34.3697i −0.845356 + 1.46420i
\(552\) 1.57664 2.73082i 0.0671061 0.116231i
\(553\) −6.91406 + 3.99183i −0.294016 + 0.169750i
\(554\) −4.61485 −0.196066
\(555\) −3.96140 + 4.61598i −0.168152 + 0.195938i
\(556\) −13.6279 −0.577950
\(557\) −27.4914 + 15.8721i −1.16485 + 0.672524i −0.952461 0.304662i \(-0.901457\pi\)
−0.212386 + 0.977186i \(0.568123\pi\)
\(558\) 3.49967 6.06161i 0.148153 0.256609i
\(559\) 2.73307 4.73381i 0.115596 0.200219i
\(560\) 1.69728 + 0.979923i 0.0717230 + 0.0414093i
\(561\) 2.35771i 0.0995428i
\(562\) 8.98032 15.5544i 0.378812 0.656122i
\(563\) 30.6776i 1.29291i −0.762953 0.646454i \(-0.776251\pi\)
0.762953 0.646454i \(-0.223749\pi\)
\(564\) 6.76466 + 11.7167i 0.284843 + 0.493363i
\(565\) 17.6626 0.743071
\(566\) −4.10224 −0.172430
\(567\) −0.979923 1.69728i −0.0411529 0.0712789i
\(568\) 2.33979 + 1.35088i 0.0981752 + 0.0566815i
\(569\) 7.51849i 0.315192i 0.987504 + 0.157596i \(0.0503743\pi\)
−0.987504 + 0.157596i \(0.949626\pi\)
\(570\) −3.95806 + 2.28518i −0.165785 + 0.0957158i
\(571\) 4.76931 + 8.26068i 0.199589 + 0.345699i 0.948395 0.317090i \(-0.102706\pi\)
−0.748806 + 0.662789i \(0.769373\pi\)
\(572\) 3.02331 1.74551i 0.126411 0.0729833i
\(573\) 1.74494 + 1.00744i 0.0728960 + 0.0420865i
\(574\) −16.5874 9.57674i −0.692345 0.399725i
\(575\) 2.73082 1.57664i 0.113883 0.0657503i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 3.03587 1.75276i 0.126385 0.0729685i −0.435475 0.900201i \(-0.643419\pi\)
0.561860 + 0.827233i \(0.310086\pi\)
\(578\) 16.0787i 0.668786i
\(579\) 9.35235 + 5.39958i 0.388671 + 0.224399i
\(580\) 4.34174 + 7.52012i 0.180281 + 0.312256i
\(581\) 10.8902 0.451803
\(582\) 1.53772 0.0637405
\(583\) −13.1120 22.7106i −0.543042 0.940576i
\(584\) 3.05026i 0.126221i
\(585\) 0.710611 1.23082i 0.0293802 0.0508879i
\(586\) 11.9721i 0.494563i
\(587\) −10.9435 6.31826i −0.451688 0.260782i 0.256855 0.966450i \(-0.417314\pi\)
−0.708543 + 0.705668i \(0.750647\pi\)
\(588\) −1.57950 + 2.73577i −0.0651375 + 0.112821i
\(589\) −15.9948 + 27.7038i −0.659054 + 1.14152i
\(590\) 6.41533 3.70389i 0.264115 0.152487i
\(591\) 14.2055 0.584336
\(592\) −4.61598 3.96140i −0.189716 0.162813i
\(593\) 4.99944 0.205302 0.102651 0.994717i \(-0.467267\pi\)
0.102651 + 0.994717i \(0.467267\pi\)
\(594\) 2.12726 1.22817i 0.0872824 0.0503925i
\(595\) 0.940576 1.62913i 0.0385599 0.0667876i
\(596\) −6.72123 + 11.6415i −0.275312 + 0.476855i
\(597\) −20.8287 12.0254i −0.852460 0.492168i
\(598\) 4.48150i 0.183262i
\(599\) 20.0086 34.6560i 0.817531 1.41601i −0.0899648 0.995945i \(-0.528675\pi\)
0.907496 0.420061i \(-0.137991\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) 11.3414 + 19.6439i 0.462625 + 0.801290i 0.999091 0.0426319i \(-0.0135743\pi\)
−0.536466 + 0.843922i \(0.680241\pi\)
\(602\) 7.53772 0.307215
\(603\) 8.46817 0.344851
\(604\) −5.96442 10.3307i −0.242689 0.420349i
\(605\) −4.30101 2.48319i −0.174861 0.100956i
\(606\) 5.16988i 0.210012i
\(607\) 28.8731 16.6699i 1.17192 0.676611i 0.217792 0.975995i \(-0.430114\pi\)
0.954133 + 0.299384i \(0.0967812\pi\)
\(608\) −2.28518 3.95806i −0.0926765 0.160520i
\(609\) 14.7383 8.50915i 0.597226 0.344808i
\(610\) −7.96035 4.59591i −0.322305 0.186083i
\(611\) 16.6521 + 9.61408i 0.673671 + 0.388944i
\(612\) 0.831252 0.479923i 0.0336014 0.0193998i
\(613\) −11.0511 19.1411i −0.446351 0.773102i 0.551795 0.833980i \(-0.313943\pi\)
−0.998145 + 0.0608781i \(0.980610\pi\)
\(614\) 12.2590 7.07771i 0.494731 0.285633i
\(615\) 9.77295i 0.394083i
\(616\) 4.16910 + 2.40703i 0.167978 + 0.0969820i
\(617\) 1.17946 + 2.04289i 0.0474833 + 0.0822436i 0.888790 0.458314i \(-0.151547\pi\)
−0.841307 + 0.540558i \(0.818213\pi\)
\(618\) 10.6296 0.427587
\(619\) −43.1657 −1.73497 −0.867487 0.497459i \(-0.834266\pi\)
−0.867487 + 0.497459i \(0.834266\pi\)
\(620\) 3.49967 + 6.06161i 0.140550 + 0.243440i
\(621\) 3.15327i 0.126537i
\(622\) 1.24756 2.16085i 0.0500228 0.0866420i
\(623\) 5.12481i 0.205321i
\(624\) 1.23082 + 0.710611i 0.0492720 + 0.0284472i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −5.19632 + 9.00030i −0.207687 + 0.359724i
\(627\) −9.72235 + 5.61320i −0.388273 + 0.224170i
\(628\) 23.7930 0.949445
\(629\) −3.80234 + 4.43064i −0.151609 + 0.176661i
\(630\) 1.95985 0.0780822
\(631\) −6.45035 + 3.72411i −0.256784 + 0.148255i −0.622867 0.782328i \(-0.714032\pi\)
0.366082 + 0.930582i \(0.380699\pi\)
\(632\) 2.03681 3.52786i 0.0810199 0.140331i
\(633\) 4.39685 7.61557i 0.174759 0.302692i
\(634\) 26.1571 + 15.1018i 1.03883 + 0.599769i
\(635\) 3.18089i 0.126230i
\(636\) 5.33799 9.24568i 0.211665 0.366615i
\(637\) 4.48964i 0.177886i
\(638\) 10.6648 + 18.4720i 0.422224 + 0.731314i
\(639\) 2.70175 0.106880
\(640\) −1.00000 −0.0395285
\(641\) −24.0317 41.6241i −0.949195 1.64405i −0.747125 0.664684i \(-0.768566\pi\)
−0.202071 0.979371i \(-0.564767\pi\)
\(642\) 8.44284 + 4.87448i 0.333212 + 0.192380i
\(643\) 12.3081i 0.485382i 0.970104 + 0.242691i \(0.0780301\pi\)
−0.970104 + 0.242691i \(0.921970\pi\)
\(644\) 5.35198 3.08997i 0.210898 0.121762i
\(645\) 1.92304 + 3.33080i 0.0757195 + 0.131150i
\(646\) −3.79913 + 2.19343i −0.149475 + 0.0862992i
\(647\) 10.6408 + 6.14347i 0.418333 + 0.241525i 0.694364 0.719624i \(-0.255686\pi\)
−0.276031 + 0.961149i \(0.589019\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 15.7583 9.09804i 0.618566 0.357129i
\(650\) 0.710611 + 1.23082i 0.0278725 + 0.0482765i
\(651\) 11.8798 6.85883i 0.465607 0.268819i
\(652\) 11.2126i 0.439121i
\(653\) 36.8075 + 21.2508i 1.44039 + 0.831610i 0.997875 0.0651515i \(-0.0207531\pi\)
0.442515 + 0.896761i \(0.354086\pi\)
\(654\) −7.40492 12.8257i −0.289555 0.501524i
\(655\) 19.3477 0.755977
\(656\) 9.77295 0.381569
\(657\) 1.52513 + 2.64160i 0.0595010 + 0.103059i
\(658\) 26.5154i 1.03368i
\(659\) −19.1518 + 33.1719i −0.746049 + 1.29219i 0.203655 + 0.979043i \(0.434718\pi\)
−0.949703 + 0.313151i \(0.898615\pi\)
\(660\) 2.45634i 0.0956131i
\(661\) 29.3666 + 16.9548i 1.14223 + 0.659467i 0.946982 0.321287i \(-0.104116\pi\)
0.195248 + 0.980754i \(0.437449\pi\)
\(662\) 6.83928 11.8460i 0.265816 0.460407i
\(663\) 0.682078 1.18139i 0.0264897 0.0458815i
\(664\) −4.81222 + 2.77834i −0.186751 + 0.107820i
\(665\) −8.95722 −0.347346
\(666\) −5.97826 1.12268i −0.231653 0.0435030i
\(667\) 27.3814 1.06021
\(668\) −9.73668 + 5.62147i −0.376723 + 0.217501i
\(669\) 6.66613 11.5461i 0.257727 0.446397i
\(670\) −4.23409 + 7.33365i −0.163577 + 0.283324i
\(671\) −19.5533 11.2891i −0.754849 0.435812i
\(672\) 1.95985i 0.0756027i
\(673\) −9.51980 + 16.4888i −0.366961 + 0.635596i −0.989089 0.147320i \(-0.952935\pi\)
0.622127 + 0.782916i \(0.286269\pi\)
\(674\) 3.43470i 0.132300i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −10.9801 −0.422313
\(677\) −15.8403 −0.608792 −0.304396 0.952546i \(-0.598455\pi\)
−0.304396 + 0.952546i \(0.598455\pi\)
\(678\) 8.83130 + 15.2963i 0.339164 + 0.587449i
\(679\) 2.60994 + 1.50685i 0.100160 + 0.0578275i
\(680\) 0.959847i 0.0368084i
\(681\) 0.418906 0.241856i 0.0160525 0.00926793i
\(682\) 8.59641 + 14.8894i 0.329173 + 0.570145i
\(683\) −39.2891 + 22.6836i −1.50336 + 0.867964i −0.503364 + 0.864074i \(0.667905\pi\)
−0.999992 + 0.00388931i \(0.998762\pi\)
\(684\) −3.95806 2.28518i −0.151340 0.0873762i
\(685\) −10.8774 6.28008i −0.415605 0.239949i
\(686\) −17.2426 + 9.95504i −0.658327 + 0.380085i
\(687\) −5.29548 9.17204i −0.202035 0.349935i
\(688\) −3.33080 + 1.92304i −0.126986 + 0.0733151i
\(689\) 15.1730i 0.578044i
\(690\) 2.73082 + 1.57664i 0.103960 + 0.0600215i
\(691\) −9.76278 16.9096i −0.371394 0.643273i 0.618387 0.785874i \(-0.287787\pi\)
−0.989780 + 0.142601i \(0.954453\pi\)
\(692\) −18.1608 −0.690371
\(693\) 4.81406 0.182871
\(694\) 6.08965 + 10.5476i 0.231160 + 0.400380i
\(695\) 13.6279i 0.516934i
\(696\) −4.34174 + 7.52012i −0.164573 + 0.285050i
\(697\) 9.38053i 0.355313i
\(698\) −21.5639 12.4499i −0.816205 0.471236i
\(699\) −0.857721 + 1.48562i −0.0324420 + 0.0561912i
\(700\) −0.979923 + 1.69728i −0.0370376 + 0.0641510i
\(701\) −43.6793 + 25.2183i −1.64974 + 0.952481i −0.672573 + 0.740031i \(0.734811\pi\)
−0.977172 + 0.212449i \(0.931856\pi\)
\(702\) 1.42122 0.0536406
\(703\) 27.3229 + 5.13107i 1.03050 + 0.193522i
\(704\) −2.45634 −0.0925770
\(705\) −11.7167 + 6.76466i −0.441277 + 0.254772i
\(706\) −11.7577 + 20.3650i −0.442508 + 0.766447i
\(707\) −5.06608 + 8.77472i −0.190530 + 0.330007i
\(708\) 6.41533 + 3.70389i 0.241103 + 0.139201i
\(709\) 0.774617i 0.0290913i −0.999894 0.0145457i \(-0.995370\pi\)
0.999894 0.0145457i \(-0.00463019\pi\)
\(710\) −1.35088 + 2.33979i −0.0506975 + 0.0878106i
\(711\) 4.07362i 0.152773i
\(712\) −1.30745 2.26457i −0.0489988 0.0848685i
\(713\) 22.0709 0.826560
\(714\) 1.88115 0.0704004
\(715\) 1.74551 + 3.02331i 0.0652782 + 0.113065i
\(716\) −16.9405 9.78063i −0.633098 0.365519i
\(717\) 0.550152i 0.0205458i
\(718\) 1.72060 0.993387i 0.0642121 0.0370729i
\(719\) −2.57835 4.46583i −0.0961561 0.166547i 0.813934 0.580957i \(-0.197321\pi\)
−0.910091 + 0.414410i \(0.863988\pi\)
\(720\) −0.866025 + 0.500000i −0.0322749 + 0.0186339i
\(721\) 18.0415 + 10.4162i 0.671899 + 0.387921i
\(722\) 1.63529 + 0.944137i 0.0608593 + 0.0351371i
\(723\) 20.2817 11.7097i 0.754286 0.435487i
\(724\) 2.38223 + 4.12613i 0.0885347 + 0.153347i
\(725\) −7.52012 + 4.34174i −0.279290 + 0.161248i
\(726\) 4.96637i 0.184319i
\(727\) 34.4957 + 19.9161i 1.27938 + 0.738648i 0.976734 0.214456i \(-0.0687979\pi\)
0.302642 + 0.953104i \(0.402131\pi\)
\(728\) 1.39269 + 2.41221i 0.0516165 + 0.0894024i
\(729\) 1.00000 0.0370370
\(730\) −3.05026 −0.112895
\(731\) 1.84582 + 3.19706i 0.0682702 + 0.118247i
\(732\) 9.19181i 0.339739i
\(733\) −2.65608 + 4.60046i −0.0981045 + 0.169922i −0.910900 0.412627i \(-0.864611\pi\)
0.812796 + 0.582549i \(0.197945\pi\)
\(734\) 17.7253i 0.654253i
\(735\) −2.73577 1.57950i −0.100911 0.0582607i
\(736\) −1.57664 + 2.73082i −0.0581156 + 0.100659i
\(737\) −10.4004 + 18.0140i −0.383103 + 0.663553i
\(738\) 8.46362 4.88647i 0.311550 0.179874i
\(739\) 1.35357 0.0497918 0.0248959 0.999690i \(-0.492075\pi\)
0.0248959 + 0.999690i \(0.492075\pi\)
\(740\) 3.96140 4.61598i 0.145624 0.169687i
\(741\) −6.49551 −0.238619
\(742\) 18.1201 10.4617i 0.665210 0.384059i
\(743\) 6.76254 11.7131i 0.248094 0.429711i −0.714903 0.699223i \(-0.753529\pi\)
0.962997 + 0.269513i \(0.0868626\pi\)
\(744\) −3.49967 + 6.06161i −0.128304 + 0.222230i
\(745\) −11.6415 6.72123i −0.426512 0.246247i
\(746\) 14.6085i 0.534854i
\(747\) −2.77834 + 4.81222i −0.101654 + 0.176070i
\(748\) 2.35771i 0.0862066i
\(749\) 9.55323 + 16.5467i 0.349067 + 0.604603i
\(750\) −1.00000 −0.0365148
\(751\) 46.7414 1.70562 0.852809 0.522223i \(-0.174897\pi\)
0.852809 + 0.522223i \(0.174897\pi\)
\(752\) −6.76466 11.7167i −0.246682 0.427265i
\(753\) −0.143765 0.0830030i −0.00523910 0.00302480i
\(754\) 12.3412i 0.449439i
\(755\) 10.3307 5.96442i 0.375972 0.217068i
\(756\) 0.979923 + 1.69728i 0.0356395 + 0.0617294i
\(757\) −26.4808 + 15.2887i −0.962460 + 0.555677i −0.896929 0.442174i \(-0.854207\pi\)
−0.0655310 + 0.997851i \(0.520874\pi\)
\(758\) −1.23658 0.713939i −0.0449146 0.0259314i
\(759\) 6.70782 + 3.87276i 0.243479 + 0.140572i
\(760\) 3.95806 2.28518i 0.143574 0.0828924i
\(761\) 3.30256 + 5.72021i 0.119718 + 0.207357i 0.919656 0.392725i \(-0.128468\pi\)
−0.799938 + 0.600083i \(0.795134\pi\)
\(762\) −2.75473 + 1.59045i −0.0997934 + 0.0576158i
\(763\) 29.0250i 1.05078i
\(764\) −1.74494 1.00744i −0.0631298 0.0364480i
\(765\) 0.479923 + 0.831252i 0.0173517 + 0.0300540i
\(766\) 7.69960 0.278198
\(767\) 10.5281 0.380148
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 11.8201i 0.426243i −0.977026 0.213122i \(-0.931637\pi\)
0.977026 0.213122i \(-0.0683630\pi\)
\(770\) −2.40703 + 4.16910i −0.0867433 + 0.150244i
\(771\) 7.29397i 0.262686i
\(772\) −9.35235 5.39958i −0.336599 0.194335i
\(773\) 12.8013 22.1725i 0.460430 0.797488i −0.538552 0.842592i \(-0.681029\pi\)
0.998982 + 0.0451041i \(0.0143620\pi\)
\(774\) −1.92304 + 3.33080i −0.0691222 + 0.119723i
\(775\) −6.06161 + 3.49967i −0.217740 + 0.125712i
\(776\) −1.53772 −0.0552009
\(777\) −9.04662 7.