Properties

Label 546.2.s.e.43.3
Level $546$
Weight $2$
Character 546.43
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
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.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.195105024.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 4 x^{5} - 20 x^{4} + 12 x^{3} + 45 x^{2} - 108 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.3
Root \(-1.58726 - 0.693255i\) of defining polynomial
Character \(\chi\) \(=\) 546.43
Dual form 546.2.s.e.127.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.52798 - 2.64654i) q^{10} +(-2.98127 - 1.72124i) q^{11} +1.00000 q^{12} +(3.25253 + 1.55596i) q^{13} +1.00000 q^{14} +(-2.64654 - 1.52798i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.41449 - 2.44997i) q^{17} -1.00000i q^{18} +(1.49425 - 0.862708i) q^{19} +(2.64654 - 1.52798i) q^{20} -1.00000i q^{21} +(-1.72124 - 2.98127i) q^{22} +(1.53130 - 2.65229i) q^{23} +(0.866025 + 0.500000i) q^{24} -4.33891 q^{25} +(2.03880 + 2.97377i) q^{26} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{28} +(-1.92531 + 3.33473i) q^{29} +(-1.52798 - 2.64654i) q^{30} -0.978370i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.98127 + 1.72124i) q^{33} -2.82898i q^{34} +(-1.52798 - 2.64654i) q^{35} +(0.500000 - 0.866025i) q^{36} +(4.58394 + 2.64654i) q^{37} +1.72542 q^{38} +(2.97377 - 2.03880i) q^{39} +3.05596 q^{40} +(8.62781 + 4.98127i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-1.51082 - 2.61681i) q^{43} -3.44247i q^{44} +(-2.64654 + 1.52798i) q^{45} +(2.65229 - 1.53130i) q^{46} +8.04447i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-3.75760 - 2.16945i) q^{50} -2.82898 q^{51} +(0.278764 + 3.59476i) q^{52} -8.33405 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-5.26003 + 9.11064i) q^{55} +(0.500000 + 0.866025i) q^{56} -1.72542i q^{57} +(-3.33473 + 1.92531i) q^{58} +(8.64080 - 4.98877i) q^{59} -3.05596i q^{60} +(5.77260 + 9.99843i) q^{61} +(0.489185 - 0.847293i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(4.75496 - 9.93962i) q^{65} -3.44247 q^{66} +(4.11410 + 2.37527i) q^{67} +(1.41449 - 2.44997i) q^{68} +(-1.53130 - 2.65229i) q^{69} -3.05596i q^{70} +(-3.17784 + 1.83473i) q^{71} +(0.866025 - 0.500000i) q^{72} +10.1119i q^{73} +(2.64654 + 4.58394i) q^{74} +(-2.16945 + 3.75760i) q^{75} +(1.49425 + 0.862708i) q^{76} -3.44247 q^{77} +(3.59476 - 0.278764i) q^{78} -4.49843 q^{79} +(2.64654 + 1.52798i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.98127 + 8.62781i) q^{82} +7.15869i q^{83} +(0.866025 - 0.500000i) q^{84} +(-7.48701 + 4.32263i) q^{85} -3.02163i q^{86} +(1.92531 + 3.33473i) q^{87} +(1.72124 - 2.98127i) q^{88} +(-6.84426 - 3.95154i) q^{89} -3.05596 q^{90} +(3.59476 - 0.278764i) q^{91} +3.06260 q^{92} +(-0.847293 - 0.489185i) q^{93} +(-4.02224 + 6.96672i) q^{94} +(-2.63640 - 4.56638i) q^{95} +1.00000i q^{96} +(-7.88016 + 4.54961i) q^{97} +(0.866025 - 0.500000i) q^{98} +3.44247i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + 6q^{10} + 6q^{11} + 8q^{12} + 12q^{13} + 8q^{14} + 6q^{15} - 4q^{16} + 2q^{17} - 12q^{19} - 6q^{20} - 4q^{22} + 8q^{23} - 24q^{25} + 6q^{26} - 8q^{27} + 2q^{29} - 6q^{30} + 6q^{33} - 6q^{35} + 4q^{36} + 18q^{37} - 4q^{38} + 12q^{40} + 12q^{41} + 4q^{42} - 8q^{43} + 6q^{45} + 18q^{46} + 4q^{48} + 4q^{49} + 12q^{50} + 4q^{51} + 12q^{52} - 12q^{53} - 22q^{55} + 4q^{56} - 24q^{58} + 18q^{59} - 8q^{61} + 8q^{62} - 8q^{64} + 46q^{65} - 8q^{66} + 18q^{67} - 2q^{68} - 8q^{69} + 6q^{71} - 6q^{74} - 12q^{75} - 12q^{76} - 8q^{77} + 6q^{78} - 4q^{79} - 6q^{80} - 4q^{81} + 10q^{82} - 54q^{85} - 2q^{87} + 4q^{88} - 18q^{89} - 12q^{90} + 6q^{91} + 16q^{92} + 30q^{93} - 2q^{94} - 50q^{95} - 54q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 3.05596i 1.36667i −0.730106 0.683334i \(-0.760529\pi\)
0.730106 0.683334i \(-0.239471\pi\)
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.52798 2.64654i 0.483190 0.836910i
\(11\) −2.98127 1.72124i −0.898886 0.518972i −0.0220475 0.999757i \(-0.507018\pi\)
−0.876839 + 0.480785i \(0.840352\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.25253 + 1.55596i 0.902091 + 0.431546i
\(14\) 1.00000 0.267261
\(15\) −2.64654 1.52798i −0.683334 0.394523i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.41449 2.44997i −0.343064 0.594205i 0.641936 0.766758i \(-0.278132\pi\)
−0.985000 + 0.172554i \(0.944798\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.49425 0.862708i 0.342805 0.197919i −0.318707 0.947853i \(-0.603248\pi\)
0.661512 + 0.749935i \(0.269915\pi\)
\(20\) 2.64654 1.52798i 0.591785 0.341667i
\(21\) 1.00000i 0.218218i
\(22\) −1.72124 2.98127i −0.366969 0.635608i
\(23\) 1.53130 2.65229i 0.319298 0.553040i −0.661044 0.750347i \(-0.729886\pi\)
0.980342 + 0.197307i \(0.0632196\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) −4.33891 −0.867781
\(26\) 2.03880 + 2.97377i 0.399841 + 0.583204i
\(27\) −1.00000 −0.192450
\(28\) 0.866025 + 0.500000i 0.163663 + 0.0944911i
\(29\) −1.92531 + 3.33473i −0.357520 + 0.619243i −0.987546 0.157331i \(-0.949711\pi\)
0.630026 + 0.776574i \(0.283044\pi\)
\(30\) −1.52798 2.64654i −0.278970 0.483190i
\(31\) 0.978370i 0.175720i −0.996133 0.0878602i \(-0.971997\pi\)
0.996133 0.0878602i \(-0.0280029\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −2.98127 + 1.72124i −0.518972 + 0.299629i
\(34\) 2.82898i 0.485166i
\(35\) −1.52798 2.64654i −0.258276 0.447347i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 4.58394 + 2.64654i 0.753596 + 0.435089i 0.826992 0.562214i \(-0.190050\pi\)
−0.0733959 + 0.997303i \(0.523384\pi\)
\(38\) 1.72542 0.279899
\(39\) 2.97377 2.03880i 0.476184 0.326469i
\(40\) 3.05596 0.483190
\(41\) 8.62781 + 4.98127i 1.34744 + 0.777943i 0.987886 0.155182i \(-0.0495964\pi\)
0.359551 + 0.933125i \(0.382930\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) −1.51082 2.61681i −0.230397 0.399060i 0.727528 0.686078i \(-0.240669\pi\)
−0.957925 + 0.287019i \(0.907336\pi\)
\(44\) 3.44247i 0.518972i
\(45\) −2.64654 + 1.52798i −0.394523 + 0.227778i
\(46\) 2.65229 1.53130i 0.391058 0.225778i
\(47\) 8.04447i 1.17341i 0.809802 + 0.586703i \(0.199575\pi\)
−0.809802 + 0.586703i \(0.800425\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −3.75760 2.16945i −0.531405 0.306807i
\(51\) −2.82898 −0.396137
\(52\) 0.278764 + 3.59476i 0.0386576 + 0.498503i
\(53\) −8.33405 −1.14477 −0.572385 0.819985i \(-0.693982\pi\)
−0.572385 + 0.819985i \(0.693982\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) −5.26003 + 9.11064i −0.709263 + 1.22848i
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 1.72542i 0.228537i
\(58\) −3.33473 + 1.92531i −0.437871 + 0.252805i
\(59\) 8.64080 4.98877i 1.12494 0.649482i 0.182279 0.983247i \(-0.441652\pi\)
0.942656 + 0.333765i \(0.108319\pi\)
\(60\) 3.05596i 0.394523i
\(61\) 5.77260 + 9.99843i 0.739106 + 1.28017i 0.952899 + 0.303289i \(0.0980849\pi\)
−0.213793 + 0.976879i \(0.568582\pi\)
\(62\) 0.489185 0.847293i 0.0621266 0.107606i
\(63\) −0.866025 0.500000i −0.109109 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 4.75496 9.93962i 0.589781 1.23286i
\(66\) −3.44247 −0.423739
\(67\) 4.11410 + 2.37527i 0.502617 + 0.290186i 0.729794 0.683668i \(-0.239616\pi\)
−0.227177 + 0.973854i \(0.572950\pi\)
\(68\) 1.41449 2.44997i 0.171532 0.297102i
\(69\) −1.53130 2.65229i −0.184347 0.319298i
\(70\) 3.05596i 0.365257i
\(71\) −3.17784 + 1.83473i −0.377140 + 0.217742i −0.676573 0.736375i \(-0.736536\pi\)
0.299433 + 0.954117i \(0.403202\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 10.1119i 1.18351i 0.806117 + 0.591756i \(0.201565\pi\)
−0.806117 + 0.591756i \(0.798435\pi\)
\(74\) 2.64654 + 4.58394i 0.307654 + 0.532873i
\(75\) −2.16945 + 3.75760i −0.250507 + 0.433891i
\(76\) 1.49425 + 0.862708i 0.171403 + 0.0989594i
\(77\) −3.44247 −0.392306
\(78\) 3.59476 0.278764i 0.407026 0.0315638i
\(79\) −4.49843 −0.506113 −0.253057 0.967451i \(-0.581436\pi\)
−0.253057 + 0.967451i \(0.581436\pi\)
\(80\) 2.64654 + 1.52798i 0.295892 + 0.170833i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.98127 + 8.62781i 0.550089 + 0.952782i
\(83\) 7.15869i 0.785768i 0.919588 + 0.392884i \(0.128523\pi\)
−0.919588 + 0.392884i \(0.871477\pi\)
\(84\) 0.866025 0.500000i 0.0944911 0.0545545i
\(85\) −7.48701 + 4.32263i −0.812081 + 0.468855i
\(86\) 3.02163i 0.325831i
\(87\) 1.92531 + 3.33473i 0.206414 + 0.357520i
\(88\) 1.72124 2.98127i 0.183484 0.317804i
\(89\) −6.84426 3.95154i −0.725490 0.418862i 0.0912800 0.995825i \(-0.470904\pi\)
−0.816770 + 0.576963i \(0.804238\pi\)
\(90\) −3.05596 −0.322127
\(91\) 3.59476 0.278764i 0.376833 0.0292224i
\(92\) 3.06260 0.319298
\(93\) −0.847293 0.489185i −0.0878602 0.0507261i
\(94\) −4.02224 + 6.96672i −0.414862 + 0.718562i
\(95\) −2.63640 4.56638i −0.270489 0.468501i
\(96\) 1.00000i 0.102062i
\(97\) −7.88016 + 4.54961i −0.800109 + 0.461943i −0.843509 0.537115i \(-0.819514\pi\)
0.0434004 + 0.999058i \(0.486181\pi\)
\(98\) 0.866025 0.500000i 0.0874818 0.0505076i
\(99\) 3.44247i 0.345981i
\(100\) −2.16945 3.75760i −0.216945 0.375760i
\(101\) 9.42664 16.3274i 0.937985 1.62464i 0.168764 0.985657i \(-0.446023\pi\)
0.769222 0.638982i \(-0.220644\pi\)
\(102\) −2.44997 1.41449i −0.242583 0.140055i
\(103\) −13.7079 −1.35068 −0.675338 0.737509i \(-0.736002\pi\)
−0.675338 + 0.737509i \(0.736002\pi\)
\(104\) −1.55596 + 3.25253i −0.152575 + 0.318937i
\(105\) −3.05596 −0.298231
\(106\) −7.21750 4.16702i −0.701025 0.404737i
\(107\) 1.65736 2.87063i 0.160223 0.277514i −0.774726 0.632297i \(-0.782112\pi\)
0.934948 + 0.354784i \(0.115445\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 8.67525i 0.830938i 0.909607 + 0.415469i \(0.136383\pi\)
−0.909607 + 0.415469i \(0.863617\pi\)
\(110\) −9.11064 + 5.26003i −0.868666 + 0.501524i
\(111\) 4.58394 2.64654i 0.435089 0.251199i
\(112\) 1.00000i 0.0944911i
\(113\) 5.60557 + 9.70914i 0.527328 + 0.913359i 0.999493 + 0.0318486i \(0.0101394\pi\)
−0.472165 + 0.881510i \(0.656527\pi\)
\(114\) 0.862708 1.49425i 0.0808000 0.139950i
\(115\) −8.10529 4.67959i −0.755822 0.436374i
\(116\) −3.85061 −0.357520
\(117\) −0.278764 3.59476i −0.0257718 0.332336i
\(118\) 9.97753 0.918506
\(119\) −2.44997 1.41449i −0.224588 0.129666i
\(120\) 1.52798 2.64654i 0.139485 0.241595i
\(121\) 0.425305 + 0.736650i 0.0386641 + 0.0669682i
\(122\) 11.5452i 1.04525i
\(123\) 8.62781 4.98127i 0.777943 0.449146i
\(124\) 0.847293 0.489185i 0.0760892 0.0439301i
\(125\) 2.02028i 0.180699i
\(126\) −0.500000 0.866025i −0.0445435 0.0771517i
\(127\) 2.55753 4.42977i 0.226944 0.393078i −0.729957 0.683493i \(-0.760460\pi\)
0.956901 + 0.290415i \(0.0937932\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −3.02163 −0.266040
\(130\) 9.08773 6.23048i 0.797047 0.546450i
\(131\) −18.7757 −1.64044 −0.820219 0.572049i \(-0.806149\pi\)
−0.820219 + 0.572049i \(0.806149\pi\)
\(132\) −2.98127 1.72124i −0.259486 0.149814i
\(133\) 0.862708 1.49425i 0.0748063 0.129568i
\(134\) 2.37527 + 4.11410i 0.205192 + 0.355404i
\(135\) 3.05596i 0.263015i
\(136\) 2.44997 1.41449i 0.210083 0.121292i
\(137\) 2.30457 1.33055i 0.196893 0.113676i −0.398312 0.917250i \(-0.630404\pi\)
0.595205 + 0.803574i \(0.297071\pi\)
\(138\) 3.06260i 0.260706i
\(139\) 8.35322 + 14.4682i 0.708511 + 1.22718i 0.965409 + 0.260739i \(0.0839662\pi\)
−0.256898 + 0.966439i \(0.582700\pi\)
\(140\) 1.52798 2.64654i 0.129138 0.223674i
\(141\) 6.96672 + 4.02224i 0.586703 + 0.338733i
\(142\) −3.66945 −0.307934
\(143\) −7.01850 10.2371i −0.586916 0.856071i
\(144\) 1.00000 0.0833333
\(145\) 10.1908 + 5.88366i 0.846300 + 0.488611i
\(146\) −5.05596 + 8.75718i −0.418434 + 0.724750i
\(147\) −0.500000 0.866025i −0.0412393 0.0714286i
\(148\) 5.29308i 0.435089i
\(149\) 2.16642 1.25078i 0.177480 0.102468i −0.408628 0.912701i \(-0.633993\pi\)
0.586108 + 0.810233i \(0.300659\pi\)
\(150\) −3.75760 + 2.16945i −0.306807 + 0.177135i
\(151\) 12.6465i 1.02916i −0.857444 0.514578i \(-0.827949\pi\)
0.857444 0.514578i \(-0.172051\pi\)
\(152\) 0.862708 + 1.49425i 0.0699749 + 0.121200i
\(153\) −1.41449 + 2.44997i −0.114355 + 0.198068i
\(154\) −2.98127 1.72124i −0.240237 0.138701i
\(155\) −2.98986 −0.240151
\(156\) 3.25253 + 1.55596i 0.260411 + 0.124577i
\(157\) 17.8131 1.42164 0.710822 0.703372i \(-0.248323\pi\)
0.710822 + 0.703372i \(0.248323\pi\)
\(158\) −3.89576 2.24922i −0.309930 0.178938i
\(159\) −4.16702 + 7.21750i −0.330467 + 0.572385i
\(160\) 1.52798 + 2.64654i 0.120798 + 0.209227i
\(161\) 3.06260i 0.241366i
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) −7.68884 + 4.43915i −0.602236 + 0.347701i −0.769921 0.638139i \(-0.779704\pi\)
0.167684 + 0.985841i \(0.446371\pi\)
\(164\) 9.96254i 0.777943i
\(165\) 5.26003 + 9.11064i 0.409493 + 0.709263i
\(166\) −3.57934 + 6.19961i −0.277811 + 0.481183i
\(167\) −8.46097 4.88494i −0.654730 0.378008i 0.135536 0.990772i \(-0.456724\pi\)
−0.790266 + 0.612764i \(0.790058\pi\)
\(168\) 1.00000 0.0771517
\(169\) 8.15796 + 10.1216i 0.627535 + 0.778588i
\(170\) −8.64526 −0.663061
\(171\) −1.49425 0.862708i −0.114268 0.0659729i
\(172\) 1.51082 2.61681i 0.115199 0.199530i
\(173\) 4.33762 + 7.51299i 0.329783 + 0.571202i 0.982469 0.186427i \(-0.0596909\pi\)
−0.652685 + 0.757629i \(0.726358\pi\)
\(174\) 3.85061i 0.291914i
\(175\) −3.75760 + 2.16945i −0.284048 + 0.163995i
\(176\) 2.98127 1.72124i 0.224722 0.129743i
\(177\) 9.97753i 0.749957i
\(178\) −3.95154 6.84426i −0.296180 0.512999i
\(179\) −11.7139 + 20.2891i −0.875540 + 1.51648i −0.0193531 + 0.999813i \(0.506161\pi\)
−0.856187 + 0.516667i \(0.827173\pi\)
\(180\) −2.64654 1.52798i −0.197262 0.113889i
\(181\) 7.66632 0.569833 0.284917 0.958552i \(-0.408034\pi\)
0.284917 + 0.958552i \(0.408034\pi\)
\(182\) 3.25253 + 1.55596i 0.241094 + 0.115336i
\(183\) 11.5452 0.853446
\(184\) 2.65229 + 1.53130i 0.195529 + 0.112889i
\(185\) 8.08773 14.0084i 0.594622 1.02992i
\(186\) −0.489185 0.847293i −0.0358688 0.0621266i
\(187\) 9.73869i 0.712163i
\(188\) −6.96672 + 4.02224i −0.508100 + 0.293352i
\(189\) −0.866025 + 0.500000i −0.0629941 + 0.0363696i
\(190\) 5.27281i 0.382530i
\(191\) −12.7472 22.0789i −0.922357 1.59757i −0.795757 0.605616i \(-0.792927\pi\)
−0.126600 0.991954i \(-0.540407\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −7.38361 4.26293i −0.531484 0.306852i 0.210137 0.977672i \(-0.432609\pi\)
−0.741621 + 0.670820i \(0.765942\pi\)
\(194\) −9.09922 −0.653286
\(195\) −6.23048 9.08773i −0.446174 0.650786i
\(196\) 1.00000 0.0714286
\(197\) 20.5094 + 11.8411i 1.46124 + 0.843645i 0.999069 0.0431470i \(-0.0137384\pi\)
0.462168 + 0.886792i \(0.347072\pi\)
\(198\) −1.72124 + 2.98127i −0.122323 + 0.211869i
\(199\) −12.4233 21.5178i −0.880666 1.52536i −0.850602 0.525810i \(-0.823762\pi\)
−0.0300637 0.999548i \(-0.509571\pi\)
\(200\) 4.33891i 0.306807i
\(201\) 4.11410 2.37527i 0.290186 0.167539i
\(202\) 16.3274 9.42664i 1.14879 0.663256i
\(203\) 3.85061i 0.270260i
\(204\) −1.41449 2.44997i −0.0990341 0.171532i
\(205\) 15.2226 26.3663i 1.06319 1.84150i
\(206\) −11.8714 6.85393i −0.827116 0.477536i
\(207\) −3.06260 −0.212865
\(208\) −2.97377 + 2.03880i −0.206194 + 0.141365i
\(209\) −5.93970 −0.410857
\(210\) −2.64654 1.52798i −0.182629 0.105441i
\(211\) −0.386509 + 0.669453i −0.0266084 + 0.0460871i −0.879023 0.476779i \(-0.841804\pi\)
0.852415 + 0.522867i \(0.175137\pi\)
\(212\) −4.16702 7.21750i −0.286192 0.495700i
\(213\) 3.66945i 0.251427i
\(214\) 2.87063 1.65736i 0.196232 0.113295i
\(215\) −7.99687 + 4.61699i −0.545382 + 0.314876i
\(216\) 1.00000i 0.0680414i
\(217\) −0.489185 0.847293i −0.0332080 0.0575180i
\(218\) −4.33762 + 7.51299i −0.293781 + 0.508844i
\(219\) 8.75718 + 5.05596i 0.591756 + 0.341650i
\(220\) −10.5201 −0.709263
\(221\) −0.788619 10.1695i −0.0530482 0.684075i
\(222\) 5.29308 0.355248
\(223\) −18.6502 10.7677i −1.24891 0.721060i −0.278019 0.960575i \(-0.589678\pi\)
−0.970892 + 0.239516i \(0.923011\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) 2.16945 + 3.75760i 0.144630 + 0.250507i
\(226\) 11.2111i 0.745754i
\(227\) 15.1939 8.77218i 1.00845 0.582230i 0.0977139 0.995215i \(-0.468847\pi\)
0.910738 + 0.412985i \(0.135514\pi\)
\(228\) 1.49425 0.862708i 0.0989594 0.0571342i
\(229\) 10.3222i 0.682109i 0.940043 + 0.341055i \(0.110784\pi\)
−0.940043 + 0.341055i \(0.889216\pi\)
\(230\) −4.67959 8.10529i −0.308563 0.534447i
\(231\) −1.72124 + 2.98127i −0.113249 + 0.196153i
\(232\) −3.33473 1.92531i −0.218936 0.126402i
\(233\) −17.8290 −1.16802 −0.584008 0.811748i \(-0.698516\pi\)
−0.584008 + 0.811748i \(0.698516\pi\)
\(234\) 1.55596 3.25253i 0.101716 0.212625i
\(235\) 24.5836 1.60366
\(236\) 8.64080 + 4.98877i 0.562468 + 0.324741i
\(237\) −2.24922 + 3.89576i −0.146102 + 0.253057i
\(238\) −1.41449 2.44997i −0.0916878 0.158808i
\(239\) 5.71271i 0.369525i 0.982783 + 0.184762i \(0.0591515\pi\)
−0.982783 + 0.184762i \(0.940848\pi\)
\(240\) 2.64654 1.52798i 0.170833 0.0986308i
\(241\) 0.868738 0.501566i 0.0559603 0.0323087i −0.471759 0.881728i \(-0.656381\pi\)
0.527719 + 0.849419i \(0.323047\pi\)
\(242\) 0.850611i 0.0546793i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −5.77260 + 9.99843i −0.369553 + 0.640084i
\(245\) −2.64654 1.52798i −0.169081 0.0976191i
\(246\) 9.96254 0.635188
\(247\) 6.20245 0.480984i 0.394653 0.0306043i
\(248\) 0.978370 0.0621266
\(249\) 6.19961 + 3.57934i 0.392884 + 0.226832i
\(250\) 1.01014 1.74961i 0.0638867 0.110655i
\(251\) −0.336293 0.582476i −0.0212266 0.0367656i 0.855217 0.518270i \(-0.173424\pi\)
−0.876444 + 0.481505i \(0.840090\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) −9.13042 + 5.27145i −0.574025 + 0.331413i
\(254\) 4.42977 2.55753i 0.277948 0.160474i
\(255\) 8.64526i 0.541387i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 12.1717 21.0820i 0.759248 1.31506i −0.183986 0.982929i \(-0.558900\pi\)
0.943234 0.332128i \(-0.107766\pi\)
\(258\) −2.61681 1.51082i −0.162915 0.0940592i
\(259\) 5.29308 0.328896
\(260\) 10.9854 0.851893i 0.681289 0.0528322i
\(261\) 3.85061 0.238347
\(262\) −16.2602 9.38784i −1.00456 0.579983i
\(263\) 8.54648 14.8029i 0.526999 0.912788i −0.472506 0.881327i \(-0.656651\pi\)
0.999505 0.0314610i \(-0.0100160\pi\)
\(264\) −1.72124 2.98127i −0.105935 0.183484i
\(265\) 25.4685i 1.56452i
\(266\) 1.49425 0.862708i 0.0916186 0.0528960i
\(267\) −6.84426 + 3.95154i −0.418862 + 0.241830i
\(268\) 4.75055i 0.290186i
\(269\) 13.3297 + 23.0877i 0.812727 + 1.40768i 0.910949 + 0.412519i \(0.135351\pi\)
−0.0982223 + 0.995165i \(0.531316\pi\)
\(270\) −1.52798 + 2.64654i −0.0929900 + 0.161063i
\(271\) 21.1739 + 12.2247i 1.28622 + 0.742600i 0.977978 0.208708i \(-0.0669257\pi\)
0.308243 + 0.951308i \(0.400259\pi\)
\(272\) 2.82898 0.171532
\(273\) 1.55596 3.25253i 0.0941711 0.196852i
\(274\) 2.66109 0.160763
\(275\) 12.9354 + 7.46828i 0.780037 + 0.450354i
\(276\) 1.53130 2.65229i 0.0921734 0.159649i
\(277\) −14.2406 24.6655i −0.855636 1.48201i −0.876054 0.482214i \(-0.839833\pi\)
0.0204175 0.999792i \(-0.493500\pi\)
\(278\) 16.7064i 1.00199i
\(279\) −0.847293 + 0.489185i −0.0507261 + 0.0292867i
\(280\) 2.64654 1.52798i 0.158161 0.0913143i
\(281\) 9.76032i 0.582252i 0.956685 + 0.291126i \(0.0940298\pi\)
−0.956685 + 0.291126i \(0.905970\pi\)
\(282\) 4.02224 + 6.96672i 0.239521 + 0.414862i
\(283\) 5.83562 10.1076i 0.346891 0.600833i −0.638804 0.769369i \(-0.720571\pi\)
0.985696 + 0.168536i \(0.0539039\pi\)
\(284\) −3.17784 1.83473i −0.188570 0.108871i
\(285\) −5.27281 −0.312334
\(286\) −0.959638 12.3749i −0.0567446 0.731741i
\(287\) 9.96254 0.588070
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) 4.49843 7.79152i 0.264614 0.458324i
\(290\) 5.88366 + 10.1908i 0.345500 + 0.598424i
\(291\) 9.09922i 0.533406i
\(292\) −8.75718 + 5.05596i −0.512475 + 0.295878i
\(293\) 18.8968 10.9101i 1.10396 0.637373i 0.166704 0.986007i \(-0.446688\pi\)
0.937259 + 0.348634i \(0.113354\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) −15.2455 26.4059i −0.887626 1.53741i
\(296\) −2.64654 + 4.58394i −0.153827 + 0.266436i
\(297\) 2.98127 + 1.72124i 0.172991 + 0.0998762i
\(298\) 2.50157 0.144912
\(299\) 9.10746 6.24401i 0.526698 0.361101i
\(300\) −4.33891 −0.250507
\(301\) −2.61681 1.51082i −0.150830 0.0870819i
\(302\) 6.32323 10.9522i 0.363861 0.630226i
\(303\) −9.42664 16.3274i −0.541546 0.937985i
\(304\) 1.72542i 0.0989594i
\(305\) 30.5548 17.6408i 1.74957 1.01011i
\(306\) −2.44997 + 1.41449i −0.140055 + 0.0808610i
\(307\) 4.87046i 0.277972i −0.990294 0.138986i \(-0.955616\pi\)
0.990294 0.138986i \(-0.0443843\pi\)
\(308\) −1.72124 2.98127i −0.0980765 0.169874i
\(309\) −6.85393 + 11.8714i −0.389906 + 0.675338i
\(310\) −2.58930 1.49493i −0.147062 0.0849064i
\(311\) −3.90344 −0.221344 −0.110672 0.993857i \(-0.535300\pi\)
−0.110672 + 0.993857i \(0.535300\pi\)
\(312\) 2.03880 + 2.97377i 0.115424 + 0.168357i
\(313\) 26.0528 1.47259 0.736297 0.676659i \(-0.236573\pi\)
0.736297 + 0.676659i \(0.236573\pi\)
\(314\) 15.4266 + 8.90657i 0.870576 + 0.502627i
\(315\) −1.52798 + 2.64654i −0.0860920 + 0.149116i
\(316\) −2.24922 3.89576i −0.126528 0.219154i
\(317\) 11.1107i 0.624040i 0.950076 + 0.312020i \(0.101006\pi\)
−0.950076 + 0.312020i \(0.898994\pi\)
\(318\) −7.21750 + 4.16702i −0.404737 + 0.233675i
\(319\) 11.4797 6.62781i 0.642740 0.371086i
\(320\) 3.05596i 0.170833i
\(321\) −1.65736 2.87063i −0.0925046 0.160223i
\(322\) 1.53130 2.65229i 0.0853359 0.147806i
\(323\) −4.22722 2.44058i −0.235209 0.135798i
\(324\) −1.00000 −0.0555556
\(325\) −14.1124 6.75118i −0.782818 0.374488i
\(326\) −8.87831 −0.491724
\(327\) 7.51299 + 4.33762i 0.415469 + 0.239871i
\(328\) −4.98127 + 8.62781i −0.275045 + 0.476391i
\(329\) 4.02224 + 6.96672i 0.221753 + 0.384087i
\(330\) 10.5201i 0.579110i
\(331\) 12.6854 7.32391i 0.697252 0.402559i −0.109071 0.994034i \(-0.534788\pi\)
0.806323 + 0.591475i \(0.201454\pi\)
\(332\) −6.19961 + 3.57934i −0.340248 + 0.196442i
\(333\) 5.29308i 0.290059i
\(334\) −4.88494 8.46097i −0.267292 0.462964i
\(335\) 7.25875 12.5725i 0.396588 0.686910i
\(336\) 0.866025 + 0.500000i 0.0472456 + 0.0272772i
\(337\) −27.5456 −1.50050 −0.750251 0.661153i \(-0.770068\pi\)
−0.750251 + 0.661153i \(0.770068\pi\)
\(338\) 2.00418 + 12.8446i 0.109013 + 0.698653i
\(339\) 11.2111 0.608906
\(340\) −7.48701 4.32263i −0.406040 0.234427i
\(341\) −1.68401 + 2.91678i −0.0911940 + 0.157953i
\(342\) −0.862708 1.49425i −0.0466499 0.0808000i
\(343\) 1.00000i 0.0539949i
\(344\) 2.61681 1.51082i 0.141089 0.0814577i
\(345\) −8.10529 + 4.67959i −0.436374 + 0.251941i
\(346\) 8.67525i 0.466384i
\(347\) −2.62073 4.53924i −0.140688 0.243679i 0.787068 0.616867i \(-0.211598\pi\)
−0.927756 + 0.373187i \(0.878265\pi\)
\(348\) −1.92531 + 3.33473i −0.103207 + 0.178760i
\(349\) −4.52901 2.61482i −0.242432 0.139968i 0.373862 0.927484i \(-0.378033\pi\)
−0.616294 + 0.787516i \(0.711367\pi\)
\(350\) −4.33891 −0.231924
\(351\) −3.25253 1.55596i −0.173607 0.0830511i
\(352\) 3.44247 0.183484
\(353\) 3.26227 + 1.88348i 0.173633 + 0.100247i 0.584298 0.811539i \(-0.301370\pi\)
−0.410665 + 0.911786i \(0.634703\pi\)
\(354\) 4.98877 8.64080i 0.265150 0.459253i
\(355\) 5.60686 + 9.71136i 0.297581 + 0.515425i
\(356\) 7.90307i 0.418862i
\(357\) −2.44997 + 1.41449i −0.129666 + 0.0748628i
\(358\) −20.2891 + 11.7139i −1.07231 + 0.619100i
\(359\) 20.6003i 1.08724i 0.839330 + 0.543622i \(0.182947\pi\)
−0.839330 + 0.543622i \(0.817053\pi\)
\(360\) −1.52798 2.64654i −0.0805317 0.139485i
\(361\) −8.01147 + 13.8763i −0.421656 + 0.730330i
\(362\) 6.63923 + 3.83316i 0.348950 + 0.201466i
\(363\) 0.850611 0.0446455
\(364\) 2.03880 + 2.97377i 0.106862 + 0.155868i
\(365\) 30.9017 1.61747
\(366\) 9.99843 + 5.77260i 0.522627 + 0.301739i
\(367\) 13.9579 24.1759i 0.728598 1.26197i −0.228877 0.973455i \(-0.573505\pi\)
0.957476 0.288514i \(-0.0931612\pi\)
\(368\) 1.53130 + 2.65229i 0.0798245 + 0.138260i
\(369\) 9.96254i 0.518629i
\(370\) 14.0084 8.08773i 0.728260 0.420461i
\(371\) −7.21750 + 4.16702i −0.374714 + 0.216341i
\(372\) 0.978370i 0.0507261i
\(373\) −15.7091 27.2090i −0.813388 1.40883i −0.910479 0.413554i \(-0.864287\pi\)
0.0970910 0.995276i \(-0.469046\pi\)
\(374\) −4.86934 + 8.43395i −0.251788 + 0.436109i
\(375\) −1.74961 1.01014i −0.0903495 0.0521633i
\(376\) −8.04447 −0.414862
\(377\) −11.4508 + 7.85061i −0.589748 + 0.404327i
\(378\) −1.00000 −0.0514344
\(379\) −27.5747 15.9203i −1.41642 0.817770i −0.420437 0.907322i \(-0.638123\pi\)
−0.995982 + 0.0895514i \(0.971457\pi\)
\(380\) 2.63640 4.56638i 0.135245 0.234251i
\(381\) −2.55753 4.42977i −0.131026 0.226944i
\(382\) 25.4945i 1.30441i
\(383\) −4.08962 + 2.36114i −0.208970 + 0.120649i −0.600832 0.799375i \(-0.705164\pi\)
0.391863 + 0.920024i \(0.371831\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 10.5201i 0.536152i
\(386\) −4.26293 7.38361i −0.216977 0.375816i
\(387\) −1.51082 + 2.61681i −0.0767990 + 0.133020i
\(388\) −7.88016 4.54961i −0.400054 0.230972i
\(389\) −30.5902 −1.55099 −0.775493 0.631356i \(-0.782499\pi\)
−0.775493 + 0.631356i \(0.782499\pi\)
\(390\) −0.851893 10.9854i −0.0431373 0.556270i
\(391\) −8.66403 −0.438159
\(392\) 0.866025 + 0.500000i 0.0437409 + 0.0252538i
\(393\) −9.38784 + 16.2602i −0.473554 + 0.820219i
\(394\) 11.8411 + 20.5094i 0.596547 + 1.03325i
\(395\) 13.7470i 0.691689i
\(396\) −2.98127 + 1.72124i −0.149814 + 0.0864954i
\(397\) 10.1133 5.83891i 0.507571 0.293046i −0.224264 0.974529i \(-0.571998\pi\)
0.731835 + 0.681482i \(0.238664\pi\)
\(398\) 24.8466i 1.24545i
\(399\) −0.862708 1.49425i −0.0431894 0.0748063i
\(400\) 2.16945 3.75760i 0.108473 0.187880i
\(401\) 8.01677 + 4.62849i 0.400339 + 0.231136i 0.686630 0.727007i \(-0.259089\pi\)
−0.286292 + 0.958143i \(0.592423\pi\)
\(402\) 4.75055 0.236936
\(403\) 1.52231 3.18218i 0.0758315 0.158516i
\(404\) 18.8533 0.937985
\(405\) 2.64654 + 1.52798i 0.131508 + 0.0759260i
\(406\) −1.92531 + 3.33473i −0.0955513 + 0.165500i
\(407\) −9.11064 15.7801i −0.451598 0.782190i
\(408\) 2.82898i 0.140055i
\(409\) −22.1693 + 12.7994i −1.09620 + 0.632891i −0.935220 0.354066i \(-0.884799\pi\)
−0.160980 + 0.986958i \(0.551465\pi\)
\(410\) 26.3663 15.2226i 1.30214 0.751789i
\(411\) 2.66109i 0.131262i
\(412\) −6.85393 11.8714i −0.337669 0.584860i
\(413\) 4.98877 8.64080i 0.245481 0.425186i
\(414\) −2.65229 1.53130i −0.130353 0.0752592i
\(415\) 21.8767 1.07388
\(416\) −3.59476 + 0.278764i −0.176248 + 0.0136675i
\(417\) 16.7064 0.818118
\(418\) −5.14393 2.96985i −0.251598 0.145260i
\(419\) −14.1018 + 24.4251i −0.688920 + 1.19324i 0.283268 + 0.959041i \(0.408581\pi\)
−0.972188 + 0.234203i \(0.924752\pi\)
\(420\) −1.52798 2.64654i −0.0745579 0.129138i
\(421\) 5.07012i 0.247102i 0.992338 + 0.123551i \(0.0394283\pi\)
−0.992338 + 0.123551i \(0.960572\pi\)
\(422\) −0.669453 + 0.386509i −0.0325885 + 0.0188150i
\(423\) 6.96672 4.02224i 0.338733 0.195568i
\(424\) 8.33405i 0.404737i
\(425\) 6.13734 + 10.6302i 0.297705 + 0.515640i
\(426\) −1.83473 + 3.17784i −0.0888928 + 0.153967i
\(427\) 9.99843 + 5.77260i 0.483858 + 0.279356i
\(428\) 3.31471 0.160223
\(429\) −12.3749 + 0.959638i −0.597464 + 0.0463318i
\(430\) −9.23399 −0.445302
\(431\) −13.9808 8.07185i −0.673434 0.388807i 0.123943 0.992289i \(-0.460446\pi\)
−0.797376 + 0.603482i \(0.793779\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −11.3014 19.5747i −0.543113 0.940699i −0.998723 0.0505195i \(-0.983912\pi\)
0.455610 0.890179i \(-0.349421\pi\)
\(434\) 0.978370i 0.0469633i
\(435\) 10.1908 5.88366i 0.488611 0.282100i
\(436\) −7.51299 + 4.33762i −0.359807 + 0.207735i
\(437\) 5.28425i 0.252780i
\(438\) 5.05596 + 8.75718i 0.241583 + 0.418434i
\(439\) 14.1486 24.5060i 0.675273 1.16961i −0.301115 0.953588i \(-0.597359\pi\)
0.976389 0.216020i \(-0.0693077\pi\)
\(440\) −9.11064 5.26003i −0.434333 0.250762i
\(441\) −1.00000 −0.0476190
\(442\) 4.40179 9.20136i 0.209372 0.437664i
\(443\) −1.38096 −0.0656112 −0.0328056 0.999462i \(-0.510444\pi\)
−0.0328056 + 0.999462i \(0.510444\pi\)
\(444\) 4.58394 + 2.64654i 0.217544 + 0.125599i
\(445\) −12.0757 + 20.9158i −0.572445 + 0.991504i
\(446\) −10.7677 18.6502i −0.509866 0.883114i
\(447\) 2.50157i 0.118320i
\(448\) −0.866025 + 0.500000i −0.0409159 + 0.0236228i
\(449\) −32.0480 + 18.5029i −1.51244 + 0.873208i −0.512547 + 0.858659i \(0.671298\pi\)
−0.999894 + 0.0145487i \(0.995369\pi\)
\(450\) 4.33891i 0.204538i
\(451\) −17.1479 29.7010i −0.807462 1.39856i
\(452\) −5.60557 + 9.70914i −0.263664 + 0.456679i
\(453\) −10.9522 6.32323i −0.514578 0.297091i
\(454\) 17.5444 0.823398
\(455\) −0.851893 10.9854i −0.0399374 0.515006i
\(456\) 1.72542 0.0808000
\(457\) 12.0530 + 6.95878i 0.563813 + 0.325518i 0.754675 0.656099i \(-0.227795\pi\)
−0.190861 + 0.981617i \(0.561128\pi\)
\(458\) −5.16109 + 8.93928i −0.241162 + 0.417705i
\(459\) 1.41449 + 2.44997i 0.0660228 + 0.114355i
\(460\) 9.35918i 0.436374i
\(461\) 4.19845 2.42397i 0.195541 0.112896i −0.399033 0.916937i \(-0.630654\pi\)
0.594574 + 0.804041i \(0.297321\pi\)
\(462\) −2.98127 + 1.72124i −0.138701 + 0.0800791i
\(463\) 24.4377i 1.13571i 0.823127 + 0.567857i \(0.192227\pi\)
−0.823127 + 0.567857i \(0.807773\pi\)
\(464\) −1.92531 3.33473i −0.0893801 0.154811i
\(465\) −1.49493 + 2.58930i −0.0693258 + 0.120076i
\(466\) −15.4404 8.91449i −0.715260 0.412956i
\(467\) −36.0027 −1.66600 −0.833002 0.553270i \(-0.813380\pi\)
−0.833002 + 0.553270i \(0.813380\pi\)
\(468\) 2.97377 2.03880i 0.137463 0.0942434i
\(469\) 4.75055 0.219360
\(470\) 21.2900 + 12.2918i 0.982035 + 0.566978i
\(471\) 8.90657 15.4266i 0.410393 0.710822i
\(472\) 4.98877 + 8.64080i 0.229627 + 0.397725i
\(473\) 10.4019i 0.478279i
\(474\) −3.89576 + 2.24922i −0.178938 + 0.103310i
\(475\) −6.48343 + 3.74321i −0.297480 + 0.171750i
\(476\) 2.82898i 0.129666i
\(477\) 4.16702 + 7.21750i 0.190795 + 0.330467i
\(478\) −2.85636 + 4.94735i −0.130647 + 0.226287i
\(479\) −8.22108 4.74644i −0.375631 0.216870i 0.300285 0.953850i \(-0.402918\pi\)
−0.675915 + 0.736979i \(0.736252\pi\)
\(480\) 3.05596 0.139485
\(481\) 10.7915 + 15.7404i 0.492051 + 0.717701i
\(482\) 1.00313 0.0456914
\(483\) −2.65229 1.53130i −0.120683 0.0696765i
\(484\) −0.425305 + 0.736650i −0.0193321 + 0.0334841i
\(485\) 13.9034 + 24.0815i 0.631323 + 1.09348i
\(486\) 1.00000i 0.0453609i
\(487\) −35.4383 + 20.4603i −1.60586 + 0.927144i −0.615578 + 0.788076i \(0.711078\pi\)
−0.990283 + 0.139069i \(0.955589\pi\)
\(488\) −9.99843 + 5.77260i −0.452608 + 0.261313i
\(489\) 8.87831i 0.401491i
\(490\) −1.52798 2.64654i −0.0690272 0.119559i
\(491\) −2.55753 + 4.42977i −0.115420 + 0.199913i −0.917947 0.396702i \(-0.870155\pi\)
0.802528 + 0.596615i \(0.203488\pi\)
\(492\) 8.62781 + 4.98127i 0.388972 + 0.224573i
\(493\) 10.8933 0.490610
\(494\) 5.61197 + 2.68468i 0.252495 + 0.120790i
\(495\) 10.5201 0.472842
\(496\) 0.847293 + 0.489185i 0.0380446 + 0.0219651i
\(497\) −1.83473 + 3.17784i −0.0822987 + 0.142546i
\(498\) 3.57934 + 6.19961i 0.160394 + 0.277811i
\(499\) 19.5827i 0.876640i 0.898819 + 0.438320i \(0.144426\pi\)
−0.898819 + 0.438320i \(0.855574\pi\)
\(500\) 1.74961 1.01014i 0.0782450 0.0451747i
\(501\) −8.46097 + 4.88494i −0.378008 + 0.218243i
\(502\) 0.672585i 0.0300189i
\(503\) 14.5429 + 25.1890i 0.648436 + 1.12312i 0.983496 + 0.180928i \(0.0579100\pi\)
−0.335060 + 0.942197i \(0.608757\pi\)
\(504\) 0.500000 0.866025i 0.0222718 0.0385758i
\(505\) −49.8960 28.8075i −2.22034 1.28191i
\(506\) −10.5429 −0.468689
\(507\) 12.8446 2.00418i 0.570448 0.0890088i
\(508\) 5.11506 0.226944
\(509\) −4.52051 2.60992i −0.200368 0.115682i 0.396459 0.918052i \(-0.370239\pi\)
−0.596827 + 0.802370i \(0.703572\pi\)
\(510\) −4.32263 + 7.48701i −0.191409 + 0.331531i
\(511\) 5.05596 + 8.75718i 0.223663 + 0.387395i
\(512\) 1.00000i 0.0441942i
\(513\) −1.49425 + 0.862708i −0.0659729 + 0.0380895i
\(514\) 21.0820 12.1717i 0.929885 0.536870i
\(515\) 41.8907i 1.84592i
\(516\) −1.51082 2.61681i −0.0665099 0.115199i
\(517\) 13.8464 23.9827i 0.608965 1.05476i
\(518\) 4.58394 + 2.64654i 0.201407 + 0.116282i
\(519\) 8.67525 0.380801
\(520\) 9.93962 + 4.75496i 0.435881 + 0.208519i
\(521\) −14.5259 −0.636389 −0.318195 0.948025i \(-0.603077\pi\)
−0.318195 + 0.948025i \(0.603077\pi\)
\(522\) 3.33473 + 1.92531i 0.145957 + 0.0842683i
\(523\) −13.9367 + 24.1391i −0.609410 + 1.05553i 0.381927 + 0.924192i \(0.375260\pi\)
−0.991338 + 0.131337i \(0.958073\pi\)
\(524\) −9.38784 16.2602i −0.410110 0.710331i
\(525\) 4.33891i 0.189365i
\(526\) 14.8029 8.54648i 0.645439 0.372644i
\(527\) −2.39698 + 1.38389i −0.104414 + 0.0602834i
\(528\) 3.44247i 0.149814i
\(529\) 6.81025 + 11.7957i 0.296098 + 0.512856i
\(530\) −12.7343 + 22.0564i −0.553141 + 0.958069i
\(531\) −8.64080 4.98877i −0.374979 0.216494i
\(532\) 1.72542 0.0748063
\(533\) 20.3116 + 29.6263i 0.879792 + 1.28326i
\(534\) −7.90307 −0.341999
\(535\) −8.77252 5.06482i −0.379269 0.218971i
\(536\) −2.37527 + 4.11410i −0.102596 + 0.177702i
\(537\) 11.7139 + 20.2891i 0.505493 + 0.875540i
\(538\) 26.6594i 1.14937i
\(539\) −2.98127 + 1.72124i −0.128412 + 0.0741389i
\(540\) −2.64654 + 1.52798i −0.113889 + 0.0657538i
\(541\) 1.42341i 0.0611970i −0.999532 0.0305985i \(-0.990259\pi\)
0.999532 0.0305985i \(-0.00974133\pi\)
\(542\) 12.2247 + 21.1739i 0.525097 + 0.909496i
\(543\) 3.83316 6.63923i 0.164497 0.284917i
\(544\) 2.44997 + 1.41449i 0.105042 + 0.0606458i
\(545\) 26.5112 1.13562
\(546\) 2.97377 2.03880i 0.127266 0.0872524i
\(547\) −9.33008 −0.398925 −0.199463 0.979905i \(-0.563920\pi\)
−0.199463 + 0.979905i \(0.563920\pi\)
\(548\) 2.30457 + 1.33055i 0.0984465 + 0.0568381i
\(549\) 5.77260 9.99843i 0.246369 0.426723i
\(550\) 7.46828 + 12.9354i 0.318449 + 0.551569i
\(551\) 6.64390i 0.283040i
\(552\) 2.65229 1.53130i 0.112889 0.0651764i
\(553\) −3.89576 + 2.24922i −0.165664 + 0.0956464i
\(554\) 28.4812i 1.21005i
\(555\) −8.08773 14.0084i −0.343305 0.594622i
\(556\) −8.35322 + 14.4682i −0.354256 + 0.613589i
\(557\) 9.34071 + 5.39286i 0.395779 + 0.228503i 0.684661 0.728862i \(-0.259950\pi\)
−0.288882 + 0.957365i \(0.593284\pi\)
\(558\) −0.978370 −0.0414177
\(559\) −0.842322 10.8620i −0.0356264 0.459415i
\(560\) 3.05596 0.129138
\(561\) 8.43395 + 4.86934i 0.356082 + 0.205584i
\(562\) −4.88016 + 8.45268i −0.205857 + 0.356555i
\(563\) 12.7541 + 22.0908i 0.537522 + 0.931016i 0.999037 + 0.0438831i \(0.0139729\pi\)
−0.461514 + 0.887133i \(0.652694\pi\)
\(564\) 8.04447i 0.338733i
\(565\) 29.6708 17.1304i 1.24826 0.720682i
\(566\) 10.1076 5.83562i 0.424853 0.245289i
\(567\) 1.00000i 0.0419961i
\(568\) −1.83473 3.17784i −0.0769834 0.133339i
\(569\) −4.10835 + 7.11587i −0.172231 + 0.298313i −0.939200 0.343372i \(-0.888431\pi\)
0.766969 + 0.641685i \(0.221764\pi\)
\(570\) −4.56638 2.63640i −0.191265 0.110427i
\(571\) 2.70500 0.113201 0.0566003 0.998397i \(-0.481974\pi\)
0.0566003 + 0.998397i \(0.481974\pi\)
\(572\) 5.35636 11.1968i 0.223961 0.468160i
\(573\) −25.4945 −1.06505
\(574\) 8.62781 + 4.98127i 0.360118 + 0.207914i
\(575\) −6.64416 + 11.5080i −0.277081 + 0.479918i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 21.4253i 0.891946i 0.895046 + 0.445973i \(0.147142\pi\)
−0.895046 + 0.445973i \(0.852858\pi\)
\(578\) 7.79152 4.49843i 0.324084 0.187110i
\(579\) −7.38361 + 4.26293i −0.306852 + 0.177161i
\(580\) 11.7673i 0.488611i
\(581\) 3.57934 + 6.19961i 0.148496 + 0.257203i
\(582\) −4.54961 + 7.88016i −0.188587 + 0.326643i
\(583\) 24.8460 + 14.3449i 1.02902 + 0.594104i
\(584\) −10.1119 −0.418434
\(585\) −10.9854 + 0.851893i −0.454192 + 0.0352214i
\(586\) 21.8202 0.901382
\(587\) −4.96515 2.86663i −0.204934 0.118319i 0.394021 0.919101i \(-0.371084\pi\)
−0.598955 + 0.800783i \(0.704417\pi\)
\(588\) 0.500000 0.866025i 0.0206197 0.0357143i
\(589\) −0.844048 1.46193i −0.0347784 0.0602379i
\(590\) 30.4910i 1.25529i
\(591\) 20.5094 11.8411i 0.843645 0.487079i
\(592\) −4.58394 + 2.64654i −0.188399 + 0.108772i
\(593\) 17.3442i 0.712240i −0.934440 0.356120i \(-0.884099\pi\)
0.934440 0.356120i \(-0.115901\pi\)
\(594\) 1.72124 + 2.98127i 0.0706232 + 0.122323i
\(595\) −4.32263 + 7.48701i −0.177211 + 0.306938i
\(596\) 2.16642 + 1.25078i 0.0887400 + 0.0512341i
\(597\) −24.8466 −1.01691
\(598\) 11.0093 0.853743i 0.450204 0.0349121i
\(599\) −31.5835 −1.29047 −0.645234 0.763985i \(-0.723240\pi\)
−0.645234 + 0.763985i \(0.723240\pi\)
\(600\) −3.75760 2.16945i −0.153404 0.0885676i
\(601\) −12.4478 + 21.5603i −0.507757 + 0.879462i 0.492202 + 0.870481i \(0.336192\pi\)
−0.999960 + 0.00898069i \(0.997141\pi\)
\(602\) −1.51082 2.61681i −0.0615762 0.106653i
\(603\) 4.75055i 0.193457i
\(604\) 10.9522 6.32323i 0.445637 0.257289i
\(605\) 2.25118 1.29972i 0.0915233 0.0528410i
\(606\) 18.8533i 0.765862i
\(607\) −7.62951 13.2147i −0.309672 0.536368i 0.668618 0.743606i \(-0.266886\pi\)
−0.978291 + 0.207238i \(0.933553\pi\)
\(608\) −0.862708 + 1.49425i −0.0349874 + 0.0606000i
\(609\) 3.33473 + 1.92531i 0.135130 + 0.0780173i
\(610\) 35.2817 1.42851
\(611\) −12.5169 + 26.1649i −0.506379 + 1.05852i
\(612\) −2.82898 −0.114355
\(613\) −39.6220 22.8757i −1.60032 0.923943i −0.991423 0.130690i \(-0.958281\pi\)
−0.608892 0.793253i \(-0.708386\pi\)
\(614\) 2.43523 4.21794i 0.0982779 0.170222i
\(615\) −15.2226 26.3663i −0.613833 1.06319i
\(616\) 3.44247i 0.138701i
\(617\) 36.6167 21.1406i 1.47413 0.851090i 0.474555 0.880226i \(-0.342609\pi\)
0.999575 + 0.0291358i \(0.00927553\pi\)
\(618\) −11.8714 + 6.85393i −0.477536 + 0.275705i
\(619\) 22.0261i 0.885303i 0.896694 + 0.442651i \(0.145962\pi\)
−0.896694 + 0.442651i \(0.854038\pi\)
\(620\) −1.49493 2.58930i −0.0600379 0.103989i
\(621\) −1.53130 + 2.65229i −0.0614489 + 0.106433i
\(622\) −3.38048 1.95172i −0.135545 0.0782569i
\(623\) −7.90307 −0.316630
\(624\) 0.278764 + 3.59476i 0.0111595 + 0.143906i
\(625\) −27.8684 −1.11474
\(626\) 22.5624 + 13.0264i 0.901775 + 0.520640i
\(627\) −2.96985 + 5.14393i −0.118604 + 0.205429i
\(628\) 8.90657 + 15.4266i 0.355411 + 0.615590i
\(629\) 14.9740i 0.597054i
\(630\) −2.64654 + 1.52798i −0.105441 + 0.0608762i
\(631\) 18.0721 10.4339i 0.719440 0.415369i −0.0951064 0.995467i \(-0.530319\pi\)
0.814547 + 0.580098i \(0.196986\pi\)
\(632\) 4.49843i 0.178938i
\(633\) 0.386509 + 0.669453i 0.0153624 + 0.0266084i
\(634\) −5.55536 + 9.62216i −0.220631 + 0.382145i
\(635\) −13.5372 7.81571i −0.537208 0.310157i
\(636\) −8.33405 −0.330467
\(637\) 2.97377 2.03880i 0.117825 0.0807800i
\(638\) 13.2556 0.524795
\(639\) 3.17784 + 1.83473i 0.125713 + 0.0725807i
\(640\) −1.52798 + 2.64654i −0.0603988 + 0.104614i
\(641\) −10.4526 18.1045i −0.412853 0.715083i 0.582347 0.812940i \(-0.302134\pi\)
−0.995200 + 0.0978574i \(0.968801\pi\)
\(642\) 3.31471i 0.130821i
\(643\) 33.8703 19.5550i 1.33571 0.771174i 0.349544 0.936920i \(-0.386337\pi\)
0.986168 + 0.165746i \(0.0530032\pi\)
\(644\) 2.65229 1.53130i 0.104515 0.0603416i
\(645\) 9.23399i 0.363588i
\(646\) −2.44058 4.22722i −0.0960235 0.166318i
\(647\) −3.96755 + 6.87201i −0.155981 + 0.270166i −0.933416 0.358797i \(-0.883187\pi\)
0.777435 + 0.628963i \(0.216520\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −34.3474 −1.34825
\(650\) −8.84615 12.9029i −0.346974 0.506094i
\(651\) −0.978370 −0.0383453
\(652\) −7.68884 4.43915i −0.301118 0.173851i
\(653\) −21.3998 + 37.0655i −0.837439 + 1.45049i 0.0545901 + 0.998509i \(0.482615\pi\)
−0.892029 + 0.451978i \(0.850719\pi\)
\(654\) 4.33762 + 7.51299i 0.169615 + 0.293781i
\(655\) 57.3778i 2.24194i
\(656\) −8.62781 + 4.98127i −0.336859 + 0.194486i
\(657\) 8.75718 5.05596i 0.341650 0.197252i
\(658\) 8.04447i 0.313606i
\(659\) −0.364274 0.630941i −0.0141901 0.0245780i 0.858843 0.512239i \(-0.171184\pi\)
−0.873033 + 0.487661i \(0.837850\pi\)
\(660\) −5.26003 + 9.11064i −0.204746 + 0.354631i
\(661\) −2.04352 1.17983i −0.0794836 0.0458899i 0.459731 0.888058i \(-0.347946\pi\)
−0.539215 + 0.842168i \(0.681279\pi\)
\(662\) 14.6478 0.569304
\(663\) −9.20136 4.40179i −0.357351 0.170951i
\(664\) −7.15869 −0.277811
\(665\) −4.56638 2.63640i −0.177077 0.102235i
\(666\) 2.64654 4.58394i 0.102551 0.177624i
\(667\) 5.89644 + 10.2129i 0.228311 + 0.395446i
\(668\) 9.76989i 0.378008i
\(669\) −18.6502 + 10.7677i −0.721060 + 0.416304i
\(670\) 12.5725 7.25875i 0.485719 0.280430i
\(671\) 39.7440i 1.53430i
\(672\) 0.500000 + 0.866025i 0.0192879 + 0.0334077i
\(673\) 15.6279 27.0682i 0.602410 1.04340i −0.390045 0.920796i \(-0.627541\pi\)
0.992455 0.122609i \(-0.0391260\pi\)
\(674\) −23.8552 13.7728i −0.918867 0.530508i
\(675\) 4.33891 0.167005
\(676\) −4.68662 + 12.1258i −0.180255 + 0.466378i
\(677\) −41.7294 −1.60379 −0.801895 0.597464i \(-0.796175\pi\)
−0.801895 + 0.597464i \(0.796175\pi\)
\(678\) 9.70914 + 5.60557i 0.372877 + 0.215281i
\(679\) −4.54961 + 7.88016i −0.174598 + 0.302413i
\(680\) −4.32263 7.48701i −0.165765 0.287114i
\(681\) 17.5444i 0.672301i
\(682\) −2.91678 + 1.68401i −0.111689 + 0.0644839i
\(683\) −7.98473 + 4.60999i −0.305527 + 0.176396i −0.644923 0.764247i \(-0.723111\pi\)
0.339396 + 0.940644i \(0.389777\pi\)
\(684\) 1.72542i 0.0659729i
\(685\) −4.06610 7.04269i −0.155358 0.269087i
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) 8.93928 + 5.16109i 0.341055 + 0.196908i
\(688\) 3.02163 0.115199
\(689\) −27.1068 12.9675i −1.03269 0.494021i
\(690\) −9.35918 −0.356298
\(691\) −7.97487 4.60429i −0.303378 0.175156i 0.340581 0.940215i \(-0.389376\pi\)
−0.643960 + 0.765060i \(0.722709\pi\)
\(692\) −4.33762 + 7.51299i −0.164892 + 0.285601i
\(693\) 1.72124 + 2.98127i 0.0653843 + 0.113249i
\(694\) 5.24146i 0.198963i
\(695\) 44.2143 25.5271i 1.67714 0.968300i
\(696\) −3.33473 + 1.92531i −0.126402 + 0.0729785i
\(697\) 28.1838i 1.06754i
\(698\) −2.61482 4.52901i −0.0989725 0.171425i
\(699\) −8.91449 + 15.4404i −0.337177 + 0.584008i
\(700\) −3.75760 2.16945i −0.142024 0.0819976i
\(701\) 20.8683 0.788184 0.394092 0.919071i \(-0.371059\pi\)
0.394092 + 0.919071i \(0.371059\pi\)
\(702\) −2.03880 2.97377i −0.0769494 0.112238i
\(703\) 9.13277 0.344449
\(704\) 2.98127 + 1.72124i 0.112361 + 0.0648715i
\(705\) 12.2918 21.2900i 0.462936 0.801829i
\(706\) 1.88348 + 3.26227i 0.0708855 + 0.122777i
\(707\) 18.8533i 0.709050i
\(708\) 8.64080 4.98877i 0.324741 0.187489i
\(709\) −12.8731 + 7.43226i −0.483458 + 0.279124i −0.721856 0.692043i \(-0.756711\pi\)
0.238399 + 0.971167i \(0.423378\pi\)
\(710\) 11.2137i 0.420843i
\(711\) 2.24922 + 3.89576i 0.0843522 + 0.146102i
\(712\) 3.95154 6.84426i 0.148090 0.256499i
\(713\) −2.59492 1.49818i −0.0971804 0.0561072i
\(714\) −2.82898 −0.105872
\(715\) −31.2843 + 21.4483i −1.16996 + 0.802120i
\(716\) −23.4278 −0.875540
\(717\) 4.94735 + 2.85636i 0.184762 + 0.106673i
\(718\) −10.3002 + 17.8404i −0.384399 + 0.665798i
\(719\) −12.8265 22.2162i −0.478349 0.828524i 0.521343 0.853347i \(-0.325431\pi\)
−0.999692 + 0.0248229i \(0.992098\pi\)
\(720\) 3.05596i 0.113889i
\(721\) −11.8714 + 6.85393i −0.442112 + 0.255254i
\(722\) −13.8763 + 8.01147i −0.516421 + 0.298156i
\(723\) 1.00313i 0.0373069i
\(724\) 3.83316 + 6.63923i 0.142458 + 0.246745i
\(725\) 8.35372 14.4691i 0.310249 0.537368i
\(726\) 0.736650 + 0.425305i 0.0273397 + 0.0157846i
\(727\) 41.6568 1.54497 0.772483 0.635036i \(-0.219015\pi\)
0.772483 + 0.635036i \(0.219015\pi\)
\(728\) 0.278764 + 3.59476i 0.0103317 + 0.133231i
\(729\) 1.00000 0.0370370
\(730\) 26.7616 + 15.4508i 0.990492 + 0.571861i
\(731\) −4.27407 + 7.40290i −0.158082 + 0.273806i
\(732\) 5.77260 + 9.99843i 0.213361 + 0.369553i
\(733\) 26.4965i 0.978671i −0.872096 0.489336i \(-0.837239\pi\)
0.872096 0.489336i \(-0.162761\pi\)
\(734\) 24.1759 13.9579i 0.892347 0.515197i
\(735\) −2.64654 + 1.52798i −0.0976191 + 0.0563604i
\(736\) 3.06260i 0.112889i
\(737\) −8.17682 14.1627i −0.301197 0.521688i
\(738\) 4.98127 8.62781i 0.183363 0.317594i
\(739\) 18.1009 + 10.4506i 0.665853 + 0.384431i 0.794504 0.607259i \(-0.207731\pi\)
−0.128650 + 0.991690i \(0.541064\pi\)
\(740\) 16.1755 0.594622
\(741\) 2.68468 5.61197i 0.0986243 0.206161i
\(742\) −8.33405 −0.305953
\(743\) 4.88999 + 2.82323i 0.179396 + 0.103574i 0.587009 0.809580i \(-0.300305\pi\)
−0.407613 + 0.913155i \(0.633639\pi\)
\(744\) 0.489185 0.847293i 0.0179344 0.0310633i
\(745\) −3.82235 6.62050i −0.140040 0.242556i
\(746\) 31.4183i 1.15030i
\(747\) 6.19961 3.57934i 0.226832 0.130961i
\(748\) −8.43395 + 4.86934i −0.308376 + 0.178041i
\(749\) 3.31471i 0.121117i
\(750\) −1.01014 1.74961i −0.0368850 0.0638867i
\(751\) 7.70439 13.3444i 0.281137 0.486944i −0.690528 0.723306i \(-0.742622\pi\)
0.971665 + 0.236362i \(0.0759551\pi\)
\(752\) −6.96672 4.02224i −0.254050 0.146676i
\(753\) −0.672585 −0.0245104
\(754\) −13.8420 + 1.07341i −0.504097 + 0.0390914i
\(755\) −38.6471 −1.40651
\(756\) −0.866025 0.500000i −0.0314970 0.0181848i
\(757\) 17.7686 30.7761i 0.645811 1.11858i −0.338303 0.941037i \(-0.609853\pi\)
0.984114 0.177540i \(-0.0568139\pi\)
\(758\) −15.9203 27.5747i −0.578251 1.00156i
\(759\) 10.5429i 0.382683i
\(760\) 4.56638 2.63640i 0.165640 0.0956324i
\(761\) 36.2213 20.9124i 1.31302 0.758073i 0.330425 0.943832i \(-0.392808\pi\)
0.982595 + 0.185759i \(0.0594745\pi\)
\(762\) 5.11506i 0.185299i
\(763\) 4.33762 + 7.51299i 0.157033 + 0.271988i
\(764\) 12.7472 22.0789i 0.461179 0.798785i
\(765\) 7.48701 + 4.32263i 0.270694 + 0.156285i
\(766\) −4.72228 −0.170623
\(767\) 35.8668 2.78138i 1.29508 0.100430i
\(768\) −1.00000 −0.0360844
\(769\) 15.4609 + 8.92635i 0.557534 + 0.321893i 0.752155 0.658986i \(-0.229014\pi\)
−0.194621 + 0.980879i \(0.562348\pi\)
\(770\) −5.26003 + 9.11064i −0.189558 + 0.328325i
\(771\) −12.1717 21.0820i −0.438352 0.759248i
\(772\) 8.52586i 0.306852i
\(773\) 10.4892 6.05596i 0.377272 0.217818i −0.299359 0.954141i \(-0.596773\pi\)
0.676630 + 0.736323i \(0.263439\pi\)
\(774\) −2.61681 + 1.51082i −0.0940592 + 0.0543051i
\(775\) 4.24506i 0.152487i
\(776\) −4.54961