Properties

Label 546.2.l.i.295.2
Level $546$
Weight $2$
Character 546.295
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.l (of order \(3\), degree \(2\), minimal)

Newform invariants

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

Embedding invariants

Embedding label 295.2
Root \(-0.780776 - 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 546.295
Dual form 546.2.l.i.211.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.561553 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.561553 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.280776 + 0.486319i) q^{10} +(0.780776 - 1.35234i) q^{11} +1.00000 q^{12} +(-0.500000 + 3.57071i) q^{13} -1.00000 q^{14} +(-0.280776 + 0.486319i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(2.34233 + 4.05703i) q^{19} +(-0.280776 - 0.486319i) q^{20} -1.00000 q^{21} +(0.780776 + 1.35234i) q^{22} +(0.438447 - 0.759413i) q^{23} +(-0.500000 + 0.866025i) q^{24} -4.68466 q^{25} +(-2.84233 - 2.21837i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(0.500000 - 0.866025i) q^{29} +(-0.280776 - 0.486319i) q^{30} -3.12311 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.780776 + 1.35234i) q^{33} -5.00000 q^{34} +(0.280776 + 0.486319i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.40388 + 9.35980i) q^{37} -4.68466 q^{38} +(-2.84233 - 2.21837i) q^{39} +0.561553 q^{40} +(2.06155 - 3.57071i) q^{41} +(0.500000 - 0.866025i) q^{42} +(5.56155 + 9.63289i) q^{43} -1.56155 q^{44} +(-0.280776 - 0.486319i) q^{45} +(0.438447 + 0.759413i) q^{46} +4.68466 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(2.34233 - 4.05703i) q^{50} -5.00000 q^{51} +(3.34233 - 1.35234i) q^{52} -12.1231 q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.438447 - 0.759413i) q^{55} +(0.500000 + 0.866025i) q^{56} -4.68466 q^{57} +(0.500000 + 0.866025i) q^{58} +(-2.43845 - 4.22351i) q^{59} +0.561553 q^{60} +(0.500000 + 0.866025i) q^{61} +(1.56155 - 2.70469i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-0.280776 + 2.00514i) q^{65} -1.56155 q^{66} +(3.56155 - 6.16879i) q^{67} +(2.50000 - 4.33013i) q^{68} +(0.438447 + 0.759413i) q^{69} -0.561553 q^{70} +(2.00000 + 3.46410i) q^{71} +(-0.500000 - 0.866025i) q^{72} -6.56155 q^{73} +(-5.40388 - 9.35980i) q^{74} +(2.34233 - 4.05703i) q^{75} +(2.34233 - 4.05703i) q^{76} +1.56155 q^{77} +(3.34233 - 1.35234i) q^{78} +5.56155 q^{79} +(-0.280776 + 0.486319i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.06155 + 3.57071i) q^{82} +6.24621 q^{83} +(0.500000 + 0.866025i) q^{84} +(1.40388 + 2.43160i) q^{85} -11.1231 q^{86} +(0.500000 + 0.866025i) q^{87} +(0.780776 - 1.35234i) q^{88} +(-1.34233 + 2.32498i) q^{89} +0.561553 q^{90} +(-3.34233 + 1.35234i) q^{91} -0.876894 q^{92} +(1.56155 - 2.70469i) q^{93} +(-2.34233 + 4.05703i) q^{94} +(1.31534 + 2.27824i) q^{95} +1.00000 q^{96} +(2.12311 + 3.67733i) q^{97} +(-0.500000 - 0.866025i) q^{98} -1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 6q^{5} - 2q^{6} + 2q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 6q^{5} - 2q^{6} + 2q^{7} + 4q^{8} - 2q^{9} + 3q^{10} - q^{11} + 4q^{12} - 2q^{13} - 4q^{14} + 3q^{15} - 2q^{16} + 10q^{17} + 4q^{18} - 3q^{19} + 3q^{20} - 4q^{21} - q^{22} + 10q^{23} - 2q^{24} + 6q^{25} + q^{26} + 4q^{27} + 2q^{28} + 2q^{29} + 3q^{30} + 4q^{31} - 2q^{32} - q^{33} - 20q^{34} - 3q^{35} - 2q^{36} - q^{37} + 6q^{38} + q^{39} - 6q^{40} + 2q^{42} + 14q^{43} + 2q^{44} + 3q^{45} + 10q^{46} - 6q^{47} - 2q^{48} - 2q^{49} - 3q^{50} - 20q^{51} + q^{52} - 32q^{53} - 2q^{54} + 10q^{55} + 2q^{56} + 6q^{57} + 2q^{58} - 18q^{59} - 6q^{60} + 2q^{61} - 2q^{62} + 2q^{63} + 4q^{64} + 3q^{65} + 2q^{66} + 6q^{67} + 10q^{68} + 10q^{69} + 6q^{70} + 8q^{71} - 2q^{72} - 18q^{73} - q^{74} - 3q^{75} - 3q^{76} - 2q^{77} + q^{78} + 14q^{79} + 3q^{80} - 2q^{81} - 8q^{83} + 2q^{84} - 15q^{85} - 28q^{86} + 2q^{87} - q^{88} + 7q^{89} - 6q^{90} - q^{91} - 20q^{92} - 2q^{93} + 3q^{94} + 30q^{95} + 4q^{96} - 8q^{97} - 2q^{98} + 2q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.561553 0.251134 0.125567 0.992085i \(-0.459925\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.280776 + 0.486319i −0.0887893 + 0.153788i
\(11\) 0.780776 1.35234i 0.235413 0.407747i −0.723980 0.689821i \(-0.757689\pi\)
0.959393 + 0.282074i \(0.0910224\pi\)
\(12\) 1.00000 0.288675
\(13\) −0.500000 + 3.57071i −0.138675 + 0.990338i
\(14\) −1.00000 −0.267261
\(15\) −0.280776 + 0.486319i −0.0724962 + 0.125567i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.50000 + 4.33013i 0.606339 + 1.05021i 0.991838 + 0.127502i \(0.0406959\pi\)
−0.385499 + 0.922708i \(0.625971\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.34233 + 4.05703i 0.537367 + 0.930747i 0.999045 + 0.0436994i \(0.0139144\pi\)
−0.461678 + 0.887048i \(0.652752\pi\)
\(20\) −0.280776 0.486319i −0.0627835 0.108744i
\(21\) −1.00000 −0.218218
\(22\) 0.780776 + 1.35234i 0.166462 + 0.288321i
\(23\) 0.438447 0.759413i 0.0914226 0.158349i −0.816687 0.577080i \(-0.804192\pi\)
0.908110 + 0.418732i \(0.137525\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −4.68466 −0.936932
\(26\) −2.84233 2.21837i −0.557427 0.435058i
\(27\) 1.00000 0.192450
\(28\) 0.500000 0.866025i 0.0944911 0.163663i
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) −0.280776 0.486319i −0.0512625 0.0887893i
\(31\) −3.12311 −0.560926 −0.280463 0.959865i \(-0.590488\pi\)
−0.280463 + 0.959865i \(0.590488\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.780776 + 1.35234i 0.135916 + 0.235413i
\(34\) −5.00000 −0.857493
\(35\) 0.280776 + 0.486319i 0.0474599 + 0.0822029i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −5.40388 + 9.35980i −0.888393 + 1.53874i −0.0466177 + 0.998913i \(0.514844\pi\)
−0.841775 + 0.539829i \(0.818489\pi\)
\(38\) −4.68466 −0.759952
\(39\) −2.84233 2.21837i −0.455137 0.355223i
\(40\) 0.561553 0.0887893
\(41\) 2.06155 3.57071i 0.321960 0.557652i −0.658932 0.752202i \(-0.728992\pi\)
0.980892 + 0.194551i \(0.0623249\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) 5.56155 + 9.63289i 0.848129 + 1.46900i 0.882876 + 0.469606i \(0.155604\pi\)
−0.0347472 + 0.999396i \(0.511063\pi\)
\(44\) −1.56155 −0.235413
\(45\) −0.280776 0.486319i −0.0418557 0.0724962i
\(46\) 0.438447 + 0.759413i 0.0646455 + 0.111969i
\(47\) 4.68466 0.683328 0.341664 0.939822i \(-0.389010\pi\)
0.341664 + 0.939822i \(0.389010\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 2.34233 4.05703i 0.331255 0.573751i
\(51\) −5.00000 −0.700140
\(52\) 3.34233 1.35234i 0.463498 0.187536i
\(53\) −12.1231 −1.66524 −0.832618 0.553847i \(-0.813159\pi\)
−0.832618 + 0.553847i \(0.813159\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0.438447 0.759413i 0.0591202 0.102399i
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) −4.68466 −0.620498
\(58\) 0.500000 + 0.866025i 0.0656532 + 0.113715i
\(59\) −2.43845 4.22351i −0.317459 0.549855i 0.662498 0.749063i \(-0.269496\pi\)
−0.979957 + 0.199209i \(0.936163\pi\)
\(60\) 0.561553 0.0724962
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 1.56155 2.70469i 0.198317 0.343496i
\(63\) 0.500000 0.866025i 0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) −0.280776 + 2.00514i −0.0348260 + 0.248708i
\(66\) −1.56155 −0.192214
\(67\) 3.56155 6.16879i 0.435113 0.753638i −0.562192 0.827007i \(-0.690042\pi\)
0.997305 + 0.0733691i \(0.0233751\pi\)
\(68\) 2.50000 4.33013i 0.303170 0.525105i
\(69\) 0.438447 + 0.759413i 0.0527828 + 0.0914226i
\(70\) −0.561553 −0.0671184
\(71\) 2.00000 + 3.46410i 0.237356 + 0.411113i 0.959955 0.280155i \(-0.0903858\pi\)
−0.722599 + 0.691268i \(0.757052\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −6.56155 −0.767972 −0.383986 0.923339i \(-0.625449\pi\)
−0.383986 + 0.923339i \(0.625449\pi\)
\(74\) −5.40388 9.35980i −0.628189 1.08805i
\(75\) 2.34233 4.05703i 0.270469 0.468466i
\(76\) 2.34233 4.05703i 0.268684 0.465374i
\(77\) 1.56155 0.177955
\(78\) 3.34233 1.35234i 0.378444 0.153123i
\(79\) 5.56155 0.625724 0.312862 0.949799i \(-0.398712\pi\)
0.312862 + 0.949799i \(0.398712\pi\)
\(80\) −0.280776 + 0.486319i −0.0313918 + 0.0543721i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.06155 + 3.57071i 0.227660 + 0.394319i
\(83\) 6.24621 0.685611 0.342805 0.939406i \(-0.388623\pi\)
0.342805 + 0.939406i \(0.388623\pi\)
\(84\) 0.500000 + 0.866025i 0.0545545 + 0.0944911i
\(85\) 1.40388 + 2.43160i 0.152272 + 0.263744i
\(86\) −11.1231 −1.19944
\(87\) 0.500000 + 0.866025i 0.0536056 + 0.0928477i
\(88\) 0.780776 1.35234i 0.0832310 0.144160i
\(89\) −1.34233 + 2.32498i −0.142287 + 0.246448i −0.928357 0.371689i \(-0.878779\pi\)
0.786071 + 0.618137i \(0.212112\pi\)
\(90\) 0.561553 0.0591929
\(91\) −3.34233 + 1.35234i −0.350371 + 0.141764i
\(92\) −0.876894 −0.0914226
\(93\) 1.56155 2.70469i 0.161925 0.280463i
\(94\) −2.34233 + 4.05703i −0.241593 + 0.418451i
\(95\) 1.31534 + 2.27824i 0.134951 + 0.233742i
\(96\) 1.00000 0.102062
\(97\) 2.12311 + 3.67733i 0.215569 + 0.373376i 0.953448 0.301556i \(-0.0975061\pi\)
−0.737880 + 0.674932i \(0.764173\pi\)
\(98\) −0.500000 0.866025i −0.0505076 0.0874818i
\(99\) −1.56155 −0.156942
\(100\) 2.34233 + 4.05703i 0.234233 + 0.405703i
\(101\) 7.71922 13.3701i 0.768091 1.33037i −0.170505 0.985357i \(-0.554540\pi\)
0.938597 0.345017i \(-0.112127\pi\)
\(102\) 2.50000 4.33013i 0.247537 0.428746i
\(103\) 13.3693 1.31732 0.658659 0.752442i \(-0.271124\pi\)
0.658659 + 0.752442i \(0.271124\pi\)
\(104\) −0.500000 + 3.57071i −0.0490290 + 0.350137i
\(105\) −0.561553 −0.0548019
\(106\) 6.06155 10.4989i 0.588750 1.01975i
\(107\) 6.78078 11.7446i 0.655522 1.13540i −0.326240 0.945287i \(-0.605782\pi\)
0.981763 0.190111i \(-0.0608848\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 9.12311 0.873835 0.436918 0.899502i \(-0.356070\pi\)
0.436918 + 0.899502i \(0.356070\pi\)
\(110\) 0.438447 + 0.759413i 0.0418043 + 0.0724072i
\(111\) −5.40388 9.35980i −0.512914 0.888393i
\(112\) −1.00000 −0.0944911
\(113\) 5.96543 + 10.3324i 0.561181 + 0.971994i 0.997394 + 0.0721503i \(0.0229861\pi\)
−0.436213 + 0.899844i \(0.643681\pi\)
\(114\) 2.34233 4.05703i 0.219379 0.379976i
\(115\) 0.246211 0.426450i 0.0229593 0.0397667i
\(116\) −1.00000 −0.0928477
\(117\) 3.34233 1.35234i 0.308998 0.125024i
\(118\) 4.87689 0.448955
\(119\) −2.50000 + 4.33013i −0.229175 + 0.396942i
\(120\) −0.280776 + 0.486319i −0.0256313 + 0.0443946i
\(121\) 4.28078 + 7.41452i 0.389161 + 0.674047i
\(122\) −1.00000 −0.0905357
\(123\) 2.06155 + 3.57071i 0.185884 + 0.321960i
\(124\) 1.56155 + 2.70469i 0.140232 + 0.242888i
\(125\) −5.43845 −0.486430
\(126\) 0.500000 + 0.866025i 0.0445435 + 0.0771517i
\(127\) 7.12311 12.3376i 0.632073 1.09478i −0.355054 0.934846i \(-0.615537\pi\)
0.987127 0.159937i \(-0.0511292\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −11.1231 −0.979335
\(130\) −1.59612 1.24573i −0.139989 0.109258i
\(131\) 16.4924 1.44095 0.720475 0.693481i \(-0.243924\pi\)
0.720475 + 0.693481i \(0.243924\pi\)
\(132\) 0.780776 1.35234i 0.0679579 0.117706i
\(133\) −2.34233 + 4.05703i −0.203106 + 0.351789i
\(134\) 3.56155 + 6.16879i 0.307671 + 0.532902i
\(135\) 0.561553 0.0483308
\(136\) 2.50000 + 4.33013i 0.214373 + 0.371305i
\(137\) −7.40388 12.8239i −0.632556 1.09562i −0.987027 0.160553i \(-0.948672\pi\)
0.354471 0.935067i \(-0.384661\pi\)
\(138\) −0.876894 −0.0746462
\(139\) −2.34233 4.05703i −0.198674 0.344113i 0.749425 0.662089i \(-0.230330\pi\)
−0.948099 + 0.317976i \(0.896997\pi\)
\(140\) 0.280776 0.486319i 0.0237299 0.0411015i
\(141\) −2.34233 + 4.05703i −0.197260 + 0.341664i
\(142\) −4.00000 −0.335673
\(143\) 4.43845 + 3.46410i 0.371162 + 0.289683i
\(144\) 1.00000 0.0833333
\(145\) 0.280776 0.486319i 0.0233172 0.0403866i
\(146\) 3.28078 5.68247i 0.271519 0.470285i
\(147\) −0.500000 0.866025i −0.0412393 0.0714286i
\(148\) 10.8078 0.888393
\(149\) −1.40388 2.43160i −0.115010 0.199204i 0.802773 0.596284i \(-0.203357\pi\)
−0.917784 + 0.397080i \(0.870024\pi\)
\(150\) 2.34233 + 4.05703i 0.191250 + 0.331255i
\(151\) −21.5616 −1.75465 −0.877327 0.479893i \(-0.840676\pi\)
−0.877327 + 0.479893i \(0.840676\pi\)
\(152\) 2.34233 + 4.05703i 0.189988 + 0.329069i
\(153\) 2.50000 4.33013i 0.202113 0.350070i
\(154\) −0.780776 + 1.35234i −0.0629168 + 0.108975i
\(155\) −1.75379 −0.140868
\(156\) −0.500000 + 3.57071i −0.0400320 + 0.285886i
\(157\) 14.8078 1.18179 0.590894 0.806749i \(-0.298775\pi\)
0.590894 + 0.806749i \(0.298775\pi\)
\(158\) −2.78078 + 4.81645i −0.221227 + 0.383176i
\(159\) 6.06155 10.4989i 0.480712 0.832618i
\(160\) −0.280776 0.486319i −0.0221973 0.0384469i
\(161\) 0.876894 0.0691090
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −3.56155 6.16879i −0.278962 0.483177i 0.692165 0.721739i \(-0.256657\pi\)
−0.971127 + 0.238563i \(0.923324\pi\)
\(164\) −4.12311 −0.321960
\(165\) 0.438447 + 0.759413i 0.0341331 + 0.0591202i
\(166\) −3.12311 + 5.40938i −0.242400 + 0.419849i
\(167\) 6.24621 10.8188i 0.483346 0.837180i −0.516471 0.856305i \(-0.672755\pi\)
0.999817 + 0.0191244i \(0.00608786\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −12.5000 3.57071i −0.961538 0.274670i
\(170\) −2.80776 −0.215346
\(171\) 2.34233 4.05703i 0.179122 0.310249i
\(172\) 5.56155 9.63289i 0.424064 0.734501i
\(173\) 6.56155 + 11.3649i 0.498866 + 0.864061i 0.999999 0.00130937i \(-0.000416786\pi\)
−0.501134 + 0.865370i \(0.667083\pi\)
\(174\) −1.00000 −0.0758098
\(175\) −2.34233 4.05703i −0.177063 0.306683i
\(176\) 0.780776 + 1.35234i 0.0588532 + 0.101937i
\(177\) 4.87689 0.366570
\(178\) −1.34233 2.32498i −0.100612 0.174265i
\(179\) −8.24621 + 14.2829i −0.616351 + 1.06755i 0.373795 + 0.927511i \(0.378056\pi\)
−0.990146 + 0.140040i \(0.955277\pi\)
\(180\) −0.280776 + 0.486319i −0.0209278 + 0.0362481i
\(181\) −3.24621 −0.241289 −0.120644 0.992696i \(-0.538496\pi\)
−0.120644 + 0.992696i \(0.538496\pi\)
\(182\) 0.500000 3.57071i 0.0370625 0.264679i
\(183\) −1.00000 −0.0739221
\(184\) 0.438447 0.759413i 0.0323228 0.0559847i
\(185\) −3.03457 + 5.25602i −0.223106 + 0.386430i
\(186\) 1.56155 + 2.70469i 0.114499 + 0.198317i
\(187\) 7.80776 0.570960
\(188\) −2.34233 4.05703i −0.170832 0.295890i
\(189\) 0.500000 + 0.866025i 0.0363696 + 0.0629941i
\(190\) −2.63068 −0.190850
\(191\) −11.1231 19.2658i −0.804840 1.39402i −0.916399 0.400265i \(-0.868918\pi\)
0.111560 0.993758i \(-0.464415\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −2.18466 + 3.78394i −0.157255 + 0.272374i −0.933878 0.357592i \(-0.883598\pi\)
0.776623 + 0.629966i \(0.216931\pi\)
\(194\) −4.24621 −0.304860
\(195\) −1.59612 1.24573i −0.114300 0.0892087i
\(196\) 1.00000 0.0714286
\(197\) −1.78078 + 3.08440i −0.126875 + 0.219754i −0.922464 0.386082i \(-0.873828\pi\)
0.795589 + 0.605836i \(0.207161\pi\)
\(198\) 0.780776 1.35234i 0.0554874 0.0961069i
\(199\) −11.8078 20.4516i −0.837030 1.44978i −0.892367 0.451311i \(-0.850956\pi\)
0.0553365 0.998468i \(-0.482377\pi\)
\(200\) −4.68466 −0.331255
\(201\) 3.56155 + 6.16879i 0.251213 + 0.435113i
\(202\) 7.71922 + 13.3701i 0.543123 + 0.940716i
\(203\) 1.00000 0.0701862
\(204\) 2.50000 + 4.33013i 0.175035 + 0.303170i
\(205\) 1.15767 2.00514i 0.0808552 0.140045i
\(206\) −6.68466 + 11.5782i −0.465742 + 0.806689i
\(207\) −0.876894 −0.0609484
\(208\) −2.84233 2.21837i −0.197080 0.153816i
\(209\) 7.31534 0.506013
\(210\) 0.280776 0.486319i 0.0193754 0.0335592i
\(211\) 5.56155 9.63289i 0.382873 0.663156i −0.608599 0.793478i \(-0.708268\pi\)
0.991472 + 0.130323i \(0.0416013\pi\)
\(212\) 6.06155 + 10.4989i 0.416309 + 0.721069i
\(213\) −4.00000 −0.274075
\(214\) 6.78078 + 11.7446i 0.463524 + 0.802848i
\(215\) 3.12311 + 5.40938i 0.212994 + 0.368916i
\(216\) 1.00000 0.0680414
\(217\) −1.56155 2.70469i −0.106005 0.183606i
\(218\) −4.56155 + 7.90084i −0.308947 + 0.535112i
\(219\) 3.28078 5.68247i 0.221694 0.383986i
\(220\) −0.876894 −0.0591202
\(221\) −16.7116 + 6.76172i −1.12415 + 0.454843i
\(222\) 10.8078 0.725370
\(223\) −8.24621 + 14.2829i −0.552207 + 0.956451i 0.445908 + 0.895079i \(0.352881\pi\)
−0.998115 + 0.0613719i \(0.980452\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) 2.34233 + 4.05703i 0.156155 + 0.270469i
\(226\) −11.9309 −0.793630
\(227\) −2.43845 4.22351i −0.161845 0.280324i 0.773685 0.633570i \(-0.218411\pi\)
−0.935531 + 0.353246i \(0.885078\pi\)
\(228\) 2.34233 + 4.05703i 0.155125 + 0.268684i
\(229\) 2.19224 0.144867 0.0724335 0.997373i \(-0.476923\pi\)
0.0724335 + 0.997373i \(0.476923\pi\)
\(230\) 0.246211 + 0.426450i 0.0162347 + 0.0281193i
\(231\) −0.780776 + 1.35234i −0.0513713 + 0.0889777i
\(232\) 0.500000 0.866025i 0.0328266 0.0568574i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −0.500000 + 3.57071i −0.0326860 + 0.233425i
\(235\) 2.63068 0.171607
\(236\) −2.43845 + 4.22351i −0.158729 + 0.274927i
\(237\) −2.78078 + 4.81645i −0.180631 + 0.312862i
\(238\) −2.50000 4.33013i −0.162051 0.280680i
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) −0.280776 0.486319i −0.0181240 0.0313918i
\(241\) −11.8423 20.5115i −0.762831 1.32126i −0.941385 0.337333i \(-0.890475\pi\)
0.178554 0.983930i \(-0.442858\pi\)
\(242\) −8.56155 −0.550357
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0.500000 0.866025i 0.0320092 0.0554416i
\(245\) −0.280776 + 0.486319i −0.0179381 + 0.0310698i
\(246\) −4.12311 −0.262880
\(247\) −15.6577 + 6.33527i −0.996274 + 0.403104i
\(248\) −3.12311 −0.198317
\(249\) −3.12311 + 5.40938i −0.197919 + 0.342805i
\(250\) 2.71922 4.70983i 0.171979 0.297876i
\(251\) 12.2462 + 21.2111i 0.772974 + 1.33883i 0.935926 + 0.352196i \(0.114565\pi\)
−0.162952 + 0.986634i \(0.552102\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −0.684658 1.18586i −0.0430441 0.0745546i
\(254\) 7.12311 + 12.3376i 0.446943 + 0.774129i
\(255\) −2.80776 −0.175829
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 15.6231 27.0600i 0.974543 1.68796i 0.293106 0.956080i \(-0.405311\pi\)
0.681436 0.731877i \(-0.261356\pi\)
\(258\) 5.56155 9.63289i 0.346247 0.599718i
\(259\) −10.8078 −0.671562
\(260\) 1.87689 0.759413i 0.116400 0.0470968i
\(261\) −1.00000 −0.0618984
\(262\) −8.24621 + 14.2829i −0.509453 + 0.882398i
\(263\) −6.24621 + 10.8188i −0.385158 + 0.667113i −0.991791 0.127869i \(-0.959186\pi\)
0.606633 + 0.794982i \(0.292520\pi\)
\(264\) 0.780776 + 1.35234i 0.0480535 + 0.0832310i
\(265\) −6.80776 −0.418198
\(266\) −2.34233 4.05703i −0.143617 0.248753i
\(267\) −1.34233 2.32498i −0.0821492 0.142287i
\(268\) −7.12311 −0.435113
\(269\) 6.56155 + 11.3649i 0.400065 + 0.692933i 0.993733 0.111777i \(-0.0356542\pi\)
−0.593668 + 0.804710i \(0.702321\pi\)
\(270\) −0.280776 + 0.486319i −0.0170875 + 0.0295964i
\(271\) −2.43845 + 4.22351i −0.148125 + 0.256560i −0.930535 0.366204i \(-0.880657\pi\)
0.782409 + 0.622764i \(0.213990\pi\)
\(272\) −5.00000 −0.303170
\(273\) 0.500000 3.57071i 0.0302614 0.216109i
\(274\) 14.8078 0.894570
\(275\) −3.65767 + 6.33527i −0.220566 + 0.382031i
\(276\) 0.438447 0.759413i 0.0263914 0.0457113i
\(277\) −0.280776 0.486319i −0.0168702 0.0292201i 0.857467 0.514539i \(-0.172037\pi\)
−0.874337 + 0.485319i \(0.838704\pi\)
\(278\) 4.68466 0.280967
\(279\) 1.56155 + 2.70469i 0.0934877 + 0.161925i
\(280\) 0.280776 + 0.486319i 0.0167796 + 0.0290631i
\(281\) −12.8078 −0.764047 −0.382024 0.924153i \(-0.624773\pi\)
−0.382024 + 0.924153i \(0.624773\pi\)
\(282\) −2.34233 4.05703i −0.139484 0.241593i
\(283\) 12.2462 21.2111i 0.727962 1.26087i −0.229782 0.973242i \(-0.573801\pi\)
0.957743 0.287624i \(-0.0928655\pi\)
\(284\) 2.00000 3.46410i 0.118678 0.205557i
\(285\) −2.63068 −0.155828
\(286\) −5.21922 + 2.11176i −0.308619 + 0.124871i
\(287\) 4.12311 0.243379
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 0.280776 + 0.486319i 0.0164878 + 0.0285576i
\(291\) −4.24621 −0.248917
\(292\) 3.28078 + 5.68247i 0.191993 + 0.332541i
\(293\) −3.84233 6.65511i −0.224471 0.388796i 0.731689 0.681638i \(-0.238732\pi\)
−0.956161 + 0.292843i \(0.905399\pi\)
\(294\) 1.00000 0.0583212
\(295\) −1.36932 2.37173i −0.0797247 0.138087i
\(296\) −5.40388 + 9.35980i −0.314094 + 0.544027i
\(297\) 0.780776 1.35234i 0.0453052 0.0784710i
\(298\) 2.80776 0.162649
\(299\) 2.49242 + 1.94528i 0.144141 + 0.112498i
\(300\) −4.68466 −0.270469
\(301\) −5.56155 + 9.63289i −0.320563 + 0.555231i
\(302\) 10.7808 18.6729i 0.620364 1.07450i
\(303\) 7.71922 + 13.3701i 0.443458 + 0.768091i
\(304\) −4.68466 −0.268684
\(305\) 0.280776 + 0.486319i 0.0160772 + 0.0278465i
\(306\) 2.50000 + 4.33013i 0.142915 + 0.247537i
\(307\) −5.06913 −0.289311 −0.144655 0.989482i \(-0.546207\pi\)
−0.144655 + 0.989482i \(0.546207\pi\)
\(308\) −0.780776 1.35234i −0.0444889 0.0770570i
\(309\) −6.68466 + 11.5782i −0.380277 + 0.658659i
\(310\) 0.876894 1.51883i 0.0498043 0.0862635i
\(311\) 18.4384 1.04555 0.522774 0.852471i \(-0.324897\pi\)
0.522774 + 0.852471i \(0.324897\pi\)
\(312\) −2.84233 2.21837i −0.160915 0.125590i
\(313\) −13.6155 −0.769595 −0.384798 0.923001i \(-0.625729\pi\)
−0.384798 + 0.923001i \(0.625729\pi\)
\(314\) −7.40388 + 12.8239i −0.417825 + 0.723695i
\(315\) 0.280776 0.486319i 0.0158200 0.0274010i
\(316\) −2.78078 4.81645i −0.156431 0.270946i
\(317\) −7.43845 −0.417785 −0.208892 0.977939i \(-0.566986\pi\)
−0.208892 + 0.977939i \(0.566986\pi\)
\(318\) 6.06155 + 10.4989i 0.339915 + 0.588750i
\(319\) −0.780776 1.35234i −0.0437151 0.0757168i
\(320\) 0.561553 0.0313918
\(321\) 6.78078 + 11.7446i 0.378466 + 0.655522i
\(322\) −0.438447 + 0.759413i −0.0244337 + 0.0423204i
\(323\) −11.7116 + 20.2852i −0.651653 + 1.12870i
\(324\) 1.00000 0.0555556
\(325\) 2.34233 16.7276i 0.129929 0.927879i
\(326\) 7.12311 0.394512
\(327\) −4.56155 + 7.90084i −0.252254 + 0.436918i
\(328\) 2.06155 3.57071i 0.113830 0.197160i
\(329\) 2.34233 + 4.05703i 0.129137 + 0.223671i
\(330\) −0.876894 −0.0482714
\(331\) 5.31534 + 9.20644i 0.292158 + 0.506032i 0.974320 0.225169i \(-0.0722935\pi\)
−0.682162 + 0.731201i \(0.738960\pi\)
\(332\) −3.12311 5.40938i −0.171403 0.296878i
\(333\) 10.8078 0.592262
\(334\) 6.24621 + 10.8188i 0.341777 + 0.591976i
\(335\) 2.00000 3.46410i 0.109272 0.189264i
\(336\) 0.500000 0.866025i 0.0272772 0.0472456i
\(337\) 3.49242 0.190244 0.0951222 0.995466i \(-0.469676\pi\)
0.0951222 + 0.995466i \(0.469676\pi\)
\(338\) 9.34233 9.03996i 0.508156 0.491709i
\(339\) −11.9309 −0.647996
\(340\) 1.40388 2.43160i 0.0761362 0.131872i
\(341\) −2.43845 + 4.22351i −0.132049 + 0.228716i
\(342\) 2.34233 + 4.05703i 0.126659 + 0.219379i
\(343\) −1.00000 −0.0539949
\(344\) 5.56155 + 9.63289i 0.299859 + 0.519371i
\(345\) 0.246211 + 0.426450i 0.0132556 + 0.0229593i
\(346\) −13.1231 −0.705503
\(347\) 6.34233 + 10.9852i 0.340474 + 0.589718i 0.984521 0.175268i \(-0.0560791\pi\)
−0.644047 + 0.764986i \(0.722746\pi\)
\(348\) 0.500000 0.866025i 0.0268028 0.0464238i
\(349\) −13.2462 + 22.9431i −0.709053 + 1.22812i 0.256155 + 0.966636i \(0.417544\pi\)
−0.965209 + 0.261481i \(0.915789\pi\)
\(350\) 4.68466 0.250406
\(351\) −0.500000 + 3.57071i −0.0266880 + 0.190591i
\(352\) −1.56155 −0.0832310
\(353\) −5.40388 + 9.35980i −0.287620 + 0.498172i −0.973241 0.229786i \(-0.926197\pi\)
0.685621 + 0.727958i \(0.259531\pi\)
\(354\) −2.43845 + 4.22351i −0.129602 + 0.224477i
\(355\) 1.12311 + 1.94528i 0.0596083 + 0.103245i
\(356\) 2.68466 0.142287
\(357\) −2.50000 4.33013i −0.132314 0.229175i
\(358\) −8.24621 14.2829i −0.435826 0.754872i
\(359\) −29.3693 −1.55005 −0.775027 0.631929i \(-0.782264\pi\)
−0.775027 + 0.631929i \(0.782264\pi\)
\(360\) −0.280776 0.486319i −0.0147982 0.0256313i
\(361\) −1.47301 + 2.55133i −0.0775270 + 0.134281i
\(362\) 1.62311 2.81130i 0.0853085 0.147759i
\(363\) −8.56155 −0.449365
\(364\) 2.84233 + 2.21837i 0.148979 + 0.116274i
\(365\) −3.68466 −0.192864
\(366\) 0.500000 0.866025i 0.0261354 0.0452679i
\(367\) 6.68466 11.5782i 0.348936 0.604375i −0.637124 0.770761i \(-0.719876\pi\)
0.986061 + 0.166385i \(0.0532096\pi\)
\(368\) 0.438447 + 0.759413i 0.0228556 + 0.0395871i
\(369\) −4.12311 −0.214640
\(370\) −3.03457 5.25602i −0.157760 0.273248i
\(371\) −6.06155 10.4989i −0.314700 0.545077i
\(372\) −3.12311 −0.161925
\(373\) −8.71922 15.1021i −0.451464 0.781959i 0.547013 0.837124i \(-0.315765\pi\)
−0.998477 + 0.0551651i \(0.982431\pi\)
\(374\) −3.90388 + 6.76172i −0.201865 + 0.349640i
\(375\) 2.71922 4.70983i 0.140420 0.243215i
\(376\) 4.68466 0.241593
\(377\) 2.84233 + 2.21837i 0.146387 + 0.114252i
\(378\) −1.00000 −0.0514344
\(379\) 16.2462 28.1393i 0.834512 1.44542i −0.0599155 0.998203i \(-0.519083\pi\)
0.894427 0.447213i \(-0.147584\pi\)
\(380\) 1.31534 2.27824i 0.0674756 0.116871i
\(381\) 7.12311 + 12.3376i 0.364928 + 0.632073i
\(382\) 22.2462 1.13822
\(383\) −10.3423 17.9134i −0.528468 0.915334i −0.999449 0.0331905i \(-0.989433\pi\)
0.470981 0.882144i \(-0.343900\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0.876894 0.0446907
\(386\) −2.18466 3.78394i −0.111196 0.192597i
\(387\) 5.56155 9.63289i 0.282710 0.489667i
\(388\) 2.12311 3.67733i 0.107784 0.186688i
\(389\) 6.31534 0.320201 0.160100 0.987101i \(-0.448818\pi\)
0.160100 + 0.987101i \(0.448818\pi\)
\(390\) 1.87689 0.759413i 0.0950402 0.0384544i
\(391\) 4.38447 0.221732
\(392\) −0.500000 + 0.866025i −0.0252538 + 0.0437409i
\(393\) −8.24621 + 14.2829i −0.415966 + 0.720475i
\(394\) −1.78078 3.08440i −0.0897142 0.155390i
\(395\) 3.12311 0.157140
\(396\) 0.780776 + 1.35234i 0.0392355 + 0.0679579i
\(397\) 5.34233 + 9.25319i 0.268124 + 0.464404i 0.968377 0.249490i \(-0.0802630\pi\)
−0.700254 + 0.713894i \(0.746930\pi\)
\(398\) 23.6155 1.18374
\(399\) −2.34233 4.05703i −0.117263 0.203106i
\(400\) 2.34233 4.05703i 0.117116 0.202852i
\(401\) 15.0885 26.1341i 0.753486 1.30508i −0.192638 0.981270i \(-0.561704\pi\)
0.946124 0.323806i \(-0.104962\pi\)
\(402\) −7.12311 −0.355268
\(403\) 1.56155 11.1517i 0.0777865 0.555507i
\(404\) −15.4384 −0.768091
\(405\) −0.280776 + 0.486319i −0.0139519 + 0.0241654i
\(406\) −0.500000 + 0.866025i −0.0248146 + 0.0429801i
\(407\) 8.43845 + 14.6158i 0.418278 + 0.724479i
\(408\) −5.00000 −0.247537
\(409\) 17.2808 + 29.9312i 0.854479 + 1.48000i 0.877127 + 0.480258i \(0.159457\pi\)
−0.0226477 + 0.999744i \(0.507210\pi\)
\(410\) 1.15767 + 2.00514i 0.0571733 + 0.0990270i
\(411\) 14.8078 0.730413
\(412\) −6.68466 11.5782i −0.329329 0.570415i
\(413\) 2.43845 4.22351i 0.119988 0.207826i
\(414\) 0.438447 0.759413i 0.0215485 0.0373231i
\(415\) 3.50758 0.172180
\(416\) 3.34233 1.35234i 0.163871 0.0663041i
\(417\) 4.68466 0.229409
\(418\) −3.65767 + 6.33527i −0.178903 + 0.309868i
\(419\) 13.3693 23.1563i 0.653134 1.13126i −0.329224 0.944252i \(-0.606787\pi\)
0.982358 0.187009i \(-0.0598795\pi\)
\(420\) 0.280776 + 0.486319i 0.0137005 + 0.0237299i
\(421\) 12.5616 0.612213 0.306106 0.951997i \(-0.400974\pi\)
0.306106 + 0.951997i \(0.400974\pi\)
\(422\) 5.56155 + 9.63289i 0.270732 + 0.468922i
\(423\) −2.34233 4.05703i −0.113888 0.197260i
\(424\) −12.1231 −0.588750
\(425\) −11.7116 20.2852i −0.568098 0.983975i
\(426\) 2.00000 3.46410i 0.0969003 0.167836i
\(427\) −0.500000 + 0.866025i −0.0241967 + 0.0419099i
\(428\) −13.5616 −0.655522
\(429\) −5.21922 + 2.11176i −0.251986 + 0.101957i
\(430\) −6.24621 −0.301219
\(431\) −15.3693 + 26.6204i −0.740314 + 1.28226i 0.212038 + 0.977261i \(0.431990\pi\)
−0.952352 + 0.305000i \(0.901344\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 8.84233 + 15.3154i 0.424935 + 0.736009i 0.996414 0.0846072i \(-0.0269635\pi\)
−0.571479 + 0.820617i \(0.693630\pi\)
\(434\) 3.12311 0.149914
\(435\) 0.280776 + 0.486319i 0.0134622 + 0.0233172i
\(436\) −4.56155 7.90084i −0.218459 0.378382i
\(437\) 4.10795 0.196510
\(438\) 3.28078 + 5.68247i 0.156762 + 0.271519i
\(439\) −2.24621 + 3.89055i −0.107206 + 0.185686i −0.914637 0.404275i \(-0.867524\pi\)
0.807431 + 0.589961i \(0.200857\pi\)
\(440\) 0.438447 0.759413i 0.0209021 0.0362036i
\(441\) 1.00000 0.0476190
\(442\) 2.50000 17.8536i 0.118913 0.849208i
\(443\) 27.4233 1.30292 0.651460 0.758683i \(-0.274157\pi\)
0.651460 + 0.758683i \(0.274157\pi\)
\(444\) −5.40388 + 9.35980i −0.256457 + 0.444196i
\(445\) −0.753789 + 1.30560i −0.0357330 + 0.0618914i
\(446\) −8.24621 14.2829i −0.390469 0.676313i
\(447\) 2.80776 0.132803
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) −9.00000 15.5885i −0.424736 0.735665i 0.571660 0.820491i \(-0.306300\pi\)
−0.996396 + 0.0848262i \(0.972967\pi\)
\(450\) −4.68466 −0.220837
\(451\) −3.21922 5.57586i −0.151587 0.262557i
\(452\) 5.96543 10.3324i 0.280590 0.485997i
\(453\) 10.7808 18.6729i 0.506525 0.877327i
\(454\) 4.87689 0.228884
\(455\) −1.87689 + 0.759413i −0.0879902 + 0.0356018i
\(456\) −4.68466 −0.219379
\(457\) 12.8423 22.2436i 0.600739 1.04051i −0.391971 0.919978i \(-0.628206\pi\)
0.992709 0.120532i \(-0.0384602\pi\)
\(458\) −1.09612 + 1.89853i −0.0512182 + 0.0887126i
\(459\) 2.50000 + 4.33013i 0.116690 + 0.202113i
\(460\) −0.492423 −0.0229593
\(461\) 3.52699 + 6.10892i 0.164268 + 0.284521i 0.936395 0.350947i \(-0.114140\pi\)
−0.772127 + 0.635468i \(0.780807\pi\)
\(462\) −0.780776 1.35234i −0.0363250 0.0629168i
\(463\) 0.684658 0.0318188 0.0159094 0.999873i \(-0.494936\pi\)
0.0159094 + 0.999873i \(0.494936\pi\)
\(464\) 0.500000 + 0.866025i 0.0232119 + 0.0402042i
\(465\) 0.876894 1.51883i 0.0406650 0.0704339i
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) 28.0000 1.29569 0.647843 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) −2.84233 2.21837i −0.131387 0.102544i
\(469\) 7.12311 0.328914
\(470\) −1.31534 + 2.27824i −0.0606722 + 0.105087i
\(471\) −7.40388 + 12.8239i −0.341153 + 0.590894i
\(472\) −2.43845 4.22351i −0.112239 0.194403i
\(473\) 17.3693 0.798642
\(474\) −2.78078 4.81645i −0.127725 0.221227i
\(475\) −10.9730 19.0058i −0.503476 0.872047i
\(476\) 5.00000 0.229175
\(477\) 6.06155 + 10.4989i 0.277539 + 0.480712i
\(478\) −2.00000 + 3.46410i −0.0914779 + 0.158444i
\(479\) −0.780776 + 1.35234i −0.0356746 + 0.0617902i −0.883311 0.468787i \(-0.844691\pi\)
0.847637 + 0.530577i \(0.178025\pi\)
\(480\) 0.561553 0.0256313
\(481\) −30.7192 23.9756i −1.40068 1.09319i
\(482\) 23.6847 1.07881
\(483\) −0.438447 + 0.759413i −0.0199500 + 0.0345545i
\(484\) 4.28078 7.41452i 0.194581 0.337024i
\(485\) 1.19224 + 2.06501i 0.0541366 + 0.0937674i
\(486\) 1.00000 0.0453609
\(487\) −5.65767 9.79937i −0.256374 0.444052i 0.708894 0.705315i \(-0.249194\pi\)
−0.965268 + 0.261263i \(0.915861\pi\)
\(488\) 0.500000 + 0.866025i 0.0226339 + 0.0392031i
\(489\) 7.12311 0.322118
\(490\) −0.280776 0.486319i −0.0126842 0.0219697i
\(491\) 9.12311 15.8017i 0.411720 0.713120i −0.583358 0.812215i \(-0.698262\pi\)
0.995078 + 0.0990952i \(0.0315948\pi\)
\(492\) 2.06155 3.57071i 0.0929420 0.160980i
\(493\) 5.00000 0.225189
\(494\) 2.34233 16.7276i 0.105386 0.752609i
\(495\) −0.876894 −0.0394135
\(496\) 1.56155 2.70469i 0.0701158 0.121444i
\(497\) −2.00000 + 3.46410i −0.0897123 + 0.155386i
\(498\) −3.12311 5.40938i −0.139950 0.242400i
\(499\) −2.63068 −0.117766 −0.0588828 0.998265i \(-0.518754\pi\)
−0.0588828 + 0.998265i \(0.518754\pi\)
\(500\) 2.71922 + 4.70983i 0.121607 + 0.210630i
\(501\) 6.24621 + 10.8188i 0.279060 + 0.483346i
\(502\) −24.4924 −1.09315
\(503\) 6.24621 + 10.8188i 0.278505 + 0.482384i 0.971013 0.239025i \(-0.0768279\pi\)
−0.692509 + 0.721410i \(0.743495\pi\)
\(504\) 0.500000 0.866025i 0.0222718 0.0385758i
\(505\) 4.33475 7.50801i 0.192894 0.334102i
\(506\) 1.36932 0.0608736
\(507\) 9.34233 9.03996i 0.414907 0.401479i
\(508\) −14.2462 −0.632073
\(509\) −19.8423 + 34.3679i −0.879496 + 1.52333i −0.0276006 + 0.999619i \(0.508787\pi\)
−0.851895 + 0.523712i \(0.824547\pi\)
\(510\) 1.40388 2.43160i 0.0621649 0.107673i
\(511\) −3.28078 5.68247i −0.145133 0.251378i
\(512\) 1.00000 0.0441942
\(513\) 2.34233 + 4.05703i 0.103416 + 0.179122i
\(514\) 15.6231 + 27.0600i 0.689106 + 1.19357i
\(515\) 7.50758 0.330823
\(516\) 5.56155 + 9.63289i 0.244834 + 0.424064i
\(517\) 3.65767 6.33527i 0.160864 0.278625i
\(518\) 5.40388 9.35980i 0.237433 0.411246i
\(519\) −13.1231 −0.576040
\(520\) −0.280776 + 2.00514i −0.0123129 + 0.0879314i
\(521\) −17.0000 −0.744784 −0.372392 0.928076i \(-0.621462\pi\)
−0.372392 + 0.928076i \(0.621462\pi\)
\(522\) 0.500000 0.866025i 0.0218844 0.0379049i
\(523\) −17.9039 + 31.0104i −0.782882 + 1.35599i 0.147374 + 0.989081i \(0.452918\pi\)
−0.930256 + 0.366911i \(0.880415\pi\)
\(524\) −8.24621 14.2829i −0.360237 0.623949i
\(525\) 4.68466 0.204455
\(526\) −6.24621 10.8188i −0.272348 0.471720i
\(527\) −7.80776 13.5234i −0.340112 0.589090i
\(528\) −1.56155 −0.0679579
\(529\) 11.1155 + 19.2527i 0.483284 + 0.837072i
\(530\) 3.40388 5.89570i 0.147855 0.256093i
\(531\) −2.43845 + 4.22351i −0.105820 + 0.183285i
\(532\) 4.68466 0.203106
\(533\) 11.7192 + 9.14657i 0.507616 + 0.396182i
\(534\) 2.68466 0.116177
\(535\) 3.80776 6.59524i 0.164624 0.285137i
\(536\) 3.56155 6.16879i 0.153836 0.266451i
\(537\) −8.24621 14.2829i −0.355850 0.616351i
\(538\) −13.1231 −0.565777
\(539\) 0.780776 + 1.35234i 0.0336304 + 0.0582496i
\(540\) −0.280776 0.486319i −0.0120827 0.0209278i
\(541\) −2.56155 −0.110130 −0.0550649 0.998483i \(-0.517537\pi\)
−0.0550649 + 0.998483i \(0.517537\pi\)
\(542\) −2.43845 4.22351i −0.104740 0.181415i
\(543\) 1.62311 2.81130i 0.0696541 0.120644i
\(544\) 2.50000 4.33013i 0.107187 0.185653i
\(545\) 5.12311 0.219450
\(546\) 2.84233 + 2.21837i 0.121640 + 0.0949375i
\(547\) 26.7386 1.14326 0.571631 0.820511i \(-0.306311\pi\)
0.571631 + 0.820511i \(0.306311\pi\)
\(548\) −7.40388 + 12.8239i −0.316278 + 0.547810i
\(549\) 0.500000 0.866025i 0.0213395 0.0369611i
\(550\) −3.65767 6.33527i −0.155964 0.270137i
\(551\) 4.68466 0.199573
\(552\) 0.438447 + 0.759413i 0.0186616 + 0.0323228i
\(553\) 2.78078 + 4.81645i 0.118251 + 0.204816i
\(554\) 0.561553 0.0238581
\(555\) −3.03457 5.25602i −0.128810 0.223106i
\(556\) −2.34233 + 4.05703i −0.0993369 + 0.172057i
\(557\) 13.8693 24.0224i 0.587662 1.01786i −0.406876 0.913483i \(-0.633382\pi\)
0.994538 0.104377i \(-0.0332848\pi\)
\(558\) −3.12311 −0.132212
\(559\) −37.1771 + 15.0423i −1.57242 + 0.636220i
\(560\) −0.561553 −0.0237299
\(561\) −3.90388 + 6.76172i −0.164822 + 0.285480i
\(562\) 6.40388 11.0918i 0.270131 0.467881i
\(563\) 12.6847 + 21.9705i 0.534595 + 0.925945i 0.999183 + 0.0404182i \(0.0128690\pi\)
−0.464588 + 0.885527i \(0.653798\pi\)
\(564\) 4.68466 0.197260
\(565\) 3.34991 + 5.80221i 0.140932 + 0.244101i
\(566\) 12.2462 + 21.2111i 0.514747 + 0.891567i
\(567\) −1.00000 −0.0419961
\(568\) 2.00000 + 3.46410i 0.0839181 + 0.145350i
\(569\) 14.8078 25.6478i 0.620774 1.07521i −0.368568 0.929601i \(-0.620152\pi\)
0.989342 0.145611i \(-0.0465148\pi\)
\(570\) 1.31534 2.27824i 0.0550936 0.0954249i
\(571\) 30.2462 1.26576 0.632882 0.774248i \(-0.281872\pi\)
0.632882 + 0.774248i \(0.281872\pi\)
\(572\) 0.780776 5.57586i 0.0326459 0.233138i
\(573\) 22.2462 0.929349
\(574\) −2.06155 + 3.57071i −0.0860476 + 0.149039i
\(575\) −2.05398 + 3.55759i −0.0856567 + 0.148362i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 43.6847 1.81862 0.909308 0.416124i \(-0.136612\pi\)
0.909308 + 0.416124i \(0.136612\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) −2.18466 3.78394i −0.0907913 0.157255i
\(580\) −0.561553 −0.0233172
\(581\) 3.12311 + 5.40938i 0.129568 + 0.224419i
\(582\) 2.12311 3.67733i 0.0880056 0.152430i
\(583\) −9.46543 + 16.3946i −0.392018 + 0.678996i
\(584\) −6.56155 −0.271519
\(585\) 1.87689 0.759413i 0.0776000 0.0313979i
\(586\) 7.68466 0.317450
\(587\) −3.31534 + 5.74234i −0.136839 + 0.237012i −0.926298 0.376791i \(-0.877028\pi\)
0.789460 + 0.613803i \(0.210361\pi\)
\(588\) −0.500000 + 0.866025i −0.0206197 + 0.0357143i
\(589\) −7.31534 12.6705i −0.301423 0.522081i
\(590\) 2.73863 0.112748
\(591\) −1.78078 3.08440i −0.0732514 0.126875i
\(592\) −5.40388 9.35980i −0.222098 0.384685i
\(593\) −8.61553 −0.353797 −0.176899 0.984229i \(-0.556606\pi\)
−0.176899 + 0.984229i \(0.556606\pi\)
\(594\) 0.780776 + 1.35234i 0.0320356 + 0.0554874i
\(595\) −1.40388 + 2.43160i −0.0575536 + 0.0996857i
\(596\) −1.40388 + 2.43160i −0.0575052 + 0.0996020i
\(597\) 23.6155 0.966519
\(598\) −2.93087 + 1.18586i −0.119852 + 0.0484936i
\(599\) −31.1231 −1.27166 −0.635828 0.771831i \(-0.719341\pi\)
−0.635828 + 0.771831i \(0.719341\pi\)
\(600\) 2.34233 4.05703i 0.0956252 0.165628i
\(601\) −4.03457 + 6.98807i −0.164573 + 0.285049i −0.936504 0.350658i \(-0.885958\pi\)
0.771930 + 0.635707i \(0.219291\pi\)
\(602\) −5.56155 9.63289i −0.226672 0.392607i
\(603\) −7.12311 −0.290075
\(604\) 10.7808 + 18.6729i 0.438664 + 0.759788i
\(605\) 2.40388 + 4.16365i 0.0977317 + 0.169276i
\(606\) −15.4384 −0.627144
\(607\) −6.43845 11.1517i −0.261329 0.452634i 0.705267 0.708942i \(-0.250827\pi\)
−0.966595 + 0.256308i \(0.917494\pi\)
\(608\) 2.34233 4.05703i 0.0949940 0.164534i
\(609\) −0.500000 + 0.866025i −0.0202610 + 0.0350931i
\(610\) −0.561553 −0.0227366
\(611\) −2.34233 + 16.7276i −0.0947605 + 0.676725i
\(612\) −5.00000 −0.202113
\(613\) 8.65009 14.9824i 0.349374 0.605133i −0.636764 0.771058i \(-0.719728\pi\)
0.986138 + 0.165925i \(0.0530609\pi\)
\(614\) 2.53457 4.39000i 0.102287 0.177166i
\(615\) 1.15767 + 2.00514i 0.0466818 + 0.0808552i
\(616\) 1.56155 0.0629168
\(617\) −17.2116 29.8114i −0.692915 1.20016i −0.970879 0.239572i \(-0.922993\pi\)
0.277964 0.960592i \(-0.410340\pi\)
\(618\) −6.68466 11.5782i −0.268896 0.465742i
\(619\) 16.6847 0.670613 0.335307 0.942109i \(-0.391160\pi\)
0.335307 + 0.942109i \(0.391160\pi\)
\(620\) 0.876894 + 1.51883i 0.0352169 + 0.0609975i
\(621\) 0.438447 0.759413i 0.0175943 0.0304742i
\(622\) −9.21922 + 15.9682i −0.369657 + 0.640265i
\(623\) −2.68466 −0.107559
\(624\) 3.34233 1.35234i 0.133800 0.0541371i
\(625\) 20.3693 0.814773
\(626\) 6.80776 11.7914i 0.272093 0.471279i
\(627\) −3.65767 + 6.33527i −0.146073 + 0.253006i
\(628\) −7.40388 12.8239i −0.295447 0.511729i
\(629\) −54.0388 −2.15467
\(630\) 0.280776 + 0.486319i 0.0111864 + 0.0193754i
\(631\) −21.9039 37.9386i −0.871980 1.51031i −0.859946 0.510386i \(-0.829503\pi\)
−0.0120342 0.999928i \(-0.503831\pi\)
\(632\) 5.56155 0.221227
\(633\) 5.56155 + 9.63289i 0.221052 + 0.382873i
\(634\) 3.71922 6.44188i 0.147709 0.255840i
\(635\) 4.00000 6.92820i 0.158735 0.274937i
\(636\) −12.1231 −0.480712
\(637\) −2.84233 2.21837i −0.112617 0.0878950i
\(638\) 1.56155 0.0618225
\(639\) 2.00000 3.46410i 0.0791188 0.137038i
\(640\) −0.280776 + 0.486319i −0.0110987 + 0.0192234i
\(641\) −4.03457 6.98807i −0.159356 0.276012i 0.775281 0.631617i \(-0.217608\pi\)
−0.934637 + 0.355604i \(0.884275\pi\)
\(642\) −13.5616 −0.535232
\(643\) 11.2192 + 19.4323i 0.442443 + 0.766334i 0.997870 0.0652314i \(-0.0207786\pi\)
−0.555427 + 0.831565i \(0.687445\pi\)
\(644\) −0.438447 0.759413i −0.0172772 0.0299251i
\(645\) −6.24621 −0.245944
\(646\) −11.7116 20.2852i −0.460789 0.798109i
\(647\) 0.0961180 0.166481i 0.00377879 0.00654505i −0.864130 0.503269i \(-0.832131\pi\)
0.867909 + 0.496724i \(0.165464\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −7.61553 −0.298936
\(650\) 13.3153 + 10.3923i 0.522271 + 0.407620i
\(651\) 3.12311 0.122404
\(652\) −3.56155 + 6.16879i −0.139481 + 0.241588i
\(653\) −0.903882 + 1.56557i −0.0353716 + 0.0612655i −0.883169 0.469054i \(-0.844595\pi\)
0.847798 + 0.530320i \(0.177928\pi\)
\(654\) −4.56155 7.90084i −0.178371 0.308947i
\(655\) 9.26137 0.361872
\(656\) 2.06155 + 3.57071i 0.0804901 + 0.139413i
\(657\) 3.28078 + 5.68247i 0.127995 + 0.221694i
\(658\) −4.68466 −0.182627
\(659\) 20.3423 + 35.2339i 0.792425 + 1.37252i 0.924462 + 0.381275i \(0.124515\pi\)
−0.132037 + 0.991245i \(0.542152\pi\)
\(660\) 0.438447 0.759413i 0.0170665 0.0295601i
\(661\) −5.40388 + 9.35980i −0.210187 + 0.364054i −0.951773 0.306804i \(-0.900741\pi\)
0.741586 + 0.670858i \(0.234074\pi\)
\(662\) −10.6307 −0.413173
\(663\) 2.50000 17.8536i 0.0970920 0.693375i
\(664\) 6.24621 0.242400
\(665\) −1.31534 + 2.27824i −0.0510068 + 0.0883463i
\(666\) −5.40388 + 9.35980i −0.209396 + 0.362685i
\(667\) −0.438447 0.759413i −0.0169767 0.0294046i
\(668\) −12.4924 −0.483346
\(669\) −8.24621 14.2829i −0.318817 0.552207i
\(670\) 2.00000 + 3.46410i 0.0772667 + 0.133830i
\(671\) 1.56155 0.0602831
\(672\) 0.500000 + 0.866025i 0.0192879 + 0.0334077i
\(673\) −12.6231 + 21.8639i −0.486585 + 0.842790i −0.999881 0.0154217i \(-0.995091\pi\)
0.513296 + 0.858212i \(0.328424\pi\)
\(674\) −1.74621 + 3.02453i −0.0672615 + 0.116500i
\(675\) −4.68466 −0.180313
\(676\) 3.15767 + 12.6107i 0.121449 + 0.485026i
\(677\) −49.6155 −1.90688 −0.953440 0.301583i \(-0.902485\pi\)
−0.953440 + 0.301583i \(0.902485\pi\)
\(678\) 5.96543 10.3324i 0.229101 0.396815i
\(679\) −2.12311 + 3.67733i −0.0814773 + 0.141123i
\(680\) 1.40388 + 2.43160i 0.0538364 + 0.0932474i
\(681\) 4.87689 0.186883
\(682\) −2.43845 4.22351i −0.0933730 0.161727i
\(683\) −2.00000 3.46410i −0.0765279 0.132550i 0.825222 0.564809i \(-0.191050\pi\)
−0.901750 + 0.432259i \(0.857717\pi\)
\(684\) −4.68466 −0.179122
\(685\) −4.15767 7.20130i −0.158856 0.275147i
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) −1.09612 + 1.89853i −0.0418195 + 0.0724335i
\(688\) −11.1231 −0.424064
\(689\) 6.06155 43.2881i 0.230927 1.64915i
\(690\) −0.492423 −0.0187462
\(691\) −2.24621 + 3.89055i −0.0854499 + 0.148004i −0.905583 0.424169i \(-0.860566\pi\)
0.820133 + 0.572173i \(0.193899\pi\)
\(692\) 6.56155 11.3649i 0.249433 0.432030i
\(693\) −0.780776 1.35234i −0.0296592 0.0513713i
\(694\) −12.6847 −0.481503
\(695\) −1.31534 2.27824i −0.0498937 0.0864185i
\(696\) 0.500000 + 0.866025i 0.0189525 + 0.0328266i
\(697\) 20.6155 0.780869
\(698\) −13.2462 22.9431i −0.501376 0.868410i
\(699\) 3.00000 5.19615i 0.113470 0.196537i
\(700\) −2.34233 + 4.05703i −0.0885317 + 0.153341i
\(701\) −28.0540 −1.05958 −0.529792 0.848128i \(-0.677730\pi\)
−0.529792 + 0.848128i \(0.677730\pi\)
\(702\) −2.84233 2.21837i −0.107277 0.0837270i
\(703\) −50.6307 −1.90957
\(704\) 0.780776 1.35234i 0.0294266 0.0509684i
\(705\) −1.31534 + 2.27824i −0.0495386 + 0.0858034i
\(706\) −5.40388 9.35980i −0.203378 0.352261i
\(707\) 15.4384 0.580623
\(708\) −2.43845 4.22351i −0.0916425 0.158729i
\(709\) 16.6501 + 28.8388i 0.625307 + 1.08306i 0.988481 + 0.151343i \(0.0483597\pi\)
−0.363174 + 0.931721i \(0.618307\pi\)
\(710\) −2.24621 −0.0842988
\(711\) −2.78078 4.81645i −0.104287 0.180631i
\(712\) −1.34233 + 2.32498i −0.0503059 + 0.0871324i
\(713\) −1.36932 + 2.37173i −0.0512813 + 0.0888219i
\(714\) 5.00000 0.187120
\(715\) 2.49242 + 1.94528i 0.0932113 + 0.0727492i
\(716\) 16.4924 0.616351
\(717\) −2.00000 + 3.46410i −0.0746914 + 0.129369i
\(718\) 14.6847 25.4346i 0.548027 0.949210i
\(719\) 3.46543 + 6.00231i 0.129239 + 0.223848i 0.923382 0.383883i \(-0.125413\pi\)
−0.794143 + 0.607731i \(0.792080\pi\)
\(720\) 0.561553 0.0209278
\(721\) 6.68466 + 11.5782i 0.248950 + 0.431194i
\(722\) −1.47301 2.55133i −0.0548198 0.0949508i
\(723\) 23.6847 0.880842
\(724\) 1.62311 + 2.81130i 0.0603222 + 0.104481i
\(725\) −2.34233 + 4.05703i −0.0869919 + 0.150674i
\(726\) 4.28078 7.41452i 0.158875 0.275179i
\(727\) 33.7538 1.25186 0.625929 0.779880i \(-0.284720\pi\)
0.625929 + 0.779880i \(0.284720\pi\)
\(728\) −3.34233 + 1.35234i −0.123875 + 0.0501212i
\(729\) 1.00000 0.0370370
\(730\) 1.84233 3.19101i 0.0681877 0.118104i
\(731\) −27.8078 + 48.1645i −1.02851 + 1.78143i
\(732\) 0.500000 + 0.866025i 0.0184805 + 0.0320092i
\(733\) −8.61553 −0.318222 −0.159111 0.987261i \(-0.550863\pi\)
−0.159111 + 0.987261i \(0.550863\pi\)
\(734\) 6.68466 + 11.5782i 0.246735 + 0.427358i
\(735\) −0.280776 0.486319i −0.0103566 0.0179381i
\(736\) −0.876894 −0.0323228
\(737\) −5.56155 9.63289i −0.204862 0.354832i
\(738\) 2.06155 3.57071i 0.0758868 0.131440i
\(739\) −11.3153 + 19.5987i −0.416242 + 0.720952i −0.995558 0.0941513i \(-0.969986\pi\)
0.579316 + 0.815103i \(0.303320\pi\)
\(740\) 6.06913 0.223106
\(741\) 2.34233 16.7276i 0.0860476 0.614503i
\(742\) 12.1231 0.445053
\(743\) −16.6847 + 28.8987i −0.612101 + 1.06019i 0.378785 + 0.925485i \(0.376342\pi\)
−0.990886 + 0.134705i \(0.956991\pi\)
\(744\) 1.56155 2.70469i 0.0572493 0.0991587i
\(745\) −0.788354 1.36547i −0.0288831 0.0500269i
\(746\) 17.4384 0.638467
\(747\) −3.12311 5.40938i −0.114268 0.197919i
\(748\) −3.90388 6.76172i −0.142740 0.247233i
\(749\) 13.5616 0.495528
\(750\) 2.71922 + 4.70983i 0.0992920 + 0.171979i
\(751\) −9.90388 + 17.1540i −0.361398 + 0.625959i −0.988191 0.153226i \(-0.951034\pi\)
0.626793 + 0.779186i \(0.284367\pi\)
\(752\) −2.34233 + 4.05703i −0.0854160 + 0.147945i
\(753\) −24.4924 −0.892553
\(754\) −3.34233 + 1.35234i −0.121720 + 0.0492495i
\(755\) −12.1080 −0.440653
\(756\) 0.500000 0.866025i 0.0181848 0.0314970i
\(757\) −0.561553 + 0.972638i −0.0204100 + 0.0353511i −0.876050 0.482220i \(-0.839830\pi\)
0.855640 + 0.517571i \(0.173164\pi\)
\(758\) 16.2462 + 28.1393i 0.590089 + 1.02206i
\(759\) 1.36932 0.0497031
\(760\) 1.31534 + 2.27824i 0.0477125 + 0.0826404i
\(761\) 4.75379 + 8.23380i 0.172325 + 0.298475i 0.939232 0.343283i \(-0.111539\pi\)
−0.766907 + 0.641758i \(0.778205\pi\)
\(762\) −14.2462 −0.516086
\(763\) 4.56155 + 7.90084i 0.165139 + 0.286030i
\(764\) −11.1231 + 19.2658i −0.402420 + 0.697012i
\(765\) 1.40388 2.43160i 0.0507575 0.0879145i
\(766\) 20.6847 0.747367
\(767\) 16.3002 6.59524i 0.588566 0.238140i
\(768\) 1.00000 0.0360844
\(769\) −21.4924 + 37.2260i −0.775037 + 1.34240i 0.159737 + 0.987160i \(0.448935\pi\)
−0.934774 + 0.355243i \(0.884398\pi\)
\(770\) −0.438447 + 0.759413i −0.0158005 + 0.0273673i
\(771\) 15.6231 + 27.0600i 0.562652 + 0.974543i
\(772\) 4.36932 0.157255
\(773\) 3.24621 + 5.62260i 0.116758 + 0.202231i 0.918481 0.395465i \(-0.129416\pi\)
−0.801723 + 0.597696i \(0.796083\pi\)
\(774\) 5.56155 + 9.63289i 0.199906 + 0.346247i
\(775\) 14.6307 0.525550
\(776\) 2.12311 + 3.67733i 0.0762151