Properties

Label 1110.2.i.o.211.2
Level $1110$
Weight $2$
Character 1110.211
Analytic conductor $8.863$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.45911232.1
Defining polynomial: \(x^{6} + 11 x^{4} - 4 x^{3} + 121 x^{2} - 22 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.2
Root \(1.61084 + 2.79005i\) of defining polynomial
Character \(\chi\) \(=\) 1110.211
Dual form 1110.2.i.o.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.210618 + 0.364801i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.210618 + 0.364801i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -3.22168 q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.500000 + 0.866025i) q^{13} +0.421236 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.28938 - 2.23328i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.11084 - 3.65608i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.210618 + 0.364801i) q^{21} +(1.61084 + 2.79005i) q^{22} -5.60088 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} -1.00000 q^{27} +(-0.210618 - 0.364801i) q^{28} -7.24380 q^{29} +(-0.500000 + 0.866025i) q^{30} -2.44335 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.61084 + 2.79005i) q^{33} +(-1.28938 + 2.23328i) q^{34} +(0.210618 + 0.364801i) q^{35} +1.00000 q^{36} +(-2.07876 - 5.71653i) q^{37} -4.22168 q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +(5.12190 - 8.87139i) q^{41} +(0.210618 - 0.364801i) q^{42} +0.842472 q^{43} +(1.61084 - 2.79005i) q^{44} -1.00000 q^{45} +(2.80044 + 4.85051i) q^{46} -8.82256 q^{47} -1.00000 q^{48} +(3.41128 + 5.90851i) q^{49} +(-0.500000 + 0.866025i) q^{50} -2.57876 q^{51} +(-0.500000 - 0.866025i) q^{52} +(1.32146 + 2.28883i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.61084 + 2.79005i) q^{55} +(-0.210618 + 0.364801i) q^{56} +(-2.11084 - 3.65608i) q^{57} +(3.62190 + 6.27331i) q^{58} +(1.03207 + 1.78761i) q^{59} +1.00000 q^{60} +(0.900221 - 1.55923i) q^{61} +(1.22168 + 2.11601i) q^{62} +0.421236 q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +3.22168 q^{66} +(1.93230 - 3.34683i) q^{67} +2.57876 q^{68} +(-2.80044 + 4.85051i) q^{69} +(0.210618 - 0.364801i) q^{70} +(3.58982 - 6.21776i) q^{71} +(-0.500000 - 0.866025i) q^{72} -8.44335 q^{73} +(-3.91128 + 4.65853i) q^{74} -1.00000 q^{75} +(2.11084 + 3.65608i) q^{76} +(0.678543 - 1.17527i) q^{77} +(0.500000 - 0.866025i) q^{78} +(-7.37921 + 12.7812i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -10.2438 q^{82} +(-7.01106 - 12.1435i) q^{83} -0.421236 q^{84} -2.57876 q^{85} +(-0.421236 - 0.729602i) q^{86} +(-3.62190 + 6.27331i) q^{87} -3.22168 q^{88} +(-3.42124 - 5.92575i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-0.210618 - 0.364801i) q^{91} +(2.80044 - 4.85051i) q^{92} +(-1.22168 + 2.11601i) q^{93} +(4.41128 + 7.64056i) q^{94} +(-2.11084 - 3.65608i) q^{95} +(0.500000 + 0.866025i) q^{96} +2.00000 q^{97} +(3.41128 - 5.90851i) q^{98} +(1.61084 + 2.79005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} + 3q^{3} - 3q^{4} + 3q^{5} - 6q^{6} - q^{7} + 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q - 3q^{2} + 3q^{3} - 3q^{4} + 3q^{5} - 6q^{6} - q^{7} + 6q^{8} - 3q^{9} - 6q^{10} + 3q^{12} - 3q^{13} + 2q^{14} - 3q^{15} - 3q^{16} - 8q^{17} - 3q^{18} + 3q^{19} + 3q^{20} + q^{21} + 4q^{23} + 3q^{24} - 3q^{25} + 6q^{26} - 6q^{27} - q^{28} + 14q^{29} - 3q^{30} + 24q^{31} - 3q^{32} - 8q^{34} + q^{35} + 6q^{36} - 13q^{37} - 6q^{38} + 3q^{39} + 3q^{40} + 2q^{41} + q^{42} + 4q^{43} - 6q^{45} - 2q^{46} + 4q^{47} - 6q^{48} - 8q^{49} - 3q^{50} - 16q^{51} - 3q^{52} - 2q^{53} + 3q^{54} - q^{56} - 3q^{57} - 7q^{58} - 4q^{59} + 6q^{60} - 4q^{61} - 12q^{62} + 2q^{63} + 6q^{64} + 3q^{65} - 8q^{67} + 16q^{68} + 2q^{69} + q^{70} + 3q^{71} - 3q^{72} - 12q^{73} + 5q^{74} - 6q^{75} + 3q^{76} + 14q^{77} + 3q^{78} - 26q^{79} - 6q^{80} - 3q^{81} - 4q^{82} - 23q^{83} - 2q^{84} - 16q^{85} - 2q^{86} + 7q^{87} - 20q^{89} + 3q^{90} - q^{91} - 2q^{92} + 12q^{93} - 2q^{94} - 3q^{95} + 3q^{96} + 12q^{97} - 8q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −1.00000 −0.408248
\(7\) −0.210618 + 0.364801i −0.0796061 + 0.137882i −0.903080 0.429472i \(-0.858700\pi\)
0.823474 + 0.567354i \(0.192033\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.00000 −0.316228
\(11\) −3.22168 −0.971372 −0.485686 0.874133i \(-0.661430\pi\)
−0.485686 + 0.874133i \(0.661430\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 0.421236 0.112580
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.28938 2.23328i −0.312721 0.541649i 0.666229 0.745747i \(-0.267907\pi\)
−0.978950 + 0.204098i \(0.934574\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 2.11084 3.65608i 0.484260 0.838762i −0.515577 0.856843i \(-0.672422\pi\)
0.999837 + 0.0180811i \(0.00575569\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 0.210618 + 0.364801i 0.0459606 + 0.0796061i
\(22\) 1.61084 + 2.79005i 0.343432 + 0.594842i
\(23\) −5.60088 −1.16786 −0.583932 0.811802i \(-0.698487\pi\)
−0.583932 + 0.811802i \(0.698487\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) −0.210618 0.364801i −0.0398031 0.0689409i
\(29\) −7.24380 −1.34514 −0.672570 0.740034i \(-0.734809\pi\)
−0.672570 + 0.740034i \(0.734809\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) −2.44335 −0.438839 −0.219420 0.975631i \(-0.570416\pi\)
−0.219420 + 0.975631i \(0.570416\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.61084 + 2.79005i −0.280411 + 0.485686i
\(34\) −1.28938 + 2.23328i −0.221127 + 0.383004i
\(35\) 0.210618 + 0.364801i 0.0356009 + 0.0616626i
\(36\) 1.00000 0.166667
\(37\) −2.07876 5.71653i −0.341747 0.939792i
\(38\) −4.22168 −0.684847
\(39\) 0.500000 + 0.866025i 0.0800641 + 0.138675i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 5.12190 8.87139i 0.799906 1.38548i −0.119771 0.992802i \(-0.538216\pi\)
0.919677 0.392676i \(-0.128451\pi\)
\(42\) 0.210618 0.364801i 0.0324991 0.0562900i
\(43\) 0.842472 0.128476 0.0642379 0.997935i \(-0.479538\pi\)
0.0642379 + 0.997935i \(0.479538\pi\)
\(44\) 1.61084 2.79005i 0.242843 0.420617i
\(45\) −1.00000 −0.149071
\(46\) 2.80044 + 4.85051i 0.412903 + 0.715168i
\(47\) −8.82256 −1.28690 −0.643451 0.765487i \(-0.722498\pi\)
−0.643451 + 0.765487i \(0.722498\pi\)
\(48\) −1.00000 −0.144338
\(49\) 3.41128 + 5.90851i 0.487326 + 0.844073i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) −2.57876 −0.361099
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) 1.32146 + 2.28883i 0.181516 + 0.314395i 0.942397 0.334496i \(-0.108566\pi\)
−0.760881 + 0.648891i \(0.775233\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −1.61084 + 2.79005i −0.217205 + 0.376211i
\(56\) −0.210618 + 0.364801i −0.0281450 + 0.0487486i
\(57\) −2.11084 3.65608i −0.279587 0.484260i
\(58\) 3.62190 + 6.27331i 0.475579 + 0.823726i
\(59\) 1.03207 + 1.78761i 0.134365 + 0.232726i 0.925355 0.379103i \(-0.123767\pi\)
−0.790990 + 0.611829i \(0.790434\pi\)
\(60\) 1.00000 0.129099
\(61\) 0.900221 1.55923i 0.115261 0.199639i −0.802623 0.596487i \(-0.796563\pi\)
0.917884 + 0.396848i \(0.129896\pi\)
\(62\) 1.22168 + 2.11601i 0.155153 + 0.268733i
\(63\) 0.421236 0.0530707
\(64\) 1.00000 0.125000
\(65\) 0.500000 + 0.866025i 0.0620174 + 0.107417i
\(66\) 3.22168 0.396561
\(67\) 1.93230 3.34683i 0.236067 0.408881i −0.723515 0.690309i \(-0.757475\pi\)
0.959582 + 0.281428i \(0.0908080\pi\)
\(68\) 2.57876 0.312721
\(69\) −2.80044 + 4.85051i −0.337134 + 0.583932i
\(70\) 0.210618 0.364801i 0.0251737 0.0436021i
\(71\) 3.58982 6.21776i 0.426034 0.737912i −0.570483 0.821310i \(-0.693244\pi\)
0.996516 + 0.0833977i \(0.0265772\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −8.44335 −0.988220 −0.494110 0.869399i \(-0.664506\pi\)
−0.494110 + 0.869399i \(0.664506\pi\)
\(74\) −3.91128 + 4.65853i −0.454677 + 0.541543i
\(75\) −1.00000 −0.115470
\(76\) 2.11084 + 3.65608i 0.242130 + 0.419381i
\(77\) 0.678543 1.17527i 0.0773272 0.133935i
\(78\) 0.500000 0.866025i 0.0566139 0.0980581i
\(79\) −7.37921 + 12.7812i −0.830225 + 1.43799i 0.0676338 + 0.997710i \(0.478455\pi\)
−0.897859 + 0.440282i \(0.854878\pi\)
\(80\) −1.00000 −0.111803
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −10.2438 −1.13124
\(83\) −7.01106 12.1435i −0.769564 1.33292i −0.937800 0.347177i \(-0.887140\pi\)
0.168236 0.985747i \(-0.446193\pi\)
\(84\) −0.421236 −0.0459606
\(85\) −2.57876 −0.279706
\(86\) −0.421236 0.729602i −0.0454230 0.0786750i
\(87\) −3.62190 + 6.27331i −0.388308 + 0.672570i
\(88\) −3.22168 −0.343432
\(89\) −3.42124 5.92575i −0.362650 0.628129i 0.625746 0.780027i \(-0.284795\pi\)
−0.988396 + 0.151898i \(0.951461\pi\)
\(90\) 0.500000 + 0.866025i 0.0527046 + 0.0912871i
\(91\) −0.210618 0.364801i −0.0220788 0.0382415i
\(92\) 2.80044 4.85051i 0.291966 0.505700i
\(93\) −1.22168 + 2.11601i −0.126682 + 0.219420i
\(94\) 4.41128 + 7.64056i 0.454989 + 0.788064i
\(95\) −2.11084 3.65608i −0.216567 0.375106i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 3.41128 5.90851i 0.344591 0.596850i
\(99\) 1.61084 + 2.79005i 0.161895 + 0.280411i
\(100\) 1.00000 0.100000
\(101\) 10.1796 1.01291 0.506456 0.862266i \(-0.330955\pi\)
0.506456 + 0.862266i \(0.330955\pi\)
\(102\) 1.28938 + 2.23328i 0.127668 + 0.221127i
\(103\) 6.86459 0.676388 0.338194 0.941076i \(-0.390184\pi\)
0.338194 + 0.941076i \(0.390184\pi\)
\(104\) −0.500000 + 0.866025i −0.0490290 + 0.0849208i
\(105\) 0.421236 0.0411084
\(106\) 1.32146 2.28883i 0.128351 0.222311i
\(107\) −8.76481 + 15.1811i −0.847326 + 1.46761i 0.0362592 + 0.999342i \(0.488456\pi\)
−0.883586 + 0.468270i \(0.844878\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 10.1440 + 17.5700i 0.971621 + 1.68290i 0.690664 + 0.723176i \(0.257318\pi\)
0.280957 + 0.959720i \(0.409348\pi\)
\(110\) 3.22168 0.307175
\(111\) −5.99004 1.05800i −0.568550 0.100421i
\(112\) 0.421236 0.0398031
\(113\) −1.20066 2.07961i −0.112949 0.195633i 0.804009 0.594617i \(-0.202696\pi\)
−0.916958 + 0.398984i \(0.869363\pi\)
\(114\) −2.11084 + 3.65608i −0.197698 + 0.342423i
\(115\) −2.80044 + 4.85051i −0.261143 + 0.452312i
\(116\) 3.62190 6.27331i 0.336285 0.582462i
\(117\) 1.00000 0.0924500
\(118\) 1.03207 1.78761i 0.0950102 0.164562i
\(119\) 1.08627 0.0995780
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) −0.620795 −0.0564359
\(122\) −1.80044 −0.163004
\(123\) −5.12190 8.87139i −0.461826 0.799906i
\(124\) 1.22168 2.11601i 0.109710 0.190023i
\(125\) −1.00000 −0.0894427
\(126\) −0.210618 0.364801i −0.0187633 0.0324991i
\(127\) −1.58982 2.75365i −0.141074 0.244347i 0.786827 0.617173i \(-0.211722\pi\)
−0.927901 + 0.372826i \(0.878389\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0.421236 0.729602i 0.0370878 0.0642379i
\(130\) 0.500000 0.866025i 0.0438529 0.0759555i
\(131\) 0.810397 + 1.40365i 0.0708047 + 0.122637i 0.899254 0.437426i \(-0.144110\pi\)
−0.828449 + 0.560064i \(0.810777\pi\)
\(132\) −1.61084 2.79005i −0.140206 0.242843i
\(133\) 0.889161 + 1.54007i 0.0771001 + 0.133541i
\(134\) −3.86459 −0.333850
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) −1.28938 2.23328i −0.110564 0.191502i
\(137\) 15.6429 1.33646 0.668232 0.743953i \(-0.267051\pi\)
0.668232 + 0.743953i \(0.267051\pi\)
\(138\) 5.60088 0.476779
\(139\) 4.95797 + 8.58745i 0.420529 + 0.728378i 0.995991 0.0894502i \(-0.0285110\pi\)
−0.575462 + 0.817829i \(0.695178\pi\)
\(140\) −0.421236 −0.0356009
\(141\) −4.41128 + 7.64056i −0.371497 + 0.643451i
\(142\) −7.17965 −0.602503
\(143\) 1.61084 2.79005i 0.134705 0.233316i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −3.62190 + 6.27331i −0.300782 + 0.520970i
\(146\) 4.22168 + 7.31216i 0.349389 + 0.605159i
\(147\) 6.82256 0.562715
\(148\) 5.99004 + 1.05800i 0.492379 + 0.0869674i
\(149\) −5.19956 −0.425964 −0.212982 0.977056i \(-0.568318\pi\)
−0.212982 + 0.977056i \(0.568318\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 0.620795 1.07525i 0.0505195 0.0875024i −0.839660 0.543113i \(-0.817246\pi\)
0.890179 + 0.455610i \(0.150579\pi\)
\(152\) 2.11084 3.65608i 0.171212 0.296547i
\(153\) −1.28938 + 2.23328i −0.104240 + 0.180550i
\(154\) −1.35709 −0.109357
\(155\) −1.22168 + 2.11601i −0.0981275 + 0.169962i
\(156\) −1.00000 −0.0800641
\(157\) −9.16503 15.8743i −0.731449 1.26691i −0.956264 0.292506i \(-0.905511\pi\)
0.224815 0.974402i \(-0.427822\pi\)
\(158\) 14.7584 1.17412
\(159\) 2.64291 0.209597
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 1.17965 2.04321i 0.0929692 0.161027i
\(162\) 1.00000 0.0785674
\(163\) −1.06770 1.84932i −0.0836291 0.144850i 0.821177 0.570673i \(-0.193318\pi\)
−0.904806 + 0.425824i \(0.859984\pi\)
\(164\) 5.12190 + 8.87139i 0.399953 + 0.692739i
\(165\) 1.61084 + 2.79005i 0.125404 + 0.217205i
\(166\) −7.01106 + 12.1435i −0.544164 + 0.942519i
\(167\) 8.25375 14.2959i 0.638695 1.10625i −0.347025 0.937856i \(-0.612808\pi\)
0.985720 0.168395i \(-0.0538586\pi\)
\(168\) 0.210618 + 0.364801i 0.0162495 + 0.0281450i
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 1.28938 + 2.23328i 0.0988911 + 0.171284i
\(171\) −4.22168 −0.322840
\(172\) −0.421236 + 0.729602i −0.0321189 + 0.0556316i
\(173\) −9.34358 16.1835i −0.710379 1.23041i −0.964715 0.263296i \(-0.915190\pi\)
0.254336 0.967116i \(-0.418143\pi\)
\(174\) 7.24380 0.549151
\(175\) 0.421236 0.0318424
\(176\) 1.61084 + 2.79005i 0.121422 + 0.210308i
\(177\) 2.06415 0.155151
\(178\) −3.42124 + 5.92575i −0.256432 + 0.444154i
\(179\) 5.15753 0.385492 0.192746 0.981249i \(-0.438261\pi\)
0.192746 + 0.981249i \(0.438261\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 8.60088 14.8972i 0.639299 1.10730i −0.346288 0.938128i \(-0.612558\pi\)
0.985587 0.169170i \(-0.0541085\pi\)
\(182\) −0.210618 + 0.364801i −0.0156120 + 0.0270409i
\(183\) −0.900221 1.55923i −0.0665462 0.115261i
\(184\) −5.60088 −0.412903
\(185\) −5.99004 1.05800i −0.440397 0.0777860i
\(186\) 2.44335 0.179155
\(187\) 4.15397 + 7.19489i 0.303769 + 0.526143i
\(188\) 4.41128 7.64056i 0.321726 0.557245i
\(189\) 0.210618 0.364801i 0.0153202 0.0265354i
\(190\) −2.11084 + 3.65608i −0.153136 + 0.265240i
\(191\) −0.243796 −0.0176405 −0.00882024 0.999961i \(-0.502808\pi\)
−0.00882024 + 0.999961i \(0.502808\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 9.71638 0.699400 0.349700 0.936862i \(-0.386283\pi\)
0.349700 + 0.936862i \(0.386283\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) 1.00000 0.0716115
\(196\) −6.82256 −0.487326
\(197\) −12.0863 20.9340i −0.861111 1.49149i −0.870858 0.491535i \(-0.836436\pi\)
0.00974662 0.999953i \(-0.496898\pi\)
\(198\) 1.61084 2.79005i 0.114477 0.198281i
\(199\) −4.97788 −0.352873 −0.176436 0.984312i \(-0.556457\pi\)
−0.176436 + 0.984312i \(0.556457\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) −1.93230 3.34683i −0.136294 0.236067i
\(202\) −5.08982 8.81583i −0.358119 0.620280i
\(203\) 1.52567 2.64254i 0.107081 0.185470i
\(204\) 1.28938 2.23328i 0.0902748 0.156361i
\(205\) −5.12190 8.87139i −0.357729 0.619605i
\(206\) −3.43230 5.94491i −0.239139 0.414202i
\(207\) 2.80044 + 4.85051i 0.194644 + 0.337134i
\(208\) 1.00000 0.0693375
\(209\) −6.80044 + 11.7787i −0.470396 + 0.814750i
\(210\) −0.210618 0.364801i −0.0145340 0.0251737i
\(211\) 12.5367 0.863064 0.431532 0.902098i \(-0.357973\pi\)
0.431532 + 0.902098i \(0.357973\pi\)
\(212\) −2.64291 −0.181516
\(213\) −3.58982 6.21776i −0.245971 0.426034i
\(214\) 17.5296 1.19830
\(215\) 0.421236 0.729602i 0.0287281 0.0497585i
\(216\) −1.00000 −0.0680414
\(217\) 0.514615 0.891339i 0.0349343 0.0605080i
\(218\) 10.1440 17.5700i 0.687040 1.18999i
\(219\) −4.22168 + 7.31216i −0.285275 + 0.494110i
\(220\) −1.61084 2.79005i −0.108603 0.188105i
\(221\) 2.57876 0.173466
\(222\) 2.07876 + 5.71653i 0.139518 + 0.383669i
\(223\) −12.8867 −0.862958 −0.431479 0.902123i \(-0.642008\pi\)
−0.431479 + 0.902123i \(0.642008\pi\)
\(224\) −0.210618 0.364801i −0.0140725 0.0243743i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) −1.20066 + 2.07961i −0.0798669 + 0.138333i
\(227\) 1.01106 1.75121i 0.0671064 0.116232i −0.830520 0.556989i \(-0.811957\pi\)
0.897626 + 0.440757i \(0.145290\pi\)
\(228\) 4.22168 0.279587
\(229\) −1.09978 + 1.90487i −0.0726755 + 0.125878i −0.900073 0.435739i \(-0.856487\pi\)
0.827398 + 0.561617i \(0.189820\pi\)
\(230\) 5.60088 0.369311
\(231\) −0.678543 1.17527i −0.0446449 0.0773272i
\(232\) −7.24380 −0.475579
\(233\) 23.8226 1.56067 0.780334 0.625363i \(-0.215049\pi\)
0.780334 + 0.625363i \(0.215049\pi\)
\(234\) −0.500000 0.866025i −0.0326860 0.0566139i
\(235\) −4.41128 + 7.64056i −0.287760 + 0.498415i
\(236\) −2.06415 −0.134365
\(237\) 7.37921 + 12.7812i 0.479331 + 0.830225i
\(238\) −0.543134 0.940736i −0.0352062 0.0609789i
\(239\) −3.11084 5.38813i −0.201223 0.348529i 0.747699 0.664037i \(-0.231158\pi\)
−0.948923 + 0.315508i \(0.897825\pi\)
\(240\) −0.500000 + 0.866025i −0.0322749 + 0.0559017i
\(241\) 11.9900 20.7674i 0.772347 1.33774i −0.163927 0.986472i \(-0.552416\pi\)
0.936274 0.351271i \(-0.114250\pi\)
\(242\) 0.310397 + 0.537624i 0.0199531 + 0.0345598i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0.900221 + 1.55923i 0.0576307 + 0.0998193i
\(245\) 6.82256 0.435877
\(246\) −5.12190 + 8.87139i −0.326560 + 0.565619i
\(247\) 2.11084 + 3.65608i 0.134309 + 0.232631i
\(248\) −2.44335 −0.155153
\(249\) −14.0221 −0.888616
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 17.2659 1.08981 0.544907 0.838496i \(-0.316565\pi\)
0.544907 + 0.838496i \(0.316565\pi\)
\(252\) −0.210618 + 0.364801i −0.0132677 + 0.0229803i
\(253\) 18.0442 1.13443
\(254\) −1.58982 + 2.75365i −0.0997544 + 0.172780i
\(255\) −1.28938 + 2.23328i −0.0807442 + 0.139853i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.64402 2.84752i −0.102551 0.177623i 0.810184 0.586176i \(-0.199367\pi\)
−0.912735 + 0.408552i \(0.866034\pi\)
\(258\) −0.842472 −0.0524500
\(259\) 2.52322 + 0.445669i 0.156785 + 0.0276925i
\(260\) −1.00000 −0.0620174
\(261\) 3.62190 + 6.27331i 0.224190 + 0.388308i
\(262\) 0.810397 1.40365i 0.0500665 0.0867177i
\(263\) −11.8867 + 20.5884i −0.732966 + 1.26953i 0.222644 + 0.974900i \(0.428531\pi\)
−0.955610 + 0.294634i \(0.904802\pi\)
\(264\) −1.61084 + 2.79005i −0.0991403 + 0.171716i
\(265\) 2.64291 0.162353
\(266\) 0.889161 1.54007i 0.0545180 0.0944279i
\(267\) −6.84247 −0.418752
\(268\) 1.93230 + 3.34683i 0.118034 + 0.204440i
\(269\) 30.7933 1.87750 0.938751 0.344595i \(-0.111984\pi\)
0.938751 + 0.344595i \(0.111984\pi\)
\(270\) 1.00000 0.0608581
\(271\) −9.51106 16.4736i −0.577756 1.00070i −0.995736 0.0922463i \(-0.970595\pi\)
0.417981 0.908456i \(-0.362738\pi\)
\(272\) −1.28938 + 2.23328i −0.0781803 + 0.135412i
\(273\) −0.421236 −0.0254944
\(274\) −7.82146 13.5472i −0.472511 0.818414i
\(275\) 1.61084 + 2.79005i 0.0971372 + 0.168247i
\(276\) −2.80044 4.85051i −0.168567 0.291966i
\(277\) 5.90132 10.2214i 0.354576 0.614144i −0.632469 0.774586i \(-0.717958\pi\)
0.987045 + 0.160442i \(0.0512918\pi\)
\(278\) 4.95797 8.58745i 0.297359 0.515041i
\(279\) 1.22168 + 2.11601i 0.0731399 + 0.126682i
\(280\) 0.210618 + 0.364801i 0.0125868 + 0.0218010i
\(281\) −9.02212 15.6268i −0.538214 0.932215i −0.999000 0.0447035i \(-0.985766\pi\)
0.460786 0.887511i \(-0.347568\pi\)
\(282\) 8.82256 0.525376
\(283\) 1.73274 3.00119i 0.103001 0.178402i −0.809919 0.586542i \(-0.800489\pi\)
0.912920 + 0.408140i \(0.133822\pi\)
\(284\) 3.58982 + 6.21776i 0.213017 + 0.368956i
\(285\) −4.22168 −0.250071
\(286\) −3.22168 −0.190502
\(287\) 2.15753 + 3.73695i 0.127355 + 0.220585i
\(288\) 1.00000 0.0589256
\(289\) 5.17499 8.96334i 0.304411 0.527255i
\(290\) 7.24380 0.425370
\(291\) 1.00000 1.73205i 0.0586210 0.101535i
\(292\) 4.22168 7.31216i 0.247055 0.427912i
\(293\) 3.95797 6.85540i 0.231227 0.400497i −0.726942 0.686698i \(-0.759059\pi\)
0.958169 + 0.286201i \(0.0923926\pi\)
\(294\) −3.41128 5.90851i −0.198950 0.344591i
\(295\) 2.06415 0.120179
\(296\) −2.07876 5.71653i −0.120826 0.332267i
\(297\) 3.22168 0.186941
\(298\) 2.59978 + 4.50295i 0.150601 + 0.260849i
\(299\) 2.80044 4.85051i 0.161954 0.280512i
\(300\) 0.500000 0.866025i 0.0288675 0.0500000i
\(301\) −0.177440 + 0.307335i −0.0102275 + 0.0177145i
\(302\) −1.24159 −0.0714454
\(303\) 5.08982 8.81583i 0.292403 0.506456i
\(304\) −4.22168 −0.242130
\(305\) −0.900221 1.55923i −0.0515465 0.0892811i
\(306\) 2.57876 0.147418
\(307\) −0.128299 −0.00732241 −0.00366120 0.999993i \(-0.501165\pi\)
−0.00366120 + 0.999993i \(0.501165\pi\)
\(308\) 0.678543 + 1.17527i 0.0386636 + 0.0669673i
\(309\) 3.43230 5.94491i 0.195256 0.338194i
\(310\) 2.44335 0.138773
\(311\) −11.3436 19.6476i −0.643235 1.11412i −0.984706 0.174224i \(-0.944258\pi\)
0.341471 0.939892i \(-0.389075\pi\)
\(312\) 0.500000 + 0.866025i 0.0283069 + 0.0490290i
\(313\) −5.86459 10.1578i −0.331486 0.574151i 0.651317 0.758806i \(-0.274217\pi\)
−0.982804 + 0.184654i \(0.940883\pi\)
\(314\) −9.16503 + 15.8743i −0.517213 + 0.895839i
\(315\) 0.210618 0.364801i 0.0118670 0.0205542i
\(316\) −7.37921 12.7812i −0.415113 0.718996i
\(317\) 10.7228 + 18.5724i 0.602251 + 1.04313i 0.992479 + 0.122412i \(0.0390628\pi\)
−0.390228 + 0.920718i \(0.627604\pi\)
\(318\) −1.32146 2.28883i −0.0741036 0.128351i
\(319\) 23.3372 1.30663
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 8.76481 + 15.1811i 0.489204 + 0.847326i
\(322\) −2.35929 −0.131478
\(323\) −10.8867 −0.605753
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 1.00000 0.0554700
\(326\) −1.06770 + 1.84932i −0.0591347 + 0.102424i
\(327\) 20.2880 1.12193
\(328\) 5.12190 8.87139i 0.282810 0.489840i
\(329\) 1.85819 3.21848i 0.102445 0.177441i
\(330\) 1.61084 2.79005i 0.0886738 0.153587i
\(331\) 8.05309 + 13.9484i 0.442638 + 0.766671i 0.997884 0.0650146i \(-0.0207094\pi\)
−0.555246 + 0.831686i \(0.687376\pi\)
\(332\) 14.0221 0.769564
\(333\) −3.91128 + 4.65853i −0.214337 + 0.255286i
\(334\) −16.5075 −0.903250
\(335\) −1.93230 3.34683i −0.105573 0.182857i
\(336\) 0.210618 0.364801i 0.0114902 0.0199015i
\(337\) 12.4591 21.5797i 0.678689 1.17552i −0.296687 0.954975i \(-0.595882\pi\)
0.975376 0.220549i \(-0.0707849\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) −2.40132 −0.130422
\(340\) 1.28938 2.23328i 0.0699266 0.121116i
\(341\) 7.87170 0.426277
\(342\) 2.11084 + 3.65608i 0.114141 + 0.197698i
\(343\) −5.82256 −0.314389
\(344\) 0.842472 0.0454230
\(345\) 2.80044 + 4.85051i 0.150771 + 0.261143i
\(346\) −9.34358 + 16.1835i −0.502314 + 0.870033i
\(347\) −6.49250 −0.348535 −0.174268 0.984698i \(-0.555756\pi\)
−0.174268 + 0.984698i \(0.555756\pi\)
\(348\) −3.62190 6.27331i −0.194154 0.336285i
\(349\) 11.6009 + 20.0933i 0.620981 + 1.07557i 0.989303 + 0.145873i \(0.0465989\pi\)
−0.368322 + 0.929698i \(0.620068\pi\)
\(350\) −0.210618 0.364801i −0.0112580 0.0194994i
\(351\) 0.500000 0.866025i 0.0266880 0.0462250i
\(352\) 1.61084 2.79005i 0.0858580 0.148710i
\(353\) −2.31040 4.00173i −0.122970 0.212990i 0.797968 0.602700i \(-0.205909\pi\)
−0.920938 + 0.389710i \(0.872575\pi\)
\(354\) −1.03207 1.78761i −0.0548542 0.0950102i
\(355\) −3.58982 6.21776i −0.190528 0.330004i
\(356\) 6.84247 0.362650
\(357\) 0.543134 0.940736i 0.0287457 0.0497890i
\(358\) −2.57876 4.46655i −0.136292 0.236065i
\(359\) −7.42344 −0.391794 −0.195897 0.980624i \(-0.562762\pi\)
−0.195897 + 0.980624i \(0.562762\pi\)
\(360\) −1.00000 −0.0527046
\(361\) 0.588720 + 1.01969i 0.0309853 + 0.0536680i
\(362\) −17.2018 −0.904105
\(363\) −0.310397 + 0.537624i −0.0162916 + 0.0282179i
\(364\) 0.421236 0.0220788
\(365\) −4.22168 + 7.31216i −0.220973 + 0.382736i
\(366\) −0.900221 + 1.55923i −0.0470553 + 0.0815022i
\(367\) −2.49004 + 4.31288i −0.129979 + 0.225131i −0.923668 0.383193i \(-0.874824\pi\)
0.793689 + 0.608324i \(0.208158\pi\)
\(368\) 2.80044 + 4.85051i 0.145983 + 0.252850i
\(369\) −10.2438 −0.533271
\(370\) 2.07876 + 5.71653i 0.108070 + 0.297188i
\(371\) −1.11329 −0.0577992
\(372\) −1.22168 2.11601i −0.0633410 0.109710i
\(373\) 14.1971 24.5901i 0.735098 1.27323i −0.219582 0.975594i \(-0.570469\pi\)
0.954680 0.297634i \(-0.0961974\pi\)
\(374\) 4.15397 7.19489i 0.214797 0.372039i
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) −8.82256 −0.454989
\(377\) 3.62190 6.27331i 0.186537 0.323092i
\(378\) −0.421236 −0.0216660
\(379\) −0.410177 0.710447i −0.0210694 0.0364932i 0.855298 0.518136i \(-0.173374\pi\)
−0.876368 + 0.481642i \(0.840040\pi\)
\(380\) 4.22168 0.216567
\(381\) −3.17965 −0.162898
\(382\) 0.121898 + 0.211134i 0.00623685 + 0.0108025i
\(383\) −2.56881 + 4.44931i −0.131260 + 0.227349i −0.924163 0.382000i \(-0.875236\pi\)
0.792903 + 0.609348i \(0.208569\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −0.678543 1.17527i −0.0345818 0.0598974i
\(386\) −4.85819 8.41463i −0.247275 0.428293i
\(387\) −0.421236 0.729602i −0.0214126 0.0370878i
\(388\) −1.00000 + 1.73205i −0.0507673 + 0.0879316i
\(389\) −15.5343 + 26.9062i −0.787619 + 1.36420i 0.139802 + 0.990179i \(0.455353\pi\)
−0.927422 + 0.374017i \(0.877980\pi\)
\(390\) −0.500000 0.866025i −0.0253185 0.0438529i
\(391\) 7.22168 + 12.5083i 0.365216 + 0.632573i
\(392\) 3.41128 + 5.90851i 0.172296 + 0.298425i
\(393\) 1.62079 0.0817583
\(394\) −12.0863 + 20.9340i −0.608897 + 1.05464i
\(395\) 7.37921 + 12.7812i 0.371288 + 0.643090i
\(396\) −3.22168 −0.161895
\(397\) 12.3792 0.621295 0.310647 0.950525i \(-0.399454\pi\)
0.310647 + 0.950525i \(0.399454\pi\)
\(398\) 2.48894 + 4.31097i 0.124759 + 0.216089i
\(399\) 1.77832 0.0890275
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −8.32786 −0.415873 −0.207937 0.978142i \(-0.566675\pi\)
−0.207937 + 0.978142i \(0.566675\pi\)
\(402\) −1.93230 + 3.34683i −0.0963741 + 0.166925i
\(403\) 1.22168 2.11601i 0.0608561 0.105406i
\(404\) −5.08982 + 8.81583i −0.253228 + 0.438604i
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) −3.05135 −0.151436
\(407\) 6.69711 + 18.4168i 0.331963 + 0.912888i
\(408\) −2.57876 −0.127668
\(409\) 2.30044 + 3.98448i 0.113750 + 0.197020i 0.917279 0.398245i \(-0.130381\pi\)
−0.803530 + 0.595265i \(0.797047\pi\)
\(410\) −5.12190 + 8.87139i −0.252953 + 0.438127i
\(411\) 7.82146 13.5472i 0.385804 0.668232i
\(412\) −3.43230 + 5.94491i −0.169097 + 0.292885i
\(413\) −0.869494 −0.0427850
\(414\) 2.80044 4.85051i 0.137634 0.238389i
\(415\) −14.0221 −0.688319
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 9.91594 0.485586
\(418\) 13.6009 0.665241
\(419\) −11.0221 19.0909i −0.538466 0.932650i −0.998987 0.0450013i \(-0.985671\pi\)
0.460521 0.887649i \(-0.347663\pi\)
\(420\) −0.210618 + 0.364801i −0.0102771 + 0.0178005i
\(421\) −25.8004 −1.25744 −0.628718 0.777633i \(-0.716420\pi\)
−0.628718 + 0.777633i \(0.716420\pi\)
\(422\) −6.26837 10.8571i −0.305139 0.528517i
\(423\) 4.41128 + 7.64056i 0.214484 + 0.371497i
\(424\) 1.32146 + 2.28883i 0.0641756 + 0.111155i
\(425\) −1.28938 + 2.23328i −0.0625442 + 0.108330i
\(426\) −3.58982 + 6.21776i −0.173928 + 0.301251i
\(427\) 0.379205 + 0.656803i 0.0183510 + 0.0317849i
\(428\) −8.76481 15.1811i −0.423663 0.733806i
\(429\) −1.61084 2.79005i −0.0777720 0.134705i
\(430\) −0.842472 −0.0406276
\(431\) −2.94691 + 5.10420i −0.141948 + 0.245861i −0.928230 0.372007i \(-0.878670\pi\)
0.786282 + 0.617867i \(0.212003\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 14.3151 0.687938 0.343969 0.938981i \(-0.388229\pi\)
0.343969 + 0.938981i \(0.388229\pi\)
\(434\) −1.02923 −0.0494046
\(435\) 3.62190 + 6.27331i 0.173657 + 0.300782i
\(436\) −20.2880 −0.971621
\(437\) −11.8226 + 20.4773i −0.565550 + 0.979561i
\(438\) 8.44335 0.403439
\(439\) 0.553090 0.957980i 0.0263975 0.0457219i −0.852525 0.522687i \(-0.824930\pi\)
0.878922 + 0.476965i \(0.158263\pi\)
\(440\) −1.61084 + 2.79005i −0.0767937 + 0.133011i
\(441\) 3.41128 5.90851i 0.162442 0.281358i
\(442\) −1.28938 2.23328i −0.0613296 0.106226i
\(443\) −14.6522 −0.696148 −0.348074 0.937467i \(-0.613164\pi\)
−0.348074 + 0.937467i \(0.613164\pi\)
\(444\) 3.91128 4.65853i 0.185621 0.221084i
\(445\) −6.84247 −0.324364
\(446\) 6.44335 + 11.1602i 0.305102 + 0.528452i
\(447\) −2.59978 + 4.50295i −0.122965 + 0.212982i
\(448\) −0.210618 + 0.364801i −0.00995077 + 0.0172352i
\(449\) −7.60088 + 13.1651i −0.358708 + 0.621300i −0.987745 0.156075i \(-0.950116\pi\)
0.629037 + 0.777375i \(0.283449\pi\)
\(450\) 1.00000 0.0471405
\(451\) −16.5011 + 28.5807i −0.777007 + 1.34581i
\(452\) 2.40132 0.112949
\(453\) −0.620795 1.07525i −0.0291675 0.0505195i
\(454\) −2.02212 −0.0949027
\(455\) −0.421236 −0.0197478
\(456\) −2.11084 3.65608i −0.0988491 0.171212i
\(457\) 1.97788 3.42579i 0.0925214 0.160252i −0.816050 0.577981i \(-0.803841\pi\)
0.908571 + 0.417729i \(0.137174\pi\)
\(458\) 2.19956 0.102779
\(459\) 1.28938 + 2.23328i 0.0601832 + 0.104240i
\(460\) −2.80044 4.85051i −0.130571 0.226156i
\(461\) 19.4024 + 33.6060i 0.903661 + 1.56519i 0.822704 + 0.568469i \(0.192464\pi\)
0.0809567 + 0.996718i \(0.474202\pi\)
\(462\) −0.678543 + 1.17527i −0.0315687 + 0.0546786i
\(463\) −0.132958 + 0.230289i −0.00617906 + 0.0107024i −0.869098 0.494639i \(-0.835300\pi\)
0.862919 + 0.505342i \(0.168634\pi\)
\(464\) 3.62190 + 6.27331i 0.168142 + 0.291231i
\(465\) 1.22168 + 2.11601i 0.0566539 + 0.0981275i
\(466\) −11.9113 20.6309i −0.551779 0.955710i
\(467\) −7.77832 −0.359938 −0.179969 0.983672i \(-0.557600\pi\)
−0.179969 + 0.983672i \(0.557600\pi\)
\(468\) −0.500000 + 0.866025i −0.0231125 + 0.0400320i
\(469\) 0.813952 + 1.40981i 0.0375848 + 0.0650988i
\(470\) 8.82256 0.406954
\(471\) −18.3301 −0.844605
\(472\) 1.03207 + 1.78761i 0.0475051 + 0.0822812i
\(473\) −2.71417 −0.124798
\(474\) 7.37921 12.7812i 0.338938 0.587058i
\(475\) −4.22168 −0.193704
\(476\) −0.543134 + 0.940736i −0.0248945 + 0.0431186i
\(477\) 1.32146 2.28883i 0.0605053 0.104798i
\(478\) −3.11084 + 5.38813i −0.142286 + 0.246447i
\(479\) 4.06415 + 7.03931i 0.185696 + 0.321634i 0.943811 0.330486i \(-0.107213\pi\)
−0.758115 + 0.652121i \(0.773879\pi\)
\(480\) 1.00000 0.0456435
\(481\) 5.99004 + 1.05800i 0.273123 + 0.0482408i
\(482\) −23.9801 −1.09226
\(483\) −1.17965 2.04321i −0.0536758 0.0929692i
\(484\) 0.310397 0.537624i 0.0141090 0.0244375i
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −21.2951 −0.964975 −0.482488 0.875903i \(-0.660267\pi\)
−0.482488 + 0.875903i \(0.660267\pi\)
\(488\) 0.900221 1.55923i 0.0407511 0.0705829i
\(489\) −2.13541 −0.0965665
\(490\) −3.41128 5.90851i −0.154106 0.266919i
\(491\) 17.6009 0.794317 0.397158 0.917750i \(-0.369996\pi\)
0.397158 + 0.917750i \(0.369996\pi\)
\(492\) 10.2438 0.461826
\(493\) 9.34002 + 16.1774i 0.420653 + 0.728593i
\(494\) 2.11084 3.65608i 0.0949711 0.164495i
\(495\) 3.22168 0.144804
\(496\) 1.22168 + 2.11601i 0.0548549 + 0.0950115i
\(497\) 1.51216 + 2.61914i 0.0678298 + 0.117485i
\(498\) 7.01106 + 12.1435i 0.314173 + 0.544164i
\(499\) −4.81150 + 8.33376i −0.215392 + 0.373071i −0.953394 0.301729i \(-0.902436\pi\)
0.738002 + 0.674799i \(0.235770\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) −8.25375 14.2959i −0.368750 0.638695i
\(502\) −8.63296 14.9527i −0.385308 0.667373i
\(503\) 5.21172 + 9.02697i 0.232379 + 0.402493i 0.958508 0.285066i \(-0.0920156\pi\)
−0.726129 + 0.687559i \(0.758682\pi\)
\(504\) 0.421236 0.0187633
\(505\) 5.08982 8.81583i 0.226494 0.392299i
\(506\) −9.02212 15.6268i −0.401082 0.694695i
\(507\) 12.0000 0.532939
\(508\) 3.17965 0.141074
\(509\) 3.33252 + 5.77209i 0.147711 + 0.255843i 0.930381 0.366594i \(-0.119476\pi\)
−0.782670 + 0.622437i \(0.786143\pi\)
\(510\) 2.57876 0.114190
\(511\) 1.77832 3.08015i 0.0786684 0.136258i
\(512\) 1.00000 0.0441942
\(513\) −2.11084 + 3.65608i −0.0931958 + 0.161420i
\(514\) −1.64402 + 2.84752i −0.0725145 + 0.125599i
\(515\) 3.43230 5.94491i 0.151245 0.261964i
\(516\) 0.421236 + 0.729602i 0.0185439 + 0.0321189i
\(517\) 28.4234 1.25006
\(518\) −0.875650 2.40801i −0.0384739 0.105802i
\(519\) −18.6872 −0.820275
\(520\) 0.500000 + 0.866025i 0.0219265 + 0.0379777i
\(521\) 8.19956 14.2021i 0.359229 0.622203i −0.628603 0.777726i \(-0.716373\pi\)
0.987832 + 0.155523i \(0.0497063\pi\)
\(522\) 3.62190 6.27331i 0.158526 0.274575i
\(523\) −17.0863 + 29.5943i −0.747130 + 1.29407i 0.202062 + 0.979373i \(0.435236\pi\)
−0.949193 + 0.314695i \(0.898098\pi\)
\(524\) −1.62079 −0.0708047
\(525\) 0.210618 0.364801i 0.00919212 0.0159212i
\(526\) 23.7734 1.03657
\(527\) 3.15042 + 5.45668i 0.137234 + 0.237697i
\(528\) 3.22168 0.140206
\(529\) 8.36989 0.363908
\(530\) −1.32146 2.28883i −0.0574004 0.0994204i
\(531\) 1.03207 1.78761i 0.0447882 0.0775755i
\(532\) −1.77832 −0.0771001
\(533\) 5.12190 + 8.87139i 0.221854 + 0.384262i
\(534\) 3.42124 + 5.92575i 0.148051 + 0.256432i
\(535\) 8.76481 + 15.1811i 0.378936 + 0.656336i
\(536\) 1.93230 3.34683i 0.0834625 0.144561i
\(537\) 2.57876 4.46655i 0.111282 0.192746i
\(538\) −15.3967 26.6678i −0.663797 1.14973i
\(539\) −10.9900 19.0353i −0.473375 0.819909i
\(540\) −0.500000 0.866025i −0.0215166 0.0372678i
\(541\) 17.4013 0.748141 0.374071 0.927400i \(-0.377962\pi\)
0.374071 + 0.927400i \(0.377962\pi\)
\(542\) −9.51106 + 16.4736i −0.408535 + 0.707603i
\(543\) −8.60088 14.8972i −0.369099 0.639299i
\(544\) 2.57876 0.110564
\(545\) 20.2880 0.869044
\(546\) 0.210618 + 0.364801i 0.00901362 + 0.0156120i
\(547\) −44.9752 −1.92300 −0.961500 0.274805i \(-0.911387\pi\)
−0.961500 + 0.274805i \(0.911387\pi\)
\(548\) −7.82146 + 13.5472i −0.334116 + 0.578706i
\(549\) −1.80044 −0.0768410
\(550\) 1.61084 2.79005i 0.0686864 0.118968i
\(551\) −15.2905 + 26.4839i −0.651397 + 1.12825i
\(552\) −2.80044 + 4.85051i −0.119195 + 0.206451i
\(553\) −3.10839 5.38388i −0.132182 0.228946i
\(554\) −11.8026 −0.501446
\(555\) −3.91128 + 4.65853i −0.166025 + 0.197744i
\(556\) −9.91594 −0.420529
\(557\) 10.6009 + 18.3613i 0.449174 + 0.777992i 0.998332 0.0577263i \(-0.0183851\pi\)
−0.549159 + 0.835718i \(0.685052\pi\)
\(558\) 1.22168 2.11601i 0.0517177 0.0895777i
\(559\) −0.421236 + 0.729602i −0.0178164 + 0.0308589i
\(560\) 0.210618 0.364801i 0.00890024 0.0154157i
\(561\) 8.30795 0.350762
\(562\) −9.02212 + 15.6268i −0.380575 + 0.659175i
\(563\) −9.09559 −0.383333 −0.191667 0.981460i \(-0.561389\pi\)
−0.191667 + 0.981460i \(0.561389\pi\)
\(564\) −4.41128 7.64056i −0.185748 0.321726i
\(565\) −2.40132 −0.101024
\(566\) −3.46547 −0.145665
\(567\) −0.210618 0.364801i −0.00884512 0.0153202i
\(568\) 3.58982 6.21776i 0.150626 0.260891i
\(569\) −38.7314 −1.62370 −0.811852 0.583863i \(-0.801540\pi\)
−0.811852 + 0.583863i \(0.801540\pi\)
\(570\) 2.11084 + 3.65608i 0.0884133 + 0.153136i
\(571\) 0.847131 + 1.46727i 0.0354513 + 0.0614035i 0.883207 0.468984i \(-0.155380\pi\)
−0.847755 + 0.530387i \(0.822046\pi\)
\(572\) 1.61084 + 2.79005i 0.0673525 + 0.116658i
\(573\) −0.121898 + 0.211134i −0.00509237 + 0.00882024i
\(574\) 2.15753 3.73695i 0.0900535 0.155977i
\(575\) 2.80044 + 4.85051i 0.116786 + 0.202280i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −17.5874 30.4622i −0.732172 1.26816i −0.955953 0.293519i \(-0.905173\pi\)
0.223781 0.974639i \(-0.428160\pi\)
\(578\) −10.3500 −0.430502
\(579\) 4.85819 8.41463i 0.201899 0.349700i
\(580\) −3.62190 6.27331i −0.150391 0.260485i
\(581\) 5.90662 0.245048
\(582\) −2.00000 −0.0829027
\(583\) −4.25731 7.37387i −0.176320 0.305395i
\(584\) −8.44335 −0.349389
\(585\) 0.500000 0.866025i 0.0206725 0.0358057i
\(586\) −7.91594 −0.327004
\(587\) 1.11724 1.93512i 0.0461134 0.0798708i −0.842047 0.539403i \(-0.818650\pi\)
0.888161 + 0.459533i \(0.151983\pi\)
\(588\) −3.41128 + 5.90851i −0.140679 + 0.243663i
\(589\) −5.15753 + 8.93310i −0.212512 + 0.368082i
\(590\) −1.03207 1.78761i −0.0424898 0.0735946i
\(591\) −24.1725 −0.994325
\(592\) −3.91128 + 4.65853i −0.160753 + 0.191464i
\(593\) −33.7805 −1.38720 −0.693600 0.720360i \(-0.743976\pi\)
−0.693600 + 0.720360i \(0.743976\pi\)
\(594\) −1.61084 2.79005i −0.0660935 0.114477i
\(595\) 0.543134 0.940736i 0.0222663 0.0385664i
\(596\) 2.59978 4.50295i 0.106491 0.184448i
\(597\) −2.48894 + 4.31097i −0.101866 + 0.176436i
\(598\) −5.60088 −0.229037
\(599\) −6.05309 + 10.4843i −0.247323 + 0.428375i −0.962782 0.270279i \(-0.912884\pi\)
0.715459 + 0.698654i \(0.246217\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −1.23163 2.13325i −0.0502394 0.0870171i 0.839812 0.542877i \(-0.182665\pi\)
−0.890051 + 0.455860i \(0.849332\pi\)
\(602\) 0.354880 0.0144638
\(603\) −3.86459 −0.157378
\(604\) 0.620795 + 1.07525i 0.0252598 + 0.0437512i
\(605\) −0.310397 + 0.537624i −0.0126194 + 0.0218575i
\(606\) −10.1796 −0.413520
\(607\) −13.2905 23.0198i −0.539444 0.934345i −0.998934 0.0461617i \(-0.985301\pi\)
0.459490 0.888183i \(-0.348032\pi\)
\(608\) 2.11084 + 3.65608i 0.0856058 + 0.148274i
\(609\) −1.52567 2.64254i −0.0618234 0.107081i
\(610\) −0.900221 + 1.55923i −0.0364489 + 0.0631313i
\(611\) 4.41128 7.64056i 0.178461 0.309104i
\(612\) −1.28938 2.23328i −0.0521202 0.0902748i
\(613\) 1.30044 + 2.25243i 0.0525243 + 0.0909748i 0.891092 0.453822i \(-0.149940\pi\)
−0.838568 + 0.544797i \(0.816607\pi\)
\(614\) 0.0641495 + 0.111110i 0.00258886 + 0.00448404i
\(615\) −10.2438 −0.413070
\(616\) 0.678543 1.17527i 0.0273393 0.0473530i
\(617\) 8.75731 + 15.1681i 0.352556 + 0.610645i 0.986697 0.162573i \(-0.0519793\pi\)
−0.634141 + 0.773218i \(0.718646\pi\)
\(618\) −6.86459 −0.276134
\(619\) −6.43055 −0.258466 −0.129233 0.991614i \(-0.541251\pi\)
−0.129233 + 0.991614i \(0.541251\pi\)
\(620\) −1.22168 2.11601i −0.0490637 0.0849809i
\(621\) 5.60088 0.224756
\(622\) −11.3436 + 19.6476i −0.454836 + 0.787799i
\(623\) 2.88230 0.115477
\(624\) 0.500000 0.866025i 0.0200160 0.0346688i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −5.86459 + 10.1578i −0.234396 + 0.405986i
\(627\) 6.80044 + 11.7787i 0.271583 + 0.470396i
\(628\) 18.3301 0.731449
\(629\) −10.0863 + 12.0132i −0.402166 + 0.478999i
\(630\) −0.421236 −0.0167824
\(631\) −16.9345 29.3314i −0.674152 1.16767i −0.976716 0.214536i \(-0.931176\pi\)
0.302564 0.953129i \(-0.402157\pi\)
\(632\) −7.37921 + 12.7812i −0.293529 + 0.508407i
\(633\) 6.26837 10.8571i 0.249145 0.431532i
\(634\) 10.7228 18.5724i 0.425856 0.737604i
\(635\) −3.17965 −0.126180
\(636\) −1.32146 + 2.28883i −0.0523992 + 0.0907580i
\(637\) −6.82256 −0.270320
\(638\) −11.6686 20.2106i −0.461964 0.800145i
\(639\) −7.17965 −0.284022
\(640\) −1.00000 −0.0395285
\(641\) 4.36569 + 7.56160i 0.172435 + 0.298665i 0.939270 0.343178i \(-0.111503\pi\)
−0.766836 + 0.641843i \(0.778170\pi\)
\(642\) 8.76481 15.1811i 0.345920 0.599150i
\(643\) 8.66724 0.341803 0.170901 0.985288i \(-0.445332\pi\)
0.170901 + 0.985288i \(0.445332\pi\)
\(644\) 1.17965 + 2.04321i 0.0464846 + 0.0805137i
\(645\) −0.421236 0.729602i −0.0165862 0.0287281i
\(646\) 5.44335 + 9.42817i 0.214166 + 0.370946i
\(647\) −19.2117 + 33.2757i −0.755291 + 1.30820i 0.189939 + 0.981796i \(0.439171\pi\)
−0.945230 + 0.326406i \(0.894162\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −3.32501 5.75909i −0.130518 0.226064i
\(650\) −0.500000 0.866025i −0.0196116 0.0339683i
\(651\) −0.514615 0.891339i −0.0201693 0.0349343i
\(652\) 2.13541 0.0836291
\(653\) −15.9381 + 27.6055i −0.623704 + 1.08029i 0.365085 + 0.930974i \(0.381040\pi\)
−0.988790 + 0.149314i \(0.952294\pi\)
\(654\) −10.1440 17.5700i −0.396662 0.687040i
\(655\) 1.62079 0.0633297
\(656\) −10.2438 −0.399953
\(657\) 4.22168 + 7.31216i 0.164703 + 0.285275i
\(658\) −3.71638 −0.144880
\(659\) 8.96793 15.5329i 0.349341 0.605076i −0.636792 0.771036i \(-0.719739\pi\)
0.986133 + 0.165960i \(0.0530722\pi\)
\(660\) −3.22168 −0.125404
\(661\) 7.62300 13.2034i 0.296500 0.513554i −0.678832 0.734293i \(-0.737514\pi\)
0.975333 + 0.220739i \(0.0708471\pi\)
\(662\) 8.05309 13.9484i 0.312992 0.542118i
\(663\) 1.28938 2.23328i 0.0500754 0.0867332i
\(664\) −7.01106 12.1435i −0.272082 0.471260i
\(665\) 1.77832 0.0689604
\(666\) 5.99004 + 1.05800i 0.232109 + 0.0409968i
\(667\) 40.5717 1.57094
\(668\) 8.25375 + 14.2959i 0.319347 + 0.553126i
\(669\) −6.44335 + 11.1602i −0.249114 + 0.431479i
\(670\) −1.93230 + 3.34683i −0.0746511 + 0.129299i
\(671\) −2.90022 + 5.02333i −0.111962 + 0.193923i
\(672\) −0.421236 −0.0162495
\(673\) 3.25731 5.64182i 0.125560 0.217476i −0.796392 0.604781i \(-0.793261\pi\)
0.921952 + 0.387305i \(0.126594\pi\)
\(674\) −24.9181 −0.959811
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −12.0000 −0.461538
\(677\) 38.0172 1.46112 0.730560 0.682848i \(-0.239259\pi\)
0.730560 + 0.682848i \(0.239259\pi\)
\(678\) 1.20066 + 2.07961i 0.0461112 + 0.0798669i
\(679\) −0.421236 + 0.729602i −0.0161656 + 0.0279996i
\(680\) −2.57876 −0.0988911
\(681\) −1.01106 1.75121i −0.0387439 0.0671064i
\(682\) −3.93585 6.81709i −0.150712 0.261040i
\(683\) −16.3079 28.2462i −0.624006 1.08081i −0.988732 0.149696i \(-0.952171\pi\)
0.364726 0.931115i \(-0.381163\pi\)
\(684\) 2.11084 3.65608i 0.0807099 0.139794i
\(685\) 7.82146 13.5472i 0.298842 0.517610i
\(686\) 2.91128 + 5.04249i 0.111153 + 0.192523i
\(687\) 1.09978 + 1.90487i 0.0419592 + 0.0726755i
\(688\) −0.421236 0.729602i −0.0160595 0.0278158i
\(689\) −2.64291 −0.100687
\(690\) 2.80044 4.85051i 0.106611 0.184656i
\(691\) 12.1551 + 21.0532i 0.462401 + 0.800902i 0.999080 0.0428846i \(-0.0136548\pi\)
−0.536679 + 0.843786i \(0.680321\pi\)
\(692\) 18.6872 0.710379
\(693\) −1.35709 −0.0515515
\(694\) 3.24625 + 5.62267i 0.123226 + 0.213433i
\(695\) 9.91594 0.376133
\(696\) −3.62190 + 6.27331i −0.137288 + 0.237789i
\(697\) −26.4163 −1.00059
\(698\) 11.6009 20.0933i 0.439100 0.760543i
\(699\) 11.9113 20.6309i 0.450526 0.780334i
\(700\) −0.210618 + 0.364801i −0.00796061 + 0.0137882i
\(701\) 18.1119 + 31.3708i 0.684079 + 1.18486i 0.973725 + 0.227725i \(0.0731288\pi\)
−0.289647 + 0.957134i \(0.593538\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −25.2880 4.46655i −0.953756 0.168459i
\(704\) −3.22168 −0.121422
\(705\) 4.41128 + 7.64056i 0.166138 + 0.287760i
\(706\) −2.31040 + 4.00173i −0.0869529 + 0.150607i
\(707\) −2.14402 + 3.71355i −0.0806341 + 0.139662i
\(708\) −1.03207 + 1.78761i −0.0387877 + 0.0671823i
\(709\) −37.2146 −1.39762 −0.698811 0.715306i \(-0.746287\pi\)
−0.698811 + 0.715306i \(0.746287\pi\)
\(710\) −3.58982 + 6.21776i −0.134724 + 0.233348i
\(711\) 14.7584 0.553484
\(712\) −3.42124 5.92575i −0.128216 0.222077i
\(713\) 13.6849 0.512505
\(714\) −1.08627 −0.0406526
\(715\) −1.61084 2.79005i −0.0602420 0.104342i
\(716\) −2.57876 + 4.46655i −0.0963729 + 0.166923i
\(717\) −6.22168 −0.232353
\(718\) 3.71172 + 6.42889i 0.138520 + 0.239924i
\(719\) −19.5920 33.9344i −0.730659 1.26554i −0.956602 0.291399i \(-0.905879\pi\)
0.225942 0.974141i \(-0.427454\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) −1.44581 + 2.50421i −0.0538446 + 0.0932617i
\(722\) 0.588720 1.01969i 0.0219099 0.0379490i
\(723\) −11.9900 20.7674i −0.445915 0.772347i
\(724\) 8.60088 + 14.8972i 0.319649 + 0.553649i
\(725\) 3.62190 + 6.27331i 0.134514 + 0.232985i
\(726\) 0.620795 0.0230398
\(727\) −22.7117 + 39.3379i −0.842331 + 1.45896i 0.0455878 + 0.998960i \(0.485484\pi\)
−0.887919 + 0.460000i \(0.847849\pi\)
\(728\) −0.210618 0.364801i −0.00780602 0.0135204i
\(729\) 1.00000 0.0370370
\(730\) 8.44335 0.312503
\(731\) −1.08627 1.88147i −0.0401771 0.0695887i
\(732\) 1.80044 0.0665462
\(733\) −1.87455 + 3.24681i −0.0692380 + 0.119924i −0.898566 0.438838i \(-0.855390\pi\)
0.829328 + 0.558762i \(0.188723\pi\)
\(734\) 4.98009 0.183818
\(735\) 3.41128 5.90851i 0.125827 0.217939i
\(736\) 2.80044 4.85051i 0.103226 0.178792i
\(737\) −6.22523 + 10.7824i −0.229309 + 0.397176i
\(738\) 5.12190 + 8.87139i 0.188540 + 0.326560i
\(739\) 36.3986 1.33895 0.669473 0.742837i \(-0.266520\pi\)
0.669473 + 0.742837i \(0.266520\pi\)
\(740\) 3.91128 4.65853i 0.143782 0.171251i
\(741\) 4.22168 0.155087
\(742\) 0.556645 + 0.964138i 0.0204351 + 0.0353946i
\(743\) −22.0564 + 38.2028i −0.809171 + 1.40153i 0.104268 + 0.994549i \(0.466750\pi\)
−0.913439 + 0.406976i \(0.866583\pi\)
\(744\) −1.22168 + 2.11601i −0.0447889 + 0.0775766i
\(745\) −2.59978 + 4.50295i −0.0952485 + 0.164975i
\(746\) −28.3942 −1.03959
\(747\) −7.01106 + 12.1435i −0.256521 + 0.444308i
\(748\) −8.30795 −0.303769
\(749\) −3.69205 6.39483i −0.134905 0.233662i
\(750\) 1.00000 0.0365148
\(751\) 47.2389 1.72377 0.861886 0.507102i \(-0.169283\pi\)
0.861886 + 0.507102i \(0.169283\pi\)
\(752\) 4.41128 + 7.64056i 0.160863 + 0.278623i
\(753\) 8.63296 14.9527i 0.314602 0.544907i
\(754\) −7.24380 −0.263803
\(755\) −0.620795 1.07525i −0.0225930 0.0391323i
\(756\) 0.210618 + 0.364801i 0.00766010 + 0.0132677i
\(757\) −16.2263 28.1048i −0.589756 1.02149i −0.994264 0.106953i \(-0.965890\pi\)
0.404508 0.914535i \(-0.367443\pi\)
\(758\) −0.410177 + 0.710447i −0.0148983 + 0.0258046i
\(759\) 9.02212 15.6268i 0.327482 0.567216i
\(760\) −2.11084 3.65608i −0.0765682 0.132620i
\(761\) −1.70066 2.94563i −0.0616490 0.106779i 0.833554 0.552439i \(-0.186303\pi\)
−0.895203 + 0.445659i \(0.852969\pi\)
\(762\) 1.58982 + 2.75365i 0.0575932 + 0.0997544i
\(763\) −8.54605 −0.309388
\(764\) 0.121898 0.211134i 0.00441012 0.00763855i
\(765\) 1.28938 + 2.23328i 0.0466177 + 0.0807442i
\(766\) 5.13762 0.185630
\(767\) −2.06415 −0.0745321
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 35.3195 1.27365 0.636826 0.771007i \(-0.280247\pi\)
0.636826 + 0.771007i \(0.280247\pi\)
\(770\) −0.678543 + 1.17527i −0.0244530 + 0.0423538i
\(771\) −3.28803 −0.118416
\(772\) −4.85819 + 8.41463i −0.174850 + 0.302849i
\(773\) −22.1860 + 38.4274i −0.797977 + 1.38214i 0.122955 + 0.992412i \(0.460763\pi\)
−0.920932 + 0.389724i \(0.872570\pi\)
\(774\) −0.421236 + 0.729602i −0.0151410 + 0.0262250i
\(775\) 1.22168 + 2.11601i 0.0438839 + 0.0760092i
\(776\) 2.00000 0.0717958
\(777\) 1.64757 1.96234i 0.0591063 0.0703986i
\(778\) 31.0686