Properties

Label 1386.2.k.u.793.1
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
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 793.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.u.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.207107 + 0.358719i) q^{5} +(-2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.207107 + 0.358719i) q^{5} +(-2.62132 - 0.358719i) q^{7} -1.00000 q^{8} +(0.207107 + 0.358719i) q^{10} +(0.500000 + 0.866025i) q^{11} -1.17157 q^{13} +(-1.62132 + 2.09077i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.08579 - 1.88064i) q^{17} +(-0.414214 + 0.717439i) q^{19} +0.414214 q^{20} +1.00000 q^{22} +(-1.62132 + 2.80821i) q^{23} +(2.41421 + 4.18154i) q^{25} +(-0.585786 + 1.01461i) q^{26} +(1.00000 + 2.44949i) q^{28} -2.82843 q^{29} +(3.24264 + 5.61642i) q^{31} +(0.500000 + 0.866025i) q^{32} -2.17157 q^{34} +(0.671573 - 0.866025i) q^{35} +(-4.82843 + 8.36308i) q^{37} +(0.414214 + 0.717439i) q^{38} +(0.207107 - 0.358719i) q^{40} -4.65685 q^{41} -2.82843 q^{43} +(0.500000 - 0.866025i) q^{44} +(1.62132 + 2.80821i) q^{46} +(-4.62132 + 8.00436i) q^{47} +(6.74264 + 1.88064i) q^{49} +4.82843 q^{50} +(0.585786 + 1.01461i) q^{52} +(-2.58579 - 4.47871i) q^{53} -0.414214 q^{55} +(2.62132 + 0.358719i) q^{56} +(-1.41421 + 2.44949i) q^{58} +(-1.82843 - 3.16693i) q^{59} +(0.792893 - 1.37333i) q^{61} +6.48528 q^{62} +1.00000 q^{64} +(0.242641 - 0.420266i) q^{65} +(6.74264 + 11.6786i) q^{67} +(-1.08579 + 1.88064i) q^{68} +(-0.414214 - 1.01461i) q^{70} -13.3137 q^{71} +(2.41421 + 4.18154i) q^{73} +(4.82843 + 8.36308i) q^{74} +0.828427 q^{76} +(-1.00000 - 2.44949i) q^{77} +(-2.37868 + 4.11999i) q^{79} +(-0.207107 - 0.358719i) q^{80} +(-2.32843 + 4.03295i) q^{82} +9.82843 q^{83} +0.899495 q^{85} +(-1.41421 + 2.44949i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(6.24264 - 10.8126i) q^{89} +(3.07107 + 0.420266i) q^{91} +3.24264 q^{92} +(4.62132 + 8.00436i) q^{94} +(-0.171573 - 0.297173i) q^{95} -10.1716 q^{97} +(5.00000 - 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} + 2q^{5} - 2q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} + 2q^{5} - 2q^{7} - 4q^{8} - 2q^{10} + 2q^{11} - 16q^{13} + 2q^{14} - 2q^{16} - 10q^{17} + 4q^{19} - 4q^{20} + 4q^{22} + 2q^{23} + 4q^{25} - 8q^{26} + 4q^{28} - 4q^{31} + 2q^{32} - 20q^{34} + 14q^{35} - 8q^{37} - 4q^{38} - 2q^{40} + 4q^{41} + 2q^{44} - 2q^{46} - 10q^{47} + 10q^{49} + 8q^{50} + 8q^{52} - 16q^{53} + 4q^{55} + 2q^{56} + 4q^{59} + 6q^{61} - 8q^{62} + 4q^{64} - 16q^{65} + 10q^{67} - 10q^{68} + 4q^{70} - 8q^{71} + 4q^{73} + 8q^{74} - 8q^{76} - 4q^{77} - 18q^{79} + 2q^{80} + 2q^{82} + 28q^{83} - 36q^{85} - 2q^{88} + 8q^{89} - 16q^{91} - 4q^{92} + 10q^{94} - 12q^{95} - 52q^{97} + 20q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.207107 + 0.358719i −0.0926210 + 0.160424i −0.908613 0.417639i \(-0.862858\pi\)
0.815992 + 0.578063i \(0.196191\pi\)
\(6\) 0 0
\(7\) −2.62132 0.358719i −0.990766 0.135583i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.207107 + 0.358719i 0.0654929 + 0.113437i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0 0
\(13\) −1.17157 −0.324936 −0.162468 0.986714i \(-0.551945\pi\)
−0.162468 + 0.986714i \(0.551945\pi\)
\(14\) −1.62132 + 2.09077i −0.433316 + 0.558782i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.08579 1.88064i −0.263342 0.456122i 0.703786 0.710412i \(-0.251491\pi\)
−0.967128 + 0.254291i \(0.918158\pi\)
\(18\) 0 0
\(19\) −0.414214 + 0.717439i −0.0950271 + 0.164592i −0.909620 0.415441i \(-0.863627\pi\)
0.814593 + 0.580033i \(0.196960\pi\)
\(20\) 0.414214 0.0926210
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −1.62132 + 2.80821i −0.338069 + 0.585552i −0.984069 0.177785i \(-0.943107\pi\)
0.646001 + 0.763337i \(0.276440\pi\)
\(24\) 0 0
\(25\) 2.41421 + 4.18154i 0.482843 + 0.836308i
\(26\) −0.585786 + 1.01461i −0.114882 + 0.198982i
\(27\) 0 0
\(28\) 1.00000 + 2.44949i 0.188982 + 0.462910i
\(29\) −2.82843 −0.525226 −0.262613 0.964901i \(-0.584584\pi\)
−0.262613 + 0.964901i \(0.584584\pi\)
\(30\) 0 0
\(31\) 3.24264 + 5.61642i 0.582395 + 1.00874i 0.995195 + 0.0979165i \(0.0312178\pi\)
−0.412799 + 0.910822i \(0.635449\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −2.17157 −0.372422
\(35\) 0.671573 0.866025i 0.113517 0.146385i
\(36\) 0 0
\(37\) −4.82843 + 8.36308i −0.793789 + 1.37488i 0.129817 + 0.991538i \(0.458561\pi\)
−0.923606 + 0.383344i \(0.874772\pi\)
\(38\) 0.414214 + 0.717439i 0.0671943 + 0.116384i
\(39\) 0 0
\(40\) 0.207107 0.358719i 0.0327465 0.0567185i
\(41\) −4.65685 −0.727278 −0.363639 0.931540i \(-0.618466\pi\)
−0.363639 + 0.931540i \(0.618466\pi\)
\(42\) 0 0
\(43\) −2.82843 −0.431331 −0.215666 0.976467i \(-0.569192\pi\)
−0.215666 + 0.976467i \(0.569192\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) 1.62132 + 2.80821i 0.239051 + 0.414048i
\(47\) −4.62132 + 8.00436i −0.674089 + 1.16756i 0.302645 + 0.953103i \(0.402130\pi\)
−0.976734 + 0.214453i \(0.931203\pi\)
\(48\) 0 0
\(49\) 6.74264 + 1.88064i 0.963234 + 0.268662i
\(50\) 4.82843 0.682843
\(51\) 0 0
\(52\) 0.585786 + 1.01461i 0.0812340 + 0.140701i
\(53\) −2.58579 4.47871i −0.355185 0.615199i 0.631965 0.774997i \(-0.282249\pi\)
−0.987150 + 0.159799i \(0.948915\pi\)
\(54\) 0 0
\(55\) −0.414214 −0.0558525
\(56\) 2.62132 + 0.358719i 0.350289 + 0.0479359i
\(57\) 0 0
\(58\) −1.41421 + 2.44949i −0.185695 + 0.321634i
\(59\) −1.82843 3.16693i −0.238041 0.412299i 0.722111 0.691777i \(-0.243172\pi\)
−0.960152 + 0.279478i \(0.909839\pi\)
\(60\) 0 0
\(61\) 0.792893 1.37333i 0.101520 0.175837i −0.810791 0.585335i \(-0.800963\pi\)
0.912311 + 0.409498i \(0.134296\pi\)
\(62\) 6.48528 0.823632
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.242641 0.420266i 0.0300959 0.0521276i
\(66\) 0 0
\(67\) 6.74264 + 11.6786i 0.823745 + 1.42677i 0.902875 + 0.429903i \(0.141452\pi\)
−0.0791303 + 0.996864i \(0.525214\pi\)
\(68\) −1.08579 + 1.88064i −0.131671 + 0.228061i
\(69\) 0 0
\(70\) −0.414214 1.01461i −0.0495080 0.121269i
\(71\) −13.3137 −1.58005 −0.790023 0.613077i \(-0.789932\pi\)
−0.790023 + 0.613077i \(0.789932\pi\)
\(72\) 0 0
\(73\) 2.41421 + 4.18154i 0.282562 + 0.489412i 0.972015 0.234918i \(-0.0754823\pi\)
−0.689453 + 0.724331i \(0.742149\pi\)
\(74\) 4.82843 + 8.36308i 0.561293 + 0.972188i
\(75\) 0 0
\(76\) 0.828427 0.0950271
\(77\) −1.00000 2.44949i −0.113961 0.279145i
\(78\) 0 0
\(79\) −2.37868 + 4.11999i −0.267622 + 0.463536i −0.968247 0.249994i \(-0.919571\pi\)
0.700625 + 0.713530i \(0.252905\pi\)
\(80\) −0.207107 0.358719i −0.0231552 0.0401061i
\(81\) 0 0
\(82\) −2.32843 + 4.03295i −0.257132 + 0.445365i
\(83\) 9.82843 1.07881 0.539405 0.842046i \(-0.318649\pi\)
0.539405 + 0.842046i \(0.318649\pi\)
\(84\) 0 0
\(85\) 0.899495 0.0975639
\(86\) −1.41421 + 2.44949i −0.152499 + 0.264135i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 6.24264 10.8126i 0.661719 1.14613i −0.318445 0.947941i \(-0.603161\pi\)
0.980164 0.198189i \(-0.0635060\pi\)
\(90\) 0 0
\(91\) 3.07107 + 0.420266i 0.321935 + 0.0440558i
\(92\) 3.24264 0.338069
\(93\) 0 0
\(94\) 4.62132 + 8.00436i 0.476653 + 0.825587i
\(95\) −0.171573 0.297173i −0.0176030 0.0304893i
\(96\) 0 0
\(97\) −10.1716 −1.03277 −0.516383 0.856358i \(-0.672722\pi\)
−0.516383 + 0.856358i \(0.672722\pi\)
\(98\) 5.00000 4.89898i 0.505076 0.494872i
\(99\) 0 0
\(100\) 2.41421 4.18154i 0.241421 0.418154i
\(101\) −7.07107 12.2474i −0.703598 1.21867i −0.967195 0.254034i \(-0.918242\pi\)
0.263598 0.964633i \(-0.415091\pi\)
\(102\) 0 0
\(103\) 4.58579 7.94282i 0.451851 0.782629i −0.546650 0.837361i \(-0.684097\pi\)
0.998501 + 0.0547323i \(0.0174305\pi\)
\(104\) 1.17157 0.114882
\(105\) 0 0
\(106\) −5.17157 −0.502308
\(107\) −8.32843 + 14.4253i −0.805139 + 1.39454i 0.111057 + 0.993814i \(0.464576\pi\)
−0.916197 + 0.400728i \(0.868757\pi\)
\(108\) 0 0
\(109\) −1.62132 2.80821i −0.155294 0.268978i 0.777872 0.628423i \(-0.216299\pi\)
−0.933166 + 0.359445i \(0.882966\pi\)
\(110\) −0.207107 + 0.358719i −0.0197469 + 0.0342026i
\(111\) 0 0
\(112\) 1.62132 2.09077i 0.153200 0.197559i
\(113\) −3.65685 −0.344008 −0.172004 0.985096i \(-0.555024\pi\)
−0.172004 + 0.985096i \(0.555024\pi\)
\(114\) 0 0
\(115\) −0.671573 1.16320i −0.0626245 0.108469i
\(116\) 1.41421 + 2.44949i 0.131306 + 0.227429i
\(117\) 0 0
\(118\) −3.65685 −0.336641
\(119\) 2.17157 + 5.31925i 0.199068 + 0.487614i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −0.792893 1.37333i −0.0717852 0.124336i
\(123\) 0 0
\(124\) 3.24264 5.61642i 0.291198 0.504369i
\(125\) −4.07107 −0.364127
\(126\) 0 0
\(127\) 1.24264 0.110267 0.0551333 0.998479i \(-0.482442\pi\)
0.0551333 + 0.998479i \(0.482442\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −0.242641 0.420266i −0.0212810 0.0368598i
\(131\) 7.65685 13.2621i 0.668982 1.15871i −0.309207 0.950995i \(-0.600063\pi\)
0.978189 0.207717i \(-0.0666032\pi\)
\(132\) 0 0
\(133\) 1.34315 1.73205i 0.116466 0.150188i
\(134\) 13.4853 1.16495
\(135\) 0 0
\(136\) 1.08579 + 1.88064i 0.0931054 + 0.161263i
\(137\) −2.41421 4.18154i −0.206260 0.357253i 0.744273 0.667875i \(-0.232796\pi\)
−0.950534 + 0.310622i \(0.899463\pi\)
\(138\) 0 0
\(139\) −6.00000 −0.508913 −0.254457 0.967084i \(-0.581897\pi\)
−0.254457 + 0.967084i \(0.581897\pi\)
\(140\) −1.08579 0.148586i −0.0917657 0.0125578i
\(141\) 0 0
\(142\) −6.65685 + 11.5300i −0.558631 + 0.967577i
\(143\) −0.585786 1.01461i −0.0489859 0.0848461i
\(144\) 0 0
\(145\) 0.585786 1.01461i 0.0486469 0.0842589i
\(146\) 4.82843 0.399603
\(147\) 0 0
\(148\) 9.65685 0.793789
\(149\) 5.65685 9.79796i 0.463428 0.802680i −0.535701 0.844407i \(-0.679953\pi\)
0.999129 + 0.0417274i \(0.0132861\pi\)
\(150\) 0 0
\(151\) −0.621320 1.07616i −0.0505623 0.0875765i 0.839637 0.543149i \(-0.182768\pi\)
−0.890199 + 0.455572i \(0.849435\pi\)
\(152\) 0.414214 0.717439i 0.0335972 0.0581920i
\(153\) 0 0
\(154\) −2.62132 0.358719i −0.211232 0.0289064i
\(155\) −2.68629 −0.215768
\(156\) 0 0
\(157\) 4.58579 + 7.94282i 0.365986 + 0.633906i 0.988934 0.148357i \(-0.0473986\pi\)
−0.622948 + 0.782263i \(0.714065\pi\)
\(158\) 2.37868 + 4.11999i 0.189238 + 0.327769i
\(159\) 0 0
\(160\) −0.414214 −0.0327465
\(161\) 5.25736 6.77962i 0.414338 0.534309i
\(162\) 0 0
\(163\) −1.50000 + 2.59808i −0.117489 + 0.203497i −0.918772 0.394789i \(-0.870818\pi\)
0.801283 + 0.598286i \(0.204151\pi\)
\(164\) 2.32843 + 4.03295i 0.181820 + 0.314921i
\(165\) 0 0
\(166\) 4.91421 8.51167i 0.381417 0.660634i
\(167\) 16.4853 1.27567 0.637835 0.770173i \(-0.279830\pi\)
0.637835 + 0.770173i \(0.279830\pi\)
\(168\) 0 0
\(169\) −11.6274 −0.894417
\(170\) 0.449747 0.778985i 0.0344941 0.0597455i
\(171\) 0 0
\(172\) 1.41421 + 2.44949i 0.107833 + 0.186772i
\(173\) −6.07107 + 10.5154i −0.461575 + 0.799471i −0.999040 0.0438152i \(-0.986049\pi\)
0.537465 + 0.843286i \(0.319382\pi\)
\(174\) 0 0
\(175\) −4.82843 11.8272i −0.364995 0.894051i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) −6.24264 10.8126i −0.467906 0.810436i
\(179\) −1.58579 2.74666i −0.118527 0.205295i 0.800657 0.599123i \(-0.204484\pi\)
−0.919184 + 0.393828i \(0.871151\pi\)
\(180\) 0 0
\(181\) −2.34315 −0.174165 −0.0870823 0.996201i \(-0.527754\pi\)
−0.0870823 + 0.996201i \(0.527754\pi\)
\(182\) 1.89949 2.44949i 0.140800 0.181568i
\(183\) 0 0
\(184\) 1.62132 2.80821i 0.119525 0.207024i
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 0 0
\(187\) 1.08579 1.88064i 0.0794006 0.137526i
\(188\) 9.24264 0.674089
\(189\) 0 0
\(190\) −0.343146 −0.0248944
\(191\) −4.65685 + 8.06591i −0.336958 + 0.583629i −0.983859 0.178945i \(-0.942731\pi\)
0.646901 + 0.762574i \(0.276065\pi\)
\(192\) 0 0
\(193\) 4.58579 + 7.94282i 0.330092 + 0.571736i 0.982530 0.186106i \(-0.0595868\pi\)
−0.652438 + 0.757843i \(0.726254\pi\)
\(194\) −5.08579 + 8.80884i −0.365138 + 0.632438i
\(195\) 0 0
\(196\) −1.74264 6.77962i −0.124474 0.484258i
\(197\) 3.51472 0.250413 0.125207 0.992131i \(-0.460041\pi\)
0.125207 + 0.992131i \(0.460041\pi\)
\(198\) 0 0
\(199\) 4.17157 + 7.22538i 0.295715 + 0.512193i 0.975151 0.221541i \(-0.0711088\pi\)
−0.679436 + 0.733735i \(0.737775\pi\)
\(200\) −2.41421 4.18154i −0.170711 0.295680i
\(201\) 0 0
\(202\) −14.1421 −0.995037
\(203\) 7.41421 + 1.01461i 0.520376 + 0.0712118i
\(204\) 0 0
\(205\) 0.964466 1.67050i 0.0673612 0.116673i
\(206\) −4.58579 7.94282i −0.319507 0.553402i
\(207\) 0 0
\(208\) 0.585786 1.01461i 0.0406170 0.0703507i
\(209\) −0.828427 −0.0573035
\(210\) 0 0
\(211\) 14.8284 1.02083 0.510416 0.859928i \(-0.329492\pi\)
0.510416 + 0.859928i \(0.329492\pi\)
\(212\) −2.58579 + 4.47871i −0.177593 + 0.307599i
\(213\) 0 0
\(214\) 8.32843 + 14.4253i 0.569320 + 0.986090i
\(215\) 0.585786 1.01461i 0.0399503 0.0691960i
\(216\) 0 0
\(217\) −6.48528 15.8856i −0.440250 1.07839i
\(218\) −3.24264 −0.219619
\(219\) 0 0
\(220\) 0.207107 + 0.358719i 0.0139631 + 0.0241849i
\(221\) 1.27208 + 2.20330i 0.0855692 + 0.148210i
\(222\) 0 0
\(223\) −13.3137 −0.891552 −0.445776 0.895145i \(-0.647072\pi\)
−0.445776 + 0.895145i \(0.647072\pi\)
\(224\) −1.00000 2.44949i −0.0668153 0.163663i
\(225\) 0 0
\(226\) −1.82843 + 3.16693i −0.121625 + 0.210661i
\(227\) 6.15685 + 10.6640i 0.408645 + 0.707794i 0.994738 0.102450i \(-0.0326682\pi\)
−0.586093 + 0.810244i \(0.699335\pi\)
\(228\) 0 0
\(229\) 5.65685 9.79796i 0.373815 0.647467i −0.616334 0.787485i \(-0.711383\pi\)
0.990149 + 0.140018i \(0.0447160\pi\)
\(230\) −1.34315 −0.0885644
\(231\) 0 0
\(232\) 2.82843 0.185695
\(233\) 4.15685 7.19988i 0.272325 0.471680i −0.697132 0.716943i \(-0.745541\pi\)
0.969457 + 0.245263i \(0.0788742\pi\)
\(234\) 0 0
\(235\) −1.91421 3.31552i −0.124870 0.216280i
\(236\) −1.82843 + 3.16693i −0.119020 + 0.206149i
\(237\) 0 0
\(238\) 5.69239 + 0.778985i 0.368983 + 0.0504941i
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 0 0
\(241\) −12.4853 21.6251i −0.804248 1.39300i −0.916798 0.399352i \(-0.869235\pi\)
0.112550 0.993646i \(-0.464098\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) −1.58579 −0.101520
\(245\) −2.07107 + 2.02922i −0.132316 + 0.129642i
\(246\) 0 0
\(247\) 0.485281 0.840532i 0.0308777 0.0534818i
\(248\) −3.24264 5.61642i −0.205908 0.356643i
\(249\) 0 0
\(250\) −2.03553 + 3.52565i −0.128738 + 0.222982i
\(251\) −26.1421 −1.65008 −0.825038 0.565077i \(-0.808847\pi\)
−0.825038 + 0.565077i \(0.808847\pi\)
\(252\) 0 0
\(253\) −3.24264 −0.203863
\(254\) 0.621320 1.07616i 0.0389851 0.0675242i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 12.5858 21.7992i 0.785080 1.35980i −0.143872 0.989596i \(-0.545955\pi\)
0.928951 0.370202i \(-0.120711\pi\)
\(258\) 0 0
\(259\) 15.6569 20.1903i 0.972870 1.25456i
\(260\) −0.485281 −0.0300959
\(261\) 0 0
\(262\) −7.65685 13.2621i −0.473042 0.819333i
\(263\) 4.65685 + 8.06591i 0.287154 + 0.497365i 0.973129 0.230260i \(-0.0739575\pi\)
−0.685975 + 0.727625i \(0.740624\pi\)
\(264\) 0 0
\(265\) 2.14214 0.131590
\(266\) −0.828427 2.02922i −0.0507941 0.124420i
\(267\) 0 0
\(268\) 6.74264 11.6786i 0.411872 0.713384i
\(269\) −4.03553 6.98975i −0.246051 0.426173i 0.716376 0.697715i \(-0.245800\pi\)
−0.962427 + 0.271542i \(0.912466\pi\)
\(270\) 0 0
\(271\) 6.65685 11.5300i 0.404375 0.700398i −0.589873 0.807496i \(-0.700822\pi\)
0.994249 + 0.107098i \(0.0341557\pi\)
\(272\) 2.17157 0.131671
\(273\) 0 0
\(274\) −4.82843 −0.291696
\(275\) −2.41421 + 4.18154i −0.145583 + 0.252156i
\(276\) 0 0
\(277\) 3.41421 + 5.91359i 0.205140 + 0.355313i 0.950177 0.311710i \(-0.100902\pi\)
−0.745037 + 0.667023i \(0.767568\pi\)
\(278\) −3.00000 + 5.19615i −0.179928 + 0.311645i
\(279\) 0 0
\(280\) −0.671573 + 0.866025i −0.0401342 + 0.0517549i
\(281\) −2.51472 −0.150016 −0.0750078 0.997183i \(-0.523898\pi\)
−0.0750078 + 0.997183i \(0.523898\pi\)
\(282\) 0 0
\(283\) 0.928932 + 1.60896i 0.0552193 + 0.0956426i 0.892314 0.451416i \(-0.149081\pi\)
−0.837094 + 0.547058i \(0.815748\pi\)
\(284\) 6.65685 + 11.5300i 0.395012 + 0.684180i
\(285\) 0 0
\(286\) −1.17157 −0.0692766
\(287\) 12.2071 + 1.67050i 0.720563 + 0.0986067i
\(288\) 0 0
\(289\) 6.14214 10.6385i 0.361302 0.625794i
\(290\) −0.585786 1.01461i −0.0343986 0.0595801i
\(291\) 0 0
\(292\) 2.41421 4.18154i 0.141281 0.244706i
\(293\) −12.8284 −0.749445 −0.374722 0.927137i \(-0.622262\pi\)
−0.374722 + 0.927137i \(0.622262\pi\)
\(294\) 0 0
\(295\) 1.51472 0.0881903
\(296\) 4.82843 8.36308i 0.280647 0.486094i
\(297\) 0 0
\(298\) −5.65685 9.79796i −0.327693 0.567581i
\(299\) 1.89949 3.29002i 0.109851 0.190267i
\(300\) 0 0
\(301\) 7.41421 + 1.01461i 0.427348 + 0.0584813i
\(302\) −1.24264 −0.0715059
\(303\) 0 0
\(304\) −0.414214 0.717439i −0.0237568 0.0411479i
\(305\) 0.328427 + 0.568852i 0.0188057 + 0.0325724i
\(306\) 0 0
\(307\) −34.6274 −1.97629 −0.988146 0.153520i \(-0.950939\pi\)
−0.988146 + 0.153520i \(0.950939\pi\)
\(308\) −1.62132 + 2.09077i −0.0923833 + 0.119133i
\(309\) 0 0
\(310\) −1.34315 + 2.32640i −0.0762856 + 0.132130i
\(311\) 5.10660 + 8.84489i 0.289569 + 0.501548i 0.973707 0.227805i \(-0.0731548\pi\)
−0.684138 + 0.729353i \(0.739821\pi\)
\(312\) 0 0
\(313\) 14.6569 25.3864i 0.828454 1.43493i −0.0707960 0.997491i \(-0.522554\pi\)
0.899250 0.437434i \(-0.144113\pi\)
\(314\) 9.17157 0.517582
\(315\) 0 0
\(316\) 4.75736 0.267622
\(317\) −16.9350 + 29.3323i −0.951166 + 1.64747i −0.208258 + 0.978074i \(0.566779\pi\)
−0.742908 + 0.669394i \(0.766554\pi\)
\(318\) 0 0
\(319\) −1.41421 2.44949i −0.0791808 0.137145i
\(320\) −0.207107 + 0.358719i −0.0115776 + 0.0200530i
\(321\) 0 0
\(322\) −3.24264 7.94282i −0.180705 0.442636i
\(323\) 1.79899 0.100098
\(324\) 0 0
\(325\) −2.82843 4.89898i −0.156893 0.271746i
\(326\) 1.50000 + 2.59808i 0.0830773 + 0.143894i
\(327\) 0 0
\(328\) 4.65685 0.257132
\(329\) 14.9853 19.3242i 0.826165 1.06538i
\(330\) 0 0
\(331\) −3.15685 + 5.46783i −0.173516 + 0.300539i −0.939647 0.342146i \(-0.888846\pi\)
0.766130 + 0.642685i \(0.222180\pi\)
\(332\) −4.91421 8.51167i −0.269703 0.467138i
\(333\) 0 0
\(334\) 8.24264 14.2767i 0.451017 0.781185i
\(335\) −5.58579 −0.305184
\(336\) 0 0
\(337\) 9.51472 0.518300 0.259150 0.965837i \(-0.416558\pi\)
0.259150 + 0.965837i \(0.416558\pi\)
\(338\) −5.81371 + 10.0696i −0.316224 + 0.547716i
\(339\) 0 0
\(340\) −0.449747 0.778985i −0.0243910 0.0422464i
\(341\) −3.24264 + 5.61642i −0.175599 + 0.304146i
\(342\) 0 0
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 2.82843 0.152499
\(345\) 0 0
\(346\) 6.07107 + 10.5154i 0.326383 + 0.565311i
\(347\) 2.42893 + 4.20703i 0.130392 + 0.225845i 0.923828 0.382809i \(-0.125043\pi\)
−0.793436 + 0.608654i \(0.791710\pi\)
\(348\) 0 0
\(349\) −15.7279 −0.841896 −0.420948 0.907085i \(-0.638303\pi\)
−0.420948 + 0.907085i \(0.638303\pi\)
\(350\) −12.6569 1.73205i −0.676537 0.0925820i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −8.41421 14.5738i −0.447843 0.775688i 0.550402 0.834900i \(-0.314474\pi\)
−0.998245 + 0.0592122i \(0.981141\pi\)
\(354\) 0 0
\(355\) 2.75736 4.77589i 0.146345 0.253478i
\(356\) −12.4853 −0.661719
\(357\) 0 0
\(358\) −3.17157 −0.167623
\(359\) −4.24264 + 7.34847i −0.223918 + 0.387837i −0.955994 0.293385i \(-0.905218\pi\)
0.732076 + 0.681223i \(0.238551\pi\)
\(360\) 0 0
\(361\) 9.15685 + 15.8601i 0.481940 + 0.834744i
\(362\) −1.17157 + 2.02922i −0.0615765 + 0.106654i
\(363\) 0 0
\(364\) −1.17157 2.86976i −0.0614071 0.150416i
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) −2.75736 4.77589i −0.143933 0.249299i 0.785041 0.619443i \(-0.212642\pi\)
−0.928974 + 0.370144i \(0.879308\pi\)
\(368\) −1.62132 2.80821i −0.0845172 0.146388i
\(369\) 0 0
\(370\) −4.00000 −0.207950
\(371\) 5.17157 + 12.6677i 0.268495 + 0.657675i
\(372\) 0 0
\(373\) 7.86396 13.6208i 0.407180 0.705257i −0.587392 0.809302i \(-0.699845\pi\)
0.994573 + 0.104045i \(0.0331787\pi\)
\(374\) −1.08579 1.88064i −0.0561447 0.0972454i
\(375\) 0 0
\(376\) 4.62132 8.00436i 0.238326 0.412793i
\(377\) 3.31371 0.170665
\(378\) 0 0
\(379\) 19.3431 0.993591 0.496795 0.867868i \(-0.334510\pi\)
0.496795 + 0.867868i \(0.334510\pi\)
\(380\) −0.171573 + 0.297173i −0.00880150 + 0.0152447i
\(381\) 0 0
\(382\) 4.65685 + 8.06591i 0.238265 + 0.412688i
\(383\) −17.1421 + 29.6910i −0.875922 + 1.51714i −0.0201451 + 0.999797i \(0.506413\pi\)
−0.855777 + 0.517345i \(0.826921\pi\)
\(384\) 0 0
\(385\) 1.08579 + 0.148586i 0.0553368 + 0.00757267i
\(386\) 9.17157 0.466821
\(387\) 0 0
\(388\) 5.08579 + 8.80884i 0.258192 + 0.447201i
\(389\) −0.863961 1.49642i −0.0438046 0.0758717i 0.843292 0.537456i \(-0.180615\pi\)
−0.887096 + 0.461584i \(0.847281\pi\)
\(390\) 0 0
\(391\) 7.04163 0.356111
\(392\) −6.74264 1.88064i −0.340555 0.0949865i
\(393\) 0 0
\(394\) 1.75736 3.04384i 0.0885345 0.153346i
\(395\) −0.985281 1.70656i −0.0495749 0.0858662i
\(396\) 0 0
\(397\) −6.24264 + 10.8126i −0.313309 + 0.542667i −0.979077 0.203492i \(-0.934771\pi\)
0.665767 + 0.746159i \(0.268104\pi\)
\(398\) 8.34315 0.418204
\(399\) 0 0
\(400\) −4.82843 −0.241421
\(401\) −7.89949 + 13.6823i −0.394482 + 0.683263i −0.993035 0.117820i \(-0.962409\pi\)
0.598553 + 0.801083i \(0.295743\pi\)
\(402\) 0 0
\(403\) −3.79899 6.58004i −0.189241 0.327775i
\(404\) −7.07107 + 12.2474i −0.351799 + 0.609333i
\(405\) 0 0
\(406\) 4.58579 5.91359i 0.227589 0.293487i
\(407\) −9.65685 −0.478672
\(408\) 0 0
\(409\) 5.72792 + 9.92105i 0.283228 + 0.490564i 0.972178 0.234244i \(-0.0752615\pi\)
−0.688950 + 0.724809i \(0.741928\pi\)
\(410\) −0.964466 1.67050i −0.0476316 0.0825003i
\(411\) 0 0
\(412\) −9.17157 −0.451851
\(413\) 3.65685 + 8.95743i 0.179942 + 0.440766i
\(414\) 0 0
\(415\) −2.03553 + 3.52565i −0.0999204 + 0.173067i
\(416\) −0.585786 1.01461i −0.0287205 0.0497454i
\(417\) 0 0
\(418\) −0.414214 + 0.717439i −0.0202598 + 0.0350911i
\(419\) 25.7990 1.26036 0.630182 0.776448i \(-0.282980\pi\)
0.630182 + 0.776448i \(0.282980\pi\)
\(420\) 0 0
\(421\) 14.8284 0.722693 0.361347 0.932432i \(-0.382317\pi\)
0.361347 + 0.932432i \(0.382317\pi\)
\(422\) 7.41421 12.8418i 0.360918 0.625129i
\(423\) 0 0
\(424\) 2.58579 + 4.47871i 0.125577 + 0.217506i
\(425\) 5.24264 9.08052i 0.254305 0.440470i
\(426\) 0 0
\(427\) −2.57107 + 3.31552i −0.124423 + 0.160449i
\(428\) 16.6569 0.805139
\(429\) 0 0
\(430\) −0.585786 1.01461i −0.0282491 0.0489289i
\(431\) −9.58579 16.6031i −0.461731 0.799742i 0.537316 0.843381i \(-0.319438\pi\)
−0.999047 + 0.0436391i \(0.986105\pi\)
\(432\) 0 0
\(433\) −26.6569 −1.28105 −0.640523 0.767939i \(-0.721283\pi\)
−0.640523 + 0.767939i \(0.721283\pi\)
\(434\) −17.0000 2.32640i −0.816026 0.111671i
\(435\) 0 0
\(436\) −1.62132 + 2.80821i −0.0776472 + 0.134489i
\(437\) −1.34315 2.32640i −0.0642514 0.111287i
\(438\) 0 0
\(439\) −1.69239 + 2.93130i −0.0807733 + 0.139903i −0.903582 0.428415i \(-0.859072\pi\)
0.822809 + 0.568318i \(0.192406\pi\)
\(440\) 0.414214 0.0197469
\(441\) 0 0
\(442\) 2.54416 0.121013
\(443\) 7.17157 12.4215i 0.340732 0.590165i −0.643837 0.765163i \(-0.722659\pi\)
0.984569 + 0.174998i \(0.0559919\pi\)
\(444\) 0 0
\(445\) 2.58579 + 4.47871i 0.122578 + 0.212311i
\(446\) −6.65685 + 11.5300i −0.315211 + 0.545962i
\(447\) 0 0
\(448\) −2.62132 0.358719i −0.123846 0.0169479i
\(449\) −23.1127 −1.09076 −0.545378 0.838190i \(-0.683614\pi\)
−0.545378 + 0.838190i \(0.683614\pi\)
\(450\) 0 0
\(451\) −2.32843 4.03295i −0.109641 0.189904i
\(452\) 1.82843 + 3.16693i 0.0860020 + 0.148960i
\(453\) 0 0
\(454\) 12.3137 0.577911
\(455\) −0.786797 + 1.01461i −0.0368856 + 0.0475657i
\(456\) 0 0
\(457\) −17.3137 + 29.9882i −0.809901 + 1.40279i 0.103031 + 0.994678i \(0.467146\pi\)
−0.912932 + 0.408112i \(0.866187\pi\)
\(458\) −5.65685 9.79796i −0.264327 0.457829i
\(459\) 0 0
\(460\) −0.671573 + 1.16320i −0.0313122 + 0.0542344i
\(461\) 23.6569 1.10181 0.550905 0.834568i \(-0.314283\pi\)
0.550905 + 0.834568i \(0.314283\pi\)
\(462\) 0 0
\(463\) 23.1127 1.07414 0.537069 0.843538i \(-0.319531\pi\)
0.537069 + 0.843538i \(0.319531\pi\)
\(464\) 1.41421 2.44949i 0.0656532 0.113715i
\(465\) 0 0
\(466\) −4.15685 7.19988i −0.192563 0.333528i
\(467\) −1.48528 + 2.57258i −0.0687306 + 0.119045i −0.898343 0.439295i \(-0.855228\pi\)
0.829612 + 0.558340i \(0.188562\pi\)
\(468\) 0 0
\(469\) −13.4853 33.0321i −0.622692 1.52528i
\(470\) −3.82843 −0.176592
\(471\) 0 0
\(472\) 1.82843 + 3.16693i 0.0841602 + 0.145770i
\(473\) −1.41421 2.44949i −0.0650256 0.112628i
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 3.52082 4.54026i 0.161376 0.208102i
\(477\) 0 0
\(478\) −10.0000 + 17.3205i −0.457389 + 0.792222i
\(479\) 2.58579 + 4.47871i 0.118148 + 0.204638i 0.919034 0.394179i \(-0.128971\pi\)
−0.800886 + 0.598817i \(0.795638\pi\)
\(480\) 0 0
\(481\) 5.65685 9.79796i 0.257930 0.446748i
\(482\) −24.9706 −1.13738
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 2.10660 3.64874i 0.0956559 0.165681i
\(486\) 0 0
\(487\) 10.6569 + 18.4582i 0.482908 + 0.836421i 0.999807 0.0196248i \(-0.00624716\pi\)
−0.516899 + 0.856046i \(0.672914\pi\)
\(488\) −0.792893 + 1.37333i −0.0358926 + 0.0621678i
\(489\) 0 0
\(490\) 0.721825 + 2.80821i 0.0326087 + 0.126862i
\(491\) 15.6274 0.705255 0.352628 0.935764i \(-0.385288\pi\)
0.352628 + 0.935764i \(0.385288\pi\)
\(492\) 0 0
\(493\) 3.07107 + 5.31925i 0.138314 + 0.239567i
\(494\) −0.485281 0.840532i −0.0218338 0.0378173i
\(495\) 0 0
\(496\) −6.48528 −0.291198
\(497\) 34.8995 + 4.77589i 1.56546 + 0.214228i
\(498\) 0 0
\(499\) −7.17157 + 12.4215i −0.321044 + 0.556064i −0.980704 0.195500i \(-0.937367\pi\)
0.659660 + 0.751564i \(0.270700\pi\)
\(500\) 2.03553 + 3.52565i 0.0910318 + 0.157672i
\(501\) 0 0
\(502\) −13.0711 + 22.6398i −0.583390 + 1.01046i
\(503\) −8.97056 −0.399978 −0.199989 0.979798i \(-0.564091\pi\)
−0.199989 + 0.979798i \(0.564091\pi\)
\(504\) 0 0
\(505\) 5.85786 0.260672
\(506\) −1.62132 + 2.80821i −0.0720765 + 0.124840i
\(507\) 0 0
\(508\) −0.621320 1.07616i −0.0275666 0.0477468i
\(509\) 12.5858 21.7992i 0.557855 0.966234i −0.439820 0.898086i \(-0.644958\pi\)
0.997675 0.0681476i \(-0.0217089\pi\)
\(510\) 0 0
\(511\) −4.82843 11.8272i −0.213597 0.523204i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −12.5858 21.7992i −0.555135 0.961522i
\(515\) 1.89949 + 3.29002i 0.0837017 + 0.144976i
\(516\) 0 0
\(517\) −9.24264 −0.406491
\(518\) −9.65685 23.6544i −0.424298 1.03931i
\(519\) 0 0
\(520\) −0.242641 + 0.420266i −0.0106405 + 0.0184299i
\(521\) 14.6569 + 25.3864i 0.642128 + 1.11220i 0.984957 + 0.172801i \(0.0552818\pi\)
−0.342828 + 0.939398i \(0.611385\pi\)
\(522\) 0 0
\(523\) 15.7279 27.2416i 0.687734 1.19119i −0.284835 0.958577i \(-0.591939\pi\)
0.972569 0.232614i \(-0.0747278\pi\)
\(524\) −15.3137 −0.668982
\(525\) 0 0
\(526\) 9.31371 0.406097
\(527\) 7.04163 12.1965i 0.306738 0.531286i
\(528\) 0 0
\(529\) 6.24264 + 10.8126i 0.271419 + 0.470112i
\(530\) 1.07107 1.85514i 0.0465242 0.0805823i
\(531\) 0 0
\(532\) −2.17157 0.297173i −0.0941496 0.0128841i
\(533\) 5.45584 0.236319
\(534\) 0 0
\(535\) −3.44975 5.97514i −0.149146 0.258328i
\(536\) −6.74264 11.6786i −0.291238 0.504439i
\(537\) 0 0
\(538\) −8.07107 −0.347968
\(539\) 1.74264 + 6.77962i 0.0750608 + 0.292019i
\(540\) 0 0
\(541\) 2.72183 4.71434i 0.117020 0.202685i −0.801565 0.597907i \(-0.795999\pi\)
0.918586 + 0.395222i \(0.129332\pi\)
\(542\) −6.65685 11.5300i −0.285936 0.495256i
\(543\) 0 0
\(544\) 1.08579 1.88064i 0.0465527 0.0806317i
\(545\) 1.34315 0.0575340
\(546\) 0 0
\(547\) −36.1421 −1.54533 −0.772663 0.634816i \(-0.781076\pi\)
−0.772663 + 0.634816i \(0.781076\pi\)
\(548\) −2.41421 + 4.18154i −0.103130 + 0.178627i
\(549\) 0 0
\(550\) 2.41421 + 4.18154i 0.102942 + 0.178301i
\(551\) 1.17157 2.02922i 0.0499107 0.0864478i
\(552\) 0 0
\(553\) 7.71320 9.94655i 0.327999 0.422970i
\(554\) 6.82843 0.290112
\(555\) 0 0
\(556\) 3.00000 + 5.19615i 0.127228 + 0.220366i
\(557\) −2.24264 3.88437i −0.0950237 0.164586i 0.814595 0.580030i \(-0.196959\pi\)
−0.909619 + 0.415445i \(0.863626\pi\)
\(558\) 0 0
\(559\) 3.31371 0.140155
\(560\) 0.414214 + 1.01461i 0.0175037 + 0.0428752i
\(561\) 0 0
\(562\) −1.25736 + 2.17781i −0.0530385 + 0.0918654i
\(563\) 12.8284 + 22.2195i 0.540654 + 0.936440i 0.998867 + 0.0475973i \(0.0151564\pi\)
−0.458213 + 0.888842i \(0.651510\pi\)
\(564\) 0 0
\(565\) 0.757359 1.31178i 0.0318623 0.0551872i
\(566\) 1.85786 0.0780919
\(567\) 0 0
\(568\) 13.3137 0.558631
\(569\) −11.0000 + 19.0526i −0.461144 + 0.798725i −0.999018 0.0443003i \(-0.985894\pi\)
0.537874 + 0.843025i \(0.319228\pi\)
\(570\) 0 0
\(571\) 10.8284 + 18.7554i 0.453156 + 0.784888i 0.998580 0.0532715i \(-0.0169649\pi\)
−0.545424 + 0.838160i \(0.683632\pi\)
\(572\) −0.585786 + 1.01461i −0.0244930 + 0.0424231i
\(573\) 0 0
\(574\) 7.55025 9.73641i 0.315141 0.406390i
\(575\) −15.6569 −0.652936
\(576\) 0 0
\(577\) −2.57107 4.45322i −0.107035 0.185390i 0.807533 0.589823i \(-0.200802\pi\)
−0.914568 + 0.404433i \(0.867469\pi\)
\(578\) −6.14214 10.6385i −0.255479 0.442503i
\(579\) 0 0
\(580\) −1.17157 −0.0486469
\(581\) −25.7635 3.52565i −1.06885 0.146269i
\(582\) 0 0
\(583\) 2.58579 4.47871i 0.107092 0.185489i
\(584\) −2.41421 4.18154i −0.0999009 0.173033i
\(585\) 0 0
\(586\) −6.41421 + 11.1097i −0.264969 + 0.458939i
\(587\) 28.1421 1.16155 0.580775 0.814064i \(-0.302750\pi\)
0.580775 + 0.814064i \(0.302750\pi\)
\(588\) 0 0
\(589\) −5.37258 −0.221373
\(590\) 0.757359 1.31178i 0.0311800 0.0540053i
\(591\) 0 0
\(592\) −4.82843 8.36308i −0.198447 0.343721i
\(593\) 19.9706 34.5900i 0.820093 1.42044i −0.0855199 0.996336i \(-0.527255\pi\)
0.905613 0.424106i \(-0.139412\pi\)
\(594\) 0 0
\(595\) −2.35786 0.322666i −0.0966630 0.0132280i
\(596\) −11.3137 −0.463428
\(597\) 0 0
\(598\) −1.89949 3.29002i −0.0776761 0.134539i
\(599\) 14.5208 + 25.1508i 0.593304 + 1.02763i 0.993784 + 0.111328i \(0.0355103\pi\)
−0.400479 + 0.916306i \(0.631156\pi\)
\(600\) 0 0
\(601\) −20.0000 −0.815817 −0.407909 0.913023i \(-0.633742\pi\)
−0.407909 + 0.913023i \(0.633742\pi\)
\(602\) 4.58579 5.91359i 0.186903 0.241020i
\(603\) 0 0
\(604\) −0.621320 + 1.07616i −0.0252812 + 0.0437883i
\(605\) −0.207107 0.358719i −0.00842009 0.0145840i
\(606\) 0 0
\(607\) −23.1066 + 40.0218i −0.937868 + 1.62444i −0.168430 + 0.985714i \(0.553870\pi\)
−0.769438 + 0.638721i \(0.779464\pi\)
\(608\) −0.828427 −0.0335972
\(609\) 0 0
\(610\) 0.656854 0.0265953
\(611\) 5.41421 9.37769i 0.219036 0.379381i
\(612\) 0 0
\(613\) 15.4497 + 26.7597i 0.624009 + 1.08082i 0.988732 + 0.149700i \(0.0478307\pi\)
−0.364722 + 0.931116i \(0.618836\pi\)
\(614\) −17.3137 + 29.9882i −0.698724 + 1.21023i
\(615\) 0 0
\(616\) 1.00000 + 2.44949i 0.0402911 + 0.0986928i
\(617\) 24.4853 0.985740 0.492870 0.870103i \(-0.335948\pi\)
0.492870 + 0.870103i \(0.335948\pi\)
\(618\) 0 0
\(619\) −0.257359 0.445759i −0.0103441 0.0179166i 0.860807 0.508932i \(-0.169959\pi\)
−0.871151 + 0.491015i \(0.836626\pi\)
\(620\) 1.34315 + 2.32640i 0.0539420 + 0.0934303i
\(621\) 0 0
\(622\) 10.2132 0.409512
\(623\) −20.2426 + 26.1039i −0.811004 + 1.04583i
\(624\) 0 0
\(625\) −11.2279 + 19.4473i −0.449117 + 0.777893i
\(626\) −14.6569 25.3864i −0.585806 1.01465i
\(627\) 0 0
\(628\) 4.58579 7.94282i 0.182993 0.316953i
\(629\) 20.9706 0.836151
\(630\) 0 0
\(631\) −1.02944 −0.0409812 −0.0204906 0.999790i \(-0.506523\pi\)
−0.0204906 + 0.999790i \(0.506523\pi\)
\(632\) 2.37868 4.11999i 0.0946188 0.163885i
\(633\) 0 0
\(634\) 16.9350 + 29.3323i 0.672576 + 1.16494i
\(635\) −0.257359 + 0.445759i −0.0102130 + 0.0176894i
\(636\) 0 0
\(637\) −7.89949 2.20330i −0.312989 0.0872981i
\(638\) −2.82843 −0.111979
\(639\) 0 0
\(640\) 0.207107 + 0.358719i 0.00818661 + 0.0141796i
\(641\) −13.6569 23.6544i −0.539413 0.934291i −0.998936 0.0461251i \(-0.985313\pi\)
0.459522 0.888166i \(-0.348021\pi\)
\(642\) 0 0
\(643\) 17.6569 0.696318 0.348159 0.937435i \(-0.386807\pi\)
0.348159 + 0.937435i \(0.386807\pi\)
\(644\) −8.50000 1.16320i −0.334947 0.0458364i
\(645\) 0 0
\(646\) 0.899495 1.55797i 0.0353902 0.0612975i
\(647\) 21.3492 + 36.9780i 0.839325 + 1.45375i 0.890460 + 0.455062i \(0.150383\pi\)
−0.0511343 + 0.998692i \(0.516284\pi\)
\(648\) 0 0
\(649\) 1.82843 3.16693i 0.0717720 0.124313i
\(650\) −5.65685 −0.221880
\(651\) 0 0
\(652\) 3.00000 0.117489
\(653\) 22.1777 38.4129i 0.867879 1.50321i 0.00371972 0.999993i \(-0.498816\pi\)
0.864160 0.503218i \(-0.167851\pi\)
\(654\) 0 0
\(655\) 3.17157 + 5.49333i 0.123924 + 0.214642i
\(656\) 2.32843 4.03295i 0.0909098 0.157460i
\(657\) 0 0
\(658\) −9.24264 22.6398i −0.360316 0.882589i
\(659\) 36.9411 1.43902 0.719511 0.694481i \(-0.244366\pi\)
0.719511 + 0.694481i \(0.244366\pi\)
\(660\) 0 0
\(661\) 19.4853 + 33.7495i 0.757890 + 1.31270i 0.943925 + 0.330160i \(0.107103\pi\)
−0.186035 + 0.982543i \(0.559564\pi\)
\(662\) 3.15685 + 5.46783i 0.122695 + 0.212513i
\(663\) 0 0
\(664\) −9.82843 −0.381417
\(665\) 0.343146 + 0.840532i 0.0133066 + 0.0325944i
\(666\) 0 0
\(667\) 4.58579 7.94282i 0.177562 0.307547i
\(668\) −8.24264 14.2767i −0.318917 0.552381i
\(669\) 0 0
\(670\) −2.79289 + 4.83743i −0.107899 + 0.186886i
\(671\) 1.58579 0.0612186
\(672\) 0 0
\(673\) 24.6274 0.949317 0.474659 0.880170i \(-0.342572\pi\)
0.474659 + 0.880170i \(0.342572\pi\)
\(674\) 4.75736 8.23999i 0.183247 0.317392i
\(675\) 0 0
\(676\) 5.81371 + 10.0696i 0.223604 + 0.387294i
\(677\) 21.3848 37.0395i 0.821884 1.42354i −0.0823941 0.996600i \(-0.526257\pi\)
0.904278 0.426945i \(-0.140410\pi\)
\(678\) 0 0
\(679\) 26.6630 + 3.64874i 1.02323 + 0.140026i
\(680\) −0.899495 −0.0344941
\(681\) 0 0
\(682\) 3.24264 + 5.61642i 0.124167 + 0.215064i
\(683\) 8.82843 + 15.2913i 0.337810 + 0.585105i 0.984021 0.178055i \(-0.0569804\pi\)
−0.646210 + 0.763159i \(0.723647\pi\)
\(684\) 0 0
\(685\) 2.00000 0.0764161
\(686\) −14.8640 + 11.0482i −0.567509 + 0.421822i
\(687\) 0 0
\(688\) 1.41421 2.44949i 0.0539164 0.0933859i
\(689\) 3.02944 + 5.24714i 0.115412 + 0.199900i
\(690\) 0 0
\(691\) −14.5711 + 25.2378i −0.554310 + 0.960092i 0.443647 + 0.896201i \(0.353684\pi\)
−0.997957 + 0.0638908i \(0.979649\pi\)
\(692\) 12.1421 0.461575
\(693\) 0 0
\(694\) 4.85786 0.184402
\(695\) 1.24264 2.15232i 0.0471360 0.0816420i
\(696\) 0 0
\(697\) 5.05635 + 8.75785i 0.191523 + 0.331727i
\(698\) −7.86396 + 13.6208i −0.297655 + 0.515554i
\(699\) 0 0
\(700\) −7.82843 + 10.0951i −0.295887 + 0.381560i
\(701\) −28.1421 −1.06291 −0.531457 0.847085i \(-0.678355\pi\)
−0.531457 + 0.847085i \(0.678355\pi\)
\(702\) 0 0
\(703\) −4.00000 6.92820i −0.150863 0.261302i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −16.8284 −0.633346
\(707\) 14.1421 + 34.6410i 0.531870 + 1.30281i
\(708\) 0 0
\(709\) −1.92893 + 3.34101i −0.0724426 + 0.125474i −0.899971 0.435949i \(-0.856413\pi\)
0.827529 + 0.561423i \(0.189746\pi\)
\(710\) −2.75736 4.77589i −0.103482 0.179236i
\(711\) 0 0
\(712\) −6.24264 + 10.8126i −0.233953 + 0.405218i
\(713\) −21.0294 −0.787559
\(714\) 0 0
\(715\) 0.485281 0.0181485
\(716\) −1.58579 + 2.74666i −0.0592636 + 0.102648i
\(717\) 0 0
\(718\) 4.24264 + 7.34847i 0.158334 + 0.274242i
\(719\) −8.10660 + 14.0410i −0.302325 + 0.523643i −0.976662 0.214781i \(-0.931096\pi\)
0.674337 + 0.738424i \(0.264430\pi\)
\(720\) 0 0
\(721\) −14.8701 + 19.1757i −0.553790 + 0.714139i
\(722\) 18.3137 0.681566
\(723\) 0 0
\(724\) 1.17157 + 2.02922i 0.0435412 + 0.0754155i
\(725\) −6.82843 11.8272i −0.253601 0.439251i
\(726\) 0 0
\(727\) −32.4853 −1.20481 −0.602406 0.798190i \(-0.705791\pi\)
−0.602406 + 0.798190i \(0.705791\pi\)
\(728\) −3.07107 0.420266i −0.113821 0.0155761i
\(729\) 0 0
\(730\) −1.00000 + 1.73205i −0.0370117 + 0.0641061i
\(731\) 3.07107 + 5.31925i 0.113588 + 0.196739i
\(732\) 0 0
\(733\) 7.37868 12.7802i 0.272538 0.472049i −0.696973 0.717097i \(-0.745470\pi\)
0.969511 + 0.245048i \(0.0788037\pi\)
\(734\) −5.51472 −0.203552
\(735\) 0 0
\(736\) −3.24264 −0.119525
\(737\) −6.74264 + 11.6786i −0.248368 + 0.430187i
\(738\) 0 0
\(739\) 17.0000 + 29.4449i 0.625355 + 1.08315i 0.988472 + 0.151403i \(0.0483792\pi\)
−0.363117 + 0.931744i \(0.618287\pi\)
\(740\) −2.00000 + 3.46410i −0.0735215 + 0.127343i
\(741\) 0 0
\(742\) 13.5563 + 1.85514i 0.497669 + 0.0681045i
\(743\) 13.6569 0.501021 0.250511 0.968114i \(-0.419401\pi\)
0.250511 + 0.968114i \(0.419401\pi\)
\(744\) 0 0
\(745\) 2.34315 + 4.05845i 0.0858462 + 0.148690i
\(746\) −7.86396 13.6208i −0.287920 0.498692i
\(747\) 0 0
\(748\) −2.17157 −0.0794006
\(749\) 27.0061 34.8257i 0.986781 1.27250i
\(750\) 0 0
\(751\) −14.8995 + 25.8067i −0.543690 + 0.941699i 0.454998 + 0.890493i \(0.349640\pi\)
−0.998688 + 0.0512066i \(0.983693\pi\)
\(752\) −4.62132 8.00436i −0.168522 0.291889i
\(753\) 0 0
\(754\) 1.65685 2.86976i 0.0603391 0.104510i
\(755\) 0.514719 0.0187325
\(756\) 0 0
\(757\) 19.6569 0.714441 0.357220 0.934020i \(-0.383725\pi\)
0.357220 + 0.934020i \(0.383725\pi\)
\(758\) 9.67157 16.7517i 0.351287 0.608448i
\(759\) 0 0
\(760\) 0.171573 + 0.297173i 0.00622360 + 0.0107796i
\(761\) 12.2279 21.1794i 0.443262 0.767752i −0.554667 0.832072i \(-0.687155\pi\)
0.997929 + 0.0643201i \(0.0204879\pi\)
\(762\) 0 0
\(763\) 3.24264 + 7.94282i 0.117391 + 0.287549i
\(764\) 9.31371 0.336958
\(765\) 0 0
\(766\) 17.1421 + 29.6910i 0.619371 + 1.07278i
\(767\) 2.14214 + 3.71029i 0.0773480 + 0.133971i
\(768\) 0 0
\(769\) 26.4853 0.955084 0.477542 0.878609i \(-0.341528\pi\)
0.477542 + 0.878609i \(0.341528\pi\)
\(770\) 0.671573 0.866025i 0.0242018 0.0312094i
\(771\) 0 0
\(772\) 4.58579 7.94282i 0.165046 0.285868i
\(773\) 15.6213 + 27.0569i 0.561860 + 0.973170i 0.997334 + 0.0729687i \(0.0232473\pi\)
−0.435474 + 0.900201i \(0.643419\pi\)
\(774\) 0 0
\(775\) −15.6569 + 27.1185i −0.562411 + 0.974124i
\(776\) 10.1716 0.365138
\(777\) 0 0
\(778\) −1.72792 −0.0619490
\(779\) 1.92893 3.34101i 0.0691112 0.119704i
\(780\) 0 0
\(781\) −6.65685 11.5300i −0.238201 0.412576i
\(782\) 3.52082 6.09823i 0.125904 0.218072i
\(783\) 0 0
\(784\) −5.00000 + 4.89898i −0.178571 + 0.174964i
\(785\) −3.79899 −0.135592
\(786\) 0 0
\(787\) 19.3848 + 33.5754i 0.690993 + 1.19683i 0.971513 + 0.236986i \(0.0761597\pi\)
−0.280520 + 0.959848i \(0.590507\pi\)
\(788\) −1.75736 3.04384i −0.0626033 0.108432i
\(789\) 0 0