Properties

Label 1170.2.bj.c.829.2
Level $1170$
Weight $2$
Character 1170.829
Analytic conductor $9.342$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 829.2
Root \(1.75374 + 1.62986i\) of defining polynomial
Character \(\chi\) \(=\) 1170.829
Dual form 1170.2.bj.c.199.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(-0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.40066 - 1.74303i) q^{5} +(-0.763837 + 1.32301i) q^{7} +1.00000 q^{8} +(-0.809179 + 2.08452i) q^{10} +(1.14057 - 0.658509i) q^{11} +(2.41225 + 2.67975i) q^{13} +1.52767 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.35904 - 0.784645i) q^{17} +(-4.18063 - 2.41369i) q^{19} +(2.20984 - 0.341491i) q^{20} +(-1.14057 - 0.658509i) q^{22} +(-7.31172 + 4.22143i) q^{23} +(-1.07631 + 4.88278i) q^{25} +(1.11461 - 3.42894i) q^{26} +(-0.763837 - 1.32301i) q^{28} +(2.21438 + 3.83543i) q^{29} -1.62745i q^{31} +(-0.500000 + 0.866025i) q^{32} +1.56929i q^{34} +(3.37591 - 0.521687i) q^{35} +(1.40148 + 2.42743i) q^{37} +4.82738i q^{38} +(-1.40066 - 1.74303i) q^{40} +(-1.35904 + 0.784645i) q^{41} +(4.58006 + 2.64430i) q^{43} +1.31702i q^{44} +(7.31172 + 4.22143i) q^{46} +4.94552 q^{47} +(2.33310 + 4.04106i) q^{49} +(4.76677 - 1.50928i) q^{50} +(-3.52686 + 0.749192i) q^{52} +13.9161i q^{53} +(-2.74535 - 1.06570i) q^{55} +(-0.763837 + 1.32301i) q^{56} +(2.21438 - 3.83543i) q^{58} +(9.07005 + 5.23660i) q^{59} +(2.49134 - 4.31513i) q^{61} +(-1.40941 + 0.813725i) q^{62} +1.00000 q^{64} +(1.29215 - 7.95804i) q^{65} +(-1.38628 - 2.40112i) q^{67} +(1.35904 - 0.784645i) q^{68} +(-2.13975 - 2.66278i) q^{70} +(12.8513 + 7.41968i) q^{71} -5.98944 q^{73} +(1.40148 - 2.42743i) q^{74} +(4.18063 - 2.41369i) q^{76} +2.01198i q^{77} +4.87632 q^{79} +(-0.809179 + 2.08452i) q^{80} +(1.35904 + 0.784645i) q^{82} -6.39020 q^{83} +(0.535898 + 3.46788i) q^{85} -5.28860i q^{86} +(1.14057 - 0.658509i) q^{88} +(-15.9738 + 9.22251i) q^{89} +(-5.38789 + 1.14452i) q^{91} -8.44285i q^{92} +(-2.47276 - 4.28295i) q^{94} +(1.64851 + 10.6677i) q^{95} +(-0.963028 + 1.66801i) q^{97} +(2.33310 - 4.04106i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.40066 1.74303i −0.626394 0.779507i
\(6\) 0 0
\(7\) −0.763837 + 1.32301i −0.288703 + 0.500049i −0.973501 0.228685i \(-0.926557\pi\)
0.684797 + 0.728734i \(0.259891\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.809179 + 2.08452i −0.255885 + 0.659184i
\(11\) 1.14057 0.658509i 0.343895 0.198548i −0.318098 0.948058i \(-0.603044\pi\)
0.661993 + 0.749510i \(0.269711\pi\)
\(12\) 0 0
\(13\) 2.41225 + 2.67975i 0.669037 + 0.743229i
\(14\) 1.52767 0.408288
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.35904 0.784645i −0.329617 0.190304i 0.326054 0.945351i \(-0.394281\pi\)
−0.655671 + 0.755047i \(0.727614\pi\)
\(18\) 0 0
\(19\) −4.18063 2.41369i −0.959103 0.553738i −0.0632058 0.998001i \(-0.520132\pi\)
−0.895897 + 0.444262i \(0.853466\pi\)
\(20\) 2.20984 0.341491i 0.494135 0.0763597i
\(21\) 0 0
\(22\) −1.14057 0.658509i −0.243171 0.140395i
\(23\) −7.31172 + 4.22143i −1.52460 + 0.880228i −0.525025 + 0.851087i \(0.675944\pi\)
−0.999575 + 0.0291412i \(0.990723\pi\)
\(24\) 0 0
\(25\) −1.07631 + 4.88278i −0.215262 + 0.976556i
\(26\) 1.11461 3.42894i 0.218593 0.672471i
\(27\) 0 0
\(28\) −0.763837 1.32301i −0.144352 0.250025i
\(29\) 2.21438 + 3.83543i 0.411201 + 0.712221i 0.995021 0.0996620i \(-0.0317762\pi\)
−0.583821 + 0.811883i \(0.698443\pi\)
\(30\) 0 0
\(31\) 1.62745i 0.292299i −0.989263 0.146149i \(-0.953312\pi\)
0.989263 0.146149i \(-0.0466880\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 1.56929i 0.269131i
\(35\) 3.37591 0.521687i 0.570634 0.0881813i
\(36\) 0 0
\(37\) 1.40148 + 2.42743i 0.230402 + 0.399067i 0.957926 0.287014i \(-0.0926627\pi\)
−0.727525 + 0.686081i \(0.759329\pi\)
\(38\) 4.82738i 0.783104i
\(39\) 0 0
\(40\) −1.40066 1.74303i −0.221464 0.275597i
\(41\) −1.35904 + 0.784645i −0.212247 + 0.122541i −0.602355 0.798228i \(-0.705771\pi\)
0.390108 + 0.920769i \(0.372438\pi\)
\(42\) 0 0
\(43\) 4.58006 + 2.64430i 0.698452 + 0.403252i 0.806771 0.590865i \(-0.201213\pi\)
−0.108318 + 0.994116i \(0.534547\pi\)
\(44\) 1.31702i 0.198548i
\(45\) 0 0
\(46\) 7.31172 + 4.22143i 1.07805 + 0.622415i
\(47\) 4.94552 0.721378 0.360689 0.932686i \(-0.382542\pi\)
0.360689 + 0.932686i \(0.382542\pi\)
\(48\) 0 0
\(49\) 2.33310 + 4.04106i 0.333301 + 0.577294i
\(50\) 4.76677 1.50928i 0.674123 0.213444i
\(51\) 0 0
\(52\) −3.52686 + 0.749192i −0.489087 + 0.103894i
\(53\) 13.9161i 1.91152i 0.294148 + 0.955760i \(0.404964\pi\)
−0.294148 + 0.955760i \(0.595036\pi\)
\(54\) 0 0
\(55\) −2.74535 1.06570i −0.370183 0.143699i
\(56\) −0.763837 + 1.32301i −0.102072 + 0.176794i
\(57\) 0 0
\(58\) 2.21438 3.83543i 0.290763 0.503616i
\(59\) 9.07005 + 5.23660i 1.18082 + 0.681747i 0.956204 0.292700i \(-0.0945539\pi\)
0.224616 + 0.974447i \(0.427887\pi\)
\(60\) 0 0
\(61\) 2.49134 4.31513i 0.318984 0.552496i −0.661293 0.750128i \(-0.729992\pi\)
0.980276 + 0.197632i \(0.0633252\pi\)
\(62\) −1.40941 + 0.813725i −0.178996 + 0.103343i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.29215 7.95804i 0.160272 0.987073i
\(66\) 0 0
\(67\) −1.38628 2.40112i −0.169362 0.293343i 0.768834 0.639448i \(-0.220837\pi\)
−0.938196 + 0.346105i \(0.887504\pi\)
\(68\) 1.35904 0.784645i 0.164808 0.0951521i
\(69\) 0 0
\(70\) −2.13975 2.66278i −0.255749 0.318264i
\(71\) 12.8513 + 7.41968i 1.52516 + 0.880554i 0.999555 + 0.0298269i \(0.00949560\pi\)
0.525608 + 0.850727i \(0.323838\pi\)
\(72\) 0 0
\(73\) −5.98944 −0.701011 −0.350505 0.936561i \(-0.613990\pi\)
−0.350505 + 0.936561i \(0.613990\pi\)
\(74\) 1.40148 2.42743i 0.162919 0.282183i
\(75\) 0 0
\(76\) 4.18063 2.41369i 0.479551 0.276869i
\(77\) 2.01198i 0.229286i
\(78\) 0 0
\(79\) 4.87632 0.548629 0.274315 0.961640i \(-0.411549\pi\)
0.274315 + 0.961640i \(0.411549\pi\)
\(80\) −0.809179 + 2.08452i −0.0904690 + 0.233057i
\(81\) 0 0
\(82\) 1.35904 + 0.784645i 0.150081 + 0.0866495i
\(83\) −6.39020 −0.701416 −0.350708 0.936485i \(-0.614059\pi\)
−0.350708 + 0.936485i \(0.614059\pi\)
\(84\) 0 0
\(85\) 0.535898 + 3.46788i 0.0581263 + 0.376144i
\(86\) 5.28860i 0.570284i
\(87\) 0 0
\(88\) 1.14057 0.658509i 0.121585 0.0701973i
\(89\) −15.9738 + 9.22251i −1.69322 + 0.977584i −0.741338 + 0.671131i \(0.765809\pi\)
−0.951886 + 0.306452i \(0.900858\pi\)
\(90\) 0 0
\(91\) −5.38789 + 1.14452i −0.564804 + 0.119978i
\(92\) 8.44285i 0.880228i
\(93\) 0 0
\(94\) −2.47276 4.28295i −0.255046 0.441752i
\(95\) 1.64851 + 10.6677i 0.169133 + 1.09449i
\(96\) 0 0
\(97\) −0.963028 + 1.66801i −0.0977807 + 0.169361i −0.910766 0.412923i \(-0.864508\pi\)
0.812985 + 0.582285i \(0.197841\pi\)
\(98\) 2.33310 4.04106i 0.235679 0.408208i
\(99\) 0 0
\(100\) −3.69046 3.37350i −0.369046 0.337350i
\(101\) −1.21929 2.11188i −0.121324 0.210140i 0.798966 0.601376i \(-0.205381\pi\)
−0.920290 + 0.391237i \(0.872047\pi\)
\(102\) 0 0
\(103\) 12.4300i 1.22477i −0.790561 0.612383i \(-0.790211\pi\)
0.790561 0.612383i \(-0.209789\pi\)
\(104\) 2.41225 + 2.67975i 0.236540 + 0.262771i
\(105\) 0 0
\(106\) 12.0517 6.95804i 1.17056 0.675824i
\(107\) −9.07302 + 5.23831i −0.877122 + 0.506407i −0.869708 0.493566i \(-0.835693\pi\)
−0.00741349 + 0.999973i \(0.502360\pi\)
\(108\) 0 0
\(109\) 17.1799i 1.64553i 0.568379 + 0.822767i \(0.307571\pi\)
−0.568379 + 0.822767i \(0.692429\pi\)
\(110\) 0.449750 + 2.91040i 0.0428820 + 0.277495i
\(111\) 0 0
\(112\) 1.52767 0.144352
\(113\) 2.25151 + 1.29991i 0.211805 + 0.122285i 0.602150 0.798383i \(-0.294311\pi\)
−0.390345 + 0.920669i \(0.627644\pi\)
\(114\) 0 0
\(115\) 17.5993 + 6.83178i 1.64114 + 0.637067i
\(116\) −4.42877 −0.411201
\(117\) 0 0
\(118\) 10.4732i 0.964136i
\(119\) 2.07618 1.19868i 0.190323 0.109883i
\(120\) 0 0
\(121\) −4.63273 + 8.02413i −0.421157 + 0.729466i
\(122\) −4.98268 −0.451111
\(123\) 0 0
\(124\) 1.40941 + 0.813725i 0.126569 + 0.0730747i
\(125\) 10.0184 4.96307i 0.896071 0.443911i
\(126\) 0 0
\(127\) −7.01552 + 4.05041i −0.622527 + 0.359416i −0.777852 0.628447i \(-0.783691\pi\)
0.155325 + 0.987863i \(0.450357\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −7.53794 + 2.85998i −0.661121 + 0.250837i
\(131\) 2.32506 0.203141 0.101571 0.994828i \(-0.467613\pi\)
0.101571 + 0.994828i \(0.467613\pi\)
\(132\) 0 0
\(133\) 6.38665 3.68733i 0.553792 0.319732i
\(134\) −1.38628 + 2.40112i −0.119757 + 0.207425i
\(135\) 0 0
\(136\) −1.35904 0.784645i −0.116537 0.0672827i
\(137\) 6.14192 10.6381i 0.524740 0.908876i −0.474845 0.880069i \(-0.657496\pi\)
0.999585 0.0288066i \(-0.00917069\pi\)
\(138\) 0 0
\(139\) −3.32861 + 5.76531i −0.282329 + 0.489008i −0.971958 0.235155i \(-0.924440\pi\)
0.689629 + 0.724163i \(0.257774\pi\)
\(140\) −1.23616 + 3.18447i −0.104475 + 0.269137i
\(141\) 0 0
\(142\) 14.8394i 1.24529i
\(143\) 4.51598 + 1.46796i 0.377645 + 0.122757i
\(144\) 0 0
\(145\) 3.58367 9.23186i 0.297607 0.766664i
\(146\) 2.99472 + 5.18700i 0.247845 + 0.429280i
\(147\) 0 0
\(148\) −2.80296 −0.230402
\(149\) 2.60768 + 1.50554i 0.213629 + 0.123339i 0.602997 0.797744i \(-0.293973\pi\)
−0.389368 + 0.921082i \(0.627306\pi\)
\(150\) 0 0
\(151\) 12.0149i 0.977759i −0.872351 0.488880i \(-0.837406\pi\)
0.872351 0.488880i \(-0.162594\pi\)
\(152\) −4.18063 2.41369i −0.339094 0.195776i
\(153\) 0 0
\(154\) 1.74242 1.00599i 0.140408 0.0810648i
\(155\) −2.83670 + 2.27950i −0.227849 + 0.183094i
\(156\) 0 0
\(157\) 3.01556i 0.240668i 0.992733 + 0.120334i \(0.0383965\pi\)
−0.992733 + 0.120334i \(0.961604\pi\)
\(158\) −2.43816 4.22302i −0.193970 0.335965i
\(159\) 0 0
\(160\) 2.20984 0.341491i 0.174703 0.0269972i
\(161\) 12.8979i 1.01650i
\(162\) 0 0
\(163\) 4.95812 8.58772i 0.388350 0.672642i −0.603878 0.797077i \(-0.706379\pi\)
0.992228 + 0.124435i \(0.0397119\pi\)
\(164\) 1.56929i 0.122541i
\(165\) 0 0
\(166\) 3.19510 + 5.53408i 0.247988 + 0.429528i
\(167\) −6.49472 11.2492i −0.502576 0.870488i −0.999996 0.00297754i \(-0.999052\pi\)
0.497419 0.867510i \(-0.334281\pi\)
\(168\) 0 0
\(169\) −1.36213 + 12.9284i −0.104779 + 0.994496i
\(170\) 2.73532 2.19804i 0.209789 0.168582i
\(171\) 0 0
\(172\) −4.58006 + 2.64430i −0.349226 + 0.201626i
\(173\) 3.35755 + 1.93848i 0.255270 + 0.147380i 0.622175 0.782878i \(-0.286249\pi\)
−0.366905 + 0.930258i \(0.619583\pi\)
\(174\) 0 0
\(175\) −5.63782 5.15361i −0.426179 0.389577i
\(176\) −1.14057 0.658509i −0.0859738 0.0496370i
\(177\) 0 0
\(178\) 15.9738 + 9.22251i 1.19729 + 0.691256i
\(179\) −7.05325 12.2166i −0.527185 0.913111i −0.999498 0.0316802i \(-0.989914\pi\)
0.472313 0.881431i \(-0.343419\pi\)
\(180\) 0 0
\(181\) −26.1472 −1.94351 −0.971753 0.236001i \(-0.924163\pi\)
−0.971753 + 0.236001i \(0.924163\pi\)
\(182\) 3.68513 + 4.09379i 0.273160 + 0.303452i
\(183\) 0 0
\(184\) −7.31172 + 4.22143i −0.539027 + 0.311208i
\(185\) 2.26809 5.84282i 0.166754 0.429573i
\(186\) 0 0
\(187\) −2.06678 −0.151138
\(188\) −2.47276 + 4.28295i −0.180345 + 0.312366i
\(189\) 0 0
\(190\) 8.41426 6.76151i 0.610435 0.490531i
\(191\) 9.42713 16.3283i 0.682123 1.18147i −0.292208 0.956355i \(-0.594390\pi\)
0.974332 0.225117i \(-0.0722766\pi\)
\(192\) 0 0
\(193\) 8.94600 + 15.4949i 0.643947 + 1.11535i 0.984544 + 0.175140i \(0.0560378\pi\)
−0.340596 + 0.940210i \(0.610629\pi\)
\(194\) 1.92606 0.138283
\(195\) 0 0
\(196\) −4.66621 −0.333301
\(197\) 0.312928 + 0.542008i 0.0222952 + 0.0386165i 0.876958 0.480567i \(-0.159569\pi\)
−0.854663 + 0.519184i \(0.826236\pi\)
\(198\) 0 0
\(199\) −8.84057 + 15.3123i −0.626691 + 1.08546i 0.361520 + 0.932364i \(0.382258\pi\)
−0.988211 + 0.153097i \(0.951075\pi\)
\(200\) −1.07631 + 4.88278i −0.0761065 + 0.345265i
\(201\) 0 0
\(202\) −1.21929 + 2.11188i −0.0857891 + 0.148591i
\(203\) −6.76572 −0.474860
\(204\) 0 0
\(205\) 3.27122 + 1.26984i 0.228472 + 0.0886892i
\(206\) −10.7647 + 6.21501i −0.750013 + 0.433020i
\(207\) 0 0
\(208\) 1.11461 3.42894i 0.0772842 0.237754i
\(209\) −6.35774 −0.439774
\(210\) 0 0
\(211\) −8.62227 14.9342i −0.593581 1.02811i −0.993745 0.111669i \(-0.964380\pi\)
0.400164 0.916443i \(-0.368953\pi\)
\(212\) −12.0517 6.95804i −0.827712 0.477880i
\(213\) 0 0
\(214\) 9.07302 + 5.23831i 0.620219 + 0.358083i
\(215\) −1.80601 11.6869i −0.123169 0.797043i
\(216\) 0 0
\(217\) 2.15313 + 1.24311i 0.146164 + 0.0843877i
\(218\) 14.8782 8.58994i 1.00768 0.581784i
\(219\) 0 0
\(220\) 2.29560 1.84469i 0.154769 0.124369i
\(221\) −1.17570 5.53466i −0.0790861 0.372301i
\(222\) 0 0
\(223\) 2.44858 + 4.24107i 0.163969 + 0.284003i 0.936289 0.351231i \(-0.114237\pi\)
−0.772320 + 0.635234i \(0.780904\pi\)
\(224\) −0.763837 1.32301i −0.0510360 0.0883970i
\(225\) 0 0
\(226\) 2.59982i 0.172938i
\(227\) 5.07567 8.79132i 0.336884 0.583500i −0.646961 0.762523i \(-0.723960\pi\)
0.983845 + 0.179023i \(0.0572936\pi\)
\(228\) 0 0
\(229\) 15.3959i 1.01739i 0.860947 + 0.508694i \(0.169871\pi\)
−0.860947 + 0.508694i \(0.830129\pi\)
\(230\) −2.88316 18.6573i −0.190110 1.23023i
\(231\) 0 0
\(232\) 2.21438 + 3.83543i 0.145381 + 0.251808i
\(233\) 9.91624i 0.649634i −0.945777 0.324817i \(-0.894697\pi\)
0.945777 0.324817i \(-0.105303\pi\)
\(234\) 0 0
\(235\) −6.92699 8.62019i −0.451867 0.562319i
\(236\) −9.07005 + 5.23660i −0.590410 + 0.340873i
\(237\) 0 0
\(238\) −2.07618 1.19868i −0.134579 0.0776990i
\(239\) 9.46167i 0.612024i −0.952028 0.306012i \(-0.901005\pi\)
0.952028 0.306012i \(-0.0989948\pi\)
\(240\) 0 0
\(241\) 11.3482 + 6.55189i 0.731002 + 0.422044i 0.818789 0.574095i \(-0.194646\pi\)
−0.0877865 + 0.996139i \(0.527979\pi\)
\(242\) 9.26546 0.595607
\(243\) 0 0
\(244\) 2.49134 + 4.31513i 0.159492 + 0.276248i
\(245\) 3.77580 9.72681i 0.241227 0.621423i
\(246\) 0 0
\(247\) −3.61663 17.0255i −0.230121 1.08330i
\(248\) 1.62745i 0.103343i
\(249\) 0 0
\(250\) −9.30734 6.19463i −0.588648 0.391783i
\(251\) −11.5822 + 20.0610i −0.731062 + 1.26624i 0.225367 + 0.974274i \(0.427642\pi\)
−0.956430 + 0.291963i \(0.905692\pi\)
\(252\) 0 0
\(253\) −5.55969 + 9.62967i −0.349535 + 0.605412i
\(254\) 7.01552 + 4.05041i 0.440193 + 0.254146i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.32895 1.92197i 0.207654 0.119889i −0.392566 0.919724i \(-0.628413\pi\)
0.600221 + 0.799834i \(0.295079\pi\)
\(258\) 0 0
\(259\) −4.28201 −0.266071
\(260\) 6.24579 + 5.09805i 0.387347 + 0.316168i
\(261\) 0 0
\(262\) −1.16253 2.01356i −0.0718213 0.124398i
\(263\) −26.5060 + 15.3032i −1.63443 + 0.943638i −0.651726 + 0.758455i \(0.725955\pi\)
−0.982704 + 0.185184i \(0.940712\pi\)
\(264\) 0 0
\(265\) 24.2561 19.4917i 1.49004 1.19736i
\(266\) −6.38665 3.68733i −0.391590 0.226085i
\(267\) 0 0
\(268\) 2.77257 0.169362
\(269\) −9.04370 + 15.6641i −0.551404 + 0.955060i 0.446769 + 0.894649i \(0.352574\pi\)
−0.998174 + 0.0604109i \(0.980759\pi\)
\(270\) 0 0
\(271\) 12.2869 7.09382i 0.746373 0.430919i −0.0780089 0.996953i \(-0.524856\pi\)
0.824382 + 0.566034i \(0.191523\pi\)
\(272\) 1.56929i 0.0951521i
\(273\) 0 0
\(274\) −12.2838 −0.742094
\(275\) 1.98775 + 6.27792i 0.119866 + 0.378573i
\(276\) 0 0
\(277\) 14.5855 + 8.42097i 0.876360 + 0.505967i 0.869457 0.494009i \(-0.164469\pi\)
0.00690380 + 0.999976i \(0.497802\pi\)
\(278\) 6.65721 0.399273
\(279\) 0 0
\(280\) 3.37591 0.521687i 0.201749 0.0311768i
\(281\) 8.61535i 0.513949i 0.966418 + 0.256974i \(0.0827256\pi\)
−0.966418 + 0.256974i \(0.917274\pi\)
\(282\) 0 0
\(283\) −23.9192 + 13.8098i −1.42185 + 0.820905i −0.996457 0.0841040i \(-0.973197\pi\)
−0.425392 + 0.905009i \(0.639864\pi\)
\(284\) −12.8513 + 7.41968i −0.762582 + 0.440277i
\(285\) 0 0
\(286\) −0.986699 4.64493i −0.0583447 0.274661i
\(287\) 2.39736i 0.141512i
\(288\) 0 0
\(289\) −7.26867 12.5897i −0.427569 0.740570i
\(290\) −9.78686 + 1.51239i −0.574704 + 0.0888103i
\(291\) 0 0
\(292\) 2.99472 5.18700i 0.175253 0.303546i
\(293\) 15.1250 26.1973i 0.883614 1.53046i 0.0363205 0.999340i \(-0.488436\pi\)
0.847294 0.531125i \(-0.178230\pi\)
\(294\) 0 0
\(295\) −3.57650 23.1441i −0.208232 1.34750i
\(296\) 1.40148 + 2.42743i 0.0814593 + 0.141092i
\(297\) 0 0
\(298\) 3.01108i 0.174427i
\(299\) −28.9501 9.41048i −1.67422 0.544222i
\(300\) 0 0
\(301\) −6.99684 + 4.03963i −0.403291 + 0.232840i
\(302\) −10.4052 + 6.00745i −0.598753 + 0.345690i
\(303\) 0 0
\(304\) 4.82738i 0.276869i
\(305\) −11.0109 + 1.70154i −0.630484 + 0.0974300i
\(306\) 0 0
\(307\) −14.1392 −0.806966 −0.403483 0.914987i \(-0.632201\pi\)
−0.403483 + 0.914987i \(0.632201\pi\)
\(308\) −1.74242 1.00599i −0.0992837 0.0573215i
\(309\) 0 0
\(310\) 3.39246 + 1.31690i 0.192679 + 0.0747948i
\(311\) 9.97427 0.565589 0.282794 0.959181i \(-0.408739\pi\)
0.282794 + 0.959181i \(0.408739\pi\)
\(312\) 0 0
\(313\) 3.08460i 0.174352i 0.996193 + 0.0871760i \(0.0277843\pi\)
−0.996193 + 0.0871760i \(0.972216\pi\)
\(314\) 2.61155 1.50778i 0.147378 0.0850888i
\(315\) 0 0
\(316\) −2.43816 + 4.22302i −0.137157 + 0.237563i
\(317\) −14.2980 −0.803054 −0.401527 0.915847i \(-0.631520\pi\)
−0.401527 + 0.915847i \(0.631520\pi\)
\(318\) 0 0
\(319\) 5.05132 + 2.91638i 0.282820 + 0.163286i
\(320\) −1.40066 1.74303i −0.0782992 0.0974384i
\(321\) 0 0
\(322\) −11.1699 + 6.44897i −0.622476 + 0.359387i
\(323\) 3.78778 + 6.56062i 0.210757 + 0.365043i
\(324\) 0 0
\(325\) −15.6810 + 8.89424i −0.869823 + 0.493363i
\(326\) −9.91624 −0.549210
\(327\) 0 0
\(328\) −1.35904 + 0.784645i −0.0750407 + 0.0433248i
\(329\) −3.77757 + 6.54295i −0.208264 + 0.360724i
\(330\) 0 0
\(331\) −9.89017 5.71009i −0.543613 0.313855i 0.202929 0.979193i \(-0.434954\pi\)
−0.746542 + 0.665338i \(0.768287\pi\)
\(332\) 3.19510 5.53408i 0.175354 0.303722i
\(333\) 0 0
\(334\) −6.49472 + 11.2492i −0.355375 + 0.615528i
\(335\) −2.24351 + 5.77948i −0.122576 + 0.315767i
\(336\) 0 0
\(337\) 5.53208i 0.301352i −0.988583 0.150676i \(-0.951855\pi\)
0.988583 0.150676i \(-0.0481450\pi\)
\(338\) 11.8774 5.28458i 0.646047 0.287443i
\(339\) 0 0
\(340\) −3.27122 1.26984i −0.177407 0.0688665i
\(341\) −1.07169 1.85622i −0.0580353 0.100520i
\(342\) 0 0
\(343\) −17.8222 −0.962307
\(344\) 4.58006 + 2.64430i 0.246940 + 0.142571i
\(345\) 0 0
\(346\) 3.87696i 0.208427i
\(347\) 2.44226 + 1.41004i 0.131107 + 0.0756949i 0.564119 0.825693i \(-0.309216\pi\)
−0.433012 + 0.901388i \(0.642549\pi\)
\(348\) 0 0
\(349\) 23.0704 13.3197i 1.23493 0.712986i 0.266875 0.963731i \(-0.414009\pi\)
0.968053 + 0.250745i \(0.0806757\pi\)
\(350\) −1.64425 + 7.45930i −0.0878889 + 0.398717i
\(351\) 0 0
\(352\) 1.31702i 0.0701973i
\(353\) −6.61308 11.4542i −0.351979 0.609645i 0.634617 0.772826i \(-0.281158\pi\)
−0.986596 + 0.163182i \(0.947824\pi\)
\(354\) 0 0
\(355\) −5.06751 32.7926i −0.268955 1.74045i
\(356\) 18.4450i 0.977584i
\(357\) 0 0
\(358\) −7.05325 + 12.2166i −0.372776 + 0.645667i
\(359\) 12.3827i 0.653532i 0.945105 + 0.326766i \(0.105959\pi\)
−0.945105 + 0.326766i \(0.894041\pi\)
\(360\) 0 0
\(361\) 2.15178 + 3.72700i 0.113252 + 0.196158i
\(362\) 13.0736 + 22.6441i 0.687133 + 1.19015i
\(363\) 0 0
\(364\) 1.70276 5.23831i 0.0892489 0.274562i
\(365\) 8.38916 + 10.4398i 0.439109 + 0.546443i
\(366\) 0 0
\(367\) 6.14226 3.54624i 0.320623 0.185112i −0.331047 0.943614i \(-0.607402\pi\)
0.651670 + 0.758502i \(0.274069\pi\)
\(368\) 7.31172 + 4.22143i 0.381150 + 0.220057i
\(369\) 0 0
\(370\) −6.19408 + 0.957185i −0.322015 + 0.0497617i
\(371\) −18.4110 10.6296i −0.955854 0.551862i
\(372\) 0 0
\(373\) −32.0259 18.4902i −1.65824 0.957384i −0.973528 0.228568i \(-0.926596\pi\)
−0.684709 0.728816i \(-0.740071\pi\)
\(374\) 1.03339 + 1.78989i 0.0534354 + 0.0925528i
\(375\) 0 0
\(376\) 4.94552 0.255046
\(377\) −4.93634 + 15.1860i −0.254235 + 0.782118i
\(378\) 0 0
\(379\) −29.6252 + 17.1041i −1.52174 + 0.878580i −0.522075 + 0.852900i \(0.674842\pi\)
−0.999670 + 0.0256802i \(0.991825\pi\)
\(380\) −10.0628 3.90621i −0.516209 0.200384i
\(381\) 0 0
\(382\) −18.8543 −0.964668
\(383\) 13.0170 22.5461i 0.665137 1.15205i −0.314111 0.949386i \(-0.601706\pi\)
0.979248 0.202665i \(-0.0649603\pi\)
\(384\) 0 0
\(385\) 3.50693 2.81809i 0.178730 0.143623i
\(386\) 8.94600 15.4949i 0.455340 0.788671i
\(387\) 0 0
\(388\) −0.963028 1.66801i −0.0488904 0.0846806i
\(389\) 6.23568 0.316162 0.158081 0.987426i \(-0.449469\pi\)
0.158081 + 0.987426i \(0.449469\pi\)
\(390\) 0 0
\(391\) 13.2493 0.670045
\(392\) 2.33310 + 4.04106i 0.117840 + 0.204104i
\(393\) 0 0
\(394\) 0.312928 0.542008i 0.0157651 0.0273060i
\(395\) −6.83007 8.49958i −0.343658 0.427660i
\(396\) 0 0
\(397\) 18.3498 31.7827i 0.920948 1.59513i 0.122997 0.992407i \(-0.460750\pi\)
0.797951 0.602722i \(-0.205917\pi\)
\(398\) 17.6811 0.886275
\(399\) 0 0
\(400\) 4.76677 1.50928i 0.238338 0.0754640i
\(401\) −24.5044 + 14.1476i −1.22369 + 0.706498i −0.965703 0.259651i \(-0.916393\pi\)
−0.257987 + 0.966148i \(0.583059\pi\)
\(402\) 0 0
\(403\) 4.36116 3.92581i 0.217245 0.195559i
\(404\) 2.43859 0.121324
\(405\) 0 0
\(406\) 3.38286 + 5.85928i 0.167888 + 0.290791i
\(407\) 3.19697 + 1.84577i 0.158468 + 0.0914915i
\(408\) 0 0
\(409\) 13.2744 + 7.66400i 0.656379 + 0.378961i 0.790896 0.611951i \(-0.209615\pi\)
−0.134517 + 0.990911i \(0.542948\pi\)
\(410\) −0.535898 3.46788i −0.0264661 0.171266i
\(411\) 0 0
\(412\) 10.7647 + 6.21501i 0.530339 + 0.306191i
\(413\) −13.8561 + 7.99982i −0.681814 + 0.393645i
\(414\) 0 0
\(415\) 8.95050 + 11.1383i 0.439363 + 0.546758i
\(416\) −3.52686 + 0.749192i −0.172918 + 0.0367322i
\(417\) 0 0
\(418\) 3.17887 + 5.50597i 0.155484 + 0.269306i
\(419\) 13.4692 + 23.3293i 0.658013 + 1.13971i 0.981129 + 0.193353i \(0.0619362\pi\)
−0.323116 + 0.946359i \(0.604730\pi\)
\(420\) 0 0
\(421\) 38.5359i 1.87812i −0.343747 0.939062i \(-0.611696\pi\)
0.343747 0.939062i \(-0.388304\pi\)
\(422\) −8.62227 + 14.9342i −0.419725 + 0.726986i
\(423\) 0 0
\(424\) 13.9161i 0.675824i
\(425\) 5.29400 5.79140i 0.256797 0.280924i
\(426\) 0 0
\(427\) 3.80596 + 6.59212i 0.184183 + 0.319015i
\(428\) 10.4766i 0.506407i
\(429\) 0 0
\(430\) −9.21818 + 7.40752i −0.444540 + 0.357222i
\(431\) −2.48744 + 1.43612i −0.119816 + 0.0691756i −0.558710 0.829363i \(-0.688704\pi\)
0.438894 + 0.898539i \(0.355370\pi\)
\(432\) 0 0
\(433\) 11.2344 + 6.48619i 0.539891 + 0.311706i 0.745035 0.667026i \(-0.232433\pi\)
−0.205144 + 0.978732i \(0.565766\pi\)
\(434\) 2.48622i 0.119342i
\(435\) 0 0
\(436\) −14.8782 8.58994i −0.712537 0.411383i
\(437\) 40.7568 1.94966
\(438\) 0 0
\(439\) −1.02411 1.77380i −0.0488779 0.0846590i 0.840551 0.541732i \(-0.182231\pi\)
−0.889429 + 0.457073i \(0.848898\pi\)
\(440\) −2.74535 1.06570i −0.130880 0.0508054i
\(441\) 0 0
\(442\) −4.20530 + 3.78551i −0.200026 + 0.180059i
\(443\) 25.7082i 1.22143i 0.791849 + 0.610717i \(0.209119\pi\)
−0.791849 + 0.610717i \(0.790881\pi\)
\(444\) 0 0
\(445\) 38.4490 + 14.9253i 1.82266 + 0.707528i
\(446\) 2.44858 4.24107i 0.115944 0.200820i
\(447\) 0 0
\(448\) −0.763837 + 1.32301i −0.0360879 + 0.0625061i
\(449\) 16.0756 + 9.28127i 0.758656 + 0.438010i 0.828813 0.559526i \(-0.189017\pi\)
−0.0701571 + 0.997536i \(0.522350\pi\)
\(450\) 0 0
\(451\) −1.03339 + 1.78989i −0.0486605 + 0.0842824i
\(452\) −2.25151 + 1.29991i −0.105902 + 0.0611427i
\(453\) 0 0
\(454\) −10.1513 −0.476426
\(455\) 9.54153 + 7.78817i 0.447314 + 0.365115i
\(456\) 0 0
\(457\) 12.3213 + 21.3412i 0.576368 + 0.998299i 0.995891 + 0.0905546i \(0.0288640\pi\)
−0.419523 + 0.907745i \(0.637803\pi\)
\(458\) 13.3332 7.69794i 0.623020 0.359701i
\(459\) 0 0
\(460\) −14.7161 + 11.8256i −0.686144 + 0.551369i
\(461\) 27.5693 + 15.9171i 1.28403 + 0.741334i 0.977582 0.210554i \(-0.0675268\pi\)
0.306446 + 0.951888i \(0.400860\pi\)
\(462\) 0 0
\(463\) −3.18319 −0.147936 −0.0739678 0.997261i \(-0.523566\pi\)
−0.0739678 + 0.997261i \(0.523566\pi\)
\(464\) 2.21438 3.83543i 0.102800 0.178055i
\(465\) 0 0
\(466\) −8.58772 + 4.95812i −0.397818 + 0.229680i
\(467\) 21.6747i 1.00298i −0.865162 0.501492i \(-0.832785\pi\)
0.865162 0.501492i \(-0.167215\pi\)
\(468\) 0 0
\(469\) 4.23559 0.195581
\(470\) −4.00181 + 10.3090i −0.184590 + 0.475521i
\(471\) 0 0
\(472\) 9.07005 + 5.23660i 0.417483 + 0.241034i
\(473\) 6.96517 0.320259
\(474\) 0 0
\(475\) 16.2852 17.8152i 0.747215 0.817419i
\(476\) 2.39736i 0.109883i
\(477\) 0 0
\(478\) −8.19404 + 4.73083i −0.374787 + 0.216383i
\(479\) 25.3765 14.6511i 1.15948 0.669426i 0.208300 0.978065i \(-0.433207\pi\)
0.951179 + 0.308639i \(0.0998735\pi\)
\(480\) 0 0
\(481\) −3.12420 + 9.61118i −0.142451 + 0.438232i
\(482\) 13.1038i 0.596861i
\(483\) 0 0
\(484\) −4.63273 8.02413i −0.210579 0.364733i
\(485\) 4.25627 0.657731i 0.193267 0.0298660i
\(486\) 0 0
\(487\) 21.2643 36.8309i 0.963579 1.66897i 0.250194 0.968196i \(-0.419506\pi\)
0.713385 0.700772i \(-0.247161\pi\)
\(488\) 2.49134 4.31513i 0.112778 0.195337i
\(489\) 0 0
\(490\) −10.3116 + 1.59347i −0.465829 + 0.0719856i
\(491\) −6.32521 10.9556i −0.285453 0.494418i 0.687266 0.726406i \(-0.258811\pi\)
−0.972719 + 0.231987i \(0.925477\pi\)
\(492\) 0 0
\(493\) 6.95002i 0.313013i
\(494\) −12.9362 + 11.6448i −0.582026 + 0.523925i
\(495\) 0 0
\(496\) −1.40941 + 0.813725i −0.0632845 + 0.0365373i
\(497\) −19.6325 + 11.3349i −0.880640 + 0.508438i
\(498\) 0 0
\(499\) 4.54007i 0.203242i −0.994823 0.101621i \(-0.967597\pi\)
0.994823 0.101621i \(-0.0324028\pi\)
\(500\) −0.711042 + 11.1577i −0.0317988 + 0.498988i
\(501\) 0 0
\(502\) 23.1644 1.03388
\(503\) −17.2476 9.95791i −0.769033 0.444001i 0.0634967 0.997982i \(-0.479775\pi\)
−0.832529 + 0.553981i \(0.813108\pi\)
\(504\) 0 0
\(505\) −1.97325 + 5.08328i −0.0878086 + 0.226203i
\(506\) 11.1194 0.494317
\(507\) 0 0
\(508\) 8.10083i 0.359416i
\(509\) 9.09532 5.25118i 0.403143 0.232755i −0.284696 0.958618i \(-0.591893\pi\)
0.687839 + 0.725863i \(0.258559\pi\)
\(510\) 0 0
\(511\) 4.57496 7.92406i 0.202384 0.350540i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.32895 1.92197i −0.146834 0.0847746i
\(515\) −21.6659 + 17.4102i −0.954713 + 0.767185i
\(516\) 0 0
\(517\) 5.64072 3.25667i 0.248078 0.143228i
\(518\) 2.14100 + 3.70833i 0.0940703 + 0.162934i
\(519\) 0 0
\(520\) 1.29215 7.95804i 0.0566646 0.348983i
\(521\) 24.5221 1.07433 0.537166 0.843477i \(-0.319495\pi\)
0.537166 + 0.843477i \(0.319495\pi\)
\(522\) 0 0
\(523\) −21.6924 + 12.5241i −0.948541 + 0.547641i −0.892627 0.450795i \(-0.851141\pi\)
−0.0559138 + 0.998436i \(0.517807\pi\)
\(524\) −1.16253 + 2.01356i −0.0507853 + 0.0879628i
\(525\) 0 0
\(526\) 26.5060 + 15.3032i 1.15572 + 0.667253i
\(527\) −1.27697 + 2.21178i −0.0556257 + 0.0963466i
\(528\) 0 0
\(529\) 24.1409 41.8132i 1.04960 1.81797i
\(530\) −29.0084 11.2606i −1.26004 0.489129i
\(531\) 0 0
\(532\) 7.37466i 0.319732i
\(533\) −5.38100 1.74914i −0.233077 0.0757638i
\(534\) 0 0
\(535\) 21.8387 + 8.47746i 0.944171 + 0.366513i
\(536\) −1.38628 2.40112i −0.0598784 0.103712i
\(537\) 0 0
\(538\) 18.0874 0.779803
\(539\) 5.32214 + 3.07274i 0.229241 + 0.132352i
\(540\) 0 0
\(541\) 20.6859i 0.889356i 0.895690 + 0.444678i \(0.146682\pi\)
−0.895690 + 0.444678i \(0.853318\pi\)
\(542\) −12.2869 7.09382i −0.527765 0.304705i
\(543\) 0 0
\(544\) 1.35904 0.784645i 0.0582686 0.0336414i
\(545\) 29.9450 24.0631i 1.28270 1.03075i
\(546\) 0 0
\(547\) 40.5960i 1.73576i 0.496773 + 0.867880i \(0.334518\pi\)
−0.496773 + 0.867880i \(0.665482\pi\)
\(548\) 6.14192 + 10.6381i 0.262370 + 0.454438i
\(549\) 0 0
\(550\) 4.44296 4.86040i 0.189449 0.207248i
\(551\) 21.3793i 0.910790i
\(552\) 0 0
\(553\) −3.72472 + 6.45140i −0.158391 + 0.274342i
\(554\) 16.8419i 0.715545i
\(555\) 0 0
\(556\) −3.32861 5.76531i −0.141164 0.244504i
\(557\) 20.6032 + 35.6858i 0.872985 + 1.51205i 0.858894 + 0.512153i \(0.171152\pi\)
0.0140907 + 0.999901i \(0.495515\pi\)
\(558\) 0 0
\(559\) 3.96217 + 18.6521i 0.167582 + 0.788900i
\(560\) −2.13975 2.66278i −0.0904210 0.112523i
\(561\) 0 0
\(562\) 7.46112 4.30768i 0.314728 0.181708i
\(563\) −13.0933 7.55940i −0.551815 0.318591i 0.198038 0.980194i \(-0.436543\pi\)
−0.749854 + 0.661603i \(0.769876\pi\)
\(564\) 0 0
\(565\) −0.887817 5.74519i −0.0373507 0.241702i
\(566\) 23.9192 + 13.8098i 1.00540 + 0.580468i
\(567\) 0 0
\(568\) 12.8513 + 7.41968i 0.539227 + 0.311323i
\(569\) 13.2995 + 23.0353i 0.557542 + 0.965692i 0.997701 + 0.0677716i \(0.0215889\pi\)
−0.440159 + 0.897920i \(0.645078\pi\)
\(570\) 0 0
\(571\) 31.8452 1.33268 0.666340 0.745648i \(-0.267860\pi\)
0.666340 + 0.745648i \(0.267860\pi\)
\(572\) −3.52928 + 3.17697i −0.147567 + 0.132836i
\(573\) 0 0
\(574\) −2.07618 + 1.19868i −0.0866580 + 0.0500320i
\(575\) −12.7426 40.2451i −0.531404 1.67834i
\(576\) 0 0
\(577\) 1.20258 0.0500639 0.0250319 0.999687i \(-0.492031\pi\)
0.0250319 + 0.999687i \(0.492031\pi\)
\(578\) −7.26867 + 12.5897i −0.302337 + 0.523662i
\(579\) 0 0
\(580\) 6.20319 + 7.71948i 0.257574 + 0.320534i
\(581\) 4.88108 8.45427i 0.202501 0.350742i
\(582\) 0 0
\(583\) 9.16386 + 15.8723i 0.379528 + 0.657362i
\(584\) −5.98944 −0.247845
\(585\) 0 0
\(586\) −30.2501 −1.24962
\(587\) −9.53243 16.5107i −0.393446 0.681468i 0.599456 0.800408i \(-0.295384\pi\)
−0.992901 + 0.118940i \(0.962050\pi\)
\(588\) 0 0
\(589\) −3.92816 + 6.80377i −0.161857 + 0.280344i
\(590\) −18.2551 + 14.6694i −0.751550 + 0.603929i
\(591\) 0 0
\(592\) 1.40148 2.42743i 0.0576004 0.0997668i
\(593\) −11.8496 −0.486606 −0.243303 0.969950i \(-0.578231\pi\)
−0.243303 + 0.969950i \(0.578231\pi\)
\(594\) 0 0
\(595\) −4.99736 1.93990i −0.204872 0.0795280i
\(596\) −2.60768 + 1.50554i −0.106815 + 0.0616694i
\(597\) 0 0
\(598\) 6.32532 + 29.7767i 0.258661 + 1.21766i
\(599\) −13.1277 −0.536382 −0.268191 0.963366i \(-0.586426\pi\)
−0.268191 + 0.963366i \(0.586426\pi\)
\(600\) 0 0
\(601\) 17.8125 + 30.8522i 0.726589 + 1.25849i 0.958317 + 0.285708i \(0.0922288\pi\)
−0.231728 + 0.972781i \(0.574438\pi\)
\(602\) 6.99684 + 4.03963i 0.285170 + 0.164643i
\(603\) 0 0
\(604\) 10.4052 + 6.00745i 0.423382 + 0.244440i
\(605\) 20.4752 3.16407i 0.832434 0.128638i
\(606\) 0 0
\(607\) 4.20075 + 2.42530i 0.170503 + 0.0984400i 0.582823 0.812599i \(-0.301948\pi\)
−0.412320 + 0.911039i \(0.635281\pi\)
\(608\) 4.18063 2.41369i 0.169547 0.0978880i
\(609\) 0 0
\(610\) 6.97904 + 8.68497i 0.282573 + 0.351644i
\(611\) 11.9298 + 13.2528i 0.482629 + 0.536149i
\(612\) 0 0
\(613\) −11.7172 20.2948i −0.473253 0.819698i 0.526279 0.850312i \(-0.323587\pi\)
−0.999531 + 0.0306146i \(0.990254\pi\)
\(614\) 7.06959 + 12.2449i 0.285306 + 0.494164i
\(615\) 0 0
\(616\) 2.01198i 0.0810648i
\(617\) −7.01830 + 12.1560i −0.282546 + 0.489384i −0.972011 0.234935i \(-0.924512\pi\)
0.689465 + 0.724319i \(0.257846\pi\)
\(618\) 0 0
\(619\) 16.1470i 0.649002i 0.945885 + 0.324501i \(0.105196\pi\)
−0.945885 + 0.324501i \(0.894804\pi\)
\(620\) −0.555760 3.59640i −0.0223199 0.144435i
\(621\) 0 0
\(622\) −4.98713 8.63797i −0.199966 0.346351i
\(623\) 28.1780i 1.12893i
\(624\) 0 0
\(625\) −22.6831 10.5108i −0.907325 0.420431i
\(626\) 2.67134 1.54230i 0.106768 0.0616428i
\(627\) 0 0
\(628\) −2.61155 1.50778i −0.104212 0.0601669i
\(629\) 4.39865i 0.175386i
\(630\) 0 0
\(631\) 16.3611 + 9.44608i 0.651325 + 0.376043i 0.788964 0.614440i \(-0.210618\pi\)
−0.137639 + 0.990483i \(0.543951\pi\)
\(632\) 4.87632 0.193970
\(633\) 0 0
\(634\) 7.14899 + 12.3824i 0.283922 + 0.491768i
\(635\) 16.8863 + 6.55502i 0.670114 + 0.260128i
\(636\) 0 0
\(637\) −5.20100 + 16.0002i −0.206071 + 0.633950i
\(638\) 5.83277i 0.230921i
\(639\) 0 0
\(640\) −0.809179 + 2.08452i −0.0319856 + 0.0823979i
\(641\) −3.57648 + 6.19465i −0.141262 + 0.244674i −0.927972 0.372649i \(-0.878449\pi\)
0.786710 + 0.617323i \(0.211783\pi\)
\(642\) 0 0
\(643\) −19.9623 + 34.5756i −0.787235 + 1.36353i 0.140420 + 0.990092i \(0.455155\pi\)
−0.927655 + 0.373438i \(0.878179\pi\)
\(644\) 11.1699 + 6.44897i 0.440157 + 0.254125i
\(645\) 0 0
\(646\) 3.78778 6.56062i 0.149028 0.258124i
\(647\) 12.0656 6.96608i 0.474348 0.273865i −0.243710 0.969848i \(-0.578365\pi\)
0.718058 + 0.695983i \(0.245031\pi\)
\(648\) 0 0
\(649\) 13.7934 0.541438
\(650\) 15.5431 + 9.13299i 0.609651 + 0.358225i
\(651\) 0 0
\(652\) 4.95812 + 8.58772i 0.194175 + 0.336321i
\(653\) −25.7670 + 14.8766i −1.00834 + 0.582165i −0.910705 0.413058i \(-0.864461\pi\)
−0.0976340 + 0.995222i \(0.531127\pi\)
\(654\) 0 0
\(655\) −3.25662 4.05265i −0.127246 0.158350i
\(656\) 1.35904 + 0.784645i 0.0530618 + 0.0306352i
\(657\) 0 0
\(658\) 7.55515 0.294530
\(659\) 14.6318 25.3431i 0.569975 0.987226i −0.426593 0.904444i \(-0.640286\pi\)
0.996568 0.0827819i \(-0.0263805\pi\)
\(660\) 0 0
\(661\) −30.0903 + 17.3726i −1.17038 + 0.675717i −0.953769 0.300541i \(-0.902833\pi\)
−0.216608 + 0.976259i \(0.569499\pi\)
\(662\) 11.4202i 0.443858i
\(663\) 0 0
\(664\) −6.39020 −0.247988
\(665\) −15.3726 5.96742i −0.596125 0.231407i
\(666\) 0 0
\(667\) −32.3819 18.6957i −1.25383 0.723901i
\(668\) 12.9894 0.502576
\(669\) 0 0
\(670\) 6.12693 0.946808i 0.236704 0.0365784i
\(671\) 6.56228i 0.253334i
\(672\) 0 0
\(673\) 28.1953 16.2786i 1.08685 0.627492i 0.154113 0.988053i \(-0.450748\pi\)
0.932736 + 0.360561i \(0.117415\pi\)
\(674\) −4.79092 + 2.76604i −0.184539 + 0.106544i
\(675\) 0 0
\(676\) −10.5153 7.64386i −0.404434 0.293995i
\(677\) 32.2002i 1.23756i 0.785566 + 0.618778i \(0.212372\pi\)
−0.785566 + 0.618778i \(0.787628\pi\)
\(678\) 0 0
\(679\) −1.47119 2.54818i −0.0564593 0.0977903i
\(680\) 0.535898 + 3.46788i 0.0205508 + 0.132987i
\(681\) 0 0
\(682\) −1.07169 + 1.85622i −0.0410372 + 0.0710784i
\(683\) 3.19280 5.53009i 0.122169 0.211603i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(684\) 0 0
\(685\) −27.1453 + 4.19482i −1.03717 + 0.160276i
\(686\) 8.91109 + 15.4345i 0.340227 + 0.589290i
\(687\) 0 0
\(688\) 5.28860i 0.201626i
\(689\) −37.2916 + 33.5690i −1.42070 + 1.27888i
\(690\) 0 0
\(691\) 13.6788 7.89748i 0.520368 0.300434i −0.216717 0.976234i \(-0.569535\pi\)
0.737085 + 0.675800i \(0.236202\pi\)
\(692\) −3.35755 + 1.93848i −0.127635 + 0.0736900i
\(693\) 0 0
\(694\) 2.82008i 0.107049i
\(695\) 14.7114 2.27338i 0.558034 0.0862342i
\(696\) 0 0
\(697\) 2.46267 0.0932803
\(698\) −23.0704 13.3197i −0.873226 0.504157i
\(699\) 0 0
\(700\) 7.28207 2.30569i 0.275236 0.0871469i
\(701\) 43.7481 1.65234 0.826171 0.563420i \(-0.190515\pi\)
0.826171 + 0.563420i \(0.190515\pi\)
\(702\) 0 0
\(703\) 13.5309i 0.510329i
\(704\) 1.14057 0.658509i 0.0429869 0.0248185i
\(705\) 0 0
\(706\) −6.61308 + 11.4542i −0.248886 + 0.431084i
\(707\) 3.72537 0.140107
\(708\) 0 0
\(709\) −30.0167 17.3302i −1.12730 0.650848i −0.184046 0.982918i \(-0.558920\pi\)
−0.943255 + 0.332070i \(0.892253\pi\)
\(710\) −25.8654 + 20.7849i −0.970713 + 0.780042i
\(711\) 0 0
\(712\) −15.9738 + 9.22251i −0.598645 + 0.345628i
\(713\) 6.87016 + 11.8995i 0.257290 + 0.445639i
\(714\) 0 0
\(715\) −3.76665 9.92760i −0.140865 0.371271i
\(716\) 14.1065 0.527185
\(717\) 0 0
\(718\) 10.7237 6.19133i 0.400205 0.231058i
\(719\) 21.9251 37.9755i 0.817670 1.41625i −0.0897253 0.995967i \(-0.528599\pi\)
0.907395 0.420279i \(-0.138068\pi\)
\(720\) 0 0
\(721\) 16.4450 + 9.49451i 0.612443 + 0.353594i
\(722\) 2.15178 3.72700i 0.0800811 0.138704i
\(723\) 0 0
\(724\) 13.0736 22.6441i 0.485876 0.841563i
\(725\) −21.1109 + 6.68425i −0.784040 + 0.248247i
\(726\) 0 0
\(727\) 17.2599i 0.640136i −0.947395 0.320068i \(-0.896294\pi\)
0.947395 0.320068i \(-0.103706\pi\)
\(728\) −5.38789 + 1.14452i −0.199688 + 0.0424188i
\(729\) 0 0
\(730\) 4.84653 12.4851i 0.179378 0.462095i
\(731\) −4.14967 7.18744i −0.153481 0.265837i
\(732\) 0 0
\(733\) 0.304799 0.0112580 0.00562900 0.999984i \(-0.498208\pi\)
0.00562900 + 0.999984i \(0.498208\pi\)
\(734\) −6.14226 3.54624i −0.226715 0.130894i
\(735\) 0 0
\(736\) 8.44285i 0.311208i
\(737\) −3.16231 1.82576i −0.116485 0.0672528i
\(738\) 0 0
\(739\) 3.14941 1.81831i 0.115853 0.0668877i −0.440954 0.897530i \(-0.645360\pi\)
0.556807 + 0.830642i \(0.312026\pi\)
\(740\) 3.92599 + 4.88564i 0.144322 + 0.179600i
\(741\) 0 0
\(742\) 21.2592i 0.780451i
\(743\) 15.1150 + 26.1800i 0.554517 + 0.960451i 0.997941 + 0.0641394i \(0.0204302\pi\)
−0.443424 + 0.896312i \(0.646236\pi\)
\(744\) 0 0
\(745\) −1.02826 6.65401i −0.0376725 0.243784i
\(746\) 36.9803i 1.35395i
\(747\) 0 0
\(748\) 1.03339 1.78989i 0.0377845 0.0654447i
\(749\) 16.0049i 0.584805i
\(750\) 0 0
\(751\) −0.00159080 0.00275535i −5.80493e−5 0.000100544i 0.865996 0.500050i \(-0.166685\pi\)
−0.866054 + 0.499950i \(0.833352\pi\)
\(752\) −2.47276 4.28295i −0.0901723 0.156183i
\(753\) 0 0
\(754\) 15.6196 3.31800i 0.568833 0.120834i
\(755\) −20.9423 + 16.8288i −0.762170 + 0.612462i
\(756\) 0 0
\(757\) −36.4328 + 21.0345i −1.32417 + 0.764512i −0.984392 0.175992i \(-0.943687\pi\)
−0.339782 + 0.940504i \(0.610353\pi\)
\(758\) 29.6252 + 17.1041i 1.07604 + 0.621250i
\(759\) 0 0
\(760\) 1.64851 + 10.6677i 0.0597976 + 0.386959i
\(761\) −21.1489 12.2103i −0.766646 0.442623i 0.0650310 0.997883i \(-0.479285\pi\)
−0.831677 + 0.555260i \(0.812619\pi\)
\(762\) 0 0
\(763\) −22.7291 13.1226i −0.822847 0.475071i
\(764\) 9.42713 + 16.3283i 0.341062 + 0.590736i
\(765\) 0 0
\(766\) −26.0340 −0.940646
\(767\) 7.84643 + 36.9374i 0.283318 + 1.33373i
\(768\) 0 0
\(769\) −28.1198 + 16.2350i −1.01403 + 0.585449i −0.912368 0.409370i \(-0.865748\pi\)
−0.101659 + 0.994819i \(0.532415\pi\)
\(770\) −4.19401 1.62805i −0.151141 0.0586708i
\(771\) 0 0
\(772\) −17.8920 −0.643947
\(773\) −4.13819 + 7.16756i −0.148840 + 0.257799i −0.930799 0.365531i \(-0.880887\pi\)
0.781959 + 0.623330i \(0.214221\pi\)
\(774\) 0 0
\(775\) 7.94649 + 1.75164i 0.285446 + 0.0629208i
\(776\) −0.963028 + 1.66801i −0.0345707 + 0.0598782i
\(777\) 0 0
\(778\) −3.11784 5.40026i −0.111780 0.193609i
\(779\) 7.57555 0.271422
\(780\) 0 0
\(781\) 19.5437 0.699328
\(782\) −6.62464 11.4742i −0.236897 0.410317i
\(783\) 0 0
\(784\) 2.33310 4.04106i 0.0833252 0.144323i
\(785\) 5.25620 4.22376i 0.187602 0.150753i
\(786\) 0 0