Properties

Label 1170.2.bj.d.829.4
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: \(x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197\)
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 829.4
Root \(-0.330925 + 1.46916i\) of defining polynomial
Character \(\chi\) \(=\) 1170.829
Dual form 1170.2.bj.d.199.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.571769 + 2.16173i) q^{5} +(-0.603137 + 1.04466i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.571769 + 2.16173i) q^{5} +(-0.603137 + 1.04466i) q^{7} -1.00000 q^{8} +(-1.58623 + 1.57603i) q^{10} +(-4.46182 + 2.57603i) q^{11} +(-2.24511 - 2.82126i) q^{13} -1.20627 q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.10150 + 2.36800i) q^{17} +(-1.84474 - 1.06506i) q^{19} +(-2.15800 - 0.585699i) q^{20} +(-4.46182 - 2.57603i) q^{22} +(-1.88293 + 1.08711i) q^{23} +(-4.34616 + 2.47202i) q^{25} +(1.32073 - 3.35495i) q^{26} +(-0.603137 - 1.04466i) q^{28} +(-2.38346 - 4.12828i) q^{29} -5.91046i q^{31} +(0.500000 - 0.866025i) q^{32} +4.73601i q^{34} +(-2.60314 - 0.706513i) q^{35} +(2.20034 + 3.81110i) q^{37} -2.13012i q^{38} +(-0.571769 - 2.16173i) q^{40} +(-4.10150 + 2.36800i) q^{41} +(-1.70944 - 0.986944i) q^{43} -5.15206i q^{44} +(-1.88293 - 1.08711i) q^{46} +0.852296 q^{47} +(2.77245 + 4.80203i) q^{49} +(-4.31391 - 2.52788i) q^{50} +(3.56583 - 0.533691i) q^{52} +4.48042i q^{53} +(-8.11982 - 8.17235i) q^{55} +(0.603137 - 1.04466i) q^{56} +(2.38346 - 4.12828i) q^{58} +(-1.68133 - 0.970715i) q^{59} +(-1.53795 + 2.66381i) q^{61} +(5.11861 - 2.95523i) q^{62} +1.00000 q^{64} +(4.81512 - 6.46642i) q^{65} +(7.02765 + 12.1723i) q^{67} +(-4.10150 + 2.36800i) q^{68} +(-0.689710 - 2.60764i) q^{70} +(0.298707 + 0.172459i) q^{71} +15.7228 q^{73} +(-2.20034 + 3.81110i) q^{74} +(1.84474 - 1.06506i) q^{76} -6.21480i q^{77} -13.5863 q^{79} +(1.58623 - 1.57603i) q^{80} +(-4.10150 - 2.36800i) q^{82} -10.2045 q^{83} +(-2.77388 + 10.2203i) q^{85} -1.97389i q^{86} +(4.46182 - 2.57603i) q^{88} +(-14.1941 + 8.19497i) q^{89} +(4.30137 - 0.643777i) q^{91} -2.17422i q^{92} +(0.426148 + 0.738110i) q^{94} +(1.24761 - 4.59679i) q^{95} +(4.24139 - 7.34631i) q^{97} +(-2.77245 + 4.80203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} + O(q^{10}) \) \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{7} - 12 q^{8} - 2 q^{10} - 6 q^{11} - 8 q^{13} - 4 q^{14} - 6 q^{16} - 18 q^{17} - 6 q^{19} - 4 q^{20} - 6 q^{22} - 6 q^{23} - 10 q^{25} + 2 q^{26} - 2 q^{28} - 14 q^{29} + 6 q^{32} - 26 q^{35} - 12 q^{37} - 2 q^{40} + 18 q^{41} - 36 q^{43} - 6 q^{46} - 16 q^{47} + 8 q^{49} + 10 q^{50} + 10 q^{52} - 28 q^{55} + 2 q^{56} + 14 q^{58} + 36 q^{59} + 10 q^{61} - 6 q^{62} + 12 q^{64} - 6 q^{65} + 4 q^{67} + 18 q^{68} - 4 q^{70} + 12 q^{71} + 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 2 q^{80} + 18 q^{82} - 72 q^{83} + 18 q^{85} + 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} + 42 q^{95} - 48 q^{97} - 8 q^{98} + O(q^{100}) \)

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
\(5\) 0.571769 + 2.16173i 0.255703 + 0.966755i
\(6\) 0 0
\(7\) −0.603137 + 1.04466i −0.227964 + 0.394846i −0.957205 0.289412i \(-0.906540\pi\)
0.729240 + 0.684258i \(0.239874\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.58623 + 1.57603i −0.501610 + 0.498385i
\(11\) −4.46182 + 2.57603i −1.34529 + 0.776703i −0.987578 0.157130i \(-0.949776\pi\)
−0.357711 + 0.933832i \(0.616443\pi\)
\(12\) 0 0
\(13\) −2.24511 2.82126i −0.622681 0.782476i
\(14\) −1.20627 −0.322390
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.10150 + 2.36800i 0.994761 + 0.574326i 0.906694 0.421789i \(-0.138598\pi\)
0.0880670 + 0.996115i \(0.471931\pi\)
\(18\) 0 0
\(19\) −1.84474 1.06506i −0.423212 0.244341i 0.273239 0.961946i \(-0.411905\pi\)
−0.696450 + 0.717605i \(0.745238\pi\)
\(20\) −2.15800 0.585699i −0.482543 0.130966i
\(21\) 0 0
\(22\) −4.46182 2.57603i −0.951263 0.549212i
\(23\) −1.88293 + 1.08711i −0.392618 + 0.226678i −0.683294 0.730144i \(-0.739453\pi\)
0.290676 + 0.956822i \(0.406120\pi\)
\(24\) 0 0
\(25\) −4.34616 + 2.47202i −0.869232 + 0.494404i
\(26\) 1.32073 3.35495i 0.259016 0.657960i
\(27\) 0 0
\(28\) −0.603137 1.04466i −0.113982 0.197423i
\(29\) −2.38346 4.12828i −0.442598 0.766602i 0.555283 0.831661i \(-0.312610\pi\)
−0.997881 + 0.0650589i \(0.979276\pi\)
\(30\) 0 0
\(31\) 5.91046i 1.06155i −0.847513 0.530775i \(-0.821901\pi\)
0.847513 0.530775i \(-0.178099\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 4.73601i 0.812219i
\(35\) −2.60314 0.706513i −0.440010 0.119423i
\(36\) 0 0
\(37\) 2.20034 + 3.81110i 0.361734 + 0.626541i 0.988246 0.152870i \(-0.0488517\pi\)
−0.626513 + 0.779411i \(0.715518\pi\)
\(38\) 2.13012i 0.345551i
\(39\) 0 0
\(40\) −0.571769 2.16173i −0.0904046 0.341800i
\(41\) −4.10150 + 2.36800i −0.640547 + 0.369820i −0.784825 0.619717i \(-0.787247\pi\)
0.144278 + 0.989537i \(0.453914\pi\)
\(42\) 0 0
\(43\) −1.70944 0.986944i −0.260687 0.150508i 0.363961 0.931414i \(-0.381424\pi\)
−0.624648 + 0.780907i \(0.714757\pi\)
\(44\) 5.15206i 0.776703i
\(45\) 0 0
\(46\) −1.88293 1.08711i −0.277623 0.160285i
\(47\) 0.852296 0.124320 0.0621600 0.998066i \(-0.480201\pi\)
0.0621600 + 0.998066i \(0.480201\pi\)
\(48\) 0 0
\(49\) 2.77245 + 4.80203i 0.396065 + 0.686004i
\(50\) −4.31391 2.52788i −0.610079 0.357496i
\(51\) 0 0
\(52\) 3.56583 0.533691i 0.494492 0.0740096i
\(53\) 4.48042i 0.615433i 0.951478 + 0.307716i \(0.0995648\pi\)
−0.951478 + 0.307716i \(0.900435\pi\)
\(54\) 0 0
\(55\) −8.11982 8.17235i −1.09488 1.10196i
\(56\) 0.603137 1.04466i 0.0805976 0.139599i
\(57\) 0 0
\(58\) 2.38346 4.12828i 0.312964 0.542070i
\(59\) −1.68133 0.970715i −0.218890 0.126376i 0.386546 0.922270i \(-0.373668\pi\)
−0.605436 + 0.795894i \(0.707001\pi\)
\(60\) 0 0
\(61\) −1.53795 + 2.66381i −0.196915 + 0.341066i −0.947527 0.319677i \(-0.896426\pi\)
0.750612 + 0.660744i \(0.229759\pi\)
\(62\) 5.11861 2.95523i 0.650064 0.375315i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.81512 6.46642i 0.597242 0.802061i
\(66\) 0 0
\(67\) 7.02765 + 12.1723i 0.858564 + 1.48708i 0.873298 + 0.487186i \(0.161977\pi\)
−0.0147340 + 0.999891i \(0.504690\pi\)
\(68\) −4.10150 + 2.36800i −0.497380 + 0.287163i
\(69\) 0 0
\(70\) −0.689710 2.60764i −0.0824361 0.311673i
\(71\) 0.298707 + 0.172459i 0.0354500 + 0.0204671i 0.517620 0.855610i \(-0.326818\pi\)
−0.482170 + 0.876078i \(0.660151\pi\)
\(72\) 0 0
\(73\) 15.7228 1.84022 0.920109 0.391662i \(-0.128100\pi\)
0.920109 + 0.391662i \(0.128100\pi\)
\(74\) −2.20034 + 3.81110i −0.255784 + 0.443031i
\(75\) 0 0
\(76\) 1.84474 1.06506i 0.211606 0.122171i
\(77\) 6.21480i 0.708242i
\(78\) 0 0
\(79\) −13.5863 −1.52858 −0.764290 0.644873i \(-0.776910\pi\)
−0.764290 + 0.644873i \(0.776910\pi\)
\(80\) 1.58623 1.57603i 0.177346 0.176206i
\(81\) 0 0
\(82\) −4.10150 2.36800i −0.452935 0.261502i
\(83\) −10.2045 −1.12009 −0.560046 0.828462i \(-0.689216\pi\)
−0.560046 + 0.828462i \(0.689216\pi\)
\(84\) 0 0
\(85\) −2.77388 + 10.2203i −0.300869 + 1.10855i
\(86\) 1.97389i 0.212850i
\(87\) 0 0
\(88\) 4.46182 2.57603i 0.475631 0.274606i
\(89\) −14.1941 + 8.19497i −1.50457 + 0.868665i −0.504586 + 0.863361i \(0.668355\pi\)
−0.999986 + 0.00530346i \(0.998312\pi\)
\(90\) 0 0
\(91\) 4.30137 0.643777i 0.450906 0.0674862i
\(92\) 2.17422i 0.226678i
\(93\) 0 0
\(94\) 0.426148 + 0.738110i 0.0439538 + 0.0761302i
\(95\) 1.24761 4.59679i 0.128002 0.471621i
\(96\) 0 0
\(97\) 4.24139 7.34631i 0.430648 0.745904i −0.566281 0.824212i \(-0.691618\pi\)
0.996929 + 0.0783078i \(0.0249517\pi\)
\(98\) −2.77245 + 4.80203i −0.280060 + 0.485078i
\(99\) 0 0
\(100\) 0.0322474 4.99990i 0.00322474 0.499990i
\(101\) −6.79121 11.7627i −0.675751 1.17044i −0.976249 0.216653i \(-0.930486\pi\)
0.300498 0.953783i \(-0.402847\pi\)
\(102\) 0 0
\(103\) 2.15696i 0.212531i −0.994338 0.106266i \(-0.966111\pi\)
0.994338 0.106266i \(-0.0338894\pi\)
\(104\) 2.24511 + 2.82126i 0.220151 + 0.276647i
\(105\) 0 0
\(106\) −3.88016 + 2.24021i −0.376874 + 0.217588i
\(107\) −7.00959 + 4.04699i −0.677642 + 0.391237i −0.798966 0.601376i \(-0.794619\pi\)
0.121324 + 0.992613i \(0.461286\pi\)
\(108\) 0 0
\(109\) 16.8839i 1.61718i 0.588370 + 0.808592i \(0.299770\pi\)
−0.588370 + 0.808592i \(0.700230\pi\)
\(110\) 3.01756 11.1181i 0.287713 1.06007i
\(111\) 0 0
\(112\) 1.20627 0.113982
\(113\) −4.28771 2.47551i −0.403354 0.232876i 0.284576 0.958653i \(-0.408147\pi\)
−0.687930 + 0.725777i \(0.741480\pi\)
\(114\) 0 0
\(115\) −3.42664 3.44881i −0.319535 0.321603i
\(116\) 4.76693 0.442598
\(117\) 0 0
\(118\) 1.94143i 0.178723i
\(119\) −4.94754 + 2.85646i −0.453540 + 0.261851i
\(120\) 0 0
\(121\) 7.77188 13.4613i 0.706535 1.22375i
\(122\) −3.07591 −0.278480
\(123\) 0 0
\(124\) 5.11861 + 2.95523i 0.459665 + 0.265388i
\(125\) −7.82884 7.98180i −0.700233 0.713914i
\(126\) 0 0
\(127\) −1.04089 + 0.600957i −0.0923639 + 0.0533263i −0.545471 0.838130i \(-0.683649\pi\)
0.453107 + 0.891456i \(0.350316\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 8.00765 + 0.936802i 0.702317 + 0.0821629i
\(131\) 6.65149 0.581143 0.290572 0.956853i \(-0.406155\pi\)
0.290572 + 0.956853i \(0.406155\pi\)
\(132\) 0 0
\(133\) 2.22526 1.28475i 0.192954 0.111402i
\(134\) −7.02765 + 12.1723i −0.607097 + 1.05152i
\(135\) 0 0
\(136\) −4.10150 2.36800i −0.351701 0.203055i
\(137\) 7.35746 12.7435i 0.628590 1.08875i −0.359245 0.933243i \(-0.616966\pi\)
0.987835 0.155507i \(-0.0497010\pi\)
\(138\) 0 0
\(139\) −7.82540 + 13.5540i −0.663742 + 1.14963i 0.315883 + 0.948798i \(0.397699\pi\)
−0.979625 + 0.200837i \(0.935634\pi\)
\(140\) 1.91343 1.90113i 0.161714 0.160674i
\(141\) 0 0
\(142\) 0.344918i 0.0289448i
\(143\) 17.2849 + 6.80447i 1.44544 + 0.569018i
\(144\) 0 0
\(145\) 7.56144 7.51283i 0.627943 0.623906i
\(146\) 7.86142 + 13.6164i 0.650615 + 1.12690i
\(147\) 0 0
\(148\) −4.40068 −0.361734
\(149\) 19.7555 + 11.4058i 1.61843 + 0.934401i 0.987327 + 0.158702i \(0.0507309\pi\)
0.631103 + 0.775699i \(0.282602\pi\)
\(150\) 0 0
\(151\) 19.8995i 1.61940i 0.586845 + 0.809699i \(0.300370\pi\)
−0.586845 + 0.809699i \(0.699630\pi\)
\(152\) 1.84474 + 1.06506i 0.149628 + 0.0863877i
\(153\) 0 0
\(154\) 5.38217 3.10740i 0.433708 0.250401i
\(155\) 12.7768 3.37942i 1.02626 0.271442i
\(156\) 0 0
\(157\) 4.74392i 0.378606i 0.981919 + 0.189303i \(0.0606228\pi\)
−0.981919 + 0.189303i \(0.939377\pi\)
\(158\) −6.79315 11.7661i −0.540434 0.936060i
\(159\) 0 0
\(160\) 2.15800 + 0.585699i 0.170605 + 0.0463036i
\(161\) 2.62270i 0.206698i
\(162\) 0 0
\(163\) 1.93329 3.34855i 0.151427 0.262279i −0.780325 0.625374i \(-0.784947\pi\)
0.931752 + 0.363095i \(0.118280\pi\)
\(164\) 4.73601i 0.369820i
\(165\) 0 0
\(166\) −5.10226 8.83737i −0.396012 0.685913i
\(167\) 11.3614 + 19.6785i 0.879173 + 1.52277i 0.852250 + 0.523134i \(0.175237\pi\)
0.0269225 + 0.999638i \(0.491429\pi\)
\(168\) 0 0
\(169\) −2.91899 + 12.6681i −0.224538 + 0.974465i
\(170\) −10.2380 + 2.70790i −0.785217 + 0.207687i
\(171\) 0 0
\(172\) 1.70944 0.986944i 0.130343 0.0752538i
\(173\) 4.06859 + 2.34900i 0.309329 + 0.178591i 0.646626 0.762807i \(-0.276179\pi\)
−0.337297 + 0.941398i \(0.609513\pi\)
\(174\) 0 0
\(175\) 0.0388991 6.03124i 0.00294050 0.455919i
\(176\) 4.46182 + 2.57603i 0.336322 + 0.194176i
\(177\) 0 0
\(178\) −14.1941 8.19497i −1.06389 0.614239i
\(179\) 4.34913 + 7.53292i 0.325069 + 0.563037i 0.981526 0.191327i \(-0.0612790\pi\)
−0.656457 + 0.754363i \(0.727946\pi\)
\(180\) 0 0
\(181\) 9.75480 0.725069 0.362534 0.931970i \(-0.381912\pi\)
0.362534 + 0.931970i \(0.381912\pi\)
\(182\) 2.70821 + 3.40321i 0.200746 + 0.252263i
\(183\) 0 0
\(184\) 1.88293 1.08711i 0.138811 0.0801427i
\(185\) −6.98049 + 6.93561i −0.513215 + 0.509916i
\(186\) 0 0
\(187\) −24.4002 −1.78432
\(188\) −0.426148 + 0.738110i −0.0310800 + 0.0538322i
\(189\) 0 0
\(190\) 4.60474 1.21794i 0.334063 0.0883583i
\(191\) 5.77729 10.0066i 0.418030 0.724049i −0.577711 0.816241i \(-0.696054\pi\)
0.995741 + 0.0921920i \(0.0293874\pi\)
\(192\) 0 0
\(193\) 5.23154 + 9.06130i 0.376575 + 0.652247i 0.990561 0.137070i \(-0.0437685\pi\)
−0.613987 + 0.789316i \(0.710435\pi\)
\(194\) 8.48278 0.609028
\(195\) 0 0
\(196\) −5.54490 −0.396065
\(197\) 8.79472 + 15.2329i 0.626598 + 1.08530i 0.988230 + 0.152978i \(0.0488865\pi\)
−0.361632 + 0.932321i \(0.617780\pi\)
\(198\) 0 0
\(199\) 12.7858 22.1457i 0.906362 1.56986i 0.0872828 0.996184i \(-0.472182\pi\)
0.819079 0.573681i \(-0.194485\pi\)
\(200\) 4.34616 2.47202i 0.307320 0.174798i
\(201\) 0 0
\(202\) 6.79121 11.7627i 0.477828 0.827623i
\(203\) 5.75022 0.403586
\(204\) 0 0
\(205\) −7.46410 7.51240i −0.521315 0.524689i
\(206\) 1.86798 1.07848i 0.130148 0.0751412i
\(207\) 0 0
\(208\) −1.32073 + 3.35495i −0.0915760 + 0.232624i
\(209\) 10.9745 0.759122
\(210\) 0 0
\(211\) −6.45984 11.1888i −0.444714 0.770267i 0.553318 0.832970i \(-0.313361\pi\)
−0.998032 + 0.0627029i \(0.980028\pi\)
\(212\) −3.88016 2.24021i −0.266490 0.153858i
\(213\) 0 0
\(214\) −7.00959 4.04699i −0.479165 0.276646i
\(215\) 1.15610 4.25965i 0.0788456 0.290505i
\(216\) 0 0
\(217\) 6.17445 + 3.56482i 0.419149 + 0.241996i
\(218\) −14.6219 + 8.44195i −0.990319 + 0.571761i
\(219\) 0 0
\(220\) 11.1374 2.94579i 0.750882 0.198605i
\(221\) −2.52757 16.8878i −0.170022 1.13600i
\(222\) 0 0
\(223\) −3.57679 6.19518i −0.239519 0.414860i 0.721057 0.692876i \(-0.243657\pi\)
−0.960576 + 0.278016i \(0.910323\pi\)
\(224\) 0.603137 + 1.04466i 0.0402988 + 0.0697995i
\(225\) 0 0
\(226\) 4.95102i 0.329337i
\(227\) −12.9192 + 22.3768i −0.857480 + 1.48520i 0.0168460 + 0.999858i \(0.494638\pi\)
−0.874325 + 0.485340i \(0.838696\pi\)
\(228\) 0 0
\(229\) 8.95153i 0.591533i 0.955260 + 0.295767i \(0.0955751\pi\)
−0.955260 + 0.295767i \(0.904425\pi\)
\(230\) 1.27344 4.69196i 0.0839680 0.309379i
\(231\) 0 0
\(232\) 2.38346 + 4.12828i 0.156482 + 0.271035i
\(233\) 3.86657i 0.253308i 0.991947 + 0.126654i \(0.0404237\pi\)
−0.991947 + 0.126654i \(0.959576\pi\)
\(234\) 0 0
\(235\) 0.487316 + 1.84243i 0.0317890 + 0.120187i
\(236\) 1.68133 0.970715i 0.109445 0.0631882i
\(237\) 0 0
\(238\) −4.94754 2.85646i −0.320701 0.185157i
\(239\) 15.4177i 0.997286i 0.866807 + 0.498643i \(0.166168\pi\)
−0.866807 + 0.498643i \(0.833832\pi\)
\(240\) 0 0
\(241\) 9.76603 + 5.63842i 0.629085 + 0.363203i 0.780398 0.625283i \(-0.215017\pi\)
−0.151312 + 0.988486i \(0.548350\pi\)
\(242\) 15.5438 0.999191
\(243\) 0 0
\(244\) −1.53795 2.66381i −0.0984574 0.170533i
\(245\) −8.79549 + 8.73894i −0.561923 + 0.558311i
\(246\) 0 0
\(247\) 1.13682 + 7.59565i 0.0723344 + 0.483299i
\(248\) 5.91046i 0.375315i
\(249\) 0 0
\(250\) 2.99802 10.7709i 0.189612 0.681210i
\(251\) −6.15329 + 10.6578i −0.388392 + 0.672715i −0.992233 0.124390i \(-0.960303\pi\)
0.603841 + 0.797104i \(0.293636\pi\)
\(252\) 0 0
\(253\) 5.60085 9.70096i 0.352123 0.609894i
\(254\) −1.04089 0.600957i −0.0653112 0.0377074i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 24.3239 14.0434i 1.51728 0.876004i 0.517490 0.855689i \(-0.326866\pi\)
0.999794 0.0203154i \(-0.00646704\pi\)
\(258\) 0 0
\(259\) −5.30842 −0.329849
\(260\) 3.19253 + 7.40323i 0.197992 + 0.459129i
\(261\) 0 0
\(262\) 3.32575 + 5.76036i 0.205465 + 0.355876i
\(263\) 6.56756 3.79178i 0.404973 0.233811i −0.283654 0.958927i \(-0.591547\pi\)
0.688628 + 0.725115i \(0.258213\pi\)
\(264\) 0 0
\(265\) −9.68546 + 2.56176i −0.594973 + 0.157368i
\(266\) 2.22526 + 1.28475i 0.136439 + 0.0787732i
\(267\) 0 0
\(268\) −14.0553 −0.858564
\(269\) 12.2355 21.1924i 0.746010 1.29213i −0.203712 0.979031i \(-0.565301\pi\)
0.949722 0.313096i \(-0.101366\pi\)
\(270\) 0 0
\(271\) 10.0199 5.78497i 0.608664 0.351412i −0.163779 0.986497i \(-0.552368\pi\)
0.772442 + 0.635085i \(0.219035\pi\)
\(272\) 4.73601i 0.287163i
\(273\) 0 0
\(274\) 14.7149 0.888961
\(275\) 13.0238 22.2256i 0.785363 1.34025i
\(276\) 0 0
\(277\) 11.2111 + 6.47271i 0.673608 + 0.388908i 0.797442 0.603395i \(-0.206186\pi\)
−0.123835 + 0.992303i \(0.539519\pi\)
\(278\) −15.6508 −0.938673
\(279\) 0 0
\(280\) 2.60314 + 0.706513i 0.155567 + 0.0422223i
\(281\) 2.57187i 0.153425i 0.997053 + 0.0767124i \(0.0244423\pi\)
−0.997053 + 0.0767124i \(0.975558\pi\)
\(282\) 0 0
\(283\) 4.80517 2.77427i 0.285638 0.164913i −0.350335 0.936624i \(-0.613932\pi\)
0.635973 + 0.771711i \(0.280599\pi\)
\(284\) −0.298707 + 0.172459i −0.0177250 + 0.0102335i
\(285\) 0 0
\(286\) 2.74961 + 18.3714i 0.162588 + 1.08632i
\(287\) 5.71292i 0.337223i
\(288\) 0 0
\(289\) 2.71489 + 4.70233i 0.159700 + 0.276608i
\(290\) 10.2870 + 2.79198i 0.604075 + 0.163951i
\(291\) 0 0
\(292\) −7.86142 + 13.6164i −0.460055 + 0.796838i
\(293\) 12.0658 20.8986i 0.704891 1.22091i −0.261840 0.965111i \(-0.584329\pi\)
0.966731 0.255795i \(-0.0823374\pi\)
\(294\) 0 0
\(295\) 1.13709 4.18960i 0.0662042 0.243928i
\(296\) −2.20034 3.81110i −0.127892 0.221516i
\(297\) 0 0
\(298\) 22.8116i 1.32144i
\(299\) 7.29439 + 2.87155i 0.421845 + 0.166066i
\(300\) 0 0
\(301\) 2.06205 1.19052i 0.118855 0.0686207i
\(302\) −17.2335 + 9.94975i −0.991675 + 0.572544i
\(303\) 0 0
\(304\) 2.13012i 0.122171i
\(305\) −6.63780 1.80156i −0.380080 0.103157i
\(306\) 0 0
\(307\) −30.3243 −1.73070 −0.865348 0.501171i \(-0.832903\pi\)
−0.865348 + 0.501171i \(0.832903\pi\)
\(308\) 5.38217 + 3.10740i 0.306678 + 0.177061i
\(309\) 0 0
\(310\) 9.31508 + 9.37535i 0.529061 + 0.532484i
\(311\) −8.76406 −0.496964 −0.248482 0.968636i \(-0.579932\pi\)
−0.248482 + 0.968636i \(0.579932\pi\)
\(312\) 0 0
\(313\) 29.0155i 1.64005i 0.572326 + 0.820026i \(0.306041\pi\)
−0.572326 + 0.820026i \(0.693959\pi\)
\(314\) −4.10836 + 2.37196i −0.231848 + 0.133857i
\(315\) 0 0
\(316\) 6.79315 11.7661i 0.382145 0.661894i
\(317\) −25.9970 −1.46014 −0.730068 0.683375i \(-0.760511\pi\)
−0.730068 + 0.683375i \(0.760511\pi\)
\(318\) 0 0
\(319\) 21.2692 + 12.2798i 1.19084 + 0.687534i
\(320\) 0.571769 + 2.16173i 0.0319629 + 0.120844i
\(321\) 0 0
\(322\) 2.27133 1.31135i 0.126576 0.0730787i
\(323\) −5.04413 8.73669i −0.280663 0.486122i
\(324\) 0 0
\(325\) 16.7318 + 6.71169i 0.928113 + 0.372297i
\(326\) 3.86657 0.214150
\(327\) 0 0
\(328\) 4.10150 2.36800i 0.226468 0.130751i
\(329\) −0.514051 + 0.890362i −0.0283405 + 0.0490873i
\(330\) 0 0
\(331\) −9.56025 5.51961i −0.525479 0.303385i 0.213694 0.976901i \(-0.431450\pi\)
−0.739173 + 0.673515i \(0.764784\pi\)
\(332\) 5.10226 8.83737i 0.280023 0.485014i
\(333\) 0 0
\(334\) −11.3614 + 19.6785i −0.621669 + 1.07676i
\(335\) −22.2949 + 22.1516i −1.21810 + 1.21027i
\(336\) 0 0
\(337\) 17.7108i 0.964769i −0.875960 0.482384i \(-0.839771\pi\)
0.875960 0.482384i \(-0.160229\pi\)
\(338\) −12.4303 + 3.80611i −0.676122 + 0.207025i
\(339\) 0 0
\(340\) −7.46410 7.51240i −0.404798 0.407417i
\(341\) 15.2255 + 26.3714i 0.824509 + 1.42809i
\(342\) 0 0
\(343\) −15.1326 −0.817083
\(344\) 1.70944 + 0.986944i 0.0921667 + 0.0532124i
\(345\) 0 0
\(346\) 4.69800i 0.252566i
\(347\) −30.0526 17.3509i −1.61331 0.931443i −0.988597 0.150587i \(-0.951884\pi\)
−0.624710 0.780857i \(-0.714783\pi\)
\(348\) 0 0
\(349\) −30.4563 + 17.5840i −1.63029 + 0.941249i −0.646288 + 0.763093i \(0.723680\pi\)
−0.984002 + 0.178156i \(0.942987\pi\)
\(350\) 5.24266 2.98193i 0.280232 0.159391i
\(351\) 0 0
\(352\) 5.15206i 0.274606i
\(353\) 5.54542 + 9.60495i 0.295153 + 0.511220i 0.975020 0.222115i \(-0.0712961\pi\)
−0.679868 + 0.733335i \(0.737963\pi\)
\(354\) 0 0
\(355\) −0.202018 + 0.744332i −0.0107220 + 0.0395050i
\(356\) 16.3899i 0.868665i
\(357\) 0 0
\(358\) −4.34913 + 7.53292i −0.229859 + 0.398127i
\(359\) 26.1575i 1.38054i 0.723552 + 0.690270i \(0.242508\pi\)
−0.723552 + 0.690270i \(0.757492\pi\)
\(360\) 0 0
\(361\) −7.23130 12.5250i −0.380595 0.659209i
\(362\) 4.87740 + 8.44791i 0.256351 + 0.444012i
\(363\) 0 0
\(364\) −1.59316 + 4.04699i −0.0835042 + 0.212120i
\(365\) 8.98983 + 33.9885i 0.470549 + 1.77904i
\(366\) 0 0
\(367\) 13.4988 7.79352i 0.704630 0.406818i −0.104440 0.994531i \(-0.533305\pi\)
0.809070 + 0.587713i \(0.199972\pi\)
\(368\) 1.88293 + 1.08711i 0.0981544 + 0.0566695i
\(369\) 0 0
\(370\) −9.49666 2.57747i −0.493708 0.133996i
\(371\) −4.68053 2.70231i −0.243001 0.140297i
\(372\) 0 0
\(373\) 0.860358 + 0.496728i 0.0445476 + 0.0257196i 0.522108 0.852879i \(-0.325146\pi\)
−0.477561 + 0.878599i \(0.658479\pi\)
\(374\) −12.2001 21.1312i −0.630853 1.09267i
\(375\) 0 0
\(376\) −0.852296 −0.0439538
\(377\) −6.29581 + 15.9928i −0.324251 + 0.823671i
\(378\) 0 0
\(379\) 23.7856 13.7326i 1.22178 0.705398i 0.256486 0.966548i \(-0.417435\pi\)
0.965298 + 0.261150i \(0.0841018\pi\)
\(380\) 3.35713 + 3.37886i 0.172217 + 0.173332i
\(381\) 0 0
\(382\) 11.5546 0.591184
\(383\) 16.2851 28.2067i 0.832132 1.44130i −0.0642122 0.997936i \(-0.520453\pi\)
0.896344 0.443359i \(-0.146213\pi\)
\(384\) 0 0
\(385\) 13.4347 3.55343i 0.684697 0.181100i
\(386\) −5.23154 + 9.06130i −0.266279 + 0.461208i
\(387\) 0 0
\(388\) 4.24139 + 7.34631i 0.215324 + 0.372952i
\(389\) 16.9110 0.857421 0.428710 0.903442i \(-0.358968\pi\)
0.428710 + 0.903442i \(0.358968\pi\)
\(390\) 0 0
\(391\) −10.2971 −0.520747
\(392\) −2.77245 4.80203i −0.140030 0.242539i
\(393\) 0 0
\(394\) −8.79472 + 15.2329i −0.443072 + 0.767423i
\(395\) −7.76823 29.3699i −0.390862 1.47776i
\(396\) 0 0
\(397\) 16.1198 27.9204i 0.809031 1.40128i −0.104504 0.994524i \(-0.533326\pi\)
0.913536 0.406759i \(-0.133341\pi\)
\(398\) 25.5716 1.28179
\(399\) 0 0
\(400\) 4.31391 + 2.52788i 0.215696 + 0.126394i
\(401\) −28.0082 + 16.1705i −1.39866 + 0.807518i −0.994253 0.107060i \(-0.965856\pi\)
−0.404410 + 0.914578i \(0.632523\pi\)
\(402\) 0 0
\(403\) −16.6749 + 13.2696i −0.830638 + 0.661007i
\(404\) 13.5824 0.675751
\(405\) 0 0
\(406\) 2.87511 + 4.97984i 0.142689 + 0.247145i
\(407\) −19.6350 11.3363i −0.973272 0.561919i
\(408\) 0 0
\(409\) 1.00971 + 0.582957i 0.0499270 + 0.0288254i 0.524756 0.851253i \(-0.324157\pi\)
−0.474829 + 0.880078i \(0.657490\pi\)
\(410\) 2.77388 10.2203i 0.136992 0.504745i
\(411\) 0 0
\(412\) 1.86798 + 1.07848i 0.0920288 + 0.0531328i
\(413\) 2.02814 1.17095i 0.0997984 0.0576186i
\(414\) 0 0
\(415\) −5.83462 22.0594i −0.286410 1.08285i
\(416\) −3.56583 + 0.533691i −0.174829 + 0.0261663i
\(417\) 0 0
\(418\) 5.48725 + 9.50420i 0.268390 + 0.464866i
\(419\) −5.91396 10.2433i −0.288916 0.500417i 0.684635 0.728886i \(-0.259961\pi\)
−0.973551 + 0.228469i \(0.926628\pi\)
\(420\) 0 0
\(421\) 23.9102i 1.16531i 0.812719 + 0.582655i \(0.197986\pi\)
−0.812719 + 0.582655i \(0.802014\pi\)
\(422\) 6.45984 11.1888i 0.314460 0.544661i
\(423\) 0 0
\(424\) 4.48042i 0.217588i
\(425\) −23.6796 0.152724i −1.14863 0.00740819i
\(426\) 0 0
\(427\) −1.85519 3.21329i −0.0897791 0.155502i
\(428\) 8.09397i 0.391237i
\(429\) 0 0
\(430\) 4.26701 1.12861i 0.205774 0.0544263i
\(431\) 22.8082 13.1683i 1.09863 0.634294i 0.162769 0.986664i \(-0.447957\pi\)
0.935861 + 0.352370i \(0.114624\pi\)
\(432\) 0 0
\(433\) 11.2232 + 6.47972i 0.539353 + 0.311396i 0.744817 0.667269i \(-0.232537\pi\)
−0.205464 + 0.978665i \(0.565870\pi\)
\(434\) 7.12964i 0.342234i
\(435\) 0 0
\(436\) −14.6219 8.44195i −0.700261 0.404296i
\(437\) 4.63134 0.221547
\(438\) 0 0
\(439\) 11.6234 + 20.1324i 0.554756 + 0.960865i 0.997922 + 0.0644259i \(0.0205216\pi\)
−0.443167 + 0.896439i \(0.646145\pi\)
\(440\) 8.11982 + 8.17235i 0.387097 + 0.389602i
\(441\) 0 0
\(442\) 13.3615 10.6328i 0.635542 0.505753i
\(443\) 23.3728i 1.11047i −0.831692 0.555237i \(-0.812627\pi\)
0.831692 0.555237i \(-0.187373\pi\)
\(444\) 0 0
\(445\) −25.8311 25.9982i −1.22451 1.23243i
\(446\) 3.57679 6.19518i 0.169366 0.293350i
\(447\) 0 0
\(448\) −0.603137 + 1.04466i −0.0284955 + 0.0493557i
\(449\) −1.20931 0.698196i −0.0570709 0.0329499i 0.471193 0.882030i \(-0.343824\pi\)
−0.528264 + 0.849080i \(0.677157\pi\)
\(450\) 0 0
\(451\) 12.2001 21.1312i 0.574481 0.995030i
\(452\) 4.28771 2.47551i 0.201677 0.116438i
\(453\) 0 0
\(454\) −25.8385 −1.21266
\(455\) 3.85106 + 8.93032i 0.180541 + 0.418660i
\(456\) 0 0
\(457\) 3.60093 + 6.23699i 0.168444 + 0.291754i 0.937873 0.346979i \(-0.112792\pi\)
−0.769429 + 0.638733i \(0.779459\pi\)
\(458\) −7.75225 + 4.47576i −0.362239 + 0.209139i
\(459\) 0 0
\(460\) 4.70007 1.24315i 0.219142 0.0579622i
\(461\) 4.10920 + 2.37245i 0.191384 + 0.110496i 0.592630 0.805474i \(-0.298089\pi\)
−0.401246 + 0.915970i \(0.631423\pi\)
\(462\) 0 0
\(463\) 15.7510 0.732012 0.366006 0.930612i \(-0.380725\pi\)
0.366006 + 0.930612i \(0.380725\pi\)
\(464\) −2.38346 + 4.12828i −0.110650 + 0.191651i
\(465\) 0 0
\(466\) −3.34855 + 1.93329i −0.155119 + 0.0895578i
\(467\) 17.9789i 0.831962i 0.909373 + 0.415981i \(0.136562\pi\)
−0.909373 + 0.415981i \(0.863438\pi\)
\(468\) 0 0
\(469\) −16.9545 −0.782888
\(470\) −1.35194 + 1.34324i −0.0623602 + 0.0619593i
\(471\) 0 0
\(472\) 1.68133 + 0.970715i 0.0773894 + 0.0446808i
\(473\) 10.1696 0.467598
\(474\) 0 0
\(475\) 10.6504 + 0.0686907i 0.488672 + 0.00315174i
\(476\) 5.71292i 0.261851i
\(477\) 0 0
\(478\) −13.3521 + 7.70884i −0.610711 + 0.352594i
\(479\) −2.83964 + 1.63947i −0.129747 + 0.0749093i −0.563468 0.826138i \(-0.690533\pi\)
0.433722 + 0.901047i \(0.357200\pi\)
\(480\) 0 0
\(481\) 5.81210 14.7640i 0.265009 0.673183i
\(482\) 11.2768i 0.513646i
\(483\) 0 0
\(484\) 7.77188 + 13.4613i 0.353267 + 0.611877i
\(485\) 18.3058 + 4.96836i 0.831225 + 0.225601i
\(486\) 0 0
\(487\) −4.98852 + 8.64037i −0.226052 + 0.391533i −0.956634 0.291291i \(-0.905915\pi\)
0.730583 + 0.682824i \(0.239248\pi\)
\(488\) 1.53795 2.66381i 0.0696199 0.120585i
\(489\) 0 0
\(490\) −11.9659 3.24764i −0.540564 0.146714i
\(491\) −10.0376 17.3857i −0.452992 0.784605i 0.545578 0.838060i \(-0.316310\pi\)
−0.998570 + 0.0534548i \(0.982977\pi\)
\(492\) 0 0
\(493\) 22.5762i 1.01678i
\(494\) −6.00961 + 4.78234i −0.270385 + 0.215168i
\(495\) 0 0
\(496\) −5.11861 + 2.95523i −0.229832 + 0.132694i
\(497\) −0.360323 + 0.208033i −0.0161627 + 0.00933153i
\(498\) 0 0
\(499\) 23.9474i 1.07203i −0.844208 0.536016i \(-0.819929\pi\)
0.844208 0.536016i \(-0.180071\pi\)
\(500\) 10.8269 2.78907i 0.484192 0.124731i
\(501\) 0 0
\(502\) −12.3066 −0.549269
\(503\) −10.5377 6.08395i −0.469853 0.271270i 0.246325 0.969187i \(-0.420777\pi\)
−0.716178 + 0.697917i \(0.754110\pi\)
\(504\) 0 0
\(505\) 21.5448 21.4063i 0.958733 0.952570i
\(506\) 11.2017 0.497977
\(507\) 0 0
\(508\) 1.20191i 0.0533263i
\(509\) −34.9666 + 20.1880i −1.54987 + 0.894817i −0.551717 + 0.834031i \(0.686027\pi\)
−0.998151 + 0.0607857i \(0.980639\pi\)
\(510\) 0 0
\(511\) −9.48302 + 16.4251i −0.419504 + 0.726602i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 24.3239 + 14.0434i 1.07288 + 0.619429i
\(515\) 4.66276 1.23328i 0.205466 0.0543449i
\(516\) 0 0
\(517\) −3.80279 + 2.19554i −0.167246 + 0.0965598i
\(518\) −2.65421 4.59723i −0.116619 0.201991i
\(519\) 0 0
\(520\) −4.81512 + 6.46642i −0.211157 + 0.283571i
\(521\) 0.259356 0.0113626 0.00568129 0.999984i \(-0.498192\pi\)
0.00568129 + 0.999984i \(0.498192\pi\)
\(522\) 0 0
\(523\) −33.4527 + 19.3139i −1.46278 + 0.844539i −0.999139 0.0414825i \(-0.986792\pi\)
−0.463645 + 0.886021i \(0.653459\pi\)
\(524\) −3.32575 + 5.76036i −0.145286 + 0.251642i
\(525\) 0 0
\(526\) 6.56756 + 3.79178i 0.286359 + 0.165330i
\(527\) 13.9960 24.2418i 0.609676 1.05599i
\(528\) 0 0
\(529\) −9.13639 + 15.8247i −0.397234 + 0.688030i
\(530\) −7.06128 7.10697i −0.306723 0.308707i
\(531\) 0 0
\(532\) 2.56951i 0.111402i
\(533\) 15.8891 + 6.25498i 0.688232 + 0.270933i
\(534\) 0 0
\(535\) −12.7564 12.8389i −0.551506 0.555074i
\(536\) −7.02765 12.1723i −0.303548 0.525761i
\(537\) 0 0
\(538\) 24.4709 1.05502
\(539\) −24.7403 14.2838i −1.06564 0.615249i
\(540\) 0 0
\(541\) 19.4443i 0.835975i −0.908453 0.417988i \(-0.862736\pi\)
0.908453 0.417988i \(-0.137264\pi\)
\(542\) 10.0199 + 5.78497i 0.430390 + 0.248486i
\(543\) 0 0
\(544\) 4.10150 2.36800i 0.175851 0.101527i
\(545\) −36.4984 + 9.65369i −1.56342 + 0.413518i
\(546\) 0 0
\(547\) 25.2121i 1.07799i −0.842308 0.538997i \(-0.818803\pi\)
0.842308 0.538997i \(-0.181197\pi\)
\(548\) 7.35746 + 12.7435i 0.314295 + 0.544375i
\(549\) 0 0
\(550\) 25.7598 + 0.166140i 1.09840 + 0.00708425i
\(551\) 10.1541i 0.432580i
\(552\) 0 0
\(553\) 8.19440 14.1931i 0.348462 0.603553i
\(554\) 12.9454i 0.549998i
\(555\) 0 0
\(556\) −7.82540 13.5540i −0.331871 0.574817i
\(557\) −5.63445 9.75916i −0.238739 0.413509i 0.721613 0.692296i \(-0.243401\pi\)
−0.960353 + 0.278787i \(0.910067\pi\)
\(558\) 0 0
\(559\) 1.05345 + 7.03856i 0.0445560 + 0.297699i
\(560\) 0.689710 + 2.60764i 0.0291456 + 0.110193i
\(561\) 0 0
\(562\) −2.22730 + 1.28593i −0.0939531 + 0.0542439i
\(563\) 14.2495 + 8.22694i 0.600544 + 0.346724i 0.769256 0.638941i \(-0.220627\pi\)
−0.168712 + 0.985665i \(0.553961\pi\)
\(564\) 0 0
\(565\) 2.89981 10.6843i 0.121996 0.449491i
\(566\) 4.80517 + 2.77427i 0.201976 + 0.116611i
\(567\) 0 0
\(568\) −0.298707 0.172459i −0.0125335 0.00723621i
\(569\) −15.2444 26.4040i −0.639077 1.10691i −0.985636 0.168886i \(-0.945983\pi\)
0.346558 0.938028i \(-0.387350\pi\)
\(570\) 0 0
\(571\) 13.0909 0.547836 0.273918 0.961753i \(-0.411680\pi\)
0.273918 + 0.961753i \(0.411680\pi\)
\(572\) −14.5353 + 11.5669i −0.607751 + 0.483638i
\(573\) 0 0
\(574\) 4.94754 2.85646i 0.206506 0.119226i
\(575\) 5.49615 9.37939i 0.229205 0.391147i
\(576\) 0 0
\(577\) 13.1315 0.546670 0.273335 0.961919i \(-0.411873\pi\)
0.273335 + 0.961919i \(0.411873\pi\)
\(578\) −2.71489 + 4.70233i −0.112925 + 0.195591i
\(579\) 0 0
\(580\) 2.72558 + 10.3048i 0.113174 + 0.427884i
\(581\) 6.15472 10.6603i 0.255341 0.442263i
\(582\) 0 0
\(583\) −11.5417 19.9908i −0.478009 0.827935i
\(584\) −15.7228 −0.650615
\(585\) 0 0
\(586\) 24.1316 0.996866
\(587\) 3.03785 + 5.26171i 0.125386 + 0.217174i 0.921884 0.387467i \(-0.126650\pi\)
−0.796498 + 0.604641i \(0.793317\pi\)
\(588\) 0 0
\(589\) −6.29499 + 10.9032i −0.259381 + 0.449260i
\(590\) 4.19685 1.11005i 0.172782 0.0457000i
\(591\) 0 0
\(592\) 2.20034 3.81110i 0.0904334 0.156635i
\(593\) 18.3609 0.753990 0.376995 0.926215i \(-0.376957\pi\)
0.376995 + 0.926215i \(0.376957\pi\)
\(594\) 0 0
\(595\) −9.00375 9.06201i −0.369118 0.371506i
\(596\) −19.7555 + 11.4058i −0.809215 + 0.467200i
\(597\) 0 0
\(598\) 1.16036 + 7.75290i 0.0474507 + 0.317040i
\(599\) −22.1098 −0.903382 −0.451691 0.892174i \(-0.649179\pi\)
−0.451691 + 0.892174i \(0.649179\pi\)
\(600\) 0 0
\(601\) −5.90349 10.2251i −0.240808 0.417092i 0.720136 0.693832i \(-0.244079\pi\)
−0.960945 + 0.276740i \(0.910746\pi\)
\(602\) 2.06205 + 1.19052i 0.0840428 + 0.0485222i
\(603\) 0 0
\(604\) −17.2335 9.94975i −0.701220 0.404850i
\(605\) 33.5434 + 9.10397i 1.36373 + 0.370129i
\(606\) 0 0
\(607\) −22.3119 12.8818i −0.905612 0.522856i −0.0265955 0.999646i \(-0.508467\pi\)
−0.879017 + 0.476791i \(0.841800\pi\)
\(608\) −1.84474 + 1.06506i −0.0748139 + 0.0431938i
\(609\) 0 0
\(610\) −1.75871 6.64928i −0.0712080 0.269222i
\(611\) −1.91349 2.40455i −0.0774117 0.0972775i
\(612\) 0 0
\(613\) −6.54178 11.3307i −0.264220 0.457642i 0.703139 0.711052i \(-0.251781\pi\)
−0.967359 + 0.253410i \(0.918448\pi\)
\(614\) −15.1621 26.2616i −0.611894 1.05983i
\(615\) 0 0
\(616\) 6.21480i 0.250401i
\(617\) −2.20914 + 3.82634i −0.0889366 + 0.154043i −0.907062 0.420997i \(-0.861680\pi\)
0.818125 + 0.575040i \(0.195014\pi\)
\(618\) 0 0
\(619\) 1.12760i 0.0453220i 0.999743 + 0.0226610i \(0.00721383\pi\)
−0.999743 + 0.0226610i \(0.992786\pi\)
\(620\) −3.46175 + 12.7548i −0.139027 + 0.512244i
\(621\) 0 0
\(622\) −4.38203 7.58990i −0.175703 0.304327i
\(623\) 19.7708i 0.792099i
\(624\) 0 0
\(625\) 12.7782 21.4876i 0.511129 0.859504i
\(626\) −25.1282 + 14.5077i −1.00432 + 0.579846i
\(627\) 0 0
\(628\) −4.10836 2.37196i −0.163941 0.0946515i
\(629\) 20.8417i 0.831011i
\(630\) 0 0
\(631\) −14.3916 8.30898i −0.572920 0.330775i 0.185395 0.982664i \(-0.440644\pi\)
−0.758315 + 0.651889i \(0.773977\pi\)
\(632\) 13.5863 0.540434
\(633\) 0 0
\(634\) −12.9985 22.5140i −0.516236 0.894147i
\(635\) −1.89426 1.90651i −0.0751712 0.0756576i
\(636\) 0 0
\(637\) 7.32331 18.6029i 0.290160 0.737072i
\(638\) 24.5595i 0.972320i
\(639\) 0 0
\(640\) −1.58623 + 1.57603i −0.0627012 + 0.0622981i
\(641\) −5.05184 + 8.75005i −0.199536 + 0.345606i −0.948378 0.317142i \(-0.897277\pi\)
0.748842 + 0.662748i \(0.230610\pi\)
\(642\) 0 0
\(643\) 17.5208 30.3469i 0.690951 1.19676i −0.280575 0.959832i \(-0.590525\pi\)
0.971526 0.236931i \(-0.0761415\pi\)
\(644\) 2.27133 + 1.31135i 0.0895028 + 0.0516745i
\(645\) 0 0
\(646\) 5.04413 8.73669i 0.198459 0.343740i
\(647\) −17.2864 + 9.98031i −0.679598 + 0.392366i −0.799704 0.600395i \(-0.795010\pi\)
0.120105 + 0.992761i \(0.461677\pi\)
\(648\) 0 0
\(649\) 10.0024 0.392628
\(650\) 2.55341 + 17.8460i 0.100153 + 0.699978i
\(651\) 0 0
\(652\) 1.93329 + 3.34855i 0.0757133 + 0.131139i
\(653\) 4.51410 2.60621i 0.176650 0.101989i −0.409068 0.912504i \(-0.634146\pi\)
0.585718 + 0.810515i \(0.300813\pi\)
\(654\) 0 0
\(655\) 3.80312 + 14.3787i 0.148600 + 0.561824i
\(656\) 4.10150 + 2.36800i 0.160137 + 0.0924551i
\(657\) 0 0
\(658\) −1.02810 −0.0400796
\(659\) −3.66183 + 6.34248i −0.142645 + 0.247068i −0.928492 0.371353i \(-0.878894\pi\)
0.785847 + 0.618421i \(0.212227\pi\)
\(660\) 0 0
\(661\) −31.7189 + 18.3129i −1.23372 + 0.712289i −0.967803 0.251707i \(-0.919008\pi\)
−0.265917 + 0.963996i \(0.585675\pi\)
\(662\) 11.0392i 0.429052i
\(663\) 0 0
\(664\) 10.2045 0.396012
\(665\) 4.04962 + 4.07583i 0.157038 + 0.158054i
\(666\) 0 0
\(667\) 8.97578 + 5.18217i 0.347543 + 0.200654i
\(668\) −22.7228 −0.879173
\(669\) 0 0
\(670\) −30.3313 8.23218i −1.17180 0.318037i
\(671\) 15.8473i 0.611777i
\(672\) 0 0
\(673\) −29.4292 + 16.9909i −1.13441 + 0.654952i −0.945041 0.326953i \(-0.893978\pi\)
−0.189370 + 0.981906i \(0.560645\pi\)
\(674\) 15.3380 8.85540i 0.590798 0.341097i
\(675\) 0 0
\(676\) −9.51136 8.86194i −0.365822 0.340844i
\(677\) 41.7902i 1.60613i −0.595894 0.803063i \(-0.703202\pi\)
0.595894 0.803063i \(-0.296798\pi\)
\(678\) 0 0
\(679\) 5.11628 + 8.86166i 0.196345 + 0.340079i
\(680\) 2.77388 10.2203i 0.106373 0.391931i
\(681\) 0 0
\(682\) −15.2255 + 26.3714i −0.583016 + 1.00981i
\(683\) 24.2071 41.9280i 0.926260 1.60433i 0.136737 0.990607i \(-0.456338\pi\)
0.789523 0.613721i \(-0.210328\pi\)
\(684\) 0 0
\(685\) 31.7548 + 8.61851i 1.21329 + 0.329296i
\(686\) −7.56629 13.1052i −0.288882 0.500359i
\(687\) 0 0
\(688\) 1.97389i 0.0752538i
\(689\) 12.6404 10.0590i 0.481562 0.383218i
\(690\) 0 0
\(691\) −23.8905 + 13.7932i −0.908837 + 0.524717i −0.880057 0.474868i \(-0.842496\pi\)
−0.0287804 + 0.999586i \(0.509162\pi\)
\(692\) −4.06859 + 2.34900i −0.154664 + 0.0892955i
\(693\) 0 0
\(694\) 34.7017i 1.31726i
\(695\) −33.7744 9.16666i −1.28114 0.347711i
\(696\) 0 0
\(697\) −22.4298 −0.849589
\(698\) −30.4563 17.5840i −1.15279 0.665563i
\(699\) 0 0
\(700\) 5.20376 + 3.04931i 0.196684 + 0.115253i
\(701\) 19.7883 0.747392 0.373696 0.927551i \(-0.378090\pi\)
0.373696 + 0.927551i \(0.378090\pi\)
\(702\) 0 0
\(703\) 9.37396i 0.353546i
\(704\) −4.46182 + 2.57603i −0.168161 + 0.0970879i
\(705\) 0 0
\(706\) −5.54542 + 9.60495i −0.208705 + 0.361487i
\(707\) 16.3841 0.616189
\(708\) 0 0
\(709\) −6.09389 3.51831i −0.228861 0.132133i 0.381186 0.924499i \(-0.375516\pi\)
−0.610046 + 0.792366i \(0.708849\pi\)
\(710\) −0.745619 + 0.197213i −0.0279826 + 0.00740128i
\(711\) 0 0
\(712\) 14.1941 8.19497i 0.531946 0.307119i
\(713\) 6.42532 + 11.1290i 0.240630 + 0.416783i
\(714\) 0 0
\(715\) −4.82646 + 41.2559i −0.180499 + 1.54288i
\(716\) −8.69827 −0.325069
\(717\) 0 0
\(718\) −22.6531 + 13.0788i −0.845405 + 0.488095i
\(719\) 5.52118 9.56296i 0.205905 0.356638i −0.744516 0.667605i \(-0.767319\pi\)
0.950421 + 0.310967i \(0.100653\pi\)
\(720\) 0 0
\(721\) 2.25330 + 1.30094i 0.0839171 + 0.0484496i
\(722\) 7.23130 12.5250i 0.269121 0.466131i
\(723\) 0 0
\(724\) −4.87740 + 8.44791i −0.181267 + 0.313964i
\(725\) 20.5641 + 12.0502i 0.763732 + 0.447533i
\(726\) 0 0
\(727\) 14.1056i 0.523147i −0.965184 0.261573i \(-0.915759\pi\)
0.965184 0.261573i \(-0.0842414\pi\)
\(728\) −4.30137 + 0.643777i −0.159419 + 0.0238600i
\(729\) 0 0
\(730\) −24.9400 + 24.7797i −0.923071 + 0.917137i
\(731\) −4.67418 8.09591i −0.172881 0.299438i
\(732\) 0 0
\(733\) 11.3855 0.420535 0.210267 0.977644i \(-0.432567\pi\)
0.210267 + 0.977644i \(0.432567\pi\)
\(734\) 13.4988 + 7.79352i 0.498249 + 0.287664i
\(735\) 0 0
\(736\) 2.17422i 0.0801427i
\(737\) −62.7122 36.2069i −2.31003 1.33370i
\(738\) 0 0
\(739\) −7.93251 + 4.57983i −0.291802 + 0.168472i −0.638754 0.769411i \(-0.720550\pi\)
0.346952 + 0.937883i \(0.387217\pi\)
\(740\) −2.51617 9.51308i −0.0924963 0.349708i
\(741\) 0 0
\(742\) 5.40461i 0.198410i
\(743\) 19.9566 + 34.5658i 0.732135 + 1.26809i 0.955969 + 0.293468i \(0.0948093\pi\)
−0.223834 + 0.974627i \(0.571857\pi\)
\(744\) 0 0
\(745\) −13.3607 + 49.2275i −0.489500 + 1.80355i
\(746\) 0.993455i 0.0363730i
\(747\) 0 0
\(748\) 12.2001 21.1312i 0.446080 0.772634i
\(749\) 9.76355i 0.356752i
\(750\) 0 0
\(751\) 8.79993 + 15.2419i 0.321114 + 0.556186i 0.980718 0.195427i \(-0.0626094\pi\)
−0.659604 + 0.751613i \(0.729276\pi\)
\(752\) −0.426148 0.738110i −0.0155400 0.0269161i
\(753\) 0 0
\(754\) −16.9981 + 2.54407i −0.619033 + 0.0926494i
\(755\) −43.0174 + 11.3779i −1.56556 + 0.414085i
\(756\) 0 0
\(757\) −19.1099 + 11.0331i −0.694560 + 0.401004i −0.805318 0.592843i \(-0.798005\pi\)
0.110758 + 0.993847i \(0.464672\pi\)
\(758\) 23.7856 + 13.7326i 0.863932 + 0.498791i
\(759\) 0 0
\(760\) −1.24761 + 4.59679i −0.0452555 + 0.166743i
\(761\) 17.4454 + 10.0721i 0.632394 + 0.365113i 0.781678 0.623682i \(-0.214364\pi\)
−0.149285 + 0.988794i \(0.547697\pi\)
\(762\) 0 0
\(763\) −17.6380 10.1833i −0.638538 0.368660i
\(764\) 5.77729 + 10.0066i 0.209015 + 0.362025i
\(765\) 0 0
\(766\) 32.5703 1.17681
\(767\) 1.03612 + 6.92282i 0.0374123 + 0.249969i
\(768\) 0 0
\(769\) 26.9356 15.5513i 0.971323 0.560794i 0.0716840 0.997427i \(-0.477163\pi\)
0.899639 + 0.436634i \(0.143829\pi\)
\(770\) 9.79472 + 9.85810i 0.352977 + 0.355261i
\(771\) 0 0
\(772\) −10.4631 −0.376575
\(773\) 0.416119 0.720739i 0.0149668 0.0259232i −0.858445 0.512906i \(-0.828569\pi\)
0.873412 + 0.486982i \(0.161902\pi\)
\(774\) 0 0
\(775\) 14.6108 + 25.6878i 0.524835 + 0.922734i
\(776\) −4.24139 + 7.34631i −0.152257 + 0.263717i
\(777\) 0 0
\(778\) 8.45549 + 14.6453i 0.303144 + 0.525061i
\(779\) 10.0883 0.361449
\(780\) 0 0
\(781\) −1.77704 −0.0635874
\(782\) −5.14856 8.91756i −0.184112 0.318891i
\(783\) 0 0
\(784\) 2.77245 4.80203i 0.0990161 0.171501i
\(785\) −10.2551 + 2.71243i −0.366019 + 0.0968106i
\(786\) 0 0
\(787\) −12.4115 + 21.4974i −0.442422 + 0.766298i −0.997869 0.0652545i \(-0.979214\pi\)
0.555446 + 0.831552i \(0.312547\pi\)
\(788\) −17.5894