Properties

Label 1170.2.bj.c.199.3
Level $1170$
Weight $2$
Character 1170.199
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 199.3
Root \(-0.330925 - 1.46916i\) of defining polynomial
Character \(\chi\) \(=\) 1170.199
Dual form 1170.2.bj.c.829.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.571769 - 2.16173i) q^{5} +(0.603137 + 1.04466i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.571769 - 2.16173i) q^{5} +(0.603137 + 1.04466i) q^{7} +1.00000 q^{8} +(2.15800 + 0.585699i) q^{10} +(-4.46182 - 2.57603i) q^{11} +(2.24511 - 2.82126i) q^{13} -1.20627 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.10150 + 2.36800i) q^{17} +(-1.84474 + 1.06506i) q^{19} +(-1.58623 + 1.57603i) q^{20} +(4.46182 - 2.57603i) q^{22} +(1.88293 + 1.08711i) q^{23} +(-4.34616 + 2.47202i) q^{25} +(1.32073 + 3.35495i) q^{26} +(0.603137 - 1.04466i) q^{28} +(-2.38346 + 4.12828i) q^{29} +5.91046i q^{31} +(-0.500000 - 0.866025i) q^{32} -4.73601i q^{34} +(1.91343 - 1.90113i) q^{35} +(-2.20034 + 3.81110i) q^{37} -2.13012i q^{38} +(-0.571769 - 2.16173i) q^{40} +(-4.10150 - 2.36800i) q^{41} +(1.70944 - 0.986944i) q^{43} +5.15206i q^{44} +(-1.88293 + 1.08711i) q^{46} -0.852296 q^{47} +(2.77245 - 4.80203i) q^{49} +(0.0322474 - 4.99990i) q^{50} +(-3.56583 - 0.533691i) q^{52} +4.48042i q^{53} +(-3.01756 + 11.1181i) q^{55} +(0.603137 + 1.04466i) q^{56} +(-2.38346 - 4.12828i) q^{58} +(-1.68133 + 0.970715i) q^{59} +(-1.53795 - 2.66381i) q^{61} +(-5.11861 - 2.95523i) q^{62} +1.00000 q^{64} +(-7.38248 - 3.24021i) q^{65} +(-7.02765 + 12.1723i) q^{67} +(4.10150 + 2.36800i) q^{68} +(0.689710 + 2.60764i) q^{70} +(0.298707 - 0.172459i) q^{71} -15.7228 q^{73} +(-2.20034 - 3.81110i) q^{74} +(1.84474 + 1.06506i) q^{76} -6.21480i q^{77} -13.5863 q^{79} +(2.15800 + 0.585699i) q^{80} +(4.10150 - 2.36800i) q^{82} +10.2045 q^{83} +(7.46410 + 7.51240i) q^{85} +1.97389i q^{86} +(-4.46182 - 2.57603i) q^{88} +(-14.1941 - 8.19497i) q^{89} +(4.30137 + 0.643777i) q^{91} -2.17422i q^{92} +(0.426148 - 0.738110i) q^{94} +(3.35713 + 3.37886i) q^{95} +(-4.24139 - 7.34631i) q^{97} +(2.77245 + 4.80203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + O(q^{10}) \) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98} + O(q^{100}) \)

Character values

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

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

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 \(-0.0934597\pi\)
−0.729240 + 0.684258i \(0.760126\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 2.15800 + 0.585699i 0.682419 + 0.185214i
\(11\) −4.46182 2.57603i −1.34529 0.776703i −0.357711 0.933832i \(-0.616443\pi\)
−0.987578 + 0.157130i \(0.949776\pi\)
\(12\) 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 \(-0.861402\pi\)
−0.0880670 + 0.996115i \(0.528069\pi\)
\(18\) 0 0
\(19\) −1.84474 + 1.06506i −0.423212 + 0.244341i −0.696450 0.717605i \(-0.745238\pi\)
0.273239 + 0.961946i \(0.411905\pi\)
\(20\) −1.58623 + 1.57603i −0.354692 + 0.352411i
\(21\) 0 0
\(22\) 4.46182 2.57603i 0.951263 0.549212i
\(23\) 1.88293 + 1.08711i 0.392618 + 0.226678i 0.683294 0.730144i \(-0.260547\pi\)
−0.290676 + 0.956822i \(0.593880\pi\)
\(24\) 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 −0.997881 0.0650589i \(-0.979276\pi\)
0.555283 + 0.831661i \(0.312610\pi\)
\(30\) 0 0
\(31\) 5.91046i 1.06155i 0.847513 + 0.530775i \(0.178099\pi\)
−0.847513 + 0.530775i \(0.821901\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 4.73601i 0.812219i
\(35\) 1.91343 1.90113i 0.323428 0.321349i
\(36\) 0 0
\(37\) −2.20034 + 3.81110i −0.361734 + 0.626541i −0.988246 0.152870i \(-0.951148\pi\)
0.626513 + 0.779411i \(0.284482\pi\)
\(38\) 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 0.144278 0.989537i \(-0.453914\pi\)
−0.784825 + 0.619717i \(0.787247\pi\)
\(42\) 0 0
\(43\) 1.70944 0.986944i 0.260687 0.150508i −0.363961 0.931414i \(-0.618576\pi\)
0.624648 + 0.780907i \(0.285243\pi\)
\(44\) 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 \(-0.519799\pi\)
−0.0621600 + 0.998066i \(0.519799\pi\)
\(48\) 0 0
\(49\) 2.77245 4.80203i 0.396065 0.686004i
\(50\) 0.0322474 4.99990i 0.00456046 0.707092i
\(51\) 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
\(55\) −3.01756 + 11.1181i −0.406888 + 1.49917i
\(56\) 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 −0.605436 0.795894i \(-0.707001\pi\)
0.386546 + 0.922270i \(0.373668\pi\)
\(60\) 0 0
\(61\) −1.53795 2.66381i −0.196915 0.341066i 0.750612 0.660744i \(-0.229759\pi\)
−0.947527 + 0.319677i \(0.896426\pi\)
\(62\) −5.11861 2.95523i −0.650064 0.375315i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −7.38248 3.24021i −0.915684 0.401899i
\(66\) 0 0
\(67\) −7.02765 + 12.1723i −0.858564 + 1.48708i 0.0147340 + 0.999891i \(0.495310\pi\)
−0.873298 + 0.487186i \(0.838023\pi\)
\(68\) 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 −0.482170 0.876078i \(-0.660151\pi\)
0.517620 + 0.855610i \(0.326818\pi\)
\(72\) 0 0
\(73\) −15.7228 −1.84022 −0.920109 0.391662i \(-0.871900\pi\)
−0.920109 + 0.391662i \(0.871900\pi\)
\(74\) −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 \(0.776910\pi\)
\(80\) 2.15800 + 0.585699i 0.241272 + 0.0654831i
\(81\) 0 0
\(82\) 4.10150 2.36800i 0.452935 0.261502i
\(83\) 10.2045 1.12009 0.560046 0.828462i \(-0.310784\pi\)
0.560046 + 0.828462i \(0.310784\pi\)
\(84\) 0 0
\(85\) 7.46410 + 7.51240i 0.809595 + 0.814834i
\(86\) 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 −0.999986 0.00530346i \(-0.998312\pi\)
−0.504586 0.863361i \(-0.668355\pi\)
\(90\) 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
\(95\) 3.35713 + 3.37886i 0.344435 + 0.346663i
\(96\) 0 0
\(97\) −4.24139 7.34631i −0.430648 0.745904i 0.566281 0.824212i \(-0.308382\pi\)
−0.996929 + 0.0783078i \(0.975048\pi\)
\(98\) 2.77245 + 4.80203i 0.280060 + 0.485078i
\(99\) 0 0
\(100\) 4.31391 + 2.52788i 0.431391 + 0.252788i
\(101\) −6.79121 + 11.7627i −0.675751 + 1.17044i 0.300498 + 0.953783i \(0.402847\pi\)
−0.976249 + 0.216653i \(0.930486\pi\)
\(102\) 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 \(-0.205381\pi\)
−0.121324 + 0.992613i \(0.538714\pi\)
\(108\) 0 0
\(109\) 16.8839i 1.61718i −0.588370 0.808592i \(-0.700230\pi\)
0.588370 0.808592i \(-0.299770\pi\)
\(110\) −8.11982 8.17235i −0.774194 0.779203i
\(111\) 0 0
\(112\) −1.20627 −0.113982
\(113\) 4.28771 2.47551i 0.403354 0.232876i −0.284576 0.958653i \(-0.591853\pi\)
0.687930 + 0.725777i \(0.258520\pi\)
\(114\) 0 0
\(115\) 1.27344 4.69196i 0.118749 0.437527i
\(116\) 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 \(-0.316351\pi\)
−0.453107 + 0.891456i \(0.649684\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 6.49734 4.77331i 0.569855 0.418647i
\(131\) 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 −0.987835 0.155507i \(-0.950299\pi\)
0.359245 0.933243i \(-0.383034\pi\)
\(138\) 0 0
\(139\) −7.82540 13.5540i −0.663742 1.14963i −0.979625 0.200837i \(-0.935634\pi\)
0.315883 0.948798i \(-0.397699\pi\)
\(140\) −2.60314 0.706513i −0.220005 0.0597113i
\(141\) 0 0
\(142\) 0.344918i 0.0289448i
\(143\) −17.2849 + 6.80447i −1.44544 + 0.569018i
\(144\) 0 0
\(145\) 10.2870 + 2.79198i 0.854290 + 0.231862i
\(146\) 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 0.631103 0.775699i \(-0.282602\pi\)
0.987327 0.158702i \(-0.0507309\pi\)
\(150\) 0 0
\(151\) 19.8995i 1.61940i −0.586845 0.809699i \(-0.699630\pi\)
0.586845 0.809699i \(-0.300370\pi\)
\(152\) −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
\(160\) −1.58623 + 1.57603i −0.125402 + 0.124596i
\(161\) 2.62270i 0.206698i
\(162\) 0 0
\(163\) −1.93329 3.34855i −0.151427 0.262279i 0.780325 0.625374i \(-0.215053\pi\)
−0.931752 + 0.363095i \(0.881720\pi\)
\(164\) 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 −0.0269225 + 0.999638i \(0.508571\pi\)
−0.852250 + 0.523134i \(0.824763\pi\)
\(168\) 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 \(-0.723821\pi\)
0.337297 + 0.941398i \(0.390487\pi\)
\(174\) 0 0
\(175\) −5.20376 3.04931i −0.393367 0.230506i
\(176\) 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 −0.656457 0.754363i \(-0.727946\pi\)
0.981526 + 0.191327i \(0.0612790\pi\)
\(180\) 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
\(185\) 9.49666 + 2.57747i 0.698208 + 0.189500i
\(186\) 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 0.995741 0.0921920i \(-0.0293874\pi\)
−0.577711 + 0.816241i \(0.696054\pi\)
\(192\) 0 0
\(193\) −5.23154 + 9.06130i −0.376575 + 0.652247i −0.990561 0.137070i \(-0.956232\pi\)
0.613987 + 0.789316i \(0.289565\pi\)
\(194\) 8.48278 0.609028
\(195\) 0 0
\(196\) −5.54490 −0.396065
\(197\) −8.79472 + 15.2329i −0.626598 + 1.08530i 0.361632 + 0.932321i \(0.382220\pi\)
−0.988230 + 0.152978i \(0.951113\pi\)
\(198\) 0 0
\(199\) 12.7858 + 22.1457i 0.906362 + 1.56986i 0.819079 + 0.573681i \(0.194485\pi\)
0.0872828 + 0.996184i \(0.472182\pi\)
\(200\) −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
\(205\) −2.77388 + 10.2203i −0.193736 + 0.713817i
\(206\) 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 −0.998032 0.0627029i \(-0.980028\pi\)
0.553318 + 0.832970i \(0.313361\pi\)
\(212\) 3.88016 2.24021i 0.266490 0.153858i
\(213\) 0 0
\(214\) −7.00959 + 4.04699i −0.479165 + 0.276646i
\(215\) −3.11091 3.13104i −0.212162 0.213535i
\(216\) 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 \(-0.756343\pi\)
0.960576 + 0.278016i \(0.0896768\pi\)
\(224\) 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 0.874325 + 0.485340i \(0.161304\pi\)
−0.0168460 + 0.999858i \(0.505362\pi\)
\(228\) 0 0
\(229\) 8.95153i 0.591533i −0.955260 0.295767i \(-0.904425\pi\)
0.955260 0.295767i \(-0.0955751\pi\)
\(230\) 3.42664 + 3.44881i 0.225946 + 0.227408i
\(231\) 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 \(-0.833832\pi\)
0.866807 0.498643i \(-0.166168\pi\)
\(240\) 0 0
\(241\) 9.76603 5.63842i 0.629085 0.363203i −0.151312 0.988486i \(-0.548350\pi\)
0.780398 + 0.625283i \(0.215017\pi\)
\(242\) −15.5438 −0.999191
\(243\) 0 0
\(244\) −1.53795 + 2.66381i −0.0984574 + 0.170533i
\(245\) −11.9659 3.24764i −0.764473 0.207484i
\(246\) 0 0
\(247\) −1.13682 + 7.59565i −0.0723344 + 0.483299i
\(248\) 5.91046i 0.375315i
\(249\) 0 0
\(250\) −10.8269 + 2.78907i −0.684751 + 0.176397i
\(251\) −6.15329 10.6578i −0.388392 0.672715i 0.603841 0.797104i \(-0.293636\pi\)
−0.992233 + 0.124390i \(0.960303\pi\)
\(252\) 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 −0.999794 0.0203154i \(-0.993533\pi\)
−0.517490 0.855689i \(-0.673134\pi\)
\(258\) 0 0
\(259\) −5.30842 −0.329849
\(260\) 0.885137 + 8.01352i 0.0548939 + 0.496978i
\(261\) 0 0
\(262\) −3.32575 + 5.76036i −0.205465 + 0.355876i
\(263\) −6.56756 3.79178i −0.404973 0.233811i 0.283654 0.958927i \(-0.408453\pi\)
−0.688628 + 0.725115i \(0.741787\pi\)
\(264\) 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 0.949722 + 0.313096i \(0.101366\pi\)
−0.203712 + 0.979031i \(0.565301\pi\)
\(270\) 0 0
\(271\) 10.0199 + 5.78497i 0.608664 + 0.351412i 0.772442 0.635085i \(-0.219035\pi\)
−0.163779 + 0.986497i \(0.552368\pi\)
\(272\) 4.73601i 0.287163i
\(273\) 0 0
\(274\) 14.7149 0.888961
\(275\) 25.7598 + 0.166140i 1.55337 + 0.0100186i
\(276\) 0 0
\(277\) −11.2111 + 6.47271i −0.673608 + 0.388908i −0.797442 0.603395i \(-0.793814\pi\)
0.123835 + 0.992303i \(0.460481\pi\)
\(278\) 15.6508 0.938673
\(279\) 0 0
\(280\) 1.91343 1.90113i 0.114349 0.113614i
\(281\) 2.57187i 0.153425i −0.997053 0.0767124i \(-0.975558\pi\)
0.997053 0.0767124i \(-0.0244423\pi\)
\(282\) 0 0
\(283\) −4.80517 2.77427i −0.285638 0.164913i 0.350335 0.936624i \(-0.386068\pi\)
−0.635973 + 0.771711i \(0.719401\pi\)
\(284\) −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
\(290\) −7.56144 + 7.51283i −0.444023 + 0.441168i
\(291\) 0 0
\(292\) 7.86142 + 13.6164i 0.460055 + 0.796838i
\(293\) −12.0658 20.8986i −0.704891 1.22091i −0.966731 0.255795i \(-0.917663\pi\)
0.261840 0.965111i \(-0.415671\pi\)
\(294\) 0 0
\(295\) 3.05976 + 3.07955i 0.178146 + 0.179299i
\(296\) −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
\(305\) −4.87910 + 4.84773i −0.279376 + 0.277580i
\(306\) 0 0
\(307\) 30.3243 1.73070 0.865348 0.501171i \(-0.167097\pi\)
0.865348 + 0.501171i \(0.167097\pi\)
\(308\) −5.38217 + 3.10740i −0.306678 + 0.177061i
\(309\) 0 0
\(310\) −3.46175 + 12.7548i −0.196614 + 0.724422i
\(311\) −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 \(-0.239489\pi\)
0.730068 + 0.683375i \(0.239489\pi\)
\(318\) 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
\(325\) −2.78339 + 17.8116i −0.154395 + 0.988009i
\(326\) 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 −0.739173 0.673515i \(-0.764784\pi\)
0.213694 + 0.976901i \(0.431450\pi\)
\(332\) −5.10226 8.83737i −0.280023 0.485014i
\(333\) 0 0
\(334\) −11.3614 19.6785i −0.621669 1.07676i
\(335\) 30.3313 + 8.23218i 1.65718 + 0.449772i
\(336\) 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
\(340\) 2.77388 10.2203i 0.150435 0.554274i
\(341\) 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 0.624710 0.780857i \(-0.285217\pi\)
0.988597 0.150587i \(-0.0481162\pi\)
\(348\) 0 0
\(349\) −30.4563 17.5840i −1.63029 0.941249i −0.984002 0.178156i \(-0.942987\pi\)
−0.646288 0.763093i \(-0.723680\pi\)
\(350\) 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 \(-0.928704\pi\)
0.679868 + 0.733335i \(0.262037\pi\)
\(354\) 0 0
\(355\) −0.543601 0.547118i −0.0288513 0.0290380i
\(356\) 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 \(-0.757492\pi\)
0.723552 0.690270i \(-0.242508\pi\)
\(360\) 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 \(-0.466695\pi\)
−0.809070 + 0.587713i \(0.800028\pi\)
\(368\) −1.88293 + 1.08711i −0.0981544 + 0.0566695i
\(369\) 0 0
\(370\) −6.98049 + 6.93561i −0.362898 + 0.360565i
\(371\) −4.68053 + 2.70231i −0.243001 + 0.140297i
\(372\) 0 0
\(373\) −0.860358 + 0.496728i −0.0445476 + 0.0257196i −0.522108 0.852879i \(-0.674854\pi\)
0.477561 + 0.878599i \(0.341521\pi\)
\(374\) −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 0.965298 0.261150i \(-0.0841018\pi\)
0.256486 + 0.966548i \(0.417435\pi\)
\(380\) 1.24761 4.59679i 0.0640009 0.235810i
\(381\) 0 0
\(382\) −11.5546 −0.591184
\(383\) −16.2851 28.2067i −0.832132 1.44130i −0.896344 0.443359i \(-0.853787\pi\)
0.0642122 0.997936i \(-0.479547\pi\)
\(384\) 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 −0.913536 0.406759i \(-0.866659\pi\)
0.104504 0.994524i \(-0.466674\pi\)
\(398\) −25.5716 −1.28179
\(399\) 0 0
\(400\) 0.0322474 4.99990i 0.00161237 0.249995i
\(401\) −28.0082 16.1705i −1.39866 0.807518i −0.404410 0.914578i \(-0.632523\pi\)
−0.994253 + 0.107060i \(0.965856\pi\)
\(402\) 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 −0.474829 0.880078i \(-0.657490\pi\)
0.524756 + 0.851253i \(0.324157\pi\)
\(410\) −7.46410 7.51240i −0.368626 0.371011i
\(411\) 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 −0.973551 0.228469i \(-0.926628\pi\)
0.684635 + 0.728886i \(0.259961\pi\)
\(420\) 0 0
\(421\) 23.9102i 1.16531i −0.812719 0.582655i \(-0.802014\pi\)
0.812719 0.582655i \(-0.197986\pi\)
\(422\) −6.45984 11.1888i −0.314460 0.544661i
\(423\) 0 0
\(424\) 4.48042i 0.217588i
\(425\) 11.9720 20.4307i 0.580729 0.991036i
\(426\) 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 0.935861 0.352370i \(-0.114624\pi\)
0.162769 + 0.986664i \(0.447957\pi\)
\(432\) 0 0
\(433\) −11.2232 + 6.47972i −0.539353 + 0.311396i −0.744817 0.667269i \(-0.767463\pi\)
0.205464 + 0.978665i \(0.434130\pi\)
\(434\) 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 −0.443167 0.896439i \(-0.646145\pi\)
0.997922 0.0644259i \(-0.0205216\pi\)
\(440\) −3.01756 + 11.1181i −0.143856 + 0.530037i
\(441\) 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
\(445\) −9.59957 + 35.3695i −0.455063 + 1.67667i
\(446\) 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 −0.528264 0.849080i \(-0.677157\pi\)
0.471193 + 0.882030i \(0.343824\pi\)
\(450\) 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
\(455\) −1.06772 9.66650i −0.0500554 0.453173i
\(456\) 0 0
\(457\) −3.60093 + 6.23699i −0.168444 + 0.291754i −0.937873 0.346979i \(-0.887208\pi\)
0.769429 + 0.638733i \(0.220541\pi\)
\(458\) 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 −0.401246 0.915970i \(-0.631423\pi\)
0.592630 + 0.805474i \(0.298089\pi\)
\(462\) 0 0
\(463\) −15.7510 −0.732012 −0.366006 0.930612i \(-0.619275\pi\)
−0.366006 + 0.930612i \(0.619275\pi\)
\(464\) −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
\(470\) −1.83925 0.499189i −0.0848384 0.0230259i
\(471\) 0 0
\(472\) −1.68133 + 0.970715i −0.0773894 + 0.0446808i
\(473\) −10.1696 −0.467598
\(474\) 0 0
\(475\) 5.38467 9.18914i 0.247066 0.421627i
\(476\) 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 0.433722 0.901047i \(-0.357200\pi\)
−0.563468 + 0.826138i \(0.690533\pi\)
\(480\) 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
\(485\) −13.4556 + 13.3691i −0.610989 + 0.607061i
\(486\) 0 0
\(487\) 4.98852 + 8.64037i 0.226052 + 0.391533i 0.956634 0.291291i \(-0.0940849\pi\)
−0.730583 + 0.682824i \(0.760752\pi\)
\(488\) −1.53795 2.66381i −0.0696199 0.120585i
\(489\) 0 0
\(490\) 8.79549 8.73894i 0.397340 0.394785i
\(491\) −10.0376 + 17.3857i −0.452992 + 0.784605i −0.998570 0.0534548i \(-0.982977\pi\)
0.545578 + 0.838060i \(0.316310\pi\)
\(492\) 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 \(0.180071\pi\)
−0.844208 + 0.536016i \(0.819929\pi\)
\(500\) 2.99802 10.7709i 0.134076 0.481688i
\(501\) 0 0
\(502\) 12.3066 0.549269
\(503\) 10.5377 6.08395i 0.469853 0.271270i −0.246325 0.969187i \(-0.579223\pi\)
0.716178 + 0.697917i \(0.245890\pi\)
\(504\) 0 0
\(505\) 29.3109 + 7.95522i 1.30432 + 0.354002i
\(506\) 11.2017 0.497977
\(507\) 0 0
\(508\) 1.20191i 0.0533263i
\(509\) −34.9666 20.1880i −1.54987 0.894817i −0.998151 0.0607857i \(-0.980639\pi\)
−0.551717 0.834031i \(-0.686027\pi\)
\(510\) 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
\(520\) −7.38248 3.24021i −0.323743 0.142093i
\(521\) 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 \(-0.0132081\pi\)
0.463645 + 0.886021i \(0.346541\pi\)
\(524\) −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
\(530\) −2.62418 + 9.66874i −0.113987 + 0.419983i
\(531\) 0 0
\(532\) 2.56951i 0.111402i
\(533\) −15.8891 + 6.25498i −0.688232 + 0.270933i
\(534\) 0 0
\(535\) 4.74063 17.4668i 0.204955 0.755155i
\(536\) −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 \(0.137264\pi\)
−0.908453 + 0.417988i \(0.862736\pi\)
\(542\) −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
\(550\) −13.0238 + 22.2256i −0.555336 + 0.947701i
\(551\) 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 \(-0.756599\pi\)
0.960353 + 0.278787i \(0.0899325\pi\)
\(558\) 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 \(-0.779373\pi\)
0.168712 + 0.985665i \(0.446039\pi\)
\(564\) 0 0
\(565\) −7.80296 7.85345i −0.328273 0.330397i
\(566\) 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 0.346558 + 0.938028i \(0.387350\pi\)
−0.985636 + 0.168886i \(0.945983\pi\)
\(570\) 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
\(575\) −10.8709 0.0701128i −0.453346 0.00292390i
\(576\) 0 0
\(577\) −13.1315 −0.546670 −0.273335 0.961919i \(-0.588127\pi\)
−0.273335 + 0.961919i \(0.588127\pi\)
\(578\) 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 \(-0.873350\pi\)
0.796498 + 0.604641i \(0.206683\pi\)
\(588\) 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 \(-0.623043\pi\)
−0.376995 + 0.926215i \(0.623043\pi\)
\(594\) 0 0
\(595\) −3.34605 + 12.3285i −0.137175 + 0.505418i
\(596\) −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 −0.960945 0.276740i \(-0.910746\pi\)
0.720136 + 0.693832i \(0.244079\pi\)
\(602\) −2.06205 + 1.19052i −0.0840428 + 0.0485222i
\(603\) 0 0
\(604\) −17.2335 + 9.94975i −0.701220 + 0.404850i
\(605\) 24.6560 24.4975i 1.00241 0.995963i
\(606\) 0 0
\(607\) 22.3119 12.8818i 0.905612 0.522856i 0.0265955 0.999646i \(-0.491533\pi\)
0.879017 + 0.476791i \(0.158200\pi\)
\(608\) 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 \(-0.748219\pi\)
0.967359 + 0.253410i \(0.0815522\pi\)
\(614\) −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 \(-0.138320\pi\)
−0.818125 + 0.575040i \(0.804986\pi\)
\(618\) 0 0
\(619\) 1.12760i 0.0453220i −0.999743 0.0226610i \(-0.992786\pi\)
0.999743 0.0226610i \(-0.00721383\pi\)
\(620\) −9.31508 9.37535i −0.374103 0.376523i
\(621\) 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 −0.758315 0.651889i \(-0.773977\pi\)
0.185395 + 0.982664i \(0.440644\pi\)
\(632\) −13.5863 −0.540434
\(633\) 0 0
\(634\) −12.9985 + 22.5140i −0.516236 + 0.894147i
\(635\) 0.703960 2.59373i 0.0279358 0.102929i
\(636\) 0 0
\(637\) −7.32331 18.6029i −0.290160 0.737072i
\(638\) 24.5595i 0.972320i
\(639\) 0 0
\(640\) 2.15800 + 0.585699i 0.0853024 + 0.0231518i
\(641\) −5.05184 8.75005i −0.199536 0.345606i 0.748842 0.662748i \(-0.230610\pi\)
−0.948378 + 0.317142i \(0.897277\pi\)
\(642\) 0 0
\(643\) −17.5208 30.3469i −0.690951 1.19676i −0.971526 0.236931i \(-0.923858\pi\)
0.280575 0.959832i \(-0.409475\pi\)
\(644\) 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 \(-0.204990\pi\)
−0.120105 + 0.992761i \(0.538323\pi\)
\(648\) 0 0
\(649\) 10.0024 0.392628
\(650\) −14.0336 11.3163i −0.550443 0.443861i
\(651\) 0 0
\(652\) −1.93329 + 3.34855i −0.0757133 + 0.131139i
\(653\) −4.51410 2.60621i −0.176650 0.101989i 0.409068 0.912504i \(-0.365854\pi\)
−0.585718 + 0.810515i \(0.699187\pi\)
\(654\) 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 0.785847 0.618421i \(-0.212227\pi\)
−0.928492 + 0.371353i \(0.878894\pi\)
\(660\) 0 0
\(661\) −31.7189 18.3129i −1.23372 0.712289i −0.265917 0.963996i \(-0.585675\pi\)
−0.967803 + 0.251707i \(0.919008\pi\)
\(662\) 11.0392i 0.429052i
\(663\) 0 0
\(664\) 10.2045 0.396012
\(665\) −1.50496 + 5.54499i −0.0583597 + 0.215025i
\(666\) 0 0
\(667\) −8.97578 + 5.18217i −0.347543 + 0.200654i
\(668\) 22.7228 0.879173
\(669\) 0 0
\(670\) −22.2949 + 22.1516i −0.861329 + 0.855791i
\(671\) 15.8473i 0.611777i
\(672\) 0 0
\(673\) 29.4292 + 16.9909i 1.13441 + 0.654952i 0.945041 0.326953i \(-0.106022\pi\)
0.189370 + 0.981906i \(0.439355\pi\)
\(674\) 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
\(680\) 7.46410 + 7.51240i 0.286235 + 0.288087i
\(681\) 0 0
\(682\) 15.2255 + 26.3714i 0.583016 + 1.00981i
\(683\) −24.2071 41.9280i −0.926260 1.60433i −0.789523 0.613721i \(-0.789672\pi\)
−0.136737 0.990607i \(-0.543662\pi\)
\(684\) 0 0
\(685\) −23.3412 + 23.1912i −0.891823 + 0.886089i
\(686\) −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 −0.0287804 0.999586i \(-0.509162\pi\)
−0.880057 + 0.474868i \(0.842496\pi\)
\(692\) 4.06859 + 2.34900i 0.154664 + 0.0892955i
\(693\) 0 0
\(694\) 34.7017i 1.31726i
\(695\) −24.8258 + 24.6662i −0.941695 + 0.935641i
\(696\) 0 0
\(697\) 22.4298 0.849589
\(698\) 30.4563 17.5840i 1.15279 0.665563i
\(699\) 0 0
\(700\) −0.0388991 + 6.03124i −0.00147025 + 0.227960i
\(701\) 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 −0.610046 0.792366i \(-0.708849\pi\)
0.381186 + 0.924499i \(0.375516\pi\)
\(710\) 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
\(715\) 24.5924 + 33.4747i 0.919704 + 1.25188i
\(716\) −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 0.950421 0.310967i \(-0.100653\pi\)
−0.744516 + 0.667605i \(0.767319\pi\)
\(720\) 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
\(725\) 0.153721 23.8341i 0.00570905 0.885178i
\(726\) 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
\(730\) −33.9298 9.20885i −1.25580 0.340835i
\(731\) −4.67418 + 8.09591i −0.172881 + 0.299438i
\(732\) 0 0
\(733\) −11.3855 −0.420535 −0.210267 0.977644i \(-0.567433\pi\)
−0.210267 + 0.977644i \(0.567433\pi\)
\(734\) 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 0.346952 0.937883i \(-0.387217\pi\)
−0.638754 + 0.769411i \(0.720550\pi\)
\(740\) −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 0.223834 + 0.974627i \(0.428143\pi\)
−0.955969 + 0.293468i \(0.905191\pi\)
\(744\) 0 0
\(745\) −35.9519 36.1845i −1.31717 1.32570i
\(746\) 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 −0.659604 0.751613i \(-0.729276\pi\)
0.980718 + 0.195427i \(0.0626094\pi\)
\(752\) 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 \(-0.201995\pi\)
−0.110758 + 0.993847i \(0.535328\pi\)
\(758\) −23.7856 + 13.7326i −0.863932 + 0.498791i
\(759\) 0 0
\(760\) 3.35713 + 3.37886i 0.121776 + 0.122564i
\(761\) 17.4454 10.0721i 0.632394 0.365113i −0.149285 0.988794i \(-0.547697\pi\)
0.781678 + 0.623682i \(0.214364\pi\)
\(762\) 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 0.899639 0.436634i \(-0.143829\pi\)
0.0716840 + 0.997427i \(0.477163\pi\)
\(770\) 3.64000 13.4115i 0.131177 0.483318i
\(771\) 0 0
\(772\) 10.4631 0.376575
\(773\) −0.416119 0.720739i −0.0149668 0.0259232i 0.858445 0.512906i \(-0.171431\pi\)
−0.873412 + 0.486982i \(0.838098\pi\)
\(774\) 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 \(-0.0207859\pi\)
−0.555446 + 0.831552i \(0.687453\pi\)