Properties

Label 819.2.n.d.172.2
Level $819$
Weight $2$
Character 819.172
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.n (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 172.2
Root \(1.16700 + 2.02131i\) of defining polynomial
Character \(\chi\) \(=\) 819.172
Dual form 819.2.n.d.100.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.952780 + 1.65026i) q^{2} +(-0.815580 - 1.41263i) q^{4} +(-0.736565 - 1.27577i) q^{5} +(-2.62736 - 0.311376i) q^{7} -0.702849 q^{8} +O(q^{10})\) \(q+(-0.952780 + 1.65026i) q^{2} +(-0.815580 - 1.41263i) q^{4} +(-0.736565 - 1.27577i) q^{5} +(-2.62736 - 0.311376i) q^{7} -0.702849 q^{8} +2.80714 q^{10} +4.39361 q^{11} +(2.69752 + 2.39236i) q^{13} +(3.01715 - 4.03917i) q^{14} +(2.30082 - 3.98514i) q^{16} +(-0.601356 - 1.04158i) q^{17} +3.24209 q^{19} +(-1.20145 + 2.08098i) q^{20} +(-4.18615 + 7.25062i) q^{22} +(-2.21855 + 3.84264i) q^{23} +(1.41494 - 2.45075i) q^{25} +(-6.51816 + 2.17223i) q^{26} +(1.70297 + 3.96543i) q^{28} +(0.0837807 + 0.145112i) q^{29} +(-2.62272 + 4.54268i) q^{31} +(3.68150 + 6.37655i) q^{32} +2.29184 q^{34} +(1.53798 + 3.58126i) q^{35} +(-3.52527 + 6.10595i) q^{37} +(-3.08900 + 5.35031i) q^{38} +(0.517694 + 0.896672i) q^{40} +(2.58195 + 4.47206i) q^{41} +(-0.0113752 + 0.0197024i) q^{43} +(-3.58334 - 6.20653i) q^{44} +(-4.22758 - 7.32239i) q^{46} +(5.84178 + 10.1183i) q^{47} +(6.80609 + 1.63620i) q^{49} +(2.69626 + 4.67006i) q^{50} +(1.17946 - 5.76175i) q^{52} +(-0.0708929 + 0.122790i) q^{53} +(-3.23618 - 5.60523i) q^{55} +(1.84664 + 0.218850i) q^{56} -0.319298 q^{58} +(-2.67177 - 4.62764i) q^{59} +11.5457 q^{61} +(-4.99774 - 8.65635i) q^{62} -4.82736 q^{64} +(1.06519 - 5.20354i) q^{65} +4.13546 q^{67} +(-0.980907 + 1.69898i) q^{68} +(-7.37537 - 0.874075i) q^{70} +(-4.98486 + 8.63403i) q^{71} +(-7.62080 + 13.1996i) q^{73} +(-6.71762 - 11.6353i) q^{74} +(-2.64418 - 4.57986i) q^{76} +(-11.5436 - 1.36807i) q^{77} +(-0.387251 - 0.670738i) q^{79} -6.77881 q^{80} -9.84011 q^{82} +16.0186 q^{83} +(-0.885875 + 1.53438i) q^{85} +(-0.0216761 - 0.0375441i) q^{86} -3.08805 q^{88} +(3.27880 - 5.67904i) q^{89} +(-6.34245 - 7.12554i) q^{91} +7.23762 q^{92} -22.2637 q^{94} +(-2.38801 - 4.13616i) q^{95} +(-1.74583 + 3.02387i) q^{97} +(-9.18486 + 9.67291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} + O(q^{10}) \) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} - 8q^{10} + 8q^{11} - 2q^{13} + 2q^{14} + 8q^{16} - 5q^{17} + 2q^{19} + q^{20} - 5q^{22} + q^{23} + 7q^{25} - 5q^{26} - 7q^{28} - 3q^{29} + 16q^{31} - 8q^{32} + 32q^{34} - 8q^{35} - 13q^{37} + 17q^{38} - 5q^{40} + 8q^{41} - 11q^{43} - 21q^{44} + 16q^{46} + q^{47} - 3q^{49} - 6q^{50} - 25q^{52} + 2q^{53} + 9q^{55} + 18q^{56} + 16q^{58} - 13q^{59} + 10q^{61} - 5q^{62} - 30q^{64} - 19q^{65} + 22q^{67} - 29q^{68} - 39q^{70} - 6q^{71} - 30q^{73} + 3q^{74} - 9q^{76} - 11q^{77} + 7q^{79} - 14q^{80} - 2q^{82} + 54q^{83} - q^{85} + 7q^{86} - 4q^{89} - 20q^{91} - 54q^{92} - 90q^{94} + 6q^{95} - 35q^{97} - 62q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.952780 + 1.65026i −0.673717 + 1.16691i 0.303125 + 0.952951i \(0.401970\pi\)
−0.976842 + 0.213962i \(0.931363\pi\)
\(3\) 0 0
\(4\) −0.815580 1.41263i −0.407790 0.706313i
\(5\) −0.736565 1.27577i −0.329402 0.570541i 0.652991 0.757365i \(-0.273514\pi\)
−0.982393 + 0.186825i \(0.940180\pi\)
\(6\) 0 0
\(7\) −2.62736 0.311376i −0.993050 0.117689i
\(8\) −0.702849 −0.248495
\(9\) 0 0
\(10\) 2.80714 0.887695
\(11\) 4.39361 1.32472 0.662362 0.749184i \(-0.269554\pi\)
0.662362 + 0.749184i \(0.269554\pi\)
\(12\) 0 0
\(13\) 2.69752 + 2.39236i 0.748158 + 0.663520i
\(14\) 3.01715 4.03917i 0.806368 1.07951i
\(15\) 0 0
\(16\) 2.30082 3.98514i 0.575205 0.996284i
\(17\) −0.601356 1.04158i −0.145850 0.252620i 0.783840 0.620963i \(-0.213258\pi\)
−0.929690 + 0.368343i \(0.879925\pi\)
\(18\) 0 0
\(19\) 3.24209 0.743787 0.371893 0.928275i \(-0.378709\pi\)
0.371893 + 0.928275i \(0.378709\pi\)
\(20\) −1.20145 + 2.08098i −0.268653 + 0.465321i
\(21\) 0 0
\(22\) −4.18615 + 7.25062i −0.892490 + 1.54584i
\(23\) −2.21855 + 3.84264i −0.462600 + 0.801246i −0.999090 0.0426603i \(-0.986417\pi\)
0.536490 + 0.843907i \(0.319750\pi\)
\(24\) 0 0
\(25\) 1.41494 2.45075i 0.282989 0.490151i
\(26\) −6.51816 + 2.17223i −1.27832 + 0.426010i
\(27\) 0 0
\(28\) 1.70297 + 3.96543i 0.321831 + 0.749396i
\(29\) 0.0837807 + 0.145112i 0.0155577 + 0.0269467i 0.873699 0.486466i \(-0.161714\pi\)
−0.858142 + 0.513413i \(0.828381\pi\)
\(30\) 0 0
\(31\) −2.62272 + 4.54268i −0.471054 + 0.815889i −0.999452 0.0331076i \(-0.989460\pi\)
0.528398 + 0.848997i \(0.322793\pi\)
\(32\) 3.68150 + 6.37655i 0.650803 + 1.12722i
\(33\) 0 0
\(34\) 2.29184 0.393047
\(35\) 1.53798 + 3.58126i 0.259966 + 0.605343i
\(36\) 0 0
\(37\) −3.52527 + 6.10595i −0.579552 + 1.00381i 0.415979 + 0.909374i \(0.363439\pi\)
−0.995531 + 0.0944386i \(0.969894\pi\)
\(38\) −3.08900 + 5.35031i −0.501102 + 0.867934i
\(39\) 0 0
\(40\) 0.517694 + 0.896672i 0.0818546 + 0.141776i
\(41\) 2.58195 + 4.47206i 0.403233 + 0.698419i 0.994114 0.108339i \(-0.0345533\pi\)
−0.590881 + 0.806758i \(0.701220\pi\)
\(42\) 0 0
\(43\) −0.0113752 + 0.0197024i −0.00173470 + 0.00300459i −0.866891 0.498497i \(-0.833886\pi\)
0.865157 + 0.501502i \(0.167219\pi\)
\(44\) −3.58334 6.20653i −0.540209 0.935670i
\(45\) 0 0
\(46\) −4.22758 7.32239i −0.623323 1.07963i
\(47\) 5.84178 + 10.1183i 0.852111 + 1.47590i 0.879300 + 0.476269i \(0.158011\pi\)
−0.0271891 + 0.999630i \(0.508656\pi\)
\(48\) 0 0
\(49\) 6.80609 + 1.63620i 0.972299 + 0.233742i
\(50\) 2.69626 + 4.67006i 0.381309 + 0.660446i
\(51\) 0 0
\(52\) 1.17946 5.76175i 0.163561 0.799010i
\(53\) −0.0708929 + 0.122790i −0.00973788 + 0.0168665i −0.870853 0.491543i \(-0.836433\pi\)
0.861115 + 0.508410i \(0.169766\pi\)
\(54\) 0 0
\(55\) −3.23618 5.60523i −0.436367 0.755809i
\(56\) 1.84664 + 0.218850i 0.246768 + 0.0292451i
\(57\) 0 0
\(58\) −0.319298 −0.0419259
\(59\) −2.67177 4.62764i −0.347835 0.602468i 0.638030 0.770012i \(-0.279750\pi\)
−0.985865 + 0.167544i \(0.946416\pi\)
\(60\) 0 0
\(61\) 11.5457 1.47828 0.739141 0.673551i \(-0.235232\pi\)
0.739141 + 0.673551i \(0.235232\pi\)
\(62\) −4.99774 8.65635i −0.634714 1.09936i
\(63\) 0 0
\(64\) −4.82736 −0.603420
\(65\) 1.06519 5.20354i 0.132121 0.645420i
\(66\) 0 0
\(67\) 4.13546 0.505226 0.252613 0.967567i \(-0.418710\pi\)
0.252613 + 0.967567i \(0.418710\pi\)
\(68\) −0.980907 + 1.69898i −0.118952 + 0.206032i
\(69\) 0 0
\(70\) −7.37537 0.874075i −0.881526 0.104472i
\(71\) −4.98486 + 8.63403i −0.591594 + 1.02467i 0.402424 + 0.915453i \(0.368168\pi\)
−0.994018 + 0.109217i \(0.965166\pi\)
\(72\) 0 0
\(73\) −7.62080 + 13.1996i −0.891947 + 1.54490i −0.0544080 + 0.998519i \(0.517327\pi\)
−0.837539 + 0.546378i \(0.816006\pi\)
\(74\) −6.71762 11.6353i −0.780908 1.35257i
\(75\) 0 0
\(76\) −2.64418 4.57986i −0.303309 0.525346i
\(77\) −11.5436 1.36807i −1.31552 0.155906i
\(78\) 0 0
\(79\) −0.387251 0.670738i −0.0435691 0.0754639i 0.843418 0.537257i \(-0.180540\pi\)
−0.886988 + 0.461793i \(0.847206\pi\)
\(80\) −6.77881 −0.757894
\(81\) 0 0
\(82\) −9.84011 −1.08666
\(83\) 16.0186 1.75827 0.879136 0.476571i \(-0.158121\pi\)
0.879136 + 0.476571i \(0.158121\pi\)
\(84\) 0 0
\(85\) −0.885875 + 1.53438i −0.0960866 + 0.166427i
\(86\) −0.0216761 0.0375441i −0.00233740 0.00404849i
\(87\) 0 0
\(88\) −3.08805 −0.329187
\(89\) 3.27880 5.67904i 0.347552 0.601977i −0.638262 0.769819i \(-0.720346\pi\)
0.985814 + 0.167842i \(0.0536797\pi\)
\(90\) 0 0
\(91\) −6.34245 7.12554i −0.664870 0.746959i
\(92\) 7.23762 0.754574
\(93\) 0 0
\(94\) −22.2637 −2.29633
\(95\) −2.38801 4.13616i −0.245005 0.424361i
\(96\) 0 0
\(97\) −1.74583 + 3.02387i −0.177262 + 0.307027i −0.940942 0.338568i \(-0.890057\pi\)
0.763680 + 0.645595i \(0.223391\pi\)
\(98\) −9.18486 + 9.67291i −0.927811 + 0.977111i
\(99\) 0 0
\(100\) −4.61600 −0.461600
\(101\) −2.57780 −0.256500 −0.128250 0.991742i \(-0.540936\pi\)
−0.128250 + 0.991742i \(0.540936\pi\)
\(102\) 0 0
\(103\) 8.43173 + 14.6042i 0.830803 + 1.43899i 0.897402 + 0.441213i \(0.145452\pi\)
−0.0665997 + 0.997780i \(0.521215\pi\)
\(104\) −1.89595 1.68146i −0.185913 0.164881i
\(105\) 0 0
\(106\) −0.135091 0.233984i −0.0131212 0.0227265i
\(107\) 4.34132 7.51939i 0.419692 0.726927i −0.576217 0.817297i \(-0.695472\pi\)
0.995908 + 0.0903697i \(0.0288049\pi\)
\(108\) 0 0
\(109\) 6.02026 10.4274i 0.576637 0.998764i −0.419225 0.907882i \(-0.637698\pi\)
0.995862 0.0908816i \(-0.0289685\pi\)
\(110\) 12.3335 1.17595
\(111\) 0 0
\(112\) −7.28597 + 9.75398i −0.688459 + 0.921665i
\(113\) 4.68616 8.11667i 0.440837 0.763552i −0.556915 0.830570i \(-0.688015\pi\)
0.997752 + 0.0670176i \(0.0213484\pi\)
\(114\) 0 0
\(115\) 6.53643 0.609525
\(116\) 0.136660 0.236701i 0.0126885 0.0219772i
\(117\) 0 0
\(118\) 10.1824 0.937369
\(119\) 1.25566 + 2.92385i 0.115106 + 0.268029i
\(120\) 0 0
\(121\) 8.30385 0.754895
\(122\) −11.0006 + 19.0535i −0.995944 + 1.72503i
\(123\) 0 0
\(124\) 8.55614 0.768364
\(125\) −11.5344 −1.03167
\(126\) 0 0
\(127\) −7.94269 13.7571i −0.704800 1.22075i −0.966764 0.255672i \(-0.917703\pi\)
0.261964 0.965078i \(-0.415630\pi\)
\(128\) −2.76359 + 4.78667i −0.244269 + 0.423086i
\(129\) 0 0
\(130\) 7.57232 + 6.71567i 0.664136 + 0.589004i
\(131\) 0.928725 + 1.60860i 0.0811430 + 0.140544i 0.903741 0.428079i \(-0.140810\pi\)
−0.822598 + 0.568623i \(0.807476\pi\)
\(132\) 0 0
\(133\) −8.51816 1.00951i −0.738618 0.0875356i
\(134\) −3.94018 + 6.82459i −0.340380 + 0.589555i
\(135\) 0 0
\(136\) 0.422662 + 0.732072i 0.0362430 + 0.0627747i
\(137\) −6.40011 11.0853i −0.546798 0.947082i −0.998491 0.0549088i \(-0.982513\pi\)
0.451693 0.892173i \(-0.350820\pi\)
\(138\) 0 0
\(139\) 0.169365 0.293348i 0.0143653 0.0248815i −0.858753 0.512389i \(-0.828761\pi\)
0.873119 + 0.487508i \(0.162094\pi\)
\(140\) 3.80463 5.09339i 0.321550 0.430470i
\(141\) 0 0
\(142\) −9.49894 16.4527i −0.797134 1.38068i
\(143\) 11.8519 + 10.5111i 0.991104 + 0.878982i
\(144\) 0 0
\(145\) 0.123420 0.213769i 0.0102495 0.0177526i
\(146\) −14.5219 25.1526i −1.20184 2.08165i
\(147\) 0 0
\(148\) 11.5006 0.945341
\(149\) −3.92316 −0.321398 −0.160699 0.987003i \(-0.551375\pi\)
−0.160699 + 0.987003i \(0.551375\pi\)
\(150\) 0 0
\(151\) 1.05939 1.83492i 0.0862122 0.149324i −0.819695 0.572800i \(-0.805857\pi\)
0.905907 + 0.423476i \(0.139190\pi\)
\(152\) −2.27870 −0.184827
\(153\) 0 0
\(154\) 13.2562 17.7466i 1.06822 1.43006i
\(155\) 7.72721 0.620664
\(156\) 0 0
\(157\) 11.0564 19.1502i 0.882397 1.52836i 0.0337285 0.999431i \(-0.489262\pi\)
0.848668 0.528925i \(-0.177405\pi\)
\(158\) 1.47586 0.117413
\(159\) 0 0
\(160\) 5.42333 9.39348i 0.428752 0.742620i
\(161\) 7.02545 9.40522i 0.553683 0.741235i
\(162\) 0 0
\(163\) 3.85214 0.301723 0.150861 0.988555i \(-0.451795\pi\)
0.150861 + 0.988555i \(0.451795\pi\)
\(164\) 4.21157 7.29465i 0.328868 0.569616i
\(165\) 0 0
\(166\) −15.2622 + 26.4349i −1.18458 + 2.05175i
\(167\) 1.06947 + 1.85238i 0.0827582 + 0.143341i 0.904434 0.426614i \(-0.140294\pi\)
−0.821676 + 0.569956i \(0.806960\pi\)
\(168\) 0 0
\(169\) 1.55326 + 12.9069i 0.119482 + 0.992836i
\(170\) −1.68809 2.92385i −0.129470 0.224249i
\(171\) 0 0
\(172\) 0.0371095 0.00282957
\(173\) 16.6133 1.26308 0.631542 0.775342i \(-0.282422\pi\)
0.631542 + 0.775342i \(0.282422\pi\)
\(174\) 0 0
\(175\) −4.48068 + 5.99845i −0.338708 + 0.453440i
\(176\) 10.1089 17.5091i 0.761988 1.31980i
\(177\) 0 0
\(178\) 6.24795 + 10.8218i 0.468303 + 0.811125i
\(179\) 0.539496 0.0403238 0.0201619 0.999797i \(-0.493582\pi\)
0.0201619 + 0.999797i \(0.493582\pi\)
\(180\) 0 0
\(181\) 2.77164 0.206014 0.103007 0.994681i \(-0.467154\pi\)
0.103007 + 0.994681i \(0.467154\pi\)
\(182\) 17.8020 3.67765i 1.31957 0.272606i
\(183\) 0 0
\(184\) 1.55931 2.70080i 0.114954 0.199105i
\(185\) 10.3864 0.763621
\(186\) 0 0
\(187\) −2.64213 4.57629i −0.193211 0.334652i
\(188\) 9.52887 16.5045i 0.694964 1.20371i
\(189\) 0 0
\(190\) 9.10100 0.660256
\(191\) 20.2407 1.46457 0.732284 0.680999i \(-0.238454\pi\)
0.732284 + 0.680999i \(0.238454\pi\)
\(192\) 0 0
\(193\) −16.3771 −1.17885 −0.589425 0.807823i \(-0.700646\pi\)
−0.589425 + 0.807823i \(0.700646\pi\)
\(194\) −3.32678 5.76216i −0.238849 0.413699i
\(195\) 0 0
\(196\) −3.23958 10.9489i −0.231398 0.782064i
\(197\) 9.86676 + 17.0897i 0.702977 + 1.21759i 0.967417 + 0.253190i \(0.0814798\pi\)
−0.264439 + 0.964402i \(0.585187\pi\)
\(198\) 0 0
\(199\) 7.05873 + 12.2261i 0.500380 + 0.866683i 1.00000 0.000438630i \(0.000139620\pi\)
−0.499620 + 0.866245i \(0.666527\pi\)
\(200\) −0.994491 + 1.72251i −0.0703212 + 0.121800i
\(201\) 0 0
\(202\) 2.45607 4.25404i 0.172809 0.299313i
\(203\) −0.174938 0.407351i −0.0122782 0.0285904i
\(204\) 0 0
\(205\) 3.80354 6.58793i 0.265651 0.460121i
\(206\) −32.1343 −2.23890
\(207\) 0 0
\(208\) 15.7404 5.24562i 1.09140 0.363718i
\(209\) 14.2445 0.985313
\(210\) 0 0
\(211\) 2.31317 + 4.00652i 0.159245 + 0.275820i 0.934597 0.355709i \(-0.115761\pi\)
−0.775352 + 0.631530i \(0.782427\pi\)
\(212\) 0.231275 0.0158840
\(213\) 0 0
\(214\) 8.27265 + 14.3287i 0.565507 + 0.979487i
\(215\) 0.0335143 0.00228565
\(216\) 0 0
\(217\) 8.30532 11.1186i 0.563802 0.754781i
\(218\) 11.4720 + 19.8700i 0.776980 + 1.34577i
\(219\) 0 0
\(220\) −5.27873 + 9.14303i −0.355892 + 0.616423i
\(221\) 0.869656 4.24834i 0.0584994 0.285774i
\(222\) 0 0
\(223\) 10.6761 + 18.4916i 0.714926 + 1.23829i 0.962988 + 0.269545i \(0.0868732\pi\)
−0.248061 + 0.968744i \(0.579793\pi\)
\(224\) −7.68714 17.8998i −0.513619 1.19598i
\(225\) 0 0
\(226\) 8.92976 + 15.4668i 0.593999 + 1.02884i
\(227\) −5.22451 9.04911i −0.346763 0.600611i 0.638910 0.769282i \(-0.279386\pi\)
−0.985672 + 0.168671i \(0.946052\pi\)
\(228\) 0 0
\(229\) −7.22901 12.5210i −0.477706 0.827412i 0.521967 0.852966i \(-0.325198\pi\)
−0.999673 + 0.0255538i \(0.991865\pi\)
\(230\) −6.22778 + 10.7868i −0.410648 + 0.711262i
\(231\) 0 0
\(232\) −0.0588852 0.101992i −0.00386600 0.00669611i
\(233\) −4.64413 8.04388i −0.304247 0.526972i 0.672846 0.739783i \(-0.265072\pi\)
−0.977093 + 0.212811i \(0.931738\pi\)
\(234\) 0 0
\(235\) 8.60570 14.9055i 0.561374 0.972328i
\(236\) −4.35808 + 7.54842i −0.283687 + 0.491360i
\(237\) 0 0
\(238\) −6.02150 0.713623i −0.390316 0.0462573i
\(239\) −19.6332 −1.26997 −0.634983 0.772526i \(-0.718993\pi\)
−0.634983 + 0.772526i \(0.718993\pi\)
\(240\) 0 0
\(241\) −3.65552 6.33155i −0.235473 0.407851i 0.723937 0.689866i \(-0.242331\pi\)
−0.959410 + 0.282015i \(0.908997\pi\)
\(242\) −7.91174 + 13.7035i −0.508586 + 0.880897i
\(243\) 0 0
\(244\) −9.41648 16.3098i −0.602828 1.04413i
\(245\) −2.92572 9.88816i −0.186917 0.631731i
\(246\) 0 0
\(247\) 8.74562 + 7.75624i 0.556470 + 0.493518i
\(248\) 1.84337 3.19282i 0.117054 0.202744i
\(249\) 0 0
\(250\) 10.9898 19.0349i 0.695055 1.20387i
\(251\) −5.93191 + 10.2744i −0.374419 + 0.648512i −0.990240 0.139374i \(-0.955491\pi\)
0.615821 + 0.787886i \(0.288824\pi\)
\(252\) 0 0
\(253\) −9.74746 + 16.8831i −0.612817 + 1.06143i
\(254\) 30.2706 1.89934
\(255\) 0 0
\(256\) −10.0935 17.4825i −0.630846 1.09266i
\(257\) −7.58608 + 13.1395i −0.473206 + 0.819618i −0.999530 0.0306670i \(-0.990237\pi\)
0.526323 + 0.850285i \(0.323570\pi\)
\(258\) 0 0
\(259\) 11.1634 14.9449i 0.693662 0.928630i
\(260\) −8.21940 + 2.73919i −0.509745 + 0.169877i
\(261\) 0 0
\(262\) −3.53948 −0.218670
\(263\) −17.1964 −1.06037 −0.530187 0.847880i \(-0.677878\pi\)
−0.530187 + 0.847880i \(0.677878\pi\)
\(264\) 0 0
\(265\) 0.208869 0.0128307
\(266\) 9.78189 13.0954i 0.599766 0.802928i
\(267\) 0 0
\(268\) −3.37279 5.84185i −0.206026 0.356848i
\(269\) 9.46102 + 16.3870i 0.576849 + 0.999131i 0.995838 + 0.0911401i \(0.0290511\pi\)
−0.418989 + 0.907991i \(0.637616\pi\)
\(270\) 0 0
\(271\) −16.0667 + 27.8283i −0.975982 + 1.69045i −0.299324 + 0.954151i \(0.596761\pi\)
−0.676657 + 0.736298i \(0.736572\pi\)
\(272\) −5.53444 −0.335575
\(273\) 0 0
\(274\) 24.3916 1.47355
\(275\) 6.21672 10.7677i 0.374882 0.649315i
\(276\) 0 0
\(277\) −9.20269 15.9395i −0.552936 0.957714i −0.998061 0.0622450i \(-0.980174\pi\)
0.445125 0.895469i \(-0.353159\pi\)
\(278\) 0.322734 + 0.558992i 0.0193563 + 0.0335261i
\(279\) 0 0
\(280\) −1.08097 2.51708i −0.0646002 0.150424i
\(281\) 14.2252 0.848603 0.424302 0.905521i \(-0.360520\pi\)
0.424302 + 0.905521i \(0.360520\pi\)
\(282\) 0 0
\(283\) −11.4289 −0.679378 −0.339689 0.940538i \(-0.610322\pi\)
−0.339689 + 0.940538i \(0.610322\pi\)
\(284\) 16.2622 0.964983
\(285\) 0 0
\(286\) −28.6383 + 9.54396i −1.69342 + 0.564346i
\(287\) −5.39123 12.5537i −0.318234 0.741022i
\(288\) 0 0
\(289\) 7.77674 13.4697i 0.457455 0.792336i
\(290\) 0.235184 + 0.407351i 0.0138105 + 0.0239205i
\(291\) 0 0
\(292\) 24.8615 1.45491
\(293\) −6.60231 + 11.4355i −0.385711 + 0.668071i −0.991868 0.127274i \(-0.959377\pi\)
0.606156 + 0.795345i \(0.292711\pi\)
\(294\) 0 0
\(295\) −3.93586 + 6.81712i −0.229155 + 0.396908i
\(296\) 2.47773 4.29156i 0.144015 0.249442i
\(297\) 0 0
\(298\) 3.73791 6.47425i 0.216531 0.375043i
\(299\) −15.1776 + 5.05805i −0.877741 + 0.292515i
\(300\) 0 0
\(301\) 0.0360216 0.0482235i 0.00207625 0.00277955i
\(302\) 2.01874 + 3.49656i 0.116165 + 0.201204i
\(303\) 0 0
\(304\) 7.45947 12.9202i 0.427830 0.741023i
\(305\) −8.50420 14.7297i −0.486949 0.843420i
\(306\) 0 0
\(307\) −6.65903 −0.380051 −0.190026 0.981779i \(-0.560857\pi\)
−0.190026 + 0.981779i \(0.560857\pi\)
\(308\) 7.48218 + 17.4226i 0.426337 + 0.992744i
\(309\) 0 0
\(310\) −7.36233 + 12.7519i −0.418152 + 0.724261i
\(311\) −1.02298 + 1.77186i −0.0580081 + 0.100473i −0.893571 0.448922i \(-0.851808\pi\)
0.835563 + 0.549395i \(0.185142\pi\)
\(312\) 0 0
\(313\) −4.70883 8.15594i −0.266159 0.461001i 0.701708 0.712465i \(-0.252421\pi\)
−0.967867 + 0.251464i \(0.919088\pi\)
\(314\) 21.0686 + 36.4919i 1.18897 + 2.05936i
\(315\) 0 0
\(316\) −0.631667 + 1.09408i −0.0355341 + 0.0615468i
\(317\) −16.6856 28.9004i −0.937159 1.62321i −0.770738 0.637153i \(-0.780112\pi\)
−0.166421 0.986055i \(-0.553221\pi\)
\(318\) 0 0
\(319\) 0.368100 + 0.637568i 0.0206097 + 0.0356970i
\(320\) 3.55567 + 6.15860i 0.198768 + 0.344276i
\(321\) 0 0
\(322\) 8.82739 + 20.5549i 0.491931 + 1.14548i
\(323\) −1.94965 3.37689i −0.108481 0.187895i
\(324\) 0 0
\(325\) 9.67992 3.22592i 0.536946 0.178942i
\(326\) −3.67024 + 6.35704i −0.203276 + 0.352084i
\(327\) 0 0
\(328\) −1.81472 3.14318i −0.100201 0.173553i
\(329\) −12.1979 28.4033i −0.672492 1.56593i
\(330\) 0 0
\(331\) 19.0660 1.04796 0.523980 0.851731i \(-0.324447\pi\)
0.523980 + 0.851731i \(0.324447\pi\)
\(332\) −13.0645 22.6283i −0.717005 1.24189i
\(333\) 0 0
\(334\) −4.07589 −0.223023
\(335\) −3.04603 5.27588i −0.166423 0.288252i
\(336\) 0 0
\(337\) −31.2849 −1.70420 −0.852098 0.523382i \(-0.824670\pi\)
−0.852098 + 0.523382i \(0.824670\pi\)
\(338\) −22.7797 9.73412i −1.23905 0.529466i
\(339\) 0 0
\(340\) 2.89001 0.156733
\(341\) −11.5232 + 19.9588i −0.624017 + 1.08083i
\(342\) 0 0
\(343\) −17.3726 6.41814i −0.938033 0.346547i
\(344\) 0.00799504 0.0138478i 0.000431064 0.000746624i
\(345\) 0 0
\(346\) −15.8288 + 27.4163i −0.850961 + 1.47391i
\(347\) 5.83759 + 10.1110i 0.313378 + 0.542787i 0.979091 0.203420i \(-0.0652058\pi\)
−0.665713 + 0.746208i \(0.731872\pi\)
\(348\) 0 0
\(349\) −11.9952 20.7763i −0.642089 1.11213i −0.984966 0.172750i \(-0.944735\pi\)
0.342877 0.939380i \(-0.388599\pi\)
\(350\) −5.62992 13.1095i −0.300932 0.700732i
\(351\) 0 0
\(352\) 16.1751 + 28.0161i 0.862135 + 1.49326i
\(353\) −12.7934 −0.680922 −0.340461 0.940259i \(-0.610583\pi\)
−0.340461 + 0.940259i \(0.610583\pi\)
\(354\) 0 0
\(355\) 14.6867 0.779488
\(356\) −10.6965 −0.566912
\(357\) 0 0
\(358\) −0.514021 + 0.890310i −0.0271668 + 0.0470544i
\(359\) 6.16986 + 10.6865i 0.325633 + 0.564012i 0.981640 0.190742i \(-0.0610894\pi\)
−0.656008 + 0.754754i \(0.727756\pi\)
\(360\) 0 0
\(361\) −8.48884 −0.446781
\(362\) −2.64076 + 4.57393i −0.138795 + 0.240401i
\(363\) 0 0
\(364\) −4.89294 + 14.7710i −0.256460 + 0.774208i
\(365\) 22.4528 1.17524
\(366\) 0 0
\(367\) 2.03077 0.106005 0.0530026 0.998594i \(-0.483121\pi\)
0.0530026 + 0.998594i \(0.483121\pi\)
\(368\) 10.2090 + 17.6825i 0.532179 + 0.921762i
\(369\) 0 0
\(370\) −9.89593 + 17.1403i −0.514465 + 0.891079i
\(371\) 0.224495 0.300540i 0.0116552 0.0156033i
\(372\) 0 0
\(373\) −3.87400 −0.200588 −0.100294 0.994958i \(-0.531978\pi\)
−0.100294 + 0.994958i \(0.531978\pi\)
\(374\) 10.0695 0.520679
\(375\) 0 0
\(376\) −4.10588 7.11160i −0.211745 0.366753i
\(377\) −0.121160 + 0.591877i −0.00624007 + 0.0304832i
\(378\) 0 0
\(379\) 7.28396 + 12.6162i 0.374152 + 0.648050i 0.990200 0.139659i \(-0.0446006\pi\)
−0.616048 + 0.787709i \(0.711267\pi\)
\(380\) −3.89523 + 6.74673i −0.199821 + 0.346100i
\(381\) 0 0
\(382\) −19.2850 + 33.4025i −0.986705 + 1.70902i
\(383\) 26.7818 1.36849 0.684243 0.729254i \(-0.260133\pi\)
0.684243 + 0.729254i \(0.260133\pi\)
\(384\) 0 0
\(385\) 6.75730 + 15.7347i 0.344384 + 0.801912i
\(386\) 15.6038 27.0266i 0.794212 1.37562i
\(387\) 0 0
\(388\) 5.69545 0.289143
\(389\) 6.00738 10.4051i 0.304586 0.527559i −0.672583 0.740022i \(-0.734815\pi\)
0.977169 + 0.212463i \(0.0681485\pi\)
\(390\) 0 0
\(391\) 5.33655 0.269881
\(392\) −4.78365 1.15000i −0.241611 0.0580837i
\(393\) 0 0
\(394\) −37.6034 −1.89443
\(395\) −0.570470 + 0.988084i −0.0287035 + 0.0497159i
\(396\) 0 0
\(397\) −1.65765 −0.0831951 −0.0415975 0.999134i \(-0.513245\pi\)
−0.0415975 + 0.999134i \(0.513245\pi\)
\(398\) −26.9017 −1.34846
\(399\) 0 0
\(400\) −6.51106 11.2775i −0.325553 0.563874i
\(401\) −10.2414 + 17.7386i −0.511430 + 0.885823i 0.488482 + 0.872574i \(0.337551\pi\)
−0.999912 + 0.0132488i \(0.995783\pi\)
\(402\) 0 0
\(403\) −17.9425 + 5.97951i −0.893782 + 0.297861i
\(404\) 2.10240 + 3.64146i 0.104598 + 0.181169i
\(405\) 0 0
\(406\) 0.838913 + 0.0994218i 0.0416346 + 0.00493422i
\(407\) −15.4887 + 26.8272i −0.767746 + 1.32978i
\(408\) 0 0
\(409\) −7.43293 12.8742i −0.367535 0.636589i 0.621645 0.783299i \(-0.286465\pi\)
−0.989180 + 0.146710i \(0.953131\pi\)
\(410\) 7.24788 + 12.5537i 0.357947 + 0.619983i
\(411\) 0 0
\(412\) 13.7535 23.8217i 0.677586 1.17361i
\(413\) 5.57878 + 12.9904i 0.274514 + 0.639217i
\(414\) 0 0
\(415\) −11.7988 20.4360i −0.579178 1.00317i
\(416\) −5.32404 + 26.0083i −0.261032 + 1.27516i
\(417\) 0 0
\(418\) −13.5719 + 23.5072i −0.663822 + 1.14977i
\(419\) −11.8087 20.4533i −0.576895 0.999211i −0.995833 0.0911962i \(-0.970931\pi\)
0.418938 0.908015i \(-0.362402\pi\)
\(420\) 0 0
\(421\) 26.0822 1.27117 0.635585 0.772031i \(-0.280759\pi\)
0.635585 + 0.772031i \(0.280759\pi\)
\(422\) −8.81576 −0.429144
\(423\) 0 0
\(424\) 0.0498269 0.0863028i 0.00241981 0.00419123i
\(425\) −3.40354 −0.165096
\(426\) 0 0
\(427\) −30.3349 3.59507i −1.46801 0.173978i
\(428\) −14.1628 −0.684584
\(429\) 0 0
\(430\) −0.0319317 + 0.0553074i −0.00153988 + 0.00266716i
\(431\) 13.3172 0.641466 0.320733 0.947170i \(-0.396071\pi\)
0.320733 + 0.947170i \(0.396071\pi\)
\(432\) 0 0
\(433\) −10.2110 + 17.6860i −0.490711 + 0.849937i −0.999943 0.0106929i \(-0.996596\pi\)
0.509232 + 0.860629i \(0.329930\pi\)
\(434\) 10.4355 + 24.2996i 0.500921 + 1.16642i
\(435\) 0 0
\(436\) −19.6400 −0.940586
\(437\) −7.19275 + 12.4582i −0.344076 + 0.595957i
\(438\) 0 0
\(439\) 4.88537 8.46171i 0.233166 0.403855i −0.725572 0.688146i \(-0.758425\pi\)
0.958738 + 0.284291i \(0.0917581\pi\)
\(440\) 2.27455 + 3.93963i 0.108435 + 0.187814i
\(441\) 0 0
\(442\) 6.18229 + 5.48290i 0.294061 + 0.260795i
\(443\) 10.5819 + 18.3285i 0.502763 + 0.870811i 0.999995 + 0.00319331i \(0.00101646\pi\)
−0.497232 + 0.867618i \(0.665650\pi\)
\(444\) 0 0
\(445\) −9.66019 −0.457937
\(446\) −40.6880 −1.92663
\(447\) 0 0
\(448\) 12.6832 + 1.50312i 0.599227 + 0.0710160i
\(449\) −9.07320 + 15.7152i −0.428191 + 0.741648i −0.996712 0.0810200i \(-0.974182\pi\)
0.568522 + 0.822668i \(0.307516\pi\)
\(450\) 0 0
\(451\) 11.3441 + 19.6485i 0.534172 + 0.925213i
\(452\) −15.2877 −0.719075
\(453\) 0 0
\(454\) 19.9112 0.934480
\(455\) −4.41890 + 13.3399i −0.207161 + 0.625385i
\(456\) 0 0
\(457\) 9.00991 15.6056i 0.421466 0.730000i −0.574617 0.818422i \(-0.694849\pi\)
0.996083 + 0.0884220i \(0.0281824\pi\)
\(458\) 27.5506 1.28736
\(459\) 0 0
\(460\) −5.33098 9.23352i −0.248558 0.430515i
\(461\) −14.8873 + 25.7855i −0.693370 + 1.20095i 0.277357 + 0.960767i \(0.410542\pi\)
−0.970727 + 0.240185i \(0.922792\pi\)
\(462\) 0 0
\(463\) 17.7067 0.822900 0.411450 0.911432i \(-0.365023\pi\)
0.411450 + 0.911432i \(0.365023\pi\)
\(464\) 0.771057 0.0357954
\(465\) 0 0
\(466\) 17.6994 0.819907
\(467\) −2.91461 5.04825i −0.134872 0.233605i 0.790677 0.612234i \(-0.209729\pi\)
−0.925549 + 0.378629i \(0.876396\pi\)
\(468\) 0 0
\(469\) −10.8654 1.28768i −0.501715 0.0594596i
\(470\) 16.3987 + 28.4033i 0.756414 + 1.31015i
\(471\) 0 0
\(472\) 1.87785 + 3.25253i 0.0864350 + 0.149710i
\(473\) −0.0499782 + 0.0865648i −0.00229800 + 0.00398025i
\(474\) 0 0
\(475\) 4.58738 7.94557i 0.210483 0.364568i
\(476\) 3.10622 4.15841i 0.142373 0.190600i
\(477\) 0 0
\(478\) 18.7061 32.4000i 0.855598 1.48194i
\(479\) −14.4913 −0.662125 −0.331062 0.943609i \(-0.607407\pi\)
−0.331062 + 0.943609i \(0.607407\pi\)
\(480\) 0 0
\(481\) −24.1171 + 8.03724i −1.09965 + 0.366467i
\(482\) 13.9316 0.634569
\(483\) 0 0
\(484\) −6.77245 11.7302i −0.307839 0.533192i
\(485\) 5.14367 0.233562
\(486\) 0 0
\(487\) 8.98006 + 15.5539i 0.406926 + 0.704816i 0.994543 0.104323i \(-0.0332675\pi\)
−0.587618 + 0.809139i \(0.699934\pi\)
\(488\) −8.11491 −0.367345
\(489\) 0 0
\(490\) 19.1056 + 4.59303i 0.863104 + 0.207492i
\(491\) −18.1505 31.4375i −0.819119 1.41876i −0.906332 0.422566i \(-0.861130\pi\)
0.0872134 0.996190i \(-0.472204\pi\)
\(492\) 0 0
\(493\) 0.100764 0.174528i 0.00453818 0.00786036i
\(494\) −21.1325 + 7.04258i −0.950796 + 0.316861i
\(495\) 0 0
\(496\) 12.0688 + 20.9038i 0.541905 + 0.938607i
\(497\) 15.7855 21.1326i 0.708075 0.947925i
\(498\) 0 0
\(499\) −11.8538 20.5314i −0.530649 0.919112i −0.999360 0.0357602i \(-0.988615\pi\)
0.468711 0.883352i \(-0.344719\pi\)
\(500\) 9.40726 + 16.2938i 0.420705 + 0.728683i
\(501\) 0 0
\(502\) −11.3036 19.5784i −0.504505 0.873828i
\(503\) 13.8876 24.0540i 0.619217 1.07252i −0.370411 0.928868i \(-0.620783\pi\)
0.989629 0.143648i \(-0.0458834\pi\)
\(504\) 0 0
\(505\) 1.89871 + 3.28867i 0.0844916 + 0.146344i
\(506\) −18.5744 32.1717i −0.825731 1.43021i
\(507\) 0 0
\(508\) −12.9558 + 22.4401i −0.574820 + 0.995618i
\(509\) 4.35208 7.53802i 0.192902 0.334117i −0.753308 0.657667i \(-0.771543\pi\)
0.946211 + 0.323551i \(0.104877\pi\)
\(510\) 0 0
\(511\) 24.1326 32.3072i 1.06757 1.42919i
\(512\) 27.4134 1.21151
\(513\) 0 0
\(514\) −14.4557 25.0380i −0.637615 1.10438i
\(515\) 12.4210 21.5139i 0.547336 0.948014i
\(516\) 0 0
\(517\) 25.6665 + 44.4557i 1.12881 + 1.95516i
\(518\) 14.0267 + 32.6618i 0.616298 + 1.43508i
\(519\) 0 0
\(520\) −0.748668 + 3.65730i −0.0328313 + 0.160383i
\(521\) −4.28573 + 7.42310i −0.187761 + 0.325212i −0.944504 0.328501i \(-0.893456\pi\)
0.756742 + 0.653713i \(0.226790\pi\)
\(522\) 0 0
\(523\) −14.9746 + 25.9369i −0.654796 + 1.13414i 0.327149 + 0.944973i \(0.393912\pi\)
−0.981945 + 0.189167i \(0.939421\pi\)
\(524\) 1.51490 2.62388i 0.0661786 0.114625i
\(525\) 0 0
\(526\) 16.3844 28.3786i 0.714393 1.23736i
\(527\) 6.30874 0.274813
\(528\) 0 0
\(529\) 1.65606 + 2.86838i 0.0720027 + 0.124712i
\(530\) −0.199006 + 0.344689i −0.00864427 + 0.0149723i
\(531\) 0 0
\(532\) 5.52118 + 12.8563i 0.239373 + 0.557391i
\(533\) −3.73391 + 18.2404i −0.161734 + 0.790081i
\(534\) 0 0
\(535\) −12.7907 −0.552989
\(536\) −2.90660 −0.125546
\(537\) 0 0
\(538\) −36.0571 −1.55453
\(539\) 29.9033 + 7.18882i 1.28803 + 0.309644i
\(540\) 0 0
\(541\) −5.24095 9.07760i −0.225326 0.390276i 0.731091 0.682280i \(-0.239011\pi\)
−0.956417 + 0.292003i \(0.905678\pi\)
\(542\) −30.6160 53.0285i −1.31507 2.27777i
\(543\) 0 0
\(544\) 4.42778 7.66914i 0.189840 0.328812i
\(545\) −17.7373 −0.759781
\(546\) 0 0
\(547\) 15.2216 0.650829 0.325415 0.945571i \(-0.394496\pi\)
0.325415 + 0.945571i \(0.394496\pi\)
\(548\) −10.4396 + 18.0819i −0.445957 + 0.772421i
\(549\) 0 0
\(550\) 11.8463 + 20.5184i 0.505129 + 0.874909i
\(551\) 0.271625 + 0.470468i 0.0115716 + 0.0200426i
\(552\) 0 0
\(553\) 0.808597 + 1.88285i 0.0343850 + 0.0800671i
\(554\) 35.0726 1.49009
\(555\) 0 0
\(556\) −0.552521 −0.0234321
\(557\) −11.8597 −0.502513 −0.251256 0.967921i \(-0.580844\pi\)
−0.251256 + 0.967921i \(0.580844\pi\)
\(558\) 0 0
\(559\) −0.0778200 + 0.0259342i −0.00329144 + 0.00109690i
\(560\) 17.8104 + 2.11076i 0.752627 + 0.0891958i
\(561\) 0 0
\(562\) −13.5535 + 23.4753i −0.571719 + 0.990246i
\(563\) 3.84675 + 6.66276i 0.162121 + 0.280802i 0.935629 0.352985i \(-0.114833\pi\)
−0.773508 + 0.633786i \(0.781500\pi\)
\(564\) 0 0
\(565\) −13.8066 −0.580850
\(566\) 10.8892 18.8607i 0.457709 0.792775i
\(567\) 0 0
\(568\) 3.50360 6.06841i 0.147008 0.254625i
\(569\) 18.7098 32.4063i 0.784355 1.35854i −0.145029 0.989427i \(-0.546327\pi\)
0.929384 0.369115i \(-0.120339\pi\)
\(570\) 0 0
\(571\) −7.08285 + 12.2679i −0.296408 + 0.513394i −0.975311 0.220834i \(-0.929122\pi\)
0.678903 + 0.734228i \(0.262456\pi\)
\(572\) 5.18208 25.3149i 0.216674 1.05847i
\(573\) 0 0
\(574\) 25.8536 + 3.06397i 1.07911 + 0.127888i
\(575\) 6.27825 + 10.8742i 0.261821 + 0.453488i
\(576\) 0 0
\(577\) 7.48776 12.9692i 0.311720 0.539914i −0.667015 0.745044i \(-0.732428\pi\)
0.978735 + 0.205130i \(0.0657617\pi\)
\(578\) 14.8190 + 25.6673i 0.616391 + 1.06762i
\(579\) 0 0
\(580\) −0.402635 −0.0167185
\(581\) −42.0867 4.98781i −1.74605 0.206929i
\(582\) 0 0
\(583\) −0.311476 + 0.539492i −0.0129000 + 0.0223435i
\(584\) 5.35627 9.27732i 0.221644 0.383898i
\(585\) 0 0
\(586\) −12.5811 21.7911i −0.519720 0.900182i
\(587\) −6.58821 11.4111i −0.271925 0.470987i 0.697430 0.716653i \(-0.254327\pi\)
−0.969355 + 0.245666i \(0.920993\pi\)
\(588\) 0 0
\(589\) −8.50309 + 14.7278i −0.350364 + 0.606848i
\(590\) −7.50003 12.9904i −0.308771 0.534807i
\(591\) 0 0
\(592\) 16.2220 + 28.0974i 0.666722 + 1.15480i
\(593\) −22.0663 38.2200i −0.906156 1.56951i −0.819357 0.573283i \(-0.805670\pi\)
−0.0867989 0.996226i \(-0.527664\pi\)
\(594\) 0 0
\(595\) 2.80529 3.75554i 0.115006 0.153962i
\(596\) 3.19965 + 5.54195i 0.131063 + 0.227007i
\(597\) 0 0
\(598\) 6.11376 29.8662i 0.250010 1.22132i
\(599\) −3.01349 + 5.21952i −0.123128 + 0.213264i −0.921000 0.389564i \(-0.872626\pi\)
0.797872 + 0.602827i \(0.205959\pi\)
\(600\) 0 0
\(601\) −1.86260 3.22612i −0.0759770 0.131596i 0.825534 0.564353i \(-0.190874\pi\)
−0.901511 + 0.432757i \(0.857541\pi\)
\(602\) 0.0452607 + 0.105392i 0.00184469 + 0.00429544i
\(603\) 0 0
\(604\) −3.45608 −0.140626
\(605\) −6.11632 10.5938i −0.248664 0.430698i
\(606\) 0 0
\(607\) −6.01651 −0.244203 −0.122101 0.992518i \(-0.538963\pi\)
−0.122101 + 0.992518i \(0.538963\pi\)
\(608\) 11.9358 + 20.6733i 0.484059 + 0.838415i
\(609\) 0 0
\(610\) 32.4105 1.31226
\(611\) −8.44814 + 41.2698i −0.341775 + 1.66960i
\(612\) 0 0
\(613\) 9.80825 0.396152 0.198076 0.980187i \(-0.436531\pi\)
0.198076 + 0.980187i \(0.436531\pi\)
\(614\) 6.34459 10.9892i 0.256047 0.443486i
\(615\) 0 0
\(616\) 8.11342 + 0.961543i 0.326899 + 0.0387417i
\(617\) 16.8838 29.2436i 0.679716 1.17730i −0.295350 0.955389i \(-0.595436\pi\)
0.975066 0.221914i \(-0.0712304\pi\)
\(618\) 0 0
\(619\) −2.04671 + 3.54501i −0.0822644 + 0.142486i −0.904222 0.427062i \(-0.859549\pi\)
0.821958 + 0.569548i \(0.192882\pi\)
\(620\) −6.30215 10.9156i −0.253100 0.438383i
\(621\) 0 0
\(622\) −1.94936 3.37639i −0.0781621 0.135381i
\(623\) −10.3829 + 13.9000i −0.415983 + 0.556891i
\(624\) 0 0
\(625\) 1.42115 + 2.46150i 0.0568459 + 0.0984599i
\(626\) 17.9459 0.717264
\(627\) 0 0
\(628\) −36.0695 −1.43933
\(629\) 8.47978 0.338111
\(630\) 0 0
\(631\) 13.3868 23.1866i 0.532921 0.923046i −0.466340 0.884605i \(-0.654428\pi\)
0.999261 0.0384402i \(-0.0122389\pi\)
\(632\) 0.272179 + 0.471427i 0.0108267 + 0.0187524i
\(633\) 0 0
\(634\) 63.5910 2.52552
\(635\) −11.7006 + 20.2661i −0.464325 + 0.804234i
\(636\) 0 0
\(637\) 14.4452 + 20.6963i 0.572340 + 0.820016i
\(638\) −1.40287 −0.0555403
\(639\) 0 0
\(640\) 8.14224 0.321850
\(641\) −9.28610 16.0840i −0.366779 0.635279i 0.622281 0.782794i \(-0.286206\pi\)
−0.989060 + 0.147514i \(0.952873\pi\)
\(642\) 0 0
\(643\) 1.96695 3.40686i 0.0775690 0.134353i −0.824632 0.565670i \(-0.808618\pi\)
0.902201 + 0.431317i \(0.141951\pi\)
\(644\) −19.0159 2.25362i −0.749330 0.0888051i
\(645\) 0 0
\(646\) 7.43035 0.292343
\(647\) 0.197076 0.00774784 0.00387392 0.999992i \(-0.498767\pi\)
0.00387392 + 0.999992i \(0.498767\pi\)
\(648\) 0 0
\(649\) −11.7387 20.3321i −0.460785 0.798104i
\(650\) −3.89922 + 19.0480i −0.152940 + 0.747125i
\(651\) 0 0
\(652\) −3.14172 5.44163i −0.123039 0.213110i
\(653\) −7.23363 + 12.5290i −0.283074 + 0.490298i −0.972140 0.234400i \(-0.924687\pi\)
0.689066 + 0.724698i \(0.258021\pi\)
\(654\) 0 0
\(655\) 1.36813 2.36967i 0.0534573 0.0925908i
\(656\) 23.7624 0.927765
\(657\) 0 0
\(658\) 58.4949 + 6.93238i 2.28037 + 0.270252i
\(659\) −11.7066 + 20.2764i −0.456024 + 0.789857i −0.998746 0.0500552i \(-0.984060\pi\)
0.542722 + 0.839912i \(0.317394\pi\)
\(660\) 0 0
\(661\) −4.04817 −0.157456 −0.0787278 0.996896i \(-0.525086\pi\)
−0.0787278 + 0.996896i \(0.525086\pi\)
\(662\) −18.1657 + 31.4638i −0.706028 + 1.22288i
\(663\) 0 0
\(664\) −11.2587 −0.436921
\(665\) 4.98628 + 11.6108i 0.193360 + 0.450246i
\(666\) 0 0
\(667\) −0.743487 −0.0287879
\(668\) 1.74448 3.02153i 0.0674959 0.116906i
\(669\) 0 0
\(670\) 11.6088 0.448487
\(671\) 50.7276 1.95832
\(672\) 0 0
\(673\) −3.64704 6.31685i −0.140583 0.243497i 0.787133 0.616783i \(-0.211564\pi\)
−0.927716 + 0.373286i \(0.878231\pi\)
\(674\) 29.8076 51.6283i 1.14815 1.98865i
\(675\) 0 0
\(676\) 16.9658 12.7208i 0.652529 0.489260i
\(677\) −7.87553 13.6408i −0.302681 0.524259i 0.674061 0.738676i \(-0.264548\pi\)
−0.976742 + 0.214416i \(0.931215\pi\)
\(678\) 0 0
\(679\) 5.52849 7.40119i 0.212164 0.284032i
\(680\) 0.622636 1.07844i 0.0238770 0.0413562i
\(681\) 0 0
\(682\) −21.9582 38.0327i −0.840822 1.45635i
\(683\) 20.7427 + 35.9274i 0.793697 + 1.37472i 0.923664 + 0.383204i \(0.125180\pi\)
−0.129967 + 0.991518i \(0.541487\pi\)
\(684\) 0 0
\(685\) −9.42819 + 16.3301i −0.360233 + 0.623941i
\(686\) 27.1439 22.5543i 1.03636 0.861127i
\(687\) 0 0
\(688\) 0.0523445 + 0.0906634i 0.00199562 + 0.00345651i
\(689\) −0.484993 + 0.161628i −0.0184767 + 0.00615754i
\(690\) 0 0
\(691\) 23.4108 40.5487i 0.890589 1.54255i 0.0514184 0.998677i \(-0.483626\pi\)
0.839171 0.543868i \(-0.183041\pi\)
\(692\) −13.5494 23.4683i −0.515073 0.892132i
\(693\) 0 0
\(694\) −22.2478 −0.844514
\(695\) −0.498992 −0.0189278
\(696\) 0 0
\(697\) 3.10534 5.37860i 0.117623 0.203729i
\(698\) 45.7152 1.73034
\(699\) 0 0
\(700\) 12.1279 + 1.43731i 0.458392 + 0.0543252i
\(701\) −29.8626 −1.12790 −0.563948 0.825810i \(-0.690718\pi\)
−0.563948 + 0.825810i \(0.690718\pi\)
\(702\) 0 0
\(703\) −11.4293 + 19.7961i −0.431063 + 0.746623i
\(704\) −21.2096 −0.799366
\(705\) 0 0
\(706\) 12.1893 21.1124i 0.458749 0.794576i
\(707\) 6.77281 + 0.802663i 0.254718 + 0.0301873i
\(708\) 0 0
\(709\) 26.9332 1.01150 0.505750 0.862680i \(-0.331216\pi\)
0.505750 + 0.862680i \(0.331216\pi\)
\(710\) −13.9932 + 24.2369i −0.525155 + 0.909595i
\(711\) 0 0
\(712\) −2.30450 + 3.99151i −0.0863647 + 0.149588i
\(713\) −11.6373 20.1563i −0.435819 0.754861i
\(714\) 0 0
\(715\) 4.68004 22.8623i 0.175023 0.855003i
\(716\) −0.440002 0.762105i −0.0164436 0.0284812i
\(717\) 0 0
\(718\) −23.5141 −0.877537
\(719\) 14.4988 0.540713 0.270356 0.962760i \(-0.412859\pi\)
0.270356 + 0.962760i \(0.412859\pi\)
\(720\) 0 0
\(721\) −17.6058 40.9959i −0.655675 1.52677i
\(722\) 8.08799 14.0088i 0.301004 0.521354i
\(723\) 0 0
\(724\) −2.26049 3.91528i −0.0840105 0.145510i
\(725\) 0.474180 0.0176106
\(726\) 0 0
\(727\) −6.26424 −0.232328 −0.116164 0.993230i \(-0.537060\pi\)
−0.116164 + 0.993230i \(0.537060\pi\)
\(728\) 4.45779 + 5.00817i 0.165217 + 0.185615i
\(729\) 0 0
\(730\) −21.3926 + 37.0531i −0.791776 + 1.37140i
\(731\) 0.0273621 0.00101203
\(732\) 0 0
\(733\) 5.99189 + 10.3783i 0.221316 + 0.383330i 0.955208 0.295936i \(-0.0956316\pi\)
−0.733892 + 0.679266i \(0.762298\pi\)
\(734\) −1.93487 + 3.35130i −0.0714175 + 0.123699i
\(735\) 0 0
\(736\) −32.6704 −1.20425
\(737\) 18.1696 0.669286
\(738\) 0 0
\(739\) 13.5254 0.497539 0.248770 0.968563i \(-0.419974\pi\)
0.248770 + 0.968563i \(0.419974\pi\)
\(740\) −8.47091 14.6721i −0.311397 0.539355i
\(741\) 0 0
\(742\) 0.282075 + 0.656825i 0.0103553 + 0.0241128i
\(743\) −19.2299 33.3072i −0.705477 1.22192i −0.966519 0.256594i \(-0.917400\pi\)
0.261043 0.965327i \(-0.415934\pi\)
\(744\) 0 0
\(745\) 2.88966 + 5.00504i 0.105869 + 0.183371i
\(746\) 3.69107 6.39312i 0.135140 0.234069i
\(747\) 0 0
\(748\) −4.30973 + 7.46466i −0.157579 + 0.272935i
\(749\) −13.7476 + 18.4044i −0.502326 + 0.672482i
\(750\) 0 0
\(751\) −5.85573 + 10.1424i −0.213679 + 0.370102i −0.952863 0.303401i \(-0.901878\pi\)
0.739184 + 0.673503i \(0.235211\pi\)
\(752\) 53.7635 1.96055
\(753\) 0 0
\(754\) −0.861315 0.763875i −0.0313672 0.0278187i
\(755\) −3.12125 −0.113594
\(756\) 0 0
\(757\) −4.65791 8.06773i −0.169295 0.293227i 0.768877 0.639396i \(-0.220816\pi\)
−0.938172 + 0.346169i \(0.887482\pi\)
\(758\) −27.7600 −1.00829
\(759\) 0 0
\(760\) 1.67841 + 2.90709i 0.0608824 + 0.105451i
\(761\) 43.9381 1.59276 0.796378 0.604799i \(-0.206747\pi\)
0.796378 + 0.604799i \(0.206747\pi\)
\(762\) 0 0
\(763\) −19.0643 + 25.5220i −0.690173 + 0.923959i
\(764\) −16.5079 28.5926i −0.597236 1.03444i
\(765\) 0 0
\(766\) −25.5172 + 44.1971i −0.921973 + 1.59690i
\(767\) 3.86381 18.8750i 0.139514 0.681537i
\(768\) 0 0
\(769\) −12.6771 21.9573i −0.457147 0.791802i 0.541662 0.840597i \(-0.317795\pi\)
−0.998809 + 0.0487946i \(0.984462\pi\)
\(770\) −32.4045 3.84035i −1.16778 0.138397i
\(771\) 0 0
\(772\) 13.3568 + 23.1347i 0.480723 + 0.832637i
\(773\) −11.5542 20.0125i −0.415576 0.719798i 0.579913 0.814678i \(-0.303087\pi\)
−0.995489 + 0.0948801i \(0.969753\pi\)
\(774\) 0 0
\(775\) 7.42200 + 12.8553i 0.266606 + 0.461775i
\(776\) 1.22705 2.12532i 0.0440487 0.0762946i
\(777\) 0 0
\(778\) 11.4474 + 19.8275i 0.410410 + 0.710851i
\(779\) 8.37091 + 14.4988i 0.299919 + 0.519475i
\(780\) 0 0
\(781\) −21.9015 + 37.9346i −0.783699 + 1.35741i
\(782\) −5.08456 + 8.80672i −0.181824 + 0.314928i
\(783\) 0 0
\(784\) 22.1800 23.3586i 0.792145 0.834236i
\(785\) −32.5750 −1.16265
\(786\) 0 0
\(787\) 12.3346 + 21.3642i 0.439682 + 0.761551i 0.997665 0.0683012i \(-0.0217579\pi\)
−0.557983 + 0.829852i \(0.688425\pi\)
\(788\) 16.0943 27.8761i 0.573334 0.993044i
\(789\) 0 0
\(790\) −1.08707