Properties

Label 380.2.i.c.121.2
Level $380$
Weight $2$
Character 380.121
Analytic conductor $3.034$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.2
Root \(0.354609 + 0.614201i\) of defining polynomial
Character \(\chi\) \(=\) 380.121
Dual form 380.2.i.c.201.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.354609 - 0.614201i) q^{3} +(-0.500000 - 0.866025i) q^{5} +3.11079 q^{7} +(1.24850 - 2.16247i) q^{9} +O(q^{10})\) \(q+(-0.354609 - 0.614201i) q^{3} +(-0.500000 - 0.866025i) q^{5} +3.11079 q^{7} +(1.24850 - 2.16247i) q^{9} -3.52922 q^{11} +(-0.200785 + 0.347770i) q^{13} +(-0.354609 + 0.614201i) q^{15} +(-1.74850 - 3.02850i) q^{17} +(4.35162 - 0.251824i) q^{19} +(-1.10311 - 1.91065i) q^{21} +(3.65851 - 6.33672i) q^{23} +(-0.500000 + 0.866025i) q^{25} -3.89858 q^{27} +(3.96540 - 6.86827i) q^{29} +5.73545 q^{31} +(1.25150 + 2.16765i) q^{33} +(-1.55539 - 2.69402i) q^{35} -10.5292 q^{37} +0.284801 q^{39} +(0.555394 + 0.961971i) q^{41} +(4.30390 + 7.45457i) q^{43} -2.49701 q^{45} +(-3.76162 + 6.51532i) q^{47} +2.67700 q^{49} +(-1.24007 + 2.14787i) q^{51} +(-5.27773 + 9.14130i) q^{53} +(1.76461 + 3.05640i) q^{55} +(-1.69779 - 2.58347i) q^{57} +(4.25618 + 7.37192i) q^{59} +(4.61079 - 7.98612i) q^{61} +(3.88383 - 6.72700i) q^{63} +0.401570 q^{65} +(-4.20623 + 7.28540i) q^{67} -5.18936 q^{69} +(4.31233 + 7.46918i) q^{71} +(-0.870717 - 1.50813i) q^{73} +0.709218 q^{75} -10.9787 q^{77} +(4.50544 + 7.80366i) q^{79} +(-2.36304 - 4.09291i) q^{81} +4.07857 q^{83} +(-1.74850 + 3.02850i) q^{85} -5.62466 q^{87} +(6.61623 - 11.4596i) q^{89} +(-0.624599 + 1.08184i) q^{91} +(-2.03384 - 3.52272i) q^{93} +(-2.39390 - 3.64270i) q^{95} +(3.85162 + 6.67120i) q^{97} +(-4.40625 + 7.63186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} - 4 q^{5} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{3} - 4 q^{5} - 5 q^{9} + 4 q^{11} + 9 q^{13} - q^{15} + q^{17} + 3 q^{19} + 8 q^{21} - 4 q^{25} + 20 q^{27} + 5 q^{29} - 20 q^{31} + 25 q^{33} - 52 q^{37} - 54 q^{39} - 8 q^{41} + 7 q^{43} + 10 q^{45} + 16 q^{47} + 20 q^{49} + 12 q^{51} + 5 q^{53} - 2 q^{55} + 27 q^{57} + 11 q^{59} + 12 q^{61} - 3 q^{63} - 18 q^{65} + 6 q^{69} + 14 q^{71} - 4 q^{73} + 2 q^{75} - 44 q^{77} + 13 q^{79} - 24 q^{81} + 10 q^{83} + q^{85} - 4 q^{87} + 5 q^{89} - 46 q^{91} - 28 q^{93} - 6 q^{95} - q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.354609 0.614201i −0.204734 0.354609i 0.745314 0.666713i \(-0.232299\pi\)
−0.950048 + 0.312104i \(0.898966\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 3.11079 1.17577 0.587884 0.808945i \(-0.299961\pi\)
0.587884 + 0.808945i \(0.299961\pi\)
\(8\) 0 0
\(9\) 1.24850 2.16247i 0.416168 0.720825i
\(10\) 0 0
\(11\) −3.52922 −1.06410 −0.532051 0.846713i \(-0.678578\pi\)
−0.532051 + 0.846713i \(0.678578\pi\)
\(12\) 0 0
\(13\) −0.200785 + 0.347770i −0.0556877 + 0.0964540i −0.892525 0.450997i \(-0.851068\pi\)
0.836838 + 0.547451i \(0.184402\pi\)
\(14\) 0 0
\(15\) −0.354609 + 0.614201i −0.0915597 + 0.158586i
\(16\) 0 0
\(17\) −1.74850 3.02850i −0.424075 0.734519i 0.572259 0.820073i \(-0.306067\pi\)
−0.996334 + 0.0855542i \(0.972734\pi\)
\(18\) 0 0
\(19\) 4.35162 0.251824i 0.998330 0.0577725i
\(20\) 0 0
\(21\) −1.10311 1.91065i −0.240719 0.416938i
\(22\) 0 0
\(23\) 3.65851 6.33672i 0.762852 1.32130i −0.178523 0.983936i \(-0.557132\pi\)
0.941375 0.337362i \(-0.109535\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −3.89858 −0.750282
\(28\) 0 0
\(29\) 3.96540 6.86827i 0.736356 1.27541i −0.217770 0.976000i \(-0.569878\pi\)
0.954126 0.299406i \(-0.0967884\pi\)
\(30\) 0 0
\(31\) 5.73545 1.03012 0.515059 0.857155i \(-0.327770\pi\)
0.515059 + 0.857155i \(0.327770\pi\)
\(32\) 0 0
\(33\) 1.25150 + 2.16765i 0.217857 + 0.377340i
\(34\) 0 0
\(35\) −1.55539 2.69402i −0.262910 0.455373i
\(36\) 0 0
\(37\) −10.5292 −1.73099 −0.865497 0.500914i \(-0.832997\pi\)
−0.865497 + 0.500914i \(0.832997\pi\)
\(38\) 0 0
\(39\) 0.284801 0.0456046
\(40\) 0 0
\(41\) 0.555394 + 0.961971i 0.0867380 + 0.150235i 0.906130 0.422998i \(-0.139022\pi\)
−0.819392 + 0.573233i \(0.805689\pi\)
\(42\) 0 0
\(43\) 4.30390 + 7.45457i 0.656338 + 1.13681i 0.981556 + 0.191172i \(0.0612290\pi\)
−0.325218 + 0.945639i \(0.605438\pi\)
\(44\) 0 0
\(45\) −2.49701 −0.372232
\(46\) 0 0
\(47\) −3.76162 + 6.51532i −0.548689 + 0.950357i 0.449676 + 0.893192i \(0.351540\pi\)
−0.998365 + 0.0571653i \(0.981794\pi\)
\(48\) 0 0
\(49\) 2.67700 0.382429
\(50\) 0 0
\(51\) −1.24007 + 2.14787i −0.173645 + 0.300762i
\(52\) 0 0
\(53\) −5.27773 + 9.14130i −0.724952 + 1.25565i 0.234042 + 0.972227i \(0.424805\pi\)
−0.958994 + 0.283427i \(0.908529\pi\)
\(54\) 0 0
\(55\) 1.76461 + 3.05640i 0.237940 + 0.412125i
\(56\) 0 0
\(57\) −1.69779 2.58347i −0.224878 0.342189i
\(58\) 0 0
\(59\) 4.25618 + 7.37192i 0.554107 + 0.959742i 0.997972 + 0.0636484i \(0.0202736\pi\)
−0.443865 + 0.896094i \(0.646393\pi\)
\(60\) 0 0
\(61\) 4.61079 7.98612i 0.590351 1.02252i −0.403834 0.914832i \(-0.632323\pi\)
0.994185 0.107686i \(-0.0343440\pi\)
\(62\) 0 0
\(63\) 3.88383 6.72700i 0.489317 0.847522i
\(64\) 0 0
\(65\) 0.401570 0.0498086
\(66\) 0 0
\(67\) −4.20623 + 7.28540i −0.513873 + 0.890053i 0.485998 + 0.873960i \(0.338456\pi\)
−0.999870 + 0.0160934i \(0.994877\pi\)
\(68\) 0 0
\(69\) −5.18936 −0.624726
\(70\) 0 0
\(71\) 4.31233 + 7.46918i 0.511780 + 0.886428i 0.999907 + 0.0136558i \(0.00434692\pi\)
−0.488127 + 0.872773i \(0.662320\pi\)
\(72\) 0 0
\(73\) −0.870717 1.50813i −0.101910 0.176513i 0.810562 0.585653i \(-0.199162\pi\)
−0.912471 + 0.409140i \(0.865829\pi\)
\(74\) 0 0
\(75\) 0.709218 0.0818935
\(76\) 0 0
\(77\) −10.9787 −1.25114
\(78\) 0 0
\(79\) 4.50544 + 7.80366i 0.506902 + 0.877980i 0.999968 + 0.00798806i \(0.00254271\pi\)
−0.493066 + 0.869992i \(0.664124\pi\)
\(80\) 0 0
\(81\) −2.36304 4.09291i −0.262560 0.454768i
\(82\) 0 0
\(83\) 4.07857 0.447682 0.223841 0.974626i \(-0.428140\pi\)
0.223841 + 0.974626i \(0.428140\pi\)
\(84\) 0 0
\(85\) −1.74850 + 3.02850i −0.189652 + 0.328487i
\(86\) 0 0
\(87\) −5.62466 −0.603027
\(88\) 0 0
\(89\) 6.61623 11.4596i 0.701319 1.21472i −0.266685 0.963784i \(-0.585928\pi\)
0.968004 0.250936i \(-0.0807385\pi\)
\(90\) 0 0
\(91\) −0.624599 + 1.08184i −0.0654758 + 0.113407i
\(92\) 0 0
\(93\) −2.03384 3.52272i −0.210900 0.365289i
\(94\) 0 0
\(95\) −2.39390 3.64270i −0.245609 0.373733i
\(96\) 0 0
\(97\) 3.85162 + 6.67120i 0.391073 + 0.677358i 0.992591 0.121501i \(-0.0387708\pi\)
−0.601519 + 0.798859i \(0.705437\pi\)
\(98\) 0 0
\(99\) −4.40625 + 7.63186i −0.442845 + 0.767030i
\(100\) 0 0
\(101\) −8.68773 + 15.0476i −0.864462 + 1.49729i 0.00311897 + 0.999995i \(0.499007\pi\)
−0.867581 + 0.497296i \(0.834326\pi\)
\(102\) 0 0
\(103\) −7.12614 −0.702159 −0.351080 0.936346i \(-0.614185\pi\)
−0.351080 + 0.936346i \(0.614185\pi\)
\(104\) 0 0
\(105\) −1.10311 + 1.91065i −0.107653 + 0.186460i
\(106\) 0 0
\(107\) 0.735452 0.0710989 0.0355494 0.999368i \(-0.488682\pi\)
0.0355494 + 0.999368i \(0.488682\pi\)
\(108\) 0 0
\(109\) 8.00468 + 13.8645i 0.766710 + 1.32798i 0.939338 + 0.342993i \(0.111441\pi\)
−0.172628 + 0.984987i \(0.555226\pi\)
\(110\) 0 0
\(111\) 3.73376 + 6.46706i 0.354393 + 0.613826i
\(112\) 0 0
\(113\) 4.34923 0.409141 0.204571 0.978852i \(-0.434420\pi\)
0.204571 + 0.978852i \(0.434420\pi\)
\(114\) 0 0
\(115\) −7.31702 −0.682315
\(116\) 0 0
\(117\) 0.501362 + 0.868384i 0.0463509 + 0.0802822i
\(118\) 0 0
\(119\) −5.43923 9.42102i −0.498613 0.863623i
\(120\) 0 0
\(121\) 1.45543 0.132312
\(122\) 0 0
\(123\) 0.393896 0.682247i 0.0355164 0.0615162i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.32300 4.02355i 0.206133 0.357032i −0.744360 0.667778i \(-0.767245\pi\)
0.950493 + 0.310746i \(0.100579\pi\)
\(128\) 0 0
\(129\) 3.05240 5.28692i 0.268749 0.465487i
\(130\) 0 0
\(131\) −5.24775 9.08936i −0.458498 0.794141i 0.540384 0.841418i \(-0.318279\pi\)
−0.998882 + 0.0472772i \(0.984946\pi\)
\(132\) 0 0
\(133\) 13.5370 0.783372i 1.17380 0.0679270i
\(134\) 0 0
\(135\) 1.94929 + 3.37627i 0.167768 + 0.290583i
\(136\) 0 0
\(137\) 0.696101 1.20568i 0.0594719 0.103008i −0.834757 0.550619i \(-0.814392\pi\)
0.894228 + 0.447611i \(0.147725\pi\)
\(138\) 0 0
\(139\) 3.03766 5.26138i 0.257651 0.446264i −0.707961 0.706251i \(-0.750385\pi\)
0.965612 + 0.259987i \(0.0837183\pi\)
\(140\) 0 0
\(141\) 5.33562 0.449340
\(142\) 0 0
\(143\) 0.708615 1.22736i 0.0592574 0.102637i
\(144\) 0 0
\(145\) −7.93079 −0.658617
\(146\) 0 0
\(147\) −0.949290 1.64422i −0.0782961 0.135613i
\(148\) 0 0
\(149\) 0.0422770 + 0.0732259i 0.00346347 + 0.00599890i 0.867752 0.496998i \(-0.165564\pi\)
−0.864288 + 0.502996i \(0.832231\pi\)
\(150\) 0 0
\(151\) −15.2216 −1.23871 −0.619357 0.785109i \(-0.712607\pi\)
−0.619357 + 0.785109i \(0.712607\pi\)
\(152\) 0 0
\(153\) −8.73207 −0.705946
\(154\) 0 0
\(155\) −2.86773 4.96705i −0.230341 0.398963i
\(156\) 0 0
\(157\) −8.12935 14.0804i −0.648793 1.12374i −0.983412 0.181388i \(-0.941941\pi\)
0.334619 0.942354i \(-0.391392\pi\)
\(158\) 0 0
\(159\) 7.48612 0.593688
\(160\) 0 0
\(161\) 11.3808 19.7122i 0.896936 1.55354i
\(162\) 0 0
\(163\) 14.9461 1.17067 0.585336 0.810791i \(-0.300963\pi\)
0.585336 + 0.810791i \(0.300963\pi\)
\(164\) 0 0
\(165\) 1.25150 2.16765i 0.0974288 0.168752i
\(166\) 0 0
\(167\) −6.26461 + 10.8506i −0.484770 + 0.839647i −0.999847 0.0174974i \(-0.994430\pi\)
0.515077 + 0.857144i \(0.327763\pi\)
\(168\) 0 0
\(169\) 6.41937 + 11.1187i 0.493798 + 0.855283i
\(170\) 0 0
\(171\) 4.88845 9.72466i 0.373829 0.743664i
\(172\) 0 0
\(173\) −8.69242 15.0557i −0.660872 1.14466i −0.980387 0.197083i \(-0.936853\pi\)
0.319515 0.947581i \(-0.396480\pi\)
\(174\) 0 0
\(175\) −1.55539 + 2.69402i −0.117577 + 0.203649i
\(176\) 0 0
\(177\) 3.01856 5.22830i 0.226889 0.392983i
\(178\) 0 0
\(179\) 20.7830 1.55340 0.776698 0.629873i \(-0.216893\pi\)
0.776698 + 0.629873i \(0.216893\pi\)
\(180\) 0 0
\(181\) −0.814564 + 1.41087i −0.0605460 + 0.104869i −0.894710 0.446648i \(-0.852618\pi\)
0.834164 + 0.551517i \(0.185951\pi\)
\(182\) 0 0
\(183\) −6.54011 −0.483459
\(184\) 0 0
\(185\) 5.26461 + 9.11858i 0.387062 + 0.670411i
\(186\) 0 0
\(187\) 6.17087 + 10.6883i 0.451258 + 0.781603i
\(188\) 0 0
\(189\) −12.1277 −0.882157
\(190\) 0 0
\(191\) −13.4016 −0.969704 −0.484852 0.874596i \(-0.661126\pi\)
−0.484852 + 0.874596i \(0.661126\pi\)
\(192\) 0 0
\(193\) 5.34693 + 9.26116i 0.384881 + 0.666633i 0.991753 0.128167i \(-0.0409092\pi\)
−0.606872 + 0.794800i \(0.707576\pi\)
\(194\) 0 0
\(195\) −0.142400 0.246645i −0.0101975 0.0176626i
\(196\) 0 0
\(197\) −7.00611 −0.499165 −0.249582 0.968354i \(-0.580293\pi\)
−0.249582 + 0.968354i \(0.580293\pi\)
\(198\) 0 0
\(199\) 10.3909 17.9976i 0.736592 1.27581i −0.217430 0.976076i \(-0.569767\pi\)
0.954021 0.299738i \(-0.0968994\pi\)
\(200\) 0 0
\(201\) 5.96627 0.420828
\(202\) 0 0
\(203\) 12.3355 21.3657i 0.865783 1.49958i
\(204\) 0 0
\(205\) 0.555394 0.961971i 0.0387904 0.0671870i
\(206\) 0 0
\(207\) −9.13533 15.8229i −0.634949 1.09976i
\(208\) 0 0
\(209\) −15.3578 + 0.888745i −1.06232 + 0.0614758i
\(210\) 0 0
\(211\) 5.61623 + 9.72760i 0.386637 + 0.669675i 0.991995 0.126278i \(-0.0403032\pi\)
−0.605358 + 0.795954i \(0.706970\pi\)
\(212\) 0 0
\(213\) 3.05838 5.29728i 0.209557 0.362963i
\(214\) 0 0
\(215\) 4.30390 7.45457i 0.293523 0.508398i
\(216\) 0 0
\(217\) 17.8418 1.21118
\(218\) 0 0
\(219\) −0.617528 + 1.06959i −0.0417287 + 0.0722762i
\(220\) 0 0
\(221\) 1.40429 0.0944630
\(222\) 0 0
\(223\) 5.45005 + 9.43976i 0.364962 + 0.632133i 0.988770 0.149445i \(-0.0477486\pi\)
−0.623808 + 0.781578i \(0.714415\pi\)
\(224\) 0 0
\(225\) 1.24850 + 2.16247i 0.0832336 + 0.144165i
\(226\) 0 0
\(227\) 3.96627 0.263250 0.131625 0.991300i \(-0.457980\pi\)
0.131625 + 0.991300i \(0.457980\pi\)
\(228\) 0 0
\(229\) −10.9139 −0.721213 −0.360606 0.932718i \(-0.617430\pi\)
−0.360606 + 0.932718i \(0.617430\pi\)
\(230\) 0 0
\(231\) 3.89314 + 6.74311i 0.256150 + 0.443664i
\(232\) 0 0
\(233\) 7.79547 + 13.5021i 0.510698 + 0.884555i 0.999923 + 0.0123973i \(0.00394628\pi\)
−0.489225 + 0.872157i \(0.662720\pi\)
\(234\) 0 0
\(235\) 7.52324 0.490762
\(236\) 0 0
\(237\) 3.19534 5.53450i 0.207560 0.359504i
\(238\) 0 0
\(239\) −8.09544 −0.523650 −0.261825 0.965115i \(-0.584324\pi\)
−0.261825 + 0.965115i \(0.584324\pi\)
\(240\) 0 0
\(241\) 12.6425 21.8974i 0.814373 1.41054i −0.0954047 0.995439i \(-0.530415\pi\)
0.909777 0.415096i \(-0.136252\pi\)
\(242\) 0 0
\(243\) −7.52378 + 13.0316i −0.482651 + 0.835976i
\(244\) 0 0
\(245\) −1.33850 2.31835i −0.0855137 0.148114i
\(246\) 0 0
\(247\) −0.786163 + 1.56392i −0.0500223 + 0.0995101i
\(248\) 0 0
\(249\) −1.44630 2.50506i −0.0916555 0.158752i
\(250\) 0 0
\(251\) −3.94461 + 6.83226i −0.248981 + 0.431248i −0.963243 0.268630i \(-0.913429\pi\)
0.714262 + 0.699878i \(0.246762\pi\)
\(252\) 0 0
\(253\) −12.9117 + 22.3637i −0.811751 + 1.40599i
\(254\) 0 0
\(255\) 2.48014 0.155313
\(256\) 0 0
\(257\) 4.59305 7.95540i 0.286507 0.496244i −0.686467 0.727161i \(-0.740839\pi\)
0.972973 + 0.230917i \(0.0741726\pi\)
\(258\) 0 0
\(259\) −32.7542 −2.03525
\(260\) 0 0
\(261\) −9.90163 17.1501i −0.612896 1.06157i
\(262\) 0 0
\(263\) −12.1217 20.9954i −0.747454 1.29463i −0.949039 0.315158i \(-0.897942\pi\)
0.201585 0.979471i \(-0.435391\pi\)
\(264\) 0 0
\(265\) 10.5555 0.648417
\(266\) 0 0
\(267\) −9.38470 −0.574335
\(268\) 0 0
\(269\) −0.712209 1.23358i −0.0434241 0.0752128i 0.843496 0.537135i \(-0.180493\pi\)
−0.886921 + 0.461922i \(0.847160\pi\)
\(270\) 0 0
\(271\) 5.19617 + 9.00002i 0.315645 + 0.546712i 0.979574 0.201083i \(-0.0644459\pi\)
−0.663930 + 0.747795i \(0.731113\pi\)
\(272\) 0 0
\(273\) 0.885955 0.0536204
\(274\) 0 0
\(275\) 1.76461 3.05640i 0.106410 0.184308i
\(276\) 0 0
\(277\) 20.3078 1.22018 0.610088 0.792334i \(-0.291134\pi\)
0.610088 + 0.792334i \(0.291134\pi\)
\(278\) 0 0
\(279\) 7.16074 12.4028i 0.428702 0.742534i
\(280\) 0 0
\(281\) −7.79547 + 13.5021i −0.465038 + 0.805470i −0.999203 0.0399101i \(-0.987293\pi\)
0.534165 + 0.845380i \(0.320626\pi\)
\(282\) 0 0
\(283\) −13.6323 23.6119i −0.810358 1.40358i −0.912613 0.408824i \(-0.865939\pi\)
0.102255 0.994758i \(-0.467394\pi\)
\(284\) 0 0
\(285\) −1.38845 + 2.76207i −0.0822448 + 0.163611i
\(286\) 0 0
\(287\) 1.72771 + 2.99249i 0.101984 + 0.176641i
\(288\) 0 0
\(289\) 2.38546 4.13174i 0.140321 0.243044i
\(290\) 0 0
\(291\) 2.73164 4.73134i 0.160131 0.277356i
\(292\) 0 0
\(293\) −12.6710 −0.740249 −0.370125 0.928982i \(-0.620685\pi\)
−0.370125 + 0.928982i \(0.620685\pi\)
\(294\) 0 0
\(295\) 4.25618 7.37192i 0.247804 0.429210i
\(296\) 0 0
\(297\) 13.7590 0.798376
\(298\) 0 0
\(299\) 1.46915 + 2.54464i 0.0849630 + 0.147160i
\(300\) 0 0
\(301\) 13.3885 + 23.1896i 0.771701 + 1.33663i
\(302\) 0 0
\(303\) 12.3230 0.707938
\(304\) 0 0
\(305\) −9.22158 −0.528026
\(306\) 0 0
\(307\) −1.28540 2.22638i −0.0733619 0.127066i 0.827011 0.562186i \(-0.190039\pi\)
−0.900373 + 0.435119i \(0.856706\pi\)
\(308\) 0 0
\(309\) 2.52699 + 4.37688i 0.143756 + 0.248992i
\(310\) 0 0
\(311\) 19.7568 1.12030 0.560152 0.828390i \(-0.310743\pi\)
0.560152 + 0.828390i \(0.310743\pi\)
\(312\) 0 0
\(313\) −11.1877 + 19.3777i −0.632368 + 1.09529i 0.354698 + 0.934981i \(0.384584\pi\)
−0.987066 + 0.160313i \(0.948750\pi\)
\(314\) 0 0
\(315\) −7.76767 −0.437658
\(316\) 0 0
\(317\) −6.65313 + 11.5236i −0.373677 + 0.647228i −0.990128 0.140166i \(-0.955236\pi\)
0.616451 + 0.787393i \(0.288570\pi\)
\(318\) 0 0
\(319\) −13.9948 + 24.2397i −0.783557 + 1.35716i
\(320\) 0 0
\(321\) −0.260798 0.451716i −0.0145563 0.0252123i
\(322\) 0 0
\(323\) −8.37148 12.7386i −0.465801 0.708792i
\(324\) 0 0
\(325\) −0.200785 0.347770i −0.0111375 0.0192908i
\(326\) 0 0
\(327\) 5.67707 9.83297i 0.313943 0.543764i
\(328\) 0 0
\(329\) −11.7016 + 20.2678i −0.645131 + 1.11740i
\(330\) 0 0
\(331\) −19.6173 −1.07826 −0.539132 0.842221i \(-0.681248\pi\)
−0.539132 + 0.842221i \(0.681248\pi\)
\(332\) 0 0
\(333\) −13.1458 + 22.7692i −0.720385 + 1.24774i
\(334\) 0 0
\(335\) 8.41246 0.459622
\(336\) 0 0
\(337\) 14.5909 + 25.2722i 0.794819 + 1.37667i 0.922954 + 0.384910i \(0.125767\pi\)
−0.128136 + 0.991757i \(0.540899\pi\)
\(338\) 0 0
\(339\) −1.54228 2.67130i −0.0837650 0.145085i
\(340\) 0 0
\(341\) −20.2417 −1.09615
\(342\) 0 0
\(343\) −13.4479 −0.726120
\(344\) 0 0
\(345\) 2.59468 + 4.49412i 0.139693 + 0.241955i
\(346\) 0 0
\(347\) 6.03935 + 10.4605i 0.324209 + 0.561547i 0.981352 0.192219i \(-0.0615684\pi\)
−0.657143 + 0.753766i \(0.728235\pi\)
\(348\) 0 0
\(349\) 20.2894 1.08607 0.543033 0.839711i \(-0.317276\pi\)
0.543033 + 0.839711i \(0.317276\pi\)
\(350\) 0 0
\(351\) 0.782776 1.35581i 0.0417815 0.0723677i
\(352\) 0 0
\(353\) 6.69387 0.356279 0.178139 0.984005i \(-0.442992\pi\)
0.178139 + 0.984005i \(0.442992\pi\)
\(354\) 0 0
\(355\) 4.31233 7.46918i 0.228875 0.396423i
\(356\) 0 0
\(357\) −3.85760 + 6.68156i −0.204166 + 0.353626i
\(358\) 0 0
\(359\) −4.94536 8.56562i −0.261006 0.452076i 0.705503 0.708707i \(-0.250721\pi\)
−0.966510 + 0.256630i \(0.917388\pi\)
\(360\) 0 0
\(361\) 18.8732 2.19169i 0.993325 0.115352i
\(362\) 0 0
\(363\) −0.516108 0.893925i −0.0270886 0.0469189i
\(364\) 0 0
\(365\) −0.870717 + 1.50813i −0.0455754 + 0.0789389i
\(366\) 0 0
\(367\) −8.09936 + 14.0285i −0.422783 + 0.732282i −0.996211 0.0869742i \(-0.972280\pi\)
0.573427 + 0.819257i \(0.305614\pi\)
\(368\) 0 0
\(369\) 2.77365 0.144390
\(370\) 0 0
\(371\) −16.4179 + 28.4366i −0.852375 + 1.47636i
\(372\) 0 0
\(373\) 10.3003 0.533328 0.266664 0.963790i \(-0.414079\pi\)
0.266664 + 0.963790i \(0.414079\pi\)
\(374\) 0 0
\(375\) −0.354609 0.614201i −0.0183119 0.0317172i
\(376\) 0 0
\(377\) 1.59238 + 2.75809i 0.0820120 + 0.142049i
\(378\) 0 0
\(379\) −21.2587 −1.09199 −0.545993 0.837790i \(-0.683847\pi\)
−0.545993 + 0.837790i \(0.683847\pi\)
\(380\) 0 0
\(381\) −3.29502 −0.168809
\(382\) 0 0
\(383\) 6.79002 + 11.7607i 0.346954 + 0.600942i 0.985707 0.168470i \(-0.0538827\pi\)
−0.638753 + 0.769412i \(0.720549\pi\)
\(384\) 0 0
\(385\) 5.48934 + 9.50781i 0.279762 + 0.484563i
\(386\) 0 0
\(387\) 21.4938 1.09259
\(388\) 0 0
\(389\) −8.98771 + 15.5672i −0.455695 + 0.789287i −0.998728 0.0504248i \(-0.983942\pi\)
0.543033 + 0.839711i \(0.317276\pi\)
\(390\) 0 0
\(391\) −25.5877 −1.29402
\(392\) 0 0
\(393\) −3.72180 + 6.44634i −0.187740 + 0.325175i
\(394\) 0 0
\(395\) 4.50544 7.80366i 0.226693 0.392645i
\(396\) 0 0
\(397\) −12.0169 20.8139i −0.603112 1.04462i −0.992347 0.123483i \(-0.960594\pi\)
0.389234 0.921139i \(-0.372740\pi\)
\(398\) 0 0
\(399\) −5.28148 8.03663i −0.264405 0.402335i
\(400\) 0 0
\(401\) 5.91076 + 10.2377i 0.295169 + 0.511248i 0.975024 0.222098i \(-0.0712906\pi\)
−0.679855 + 0.733347i \(0.737957\pi\)
\(402\) 0 0
\(403\) −1.15159 + 1.99462i −0.0573649 + 0.0993589i
\(404\) 0 0
\(405\) −2.36304 + 4.09291i −0.117421 + 0.203378i
\(406\) 0 0
\(407\) 37.1600 1.84195
\(408\) 0 0
\(409\) 15.6300 27.0719i 0.772851 1.33862i −0.163143 0.986602i \(-0.552163\pi\)
0.935994 0.352015i \(-0.114504\pi\)
\(410\) 0 0
\(411\) −0.987375 −0.0487036
\(412\) 0 0
\(413\) 13.2401 + 22.9325i 0.651501 + 1.12843i
\(414\) 0 0
\(415\) −2.03929 3.53215i −0.100105 0.173386i
\(416\) 0 0
\(417\) −4.30872 −0.210999
\(418\) 0 0
\(419\) −22.4217 −1.09537 −0.547686 0.836684i \(-0.684491\pi\)
−0.547686 + 0.836684i \(0.684491\pi\)
\(420\) 0 0
\(421\) −13.6431 23.6305i −0.664922 1.15168i −0.979306 0.202384i \(-0.935131\pi\)
0.314384 0.949296i \(-0.398202\pi\)
\(422\) 0 0
\(423\) 9.39281 + 16.2688i 0.456694 + 0.791017i
\(424\) 0 0
\(425\) 3.49701 0.169630
\(426\) 0 0
\(427\) 14.3432 24.8431i 0.694115 1.20224i
\(428\) 0 0
\(429\) −1.00513 −0.0485279
\(430\) 0 0
\(431\) −13.6686 + 23.6748i −0.658395 + 1.14037i 0.322636 + 0.946523i \(0.395431\pi\)
−0.981031 + 0.193850i \(0.937902\pi\)
\(432\) 0 0
\(433\) 3.67761 6.36980i 0.176734 0.306113i −0.764026 0.645186i \(-0.776780\pi\)
0.940760 + 0.339073i \(0.110113\pi\)
\(434\) 0 0
\(435\) 2.81233 + 4.87110i 0.134841 + 0.233551i
\(436\) 0 0
\(437\) 14.3247 28.4963i 0.685243 1.36316i
\(438\) 0 0
\(439\) −2.11862 3.66955i −0.101116 0.175138i 0.811029 0.585006i \(-0.198908\pi\)
−0.912145 + 0.409868i \(0.865575\pi\)
\(440\) 0 0
\(441\) 3.34225 5.78895i 0.159155 0.275664i
\(442\) 0 0
\(443\) 11.1310 19.2794i 0.528849 0.915993i −0.470585 0.882354i \(-0.655957\pi\)
0.999434 0.0336383i \(-0.0107094\pi\)
\(444\) 0 0
\(445\) −13.2325 −0.627279
\(446\) 0 0
\(447\) 0.0299836 0.0519332i 0.00141818 0.00245635i
\(448\) 0 0
\(449\) 4.46328 0.210635 0.105318 0.994439i \(-0.466414\pi\)
0.105318 + 0.994439i \(0.466414\pi\)
\(450\) 0 0
\(451\) −1.96011 3.39501i −0.0922980 0.159865i
\(452\) 0 0
\(453\) 5.39771 + 9.34911i 0.253607 + 0.439259i
\(454\) 0 0
\(455\) 1.24920 0.0585634
\(456\) 0 0
\(457\) 10.7463 0.502692 0.251346 0.967897i \(-0.419127\pi\)
0.251346 + 0.967897i \(0.419127\pi\)
\(458\) 0 0
\(459\) 6.81668 + 11.8068i 0.318176 + 0.551096i
\(460\) 0 0
\(461\) −11.9163 20.6397i −0.554998 0.961285i −0.997904 0.0647167i \(-0.979386\pi\)
0.442906 0.896568i \(-0.353948\pi\)
\(462\) 0 0
\(463\) −25.3695 −1.17902 −0.589510 0.807761i \(-0.700679\pi\)
−0.589510 + 0.807761i \(0.700679\pi\)
\(464\) 0 0
\(465\) −2.03384 + 3.52272i −0.0943172 + 0.163362i
\(466\) 0 0
\(467\) 5.62020 0.260072 0.130036 0.991509i \(-0.458491\pi\)
0.130036 + 0.991509i \(0.458491\pi\)
\(468\) 0 0
\(469\) −13.0847 + 22.6633i −0.604195 + 1.04650i
\(470\) 0 0
\(471\) −5.76548 + 9.98611i −0.265659 + 0.460136i
\(472\) 0 0
\(473\) −15.1894 26.3089i −0.698411 1.20968i
\(474\) 0 0
\(475\) −1.95772 + 3.89452i −0.0898265 + 0.178693i
\(476\) 0 0
\(477\) 13.1785 + 22.8259i 0.603404 + 1.04513i
\(478\) 0 0
\(479\) −6.83611 + 11.8405i −0.312350 + 0.541006i −0.978871 0.204480i \(-0.934450\pi\)
0.666521 + 0.745487i \(0.267783\pi\)
\(480\) 0 0
\(481\) 2.11411 3.66175i 0.0963951 0.166961i
\(482\) 0 0
\(483\) −16.1430 −0.734532
\(484\) 0 0
\(485\) 3.85162 6.67120i 0.174893 0.302924i
\(486\) 0 0
\(487\) −7.39233 −0.334979 −0.167489 0.985874i \(-0.553566\pi\)
−0.167489 + 0.985874i \(0.553566\pi\)
\(488\) 0 0
\(489\) −5.30004 9.17994i −0.239676 0.415131i
\(490\) 0 0
\(491\) −0.979053 1.69577i −0.0441840 0.0765290i 0.843088 0.537776i \(-0.180735\pi\)
−0.887272 + 0.461247i \(0.847402\pi\)
\(492\) 0 0
\(493\) −27.7341 −1.24908
\(494\) 0 0
\(495\) 8.81251 0.396093
\(496\) 0 0
\(497\) 13.4148 + 23.2350i 0.601734 + 1.04223i
\(498\) 0 0
\(499\) −2.72234 4.71522i −0.121868 0.211082i 0.798636 0.601814i \(-0.205555\pi\)
−0.920505 + 0.390732i \(0.872222\pi\)
\(500\) 0 0
\(501\) 8.88595 0.396995
\(502\) 0 0
\(503\) 8.29629 14.3696i 0.369913 0.640709i −0.619638 0.784887i \(-0.712721\pi\)
0.989552 + 0.144179i \(0.0460541\pi\)
\(504\) 0 0
\(505\) 17.3755 0.773198
\(506\) 0 0
\(507\) 4.55273 7.88557i 0.202194 0.350210i
\(508\) 0 0
\(509\) −6.06552 + 10.5058i −0.268849 + 0.465661i −0.968565 0.248761i \(-0.919977\pi\)
0.699716 + 0.714422i \(0.253310\pi\)
\(510\) 0 0
\(511\) −2.70862 4.69146i −0.119822 0.207538i
\(512\) 0 0
\(513\) −16.9651 + 0.981757i −0.749029 + 0.0433456i
\(514\) 0 0
\(515\) 3.56307 + 6.17142i 0.157008 + 0.271945i
\(516\) 0 0
\(517\) 13.2756 22.9940i 0.583861 1.01128i
\(518\) 0 0
\(519\) −6.16482 + 10.6778i −0.270606 + 0.468703i
\(520\) 0 0
\(521\) 14.1249 0.618824 0.309412 0.950928i \(-0.399868\pi\)
0.309412 + 0.950928i \(0.399868\pi\)
\(522\) 0 0
\(523\) 13.1840 22.8353i 0.576495 0.998519i −0.419382 0.907810i \(-0.637753\pi\)
0.995877 0.0907094i \(-0.0289134\pi\)
\(524\) 0 0
\(525\) 2.20623 0.0962877
\(526\) 0 0
\(527\) −10.0285 17.3698i −0.436847 0.756641i
\(528\) 0 0
\(529\) −15.2694 26.4473i −0.663885 1.14988i
\(530\) 0 0
\(531\) 21.2554 0.922407
\(532\) 0 0
\(533\) −0.446059 −0.0193210
\(534\) 0 0
\(535\) −0.367726 0.636920i −0.0158982 0.0275365i
\(536\) 0 0
\(537\) −7.36985 12.7649i −0.318032 0.550848i
\(538\) 0 0
\(539\) −9.44775 −0.406943
\(540\) 0 0
\(541\) 14.6986 25.4586i 0.631940 1.09455i −0.355214 0.934785i \(-0.615592\pi\)
0.987155 0.159768i \(-0.0510745\pi\)
\(542\) 0 0
\(543\) 1.15541 0.0495833
\(544\) 0 0
\(545\) 8.00468 13.8645i 0.342883 0.593891i
\(546\) 0 0
\(547\) −10.8762 + 18.8381i −0.465031 + 0.805457i −0.999203 0.0399185i \(-0.987290\pi\)
0.534172 + 0.845376i \(0.320623\pi\)
\(548\) 0 0
\(549\) −11.5132 19.9414i −0.491371 0.851079i
\(550\) 0 0
\(551\) 15.5263 30.8867i 0.661443 1.31582i
\(552\) 0 0
\(553\) 14.0155 + 24.2755i 0.595999 + 1.03230i
\(554\) 0 0
\(555\) 3.73376 6.46706i 0.158489 0.274511i
\(556\) 0 0
\(557\) 12.0716 20.9086i 0.511489 0.885924i −0.488423 0.872607i \(-0.662428\pi\)
0.999911 0.0133172i \(-0.00423912\pi\)
\(558\) 0 0
\(559\) −3.45663 −0.146200
\(560\) 0 0
\(561\) 4.37649 7.58030i 0.184776 0.320041i
\(562\) 0 0
\(563\) −15.0693 −0.635097 −0.317548 0.948242i \(-0.602860\pi\)
−0.317548 + 0.948242i \(0.602860\pi\)
\(564\) 0 0
\(565\) −2.17462 3.76654i −0.0914868 0.158460i
\(566\) 0 0
\(567\) −7.35092 12.7322i −0.308710 0.534701i
\(568\) 0 0
\(569\) 0.302873 0.0126971 0.00634855 0.999980i \(-0.497979\pi\)
0.00634855 + 0.999980i \(0.497979\pi\)
\(570\) 0 0
\(571\) 30.3107 1.26846 0.634232 0.773143i \(-0.281316\pi\)
0.634232 + 0.773143i \(0.281316\pi\)
\(572\) 0 0
\(573\) 4.75232 + 8.23126i 0.198531 + 0.343866i
\(574\) 0 0
\(575\) 3.65851 + 6.33672i 0.152570 + 0.264260i
\(576\) 0 0
\(577\) 18.6601 0.776832 0.388416 0.921484i \(-0.373022\pi\)
0.388416 + 0.921484i \(0.373022\pi\)
\(578\) 0 0
\(579\) 3.79214 6.56819i 0.157596 0.272964i
\(580\) 0 0
\(581\) 12.6876 0.526369
\(582\) 0 0
\(583\) 18.6263 32.2617i 0.771422 1.33614i
\(584\) 0 0
\(585\) 0.501362 0.868384i 0.0207288 0.0359033i
\(586\) 0 0
\(587\) 13.5986 + 23.5535i 0.561275 + 0.972156i 0.997386 + 0.0722631i \(0.0230221\pi\)
−0.436111 + 0.899893i \(0.643645\pi\)
\(588\) 0 0
\(589\) 24.9585 1.44433i 1.02840 0.0595124i
\(590\) 0 0
\(591\) 2.48443 + 4.30316i 0.102196 + 0.177008i
\(592\) 0 0
\(593\) 14.7987 25.6321i 0.607709 1.05258i −0.383908 0.923371i \(-0.625422\pi\)
0.991617 0.129211i \(-0.0412446\pi\)
\(594\) 0 0
\(595\) −5.43923 + 9.42102i −0.222987 + 0.386224i
\(596\) 0 0
\(597\) −14.7388 −0.603221
\(598\) 0 0
\(599\) −7.54404 + 13.0667i −0.308241 + 0.533889i −0.977978 0.208710i \(-0.933074\pi\)
0.669737 + 0.742599i \(0.266407\pi\)
\(600\) 0 0
\(601\) −44.9249 −1.83253 −0.916263 0.400576i \(-0.868810\pi\)
−0.916263 + 0.400576i \(0.868810\pi\)
\(602\) 0 0
\(603\) 10.5030 + 18.1917i 0.427715 + 0.740824i
\(604\) 0 0
\(605\) −0.727713 1.26044i −0.0295858 0.0512440i
\(606\) 0 0
\(607\) −24.9570 −1.01297 −0.506487 0.862247i \(-0.669056\pi\)
−0.506487 + 0.862247i \(0.669056\pi\)
\(608\) 0 0
\(609\) −17.4971 −0.709020
\(610\) 0 0
\(611\) −1.51055 2.61636i −0.0611105 0.105846i
\(612\) 0 0
\(613\) 9.64316 + 16.7024i 0.389484 + 0.674605i 0.992380 0.123214i \(-0.0393202\pi\)
−0.602897 + 0.797819i \(0.705987\pi\)
\(614\) 0 0
\(615\) −0.787791 −0.0317668
\(616\) 0 0
\(617\) −9.72294 + 16.8406i −0.391431 + 0.677978i −0.992639 0.121115i \(-0.961353\pi\)
0.601208 + 0.799093i \(0.294686\pi\)
\(618\) 0 0
\(619\) −1.70324 −0.0684589 −0.0342294 0.999414i \(-0.510898\pi\)
−0.0342294 + 0.999414i \(0.510898\pi\)
\(620\) 0 0
\(621\) −14.2630 + 24.7042i −0.572354 + 0.991346i
\(622\) 0 0
\(623\) 20.5817 35.6485i 0.824588 1.42823i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 5.99190 + 9.11764i 0.239293 + 0.364124i
\(628\) 0 0
\(629\) 18.4104 + 31.8877i 0.734071 + 1.27145i
\(630\) 0 0
\(631\) 4.39314 7.60914i 0.174888 0.302915i −0.765235 0.643752i \(-0.777377\pi\)
0.940123 + 0.340837i \(0.110710\pi\)
\(632\) 0 0
\(633\) 3.98313 6.89899i 0.158315 0.274210i
\(634\) 0 0
\(635\) −4.64599 −0.184371
\(636\) 0 0
\(637\) −0.537502 + 0.930981i −0.0212966 + 0.0368868i
\(638\) 0 0
\(639\) 21.5359 0.851946
\(640\) 0 0
\(641\) 17.9033 + 31.0095i 0.707139 + 1.22480i 0.965914 + 0.258863i \(0.0833478\pi\)
−0.258775 + 0.965938i \(0.583319\pi\)
\(642\) 0 0
\(643\) −1.30758 2.26480i −0.0515661 0.0893150i 0.839090 0.543992i \(-0.183088\pi\)
−0.890656 + 0.454677i \(0.849755\pi\)
\(644\) 0 0
\(645\) −6.10481 −0.240377
\(646\) 0 0
\(647\) 30.8849 1.21421 0.607105 0.794622i \(-0.292331\pi\)
0.607105 + 0.794622i \(0.292331\pi\)
\(648\) 0 0
\(649\) −15.0210 26.0172i −0.589626 1.02126i
\(650\) 0 0
\(651\) −6.32686 10.9584i −0.247969 0.429495i
\(652\) 0 0
\(653\) −17.2198 −0.673864 −0.336932 0.941529i \(-0.609389\pi\)
−0.336932 + 0.941529i \(0.609389\pi\)
\(654\) 0 0
\(655\) −5.24775 + 9.08936i −0.205046 + 0.355151i
\(656\) 0 0
\(657\) −4.34838 −0.169646
\(658\) 0 0
\(659\) 0.0769444 0.133272i 0.00299733 0.00519153i −0.864523 0.502594i \(-0.832379\pi\)
0.867520 + 0.497402i \(0.165713\pi\)
\(660\) 0 0
\(661\) 13.8595 24.0054i 0.539073 0.933701i −0.459882 0.887980i \(-0.652108\pi\)
0.998954 0.0457209i \(-0.0145585\pi\)
\(662\) 0 0
\(663\) −0.497975 0.862519i −0.0193398 0.0334975i
\(664\) 0 0
\(665\) −7.44690 11.3317i −0.288778 0.439423i
\(666\) 0 0
\(667\) −29.0149 50.2552i −1.12346 1.94589i
\(668\) 0 0
\(669\) 3.86527 6.69485i 0.149440 0.258838i
\(670\) 0 0
\(671\) −16.2725 + 28.1848i −0.628193 + 1.08806i
\(672\) 0 0
\(673\) −48.0820 −1.85342 −0.926712 0.375773i \(-0.877377\pi\)
−0.926712 + 0.375773i \(0.877377\pi\)
\(674\) 0 0
\(675\) 1.94929 3.37627i 0.0750282 0.129953i
\(676\) 0 0
\(677\) −42.8392 −1.64644 −0.823222 0.567720i \(-0.807826\pi\)
−0.823222 + 0.567720i \(0.807826\pi\)
\(678\) 0 0
\(679\) 11.9816 + 20.7527i 0.459810 + 0.796415i
\(680\) 0 0
\(681\) −1.40647 2.43609i −0.0538962 0.0933510i
\(682\) 0 0
\(683\) 41.4022 1.58421 0.792106 0.610383i \(-0.208985\pi\)
0.792106 + 0.610383i \(0.208985\pi\)
\(684\) 0 0
\(685\) −1.39220 −0.0531933
\(686\) 0 0
\(687\) 3.87018 + 6.70335i 0.147657 + 0.255749i
\(688\) 0 0
\(689\) −2.11938 3.67087i −0.0807418 0.139849i
\(690\) 0 0
\(691\) 16.9248 0.643850 0.321925 0.946765i \(-0.395670\pi\)
0.321925 + 0.946765i \(0.395670\pi\)
\(692\) 0 0
\(693\) −13.7069 + 23.7411i −0.520683 + 0.901849i
\(694\) 0 0
\(695\) −6.07532 −0.230450
\(696\) 0 0
\(697\) 1.94222 3.36402i 0.0735668 0.127421i
\(698\) 0 0
\(699\) 5.52869 9.57597i 0.209114 0.362196i
\(700\) 0 0
\(701\) 18.7780 + 32.5244i 0.709233 + 1.22843i 0.965142 + 0.261727i \(0.0842921\pi\)
−0.255908 + 0.966701i \(0.582375\pi\)
\(702\) 0 0
\(703\) −45.8192 + 2.65152i −1.72810 + 0.100004i
\(704\) 0 0
\(705\) −2.66781 4.62078i −0.100476 0.174029i
\(706\) 0 0
\(707\) −27.0257 + 46.8099i −1.01641 + 1.76047i
\(708\) 0 0
\(709\) 15.3872 26.6514i 0.577879 1.00092i −0.417843 0.908519i \(-0.637214\pi\)
0.995722 0.0923969i \(-0.0294529\pi\)
\(710\) 0 0
\(711\) 22.5003 0.843826
\(712\) 0 0
\(713\) 20.9832 36.3440i 0.785827 1.36109i
\(714\) 0 0
\(715\) −1.41723 −0.0530014
\(716\) 0 0
\(717\) 2.87072 + 4.97223i 0.107209 + 0.185691i
\(718\) 0 0
\(719\) 23.1509 + 40.0985i 0.863383 + 1.49542i 0.868644 + 0.495437i \(0.164992\pi\)
−0.00526119 + 0.999986i \(0.501675\pi\)
\(720\) 0 0
\(721\) −22.1679 −0.825576
\(722\) 0 0
\(723\) −17.9325 −0.666918
\(724\) 0 0
\(725\) 3.96540 + 6.86827i 0.147271 + 0.255081i
\(726\) 0 0
\(727\) 2.93454 + 5.08278i 0.108836 + 0.188510i 0.915299 0.402775i \(-0.131954\pi\)
−0.806463 + 0.591285i \(0.798621\pi\)
\(728\) 0 0
\(729\) −3.50625 −0.129861
\(730\) 0 0
\(731\) 15.0508 26.0687i 0.556673 0.964186i
\(732\) 0 0
\(733\) 11.3955 0.420901 0.210450 0.977605i \(-0.432507\pi\)
0.210450 + 0.977605i \(0.432507\pi\)
\(734\) 0 0
\(735\) −0.949290 + 1.64422i −0.0350151 + 0.0606479i
\(736\) 0 0
\(737\) 14.8447 25.7118i 0.546812 0.947107i
\(738\) 0 0
\(739\) −6.86621 11.8926i −0.252578 0.437477i 0.711657 0.702527i \(-0.247945\pi\)
−0.964235 + 0.265050i \(0.914612\pi\)
\(740\) 0 0
\(741\) 1.23934 0.0717198i 0.0455284 0.00263469i
\(742\) 0 0
\(743\) 4.33763 + 7.51300i 0.159132 + 0.275625i 0.934556 0.355816i \(-0.115797\pi\)
−0.775424 + 0.631441i \(0.782464\pi\)
\(744\) 0 0
\(745\) 0.0422770 0.0732259i 0.00154891 0.00268279i
\(746\) 0 0
\(747\) 5.09212 8.81981i 0.186311 0.322700i
\(748\) 0 0
\(749\) 2.28784 0.0835957
\(750\) 0 0
\(751\) −3.35314 + 5.80780i −0.122358 + 0.211930i −0.920697 0.390278i \(-0.872379\pi\)
0.798339 + 0.602208i \(0.205712\pi\)
\(752\) 0 0
\(753\) 5.59517 0.203899
\(754\) 0 0
\(755\) 7.61079 + 13.1823i 0.276985 + 0.479752i
\(756\) 0 0
\(757\) −7.19480 12.4618i −0.261500 0.452931i 0.705141 0.709067i \(-0.250884\pi\)
−0.966641 + 0.256136i \(0.917550\pi\)
\(758\) 0 0
\(759\) 18.3144 0.664771
\(760\) 0 0
\(761\) −50.9650 −1.84748 −0.923740 0.383020i \(-0.874884\pi\)
−0.923740 + 0.383020i \(0.874884\pi\)
\(762\) 0 0
\(763\) 24.9009 + 43.1296i 0.901472 + 1.56140i
\(764\) 0 0
\(765\) 4.36603 + 7.56219i 0.157854 + 0.273412i
\(766\) 0 0
\(767\) −3.41831 −0.123428
\(768\) 0 0
\(769\) −11.9988 + 20.7825i −0.432687 + 0.749435i −0.997104 0.0760546i \(-0.975768\pi\)
0.564417 + 0.825490i \(0.309101\pi\)
\(770\) 0 0
\(771\) −6.51495 −0.234630
\(772\) 0 0
\(773\) 21.9925 38.0920i 0.791014 1.37008i −0.134326 0.990937i \(-0.542887\pi\)
0.925340 0.379139i \(-0.123780\pi\)
\(774\) 0 0
\(775\) −2.86773 + 4.96705i −0.103012 + 0.178422i
\(776\) 0 0
\(777\) 11.6149 + 20.1177i 0.416683 + 0.721717i
\(778\) 0 0
\(779\) 2.65911 + 4.04627i 0.0952725 + 0.144973i
\(780\) 0 0
\(781\) −15.2192 26.3604i −0.544585 0.943250i
\(782\) 0 0
\(783\) −15.4594 + 26.7765i −0.552474 + 0.956914i
\(784\) 0 0
\(785\) −8.12935 + 14.0804i −0.290149 + 0.502553i
\(786\) 0 0
\(787\) 16.4815 0.587501 0.293751 0.955882i \(-0.405096\pi\)
0.293751 + 0.955882i \(0.405096\pi\)
\(788\) 0 0
\(789\) −8.59691 + 14.8903i −0.306058 + 0.530108i
\(790\) 0 0
\(791\) 13.5295 0.481055
\(792\) 0 0
\(793\) 1.85155 + 3.20699i 0.0657506 + 0.113883i
\(794\) 0 0
\(795\) −3.74306