Properties

Label 1900.2.i.d.501.3
Level $1900$
Weight $2$
Character 1900.501
Analytic conductor $15.172$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} + 9 x^{6} + 2 x^{5} + 65 x^{4} - 20 x^{3} + 25 x^{2} + 6 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 501.3
Root \(0.354609 + 0.614201i\) of defining polynomial
Character \(\chi\) \(=\) 1900.501
Dual form 1900.2.i.d.201.3

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0.950048 0.312104i \(-0.101034\pi\)
−0.745314 + 0.666713i \(0.767701\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.11079 −1.17577 −0.587884 0.808945i \(-0.700039\pi\)
−0.587884 + 0.808945i \(0.700039\pi\)
\(8\) 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 −0.836838 0.547451i \(-0.815598\pi\)
0.892525 + 0.450997i \(0.148932\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.74850 + 3.02850i 0.424075 + 0.734519i 0.996334 0.0855542i \(-0.0272661\pi\)
−0.572259 + 0.820073i \(0.693933\pi\)
\(18\) 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 \(0.442868\pi\)
−0.941375 + 0.337362i \(0.890465\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 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
\(35\) 0 0
\(36\) 0 0
\(37\) 10.5292 1.73099 0.865497 0.500914i \(-0.167003\pi\)
0.865497 + 0.500914i \(0.167003\pi\)
\(38\) 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 \(-0.938771\pi\)
0.325218 0.945639i \(-0.394562\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.76162 6.51532i 0.548689 0.950357i −0.449676 0.893192i \(-0.648460\pi\)
0.998365 0.0571653i \(-0.0182062\pi\)
\(48\) 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 \(-0.575195\pi\)
0.958994 0.283427i \(-0.0914714\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 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 0
\(66\) 0 0
\(67\) 4.20623 7.28540i 0.513873 0.890053i −0.485998 0.873960i \(-0.661544\pi\)
0.999870 0.0160934i \(-0.00512290\pi\)
\(68\) 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 0.912471 0.409140i \(-0.134171\pi\)
−0.810562 + 0.585653i \(0.800838\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 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 \(-0.571860\pi\)
−0.223841 + 0.974626i \(0.571860\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 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
\(95\) 0 0
\(96\) 0 0
\(97\) −3.85162 6.67120i −0.391073 0.677358i 0.601519 0.798859i \(-0.294563\pi\)
−0.992591 + 0.121501i \(0.961229\pi\)
\(98\) 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 \(-0.385815\pi\)
0.351080 + 0.936346i \(0.385815\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.735452 −0.0710989 −0.0355494 0.999368i \(-0.511318\pi\)
−0.0355494 + 0.999368i \(0.511318\pi\)
\(108\) 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 \(-0.565580\pi\)
−0.204571 + 0.978852i \(0.565580\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 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
\(125\) 0 0
\(126\) 0 0
\(127\) −2.32300 + 4.02355i −0.206133 + 0.357032i −0.950493 0.310746i \(-0.899421\pi\)
0.744360 + 0.667778i \(0.232755\pi\)
\(128\) 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
\(135\) 0 0
\(136\) 0 0
\(137\) −0.696101 + 1.20568i −0.0594719 + 0.103008i −0.894228 0.447611i \(-0.852275\pi\)
0.834757 + 0.550619i \(0.185608\pi\)
\(138\) 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
\(145\) 0 0
\(146\) 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
\(155\) 0 0
\(156\) 0 0
\(157\) 8.12935 + 14.0804i 0.648793 + 1.12374i 0.983412 + 0.181388i \(0.0580591\pi\)
−0.334619 + 0.942354i \(0.608608\pi\)
\(158\) 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 \(-0.699037\pi\)
−0.585336 + 0.810791i \(0.699037\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.26461 10.8506i 0.484770 0.839647i −0.515077 0.857144i \(-0.672237\pi\)
0.999847 + 0.0174974i \(0.00556988\pi\)
\(168\) 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 \(0.0631468\pi\)
−0.319515 + 0.947581i \(0.603520\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 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
\(185\) 0 0
\(186\) 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 0.606872 0.794800i \(-0.292424\pi\)
−0.991753 + 0.128167i \(0.959091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.00611 0.499165 0.249582 0.968354i \(-0.419707\pi\)
0.249582 + 0.968354i \(0.419707\pi\)
\(198\) 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 0
\(206\) 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
\(215\) 0 0
\(216\) 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 0.623808 0.781578i \(-0.285585\pi\)
−0.988770 + 0.149445i \(0.952251\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.96627 −0.263250 −0.131625 0.991300i \(-0.542020\pi\)
−0.131625 + 0.991300i \(0.542020\pi\)
\(228\) 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 \(-0.996054\pi\)
0.489225 0.872157i \(-0.337280\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 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
\(245\) 0 0
\(246\) 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
\(255\) 0 0
\(256\) 0 0
\(257\) −4.59305 + 7.95540i −0.286507 + 0.496244i −0.972973 0.230917i \(-0.925827\pi\)
0.686467 + 0.727161i \(0.259161\pi\)
\(258\) 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 \(0.102058\pi\)
−0.201585 + 0.979471i \(0.564609\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 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
\(275\) 0 0
\(276\) 0 0
\(277\) −20.3078 −1.22018 −0.610088 0.792334i \(-0.708866\pi\)
−0.610088 + 0.792334i \(0.708866\pi\)
\(278\) 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 \(0.134061\pi\)
−0.102255 + 0.994758i \(0.532606\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 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 \(-0.379315\pi\)
0.370125 + 0.928982i \(0.379315\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 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
\(305\) 0 0
\(306\) 0 0
\(307\) 1.28540 + 2.22638i 0.0733619 + 0.127066i 0.900373 0.435119i \(-0.143294\pi\)
−0.827011 + 0.562186i \(0.809961\pi\)
\(308\) 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 \(-0.615416\pi\)
0.987066 0.160313i \(-0.0512503\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.65313 11.5236i 0.373677 0.647228i −0.616451 0.787393i \(-0.711430\pi\)
0.990128 + 0.140166i \(0.0447635\pi\)
\(318\) 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 0
\(326\) 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
\(335\) 0 0
\(336\) 0 0
\(337\) −14.5909 25.2722i −0.794819 1.37667i −0.922954 0.384910i \(-0.874233\pi\)
0.128136 0.991757i \(-0.459101\pi\)
\(338\) 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
\(345\) 0 0
\(346\) 0 0
\(347\) −6.03935 10.4605i −0.324209 0.561547i 0.657143 0.753766i \(-0.271765\pi\)
−0.981352 + 0.192219i \(0.938432\pi\)
\(348\) 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 \(-0.557008\pi\)
−0.178139 + 0.984005i \(0.557008\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 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 0
\(366\) 0 0
\(367\) 8.09936 14.0285i 0.422783 0.732282i −0.573427 0.819257i \(-0.694386\pi\)
0.996211 + 0.0869742i \(0.0277198\pi\)
\(368\) 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 \(-0.585921\pi\)
−0.266664 + 0.963790i \(0.585921\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 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 0.638753 0.769412i \(-0.279451\pi\)
−0.985707 + 0.168470i \(0.946117\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 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
\(395\) 0 0
\(396\) 0 0
\(397\) 12.0169 + 20.8139i 0.603112 + 1.04462i 0.992347 + 0.123483i \(0.0394063\pi\)
−0.389234 + 0.921139i \(0.627260\pi\)
\(398\) 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
\(405\) 0 0
\(406\) 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
\(415\) 0 0
\(416\) 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
\(425\) 0 0
\(426\) 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 −0.940760 0.339073i \(-0.889887\pi\)
0.764026 + 0.645186i \(0.223220\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 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 \(0.344043\pi\)
−0.999434 + 0.0336383i \(0.989291\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 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
\(455\) 0 0
\(456\) 0 0
\(457\) −10.7463 −0.502692 −0.251346 0.967897i \(-0.580873\pi\)
−0.251346 + 0.967897i \(0.580873\pi\)
\(458\) 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 \(-0.299321\pi\)
0.589510 + 0.807761i \(0.299321\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.62020 −0.260072 −0.130036 0.991509i \(-0.541509\pi\)
−0.130036 + 0.991509i \(0.541509\pi\)
\(468\) 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
\(475\) 0 0
\(476\) 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
\(485\) 0 0
\(486\) 0 0
\(487\) 7.39233 0.334979 0.167489 0.985874i \(-0.446434\pi\)
0.167489 + 0.985874i \(0.446434\pi\)
\(488\) 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
\(495\) 0 0
\(496\) 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 −0.989552 0.144179i \(-0.953946\pi\)
0.619638 + 0.784887i \(0.287279\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 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
\(515\) 0 0
\(516\) 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 \(0.362247\pi\)
−0.995877 + 0.0907094i \(0.971087\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 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 0
\(536\) 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
\(545\) 0 0
\(546\) 0 0
\(547\) 10.8762 18.8381i 0.465031 0.805457i −0.534172 0.845376i \(-0.679377\pi\)
0.999203 + 0.0399185i \(0.0127098\pi\)
\(548\) 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
\(555\) 0 0
\(556\) 0 0
\(557\) −12.0716 + 20.9086i −0.511489 + 0.885924i 0.488423 + 0.872607i \(0.337572\pi\)
−0.999911 + 0.0133172i \(0.995761\pi\)
\(558\) 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 \(-0.397140\pi\)
0.317548 + 0.948242i \(0.397140\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 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
\(575\) 0 0
\(576\) 0 0
\(577\) −18.6601 −0.776832 −0.388416 0.921484i \(-0.626978\pi\)
−0.388416 + 0.921484i \(0.626978\pi\)
\(578\) 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 0
\(586\) 0 0
\(587\) −13.5986 23.5535i −0.561275 0.972156i −0.997386 0.0722631i \(-0.976978\pi\)
0.436111 0.899893i \(-0.356355\pi\)
\(588\) 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 \(0.374578\pi\)
−0.991617 + 0.129211i \(0.958755\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 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 0
\(606\) 0 0
\(607\) 24.9570 1.01297 0.506487 0.862247i \(-0.330944\pi\)
0.506487 + 0.862247i \(0.330944\pi\)
\(608\) 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 0.602897 0.797819i \(-0.294013\pi\)
−0.992380 + 0.123214i \(0.960680\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.72294 16.8406i 0.391431 0.677978i −0.601208 0.799093i \(-0.705314\pi\)
0.992639 + 0.121115i \(0.0386469\pi\)
\(618\) 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 0
\(626\) 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
\(635\) 0 0
\(636\) 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 0.890656 0.454677i \(-0.150245\pi\)
−0.839090 + 0.543992i \(0.816912\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.8849 −1.21421 −0.607105 0.794622i \(-0.707669\pi\)
−0.607105 + 0.794622i \(0.707669\pi\)
\(648\) 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 \(-0.390611\pi\)
0.336932 + 0.941529i \(0.390611\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 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
\(665\) 0 0
\(666\) 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 \(-0.122623\pi\)
0.926712 + 0.375773i \(0.122623\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 42.8392 1.64644 0.823222 0.567720i \(-0.192174\pi\)
0.823222 + 0.567720i \(0.192174\pi\)
\(678\) 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 \(-0.791015\pi\)
−0.792106 + 0.610383i \(0.791015\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 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
\(695\) 0 0
\(696\) 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
\(705\) 0 0
\(706\) 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
\(715\) 0 0
\(716\) 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
\(725\) 0 0
\(726\) 0 0
\(727\) −2.93454 5.08278i −0.108836 0.188510i 0.806463 0.591285i \(-0.201379\pi\)
−0.915299 + 0.402775i \(0.868046\pi\)
\(728\) 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 \(-0.567493\pi\)
−0.210450 + 0.977605i \(0.567493\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 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 0.775424 0.631441i \(-0.217536\pi\)
−0.934556 + 0.355816i \(0.884203\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 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
\(755\) 0 0
\(756\) 0 0
\(757\) 7.19480 + 12.4618i 0.261500 + 0.452931i 0.966641 0.256136i \(-0.0824497\pi\)
−0.705141 + 0.709067i \(0.749116\pi\)
\(758\) 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
\(765\) 0 0
\(766\) 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 \(0.457113\pi\)
−0.925340 + 0.379139i \(0.876220\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 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
\(785\) 0 0
\(786\) 0 0
\(787\) −16.4815 −0.587501 −0.293751 0.955882i \(-0.594904\pi\)
−0.293751 + 0.955882i \(0.594904\pi\)
\(788\) 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
\(795\) 0 0
\(796\) 0 0
\(797\) 47.9346 1.69793 0.848966 0.528448i \(-0.177226\pi\)
0.848966 + 0.528448i \(0.177226\pi\)
\(798\) 0 0
\(799\) 26.3089 0.930740
\(800\) 0 0
\(801\) −16.5208 28.6149i −0.583733