Properties

Label 819.2.et.c.136.7
Level $819$
Weight $2$
Character 819.136
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
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.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 136.7
Character \(\chi\) \(=\) 819.136
Dual form 819.2.et.c.271.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.20543 - 1.20543i) q^{2} -0.906108i q^{4} +(-0.363968 + 1.35835i) q^{5} +(0.864271 - 2.50061i) q^{7} +(1.31861 + 1.31861i) q^{8} +O(q^{10})\) \(q+(1.20543 - 1.20543i) q^{2} -0.906108i q^{4} +(-0.363968 + 1.35835i) q^{5} +(0.864271 - 2.50061i) q^{7} +(1.31861 + 1.31861i) q^{8} +(1.19865 + 2.07613i) q^{10} +(-0.392515 + 1.46489i) q^{11} +(-1.37191 - 3.33435i) q^{13} +(-1.97248 - 4.05611i) q^{14} +4.99118 q^{16} +5.17026 q^{17} +(4.68519 - 1.25539i) q^{19} +(1.23081 + 0.329795i) q^{20} +(1.29267 + 2.23896i) q^{22} -2.14980i q^{23} +(2.61749 + 1.51121i) q^{25} +(-5.67305 - 2.36557i) q^{26} +(-2.26582 - 0.783122i) q^{28} +(0.744307 - 1.28918i) q^{29} +(1.89045 - 0.506544i) q^{31} +(3.37929 - 3.37929i) q^{32} +(6.23237 - 6.23237i) q^{34} +(3.08213 + 2.08412i) q^{35} +(6.70890 + 6.70890i) q^{37} +(4.13437 - 7.16094i) q^{38} +(-2.27106 + 1.31120i) q^{40} +(-6.34762 + 1.70084i) q^{41} +(-7.27334 + 4.19927i) q^{43} +(1.32735 + 0.355661i) q^{44} +(-2.59143 - 2.59143i) q^{46} +(-6.20311 - 1.66212i) q^{47} +(-5.50607 - 4.32240i) q^{49} +(4.97684 - 1.33354i) q^{50} +(-3.02128 + 1.24310i) q^{52} +(-1.87579 + 3.24897i) q^{53} +(-1.84696 - 1.06635i) q^{55} +(4.43695 - 2.15769i) q^{56} +(-0.656802 - 2.45122i) q^{58} +(5.98603 - 5.98603i) q^{59} +(-2.79969 - 1.61640i) q^{61} +(1.66819 - 2.88940i) q^{62} +1.83539i q^{64} +(5.02854 - 0.649937i) q^{65} +(-12.5811 - 3.37110i) q^{67} -4.68481i q^{68} +(6.22754 - 1.20302i) q^{70} +(2.71213 + 0.726713i) q^{71} +(-3.82844 - 14.2879i) q^{73} +16.1742 q^{74} +(-1.13752 - 4.24529i) q^{76} +(3.32387 + 2.24759i) q^{77} +(3.67744 + 6.36951i) q^{79} +(-1.81663 + 6.77977i) q^{80} +(-5.60135 + 9.70182i) q^{82} +(-0.0684765 - 0.0684765i) q^{83} +(-1.88181 + 7.02301i) q^{85} +(-3.70557 + 13.8294i) q^{86} +(-2.44918 + 1.41404i) q^{88} +(-7.89157 + 7.89157i) q^{89} +(-9.52359 + 0.548833i) q^{91} -1.94795 q^{92} +(-9.48096 + 5.47383i) q^{94} +6.82105i q^{95} +(-3.39415 + 12.6671i) q^{97} +(-11.8475 + 1.42683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20543 1.20543i 0.852365 0.852365i −0.138059 0.990424i \(-0.544086\pi\)
0.990424 + 0.138059i \(0.0440862\pi\)
\(3\) 0 0
\(4\) 0.906108i 0.453054i
\(5\) −0.363968 + 1.35835i −0.162772 + 0.607472i 0.835542 + 0.549426i \(0.185154\pi\)
−0.998314 + 0.0580459i \(0.981513\pi\)
\(6\) 0 0
\(7\) 0.864271 2.50061i 0.326664 0.945141i
\(8\) 1.31861 + 1.31861i 0.466198 + 0.466198i
\(9\) 0 0
\(10\) 1.19865 + 2.07613i 0.379047 + 0.656529i
\(11\) −0.392515 + 1.46489i −0.118348 + 0.441680i −0.999516 0.0311237i \(-0.990091\pi\)
0.881168 + 0.472804i \(0.156758\pi\)
\(12\) 0 0
\(13\) −1.37191 3.33435i −0.380500 0.924781i
\(14\) −1.97248 4.05611i −0.527169 1.08404i
\(15\) 0 0
\(16\) 4.99118 1.24780
\(17\) 5.17026 1.25397 0.626986 0.779031i \(-0.284288\pi\)
0.626986 + 0.779031i \(0.284288\pi\)
\(18\) 0 0
\(19\) 4.68519 1.25539i 1.07486 0.288007i 0.322370 0.946614i \(-0.395521\pi\)
0.752487 + 0.658607i \(0.228854\pi\)
\(20\) 1.23081 + 0.329795i 0.275218 + 0.0737443i
\(21\) 0 0
\(22\) 1.29267 + 2.23896i 0.275597 + 0.477348i
\(23\) 2.14980i 0.448264i −0.974559 0.224132i \(-0.928045\pi\)
0.974559 0.224132i \(-0.0719547\pi\)
\(24\) 0 0
\(25\) 2.61749 + 1.51121i 0.523498 + 0.302242i
\(26\) −5.67305 2.36557i −1.11258 0.463927i
\(27\) 0 0
\(28\) −2.26582 0.783122i −0.428200 0.147996i
\(29\) 0.744307 1.28918i 0.138214 0.239394i −0.788606 0.614898i \(-0.789197\pi\)
0.926821 + 0.375504i \(0.122530\pi\)
\(30\) 0 0
\(31\) 1.89045 0.506544i 0.339534 0.0909779i −0.0850231 0.996379i \(-0.527096\pi\)
0.424557 + 0.905401i \(0.360430\pi\)
\(32\) 3.37929 3.37929i 0.597380 0.597380i
\(33\) 0 0
\(34\) 6.23237 6.23237i 1.06884 1.06884i
\(35\) 3.08213 + 2.08412i 0.520975 + 0.352281i
\(36\) 0 0
\(37\) 6.70890 + 6.70890i 1.10294 + 1.10294i 0.994055 + 0.108882i \(0.0347270\pi\)
0.108882 + 0.994055i \(0.465273\pi\)
\(38\) 4.13437 7.16094i 0.670684 1.16166i
\(39\) 0 0
\(40\) −2.27106 + 1.31120i −0.359086 + 0.207318i
\(41\) −6.34762 + 1.70084i −0.991331 + 0.265626i −0.717810 0.696239i \(-0.754855\pi\)
−0.273522 + 0.961866i \(0.588188\pi\)
\(42\) 0 0
\(43\) −7.27334 + 4.19927i −1.10917 + 0.640382i −0.938615 0.344965i \(-0.887891\pi\)
−0.170559 + 0.985347i \(0.554557\pi\)
\(44\) 1.32735 + 0.355661i 0.200105 + 0.0536179i
\(45\) 0 0
\(46\) −2.59143 2.59143i −0.382085 0.382085i
\(47\) −6.20311 1.66212i −0.904817 0.242445i −0.223733 0.974650i \(-0.571824\pi\)
−0.681084 + 0.732206i \(0.738491\pi\)
\(48\) 0 0
\(49\) −5.50607 4.32240i −0.786582 0.617486i
\(50\) 4.97684 1.33354i 0.703832 0.188591i
\(51\) 0 0
\(52\) −3.02128 + 1.24310i −0.418976 + 0.172387i
\(53\) −1.87579 + 3.24897i −0.257660 + 0.446280i −0.965615 0.259978i \(-0.916285\pi\)
0.707955 + 0.706258i \(0.249618\pi\)
\(54\) 0 0
\(55\) −1.84696 1.06635i −0.249045 0.143786i
\(56\) 4.43695 2.15769i 0.592913 0.288333i
\(57\) 0 0
\(58\) −0.656802 2.45122i −0.0862423 0.321861i
\(59\) 5.98603 5.98603i 0.779315 0.779315i −0.200399 0.979714i \(-0.564224\pi\)
0.979714 + 0.200399i \(0.0642239\pi\)
\(60\) 0 0
\(61\) −2.79969 1.61640i −0.358463 0.206959i 0.309943 0.950755i \(-0.399690\pi\)
−0.668407 + 0.743796i \(0.733023\pi\)
\(62\) 1.66819 2.88940i 0.211861 0.366954i
\(63\) 0 0
\(64\) 1.83539i 0.229423i
\(65\) 5.02854 0.649937i 0.623713 0.0806147i
\(66\) 0 0
\(67\) −12.5811 3.37110i −1.53703 0.411845i −0.611723 0.791072i \(-0.709523\pi\)
−0.925304 + 0.379227i \(0.876190\pi\)
\(68\) 4.68481i 0.568117i
\(69\) 0 0
\(70\) 6.22754 1.20302i 0.744333 0.143789i
\(71\) 2.71213 + 0.726713i 0.321870 + 0.0862449i 0.416137 0.909302i \(-0.363384\pi\)
−0.0942662 + 0.995547i \(0.530050\pi\)
\(72\) 0 0
\(73\) −3.82844 14.2879i −0.448085 1.67228i −0.707660 0.706554i \(-0.750249\pi\)
0.259574 0.965723i \(-0.416418\pi\)
\(74\) 16.1742 1.88021
\(75\) 0 0
\(76\) −1.13752 4.24529i −0.130483 0.486968i
\(77\) 3.32387 + 2.24759i 0.378790 + 0.256136i
\(78\) 0 0
\(79\) 3.67744 + 6.36951i 0.413744 + 0.716626i 0.995296 0.0968836i \(-0.0308874\pi\)
−0.581551 + 0.813510i \(0.697554\pi\)
\(80\) −1.81663 + 6.77977i −0.203106 + 0.758001i
\(81\) 0 0
\(82\) −5.60135 + 9.70182i −0.618566 + 1.07139i
\(83\) −0.0684765 0.0684765i −0.00751627 0.00751627i 0.703339 0.710855i \(-0.251692\pi\)
−0.710855 + 0.703339i \(0.751692\pi\)
\(84\) 0 0
\(85\) −1.88181 + 7.02301i −0.204111 + 0.761753i
\(86\) −3.70557 + 13.8294i −0.399582 + 1.49126i
\(87\) 0 0
\(88\) −2.44918 + 1.41404i −0.261084 + 0.150737i
\(89\) −7.89157 + 7.89157i −0.836505 + 0.836505i −0.988397 0.151892i \(-0.951463\pi\)
0.151892 + 0.988397i \(0.451463\pi\)
\(90\) 0 0
\(91\) −9.52359 + 0.548833i −0.998344 + 0.0575333i
\(92\) −1.94795 −0.203088
\(93\) 0 0
\(94\) −9.48096 + 5.47383i −0.977886 + 0.564583i
\(95\) 6.82105i 0.699825i
\(96\) 0 0
\(97\) −3.39415 + 12.6671i −0.344624 + 1.28615i 0.548428 + 0.836198i \(0.315227\pi\)
−0.893051 + 0.449955i \(0.851440\pi\)
\(98\) −11.8475 + 1.42683i −1.19678 + 0.144131i
\(99\) 0 0
\(100\) 1.36932 2.37173i 0.136932 0.237173i
\(101\) −8.59776 14.8918i −0.855509 1.48179i −0.876172 0.481999i \(-0.839911\pi\)
0.0206627 0.999787i \(-0.493422\pi\)
\(102\) 0 0
\(103\) 0.176474 + 0.305661i 0.0173885 + 0.0301177i 0.874589 0.484866i \(-0.161131\pi\)
−0.857200 + 0.514983i \(0.827798\pi\)
\(104\) 2.58768 6.20570i 0.253743 0.608519i
\(105\) 0 0
\(106\) 1.65526 + 6.17753i 0.160773 + 0.600014i
\(107\) −13.4093 −1.29633 −0.648164 0.761500i \(-0.724463\pi\)
−0.648164 + 0.761500i \(0.724463\pi\)
\(108\) 0 0
\(109\) 2.54648 + 9.50358i 0.243908 + 0.910277i 0.973929 + 0.226853i \(0.0728436\pi\)
−0.730021 + 0.683425i \(0.760490\pi\)
\(110\) −3.51178 + 0.940979i −0.334835 + 0.0897188i
\(111\) 0 0
\(112\) 4.31373 12.4810i 0.407610 1.17934i
\(113\) −0.325800 0.564301i −0.0306486 0.0530850i 0.850294 0.526308i \(-0.176424\pi\)
−0.880943 + 0.473223i \(0.843091\pi\)
\(114\) 0 0
\(115\) 2.92018 + 0.782460i 0.272308 + 0.0729647i
\(116\) −1.16813 0.674422i −0.108458 0.0626185i
\(117\) 0 0
\(118\) 14.4315i 1.32852i
\(119\) 4.46850 12.9288i 0.409627 1.18518i
\(120\) 0 0
\(121\) 7.53445 + 4.35002i 0.684950 + 0.395456i
\(122\) −5.32327 + 1.42637i −0.481947 + 0.129137i
\(123\) 0 0
\(124\) −0.458983 1.71295i −0.0412179 0.153827i
\(125\) −7.97733 + 7.97733i −0.713514 + 0.713514i
\(126\) 0 0
\(127\) −1.63609 0.944595i −0.145179 0.0838192i 0.425651 0.904887i \(-0.360045\pi\)
−0.570830 + 0.821068i \(0.693378\pi\)
\(128\) 8.97101 + 8.97101i 0.792933 + 0.792933i
\(129\) 0 0
\(130\) 5.27808 6.84498i 0.462918 0.600345i
\(131\) −8.89476 + 5.13539i −0.777139 + 0.448681i −0.835415 0.549619i \(-0.814773\pi\)
0.0582763 + 0.998300i \(0.481440\pi\)
\(132\) 0 0
\(133\) 0.910028 12.8008i 0.0789095 1.10997i
\(134\) −19.2292 + 11.1020i −1.66115 + 0.959066i
\(135\) 0 0
\(136\) 6.81754 + 6.81754i 0.584599 + 0.584599i
\(137\) −6.59189 6.59189i −0.563183 0.563183i 0.367027 0.930210i \(-0.380376\pi\)
−0.930210 + 0.367027i \(0.880376\pi\)
\(138\) 0 0
\(139\) 0.141825 0.0818824i 0.0120294 0.00694518i −0.493973 0.869477i \(-0.664456\pi\)
0.506003 + 0.862532i \(0.331123\pi\)
\(140\) 1.88844 2.79274i 0.159602 0.236030i
\(141\) 0 0
\(142\) 4.14527 2.39327i 0.347863 0.200839i
\(143\) 5.42294 0.700913i 0.453489 0.0586133i
\(144\) 0 0
\(145\) 1.48025 + 1.48025i 0.122928 + 0.122928i
\(146\) −21.8380 12.6082i −1.80732 1.04346i
\(147\) 0 0
\(148\) 6.07899 6.07899i 0.499690 0.499690i
\(149\) 5.39257 + 20.1254i 0.441777 + 1.64873i 0.724309 + 0.689476i \(0.242159\pi\)
−0.282532 + 0.959258i \(0.591174\pi\)
\(150\) 0 0
\(151\) 3.50140 0.938197i 0.284940 0.0763494i −0.113518 0.993536i \(-0.536212\pi\)
0.398458 + 0.917187i \(0.369545\pi\)
\(152\) 7.83330 + 4.52256i 0.635365 + 0.366828i
\(153\) 0 0
\(154\) 6.71598 1.29738i 0.541189 0.104546i
\(155\) 2.75225i 0.221066i
\(156\) 0 0
\(157\) 12.8664 + 7.42842i 1.02685 + 0.592852i 0.916081 0.400994i \(-0.131335\pi\)
0.110770 + 0.993846i \(0.464668\pi\)
\(158\) 12.1109 + 3.24510i 0.963489 + 0.258166i
\(159\) 0 0
\(160\) 3.36030 + 5.82021i 0.265655 + 0.460128i
\(161\) −5.37581 1.85801i −0.423673 0.146432i
\(162\) 0 0
\(163\) −15.5228 + 4.15931i −1.21584 + 0.325782i −0.809050 0.587740i \(-0.800018\pi\)
−0.406787 + 0.913523i \(0.633351\pi\)
\(164\) 1.54114 + 5.75162i 0.120343 + 0.449126i
\(165\) 0 0
\(166\) −0.165087 −0.0128132
\(167\) −3.41310 12.7379i −0.264114 0.985686i −0.962791 0.270249i \(-0.912894\pi\)
0.698677 0.715438i \(-0.253773\pi\)
\(168\) 0 0
\(169\) −9.23572 + 9.14885i −0.710440 + 0.703758i
\(170\) 6.19734 + 10.7341i 0.475315 + 0.823269i
\(171\) 0 0
\(172\) 3.80499 + 6.59043i 0.290128 + 0.502516i
\(173\) 7.01638 12.1527i 0.533445 0.923954i −0.465791 0.884895i \(-0.654230\pi\)
0.999237 0.0390600i \(-0.0124363\pi\)
\(174\) 0 0
\(175\) 6.04116 5.23922i 0.456668 0.396048i
\(176\) −1.95912 + 7.31152i −0.147674 + 0.551127i
\(177\) 0 0
\(178\) 19.0254i 1.42602i
\(179\) 15.5849 8.99797i 1.16487 0.672540i 0.212406 0.977182i \(-0.431870\pi\)
0.952467 + 0.304642i \(0.0985368\pi\)
\(180\) 0 0
\(181\) 14.8428 1.10325 0.551627 0.834091i \(-0.314007\pi\)
0.551627 + 0.834091i \(0.314007\pi\)
\(182\) −10.8184 + 12.1416i −0.801914 + 0.899993i
\(183\) 0 0
\(184\) 2.83474 2.83474i 0.208980 0.208980i
\(185\) −11.5549 + 6.67120i −0.849530 + 0.490476i
\(186\) 0 0
\(187\) −2.02941 + 7.57385i −0.148405 + 0.553854i
\(188\) −1.50606 + 5.62069i −0.109841 + 0.409931i
\(189\) 0 0
\(190\) 8.22228 + 8.22228i 0.596507 + 0.596507i
\(191\) 7.23283 12.5276i 0.523349 0.906468i −0.476281 0.879293i \(-0.658016\pi\)
0.999631 0.0271748i \(-0.00865108\pi\)
\(192\) 0 0
\(193\) 4.69718 17.5301i 0.338111 1.26185i −0.562346 0.826902i \(-0.690101\pi\)
0.900457 0.434945i \(-0.143232\pi\)
\(194\) 11.1779 + 19.3607i 0.802527 + 1.39002i
\(195\) 0 0
\(196\) −3.91656 + 4.98909i −0.279754 + 0.356364i
\(197\) 6.18216 + 23.0721i 0.440460 + 1.64382i 0.727651 + 0.685947i \(0.240612\pi\)
−0.287191 + 0.957873i \(0.592721\pi\)
\(198\) 0 0
\(199\) 2.98353 0.211497 0.105749 0.994393i \(-0.466276\pi\)
0.105749 + 0.994393i \(0.466276\pi\)
\(200\) 1.45875 + 5.44413i 0.103149 + 0.384958i
\(201\) 0 0
\(202\) −28.3149 7.58695i −1.99223 0.533816i
\(203\) −2.58044 2.97542i −0.181112 0.208833i
\(204\) 0 0
\(205\) 9.24133i 0.645442i
\(206\) 0.581178 + 0.155726i 0.0404926 + 0.0108500i
\(207\) 0 0
\(208\) −6.84746 16.6423i −0.474786 1.15394i
\(209\) 7.35604i 0.508828i
\(210\) 0 0
\(211\) −2.05578 + 3.56072i −0.141526 + 0.245130i −0.928071 0.372402i \(-0.878534\pi\)
0.786546 + 0.617532i \(0.211867\pi\)
\(212\) 2.94392 + 1.69967i 0.202189 + 0.116734i
\(213\) 0 0
\(214\) −16.1640 + 16.1640i −1.10495 + 1.10495i
\(215\) −3.05680 11.4081i −0.208472 0.778028i
\(216\) 0 0
\(217\) 0.367191 5.16506i 0.0249265 0.350627i
\(218\) 14.5255 + 8.38628i 0.983788 + 0.567990i
\(219\) 0 0
\(220\) −0.966224 + 1.67355i −0.0651428 + 0.112831i
\(221\) −7.09313 17.2394i −0.477136 1.15965i
\(222\) 0 0
\(223\) −16.9482 + 4.54125i −1.13493 + 0.304105i −0.776912 0.629609i \(-0.783215\pi\)
−0.358022 + 0.933713i \(0.616549\pi\)
\(224\) −5.52966 11.3709i −0.369466 0.759751i
\(225\) 0 0
\(226\) −1.07295 0.287496i −0.0713717 0.0191240i
\(227\) 4.90655 + 4.90655i 0.325659 + 0.325659i 0.850933 0.525274i \(-0.176037\pi\)
−0.525274 + 0.850933i \(0.676037\pi\)
\(228\) 0 0
\(229\) 8.65510 + 2.31913i 0.571945 + 0.153252i 0.533189 0.845996i \(-0.320994\pi\)
0.0387566 + 0.999249i \(0.487660\pi\)
\(230\) 4.46326 2.57686i 0.294299 0.169913i
\(231\) 0 0
\(232\) 2.68137 0.718470i 0.176040 0.0471699i
\(233\) −5.51653 + 3.18497i −0.361400 + 0.208654i −0.669695 0.742636i \(-0.733575\pi\)
0.308295 + 0.951291i \(0.400242\pi\)
\(234\) 0 0
\(235\) 4.51547 7.82103i 0.294557 0.510188i
\(236\) −5.42399 5.42399i −0.353072 0.353072i
\(237\) 0 0
\(238\) −10.1983 20.9712i −0.661055 1.35936i
\(239\) 11.4926 11.4926i 0.743396 0.743396i −0.229834 0.973230i \(-0.573818\pi\)
0.973230 + 0.229834i \(0.0738183\pi\)
\(240\) 0 0
\(241\) −0.164298 + 0.164298i −0.0105834 + 0.0105834i −0.712379 0.701795i \(-0.752382\pi\)
0.701795 + 0.712379i \(0.252382\pi\)
\(242\) 14.3259 3.83860i 0.920901 0.246755i
\(243\) 0 0
\(244\) −1.46463 + 2.53682i −0.0937636 + 0.162403i
\(245\) 7.87537 5.90595i 0.503139 0.377317i
\(246\) 0 0
\(247\) −10.6136 13.8998i −0.675326 0.884421i
\(248\) 3.16069 + 1.82482i 0.200704 + 0.115876i
\(249\) 0 0
\(250\) 19.2322i 1.21635i
\(251\) −4.39247 7.60798i −0.277250 0.480211i 0.693450 0.720504i \(-0.256090\pi\)
−0.970700 + 0.240293i \(0.922756\pi\)
\(252\) 0 0
\(253\) 3.14922 + 0.843830i 0.197989 + 0.0530511i
\(254\) −3.11082 + 0.833542i −0.195190 + 0.0523011i
\(255\) 0 0
\(256\) 17.9570 1.12231
\(257\) −22.7247 −1.41753 −0.708763 0.705447i \(-0.750746\pi\)
−0.708763 + 0.705447i \(0.750746\pi\)
\(258\) 0 0
\(259\) 22.5746 10.9780i 1.40272 0.682141i
\(260\) −0.588913 4.55640i −0.0365228 0.282576i
\(261\) 0 0
\(262\) −4.53164 + 16.9123i −0.279966 + 1.04485i
\(263\) −4.09771 7.09745i −0.252676 0.437647i 0.711586 0.702599i \(-0.247977\pi\)
−0.964262 + 0.264952i \(0.914644\pi\)
\(264\) 0 0
\(265\) −3.73050 3.73050i −0.229163 0.229163i
\(266\) −14.3335 16.5274i −0.878843 1.01336i
\(267\) 0 0
\(268\) −3.05458 + 11.3998i −0.186588 + 0.696356i
\(269\) 24.5019i 1.49391i 0.664875 + 0.746954i \(0.268485\pi\)
−0.664875 + 0.746954i \(0.731515\pi\)
\(270\) 0 0
\(271\) −5.87162 + 5.87162i −0.356675 + 0.356675i −0.862586 0.505910i \(-0.831157\pi\)
0.505910 + 0.862586i \(0.331157\pi\)
\(272\) 25.8057 1.56470
\(273\) 0 0
\(274\) −15.8921 −0.960076
\(275\) −3.24115 + 3.24115i −0.195449 + 0.195449i
\(276\) 0 0
\(277\) 1.49932i 0.0900852i 0.998985 + 0.0450426i \(0.0143424\pi\)
−0.998985 + 0.0450426i \(0.985658\pi\)
\(278\) 0.0722558 0.269662i 0.00433362 0.0161733i
\(279\) 0 0
\(280\) 1.31598 + 6.81226i 0.0786447 + 0.407110i
\(281\) −19.5020 19.5020i −1.16339 1.16339i −0.983728 0.179665i \(-0.942499\pi\)
−0.179665 0.983728i \(-0.557501\pi\)
\(282\) 0 0
\(283\) −7.83136 13.5643i −0.465526 0.806315i 0.533699 0.845674i \(-0.320802\pi\)
−0.999225 + 0.0393597i \(0.987468\pi\)
\(284\) 0.658480 2.45748i 0.0390736 0.145825i
\(285\) 0 0
\(286\) 5.69205 7.38185i 0.336578 0.436498i
\(287\) −1.23293 + 17.3429i −0.0727775 + 1.02372i
\(288\) 0 0
\(289\) 9.73158 0.572446
\(290\) 3.56866 0.209559
\(291\) 0 0
\(292\) −12.9464 + 3.46898i −0.757631 + 0.203007i
\(293\) −13.6614 3.66056i −0.798107 0.213852i −0.163354 0.986567i \(-0.552231\pi\)
−0.634753 + 0.772715i \(0.718898\pi\)
\(294\) 0 0
\(295\) 5.95239 + 10.3098i 0.346562 + 0.600263i
\(296\) 17.6928i 1.02837i
\(297\) 0 0
\(298\) 30.7600 + 17.7593i 1.78188 + 1.02877i
\(299\) −7.16818 + 2.94933i −0.414546 + 0.170564i
\(300\) 0 0
\(301\) 4.21458 + 21.8171i 0.242924 + 1.25752i
\(302\) 3.08975 5.35161i 0.177795 0.307950i
\(303\) 0 0
\(304\) 23.3847 6.26590i 1.34120 0.359374i
\(305\) 3.21464 3.21464i 0.184069 0.184069i
\(306\) 0 0
\(307\) 0.977336 0.977336i 0.0557795 0.0557795i −0.678667 0.734446i \(-0.737442\pi\)
0.734446 + 0.678667i \(0.237442\pi\)
\(308\) 2.03655 3.01178i 0.116043 0.171612i
\(309\) 0 0
\(310\) 3.31764 + 3.31764i 0.188429 + 0.188429i
\(311\) 4.20663 7.28609i 0.238536 0.413156i −0.721759 0.692145i \(-0.756666\pi\)
0.960294 + 0.278989i \(0.0899992\pi\)
\(312\) 0 0
\(313\) −14.4104 + 8.31988i −0.814527 + 0.470267i −0.848525 0.529155i \(-0.822509\pi\)
0.0339987 + 0.999422i \(0.489176\pi\)
\(314\) 24.4639 6.55509i 1.38058 0.369925i
\(315\) 0 0
\(316\) 5.77146 3.33216i 0.324670 0.187448i
\(317\) 8.06223 + 2.16027i 0.452820 + 0.121333i 0.478019 0.878350i \(-0.341355\pi\)
−0.0251986 + 0.999682i \(0.508022\pi\)
\(318\) 0 0
\(319\) 1.59635 + 1.59635i 0.0893783 + 0.0893783i
\(320\) −2.49310 0.668023i −0.139368 0.0373436i
\(321\) 0 0
\(322\) −8.71984 + 4.24045i −0.485937 + 0.236311i
\(323\) 24.2237 6.49071i 1.34784 0.361153i
\(324\) 0 0
\(325\) 1.44793 10.8009i 0.0803166 0.599124i
\(326\) −13.6978 + 23.7253i −0.758652 + 1.31402i
\(327\) 0 0
\(328\) −10.6128 6.12727i −0.585991 0.338322i
\(329\) −9.51747 + 14.0750i −0.524715 + 0.775981i
\(330\) 0 0
\(331\) 1.91640 + 7.15210i 0.105335 + 0.393115i 0.998383 0.0568462i \(-0.0181045\pi\)
−0.893048 + 0.449961i \(0.851438\pi\)
\(332\) −0.0620471 + 0.0620471i −0.00340528 + 0.00340528i
\(333\) 0 0
\(334\) −19.4688 11.2403i −1.06529 0.615043i
\(335\) 9.15825 15.8626i 0.500369 0.866664i
\(336\) 0 0
\(337\) 27.7667i 1.51255i −0.654256 0.756273i \(-0.727018\pi\)
0.654256 0.756273i \(-0.272982\pi\)
\(338\) −0.104718 + 22.1613i −0.00569593 + 1.20541i
\(339\) 0 0
\(340\) 6.36361 + 1.70512i 0.345115 + 0.0924733i
\(341\) 2.96812i 0.160733i
\(342\) 0 0
\(343\) −15.5674 + 10.0328i −0.840559 + 0.541720i
\(344\) −15.1279 4.05350i −0.815640 0.218550i
\(345\) 0 0
\(346\) −6.19149 23.1070i −0.332856 1.24224i
\(347\) 10.8321 0.581499 0.290750 0.956799i \(-0.406095\pi\)
0.290750 + 0.956799i \(0.406095\pi\)
\(348\) 0 0
\(349\) 0.622157 + 2.32192i 0.0333033 + 0.124290i 0.980576 0.196138i \(-0.0628401\pi\)
−0.947273 + 0.320428i \(0.896173\pi\)
\(350\) 0.966677 13.5977i 0.0516710 0.726826i
\(351\) 0 0
\(352\) 3.62386 + 6.27671i 0.193152 + 0.334550i
\(353\) −3.11894 + 11.6401i −0.166005 + 0.619538i 0.831905 + 0.554918i \(0.187250\pi\)
−0.997910 + 0.0646202i \(0.979416\pi\)
\(354\) 0 0
\(355\) −1.97426 + 3.41952i −0.104783 + 0.181489i
\(356\) 7.15062 + 7.15062i 0.378982 + 0.378982i
\(357\) 0 0
\(358\) 7.94011 29.6329i 0.419648 1.56615i
\(359\) 7.12307 26.5837i 0.375941 1.40303i −0.476023 0.879433i \(-0.657922\pi\)
0.851965 0.523599i \(-0.175411\pi\)
\(360\) 0 0
\(361\) 3.92054 2.26352i 0.206344 0.119133i
\(362\) 17.8919 17.8919i 0.940376 0.940376i
\(363\) 0 0
\(364\) 0.497302 + 8.62940i 0.0260657 + 0.452303i
\(365\) 20.8014 1.08880
\(366\) 0 0
\(367\) 12.2228 7.05683i 0.638024 0.368363i −0.145829 0.989310i \(-0.546585\pi\)
0.783853 + 0.620946i \(0.213252\pi\)
\(368\) 10.7301i 0.559343i
\(369\) 0 0
\(370\) −5.88689 + 21.9702i −0.306045 + 1.14218i
\(371\) 6.50320 + 7.49861i 0.337629 + 0.389308i
\(372\) 0 0
\(373\) −14.9945 + 25.9713i −0.776387 + 1.34474i 0.157624 + 0.987499i \(0.449616\pi\)
−0.934012 + 0.357243i \(0.883717\pi\)
\(374\) 6.68342 + 11.5760i 0.345591 + 0.598582i
\(375\) 0 0
\(376\) −5.98778 10.3711i −0.308796 0.534851i
\(377\) −5.31969 0.713140i −0.273978 0.0367286i
\(378\) 0 0
\(379\) −6.76234 25.2374i −0.347358 1.29636i −0.889833 0.456286i \(-0.849179\pi\)
0.542475 0.840072i \(-0.317487\pi\)
\(380\) 6.18061 0.317058
\(381\) 0 0
\(382\) −6.38250 23.8198i −0.326557 1.21873i
\(383\) −30.7142 + 8.22985i −1.56942 + 0.420526i −0.935632 0.352978i \(-0.885169\pi\)
−0.633792 + 0.773504i \(0.718502\pi\)
\(384\) 0 0
\(385\) −4.26279 + 3.69692i −0.217252 + 0.188413i
\(386\) −15.4692 26.7934i −0.787360 1.36375i
\(387\) 0 0
\(388\) 11.4778 + 3.07546i 0.582697 + 0.156133i
\(389\) −12.1261 7.00102i −0.614818 0.354966i 0.160030 0.987112i \(-0.448841\pi\)
−0.774849 + 0.632147i \(0.782174\pi\)
\(390\) 0 0
\(391\) 11.1150i 0.562111i
\(392\) −1.56080 12.9599i −0.0788321 0.654574i
\(393\) 0 0
\(394\) 35.2639 + 20.3596i 1.77657 + 1.02570i
\(395\) −9.99049 + 2.67694i −0.502676 + 0.134692i
\(396\) 0 0
\(397\) −4.60637 17.1912i −0.231187 0.862802i −0.979831 0.199829i \(-0.935961\pi\)
0.748644 0.662973i \(-0.230705\pi\)
\(398\) 3.59643 3.59643i 0.180273 0.180273i
\(399\) 0 0
\(400\) 13.0644 + 7.54272i 0.653218 + 0.377136i
\(401\) −1.38205 1.38205i −0.0690162 0.0690162i 0.671756 0.740772i \(-0.265540\pi\)
−0.740772 + 0.671756i \(0.765540\pi\)
\(402\) 0 0
\(403\) −4.28252 5.60847i −0.213327 0.279378i
\(404\) −13.4935 + 7.79050i −0.671329 + 0.387592i
\(405\) 0 0
\(406\) −6.69718 0.476112i −0.332376 0.0236290i
\(407\) −12.4611 + 7.19444i −0.617675 + 0.356615i
\(408\) 0 0
\(409\) −11.0600 11.0600i −0.546882 0.546882i 0.378656 0.925538i \(-0.376387\pi\)
−0.925538 + 0.378656i \(0.876387\pi\)
\(410\) −11.1397 11.1397i −0.550153 0.550153i
\(411\) 0 0
\(412\) 0.276962 0.159904i 0.0136449 0.00787791i
\(413\) −9.79517 20.1423i −0.481989 0.991136i
\(414\) 0 0
\(415\) 0.117938 0.0680917i 0.00578936 0.00334249i
\(416\) −15.9038 6.63164i −0.779749 0.325143i
\(417\) 0 0
\(418\) 8.86717 + 8.86717i 0.433707 + 0.433707i
\(419\) 32.1543 + 18.5643i 1.57084 + 0.906924i 0.996066 + 0.0886099i \(0.0282425\pi\)
0.574772 + 0.818314i \(0.305091\pi\)
\(420\) 0 0
\(421\) −23.1846 + 23.1846i −1.12995 + 1.12995i −0.139764 + 0.990185i \(0.544634\pi\)
−0.990185 + 0.139764i \(0.955366\pi\)
\(422\) 1.81409 + 6.77028i 0.0883085 + 0.329572i
\(423\) 0 0
\(424\) −6.75755 + 1.81068i −0.328176 + 0.0879344i
\(425\) 13.5331 + 7.81334i 0.656451 + 0.379002i
\(426\) 0 0
\(427\) −6.46167 + 5.60391i −0.312702 + 0.271192i
\(428\) 12.1503i 0.587307i
\(429\) 0 0
\(430\) −17.4364 10.0669i −0.840859 0.485470i
\(431\) 15.9999 + 4.28716i 0.770688 + 0.206505i 0.622675 0.782480i \(-0.286046\pi\)
0.148012 + 0.988986i \(0.452712\pi\)
\(432\) 0 0
\(433\) 0.814551 + 1.41084i 0.0391448 + 0.0678008i 0.884934 0.465716i \(-0.154203\pi\)
−0.845789 + 0.533517i \(0.820870\pi\)
\(434\) −5.78347 6.66872i −0.277616 0.320109i
\(435\) 0 0
\(436\) 8.61126 2.30738i 0.412405 0.110504i
\(437\) −2.69885 10.0722i −0.129103 0.481820i
\(438\) 0 0
\(439\) 27.9803 1.33543 0.667713 0.744419i \(-0.267273\pi\)
0.667713 + 0.744419i \(0.267273\pi\)
\(440\) −1.02933 3.84151i −0.0490714 0.183137i
\(441\) 0 0
\(442\) −29.3311 12.2306i −1.39514 0.581751i
\(443\) −12.7182 22.0285i −0.604258 1.04661i −0.992168 0.124908i \(-0.960136\pi\)
0.387910 0.921697i \(-0.373197\pi\)
\(444\) 0 0
\(445\) −7.84723 13.5918i −0.371994 0.644313i
\(446\) −14.9556 + 25.9039i −0.708170 + 1.22659i
\(447\) 0 0
\(448\) 4.58958 + 1.58627i 0.216837 + 0.0749443i
\(449\) 0.665392 2.48328i 0.0314018 0.117193i −0.948446 0.316939i \(-0.897345\pi\)
0.979848 + 0.199746i \(0.0640116\pi\)
\(450\) 0 0
\(451\) 9.96615i 0.469288i
\(452\) −0.511318 + 0.295209i −0.0240504 + 0.0138855i
\(453\) 0 0
\(454\) 11.8290 0.555162
\(455\) 2.72078 13.1361i 0.127552 0.615831i
\(456\) 0 0
\(457\) −10.0248 + 10.0248i −0.468940 + 0.468940i −0.901571 0.432631i \(-0.857585\pi\)
0.432631 + 0.901571i \(0.357585\pi\)
\(458\) 13.2286 7.63755i 0.618133 0.356879i
\(459\) 0 0
\(460\) 0.708993 2.64600i 0.0330570 0.123370i
\(461\) −10.8132 + 40.3552i −0.503619 + 1.87953i −0.0285297 + 0.999593i \(0.509083\pi\)
−0.475089 + 0.879938i \(0.657584\pi\)
\(462\) 0 0
\(463\) 19.6177 + 19.6177i 0.911713 + 0.911713i 0.996407 0.0846939i \(-0.0269912\pi\)
−0.0846939 + 0.996407i \(0.526991\pi\)
\(464\) 3.71497 6.43452i 0.172463 0.298715i
\(465\) 0 0
\(466\) −2.81053 + 10.4890i −0.130195 + 0.485895i
\(467\) 14.6509 + 25.3761i 0.677962 + 1.17426i 0.975594 + 0.219584i \(0.0704700\pi\)
−0.297632 + 0.954681i \(0.596197\pi\)
\(468\) 0 0
\(469\) −19.3033 + 28.5469i −0.891342 + 1.31817i
\(470\) −3.98461 14.8707i −0.183796 0.685937i
\(471\) 0 0
\(472\) 15.7865 0.726630
\(473\) −3.29655 12.3029i −0.151576 0.565688i
\(474\) 0 0
\(475\) 14.1606 + 3.79432i 0.649733 + 0.174095i
\(476\) −11.7149 4.04894i −0.536950 0.185583i
\(477\) 0 0
\(478\) 27.7070i 1.26729i
\(479\) 8.64079 + 2.31529i 0.394808 + 0.105788i 0.450760 0.892645i \(-0.351153\pi\)
−0.0559526 + 0.998433i \(0.517820\pi\)
\(480\) 0 0
\(481\) 13.1658 31.5738i 0.600308 1.43964i
\(482\) 0.396098i 0.0180418i
\(483\) 0 0
\(484\) 3.94159 6.82703i 0.179163 0.310319i
\(485\) −15.9710 9.22088i −0.725207 0.418698i
\(486\) 0 0
\(487\) 14.5064 14.5064i 0.657346 0.657346i −0.297406 0.954751i \(-0.596121\pi\)
0.954751 + 0.297406i \(0.0961214\pi\)
\(488\) −1.56029 5.82309i −0.0706311 0.263599i
\(489\) 0 0
\(490\) 2.37399 16.6124i 0.107246 0.750470i
\(491\) 27.6274 + 15.9507i 1.24681 + 0.719845i 0.970472 0.241216i \(-0.0775461\pi\)
0.276337 + 0.961061i \(0.410879\pi\)
\(492\) 0 0
\(493\) 3.84826 6.66538i 0.173317 0.300194i
\(494\) −29.5490 3.96125i −1.32947 0.178225i
\(495\) 0 0
\(496\) 9.43557 2.52825i 0.423669 0.113522i
\(497\) 4.16124 6.15389i 0.186657 0.276040i
\(498\) 0 0
\(499\) −22.1352 5.93111i −0.990907 0.265513i −0.273276 0.961936i \(-0.588107\pi\)
−0.717632 + 0.696423i \(0.754774\pi\)
\(500\) 7.22832 + 7.22832i 0.323260 + 0.323260i
\(501\) 0 0
\(502\) −14.4657 3.87606i −0.645634 0.172997i
\(503\) 23.9880 13.8495i 1.06957 0.617518i 0.141508 0.989937i \(-0.454805\pi\)
0.928065 + 0.372419i \(0.121472\pi\)
\(504\) 0 0
\(505\) 23.3575 6.25863i 1.03940 0.278505i
\(506\) 4.81332 2.77897i 0.213978 0.123540i
\(507\) 0 0
\(508\) −0.855905 + 1.48247i −0.0379746 + 0.0657740i
\(509\) −30.4769 30.4769i −1.35087 1.35087i −0.884693 0.466174i \(-0.845632\pi\)
−0.466174 0.884693i \(-0.654368\pi\)
\(510\) 0 0
\(511\) −39.0373 2.77522i −1.72691 0.122768i
\(512\) 3.70385 3.70385i 0.163689 0.163689i
\(513\) 0 0
\(514\) −27.3929 + 27.3929i −1.20825 + 1.20825i
\(515\) −0.479425 + 0.128462i −0.0211260 + 0.00566070i
\(516\) 0 0
\(517\) 4.86963 8.43445i 0.214166 0.370947i
\(518\) 13.9789 40.4453i 0.614196 1.77706i
\(519\) 0 0
\(520\) 7.48768 + 5.77365i 0.328356 + 0.253191i
\(521\) −1.66737 0.962655i −0.0730487 0.0421747i 0.463031 0.886342i \(-0.346762\pi\)
−0.536079 + 0.844168i \(0.680095\pi\)
\(522\) 0 0
\(523\) 1.27342i 0.0556829i 0.999612 + 0.0278414i \(0.00886335\pi\)
−0.999612 + 0.0278414i \(0.991137\pi\)
\(524\) 4.65322 + 8.05961i 0.203277 + 0.352086i
\(525\) 0 0
\(526\) −13.4949 3.61596i −0.588408 0.157663i
\(527\) 9.77410 2.61896i 0.425766 0.114084i
\(528\) 0 0
\(529\) 18.3784 0.799059
\(530\) −8.99370 −0.390661
\(531\) 0 0
\(532\) −11.5989 0.824584i −0.502877 0.0357502i
\(533\) 14.3795 + 18.8317i 0.622847 + 0.815694i
\(534\) 0 0
\(535\) 4.88057 18.2145i 0.211006 0.787483i
\(536\) −12.1444 21.0347i −0.524557 0.908560i
\(537\) 0 0
\(538\) 29.5353 + 29.5353i 1.27336 + 1.27336i
\(539\) 8.49305 6.36917i 0.365822 0.274339i
\(540\) 0 0
\(541\) −6.06372 + 22.6301i −0.260700 + 0.972944i 0.704131 + 0.710070i \(0.251337\pi\)
−0.964830 + 0.262874i \(0.915330\pi\)
\(542\) 14.1556i 0.608036i
\(543\) 0 0
\(544\) 17.4718 17.4718i 0.749098 0.749098i
\(545\) −13.8360 −0.592669
\(546\) 0 0
\(547\) 39.4093 1.68502 0.842510 0.538680i \(-0.181077\pi\)
0.842510 + 0.538680i \(0.181077\pi\)
\(548\) −5.97296 + 5.97296i −0.255152 + 0.255152i
\(549\) 0 0
\(550\) 7.81395i 0.333188i
\(551\) 1.86880 6.97444i 0.0796134 0.297121i
\(552\) 0 0
\(553\) 19.1059 3.69085i 0.812468 0.156951i
\(554\) 1.80732 + 1.80732i 0.0767855 + 0.0767855i
\(555\) 0 0
\(556\) −0.0741943 0.128508i −0.00314654 0.00544997i
\(557\) −3.89152 + 14.5233i −0.164889 + 0.615374i 0.833165 + 0.553024i \(0.186526\pi\)
−0.998054 + 0.0623501i \(0.980140\pi\)
\(558\) 0 0
\(559\) 23.9802 + 18.4908i 1.01425 + 0.782078i
\(560\) 15.3835 + 10.4022i 0.650070 + 0.439575i
\(561\) 0 0
\(562\) −47.0165 −1.98327
\(563\) 17.2519 0.727081 0.363541 0.931578i \(-0.381568\pi\)
0.363541 + 0.931578i \(0.381568\pi\)
\(564\) 0 0
\(565\) 0.885099 0.237161i 0.0372364 0.00997746i
\(566\) −25.7909 6.91066i −1.08407 0.290477i
\(567\) 0 0
\(568\) 2.61798 + 4.53448i 0.109848 + 0.190263i
\(569\) 10.5691i 0.443081i −0.975151 0.221540i \(-0.928892\pi\)
0.975151 0.221540i \(-0.0711085\pi\)
\(570\) 0 0
\(571\) −4.73797 2.73547i −0.198278 0.114476i 0.397574 0.917570i \(-0.369852\pi\)
−0.595852 + 0.803094i \(0.703185\pi\)
\(572\) −0.635102 4.91376i −0.0265550 0.205455i
\(573\) 0 0
\(574\) 19.4194 + 22.3918i 0.810549 + 0.934615i
\(575\) 3.24880 5.62708i 0.135484 0.234665i
\(576\) 0 0
\(577\) −19.3289 + 5.17915i −0.804671 + 0.215611i −0.637634 0.770340i \(-0.720087\pi\)
−0.167037 + 0.985951i \(0.553420\pi\)
\(578\) 11.7307 11.7307i 0.487933 0.487933i
\(579\) 0 0
\(580\) 1.34126 1.34126i 0.0556930 0.0556930i
\(581\) −0.230415 + 0.112051i −0.00955923 + 0.00464864i
\(582\) 0 0
\(583\) −4.02310 4.02310i −0.166620 0.166620i
\(584\) 13.7920 23.8884i 0.570716 0.988508i
\(585\) 0 0
\(586\) −20.8803 + 12.0553i −0.862559 + 0.497999i
\(587\) 1.59431 0.427193i 0.0658041 0.0176321i −0.225767 0.974181i \(-0.572489\pi\)
0.291571 + 0.956549i \(0.405822\pi\)
\(588\) 0 0
\(589\) 8.22120 4.74651i 0.338748 0.195577i
\(590\) 19.6029 + 5.25259i 0.807040 + 0.216246i
\(591\) 0 0
\(592\) 33.4854 + 33.4854i 1.37624 + 1.37624i
\(593\) 34.8670 + 9.34258i 1.43182 + 0.383654i 0.889660 0.456624i \(-0.150941\pi\)
0.542156 + 0.840278i \(0.317608\pi\)
\(594\) 0 0
\(595\) 15.9354 + 10.7755i 0.653288 + 0.441751i
\(596\) 18.2357 4.88625i 0.746965 0.200149i
\(597\) 0 0
\(598\) −5.08551 + 12.1959i −0.207962 + 0.498728i
\(599\) 5.29544 9.17197i 0.216366 0.374757i −0.737328 0.675534i \(-0.763913\pi\)
0.953694 + 0.300778i \(0.0972463\pi\)
\(600\) 0 0
\(601\) −24.1270 13.9297i −0.984160 0.568205i −0.0806362 0.996744i \(-0.525695\pi\)
−0.903523 + 0.428539i \(0.859029\pi\)
\(602\) 31.3793 + 21.2185i 1.27892 + 0.864802i
\(603\) 0 0
\(604\) −0.850107 3.17264i −0.0345904 0.129093i
\(605\) −8.65115 + 8.65115i −0.351719 + 0.351719i
\(606\) 0 0
\(607\) 19.2975 + 11.1414i 0.783262 + 0.452216i 0.837585 0.546307i \(-0.183967\pi\)
−0.0543233 + 0.998523i \(0.517300\pi\)
\(608\) 11.5903 20.0750i 0.470049 0.814148i
\(609\) 0 0
\(610\) 7.75001i 0.313789i
\(611\) 2.96804 + 22.9636i 0.120074 + 0.929007i
\(612\) 0 0
\(613\) −37.2994 9.99436i −1.50651 0.403668i −0.591236 0.806499i \(-0.701360\pi\)
−0.915275 + 0.402831i \(0.868026\pi\)
\(614\) 2.35621i 0.0950890i
\(615\) 0 0
\(616\) 1.41919 + 7.34656i 0.0571809 + 0.296001i
\(617\) −19.0276 5.09843i −0.766022 0.205255i −0.145409 0.989372i \(-0.546450\pi\)
−0.620613 + 0.784117i \(0.713116\pi\)
\(618\) 0 0
\(619\) −9.15720 34.1751i −0.368059 1.37361i −0.863226 0.504817i \(-0.831560\pi\)
0.495167 0.868798i \(-0.335107\pi\)
\(620\) 2.49384 0.100155
\(621\) 0 0
\(622\) −3.71207 13.8536i −0.148840 0.555480i
\(623\) 12.9133 + 26.5542i 0.517359 + 1.06387i
\(624\) 0 0
\(625\) −0.376462 0.652052i −0.0150585 0.0260821i
\(626\) −7.34174 + 27.3997i −0.293435 + 1.09511i
\(627\) 0 0
\(628\) 6.73095 11.6583i 0.268594 0.465219i
\(629\) 34.6868 + 34.6868i 1.38305 + 1.38305i
\(630\) 0 0
\(631\) 1.11023 4.14343i 0.0441976 0.164948i −0.940300 0.340348i \(-0.889455\pi\)
0.984497 + 0.175400i \(0.0561219\pi\)
\(632\) −3.54979 + 13.2480i −0.141203 + 0.526976i
\(633\) 0 0
\(634\) 12.3225 7.11439i 0.489388 0.282548i
\(635\) 1.87857 1.87857i 0.0745489 0.0745489i
\(636\) 0 0
\(637\) −6.85854 + 24.2891i −0.271745 + 0.962369i
\(638\) 3.84856 0.152366
\(639\) 0 0
\(640\) −15.4509 + 8.92060i −0.610752 + 0.352618i
\(641\) 35.3132i 1.39479i 0.716689 + 0.697393i \(0.245657\pi\)
−0.716689 + 0.697393i \(0.754343\pi\)
\(642\) 0 0
\(643\) −2.90713 + 10.8495i −0.114646 + 0.427864i −0.999260 0.0384591i \(-0.987755\pi\)
0.884614 + 0.466323i \(0.154422\pi\)
\(644\) −1.68356 + 4.87106i −0.0663414 + 0.191947i
\(645\) 0 0
\(646\) 21.3758 37.0239i 0.841019 1.45669i
\(647\) −6.78354 11.7494i −0.266689 0.461918i 0.701316 0.712851i \(-0.252596\pi\)
−0.968005 + 0.250932i \(0.919263\pi\)
\(648\) 0 0
\(649\) 6.41925 + 11.1185i 0.251978 + 0.436438i
\(650\) −11.2743 14.7650i −0.442213 0.579131i
\(651\) 0 0
\(652\) 3.76878 + 14.0653i 0.147597 + 0.550839i
\(653\) 14.6552 0.573501 0.286751 0.958005i \(-0.407425\pi\)
0.286751 + 0.958005i \(0.407425\pi\)
\(654\) 0 0
\(655\) −3.73824 13.9513i −0.146065 0.545123i
\(656\) −31.6821 + 8.48920i −1.23698 + 0.331448i
\(657\) 0 0
\(658\) 5.49379 + 28.4390i 0.214170 + 1.10867i
\(659\) 25.1178 + 43.5054i 0.978452 + 1.69473i 0.668037 + 0.744128i \(0.267135\pi\)
0.310415 + 0.950601i \(0.399532\pi\)
\(660\) 0 0
\(661\) −1.25098 0.335198i −0.0486574 0.0130377i 0.234408 0.972138i \(-0.424685\pi\)
−0.283066 + 0.959101i \(0.591351\pi\)
\(662\) 10.9314 + 6.31125i 0.424861 + 0.245294i
\(663\) 0 0
\(664\) 0.180587i 0.00700814i
\(665\) 17.0568 + 5.89523i 0.661433 + 0.228607i
\(666\) 0 0
\(667\) −2.77147 1.60011i −0.107312 0.0619566i
\(668\) −11.5419 + 3.09264i −0.446569 + 0.119658i
\(669\) 0 0
\(670\) −8.08155 30.1607i −0.312217 1.16521i
\(671\) 3.46677 3.46677i 0.133833 0.133833i
\(672\) 0 0
\(673\) 19.6264 + 11.3313i 0.756543 + 0.436790i 0.828053 0.560650i \(-0.189449\pi\)
−0.0715103 + 0.997440i \(0.522782\pi\)
\(674\) −33.4707 33.4707i −1.28924 1.28924i
\(675\) 0 0
\(676\) 8.28984 + 8.36856i 0.318840 + 0.321868i
\(677\) 23.6738 13.6681i 0.909859 0.525307i 0.0294729 0.999566i \(-0.490617\pi\)
0.880386 + 0.474258i \(0.157284\pi\)
\(678\) 0 0
\(679\) 28.7421 + 19.4353i 1.10302 + 0.745857i
\(680\) −11.7420 + 6.77923i −0.450284 + 0.259972i
\(681\) 0 0
\(682\) 3.57785 + 3.57785i 0.137003 + 0.137003i
\(683\) −20.0961 20.0961i −0.768954 0.768954i 0.208968 0.977922i \(-0.432989\pi\)
−0.977922 + 0.208968i \(0.932989\pi\)
\(684\) 0 0
\(685\) 11.3533 6.55485i 0.433788 0.250448i
\(686\) −6.67152 + 30.8591i −0.254720 + 1.17821i
\(687\) 0 0
\(688\) −36.3026 + 20.9593i −1.38402 + 0.799066i
\(689\) 13.4066 + 1.79725i 0.510751 + 0.0684697i
\(690\) 0 0
\(691\) 7.07012 + 7.07012i 0.268960 + 0.268960i 0.828681 0.559721i \(-0.189092\pi\)
−0.559721 + 0.828681i \(0.689092\pi\)
\(692\) −11.0117 6.35759i −0.418601 0.241679i
\(693\) 0 0
\(694\) 13.0573 13.0573i 0.495650 0.495650i
\(695\) 0.0596052 + 0.222450i 0.00226096 + 0.00843800i
\(696\) 0 0
\(697\) −32.8188 + 8.79378i −1.24310 + 0.333088i
\(698\) 3.54887 + 2.04894i 0.134327 + 0.0775536i
\(699\) 0 0
\(700\) −4.74730 5.47394i −0.179431 0.206895i
\(701\) 36.1836i 1.36664i −0.730121 0.683318i \(-0.760536\pi\)
0.730121 0.683318i \(-0.239464\pi\)
\(702\) 0 0
\(703\) 39.8548 + 23.0102i 1.50315 + 0.867846i
\(704\) −2.68864 0.720418i −0.101332 0.0271518i
\(705\) 0 0
\(706\) 10.2716 + 17.7909i 0.386576 + 0.669569i
\(707\) −44.6692 + 8.62911i −1.67996 + 0.324531i
\(708\) 0 0
\(709\) −30.8750 + 8.27293i −1.15954 + 0.310697i −0.786780 0.617233i \(-0.788253\pi\)
−0.372755 + 0.927930i \(0.621587\pi\)
\(710\) 1.74215 + 6.50180i 0.0653818 + 0.244008i
\(711\) 0 0
\(712\) −20.8118 −0.779954
\(713\) −1.08897 4.06408i −0.0407822 0.152201i
\(714\) 0 0
\(715\) −1.02169 + 7.62135i −0.0382092 + 0.285022i
\(716\) −8.15313 14.1216i −0.304697 0.527750i
\(717\) 0 0
\(718\) −23.4583 40.6310i −0.875457 1.51634i
\(719\) 10.5168 18.2157i 0.392212 0.679330i −0.600529 0.799603i \(-0.705043\pi\)
0.992741 + 0.120272i \(0.0383768\pi\)
\(720\) 0 0
\(721\) 0.916860 0.177117i 0.0341456 0.00659619i
\(722\) 1.99741 7.45444i 0.0743359 0.277425i
\(723\) 0 0
\(724\) 13.4491i 0.499833i
\(725\) 3.89643 2.24961i 0.144710 0.0835482i
\(726\) 0 0
\(727\) −31.1689 −1.15599 −0.577995 0.816040i \(-0.696165\pi\)
−0.577995 + 0.816040i \(0.696165\pi\)
\(728\) −13.2816 11.8342i −0.492248 0.438604i
\(729\) 0 0
\(730\) 25.0746 25.0746i 0.928053 0.928053i
\(731\) −37.6051 + 21.7113i −1.39087 + 0.803021i
\(732\) 0 0
\(733\) 1.40351 5.23797i 0.0518398 0.193469i −0.935150 0.354252i \(-0.884735\pi\)
0.986990 + 0.160783i \(0.0514021\pi\)
\(734\) 6.22718 23.2402i 0.229849 0.857810i
\(735\) 0 0
\(736\) −7.26481 7.26481i −0.267784 0.267784i
\(737\) 9.87655 17.1067i 0.363807 0.630133i
\(738\) 0 0
\(739\) 7.93352 29.6083i 0.291839 1.08916i −0.651856 0.758343i \(-0.726009\pi\)
0.943695 0.330816i \(-0.107324\pi\)
\(740\) 6.04482 + 10.4699i 0.222212 + 0.384883i
\(741\) 0 0
\(742\) 16.8782 + 1.19989i 0.619617 + 0.0440494i
\(743\) 1.70775 + 6.37341i 0.0626512 + 0.233818i 0.990150 0.140008i \(-0.0447127\pi\)
−0.927499 + 0.373825i \(0.878046\pi\)
\(744\) 0 0
\(745\) −29.3000 −1.07347
\(746\) 13.2317 + 49.3813i 0.484446 + 1.80798i
\(747\) 0 0
\(748\) 6.86272 + 1.83886i 0.250926 + 0.0672354i
\(749\) −11.5893 + 33.5315i −0.423463 + 1.22521i
\(750\) 0 0
\(751\) 8.46455i 0.308876i −0.988002 0.154438i \(-0.950643\pi\)
0.988002 0.154438i \(-0.0493567\pi\)
\(752\) −30.9609 8.29594i −1.12903 0.302522i
\(753\) 0 0
\(754\) −7.27213 + 5.55285i −0.264835 + 0.202223i
\(755\) 5.09759i 0.185520i
\(756\) 0 0
\(757\) 13.5330 23.4399i 0.491866 0.851937i −0.508090 0.861304i \(-0.669648\pi\)
0.999956 + 0.00936661i \(0.00298153\pi\)
\(758\) −38.5734 22.2703i −1.40105 0.808895i
\(759\) 0 0
\(760\) −8.99429 + 8.99429i −0.326257 + 0.326257i
\(761\) 4.69735 + 17.5308i 0.170279 + 0.635489i 0.997308 + 0.0733299i \(0.0233626\pi\)
−0.827029 + 0.562159i \(0.809971\pi\)
\(762\) 0 0
\(763\) 25.9656 + 1.84593i 0.940016 + 0.0668270i
\(764\) −11.3514 6.55373i −0.410679 0.237105i
\(765\) 0 0
\(766\) −27.1033 + 46.9442i −0.979281 + 1.69616i
\(767\) −28.1718 11.7472i −1.01723 0.424167i
\(768\) 0 0
\(769\) 39.4162 10.5616i 1.42139 0.380859i 0.535411 0.844592i \(-0.320157\pi\)
0.885975 + 0.463732i \(0.153490\pi\)
\(770\) −0.682111 + 9.59485i −0.0245816 + 0.345774i
\(771\) 0 0
\(772\) −15.8842 4.25616i −0.571684 0.153182i
\(773\) 7.87836 + 7.87836i 0.283365 + 0.283365i 0.834449 0.551085i \(-0.185786\pi\)
−0.551085 + 0.834449i \(0.685786\pi\)
\(774\) 0 0
\(775\) 5.71372 + 1.53099i 0.205243 + 0.0549946i
\(776\) −21.1785 + 12.2274i −0.760265 + 0.438939i
\(777\) 0 0
\(778\) −23.0564 + 6.17793i −0.826610 + 0.221490i
\(779\) −27.6046 + 15.9375i −0.989037 + 0.571021i
\(780\) 0 0
\(781\) −2.12910 + 3.68772i −0.0761853 + 0.131957i
\(782\) −13.3983 13.3983i −0.479124 0.479124i
\(783\) 0 0
\(784\) −27.4818 21.5739i −0.981494 0.770497i
\(785\) −14.7733 + 14.7733i −0.527283 + 0.527283i
\(786\) 0 0
\(787\) −0.429238 + 0.429238i −0.0153007 + 0.0153007i −0.714716 0.699415i \(-0.753444\pi\)
0.699415 + 0.714716i \(0.253444\pi\)
\(788\) 20.9058 5.60170i 0.744739 0.199552i