Properties

Label 229.2.b.a.228.1
Level 229
Weight 2
Character 229.228
Analytic conductor 1.829
Analytic rank 0
Dimension 2
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 229.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(1.82857420629\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-5}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 228.1
Root \(-2.23607i\)
Character \(\chi\) = 229.228
Dual form 229.2.b.a.228.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.23607i q^{2}\) \(+1.00000 q^{3}\) \(-3.00000 q^{4}\) \(+3.00000 q^{5}\) \(-2.23607i q^{6}\) \(+2.23607i q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.23607i q^{2}\) \(+1.00000 q^{3}\) \(-3.00000 q^{4}\) \(+3.00000 q^{5}\) \(-2.23607i q^{6}\) \(+2.23607i q^{8}\) \(-2.00000 q^{9}\) \(-6.70820i q^{10}\) \(+3.00000 q^{11}\) \(-3.00000 q^{12}\) \(+3.00000 q^{15}\) \(-1.00000 q^{16}\) \(-3.00000 q^{17}\) \(+4.47214i q^{18}\) \(-1.00000 q^{19}\) \(-9.00000 q^{20}\) \(-6.70820i q^{22}\) \(+4.47214i q^{23}\) \(+2.23607i q^{24}\) \(+4.00000 q^{25}\) \(-5.00000 q^{27}\) \(+4.47214i q^{29}\) \(-6.70820i q^{30}\) \(+6.70820i q^{32}\) \(+3.00000 q^{33}\) \(+6.70820i q^{34}\) \(+6.00000 q^{36}\) \(+2.00000 q^{37}\) \(+2.23607i q^{38}\) \(+6.70820i q^{40}\) \(+4.47214i q^{41}\) \(-1.00000 q^{43}\) \(-9.00000 q^{44}\) \(-6.00000 q^{45}\) \(+10.0000 q^{46}\) \(-8.94427i q^{47}\) \(-1.00000 q^{48}\) \(+7.00000 q^{49}\) \(-8.94427i q^{50}\) \(-3.00000 q^{51}\) \(+6.00000 q^{53}\) \(+11.1803i q^{54}\) \(+9.00000 q^{55}\) \(-1.00000 q^{57}\) \(+10.0000 q^{58}\) \(-8.94427i q^{59}\) \(-9.00000 q^{60}\) \(+5.00000 q^{61}\) \(+13.0000 q^{64}\) \(-6.70820i q^{66}\) \(-13.4164i q^{67}\) \(+9.00000 q^{68}\) \(+4.47214i q^{69}\) \(-15.0000 q^{71}\) \(-4.47214i q^{72}\) \(+13.4164i q^{73}\) \(-4.47214i q^{74}\) \(+4.00000 q^{75}\) \(+3.00000 q^{76}\) \(+13.4164i q^{79}\) \(-3.00000 q^{80}\) \(+1.00000 q^{81}\) \(+10.0000 q^{82}\) \(-9.00000 q^{83}\) \(-9.00000 q^{85}\) \(+2.23607i q^{86}\) \(+4.47214i q^{87}\) \(+6.70820i q^{88}\) \(+17.8885i q^{89}\) \(+13.4164i q^{90}\) \(-13.4164i q^{92}\) \(-20.0000 q^{94}\) \(-3.00000 q^{95}\) \(+6.70820i q^{96}\) \(-7.00000 q^{97}\) \(-15.6525i q^{98}\) \(-6.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 18q^{20} \) \(\mathstrut +\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{44} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 14q^{49} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut +\mathstrut 20q^{58} \) \(\mathstrut -\mathstrut 18q^{60} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 26q^{64} \) \(\mathstrut +\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 30q^{71} \) \(\mathstrut +\mathstrut 8q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 18q^{85} \) \(\mathstrut -\mathstrut 40q^{94} \) \(\mathstrut -\mathstrut 6q^{95} \) \(\mathstrut -\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/229\mathbb{Z}\right)^\times\).

\(n\) \(6\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.23607i 1.58114i −0.612372 0.790569i \(-0.709785\pi\)
0.612372 0.790569i \(-0.290215\pi\)
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) −3.00000 −1.50000
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 2.23607i 0.912871i
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 2.23607i 0.790569i
\(9\) −2.00000 −0.666667
\(10\) 6.70820i 2.12132i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) −3.00000 −0.866025
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) −1.00000 −0.250000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 4.47214i 1.05409i
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −9.00000 −2.01246
\(21\) 0 0
\(22\) 6.70820i 1.43019i
\(23\) 4.47214i 0.932505i 0.884652 + 0.466252i \(0.154396\pi\)
−0.884652 + 0.466252i \(0.845604\pi\)
\(24\) 2.23607i 0.456435i
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 4.47214i 0.830455i 0.909718 + 0.415227i \(0.136298\pi\)
−0.909718 + 0.415227i \(0.863702\pi\)
\(30\) 6.70820i 1.22474i
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 6.70820i 1.18585i
\(33\) 3.00000 0.522233
\(34\) 6.70820i 1.15045i
\(35\) 0 0
\(36\) 6.00000 1.00000
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 2.23607i 0.362738i
\(39\) 0 0
\(40\) 6.70820i 1.06066i
\(41\) 4.47214i 0.698430i 0.937043 + 0.349215i \(0.113552\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) −9.00000 −1.35680
\(45\) −6.00000 −0.894427
\(46\) 10.0000 1.47442
\(47\) 8.94427i 1.30466i −0.757937 0.652328i \(-0.773792\pi\)
0.757937 0.652328i \(-0.226208\pi\)
\(48\) −1.00000 −0.144338
\(49\) 7.00000 1.00000
\(50\) 8.94427i 1.26491i
\(51\) −3.00000 −0.420084
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 11.1803i 1.52145i
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 10.0000 1.31306
\(59\) 8.94427i 1.16445i −0.813029 0.582223i \(-0.802183\pi\)
0.813029 0.582223i \(-0.197817\pi\)
\(60\) −9.00000 −1.16190
\(61\) 5.00000 0.640184 0.320092 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 13.0000 1.62500
\(65\) 0 0
\(66\) 6.70820i 0.825723i
\(67\) 13.4164i 1.63908i −0.573025 0.819538i \(-0.694230\pi\)
0.573025 0.819538i \(-0.305770\pi\)
\(68\) 9.00000 1.09141
\(69\) 4.47214i 0.538382i
\(70\) 0 0
\(71\) −15.0000 −1.78017 −0.890086 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 4.47214i 0.527046i
\(73\) 13.4164i 1.57027i 0.619324 + 0.785136i \(0.287407\pi\)
−0.619324 + 0.785136i \(0.712593\pi\)
\(74\) 4.47214i 0.519875i
\(75\) 4.00000 0.461880
\(76\) 3.00000 0.344124
\(77\) 0 0
\(78\) 0 0
\(79\) 13.4164i 1.50946i 0.656033 + 0.754732i \(0.272233\pi\)
−0.656033 + 0.754732i \(0.727767\pi\)
\(80\) −3.00000 −0.335410
\(81\) 1.00000 0.111111
\(82\) 10.0000 1.10432
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 0 0
\(85\) −9.00000 −0.976187
\(86\) 2.23607i 0.241121i
\(87\) 4.47214i 0.479463i
\(88\) 6.70820i 0.715097i
\(89\) 17.8885i 1.89618i 0.317999 + 0.948091i \(0.396989\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 13.4164i 1.41421i
\(91\) 0 0
\(92\) 13.4164i 1.39876i
\(93\) 0 0
\(94\) −20.0000 −2.06284
\(95\) −3.00000 −0.307794
\(96\) 6.70820i 0.684653i
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 15.6525i 1.58114i
\(99\) −6.00000 −0.603023
\(100\) −12.0000 −1.20000
\(101\) 4.47214i 0.444994i 0.974933 + 0.222497i \(0.0714208\pi\)
−0.974933 + 0.222497i \(0.928579\pi\)
\(102\) 6.70820i 0.664211i
\(103\) 11.0000 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 13.4164i 1.30312i
\(107\) 8.94427i 0.864675i −0.901712 0.432338i \(-0.857689\pi\)
0.901712 0.432338i \(-0.142311\pi\)
\(108\) 15.0000 1.44338
\(109\) 13.4164i 1.28506i −0.766261 0.642529i \(-0.777885\pi\)
0.766261 0.642529i \(-0.222115\pi\)
\(110\) 20.1246i 1.91881i
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) 8.94427i 0.841406i −0.907198 0.420703i \(-0.861783\pi\)
0.907198 0.420703i \(-0.138217\pi\)
\(114\) 2.23607i 0.209427i
\(115\) 13.4164i 1.25109i
\(116\) 13.4164i 1.24568i
\(117\) 0 0
\(118\) −20.0000 −1.84115
\(119\) 0 0
\(120\) 6.70820i 0.612372i
\(121\) −2.00000 −0.181818
\(122\) 11.1803i 1.01222i
\(123\) 4.47214i 0.403239i
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 15.6525i 1.38350i
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) 4.47214i 0.390732i 0.980730 + 0.195366i \(0.0625895\pi\)
−0.980730 + 0.195366i \(0.937410\pi\)
\(132\) −9.00000 −0.783349
\(133\) 0 0
\(134\) −30.0000 −2.59161
\(135\) −15.0000 −1.29099
\(136\) 6.70820i 0.575224i
\(137\) 8.94427i 0.764161i −0.924129 0.382080i \(-0.875208\pi\)
0.924129 0.382080i \(-0.124792\pi\)
\(138\) 10.0000 0.851257
\(139\) 13.4164i 1.13796i −0.822350 0.568982i \(-0.807337\pi\)
0.822350 0.568982i \(-0.192663\pi\)
\(140\) 0 0
\(141\) 8.94427i 0.753244i
\(142\) 33.5410i 2.81470i
\(143\) 0 0
\(144\) 2.00000 0.166667
\(145\) 13.4164i 1.11417i
\(146\) 30.0000 2.48282
\(147\) 7.00000 0.577350
\(148\) −6.00000 −0.493197
\(149\) −21.0000 −1.72039 −0.860194 0.509968i \(-0.829657\pi\)
−0.860194 + 0.509968i \(0.829657\pi\)
\(150\) 8.94427i 0.730297i
\(151\) −7.00000 −0.569652 −0.284826 0.958579i \(-0.591936\pi\)
−0.284826 + 0.958579i \(0.591936\pi\)
\(152\) 2.23607i 0.181369i
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 13.4164i 1.07075i −0.844616 0.535373i \(-0.820171\pi\)
0.844616 0.535373i \(-0.179829\pi\)
\(158\) 30.0000 2.38667
\(159\) 6.00000 0.475831
\(160\) 20.1246i 1.59099i
\(161\) 0 0
\(162\) 2.23607i 0.175682i
\(163\) 13.4164i 1.05085i −0.850839 0.525427i \(-0.823906\pi\)
0.850839 0.525427i \(-0.176094\pi\)
\(164\) 13.4164i 1.04765i
\(165\) 9.00000 0.700649
\(166\) 20.1246i 1.56197i
\(167\) 3.00000 0.232147 0.116073 0.993241i \(-0.462969\pi\)
0.116073 + 0.993241i \(0.462969\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 20.1246i 1.54349i
\(171\) 2.00000 0.152944
\(172\) 3.00000 0.228748
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 10.0000 0.758098
\(175\) 0 0
\(176\) −3.00000 −0.226134
\(177\) 8.94427i 0.672293i
\(178\) 40.0000 2.99813
\(179\) 17.8885i 1.33705i 0.743689 + 0.668526i \(0.233075\pi\)
−0.743689 + 0.668526i \(0.766925\pi\)
\(180\) 18.0000 1.34164
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 5.00000 0.369611
\(184\) −10.0000 −0.737210
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −9.00000 −0.658145
\(188\) 26.8328i 1.95698i
\(189\) 0 0
\(190\) 6.70820i 0.486664i
\(191\) 8.94427i 0.647185i −0.946197 0.323592i \(-0.895109\pi\)
0.946197 0.323592i \(-0.104891\pi\)
\(192\) 13.0000 0.938194
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 15.6525i 1.12378i
\(195\) 0 0
\(196\) −21.0000 −1.50000
\(197\) 17.8885i 1.27451i 0.770655 + 0.637253i \(0.219929\pi\)
−0.770655 + 0.637253i \(0.780071\pi\)
\(198\) 13.4164i 0.953463i
\(199\) 13.4164i 0.951064i −0.879698 0.475532i \(-0.842256\pi\)
0.879698 0.475532i \(-0.157744\pi\)
\(200\) 8.94427i 0.632456i
\(201\) 13.4164i 0.946320i
\(202\) 10.0000 0.703598
\(203\) 0 0
\(204\) 9.00000 0.630126
\(205\) 13.4164i 0.937043i
\(206\) 24.5967i 1.71374i
\(207\) 8.94427i 0.621670i
\(208\) 0 0
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) 13.4164i 0.923624i −0.886978 0.461812i \(-0.847200\pi\)
0.886978 0.461812i \(-0.152800\pi\)
\(212\) −18.0000 −1.23625
\(213\) −15.0000 −1.02778
\(214\) −20.0000 −1.36717
\(215\) −3.00000 −0.204598
\(216\) 11.1803i 0.760726i
\(217\) 0 0
\(218\) −30.0000 −2.03186
\(219\) 13.4164i 0.906597i
\(220\) −27.0000 −1.82034
\(221\) 0 0
\(222\) 4.47214i 0.300150i
\(223\) 13.4164i 0.898429i −0.893424 0.449215i \(-0.851704\pi\)
0.893424 0.449215i \(-0.148296\pi\)
\(224\) 0 0
\(225\) −8.00000 −0.533333
\(226\) −20.0000 −1.33038
\(227\) 4.47214i 0.296826i 0.988925 + 0.148413i \(0.0474165\pi\)
−0.988925 + 0.148413i \(0.952583\pi\)
\(228\) 3.00000 0.198680
\(229\) 7.00000 13.4164i 0.462573 0.886581i
\(230\) 30.0000 1.97814
\(231\) 0 0
\(232\) −10.0000 −0.656532
\(233\) 9.00000 0.589610 0.294805 0.955557i \(-0.404745\pi\)
0.294805 + 0.955557i \(0.404745\pi\)
\(234\) 0 0
\(235\) 26.8328i 1.75038i
\(236\) 26.8328i 1.74667i
\(237\) 13.4164i 0.871489i
\(238\) 0 0
\(239\) 22.3607i 1.44639i −0.690643 0.723196i \(-0.742672\pi\)
0.690643 0.723196i \(-0.257328\pi\)
\(240\) −3.00000 −0.193649
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 4.47214i 0.287480i
\(243\) 16.0000 1.02640
\(244\) −15.0000 −0.960277
\(245\) 21.0000 1.34164
\(246\) 10.0000 0.637577
\(247\) 0 0
\(248\) 0 0
\(249\) −9.00000 −0.570352
\(250\) 6.70820i 0.424264i
\(251\) 17.8885i 1.12911i 0.825394 + 0.564557i \(0.190953\pi\)
−0.825394 + 0.564557i \(0.809047\pi\)
\(252\) 0 0
\(253\) 13.4164i 0.843482i
\(254\) 0 0
\(255\) −9.00000 −0.563602
\(256\) −9.00000 −0.562500
\(257\) 17.8885i 1.11586i 0.829889 + 0.557928i \(0.188404\pi\)
−0.829889 + 0.557928i \(0.811596\pi\)
\(258\) 2.23607i 0.139212i
\(259\) 0 0
\(260\) 0 0
\(261\) 8.94427i 0.553637i
\(262\) 10.0000 0.617802
\(263\) 4.47214i 0.275764i 0.990449 + 0.137882i \(0.0440294\pi\)
−0.990449 + 0.137882i \(0.955971\pi\)
\(264\) 6.70820i 0.412861i
\(265\) 18.0000 1.10573
\(266\) 0 0
\(267\) 17.8885i 1.09476i
\(268\) 40.2492i 2.45861i
\(269\) 22.3607i 1.36335i −0.731653 0.681677i \(-0.761251\pi\)
0.731653 0.681677i \(-0.238749\pi\)
\(270\) 33.5410i 2.04124i
\(271\) −25.0000 −1.51864 −0.759321 0.650716i \(-0.774469\pi\)
−0.759321 + 0.650716i \(0.774469\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) −20.0000 −1.20824
\(275\) 12.0000 0.723627
\(276\) 13.4164i 0.807573i
\(277\) 17.0000 1.02143 0.510716 0.859750i \(-0.329381\pi\)
0.510716 + 0.859750i \(0.329381\pi\)
\(278\) −30.0000 −1.79928
\(279\) 0 0
\(280\) 0 0
\(281\) 31.3050i 1.86750i 0.357930 + 0.933748i \(0.383483\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) −20.0000 −1.19098
\(283\) 13.4164i 0.797523i −0.917055 0.398761i \(-0.869440\pi\)
0.917055 0.398761i \(-0.130560\pi\)
\(284\) 45.0000 2.67026
\(285\) −3.00000 −0.177705
\(286\) 0 0
\(287\) 0 0
\(288\) 13.4164i 0.790569i
\(289\) −8.00000 −0.470588
\(290\) 30.0000 1.76166
\(291\) −7.00000 −0.410347
\(292\) 40.2492i 2.35541i
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 15.6525i 0.912871i
\(295\) 26.8328i 1.56227i
\(296\) 4.47214i 0.259938i
\(297\) −15.0000 −0.870388
\(298\) 46.9574i 2.72017i
\(299\) 0 0
\(300\) −12.0000 −0.692820
\(301\) 0 0
\(302\) 15.6525i 0.900699i
\(303\) 4.47214i 0.256917i
\(304\) 1.00000 0.0573539
\(305\) 15.0000 0.858898
\(306\) 13.4164i 0.766965i
\(307\) 17.0000 0.970241 0.485121 0.874447i \(-0.338776\pi\)
0.485121 + 0.874447i \(0.338776\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) 15.0000 0.850572 0.425286 0.905059i \(-0.360174\pi\)
0.425286 + 0.905059i \(0.360174\pi\)
\(312\) 0 0
\(313\) 13.4164i 0.758340i 0.925327 + 0.379170i \(0.123790\pi\)
−0.925327 + 0.379170i \(0.876210\pi\)
\(314\) −30.0000 −1.69300
\(315\) 0 0
\(316\) 40.2492i 2.26420i
\(317\) 8.94427i 0.502360i −0.967940 0.251180i \(-0.919181\pi\)
0.967940 0.251180i \(-0.0808187\pi\)
\(318\) 13.4164i 0.752355i
\(319\) 13.4164i 0.751175i
\(320\) 39.0000 2.18017
\(321\) 8.94427i 0.499221i
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) −3.00000 −0.166667
\(325\) 0 0
\(326\) −30.0000 −1.66155
\(327\) 13.4164i 0.741929i
\(328\) −10.0000 −0.552158
\(329\) 0 0
\(330\) 20.1246i 1.10782i
\(331\) 13.4164i 0.737432i 0.929542 + 0.368716i \(0.120203\pi\)
−0.929542 + 0.368716i \(0.879797\pi\)
\(332\) 27.0000 1.48182
\(333\) −4.00000 −0.219199
\(334\) 6.70820i 0.367057i
\(335\) 40.2492i 2.19905i
\(336\) 0 0
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) 29.0689i 1.58114i
\(339\) 8.94427i 0.485786i
\(340\) 27.0000 1.46428
\(341\) 0 0
\(342\) 4.47214i 0.241825i
\(343\) 0 0
\(344\) 2.23607i 0.120561i
\(345\) 13.4164i 0.722315i
\(346\) 13.4164i 0.721271i
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 13.4164i 0.719195i
\(349\) 13.4164i 0.718164i −0.933306 0.359082i \(-0.883090\pi\)
0.933306 0.359082i \(-0.116910\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 20.1246i 1.07265i
\(353\) 8.94427i 0.476056i −0.971258 0.238028i \(-0.923499\pi\)
0.971258 0.238028i \(-0.0765009\pi\)
\(354\) −20.0000 −1.06299
\(355\) −45.0000 −2.38835
\(356\) 53.6656i 2.84427i
\(357\) 0 0
\(358\) 40.0000 2.11407
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 13.4164i 0.707107i
\(361\) −18.0000 −0.947368
\(362\) 15.6525i 0.822676i
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 40.2492i 2.10674i
\(366\) 11.1803i 0.584406i
\(367\) 17.0000 0.887393 0.443696 0.896177i \(-0.353667\pi\)
0.443696 + 0.896177i \(0.353667\pi\)
\(368\) 4.47214i 0.233126i
\(369\) 8.94427i 0.465620i
\(370\) 13.4164i 0.697486i
\(371\) 0 0
\(372\) 0 0
\(373\) −19.0000 −0.983783 −0.491891 0.870657i \(-0.663694\pi\)
−0.491891 + 0.870657i \(0.663694\pi\)
\(374\) 20.1246i 1.04062i
\(375\) −3.00000 −0.154919
\(376\) 20.0000 1.03142
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 9.00000 0.461690
\(381\) 0 0
\(382\) −20.0000 −1.02329
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 15.6525i 0.798762i
\(385\) 0 0
\(386\) 31.3050i 1.59338i
\(387\) 2.00000 0.101666
\(388\) 21.0000 1.06611
\(389\) 31.3050i 1.58722i 0.608424 + 0.793612i \(0.291802\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) 13.4164i 0.678497i
\(392\) 15.6525i 0.790569i
\(393\) 4.47214i 0.225589i
\(394\) 40.0000 2.01517
\(395\) 40.2492i 2.02516i
\(396\) 18.0000 0.904534
\(397\) 23.0000 1.15434 0.577168 0.816625i \(-0.304158\pi\)
0.577168 + 0.816625i \(0.304158\pi\)
\(398\) −30.0000 −1.50376
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 27.0000 1.34832 0.674158 0.738587i \(-0.264507\pi\)
0.674158 + 0.738587i \(0.264507\pi\)
\(402\) −30.0000 −1.49626
\(403\) 0 0
\(404\) 13.4164i 0.667491i
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 6.70820i 0.332106i
\(409\) 35.0000 1.73064 0.865319 0.501221i \(-0.167116\pi\)
0.865319 + 0.501221i \(0.167116\pi\)
\(410\) 30.0000 1.48159
\(411\) 8.94427i 0.441188i
\(412\) −33.0000 −1.62579
\(413\) 0 0
\(414\) −20.0000 −0.982946
\(415\) −27.0000 −1.32538
\(416\) 0 0
\(417\) 13.4164i 0.657004i
\(418\) 6.70820i 0.328109i
\(419\) 4.47214i 0.218478i 0.994016 + 0.109239i \(0.0348414\pi\)
−0.994016 + 0.109239i \(0.965159\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) −30.0000 −1.46038
\(423\) 17.8885i 0.869771i
\(424\) 13.4164i 0.651558i
\(425\) −12.0000 −0.582086
\(426\) 33.5410i 1.62507i
\(427\) 0 0
\(428\) 26.8328i 1.29701i
\(429\) 0 0
\(430\) 6.70820i 0.323498i
\(431\) 15.0000 0.722525 0.361262 0.932464i \(-0.382346\pi\)
0.361262 + 0.932464i \(0.382346\pi\)
\(432\) 5.00000 0.240563
\(433\) −19.0000 −0.913082 −0.456541 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) 0 0
\(435\) 13.4164i 0.643268i
\(436\) 40.2492i 1.92759i
\(437\) 4.47214i 0.213931i
\(438\) 30.0000 1.43346
\(439\) 20.0000 0.954548 0.477274 0.878755i \(-0.341625\pi\)
0.477274 + 0.878755i \(0.341625\pi\)
\(440\) 20.1246i 0.959403i
\(441\) −14.0000 −0.666667
\(442\) 0 0
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) −6.00000 −0.284747
\(445\) 53.6656i 2.54399i
\(446\) −30.0000 −1.42054
\(447\) −21.0000 −0.993266
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 17.8885i 0.843274i
\(451\) 13.4164i 0.631754i
\(452\) 26.8328i 1.26211i
\(453\) −7.00000 −0.328889
\(454\) 10.0000 0.469323
\(455\) 0 0
\(456\) 2.23607i 0.104713i
\(457\) 23.0000 1.07589 0.537947 0.842978i \(-0.319200\pi\)
0.537947 + 0.842978i \(0.319200\pi\)
\(458\) −30.0000 15.6525i −1.40181 0.731392i
\(459\) 15.0000 0.700140
\(460\) 40.2492i 1.87663i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) 4.47214i 0.207614i
\(465\) 0 0
\(466\) 20.1246i 0.932255i
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −60.0000 −2.76759
\(471\) 13.4164i 0.618195i
\(472\) 20.0000 0.920575
\(473\) −3.00000 −0.137940
\(474\) 30.0000 1.37795
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) −50.0000 −2.28695
\(479\) 8.94427i 0.408674i −0.978901 0.204337i \(-0.934496\pi\)
0.978901 0.204337i \(-0.0655039\pi\)
\(480\) 20.1246i 0.918559i
\(481\) 0 0
\(482\) 22.3607i 1.01850i
\(483\) 0 0
\(484\) 6.00000 0.272727
\(485\) −21.0000 −0.953561
\(486\) 35.7771i 1.62288i
\(487\) 13.4164i 0.607955i 0.952679 + 0.303978i \(0.0983148\pi\)
−0.952679 + 0.303978i \(0.901685\pi\)
\(488\) 11.1803i 0.506110i
\(489\) 13.4164i 0.606711i
\(490\) 46.9574i 2.12132i
\(491\) −15.0000 −0.676941 −0.338470 0.940977i \(-0.609909\pi\)
−0.338470 + 0.940977i \(0.609909\pi\)
\(492\) 13.4164i 0.604858i
\(493\) 13.4164i 0.604245i
\(494\) 0 0
\(495\) −18.0000 −0.809040
\(496\) 0 0
\(497\) 0 0
\(498\) 20.1246i 0.901805i
\(499\) 26.8328i 1.20120i 0.799549 + 0.600601i \(0.205072\pi\)
−0.799549 + 0.600601i \(0.794928\pi\)
\(500\) 9.00000 0.402492
\(501\) 3.00000 0.134030
\(502\) 40.0000 1.78529
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 13.4164i 0.597022i
\(506\) 30.0000 1.33366
\(507\) 13.0000 0.577350
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 20.1246i 0.891133i
\(511\) 0 0
\(512\) 11.1803i 0.494106i
\(513\) 5.00000 0.220755
\(514\) 40.0000 1.76432
\(515\) 33.0000 1.45415
\(516\) 3.00000 0.132068
\(517\) 26.8328i 1.18011i
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 31.3050i 1.37149i 0.727840 + 0.685747i \(0.240525\pi\)
−0.727840 + 0.685747i \(0.759475\pi\)
\(522\) −20.0000 −0.875376
\(523\) 26.8328i 1.17332i 0.809834 + 0.586659i \(0.199557\pi\)
−0.809834 + 0.586659i \(0.800443\pi\)
\(524\) 13.4164i 0.586098i
\(525\) 0 0
\(526\) 10.0000 0.436021
\(527\) 0 0
\(528\) −3.00000 −0.130558
\(529\) 3.00000 0.130435
\(530\) 40.2492i 1.74831i
\(531\) 17.8885i 0.776297i
\(532\) 0 0
\(533\) 0 0
\(534\) 40.0000 1.73097
\(535\) 26.8328i 1.16008i
\(536\) 30.0000 1.29580
\(537\) 17.8885i 0.771948i
\(538\) −50.0000 −2.15565
\(539\) 21.0000 0.904534
\(540\) 45.0000 1.93649
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 55.9017i 2.40118i
\(543\) −7.00000 −0.300399
\(544\) 20.1246i 0.862836i
\(545\) 40.2492i 1.72409i
\(546\) 0 0
\(547\) 13.4164i 0.573644i −0.957984 0.286822i \(-0.907401\pi\)
0.957984 0.286822i \(-0.0925989\pi\)
\(548\) 26.8328i 1.14624i
\(549\) −10.0000 −0.426790
\(550\) 26.8328i 1.14416i
\(551\) 4.47214i 0.190519i
\(552\) −10.0000 −0.425628
\(553\) 0 0
\(554\) 38.0132i 1.61502i
\(555\) 6.00000 0.254686
\(556\) 40.2492i 1.70695i
\(557\) −3.00000 −0.127114 −0.0635570 0.997978i \(-0.520244\pi\)
−0.0635570 + 0.997978i \(0.520244\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 70.0000 2.95277
\(563\) 44.7214i 1.88478i 0.334515 + 0.942390i \(0.391427\pi\)
−0.334515 + 0.942390i \(0.608573\pi\)
\(564\) 26.8328i 1.12987i
\(565\) 26.8328i 1.12887i
\(566\) −30.0000 −1.26099
\(567\) 0 0
\(568\) 33.5410i 1.40735i
\(569\) 45.0000 1.88650 0.943249 0.332086i \(-0.107752\pi\)
0.943249 + 0.332086i \(0.107752\pi\)
\(570\) 6.70820i 0.280976i
\(571\) 26.8328i 1.12292i 0.827504 + 0.561459i \(0.189760\pi\)
−0.827504 + 0.561459i \(0.810240\pi\)
\(572\) 0 0
\(573\) 8.94427i 0.373652i
\(574\) 0 0
\(575\) 17.8885i 0.746004i
\(576\) −26.0000 −1.08333
\(577\) 40.2492i 1.67560i −0.545979 0.837799i \(-0.683842\pi\)
0.545979 0.837799i \(-0.316158\pi\)
\(578\) 17.8885i 0.744065i
\(579\) 14.0000 0.581820
\(580\) 40.2492i 1.67126i
\(581\) 0 0
\(582\) 15.6525i 0.648816i
\(583\) 18.0000 0.745484
\(584\) −30.0000 −1.24141
\(585\) 0 0
\(586\) 20.1246i 0.831340i
\(587\) −27.0000 −1.11441 −0.557205 0.830375i \(-0.688126\pi\)
−0.557205 + 0.830375i \(0.688126\pi\)
\(588\) −21.0000 −0.866025
\(589\) 0 0
\(590\) −60.0000 −2.47016
\(591\) 17.8885i 0.735836i
\(592\) −2.00000 −0.0821995
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 33.5410i 1.37620i
\(595\) 0 0
\(596\) 63.0000 2.58058
\(597\) 13.4164i 0.549097i
\(598\) 0 0
\(599\) 8.94427i 0.365453i −0.983164 0.182727i \(-0.941508\pi\)
0.983164 0.182727i \(-0.0584923\pi\)
\(600\) 8.94427i 0.365148i
\(601\) 40.2492i 1.64180i 0.571072 + 0.820900i \(0.306528\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) 0 0
\(603\) 26.8328i 1.09272i
\(604\) 21.0000 0.854478
\(605\) −6.00000 −0.243935
\(606\) 10.0000 0.406222
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 6.70820i 0.272054i
\(609\) 0 0
\(610\) 33.5410i 1.35804i
\(611\) 0 0
\(612\) −18.0000 −0.727607
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 38.0132i 1.53409i
\(615\) 13.4164i 0.541002i
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 24.5967i 0.989426i
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 22.3607i 0.897303i
\(622\) 33.5410i 1.34487i
\(623\) 0 0
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 30.0000 1.19904
\(627\) −3.00000 −0.119808
\(628\) 40.2492i 1.60612i
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) −43.0000 −1.71180 −0.855901 0.517139i \(-0.826997\pi\)
−0.855901 + 0.517139i \(0.826997\pi\)
\(632\) −30.0000 −1.19334
\(633\) 13.4164i 0.533254i
\(634\) −20.0000 −0.794301
\(635\) 0 0
\(636\) −18.0000 −0.713746
\(637\) 0 0
\(638\) 30.0000 1.18771
\(639\) 30.0000 1.18678
\(640\) 46.9574i 1.85616i
\(641\) −45.0000 −1.77739 −0.888697 0.458496i \(-0.848388\pi\)
−0.888697 + 0.458496i \(0.848388\pi\)
\(642\) −20.0000 −0.789337
\(643\) 44.0000 1.73519 0.867595 0.497271i \(-0.165665\pi\)
0.867595 + 0.497271i \(0.165665\pi\)
\(644\) 0 0
\(645\) −3.00000 −0.118125
\(646\) 6.70820i 0.263931i
\(647\) 17.8885i 0.703271i 0.936137 + 0.351636i \(0.114374\pi\)
−0.936137 + 0.351636i \(0.885626\pi\)
\(648\) 2.23607i 0.0878410i
\(649\) 26.8328i 1.05328i
\(650\) 0 0
\(651\) 0 0
\(652\) 40.2492i 1.57628i
\(653\) 35.7771i 1.40007i −0.714111 0.700033i \(-0.753169\pi\)
0.714111 0.700033i \(-0.246831\pi\)
\(654\) −30.0000 −1.17309
\(655\) 13.4164i 0.524222i
\(656\) 4.47214i 0.174608i
\(657\) 26.8328i 1.04685i
\(658\) 0 0
\(659\) 31.3050i 1.21947i 0.792606 + 0.609734i \(0.208724\pi\)
−0.792606 + 0.609734i \(0.791276\pi\)
\(660\) −27.0000 −1.05097
\(661\) −13.0000 −0.505641 −0.252821 0.967513i \(-0.581358\pi\)
−0.252821 + 0.967513i \(0.581358\pi\)
\(662\) 30.0000 1.16598
\(663\) 0 0
\(664\) 20.1246i 0.780986i
\(665\) 0 0
\(666\) 8.94427i 0.346583i
\(667\) −20.0000 −0.774403
\(668\) −9.00000 −0.348220
\(669\) 13.4164i 0.518708i
\(670\) −90.0000 −3.47700
\(671\) 15.0000 0.579069
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 29.0689i 1.11969i
\(675\) −20.0000 −0.769800
\(676\) −39.0000 −1.50000
\(677\) 8.94427i 0.343756i −0.985118 0.171878i \(-0.945016\pi\)
0.985118 0.171878i \(-0.0549835\pi\)
\(678\) −20.0000 −0.768095
\(679\) 0 0
\(680\) 20.1246i 0.771744i
\(681\) 4.47214i 0.171373i
\(682\) 0 0
\(683\) 9.00000 0.344375 0.172188 0.985064i \(-0.444916\pi\)
0.172188 + 0.985064i \(0.444916\pi\)
\(684\) −6.00000 −0.229416
\(685\) 26.8328i 1.02523i
\(686\) 0 0
\(687\) 7.00000 13.4164i 0.267067 0.511868i
\(688\) 1.00000 0.0381246
\(689\) 0 0
\(690\) 30.0000 1.14208
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) 26.8328i 1.01856i
\(695\) 40.2492i 1.52674i
\(696\) −10.0000 −0.379049
\(697\) 13.4164i 0.508183i
\(698\) −30.0000 −1.13552
\(699\) 9.00000 0.340411
\(700\) 0 0
\(701\) 33.0000 1.24639 0.623196 0.782065i \(-0.285834\pi\)
0.623196 + 0.782065i \(0.285834\pi\)
\(702\) 0 0
\(703\) −2.00000 −0.0754314
\(704\) 39.0000 1.46987
\(705\) 26.8328i 1.01058i
\(706\) −20.0000 −0.752710
\(707\) 0 0
\(708\) 26.8328i 1.00844i
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 100.623i 3.77632i
\(711\) 26.8328i 1.00631i
\(712\) −40.0000 −1.49906
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 53.6656i 2.00558i
\(717\) 22.3607i 0.835075i
\(718\) 53.6656i 2.00278i
\(719\) 4.47214i 0.166783i 0.996517 + 0.0833913i \(0.0265751\pi\)
−0.996517 + 0.0833913i \(0.973425\pi\)
\(720\) 6.00000 0.223607
\(721\) 0 0
\(722\) 40.2492i 1.49792i
\(723\) −10.0000 −0.371904
\(724\) 21.0000 0.780459
\(725\) 17.8885i 0.664364i
\(726\) 4.47214i 0.165977i
\(727\) 26.8328i 0.995174i −0.867414 0.497587i \(-0.834220\pi\)
0.867414 0.497587i \(-0.165780\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 90.0000 3.33105
\(731\) 3.00000 0.110959
\(732\) −15.0000 −0.554416
\(733\) 11.0000 0.406294 0.203147 0.979148i \(-0.434883\pi\)
0.203147 + 0.979148i \(0.434883\pi\)
\(734\) 38.0132i 1.40309i
\(735\) 21.0000 0.774597
\(736\) −30.0000 −1.10581
\(737\) 40.2492i 1.48260i
\(738\) −20.0000 −0.736210
\(739\) 13.4164i 0.493531i −0.969075 0.246765i \(-0.920632\pi\)
0.969075 0.246765i \(-0.0793677\pi\)
\(740\) −18.0000 −0.661693
\(741\) 0 0
\(742\) 0 0
\(743\) −39.0000 −1.43077 −0.715386 0.698730i \(-0.753749\pi\)
−0.715386 + 0.698730i \(0.753749\pi\)
\(744\) 0 0
\(745\) −63.0000 −2.30814
\(746\) 42.4853i 1.55550i
\(747\) 18.0000 0.658586
\(748\) 27.0000 0.987218
\(749\) 0 0
\(750\) 6.70820i 0.244949i
\(751\) 5.00000 0.182453 0.0912263 0.995830i \(-0.470921\pi\)
0.0912263 + 0.995830i \(0.470921\pi\)
\(752\) 8.94427i 0.326164i
\(753\) 17.8885i 0.651895i
\(754\) 0 0
\(755\) −21.0000 −0.764268
\(756\) 0 0
\(757\) −13.0000 −0.472493 −0.236247 0.971693i \(-0.575917\pi\)
−0.236247 + 0.971693i \(0.575917\pi\)
\(758\) 0 0
\(759\) 13.4164i 0.486985i
\(760\) 6.70820i 0.243332i
\(761\) 44.7214i 1.62115i 0.585636 + 0.810574i \(0.300845\pi\)
−0.585636 + 0.810574i \(0.699155\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 26.8328i 0.970777i
\(765\) 18.0000 0.650791
\(766\) 53.6656i 1.93902i
\(767\) 0 0
\(768\) −9.00000 −0.324760
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) 17.8885i 0.644240i
\(772\) −42.0000 −1.51161
\(773\) 35.7771i 1.28681i −0.765525 0.643406i \(-0.777521\pi\)
0.765525 0.643406i \(-0.222479\pi\)
\(774\) 4.47214i 0.160748i
\(775\) 0 0
\(776\) 15.6525i 0.561891i
\(777\) 0 0
\(778\) 70.0000 2.50962
\(779\) 4.47214i 0.160231i
\(780\) 0 0
\(781\) −45.0000 −1.61023
\(782\) −30.0000 −1.07280
\(783\) 22.3607i 0.799106i
\(784\) −7.00000 −0.250000
\(785\) 40.2492i 1.43656i
\(786\) 10.0000 0.356688
\(787\) 23.0000 0.819861 0.409931 0.912117i \(-0.365553\pi\)
0.409931 + 0.912117i \(0.365553\pi\)
\(788\) 53.6656i 1.91176i
\(789\) 4.47214i 0.159212i
\(790\) 90.0000 3.20206
\(791\) 0 0
\(792\) 13.4164i 0.476731i
\(793\) 0 0
\(794\) 51.4296i 1.82517i
\(795\) 18.0000 0.638394
\(796\) 40.2492i 1.42660i
\(797\) 44.7214i 1.58411i 0.610449 + 0.792056i \(0.290989\pi\)
−0.610449 + 0.792056i \(0.709011\pi\)
\(798\) 0 0
\(799\) 26.8328i 0.949277i
\(800\) 26.8328i 0.948683i
\(801\) 35.7771i 1.26412i
\(802\) 60.3738i 2.13187i
\(803\) 40.2492i 1.42036i
\(804\) 40.2492i 1.41948i
\(805\) 0 0
\(806\) 0 0
\(807\) 22.3607i 0.787133i
\(808\) −10.0000 −0.351799
\(809\) 4.47214i