Properties

Label 429.2.b.b.298.10
Level $429$
Weight $2$
Character 429.298
Analytic conductor $3.426$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
Defining polynomial: \(x^{14} + 23 x^{12} + 201 x^{10} + 835 x^{8} + 1695 x^{6} + 1565 x^{4} + 511 x^{2} + 49\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 298.10
Root \(1.36814i\) of defining polynomial
Character \(\chi\) \(=\) 429.298
Dual form 429.2.b.b.298.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.36814i q^{2} +1.00000 q^{3} +0.128197 q^{4} -2.18365i q^{5} +1.36814i q^{6} -4.27070i q^{7} +2.91167i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.36814i q^{2} +1.00000 q^{3} +0.128197 q^{4} -2.18365i q^{5} +1.36814i q^{6} -4.27070i q^{7} +2.91167i q^{8} +1.00000 q^{9} +2.98753 q^{10} +1.00000i q^{11} +0.128197 q^{12} +(-0.922450 - 3.48555i) q^{13} +5.84291 q^{14} -2.18365i q^{15} -3.72717 q^{16} +3.79173 q^{17} +1.36814i q^{18} +3.17118i q^{19} -0.279937i q^{20} -4.27070i q^{21} -1.36814 q^{22} +4.94243 q^{23} +2.91167i q^{24} +0.231676 q^{25} +(4.76872 - 1.26204i) q^{26} +1.00000 q^{27} -0.547491i q^{28} -7.35483 q^{29} +2.98753 q^{30} -0.0727448i q^{31} +0.724050i q^{32} +1.00000i q^{33} +5.18761i q^{34} -9.32571 q^{35} +0.128197 q^{36} +3.66658i q^{37} -4.33862 q^{38} +(-0.922450 - 3.48555i) q^{39} +6.35806 q^{40} +4.16722i q^{41} +5.84291 q^{42} -7.11697 q^{43} +0.128197i q^{44} -2.18365i q^{45} +6.76193i q^{46} +11.6337i q^{47} -3.72717 q^{48} -11.2389 q^{49} +0.316965i q^{50} +3.79173 q^{51} +(-0.118255 - 0.446838i) q^{52} +5.11268 q^{53} +1.36814i q^{54} +2.18365 q^{55} +12.4349 q^{56} +3.17118i q^{57} -10.0624i q^{58} +5.62765i q^{59} -0.279937i q^{60} -5.40800 q^{61} +0.0995250 q^{62} -4.27070i q^{63} -8.44494 q^{64} +(-7.61123 + 2.01431i) q^{65} -1.36814 q^{66} -10.1145i q^{67} +0.486088 q^{68} +4.94243 q^{69} -12.7589i q^{70} -9.62239i q^{71} +2.91167i q^{72} +6.44736i q^{73} -5.01639 q^{74} +0.231676 q^{75} +0.406536i q^{76} +4.27070 q^{77} +(4.76872 - 1.26204i) q^{78} +10.1209 q^{79} +8.13884i q^{80} +1.00000 q^{81} -5.70134 q^{82} +7.80918i q^{83} -0.547491i q^{84} -8.27981i q^{85} -9.73700i q^{86} -7.35483 q^{87} -2.91167 q^{88} +2.87912i q^{89} +2.98753 q^{90} +(-14.8858 + 3.93951i) q^{91} +0.633605 q^{92} -0.0727448i q^{93} -15.9166 q^{94} +6.92475 q^{95} +0.724050i q^{96} -3.79281i q^{97} -15.3764i q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} + O(q^{10}) \) \( 14q + 14q^{3} - 18q^{4} + 14q^{9} - 18q^{12} + 16q^{14} + 34q^{16} + 4q^{17} + 6q^{22} - 8q^{23} - 26q^{25} - 6q^{26} + 14q^{27} - 24q^{29} - 8q^{35} - 18q^{36} - 32q^{38} - 20q^{40} + 16q^{42} + 32q^{43} + 34q^{48} - 46q^{49} + 4q^{51} + 4q^{52} + 20q^{53} + 12q^{55} - 32q^{56} - 20q^{61} + 72q^{62} - 58q^{64} + 12q^{65} + 6q^{66} - 20q^{68} - 8q^{69} - 26q^{75} - 12q^{77} - 6q^{78} + 12q^{79} + 14q^{81} + 20q^{82} - 24q^{87} - 30q^{88} + 16q^{91} - 24q^{92} + 64q^{94} - 36q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36814i 0.967420i 0.875228 + 0.483710i \(0.160711\pi\)
−0.875228 + 0.483710i \(0.839289\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.128197 0.0640985
\(5\) 2.18365i 0.976558i −0.872688 0.488279i \(-0.837625\pi\)
0.872688 0.488279i \(-0.162375\pi\)
\(6\) 1.36814i 0.558540i
\(7\) 4.27070i 1.61417i −0.590433 0.807087i \(-0.701043\pi\)
0.590433 0.807087i \(-0.298957\pi\)
\(8\) 2.91167i 1.02943i
\(9\) 1.00000 0.333333
\(10\) 2.98753 0.944741
\(11\) 1.00000i 0.301511i
\(12\) 0.128197 0.0370073
\(13\) −0.922450 3.48555i −0.255842 0.966719i
\(14\) 5.84291 1.56158
\(15\) 2.18365i 0.563816i
\(16\) −3.72717 −0.931793
\(17\) 3.79173 0.919629 0.459815 0.888015i \(-0.347916\pi\)
0.459815 + 0.888015i \(0.347916\pi\)
\(18\) 1.36814i 0.322473i
\(19\) 3.17118i 0.727519i 0.931493 + 0.363760i \(0.118507\pi\)
−0.931493 + 0.363760i \(0.881493\pi\)
\(20\) 0.279937i 0.0625959i
\(21\) 4.27070i 0.931943i
\(22\) −1.36814 −0.291688
\(23\) 4.94243 1.03057 0.515284 0.857020i \(-0.327687\pi\)
0.515284 + 0.857020i \(0.327687\pi\)
\(24\) 2.91167i 0.594342i
\(25\) 0.231676 0.0463352
\(26\) 4.76872 1.26204i 0.935223 0.247506i
\(27\) 1.00000 0.192450
\(28\) 0.547491i 0.103466i
\(29\) −7.35483 −1.36576 −0.682879 0.730531i \(-0.739272\pi\)
−0.682879 + 0.730531i \(0.739272\pi\)
\(30\) 2.98753 0.545447
\(31\) 0.0727448i 0.0130654i −0.999979 0.00653268i \(-0.997921\pi\)
0.999979 0.00653268i \(-0.00207943\pi\)
\(32\) 0.724050i 0.127995i
\(33\) 1.00000i 0.174078i
\(34\) 5.18761i 0.889668i
\(35\) −9.32571 −1.57633
\(36\) 0.128197 0.0213662
\(37\) 3.66658i 0.602782i 0.953501 + 0.301391i \(0.0974510\pi\)
−0.953501 + 0.301391i \(0.902549\pi\)
\(38\) −4.33862 −0.703817
\(39\) −0.922450 3.48555i −0.147710 0.558135i
\(40\) 6.35806 1.00530
\(41\) 4.16722i 0.650811i 0.945575 + 0.325405i \(0.105501\pi\)
−0.945575 + 0.325405i \(0.894499\pi\)
\(42\) 5.84291 0.901581
\(43\) −7.11697 −1.08533 −0.542664 0.839950i \(-0.682584\pi\)
−0.542664 + 0.839950i \(0.682584\pi\)
\(44\) 0.128197i 0.0193264i
\(45\) 2.18365i 0.325519i
\(46\) 6.76193i 0.996992i
\(47\) 11.6337i 1.69695i 0.529232 + 0.848477i \(0.322480\pi\)
−0.529232 + 0.848477i \(0.677520\pi\)
\(48\) −3.72717 −0.537971
\(49\) −11.2389 −1.60556
\(50\) 0.316965i 0.0448256i
\(51\) 3.79173 0.530948
\(52\) −0.118255 0.446838i −0.0163991 0.0619652i
\(53\) 5.11268 0.702281 0.351140 0.936323i \(-0.385794\pi\)
0.351140 + 0.936323i \(0.385794\pi\)
\(54\) 1.36814i 0.186180i
\(55\) 2.18365 0.294443
\(56\) 12.4349 1.66168
\(57\) 3.17118i 0.420034i
\(58\) 10.0624i 1.32126i
\(59\) 5.62765i 0.732658i 0.930485 + 0.366329i \(0.119386\pi\)
−0.930485 + 0.366329i \(0.880614\pi\)
\(60\) 0.279937i 0.0361398i
\(61\) −5.40800 −0.692424 −0.346212 0.938156i \(-0.612532\pi\)
−0.346212 + 0.938156i \(0.612532\pi\)
\(62\) 0.0995250 0.0126397
\(63\) 4.27070i 0.538058i
\(64\) −8.44494 −1.05562
\(65\) −7.61123 + 2.01431i −0.944057 + 0.249844i
\(66\) −1.36814 −0.168406
\(67\) 10.1145i 1.23569i −0.786302 0.617843i \(-0.788007\pi\)
0.786302 0.617843i \(-0.211993\pi\)
\(68\) 0.486088 0.0589469
\(69\) 4.94243 0.594998
\(70\) 12.7589i 1.52498i
\(71\) 9.62239i 1.14197i −0.820961 0.570984i \(-0.806562\pi\)
0.820961 0.570984i \(-0.193438\pi\)
\(72\) 2.91167i 0.343143i
\(73\) 6.44736i 0.754607i 0.926090 + 0.377303i \(0.123149\pi\)
−0.926090 + 0.377303i \(0.876851\pi\)
\(74\) −5.01639 −0.583144
\(75\) 0.231676 0.0267516
\(76\) 0.406536i 0.0466329i
\(77\) 4.27070 0.486692
\(78\) 4.76872 1.26204i 0.539951 0.142898i
\(79\) 10.1209 1.13869 0.569347 0.822097i \(-0.307196\pi\)
0.569347 + 0.822097i \(0.307196\pi\)
\(80\) 8.13884i 0.909949i
\(81\) 1.00000 0.111111
\(82\) −5.70134 −0.629607
\(83\) 7.80918i 0.857169i 0.903502 + 0.428585i \(0.140988\pi\)
−0.903502 + 0.428585i \(0.859012\pi\)
\(84\) 0.547491i 0.0597362i
\(85\) 8.27981i 0.898071i
\(86\) 9.73700i 1.04997i
\(87\) −7.35483 −0.788521
\(88\) −2.91167 −0.310385
\(89\) 2.87912i 0.305187i 0.988289 + 0.152593i \(0.0487624\pi\)
−0.988289 + 0.152593i \(0.951238\pi\)
\(90\) 2.98753 0.314914
\(91\) −14.8858 + 3.93951i −1.56045 + 0.412973i
\(92\) 0.633605 0.0660579
\(93\) 0.0727448i 0.00754329i
\(94\) −15.9166 −1.64167
\(95\) 6.92475 0.710465
\(96\) 0.724050i 0.0738980i
\(97\) 3.79281i 0.385101i −0.981287 0.192551i \(-0.938324\pi\)
0.981287 0.192551i \(-0.0616760\pi\)
\(98\) 15.3764i 1.55325i
\(99\) 1.00000i 0.100504i
\(100\) 0.0297002 0.00297002
\(101\) −12.8641 −1.28003 −0.640014 0.768363i \(-0.721072\pi\)
−0.640014 + 0.768363i \(0.721072\pi\)
\(102\) 5.18761i 0.513650i
\(103\) 16.9975 1.67482 0.837409 0.546577i \(-0.184070\pi\)
0.837409 + 0.546577i \(0.184070\pi\)
\(104\) 10.1488 2.68587i 0.995169 0.263371i
\(105\) −9.32571 −0.910096
\(106\) 6.99486i 0.679400i
\(107\) −12.6819 −1.22600 −0.613001 0.790082i \(-0.710038\pi\)
−0.613001 + 0.790082i \(0.710038\pi\)
\(108\) 0.128197 0.0123358
\(109\) 8.89607i 0.852089i −0.904702 0.426045i \(-0.859907\pi\)
0.904702 0.426045i \(-0.140093\pi\)
\(110\) 2.98753i 0.284850i
\(111\) 3.66658i 0.348017i
\(112\) 15.9176i 1.50408i
\(113\) 1.36552 0.128457 0.0642287 0.997935i \(-0.479541\pi\)
0.0642287 + 0.997935i \(0.479541\pi\)
\(114\) −4.33862 −0.406349
\(115\) 10.7925i 1.00641i
\(116\) −0.942868 −0.0875431
\(117\) −0.922450 3.48555i −0.0852805 0.322240i
\(118\) −7.69941 −0.708788
\(119\) 16.1933i 1.48444i
\(120\) 6.35806 0.580409
\(121\) −1.00000 −0.0909091
\(122\) 7.39890i 0.669865i
\(123\) 4.16722i 0.375746i
\(124\) 0.00932567i 0.000837470i
\(125\) 11.4241i 1.02181i
\(126\) 5.84291 0.520528
\(127\) −10.4027 −0.923093 −0.461546 0.887116i \(-0.652705\pi\)
−0.461546 + 0.887116i \(0.652705\pi\)
\(128\) 10.1058i 0.893231i
\(129\) −7.11697 −0.626614
\(130\) −2.75585 10.4132i −0.241704 0.913299i
\(131\) −12.0678 −1.05437 −0.527183 0.849752i \(-0.676752\pi\)
−0.527183 + 0.849752i \(0.676752\pi\)
\(132\) 0.128197i 0.0111581i
\(133\) 13.5432 1.17434
\(134\) 13.8381 1.19543
\(135\) 2.18365i 0.187939i
\(136\) 11.0403i 0.946694i
\(137\) 3.96114i 0.338423i 0.985580 + 0.169211i \(0.0541221\pi\)
−0.985580 + 0.169211i \(0.945878\pi\)
\(138\) 6.76193i 0.575613i
\(139\) 18.2437 1.54741 0.773703 0.633548i \(-0.218402\pi\)
0.773703 + 0.633548i \(0.218402\pi\)
\(140\) −1.19553 −0.101041
\(141\) 11.6337i 0.979737i
\(142\) 13.1648 1.10476
\(143\) 3.48555 0.922450i 0.291477 0.0771391i
\(144\) −3.72717 −0.310598
\(145\) 16.0604i 1.33374i
\(146\) −8.82089 −0.730022
\(147\) −11.2389 −0.926968
\(148\) 0.470045i 0.0386375i
\(149\) 13.8984i 1.13860i −0.822131 0.569299i \(-0.807215\pi\)
0.822131 0.569299i \(-0.192785\pi\)
\(150\) 0.316965i 0.0258801i
\(151\) 2.29739i 0.186959i −0.995621 0.0934795i \(-0.970201\pi\)
0.995621 0.0934795i \(-0.0297990\pi\)
\(152\) −9.23344 −0.748931
\(153\) 3.79173 0.306543
\(154\) 5.84291i 0.470835i
\(155\) −0.158849 −0.0127591
\(156\) −0.118255 0.446838i −0.00946801 0.0357756i
\(157\) −15.6293 −1.24736 −0.623678 0.781682i \(-0.714362\pi\)
−0.623678 + 0.781682i \(0.714362\pi\)
\(158\) 13.8468i 1.10160i
\(159\) 5.11268 0.405462
\(160\) 1.58107 0.124995
\(161\) 21.1076i 1.66351i
\(162\) 1.36814i 0.107491i
\(163\) 1.25583i 0.0983643i 0.998790 + 0.0491822i \(0.0156615\pi\)
−0.998790 + 0.0491822i \(0.984339\pi\)
\(164\) 0.534226i 0.0417160i
\(165\) 2.18365 0.169997
\(166\) −10.6840 −0.829243
\(167\) 17.3823i 1.34509i 0.740058 + 0.672543i \(0.234798\pi\)
−0.740058 + 0.672543i \(0.765202\pi\)
\(168\) 12.4349 0.959371
\(169\) −11.2982 + 6.43050i −0.869090 + 0.494654i
\(170\) 11.3279 0.868812
\(171\) 3.17118i 0.242506i
\(172\) −0.912375 −0.0695679
\(173\) 12.0899 0.919178 0.459589 0.888132i \(-0.347997\pi\)
0.459589 + 0.888132i \(0.347997\pi\)
\(174\) 10.0624i 0.762831i
\(175\) 0.989418i 0.0747930i
\(176\) 3.72717i 0.280946i
\(177\) 5.62765i 0.423000i
\(178\) −3.93904 −0.295244
\(179\) 5.13094 0.383504 0.191752 0.981443i \(-0.438583\pi\)
0.191752 + 0.981443i \(0.438583\pi\)
\(180\) 0.279937i 0.0208653i
\(181\) 23.3170 1.73314 0.866568 0.499059i \(-0.166321\pi\)
0.866568 + 0.499059i \(0.166321\pi\)
\(182\) −5.38979 20.3658i −0.399518 1.50961i
\(183\) −5.40800 −0.399771
\(184\) 14.3907i 1.06090i
\(185\) 8.00653 0.588652
\(186\) 0.0995250 0.00729753
\(187\) 3.79173i 0.277279i
\(188\) 1.49141i 0.108772i
\(189\) 4.27070i 0.310648i
\(190\) 9.47402i 0.687318i
\(191\) 11.1231 0.804838 0.402419 0.915456i \(-0.368169\pi\)
0.402419 + 0.915456i \(0.368169\pi\)
\(192\) −8.44494 −0.609461
\(193\) 23.1664i 1.66756i 0.552099 + 0.833778i \(0.313827\pi\)
−0.552099 + 0.833778i \(0.686173\pi\)
\(194\) 5.18909 0.372555
\(195\) −7.61123 + 2.01431i −0.545051 + 0.144248i
\(196\) −1.44079 −0.102914
\(197\) 9.18435i 0.654358i −0.944962 0.327179i \(-0.893902\pi\)
0.944962 0.327179i \(-0.106098\pi\)
\(198\) −1.36814 −0.0972294
\(199\) −6.38937 −0.452930 −0.226465 0.974019i \(-0.572717\pi\)
−0.226465 + 0.974019i \(0.572717\pi\)
\(200\) 0.674563i 0.0476988i
\(201\) 10.1145i 0.713423i
\(202\) 17.5999i 1.23833i
\(203\) 31.4103i 2.20457i
\(204\) 0.486088 0.0340330
\(205\) 9.09975 0.635554
\(206\) 23.2550i 1.62025i
\(207\) 4.94243 0.343522
\(208\) 3.43813 + 12.9913i 0.238391 + 0.900782i
\(209\) −3.17118 −0.219355
\(210\) 12.7589i 0.880446i
\(211\) 22.4436 1.54508 0.772541 0.634965i \(-0.218985\pi\)
0.772541 + 0.634965i \(0.218985\pi\)
\(212\) 0.655431 0.0450152
\(213\) 9.62239i 0.659315i
\(214\) 17.3505i 1.18606i
\(215\) 15.5410i 1.05989i
\(216\) 2.91167i 0.198114i
\(217\) −0.310671 −0.0210897
\(218\) 12.1711 0.824328
\(219\) 6.44736i 0.435673i
\(220\) 0.279937 0.0188734
\(221\) −3.49768 13.2163i −0.235279 0.889023i
\(222\) −5.01639 −0.336678
\(223\) 16.5344i 1.10722i 0.832775 + 0.553611i \(0.186751\pi\)
−0.832775 + 0.553611i \(0.813249\pi\)
\(224\) 3.09220 0.206606
\(225\) 0.231676 0.0154451
\(226\) 1.86822i 0.124272i
\(227\) 19.9826i 1.32630i 0.748489 + 0.663148i \(0.230780\pi\)
−0.748489 + 0.663148i \(0.769220\pi\)
\(228\) 0.406536i 0.0269235i
\(229\) 15.8459i 1.04713i 0.851986 + 0.523564i \(0.175398\pi\)
−0.851986 + 0.523564i \(0.824602\pi\)
\(230\) 14.7657 0.973620
\(231\) 4.27070 0.280992
\(232\) 21.4148i 1.40595i
\(233\) −15.9195 −1.04292 −0.521460 0.853276i \(-0.674612\pi\)
−0.521460 + 0.853276i \(0.674612\pi\)
\(234\) 4.76872 1.26204i 0.311741 0.0825021i
\(235\) 25.4040 1.65717
\(236\) 0.721449i 0.0469623i
\(237\) 10.1209 0.657425
\(238\) 22.1547 1.43608
\(239\) 16.9898i 1.09898i −0.835500 0.549491i \(-0.814822\pi\)
0.835500 0.549491i \(-0.185178\pi\)
\(240\) 8.13884i 0.525360i
\(241\) 21.9883i 1.41639i −0.706015 0.708197i \(-0.749509\pi\)
0.706015 0.708197i \(-0.250491\pi\)
\(242\) 1.36814i 0.0879473i
\(243\) 1.00000 0.0641500
\(244\) −0.693290 −0.0443834
\(245\) 24.5418i 1.56792i
\(246\) −5.70134 −0.363504
\(247\) 11.0533 2.92526i 0.703307 0.186130i
\(248\) 0.211809 0.0134499
\(249\) 7.80918i 0.494887i
\(250\) 15.6298 0.988516
\(251\) −11.9461 −0.754029 −0.377015 0.926207i \(-0.623049\pi\)
−0.377015 + 0.926207i \(0.623049\pi\)
\(252\) 0.547491i 0.0344887i
\(253\) 4.94243i 0.310728i
\(254\) 14.2324i 0.893019i
\(255\) 8.27981i 0.518502i
\(256\) −3.06382 −0.191489
\(257\) −28.3671 −1.76949 −0.884746 0.466074i \(-0.845668\pi\)
−0.884746 + 0.466074i \(0.845668\pi\)
\(258\) 9.73700i 0.606199i
\(259\) 15.6589 0.972995
\(260\) −0.975737 + 0.258228i −0.0605126 + 0.0160146i
\(261\) −7.35483 −0.455253
\(262\) 16.5104i 1.02001i
\(263\) −1.37798 −0.0849699 −0.0424849 0.999097i \(-0.513527\pi\)
−0.0424849 + 0.999097i \(0.513527\pi\)
\(264\) −2.91167 −0.179201
\(265\) 11.1643i 0.685818i
\(266\) 18.5289i 1.13608i
\(267\) 2.87912i 0.176200i
\(268\) 1.29665i 0.0792056i
\(269\) −14.6274 −0.891847 −0.445923 0.895071i \(-0.647125\pi\)
−0.445923 + 0.895071i \(0.647125\pi\)
\(270\) 2.98753 0.181816
\(271\) 13.3040i 0.808158i 0.914724 + 0.404079i \(0.132408\pi\)
−0.914724 + 0.404079i \(0.867592\pi\)
\(272\) −14.1324 −0.856904
\(273\) −14.8858 + 3.93951i −0.900927 + 0.238430i
\(274\) −5.41938 −0.327397
\(275\) 0.231676i 0.0139706i
\(276\) 0.633605 0.0381385
\(277\) −22.1581 −1.33135 −0.665676 0.746241i \(-0.731857\pi\)
−0.665676 + 0.746241i \(0.731857\pi\)
\(278\) 24.9598i 1.49699i
\(279\) 0.0727448i 0.00435512i
\(280\) 27.1534i 1.62273i
\(281\) 2.12589i 0.126820i −0.997988 0.0634100i \(-0.979802\pi\)
0.997988 0.0634100i \(-0.0201976\pi\)
\(282\) −15.9166 −0.947817
\(283\) 31.1036 1.84892 0.924458 0.381283i \(-0.124518\pi\)
0.924458 + 0.381283i \(0.124518\pi\)
\(284\) 1.23356i 0.0731984i
\(285\) 6.92475 0.410187
\(286\) 1.26204 + 4.76872i 0.0746259 + 0.281980i
\(287\) 17.7970 1.05052
\(288\) 0.724050i 0.0426650i
\(289\) −2.62279 −0.154282
\(290\) −21.9728 −1.29029
\(291\) 3.79281i 0.222338i
\(292\) 0.826533i 0.0483692i
\(293\) 16.9009i 0.987363i 0.869643 + 0.493682i \(0.164349\pi\)
−0.869643 + 0.493682i \(0.835651\pi\)
\(294\) 15.3764i 0.896767i
\(295\) 12.2888 0.715483
\(296\) −10.6759 −0.620523
\(297\) 1.00000i 0.0580259i
\(298\) 19.0149 1.10150
\(299\) −4.55914 17.2271i −0.263662 0.996269i
\(300\) 0.0297002 0.00171474
\(301\) 30.3945i 1.75191i
\(302\) 3.14315 0.180868
\(303\) −12.8641 −0.739025
\(304\) 11.8195i 0.677897i
\(305\) 11.8092i 0.676192i
\(306\) 5.18761i 0.296556i
\(307\) 24.6110i 1.40462i −0.711869 0.702312i \(-0.752151\pi\)
0.711869 0.702312i \(-0.247849\pi\)
\(308\) 0.547491 0.0311962
\(309\) 16.9975 0.966956
\(310\) 0.217328i 0.0123434i
\(311\) 1.00504 0.0569904 0.0284952 0.999594i \(-0.490928\pi\)
0.0284952 + 0.999594i \(0.490928\pi\)
\(312\) 10.1488 2.68587i 0.574561 0.152057i
\(313\) −13.8744 −0.784227 −0.392114 0.919917i \(-0.628256\pi\)
−0.392114 + 0.919917i \(0.628256\pi\)
\(314\) 21.3831i 1.20672i
\(315\) −9.32571 −0.525444
\(316\) 1.29747 0.0729886
\(317\) 15.6405i 0.878460i −0.898375 0.439230i \(-0.855251\pi\)
0.898375 0.439230i \(-0.144749\pi\)
\(318\) 6.99486i 0.392252i
\(319\) 7.35483i 0.411792i
\(320\) 18.4408i 1.03087i
\(321\) −12.6819 −0.707832
\(322\) 28.8782 1.60932
\(323\) 12.0243i 0.669048i
\(324\) 0.128197 0.00712206
\(325\) −0.213709 0.807519i −0.0118545 0.0447931i
\(326\) −1.71815 −0.0951596
\(327\) 8.89607i 0.491954i
\(328\) −12.1336 −0.669964
\(329\) 49.6842 2.73918
\(330\) 2.98753i 0.164458i
\(331\) 23.1426i 1.27203i −0.771675 0.636017i \(-0.780581\pi\)
0.771675 0.636017i \(-0.219419\pi\)
\(332\) 1.00111i 0.0549433i
\(333\) 3.66658i 0.200927i
\(334\) −23.7814 −1.30126
\(335\) −22.0866 −1.20672
\(336\) 15.9176i 0.868378i
\(337\) −15.1946 −0.827705 −0.413853 0.910344i \(-0.635817\pi\)
−0.413853 + 0.910344i \(0.635817\pi\)
\(338\) −8.79781 15.4575i −0.478538 0.840775i
\(339\) 1.36552 0.0741650
\(340\) 1.06145i 0.0575650i
\(341\) 0.0727448 0.00393935
\(342\) −4.33862 −0.234606
\(343\) 18.1030i 0.977472i
\(344\) 20.7223i 1.11727i
\(345\) 10.7925i 0.581050i
\(346\) 16.5407i 0.889231i
\(347\) 16.6545 0.894061 0.447030 0.894519i \(-0.352482\pi\)
0.447030 + 0.894519i \(0.352482\pi\)
\(348\) −0.942868 −0.0505430
\(349\) 29.1080i 1.55812i −0.626952 0.779058i \(-0.715698\pi\)
0.626952 0.779058i \(-0.284302\pi\)
\(350\) 1.35366 0.0723562
\(351\) −0.922450 3.48555i −0.0492367 0.186045i
\(352\) −0.724050 −0.0385920
\(353\) 29.1723i 1.55268i −0.630312 0.776342i \(-0.717073\pi\)
0.630312 0.776342i \(-0.282927\pi\)
\(354\) −7.69941 −0.409219
\(355\) −21.0119 −1.11520
\(356\) 0.369095i 0.0195620i
\(357\) 16.1933i 0.857043i
\(358\) 7.01983i 0.371010i
\(359\) 18.0809i 0.954271i −0.878830 0.477136i \(-0.841675\pi\)
0.878830 0.477136i \(-0.158325\pi\)
\(360\) 6.35806 0.335099
\(361\) 8.94359 0.470715
\(362\) 31.9008i 1.67667i
\(363\) −1.00000 −0.0524864
\(364\) −1.90831 + 0.505033i −0.100023 + 0.0264709i
\(365\) 14.0788 0.736917
\(366\) 7.39890i 0.386747i
\(367\) 18.1338 0.946578 0.473289 0.880907i \(-0.343067\pi\)
0.473289 + 0.880907i \(0.343067\pi\)
\(368\) −18.4213 −0.960275
\(369\) 4.16722i 0.216937i
\(370\) 10.9540i 0.569474i
\(371\) 21.8347i 1.13360i
\(372\) 0.00932567i 0.000483513i
\(373\) −15.8564 −0.821012 −0.410506 0.911858i \(-0.634648\pi\)
−0.410506 + 0.911858i \(0.634648\pi\)
\(374\) −5.18761 −0.268245
\(375\) 11.4241i 0.589940i
\(376\) −33.8736 −1.74690
\(377\) 6.78447 + 25.6357i 0.349418 + 1.32030i
\(378\) 5.84291 0.300527
\(379\) 18.3431i 0.942224i 0.882073 + 0.471112i \(0.156147\pi\)
−0.882073 + 0.471112i \(0.843853\pi\)
\(380\) 0.887733 0.0455397
\(381\) −10.4027 −0.532948
\(382\) 15.2179i 0.778617i
\(383\) 16.1019i 0.822768i −0.911462 0.411384i \(-0.865046\pi\)
0.911462 0.411384i \(-0.134954\pi\)
\(384\) 10.1058i 0.515707i
\(385\) 9.32571i 0.475282i
\(386\) −31.6949 −1.61323
\(387\) −7.11697 −0.361776
\(388\) 0.486227i 0.0246844i
\(389\) −32.7166 −1.65880 −0.829400 0.558655i \(-0.811317\pi\)
−0.829400 + 0.558655i \(0.811317\pi\)
\(390\) −2.75585 10.4132i −0.139548 0.527294i
\(391\) 18.7403 0.947740
\(392\) 32.7239i 1.65281i
\(393\) −12.0678 −0.608738
\(394\) 12.5655 0.633039
\(395\) 22.1006i 1.11200i
\(396\) 0.128197i 0.00644214i
\(397\) 3.51685i 0.176506i 0.996098 + 0.0882529i \(0.0281284\pi\)
−0.996098 + 0.0882529i \(0.971872\pi\)
\(398\) 8.74154i 0.438174i
\(399\) 13.5432 0.678007
\(400\) −0.863496 −0.0431748
\(401\) 18.6231i 0.929992i −0.885313 0.464996i \(-0.846056\pi\)
0.885313 0.464996i \(-0.153944\pi\)
\(402\) 13.8381 0.690180
\(403\) −0.253556 + 0.0671034i −0.0126305 + 0.00334266i
\(404\) −1.64914 −0.0820480
\(405\) 2.18365i 0.108506i
\(406\) −42.9736 −2.13275
\(407\) −3.66658 −0.181746
\(408\) 11.0403i 0.546574i
\(409\) 17.6809i 0.874262i −0.899398 0.437131i \(-0.855995\pi\)
0.899398 0.437131i \(-0.144005\pi\)
\(410\) 12.4497i 0.614848i
\(411\) 3.96114i 0.195388i
\(412\) 2.17903 0.107353
\(413\) 24.0340 1.18264
\(414\) 6.76193i 0.332331i
\(415\) 17.0525 0.837075
\(416\) 2.52371 0.667900i 0.123735 0.0327465i
\(417\) 18.2437 0.893395
\(418\) 4.33862i 0.212209i
\(419\) −1.93036 −0.0943044 −0.0471522 0.998888i \(-0.515015\pi\)
−0.0471522 + 0.998888i \(0.515015\pi\)
\(420\) −1.19553 −0.0583358
\(421\) 7.21742i 0.351756i 0.984412 + 0.175878i \(0.0562764\pi\)
−0.984412 + 0.175878i \(0.943724\pi\)
\(422\) 30.7060i 1.49474i
\(423\) 11.6337i 0.565651i
\(424\) 14.8864i 0.722949i
\(425\) 0.878452 0.0426112
\(426\) 13.1648 0.637835
\(427\) 23.0960i 1.11769i
\(428\) −1.62578 −0.0785849
\(429\) 3.48555 0.922450i 0.168284 0.0445363i
\(430\) −21.2622 −1.02535
\(431\) 29.7876i 1.43482i 0.696653 + 0.717408i \(0.254672\pi\)
−0.696653 + 0.717408i \(0.745328\pi\)
\(432\) −3.72717 −0.179324
\(433\) 25.2468 1.21329 0.606643 0.794975i \(-0.292516\pi\)
0.606643 + 0.794975i \(0.292516\pi\)
\(434\) 0.425041i 0.0204026i
\(435\) 16.0604i 0.770036i
\(436\) 1.14045i 0.0546177i
\(437\) 15.6733i 0.749758i
\(438\) −8.82089 −0.421478
\(439\) 9.07110 0.432940 0.216470 0.976289i \(-0.430546\pi\)
0.216470 + 0.976289i \(0.430546\pi\)
\(440\) 6.35806i 0.303109i
\(441\) −11.2389 −0.535185
\(442\) 18.0817 4.78531i 0.860059 0.227614i
\(443\) −12.0753 −0.573715 −0.286858 0.957973i \(-0.592611\pi\)
−0.286858 + 0.957973i \(0.592611\pi\)
\(444\) 0.470045i 0.0223074i
\(445\) 6.28700 0.298032
\(446\) −22.6213 −1.07115
\(447\) 13.8984i 0.657370i
\(448\) 36.0658i 1.70395i
\(449\) 8.94438i 0.422111i 0.977474 + 0.211056i \(0.0676901\pi\)
−0.977474 + 0.211056i \(0.932310\pi\)
\(450\) 0.316965i 0.0149419i
\(451\) −4.16722 −0.196227
\(452\) 0.175056 0.00823394
\(453\) 2.29739i 0.107941i
\(454\) −27.3390 −1.28308
\(455\) 8.60250 + 32.5053i 0.403292 + 1.52387i
\(456\) −9.23344 −0.432395
\(457\) 28.4975i 1.33305i 0.745481 + 0.666527i \(0.232220\pi\)
−0.745481 + 0.666527i \(0.767780\pi\)
\(458\) −21.6794 −1.01301
\(459\) 3.79173 0.176983
\(460\) 1.38357i 0.0645093i
\(461\) 19.2580i 0.896932i 0.893800 + 0.448466i \(0.148030\pi\)
−0.893800 + 0.448466i \(0.851970\pi\)
\(462\) 5.84291i 0.271837i
\(463\) 36.3639i 1.68997i 0.534787 + 0.844987i \(0.320392\pi\)
−0.534787 + 0.844987i \(0.679608\pi\)
\(464\) 27.4127 1.27260
\(465\) −0.158849 −0.00736645
\(466\) 21.7801i 1.00894i
\(467\) −1.70345 −0.0788264 −0.0394132 0.999223i \(-0.512549\pi\)
−0.0394132 + 0.999223i \(0.512549\pi\)
\(468\) −0.118255 0.446838i −0.00546636 0.0206551i
\(469\) −43.1961 −1.99461
\(470\) 34.7562i 1.60318i
\(471\) −15.6293 −0.720161
\(472\) −16.3859 −0.754220
\(473\) 7.11697i 0.327239i
\(474\) 13.8468i 0.636006i
\(475\) 0.734687i 0.0337097i
\(476\) 2.07594i 0.0951505i
\(477\) 5.11268 0.234094
\(478\) 23.2444 1.06318
\(479\) 24.5812i 1.12314i −0.827429 0.561571i \(-0.810197\pi\)
0.827429 0.561571i \(-0.189803\pi\)
\(480\) 1.58107 0.0721657
\(481\) 12.7801 3.38224i 0.582721 0.154217i
\(482\) 30.0831 1.37025
\(483\) 21.1076i 0.960431i
\(484\) −0.128197 −0.00582714
\(485\) −8.28216 −0.376074
\(486\) 1.36814i 0.0620600i
\(487\) 40.5270i 1.83646i −0.396053 0.918228i \(-0.629620\pi\)
0.396053 0.918228i \(-0.370380\pi\)
\(488\) 15.7463i 0.712802i
\(489\) 1.25583i 0.0567907i
\(490\) −33.5766 −1.51683
\(491\) −16.8245 −0.759277 −0.379639 0.925135i \(-0.623952\pi\)
−0.379639 + 0.925135i \(0.623952\pi\)
\(492\) 0.534226i 0.0240848i
\(493\) −27.8875 −1.25599
\(494\) 4.00216 + 15.1225i 0.180066 + 0.680393i
\(495\) 2.18365 0.0981477
\(496\) 0.271132i 0.0121742i
\(497\) −41.0943 −1.84333
\(498\) −10.6840 −0.478764
\(499\) 28.5150i 1.27651i −0.769826 0.638254i \(-0.779657\pi\)
0.769826 0.638254i \(-0.220343\pi\)
\(500\) 1.46454i 0.0654963i
\(501\) 17.3823i 0.776586i
\(502\) 16.3439i 0.729463i
\(503\) 27.4200 1.22260 0.611299 0.791400i \(-0.290647\pi\)
0.611299 + 0.791400i \(0.290647\pi\)
\(504\) 12.4349 0.553893
\(505\) 28.0908i 1.25002i
\(506\) −6.76193 −0.300604
\(507\) −11.2982 + 6.43050i −0.501769 + 0.285588i
\(508\) −1.33360 −0.0591689
\(509\) 25.4659i 1.12876i 0.825516 + 0.564378i \(0.190884\pi\)
−0.825516 + 0.564378i \(0.809116\pi\)
\(510\) 11.3279 0.501609
\(511\) 27.5348 1.21807
\(512\) 24.4032i 1.07848i
\(513\) 3.17118i 0.140011i
\(514\) 38.8101i 1.71184i
\(515\) 37.1167i 1.63556i
\(516\) −0.912375 −0.0401651
\(517\) −11.6337 −0.511651
\(518\) 21.4235i 0.941295i
\(519\) 12.0899 0.530688
\(520\) −5.86499 22.1614i −0.257197 0.971840i
\(521\) 2.38806 0.104623 0.0523113 0.998631i \(-0.483341\pi\)
0.0523113 + 0.998631i \(0.483341\pi\)
\(522\) 10.0624i 0.440421i
\(523\) 45.6041 1.99413 0.997064 0.0765769i \(-0.0243991\pi\)
0.997064 + 0.0765769i \(0.0243991\pi\)
\(524\) −1.54705 −0.0675833
\(525\) 0.989418i 0.0431818i
\(526\) 1.88527i 0.0822015i
\(527\) 0.275829i 0.0120153i
\(528\) 3.72717i 0.162204i
\(529\) 1.42760 0.0620694
\(530\) 15.2743 0.663474
\(531\) 5.62765i 0.244219i
\(532\) 1.73620 0.0752736
\(533\) 14.5251 3.84405i 0.629151 0.166504i
\(534\) −3.93904 −0.170459
\(535\) 27.6927i 1.19726i
\(536\) 29.4501 1.27205
\(537\) 5.13094 0.221416
\(538\) 20.0123i 0.862791i
\(539\) 11.2389i 0.484093i
\(540\) 0.279937i 0.0120466i
\(541\) 29.4997i 1.26829i −0.773214 0.634145i \(-0.781352\pi\)
0.773214 0.634145i \(-0.218648\pi\)
\(542\) −18.2017 −0.781828
\(543\) 23.3170 1.00063
\(544\) 2.74540i 0.117708i
\(545\) −19.4259 −0.832114
\(546\) −5.38979 20.3658i −0.230662 0.871575i
\(547\) 7.75142 0.331427 0.165713 0.986174i \(-0.447007\pi\)
0.165713 + 0.986174i \(0.447007\pi\)
\(548\) 0.507806i 0.0216924i
\(549\) −5.40800 −0.230808
\(550\) −0.316965 −0.0135154
\(551\) 23.3235i 0.993616i
\(552\) 14.3907i 0.612509i
\(553\) 43.2235i 1.83805i
\(554\) 30.3153i 1.28798i
\(555\) 8.00653 0.339858
\(556\) 2.33878 0.0991865
\(557\) 20.2857i 0.859534i −0.902940 0.429767i \(-0.858596\pi\)
0.902940 0.429767i \(-0.141404\pi\)
\(558\) 0.0995250 0.00421323
\(559\) 6.56505 + 24.8066i 0.277672 + 1.04921i
\(560\) 34.7585 1.46882
\(561\) 3.79173i 0.160087i
\(562\) 2.90851 0.122688
\(563\) 32.7633 1.38081 0.690403 0.723425i \(-0.257433\pi\)
0.690403 + 0.723425i \(0.257433\pi\)
\(564\) 1.49141i 0.0627997i
\(565\) 2.98182i 0.125446i
\(566\) 42.5540i 1.78868i
\(567\) 4.27070i 0.179353i
\(568\) 28.0172 1.17558
\(569\) −27.8002 −1.16545 −0.582723 0.812671i \(-0.698013\pi\)
−0.582723 + 0.812671i \(0.698013\pi\)
\(570\) 9.47402i 0.396823i
\(571\) −43.4425 −1.81801 −0.909007 0.416782i \(-0.863158\pi\)
−0.909007 + 0.416782i \(0.863158\pi\)
\(572\) 0.446838 0.118255i 0.0186832 0.00494450i
\(573\) 11.1231 0.464674
\(574\) 24.3487i 1.01630i
\(575\) 1.14504 0.0477515
\(576\) −8.44494 −0.351873
\(577\) 25.7084i 1.07025i −0.844772 0.535127i \(-0.820264\pi\)
0.844772 0.535127i \(-0.179736\pi\)
\(578\) 3.58834i 0.149255i
\(579\) 23.1664i 0.962764i
\(580\) 2.05889i 0.0854909i
\(581\) 33.3507 1.38362
\(582\) 5.18909 0.215095
\(583\) 5.11268i 0.211746i
\(584\) −18.7726 −0.776815
\(585\) −7.61123 + 2.01431i −0.314686 + 0.0832814i
\(586\) −23.1228 −0.955195
\(587\) 1.44805i 0.0597673i −0.999553 0.0298837i \(-0.990486\pi\)
0.999553 0.0298837i \(-0.00951368\pi\)
\(588\) −1.44079 −0.0594173
\(589\) 0.230687 0.00950530
\(590\) 16.8128i 0.692173i
\(591\) 9.18435i 0.377794i
\(592\) 13.6660i 0.561668i
\(593\) 4.27539i 0.175569i 0.996139 + 0.0877845i \(0.0279787\pi\)
−0.996139 + 0.0877845i \(0.972021\pi\)
\(594\) −1.36814 −0.0561354
\(595\) −35.3606 −1.44964
\(596\) 1.78173i 0.0729824i
\(597\) −6.38937 −0.261499
\(598\) 23.5691 6.23754i 0.963810 0.255072i
\(599\) 15.9807 0.652953 0.326476 0.945205i \(-0.394139\pi\)
0.326476 + 0.945205i \(0.394139\pi\)
\(600\) 0.674563i 0.0275389i
\(601\) −25.2647 −1.03057 −0.515283 0.857020i \(-0.672313\pi\)
−0.515283 + 0.857020i \(0.672313\pi\)
\(602\) −41.5838 −1.69483
\(603\) 10.1145i 0.411895i
\(604\) 0.294519i 0.0119838i
\(605\) 2.18365i 0.0887780i
\(606\) 17.5999i 0.714948i
\(607\) 41.6506 1.69055 0.845273 0.534334i \(-0.179437\pi\)
0.845273 + 0.534334i \(0.179437\pi\)
\(608\) −2.29610 −0.0931190
\(609\) 31.4103i 1.27281i
\(610\) −16.1566 −0.654162
\(611\) 40.5500 10.7315i 1.64048 0.434151i
\(612\) 0.486088 0.0196490
\(613\) 16.1620i 0.652777i −0.945236 0.326388i \(-0.894168\pi\)
0.945236 0.326388i \(-0.105832\pi\)
\(614\) 33.6713 1.35886
\(615\) 9.09975 0.366937
\(616\) 12.4349i 0.501015i
\(617\) 8.12561i 0.327125i −0.986533 0.163562i \(-0.947701\pi\)
0.986533 0.163562i \(-0.0522985\pi\)
\(618\) 23.2550i 0.935453i
\(619\) 7.09593i 0.285209i 0.989780 + 0.142605i \(0.0455478\pi\)
−0.989780 + 0.142605i \(0.954452\pi\)
\(620\) −0.0203640 −0.000817838
\(621\) 4.94243 0.198333
\(622\) 1.37503i 0.0551337i
\(623\) 12.2959 0.492624
\(624\) 3.43813 + 12.9913i 0.137635 + 0.520066i
\(625\) −23.7879 −0.951518
\(626\) 18.9821i 0.758677i
\(627\) −3.17118 −0.126645
\(628\) −2.00363 −0.0799536
\(629\) 13.9027i 0.554337i
\(630\) 12.7589i 0.508325i
\(631\) 3.62153i 0.144171i 0.997398 + 0.0720854i \(0.0229654\pi\)
−0.997398 + 0.0720854i \(0.977035\pi\)
\(632\) 29.4688i 1.17221i
\(633\) 22.4436 0.892053
\(634\) 21.3984 0.849840
\(635\) 22.7159i 0.901453i
\(636\) 0.655431 0.0259895
\(637\) 10.3673 + 39.1738i 0.410768 + 1.55212i
\(638\) 10.0624 0.398375
\(639\) 9.62239i 0.380656i
\(640\) −22.0674 −0.872291
\(641\) 8.81244 0.348070 0.174035 0.984739i \(-0.444319\pi\)
0.174035 + 0.984739i \(0.444319\pi\)
\(642\) 17.3505i 0.684771i
\(643\) 47.2262i 1.86242i 0.364484 + 0.931210i \(0.381245\pi\)
−0.364484 + 0.931210i \(0.618755\pi\)
\(644\) 2.70594i 0.106629i
\(645\) 15.5410i 0.611925i
\(646\) −16.4509 −0.647251
\(647\) −41.0552 −1.61405 −0.807023 0.590520i \(-0.798923\pi\)
−0.807023 + 0.590520i \(0.798923\pi\)
\(648\) 2.91167i 0.114381i
\(649\) −5.62765 −0.220905
\(650\) 1.10480 0.292384i 0.0433337 0.0114682i
\(651\) −0.310671 −0.0121762
\(652\) 0.160994i 0.00630501i
\(653\) 36.9362 1.44542 0.722712 0.691149i \(-0.242895\pi\)
0.722712 + 0.691149i \(0.242895\pi\)
\(654\) 12.1711 0.475926
\(655\) 26.3518i 1.02965i
\(656\) 15.5320i 0.606421i
\(657\) 6.44736i 0.251536i
\(658\) 67.9748i 2.64994i
\(659\) 39.7980 1.55031 0.775154 0.631772i \(-0.217672\pi\)
0.775154 + 0.631772i \(0.217672\pi\)
\(660\) 0.279937 0.0108965
\(661\) 21.8622i 0.850342i −0.905113 0.425171i \(-0.860214\pi\)
0.905113 0.425171i \(-0.139786\pi\)
\(662\) 31.6623 1.23059
\(663\) −3.49768 13.2163i −0.135839 0.513278i
\(664\) −22.7378 −0.882396
\(665\) 29.5736i 1.14681i
\(666\) −5.01639 −0.194381
\(667\) −36.3507 −1.40751
\(668\) 2.22836i 0.0862180i
\(669\) 16.5344i 0.639255i
\(670\) 30.2175i 1.16740i
\(671\) 5.40800i 0.208774i
\(672\) 3.09220 0.119284
\(673\) 32.3152 1.24566 0.622830 0.782357i \(-0.285983\pi\)
0.622830 + 0.782357i \(0.285983\pi\)
\(674\) 20.7884i 0.800739i
\(675\) 0.231676 0.00891721
\(676\) −1.44839 + 0.824371i −0.0557074 + 0.0317066i
\(677\) −21.1472 −0.812753 −0.406376 0.913706i \(-0.633208\pi\)
−0.406376 + 0.913706i \(0.633208\pi\)
\(678\) 1.86822i 0.0717487i
\(679\) −16.1979 −0.621620
\(680\) 24.1081 0.924502
\(681\) 19.9826i 0.765737i
\(682\) 0.0995250i 0.00381101i
\(683\) 24.7401i 0.946654i −0.880887 0.473327i \(-0.843053\pi\)
0.880887 0.473327i \(-0.156947\pi\)
\(684\) 0.406536i 0.0155443i
\(685\) 8.64973 0.330489
\(686\) −24.7675 −0.945626
\(687\) 15.8459i 0.604560i
\(688\) 26.5262 1.01130
\(689\) −4.71619 17.8205i −0.179673 0.678908i
\(690\) 14.7657 0.562120
\(691\) 22.7394i 0.865047i −0.901623 0.432523i \(-0.857623\pi\)
0.901623 0.432523i \(-0.142377\pi\)
\(692\) 1.54989 0.0589180
\(693\) 4.27070 0.162231
\(694\) 22.7857i 0.864932i
\(695\) 39.8377i 1.51113i
\(696\) 21.4148i 0.811727i
\(697\) 15.8010i 0.598505i
\(698\) 39.8238 1.50735
\(699\) −15.9195 −0.602130
\(700\) 0.126840i 0.00479412i
\(701\) 23.8173 0.899567 0.449783 0.893138i \(-0.351501\pi\)
0.449783 + 0.893138i \(0.351501\pi\)
\(702\) 4.76872 1.26204i 0.179984 0.0476326i
\(703\) −11.6274 −0.438536
\(704\) 8.44494i 0.318281i
\(705\) 25.4040 0.956769
\(706\) 39.9117 1.50210
\(707\) 54.9389i 2.06619i
\(708\) 0.721449i 0.0271137i
\(709\) 15.8902i 0.596770i 0.954446 + 0.298385i \(0.0964480\pi\)
−0.954446 + 0.298385i \(0.903552\pi\)
\(710\) 28.7472i 1.07886i
\(711\) 10.1209 0.379565
\(712\) −8.38305 −0.314168
\(713\) 0.359536i 0.0134647i
\(714\) 22.1547 0.829120
\(715\) −2.01431 7.61123i −0.0753308 0.284644i
\(716\) 0.657771 0.0245821
\(717\) 16.9898i 0.634497i
\(718\) 24.7371 0.923181
\(719\) −4.64051 −0.173062 −0.0865309 0.996249i \(-0.527578\pi\)
−0.0865309 + 0.996249i \(0.527578\pi\)
\(720\) 8.13884i 0.303316i
\(721\) 72.5914i 2.70345i
\(722\) 12.2361i 0.455379i
\(723\) 21.9883i 0.817755i
\(724\) 2.98917 0.111091
\(725\) −1.70394 −0.0632826
\(726\) 1.36814i 0.0507764i
\(727\) 14.5583 0.539938 0.269969 0.962869i \(-0.412987\pi\)
0.269969 + 0.962869i \(0.412987\pi\)
\(728\) −11.4705 43.3424i −0.425127 1.60638i
\(729\) 1.00000 0.0370370
\(730\) 19.2617i 0.712908i
\(731\) −26.9856 −0.998100
\(732\) −0.693290 −0.0256247
\(733\) 34.2475i 1.26496i −0.774576 0.632480i \(-0.782037\pi\)
0.774576 0.632480i \(-0.217963\pi\)
\(734\) 24.8096i 0.915738i
\(735\) 24.5418i 0.905238i
\(736\) 3.57856i 0.131908i
\(737\) 10.1145 0.372573
\(738\) −5.70134 −0.209869
\(739\) 30.5325i 1.12316i −0.827424 0.561578i \(-0.810194\pi\)
0.827424 0.561578i \(-0.189806\pi\)
\(740\) 1.02641 0.0377317
\(741\) 11.0533 2.92526i 0.406054 0.107462i
\(742\) 29.8729 1.09667
\(743\) 2.86476i 0.105098i −0.998618 0.0525490i \(-0.983265\pi\)
0.998618 0.0525490i \(-0.0167346\pi\)
\(744\) 0.211809 0.00776529
\(745\) −30.3491 −1.11191
\(746\) 21.6937i 0.794263i
\(747\) 7.80918i 0.285723i
\(748\) 0.486088i 0.0177732i
\(749\) 54.1604i 1.97898i
\(750\) 15.6298 0.570720
\(751\) −38.1810 −1.39324 −0.696621 0.717439i \(-0.745314\pi\)
−0.696621 + 0.717439i \(0.745314\pi\)
\(752\) 43.3609i 1.58121i
\(753\) −11.9461 −0.435339
\(754\) −35.0731 + 9.28209i −1.27729 + 0.338034i
\(755\) −5.01670 −0.182576
\(756\) 0.547491i 0.0199121i
\(757\) −38.9456 −1.41550 −0.707750 0.706463i \(-0.750290\pi\)
−0.707750 + 0.706463i \(0.750290\pi\)
\(758\) −25.0960 −0.911526
\(759\) 4.94243i 0.179399i
\(760\) 20.1626i 0.731374i
\(761\) 26.9359i 0.976427i −0.872724 0.488214i \(-0.837649\pi\)
0.872724 0.488214i \(-0.162351\pi\)
\(762\) 14.2324i 0.515585i
\(763\) −37.9925 −1.37542
\(764\) 1.42595 0.0515889
\(765\) 8.27981i 0.299357i
\(766\) 22.0296 0.795962
\(767\) 19.6155 5.19123i 0.708274 0.187444i
\(768\) −3.06382 −0.110556
\(769\) 3.83575i 0.138321i −0.997606 0.0691603i \(-0.977968\pi\)
0.997606 0.0691603i \(-0.0220320\pi\)
\(770\) 12.7589 0.459798
\(771\) −28.3671 −1.02162
\(772\) 2.96987i 0.106888i
\(773\) 21.7215i 0.781267i −0.920546 0.390633i \(-0.872256\pi\)
0.920546 0.390633i \(-0.127744\pi\)
\(774\) 9.73700i 0.349989i
\(775\) 0.0168532i 0.000605385i
\(776\) 11.0434 0.396435
\(777\) 15.6589 0.561759
\(778\) 44.7609i 1.60476i
\(779\) −13.2150 −0.473478
\(780\) −0.975737 + 0.258228i −0.0349370 + 0.00924605i
\(781\) 9.62239 0.344316
\(782\) 25.6394i 0.916863i
\(783\) −7.35483 −0.262840
\(784\) 41.8893 1.49605
\(785\) 34.1290i 1.21811i
\(786\) 16.5104i 0.588905i
\(787\) 32.8705i 1.17171i 0.810417 + 0.585853i \(0.199240\pi\)
−0.810417 + 0.585853i \(0.800760\pi\)
\(788\) 1.17741i 0.0419434i
\(789\) −1.37798 −0.0490574
\(790\) 30.2366 1.07577
\(791\) 5.83174i