Properties

Label 4730.2.a.z.1.7
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.41316\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.41316 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41316 q^{6} -5.00890 q^{7} -1.00000 q^{8} +2.82333 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.41316 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.41316 q^{6} -5.00890 q^{7} -1.00000 q^{8} +2.82333 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.41316 q^{12} +7.13007 q^{13} +5.00890 q^{14} +2.41316 q^{15} +1.00000 q^{16} -2.68227 q^{17} -2.82333 q^{18} -3.51382 q^{19} +1.00000 q^{20} -12.0873 q^{21} -1.00000 q^{22} +6.05399 q^{23} -2.41316 q^{24} +1.00000 q^{25} -7.13007 q^{26} -0.426321 q^{27} -5.00890 q^{28} -7.74615 q^{29} -2.41316 q^{30} +7.62662 q^{31} -1.00000 q^{32} +2.41316 q^{33} +2.68227 q^{34} -5.00890 q^{35} +2.82333 q^{36} +3.83869 q^{37} +3.51382 q^{38} +17.2060 q^{39} -1.00000 q^{40} +3.90400 q^{41} +12.0873 q^{42} +1.00000 q^{43} +1.00000 q^{44} +2.82333 q^{45} -6.05399 q^{46} -0.876784 q^{47} +2.41316 q^{48} +18.0890 q^{49} -1.00000 q^{50} -6.47274 q^{51} +7.13007 q^{52} -1.81678 q^{53} +0.426321 q^{54} +1.00000 q^{55} +5.00890 q^{56} -8.47940 q^{57} +7.74615 q^{58} +1.02302 q^{59} +2.41316 q^{60} +1.82530 q^{61} -7.62662 q^{62} -14.1418 q^{63} +1.00000 q^{64} +7.13007 q^{65} -2.41316 q^{66} +8.02353 q^{67} -2.68227 q^{68} +14.6092 q^{69} +5.00890 q^{70} +8.89481 q^{71} -2.82333 q^{72} -1.68829 q^{73} -3.83869 q^{74} +2.41316 q^{75} -3.51382 q^{76} -5.00890 q^{77} -17.2060 q^{78} +10.0241 q^{79} +1.00000 q^{80} -9.49878 q^{81} -3.90400 q^{82} +7.73554 q^{83} -12.0873 q^{84} -2.68227 q^{85} -1.00000 q^{86} -18.6927 q^{87} -1.00000 q^{88} -9.35787 q^{89} -2.82333 q^{90} -35.7138 q^{91} +6.05399 q^{92} +18.4042 q^{93} +0.876784 q^{94} -3.51382 q^{95} -2.41316 q^{96} -11.8989 q^{97} -18.0890 q^{98} +2.82333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} - 10q^{10} + 10q^{11} + 8q^{12} + 7q^{13} - 3q^{14} + 8q^{15} + 10q^{16} + 2q^{17} - 14q^{18} - 7q^{19} + 10q^{20} - 2q^{21} - 10q^{22} + 12q^{23} - 8q^{24} + 10q^{25} - 7q^{26} + 23q^{27} + 3q^{28} - 12q^{29} - 8q^{30} + 16q^{31} - 10q^{32} + 8q^{33} - 2q^{34} + 3q^{35} + 14q^{36} + 19q^{37} + 7q^{38} + 6q^{39} - 10q^{40} + 9q^{41} + 2q^{42} + 10q^{43} + 10q^{44} + 14q^{45} - 12q^{46} + 29q^{47} + 8q^{48} + 23q^{49} - 10q^{50} - 7q^{51} + 7q^{52} + 6q^{53} - 23q^{54} + 10q^{55} - 3q^{56} + 23q^{57} + 12q^{58} + 29q^{59} + 8q^{60} - 4q^{61} - 16q^{62} + 10q^{64} + 7q^{65} - 8q^{66} + 45q^{67} + 2q^{68} + 24q^{69} - 3q^{70} - 18q^{71} - 14q^{72} + 3q^{73} - 19q^{74} + 8q^{75} - 7q^{76} + 3q^{77} - 6q^{78} - 14q^{79} + 10q^{80} + 6q^{81} - 9q^{82} + 23q^{83} - 2q^{84} + 2q^{85} - 10q^{86} + 25q^{87} - 10q^{88} + q^{89} - 14q^{90} + q^{91} + 12q^{92} + 35q^{93} - 29q^{94} - 7q^{95} - 8q^{96} + 30q^{97} - 23q^{98} + 14q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 2.41316 1.39324 0.696619 0.717441i \(-0.254687\pi\)
0.696619 + 0.717441i \(0.254687\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.41316 −0.985168
\(7\) −5.00890 −1.89319 −0.946593 0.322432i \(-0.895500\pi\)
−0.946593 + 0.322432i \(0.895500\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.82333 0.941112
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 2.41316 0.696619
\(13\) 7.13007 1.97752 0.988762 0.149495i \(-0.0477648\pi\)
0.988762 + 0.149495i \(0.0477648\pi\)
\(14\) 5.00890 1.33868
\(15\) 2.41316 0.623075
\(16\) 1.00000 0.250000
\(17\) −2.68227 −0.650546 −0.325273 0.945620i \(-0.605456\pi\)
−0.325273 + 0.945620i \(0.605456\pi\)
\(18\) −2.82333 −0.665466
\(19\) −3.51382 −0.806125 −0.403063 0.915172i \(-0.632054\pi\)
−0.403063 + 0.915172i \(0.632054\pi\)
\(20\) 1.00000 0.223607
\(21\) −12.0873 −2.63766
\(22\) −1.00000 −0.213201
\(23\) 6.05399 1.26234 0.631172 0.775643i \(-0.282574\pi\)
0.631172 + 0.775643i \(0.282574\pi\)
\(24\) −2.41316 −0.492584
\(25\) 1.00000 0.200000
\(26\) −7.13007 −1.39832
\(27\) −0.426321 −0.0820455
\(28\) −5.00890 −0.946593
\(29\) −7.74615 −1.43842 −0.719212 0.694790i \(-0.755497\pi\)
−0.719212 + 0.694790i \(0.755497\pi\)
\(30\) −2.41316 −0.440580
\(31\) 7.62662 1.36978 0.684891 0.728646i \(-0.259850\pi\)
0.684891 + 0.728646i \(0.259850\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.41316 0.420077
\(34\) 2.68227 0.460005
\(35\) −5.00890 −0.846658
\(36\) 2.82333 0.470556
\(37\) 3.83869 0.631076 0.315538 0.948913i \(-0.397815\pi\)
0.315538 + 0.948913i \(0.397815\pi\)
\(38\) 3.51382 0.570017
\(39\) 17.2060 2.75516
\(40\) −1.00000 −0.158114
\(41\) 3.90400 0.609703 0.304851 0.952400i \(-0.401393\pi\)
0.304851 + 0.952400i \(0.401393\pi\)
\(42\) 12.0873 1.86511
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) 2.82333 0.420878
\(46\) −6.05399 −0.892612
\(47\) −0.876784 −0.127892 −0.0639461 0.997953i \(-0.520369\pi\)
−0.0639461 + 0.997953i \(0.520369\pi\)
\(48\) 2.41316 0.348309
\(49\) 18.0890 2.58415
\(50\) −1.00000 −0.141421
\(51\) −6.47274 −0.906365
\(52\) 7.13007 0.988762
\(53\) −1.81678 −0.249553 −0.124777 0.992185i \(-0.539821\pi\)
−0.124777 + 0.992185i \(0.539821\pi\)
\(54\) 0.426321 0.0580149
\(55\) 1.00000 0.134840
\(56\) 5.00890 0.669342
\(57\) −8.47940 −1.12312
\(58\) 7.74615 1.01712
\(59\) 1.02302 0.133186 0.0665932 0.997780i \(-0.478787\pi\)
0.0665932 + 0.997780i \(0.478787\pi\)
\(60\) 2.41316 0.311537
\(61\) 1.82530 0.233706 0.116853 0.993149i \(-0.462719\pi\)
0.116853 + 0.993149i \(0.462719\pi\)
\(62\) −7.62662 −0.968582
\(63\) −14.1418 −1.78170
\(64\) 1.00000 0.125000
\(65\) 7.13007 0.884376
\(66\) −2.41316 −0.297039
\(67\) 8.02353 0.980231 0.490115 0.871658i \(-0.336955\pi\)
0.490115 + 0.871658i \(0.336955\pi\)
\(68\) −2.68227 −0.325273
\(69\) 14.6092 1.75875
\(70\) 5.00890 0.598678
\(71\) 8.89481 1.05562 0.527810 0.849363i \(-0.323013\pi\)
0.527810 + 0.849363i \(0.323013\pi\)
\(72\) −2.82333 −0.332733
\(73\) −1.68829 −0.197600 −0.0988000 0.995107i \(-0.531500\pi\)
−0.0988000 + 0.995107i \(0.531500\pi\)
\(74\) −3.83869 −0.446238
\(75\) 2.41316 0.278648
\(76\) −3.51382 −0.403063
\(77\) −5.00890 −0.570817
\(78\) −17.2060 −1.94819
\(79\) 10.0241 1.12780 0.563902 0.825842i \(-0.309300\pi\)
0.563902 + 0.825842i \(0.309300\pi\)
\(80\) 1.00000 0.111803
\(81\) −9.49878 −1.05542
\(82\) −3.90400 −0.431125
\(83\) 7.73554 0.849086 0.424543 0.905408i \(-0.360435\pi\)
0.424543 + 0.905408i \(0.360435\pi\)
\(84\) −12.0873 −1.31883
\(85\) −2.68227 −0.290933
\(86\) −1.00000 −0.107833
\(87\) −18.6927 −2.00407
\(88\) −1.00000 −0.106600
\(89\) −9.35787 −0.991932 −0.495966 0.868342i \(-0.665186\pi\)
−0.495966 + 0.868342i \(0.665186\pi\)
\(90\) −2.82333 −0.297606
\(91\) −35.7138 −3.74382
\(92\) 6.05399 0.631172
\(93\) 18.4042 1.90843
\(94\) 0.876784 0.0904334
\(95\) −3.51382 −0.360510
\(96\) −2.41316 −0.246292
\(97\) −11.8989 −1.20815 −0.604076 0.796926i \(-0.706458\pi\)
−0.604076 + 0.796926i \(0.706458\pi\)
\(98\) −18.0890 −1.82727
\(99\) 2.82333 0.283756
\(100\) 1.00000 0.100000
\(101\) 11.1320 1.10767 0.553836 0.832626i \(-0.313164\pi\)
0.553836 + 0.832626i \(0.313164\pi\)
\(102\) 6.47274 0.640897
\(103\) −8.64427 −0.851745 −0.425872 0.904783i \(-0.640033\pi\)
−0.425872 + 0.904783i \(0.640033\pi\)
\(104\) −7.13007 −0.699161
\(105\) −12.0873 −1.17960
\(106\) 1.81678 0.176461
\(107\) 15.4780 1.49631 0.748155 0.663523i \(-0.230940\pi\)
0.748155 + 0.663523i \(0.230940\pi\)
\(108\) −0.426321 −0.0410228
\(109\) 5.43714 0.520784 0.260392 0.965503i \(-0.416148\pi\)
0.260392 + 0.965503i \(0.416148\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 9.26336 0.879239
\(112\) −5.00890 −0.473296
\(113\) 6.86930 0.646210 0.323105 0.946363i \(-0.395273\pi\)
0.323105 + 0.946363i \(0.395273\pi\)
\(114\) 8.47940 0.794169
\(115\) 6.05399 0.564537
\(116\) −7.74615 −0.719212
\(117\) 20.1306 1.86107
\(118\) −1.02302 −0.0941770
\(119\) 13.4352 1.23160
\(120\) −2.41316 −0.220290
\(121\) 1.00000 0.0909091
\(122\) −1.82530 −0.165255
\(123\) 9.42097 0.849461
\(124\) 7.62662 0.684891
\(125\) 1.00000 0.0894427
\(126\) 14.1418 1.25985
\(127\) 1.54738 0.137308 0.0686540 0.997641i \(-0.478130\pi\)
0.0686540 + 0.997641i \(0.478130\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.41316 0.212467
\(130\) −7.13007 −0.625348
\(131\) −14.1171 −1.23341 −0.616706 0.787193i \(-0.711533\pi\)
−0.616706 + 0.787193i \(0.711533\pi\)
\(132\) 2.41316 0.210039
\(133\) 17.6004 1.52614
\(134\) −8.02353 −0.693128
\(135\) −0.426321 −0.0366919
\(136\) 2.68227 0.230003
\(137\) 3.23436 0.276330 0.138165 0.990409i \(-0.455880\pi\)
0.138165 + 0.990409i \(0.455880\pi\)
\(138\) −14.6092 −1.24362
\(139\) −4.86705 −0.412818 −0.206409 0.978466i \(-0.566178\pi\)
−0.206409 + 0.978466i \(0.566178\pi\)
\(140\) −5.00890 −0.423329
\(141\) −2.11582 −0.178184
\(142\) −8.89481 −0.746436
\(143\) 7.13007 0.596246
\(144\) 2.82333 0.235278
\(145\) −7.74615 −0.643283
\(146\) 1.68829 0.139724
\(147\) 43.6517 3.60034
\(148\) 3.83869 0.315538
\(149\) 8.90513 0.729537 0.364768 0.931098i \(-0.381148\pi\)
0.364768 + 0.931098i \(0.381148\pi\)
\(150\) −2.41316 −0.197034
\(151\) −13.8455 −1.12673 −0.563364 0.826209i \(-0.690493\pi\)
−0.563364 + 0.826209i \(0.690493\pi\)
\(152\) 3.51382 0.285008
\(153\) −7.57294 −0.612236
\(154\) 5.00890 0.403628
\(155\) 7.62662 0.612585
\(156\) 17.2060 1.37758
\(157\) −1.35382 −0.108047 −0.0540234 0.998540i \(-0.517205\pi\)
−0.0540234 + 0.998540i \(0.517205\pi\)
\(158\) −10.0241 −0.797477
\(159\) −4.38417 −0.347687
\(160\) −1.00000 −0.0790569
\(161\) −30.3238 −2.38985
\(162\) 9.49878 0.746295
\(163\) 14.2012 1.11232 0.556161 0.831074i \(-0.312274\pi\)
0.556161 + 0.831074i \(0.312274\pi\)
\(164\) 3.90400 0.304851
\(165\) 2.41316 0.187864
\(166\) −7.73554 −0.600395
\(167\) 17.1331 1.32580 0.662898 0.748709i \(-0.269326\pi\)
0.662898 + 0.748709i \(0.269326\pi\)
\(168\) 12.0873 0.932553
\(169\) 37.8379 2.91061
\(170\) 2.68227 0.205721
\(171\) −9.92068 −0.758654
\(172\) 1.00000 0.0762493
\(173\) −7.33843 −0.557930 −0.278965 0.960301i \(-0.589991\pi\)
−0.278965 + 0.960301i \(0.589991\pi\)
\(174\) 18.6927 1.41709
\(175\) −5.00890 −0.378637
\(176\) 1.00000 0.0753778
\(177\) 2.46872 0.185560
\(178\) 9.35787 0.701402
\(179\) 20.5062 1.53271 0.766353 0.642420i \(-0.222070\pi\)
0.766353 + 0.642420i \(0.222070\pi\)
\(180\) 2.82333 0.210439
\(181\) −10.2191 −0.759579 −0.379790 0.925073i \(-0.624004\pi\)
−0.379790 + 0.925073i \(0.624004\pi\)
\(182\) 35.7138 2.64728
\(183\) 4.40474 0.325608
\(184\) −6.05399 −0.446306
\(185\) 3.83869 0.282226
\(186\) −18.4042 −1.34946
\(187\) −2.68227 −0.196147
\(188\) −0.876784 −0.0639461
\(189\) 2.13540 0.155327
\(190\) 3.51382 0.254919
\(191\) 8.94039 0.646904 0.323452 0.946245i \(-0.395157\pi\)
0.323452 + 0.946245i \(0.395157\pi\)
\(192\) 2.41316 0.174155
\(193\) 23.5154 1.69268 0.846339 0.532644i \(-0.178802\pi\)
0.846339 + 0.532644i \(0.178802\pi\)
\(194\) 11.8989 0.854293
\(195\) 17.2060 1.23215
\(196\) 18.0890 1.29207
\(197\) −0.533015 −0.0379757 −0.0189879 0.999820i \(-0.506044\pi\)
−0.0189879 + 0.999820i \(0.506044\pi\)
\(198\) −2.82333 −0.200646
\(199\) −8.70787 −0.617284 −0.308642 0.951178i \(-0.599875\pi\)
−0.308642 + 0.951178i \(0.599875\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 19.3621 1.36569
\(202\) −11.1320 −0.783242
\(203\) 38.7997 2.72320
\(204\) −6.47274 −0.453182
\(205\) 3.90400 0.272667
\(206\) 8.64427 0.602275
\(207\) 17.0924 1.18801
\(208\) 7.13007 0.494381
\(209\) −3.51382 −0.243056
\(210\) 12.0873 0.834100
\(211\) 21.4706 1.47810 0.739050 0.673651i \(-0.235275\pi\)
0.739050 + 0.673651i \(0.235275\pi\)
\(212\) −1.81678 −0.124777
\(213\) 21.4646 1.47073
\(214\) −15.4780 −1.05805
\(215\) 1.00000 0.0681994
\(216\) 0.426321 0.0290075
\(217\) −38.2010 −2.59325
\(218\) −5.43714 −0.368250
\(219\) −4.07412 −0.275304
\(220\) 1.00000 0.0674200
\(221\) −19.1248 −1.28647
\(222\) −9.26336 −0.621716
\(223\) 25.6498 1.71764 0.858819 0.512279i \(-0.171199\pi\)
0.858819 + 0.512279i \(0.171199\pi\)
\(224\) 5.00890 0.334671
\(225\) 2.82333 0.188222
\(226\) −6.86930 −0.456939
\(227\) 18.1130 1.20220 0.601100 0.799174i \(-0.294729\pi\)
0.601100 + 0.799174i \(0.294729\pi\)
\(228\) −8.47940 −0.561562
\(229\) −27.1746 −1.79575 −0.897873 0.440255i \(-0.854888\pi\)
−0.897873 + 0.440255i \(0.854888\pi\)
\(230\) −6.05399 −0.399188
\(231\) −12.0873 −0.795284
\(232\) 7.74615 0.508560
\(233\) 0.871375 0.0570857 0.0285428 0.999593i \(-0.490913\pi\)
0.0285428 + 0.999593i \(0.490913\pi\)
\(234\) −20.1306 −1.31598
\(235\) −0.876784 −0.0571951
\(236\) 1.02302 0.0665932
\(237\) 24.1898 1.57130
\(238\) −13.4352 −0.870875
\(239\) −9.08899 −0.587918 −0.293959 0.955818i \(-0.594973\pi\)
−0.293959 + 0.955818i \(0.594973\pi\)
\(240\) 2.41316 0.155769
\(241\) −14.6619 −0.944453 −0.472227 0.881477i \(-0.656550\pi\)
−0.472227 + 0.881477i \(0.656550\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −21.6431 −1.38841
\(244\) 1.82530 0.116853
\(245\) 18.0890 1.15567
\(246\) −9.42097 −0.600659
\(247\) −25.0538 −1.59413
\(248\) −7.62662 −0.484291
\(249\) 18.6671 1.18298
\(250\) −1.00000 −0.0632456
\(251\) −1.80652 −0.114026 −0.0570132 0.998373i \(-0.518158\pi\)
−0.0570132 + 0.998373i \(0.518158\pi\)
\(252\) −14.1418 −0.890849
\(253\) 6.05399 0.380611
\(254\) −1.54738 −0.0970915
\(255\) −6.47274 −0.405339
\(256\) 1.00000 0.0625000
\(257\) −11.5395 −0.719817 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(258\) −2.41316 −0.150237
\(259\) −19.2276 −1.19474
\(260\) 7.13007 0.442188
\(261\) −21.8700 −1.35372
\(262\) 14.1171 0.872154
\(263\) 14.8920 0.918279 0.459139 0.888364i \(-0.348158\pi\)
0.459139 + 0.888364i \(0.348158\pi\)
\(264\) −2.41316 −0.148520
\(265\) −1.81678 −0.111604
\(266\) −17.6004 −1.07915
\(267\) −22.5820 −1.38200
\(268\) 8.02353 0.490115
\(269\) −11.9970 −0.731470 −0.365735 0.930719i \(-0.619182\pi\)
−0.365735 + 0.930719i \(0.619182\pi\)
\(270\) 0.426321 0.0259451
\(271\) −8.55250 −0.519528 −0.259764 0.965672i \(-0.583645\pi\)
−0.259764 + 0.965672i \(0.583645\pi\)
\(272\) −2.68227 −0.162636
\(273\) −86.1830 −5.21603
\(274\) −3.23436 −0.195395
\(275\) 1.00000 0.0603023
\(276\) 14.6092 0.879373
\(277\) −2.61654 −0.157213 −0.0786064 0.996906i \(-0.525047\pi\)
−0.0786064 + 0.996906i \(0.525047\pi\)
\(278\) 4.86705 0.291906
\(279\) 21.5325 1.28912
\(280\) 5.00890 0.299339
\(281\) −11.3870 −0.679293 −0.339646 0.940553i \(-0.610307\pi\)
−0.339646 + 0.940553i \(0.610307\pi\)
\(282\) 2.11582 0.125995
\(283\) 23.6527 1.40600 0.703002 0.711188i \(-0.251842\pi\)
0.703002 + 0.711188i \(0.251842\pi\)
\(284\) 8.89481 0.527810
\(285\) −8.47940 −0.502276
\(286\) −7.13007 −0.421610
\(287\) −19.5547 −1.15428
\(288\) −2.82333 −0.166367
\(289\) −9.80543 −0.576790
\(290\) 7.74615 0.454870
\(291\) −28.7140 −1.68324
\(292\) −1.68829 −0.0988000
\(293\) −9.36175 −0.546920 −0.273460 0.961883i \(-0.588168\pi\)
−0.273460 + 0.961883i \(0.588168\pi\)
\(294\) −43.6517 −2.54582
\(295\) 1.02302 0.0595627
\(296\) −3.83869 −0.223119
\(297\) −0.426321 −0.0247377
\(298\) −8.90513 −0.515860
\(299\) 43.1653 2.49632
\(300\) 2.41316 0.139324
\(301\) −5.00890 −0.288708
\(302\) 13.8455 0.796716
\(303\) 26.8632 1.54325
\(304\) −3.51382 −0.201531
\(305\) 1.82530 0.104516
\(306\) 7.57294 0.432916
\(307\) 30.2823 1.72830 0.864152 0.503231i \(-0.167855\pi\)
0.864152 + 0.503231i \(0.167855\pi\)
\(308\) −5.00890 −0.285408
\(309\) −20.8600 −1.18668
\(310\) −7.62662 −0.433163
\(311\) −25.0684 −1.42150 −0.710750 0.703445i \(-0.751644\pi\)
−0.710750 + 0.703445i \(0.751644\pi\)
\(312\) −17.2060 −0.974097
\(313\) −23.4292 −1.32430 −0.662149 0.749372i \(-0.730355\pi\)
−0.662149 + 0.749372i \(0.730355\pi\)
\(314\) 1.35382 0.0764007
\(315\) −14.1418 −0.796800
\(316\) 10.0241 0.563902
\(317\) −10.6997 −0.600952 −0.300476 0.953789i \(-0.597146\pi\)
−0.300476 + 0.953789i \(0.597146\pi\)
\(318\) 4.38417 0.245852
\(319\) −7.74615 −0.433701
\(320\) 1.00000 0.0559017
\(321\) 37.3508 2.08472
\(322\) 30.3238 1.68988
\(323\) 9.42500 0.524421
\(324\) −9.49878 −0.527710
\(325\) 7.13007 0.395505
\(326\) −14.2012 −0.786531
\(327\) 13.1207 0.725576
\(328\) −3.90400 −0.215562
\(329\) 4.39172 0.242124
\(330\) −2.41316 −0.132840
\(331\) 20.3200 1.11689 0.558445 0.829541i \(-0.311398\pi\)
0.558445 + 0.829541i \(0.311398\pi\)
\(332\) 7.73554 0.424543
\(333\) 10.8379 0.593913
\(334\) −17.1331 −0.937480
\(335\) 8.02353 0.438372
\(336\) −12.0873 −0.659414
\(337\) 9.75296 0.531278 0.265639 0.964073i \(-0.414417\pi\)
0.265639 + 0.964073i \(0.414417\pi\)
\(338\) −37.8379 −2.05811
\(339\) 16.5767 0.900324
\(340\) −2.68227 −0.145466
\(341\) 7.62662 0.413005
\(342\) 9.92068 0.536449
\(343\) −55.5439 −2.99909
\(344\) −1.00000 −0.0539164
\(345\) 14.6092 0.786535
\(346\) 7.33843 0.394516
\(347\) −27.3345 −1.46739 −0.733696 0.679478i \(-0.762206\pi\)
−0.733696 + 0.679478i \(0.762206\pi\)
\(348\) −18.6927 −1.00203
\(349\) −16.3076 −0.872925 −0.436462 0.899723i \(-0.643769\pi\)
−0.436462 + 0.899723i \(0.643769\pi\)
\(350\) 5.00890 0.267737
\(351\) −3.03970 −0.162247
\(352\) −1.00000 −0.0533002
\(353\) 0.703139 0.0374243 0.0187122 0.999825i \(-0.494043\pi\)
0.0187122 + 0.999825i \(0.494043\pi\)
\(354\) −2.46872 −0.131211
\(355\) 8.89481 0.472088
\(356\) −9.35787 −0.495966
\(357\) 32.4213 1.71592
\(358\) −20.5062 −1.08379
\(359\) −12.3095 −0.649669 −0.324834 0.945771i \(-0.605309\pi\)
−0.324834 + 0.945771i \(0.605309\pi\)
\(360\) −2.82333 −0.148803
\(361\) −6.65308 −0.350162
\(362\) 10.2191 0.537104
\(363\) 2.41316 0.126658
\(364\) −35.7138 −1.87191
\(365\) −1.68829 −0.0883694
\(366\) −4.40474 −0.230239
\(367\) −17.8166 −0.930020 −0.465010 0.885305i \(-0.653949\pi\)
−0.465010 + 0.885305i \(0.653949\pi\)
\(368\) 6.05399 0.315586
\(369\) 11.0223 0.573798
\(370\) −3.83869 −0.199564
\(371\) 9.10004 0.472451
\(372\) 18.4042 0.954216
\(373\) −17.9785 −0.930894 −0.465447 0.885076i \(-0.654106\pi\)
−0.465447 + 0.885076i \(0.654106\pi\)
\(374\) 2.68227 0.138697
\(375\) 2.41316 0.124615
\(376\) 0.876784 0.0452167
\(377\) −55.2306 −2.84452
\(378\) −2.13540 −0.109833
\(379\) 37.0463 1.90294 0.951472 0.307737i \(-0.0995716\pi\)
0.951472 + 0.307737i \(0.0995716\pi\)
\(380\) −3.51382 −0.180255
\(381\) 3.73408 0.191303
\(382\) −8.94039 −0.457430
\(383\) −10.1265 −0.517441 −0.258720 0.965952i \(-0.583301\pi\)
−0.258720 + 0.965952i \(0.583301\pi\)
\(384\) −2.41316 −0.123146
\(385\) −5.00890 −0.255277
\(386\) −23.5154 −1.19690
\(387\) 2.82333 0.143518
\(388\) −11.8989 −0.604076
\(389\) −29.9366 −1.51785 −0.758923 0.651181i \(-0.774274\pi\)
−0.758923 + 0.651181i \(0.774274\pi\)
\(390\) −17.2060 −0.871259
\(391\) −16.2384 −0.821212
\(392\) −18.0890 −0.913635
\(393\) −34.0667 −1.71844
\(394\) 0.533015 0.0268529
\(395\) 10.0241 0.504369
\(396\) 2.82333 0.141878
\(397\) 30.8013 1.54587 0.772937 0.634483i \(-0.218787\pi\)
0.772937 + 0.634483i \(0.218787\pi\)
\(398\) 8.70787 0.436486
\(399\) 42.4724 2.12628
\(400\) 1.00000 0.0500000
\(401\) 22.3222 1.11472 0.557358 0.830272i \(-0.311815\pi\)
0.557358 + 0.830272i \(0.311815\pi\)
\(402\) −19.3621 −0.965692
\(403\) 54.3783 2.70878
\(404\) 11.1320 0.553836
\(405\) −9.49878 −0.471998
\(406\) −38.7997 −1.92560
\(407\) 3.83869 0.190277
\(408\) 6.47274 0.320448
\(409\) 32.8009 1.62190 0.810951 0.585114i \(-0.198950\pi\)
0.810951 + 0.585114i \(0.198950\pi\)
\(410\) −3.90400 −0.192805
\(411\) 7.80503 0.384994
\(412\) −8.64427 −0.425872
\(413\) −5.12422 −0.252146
\(414\) −17.0924 −0.840047
\(415\) 7.73554 0.379723
\(416\) −7.13007 −0.349580
\(417\) −11.7450 −0.575153
\(418\) 3.51382 0.171866
\(419\) −28.5131 −1.39296 −0.696479 0.717578i \(-0.745251\pi\)
−0.696479 + 0.717578i \(0.745251\pi\)
\(420\) −12.0873 −0.589798
\(421\) 28.9496 1.41092 0.705458 0.708752i \(-0.250742\pi\)
0.705458 + 0.708752i \(0.250742\pi\)
\(422\) −21.4706 −1.04517
\(423\) −2.47546 −0.120361
\(424\) 1.81678 0.0882304
\(425\) −2.68227 −0.130109
\(426\) −21.4646 −1.03996
\(427\) −9.14274 −0.442448
\(428\) 15.4780 0.748155
\(429\) 17.2060 0.830713
\(430\) −1.00000 −0.0482243
\(431\) −20.9481 −1.00903 −0.504516 0.863402i \(-0.668329\pi\)
−0.504516 + 0.863402i \(0.668329\pi\)
\(432\) −0.426321 −0.0205114
\(433\) −2.69386 −0.129458 −0.0647292 0.997903i \(-0.520618\pi\)
−0.0647292 + 0.997903i \(0.520618\pi\)
\(434\) 38.2010 1.83370
\(435\) −18.6927 −0.896246
\(436\) 5.43714 0.260392
\(437\) −21.2726 −1.01761
\(438\) 4.07412 0.194669
\(439\) 39.6125 1.89060 0.945302 0.326198i \(-0.105768\pi\)
0.945302 + 0.326198i \(0.105768\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 51.0714 2.43197
\(442\) 19.1248 0.909672
\(443\) 9.40525 0.446857 0.223428 0.974720i \(-0.428275\pi\)
0.223428 + 0.974720i \(0.428275\pi\)
\(444\) 9.26336 0.439619
\(445\) −9.35787 −0.443605
\(446\) −25.6498 −1.21455
\(447\) 21.4895 1.01642
\(448\) −5.00890 −0.236648
\(449\) −38.2727 −1.80620 −0.903101 0.429429i \(-0.858715\pi\)
−0.903101 + 0.429429i \(0.858715\pi\)
\(450\) −2.82333 −0.133093
\(451\) 3.90400 0.183832
\(452\) 6.86930 0.323105
\(453\) −33.4113 −1.56980
\(454\) −18.1130 −0.850084
\(455\) −35.7138 −1.67429
\(456\) 8.47940 0.397084
\(457\) 13.7202 0.641802 0.320901 0.947113i \(-0.396014\pi\)
0.320901 + 0.947113i \(0.396014\pi\)
\(458\) 27.1746 1.26978
\(459\) 1.14351 0.0533744
\(460\) 6.05399 0.282269
\(461\) −15.7395 −0.733063 −0.366532 0.930406i \(-0.619455\pi\)
−0.366532 + 0.930406i \(0.619455\pi\)
\(462\) 12.0873 0.562350
\(463\) 10.4522 0.485754 0.242877 0.970057i \(-0.421909\pi\)
0.242877 + 0.970057i \(0.421909\pi\)
\(464\) −7.74615 −0.359606
\(465\) 18.4042 0.853476
\(466\) −0.871375 −0.0403657
\(467\) 32.0595 1.48354 0.741768 0.670657i \(-0.233988\pi\)
0.741768 + 0.670657i \(0.233988\pi\)
\(468\) 20.1306 0.930536
\(469\) −40.1890 −1.85576
\(470\) 0.876784 0.0404431
\(471\) −3.26699 −0.150535
\(472\) −1.02302 −0.0470885
\(473\) 1.00000 0.0459800
\(474\) −24.1898 −1.11108
\(475\) −3.51382 −0.161225
\(476\) 13.4352 0.615802
\(477\) −5.12937 −0.234857
\(478\) 9.08899 0.415721
\(479\) −0.619319 −0.0282974 −0.0141487 0.999900i \(-0.504504\pi\)
−0.0141487 + 0.999900i \(0.504504\pi\)
\(480\) −2.41316 −0.110145
\(481\) 27.3701 1.24797
\(482\) 14.6619 0.667829
\(483\) −73.1762 −3.32963
\(484\) 1.00000 0.0454545
\(485\) −11.8989 −0.540302
\(486\) 21.6431 0.981752
\(487\) 24.5740 1.11356 0.556778 0.830662i \(-0.312038\pi\)
0.556778 + 0.830662i \(0.312038\pi\)
\(488\) −1.82530 −0.0826275
\(489\) 34.2697 1.54973
\(490\) −18.0890 −0.817180
\(491\) −3.57682 −0.161420 −0.0807099 0.996738i \(-0.525719\pi\)
−0.0807099 + 0.996738i \(0.525719\pi\)
\(492\) 9.42097 0.424730
\(493\) 20.7773 0.935761
\(494\) 25.0538 1.12722
\(495\) 2.82333 0.126899
\(496\) 7.62662 0.342445
\(497\) −44.5532 −1.99848
\(498\) −18.6671 −0.836492
\(499\) 9.76592 0.437182 0.218591 0.975817i \(-0.429854\pi\)
0.218591 + 0.975817i \(0.429854\pi\)
\(500\) 1.00000 0.0447214
\(501\) 41.3448 1.84715
\(502\) 1.80652 0.0806288
\(503\) −6.21085 −0.276928 −0.138464 0.990367i \(-0.544217\pi\)
−0.138464 + 0.990367i \(0.544217\pi\)
\(504\) 14.1418 0.629926
\(505\) 11.1320 0.495366
\(506\) −6.05399 −0.269133
\(507\) 91.3088 4.05517
\(508\) 1.54738 0.0686540
\(509\) −21.4408 −0.950348 −0.475174 0.879892i \(-0.657615\pi\)
−0.475174 + 0.879892i \(0.657615\pi\)
\(510\) 6.47274 0.286618
\(511\) 8.45649 0.374093
\(512\) −1.00000 −0.0441942
\(513\) 1.49801 0.0661389
\(514\) 11.5395 0.508987
\(515\) −8.64427 −0.380912
\(516\) 2.41316 0.106233
\(517\) −0.876784 −0.0385609
\(518\) 19.2276 0.844811
\(519\) −17.7088 −0.777330
\(520\) −7.13007 −0.312674
\(521\) 19.7143 0.863701 0.431851 0.901945i \(-0.357861\pi\)
0.431851 + 0.901945i \(0.357861\pi\)
\(522\) 21.8700 0.957223
\(523\) −35.0075 −1.53077 −0.765385 0.643572i \(-0.777452\pi\)
−0.765385 + 0.643572i \(0.777452\pi\)
\(524\) −14.1171 −0.616706
\(525\) −12.0873 −0.527531
\(526\) −14.8920 −0.649321
\(527\) −20.4566 −0.891106
\(528\) 2.41316 0.105019
\(529\) 13.6508 0.593512
\(530\) 1.81678 0.0789157
\(531\) 2.88834 0.125343
\(532\) 17.6004 0.763072
\(533\) 27.8358 1.20570
\(534\) 22.5820 0.977220
\(535\) 15.4780 0.669171
\(536\) −8.02353 −0.346564
\(537\) 49.4847 2.13542
\(538\) 11.9970 0.517228
\(539\) 18.0890 0.779150
\(540\) −0.426321 −0.0183459
\(541\) 8.26716 0.355433 0.177717 0.984082i \(-0.443129\pi\)
0.177717 + 0.984082i \(0.443129\pi\)
\(542\) 8.55250 0.367361
\(543\) −24.6603 −1.05827
\(544\) 2.68227 0.115001
\(545\) 5.43714 0.232902
\(546\) 86.1830 3.68829
\(547\) −32.2978 −1.38096 −0.690478 0.723353i \(-0.742600\pi\)
−0.690478 + 0.723353i \(0.742600\pi\)
\(548\) 3.23436 0.138165
\(549\) 5.15343 0.219943
\(550\) −1.00000 −0.0426401
\(551\) 27.2186 1.15955
\(552\) −14.6092 −0.621810
\(553\) −50.2098 −2.13514
\(554\) 2.61654 0.111166
\(555\) 9.26336 0.393208
\(556\) −4.86705 −0.206409
\(557\) −1.38006 −0.0584749 −0.0292374 0.999572i \(-0.509308\pi\)
−0.0292374 + 0.999572i \(0.509308\pi\)
\(558\) −21.5325 −0.911544
\(559\) 7.13007 0.301570
\(560\) −5.00890 −0.211665
\(561\) −6.47274 −0.273279
\(562\) 11.3870 0.480332
\(563\) −44.9494 −1.89439 −0.947195 0.320657i \(-0.896096\pi\)
−0.947195 + 0.320657i \(0.896096\pi\)
\(564\) −2.11582 −0.0890921
\(565\) 6.86930 0.288994
\(566\) −23.6527 −0.994195
\(567\) 47.5784 1.99811
\(568\) −8.89481 −0.373218
\(569\) −3.97796 −0.166765 −0.0833823 0.996518i \(-0.526572\pi\)
−0.0833823 + 0.996518i \(0.526572\pi\)
\(570\) 8.47940 0.355163
\(571\) 18.1519 0.759631 0.379816 0.925062i \(-0.375987\pi\)
0.379816 + 0.925062i \(0.375987\pi\)
\(572\) 7.13007 0.298123
\(573\) 21.5746 0.901292
\(574\) 19.5547 0.816199
\(575\) 6.05399 0.252469
\(576\) 2.82333 0.117639
\(577\) 19.7959 0.824116 0.412058 0.911158i \(-0.364810\pi\)
0.412058 + 0.911158i \(0.364810\pi\)
\(578\) 9.80543 0.407852
\(579\) 56.7465 2.35830
\(580\) −7.74615 −0.321641
\(581\) −38.7465 −1.60748
\(582\) 28.7140 1.19023
\(583\) −1.81678 −0.0752431
\(584\) 1.68829 0.0698621
\(585\) 20.1306 0.832297
\(586\) 9.36175 0.386731
\(587\) 12.0348 0.496727 0.248364 0.968667i \(-0.420107\pi\)
0.248364 + 0.968667i \(0.420107\pi\)
\(588\) 43.6517 1.80017
\(589\) −26.7986 −1.10422
\(590\) −1.02302 −0.0421172
\(591\) −1.28625 −0.0529092
\(592\) 3.83869 0.157769
\(593\) 9.27281 0.380789 0.190394 0.981708i \(-0.439023\pi\)
0.190394 + 0.981708i \(0.439023\pi\)
\(594\) 0.426321 0.0174922
\(595\) 13.4352 0.550790
\(596\) 8.90513 0.364768
\(597\) −21.0135 −0.860024
\(598\) −43.1653 −1.76516
\(599\) −21.8347 −0.892140 −0.446070 0.894998i \(-0.647177\pi\)
−0.446070 + 0.894998i \(0.647177\pi\)
\(600\) −2.41316 −0.0985168
\(601\) −37.4782 −1.52877 −0.764383 0.644762i \(-0.776956\pi\)
−0.764383 + 0.644762i \(0.776956\pi\)
\(602\) 5.00890 0.204147
\(603\) 22.6531 0.922506
\(604\) −13.8455 −0.563364
\(605\) 1.00000 0.0406558
\(606\) −26.8632 −1.09124
\(607\) −17.2676 −0.700869 −0.350435 0.936587i \(-0.613966\pi\)
−0.350435 + 0.936587i \(0.613966\pi\)
\(608\) 3.51382 0.142504
\(609\) 93.6298 3.79407
\(610\) −1.82530 −0.0739043
\(611\) −6.25153 −0.252910
\(612\) −7.57294 −0.306118
\(613\) −34.8338 −1.40692 −0.703461 0.710734i \(-0.748363\pi\)
−0.703461 + 0.710734i \(0.748363\pi\)
\(614\) −30.2823 −1.22210
\(615\) 9.42097 0.379890
\(616\) 5.00890 0.201814
\(617\) −2.11051 −0.0849657 −0.0424829 0.999097i \(-0.513527\pi\)
−0.0424829 + 0.999097i \(0.513527\pi\)
\(618\) 20.8600 0.839112
\(619\) −38.1171 −1.53206 −0.766028 0.642807i \(-0.777770\pi\)
−0.766028 + 0.642807i \(0.777770\pi\)
\(620\) 7.62662 0.306292
\(621\) −2.58094 −0.103570
\(622\) 25.0684 1.00515
\(623\) 46.8726 1.87791
\(624\) 17.2060 0.688791
\(625\) 1.00000 0.0400000
\(626\) 23.4292 0.936420
\(627\) −8.47940 −0.338635
\(628\) −1.35382 −0.0540234
\(629\) −10.2964 −0.410544
\(630\) 14.1418 0.563423
\(631\) 1.36200 0.0542205 0.0271102 0.999632i \(-0.491369\pi\)
0.0271102 + 0.999632i \(0.491369\pi\)
\(632\) −10.0241 −0.398739
\(633\) 51.8120 2.05934
\(634\) 10.6997 0.424937
\(635\) 1.54738 0.0614060
\(636\) −4.38417 −0.173844
\(637\) 128.976 5.11022
\(638\) 7.74615 0.306673
\(639\) 25.1130 0.993456
\(640\) −1.00000 −0.0395285
\(641\) 43.8228 1.73090 0.865449 0.500997i \(-0.167033\pi\)
0.865449 + 0.500997i \(0.167033\pi\)
\(642\) −37.3508 −1.47412
\(643\) 8.56830 0.337901 0.168950 0.985625i \(-0.445962\pi\)
0.168950 + 0.985625i \(0.445962\pi\)
\(644\) −30.3238 −1.19493
\(645\) 2.41316 0.0950180
\(646\) −9.42500 −0.370822
\(647\) −1.02232 −0.0401915 −0.0200958 0.999798i \(-0.506397\pi\)
−0.0200958 + 0.999798i \(0.506397\pi\)
\(648\) 9.49878 0.373148
\(649\) 1.02302 0.0401572
\(650\) −7.13007 −0.279664
\(651\) −92.1850 −3.61301
\(652\) 14.2012 0.556161
\(653\) 36.1755 1.41566 0.707829 0.706384i \(-0.249675\pi\)
0.707829 + 0.706384i \(0.249675\pi\)
\(654\) −13.1207 −0.513060
\(655\) −14.1171 −0.551599
\(656\) 3.90400 0.152426
\(657\) −4.76662 −0.185964
\(658\) −4.39172 −0.171207
\(659\) −11.2549 −0.438430 −0.219215 0.975677i \(-0.570350\pi\)
−0.219215 + 0.975677i \(0.570350\pi\)
\(660\) 2.41316 0.0939321
\(661\) −20.9086 −0.813251 −0.406625 0.913595i \(-0.633295\pi\)
−0.406625 + 0.913595i \(0.633295\pi\)
\(662\) −20.3200 −0.789761
\(663\) −46.1511 −1.79236
\(664\) −7.73554 −0.300197
\(665\) 17.6004 0.682512
\(666\) −10.8379 −0.419960
\(667\) −46.8951 −1.81579
\(668\) 17.1331 0.662898
\(669\) 61.8970 2.39308
\(670\) −8.02353 −0.309976
\(671\) 1.82530 0.0704649
\(672\) 12.0873 0.466276
\(673\) 5.90228 0.227516 0.113758 0.993508i \(-0.463711\pi\)
0.113758 + 0.993508i \(0.463711\pi\)
\(674\) −9.75296 −0.375670
\(675\) −0.426321 −0.0164091
\(676\) 37.8379 1.45530
\(677\) −33.8782 −1.30205 −0.651023 0.759058i \(-0.725660\pi\)
−0.651023 + 0.759058i \(0.725660\pi\)
\(678\) −16.5767 −0.636625
\(679\) 59.6005 2.28726
\(680\) 2.68227 0.102860
\(681\) 43.7095 1.67495
\(682\) −7.62662 −0.292038
\(683\) 1.47337 0.0563769 0.0281885 0.999603i \(-0.491026\pi\)
0.0281885 + 0.999603i \(0.491026\pi\)
\(684\) −9.92068 −0.379327
\(685\) 3.23436 0.123579
\(686\) 55.5439 2.12068
\(687\) −65.5765 −2.50190
\(688\) 1.00000 0.0381246
\(689\) −12.9537 −0.493498
\(690\) −14.6092 −0.556164
\(691\) −9.84859 −0.374658 −0.187329 0.982297i \(-0.559983\pi\)
−0.187329 + 0.982297i \(0.559983\pi\)
\(692\) −7.33843 −0.278965
\(693\) −14.1418 −0.537202
\(694\) 27.3345 1.03760
\(695\) −4.86705 −0.184618
\(696\) 18.6927 0.708545
\(697\) −10.4716 −0.396639
\(698\) 16.3076 0.617251
\(699\) 2.10277 0.0795339
\(700\) −5.00890 −0.189319
\(701\) 10.5295 0.397695 0.198848 0.980030i \(-0.436280\pi\)
0.198848 + 0.980030i \(0.436280\pi\)
\(702\) 3.03970 0.114726
\(703\) −13.4884 −0.508726
\(704\) 1.00000 0.0376889
\(705\) −2.11582 −0.0796864
\(706\) −0.703139 −0.0264630
\(707\) −55.7588 −2.09703
\(708\) 2.46872 0.0927801
\(709\) 3.05531 0.114745 0.0573723 0.998353i \(-0.481728\pi\)
0.0573723 + 0.998353i \(0.481728\pi\)
\(710\) −8.89481 −0.333816
\(711\) 28.3015 1.06139
\(712\) 9.35787 0.350701
\(713\) 46.1715 1.72914
\(714\) −32.4213 −1.21334
\(715\) 7.13007 0.266649
\(716\) 20.5062 0.766353
\(717\) −21.9332 −0.819109
\(718\) 12.3095 0.459385
\(719\) −19.4827 −0.726583 −0.363292 0.931676i \(-0.618347\pi\)
−0.363292 + 0.931676i \(0.618347\pi\)
\(720\) 2.82333 0.105219
\(721\) 43.2982 1.61251
\(722\) 6.65308 0.247602
\(723\) −35.3814 −1.31585
\(724\) −10.2191 −0.379790
\(725\) −7.74615 −0.287685
\(726\) −2.41316 −0.0895607
\(727\) 18.5835 0.689226 0.344613 0.938745i \(-0.388010\pi\)
0.344613 + 0.938745i \(0.388010\pi\)
\(728\) 35.7138 1.32364
\(729\) −23.7319 −0.878960
\(730\) 1.68829 0.0624866
\(731\) −2.68227 −0.0992073
\(732\) 4.40474 0.162804
\(733\) −25.6473 −0.947304 −0.473652 0.880712i \(-0.657065\pi\)
−0.473652 + 0.880712i \(0.657065\pi\)
\(734\) 17.8166 0.657623
\(735\) 43.6517 1.61012
\(736\) −6.05399 −0.223153
\(737\) 8.02353 0.295551
\(738\) −11.0223 −0.405737
\(739\) −43.2282 −1.59017 −0.795087 0.606495i \(-0.792575\pi\)
−0.795087 + 0.606495i \(0.792575\pi\)
\(740\) 3.83869 0.141113
\(741\) −60.4587 −2.22101
\(742\) −9.10004 −0.334073
\(743\) −1.53966 −0.0564847 −0.0282423 0.999601i \(-0.508991\pi\)
−0.0282423 + 0.999601i \(0.508991\pi\)
\(744\) −18.4042 −0.674732
\(745\) 8.90513 0.326259
\(746\) 17.9785 0.658241
\(747\) 21.8400 0.799085
\(748\) −2.68227 −0.0980735
\(749\) −77.5275 −2.83279
\(750\) −2.41316 −0.0881161
\(751\) −35.2472 −1.28619 −0.643094 0.765787i \(-0.722349\pi\)
−0.643094 + 0.765787i \(0.722349\pi\)
\(752\) −0.876784 −0.0319730
\(753\) −4.35941 −0.158866
\(754\) 55.2306 2.01138
\(755\) −13.8455 −0.503888
\(756\) 2.13540 0.0776637
\(757\) 28.8163 1.04735 0.523673 0.851919i \(-0.324561\pi\)
0.523673 + 0.851919i \(0.324561\pi\)
\(758\) −37.0463 −1.34558
\(759\) 14.6092 0.530282
\(760\) 3.51382 0.127460
\(761\) −38.3711 −1.39095 −0.695476 0.718549i \(-0.744806\pi\)
−0.695476 + 0.718549i \(0.744806\pi\)
\(762\) −3.73408 −0.135272
\(763\) −27.2341 −0.985940
\(764\) 8.94039 0.323452
\(765\) −7.57294 −0.273800
\(766\) 10.1265 0.365886
\(767\) 7.29423 0.263379
\(768\) 2.41316 0.0870774
\(769\) 22.5187 0.812044 0.406022 0.913863i \(-0.366916\pi\)
0.406022 + 0.913863i \(0.366916\pi\)
\(770\) 5.00890 0.180508
\(771\) −27.8467 −1.00288
\(772\) 23.5154 0.846339
\(773\) −33.3659 −1.20009 −0.600044 0.799967i \(-0.704850\pi\)
−0.600044 + 0.799967i \(0.704850\pi\)
\(774\) −2.82333 −0.101483
\(775\) 7.62662 0.273956
\(776\) 11.8989 0.427147
\(777\) −46.3992 −1.66456
\(778\) 29.9366 1.07328
\(779\) −13.7179 −0.491497
\(780\) 17.2060 0.616073
\(781\) 8.89481 0.318281
\(782\) 16.2384 0.580685
\(783\) 3.30235 0.118016
\(784\) 18.0890 0.646037
\(785\) −1.35382 −0.0483200
\(786\) 34.0667 1.21512
\(787\) −38.9605 −1.38879 −0.694396 0.719593i \(-0.744328\pi\)
−0.694396 + 0.719593i \(0.744328\pi\)
\(788\) −0.533015 −0.0189879
\(789\) 35.9367 1.27938
\(790\) −10.0241 −0.356643
\(791\) −34.4076 −1.22339
\(792\) −2.82333 −0.100323
\(793\) 13.0145 0.462159
\(794\) −30.8013 −1.09310
\(795\) −4.38417 −0.155490
\(796\) −8.70787 −0.308642
\(797\) −20.8370 −0.738084 −0.369042 0.929413i \(-0.620314\pi\)
−0.369042 + 0.929413i \(0.620314\pi\)
\(798\) −42.4724 −1.50351
\(799\) 2.35177 0.0831997
\(800\) −1.00000 −0.0353553
\(801\) −26.4204 −0.933519
\(802\) −22.3222 −0.788223
\(803\) −1.68829 −0.0595786
\(804\) 19.3621 0.682847
\(805\) −30.3238 −1.06877
\(806\) −54.3783 −1.91539
\(807\) −28.9507 −1.01911
\(808\) −11.1320 −0.391621
\(809\) 15.6011 0.548506 0.274253 0.961658i \(-0.411569\pi\)
0.274253 + 0.961658i \(0.411569\pi\)
\(810\) 9.49878 0.333753
\(811\) −36.8109 −1.29260 −0.646302 0.763081i \(-0.723686\pi\)
−0.646302 + 0.763081i \(0.723686\pi\)
\(812\) 38.7997 1.36160
\(813\) −20.6385 −0.723825
\(814\) −3.83869 −0.134546
\(815\) 14.2012 0.497446
\(816\) −6.47274 −0.226591
\(817\) −3.51382 −0.122933
\(818\) −32.8009 −1.14686
\(819\) −100.832 −3.52335
\(820\) 3.90400 0.136334
\(821\) −3.04007 −0.106099 −0.0530495 0.998592i \(-0.516894\pi\)
−0.0530495 + 0.998592i \(0.516894\pi\)
\(822\) −7.80503 −0.272232
\(823\) −36.5627 −1.27450 −0.637248 0.770659i \(-0.719927\pi\)
−0.637248 + 0.770659i \(0.719927\pi\)
\(824\) 8.64427 0.301137
\(825\) 2.41316 0.0840154
\(826\) 5.12422 0.178294
\(827\) 8.76539 0.304802 0.152401 0.988319i \(-0.451299\pi\)
0.152401 + 0.988319i \(0.451299\pi\)
\(828\) 17.0924 0.594003
\(829\) −35.6384 −1.23777 −0.618887 0.785480i \(-0.712416\pi\)
−0.618887 + 0.785480i \(0.712416\pi\)
\(830\) −7.73554 −0.268505
\(831\) −6.31413 −0.219035
\(832\) 7.13007 0.247191
\(833\) −48.5197 −1.68111
\(834\) 11.7450 0.406695
\(835\) 17.1331 0.592914
\(836\) −3.51382 −0.121528
\(837\) −3.25139 −0.112384
\(838\) 28.5131 0.984970
\(839\) 25.0754 0.865698 0.432849 0.901467i \(-0.357508\pi\)
0.432849 + 0.901467i \(0.357508\pi\)
\(840\) 12.0873 0.417050
\(841\) 31.0029 1.06906
\(842\) −28.9496 −0.997668
\(843\) −27.4787 −0.946416
\(844\) 21.4706 0.739050
\(845\) 37.8379 1.30166
\(846\) 2.47546 0.0851079
\(847\) −5.00890 −0.172108
\(848\) −1.81678 −0.0623883
\(849\) 57.0776 1.95890
\(850\) 2.68227 0.0920011
\(851\) 23.2394 0.796635
\(852\) 21.4646 0.735365
\(853\) 12.7351 0.436041 0.218020 0.975944i \(-0.430040\pi\)
0.218020 + 0.975944i \(0.430040\pi\)
\(854\) 9.14274 0.312858
\(855\) −9.92068 −0.339280
\(856\) −15.4780 −0.529026
\(857\) −2.74444 −0.0937484 −0.0468742 0.998901i \(-0.514926\pi\)
−0.0468742 + 0.998901i \(0.514926\pi\)
\(858\) −17.2060 −0.587403
\(859\) −10.8500 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(860\) 1.00000 0.0340997
\(861\) −47.1887 −1.60819
\(862\) 20.9481 0.713494
\(863\) 42.9042 1.46048 0.730238 0.683193i \(-0.239409\pi\)
0.730238 + 0.683193i \(0.239409\pi\)
\(864\) 0.426321 0.0145037
\(865\) −7.33843 −0.249514
\(866\) 2.69386 0.0915410
\(867\) −23.6621 −0.803606
\(868\) −38.2010 −1.29662
\(869\) 10.0241 0.340045
\(870\) 18.6927 0.633742
\(871\) 57.2083 1.93843
\(872\) −5.43714 −0.184125
\(873\) −33.5946 −1.13701
\(874\) 21.2726 0.719557
\(875\) −5.00890 −0.169332
\(876\) −4.07412 −0.137652
\(877\) 34.6807 1.17109 0.585543 0.810642i \(-0.300881\pi\)
0.585543 + 0.810642i \(0.300881\pi\)
\(878\) −39.6125 −1.33686
\(879\) −22.5914 −0.761989
\(880\) 1.00000 0.0337100
\(881\) 8.45493 0.284854 0.142427 0.989805i \(-0.454509\pi\)
0.142427 + 0.989805i \(0.454509\pi\)
\(882\) −51.0714 −1.71966
\(883\) 30.2302 1.01733 0.508664 0.860965i \(-0.330139\pi\)
0.508664 + 0.860965i \(0.330139\pi\)
\(884\) −19.1248 −0.643235
\(885\) 2.46872 0.0829851
\(886\) −9.40525 −0.315976
\(887\) 49.6709 1.66779 0.833893 0.551926i \(-0.186107\pi\)
0.833893 + 0.551926i \(0.186107\pi\)
\(888\) −9.26336 −0.310858
\(889\) −7.75068 −0.259950
\(890\) 9.35787 0.313676
\(891\) −9.49878 −0.318221
\(892\) 25.6498 0.858819
\(893\) 3.08086 0.103097
\(894\) −21.4895 −0.718716
\(895\) 20.5062 0.685447
\(896\) 5.00890 0.167335
\(897\) 104.165 3.47796
\(898\) 38.2727 1.27718
\(899\) −59.0770 −1.97033
\(900\) 2.82333 0.0941112
\(901\) 4.87308 0.162346
\(902\) −3.90400 −0.129989
\(903\) −12.0873 −0.402239
\(904\) −6.86930 −0.228470
\(905\) −10.2191 −0.339694
\(906\) 33.4113 1.11002
\(907\) 8.18916 0.271917 0.135958 0.990715i \(-0.456589\pi\)
0.135958 + 0.990715i \(0.456589\pi\)
\(908\) 18.1130 0.601100
\(909\) 31.4293 1.04244
\(910\) 35.7138 1.18390
\(911\) −24.0013 −0.795199 −0.397600 0.917559i \(-0.630157\pi\)
−0.397600 + 0.917559i \(0.630157\pi\)
\(912\) −8.47940 −0.280781
\(913\) 7.73554 0.256009
\(914\) −13.7202 −0.453823
\(915\) 4.40474 0.145616
\(916\) −27.1746 −0.897873
\(917\) 70.7109 2.33508
\(918\) −1.14351 −0.0377414
\(919\) −36.7718 −1.21299 −0.606496 0.795087i \(-0.707425\pi\)
−0.606496 + 0.795087i \(0.707425\pi\)
\(920\) −6.05399 −0.199594
\(921\) 73.0761 2.40794
\(922\) 15.7395 0.518354
\(923\) 63.4206 2.08751
\(924\) −12.0873 −0.397642
\(925\) 3.83869 0.126215
\(926\) −10.4522 −0.343480
\(927\) −24.4057 −0.801587
\(928\) 7.74615 0.254280
\(929\) −30.6815 −1.00663 −0.503314 0.864104i \(-0.667886\pi\)
−0.503314 + 0.864104i \(0.667886\pi\)
\(930\) −18.4042 −0.603499
\(931\) −63.5616 −2.08315
\(932\) 0.871375 0.0285428
\(933\) −60.4941 −1.98049
\(934\) −32.0595 −1.04902
\(935\) −2.68227 −0.0877196
\(936\) −20.1306 −0.657988
\(937\) 53.5103 1.74810 0.874052 0.485832i \(-0.161483\pi\)
0.874052 + 0.485832i \(0.161483\pi\)
\(938\) 40.1890 1.31222
\(939\) −56.5384 −1.84506
\(940\) −0.876784 −0.0285976
\(941\) −47.9431 −1.56290 −0.781450 0.623968i \(-0.785519\pi\)
−0.781450 + 0.623968i \(0.785519\pi\)
\(942\) 3.26699 0.106444
\(943\) 23.6348 0.769654
\(944\) 1.02302 0.0332966
\(945\) 2.13540 0.0694645
\(946\) −1.00000 −0.0325128
\(947\) 7.10057 0.230738 0.115369 0.993323i \(-0.463195\pi\)
0.115369 + 0.993323i \(0.463195\pi\)
\(948\) 24.1898 0.785649
\(949\) −12.0377 −0.390759
\(950\) 3.51382 0.114003
\(951\) −25.8200 −0.837270
\(952\) −13.4352 −0.435438
\(953\) −31.9647 −1.03544 −0.517719 0.855550i \(-0.673219\pi\)
−0.517719 + 0.855550i \(0.673219\pi\)
\(954\) 5.12937 0.166069
\(955\) 8.94039 0.289304
\(956\) −9.08899 −0.293959
\(957\) −18.6927 −0.604249
\(958\) 0.619319 0.0200093
\(959\) −16.2006 −0.523144
\(960\) 2.41316 0.0778844
\(961\) 27.1653 0.876301
\(962\) −27.3701 −0.882447
\(963\) 43.6995 1.40820
\(964\) −14.6619 −0.472227
\(965\) 23.5154 0.756989
\(966\) 73.1762 2.35440
\(967\) −19.1061 −0.614411 −0.307206 0.951643i \(-0.599394\pi\)
−0.307206 + 0.951643i \(0.599394\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 22.7440 0.730644
\(970\) 11.8989 0.382051
\(971\) −38.7112 −1.24230 −0.621150 0.783692i \(-0.713334\pi\)
−0.621150 + 0.783692i \(0.713334\pi\)
\(972\) −21.6431 −0.694203
\(973\) 24.3785 0.781540
\(974\) −24.5740 −0.787402
\(975\) 17.2060 0.551033
\(976\) 1.82530 0.0584264
\(977\) −2.58123 −0.0825807 −0.0412904 0.999147i \(-0.513147\pi\)
−0.0412904 + 0.999147i \(0.513147\pi\)
\(978\) −34.2697 −1.09582
\(979\) −9.35787 −0.299079
\(980\) 18.0890 0.577833
\(981\) 15.3509 0.490116
\(982\) 3.57682 0.114141
\(983\) −35.2738 −1.12506 −0.562530 0.826777i \(-0.690172\pi\)
−0.562530 + 0.826777i \(0.690172\pi\)
\(984\) −9.42097 −0.300330
\(985\) −0.533015 −0.0169833
\(986\) −20.7773 −0.661683
\(987\) 10.5979 0.337336
\(988\) −25.0538 −0.797066
\(989\) 6.05399 0.192506
\(990\) −2.82333 −0.0897315
\(991\) −51.7141 −1.64275 −0.821376 0.570387i \(-0.806793\pi\)
−0.821376 + 0.570387i \(0.806793\pi\)
\(992\) −7.62662 −0.242145
\(993\) 49.0355 1.55609
\(994\) 44.5532 1.41314
\(995\) −8.70787 −0.276058
\(996\) 18.6671 0.591489
\(997\) 6.87510 0.217736 0.108868 0.994056i \(-0.465277\pi\)
0.108868 + 0.994056i \(0.465277\pi\)
\(998\) −9.76592 −0.309135
\(999\) −1.63651 −0.0517770
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4730.2.a.z.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.z.1.7 10 1.1 even 1 trivial