Properties

Label 4026.2.a.u.1.5
Level 4026
Weight 2
Character 4026.1
Self dual yes
Analytic conductor 32.148
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.9176805.1
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 1.5
Root \(-2.48204\) of \(x^{5} - x^{4} - 12 x^{3} + 7 x^{2} + 30 x - 20\)
Character \(\chi\) \(=\) 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48204 q^{5} -1.00000 q^{6} +1.57766 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.48204 q^{5} -1.00000 q^{6} +1.57766 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.48204 q^{10} -1.00000 q^{11} +1.00000 q^{12} -4.97551 q^{13} -1.57766 q^{14} +2.48204 q^{15} +1.00000 q^{16} +7.22020 q^{17} -1.00000 q^{18} +5.46325 q^{19} +2.48204 q^{20} +1.57766 q^{21} +1.00000 q^{22} -1.75531 q^{23} -1.00000 q^{24} +1.16050 q^{25} +4.97551 q^{26} +1.00000 q^{27} +1.57766 q^{28} +2.32153 q^{29} -2.48204 q^{30} -2.23734 q^{31} -1.00000 q^{32} -1.00000 q^{33} -7.22020 q^{34} +3.91581 q^{35} +1.00000 q^{36} +3.65450 q^{37} -5.46325 q^{38} -4.97551 q^{39} -2.48204 q^{40} -0.0841890 q^{41} -1.57766 q^{42} +3.92316 q^{43} -1.00000 q^{44} +2.48204 q^{45} +1.75531 q^{46} -5.61805 q^{47} +1.00000 q^{48} -4.51099 q^{49} -1.16050 q^{50} +7.22020 q^{51} -4.97551 q^{52} +0.738164 q^{53} -1.00000 q^{54} -2.48204 q^{55} -1.57766 q^{56} +5.46325 q^{57} -2.32153 q^{58} +6.61123 q^{59} +2.48204 q^{60} -1.00000 q^{61} +2.23734 q^{62} +1.57766 q^{63} +1.00000 q^{64} -12.3494 q^{65} +1.00000 q^{66} +7.08992 q^{67} +7.22020 q^{68} -1.75531 q^{69} -3.91581 q^{70} +1.20142 q^{71} -1.00000 q^{72} +12.1189 q^{73} -3.65450 q^{74} +1.16050 q^{75} +5.46325 q^{76} -1.57766 q^{77} +4.97551 q^{78} +10.4861 q^{79} +2.48204 q^{80} +1.00000 q^{81} +0.0841890 q^{82} +0.359100 q^{83} +1.57766 q^{84} +17.9208 q^{85} -3.92316 q^{86} +2.32153 q^{87} +1.00000 q^{88} +4.63572 q^{89} -2.48204 q^{90} -7.84966 q^{91} -1.75531 q^{92} -2.23734 q^{93} +5.61805 q^{94} +13.5600 q^{95} -1.00000 q^{96} +5.94529 q^{97} +4.51099 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + O(q^{10}) \) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + q^{10} - 5q^{11} + 5q^{12} + 2q^{13} + 3q^{14} - q^{15} + 5q^{16} + 6q^{17} - 5q^{18} + 7q^{19} - q^{20} - 3q^{21} + 5q^{22} - 12q^{23} - 5q^{24} - 2q^{26} + 5q^{27} - 3q^{28} + 4q^{29} + q^{30} - q^{31} - 5q^{32} - 5q^{33} - 6q^{34} + 17q^{35} + 5q^{36} + 3q^{37} - 7q^{38} + 2q^{39} + q^{40} - 3q^{41} + 3q^{42} + 24q^{43} - 5q^{44} - q^{45} + 12q^{46} + 18q^{47} + 5q^{48} + 26q^{49} + 6q^{51} + 2q^{52} - 13q^{53} - 5q^{54} + q^{55} + 3q^{56} + 7q^{57} - 4q^{58} - 16q^{59} - q^{60} - 5q^{61} + q^{62} - 3q^{63} + 5q^{64} + 4q^{65} + 5q^{66} + 18q^{67} + 6q^{68} - 12q^{69} - 17q^{70} - 31q^{71} - 5q^{72} + 8q^{73} - 3q^{74} + 7q^{76} + 3q^{77} - 2q^{78} + 32q^{79} - q^{80} + 5q^{81} + 3q^{82} + 8q^{83} - 3q^{84} + 29q^{85} - 24q^{86} + 4q^{87} + 5q^{88} + q^{89} + q^{90} - 3q^{91} - 12q^{92} - q^{93} - 18q^{94} + 33q^{95} - 5q^{96} - 4q^{97} - 26q^{98} - 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 2.48204 1.11000 0.555000 0.831850i \(-0.312718\pi\)
0.555000 + 0.831850i \(0.312718\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.57766 0.596300 0.298150 0.954519i \(-0.403630\pi\)
0.298150 + 0.954519i \(0.403630\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.48204 −0.784889
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) −4.97551 −1.37996 −0.689979 0.723830i \(-0.742380\pi\)
−0.689979 + 0.723830i \(0.742380\pi\)
\(14\) −1.57766 −0.421648
\(15\) 2.48204 0.640859
\(16\) 1.00000 0.250000
\(17\) 7.22020 1.75116 0.875578 0.483077i \(-0.160481\pi\)
0.875578 + 0.483077i \(0.160481\pi\)
\(18\) −1.00000 −0.235702
\(19\) 5.46325 1.25336 0.626678 0.779278i \(-0.284414\pi\)
0.626678 + 0.779278i \(0.284414\pi\)
\(20\) 2.48204 0.555000
\(21\) 1.57766 0.344274
\(22\) 1.00000 0.213201
\(23\) −1.75531 −0.366007 −0.183004 0.983112i \(-0.558582\pi\)
−0.183004 + 0.983112i \(0.558582\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.16050 0.232101
\(26\) 4.97551 0.975777
\(27\) 1.00000 0.192450
\(28\) 1.57766 0.298150
\(29\) 2.32153 0.431098 0.215549 0.976493i \(-0.430846\pi\)
0.215549 + 0.976493i \(0.430846\pi\)
\(30\) −2.48204 −0.453156
\(31\) −2.23734 −0.401839 −0.200919 0.979608i \(-0.564393\pi\)
−0.200919 + 0.979608i \(0.564393\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) −7.22020 −1.23825
\(35\) 3.91581 0.661893
\(36\) 1.00000 0.166667
\(37\) 3.65450 0.600796 0.300398 0.953814i \(-0.402880\pi\)
0.300398 + 0.953814i \(0.402880\pi\)
\(38\) −5.46325 −0.886257
\(39\) −4.97551 −0.796719
\(40\) −2.48204 −0.392444
\(41\) −0.0841890 −0.0131481 −0.00657406 0.999978i \(-0.502093\pi\)
−0.00657406 + 0.999978i \(0.502093\pi\)
\(42\) −1.57766 −0.243438
\(43\) 3.92316 0.598276 0.299138 0.954210i \(-0.403301\pi\)
0.299138 + 0.954210i \(0.403301\pi\)
\(44\) −1.00000 −0.150756
\(45\) 2.48204 0.370000
\(46\) 1.75531 0.258806
\(47\) −5.61805 −0.819476 −0.409738 0.912203i \(-0.634380\pi\)
−0.409738 + 0.912203i \(0.634380\pi\)
\(48\) 1.00000 0.144338
\(49\) −4.51099 −0.644427
\(50\) −1.16050 −0.164120
\(51\) 7.22020 1.01103
\(52\) −4.97551 −0.689979
\(53\) 0.738164 0.101395 0.0506973 0.998714i \(-0.483856\pi\)
0.0506973 + 0.998714i \(0.483856\pi\)
\(54\) −1.00000 −0.136083
\(55\) −2.48204 −0.334678
\(56\) −1.57766 −0.210824
\(57\) 5.46325 0.723625
\(58\) −2.32153 −0.304832
\(59\) 6.61123 0.860708 0.430354 0.902660i \(-0.358389\pi\)
0.430354 + 0.902660i \(0.358389\pi\)
\(60\) 2.48204 0.320429
\(61\) −1.00000 −0.128037
\(62\) 2.23734 0.284143
\(63\) 1.57766 0.198767
\(64\) 1.00000 0.125000
\(65\) −12.3494 −1.53175
\(66\) 1.00000 0.123091
\(67\) 7.08992 0.866171 0.433086 0.901353i \(-0.357425\pi\)
0.433086 + 0.901353i \(0.357425\pi\)
\(68\) 7.22020 0.875578
\(69\) −1.75531 −0.211314
\(70\) −3.91581 −0.468029
\(71\) 1.20142 0.142582 0.0712909 0.997456i \(-0.477288\pi\)
0.0712909 + 0.997456i \(0.477288\pi\)
\(72\) −1.00000 −0.117851
\(73\) 12.1189 1.41841 0.709203 0.705004i \(-0.249055\pi\)
0.709203 + 0.705004i \(0.249055\pi\)
\(74\) −3.65450 −0.424827
\(75\) 1.16050 0.134003
\(76\) 5.46325 0.626678
\(77\) −1.57766 −0.179791
\(78\) 4.97551 0.563365
\(79\) 10.4861 1.17978 0.589891 0.807483i \(-0.299171\pi\)
0.589891 + 0.807483i \(0.299171\pi\)
\(80\) 2.48204 0.277500
\(81\) 1.00000 0.111111
\(82\) 0.0841890 0.00929712
\(83\) 0.359100 0.0394164 0.0197082 0.999806i \(-0.493726\pi\)
0.0197082 + 0.999806i \(0.493726\pi\)
\(84\) 1.57766 0.172137
\(85\) 17.9208 1.94378
\(86\) −3.92316 −0.423045
\(87\) 2.32153 0.248894
\(88\) 1.00000 0.106600
\(89\) 4.63572 0.491385 0.245693 0.969348i \(-0.420985\pi\)
0.245693 + 0.969348i \(0.420985\pi\)
\(90\) −2.48204 −0.261630
\(91\) −7.84966 −0.822868
\(92\) −1.75531 −0.183004
\(93\) −2.23734 −0.232002
\(94\) 5.61805 0.579457
\(95\) 13.5600 1.39123
\(96\) −1.00000 −0.102062
\(97\) 5.94529 0.603653 0.301826 0.953363i \(-0.402404\pi\)
0.301826 + 0.953363i \(0.402404\pi\)
\(98\) 4.51099 0.455678
\(99\) −1.00000 −0.100504
\(100\) 1.16050 0.116050
\(101\) −12.6243 −1.25616 −0.628082 0.778147i \(-0.716160\pi\)
−0.628082 + 0.778147i \(0.716160\pi\)
\(102\) −7.22020 −0.714906
\(103\) 10.1900 1.00405 0.502024 0.864854i \(-0.332589\pi\)
0.502024 + 0.864854i \(0.332589\pi\)
\(104\) 4.97551 0.487889
\(105\) 3.91581 0.382144
\(106\) −0.738164 −0.0716968
\(107\) −1.35801 −0.131283 −0.0656417 0.997843i \(-0.520909\pi\)
−0.0656417 + 0.997843i \(0.520909\pi\)
\(108\) 1.00000 0.0962250
\(109\) 6.58337 0.630572 0.315286 0.948997i \(-0.397899\pi\)
0.315286 + 0.948997i \(0.397899\pi\)
\(110\) 2.48204 0.236653
\(111\) 3.65450 0.346870
\(112\) 1.57766 0.149075
\(113\) −4.58448 −0.431272 −0.215636 0.976474i \(-0.569182\pi\)
−0.215636 + 0.976474i \(0.569182\pi\)
\(114\) −5.46325 −0.511680
\(115\) −4.35674 −0.406268
\(116\) 2.32153 0.215549
\(117\) −4.97551 −0.459986
\(118\) −6.61123 −0.608613
\(119\) 11.3910 1.04421
\(120\) −2.48204 −0.226578
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) −0.0841890 −0.00759107
\(124\) −2.23734 −0.200919
\(125\) −9.52977 −0.852369
\(126\) −1.57766 −0.140549
\(127\) −6.83090 −0.606144 −0.303072 0.952968i \(-0.598012\pi\)
−0.303072 + 0.952968i \(0.598012\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.92316 0.345415
\(130\) 12.3494 1.08311
\(131\) 6.39323 0.558579 0.279290 0.960207i \(-0.409901\pi\)
0.279290 + 0.960207i \(0.409901\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 8.61916 0.747376
\(134\) −7.08992 −0.612475
\(135\) 2.48204 0.213620
\(136\) −7.22020 −0.619127
\(137\) −2.37624 −0.203016 −0.101508 0.994835i \(-0.532367\pi\)
−0.101508 + 0.994835i \(0.532367\pi\)
\(138\) 1.75531 0.149422
\(139\) 6.12294 0.519341 0.259670 0.965697i \(-0.416386\pi\)
0.259670 + 0.965697i \(0.416386\pi\)
\(140\) 3.91581 0.330946
\(141\) −5.61805 −0.473125
\(142\) −1.20142 −0.100821
\(143\) 4.97551 0.416073
\(144\) 1.00000 0.0833333
\(145\) 5.76213 0.478519
\(146\) −12.1189 −1.00296
\(147\) −4.51099 −0.372060
\(148\) 3.65450 0.300398
\(149\) 14.0581 1.15168 0.575841 0.817562i \(-0.304675\pi\)
0.575841 + 0.817562i \(0.304675\pi\)
\(150\) −1.16050 −0.0947547
\(151\) −10.2538 −0.834440 −0.417220 0.908806i \(-0.636995\pi\)
−0.417220 + 0.908806i \(0.636995\pi\)
\(152\) −5.46325 −0.443128
\(153\) 7.22020 0.583719
\(154\) 1.57766 0.127132
\(155\) −5.55317 −0.446041
\(156\) −4.97551 −0.398359
\(157\) −8.82517 −0.704325 −0.352163 0.935939i \(-0.614554\pi\)
−0.352163 + 0.935939i \(0.614554\pi\)
\(158\) −10.4861 −0.834231
\(159\) 0.738164 0.0585402
\(160\) −2.48204 −0.196222
\(161\) −2.76928 −0.218250
\(162\) −1.00000 −0.0785674
\(163\) −11.7260 −0.918452 −0.459226 0.888320i \(-0.651873\pi\)
−0.459226 + 0.888320i \(0.651873\pi\)
\(164\) −0.0841890 −0.00657406
\(165\) −2.48204 −0.193226
\(166\) −0.359100 −0.0278716
\(167\) 3.73191 0.288784 0.144392 0.989521i \(-0.453877\pi\)
0.144392 + 0.989521i \(0.453877\pi\)
\(168\) −1.57766 −0.121719
\(169\) 11.7557 0.904283
\(170\) −17.9208 −1.37446
\(171\) 5.46325 0.417785
\(172\) 3.92316 0.299138
\(173\) −15.7364 −1.19641 −0.598207 0.801342i \(-0.704120\pi\)
−0.598207 + 0.801342i \(0.704120\pi\)
\(174\) −2.32153 −0.175995
\(175\) 1.83088 0.138402
\(176\) −1.00000 −0.0753778
\(177\) 6.61123 0.496930
\(178\) −4.63572 −0.347462
\(179\) −13.1480 −0.982726 −0.491363 0.870955i \(-0.663501\pi\)
−0.491363 + 0.870955i \(0.663501\pi\)
\(180\) 2.48204 0.185000
\(181\) −23.7767 −1.76731 −0.883655 0.468139i \(-0.844925\pi\)
−0.883655 + 0.468139i \(0.844925\pi\)
\(182\) 7.84966 0.581856
\(183\) −1.00000 −0.0739221
\(184\) 1.75531 0.129403
\(185\) 9.07061 0.666884
\(186\) 2.23734 0.164050
\(187\) −7.22020 −0.527993
\(188\) −5.61805 −0.409738
\(189\) 1.57766 0.114758
\(190\) −13.5600 −0.983745
\(191\) −22.9311 −1.65924 −0.829619 0.558329i \(-0.811443\pi\)
−0.829619 + 0.558329i \(0.811443\pi\)
\(192\) 1.00000 0.0721688
\(193\) 15.2772 1.09967 0.549837 0.835272i \(-0.314690\pi\)
0.549837 + 0.835272i \(0.314690\pi\)
\(194\) −5.94529 −0.426847
\(195\) −12.3494 −0.884358
\(196\) −4.51099 −0.322213
\(197\) −9.38641 −0.668754 −0.334377 0.942439i \(-0.608526\pi\)
−0.334377 + 0.942439i \(0.608526\pi\)
\(198\) 1.00000 0.0710669
\(199\) 11.3483 0.804461 0.402230 0.915538i \(-0.368235\pi\)
0.402230 + 0.915538i \(0.368235\pi\)
\(200\) −1.16050 −0.0820600
\(201\) 7.08992 0.500084
\(202\) 12.6243 0.888243
\(203\) 3.66259 0.257064
\(204\) 7.22020 0.505515
\(205\) −0.208960 −0.0145944
\(206\) −10.1900 −0.709970
\(207\) −1.75531 −0.122002
\(208\) −4.97551 −0.344989
\(209\) −5.46325 −0.377901
\(210\) −3.91581 −0.270217
\(211\) 19.7222 1.35773 0.678866 0.734262i \(-0.262472\pi\)
0.678866 + 0.734262i \(0.262472\pi\)
\(212\) 0.738164 0.0506973
\(213\) 1.20142 0.0823197
\(214\) 1.35801 0.0928314
\(215\) 9.73742 0.664087
\(216\) −1.00000 −0.0680414
\(217\) −3.52977 −0.239616
\(218\) −6.58337 −0.445882
\(219\) 12.1189 0.818917
\(220\) −2.48204 −0.167339
\(221\) −35.9242 −2.41652
\(222\) −3.65450 −0.245274
\(223\) −12.0039 −0.803843 −0.401921 0.915674i \(-0.631657\pi\)
−0.401921 + 0.915674i \(0.631657\pi\)
\(224\) −1.57766 −0.105412
\(225\) 1.16050 0.0773669
\(226\) 4.58448 0.304955
\(227\) 3.72526 0.247254 0.123627 0.992329i \(-0.460547\pi\)
0.123627 + 0.992329i \(0.460547\pi\)
\(228\) 5.46325 0.361813
\(229\) 23.6720 1.56429 0.782146 0.623095i \(-0.214125\pi\)
0.782146 + 0.623095i \(0.214125\pi\)
\(230\) 4.35674 0.287275
\(231\) −1.57766 −0.103802
\(232\) −2.32153 −0.152416
\(233\) −10.8622 −0.711607 −0.355804 0.934561i \(-0.615793\pi\)
−0.355804 + 0.934561i \(0.615793\pi\)
\(234\) 4.97551 0.325259
\(235\) −13.9442 −0.909619
\(236\) 6.61123 0.430354
\(237\) 10.4861 0.681147
\(238\) −11.3910 −0.738371
\(239\) 1.82533 0.118071 0.0590353 0.998256i \(-0.481198\pi\)
0.0590353 + 0.998256i \(0.481198\pi\)
\(240\) 2.48204 0.160215
\(241\) 17.4546 1.12435 0.562176 0.827018i \(-0.309964\pi\)
0.562176 + 0.827018i \(0.309964\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −11.1964 −0.715314
\(246\) 0.0841890 0.00536769
\(247\) −27.1825 −1.72958
\(248\) 2.23734 0.142071
\(249\) 0.359100 0.0227571
\(250\) 9.52977 0.602716
\(251\) 20.2679 1.27930 0.639650 0.768666i \(-0.279079\pi\)
0.639650 + 0.768666i \(0.279079\pi\)
\(252\) 1.57766 0.0993833
\(253\) 1.75531 0.110355
\(254\) 6.83090 0.428609
\(255\) 17.9208 1.12224
\(256\) 1.00000 0.0625000
\(257\) 7.60217 0.474210 0.237105 0.971484i \(-0.423801\pi\)
0.237105 + 0.971484i \(0.423801\pi\)
\(258\) −3.92316 −0.244245
\(259\) 5.76556 0.358255
\(260\) −12.3494 −0.765877
\(261\) 2.32153 0.143699
\(262\) −6.39323 −0.394975
\(263\) 4.33404 0.267248 0.133624 0.991032i \(-0.457338\pi\)
0.133624 + 0.991032i \(0.457338\pi\)
\(264\) 1.00000 0.0615457
\(265\) 1.83215 0.112548
\(266\) −8.61916 −0.528475
\(267\) 4.63572 0.283701
\(268\) 7.08992 0.433086
\(269\) −11.4364 −0.697289 −0.348645 0.937255i \(-0.613358\pi\)
−0.348645 + 0.937255i \(0.613358\pi\)
\(270\) −2.48204 −0.151052
\(271\) 6.09101 0.370002 0.185001 0.982738i \(-0.440771\pi\)
0.185001 + 0.982738i \(0.440771\pi\)
\(272\) 7.22020 0.437789
\(273\) −7.84966 −0.475083
\(274\) 2.37624 0.143554
\(275\) −1.16050 −0.0699810
\(276\) −1.75531 −0.105657
\(277\) 9.24397 0.555416 0.277708 0.960665i \(-0.410425\pi\)
0.277708 + 0.960665i \(0.410425\pi\)
\(278\) −6.12294 −0.367229
\(279\) −2.23734 −0.133946
\(280\) −3.91581 −0.234014
\(281\) 4.42234 0.263815 0.131907 0.991262i \(-0.457890\pi\)
0.131907 + 0.991262i \(0.457890\pi\)
\(282\) 5.61805 0.334550
\(283\) −12.6077 −0.749449 −0.374725 0.927136i \(-0.622263\pi\)
−0.374725 + 0.927136i \(0.622263\pi\)
\(284\) 1.20142 0.0712909
\(285\) 13.5600 0.803224
\(286\) −4.97551 −0.294208
\(287\) −0.132822 −0.00784022
\(288\) −1.00000 −0.0589256
\(289\) 35.1313 2.06655
\(290\) −5.76213 −0.338364
\(291\) 5.94529 0.348519
\(292\) 12.1189 0.709203
\(293\) 5.90312 0.344864 0.172432 0.985021i \(-0.444837\pi\)
0.172432 + 0.985021i \(0.444837\pi\)
\(294\) 4.51099 0.263086
\(295\) 16.4093 0.955386
\(296\) −3.65450 −0.212414
\(297\) −1.00000 −0.0580259
\(298\) −14.0581 −0.814362
\(299\) 8.73355 0.505074
\(300\) 1.16050 0.0670017
\(301\) 6.18941 0.356752
\(302\) 10.2538 0.590038
\(303\) −12.6243 −0.725247
\(304\) 5.46325 0.313339
\(305\) −2.48204 −0.142121
\(306\) −7.22020 −0.412751
\(307\) 18.1342 1.03497 0.517487 0.855691i \(-0.326868\pi\)
0.517487 + 0.855691i \(0.326868\pi\)
\(308\) −1.57766 −0.0898956
\(309\) 10.1900 0.579688
\(310\) 5.55317 0.315399
\(311\) −14.9799 −0.849435 −0.424717 0.905326i \(-0.639627\pi\)
−0.424717 + 0.905326i \(0.639627\pi\)
\(312\) 4.97551 0.281683
\(313\) −12.9832 −0.733855 −0.366928 0.930249i \(-0.619590\pi\)
−0.366928 + 0.930249i \(0.619590\pi\)
\(314\) 8.82517 0.498033
\(315\) 3.91581 0.220631
\(316\) 10.4861 0.589891
\(317\) −29.4666 −1.65501 −0.827505 0.561458i \(-0.810241\pi\)
−0.827505 + 0.561458i \(0.810241\pi\)
\(318\) −0.738164 −0.0413942
\(319\) −2.32153 −0.129981
\(320\) 2.48204 0.138750
\(321\) −1.35801 −0.0757966
\(322\) 2.76928 0.154326
\(323\) 39.4458 2.19482
\(324\) 1.00000 0.0555556
\(325\) −5.77409 −0.320289
\(326\) 11.7260 0.649443
\(327\) 6.58337 0.364061
\(328\) 0.0841890 0.00464856
\(329\) −8.86337 −0.488654
\(330\) 2.48204 0.136632
\(331\) −13.0564 −0.717642 −0.358821 0.933406i \(-0.616821\pi\)
−0.358821 + 0.933406i \(0.616821\pi\)
\(332\) 0.359100 0.0197082
\(333\) 3.65450 0.200265
\(334\) −3.73191 −0.204201
\(335\) 17.5974 0.961450
\(336\) 1.57766 0.0860685
\(337\) 5.16212 0.281199 0.140599 0.990067i \(-0.455097\pi\)
0.140599 + 0.990067i \(0.455097\pi\)
\(338\) −11.7557 −0.639425
\(339\) −4.58448 −0.248995
\(340\) 17.9208 0.971892
\(341\) 2.23734 0.121159
\(342\) −5.46325 −0.295419
\(343\) −18.1604 −0.980571
\(344\) −3.92316 −0.211523
\(345\) −4.35674 −0.234559
\(346\) 15.7364 0.845992
\(347\) 12.2368 0.656905 0.328452 0.944521i \(-0.393473\pi\)
0.328452 + 0.944521i \(0.393473\pi\)
\(348\) 2.32153 0.124447
\(349\) −18.5418 −0.992521 −0.496260 0.868174i \(-0.665294\pi\)
−0.496260 + 0.868174i \(0.665294\pi\)
\(350\) −1.83088 −0.0978647
\(351\) −4.97551 −0.265573
\(352\) 1.00000 0.0533002
\(353\) 1.97315 0.105020 0.0525100 0.998620i \(-0.483278\pi\)
0.0525100 + 0.998620i \(0.483278\pi\)
\(354\) −6.61123 −0.351383
\(355\) 2.98196 0.158266
\(356\) 4.63572 0.245693
\(357\) 11.3910 0.602877
\(358\) 13.1480 0.694892
\(359\) −9.23490 −0.487399 −0.243700 0.969851i \(-0.578361\pi\)
−0.243700 + 0.969851i \(0.578361\pi\)
\(360\) −2.48204 −0.130815
\(361\) 10.8471 0.570901
\(362\) 23.7767 1.24968
\(363\) 1.00000 0.0524864
\(364\) −7.84966 −0.411434
\(365\) 30.0795 1.57443
\(366\) 1.00000 0.0522708
\(367\) 23.3975 1.22134 0.610670 0.791885i \(-0.290900\pi\)
0.610670 + 0.791885i \(0.290900\pi\)
\(368\) −1.75531 −0.0915018
\(369\) −0.0841890 −0.00438270
\(370\) −9.07061 −0.471558
\(371\) 1.16457 0.0604616
\(372\) −2.23734 −0.116001
\(373\) 6.44001 0.333451 0.166726 0.986003i \(-0.446681\pi\)
0.166726 + 0.986003i \(0.446681\pi\)
\(374\) 7.22020 0.373348
\(375\) −9.52977 −0.492115
\(376\) 5.61805 0.289729
\(377\) −11.5508 −0.594897
\(378\) −1.57766 −0.0811461
\(379\) 13.5104 0.693985 0.346992 0.937868i \(-0.387203\pi\)
0.346992 + 0.937868i \(0.387203\pi\)
\(380\) 13.5600 0.695613
\(381\) −6.83090 −0.349958
\(382\) 22.9311 1.17326
\(383\) −16.5203 −0.844146 −0.422073 0.906562i \(-0.638697\pi\)
−0.422073 + 0.906562i \(0.638697\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −3.91581 −0.199568
\(386\) −15.2772 −0.777587
\(387\) 3.92316 0.199425
\(388\) 5.94529 0.301826
\(389\) −11.1952 −0.567617 −0.283809 0.958881i \(-0.591598\pi\)
−0.283809 + 0.958881i \(0.591598\pi\)
\(390\) 12.3494 0.625336
\(391\) −12.6737 −0.640935
\(392\) 4.51099 0.227839
\(393\) 6.39323 0.322496
\(394\) 9.38641 0.472881
\(395\) 26.0269 1.30956
\(396\) −1.00000 −0.0502519
\(397\) −21.6990 −1.08904 −0.544520 0.838748i \(-0.683288\pi\)
−0.544520 + 0.838748i \(0.683288\pi\)
\(398\) −11.3483 −0.568840
\(399\) 8.61916 0.431498
\(400\) 1.16050 0.0580251
\(401\) −18.4153 −0.919618 −0.459809 0.888018i \(-0.652082\pi\)
−0.459809 + 0.888018i \(0.652082\pi\)
\(402\) −7.08992 −0.353613
\(403\) 11.1319 0.554521
\(404\) −12.6243 −0.628082
\(405\) 2.48204 0.123333
\(406\) −3.66259 −0.181771
\(407\) −3.65450 −0.181147
\(408\) −7.22020 −0.357453
\(409\) 4.30492 0.212864 0.106432 0.994320i \(-0.466057\pi\)
0.106432 + 0.994320i \(0.466057\pi\)
\(410\) 0.208960 0.0103198
\(411\) −2.37624 −0.117212
\(412\) 10.1900 0.502024
\(413\) 10.4303 0.513240
\(414\) 1.75531 0.0862687
\(415\) 0.891300 0.0437522
\(416\) 4.97551 0.243944
\(417\) 6.12294 0.299841
\(418\) 5.46325 0.267216
\(419\) −7.35619 −0.359373 −0.179687 0.983724i \(-0.557508\pi\)
−0.179687 + 0.983724i \(0.557508\pi\)
\(420\) 3.91581 0.191072
\(421\) 26.5246 1.29273 0.646365 0.763028i \(-0.276288\pi\)
0.646365 + 0.763028i \(0.276288\pi\)
\(422\) −19.7222 −0.960062
\(423\) −5.61805 −0.273159
\(424\) −0.738164 −0.0358484
\(425\) 8.37906 0.406444
\(426\) −1.20142 −0.0582088
\(427\) −1.57766 −0.0763484
\(428\) −1.35801 −0.0656417
\(429\) 4.97551 0.240220
\(430\) −9.73742 −0.469580
\(431\) 22.2025 1.06946 0.534729 0.845024i \(-0.320414\pi\)
0.534729 + 0.845024i \(0.320414\pi\)
\(432\) 1.00000 0.0481125
\(433\) 16.1513 0.776183 0.388091 0.921621i \(-0.373134\pi\)
0.388091 + 0.921621i \(0.373134\pi\)
\(434\) 3.52977 0.169434
\(435\) 5.76213 0.276273
\(436\) 6.58337 0.315286
\(437\) −9.58969 −0.458737
\(438\) −12.1189 −0.579062
\(439\) 3.76764 0.179820 0.0899099 0.995950i \(-0.471342\pi\)
0.0899099 + 0.995950i \(0.471342\pi\)
\(440\) 2.48204 0.118326
\(441\) −4.51099 −0.214809
\(442\) 35.9242 1.70874
\(443\) −28.9033 −1.37324 −0.686618 0.727018i \(-0.740906\pi\)
−0.686618 + 0.727018i \(0.740906\pi\)
\(444\) 3.65450 0.173435
\(445\) 11.5060 0.545438
\(446\) 12.0039 0.568403
\(447\) 14.0581 0.664924
\(448\) 1.57766 0.0745375
\(449\) −17.3249 −0.817612 −0.408806 0.912621i \(-0.634055\pi\)
−0.408806 + 0.912621i \(0.634055\pi\)
\(450\) −1.16050 −0.0547066
\(451\) 0.0841890 0.00396431
\(452\) −4.58448 −0.215636
\(453\) −10.2538 −0.481764
\(454\) −3.72526 −0.174835
\(455\) −19.4831 −0.913384
\(456\) −5.46325 −0.255840
\(457\) −27.9527 −1.30757 −0.653787 0.756679i \(-0.726821\pi\)
−0.653787 + 0.756679i \(0.726821\pi\)
\(458\) −23.6720 −1.10612
\(459\) 7.22020 0.337010
\(460\) −4.35674 −0.203134
\(461\) −19.7301 −0.918922 −0.459461 0.888198i \(-0.651957\pi\)
−0.459461 + 0.888198i \(0.651957\pi\)
\(462\) 1.57766 0.0733994
\(463\) −35.0083 −1.62698 −0.813488 0.581582i \(-0.802434\pi\)
−0.813488 + 0.581582i \(0.802434\pi\)
\(464\) 2.32153 0.107774
\(465\) −5.55317 −0.257522
\(466\) 10.8622 0.503182
\(467\) 2.95172 0.136589 0.0682947 0.997665i \(-0.478244\pi\)
0.0682947 + 0.997665i \(0.478244\pi\)
\(468\) −4.97551 −0.229993
\(469\) 11.1855 0.516498
\(470\) 13.9442 0.643198
\(471\) −8.82517 −0.406642
\(472\) −6.61123 −0.304306
\(473\) −3.92316 −0.180387
\(474\) −10.4861 −0.481644
\(475\) 6.34012 0.290905
\(476\) 11.3910 0.522107
\(477\) 0.738164 0.0337982
\(478\) −1.82533 −0.0834886
\(479\) 13.6000 0.621398 0.310699 0.950508i \(-0.399437\pi\)
0.310699 + 0.950508i \(0.399437\pi\)
\(480\) −2.48204 −0.113289
\(481\) −18.1830 −0.829074
\(482\) −17.4546 −0.795037
\(483\) −2.76928 −0.126007
\(484\) 1.00000 0.0454545
\(485\) 14.7564 0.670055
\(486\) −1.00000 −0.0453609
\(487\) 29.5866 1.34070 0.670348 0.742047i \(-0.266145\pi\)
0.670348 + 0.742047i \(0.266145\pi\)
\(488\) 1.00000 0.0452679
\(489\) −11.7260 −0.530268
\(490\) 11.1964 0.505803
\(491\) −7.69301 −0.347180 −0.173590 0.984818i \(-0.555537\pi\)
−0.173590 + 0.984818i \(0.555537\pi\)
\(492\) −0.0841890 −0.00379553
\(493\) 16.7619 0.754919
\(494\) 27.1825 1.22300
\(495\) −2.48204 −0.111559
\(496\) −2.23734 −0.100460
\(497\) 1.89543 0.0850215
\(498\) −0.359100 −0.0160917
\(499\) −1.53213 −0.0685877 −0.0342938 0.999412i \(-0.510918\pi\)
−0.0342938 + 0.999412i \(0.510918\pi\)
\(500\) −9.52977 −0.426184
\(501\) 3.73191 0.166729
\(502\) −20.2679 −0.904602
\(503\) 11.5692 0.515846 0.257923 0.966165i \(-0.416962\pi\)
0.257923 + 0.966165i \(0.416962\pi\)
\(504\) −1.57766 −0.0702746
\(505\) −31.3340 −1.39434
\(506\) −1.75531 −0.0780330
\(507\) 11.7557 0.522088
\(508\) −6.83090 −0.303072
\(509\) 7.65272 0.339201 0.169601 0.985513i \(-0.445752\pi\)
0.169601 + 0.985513i \(0.445752\pi\)
\(510\) −17.9208 −0.793546
\(511\) 19.1195 0.845795
\(512\) −1.00000 −0.0441942
\(513\) 5.46325 0.241208
\(514\) −7.60217 −0.335317
\(515\) 25.2919 1.11449
\(516\) 3.92316 0.172707
\(517\) 5.61805 0.247081
\(518\) −5.76556 −0.253324
\(519\) −15.7364 −0.690750
\(520\) 12.3494 0.541557
\(521\) −13.2638 −0.581099 −0.290549 0.956860i \(-0.593838\pi\)
−0.290549 + 0.956860i \(0.593838\pi\)
\(522\) −2.32153 −0.101611
\(523\) 12.6709 0.554061 0.277030 0.960861i \(-0.410650\pi\)
0.277030 + 0.960861i \(0.410650\pi\)
\(524\) 6.39323 0.279290
\(525\) 1.83088 0.0799062
\(526\) −4.33404 −0.188973
\(527\) −16.1541 −0.703682
\(528\) −1.00000 −0.0435194
\(529\) −19.9189 −0.866039
\(530\) −1.83215 −0.0795835
\(531\) 6.61123 0.286903
\(532\) 8.61916 0.373688
\(533\) 0.418883 0.0181438
\(534\) −4.63572 −0.200607
\(535\) −3.37062 −0.145725
\(536\) −7.08992 −0.306238
\(537\) −13.1480 −0.567377
\(538\) 11.4364 0.493058
\(539\) 4.51099 0.194302
\(540\) 2.48204 0.106810
\(541\) −1.05233 −0.0452432 −0.0226216 0.999744i \(-0.507201\pi\)
−0.0226216 + 0.999744i \(0.507201\pi\)
\(542\) −6.09101 −0.261631
\(543\) −23.7767 −1.02036
\(544\) −7.22020 −0.309564
\(545\) 16.3402 0.699936
\(546\) 7.84966 0.335935
\(547\) 27.8952 1.19271 0.596357 0.802720i \(-0.296614\pi\)
0.596357 + 0.802720i \(0.296614\pi\)
\(548\) −2.37624 −0.101508
\(549\) −1.00000 −0.0426790
\(550\) 1.16050 0.0494840
\(551\) 12.6831 0.540319
\(552\) 1.75531 0.0747109
\(553\) 16.5435 0.703503
\(554\) −9.24397 −0.392739
\(555\) 9.07061 0.385026
\(556\) 6.12294 0.259670
\(557\) 12.6051 0.534097 0.267049 0.963683i \(-0.413952\pi\)
0.267049 + 0.963683i \(0.413952\pi\)
\(558\) 2.23734 0.0947143
\(559\) −19.5197 −0.825596
\(560\) 3.91581 0.165473
\(561\) −7.22020 −0.304837
\(562\) −4.42234 −0.186545
\(563\) 33.6327 1.41745 0.708724 0.705486i \(-0.249271\pi\)
0.708724 + 0.705486i \(0.249271\pi\)
\(564\) −5.61805 −0.236562
\(565\) −11.3788 −0.478712
\(566\) 12.6077 0.529940
\(567\) 1.57766 0.0662555
\(568\) −1.20142 −0.0504103
\(569\) 0.260216 0.0109088 0.00545440 0.999985i \(-0.498264\pi\)
0.00545440 + 0.999985i \(0.498264\pi\)
\(570\) −13.5600 −0.567965
\(571\) 6.25904 0.261933 0.130966 0.991387i \(-0.458192\pi\)
0.130966 + 0.991387i \(0.458192\pi\)
\(572\) 4.97551 0.208036
\(573\) −22.9311 −0.957962
\(574\) 0.132822 0.00554387
\(575\) −2.03704 −0.0849504
\(576\) 1.00000 0.0416667
\(577\) −41.0482 −1.70886 −0.854429 0.519568i \(-0.826093\pi\)
−0.854429 + 0.519568i \(0.826093\pi\)
\(578\) −35.1313 −1.46127
\(579\) 15.2772 0.634897
\(580\) 5.76213 0.239259
\(581\) 0.566539 0.0235040
\(582\) −5.94529 −0.246440
\(583\) −0.738164 −0.0305716
\(584\) −12.1189 −0.501482
\(585\) −12.3494 −0.510584
\(586\) −5.90312 −0.243856
\(587\) −44.9987 −1.85730 −0.928649 0.370961i \(-0.879028\pi\)
−0.928649 + 0.370961i \(0.879028\pi\)
\(588\) −4.51099 −0.186030
\(589\) −12.2232 −0.503647
\(590\) −16.4093 −0.675560
\(591\) −9.38641 −0.386105
\(592\) 3.65450 0.150199
\(593\) −38.2024 −1.56878 −0.784391 0.620266i \(-0.787025\pi\)
−0.784391 + 0.620266i \(0.787025\pi\)
\(594\) 1.00000 0.0410305
\(595\) 28.2729 1.15908
\(596\) 14.0581 0.575841
\(597\) 11.3483 0.464456
\(598\) −8.73355 −0.357141
\(599\) 15.2200 0.621874 0.310937 0.950431i \(-0.399357\pi\)
0.310937 + 0.950431i \(0.399357\pi\)
\(600\) −1.16050 −0.0473773
\(601\) −15.8396 −0.646112 −0.323056 0.946380i \(-0.604710\pi\)
−0.323056 + 0.946380i \(0.604710\pi\)
\(602\) −6.18941 −0.252262
\(603\) 7.08992 0.288724
\(604\) −10.2538 −0.417220
\(605\) 2.48204 0.100909
\(606\) 12.6243 0.512827
\(607\) 15.1823 0.616229 0.308115 0.951349i \(-0.400302\pi\)
0.308115 + 0.951349i \(0.400302\pi\)
\(608\) −5.46325 −0.221564
\(609\) 3.66259 0.148416
\(610\) 2.48204 0.100495
\(611\) 27.9526 1.13084
\(612\) 7.22020 0.291859
\(613\) 3.87932 0.156684 0.0783421 0.996927i \(-0.475037\pi\)
0.0783421 + 0.996927i \(0.475037\pi\)
\(614\) −18.1342 −0.731837
\(615\) −0.208960 −0.00842609
\(616\) 1.57766 0.0635658
\(617\) 19.1740 0.771916 0.385958 0.922516i \(-0.373871\pi\)
0.385958 + 0.922516i \(0.373871\pi\)
\(618\) −10.1900 −0.409901
\(619\) 7.44720 0.299328 0.149664 0.988737i \(-0.452181\pi\)
0.149664 + 0.988737i \(0.452181\pi\)
\(620\) −5.55317 −0.223021
\(621\) −1.75531 −0.0704381
\(622\) 14.9799 0.600641
\(623\) 7.31359 0.293013
\(624\) −4.97551 −0.199180
\(625\) −29.4557 −1.17823
\(626\) 12.9832 0.518914
\(627\) −5.46325 −0.218181
\(628\) −8.82517 −0.352163
\(629\) 26.3862 1.05209
\(630\) −3.91581 −0.156010
\(631\) 4.60480 0.183314 0.0916570 0.995791i \(-0.470784\pi\)
0.0916570 + 0.995791i \(0.470784\pi\)
\(632\) −10.4861 −0.417116
\(633\) 19.7222 0.783887
\(634\) 29.4666 1.17027
\(635\) −16.9545 −0.672820
\(636\) 0.738164 0.0292701
\(637\) 22.4444 0.889281
\(638\) 2.32153 0.0919104
\(639\) 1.20142 0.0475273
\(640\) −2.48204 −0.0981111
\(641\) −3.00269 −0.118599 −0.0592996 0.998240i \(-0.518887\pi\)
−0.0592996 + 0.998240i \(0.518887\pi\)
\(642\) 1.35801 0.0535963
\(643\) −18.0116 −0.710310 −0.355155 0.934807i \(-0.615572\pi\)
−0.355155 + 0.934807i \(0.615572\pi\)
\(644\) −2.76928 −0.109125
\(645\) 9.73742 0.383411
\(646\) −39.4458 −1.55197
\(647\) 49.1170 1.93099 0.965493 0.260427i \(-0.0838634\pi\)
0.965493 + 0.260427i \(0.0838634\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −6.61123 −0.259513
\(650\) 5.77409 0.226479
\(651\) −3.52977 −0.138343
\(652\) −11.7260 −0.459226
\(653\) 17.1394 0.670718 0.335359 0.942090i \(-0.391142\pi\)
0.335359 + 0.942090i \(0.391142\pi\)
\(654\) −6.58337 −0.257430
\(655\) 15.8682 0.620023
\(656\) −0.0841890 −0.00328703
\(657\) 12.1189 0.472802
\(658\) 8.86337 0.345530
\(659\) 2.75457 0.107303 0.0536513 0.998560i \(-0.482914\pi\)
0.0536513 + 0.998560i \(0.482914\pi\)
\(660\) −2.48204 −0.0966131
\(661\) 32.8559 1.27795 0.638973 0.769230i \(-0.279360\pi\)
0.638973 + 0.769230i \(0.279360\pi\)
\(662\) 13.0564 0.507449
\(663\) −35.9242 −1.39518
\(664\) −0.359100 −0.0139358
\(665\) 21.3931 0.829587
\(666\) −3.65450 −0.141609
\(667\) −4.07501 −0.157785
\(668\) 3.73191 0.144392
\(669\) −12.0039 −0.464099
\(670\) −17.5974 −0.679848
\(671\) 1.00000 0.0386046
\(672\) −1.57766 −0.0608596
\(673\) −2.74514 −0.105817 −0.0529087 0.998599i \(-0.516849\pi\)
−0.0529087 + 0.998599i \(0.516849\pi\)
\(674\) −5.16212 −0.198838
\(675\) 1.16050 0.0446678
\(676\) 11.7557 0.452141
\(677\) −21.9923 −0.845234 −0.422617 0.906308i \(-0.638888\pi\)
−0.422617 + 0.906308i \(0.638888\pi\)
\(678\) 4.58448 0.176066
\(679\) 9.37965 0.359958
\(680\) −17.9208 −0.687231
\(681\) 3.72526 0.142752
\(682\) −2.23734 −0.0856723
\(683\) −35.2564 −1.34905 −0.674525 0.738252i \(-0.735651\pi\)
−0.674525 + 0.738252i \(0.735651\pi\)
\(684\) 5.46325 0.208893
\(685\) −5.89792 −0.225348
\(686\) 18.1604 0.693369
\(687\) 23.6720 0.903144
\(688\) 3.92316 0.149569
\(689\) −3.67274 −0.139920
\(690\) 4.35674 0.165858
\(691\) 28.0494 1.06705 0.533524 0.845785i \(-0.320867\pi\)
0.533524 + 0.845785i \(0.320867\pi\)
\(692\) −15.7364 −0.598207
\(693\) −1.57766 −0.0599304
\(694\) −12.2368 −0.464502
\(695\) 15.1973 0.576468
\(696\) −2.32153 −0.0879975
\(697\) −0.607861 −0.0230244
\(698\) 18.5418 0.701818
\(699\) −10.8622 −0.410847
\(700\) 1.83088 0.0692008
\(701\) 2.85019 0.107650 0.0538251 0.998550i \(-0.482859\pi\)
0.0538251 + 0.998550i \(0.482859\pi\)
\(702\) 4.97551 0.187788
\(703\) 19.9655 0.753012
\(704\) −1.00000 −0.0376889
\(705\) −13.9442 −0.525169
\(706\) −1.97315 −0.0742603
\(707\) −19.9169 −0.749051
\(708\) 6.61123 0.248465
\(709\) 17.2618 0.648279 0.324140 0.946009i \(-0.394925\pi\)
0.324140 + 0.946009i \(0.394925\pi\)
\(710\) −2.98196 −0.111911
\(711\) 10.4861 0.393260
\(712\) −4.63572 −0.173731
\(713\) 3.92723 0.147076
\(714\) −11.3910 −0.426298
\(715\) 12.3494 0.461841
\(716\) −13.1480 −0.491363
\(717\) 1.82533 0.0681681
\(718\) 9.23490 0.344643
\(719\) 37.7255 1.40692 0.703462 0.710733i \(-0.251637\pi\)
0.703462 + 0.710733i \(0.251637\pi\)
\(720\) 2.48204 0.0925000
\(721\) 16.0763 0.598714
\(722\) −10.8471 −0.403688
\(723\) 17.4546 0.649145
\(724\) −23.7767 −0.883655
\(725\) 2.69415 0.100058
\(726\) −1.00000 −0.0371135
\(727\) −30.4200 −1.12821 −0.564107 0.825702i \(-0.690780\pi\)
−0.564107 + 0.825702i \(0.690780\pi\)
\(728\) 7.84966 0.290928
\(729\) 1.00000 0.0370370
\(730\) −30.0795 −1.11329
\(731\) 28.3260 1.04767
\(732\) −1.00000 −0.0369611
\(733\) 21.8473 0.806949 0.403475 0.914991i \(-0.367802\pi\)
0.403475 + 0.914991i \(0.367802\pi\)
\(734\) −23.3975 −0.863617
\(735\) −11.1964 −0.412987
\(736\) 1.75531 0.0647015
\(737\) −7.08992 −0.261160
\(738\) 0.0841890 0.00309904
\(739\) 3.62541 0.133363 0.0666815 0.997774i \(-0.478759\pi\)
0.0666815 + 0.997774i \(0.478759\pi\)
\(740\) 9.07061 0.333442
\(741\) −27.1825 −0.998572
\(742\) −1.16457 −0.0427528
\(743\) −28.6055 −1.04944 −0.524718 0.851276i \(-0.675829\pi\)
−0.524718 + 0.851276i \(0.675829\pi\)
\(744\) 2.23734 0.0820250
\(745\) 34.8927 1.27837
\(746\) −6.44001 −0.235786
\(747\) 0.359100 0.0131388
\(748\) −7.22020 −0.263997
\(749\) −2.14247 −0.0782843
\(750\) 9.52977 0.347978
\(751\) 4.90312 0.178918 0.0894588 0.995991i \(-0.471486\pi\)
0.0894588 + 0.995991i \(0.471486\pi\)
\(752\) −5.61805 −0.204869
\(753\) 20.2679 0.738605
\(754\) 11.5508 0.420656
\(755\) −25.4502 −0.926228
\(756\) 1.57766 0.0573790
\(757\) 45.3746 1.64917 0.824583 0.565741i \(-0.191410\pi\)
0.824583 + 0.565741i \(0.191410\pi\)
\(758\) −13.5104 −0.490721
\(759\) 1.75531 0.0637136
\(760\) −13.5600 −0.491873
\(761\) −32.0786 −1.16285 −0.581424 0.813601i \(-0.697504\pi\)
−0.581424 + 0.813601i \(0.697504\pi\)
\(762\) 6.83090 0.247457
\(763\) 10.3863 0.376010
\(764\) −22.9311 −0.829619
\(765\) 17.9208 0.647928
\(766\) 16.5203 0.596901
\(767\) −32.8942 −1.18774
\(768\) 1.00000 0.0360844
\(769\) −22.0409 −0.794815 −0.397407 0.917642i \(-0.630090\pi\)
−0.397407 + 0.917642i \(0.630090\pi\)
\(770\) 3.91581 0.141116
\(771\) 7.60217 0.273786
\(772\) 15.2772 0.549837
\(773\) 1.84767 0.0664562 0.0332281 0.999448i \(-0.489421\pi\)
0.0332281 + 0.999448i \(0.489421\pi\)
\(774\) −3.92316 −0.141015
\(775\) −2.59644 −0.0932670
\(776\) −5.94529 −0.213423
\(777\) 5.76556 0.206838
\(778\) 11.1952 0.401366
\(779\) −0.459946 −0.0164793
\(780\) −12.3494 −0.442179
\(781\) −1.20142 −0.0429901
\(782\) 12.6737 0.453210
\(783\) 2.32153 0.0829648
\(784\) −4.51099 −0.161107
\(785\) −21.9044 −0.781801
\(786\) −6.39323 −0.228039
\(787\) −35.6316 −1.27013 −0.635064 0.772459i \(-0.719026\pi\)
−0.635064 + 0.772459i \(0.719026\pi\)
\(788\) −9.38641 −0.334377
\(789\) 4.33404 0.154296
\(790\) −26.0269 −0.925997
\(791\) −7.23276 −0.257167
\(792\) 1.00000 0.0355335
\(793\) 4.97551 0.176685
\(794\) 21.6990 0.770068
\(795\) 1.83215 0.0649796
\(796\) 11.3483 0.402230
\(797\) −7.69723 −0.272650 −0.136325 0.990664i \(-0.543529\pi\)
−0.136325 + 0.990664i \(0.543529\pi\)
\(798\) −8.61916 −0.305115
\(799\) −40.5634 −1.43503
\(800\) −1.16050 −0.0410300
\(801\) 4.63572 0.163795
\(802\) 18.4153 0.650268
\(803\) −12.1189 −0.427666
\(804\) 7.08992 0.250042
\(805\) −6.87345 −0.242257
\(806\) −11.1319 −0.392105
\(807\) −11.4364 −0.402580
\(808\) 12.6243 0.444121
\(809\) −25.4627 −0.895222 −0.447611 0.894228i \(-0.647725\pi\)
−0.447611 + 0.894228i \(0.647725\pi\)
\(810\) −2.48204 −0.0872099
\(811\) −46.0069 −1.61552 −0.807760 0.589511i \(-0.799321\pi\)
−0.807760 + 0.589511i \(0.799321\pi\)
\(812\) 3.66259 0.128532
\(813\) 6.09101 0.213621
\(814\) 3.65450 0.128090
\(815\) −29.1044 −1.01948
\(816\) 7.22020 0.252758
\(817\) 21.4332 0.749853
\(818\) −4.30492 −0.150518
\(819\) −7.84966 −0.274289
\(820\) −0.208960 −0.00729720
\(821\) −55.5046 −1.93712 −0.968562 0.248771i \(-0.919973\pi\)
−0.968562 + 0.248771i \(0.919973\pi\)
\(822\) 2.37624 0.0828810
\(823\) 15.8969 0.554130 0.277065 0.960851i \(-0.410638\pi\)
0.277065 + 0.960851i \(0.410638\pi\)
\(824\) −10.1900 −0.354985
\(825\) −1.16050 −0.0404035
\(826\) −10.4303 −0.362916
\(827\) 31.5467 1.09699 0.548493 0.836155i \(-0.315202\pi\)
0.548493 + 0.836155i \(0.315202\pi\)
\(828\) −1.75531 −0.0610012
\(829\) 23.0397 0.800203 0.400101 0.916471i \(-0.368975\pi\)
0.400101 + 0.916471i \(0.368975\pi\)
\(830\) −0.891300 −0.0309375
\(831\) 9.24397 0.320670
\(832\) −4.97551 −0.172495
\(833\) −32.5702 −1.12849
\(834\) −6.12294 −0.212020
\(835\) 9.26273 0.320550
\(836\) −5.46325 −0.188951
\(837\) −2.23734 −0.0773339
\(838\) 7.35619 0.254115
\(839\) −18.9841 −0.655405 −0.327703 0.944781i \(-0.606274\pi\)
−0.327703 + 0.944781i \(0.606274\pi\)
\(840\) −3.91581 −0.135108
\(841\) −23.6105 −0.814155
\(842\) −26.5246 −0.914098
\(843\) 4.42234 0.152313
\(844\) 19.7222 0.678866
\(845\) 29.1780 1.00375
\(846\) 5.61805 0.193152
\(847\) 1.57766 0.0542091
\(848\) 0.738164 0.0253486
\(849\) −12.6077 −0.432695
\(850\) −8.37906 −0.287400
\(851\) −6.41478 −0.219896
\(852\) 1.20142 0.0411598
\(853\) −17.8157 −0.610000 −0.305000 0.952352i \(-0.598656\pi\)
−0.305000 + 0.952352i \(0.598656\pi\)
\(854\) 1.57766 0.0539864
\(855\) 13.5600 0.463742
\(856\) 1.35801 0.0464157
\(857\) −23.7992 −0.812966 −0.406483 0.913658i \(-0.633245\pi\)
−0.406483 + 0.913658i \(0.633245\pi\)
\(858\) −4.97551 −0.169861
\(859\) −36.6484 −1.25043 −0.625214 0.780453i \(-0.714988\pi\)
−0.625214 + 0.780453i \(0.714988\pi\)
\(860\) 9.73742 0.332043
\(861\) −0.132822 −0.00452655
\(862\) −22.2025 −0.756221
\(863\) 2.33478 0.0794770 0.0397385 0.999210i \(-0.487348\pi\)
0.0397385 + 0.999210i \(0.487348\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −39.0582 −1.32802
\(866\) −16.1513 −0.548844
\(867\) 35.1313 1.19312
\(868\) −3.52977 −0.119808
\(869\) −10.4861 −0.355717
\(870\) −5.76213 −0.195354
\(871\) −35.2759 −1.19528
\(872\) −6.58337 −0.222941
\(873\) 5.94529 0.201218
\(874\) 9.58969 0.324376
\(875\) −15.0347 −0.508267
\(876\) 12.1189 0.409459
\(877\) −30.5720 −1.03234 −0.516172 0.856485i \(-0.672644\pi\)
−0.516172 + 0.856485i \(0.672644\pi\)
\(878\) −3.76764 −0.127152
\(879\) 5.90312 0.199107
\(880\) −2.48204 −0.0836694
\(881\) 39.6527 1.33593 0.667966 0.744192i \(-0.267165\pi\)
0.667966 + 0.744192i \(0.267165\pi\)
\(882\) 4.51099 0.151893
\(883\) 24.9384 0.839246 0.419623 0.907699i \(-0.362162\pi\)
0.419623 + 0.907699i \(0.362162\pi\)
\(884\) −35.9242 −1.20826
\(885\) 16.4093 0.551593
\(886\) 28.9033 0.971025
\(887\) −35.3662 −1.18748 −0.593740 0.804657i \(-0.702349\pi\)
−0.593740 + 0.804657i \(0.702349\pi\)
\(888\) −3.65450 −0.122637
\(889\) −10.7768 −0.361444
\(890\) −11.5060 −0.385683
\(891\) −1.00000 −0.0335013
\(892\) −12.0039 −0.401921
\(893\) −30.6928 −1.02710
\(894\) −14.0581 −0.470172
\(895\) −32.6337 −1.09083
\(896\) −1.57766 −0.0527059
\(897\) 8.73355 0.291605
\(898\) 17.3249 0.578139
\(899\) −5.19407 −0.173232
\(900\) 1.16050 0.0386834
\(901\) 5.32969 0.177558
\(902\) −0.0841890 −0.00280319
\(903\) 6.18941 0.205971
\(904\) 4.58448 0.152478
\(905\) −59.0147 −1.96171
\(906\) 10.2538 0.340659
\(907\) −24.1847 −0.803041 −0.401520 0.915850i \(-0.631518\pi\)
−0.401520 + 0.915850i \(0.631518\pi\)
\(908\) 3.72526 0.123627
\(909\) −12.6243 −0.418722
\(910\) 19.4831 0.645860
\(911\) −30.1740 −0.999710 −0.499855 0.866109i \(-0.666613\pi\)
−0.499855 + 0.866109i \(0.666613\pi\)
\(912\) 5.46325 0.180906
\(913\) −0.359100 −0.0118845
\(914\) 27.9527 0.924594
\(915\) −2.48204 −0.0820536
\(916\) 23.6720 0.782146
\(917\) 10.0864 0.333081
\(918\) −7.22020 −0.238302
\(919\) 44.9120 1.48151 0.740755 0.671775i \(-0.234468\pi\)
0.740755 + 0.671775i \(0.234468\pi\)
\(920\) 4.35674 0.143637
\(921\) 18.1342 0.597543
\(922\) 19.7301 0.649776
\(923\) −5.97766 −0.196757
\(924\) −1.57766 −0.0519012
\(925\) 4.24106 0.139445
\(926\) 35.0083 1.15045
\(927\) 10.1900 0.334683
\(928\) −2.32153 −0.0762081
\(929\) −58.7619 −1.92791 −0.963957 0.266057i \(-0.914279\pi\)
−0.963957 + 0.266057i \(0.914279\pi\)
\(930\) 5.55317 0.182096
\(931\) −24.6447 −0.807696
\(932\) −10.8622 −0.355804
\(933\) −14.9799 −0.490421
\(934\) −2.95172 −0.0965832
\(935\) −17.9208 −0.586073
\(936\) 4.97551 0.162630
\(937\) −40.8754 −1.33534 −0.667671 0.744457i \(-0.732709\pi\)
−0.667671 + 0.744457i \(0.732709\pi\)
\(938\) −11.1855 −0.365219
\(939\) −12.9832 −0.423692
\(940\) −13.9442 −0.454809
\(941\) 2.90275 0.0946271 0.0473135 0.998880i \(-0.484934\pi\)
0.0473135 + 0.998880i \(0.484934\pi\)
\(942\) 8.82517 0.287540
\(943\) 0.147778 0.00481230
\(944\) 6.61123 0.215177
\(945\) 3.91581 0.127381
\(946\) 3.92316 0.127553
\(947\) 16.0737 0.522324 0.261162 0.965295i \(-0.415894\pi\)
0.261162 + 0.965295i \(0.415894\pi\)
\(948\) 10.4861 0.340573
\(949\) −60.2975 −1.95734
\(950\) −6.34012 −0.205701
\(951\) −29.4666 −0.955521
\(952\) −11.3910 −0.369185
\(953\) 49.3712 1.59929 0.799645 0.600473i \(-0.205021\pi\)
0.799645 + 0.600473i \(0.205021\pi\)
\(954\) −0.738164 −0.0238989
\(955\) −56.9159 −1.84176
\(956\) 1.82533 0.0590353
\(957\) −2.32153 −0.0750445
\(958\) −13.6000 −0.439395
\(959\) −3.74891 −0.121059
\(960\) 2.48204 0.0801074
\(961\) −25.9943 −0.838526
\(962\) 18.1830 0.586244
\(963\) −1.35801 −0.0437612
\(964\) 17.4546 0.562176
\(965\) 37.9185 1.22064
\(966\) 2.76928 0.0891001
\(967\) 32.1599 1.03419 0.517096 0.855927i \(-0.327013\pi\)
0.517096 + 0.855927i \(0.327013\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 39.4458 1.26718
\(970\) −14.7564 −0.473800
\(971\) −8.44075 −0.270877 −0.135438 0.990786i \(-0.543244\pi\)
−0.135438 + 0.990786i \(0.543244\pi\)
\(972\) 1.00000 0.0320750
\(973\) 9.65992 0.309683
\(974\) −29.5866 −0.948015
\(975\) −5.77409 −0.184919
\(976\) −1.00000 −0.0320092
\(977\) −57.5522 −1.84126 −0.920629 0.390439i \(-0.872323\pi\)
−0.920629 + 0.390439i \(0.872323\pi\)
\(978\) 11.7260 0.374956
\(979\) −4.63572 −0.148158
\(980\) −11.1964 −0.357657
\(981\) 6.58337 0.210191
\(982\) 7.69301 0.245494
\(983\) −12.4597 −0.397404 −0.198702 0.980060i \(-0.563673\pi\)
−0.198702 + 0.980060i \(0.563673\pi\)
\(984\) 0.0841890 0.00268385
\(985\) −23.2974 −0.742317
\(986\) −16.7619 −0.533809
\(987\) −8.86337 −0.282124
\(988\) −27.1825 −0.864789
\(989\) −6.88635 −0.218973
\(990\) 2.48204 0.0788843
\(991\) −27.3577 −0.869046 −0.434523 0.900661i \(-0.643083\pi\)
−0.434523 + 0.900661i \(0.643083\pi\)
\(992\) 2.23734 0.0710357
\(993\) −13.0564 −0.414331
\(994\) −1.89543 −0.0601193
\(995\) 28.1669 0.892952
\(996\) 0.359100 0.0113785
\(997\) −49.6451 −1.57228 −0.786138 0.618051i \(-0.787922\pi\)
−0.786138 + 0.618051i \(0.787922\pi\)
\(998\) 1.53213 0.0484988
\(999\) 3.65450 0.115623
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 4026.2.a.u.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.u.1.5 5 1.1 even 1 trivial