Properties

Label 4235.2.a.bc.1.2
Level $4235$
Weight $2$
Character 4235.1
Self dual yes
Analytic conductor $33.817$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4235.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.8166452560\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.288385.1
Defining polynomial: \(x^{5} - 7 x^{3} - 2 x^{2} + 10 x + 3\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.35681\) of defining polynomial
Character \(\chi\) \(=\) 4235.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} +0.329669 q^{6} -1.00000 q^{7} +2.92945 q^{8} -2.94096 q^{9} +O(q^{10})\) \(q-1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} +0.329669 q^{6} -1.00000 q^{7} +2.92945 q^{8} -2.94096 q^{9} -1.35681 q^{10} +0.0386517 q^{12} -2.34529 q^{13} +1.35681 q^{14} -0.242974 q^{15} -3.65654 q^{16} -0.927617 q^{17} +3.99032 q^{18} +1.95659 q^{19} -0.159077 q^{20} +0.242974 q^{21} +2.68368 q^{23} -0.711781 q^{24} +1.00000 q^{25} +3.18211 q^{26} +1.44350 q^{27} +0.159077 q^{28} +0.245772 q^{29} +0.329669 q^{30} +2.99032 q^{31} -0.897683 q^{32} +1.25860 q^{34} -1.00000 q^{35} +0.467840 q^{36} +6.23609 q^{37} -2.65471 q^{38} +0.569845 q^{39} +2.92945 q^{40} +6.05663 q^{41} -0.329669 q^{42} -9.64965 q^{43} -2.94096 q^{45} -3.64123 q^{46} +5.84459 q^{47} +0.888445 q^{48} +1.00000 q^{49} -1.35681 q^{50} +0.225387 q^{51} +0.373082 q^{52} -4.58827 q^{53} -1.95855 q^{54} -2.92945 q^{56} -0.475400 q^{57} -0.333465 q^{58} -9.66792 q^{59} +0.0386517 q^{60} -2.82941 q^{61} -4.05728 q^{62} +2.94096 q^{63} +8.53106 q^{64} -2.34529 q^{65} +15.0109 q^{67} +0.147563 q^{68} -0.652064 q^{69} +1.35681 q^{70} -2.21995 q^{71} -8.61540 q^{72} -0.100173 q^{73} -8.46116 q^{74} -0.242974 q^{75} -0.311248 q^{76} -0.773170 q^{78} -6.31847 q^{79} -3.65654 q^{80} +8.47216 q^{81} -8.21767 q^{82} -16.4112 q^{83} -0.0386517 q^{84} -0.927617 q^{85} +13.0927 q^{86} -0.0597162 q^{87} +2.73384 q^{89} +3.99032 q^{90} +2.34529 q^{91} -0.426912 q^{92} -0.726570 q^{93} -7.92997 q^{94} +1.95659 q^{95} +0.218114 q^{96} +3.11103 q^{97} -1.35681 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 2q^{3} + 4q^{4} + 5q^{5} - 9q^{6} - 5q^{7} - 6q^{8} + 7q^{9} + O(q^{10}) \) \( 5q + 2q^{3} + 4q^{4} + 5q^{5} - 9q^{6} - 5q^{7} - 6q^{8} + 7q^{9} + 3q^{12} - 6q^{13} + 2q^{15} - 6q^{16} - 2q^{17} + 3q^{18} - 7q^{19} + 4q^{20} - 2q^{21} + 5q^{23} - 8q^{24} + 5q^{25} + 9q^{26} - 7q^{27} - 4q^{28} - 11q^{29} - 9q^{30} - 2q^{31} - 7q^{32} + 8q^{34} - 5q^{35} + q^{36} + 2q^{37} - 19q^{38} - 2q^{39} - 6q^{40} - 13q^{41} + 9q^{42} - 10q^{43} + 7q^{45} - 2q^{46} - 2q^{47} + 32q^{48} + 5q^{49} - 30q^{51} + 8q^{52} - 14q^{53} - 16q^{54} + 6q^{56} - 6q^{57} + 4q^{58} + 6q^{59} + 3q^{60} - 20q^{61} + 15q^{62} - 7q^{63} - 6q^{64} - 6q^{65} - 9q^{67} - 3q^{68} - 30q^{69} - 10q^{71} - 38q^{72} - 15q^{73} + 19q^{74} + 2q^{75} + 5q^{76} + 21q^{78} - 23q^{79} - 6q^{80} + 13q^{81} - 16q^{82} - 8q^{83} - 3q^{84} - 2q^{85} - 29q^{86} + 22q^{87} + 7q^{89} + 3q^{90} + 6q^{91} + 26q^{92} - 45q^{93} + 14q^{94} - 7q^{95} + 18q^{96} + 21q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35681 −0.959407 −0.479703 0.877431i \(-0.659256\pi\)
−0.479703 + 0.877431i \(0.659256\pi\)
\(3\) −0.242974 −0.140281 −0.0701406 0.997537i \(-0.522345\pi\)
−0.0701406 + 0.997537i \(0.522345\pi\)
\(4\) −0.159077 −0.0795386
\(5\) 1.00000 0.447214
\(6\) 0.329669 0.134587
\(7\) −1.00000 −0.377964
\(8\) 2.92945 1.03572
\(9\) −2.94096 −0.980321
\(10\) −1.35681 −0.429060
\(11\) 0 0
\(12\) 0.0386517 0.0111578
\(13\) −2.34529 −0.650467 −0.325233 0.945634i \(-0.605443\pi\)
−0.325233 + 0.945634i \(0.605443\pi\)
\(14\) 1.35681 0.362622
\(15\) −0.242974 −0.0627357
\(16\) −3.65654 −0.914135
\(17\) −0.927617 −0.224980 −0.112490 0.993653i \(-0.535883\pi\)
−0.112490 + 0.993653i \(0.535883\pi\)
\(18\) 3.99032 0.940527
\(19\) 1.95659 0.448872 0.224436 0.974489i \(-0.427946\pi\)
0.224436 + 0.974489i \(0.427946\pi\)
\(20\) −0.159077 −0.0355707
\(21\) 0.242974 0.0530213
\(22\) 0 0
\(23\) 2.68368 0.559585 0.279793 0.960060i \(-0.409734\pi\)
0.279793 + 0.960060i \(0.409734\pi\)
\(24\) −0.711781 −0.145292
\(25\) 1.00000 0.200000
\(26\) 3.18211 0.624062
\(27\) 1.44350 0.277802
\(28\) 0.159077 0.0300628
\(29\) 0.245772 0.0456387 0.0228193 0.999740i \(-0.492736\pi\)
0.0228193 + 0.999740i \(0.492736\pi\)
\(30\) 0.329669 0.0601890
\(31\) 2.99032 0.537077 0.268538 0.963269i \(-0.413459\pi\)
0.268538 + 0.963269i \(0.413459\pi\)
\(32\) −0.897683 −0.158689
\(33\) 0 0
\(34\) 1.25860 0.215848
\(35\) −1.00000 −0.169031
\(36\) 0.467840 0.0779734
\(37\) 6.23609 1.02521 0.512603 0.858626i \(-0.328681\pi\)
0.512603 + 0.858626i \(0.328681\pi\)
\(38\) −2.65471 −0.430651
\(39\) 0.569845 0.0912483
\(40\) 2.92945 0.463187
\(41\) 6.05663 0.945886 0.472943 0.881093i \(-0.343192\pi\)
0.472943 + 0.881093i \(0.343192\pi\)
\(42\) −0.329669 −0.0508690
\(43\) −9.64965 −1.47156 −0.735779 0.677221i \(-0.763184\pi\)
−0.735779 + 0.677221i \(0.763184\pi\)
\(44\) 0 0
\(45\) −2.94096 −0.438413
\(46\) −3.64123 −0.536870
\(47\) 5.84459 0.852521 0.426260 0.904601i \(-0.359831\pi\)
0.426260 + 0.904601i \(0.359831\pi\)
\(48\) 0.888445 0.128236
\(49\) 1.00000 0.142857
\(50\) −1.35681 −0.191881
\(51\) 0.225387 0.0315605
\(52\) 0.373082 0.0517372
\(53\) −4.58827 −0.630247 −0.315123 0.949051i \(-0.602046\pi\)
−0.315123 + 0.949051i \(0.602046\pi\)
\(54\) −1.95855 −0.266525
\(55\) 0 0
\(56\) −2.92945 −0.391464
\(57\) −0.475400 −0.0629683
\(58\) −0.333465 −0.0437861
\(59\) −9.66792 −1.25866 −0.629328 0.777140i \(-0.716670\pi\)
−0.629328 + 0.777140i \(0.716670\pi\)
\(60\) 0.0386517 0.00498991
\(61\) −2.82941 −0.362269 −0.181134 0.983458i \(-0.557977\pi\)
−0.181134 + 0.983458i \(0.557977\pi\)
\(62\) −4.05728 −0.515275
\(63\) 2.94096 0.370527
\(64\) 8.53106 1.06638
\(65\) −2.34529 −0.290898
\(66\) 0 0
\(67\) 15.0109 1.83388 0.916939 0.399028i \(-0.130652\pi\)
0.916939 + 0.399028i \(0.130652\pi\)
\(68\) 0.147563 0.0178946
\(69\) −0.652064 −0.0784993
\(70\) 1.35681 0.162169
\(71\) −2.21995 −0.263459 −0.131730 0.991286i \(-0.542053\pi\)
−0.131730 + 0.991286i \(0.542053\pi\)
\(72\) −8.61540 −1.01533
\(73\) −0.100173 −0.0117244 −0.00586220 0.999983i \(-0.501866\pi\)
−0.00586220 + 0.999983i \(0.501866\pi\)
\(74\) −8.46116 −0.983590
\(75\) −0.242974 −0.0280562
\(76\) −0.311248 −0.0357026
\(77\) 0 0
\(78\) −0.773170 −0.0875442
\(79\) −6.31847 −0.710883 −0.355442 0.934699i \(-0.615669\pi\)
−0.355442 + 0.934699i \(0.615669\pi\)
\(80\) −3.65654 −0.408814
\(81\) 8.47216 0.941351
\(82\) −8.21767 −0.907490
\(83\) −16.4112 −1.80136 −0.900679 0.434485i \(-0.856931\pi\)
−0.900679 + 0.434485i \(0.856931\pi\)
\(84\) −0.0386517 −0.00421724
\(85\) −0.927617 −0.100614
\(86\) 13.0927 1.41182
\(87\) −0.0597162 −0.00640225
\(88\) 0 0
\(89\) 2.73384 0.289787 0.144893 0.989447i \(-0.453716\pi\)
0.144893 + 0.989447i \(0.453716\pi\)
\(90\) 3.99032 0.420616
\(91\) 2.34529 0.245853
\(92\) −0.426912 −0.0445086
\(93\) −0.726570 −0.0753418
\(94\) −7.92997 −0.817914
\(95\) 1.95659 0.200742
\(96\) 0.218114 0.0222611
\(97\) 3.11103 0.315878 0.157939 0.987449i \(-0.449515\pi\)
0.157939 + 0.987449i \(0.449515\pi\)
\(98\) −1.35681 −0.137058
\(99\) 0 0
\(100\) −0.159077 −0.0159077
\(101\) −14.9247 −1.48506 −0.742531 0.669812i \(-0.766375\pi\)
−0.742531 + 0.669812i \(0.766375\pi\)
\(102\) −0.305807 −0.0302794
\(103\) 0.991937 0.0977384 0.0488692 0.998805i \(-0.484438\pi\)
0.0488692 + 0.998805i \(0.484438\pi\)
\(104\) −6.87041 −0.673699
\(105\) 0.242974 0.0237119
\(106\) 6.22539 0.604663
\(107\) 3.31075 0.320062 0.160031 0.987112i \(-0.448841\pi\)
0.160031 + 0.987112i \(0.448841\pi\)
\(108\) −0.229628 −0.0220960
\(109\) 6.08363 0.582706 0.291353 0.956616i \(-0.405895\pi\)
0.291353 + 0.956616i \(0.405895\pi\)
\(110\) 0 0
\(111\) −1.51521 −0.143817
\(112\) 3.65654 0.345511
\(113\) −9.54323 −0.897751 −0.448876 0.893594i \(-0.648175\pi\)
−0.448876 + 0.893594i \(0.648175\pi\)
\(114\) 0.645026 0.0604122
\(115\) 2.68368 0.250254
\(116\) −0.0390967 −0.00363004
\(117\) 6.89742 0.637666
\(118\) 13.1175 1.20756
\(119\) 0.927617 0.0850346
\(120\) −0.711781 −0.0649764
\(121\) 0 0
\(122\) 3.83896 0.347563
\(123\) −1.47160 −0.132690
\(124\) −0.475691 −0.0427183
\(125\) 1.00000 0.0894427
\(126\) −3.99032 −0.355486
\(127\) −10.1792 −0.903256 −0.451628 0.892206i \(-0.649157\pi\)
−0.451628 + 0.892206i \(0.649157\pi\)
\(128\) −9.77963 −0.864405
\(129\) 2.34462 0.206432
\(130\) 3.18211 0.279089
\(131\) 12.4893 1.09119 0.545596 0.838048i \(-0.316303\pi\)
0.545596 + 0.838048i \(0.316303\pi\)
\(132\) 0 0
\(133\) −1.95659 −0.169658
\(134\) −20.3669 −1.75943
\(135\) 1.44350 0.124237
\(136\) −2.71741 −0.233016
\(137\) 16.6161 1.41961 0.709805 0.704398i \(-0.248783\pi\)
0.709805 + 0.704398i \(0.248783\pi\)
\(138\) 0.884725 0.0753128
\(139\) −0.420472 −0.0356640 −0.0178320 0.999841i \(-0.505676\pi\)
−0.0178320 + 0.999841i \(0.505676\pi\)
\(140\) 0.159077 0.0134445
\(141\) −1.42008 −0.119593
\(142\) 3.01204 0.252764
\(143\) 0 0
\(144\) 10.7538 0.896146
\(145\) 0.245772 0.0204102
\(146\) 0.135916 0.0112485
\(147\) −0.242974 −0.0200402
\(148\) −0.992020 −0.0815435
\(149\) −10.1747 −0.833544 −0.416772 0.909011i \(-0.636839\pi\)
−0.416772 + 0.909011i \(0.636839\pi\)
\(150\) 0.329669 0.0269173
\(151\) 5.10643 0.415555 0.207778 0.978176i \(-0.433377\pi\)
0.207778 + 0.978176i \(0.433377\pi\)
\(152\) 5.73172 0.464904
\(153\) 2.72809 0.220553
\(154\) 0 0
\(155\) 2.99032 0.240188
\(156\) −0.0906494 −0.00725776
\(157\) 3.85612 0.307752 0.153876 0.988090i \(-0.450824\pi\)
0.153876 + 0.988090i \(0.450824\pi\)
\(158\) 8.57293 0.682026
\(159\) 1.11483 0.0884118
\(160\) −0.897683 −0.0709680
\(161\) −2.68368 −0.211503
\(162\) −11.4951 −0.903138
\(163\) −8.98048 −0.703406 −0.351703 0.936112i \(-0.614397\pi\)
−0.351703 + 0.936112i \(0.614397\pi\)
\(164\) −0.963471 −0.0752345
\(165\) 0 0
\(166\) 22.2668 1.72824
\(167\) 0.0644782 0.00498947 0.00249474 0.999997i \(-0.499206\pi\)
0.00249474 + 0.999997i \(0.499206\pi\)
\(168\) 0.711781 0.0549151
\(169\) −7.49961 −0.576893
\(170\) 1.25860 0.0965300
\(171\) −5.75425 −0.440038
\(172\) 1.53504 0.117046
\(173\) 17.2202 1.30923 0.654613 0.755964i \(-0.272832\pi\)
0.654613 + 0.755964i \(0.272832\pi\)
\(174\) 0.0810233 0.00614236
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) 2.34906 0.176566
\(178\) −3.70930 −0.278023
\(179\) −18.2017 −1.36046 −0.680230 0.732999i \(-0.738120\pi\)
−0.680230 + 0.732999i \(0.738120\pi\)
\(180\) 0.467840 0.0348708
\(181\) −9.54258 −0.709294 −0.354647 0.935000i \(-0.615399\pi\)
−0.354647 + 0.935000i \(0.615399\pi\)
\(182\) −3.18211 −0.235873
\(183\) 0.687473 0.0508195
\(184\) 7.86170 0.579572
\(185\) 6.23609 0.458486
\(186\) 0.985814 0.0722834
\(187\) 0 0
\(188\) −0.929741 −0.0678083
\(189\) −1.44350 −0.104999
\(190\) −2.65471 −0.192593
\(191\) 10.0070 0.724078 0.362039 0.932163i \(-0.382081\pi\)
0.362039 + 0.932163i \(0.382081\pi\)
\(192\) −2.07283 −0.149593
\(193\) −13.5332 −0.974141 −0.487071 0.873363i \(-0.661935\pi\)
−0.487071 + 0.873363i \(0.661935\pi\)
\(194\) −4.22107 −0.303055
\(195\) 0.569845 0.0408075
\(196\) −0.159077 −0.0113627
\(197\) −22.2486 −1.58515 −0.792575 0.609774i \(-0.791260\pi\)
−0.792575 + 0.609774i \(0.791260\pi\)
\(198\) 0 0
\(199\) −9.44551 −0.669575 −0.334787 0.942294i \(-0.608664\pi\)
−0.334787 + 0.942294i \(0.608664\pi\)
\(200\) 2.92945 0.207143
\(201\) −3.64727 −0.257259
\(202\) 20.2499 1.42478
\(203\) −0.245772 −0.0172498
\(204\) −0.0358540 −0.00251028
\(205\) 6.05663 0.423013
\(206\) −1.34587 −0.0937709
\(207\) −7.89260 −0.548573
\(208\) 8.57565 0.594615
\(209\) 0 0
\(210\) −0.329669 −0.0227493
\(211\) −4.75884 −0.327612 −0.163806 0.986493i \(-0.552377\pi\)
−0.163806 + 0.986493i \(0.552377\pi\)
\(212\) 0.729889 0.0501290
\(213\) 0.539389 0.0369584
\(214\) −4.49204 −0.307070
\(215\) −9.64965 −0.658101
\(216\) 4.22866 0.287724
\(217\) −2.99032 −0.202996
\(218\) −8.25431 −0.559052
\(219\) 0.0243395 0.00164471
\(220\) 0 0
\(221\) 2.17553 0.146342
\(222\) 2.05584 0.137979
\(223\) 19.6049 1.31284 0.656422 0.754394i \(-0.272069\pi\)
0.656422 + 0.754394i \(0.272069\pi\)
\(224\) 0.897683 0.0599789
\(225\) −2.94096 −0.196064
\(226\) 12.9483 0.861309
\(227\) −8.13362 −0.539847 −0.269924 0.962882i \(-0.586998\pi\)
−0.269924 + 0.962882i \(0.586998\pi\)
\(228\) 0.0756253 0.00500841
\(229\) 12.5891 0.831910 0.415955 0.909385i \(-0.363447\pi\)
0.415955 + 0.909385i \(0.363447\pi\)
\(230\) −3.64123 −0.240096
\(231\) 0 0
\(232\) 0.719976 0.0472688
\(233\) −2.77199 −0.181599 −0.0907996 0.995869i \(-0.528942\pi\)
−0.0907996 + 0.995869i \(0.528942\pi\)
\(234\) −9.35846 −0.611782
\(235\) 5.84459 0.381259
\(236\) 1.53795 0.100112
\(237\) 1.53522 0.0997235
\(238\) −1.25860 −0.0815827
\(239\) 1.04527 0.0676130 0.0338065 0.999428i \(-0.489237\pi\)
0.0338065 + 0.999428i \(0.489237\pi\)
\(240\) 0.888445 0.0573489
\(241\) −24.2918 −1.56477 −0.782385 0.622796i \(-0.785997\pi\)
−0.782385 + 0.622796i \(0.785997\pi\)
\(242\) 0 0
\(243\) −6.38902 −0.409856
\(244\) 0.450094 0.0288143
\(245\) 1.00000 0.0638877
\(246\) 1.99668 0.127304
\(247\) −4.58877 −0.291976
\(248\) 8.75998 0.556259
\(249\) 3.98749 0.252697
\(250\) −1.35681 −0.0858120
\(251\) −15.7101 −0.991610 −0.495805 0.868434i \(-0.665127\pi\)
−0.495805 + 0.868434i \(0.665127\pi\)
\(252\) −0.467840 −0.0294712
\(253\) 0 0
\(254\) 13.8112 0.866590
\(255\) 0.225387 0.0141143
\(256\) −3.79306 −0.237066
\(257\) 24.4875 1.52749 0.763745 0.645519i \(-0.223359\pi\)
0.763745 + 0.645519i \(0.223359\pi\)
\(258\) −3.18119 −0.198052
\(259\) −6.23609 −0.387492
\(260\) 0.373082 0.0231376
\(261\) −0.722806 −0.0447406
\(262\) −16.9455 −1.04690
\(263\) 21.7093 1.33865 0.669325 0.742969i \(-0.266583\pi\)
0.669325 + 0.742969i \(0.266583\pi\)
\(264\) 0 0
\(265\) −4.58827 −0.281855
\(266\) 2.65471 0.162771
\(267\) −0.664253 −0.0406516
\(268\) −2.38790 −0.145864
\(269\) −10.5726 −0.644621 −0.322310 0.946634i \(-0.604459\pi\)
−0.322310 + 0.946634i \(0.604459\pi\)
\(270\) −1.95855 −0.119194
\(271\) −23.8119 −1.44647 −0.723235 0.690602i \(-0.757346\pi\)
−0.723235 + 0.690602i \(0.757346\pi\)
\(272\) 3.39187 0.205662
\(273\) −0.569845 −0.0344886
\(274\) −22.5448 −1.36198
\(275\) 0 0
\(276\) 0.103729 0.00624373
\(277\) 0.357431 0.0214759 0.0107380 0.999942i \(-0.496582\pi\)
0.0107380 + 0.999942i \(0.496582\pi\)
\(278\) 0.570499 0.0342162
\(279\) −8.79441 −0.526508
\(280\) −2.92945 −0.175068
\(281\) 6.93387 0.413640 0.206820 0.978379i \(-0.433689\pi\)
0.206820 + 0.978379i \(0.433689\pi\)
\(282\) 1.92678 0.114738
\(283\) 12.2813 0.730050 0.365025 0.930998i \(-0.381061\pi\)
0.365025 + 0.930998i \(0.381061\pi\)
\(284\) 0.353143 0.0209552
\(285\) −0.475400 −0.0281603
\(286\) 0 0
\(287\) −6.05663 −0.357511
\(288\) 2.64005 0.155567
\(289\) −16.1395 −0.949384
\(290\) −0.333465 −0.0195817
\(291\) −0.755901 −0.0443117
\(292\) 0.0159353 0.000932543 0
\(293\) −18.4314 −1.07678 −0.538388 0.842697i \(-0.680966\pi\)
−0.538388 + 0.842697i \(0.680966\pi\)
\(294\) 0.329669 0.0192267
\(295\) −9.66792 −0.562888
\(296\) 18.2683 1.06182
\(297\) 0 0
\(298\) 13.8051 0.799708
\(299\) −6.29401 −0.363992
\(300\) 0.0386517 0.00223155
\(301\) 9.64965 0.556197
\(302\) −6.92843 −0.398686
\(303\) 3.62631 0.208326
\(304\) −7.15434 −0.410329
\(305\) −2.82941 −0.162011
\(306\) −3.70149 −0.211600
\(307\) −27.8266 −1.58815 −0.794074 0.607821i \(-0.792044\pi\)
−0.794074 + 0.607821i \(0.792044\pi\)
\(308\) 0 0
\(309\) −0.241015 −0.0137109
\(310\) −4.05728 −0.230438
\(311\) −18.5140 −1.04983 −0.524916 0.851154i \(-0.675903\pi\)
−0.524916 + 0.851154i \(0.675903\pi\)
\(312\) 1.66933 0.0945074
\(313\) −9.40487 −0.531595 −0.265797 0.964029i \(-0.585635\pi\)
−0.265797 + 0.964029i \(0.585635\pi\)
\(314\) −5.23201 −0.295259
\(315\) 2.94096 0.165705
\(316\) 1.00512 0.0565427
\(317\) −14.1532 −0.794924 −0.397462 0.917619i \(-0.630109\pi\)
−0.397462 + 0.917619i \(0.630109\pi\)
\(318\) −1.51261 −0.0848229
\(319\) 0 0
\(320\) 8.53106 0.476901
\(321\) −0.804426 −0.0448987
\(322\) 3.64123 0.202918
\(323\) −1.81496 −0.100987
\(324\) −1.34773 −0.0748737
\(325\) −2.34529 −0.130093
\(326\) 12.1848 0.674852
\(327\) −1.47817 −0.0817427
\(328\) 17.7426 0.979670
\(329\) −5.84459 −0.322222
\(330\) 0 0
\(331\) −24.4577 −1.34432 −0.672159 0.740407i \(-0.734633\pi\)
−0.672159 + 0.740407i \(0.734633\pi\)
\(332\) 2.61064 0.143278
\(333\) −18.3401 −1.00503
\(334\) −0.0874844 −0.00478693
\(335\) 15.0109 0.820135
\(336\) −0.888445 −0.0484686
\(337\) 23.7769 1.29521 0.647605 0.761976i \(-0.275771\pi\)
0.647605 + 0.761976i \(0.275771\pi\)
\(338\) 10.1755 0.553475
\(339\) 2.31876 0.125938
\(340\) 0.147563 0.00800272
\(341\) 0 0
\(342\) 7.80740 0.422176
\(343\) −1.00000 −0.0539949
\(344\) −28.2682 −1.52412
\(345\) −0.652064 −0.0351060
\(346\) −23.3644 −1.25608
\(347\) 2.31154 0.124090 0.0620450 0.998073i \(-0.480238\pi\)
0.0620450 + 0.998073i \(0.480238\pi\)
\(348\) 0.00949949 0.000509226 0
\(349\) −36.2674 −1.94135 −0.970675 0.240395i \(-0.922723\pi\)
−0.970675 + 0.240395i \(0.922723\pi\)
\(350\) 1.35681 0.0725243
\(351\) −3.38543 −0.180701
\(352\) 0 0
\(353\) −10.6567 −0.567200 −0.283600 0.958943i \(-0.591529\pi\)
−0.283600 + 0.958943i \(0.591529\pi\)
\(354\) −3.18721 −0.169398
\(355\) −2.21995 −0.117822
\(356\) −0.434892 −0.0230492
\(357\) −0.225387 −0.0119287
\(358\) 24.6962 1.30523
\(359\) −22.4588 −1.18533 −0.592664 0.805450i \(-0.701924\pi\)
−0.592664 + 0.805450i \(0.701924\pi\)
\(360\) −8.61540 −0.454072
\(361\) −15.1718 −0.798514
\(362\) 12.9474 0.680502
\(363\) 0 0
\(364\) −0.373082 −0.0195548
\(365\) −0.100173 −0.00524331
\(366\) −0.932768 −0.0487566
\(367\) 15.1093 0.788698 0.394349 0.918961i \(-0.370970\pi\)
0.394349 + 0.918961i \(0.370970\pi\)
\(368\) −9.81297 −0.511537
\(369\) −17.8123 −0.927272
\(370\) −8.46116 −0.439875
\(371\) 4.58827 0.238211
\(372\) 0.115581 0.00599258
\(373\) 22.7153 1.17616 0.588078 0.808804i \(-0.299885\pi\)
0.588078 + 0.808804i \(0.299885\pi\)
\(374\) 0 0
\(375\) −0.242974 −0.0125471
\(376\) 17.1214 0.882970
\(377\) −0.576407 −0.0296865
\(378\) 1.95855 0.100737
\(379\) −1.50696 −0.0774072 −0.0387036 0.999251i \(-0.512323\pi\)
−0.0387036 + 0.999251i \(0.512323\pi\)
\(380\) −0.311248 −0.0159667
\(381\) 2.47328 0.126710
\(382\) −13.5775 −0.694686
\(383\) −14.8062 −0.756564 −0.378282 0.925690i \(-0.623485\pi\)
−0.378282 + 0.925690i \(0.623485\pi\)
\(384\) 2.37620 0.121260
\(385\) 0 0
\(386\) 18.3619 0.934598
\(387\) 28.3793 1.44260
\(388\) −0.494895 −0.0251245
\(389\) −33.6017 −1.70368 −0.851838 0.523806i \(-0.824512\pi\)
−0.851838 + 0.523806i \(0.824512\pi\)
\(390\) −0.773170 −0.0391510
\(391\) −2.48943 −0.125896
\(392\) 2.92945 0.147960
\(393\) −3.03457 −0.153074
\(394\) 30.1871 1.52080
\(395\) −6.31847 −0.317917
\(396\) 0 0
\(397\) −23.7402 −1.19149 −0.595744 0.803174i \(-0.703143\pi\)
−0.595744 + 0.803174i \(0.703143\pi\)
\(398\) 12.8157 0.642394
\(399\) 0.475400 0.0237998
\(400\) −3.65654 −0.182827
\(401\) 25.6299 1.27990 0.639949 0.768417i \(-0.278955\pi\)
0.639949 + 0.768417i \(0.278955\pi\)
\(402\) 4.94864 0.246816
\(403\) −7.01317 −0.349351
\(404\) 2.37418 0.118120
\(405\) 8.47216 0.420985
\(406\) 0.333465 0.0165496
\(407\) 0 0
\(408\) 0.660260 0.0326877
\(409\) −26.5551 −1.31306 −0.656532 0.754299i \(-0.727977\pi\)
−0.656532 + 0.754299i \(0.727977\pi\)
\(410\) −8.21767 −0.405842
\(411\) −4.03728 −0.199145
\(412\) −0.157795 −0.00777398
\(413\) 9.66792 0.475727
\(414\) 10.7087 0.526305
\(415\) −16.4112 −0.805592
\(416\) 2.10533 0.103222
\(417\) 0.102164 0.00500298
\(418\) 0 0
\(419\) −34.6824 −1.69435 −0.847174 0.531316i \(-0.821698\pi\)
−0.847174 + 0.531316i \(0.821698\pi\)
\(420\) −0.0386517 −0.00188601
\(421\) 24.7907 1.20823 0.604113 0.796899i \(-0.293527\pi\)
0.604113 + 0.796899i \(0.293527\pi\)
\(422\) 6.45682 0.314313
\(423\) −17.1887 −0.835744
\(424\) −13.4411 −0.652757
\(425\) −0.927617 −0.0449961
\(426\) −0.731847 −0.0354581
\(427\) 2.82941 0.136925
\(428\) −0.526665 −0.0254573
\(429\) 0 0
\(430\) 13.0927 0.631387
\(431\) 6.59999 0.317910 0.158955 0.987286i \(-0.449187\pi\)
0.158955 + 0.987286i \(0.449187\pi\)
\(432\) −5.27822 −0.253948
\(433\) 20.0200 0.962101 0.481050 0.876693i \(-0.340255\pi\)
0.481050 + 0.876693i \(0.340255\pi\)
\(434\) 4.05728 0.194756
\(435\) −0.0597162 −0.00286317
\(436\) −0.967767 −0.0463476
\(437\) 5.25085 0.251182
\(438\) −0.0330240 −0.00157795
\(439\) 26.6216 1.27058 0.635290 0.772274i \(-0.280881\pi\)
0.635290 + 0.772274i \(0.280881\pi\)
\(440\) 0 0
\(441\) −2.94096 −0.140046
\(442\) −2.95178 −0.140402
\(443\) 7.35380 0.349389 0.174695 0.984623i \(-0.444106\pi\)
0.174695 + 0.984623i \(0.444106\pi\)
\(444\) 0.241035 0.0114390
\(445\) 2.73384 0.129597
\(446\) −26.6001 −1.25955
\(447\) 2.47219 0.116931
\(448\) −8.53106 −0.403055
\(449\) 1.75184 0.0826744 0.0413372 0.999145i \(-0.486838\pi\)
0.0413372 + 0.999145i \(0.486838\pi\)
\(450\) 3.99032 0.188105
\(451\) 0 0
\(452\) 1.51811 0.0714059
\(453\) −1.24073 −0.0582946
\(454\) 11.0357 0.517933
\(455\) 2.34529 0.109949
\(456\) −1.39266 −0.0652173
\(457\) −17.7181 −0.828817 −0.414409 0.910091i \(-0.636012\pi\)
−0.414409 + 0.910091i \(0.636012\pi\)
\(458\) −17.0809 −0.798140
\(459\) −1.33902 −0.0624999
\(460\) −0.426912 −0.0199049
\(461\) −20.6171 −0.960235 −0.480118 0.877204i \(-0.659406\pi\)
−0.480118 + 0.877204i \(0.659406\pi\)
\(462\) 0 0
\(463\) −13.1323 −0.610309 −0.305154 0.952303i \(-0.598708\pi\)
−0.305154 + 0.952303i \(0.598708\pi\)
\(464\) −0.898675 −0.0417199
\(465\) −0.726570 −0.0336939
\(466\) 3.76105 0.174228
\(467\) 30.8738 1.42867 0.714334 0.699805i \(-0.246730\pi\)
0.714334 + 0.699805i \(0.246730\pi\)
\(468\) −1.09722 −0.0507191
\(469\) −15.0109 −0.693141
\(470\) −7.92997 −0.365782
\(471\) −0.936938 −0.0431718
\(472\) −28.3217 −1.30361
\(473\) 0 0
\(474\) −2.08300 −0.0956754
\(475\) 1.95659 0.0897743
\(476\) −0.147563 −0.00676353
\(477\) 13.4939 0.617844
\(478\) −1.41823 −0.0648684
\(479\) 36.4945 1.66748 0.833739 0.552159i \(-0.186196\pi\)
0.833739 + 0.552159i \(0.186196\pi\)
\(480\) 0.218114 0.00995548
\(481\) −14.6254 −0.666863
\(482\) 32.9592 1.50125
\(483\) 0.652064 0.0296700
\(484\) 0 0
\(485\) 3.11103 0.141265
\(486\) 8.66866 0.393218
\(487\) −29.0277 −1.31537 −0.657685 0.753293i \(-0.728464\pi\)
−0.657685 + 0.753293i \(0.728464\pi\)
\(488\) −8.28861 −0.375208
\(489\) 2.18203 0.0986746
\(490\) −1.35681 −0.0612943
\(491\) −28.1964 −1.27249 −0.636244 0.771488i \(-0.719513\pi\)
−0.636244 + 0.771488i \(0.719513\pi\)
\(492\) 0.234099 0.0105540
\(493\) −0.227982 −0.0102678
\(494\) 6.22607 0.280124
\(495\) 0 0
\(496\) −10.9342 −0.490961
\(497\) 2.21995 0.0995782
\(498\) −5.41025 −0.242439
\(499\) −12.1817 −0.545326 −0.272663 0.962110i \(-0.587904\pi\)
−0.272663 + 0.962110i \(0.587904\pi\)
\(500\) −0.159077 −0.00711415
\(501\) −0.0156665 −0.000699929 0
\(502\) 21.3155 0.951357
\(503\) −9.57390 −0.426879 −0.213439 0.976956i \(-0.568467\pi\)
−0.213439 + 0.976956i \(0.568467\pi\)
\(504\) 8.61540 0.383761
\(505\) −14.9247 −0.664140
\(506\) 0 0
\(507\) 1.82221 0.0809272
\(508\) 1.61927 0.0718437
\(509\) −28.2988 −1.25432 −0.627161 0.778889i \(-0.715783\pi\)
−0.627161 + 0.778889i \(0.715783\pi\)
\(510\) −0.305807 −0.0135413
\(511\) 0.100173 0.00443141
\(512\) 24.7057 1.09185
\(513\) 2.82433 0.124697
\(514\) −33.2248 −1.46548
\(515\) 0.991937 0.0437100
\(516\) −0.372975 −0.0164193
\(517\) 0 0
\(518\) 8.46116 0.371762
\(519\) −4.18406 −0.183660
\(520\) −6.87041 −0.301288
\(521\) −6.04860 −0.264994 −0.132497 0.991183i \(-0.542299\pi\)
−0.132497 + 0.991183i \(0.542299\pi\)
\(522\) 0.980708 0.0429244
\(523\) −15.3496 −0.671192 −0.335596 0.942006i \(-0.608938\pi\)
−0.335596 + 0.942006i \(0.608938\pi\)
\(524\) −1.98676 −0.0867919
\(525\) 0.242974 0.0106043
\(526\) −29.4553 −1.28431
\(527\) −2.77387 −0.120832
\(528\) 0 0
\(529\) −15.7979 −0.686864
\(530\) 6.22539 0.270414
\(531\) 28.4330 1.23389
\(532\) 0.311248 0.0134943
\(533\) −14.2046 −0.615268
\(534\) 0.901263 0.0390015
\(535\) 3.31075 0.143136
\(536\) 43.9738 1.89938
\(537\) 4.42254 0.190847
\(538\) 14.3449 0.618453
\(539\) 0 0
\(540\) −0.229628 −0.00988162
\(541\) 31.1468 1.33911 0.669553 0.742765i \(-0.266486\pi\)
0.669553 + 0.742765i \(0.266486\pi\)
\(542\) 32.3081 1.38775
\(543\) 2.31860 0.0995006
\(544\) 0.832706 0.0357020
\(545\) 6.08363 0.260594
\(546\) 0.773170 0.0330886
\(547\) −2.82444 −0.120764 −0.0603821 0.998175i \(-0.519232\pi\)
−0.0603821 + 0.998175i \(0.519232\pi\)
\(548\) −2.64324 −0.112914
\(549\) 8.32119 0.355140
\(550\) 0 0
\(551\) 0.480874 0.0204859
\(552\) −1.91019 −0.0813030
\(553\) 6.31847 0.268689
\(554\) −0.484965 −0.0206042
\(555\) −1.51521 −0.0643170
\(556\) 0.0668875 0.00283666
\(557\) −5.32104 −0.225460 −0.112730 0.993626i \(-0.535959\pi\)
−0.112730 + 0.993626i \(0.535959\pi\)
\(558\) 11.9323 0.505135
\(559\) 22.6313 0.957200
\(560\) 3.65654 0.154517
\(561\) 0 0
\(562\) −9.40792 −0.396849
\(563\) −1.88609 −0.0794893 −0.0397447 0.999210i \(-0.512654\pi\)
−0.0397447 + 0.999210i \(0.512654\pi\)
\(564\) 0.225903 0.00951223
\(565\) −9.54323 −0.401487
\(566\) −16.6634 −0.700415
\(567\) −8.47216 −0.355797
\(568\) −6.50322 −0.272869
\(569\) −4.30097 −0.180306 −0.0901529 0.995928i \(-0.528736\pi\)
−0.0901529 + 0.995928i \(0.528736\pi\)
\(570\) 0.645026 0.0270171
\(571\) 10.5416 0.441153 0.220577 0.975370i \(-0.429206\pi\)
0.220577 + 0.975370i \(0.429206\pi\)
\(572\) 0 0
\(573\) −2.43143 −0.101575
\(574\) 8.21767 0.342999
\(575\) 2.68368 0.111917
\(576\) −25.0895 −1.04540
\(577\) −2.05286 −0.0854618 −0.0427309 0.999087i \(-0.513606\pi\)
−0.0427309 + 0.999087i \(0.513606\pi\)
\(578\) 21.8982 0.910845
\(579\) 3.28822 0.136654
\(580\) −0.0390967 −0.00162340
\(581\) 16.4112 0.680849
\(582\) 1.02561 0.0425129
\(583\) 0 0
\(584\) −0.293453 −0.0121432
\(585\) 6.89742 0.285173
\(586\) 25.0079 1.03307
\(587\) 25.9972 1.07302 0.536510 0.843894i \(-0.319742\pi\)
0.536510 + 0.843894i \(0.319742\pi\)
\(588\) 0.0386517 0.00159397
\(589\) 5.85081 0.241079
\(590\) 13.1175 0.540039
\(591\) 5.40585 0.222367
\(592\) −22.8025 −0.937177
\(593\) 11.1931 0.459645 0.229823 0.973233i \(-0.426185\pi\)
0.229823 + 0.973233i \(0.426185\pi\)
\(594\) 0 0
\(595\) 0.927617 0.0380286
\(596\) 1.61856 0.0662989
\(597\) 2.29502 0.0939287
\(598\) 8.53975 0.349216
\(599\) 33.8637 1.38363 0.691817 0.722073i \(-0.256811\pi\)
0.691817 + 0.722073i \(0.256811\pi\)
\(600\) −0.711781 −0.0290583
\(601\) −42.1489 −1.71929 −0.859645 0.510892i \(-0.829315\pi\)
−0.859645 + 0.510892i \(0.829315\pi\)
\(602\) −13.0927 −0.533619
\(603\) −44.1466 −1.79779
\(604\) −0.812316 −0.0330527
\(605\) 0 0
\(606\) −4.92020 −0.199870
\(607\) 22.4797 0.912422 0.456211 0.889872i \(-0.349206\pi\)
0.456211 + 0.889872i \(0.349206\pi\)
\(608\) −1.75639 −0.0712312
\(609\) 0.0597162 0.00241982
\(610\) 3.83896 0.155435
\(611\) −13.7073 −0.554536
\(612\) −0.433977 −0.0175425
\(613\) 8.61975 0.348148 0.174074 0.984733i \(-0.444307\pi\)
0.174074 + 0.984733i \(0.444307\pi\)
\(614\) 37.7553 1.52368
\(615\) −1.47160 −0.0593408
\(616\) 0 0
\(617\) −1.79131 −0.0721154 −0.0360577 0.999350i \(-0.511480\pi\)
−0.0360577 + 0.999350i \(0.511480\pi\)
\(618\) 0.327011 0.0131543
\(619\) 12.4154 0.499016 0.249508 0.968373i \(-0.419731\pi\)
0.249508 + 0.968373i \(0.419731\pi\)
\(620\) −0.475691 −0.0191042
\(621\) 3.87389 0.155454
\(622\) 25.1199 1.00722
\(623\) −2.73384 −0.109529
\(624\) −2.08366 −0.0834132
\(625\) 1.00000 0.0400000
\(626\) 12.7606 0.510016
\(627\) 0 0
\(628\) −0.613421 −0.0244782
\(629\) −5.78471 −0.230651
\(630\) −3.99032 −0.158978
\(631\) −6.81348 −0.271240 −0.135620 0.990761i \(-0.543303\pi\)
−0.135620 + 0.990761i \(0.543303\pi\)
\(632\) −18.5096 −0.736273
\(633\) 1.15627 0.0459578
\(634\) 19.2032 0.762655
\(635\) −10.1792 −0.403948
\(636\) −0.177344 −0.00703215
\(637\) −2.34529 −0.0929238
\(638\) 0 0
\(639\) 6.52878 0.258274
\(640\) −9.77963 −0.386574
\(641\) −48.3163 −1.90838 −0.954190 0.299202i \(-0.903280\pi\)
−0.954190 + 0.299202i \(0.903280\pi\)
\(642\) 1.09145 0.0430761
\(643\) −45.7624 −1.80469 −0.902346 0.431012i \(-0.858157\pi\)
−0.902346 + 0.431012i \(0.858157\pi\)
\(644\) 0.426912 0.0168227
\(645\) 2.34462 0.0923192
\(646\) 2.46255 0.0968879
\(647\) −14.5828 −0.573310 −0.286655 0.958034i \(-0.592543\pi\)
−0.286655 + 0.958034i \(0.592543\pi\)
\(648\) 24.8188 0.974973
\(649\) 0 0
\(650\) 3.18211 0.124812
\(651\) 0.726570 0.0284765
\(652\) 1.42859 0.0559479
\(653\) 17.5533 0.686913 0.343456 0.939169i \(-0.388402\pi\)
0.343456 + 0.939169i \(0.388402\pi\)
\(654\) 2.00558 0.0784245
\(655\) 12.4893 0.487996
\(656\) −22.1463 −0.864668
\(657\) 0.294606 0.0114937
\(658\) 7.92997 0.309142
\(659\) −15.1180 −0.588915 −0.294458 0.955665i \(-0.595139\pi\)
−0.294458 + 0.955665i \(0.595139\pi\)
\(660\) 0 0
\(661\) −38.6231 −1.50226 −0.751132 0.660152i \(-0.770492\pi\)
−0.751132 + 0.660152i \(0.770492\pi\)
\(662\) 33.1844 1.28975
\(663\) −0.528598 −0.0205291
\(664\) −48.0756 −1.86570
\(665\) −1.95659 −0.0758732
\(666\) 24.8840 0.964234
\(667\) 0.659572 0.0255387
\(668\) −0.0102570 −0.000396856 0
\(669\) −4.76349 −0.184167
\(670\) −20.3669 −0.786843
\(671\) 0 0
\(672\) −0.218114 −0.00841392
\(673\) −41.8975 −1.61503 −0.807515 0.589847i \(-0.799188\pi\)
−0.807515 + 0.589847i \(0.799188\pi\)
\(674\) −32.2606 −1.24263
\(675\) 1.44350 0.0555604
\(676\) 1.19302 0.0458853
\(677\) 15.8363 0.608637 0.304318 0.952570i \(-0.401571\pi\)
0.304318 + 0.952570i \(0.401571\pi\)
\(678\) −3.14611 −0.120825
\(679\) −3.11103 −0.119391
\(680\) −2.71741 −0.104208
\(681\) 1.97626 0.0757304
\(682\) 0 0
\(683\) 16.7634 0.641434 0.320717 0.947175i \(-0.396076\pi\)
0.320717 + 0.947175i \(0.396076\pi\)
\(684\) 0.915370 0.0350000
\(685\) 16.6161 0.634869
\(686\) 1.35681 0.0518031
\(687\) −3.05882 −0.116701
\(688\) 35.2843 1.34520
\(689\) 10.7608 0.409955
\(690\) 0.884725 0.0336809
\(691\) −0.259485 −0.00987129 −0.00493564 0.999988i \(-0.501571\pi\)
−0.00493564 + 0.999988i \(0.501571\pi\)
\(692\) −2.73934 −0.104134
\(693\) 0 0
\(694\) −3.13631 −0.119053
\(695\) −0.420472 −0.0159494
\(696\) −0.174936 −0.00663092
\(697\) −5.61823 −0.212806
\(698\) 49.2079 1.86254
\(699\) 0.673522 0.0254750
\(700\) 0.159077 0.00601255
\(701\) 14.0986 0.532498 0.266249 0.963904i \(-0.414216\pi\)
0.266249 + 0.963904i \(0.414216\pi\)
\(702\) 4.59337 0.173366
\(703\) 12.2014 0.460186
\(704\) 0 0
\(705\) −1.42008 −0.0534834
\(706\) 14.4591 0.544176
\(707\) 14.9247 0.561301
\(708\) −0.373681 −0.0140438
\(709\) 18.0034 0.676131 0.338065 0.941123i \(-0.390227\pi\)
0.338065 + 0.941123i \(0.390227\pi\)
\(710\) 3.01204 0.113040
\(711\) 18.5824 0.696894
\(712\) 8.00865 0.300137
\(713\) 8.02505 0.300540
\(714\) 0.305807 0.0114445
\(715\) 0 0
\(716\) 2.89548 0.108209
\(717\) −0.253974 −0.00948483
\(718\) 30.4722 1.13721
\(719\) −20.5769 −0.767387 −0.383694 0.923460i \(-0.625348\pi\)
−0.383694 + 0.923460i \(0.625348\pi\)
\(720\) 10.7538 0.400769
\(721\) −0.991937 −0.0369417
\(722\) 20.5851 0.766100
\(723\) 5.90227 0.219508
\(724\) 1.51801 0.0564163
\(725\) 0.245772 0.00912774
\(726\) 0 0
\(727\) −2.37912 −0.0882368 −0.0441184 0.999026i \(-0.514048\pi\)
−0.0441184 + 0.999026i \(0.514048\pi\)
\(728\) 6.87041 0.254634
\(729\) −23.8641 −0.883856
\(730\) 0.135916 0.00503047
\(731\) 8.95119 0.331072
\(732\) −0.109361 −0.00404211
\(733\) 9.09774 0.336033 0.168016 0.985784i \(-0.446264\pi\)
0.168016 + 0.985784i \(0.446264\pi\)
\(734\) −20.5004 −0.756682
\(735\) −0.242974 −0.00896224
\(736\) −2.40909 −0.0888002
\(737\) 0 0
\(738\) 24.1679 0.889631
\(739\) 12.3131 0.452944 0.226472 0.974018i \(-0.427281\pi\)
0.226472 + 0.974018i \(0.427281\pi\)
\(740\) −0.992020 −0.0364674
\(741\) 1.11495 0.0409588
\(742\) −6.22539 −0.228541
\(743\) 51.7175 1.89733 0.948666 0.316279i \(-0.102434\pi\)
0.948666 + 0.316279i \(0.102434\pi\)
\(744\) −2.12845 −0.0780327
\(745\) −10.1747 −0.372772
\(746\) −30.8203 −1.12841
\(747\) 48.2646 1.76591
\(748\) 0 0
\(749\) −3.31075 −0.120972
\(750\) 0.329669 0.0120378
\(751\) 13.7321 0.501093 0.250546 0.968105i \(-0.419390\pi\)
0.250546 + 0.968105i \(0.419390\pi\)
\(752\) −21.3710 −0.779319
\(753\) 3.81714 0.139104
\(754\) 0.782072 0.0284814
\(755\) 5.10643 0.185842
\(756\) 0.229628 0.00835149
\(757\) −49.2807 −1.79114 −0.895568 0.444924i \(-0.853231\pi\)
−0.895568 + 0.444924i \(0.853231\pi\)
\(758\) 2.04465 0.0742650
\(759\) 0 0
\(760\) 5.73172 0.207911
\(761\) −12.4590 −0.451637 −0.225818 0.974169i \(-0.572506\pi\)
−0.225818 + 0.974169i \(0.572506\pi\)
\(762\) −3.35576 −0.121566
\(763\) −6.08363 −0.220242
\(764\) −1.59188 −0.0575922
\(765\) 2.72809 0.0986343
\(766\) 20.0892 0.725853
\(767\) 22.6741 0.818714
\(768\) 0.921616 0.0332559
\(769\) 21.9501 0.791540 0.395770 0.918350i \(-0.370478\pi\)
0.395770 + 0.918350i \(0.370478\pi\)
\(770\) 0 0
\(771\) −5.94983 −0.214278
\(772\) 2.15282 0.0774819
\(773\) 23.0657 0.829617 0.414808 0.909909i \(-0.363849\pi\)
0.414808 + 0.909909i \(0.363849\pi\)
\(774\) −38.5052 −1.38404
\(775\) 2.99032 0.107415
\(776\) 9.11362 0.327160
\(777\) 1.51521 0.0543578
\(778\) 45.5910 1.63452
\(779\) 11.8503 0.424582
\(780\) −0.0906494 −0.00324577
\(781\) 0 0
\(782\) 3.37767 0.120785
\(783\) 0.354772 0.0126785
\(784\) −3.65654 −0.130591
\(785\) 3.85612 0.137631
\(786\) 4.11732 0.146860
\(787\) 46.7274 1.66565 0.832826 0.553534i \(-0.186721\pi\)
0.832826 + 0.553534i \(0.186721\pi\)
\(788\) 3.53925 0.126081
\(789\) −5.27479 −0.187788
\(790\) 8.57293 0.305011
\(791\) 9.54323 0.339318
\(792\) 0 0
\(793\) 6.63579 0.235644
\(794\) 32.2109 1.14312
\(795\) 1.11483 0.0395390
\(796\) 1.50257 0.0532570
\(797\) 49.0362 1.73695 0.868475 0.495732i \(-0.165100\pi\)
0.868475 + 0.495732i \(0.165100\pi\)
\(798\) −0.645026 −0.0228337
\(799\) −5.42154 −0.191800
\(800\) −0.897683 −0.0317379
\(801\) −8.04013 −0.284084
\(802\) −34.7749 −1.22794
\(803\) 0 0
\(804\) 0.580198 0.0204620
\(805\) −2.68368 −0.0945872
\(806\) 9.51551 0.335169
\(807\) 2.56886 0.0904282
\(808\) −43.7211 −1.53810
\(809\) 9.38528 0.329969 0.164984 0.986296i \(-0.447243\pi\)
0.164984 + 0.986296i \(0.447243\pi\)
\(810\) −11.4951 −0.403896
\(811\) −9.21722 −0.323660 −0.161830 0.986819i \(-0.551740\pi\)
−0.161830 + 0.986819i \(0.551740\pi\)
\(812\) 0.0390967 0.00137203
\(813\) 5.78568 0.202913
\(814\) 0 0
\(815\) −8.98048 −0.314573
\(816\) −0.824137 −0.0288506
\(817\) −18.8804 −0.660541
\(818\) 36.0301 1.25976
\(819\) −6.89742 −0.241015
\(820\) −0.963471 −0.0336459
\(821\) 17.3336 0.604946 0.302473 0.953158i \(-0.402188\pi\)
0.302473 + 0.953158i \(0.402188\pi\)
\(822\) 5.47781 0.191061
\(823\) −42.7706 −1.49089 −0.745445 0.666567i \(-0.767763\pi\)
−0.745445 + 0.666567i \(0.767763\pi\)
\(824\) 2.90583 0.101229
\(825\) 0 0
\(826\) −13.1175 −0.456416
\(827\) −19.0832 −0.663589 −0.331794 0.943352i \(-0.607654\pi\)
−0.331794 + 0.943352i \(0.607654\pi\)
\(828\) 1.25553 0.0436328
\(829\) −40.8201 −1.41774 −0.708870 0.705340i \(-0.750795\pi\)
−0.708870 + 0.705340i \(0.750795\pi\)
\(830\) 22.2668 0.772890
\(831\) −0.0868465 −0.00301267
\(832\) −20.0078 −0.693647
\(833\) −0.927617 −0.0321400
\(834\) −0.138617 −0.00479990
\(835\) 0.0644782 0.00223136
\(836\) 0 0
\(837\) 4.31653 0.149201
\(838\) 47.0573 1.62557
\(839\) 33.0074 1.13954 0.569771 0.821804i \(-0.307032\pi\)
0.569771 + 0.821804i \(0.307032\pi\)
\(840\) 0.711781 0.0245588
\(841\) −28.9396 −0.997917
\(842\) −33.6362 −1.15918
\(843\) −1.68475 −0.0580259
\(844\) 0.757022 0.0260578
\(845\) −7.49961 −0.257994
\(846\) 23.3218 0.801818
\(847\) 0 0
\(848\) 16.7772 0.576131
\(849\) −2.98405 −0.102412
\(850\) 1.25860 0.0431695
\(851\) 16.7357 0.573691
\(852\) −0.0858046 −0.00293962
\(853\) −48.6092 −1.66435 −0.832173 0.554516i \(-0.812903\pi\)
−0.832173 + 0.554516i \(0.812903\pi\)
\(854\) −3.83896 −0.131366
\(855\) −5.75425 −0.196791
\(856\) 9.69867 0.331494
\(857\) −18.1003 −0.618294 −0.309147 0.951014i \(-0.600043\pi\)
−0.309147 + 0.951014i \(0.600043\pi\)
\(858\) 0 0
\(859\) −7.23154 −0.246737 −0.123368 0.992361i \(-0.539370\pi\)
−0.123368 + 0.992361i \(0.539370\pi\)
\(860\) 1.53504 0.0523444
\(861\) 1.47160 0.0501521
\(862\) −8.95491 −0.305005
\(863\) 30.3494 1.03310 0.516552 0.856256i \(-0.327215\pi\)
0.516552 + 0.856256i \(0.327215\pi\)
\(864\) −1.29581 −0.0440842
\(865\) 17.2202 0.585504
\(866\) −27.1633 −0.923046
\(867\) 3.92149 0.133181
\(868\) 0.475691 0.0161460
\(869\) 0 0
\(870\) 0.0810233 0.00274695
\(871\) −35.2050 −1.19288
\(872\) 17.8217 0.603519
\(873\) −9.14944 −0.309662
\(874\) −7.12438 −0.240986
\(875\) −1.00000 −0.0338062
\(876\) −0.00387187 −0.000130818 0
\(877\) −32.3026 −1.09078 −0.545391 0.838182i \(-0.683619\pi\)
−0.545391 + 0.838182i \(0.683619\pi\)
\(878\) −36.1203 −1.21900
\(879\) 4.47836 0.151051
\(880\) 0 0
\(881\) 23.1158 0.778792 0.389396 0.921070i \(-0.372684\pi\)
0.389396 + 0.921070i \(0.372684\pi\)
\(882\) 3.99032 0.134361
\(883\) 47.4436 1.59661 0.798303 0.602257i \(-0.205732\pi\)
0.798303 + 0.602257i \(0.205732\pi\)
\(884\) −0.346078 −0.0116399
\(885\) 2.34906 0.0789626
\(886\) −9.97768 −0.335207
\(887\) 49.3267 1.65623 0.828114 0.560560i \(-0.189414\pi\)
0.828114 + 0.560560i \(0.189414\pi\)
\(888\) −4.43873 −0.148954
\(889\) 10.1792 0.341399
\(890\) −3.70930 −0.124336
\(891\) 0 0
\(892\) −3.11870 −0.104422
\(893\) 11.4354 0.382672
\(894\) −3.35428 −0.112184
\(895\) −18.2017 −0.608416
\(896\) 9.77963 0.326715
\(897\) 1.52928 0.0510612
\(898\) −2.37691 −0.0793184
\(899\) 0.734936 0.0245115
\(900\) 0.467840 0.0155947
\(901\) 4.25616 0.141793
\(902\) 0 0
\(903\) −2.34462 −0.0780240
\(904\) −27.9564 −0.929816
\(905\) −9.54258 −0.317206
\(906\) 1.68343 0.0559282
\(907\) 32.7141 1.08625 0.543126 0.839651i \(-0.317240\pi\)
0.543126 + 0.839651i \(0.317240\pi\)
\(908\) 1.29387 0.0429387
\(909\) 43.8930 1.45584
\(910\) −3.18211 −0.105486
\(911\) −15.9930 −0.529870 −0.264935 0.964266i \(-0.585351\pi\)
−0.264935 + 0.964266i \(0.585351\pi\)
\(912\) 1.73832 0.0575615
\(913\) 0 0
\(914\) 24.0400 0.795173
\(915\) 0.687473 0.0227272
\(916\) −2.00264 −0.0661689
\(917\) −12.4893 −0.412432
\(918\) 1.81679 0.0599629
\(919\) −47.6485 −1.57178 −0.785890 0.618366i \(-0.787795\pi\)
−0.785890 + 0.618366i \(0.787795\pi\)
\(920\) 7.86170 0.259192
\(921\) 6.76115 0.222787
\(922\) 27.9734 0.921256
\(923\) 5.20642 0.171371
\(924\) 0 0
\(925\) 6.23609 0.205041
\(926\) 17.8179 0.585534
\(927\) −2.91725 −0.0958151
\(928\) −0.220625 −0.00724237
\(929\) 53.3770 1.75124 0.875622 0.482998i \(-0.160452\pi\)
0.875622 + 0.482998i \(0.160452\pi\)
\(930\) 0.985814 0.0323261
\(931\) 1.95659 0.0641245
\(932\) 0.440961 0.0144441
\(933\) 4.49842 0.147272
\(934\) −41.8897 −1.37067
\(935\) 0 0
\(936\) 20.2056 0.660442
\(937\) −13.0806 −0.427326 −0.213663 0.976907i \(-0.568539\pi\)
−0.213663 + 0.976907i \(0.568539\pi\)
\(938\) 20.3669 0.665004
\(939\) 2.28514 0.0745727
\(940\) −0.929741 −0.0303248
\(941\) 40.1799 1.30983 0.654913 0.755704i \(-0.272705\pi\)
0.654913 + 0.755704i \(0.272705\pi\)
\(942\) 1.27124 0.0414193
\(943\) 16.2540 0.529304
\(944\) 35.3511 1.15058
\(945\) −1.44350 −0.0469571
\(946\) 0 0
\(947\) 21.1138 0.686105 0.343053 0.939316i \(-0.388539\pi\)
0.343053 + 0.939316i \(0.388539\pi\)
\(948\) −0.244219 −0.00793187
\(949\) 0.234936 0.00762634
\(950\) −2.65471 −0.0861301
\(951\) 3.43887 0.111513
\(952\) 2.71741 0.0880717
\(953\) 36.3562 1.17769 0.588846 0.808245i \(-0.299582\pi\)
0.588846 + 0.808245i \(0.299582\pi\)
\(954\) −18.3086 −0.592764
\(955\) 10.0070 0.323818
\(956\) −0.166279 −0.00537784
\(957\) 0 0
\(958\) −49.5160 −1.59979
\(959\) −16.6161 −0.536562
\(960\) −2.07283 −0.0669002
\(961\) −22.0580 −0.711548
\(962\) 19.8439 0.639793
\(963\) −9.73679 −0.313764
\(964\) 3.86426 0.124460
\(965\) −13.5332 −0.435649
\(966\) −0.884725 −0.0284656
\(967\) 3.01730 0.0970299 0.0485149 0.998822i \(-0.484551\pi\)
0.0485149 + 0.998822i \(0.484551\pi\)
\(968\) 0 0
\(969\) 0.440989 0.0141666
\(970\) −4.22107 −0.135530
\(971\) 49.6294 1.59268 0.796341 0.604847i \(-0.206766\pi\)
0.796341 + 0.604847i \(0.206766\pi\)
\(972\) 1.01635 0.0325994
\(973\) 0.420472 0.0134797
\(974\) 39.3849 1.26197
\(975\) 0.569845 0.0182497
\(976\) 10.3458 0.331162
\(977\) −11.0956 −0.354979 −0.177490 0.984123i \(-0.556798\pi\)
−0.177490 + 0.984123i \(0.556798\pi\)
\(978\) −2.96058 −0.0946691
\(979\) 0 0
\(980\) −0.159077 −0.00508154
\(981\) −17.8917 −0.571239
\(982\) 38.2571 1.22083
\(983\) 16.2497 0.518283 0.259142 0.965839i \(-0.416560\pi\)
0.259142 + 0.965839i \(0.416560\pi\)
\(984\) −4.31099 −0.137429
\(985\) −22.2486 −0.708901
\(986\) 0.309328 0.00985100
\(987\) 1.42008 0.0452018
\(988\) 0.729968 0.0232234
\(989\) −25.8966 −0.823463
\(990\) 0 0
\(991\) −31.8831 −1.01280 −0.506400 0.862299i \(-0.669024\pi\)
−0.506400 + 0.862299i \(0.669024\pi\)
\(992\) −2.68436 −0.0852284
\(993\) 5.94259 0.188582
\(994\) −3.01204 −0.0955360
\(995\) −9.44551 −0.299443
\(996\) −0.634318 −0.0200991
\(997\) 10.3751 0.328584 0.164292 0.986412i \(-0.447466\pi\)
0.164292 + 0.986412i \(0.447466\pi\)
\(998\) 16.5282 0.523190
\(999\) 9.00180 0.284804
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 4235.2.a.bc.1.2 5
11.10 odd 2 4235.2.a.bd.1.4 yes 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4235.2.a.bc.1.2 5 1.1 even 1 trivial
4235.2.a.bd.1.4 yes 5 11.10 odd 2