Properties

Label 4730.2.a.w.1.8
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 1
Dimension 8
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(2.70201\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.70201 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.70201 q^{6} +0.961819 q^{7} -1.00000 q^{8} -0.103166 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.70201 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.70201 q^{6} +0.961819 q^{7} -1.00000 q^{8} -0.103166 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.70201 q^{12} -2.37582 q^{13} -0.961819 q^{14} +1.70201 q^{15} +1.00000 q^{16} +0.206466 q^{17} +0.103166 q^{18} -0.413677 q^{19} +1.00000 q^{20} +1.63702 q^{21} -1.00000 q^{22} -4.37582 q^{23} -1.70201 q^{24} +1.00000 q^{25} +2.37582 q^{26} -5.28162 q^{27} +0.961819 q^{28} -5.05157 q^{29} -1.70201 q^{30} -6.59571 q^{31} -1.00000 q^{32} +1.70201 q^{33} -0.206466 q^{34} +0.961819 q^{35} -0.103166 q^{36} -9.05446 q^{37} +0.413677 q^{38} -4.04367 q^{39} -1.00000 q^{40} -7.15062 q^{41} -1.63702 q^{42} -1.00000 q^{43} +1.00000 q^{44} -0.103166 q^{45} +4.37582 q^{46} -10.4220 q^{47} +1.70201 q^{48} -6.07490 q^{49} -1.00000 q^{50} +0.351408 q^{51} -2.37582 q^{52} +9.81295 q^{53} +5.28162 q^{54} +1.00000 q^{55} -0.961819 q^{56} -0.704082 q^{57} +5.05157 q^{58} +5.21881 q^{59} +1.70201 q^{60} +7.54665 q^{61} +6.59571 q^{62} -0.0992265 q^{63} +1.00000 q^{64} -2.37582 q^{65} -1.70201 q^{66} +7.11705 q^{67} +0.206466 q^{68} -7.44769 q^{69} -0.961819 q^{70} +1.63446 q^{71} +0.103166 q^{72} -9.11062 q^{73} +9.05446 q^{74} +1.70201 q^{75} -0.413677 q^{76} +0.961819 q^{77} +4.04367 q^{78} +2.19376 q^{79} +1.00000 q^{80} -8.67986 q^{81} +7.15062 q^{82} -5.54961 q^{83} +1.63702 q^{84} +0.206466 q^{85} +1.00000 q^{86} -8.59782 q^{87} -1.00000 q^{88} -16.7071 q^{89} +0.103166 q^{90} -2.28511 q^{91} -4.37582 q^{92} -11.2260 q^{93} +10.4220 q^{94} -0.413677 q^{95} -1.70201 q^{96} +2.79975 q^{97} +6.07490 q^{98} -0.103166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} + O(q^{10}) \) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} - 8q^{10} + 8q^{11} - 7q^{12} - 2q^{13} + 6q^{14} - 7q^{15} + 8q^{16} - 8q^{17} - 7q^{18} + 8q^{20} + 14q^{21} - 8q^{22} - 18q^{23} + 7q^{24} + 8q^{25} + 2q^{26} - 22q^{27} - 6q^{28} + 8q^{29} + 7q^{30} - 11q^{31} - 8q^{32} - 7q^{33} + 8q^{34} - 6q^{35} + 7q^{36} - 17q^{37} - 6q^{39} - 8q^{40} + 12q^{41} - 14q^{42} - 8q^{43} + 8q^{44} + 7q^{45} + 18q^{46} - 19q^{47} - 7q^{48} - 2q^{49} - 8q^{50} - q^{51} - 2q^{52} - 7q^{53} + 22q^{54} + 8q^{55} + 6q^{56} - 3q^{57} - 8q^{58} + q^{59} - 7q^{60} + 6q^{61} + 11q^{62} - 15q^{63} + 8q^{64} - 2q^{65} + 7q^{66} - 22q^{67} - 8q^{68} + 8q^{69} + 6q^{70} - 14q^{71} - 7q^{72} - 13q^{73} + 17q^{74} - 7q^{75} - 6q^{77} + 6q^{78} - 8q^{79} + 8q^{80} + 28q^{81} - 12q^{82} - 4q^{83} + 14q^{84} - 8q^{85} + 8q^{86} - 30q^{87} - 8q^{88} + 5q^{89} - 7q^{90} - 8q^{91} - 18q^{92} + q^{93} + 19q^{94} + 7q^{96} - 23q^{97} + 2q^{98} + 7q^{99} + O(q^{100}) \)

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
\(3\) 1.70201 0.982655 0.491328 0.870975i \(-0.336512\pi\)
0.491328 + 0.870975i \(0.336512\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.70201 −0.694842
\(7\) 0.961819 0.363533 0.181767 0.983342i \(-0.441818\pi\)
0.181767 + 0.983342i \(0.441818\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.103166 −0.0343885
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 1.70201 0.491328
\(13\) −2.37582 −0.658935 −0.329468 0.944167i \(-0.606869\pi\)
−0.329468 + 0.944167i \(0.606869\pi\)
\(14\) −0.961819 −0.257057
\(15\) 1.70201 0.439457
\(16\) 1.00000 0.250000
\(17\) 0.206466 0.0500755 0.0250377 0.999687i \(-0.492029\pi\)
0.0250377 + 0.999687i \(0.492029\pi\)
\(18\) 0.103166 0.0243163
\(19\) −0.413677 −0.0949041 −0.0474520 0.998874i \(-0.515110\pi\)
−0.0474520 + 0.998874i \(0.515110\pi\)
\(20\) 1.00000 0.223607
\(21\) 1.63702 0.357228
\(22\) −1.00000 −0.213201
\(23\) −4.37582 −0.912422 −0.456211 0.889872i \(-0.650794\pi\)
−0.456211 + 0.889872i \(0.650794\pi\)
\(24\) −1.70201 −0.347421
\(25\) 1.00000 0.200000
\(26\) 2.37582 0.465937
\(27\) −5.28162 −1.01645
\(28\) 0.961819 0.181767
\(29\) −5.05157 −0.938053 −0.469026 0.883184i \(-0.655395\pi\)
−0.469026 + 0.883184i \(0.655395\pi\)
\(30\) −1.70201 −0.310743
\(31\) −6.59571 −1.18462 −0.592312 0.805709i \(-0.701785\pi\)
−0.592312 + 0.805709i \(0.701785\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.70201 0.296282
\(34\) −0.206466 −0.0354087
\(35\) 0.961819 0.162577
\(36\) −0.103166 −0.0171943
\(37\) −9.05446 −1.48854 −0.744272 0.667877i \(-0.767203\pi\)
−0.744272 + 0.667877i \(0.767203\pi\)
\(38\) 0.413677 0.0671073
\(39\) −4.04367 −0.647506
\(40\) −1.00000 −0.158114
\(41\) −7.15062 −1.11674 −0.558370 0.829592i \(-0.688573\pi\)
−0.558370 + 0.829592i \(0.688573\pi\)
\(42\) −1.63702 −0.252598
\(43\) −1.00000 −0.152499
\(44\) 1.00000 0.150756
\(45\) −0.103166 −0.0153790
\(46\) 4.37582 0.645180
\(47\) −10.4220 −1.52020 −0.760102 0.649804i \(-0.774851\pi\)
−0.760102 + 0.649804i \(0.774851\pi\)
\(48\) 1.70201 0.245664
\(49\) −6.07490 −0.867843
\(50\) −1.00000 −0.141421
\(51\) 0.351408 0.0492069
\(52\) −2.37582 −0.329468
\(53\) 9.81295 1.34791 0.673956 0.738771i \(-0.264594\pi\)
0.673956 + 0.738771i \(0.264594\pi\)
\(54\) 5.28162 0.718737
\(55\) 1.00000 0.134840
\(56\) −0.961819 −0.128528
\(57\) −0.704082 −0.0932580
\(58\) 5.05157 0.663303
\(59\) 5.21881 0.679431 0.339716 0.940528i \(-0.389669\pi\)
0.339716 + 0.940528i \(0.389669\pi\)
\(60\) 1.70201 0.219728
\(61\) 7.54665 0.966249 0.483124 0.875552i \(-0.339502\pi\)
0.483124 + 0.875552i \(0.339502\pi\)
\(62\) 6.59571 0.837656
\(63\) −0.0992265 −0.0125014
\(64\) 1.00000 0.125000
\(65\) −2.37582 −0.294685
\(66\) −1.70201 −0.209503
\(67\) 7.11705 0.869486 0.434743 0.900555i \(-0.356839\pi\)
0.434743 + 0.900555i \(0.356839\pi\)
\(68\) 0.206466 0.0250377
\(69\) −7.44769 −0.896597
\(70\) −0.961819 −0.114959
\(71\) 1.63446 0.193974 0.0969872 0.995286i \(-0.469079\pi\)
0.0969872 + 0.995286i \(0.469079\pi\)
\(72\) 0.103166 0.0121582
\(73\) −9.11062 −1.06632 −0.533159 0.846015i \(-0.678995\pi\)
−0.533159 + 0.846015i \(0.678995\pi\)
\(74\) 9.05446 1.05256
\(75\) 1.70201 0.196531
\(76\) −0.413677 −0.0474520
\(77\) 0.961819 0.109609
\(78\) 4.04367 0.457856
\(79\) 2.19376 0.246818 0.123409 0.992356i \(-0.460617\pi\)
0.123409 + 0.992356i \(0.460617\pi\)
\(80\) 1.00000 0.111803
\(81\) −8.67986 −0.964429
\(82\) 7.15062 0.789654
\(83\) −5.54961 −0.609148 −0.304574 0.952489i \(-0.598514\pi\)
−0.304574 + 0.952489i \(0.598514\pi\)
\(84\) 1.63702 0.178614
\(85\) 0.206466 0.0223944
\(86\) 1.00000 0.107833
\(87\) −8.59782 −0.921783
\(88\) −1.00000 −0.106600
\(89\) −16.7071 −1.77095 −0.885474 0.464689i \(-0.846166\pi\)
−0.885474 + 0.464689i \(0.846166\pi\)
\(90\) 0.103166 0.0108746
\(91\) −2.28511 −0.239545
\(92\) −4.37582 −0.456211
\(93\) −11.2260 −1.16408
\(94\) 10.4220 1.07495
\(95\) −0.413677 −0.0424424
\(96\) −1.70201 −0.173711
\(97\) 2.79975 0.284271 0.142136 0.989847i \(-0.454603\pi\)
0.142136 + 0.989847i \(0.454603\pi\)
\(98\) 6.07490 0.613658
\(99\) −0.103166 −0.0103685
\(100\) 1.00000 0.100000
\(101\) 18.4724 1.83807 0.919036 0.394174i \(-0.128969\pi\)
0.919036 + 0.394174i \(0.128969\pi\)
\(102\) −0.351408 −0.0347945
\(103\) −14.9220 −1.47031 −0.735153 0.677901i \(-0.762890\pi\)
−0.735153 + 0.677901i \(0.762890\pi\)
\(104\) 2.37582 0.232969
\(105\) 1.63702 0.159757
\(106\) −9.81295 −0.953118
\(107\) 17.2230 1.66501 0.832503 0.554020i \(-0.186907\pi\)
0.832503 + 0.554020i \(0.186907\pi\)
\(108\) −5.28162 −0.508224
\(109\) 4.94258 0.473413 0.236706 0.971581i \(-0.423932\pi\)
0.236706 + 0.971581i \(0.423932\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −15.4108 −1.46273
\(112\) 0.961819 0.0908833
\(113\) −1.33914 −0.125976 −0.0629880 0.998014i \(-0.520063\pi\)
−0.0629880 + 0.998014i \(0.520063\pi\)
\(114\) 0.704082 0.0659434
\(115\) −4.37582 −0.408048
\(116\) −5.05157 −0.469026
\(117\) 0.245103 0.0226598
\(118\) −5.21881 −0.480431
\(119\) 0.198583 0.0182041
\(120\) −1.70201 −0.155371
\(121\) 1.00000 0.0909091
\(122\) −7.54665 −0.683241
\(123\) −12.1704 −1.09737
\(124\) −6.59571 −0.592312
\(125\) 1.00000 0.0894427
\(126\) 0.0992265 0.00883980
\(127\) −2.61565 −0.232101 −0.116051 0.993243i \(-0.537024\pi\)
−0.116051 + 0.993243i \(0.537024\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.70201 −0.149854
\(130\) 2.37582 0.208374
\(131\) −9.98567 −0.872452 −0.436226 0.899837i \(-0.643685\pi\)
−0.436226 + 0.899837i \(0.643685\pi\)
\(132\) 1.70201 0.148141
\(133\) −0.397883 −0.0345008
\(134\) −7.11705 −0.614820
\(135\) −5.28162 −0.454569
\(136\) −0.206466 −0.0177043
\(137\) −15.5593 −1.32932 −0.664661 0.747145i \(-0.731424\pi\)
−0.664661 + 0.747145i \(0.731424\pi\)
\(138\) 7.44769 0.633990
\(139\) 9.87107 0.837253 0.418627 0.908158i \(-0.362512\pi\)
0.418627 + 0.908158i \(0.362512\pi\)
\(140\) 0.961819 0.0812885
\(141\) −17.7383 −1.49384
\(142\) −1.63446 −0.137161
\(143\) −2.37582 −0.198676
\(144\) −0.103166 −0.00859713
\(145\) −5.05157 −0.419510
\(146\) 9.11062 0.754000
\(147\) −10.3395 −0.852791
\(148\) −9.05446 −0.744272
\(149\) 19.6052 1.60612 0.803060 0.595898i \(-0.203204\pi\)
0.803060 + 0.595898i \(0.203204\pi\)
\(150\) −1.70201 −0.138968
\(151\) −8.91621 −0.725591 −0.362795 0.931869i \(-0.618178\pi\)
−0.362795 + 0.931869i \(0.618178\pi\)
\(152\) 0.413677 0.0335537
\(153\) −0.0213002 −0.00172202
\(154\) −0.961819 −0.0775056
\(155\) −6.59571 −0.529780
\(156\) −4.04367 −0.323753
\(157\) 13.1048 1.04588 0.522940 0.852369i \(-0.324835\pi\)
0.522940 + 0.852369i \(0.324835\pi\)
\(158\) −2.19376 −0.174527
\(159\) 16.7017 1.32453
\(160\) −1.00000 −0.0790569
\(161\) −4.20875 −0.331696
\(162\) 8.67986 0.681954
\(163\) 9.93240 0.777965 0.388983 0.921245i \(-0.372827\pi\)
0.388983 + 0.921245i \(0.372827\pi\)
\(164\) −7.15062 −0.558370
\(165\) 1.70201 0.132501
\(166\) 5.54961 0.430733
\(167\) 5.82283 0.450584 0.225292 0.974291i \(-0.427666\pi\)
0.225292 + 0.974291i \(0.427666\pi\)
\(168\) −1.63702 −0.126299
\(169\) −7.35546 −0.565805
\(170\) −0.206466 −0.0158353
\(171\) 0.0426772 0.00326361
\(172\) −1.00000 −0.0762493
\(173\) 21.4892 1.63379 0.816897 0.576784i \(-0.195693\pi\)
0.816897 + 0.576784i \(0.195693\pi\)
\(174\) 8.59782 0.651799
\(175\) 0.961819 0.0727067
\(176\) 1.00000 0.0753778
\(177\) 8.88246 0.667647
\(178\) 16.7071 1.25225
\(179\) −5.87243 −0.438926 −0.219463 0.975621i \(-0.570431\pi\)
−0.219463 + 0.975621i \(0.570431\pi\)
\(180\) −0.103166 −0.00768950
\(181\) 2.70569 0.201113 0.100556 0.994931i \(-0.467938\pi\)
0.100556 + 0.994931i \(0.467938\pi\)
\(182\) 2.28511 0.169384
\(183\) 12.8445 0.949490
\(184\) 4.37582 0.322590
\(185\) −9.05446 −0.665697
\(186\) 11.2260 0.823127
\(187\) 0.206466 0.0150983
\(188\) −10.4220 −0.760102
\(189\) −5.07996 −0.369513
\(190\) 0.413677 0.0300113
\(191\) 17.2199 1.24599 0.622994 0.782227i \(-0.285916\pi\)
0.622994 + 0.782227i \(0.285916\pi\)
\(192\) 1.70201 0.122832
\(193\) −9.74778 −0.701660 −0.350830 0.936439i \(-0.614101\pi\)
−0.350830 + 0.936439i \(0.614101\pi\)
\(194\) −2.79975 −0.201010
\(195\) −4.04367 −0.289574
\(196\) −6.07490 −0.433922
\(197\) −20.1939 −1.43875 −0.719377 0.694619i \(-0.755573\pi\)
−0.719377 + 0.694619i \(0.755573\pi\)
\(198\) 0.103166 0.00733165
\(199\) −11.4718 −0.813216 −0.406608 0.913603i \(-0.633289\pi\)
−0.406608 + 0.913603i \(0.633289\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 12.1133 0.854405
\(202\) −18.4724 −1.29971
\(203\) −4.85869 −0.341013
\(204\) 0.351408 0.0246035
\(205\) −7.15062 −0.499421
\(206\) 14.9220 1.03966
\(207\) 0.451434 0.0313768
\(208\) −2.37582 −0.164734
\(209\) −0.413677 −0.0286147
\(210\) −1.63702 −0.112965
\(211\) −4.90180 −0.337454 −0.168727 0.985663i \(-0.553966\pi\)
−0.168727 + 0.985663i \(0.553966\pi\)
\(212\) 9.81295 0.673956
\(213\) 2.78186 0.190610
\(214\) −17.2230 −1.17734
\(215\) −1.00000 −0.0681994
\(216\) 5.28162 0.359368
\(217\) −6.34388 −0.430650
\(218\) −4.94258 −0.334753
\(219\) −15.5064 −1.04782
\(220\) 1.00000 0.0674200
\(221\) −0.490528 −0.0329965
\(222\) 15.4108 1.03430
\(223\) 23.1695 1.55155 0.775773 0.631012i \(-0.217360\pi\)
0.775773 + 0.631012i \(0.217360\pi\)
\(224\) −0.961819 −0.0642642
\(225\) −0.103166 −0.00687770
\(226\) 1.33914 0.0890785
\(227\) 1.95283 0.129614 0.0648068 0.997898i \(-0.479357\pi\)
0.0648068 + 0.997898i \(0.479357\pi\)
\(228\) −0.704082 −0.0466290
\(229\) −27.9257 −1.84538 −0.922692 0.385537i \(-0.874016\pi\)
−0.922692 + 0.385537i \(0.874016\pi\)
\(230\) 4.37582 0.288533
\(231\) 1.63702 0.107708
\(232\) 5.05157 0.331652
\(233\) −17.6982 −1.15945 −0.579724 0.814813i \(-0.696840\pi\)
−0.579724 + 0.814813i \(0.696840\pi\)
\(234\) −0.245103 −0.0160229
\(235\) −10.4220 −0.679856
\(236\) 5.21881 0.339716
\(237\) 3.73381 0.242537
\(238\) −0.198583 −0.0128722
\(239\) 1.11014 0.0718088 0.0359044 0.999355i \(-0.488569\pi\)
0.0359044 + 0.999355i \(0.488569\pi\)
\(240\) 1.70201 0.109864
\(241\) 7.88619 0.507994 0.253997 0.967205i \(-0.418255\pi\)
0.253997 + 0.967205i \(0.418255\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.07165 0.0687461
\(244\) 7.54665 0.483124
\(245\) −6.07490 −0.388111
\(246\) 12.1704 0.775958
\(247\) 0.982824 0.0625356
\(248\) 6.59571 0.418828
\(249\) −9.44548 −0.598583
\(250\) −1.00000 −0.0632456
\(251\) 15.9387 1.00604 0.503020 0.864275i \(-0.332222\pi\)
0.503020 + 0.864275i \(0.332222\pi\)
\(252\) −0.0992265 −0.00625068
\(253\) −4.37582 −0.275106
\(254\) 2.61565 0.164121
\(255\) 0.351408 0.0220060
\(256\) 1.00000 0.0625000
\(257\) 1.73607 0.108293 0.0541465 0.998533i \(-0.482756\pi\)
0.0541465 + 0.998533i \(0.482756\pi\)
\(258\) 1.70201 0.105962
\(259\) −8.70875 −0.541135
\(260\) −2.37582 −0.147342
\(261\) 0.521148 0.0322582
\(262\) 9.98567 0.616917
\(263\) 3.85858 0.237931 0.118965 0.992898i \(-0.462042\pi\)
0.118965 + 0.992898i \(0.462042\pi\)
\(264\) −1.70201 −0.104751
\(265\) 9.81295 0.602805
\(266\) 0.397883 0.0243957
\(267\) −28.4356 −1.74023
\(268\) 7.11705 0.434743
\(269\) −0.849440 −0.0517913 −0.0258957 0.999665i \(-0.508244\pi\)
−0.0258957 + 0.999665i \(0.508244\pi\)
\(270\) 5.28162 0.321429
\(271\) 8.59360 0.522024 0.261012 0.965336i \(-0.415944\pi\)
0.261012 + 0.965336i \(0.415944\pi\)
\(272\) 0.206466 0.0125189
\(273\) −3.88928 −0.235390
\(274\) 15.5593 0.939972
\(275\) 1.00000 0.0603023
\(276\) −7.44769 −0.448298
\(277\) 9.73658 0.585015 0.292507 0.956263i \(-0.405510\pi\)
0.292507 + 0.956263i \(0.405510\pi\)
\(278\) −9.87107 −0.592028
\(279\) 0.680450 0.0407374
\(280\) −0.961819 −0.0574797
\(281\) −8.69294 −0.518578 −0.259289 0.965800i \(-0.583488\pi\)
−0.259289 + 0.965800i \(0.583488\pi\)
\(282\) 17.7383 1.05630
\(283\) −8.80745 −0.523548 −0.261774 0.965129i \(-0.584308\pi\)
−0.261774 + 0.965129i \(0.584308\pi\)
\(284\) 1.63446 0.0969872
\(285\) −0.704082 −0.0417062
\(286\) 2.37582 0.140485
\(287\) −6.87760 −0.405972
\(288\) 0.103166 0.00607909
\(289\) −16.9574 −0.997492
\(290\) 5.05157 0.296638
\(291\) 4.76520 0.279341
\(292\) −9.11062 −0.533159
\(293\) 9.46882 0.553174 0.276587 0.960989i \(-0.410797\pi\)
0.276587 + 0.960989i \(0.410797\pi\)
\(294\) 10.3395 0.603014
\(295\) 5.21881 0.303851
\(296\) 9.05446 0.526280
\(297\) −5.28162 −0.306470
\(298\) −19.6052 −1.13570
\(299\) 10.3962 0.601227
\(300\) 1.70201 0.0982655
\(301\) −0.961819 −0.0554383
\(302\) 8.91621 0.513070
\(303\) 31.4402 1.80619
\(304\) −0.413677 −0.0237260
\(305\) 7.54665 0.432120
\(306\) 0.0213002 0.00121765
\(307\) −8.96899 −0.511887 −0.255944 0.966692i \(-0.582386\pi\)
−0.255944 + 0.966692i \(0.582386\pi\)
\(308\) 0.961819 0.0548047
\(309\) −25.3973 −1.44480
\(310\) 6.59571 0.374611
\(311\) 18.6547 1.05781 0.528905 0.848681i \(-0.322603\pi\)
0.528905 + 0.848681i \(0.322603\pi\)
\(312\) 4.04367 0.228928
\(313\) 25.3697 1.43398 0.716990 0.697084i \(-0.245519\pi\)
0.716990 + 0.697084i \(0.245519\pi\)
\(314\) −13.1048 −0.739549
\(315\) −0.0992265 −0.00559078
\(316\) 2.19376 0.123409
\(317\) −28.8646 −1.62120 −0.810600 0.585600i \(-0.800859\pi\)
−0.810600 + 0.585600i \(0.800859\pi\)
\(318\) −16.7017 −0.936586
\(319\) −5.05157 −0.282834
\(320\) 1.00000 0.0559017
\(321\) 29.3136 1.63613
\(322\) 4.20875 0.234545
\(323\) −0.0854105 −0.00475236
\(324\) −8.67986 −0.482214
\(325\) −2.37582 −0.131787
\(326\) −9.93240 −0.550105
\(327\) 8.41231 0.465202
\(328\) 7.15062 0.394827
\(329\) −10.0241 −0.552645
\(330\) −1.70201 −0.0936925
\(331\) 32.7920 1.80241 0.901205 0.433394i \(-0.142684\pi\)
0.901205 + 0.433394i \(0.142684\pi\)
\(332\) −5.54961 −0.304574
\(333\) 0.934108 0.0511888
\(334\) −5.82283 −0.318611
\(335\) 7.11705 0.388846
\(336\) 1.63702 0.0893070
\(337\) −26.1589 −1.42497 −0.712483 0.701689i \(-0.752430\pi\)
−0.712483 + 0.701689i \(0.752430\pi\)
\(338\) 7.35546 0.400084
\(339\) −2.27923 −0.123791
\(340\) 0.206466 0.0111972
\(341\) −6.59571 −0.357178
\(342\) −0.0426772 −0.00230772
\(343\) −12.5757 −0.679023
\(344\) 1.00000 0.0539164
\(345\) −7.44769 −0.400970
\(346\) −21.4892 −1.15527
\(347\) 17.0650 0.916099 0.458049 0.888927i \(-0.348548\pi\)
0.458049 + 0.888927i \(0.348548\pi\)
\(348\) −8.59782 −0.460891
\(349\) 22.3693 1.19740 0.598701 0.800973i \(-0.295684\pi\)
0.598701 + 0.800973i \(0.295684\pi\)
\(350\) −0.961819 −0.0514114
\(351\) 12.5482 0.669773
\(352\) −1.00000 −0.0533002
\(353\) 31.2738 1.66454 0.832269 0.554372i \(-0.187042\pi\)
0.832269 + 0.554372i \(0.187042\pi\)
\(354\) −8.88246 −0.472098
\(355\) 1.63446 0.0867480
\(356\) −16.7071 −0.885474
\(357\) 0.337991 0.0178884
\(358\) 5.87243 0.310368
\(359\) 24.3617 1.28576 0.642881 0.765966i \(-0.277739\pi\)
0.642881 + 0.765966i \(0.277739\pi\)
\(360\) 0.103166 0.00543730
\(361\) −18.8289 −0.990993
\(362\) −2.70569 −0.142208
\(363\) 1.70201 0.0893323
\(364\) −2.28511 −0.119772
\(365\) −9.11062 −0.476872
\(366\) −12.8445 −0.671391
\(367\) −30.0924 −1.57081 −0.785404 0.618983i \(-0.787545\pi\)
−0.785404 + 0.618983i \(0.787545\pi\)
\(368\) −4.37582 −0.228106
\(369\) 0.737698 0.0384030
\(370\) 9.05446 0.470719
\(371\) 9.43828 0.490011
\(372\) −11.2260 −0.582039
\(373\) 7.87615 0.407811 0.203906 0.978991i \(-0.434636\pi\)
0.203906 + 0.978991i \(0.434636\pi\)
\(374\) −0.206466 −0.0106761
\(375\) 1.70201 0.0878914
\(376\) 10.4220 0.537473
\(377\) 12.0016 0.618116
\(378\) 5.07996 0.261285
\(379\) −33.5862 −1.72521 −0.862603 0.505882i \(-0.831167\pi\)
−0.862603 + 0.505882i \(0.831167\pi\)
\(380\) −0.413677 −0.0212212
\(381\) −4.45186 −0.228076
\(382\) −17.2199 −0.881046
\(383\) −35.5745 −1.81777 −0.908886 0.417044i \(-0.863066\pi\)
−0.908886 + 0.417044i \(0.863066\pi\)
\(384\) −1.70201 −0.0868553
\(385\) 0.961819 0.0490188
\(386\) 9.74778 0.496149
\(387\) 0.103166 0.00524420
\(388\) 2.79975 0.142136
\(389\) −9.06568 −0.459648 −0.229824 0.973232i \(-0.573815\pi\)
−0.229824 + 0.973232i \(0.573815\pi\)
\(390\) 4.04367 0.204759
\(391\) −0.903461 −0.0456900
\(392\) 6.07490 0.306829
\(393\) −16.9957 −0.857319
\(394\) 20.1939 1.01735
\(395\) 2.19376 0.110380
\(396\) −0.103166 −0.00518426
\(397\) −13.6754 −0.686350 −0.343175 0.939272i \(-0.611502\pi\)
−0.343175 + 0.939272i \(0.611502\pi\)
\(398\) 11.4718 0.575031
\(399\) −0.677200 −0.0339024
\(400\) 1.00000 0.0500000
\(401\) 21.7514 1.08622 0.543108 0.839663i \(-0.317247\pi\)
0.543108 + 0.839663i \(0.317247\pi\)
\(402\) −12.1133 −0.604156
\(403\) 15.6702 0.780590
\(404\) 18.4724 0.919036
\(405\) −8.67986 −0.431306
\(406\) 4.85869 0.241133
\(407\) −9.05446 −0.448813
\(408\) −0.351408 −0.0173973
\(409\) 19.7331 0.975737 0.487869 0.872917i \(-0.337775\pi\)
0.487869 + 0.872917i \(0.337775\pi\)
\(410\) 7.15062 0.353144
\(411\) −26.4821 −1.30626
\(412\) −14.9220 −0.735153
\(413\) 5.01955 0.246996
\(414\) −0.451434 −0.0221868
\(415\) −5.54961 −0.272419
\(416\) 2.37582 0.116484
\(417\) 16.8007 0.822731
\(418\) 0.413677 0.0202336
\(419\) −33.4352 −1.63342 −0.816708 0.577052i \(-0.804203\pi\)
−0.816708 + 0.577052i \(0.804203\pi\)
\(420\) 1.63702 0.0798786
\(421\) 16.1852 0.788820 0.394410 0.918935i \(-0.370949\pi\)
0.394410 + 0.918935i \(0.370949\pi\)
\(422\) 4.90180 0.238616
\(423\) 1.07519 0.0522775
\(424\) −9.81295 −0.476559
\(425\) 0.206466 0.0100151
\(426\) −2.78186 −0.134782
\(427\) 7.25851 0.351264
\(428\) 17.2230 0.832503
\(429\) −4.04367 −0.195230
\(430\) 1.00000 0.0482243
\(431\) 23.9093 1.15167 0.575834 0.817566i \(-0.304677\pi\)
0.575834 + 0.817566i \(0.304677\pi\)
\(432\) −5.28162 −0.254112
\(433\) −26.9709 −1.29614 −0.648069 0.761581i \(-0.724423\pi\)
−0.648069 + 0.761581i \(0.724423\pi\)
\(434\) 6.34388 0.304516
\(435\) −8.59782 −0.412234
\(436\) 4.94258 0.236706
\(437\) 1.81018 0.0865926
\(438\) 15.5064 0.740923
\(439\) −34.1093 −1.62795 −0.813974 0.580901i \(-0.802700\pi\)
−0.813974 + 0.580901i \(0.802700\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 0.626721 0.0298438
\(442\) 0.490528 0.0233320
\(443\) −16.1902 −0.769220 −0.384610 0.923079i \(-0.625664\pi\)
−0.384610 + 0.923079i \(0.625664\pi\)
\(444\) −15.4108 −0.731363
\(445\) −16.7071 −0.791992
\(446\) −23.1695 −1.09711
\(447\) 33.3682 1.57826
\(448\) 0.961819 0.0454417
\(449\) 15.2420 0.719315 0.359657 0.933084i \(-0.382894\pi\)
0.359657 + 0.933084i \(0.382894\pi\)
\(450\) 0.103166 0.00486327
\(451\) −7.15062 −0.336710
\(452\) −1.33914 −0.0629880
\(453\) −15.1755 −0.713006
\(454\) −1.95283 −0.0916507
\(455\) −2.28511 −0.107128
\(456\) 0.704082 0.0329717
\(457\) −12.3146 −0.576054 −0.288027 0.957622i \(-0.592999\pi\)
−0.288027 + 0.957622i \(0.592999\pi\)
\(458\) 27.9257 1.30488
\(459\) −1.09048 −0.0508991
\(460\) −4.37582 −0.204024
\(461\) −7.78904 −0.362772 −0.181386 0.983412i \(-0.558058\pi\)
−0.181386 + 0.983412i \(0.558058\pi\)
\(462\) −1.63702 −0.0761613
\(463\) −32.6817 −1.51885 −0.759424 0.650596i \(-0.774519\pi\)
−0.759424 + 0.650596i \(0.774519\pi\)
\(464\) −5.05157 −0.234513
\(465\) −11.2260 −0.520591
\(466\) 17.6982 0.819853
\(467\) 4.73048 0.218900 0.109450 0.993992i \(-0.465091\pi\)
0.109450 + 0.993992i \(0.465091\pi\)
\(468\) 0.245103 0.0113299
\(469\) 6.84531 0.316087
\(470\) 10.4220 0.480731
\(471\) 22.3046 1.02774
\(472\) −5.21881 −0.240215
\(473\) −1.00000 −0.0459800
\(474\) −3.73381 −0.171499
\(475\) −0.413677 −0.0189808
\(476\) 0.198583 0.00910205
\(477\) −1.01236 −0.0463527
\(478\) −1.11014 −0.0507765
\(479\) 4.04389 0.184770 0.0923851 0.995723i \(-0.470551\pi\)
0.0923851 + 0.995723i \(0.470551\pi\)
\(480\) −1.70201 −0.0776857
\(481\) 21.5118 0.980854
\(482\) −7.88619 −0.359206
\(483\) −7.16333 −0.325943
\(484\) 1.00000 0.0454545
\(485\) 2.79975 0.127130
\(486\) −1.07165 −0.0486109
\(487\) −3.81325 −0.172795 −0.0863975 0.996261i \(-0.527536\pi\)
−0.0863975 + 0.996261i \(0.527536\pi\)
\(488\) −7.54665 −0.341621
\(489\) 16.9050 0.764472
\(490\) 6.07490 0.274436
\(491\) −34.9008 −1.57505 −0.787526 0.616281i \(-0.788639\pi\)
−0.787526 + 0.616281i \(0.788639\pi\)
\(492\) −12.1704 −0.548685
\(493\) −1.04298 −0.0469734
\(494\) −0.982824 −0.0442194
\(495\) −0.103166 −0.00463694
\(496\) −6.59571 −0.296156
\(497\) 1.57205 0.0705162
\(498\) 9.44548 0.423262
\(499\) −14.5870 −0.653005 −0.326502 0.945196i \(-0.605870\pi\)
−0.326502 + 0.945196i \(0.605870\pi\)
\(500\) 1.00000 0.0447214
\(501\) 9.91050 0.442769
\(502\) −15.9387 −0.711378
\(503\) −12.2195 −0.544840 −0.272420 0.962179i \(-0.587824\pi\)
−0.272420 + 0.962179i \(0.587824\pi\)
\(504\) 0.0992265 0.00441990
\(505\) 18.4724 0.822011
\(506\) 4.37582 0.194529
\(507\) −12.5191 −0.555991
\(508\) −2.61565 −0.116051
\(509\) 11.9850 0.531226 0.265613 0.964080i \(-0.414426\pi\)
0.265613 + 0.964080i \(0.414426\pi\)
\(510\) −0.351408 −0.0155606
\(511\) −8.76277 −0.387642
\(512\) −1.00000 −0.0441942
\(513\) 2.18488 0.0964650
\(514\) −1.73607 −0.0765747
\(515\) −14.9220 −0.657541
\(516\) −1.70201 −0.0749268
\(517\) −10.4220 −0.458359
\(518\) 8.70875 0.382641
\(519\) 36.5748 1.60546
\(520\) 2.37582 0.104187
\(521\) 12.3064 0.539151 0.269576 0.962979i \(-0.413117\pi\)
0.269576 + 0.962979i \(0.413117\pi\)
\(522\) −0.521148 −0.0228100
\(523\) 24.2620 1.06090 0.530451 0.847715i \(-0.322022\pi\)
0.530451 + 0.847715i \(0.322022\pi\)
\(524\) −9.98567 −0.436226
\(525\) 1.63702 0.0714456
\(526\) −3.85858 −0.168242
\(527\) −1.36179 −0.0593206
\(528\) 1.70201 0.0740704
\(529\) −3.85216 −0.167485
\(530\) −9.81295 −0.426247
\(531\) −0.538401 −0.0233646
\(532\) −0.397883 −0.0172504
\(533\) 16.9886 0.735859
\(534\) 28.4356 1.23053
\(535\) 17.2230 0.744614
\(536\) −7.11705 −0.307410
\(537\) −9.99493 −0.431313
\(538\) 0.849440 0.0366220
\(539\) −6.07490 −0.261665
\(540\) −5.28162 −0.227285
\(541\) 3.56831 0.153414 0.0767068 0.997054i \(-0.475559\pi\)
0.0767068 + 0.997054i \(0.475559\pi\)
\(542\) −8.59360 −0.369127
\(543\) 4.60511 0.197624
\(544\) −0.206466 −0.00885217
\(545\) 4.94258 0.211717
\(546\) 3.88928 0.166446
\(547\) 15.1247 0.646684 0.323342 0.946282i \(-0.395194\pi\)
0.323342 + 0.946282i \(0.395194\pi\)
\(548\) −15.5593 −0.664661
\(549\) −0.778553 −0.0332279
\(550\) −1.00000 −0.0426401
\(551\) 2.08972 0.0890250
\(552\) 7.44769 0.316995
\(553\) 2.11000 0.0897265
\(554\) −9.73658 −0.413668
\(555\) −15.4108 −0.654151
\(556\) 9.87107 0.418627
\(557\) −0.572118 −0.0242414 −0.0121207 0.999927i \(-0.503858\pi\)
−0.0121207 + 0.999927i \(0.503858\pi\)
\(558\) −0.680450 −0.0288057
\(559\) 2.37582 0.100487
\(560\) 0.961819 0.0406443
\(561\) 0.351408 0.0148364
\(562\) 8.69294 0.366690
\(563\) 37.1756 1.56676 0.783382 0.621540i \(-0.213493\pi\)
0.783382 + 0.621540i \(0.213493\pi\)
\(564\) −17.7383 −0.746918
\(565\) −1.33914 −0.0563382
\(566\) 8.80745 0.370205
\(567\) −8.34845 −0.350602
\(568\) −1.63446 −0.0685803
\(569\) 14.7054 0.616482 0.308241 0.951308i \(-0.400260\pi\)
0.308241 + 0.951308i \(0.400260\pi\)
\(570\) 0.704082 0.0294908
\(571\) 22.3192 0.934029 0.467014 0.884250i \(-0.345330\pi\)
0.467014 + 0.884250i \(0.345330\pi\)
\(572\) −2.37582 −0.0993382
\(573\) 29.3084 1.22438
\(574\) 6.87760 0.287066
\(575\) −4.37582 −0.182484
\(576\) −0.103166 −0.00429856
\(577\) −29.7288 −1.23763 −0.618814 0.785538i \(-0.712387\pi\)
−0.618814 + 0.785538i \(0.712387\pi\)
\(578\) 16.9574 0.705334
\(579\) −16.5908 −0.689490
\(580\) −5.05157 −0.209755
\(581\) −5.33772 −0.221446
\(582\) −4.76520 −0.197524
\(583\) 9.81295 0.406411
\(584\) 9.11062 0.377000
\(585\) 0.245103 0.0101338
\(586\) −9.46882 −0.391153
\(587\) −27.2434 −1.12445 −0.562227 0.826983i \(-0.690055\pi\)
−0.562227 + 0.826983i \(0.690055\pi\)
\(588\) −10.3395 −0.426396
\(589\) 2.72849 0.112426
\(590\) −5.21881 −0.214855
\(591\) −34.3702 −1.41380
\(592\) −9.05446 −0.372136
\(593\) −10.1627 −0.417333 −0.208666 0.977987i \(-0.566912\pi\)
−0.208666 + 0.977987i \(0.566912\pi\)
\(594\) 5.28162 0.216707
\(595\) 0.198583 0.00814112
\(596\) 19.6052 0.803060
\(597\) −19.5251 −0.799111
\(598\) −10.3962 −0.425132
\(599\) 8.32534 0.340164 0.170082 0.985430i \(-0.445597\pi\)
0.170082 + 0.985430i \(0.445597\pi\)
\(600\) −1.70201 −0.0694842
\(601\) −15.7094 −0.640799 −0.320400 0.947282i \(-0.603817\pi\)
−0.320400 + 0.947282i \(0.603817\pi\)
\(602\) 0.961819 0.0392008
\(603\) −0.734234 −0.0299003
\(604\) −8.91621 −0.362795
\(605\) 1.00000 0.0406558
\(606\) −31.4402 −1.27717
\(607\) −32.9503 −1.33741 −0.668706 0.743527i \(-0.733151\pi\)
−0.668706 + 0.743527i \(0.733151\pi\)
\(608\) 0.413677 0.0167768
\(609\) −8.26954 −0.335099
\(610\) −7.54665 −0.305555
\(611\) 24.7608 1.00172
\(612\) −0.0213002 −0.000861010 0
\(613\) −28.9790 −1.17045 −0.585226 0.810870i \(-0.698994\pi\)
−0.585226 + 0.810870i \(0.698994\pi\)
\(614\) 8.96899 0.361959
\(615\) −12.1704 −0.490759
\(616\) −0.961819 −0.0387528
\(617\) −17.1103 −0.688833 −0.344416 0.938817i \(-0.611923\pi\)
−0.344416 + 0.938817i \(0.611923\pi\)
\(618\) 25.3973 1.02163
\(619\) 7.74766 0.311405 0.155702 0.987804i \(-0.450236\pi\)
0.155702 + 0.987804i \(0.450236\pi\)
\(620\) −6.59571 −0.264890
\(621\) 23.1114 0.927429
\(622\) −18.6547 −0.747985
\(623\) −16.0692 −0.643799
\(624\) −4.04367 −0.161877
\(625\) 1.00000 0.0400000
\(626\) −25.3697 −1.01398
\(627\) −0.704082 −0.0281183
\(628\) 13.1048 0.522940
\(629\) −1.86944 −0.0745395
\(630\) 0.0992265 0.00395328
\(631\) −11.5964 −0.461646 −0.230823 0.972996i \(-0.574142\pi\)
−0.230823 + 0.972996i \(0.574142\pi\)
\(632\) −2.19376 −0.0872633
\(633\) −8.34291 −0.331601
\(634\) 28.8646 1.14636
\(635\) −2.61565 −0.103799
\(636\) 16.7017 0.662267
\(637\) 14.4329 0.571853
\(638\) 5.05157 0.199994
\(639\) −0.168620 −0.00667049
\(640\) −1.00000 −0.0395285
\(641\) 3.15569 0.124642 0.0623211 0.998056i \(-0.480150\pi\)
0.0623211 + 0.998056i \(0.480150\pi\)
\(642\) −29.3136 −1.15692
\(643\) −23.6766 −0.933715 −0.466858 0.884332i \(-0.654614\pi\)
−0.466858 + 0.884332i \(0.654614\pi\)
\(644\) −4.20875 −0.165848
\(645\) −1.70201 −0.0670165
\(646\) 0.0854105 0.00336043
\(647\) 33.0208 1.29818 0.649091 0.760710i \(-0.275149\pi\)
0.649091 + 0.760710i \(0.275149\pi\)
\(648\) 8.67986 0.340977
\(649\) 5.21881 0.204856
\(650\) 2.37582 0.0931875
\(651\) −10.7973 −0.423181
\(652\) 9.93240 0.388983
\(653\) −39.1416 −1.53173 −0.765865 0.643001i \(-0.777689\pi\)
−0.765865 + 0.643001i \(0.777689\pi\)
\(654\) −8.41231 −0.328947
\(655\) −9.98567 −0.390172
\(656\) −7.15062 −0.279185
\(657\) 0.939902 0.0366691
\(658\) 10.0241 0.390779
\(659\) −33.6319 −1.31011 −0.655056 0.755580i \(-0.727355\pi\)
−0.655056 + 0.755580i \(0.727355\pi\)
\(660\) 1.70201 0.0662506
\(661\) 43.8811 1.70678 0.853389 0.521275i \(-0.174543\pi\)
0.853389 + 0.521275i \(0.174543\pi\)
\(662\) −32.7920 −1.27450
\(663\) −0.834883 −0.0324242
\(664\) 5.54961 0.215366
\(665\) −0.397883 −0.0154292
\(666\) −0.934108 −0.0361959
\(667\) 22.1048 0.855900
\(668\) 5.82283 0.225292
\(669\) 39.4347 1.52463
\(670\) −7.11705 −0.274956
\(671\) 7.54665 0.291335
\(672\) −1.63702 −0.0631496
\(673\) −14.1334 −0.544802 −0.272401 0.962184i \(-0.587818\pi\)
−0.272401 + 0.962184i \(0.587818\pi\)
\(674\) 26.1589 1.00760
\(675\) −5.28162 −0.203289
\(676\) −7.35546 −0.282902
\(677\) −20.3729 −0.782995 −0.391498 0.920179i \(-0.628043\pi\)
−0.391498 + 0.920179i \(0.628043\pi\)
\(678\) 2.27923 0.0875334
\(679\) 2.69285 0.103342
\(680\) −0.206466 −0.00791763
\(681\) 3.32373 0.127366
\(682\) 6.59571 0.252563
\(683\) 16.1894 0.619471 0.309736 0.950823i \(-0.399759\pi\)
0.309736 + 0.950823i \(0.399759\pi\)
\(684\) 0.0426772 0.00163180
\(685\) −15.5593 −0.594491
\(686\) 12.5757 0.480142
\(687\) −47.5299 −1.81338
\(688\) −1.00000 −0.0381246
\(689\) −23.3138 −0.888187
\(690\) 7.44769 0.283529
\(691\) 10.5271 0.400470 0.200235 0.979748i \(-0.435829\pi\)
0.200235 + 0.979748i \(0.435829\pi\)
\(692\) 21.4892 0.816897
\(693\) −0.0992265 −0.00376930
\(694\) −17.0650 −0.647779
\(695\) 9.87107 0.374431
\(696\) 8.59782 0.325899
\(697\) −1.47636 −0.0559212
\(698\) −22.3693 −0.846690
\(699\) −30.1225 −1.13934
\(700\) 0.961819 0.0363533
\(701\) 37.6120 1.42059 0.710293 0.703906i \(-0.248562\pi\)
0.710293 + 0.703906i \(0.248562\pi\)
\(702\) −12.5482 −0.473601
\(703\) 3.74562 0.141269
\(704\) 1.00000 0.0376889
\(705\) −17.7383 −0.668064
\(706\) −31.2738 −1.17701
\(707\) 17.7671 0.668200
\(708\) 8.88246 0.333823
\(709\) −5.33959 −0.200532 −0.100266 0.994961i \(-0.531969\pi\)
−0.100266 + 0.994961i \(0.531969\pi\)
\(710\) −1.63446 −0.0613401
\(711\) −0.226321 −0.00848769
\(712\) 16.7071 0.626125
\(713\) 28.8617 1.08088
\(714\) −0.337991 −0.0126490
\(715\) −2.37582 −0.0888508
\(716\) −5.87243 −0.219463
\(717\) 1.88946 0.0705633
\(718\) −24.3617 −0.909171
\(719\) 28.7331 1.07156 0.535782 0.844356i \(-0.320017\pi\)
0.535782 + 0.844356i \(0.320017\pi\)
\(720\) −0.103166 −0.00384475
\(721\) −14.3522 −0.534505
\(722\) 18.8289 0.700738
\(723\) 13.4224 0.499183
\(724\) 2.70569 0.100556
\(725\) −5.05157 −0.187611
\(726\) −1.70201 −0.0631675
\(727\) −40.7811 −1.51249 −0.756244 0.654289i \(-0.772968\pi\)
−0.756244 + 0.654289i \(0.772968\pi\)
\(728\) 2.28511 0.0846919
\(729\) 27.8635 1.03198
\(730\) 9.11062 0.337199
\(731\) −0.206466 −0.00763644
\(732\) 12.8445 0.474745
\(733\) −0.227142 −0.00838967 −0.00419484 0.999991i \(-0.501335\pi\)
−0.00419484 + 0.999991i \(0.501335\pi\)
\(734\) 30.0924 1.11073
\(735\) −10.3395 −0.381380
\(736\) 4.37582 0.161295
\(737\) 7.11705 0.262160
\(738\) −0.737698 −0.0271550
\(739\) −20.3171 −0.747375 −0.373688 0.927555i \(-0.621907\pi\)
−0.373688 + 0.927555i \(0.621907\pi\)
\(740\) −9.05446 −0.332849
\(741\) 1.67278 0.0614510
\(742\) −9.43828 −0.346490
\(743\) 34.4385 1.26343 0.631713 0.775202i \(-0.282352\pi\)
0.631713 + 0.775202i \(0.282352\pi\)
\(744\) 11.2260 0.411563
\(745\) 19.6052 0.718279
\(746\) −7.87615 −0.288366
\(747\) 0.572528 0.0209477
\(748\) 0.206466 0.00754916
\(749\) 16.5654 0.605286
\(750\) −1.70201 −0.0621486
\(751\) 17.0082 0.620638 0.310319 0.950632i \(-0.399564\pi\)
0.310319 + 0.950632i \(0.399564\pi\)
\(752\) −10.4220 −0.380051
\(753\) 27.1278 0.988591
\(754\) −12.0016 −0.437074
\(755\) −8.91621 −0.324494
\(756\) −5.07996 −0.184756
\(757\) −14.1239 −0.513342 −0.256671 0.966499i \(-0.582626\pi\)
−0.256671 + 0.966499i \(0.582626\pi\)
\(758\) 33.5862 1.21990
\(759\) −7.44769 −0.270334
\(760\) 0.413677 0.0150057
\(761\) −44.1831 −1.60163 −0.800817 0.598909i \(-0.795601\pi\)
−0.800817 + 0.598909i \(0.795601\pi\)
\(762\) 4.45186 0.161274
\(763\) 4.75386 0.172101
\(764\) 17.2199 0.622994
\(765\) −0.0213002 −0.000770111 0
\(766\) 35.5745 1.28536
\(767\) −12.3990 −0.447701
\(768\) 1.70201 0.0614160
\(769\) −4.06495 −0.146586 −0.0732929 0.997310i \(-0.523351\pi\)
−0.0732929 + 0.997310i \(0.523351\pi\)
\(770\) −0.961819 −0.0346615
\(771\) 2.95480 0.106415
\(772\) −9.74778 −0.350830
\(773\) 13.8922 0.499669 0.249834 0.968289i \(-0.419624\pi\)
0.249834 + 0.968289i \(0.419624\pi\)
\(774\) −0.103166 −0.00370821
\(775\) −6.59571 −0.236925
\(776\) −2.79975 −0.100505
\(777\) −14.8224 −0.531750
\(778\) 9.06568 0.325020
\(779\) 2.95805 0.105983
\(780\) −4.04367 −0.144787
\(781\) 1.63446 0.0584855
\(782\) 0.903461 0.0323077
\(783\) 26.6804 0.953481
\(784\) −6.07490 −0.216961
\(785\) 13.1048 0.467732
\(786\) 16.9957 0.606216
\(787\) −16.0702 −0.572840 −0.286420 0.958104i \(-0.592465\pi\)
−0.286420 + 0.958104i \(0.592465\pi\)
\(788\) −20.1939 −0.719377
\(789\) 6.56735 0.233804
\(790\) −2.19376 −0.0780506
\(791\) −1.28801 −0.0457965
\(792\) 0.103166 0.00366583
\(793\) −17.9295 −0.636695
\(794\) 13.6754 0.485323
\(795\) 16.7017 0.592349
\(796\) −11.4718 −0.406608
\(797\) −24.5095 −0.868172 −0.434086 0.900872i \(-0.642929\pi\)
−0.434086 + 0.900872i \(0.642929\pi\)
\(798\) 0.677200 0.0239726
\(799\) −2.15179 −0.0761249
\(800\) −1.00000 −0.0353553
\(801\) 1.72360 0.0609002
\(802\) −21.7514 −0.768070
\(803\) −9.11062 −0.321507
\(804\) 12.1133 0.427203
\(805\) −4.20875 −0.148339
\(806\) −15.6702 −0.551961
\(807\) −1.44576 −0.0508930
\(808\) −18.4724 −0.649856
\(809\) −22.7326 −0.799237 −0.399618 0.916682i \(-0.630857\pi\)
−0.399618 + 0.916682i \(0.630857\pi\)
\(810\) 8.67986 0.304979
\(811\) 8.81751 0.309625 0.154812 0.987944i \(-0.450523\pi\)
0.154812 + 0.987944i \(0.450523\pi\)
\(812\) −4.85869 −0.170507
\(813\) 14.6264 0.512970
\(814\) 9.05446 0.317359
\(815\) 9.93240 0.347917
\(816\) 0.351408 0.0123017
\(817\) 0.413677 0.0144727
\(818\) −19.7331 −0.689950
\(819\) 0.235745 0.00823759
\(820\) −7.15062 −0.249711
\(821\) 39.0023 1.36119 0.680595 0.732660i \(-0.261721\pi\)
0.680595 + 0.732660i \(0.261721\pi\)
\(822\) 26.4821 0.923669
\(823\) −31.2002 −1.08757 −0.543786 0.839224i \(-0.683010\pi\)
−0.543786 + 0.839224i \(0.683010\pi\)
\(824\) 14.9220 0.519832
\(825\) 1.70201 0.0592563
\(826\) −5.01955 −0.174653
\(827\) −55.4006 −1.92647 −0.963234 0.268664i \(-0.913418\pi\)
−0.963234 + 0.268664i \(0.913418\pi\)
\(828\) 0.451434 0.0156884
\(829\) 1.43127 0.0497101 0.0248551 0.999691i \(-0.492088\pi\)
0.0248551 + 0.999691i \(0.492088\pi\)
\(830\) 5.54961 0.192630
\(831\) 16.5718 0.574868
\(832\) −2.37582 −0.0823669
\(833\) −1.25426 −0.0434577
\(834\) −16.8007 −0.581759
\(835\) 5.82283 0.201507
\(836\) −0.413677 −0.0143073
\(837\) 34.8360 1.20411
\(838\) 33.4352 1.15500
\(839\) 2.47077 0.0853005 0.0426503 0.999090i \(-0.486420\pi\)
0.0426503 + 0.999090i \(0.486420\pi\)
\(840\) −1.63702 −0.0564827
\(841\) −3.48165 −0.120057
\(842\) −16.1852 −0.557780
\(843\) −14.7955 −0.509583
\(844\) −4.90180 −0.168727
\(845\) −7.35546 −0.253035
\(846\) −1.07519 −0.0369658
\(847\) 0.961819 0.0330485
\(848\) 9.81295 0.336978
\(849\) −14.9904 −0.514468
\(850\) −0.206466 −0.00708174
\(851\) 39.6207 1.35818
\(852\) 2.78186 0.0953050
\(853\) −49.5735 −1.69736 −0.848682 0.528903i \(-0.822604\pi\)
−0.848682 + 0.528903i \(0.822604\pi\)
\(854\) −7.25851 −0.248381
\(855\) 0.0426772 0.00145953
\(856\) −17.2230 −0.588669
\(857\) −32.4395 −1.10811 −0.554056 0.832479i \(-0.686921\pi\)
−0.554056 + 0.832479i \(0.686921\pi\)
\(858\) 4.04367 0.138049
\(859\) −2.78379 −0.0949816 −0.0474908 0.998872i \(-0.515122\pi\)
−0.0474908 + 0.998872i \(0.515122\pi\)
\(860\) −1.00000 −0.0340997
\(861\) −11.7057 −0.398931
\(862\) −23.9093 −0.814353
\(863\) −37.1206 −1.26360 −0.631801 0.775131i \(-0.717684\pi\)
−0.631801 + 0.775131i \(0.717684\pi\)
\(864\) 5.28162 0.179684
\(865\) 21.4892 0.730655
\(866\) 26.9709 0.916508
\(867\) −28.8616 −0.980191
\(868\) −6.34388 −0.215325
\(869\) 2.19376 0.0744184
\(870\) 8.59782 0.291493
\(871\) −16.9089 −0.572935
\(872\) −4.94258 −0.167377
\(873\) −0.288838 −0.00977567
\(874\) −1.81018 −0.0612302
\(875\) 0.961819 0.0325154
\(876\) −15.5064 −0.523911
\(877\) −41.3812 −1.39734 −0.698672 0.715442i \(-0.746225\pi\)
−0.698672 + 0.715442i \(0.746225\pi\)
\(878\) 34.1093 1.15113
\(879\) 16.1160 0.543580
\(880\) 1.00000 0.0337100
\(881\) 50.3228 1.69542 0.847709 0.530462i \(-0.177982\pi\)
0.847709 + 0.530462i \(0.177982\pi\)
\(882\) −0.626721 −0.0211028
\(883\) 9.51376 0.320163 0.160082 0.987104i \(-0.448824\pi\)
0.160082 + 0.987104i \(0.448824\pi\)
\(884\) −0.490528 −0.0164982
\(885\) 8.88246 0.298581
\(886\) 16.1902 0.543920
\(887\) 49.4737 1.66116 0.830582 0.556896i \(-0.188008\pi\)
0.830582 + 0.556896i \(0.188008\pi\)
\(888\) 15.4108 0.517152
\(889\) −2.51578 −0.0843766
\(890\) 16.7071 0.560023
\(891\) −8.67986 −0.290786
\(892\) 23.1695 0.775773
\(893\) 4.31134 0.144273
\(894\) −33.3682 −1.11600
\(895\) −5.87243 −0.196294
\(896\) −0.961819 −0.0321321
\(897\) 17.6944 0.590799
\(898\) −15.2420 −0.508632
\(899\) 33.3187 1.11124
\(900\) −0.103166 −0.00343885
\(901\) 2.02604 0.0674973
\(902\) 7.15062 0.238090
\(903\) −1.63702 −0.0544768
\(904\) 1.33914 0.0445392
\(905\) 2.70569 0.0899403
\(906\) 15.1755 0.504171
\(907\) 36.9144 1.22572 0.612862 0.790190i \(-0.290018\pi\)
0.612862 + 0.790190i \(0.290018\pi\)
\(908\) 1.95283 0.0648068
\(909\) −1.90571 −0.0632085
\(910\) 2.28511 0.0757508
\(911\) −20.1105 −0.666291 −0.333146 0.942875i \(-0.608110\pi\)
−0.333146 + 0.942875i \(0.608110\pi\)
\(912\) −0.704082 −0.0233145
\(913\) −5.54961 −0.183665
\(914\) 12.3146 0.407331
\(915\) 12.8445 0.424625
\(916\) −27.9257 −0.922692
\(917\) −9.60440 −0.317165
\(918\) 1.09048 0.0359911
\(919\) −3.83727 −0.126580 −0.0632899 0.997995i \(-0.520159\pi\)
−0.0632899 + 0.997995i \(0.520159\pi\)
\(920\) 4.37582 0.144267
\(921\) −15.2653 −0.503009
\(922\) 7.78904 0.256518
\(923\) −3.88318 −0.127817
\(924\) 1.63702 0.0538542
\(925\) −9.05446 −0.297709
\(926\) 32.6817 1.07399
\(927\) 1.53943 0.0505616
\(928\) 5.05157 0.165826
\(929\) 57.2835 1.87941 0.939705 0.341985i \(-0.111099\pi\)
0.939705 + 0.341985i \(0.111099\pi\)
\(930\) 11.2260 0.368114
\(931\) 2.51305 0.0823619
\(932\) −17.6982 −0.579724
\(933\) 31.7505 1.03946
\(934\) −4.73048 −0.154786
\(935\) 0.206466 0.00675217
\(936\) −0.245103 −0.00801145
\(937\) 17.9301 0.585751 0.292876 0.956151i \(-0.405388\pi\)
0.292876 + 0.956151i \(0.405388\pi\)
\(938\) −6.84531 −0.223507
\(939\) 43.1794 1.40911
\(940\) −10.4220 −0.339928
\(941\) 42.8854 1.39802 0.699012 0.715110i \(-0.253623\pi\)
0.699012 + 0.715110i \(0.253623\pi\)
\(942\) −22.3046 −0.726722
\(943\) 31.2899 1.01894
\(944\) 5.21881 0.169858
\(945\) −5.07996 −0.165251
\(946\) 1.00000 0.0325128
\(947\) −16.2404 −0.527742 −0.263871 0.964558i \(-0.584999\pi\)
−0.263871 + 0.964558i \(0.584999\pi\)
\(948\) 3.73381 0.121268
\(949\) 21.6452 0.702634
\(950\) 0.413677 0.0134215
\(951\) −49.1279 −1.59308
\(952\) −0.198583 −0.00643612
\(953\) 42.8358 1.38759 0.693794 0.720173i \(-0.255938\pi\)
0.693794 + 0.720173i \(0.255938\pi\)
\(954\) 1.01236 0.0327763
\(955\) 17.2199 0.557223
\(956\) 1.11014 0.0359044
\(957\) −8.59782 −0.277928
\(958\) −4.04389 −0.130652
\(959\) −14.9652 −0.483253
\(960\) 1.70201 0.0549321
\(961\) 12.5034 0.403334
\(962\) −21.5118 −0.693568
\(963\) −1.77682 −0.0572571
\(964\) 7.88619 0.253997
\(965\) −9.74778 −0.313792
\(966\) 7.16333 0.230476
\(967\) 47.4970 1.52740 0.763700 0.645572i \(-0.223381\pi\)
0.763700 + 0.645572i \(0.223381\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −0.145369 −0.00466994
\(970\) −2.79975 −0.0898945
\(971\) 1.33889 0.0429669 0.0214835 0.999769i \(-0.493161\pi\)
0.0214835 + 0.999769i \(0.493161\pi\)
\(972\) 1.07165 0.0343731
\(973\) 9.49418 0.304370
\(974\) 3.81325 0.122185
\(975\) −4.04367 −0.129501
\(976\) 7.54665 0.241562
\(977\) 21.7838 0.696926 0.348463 0.937323i \(-0.386704\pi\)
0.348463 + 0.937323i \(0.386704\pi\)
\(978\) −16.9050 −0.540563
\(979\) −16.7071 −0.533961
\(980\) −6.07490 −0.194056
\(981\) −0.509903 −0.0162800
\(982\) 34.9008 1.11373
\(983\) 12.9448 0.412873 0.206437 0.978460i \(-0.433813\pi\)
0.206437 + 0.978460i \(0.433813\pi\)
\(984\) 12.1704 0.387979
\(985\) −20.1939 −0.643431
\(986\) 1.04298 0.0332152
\(987\) −17.0611 −0.543059
\(988\) 0.982824 0.0312678
\(989\) 4.37582 0.139143
\(990\) 0.103166 0.00327881
\(991\) −47.3675 −1.50468 −0.752340 0.658775i \(-0.771075\pi\)
−0.752340 + 0.658775i \(0.771075\pi\)
\(992\) 6.59571 0.209414
\(993\) 55.8122 1.77115
\(994\) −1.57205 −0.0498625
\(995\) −11.4718 −0.363681
\(996\) −9.44548 −0.299291
\(997\) 13.6998 0.433877 0.216939 0.976185i \(-0.430393\pi\)
0.216939 + 0.976185i \(0.430393\pi\)
\(998\) 14.5870 0.461744
\(999\) 47.8222 1.51303
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.w.1.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.w.1.8 8 1.1 even 1 trivial