Properties

Label 4026.2.a.u.1.4
Level 4026
Weight 2
Character 4026.1
Self dual yes
Analytic conductor 32.148
Analytic rank 0
Dimension 5
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.4
Root \(-2.15973\) of \(x^{5} - x^{4} - 12 x^{3} + 7 x^{2} + 30 x - 20\)
Character \(\chi\) \(=\) 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.15973 q^{5} -1.00000 q^{6} -1.48663 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.15973 q^{5} -1.00000 q^{6} -1.48663 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.15973 q^{10} -1.00000 q^{11} +1.00000 q^{12} +5.53760 q^{13} +1.48663 q^{14} +2.15973 q^{15} +1.00000 q^{16} +2.33751 q^{17} -1.00000 q^{18} +3.42627 q^{19} +2.15973 q^{20} -1.48663 q^{21} +1.00000 q^{22} +3.87512 q^{23} -1.00000 q^{24} -0.335585 q^{25} -5.53760 q^{26} +1.00000 q^{27} -1.48663 q^{28} +3.49531 q^{29} -2.15973 q^{30} +3.71539 q^{31} -1.00000 q^{32} -1.00000 q^{33} -2.33751 q^{34} -3.21070 q^{35} +1.00000 q^{36} -3.86643 q^{37} -3.42627 q^{38} +5.53760 q^{39} -2.15973 q^{40} -7.21070 q^{41} +1.48663 q^{42} +8.37981 q^{43} -1.00000 q^{44} +2.15973 q^{45} -3.87512 q^{46} +6.71346 q^{47} +1.00000 q^{48} -4.78994 q^{49} +0.335585 q^{50} +2.33751 q^{51} +5.53760 q^{52} -3.82221 q^{53} -1.00000 q^{54} -2.15973 q^{55} +1.48663 q^{56} +3.42627 q^{57} -3.49531 q^{58} -13.1375 q^{59} +2.15973 q^{60} -1.00000 q^{61} -3.71539 q^{62} -1.48663 q^{63} +1.00000 q^{64} +11.9597 q^{65} +1.00000 q^{66} -4.45050 q^{67} +2.33751 q^{68} +3.87512 q^{69} +3.21070 q^{70} -5.39594 q^{71} -1.00000 q^{72} +1.17972 q^{73} +3.86643 q^{74} -0.335585 q^{75} +3.42627 q^{76} +1.48663 q^{77} -5.53760 q^{78} -11.2878 q^{79} +2.15973 q^{80} +1.00000 q^{81} +7.21070 q^{82} +4.96222 q^{83} -1.48663 q^{84} +5.04839 q^{85} -8.37981 q^{86} +3.49531 q^{87} +1.00000 q^{88} -4.59989 q^{89} -2.15973 q^{90} -8.23235 q^{91} +3.87512 q^{92} +3.71539 q^{93} -6.71346 q^{94} +7.39980 q^{95} -1.00000 q^{96} +3.58599 q^{97} +4.78994 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + O(q^{10}) \) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + q^{10} - 5q^{11} + 5q^{12} + 2q^{13} + 3q^{14} - q^{15} + 5q^{16} + 6q^{17} - 5q^{18} + 7q^{19} - q^{20} - 3q^{21} + 5q^{22} - 12q^{23} - 5q^{24} - 2q^{26} + 5q^{27} - 3q^{28} + 4q^{29} + q^{30} - q^{31} - 5q^{32} - 5q^{33} - 6q^{34} + 17q^{35} + 5q^{36} + 3q^{37} - 7q^{38} + 2q^{39} + q^{40} - 3q^{41} + 3q^{42} + 24q^{43} - 5q^{44} - q^{45} + 12q^{46} + 18q^{47} + 5q^{48} + 26q^{49} + 6q^{51} + 2q^{52} - 13q^{53} - 5q^{54} + q^{55} + 3q^{56} + 7q^{57} - 4q^{58} - 16q^{59} - q^{60} - 5q^{61} + q^{62} - 3q^{63} + 5q^{64} + 4q^{65} + 5q^{66} + 18q^{67} + 6q^{68} - 12q^{69} - 17q^{70} - 31q^{71} - 5q^{72} + 8q^{73} - 3q^{74} + 7q^{76} + 3q^{77} - 2q^{78} + 32q^{79} - q^{80} + 5q^{81} + 3q^{82} + 8q^{83} - 3q^{84} + 29q^{85} - 24q^{86} + 4q^{87} + 5q^{88} + q^{89} + q^{90} - 3q^{91} - 12q^{92} - q^{93} - 18q^{94} + 33q^{95} - 5q^{96} - 4q^{97} - 26q^{98} - 5q^{99} + O(q^{100}) \)

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
\(5\) 2.15973 0.965859 0.482929 0.875659i \(-0.339573\pi\)
0.482929 + 0.875659i \(0.339573\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.48663 −0.561892 −0.280946 0.959724i \(-0.590648\pi\)
−0.280946 + 0.959724i \(0.590648\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.15973 −0.682965
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) 5.53760 1.53586 0.767928 0.640537i \(-0.221288\pi\)
0.767928 + 0.640537i \(0.221288\pi\)
\(14\) 1.48663 0.397317
\(15\) 2.15973 0.557639
\(16\) 1.00000 0.250000
\(17\) 2.33751 0.566931 0.283465 0.958982i \(-0.408516\pi\)
0.283465 + 0.958982i \(0.408516\pi\)
\(18\) −1.00000 −0.235702
\(19\) 3.42627 0.786040 0.393020 0.919530i \(-0.371430\pi\)
0.393020 + 0.919530i \(0.371430\pi\)
\(20\) 2.15973 0.482929
\(21\) −1.48663 −0.324408
\(22\) 1.00000 0.213201
\(23\) 3.87512 0.808018 0.404009 0.914755i \(-0.367616\pi\)
0.404009 + 0.914755i \(0.367616\pi\)
\(24\) −1.00000 −0.204124
\(25\) −0.335585 −0.0671170
\(26\) −5.53760 −1.08601
\(27\) 1.00000 0.192450
\(28\) −1.48663 −0.280946
\(29\) 3.49531 0.649063 0.324531 0.945875i \(-0.394793\pi\)
0.324531 + 0.945875i \(0.394793\pi\)
\(30\) −2.15973 −0.394310
\(31\) 3.71539 0.667304 0.333652 0.942696i \(-0.391719\pi\)
0.333652 + 0.942696i \(0.391719\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) −2.33751 −0.400880
\(35\) −3.21070 −0.542708
\(36\) 1.00000 0.166667
\(37\) −3.86643 −0.635638 −0.317819 0.948151i \(-0.602950\pi\)
−0.317819 + 0.948151i \(0.602950\pi\)
\(38\) −3.42627 −0.555814
\(39\) 5.53760 0.886726
\(40\) −2.15973 −0.341483
\(41\) −7.21070 −1.12612 −0.563061 0.826415i \(-0.690377\pi\)
−0.563061 + 0.826415i \(0.690377\pi\)
\(42\) 1.48663 0.229391
\(43\) 8.37981 1.27791 0.638954 0.769245i \(-0.279367\pi\)
0.638954 + 0.769245i \(0.279367\pi\)
\(44\) −1.00000 −0.150756
\(45\) 2.15973 0.321953
\(46\) −3.87512 −0.571355
\(47\) 6.71346 0.979259 0.489630 0.871930i \(-0.337132\pi\)
0.489630 + 0.871930i \(0.337132\pi\)
\(48\) 1.00000 0.144338
\(49\) −4.78994 −0.684278
\(50\) 0.335585 0.0474589
\(51\) 2.33751 0.327318
\(52\) 5.53760 0.767928
\(53\) −3.82221 −0.525021 −0.262511 0.964929i \(-0.584550\pi\)
−0.262511 + 0.964929i \(0.584550\pi\)
\(54\) −1.00000 −0.136083
\(55\) −2.15973 −0.291217
\(56\) 1.48663 0.198659
\(57\) 3.42627 0.453820
\(58\) −3.49531 −0.458957
\(59\) −13.1375 −1.71036 −0.855178 0.518334i \(-0.826552\pi\)
−0.855178 + 0.518334i \(0.826552\pi\)
\(60\) 2.15973 0.278819
\(61\) −1.00000 −0.128037
\(62\) −3.71539 −0.471855
\(63\) −1.48663 −0.187297
\(64\) 1.00000 0.125000
\(65\) 11.9597 1.48342
\(66\) 1.00000 0.123091
\(67\) −4.45050 −0.543715 −0.271858 0.962338i \(-0.587638\pi\)
−0.271858 + 0.962338i \(0.587638\pi\)
\(68\) 2.33751 0.283465
\(69\) 3.87512 0.466510
\(70\) 3.21070 0.383753
\(71\) −5.39594 −0.640381 −0.320190 0.947353i \(-0.603747\pi\)
−0.320190 + 0.947353i \(0.603747\pi\)
\(72\) −1.00000 −0.117851
\(73\) 1.17972 0.138076 0.0690378 0.997614i \(-0.478007\pi\)
0.0690378 + 0.997614i \(0.478007\pi\)
\(74\) 3.86643 0.449464
\(75\) −0.335585 −0.0387500
\(76\) 3.42627 0.393020
\(77\) 1.48663 0.169417
\(78\) −5.53760 −0.627010
\(79\) −11.2878 −1.26998 −0.634991 0.772520i \(-0.718996\pi\)
−0.634991 + 0.772520i \(0.718996\pi\)
\(80\) 2.15973 0.241465
\(81\) 1.00000 0.111111
\(82\) 7.21070 0.796289
\(83\) 4.96222 0.544675 0.272337 0.962202i \(-0.412203\pi\)
0.272337 + 0.962202i \(0.412203\pi\)
\(84\) −1.48663 −0.162204
\(85\) 5.04839 0.547575
\(86\) −8.37981 −0.903618
\(87\) 3.49531 0.374737
\(88\) 1.00000 0.106600
\(89\) −4.59989 −0.487587 −0.243794 0.969827i \(-0.578392\pi\)
−0.243794 + 0.969827i \(0.578392\pi\)
\(90\) −2.15973 −0.227655
\(91\) −8.23235 −0.862984
\(92\) 3.87512 0.404009
\(93\) 3.71539 0.385268
\(94\) −6.71346 −0.692441
\(95\) 7.39980 0.759204
\(96\) −1.00000 −0.102062
\(97\) 3.58599 0.364103 0.182051 0.983289i \(-0.441726\pi\)
0.182051 + 0.983289i \(0.441726\pi\)
\(98\) 4.78994 0.483857
\(99\) −1.00000 −0.100504
\(100\) −0.335585 −0.0335585
\(101\) 14.2082 1.41377 0.706884 0.707330i \(-0.250100\pi\)
0.706884 + 0.707330i \(0.250100\pi\)
\(102\) −2.33751 −0.231448
\(103\) 13.4611 1.32636 0.663181 0.748459i \(-0.269206\pi\)
0.663181 + 0.748459i \(0.269206\pi\)
\(104\) −5.53760 −0.543007
\(105\) −3.21070 −0.313333
\(106\) 3.82221 0.371246
\(107\) 20.1230 1.94536 0.972682 0.232140i \(-0.0745727\pi\)
0.972682 + 0.232140i \(0.0745727\pi\)
\(108\) 1.00000 0.0962250
\(109\) 12.3175 1.17980 0.589902 0.807475i \(-0.299166\pi\)
0.589902 + 0.807475i \(0.299166\pi\)
\(110\) 2.15973 0.205922
\(111\) −3.86643 −0.366986
\(112\) −1.48663 −0.140473
\(113\) −8.93741 −0.840760 −0.420380 0.907348i \(-0.638103\pi\)
−0.420380 + 0.907348i \(0.638103\pi\)
\(114\) −3.42627 −0.320899
\(115\) 8.36919 0.780431
\(116\) 3.49531 0.324531
\(117\) 5.53760 0.511952
\(118\) 13.1375 1.20940
\(119\) −3.47501 −0.318554
\(120\) −2.15973 −0.197155
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) −7.21070 −0.650167
\(124\) 3.71539 0.333652
\(125\) −11.5234 −1.03068
\(126\) 1.48663 0.132439
\(127\) 21.9665 1.94921 0.974604 0.223935i \(-0.0718903\pi\)
0.974604 + 0.223935i \(0.0718903\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.37981 0.737801
\(130\) −11.9597 −1.04894
\(131\) 16.2301 1.41803 0.709016 0.705193i \(-0.249140\pi\)
0.709016 + 0.705193i \(0.249140\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −5.09358 −0.441669
\(134\) 4.45050 0.384465
\(135\) 2.15973 0.185880
\(136\) −2.33751 −0.200440
\(137\) −5.90932 −0.504867 −0.252433 0.967614i \(-0.581231\pi\)
−0.252433 + 0.967614i \(0.581231\pi\)
\(138\) −3.87512 −0.329872
\(139\) 1.19750 0.101571 0.0507854 0.998710i \(-0.483828\pi\)
0.0507854 + 0.998710i \(0.483828\pi\)
\(140\) −3.21070 −0.271354
\(141\) 6.71346 0.565376
\(142\) 5.39594 0.452817
\(143\) −5.53760 −0.463078
\(144\) 1.00000 0.0833333
\(145\) 7.54891 0.626903
\(146\) −1.17972 −0.0976342
\(147\) −4.78994 −0.395068
\(148\) −3.86643 −0.317819
\(149\) −19.5786 −1.60394 −0.801971 0.597362i \(-0.796215\pi\)
−0.801971 + 0.597362i \(0.796215\pi\)
\(150\) 0.335585 0.0274004
\(151\) 11.3134 0.920668 0.460334 0.887746i \(-0.347730\pi\)
0.460334 + 0.887746i \(0.347730\pi\)
\(152\) −3.42627 −0.277907
\(153\) 2.33751 0.188977
\(154\) −1.48663 −0.119796
\(155\) 8.02423 0.644522
\(156\) 5.53760 0.443363
\(157\) 1.30526 0.104171 0.0520855 0.998643i \(-0.483413\pi\)
0.0520855 + 0.998643i \(0.483413\pi\)
\(158\) 11.2878 0.898013
\(159\) −3.82221 −0.303121
\(160\) −2.15973 −0.170741
\(161\) −5.76085 −0.454019
\(162\) −1.00000 −0.0785674
\(163\) −2.48979 −0.195016 −0.0975078 0.995235i \(-0.531087\pi\)
−0.0975078 + 0.995235i \(0.531087\pi\)
\(164\) −7.21070 −0.563061
\(165\) −2.15973 −0.168134
\(166\) −4.96222 −0.385143
\(167\) 13.6725 1.05801 0.529005 0.848618i \(-0.322565\pi\)
0.529005 + 0.848618i \(0.322565\pi\)
\(168\) 1.48663 0.114696
\(169\) 17.6651 1.35885
\(170\) −5.04839 −0.387194
\(171\) 3.42627 0.262013
\(172\) 8.37981 0.638954
\(173\) −15.7651 −1.19860 −0.599300 0.800524i \(-0.704554\pi\)
−0.599300 + 0.800524i \(0.704554\pi\)
\(174\) −3.49531 −0.264979
\(175\) 0.498890 0.0377125
\(176\) −1.00000 −0.0753778
\(177\) −13.1375 −0.987475
\(178\) 4.59989 0.344776
\(179\) 4.56376 0.341112 0.170556 0.985348i \(-0.445444\pi\)
0.170556 + 0.985348i \(0.445444\pi\)
\(180\) 2.15973 0.160976
\(181\) 3.21399 0.238894 0.119447 0.992841i \(-0.461888\pi\)
0.119447 + 0.992841i \(0.461888\pi\)
\(182\) 8.23235 0.610222
\(183\) −1.00000 −0.0739221
\(184\) −3.87512 −0.285678
\(185\) −8.35044 −0.613936
\(186\) −3.71539 −0.272426
\(187\) −2.33751 −0.170936
\(188\) 6.71346 0.489630
\(189\) −1.48663 −0.108136
\(190\) −7.39980 −0.536838
\(191\) 25.8939 1.87362 0.936808 0.349843i \(-0.113765\pi\)
0.936808 + 0.349843i \(0.113765\pi\)
\(192\) 1.00000 0.0721688
\(193\) −21.8610 −1.57359 −0.786794 0.617216i \(-0.788261\pi\)
−0.786794 + 0.617216i \(0.788261\pi\)
\(194\) −3.58599 −0.257459
\(195\) 11.9597 0.856452
\(196\) −4.78994 −0.342139
\(197\) −11.8061 −0.841148 −0.420574 0.907258i \(-0.638171\pi\)
−0.420574 + 0.907258i \(0.638171\pi\)
\(198\) 1.00000 0.0710669
\(199\) 6.17268 0.437570 0.218785 0.975773i \(-0.429791\pi\)
0.218785 + 0.975773i \(0.429791\pi\)
\(200\) 0.335585 0.0237295
\(201\) −4.45050 −0.313914
\(202\) −14.2082 −0.999684
\(203\) −5.19622 −0.364703
\(204\) 2.33751 0.163659
\(205\) −15.5731 −1.08768
\(206\) −13.4611 −0.937880
\(207\) 3.87512 0.269339
\(208\) 5.53760 0.383964
\(209\) −3.42627 −0.237000
\(210\) 3.21070 0.221560
\(211\) 0.750581 0.0516721 0.0258361 0.999666i \(-0.491775\pi\)
0.0258361 + 0.999666i \(0.491775\pi\)
\(212\) −3.82221 −0.262511
\(213\) −5.39594 −0.369724
\(214\) −20.1230 −1.37558
\(215\) 18.0981 1.23428
\(216\) −1.00000 −0.0680414
\(217\) −5.52340 −0.374953
\(218\) −12.3175 −0.834248
\(219\) 1.17972 0.0797180
\(220\) −2.15973 −0.145609
\(221\) 12.9442 0.870723
\(222\) 3.86643 0.259498
\(223\) 2.07387 0.138876 0.0694382 0.997586i \(-0.477879\pi\)
0.0694382 + 0.997586i \(0.477879\pi\)
\(224\) 1.48663 0.0993294
\(225\) −0.335585 −0.0223723
\(226\) 8.93741 0.594507
\(227\) −28.5906 −1.89762 −0.948811 0.315843i \(-0.897713\pi\)
−0.948811 + 0.315843i \(0.897713\pi\)
\(228\) 3.42627 0.226910
\(229\) −0.844512 −0.0558069 −0.0279035 0.999611i \(-0.508883\pi\)
−0.0279035 + 0.999611i \(0.508883\pi\)
\(230\) −8.36919 −0.551848
\(231\) 1.48663 0.0978128
\(232\) −3.49531 −0.229478
\(233\) 0.00482589 0.000316155 0 0.000158077 1.00000i \(-0.499950\pi\)
0.000158077 1.00000i \(0.499950\pi\)
\(234\) −5.53760 −0.362005
\(235\) 14.4992 0.945826
\(236\) −13.1375 −0.855178
\(237\) −11.2878 −0.733224
\(238\) 3.47501 0.225251
\(239\) −15.6790 −1.01419 −0.507094 0.861891i \(-0.669280\pi\)
−0.507094 + 0.861891i \(0.669280\pi\)
\(240\) 2.15973 0.139410
\(241\) 12.5896 0.810966 0.405483 0.914103i \(-0.367103\pi\)
0.405483 + 0.914103i \(0.367103\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −10.3450 −0.660915
\(246\) 7.21070 0.459738
\(247\) 18.9733 1.20724
\(248\) −3.71539 −0.235928
\(249\) 4.96222 0.314468
\(250\) 11.5234 0.728804
\(251\) 17.7012 1.11729 0.558645 0.829407i \(-0.311322\pi\)
0.558645 + 0.829407i \(0.311322\pi\)
\(252\) −1.48663 −0.0936486
\(253\) −3.87512 −0.243627
\(254\) −21.9665 −1.37830
\(255\) 5.04839 0.316142
\(256\) 1.00000 0.0625000
\(257\) −12.4144 −0.774387 −0.387194 0.921998i \(-0.626556\pi\)
−0.387194 + 0.921998i \(0.626556\pi\)
\(258\) −8.37981 −0.521704
\(259\) 5.74794 0.357160
\(260\) 11.9597 0.741709
\(261\) 3.49531 0.216354
\(262\) −16.2301 −1.00270
\(263\) −23.4941 −1.44871 −0.724355 0.689427i \(-0.757862\pi\)
−0.724355 + 0.689427i \(0.757862\pi\)
\(264\) 1.00000 0.0615457
\(265\) −8.25493 −0.507096
\(266\) 5.09358 0.312307
\(267\) −4.59989 −0.281509
\(268\) −4.45050 −0.271858
\(269\) 18.4428 1.12447 0.562237 0.826976i \(-0.309941\pi\)
0.562237 + 0.826976i \(0.309941\pi\)
\(270\) −2.15973 −0.131437
\(271\) 20.6347 1.25347 0.626735 0.779232i \(-0.284391\pi\)
0.626735 + 0.779232i \(0.284391\pi\)
\(272\) 2.33751 0.141733
\(273\) −8.23235 −0.498244
\(274\) 5.90932 0.356995
\(275\) 0.335585 0.0202365
\(276\) 3.87512 0.233255
\(277\) 0.330066 0.0198317 0.00991586 0.999951i \(-0.496844\pi\)
0.00991586 + 0.999951i \(0.496844\pi\)
\(278\) −1.19750 −0.0718214
\(279\) 3.71539 0.222435
\(280\) 3.21070 0.191876
\(281\) 7.48663 0.446615 0.223307 0.974748i \(-0.428315\pi\)
0.223307 + 0.974748i \(0.428315\pi\)
\(282\) −6.71346 −0.399781
\(283\) 8.98880 0.534329 0.267164 0.963651i \(-0.413913\pi\)
0.267164 + 0.963651i \(0.413913\pi\)
\(284\) −5.39594 −0.320190
\(285\) 7.39980 0.438326
\(286\) 5.53760 0.327445
\(287\) 10.7196 0.632759
\(288\) −1.00000 −0.0589256
\(289\) −11.5360 −0.678590
\(290\) −7.54891 −0.443287
\(291\) 3.58599 0.210215
\(292\) 1.17972 0.0690378
\(293\) −10.0652 −0.588014 −0.294007 0.955803i \(-0.594989\pi\)
−0.294007 + 0.955803i \(0.594989\pi\)
\(294\) 4.78994 0.279355
\(295\) −28.3734 −1.65196
\(296\) 3.86643 0.224732
\(297\) −1.00000 −0.0580259
\(298\) 19.5786 1.13416
\(299\) 21.4589 1.24100
\(300\) −0.335585 −0.0193750
\(301\) −12.4576 −0.718046
\(302\) −11.3134 −0.651010
\(303\) 14.2082 0.816239
\(304\) 3.42627 0.196510
\(305\) −2.15973 −0.123666
\(306\) −2.33751 −0.133627
\(307\) 10.7141 0.611489 0.305744 0.952114i \(-0.401095\pi\)
0.305744 + 0.952114i \(0.401095\pi\)
\(308\) 1.48663 0.0847084
\(309\) 13.4611 0.765776
\(310\) −8.02423 −0.455746
\(311\) −22.0204 −1.24866 −0.624330 0.781161i \(-0.714628\pi\)
−0.624330 + 0.781161i \(0.714628\pi\)
\(312\) −5.53760 −0.313505
\(313\) −25.5931 −1.44661 −0.723303 0.690530i \(-0.757377\pi\)
−0.723303 + 0.690530i \(0.757377\pi\)
\(314\) −1.30526 −0.0736600
\(315\) −3.21070 −0.180903
\(316\) −11.2878 −0.634991
\(317\) 8.56635 0.481134 0.240567 0.970632i \(-0.422667\pi\)
0.240567 + 0.970632i \(0.422667\pi\)
\(318\) 3.82221 0.214339
\(319\) −3.49531 −0.195700
\(320\) 2.15973 0.120732
\(321\) 20.1230 1.12316
\(322\) 5.76085 0.321040
\(323\) 8.00895 0.445630
\(324\) 1.00000 0.0555556
\(325\) −1.85834 −0.103082
\(326\) 2.48979 0.137897
\(327\) 12.3175 0.681161
\(328\) 7.21070 0.398145
\(329\) −9.98041 −0.550238
\(330\) 2.15973 0.118889
\(331\) −18.2004 −1.00038 −0.500191 0.865915i \(-0.666737\pi\)
−0.500191 + 0.865915i \(0.666737\pi\)
\(332\) 4.96222 0.272337
\(333\) −3.86643 −0.211879
\(334\) −13.6725 −0.748127
\(335\) −9.61186 −0.525152
\(336\) −1.48663 −0.0811021
\(337\) 33.9161 1.84753 0.923765 0.382961i \(-0.125095\pi\)
0.923765 + 0.382961i \(0.125095\pi\)
\(338\) −17.6651 −0.960853
\(339\) −8.93741 −0.485413
\(340\) 5.04839 0.273787
\(341\) −3.71539 −0.201200
\(342\) −3.42627 −0.185271
\(343\) 17.5272 0.946382
\(344\) −8.37981 −0.451809
\(345\) 8.36919 0.450582
\(346\) 15.7651 0.847538
\(347\) −15.6341 −0.839285 −0.419642 0.907689i \(-0.637845\pi\)
−0.419642 + 0.907689i \(0.637845\pi\)
\(348\) 3.49531 0.187368
\(349\) 26.7325 1.43096 0.715480 0.698634i \(-0.246208\pi\)
0.715480 + 0.698634i \(0.246208\pi\)
\(350\) −0.498890 −0.0266668
\(351\) 5.53760 0.295575
\(352\) 1.00000 0.0533002
\(353\) −25.8690 −1.37687 −0.688435 0.725298i \(-0.741702\pi\)
−0.688435 + 0.725298i \(0.741702\pi\)
\(354\) 13.1375 0.698250
\(355\) −11.6538 −0.618517
\(356\) −4.59989 −0.243794
\(357\) −3.47501 −0.183917
\(358\) −4.56376 −0.241202
\(359\) −27.5185 −1.45237 −0.726186 0.687498i \(-0.758709\pi\)
−0.726186 + 0.687498i \(0.758709\pi\)
\(360\) −2.15973 −0.113828
\(361\) −7.26068 −0.382141
\(362\) −3.21399 −0.168923
\(363\) 1.00000 0.0524864
\(364\) −8.23235 −0.431492
\(365\) 2.54787 0.133362
\(366\) 1.00000 0.0522708
\(367\) 12.9441 0.675679 0.337840 0.941204i \(-0.390304\pi\)
0.337840 + 0.941204i \(0.390304\pi\)
\(368\) 3.87512 0.202005
\(369\) −7.21070 −0.375374
\(370\) 8.35044 0.434119
\(371\) 5.68220 0.295005
\(372\) 3.71539 0.192634
\(373\) 12.6002 0.652414 0.326207 0.945298i \(-0.394229\pi\)
0.326207 + 0.945298i \(0.394229\pi\)
\(374\) 2.33751 0.120870
\(375\) −11.5234 −0.595066
\(376\) −6.71346 −0.346220
\(377\) 19.3556 0.996867
\(378\) 1.48663 0.0764638
\(379\) 37.0888 1.90512 0.952562 0.304344i \(-0.0984372\pi\)
0.952562 + 0.304344i \(0.0984372\pi\)
\(380\) 7.39980 0.379602
\(381\) 21.9665 1.12538
\(382\) −25.8939 −1.32485
\(383\) 0.0199579 0.00101980 0.000509902 1.00000i \(-0.499838\pi\)
0.000509902 1.00000i \(0.499838\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 3.21070 0.163633
\(386\) 21.8610 1.11269
\(387\) 8.37981 0.425970
\(388\) 3.58599 0.182051
\(389\) −19.0988 −0.968347 −0.484173 0.874972i \(-0.660880\pi\)
−0.484173 + 0.874972i \(0.660880\pi\)
\(390\) −11.9597 −0.605603
\(391\) 9.05815 0.458090
\(392\) 4.78994 0.241929
\(393\) 16.2301 0.818701
\(394\) 11.8061 0.594782
\(395\) −24.3786 −1.22662
\(396\) −1.00000 −0.0502519
\(397\) 16.5408 0.830161 0.415080 0.909785i \(-0.363753\pi\)
0.415080 + 0.909785i \(0.363753\pi\)
\(398\) −6.17268 −0.309409
\(399\) −5.09358 −0.254998
\(400\) −0.335585 −0.0167793
\(401\) 23.7813 1.18758 0.593791 0.804619i \(-0.297630\pi\)
0.593791 + 0.804619i \(0.297630\pi\)
\(402\) 4.45050 0.221971
\(403\) 20.5744 1.02488
\(404\) 14.2082 0.706884
\(405\) 2.15973 0.107318
\(406\) 5.19622 0.257884
\(407\) 3.86643 0.191652
\(408\) −2.33751 −0.115724
\(409\) 10.7147 0.529808 0.264904 0.964275i \(-0.414660\pi\)
0.264904 + 0.964275i \(0.414660\pi\)
\(410\) 15.5731 0.769103
\(411\) −5.90932 −0.291485
\(412\) 13.4611 0.663181
\(413\) 19.5305 0.961035
\(414\) −3.87512 −0.190452
\(415\) 10.7170 0.526079
\(416\) −5.53760 −0.271503
\(417\) 1.19750 0.0586419
\(418\) 3.42627 0.167584
\(419\) −17.9297 −0.875922 −0.437961 0.898994i \(-0.644299\pi\)
−0.437961 + 0.898994i \(0.644299\pi\)
\(420\) −3.21070 −0.156666
\(421\) −3.57962 −0.174460 −0.0872299 0.996188i \(-0.527801\pi\)
−0.0872299 + 0.996188i \(0.527801\pi\)
\(422\) −0.750581 −0.0365377
\(423\) 6.71346 0.326420
\(424\) 3.82221 0.185623
\(425\) −0.784435 −0.0380507
\(426\) 5.39594 0.261434
\(427\) 1.48663 0.0719429
\(428\) 20.1230 0.972682
\(429\) −5.53760 −0.267358
\(430\) −18.0981 −0.872767
\(431\) 14.2239 0.685143 0.342572 0.939492i \(-0.388702\pi\)
0.342572 + 0.939492i \(0.388702\pi\)
\(432\) 1.00000 0.0481125
\(433\) −10.0910 −0.484944 −0.242472 0.970158i \(-0.577958\pi\)
−0.242472 + 0.970158i \(0.577958\pi\)
\(434\) 5.52340 0.265132
\(435\) 7.54891 0.361943
\(436\) 12.3175 0.589902
\(437\) 13.2772 0.635135
\(438\) −1.17972 −0.0563691
\(439\) 3.97449 0.189692 0.0948460 0.995492i \(-0.469764\pi\)
0.0948460 + 0.995492i \(0.469764\pi\)
\(440\) 2.15973 0.102961
\(441\) −4.78994 −0.228093
\(442\) −12.9442 −0.615694
\(443\) −5.56112 −0.264217 −0.132108 0.991235i \(-0.542175\pi\)
−0.132108 + 0.991235i \(0.542175\pi\)
\(444\) −3.86643 −0.183493
\(445\) −9.93450 −0.470941
\(446\) −2.07387 −0.0982005
\(447\) −19.5786 −0.926037
\(448\) −1.48663 −0.0702365
\(449\) 17.4973 0.825749 0.412875 0.910788i \(-0.364525\pi\)
0.412875 + 0.910788i \(0.364525\pi\)
\(450\) 0.335585 0.0158196
\(451\) 7.21070 0.339539
\(452\) −8.93741 −0.420380
\(453\) 11.3134 0.531548
\(454\) 28.5906 1.34182
\(455\) −17.7796 −0.833521
\(456\) −3.42627 −0.160450
\(457\) 31.8542 1.49008 0.745038 0.667022i \(-0.232431\pi\)
0.745038 + 0.667022i \(0.232431\pi\)
\(458\) 0.844512 0.0394614
\(459\) 2.33751 0.109106
\(460\) 8.36919 0.390216
\(461\) 10.9578 0.510355 0.255177 0.966894i \(-0.417866\pi\)
0.255177 + 0.966894i \(0.417866\pi\)
\(462\) −1.48663 −0.0691641
\(463\) 6.73353 0.312934 0.156467 0.987683i \(-0.449990\pi\)
0.156467 + 0.987683i \(0.449990\pi\)
\(464\) 3.49531 0.162266
\(465\) 8.02423 0.372115
\(466\) −0.00482589 −0.000223555 0
\(467\) 23.9352 1.10759 0.553794 0.832653i \(-0.313179\pi\)
0.553794 + 0.832653i \(0.313179\pi\)
\(468\) 5.53760 0.255976
\(469\) 6.61623 0.305509
\(470\) −14.4992 −0.668800
\(471\) 1.30526 0.0601431
\(472\) 13.1375 0.604702
\(473\) −8.37981 −0.385304
\(474\) 11.2878 0.518468
\(475\) −1.14980 −0.0527567
\(476\) −3.47501 −0.159277
\(477\) −3.82221 −0.175007
\(478\) 15.6790 0.717139
\(479\) −31.1195 −1.42189 −0.710943 0.703250i \(-0.751732\pi\)
−0.710943 + 0.703250i \(0.751732\pi\)
\(480\) −2.15973 −0.0985775
\(481\) −21.4108 −0.976248
\(482\) −12.5896 −0.573439
\(483\) −5.76085 −0.262128
\(484\) 1.00000 0.0454545
\(485\) 7.74476 0.351672
\(486\) −1.00000 −0.0453609
\(487\) 6.69860 0.303543 0.151771 0.988416i \(-0.451502\pi\)
0.151771 + 0.988416i \(0.451502\pi\)
\(488\) 1.00000 0.0452679
\(489\) −2.48979 −0.112592
\(490\) 10.3450 0.467338
\(491\) −37.0594 −1.67247 −0.836234 0.548373i \(-0.815247\pi\)
−0.836234 + 0.548373i \(0.815247\pi\)
\(492\) −7.21070 −0.325084
\(493\) 8.17034 0.367974
\(494\) −18.9733 −0.853650
\(495\) −2.15973 −0.0970724
\(496\) 3.71539 0.166826
\(497\) 8.02175 0.359825
\(498\) −4.96222 −0.222363
\(499\) −20.8548 −0.933590 −0.466795 0.884366i \(-0.654591\pi\)
−0.466795 + 0.884366i \(0.654591\pi\)
\(500\) −11.5234 −0.515342
\(501\) 13.6725 0.610843
\(502\) −17.7012 −0.790043
\(503\) −29.1624 −1.30029 −0.650143 0.759812i \(-0.725291\pi\)
−0.650143 + 0.759812i \(0.725291\pi\)
\(504\) 1.48663 0.0662196
\(505\) 30.6858 1.36550
\(506\) 3.87512 0.172270
\(507\) 17.6651 0.784533
\(508\) 21.9665 0.974604
\(509\) −22.7444 −1.00813 −0.504065 0.863666i \(-0.668163\pi\)
−0.504065 + 0.863666i \(0.668163\pi\)
\(510\) −5.04839 −0.223546
\(511\) −1.75380 −0.0775835
\(512\) −1.00000 −0.0441942
\(513\) 3.42627 0.151273
\(514\) 12.4144 0.547575
\(515\) 29.0723 1.28108
\(516\) 8.37981 0.368900
\(517\) −6.71346 −0.295258
\(518\) −5.74794 −0.252550
\(519\) −15.7651 −0.692012
\(520\) −11.9597 −0.524468
\(521\) 13.0689 0.572557 0.286279 0.958146i \(-0.407582\pi\)
0.286279 + 0.958146i \(0.407582\pi\)
\(522\) −3.49531 −0.152986
\(523\) −10.4644 −0.457576 −0.228788 0.973476i \(-0.573476\pi\)
−0.228788 + 0.973476i \(0.573476\pi\)
\(524\) 16.2301 0.709016
\(525\) 0.498890 0.0217733
\(526\) 23.4941 1.02439
\(527\) 8.68479 0.378315
\(528\) −1.00000 −0.0435194
\(529\) −7.98345 −0.347107
\(530\) 8.25493 0.358571
\(531\) −13.1375 −0.570119
\(532\) −5.09358 −0.220835
\(533\) −39.9300 −1.72956
\(534\) 4.59989 0.199057
\(535\) 43.4602 1.87895
\(536\) 4.45050 0.192232
\(537\) 4.56376 0.196941
\(538\) −18.4428 −0.795124
\(539\) 4.78994 0.206317
\(540\) 2.15973 0.0929398
\(541\) −13.5479 −0.582471 −0.291236 0.956651i \(-0.594066\pi\)
−0.291236 + 0.956651i \(0.594066\pi\)
\(542\) −20.6347 −0.886338
\(543\) 3.21399 0.137925
\(544\) −2.33751 −0.100220
\(545\) 26.6025 1.13952
\(546\) 8.23235 0.352312
\(547\) −21.5744 −0.922457 −0.461228 0.887281i \(-0.652591\pi\)
−0.461228 + 0.887281i \(0.652591\pi\)
\(548\) −5.90932 −0.252433
\(549\) −1.00000 −0.0426790
\(550\) −0.335585 −0.0143094
\(551\) 11.9759 0.510189
\(552\) −3.87512 −0.164936
\(553\) 16.7808 0.713592
\(554\) −0.330066 −0.0140231
\(555\) −8.35044 −0.354456
\(556\) 1.19750 0.0507854
\(557\) −27.4818 −1.16444 −0.582221 0.813030i \(-0.697816\pi\)
−0.582221 + 0.813030i \(0.697816\pi\)
\(558\) −3.71539 −0.157285
\(559\) 46.4041 1.96268
\(560\) −3.21070 −0.135677
\(561\) −2.33751 −0.0986899
\(562\) −7.48663 −0.315804
\(563\) 10.2759 0.433078 0.216539 0.976274i \(-0.430523\pi\)
0.216539 + 0.976274i \(0.430523\pi\)
\(564\) 6.71346 0.282688
\(565\) −19.3023 −0.812056
\(566\) −8.98880 −0.377827
\(567\) −1.48663 −0.0624324
\(568\) 5.39594 0.226409
\(569\) −25.4295 −1.06606 −0.533030 0.846096i \(-0.678947\pi\)
−0.533030 + 0.846096i \(0.678947\pi\)
\(570\) −7.39980 −0.309944
\(571\) −3.94939 −0.165277 −0.0826384 0.996580i \(-0.526335\pi\)
−0.0826384 + 0.996580i \(0.526335\pi\)
\(572\) −5.53760 −0.231539
\(573\) 25.8939 1.08173
\(574\) −10.7196 −0.447428
\(575\) −1.30043 −0.0542318
\(576\) 1.00000 0.0416667
\(577\) 31.8791 1.32715 0.663573 0.748112i \(-0.269039\pi\)
0.663573 + 0.748112i \(0.269039\pi\)
\(578\) 11.5360 0.479835
\(579\) −21.8610 −0.908512
\(580\) 7.54891 0.313452
\(581\) −7.37697 −0.306048
\(582\) −3.58599 −0.148644
\(583\) 3.82221 0.158300
\(584\) −1.17972 −0.0488171
\(585\) 11.9597 0.494473
\(586\) 10.0652 0.415789
\(587\) −26.2885 −1.08504 −0.542521 0.840043i \(-0.682530\pi\)
−0.542521 + 0.840043i \(0.682530\pi\)
\(588\) −4.78994 −0.197534
\(589\) 12.7299 0.524528
\(590\) 28.3734 1.16811
\(591\) −11.8061 −0.485637
\(592\) −3.86643 −0.158909
\(593\) 7.61998 0.312915 0.156458 0.987685i \(-0.449993\pi\)
0.156458 + 0.987685i \(0.449993\pi\)
\(594\) 1.00000 0.0410305
\(595\) −7.50507 −0.307678
\(596\) −19.5786 −0.801971
\(597\) 6.17268 0.252631
\(598\) −21.4589 −0.877519
\(599\) 17.7112 0.723661 0.361830 0.932244i \(-0.382152\pi\)
0.361830 + 0.932244i \(0.382152\pi\)
\(600\) 0.335585 0.0137002
\(601\) 6.47749 0.264222 0.132111 0.991235i \(-0.457824\pi\)
0.132111 + 0.991235i \(0.457824\pi\)
\(602\) 12.4576 0.507736
\(603\) −4.45050 −0.181238
\(604\) 11.3134 0.460334
\(605\) 2.15973 0.0878053
\(606\) −14.2082 −0.577168
\(607\) −4.66958 −0.189532 −0.0947662 0.995500i \(-0.530210\pi\)
−0.0947662 + 0.995500i \(0.530210\pi\)
\(608\) −3.42627 −0.138954
\(609\) −5.19622 −0.210561
\(610\) 2.15973 0.0874447
\(611\) 37.1765 1.50400
\(612\) 2.33751 0.0944884
\(613\) −25.8100 −1.04246 −0.521228 0.853417i \(-0.674526\pi\)
−0.521228 + 0.853417i \(0.674526\pi\)
\(614\) −10.7141 −0.432388
\(615\) −15.5731 −0.627970
\(616\) −1.48663 −0.0598979
\(617\) −37.1837 −1.49696 −0.748480 0.663157i \(-0.769216\pi\)
−0.748480 + 0.663157i \(0.769216\pi\)
\(618\) −13.4611 −0.541485
\(619\) −40.1186 −1.61250 −0.806251 0.591574i \(-0.798507\pi\)
−0.806251 + 0.591574i \(0.798507\pi\)
\(620\) 8.02423 0.322261
\(621\) 3.87512 0.155503
\(622\) 22.0204 0.882936
\(623\) 6.83832 0.273971
\(624\) 5.53760 0.221682
\(625\) −23.2095 −0.928378
\(626\) 25.5931 1.02291
\(627\) −3.42627 −0.136832
\(628\) 1.30526 0.0520855
\(629\) −9.03785 −0.360363
\(630\) 3.21070 0.127918
\(631\) 34.1963 1.36133 0.680666 0.732594i \(-0.261690\pi\)
0.680666 + 0.732594i \(0.261690\pi\)
\(632\) 11.2878 0.449006
\(633\) 0.750581 0.0298329
\(634\) −8.56635 −0.340213
\(635\) 47.4415 1.88266
\(636\) −3.82221 −0.151561
\(637\) −26.5248 −1.05095
\(638\) 3.49531 0.138381
\(639\) −5.39594 −0.213460
\(640\) −2.15973 −0.0853707
\(641\) −14.1193 −0.557680 −0.278840 0.960338i \(-0.589950\pi\)
−0.278840 + 0.960338i \(0.589950\pi\)
\(642\) −20.1230 −0.794192
\(643\) −27.0568 −1.06702 −0.533509 0.845795i \(-0.679127\pi\)
−0.533509 + 0.845795i \(0.679127\pi\)
\(644\) −5.76085 −0.227009
\(645\) 18.0981 0.712611
\(646\) −8.00895 −0.315108
\(647\) −9.17687 −0.360780 −0.180390 0.983595i \(-0.557736\pi\)
−0.180390 + 0.983595i \(0.557736\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 13.1375 0.515692
\(650\) 1.85834 0.0728900
\(651\) −5.52340 −0.216479
\(652\) −2.48979 −0.0975078
\(653\) 30.7912 1.20495 0.602476 0.798137i \(-0.294181\pi\)
0.602476 + 0.798137i \(0.294181\pi\)
\(654\) −12.3175 −0.481653
\(655\) 35.0526 1.36962
\(656\) −7.21070 −0.281531
\(657\) 1.17972 0.0460252
\(658\) 9.98041 0.389077
\(659\) 10.0452 0.391305 0.195652 0.980673i \(-0.437318\pi\)
0.195652 + 0.980673i \(0.437318\pi\)
\(660\) −2.15973 −0.0840672
\(661\) −42.9194 −1.66937 −0.834685 0.550727i \(-0.814350\pi\)
−0.834685 + 0.550727i \(0.814350\pi\)
\(662\) 18.2004 0.707377
\(663\) 12.9442 0.502712
\(664\) −4.96222 −0.192572
\(665\) −11.0007 −0.426590
\(666\) 3.86643 0.149821
\(667\) 13.5447 0.524455
\(668\) 13.6725 0.529005
\(669\) 2.07387 0.0801804
\(670\) 9.61186 0.371338
\(671\) 1.00000 0.0386046
\(672\) 1.48663 0.0573478
\(673\) 1.77188 0.0683010 0.0341505 0.999417i \(-0.489127\pi\)
0.0341505 + 0.999417i \(0.489127\pi\)
\(674\) −33.9161 −1.30640
\(675\) −0.335585 −0.0129167
\(676\) 17.6651 0.679425
\(677\) −25.1569 −0.966858 −0.483429 0.875384i \(-0.660609\pi\)
−0.483429 + 0.875384i \(0.660609\pi\)
\(678\) 8.93741 0.343239
\(679\) −5.33103 −0.204586
\(680\) −5.04839 −0.193597
\(681\) −28.5906 −1.09559
\(682\) 3.71539 0.142270
\(683\) −8.36659 −0.320139 −0.160069 0.987106i \(-0.551172\pi\)
−0.160069 + 0.987106i \(0.551172\pi\)
\(684\) 3.42627 0.131007
\(685\) −12.7625 −0.487630
\(686\) −17.5272 −0.669193
\(687\) −0.844512 −0.0322201
\(688\) 8.37981 0.319477
\(689\) −21.1659 −0.806356
\(690\) −8.36919 −0.318610
\(691\) 33.1500 1.26109 0.630543 0.776154i \(-0.282832\pi\)
0.630543 + 0.776154i \(0.282832\pi\)
\(692\) −15.7651 −0.599300
\(693\) 1.48663 0.0564722
\(694\) 15.6341 0.593464
\(695\) 2.58627 0.0981030
\(696\) −3.49531 −0.132489
\(697\) −16.8551 −0.638433
\(698\) −26.7325 −1.01184
\(699\) 0.00482589 0.000182532 0
\(700\) 0.498890 0.0188563
\(701\) 7.39883 0.279450 0.139725 0.990190i \(-0.455378\pi\)
0.139725 + 0.990190i \(0.455378\pi\)
\(702\) −5.53760 −0.209003
\(703\) −13.2474 −0.499637
\(704\) −1.00000 −0.0376889
\(705\) 14.4992 0.546073
\(706\) 25.8690 0.973594
\(707\) −21.1223 −0.794384
\(708\) −13.1375 −0.493737
\(709\) −12.3694 −0.464544 −0.232272 0.972651i \(-0.574616\pi\)
−0.232272 + 0.972651i \(0.574616\pi\)
\(710\) 11.6538 0.437358
\(711\) −11.2878 −0.423327
\(712\) 4.59989 0.172388
\(713\) 14.3976 0.539194
\(714\) 3.47501 0.130049
\(715\) −11.9597 −0.447268
\(716\) 4.56376 0.170556
\(717\) −15.6790 −0.585541
\(718\) 27.5185 1.02698
\(719\) −3.14204 −0.117178 −0.0585892 0.998282i \(-0.518660\pi\)
−0.0585892 + 0.998282i \(0.518660\pi\)
\(720\) 2.15973 0.0804882
\(721\) −20.0116 −0.745272
\(722\) 7.26068 0.270215
\(723\) 12.5896 0.468211
\(724\) 3.21399 0.119447
\(725\) −1.17297 −0.0435632
\(726\) −1.00000 −0.0371135
\(727\) −16.1552 −0.599163 −0.299582 0.954071i \(-0.596847\pi\)
−0.299582 + 0.954071i \(0.596847\pi\)
\(728\) 8.23235 0.305111
\(729\) 1.00000 0.0370370
\(730\) −2.54787 −0.0943008
\(731\) 19.5879 0.724486
\(732\) −1.00000 −0.0369611
\(733\) −22.5644 −0.833436 −0.416718 0.909036i \(-0.636820\pi\)
−0.416718 + 0.909036i \(0.636820\pi\)
\(734\) −12.9441 −0.477777
\(735\) −10.3450 −0.381580
\(736\) −3.87512 −0.142839
\(737\) 4.45050 0.163936
\(738\) 7.21070 0.265430
\(739\) −24.5883 −0.904495 −0.452248 0.891892i \(-0.649378\pi\)
−0.452248 + 0.891892i \(0.649378\pi\)
\(740\) −8.35044 −0.306968
\(741\) 18.9733 0.697002
\(742\) −5.68220 −0.208600
\(743\) 27.4070 1.00547 0.502733 0.864442i \(-0.332328\pi\)
0.502733 + 0.864442i \(0.332328\pi\)
\(744\) −3.71539 −0.136213
\(745\) −42.2844 −1.54918
\(746\) −12.6002 −0.461326
\(747\) 4.96222 0.181558
\(748\) −2.33751 −0.0854680
\(749\) −29.9154 −1.09308
\(750\) 11.5234 0.420775
\(751\) −11.0652 −0.403774 −0.201887 0.979409i \(-0.564707\pi\)
−0.201887 + 0.979409i \(0.564707\pi\)
\(752\) 6.71346 0.244815
\(753\) 17.7012 0.645067
\(754\) −19.3556 −0.704891
\(755\) 24.4337 0.889235
\(756\) −1.48663 −0.0540681
\(757\) −15.5340 −0.564595 −0.282297 0.959327i \(-0.591096\pi\)
−0.282297 + 0.959327i \(0.591096\pi\)
\(758\) −37.0888 −1.34713
\(759\) −3.87512 −0.140658
\(760\) −7.39980 −0.268419
\(761\) 11.1588 0.404506 0.202253 0.979333i \(-0.435174\pi\)
0.202253 + 0.979333i \(0.435174\pi\)
\(762\) −21.9665 −0.795761
\(763\) −18.3115 −0.662923
\(764\) 25.8939 0.936808
\(765\) 5.04839 0.182525
\(766\) −0.0199579 −0.000721110 0
\(767\) −72.7503 −2.62686
\(768\) 1.00000 0.0360844
\(769\) 28.2780 1.01973 0.509865 0.860254i \(-0.329695\pi\)
0.509865 + 0.860254i \(0.329695\pi\)
\(770\) −3.21070 −0.115706
\(771\) −12.4144 −0.447093
\(772\) −21.8610 −0.786794
\(773\) −39.5596 −1.42286 −0.711429 0.702758i \(-0.751952\pi\)
−0.711429 + 0.702758i \(0.751952\pi\)
\(774\) −8.37981 −0.301206
\(775\) −1.24683 −0.0447875
\(776\) −3.58599 −0.128730
\(777\) 5.74794 0.206206
\(778\) 19.0988 0.684724
\(779\) −24.7058 −0.885178
\(780\) 11.9597 0.428226
\(781\) 5.39594 0.193082
\(782\) −9.05815 −0.323919
\(783\) 3.49531 0.124912
\(784\) −4.78994 −0.171069
\(785\) 2.81900 0.100614
\(786\) −16.2301 −0.578909
\(787\) 13.8093 0.492249 0.246125 0.969238i \(-0.420843\pi\)
0.246125 + 0.969238i \(0.420843\pi\)
\(788\) −11.8061 −0.420574
\(789\) −23.4941 −0.836413
\(790\) 24.3786 0.867353
\(791\) 13.2866 0.472416
\(792\) 1.00000 0.0355335
\(793\) −5.53760 −0.196646
\(794\) −16.5408 −0.587012
\(795\) −8.25493 −0.292772
\(796\) 6.17268 0.218785
\(797\) −35.7035 −1.26468 −0.632341 0.774690i \(-0.717906\pi\)
−0.632341 + 0.774690i \(0.717906\pi\)
\(798\) 5.09358 0.180311
\(799\) 15.6928 0.555172
\(800\) 0.335585 0.0118647
\(801\) −4.59989 −0.162529
\(802\) −23.7813 −0.839748
\(803\) −1.17972 −0.0416314
\(804\) −4.45050 −0.156957
\(805\) −12.4419 −0.438518
\(806\) −20.5744 −0.724702
\(807\) 18.4428 0.649216
\(808\) −14.2082 −0.499842
\(809\) 53.4232 1.87826 0.939130 0.343563i \(-0.111634\pi\)
0.939130 + 0.343563i \(0.111634\pi\)
\(810\) −2.15973 −0.0758850
\(811\) −47.8593 −1.68057 −0.840284 0.542146i \(-0.817612\pi\)
−0.840284 + 0.542146i \(0.817612\pi\)
\(812\) −5.19622 −0.182352
\(813\) 20.6347 0.723692
\(814\) −3.86643 −0.135518
\(815\) −5.37727 −0.188357
\(816\) 2.33751 0.0818294
\(817\) 28.7115 1.00449
\(818\) −10.7147 −0.374631
\(819\) −8.23235 −0.287661
\(820\) −15.5731 −0.543838
\(821\) 54.3422 1.89656 0.948278 0.317440i \(-0.102823\pi\)
0.948278 + 0.317440i \(0.102823\pi\)
\(822\) 5.90932 0.206111
\(823\) 14.4295 0.502982 0.251491 0.967860i \(-0.419079\pi\)
0.251491 + 0.967860i \(0.419079\pi\)
\(824\) −13.4611 −0.468940
\(825\) 0.335585 0.0116836
\(826\) −19.5305 −0.679554
\(827\) 22.0919 0.768211 0.384106 0.923289i \(-0.374510\pi\)
0.384106 + 0.923289i \(0.374510\pi\)
\(828\) 3.87512 0.134670
\(829\) −14.8719 −0.516522 −0.258261 0.966075i \(-0.583149\pi\)
−0.258261 + 0.966075i \(0.583149\pi\)
\(830\) −10.7170 −0.371994
\(831\) 0.330066 0.0114498
\(832\) 5.53760 0.191982
\(833\) −11.1966 −0.387938
\(834\) −1.19750 −0.0414661
\(835\) 29.5289 1.02189
\(836\) −3.42627 −0.118500
\(837\) 3.71539 0.128423
\(838\) 17.9297 0.619370
\(839\) 16.1663 0.558121 0.279061 0.960273i \(-0.409977\pi\)
0.279061 + 0.960273i \(0.409977\pi\)
\(840\) 3.21070 0.110780
\(841\) −16.7828 −0.578717
\(842\) 3.57962 0.123362
\(843\) 7.48663 0.257853
\(844\) 0.750581 0.0258361
\(845\) 38.1517 1.31246
\(846\) −6.71346 −0.230814
\(847\) −1.48663 −0.0510811
\(848\) −3.82221 −0.131255
\(849\) 8.98880 0.308495
\(850\) 0.784435 0.0269059
\(851\) −14.9829 −0.513607
\(852\) −5.39594 −0.184862
\(853\) 4.12232 0.141145 0.0705727 0.997507i \(-0.477517\pi\)
0.0705727 + 0.997507i \(0.477517\pi\)
\(854\) −1.48663 −0.0508713
\(855\) 7.39980 0.253068
\(856\) −20.1230 −0.687790
\(857\) 34.4683 1.17741 0.588707 0.808347i \(-0.299637\pi\)
0.588707 + 0.808347i \(0.299637\pi\)
\(858\) 5.53760 0.189051
\(859\) −17.3245 −0.591106 −0.295553 0.955326i \(-0.595504\pi\)
−0.295553 + 0.955326i \(0.595504\pi\)
\(860\) 18.0981 0.617140
\(861\) 10.7196 0.365324
\(862\) −14.2239 −0.484469
\(863\) −38.4144 −1.30764 −0.653821 0.756649i \(-0.726835\pi\)
−0.653821 + 0.756649i \(0.726835\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −34.0483 −1.15768
\(866\) 10.0910 0.342907
\(867\) −11.5360 −0.391784
\(868\) −5.52340 −0.187476
\(869\) 11.2878 0.382914
\(870\) −7.54891 −0.255932
\(871\) −24.6451 −0.835068
\(872\) −12.3175 −0.417124
\(873\) 3.58599 0.121368
\(874\) −13.2772 −0.449108
\(875\) 17.1310 0.579133
\(876\) 1.17972 0.0398590
\(877\) 22.8561 0.771796 0.385898 0.922541i \(-0.373892\pi\)
0.385898 + 0.922541i \(0.373892\pi\)
\(878\) −3.97449 −0.134132
\(879\) −10.0652 −0.339490
\(880\) −2.15973 −0.0728043
\(881\) 18.9686 0.639069 0.319535 0.947575i \(-0.396473\pi\)
0.319535 + 0.947575i \(0.396473\pi\)
\(882\) 4.78994 0.161286
\(883\) −30.0557 −1.01145 −0.505727 0.862694i \(-0.668776\pi\)
−0.505727 + 0.862694i \(0.668776\pi\)
\(884\) 12.9442 0.435362
\(885\) −28.3734 −0.953761
\(886\) 5.56112 0.186829
\(887\) −34.4479 −1.15665 −0.578323 0.815808i \(-0.696293\pi\)
−0.578323 + 0.815808i \(0.696293\pi\)
\(888\) 3.86643 0.129749
\(889\) −32.6559 −1.09524
\(890\) 9.93450 0.333005
\(891\) −1.00000 −0.0335013
\(892\) 2.07387 0.0694382
\(893\) 23.0021 0.769737
\(894\) 19.5786 0.654807
\(895\) 9.85648 0.329466
\(896\) 1.48663 0.0496647
\(897\) 21.4589 0.716491
\(898\) −17.4973 −0.583893
\(899\) 12.9865 0.433123
\(900\) −0.335585 −0.0111862
\(901\) −8.93447 −0.297650
\(902\) −7.21070 −0.240090
\(903\) −12.4576 −0.414564
\(904\) 8.93741 0.297254
\(905\) 6.94133 0.230738
\(906\) −11.3134 −0.375861
\(907\) 11.3682 0.377475 0.188737 0.982028i \(-0.439560\pi\)
0.188737 + 0.982028i \(0.439560\pi\)
\(908\) −28.5906 −0.948811
\(909\) 14.2082 0.471256
\(910\) 17.7796 0.589388
\(911\) 53.6491 1.77747 0.888736 0.458418i \(-0.151584\pi\)
0.888736 + 0.458418i \(0.151584\pi\)
\(912\) 3.42627 0.113455
\(913\) −4.96222 −0.164226
\(914\) −31.8542 −1.05364
\(915\) −2.15973 −0.0713983
\(916\) −0.844512 −0.0279035
\(917\) −24.1281 −0.796780
\(918\) −2.33751 −0.0771495
\(919\) 36.5854 1.20684 0.603420 0.797423i \(-0.293804\pi\)
0.603420 + 0.797423i \(0.293804\pi\)
\(920\) −8.36919 −0.275924
\(921\) 10.7141 0.353043
\(922\) −10.9578 −0.360875
\(923\) −29.8806 −0.983532
\(924\) 1.48663 0.0489064
\(925\) 1.29752 0.0426621
\(926\) −6.73353 −0.221277
\(927\) 13.4611 0.442121
\(928\) −3.49531 −0.114739
\(929\) 11.4867 0.376865 0.188433 0.982086i \(-0.439659\pi\)
0.188433 + 0.982086i \(0.439659\pi\)
\(930\) −8.02423 −0.263125
\(931\) −16.4116 −0.537870
\(932\) 0.00482589 0.000158077 0
\(933\) −22.0204 −0.720914
\(934\) −23.9352 −0.783184
\(935\) −5.04839 −0.165100
\(936\) −5.53760 −0.181002
\(937\) −43.0161 −1.40528 −0.702638 0.711548i \(-0.747995\pi\)
−0.702638 + 0.711548i \(0.747995\pi\)
\(938\) −6.61623 −0.216027
\(939\) −25.5931 −0.835199
\(940\) 14.4992 0.472913
\(941\) −24.6054 −0.802112 −0.401056 0.916054i \(-0.631357\pi\)
−0.401056 + 0.916054i \(0.631357\pi\)
\(942\) −1.30526 −0.0425276
\(943\) −27.9423 −0.909928
\(944\) −13.1375 −0.427589
\(945\) −3.21070 −0.104444
\(946\) 8.37981 0.272451
\(947\) 21.3091 0.692452 0.346226 0.938151i \(-0.387463\pi\)
0.346226 + 0.938151i \(0.387463\pi\)
\(948\) −11.2878 −0.366612
\(949\) 6.53281 0.212064
\(950\) 1.14980 0.0373046
\(951\) 8.56635 0.277783
\(952\) 3.47501 0.112626
\(953\) −12.2237 −0.395966 −0.197983 0.980205i \(-0.563439\pi\)
−0.197983 + 0.980205i \(0.563439\pi\)
\(954\) 3.82221 0.123749
\(955\) 55.9237 1.80965
\(956\) −15.6790 −0.507094
\(957\) −3.49531 −0.112987
\(958\) 31.1195 1.00543
\(959\) 8.78494 0.283681
\(960\) 2.15973 0.0697048
\(961\) −17.1959 −0.554705
\(962\) 21.4108 0.690311
\(963\) 20.1230 0.648455
\(964\) 12.5896 0.405483
\(965\) −47.2137 −1.51986
\(966\) 5.76085 0.185352
\(967\) −52.9113 −1.70151 −0.850757 0.525559i \(-0.823856\pi\)
−0.850757 + 0.525559i \(0.823856\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 8.00895 0.257285
\(970\) −7.74476 −0.248669
\(971\) −37.6806 −1.20923 −0.604613 0.796519i \(-0.706672\pi\)
−0.604613 + 0.796519i \(0.706672\pi\)
\(972\) 1.00000 0.0320750
\(973\) −1.78024 −0.0570718
\(974\) −6.69860 −0.214637
\(975\) −1.85834 −0.0595144
\(976\) −1.00000 −0.0320092
\(977\) 42.6049 1.36305 0.681525 0.731795i \(-0.261317\pi\)
0.681525 + 0.731795i \(0.261317\pi\)
\(978\) 2.48979 0.0796147
\(979\) 4.59989 0.147013
\(980\) −10.3450 −0.330458
\(981\) 12.3175 0.393268
\(982\) 37.0594 1.18261
\(983\) 18.8904 0.602510 0.301255 0.953544i \(-0.402595\pi\)
0.301255 + 0.953544i \(0.402595\pi\)
\(984\) 7.21070 0.229869
\(985\) −25.4979 −0.812430
\(986\) −8.17034 −0.260197
\(987\) −9.98041 −0.317680
\(988\) 18.9733 0.603622
\(989\) 32.4728 1.03257
\(990\) 2.15973 0.0686406
\(991\) −20.6244 −0.655155 −0.327578 0.944824i \(-0.606232\pi\)
−0.327578 + 0.944824i \(0.606232\pi\)
\(992\) −3.71539 −0.117964
\(993\) −18.2004 −0.577571
\(994\) −8.02175 −0.254434
\(995\) 13.3313 0.422631
\(996\) 4.96222 0.157234
\(997\) −38.8518 −1.23045 −0.615225 0.788352i \(-0.710935\pi\)
−0.615225 + 0.788352i \(0.710935\pi\)
\(998\) 20.8548 0.660148
\(999\) −3.86643 −0.122329
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.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.u.1.4 5 1.1 even 1 trivial