Properties

Label 4003.2.a.c.1.7
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61690 q^{2} -2.40767 q^{3} +4.84815 q^{4} +1.76120 q^{5} +6.30063 q^{6} -1.48829 q^{7} -7.45330 q^{8} +2.79688 q^{9} +O(q^{10})\) \(q-2.61690 q^{2} -2.40767 q^{3} +4.84815 q^{4} +1.76120 q^{5} +6.30063 q^{6} -1.48829 q^{7} -7.45330 q^{8} +2.79688 q^{9} -4.60888 q^{10} -4.43026 q^{11} -11.6727 q^{12} +3.63606 q^{13} +3.89470 q^{14} -4.24040 q^{15} +9.80823 q^{16} -3.52069 q^{17} -7.31915 q^{18} -7.25290 q^{19} +8.53856 q^{20} +3.58331 q^{21} +11.5935 q^{22} -0.195235 q^{23} +17.9451 q^{24} -1.89817 q^{25} -9.51518 q^{26} +0.489037 q^{27} -7.21545 q^{28} -5.52454 q^{29} +11.0967 q^{30} -10.6216 q^{31} -10.7605 q^{32} +10.6666 q^{33} +9.21329 q^{34} -2.62118 q^{35} +13.5597 q^{36} -10.2608 q^{37} +18.9801 q^{38} -8.75443 q^{39} -13.1268 q^{40} +3.71977 q^{41} -9.37716 q^{42} -10.5086 q^{43} -21.4786 q^{44} +4.92588 q^{45} +0.510910 q^{46} -0.699387 q^{47} -23.6150 q^{48} -4.78499 q^{49} +4.96731 q^{50} +8.47667 q^{51} +17.6281 q^{52} +10.9746 q^{53} -1.27976 q^{54} -7.80259 q^{55} +11.0927 q^{56} +17.4626 q^{57} +14.4572 q^{58} -0.122480 q^{59} -20.5581 q^{60} +6.99841 q^{61} +27.7956 q^{62} -4.16258 q^{63} +8.54267 q^{64} +6.40383 q^{65} -27.9134 q^{66} -3.16616 q^{67} -17.0688 q^{68} +0.470062 q^{69} +6.85935 q^{70} -6.44739 q^{71} -20.8460 q^{72} +6.88859 q^{73} +26.8515 q^{74} +4.57017 q^{75} -35.1631 q^{76} +6.59352 q^{77} +22.9094 q^{78} -1.12889 q^{79} +17.2743 q^{80} -9.56809 q^{81} -9.73425 q^{82} +11.3563 q^{83} +17.3724 q^{84} -6.20065 q^{85} +27.5000 q^{86} +13.3013 q^{87} +33.0201 q^{88} +14.1517 q^{89} -12.8905 q^{90} -5.41151 q^{91} -0.946529 q^{92} +25.5733 q^{93} +1.83022 q^{94} -12.7738 q^{95} +25.9078 q^{96} -9.84146 q^{97} +12.5218 q^{98} -12.3909 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61690 −1.85043 −0.925213 0.379449i \(-0.876113\pi\)
−0.925213 + 0.379449i \(0.876113\pi\)
\(3\) −2.40767 −1.39007 −0.695035 0.718976i \(-0.744611\pi\)
−0.695035 + 0.718976i \(0.744611\pi\)
\(4\) 4.84815 2.42407
\(5\) 1.76120 0.787633 0.393817 0.919189i \(-0.371154\pi\)
0.393817 + 0.919189i \(0.371154\pi\)
\(6\) 6.30063 2.57222
\(7\) −1.48829 −0.562521 −0.281260 0.959631i \(-0.590752\pi\)
−0.281260 + 0.959631i \(0.590752\pi\)
\(8\) −7.45330 −2.63514
\(9\) 2.79688 0.932295
\(10\) −4.60888 −1.45746
\(11\) −4.43026 −1.33577 −0.667887 0.744263i \(-0.732801\pi\)
−0.667887 + 0.744263i \(0.732801\pi\)
\(12\) −11.6727 −3.36963
\(13\) 3.63606 1.00846 0.504230 0.863569i \(-0.331776\pi\)
0.504230 + 0.863569i \(0.331776\pi\)
\(14\) 3.89470 1.04090
\(15\) −4.24040 −1.09487
\(16\) 9.80823 2.45206
\(17\) −3.52069 −0.853894 −0.426947 0.904277i \(-0.640411\pi\)
−0.426947 + 0.904277i \(0.640411\pi\)
\(18\) −7.31915 −1.72514
\(19\) −7.25290 −1.66393 −0.831965 0.554829i \(-0.812784\pi\)
−0.831965 + 0.554829i \(0.812784\pi\)
\(20\) 8.53856 1.90928
\(21\) 3.58331 0.781943
\(22\) 11.5935 2.47175
\(23\) −0.195235 −0.0407093 −0.0203547 0.999793i \(-0.506480\pi\)
−0.0203547 + 0.999793i \(0.506480\pi\)
\(24\) 17.9451 3.66303
\(25\) −1.89817 −0.379634
\(26\) −9.51518 −1.86608
\(27\) 0.489037 0.0941152
\(28\) −7.21545 −1.36359
\(29\) −5.52454 −1.02588 −0.512941 0.858424i \(-0.671444\pi\)
−0.512941 + 0.858424i \(0.671444\pi\)
\(30\) 11.0967 2.02597
\(31\) −10.6216 −1.90769 −0.953847 0.300293i \(-0.902916\pi\)
−0.953847 + 0.300293i \(0.902916\pi\)
\(32\) −10.7605 −1.90221
\(33\) 10.6666 1.85682
\(34\) 9.21329 1.58007
\(35\) −2.62118 −0.443060
\(36\) 13.5597 2.25995
\(37\) −10.2608 −1.68687 −0.843434 0.537232i \(-0.819470\pi\)
−0.843434 + 0.537232i \(0.819470\pi\)
\(38\) 18.9801 3.07898
\(39\) −8.75443 −1.40183
\(40\) −13.1268 −2.07552
\(41\) 3.71977 0.580930 0.290465 0.956886i \(-0.406190\pi\)
0.290465 + 0.956886i \(0.406190\pi\)
\(42\) −9.37716 −1.44693
\(43\) −10.5086 −1.60255 −0.801275 0.598296i \(-0.795845\pi\)
−0.801275 + 0.598296i \(0.795845\pi\)
\(44\) −21.4786 −3.23801
\(45\) 4.92588 0.734306
\(46\) 0.510910 0.0753296
\(47\) −0.699387 −0.102016 −0.0510080 0.998698i \(-0.516243\pi\)
−0.0510080 + 0.998698i \(0.516243\pi\)
\(48\) −23.6150 −3.40853
\(49\) −4.78499 −0.683570
\(50\) 4.96731 0.702484
\(51\) 8.47667 1.18697
\(52\) 17.6281 2.44458
\(53\) 10.9746 1.50748 0.753739 0.657174i \(-0.228248\pi\)
0.753739 + 0.657174i \(0.228248\pi\)
\(54\) −1.27976 −0.174153
\(55\) −7.80259 −1.05210
\(56\) 11.0927 1.48232
\(57\) 17.4626 2.31298
\(58\) 14.4572 1.89832
\(59\) −0.122480 −0.0159455 −0.00797275 0.999968i \(-0.502538\pi\)
−0.00797275 + 0.999968i \(0.502538\pi\)
\(60\) −20.5581 −2.65403
\(61\) 6.99841 0.896055 0.448028 0.894020i \(-0.352127\pi\)
0.448028 + 0.894020i \(0.352127\pi\)
\(62\) 27.7956 3.53005
\(63\) −4.16258 −0.524435
\(64\) 8.54267 1.06783
\(65\) 6.40383 0.794297
\(66\) −27.9134 −3.43591
\(67\) −3.16616 −0.386808 −0.193404 0.981119i \(-0.561953\pi\)
−0.193404 + 0.981119i \(0.561953\pi\)
\(68\) −17.0688 −2.06990
\(69\) 0.470062 0.0565888
\(70\) 6.85935 0.819850
\(71\) −6.44739 −0.765164 −0.382582 0.923922i \(-0.624965\pi\)
−0.382582 + 0.923922i \(0.624965\pi\)
\(72\) −20.8460 −2.45673
\(73\) 6.88859 0.806249 0.403124 0.915145i \(-0.367924\pi\)
0.403124 + 0.915145i \(0.367924\pi\)
\(74\) 26.8515 3.12142
\(75\) 4.57017 0.527718
\(76\) −35.1631 −4.03349
\(77\) 6.59352 0.751401
\(78\) 22.9094 2.59398
\(79\) −1.12889 −0.127011 −0.0635053 0.997982i \(-0.520228\pi\)
−0.0635053 + 0.997982i \(0.520228\pi\)
\(80\) 17.2743 1.93132
\(81\) −9.56809 −1.06312
\(82\) −9.73425 −1.07497
\(83\) 11.3563 1.24651 0.623256 0.782018i \(-0.285809\pi\)
0.623256 + 0.782018i \(0.285809\pi\)
\(84\) 17.3724 1.89549
\(85\) −6.20065 −0.672555
\(86\) 27.5000 2.96540
\(87\) 13.3013 1.42605
\(88\) 33.0201 3.51995
\(89\) 14.1517 1.50007 0.750037 0.661396i \(-0.230036\pi\)
0.750037 + 0.661396i \(0.230036\pi\)
\(90\) −12.8905 −1.35878
\(91\) −5.41151 −0.567280
\(92\) −0.946529 −0.0986824
\(93\) 25.5733 2.65183
\(94\) 1.83022 0.188773
\(95\) −12.7738 −1.31057
\(96\) 25.9078 2.64420
\(97\) −9.84146 −0.999249 −0.499624 0.866242i \(-0.666529\pi\)
−0.499624 + 0.866242i \(0.666529\pi\)
\(98\) 12.5218 1.26490
\(99\) −12.3909 −1.24534
\(100\) −9.20260 −0.920260
\(101\) 6.07715 0.604699 0.302349 0.953197i \(-0.402229\pi\)
0.302349 + 0.953197i \(0.402229\pi\)
\(102\) −22.1826 −2.19640
\(103\) 9.32815 0.919130 0.459565 0.888144i \(-0.348005\pi\)
0.459565 + 0.888144i \(0.348005\pi\)
\(104\) −27.1006 −2.65744
\(105\) 6.31094 0.615885
\(106\) −28.7194 −2.78947
\(107\) 3.10481 0.300154 0.150077 0.988674i \(-0.452048\pi\)
0.150077 + 0.988674i \(0.452048\pi\)
\(108\) 2.37092 0.228142
\(109\) −15.8448 −1.51766 −0.758830 0.651289i \(-0.774229\pi\)
−0.758830 + 0.651289i \(0.774229\pi\)
\(110\) 20.4186 1.94683
\(111\) 24.7047 2.34487
\(112\) −14.5975 −1.37933
\(113\) −4.31065 −0.405512 −0.202756 0.979229i \(-0.564990\pi\)
−0.202756 + 0.979229i \(0.564990\pi\)
\(114\) −45.6978 −4.27999
\(115\) −0.343848 −0.0320640
\(116\) −26.7838 −2.48681
\(117\) 10.1696 0.940182
\(118\) 0.320517 0.0295060
\(119\) 5.23981 0.480333
\(120\) 31.6049 2.88512
\(121\) 8.62723 0.784293
\(122\) −18.3141 −1.65808
\(123\) −8.95598 −0.807534
\(124\) −51.4950 −4.62439
\(125\) −12.1491 −1.08665
\(126\) 10.8930 0.970428
\(127\) 8.51277 0.755387 0.377693 0.925931i \(-0.376717\pi\)
0.377693 + 0.925931i \(0.376717\pi\)
\(128\) −0.834281 −0.0737407
\(129\) 25.3013 2.22766
\(130\) −16.7582 −1.46979
\(131\) −7.91504 −0.691540 −0.345770 0.938319i \(-0.612382\pi\)
−0.345770 + 0.938319i \(0.612382\pi\)
\(132\) 51.7133 4.50107
\(133\) 10.7944 0.935995
\(134\) 8.28551 0.715759
\(135\) 0.861293 0.0741283
\(136\) 26.2408 2.25013
\(137\) −20.2312 −1.72847 −0.864236 0.503087i \(-0.832198\pi\)
−0.864236 + 0.503087i \(0.832198\pi\)
\(138\) −1.23010 −0.104713
\(139\) 1.94813 0.165238 0.0826191 0.996581i \(-0.473672\pi\)
0.0826191 + 0.996581i \(0.473672\pi\)
\(140\) −12.7079 −1.07401
\(141\) 1.68389 0.141809
\(142\) 16.8721 1.41588
\(143\) −16.1087 −1.34708
\(144\) 27.4325 2.28604
\(145\) −9.72984 −0.808019
\(146\) −18.0267 −1.49190
\(147\) 11.5207 0.950211
\(148\) −49.7460 −4.08909
\(149\) −13.0589 −1.06983 −0.534913 0.844907i \(-0.679656\pi\)
−0.534913 + 0.844907i \(0.679656\pi\)
\(150\) −11.9597 −0.976502
\(151\) −14.8544 −1.20883 −0.604417 0.796668i \(-0.706594\pi\)
−0.604417 + 0.796668i \(0.706594\pi\)
\(152\) 54.0580 4.38469
\(153\) −9.84697 −0.796080
\(154\) −17.2545 −1.39041
\(155\) −18.7068 −1.50256
\(156\) −42.4428 −3.39814
\(157\) 22.9854 1.83443 0.917216 0.398390i \(-0.130431\pi\)
0.917216 + 0.398390i \(0.130431\pi\)
\(158\) 2.95420 0.235023
\(159\) −26.4232 −2.09550
\(160\) −18.9514 −1.49824
\(161\) 0.290567 0.0228999
\(162\) 25.0387 1.96723
\(163\) −15.1865 −1.18950 −0.594750 0.803911i \(-0.702749\pi\)
−0.594750 + 0.803911i \(0.702749\pi\)
\(164\) 18.0340 1.40822
\(165\) 18.7861 1.46249
\(166\) −29.7182 −2.30658
\(167\) −13.4947 −1.04425 −0.522126 0.852868i \(-0.674861\pi\)
−0.522126 + 0.852868i \(0.674861\pi\)
\(168\) −26.7075 −2.06053
\(169\) 0.220908 0.0169929
\(170\) 16.2265 1.24451
\(171\) −20.2855 −1.55127
\(172\) −50.9473 −3.88470
\(173\) 14.5178 1.10377 0.551886 0.833920i \(-0.313908\pi\)
0.551886 + 0.833920i \(0.313908\pi\)
\(174\) −34.8081 −2.63879
\(175\) 2.82503 0.213552
\(176\) −43.4530 −3.27539
\(177\) 0.294891 0.0221654
\(178\) −37.0334 −2.77577
\(179\) −7.92449 −0.592304 −0.296152 0.955141i \(-0.595704\pi\)
−0.296152 + 0.955141i \(0.595704\pi\)
\(180\) 23.8814 1.78001
\(181\) 4.17278 0.310160 0.155080 0.987902i \(-0.450436\pi\)
0.155080 + 0.987902i \(0.450436\pi\)
\(182\) 14.1614 1.04971
\(183\) −16.8499 −1.24558
\(184\) 1.45515 0.107275
\(185\) −18.0714 −1.32863
\(186\) −66.9227 −4.90701
\(187\) 15.5976 1.14061
\(188\) −3.39073 −0.247294
\(189\) −0.727829 −0.0529418
\(190\) 33.4278 2.42510
\(191\) 23.1021 1.67161 0.835806 0.549025i \(-0.185001\pi\)
0.835806 + 0.549025i \(0.185001\pi\)
\(192\) −20.5680 −1.48436
\(193\) 4.70682 0.338805 0.169402 0.985547i \(-0.445816\pi\)
0.169402 + 0.985547i \(0.445816\pi\)
\(194\) 25.7541 1.84903
\(195\) −15.4183 −1.10413
\(196\) −23.1983 −1.65702
\(197\) 2.45191 0.174691 0.0873455 0.996178i \(-0.472162\pi\)
0.0873455 + 0.996178i \(0.472162\pi\)
\(198\) 32.4258 2.30440
\(199\) −0.434301 −0.0307868 −0.0153934 0.999882i \(-0.504900\pi\)
−0.0153934 + 0.999882i \(0.504900\pi\)
\(200\) 14.1476 1.00039
\(201\) 7.62308 0.537690
\(202\) −15.9033 −1.11895
\(203\) 8.22213 0.577080
\(204\) 41.0962 2.87731
\(205\) 6.55126 0.457560
\(206\) −24.4108 −1.70078
\(207\) −0.546050 −0.0379531
\(208\) 35.6633 2.47280
\(209\) 32.1322 2.22263
\(210\) −16.5151 −1.13965
\(211\) −23.1304 −1.59236 −0.796180 0.605060i \(-0.793149\pi\)
−0.796180 + 0.605060i \(0.793149\pi\)
\(212\) 53.2065 3.65424
\(213\) 15.5232 1.06363
\(214\) −8.12497 −0.555412
\(215\) −18.5078 −1.26222
\(216\) −3.64494 −0.248007
\(217\) 15.8080 1.07312
\(218\) 41.4643 2.80831
\(219\) −16.5855 −1.12074
\(220\) −37.8281 −2.55037
\(221\) −12.8014 −0.861118
\(222\) −64.6496 −4.33900
\(223\) 28.6313 1.91730 0.958648 0.284595i \(-0.0918590\pi\)
0.958648 + 0.284595i \(0.0918590\pi\)
\(224\) 16.0148 1.07003
\(225\) −5.30896 −0.353931
\(226\) 11.2805 0.750369
\(227\) 11.3003 0.750030 0.375015 0.927019i \(-0.377638\pi\)
0.375015 + 0.927019i \(0.377638\pi\)
\(228\) 84.6612 5.60683
\(229\) −24.1168 −1.59368 −0.796840 0.604190i \(-0.793497\pi\)
−0.796840 + 0.604190i \(0.793497\pi\)
\(230\) 0.899816 0.0593321
\(231\) −15.8750 −1.04450
\(232\) 41.1761 2.70334
\(233\) 22.9575 1.50400 0.751999 0.659165i \(-0.229090\pi\)
0.751999 + 0.659165i \(0.229090\pi\)
\(234\) −26.6129 −1.73974
\(235\) −1.23176 −0.0803513
\(236\) −0.593799 −0.0386531
\(237\) 2.71801 0.176554
\(238\) −13.7120 −0.888820
\(239\) −5.38387 −0.348254 −0.174127 0.984723i \(-0.555710\pi\)
−0.174127 + 0.984723i \(0.555710\pi\)
\(240\) −41.5908 −2.68467
\(241\) 11.0695 0.713051 0.356525 0.934286i \(-0.383961\pi\)
0.356525 + 0.934286i \(0.383961\pi\)
\(242\) −22.5766 −1.45128
\(243\) 21.5697 1.38370
\(244\) 33.9293 2.17210
\(245\) −8.42734 −0.538403
\(246\) 23.4369 1.49428
\(247\) −26.3720 −1.67801
\(248\) 79.1659 5.02704
\(249\) −27.3422 −1.73274
\(250\) 31.7928 2.01076
\(251\) −3.36425 −0.212350 −0.106175 0.994347i \(-0.533860\pi\)
−0.106175 + 0.994347i \(0.533860\pi\)
\(252\) −20.1808 −1.27127
\(253\) 0.864943 0.0543785
\(254\) −22.2770 −1.39779
\(255\) 14.9291 0.934899
\(256\) −14.9021 −0.931383
\(257\) −10.8281 −0.675440 −0.337720 0.941247i \(-0.609656\pi\)
−0.337720 + 0.941247i \(0.609656\pi\)
\(258\) −66.2109 −4.12211
\(259\) 15.2711 0.948899
\(260\) 31.0467 1.92543
\(261\) −15.4515 −0.956424
\(262\) 20.7128 1.27964
\(263\) −20.8743 −1.28717 −0.643584 0.765376i \(-0.722553\pi\)
−0.643584 + 0.765376i \(0.722553\pi\)
\(264\) −79.5015 −4.89298
\(265\) 19.3285 1.18734
\(266\) −28.2479 −1.73199
\(267\) −34.0726 −2.08521
\(268\) −15.3500 −0.937651
\(269\) −24.4283 −1.48942 −0.744710 0.667389i \(-0.767412\pi\)
−0.744710 + 0.667389i \(0.767412\pi\)
\(270\) −2.25391 −0.137169
\(271\) 25.2413 1.53330 0.766651 0.642064i \(-0.221922\pi\)
0.766651 + 0.642064i \(0.221922\pi\)
\(272\) −34.5318 −2.09380
\(273\) 13.0291 0.788559
\(274\) 52.9431 3.19841
\(275\) 8.40939 0.507105
\(276\) 2.27893 0.137175
\(277\) −21.1908 −1.27323 −0.636617 0.771180i \(-0.719667\pi\)
−0.636617 + 0.771180i \(0.719667\pi\)
\(278\) −5.09805 −0.305761
\(279\) −29.7074 −1.77853
\(280\) 19.5364 1.16753
\(281\) −24.5594 −1.46509 −0.732546 0.680717i \(-0.761668\pi\)
−0.732546 + 0.680717i \(0.761668\pi\)
\(282\) −4.40658 −0.262408
\(283\) −3.27857 −0.194891 −0.0974454 0.995241i \(-0.531067\pi\)
−0.0974454 + 0.995241i \(0.531067\pi\)
\(284\) −31.2579 −1.85481
\(285\) 30.7552 1.82178
\(286\) 42.1548 2.49266
\(287\) −5.53610 −0.326785
\(288\) −30.0959 −1.77342
\(289\) −4.60472 −0.270866
\(290\) 25.4620 1.49518
\(291\) 23.6950 1.38903
\(292\) 33.3969 1.95441
\(293\) −25.3559 −1.48131 −0.740653 0.671888i \(-0.765484\pi\)
−0.740653 + 0.671888i \(0.765484\pi\)
\(294\) −30.1485 −1.75829
\(295\) −0.215711 −0.0125592
\(296\) 76.4770 4.44514
\(297\) −2.16656 −0.125717
\(298\) 34.1737 1.97963
\(299\) −0.709886 −0.0410538
\(300\) 22.1568 1.27923
\(301\) 15.6399 0.901468
\(302\) 38.8724 2.23686
\(303\) −14.6318 −0.840574
\(304\) −71.1381 −4.08005
\(305\) 12.3256 0.705763
\(306\) 25.7685 1.47309
\(307\) −12.5025 −0.713557 −0.356779 0.934189i \(-0.616125\pi\)
−0.356779 + 0.934189i \(0.616125\pi\)
\(308\) 31.9663 1.82145
\(309\) −22.4591 −1.27765
\(310\) 48.9537 2.78038
\(311\) 21.0691 1.19472 0.597359 0.801974i \(-0.296217\pi\)
0.597359 + 0.801974i \(0.296217\pi\)
\(312\) 65.2494 3.69402
\(313\) −18.4189 −1.04110 −0.520550 0.853831i \(-0.674273\pi\)
−0.520550 + 0.853831i \(0.674273\pi\)
\(314\) −60.1503 −3.39448
\(315\) −7.33113 −0.413063
\(316\) −5.47304 −0.307883
\(317\) 28.9100 1.62375 0.811874 0.583833i \(-0.198448\pi\)
0.811874 + 0.583833i \(0.198448\pi\)
\(318\) 69.1469 3.87756
\(319\) 24.4752 1.37035
\(320\) 15.0454 0.841062
\(321\) −7.47537 −0.417235
\(322\) −0.760383 −0.0423745
\(323\) 25.5352 1.42082
\(324\) −46.3875 −2.57708
\(325\) −6.90185 −0.382846
\(326\) 39.7415 2.20108
\(327\) 38.1491 2.10965
\(328\) −27.7246 −1.53083
\(329\) 1.04089 0.0573862
\(330\) −49.1612 −2.70623
\(331\) 16.5980 0.912311 0.456156 0.889900i \(-0.349226\pi\)
0.456156 + 0.889900i \(0.349226\pi\)
\(332\) 55.0568 3.02164
\(333\) −28.6983 −1.57266
\(334\) 35.3143 1.93231
\(335\) −5.57625 −0.304663
\(336\) 35.1460 1.91737
\(337\) −18.4316 −1.00403 −0.502015 0.864859i \(-0.667408\pi\)
−0.502015 + 0.864859i \(0.667408\pi\)
\(338\) −0.578092 −0.0314441
\(339\) 10.3786 0.563689
\(340\) −30.0617 −1.63032
\(341\) 47.0564 2.54825
\(342\) 53.0851 2.87051
\(343\) 17.5395 0.947043
\(344\) 78.3239 4.22294
\(345\) 0.827874 0.0445713
\(346\) −37.9917 −2.04245
\(347\) 0.788247 0.0423153 0.0211577 0.999776i \(-0.493265\pi\)
0.0211577 + 0.999776i \(0.493265\pi\)
\(348\) 64.4866 3.45684
\(349\) 19.5283 1.04532 0.522662 0.852540i \(-0.324939\pi\)
0.522662 + 0.852540i \(0.324939\pi\)
\(350\) −7.39280 −0.395162
\(351\) 1.77817 0.0949115
\(352\) 47.6719 2.54092
\(353\) −3.56229 −0.189602 −0.0948008 0.995496i \(-0.530221\pi\)
−0.0948008 + 0.995496i \(0.530221\pi\)
\(354\) −0.771699 −0.0410153
\(355\) −11.3551 −0.602669
\(356\) 68.6093 3.63629
\(357\) −12.6158 −0.667696
\(358\) 20.7376 1.09602
\(359\) 13.6592 0.720904 0.360452 0.932778i \(-0.382623\pi\)
0.360452 + 0.932778i \(0.382623\pi\)
\(360\) −36.7140 −1.93500
\(361\) 33.6045 1.76866
\(362\) −10.9197 −0.573928
\(363\) −20.7715 −1.09022
\(364\) −26.2358 −1.37513
\(365\) 12.1322 0.635028
\(366\) 44.0944 2.30485
\(367\) −1.58747 −0.0828653 −0.0414326 0.999141i \(-0.513192\pi\)
−0.0414326 + 0.999141i \(0.513192\pi\)
\(368\) −1.91491 −0.0998216
\(369\) 10.4038 0.541598
\(370\) 47.2909 2.45854
\(371\) −16.3334 −0.847987
\(372\) 123.983 6.42823
\(373\) 22.6914 1.17491 0.587457 0.809255i \(-0.300129\pi\)
0.587457 + 0.809255i \(0.300129\pi\)
\(374\) −40.8173 −2.11061
\(375\) 29.2510 1.51051
\(376\) 5.21274 0.268827
\(377\) −20.0876 −1.03456
\(378\) 1.90465 0.0979648
\(379\) 18.2407 0.936963 0.468481 0.883473i \(-0.344801\pi\)
0.468481 + 0.883473i \(0.344801\pi\)
\(380\) −61.9293 −3.17691
\(381\) −20.4960 −1.05004
\(382\) −60.4559 −3.09319
\(383\) 2.45006 0.125192 0.0625961 0.998039i \(-0.480062\pi\)
0.0625961 + 0.998039i \(0.480062\pi\)
\(384\) 2.00867 0.102505
\(385\) 11.6125 0.591828
\(386\) −12.3173 −0.626933
\(387\) −29.3914 −1.49405
\(388\) −47.7128 −2.42225
\(389\) 34.3681 1.74253 0.871265 0.490813i \(-0.163300\pi\)
0.871265 + 0.490813i \(0.163300\pi\)
\(390\) 40.3481 2.04311
\(391\) 0.687363 0.0347614
\(392\) 35.6640 1.80130
\(393\) 19.0568 0.961289
\(394\) −6.41638 −0.323253
\(395\) −1.98821 −0.100038
\(396\) −60.0730 −3.01878
\(397\) 30.2228 1.51684 0.758421 0.651765i \(-0.225971\pi\)
0.758421 + 0.651765i \(0.225971\pi\)
\(398\) 1.13652 0.0569687
\(399\) −25.9894 −1.30110
\(400\) −18.6177 −0.930883
\(401\) 17.5844 0.878124 0.439062 0.898457i \(-0.355311\pi\)
0.439062 + 0.898457i \(0.355311\pi\)
\(402\) −19.9488 −0.994956
\(403\) −38.6207 −1.92383
\(404\) 29.4629 1.46583
\(405\) −16.8513 −0.837350
\(406\) −21.5164 −1.06784
\(407\) 45.4581 2.25328
\(408\) −63.1792 −3.12784
\(409\) −38.3349 −1.89554 −0.947770 0.318954i \(-0.896668\pi\)
−0.947770 + 0.318954i \(0.896668\pi\)
\(410\) −17.1440 −0.846681
\(411\) 48.7102 2.40270
\(412\) 45.2242 2.22804
\(413\) 0.182285 0.00896968
\(414\) 1.42896 0.0702294
\(415\) 20.0007 0.981795
\(416\) −39.1258 −1.91830
\(417\) −4.69046 −0.229693
\(418\) −84.0868 −4.11282
\(419\) −24.3393 −1.18905 −0.594527 0.804076i \(-0.702661\pi\)
−0.594527 + 0.804076i \(0.702661\pi\)
\(420\) 30.5964 1.49295
\(421\) 6.91001 0.336773 0.168387 0.985721i \(-0.446144\pi\)
0.168387 + 0.985721i \(0.446144\pi\)
\(422\) 60.5298 2.94654
\(423\) −1.95610 −0.0951090
\(424\) −81.7970 −3.97241
\(425\) 6.68287 0.324167
\(426\) −40.6226 −1.96817
\(427\) −10.4157 −0.504050
\(428\) 15.0526 0.727594
\(429\) 38.7844 1.87253
\(430\) 48.4330 2.33565
\(431\) −36.3378 −1.75033 −0.875166 0.483823i \(-0.839248\pi\)
−0.875166 + 0.483823i \(0.839248\pi\)
\(432\) 4.79659 0.230776
\(433\) 10.2929 0.494646 0.247323 0.968933i \(-0.420449\pi\)
0.247323 + 0.968933i \(0.420449\pi\)
\(434\) −41.3679 −1.98572
\(435\) 23.4263 1.12320
\(436\) −76.8180 −3.67892
\(437\) 1.41602 0.0677375
\(438\) 43.4024 2.07385
\(439\) −11.1746 −0.533335 −0.266668 0.963789i \(-0.585923\pi\)
−0.266668 + 0.963789i \(0.585923\pi\)
\(440\) 58.1550 2.77243
\(441\) −13.3831 −0.637289
\(442\) 33.5000 1.59343
\(443\) 23.6305 1.12272 0.561360 0.827572i \(-0.310278\pi\)
0.561360 + 0.827572i \(0.310278\pi\)
\(444\) 119.772 5.68412
\(445\) 24.9239 1.18151
\(446\) −74.9252 −3.54781
\(447\) 31.4415 1.48713
\(448\) −12.7140 −0.600679
\(449\) 26.0017 1.22710 0.613548 0.789658i \(-0.289742\pi\)
0.613548 + 0.789658i \(0.289742\pi\)
\(450\) 13.8930 0.654922
\(451\) −16.4796 −0.775992
\(452\) −20.8986 −0.982989
\(453\) 35.7645 1.68036
\(454\) −29.5718 −1.38787
\(455\) −9.53076 −0.446809
\(456\) −130.154 −6.09502
\(457\) −9.27877 −0.434043 −0.217021 0.976167i \(-0.569634\pi\)
−0.217021 + 0.976167i \(0.569634\pi\)
\(458\) 63.1111 2.94899
\(459\) −1.72175 −0.0803644
\(460\) −1.66703 −0.0777256
\(461\) −2.80330 −0.130563 −0.0652813 0.997867i \(-0.520794\pi\)
−0.0652813 + 0.997867i \(0.520794\pi\)
\(462\) 41.5433 1.93277
\(463\) 4.14501 0.192635 0.0963175 0.995351i \(-0.469294\pi\)
0.0963175 + 0.995351i \(0.469294\pi\)
\(464\) −54.1860 −2.51552
\(465\) 45.0397 2.08867
\(466\) −60.0774 −2.78303
\(467\) 16.2885 0.753743 0.376871 0.926266i \(-0.377000\pi\)
0.376871 + 0.926266i \(0.377000\pi\)
\(468\) 49.3038 2.27907
\(469\) 4.71217 0.217588
\(470\) 3.22339 0.148684
\(471\) −55.3412 −2.54999
\(472\) 0.912878 0.0420186
\(473\) 46.5559 2.14064
\(474\) −7.11274 −0.326699
\(475\) 13.7672 0.631684
\(476\) 25.4034 1.16436
\(477\) 30.6947 1.40541
\(478\) 14.0890 0.644418
\(479\) −8.24999 −0.376952 −0.188476 0.982078i \(-0.560355\pi\)
−0.188476 + 0.982078i \(0.560355\pi\)
\(480\) 45.6288 2.08266
\(481\) −37.3089 −1.70114
\(482\) −28.9678 −1.31945
\(483\) −0.699589 −0.0318324
\(484\) 41.8260 1.90118
\(485\) −17.3328 −0.787042
\(486\) −56.4457 −2.56043
\(487\) −16.5879 −0.751671 −0.375836 0.926686i \(-0.622644\pi\)
−0.375836 + 0.926686i \(0.622644\pi\)
\(488\) −52.1613 −2.36123
\(489\) 36.5641 1.65349
\(490\) 22.0535 0.996274
\(491\) 4.73711 0.213783 0.106891 0.994271i \(-0.465910\pi\)
0.106891 + 0.994271i \(0.465910\pi\)
\(492\) −43.4199 −1.95752
\(493\) 19.4502 0.875994
\(494\) 69.0127 3.10503
\(495\) −21.8229 −0.980868
\(496\) −104.179 −4.67777
\(497\) 9.59558 0.430421
\(498\) 71.5516 3.20630
\(499\) 7.17103 0.321019 0.160510 0.987034i \(-0.448686\pi\)
0.160510 + 0.987034i \(0.448686\pi\)
\(500\) −58.9004 −2.63411
\(501\) 32.4909 1.45158
\(502\) 8.80390 0.392937
\(503\) 10.6565 0.475151 0.237575 0.971369i \(-0.423647\pi\)
0.237575 + 0.971369i \(0.423647\pi\)
\(504\) 31.0249 1.38196
\(505\) 10.7031 0.476281
\(506\) −2.26347 −0.100623
\(507\) −0.531873 −0.0236213
\(508\) 41.2712 1.83111
\(509\) 23.2019 1.02841 0.514203 0.857669i \(-0.328088\pi\)
0.514203 + 0.857669i \(0.328088\pi\)
\(510\) −39.0680 −1.72996
\(511\) −10.2522 −0.453532
\(512\) 40.6659 1.79719
\(513\) −3.54694 −0.156601
\(514\) 28.3361 1.24985
\(515\) 16.4288 0.723937
\(516\) 122.664 5.40000
\(517\) 3.09847 0.136270
\(518\) −39.9628 −1.75587
\(519\) −34.9542 −1.53432
\(520\) −47.7297 −2.09308
\(521\) 22.1982 0.972522 0.486261 0.873814i \(-0.338360\pi\)
0.486261 + 0.873814i \(0.338360\pi\)
\(522\) 40.4350 1.76979
\(523\) −40.3270 −1.76338 −0.881688 0.471832i \(-0.843593\pi\)
−0.881688 + 0.471832i \(0.843593\pi\)
\(524\) −38.3733 −1.67634
\(525\) −6.80174 −0.296852
\(526\) 54.6260 2.38181
\(527\) 37.3954 1.62897
\(528\) 104.621 4.55303
\(529\) −22.9619 −0.998343
\(530\) −50.5806 −2.19708
\(531\) −0.342562 −0.0148659
\(532\) 52.3329 2.26892
\(533\) 13.5253 0.585845
\(534\) 89.1644 3.85852
\(535\) 5.46820 0.236411
\(536\) 23.5984 1.01929
\(537\) 19.0796 0.823345
\(538\) 63.9263 2.75606
\(539\) 21.1988 0.913096
\(540\) 4.17567 0.179692
\(541\) −30.7491 −1.32201 −0.661003 0.750383i \(-0.729869\pi\)
−0.661003 + 0.750383i \(0.729869\pi\)
\(542\) −66.0539 −2.83726
\(543\) −10.0467 −0.431144
\(544\) 37.8844 1.62428
\(545\) −27.9059 −1.19536
\(546\) −34.0959 −1.45917
\(547\) 5.79418 0.247741 0.123871 0.992298i \(-0.460469\pi\)
0.123871 + 0.992298i \(0.460469\pi\)
\(548\) −98.0840 −4.18994
\(549\) 19.5738 0.835387
\(550\) −22.0065 −0.938360
\(551\) 40.0690 1.70700
\(552\) −3.50352 −0.149120
\(553\) 1.68012 0.0714461
\(554\) 55.4542 2.35602
\(555\) 43.5099 1.84689
\(556\) 9.44481 0.400549
\(557\) 12.2178 0.517687 0.258843 0.965919i \(-0.416659\pi\)
0.258843 + 0.965919i \(0.416659\pi\)
\(558\) 77.7411 3.29104
\(559\) −38.2099 −1.61611
\(560\) −25.7091 −1.08641
\(561\) −37.5539 −1.58553
\(562\) 64.2695 2.71104
\(563\) −13.0681 −0.550755 −0.275377 0.961336i \(-0.588803\pi\)
−0.275377 + 0.961336i \(0.588803\pi\)
\(564\) 8.16376 0.343757
\(565\) −7.59192 −0.319394
\(566\) 8.57968 0.360631
\(567\) 14.2401 0.598028
\(568\) 48.0543 2.01631
\(569\) −13.2688 −0.556256 −0.278128 0.960544i \(-0.589714\pi\)
−0.278128 + 0.960544i \(0.589714\pi\)
\(570\) −80.4831 −3.37106
\(571\) −5.33049 −0.223074 −0.111537 0.993760i \(-0.535577\pi\)
−0.111537 + 0.993760i \(0.535577\pi\)
\(572\) −78.0973 −3.26541
\(573\) −55.6224 −2.32366
\(574\) 14.4874 0.604692
\(575\) 0.370589 0.0154546
\(576\) 23.8929 0.995536
\(577\) 22.6552 0.943149 0.471575 0.881826i \(-0.343686\pi\)
0.471575 + 0.881826i \(0.343686\pi\)
\(578\) 12.0501 0.501217
\(579\) −11.3325 −0.470962
\(580\) −47.1717 −1.95870
\(581\) −16.9014 −0.701189
\(582\) −62.0074 −2.57029
\(583\) −48.6204 −2.01365
\(584\) −51.3427 −2.12458
\(585\) 17.9108 0.740519
\(586\) 66.3537 2.74104
\(587\) −8.55594 −0.353141 −0.176571 0.984288i \(-0.556500\pi\)
−0.176571 + 0.984288i \(0.556500\pi\)
\(588\) 55.8540 2.30338
\(589\) 77.0373 3.17427
\(590\) 0.564494 0.0232399
\(591\) −5.90338 −0.242833
\(592\) −100.640 −4.13630
\(593\) −6.46079 −0.265313 −0.132656 0.991162i \(-0.542351\pi\)
−0.132656 + 0.991162i \(0.542351\pi\)
\(594\) 5.66967 0.232629
\(595\) 9.22837 0.378326
\(596\) −63.3114 −2.59333
\(597\) 1.04565 0.0427958
\(598\) 1.85770 0.0759669
\(599\) −38.3984 −1.56892 −0.784458 0.620182i \(-0.787059\pi\)
−0.784458 + 0.620182i \(0.787059\pi\)
\(600\) −34.0628 −1.39061
\(601\) 33.8140 1.37930 0.689652 0.724141i \(-0.257764\pi\)
0.689652 + 0.724141i \(0.257764\pi\)
\(602\) −40.9279 −1.66810
\(603\) −8.85538 −0.360619
\(604\) −72.0163 −2.93030
\(605\) 15.1943 0.617735
\(606\) 38.2898 1.55542
\(607\) 7.56070 0.306880 0.153440 0.988158i \(-0.450965\pi\)
0.153440 + 0.988158i \(0.450965\pi\)
\(608\) 78.0449 3.16514
\(609\) −19.7962 −0.802182
\(610\) −32.2549 −1.30596
\(611\) −2.54301 −0.102879
\(612\) −47.7395 −1.92976
\(613\) 7.21496 0.291409 0.145705 0.989328i \(-0.453455\pi\)
0.145705 + 0.989328i \(0.453455\pi\)
\(614\) 32.7178 1.32038
\(615\) −15.7733 −0.636040
\(616\) −49.1435 −1.98005
\(617\) −35.2460 −1.41895 −0.709475 0.704731i \(-0.751068\pi\)
−0.709475 + 0.704731i \(0.751068\pi\)
\(618\) 58.7732 2.36420
\(619\) −3.86634 −0.155401 −0.0777007 0.996977i \(-0.524758\pi\)
−0.0777007 + 0.996977i \(0.524758\pi\)
\(620\) −90.6931 −3.64232
\(621\) −0.0954772 −0.00383137
\(622\) −55.1356 −2.21074
\(623\) −21.0618 −0.843823
\(624\) −85.8654 −3.43737
\(625\) −11.9061 −0.476244
\(626\) 48.2005 1.92648
\(627\) −77.3639 −3.08962
\(628\) 111.436 4.44680
\(629\) 36.1252 1.44041
\(630\) 19.1848 0.764341
\(631\) 38.0254 1.51377 0.756883 0.653550i \(-0.226721\pi\)
0.756883 + 0.653550i \(0.226721\pi\)
\(632\) 8.41399 0.334691
\(633\) 55.6903 2.21349
\(634\) −75.6545 −3.00462
\(635\) 14.9927 0.594968
\(636\) −128.104 −5.07964
\(637\) −17.3985 −0.689354
\(638\) −64.0490 −2.53572
\(639\) −18.0326 −0.713358
\(640\) −1.46934 −0.0580806
\(641\) 3.60359 0.142333 0.0711666 0.997464i \(-0.477328\pi\)
0.0711666 + 0.997464i \(0.477328\pi\)
\(642\) 19.5623 0.772061
\(643\) 10.1135 0.398836 0.199418 0.979915i \(-0.436095\pi\)
0.199418 + 0.979915i \(0.436095\pi\)
\(644\) 1.40871 0.0555109
\(645\) 44.5607 1.75458
\(646\) −66.8231 −2.62912
\(647\) 8.75023 0.344007 0.172003 0.985096i \(-0.444976\pi\)
0.172003 + 0.985096i \(0.444976\pi\)
\(648\) 71.3139 2.80147
\(649\) 0.542617 0.0212996
\(650\) 18.0614 0.708427
\(651\) −38.0605 −1.49171
\(652\) −73.6264 −2.88343
\(653\) 14.7981 0.579093 0.289546 0.957164i \(-0.406496\pi\)
0.289546 + 0.957164i \(0.406496\pi\)
\(654\) −99.8324 −3.90375
\(655\) −13.9400 −0.544680
\(656\) 36.4843 1.42447
\(657\) 19.2666 0.751661
\(658\) −2.72390 −0.106189
\(659\) 7.43544 0.289644 0.144822 0.989458i \(-0.453739\pi\)
0.144822 + 0.989458i \(0.453739\pi\)
\(660\) 91.0776 3.54519
\(661\) −30.2159 −1.17526 −0.587632 0.809129i \(-0.699940\pi\)
−0.587632 + 0.809129i \(0.699940\pi\)
\(662\) −43.4354 −1.68816
\(663\) 30.8217 1.19701
\(664\) −84.6417 −3.28473
\(665\) 19.0111 0.737221
\(666\) 75.1005 2.91009
\(667\) 1.07859 0.0417630
\(668\) −65.4244 −2.53134
\(669\) −68.9349 −2.66518
\(670\) 14.5925 0.563756
\(671\) −31.0048 −1.19693
\(672\) −38.5583 −1.48742
\(673\) 15.5550 0.599601 0.299801 0.954002i \(-0.403080\pi\)
0.299801 + 0.954002i \(0.403080\pi\)
\(674\) 48.2335 1.85788
\(675\) −0.928275 −0.0357293
\(676\) 1.07099 0.0411920
\(677\) −13.4736 −0.517831 −0.258915 0.965900i \(-0.583365\pi\)
−0.258915 + 0.965900i \(0.583365\pi\)
\(678\) −27.1598 −1.04306
\(679\) 14.6469 0.562098
\(680\) 46.2153 1.77228
\(681\) −27.2075 −1.04259
\(682\) −123.142 −4.71534
\(683\) 40.6659 1.55604 0.778019 0.628240i \(-0.216225\pi\)
0.778019 + 0.628240i \(0.216225\pi\)
\(684\) −98.3471 −3.76040
\(685\) −35.6313 −1.36140
\(686\) −45.8990 −1.75243
\(687\) 58.0653 2.21533
\(688\) −103.071 −3.92954
\(689\) 39.9043 1.52023
\(690\) −2.16646 −0.0824758
\(691\) 25.3391 0.963945 0.481972 0.876186i \(-0.339921\pi\)
0.481972 + 0.876186i \(0.339921\pi\)
\(692\) 70.3846 2.67562
\(693\) 18.4413 0.700527
\(694\) −2.06276 −0.0783014
\(695\) 3.43105 0.130147
\(696\) −99.1385 −3.75784
\(697\) −13.0962 −0.496053
\(698\) −51.1034 −1.93429
\(699\) −55.2742 −2.09066
\(700\) 13.6961 0.517665
\(701\) 37.2790 1.40801 0.704004 0.710196i \(-0.251394\pi\)
0.704004 + 0.710196i \(0.251394\pi\)
\(702\) −4.65328 −0.175627
\(703\) 74.4207 2.80683
\(704\) −37.8463 −1.42639
\(705\) 2.96568 0.111694
\(706\) 9.32214 0.350843
\(707\) −9.04456 −0.340156
\(708\) 1.42967 0.0537305
\(709\) −43.4171 −1.63056 −0.815282 0.579065i \(-0.803418\pi\)
−0.815282 + 0.579065i \(0.803418\pi\)
\(710\) 29.7152 1.11519
\(711\) −3.15739 −0.118411
\(712\) −105.477 −3.95290
\(713\) 2.07371 0.0776610
\(714\) 33.0141 1.23552
\(715\) −28.3706 −1.06100
\(716\) −38.4191 −1.43579
\(717\) 12.9626 0.484097
\(718\) −35.7446 −1.33398
\(719\) −15.2021 −0.566944 −0.283472 0.958981i \(-0.591486\pi\)
−0.283472 + 0.958981i \(0.591486\pi\)
\(720\) 48.3141 1.80056
\(721\) −13.8830 −0.517030
\(722\) −87.9396 −3.27277
\(723\) −26.6518 −0.991190
\(724\) 20.2302 0.751850
\(725\) 10.4865 0.389460
\(726\) 54.3569 2.01737
\(727\) −7.01976 −0.260349 −0.130174 0.991491i \(-0.541554\pi\)
−0.130174 + 0.991491i \(0.541554\pi\)
\(728\) 40.3336 1.49486
\(729\) −23.2285 −0.860316
\(730\) −31.7487 −1.17507
\(731\) 36.9976 1.36841
\(732\) −81.6907 −3.01938
\(733\) −14.8121 −0.547098 −0.273549 0.961858i \(-0.588198\pi\)
−0.273549 + 0.961858i \(0.588198\pi\)
\(734\) 4.15425 0.153336
\(735\) 20.2903 0.748417
\(736\) 2.10083 0.0774376
\(737\) 14.0269 0.516688
\(738\) −27.2256 −1.00219
\(739\) 23.2873 0.856635 0.428318 0.903628i \(-0.359106\pi\)
0.428318 + 0.903628i \(0.359106\pi\)
\(740\) −87.6127 −3.22071
\(741\) 63.4950 2.33255
\(742\) 42.7428 1.56914
\(743\) −54.0546 −1.98307 −0.991536 0.129829i \(-0.958557\pi\)
−0.991536 + 0.129829i \(0.958557\pi\)
\(744\) −190.606 −6.98794
\(745\) −22.9993 −0.842630
\(746\) −59.3809 −2.17409
\(747\) 31.7622 1.16212
\(748\) 75.6194 2.76492
\(749\) −4.62086 −0.168843
\(750\) −76.5467 −2.79509
\(751\) −2.26744 −0.0827399 −0.0413700 0.999144i \(-0.513172\pi\)
−0.0413700 + 0.999144i \(0.513172\pi\)
\(752\) −6.85975 −0.250149
\(753\) 8.10002 0.295181
\(754\) 52.5670 1.91438
\(755\) −26.1616 −0.952118
\(756\) −3.52862 −0.128335
\(757\) 4.18030 0.151936 0.0759678 0.997110i \(-0.475795\pi\)
0.0759678 + 0.997110i \(0.475795\pi\)
\(758\) −47.7341 −1.73378
\(759\) −2.08250 −0.0755899
\(760\) 95.2071 3.45353
\(761\) 5.73786 0.207997 0.103999 0.994577i \(-0.466836\pi\)
0.103999 + 0.994577i \(0.466836\pi\)
\(762\) 53.6358 1.94302
\(763\) 23.5817 0.853715
\(764\) 112.003 4.05211
\(765\) −17.3425 −0.627019
\(766\) −6.41155 −0.231659
\(767\) −0.445343 −0.0160804
\(768\) 35.8794 1.29469
\(769\) −5.59268 −0.201677 −0.100839 0.994903i \(-0.532153\pi\)
−0.100839 + 0.994903i \(0.532153\pi\)
\(770\) −30.3887 −1.09513
\(771\) 26.0706 0.938909
\(772\) 22.8194 0.821287
\(773\) −3.01849 −0.108567 −0.0542837 0.998526i \(-0.517288\pi\)
−0.0542837 + 0.998526i \(0.517288\pi\)
\(774\) 76.9142 2.76462
\(775\) 20.1616 0.724225
\(776\) 73.3514 2.63316
\(777\) −36.7678 −1.31904
\(778\) −89.9376 −3.22442
\(779\) −26.9791 −0.966627
\(780\) −74.7503 −2.67649
\(781\) 28.5636 1.02209
\(782\) −1.79876 −0.0643235
\(783\) −2.70171 −0.0965511
\(784\) −46.9323 −1.67615
\(785\) 40.4819 1.44486
\(786\) −49.8697 −1.77879
\(787\) −17.3078 −0.616957 −0.308478 0.951231i \(-0.599820\pi\)
−0.308478 + 0.951231i \(0.599820\pi\)
\(788\) 11.8872 0.423464
\(789\) 50.2586 1.78925
\(790\) 5.20294 0.185112
\(791\) 6.41549 0.228109
\(792\) 92.3533 3.28163
\(793\) 25.4466 0.903636
\(794\) −79.0901 −2.80680
\(795\) −46.5367 −1.65048
\(796\) −2.10556 −0.0746294
\(797\) 7.31305 0.259041 0.129521 0.991577i \(-0.458656\pi\)
0.129521 + 0.991577i \(0.458656\pi\)
\(798\) 68.0116 2.40759
\(799\) 2.46233 0.0871109
\(800\) 20.4253 0.722142
\(801\) 39.5806 1.39851
\(802\) −46.0166 −1.62490
\(803\) −30.5183 −1.07697
\(804\) 36.9578 1.30340
\(805\) 0.511746 0.0180367
\(806\) 101.066 3.55991
\(807\) 58.8153 2.07040
\(808\) −45.2948 −1.59347
\(809\) −7.05694 −0.248109 −0.124054 0.992275i \(-0.539590\pi\)
−0.124054 + 0.992275i \(0.539590\pi\)
\(810\) 44.0982 1.54945
\(811\) 56.2616 1.97561 0.987806 0.155690i \(-0.0497602\pi\)
0.987806 + 0.155690i \(0.0497602\pi\)
\(812\) 39.8621 1.39888
\(813\) −60.7728 −2.13140
\(814\) −118.959 −4.16952
\(815\) −26.7465 −0.936890
\(816\) 83.1411 2.91052
\(817\) 76.2180 2.66653
\(818\) 100.319 3.50756
\(819\) −15.1354 −0.528872
\(820\) 31.7615 1.10916
\(821\) −15.7078 −0.548205 −0.274102 0.961701i \(-0.588381\pi\)
−0.274102 + 0.961701i \(0.588381\pi\)
\(822\) −127.470 −4.44601
\(823\) −16.1712 −0.563692 −0.281846 0.959460i \(-0.590947\pi\)
−0.281846 + 0.959460i \(0.590947\pi\)
\(824\) −69.5255 −2.42204
\(825\) −20.2470 −0.704912
\(826\) −0.477022 −0.0165977
\(827\) −18.0781 −0.628635 −0.314318 0.949318i \(-0.601776\pi\)
−0.314318 + 0.949318i \(0.601776\pi\)
\(828\) −2.64733 −0.0920011
\(829\) −3.67232 −0.127545 −0.0637724 0.997964i \(-0.520313\pi\)
−0.0637724 + 0.997964i \(0.520313\pi\)
\(830\) −52.3397 −1.81674
\(831\) 51.0206 1.76988
\(832\) 31.0616 1.07687
\(833\) 16.8465 0.583696
\(834\) 12.2744 0.425029
\(835\) −23.7669 −0.822488
\(836\) 155.782 5.38783
\(837\) −5.19435 −0.179543
\(838\) 63.6935 2.20025
\(839\) 1.42606 0.0492330 0.0246165 0.999697i \(-0.492164\pi\)
0.0246165 + 0.999697i \(0.492164\pi\)
\(840\) −47.0373 −1.62294
\(841\) 1.52059 0.0524341
\(842\) −18.0828 −0.623174
\(843\) 59.1310 2.03658
\(844\) −112.139 −3.86000
\(845\) 0.389063 0.0133842
\(846\) 5.11892 0.175992
\(847\) −12.8398 −0.441181
\(848\) 107.641 3.69642
\(849\) 7.89373 0.270912
\(850\) −17.4884 −0.599846
\(851\) 2.00327 0.0686713
\(852\) 75.2587 2.57832
\(853\) −8.38552 −0.287115 −0.143557 0.989642i \(-0.545854\pi\)
−0.143557 + 0.989642i \(0.545854\pi\)
\(854\) 27.2567 0.932706
\(855\) −35.7269 −1.22183
\(856\) −23.1411 −0.790947
\(857\) −28.6399 −0.978319 −0.489159 0.872194i \(-0.662696\pi\)
−0.489159 + 0.872194i \(0.662696\pi\)
\(858\) −101.495 −3.46498
\(859\) 19.5413 0.666740 0.333370 0.942796i \(-0.391814\pi\)
0.333370 + 0.942796i \(0.391814\pi\)
\(860\) −89.7285 −3.05972
\(861\) 13.3291 0.454255
\(862\) 95.0923 3.23886
\(863\) −45.7404 −1.55702 −0.778511 0.627631i \(-0.784025\pi\)
−0.778511 + 0.627631i \(0.784025\pi\)
\(864\) −5.26229 −0.179027
\(865\) 25.5689 0.869367
\(866\) −26.9355 −0.915306
\(867\) 11.0867 0.376522
\(868\) 76.6395 2.60132
\(869\) 5.00130 0.169657
\(870\) −61.3041 −2.07840
\(871\) −11.5123 −0.390081
\(872\) 118.096 3.99925
\(873\) −27.5254 −0.931594
\(874\) −3.70558 −0.125343
\(875\) 18.0813 0.611261
\(876\) −80.4088 −2.71676
\(877\) −48.3925 −1.63410 −0.817050 0.576567i \(-0.804392\pi\)
−0.817050 + 0.576567i \(0.804392\pi\)
\(878\) 29.2428 0.986896
\(879\) 61.0486 2.05912
\(880\) −76.5295 −2.57981
\(881\) 40.2197 1.35504 0.677519 0.735505i \(-0.263055\pi\)
0.677519 + 0.735505i \(0.263055\pi\)
\(882\) 35.0221 1.17926
\(883\) 39.4907 1.32897 0.664484 0.747302i \(-0.268651\pi\)
0.664484 + 0.747302i \(0.268651\pi\)
\(884\) −62.0632 −2.08741
\(885\) 0.519362 0.0174582
\(886\) −61.8386 −2.07751
\(887\) 22.4731 0.754573 0.377286 0.926097i \(-0.376857\pi\)
0.377286 + 0.926097i \(0.376857\pi\)
\(888\) −184.132 −6.17905
\(889\) −12.6695 −0.424921
\(890\) −65.2234 −2.18629
\(891\) 42.3892 1.42009
\(892\) 138.809 4.64767
\(893\) 5.07258 0.169748
\(894\) −82.2792 −2.75183
\(895\) −13.9566 −0.466519
\(896\) 1.24165 0.0414807
\(897\) 1.70917 0.0570676
\(898\) −68.0437 −2.27065
\(899\) 58.6795 1.95707
\(900\) −25.7386 −0.857953
\(901\) −38.6382 −1.28723
\(902\) 43.1253 1.43591
\(903\) −37.6557 −1.25310
\(904\) 32.1286 1.06858
\(905\) 7.34910 0.244292
\(906\) −93.5920 −3.10939
\(907\) −12.6097 −0.418700 −0.209350 0.977841i \(-0.567135\pi\)
−0.209350 + 0.977841i \(0.567135\pi\)
\(908\) 54.7857 1.81813
\(909\) 16.9971 0.563757
\(910\) 24.9410 0.826786
\(911\) −17.6461 −0.584642 −0.292321 0.956320i \(-0.594428\pi\)
−0.292321 + 0.956320i \(0.594428\pi\)
\(912\) 171.277 5.67155
\(913\) −50.3112 −1.66506
\(914\) 24.2816 0.803163
\(915\) −29.6760 −0.981060
\(916\) −116.922 −3.86320
\(917\) 11.7799 0.389006
\(918\) 4.50564 0.148708
\(919\) −47.2687 −1.55925 −0.779625 0.626246i \(-0.784590\pi\)
−0.779625 + 0.626246i \(0.784590\pi\)
\(920\) 2.56281 0.0844932
\(921\) 30.1020 0.991894
\(922\) 7.33594 0.241596
\(923\) −23.4431 −0.771638
\(924\) −76.9644 −2.53194
\(925\) 19.4768 0.640392
\(926\) −10.8471 −0.356457
\(927\) 26.0898 0.856900
\(928\) 59.4469 1.95144
\(929\) 6.97371 0.228800 0.114400 0.993435i \(-0.463505\pi\)
0.114400 + 0.993435i \(0.463505\pi\)
\(930\) −117.864 −3.86492
\(931\) 34.7051 1.13741
\(932\) 111.301 3.64580
\(933\) −50.7275 −1.66074
\(934\) −42.6254 −1.39474
\(935\) 27.4705 0.898382
\(936\) −75.7973 −2.47751
\(937\) 37.8474 1.23642 0.618210 0.786013i \(-0.287858\pi\)
0.618210 + 0.786013i \(0.287858\pi\)
\(938\) −12.3313 −0.402630
\(939\) 44.3468 1.44720
\(940\) −5.97176 −0.194777
\(941\) −54.7566 −1.78501 −0.892507 0.451034i \(-0.851055\pi\)
−0.892507 + 0.451034i \(0.851055\pi\)
\(942\) 144.822 4.71856
\(943\) −0.726230 −0.0236493
\(944\) −1.20131 −0.0390993
\(945\) −1.28185 −0.0416987
\(946\) −121.832 −3.96110
\(947\) 30.9147 1.00459 0.502297 0.864695i \(-0.332489\pi\)
0.502297 + 0.864695i \(0.332489\pi\)
\(948\) 13.1773 0.427979
\(949\) 25.0473 0.813070
\(950\) −36.0274 −1.16888
\(951\) −69.6058 −2.25712
\(952\) −39.0539 −1.26574
\(953\) 12.5376 0.406134 0.203067 0.979165i \(-0.434909\pi\)
0.203067 + 0.979165i \(0.434909\pi\)
\(954\) −80.3248 −2.60061
\(955\) 40.6875 1.31662
\(956\) −26.1018 −0.844193
\(957\) −58.9282 −1.90488
\(958\) 21.5894 0.697521
\(959\) 30.1100 0.972301
\(960\) −36.2243 −1.16913
\(961\) 81.8182 2.63930
\(962\) 97.6336 3.14783
\(963\) 8.68380 0.279832
\(964\) 53.6667 1.72849
\(965\) 8.28967 0.266854
\(966\) 1.83075 0.0589035
\(967\) −35.4798 −1.14095 −0.570477 0.821313i \(-0.693242\pi\)
−0.570477 + 0.821313i \(0.693242\pi\)
\(968\) −64.3013 −2.06672
\(969\) −61.4805 −1.97504
\(970\) 45.3581 1.45636
\(971\) 26.7694 0.859072 0.429536 0.903050i \(-0.358677\pi\)
0.429536 + 0.903050i \(0.358677\pi\)
\(972\) 104.573 3.35418
\(973\) −2.89938 −0.0929499
\(974\) 43.4089 1.39091
\(975\) 16.6174 0.532182
\(976\) 68.6420 2.19718
\(977\) 14.1184 0.451687 0.225843 0.974164i \(-0.427486\pi\)
0.225843 + 0.974164i \(0.427486\pi\)
\(978\) −95.6846 −3.05966
\(979\) −62.6956 −2.00376
\(980\) −40.8570 −1.30513
\(981\) −44.3161 −1.41491
\(982\) −12.3965 −0.395589
\(983\) 24.0925 0.768431 0.384216 0.923243i \(-0.374472\pi\)
0.384216 + 0.923243i \(0.374472\pi\)
\(984\) 66.7516 2.12796
\(985\) 4.31830 0.137592
\(986\) −50.8992 −1.62096
\(987\) −2.50612 −0.0797708
\(988\) −127.855 −4.06761
\(989\) 2.05165 0.0652387
\(990\) 57.1083 1.81502
\(991\) 9.61494 0.305429 0.152714 0.988270i \(-0.451199\pi\)
0.152714 + 0.988270i \(0.451199\pi\)
\(992\) 114.294 3.62883
\(993\) −39.9627 −1.26818
\(994\) −25.1106 −0.796461
\(995\) −0.764892 −0.0242487
\(996\) −132.559 −4.20029
\(997\) 34.8116 1.10249 0.551247 0.834342i \(-0.314152\pi\)
0.551247 + 0.834342i \(0.314152\pi\)
\(998\) −18.7658 −0.594022
\(999\) −5.01792 −0.158760
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 4003.2.a.c.1.7 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.7 179 1.1 even 1 trivial