Properties

Label 4029.2.a.l.1.3
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.57711 q^{2} -1.00000 q^{3} +4.64151 q^{4} +2.80201 q^{5} +2.57711 q^{6} -2.75409 q^{7} -6.80748 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.57711 q^{2} -1.00000 q^{3} +4.64151 q^{4} +2.80201 q^{5} +2.57711 q^{6} -2.75409 q^{7} -6.80748 q^{8} +1.00000 q^{9} -7.22109 q^{10} +5.08930 q^{11} -4.64151 q^{12} +1.22692 q^{13} +7.09760 q^{14} -2.80201 q^{15} +8.26062 q^{16} -1.00000 q^{17} -2.57711 q^{18} +4.27531 q^{19} +13.0056 q^{20} +2.75409 q^{21} -13.1157 q^{22} +3.53882 q^{23} +6.80748 q^{24} +2.85124 q^{25} -3.16191 q^{26} -1.00000 q^{27} -12.7831 q^{28} +5.81249 q^{29} +7.22109 q^{30} +6.37475 q^{31} -7.67360 q^{32} -5.08930 q^{33} +2.57711 q^{34} -7.71697 q^{35} +4.64151 q^{36} +5.23507 q^{37} -11.0179 q^{38} -1.22692 q^{39} -19.0746 q^{40} -0.440553 q^{41} -7.09760 q^{42} -1.81039 q^{43} +23.6220 q^{44} +2.80201 q^{45} -9.11995 q^{46} -6.02387 q^{47} -8.26062 q^{48} +0.585005 q^{49} -7.34797 q^{50} +1.00000 q^{51} +5.69475 q^{52} -11.2066 q^{53} +2.57711 q^{54} +14.2602 q^{55} +18.7484 q^{56} -4.27531 q^{57} -14.9794 q^{58} -4.07358 q^{59} -13.0056 q^{60} +7.50948 q^{61} -16.4284 q^{62} -2.75409 q^{63} +3.25449 q^{64} +3.43783 q^{65} +13.1157 q^{66} +12.4723 q^{67} -4.64151 q^{68} -3.53882 q^{69} +19.8875 q^{70} +5.18453 q^{71} -6.80748 q^{72} +7.17842 q^{73} -13.4914 q^{74} -2.85124 q^{75} +19.8439 q^{76} -14.0164 q^{77} +3.16191 q^{78} +1.00000 q^{79} +23.1463 q^{80} +1.00000 q^{81} +1.13535 q^{82} +7.95637 q^{83} +12.7831 q^{84} -2.80201 q^{85} +4.66557 q^{86} -5.81249 q^{87} -34.6453 q^{88} -9.67764 q^{89} -7.22109 q^{90} -3.37904 q^{91} +16.4255 q^{92} -6.37475 q^{93} +15.5242 q^{94} +11.9794 q^{95} +7.67360 q^{96} +6.88466 q^{97} -1.50763 q^{98} +5.08930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57711 −1.82229 −0.911147 0.412081i \(-0.864802\pi\)
−0.911147 + 0.412081i \(0.864802\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.64151 2.32076
\(5\) 2.80201 1.25310 0.626548 0.779383i \(-0.284467\pi\)
0.626548 + 0.779383i \(0.284467\pi\)
\(6\) 2.57711 1.05210
\(7\) −2.75409 −1.04095 −0.520474 0.853878i \(-0.674245\pi\)
−0.520474 + 0.853878i \(0.674245\pi\)
\(8\) −6.80748 −2.40681
\(9\) 1.00000 0.333333
\(10\) −7.22109 −2.28351
\(11\) 5.08930 1.53448 0.767241 0.641359i \(-0.221629\pi\)
0.767241 + 0.641359i \(0.221629\pi\)
\(12\) −4.64151 −1.33989
\(13\) 1.22692 0.340286 0.170143 0.985419i \(-0.445577\pi\)
0.170143 + 0.985419i \(0.445577\pi\)
\(14\) 7.09760 1.89691
\(15\) −2.80201 −0.723475
\(16\) 8.26062 2.06516
\(17\) −1.00000 −0.242536
\(18\) −2.57711 −0.607431
\(19\) 4.27531 0.980823 0.490411 0.871491i \(-0.336847\pi\)
0.490411 + 0.871491i \(0.336847\pi\)
\(20\) 13.0056 2.90813
\(21\) 2.75409 0.600991
\(22\) −13.1157 −2.79628
\(23\) 3.53882 0.737896 0.368948 0.929450i \(-0.379718\pi\)
0.368948 + 0.929450i \(0.379718\pi\)
\(24\) 6.80748 1.38957
\(25\) 2.85124 0.570248
\(26\) −3.16191 −0.620101
\(27\) −1.00000 −0.192450
\(28\) −12.7831 −2.41579
\(29\) 5.81249 1.07935 0.539676 0.841873i \(-0.318547\pi\)
0.539676 + 0.841873i \(0.318547\pi\)
\(30\) 7.22109 1.31838
\(31\) 6.37475 1.14494 0.572469 0.819926i \(-0.305986\pi\)
0.572469 + 0.819926i \(0.305986\pi\)
\(32\) −7.67360 −1.35651
\(33\) −5.08930 −0.885933
\(34\) 2.57711 0.441971
\(35\) −7.71697 −1.30441
\(36\) 4.64151 0.773586
\(37\) 5.23507 0.860641 0.430320 0.902676i \(-0.358401\pi\)
0.430320 + 0.902676i \(0.358401\pi\)
\(38\) −11.0179 −1.78735
\(39\) −1.22692 −0.196464
\(40\) −19.0746 −3.01596
\(41\) −0.440553 −0.0688028 −0.0344014 0.999408i \(-0.510952\pi\)
−0.0344014 + 0.999408i \(0.510952\pi\)
\(42\) −7.09760 −1.09518
\(43\) −1.81039 −0.276081 −0.138041 0.990427i \(-0.544080\pi\)
−0.138041 + 0.990427i \(0.544080\pi\)
\(44\) 23.6220 3.56116
\(45\) 2.80201 0.417698
\(46\) −9.11995 −1.34466
\(47\) −6.02387 −0.878672 −0.439336 0.898323i \(-0.644786\pi\)
−0.439336 + 0.898323i \(0.644786\pi\)
\(48\) −8.26062 −1.19232
\(49\) 0.585005 0.0835722
\(50\) −7.34797 −1.03916
\(51\) 1.00000 0.140028
\(52\) 5.69475 0.789720
\(53\) −11.2066 −1.53934 −0.769672 0.638440i \(-0.779580\pi\)
−0.769672 + 0.638440i \(0.779580\pi\)
\(54\) 2.57711 0.350701
\(55\) 14.2602 1.92285
\(56\) 18.7484 2.50536
\(57\) −4.27531 −0.566278
\(58\) −14.9794 −1.96690
\(59\) −4.07358 −0.530335 −0.265168 0.964202i \(-0.585427\pi\)
−0.265168 + 0.964202i \(0.585427\pi\)
\(60\) −13.0056 −1.67901
\(61\) 7.50948 0.961490 0.480745 0.876860i \(-0.340366\pi\)
0.480745 + 0.876860i \(0.340366\pi\)
\(62\) −16.4284 −2.08641
\(63\) −2.75409 −0.346983
\(64\) 3.25449 0.406811
\(65\) 3.43783 0.426410
\(66\) 13.1157 1.61443
\(67\) 12.4723 1.52373 0.761866 0.647735i \(-0.224283\pi\)
0.761866 + 0.647735i \(0.224283\pi\)
\(68\) −4.64151 −0.562866
\(69\) −3.53882 −0.426024
\(70\) 19.8875 2.37701
\(71\) 5.18453 0.615290 0.307645 0.951501i \(-0.400459\pi\)
0.307645 + 0.951501i \(0.400459\pi\)
\(72\) −6.80748 −0.802269
\(73\) 7.17842 0.840170 0.420085 0.907485i \(-0.362000\pi\)
0.420085 + 0.907485i \(0.362000\pi\)
\(74\) −13.4914 −1.56834
\(75\) −2.85124 −0.329233
\(76\) 19.8439 2.27625
\(77\) −14.0164 −1.59731
\(78\) 3.16191 0.358015
\(79\) 1.00000 0.112509
\(80\) 23.1463 2.58784
\(81\) 1.00000 0.111111
\(82\) 1.13535 0.125379
\(83\) 7.95637 0.873325 0.436662 0.899625i \(-0.356160\pi\)
0.436662 + 0.899625i \(0.356160\pi\)
\(84\) 12.7831 1.39475
\(85\) −2.80201 −0.303920
\(86\) 4.66557 0.503101
\(87\) −5.81249 −0.623164
\(88\) −34.6453 −3.69320
\(89\) −9.67764 −1.02583 −0.512914 0.858440i \(-0.671434\pi\)
−0.512914 + 0.858440i \(0.671434\pi\)
\(90\) −7.22109 −0.761170
\(91\) −3.37904 −0.354220
\(92\) 16.4255 1.71248
\(93\) −6.37475 −0.661030
\(94\) 15.5242 1.60120
\(95\) 11.9794 1.22906
\(96\) 7.67360 0.783183
\(97\) 6.88466 0.699031 0.349515 0.936931i \(-0.386346\pi\)
0.349515 + 0.936931i \(0.386346\pi\)
\(98\) −1.50763 −0.152293
\(99\) 5.08930 0.511494
\(100\) 13.2341 1.32341
\(101\) 5.54339 0.551588 0.275794 0.961217i \(-0.411059\pi\)
0.275794 + 0.961217i \(0.411059\pi\)
\(102\) −2.57711 −0.255172
\(103\) −8.01343 −0.789587 −0.394793 0.918770i \(-0.629184\pi\)
−0.394793 + 0.918770i \(0.629184\pi\)
\(104\) −8.35222 −0.819002
\(105\) 7.71697 0.753100
\(106\) 28.8806 2.80514
\(107\) 16.4057 1.58600 0.793001 0.609220i \(-0.208517\pi\)
0.793001 + 0.609220i \(0.208517\pi\)
\(108\) −4.64151 −0.446630
\(109\) 13.8530 1.32687 0.663437 0.748232i \(-0.269097\pi\)
0.663437 + 0.748232i \(0.269097\pi\)
\(110\) −36.7503 −3.50400
\(111\) −5.23507 −0.496891
\(112\) −22.7505 −2.14972
\(113\) −14.5297 −1.36684 −0.683418 0.730028i \(-0.739507\pi\)
−0.683418 + 0.730028i \(0.739507\pi\)
\(114\) 11.0179 1.03193
\(115\) 9.91581 0.924654
\(116\) 26.9787 2.50491
\(117\) 1.22692 0.113429
\(118\) 10.4981 0.966427
\(119\) 2.75409 0.252467
\(120\) 19.0746 1.74127
\(121\) 14.9010 1.35463
\(122\) −19.3528 −1.75212
\(123\) 0.440553 0.0397233
\(124\) 29.5885 2.65712
\(125\) −6.02084 −0.538520
\(126\) 7.09760 0.632304
\(127\) −4.98610 −0.442445 −0.221222 0.975223i \(-0.571005\pi\)
−0.221222 + 0.975223i \(0.571005\pi\)
\(128\) 6.96001 0.615184
\(129\) 1.81039 0.159396
\(130\) −8.85968 −0.777045
\(131\) −18.6708 −1.63128 −0.815639 0.578561i \(-0.803615\pi\)
−0.815639 + 0.578561i \(0.803615\pi\)
\(132\) −23.6220 −2.05604
\(133\) −11.7746 −1.02099
\(134\) −32.1425 −2.77669
\(135\) −2.80201 −0.241158
\(136\) 6.80748 0.583737
\(137\) −10.2748 −0.877833 −0.438916 0.898528i \(-0.644638\pi\)
−0.438916 + 0.898528i \(0.644638\pi\)
\(138\) 9.11995 0.776342
\(139\) 7.55783 0.641047 0.320524 0.947241i \(-0.396141\pi\)
0.320524 + 0.947241i \(0.396141\pi\)
\(140\) −35.8184 −3.02721
\(141\) 6.02387 0.507302
\(142\) −13.3611 −1.12124
\(143\) 6.24415 0.522162
\(144\) 8.26062 0.688385
\(145\) 16.2866 1.35253
\(146\) −18.4996 −1.53104
\(147\) −0.585005 −0.0482504
\(148\) 24.2987 1.99734
\(149\) −5.74625 −0.470751 −0.235376 0.971905i \(-0.575632\pi\)
−0.235376 + 0.971905i \(0.575632\pi\)
\(150\) 7.34797 0.599959
\(151\) −4.21207 −0.342774 −0.171387 0.985204i \(-0.554825\pi\)
−0.171387 + 0.985204i \(0.554825\pi\)
\(152\) −29.1041 −2.36065
\(153\) −1.00000 −0.0808452
\(154\) 36.1218 2.91078
\(155\) 17.8621 1.43472
\(156\) −5.69475 −0.455945
\(157\) −14.4654 −1.15446 −0.577232 0.816580i \(-0.695867\pi\)
−0.577232 + 0.816580i \(0.695867\pi\)
\(158\) −2.57711 −0.205024
\(159\) 11.2066 0.888740
\(160\) −21.5015 −1.69984
\(161\) −9.74624 −0.768111
\(162\) −2.57711 −0.202477
\(163\) 3.54647 0.277781 0.138891 0.990308i \(-0.455646\pi\)
0.138891 + 0.990308i \(0.455646\pi\)
\(164\) −2.04483 −0.159675
\(165\) −14.2602 −1.11016
\(166\) −20.5045 −1.59146
\(167\) −6.13316 −0.474598 −0.237299 0.971437i \(-0.576262\pi\)
−0.237299 + 0.971437i \(0.576262\pi\)
\(168\) −18.7484 −1.44647
\(169\) −11.4947 −0.884206
\(170\) 7.22109 0.553832
\(171\) 4.27531 0.326941
\(172\) −8.40293 −0.640717
\(173\) 13.9274 1.05888 0.529439 0.848348i \(-0.322402\pi\)
0.529439 + 0.848348i \(0.322402\pi\)
\(174\) 14.9794 1.13559
\(175\) −7.85257 −0.593598
\(176\) 42.0408 3.16894
\(177\) 4.07358 0.306189
\(178\) 24.9404 1.86936
\(179\) −3.49755 −0.261419 −0.130710 0.991421i \(-0.541726\pi\)
−0.130710 + 0.991421i \(0.541726\pi\)
\(180\) 13.0056 0.969377
\(181\) −17.4680 −1.29838 −0.649191 0.760625i \(-0.724893\pi\)
−0.649191 + 0.760625i \(0.724893\pi\)
\(182\) 8.70817 0.645492
\(183\) −7.50948 −0.555117
\(184\) −24.0905 −1.77597
\(185\) 14.6687 1.07846
\(186\) 16.4284 1.20459
\(187\) −5.08930 −0.372166
\(188\) −27.9599 −2.03918
\(189\) 2.75409 0.200330
\(190\) −30.8724 −2.23972
\(191\) −14.7246 −1.06543 −0.532716 0.846294i \(-0.678828\pi\)
−0.532716 + 0.846294i \(0.678828\pi\)
\(192\) −3.25449 −0.234872
\(193\) 7.14114 0.514030 0.257015 0.966407i \(-0.417261\pi\)
0.257015 + 0.966407i \(0.417261\pi\)
\(194\) −17.7425 −1.27384
\(195\) −3.43783 −0.246188
\(196\) 2.71531 0.193951
\(197\) −12.5727 −0.895770 −0.447885 0.894091i \(-0.647823\pi\)
−0.447885 + 0.894091i \(0.647823\pi\)
\(198\) −13.1157 −0.932092
\(199\) 25.6563 1.81873 0.909364 0.416001i \(-0.136569\pi\)
0.909364 + 0.416001i \(0.136569\pi\)
\(200\) −19.4098 −1.37248
\(201\) −12.4723 −0.879727
\(202\) −14.2859 −1.00516
\(203\) −16.0081 −1.12355
\(204\) 4.64151 0.324971
\(205\) −1.23443 −0.0862165
\(206\) 20.6515 1.43886
\(207\) 3.53882 0.245965
\(208\) 10.1351 0.702743
\(209\) 21.7583 1.50505
\(210\) −19.8875 −1.37237
\(211\) −8.62202 −0.593565 −0.296782 0.954945i \(-0.595914\pi\)
−0.296782 + 0.954945i \(0.595914\pi\)
\(212\) −52.0155 −3.57244
\(213\) −5.18453 −0.355238
\(214\) −42.2795 −2.89016
\(215\) −5.07271 −0.345956
\(216\) 6.80748 0.463190
\(217\) −17.5566 −1.19182
\(218\) −35.7007 −2.41795
\(219\) −7.17842 −0.485073
\(220\) 66.1891 4.46247
\(221\) −1.22692 −0.0825314
\(222\) 13.4914 0.905482
\(223\) 22.8458 1.52987 0.764934 0.644109i \(-0.222772\pi\)
0.764934 + 0.644109i \(0.222772\pi\)
\(224\) 21.1338 1.41206
\(225\) 2.85124 0.190083
\(226\) 37.4446 2.49078
\(227\) 29.4109 1.95207 0.976034 0.217618i \(-0.0698287\pi\)
0.976034 + 0.217618i \(0.0698287\pi\)
\(228\) −19.8439 −1.31419
\(229\) −21.7889 −1.43985 −0.719926 0.694051i \(-0.755824\pi\)
−0.719926 + 0.694051i \(0.755824\pi\)
\(230\) −25.5542 −1.68499
\(231\) 14.0164 0.922210
\(232\) −39.5684 −2.59779
\(233\) 9.90516 0.648909 0.324454 0.945901i \(-0.394819\pi\)
0.324454 + 0.945901i \(0.394819\pi\)
\(234\) −3.16191 −0.206700
\(235\) −16.8789 −1.10106
\(236\) −18.9076 −1.23078
\(237\) −1.00000 −0.0649570
\(238\) −7.09760 −0.460069
\(239\) 5.28546 0.341888 0.170944 0.985281i \(-0.445318\pi\)
0.170944 + 0.985281i \(0.445318\pi\)
\(240\) −23.1463 −1.49409
\(241\) −13.7238 −0.884029 −0.442014 0.897008i \(-0.645736\pi\)
−0.442014 + 0.897008i \(0.645736\pi\)
\(242\) −38.4015 −2.46854
\(243\) −1.00000 −0.0641500
\(244\) 34.8554 2.23139
\(245\) 1.63919 0.104724
\(246\) −1.13535 −0.0723876
\(247\) 5.24545 0.333760
\(248\) −43.3960 −2.75565
\(249\) −7.95637 −0.504214
\(250\) 15.5164 0.981342
\(251\) 8.56079 0.540352 0.270176 0.962811i \(-0.412918\pi\)
0.270176 + 0.962811i \(0.412918\pi\)
\(252\) −12.7831 −0.805262
\(253\) 18.0101 1.13229
\(254\) 12.8497 0.806264
\(255\) 2.80201 0.175468
\(256\) −24.4457 −1.52786
\(257\) −6.86639 −0.428313 −0.214157 0.976799i \(-0.568700\pi\)
−0.214157 + 0.976799i \(0.568700\pi\)
\(258\) −4.66557 −0.290466
\(259\) −14.4179 −0.895882
\(260\) 15.9567 0.989595
\(261\) 5.81249 0.359784
\(262\) 48.1169 2.97267
\(263\) −12.7383 −0.785477 −0.392739 0.919650i \(-0.628472\pi\)
−0.392739 + 0.919650i \(0.628472\pi\)
\(264\) 34.6453 2.13227
\(265\) −31.4009 −1.92894
\(266\) 30.3444 1.86054
\(267\) 9.67764 0.592262
\(268\) 57.8903 3.53621
\(269\) −2.65708 −0.162005 −0.0810026 0.996714i \(-0.525812\pi\)
−0.0810026 + 0.996714i \(0.525812\pi\)
\(270\) 7.22109 0.439461
\(271\) 12.7171 0.772508 0.386254 0.922392i \(-0.373769\pi\)
0.386254 + 0.922392i \(0.373769\pi\)
\(272\) −8.26062 −0.500874
\(273\) 3.37904 0.204509
\(274\) 26.4792 1.59967
\(275\) 14.5108 0.875035
\(276\) −16.4255 −0.988699
\(277\) 3.12729 0.187900 0.0939502 0.995577i \(-0.470051\pi\)
0.0939502 + 0.995577i \(0.470051\pi\)
\(278\) −19.4774 −1.16818
\(279\) 6.37475 0.381646
\(280\) 52.5332 3.13946
\(281\) −29.2396 −1.74429 −0.872145 0.489248i \(-0.837271\pi\)
−0.872145 + 0.489248i \(0.837271\pi\)
\(282\) −15.5242 −0.924453
\(283\) −24.5281 −1.45805 −0.729024 0.684489i \(-0.760026\pi\)
−0.729024 + 0.684489i \(0.760026\pi\)
\(284\) 24.0641 1.42794
\(285\) −11.9794 −0.709601
\(286\) −16.0919 −0.951533
\(287\) 1.21332 0.0716201
\(288\) −7.67360 −0.452171
\(289\) 1.00000 0.0588235
\(290\) −41.9725 −2.46471
\(291\) −6.88466 −0.403586
\(292\) 33.3187 1.94983
\(293\) −27.0550 −1.58057 −0.790285 0.612739i \(-0.790068\pi\)
−0.790285 + 0.612739i \(0.790068\pi\)
\(294\) 1.50763 0.0879265
\(295\) −11.4142 −0.664560
\(296\) −35.6376 −2.07140
\(297\) −5.08930 −0.295311
\(298\) 14.8087 0.857847
\(299\) 4.34185 0.251095
\(300\) −13.2341 −0.764069
\(301\) 4.98596 0.287386
\(302\) 10.8550 0.624634
\(303\) −5.54339 −0.318459
\(304\) 35.3167 2.02555
\(305\) 21.0416 1.20484
\(306\) 2.57711 0.147324
\(307\) 8.14904 0.465090 0.232545 0.972586i \(-0.425295\pi\)
0.232545 + 0.972586i \(0.425295\pi\)
\(308\) −65.0572 −3.70698
\(309\) 8.01343 0.455868
\(310\) −46.0326 −2.61448
\(311\) 13.4755 0.764127 0.382063 0.924136i \(-0.375214\pi\)
0.382063 + 0.924136i \(0.375214\pi\)
\(312\) 8.35222 0.472851
\(313\) 14.1793 0.801460 0.400730 0.916196i \(-0.368757\pi\)
0.400730 + 0.916196i \(0.368757\pi\)
\(314\) 37.2789 2.10377
\(315\) −7.71697 −0.434802
\(316\) 4.64151 0.261106
\(317\) 1.59717 0.0897061 0.0448530 0.998994i \(-0.485718\pi\)
0.0448530 + 0.998994i \(0.485718\pi\)
\(318\) −28.8806 −1.61955
\(319\) 29.5815 1.65624
\(320\) 9.11909 0.509773
\(321\) −16.4057 −0.915679
\(322\) 25.1172 1.39972
\(323\) −4.27531 −0.237884
\(324\) 4.64151 0.257862
\(325\) 3.49824 0.194047
\(326\) −9.13966 −0.506199
\(327\) −13.8530 −0.766071
\(328\) 2.99905 0.165595
\(329\) 16.5903 0.914652
\(330\) 36.7503 2.02304
\(331\) −18.4099 −1.01190 −0.505949 0.862564i \(-0.668857\pi\)
−0.505949 + 0.862564i \(0.668857\pi\)
\(332\) 36.9296 2.02677
\(333\) 5.23507 0.286880
\(334\) 15.8059 0.864858
\(335\) 34.9474 1.90938
\(336\) 22.7505 1.24114
\(337\) 18.4240 1.00362 0.501809 0.864978i \(-0.332668\pi\)
0.501809 + 0.864978i \(0.332668\pi\)
\(338\) 29.6231 1.61128
\(339\) 14.5297 0.789143
\(340\) −13.0056 −0.705325
\(341\) 32.4430 1.75689
\(342\) −11.0179 −0.595782
\(343\) 17.6675 0.953953
\(344\) 12.3242 0.664474
\(345\) −9.91581 −0.533849
\(346\) −35.8924 −1.92959
\(347\) −10.7338 −0.576218 −0.288109 0.957598i \(-0.593027\pi\)
−0.288109 + 0.957598i \(0.593027\pi\)
\(348\) −26.9787 −1.44621
\(349\) −2.86848 −0.153546 −0.0767730 0.997049i \(-0.524462\pi\)
−0.0767730 + 0.997049i \(0.524462\pi\)
\(350\) 20.2370 1.08171
\(351\) −1.22692 −0.0654880
\(352\) −39.0532 −2.08154
\(353\) 24.4997 1.30399 0.651995 0.758223i \(-0.273932\pi\)
0.651995 + 0.758223i \(0.273932\pi\)
\(354\) −10.4981 −0.557967
\(355\) 14.5271 0.771018
\(356\) −44.9189 −2.38070
\(357\) −2.75409 −0.145762
\(358\) 9.01358 0.476382
\(359\) 12.1833 0.643011 0.321505 0.946908i \(-0.395811\pi\)
0.321505 + 0.946908i \(0.395811\pi\)
\(360\) −19.0746 −1.00532
\(361\) −0.721754 −0.0379870
\(362\) 45.0169 2.36604
\(363\) −14.9010 −0.782098
\(364\) −15.6839 −0.822058
\(365\) 20.1140 1.05281
\(366\) 19.3528 1.01159
\(367\) −22.5406 −1.17661 −0.588305 0.808639i \(-0.700205\pi\)
−0.588305 + 0.808639i \(0.700205\pi\)
\(368\) 29.2329 1.52387
\(369\) −0.440553 −0.0229343
\(370\) −37.8029 −1.96528
\(371\) 30.8639 1.60238
\(372\) −29.5885 −1.53409
\(373\) 4.22920 0.218979 0.109490 0.993988i \(-0.465078\pi\)
0.109490 + 0.993988i \(0.465078\pi\)
\(374\) 13.1157 0.678197
\(375\) 6.02084 0.310915
\(376\) 41.0074 2.11480
\(377\) 7.13144 0.367288
\(378\) −7.09760 −0.365061
\(379\) 26.6704 1.36996 0.684982 0.728560i \(-0.259810\pi\)
0.684982 + 0.728560i \(0.259810\pi\)
\(380\) 55.6027 2.85236
\(381\) 4.98610 0.255445
\(382\) 37.9468 1.94153
\(383\) 17.5451 0.896514 0.448257 0.893905i \(-0.352045\pi\)
0.448257 + 0.893905i \(0.352045\pi\)
\(384\) −6.96001 −0.355177
\(385\) −39.2740 −2.00159
\(386\) −18.4035 −0.936715
\(387\) −1.81039 −0.0920271
\(388\) 31.9552 1.62228
\(389\) 25.4334 1.28952 0.644761 0.764384i \(-0.276957\pi\)
0.644761 + 0.764384i \(0.276957\pi\)
\(390\) 8.85968 0.448627
\(391\) −3.53882 −0.178966
\(392\) −3.98241 −0.201142
\(393\) 18.6708 0.941819
\(394\) 32.4013 1.63236
\(395\) 2.80201 0.140984
\(396\) 23.6220 1.18705
\(397\) 15.1674 0.761229 0.380615 0.924734i \(-0.375712\pi\)
0.380615 + 0.924734i \(0.375712\pi\)
\(398\) −66.1192 −3.31426
\(399\) 11.7746 0.589466
\(400\) 23.5530 1.17765
\(401\) −6.03797 −0.301522 −0.150761 0.988570i \(-0.548172\pi\)
−0.150761 + 0.988570i \(0.548172\pi\)
\(402\) 32.1425 1.60312
\(403\) 7.82129 0.389606
\(404\) 25.7297 1.28010
\(405\) 2.80201 0.139233
\(406\) 41.2547 2.04744
\(407\) 26.6428 1.32064
\(408\) −6.80748 −0.337020
\(409\) 38.1362 1.88571 0.942856 0.333201i \(-0.108129\pi\)
0.942856 + 0.333201i \(0.108129\pi\)
\(410\) 3.18127 0.157112
\(411\) 10.2748 0.506817
\(412\) −37.1944 −1.83244
\(413\) 11.2190 0.552051
\(414\) −9.11995 −0.448221
\(415\) 22.2938 1.09436
\(416\) −9.41487 −0.461602
\(417\) −7.55783 −0.370109
\(418\) −56.0736 −2.74265
\(419\) −36.4253 −1.77949 −0.889746 0.456456i \(-0.849119\pi\)
−0.889746 + 0.456456i \(0.849119\pi\)
\(420\) 35.8184 1.74776
\(421\) 29.2984 1.42792 0.713958 0.700188i \(-0.246901\pi\)
0.713958 + 0.700188i \(0.246901\pi\)
\(422\) 22.2199 1.08165
\(423\) −6.02387 −0.292891
\(424\) 76.2886 3.70490
\(425\) −2.85124 −0.138305
\(426\) 13.3611 0.647348
\(427\) −20.6818 −1.00086
\(428\) 76.1475 3.68073
\(429\) −6.24415 −0.301470
\(430\) 13.0730 0.630434
\(431\) −13.2517 −0.638311 −0.319156 0.947702i \(-0.603399\pi\)
−0.319156 + 0.947702i \(0.603399\pi\)
\(432\) −8.26062 −0.397439
\(433\) 12.0821 0.580629 0.290315 0.956931i \(-0.406240\pi\)
0.290315 + 0.956931i \(0.406240\pi\)
\(434\) 45.2454 2.17185
\(435\) −16.2866 −0.780884
\(436\) 64.2987 3.07935
\(437\) 15.1296 0.723745
\(438\) 18.4996 0.883945
\(439\) 19.4448 0.928048 0.464024 0.885823i \(-0.346405\pi\)
0.464024 + 0.885823i \(0.346405\pi\)
\(440\) −97.0764 −4.62793
\(441\) 0.585005 0.0278574
\(442\) 3.16191 0.150397
\(443\) −12.8617 −0.611078 −0.305539 0.952180i \(-0.598837\pi\)
−0.305539 + 0.952180i \(0.598837\pi\)
\(444\) −24.2987 −1.15316
\(445\) −27.1168 −1.28546
\(446\) −58.8762 −2.78787
\(447\) 5.74625 0.271788
\(448\) −8.96315 −0.423469
\(449\) 0.817399 0.0385755 0.0192877 0.999814i \(-0.493860\pi\)
0.0192877 + 0.999814i \(0.493860\pi\)
\(450\) −7.34797 −0.346387
\(451\) −2.24210 −0.105577
\(452\) −67.4396 −3.17209
\(453\) 4.21207 0.197900
\(454\) −75.7952 −3.55724
\(455\) −9.46809 −0.443871
\(456\) 29.1041 1.36292
\(457\) −0.511214 −0.0239136 −0.0119568 0.999929i \(-0.503806\pi\)
−0.0119568 + 0.999929i \(0.503806\pi\)
\(458\) 56.1525 2.62383
\(459\) 1.00000 0.0466760
\(460\) 46.0244 2.14590
\(461\) 30.7659 1.43291 0.716456 0.697632i \(-0.245763\pi\)
0.716456 + 0.697632i \(0.245763\pi\)
\(462\) −36.1218 −1.68054
\(463\) 8.17038 0.379710 0.189855 0.981812i \(-0.439198\pi\)
0.189855 + 0.981812i \(0.439198\pi\)
\(464\) 48.0147 2.22903
\(465\) −17.8621 −0.828334
\(466\) −25.5267 −1.18250
\(467\) −0.987753 −0.0457078 −0.0228539 0.999739i \(-0.507275\pi\)
−0.0228539 + 0.999739i \(0.507275\pi\)
\(468\) 5.69475 0.263240
\(469\) −34.3498 −1.58613
\(470\) 43.4989 2.00646
\(471\) 14.4654 0.666530
\(472\) 27.7308 1.27641
\(473\) −9.21359 −0.423641
\(474\) 2.57711 0.118371
\(475\) 12.1899 0.559312
\(476\) 12.7831 0.585914
\(477\) −11.2066 −0.513114
\(478\) −13.6212 −0.623021
\(479\) 13.2194 0.604012 0.302006 0.953306i \(-0.402344\pi\)
0.302006 + 0.953306i \(0.402344\pi\)
\(480\) 21.5015 0.981403
\(481\) 6.42300 0.292864
\(482\) 35.3678 1.61096
\(483\) 9.74624 0.443469
\(484\) 69.1630 3.14377
\(485\) 19.2909 0.875952
\(486\) 2.57711 0.116900
\(487\) 28.3574 1.28500 0.642498 0.766288i \(-0.277898\pi\)
0.642498 + 0.766288i \(0.277898\pi\)
\(488\) −51.1206 −2.31412
\(489\) −3.54647 −0.160377
\(490\) −4.22438 −0.190838
\(491\) 18.3357 0.827478 0.413739 0.910396i \(-0.364223\pi\)
0.413739 + 0.910396i \(0.364223\pi\)
\(492\) 2.04483 0.0921881
\(493\) −5.81249 −0.261781
\(494\) −13.5181 −0.608209
\(495\) 14.2602 0.640950
\(496\) 52.6594 2.36448
\(497\) −14.2787 −0.640485
\(498\) 20.5045 0.918827
\(499\) −2.15154 −0.0963163 −0.0481581 0.998840i \(-0.515335\pi\)
−0.0481581 + 0.998840i \(0.515335\pi\)
\(500\) −27.9458 −1.24977
\(501\) 6.13316 0.274010
\(502\) −22.0621 −0.984681
\(503\) 15.2893 0.681718 0.340859 0.940114i \(-0.389282\pi\)
0.340859 + 0.940114i \(0.389282\pi\)
\(504\) 18.7484 0.835120
\(505\) 15.5326 0.691192
\(506\) −46.4142 −2.06336
\(507\) 11.4947 0.510496
\(508\) −23.1430 −1.02681
\(509\) −13.6807 −0.606385 −0.303192 0.952929i \(-0.598052\pi\)
−0.303192 + 0.952929i \(0.598052\pi\)
\(510\) −7.22109 −0.319755
\(511\) −19.7700 −0.874574
\(512\) 49.0793 2.16902
\(513\) −4.27531 −0.188759
\(514\) 17.6955 0.780513
\(515\) −22.4537 −0.989427
\(516\) 8.40293 0.369918
\(517\) −30.6573 −1.34831
\(518\) 37.1564 1.63256
\(519\) −13.9274 −0.611344
\(520\) −23.4030 −1.02629
\(521\) −30.2671 −1.32603 −0.663013 0.748608i \(-0.730723\pi\)
−0.663013 + 0.748608i \(0.730723\pi\)
\(522\) −14.9794 −0.655632
\(523\) 26.0430 1.13878 0.569391 0.822067i \(-0.307179\pi\)
0.569391 + 0.822067i \(0.307179\pi\)
\(524\) −86.6609 −3.78580
\(525\) 7.85257 0.342714
\(526\) 32.8280 1.43137
\(527\) −6.37475 −0.277688
\(528\) −42.0408 −1.82959
\(529\) −10.4767 −0.455510
\(530\) 80.9238 3.51510
\(531\) −4.07358 −0.176778
\(532\) −54.6518 −2.36946
\(533\) −0.540522 −0.0234126
\(534\) −24.9404 −1.07928
\(535\) 45.9690 1.98741
\(536\) −84.9048 −3.66733
\(537\) 3.49755 0.150930
\(538\) 6.84761 0.295221
\(539\) 2.97727 0.128240
\(540\) −13.0056 −0.559670
\(541\) 2.78093 0.119561 0.0597807 0.998212i \(-0.480960\pi\)
0.0597807 + 0.998212i \(0.480960\pi\)
\(542\) −32.7734 −1.40774
\(543\) 17.4680 0.749621
\(544\) 7.67360 0.329003
\(545\) 38.8161 1.66270
\(546\) −8.70817 −0.372675
\(547\) 16.6007 0.709795 0.354898 0.934905i \(-0.384516\pi\)
0.354898 + 0.934905i \(0.384516\pi\)
\(548\) −47.6905 −2.03724
\(549\) 7.50948 0.320497
\(550\) −37.3960 −1.59457
\(551\) 24.8502 1.05865
\(552\) 24.0905 1.02536
\(553\) −2.75409 −0.117116
\(554\) −8.05937 −0.342410
\(555\) −14.6687 −0.622652
\(556\) 35.0798 1.48771
\(557\) −24.6908 −1.04618 −0.523092 0.852276i \(-0.675222\pi\)
−0.523092 + 0.852276i \(0.675222\pi\)
\(558\) −16.4284 −0.695471
\(559\) −2.22119 −0.0939465
\(560\) −63.7470 −2.69380
\(561\) 5.08930 0.214870
\(562\) 75.3538 3.17861
\(563\) 1.92738 0.0812293 0.0406146 0.999175i \(-0.487068\pi\)
0.0406146 + 0.999175i \(0.487068\pi\)
\(564\) 27.9599 1.17732
\(565\) −40.7122 −1.71278
\(566\) 63.2118 2.65699
\(567\) −2.75409 −0.115661
\(568\) −35.2936 −1.48089
\(569\) 33.3052 1.39623 0.698114 0.715987i \(-0.254023\pi\)
0.698114 + 0.715987i \(0.254023\pi\)
\(570\) 30.8724 1.29310
\(571\) 31.6065 1.32269 0.661346 0.750081i \(-0.269986\pi\)
0.661346 + 0.750081i \(0.269986\pi\)
\(572\) 28.9823 1.21181
\(573\) 14.7246 0.615127
\(574\) −3.12687 −0.130513
\(575\) 10.0900 0.420784
\(576\) 3.25449 0.135604
\(577\) −25.2984 −1.05319 −0.526594 0.850117i \(-0.676531\pi\)
−0.526594 + 0.850117i \(0.676531\pi\)
\(578\) −2.57711 −0.107194
\(579\) −7.14114 −0.296776
\(580\) 75.5946 3.13889
\(581\) −21.9125 −0.909086
\(582\) 17.7425 0.735452
\(583\) −57.0337 −2.36209
\(584\) −48.8669 −2.02213
\(585\) 3.43783 0.142137
\(586\) 69.7238 2.88026
\(587\) −29.5672 −1.22037 −0.610184 0.792260i \(-0.708905\pi\)
−0.610184 + 0.792260i \(0.708905\pi\)
\(588\) −2.71531 −0.111978
\(589\) 27.2540 1.12298
\(590\) 29.4157 1.21102
\(591\) 12.5727 0.517173
\(592\) 43.2449 1.77736
\(593\) 34.0643 1.39885 0.699427 0.714704i \(-0.253438\pi\)
0.699427 + 0.714704i \(0.253438\pi\)
\(594\) 13.1157 0.538144
\(595\) 7.71697 0.316365
\(596\) −26.6713 −1.09250
\(597\) −25.6563 −1.05004
\(598\) −11.1894 −0.457570
\(599\) 10.4664 0.427646 0.213823 0.976872i \(-0.431408\pi\)
0.213823 + 0.976872i \(0.431408\pi\)
\(600\) 19.4098 0.792400
\(601\) 2.79728 0.114103 0.0570516 0.998371i \(-0.481830\pi\)
0.0570516 + 0.998371i \(0.481830\pi\)
\(602\) −12.8494 −0.523702
\(603\) 12.4723 0.507911
\(604\) −19.5504 −0.795494
\(605\) 41.7526 1.69748
\(606\) 14.2859 0.580327
\(607\) −40.7507 −1.65402 −0.827011 0.562186i \(-0.809960\pi\)
−0.827011 + 0.562186i \(0.809960\pi\)
\(608\) −32.8070 −1.33050
\(609\) 16.0081 0.648681
\(610\) −54.2266 −2.19557
\(611\) −7.39080 −0.299000
\(612\) −4.64151 −0.187622
\(613\) −2.33241 −0.0942052 −0.0471026 0.998890i \(-0.514999\pi\)
−0.0471026 + 0.998890i \(0.514999\pi\)
\(614\) −21.0010 −0.847532
\(615\) 1.23443 0.0497771
\(616\) 95.4162 3.84443
\(617\) 0.890091 0.0358337 0.0179168 0.999839i \(-0.494297\pi\)
0.0179168 + 0.999839i \(0.494297\pi\)
\(618\) −20.6515 −0.830726
\(619\) 25.6620 1.03144 0.515722 0.856756i \(-0.327524\pi\)
0.515722 + 0.856756i \(0.327524\pi\)
\(620\) 82.9071 3.32963
\(621\) −3.53882 −0.142008
\(622\) −34.7279 −1.39246
\(623\) 26.6531 1.06783
\(624\) −10.1351 −0.405729
\(625\) −31.1266 −1.24507
\(626\) −36.5416 −1.46050
\(627\) −21.7583 −0.868943
\(628\) −67.1413 −2.67923
\(629\) −5.23507 −0.208736
\(630\) 19.8875 0.792338
\(631\) −28.9704 −1.15329 −0.576647 0.816994i \(-0.695639\pi\)
−0.576647 + 0.816994i \(0.695639\pi\)
\(632\) −6.80748 −0.270787
\(633\) 8.62202 0.342695
\(634\) −4.11609 −0.163471
\(635\) −13.9711 −0.554425
\(636\) 52.0155 2.06255
\(637\) 0.717753 0.0284384
\(638\) −76.2348 −3.01817
\(639\) 5.18453 0.205097
\(640\) 19.5020 0.770884
\(641\) −40.2458 −1.58961 −0.794807 0.606863i \(-0.792428\pi\)
−0.794807 + 0.606863i \(0.792428\pi\)
\(642\) 42.2795 1.66864
\(643\) −43.7309 −1.72458 −0.862289 0.506416i \(-0.830970\pi\)
−0.862289 + 0.506416i \(0.830970\pi\)
\(644\) −45.2373 −1.78260
\(645\) 5.07271 0.199738
\(646\) 11.0179 0.433495
\(647\) −18.0131 −0.708168 −0.354084 0.935214i \(-0.615207\pi\)
−0.354084 + 0.935214i \(0.615207\pi\)
\(648\) −6.80748 −0.267423
\(649\) −20.7317 −0.813789
\(650\) −9.01535 −0.353611
\(651\) 17.5566 0.688098
\(652\) 16.4610 0.644663
\(653\) 21.4209 0.838265 0.419132 0.907925i \(-0.362334\pi\)
0.419132 + 0.907925i \(0.362334\pi\)
\(654\) 35.7007 1.39601
\(655\) −52.3158 −2.04415
\(656\) −3.63924 −0.142088
\(657\) 7.17842 0.280057
\(658\) −42.7550 −1.66676
\(659\) 16.6786 0.649705 0.324852 0.945765i \(-0.394685\pi\)
0.324852 + 0.945765i \(0.394685\pi\)
\(660\) −66.1891 −2.57641
\(661\) 21.3001 0.828479 0.414239 0.910168i \(-0.364048\pi\)
0.414239 + 0.910168i \(0.364048\pi\)
\(662\) 47.4443 1.84397
\(663\) 1.22692 0.0476495
\(664\) −54.1628 −2.10192
\(665\) −32.9924 −1.27939
\(666\) −13.4914 −0.522780
\(667\) 20.5694 0.796449
\(668\) −28.4672 −1.10143
\(669\) −22.8458 −0.883270
\(670\) −90.0635 −3.47946
\(671\) 38.2180 1.47539
\(672\) −21.1338 −0.815253
\(673\) −24.5742 −0.947267 −0.473633 0.880722i \(-0.657058\pi\)
−0.473633 + 0.880722i \(0.657058\pi\)
\(674\) −47.4807 −1.82889
\(675\) −2.85124 −0.109744
\(676\) −53.3527 −2.05203
\(677\) −0.965852 −0.0371207 −0.0185603 0.999828i \(-0.505908\pi\)
−0.0185603 + 0.999828i \(0.505908\pi\)
\(678\) −37.4446 −1.43805
\(679\) −18.9610 −0.727655
\(680\) 19.0746 0.731478
\(681\) −29.4109 −1.12703
\(682\) −83.6093 −3.20156
\(683\) 31.2478 1.19566 0.597831 0.801622i \(-0.296029\pi\)
0.597831 + 0.801622i \(0.296029\pi\)
\(684\) 19.8439 0.758750
\(685\) −28.7900 −1.10001
\(686\) −45.5311 −1.73838
\(687\) 21.7889 0.831298
\(688\) −14.9549 −0.570150
\(689\) −13.7496 −0.523817
\(690\) 25.5542 0.972830
\(691\) 21.5915 0.821379 0.410690 0.911775i \(-0.365288\pi\)
0.410690 + 0.911775i \(0.365288\pi\)
\(692\) 64.6441 2.45740
\(693\) −14.0164 −0.532438
\(694\) 27.6621 1.05004
\(695\) 21.1771 0.803293
\(696\) 39.5684 1.49984
\(697\) 0.440553 0.0166871
\(698\) 7.39239 0.279806
\(699\) −9.90516 −0.374648
\(700\) −36.4478 −1.37760
\(701\) −42.9615 −1.62263 −0.811316 0.584608i \(-0.801248\pi\)
−0.811316 + 0.584608i \(0.801248\pi\)
\(702\) 3.16191 0.119338
\(703\) 22.3815 0.844136
\(704\) 16.5631 0.624244
\(705\) 16.8789 0.635697
\(706\) −63.1386 −2.37625
\(707\) −15.2670 −0.574174
\(708\) 18.9076 0.710590
\(709\) 12.7478 0.478755 0.239377 0.970927i \(-0.423057\pi\)
0.239377 + 0.970927i \(0.423057\pi\)
\(710\) −37.4379 −1.40502
\(711\) 1.00000 0.0375029
\(712\) 65.8803 2.46897
\(713\) 22.5591 0.844845
\(714\) 7.09760 0.265621
\(715\) 17.4962 0.654319
\(716\) −16.2339 −0.606690
\(717\) −5.28546 −0.197389
\(718\) −31.3978 −1.17175
\(719\) 47.6229 1.77603 0.888017 0.459810i \(-0.152083\pi\)
0.888017 + 0.459810i \(0.152083\pi\)
\(720\) 23.1463 0.862612
\(721\) 22.0697 0.821918
\(722\) 1.86004 0.0692236
\(723\) 13.7238 0.510394
\(724\) −81.0777 −3.01323
\(725\) 16.5728 0.615498
\(726\) 38.4015 1.42521
\(727\) 19.5951 0.726743 0.363371 0.931644i \(-0.381626\pi\)
0.363371 + 0.931644i \(0.381626\pi\)
\(728\) 23.0027 0.852539
\(729\) 1.00000 0.0370370
\(730\) −51.8360 −1.91854
\(731\) 1.81039 0.0669595
\(732\) −34.8554 −1.28829
\(733\) 5.04366 0.186292 0.0931459 0.995652i \(-0.470308\pi\)
0.0931459 + 0.995652i \(0.470308\pi\)
\(734\) 58.0897 2.14413
\(735\) −1.63919 −0.0604624
\(736\) −27.1555 −1.00097
\(737\) 63.4752 2.33814
\(738\) 1.13535 0.0417930
\(739\) −17.1244 −0.629931 −0.314965 0.949103i \(-0.601993\pi\)
−0.314965 + 0.949103i \(0.601993\pi\)
\(740\) 68.0850 2.50285
\(741\) −5.24545 −0.192696
\(742\) −79.5399 −2.92000
\(743\) 19.2144 0.704909 0.352455 0.935829i \(-0.385347\pi\)
0.352455 + 0.935829i \(0.385347\pi\)
\(744\) 43.3960 1.59097
\(745\) −16.1010 −0.589896
\(746\) −10.8991 −0.399045
\(747\) 7.95637 0.291108
\(748\) −23.6220 −0.863708
\(749\) −45.1829 −1.65095
\(750\) −15.5164 −0.566578
\(751\) −18.2066 −0.664368 −0.332184 0.943215i \(-0.607785\pi\)
−0.332184 + 0.943215i \(0.607785\pi\)
\(752\) −49.7609 −1.81459
\(753\) −8.56079 −0.311972
\(754\) −18.3785 −0.669307
\(755\) −11.8023 −0.429528
\(756\) 12.7831 0.464918
\(757\) −0.914931 −0.0332537 −0.0166269 0.999862i \(-0.505293\pi\)
−0.0166269 + 0.999862i \(0.505293\pi\)
\(758\) −68.7325 −2.49648
\(759\) −18.0101 −0.653726
\(760\) −81.5498 −2.95812
\(761\) 48.7468 1.76707 0.883534 0.468367i \(-0.155157\pi\)
0.883534 + 0.468367i \(0.155157\pi\)
\(762\) −12.8497 −0.465497
\(763\) −38.1523 −1.38121
\(764\) −68.3442 −2.47261
\(765\) −2.80201 −0.101307
\(766\) −45.2158 −1.63371
\(767\) −4.99795 −0.180465
\(768\) 24.4457 0.882109
\(769\) 18.9249 0.682451 0.341225 0.939982i \(-0.389158\pi\)
0.341225 + 0.939982i \(0.389158\pi\)
\(770\) 101.214 3.64748
\(771\) 6.86639 0.247287
\(772\) 33.1457 1.19294
\(773\) −4.36566 −0.157022 −0.0785109 0.996913i \(-0.525017\pi\)
−0.0785109 + 0.996913i \(0.525017\pi\)
\(774\) 4.66557 0.167700
\(775\) 18.1759 0.652899
\(776\) −46.8672 −1.68243
\(777\) 14.4179 0.517238
\(778\) −65.5446 −2.34989
\(779\) −1.88350 −0.0674833
\(780\) −15.9567 −0.571343
\(781\) 26.3856 0.944152
\(782\) 9.11995 0.326129
\(783\) −5.81249 −0.207721
\(784\) 4.83251 0.172590
\(785\) −40.5321 −1.44665
\(786\) −48.1169 −1.71627
\(787\) 24.4857 0.872820 0.436410 0.899748i \(-0.356250\pi\)
0.436410 + 0.899748i \(0.356250\pi\)
\(788\) −58.3565 −2.07886
\(789\) 12.7383 0.453496
\(790\) −7.22109 −0.256915
\(791\) 40.0160 1.42280
\(792\) −34.6453 −1.23107
\(793\) 9.21351 0.327181
\(794\) −39.0881 −1.38718
\(795\) 31.4009 1.11368
\(796\) 119.084 4.22083
\(797\) 11.1652 0.395493 0.197747 0.980253i \(-0.436638\pi\)
0.197747 + 0.980253i \(0.436638\pi\)
\(798\) −30.3444 −1.07418
\(799\) 6.02387 0.213109
\(800\) −21.8793 −0.773549
\(801\) −9.67764 −0.341943
\(802\) 15.5605 0.549461
\(803\) 36.5331 1.28923
\(804\) −57.8903 −2.04163
\(805\) −27.3090 −0.962516
\(806\) −20.1563 −0.709977
\(807\) 2.65708 0.0935338
\(808\) −37.7365 −1.32757
\(809\) −37.5180 −1.31906 −0.659531 0.751678i \(-0.729245\pi\)
−0.659531 + 0.751678i \(0.729245\pi\)
\(810\) −7.22109 −0.253723
\(811\) −25.2277 −0.885866 −0.442933 0.896555i \(-0.646062\pi\)
−0.442933 + 0.896555i \(0.646062\pi\)
\(812\) −74.3018 −2.60748
\(813\) −12.7171 −0.446008
\(814\) −68.6616 −2.40659
\(815\) 9.93724 0.348086
\(816\) 8.26062 0.289180
\(817\) −7.73995 −0.270787
\(818\) −98.2812 −3.43632
\(819\) −3.37904 −0.118073
\(820\) −5.72963 −0.200087
\(821\) −39.6582 −1.38408 −0.692041 0.721859i \(-0.743288\pi\)
−0.692041 + 0.721859i \(0.743288\pi\)
\(822\) −26.4792 −0.923570
\(823\) −7.60901 −0.265234 −0.132617 0.991167i \(-0.542338\pi\)
−0.132617 + 0.991167i \(0.542338\pi\)
\(824\) 54.5513 1.90038
\(825\) −14.5108 −0.505202
\(826\) −28.9126 −1.00600
\(827\) 19.4383 0.675936 0.337968 0.941158i \(-0.390260\pi\)
0.337968 + 0.941158i \(0.390260\pi\)
\(828\) 16.4255 0.570826
\(829\) −38.1869 −1.32629 −0.663143 0.748492i \(-0.730778\pi\)
−0.663143 + 0.748492i \(0.730778\pi\)
\(830\) −57.4536 −1.99424
\(831\) −3.12729 −0.108484
\(832\) 3.99299 0.138432
\(833\) −0.585005 −0.0202692
\(834\) 19.4774 0.674447
\(835\) −17.1852 −0.594717
\(836\) 100.992 3.49286
\(837\) −6.37475 −0.220343
\(838\) 93.8721 3.24276
\(839\) 29.0385 1.00252 0.501260 0.865297i \(-0.332870\pi\)
0.501260 + 0.865297i \(0.332870\pi\)
\(840\) −52.5332 −1.81257
\(841\) 4.78499 0.165000
\(842\) −75.5053 −2.60208
\(843\) 29.2396 1.00707
\(844\) −40.0192 −1.37752
\(845\) −32.2081 −1.10799
\(846\) 15.5242 0.533733
\(847\) −41.0386 −1.41010
\(848\) −92.5734 −3.17898
\(849\) 24.5281 0.841804
\(850\) 7.34797 0.252033
\(851\) 18.5260 0.635063
\(852\) −24.0641 −0.824421
\(853\) −39.3760 −1.34821 −0.674105 0.738636i \(-0.735470\pi\)
−0.674105 + 0.738636i \(0.735470\pi\)
\(854\) 53.2993 1.82386
\(855\) 11.9794 0.409688
\(856\) −111.682 −3.81720
\(857\) −22.4273 −0.766103 −0.383052 0.923727i \(-0.625127\pi\)
−0.383052 + 0.923727i \(0.625127\pi\)
\(858\) 16.0919 0.549368
\(859\) −26.9153 −0.918339 −0.459170 0.888349i \(-0.651853\pi\)
−0.459170 + 0.888349i \(0.651853\pi\)
\(860\) −23.5451 −0.802880
\(861\) −1.21332 −0.0413499
\(862\) 34.1511 1.16319
\(863\) 19.3259 0.657861 0.328930 0.944354i \(-0.393312\pi\)
0.328930 + 0.944354i \(0.393312\pi\)
\(864\) 7.67360 0.261061
\(865\) 39.0246 1.32688
\(866\) −31.1370 −1.05808
\(867\) −1.00000 −0.0339618
\(868\) −81.4893 −2.76593
\(869\) 5.08930 0.172643
\(870\) 41.9725 1.42300
\(871\) 15.3025 0.518504
\(872\) −94.3038 −3.19353
\(873\) 6.88466 0.233010
\(874\) −38.9906 −1.31888
\(875\) 16.5819 0.560571
\(876\) −33.3187 −1.12574
\(877\) −1.19412 −0.0403224 −0.0201612 0.999797i \(-0.506418\pi\)
−0.0201612 + 0.999797i \(0.506418\pi\)
\(878\) −50.1114 −1.69118
\(879\) 27.0550 0.912543
\(880\) 117.799 3.97099
\(881\) 11.9002 0.400929 0.200465 0.979701i \(-0.435755\pi\)
0.200465 + 0.979701i \(0.435755\pi\)
\(882\) −1.50763 −0.0507644
\(883\) 34.0166 1.14475 0.572375 0.819992i \(-0.306022\pi\)
0.572375 + 0.819992i \(0.306022\pi\)
\(884\) −5.69475 −0.191535
\(885\) 11.4142 0.383684
\(886\) 33.1461 1.11356
\(887\) 41.8345 1.40466 0.702332 0.711850i \(-0.252142\pi\)
0.702332 + 0.711850i \(0.252142\pi\)
\(888\) 35.6376 1.19592
\(889\) 13.7322 0.460562
\(890\) 69.8831 2.34249
\(891\) 5.08930 0.170498
\(892\) 106.039 3.55045
\(893\) −25.7539 −0.861822
\(894\) −14.8087 −0.495278
\(895\) −9.80015 −0.327583
\(896\) −19.1685 −0.640374
\(897\) −4.34185 −0.144970
\(898\) −2.10653 −0.0702958
\(899\) 37.0531 1.23579
\(900\) 13.2341 0.441136
\(901\) 11.2066 0.373346
\(902\) 5.77816 0.192392
\(903\) −4.98596 −0.165922
\(904\) 98.9104 3.28971
\(905\) −48.9453 −1.62700
\(906\) −10.8550 −0.360633
\(907\) 48.3897 1.60675 0.803377 0.595471i \(-0.203034\pi\)
0.803377 + 0.595471i \(0.203034\pi\)
\(908\) 136.511 4.53028
\(909\) 5.54339 0.183863
\(910\) 24.4003 0.808864
\(911\) 27.9654 0.926533 0.463267 0.886219i \(-0.346677\pi\)
0.463267 + 0.886219i \(0.346677\pi\)
\(912\) −35.3167 −1.16945
\(913\) 40.4923 1.34010
\(914\) 1.31746 0.0435775
\(915\) −21.0416 −0.695614
\(916\) −101.133 −3.34154
\(917\) 51.4211 1.69808
\(918\) −2.57711 −0.0850574
\(919\) −43.4493 −1.43326 −0.716631 0.697453i \(-0.754317\pi\)
−0.716631 + 0.697453i \(0.754317\pi\)
\(920\) −67.5017 −2.22546
\(921\) −8.14904 −0.268520
\(922\) −79.2873 −2.61119
\(923\) 6.36099 0.209375
\(924\) 65.0572 2.14023
\(925\) 14.9264 0.490779
\(926\) −21.0560 −0.691943
\(927\) −8.01343 −0.263196
\(928\) −44.6027 −1.46415
\(929\) −31.0643 −1.01919 −0.509594 0.860415i \(-0.670204\pi\)
−0.509594 + 0.860415i \(0.670204\pi\)
\(930\) 46.0326 1.50947
\(931\) 2.50108 0.0819695
\(932\) 45.9750 1.50596
\(933\) −13.4755 −0.441169
\(934\) 2.54555 0.0832930
\(935\) −14.2602 −0.466360
\(936\) −8.35222 −0.273001
\(937\) 29.5595 0.965668 0.482834 0.875712i \(-0.339608\pi\)
0.482834 + 0.875712i \(0.339608\pi\)
\(938\) 88.5233 2.89039
\(939\) −14.1793 −0.462723
\(940\) −78.3438 −2.55529
\(941\) −58.8939 −1.91989 −0.959943 0.280197i \(-0.909600\pi\)
−0.959943 + 0.280197i \(0.909600\pi\)
\(942\) −37.2789 −1.21461
\(943\) −1.55904 −0.0507693
\(944\) −33.6503 −1.09522
\(945\) 7.71697 0.251033
\(946\) 23.7445 0.771999
\(947\) −41.5581 −1.35046 −0.675228 0.737609i \(-0.735955\pi\)
−0.675228 + 0.737609i \(0.735955\pi\)
\(948\) −4.64151 −0.150749
\(949\) 8.80733 0.285898
\(950\) −31.4148 −1.01923
\(951\) −1.59717 −0.0517918
\(952\) −18.7484 −0.607639
\(953\) 2.91263 0.0943494 0.0471747 0.998887i \(-0.484978\pi\)
0.0471747 + 0.998887i \(0.484978\pi\)
\(954\) 28.8806 0.935046
\(955\) −41.2583 −1.33509
\(956\) 24.5325 0.793439
\(957\) −29.5815 −0.956233
\(958\) −34.0680 −1.10069
\(959\) 28.2976 0.913778
\(960\) −9.11909 −0.294317
\(961\) 9.63739 0.310883
\(962\) −16.5528 −0.533684
\(963\) 16.4057 0.528668
\(964\) −63.6993 −2.05162
\(965\) 20.0095 0.644129
\(966\) −25.1172 −0.808131
\(967\) −2.35895 −0.0758586 −0.0379293 0.999280i \(-0.512076\pi\)
−0.0379293 + 0.999280i \(0.512076\pi\)
\(968\) −101.438 −3.26034
\(969\) 4.27531 0.137343
\(970\) −49.7147 −1.59624
\(971\) 35.3450 1.13427 0.567137 0.823623i \(-0.308051\pi\)
0.567137 + 0.823623i \(0.308051\pi\)
\(972\) −4.64151 −0.148877
\(973\) −20.8149 −0.667297
\(974\) −73.0802 −2.34164
\(975\) −3.49824 −0.112033
\(976\) 62.0330 1.98563
\(977\) −7.53500 −0.241066 −0.120533 0.992709i \(-0.538460\pi\)
−0.120533 + 0.992709i \(0.538460\pi\)
\(978\) 9.13966 0.292254
\(979\) −49.2524 −1.57411
\(980\) 7.60832 0.243039
\(981\) 13.8530 0.442291
\(982\) −47.2531 −1.50791
\(983\) 48.2940 1.54034 0.770169 0.637839i \(-0.220172\pi\)
0.770169 + 0.637839i \(0.220172\pi\)
\(984\) −2.99905 −0.0956064
\(985\) −35.2289 −1.12248
\(986\) 14.9794 0.477042
\(987\) −16.5903 −0.528075
\(988\) 24.3468 0.774576
\(989\) −6.40664 −0.203719
\(990\) −36.7503 −1.16800
\(991\) 58.9217 1.87171 0.935854 0.352387i \(-0.114630\pi\)
0.935854 + 0.352387i \(0.114630\pi\)
\(992\) −48.9172 −1.55312
\(993\) 18.4099 0.584219
\(994\) 36.7977 1.16715
\(995\) 71.8892 2.27904
\(996\) −36.9296 −1.17016
\(997\) −32.2089 −1.02007 −0.510034 0.860154i \(-0.670367\pi\)
−0.510034 + 0.860154i \(0.670367\pi\)
\(998\) 5.54477 0.175517
\(999\) −5.23507 −0.165630
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 4029.2.a.l.1.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.3 32 1.1 even 1 trivial