Properties

Label 4029.2.a.k.1.3
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
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: \(31\)
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

\(f(q)\) \(=\) \(q-2.41826 q^{2} +1.00000 q^{3} +3.84800 q^{4} +1.43707 q^{5} -2.41826 q^{6} +3.74160 q^{7} -4.46895 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.41826 q^{2} +1.00000 q^{3} +3.84800 q^{4} +1.43707 q^{5} -2.41826 q^{6} +3.74160 q^{7} -4.46895 q^{8} +1.00000 q^{9} -3.47522 q^{10} +4.27025 q^{11} +3.84800 q^{12} +2.58959 q^{13} -9.04818 q^{14} +1.43707 q^{15} +3.11110 q^{16} +1.00000 q^{17} -2.41826 q^{18} -7.71172 q^{19} +5.52985 q^{20} +3.74160 q^{21} -10.3266 q^{22} +3.97190 q^{23} -4.46895 q^{24} -2.93482 q^{25} -6.26230 q^{26} +1.00000 q^{27} +14.3977 q^{28} -2.55730 q^{29} -3.47522 q^{30} -1.53032 q^{31} +1.41444 q^{32} +4.27025 q^{33} -2.41826 q^{34} +5.37695 q^{35} +3.84800 q^{36} -2.68852 q^{37} +18.6490 q^{38} +2.58959 q^{39} -6.42220 q^{40} +8.65508 q^{41} -9.04818 q^{42} -2.21466 q^{43} +16.4319 q^{44} +1.43707 q^{45} -9.60509 q^{46} +2.63011 q^{47} +3.11110 q^{48} +6.99958 q^{49} +7.09717 q^{50} +1.00000 q^{51} +9.96472 q^{52} -0.811178 q^{53} -2.41826 q^{54} +6.13666 q^{55} -16.7210 q^{56} -7.71172 q^{57} +6.18424 q^{58} +8.80098 q^{59} +5.52985 q^{60} +1.53092 q^{61} +3.70072 q^{62} +3.74160 q^{63} -9.64269 q^{64} +3.72142 q^{65} -10.3266 q^{66} +2.18684 q^{67} +3.84800 q^{68} +3.97190 q^{69} -13.0029 q^{70} -1.36413 q^{71} -4.46895 q^{72} +3.33586 q^{73} +6.50156 q^{74} -2.93482 q^{75} -29.6747 q^{76} +15.9776 q^{77} -6.26230 q^{78} +1.00000 q^{79} +4.47087 q^{80} +1.00000 q^{81} -20.9303 q^{82} +0.585100 q^{83} +14.3977 q^{84} +1.43707 q^{85} +5.35564 q^{86} -2.55730 q^{87} -19.0835 q^{88} +10.0870 q^{89} -3.47522 q^{90} +9.68920 q^{91} +15.2839 q^{92} -1.53032 q^{93} -6.36031 q^{94} -11.0823 q^{95} +1.41444 q^{96} +1.60550 q^{97} -16.9268 q^{98} +4.27025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41826 −1.70997 −0.854985 0.518652i \(-0.826434\pi\)
−0.854985 + 0.518652i \(0.826434\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.84800 1.92400
\(5\) 1.43707 0.642678 0.321339 0.946964i \(-0.395867\pi\)
0.321339 + 0.946964i \(0.395867\pi\)
\(6\) −2.41826 −0.987252
\(7\) 3.74160 1.41419 0.707096 0.707117i \(-0.250005\pi\)
0.707096 + 0.707117i \(0.250005\pi\)
\(8\) −4.46895 −1.58001
\(9\) 1.00000 0.333333
\(10\) −3.47522 −1.09896
\(11\) 4.27025 1.28753 0.643765 0.765223i \(-0.277372\pi\)
0.643765 + 0.765223i \(0.277372\pi\)
\(12\) 3.84800 1.11082
\(13\) 2.58959 0.718222 0.359111 0.933295i \(-0.383080\pi\)
0.359111 + 0.933295i \(0.383080\pi\)
\(14\) −9.04818 −2.41823
\(15\) 1.43707 0.371051
\(16\) 3.11110 0.777775
\(17\) 1.00000 0.242536
\(18\) −2.41826 −0.569990
\(19\) −7.71172 −1.76919 −0.884595 0.466360i \(-0.845565\pi\)
−0.884595 + 0.466360i \(0.845565\pi\)
\(20\) 5.52985 1.23651
\(21\) 3.74160 0.816484
\(22\) −10.3266 −2.20164
\(23\) 3.97190 0.828198 0.414099 0.910232i \(-0.364097\pi\)
0.414099 + 0.910232i \(0.364097\pi\)
\(24\) −4.46895 −0.912220
\(25\) −2.93482 −0.586964
\(26\) −6.26230 −1.22814
\(27\) 1.00000 0.192450
\(28\) 14.3977 2.72091
\(29\) −2.55730 −0.474880 −0.237440 0.971402i \(-0.576308\pi\)
−0.237440 + 0.971402i \(0.576308\pi\)
\(30\) −3.47522 −0.634486
\(31\) −1.53032 −0.274853 −0.137427 0.990512i \(-0.543883\pi\)
−0.137427 + 0.990512i \(0.543883\pi\)
\(32\) 1.41444 0.250040
\(33\) 4.27025 0.743355
\(34\) −2.41826 −0.414729
\(35\) 5.37695 0.908871
\(36\) 3.84800 0.641333
\(37\) −2.68852 −0.441990 −0.220995 0.975275i \(-0.570931\pi\)
−0.220995 + 0.975275i \(0.570931\pi\)
\(38\) 18.6490 3.02526
\(39\) 2.58959 0.414666
\(40\) −6.42220 −1.01544
\(41\) 8.65508 1.35170 0.675848 0.737041i \(-0.263778\pi\)
0.675848 + 0.737041i \(0.263778\pi\)
\(42\) −9.04818 −1.39616
\(43\) −2.21466 −0.337733 −0.168867 0.985639i \(-0.554011\pi\)
−0.168867 + 0.985639i \(0.554011\pi\)
\(44\) 16.4319 2.47721
\(45\) 1.43707 0.214226
\(46\) −9.60509 −1.41619
\(47\) 2.63011 0.383642 0.191821 0.981430i \(-0.438561\pi\)
0.191821 + 0.981430i \(0.438561\pi\)
\(48\) 3.11110 0.449048
\(49\) 6.99958 0.999940
\(50\) 7.09717 1.00369
\(51\) 1.00000 0.140028
\(52\) 9.96472 1.38186
\(53\) −0.811178 −0.111424 −0.0557119 0.998447i \(-0.517743\pi\)
−0.0557119 + 0.998447i \(0.517743\pi\)
\(54\) −2.41826 −0.329084
\(55\) 6.13666 0.827467
\(56\) −16.7210 −2.23444
\(57\) −7.71172 −1.02144
\(58\) 6.18424 0.812030
\(59\) 8.80098 1.14579 0.572895 0.819629i \(-0.305820\pi\)
0.572895 + 0.819629i \(0.305820\pi\)
\(60\) 5.52985 0.713901
\(61\) 1.53092 0.196014 0.0980069 0.995186i \(-0.468753\pi\)
0.0980069 + 0.995186i \(0.468753\pi\)
\(62\) 3.70072 0.469991
\(63\) 3.74160 0.471397
\(64\) −9.64269 −1.20534
\(65\) 3.72142 0.461586
\(66\) −10.3266 −1.27112
\(67\) 2.18684 0.267166 0.133583 0.991038i \(-0.457352\pi\)
0.133583 + 0.991038i \(0.457352\pi\)
\(68\) 3.84800 0.466638
\(69\) 3.97190 0.478160
\(70\) −13.0029 −1.55414
\(71\) −1.36413 −0.161893 −0.0809465 0.996718i \(-0.525794\pi\)
−0.0809465 + 0.996718i \(0.525794\pi\)
\(72\) −4.46895 −0.526671
\(73\) 3.33586 0.390433 0.195217 0.980760i \(-0.437459\pi\)
0.195217 + 0.980760i \(0.437459\pi\)
\(74\) 6.50156 0.755791
\(75\) −2.93482 −0.338884
\(76\) −29.6747 −3.40392
\(77\) 15.9776 1.82081
\(78\) −6.26230 −0.709066
\(79\) 1.00000 0.112509
\(80\) 4.47087 0.499859
\(81\) 1.00000 0.111111
\(82\) −20.9303 −2.31136
\(83\) 0.585100 0.0642231 0.0321115 0.999484i \(-0.489777\pi\)
0.0321115 + 0.999484i \(0.489777\pi\)
\(84\) 14.3977 1.57092
\(85\) 1.43707 0.155872
\(86\) 5.35564 0.577514
\(87\) −2.55730 −0.274172
\(88\) −19.0835 −2.03431
\(89\) 10.0870 1.06922 0.534610 0.845099i \(-0.320458\pi\)
0.534610 + 0.845099i \(0.320458\pi\)
\(90\) −3.47522 −0.366320
\(91\) 9.68920 1.01570
\(92\) 15.2839 1.59345
\(93\) −1.53032 −0.158687
\(94\) −6.36031 −0.656016
\(95\) −11.0823 −1.13702
\(96\) 1.41444 0.144361
\(97\) 1.60550 0.163014 0.0815068 0.996673i \(-0.474027\pi\)
0.0815068 + 0.996673i \(0.474027\pi\)
\(98\) −16.9268 −1.70987
\(99\) 4.27025 0.429176
\(100\) −11.2932 −1.12932
\(101\) −16.1021 −1.60221 −0.801107 0.598521i \(-0.795755\pi\)
−0.801107 + 0.598521i \(0.795755\pi\)
\(102\) −2.41826 −0.239444
\(103\) −2.66118 −0.262214 −0.131107 0.991368i \(-0.541853\pi\)
−0.131107 + 0.991368i \(0.541853\pi\)
\(104\) −11.5727 −1.13480
\(105\) 5.37695 0.524737
\(106\) 1.96164 0.190532
\(107\) 10.4918 1.01428 0.507138 0.861865i \(-0.330703\pi\)
0.507138 + 0.861865i \(0.330703\pi\)
\(108\) 3.84800 0.370274
\(109\) 10.1201 0.969326 0.484663 0.874701i \(-0.338942\pi\)
0.484663 + 0.874701i \(0.338942\pi\)
\(110\) −14.8401 −1.41495
\(111\) −2.68852 −0.255183
\(112\) 11.6405 1.09992
\(113\) 17.0041 1.59961 0.799803 0.600262i \(-0.204937\pi\)
0.799803 + 0.600262i \(0.204937\pi\)
\(114\) 18.6490 1.74664
\(115\) 5.70791 0.532265
\(116\) −9.84050 −0.913668
\(117\) 2.58959 0.239407
\(118\) −21.2831 −1.95927
\(119\) 3.74160 0.342992
\(120\) −6.42220 −0.586264
\(121\) 7.23505 0.657732
\(122\) −3.70216 −0.335178
\(123\) 8.65508 0.780402
\(124\) −5.88867 −0.528818
\(125\) −11.4029 −1.01991
\(126\) −9.04818 −0.806076
\(127\) 11.1393 0.988455 0.494227 0.869333i \(-0.335451\pi\)
0.494227 + 0.869333i \(0.335451\pi\)
\(128\) 20.4897 1.81105
\(129\) −2.21466 −0.194990
\(130\) −8.99938 −0.789298
\(131\) −2.37479 −0.207486 −0.103743 0.994604i \(-0.533082\pi\)
−0.103743 + 0.994604i \(0.533082\pi\)
\(132\) 16.4319 1.43022
\(133\) −28.8542 −2.50198
\(134\) −5.28837 −0.456845
\(135\) 1.43707 0.123684
\(136\) −4.46895 −0.383209
\(137\) −14.8950 −1.27257 −0.636284 0.771455i \(-0.719529\pi\)
−0.636284 + 0.771455i \(0.719529\pi\)
\(138\) −9.60509 −0.817640
\(139\) 21.2326 1.80093 0.900463 0.434932i \(-0.143228\pi\)
0.900463 + 0.434932i \(0.143228\pi\)
\(140\) 20.6905 1.74867
\(141\) 2.63011 0.221496
\(142\) 3.29884 0.276832
\(143\) 11.0582 0.924732
\(144\) 3.11110 0.259258
\(145\) −3.67503 −0.305195
\(146\) −8.06699 −0.667629
\(147\) 6.99958 0.577316
\(148\) −10.3454 −0.850389
\(149\) 4.30985 0.353076 0.176538 0.984294i \(-0.443510\pi\)
0.176538 + 0.984294i \(0.443510\pi\)
\(150\) 7.09717 0.579482
\(151\) −19.7238 −1.60510 −0.802550 0.596585i \(-0.796524\pi\)
−0.802550 + 0.596585i \(0.796524\pi\)
\(152\) 34.4633 2.79534
\(153\) 1.00000 0.0808452
\(154\) −38.6380 −3.11354
\(155\) −2.19918 −0.176642
\(156\) 9.96472 0.797816
\(157\) 14.6968 1.17293 0.586467 0.809973i \(-0.300518\pi\)
0.586467 + 0.809973i \(0.300518\pi\)
\(158\) −2.41826 −0.192387
\(159\) −0.811178 −0.0643306
\(160\) 2.03266 0.160696
\(161\) 14.8613 1.17123
\(162\) −2.41826 −0.189997
\(163\) 0.0695570 0.00544813 0.00272406 0.999996i \(-0.499133\pi\)
0.00272406 + 0.999996i \(0.499133\pi\)
\(164\) 33.3047 2.60066
\(165\) 6.13666 0.477739
\(166\) −1.41493 −0.109820
\(167\) −0.744912 −0.0576430 −0.0288215 0.999585i \(-0.509175\pi\)
−0.0288215 + 0.999585i \(0.509175\pi\)
\(168\) −16.7210 −1.29006
\(169\) −6.29405 −0.484157
\(170\) −3.47522 −0.266537
\(171\) −7.71172 −0.589730
\(172\) −8.52202 −0.649798
\(173\) 7.23891 0.550364 0.275182 0.961392i \(-0.411262\pi\)
0.275182 + 0.961392i \(0.411262\pi\)
\(174\) 6.18424 0.468826
\(175\) −10.9809 −0.830081
\(176\) 13.2852 1.00141
\(177\) 8.80098 0.661522
\(178\) −24.3930 −1.82834
\(179\) −13.5003 −1.00906 −0.504528 0.863395i \(-0.668334\pi\)
−0.504528 + 0.863395i \(0.668334\pi\)
\(180\) 5.52985 0.412171
\(181\) −19.2944 −1.43414 −0.717070 0.697001i \(-0.754517\pi\)
−0.717070 + 0.697001i \(0.754517\pi\)
\(182\) −23.4310 −1.73682
\(183\) 1.53092 0.113169
\(184\) −17.7502 −1.30856
\(185\) −3.86360 −0.284058
\(186\) 3.70072 0.271350
\(187\) 4.27025 0.312272
\(188\) 10.1207 0.738126
\(189\) 3.74160 0.272161
\(190\) 26.7999 1.94427
\(191\) −20.7925 −1.50449 −0.752247 0.658882i \(-0.771030\pi\)
−0.752247 + 0.658882i \(0.771030\pi\)
\(192\) −9.64269 −0.695901
\(193\) 4.40761 0.317267 0.158633 0.987338i \(-0.449291\pi\)
0.158633 + 0.987338i \(0.449291\pi\)
\(194\) −3.88252 −0.278749
\(195\) 3.72142 0.266497
\(196\) 26.9344 1.92388
\(197\) 10.7014 0.762441 0.381221 0.924484i \(-0.375504\pi\)
0.381221 + 0.924484i \(0.375504\pi\)
\(198\) −10.3266 −0.733879
\(199\) 12.1396 0.860550 0.430275 0.902698i \(-0.358417\pi\)
0.430275 + 0.902698i \(0.358417\pi\)
\(200\) 13.1156 0.927411
\(201\) 2.18684 0.154248
\(202\) 38.9390 2.73974
\(203\) −9.56841 −0.671571
\(204\) 3.84800 0.269414
\(205\) 12.4380 0.868706
\(206\) 6.43544 0.448378
\(207\) 3.97190 0.276066
\(208\) 8.05646 0.558615
\(209\) −32.9310 −2.27788
\(210\) −13.0029 −0.897285
\(211\) −9.19535 −0.633034 −0.316517 0.948587i \(-0.602513\pi\)
−0.316517 + 0.948587i \(0.602513\pi\)
\(212\) −3.12141 −0.214379
\(213\) −1.36413 −0.0934690
\(214\) −25.3718 −1.73438
\(215\) −3.18263 −0.217054
\(216\) −4.46895 −0.304073
\(217\) −5.72584 −0.388696
\(218\) −24.4730 −1.65752
\(219\) 3.33586 0.225417
\(220\) 23.6139 1.59205
\(221\) 2.58959 0.174194
\(222\) 6.50156 0.436356
\(223\) −4.41708 −0.295790 −0.147895 0.989003i \(-0.547250\pi\)
−0.147895 + 0.989003i \(0.547250\pi\)
\(224\) 5.29228 0.353605
\(225\) −2.93482 −0.195655
\(226\) −41.1203 −2.73528
\(227\) 9.11347 0.604882 0.302441 0.953168i \(-0.402198\pi\)
0.302441 + 0.953168i \(0.402198\pi\)
\(228\) −29.6747 −1.96525
\(229\) 15.4085 1.01822 0.509110 0.860701i \(-0.329975\pi\)
0.509110 + 0.860701i \(0.329975\pi\)
\(230\) −13.8032 −0.910157
\(231\) 15.9776 1.05125
\(232\) 11.4285 0.750315
\(233\) −6.27810 −0.411292 −0.205646 0.978626i \(-0.565930\pi\)
−0.205646 + 0.978626i \(0.565930\pi\)
\(234\) −6.26230 −0.409379
\(235\) 3.77967 0.246558
\(236\) 33.8662 2.20450
\(237\) 1.00000 0.0649570
\(238\) −9.04818 −0.586506
\(239\) −10.1095 −0.653932 −0.326966 0.945036i \(-0.606026\pi\)
−0.326966 + 0.945036i \(0.606026\pi\)
\(240\) 4.47087 0.288594
\(241\) −17.0269 −1.09680 −0.548399 0.836217i \(-0.684763\pi\)
−0.548399 + 0.836217i \(0.684763\pi\)
\(242\) −17.4963 −1.12470
\(243\) 1.00000 0.0641500
\(244\) 5.89097 0.377130
\(245\) 10.0589 0.642640
\(246\) −20.9303 −1.33446
\(247\) −19.9702 −1.27067
\(248\) 6.83892 0.434272
\(249\) 0.585100 0.0370792
\(250\) 27.5753 1.74401
\(251\) −19.8391 −1.25223 −0.626117 0.779729i \(-0.715357\pi\)
−0.626117 + 0.779729i \(0.715357\pi\)
\(252\) 14.3977 0.906969
\(253\) 16.9610 1.06633
\(254\) −26.9378 −1.69023
\(255\) 1.43707 0.0899930
\(256\) −30.2641 −1.89150
\(257\) 8.49648 0.529996 0.264998 0.964249i \(-0.414629\pi\)
0.264998 + 0.964249i \(0.414629\pi\)
\(258\) 5.35564 0.333428
\(259\) −10.0594 −0.625060
\(260\) 14.3200 0.888091
\(261\) −2.55730 −0.158293
\(262\) 5.74287 0.354796
\(263\) −16.5873 −1.02281 −0.511407 0.859339i \(-0.670876\pi\)
−0.511407 + 0.859339i \(0.670876\pi\)
\(264\) −19.0835 −1.17451
\(265\) −1.16572 −0.0716097
\(266\) 69.7770 4.27830
\(267\) 10.0870 0.617315
\(268\) 8.41498 0.514027
\(269\) −3.01940 −0.184096 −0.0920480 0.995755i \(-0.529341\pi\)
−0.0920480 + 0.995755i \(0.529341\pi\)
\(270\) −3.47522 −0.211495
\(271\) 10.0368 0.609694 0.304847 0.952401i \(-0.401395\pi\)
0.304847 + 0.952401i \(0.401395\pi\)
\(272\) 3.11110 0.188638
\(273\) 9.68920 0.586417
\(274\) 36.0201 2.17605
\(275\) −12.5324 −0.755734
\(276\) 15.2839 0.919980
\(277\) −28.7577 −1.72788 −0.863940 0.503594i \(-0.832011\pi\)
−0.863940 + 0.503594i \(0.832011\pi\)
\(278\) −51.3460 −3.07953
\(279\) −1.53032 −0.0916178
\(280\) −24.0293 −1.43603
\(281\) −0.250260 −0.0149293 −0.00746464 0.999972i \(-0.502376\pi\)
−0.00746464 + 0.999972i \(0.502376\pi\)
\(282\) −6.36031 −0.378751
\(283\) −18.1370 −1.07813 −0.539067 0.842263i \(-0.681223\pi\)
−0.539067 + 0.842263i \(0.681223\pi\)
\(284\) −5.24919 −0.311482
\(285\) −11.0823 −0.656459
\(286\) −26.7416 −1.58126
\(287\) 32.3839 1.91156
\(288\) 1.41444 0.0833468
\(289\) 1.00000 0.0588235
\(290\) 8.88720 0.521874
\(291\) 1.60550 0.0941160
\(292\) 12.8364 0.751193
\(293\) 8.82213 0.515394 0.257697 0.966226i \(-0.417036\pi\)
0.257697 + 0.966226i \(0.417036\pi\)
\(294\) −16.9268 −0.987193
\(295\) 12.6477 0.736375
\(296\) 12.0149 0.698350
\(297\) 4.27025 0.247785
\(298\) −10.4223 −0.603750
\(299\) 10.2856 0.594830
\(300\) −11.2932 −0.652013
\(301\) −8.28639 −0.477619
\(302\) 47.6973 2.74467
\(303\) −16.1021 −0.925039
\(304\) −23.9919 −1.37603
\(305\) 2.20004 0.125974
\(306\) −2.41826 −0.138243
\(307\) −14.0933 −0.804346 −0.402173 0.915564i \(-0.631745\pi\)
−0.402173 + 0.915564i \(0.631745\pi\)
\(308\) 61.4817 3.50325
\(309\) −2.66118 −0.151389
\(310\) 5.31820 0.302053
\(311\) 8.54992 0.484822 0.242411 0.970174i \(-0.422062\pi\)
0.242411 + 0.970174i \(0.422062\pi\)
\(312\) −11.5727 −0.655177
\(313\) −20.4335 −1.15497 −0.577484 0.816402i \(-0.695966\pi\)
−0.577484 + 0.816402i \(0.695966\pi\)
\(314\) −35.5408 −2.00568
\(315\) 5.37695 0.302957
\(316\) 3.84800 0.216467
\(317\) 18.3470 1.03047 0.515236 0.857048i \(-0.327704\pi\)
0.515236 + 0.857048i \(0.327704\pi\)
\(318\) 1.96164 0.110003
\(319\) −10.9203 −0.611421
\(320\) −13.8572 −0.774644
\(321\) 10.4918 0.585593
\(322\) −35.9384 −2.00277
\(323\) −7.71172 −0.429092
\(324\) 3.84800 0.213778
\(325\) −7.59997 −0.421571
\(326\) −0.168207 −0.00931614
\(327\) 10.1201 0.559641
\(328\) −38.6791 −2.13570
\(329\) 9.84084 0.542543
\(330\) −14.8401 −0.816919
\(331\) 29.2454 1.60747 0.803736 0.594987i \(-0.202843\pi\)
0.803736 + 0.594987i \(0.202843\pi\)
\(332\) 2.25146 0.123565
\(333\) −2.68852 −0.147330
\(334\) 1.80139 0.0985679
\(335\) 3.14266 0.171702
\(336\) 11.6405 0.635041
\(337\) −16.2320 −0.884212 −0.442106 0.896963i \(-0.645769\pi\)
−0.442106 + 0.896963i \(0.645769\pi\)
\(338\) 15.2207 0.827895
\(339\) 17.0041 0.923533
\(340\) 5.52985 0.299898
\(341\) −6.53485 −0.353882
\(342\) 18.6490 1.00842
\(343\) −0.00156242 −8.43626e−5 0
\(344\) 9.89722 0.533622
\(345\) 5.70791 0.307303
\(346\) −17.5056 −0.941106
\(347\) −8.67217 −0.465546 −0.232773 0.972531i \(-0.574780\pi\)
−0.232773 + 0.972531i \(0.574780\pi\)
\(348\) −9.84050 −0.527506
\(349\) 6.54812 0.350513 0.175256 0.984523i \(-0.443925\pi\)
0.175256 + 0.984523i \(0.443925\pi\)
\(350\) 26.5548 1.41941
\(351\) 2.58959 0.138222
\(352\) 6.04002 0.321934
\(353\) −16.5315 −0.879883 −0.439941 0.898026i \(-0.645001\pi\)
−0.439941 + 0.898026i \(0.645001\pi\)
\(354\) −21.2831 −1.13118
\(355\) −1.96036 −0.104045
\(356\) 38.8148 2.05718
\(357\) 3.74160 0.198027
\(358\) 32.6472 1.72546
\(359\) 27.4632 1.44945 0.724725 0.689038i \(-0.241967\pi\)
0.724725 + 0.689038i \(0.241967\pi\)
\(360\) −6.42220 −0.338480
\(361\) 40.4706 2.13003
\(362\) 46.6589 2.45234
\(363\) 7.23505 0.379742
\(364\) 37.2840 1.95421
\(365\) 4.79388 0.250923
\(366\) −3.70216 −0.193515
\(367\) 1.16447 0.0607850 0.0303925 0.999538i \(-0.490324\pi\)
0.0303925 + 0.999538i \(0.490324\pi\)
\(368\) 12.3570 0.644151
\(369\) 8.65508 0.450565
\(370\) 9.34321 0.485730
\(371\) −3.03510 −0.157575
\(372\) −5.88867 −0.305313
\(373\) 26.0396 1.34828 0.674141 0.738603i \(-0.264514\pi\)
0.674141 + 0.738603i \(0.264514\pi\)
\(374\) −10.3266 −0.533976
\(375\) −11.4029 −0.588844
\(376\) −11.7538 −0.606158
\(377\) −6.62236 −0.341069
\(378\) −9.04818 −0.465388
\(379\) 20.2683 1.04111 0.520557 0.853827i \(-0.325724\pi\)
0.520557 + 0.853827i \(0.325724\pi\)
\(380\) −42.6447 −2.18763
\(381\) 11.1393 0.570685
\(382\) 50.2818 2.57264
\(383\) −30.1723 −1.54173 −0.770867 0.636996i \(-0.780177\pi\)
−0.770867 + 0.636996i \(0.780177\pi\)
\(384\) 20.4897 1.04561
\(385\) 22.9609 1.17020
\(386\) −10.6588 −0.542517
\(387\) −2.21466 −0.112578
\(388\) 6.17796 0.313638
\(389\) 34.9455 1.77181 0.885903 0.463871i \(-0.153540\pi\)
0.885903 + 0.463871i \(0.153540\pi\)
\(390\) −8.99938 −0.455701
\(391\) 3.97190 0.200867
\(392\) −31.2808 −1.57992
\(393\) −2.37479 −0.119792
\(394\) −25.8787 −1.30375
\(395\) 1.43707 0.0723070
\(396\) 16.4319 0.825735
\(397\) −22.0369 −1.10600 −0.552999 0.833182i \(-0.686517\pi\)
−0.552999 + 0.833182i \(0.686517\pi\)
\(398\) −29.3566 −1.47152
\(399\) −28.8542 −1.44452
\(400\) −9.13052 −0.456526
\(401\) 5.52505 0.275908 0.137954 0.990439i \(-0.455947\pi\)
0.137954 + 0.990439i \(0.455947\pi\)
\(402\) −5.28837 −0.263760
\(403\) −3.96289 −0.197406
\(404\) −61.9607 −3.08266
\(405\) 1.43707 0.0714087
\(406\) 23.1389 1.14837
\(407\) −11.4807 −0.569076
\(408\) −4.46895 −0.221246
\(409\) −23.9969 −1.18657 −0.593286 0.804992i \(-0.702170\pi\)
−0.593286 + 0.804992i \(0.702170\pi\)
\(410\) −30.0783 −1.48546
\(411\) −14.8950 −0.734717
\(412\) −10.2402 −0.504499
\(413\) 32.9298 1.62037
\(414\) −9.60509 −0.472065
\(415\) 0.840831 0.0412748
\(416\) 3.66282 0.179584
\(417\) 21.2326 1.03977
\(418\) 79.6358 3.89512
\(419\) −8.62002 −0.421115 −0.210558 0.977581i \(-0.567528\pi\)
−0.210558 + 0.977581i \(0.567528\pi\)
\(420\) 20.6905 1.00959
\(421\) −14.8641 −0.724433 −0.362217 0.932094i \(-0.617980\pi\)
−0.362217 + 0.932094i \(0.617980\pi\)
\(422\) 22.2368 1.08247
\(423\) 2.63011 0.127881
\(424\) 3.62511 0.176051
\(425\) −2.93482 −0.142360
\(426\) 3.29884 0.159829
\(427\) 5.72808 0.277201
\(428\) 40.3723 1.95147
\(429\) 11.0582 0.533894
\(430\) 7.69644 0.371156
\(431\) 17.4944 0.842676 0.421338 0.906904i \(-0.361561\pi\)
0.421338 + 0.906904i \(0.361561\pi\)
\(432\) 3.11110 0.149683
\(433\) −6.42272 −0.308656 −0.154328 0.988020i \(-0.549321\pi\)
−0.154328 + 0.988020i \(0.549321\pi\)
\(434\) 13.8466 0.664658
\(435\) −3.67503 −0.176204
\(436\) 38.9420 1.86498
\(437\) −30.6302 −1.46524
\(438\) −8.06699 −0.385456
\(439\) 11.2816 0.538441 0.269220 0.963079i \(-0.413234\pi\)
0.269220 + 0.963079i \(0.413234\pi\)
\(440\) −27.4244 −1.30741
\(441\) 6.99958 0.333313
\(442\) −6.26230 −0.297867
\(443\) 18.6312 0.885195 0.442598 0.896720i \(-0.354057\pi\)
0.442598 + 0.896720i \(0.354057\pi\)
\(444\) −10.3454 −0.490973
\(445\) 14.4958 0.687165
\(446\) 10.6817 0.505792
\(447\) 4.30985 0.203849
\(448\) −36.0791 −1.70458
\(449\) −28.6311 −1.35118 −0.675592 0.737276i \(-0.736112\pi\)
−0.675592 + 0.737276i \(0.736112\pi\)
\(450\) 7.09717 0.334564
\(451\) 36.9594 1.74035
\(452\) 65.4316 3.07764
\(453\) −19.7238 −0.926704
\(454\) −22.0388 −1.03433
\(455\) 13.9241 0.652771
\(456\) 34.4633 1.61389
\(457\) −18.8263 −0.880657 −0.440329 0.897837i \(-0.645138\pi\)
−0.440329 + 0.897837i \(0.645138\pi\)
\(458\) −37.2617 −1.74113
\(459\) 1.00000 0.0466760
\(460\) 21.9640 1.02408
\(461\) 18.7948 0.875363 0.437681 0.899130i \(-0.355800\pi\)
0.437681 + 0.899130i \(0.355800\pi\)
\(462\) −38.6380 −1.79760
\(463\) 28.4842 1.32377 0.661886 0.749605i \(-0.269756\pi\)
0.661886 + 0.749605i \(0.269756\pi\)
\(464\) −7.95603 −0.369349
\(465\) −2.19918 −0.101985
\(466\) 15.1821 0.703297
\(467\) −30.7207 −1.42159 −0.710793 0.703402i \(-0.751664\pi\)
−0.710793 + 0.703402i \(0.751664\pi\)
\(468\) 9.96472 0.460620
\(469\) 8.18230 0.377824
\(470\) −9.14023 −0.421607
\(471\) 14.6968 0.677194
\(472\) −39.3311 −1.81036
\(473\) −9.45717 −0.434841
\(474\) −2.41826 −0.111075
\(475\) 22.6325 1.03845
\(476\) 14.3977 0.659917
\(477\) −0.811178 −0.0371413
\(478\) 24.4476 1.11821
\(479\) 23.9174 1.09281 0.546407 0.837520i \(-0.315995\pi\)
0.546407 + 0.837520i \(0.315995\pi\)
\(480\) 2.03266 0.0927776
\(481\) −6.96216 −0.317447
\(482\) 41.1755 1.87549
\(483\) 14.8613 0.676211
\(484\) 27.8405 1.26548
\(485\) 2.30722 0.104765
\(486\) −2.41826 −0.109695
\(487\) 7.44745 0.337476 0.168738 0.985661i \(-0.446031\pi\)
0.168738 + 0.985661i \(0.446031\pi\)
\(488\) −6.84159 −0.309704
\(489\) 0.0695570 0.00314548
\(490\) −24.3251 −1.09890
\(491\) 12.6240 0.569713 0.284856 0.958570i \(-0.408054\pi\)
0.284856 + 0.958570i \(0.408054\pi\)
\(492\) 33.3047 1.50149
\(493\) −2.55730 −0.115175
\(494\) 48.2931 2.17281
\(495\) 6.13666 0.275822
\(496\) −4.76097 −0.213774
\(497\) −5.10405 −0.228948
\(498\) −1.41493 −0.0634044
\(499\) 31.3716 1.40439 0.702193 0.711987i \(-0.252204\pi\)
0.702193 + 0.711987i \(0.252204\pi\)
\(500\) −43.8784 −1.96230
\(501\) −0.744912 −0.0332802
\(502\) 47.9762 2.14128
\(503\) −18.1364 −0.808661 −0.404331 0.914613i \(-0.632495\pi\)
−0.404331 + 0.914613i \(0.632495\pi\)
\(504\) −16.7210 −0.744814
\(505\) −23.1398 −1.02971
\(506\) −41.0162 −1.82339
\(507\) −6.29405 −0.279528
\(508\) 42.8641 1.90179
\(509\) 20.9859 0.930182 0.465091 0.885263i \(-0.346022\pi\)
0.465091 + 0.885263i \(0.346022\pi\)
\(510\) −3.47522 −0.153885
\(511\) 12.4815 0.552148
\(512\) 32.2071 1.42337
\(513\) −7.71172 −0.340481
\(514\) −20.5467 −0.906278
\(515\) −3.82431 −0.168519
\(516\) −8.52202 −0.375161
\(517\) 11.2312 0.493950
\(518\) 24.3262 1.06883
\(519\) 7.23891 0.317753
\(520\) −16.6309 −0.729311
\(521\) 1.66328 0.0728696 0.0364348 0.999336i \(-0.488400\pi\)
0.0364348 + 0.999336i \(0.488400\pi\)
\(522\) 6.18424 0.270677
\(523\) 0.533569 0.0233313 0.0116657 0.999932i \(-0.496287\pi\)
0.0116657 + 0.999932i \(0.496287\pi\)
\(524\) −9.13819 −0.399204
\(525\) −10.9809 −0.479247
\(526\) 40.1124 1.74898
\(527\) −1.53032 −0.0666617
\(528\) 13.2852 0.578163
\(529\) −7.22403 −0.314088
\(530\) 2.81902 0.122451
\(531\) 8.80098 0.381930
\(532\) −111.031 −4.81380
\(533\) 22.4131 0.970818
\(534\) −24.3930 −1.05559
\(535\) 15.0774 0.651854
\(536\) −9.77290 −0.422125
\(537\) −13.5003 −0.582579
\(538\) 7.30170 0.314799
\(539\) 29.8900 1.28745
\(540\) 5.52985 0.237967
\(541\) 13.1043 0.563399 0.281700 0.959503i \(-0.409102\pi\)
0.281700 + 0.959503i \(0.409102\pi\)
\(542\) −24.2717 −1.04256
\(543\) −19.2944 −0.828001
\(544\) 1.41444 0.0606437
\(545\) 14.5433 0.622965
\(546\) −23.4310 −1.00276
\(547\) −39.8637 −1.70445 −0.852224 0.523178i \(-0.824746\pi\)
−0.852224 + 0.523178i \(0.824746\pi\)
\(548\) −57.3160 −2.44842
\(549\) 1.53092 0.0653379
\(550\) 30.3067 1.29228
\(551\) 19.7212 0.840152
\(552\) −17.7502 −0.755499
\(553\) 3.74160 0.159109
\(554\) 69.5436 2.95462
\(555\) −3.86360 −0.164001
\(556\) 81.7031 3.46498
\(557\) 16.0410 0.679678 0.339839 0.940484i \(-0.389627\pi\)
0.339839 + 0.940484i \(0.389627\pi\)
\(558\) 3.70072 0.156664
\(559\) −5.73506 −0.242567
\(560\) 16.7282 0.706897
\(561\) 4.27025 0.180290
\(562\) 0.605195 0.0255286
\(563\) 9.05973 0.381822 0.190911 0.981607i \(-0.438856\pi\)
0.190911 + 0.981607i \(0.438856\pi\)
\(564\) 10.1207 0.426157
\(565\) 24.4361 1.02803
\(566\) 43.8601 1.84358
\(567\) 3.74160 0.157132
\(568\) 6.09625 0.255793
\(569\) 2.60152 0.109062 0.0545308 0.998512i \(-0.482634\pi\)
0.0545308 + 0.998512i \(0.482634\pi\)
\(570\) 26.7999 1.12253
\(571\) −25.1548 −1.05270 −0.526349 0.850269i \(-0.676439\pi\)
−0.526349 + 0.850269i \(0.676439\pi\)
\(572\) 42.5519 1.77918
\(573\) −20.7925 −0.868620
\(574\) −78.3127 −3.26871
\(575\) −11.6568 −0.486123
\(576\) −9.64269 −0.401779
\(577\) −35.3344 −1.47099 −0.735495 0.677530i \(-0.763050\pi\)
−0.735495 + 0.677530i \(0.763050\pi\)
\(578\) −2.41826 −0.100587
\(579\) 4.40761 0.183174
\(580\) −14.1415 −0.587195
\(581\) 2.18921 0.0908238
\(582\) −3.88252 −0.160936
\(583\) −3.46393 −0.143461
\(584\) −14.9078 −0.616889
\(585\) 3.72142 0.153862
\(586\) −21.3342 −0.881309
\(587\) −36.0425 −1.48763 −0.743816 0.668384i \(-0.766986\pi\)
−0.743816 + 0.668384i \(0.766986\pi\)
\(588\) 26.9344 1.11076
\(589\) 11.8014 0.486268
\(590\) −30.5854 −1.25918
\(591\) 10.7014 0.440196
\(592\) −8.36426 −0.343769
\(593\) 15.7996 0.648813 0.324406 0.945918i \(-0.394836\pi\)
0.324406 + 0.945918i \(0.394836\pi\)
\(594\) −10.3266 −0.423705
\(595\) 5.37695 0.220434
\(596\) 16.5843 0.679319
\(597\) 12.1396 0.496839
\(598\) −24.8732 −1.01714
\(599\) 32.9095 1.34465 0.672323 0.740258i \(-0.265297\pi\)
0.672323 + 0.740258i \(0.265297\pi\)
\(600\) 13.1156 0.535441
\(601\) −4.42825 −0.180632 −0.0903160 0.995913i \(-0.528788\pi\)
−0.0903160 + 0.995913i \(0.528788\pi\)
\(602\) 20.0387 0.816715
\(603\) 2.18684 0.0890552
\(604\) −75.8971 −3.08821
\(605\) 10.3973 0.422710
\(606\) 38.9390 1.58179
\(607\) −4.34059 −0.176179 −0.0880896 0.996113i \(-0.528076\pi\)
−0.0880896 + 0.996113i \(0.528076\pi\)
\(608\) −10.9078 −0.442369
\(609\) −9.56841 −0.387732
\(610\) −5.32027 −0.215412
\(611\) 6.81091 0.275540
\(612\) 3.84800 0.155546
\(613\) 26.5860 1.07380 0.536898 0.843647i \(-0.319596\pi\)
0.536898 + 0.843647i \(0.319596\pi\)
\(614\) 34.0813 1.37541
\(615\) 12.4380 0.501548
\(616\) −71.4030 −2.87691
\(617\) 14.5692 0.586533 0.293266 0.956031i \(-0.405258\pi\)
0.293266 + 0.956031i \(0.405258\pi\)
\(618\) 6.43544 0.258871
\(619\) −26.1438 −1.05081 −0.525404 0.850853i \(-0.676086\pi\)
−0.525404 + 0.850853i \(0.676086\pi\)
\(620\) −8.46244 −0.339860
\(621\) 3.97190 0.159387
\(622\) −20.6760 −0.829031
\(623\) 37.7416 1.51208
\(624\) 8.05646 0.322516
\(625\) −1.71271 −0.0685085
\(626\) 49.4136 1.97496
\(627\) −32.9310 −1.31514
\(628\) 56.5534 2.25672
\(629\) −2.68852 −0.107198
\(630\) −13.0029 −0.518048
\(631\) −44.3335 −1.76489 −0.882444 0.470417i \(-0.844103\pi\)
−0.882444 + 0.470417i \(0.844103\pi\)
\(632\) −4.46895 −0.177765
\(633\) −9.19535 −0.365483
\(634\) −44.3679 −1.76208
\(635\) 16.0080 0.635259
\(636\) −3.12141 −0.123772
\(637\) 18.1260 0.718179
\(638\) 26.4082 1.04551
\(639\) −1.36413 −0.0539643
\(640\) 29.4452 1.16392
\(641\) −9.00144 −0.355536 −0.177768 0.984072i \(-0.556888\pi\)
−0.177768 + 0.984072i \(0.556888\pi\)
\(642\) −25.3718 −1.00135
\(643\) −22.9213 −0.903929 −0.451965 0.892036i \(-0.649277\pi\)
−0.451965 + 0.892036i \(0.649277\pi\)
\(644\) 57.1861 2.25345
\(645\) −3.18263 −0.125316
\(646\) 18.6490 0.733734
\(647\) −45.1176 −1.77376 −0.886879 0.462002i \(-0.847131\pi\)
−0.886879 + 0.462002i \(0.847131\pi\)
\(648\) −4.46895 −0.175557
\(649\) 37.5824 1.47524
\(650\) 18.3787 0.720873
\(651\) −5.72584 −0.224414
\(652\) 0.267655 0.0104822
\(653\) 48.0075 1.87868 0.939338 0.342992i \(-0.111440\pi\)
0.939338 + 0.342992i \(0.111440\pi\)
\(654\) −24.4730 −0.956969
\(655\) −3.41275 −0.133347
\(656\) 26.9268 1.05132
\(657\) 3.33586 0.130144
\(658\) −23.7977 −0.927733
\(659\) 34.3792 1.33922 0.669612 0.742711i \(-0.266460\pi\)
0.669612 + 0.742711i \(0.266460\pi\)
\(660\) 23.6139 0.919169
\(661\) 19.7035 0.766378 0.383189 0.923670i \(-0.374826\pi\)
0.383189 + 0.923670i \(0.374826\pi\)
\(662\) −70.7230 −2.74873
\(663\) 2.58959 0.100571
\(664\) −2.61478 −0.101473
\(665\) −41.4656 −1.60797
\(666\) 6.50156 0.251930
\(667\) −10.1574 −0.393294
\(668\) −2.86642 −0.110905
\(669\) −4.41708 −0.170774
\(670\) −7.59977 −0.293605
\(671\) 6.53740 0.252374
\(672\) 5.29228 0.204154
\(673\) 43.1029 1.66150 0.830748 0.556648i \(-0.187913\pi\)
0.830748 + 0.556648i \(0.187913\pi\)
\(674\) 39.2532 1.51198
\(675\) −2.93482 −0.112961
\(676\) −24.2195 −0.931519
\(677\) 46.8286 1.79977 0.899886 0.436126i \(-0.143650\pi\)
0.899886 + 0.436126i \(0.143650\pi\)
\(678\) −41.1203 −1.57922
\(679\) 6.00714 0.230533
\(680\) −6.42220 −0.246280
\(681\) 9.11347 0.349229
\(682\) 15.8030 0.605128
\(683\) −35.4834 −1.35774 −0.678868 0.734261i \(-0.737529\pi\)
−0.678868 + 0.734261i \(0.737529\pi\)
\(684\) −29.6747 −1.13464
\(685\) −21.4052 −0.817851
\(686\) 0.00377834 0.000144258 0
\(687\) 15.4085 0.587870
\(688\) −6.89004 −0.262680
\(689\) −2.10061 −0.0800271
\(690\) −13.8032 −0.525480
\(691\) −1.16284 −0.0442365 −0.0221183 0.999755i \(-0.507041\pi\)
−0.0221183 + 0.999755i \(0.507041\pi\)
\(692\) 27.8553 1.05890
\(693\) 15.9776 0.606938
\(694\) 20.9716 0.796070
\(695\) 30.5128 1.15742
\(696\) 11.4285 0.433195
\(697\) 8.65508 0.327834
\(698\) −15.8351 −0.599367
\(699\) −6.27810 −0.237459
\(700\) −42.2546 −1.59707
\(701\) −2.68744 −0.101503 −0.0507516 0.998711i \(-0.516162\pi\)
−0.0507516 + 0.998711i \(0.516162\pi\)
\(702\) −6.26230 −0.236355
\(703\) 20.7331 0.781965
\(704\) −41.1767 −1.55191
\(705\) 3.77967 0.142350
\(706\) 39.9775 1.50457
\(707\) −60.2475 −2.26584
\(708\) 33.8662 1.27277
\(709\) −28.8031 −1.08172 −0.540862 0.841111i \(-0.681902\pi\)
−0.540862 + 0.841111i \(0.681902\pi\)
\(710\) 4.74067 0.177914
\(711\) 1.00000 0.0375029
\(712\) −45.0783 −1.68938
\(713\) −6.07827 −0.227633
\(714\) −9.04818 −0.338620
\(715\) 15.8914 0.594305
\(716\) −51.9490 −1.94142
\(717\) −10.1095 −0.377548
\(718\) −66.4132 −2.47852
\(719\) −2.22656 −0.0830368 −0.0415184 0.999138i \(-0.513220\pi\)
−0.0415184 + 0.999138i \(0.513220\pi\)
\(720\) 4.47087 0.166620
\(721\) −9.95708 −0.370821
\(722\) −97.8686 −3.64229
\(723\) −17.0269 −0.633237
\(724\) −74.2448 −2.75929
\(725\) 7.50523 0.278737
\(726\) −17.4963 −0.649347
\(727\) −11.9538 −0.443341 −0.221671 0.975122i \(-0.571151\pi\)
−0.221671 + 0.975122i \(0.571151\pi\)
\(728\) −43.3005 −1.60482
\(729\) 1.00000 0.0370370
\(730\) −11.5929 −0.429071
\(731\) −2.21466 −0.0819123
\(732\) 5.89097 0.217736
\(733\) 33.3616 1.23224 0.616120 0.787652i \(-0.288704\pi\)
0.616120 + 0.787652i \(0.288704\pi\)
\(734\) −2.81600 −0.103941
\(735\) 10.0589 0.371028
\(736\) 5.61802 0.207083
\(737\) 9.33838 0.343984
\(738\) −20.9303 −0.770454
\(739\) 29.3361 1.07915 0.539573 0.841939i \(-0.318586\pi\)
0.539573 + 0.841939i \(0.318586\pi\)
\(740\) −14.8671 −0.546527
\(741\) −19.9702 −0.733622
\(742\) 7.33968 0.269448
\(743\) −22.9459 −0.841804 −0.420902 0.907106i \(-0.638286\pi\)
−0.420902 + 0.907106i \(0.638286\pi\)
\(744\) 6.83892 0.250727
\(745\) 6.19356 0.226915
\(746\) −62.9707 −2.30552
\(747\) 0.585100 0.0214077
\(748\) 16.4319 0.600811
\(749\) 39.2560 1.43438
\(750\) 27.5753 1.00691
\(751\) −40.3686 −1.47307 −0.736536 0.676399i \(-0.763540\pi\)
−0.736536 + 0.676399i \(0.763540\pi\)
\(752\) 8.18254 0.298387
\(753\) −19.8391 −0.722977
\(754\) 16.0146 0.583218
\(755\) −28.3445 −1.03156
\(756\) 14.3977 0.523639
\(757\) −20.5814 −0.748043 −0.374022 0.927420i \(-0.622021\pi\)
−0.374022 + 0.927420i \(0.622021\pi\)
\(758\) −49.0142 −1.78027
\(759\) 16.9610 0.615645
\(760\) 49.5262 1.79651
\(761\) 14.3261 0.519320 0.259660 0.965700i \(-0.416389\pi\)
0.259660 + 0.965700i \(0.416389\pi\)
\(762\) −26.9378 −0.975854
\(763\) 37.8653 1.37081
\(764\) −80.0096 −2.89464
\(765\) 1.43707 0.0519575
\(766\) 72.9647 2.63632
\(767\) 22.7909 0.822932
\(768\) −30.2641 −1.09206
\(769\) 29.3853 1.05966 0.529830 0.848104i \(-0.322256\pi\)
0.529830 + 0.848104i \(0.322256\pi\)
\(770\) −55.5256 −2.00100
\(771\) 8.49648 0.305993
\(772\) 16.9605 0.610421
\(773\) −43.7678 −1.57422 −0.787108 0.616815i \(-0.788423\pi\)
−0.787108 + 0.616815i \(0.788423\pi\)
\(774\) 5.35564 0.192505
\(775\) 4.49121 0.161329
\(776\) −7.17489 −0.257564
\(777\) −10.0594 −0.360878
\(778\) −84.5074 −3.02974
\(779\) −66.7455 −2.39141
\(780\) 14.3200 0.512739
\(781\) −5.82520 −0.208442
\(782\) −9.60509 −0.343477
\(783\) −2.55730 −0.0913906
\(784\) 21.7764 0.777728
\(785\) 21.1204 0.753820
\(786\) 5.74287 0.204841
\(787\) −1.53726 −0.0547975 −0.0273988 0.999625i \(-0.508722\pi\)
−0.0273988 + 0.999625i \(0.508722\pi\)
\(788\) 41.1789 1.46694
\(789\) −16.5873 −0.590522
\(790\) −3.47522 −0.123643
\(791\) 63.6224 2.26215
\(792\) −19.0835 −0.678104
\(793\) 3.96444 0.140781
\(794\) 53.2910 1.89123
\(795\) −1.16572 −0.0413439
\(796\) 46.7130 1.65570
\(797\) −52.3005 −1.85258 −0.926290 0.376811i \(-0.877021\pi\)
−0.926290 + 0.376811i \(0.877021\pi\)
\(798\) 69.7770 2.47008
\(799\) 2.63011 0.0930467
\(800\) −4.15113 −0.146765
\(801\) 10.0870 0.356407
\(802\) −13.3610 −0.471794
\(803\) 14.2450 0.502694
\(804\) 8.41498 0.296773
\(805\) 21.3567 0.752725
\(806\) 9.58332 0.337558
\(807\) −3.01940 −0.106288
\(808\) 71.9593 2.53152
\(809\) 21.7755 0.765585 0.382792 0.923834i \(-0.374962\pi\)
0.382792 + 0.923834i \(0.374962\pi\)
\(810\) −3.47522 −0.122107
\(811\) −7.72144 −0.271136 −0.135568 0.990768i \(-0.543286\pi\)
−0.135568 + 0.990768i \(0.543286\pi\)
\(812\) −36.8192 −1.29210
\(813\) 10.0368 0.352007
\(814\) 27.7633 0.973103
\(815\) 0.0999585 0.00350139
\(816\) 3.11110 0.108910
\(817\) 17.0789 0.597514
\(818\) 58.0309 2.02900
\(819\) 9.68920 0.338568
\(820\) 47.8613 1.67139
\(821\) −51.1834 −1.78631 −0.893157 0.449746i \(-0.851515\pi\)
−0.893157 + 0.449746i \(0.851515\pi\)
\(822\) 36.0201 1.25634
\(823\) −41.6829 −1.45298 −0.726488 0.687179i \(-0.758849\pi\)
−0.726488 + 0.687179i \(0.758849\pi\)
\(824\) 11.8927 0.414301
\(825\) −12.5324 −0.436323
\(826\) −79.6329 −2.77078
\(827\) −33.8667 −1.17766 −0.588830 0.808257i \(-0.700411\pi\)
−0.588830 + 0.808257i \(0.700411\pi\)
\(828\) 15.2839 0.531151
\(829\) −26.7372 −0.928622 −0.464311 0.885672i \(-0.653698\pi\)
−0.464311 + 0.885672i \(0.653698\pi\)
\(830\) −2.03335 −0.0705787
\(831\) −28.7577 −0.997592
\(832\) −24.9706 −0.865699
\(833\) 6.99958 0.242521
\(834\) −51.3460 −1.77797
\(835\) −1.07049 −0.0370459
\(836\) −126.718 −4.38265
\(837\) −1.53032 −0.0528956
\(838\) 20.8455 0.720095
\(839\) −16.8465 −0.581605 −0.290803 0.956783i \(-0.593922\pi\)
−0.290803 + 0.956783i \(0.593922\pi\)
\(840\) −24.0293 −0.829091
\(841\) −22.4602 −0.774489
\(842\) 35.9454 1.23876
\(843\) −0.250260 −0.00861942
\(844\) −35.3837 −1.21796
\(845\) −9.04500 −0.311158
\(846\) −6.36031 −0.218672
\(847\) 27.0707 0.930160
\(848\) −2.52365 −0.0866626
\(849\) −18.1370 −0.622461
\(850\) 7.09717 0.243431
\(851\) −10.6785 −0.366056
\(852\) −5.24919 −0.179834
\(853\) −22.6295 −0.774818 −0.387409 0.921908i \(-0.626630\pi\)
−0.387409 + 0.921908i \(0.626630\pi\)
\(854\) −13.8520 −0.474006
\(855\) −11.0823 −0.379007
\(856\) −46.8871 −1.60257
\(857\) −35.5254 −1.21353 −0.606763 0.794883i \(-0.707532\pi\)
−0.606763 + 0.794883i \(0.707532\pi\)
\(858\) −26.7416 −0.912943
\(859\) 38.9522 1.32903 0.664516 0.747274i \(-0.268638\pi\)
0.664516 + 0.747274i \(0.268638\pi\)
\(860\) −12.2468 −0.417611
\(861\) 32.3839 1.10364
\(862\) −42.3061 −1.44095
\(863\) −40.9279 −1.39320 −0.696601 0.717458i \(-0.745305\pi\)
−0.696601 + 0.717458i \(0.745305\pi\)
\(864\) 1.41444 0.0481203
\(865\) 10.4028 0.353707
\(866\) 15.5318 0.527793
\(867\) 1.00000 0.0339618
\(868\) −22.0330 −0.747850
\(869\) 4.27025 0.144858
\(870\) 8.88720 0.301304
\(871\) 5.66302 0.191884
\(872\) −45.2261 −1.53155
\(873\) 1.60550 0.0543379
\(874\) 74.0718 2.50552
\(875\) −42.6652 −1.44235
\(876\) 12.8364 0.433702
\(877\) −30.4423 −1.02797 −0.513983 0.857801i \(-0.671830\pi\)
−0.513983 + 0.857801i \(0.671830\pi\)
\(878\) −27.2818 −0.920717
\(879\) 8.82213 0.297563
\(880\) 19.0918 0.643583
\(881\) −44.4180 −1.49648 −0.748241 0.663427i \(-0.769101\pi\)
−0.748241 + 0.663427i \(0.769101\pi\)
\(882\) −16.9268 −0.569956
\(883\) 2.84344 0.0956892 0.0478446 0.998855i \(-0.484765\pi\)
0.0478446 + 0.998855i \(0.484765\pi\)
\(884\) 9.96472 0.335150
\(885\) 12.6477 0.425146
\(886\) −45.0552 −1.51366
\(887\) −12.0071 −0.403159 −0.201580 0.979472i \(-0.564608\pi\)
−0.201580 + 0.979472i \(0.564608\pi\)
\(888\) 12.0149 0.403193
\(889\) 41.6789 1.39787
\(890\) −35.0546 −1.17503
\(891\) 4.27025 0.143059
\(892\) −16.9969 −0.569099
\(893\) −20.2827 −0.678735
\(894\) −10.4223 −0.348575
\(895\) −19.4008 −0.648499
\(896\) 76.6642 2.56117
\(897\) 10.2856 0.343425
\(898\) 69.2374 2.31048
\(899\) 3.91349 0.130522
\(900\) −11.2932 −0.376440
\(901\) −0.811178 −0.0270243
\(902\) −89.3775 −2.97595
\(903\) −8.28639 −0.275754
\(904\) −75.9903 −2.52740
\(905\) −27.7274 −0.921691
\(906\) 47.6973 1.58464
\(907\) 56.4484 1.87434 0.937168 0.348877i \(-0.113437\pi\)
0.937168 + 0.348877i \(0.113437\pi\)
\(908\) 35.0686 1.16379
\(909\) −16.1021 −0.534072
\(910\) −33.6721 −1.11622
\(911\) 20.1045 0.666091 0.333045 0.942911i \(-0.391924\pi\)
0.333045 + 0.942911i \(0.391924\pi\)
\(912\) −23.9919 −0.794452
\(913\) 2.49852 0.0826891
\(914\) 45.5270 1.50590
\(915\) 2.20004 0.0727310
\(916\) 59.2918 1.95905
\(917\) −8.88552 −0.293426
\(918\) −2.41826 −0.0798146
\(919\) 28.2551 0.932049 0.466025 0.884772i \(-0.345686\pi\)
0.466025 + 0.884772i \(0.345686\pi\)
\(920\) −25.5083 −0.840985
\(921\) −14.0933 −0.464390
\(922\) −45.4509 −1.49684
\(923\) −3.53254 −0.116275
\(924\) 61.4817 2.02260
\(925\) 7.89034 0.259433
\(926\) −68.8822 −2.26361
\(927\) −2.66118 −0.0874046
\(928\) −3.61716 −0.118739
\(929\) −4.72062 −0.154878 −0.0774392 0.996997i \(-0.524674\pi\)
−0.0774392 + 0.996997i \(0.524674\pi\)
\(930\) 5.31820 0.174391
\(931\) −53.9788 −1.76908
\(932\) −24.1581 −0.791325
\(933\) 8.54992 0.279912
\(934\) 74.2908 2.43087
\(935\) 6.13666 0.200690
\(936\) −11.5727 −0.378266
\(937\) 2.14740 0.0701524 0.0350762 0.999385i \(-0.488833\pi\)
0.0350762 + 0.999385i \(0.488833\pi\)
\(938\) −19.7870 −0.646067
\(939\) −20.4335 −0.666822
\(940\) 14.5441 0.474378
\(941\) 13.0863 0.426603 0.213301 0.976986i \(-0.431578\pi\)
0.213301 + 0.976986i \(0.431578\pi\)
\(942\) −35.5408 −1.15798
\(943\) 34.3771 1.11947
\(944\) 27.3807 0.891167
\(945\) 5.37695 0.174912
\(946\) 22.8699 0.743566
\(947\) −3.34712 −0.108767 −0.0543834 0.998520i \(-0.517319\pi\)
−0.0543834 + 0.998520i \(0.517319\pi\)
\(948\) 3.84800 0.124977
\(949\) 8.63850 0.280418
\(950\) −54.7314 −1.77572
\(951\) 18.3470 0.594943
\(952\) −16.7210 −0.541932
\(953\) 15.9799 0.517640 0.258820 0.965926i \(-0.416666\pi\)
0.258820 + 0.965926i \(0.416666\pi\)
\(954\) 1.96164 0.0635105
\(955\) −29.8804 −0.966905
\(956\) −38.9015 −1.25817
\(957\) −10.9203 −0.353004
\(958\) −57.8386 −1.86868
\(959\) −55.7312 −1.79965
\(960\) −13.8572 −0.447241
\(961\) −28.6581 −0.924456
\(962\) 16.8363 0.542825
\(963\) 10.4918 0.338092
\(964\) −65.5195 −2.11024
\(965\) 6.33406 0.203901
\(966\) −35.9384 −1.15630
\(967\) −38.5404 −1.23938 −0.619688 0.784848i \(-0.712741\pi\)
−0.619688 + 0.784848i \(0.712741\pi\)
\(968\) −32.3331 −1.03922
\(969\) −7.71172 −0.247736
\(970\) −5.57946 −0.179146
\(971\) 34.7449 1.11502 0.557508 0.830171i \(-0.311757\pi\)
0.557508 + 0.830171i \(0.311757\pi\)
\(972\) 3.84800 0.123425
\(973\) 79.4440 2.54686
\(974\) −18.0099 −0.577074
\(975\) −7.59997 −0.243394
\(976\) 4.76283 0.152455
\(977\) −31.7248 −1.01497 −0.507484 0.861661i \(-0.669424\pi\)
−0.507484 + 0.861661i \(0.669424\pi\)
\(978\) −0.168207 −0.00537868
\(979\) 43.0741 1.37665
\(980\) 38.7067 1.23644
\(981\) 10.1201 0.323109
\(982\) −30.5281 −0.974192
\(983\) 16.5416 0.527594 0.263797 0.964578i \(-0.415025\pi\)
0.263797 + 0.964578i \(0.415025\pi\)
\(984\) −38.6791 −1.23304
\(985\) 15.3787 0.490005
\(986\) 6.18424 0.196946
\(987\) 9.84084 0.313237
\(988\) −76.8452 −2.44477
\(989\) −8.79642 −0.279710
\(990\) −14.8401 −0.471648
\(991\) 10.7711 0.342157 0.171078 0.985257i \(-0.445275\pi\)
0.171078 + 0.985257i \(0.445275\pi\)
\(992\) −2.16455 −0.0687244
\(993\) 29.2454 0.928074
\(994\) 12.3429 0.391494
\(995\) 17.4454 0.553057
\(996\) 2.25146 0.0713404
\(997\) −17.2258 −0.545546 −0.272773 0.962078i \(-0.587941\pi\)
−0.272773 + 0.962078i \(0.587941\pi\)
\(998\) −75.8648 −2.40146
\(999\) −2.68852 −0.0850611
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.k.1.3 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.3 31 1.1 even 1 trivial