Properties

Label 6001.2.a.d.1.4
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66371 q^{2} -2.14217 q^{3} +5.09536 q^{4} -3.47946 q^{5} +5.70612 q^{6} -4.33919 q^{7} -8.24515 q^{8} +1.58889 q^{9} +O(q^{10})\) \(q-2.66371 q^{2} -2.14217 q^{3} +5.09536 q^{4} -3.47946 q^{5} +5.70612 q^{6} -4.33919 q^{7} -8.24515 q^{8} +1.58889 q^{9} +9.26828 q^{10} +0.107375 q^{11} -10.9151 q^{12} -4.16356 q^{13} +11.5584 q^{14} +7.45359 q^{15} +11.7720 q^{16} +1.00000 q^{17} -4.23236 q^{18} +4.46125 q^{19} -17.7291 q^{20} +9.29529 q^{21} -0.286015 q^{22} +4.06668 q^{23} +17.6625 q^{24} +7.10664 q^{25} +11.0905 q^{26} +3.02283 q^{27} -22.1097 q^{28} +7.04676 q^{29} -19.8542 q^{30} +5.21206 q^{31} -14.8669 q^{32} -0.230015 q^{33} -2.66371 q^{34} +15.0980 q^{35} +8.09599 q^{36} -1.68423 q^{37} -11.8835 q^{38} +8.91906 q^{39} +28.6887 q^{40} -0.249757 q^{41} -24.7600 q^{42} -10.7881 q^{43} +0.547113 q^{44} -5.52849 q^{45} -10.8325 q^{46} +13.0494 q^{47} -25.2176 q^{48} +11.8286 q^{49} -18.9300 q^{50} -2.14217 q^{51} -21.2149 q^{52} -3.53670 q^{53} -8.05195 q^{54} -0.373606 q^{55} +35.7773 q^{56} -9.55675 q^{57} -18.7705 q^{58} -9.90992 q^{59} +37.9787 q^{60} -11.5256 q^{61} -13.8834 q^{62} -6.89452 q^{63} +16.0571 q^{64} +14.4869 q^{65} +0.612693 q^{66} -6.10444 q^{67} +5.09536 q^{68} -8.71152 q^{69} -40.2168 q^{70} +6.93075 q^{71} -13.1007 q^{72} +5.78929 q^{73} +4.48629 q^{74} -15.2236 q^{75} +22.7317 q^{76} -0.465919 q^{77} -23.7578 q^{78} -12.8255 q^{79} -40.9601 q^{80} -11.2421 q^{81} +0.665282 q^{82} -6.26444 q^{83} +47.3628 q^{84} -3.47946 q^{85} +28.7363 q^{86} -15.0954 q^{87} -0.885320 q^{88} +15.7359 q^{89} +14.7263 q^{90} +18.0665 q^{91} +20.7212 q^{92} -11.1651 q^{93} -34.7598 q^{94} -15.5227 q^{95} +31.8473 q^{96} +4.41738 q^{97} -31.5079 q^{98} +0.170607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66371 −1.88353 −0.941764 0.336274i \(-0.890833\pi\)
−0.941764 + 0.336274i \(0.890833\pi\)
\(3\) −2.14217 −1.23678 −0.618391 0.785870i \(-0.712215\pi\)
−0.618391 + 0.785870i \(0.712215\pi\)
\(4\) 5.09536 2.54768
\(5\) −3.47946 −1.55606 −0.778031 0.628226i \(-0.783781\pi\)
−0.778031 + 0.628226i \(0.783781\pi\)
\(6\) 5.70612 2.32952
\(7\) −4.33919 −1.64006 −0.820030 0.572320i \(-0.806043\pi\)
−0.820030 + 0.572320i \(0.806043\pi\)
\(8\) −8.24515 −2.91510
\(9\) 1.58889 0.529631
\(10\) 9.26828 2.93089
\(11\) 0.107375 0.0323747 0.0161873 0.999869i \(-0.494847\pi\)
0.0161873 + 0.999869i \(0.494847\pi\)
\(12\) −10.9151 −3.15093
\(13\) −4.16356 −1.15476 −0.577382 0.816474i \(-0.695926\pi\)
−0.577382 + 0.816474i \(0.695926\pi\)
\(14\) 11.5584 3.08910
\(15\) 7.45359 1.92451
\(16\) 11.7720 2.94299
\(17\) 1.00000 0.242536
\(18\) −4.23236 −0.997576
\(19\) 4.46125 1.02348 0.511740 0.859140i \(-0.329001\pi\)
0.511740 + 0.859140i \(0.329001\pi\)
\(20\) −17.7291 −3.96435
\(21\) 9.29529 2.02840
\(22\) −0.286015 −0.0609786
\(23\) 4.06668 0.847962 0.423981 0.905671i \(-0.360632\pi\)
0.423981 + 0.905671i \(0.360632\pi\)
\(24\) 17.6625 3.60534
\(25\) 7.10664 1.42133
\(26\) 11.0905 2.17503
\(27\) 3.02283 0.581744
\(28\) −22.1097 −4.17835
\(29\) 7.04676 1.30855 0.654276 0.756256i \(-0.272974\pi\)
0.654276 + 0.756256i \(0.272974\pi\)
\(30\) −19.8542 −3.62487
\(31\) 5.21206 0.936114 0.468057 0.883698i \(-0.344954\pi\)
0.468057 + 0.883698i \(0.344954\pi\)
\(32\) −14.8669 −2.62811
\(33\) −0.230015 −0.0400404
\(34\) −2.66371 −0.456823
\(35\) 15.0980 2.55203
\(36\) 8.09599 1.34933
\(37\) −1.68423 −0.276885 −0.138443 0.990370i \(-0.544210\pi\)
−0.138443 + 0.990370i \(0.544210\pi\)
\(38\) −11.8835 −1.92775
\(39\) 8.91906 1.42819
\(40\) 28.6887 4.53607
\(41\) −0.249757 −0.0390056 −0.0195028 0.999810i \(-0.506208\pi\)
−0.0195028 + 0.999810i \(0.506208\pi\)
\(42\) −24.7600 −3.82055
\(43\) −10.7881 −1.64517 −0.822584 0.568644i \(-0.807468\pi\)
−0.822584 + 0.568644i \(0.807468\pi\)
\(44\) 0.547113 0.0824803
\(45\) −5.52849 −0.824139
\(46\) −10.8325 −1.59716
\(47\) 13.0494 1.90345 0.951723 0.306957i \(-0.0993109\pi\)
0.951723 + 0.306957i \(0.0993109\pi\)
\(48\) −25.2176 −3.63984
\(49\) 11.8286 1.68980
\(50\) −18.9300 −2.67711
\(51\) −2.14217 −0.299964
\(52\) −21.2149 −2.94197
\(53\) −3.53670 −0.485803 −0.242902 0.970051i \(-0.578099\pi\)
−0.242902 + 0.970051i \(0.578099\pi\)
\(54\) −8.05195 −1.09573
\(55\) −0.373606 −0.0503770
\(56\) 35.7773 4.78094
\(57\) −9.55675 −1.26582
\(58\) −18.7705 −2.46469
\(59\) −9.90992 −1.29016 −0.645081 0.764114i \(-0.723176\pi\)
−0.645081 + 0.764114i \(0.723176\pi\)
\(60\) 37.9787 4.90304
\(61\) −11.5256 −1.47570 −0.737851 0.674964i \(-0.764159\pi\)
−0.737851 + 0.674964i \(0.764159\pi\)
\(62\) −13.8834 −1.76320
\(63\) −6.89452 −0.868627
\(64\) 16.0571 2.00713
\(65\) 14.4869 1.79688
\(66\) 0.612693 0.0754173
\(67\) −6.10444 −0.745776 −0.372888 0.927876i \(-0.621632\pi\)
−0.372888 + 0.927876i \(0.621632\pi\)
\(68\) 5.09536 0.617903
\(69\) −8.71152 −1.04874
\(70\) −40.2168 −4.80683
\(71\) 6.93075 0.822529 0.411264 0.911516i \(-0.365087\pi\)
0.411264 + 0.911516i \(0.365087\pi\)
\(72\) −13.1007 −1.54393
\(73\) 5.78929 0.677585 0.338792 0.940861i \(-0.389982\pi\)
0.338792 + 0.940861i \(0.389982\pi\)
\(74\) 4.48629 0.521521
\(75\) −15.2236 −1.75787
\(76\) 22.7317 2.60750
\(77\) −0.465919 −0.0530964
\(78\) −23.7578 −2.69004
\(79\) −12.8255 −1.44298 −0.721491 0.692423i \(-0.756543\pi\)
−0.721491 + 0.692423i \(0.756543\pi\)
\(80\) −40.9601 −4.57948
\(81\) −11.2421 −1.24912
\(82\) 0.665282 0.0734681
\(83\) −6.26444 −0.687612 −0.343806 0.939041i \(-0.611716\pi\)
−0.343806 + 0.939041i \(0.611716\pi\)
\(84\) 47.3628 5.16771
\(85\) −3.47946 −0.377400
\(86\) 28.7363 3.09872
\(87\) −15.0954 −1.61839
\(88\) −0.885320 −0.0943754
\(89\) 15.7359 1.66800 0.833999 0.551766i \(-0.186046\pi\)
0.833999 + 0.551766i \(0.186046\pi\)
\(90\) 14.7263 1.55229
\(91\) 18.0665 1.89388
\(92\) 20.7212 2.16034
\(93\) −11.1651 −1.15777
\(94\) −34.7598 −3.58520
\(95\) −15.5227 −1.59260
\(96\) 31.8473 3.25040
\(97\) 4.41738 0.448517 0.224259 0.974530i \(-0.428004\pi\)
0.224259 + 0.974530i \(0.428004\pi\)
\(98\) −31.5079 −3.18278
\(99\) 0.170607 0.0171466
\(100\) 36.2109 3.62109
\(101\) −9.87180 −0.982281 −0.491140 0.871080i \(-0.663420\pi\)
−0.491140 + 0.871080i \(0.663420\pi\)
\(102\) 5.70612 0.564990
\(103\) −5.00059 −0.492722 −0.246361 0.969178i \(-0.579235\pi\)
−0.246361 + 0.969178i \(0.579235\pi\)
\(104\) 34.3292 3.36625
\(105\) −32.3426 −3.15631
\(106\) 9.42076 0.915025
\(107\) −14.7928 −1.43008 −0.715039 0.699084i \(-0.753591\pi\)
−0.715039 + 0.699084i \(0.753591\pi\)
\(108\) 15.4024 1.48210
\(109\) 3.83758 0.367573 0.183787 0.982966i \(-0.441164\pi\)
0.183787 + 0.982966i \(0.441164\pi\)
\(110\) 0.995178 0.0948865
\(111\) 3.60790 0.342447
\(112\) −51.0809 −4.82669
\(113\) 15.1635 1.42646 0.713232 0.700929i \(-0.247231\pi\)
0.713232 + 0.700929i \(0.247231\pi\)
\(114\) 25.4564 2.38421
\(115\) −14.1499 −1.31948
\(116\) 35.9058 3.33377
\(117\) −6.61546 −0.611600
\(118\) 26.3972 2.43006
\(119\) −4.33919 −0.397773
\(120\) −61.4560 −5.61014
\(121\) −10.9885 −0.998952
\(122\) 30.7009 2.77953
\(123\) 0.535023 0.0482414
\(124\) 26.5573 2.38492
\(125\) −7.32996 −0.655612
\(126\) 18.3650 1.63608
\(127\) −8.74930 −0.776375 −0.388187 0.921580i \(-0.626899\pi\)
−0.388187 + 0.921580i \(0.626899\pi\)
\(128\) −13.0377 −1.15238
\(129\) 23.1099 2.03471
\(130\) −38.5891 −3.38448
\(131\) −19.0364 −1.66322 −0.831608 0.555362i \(-0.812580\pi\)
−0.831608 + 0.555362i \(0.812580\pi\)
\(132\) −1.17201 −0.102010
\(133\) −19.3582 −1.67857
\(134\) 16.2605 1.40469
\(135\) −10.5178 −0.905229
\(136\) −8.24515 −0.707016
\(137\) −9.89062 −0.845012 −0.422506 0.906360i \(-0.638850\pi\)
−0.422506 + 0.906360i \(0.638850\pi\)
\(138\) 23.2050 1.97534
\(139\) 10.2455 0.869008 0.434504 0.900670i \(-0.356924\pi\)
0.434504 + 0.900670i \(0.356924\pi\)
\(140\) 76.9300 6.50177
\(141\) −27.9540 −2.35415
\(142\) −18.4615 −1.54926
\(143\) −0.447061 −0.0373851
\(144\) 18.7044 1.55870
\(145\) −24.5189 −2.03619
\(146\) −15.4210 −1.27625
\(147\) −25.3388 −2.08991
\(148\) −8.58174 −0.705415
\(149\) 16.6339 1.36270 0.681350 0.731957i \(-0.261393\pi\)
0.681350 + 0.731957i \(0.261393\pi\)
\(150\) 40.5514 3.31100
\(151\) −15.7251 −1.27969 −0.639845 0.768504i \(-0.721002\pi\)
−0.639845 + 0.768504i \(0.721002\pi\)
\(152\) −36.7836 −2.98355
\(153\) 1.58889 0.128454
\(154\) 1.24107 0.100009
\(155\) −18.1352 −1.45665
\(156\) 45.4458 3.63858
\(157\) 11.3060 0.902319 0.451159 0.892443i \(-0.351011\pi\)
0.451159 + 0.892443i \(0.351011\pi\)
\(158\) 34.1635 2.71790
\(159\) 7.57622 0.600833
\(160\) 51.7286 4.08951
\(161\) −17.6461 −1.39071
\(162\) 29.9457 2.35276
\(163\) 17.5592 1.37534 0.687670 0.726024i \(-0.258634\pi\)
0.687670 + 0.726024i \(0.258634\pi\)
\(164\) −1.27260 −0.0993737
\(165\) 0.800327 0.0623054
\(166\) 16.6867 1.29514
\(167\) 7.46380 0.577566 0.288783 0.957395i \(-0.406749\pi\)
0.288783 + 0.957395i \(0.406749\pi\)
\(168\) −76.6410 −5.91298
\(169\) 4.33526 0.333481
\(170\) 9.26828 0.710844
\(171\) 7.08845 0.542067
\(172\) −54.9692 −4.19136
\(173\) 7.43932 0.565601 0.282800 0.959179i \(-0.408737\pi\)
0.282800 + 0.959179i \(0.408737\pi\)
\(174\) 40.2097 3.04829
\(175\) −30.8371 −2.33106
\(176\) 1.26401 0.0952785
\(177\) 21.2287 1.59565
\(178\) −41.9158 −3.14172
\(179\) 18.2448 1.36368 0.681842 0.731500i \(-0.261179\pi\)
0.681842 + 0.731500i \(0.261179\pi\)
\(180\) −28.1697 −2.09964
\(181\) 3.46671 0.257679 0.128839 0.991665i \(-0.458875\pi\)
0.128839 + 0.991665i \(0.458875\pi\)
\(182\) −48.1239 −3.56718
\(183\) 24.6898 1.82512
\(184\) −33.5304 −2.47189
\(185\) 5.86020 0.430850
\(186\) 29.7407 2.18069
\(187\) 0.107375 0.00785201
\(188\) 66.4913 4.84937
\(189\) −13.1166 −0.954095
\(190\) 41.3481 2.99971
\(191\) 22.4947 1.62766 0.813830 0.581103i \(-0.197379\pi\)
0.813830 + 0.581103i \(0.197379\pi\)
\(192\) −34.3970 −2.48239
\(193\) 21.7503 1.56562 0.782810 0.622261i \(-0.213786\pi\)
0.782810 + 0.622261i \(0.213786\pi\)
\(194\) −11.7666 −0.844796
\(195\) −31.0335 −2.22236
\(196\) 60.2709 4.30506
\(197\) 14.0463 1.00076 0.500380 0.865806i \(-0.333194\pi\)
0.500380 + 0.865806i \(0.333194\pi\)
\(198\) −0.454448 −0.0322962
\(199\) −5.37630 −0.381116 −0.190558 0.981676i \(-0.561030\pi\)
−0.190558 + 0.981676i \(0.561030\pi\)
\(200\) −58.5953 −4.14331
\(201\) 13.0767 0.922363
\(202\) 26.2956 1.85015
\(203\) −30.5773 −2.14610
\(204\) −10.9151 −0.764212
\(205\) 0.869021 0.0606951
\(206\) 13.3201 0.928057
\(207\) 6.46153 0.449107
\(208\) −49.0134 −3.39846
\(209\) 0.479025 0.0331349
\(210\) 86.1513 5.94500
\(211\) −16.7705 −1.15453 −0.577264 0.816558i \(-0.695880\pi\)
−0.577264 + 0.816558i \(0.695880\pi\)
\(212\) −18.0208 −1.23767
\(213\) −14.8468 −1.01729
\(214\) 39.4039 2.69359
\(215\) 37.5367 2.55998
\(216\) −24.9237 −1.69584
\(217\) −22.6161 −1.53528
\(218\) −10.2222 −0.692335
\(219\) −12.4016 −0.838025
\(220\) −1.90366 −0.128344
\(221\) −4.16356 −0.280072
\(222\) −9.61041 −0.645008
\(223\) 13.8527 0.927645 0.463822 0.885928i \(-0.346478\pi\)
0.463822 + 0.885928i \(0.346478\pi\)
\(224\) 64.5101 4.31026
\(225\) 11.2917 0.752780
\(226\) −40.3912 −2.68678
\(227\) 3.05127 0.202520 0.101260 0.994860i \(-0.467713\pi\)
0.101260 + 0.994860i \(0.467713\pi\)
\(228\) −48.6951 −3.22491
\(229\) −9.75011 −0.644305 −0.322153 0.946688i \(-0.604406\pi\)
−0.322153 + 0.946688i \(0.604406\pi\)
\(230\) 37.6911 2.48528
\(231\) 0.998078 0.0656687
\(232\) −58.1016 −3.81456
\(233\) −13.1687 −0.862709 −0.431355 0.902182i \(-0.641964\pi\)
−0.431355 + 0.902182i \(0.641964\pi\)
\(234\) 17.6217 1.15197
\(235\) −45.4048 −2.96188
\(236\) −50.4946 −3.28692
\(237\) 27.4744 1.78466
\(238\) 11.5584 0.749217
\(239\) 14.5922 0.943888 0.471944 0.881629i \(-0.343552\pi\)
0.471944 + 0.881629i \(0.343552\pi\)
\(240\) 87.7435 5.66382
\(241\) −12.7327 −0.820185 −0.410093 0.912044i \(-0.634504\pi\)
−0.410093 + 0.912044i \(0.634504\pi\)
\(242\) 29.2701 1.88155
\(243\) 15.0140 0.963149
\(244\) −58.7271 −3.75962
\(245\) −41.1571 −2.62943
\(246\) −1.42515 −0.0908641
\(247\) −18.5747 −1.18188
\(248\) −42.9742 −2.72887
\(249\) 13.4195 0.850426
\(250\) 19.5249 1.23486
\(251\) 9.20328 0.580906 0.290453 0.956889i \(-0.406194\pi\)
0.290453 + 0.956889i \(0.406194\pi\)
\(252\) −35.1300 −2.21298
\(253\) 0.436659 0.0274525
\(254\) 23.3056 1.46232
\(255\) 7.45359 0.466762
\(256\) 2.61448 0.163405
\(257\) −25.1389 −1.56812 −0.784060 0.620686i \(-0.786854\pi\)
−0.784060 + 0.620686i \(0.786854\pi\)
\(258\) −61.5581 −3.83244
\(259\) 7.30818 0.454108
\(260\) 73.8162 4.57789
\(261\) 11.1966 0.693050
\(262\) 50.7074 3.13272
\(263\) −23.4570 −1.44642 −0.723209 0.690629i \(-0.757334\pi\)
−0.723209 + 0.690629i \(0.757334\pi\)
\(264\) 1.89651 0.116722
\(265\) 12.3058 0.755940
\(266\) 51.5647 3.16163
\(267\) −33.7089 −2.06295
\(268\) −31.1043 −1.90000
\(269\) −24.9789 −1.52299 −0.761496 0.648169i \(-0.775535\pi\)
−0.761496 + 0.648169i \(0.775535\pi\)
\(270\) 28.0164 1.70503
\(271\) −17.9907 −1.09286 −0.546430 0.837505i \(-0.684014\pi\)
−0.546430 + 0.837505i \(0.684014\pi\)
\(272\) 11.7720 0.713781
\(273\) −38.7015 −2.34232
\(274\) 26.3457 1.59160
\(275\) 0.763073 0.0460150
\(276\) −44.3884 −2.67186
\(277\) 20.1356 1.20983 0.604916 0.796290i \(-0.293207\pi\)
0.604916 + 0.796290i \(0.293207\pi\)
\(278\) −27.2909 −1.63680
\(279\) 8.28142 0.495795
\(280\) −124.486 −7.43944
\(281\) −13.9460 −0.831950 −0.415975 0.909376i \(-0.636560\pi\)
−0.415975 + 0.909376i \(0.636560\pi\)
\(282\) 74.4613 4.43411
\(283\) −3.74443 −0.222583 −0.111292 0.993788i \(-0.535499\pi\)
−0.111292 + 0.993788i \(0.535499\pi\)
\(284\) 35.3147 2.09554
\(285\) 33.2523 1.96970
\(286\) 1.19084 0.0704160
\(287\) 1.08375 0.0639715
\(288\) −23.6219 −1.39193
\(289\) 1.00000 0.0588235
\(290\) 65.3114 3.83522
\(291\) −9.46279 −0.554719
\(292\) 29.4985 1.72627
\(293\) −25.4953 −1.48945 −0.744725 0.667371i \(-0.767419\pi\)
−0.744725 + 0.667371i \(0.767419\pi\)
\(294\) 67.4954 3.93641
\(295\) 34.4812 2.00757
\(296\) 13.8867 0.807148
\(297\) 0.324575 0.0188338
\(298\) −44.3079 −2.56669
\(299\) −16.9319 −0.979196
\(300\) −77.5699 −4.47850
\(301\) 46.8116 2.69817
\(302\) 41.8871 2.41033
\(303\) 21.1471 1.21487
\(304\) 52.5177 3.01210
\(305\) 40.1029 2.29628
\(306\) −4.23236 −0.241948
\(307\) −5.63105 −0.321381 −0.160691 0.987005i \(-0.551372\pi\)
−0.160691 + 0.987005i \(0.551372\pi\)
\(308\) −2.37403 −0.135273
\(309\) 10.7121 0.609390
\(310\) 48.3068 2.74364
\(311\) 26.7825 1.51869 0.759347 0.650686i \(-0.225518\pi\)
0.759347 + 0.650686i \(0.225518\pi\)
\(312\) −73.5390 −4.16332
\(313\) 1.36924 0.0773938 0.0386969 0.999251i \(-0.487679\pi\)
0.0386969 + 0.999251i \(0.487679\pi\)
\(314\) −30.1160 −1.69954
\(315\) 23.9892 1.35164
\(316\) −65.3506 −3.67626
\(317\) 12.2841 0.689944 0.344972 0.938613i \(-0.387888\pi\)
0.344972 + 0.938613i \(0.387888\pi\)
\(318\) −20.1809 −1.13169
\(319\) 0.756644 0.0423639
\(320\) −55.8699 −3.12322
\(321\) 31.6888 1.76870
\(322\) 47.0042 2.61944
\(323\) 4.46125 0.248230
\(324\) −57.2825 −3.18236
\(325\) −29.5889 −1.64130
\(326\) −46.7725 −2.59049
\(327\) −8.22074 −0.454608
\(328\) 2.05929 0.113705
\(329\) −56.6237 −3.12177
\(330\) −2.13184 −0.117354
\(331\) −7.37182 −0.405192 −0.202596 0.979262i \(-0.564938\pi\)
−0.202596 + 0.979262i \(0.564938\pi\)
\(332\) −31.9196 −1.75181
\(333\) −2.67606 −0.146647
\(334\) −19.8814 −1.08786
\(335\) 21.2402 1.16047
\(336\) 109.424 5.96956
\(337\) −23.4917 −1.27967 −0.639837 0.768510i \(-0.720998\pi\)
−0.639837 + 0.768510i \(0.720998\pi\)
\(338\) −11.5479 −0.628122
\(339\) −32.4828 −1.76422
\(340\) −17.7291 −0.961495
\(341\) 0.559644 0.0303064
\(342\) −18.8816 −1.02100
\(343\) −20.9522 −1.13131
\(344\) 88.9493 4.79583
\(345\) 30.3114 1.63191
\(346\) −19.8162 −1.06533
\(347\) −22.0907 −1.18589 −0.592944 0.805243i \(-0.702035\pi\)
−0.592944 + 0.805243i \(0.702035\pi\)
\(348\) −76.9163 −4.12315
\(349\) 6.77381 0.362593 0.181297 0.983428i \(-0.441971\pi\)
0.181297 + 0.983428i \(0.441971\pi\)
\(350\) 82.1411 4.39062
\(351\) −12.5857 −0.671777
\(352\) −1.59632 −0.0850843
\(353\) −1.00000 −0.0532246
\(354\) −56.5472 −3.00545
\(355\) −24.1153 −1.27991
\(356\) 80.1799 4.24953
\(357\) 9.29529 0.491959
\(358\) −48.5990 −2.56854
\(359\) −2.23522 −0.117970 −0.0589851 0.998259i \(-0.518786\pi\)
−0.0589851 + 0.998259i \(0.518786\pi\)
\(360\) 45.5832 2.40245
\(361\) 0.902737 0.0475125
\(362\) −9.23432 −0.485345
\(363\) 23.5392 1.23549
\(364\) 92.0553 4.82501
\(365\) −20.1436 −1.05436
\(366\) −65.7665 −3.43767
\(367\) 14.5305 0.758484 0.379242 0.925297i \(-0.376185\pi\)
0.379242 + 0.925297i \(0.376185\pi\)
\(368\) 47.8729 2.49555
\(369\) −0.396838 −0.0206586
\(370\) −15.6099 −0.811519
\(371\) 15.3464 0.796747
\(372\) −56.8903 −2.94963
\(373\) 0.722633 0.0374165 0.0187083 0.999825i \(-0.494045\pi\)
0.0187083 + 0.999825i \(0.494045\pi\)
\(374\) −0.286015 −0.0147895
\(375\) 15.7020 0.810849
\(376\) −107.594 −5.54874
\(377\) −29.3396 −1.51107
\(378\) 34.9389 1.79707
\(379\) 0.337308 0.0173263 0.00866317 0.999962i \(-0.497242\pi\)
0.00866317 + 0.999962i \(0.497242\pi\)
\(380\) −79.0939 −4.05743
\(381\) 18.7425 0.960207
\(382\) −59.9194 −3.06574
\(383\) 2.84622 0.145435 0.0727175 0.997353i \(-0.476833\pi\)
0.0727175 + 0.997353i \(0.476833\pi\)
\(384\) 27.9289 1.42524
\(385\) 1.62115 0.0826213
\(386\) −57.9365 −2.94889
\(387\) −17.1411 −0.871332
\(388\) 22.5082 1.14268
\(389\) 6.95745 0.352757 0.176378 0.984322i \(-0.443562\pi\)
0.176378 + 0.984322i \(0.443562\pi\)
\(390\) 82.6643 4.18587
\(391\) 4.06668 0.205661
\(392\) −97.5284 −4.92593
\(393\) 40.7792 2.05704
\(394\) −37.4154 −1.88496
\(395\) 44.6258 2.24537
\(396\) 0.869304 0.0436842
\(397\) −33.2791 −1.67023 −0.835116 0.550074i \(-0.814599\pi\)
−0.835116 + 0.550074i \(0.814599\pi\)
\(398\) 14.3209 0.717843
\(399\) 41.4686 2.07603
\(400\) 83.6592 4.18296
\(401\) −24.1828 −1.20763 −0.603815 0.797125i \(-0.706353\pi\)
−0.603815 + 0.797125i \(0.706353\pi\)
\(402\) −34.8327 −1.73730
\(403\) −21.7008 −1.08099
\(404\) −50.3004 −2.50254
\(405\) 39.1164 1.94371
\(406\) 81.4490 4.04225
\(407\) −0.180843 −0.00896407
\(408\) 17.6625 0.874425
\(409\) −0.0721842 −0.00356928 −0.00178464 0.999998i \(-0.500568\pi\)
−0.00178464 + 0.999998i \(0.500568\pi\)
\(410\) −2.31482 −0.114321
\(411\) 21.1874 1.04510
\(412\) −25.4798 −1.25530
\(413\) 43.0010 2.11594
\(414\) −17.2116 −0.845906
\(415\) 21.7969 1.06997
\(416\) 61.8991 3.03485
\(417\) −21.9475 −1.07477
\(418\) −1.27598 −0.0624104
\(419\) −19.1459 −0.935341 −0.467670 0.883903i \(-0.654907\pi\)
−0.467670 + 0.883903i \(0.654907\pi\)
\(420\) −164.797 −8.04127
\(421\) −34.4401 −1.67851 −0.839254 0.543739i \(-0.817008\pi\)
−0.839254 + 0.543739i \(0.817008\pi\)
\(422\) 44.6717 2.17459
\(423\) 20.7341 1.00812
\(424\) 29.1606 1.41617
\(425\) 7.10664 0.344723
\(426\) 39.5477 1.91609
\(427\) 50.0118 2.42024
\(428\) −75.3749 −3.64338
\(429\) 0.957681 0.0462373
\(430\) −99.9869 −4.82180
\(431\) −13.6659 −0.658262 −0.329131 0.944284i \(-0.606756\pi\)
−0.329131 + 0.944284i \(0.606756\pi\)
\(432\) 35.5847 1.71207
\(433\) 10.9637 0.526879 0.263440 0.964676i \(-0.415143\pi\)
0.263440 + 0.964676i \(0.415143\pi\)
\(434\) 60.2429 2.89175
\(435\) 52.5237 2.51832
\(436\) 19.5538 0.936459
\(437\) 18.1425 0.867872
\(438\) 33.0344 1.57844
\(439\) 3.63913 0.173686 0.0868431 0.996222i \(-0.472322\pi\)
0.0868431 + 0.996222i \(0.472322\pi\)
\(440\) 3.08043 0.146854
\(441\) 18.7944 0.894970
\(442\) 11.0905 0.527523
\(443\) 5.89216 0.279945 0.139973 0.990155i \(-0.455299\pi\)
0.139973 + 0.990155i \(0.455299\pi\)
\(444\) 18.3836 0.872445
\(445\) −54.7523 −2.59551
\(446\) −36.8996 −1.74725
\(447\) −35.6326 −1.68536
\(448\) −69.6747 −3.29182
\(449\) 33.7957 1.59492 0.797460 0.603372i \(-0.206177\pi\)
0.797460 + 0.603372i \(0.206177\pi\)
\(450\) −30.0778 −1.41788
\(451\) −0.0268176 −0.00126279
\(452\) 77.2635 3.63417
\(453\) 33.6859 1.58270
\(454\) −8.12771 −0.381452
\(455\) −62.8617 −2.94700
\(456\) 78.7968 3.69000
\(457\) −35.9823 −1.68318 −0.841590 0.540116i \(-0.818380\pi\)
−0.841590 + 0.540116i \(0.818380\pi\)
\(458\) 25.9715 1.21357
\(459\) 3.02283 0.141094
\(460\) −72.0986 −3.36161
\(461\) 19.1568 0.892221 0.446110 0.894978i \(-0.352809\pi\)
0.446110 + 0.894978i \(0.352809\pi\)
\(462\) −2.65859 −0.123689
\(463\) −11.0864 −0.515230 −0.257615 0.966248i \(-0.582937\pi\)
−0.257615 + 0.966248i \(0.582937\pi\)
\(464\) 82.9543 3.85106
\(465\) 38.8486 1.80156
\(466\) 35.0776 1.62494
\(467\) 15.3154 0.708714 0.354357 0.935110i \(-0.384700\pi\)
0.354357 + 0.935110i \(0.384700\pi\)
\(468\) −33.7082 −1.55816
\(469\) 26.4883 1.22312
\(470\) 120.945 5.57879
\(471\) −24.2194 −1.11597
\(472\) 81.7087 3.76095
\(473\) −1.15837 −0.0532618
\(474\) −73.1840 −3.36145
\(475\) 31.7045 1.45470
\(476\) −22.1097 −1.01340
\(477\) −5.61945 −0.257297
\(478\) −38.8693 −1.77784
\(479\) 20.0057 0.914083 0.457041 0.889445i \(-0.348909\pi\)
0.457041 + 0.889445i \(0.348909\pi\)
\(480\) −110.811 −5.05783
\(481\) 7.01239 0.319737
\(482\) 33.9162 1.54484
\(483\) 37.8010 1.72000
\(484\) −55.9902 −2.54501
\(485\) −15.3701 −0.697921
\(486\) −39.9930 −1.81412
\(487\) 32.0094 1.45049 0.725243 0.688493i \(-0.241728\pi\)
0.725243 + 0.688493i \(0.241728\pi\)
\(488\) 95.0303 4.30182
\(489\) −37.6147 −1.70100
\(490\) 109.631 4.95261
\(491\) 26.4712 1.19463 0.597315 0.802007i \(-0.296234\pi\)
0.597315 + 0.802007i \(0.296234\pi\)
\(492\) 2.72614 0.122904
\(493\) 7.04676 0.317370
\(494\) 49.4776 2.22610
\(495\) −0.593620 −0.0266812
\(496\) 61.3563 2.75498
\(497\) −30.0739 −1.34900
\(498\) −35.7457 −1.60180
\(499\) −14.2651 −0.638595 −0.319298 0.947654i \(-0.603447\pi\)
−0.319298 + 0.947654i \(0.603447\pi\)
\(500\) −37.3488 −1.67029
\(501\) −15.9887 −0.714324
\(502\) −24.5149 −1.09415
\(503\) 14.3195 0.638477 0.319238 0.947674i \(-0.396573\pi\)
0.319238 + 0.947674i \(0.396573\pi\)
\(504\) 56.8463 2.53214
\(505\) 34.3485 1.52849
\(506\) −1.16313 −0.0517075
\(507\) −9.28686 −0.412444
\(508\) −44.5808 −1.97795
\(509\) −27.3140 −1.21067 −0.605337 0.795970i \(-0.706961\pi\)
−0.605337 + 0.795970i \(0.706961\pi\)
\(510\) −19.8542 −0.879160
\(511\) −25.1208 −1.11128
\(512\) 19.1111 0.844600
\(513\) 13.4856 0.595404
\(514\) 66.9627 2.95360
\(515\) 17.3993 0.766706
\(516\) 117.753 5.18380
\(517\) 1.40117 0.0616235
\(518\) −19.4669 −0.855326
\(519\) −15.9363 −0.699525
\(520\) −119.447 −5.23810
\(521\) −11.2984 −0.494993 −0.247497 0.968889i \(-0.579608\pi\)
−0.247497 + 0.968889i \(0.579608\pi\)
\(522\) −29.8244 −1.30538
\(523\) 27.5978 1.20677 0.603385 0.797450i \(-0.293818\pi\)
0.603385 + 0.797450i \(0.293818\pi\)
\(524\) −96.9972 −4.23734
\(525\) 66.0582 2.88302
\(526\) 62.4826 2.72437
\(527\) 5.21206 0.227041
\(528\) −2.70773 −0.117839
\(529\) −6.46210 −0.280961
\(530\) −32.7791 −1.42383
\(531\) −15.7458 −0.683310
\(532\) −98.6371 −4.27646
\(533\) 1.03988 0.0450422
\(534\) 89.7908 3.88563
\(535\) 51.4711 2.22529
\(536\) 50.3320 2.17401
\(537\) −39.0836 −1.68658
\(538\) 66.5367 2.86860
\(539\) 1.27009 0.0547067
\(540\) −53.5920 −2.30623
\(541\) −7.26006 −0.312134 −0.156067 0.987746i \(-0.549882\pi\)
−0.156067 + 0.987746i \(0.549882\pi\)
\(542\) 47.9222 2.05843
\(543\) −7.42629 −0.318692
\(544\) −14.8669 −0.637411
\(545\) −13.3527 −0.571967
\(546\) 103.090 4.41183
\(547\) 42.6554 1.82381 0.911906 0.410399i \(-0.134611\pi\)
0.911906 + 0.410399i \(0.134611\pi\)
\(548\) −50.3962 −2.15282
\(549\) −18.3130 −0.781578
\(550\) −2.03261 −0.0866706
\(551\) 31.4374 1.33928
\(552\) 71.8278 3.05719
\(553\) 55.6524 2.36658
\(554\) −53.6354 −2.27875
\(555\) −12.5535 −0.532868
\(556\) 52.2043 2.21395
\(557\) 24.4792 1.03722 0.518609 0.855012i \(-0.326450\pi\)
0.518609 + 0.855012i \(0.326450\pi\)
\(558\) −22.0593 −0.933845
\(559\) 44.9169 1.89978
\(560\) 177.734 7.51062
\(561\) −0.230015 −0.00971123
\(562\) 37.1482 1.56700
\(563\) −38.9746 −1.64258 −0.821291 0.570510i \(-0.806746\pi\)
−0.821291 + 0.570510i \(0.806746\pi\)
\(564\) −142.436 −5.99762
\(565\) −52.7608 −2.21966
\(566\) 9.97408 0.419242
\(567\) 48.7816 2.04864
\(568\) −57.1450 −2.39775
\(569\) −40.7485 −1.70826 −0.854132 0.520056i \(-0.825911\pi\)
−0.854132 + 0.520056i \(0.825911\pi\)
\(570\) −88.5746 −3.70998
\(571\) 13.4416 0.562515 0.281257 0.959632i \(-0.409249\pi\)
0.281257 + 0.959632i \(0.409249\pi\)
\(572\) −2.27794 −0.0952454
\(573\) −48.1875 −2.01306
\(574\) −2.88679 −0.120492
\(575\) 28.9004 1.20523
\(576\) 25.5130 1.06304
\(577\) −19.6633 −0.818593 −0.409297 0.912401i \(-0.634226\pi\)
−0.409297 + 0.912401i \(0.634226\pi\)
\(578\) −2.66371 −0.110796
\(579\) −46.5928 −1.93633
\(580\) −124.933 −5.18755
\(581\) 27.1826 1.12772
\(582\) 25.2061 1.04483
\(583\) −0.379752 −0.0157277
\(584\) −47.7335 −1.97523
\(585\) 23.0182 0.951686
\(586\) 67.9121 2.80542
\(587\) −13.2802 −0.548133 −0.274067 0.961711i \(-0.588369\pi\)
−0.274067 + 0.961711i \(0.588369\pi\)
\(588\) −129.111 −5.32443
\(589\) 23.2523 0.958095
\(590\) −91.8479 −3.78132
\(591\) −30.0897 −1.23772
\(592\) −19.8267 −0.814871
\(593\) −2.22802 −0.0914937 −0.0457469 0.998953i \(-0.514567\pi\)
−0.0457469 + 0.998953i \(0.514567\pi\)
\(594\) −0.864575 −0.0354739
\(595\) 15.0980 0.618959
\(596\) 84.7556 3.47173
\(597\) 11.5170 0.471358
\(598\) 45.1017 1.84434
\(599\) −18.8120 −0.768636 −0.384318 0.923201i \(-0.625563\pi\)
−0.384318 + 0.923201i \(0.625563\pi\)
\(600\) 125.521 5.12438
\(601\) 20.2967 0.827918 0.413959 0.910296i \(-0.364146\pi\)
0.413959 + 0.910296i \(0.364146\pi\)
\(602\) −124.693 −5.08209
\(603\) −9.69931 −0.394986
\(604\) −80.1251 −3.26024
\(605\) 38.2339 1.55443
\(606\) −56.3297 −2.28824
\(607\) 42.2314 1.71412 0.857059 0.515218i \(-0.172289\pi\)
0.857059 + 0.515218i \(0.172289\pi\)
\(608\) −66.3247 −2.68982
\(609\) 65.5017 2.65426
\(610\) −106.822 −4.32511
\(611\) −54.3319 −2.19803
\(612\) 8.09599 0.327261
\(613\) 7.24682 0.292696 0.146348 0.989233i \(-0.453248\pi\)
0.146348 + 0.989233i \(0.453248\pi\)
\(614\) 14.9995 0.605330
\(615\) −1.86159 −0.0750666
\(616\) 3.84157 0.154781
\(617\) −6.94633 −0.279649 −0.139824 0.990176i \(-0.544654\pi\)
−0.139824 + 0.990176i \(0.544654\pi\)
\(618\) −28.5340 −1.14780
\(619\) −9.04042 −0.363365 −0.181683 0.983357i \(-0.558154\pi\)
−0.181683 + 0.983357i \(0.558154\pi\)
\(620\) −92.4052 −3.71108
\(621\) 12.2929 0.493296
\(622\) −71.3408 −2.86050
\(623\) −68.2809 −2.73562
\(624\) 104.995 4.20316
\(625\) −10.0289 −0.401156
\(626\) −3.64725 −0.145773
\(627\) −1.02615 −0.0409806
\(628\) 57.6083 2.29882
\(629\) −1.68423 −0.0671545
\(630\) −63.9003 −2.54585
\(631\) −6.02879 −0.240002 −0.120001 0.992774i \(-0.538290\pi\)
−0.120001 + 0.992774i \(0.538290\pi\)
\(632\) 105.748 4.20644
\(633\) 35.9252 1.42790
\(634\) −32.7213 −1.29953
\(635\) 30.4428 1.20809
\(636\) 38.6036 1.53073
\(637\) −49.2491 −1.95132
\(638\) −2.01548 −0.0797937
\(639\) 11.0122 0.435637
\(640\) 45.3641 1.79317
\(641\) −7.05661 −0.278719 −0.139360 0.990242i \(-0.544504\pi\)
−0.139360 + 0.990242i \(0.544504\pi\)
\(642\) −84.4098 −3.33139
\(643\) −14.4408 −0.569489 −0.284745 0.958603i \(-0.591909\pi\)
−0.284745 + 0.958603i \(0.591909\pi\)
\(644\) −89.9133 −3.54308
\(645\) −80.4100 −3.16614
\(646\) −11.8835 −0.467549
\(647\) 41.8281 1.64443 0.822216 0.569175i \(-0.192737\pi\)
0.822216 + 0.569175i \(0.192737\pi\)
\(648\) 92.6927 3.64132
\(649\) −1.06407 −0.0417686
\(650\) 78.8164 3.09143
\(651\) 48.4476 1.89881
\(652\) 89.4702 3.50392
\(653\) 1.12686 0.0440975 0.0220488 0.999757i \(-0.492981\pi\)
0.0220488 + 0.999757i \(0.492981\pi\)
\(654\) 21.8977 0.856268
\(655\) 66.2363 2.58807
\(656\) −2.94014 −0.114793
\(657\) 9.19856 0.358870
\(658\) 150.829 5.87994
\(659\) 3.31591 0.129170 0.0645848 0.997912i \(-0.479428\pi\)
0.0645848 + 0.997912i \(0.479428\pi\)
\(660\) 4.07796 0.158734
\(661\) 36.8442 1.43307 0.716537 0.697549i \(-0.245726\pi\)
0.716537 + 0.697549i \(0.245726\pi\)
\(662\) 19.6364 0.763190
\(663\) 8.91906 0.346388
\(664\) 51.6512 2.00446
\(665\) 67.3561 2.61196
\(666\) 7.12825 0.276214
\(667\) 28.6569 1.10960
\(668\) 38.0307 1.47145
\(669\) −29.6748 −1.14730
\(670\) −56.5776 −2.18578
\(671\) −1.23756 −0.0477754
\(672\) −138.192 −5.33086
\(673\) 41.1993 1.58812 0.794058 0.607842i \(-0.207965\pi\)
0.794058 + 0.607842i \(0.207965\pi\)
\(674\) 62.5751 2.41030
\(675\) 21.4822 0.826849
\(676\) 22.0897 0.849604
\(677\) −45.0236 −1.73040 −0.865198 0.501431i \(-0.832807\pi\)
−0.865198 + 0.501431i \(0.832807\pi\)
\(678\) 86.5249 3.32297
\(679\) −19.1679 −0.735596
\(680\) 28.6887 1.10016
\(681\) −6.53635 −0.250473
\(682\) −1.49073 −0.0570830
\(683\) 19.0097 0.727386 0.363693 0.931519i \(-0.381516\pi\)
0.363693 + 0.931519i \(0.381516\pi\)
\(684\) 36.1182 1.38101
\(685\) 34.4140 1.31489
\(686\) 55.8105 2.13086
\(687\) 20.8864 0.796866
\(688\) −126.997 −4.84172
\(689\) 14.7253 0.560989
\(690\) −80.7408 −3.07375
\(691\) 23.3578 0.888572 0.444286 0.895885i \(-0.353457\pi\)
0.444286 + 0.895885i \(0.353457\pi\)
\(692\) 37.9060 1.44097
\(693\) −0.740296 −0.0281215
\(694\) 58.8431 2.23366
\(695\) −35.6486 −1.35223
\(696\) 124.464 4.71778
\(697\) −0.249757 −0.00946024
\(698\) −18.0435 −0.682955
\(699\) 28.2096 1.06698
\(700\) −157.126 −5.93880
\(701\) −19.7073 −0.744334 −0.372167 0.928166i \(-0.621385\pi\)
−0.372167 + 0.928166i \(0.621385\pi\)
\(702\) 33.5248 1.26531
\(703\) −7.51375 −0.283387
\(704\) 1.72412 0.0649803
\(705\) 97.2647 3.66320
\(706\) 2.66371 0.100250
\(707\) 42.8356 1.61100
\(708\) 108.168 4.06520
\(709\) −21.2053 −0.796380 −0.398190 0.917303i \(-0.630362\pi\)
−0.398190 + 0.917303i \(0.630362\pi\)
\(710\) 64.2361 2.41074
\(711\) −20.3784 −0.764249
\(712\) −129.745 −4.86238
\(713\) 21.1958 0.793789
\(714\) −24.7600 −0.926619
\(715\) 1.55553 0.0581736
\(716\) 92.9640 3.47423
\(717\) −31.2589 −1.16738
\(718\) 5.95398 0.222200
\(719\) 42.8397 1.59765 0.798826 0.601563i \(-0.205455\pi\)
0.798826 + 0.601563i \(0.205455\pi\)
\(720\) −65.0813 −2.42544
\(721\) 21.6985 0.808094
\(722\) −2.40463 −0.0894911
\(723\) 27.2756 1.01439
\(724\) 17.6641 0.656483
\(725\) 50.0788 1.85988
\(726\) −62.7016 −2.32707
\(727\) 2.25209 0.0835253 0.0417627 0.999128i \(-0.486703\pi\)
0.0417627 + 0.999128i \(0.486703\pi\)
\(728\) −148.961 −5.52086
\(729\) 1.56375 0.0579166
\(730\) 53.6567 1.98592
\(731\) −10.7881 −0.399012
\(732\) 125.803 4.64983
\(733\) −23.3510 −0.862488 −0.431244 0.902235i \(-0.641925\pi\)
−0.431244 + 0.902235i \(0.641925\pi\)
\(734\) −38.7050 −1.42863
\(735\) 88.1655 3.25203
\(736\) −60.4588 −2.22854
\(737\) −0.655462 −0.0241443
\(738\) 1.05706 0.0389110
\(739\) −29.1945 −1.07394 −0.536969 0.843602i \(-0.680431\pi\)
−0.536969 + 0.843602i \(0.680431\pi\)
\(740\) 29.8598 1.09767
\(741\) 39.7901 1.46173
\(742\) −40.8785 −1.50070
\(743\) 12.4480 0.456674 0.228337 0.973582i \(-0.426671\pi\)
0.228337 + 0.973582i \(0.426671\pi\)
\(744\) 92.0581 3.37501
\(745\) −57.8769 −2.12045
\(746\) −1.92489 −0.0704751
\(747\) −9.95353 −0.364181
\(748\) 0.547113 0.0200044
\(749\) 64.1890 2.34541
\(750\) −41.8257 −1.52726
\(751\) −9.62616 −0.351264 −0.175632 0.984456i \(-0.556197\pi\)
−0.175632 + 0.984456i \(0.556197\pi\)
\(752\) 153.617 5.60183
\(753\) −19.7150 −0.718455
\(754\) 78.1524 2.84614
\(755\) 54.7149 1.99128
\(756\) −66.8340 −2.43073
\(757\) −51.8366 −1.88403 −0.942017 0.335564i \(-0.891073\pi\)
−0.942017 + 0.335564i \(0.891073\pi\)
\(758\) −0.898491 −0.0326347
\(759\) −0.935397 −0.0339528
\(760\) 127.987 4.64258
\(761\) 7.61783 0.276146 0.138073 0.990422i \(-0.455909\pi\)
0.138073 + 0.990422i \(0.455909\pi\)
\(762\) −49.9246 −1.80858
\(763\) −16.6520 −0.602842
\(764\) 114.619 4.14676
\(765\) −5.52849 −0.199883
\(766\) −7.58151 −0.273931
\(767\) 41.2606 1.48983
\(768\) −5.60067 −0.202097
\(769\) −21.9534 −0.791660 −0.395830 0.918324i \(-0.629543\pi\)
−0.395830 + 0.918324i \(0.629543\pi\)
\(770\) −4.31827 −0.155620
\(771\) 53.8517 1.93942
\(772\) 110.826 3.98870
\(773\) −32.4934 −1.16871 −0.584354 0.811499i \(-0.698652\pi\)
−0.584354 + 0.811499i \(0.698652\pi\)
\(774\) 45.6590 1.64118
\(775\) 37.0402 1.33052
\(776\) −36.4220 −1.30747
\(777\) −15.6554 −0.561633
\(778\) −18.5326 −0.664427
\(779\) −1.11423 −0.0399214
\(780\) −158.127 −5.66185
\(781\) 0.744187 0.0266291
\(782\) −10.8325 −0.387368
\(783\) 21.3012 0.761242
\(784\) 139.246 4.97306
\(785\) −39.3388 −1.40406
\(786\) −108.624 −3.87449
\(787\) 43.1998 1.53991 0.769953 0.638101i \(-0.220280\pi\)
0.769953 + 0.638101i \(0.220280\pi\)
\(788\) 71.5712 2.54962
\(789\) 50.2488 1.78890
\(790\) −118.870 −4.22922
\(791\) −65.7974 −2.33949
\(792\) −1.40668 −0.0499842
\(793\) 47.9876 1.70409
\(794\) 88.6460 3.14593
\(795\) −26.3612 −0.934934
\(796\) −27.3942 −0.970962
\(797\) −22.1213 −0.783578 −0.391789 0.920055i \(-0.628144\pi\)
−0.391789 + 0.920055i \(0.628144\pi\)
\(798\) −110.460 −3.91025
\(799\) 13.0494 0.461654
\(800\) −105.653 −3.73541
\(801\) 25.0026 0.883424
\(802\) 64.4159 2.27460
\(803\) 0.621623 0.0219366
\(804\) 66.6308 2.34989
\(805\) 61.3989 2.16403
\(806\) 57.8046 2.03608
\(807\) 53.5091 1.88361
\(808\) 81.3945 2.86345
\(809\) −11.6081 −0.408120 −0.204060 0.978958i \(-0.565414\pi\)
−0.204060 + 0.978958i \(0.565414\pi\)
\(810\) −104.195 −3.66103
\(811\) 15.7909 0.554492 0.277246 0.960799i \(-0.410578\pi\)
0.277246 + 0.960799i \(0.410578\pi\)
\(812\) −155.802 −5.46758
\(813\) 38.5392 1.35163
\(814\) 0.481714 0.0168841
\(815\) −61.0964 −2.14011
\(816\) −25.2176 −0.882792
\(817\) −48.1283 −1.68380
\(818\) 0.192278 0.00672284
\(819\) 28.7058 1.00306
\(820\) 4.42797 0.154632
\(821\) −39.5939 −1.38184 −0.690918 0.722933i \(-0.742793\pi\)
−0.690918 + 0.722933i \(0.742793\pi\)
\(822\) −56.4371 −1.96847
\(823\) −46.4395 −1.61878 −0.809389 0.587273i \(-0.800201\pi\)
−0.809389 + 0.587273i \(0.800201\pi\)
\(824\) 41.2306 1.43633
\(825\) −1.63463 −0.0569106
\(826\) −114.542 −3.98544
\(827\) 1.38325 0.0481004 0.0240502 0.999711i \(-0.492344\pi\)
0.0240502 + 0.999711i \(0.492344\pi\)
\(828\) 32.9238 1.14418
\(829\) −40.4611 −1.40527 −0.702637 0.711549i \(-0.747994\pi\)
−0.702637 + 0.711549i \(0.747994\pi\)
\(830\) −58.0606 −2.01531
\(831\) −43.1339 −1.49630
\(832\) −66.8546 −2.31777
\(833\) 11.8286 0.409836
\(834\) 58.4618 2.02437
\(835\) −25.9700 −0.898728
\(836\) 2.44080 0.0844170
\(837\) 15.7552 0.544579
\(838\) 50.9993 1.76174
\(839\) −4.68742 −0.161828 −0.0809138 0.996721i \(-0.525784\pi\)
−0.0809138 + 0.996721i \(0.525784\pi\)
\(840\) 266.669 9.20097
\(841\) 20.6569 0.712306
\(842\) 91.7385 3.16152
\(843\) 29.8748 1.02894
\(844\) −85.4516 −2.94137
\(845\) −15.0844 −0.518918
\(846\) −55.2296 −1.89883
\(847\) 47.6811 1.63834
\(848\) −41.6340 −1.42972
\(849\) 8.02121 0.275287
\(850\) −18.9300 −0.649295
\(851\) −6.84921 −0.234788
\(852\) −75.6500 −2.59173
\(853\) −39.5992 −1.35585 −0.677926 0.735130i \(-0.737121\pi\)
−0.677926 + 0.735130i \(0.737121\pi\)
\(854\) −133.217 −4.55859
\(855\) −24.6640 −0.843490
\(856\) 121.969 4.16882
\(857\) −36.1159 −1.23370 −0.616848 0.787082i \(-0.711591\pi\)
−0.616848 + 0.787082i \(0.711591\pi\)
\(858\) −2.55099 −0.0870892
\(859\) −9.45099 −0.322464 −0.161232 0.986917i \(-0.551547\pi\)
−0.161232 + 0.986917i \(0.551547\pi\)
\(860\) 191.263 6.52201
\(861\) −2.32157 −0.0791188
\(862\) 36.4019 1.23986
\(863\) 22.5235 0.766707 0.383354 0.923602i \(-0.374769\pi\)
0.383354 + 0.923602i \(0.374769\pi\)
\(864\) −44.9400 −1.52889
\(865\) −25.8848 −0.880109
\(866\) −29.2040 −0.992392
\(867\) −2.14217 −0.0727519
\(868\) −115.237 −3.91141
\(869\) −1.37713 −0.0467161
\(870\) −139.908 −4.74333
\(871\) 25.4162 0.861196
\(872\) −31.6414 −1.07151
\(873\) 7.01876 0.237549
\(874\) −48.3263 −1.63466
\(875\) 31.8061 1.07524
\(876\) −63.1908 −2.13502
\(877\) −13.5387 −0.457169 −0.228585 0.973524i \(-0.573410\pi\)
−0.228585 + 0.973524i \(0.573410\pi\)
\(878\) −9.69359 −0.327143
\(879\) 54.6152 1.84213
\(880\) −4.39808 −0.148259
\(881\) 30.3322 1.02192 0.510960 0.859605i \(-0.329290\pi\)
0.510960 + 0.859605i \(0.329290\pi\)
\(882\) −50.0628 −1.68570
\(883\) −25.9146 −0.872097 −0.436048 0.899923i \(-0.643622\pi\)
−0.436048 + 0.899923i \(0.643622\pi\)
\(884\) −21.2149 −0.713533
\(885\) −73.8645 −2.48293
\(886\) −15.6950 −0.527285
\(887\) 30.4774 1.02333 0.511666 0.859185i \(-0.329029\pi\)
0.511666 + 0.859185i \(0.329029\pi\)
\(888\) −29.7477 −0.998267
\(889\) 37.9649 1.27330
\(890\) 145.844 4.88871
\(891\) −1.20712 −0.0404399
\(892\) 70.5845 2.36334
\(893\) 58.2165 1.94814
\(894\) 94.9150 3.17443
\(895\) −63.4822 −2.12198
\(896\) 56.5730 1.88997
\(897\) 36.2710 1.21105
\(898\) −90.0221 −3.00408
\(899\) 36.7282 1.22495
\(900\) 57.5352 1.91784
\(901\) −3.53670 −0.117825
\(902\) 0.0714344 0.00237851
\(903\) −100.278 −3.33705
\(904\) −125.025 −4.15828
\(905\) −12.0623 −0.400964
\(906\) −89.7294 −2.98106
\(907\) −13.8322 −0.459292 −0.229646 0.973274i \(-0.573757\pi\)
−0.229646 + 0.973274i \(0.573757\pi\)
\(908\) 15.5473 0.515956
\(909\) −15.6852 −0.520247
\(910\) 167.445 5.55076
\(911\) −18.5334 −0.614038 −0.307019 0.951703i \(-0.599332\pi\)
−0.307019 + 0.951703i \(0.599332\pi\)
\(912\) −112.502 −3.72531
\(913\) −0.672642 −0.0222612
\(914\) 95.8465 3.17032
\(915\) −85.9071 −2.84000
\(916\) −49.6803 −1.64148
\(917\) 82.6025 2.72778
\(918\) −8.05195 −0.265754
\(919\) 52.3403 1.72655 0.863274 0.504736i \(-0.168410\pi\)
0.863274 + 0.504736i \(0.168410\pi\)
\(920\) 116.668 3.84642
\(921\) 12.0627 0.397479
\(922\) −51.0282 −1.68052
\(923\) −28.8566 −0.949827
\(924\) 5.08557 0.167303
\(925\) −11.9692 −0.393545
\(926\) 29.5311 0.970451
\(927\) −7.94540 −0.260961
\(928\) −104.763 −3.43902
\(929\) −21.2353 −0.696706 −0.348353 0.937363i \(-0.613259\pi\)
−0.348353 + 0.937363i \(0.613259\pi\)
\(930\) −103.481 −3.39329
\(931\) 52.7703 1.72948
\(932\) −67.0992 −2.19791
\(933\) −57.3726 −1.87830
\(934\) −40.7959 −1.33488
\(935\) −0.373606 −0.0122182
\(936\) 54.5454 1.78287
\(937\) −18.3183 −0.598433 −0.299217 0.954185i \(-0.596725\pi\)
−0.299217 + 0.954185i \(0.596725\pi\)
\(938\) −70.5573 −2.30378
\(939\) −2.93314 −0.0957193
\(940\) −231.354 −7.54592
\(941\) 29.0984 0.948582 0.474291 0.880368i \(-0.342705\pi\)
0.474291 + 0.880368i \(0.342705\pi\)
\(942\) 64.5136 2.10197
\(943\) −1.01568 −0.0330752
\(944\) −116.659 −3.79694
\(945\) 45.6388 1.48463
\(946\) 3.08556 0.100320
\(947\) −48.6699 −1.58156 −0.790780 0.612100i \(-0.790325\pi\)
−0.790780 + 0.612100i \(0.790325\pi\)
\(948\) 139.992 4.54673
\(949\) −24.1041 −0.782451
\(950\) −84.4516 −2.73997
\(951\) −26.3147 −0.853311
\(952\) 35.7773 1.15955
\(953\) 0.235312 0.00762251 0.00381126 0.999993i \(-0.498787\pi\)
0.00381126 + 0.999993i \(0.498787\pi\)
\(954\) 14.9686 0.484626
\(955\) −78.2694 −2.53274
\(956\) 74.3523 2.40472
\(957\) −1.62086 −0.0523950
\(958\) −53.2894 −1.72170
\(959\) 42.9173 1.38587
\(960\) 119.683 3.86275
\(961\) −3.83440 −0.123690
\(962\) −18.6790 −0.602234
\(963\) −23.5043 −0.757414
\(964\) −64.8777 −2.08957
\(965\) −75.6793 −2.43620
\(966\) −100.691 −3.23968
\(967\) −42.0355 −1.35177 −0.675885 0.737007i \(-0.736239\pi\)
−0.675885 + 0.737007i \(0.736239\pi\)
\(968\) 90.6016 2.91204
\(969\) −9.55675 −0.307007
\(970\) 40.9415 1.31455
\(971\) 25.6222 0.822255 0.411128 0.911578i \(-0.365135\pi\)
0.411128 + 0.911578i \(0.365135\pi\)
\(972\) 76.5017 2.45379
\(973\) −44.4570 −1.42523
\(974\) −85.2639 −2.73203
\(975\) 63.3845 2.02993
\(976\) −135.679 −4.34298
\(977\) 1.66752 0.0533485 0.0266743 0.999644i \(-0.491508\pi\)
0.0266743 + 0.999644i \(0.491508\pi\)
\(978\) 100.195 3.20387
\(979\) 1.68963 0.0540009
\(980\) −209.710 −6.69895
\(981\) 6.09750 0.194678
\(982\) −70.5117 −2.25012
\(983\) −8.40787 −0.268169 −0.134085 0.990970i \(-0.542809\pi\)
−0.134085 + 0.990970i \(0.542809\pi\)
\(984\) −4.41134 −0.140628
\(985\) −48.8737 −1.55724
\(986\) −18.7705 −0.597776
\(987\) 121.298 3.86095
\(988\) −94.6447 −3.01105
\(989\) −43.8717 −1.39504
\(990\) 1.58123 0.0502549
\(991\) −25.5265 −0.810877 −0.405438 0.914122i \(-0.632881\pi\)
−0.405438 + 0.914122i \(0.632881\pi\)
\(992\) −77.4870 −2.46021
\(993\) 15.7917 0.501134
\(994\) 80.1081 2.54087
\(995\) 18.7066 0.593040
\(996\) 68.3772 2.16661
\(997\) −18.6529 −0.590744 −0.295372 0.955382i \(-0.595444\pi\)
−0.295372 + 0.955382i \(0.595444\pi\)
\(998\) 37.9982 1.20281
\(999\) −5.09113 −0.161076
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 6001.2.a.d.1.4 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.4 121 1.1 even 1 trivial