Properties

Label 4027.2.a.c.1.9
Level 4027
Weight 2
Character 4027.1
Self dual yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.53459 q^{2} +2.56413 q^{3} +4.42415 q^{4} -2.01095 q^{5} -6.49903 q^{6} -2.72523 q^{7} -6.14422 q^{8} +3.57478 q^{9} +O(q^{10})\) \(q-2.53459 q^{2} +2.56413 q^{3} +4.42415 q^{4} -2.01095 q^{5} -6.49903 q^{6} -2.72523 q^{7} -6.14422 q^{8} +3.57478 q^{9} +5.09695 q^{10} -5.31951 q^{11} +11.3441 q^{12} -4.97223 q^{13} +6.90734 q^{14} -5.15635 q^{15} +6.72478 q^{16} +5.38535 q^{17} -9.06060 q^{18} -4.08068 q^{19} -8.89676 q^{20} -6.98785 q^{21} +13.4828 q^{22} -3.66483 q^{23} -15.7546 q^{24} -0.956062 q^{25} +12.6026 q^{26} +1.47381 q^{27} -12.0568 q^{28} +4.17497 q^{29} +13.0692 q^{30} +3.40622 q^{31} -4.75613 q^{32} -13.6399 q^{33} -13.6496 q^{34} +5.48031 q^{35} +15.8153 q^{36} -0.551233 q^{37} +10.3428 q^{38} -12.7495 q^{39} +12.3557 q^{40} +0.256698 q^{41} +17.7113 q^{42} +1.62862 q^{43} -23.5343 q^{44} -7.18872 q^{45} +9.28884 q^{46} +8.56541 q^{47} +17.2432 q^{48} +0.426869 q^{49} +2.42322 q^{50} +13.8087 q^{51} -21.9979 q^{52} -1.26818 q^{53} -3.73550 q^{54} +10.6973 q^{55} +16.7444 q^{56} -10.4634 q^{57} -10.5818 q^{58} -2.84160 q^{59} -22.8125 q^{60} +4.17697 q^{61} -8.63337 q^{62} -9.74209 q^{63} -1.39472 q^{64} +9.99893 q^{65} +34.5716 q^{66} -9.17328 q^{67} +23.8256 q^{68} -9.39711 q^{69} -13.8903 q^{70} -4.31676 q^{71} -21.9642 q^{72} +2.53212 q^{73} +1.39715 q^{74} -2.45147 q^{75} -18.0535 q^{76} +14.4969 q^{77} +32.3146 q^{78} +6.09135 q^{79} -13.5232 q^{80} -6.94530 q^{81} -0.650623 q^{82} +6.95608 q^{83} -30.9153 q^{84} -10.8297 q^{85} -4.12788 q^{86} +10.7052 q^{87} +32.6842 q^{88} -2.68794 q^{89} +18.2204 q^{90} +13.5505 q^{91} -16.2137 q^{92} +8.73400 q^{93} -21.7098 q^{94} +8.20606 q^{95} -12.1954 q^{96} -10.1869 q^{97} -1.08194 q^{98} -19.0161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + O(q^{10}) \) \( 174q + 21q^{2} + 17q^{3} + 187q^{4} + 72q^{5} + 21q^{6} + 24q^{7} + 54q^{8} + 197q^{9} + 20q^{10} + 35q^{11} + 23q^{12} + 91q^{13} + 18q^{14} + 16q^{15} + 201q^{16} + 148q^{17} + 39q^{18} + 36q^{19} + 128q^{20} + 57q^{21} + 17q^{22} + 96q^{23} + 24q^{24} + 226q^{25} + 44q^{26} + 62q^{27} + 32q^{28} + 122q^{29} + 25q^{30} + 23q^{31} + 104q^{32} + 91q^{33} + 6q^{34} + 80q^{35} + 222q^{36} + 71q^{37} + 125q^{38} + 16q^{39} + 53q^{40} + 97q^{41} + 14q^{42} + 38q^{43} + 70q^{44} + 185q^{45} - 23q^{46} + 110q^{47} + 36q^{48} + 210q^{49} + 51q^{50} + 33q^{51} + 118q^{52} + 214q^{53} + 8q^{54} + 37q^{55} + 41q^{56} + 76q^{57} + 2q^{58} + 66q^{59} - 12q^{60} + 114q^{61} + 175q^{62} + 62q^{63} + 190q^{64} + 128q^{65} + 12q^{66} - 6q^{67} + 348q^{68} + 115q^{69} - 38q^{70} + 54q^{71} + 101q^{72} + 107q^{73} + 71q^{74} - q^{75} + 31q^{76} + 368q^{77} - 14q^{78} - 14q^{79} + 205q^{80} + 222q^{81} + 26q^{82} + 246q^{83} + 41q^{84} + 87q^{85} + 33q^{86} + 100q^{87} - 6q^{88} + 147q^{89} + 50q^{90} - 23q^{91} + 189q^{92} + 117q^{93} + 23q^{94} + 42q^{95} + 38q^{96} + 52q^{97} + 148q^{98} + 38q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53459 −1.79223 −0.896113 0.443826i \(-0.853621\pi\)
−0.896113 + 0.443826i \(0.853621\pi\)
\(3\) 2.56413 1.48040 0.740201 0.672385i \(-0.234730\pi\)
0.740201 + 0.672385i \(0.234730\pi\)
\(4\) 4.42415 2.21207
\(5\) −2.01095 −0.899326 −0.449663 0.893198i \(-0.648456\pi\)
−0.449663 + 0.893198i \(0.648456\pi\)
\(6\) −6.49903 −2.65322
\(7\) −2.72523 −1.03004 −0.515020 0.857178i \(-0.672215\pi\)
−0.515020 + 0.857178i \(0.672215\pi\)
\(8\) −6.14422 −2.17231
\(9\) 3.57478 1.19159
\(10\) 5.09695 1.61180
\(11\) −5.31951 −1.60389 −0.801947 0.597396i \(-0.796202\pi\)
−0.801947 + 0.597396i \(0.796202\pi\)
\(12\) 11.3441 3.27476
\(13\) −4.97223 −1.37905 −0.689524 0.724263i \(-0.742180\pi\)
−0.689524 + 0.724263i \(0.742180\pi\)
\(14\) 6.90734 1.84606
\(15\) −5.15635 −1.33137
\(16\) 6.72478 1.68120
\(17\) 5.38535 1.30614 0.653069 0.757298i \(-0.273481\pi\)
0.653069 + 0.757298i \(0.273481\pi\)
\(18\) −9.06060 −2.13560
\(19\) −4.08068 −0.936172 −0.468086 0.883683i \(-0.655056\pi\)
−0.468086 + 0.883683i \(0.655056\pi\)
\(20\) −8.89676 −1.98938
\(21\) −6.98785 −1.52487
\(22\) 13.4828 2.87454
\(23\) −3.66483 −0.764170 −0.382085 0.924127i \(-0.624794\pi\)
−0.382085 + 0.924127i \(0.624794\pi\)
\(24\) −15.7546 −3.21589
\(25\) −0.956062 −0.191212
\(26\) 12.6026 2.47157
\(27\) 1.47381 0.283634
\(28\) −12.0568 −2.27852
\(29\) 4.17497 0.775272 0.387636 0.921812i \(-0.373292\pi\)
0.387636 + 0.921812i \(0.373292\pi\)
\(30\) 13.0692 2.38611
\(31\) 3.40622 0.611775 0.305888 0.952068i \(-0.401047\pi\)
0.305888 + 0.952068i \(0.401047\pi\)
\(32\) −4.75613 −0.840773
\(33\) −13.6399 −2.37441
\(34\) −13.6496 −2.34090
\(35\) 5.48031 0.926341
\(36\) 15.8153 2.63589
\(37\) −0.551233 −0.0906221 −0.0453110 0.998973i \(-0.514428\pi\)
−0.0453110 + 0.998973i \(0.514428\pi\)
\(38\) 10.3428 1.67783
\(39\) −12.7495 −2.04155
\(40\) 12.3557 1.95361
\(41\) 0.256698 0.0400894 0.0200447 0.999799i \(-0.493619\pi\)
0.0200447 + 0.999799i \(0.493619\pi\)
\(42\) 17.7113 2.73292
\(43\) 1.62862 0.248362 0.124181 0.992260i \(-0.460370\pi\)
0.124181 + 0.992260i \(0.460370\pi\)
\(44\) −23.5343 −3.54793
\(45\) −7.18872 −1.07163
\(46\) 9.28884 1.36957
\(47\) 8.56541 1.24939 0.624697 0.780867i \(-0.285223\pi\)
0.624697 + 0.780867i \(0.285223\pi\)
\(48\) 17.2432 2.48885
\(49\) 0.426869 0.0609813
\(50\) 2.42322 0.342696
\(51\) 13.8087 1.93361
\(52\) −21.9979 −3.05056
\(53\) −1.26818 −0.174199 −0.0870993 0.996200i \(-0.527760\pi\)
−0.0870993 + 0.996200i \(0.527760\pi\)
\(54\) −3.73550 −0.508337
\(55\) 10.6973 1.44242
\(56\) 16.7444 2.23756
\(57\) −10.4634 −1.38591
\(58\) −10.5818 −1.38946
\(59\) −2.84160 −0.369945 −0.184973 0.982744i \(-0.559220\pi\)
−0.184973 + 0.982744i \(0.559220\pi\)
\(60\) −22.8125 −2.94508
\(61\) 4.17697 0.534806 0.267403 0.963585i \(-0.413835\pi\)
0.267403 + 0.963585i \(0.413835\pi\)
\(62\) −8.63337 −1.09644
\(63\) −9.74209 −1.22739
\(64\) −1.39472 −0.174340
\(65\) 9.99893 1.24021
\(66\) 34.5716 4.25548
\(67\) −9.17328 −1.12069 −0.560347 0.828258i \(-0.689332\pi\)
−0.560347 + 0.828258i \(0.689332\pi\)
\(68\) 23.8256 2.88927
\(69\) −9.39711 −1.13128
\(70\) −13.8903 −1.66021
\(71\) −4.31676 −0.512305 −0.256153 0.966636i \(-0.582455\pi\)
−0.256153 + 0.966636i \(0.582455\pi\)
\(72\) −21.9642 −2.58851
\(73\) 2.53212 0.296362 0.148181 0.988960i \(-0.452658\pi\)
0.148181 + 0.988960i \(0.452658\pi\)
\(74\) 1.39715 0.162415
\(75\) −2.45147 −0.283071
\(76\) −18.0535 −2.07088
\(77\) 14.4969 1.65207
\(78\) 32.3146 3.65891
\(79\) 6.09135 0.685330 0.342665 0.939458i \(-0.388670\pi\)
0.342665 + 0.939458i \(0.388670\pi\)
\(80\) −13.5232 −1.51194
\(81\) −6.94530 −0.771700
\(82\) −0.650623 −0.0718493
\(83\) 6.95608 0.763529 0.381764 0.924260i \(-0.375317\pi\)
0.381764 + 0.924260i \(0.375317\pi\)
\(84\) −30.9153 −3.37313
\(85\) −10.8297 −1.17464
\(86\) −4.12788 −0.445121
\(87\) 10.7052 1.14772
\(88\) 32.6842 3.48415
\(89\) −2.68794 −0.284921 −0.142461 0.989800i \(-0.545501\pi\)
−0.142461 + 0.989800i \(0.545501\pi\)
\(90\) 18.2204 1.92060
\(91\) 13.5505 1.42047
\(92\) −16.2137 −1.69040
\(93\) 8.73400 0.905674
\(94\) −21.7098 −2.23920
\(95\) 8.20606 0.841924
\(96\) −12.1954 −1.24468
\(97\) −10.1869 −1.03433 −0.517163 0.855887i \(-0.673012\pi\)
−0.517163 + 0.855887i \(0.673012\pi\)
\(98\) −1.08194 −0.109292
\(99\) −19.0161 −1.91119
\(100\) −4.22976 −0.422976
\(101\) 10.7100 1.06569 0.532843 0.846214i \(-0.321124\pi\)
0.532843 + 0.846214i \(0.321124\pi\)
\(102\) −34.9995 −3.46547
\(103\) −1.68724 −0.166249 −0.0831245 0.996539i \(-0.526490\pi\)
−0.0831245 + 0.996539i \(0.526490\pi\)
\(104\) 30.5505 2.99572
\(105\) 14.0522 1.37136
\(106\) 3.21433 0.312203
\(107\) 15.3667 1.48555 0.742775 0.669541i \(-0.233509\pi\)
0.742775 + 0.669541i \(0.233509\pi\)
\(108\) 6.52034 0.627420
\(109\) −6.36460 −0.609618 −0.304809 0.952413i \(-0.598593\pi\)
−0.304809 + 0.952413i \(0.598593\pi\)
\(110\) −27.1133 −2.58515
\(111\) −1.41343 −0.134157
\(112\) −18.3266 −1.73170
\(113\) −7.23314 −0.680437 −0.340218 0.940346i \(-0.610501\pi\)
−0.340218 + 0.940346i \(0.610501\pi\)
\(114\) 26.5204 2.48387
\(115\) 7.36981 0.687238
\(116\) 18.4707 1.71496
\(117\) −17.7746 −1.64326
\(118\) 7.20230 0.663025
\(119\) −14.6763 −1.34537
\(120\) 31.6818 2.89214
\(121\) 17.2972 1.57247
\(122\) −10.5869 −0.958493
\(123\) 0.658207 0.0593485
\(124\) 15.0696 1.35329
\(125\) 11.9774 1.07129
\(126\) 24.6922 2.19976
\(127\) −14.7645 −1.31014 −0.655069 0.755569i \(-0.727360\pi\)
−0.655069 + 0.755569i \(0.727360\pi\)
\(128\) 13.0473 1.15323
\(129\) 4.17599 0.367676
\(130\) −25.3432 −2.22274
\(131\) 6.82979 0.596722 0.298361 0.954453i \(-0.403560\pi\)
0.298361 + 0.954453i \(0.403560\pi\)
\(132\) −60.3451 −5.25237
\(133\) 11.1208 0.964294
\(134\) 23.2505 2.00854
\(135\) −2.96376 −0.255080
\(136\) −33.0888 −2.83734
\(137\) 14.1299 1.20720 0.603601 0.797287i \(-0.293732\pi\)
0.603601 + 0.797287i \(0.293732\pi\)
\(138\) 23.8178 2.02751
\(139\) 3.79122 0.321567 0.160784 0.986990i \(-0.448598\pi\)
0.160784 + 0.986990i \(0.448598\pi\)
\(140\) 24.2457 2.04914
\(141\) 21.9629 1.84961
\(142\) 10.9412 0.918166
\(143\) 26.4498 2.21185
\(144\) 24.0396 2.00330
\(145\) −8.39567 −0.697223
\(146\) −6.41788 −0.531148
\(147\) 1.09455 0.0902768
\(148\) −2.43873 −0.200463
\(149\) −1.68530 −0.138065 −0.0690326 0.997614i \(-0.521991\pi\)
−0.0690326 + 0.997614i \(0.521991\pi\)
\(150\) 6.21347 0.507328
\(151\) 16.5292 1.34513 0.672564 0.740039i \(-0.265193\pi\)
0.672564 + 0.740039i \(0.265193\pi\)
\(152\) 25.0726 2.03366
\(153\) 19.2514 1.55639
\(154\) −36.7437 −2.96089
\(155\) −6.84975 −0.550185
\(156\) −56.4055 −4.51605
\(157\) 23.7652 1.89667 0.948334 0.317273i \(-0.102767\pi\)
0.948334 + 0.317273i \(0.102767\pi\)
\(158\) −15.4391 −1.22827
\(159\) −3.25179 −0.257884
\(160\) 9.56436 0.756129
\(161\) 9.98750 0.787125
\(162\) 17.6035 1.38306
\(163\) 13.4732 1.05530 0.527652 0.849460i \(-0.323072\pi\)
0.527652 + 0.849460i \(0.323072\pi\)
\(164\) 1.13567 0.0886807
\(165\) 27.4293 2.13537
\(166\) −17.6308 −1.36842
\(167\) 20.7333 1.60439 0.802195 0.597062i \(-0.203665\pi\)
0.802195 + 0.597062i \(0.203665\pi\)
\(168\) 42.9349 3.31250
\(169\) 11.7231 0.901774
\(170\) 27.4488 2.10523
\(171\) −14.5875 −1.11554
\(172\) 7.20525 0.549395
\(173\) 5.84549 0.444424 0.222212 0.974998i \(-0.428672\pi\)
0.222212 + 0.974998i \(0.428672\pi\)
\(174\) −27.1332 −2.05697
\(175\) 2.60549 0.196956
\(176\) −35.7726 −2.69646
\(177\) −7.28625 −0.547668
\(178\) 6.81283 0.510643
\(179\) −19.6199 −1.46646 −0.733231 0.679980i \(-0.761988\pi\)
−0.733231 + 0.679980i \(0.761988\pi\)
\(180\) −31.8039 −2.37053
\(181\) 13.3320 0.990962 0.495481 0.868619i \(-0.334992\pi\)
0.495481 + 0.868619i \(0.334992\pi\)
\(182\) −34.3449 −2.54581
\(183\) 10.7103 0.791728
\(184\) 22.5175 1.66001
\(185\) 1.10850 0.0814988
\(186\) −22.1371 −1.62317
\(187\) −28.6474 −2.09491
\(188\) 37.8946 2.76375
\(189\) −4.01646 −0.292155
\(190\) −20.7990 −1.50892
\(191\) 6.86299 0.496589 0.248294 0.968685i \(-0.420130\pi\)
0.248294 + 0.968685i \(0.420130\pi\)
\(192\) −3.57626 −0.258094
\(193\) −7.87184 −0.566628 −0.283314 0.959027i \(-0.591434\pi\)
−0.283314 + 0.959027i \(0.591434\pi\)
\(194\) 25.8197 1.85374
\(195\) 25.6386 1.83602
\(196\) 1.88853 0.134895
\(197\) 3.95538 0.281809 0.140905 0.990023i \(-0.454999\pi\)
0.140905 + 0.990023i \(0.454999\pi\)
\(198\) 48.1980 3.42528
\(199\) 8.97566 0.636267 0.318134 0.948046i \(-0.396944\pi\)
0.318134 + 0.948046i \(0.396944\pi\)
\(200\) 5.87425 0.415372
\(201\) −23.5215 −1.65908
\(202\) −27.1455 −1.90995
\(203\) −11.3777 −0.798561
\(204\) 61.0919 4.27729
\(205\) −0.516207 −0.0360535
\(206\) 4.27647 0.297956
\(207\) −13.1010 −0.910579
\(208\) −33.4372 −2.31845
\(209\) 21.7072 1.50152
\(210\) −35.6167 −2.45778
\(211\) −12.3541 −0.850489 −0.425245 0.905078i \(-0.639812\pi\)
−0.425245 + 0.905078i \(0.639812\pi\)
\(212\) −5.61064 −0.385340
\(213\) −11.0687 −0.758418
\(214\) −38.9482 −2.66244
\(215\) −3.27508 −0.223358
\(216\) −9.05539 −0.616142
\(217\) −9.28273 −0.630152
\(218\) 16.1317 1.09257
\(219\) 6.49269 0.438735
\(220\) 47.3264 3.19075
\(221\) −26.7772 −1.80123
\(222\) 3.58248 0.240440
\(223\) −24.6174 −1.64850 −0.824252 0.566224i \(-0.808404\pi\)
−0.824252 + 0.566224i \(0.808404\pi\)
\(224\) 12.9615 0.866030
\(225\) −3.41771 −0.227847
\(226\) 18.3330 1.21950
\(227\) 1.91492 0.127097 0.0635487 0.997979i \(-0.479758\pi\)
0.0635487 + 0.997979i \(0.479758\pi\)
\(228\) −46.2916 −3.06574
\(229\) 17.5825 1.16189 0.580943 0.813945i \(-0.302684\pi\)
0.580943 + 0.813945i \(0.302684\pi\)
\(230\) −18.6794 −1.23169
\(231\) 37.1719 2.44573
\(232\) −25.6519 −1.68413
\(233\) −0.582736 −0.0381763 −0.0190882 0.999818i \(-0.506076\pi\)
−0.0190882 + 0.999818i \(0.506076\pi\)
\(234\) 45.0514 2.94510
\(235\) −17.2247 −1.12361
\(236\) −12.5717 −0.818346
\(237\) 15.6190 1.01456
\(238\) 37.1984 2.41121
\(239\) 17.0557 1.10324 0.551620 0.834096i \(-0.314010\pi\)
0.551620 + 0.834096i \(0.314010\pi\)
\(240\) −34.6754 −2.23829
\(241\) −28.3989 −1.82934 −0.914668 0.404207i \(-0.867548\pi\)
−0.914668 + 0.404207i \(0.867548\pi\)
\(242\) −43.8413 −2.81823
\(243\) −22.2301 −1.42606
\(244\) 18.4795 1.18303
\(245\) −0.858414 −0.0548421
\(246\) −1.66828 −0.106366
\(247\) 20.2901 1.29103
\(248\) −20.9286 −1.32896
\(249\) 17.8363 1.13033
\(250\) −30.3577 −1.91999
\(251\) −18.9155 −1.19394 −0.596969 0.802264i \(-0.703629\pi\)
−0.596969 + 0.802264i \(0.703629\pi\)
\(252\) −43.1004 −2.71507
\(253\) 19.4951 1.22565
\(254\) 37.4220 2.34806
\(255\) −27.7688 −1.73895
\(256\) −30.2801 −1.89251
\(257\) 9.03146 0.563367 0.281683 0.959507i \(-0.409107\pi\)
0.281683 + 0.959507i \(0.409107\pi\)
\(258\) −10.5844 −0.658958
\(259\) 1.50223 0.0933443
\(260\) 44.2367 2.74344
\(261\) 14.9246 0.923809
\(262\) −17.3107 −1.06946
\(263\) 21.2681 1.31145 0.655723 0.755002i \(-0.272364\pi\)
0.655723 + 0.755002i \(0.272364\pi\)
\(264\) 83.8068 5.15795
\(265\) 2.55026 0.156661
\(266\) −28.1866 −1.72823
\(267\) −6.89224 −0.421798
\(268\) −40.5839 −2.47906
\(269\) −13.2904 −0.810331 −0.405166 0.914243i \(-0.632786\pi\)
−0.405166 + 0.914243i \(0.632786\pi\)
\(270\) 7.51191 0.457161
\(271\) −30.0848 −1.82752 −0.913760 0.406254i \(-0.866835\pi\)
−0.913760 + 0.406254i \(0.866835\pi\)
\(272\) 36.2153 2.19588
\(273\) 34.7452 2.10287
\(274\) −35.8136 −2.16358
\(275\) 5.08578 0.306684
\(276\) −41.5742 −2.50247
\(277\) 23.9839 1.44105 0.720527 0.693427i \(-0.243900\pi\)
0.720527 + 0.693427i \(0.243900\pi\)
\(278\) −9.60920 −0.576321
\(279\) 12.1765 0.728987
\(280\) −33.6722 −2.01230
\(281\) 12.7082 0.758109 0.379055 0.925374i \(-0.376249\pi\)
0.379055 + 0.925374i \(0.376249\pi\)
\(282\) −55.6668 −3.31491
\(283\) −11.1050 −0.660122 −0.330061 0.943960i \(-0.607069\pi\)
−0.330061 + 0.943960i \(0.607069\pi\)
\(284\) −19.0980 −1.13326
\(285\) 21.0414 1.24639
\(286\) −67.0395 −3.96413
\(287\) −0.699559 −0.0412937
\(288\) −17.0021 −1.00186
\(289\) 12.0020 0.705998
\(290\) 21.2796 1.24958
\(291\) −26.1206 −1.53122
\(292\) 11.2025 0.655575
\(293\) −8.06426 −0.471119 −0.235560 0.971860i \(-0.575692\pi\)
−0.235560 + 0.971860i \(0.575692\pi\)
\(294\) −2.77423 −0.161797
\(295\) 5.71433 0.332701
\(296\) 3.38689 0.196859
\(297\) −7.83993 −0.454919
\(298\) 4.27155 0.247444
\(299\) 18.2224 1.05383
\(300\) −10.8457 −0.626175
\(301\) −4.43836 −0.255823
\(302\) −41.8948 −2.41077
\(303\) 27.4619 1.57764
\(304\) −27.4417 −1.57389
\(305\) −8.39969 −0.480965
\(306\) −48.7945 −2.78939
\(307\) −33.3364 −1.90261 −0.951304 0.308253i \(-0.900256\pi\)
−0.951304 + 0.308253i \(0.900256\pi\)
\(308\) 64.1363 3.65451
\(309\) −4.32631 −0.246115
\(310\) 17.3613 0.986056
\(311\) −18.2611 −1.03549 −0.517747 0.855534i \(-0.673229\pi\)
−0.517747 + 0.855534i \(0.673229\pi\)
\(312\) 78.3355 4.43487
\(313\) −6.78381 −0.383443 −0.191722 0.981449i \(-0.561407\pi\)
−0.191722 + 0.981449i \(0.561407\pi\)
\(314\) −60.2350 −3.39926
\(315\) 19.5909 1.10382
\(316\) 26.9490 1.51600
\(317\) 7.60501 0.427140 0.213570 0.976928i \(-0.431491\pi\)
0.213570 + 0.976928i \(0.431491\pi\)
\(318\) 8.24197 0.462187
\(319\) −22.2088 −1.24345
\(320\) 2.80473 0.156789
\(321\) 39.4022 2.19921
\(322\) −25.3142 −1.41071
\(323\) −21.9759 −1.22277
\(324\) −30.7270 −1.70706
\(325\) 4.75376 0.263691
\(326\) −34.1491 −1.89134
\(327\) −16.3197 −0.902481
\(328\) −1.57721 −0.0870866
\(329\) −23.3427 −1.28692
\(330\) −69.5220 −3.82706
\(331\) 21.7815 1.19722 0.598610 0.801041i \(-0.295720\pi\)
0.598610 + 0.801041i \(0.295720\pi\)
\(332\) 30.7747 1.68898
\(333\) −1.97053 −0.107985
\(334\) −52.5504 −2.87543
\(335\) 18.4470 1.00787
\(336\) −46.9918 −2.56361
\(337\) −19.4266 −1.05823 −0.529117 0.848549i \(-0.677477\pi\)
−0.529117 + 0.848549i \(0.677477\pi\)
\(338\) −29.7131 −1.61618
\(339\) −18.5467 −1.00732
\(340\) −47.9121 −2.59840
\(341\) −18.1194 −0.981222
\(342\) 36.9734 1.99929
\(343\) 17.9133 0.967226
\(344\) −10.0066 −0.539519
\(345\) 18.8972 1.01739
\(346\) −14.8159 −0.796508
\(347\) −16.3367 −0.877003 −0.438501 0.898731i \(-0.644491\pi\)
−0.438501 + 0.898731i \(0.644491\pi\)
\(348\) 47.3613 2.53883
\(349\) 21.4882 1.15024 0.575119 0.818070i \(-0.304956\pi\)
0.575119 + 0.818070i \(0.304956\pi\)
\(350\) −6.60384 −0.352990
\(351\) −7.32811 −0.391145
\(352\) 25.3003 1.34851
\(353\) 33.7957 1.79876 0.899382 0.437163i \(-0.144017\pi\)
0.899382 + 0.437163i \(0.144017\pi\)
\(354\) 18.4677 0.981545
\(355\) 8.68081 0.460729
\(356\) −11.8918 −0.630266
\(357\) −37.6320 −1.99170
\(358\) 49.7284 2.62823
\(359\) 28.8856 1.52452 0.762261 0.647270i \(-0.224089\pi\)
0.762261 + 0.647270i \(0.224089\pi\)
\(360\) 44.1690 2.32791
\(361\) −2.34806 −0.123582
\(362\) −33.7912 −1.77603
\(363\) 44.3523 2.32789
\(364\) 59.9492 3.14219
\(365\) −5.09198 −0.266526
\(366\) −27.1462 −1.41896
\(367\) −24.3881 −1.27305 −0.636525 0.771256i \(-0.719629\pi\)
−0.636525 + 0.771256i \(0.719629\pi\)
\(368\) −24.6452 −1.28472
\(369\) 0.917637 0.0477703
\(370\) −2.80960 −0.146064
\(371\) 3.45609 0.179431
\(372\) 38.6405 2.00342
\(373\) 4.89725 0.253570 0.126785 0.991930i \(-0.459534\pi\)
0.126785 + 0.991930i \(0.459534\pi\)
\(374\) 72.6095 3.75455
\(375\) 30.7116 1.58594
\(376\) −52.6278 −2.71407
\(377\) −20.7589 −1.06914
\(378\) 10.1801 0.523607
\(379\) −0.658380 −0.0338187 −0.0169094 0.999857i \(-0.505383\pi\)
−0.0169094 + 0.999857i \(0.505383\pi\)
\(380\) 36.3048 1.86240
\(381\) −37.8582 −1.93953
\(382\) −17.3949 −0.889999
\(383\) −32.7314 −1.67250 −0.836249 0.548350i \(-0.815256\pi\)
−0.836249 + 0.548350i \(0.815256\pi\)
\(384\) 33.4551 1.70725
\(385\) −29.1526 −1.48575
\(386\) 19.9519 1.01552
\(387\) 5.82195 0.295946
\(388\) −45.0684 −2.28800
\(389\) 13.1409 0.666268 0.333134 0.942879i \(-0.391894\pi\)
0.333134 + 0.942879i \(0.391894\pi\)
\(390\) −64.9833 −3.29056
\(391\) −19.7364 −0.998112
\(392\) −2.62278 −0.132470
\(393\) 17.5125 0.883388
\(394\) −10.0253 −0.505066
\(395\) −12.2494 −0.616335
\(396\) −84.1299 −4.22769
\(397\) 39.3440 1.97462 0.987309 0.158813i \(-0.0507666\pi\)
0.987309 + 0.158813i \(0.0507666\pi\)
\(398\) −22.7496 −1.14034
\(399\) 28.5152 1.42754
\(400\) −6.42931 −0.321465
\(401\) −35.6424 −1.77989 −0.889947 0.456064i \(-0.849259\pi\)
−0.889947 + 0.456064i \(0.849259\pi\)
\(402\) 59.6174 2.97345
\(403\) −16.9365 −0.843667
\(404\) 47.3826 2.35737
\(405\) 13.9667 0.694010
\(406\) 28.8379 1.43120
\(407\) 2.93229 0.145348
\(408\) −84.8440 −4.20040
\(409\) −9.10168 −0.450049 −0.225025 0.974353i \(-0.572246\pi\)
−0.225025 + 0.974353i \(0.572246\pi\)
\(410\) 1.30837 0.0646160
\(411\) 36.2310 1.78714
\(412\) −7.46461 −0.367755
\(413\) 7.74402 0.381058
\(414\) 33.2056 1.63196
\(415\) −13.9884 −0.686661
\(416\) 23.6486 1.15947
\(417\) 9.72120 0.476049
\(418\) −55.0189 −2.69106
\(419\) −0.525874 −0.0256906 −0.0128453 0.999917i \(-0.504089\pi\)
−0.0128453 + 0.999917i \(0.504089\pi\)
\(420\) 62.1692 3.03355
\(421\) 24.4813 1.19315 0.596573 0.802559i \(-0.296529\pi\)
0.596573 + 0.802559i \(0.296529\pi\)
\(422\) 31.3125 1.52427
\(423\) 30.6194 1.48877
\(424\) 7.79201 0.378413
\(425\) −5.14873 −0.249750
\(426\) 28.0547 1.35926
\(427\) −11.3832 −0.550871
\(428\) 67.9844 3.28615
\(429\) 67.8209 3.27442
\(430\) 8.30098 0.400309
\(431\) 7.44823 0.358769 0.179384 0.983779i \(-0.442589\pi\)
0.179384 + 0.983779i \(0.442589\pi\)
\(432\) 9.91103 0.476845
\(433\) −3.03056 −0.145640 −0.0728198 0.997345i \(-0.523200\pi\)
−0.0728198 + 0.997345i \(0.523200\pi\)
\(434\) 23.5279 1.12938
\(435\) −21.5276 −1.03217
\(436\) −28.1579 −1.34852
\(437\) 14.9550 0.715395
\(438\) −16.4563 −0.786313
\(439\) 18.5097 0.883419 0.441710 0.897158i \(-0.354372\pi\)
0.441710 + 0.897158i \(0.354372\pi\)
\(440\) −65.7265 −3.13339
\(441\) 1.52596 0.0726648
\(442\) 67.8692 3.22821
\(443\) 7.84447 0.372702 0.186351 0.982483i \(-0.440334\pi\)
0.186351 + 0.982483i \(0.440334\pi\)
\(444\) −6.25324 −0.296766
\(445\) 5.40533 0.256237
\(446\) 62.3950 2.95449
\(447\) −4.32134 −0.204392
\(448\) 3.80094 0.179578
\(449\) −0.568702 −0.0268387 −0.0134193 0.999910i \(-0.504272\pi\)
−0.0134193 + 0.999910i \(0.504272\pi\)
\(450\) 8.66249 0.408354
\(451\) −1.36551 −0.0642991
\(452\) −32.0005 −1.50518
\(453\) 42.3831 1.99133
\(454\) −4.85353 −0.227787
\(455\) −27.2494 −1.27747
\(456\) 64.2895 3.01063
\(457\) 31.8862 1.49157 0.745786 0.666186i \(-0.232074\pi\)
0.745786 + 0.666186i \(0.232074\pi\)
\(458\) −44.5645 −2.08236
\(459\) 7.93696 0.370466
\(460\) 32.6051 1.52022
\(461\) −14.6034 −0.680148 −0.340074 0.940399i \(-0.610452\pi\)
−0.340074 + 0.940399i \(0.610452\pi\)
\(462\) −94.2156 −4.38331
\(463\) −14.4255 −0.670410 −0.335205 0.942145i \(-0.608806\pi\)
−0.335205 + 0.942145i \(0.608806\pi\)
\(464\) 28.0758 1.30338
\(465\) −17.5637 −0.814496
\(466\) 1.47700 0.0684206
\(467\) 32.6772 1.51212 0.756060 0.654502i \(-0.227122\pi\)
0.756060 + 0.654502i \(0.227122\pi\)
\(468\) −78.6375 −3.63502
\(469\) 24.9993 1.15436
\(470\) 43.6574 2.01377
\(471\) 60.9371 2.80783
\(472\) 17.4594 0.803635
\(473\) −8.66345 −0.398346
\(474\) −39.5878 −1.81833
\(475\) 3.90138 0.179008
\(476\) −64.9301 −2.97607
\(477\) −4.53348 −0.207574
\(478\) −43.2291 −1.97725
\(479\) −12.1253 −0.554020 −0.277010 0.960867i \(-0.589344\pi\)
−0.277010 + 0.960867i \(0.589344\pi\)
\(480\) 24.5243 1.11938
\(481\) 2.74085 0.124972
\(482\) 71.9796 3.27858
\(483\) 25.6093 1.16526
\(484\) 76.5254 3.47843
\(485\) 20.4854 0.930196
\(486\) 56.3442 2.55582
\(487\) −6.72766 −0.304859 −0.152430 0.988314i \(-0.548710\pi\)
−0.152430 + 0.988314i \(0.548710\pi\)
\(488\) −25.6642 −1.16176
\(489\) 34.5472 1.56228
\(490\) 2.17573 0.0982893
\(491\) 28.5022 1.28629 0.643143 0.765746i \(-0.277630\pi\)
0.643143 + 0.765746i \(0.277630\pi\)
\(492\) 2.91200 0.131283
\(493\) 22.4837 1.01261
\(494\) −51.4270 −2.31381
\(495\) 38.2405 1.71878
\(496\) 22.9061 1.02851
\(497\) 11.7642 0.527694
\(498\) −45.2077 −2.02581
\(499\) −7.27892 −0.325849 −0.162925 0.986639i \(-0.552093\pi\)
−0.162925 + 0.986639i \(0.552093\pi\)
\(500\) 52.9896 2.36977
\(501\) 53.1629 2.37514
\(502\) 47.9432 2.13981
\(503\) 9.40468 0.419334 0.209667 0.977773i \(-0.432762\pi\)
0.209667 + 0.977773i \(0.432762\pi\)
\(504\) 59.8575 2.66627
\(505\) −21.5373 −0.958398
\(506\) −49.4121 −2.19664
\(507\) 30.0595 1.33499
\(508\) −65.3203 −2.89812
\(509\) −1.34232 −0.0594974 −0.0297487 0.999557i \(-0.509471\pi\)
−0.0297487 + 0.999557i \(0.509471\pi\)
\(510\) 70.3824 3.11659
\(511\) −6.90060 −0.305265
\(512\) 50.6531 2.23857
\(513\) −6.01413 −0.265531
\(514\) −22.8910 −1.00968
\(515\) 3.39297 0.149512
\(516\) 18.4752 0.813326
\(517\) −45.5638 −2.00389
\(518\) −3.80755 −0.167294
\(519\) 14.9886 0.657927
\(520\) −61.4356 −2.69413
\(521\) −13.6515 −0.598084 −0.299042 0.954240i \(-0.596667\pi\)
−0.299042 + 0.954240i \(0.596667\pi\)
\(522\) −37.8277 −1.65567
\(523\) 0.598206 0.0261577 0.0130789 0.999914i \(-0.495837\pi\)
0.0130789 + 0.999914i \(0.495837\pi\)
\(524\) 30.2160 1.31999
\(525\) 6.68081 0.291575
\(526\) −53.9058 −2.35041
\(527\) 18.3437 0.799063
\(528\) −91.7256 −3.99185
\(529\) −9.56902 −0.416044
\(530\) −6.46387 −0.280773
\(531\) −10.1581 −0.440824
\(532\) 49.2000 2.13309
\(533\) −1.27636 −0.0552852
\(534\) 17.4690 0.755957
\(535\) −30.9017 −1.33599
\(536\) 56.3626 2.43450
\(537\) −50.3081 −2.17095
\(538\) 33.6858 1.45230
\(539\) −2.27073 −0.0978074
\(540\) −13.1121 −0.564255
\(541\) −21.9071 −0.941860 −0.470930 0.882171i \(-0.656082\pi\)
−0.470930 + 0.882171i \(0.656082\pi\)
\(542\) 76.2526 3.27533
\(543\) 34.1851 1.46702
\(544\) −25.6134 −1.09817
\(545\) 12.7989 0.548246
\(546\) −88.0648 −3.76882
\(547\) 11.2969 0.483020 0.241510 0.970398i \(-0.422357\pi\)
0.241510 + 0.970398i \(0.422357\pi\)
\(548\) 62.5129 2.67042
\(549\) 14.9317 0.637271
\(550\) −12.8904 −0.549647
\(551\) −17.0367 −0.725788
\(552\) 57.7379 2.45749
\(553\) −16.6003 −0.705917
\(554\) −60.7894 −2.58269
\(555\) 2.84235 0.120651
\(556\) 16.7729 0.711331
\(557\) −29.7616 −1.26104 −0.630521 0.776172i \(-0.717159\pi\)
−0.630521 + 0.776172i \(0.717159\pi\)
\(558\) −30.8624 −1.30651
\(559\) −8.09786 −0.342503
\(560\) 36.8539 1.55736
\(561\) −73.4558 −3.10131
\(562\) −32.2102 −1.35870
\(563\) 42.4340 1.78838 0.894190 0.447688i \(-0.147753\pi\)
0.894190 + 0.447688i \(0.147753\pi\)
\(564\) 97.1669 4.09146
\(565\) 14.5455 0.611935
\(566\) 28.1466 1.18309
\(567\) 18.9275 0.794881
\(568\) 26.5231 1.11289
\(569\) −16.6322 −0.697257 −0.348629 0.937261i \(-0.613353\pi\)
−0.348629 + 0.937261i \(0.613353\pi\)
\(570\) −53.3314 −2.23381
\(571\) 6.07093 0.254061 0.127030 0.991899i \(-0.459455\pi\)
0.127030 + 0.991899i \(0.459455\pi\)
\(572\) 117.018 4.89277
\(573\) 17.5976 0.735151
\(574\) 1.77310 0.0740076
\(575\) 3.50380 0.146119
\(576\) −4.98583 −0.207743
\(577\) 27.1115 1.12867 0.564333 0.825547i \(-0.309133\pi\)
0.564333 + 0.825547i \(0.309133\pi\)
\(578\) −30.4201 −1.26531
\(579\) −20.1844 −0.838837
\(580\) −37.1437 −1.54231
\(581\) −18.9569 −0.786465
\(582\) 66.2051 2.74429
\(583\) 6.74612 0.279396
\(584\) −15.5579 −0.643790
\(585\) 35.7439 1.47783
\(586\) 20.4396 0.844352
\(587\) −19.6491 −0.811005 −0.405502 0.914094i \(-0.632903\pi\)
−0.405502 + 0.914094i \(0.632903\pi\)
\(588\) 4.84244 0.199699
\(589\) −13.8997 −0.572727
\(590\) −14.4835 −0.596276
\(591\) 10.1421 0.417191
\(592\) −3.70692 −0.152353
\(593\) 24.4317 1.00329 0.501645 0.865073i \(-0.332728\pi\)
0.501645 + 0.865073i \(0.332728\pi\)
\(594\) 19.8710 0.815318
\(595\) 29.5134 1.20993
\(596\) −7.45602 −0.305411
\(597\) 23.0148 0.941932
\(598\) −46.1863 −1.88870
\(599\) −22.9622 −0.938208 −0.469104 0.883143i \(-0.655423\pi\)
−0.469104 + 0.883143i \(0.655423\pi\)
\(600\) 15.0624 0.614919
\(601\) −1.52929 −0.0623812 −0.0311906 0.999513i \(-0.509930\pi\)
−0.0311906 + 0.999513i \(0.509930\pi\)
\(602\) 11.2494 0.458492
\(603\) −32.7924 −1.33541
\(604\) 73.1277 2.97552
\(605\) −34.7839 −1.41417
\(606\) −69.6046 −2.82749
\(607\) −42.8062 −1.73745 −0.868725 0.495295i \(-0.835060\pi\)
−0.868725 + 0.495295i \(0.835060\pi\)
\(608\) 19.4082 0.787108
\(609\) −29.1741 −1.18219
\(610\) 21.2898 0.861997
\(611\) −42.5892 −1.72297
\(612\) 85.1711 3.44284
\(613\) 40.7951 1.64770 0.823848 0.566810i \(-0.191823\pi\)
0.823848 + 0.566810i \(0.191823\pi\)
\(614\) 84.4941 3.40990
\(615\) −1.32362 −0.0533737
\(616\) −89.0720 −3.58881
\(617\) 40.2711 1.62125 0.810627 0.585563i \(-0.199127\pi\)
0.810627 + 0.585563i \(0.199127\pi\)
\(618\) 10.9654 0.441094
\(619\) −22.9423 −0.922130 −0.461065 0.887366i \(-0.652533\pi\)
−0.461065 + 0.887366i \(0.652533\pi\)
\(620\) −30.3043 −1.21705
\(621\) −5.40125 −0.216745
\(622\) 46.2845 1.85584
\(623\) 7.32525 0.293480
\(624\) −85.7373 −3.43224
\(625\) −19.3056 −0.772225
\(626\) 17.1942 0.687217
\(627\) 55.6602 2.22285
\(628\) 105.141 4.19557
\(629\) −2.96858 −0.118365
\(630\) −49.6549 −1.97830
\(631\) 5.65218 0.225010 0.112505 0.993651i \(-0.464113\pi\)
0.112505 + 0.993651i \(0.464113\pi\)
\(632\) −37.4266 −1.48875
\(633\) −31.6775 −1.25907
\(634\) −19.2756 −0.765531
\(635\) 29.6908 1.17824
\(636\) −14.3864 −0.570459
\(637\) −2.12249 −0.0840961
\(638\) 56.2902 2.22855
\(639\) −15.4315 −0.610459
\(640\) −26.2376 −1.03713
\(641\) −22.1634 −0.875402 −0.437701 0.899121i \(-0.644207\pi\)
−0.437701 + 0.899121i \(0.644207\pi\)
\(642\) −99.8683 −3.94149
\(643\) 27.7299 1.09356 0.546780 0.837276i \(-0.315853\pi\)
0.546780 + 0.837276i \(0.315853\pi\)
\(644\) 44.1862 1.74118
\(645\) −8.39773 −0.330660
\(646\) 55.6998 2.19148
\(647\) −33.7906 −1.32844 −0.664222 0.747535i \(-0.731237\pi\)
−0.664222 + 0.747535i \(0.731237\pi\)
\(648\) 42.6734 1.67637
\(649\) 15.1159 0.593353
\(650\) −12.0488 −0.472594
\(651\) −23.8021 −0.932880
\(652\) 59.6076 2.33441
\(653\) −11.4793 −0.449218 −0.224609 0.974449i \(-0.572110\pi\)
−0.224609 + 0.974449i \(0.572110\pi\)
\(654\) 41.3637 1.61745
\(655\) −13.7344 −0.536647
\(656\) 1.72624 0.0673982
\(657\) 9.05176 0.353143
\(658\) 59.1642 2.30646
\(659\) 16.9988 0.662179 0.331089 0.943599i \(-0.392584\pi\)
0.331089 + 0.943599i \(0.392584\pi\)
\(660\) 121.351 4.72359
\(661\) −6.37293 −0.247878 −0.123939 0.992290i \(-0.539553\pi\)
−0.123939 + 0.992290i \(0.539553\pi\)
\(662\) −55.2072 −2.14569
\(663\) −68.6603 −2.66654
\(664\) −42.7397 −1.65862
\(665\) −22.3634 −0.867215
\(666\) 4.99450 0.193533
\(667\) −15.3006 −0.592440
\(668\) 91.7271 3.54903
\(669\) −63.1223 −2.44045
\(670\) −46.7557 −1.80633
\(671\) −22.2194 −0.857771
\(672\) 33.2351 1.28207
\(673\) 47.6245 1.83579 0.917895 0.396823i \(-0.129887\pi\)
0.917895 + 0.396823i \(0.129887\pi\)
\(674\) 49.2384 1.89659
\(675\) −1.40905 −0.0542344
\(676\) 51.8645 1.99479
\(677\) 10.1943 0.391797 0.195898 0.980624i \(-0.437238\pi\)
0.195898 + 0.980624i \(0.437238\pi\)
\(678\) 47.0084 1.80535
\(679\) 27.7617 1.06540
\(680\) 66.5400 2.55169
\(681\) 4.91010 0.188155
\(682\) 45.9253 1.75857
\(683\) −15.5480 −0.594927 −0.297464 0.954733i \(-0.596141\pi\)
−0.297464 + 0.954733i \(0.596141\pi\)
\(684\) −64.5373 −2.46765
\(685\) −28.4146 −1.08567
\(686\) −45.4028 −1.73349
\(687\) 45.0839 1.72006
\(688\) 10.9521 0.417545
\(689\) 6.30571 0.240228
\(690\) −47.8966 −1.82339
\(691\) −30.7649 −1.17035 −0.585175 0.810907i \(-0.698974\pi\)
−0.585175 + 0.810907i \(0.698974\pi\)
\(692\) 25.8613 0.983099
\(693\) 51.8231 1.96860
\(694\) 41.4070 1.57179
\(695\) −7.62398 −0.289194
\(696\) −65.7750 −2.49319
\(697\) 1.38241 0.0523623
\(698\) −54.4638 −2.06149
\(699\) −1.49421 −0.0565163
\(700\) 11.5271 0.435682
\(701\) 22.8103 0.861532 0.430766 0.902464i \(-0.358243\pi\)
0.430766 + 0.902464i \(0.358243\pi\)
\(702\) 18.5737 0.701021
\(703\) 2.24940 0.0848379
\(704\) 7.41925 0.279623
\(705\) −44.1663 −1.66340
\(706\) −85.6583 −3.22379
\(707\) −29.1872 −1.09770
\(708\) −32.2354 −1.21148
\(709\) −31.4901 −1.18264 −0.591318 0.806439i \(-0.701392\pi\)
−0.591318 + 0.806439i \(0.701392\pi\)
\(710\) −22.0023 −0.825731
\(711\) 21.7752 0.816634
\(712\) 16.5153 0.618937
\(713\) −12.4832 −0.467500
\(714\) 95.3817 3.56957
\(715\) −53.1894 −1.98917
\(716\) −86.8014 −3.24392
\(717\) 43.7330 1.63324
\(718\) −73.2130 −2.73229
\(719\) −48.7555 −1.81827 −0.909137 0.416497i \(-0.863258\pi\)
−0.909137 + 0.416497i \(0.863258\pi\)
\(720\) −48.3426 −1.80162
\(721\) 4.59812 0.171243
\(722\) 5.95136 0.221487
\(723\) −72.8186 −2.70815
\(724\) 58.9829 2.19208
\(725\) −3.99153 −0.148242
\(726\) −112.415 −4.17211
\(727\) −19.8875 −0.737588 −0.368794 0.929511i \(-0.620229\pi\)
−0.368794 + 0.929511i \(0.620229\pi\)
\(728\) −83.2570 −3.08571
\(729\) −36.1650 −1.33944
\(730\) 12.9061 0.477675
\(731\) 8.77067 0.324395
\(732\) 47.3839 1.75136
\(733\) −6.38470 −0.235824 −0.117912 0.993024i \(-0.537620\pi\)
−0.117912 + 0.993024i \(0.537620\pi\)
\(734\) 61.8139 2.28159
\(735\) −2.20109 −0.0811883
\(736\) 17.4304 0.642494
\(737\) 48.7974 1.79747
\(738\) −2.32583 −0.0856151
\(739\) 49.5631 1.82321 0.911605 0.411068i \(-0.134844\pi\)
0.911605 + 0.411068i \(0.134844\pi\)
\(740\) 4.90418 0.180281
\(741\) 52.0264 1.91124
\(742\) −8.75978 −0.321582
\(743\) −7.81432 −0.286680 −0.143340 0.989674i \(-0.545784\pi\)
−0.143340 + 0.989674i \(0.545784\pi\)
\(744\) −53.6636 −1.96740
\(745\) 3.38907 0.124166
\(746\) −12.4125 −0.454455
\(747\) 24.8664 0.909815
\(748\) −126.740 −4.63409
\(749\) −41.8777 −1.53018
\(750\) −77.8412 −2.84236
\(751\) 35.4501 1.29359 0.646796 0.762663i \(-0.276109\pi\)
0.646796 + 0.762663i \(0.276109\pi\)
\(752\) 57.6005 2.10048
\(753\) −48.5020 −1.76751
\(754\) 52.6153 1.91614
\(755\) −33.2395 −1.20971
\(756\) −17.7694 −0.646267
\(757\) 20.1642 0.732882 0.366441 0.930441i \(-0.380576\pi\)
0.366441 + 0.930441i \(0.380576\pi\)
\(758\) 1.66872 0.0606108
\(759\) 49.9881 1.81445
\(760\) −50.4198 −1.82892
\(761\) −16.4203 −0.595237 −0.297618 0.954685i \(-0.596192\pi\)
−0.297618 + 0.954685i \(0.596192\pi\)
\(762\) 95.9549 3.47608
\(763\) 17.3450 0.627931
\(764\) 30.3629 1.09849
\(765\) −38.7137 −1.39970
\(766\) 82.9608 2.99749
\(767\) 14.1291 0.510172
\(768\) −77.6423 −2.80168
\(769\) 22.4424 0.809293 0.404647 0.914473i \(-0.367395\pi\)
0.404647 + 0.914473i \(0.367395\pi\)
\(770\) 73.8898 2.66280
\(771\) 23.1579 0.834010
\(772\) −34.8262 −1.25342
\(773\) 21.7861 0.783591 0.391796 0.920052i \(-0.371854\pi\)
0.391796 + 0.920052i \(0.371854\pi\)
\(774\) −14.7563 −0.530402
\(775\) −3.25656 −0.116979
\(776\) 62.5907 2.24687
\(777\) 3.85193 0.138187
\(778\) −33.3067 −1.19410
\(779\) −1.04750 −0.0375306
\(780\) 113.429 4.06140
\(781\) 22.9631 0.821683
\(782\) 50.0237 1.78884
\(783\) 6.15310 0.219894
\(784\) 2.87060 0.102521
\(785\) −47.7907 −1.70572
\(786\) −44.3870 −1.58323
\(787\) 43.5528 1.55249 0.776246 0.630431i \(-0.217122\pi\)
0.776246 + 0.630431i \(0.217122\pi\)
\(788\) 17.4992 0.623383
\(789\) 54.5342 1.94147
\(790\) 31.0473 1.10461
\(791\) 19.7120 0.700877
\(792\) 116.839 4.15169
\(793\) −20.7688 −0.737523
\(794\) −99.7208 −3.53896
\(795\) 6.53921 0.231922
\(796\) 39.7096 1.40747
\(797\) 26.6815 0.945107 0.472553 0.881302i \(-0.343332\pi\)
0.472553 + 0.881302i \(0.343332\pi\)
\(798\) −72.2743 −2.55848
\(799\) 46.1277 1.63188
\(800\) 4.54716 0.160766
\(801\) −9.60879 −0.339510
\(802\) 90.3388 3.18997
\(803\) −13.4696 −0.475333
\(804\) −104.063 −3.67001
\(805\) −20.0844 −0.707882
\(806\) 42.9271 1.51204
\(807\) −34.0784 −1.19962
\(808\) −65.8046 −2.31500
\(809\) 15.7917 0.555207 0.277603 0.960696i \(-0.410460\pi\)
0.277603 + 0.960696i \(0.410460\pi\)
\(810\) −35.3998 −1.24382
\(811\) −1.00853 −0.0354144 −0.0177072 0.999843i \(-0.505637\pi\)
−0.0177072 + 0.999843i \(0.505637\pi\)
\(812\) −50.3368 −1.76648
\(813\) −77.1414 −2.70547
\(814\) −7.43215 −0.260497
\(815\) −27.0941 −0.949063
\(816\) 92.8608 3.25078
\(817\) −6.64587 −0.232509
\(818\) 23.0690 0.806590
\(819\) 48.4399 1.69263
\(820\) −2.28378 −0.0797529
\(821\) −35.6536 −1.24432 −0.622160 0.782890i \(-0.713745\pi\)
−0.622160 + 0.782890i \(0.713745\pi\)
\(822\) −91.8308 −3.20297
\(823\) 0.677853 0.0236285 0.0118142 0.999930i \(-0.496239\pi\)
0.0118142 + 0.999930i \(0.496239\pi\)
\(824\) 10.3668 0.361144
\(825\) 13.0406 0.454016
\(826\) −19.6279 −0.682942
\(827\) 20.1792 0.701699 0.350849 0.936432i \(-0.385893\pi\)
0.350849 + 0.936432i \(0.385893\pi\)
\(828\) −57.9606 −2.01427
\(829\) −3.24765 −0.112796 −0.0563978 0.998408i \(-0.517962\pi\)
−0.0563978 + 0.998408i \(0.517962\pi\)
\(830\) 35.4547 1.23065
\(831\) 61.4980 2.13334
\(832\) 6.93488 0.240424
\(833\) 2.29884 0.0796500
\(834\) −24.6393 −0.853188
\(835\) −41.6937 −1.44287
\(836\) 96.0359 3.32147
\(837\) 5.02011 0.173520
\(838\) 1.33288 0.0460434
\(839\) 51.2298 1.76865 0.884324 0.466874i \(-0.154620\pi\)
0.884324 + 0.466874i \(0.154620\pi\)
\(840\) −86.3401 −2.97902
\(841\) −11.5696 −0.398953
\(842\) −62.0501 −2.13839
\(843\) 32.5856 1.12231
\(844\) −54.6562 −1.88134
\(845\) −23.5745 −0.810989
\(846\) −77.6077 −2.66821
\(847\) −47.1388 −1.61971
\(848\) −8.52827 −0.292862
\(849\) −28.4746 −0.977247
\(850\) 13.0499 0.447608
\(851\) 2.02017 0.0692507
\(852\) −48.9698 −1.67768
\(853\) 35.2658 1.20748 0.603740 0.797181i \(-0.293677\pi\)
0.603740 + 0.797181i \(0.293677\pi\)
\(854\) 28.8517 0.987285
\(855\) 29.3348 1.00323
\(856\) −94.4161 −3.22708
\(857\) −38.8801 −1.32812 −0.664059 0.747680i \(-0.731168\pi\)
−0.664059 + 0.747680i \(0.731168\pi\)
\(858\) −171.898 −5.86851
\(859\) −5.28982 −0.180486 −0.0902432 0.995920i \(-0.528764\pi\)
−0.0902432 + 0.995920i \(0.528764\pi\)
\(860\) −14.4894 −0.494085
\(861\) −1.79376 −0.0611313
\(862\) −18.8782 −0.642994
\(863\) −20.6293 −0.702228 −0.351114 0.936333i \(-0.614197\pi\)
−0.351114 + 0.936333i \(0.614197\pi\)
\(864\) −7.00962 −0.238472
\(865\) −11.7550 −0.399682
\(866\) 7.68124 0.261019
\(867\) 30.7746 1.04516
\(868\) −41.0681 −1.39394
\(869\) −32.4030 −1.09920
\(870\) 54.5637 1.84988
\(871\) 45.6116 1.54549
\(872\) 39.1055 1.32428
\(873\) −36.4160 −1.23249
\(874\) −37.9048 −1.28215
\(875\) −32.6411 −1.10347
\(876\) 28.7246 0.970515
\(877\) −48.9826 −1.65403 −0.827013 0.562183i \(-0.809961\pi\)
−0.827013 + 0.562183i \(0.809961\pi\)
\(878\) −46.9145 −1.58329
\(879\) −20.6778 −0.697446
\(880\) 71.9370 2.42500
\(881\) 23.4578 0.790313 0.395156 0.918614i \(-0.370690\pi\)
0.395156 + 0.918614i \(0.370690\pi\)
\(882\) −3.86769 −0.130232
\(883\) 8.82855 0.297104 0.148552 0.988905i \(-0.452539\pi\)
0.148552 + 0.988905i \(0.452539\pi\)
\(884\) −118.466 −3.98445
\(885\) 14.6523 0.492532
\(886\) −19.8825 −0.667966
\(887\) 12.1826 0.409053 0.204526 0.978861i \(-0.434435\pi\)
0.204526 + 0.978861i \(0.434435\pi\)
\(888\) 8.68445 0.291431
\(889\) 40.2366 1.34949
\(890\) −13.7003 −0.459235
\(891\) 36.9456 1.23772
\(892\) −108.911 −3.64661
\(893\) −34.9527 −1.16965
\(894\) 10.9528 0.366317
\(895\) 39.4548 1.31883
\(896\) −35.5569 −1.18787
\(897\) 46.7246 1.56009
\(898\) 1.44143 0.0481010
\(899\) 14.2209 0.474292
\(900\) −15.1204 −0.504015
\(901\) −6.82962 −0.227528
\(902\) 3.46100 0.115239
\(903\) −11.3805 −0.378720
\(904\) 44.4420 1.47812
\(905\) −26.8101 −0.891198
\(906\) −107.424 −3.56892
\(907\) 39.9599 1.32685 0.663424 0.748244i \(-0.269103\pi\)
0.663424 + 0.748244i \(0.269103\pi\)
\(908\) 8.47187 0.281149
\(909\) 38.2859 1.26986
\(910\) 69.0659 2.28951
\(911\) −19.4942 −0.645872 −0.322936 0.946421i \(-0.604670\pi\)
−0.322936 + 0.946421i \(0.604670\pi\)
\(912\) −70.3641 −2.32999
\(913\) −37.0029 −1.22462
\(914\) −80.8183 −2.67323
\(915\) −21.5379 −0.712022
\(916\) 77.7876 2.57018
\(917\) −18.6127 −0.614647
\(918\) −20.1170 −0.663958
\(919\) −9.36735 −0.309000 −0.154500 0.987993i \(-0.549377\pi\)
−0.154500 + 0.987993i \(0.549377\pi\)
\(920\) −45.2817 −1.49289
\(921\) −85.4789 −2.81663
\(922\) 37.0136 1.21898
\(923\) 21.4639 0.706493
\(924\) 164.454 5.41014
\(925\) 0.527012 0.0173281
\(926\) 36.5628 1.20153
\(927\) −6.03152 −0.198101
\(928\) −19.8567 −0.651828
\(929\) −35.6904 −1.17096 −0.585482 0.810685i \(-0.699095\pi\)
−0.585482 + 0.810685i \(0.699095\pi\)
\(930\) 44.5167 1.45976
\(931\) −1.74192 −0.0570890
\(932\) −2.57811 −0.0844488
\(933\) −46.8240 −1.53295
\(934\) −82.8233 −2.71006
\(935\) 57.6087 1.88400
\(936\) 109.211 3.56968
\(937\) 52.0532 1.70050 0.850252 0.526375i \(-0.176449\pi\)
0.850252 + 0.526375i \(0.176449\pi\)
\(938\) −63.3629 −2.06887
\(939\) −17.3946 −0.567651
\(940\) −76.2044 −2.48551
\(941\) −37.7244 −1.22978 −0.614891 0.788612i \(-0.710800\pi\)
−0.614891 + 0.788612i \(0.710800\pi\)
\(942\) −154.451 −5.03227
\(943\) −0.940753 −0.0306351
\(944\) −19.1092 −0.621950
\(945\) 8.07692 0.262742
\(946\) 21.9583 0.713926
\(947\) −24.2687 −0.788627 −0.394313 0.918976i \(-0.629018\pi\)
−0.394313 + 0.918976i \(0.629018\pi\)
\(948\) 69.1009 2.24429
\(949\) −12.5903 −0.408698
\(950\) −9.88840 −0.320822
\(951\) 19.5002 0.632339
\(952\) 90.1744 2.92257
\(953\) −40.3241 −1.30623 −0.653113 0.757260i \(-0.726537\pi\)
−0.653113 + 0.757260i \(0.726537\pi\)
\(954\) 11.4905 0.372019
\(955\) −13.8012 −0.446595
\(956\) 75.4568 2.44045
\(957\) −56.9463 −1.84081
\(958\) 30.7327 0.992930
\(959\) −38.5073 −1.24346
\(960\) 7.19169 0.232111
\(961\) −19.3977 −0.625731
\(962\) −6.94694 −0.223978
\(963\) 54.9324 1.77017
\(964\) −125.641 −4.04662
\(965\) 15.8299 0.509583
\(966\) −64.9090 −2.08841
\(967\) 12.3319 0.396567 0.198283 0.980145i \(-0.436463\pi\)
0.198283 + 0.980145i \(0.436463\pi\)
\(968\) −106.278 −3.41590
\(969\) −56.3491 −1.81019
\(970\) −51.9222 −1.66712
\(971\) −44.3784 −1.42417 −0.712085 0.702093i \(-0.752249\pi\)
−0.712085 + 0.702093i \(0.752249\pi\)
\(972\) −98.3492 −3.15455
\(973\) −10.3319 −0.331227
\(974\) 17.0519 0.546377
\(975\) 12.1893 0.390369
\(976\) 28.0892 0.899113
\(977\) 6.74466 0.215781 0.107890 0.994163i \(-0.465590\pi\)
0.107890 + 0.994163i \(0.465590\pi\)
\(978\) −87.5629 −2.79995
\(979\) 14.2985 0.456983
\(980\) −3.79775 −0.121315
\(981\) −22.7520 −0.726417
\(982\) −72.2414 −2.30532
\(983\) 33.3640 1.06415 0.532074 0.846698i \(-0.321413\pi\)
0.532074 + 0.846698i \(0.321413\pi\)
\(984\) −4.04417 −0.128923
\(985\) −7.95410 −0.253439
\(986\) −56.9869 −1.81483
\(987\) −59.8538 −1.90517
\(988\) 89.7663 2.85585
\(989\) −5.96861 −0.189791
\(990\) −96.9239 −3.08044
\(991\) 27.8321 0.884116 0.442058 0.896987i \(-0.354249\pi\)
0.442058 + 0.896987i \(0.354249\pi\)
\(992\) −16.2004 −0.514364
\(993\) 55.8507 1.77237
\(994\) −29.8173 −0.945748
\(995\) −18.0496 −0.572212
\(996\) 78.9104 2.50037
\(997\) −48.9314 −1.54967 −0.774837 0.632161i \(-0.782168\pi\)
−0.774837 + 0.632161i \(0.782168\pi\)
\(998\) 18.4491 0.583995
\(999\) −0.812411 −0.0257035
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 4027.2.a.c.1.9 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.c.1.9 174 1.1 even 1 trivial