Properties

Label 1849.4.a.j.1.25
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(50\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.25
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.213850 q^{2} -7.23549 q^{3} -7.95427 q^{4} -3.30603 q^{5} -1.54731 q^{6} -30.5623 q^{7} -3.41181 q^{8} +25.3524 q^{9} +O(q^{10})\) \(q+0.213850 q^{2} -7.23549 q^{3} -7.95427 q^{4} -3.30603 q^{5} -1.54731 q^{6} -30.5623 q^{7} -3.41181 q^{8} +25.3524 q^{9} -0.706992 q^{10} -66.6639 q^{11} +57.5531 q^{12} +32.7495 q^{13} -6.53574 q^{14} +23.9207 q^{15} +62.9045 q^{16} -58.7055 q^{17} +5.42159 q^{18} -53.7524 q^{19} +26.2970 q^{20} +221.134 q^{21} -14.2560 q^{22} -169.539 q^{23} +24.6862 q^{24} -114.070 q^{25} +7.00348 q^{26} +11.9214 q^{27} +243.101 q^{28} +67.9267 q^{29} +5.11544 q^{30} -2.72881 q^{31} +40.7466 q^{32} +482.346 q^{33} -12.5541 q^{34} +101.040 q^{35} -201.660 q^{36} +335.946 q^{37} -11.4949 q^{38} -236.959 q^{39} +11.2795 q^{40} +113.357 q^{41} +47.2893 q^{42} +530.262 q^{44} -83.8156 q^{45} -36.2558 q^{46} -24.6905 q^{47} -455.145 q^{48} +591.057 q^{49} -24.3939 q^{50} +424.763 q^{51} -260.499 q^{52} -597.346 q^{53} +2.54938 q^{54} +220.393 q^{55} +104.273 q^{56} +388.925 q^{57} +14.5261 q^{58} +206.000 q^{59} -190.272 q^{60} +392.622 q^{61} -0.583554 q^{62} -774.828 q^{63} -494.523 q^{64} -108.271 q^{65} +103.150 q^{66} +607.078 q^{67} +466.959 q^{68} +1226.70 q^{69} +21.6073 q^{70} -98.1848 q^{71} -86.4976 q^{72} +874.055 q^{73} +71.8418 q^{74} +825.354 q^{75} +427.561 q^{76} +2037.40 q^{77} -50.6736 q^{78} +788.085 q^{79} -207.964 q^{80} -770.771 q^{81} +24.2414 q^{82} -495.384 q^{83} -1758.96 q^{84} +194.082 q^{85} -491.483 q^{87} +227.445 q^{88} -528.746 q^{89} -17.9239 q^{90} -1000.90 q^{91} +1348.56 q^{92} +19.7443 q^{93} -5.28004 q^{94} +177.707 q^{95} -294.822 q^{96} +2.16686 q^{97} +126.397 q^{98} -1690.09 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.213850 0.0756072 0.0378036 0.999285i \(-0.487964\pi\)
0.0378036 + 0.999285i \(0.487964\pi\)
\(3\) −7.23549 −1.39247 −0.696236 0.717813i \(-0.745143\pi\)
−0.696236 + 0.717813i \(0.745143\pi\)
\(4\) −7.95427 −0.994284
\(5\) −3.30603 −0.295700 −0.147850 0.989010i \(-0.547235\pi\)
−0.147850 + 0.989010i \(0.547235\pi\)
\(6\) −1.54731 −0.105281
\(7\) −30.5623 −1.65021 −0.825106 0.564979i \(-0.808884\pi\)
−0.825106 + 0.564979i \(0.808884\pi\)
\(8\) −3.41181 −0.150782
\(9\) 25.3524 0.938977
\(10\) −0.706992 −0.0223571
\(11\) −66.6639 −1.82727 −0.913633 0.406541i \(-0.866735\pi\)
−0.913633 + 0.406541i \(0.866735\pi\)
\(12\) 57.5531 1.38451
\(13\) 32.7495 0.698699 0.349350 0.936992i \(-0.386403\pi\)
0.349350 + 0.936992i \(0.386403\pi\)
\(14\) −6.53574 −0.124768
\(15\) 23.9207 0.411754
\(16\) 62.9045 0.982883
\(17\) −58.7055 −0.837540 −0.418770 0.908092i \(-0.637539\pi\)
−0.418770 + 0.908092i \(0.637539\pi\)
\(18\) 5.42159 0.0709934
\(19\) −53.7524 −0.649034 −0.324517 0.945880i \(-0.605202\pi\)
−0.324517 + 0.945880i \(0.605202\pi\)
\(20\) 26.2970 0.294010
\(21\) 221.134 2.29787
\(22\) −14.2560 −0.138154
\(23\) −169.539 −1.53701 −0.768505 0.639843i \(-0.778999\pi\)
−0.768505 + 0.639843i \(0.778999\pi\)
\(24\) 24.6862 0.209960
\(25\) −114.070 −0.912562
\(26\) 7.00348 0.0528267
\(27\) 11.9214 0.0849731
\(28\) 243.101 1.64078
\(29\) 67.9267 0.434954 0.217477 0.976065i \(-0.430217\pi\)
0.217477 + 0.976065i \(0.430217\pi\)
\(30\) 5.11544 0.0311316
\(31\) −2.72881 −0.0158099 −0.00790497 0.999969i \(-0.502516\pi\)
−0.00790497 + 0.999969i \(0.502516\pi\)
\(32\) 40.7466 0.225095
\(33\) 482.346 2.54442
\(34\) −12.5541 −0.0633241
\(35\) 101.040 0.487967
\(36\) −201.660 −0.933609
\(37\) 335.946 1.49268 0.746339 0.665566i \(-0.231810\pi\)
0.746339 + 0.665566i \(0.231810\pi\)
\(38\) −11.4949 −0.0490717
\(39\) −236.959 −0.972919
\(40\) 11.2795 0.0445863
\(41\) 113.357 0.431791 0.215896 0.976416i \(-0.430733\pi\)
0.215896 + 0.976416i \(0.430733\pi\)
\(42\) 47.2893 0.173736
\(43\) 0 0
\(44\) 530.262 1.81682
\(45\) −83.8156 −0.277655
\(46\) −36.2558 −0.116209
\(47\) −24.6905 −0.0766271 −0.0383135 0.999266i \(-0.512199\pi\)
−0.0383135 + 0.999266i \(0.512199\pi\)
\(48\) −455.145 −1.36864
\(49\) 591.057 1.72320
\(50\) −24.3939 −0.0689963
\(51\) 424.763 1.16625
\(52\) −260.499 −0.694705
\(53\) −597.346 −1.54815 −0.774073 0.633096i \(-0.781784\pi\)
−0.774073 + 0.633096i \(0.781784\pi\)
\(54\) 2.54938 0.00642458
\(55\) 220.393 0.540322
\(56\) 104.273 0.248823
\(57\) 388.925 0.903761
\(58\) 14.5261 0.0328857
\(59\) 206.000 0.454557 0.227278 0.973830i \(-0.427017\pi\)
0.227278 + 0.973830i \(0.427017\pi\)
\(60\) −190.272 −0.409400
\(61\) 392.622 0.824100 0.412050 0.911161i \(-0.364813\pi\)
0.412050 + 0.911161i \(0.364813\pi\)
\(62\) −0.583554 −0.00119535
\(63\) −774.828 −1.54951
\(64\) −494.523 −0.965864
\(65\) −108.271 −0.206605
\(66\) 103.150 0.192376
\(67\) 607.078 1.10696 0.553481 0.832862i \(-0.313299\pi\)
0.553481 + 0.832862i \(0.313299\pi\)
\(68\) 466.959 0.832752
\(69\) 1226.70 2.14024
\(70\) 21.6073 0.0368939
\(71\) −98.1848 −0.164118 −0.0820591 0.996627i \(-0.526150\pi\)
−0.0820591 + 0.996627i \(0.526150\pi\)
\(72\) −86.4976 −0.141581
\(73\) 874.055 1.40138 0.700688 0.713468i \(-0.252877\pi\)
0.700688 + 0.713468i \(0.252877\pi\)
\(74\) 71.8418 0.112857
\(75\) 825.354 1.27072
\(76\) 427.561 0.645324
\(77\) 2037.40 3.01537
\(78\) −50.6736 −0.0735597
\(79\) 788.085 1.12236 0.561180 0.827694i \(-0.310348\pi\)
0.561180 + 0.827694i \(0.310348\pi\)
\(80\) −207.964 −0.290639
\(81\) −770.771 −1.05730
\(82\) 24.2414 0.0326466
\(83\) −495.384 −0.655126 −0.327563 0.944829i \(-0.606227\pi\)
−0.327563 + 0.944829i \(0.606227\pi\)
\(84\) −1758.96 −2.28474
\(85\) 194.082 0.247660
\(86\) 0 0
\(87\) −491.483 −0.605661
\(88\) 227.445 0.275519
\(89\) −528.746 −0.629741 −0.314870 0.949135i \(-0.601961\pi\)
−0.314870 + 0.949135i \(0.601961\pi\)
\(90\) −17.9239 −0.0209928
\(91\) −1000.90 −1.15300
\(92\) 1348.56 1.52822
\(93\) 19.7443 0.0220149
\(94\) −5.28004 −0.00579356
\(95\) 177.707 0.191919
\(96\) −294.822 −0.313439
\(97\) 2.16686 0.00226815 0.00113408 0.999999i \(-0.499639\pi\)
0.00113408 + 0.999999i \(0.499639\pi\)
\(98\) 126.397 0.130286
\(99\) −1690.09 −1.71576
\(100\) 907.345 0.907345
\(101\) −748.226 −0.737141 −0.368570 0.929600i \(-0.620153\pi\)
−0.368570 + 0.929600i \(0.620153\pi\)
\(102\) 90.8355 0.0881770
\(103\) 1963.62 1.87846 0.939231 0.343285i \(-0.111540\pi\)
0.939231 + 0.343285i \(0.111540\pi\)
\(104\) −111.735 −0.105351
\(105\) −731.073 −0.679481
\(106\) −127.742 −0.117051
\(107\) −1394.58 −1.26000 −0.629998 0.776597i \(-0.716944\pi\)
−0.629998 + 0.776597i \(0.716944\pi\)
\(108\) −94.8260 −0.0844873
\(109\) −518.030 −0.455214 −0.227607 0.973753i \(-0.573090\pi\)
−0.227607 + 0.973753i \(0.573090\pi\)
\(110\) 47.1308 0.0408523
\(111\) −2430.73 −2.07851
\(112\) −1922.51 −1.62197
\(113\) 383.171 0.318988 0.159494 0.987199i \(-0.449014\pi\)
0.159494 + 0.987199i \(0.449014\pi\)
\(114\) 83.1714 0.0683309
\(115\) 560.499 0.454494
\(116\) −540.307 −0.432468
\(117\) 830.279 0.656062
\(118\) 44.0529 0.0343678
\(119\) 1794.18 1.38212
\(120\) −81.6131 −0.0620852
\(121\) 3113.07 2.33890
\(122\) 83.9620 0.0623079
\(123\) −820.197 −0.601257
\(124\) 21.7057 0.0157196
\(125\) 790.372 0.565544
\(126\) −165.697 −0.117154
\(127\) 60.9317 0.0425733 0.0212867 0.999773i \(-0.493224\pi\)
0.0212867 + 0.999773i \(0.493224\pi\)
\(128\) −431.726 −0.298122
\(129\) 0 0
\(130\) −23.1537 −0.0156209
\(131\) −1069.06 −0.713008 −0.356504 0.934294i \(-0.616031\pi\)
−0.356504 + 0.934294i \(0.616031\pi\)
\(132\) −3836.71 −2.52987
\(133\) 1642.80 1.07104
\(134\) 129.823 0.0836943
\(135\) −39.4124 −0.0251265
\(136\) 200.292 0.126286
\(137\) −1551.04 −0.967260 −0.483630 0.875272i \(-0.660682\pi\)
−0.483630 + 0.875272i \(0.660682\pi\)
\(138\) 262.328 0.161818
\(139\) −818.479 −0.499442 −0.249721 0.968318i \(-0.580339\pi\)
−0.249721 + 0.968318i \(0.580339\pi\)
\(140\) −803.698 −0.485178
\(141\) 178.648 0.106701
\(142\) −20.9968 −0.0124085
\(143\) −2183.21 −1.27671
\(144\) 1594.78 0.922905
\(145\) −224.567 −0.128616
\(146\) 186.916 0.105954
\(147\) −4276.59 −2.39950
\(148\) −2672.20 −1.48415
\(149\) 593.512 0.326325 0.163163 0.986599i \(-0.447831\pi\)
0.163163 + 0.986599i \(0.447831\pi\)
\(150\) 176.502 0.0960753
\(151\) −1565.64 −0.843772 −0.421886 0.906649i \(-0.638632\pi\)
−0.421886 + 0.906649i \(0.638632\pi\)
\(152\) 183.393 0.0978628
\(153\) −1488.32 −0.786431
\(154\) 435.698 0.227984
\(155\) 9.02150 0.00467500
\(156\) 1884.84 0.967357
\(157\) 2808.47 1.42765 0.713823 0.700326i \(-0.246962\pi\)
0.713823 + 0.700326i \(0.246962\pi\)
\(158\) 168.532 0.0848586
\(159\) 4322.09 2.15575
\(160\) −134.709 −0.0665607
\(161\) 5181.50 2.53639
\(162\) −164.829 −0.0799395
\(163\) −1654.13 −0.794856 −0.397428 0.917633i \(-0.630097\pi\)
−0.397428 + 0.917633i \(0.630097\pi\)
\(164\) −901.675 −0.429323
\(165\) −1594.65 −0.752383
\(166\) −105.938 −0.0495323
\(167\) −820.480 −0.380183 −0.190092 0.981766i \(-0.560879\pi\)
−0.190092 + 0.981766i \(0.560879\pi\)
\(168\) −754.467 −0.346478
\(169\) −1124.47 −0.511819
\(170\) 41.5043 0.0187249
\(171\) −1362.75 −0.609428
\(172\) 0 0
\(173\) −3090.35 −1.35812 −0.679060 0.734083i \(-0.737612\pi\)
−0.679060 + 0.734083i \(0.737612\pi\)
\(174\) −105.103 −0.0457924
\(175\) 3486.25 1.50592
\(176\) −4193.46 −1.79599
\(177\) −1490.51 −0.632958
\(178\) −113.072 −0.0476130
\(179\) −443.168 −0.185050 −0.0925249 0.995710i \(-0.529494\pi\)
−0.0925249 + 0.995710i \(0.529494\pi\)
\(180\) 666.692 0.276068
\(181\) 2436.76 1.00068 0.500339 0.865830i \(-0.333209\pi\)
0.500339 + 0.865830i \(0.333209\pi\)
\(182\) −214.043 −0.0871753
\(183\) −2840.81 −1.14754
\(184\) 578.434 0.231754
\(185\) −1110.64 −0.441385
\(186\) 4.22230 0.00166448
\(187\) 3913.54 1.53041
\(188\) 196.395 0.0761891
\(189\) −364.346 −0.140224
\(190\) 38.0025 0.0145105
\(191\) 3887.50 1.47272 0.736360 0.676590i \(-0.236543\pi\)
0.736360 + 0.676590i \(0.236543\pi\)
\(192\) 3578.12 1.34494
\(193\) −984.557 −0.367202 −0.183601 0.983001i \(-0.558775\pi\)
−0.183601 + 0.983001i \(0.558775\pi\)
\(194\) 0.463381 0.000171489 0
\(195\) 783.393 0.287692
\(196\) −4701.42 −1.71335
\(197\) 4103.62 1.48412 0.742058 0.670336i \(-0.233850\pi\)
0.742058 + 0.670336i \(0.233850\pi\)
\(198\) −361.425 −0.129724
\(199\) −1387.37 −0.494212 −0.247106 0.968988i \(-0.579480\pi\)
−0.247106 + 0.968988i \(0.579480\pi\)
\(200\) 389.186 0.137598
\(201\) −4392.51 −1.54141
\(202\) −160.008 −0.0557332
\(203\) −2076.00 −0.717766
\(204\) −3378.68 −1.15958
\(205\) −374.762 −0.127681
\(206\) 419.920 0.142025
\(207\) −4298.21 −1.44322
\(208\) 2060.10 0.686740
\(209\) 3583.34 1.18596
\(210\) −156.340 −0.0513736
\(211\) −1794.07 −0.585349 −0.292675 0.956212i \(-0.594545\pi\)
−0.292675 + 0.956212i \(0.594545\pi\)
\(212\) 4751.45 1.53930
\(213\) 710.416 0.228530
\(214\) −298.231 −0.0952648
\(215\) 0 0
\(216\) −40.6736 −0.0128124
\(217\) 83.3987 0.0260897
\(218\) −110.780 −0.0344174
\(219\) −6324.22 −1.95138
\(220\) −1753.06 −0.537233
\(221\) −1922.58 −0.585189
\(222\) −519.811 −0.157151
\(223\) 3494.65 1.04941 0.524706 0.851284i \(-0.324175\pi\)
0.524706 + 0.851284i \(0.324175\pi\)
\(224\) −1245.31 −0.371455
\(225\) −2891.95 −0.856874
\(226\) 81.9409 0.0241178
\(227\) −5846.94 −1.70958 −0.854790 0.518974i \(-0.826314\pi\)
−0.854790 + 0.518974i \(0.826314\pi\)
\(228\) −3093.61 −0.898595
\(229\) 243.067 0.0701410 0.0350705 0.999385i \(-0.488834\pi\)
0.0350705 + 0.999385i \(0.488834\pi\)
\(230\) 119.862 0.0343630
\(231\) −14741.6 −4.19882
\(232\) −231.753 −0.0655834
\(233\) −459.249 −0.129126 −0.0645630 0.997914i \(-0.520565\pi\)
−0.0645630 + 0.997914i \(0.520565\pi\)
\(234\) 177.555 0.0496031
\(235\) 81.6273 0.0226586
\(236\) −1638.58 −0.451958
\(237\) −5702.18 −1.56285
\(238\) 383.684 0.104498
\(239\) −5216.79 −1.41191 −0.705954 0.708258i \(-0.749481\pi\)
−0.705954 + 0.708258i \(0.749481\pi\)
\(240\) 1504.72 0.404706
\(241\) 4016.94 1.07367 0.536833 0.843688i \(-0.319620\pi\)
0.536833 + 0.843688i \(0.319620\pi\)
\(242\) 665.730 0.176838
\(243\) 5255.03 1.38729
\(244\) −3123.02 −0.819389
\(245\) −1954.05 −0.509549
\(246\) −175.399 −0.0454594
\(247\) −1760.37 −0.453479
\(248\) 9.31018 0.00238386
\(249\) 3584.35 0.912245
\(250\) 169.021 0.0427592
\(251\) −6018.47 −1.51348 −0.756739 0.653718i \(-0.773208\pi\)
−0.756739 + 0.653718i \(0.773208\pi\)
\(252\) 6163.19 1.54065
\(253\) 11302.1 2.80853
\(254\) 13.0302 0.00321885
\(255\) −1404.28 −0.344860
\(256\) 3863.86 0.943324
\(257\) 7266.87 1.76379 0.881897 0.471442i \(-0.156266\pi\)
0.881897 + 0.471442i \(0.156266\pi\)
\(258\) 0 0
\(259\) −10267.3 −2.46324
\(260\) 861.215 0.205424
\(261\) 1722.10 0.408412
\(262\) −228.618 −0.0539086
\(263\) 2259.66 0.529796 0.264898 0.964276i \(-0.414662\pi\)
0.264898 + 0.964276i \(0.414662\pi\)
\(264\) −1645.68 −0.383653
\(265\) 1974.84 0.457787
\(266\) 351.312 0.0809786
\(267\) 3825.74 0.876896
\(268\) −4828.86 −1.10063
\(269\) 5104.54 1.15699 0.578493 0.815687i \(-0.303641\pi\)
0.578493 + 0.815687i \(0.303641\pi\)
\(270\) −8.42833 −0.00189975
\(271\) −2818.35 −0.631744 −0.315872 0.948802i \(-0.602297\pi\)
−0.315872 + 0.948802i \(0.602297\pi\)
\(272\) −3692.84 −0.823204
\(273\) 7242.03 1.60552
\(274\) −331.690 −0.0731319
\(275\) 7604.36 1.66749
\(276\) −9757.47 −2.12801
\(277\) −3983.20 −0.863998 −0.431999 0.901874i \(-0.642192\pi\)
−0.431999 + 0.901874i \(0.642192\pi\)
\(278\) −175.031 −0.0377614
\(279\) −69.1817 −0.0148452
\(280\) −344.729 −0.0735768
\(281\) −3607.30 −0.765813 −0.382906 0.923787i \(-0.625077\pi\)
−0.382906 + 0.923787i \(0.625077\pi\)
\(282\) 38.2037 0.00806737
\(283\) 8143.20 1.71047 0.855235 0.518240i \(-0.173413\pi\)
0.855235 + 0.518240i \(0.173413\pi\)
\(284\) 780.988 0.163180
\(285\) −1285.80 −0.267242
\(286\) −466.879 −0.0965284
\(287\) −3464.47 −0.712547
\(288\) 1033.02 0.211359
\(289\) −1466.66 −0.298527
\(290\) −48.0236 −0.00972429
\(291\) −15.6783 −0.00315834
\(292\) −6952.47 −1.39336
\(293\) −5015.12 −0.999954 −0.499977 0.866039i \(-0.666658\pi\)
−0.499977 + 0.866039i \(0.666658\pi\)
\(294\) −914.546 −0.181420
\(295\) −681.040 −0.134412
\(296\) −1146.18 −0.225069
\(297\) −794.726 −0.155268
\(298\) 126.922 0.0246725
\(299\) −5552.31 −1.07391
\(300\) −6565.09 −1.26345
\(301\) 0 0
\(302\) −334.810 −0.0637953
\(303\) 5413.78 1.02645
\(304\) −3381.27 −0.637924
\(305\) −1298.02 −0.243686
\(306\) −318.277 −0.0594598
\(307\) −4183.41 −0.777720 −0.388860 0.921297i \(-0.627131\pi\)
−0.388860 + 0.921297i \(0.627131\pi\)
\(308\) −16206.1 −2.99814
\(309\) −14207.8 −2.61571
\(310\) 1.92924 0.000353464 0
\(311\) 10090.2 1.83975 0.919875 0.392211i \(-0.128290\pi\)
0.919875 + 0.392211i \(0.128290\pi\)
\(312\) 808.460 0.146699
\(313\) 7623.64 1.37672 0.688360 0.725369i \(-0.258331\pi\)
0.688360 + 0.725369i \(0.258331\pi\)
\(314\) 600.591 0.107940
\(315\) 2561.60 0.458190
\(316\) −6268.64 −1.11594
\(317\) −2555.28 −0.452740 −0.226370 0.974041i \(-0.572686\pi\)
−0.226370 + 0.974041i \(0.572686\pi\)
\(318\) 924.277 0.162990
\(319\) −4528.26 −0.794777
\(320\) 1634.90 0.285606
\(321\) 10090.5 1.75451
\(322\) 1108.06 0.191770
\(323\) 3155.56 0.543592
\(324\) 6130.92 1.05126
\(325\) −3735.75 −0.637606
\(326\) −353.735 −0.0600969
\(327\) 3748.20 0.633872
\(328\) −386.754 −0.0651065
\(329\) 754.598 0.126451
\(330\) −341.015 −0.0568856
\(331\) 4133.00 0.686315 0.343157 0.939278i \(-0.388504\pi\)
0.343157 + 0.939278i \(0.388504\pi\)
\(332\) 3940.42 0.651381
\(333\) 8517.02 1.40159
\(334\) −175.459 −0.0287446
\(335\) −2007.02 −0.327328
\(336\) 13910.3 2.25854
\(337\) −1330.25 −0.215024 −0.107512 0.994204i \(-0.534288\pi\)
−0.107512 + 0.994204i \(0.534288\pi\)
\(338\) −240.467 −0.0386972
\(339\) −2772.43 −0.444182
\(340\) −1543.78 −0.246245
\(341\) 181.913 0.0288890
\(342\) −291.424 −0.0460771
\(343\) −7581.19 −1.19343
\(344\) 0 0
\(345\) −4055.49 −0.632870
\(346\) −660.869 −0.102684
\(347\) −8891.64 −1.37559 −0.687793 0.725907i \(-0.741420\pi\)
−0.687793 + 0.725907i \(0.741420\pi\)
\(348\) 3909.39 0.602199
\(349\) −6098.16 −0.935320 −0.467660 0.883908i \(-0.654903\pi\)
−0.467660 + 0.883908i \(0.654903\pi\)
\(350\) 745.533 0.113858
\(351\) 390.420 0.0593706
\(352\) −2716.33 −0.411309
\(353\) 7243.90 1.09222 0.546110 0.837713i \(-0.316108\pi\)
0.546110 + 0.837713i \(0.316108\pi\)
\(354\) −318.745 −0.0478562
\(355\) 324.601 0.0485297
\(356\) 4205.79 0.626141
\(357\) −12981.8 −1.92456
\(358\) −94.7712 −0.0139911
\(359\) −496.292 −0.0729618 −0.0364809 0.999334i \(-0.511615\pi\)
−0.0364809 + 0.999334i \(0.511615\pi\)
\(360\) 285.963 0.0418655
\(361\) −3969.68 −0.578755
\(362\) 521.099 0.0756585
\(363\) −22524.6 −3.25685
\(364\) 7961.45 1.14641
\(365\) −2889.65 −0.414387
\(366\) −607.507 −0.0867620
\(367\) −1824.67 −0.259529 −0.129765 0.991545i \(-0.541422\pi\)
−0.129765 + 0.991545i \(0.541422\pi\)
\(368\) −10664.7 −1.51070
\(369\) 2873.88 0.405442
\(370\) −237.511 −0.0333719
\(371\) 18256.3 2.55477
\(372\) −157.051 −0.0218890
\(373\) −9254.89 −1.28472 −0.642359 0.766404i \(-0.722044\pi\)
−0.642359 + 0.766404i \(0.722044\pi\)
\(374\) 836.908 0.115710
\(375\) −5718.73 −0.787504
\(376\) 84.2392 0.0115540
\(377\) 2224.57 0.303902
\(378\) −77.9152 −0.0106019
\(379\) −1365.96 −0.185131 −0.0925653 0.995707i \(-0.529507\pi\)
−0.0925653 + 0.995707i \(0.529507\pi\)
\(380\) −1413.53 −0.190822
\(381\) −440.871 −0.0592822
\(382\) 831.339 0.111348
\(383\) 5408.14 0.721522 0.360761 0.932658i \(-0.382517\pi\)
0.360761 + 0.932658i \(0.382517\pi\)
\(384\) 3123.75 0.415126
\(385\) −6735.71 −0.891646
\(386\) −210.547 −0.0277631
\(387\) 0 0
\(388\) −17.2358 −0.00225519
\(389\) −4751.47 −0.619304 −0.309652 0.950850i \(-0.600212\pi\)
−0.309652 + 0.950850i \(0.600212\pi\)
\(390\) 167.528 0.0217516
\(391\) 9952.85 1.28731
\(392\) −2016.57 −0.259828
\(393\) 7735.17 0.992843
\(394\) 877.558 0.112210
\(395\) −2605.43 −0.331882
\(396\) 13443.4 1.70595
\(397\) 1510.65 0.190975 0.0954876 0.995431i \(-0.469559\pi\)
0.0954876 + 0.995431i \(0.469559\pi\)
\(398\) −296.689 −0.0373660
\(399\) −11886.5 −1.49140
\(400\) −7175.53 −0.896942
\(401\) −4681.87 −0.583046 −0.291523 0.956564i \(-0.594162\pi\)
−0.291523 + 0.956564i \(0.594162\pi\)
\(402\) −939.337 −0.116542
\(403\) −89.3672 −0.0110464
\(404\) 5951.59 0.732927
\(405\) 2548.19 0.312643
\(406\) −443.951 −0.0542683
\(407\) −22395.4 −2.72752
\(408\) −1449.21 −0.175850
\(409\) −6753.27 −0.816449 −0.408224 0.912882i \(-0.633852\pi\)
−0.408224 + 0.912882i \(0.633852\pi\)
\(410\) −80.1428 −0.00965358
\(411\) 11222.6 1.34688
\(412\) −15619.2 −1.86772
\(413\) −6295.83 −0.750115
\(414\) −919.169 −0.109118
\(415\) 1637.75 0.193721
\(416\) 1334.43 0.157274
\(417\) 5922.10 0.695459
\(418\) 766.296 0.0896669
\(419\) 10883.5 1.26896 0.634481 0.772939i \(-0.281214\pi\)
0.634481 + 0.772939i \(0.281214\pi\)
\(420\) 5815.15 0.675596
\(421\) 12444.8 1.44067 0.720334 0.693628i \(-0.243989\pi\)
0.720334 + 0.693628i \(0.243989\pi\)
\(422\) −383.661 −0.0442566
\(423\) −625.962 −0.0719511
\(424\) 2038.03 0.233433
\(425\) 6696.55 0.764307
\(426\) 151.922 0.0172785
\(427\) −11999.4 −1.35994
\(428\) 11092.9 1.25279
\(429\) 15796.6 1.77778
\(430\) 0 0
\(431\) 7870.01 0.879547 0.439774 0.898109i \(-0.355059\pi\)
0.439774 + 0.898109i \(0.355059\pi\)
\(432\) 749.910 0.0835186
\(433\) 2427.39 0.269407 0.134703 0.990886i \(-0.456992\pi\)
0.134703 + 0.990886i \(0.456992\pi\)
\(434\) 17.8348 0.00197257
\(435\) 1624.86 0.179094
\(436\) 4120.55 0.452611
\(437\) 9113.10 0.997572
\(438\) −1352.43 −0.147538
\(439\) −9708.09 −1.05545 −0.527724 0.849416i \(-0.676955\pi\)
−0.527724 + 0.849416i \(0.676955\pi\)
\(440\) −751.938 −0.0814710
\(441\) 14984.7 1.61804
\(442\) −411.143 −0.0442445
\(443\) −1853.67 −0.198805 −0.0994023 0.995047i \(-0.531693\pi\)
−0.0994023 + 0.995047i \(0.531693\pi\)
\(444\) 19334.7 2.06663
\(445\) 1748.05 0.186214
\(446\) 747.329 0.0793431
\(447\) −4294.36 −0.454398
\(448\) 15113.8 1.59388
\(449\) 12703.8 1.33525 0.667627 0.744496i \(-0.267310\pi\)
0.667627 + 0.744496i \(0.267310\pi\)
\(450\) −618.442 −0.0647859
\(451\) −7556.84 −0.788997
\(452\) −3047.84 −0.317165
\(453\) 11328.1 1.17493
\(454\) −1250.36 −0.129257
\(455\) 3309.01 0.340942
\(456\) −1326.94 −0.136271
\(457\) 3614.91 0.370018 0.185009 0.982737i \(-0.440769\pi\)
0.185009 + 0.982737i \(0.440769\pi\)
\(458\) 51.9797 0.00530317
\(459\) −699.852 −0.0711683
\(460\) −4458.36 −0.451896
\(461\) −1454.92 −0.146990 −0.0734948 0.997296i \(-0.523415\pi\)
−0.0734948 + 0.997296i \(0.523415\pi\)
\(462\) −3152.49 −0.317461
\(463\) 1007.60 0.101139 0.0505694 0.998721i \(-0.483896\pi\)
0.0505694 + 0.998721i \(0.483896\pi\)
\(464\) 4272.90 0.427509
\(465\) −65.2750 −0.00650980
\(466\) −98.2101 −0.00976286
\(467\) 12311.1 1.21989 0.609946 0.792443i \(-0.291191\pi\)
0.609946 + 0.792443i \(0.291191\pi\)
\(468\) −6604.26 −0.652312
\(469\) −18553.7 −1.82672
\(470\) 17.4560 0.00171316
\(471\) −20320.7 −1.98796
\(472\) −702.832 −0.0685391
\(473\) 0 0
\(474\) −1219.41 −0.118163
\(475\) 6131.54 0.592283
\(476\) −14271.4 −1.37422
\(477\) −15144.1 −1.45367
\(478\) −1115.61 −0.106750
\(479\) 15343.4 1.46359 0.731795 0.681524i \(-0.238683\pi\)
0.731795 + 0.681524i \(0.238683\pi\)
\(480\) 974.689 0.0926838
\(481\) 11002.1 1.04293
\(482\) 859.020 0.0811770
\(483\) −37490.7 −3.53185
\(484\) −24762.2 −2.32553
\(485\) −7.16368 −0.000670693 0
\(486\) 1123.79 0.104889
\(487\) 1291.92 0.120211 0.0601053 0.998192i \(-0.480856\pi\)
0.0601053 + 0.998192i \(0.480856\pi\)
\(488\) −1339.55 −0.124260
\(489\) 11968.5 1.10681
\(490\) −417.872 −0.0385256
\(491\) −8952.69 −0.822870 −0.411435 0.911439i \(-0.634972\pi\)
−0.411435 + 0.911439i \(0.634972\pi\)
\(492\) 6524.06 0.597820
\(493\) −3987.67 −0.364291
\(494\) −376.454 −0.0342863
\(495\) 5587.47 0.507350
\(496\) −171.654 −0.0155393
\(497\) 3000.76 0.270830
\(498\) 766.512 0.0689723
\(499\) 18751.4 1.68222 0.841110 0.540864i \(-0.181903\pi\)
0.841110 + 0.540864i \(0.181903\pi\)
\(500\) −6286.83 −0.562311
\(501\) 5936.57 0.529394
\(502\) −1287.05 −0.114430
\(503\) 1320.15 0.117023 0.0585116 0.998287i \(-0.481365\pi\)
0.0585116 + 0.998287i \(0.481365\pi\)
\(504\) 2643.57 0.233639
\(505\) 2473.65 0.217972
\(506\) 2416.95 0.212345
\(507\) 8136.07 0.712694
\(508\) −484.667 −0.0423300
\(509\) 15917.4 1.38610 0.693049 0.720890i \(-0.256267\pi\)
0.693049 + 0.720890i \(0.256267\pi\)
\(510\) −300.304 −0.0260739
\(511\) −26713.2 −2.31257
\(512\) 4280.09 0.369444
\(513\) −640.803 −0.0551504
\(514\) 1554.02 0.133356
\(515\) −6491.79 −0.555461
\(516\) 0 0
\(517\) 1645.96 0.140018
\(518\) −2195.65 −0.186238
\(519\) 22360.2 1.89114
\(520\) 369.400 0.0311524
\(521\) −12988.8 −1.09223 −0.546115 0.837710i \(-0.683894\pi\)
−0.546115 + 0.837710i \(0.683894\pi\)
\(522\) 368.271 0.0308789
\(523\) −6216.75 −0.519770 −0.259885 0.965640i \(-0.583685\pi\)
−0.259885 + 0.965640i \(0.583685\pi\)
\(524\) 8503.58 0.708932
\(525\) −25224.8 −2.09695
\(526\) 483.227 0.0400564
\(527\) 160.196 0.0132415
\(528\) 30341.8 2.50086
\(529\) 16576.3 1.36240
\(530\) 422.319 0.0346120
\(531\) 5222.58 0.426818
\(532\) −13067.3 −1.06492
\(533\) 3712.40 0.301692
\(534\) 818.132 0.0662997
\(535\) 4610.53 0.372580
\(536\) −2071.24 −0.166910
\(537\) 3206.54 0.257677
\(538\) 1091.60 0.0874765
\(539\) −39402.1 −3.14874
\(540\) 313.497 0.0249829
\(541\) 5366.36 0.426465 0.213233 0.977001i \(-0.431601\pi\)
0.213233 + 0.977001i \(0.431601\pi\)
\(542\) −602.703 −0.0477644
\(543\) −17631.1 −1.39341
\(544\) −2392.05 −0.188526
\(545\) 1712.62 0.134607
\(546\) 1548.70 0.121389
\(547\) 8933.86 0.698326 0.349163 0.937062i \(-0.386466\pi\)
0.349163 + 0.937062i \(0.386466\pi\)
\(548\) 12337.4 0.961731
\(549\) 9953.90 0.773810
\(550\) 1626.19 0.126074
\(551\) −3651.22 −0.282300
\(552\) −4185.26 −0.322711
\(553\) −24085.7 −1.85213
\(554\) −851.806 −0.0653245
\(555\) 8036.06 0.614616
\(556\) 6510.40 0.496587
\(557\) 11275.9 0.857762 0.428881 0.903361i \(-0.358908\pi\)
0.428881 + 0.903361i \(0.358908\pi\)
\(558\) −14.7945 −0.00112240
\(559\) 0 0
\(560\) 6355.87 0.479615
\(561\) −28316.4 −2.13105
\(562\) −771.419 −0.0579010
\(563\) −1065.62 −0.0797704 −0.0398852 0.999204i \(-0.512699\pi\)
−0.0398852 + 0.999204i \(0.512699\pi\)
\(564\) −1421.01 −0.106091
\(565\) −1266.77 −0.0943248
\(566\) 1741.42 0.129324
\(567\) 23556.6 1.74477
\(568\) 334.988 0.0247461
\(569\) 14804.4 1.09074 0.545370 0.838196i \(-0.316389\pi\)
0.545370 + 0.838196i \(0.316389\pi\)
\(570\) −274.967 −0.0202054
\(571\) −16641.0 −1.21962 −0.609812 0.792546i \(-0.708755\pi\)
−0.609812 + 0.792546i \(0.708755\pi\)
\(572\) 17365.9 1.26941
\(573\) −28128.0 −2.05072
\(574\) −740.875 −0.0538737
\(575\) 19339.3 1.40262
\(576\) −12537.3 −0.906924
\(577\) −12019.2 −0.867183 −0.433591 0.901110i \(-0.642754\pi\)
−0.433591 + 0.901110i \(0.642754\pi\)
\(578\) −313.645 −0.0225708
\(579\) 7123.76 0.511318
\(580\) 1786.27 0.127881
\(581\) 15140.1 1.08110
\(582\) −3.35279 −0.000238793 0
\(583\) 39821.4 2.82887
\(584\) −2982.11 −0.211303
\(585\) −2744.92 −0.193998
\(586\) −1072.48 −0.0756038
\(587\) 14904.6 1.04801 0.524004 0.851716i \(-0.324438\pi\)
0.524004 + 0.851716i \(0.324438\pi\)
\(588\) 34017.1 2.38579
\(589\) 146.680 0.0102612
\(590\) −145.640 −0.0101626
\(591\) −29691.7 −2.06659
\(592\) 21132.5 1.46713
\(593\) 11518.4 0.797649 0.398824 0.917027i \(-0.369418\pi\)
0.398824 + 0.917027i \(0.369418\pi\)
\(594\) −169.952 −0.0117394
\(595\) −5931.60 −0.408692
\(596\) −4720.96 −0.324460
\(597\) 10038.3 0.688177
\(598\) −1187.36 −0.0811952
\(599\) 4433.16 0.302394 0.151197 0.988504i \(-0.451687\pi\)
0.151197 + 0.988504i \(0.451687\pi\)
\(600\) −2815.95 −0.191601
\(601\) 25109.7 1.70424 0.852119 0.523347i \(-0.175317\pi\)
0.852119 + 0.523347i \(0.175317\pi\)
\(602\) 0 0
\(603\) 15390.9 1.03941
\(604\) 12453.5 0.838949
\(605\) −10291.9 −0.691612
\(606\) 1157.73 0.0776069
\(607\) 2512.35 0.167995 0.0839976 0.996466i \(-0.473231\pi\)
0.0839976 + 0.996466i \(0.473231\pi\)
\(608\) −2190.23 −0.146094
\(609\) 15020.9 0.999469
\(610\) −277.581 −0.0184244
\(611\) −808.601 −0.0535393
\(612\) 11838.5 0.781935
\(613\) −19653.8 −1.29496 −0.647479 0.762083i \(-0.724177\pi\)
−0.647479 + 0.762083i \(0.724177\pi\)
\(614\) −894.621 −0.0588013
\(615\) 2711.59 0.177792
\(616\) −6951.24 −0.454665
\(617\) −2093.92 −0.136626 −0.0683129 0.997664i \(-0.521762\pi\)
−0.0683129 + 0.997664i \(0.521762\pi\)
\(618\) −3038.33 −0.197766
\(619\) 13916.5 0.903635 0.451817 0.892110i \(-0.350776\pi\)
0.451817 + 0.892110i \(0.350776\pi\)
\(620\) −71.7595 −0.00464827
\(621\) −2021.14 −0.130605
\(622\) 2157.78 0.139098
\(623\) 16159.7 1.03921
\(624\) −14905.8 −0.956266
\(625\) 11645.8 0.745330
\(626\) 1630.31 0.104090
\(627\) −25927.3 −1.65141
\(628\) −22339.3 −1.41949
\(629\) −19721.9 −1.25018
\(630\) 547.797 0.0346425
\(631\) 8609.66 0.543178 0.271589 0.962413i \(-0.412451\pi\)
0.271589 + 0.962413i \(0.412451\pi\)
\(632\) −2688.80 −0.169232
\(633\) 12981.0 0.815082
\(634\) −546.444 −0.0342304
\(635\) −201.442 −0.0125889
\(636\) −34379.1 −2.14343
\(637\) 19356.8 1.20400
\(638\) −968.366 −0.0600909
\(639\) −2489.22 −0.154103
\(640\) 1427.30 0.0881546
\(641\) 13316.9 0.820570 0.410285 0.911957i \(-0.365429\pi\)
0.410285 + 0.911957i \(0.365429\pi\)
\(642\) 2157.85 0.132653
\(643\) 17434.2 1.06927 0.534633 0.845084i \(-0.320450\pi\)
0.534633 + 0.845084i \(0.320450\pi\)
\(644\) −41215.0 −2.52189
\(645\) 0 0
\(646\) 674.815 0.0410995
\(647\) 12415.4 0.754402 0.377201 0.926131i \(-0.376887\pi\)
0.377201 + 0.926131i \(0.376887\pi\)
\(648\) 2629.73 0.159422
\(649\) −13732.7 −0.830596
\(650\) −798.888 −0.0482076
\(651\) −603.431 −0.0363292
\(652\) 13157.4 0.790312
\(653\) 13796.2 0.826781 0.413390 0.910554i \(-0.364345\pi\)
0.413390 + 0.910554i \(0.364345\pi\)
\(654\) 801.552 0.0479253
\(655\) 3534.33 0.210836
\(656\) 7130.69 0.424401
\(657\) 22159.4 1.31586
\(658\) 161.370 0.00956060
\(659\) 20453.4 1.20903 0.604516 0.796593i \(-0.293366\pi\)
0.604516 + 0.796593i \(0.293366\pi\)
\(660\) 12684.3 0.748082
\(661\) 6563.71 0.386231 0.193116 0.981176i \(-0.438141\pi\)
0.193116 + 0.981176i \(0.438141\pi\)
\(662\) 883.840 0.0518904
\(663\) 13910.8 0.814858
\(664\) 1690.16 0.0987814
\(665\) −5431.13 −0.316707
\(666\) 1821.36 0.105970
\(667\) −11516.2 −0.668529
\(668\) 6526.31 0.378010
\(669\) −25285.5 −1.46128
\(670\) −429.200 −0.0247484
\(671\) −26173.7 −1.50585
\(672\) 9010.45 0.517240
\(673\) −11849.9 −0.678720 −0.339360 0.940657i \(-0.610210\pi\)
−0.339360 + 0.940657i \(0.610210\pi\)
\(674\) −284.473 −0.0162574
\(675\) −1359.88 −0.0775432
\(676\) 8944.31 0.508894
\(677\) −4684.29 −0.265926 −0.132963 0.991121i \(-0.542449\pi\)
−0.132963 + 0.991121i \(0.542449\pi\)
\(678\) −592.883 −0.0335834
\(679\) −66.2242 −0.00374293
\(680\) −662.171 −0.0373428
\(681\) 42305.5 2.38054
\(682\) 38.9020 0.00218421
\(683\) 5928.82 0.332152 0.166076 0.986113i \(-0.446890\pi\)
0.166076 + 0.986113i \(0.446890\pi\)
\(684\) 10839.7 0.605944
\(685\) 5127.79 0.286019
\(686\) −1621.23 −0.0902318
\(687\) −1758.71 −0.0976694
\(688\) 0 0
\(689\) −19562.8 −1.08169
\(690\) −867.264 −0.0478495
\(691\) −19182.3 −1.05605 −0.528025 0.849229i \(-0.677067\pi\)
−0.528025 + 0.849229i \(0.677067\pi\)
\(692\) 24581.4 1.35036
\(693\) 51653.0 2.83137
\(694\) −1901.47 −0.104004
\(695\) 2705.91 0.147685
\(696\) 1676.85 0.0913230
\(697\) −6654.70 −0.361643
\(698\) −1304.09 −0.0707170
\(699\) 3322.89 0.179804
\(700\) −27730.6 −1.49731
\(701\) 14967.8 0.806457 0.403229 0.915099i \(-0.367888\pi\)
0.403229 + 0.915099i \(0.367888\pi\)
\(702\) 83.4912 0.00448885
\(703\) −18057.9 −0.968799
\(704\) 32966.8 1.76489
\(705\) −590.614 −0.0315515
\(706\) 1549.10 0.0825798
\(707\) 22867.5 1.21644
\(708\) 11855.9 0.629339
\(709\) −3735.54 −0.197872 −0.0989360 0.995094i \(-0.531544\pi\)
−0.0989360 + 0.995094i \(0.531544\pi\)
\(710\) 69.4159 0.00366920
\(711\) 19979.8 1.05387
\(712\) 1803.98 0.0949538
\(713\) 462.638 0.0243000
\(714\) −2776.14 −0.145511
\(715\) 7217.76 0.377523
\(716\) 3525.07 0.183992
\(717\) 37746.0 1.96604
\(718\) −106.132 −0.00551644
\(719\) −21766.2 −1.12899 −0.564493 0.825438i \(-0.690928\pi\)
−0.564493 + 0.825438i \(0.690928\pi\)
\(720\) −5272.38 −0.272903
\(721\) −60012.9 −3.09986
\(722\) −848.915 −0.0437581
\(723\) −29064.5 −1.49505
\(724\) −19382.6 −0.994957
\(725\) −7748.41 −0.396922
\(726\) −4816.88 −0.246241
\(727\) −13634.0 −0.695537 −0.347769 0.937580i \(-0.613061\pi\)
−0.347769 + 0.937580i \(0.613061\pi\)
\(728\) 3414.89 0.173852
\(729\) −17211.9 −0.874457
\(730\) −617.950 −0.0313306
\(731\) 0 0
\(732\) 22596.6 1.14098
\(733\) 6863.64 0.345859 0.172929 0.984934i \(-0.444677\pi\)
0.172929 + 0.984934i \(0.444677\pi\)
\(734\) −390.206 −0.0196223
\(735\) 14138.5 0.709533
\(736\) −6908.12 −0.345974
\(737\) −40470.2 −2.02271
\(738\) 614.578 0.0306544
\(739\) −22700.3 −1.12996 −0.564982 0.825103i \(-0.691117\pi\)
−0.564982 + 0.825103i \(0.691117\pi\)
\(740\) 8834.37 0.438862
\(741\) 12737.1 0.631457
\(742\) 3904.10 0.193159
\(743\) −33576.5 −1.65788 −0.828939 0.559339i \(-0.811055\pi\)
−0.828939 + 0.559339i \(0.811055\pi\)
\(744\) −67.3637 −0.00331945
\(745\) −1962.17 −0.0964943
\(746\) −1979.15 −0.0971340
\(747\) −12559.2 −0.615148
\(748\) −31129.3 −1.52166
\(749\) 42621.7 2.07926
\(750\) −1222.95 −0.0595410
\(751\) −24851.7 −1.20753 −0.603763 0.797164i \(-0.706333\pi\)
−0.603763 + 0.797164i \(0.706333\pi\)
\(752\) −1553.14 −0.0753155
\(753\) 43546.6 2.10747
\(754\) 475.723 0.0229772
\(755\) 5176.03 0.249503
\(756\) 2898.10 0.139422
\(757\) 7571.57 0.363532 0.181766 0.983342i \(-0.441819\pi\)
0.181766 + 0.983342i \(0.441819\pi\)
\(758\) −292.109 −0.0139972
\(759\) −81776.3 −3.91079
\(760\) −606.302 −0.0289380
\(761\) −9150.62 −0.435887 −0.217943 0.975961i \(-0.569935\pi\)
−0.217943 + 0.975961i \(0.569935\pi\)
\(762\) −94.2801 −0.00448216
\(763\) 15832.2 0.751198
\(764\) −30922.2 −1.46430
\(765\) 4920.44 0.232547
\(766\) 1156.53 0.0545523
\(767\) 6746.39 0.317599
\(768\) −27956.9 −1.31355
\(769\) −14125.8 −0.662404 −0.331202 0.943560i \(-0.607454\pi\)
−0.331202 + 0.943560i \(0.607454\pi\)
\(770\) −1440.43 −0.0674149
\(771\) −52579.4 −2.45603
\(772\) 7831.43 0.365103
\(773\) 12974.0 0.603678 0.301839 0.953359i \(-0.402399\pi\)
0.301839 + 0.953359i \(0.402399\pi\)
\(774\) 0 0
\(775\) 311.275 0.0144275
\(776\) −7.39291 −0.000341997 0
\(777\) 74288.9 3.42998
\(778\) −1016.10 −0.0468238
\(779\) −6093.23 −0.280247
\(780\) −6231.32 −0.286047
\(781\) 6545.38 0.299888
\(782\) 2128.41 0.0973298
\(783\) 809.781 0.0369594
\(784\) 37180.1 1.69370
\(785\) −9284.88 −0.422155
\(786\) 1654.16 0.0750662
\(787\) 14982.2 0.678600 0.339300 0.940678i \(-0.389810\pi\)
0.339300 + 0.940678i \(0.389810\pi\)
\(788\) −32641.3 −1.47563
\(789\) −16349.7 −0.737726
\(790\) −557.170 −0.0250927
\(791\) −11710.6 −0.526398
\(792\) 5766.26 0.258706
\(793\) 12858.2 0.575798
\(794\) 323.051 0.0144391
\(795\) −14288.9 −0.637455
\(796\) 11035.5 0.491387
\(797\) 6159.90 0.273770 0.136885 0.990587i \(-0.456291\pi\)
0.136885 + 0.990587i \(0.456291\pi\)
\(798\) −2541.91 −0.112760
\(799\) 1449.47 0.0641782
\(800\) −4647.97 −0.205413
\(801\) −13405.0 −0.591312
\(802\) −1001.22 −0.0440825
\(803\) −58267.9 −2.56068
\(804\) 34939.2 1.53260
\(805\) −17130.2 −0.750011
\(806\) −19.1111 −0.000835187 0
\(807\) −36933.9 −1.61107
\(808\) 2552.81 0.111148
\(809\) 1822.38 0.0791982 0.0395991 0.999216i \(-0.487392\pi\)
0.0395991 + 0.999216i \(0.487392\pi\)
\(810\) 544.929 0.0236381
\(811\) 11549.1 0.500053 0.250027 0.968239i \(-0.419561\pi\)
0.250027 + 0.968239i \(0.419561\pi\)
\(812\) 16513.0 0.713663
\(813\) 20392.2 0.879685
\(814\) −4789.25 −0.206220
\(815\) 5468.60 0.235039
\(816\) 26719.5 1.14629
\(817\) 0 0
\(818\) −1444.18 −0.0617294
\(819\) −25375.3 −1.08264
\(820\) 2980.96 0.126951
\(821\) 18127.6 0.770593 0.385296 0.922793i \(-0.374099\pi\)
0.385296 + 0.922793i \(0.374099\pi\)
\(822\) 2399.94 0.101834
\(823\) −5421.11 −0.229609 −0.114804 0.993388i \(-0.536624\pi\)
−0.114804 + 0.993388i \(0.536624\pi\)
\(824\) −6699.52 −0.283239
\(825\) −55021.3 −2.32194
\(826\) −1346.36 −0.0567141
\(827\) −19267.7 −0.810160 −0.405080 0.914281i \(-0.632756\pi\)
−0.405080 + 0.914281i \(0.632756\pi\)
\(828\) 34189.1 1.43497
\(829\) −4914.30 −0.205887 −0.102944 0.994687i \(-0.532826\pi\)
−0.102944 + 0.994687i \(0.532826\pi\)
\(830\) 350.233 0.0146467
\(831\) 28820.4 1.20309
\(832\) −16195.4 −0.674849
\(833\) −34698.3 −1.44325
\(834\) 1266.44 0.0525817
\(835\) 2712.53 0.112420
\(836\) −28502.9 −1.17918
\(837\) −32.5312 −0.00134342
\(838\) 2327.44 0.0959427
\(839\) 32743.9 1.34737 0.673687 0.739017i \(-0.264710\pi\)
0.673687 + 0.739017i \(0.264710\pi\)
\(840\) 2494.29 0.102454
\(841\) −19775.0 −0.810815
\(842\) 2661.31 0.108925
\(843\) 26100.6 1.06637
\(844\) 14270.5 0.582003
\(845\) 3717.52 0.151345
\(846\) −133.862 −0.00544002
\(847\) −95142.8 −3.85968
\(848\) −37575.8 −1.52165
\(849\) −58920.1 −2.38178
\(850\) 1432.05 0.0577871
\(851\) −56955.7 −2.29426
\(852\) −5650.84 −0.227224
\(853\) −12007.0 −0.481959 −0.240979 0.970530i \(-0.577469\pi\)
−0.240979 + 0.970530i \(0.577469\pi\)
\(854\) −2566.08 −0.102821
\(855\) 4505.29 0.180208
\(856\) 4758.06 0.189985
\(857\) 38581.8 1.53784 0.768921 0.639344i \(-0.220794\pi\)
0.768921 + 0.639344i \(0.220794\pi\)
\(858\) 3378.10 0.134413
\(859\) −6919.06 −0.274826 −0.137413 0.990514i \(-0.543879\pi\)
−0.137413 + 0.990514i \(0.543879\pi\)
\(860\) 0 0
\(861\) 25067.1 0.992201
\(862\) 1683.00 0.0665002
\(863\) −12317.1 −0.485841 −0.242920 0.970046i \(-0.578105\pi\)
−0.242920 + 0.970046i \(0.578105\pi\)
\(864\) 485.756 0.0191270
\(865\) 10216.8 0.401596
\(866\) 519.097 0.0203691
\(867\) 10612.0 0.415690
\(868\) −663.376 −0.0259406
\(869\) −52536.8 −2.05085
\(870\) 347.475 0.0135408
\(871\) 19881.5 0.773433
\(872\) 1767.42 0.0686381
\(873\) 54.9349 0.00212974
\(874\) 1948.83 0.0754236
\(875\) −24155.6 −0.933267
\(876\) 50304.5 1.94022
\(877\) 18339.0 0.706115 0.353058 0.935602i \(-0.385142\pi\)
0.353058 + 0.935602i \(0.385142\pi\)
\(878\) −2076.07 −0.0797996
\(879\) 36286.9 1.39241
\(880\) 13863.7 0.531074
\(881\) −22751.1 −0.870040 −0.435020 0.900421i \(-0.643259\pi\)
−0.435020 + 0.900421i \(0.643259\pi\)
\(882\) 3204.47 0.122336
\(883\) 22792.2 0.868649 0.434325 0.900756i \(-0.356987\pi\)
0.434325 + 0.900756i \(0.356987\pi\)
\(884\) 15292.7 0.581843
\(885\) 4927.66 0.187165
\(886\) −396.406 −0.0150311
\(887\) −15601.2 −0.590572 −0.295286 0.955409i \(-0.595415\pi\)
−0.295286 + 0.955409i \(0.595415\pi\)
\(888\) 8293.20 0.313403
\(889\) −1862.22 −0.0702550
\(890\) 373.819 0.0140792
\(891\) 51382.6 1.93197
\(892\) −27797.4 −1.04341
\(893\) 1327.17 0.0497336
\(894\) −918.346 −0.0343558
\(895\) 1465.12 0.0547192
\(896\) 13194.6 0.491964
\(897\) 40173.7 1.49539
\(898\) 2716.70 0.100955
\(899\) −185.359 −0.00687660
\(900\) 23003.3 0.851976
\(901\) 35067.5 1.29663
\(902\) −1616.03 −0.0596539
\(903\) 0 0
\(904\) −1307.31 −0.0480978
\(905\) −8055.98 −0.295900
\(906\) 2422.52 0.0888331
\(907\) 8836.95 0.323513 0.161756 0.986831i \(-0.448284\pi\)
0.161756 + 0.986831i \(0.448284\pi\)
\(908\) 46508.1 1.69981
\(909\) −18969.3 −0.692158
\(910\) 707.630 0.0257777
\(911\) −18084.8 −0.657711 −0.328856 0.944380i \(-0.606663\pi\)
−0.328856 + 0.944380i \(0.606663\pi\)
\(912\) 24465.1 0.888292
\(913\) 33024.2 1.19709
\(914\) 773.047 0.0279761
\(915\) 9391.80 0.339326
\(916\) −1933.42 −0.0697401
\(917\) 32672.9 1.17661
\(918\) −149.663 −0.00538084
\(919\) 12681.9 0.455210 0.227605 0.973754i \(-0.426911\pi\)
0.227605 + 0.973754i \(0.426911\pi\)
\(920\) −1912.32 −0.0685296
\(921\) 30269.1 1.08295
\(922\) −311.133 −0.0111135
\(923\) −3215.51 −0.114669
\(924\) 117259. 4.17482
\(925\) −38321.4 −1.36216
\(926\) 215.476 0.00764683
\(927\) 49782.5 1.76383
\(928\) 2767.78 0.0979062
\(929\) 47824.0 1.68897 0.844486 0.535577i \(-0.179906\pi\)
0.844486 + 0.535577i \(0.179906\pi\)
\(930\) −13.9590 −0.000492188 0
\(931\) −31770.7 −1.11841
\(932\) 3652.99 0.128388
\(933\) −73007.5 −2.56180
\(934\) 2632.72 0.0922327
\(935\) −12938.3 −0.452541
\(936\) −2832.76 −0.0989226
\(937\) −21397.1 −0.746011 −0.373006 0.927829i \(-0.621673\pi\)
−0.373006 + 0.927829i \(0.621673\pi\)
\(938\) −3967.71 −0.138113
\(939\) −55160.8 −1.91704
\(940\) −649.285 −0.0225291
\(941\) 40280.0 1.39542 0.697710 0.716381i \(-0.254203\pi\)
0.697710 + 0.716381i \(0.254203\pi\)
\(942\) −4345.57 −0.150304
\(943\) −19218.4 −0.663668
\(944\) 12958.3 0.446776
\(945\) 1204.54 0.0414641
\(946\) 0 0
\(947\) 9.77531 0.000335433 0 0.000167716 1.00000i \(-0.499947\pi\)
0.000167716 1.00000i \(0.499947\pi\)
\(948\) 45356.7 1.55392
\(949\) 28624.9 0.979140
\(950\) 1311.23 0.0447809
\(951\) 18488.7 0.630427
\(952\) −6121.40 −0.208399
\(953\) −42128.3 −1.43197 −0.715985 0.698115i \(-0.754022\pi\)
−0.715985 + 0.698115i \(0.754022\pi\)
\(954\) −3238.57 −0.109908
\(955\) −12852.2 −0.435483
\(956\) 41495.7 1.40384
\(957\) 32764.2 1.10670
\(958\) 3281.19 0.110658
\(959\) 47403.5 1.59618
\(960\) −11829.3 −0.397698
\(961\) −29783.6 −0.999750
\(962\) 2352.79 0.0788533
\(963\) −35356.0 −1.18311
\(964\) −31951.8 −1.06753
\(965\) 3254.97 0.108582
\(966\) −8017.37 −0.267034
\(967\) 33902.0 1.12742 0.563710 0.825973i \(-0.309373\pi\)
0.563710 + 0.825973i \(0.309373\pi\)
\(968\) −10621.2 −0.352665
\(969\) −22832.0 −0.756936
\(970\) −1.53195 −5.07092e−5 0
\(971\) 8561.31 0.282951 0.141476 0.989942i \(-0.454815\pi\)
0.141476 + 0.989942i \(0.454815\pi\)
\(972\) −41799.9 −1.37936
\(973\) 25014.6 0.824185
\(974\) 276.277 0.00908878
\(975\) 27030.0 0.887848
\(976\) 24697.7 0.809994
\(977\) −42596.6 −1.39487 −0.697434 0.716649i \(-0.745675\pi\)
−0.697434 + 0.716649i \(0.745675\pi\)
\(978\) 2559.45 0.0836832
\(979\) 35248.3 1.15070
\(980\) 15543.0 0.506636
\(981\) −13133.3 −0.427435
\(982\) −1914.53 −0.0622150
\(983\) −20090.7 −0.651875 −0.325938 0.945391i \(-0.605680\pi\)
−0.325938 + 0.945391i \(0.605680\pi\)
\(984\) 2798.36 0.0906589
\(985\) −13566.7 −0.438853
\(986\) −852.762 −0.0275431
\(987\) −5459.89 −0.176079
\(988\) 14002.4 0.450887
\(989\) 0 0
\(990\) 1194.88 0.0383593
\(991\) 14315.0 0.458861 0.229430 0.973325i \(-0.426314\pi\)
0.229430 + 0.973325i \(0.426314\pi\)
\(992\) −111.190 −0.00355874
\(993\) −29904.3 −0.955674
\(994\) 641.711 0.0204767
\(995\) 4586.69 0.146139
\(996\) −28510.9 −0.907030
\(997\) 49560.0 1.57430 0.787151 0.616760i \(-0.211555\pi\)
0.787151 + 0.616760i \(0.211555\pi\)
\(998\) 4009.98 0.127188
\(999\) 4004.94 0.126837
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 1849.4.a.j.1.25 yes 50
43.42 odd 2 1849.4.a.i.1.26 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.26 50 43.42 odd 2
1849.4.a.j.1.25 yes 50 1.1 even 1 trivial