Properties

Label 1849.4.a.i.1.26
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 1.26
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 \(-0.512036\pi\)
−0.0378036 + 0.999285i \(0.512036\pi\)
\(3\) 7.23549 1.39247 0.696236 0.717813i \(-0.254857\pi\)
0.696236 + 0.717813i \(0.254857\pi\)
\(4\) −7.95427 −0.994284
\(5\) 3.30603 0.295700 0.147850 0.989010i \(-0.452765\pi\)
0.147850 + 0.989010i \(0.452765\pi\)
\(6\) −1.54731 −0.105281
\(7\) 30.5623 1.65021 0.825106 0.564979i \(-0.191116\pi\)
0.825106 + 0.564979i \(0.191116\pi\)
\(8\) 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 \(-0.394798\pi\)
0.324517 + 0.945880i \(0.394798\pi\)
\(20\) −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 \(-0.569783\pi\)
−0.217477 + 0.976065i \(0.569783\pi\)
\(30\) −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 \(-0.768190\pi\)
−0.746339 + 0.665566i \(0.768190\pi\)
\(38\) −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 \(-0.635187\pi\)
−0.412050 + 0.911161i \(0.635187\pi\)
\(62\) 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 \(-0.473850\pi\)
0.0820591 + 0.996627i \(0.473850\pi\)
\(72\) 86.4976 0.141581
\(73\) −874.055 −1.40138 −0.700688 0.713468i \(-0.747123\pi\)
−0.700688 + 0.713468i \(0.747123\pi\)
\(74\) 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 \(-0.398039\pi\)
0.314870 + 0.949135i \(0.398039\pi\)
\(90\) −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 \(-0.550986\pi\)
−0.159494 + 0.987199i \(0.550986\pi\)
\(114\) −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 \(-0.383969\pi\)
0.356504 + 0.934294i \(0.383969\pi\)
\(132\) 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 \(-0.339318\pi\)
0.483630 + 0.875272i \(0.339318\pi\)
\(138\) 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 \(-0.552169\pi\)
−0.163163 + 0.986599i \(0.552169\pi\)
\(150\) 176.502 0.0960753
\(151\) 1565.64 0.843772 0.421886 0.906649i \(-0.361368\pi\)
0.421886 + 0.906649i \(0.361368\pi\)
\(152\) 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 \(-0.753038\pi\)
−0.713823 + 0.700326i \(0.753038\pi\)
\(158\) −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 \(-0.369903\pi\)
0.397428 + 0.917633i \(0.369903\pi\)
\(164\) −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 \(-0.470506\pi\)
0.0925249 + 0.995710i \(0.470506\pi\)
\(180\) −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 \(-0.763457\pi\)
−0.736360 + 0.676590i \(0.763457\pi\)
\(192\) −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 \(-0.420520\pi\)
0.247106 + 0.968988i \(0.420520\pi\)
\(200\) −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 \(-0.405455\pi\)
0.292675 + 0.956212i \(0.405455\pi\)
\(212\) 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 \(-0.675825\pi\)
−0.524706 + 0.851284i \(0.675825\pi\)
\(224\) −1245.31 −0.371455
\(225\) −2891.95 −0.856874
\(226\) 81.9409 0.0241178
\(227\) 5846.94 1.70958 0.854790 0.518974i \(-0.173686\pi\)
0.854790 + 0.518974i \(0.173686\pi\)
\(228\) −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 \(-0.479435\pi\)
0.0645630 + 0.997914i \(0.479435\pi\)
\(234\) −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 \(-0.680380\pi\)
−0.536833 + 0.843688i \(0.680380\pi\)
\(242\) −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 \(-0.843734\pi\)
−0.881897 + 0.471442i \(0.843734\pi\)
\(258\) 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 \(-0.585338\pi\)
−0.264898 + 0.964276i \(0.585338\pi\)
\(264\) −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 \(-0.357808\pi\)
0.431999 + 0.901874i \(0.357808\pi\)
\(278\) 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 \(-0.741669\pi\)
−0.688360 + 0.725369i \(0.741669\pi\)
\(314\) 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 \(-0.611496\pi\)
−0.343157 + 0.939278i \(0.611496\pi\)
\(332\) 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 \(-0.258580\pi\)
0.687793 + 0.725907i \(0.258580\pi\)
\(348\) 3909.39 0.602199
\(349\) 6098.16 0.935320 0.467660 0.883908i \(-0.345097\pi\)
0.467660 + 0.883908i \(0.345097\pi\)
\(350\) 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 \(-0.277956\pi\)
0.642359 + 0.766404i \(0.277956\pi\)
\(374\) −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 \(-0.617483\pi\)
−0.360761 + 0.932658i \(0.617483\pi\)
\(384\) 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 \(-0.399788\pi\)
0.309652 + 0.950850i \(0.399788\pi\)
\(390\) −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 \(-0.366148\pi\)
0.408224 + 0.912882i \(0.366148\pi\)
\(410\) −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 \(-0.718786\pi\)
−0.634481 + 0.772939i \(0.718786\pi\)
\(420\) −5815.15 −0.675596
\(421\) −12444.8 −1.44067 −0.720334 0.693628i \(-0.756011\pi\)
−0.720334 + 0.693628i \(0.756011\pi\)
\(422\) −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 \(-0.543008\pi\)
−0.134703 + 0.990886i \(0.543008\pi\)
\(434\) 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 \(-0.732690\pi\)
−0.667627 + 0.744496i \(0.732690\pi\)
\(450\) 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 \(-0.559231\pi\)
−0.185009 + 0.982737i \(0.559231\pi\)
\(458\) −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 \(-0.516104\pi\)
−0.0505694 + 0.998721i \(0.516104\pi\)
\(464\) −4272.90 −0.427509
\(465\) −65.2750 −0.00650980
\(466\) −98.2101 −0.00976286
\(467\) −12311.1 −1.21989 −0.609946 0.792443i \(-0.708809\pi\)
−0.609946 + 0.792443i \(0.708809\pi\)
\(468\) −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 \(-0.365028\pi\)
0.411435 + 0.911439i \(0.365028\pi\)
\(492\) −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 \(-0.818097\pi\)
−0.841110 + 0.540864i \(0.818097\pi\)
\(500\) 6286.83 0.562311
\(501\) −5936.57 −0.529394
\(502\) 1287.05 0.114430
\(503\) −1320.15 −0.117023 −0.0585116 0.998287i \(-0.518635\pi\)
−0.0585116 + 0.998287i \(0.518635\pi\)
\(504\) 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 \(-0.316106\pi\)
0.546115 + 0.837710i \(0.316106\pi\)
\(522\) 368.271 0.0308789
\(523\) 6216.75 0.519770 0.259885 0.965640i \(-0.416315\pi\)
0.259885 + 0.965640i \(0.416315\pi\)
\(524\) −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 \(-0.291245\pi\)
0.609812 + 0.792546i \(0.291245\pi\)
\(572\) 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 \(-0.357246\pi\)
0.433591 + 0.901110i \(0.357246\pi\)
\(578\) 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 \(-0.675562\pi\)
−0.524004 + 0.851716i \(0.675562\pi\)
\(588\) −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 \(-0.630582\pi\)
−0.398824 + 0.917027i \(0.630582\pi\)
\(594\) −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 \(-0.824683\pi\)
−0.852119 + 0.523347i \(0.824683\pi\)
\(602\) 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 \(-0.526769\pi\)
−0.0839976 + 0.996466i \(0.526769\pi\)
\(608\) −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 \(-0.587549\pi\)
−0.271589 + 0.962413i \(0.587549\pi\)
\(632\) 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 \(-0.634571\pi\)
−0.410285 + 0.911957i \(0.634571\pi\)
\(642\) 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 \(-0.623113\pi\)
−0.377201 + 0.926131i \(0.623113\pi\)
\(648\) −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 \(-0.635655\pi\)
−0.413390 + 0.910554i \(0.635655\pi\)
\(654\) 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 \(-0.389790\pi\)
0.339360 + 0.940657i \(0.389790\pi\)
\(674\) 284.473 0.0162574
\(675\) 1359.88 0.0775432
\(676\) 8944.31 0.508894
\(677\) 4684.29 0.265926 0.132963 0.991121i \(-0.457551\pi\)
0.132963 + 0.991121i \(0.457551\pi\)
\(678\) 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 \(-0.322933\pi\)
0.528025 + 0.849229i \(0.322933\pi\)
\(692\) 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 \(-0.386939\pi\)
0.347769 + 0.937580i \(0.386939\pi\)
\(728\) 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 \(-0.555323\pi\)
−0.172929 + 0.984934i \(0.555323\pi\)
\(734\) 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 \(-0.308883\pi\)
0.564982 + 0.825103i \(0.308883\pi\)
\(740\) 8834.37 0.438862
\(741\) 12737.1 0.631457
\(742\) 3904.10 0.193159
\(743\) 33576.5 1.65788 0.828939 0.559339i \(-0.188945\pi\)
0.828939 + 0.559339i \(0.188945\pi\)
\(744\) −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 \(-0.293667\pi\)
0.603763 + 0.797164i \(0.293667\pi\)
\(752\) −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 \(-0.558181\pi\)
−0.181766 + 0.983342i \(0.558181\pi\)
\(758\) 292.109 0.0139972
\(759\) 81776.3 3.91079
\(760\) 606.302 0.0289380
\(761\) 9150.62 0.435887 0.217943 0.975961i \(-0.430065\pi\)
0.217943 + 0.975961i \(0.430065\pi\)
\(762\) −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 \(-0.597601\pi\)
−0.301839 + 0.953359i \(0.597601\pi\)
\(774\) 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 \(-0.580439\pi\)
−0.250027 + 0.968239i \(0.580439\pi\)
\(812\) 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 \(-0.467174\pi\)
0.102944 + 0.994687i \(0.467174\pi\)
\(830\) 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 \(-0.735290\pi\)
−0.673687 + 0.739017i \(0.735290\pi\)
\(840\) 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 \(-0.456121\pi\)
0.137413 + 0.990514i \(0.456121\pi\)
\(860\) 0 0
\(861\) 25067.1 0.992201
\(862\) −1683.00 −0.0665002
\(863\) 12317.1 0.485841 0.242920 0.970046i \(-0.421895\pi\)
0.242920 + 0.970046i \(0.421895\pi\)
\(864\) 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 \(-0.404585\pi\)
0.295286 + 0.955409i \(0.404585\pi\)
\(888\) −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 \(-0.393337\pi\)
0.328856 + 0.944380i \(0.393337\pi\)
\(912\) 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 \(-0.820094\pi\)
−0.844486 + 0.535577i \(0.820094\pi\)
\(930\) 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 \(-0.378327\pi\)
0.373006 + 0.927829i \(0.378327\pi\)
\(938\) −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 \(-0.245978\pi\)
0.715985 + 0.698115i \(0.245978\pi\)
\(954\) 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 \(-0.394320\pi\)
0.325938 + 0.945391i \(0.394320\pi\)
\(984\) 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 \(-0.573686\pi\)
−0.229430 + 0.973325i \(0.573686\pi\)
\(992\) 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 \(-0.788445\pi\)
−0.787151 + 0.616760i \(0.788445\pi\)
\(998\) 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.i.1.26 50
43.42 odd 2 1849.4.a.j.1.25 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.26 50 1.1 even 1 trivial
1849.4.a.j.1.25 yes 50 43.42 odd 2