Properties

Label 1849.4.a.i.1.30
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 1.30
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.06529 q^{2} +0.463524 q^{3} -6.86516 q^{4} +5.41130 q^{5} +0.493788 q^{6} +4.55619 q^{7} -15.8357 q^{8} -26.7851 q^{9} +O(q^{10})\) \(q+1.06529 q^{2} +0.463524 q^{3} -6.86516 q^{4} +5.41130 q^{5} +0.493788 q^{6} +4.55619 q^{7} -15.8357 q^{8} -26.7851 q^{9} +5.76461 q^{10} +10.2865 q^{11} -3.18216 q^{12} +4.48831 q^{13} +4.85366 q^{14} +2.50827 q^{15} +38.0516 q^{16} -32.2212 q^{17} -28.5340 q^{18} +54.9889 q^{19} -37.1494 q^{20} +2.11190 q^{21} +10.9581 q^{22} +136.229 q^{23} -7.34023 q^{24} -95.7178 q^{25} +4.78136 q^{26} -24.9307 q^{27} -31.2789 q^{28} +87.3472 q^{29} +2.67203 q^{30} +27.1204 q^{31} +167.222 q^{32} +4.76801 q^{33} -34.3250 q^{34} +24.6549 q^{35} +183.884 q^{36} -287.935 q^{37} +58.5791 q^{38} +2.08044 q^{39} -85.6918 q^{40} +285.555 q^{41} +2.24979 q^{42} -70.6181 q^{44} -144.942 q^{45} +145.124 q^{46} -62.1624 q^{47} +17.6378 q^{48} -322.241 q^{49} -101.967 q^{50} -14.9353 q^{51} -30.8129 q^{52} +310.227 q^{53} -26.5584 q^{54} +55.6631 q^{55} -72.1505 q^{56} +25.4886 q^{57} +93.0501 q^{58} +561.966 q^{59} -17.2196 q^{60} -381.217 q^{61} +28.8911 q^{62} -122.038 q^{63} -126.273 q^{64} +24.2876 q^{65} +5.07932 q^{66} -167.929 q^{67} +221.204 q^{68} +63.1455 q^{69} +26.2646 q^{70} -328.805 q^{71} +424.162 q^{72} -1034.34 q^{73} -306.735 q^{74} -44.3675 q^{75} -377.507 q^{76} +46.8670 q^{77} +2.21627 q^{78} -496.972 q^{79} +205.909 q^{80} +711.643 q^{81} +304.199 q^{82} +374.134 q^{83} -14.4985 q^{84} -174.359 q^{85} +40.4875 q^{87} -162.893 q^{88} +270.772 q^{89} -154.406 q^{90} +20.4496 q^{91} -935.236 q^{92} +12.5709 q^{93} -66.2210 q^{94} +297.561 q^{95} +77.5112 q^{96} -1118.35 q^{97} -343.281 q^{98} -275.524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06529 0.376637 0.188319 0.982108i \(-0.439696\pi\)
0.188319 + 0.982108i \(0.439696\pi\)
\(3\) 0.463524 0.0892052 0.0446026 0.999005i \(-0.485798\pi\)
0.0446026 + 0.999005i \(0.485798\pi\)
\(4\) −6.86516 −0.858144
\(5\) 5.41130 0.484001 0.242001 0.970276i \(-0.422196\pi\)
0.242001 + 0.970276i \(0.422196\pi\)
\(6\) 0.493788 0.0335980
\(7\) 4.55619 0.246011 0.123005 0.992406i \(-0.460747\pi\)
0.123005 + 0.992406i \(0.460747\pi\)
\(8\) −15.8357 −0.699846
\(9\) −26.7851 −0.992042
\(10\) 5.76461 0.182293
\(11\) 10.2865 0.281953 0.140976 0.990013i \(-0.454976\pi\)
0.140976 + 0.990013i \(0.454976\pi\)
\(12\) −3.18216 −0.0765509
\(13\) 4.48831 0.0957564 0.0478782 0.998853i \(-0.484754\pi\)
0.0478782 + 0.998853i \(0.484754\pi\)
\(14\) 4.85366 0.0926569
\(15\) 2.50827 0.0431754
\(16\) 38.0516 0.594556
\(17\) −32.2212 −0.459694 −0.229847 0.973227i \(-0.573823\pi\)
−0.229847 + 0.973227i \(0.573823\pi\)
\(18\) −28.5340 −0.373640
\(19\) 54.9889 0.663964 0.331982 0.943286i \(-0.392283\pi\)
0.331982 + 0.943286i \(0.392283\pi\)
\(20\) −37.1494 −0.415343
\(21\) 2.11190 0.0219454
\(22\) 10.9581 0.106194
\(23\) 136.229 1.23503 0.617517 0.786558i \(-0.288139\pi\)
0.617517 + 0.786558i \(0.288139\pi\)
\(24\) −7.34023 −0.0624299
\(25\) −95.7178 −0.765743
\(26\) 4.78136 0.0360654
\(27\) −24.9307 −0.177700
\(28\) −31.2789 −0.211113
\(29\) 87.3472 0.559309 0.279654 0.960101i \(-0.409780\pi\)
0.279654 + 0.960101i \(0.409780\pi\)
\(30\) 2.67203 0.0162615
\(31\) 27.1204 0.157128 0.0785639 0.996909i \(-0.474967\pi\)
0.0785639 + 0.996909i \(0.474967\pi\)
\(32\) 167.222 0.923778
\(33\) 4.76801 0.0251517
\(34\) −34.3250 −0.173138
\(35\) 24.6549 0.119070
\(36\) 183.884 0.851316
\(37\) −287.935 −1.27936 −0.639680 0.768642i \(-0.720933\pi\)
−0.639680 + 0.768642i \(0.720933\pi\)
\(38\) 58.5791 0.250073
\(39\) 2.08044 0.00854197
\(40\) −85.6918 −0.338727
\(41\) 285.555 1.08771 0.543856 0.839179i \(-0.316964\pi\)
0.543856 + 0.839179i \(0.316964\pi\)
\(42\) 2.24979 0.00826547
\(43\) 0 0
\(44\) −70.6181 −0.241956
\(45\) −144.942 −0.480150
\(46\) 145.124 0.465160
\(47\) −62.1624 −0.192922 −0.0964608 0.995337i \(-0.530752\pi\)
−0.0964608 + 0.995337i \(0.530752\pi\)
\(48\) 17.6378 0.0530375
\(49\) −322.241 −0.939479
\(50\) −101.967 −0.288407
\(51\) −14.9353 −0.0410071
\(52\) −30.8129 −0.0821728
\(53\) 310.227 0.804019 0.402010 0.915635i \(-0.368312\pi\)
0.402010 + 0.915635i \(0.368312\pi\)
\(54\) −26.5584 −0.0669286
\(55\) 55.6631 0.136466
\(56\) −72.1505 −0.172170
\(57\) 25.4886 0.0592290
\(58\) 93.0501 0.210657
\(59\) 561.966 1.24003 0.620015 0.784590i \(-0.287126\pi\)
0.620015 + 0.784590i \(0.287126\pi\)
\(60\) −17.2196 −0.0370507
\(61\) −381.217 −0.800162 −0.400081 0.916480i \(-0.631018\pi\)
−0.400081 + 0.916480i \(0.631018\pi\)
\(62\) 28.8911 0.0591802
\(63\) −122.038 −0.244053
\(64\) −126.273 −0.246627
\(65\) 24.2876 0.0463462
\(66\) 5.07932 0.00947305
\(67\) −167.929 −0.306206 −0.153103 0.988210i \(-0.548927\pi\)
−0.153103 + 0.988210i \(0.548927\pi\)
\(68\) 221.204 0.394484
\(69\) 63.1455 0.110171
\(70\) 26.2646 0.0448460
\(71\) −328.805 −0.549605 −0.274802 0.961501i \(-0.588612\pi\)
−0.274802 + 0.961501i \(0.588612\pi\)
\(72\) 424.162 0.694277
\(73\) −1034.34 −1.65836 −0.829178 0.558985i \(-0.811191\pi\)
−0.829178 + 0.558985i \(0.811191\pi\)
\(74\) −306.735 −0.481854
\(75\) −44.3675 −0.0683082
\(76\) −377.507 −0.569777
\(77\) 46.8670 0.0693635
\(78\) 2.21627 0.00321722
\(79\) −496.972 −0.707768 −0.353884 0.935289i \(-0.615139\pi\)
−0.353884 + 0.935289i \(0.615139\pi\)
\(80\) 205.909 0.287766
\(81\) 711.643 0.976191
\(82\) 304.199 0.409672
\(83\) 374.134 0.494777 0.247389 0.968916i \(-0.420428\pi\)
0.247389 + 0.968916i \(0.420428\pi\)
\(84\) −14.4985 −0.0188324
\(85\) −174.359 −0.222493
\(86\) 0 0
\(87\) 40.4875 0.0498933
\(88\) −162.893 −0.197324
\(89\) 270.772 0.322492 0.161246 0.986914i \(-0.448449\pi\)
0.161246 + 0.986914i \(0.448449\pi\)
\(90\) −154.406 −0.180842
\(91\) 20.4496 0.0235571
\(92\) −935.236 −1.05984
\(93\) 12.5709 0.0140166
\(94\) −66.2210 −0.0726615
\(95\) 297.561 0.321359
\(96\) 77.5112 0.0824058
\(97\) −1118.35 −1.17063 −0.585314 0.810807i \(-0.699029\pi\)
−0.585314 + 0.810807i \(0.699029\pi\)
\(98\) −343.281 −0.353843
\(99\) −275.524 −0.279709
\(100\) 657.118 0.657118
\(101\) 4.71204 0.00464223 0.00232112 0.999997i \(-0.499261\pi\)
0.00232112 + 0.999997i \(0.499261\pi\)
\(102\) −15.9105 −0.0154448
\(103\) 1132.30 1.08319 0.541594 0.840640i \(-0.317821\pi\)
0.541594 + 0.840640i \(0.317821\pi\)
\(104\) −71.0756 −0.0670148
\(105\) 11.4281 0.0106216
\(106\) 330.482 0.302823
\(107\) −1718.40 −1.55256 −0.776279 0.630389i \(-0.782895\pi\)
−0.776279 + 0.630389i \(0.782895\pi\)
\(108\) 171.153 0.152493
\(109\) −778.298 −0.683921 −0.341961 0.939714i \(-0.611091\pi\)
−0.341961 + 0.939714i \(0.611091\pi\)
\(110\) 59.2974 0.0513980
\(111\) −133.465 −0.114125
\(112\) 173.370 0.146267
\(113\) −1039.73 −0.865568 −0.432784 0.901498i \(-0.642469\pi\)
−0.432784 + 0.901498i \(0.642469\pi\)
\(114\) 27.1528 0.0223078
\(115\) 737.178 0.597758
\(116\) −599.652 −0.479968
\(117\) −120.220 −0.0949944
\(118\) 598.658 0.467042
\(119\) −146.806 −0.113090
\(120\) −39.7202 −0.0302162
\(121\) −1225.19 −0.920503
\(122\) −406.107 −0.301371
\(123\) 132.361 0.0970294
\(124\) −186.186 −0.134838
\(125\) −1194.37 −0.854622
\(126\) −130.006 −0.0919195
\(127\) −289.845 −0.202516 −0.101258 0.994860i \(-0.532287\pi\)
−0.101258 + 0.994860i \(0.532287\pi\)
\(128\) −1472.29 −1.01667
\(129\) 0 0
\(130\) 25.8733 0.0174557
\(131\) −1123.68 −0.749441 −0.374720 0.927138i \(-0.622261\pi\)
−0.374720 + 0.927138i \(0.622261\pi\)
\(132\) −32.7332 −0.0215838
\(133\) 250.539 0.163342
\(134\) −178.893 −0.115329
\(135\) −134.907 −0.0860073
\(136\) 510.247 0.321715
\(137\) 2215.34 1.38153 0.690764 0.723080i \(-0.257274\pi\)
0.690764 + 0.723080i \(0.257274\pi\)
\(138\) 67.2684 0.0414947
\(139\) 1955.65 1.19335 0.596676 0.802482i \(-0.296488\pi\)
0.596676 + 0.802482i \(0.296488\pi\)
\(140\) −169.260 −0.102179
\(141\) −28.8137 −0.0172096
\(142\) −350.273 −0.207002
\(143\) 46.1688 0.0269988
\(144\) −1019.22 −0.589825
\(145\) 472.662 0.270706
\(146\) −1101.87 −0.624598
\(147\) −149.366 −0.0838064
\(148\) 1976.72 1.09787
\(149\) −1648.94 −0.906618 −0.453309 0.891353i \(-0.649757\pi\)
−0.453309 + 0.891353i \(0.649757\pi\)
\(150\) −47.2643 −0.0257274
\(151\) −2643.96 −1.42492 −0.712459 0.701713i \(-0.752419\pi\)
−0.712459 + 0.701713i \(0.752419\pi\)
\(152\) −870.788 −0.464673
\(153\) 863.051 0.456036
\(154\) 49.9270 0.0261249
\(155\) 146.757 0.0760501
\(156\) −14.2825 −0.00733024
\(157\) 174.029 0.0884651 0.0442326 0.999021i \(-0.485916\pi\)
0.0442326 + 0.999021i \(0.485916\pi\)
\(158\) −529.419 −0.266572
\(159\) 143.798 0.0717227
\(160\) 904.887 0.447110
\(161\) 620.686 0.303832
\(162\) 758.107 0.367670
\(163\) 2791.23 1.34126 0.670631 0.741791i \(-0.266023\pi\)
0.670631 + 0.741791i \(0.266023\pi\)
\(164\) −1960.38 −0.933413
\(165\) 25.8011 0.0121734
\(166\) 398.561 0.186352
\(167\) 1898.85 0.879865 0.439932 0.898031i \(-0.355002\pi\)
0.439932 + 0.898031i \(0.355002\pi\)
\(168\) −33.4434 −0.0153584
\(169\) −2176.86 −0.990831
\(170\) −185.743 −0.0837990
\(171\) −1472.88 −0.658680
\(172\) 0 0
\(173\) −1658.22 −0.728740 −0.364370 0.931254i \(-0.618716\pi\)
−0.364370 + 0.931254i \(0.618716\pi\)
\(174\) 43.1309 0.0187917
\(175\) −436.108 −0.188381
\(176\) 391.416 0.167637
\(177\) 260.485 0.110617
\(178\) 288.451 0.121463
\(179\) 3555.98 1.48484 0.742420 0.669934i \(-0.233678\pi\)
0.742420 + 0.669934i \(0.233678\pi\)
\(180\) 995.052 0.412038
\(181\) −3643.83 −1.49637 −0.748187 0.663488i \(-0.769075\pi\)
−0.748187 + 0.663488i \(0.769075\pi\)
\(182\) 21.7847 0.00887249
\(183\) −176.703 −0.0713786
\(184\) −2157.29 −0.864334
\(185\) −1558.10 −0.619212
\(186\) 13.3917 0.00527918
\(187\) −331.442 −0.129612
\(188\) 426.755 0.165555
\(189\) −113.589 −0.0437163
\(190\) 316.989 0.121036
\(191\) 3297.38 1.24916 0.624581 0.780960i \(-0.285270\pi\)
0.624581 + 0.780960i \(0.285270\pi\)
\(192\) −58.5305 −0.0220004
\(193\) −3679.64 −1.37236 −0.686182 0.727430i \(-0.740715\pi\)
−0.686182 + 0.727430i \(0.740715\pi\)
\(194\) −1191.36 −0.440902
\(195\) 11.2579 0.00413432
\(196\) 2212.24 0.806208
\(197\) −2520.85 −0.911692 −0.455846 0.890059i \(-0.650663\pi\)
−0.455846 + 0.890059i \(0.650663\pi\)
\(198\) −293.513 −0.105349
\(199\) −4762.22 −1.69641 −0.848203 0.529672i \(-0.822315\pi\)
−0.848203 + 0.529672i \(0.822315\pi\)
\(200\) 1515.76 0.535902
\(201\) −77.8391 −0.0273151
\(202\) 5.01969 0.00174844
\(203\) 397.970 0.137596
\(204\) 102.533 0.0351900
\(205\) 1545.22 0.526454
\(206\) 1206.22 0.407969
\(207\) −3648.92 −1.22521
\(208\) 170.787 0.0569326
\(209\) 565.640 0.187206
\(210\) 12.1743 0.00400050
\(211\) −581.138 −0.189607 −0.0948037 0.995496i \(-0.530222\pi\)
−0.0948037 + 0.995496i \(0.530222\pi\)
\(212\) −2129.76 −0.689964
\(213\) −152.409 −0.0490276
\(214\) −1830.59 −0.584752
\(215\) 0 0
\(216\) 394.795 0.124363
\(217\) 123.565 0.0386552
\(218\) −829.114 −0.257590
\(219\) −479.439 −0.147934
\(220\) −382.136 −0.117107
\(221\) −144.619 −0.0440187
\(222\) −142.179 −0.0429839
\(223\) 5483.83 1.64675 0.823374 0.567500i \(-0.192089\pi\)
0.823374 + 0.567500i \(0.192089\pi\)
\(224\) 761.893 0.227260
\(225\) 2563.82 0.759649
\(226\) −1107.61 −0.326005
\(227\) −5427.63 −1.58698 −0.793490 0.608584i \(-0.791738\pi\)
−0.793490 + 0.608584i \(0.791738\pi\)
\(228\) −174.983 −0.0508270
\(229\) 513.813 0.148269 0.0741347 0.997248i \(-0.476381\pi\)
0.0741347 + 0.997248i \(0.476381\pi\)
\(230\) 785.309 0.225138
\(231\) 21.7240 0.00618758
\(232\) −1383.20 −0.391430
\(233\) −748.209 −0.210373 −0.105186 0.994453i \(-0.533544\pi\)
−0.105186 + 0.994453i \(0.533544\pi\)
\(234\) −128.069 −0.0357784
\(235\) −336.379 −0.0933743
\(236\) −3857.99 −1.06412
\(237\) −230.358 −0.0631366
\(238\) −156.391 −0.0425938
\(239\) 5232.24 1.41609 0.708045 0.706167i \(-0.249577\pi\)
0.708045 + 0.706167i \(0.249577\pi\)
\(240\) 95.4435 0.0256702
\(241\) 3231.66 0.863774 0.431887 0.901928i \(-0.357848\pi\)
0.431887 + 0.901928i \(0.357848\pi\)
\(242\) −1305.18 −0.346696
\(243\) 1002.99 0.264782
\(244\) 2617.12 0.686655
\(245\) −1743.74 −0.454709
\(246\) 141.003 0.0365449
\(247\) 246.807 0.0635788
\(248\) −429.471 −0.109965
\(249\) 173.420 0.0441367
\(250\) −1272.35 −0.321882
\(251\) −2668.67 −0.671094 −0.335547 0.942023i \(-0.608921\pi\)
−0.335547 + 0.942023i \(0.608921\pi\)
\(252\) 837.810 0.209433
\(253\) 1401.32 0.348221
\(254\) −308.769 −0.0762752
\(255\) −80.8194 −0.0198475
\(256\) −558.235 −0.136288
\(257\) −4140.36 −1.00494 −0.502469 0.864595i \(-0.667575\pi\)
−0.502469 + 0.864595i \(0.667575\pi\)
\(258\) 0 0
\(259\) −1311.89 −0.314736
\(260\) −166.738 −0.0397718
\(261\) −2339.61 −0.554858
\(262\) −1197.05 −0.282267
\(263\) −5040.77 −1.18185 −0.590926 0.806726i \(-0.701237\pi\)
−0.590926 + 0.806726i \(0.701237\pi\)
\(264\) −75.5049 −0.0176023
\(265\) 1678.73 0.389146
\(266\) 266.897 0.0615208
\(267\) 125.509 0.0287680
\(268\) 1152.86 0.262769
\(269\) −6767.05 −1.53381 −0.766904 0.641762i \(-0.778204\pi\)
−0.766904 + 0.641762i \(0.778204\pi\)
\(270\) −143.716 −0.0323935
\(271\) −7973.39 −1.78727 −0.893633 0.448799i \(-0.851852\pi\)
−0.893633 + 0.448799i \(0.851852\pi\)
\(272\) −1226.07 −0.273314
\(273\) 9.47886 0.00210142
\(274\) 2359.98 0.520335
\(275\) −984.597 −0.215903
\(276\) −433.504 −0.0945430
\(277\) 1476.35 0.320236 0.160118 0.987098i \(-0.448813\pi\)
0.160118 + 0.987098i \(0.448813\pi\)
\(278\) 2083.34 0.449461
\(279\) −726.423 −0.155878
\(280\) −390.428 −0.0833304
\(281\) −6880.43 −1.46068 −0.730341 0.683082i \(-0.760639\pi\)
−0.730341 + 0.683082i \(0.760639\pi\)
\(282\) −30.6950 −0.00648178
\(283\) −275.458 −0.0578597 −0.0289299 0.999581i \(-0.509210\pi\)
−0.0289299 + 0.999581i \(0.509210\pi\)
\(284\) 2257.30 0.471640
\(285\) 137.927 0.0286669
\(286\) 49.1832 0.0101687
\(287\) 1301.04 0.267589
\(288\) −4479.06 −0.916427
\(289\) −3874.79 −0.788681
\(290\) 503.522 0.101958
\(291\) −518.380 −0.104426
\(292\) 7100.88 1.42311
\(293\) −4500.88 −0.897420 −0.448710 0.893678i \(-0.648116\pi\)
−0.448710 + 0.893678i \(0.648116\pi\)
\(294\) −159.119 −0.0315646
\(295\) 3040.97 0.600176
\(296\) 4559.66 0.895355
\(297\) −256.448 −0.0501032
\(298\) −1756.60 −0.341466
\(299\) 611.439 0.118262
\(300\) 304.590 0.0586183
\(301\) 0 0
\(302\) −2816.59 −0.536677
\(303\) 2.18414 0.000414111 0
\(304\) 2092.41 0.394764
\(305\) −2062.88 −0.387279
\(306\) 919.400 0.171760
\(307\) −8303.21 −1.54361 −0.771806 0.635858i \(-0.780646\pi\)
−0.771806 + 0.635858i \(0.780646\pi\)
\(308\) −321.749 −0.0595239
\(309\) 524.846 0.0966260
\(310\) 156.338 0.0286433
\(311\) 9034.89 1.64734 0.823668 0.567073i \(-0.191924\pi\)
0.823668 + 0.567073i \(0.191924\pi\)
\(312\) −32.9452 −0.00597806
\(313\) −4408.24 −0.796065 −0.398032 0.917371i \(-0.630307\pi\)
−0.398032 + 0.917371i \(0.630307\pi\)
\(314\) 185.392 0.0333193
\(315\) −660.385 −0.118122
\(316\) 3411.79 0.607367
\(317\) −1062.85 −0.188314 −0.0941569 0.995557i \(-0.530016\pi\)
−0.0941569 + 0.995557i \(0.530016\pi\)
\(318\) 153.186 0.0270134
\(319\) 898.492 0.157699
\(320\) −683.301 −0.119368
\(321\) −796.518 −0.138496
\(322\) 661.211 0.114434
\(323\) −1771.81 −0.305220
\(324\) −4885.54 −0.837713
\(325\) −429.611 −0.0733248
\(326\) 2973.47 0.505170
\(327\) −360.760 −0.0610093
\(328\) −4521.96 −0.761231
\(329\) −283.223 −0.0474608
\(330\) 27.4857 0.00458497
\(331\) −9875.05 −1.63982 −0.819912 0.572489i \(-0.805978\pi\)
−0.819912 + 0.572489i \(0.805978\pi\)
\(332\) −2568.49 −0.424590
\(333\) 7712.39 1.26918
\(334\) 2022.83 0.331390
\(335\) −908.714 −0.148204
\(336\) 80.3612 0.0130478
\(337\) −4547.10 −0.735004 −0.367502 0.930023i \(-0.619787\pi\)
−0.367502 + 0.930023i \(0.619787\pi\)
\(338\) −2318.98 −0.373184
\(339\) −481.937 −0.0772131
\(340\) 1197.00 0.190931
\(341\) 278.972 0.0443027
\(342\) −1569.05 −0.248084
\(343\) −3030.96 −0.477133
\(344\) 0 0
\(345\) 341.699 0.0533231
\(346\) −1766.49 −0.274471
\(347\) 10601.8 1.64016 0.820081 0.572247i \(-0.193928\pi\)
0.820081 + 0.572247i \(0.193928\pi\)
\(348\) −277.953 −0.0428156
\(349\) −10990.8 −1.68574 −0.842870 0.538117i \(-0.819136\pi\)
−0.842870 + 0.538117i \(0.819136\pi\)
\(350\) −464.582 −0.0709513
\(351\) −111.897 −0.0170160
\(352\) 1720.12 0.260462
\(353\) −290.232 −0.0437606 −0.0218803 0.999761i \(-0.506965\pi\)
−0.0218803 + 0.999761i \(0.506965\pi\)
\(354\) 277.492 0.0416625
\(355\) −1779.26 −0.266010
\(356\) −1858.89 −0.276745
\(357\) −68.0480 −0.0100882
\(358\) 3788.15 0.559246
\(359\) 3441.15 0.505896 0.252948 0.967480i \(-0.418600\pi\)
0.252948 + 0.967480i \(0.418600\pi\)
\(360\) 2295.27 0.336031
\(361\) −3835.22 −0.559152
\(362\) −3881.74 −0.563590
\(363\) −567.904 −0.0821136
\(364\) −140.389 −0.0202154
\(365\) −5597.10 −0.802646
\(366\) −188.240 −0.0268838
\(367\) 6785.05 0.965060 0.482530 0.875880i \(-0.339718\pi\)
0.482530 + 0.875880i \(0.339718\pi\)
\(368\) 5183.74 0.734297
\(369\) −7648.62 −1.07906
\(370\) −1659.83 −0.233218
\(371\) 1413.45 0.197797
\(372\) −86.3014 −0.0120283
\(373\) 8819.35 1.22426 0.612129 0.790758i \(-0.290313\pi\)
0.612129 + 0.790758i \(0.290313\pi\)
\(374\) −353.082 −0.0488167
\(375\) −553.619 −0.0762367
\(376\) 984.386 0.135016
\(377\) 392.041 0.0535574
\(378\) −121.005 −0.0164652
\(379\) 2684.12 0.363784 0.181892 0.983319i \(-0.441778\pi\)
0.181892 + 0.983319i \(0.441778\pi\)
\(380\) −2042.80 −0.275773
\(381\) −134.350 −0.0180655
\(382\) 3512.67 0.470481
\(383\) 4907.07 0.654673 0.327336 0.944908i \(-0.393849\pi\)
0.327336 + 0.944908i \(0.393849\pi\)
\(384\) −682.442 −0.0906920
\(385\) 253.611 0.0335720
\(386\) −3919.89 −0.516884
\(387\) 0 0
\(388\) 7677.62 1.00457
\(389\) −1999.95 −0.260672 −0.130336 0.991470i \(-0.541606\pi\)
−0.130336 + 0.991470i \(0.541606\pi\)
\(390\) 11.9929 0.00155714
\(391\) −4389.48 −0.567738
\(392\) 5102.92 0.657491
\(393\) −520.854 −0.0668540
\(394\) −2685.44 −0.343377
\(395\) −2689.26 −0.342561
\(396\) 1891.52 0.240031
\(397\) 9540.63 1.20612 0.603061 0.797695i \(-0.293947\pi\)
0.603061 + 0.797695i \(0.293947\pi\)
\(398\) −5073.15 −0.638929
\(399\) 116.131 0.0145710
\(400\) −3642.22 −0.455277
\(401\) 6723.57 0.837304 0.418652 0.908147i \(-0.362503\pi\)
0.418652 + 0.908147i \(0.362503\pi\)
\(402\) −82.9213 −0.0102879
\(403\) 121.725 0.0150460
\(404\) −32.3489 −0.00398371
\(405\) 3850.91 0.472478
\(406\) 423.954 0.0518238
\(407\) −2961.83 −0.360719
\(408\) 236.511 0.0286987
\(409\) −3107.78 −0.375720 −0.187860 0.982196i \(-0.560155\pi\)
−0.187860 + 0.982196i \(0.560155\pi\)
\(410\) 1646.11 0.198282
\(411\) 1026.86 0.123239
\(412\) −7773.38 −0.929532
\(413\) 2560.42 0.305061
\(414\) −3887.16 −0.461458
\(415\) 2024.55 0.239473
\(416\) 750.543 0.0884577
\(417\) 906.490 0.106453
\(418\) 602.571 0.0705089
\(419\) 16291.9 1.89955 0.949776 0.312931i \(-0.101311\pi\)
0.949776 + 0.312931i \(0.101311\pi\)
\(420\) −78.4558 −0.00911489
\(421\) 2863.80 0.331528 0.165764 0.986165i \(-0.446991\pi\)
0.165764 + 0.986165i \(0.446991\pi\)
\(422\) −619.081 −0.0714132
\(423\) 1665.03 0.191386
\(424\) −4912.67 −0.562690
\(425\) 3084.15 0.352007
\(426\) −162.360 −0.0184656
\(427\) −1736.90 −0.196849
\(428\) 11797.1 1.33232
\(429\) 21.4003 0.00240843
\(430\) 0 0
\(431\) −4365.79 −0.487918 −0.243959 0.969786i \(-0.578446\pi\)
−0.243959 + 0.969786i \(0.578446\pi\)
\(432\) −948.653 −0.105653
\(433\) 1671.29 0.185489 0.0927447 0.995690i \(-0.470436\pi\)
0.0927447 + 0.995690i \(0.470436\pi\)
\(434\) 131.633 0.0145590
\(435\) 219.090 0.0241484
\(436\) 5343.14 0.586903
\(437\) 7491.10 0.820018
\(438\) −510.742 −0.0557174
\(439\) −5823.57 −0.633129 −0.316564 0.948571i \(-0.602529\pi\)
−0.316564 + 0.948571i \(0.602529\pi\)
\(440\) −881.464 −0.0955049
\(441\) 8631.28 0.932003
\(442\) −154.061 −0.0165791
\(443\) −1022.42 −0.109654 −0.0548270 0.998496i \(-0.517461\pi\)
−0.0548270 + 0.998496i \(0.517461\pi\)
\(444\) 916.257 0.0979361
\(445\) 1465.23 0.156087
\(446\) 5841.88 0.620226
\(447\) −764.321 −0.0808750
\(448\) −575.323 −0.0606729
\(449\) 9630.11 1.01219 0.506095 0.862478i \(-0.331089\pi\)
0.506095 + 0.862478i \(0.331089\pi\)
\(450\) 2731.21 0.286112
\(451\) 2937.34 0.306683
\(452\) 7137.88 0.742782
\(453\) −1225.54 −0.127110
\(454\) −5782.00 −0.597715
\(455\) 110.659 0.0114017
\(456\) −403.631 −0.0414512
\(457\) 5577.69 0.570926 0.285463 0.958390i \(-0.407853\pi\)
0.285463 + 0.958390i \(0.407853\pi\)
\(458\) 547.360 0.0558438
\(459\) 803.298 0.0816879
\(460\) −5060.84 −0.512963
\(461\) −4598.29 −0.464563 −0.232282 0.972649i \(-0.574619\pi\)
−0.232282 + 0.972649i \(0.574619\pi\)
\(462\) 23.1423 0.00233047
\(463\) −463.742 −0.0465484 −0.0232742 0.999729i \(-0.507409\pi\)
−0.0232742 + 0.999729i \(0.507409\pi\)
\(464\) 3323.70 0.332541
\(465\) 68.0251 0.00678406
\(466\) −797.060 −0.0792341
\(467\) 1238.06 0.122678 0.0613388 0.998117i \(-0.480463\pi\)
0.0613388 + 0.998117i \(0.480463\pi\)
\(468\) 825.329 0.0815189
\(469\) −765.116 −0.0753300
\(470\) −358.342 −0.0351683
\(471\) 80.6666 0.00789155
\(472\) −8899.14 −0.867831
\(473\) 0 0
\(474\) −245.398 −0.0237796
\(475\) −5263.42 −0.508425
\(476\) 1007.85 0.0970474
\(477\) −8309.49 −0.797621
\(478\) 5573.86 0.533352
\(479\) 6374.43 0.608048 0.304024 0.952664i \(-0.401670\pi\)
0.304024 + 0.952664i \(0.401670\pi\)
\(480\) 419.437 0.0398845
\(481\) −1292.34 −0.122507
\(482\) 3442.66 0.325330
\(483\) 287.703 0.0271034
\(484\) 8411.11 0.789924
\(485\) −6051.71 −0.566586
\(486\) 1068.48 0.0997267
\(487\) −8076.69 −0.751519 −0.375759 0.926717i \(-0.622618\pi\)
−0.375759 + 0.926717i \(0.622618\pi\)
\(488\) 6036.85 0.559990
\(489\) 1293.80 0.119648
\(490\) −1857.59 −0.171260
\(491\) −10183.8 −0.936028 −0.468014 0.883721i \(-0.655030\pi\)
−0.468014 + 0.883721i \(0.655030\pi\)
\(492\) −908.681 −0.0832653
\(493\) −2814.43 −0.257111
\(494\) 262.921 0.0239461
\(495\) −1490.94 −0.135380
\(496\) 1031.97 0.0934214
\(497\) −1498.10 −0.135209
\(498\) 184.743 0.0166235
\(499\) 9449.18 0.847702 0.423851 0.905732i \(-0.360678\pi\)
0.423851 + 0.905732i \(0.360678\pi\)
\(500\) 8199.54 0.733389
\(501\) 880.162 0.0784885
\(502\) −2842.91 −0.252759
\(503\) 14140.8 1.25349 0.626747 0.779223i \(-0.284386\pi\)
0.626747 + 0.779223i \(0.284386\pi\)
\(504\) 1932.56 0.170800
\(505\) 25.4983 0.00224685
\(506\) 1492.81 0.131153
\(507\) −1009.02 −0.0883872
\(508\) 1989.83 0.173788
\(509\) −192.153 −0.0167329 −0.00836643 0.999965i \(-0.502663\pi\)
−0.00836643 + 0.999965i \(0.502663\pi\)
\(510\) −86.0962 −0.00747530
\(511\) −4712.63 −0.407973
\(512\) 11183.6 0.965336
\(513\) −1370.91 −0.117987
\(514\) −4410.69 −0.378497
\(515\) 6127.19 0.524265
\(516\) 0 0
\(517\) −639.430 −0.0543948
\(518\) −1397.54 −0.118541
\(519\) −768.624 −0.0650074
\(520\) −384.611 −0.0324352
\(521\) −10001.7 −0.841038 −0.420519 0.907284i \(-0.638152\pi\)
−0.420519 + 0.907284i \(0.638152\pi\)
\(522\) −2492.36 −0.208980
\(523\) −1686.23 −0.140982 −0.0704912 0.997512i \(-0.522457\pi\)
−0.0704912 + 0.997512i \(0.522457\pi\)
\(524\) 7714.27 0.643128
\(525\) −202.146 −0.0168046
\(526\) −5369.88 −0.445129
\(527\) −873.853 −0.0722308
\(528\) 181.431 0.0149541
\(529\) 6391.44 0.525309
\(530\) 1788.34 0.146567
\(531\) −15052.3 −1.23016
\(532\) −1719.99 −0.140171
\(533\) 1281.66 0.104155
\(534\) 133.704 0.0108351
\(535\) −9298.77 −0.751441
\(536\) 2659.28 0.214297
\(537\) 1648.28 0.132455
\(538\) −7208.87 −0.577689
\(539\) −3314.72 −0.264889
\(540\) 926.160 0.0738067
\(541\) 4269.53 0.339300 0.169650 0.985504i \(-0.445736\pi\)
0.169650 + 0.985504i \(0.445736\pi\)
\(542\) −8493.98 −0.673151
\(543\) −1689.00 −0.133484
\(544\) −5388.09 −0.424656
\(545\) −4211.60 −0.331019
\(546\) 10.0977 0.000791472 0
\(547\) −5089.79 −0.397849 −0.198925 0.980015i \(-0.563745\pi\)
−0.198925 + 0.980015i \(0.563745\pi\)
\(548\) −15208.7 −1.18555
\(549\) 10211.0 0.793795
\(550\) −1048.88 −0.0813172
\(551\) 4803.12 0.371361
\(552\) −999.955 −0.0771031
\(553\) −2264.29 −0.174119
\(554\) 1572.74 0.120613
\(555\) −722.218 −0.0552369
\(556\) −13425.8 −1.02407
\(557\) −211.814 −0.0161128 −0.00805641 0.999968i \(-0.502564\pi\)
−0.00805641 + 0.999968i \(0.502564\pi\)
\(558\) −773.852 −0.0587093
\(559\) 0 0
\(560\) 938.158 0.0707936
\(561\) −153.631 −0.0115621
\(562\) −7329.66 −0.550148
\(563\) 9751.04 0.729942 0.364971 0.931019i \(-0.381079\pi\)
0.364971 + 0.931019i \(0.381079\pi\)
\(564\) 197.811 0.0147683
\(565\) −5626.27 −0.418936
\(566\) −293.443 −0.0217921
\(567\) 3242.38 0.240154
\(568\) 5206.86 0.384639
\(569\) −13596.2 −1.00173 −0.500865 0.865526i \(-0.666985\pi\)
−0.500865 + 0.865526i \(0.666985\pi\)
\(570\) 146.932 0.0107970
\(571\) 5131.18 0.376065 0.188033 0.982163i \(-0.439789\pi\)
0.188033 + 0.982163i \(0.439789\pi\)
\(572\) −316.956 −0.0231689
\(573\) 1528.41 0.111432
\(574\) 1385.99 0.100784
\(575\) −13039.6 −0.945718
\(576\) 3382.24 0.244664
\(577\) 20274.6 1.46281 0.731405 0.681944i \(-0.238865\pi\)
0.731405 + 0.681944i \(0.238865\pi\)
\(578\) −4127.78 −0.297047
\(579\) −1705.60 −0.122422
\(580\) −3244.90 −0.232305
\(581\) 1704.62 0.121721
\(582\) −552.226 −0.0393307
\(583\) 3191.14 0.226695
\(584\) 16379.5 1.16059
\(585\) −650.547 −0.0459774
\(586\) −4794.74 −0.338002
\(587\) 21105.5 1.48402 0.742009 0.670390i \(-0.233873\pi\)
0.742009 + 0.670390i \(0.233873\pi\)
\(588\) 1025.42 0.0719180
\(589\) 1491.32 0.104327
\(590\) 3239.52 0.226049
\(591\) −1168.47 −0.0813276
\(592\) −10956.4 −0.760651
\(593\) −11899.5 −0.824035 −0.412017 0.911176i \(-0.635176\pi\)
−0.412017 + 0.911176i \(0.635176\pi\)
\(594\) −273.192 −0.0188707
\(595\) −794.411 −0.0547356
\(596\) 11320.2 0.778009
\(597\) −2207.40 −0.151328
\(598\) 651.361 0.0445420
\(599\) 25065.9 1.70979 0.854894 0.518802i \(-0.173622\pi\)
0.854894 + 0.518802i \(0.173622\pi\)
\(600\) 702.591 0.0478053
\(601\) 24254.1 1.64616 0.823081 0.567924i \(-0.192253\pi\)
0.823081 + 0.567924i \(0.192253\pi\)
\(602\) 0 0
\(603\) 4498.00 0.303769
\(604\) 18151.2 1.22279
\(605\) −6629.86 −0.445525
\(606\) 2.32675 0.000155970 0
\(607\) 6830.29 0.456726 0.228363 0.973576i \(-0.426663\pi\)
0.228363 + 0.973576i \(0.426663\pi\)
\(608\) 9195.34 0.613355
\(609\) 184.468 0.0122743
\(610\) −2197.57 −0.145864
\(611\) −279.004 −0.0184735
\(612\) −5924.98 −0.391345
\(613\) −9630.02 −0.634507 −0.317253 0.948341i \(-0.602761\pi\)
−0.317253 + 0.948341i \(0.602761\pi\)
\(614\) −8845.33 −0.581382
\(615\) 716.247 0.0469624
\(616\) −742.172 −0.0485438
\(617\) 2856.28 0.186369 0.0931844 0.995649i \(-0.470295\pi\)
0.0931844 + 0.995649i \(0.470295\pi\)
\(618\) 559.113 0.0363929
\(619\) 16879.5 1.09603 0.548016 0.836468i \(-0.315383\pi\)
0.548016 + 0.836468i \(0.315383\pi\)
\(620\) −1007.51 −0.0652620
\(621\) −3396.29 −0.219466
\(622\) 9624.78 0.620448
\(623\) 1233.69 0.0793366
\(624\) 79.1640 0.00507868
\(625\) 5501.63 0.352105
\(626\) −4696.06 −0.299828
\(627\) 262.188 0.0166998
\(628\) −1194.74 −0.0759159
\(629\) 9277.64 0.588114
\(630\) −703.502 −0.0444892
\(631\) −19957.6 −1.25911 −0.629555 0.776956i \(-0.716763\pi\)
−0.629555 + 0.776956i \(0.716763\pi\)
\(632\) 7869.90 0.495329
\(633\) −269.371 −0.0169140
\(634\) −1132.24 −0.0709260
\(635\) −1568.44 −0.0980182
\(636\) −987.194 −0.0615484
\(637\) −1446.32 −0.0899611
\(638\) 957.156 0.0593952
\(639\) 8807.08 0.545231
\(640\) −7967.01 −0.492068
\(641\) −22207.7 −1.36841 −0.684204 0.729290i \(-0.739850\pi\)
−0.684204 + 0.729290i \(0.739850\pi\)
\(642\) −848.524 −0.0521629
\(643\) −19400.5 −1.18986 −0.594932 0.803776i \(-0.702821\pi\)
−0.594932 + 0.803776i \(0.702821\pi\)
\(644\) −4261.11 −0.260732
\(645\) 0 0
\(646\) −1887.49 −0.114957
\(647\) −5574.01 −0.338697 −0.169349 0.985556i \(-0.554166\pi\)
−0.169349 + 0.985556i \(0.554166\pi\)
\(648\) −11269.4 −0.683183
\(649\) 5780.64 0.349630
\(650\) −457.661 −0.0276168
\(651\) 57.2755 0.00344824
\(652\) −19162.2 −1.15100
\(653\) −16231.9 −0.972747 −0.486374 0.873751i \(-0.661681\pi\)
−0.486374 + 0.873751i \(0.661681\pi\)
\(654\) −384.314 −0.0229784
\(655\) −6080.59 −0.362730
\(656\) 10865.8 0.646705
\(657\) 27704.9 1.64516
\(658\) −301.715 −0.0178755
\(659\) −21111.1 −1.24791 −0.623955 0.781461i \(-0.714475\pi\)
−0.623955 + 0.781461i \(0.714475\pi\)
\(660\) −177.129 −0.0104466
\(661\) −12591.6 −0.740935 −0.370467 0.928845i \(-0.620802\pi\)
−0.370467 + 0.928845i \(0.620802\pi\)
\(662\) −10519.8 −0.617619
\(663\) −67.0343 −0.00392669
\(664\) −5924.68 −0.346268
\(665\) 1355.74 0.0790579
\(666\) 8215.94 0.478020
\(667\) 11899.2 0.690766
\(668\) −13035.9 −0.755051
\(669\) 2541.89 0.146898
\(670\) −968.045 −0.0558192
\(671\) −3921.37 −0.225608
\(672\) 353.156 0.0202727
\(673\) −13408.2 −0.767979 −0.383989 0.923337i \(-0.625450\pi\)
−0.383989 + 0.923337i \(0.625450\pi\)
\(674\) −4843.98 −0.276830
\(675\) 2386.31 0.136073
\(676\) 14944.4 0.850276
\(677\) −32507.8 −1.84546 −0.922731 0.385445i \(-0.874048\pi\)
−0.922731 + 0.385445i \(0.874048\pi\)
\(678\) −513.404 −0.0290813
\(679\) −5095.40 −0.287987
\(680\) 2761.10 0.155711
\(681\) −2515.83 −0.141567
\(682\) 297.187 0.0166860
\(683\) −14676.1 −0.822203 −0.411101 0.911590i \(-0.634856\pi\)
−0.411101 + 0.911590i \(0.634856\pi\)
\(684\) 10111.6 0.565243
\(685\) 11987.9 0.668661
\(686\) −3228.86 −0.179706
\(687\) 238.164 0.0132264
\(688\) 0 0
\(689\) 1392.40 0.0769900
\(690\) 364.009 0.0200835
\(691\) −2412.12 −0.132795 −0.0663974 0.997793i \(-0.521151\pi\)
−0.0663974 + 0.997793i \(0.521151\pi\)
\(692\) 11383.9 0.625364
\(693\) −1255.34 −0.0688115
\(694\) 11294.0 0.617746
\(695\) 10582.6 0.577584
\(696\) −641.148 −0.0349176
\(697\) −9200.93 −0.500014
\(698\) −11708.4 −0.634913
\(699\) −346.813 −0.0187663
\(700\) 2993.95 0.161658
\(701\) 13310.0 0.717136 0.358568 0.933504i \(-0.383265\pi\)
0.358568 + 0.933504i \(0.383265\pi\)
\(702\) −119.202 −0.00640884
\(703\) −15833.2 −0.849448
\(704\) −1298.90 −0.0695372
\(705\) −155.920 −0.00832947
\(706\) −309.182 −0.0164819
\(707\) 21.4689 0.00114204
\(708\) −1788.27 −0.0949254
\(709\) 31617.1 1.67476 0.837381 0.546620i \(-0.184086\pi\)
0.837381 + 0.546620i \(0.184086\pi\)
\(710\) −1895.43 −0.100189
\(711\) 13311.5 0.702136
\(712\) −4287.87 −0.225695
\(713\) 3694.59 0.194058
\(714\) −72.4910 −0.00379959
\(715\) 249.833 0.0130674
\(716\) −24412.4 −1.27421
\(717\) 2425.27 0.126323
\(718\) 3665.82 0.190539
\(719\) 15564.1 0.807294 0.403647 0.914915i \(-0.367742\pi\)
0.403647 + 0.914915i \(0.367742\pi\)
\(720\) −5515.29 −0.285476
\(721\) 5158.95 0.266476
\(722\) −4085.63 −0.210597
\(723\) 1497.95 0.0770531
\(724\) 25015.4 1.28410
\(725\) −8360.68 −0.428287
\(726\) −604.983 −0.0309270
\(727\) −29265.4 −1.49298 −0.746488 0.665399i \(-0.768261\pi\)
−0.746488 + 0.665399i \(0.768261\pi\)
\(728\) −323.834 −0.0164864
\(729\) −18749.4 −0.952571
\(730\) −5962.54 −0.302306
\(731\) 0 0
\(732\) 1213.10 0.0612531
\(733\) 17131.8 0.863270 0.431635 0.902048i \(-0.357937\pi\)
0.431635 + 0.902048i \(0.357937\pi\)
\(734\) 7228.05 0.363477
\(735\) −808.266 −0.0405624
\(736\) 22780.5 1.14090
\(737\) −1727.39 −0.0863356
\(738\) −8148.01 −0.406412
\(739\) −16971.4 −0.844794 −0.422397 0.906411i \(-0.638811\pi\)
−0.422397 + 0.906411i \(0.638811\pi\)
\(740\) 10696.6 0.531373
\(741\) 114.401 0.00567156
\(742\) 1505.74 0.0744979
\(743\) 18171.5 0.897238 0.448619 0.893723i \(-0.351916\pi\)
0.448619 + 0.893723i \(0.351916\pi\)
\(744\) −199.070 −0.00980948
\(745\) −8922.88 −0.438804
\(746\) 9395.17 0.461101
\(747\) −10021.2 −0.490840
\(748\) 2275.40 0.111226
\(749\) −7829.34 −0.381946
\(750\) −589.765 −0.0287136
\(751\) −13978.9 −0.679223 −0.339612 0.940566i \(-0.610296\pi\)
−0.339612 + 0.940566i \(0.610296\pi\)
\(752\) −2365.38 −0.114703
\(753\) −1236.99 −0.0598651
\(754\) 417.638 0.0201717
\(755\) −14307.3 −0.689663
\(756\) 779.805 0.0375149
\(757\) −19774.5 −0.949426 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(758\) 2859.37 0.137015
\(759\) 649.543 0.0310631
\(760\) −4712.10 −0.224902
\(761\) 34351.4 1.63632 0.818158 0.574994i \(-0.194996\pi\)
0.818158 + 0.574994i \(0.194996\pi\)
\(762\) −143.122 −0.00680415
\(763\) −3546.07 −0.168252
\(764\) −22637.0 −1.07196
\(765\) 4670.23 0.220722
\(766\) 5227.46 0.246574
\(767\) 2522.28 0.118741
\(768\) −258.755 −0.0121576
\(769\) −19063.9 −0.893969 −0.446984 0.894542i \(-0.647502\pi\)
−0.446984 + 0.894542i \(0.647502\pi\)
\(770\) 270.170 0.0126445
\(771\) −1919.16 −0.0896456
\(772\) 25261.3 1.17769
\(773\) 36197.4 1.68426 0.842129 0.539276i \(-0.181302\pi\)
0.842129 + 0.539276i \(0.181302\pi\)
\(774\) 0 0
\(775\) −2595.90 −0.120320
\(776\) 17709.8 0.819260
\(777\) −608.091 −0.0280761
\(778\) −2130.53 −0.0981789
\(779\) 15702.3 0.722201
\(780\) −77.2870 −0.00354785
\(781\) −3382.23 −0.154963
\(782\) −4676.07 −0.213831
\(783\) −2177.62 −0.0993895
\(784\) −12261.8 −0.558573
\(785\) 941.723 0.0428172
\(786\) −554.861 −0.0251797
\(787\) 18293.2 0.828567 0.414284 0.910148i \(-0.364032\pi\)
0.414284 + 0.910148i \(0.364032\pi\)
\(788\) 17306.0 0.782363
\(789\) −2336.51 −0.105427
\(790\) −2864.85 −0.129021
\(791\) −4737.18 −0.212939
\(792\) 4363.12 0.195753
\(793\) −1711.02 −0.0766206
\(794\) 10163.6 0.454271
\(795\) 778.133 0.0347139
\(796\) 32693.4 1.45576
\(797\) 31454.9 1.39798 0.698989 0.715133i \(-0.253634\pi\)
0.698989 + 0.715133i \(0.253634\pi\)
\(798\) 123.713 0.00548797
\(799\) 2002.95 0.0886850
\(800\) −16006.1 −0.707377
\(801\) −7252.67 −0.319926
\(802\) 7162.56 0.315360
\(803\) −10639.7 −0.467578
\(804\) 534.377 0.0234403
\(805\) 3358.72 0.147055
\(806\) 129.672 0.00566688
\(807\) −3136.69 −0.136824
\(808\) −74.6185 −0.00324885
\(809\) 25771.0 1.11998 0.559989 0.828500i \(-0.310805\pi\)
0.559989 + 0.828500i \(0.310805\pi\)
\(810\) 4102.34 0.177953
\(811\) −33599.7 −1.45480 −0.727402 0.686212i \(-0.759272\pi\)
−0.727402 + 0.686212i \(0.759272\pi\)
\(812\) −2732.12 −0.118077
\(813\) −3695.86 −0.159433
\(814\) −3155.21 −0.135860
\(815\) 15104.2 0.649173
\(816\) −568.312 −0.0243810
\(817\) 0 0
\(818\) −3310.69 −0.141510
\(819\) −547.745 −0.0233697
\(820\) −10608.2 −0.451773
\(821\) 36051.3 1.53252 0.766260 0.642531i \(-0.222116\pi\)
0.766260 + 0.642531i \(0.222116\pi\)
\(822\) 1093.91 0.0464166
\(823\) 5404.48 0.228905 0.114452 0.993429i \(-0.463489\pi\)
0.114452 + 0.993429i \(0.463489\pi\)
\(824\) −17930.7 −0.758065
\(825\) −456.384 −0.0192597
\(826\) 2727.59 0.114897
\(827\) −19906.0 −0.837000 −0.418500 0.908217i \(-0.637444\pi\)
−0.418500 + 0.908217i \(0.637444\pi\)
\(828\) 25050.4 1.05140
\(829\) 25969.3 1.08800 0.543999 0.839086i \(-0.316910\pi\)
0.543999 + 0.839086i \(0.316910\pi\)
\(830\) 2156.74 0.0901944
\(831\) 684.324 0.0285667
\(832\) −566.752 −0.0236161
\(833\) 10383.0 0.431873
\(834\) 965.676 0.0400943
\(835\) 10275.2 0.425856
\(836\) −3883.21 −0.160650
\(837\) −676.130 −0.0279217
\(838\) 17355.6 0.715442
\(839\) −26178.3 −1.07721 −0.538603 0.842560i \(-0.681048\pi\)
−0.538603 + 0.842560i \(0.681048\pi\)
\(840\) −180.973 −0.00743351
\(841\) −16759.5 −0.687174
\(842\) 3050.78 0.124866
\(843\) −3189.24 −0.130300
\(844\) 3989.60 0.162711
\(845\) −11779.6 −0.479563
\(846\) 1773.74 0.0720833
\(847\) −5582.19 −0.226454
\(848\) 11804.6 0.478034
\(849\) −127.681 −0.00516139
\(850\) 3285.52 0.132579
\(851\) −39225.2 −1.58005
\(852\) 1046.31 0.0420728
\(853\) 45066.9 1.80898 0.904490 0.426495i \(-0.140252\pi\)
0.904490 + 0.426495i \(0.140252\pi\)
\(854\) −1850.30 −0.0741405
\(855\) −7970.22 −0.318802
\(856\) 27212.1 1.08655
\(857\) 20163.4 0.803695 0.401848 0.915706i \(-0.368368\pi\)
0.401848 + 0.915706i \(0.368368\pi\)
\(858\) 22.7976 0.000907105 0
\(859\) 38656.8 1.53545 0.767726 0.640778i \(-0.221388\pi\)
0.767726 + 0.640778i \(0.221388\pi\)
\(860\) 0 0
\(861\) 603.063 0.0238703
\(862\) −4650.83 −0.183768
\(863\) 11938.0 0.470886 0.235443 0.971888i \(-0.424346\pi\)
0.235443 + 0.971888i \(0.424346\pi\)
\(864\) −4168.95 −0.164156
\(865\) −8973.12 −0.352711
\(866\) 1780.41 0.0698622
\(867\) −1796.06 −0.0703544
\(868\) −848.296 −0.0331717
\(869\) −5112.07 −0.199557
\(870\) 233.394 0.00909519
\(871\) −753.717 −0.0293212
\(872\) 12324.9 0.478640
\(873\) 29955.1 1.16131
\(874\) 7980.20 0.308849
\(875\) −5441.77 −0.210246
\(876\) 3291.43 0.126949
\(877\) 898.663 0.0346017 0.0173008 0.999850i \(-0.494493\pi\)
0.0173008 + 0.999850i \(0.494493\pi\)
\(878\) −6203.79 −0.238460
\(879\) −2086.26 −0.0800545
\(880\) 2118.07 0.0811364
\(881\) −4887.81 −0.186918 −0.0934588 0.995623i \(-0.529792\pi\)
−0.0934588 + 0.995623i \(0.529792\pi\)
\(882\) 9194.82 0.351027
\(883\) 27593.4 1.05163 0.525816 0.850598i \(-0.323760\pi\)
0.525816 + 0.850598i \(0.323760\pi\)
\(884\) 992.831 0.0377744
\(885\) 1409.56 0.0535388
\(886\) −1089.18 −0.0412998
\(887\) 44465.6 1.68321 0.841606 0.540092i \(-0.181610\pi\)
0.841606 + 0.540092i \(0.181610\pi\)
\(888\) 2113.51 0.0798703
\(889\) −1320.59 −0.0498213
\(890\) 1560.90 0.0587880
\(891\) 7320.28 0.275240
\(892\) −37647.4 −1.41315
\(893\) −3418.24 −0.128093
\(894\) −814.224 −0.0304605
\(895\) 19242.5 0.718665
\(896\) −6708.03 −0.250111
\(897\) 283.417 0.0105496
\(898\) 10258.9 0.381228
\(899\) 2368.89 0.0878830
\(900\) −17601.0 −0.651889
\(901\) −9995.91 −0.369603
\(902\) 3129.13 0.115508
\(903\) 0 0
\(904\) 16464.8 0.605764
\(905\) −19717.8 −0.724247
\(906\) −1305.56 −0.0478744
\(907\) −13410.8 −0.490958 −0.245479 0.969402i \(-0.578945\pi\)
−0.245479 + 0.969402i \(0.578945\pi\)
\(908\) 37261.5 1.36186
\(909\) −126.213 −0.00460529
\(910\) 117.884 0.00429430
\(911\) −24002.1 −0.872914 −0.436457 0.899725i \(-0.643767\pi\)
−0.436457 + 0.899725i \(0.643767\pi\)
\(912\) 969.884 0.0352150
\(913\) 3848.51 0.139504
\(914\) 5941.86 0.215032
\(915\) −956.194 −0.0345473
\(916\) −3527.40 −0.127237
\(917\) −5119.71 −0.184371
\(918\) 855.746 0.0307667
\(919\) 28960.1 1.03950 0.519752 0.854317i \(-0.326024\pi\)
0.519752 + 0.854317i \(0.326024\pi\)
\(920\) −11673.7 −0.418339
\(921\) −3848.73 −0.137698
\(922\) −4898.52 −0.174972
\(923\) −1475.78 −0.0526282
\(924\) −149.138 −0.00530984
\(925\) 27560.6 0.979660
\(926\) −494.020 −0.0175318
\(927\) −30328.7 −1.07457
\(928\) 14606.3 0.516678
\(929\) 30584.7 1.08014 0.540071 0.841619i \(-0.318397\pi\)
0.540071 + 0.841619i \(0.318397\pi\)
\(930\) 72.4665 0.00255513
\(931\) −17719.7 −0.623780
\(932\) 5136.57 0.180530
\(933\) 4187.88 0.146951
\(934\) 1318.89 0.0462050
\(935\) −1793.53 −0.0627324
\(936\) 1903.77 0.0664815
\(937\) −45835.7 −1.59807 −0.799033 0.601287i \(-0.794655\pi\)
−0.799033 + 0.601287i \(0.794655\pi\)
\(938\) −815.071 −0.0283721
\(939\) −2043.32 −0.0710131
\(940\) 2309.30 0.0801287
\(941\) −2785.96 −0.0965140 −0.0482570 0.998835i \(-0.515367\pi\)
−0.0482570 + 0.998835i \(0.515367\pi\)
\(942\) 85.9334 0.00297225
\(943\) 38900.9 1.34336
\(944\) 21383.7 0.737268
\(945\) −614.663 −0.0211587
\(946\) 0 0
\(947\) −12107.3 −0.415454 −0.207727 0.978187i \(-0.566606\pi\)
−0.207727 + 0.978187i \(0.566606\pi\)
\(948\) 1581.44 0.0541803
\(949\) −4642.42 −0.158798
\(950\) −5607.07 −0.191492
\(951\) −492.655 −0.0167986
\(952\) 2324.78 0.0791455
\(953\) 17220.7 0.585343 0.292671 0.956213i \(-0.405456\pi\)
0.292671 + 0.956213i \(0.405456\pi\)
\(954\) −8852.02 −0.300414
\(955\) 17843.1 0.604597
\(956\) −35920.2 −1.21521
\(957\) 416.472 0.0140675
\(958\) 6790.62 0.229014
\(959\) 10093.5 0.339871
\(960\) −316.726 −0.0106482
\(961\) −29055.5 −0.975311
\(962\) −1376.72 −0.0461406
\(963\) 46027.5 1.54020
\(964\) −22185.9 −0.741243
\(965\) −19911.6 −0.664226
\(966\) 306.487 0.0102081
\(967\) 36590.1 1.21681 0.608407 0.793625i \(-0.291809\pi\)
0.608407 + 0.793625i \(0.291809\pi\)
\(968\) 19401.7 0.644210
\(969\) −821.276 −0.0272272
\(970\) −6446.83 −0.213397
\(971\) 14970.4 0.494771 0.247386 0.968917i \(-0.420429\pi\)
0.247386 + 0.968917i \(0.420429\pi\)
\(972\) −6885.70 −0.227221
\(973\) 8910.30 0.293578
\(974\) −8604.02 −0.283050
\(975\) −199.135 −0.00654095
\(976\) −14505.9 −0.475741
\(977\) −55910.8 −1.83086 −0.915428 0.402483i \(-0.868147\pi\)
−0.915428 + 0.402483i \(0.868147\pi\)
\(978\) 1378.27 0.0450637
\(979\) 2785.28 0.0909276
\(980\) 11971.1 0.390206
\(981\) 20846.8 0.678479
\(982\) −10848.7 −0.352543
\(983\) 3092.53 0.100342 0.0501710 0.998741i \(-0.484023\pi\)
0.0501710 + 0.998741i \(0.484023\pi\)
\(984\) −2096.04 −0.0679057
\(985\) −13641.1 −0.441260
\(986\) −2998.19 −0.0968376
\(987\) −131.281 −0.00423375
\(988\) −1694.37 −0.0545598
\(989\) 0 0
\(990\) −1588.29 −0.0509890
\(991\) −12923.0 −0.414242 −0.207121 0.978315i \(-0.566409\pi\)
−0.207121 + 0.978315i \(0.566409\pi\)
\(992\) 4535.12 0.145151
\(993\) −4577.32 −0.146281
\(994\) −1595.91 −0.0509247
\(995\) −25769.8 −0.821062
\(996\) −1190.55 −0.0378757
\(997\) −25871.0 −0.821807 −0.410904 0.911679i \(-0.634787\pi\)
−0.410904 + 0.911679i \(0.634787\pi\)
\(998\) 10066.1 0.319276
\(999\) 7178.43 0.227343
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.1.30 50
43.42 odd 2 1849.4.a.j.1.21 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.30 50 1.1 even 1 trivial
1849.4.a.j.1.21 yes 50 43.42 odd 2