Properties

Label 1849.4.a.j.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

\(f(q)\) \(=\) \(q+0.702850 q^{2} -4.82523 q^{3} -7.50600 q^{4} -8.51327 q^{5} -3.39141 q^{6} -25.5957 q^{7} -10.8984 q^{8} -3.71712 q^{9} +O(q^{10})\) \(q+0.702850 q^{2} -4.82523 q^{3} -7.50600 q^{4} -8.51327 q^{5} -3.39141 q^{6} -25.5957 q^{7} -10.8984 q^{8} -3.71712 q^{9} -5.98355 q^{10} -28.9564 q^{11} +36.2182 q^{12} -77.8657 q^{13} -17.9899 q^{14} +41.0785 q^{15} +52.3881 q^{16} +87.6620 q^{17} -2.61258 q^{18} -15.5698 q^{19} +63.9006 q^{20} +123.505 q^{21} -20.3520 q^{22} -9.68121 q^{23} +52.5873 q^{24} -52.5243 q^{25} -54.7279 q^{26} +148.217 q^{27} +192.121 q^{28} +189.097 q^{29} +28.8720 q^{30} +260.919 q^{31} +124.008 q^{32} +139.721 q^{33} +61.6132 q^{34} +217.903 q^{35} +27.9007 q^{36} -57.5937 q^{37} -10.9432 q^{38} +375.720 q^{39} +92.7809 q^{40} -296.291 q^{41} +86.8055 q^{42} +217.347 q^{44} +31.6448 q^{45} -6.80444 q^{46} -360.808 q^{47} -252.785 q^{48} +312.138 q^{49} -36.9167 q^{50} -422.990 q^{51} +584.460 q^{52} +352.316 q^{53} +104.174 q^{54} +246.514 q^{55} +278.952 q^{56} +75.1279 q^{57} +132.907 q^{58} -711.248 q^{59} -308.335 q^{60} -456.857 q^{61} +183.387 q^{62} +95.1422 q^{63} -331.946 q^{64} +662.891 q^{65} +98.2032 q^{66} -488.166 q^{67} -657.991 q^{68} +46.7141 q^{69} +153.153 q^{70} +924.781 q^{71} +40.5106 q^{72} +708.211 q^{73} -40.4797 q^{74} +253.442 q^{75} +116.867 q^{76} +741.159 q^{77} +264.075 q^{78} +191.956 q^{79} -445.994 q^{80} -614.821 q^{81} -208.248 q^{82} +962.592 q^{83} -927.030 q^{84} -746.290 q^{85} -912.436 q^{87} +315.578 q^{88} -158.267 q^{89} +22.2416 q^{90} +1993.02 q^{91} +72.6672 q^{92} -1259.00 q^{93} -253.594 q^{94} +132.550 q^{95} -598.368 q^{96} -1264.08 q^{97} +219.386 q^{98} +107.635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.702850 0.248495 0.124247 0.992251i \(-0.460348\pi\)
0.124247 + 0.992251i \(0.460348\pi\)
\(3\) −4.82523 −0.928617 −0.464308 0.885674i \(-0.653697\pi\)
−0.464308 + 0.885674i \(0.653697\pi\)
\(4\) −7.50600 −0.938250
\(5\) −8.51327 −0.761450 −0.380725 0.924688i \(-0.624325\pi\)
−0.380725 + 0.924688i \(0.624325\pi\)
\(6\) −3.39141 −0.230757
\(7\) −25.5957 −1.38204 −0.691018 0.722837i \(-0.742838\pi\)
−0.691018 + 0.722837i \(0.742838\pi\)
\(8\) −10.8984 −0.481645
\(9\) −3.71712 −0.137671
\(10\) −5.98355 −0.189216
\(11\) −28.9564 −0.793699 −0.396850 0.917884i \(-0.629897\pi\)
−0.396850 + 0.917884i \(0.629897\pi\)
\(12\) 36.2182 0.871275
\(13\) −77.8657 −1.66124 −0.830618 0.556843i \(-0.812012\pi\)
−0.830618 + 0.556843i \(0.812012\pi\)
\(14\) −17.9899 −0.343429
\(15\) 41.0785 0.707095
\(16\) 52.3881 0.818564
\(17\) 87.6620 1.25066 0.625328 0.780362i \(-0.284965\pi\)
0.625328 + 0.780362i \(0.284965\pi\)
\(18\) −2.61258 −0.0342106
\(19\) −15.5698 −0.187998 −0.0939989 0.995572i \(-0.529965\pi\)
−0.0939989 + 0.995572i \(0.529965\pi\)
\(20\) 63.9006 0.714430
\(21\) 123.505 1.28338
\(22\) −20.3520 −0.197230
\(23\) −9.68121 −0.0877684 −0.0438842 0.999037i \(-0.513973\pi\)
−0.0438842 + 0.999037i \(0.513973\pi\)
\(24\) 52.5873 0.447264
\(25\) −52.5243 −0.420194
\(26\) −54.7279 −0.412809
\(27\) 148.217 1.05646
\(28\) 192.121 1.29670
\(29\) 189.097 1.21084 0.605421 0.795906i \(-0.293005\pi\)
0.605421 + 0.795906i \(0.293005\pi\)
\(30\) 28.8720 0.175709
\(31\) 260.919 1.51169 0.755847 0.654748i \(-0.227225\pi\)
0.755847 + 0.654748i \(0.227225\pi\)
\(32\) 124.008 0.685054
\(33\) 139.721 0.737042
\(34\) 61.6132 0.310782
\(35\) 217.903 1.05235
\(36\) 27.9007 0.129170
\(37\) −57.5937 −0.255901 −0.127951 0.991781i \(-0.540840\pi\)
−0.127951 + 0.991781i \(0.540840\pi\)
\(38\) −10.9432 −0.0467165
\(39\) 375.720 1.54265
\(40\) 92.7809 0.366749
\(41\) −296.291 −1.12861 −0.564303 0.825568i \(-0.690855\pi\)
−0.564303 + 0.825568i \(0.690855\pi\)
\(42\) 86.8055 0.318914
\(43\) 0 0
\(44\) 217.347 0.744688
\(45\) 31.6448 0.104830
\(46\) −6.80444 −0.0218100
\(47\) −360.808 −1.11977 −0.559886 0.828570i \(-0.689155\pi\)
−0.559886 + 0.828570i \(0.689155\pi\)
\(48\) −252.785 −0.760132
\(49\) 312.138 0.910025
\(50\) −36.9167 −0.104416
\(51\) −422.990 −1.16138
\(52\) 584.460 1.55865
\(53\) 352.316 0.913101 0.456551 0.889697i \(-0.349085\pi\)
0.456551 + 0.889697i \(0.349085\pi\)
\(54\) 104.174 0.262525
\(55\) 246.514 0.604362
\(56\) 278.952 0.665651
\(57\) 75.1279 0.174578
\(58\) 132.907 0.300888
\(59\) −711.248 −1.56943 −0.784717 0.619854i \(-0.787192\pi\)
−0.784717 + 0.619854i \(0.787192\pi\)
\(60\) −308.335 −0.663432
\(61\) −456.857 −0.958926 −0.479463 0.877562i \(-0.659169\pi\)
−0.479463 + 0.877562i \(0.659169\pi\)
\(62\) 183.387 0.375648
\(63\) 95.1422 0.190267
\(64\) −331.946 −0.648331
\(65\) 662.891 1.26495
\(66\) 98.2032 0.183151
\(67\) −488.166 −0.890134 −0.445067 0.895497i \(-0.646820\pi\)
−0.445067 + 0.895497i \(0.646820\pi\)
\(68\) −657.991 −1.17343
\(69\) 46.7141 0.0815032
\(70\) 153.153 0.261504
\(71\) 924.781 1.54579 0.772896 0.634532i \(-0.218807\pi\)
0.772896 + 0.634532i \(0.218807\pi\)
\(72\) 40.5106 0.0663087
\(73\) 708.211 1.13548 0.567739 0.823209i \(-0.307818\pi\)
0.567739 + 0.823209i \(0.307818\pi\)
\(74\) −40.4797 −0.0635902
\(75\) 253.442 0.390200
\(76\) 116.867 0.176389
\(77\) 741.159 1.09692
\(78\) 264.075 0.383341
\(79\) 191.956 0.273377 0.136688 0.990614i \(-0.456354\pi\)
0.136688 + 0.990614i \(0.456354\pi\)
\(80\) −445.994 −0.623295
\(81\) −614.821 −0.843376
\(82\) −208.248 −0.280453
\(83\) 962.592 1.27299 0.636495 0.771281i \(-0.280384\pi\)
0.636495 + 0.771281i \(0.280384\pi\)
\(84\) −927.030 −1.20413
\(85\) −746.290 −0.952312
\(86\) 0 0
\(87\) −912.436 −1.12441
\(88\) 315.578 0.382281
\(89\) −158.267 −0.188498 −0.0942489 0.995549i \(-0.530045\pi\)
−0.0942489 + 0.995549i \(0.530045\pi\)
\(90\) 22.2416 0.0260496
\(91\) 1993.02 2.29589
\(92\) 72.6672 0.0823487
\(93\) −1259.00 −1.40378
\(94\) −253.594 −0.278257
\(95\) 132.550 0.143151
\(96\) −598.368 −0.636153
\(97\) −1264.08 −1.32318 −0.661589 0.749867i \(-0.730118\pi\)
−0.661589 + 0.749867i \(0.730118\pi\)
\(98\) 219.386 0.226136
\(99\) 107.635 0.109269
\(100\) 394.248 0.394248
\(101\) 347.859 0.342705 0.171353 0.985210i \(-0.445186\pi\)
0.171353 + 0.985210i \(0.445186\pi\)
\(102\) −297.298 −0.288597
\(103\) −572.571 −0.547739 −0.273869 0.961767i \(-0.588304\pi\)
−0.273869 + 0.961767i \(0.588304\pi\)
\(104\) 848.611 0.800126
\(105\) −1051.43 −0.977231
\(106\) 247.625 0.226901
\(107\) 545.798 0.493124 0.246562 0.969127i \(-0.420699\pi\)
0.246562 + 0.969127i \(0.420699\pi\)
\(108\) −1112.52 −0.991224
\(109\) 1658.16 1.45709 0.728547 0.684996i \(-0.240196\pi\)
0.728547 + 0.684996i \(0.240196\pi\)
\(110\) 173.262 0.150181
\(111\) 277.903 0.237634
\(112\) −1340.91 −1.13129
\(113\) −492.200 −0.409755 −0.204877 0.978788i \(-0.565680\pi\)
−0.204877 + 0.978788i \(0.565680\pi\)
\(114\) 52.8036 0.0433817
\(115\) 82.4187 0.0668312
\(116\) −1419.36 −1.13607
\(117\) 289.436 0.228704
\(118\) −499.901 −0.389996
\(119\) −2243.77 −1.72845
\(120\) −447.689 −0.340569
\(121\) −492.526 −0.370042
\(122\) −321.102 −0.238288
\(123\) 1429.67 1.04804
\(124\) −1958.46 −1.41835
\(125\) 1511.31 1.08141
\(126\) 66.8707 0.0472803
\(127\) 858.473 0.599820 0.299910 0.953968i \(-0.403043\pi\)
0.299910 + 0.953968i \(0.403043\pi\)
\(128\) −1225.37 −0.846161
\(129\) 0 0
\(130\) 465.913 0.314333
\(131\) 67.8806 0.0452729 0.0226365 0.999744i \(-0.492794\pi\)
0.0226365 + 0.999744i \(0.492794\pi\)
\(132\) −1048.75 −0.691530
\(133\) 398.519 0.259820
\(134\) −343.107 −0.221194
\(135\) −1261.81 −0.804441
\(136\) −955.374 −0.602373
\(137\) 1944.29 1.21249 0.606247 0.795276i \(-0.292674\pi\)
0.606247 + 0.795276i \(0.292674\pi\)
\(138\) 32.8330 0.0202531
\(139\) −531.190 −0.324136 −0.162068 0.986780i \(-0.551816\pi\)
−0.162068 + 0.986780i \(0.551816\pi\)
\(140\) −1635.58 −0.987369
\(141\) 1740.98 1.03984
\(142\) 649.982 0.384122
\(143\) 2254.71 1.31852
\(144\) −194.733 −0.112693
\(145\) −1609.83 −0.921995
\(146\) 497.766 0.282160
\(147\) −1506.14 −0.845064
\(148\) 432.298 0.240099
\(149\) 110.710 0.0608708 0.0304354 0.999537i \(-0.490311\pi\)
0.0304354 + 0.999537i \(0.490311\pi\)
\(150\) 178.132 0.0969626
\(151\) −123.313 −0.0664572 −0.0332286 0.999448i \(-0.510579\pi\)
−0.0332286 + 0.999448i \(0.510579\pi\)
\(152\) 169.686 0.0905482
\(153\) −325.850 −0.172179
\(154\) 520.923 0.272579
\(155\) −2221.28 −1.15108
\(156\) −2820.16 −1.44739
\(157\) 2208.42 1.12262 0.561308 0.827607i \(-0.310298\pi\)
0.561308 + 0.827607i \(0.310298\pi\)
\(158\) 134.916 0.0679327
\(159\) −1700.01 −0.847921
\(160\) −1055.71 −0.521634
\(161\) 247.797 0.121299
\(162\) −432.127 −0.209575
\(163\) −3433.18 −1.64974 −0.824868 0.565325i \(-0.808751\pi\)
−0.824868 + 0.565325i \(0.808751\pi\)
\(164\) 2223.96 1.05891
\(165\) −1189.49 −0.561220
\(166\) 676.558 0.316332
\(167\) 1177.83 0.545770 0.272885 0.962047i \(-0.412022\pi\)
0.272885 + 0.962047i \(0.412022\pi\)
\(168\) −1346.01 −0.618135
\(169\) 3866.07 1.75970
\(170\) −524.530 −0.236645
\(171\) 57.8748 0.0258819
\(172\) 0 0
\(173\) 3101.92 1.36321 0.681603 0.731722i \(-0.261283\pi\)
0.681603 + 0.731722i \(0.261283\pi\)
\(174\) −641.306 −0.279410
\(175\) 1344.40 0.580724
\(176\) −1516.97 −0.649693
\(177\) 3431.94 1.45740
\(178\) −111.238 −0.0468407
\(179\) 3524.06 1.47151 0.735756 0.677246i \(-0.236827\pi\)
0.735756 + 0.677246i \(0.236827\pi\)
\(180\) −237.526 −0.0983564
\(181\) −4695.34 −1.92819 −0.964093 0.265565i \(-0.914442\pi\)
−0.964093 + 0.265565i \(0.914442\pi\)
\(182\) 1400.80 0.570516
\(183\) 2204.44 0.890475
\(184\) 105.510 0.0422732
\(185\) 490.310 0.194856
\(186\) −884.886 −0.348833
\(187\) −2538.38 −0.992645
\(188\) 2708.22 1.05063
\(189\) −3793.72 −1.46007
\(190\) 93.1626 0.0355722
\(191\) 845.793 0.320416 0.160208 0.987083i \(-0.448783\pi\)
0.160208 + 0.987083i \(0.448783\pi\)
\(192\) 1601.72 0.602051
\(193\) −4042.09 −1.50754 −0.753772 0.657136i \(-0.771768\pi\)
−0.753772 + 0.657136i \(0.771768\pi\)
\(194\) −888.461 −0.328803
\(195\) −3198.61 −1.17465
\(196\) −2342.91 −0.853831
\(197\) −1036.95 −0.375025 −0.187512 0.982262i \(-0.560042\pi\)
−0.187512 + 0.982262i \(0.560042\pi\)
\(198\) 75.6509 0.0271529
\(199\) −2419.84 −0.862001 −0.431001 0.902352i \(-0.641839\pi\)
−0.431001 + 0.902352i \(0.641839\pi\)
\(200\) 572.430 0.202385
\(201\) 2355.51 0.826593
\(202\) 244.492 0.0851605
\(203\) −4840.06 −1.67343
\(204\) 3174.96 1.08967
\(205\) 2522.40 0.859377
\(206\) −402.431 −0.136110
\(207\) 35.9862 0.0120832
\(208\) −4079.23 −1.35983
\(209\) 450.846 0.149214
\(210\) −738.998 −0.242837
\(211\) −86.7026 −0.0282884 −0.0141442 0.999900i \(-0.504502\pi\)
−0.0141442 + 0.999900i \(0.504502\pi\)
\(212\) −2644.49 −0.856718
\(213\) −4462.28 −1.43545
\(214\) 383.614 0.122539
\(215\) 0 0
\(216\) −1615.33 −0.508839
\(217\) −6678.41 −2.08922
\(218\) 1165.44 0.362081
\(219\) −3417.29 −1.05442
\(220\) −1850.33 −0.567043
\(221\) −6825.86 −2.07763
\(222\) 195.324 0.0590509
\(223\) −5215.36 −1.56613 −0.783063 0.621942i \(-0.786344\pi\)
−0.783063 + 0.621942i \(0.786344\pi\)
\(224\) −3174.07 −0.946770
\(225\) 195.239 0.0578487
\(226\) −345.943 −0.101822
\(227\) 6096.41 1.78252 0.891261 0.453490i \(-0.149821\pi\)
0.891261 + 0.453490i \(0.149821\pi\)
\(228\) −563.910 −0.163798
\(229\) 1061.19 0.306225 0.153113 0.988209i \(-0.451070\pi\)
0.153113 + 0.988209i \(0.451070\pi\)
\(230\) 57.9280 0.0166072
\(231\) −3576.27 −1.01862
\(232\) −2060.85 −0.583196
\(233\) −5539.60 −1.55756 −0.778779 0.627298i \(-0.784161\pi\)
−0.778779 + 0.627298i \(0.784161\pi\)
\(234\) 203.430 0.0568318
\(235\) 3071.65 0.852649
\(236\) 5338.63 1.47252
\(237\) −926.233 −0.253862
\(238\) −1577.03 −0.429512
\(239\) 3252.71 0.880337 0.440169 0.897915i \(-0.354919\pi\)
0.440169 + 0.897915i \(0.354919\pi\)
\(240\) 2152.02 0.578802
\(241\) 6590.62 1.76157 0.880787 0.473513i \(-0.157014\pi\)
0.880787 + 0.473513i \(0.157014\pi\)
\(242\) −346.172 −0.0919535
\(243\) −1035.21 −0.273288
\(244\) 3429.17 0.899713
\(245\) −2657.32 −0.692938
\(246\) 1004.84 0.260433
\(247\) 1212.35 0.312308
\(248\) −2843.60 −0.728100
\(249\) −4644.73 −1.18212
\(250\) 1062.22 0.268724
\(251\) −6086.84 −1.53067 −0.765334 0.643633i \(-0.777426\pi\)
−0.765334 + 0.643633i \(0.777426\pi\)
\(252\) −714.138 −0.178518
\(253\) 280.333 0.0696617
\(254\) 603.377 0.149052
\(255\) 3601.02 0.884332
\(256\) 1794.31 0.438065
\(257\) 6729.20 1.63329 0.816646 0.577138i \(-0.195831\pi\)
0.816646 + 0.577138i \(0.195831\pi\)
\(258\) 0 0
\(259\) 1474.15 0.353665
\(260\) −4975.66 −1.18684
\(261\) −702.896 −0.166698
\(262\) 47.7098 0.0112501
\(263\) 5288.13 1.23985 0.619924 0.784662i \(-0.287163\pi\)
0.619924 + 0.784662i \(0.287163\pi\)
\(264\) −1522.74 −0.354993
\(265\) −2999.36 −0.695281
\(266\) 280.099 0.0645639
\(267\) 763.677 0.175042
\(268\) 3664.17 0.835168
\(269\) −7705.95 −1.74662 −0.873309 0.487166i \(-0.838031\pi\)
−0.873309 + 0.487166i \(0.838031\pi\)
\(270\) −886.865 −0.199900
\(271\) −474.184 −0.106290 −0.0531450 0.998587i \(-0.516925\pi\)
−0.0531450 + 0.998587i \(0.516925\pi\)
\(272\) 4592.44 1.02374
\(273\) −9616.81 −2.13200
\(274\) 1366.54 0.301299
\(275\) 1520.92 0.333508
\(276\) −350.636 −0.0764704
\(277\) 2161.04 0.468752 0.234376 0.972146i \(-0.424695\pi\)
0.234376 + 0.972146i \(0.424695\pi\)
\(278\) −373.346 −0.0805462
\(279\) −969.869 −0.208117
\(280\) −2374.79 −0.506860
\(281\) −2131.11 −0.452426 −0.226213 0.974078i \(-0.572634\pi\)
−0.226213 + 0.974078i \(0.572634\pi\)
\(282\) 1223.65 0.258394
\(283\) 4185.92 0.879249 0.439624 0.898182i \(-0.355112\pi\)
0.439624 + 0.898182i \(0.355112\pi\)
\(284\) −6941.41 −1.45034
\(285\) −639.584 −0.132932
\(286\) 1584.72 0.327646
\(287\) 7583.76 1.55977
\(288\) −460.953 −0.0943122
\(289\) 2771.62 0.564141
\(290\) −1131.47 −0.229111
\(291\) 6099.50 1.22872
\(292\) −5315.84 −1.06536
\(293\) 5909.60 1.17830 0.589151 0.808023i \(-0.299462\pi\)
0.589151 + 0.808023i \(0.299462\pi\)
\(294\) −1058.59 −0.209994
\(295\) 6055.04 1.19505
\(296\) 627.679 0.123254
\(297\) −4291.84 −0.838512
\(298\) 77.8127 0.0151261
\(299\) 753.834 0.145804
\(300\) −1902.34 −0.366105
\(301\) 0 0
\(302\) −86.6702 −0.0165143
\(303\) −1678.50 −0.318242
\(304\) −815.672 −0.153888
\(305\) 3889.34 0.730174
\(306\) −229.024 −0.0427857
\(307\) −4281.17 −0.795893 −0.397946 0.917409i \(-0.630277\pi\)
−0.397946 + 0.917409i \(0.630277\pi\)
\(308\) −5563.14 −1.02919
\(309\) 2762.79 0.508639
\(310\) −1561.22 −0.286037
\(311\) −7076.50 −1.29026 −0.645131 0.764072i \(-0.723197\pi\)
−0.645131 + 0.764072i \(0.723197\pi\)
\(312\) −4094.74 −0.743011
\(313\) −334.959 −0.0604889 −0.0302444 0.999543i \(-0.509629\pi\)
−0.0302444 + 0.999543i \(0.509629\pi\)
\(314\) 1552.18 0.278965
\(315\) −809.971 −0.144878
\(316\) −1440.82 −0.256496
\(317\) 3536.49 0.626591 0.313295 0.949656i \(-0.398567\pi\)
0.313295 + 0.949656i \(0.398567\pi\)
\(318\) −1194.85 −0.210704
\(319\) −5475.57 −0.961044
\(320\) 2825.94 0.493672
\(321\) −2633.60 −0.457924
\(322\) 174.164 0.0301422
\(323\) −1364.88 −0.235120
\(324\) 4614.85 0.791297
\(325\) 4089.84 0.698042
\(326\) −2413.01 −0.409951
\(327\) −8001.03 −1.35308
\(328\) 3229.09 0.543588
\(329\) 9235.12 1.54756
\(330\) −836.030 −0.139460
\(331\) −1925.31 −0.319712 −0.159856 0.987140i \(-0.551103\pi\)
−0.159856 + 0.987140i \(0.551103\pi\)
\(332\) −7225.22 −1.19438
\(333\) 214.083 0.0352302
\(334\) 827.841 0.135621
\(335\) 4155.89 0.677792
\(336\) 6470.20 1.05053
\(337\) −2426.42 −0.392212 −0.196106 0.980583i \(-0.562830\pi\)
−0.196106 + 0.980583i \(0.562830\pi\)
\(338\) 2717.26 0.437277
\(339\) 2374.98 0.380505
\(340\) 5601.65 0.893507
\(341\) −7555.29 −1.19983
\(342\) 40.6773 0.00643151
\(343\) 789.923 0.124349
\(344\) 0 0
\(345\) −397.690 −0.0620605
\(346\) 2180.18 0.338750
\(347\) −588.164 −0.0909922 −0.0454961 0.998965i \(-0.514487\pi\)
−0.0454961 + 0.998965i \(0.514487\pi\)
\(348\) 6848.75 1.05498
\(349\) 8121.04 1.24558 0.622792 0.782387i \(-0.285998\pi\)
0.622792 + 0.782387i \(0.285998\pi\)
\(350\) 944.908 0.144307
\(351\) −11541.0 −1.75503
\(352\) −3590.83 −0.543727
\(353\) 7819.91 1.17907 0.589535 0.807743i \(-0.299311\pi\)
0.589535 + 0.807743i \(0.299311\pi\)
\(354\) 2412.14 0.362157
\(355\) −7872.90 −1.17704
\(356\) 1187.95 0.176858
\(357\) 10826.7 1.60507
\(358\) 2476.89 0.365663
\(359\) 6276.39 0.922716 0.461358 0.887214i \(-0.347362\pi\)
0.461358 + 0.887214i \(0.347362\pi\)
\(360\) −344.878 −0.0504907
\(361\) −6616.58 −0.964657
\(362\) −3300.12 −0.479144
\(363\) 2376.55 0.343627
\(364\) −14959.6 −2.15412
\(365\) −6029.19 −0.864609
\(366\) 1549.39 0.221278
\(367\) 817.330 0.116251 0.0581257 0.998309i \(-0.481488\pi\)
0.0581257 + 0.998309i \(0.481488\pi\)
\(368\) −507.180 −0.0718440
\(369\) 1101.35 0.155376
\(370\) 344.615 0.0484207
\(371\) −9017.77 −1.26194
\(372\) 9450.04 1.31710
\(373\) 8113.99 1.12635 0.563173 0.826339i \(-0.309581\pi\)
0.563173 + 0.826339i \(0.309581\pi\)
\(374\) −1784.10 −0.246667
\(375\) −7292.43 −1.00421
\(376\) 3932.23 0.539333
\(377\) −14724.2 −2.01149
\(378\) −2666.42 −0.362819
\(379\) 95.6236 0.0129600 0.00648002 0.999979i \(-0.497937\pi\)
0.00648002 + 0.999979i \(0.497937\pi\)
\(380\) −994.919 −0.134311
\(381\) −4142.33 −0.557003
\(382\) 594.466 0.0796218
\(383\) −7564.64 −1.00923 −0.504615 0.863345i \(-0.668365\pi\)
−0.504615 + 0.863345i \(0.668365\pi\)
\(384\) 5912.71 0.785760
\(385\) −6309.68 −0.835250
\(386\) −2840.98 −0.374617
\(387\) 0 0
\(388\) 9488.21 1.24147
\(389\) −5243.67 −0.683457 −0.341729 0.939799i \(-0.611012\pi\)
−0.341729 + 0.939799i \(0.611012\pi\)
\(390\) −2248.14 −0.291895
\(391\) −848.674 −0.109768
\(392\) −3401.81 −0.438309
\(393\) −327.540 −0.0420412
\(394\) −728.823 −0.0931918
\(395\) −1634.17 −0.208163
\(396\) −807.905 −0.102522
\(397\) −5525.23 −0.698497 −0.349249 0.937030i \(-0.613563\pi\)
−0.349249 + 0.937030i \(0.613563\pi\)
\(398\) −1700.79 −0.214203
\(399\) −1922.95 −0.241273
\(400\) −2751.65 −0.343956
\(401\) 5427.82 0.675941 0.337971 0.941157i \(-0.390260\pi\)
0.337971 + 0.941157i \(0.390260\pi\)
\(402\) 1655.57 0.205404
\(403\) −20316.7 −2.51128
\(404\) −2611.03 −0.321543
\(405\) 5234.13 0.642188
\(406\) −3401.84 −0.415838
\(407\) 1667.71 0.203109
\(408\) 4609.90 0.559373
\(409\) 4847.71 0.586073 0.293037 0.956101i \(-0.405334\pi\)
0.293037 + 0.956101i \(0.405334\pi\)
\(410\) 1772.87 0.213551
\(411\) −9381.65 −1.12594
\(412\) 4297.72 0.513916
\(413\) 18204.9 2.16902
\(414\) 25.2929 0.00300261
\(415\) −8194.80 −0.969318
\(416\) −9655.98 −1.13804
\(417\) 2563.11 0.300998
\(418\) 316.877 0.0370788
\(419\) 6156.12 0.717771 0.358886 0.933382i \(-0.383157\pi\)
0.358886 + 0.933382i \(0.383157\pi\)
\(420\) 7892.05 0.916887
\(421\) 5676.26 0.657111 0.328556 0.944485i \(-0.393438\pi\)
0.328556 + 0.944485i \(0.393438\pi\)
\(422\) −60.9389 −0.00702952
\(423\) 1341.17 0.154160
\(424\) −3839.68 −0.439791
\(425\) −4604.39 −0.525519
\(426\) −3136.31 −0.356702
\(427\) 11693.6 1.32527
\(428\) −4096.76 −0.462674
\(429\) −10879.5 −1.22440
\(430\) 0 0
\(431\) −10888.1 −1.21685 −0.608425 0.793612i \(-0.708198\pi\)
−0.608425 + 0.793612i \(0.708198\pi\)
\(432\) 7764.82 0.864780
\(433\) −2719.36 −0.301811 −0.150905 0.988548i \(-0.548219\pi\)
−0.150905 + 0.988548i \(0.548219\pi\)
\(434\) −4693.92 −0.519160
\(435\) 7767.81 0.856180
\(436\) −12446.2 −1.36712
\(437\) 150.735 0.0165003
\(438\) −2401.84 −0.262019
\(439\) 857.486 0.0932245 0.0466123 0.998913i \(-0.485157\pi\)
0.0466123 + 0.998913i \(0.485157\pi\)
\(440\) −2686.60 −0.291088
\(441\) −1160.26 −0.125284
\(442\) −4797.55 −0.516281
\(443\) 12384.2 1.32819 0.664097 0.747646i \(-0.268816\pi\)
0.664097 + 0.747646i \(0.268816\pi\)
\(444\) −2085.94 −0.222960
\(445\) 1347.37 0.143532
\(446\) −3665.61 −0.389174
\(447\) −534.203 −0.0565256
\(448\) 8496.37 0.896018
\(449\) 8314.20 0.873878 0.436939 0.899491i \(-0.356063\pi\)
0.436939 + 0.899491i \(0.356063\pi\)
\(450\) 137.224 0.0143751
\(451\) 8579.52 0.895773
\(452\) 3694.45 0.384452
\(453\) 595.012 0.0617132
\(454\) 4284.86 0.442948
\(455\) −16967.1 −1.74820
\(456\) −818.773 −0.0840846
\(457\) 4900.06 0.501565 0.250782 0.968043i \(-0.419312\pi\)
0.250782 + 0.968043i \(0.419312\pi\)
\(458\) 745.859 0.0760954
\(459\) 12993.0 1.32127
\(460\) −618.635 −0.0627044
\(461\) 10050.6 1.01541 0.507706 0.861530i \(-0.330494\pi\)
0.507706 + 0.861530i \(0.330494\pi\)
\(462\) −2513.58 −0.253122
\(463\) −4096.77 −0.411217 −0.205608 0.978634i \(-0.565917\pi\)
−0.205608 + 0.978634i \(0.565917\pi\)
\(464\) 9906.42 0.991151
\(465\) 10718.2 1.06891
\(466\) −3893.50 −0.387045
\(467\) 8517.70 0.844009 0.422005 0.906594i \(-0.361327\pi\)
0.422005 + 0.906594i \(0.361327\pi\)
\(468\) −2172.51 −0.214582
\(469\) 12494.9 1.23020
\(470\) 2158.91 0.211879
\(471\) −10656.1 −1.04248
\(472\) 7751.46 0.755911
\(473\) 0 0
\(474\) −651.003 −0.0630834
\(475\) 817.793 0.0789956
\(476\) 16841.7 1.62172
\(477\) −1309.60 −0.125708
\(478\) 2286.17 0.218759
\(479\) 8478.48 0.808751 0.404375 0.914593i \(-0.367489\pi\)
0.404375 + 0.914593i \(0.367489\pi\)
\(480\) 5094.06 0.484398
\(481\) 4484.57 0.425112
\(482\) 4632.22 0.437742
\(483\) −1195.68 −0.112640
\(484\) 3696.90 0.347192
\(485\) 10761.5 1.00753
\(486\) −727.599 −0.0679106
\(487\) −13015.1 −1.21102 −0.605512 0.795836i \(-0.707032\pi\)
−0.605512 + 0.795836i \(0.707032\pi\)
\(488\) 4979.00 0.461862
\(489\) 16565.9 1.53197
\(490\) −1867.69 −0.172192
\(491\) −13090.1 −1.20315 −0.601577 0.798815i \(-0.705461\pi\)
−0.601577 + 0.798815i \(0.705461\pi\)
\(492\) −10731.1 −0.983326
\(493\) 16576.6 1.51435
\(494\) 852.102 0.0776071
\(495\) −916.321 −0.0832032
\(496\) 13669.1 1.23742
\(497\) −23670.4 −2.13634
\(498\) −3264.55 −0.293751
\(499\) −15411.4 −1.38258 −0.691290 0.722578i \(-0.742957\pi\)
−0.691290 + 0.722578i \(0.742957\pi\)
\(500\) −11343.9 −1.01463
\(501\) −5683.33 −0.506811
\(502\) −4278.13 −0.380363
\(503\) 19402.6 1.71991 0.859957 0.510366i \(-0.170490\pi\)
0.859957 + 0.510366i \(0.170490\pi\)
\(504\) −1036.90 −0.0916410
\(505\) −2961.41 −0.260953
\(506\) 197.032 0.0173106
\(507\) −18654.7 −1.63409
\(508\) −6443.70 −0.562781
\(509\) −12.0380 −0.00104828 −0.000524140 1.00000i \(-0.500167\pi\)
−0.000524140 1.00000i \(0.500167\pi\)
\(510\) 2530.98 0.219752
\(511\) −18127.1 −1.56927
\(512\) 11064.1 0.955018
\(513\) −2307.71 −0.198612
\(514\) 4729.62 0.405865
\(515\) 4874.45 0.417076
\(516\) 0 0
\(517\) 10447.7 0.888761
\(518\) 1036.11 0.0878839
\(519\) −14967.5 −1.26590
\(520\) −7224.45 −0.609256
\(521\) 1360.35 0.114391 0.0571956 0.998363i \(-0.481784\pi\)
0.0571956 + 0.998363i \(0.481784\pi\)
\(522\) −494.030 −0.0414236
\(523\) −6659.15 −0.556757 −0.278379 0.960471i \(-0.589797\pi\)
−0.278379 + 0.960471i \(0.589797\pi\)
\(524\) −509.512 −0.0424773
\(525\) −6487.02 −0.539270
\(526\) 3716.76 0.308096
\(527\) 22872.7 1.89061
\(528\) 7319.74 0.603316
\(529\) −12073.3 −0.992297
\(530\) −2108.10 −0.172774
\(531\) 2643.80 0.216066
\(532\) −2991.29 −0.243776
\(533\) 23070.9 1.87488
\(534\) 536.750 0.0434971
\(535\) −4646.53 −0.375489
\(536\) 5320.22 0.428729
\(537\) −17004.4 −1.36647
\(538\) −5416.13 −0.434026
\(539\) −9038.41 −0.722286
\(540\) 9471.17 0.754767
\(541\) 19303.1 1.53402 0.767009 0.641636i \(-0.221744\pi\)
0.767009 + 0.641636i \(0.221744\pi\)
\(542\) −333.280 −0.0264125
\(543\) 22656.1 1.79055
\(544\) 10870.8 0.856767
\(545\) −14116.4 −1.10950
\(546\) −6759.17 −0.529791
\(547\) 16113.9 1.25956 0.629782 0.776772i \(-0.283144\pi\)
0.629782 + 0.776772i \(0.283144\pi\)
\(548\) −14593.8 −1.13762
\(549\) 1698.19 0.132016
\(550\) 1068.98 0.0828750
\(551\) −2944.20 −0.227635
\(552\) −509.109 −0.0392556
\(553\) −4913.25 −0.377816
\(554\) 1518.89 0.116483
\(555\) −2365.86 −0.180946
\(556\) 3987.11 0.304121
\(557\) 7897.57 0.600773 0.300387 0.953818i \(-0.402884\pi\)
0.300387 + 0.953818i \(0.402884\pi\)
\(558\) −681.672 −0.0517159
\(559\) 0 0
\(560\) 11415.5 0.861417
\(561\) 12248.3 0.921786
\(562\) −1497.85 −0.112425
\(563\) −11672.7 −0.873790 −0.436895 0.899513i \(-0.643922\pi\)
−0.436895 + 0.899513i \(0.643922\pi\)
\(564\) −13067.8 −0.975628
\(565\) 4190.23 0.312008
\(566\) 2942.08 0.218489
\(567\) 15736.8 1.16558
\(568\) −10078.6 −0.744524
\(569\) 13214.7 0.973622 0.486811 0.873507i \(-0.338160\pi\)
0.486811 + 0.873507i \(0.338160\pi\)
\(570\) −449.531 −0.0330330
\(571\) 6180.52 0.452972 0.226486 0.974014i \(-0.427276\pi\)
0.226486 + 0.974014i \(0.427276\pi\)
\(572\) −16923.9 −1.23710
\(573\) −4081.15 −0.297544
\(574\) 5330.24 0.387596
\(575\) 508.499 0.0368798
\(576\) 1233.88 0.0892565
\(577\) 2583.84 0.186424 0.0932120 0.995646i \(-0.470287\pi\)
0.0932120 + 0.995646i \(0.470287\pi\)
\(578\) 1948.03 0.140186
\(579\) 19504.0 1.39993
\(580\) 12083.4 0.865062
\(581\) −24638.2 −1.75932
\(582\) 4287.03 0.305332
\(583\) −10201.8 −0.724728
\(584\) −7718.36 −0.546898
\(585\) −2464.05 −0.174147
\(586\) 4153.56 0.292802
\(587\) −4777.54 −0.335929 −0.167964 0.985793i \(-0.553719\pi\)
−0.167964 + 0.985793i \(0.553719\pi\)
\(588\) 11305.1 0.792881
\(589\) −4062.46 −0.284195
\(590\) 4255.79 0.296963
\(591\) 5003.54 0.348254
\(592\) −3017.22 −0.209472
\(593\) −6495.84 −0.449835 −0.224918 0.974378i \(-0.572211\pi\)
−0.224918 + 0.974378i \(0.572211\pi\)
\(594\) −3016.52 −0.208366
\(595\) 19101.8 1.31613
\(596\) −830.992 −0.0571120
\(597\) 11676.3 0.800469
\(598\) 529.832 0.0362315
\(599\) 3799.23 0.259152 0.129576 0.991569i \(-0.458638\pi\)
0.129576 + 0.991569i \(0.458638\pi\)
\(600\) −2762.11 −0.187938
\(601\) −7204.53 −0.488983 −0.244492 0.969651i \(-0.578621\pi\)
−0.244492 + 0.969651i \(0.578621\pi\)
\(602\) 0 0
\(603\) 1814.57 0.122546
\(604\) 925.584 0.0623535
\(605\) 4193.00 0.281768
\(606\) −1179.73 −0.0790814
\(607\) −16521.2 −1.10474 −0.552368 0.833601i \(-0.686276\pi\)
−0.552368 + 0.833601i \(0.686276\pi\)
\(608\) −1930.78 −0.128789
\(609\) 23354.4 1.55397
\(610\) 2733.62 0.181445
\(611\) 28094.6 1.86020
\(612\) 2445.83 0.161547
\(613\) 12480.3 0.822307 0.411153 0.911566i \(-0.365126\pi\)
0.411153 + 0.911566i \(0.365126\pi\)
\(614\) −3009.02 −0.197775
\(615\) −12171.2 −0.798031
\(616\) −8077.44 −0.528327
\(617\) −10157.2 −0.662745 −0.331372 0.943500i \(-0.607512\pi\)
−0.331372 + 0.943500i \(0.607512\pi\)
\(618\) 1941.83 0.126394
\(619\) 303.903 0.0197333 0.00986664 0.999951i \(-0.496859\pi\)
0.00986664 + 0.999951i \(0.496859\pi\)
\(620\) 16672.9 1.08000
\(621\) −1434.92 −0.0927238
\(622\) −4973.72 −0.320623
\(623\) 4050.96 0.260511
\(624\) 19683.3 1.26276
\(625\) −6300.66 −0.403242
\(626\) −235.426 −0.0150312
\(627\) −2175.44 −0.138562
\(628\) −16576.4 −1.05330
\(629\) −5048.78 −0.320044
\(630\) −569.288 −0.0360015
\(631\) −24763.4 −1.56231 −0.781153 0.624340i \(-0.785368\pi\)
−0.781153 + 0.624340i \(0.785368\pi\)
\(632\) −2092.01 −0.131671
\(633\) 418.360 0.0262691
\(634\) 2485.62 0.155705
\(635\) −7308.41 −0.456733
\(636\) 12760.3 0.795562
\(637\) −24304.9 −1.51176
\(638\) −3848.50 −0.238814
\(639\) −3437.52 −0.212811
\(640\) 10431.9 0.644309
\(641\) −17677.2 −1.08925 −0.544624 0.838680i \(-0.683328\pi\)
−0.544624 + 0.838680i \(0.683328\pi\)
\(642\) −1851.03 −0.113792
\(643\) 1817.63 0.111478 0.0557390 0.998445i \(-0.482249\pi\)
0.0557390 + 0.998445i \(0.482249\pi\)
\(644\) −1859.97 −0.113809
\(645\) 0 0
\(646\) −959.305 −0.0584262
\(647\) −7234.22 −0.439578 −0.219789 0.975547i \(-0.570537\pi\)
−0.219789 + 0.975547i \(0.570537\pi\)
\(648\) 6700.56 0.406208
\(649\) 20595.2 1.24566
\(650\) 2874.54 0.173460
\(651\) 32224.9 1.94008
\(652\) 25769.4 1.54787
\(653\) −13094.2 −0.784710 −0.392355 0.919814i \(-0.628339\pi\)
−0.392355 + 0.919814i \(0.628339\pi\)
\(654\) −5623.52 −0.336234
\(655\) −577.885 −0.0344730
\(656\) −15522.1 −0.923836
\(657\) −2632.51 −0.156323
\(658\) 6490.90 0.384562
\(659\) 23832.6 1.40878 0.704391 0.709813i \(-0.251220\pi\)
0.704391 + 0.709813i \(0.251220\pi\)
\(660\) 8928.29 0.526565
\(661\) −6199.16 −0.364780 −0.182390 0.983226i \(-0.558383\pi\)
−0.182390 + 0.983226i \(0.558383\pi\)
\(662\) −1353.20 −0.0794468
\(663\) 32936.4 1.92933
\(664\) −10490.7 −0.613130
\(665\) −3392.70 −0.197840
\(666\) 150.468 0.00875453
\(667\) −1830.69 −0.106274
\(668\) −8840.83 −0.512069
\(669\) 25165.3 1.45433
\(670\) 2920.96 0.168428
\(671\) 13228.9 0.761099
\(672\) 15315.6 0.879186
\(673\) −14970.2 −0.857442 −0.428721 0.903437i \(-0.641036\pi\)
−0.428721 + 0.903437i \(0.641036\pi\)
\(674\) −1705.41 −0.0974626
\(675\) −7785.01 −0.443919
\(676\) −29018.7 −1.65104
\(677\) 14646.4 0.831470 0.415735 0.909486i \(-0.363524\pi\)
0.415735 + 0.909486i \(0.363524\pi\)
\(678\) 1669.25 0.0945536
\(679\) 32355.1 1.82868
\(680\) 8133.36 0.458676
\(681\) −29416.6 −1.65528
\(682\) −5310.24 −0.298152
\(683\) −18578.7 −1.04084 −0.520420 0.853910i \(-0.674225\pi\)
−0.520420 + 0.853910i \(0.674225\pi\)
\(684\) −434.408 −0.0242837
\(685\) −16552.2 −0.923254
\(686\) 555.197 0.0309002
\(687\) −5120.50 −0.284366
\(688\) 0 0
\(689\) −27433.4 −1.51688
\(690\) −279.516 −0.0154217
\(691\) 20405.3 1.12338 0.561690 0.827348i \(-0.310151\pi\)
0.561690 + 0.827348i \(0.310151\pi\)
\(692\) −23283.0 −1.27903
\(693\) −2754.98 −0.151014
\(694\) −413.391 −0.0226111
\(695\) 4522.16 0.246813
\(696\) 9944.09 0.541566
\(697\) −25973.4 −1.41150
\(698\) 5707.87 0.309522
\(699\) 26729.8 1.44637
\(700\) −10091.0 −0.544865
\(701\) −9377.79 −0.505270 −0.252635 0.967562i \(-0.581297\pi\)
−0.252635 + 0.967562i \(0.581297\pi\)
\(702\) −8111.62 −0.436116
\(703\) 896.722 0.0481088
\(704\) 9611.96 0.514580
\(705\) −14821.4 −0.791784
\(706\) 5496.22 0.292993
\(707\) −8903.67 −0.473631
\(708\) −25760.1 −1.36741
\(709\) −23415.3 −1.24031 −0.620155 0.784479i \(-0.712930\pi\)
−0.620155 + 0.784479i \(0.712930\pi\)
\(710\) −5533.47 −0.292489
\(711\) −713.524 −0.0376361
\(712\) 1724.86 0.0907891
\(713\) −2526.02 −0.132679
\(714\) 7609.54 0.398852
\(715\) −19195.0 −1.00399
\(716\) −26451.6 −1.38065
\(717\) −15695.1 −0.817496
\(718\) 4411.36 0.229290
\(719\) 17381.0 0.901531 0.450765 0.892642i \(-0.351151\pi\)
0.450765 + 0.892642i \(0.351151\pi\)
\(720\) 1657.81 0.0858098
\(721\) 14655.3 0.756995
\(722\) −4650.46 −0.239712
\(723\) −31801.3 −1.63583
\(724\) 35243.2 1.80912
\(725\) −9932.18 −0.508789
\(726\) 1670.36 0.0853896
\(727\) −10089.7 −0.514728 −0.257364 0.966315i \(-0.582854\pi\)
−0.257364 + 0.966315i \(0.582854\pi\)
\(728\) −21720.8 −1.10580
\(729\) 21595.3 1.09716
\(730\) −4237.62 −0.214851
\(731\) 0 0
\(732\) −16546.5 −0.835488
\(733\) 18021.1 0.908081 0.454041 0.890981i \(-0.349982\pi\)
0.454041 + 0.890981i \(0.349982\pi\)
\(734\) 574.460 0.0288879
\(735\) 12822.2 0.643474
\(736\) −1200.55 −0.0601261
\(737\) 14135.5 0.706498
\(738\) 774.083 0.0386103
\(739\) −10773.6 −0.536284 −0.268142 0.963379i \(-0.586410\pi\)
−0.268142 + 0.963379i \(0.586410\pi\)
\(740\) −3680.27 −0.182824
\(741\) −5849.89 −0.290015
\(742\) −6338.14 −0.313585
\(743\) −14689.6 −0.725316 −0.362658 0.931922i \(-0.618131\pi\)
−0.362658 + 0.931922i \(0.618131\pi\)
\(744\) 13721.0 0.676126
\(745\) −942.507 −0.0463500
\(746\) 5702.92 0.279891
\(747\) −3578.07 −0.175254
\(748\) 19053.1 0.931349
\(749\) −13970.1 −0.681516
\(750\) −5125.48 −0.249542
\(751\) −24097.2 −1.17086 −0.585432 0.810721i \(-0.699075\pi\)
−0.585432 + 0.810721i \(0.699075\pi\)
\(752\) −18902.0 −0.916604
\(753\) 29370.4 1.42140
\(754\) −10348.9 −0.499846
\(755\) 1049.79 0.0506038
\(756\) 28475.7 1.36991
\(757\) 21261.7 1.02083 0.510415 0.859928i \(-0.329492\pi\)
0.510415 + 0.859928i \(0.329492\pi\)
\(758\) 67.2090 0.00322050
\(759\) −1352.67 −0.0646890
\(760\) −1444.58 −0.0689479
\(761\) 12987.5 0.618657 0.309328 0.950955i \(-0.399896\pi\)
0.309328 + 0.950955i \(0.399896\pi\)
\(762\) −2911.44 −0.138412
\(763\) −42441.8 −2.01376
\(764\) −6348.53 −0.300630
\(765\) 2774.05 0.131106
\(766\) −5316.80 −0.250788
\(767\) 55381.8 2.60720
\(768\) −8657.98 −0.406794
\(769\) 19917.6 0.934001 0.467000 0.884257i \(-0.345335\pi\)
0.467000 + 0.884257i \(0.345335\pi\)
\(770\) −4434.76 −0.207555
\(771\) −32470.0 −1.51670
\(772\) 30339.9 1.41445
\(773\) 28483.0 1.32531 0.662653 0.748927i \(-0.269431\pi\)
0.662653 + 0.748927i \(0.269431\pi\)
\(774\) 0 0
\(775\) −13704.6 −0.635205
\(776\) 13776.5 0.637302
\(777\) −7113.12 −0.328419
\(778\) −3685.51 −0.169836
\(779\) 4613.19 0.212175
\(780\) 24008.7 1.10212
\(781\) −26778.3 −1.22689
\(782\) −596.490 −0.0272768
\(783\) 28027.4 1.27921
\(784\) 16352.3 0.744913
\(785\) −18800.8 −0.854816
\(786\) −230.211 −0.0104470
\(787\) 14243.4 0.645135 0.322567 0.946547i \(-0.395454\pi\)
0.322567 + 0.946547i \(0.395454\pi\)
\(788\) 7783.38 0.351867
\(789\) −25516.5 −1.15134
\(790\) −1148.58 −0.0517273
\(791\) 12598.2 0.566296
\(792\) −1173.04 −0.0526291
\(793\) 35573.5 1.59300
\(794\) −3883.41 −0.173573
\(795\) 14472.6 0.645649
\(796\) 18163.4 0.808773
\(797\) −5179.01 −0.230176 −0.115088 0.993355i \(-0.536715\pi\)
−0.115088 + 0.993355i \(0.536715\pi\)
\(798\) −1351.54 −0.0599551
\(799\) −31629.1 −1.40045
\(800\) −6513.44 −0.287856
\(801\) 588.299 0.0259507
\(802\) 3814.94 0.167968
\(803\) −20507.3 −0.901228
\(804\) −17680.5 −0.775551
\(805\) −2109.56 −0.0923631
\(806\) −14279.6 −0.624040
\(807\) 37183.0 1.62194
\(808\) −3791.10 −0.165062
\(809\) −25454.2 −1.10621 −0.553103 0.833113i \(-0.686556\pi\)
−0.553103 + 0.833113i \(0.686556\pi\)
\(810\) 3678.81 0.159580
\(811\) −654.805 −0.0283518 −0.0141759 0.999900i \(-0.504512\pi\)
−0.0141759 + 0.999900i \(0.504512\pi\)
\(812\) 36329.5 1.57009
\(813\) 2288.05 0.0987027
\(814\) 1172.15 0.0504714
\(815\) 29227.5 1.25619
\(816\) −22159.6 −0.950664
\(817\) 0 0
\(818\) 3407.21 0.145636
\(819\) −7408.31 −0.316077
\(820\) −18933.2 −0.806310
\(821\) 39663.1 1.68606 0.843029 0.537869i \(-0.180770\pi\)
0.843029 + 0.537869i \(0.180770\pi\)
\(822\) −6593.89 −0.279791
\(823\) −23291.6 −0.986507 −0.493254 0.869886i \(-0.664193\pi\)
−0.493254 + 0.869886i \(0.664193\pi\)
\(824\) 6240.10 0.263816
\(825\) −7338.78 −0.309701
\(826\) 12795.3 0.538989
\(827\) −17656.3 −0.742404 −0.371202 0.928552i \(-0.621054\pi\)
−0.371202 + 0.928552i \(0.621054\pi\)
\(828\) −270.113 −0.0113370
\(829\) −36113.7 −1.51300 −0.756502 0.653991i \(-0.773093\pi\)
−0.756502 + 0.653991i \(0.773093\pi\)
\(830\) −5759.71 −0.240871
\(831\) −10427.5 −0.435291
\(832\) 25847.2 1.07703
\(833\) 27362.7 1.13813
\(834\) 1801.48 0.0747965
\(835\) −10027.2 −0.415576
\(836\) −3384.05 −0.140000
\(837\) 38672.8 1.59704
\(838\) 4326.83 0.178363
\(839\) −23151.9 −0.952674 −0.476337 0.879263i \(-0.658036\pi\)
−0.476337 + 0.879263i \(0.658036\pi\)
\(840\) 11458.9 0.470679
\(841\) 11368.6 0.466137
\(842\) 3989.56 0.163289
\(843\) 10283.1 0.420130
\(844\) 650.790 0.0265416
\(845\) −32912.9 −1.33992
\(846\) 942.639 0.0383080
\(847\) 12606.5 0.511411
\(848\) 18457.2 0.747432
\(849\) −20198.1 −0.816485
\(850\) −3236.19 −0.130589
\(851\) 557.577 0.0224600
\(852\) 33493.9 1.34681
\(853\) −14236.2 −0.571441 −0.285721 0.958313i \(-0.592233\pi\)
−0.285721 + 0.958313i \(0.592233\pi\)
\(854\) 8218.81 0.329323
\(855\) −492.704 −0.0197077
\(856\) −5948.32 −0.237511
\(857\) −12778.3 −0.509332 −0.254666 0.967029i \(-0.581965\pi\)
−0.254666 + 0.967029i \(0.581965\pi\)
\(858\) −7646.66 −0.304257
\(859\) 8165.70 0.324342 0.162171 0.986763i \(-0.448150\pi\)
0.162171 + 0.986763i \(0.448150\pi\)
\(860\) 0 0
\(861\) −36593.4 −1.44843
\(862\) −7652.71 −0.302381
\(863\) −8527.22 −0.336350 −0.168175 0.985757i \(-0.553787\pi\)
−0.168175 + 0.985757i \(0.553787\pi\)
\(864\) 18380.1 0.723733
\(865\) −26407.5 −1.03801
\(866\) −1911.30 −0.0749984
\(867\) −13373.7 −0.523870
\(868\) 50128.1 1.96021
\(869\) −5558.36 −0.216979
\(870\) 5459.61 0.212756
\(871\) 38011.4 1.47872
\(872\) −18071.3 −0.701803
\(873\) 4698.75 0.182163
\(874\) 105.944 0.00410023
\(875\) −38683.0 −1.49454
\(876\) 25650.2 0.989313
\(877\) 6640.78 0.255694 0.127847 0.991794i \(-0.459193\pi\)
0.127847 + 0.991794i \(0.459193\pi\)
\(878\) 602.684 0.0231658
\(879\) −28515.2 −1.09419
\(880\) 12914.4 0.494709
\(881\) 442.425 0.0169190 0.00845952 0.999964i \(-0.497307\pi\)
0.00845952 + 0.999964i \(0.497307\pi\)
\(882\) −815.486 −0.0311325
\(883\) −12877.2 −0.490773 −0.245386 0.969425i \(-0.578915\pi\)
−0.245386 + 0.969425i \(0.578915\pi\)
\(884\) 51234.9 1.94934
\(885\) −29217.0 −1.10974
\(886\) 8704.22 0.330050
\(887\) 41065.2 1.55449 0.777246 0.629196i \(-0.216616\pi\)
0.777246 + 0.629196i \(0.216616\pi\)
\(888\) −3028.70 −0.114455
\(889\) −21973.2 −0.828973
\(890\) 947.000 0.0356669
\(891\) 17803.0 0.669386
\(892\) 39146.5 1.46942
\(893\) 5617.71 0.210514
\(894\) −375.465 −0.0140463
\(895\) −30001.3 −1.12048
\(896\) 31364.2 1.16943
\(897\) −3637.43 −0.135396
\(898\) 5843.63 0.217154
\(899\) 49339.0 1.83042
\(900\) −1465.47 −0.0542765
\(901\) 30884.7 1.14198
\(902\) 6030.11 0.222595
\(903\) 0 0
\(904\) 5364.19 0.197356
\(905\) 39972.7 1.46822
\(906\) 418.204 0.0153354
\(907\) 10096.2 0.369614 0.184807 0.982775i \(-0.440834\pi\)
0.184807 + 0.982775i \(0.440834\pi\)
\(908\) −45759.6 −1.67245
\(909\) −1293.03 −0.0471806
\(910\) −11925.4 −0.434419
\(911\) −33124.2 −1.20467 −0.602334 0.798244i \(-0.705762\pi\)
−0.602334 + 0.798244i \(0.705762\pi\)
\(912\) 3935.81 0.142903
\(913\) −27873.2 −1.01037
\(914\) 3444.01 0.124636
\(915\) −18767.0 −0.678052
\(916\) −7965.32 −0.287316
\(917\) −1737.45 −0.0625688
\(918\) 9132.14 0.328329
\(919\) 41284.6 1.48189 0.740944 0.671567i \(-0.234379\pi\)
0.740944 + 0.671567i \(0.234379\pi\)
\(920\) −898.231 −0.0321889
\(921\) 20657.6 0.739079
\(922\) 7064.09 0.252325
\(923\) −72008.7 −2.56793
\(924\) 26843.5 0.955720
\(925\) 3025.07 0.107528
\(926\) −2879.42 −0.102185
\(927\) 2128.32 0.0754078
\(928\) 23449.5 0.829492
\(929\) 24029.9 0.848650 0.424325 0.905510i \(-0.360511\pi\)
0.424325 + 0.905510i \(0.360511\pi\)
\(930\) 7533.27 0.265619
\(931\) −4859.93 −0.171083
\(932\) 41580.2 1.46138
\(933\) 34145.8 1.19816
\(934\) 5986.67 0.209732
\(935\) 21609.9 0.755849
\(936\) −3154.39 −0.110154
\(937\) 3930.36 0.137032 0.0685162 0.997650i \(-0.478174\pi\)
0.0685162 + 0.997650i \(0.478174\pi\)
\(938\) 8782.06 0.305698
\(939\) 1616.26 0.0561710
\(940\) −23055.8 −0.799998
\(941\) 20402.1 0.706790 0.353395 0.935474i \(-0.385027\pi\)
0.353395 + 0.935474i \(0.385027\pi\)
\(942\) −7489.65 −0.259051
\(943\) 2868.45 0.0990559
\(944\) −37260.9 −1.28468
\(945\) 32297.0 1.11177
\(946\) 0 0
\(947\) 31210.9 1.07098 0.535491 0.844541i \(-0.320127\pi\)
0.535491 + 0.844541i \(0.320127\pi\)
\(948\) 6952.31 0.238186
\(949\) −55145.4 −1.88630
\(950\) 574.786 0.0196300
\(951\) −17064.4 −0.581863
\(952\) 24453.5 0.832501
\(953\) 30067.7 1.02202 0.511011 0.859574i \(-0.329271\pi\)
0.511011 + 0.859574i \(0.329271\pi\)
\(954\) −920.454 −0.0312377
\(955\) −7200.46 −0.243981
\(956\) −24414.9 −0.825977
\(957\) 26420.9 0.892441
\(958\) 5959.10 0.200970
\(959\) −49765.4 −1.67571
\(960\) −13635.8 −0.458432
\(961\) 38287.9 1.28522
\(962\) 3151.98 0.105638
\(963\) −2028.80 −0.0678890
\(964\) −49469.2 −1.65280
\(965\) 34411.4 1.14792
\(966\) −840.383 −0.0279906
\(967\) 13292.5 0.442046 0.221023 0.975269i \(-0.429060\pi\)
0.221023 + 0.975269i \(0.429060\pi\)
\(968\) 5367.74 0.178229
\(969\) 6585.86 0.218337
\(970\) 7563.70 0.250367
\(971\) 8526.63 0.281805 0.140902 0.990023i \(-0.455000\pi\)
0.140902 + 0.990023i \(0.455000\pi\)
\(972\) 7770.31 0.256412
\(973\) 13596.2 0.447968
\(974\) −9147.63 −0.300933
\(975\) −19734.4 −0.648213
\(976\) −23933.8 −0.784942
\(977\) 18477.0 0.605049 0.302524 0.953142i \(-0.402171\pi\)
0.302524 + 0.953142i \(0.402171\pi\)
\(978\) 11643.3 0.380687
\(979\) 4582.86 0.149611
\(980\) 19945.8 0.650149
\(981\) −6163.60 −0.200600
\(982\) −9200.38 −0.298978
\(983\) −9172.54 −0.297618 −0.148809 0.988866i \(-0.547544\pi\)
−0.148809 + 0.988866i \(0.547544\pi\)
\(984\) −15581.1 −0.504785
\(985\) 8827.86 0.285562
\(986\) 11650.9 0.376307
\(987\) −44561.6 −1.43709
\(988\) −9099.92 −0.293023
\(989\) 0 0
\(990\) −644.036 −0.0206756
\(991\) −48061.3 −1.54058 −0.770292 0.637691i \(-0.779890\pi\)
−0.770292 + 0.637691i \(0.779890\pi\)
\(992\) 32356.1 1.03559
\(993\) 9290.08 0.296890
\(994\) −16636.7 −0.530870
\(995\) 20600.8 0.656371
\(996\) 34863.4 1.10912
\(997\) −49132.9 −1.56074 −0.780369 0.625320i \(-0.784969\pi\)
−0.780369 + 0.625320i \(0.784969\pi\)
\(998\) −10831.9 −0.343564
\(999\) −8536.38 −0.270350
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.1.26 yes 50
43.42 odd 2 1849.4.a.i.1.25 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.25 50 43.42 odd 2
1849.4.a.j.1.26 yes 50 1.1 even 1 trivial