Properties

Label 1849.4.a.i.1.33
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 1.33
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.84969 q^{2} -3.08645 q^{3} -4.57866 q^{4} -18.1899 q^{5} -5.70896 q^{6} +24.2083 q^{7} -23.2666 q^{8} -17.4738 q^{9} +O(q^{10})\) \(q+1.84969 q^{2} -3.08645 q^{3} -4.57866 q^{4} -18.1899 q^{5} -5.70896 q^{6} +24.2083 q^{7} -23.2666 q^{8} -17.4738 q^{9} -33.6456 q^{10} +49.5002 q^{11} +14.1318 q^{12} -23.1645 q^{13} +44.7778 q^{14} +56.1421 q^{15} -6.40651 q^{16} -2.27673 q^{17} -32.3211 q^{18} -103.752 q^{19} +83.2854 q^{20} -74.7178 q^{21} +91.5597 q^{22} -159.479 q^{23} +71.8111 q^{24} +205.872 q^{25} -42.8469 q^{26} +137.266 q^{27} -110.842 q^{28} +309.695 q^{29} +103.845 q^{30} +93.3796 q^{31} +174.283 q^{32} -152.780 q^{33} -4.21124 q^{34} -440.347 q^{35} +80.0068 q^{36} +1.12136 q^{37} -191.909 q^{38} +71.4959 q^{39} +423.216 q^{40} +386.766 q^{41} -138.204 q^{42} -226.645 q^{44} +317.847 q^{45} -294.985 q^{46} +214.825 q^{47} +19.7734 q^{48} +243.043 q^{49} +380.798 q^{50} +7.02702 q^{51} +106.062 q^{52} -96.4065 q^{53} +253.899 q^{54} -900.402 q^{55} -563.245 q^{56} +320.226 q^{57} +572.838 q^{58} -135.840 q^{59} -257.056 q^{60} +374.631 q^{61} +172.723 q^{62} -423.012 q^{63} +373.620 q^{64} +421.359 q^{65} -282.594 q^{66} +266.093 q^{67} +10.4244 q^{68} +492.223 q^{69} -814.503 q^{70} -438.610 q^{71} +406.556 q^{72} +809.464 q^{73} +2.07417 q^{74} -635.413 q^{75} +475.047 q^{76} +1198.32 q^{77} +132.245 q^{78} -1055.64 q^{79} +116.534 q^{80} +48.1284 q^{81} +715.396 q^{82} -429.900 q^{83} +342.108 q^{84} +41.4135 q^{85} -955.857 q^{87} -1151.70 q^{88} +136.454 q^{89} +587.917 q^{90} -560.773 q^{91} +730.200 q^{92} -288.211 q^{93} +397.358 q^{94} +1887.24 q^{95} -537.914 q^{96} +25.6218 q^{97} +449.553 q^{98} -864.958 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84969 0.653962 0.326981 0.945031i \(-0.393969\pi\)
0.326981 + 0.945031i \(0.393969\pi\)
\(3\) −3.08645 −0.593987 −0.296994 0.954879i \(-0.595984\pi\)
−0.296994 + 0.954879i \(0.595984\pi\)
\(4\) −4.57866 −0.572333
\(5\) −18.1899 −1.62695 −0.813476 0.581598i \(-0.802428\pi\)
−0.813476 + 0.581598i \(0.802428\pi\)
\(6\) −5.70896 −0.388445
\(7\) 24.2083 1.30713 0.653563 0.756872i \(-0.273273\pi\)
0.653563 + 0.756872i \(0.273273\pi\)
\(8\) −23.2666 −1.02825
\(9\) −17.4738 −0.647179
\(10\) −33.6456 −1.06397
\(11\) 49.5002 1.35681 0.678403 0.734690i \(-0.262673\pi\)
0.678403 + 0.734690i \(0.262673\pi\)
\(12\) 14.1318 0.339959
\(13\) −23.1645 −0.494205 −0.247102 0.968989i \(-0.579478\pi\)
−0.247102 + 0.968989i \(0.579478\pi\)
\(14\) 44.7778 0.854812
\(15\) 56.1421 0.966389
\(16\) −6.40651 −0.100102
\(17\) −2.27673 −0.0324817 −0.0162409 0.999868i \(-0.505170\pi\)
−0.0162409 + 0.999868i \(0.505170\pi\)
\(18\) −32.3211 −0.423231
\(19\) −103.752 −1.25276 −0.626379 0.779519i \(-0.715464\pi\)
−0.626379 + 0.779519i \(0.715464\pi\)
\(20\) 83.2854 0.931159
\(21\) −74.7178 −0.776417
\(22\) 91.5597 0.887300
\(23\) −159.479 −1.44581 −0.722905 0.690948i \(-0.757193\pi\)
−0.722905 + 0.690948i \(0.757193\pi\)
\(24\) 71.8111 0.610766
\(25\) 205.872 1.64697
\(26\) −42.8469 −0.323191
\(27\) 137.266 0.978404
\(28\) −110.842 −0.748112
\(29\) 309.695 1.98306 0.991532 0.129863i \(-0.0414536\pi\)
0.991532 + 0.129863i \(0.0414536\pi\)
\(30\) 103.845 0.631982
\(31\) 93.3796 0.541015 0.270508 0.962718i \(-0.412809\pi\)
0.270508 + 0.962718i \(0.412809\pi\)
\(32\) 174.283 0.962784
\(33\) −152.780 −0.805925
\(34\) −4.21124 −0.0212418
\(35\) −440.347 −2.12663
\(36\) 80.0068 0.370402
\(37\) 1.12136 0.00498247 0.00249123 0.999997i \(-0.499207\pi\)
0.00249123 + 0.999997i \(0.499207\pi\)
\(38\) −191.909 −0.819257
\(39\) 71.4959 0.293551
\(40\) 423.216 1.67291
\(41\) 386.766 1.47324 0.736619 0.676308i \(-0.236421\pi\)
0.736619 + 0.676308i \(0.236421\pi\)
\(42\) −138.204 −0.507747
\(43\) 0 0
\(44\) −226.645 −0.776545
\(45\) 317.847 1.05293
\(46\) −294.985 −0.945505
\(47\) 214.825 0.666710 0.333355 0.942801i \(-0.391819\pi\)
0.333355 + 0.942801i \(0.391819\pi\)
\(48\) 19.7734 0.0594592
\(49\) 243.043 0.708581
\(50\) 380.798 1.07706
\(51\) 7.02702 0.0192937
\(52\) 106.062 0.282850
\(53\) −96.4065 −0.249858 −0.124929 0.992166i \(-0.539870\pi\)
−0.124929 + 0.992166i \(0.539870\pi\)
\(54\) 253.899 0.639839
\(55\) −900.402 −2.20746
\(56\) −563.245 −1.34405
\(57\) 320.226 0.744122
\(58\) 572.838 1.29685
\(59\) −135.840 −0.299744 −0.149872 0.988705i \(-0.547886\pi\)
−0.149872 + 0.988705i \(0.547886\pi\)
\(60\) −257.056 −0.553097
\(61\) 374.631 0.786337 0.393169 0.919466i \(-0.371379\pi\)
0.393169 + 0.919466i \(0.371379\pi\)
\(62\) 172.723 0.353804
\(63\) −423.012 −0.845945
\(64\) 373.620 0.729726
\(65\) 421.359 0.804048
\(66\) −282.594 −0.527045
\(67\) 266.093 0.485200 0.242600 0.970126i \(-0.422000\pi\)
0.242600 + 0.970126i \(0.422000\pi\)
\(68\) 10.4244 0.0185904
\(69\) 492.223 0.858792
\(70\) −814.503 −1.39074
\(71\) −438.610 −0.733147 −0.366574 0.930389i \(-0.619469\pi\)
−0.366574 + 0.930389i \(0.619469\pi\)
\(72\) 406.556 0.665460
\(73\) 809.464 1.29782 0.648908 0.760867i \(-0.275226\pi\)
0.648908 + 0.760867i \(0.275226\pi\)
\(74\) 2.07417 0.00325835
\(75\) −635.413 −0.978282
\(76\) 475.047 0.716995
\(77\) 1198.32 1.77352
\(78\) 132.245 0.191972
\(79\) −1055.64 −1.50341 −0.751704 0.659501i \(-0.770768\pi\)
−0.751704 + 0.659501i \(0.770768\pi\)
\(80\) 116.534 0.162861
\(81\) 48.1284 0.0660197
\(82\) 715.396 0.963443
\(83\) −429.900 −0.568526 −0.284263 0.958746i \(-0.591749\pi\)
−0.284263 + 0.958746i \(0.591749\pi\)
\(84\) 342.108 0.444369
\(85\) 41.4135 0.0528462
\(86\) 0 0
\(87\) −955.857 −1.17791
\(88\) −1151.70 −1.39513
\(89\) 136.454 0.162517 0.0812587 0.996693i \(-0.474106\pi\)
0.0812587 + 0.996693i \(0.474106\pi\)
\(90\) 587.917 0.688576
\(91\) −560.773 −0.645988
\(92\) 730.200 0.827485
\(93\) −288.211 −0.321356
\(94\) 397.358 0.436003
\(95\) 1887.24 2.03818
\(96\) −537.914 −0.571882
\(97\) 25.6218 0.0268196 0.0134098 0.999910i \(-0.495731\pi\)
0.0134098 + 0.999910i \(0.495731\pi\)
\(98\) 449.553 0.463385
\(99\) −864.958 −0.878096
\(100\) −942.618 −0.942618
\(101\) −1661.81 −1.63719 −0.818593 0.574373i \(-0.805246\pi\)
−0.818593 + 0.574373i \(0.805246\pi\)
\(102\) 12.9978 0.0126174
\(103\) 22.0462 0.0210901 0.0105450 0.999944i \(-0.496643\pi\)
0.0105450 + 0.999944i \(0.496643\pi\)
\(104\) 538.957 0.508165
\(105\) 1359.11 1.26319
\(106\) −178.322 −0.163397
\(107\) −891.422 −0.805392 −0.402696 0.915334i \(-0.631927\pi\)
−0.402696 + 0.915334i \(0.631927\pi\)
\(108\) −628.496 −0.559973
\(109\) 1372.93 1.20644 0.603222 0.797573i \(-0.293883\pi\)
0.603222 + 0.797573i \(0.293883\pi\)
\(110\) −1665.46 −1.44359
\(111\) −3.46104 −0.00295952
\(112\) −155.091 −0.130846
\(113\) −938.442 −0.781249 −0.390625 0.920550i \(-0.627741\pi\)
−0.390625 + 0.920550i \(0.627741\pi\)
\(114\) 592.317 0.486628
\(115\) 2900.90 2.35226
\(116\) −1417.99 −1.13497
\(117\) 404.772 0.319839
\(118\) −251.262 −0.196021
\(119\) −55.1159 −0.0424577
\(120\) −1306.24 −0.993687
\(121\) 1119.27 0.840921
\(122\) 692.949 0.514235
\(123\) −1193.73 −0.875085
\(124\) −427.554 −0.309641
\(125\) −1471.05 −1.05260
\(126\) −782.440 −0.553216
\(127\) −2503.68 −1.74934 −0.874669 0.484721i \(-0.838921\pi\)
−0.874669 + 0.484721i \(0.838921\pi\)
\(128\) −703.181 −0.485570
\(129\) 0 0
\(130\) 779.381 0.525817
\(131\) −168.167 −0.112159 −0.0560794 0.998426i \(-0.517860\pi\)
−0.0560794 + 0.998426i \(0.517860\pi\)
\(132\) 699.527 0.461258
\(133\) −2511.67 −1.63751
\(134\) 492.188 0.317303
\(135\) −2496.86 −1.59182
\(136\) 52.9718 0.0333992
\(137\) 357.390 0.222875 0.111438 0.993771i \(-0.464454\pi\)
0.111438 + 0.993771i \(0.464454\pi\)
\(138\) 910.457 0.561618
\(139\) 493.366 0.301056 0.150528 0.988606i \(-0.451903\pi\)
0.150528 + 0.988606i \(0.451903\pi\)
\(140\) 2016.20 1.21714
\(141\) −663.045 −0.396017
\(142\) −811.291 −0.479451
\(143\) −1146.64 −0.670540
\(144\) 111.946 0.0647837
\(145\) −5633.31 −3.22635
\(146\) 1497.25 0.848723
\(147\) −750.140 −0.420888
\(148\) −5.13435 −0.00285163
\(149\) 187.920 0.103322 0.0516610 0.998665i \(-0.483548\pi\)
0.0516610 + 0.998665i \(0.483548\pi\)
\(150\) −1175.31 −0.639760
\(151\) −1664.02 −0.896794 −0.448397 0.893834i \(-0.648005\pi\)
−0.448397 + 0.893834i \(0.648005\pi\)
\(152\) 2413.96 1.28814
\(153\) 39.7833 0.0210215
\(154\) 2216.51 1.15981
\(155\) −1698.56 −0.880206
\(156\) −327.356 −0.168009
\(157\) −3303.37 −1.67922 −0.839611 0.543188i \(-0.817217\pi\)
−0.839611 + 0.543188i \(0.817217\pi\)
\(158\) −1952.61 −0.983172
\(159\) 297.554 0.148412
\(160\) −3170.18 −1.56640
\(161\) −3860.71 −1.88986
\(162\) 89.0223 0.0431744
\(163\) −1552.90 −0.746212 −0.373106 0.927789i \(-0.621707\pi\)
−0.373106 + 0.927789i \(0.621707\pi\)
\(164\) −1770.87 −0.843183
\(165\) 2779.04 1.31120
\(166\) −795.180 −0.371795
\(167\) 2180.15 1.01021 0.505105 0.863058i \(-0.331454\pi\)
0.505105 + 0.863058i \(0.331454\pi\)
\(168\) 1738.43 0.798348
\(169\) −1660.41 −0.755762
\(170\) 76.6020 0.0345594
\(171\) 1812.95 0.810759
\(172\) 0 0
\(173\) −1547.13 −0.679918 −0.339959 0.940440i \(-0.610413\pi\)
−0.339959 + 0.940440i \(0.610413\pi\)
\(174\) −1768.03 −0.770312
\(175\) 4983.81 2.15280
\(176\) −317.123 −0.135819
\(177\) 419.264 0.178044
\(178\) 252.396 0.106280
\(179\) 2721.23 1.13628 0.568140 0.822932i \(-0.307663\pi\)
0.568140 + 0.822932i \(0.307663\pi\)
\(180\) −1455.31 −0.602626
\(181\) −973.771 −0.399889 −0.199944 0.979807i \(-0.564076\pi\)
−0.199944 + 0.979807i \(0.564076\pi\)
\(182\) −1037.25 −0.422452
\(183\) −1156.28 −0.467074
\(184\) 3710.52 1.48665
\(185\) −20.3975 −0.00810624
\(186\) −533.100 −0.210155
\(187\) −112.699 −0.0440713
\(188\) −983.610 −0.381580
\(189\) 3322.99 1.27890
\(190\) 3490.80 1.33289
\(191\) 741.917 0.281064 0.140532 0.990076i \(-0.455119\pi\)
0.140532 + 0.990076i \(0.455119\pi\)
\(192\) −1153.16 −0.433448
\(193\) 437.336 0.163109 0.0815547 0.996669i \(-0.474011\pi\)
0.0815547 + 0.996669i \(0.474011\pi\)
\(194\) 47.3923 0.0175390
\(195\) −1300.50 −0.477594
\(196\) −1112.81 −0.405544
\(197\) 1769.20 0.639848 0.319924 0.947443i \(-0.396343\pi\)
0.319924 + 0.947443i \(0.396343\pi\)
\(198\) −1599.90 −0.574242
\(199\) 2442.81 0.870181 0.435091 0.900387i \(-0.356716\pi\)
0.435091 + 0.900387i \(0.356716\pi\)
\(200\) −4789.93 −1.69350
\(201\) −821.282 −0.288203
\(202\) −3073.82 −1.07066
\(203\) 7497.19 2.59212
\(204\) −32.1744 −0.0110424
\(205\) −7035.24 −2.39689
\(206\) 40.7785 0.0137921
\(207\) 2786.70 0.935697
\(208\) 148.403 0.0494708
\(209\) −5135.75 −1.69975
\(210\) 2513.92 0.826081
\(211\) 2447.16 0.798433 0.399217 0.916857i \(-0.369282\pi\)
0.399217 + 0.916857i \(0.369282\pi\)
\(212\) 441.413 0.143002
\(213\) 1353.75 0.435480
\(214\) −1648.85 −0.526696
\(215\) 0 0
\(216\) −3193.71 −1.00604
\(217\) 2260.56 0.707175
\(218\) 2539.48 0.788970
\(219\) −2498.37 −0.770886
\(220\) 4122.64 1.26340
\(221\) 52.7393 0.0160526
\(222\) −6.40183 −0.00193542
\(223\) −1162.40 −0.349059 −0.174529 0.984652i \(-0.555840\pi\)
−0.174529 + 0.984652i \(0.555840\pi\)
\(224\) 4219.09 1.25848
\(225\) −3597.37 −1.06589
\(226\) −1735.82 −0.510908
\(227\) −3586.53 −1.04866 −0.524332 0.851514i \(-0.675685\pi\)
−0.524332 + 0.851514i \(0.675685\pi\)
\(228\) −1466.21 −0.425886
\(229\) −3162.75 −0.912666 −0.456333 0.889809i \(-0.650837\pi\)
−0.456333 + 0.889809i \(0.650837\pi\)
\(230\) 5365.75 1.53829
\(231\) −3698.54 −1.05345
\(232\) −7205.53 −2.03908
\(233\) 3331.29 0.936652 0.468326 0.883556i \(-0.344857\pi\)
0.468326 + 0.883556i \(0.344857\pi\)
\(234\) 748.700 0.209163
\(235\) −3907.63 −1.08471
\(236\) 621.967 0.171553
\(237\) 3258.19 0.893005
\(238\) −101.947 −0.0277657
\(239\) −3470.98 −0.939410 −0.469705 0.882823i \(-0.655640\pi\)
−0.469705 + 0.882823i \(0.655640\pi\)
\(240\) −359.675 −0.0967372
\(241\) 3904.03 1.04349 0.521744 0.853102i \(-0.325282\pi\)
0.521744 + 0.853102i \(0.325282\pi\)
\(242\) 2070.29 0.549931
\(243\) −3854.73 −1.01762
\(244\) −1715.31 −0.450047
\(245\) −4420.93 −1.15283
\(246\) −2208.03 −0.572273
\(247\) 2403.36 0.619119
\(248\) −2172.62 −0.556297
\(249\) 1326.86 0.337697
\(250\) −2720.98 −0.688359
\(251\) −5320.94 −1.33807 −0.669034 0.743232i \(-0.733292\pi\)
−0.669034 + 0.743232i \(0.733292\pi\)
\(252\) 1936.83 0.484162
\(253\) −7894.22 −1.96168
\(254\) −4631.03 −1.14400
\(255\) −127.821 −0.0313900
\(256\) −4289.62 −1.04727
\(257\) −21.4980 −0.00521793 −0.00260896 0.999997i \(-0.500830\pi\)
−0.00260896 + 0.999997i \(0.500830\pi\)
\(258\) 0 0
\(259\) 27.1464 0.00651272
\(260\) −1929.26 −0.460183
\(261\) −5411.55 −1.28340
\(262\) −311.056 −0.0733477
\(263\) 2887.95 0.677105 0.338553 0.940947i \(-0.390063\pi\)
0.338553 + 0.940947i \(0.390063\pi\)
\(264\) 3554.66 0.828690
\(265\) 1753.62 0.406506
\(266\) −4645.80 −1.07087
\(267\) −421.157 −0.0965333
\(268\) −1218.35 −0.277696
\(269\) −6873.83 −1.55801 −0.779005 0.627018i \(-0.784275\pi\)
−0.779005 + 0.627018i \(0.784275\pi\)
\(270\) −4618.40 −1.04099
\(271\) −6722.51 −1.50688 −0.753438 0.657518i \(-0.771606\pi\)
−0.753438 + 0.657518i \(0.771606\pi\)
\(272\) 14.5859 0.00325147
\(273\) 1730.80 0.383709
\(274\) 661.060 0.145752
\(275\) 10190.7 2.23462
\(276\) −2253.72 −0.491515
\(277\) 7511.83 1.62939 0.814697 0.579887i \(-0.196903\pi\)
0.814697 + 0.579887i \(0.196903\pi\)
\(278\) 912.571 0.196879
\(279\) −1631.70 −0.350134
\(280\) 10245.4 2.18670
\(281\) −6564.63 −1.39364 −0.696820 0.717246i \(-0.745403\pi\)
−0.696820 + 0.717246i \(0.745403\pi\)
\(282\) −1226.42 −0.258981
\(283\) 982.494 0.206372 0.103186 0.994662i \(-0.467096\pi\)
0.103186 + 0.994662i \(0.467096\pi\)
\(284\) 2008.25 0.419605
\(285\) −5824.87 −1.21065
\(286\) −2120.93 −0.438508
\(287\) 9362.97 1.92571
\(288\) −3045.38 −0.623094
\(289\) −4907.82 −0.998945
\(290\) −10419.8 −2.10991
\(291\) −79.0805 −0.0159305
\(292\) −3706.26 −0.742783
\(293\) 4099.32 0.817354 0.408677 0.912679i \(-0.365990\pi\)
0.408677 + 0.912679i \(0.365990\pi\)
\(294\) −1387.52 −0.275245
\(295\) 2470.92 0.487669
\(296\) −26.0903 −0.00512321
\(297\) 6794.70 1.32750
\(298\) 347.592 0.0675687
\(299\) 3694.24 0.714526
\(300\) 2909.34 0.559903
\(301\) 0 0
\(302\) −3077.91 −0.586470
\(303\) 5129.08 0.972468
\(304\) 664.690 0.125403
\(305\) −6814.49 −1.27933
\(306\) 73.5865 0.0137473
\(307\) 6286.95 1.16878 0.584390 0.811473i \(-0.301334\pi\)
0.584390 + 0.811473i \(0.301334\pi\)
\(308\) −5486.69 −1.01504
\(309\) −68.0445 −0.0125272
\(310\) −3141.81 −0.575622
\(311\) −9190.56 −1.67572 −0.837860 0.545885i \(-0.816193\pi\)
−0.837860 + 0.545885i \(0.816193\pi\)
\(312\) −1663.46 −0.301843
\(313\) 2173.57 0.392516 0.196258 0.980552i \(-0.437121\pi\)
0.196258 + 0.980552i \(0.437121\pi\)
\(314\) −6110.20 −1.09815
\(315\) 7694.54 1.37631
\(316\) 4833.44 0.860450
\(317\) 8485.50 1.50345 0.751724 0.659478i \(-0.229223\pi\)
0.751724 + 0.659478i \(0.229223\pi\)
\(318\) 550.381 0.0970560
\(319\) 15329.9 2.69063
\(320\) −6796.10 −1.18723
\(321\) 2751.33 0.478393
\(322\) −7141.10 −1.23589
\(323\) 236.216 0.0406917
\(324\) −220.364 −0.0377853
\(325\) −4768.91 −0.813943
\(326\) −2872.38 −0.487995
\(327\) −4237.47 −0.716613
\(328\) −8998.73 −1.51485
\(329\) 5200.54 0.871475
\(330\) 5140.36 0.857477
\(331\) 3108.26 0.516149 0.258075 0.966125i \(-0.416912\pi\)
0.258075 + 0.966125i \(0.416912\pi\)
\(332\) 1968.37 0.325386
\(333\) −19.5945 −0.00322455
\(334\) 4032.59 0.660640
\(335\) −4840.20 −0.789398
\(336\) 478.680 0.0777207
\(337\) 6066.72 0.980639 0.490319 0.871543i \(-0.336880\pi\)
0.490319 + 0.871543i \(0.336880\pi\)
\(338\) −3071.23 −0.494240
\(339\) 2896.45 0.464052
\(340\) −189.619 −0.0302456
\(341\) 4622.30 0.734052
\(342\) 3353.39 0.530206
\(343\) −2419.79 −0.380922
\(344\) 0 0
\(345\) −8953.48 −1.39721
\(346\) −2861.70 −0.444641
\(347\) 1685.20 0.260710 0.130355 0.991467i \(-0.458388\pi\)
0.130355 + 0.991467i \(0.458388\pi\)
\(348\) 4376.55 0.674160
\(349\) 6257.79 0.959805 0.479902 0.877322i \(-0.340672\pi\)
0.479902 + 0.877322i \(0.340672\pi\)
\(350\) 9218.49 1.40785
\(351\) −3179.70 −0.483532
\(352\) 8627.01 1.30631
\(353\) 5204.31 0.784695 0.392347 0.919817i \(-0.371663\pi\)
0.392347 + 0.919817i \(0.371663\pi\)
\(354\) 775.506 0.116434
\(355\) 7978.27 1.19280
\(356\) −624.775 −0.0930141
\(357\) 170.112 0.0252193
\(358\) 5033.41 0.743084
\(359\) 6365.10 0.935758 0.467879 0.883793i \(-0.345018\pi\)
0.467879 + 0.883793i \(0.345018\pi\)
\(360\) −7395.21 −1.08267
\(361\) 3905.53 0.569403
\(362\) −1801.17 −0.261512
\(363\) −3454.56 −0.499496
\(364\) 2567.59 0.369721
\(365\) −14724.0 −2.11148
\(366\) −2138.75 −0.305449
\(367\) 6551.85 0.931891 0.465945 0.884813i \(-0.345714\pi\)
0.465945 + 0.884813i \(0.345714\pi\)
\(368\) 1021.70 0.144728
\(369\) −6758.29 −0.953449
\(370\) −37.7289 −0.00530117
\(371\) −2333.84 −0.326595
\(372\) 1319.62 0.183923
\(373\) 5826.94 0.808868 0.404434 0.914567i \(-0.367469\pi\)
0.404434 + 0.914567i \(0.367469\pi\)
\(374\) −208.457 −0.0288210
\(375\) 4540.32 0.625230
\(376\) −4998.23 −0.685543
\(377\) −7173.91 −0.980040
\(378\) 6146.48 0.836351
\(379\) −1125.98 −0.152607 −0.0763033 0.997085i \(-0.524312\pi\)
−0.0763033 + 0.997085i \(0.524312\pi\)
\(380\) −8641.05 −1.16652
\(381\) 7727.49 1.03908
\(382\) 1372.31 0.183805
\(383\) −8568.62 −1.14318 −0.571588 0.820541i \(-0.693672\pi\)
−0.571588 + 0.820541i \(0.693672\pi\)
\(384\) 2170.33 0.288423
\(385\) −21797.2 −2.88543
\(386\) 808.933 0.106667
\(387\) 0 0
\(388\) −117.314 −0.0153498
\(389\) 14675.3 1.91277 0.956383 0.292117i \(-0.0943596\pi\)
0.956383 + 0.292117i \(0.0943596\pi\)
\(390\) −2405.52 −0.312329
\(391\) 363.091 0.0469623
\(392\) −5654.78 −0.728596
\(393\) 519.039 0.0666210
\(394\) 3272.46 0.418437
\(395\) 19202.0 2.44597
\(396\) 3960.35 0.502563
\(397\) −10358.3 −1.30950 −0.654748 0.755848i \(-0.727225\pi\)
−0.654748 + 0.755848i \(0.727225\pi\)
\(398\) 4518.43 0.569066
\(399\) 7752.14 0.972662
\(400\) −1318.92 −0.164865
\(401\) 2134.79 0.265851 0.132926 0.991126i \(-0.457563\pi\)
0.132926 + 0.991126i \(0.457563\pi\)
\(402\) −1519.11 −0.188474
\(403\) −2163.09 −0.267372
\(404\) 7608.85 0.937016
\(405\) −875.449 −0.107411
\(406\) 13867.4 1.69515
\(407\) 55.5077 0.00676024
\(408\) −163.495 −0.0198387
\(409\) 2284.74 0.276218 0.138109 0.990417i \(-0.455898\pi\)
0.138109 + 0.990417i \(0.455898\pi\)
\(410\) −13013.0 −1.56748
\(411\) −1103.07 −0.132385
\(412\) −100.942 −0.0120705
\(413\) −3288.46 −0.391803
\(414\) 5154.53 0.611911
\(415\) 7819.83 0.924965
\(416\) −4037.16 −0.475813
\(417\) −1522.75 −0.178823
\(418\) −9499.53 −1.11157
\(419\) 2378.66 0.277340 0.138670 0.990339i \(-0.455717\pi\)
0.138670 + 0.990339i \(0.455717\pi\)
\(420\) −6222.90 −0.722967
\(421\) −14655.8 −1.69663 −0.848313 0.529496i \(-0.822381\pi\)
−0.848313 + 0.529496i \(0.822381\pi\)
\(422\) 4526.48 0.522145
\(423\) −3753.81 −0.431481
\(424\) 2243.05 0.256915
\(425\) −468.715 −0.0534965
\(426\) 2504.01 0.284788
\(427\) 9069.19 1.02784
\(428\) 4081.52 0.460953
\(429\) 3539.06 0.398292
\(430\) 0 0
\(431\) −2467.24 −0.275738 −0.137869 0.990450i \(-0.544025\pi\)
−0.137869 + 0.990450i \(0.544025\pi\)
\(432\) −879.397 −0.0979399
\(433\) 14202.3 1.57626 0.788128 0.615512i \(-0.211051\pi\)
0.788128 + 0.615512i \(0.211051\pi\)
\(434\) 4181.33 0.462466
\(435\) 17386.9 1.91641
\(436\) −6286.17 −0.690488
\(437\) 16546.3 1.81125
\(438\) −4621.19 −0.504131
\(439\) −11109.1 −1.20776 −0.603881 0.797075i \(-0.706380\pi\)
−0.603881 + 0.797075i \(0.706380\pi\)
\(440\) 20949.3 2.26981
\(441\) −4246.90 −0.458578
\(442\) 97.5511 0.0104978
\(443\) −3377.46 −0.362230 −0.181115 0.983462i \(-0.557971\pi\)
−0.181115 + 0.983462i \(0.557971\pi\)
\(444\) 15.8469 0.00169383
\(445\) −2482.07 −0.264408
\(446\) −2150.07 −0.228271
\(447\) −580.004 −0.0613719
\(448\) 9044.71 0.953845
\(449\) −8468.28 −0.890073 −0.445036 0.895512i \(-0.646809\pi\)
−0.445036 + 0.895512i \(0.646809\pi\)
\(450\) −6654.00 −0.697050
\(451\) 19145.0 1.99890
\(452\) 4296.81 0.447135
\(453\) 5135.91 0.532684
\(454\) −6633.96 −0.685787
\(455\) 10200.4 1.05099
\(456\) −7450.56 −0.765142
\(457\) −1014.40 −0.103833 −0.0519163 0.998651i \(-0.516533\pi\)
−0.0519163 + 0.998651i \(0.516533\pi\)
\(458\) −5850.10 −0.596850
\(459\) −312.519 −0.0317802
\(460\) −13282.2 −1.34628
\(461\) −7226.46 −0.730086 −0.365043 0.930991i \(-0.618946\pi\)
−0.365043 + 0.930991i \(0.618946\pi\)
\(462\) −6841.14 −0.688914
\(463\) 15866.5 1.59261 0.796304 0.604897i \(-0.206786\pi\)
0.796304 + 0.604897i \(0.206786\pi\)
\(464\) −1984.06 −0.198508
\(465\) 5242.53 0.522831
\(466\) 6161.84 0.612535
\(467\) −15440.6 −1.52999 −0.764996 0.644035i \(-0.777259\pi\)
−0.764996 + 0.644035i \(0.777259\pi\)
\(468\) −1853.31 −0.183054
\(469\) 6441.66 0.634218
\(470\) −7227.89 −0.709357
\(471\) 10195.7 0.997437
\(472\) 3160.53 0.308211
\(473\) 0 0
\(474\) 6026.63 0.583992
\(475\) −21359.7 −2.06326
\(476\) 252.357 0.0243000
\(477\) 1684.59 0.161703
\(478\) −6420.22 −0.614339
\(479\) −15315.4 −1.46092 −0.730460 0.682956i \(-0.760694\pi\)
−0.730460 + 0.682956i \(0.760694\pi\)
\(480\) 9784.59 0.930424
\(481\) −25.9758 −0.00246236
\(482\) 7221.23 0.682402
\(483\) 11915.9 1.12255
\(484\) −5124.74 −0.481287
\(485\) −466.058 −0.0436343
\(486\) −7130.04 −0.665484
\(487\) −4260.84 −0.396462 −0.198231 0.980155i \(-0.563520\pi\)
−0.198231 + 0.980155i \(0.563520\pi\)
\(488\) −8716.38 −0.808549
\(489\) 4792.95 0.443240
\(490\) −8177.32 −0.753906
\(491\) −8952.64 −0.822865 −0.411433 0.911440i \(-0.634971\pi\)
−0.411433 + 0.911440i \(0.634971\pi\)
\(492\) 5465.71 0.500840
\(493\) −705.092 −0.0644133
\(494\) 4445.47 0.404881
\(495\) 15733.5 1.42862
\(496\) −598.237 −0.0541565
\(497\) −10618.0 −0.958317
\(498\) 2454.28 0.220841
\(499\) −736.403 −0.0660640 −0.0330320 0.999454i \(-0.510516\pi\)
−0.0330320 + 0.999454i \(0.510516\pi\)
\(500\) 6735.44 0.602436
\(501\) −6728.93 −0.600052
\(502\) −9842.07 −0.875046
\(503\) −995.504 −0.0882451 −0.0441226 0.999026i \(-0.514049\pi\)
−0.0441226 + 0.999026i \(0.514049\pi\)
\(504\) 9842.04 0.869840
\(505\) 30228.1 2.66363
\(506\) −14601.8 −1.28287
\(507\) 5124.76 0.448913
\(508\) 11463.5 1.00120
\(509\) −12419.0 −1.08146 −0.540731 0.841195i \(-0.681852\pi\)
−0.540731 + 0.841195i \(0.681852\pi\)
\(510\) −236.428 −0.0205279
\(511\) 19595.8 1.69641
\(512\) −2309.00 −0.199306
\(513\) −14241.7 −1.22570
\(514\) −39.7645 −0.00341233
\(515\) −401.018 −0.0343125
\(516\) 0 0
\(517\) 10633.8 0.904596
\(518\) 50.2122 0.00425907
\(519\) 4775.13 0.403863
\(520\) −9803.57 −0.826760
\(521\) −10956.4 −0.921325 −0.460662 0.887575i \(-0.652388\pi\)
−0.460662 + 0.887575i \(0.652388\pi\)
\(522\) −10009.7 −0.839294
\(523\) −7978.77 −0.667088 −0.333544 0.942734i \(-0.608245\pi\)
−0.333544 + 0.942734i \(0.608245\pi\)
\(524\) 769.980 0.0641922
\(525\) −15382.3 −1.27874
\(526\) 5341.80 0.442801
\(527\) −212.600 −0.0175731
\(528\) 978.785 0.0806745
\(529\) 13266.5 1.09036
\(530\) 3243.65 0.265840
\(531\) 2373.65 0.193988
\(532\) 11500.1 0.937203
\(533\) −8959.23 −0.728082
\(534\) −779.008 −0.0631291
\(535\) 16214.9 1.31034
\(536\) −6191.07 −0.498906
\(537\) −8398.93 −0.674936
\(538\) −12714.4 −1.01888
\(539\) 12030.7 0.961406
\(540\) 11432.3 0.911049
\(541\) 15193.0 1.20739 0.603697 0.797214i \(-0.293694\pi\)
0.603697 + 0.797214i \(0.293694\pi\)
\(542\) −12434.5 −0.985441
\(543\) 3005.49 0.237529
\(544\) −396.795 −0.0312729
\(545\) −24973.4 −1.96283
\(546\) 3201.43 0.250931
\(547\) −5211.42 −0.407357 −0.203678 0.979038i \(-0.565290\pi\)
−0.203678 + 0.979038i \(0.565290\pi\)
\(548\) −1636.37 −0.127559
\(549\) −6546.24 −0.508901
\(550\) 18849.6 1.46136
\(551\) −32131.5 −2.48430
\(552\) −11452.3 −0.883051
\(553\) −25555.4 −1.96515
\(554\) 13894.5 1.06556
\(555\) 62.9558 0.00481500
\(556\) −2258.96 −0.172304
\(557\) −5979.23 −0.454844 −0.227422 0.973796i \(-0.573030\pi\)
−0.227422 + 0.973796i \(0.573030\pi\)
\(558\) −3018.13 −0.228974
\(559\) 0 0
\(560\) 2821.09 0.212880
\(561\) 347.839 0.0261778
\(562\) −12142.5 −0.911389
\(563\) −12821.9 −0.959819 −0.479910 0.877318i \(-0.659331\pi\)
−0.479910 + 0.877318i \(0.659331\pi\)
\(564\) 3035.86 0.226654
\(565\) 17070.1 1.27106
\(566\) 1817.30 0.134959
\(567\) 1165.11 0.0862961
\(568\) 10205.0 0.753857
\(569\) −17386.3 −1.28097 −0.640486 0.767970i \(-0.721267\pi\)
−0.640486 + 0.767970i \(0.721267\pi\)
\(570\) −10774.2 −0.791721
\(571\) 17303.9 1.26821 0.634105 0.773247i \(-0.281369\pi\)
0.634105 + 0.773247i \(0.281369\pi\)
\(572\) 5250.10 0.383772
\(573\) −2289.89 −0.166949
\(574\) 17318.5 1.25934
\(575\) −32832.2 −2.38121
\(576\) −6528.57 −0.472264
\(577\) −26932.4 −1.94317 −0.971587 0.236683i \(-0.923940\pi\)
−0.971587 + 0.236683i \(0.923940\pi\)
\(578\) −9077.92 −0.653272
\(579\) −1349.81 −0.0968849
\(580\) 25793.0 1.84655
\(581\) −10407.2 −0.743135
\(582\) −146.274 −0.0104180
\(583\) −4772.14 −0.339008
\(584\) −18833.4 −1.33447
\(585\) −7362.75 −0.520363
\(586\) 7582.45 0.534519
\(587\) 11169.9 0.785406 0.392703 0.919665i \(-0.371540\pi\)
0.392703 + 0.919665i \(0.371540\pi\)
\(588\) 3434.64 0.240888
\(589\) −9688.34 −0.677761
\(590\) 4570.42 0.318917
\(591\) −5460.54 −0.380062
\(592\) −7.18404 −0.000498753 0
\(593\) −1545.81 −0.107047 −0.0535234 0.998567i \(-0.517045\pi\)
−0.0535234 + 0.998567i \(0.517045\pi\)
\(594\) 12568.1 0.868137
\(595\) 1002.55 0.0690767
\(596\) −860.421 −0.0591346
\(597\) −7539.60 −0.516877
\(598\) 6833.18 0.467273
\(599\) 7624.14 0.520057 0.260028 0.965601i \(-0.416268\pi\)
0.260028 + 0.965601i \(0.416268\pi\)
\(600\) 14783.9 1.00592
\(601\) −13723.7 −0.931448 −0.465724 0.884930i \(-0.654206\pi\)
−0.465724 + 0.884930i \(0.654206\pi\)
\(602\) 0 0
\(603\) −4649.66 −0.314011
\(604\) 7618.98 0.513265
\(605\) −20359.3 −1.36814
\(606\) 9487.18 0.635958
\(607\) 15914.5 1.06417 0.532083 0.846692i \(-0.321409\pi\)
0.532083 + 0.846692i \(0.321409\pi\)
\(608\) −18082.2 −1.20614
\(609\) −23139.7 −1.53968
\(610\) −12604.7 −0.836636
\(611\) −4976.29 −0.329491
\(612\) −182.154 −0.0120313
\(613\) 19139.8 1.26109 0.630546 0.776152i \(-0.282831\pi\)
0.630546 + 0.776152i \(0.282831\pi\)
\(614\) 11628.9 0.764338
\(615\) 21713.9 1.42372
\(616\) −27880.7 −1.82361
\(617\) −20419.1 −1.33232 −0.666160 0.745809i \(-0.732063\pi\)
−0.666160 + 0.745809i \(0.732063\pi\)
\(618\) −125.861 −0.00819234
\(619\) −741.929 −0.0481755 −0.0240878 0.999710i \(-0.507668\pi\)
−0.0240878 + 0.999710i \(0.507668\pi\)
\(620\) 7777.15 0.503771
\(621\) −21891.0 −1.41458
\(622\) −16999.6 −1.09586
\(623\) 3303.31 0.212431
\(624\) −458.039 −0.0293850
\(625\) 1024.24 0.0655512
\(626\) 4020.42 0.256691
\(627\) 15851.2 1.00963
\(628\) 15125.0 0.961074
\(629\) −2.55305 −0.000161839 0
\(630\) 14232.5 0.900057
\(631\) 14781.2 0.932533 0.466266 0.884644i \(-0.345599\pi\)
0.466266 + 0.884644i \(0.345599\pi\)
\(632\) 24561.2 1.54587
\(633\) −7553.03 −0.474259
\(634\) 15695.5 0.983199
\(635\) 45541.7 2.84609
\(636\) −1362.40 −0.0849412
\(637\) −5629.96 −0.350184
\(638\) 28355.6 1.75957
\(639\) 7664.20 0.474478
\(640\) 12790.8 0.790000
\(641\) 3976.97 0.245056 0.122528 0.992465i \(-0.460900\pi\)
0.122528 + 0.992465i \(0.460900\pi\)
\(642\) 5089.09 0.312851
\(643\) −2640.34 −0.161936 −0.0809679 0.996717i \(-0.525801\pi\)
−0.0809679 + 0.996717i \(0.525801\pi\)
\(644\) 17676.9 1.08163
\(645\) 0 0
\(646\) 436.926 0.0266109
\(647\) 11975.9 0.727697 0.363848 0.931458i \(-0.381463\pi\)
0.363848 + 0.931458i \(0.381463\pi\)
\(648\) −1119.78 −0.0678845
\(649\) −6724.11 −0.406694
\(650\) −8820.98 −0.532288
\(651\) −6977.11 −0.420053
\(652\) 7110.21 0.427082
\(653\) −27053.1 −1.62124 −0.810619 0.585574i \(-0.800869\pi\)
−0.810619 + 0.585574i \(0.800869\pi\)
\(654\) −7837.98 −0.468638
\(655\) 3058.94 0.182477
\(656\) −2477.82 −0.147474
\(657\) −14144.4 −0.839919
\(658\) 9619.37 0.569912
\(659\) 27557.4 1.62896 0.814478 0.580194i \(-0.197023\pi\)
0.814478 + 0.580194i \(0.197023\pi\)
\(660\) −12724.3 −0.750444
\(661\) 17087.7 1.00550 0.502751 0.864432i \(-0.332321\pi\)
0.502751 + 0.864432i \(0.332321\pi\)
\(662\) 5749.30 0.337542
\(663\) −162.777 −0.00953505
\(664\) 10002.3 0.584585
\(665\) 45687.0 2.66416
\(666\) −36.2437 −0.00210873
\(667\) −49389.7 −2.86713
\(668\) −9982.18 −0.578177
\(669\) 3587.69 0.207336
\(670\) −8952.84 −0.516237
\(671\) 18544.3 1.06691
\(672\) −13022.0 −0.747522
\(673\) −7916.77 −0.453446 −0.226723 0.973959i \(-0.572801\pi\)
−0.226723 + 0.973959i \(0.572801\pi\)
\(674\) 11221.5 0.641301
\(675\) 28259.2 1.61141
\(676\) 7602.45 0.432547
\(677\) −19951.0 −1.13262 −0.566308 0.824194i \(-0.691629\pi\)
−0.566308 + 0.824194i \(0.691629\pi\)
\(678\) 5357.53 0.303473
\(679\) 620.262 0.0350566
\(680\) −963.550 −0.0543389
\(681\) 11069.7 0.622893
\(682\) 8549.81 0.480043
\(683\) −28013.0 −1.56938 −0.784692 0.619886i \(-0.787179\pi\)
−0.784692 + 0.619886i \(0.787179\pi\)
\(684\) −8300.89 −0.464024
\(685\) −6500.89 −0.362608
\(686\) −4475.85 −0.249109
\(687\) 9761.68 0.542112
\(688\) 0 0
\(689\) 2233.20 0.123481
\(690\) −16561.1 −0.913726
\(691\) −21559.9 −1.18694 −0.593471 0.804855i \(-0.702243\pi\)
−0.593471 + 0.804855i \(0.702243\pi\)
\(692\) 7083.77 0.389140
\(693\) −20939.2 −1.14778
\(694\) 3117.10 0.170495
\(695\) −8974.26 −0.489803
\(696\) 22239.5 1.21119
\(697\) −880.564 −0.0478533
\(698\) 11574.9 0.627676
\(699\) −10281.9 −0.556360
\(700\) −22819.2 −1.23212
\(701\) 4705.35 0.253522 0.126761 0.991933i \(-0.459542\pi\)
0.126761 + 0.991933i \(0.459542\pi\)
\(702\) −5881.44 −0.316212
\(703\) −116.344 −0.00624183
\(704\) 18494.2 0.990097
\(705\) 12060.7 0.644302
\(706\) 9626.33 0.513161
\(707\) −40229.5 −2.14001
\(708\) −1919.67 −0.101900
\(709\) −25069.4 −1.32793 −0.663963 0.747765i \(-0.731127\pi\)
−0.663963 + 0.747765i \(0.731127\pi\)
\(710\) 14757.3 0.780044
\(711\) 18446.1 0.972974
\(712\) −3174.81 −0.167108
\(713\) −14892.1 −0.782205
\(714\) 314.654 0.0164925
\(715\) 20857.3 1.09094
\(716\) −12459.6 −0.650330
\(717\) 10713.0 0.557998
\(718\) 11773.4 0.611950
\(719\) −31411.2 −1.62926 −0.814631 0.579979i \(-0.803061\pi\)
−0.814631 + 0.579979i \(0.803061\pi\)
\(720\) −2036.29 −0.105400
\(721\) 533.702 0.0275674
\(722\) 7224.01 0.372368
\(723\) −12049.6 −0.619819
\(724\) 4458.57 0.228869
\(725\) 63757.4 3.26606
\(726\) −6389.84 −0.326652
\(727\) −21425.3 −1.09301 −0.546506 0.837455i \(-0.684042\pi\)
−0.546506 + 0.837455i \(0.684042\pi\)
\(728\) 13047.3 0.664236
\(729\) 10598.0 0.538433
\(730\) −27234.9 −1.38083
\(731\) 0 0
\(732\) 5294.21 0.267322
\(733\) −3241.88 −0.163358 −0.0816791 0.996659i \(-0.526028\pi\)
−0.0816791 + 0.996659i \(0.526028\pi\)
\(734\) 12118.9 0.609422
\(735\) 13645.0 0.684765
\(736\) −27794.4 −1.39200
\(737\) 13171.6 0.658322
\(738\) −12500.7 −0.623520
\(739\) −352.220 −0.0175326 −0.00876632 0.999962i \(-0.502790\pi\)
−0.00876632 + 0.999962i \(0.502790\pi\)
\(740\) 93.3933 0.00463947
\(741\) −7417.86 −0.367749
\(742\) −4316.87 −0.213581
\(743\) −23682.7 −1.16936 −0.584679 0.811265i \(-0.698779\pi\)
−0.584679 + 0.811265i \(0.698779\pi\)
\(744\) 6705.69 0.330433
\(745\) −3418.23 −0.168100
\(746\) 10778.0 0.528969
\(747\) 7512.00 0.367938
\(748\) 516.009 0.0252235
\(749\) −21579.8 −1.05275
\(750\) 8398.16 0.408877
\(751\) 3352.04 0.162873 0.0814364 0.996679i \(-0.474049\pi\)
0.0814364 + 0.996679i \(0.474049\pi\)
\(752\) −1376.28 −0.0667388
\(753\) 16422.8 0.794795
\(754\) −13269.5 −0.640909
\(755\) 30268.3 1.45904
\(756\) −15214.8 −0.731955
\(757\) 20731.0 0.995352 0.497676 0.867363i \(-0.334187\pi\)
0.497676 + 0.867363i \(0.334187\pi\)
\(758\) −2082.72 −0.0997990
\(759\) 24365.1 1.16521
\(760\) −43909.6 −2.09575
\(761\) −15049.1 −0.716860 −0.358430 0.933557i \(-0.616688\pi\)
−0.358430 + 0.933557i \(0.616688\pi\)
\(762\) 14293.4 0.679522
\(763\) 33236.2 1.57698
\(764\) −3396.99 −0.160862
\(765\) −723.653 −0.0342009
\(766\) −15849.3 −0.747594
\(767\) 3146.66 0.148135
\(768\) 13239.7 0.622066
\(769\) −7250.41 −0.339995 −0.169998 0.985444i \(-0.554376\pi\)
−0.169998 + 0.985444i \(0.554376\pi\)
\(770\) −40318.0 −1.88696
\(771\) 66.3524 0.00309938
\(772\) −2002.41 −0.0933529
\(773\) −2947.00 −0.137123 −0.0685615 0.997647i \(-0.521841\pi\)
−0.0685615 + 0.997647i \(0.521841\pi\)
\(774\) 0 0
\(775\) 19224.2 0.891038
\(776\) −596.132 −0.0275772
\(777\) −83.7859 −0.00386847
\(778\) 27144.6 1.25088
\(779\) −40127.9 −1.84561
\(780\) 5954.56 0.273343
\(781\) −21711.3 −0.994738
\(782\) 671.603 0.0307116
\(783\) 42510.6 1.94024
\(784\) −1557.06 −0.0709301
\(785\) 60088.0 2.73201
\(786\) 960.058 0.0435676
\(787\) −27036.2 −1.22457 −0.612285 0.790637i \(-0.709749\pi\)
−0.612285 + 0.790637i \(0.709749\pi\)
\(788\) −8100.56 −0.366206
\(789\) −8913.51 −0.402192
\(790\) 35517.7 1.59958
\(791\) −22718.1 −1.02119
\(792\) 20124.6 0.902899
\(793\) −8678.12 −0.388612
\(794\) −19159.6 −0.856361
\(795\) −5412.47 −0.241460
\(796\) −11184.8 −0.498034
\(797\) 33.4802 0.00148799 0.000743997 1.00000i \(-0.499763\pi\)
0.000743997 1.00000i \(0.499763\pi\)
\(798\) 14339.0 0.636085
\(799\) −489.098 −0.0216559
\(800\) 35879.9 1.58568
\(801\) −2384.37 −0.105178
\(802\) 3948.69 0.173857
\(803\) 40068.6 1.76088
\(804\) 3760.38 0.164948
\(805\) 70225.9 3.07471
\(806\) −4001.03 −0.174851
\(807\) 21215.7 0.925438
\(808\) 38664.5 1.68343
\(809\) 42225.4 1.83506 0.917531 0.397665i \(-0.130179\pi\)
0.917531 + 0.397665i \(0.130179\pi\)
\(810\) −1619.31 −0.0702427
\(811\) 5553.35 0.240449 0.120225 0.992747i \(-0.461639\pi\)
0.120225 + 0.992747i \(0.461639\pi\)
\(812\) −34327.1 −1.48355
\(813\) 20748.7 0.895066
\(814\) 102.672 0.00442094
\(815\) 28247.1 1.21405
\(816\) −45.0187 −0.00193133
\(817\) 0 0
\(818\) 4226.04 0.180636
\(819\) 9798.85 0.418070
\(820\) 32212.0 1.37182
\(821\) 23869.5 1.01468 0.507338 0.861747i \(-0.330629\pi\)
0.507338 + 0.861747i \(0.330629\pi\)
\(822\) −2040.33 −0.0865749
\(823\) −26707.2 −1.13117 −0.565587 0.824689i \(-0.691350\pi\)
−0.565587 + 0.824689i \(0.691350\pi\)
\(824\) −512.940 −0.0216858
\(825\) −31453.0 −1.32734
\(826\) −6082.62 −0.256225
\(827\) 14209.8 0.597489 0.298744 0.954333i \(-0.403432\pi\)
0.298744 + 0.954333i \(0.403432\pi\)
\(828\) −12759.4 −0.535531
\(829\) 26345.6 1.10376 0.551882 0.833922i \(-0.313910\pi\)
0.551882 + 0.833922i \(0.313910\pi\)
\(830\) 14464.2 0.604892
\(831\) −23184.9 −0.967839
\(832\) −8654.70 −0.360634
\(833\) −553.344 −0.0230159
\(834\) −2816.60 −0.116944
\(835\) −39656.7 −1.64356
\(836\) 23514.9 0.972823
\(837\) 12817.9 0.529331
\(838\) 4399.78 0.181370
\(839\) 6078.93 0.250141 0.125070 0.992148i \(-0.460084\pi\)
0.125070 + 0.992148i \(0.460084\pi\)
\(840\) −31621.8 −1.29887
\(841\) 71521.8 2.93254
\(842\) −27108.6 −1.10953
\(843\) 20261.4 0.827805
\(844\) −11204.7 −0.456970
\(845\) 30202.6 1.22959
\(846\) −6943.36 −0.282172
\(847\) 27095.5 1.09919
\(848\) 617.629 0.0250112
\(849\) −3032.42 −0.122582
\(850\) −866.976 −0.0349847
\(851\) −178.834 −0.00720370
\(852\) −6198.36 −0.249240
\(853\) 28429.0 1.14114 0.570569 0.821249i \(-0.306723\pi\)
0.570569 + 0.821249i \(0.306723\pi\)
\(854\) 16775.1 0.672170
\(855\) −32977.3 −1.31907
\(856\) 20740.3 0.828142
\(857\) −3079.93 −0.122764 −0.0613818 0.998114i \(-0.519551\pi\)
−0.0613818 + 0.998114i \(0.519551\pi\)
\(858\) 6546.14 0.260468
\(859\) 14493.8 0.575696 0.287848 0.957676i \(-0.407060\pi\)
0.287848 + 0.957676i \(0.407060\pi\)
\(860\) 0 0
\(861\) −28898.3 −1.14385
\(862\) −4563.62 −0.180322
\(863\) −32404.8 −1.27818 −0.639092 0.769130i \(-0.720690\pi\)
−0.639092 + 0.769130i \(0.720690\pi\)
\(864\) 23923.1 0.941991
\(865\) 28142.0 1.10619
\(866\) 26269.8 1.03081
\(867\) 15147.7 0.593361
\(868\) −10350.4 −0.404740
\(869\) −52254.6 −2.03983
\(870\) 32160.3 1.25326
\(871\) −6163.90 −0.239788
\(872\) −31943.3 −1.24052
\(873\) −447.712 −0.0173571
\(874\) 30605.4 1.18449
\(875\) −35611.6 −1.37588
\(876\) 11439.2 0.441204
\(877\) −19866.3 −0.764923 −0.382461 0.923971i \(-0.624924\pi\)
−0.382461 + 0.923971i \(0.624924\pi\)
\(878\) −20548.3 −0.789831
\(879\) −12652.3 −0.485498
\(880\) 5768.43 0.220970
\(881\) 14081.8 0.538512 0.269256 0.963069i \(-0.413222\pi\)
0.269256 + 0.963069i \(0.413222\pi\)
\(882\) −7855.42 −0.299893
\(883\) 24474.0 0.932748 0.466374 0.884588i \(-0.345560\pi\)
0.466374 + 0.884588i \(0.345560\pi\)
\(884\) −241.476 −0.00918744
\(885\) −7626.36 −0.289669
\(886\) −6247.24 −0.236885
\(887\) 1361.28 0.0515301 0.0257651 0.999668i \(-0.491798\pi\)
0.0257651 + 0.999668i \(0.491798\pi\)
\(888\) 80.5264 0.00304312
\(889\) −60610.0 −2.28661
\(890\) −4591.06 −0.172913
\(891\) 2382.36 0.0895759
\(892\) 5322.24 0.199778
\(893\) −22288.5 −0.835227
\(894\) −1072.83 −0.0401349
\(895\) −49498.8 −1.84867
\(896\) −17022.8 −0.634702
\(897\) −11402.1 −0.424419
\(898\) −15663.6 −0.582074
\(899\) 28919.2 1.07287
\(900\) 16471.2 0.610043
\(901\) 219.492 0.00811580
\(902\) 35412.2 1.30720
\(903\) 0 0
\(904\) 21834.3 0.803317
\(905\) 17712.8 0.650600
\(906\) 9499.81 0.348356
\(907\) 10369.2 0.379609 0.189804 0.981822i \(-0.439215\pi\)
0.189804 + 0.981822i \(0.439215\pi\)
\(908\) 16421.5 0.600185
\(909\) 29038.1 1.05955
\(910\) 18867.5 0.687310
\(911\) −6938.26 −0.252333 −0.126166 0.992009i \(-0.540267\pi\)
−0.126166 + 0.992009i \(0.540267\pi\)
\(912\) −2051.53 −0.0744879
\(913\) −21280.1 −0.771379
\(914\) −1876.31 −0.0679026
\(915\) 21032.6 0.759908
\(916\) 14481.2 0.522349
\(917\) −4071.04 −0.146606
\(918\) −578.061 −0.0207831
\(919\) −5381.77 −0.193175 −0.0965876 0.995324i \(-0.530793\pi\)
−0.0965876 + 0.995324i \(0.530793\pi\)
\(920\) −67494.0 −2.41871
\(921\) −19404.4 −0.694240
\(922\) −13366.7 −0.477449
\(923\) 10160.2 0.362325
\(924\) 16934.4 0.602922
\(925\) 230.857 0.00820600
\(926\) 29348.0 1.04151
\(927\) −385.232 −0.0136490
\(928\) 53974.4 1.90926
\(929\) −11294.7 −0.398888 −0.199444 0.979909i \(-0.563914\pi\)
−0.199444 + 0.979909i \(0.563914\pi\)
\(930\) 9697.03 0.341912
\(931\) −25216.3 −0.887680
\(932\) −15252.9 −0.536077
\(933\) 28366.2 0.995356
\(934\) −28560.3 −1.00056
\(935\) 2049.98 0.0717020
\(936\) −9417.65 −0.328873
\(937\) −46811.1 −1.63207 −0.816037 0.578000i \(-0.803833\pi\)
−0.816037 + 0.578000i \(0.803833\pi\)
\(938\) 11915.1 0.414755
\(939\) −6708.61 −0.233149
\(940\) 17891.7 0.620813
\(941\) 416.802 0.0144393 0.00721963 0.999974i \(-0.497702\pi\)
0.00721963 + 0.999974i \(0.497702\pi\)
\(942\) 18858.8 0.652286
\(943\) −61681.0 −2.13002
\(944\) 870.261 0.0300049
\(945\) −60444.7 −2.08071
\(946\) 0 0
\(947\) 25431.0 0.872648 0.436324 0.899790i \(-0.356280\pi\)
0.436324 + 0.899790i \(0.356280\pi\)
\(948\) −14918.2 −0.511097
\(949\) −18750.8 −0.641387
\(950\) −39508.7 −1.34930
\(951\) −26190.1 −0.893029
\(952\) 1282.36 0.0436570
\(953\) −23225.7 −0.789460 −0.394730 0.918797i \(-0.629162\pi\)
−0.394730 + 0.918797i \(0.629162\pi\)
\(954\) 3115.96 0.105747
\(955\) −13495.4 −0.457278
\(956\) 15892.5 0.537656
\(957\) −47315.1 −1.59820
\(958\) −28328.8 −0.955387
\(959\) 8651.83 0.291326
\(960\) 20975.8 0.705200
\(961\) −21071.3 −0.707303
\(962\) −48.0471 −0.00161029
\(963\) 15576.6 0.521233
\(964\) −17875.2 −0.597223
\(965\) −7955.09 −0.265371
\(966\) 22040.7 0.734106
\(967\) 7103.25 0.236220 0.118110 0.993000i \(-0.462316\pi\)
0.118110 + 0.993000i \(0.462316\pi\)
\(968\) −26041.5 −0.864674
\(969\) −729.069 −0.0241704
\(970\) −862.061 −0.0285352
\(971\) −279.508 −0.00923774 −0.00461887 0.999989i \(-0.501470\pi\)
−0.00461887 + 0.999989i \(0.501470\pi\)
\(972\) 17649.5 0.582417
\(973\) 11943.6 0.393518
\(974\) −7881.20 −0.259271
\(975\) 14719.0 0.483472
\(976\) −2400.08 −0.0787137
\(977\) 2433.91 0.0797007 0.0398504 0.999206i \(-0.487312\pi\)
0.0398504 + 0.999206i \(0.487312\pi\)
\(978\) 8865.44 0.289863
\(979\) 6754.47 0.220504
\(980\) 20241.9 0.659801
\(981\) −23990.3 −0.780786
\(982\) −16559.6 −0.538123
\(983\) −52451.6 −1.70188 −0.850940 0.525264i \(-0.823967\pi\)
−0.850940 + 0.525264i \(0.823967\pi\)
\(984\) 27774.1 0.899803
\(985\) −32181.5 −1.04100
\(986\) −1304.20 −0.0421239
\(987\) −16051.2 −0.517645
\(988\) −11004.2 −0.354342
\(989\) 0 0
\(990\) 29102.0 0.934264
\(991\) 6191.90 0.198478 0.0992392 0.995064i \(-0.468359\pi\)
0.0992392 + 0.995064i \(0.468359\pi\)
\(992\) 16274.4 0.520881
\(993\) −9593.48 −0.306586
\(994\) −19640.0 −0.626703
\(995\) −44434.4 −1.41574
\(996\) −6075.27 −0.193275
\(997\) 6156.43 0.195563 0.0977814 0.995208i \(-0.468825\pi\)
0.0977814 + 0.995208i \(0.468825\pi\)
\(998\) −1362.11 −0.0432033
\(999\) 153.926 0.00487486
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.1.33 50
43.42 odd 2 1849.4.a.j.1.18 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.33 50 1.1 even 1 trivial
1849.4.a.j.1.18 yes 50 43.42 odd 2