Properties

Label 1849.4.a.i.1.8
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 1.8
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.52050 q^{2} -1.75128 q^{3} +12.4349 q^{4} -13.0472 q^{5} +7.91667 q^{6} +4.32755 q^{7} -20.0482 q^{8} -23.9330 q^{9} +O(q^{10})\) \(q-4.52050 q^{2} -1.75128 q^{3} +12.4349 q^{4} -13.0472 q^{5} +7.91667 q^{6} +4.32755 q^{7} -20.0482 q^{8} -23.9330 q^{9} +58.9799 q^{10} -55.2516 q^{11} -21.7771 q^{12} -37.7658 q^{13} -19.5627 q^{14} +22.8493 q^{15} -8.85170 q^{16} -24.9093 q^{17} +108.189 q^{18} +39.7201 q^{19} -162.241 q^{20} -7.57876 q^{21} +249.765 q^{22} -2.55110 q^{23} +35.1100 q^{24} +45.2293 q^{25} +170.720 q^{26} +89.1980 q^{27} +53.8129 q^{28} -238.086 q^{29} -103.290 q^{30} +263.063 q^{31} +200.400 q^{32} +96.7611 q^{33} +112.603 q^{34} -56.4624 q^{35} -297.606 q^{36} +353.428 q^{37} -179.555 q^{38} +66.1386 q^{39} +261.573 q^{40} +254.188 q^{41} +34.2598 q^{42} -687.051 q^{44} +312.259 q^{45} +11.5323 q^{46} -386.866 q^{47} +15.5018 q^{48} -324.272 q^{49} -204.459 q^{50} +43.6232 q^{51} -469.616 q^{52} -35.7551 q^{53} -403.220 q^{54} +720.878 q^{55} -86.7595 q^{56} -69.5611 q^{57} +1076.27 q^{58} -87.4154 q^{59} +284.130 q^{60} +890.643 q^{61} -1189.18 q^{62} -103.571 q^{63} -835.093 q^{64} +492.738 q^{65} -437.409 q^{66} -998.120 q^{67} -309.746 q^{68} +4.46769 q^{69} +255.238 q^{70} +443.994 q^{71} +479.813 q^{72} -70.5226 q^{73} -1597.67 q^{74} -79.2092 q^{75} +493.917 q^{76} -239.104 q^{77} -298.980 q^{78} +975.256 q^{79} +115.490 q^{80} +489.980 q^{81} -1149.06 q^{82} +836.712 q^{83} -94.2415 q^{84} +324.997 q^{85} +416.956 q^{87} +1107.69 q^{88} -1086.38 q^{89} -1411.57 q^{90} -163.434 q^{91} -31.7228 q^{92} -460.697 q^{93} +1748.83 q^{94} -518.236 q^{95} -350.956 q^{96} -1132.50 q^{97} +1465.87 q^{98} +1322.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.52050 −1.59824 −0.799120 0.601172i \(-0.794701\pi\)
−0.799120 + 0.601172i \(0.794701\pi\)
\(3\) −1.75128 −0.337034 −0.168517 0.985699i \(-0.553898\pi\)
−0.168517 + 0.985699i \(0.553898\pi\)
\(4\) 12.4349 1.55437
\(5\) −13.0472 −1.16698 −0.583488 0.812122i \(-0.698313\pi\)
−0.583488 + 0.812122i \(0.698313\pi\)
\(6\) 7.91667 0.538661
\(7\) 4.32755 0.233666 0.116833 0.993152i \(-0.462726\pi\)
0.116833 + 0.993152i \(0.462726\pi\)
\(8\) −20.0482 −0.886013
\(9\) −23.9330 −0.886408
\(10\) 58.9799 1.86511
\(11\) −55.2516 −1.51445 −0.757227 0.653152i \(-0.773446\pi\)
−0.757227 + 0.653152i \(0.773446\pi\)
\(12\) −21.7771 −0.523875
\(13\) −37.7658 −0.805719 −0.402860 0.915262i \(-0.631984\pi\)
−0.402860 + 0.915262i \(0.631984\pi\)
\(14\) −19.5627 −0.373454
\(15\) 22.8493 0.393311
\(16\) −8.85170 −0.138308
\(17\) −24.9093 −0.355376 −0.177688 0.984087i \(-0.556862\pi\)
−0.177688 + 0.984087i \(0.556862\pi\)
\(18\) 108.189 1.41669
\(19\) 39.7201 0.479601 0.239800 0.970822i \(-0.422918\pi\)
0.239800 + 0.970822i \(0.422918\pi\)
\(20\) −162.241 −1.81391
\(21\) −7.57876 −0.0787534
\(22\) 249.765 2.42046
\(23\) −2.55110 −0.0231279 −0.0115639 0.999933i \(-0.503681\pi\)
−0.0115639 + 0.999933i \(0.503681\pi\)
\(24\) 35.1100 0.298617
\(25\) 45.2293 0.361834
\(26\) 170.720 1.28773
\(27\) 89.1980 0.635784
\(28\) 53.8129 0.363203
\(29\) −238.086 −1.52454 −0.762268 0.647262i \(-0.775914\pi\)
−0.762268 + 0.647262i \(0.775914\pi\)
\(30\) −103.290 −0.628605
\(31\) 263.063 1.52411 0.762056 0.647512i \(-0.224190\pi\)
0.762056 + 0.647512i \(0.224190\pi\)
\(32\) 200.400 1.10706
\(33\) 96.7611 0.510423
\(34\) 112.603 0.567977
\(35\) −56.4624 −0.272682
\(36\) −297.606 −1.37780
\(37\) 353.428 1.57036 0.785178 0.619270i \(-0.212571\pi\)
0.785178 + 0.619270i \(0.212571\pi\)
\(38\) −179.555 −0.766517
\(39\) 66.1386 0.271555
\(40\) 261.573 1.03396
\(41\) 254.188 0.968233 0.484117 0.875004i \(-0.339141\pi\)
0.484117 + 0.875004i \(0.339141\pi\)
\(42\) 34.2598 0.125867
\(43\) 0 0
\(44\) −687.051 −2.35402
\(45\) 312.259 1.03442
\(46\) 11.5323 0.0369639
\(47\) −386.866 −1.20064 −0.600321 0.799759i \(-0.704961\pi\)
−0.600321 + 0.799759i \(0.704961\pi\)
\(48\) 15.5018 0.0466145
\(49\) −324.272 −0.945400
\(50\) −204.459 −0.578297
\(51\) 43.6232 0.119774
\(52\) −469.616 −1.25238
\(53\) −35.7551 −0.0926668 −0.0463334 0.998926i \(-0.514754\pi\)
−0.0463334 + 0.998926i \(0.514754\pi\)
\(54\) −403.220 −1.01614
\(55\) 720.878 1.76733
\(56\) −86.7595 −0.207031
\(57\) −69.5611 −0.161642
\(58\) 1076.27 2.43657
\(59\) −87.4154 −0.192890 −0.0964451 0.995338i \(-0.530747\pi\)
−0.0964451 + 0.995338i \(0.530747\pi\)
\(60\) 284.130 0.611350
\(61\) 890.643 1.86943 0.934714 0.355400i \(-0.115655\pi\)
0.934714 + 0.355400i \(0.115655\pi\)
\(62\) −1189.18 −2.43589
\(63\) −103.571 −0.207123
\(64\) −835.093 −1.63104
\(65\) 492.738 0.940256
\(66\) −437.409 −0.815777
\(67\) −998.120 −1.82000 −0.909998 0.414612i \(-0.863917\pi\)
−0.909998 + 0.414612i \(0.863917\pi\)
\(68\) −309.746 −0.552386
\(69\) 4.46769 0.00779489
\(70\) 255.238 0.435812
\(71\) 443.994 0.742146 0.371073 0.928604i \(-0.378990\pi\)
0.371073 + 0.928604i \(0.378990\pi\)
\(72\) 479.813 0.785369
\(73\) −70.5226 −0.113069 −0.0565346 0.998401i \(-0.518005\pi\)
−0.0565346 + 0.998401i \(0.518005\pi\)
\(74\) −1597.67 −2.50980
\(75\) −79.2092 −0.121951
\(76\) 493.917 0.745476
\(77\) −239.104 −0.353876
\(78\) −298.980 −0.434010
\(79\) 975.256 1.38892 0.694461 0.719530i \(-0.255643\pi\)
0.694461 + 0.719530i \(0.255643\pi\)
\(80\) 115.490 0.161402
\(81\) 489.980 0.672127
\(82\) −1149.06 −1.54747
\(83\) 836.712 1.10652 0.553260 0.833009i \(-0.313384\pi\)
0.553260 + 0.833009i \(0.313384\pi\)
\(84\) −94.2415 −0.122412
\(85\) 324.997 0.414716
\(86\) 0 0
\(87\) 416.956 0.513821
\(88\) 1107.69 1.34182
\(89\) −1086.38 −1.29389 −0.646944 0.762537i \(-0.723953\pi\)
−0.646944 + 0.762537i \(0.723953\pi\)
\(90\) −1411.57 −1.65325
\(91\) −163.434 −0.188269
\(92\) −31.7228 −0.0359492
\(93\) −460.697 −0.513678
\(94\) 1748.83 1.91891
\(95\) −518.236 −0.559683
\(96\) −350.956 −0.373118
\(97\) −1132.50 −1.18544 −0.592720 0.805408i \(-0.701946\pi\)
−0.592720 + 0.805408i \(0.701946\pi\)
\(98\) 1465.87 1.51098
\(99\) 1322.34 1.34242
\(100\) 562.423 0.562423
\(101\) 1437.96 1.41665 0.708326 0.705885i \(-0.249450\pi\)
0.708326 + 0.705885i \(0.249450\pi\)
\(102\) −197.199 −0.191428
\(103\) 1763.53 1.68704 0.843521 0.537096i \(-0.180479\pi\)
0.843521 + 0.537096i \(0.180479\pi\)
\(104\) 757.136 0.713878
\(105\) 98.8816 0.0919033
\(106\) 161.631 0.148104
\(107\) 166.103 0.150073 0.0750365 0.997181i \(-0.476093\pi\)
0.0750365 + 0.997181i \(0.476093\pi\)
\(108\) 1109.17 0.988243
\(109\) −441.796 −0.388224 −0.194112 0.980979i \(-0.562182\pi\)
−0.194112 + 0.980979i \(0.562182\pi\)
\(110\) −3258.73 −2.82462
\(111\) −618.951 −0.529264
\(112\) −38.3062 −0.0323178
\(113\) −971.442 −0.808722 −0.404361 0.914599i \(-0.632506\pi\)
−0.404361 + 0.914599i \(0.632506\pi\)
\(114\) 314.451 0.258342
\(115\) 33.2847 0.0269897
\(116\) −2960.59 −2.36969
\(117\) 903.850 0.714196
\(118\) 395.162 0.308285
\(119\) −107.796 −0.0830393
\(120\) −458.087 −0.348479
\(121\) 1721.74 1.29357
\(122\) −4026.15 −2.98779
\(123\) −445.155 −0.326328
\(124\) 3271.17 2.36903
\(125\) 1040.78 0.744725
\(126\) 468.195 0.331032
\(127\) −1595.77 −1.11498 −0.557489 0.830185i \(-0.688235\pi\)
−0.557489 + 0.830185i \(0.688235\pi\)
\(128\) 2171.84 1.49973
\(129\) 0 0
\(130\) −2227.42 −1.50275
\(131\) 55.8044 0.0372187 0.0186094 0.999827i \(-0.494076\pi\)
0.0186094 + 0.999827i \(0.494076\pi\)
\(132\) 1203.22 0.793385
\(133\) 171.891 0.112066
\(134\) 4512.00 2.90879
\(135\) −1163.78 −0.741945
\(136\) 499.387 0.314868
\(137\) 137.795 0.0859316 0.0429658 0.999077i \(-0.486319\pi\)
0.0429658 + 0.999077i \(0.486319\pi\)
\(138\) −20.1962 −0.0124581
\(139\) 1016.38 0.620206 0.310103 0.950703i \(-0.399637\pi\)
0.310103 + 0.950703i \(0.399637\pi\)
\(140\) −702.107 −0.423849
\(141\) 677.511 0.404658
\(142\) −2007.08 −1.18613
\(143\) 2086.62 1.22022
\(144\) 211.848 0.122597
\(145\) 3106.36 1.77910
\(146\) 318.798 0.180712
\(147\) 567.892 0.318632
\(148\) 4394.85 2.44091
\(149\) −2725.90 −1.49876 −0.749378 0.662142i \(-0.769648\pi\)
−0.749378 + 0.662142i \(0.769648\pi\)
\(150\) 358.065 0.194906
\(151\) 1350.49 0.727822 0.363911 0.931434i \(-0.381441\pi\)
0.363911 + 0.931434i \(0.381441\pi\)
\(152\) −796.315 −0.424932
\(153\) 596.155 0.315008
\(154\) 1080.87 0.565578
\(155\) −3432.23 −1.77860
\(156\) 822.430 0.422097
\(157\) 2623.54 1.33364 0.666818 0.745220i \(-0.267656\pi\)
0.666818 + 0.745220i \(0.267656\pi\)
\(158\) −4408.65 −2.21983
\(159\) 62.6172 0.0312319
\(160\) −2614.65 −1.29192
\(161\) −11.0400 −0.00540419
\(162\) −2214.96 −1.07422
\(163\) 407.303 0.195721 0.0978603 0.995200i \(-0.468800\pi\)
0.0978603 + 0.995200i \(0.468800\pi\)
\(164\) 3160.82 1.50499
\(165\) −1262.46 −0.595651
\(166\) −3782.36 −1.76848
\(167\) 1743.79 0.808015 0.404008 0.914756i \(-0.367617\pi\)
0.404008 + 0.914756i \(0.367617\pi\)
\(168\) 151.940 0.0697765
\(169\) −770.743 −0.350816
\(170\) −1469.15 −0.662815
\(171\) −950.621 −0.425122
\(172\) 0 0
\(173\) 1182.29 0.519584 0.259792 0.965665i \(-0.416346\pi\)
0.259792 + 0.965665i \(0.416346\pi\)
\(174\) −1884.85 −0.821208
\(175\) 195.732 0.0845483
\(176\) 489.071 0.209461
\(177\) 153.089 0.0650106
\(178\) 4910.99 2.06794
\(179\) 4505.20 1.88120 0.940600 0.339517i \(-0.110263\pi\)
0.940600 + 0.339517i \(0.110263\pi\)
\(180\) 3882.92 1.60787
\(181\) −2610.79 −1.07215 −0.536073 0.844172i \(-0.680093\pi\)
−0.536073 + 0.844172i \(0.680093\pi\)
\(182\) 738.802 0.300899
\(183\) −1559.77 −0.630061
\(184\) 51.1449 0.0204916
\(185\) −4611.24 −1.83257
\(186\) 2082.58 0.820980
\(187\) 1376.28 0.538201
\(188\) −4810.66 −1.86624
\(189\) 386.009 0.148561
\(190\) 2342.69 0.894507
\(191\) 2992.98 1.13384 0.566922 0.823771i \(-0.308134\pi\)
0.566922 + 0.823771i \(0.308134\pi\)
\(192\) 1462.48 0.549717
\(193\) −842.048 −0.314051 −0.157026 0.987595i \(-0.550191\pi\)
−0.157026 + 0.987595i \(0.550191\pi\)
\(194\) 5119.46 1.89462
\(195\) −862.923 −0.316898
\(196\) −4032.31 −1.46950
\(197\) 1391.04 0.503082 0.251541 0.967847i \(-0.419063\pi\)
0.251541 + 0.967847i \(0.419063\pi\)
\(198\) −5977.63 −2.14551
\(199\) 989.587 0.352512 0.176256 0.984344i \(-0.443601\pi\)
0.176256 + 0.984344i \(0.443601\pi\)
\(200\) −906.764 −0.320590
\(201\) 1747.99 0.613401
\(202\) −6500.28 −2.26415
\(203\) −1030.33 −0.356232
\(204\) 542.453 0.186173
\(205\) −3316.45 −1.12991
\(206\) −7972.02 −2.69630
\(207\) 61.0555 0.0205007
\(208\) 334.292 0.111437
\(209\) −2194.60 −0.726333
\(210\) −446.994 −0.146884
\(211\) −943.172 −0.307728 −0.153864 0.988092i \(-0.549172\pi\)
−0.153864 + 0.988092i \(0.549172\pi\)
\(212\) −444.612 −0.144038
\(213\) −777.558 −0.250129
\(214\) −750.871 −0.239853
\(215\) 0 0
\(216\) −1788.26 −0.563313
\(217\) 1138.42 0.356133
\(218\) 1997.14 0.620474
\(219\) 123.505 0.0381082
\(220\) 8964.08 2.74708
\(221\) 940.721 0.286334
\(222\) 2797.97 0.845890
\(223\) 4371.74 1.31280 0.656398 0.754415i \(-0.272079\pi\)
0.656398 + 0.754415i \(0.272079\pi\)
\(224\) 867.240 0.258682
\(225\) −1082.47 −0.320733
\(226\) 4391.41 1.29253
\(227\) −1293.65 −0.378249 −0.189124 0.981953i \(-0.560565\pi\)
−0.189124 + 0.981953i \(0.560565\pi\)
\(228\) −864.988 −0.251251
\(229\) 2720.83 0.785141 0.392570 0.919722i \(-0.371586\pi\)
0.392570 + 0.919722i \(0.371586\pi\)
\(230\) −150.464 −0.0431360
\(231\) 418.739 0.119268
\(232\) 4773.20 1.35076
\(233\) −1824.91 −0.513108 −0.256554 0.966530i \(-0.582587\pi\)
−0.256554 + 0.966530i \(0.582587\pi\)
\(234\) −4085.86 −1.14146
\(235\) 5047.52 1.40112
\(236\) −1087.01 −0.299822
\(237\) −1707.95 −0.468114
\(238\) 487.294 0.132717
\(239\) 2517.89 0.681460 0.340730 0.940161i \(-0.389326\pi\)
0.340730 + 0.940161i \(0.389326\pi\)
\(240\) −202.255 −0.0543980
\(241\) −2023.30 −0.540797 −0.270398 0.962749i \(-0.587155\pi\)
−0.270398 + 0.962749i \(0.587155\pi\)
\(242\) −7783.13 −2.06743
\(243\) −3266.44 −0.862314
\(244\) 11075.1 2.90578
\(245\) 4230.84 1.10326
\(246\) 2012.33 0.521550
\(247\) −1500.06 −0.386424
\(248\) −5273.93 −1.35038
\(249\) −1465.32 −0.372935
\(250\) −4704.87 −1.19025
\(251\) −2200.46 −0.553355 −0.276677 0.960963i \(-0.589233\pi\)
−0.276677 + 0.960963i \(0.589233\pi\)
\(252\) −1287.90 −0.321946
\(253\) 140.952 0.0350261
\(254\) 7213.71 1.78200
\(255\) −569.161 −0.139773
\(256\) −3137.08 −0.765890
\(257\) 869.760 0.211106 0.105553 0.994414i \(-0.466339\pi\)
0.105553 + 0.994414i \(0.466339\pi\)
\(258\) 0 0
\(259\) 1529.48 0.366938
\(260\) 6127.17 1.46150
\(261\) 5698.12 1.35136
\(262\) −252.264 −0.0594844
\(263\) −4849.52 −1.13701 −0.568506 0.822679i \(-0.692478\pi\)
−0.568506 + 0.822679i \(0.692478\pi\)
\(264\) −1939.88 −0.452241
\(265\) 466.503 0.108140
\(266\) −777.032 −0.179109
\(267\) 1902.56 0.436085
\(268\) −12411.6 −2.82894
\(269\) 432.453 0.0980191 0.0490096 0.998798i \(-0.484394\pi\)
0.0490096 + 0.998798i \(0.484394\pi\)
\(270\) 5260.89 1.18581
\(271\) 861.175 0.193036 0.0965179 0.995331i \(-0.469230\pi\)
0.0965179 + 0.995331i \(0.469230\pi\)
\(272\) 220.490 0.0491514
\(273\) 286.218 0.0634531
\(274\) −622.903 −0.137339
\(275\) −2498.99 −0.547981
\(276\) 55.5555 0.0121161
\(277\) −2228.63 −0.483412 −0.241706 0.970350i \(-0.577707\pi\)
−0.241706 + 0.970350i \(0.577707\pi\)
\(278\) −4594.57 −0.991237
\(279\) −6295.88 −1.35098
\(280\) 1131.97 0.241600
\(281\) −5991.67 −1.27200 −0.636002 0.771688i \(-0.719413\pi\)
−0.636002 + 0.771688i \(0.719413\pi\)
\(282\) −3062.69 −0.646740
\(283\) 1125.62 0.236434 0.118217 0.992988i \(-0.462282\pi\)
0.118217 + 0.992988i \(0.462282\pi\)
\(284\) 5521.04 1.15357
\(285\) 907.577 0.188632
\(286\) −9432.58 −1.95021
\(287\) 1100.01 0.226243
\(288\) −4796.17 −0.981308
\(289\) −4292.53 −0.873708
\(290\) −14042.3 −2.84342
\(291\) 1983.32 0.399534
\(292\) −876.945 −0.175751
\(293\) 6457.05 1.28746 0.643729 0.765254i \(-0.277387\pi\)
0.643729 + 0.765254i \(0.277387\pi\)
\(294\) −2567.16 −0.509251
\(295\) 1140.53 0.225098
\(296\) −7085.58 −1.39136
\(297\) −4928.33 −0.962865
\(298\) 12322.5 2.39537
\(299\) 96.3444 0.0186346
\(300\) −984.962 −0.189556
\(301\) 0 0
\(302\) −6104.88 −1.16323
\(303\) −2518.27 −0.477461
\(304\) −351.590 −0.0663325
\(305\) −11620.4 −2.18158
\(306\) −2694.92 −0.503459
\(307\) 7900.21 1.46869 0.734347 0.678775i \(-0.237489\pi\)
0.734347 + 0.678775i \(0.237489\pi\)
\(308\) −2973.25 −0.550053
\(309\) −3088.43 −0.568591
\(310\) 15515.4 2.84263
\(311\) 3923.50 0.715374 0.357687 0.933841i \(-0.383565\pi\)
0.357687 + 0.933841i \(0.383565\pi\)
\(312\) −1325.96 −0.240601
\(313\) −7259.87 −1.31103 −0.655515 0.755182i \(-0.727548\pi\)
−0.655515 + 0.755182i \(0.727548\pi\)
\(314\) −11859.7 −2.13147
\(315\) 1351.32 0.241708
\(316\) 12127.3 2.15890
\(317\) −5967.29 −1.05728 −0.528638 0.848847i \(-0.677297\pi\)
−0.528638 + 0.848847i \(0.677297\pi\)
\(318\) −283.061 −0.0499160
\(319\) 13154.7 2.30884
\(320\) 10895.6 1.90339
\(321\) −290.894 −0.0505798
\(322\) 49.9064 0.00863719
\(323\) −989.401 −0.170439
\(324\) 6092.88 1.04473
\(325\) −1708.12 −0.291537
\(326\) −1841.22 −0.312808
\(327\) 773.709 0.130845
\(328\) −5096.01 −0.857867
\(329\) −1674.18 −0.280549
\(330\) 5706.96 0.951993
\(331\) 7412.74 1.23094 0.615470 0.788161i \(-0.288966\pi\)
0.615470 + 0.788161i \(0.288966\pi\)
\(332\) 10404.5 1.71994
\(333\) −8458.59 −1.39198
\(334\) −7882.81 −1.29140
\(335\) 13022.7 2.12389
\(336\) 67.0849 0.0108922
\(337\) 12010.9 1.94147 0.970733 0.240160i \(-0.0771998\pi\)
0.970733 + 0.240160i \(0.0771998\pi\)
\(338\) 3484.15 0.560688
\(339\) 1701.27 0.272567
\(340\) 4041.32 0.644621
\(341\) −14534.6 −2.30819
\(342\) 4297.29 0.679446
\(343\) −2887.66 −0.454574
\(344\) 0 0
\(345\) −58.2909 −0.00909645
\(346\) −5344.56 −0.830419
\(347\) −2376.88 −0.367716 −0.183858 0.982953i \(-0.558859\pi\)
−0.183858 + 0.982953i \(0.558859\pi\)
\(348\) 5184.83 0.798666
\(349\) −2443.29 −0.374747 −0.187373 0.982289i \(-0.559997\pi\)
−0.187373 + 0.982289i \(0.559997\pi\)
\(350\) −884.807 −0.135128
\(351\) −3368.64 −0.512264
\(352\) −11072.4 −1.67659
\(353\) −6845.61 −1.03217 −0.516084 0.856538i \(-0.672611\pi\)
−0.516084 + 0.856538i \(0.672611\pi\)
\(354\) −692.039 −0.103902
\(355\) −5792.88 −0.866067
\(356\) −13509.1 −2.01118
\(357\) 188.782 0.0279871
\(358\) −20365.8 −3.00661
\(359\) −8886.04 −1.30637 −0.653185 0.757198i \(-0.726568\pi\)
−0.653185 + 0.757198i \(0.726568\pi\)
\(360\) −6260.22 −0.916507
\(361\) −5281.31 −0.769983
\(362\) 11802.1 1.71354
\(363\) −3015.25 −0.435977
\(364\) −2032.29 −0.292639
\(365\) 920.122 0.131949
\(366\) 7050.93 1.00699
\(367\) 1772.16 0.252060 0.126030 0.992026i \(-0.459776\pi\)
0.126030 + 0.992026i \(0.459776\pi\)
\(368\) 22.5816 0.00319877
\(369\) −6083.49 −0.858249
\(370\) 20845.1 2.92888
\(371\) −154.732 −0.0216531
\(372\) −5728.74 −0.798444
\(373\) 2089.79 0.290095 0.145047 0.989425i \(-0.453667\pi\)
0.145047 + 0.989425i \(0.453667\pi\)
\(374\) −6221.48 −0.860174
\(375\) −1822.71 −0.250998
\(376\) 7755.96 1.06378
\(377\) 8991.53 1.22835
\(378\) −1744.96 −0.237436
\(379\) −12958.0 −1.75622 −0.878108 0.478462i \(-0.841194\pi\)
−0.878108 + 0.478462i \(0.841194\pi\)
\(380\) −6444.23 −0.869953
\(381\) 2794.65 0.375786
\(382\) −13529.8 −1.81215
\(383\) −2891.35 −0.385747 −0.192874 0.981224i \(-0.561781\pi\)
−0.192874 + 0.981224i \(0.561781\pi\)
\(384\) −3803.51 −0.505461
\(385\) 3119.64 0.412965
\(386\) 3806.48 0.501929
\(387\) 0 0
\(388\) −14082.5 −1.84261
\(389\) −8007.52 −1.04370 −0.521848 0.853039i \(-0.674757\pi\)
−0.521848 + 0.853039i \(0.674757\pi\)
\(390\) 3900.84 0.506479
\(391\) 63.5462 0.00821910
\(392\) 6501.07 0.837637
\(393\) −97.7292 −0.0125440
\(394\) −6288.18 −0.804046
\(395\) −12724.4 −1.62084
\(396\) 16443.2 2.08662
\(397\) −5407.44 −0.683606 −0.341803 0.939772i \(-0.611038\pi\)
−0.341803 + 0.939772i \(0.611038\pi\)
\(398\) −4473.43 −0.563399
\(399\) −301.029 −0.0377702
\(400\) −400.356 −0.0500445
\(401\) −11696.4 −1.45658 −0.728290 0.685269i \(-0.759684\pi\)
−0.728290 + 0.685269i \(0.759684\pi\)
\(402\) −7901.79 −0.980362
\(403\) −9934.78 −1.22801
\(404\) 17880.9 2.20200
\(405\) −6392.87 −0.784356
\(406\) 4657.61 0.569344
\(407\) −19527.4 −2.37823
\(408\) −874.567 −0.106121
\(409\) −4629.41 −0.559681 −0.279840 0.960047i \(-0.590282\pi\)
−0.279840 + 0.960047i \(0.590282\pi\)
\(410\) 14992.0 1.80586
\(411\) −241.318 −0.0289619
\(412\) 21929.4 2.62229
\(413\) −378.295 −0.0450718
\(414\) −276.002 −0.0327651
\(415\) −10916.7 −1.29128
\(416\) −7568.25 −0.891981
\(417\) −1779.97 −0.209031
\(418\) 9920.69 1.16085
\(419\) 3307.85 0.385678 0.192839 0.981230i \(-0.438230\pi\)
0.192839 + 0.981230i \(0.438230\pi\)
\(420\) 1229.59 0.142852
\(421\) −242.081 −0.0280245 −0.0140122 0.999902i \(-0.504460\pi\)
−0.0140122 + 0.999902i \(0.504460\pi\)
\(422\) 4263.61 0.491823
\(423\) 9258.87 1.06426
\(424\) 716.824 0.0821039
\(425\) −1126.63 −0.128587
\(426\) 3514.95 0.399766
\(427\) 3854.30 0.436821
\(428\) 2065.49 0.233269
\(429\) −3654.26 −0.411257
\(430\) 0 0
\(431\) −16410.0 −1.83398 −0.916989 0.398913i \(-0.869387\pi\)
−0.916989 + 0.398913i \(0.869387\pi\)
\(432\) −789.555 −0.0879339
\(433\) 6230.06 0.691450 0.345725 0.938336i \(-0.387633\pi\)
0.345725 + 0.938336i \(0.387633\pi\)
\(434\) −5146.22 −0.569185
\(435\) −5440.11 −0.599617
\(436\) −5493.71 −0.603442
\(437\) −101.330 −0.0110921
\(438\) −558.305 −0.0609060
\(439\) −4436.43 −0.482322 −0.241161 0.970485i \(-0.577528\pi\)
−0.241161 + 0.970485i \(0.577528\pi\)
\(440\) −14452.3 −1.56588
\(441\) 7760.81 0.838010
\(442\) −4252.53 −0.457630
\(443\) −13607.7 −1.45941 −0.729707 0.683760i \(-0.760343\pi\)
−0.729707 + 0.683760i \(0.760343\pi\)
\(444\) −7696.63 −0.822671
\(445\) 14174.2 1.50994
\(446\) −19762.5 −2.09816
\(447\) 4773.82 0.505132
\(448\) −3613.91 −0.381119
\(449\) −3677.16 −0.386494 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(450\) 4893.32 0.512607
\(451\) −14044.3 −1.46634
\(452\) −12079.8 −1.25705
\(453\) −2365.08 −0.245301
\(454\) 5847.94 0.604532
\(455\) 2132.35 0.219706
\(456\) 1394.57 0.143217
\(457\) 9654.94 0.988270 0.494135 0.869385i \(-0.335485\pi\)
0.494135 + 0.869385i \(0.335485\pi\)
\(458\) −12299.5 −1.25484
\(459\) −2221.86 −0.225943
\(460\) 413.893 0.0419519
\(461\) 6387.32 0.645308 0.322654 0.946517i \(-0.395425\pi\)
0.322654 + 0.946517i \(0.395425\pi\)
\(462\) −1892.91 −0.190619
\(463\) 8369.16 0.840060 0.420030 0.907510i \(-0.362019\pi\)
0.420030 + 0.907510i \(0.362019\pi\)
\(464\) 2107.47 0.210855
\(465\) 6010.80 0.599450
\(466\) 8249.53 0.820069
\(467\) −11897.9 −1.17895 −0.589475 0.807786i \(-0.700666\pi\)
−0.589475 + 0.807786i \(0.700666\pi\)
\(468\) 11239.3 1.11012
\(469\) −4319.41 −0.425271
\(470\) −22817.3 −2.23933
\(471\) −4594.55 −0.449481
\(472\) 1752.52 0.170903
\(473\) 0 0
\(474\) 7720.78 0.748159
\(475\) 1796.51 0.173536
\(476\) −1340.44 −0.129074
\(477\) 855.727 0.0821405
\(478\) −11382.1 −1.08914
\(479\) −5313.81 −0.506877 −0.253438 0.967352i \(-0.581562\pi\)
−0.253438 + 0.967352i \(0.581562\pi\)
\(480\) 4578.99 0.435420
\(481\) −13347.5 −1.26527
\(482\) 9146.32 0.864322
\(483\) 19.3342 0.00182140
\(484\) 21409.7 2.01068
\(485\) 14775.9 1.38338
\(486\) 14766.0 1.37818
\(487\) 10792.5 1.00422 0.502110 0.864804i \(-0.332557\pi\)
0.502110 + 0.864804i \(0.332557\pi\)
\(488\) −17855.8 −1.65634
\(489\) −713.303 −0.0659645
\(490\) −19125.5 −1.76327
\(491\) −2458.96 −0.226011 −0.113006 0.993594i \(-0.536048\pi\)
−0.113006 + 0.993594i \(0.536048\pi\)
\(492\) −5535.48 −0.507233
\(493\) 5930.57 0.541784
\(494\) 6781.03 0.617597
\(495\) −17252.8 −1.56658
\(496\) −2328.55 −0.210797
\(497\) 1921.41 0.173414
\(498\) 6623.98 0.596039
\(499\) −8744.82 −0.784513 −0.392256 0.919856i \(-0.628305\pi\)
−0.392256 + 0.919856i \(0.628305\pi\)
\(500\) 12942.1 1.15758
\(501\) −3053.87 −0.272329
\(502\) 9947.20 0.884393
\(503\) 12931.7 1.14631 0.573157 0.819446i \(-0.305719\pi\)
0.573157 + 0.819446i \(0.305719\pi\)
\(504\) 2076.42 0.183514
\(505\) −18761.3 −1.65320
\(506\) −637.175 −0.0559800
\(507\) 1349.79 0.118237
\(508\) −19843.4 −1.73309
\(509\) 19155.2 1.66805 0.834026 0.551726i \(-0.186030\pi\)
0.834026 + 0.551726i \(0.186030\pi\)
\(510\) 2572.89 0.223391
\(511\) −305.190 −0.0264204
\(512\) −3193.56 −0.275658
\(513\) 3542.95 0.304923
\(514\) −3931.75 −0.337397
\(515\) −23009.1 −1.96874
\(516\) 0 0
\(517\) 21375.0 1.81832
\(518\) −6914.00 −0.586455
\(519\) −2070.53 −0.175118
\(520\) −9878.50 −0.833079
\(521\) −2030.86 −0.170775 −0.0853875 0.996348i \(-0.527213\pi\)
−0.0853875 + 0.996348i \(0.527213\pi\)
\(522\) −25758.4 −2.15980
\(523\) 13361.0 1.11708 0.558542 0.829477i \(-0.311361\pi\)
0.558542 + 0.829477i \(0.311361\pi\)
\(524\) 693.925 0.0578516
\(525\) −342.782 −0.0284957
\(526\) 21922.2 1.81722
\(527\) −6552.71 −0.541633
\(528\) −856.501 −0.0705955
\(529\) −12160.5 −0.999465
\(530\) −2108.83 −0.172833
\(531\) 2092.11 0.170979
\(532\) 2137.45 0.174192
\(533\) −9599.63 −0.780124
\(534\) −8600.52 −0.696968
\(535\) −2167.18 −0.175132
\(536\) 20010.5 1.61254
\(537\) −7889.88 −0.634029
\(538\) −1954.91 −0.156658
\(539\) 17916.6 1.43176
\(540\) −14471.6 −1.15326
\(541\) −1543.79 −0.122685 −0.0613425 0.998117i \(-0.519538\pi\)
−0.0613425 + 0.998117i \(0.519538\pi\)
\(542\) −3892.95 −0.308517
\(543\) 4572.22 0.361350
\(544\) −4991.82 −0.393424
\(545\) 5764.20 0.453048
\(546\) −1293.85 −0.101413
\(547\) −15805.6 −1.23546 −0.617731 0.786390i \(-0.711948\pi\)
−0.617731 + 0.786390i \(0.711948\pi\)
\(548\) 1713.47 0.133569
\(549\) −21315.8 −1.65708
\(550\) 11296.7 0.875804
\(551\) −9456.81 −0.731168
\(552\) −89.5691 −0.00690637
\(553\) 4220.47 0.324544
\(554\) 10074.5 0.772608
\(555\) 8075.58 0.617638
\(556\) 12638.7 0.964028
\(557\) 552.342 0.0420170 0.0210085 0.999779i \(-0.493312\pi\)
0.0210085 + 0.999779i \(0.493312\pi\)
\(558\) 28460.6 2.15920
\(559\) 0 0
\(560\) 499.788 0.0377141
\(561\) −2410.25 −0.181392
\(562\) 27085.4 2.03297
\(563\) 12098.2 0.905644 0.452822 0.891601i \(-0.350417\pi\)
0.452822 + 0.891601i \(0.350417\pi\)
\(564\) 8424.81 0.628987
\(565\) 12674.6 0.943760
\(566\) −5088.35 −0.377878
\(567\) 2120.42 0.157053
\(568\) −8901.27 −0.657551
\(569\) 519.978 0.0383104 0.0191552 0.999817i \(-0.493902\pi\)
0.0191552 + 0.999817i \(0.493902\pi\)
\(570\) −4102.70 −0.301479
\(571\) 13553.9 0.993365 0.496682 0.867932i \(-0.334551\pi\)
0.496682 + 0.867932i \(0.334551\pi\)
\(572\) 25947.0 1.89668
\(573\) −5241.55 −0.382144
\(574\) −4972.61 −0.361590
\(575\) −115.384 −0.00836845
\(576\) 19986.3 1.44577
\(577\) 6324.19 0.456290 0.228145 0.973627i \(-0.426734\pi\)
0.228145 + 0.973627i \(0.426734\pi\)
\(578\) 19404.4 1.39639
\(579\) 1474.66 0.105846
\(580\) 38627.4 2.76537
\(581\) 3620.92 0.258556
\(582\) −8965.61 −0.638551
\(583\) 1975.53 0.140339
\(584\) 1413.85 0.100181
\(585\) −11792.7 −0.833450
\(586\) −29189.1 −2.05766
\(587\) 21394.9 1.50437 0.752183 0.658954i \(-0.229001\pi\)
0.752183 + 0.658954i \(0.229001\pi\)
\(588\) 7061.71 0.495272
\(589\) 10448.9 0.730965
\(590\) −5155.75 −0.359761
\(591\) −2436.10 −0.169556
\(592\) −3128.44 −0.217193
\(593\) −17243.2 −1.19409 −0.597043 0.802209i \(-0.703658\pi\)
−0.597043 + 0.802209i \(0.703658\pi\)
\(594\) 22278.5 1.53889
\(595\) 1406.44 0.0969049
\(596\) −33896.5 −2.32962
\(597\) −1733.04 −0.118809
\(598\) −435.525 −0.0297825
\(599\) 1214.43 0.0828387 0.0414193 0.999142i \(-0.486812\pi\)
0.0414193 + 0.999142i \(0.486812\pi\)
\(600\) 1588.00 0.108050
\(601\) −3251.39 −0.220677 −0.110338 0.993894i \(-0.535193\pi\)
−0.110338 + 0.993894i \(0.535193\pi\)
\(602\) 0 0
\(603\) 23888.0 1.61326
\(604\) 16793.2 1.13130
\(605\) −22463.9 −1.50956
\(606\) 11383.8 0.763096
\(607\) −13945.8 −0.932526 −0.466263 0.884646i \(-0.654400\pi\)
−0.466263 + 0.884646i \(0.654400\pi\)
\(608\) 7959.89 0.530948
\(609\) 1804.40 0.120062
\(610\) 52530.0 3.48668
\(611\) 14610.3 0.967381
\(612\) 7413.16 0.489639
\(613\) 8980.34 0.591701 0.295850 0.955234i \(-0.404397\pi\)
0.295850 + 0.955234i \(0.404397\pi\)
\(614\) −35712.9 −2.34732
\(615\) 5808.03 0.380817
\(616\) 4793.60 0.313539
\(617\) −9450.64 −0.616642 −0.308321 0.951282i \(-0.599767\pi\)
−0.308321 + 0.951282i \(0.599767\pi\)
\(618\) 13961.3 0.908745
\(619\) −9340.01 −0.606473 −0.303237 0.952915i \(-0.598067\pi\)
−0.303237 + 0.952915i \(0.598067\pi\)
\(620\) −42679.6 −2.76460
\(621\) −227.553 −0.0147043
\(622\) −17736.2 −1.14334
\(623\) −4701.37 −0.302337
\(624\) −585.439 −0.0375582
\(625\) −19233.0 −1.23091
\(626\) 32818.3 2.09534
\(627\) 3843.36 0.244799
\(628\) 32623.5 2.07296
\(629\) −8803.65 −0.558067
\(630\) −6108.62 −0.386307
\(631\) 9633.83 0.607792 0.303896 0.952705i \(-0.401712\pi\)
0.303896 + 0.952705i \(0.401712\pi\)
\(632\) −19552.1 −1.23060
\(633\) 1651.76 0.103715
\(634\) 26975.2 1.68978
\(635\) 20820.4 1.30115
\(636\) 778.642 0.0485458
\(637\) 12246.4 0.761727
\(638\) −59465.6 −3.69007
\(639\) −10626.1 −0.657844
\(640\) −28336.5 −1.75015
\(641\) 10806.5 0.665885 0.332943 0.942947i \(-0.391958\pi\)
0.332943 + 0.942947i \(0.391958\pi\)
\(642\) 1314.99 0.0808386
\(643\) 5396.16 0.330955 0.165477 0.986214i \(-0.447084\pi\)
0.165477 + 0.986214i \(0.447084\pi\)
\(644\) −137.282 −0.00840011
\(645\) 0 0
\(646\) 4472.59 0.272402
\(647\) −13276.4 −0.806722 −0.403361 0.915041i \(-0.632158\pi\)
−0.403361 + 0.915041i \(0.632158\pi\)
\(648\) −9823.22 −0.595513
\(649\) 4829.84 0.292123
\(650\) 7721.56 0.465945
\(651\) −1993.69 −0.120029
\(652\) 5064.79 0.304222
\(653\) −7560.53 −0.453088 −0.226544 0.974001i \(-0.572743\pi\)
−0.226544 + 0.974001i \(0.572743\pi\)
\(654\) −3497.55 −0.209121
\(655\) −728.091 −0.0434334
\(656\) −2250.00 −0.133914
\(657\) 1687.82 0.100225
\(658\) 7568.15 0.448385
\(659\) 17888.9 1.05744 0.528718 0.848797i \(-0.322673\pi\)
0.528718 + 0.848797i \(0.322673\pi\)
\(660\) −15698.6 −0.925861
\(661\) 28643.1 1.68546 0.842729 0.538337i \(-0.180947\pi\)
0.842729 + 0.538337i \(0.180947\pi\)
\(662\) −33509.3 −1.96733
\(663\) −1647.47 −0.0965043
\(664\) −16774.6 −0.980390
\(665\) −2242.69 −0.130779
\(666\) 38237.1 2.22471
\(667\) 607.382 0.0352593
\(668\) 21683.9 1.25595
\(669\) −7656.15 −0.442457
\(670\) −58869.0 −3.39449
\(671\) −49209.4 −2.83116
\(672\) −1518.78 −0.0871849
\(673\) 26681.2 1.52821 0.764105 0.645091i \(-0.223181\pi\)
0.764105 + 0.645091i \(0.223181\pi\)
\(674\) −54295.2 −3.10293
\(675\) 4034.36 0.230048
\(676\) −9584.15 −0.545297
\(677\) 24196.9 1.37365 0.686826 0.726821i \(-0.259003\pi\)
0.686826 + 0.726821i \(0.259003\pi\)
\(678\) −7690.59 −0.435627
\(679\) −4900.94 −0.276997
\(680\) −6515.60 −0.367444
\(681\) 2265.54 0.127483
\(682\) 65703.8 3.68905
\(683\) 33758.8 1.89128 0.945641 0.325213i \(-0.105436\pi\)
0.945641 + 0.325213i \(0.105436\pi\)
\(684\) −11820.9 −0.660796
\(685\) −1797.84 −0.100280
\(686\) 13053.7 0.726517
\(687\) −4764.93 −0.264619
\(688\) 0 0
\(689\) 1350.32 0.0746634
\(690\) 263.504 0.0145383
\(691\) −18145.5 −0.998970 −0.499485 0.866322i \(-0.666477\pi\)
−0.499485 + 0.866322i \(0.666477\pi\)
\(692\) 14701.7 0.807625
\(693\) 5722.48 0.313678
\(694\) 10744.7 0.587698
\(695\) −13261.0 −0.723765
\(696\) −8359.21 −0.455252
\(697\) −6331.66 −0.344087
\(698\) 11044.9 0.598935
\(699\) 3195.94 0.172935
\(700\) 2433.92 0.131419
\(701\) −21944.9 −1.18238 −0.591189 0.806533i \(-0.701341\pi\)
−0.591189 + 0.806533i \(0.701341\pi\)
\(702\) 15227.9 0.818720
\(703\) 14038.2 0.753144
\(704\) 46140.2 2.47014
\(705\) −8839.62 −0.472226
\(706\) 30945.6 1.64965
\(707\) 6222.83 0.331023
\(708\) 1903.65 0.101050
\(709\) −36958.0 −1.95767 −0.978834 0.204656i \(-0.934392\pi\)
−0.978834 + 0.204656i \(0.934392\pi\)
\(710\) 26186.7 1.38418
\(711\) −23340.8 −1.23115
\(712\) 21779.9 1.14640
\(713\) −671.099 −0.0352494
\(714\) −853.389 −0.0447301
\(715\) −27224.6 −1.42397
\(716\) 56022.0 2.92408
\(717\) −4409.54 −0.229675
\(718\) 40169.4 2.08789
\(719\) 5395.23 0.279845 0.139922 0.990162i \(-0.455315\pi\)
0.139922 + 0.990162i \(0.455315\pi\)
\(720\) −2764.02 −0.143068
\(721\) 7631.75 0.394204
\(722\) 23874.2 1.23062
\(723\) 3543.36 0.182267
\(724\) −32465.0 −1.66651
\(725\) −10768.5 −0.551629
\(726\) 13630.4 0.696795
\(727\) 9561.59 0.487785 0.243892 0.969802i \(-0.421576\pi\)
0.243892 + 0.969802i \(0.421576\pi\)
\(728\) 3276.54 0.166809
\(729\) −7509.02 −0.381497
\(730\) −4159.42 −0.210886
\(731\) 0 0
\(732\) −19395.6 −0.979347
\(733\) −13308.7 −0.670623 −0.335312 0.942107i \(-0.608842\pi\)
−0.335312 + 0.942107i \(0.608842\pi\)
\(734\) −8011.05 −0.402852
\(735\) −7409.40 −0.371836
\(736\) −511.239 −0.0256040
\(737\) 55147.7 2.75630
\(738\) 27500.5 1.37169
\(739\) 16167.3 0.804768 0.402384 0.915471i \(-0.368182\pi\)
0.402384 + 0.915471i \(0.368182\pi\)
\(740\) −57340.5 −2.84849
\(741\) 2627.03 0.130238
\(742\) 699.466 0.0346068
\(743\) 25680.2 1.26799 0.633994 0.773338i \(-0.281415\pi\)
0.633994 + 0.773338i \(0.281415\pi\)
\(744\) 9236.13 0.455125
\(745\) 35565.4 1.74901
\(746\) −9446.91 −0.463641
\(747\) −20025.0 −0.980828
\(748\) 17114.0 0.836562
\(749\) 718.821 0.0350669
\(750\) 8239.55 0.401154
\(751\) 12689.2 0.616559 0.308279 0.951296i \(-0.400247\pi\)
0.308279 + 0.951296i \(0.400247\pi\)
\(752\) 3424.42 0.166058
\(753\) 3853.63 0.186500
\(754\) −40646.2 −1.96319
\(755\) −17620.1 −0.849351
\(756\) 4800.00 0.230918
\(757\) −17431.3 −0.836926 −0.418463 0.908234i \(-0.637431\pi\)
−0.418463 + 0.908234i \(0.637431\pi\)
\(758\) 58576.5 2.80685
\(759\) −246.847 −0.0118050
\(760\) 10389.7 0.495886
\(761\) −16997.5 −0.809670 −0.404835 0.914390i \(-0.632671\pi\)
−0.404835 + 0.914390i \(0.632671\pi\)
\(762\) −12633.2 −0.600595
\(763\) −1911.89 −0.0907146
\(764\) 37217.5 1.76241
\(765\) −7778.15 −0.367607
\(766\) 13070.4 0.616516
\(767\) 3301.31 0.155415
\(768\) 5493.92 0.258131
\(769\) −29896.1 −1.40193 −0.700963 0.713198i \(-0.747246\pi\)
−0.700963 + 0.713198i \(0.747246\pi\)
\(770\) −14102.3 −0.660017
\(771\) −1523.19 −0.0711498
\(772\) −10470.8 −0.488152
\(773\) −18464.3 −0.859138 −0.429569 0.903034i \(-0.641335\pi\)
−0.429569 + 0.903034i \(0.641335\pi\)
\(774\) 0 0
\(775\) 11898.1 0.551475
\(776\) 22704.5 1.05032
\(777\) −2678.54 −0.123671
\(778\) 36198.0 1.66807
\(779\) 10096.4 0.464365
\(780\) −10730.4 −0.492577
\(781\) −24531.4 −1.12395
\(782\) −287.261 −0.0131361
\(783\) −21236.8 −0.969275
\(784\) 2870.36 0.130756
\(785\) −34229.8 −1.55632
\(786\) 441.785 0.0200483
\(787\) −7383.94 −0.334446 −0.167223 0.985919i \(-0.553480\pi\)
−0.167223 + 0.985919i \(0.553480\pi\)
\(788\) 17297.5 0.781975
\(789\) 8492.87 0.383212
\(790\) 57520.5 2.59049
\(791\) −4203.97 −0.188971
\(792\) −26510.5 −1.18940
\(793\) −33635.9 −1.50623
\(794\) 24444.3 1.09257
\(795\) −816.979 −0.0364469
\(796\) 12305.5 0.547934
\(797\) 23799.0 1.05772 0.528860 0.848709i \(-0.322620\pi\)
0.528860 + 0.848709i \(0.322620\pi\)
\(798\) 1360.80 0.0603658
\(799\) 9636.57 0.426680
\(800\) 9063.93 0.400573
\(801\) 26000.4 1.14691
\(802\) 52873.4 2.32796
\(803\) 3896.49 0.171238
\(804\) 21736.1 0.953451
\(805\) 144.041 0.00630657
\(806\) 44910.2 1.96265
\(807\) −757.348 −0.0330358
\(808\) −28828.4 −1.25517
\(809\) 2665.36 0.115833 0.0579166 0.998321i \(-0.481554\pi\)
0.0579166 + 0.998321i \(0.481554\pi\)
\(810\) 28899.0 1.25359
\(811\) 36736.8 1.59063 0.795317 0.606194i \(-0.207305\pi\)
0.795317 + 0.606194i \(0.207305\pi\)
\(812\) −12812.1 −0.553715
\(813\) −1508.16 −0.0650597
\(814\) 88273.9 3.80098
\(815\) −5314.16 −0.228401
\(816\) −386.140 −0.0165657
\(817\) 0 0
\(818\) 20927.2 0.894504
\(819\) 3911.46 0.166883
\(820\) −41239.8 −1.75629
\(821\) −13460.1 −0.572180 −0.286090 0.958203i \(-0.592356\pi\)
−0.286090 + 0.958203i \(0.592356\pi\)
\(822\) 1090.88 0.0462880
\(823\) −25589.3 −1.08382 −0.541912 0.840435i \(-0.682300\pi\)
−0.541912 + 0.840435i \(0.682300\pi\)
\(824\) −35355.5 −1.49474
\(825\) 4376.43 0.184688
\(826\) 1710.08 0.0720355
\(827\) 24201.4 1.01761 0.508807 0.860881i \(-0.330087\pi\)
0.508807 + 0.860881i \(0.330087\pi\)
\(828\) 759.222 0.0318657
\(829\) 15933.9 0.667560 0.333780 0.942651i \(-0.391676\pi\)
0.333780 + 0.942651i \(0.391676\pi\)
\(830\) 49349.2 2.06378
\(831\) 3902.95 0.162926
\(832\) 31538.0 1.31416
\(833\) 8077.41 0.335973
\(834\) 8046.38 0.334081
\(835\) −22751.6 −0.942935
\(836\) −27289.7 −1.12899
\(837\) 23464.7 0.969006
\(838\) −14953.2 −0.616406
\(839\) 23536.8 0.968512 0.484256 0.874926i \(-0.339090\pi\)
0.484256 + 0.874926i \(0.339090\pi\)
\(840\) −1982.40 −0.0814275
\(841\) 32296.1 1.32421
\(842\) 1094.33 0.0447898
\(843\) 10493.1 0.428709
\(844\) −11728.3 −0.478323
\(845\) 10056.0 0.409394
\(846\) −41854.7 −1.70094
\(847\) 7450.91 0.302263
\(848\) 316.493 0.0128165
\(849\) −1971.27 −0.0796864
\(850\) 5092.94 0.205513
\(851\) −901.629 −0.0363190
\(852\) −9668.90 −0.388792
\(853\) 14346.0 0.575845 0.287923 0.957654i \(-0.407035\pi\)
0.287923 + 0.957654i \(0.407035\pi\)
\(854\) −17423.4 −0.698145
\(855\) 12402.9 0.496107
\(856\) −3330.07 −0.132967
\(857\) −25049.7 −0.998462 −0.499231 0.866469i \(-0.666384\pi\)
−0.499231 + 0.866469i \(0.666384\pi\)
\(858\) 16519.1 0.657288
\(859\) 26179.1 1.03983 0.519917 0.854217i \(-0.325963\pi\)
0.519917 + 0.854217i \(0.325963\pi\)
\(860\) 0 0
\(861\) −1926.43 −0.0762516
\(862\) 74181.7 2.93113
\(863\) −10987.8 −0.433404 −0.216702 0.976238i \(-0.569530\pi\)
−0.216702 + 0.976238i \(0.569530\pi\)
\(864\) 17875.3 0.703852
\(865\) −15425.6 −0.606342
\(866\) −28163.0 −1.10510
\(867\) 7517.42 0.294469
\(868\) 14156.2 0.553561
\(869\) −53884.4 −2.10346
\(870\) 24592.0 0.958331
\(871\) 37694.8 1.46641
\(872\) 8857.20 0.343971
\(873\) 27104.1 1.05078
\(874\) 458.062 0.0177279
\(875\) 4504.05 0.174017
\(876\) 1535.78 0.0592341
\(877\) 43452.2 1.67306 0.836531 0.547919i \(-0.184580\pi\)
0.836531 + 0.547919i \(0.184580\pi\)
\(878\) 20054.9 0.770865
\(879\) −11308.1 −0.433917
\(880\) −6381.00 −0.244436
\(881\) −10548.4 −0.403389 −0.201694 0.979449i \(-0.564645\pi\)
−0.201694 + 0.979449i \(0.564645\pi\)
\(882\) −35082.8 −1.33934
\(883\) −12217.7 −0.465637 −0.232818 0.972520i \(-0.574795\pi\)
−0.232818 + 0.972520i \(0.574795\pi\)
\(884\) 11697.8 0.445068
\(885\) −1997.38 −0.0758658
\(886\) 61513.5 2.33249
\(887\) 39821.5 1.50741 0.753706 0.657212i \(-0.228264\pi\)
0.753706 + 0.657212i \(0.228264\pi\)
\(888\) 12408.9 0.468934
\(889\) −6905.80 −0.260532
\(890\) −64074.6 −2.41324
\(891\) −27072.2 −1.01790
\(892\) 54362.4 2.04057
\(893\) −15366.4 −0.575829
\(894\) −21580.1 −0.807322
\(895\) −58780.3 −2.19532
\(896\) 9398.77 0.350436
\(897\) −168.726 −0.00628049
\(898\) 16622.6 0.617710
\(899\) −62631.6 −2.32356
\(900\) −13460.5 −0.498537
\(901\) 890.635 0.0329316
\(902\) 63487.4 2.34357
\(903\) 0 0
\(904\) 19475.6 0.716538
\(905\) 34063.4 1.25117
\(906\) 10691.4 0.392049
\(907\) −32895.0 −1.20426 −0.602128 0.798399i \(-0.705680\pi\)
−0.602128 + 0.798399i \(0.705680\pi\)
\(908\) −16086.5 −0.587938
\(909\) −34414.6 −1.25573
\(910\) −9639.29 −0.351142
\(911\) 14491.2 0.527019 0.263509 0.964657i \(-0.415120\pi\)
0.263509 + 0.964657i \(0.415120\pi\)
\(912\) 615.734 0.0223563
\(913\) −46229.7 −1.67577
\(914\) −43645.2 −1.57949
\(915\) 20350.6 0.735267
\(916\) 33833.3 1.22040
\(917\) 241.496 0.00869675
\(918\) 10043.9 0.361110
\(919\) 3819.84 0.137111 0.0685554 0.997647i \(-0.478161\pi\)
0.0685554 + 0.997647i \(0.478161\pi\)
\(920\) −667.298 −0.0239132
\(921\) −13835.5 −0.495000
\(922\) −28873.9 −1.03136
\(923\) −16767.8 −0.597962
\(924\) 5206.99 0.185387
\(925\) 15985.3 0.568208
\(926\) −37832.8 −1.34262
\(927\) −42206.5 −1.49541
\(928\) −47712.4 −1.68775
\(929\) −6597.01 −0.232983 −0.116491 0.993192i \(-0.537165\pi\)
−0.116491 + 0.993192i \(0.537165\pi\)
\(930\) −27171.8 −0.958064
\(931\) −12880.1 −0.453415
\(932\) −22692.7 −0.797559
\(933\) −6871.16 −0.241106
\(934\) 53784.6 1.88425
\(935\) −17956.6 −0.628068
\(936\) −18120.5 −0.632787
\(937\) 22841.5 0.796370 0.398185 0.917305i \(-0.369640\pi\)
0.398185 + 0.917305i \(0.369640\pi\)
\(938\) 19525.9 0.679685
\(939\) 12714.1 0.441862
\(940\) 62765.6 2.17786
\(941\) 36677.3 1.27061 0.635306 0.772261i \(-0.280874\pi\)
0.635306 + 0.772261i \(0.280874\pi\)
\(942\) 20769.7 0.718378
\(943\) −648.460 −0.0223932
\(944\) 773.775 0.0266782
\(945\) −5036.34 −0.173367
\(946\) 0 0
\(947\) −19733.4 −0.677138 −0.338569 0.940942i \(-0.609943\pi\)
−0.338569 + 0.940942i \(0.609943\pi\)
\(948\) −21238.2 −0.727622
\(949\) 2663.34 0.0911020
\(950\) −8121.13 −0.277352
\(951\) 10450.4 0.356338
\(952\) 2161.12 0.0735739
\(953\) 12496.6 0.424768 0.212384 0.977186i \(-0.431877\pi\)
0.212384 + 0.977186i \(0.431877\pi\)
\(954\) −3868.32 −0.131280
\(955\) −39050.0 −1.32317
\(956\) 31309.9 1.05924
\(957\) −23037.5 −0.778157
\(958\) 24021.1 0.810111
\(959\) 596.315 0.0200793
\(960\) −19081.3 −0.641507
\(961\) 39411.0 1.32291
\(962\) 60337.4 2.02220
\(963\) −3975.35 −0.133026
\(964\) −25159.6 −0.840597
\(965\) 10986.4 0.366491
\(966\) −87.4002 −0.00291103
\(967\) −1702.88 −0.0566297 −0.0283149 0.999599i \(-0.509014\pi\)
−0.0283149 + 0.999599i \(0.509014\pi\)
\(968\) −34517.7 −1.14612
\(969\) 1732.72 0.0574437
\(970\) −66794.6 −2.21097
\(971\) −3923.91 −0.129685 −0.0648426 0.997896i \(-0.520655\pi\)
−0.0648426 + 0.997896i \(0.520655\pi\)
\(972\) −40618.0 −1.34035
\(973\) 4398.45 0.144921
\(974\) −48787.5 −1.60498
\(975\) 2991.40 0.0982579
\(976\) −7883.71 −0.258557
\(977\) −24540.8 −0.803614 −0.401807 0.915724i \(-0.631618\pi\)
−0.401807 + 0.915724i \(0.631618\pi\)
\(978\) 3224.49 0.105427
\(979\) 60024.2 1.95953
\(980\) 52610.3 1.71487
\(981\) 10573.5 0.344124
\(982\) 11115.8 0.361220
\(983\) −10646.8 −0.345453 −0.172727 0.984970i \(-0.555258\pi\)
−0.172727 + 0.984970i \(0.555258\pi\)
\(984\) 8924.56 0.289131
\(985\) −18149.1 −0.587085
\(986\) −26809.2 −0.865900
\(987\) 2931.96 0.0945547
\(988\) −18653.2 −0.600645
\(989\) 0 0
\(990\) 77991.3 2.50376
\(991\) −68.7730 −0.00220449 −0.00110224 0.999999i \(-0.500351\pi\)
−0.00110224 + 0.999999i \(0.500351\pi\)
\(992\) 52717.6 1.68729
\(993\) −12981.8 −0.414869
\(994\) −8685.72 −0.277157
\(995\) −12911.3 −0.411373
\(996\) −18221.2 −0.579678
\(997\) −56204.3 −1.78536 −0.892682 0.450686i \(-0.851179\pi\)
−0.892682 + 0.450686i \(0.851179\pi\)
\(998\) 39531.0 1.25384
\(999\) 31525.1 0.998407
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.1.8 50
43.42 odd 2 1849.4.a.j.1.43 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.8 50 1.1 even 1 trivial
1849.4.a.j.1.43 yes 50 43.42 odd 2