Properties

Label 1849.4.a.j.1.40
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.40
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.53489 q^{2} -7.81725 q^{3} +4.49548 q^{4} -1.07981 q^{5} -27.6332 q^{6} +33.3014 q^{7} -12.3881 q^{8} +34.1094 q^{9} +O(q^{10})\) \(q+3.53489 q^{2} -7.81725 q^{3} +4.49548 q^{4} -1.07981 q^{5} -27.6332 q^{6} +33.3014 q^{7} -12.3881 q^{8} +34.1094 q^{9} -3.81700 q^{10} -6.35516 q^{11} -35.1423 q^{12} +16.4672 q^{13} +117.717 q^{14} +8.44112 q^{15} -79.7545 q^{16} +8.35561 q^{17} +120.573 q^{18} -141.509 q^{19} -4.85424 q^{20} -260.325 q^{21} -22.4648 q^{22} +123.588 q^{23} +96.8411 q^{24} -123.834 q^{25} +58.2100 q^{26} -55.5761 q^{27} +149.706 q^{28} +54.4135 q^{29} +29.8385 q^{30} -253.413 q^{31} -182.819 q^{32} +49.6799 q^{33} +29.5362 q^{34} -35.9591 q^{35} +153.338 q^{36} +246.339 q^{37} -500.219 q^{38} -128.729 q^{39} +13.3768 q^{40} +492.491 q^{41} -920.222 q^{42} -28.5695 q^{44} -36.8316 q^{45} +436.871 q^{46} -335.420 q^{47} +623.461 q^{48} +765.982 q^{49} -437.740 q^{50} -65.3179 q^{51} +74.0281 q^{52} +386.753 q^{53} -196.456 q^{54} +6.86235 q^{55} -412.542 q^{56} +1106.21 q^{57} +192.346 q^{58} -480.563 q^{59} +37.9468 q^{60} +264.683 q^{61} -895.789 q^{62} +1135.89 q^{63} -8.20876 q^{64} -17.7814 q^{65} +175.613 q^{66} -308.944 q^{67} +37.5624 q^{68} -966.120 q^{69} -127.111 q^{70} +67.5365 q^{71} -422.552 q^{72} -835.918 q^{73} +870.782 q^{74} +968.042 q^{75} -636.150 q^{76} -211.636 q^{77} -455.042 q^{78} -17.9914 q^{79} +86.1195 q^{80} -486.502 q^{81} +1740.90 q^{82} +1011.82 q^{83} -1170.29 q^{84} -9.02244 q^{85} -425.364 q^{87} +78.7286 q^{88} -1240.09 q^{89} -130.196 q^{90} +548.382 q^{91} +555.588 q^{92} +1980.99 q^{93} -1185.67 q^{94} +152.802 q^{95} +1429.14 q^{96} -287.048 q^{97} +2707.67 q^{98} -216.771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q + 10q^{2} + 2q^{3} + 186q^{4} - 8q^{5} - 51q^{6} + 6q^{7} + 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} + 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} + 386q^{18} - 12q^{19} - 108q^{20} - 408q^{21} - 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} - 1493q^{26} - 10q^{27} + 242q^{28} - 208q^{29} + 48q^{30} - 932q^{31} + 1124q^{32} - 254q^{33} - 765q^{34} - 1452q^{35} + 747q^{36} + 90q^{37} - 1213q^{38} + 1610q^{39} - 1693q^{40} - 1354q^{41} + 16q^{42} - 2704q^{44} - 4508q^{45} - 233q^{46} - 3484q^{47} + 376q^{48} + 1324q^{49} + 408q^{50} - 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} + 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} - 1172q^{61} + 1546q^{62} + 3686q^{63} + 606q^{64} - 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} - 136q^{69} + 1310q^{70} - 162q^{71} + 5814q^{72} - 746q^{73} - 4332q^{74} - 236q^{75} - 1338q^{76} - 2024q^{77} - 2782q^{78} - 2656q^{79} + 5713q^{80} - 86q^{81} + 4168q^{82} - 3514q^{83} - 4269q^{84} + 7558q^{85} - 10278q^{87} - 11692q^{88} - 2640q^{89} - 8286q^{90} + 5946q^{91} - 4271q^{92} + 2q^{93} - 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} + 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.53489 1.24977 0.624887 0.780715i \(-0.285145\pi\)
0.624887 + 0.780715i \(0.285145\pi\)
\(3\) −7.81725 −1.50443 −0.752215 0.658917i \(-0.771015\pi\)
−0.752215 + 0.658917i \(0.771015\pi\)
\(4\) 4.49548 0.561934
\(5\) −1.07981 −0.0965809 −0.0482904 0.998833i \(-0.515377\pi\)
−0.0482904 + 0.998833i \(0.515377\pi\)
\(6\) −27.6332 −1.88020
\(7\) 33.3014 1.79811 0.899053 0.437840i \(-0.144256\pi\)
0.899053 + 0.437840i \(0.144256\pi\)
\(8\) −12.3881 −0.547483
\(9\) 34.1094 1.26331
\(10\) −3.81700 −0.120704
\(11\) −6.35516 −0.174196 −0.0870979 0.996200i \(-0.527759\pi\)
−0.0870979 + 0.996200i \(0.527759\pi\)
\(12\) −35.1423 −0.845391
\(13\) 16.4672 0.351323 0.175661 0.984451i \(-0.443794\pi\)
0.175661 + 0.984451i \(0.443794\pi\)
\(14\) 117.717 2.24723
\(15\) 8.44112 0.145299
\(16\) −79.7545 −1.24616
\(17\) 8.35561 0.119208 0.0596039 0.998222i \(-0.481016\pi\)
0.0596039 + 0.998222i \(0.481016\pi\)
\(18\) 120.573 1.57885
\(19\) −141.509 −1.70865 −0.854326 0.519738i \(-0.826030\pi\)
−0.854326 + 0.519738i \(0.826030\pi\)
\(20\) −4.85424 −0.0542721
\(21\) −260.325 −2.70513
\(22\) −22.4648 −0.217705
\(23\) 123.588 1.12043 0.560216 0.828347i \(-0.310718\pi\)
0.560216 + 0.828347i \(0.310718\pi\)
\(24\) 96.8411 0.823650
\(25\) −123.834 −0.990672
\(26\) 58.2100 0.439074
\(27\) −55.5761 −0.396134
\(28\) 149.706 1.01042
\(29\) 54.4135 0.348425 0.174213 0.984708i \(-0.444262\pi\)
0.174213 + 0.984708i \(0.444262\pi\)
\(30\) 29.8385 0.181591
\(31\) −253.413 −1.46820 −0.734102 0.679039i \(-0.762397\pi\)
−0.734102 + 0.679039i \(0.762397\pi\)
\(32\) −182.819 −1.00994
\(33\) 49.6799 0.262066
\(34\) 29.5362 0.148983
\(35\) −35.9591 −0.173663
\(36\) 153.338 0.709898
\(37\) 246.339 1.09454 0.547269 0.836957i \(-0.315668\pi\)
0.547269 + 0.836957i \(0.315668\pi\)
\(38\) −500.219 −2.13543
\(39\) −128.729 −0.528540
\(40\) 13.3768 0.0528764
\(41\) 492.491 1.87596 0.937978 0.346695i \(-0.112696\pi\)
0.937978 + 0.346695i \(0.112696\pi\)
\(42\) −920.222 −3.38079
\(43\) 0 0
\(44\) −28.5695 −0.0978866
\(45\) −36.8316 −0.122012
\(46\) 436.871 1.40029
\(47\) −335.420 −1.04098 −0.520489 0.853868i \(-0.674250\pi\)
−0.520489 + 0.853868i \(0.674250\pi\)
\(48\) 623.461 1.87477
\(49\) 765.982 2.23318
\(50\) −437.740 −1.23812
\(51\) −65.3179 −0.179340
\(52\) 74.0281 0.197420
\(53\) 386.753 1.00235 0.501176 0.865345i \(-0.332901\pi\)
0.501176 + 0.865345i \(0.332901\pi\)
\(54\) −196.456 −0.495078
\(55\) 6.86235 0.0168240
\(56\) −412.542 −0.984432
\(57\) 1106.21 2.57055
\(58\) 192.346 0.435452
\(59\) −480.563 −1.06041 −0.530203 0.847871i \(-0.677884\pi\)
−0.530203 + 0.847871i \(0.677884\pi\)
\(60\) 37.9468 0.0816486
\(61\) 264.683 0.555560 0.277780 0.960645i \(-0.410401\pi\)
0.277780 + 0.960645i \(0.410401\pi\)
\(62\) −895.789 −1.83492
\(63\) 1135.89 2.27157
\(64\) −8.20876 −0.0160327
\(65\) −17.7814 −0.0339310
\(66\) 175.613 0.327523
\(67\) −308.944 −0.563337 −0.281668 0.959512i \(-0.590888\pi\)
−0.281668 + 0.959512i \(0.590888\pi\)
\(68\) 37.5624 0.0669869
\(69\) −966.120 −1.68561
\(70\) −127.111 −0.217039
\(71\) 67.5365 0.112889 0.0564444 0.998406i \(-0.482024\pi\)
0.0564444 + 0.998406i \(0.482024\pi\)
\(72\) −422.552 −0.691642
\(73\) −835.918 −1.34023 −0.670115 0.742257i \(-0.733755\pi\)
−0.670115 + 0.742257i \(0.733755\pi\)
\(74\) 870.782 1.36792
\(75\) 968.042 1.49040
\(76\) −636.150 −0.960150
\(77\) −211.636 −0.313223
\(78\) −455.042 −0.660556
\(79\) −17.9914 −0.0256226 −0.0128113 0.999918i \(-0.504078\pi\)
−0.0128113 + 0.999918i \(0.504078\pi\)
\(80\) 86.1195 0.120356
\(81\) −486.502 −0.667355
\(82\) 1740.90 2.34452
\(83\) 1011.82 1.33809 0.669046 0.743221i \(-0.266703\pi\)
0.669046 + 0.743221i \(0.266703\pi\)
\(84\) −1170.29 −1.52010
\(85\) −9.02244 −0.0115132
\(86\) 0 0
\(87\) −425.364 −0.524181
\(88\) 78.7286 0.0953692
\(89\) −1240.09 −1.47696 −0.738480 0.674276i \(-0.764456\pi\)
−0.738480 + 0.674276i \(0.764456\pi\)
\(90\) −130.196 −0.152487
\(91\) 548.382 0.631715
\(92\) 555.588 0.629609
\(93\) 1980.99 2.20881
\(94\) −1185.67 −1.30099
\(95\) 152.802 0.165023
\(96\) 1429.14 1.51939
\(97\) −287.048 −0.300467 −0.150233 0.988651i \(-0.548002\pi\)
−0.150233 + 0.988651i \(0.548002\pi\)
\(98\) 2707.67 2.79098
\(99\) −216.771 −0.220064
\(100\) −556.693 −0.556693
\(101\) 182.090 0.179392 0.0896960 0.995969i \(-0.471410\pi\)
0.0896960 + 0.995969i \(0.471410\pi\)
\(102\) −230.892 −0.224134
\(103\) −1002.89 −0.959398 −0.479699 0.877433i \(-0.659254\pi\)
−0.479699 + 0.877433i \(0.659254\pi\)
\(104\) −203.998 −0.192343
\(105\) 281.101 0.261263
\(106\) 1367.13 1.25271
\(107\) −574.209 −0.518793 −0.259397 0.965771i \(-0.583524\pi\)
−0.259397 + 0.965771i \(0.583524\pi\)
\(108\) −249.841 −0.222601
\(109\) −817.925 −0.718743 −0.359372 0.933195i \(-0.617009\pi\)
−0.359372 + 0.933195i \(0.617009\pi\)
\(110\) 24.2577 0.0210262
\(111\) −1925.69 −1.64666
\(112\) −2655.94 −2.24073
\(113\) −1835.80 −1.52830 −0.764148 0.645040i \(-0.776841\pi\)
−0.764148 + 0.645040i \(0.776841\pi\)
\(114\) 3910.34 3.21260
\(115\) −133.451 −0.108212
\(116\) 244.614 0.195792
\(117\) 561.688 0.443830
\(118\) −1698.74 −1.32527
\(119\) 278.253 0.214348
\(120\) −104.570 −0.0795488
\(121\) −1290.61 −0.969656
\(122\) 935.626 0.694324
\(123\) −3849.93 −2.82225
\(124\) −1139.21 −0.825035
\(125\) 268.693 0.192261
\(126\) 4015.25 2.83895
\(127\) −2487.57 −1.73808 −0.869040 0.494742i \(-0.835263\pi\)
−0.869040 + 0.494742i \(0.835263\pi\)
\(128\) 1433.53 0.989903
\(129\) 0 0
\(130\) −62.8555 −0.0424061
\(131\) 1043.93 0.696250 0.348125 0.937448i \(-0.386818\pi\)
0.348125 + 0.937448i \(0.386818\pi\)
\(132\) 223.335 0.147264
\(133\) −4712.44 −3.07234
\(134\) −1092.09 −0.704044
\(135\) 60.0114 0.0382590
\(136\) −103.510 −0.0652642
\(137\) 1036.27 0.646238 0.323119 0.946358i \(-0.395269\pi\)
0.323119 + 0.946358i \(0.395269\pi\)
\(138\) −3415.13 −2.10663
\(139\) −2253.15 −1.37489 −0.687444 0.726237i \(-0.741267\pi\)
−0.687444 + 0.726237i \(0.741267\pi\)
\(140\) −161.653 −0.0975870
\(141\) 2622.06 1.56608
\(142\) 238.734 0.141085
\(143\) −104.652 −0.0611989
\(144\) −2720.38 −1.57429
\(145\) −58.7560 −0.0336512
\(146\) −2954.88 −1.67498
\(147\) −5987.88 −3.35967
\(148\) 1107.41 0.615058
\(149\) 326.948 0.179763 0.0898813 0.995952i \(-0.471351\pi\)
0.0898813 + 0.995952i \(0.471351\pi\)
\(150\) 3421.92 1.86266
\(151\) 1201.25 0.647393 0.323696 0.946161i \(-0.395074\pi\)
0.323696 + 0.946161i \(0.395074\pi\)
\(152\) 1753.03 0.935457
\(153\) 285.005 0.150597
\(154\) −748.110 −0.391457
\(155\) 273.637 0.141800
\(156\) −578.696 −0.297005
\(157\) −446.815 −0.227132 −0.113566 0.993530i \(-0.536227\pi\)
−0.113566 + 0.993530i \(0.536227\pi\)
\(158\) −63.5976 −0.0320225
\(159\) −3023.35 −1.50797
\(160\) 197.409 0.0975409
\(161\) 4115.66 2.01465
\(162\) −1719.73 −0.834043
\(163\) 2436.57 1.17084 0.585420 0.810730i \(-0.300930\pi\)
0.585420 + 0.810730i \(0.300930\pi\)
\(164\) 2213.98 1.05416
\(165\) −53.6447 −0.0253105
\(166\) 3576.68 1.67231
\(167\) −941.174 −0.436109 −0.218055 0.975937i \(-0.569971\pi\)
−0.218055 + 0.975937i \(0.569971\pi\)
\(168\) 3224.94 1.48101
\(169\) −1925.83 −0.876572
\(170\) −31.8934 −0.0143889
\(171\) −4826.79 −2.15856
\(172\) 0 0
\(173\) −3622.60 −1.59203 −0.796015 0.605276i \(-0.793063\pi\)
−0.796015 + 0.605276i \(0.793063\pi\)
\(174\) −1503.62 −0.655108
\(175\) −4123.84 −1.78133
\(176\) 506.853 0.217077
\(177\) 3756.68 1.59531
\(178\) −4383.59 −1.84587
\(179\) −1272.84 −0.531490 −0.265745 0.964043i \(-0.585618\pi\)
−0.265745 + 0.964043i \(0.585618\pi\)
\(180\) −165.575 −0.0685626
\(181\) 388.903 0.159707 0.0798535 0.996807i \(-0.474555\pi\)
0.0798535 + 0.996807i \(0.474555\pi\)
\(182\) 1938.47 0.789501
\(183\) −2069.09 −0.835802
\(184\) −1531.03 −0.613417
\(185\) −265.998 −0.105711
\(186\) 7002.61 2.76052
\(187\) −53.1013 −0.0207655
\(188\) −1507.87 −0.584961
\(189\) −1850.76 −0.712291
\(190\) 540.140 0.206241
\(191\) −1090.91 −0.413273 −0.206637 0.978418i \(-0.566252\pi\)
−0.206637 + 0.978418i \(0.566252\pi\)
\(192\) 64.1699 0.0241201
\(193\) −1563.18 −0.583006 −0.291503 0.956570i \(-0.594155\pi\)
−0.291503 + 0.956570i \(0.594155\pi\)
\(194\) −1014.68 −0.375515
\(195\) 139.002 0.0510469
\(196\) 3443.45 1.25490
\(197\) 1743.94 0.630714 0.315357 0.948973i \(-0.397876\pi\)
0.315357 + 0.948973i \(0.397876\pi\)
\(198\) −766.262 −0.275030
\(199\) −2681.34 −0.955153 −0.477576 0.878590i \(-0.658485\pi\)
−0.477576 + 0.878590i \(0.658485\pi\)
\(200\) 1534.07 0.542376
\(201\) 2415.10 0.847501
\(202\) 643.668 0.224199
\(203\) 1812.04 0.626505
\(204\) −293.635 −0.100777
\(205\) −531.795 −0.181181
\(206\) −3545.12 −1.19903
\(207\) 4215.52 1.41545
\(208\) −1313.34 −0.437806
\(209\) 899.313 0.297640
\(210\) 993.662 0.326520
\(211\) 1214.47 0.396246 0.198123 0.980177i \(-0.436515\pi\)
0.198123 + 0.980177i \(0.436515\pi\)
\(212\) 1738.64 0.563256
\(213\) −527.949 −0.169833
\(214\) −2029.77 −0.648374
\(215\) 0 0
\(216\) 688.484 0.216877
\(217\) −8439.01 −2.63999
\(218\) −2891.28 −0.898267
\(219\) 6534.58 2.01628
\(220\) 30.8495 0.00945397
\(221\) 137.594 0.0418804
\(222\) −6807.12 −2.05795
\(223\) 1371.11 0.411733 0.205866 0.978580i \(-0.433999\pi\)
0.205866 + 0.978580i \(0.433999\pi\)
\(224\) −6088.12 −1.81598
\(225\) −4223.91 −1.25153
\(226\) −6489.36 −1.91003
\(227\) −6269.63 −1.83317 −0.916586 0.399837i \(-0.869067\pi\)
−0.916586 + 0.399837i \(0.869067\pi\)
\(228\) 4972.94 1.44448
\(229\) 2566.13 0.740502 0.370251 0.928932i \(-0.379272\pi\)
0.370251 + 0.928932i \(0.379272\pi\)
\(230\) −471.736 −0.135241
\(231\) 1654.41 0.471222
\(232\) −674.081 −0.190757
\(233\) −2868.19 −0.806443 −0.403222 0.915102i \(-0.632110\pi\)
−0.403222 + 0.915102i \(0.632110\pi\)
\(234\) 1985.51 0.554687
\(235\) 362.188 0.100539
\(236\) −2160.36 −0.595879
\(237\) 140.643 0.0385475
\(238\) 983.596 0.267887
\(239\) −2256.13 −0.610614 −0.305307 0.952254i \(-0.598759\pi\)
−0.305307 + 0.952254i \(0.598759\pi\)
\(240\) −673.217 −0.181067
\(241\) 3471.87 0.927978 0.463989 0.885841i \(-0.346418\pi\)
0.463989 + 0.885841i \(0.346418\pi\)
\(242\) −4562.18 −1.21185
\(243\) 5303.66 1.40012
\(244\) 1189.88 0.312188
\(245\) −827.113 −0.215683
\(246\) −13609.1 −3.52717
\(247\) −2330.26 −0.600288
\(248\) 3139.31 0.803817
\(249\) −7909.65 −2.01307
\(250\) 949.800 0.240283
\(251\) 1420.71 0.357268 0.178634 0.983916i \(-0.442832\pi\)
0.178634 + 0.983916i \(0.442832\pi\)
\(252\) 5106.37 1.27647
\(253\) −785.423 −0.195174
\(254\) −8793.30 −2.17221
\(255\) 70.5307 0.0173208
\(256\) 5133.06 1.25319
\(257\) 2942.79 0.714265 0.357132 0.934054i \(-0.383754\pi\)
0.357132 + 0.934054i \(0.383754\pi\)
\(258\) 0 0
\(259\) 8203.43 1.96809
\(260\) −79.9361 −0.0190670
\(261\) 1856.01 0.440169
\(262\) 3690.19 0.870155
\(263\) 6616.80 1.55137 0.775684 0.631122i \(-0.217405\pi\)
0.775684 + 0.631122i \(0.217405\pi\)
\(264\) −615.441 −0.143476
\(265\) −417.619 −0.0968080
\(266\) −16658.0 −3.83972
\(267\) 9694.10 2.22198
\(268\) −1388.85 −0.316558
\(269\) −4982.02 −1.12922 −0.564608 0.825359i \(-0.690973\pi\)
−0.564608 + 0.825359i \(0.690973\pi\)
\(270\) 212.134 0.0478151
\(271\) 677.961 0.151967 0.0759837 0.997109i \(-0.475790\pi\)
0.0759837 + 0.997109i \(0.475790\pi\)
\(272\) −666.397 −0.148552
\(273\) −4286.84 −0.950372
\(274\) 3663.11 0.807651
\(275\) 786.986 0.172571
\(276\) −4343.17 −0.947203
\(277\) −1893.18 −0.410651 −0.205326 0.978694i \(-0.565825\pi\)
−0.205326 + 0.978694i \(0.565825\pi\)
\(278\) −7964.64 −1.71830
\(279\) −8643.78 −1.85480
\(280\) 445.465 0.0950773
\(281\) −2436.21 −0.517196 −0.258598 0.965985i \(-0.583261\pi\)
−0.258598 + 0.965985i \(0.583261\pi\)
\(282\) 9268.70 1.95724
\(283\) −3181.08 −0.668181 −0.334091 0.942541i \(-0.608429\pi\)
−0.334091 + 0.942541i \(0.608429\pi\)
\(284\) 303.608 0.0634361
\(285\) −1194.49 −0.248266
\(286\) −369.934 −0.0764848
\(287\) 16400.6 3.37317
\(288\) −6235.84 −1.27587
\(289\) −4843.18 −0.985790
\(290\) −207.696 −0.0420564
\(291\) 2243.92 0.452031
\(292\) −3757.85 −0.753121
\(293\) −3835.76 −0.764804 −0.382402 0.923996i \(-0.624903\pi\)
−0.382402 + 0.923996i \(0.624903\pi\)
\(294\) −21166.5 −4.19883
\(295\) 518.915 0.102415
\(296\) −3051.68 −0.599240
\(297\) 353.195 0.0690049
\(298\) 1155.73 0.224662
\(299\) 2035.16 0.393633
\(300\) 4351.81 0.837506
\(301\) 0 0
\(302\) 4246.29 0.809095
\(303\) −1423.44 −0.269883
\(304\) 11286.0 2.12926
\(305\) −285.806 −0.0536565
\(306\) 1007.46 0.188212
\(307\) −1959.51 −0.364284 −0.182142 0.983272i \(-0.558303\pi\)
−0.182142 + 0.983272i \(0.558303\pi\)
\(308\) −951.403 −0.176011
\(309\) 7839.87 1.44335
\(310\) 967.279 0.177219
\(311\) −499.497 −0.0910735 −0.0455368 0.998963i \(-0.514500\pi\)
−0.0455368 + 0.998963i \(0.514500\pi\)
\(312\) 1594.71 0.289367
\(313\) 2114.30 0.381812 0.190906 0.981608i \(-0.438857\pi\)
0.190906 + 0.981608i \(0.438857\pi\)
\(314\) −1579.44 −0.283863
\(315\) −1226.54 −0.219390
\(316\) −80.8798 −0.0143982
\(317\) −5233.27 −0.927223 −0.463611 0.886039i \(-0.653447\pi\)
−0.463611 + 0.886039i \(0.653447\pi\)
\(318\) −10687.2 −1.88462
\(319\) −345.806 −0.0606942
\(320\) 8.86387 0.00154845
\(321\) 4488.74 0.780489
\(322\) 14548.4 2.51786
\(323\) −1182.39 −0.203685
\(324\) −2187.06 −0.375010
\(325\) −2039.21 −0.348045
\(326\) 8613.01 1.46328
\(327\) 6393.93 1.08130
\(328\) −6101.04 −1.02705
\(329\) −11169.9 −1.87179
\(330\) −189.628 −0.0316324
\(331\) 1835.50 0.304798 0.152399 0.988319i \(-0.451300\pi\)
0.152399 + 0.988319i \(0.451300\pi\)
\(332\) 4548.61 0.751920
\(333\) 8402.48 1.38274
\(334\) −3326.95 −0.545038
\(335\) 333.600 0.0544076
\(336\) 20762.1 3.37103
\(337\) −579.996 −0.0937519 −0.0468759 0.998901i \(-0.514927\pi\)
−0.0468759 + 0.998901i \(0.514927\pi\)
\(338\) −6807.60 −1.09552
\(339\) 14350.9 2.29922
\(340\) −40.5602 −0.00646966
\(341\) 1610.48 0.255755
\(342\) −17062.2 −2.69771
\(343\) 14085.9 2.21740
\(344\) 0 0
\(345\) 1043.22 0.162798
\(346\) −12805.5 −1.98968
\(347\) 21.1393 0.00327037 0.00163518 0.999999i \(-0.499480\pi\)
0.00163518 + 0.999999i \(0.499480\pi\)
\(348\) −1912.21 −0.294555
\(349\) 6876.17 1.05465 0.527325 0.849664i \(-0.323195\pi\)
0.527325 + 0.849664i \(0.323195\pi\)
\(350\) −14577.4 −2.22626
\(351\) −915.185 −0.139171
\(352\) 1161.84 0.175927
\(353\) −7977.84 −1.20288 −0.601442 0.798917i \(-0.705407\pi\)
−0.601442 + 0.798917i \(0.705407\pi\)
\(354\) 13279.5 1.99377
\(355\) −72.9263 −0.0109029
\(356\) −5574.80 −0.829954
\(357\) −2175.18 −0.322472
\(358\) −4499.36 −0.664242
\(359\) −8138.55 −1.19648 −0.598240 0.801317i \(-0.704133\pi\)
−0.598240 + 0.801317i \(0.704133\pi\)
\(360\) 456.274 0.0667993
\(361\) 13165.8 1.91949
\(362\) 1374.73 0.199598
\(363\) 10089.0 1.45878
\(364\) 2465.24 0.354982
\(365\) 902.630 0.129441
\(366\) −7314.02 −1.04456
\(367\) −318.114 −0.0452464 −0.0226232 0.999744i \(-0.507202\pi\)
−0.0226232 + 0.999744i \(0.507202\pi\)
\(368\) −9856.71 −1.39624
\(369\) 16798.6 2.36992
\(370\) −940.276 −0.132115
\(371\) 12879.4 1.80234
\(372\) 8905.51 1.24121
\(373\) 337.098 0.0467943 0.0233972 0.999726i \(-0.492552\pi\)
0.0233972 + 0.999726i \(0.492552\pi\)
\(374\) −187.707 −0.0259522
\(375\) −2100.44 −0.289243
\(376\) 4155.22 0.569918
\(377\) 896.040 0.122410
\(378\) −6542.24 −0.890203
\(379\) −1600.93 −0.216976 −0.108488 0.994098i \(-0.534601\pi\)
−0.108488 + 0.994098i \(0.534601\pi\)
\(380\) 686.919 0.0927321
\(381\) 19446.0 2.61482
\(382\) −3856.24 −0.516498
\(383\) −3960.47 −0.528383 −0.264191 0.964470i \(-0.585105\pi\)
−0.264191 + 0.964470i \(0.585105\pi\)
\(384\) −11206.3 −1.48924
\(385\) 228.526 0.0302513
\(386\) −5525.68 −0.728626
\(387\) 0 0
\(388\) −1290.42 −0.168843
\(389\) −2377.10 −0.309830 −0.154915 0.987928i \(-0.549510\pi\)
−0.154915 + 0.987928i \(0.549510\pi\)
\(390\) 491.357 0.0637971
\(391\) 1032.65 0.133564
\(392\) −9489.08 −1.22263
\(393\) −8160.68 −1.04746
\(394\) 6164.65 0.788250
\(395\) 19.4272 0.00247466
\(396\) −974.488 −0.123661
\(397\) −5522.04 −0.698094 −0.349047 0.937105i \(-0.613495\pi\)
−0.349047 + 0.937105i \(0.613495\pi\)
\(398\) −9478.26 −1.19372
\(399\) 36838.4 4.62212
\(400\) 9876.32 1.23454
\(401\) −5659.01 −0.704732 −0.352366 0.935862i \(-0.614623\pi\)
−0.352366 + 0.935862i \(0.614623\pi\)
\(402\) 8537.11 1.05918
\(403\) −4173.02 −0.515814
\(404\) 818.580 0.100807
\(405\) 525.328 0.0644537
\(406\) 6405.38 0.782990
\(407\) −1565.52 −0.190664
\(408\) 809.166 0.0981855
\(409\) −51.5079 −0.00622715 −0.00311357 0.999995i \(-0.500991\pi\)
−0.00311357 + 0.999995i \(0.500991\pi\)
\(410\) −1879.84 −0.226436
\(411\) −8100.79 −0.972220
\(412\) −4508.48 −0.539119
\(413\) −16003.4 −1.90672
\(414\) 14901.4 1.76900
\(415\) −1092.57 −0.129234
\(416\) −3010.52 −0.354815
\(417\) 17613.4 2.06842
\(418\) 3178.97 0.371983
\(419\) −9152.59 −1.06714 −0.533572 0.845755i \(-0.679151\pi\)
−0.533572 + 0.845755i \(0.679151\pi\)
\(420\) 1263.68 0.146813
\(421\) 6750.56 0.781478 0.390739 0.920502i \(-0.372220\pi\)
0.390739 + 0.920502i \(0.372220\pi\)
\(422\) 4293.04 0.495218
\(423\) −11441.0 −1.31508
\(424\) −4791.15 −0.548771
\(425\) −1034.71 −0.118096
\(426\) −1866.25 −0.212253
\(427\) 8814.30 0.998956
\(428\) −2581.34 −0.291528
\(429\) 818.092 0.0920695
\(430\) 0 0
\(431\) 2652.89 0.296485 0.148243 0.988951i \(-0.452638\pi\)
0.148243 + 0.988951i \(0.452638\pi\)
\(432\) 4432.44 0.493648
\(433\) −5593.70 −0.620822 −0.310411 0.950602i \(-0.600467\pi\)
−0.310411 + 0.950602i \(0.600467\pi\)
\(434\) −29831.0 −3.29939
\(435\) 459.311 0.0506259
\(436\) −3676.96 −0.403887
\(437\) −17488.8 −1.91443
\(438\) 23099.0 2.51990
\(439\) −17064.4 −1.85521 −0.927605 0.373563i \(-0.878136\pi\)
−0.927605 + 0.373563i \(0.878136\pi\)
\(440\) −85.0116 −0.00921084
\(441\) 26127.2 2.82121
\(442\) 486.380 0.0523410
\(443\) −5178.57 −0.555398 −0.277699 0.960668i \(-0.589572\pi\)
−0.277699 + 0.960668i \(0.589572\pi\)
\(444\) −8656.91 −0.925312
\(445\) 1339.06 0.142646
\(446\) 4846.73 0.514573
\(447\) −2555.83 −0.270440
\(448\) −273.363 −0.0288285
\(449\) 10238.7 1.07616 0.538079 0.842894i \(-0.319150\pi\)
0.538079 + 0.842894i \(0.319150\pi\)
\(450\) −14931.1 −1.56413
\(451\) −3129.86 −0.326784
\(452\) −8252.79 −0.858803
\(453\) −9390.47 −0.973958
\(454\) −22162.5 −2.29105
\(455\) −592.147 −0.0610116
\(456\) −13703.9 −1.40733
\(457\) −6009.74 −0.615150 −0.307575 0.951524i \(-0.599518\pi\)
−0.307575 + 0.951524i \(0.599518\pi\)
\(458\) 9071.01 0.925460
\(459\) −464.372 −0.0472223
\(460\) −599.927 −0.0608082
\(461\) 13361.1 1.34987 0.674933 0.737879i \(-0.264173\pi\)
0.674933 + 0.737879i \(0.264173\pi\)
\(462\) 5848.16 0.588920
\(463\) −14853.4 −1.49092 −0.745461 0.666550i \(-0.767771\pi\)
−0.745461 + 0.666550i \(0.767771\pi\)
\(464\) −4339.72 −0.434195
\(465\) −2139.09 −0.213329
\(466\) −10138.7 −1.00787
\(467\) −4779.44 −0.473589 −0.236794 0.971560i \(-0.576097\pi\)
−0.236794 + 0.971560i \(0.576097\pi\)
\(468\) 2525.06 0.249403
\(469\) −10288.3 −1.01294
\(470\) 1280.30 0.125650
\(471\) 3492.86 0.341704
\(472\) 5953.27 0.580554
\(473\) 0 0
\(474\) 497.158 0.0481756
\(475\) 17523.6 1.69271
\(476\) 1250.88 0.120450
\(477\) 13191.9 1.26628
\(478\) −7975.17 −0.763129
\(479\) −12824.8 −1.22334 −0.611670 0.791113i \(-0.709502\pi\)
−0.611670 + 0.791113i \(0.709502\pi\)
\(480\) −1543.19 −0.146744
\(481\) 4056.52 0.384536
\(482\) 12272.7 1.15976
\(483\) −32173.1 −3.03091
\(484\) −5801.91 −0.544883
\(485\) 309.956 0.0290193
\(486\) 18747.9 1.74984
\(487\) 2927.00 0.272351 0.136175 0.990685i \(-0.456519\pi\)
0.136175 + 0.990685i \(0.456519\pi\)
\(488\) −3278.92 −0.304160
\(489\) −19047.3 −1.76145
\(490\) −2923.76 −0.269555
\(491\) 20421.5 1.87700 0.938501 0.345275i \(-0.112214\pi\)
0.938501 + 0.345275i \(0.112214\pi\)
\(492\) −17307.2 −1.58592
\(493\) 454.657 0.0415350
\(494\) −8237.23 −0.750224
\(495\) 234.071 0.0212539
\(496\) 20210.8 1.82962
\(497\) 2249.06 0.202986
\(498\) −27959.8 −2.51588
\(499\) 14855.3 1.33270 0.666348 0.745641i \(-0.267856\pi\)
0.666348 + 0.745641i \(0.267856\pi\)
\(500\) 1207.90 0.108038
\(501\) 7357.39 0.656096
\(502\) 5022.06 0.446505
\(503\) −11694.4 −1.03663 −0.518317 0.855188i \(-0.673441\pi\)
−0.518317 + 0.855188i \(0.673441\pi\)
\(504\) −14071.6 −1.24364
\(505\) −196.622 −0.0173258
\(506\) −2776.39 −0.243924
\(507\) 15054.7 1.31874
\(508\) −11182.8 −0.976687
\(509\) 13214.1 1.15070 0.575348 0.817909i \(-0.304867\pi\)
0.575348 + 0.817909i \(0.304867\pi\)
\(510\) 249.318 0.0216471
\(511\) −27837.2 −2.40988
\(512\) 6676.55 0.576298
\(513\) 7864.51 0.676855
\(514\) 10402.4 0.892670
\(515\) 1082.93 0.0926595
\(516\) 0 0
\(517\) 2131.65 0.181334
\(518\) 28998.2 2.45967
\(519\) 28318.8 2.39510
\(520\) 220.279 0.0185767
\(521\) 14682.6 1.23465 0.617327 0.786707i \(-0.288216\pi\)
0.617327 + 0.786707i \(0.288216\pi\)
\(522\) 6560.80 0.550112
\(523\) 13237.8 1.10679 0.553394 0.832920i \(-0.313332\pi\)
0.553394 + 0.832920i \(0.313332\pi\)
\(524\) 4692.97 0.391247
\(525\) 32237.1 2.67989
\(526\) 23389.7 1.93886
\(527\) −2117.42 −0.175021
\(528\) −3962.20 −0.326577
\(529\) 3107.04 0.255366
\(530\) −1476.24 −0.120988
\(531\) −16391.7 −1.33962
\(532\) −21184.7 −1.72645
\(533\) 8109.97 0.659066
\(534\) 34267.6 2.77698
\(535\) 620.035 0.0501055
\(536\) 3827.24 0.308417
\(537\) 9950.13 0.799590
\(538\) −17610.9 −1.41126
\(539\) −4867.94 −0.389011
\(540\) 269.780 0.0214990
\(541\) 16167.1 1.28480 0.642400 0.766370i \(-0.277939\pi\)
0.642400 + 0.766370i \(0.277939\pi\)
\(542\) 2396.52 0.189925
\(543\) −3040.15 −0.240268
\(544\) −1527.56 −0.120393
\(545\) 883.201 0.0694169
\(546\) −15153.5 −1.18775
\(547\) 10235.6 0.800077 0.400038 0.916498i \(-0.368997\pi\)
0.400038 + 0.916498i \(0.368997\pi\)
\(548\) 4658.53 0.363143
\(549\) 9028.18 0.701846
\(550\) 2781.91 0.215675
\(551\) −7699.99 −0.595337
\(552\) 11968.4 0.922843
\(553\) −599.138 −0.0460722
\(554\) −6692.21 −0.513221
\(555\) 2079.38 0.159035
\(556\) −10129.0 −0.772597
\(557\) −16151.9 −1.22868 −0.614342 0.789040i \(-0.710578\pi\)
−0.614342 + 0.789040i \(0.710578\pi\)
\(558\) −30554.8 −2.31808
\(559\) 0 0
\(560\) 2867.90 0.216412
\(561\) 415.106 0.0312403
\(562\) −8611.74 −0.646378
\(563\) 18574.5 1.39045 0.695224 0.718793i \(-0.255305\pi\)
0.695224 + 0.718793i \(0.255305\pi\)
\(564\) 11787.4 0.880034
\(565\) 1982.31 0.147604
\(566\) −11244.8 −0.835076
\(567\) −16201.2 −1.19998
\(568\) −836.650 −0.0618047
\(569\) 9426.53 0.694518 0.347259 0.937769i \(-0.387113\pi\)
0.347259 + 0.937769i \(0.387113\pi\)
\(570\) −4222.41 −0.310276
\(571\) 4825.73 0.353679 0.176839 0.984240i \(-0.443413\pi\)
0.176839 + 0.984240i \(0.443413\pi\)
\(572\) −470.461 −0.0343898
\(573\) 8527.89 0.621741
\(574\) 57974.5 4.21570
\(575\) −15304.4 −1.10998
\(576\) −279.996 −0.0202543
\(577\) −9870.62 −0.712165 −0.356083 0.934455i \(-0.615888\pi\)
−0.356083 + 0.934455i \(0.615888\pi\)
\(578\) −17120.1 −1.23201
\(579\) 12219.8 0.877093
\(580\) −264.136 −0.0189098
\(581\) 33695.0 2.40603
\(582\) 7932.03 0.564937
\(583\) −2457.88 −0.174606
\(584\) 10355.5 0.733753
\(585\) −606.515 −0.0428655
\(586\) −13559.0 −0.955833
\(587\) −22261.7 −1.56531 −0.782657 0.622453i \(-0.786136\pi\)
−0.782657 + 0.622453i \(0.786136\pi\)
\(588\) −26918.3 −1.88791
\(589\) 35860.2 2.50865
\(590\) 1834.31 0.127995
\(591\) −13632.8 −0.948866
\(592\) −19646.6 −1.36397
\(593\) 6241.50 0.432222 0.216111 0.976369i \(-0.430663\pi\)
0.216111 + 0.976369i \(0.430663\pi\)
\(594\) 1248.51 0.0862406
\(595\) −300.460 −0.0207019
\(596\) 1469.79 0.101015
\(597\) 20960.7 1.43696
\(598\) 7194.07 0.491952
\(599\) 735.572 0.0501747 0.0250873 0.999685i \(-0.492014\pi\)
0.0250873 + 0.999685i \(0.492014\pi\)
\(600\) −11992.2 −0.815967
\(601\) −15890.1 −1.07848 −0.539242 0.842151i \(-0.681289\pi\)
−0.539242 + 0.842151i \(0.681289\pi\)
\(602\) 0 0
\(603\) −10537.9 −0.711670
\(604\) 5400.19 0.363792
\(605\) 1393.61 0.0936502
\(606\) −5031.71 −0.337293
\(607\) 12391.3 0.828580 0.414290 0.910145i \(-0.364030\pi\)
0.414290 + 0.910145i \(0.364030\pi\)
\(608\) 25870.5 1.72564
\(609\) −14165.2 −0.942533
\(610\) −1010.30 −0.0670584
\(611\) −5523.44 −0.365719
\(612\) 1281.23 0.0846254
\(613\) 15142.2 0.997699 0.498850 0.866689i \(-0.333756\pi\)
0.498850 + 0.866689i \(0.333756\pi\)
\(614\) −6926.66 −0.455273
\(615\) 4157.18 0.272575
\(616\) 2621.77 0.171484
\(617\) 19712.7 1.28623 0.643113 0.765771i \(-0.277643\pi\)
0.643113 + 0.765771i \(0.277643\pi\)
\(618\) 27713.1 1.80386
\(619\) 18495.4 1.20096 0.600478 0.799641i \(-0.294977\pi\)
0.600478 + 0.799641i \(0.294977\pi\)
\(620\) 1230.13 0.0796826
\(621\) −6868.55 −0.443841
\(622\) −1765.67 −0.113821
\(623\) −41296.7 −2.65573
\(624\) 10266.7 0.658648
\(625\) 15189.1 0.972103
\(626\) 7473.83 0.477179
\(627\) −7030.15 −0.447779
\(628\) −2008.64 −0.127633
\(629\) 2058.31 0.130477
\(630\) −4335.70 −0.274188
\(631\) −5867.54 −0.370179 −0.185090 0.982722i \(-0.559258\pi\)
−0.185090 + 0.982722i \(0.559258\pi\)
\(632\) 222.879 0.0140280
\(633\) −9493.85 −0.596124
\(634\) −18499.0 −1.15882
\(635\) 2686.10 0.167865
\(636\) −13591.4 −0.847380
\(637\) 12613.6 0.784568
\(638\) −1222.39 −0.0758540
\(639\) 2303.63 0.142614
\(640\) −1547.94 −0.0956057
\(641\) 16245.6 1.00103 0.500517 0.865727i \(-0.333143\pi\)
0.500517 + 0.865727i \(0.333143\pi\)
\(642\) 15867.2 0.975434
\(643\) 18563.9 1.13855 0.569276 0.822147i \(-0.307224\pi\)
0.569276 + 0.822147i \(0.307224\pi\)
\(644\) 18501.8 1.13210
\(645\) 0 0
\(646\) −4179.63 −0.254560
\(647\) −25883.5 −1.57277 −0.786386 0.617735i \(-0.788050\pi\)
−0.786386 + 0.617735i \(0.788050\pi\)
\(648\) 6026.85 0.365366
\(649\) 3054.06 0.184718
\(650\) −7208.38 −0.434978
\(651\) 65969.9 3.97168
\(652\) 10953.5 0.657935
\(653\) −26760.2 −1.60369 −0.801843 0.597535i \(-0.796147\pi\)
−0.801843 + 0.597535i \(0.796147\pi\)
\(654\) 22601.9 1.35138
\(655\) −1127.25 −0.0672444
\(656\) −39278.4 −2.33775
\(657\) −28512.7 −1.69313
\(658\) −39484.5 −2.33931
\(659\) −1429.13 −0.0844781 −0.0422390 0.999108i \(-0.513449\pi\)
−0.0422390 + 0.999108i \(0.513449\pi\)
\(660\) −241.158 −0.0142228
\(661\) 20836.3 1.22608 0.613040 0.790052i \(-0.289946\pi\)
0.613040 + 0.790052i \(0.289946\pi\)
\(662\) 6488.30 0.380929
\(663\) −1075.61 −0.0630061
\(664\) −12534.5 −0.732583
\(665\) 5088.53 0.296729
\(666\) 29701.9 1.72811
\(667\) 6724.86 0.390386
\(668\) −4231.02 −0.245065
\(669\) −10718.3 −0.619423
\(670\) 1179.24 0.0679971
\(671\) −1682.10 −0.0967763
\(672\) 47592.3 2.73202
\(673\) 8550.02 0.489716 0.244858 0.969559i \(-0.421259\pi\)
0.244858 + 0.969559i \(0.421259\pi\)
\(674\) −2050.22 −0.117169
\(675\) 6882.21 0.392439
\(676\) −8657.52 −0.492576
\(677\) 22443.6 1.27412 0.637059 0.770815i \(-0.280151\pi\)
0.637059 + 0.770815i \(0.280151\pi\)
\(678\) 50728.9 2.87350
\(679\) −9559.08 −0.540271
\(680\) 111.771 0.00630327
\(681\) 49011.3 2.75788
\(682\) 5692.89 0.319636
\(683\) −28556.4 −1.59982 −0.799912 0.600118i \(-0.795120\pi\)
−0.799912 + 0.600118i \(0.795120\pi\)
\(684\) −21698.7 −1.21297
\(685\) −1118.97 −0.0624142
\(686\) 49792.1 2.77124
\(687\) −20060.1 −1.11403
\(688\) 0 0
\(689\) 6368.76 0.352149
\(690\) 3687.68 0.203460
\(691\) −13020.8 −0.716837 −0.358418 0.933561i \(-0.616684\pi\)
−0.358418 + 0.933561i \(0.616684\pi\)
\(692\) −16285.3 −0.894617
\(693\) −7218.77 −0.395698
\(694\) 74.7252 0.00408722
\(695\) 2432.96 0.132788
\(696\) 5269.46 0.286980
\(697\) 4115.06 0.223629
\(698\) 24306.5 1.31807
\(699\) 22421.3 1.21324
\(700\) −18538.6 −1.00099
\(701\) −13786.5 −0.742811 −0.371405 0.928471i \(-0.621124\pi\)
−0.371405 + 0.928471i \(0.621124\pi\)
\(702\) −3235.08 −0.173932
\(703\) −34859.2 −1.87018
\(704\) 52.1680 0.00279283
\(705\) −2831.32 −0.151253
\(706\) −28200.8 −1.50333
\(707\) 6063.84 0.322566
\(708\) 16888.1 0.896458
\(709\) −1202.37 −0.0636895 −0.0318448 0.999493i \(-0.510138\pi\)
−0.0318448 + 0.999493i \(0.510138\pi\)
\(710\) −257.787 −0.0136262
\(711\) −613.675 −0.0323694
\(712\) 15362.4 0.808610
\(713\) −31318.9 −1.64502
\(714\) −7689.02 −0.403017
\(715\) 113.004 0.00591064
\(716\) −5722.03 −0.298663
\(717\) 17636.7 0.918626
\(718\) −28768.9 −1.49533
\(719\) 10079.5 0.522814 0.261407 0.965229i \(-0.415814\pi\)
0.261407 + 0.965229i \(0.415814\pi\)
\(720\) 2937.48 0.152047
\(721\) −33397.7 −1.72510
\(722\) 46539.6 2.39893
\(723\) −27140.5 −1.39608
\(724\) 1748.31 0.0897448
\(725\) −6738.24 −0.345175
\(726\) 35663.7 1.82314
\(727\) 28825.4 1.47053 0.735265 0.677779i \(-0.237058\pi\)
0.735265 + 0.677779i \(0.237058\pi\)
\(728\) −6793.43 −0.345853
\(729\) −28324.5 −1.43903
\(730\) 3190.70 0.161771
\(731\) 0 0
\(732\) −9301.55 −0.469666
\(733\) −19783.5 −0.996892 −0.498446 0.866921i \(-0.666096\pi\)
−0.498446 + 0.866921i \(0.666096\pi\)
\(734\) −1124.50 −0.0565478
\(735\) 6465.75 0.324480
\(736\) −22594.2 −1.13157
\(737\) 1963.39 0.0981309
\(738\) 59381.2 2.96186
\(739\) 946.083 0.0470937 0.0235468 0.999723i \(-0.492504\pi\)
0.0235468 + 0.999723i \(0.492504\pi\)
\(740\) −1195.79 −0.0594028
\(741\) 18216.3 0.903091
\(742\) 45527.4 2.25251
\(743\) 2376.31 0.117333 0.0586664 0.998278i \(-0.481315\pi\)
0.0586664 + 0.998278i \(0.481315\pi\)
\(744\) −24540.8 −1.20929
\(745\) −353.041 −0.0173616
\(746\) 1191.61 0.0584823
\(747\) 34512.6 1.69043
\(748\) −238.715 −0.0116688
\(749\) −19122.0 −0.932845
\(750\) −7424.83 −0.361488
\(751\) 6844.89 0.332588 0.166294 0.986076i \(-0.446820\pi\)
0.166294 + 0.986076i \(0.446820\pi\)
\(752\) 26751.2 1.29723
\(753\) −11106.0 −0.537485
\(754\) 3167.41 0.152984
\(755\) −1297.12 −0.0625258
\(756\) −8320.05 −0.400261
\(757\) 30909.6 1.48406 0.742028 0.670369i \(-0.233864\pi\)
0.742028 + 0.670369i \(0.233864\pi\)
\(758\) −5659.10 −0.271171
\(759\) 6139.85 0.293626
\(760\) −1892.93 −0.0903473
\(761\) 22285.2 1.06155 0.530774 0.847513i \(-0.321901\pi\)
0.530774 + 0.847513i \(0.321901\pi\)
\(762\) 68739.4 3.26793
\(763\) −27238.0 −1.29238
\(764\) −4904.14 −0.232232
\(765\) −307.750 −0.0145447
\(766\) −13999.8 −0.660359
\(767\) −7913.55 −0.372545
\(768\) −40126.4 −1.88533
\(769\) −2946.09 −0.138152 −0.0690758 0.997611i \(-0.522005\pi\)
−0.0690758 + 0.997611i \(0.522005\pi\)
\(770\) 807.814 0.0378073
\(771\) −23004.5 −1.07456
\(772\) −7027.24 −0.327611
\(773\) 36175.2 1.68322 0.841612 0.540082i \(-0.181607\pi\)
0.841612 + 0.540082i \(0.181607\pi\)
\(774\) 0 0
\(775\) 31381.2 1.45451
\(776\) 3555.98 0.164500
\(777\) −64128.3 −2.96086
\(778\) −8402.81 −0.387218
\(779\) −69691.9 −3.20535
\(780\) 624.880 0.0286850
\(781\) −429.205 −0.0196648
\(782\) 3650.32 0.166925
\(783\) −3024.09 −0.138023
\(784\) −61090.5 −2.78291
\(785\) 482.473 0.0219366
\(786\) −28847.1 −1.30909
\(787\) −2197.30 −0.0995237 −0.0497619 0.998761i \(-0.515846\pi\)
−0.0497619 + 0.998761i \(0.515846\pi\)
\(788\) 7839.85 0.354420
\(789\) −51725.2 −2.33392
\(790\) 68.6731 0.00309276
\(791\) −61134.7 −2.74804
\(792\) 2685.39 0.120481
\(793\) 4358.60 0.195181
\(794\) −19519.8 −0.872460
\(795\) 3264.63 0.145641
\(796\) −12053.9 −0.536733
\(797\) −26747.2 −1.18875 −0.594375 0.804188i \(-0.702600\pi\)
−0.594375 + 0.804188i \(0.702600\pi\)
\(798\) 130220. 5.77660
\(799\) −2802.63 −0.124093
\(800\) 22639.2 1.00052
\(801\) −42298.8 −1.86586
\(802\) −20004.0 −0.880756
\(803\) 5312.40 0.233462
\(804\) 10857.0 0.476240
\(805\) −4444.12 −0.194577
\(806\) −14751.2 −0.644650
\(807\) 38945.7 1.69883
\(808\) −2255.75 −0.0982141
\(809\) −24269.0 −1.05470 −0.527351 0.849648i \(-0.676815\pi\)
−0.527351 + 0.849648i \(0.676815\pi\)
\(810\) 1856.98 0.0805526
\(811\) −39266.0 −1.70014 −0.850071 0.526668i \(-0.823441\pi\)
−0.850071 + 0.526668i \(0.823441\pi\)
\(812\) 8146.00 0.352055
\(813\) −5299.79 −0.228625
\(814\) −5533.96 −0.238287
\(815\) −2631.02 −0.113081
\(816\) 5209.39 0.223487
\(817\) 0 0
\(818\) −182.075 −0.00778253
\(819\) 18705.0 0.798053
\(820\) −2390.67 −0.101812
\(821\) 15760.0 0.669950 0.334975 0.942227i \(-0.391272\pi\)
0.334975 + 0.942227i \(0.391272\pi\)
\(822\) −28635.4 −1.21505
\(823\) −11856.7 −0.502185 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(824\) 12424.0 0.525254
\(825\) −6152.06 −0.259621
\(826\) −56570.4 −2.38297
\(827\) 5549.47 0.233342 0.116671 0.993171i \(-0.462778\pi\)
0.116671 + 0.993171i \(0.462778\pi\)
\(828\) 18950.8 0.795392
\(829\) −11901.0 −0.498600 −0.249300 0.968426i \(-0.580201\pi\)
−0.249300 + 0.968426i \(0.580201\pi\)
\(830\) −3862.12 −0.161513
\(831\) 14799.5 0.617796
\(832\) −135.176 −0.00563266
\(833\) 6400.25 0.266213
\(834\) 62261.6 2.58506
\(835\) 1016.29 0.0421198
\(836\) 4042.84 0.167254
\(837\) 14083.7 0.581606
\(838\) −32353.4 −1.33369
\(839\) −13419.6 −0.552200 −0.276100 0.961129i \(-0.589042\pi\)
−0.276100 + 0.961129i \(0.589042\pi\)
\(840\) −3482.31 −0.143037
\(841\) −21428.2 −0.878600
\(842\) 23862.5 0.976670
\(843\) 19044.5 0.778086
\(844\) 5459.64 0.222664
\(845\) 2079.52 0.0846601
\(846\) −40442.6 −1.64355
\(847\) −42979.2 −1.74354
\(848\) −30845.3 −1.24910
\(849\) 24867.3 1.00523
\(850\) −3657.58 −0.147593
\(851\) 30444.6 1.22635
\(852\) −2373.38 −0.0954352
\(853\) 36696.4 1.47299 0.736496 0.676442i \(-0.236479\pi\)
0.736496 + 0.676442i \(0.236479\pi\)
\(854\) 31157.6 1.24847
\(855\) 5212.00 0.208476
\(856\) 7113.37 0.284030
\(857\) −39381.5 −1.56971 −0.784857 0.619677i \(-0.787264\pi\)
−0.784857 + 0.619677i \(0.787264\pi\)
\(858\) 2891.87 0.115066
\(859\) 6521.17 0.259022 0.129511 0.991578i \(-0.458659\pi\)
0.129511 + 0.991578i \(0.458659\pi\)
\(860\) 0 0
\(861\) −128208. −5.07470
\(862\) 9377.68 0.370540
\(863\) 11989.4 0.472912 0.236456 0.971642i \(-0.424014\pi\)
0.236456 + 0.971642i \(0.424014\pi\)
\(864\) 10160.4 0.400072
\(865\) 3911.71 0.153760
\(866\) −19773.1 −0.775887
\(867\) 37860.4 1.48305
\(868\) −37937.4 −1.48350
\(869\) 114.338 0.00446336
\(870\) 1623.61 0.0632709
\(871\) −5087.46 −0.197913
\(872\) 10132.6 0.393500
\(873\) −9791.02 −0.379583
\(874\) −61821.2 −2.39260
\(875\) 8947.84 0.345705
\(876\) 29376.0 1.13302
\(877\) −11656.2 −0.448807 −0.224403 0.974496i \(-0.572043\pi\)
−0.224403 + 0.974496i \(0.572043\pi\)
\(878\) −60320.7 −2.31859
\(879\) 29985.1 1.15060
\(880\) −547.303 −0.0209654
\(881\) 2593.62 0.0991843 0.0495922 0.998770i \(-0.484208\pi\)
0.0495922 + 0.998770i \(0.484208\pi\)
\(882\) 92356.9 3.52587
\(883\) −6995.75 −0.266620 −0.133310 0.991074i \(-0.542561\pi\)
−0.133310 + 0.991074i \(0.542561\pi\)
\(884\) 618.550 0.0235340
\(885\) −4056.49 −0.154076
\(886\) −18305.7 −0.694122
\(887\) 6259.93 0.236965 0.118482 0.992956i \(-0.462197\pi\)
0.118482 + 0.992956i \(0.462197\pi\)
\(888\) 23855.7 0.901516
\(889\) −82839.5 −3.12525
\(890\) 4733.43 0.178275
\(891\) 3091.80 0.116251
\(892\) 6163.79 0.231367
\(893\) 47464.9 1.77867
\(894\) −9034.60 −0.337989
\(895\) 1374.42 0.0513318
\(896\) 47738.6 1.77995
\(897\) −15909.3 −0.592193
\(898\) 36192.8 1.34496
\(899\) −13789.1 −0.511559
\(900\) −18988.5 −0.703276
\(901\) 3231.56 0.119488
\(902\) −11063.7 −0.408406
\(903\) 0 0
\(904\) 22742.1 0.836716
\(905\) −419.940 −0.0154246
\(906\) −33194.3 −1.21723
\(907\) −29084.2 −1.06475 −0.532373 0.846510i \(-0.678700\pi\)
−0.532373 + 0.846510i \(0.678700\pi\)
\(908\) −28185.0 −1.03012
\(909\) 6210.97 0.226628
\(910\) −2093.18 −0.0762507
\(911\) 50509.9 1.83696 0.918478 0.395472i \(-0.129419\pi\)
0.918478 + 0.395472i \(0.129419\pi\)
\(912\) −88225.3 −3.20332
\(913\) −6430.28 −0.233090
\(914\) −21243.8 −0.768799
\(915\) 2234.22 0.0807224
\(916\) 11536.0 0.416113
\(917\) 34764.4 1.25193
\(918\) −1641.51 −0.0590172
\(919\) 43794.2 1.57197 0.785984 0.618247i \(-0.212157\pi\)
0.785984 + 0.618247i \(0.212157\pi\)
\(920\) 1653.21 0.0592443
\(921\) 15318.0 0.548040
\(922\) 47230.0 1.68703
\(923\) 1112.14 0.0396604
\(924\) 7437.36 0.264796
\(925\) −30505.1 −1.08433
\(926\) −52505.2 −1.86331
\(927\) −34208.1 −1.21202
\(928\) −9947.80 −0.351888
\(929\) −20727.8 −0.732030 −0.366015 0.930609i \(-0.619278\pi\)
−0.366015 + 0.930609i \(0.619278\pi\)
\(930\) −7561.46 −0.266613
\(931\) −108393. −3.81573
\(932\) −12893.9 −0.453168
\(933\) 3904.69 0.137014
\(934\) −16894.8 −0.591879
\(935\) 57.3391 0.00200555
\(936\) −6958.26 −0.242989
\(937\) −21684.7 −0.756037 −0.378018 0.925798i \(-0.623394\pi\)
−0.378018 + 0.925798i \(0.623394\pi\)
\(938\) −36368.0 −1.26594
\(939\) −16528.0 −0.574410
\(940\) 1628.21 0.0564961
\(941\) 20387.6 0.706287 0.353144 0.935569i \(-0.385113\pi\)
0.353144 + 0.935569i \(0.385113\pi\)
\(942\) 12346.9 0.427053
\(943\) 60866.1 2.10188
\(944\) 38327.1 1.32144
\(945\) 1998.46 0.0687937
\(946\) 0 0
\(947\) −51110.0 −1.75380 −0.876902 0.480669i \(-0.840394\pi\)
−0.876902 + 0.480669i \(0.840394\pi\)
\(948\) 632.258 0.0216612
\(949\) −13765.3 −0.470853
\(950\) 61944.1 2.11551
\(951\) 40909.8 1.39494
\(952\) −3447.04 −0.117352
\(953\) 2618.42 0.0890019 0.0445009 0.999009i \(-0.485830\pi\)
0.0445009 + 0.999009i \(0.485830\pi\)
\(954\) 46632.1 1.58257
\(955\) 1177.97 0.0399143
\(956\) −10142.4 −0.343125
\(957\) 2703.26 0.0913102
\(958\) −45334.3 −1.52890
\(959\) 34509.2 1.16200
\(960\) −69.2911 −0.00232954
\(961\) 34427.3 1.15563
\(962\) 14339.4 0.480582
\(963\) −19585.9 −0.655398
\(964\) 15607.7 0.521463
\(965\) 1687.93 0.0563073
\(966\) −113729. −3.78795
\(967\) 34263.7 1.13945 0.569724 0.821836i \(-0.307050\pi\)
0.569724 + 0.821836i \(0.307050\pi\)
\(968\) 15988.3 0.530870
\(969\) 9243.06 0.306429
\(970\) 1095.66 0.0362676
\(971\) −30032.7 −0.992581 −0.496290 0.868157i \(-0.665305\pi\)
−0.496290 + 0.868157i \(0.665305\pi\)
\(972\) 23842.5 0.786778
\(973\) −75032.9 −2.47220
\(974\) 10346.6 0.340377
\(975\) 15941.0 0.523610
\(976\) −21109.6 −0.692319
\(977\) 10403.9 0.340686 0.170343 0.985385i \(-0.445512\pi\)
0.170343 + 0.985385i \(0.445512\pi\)
\(978\) −67330.1 −2.20141
\(979\) 7880.98 0.257280
\(980\) −3718.26 −0.121200
\(981\) −27899.0 −0.907997
\(982\) 72187.8 2.34583
\(983\) −53412.2 −1.73305 −0.866523 0.499138i \(-0.833650\pi\)
−0.866523 + 0.499138i \(0.833650\pi\)
\(984\) 47693.4 1.54513
\(985\) −1883.12 −0.0609149
\(986\) 1607.17 0.0519093
\(987\) 87318.2 2.81598
\(988\) −10475.6 −0.337322
\(989\) 0 0
\(990\) 827.415 0.0265626
\(991\) −23203.1 −0.743765 −0.371882 0.928280i \(-0.621288\pi\)
−0.371882 + 0.928280i \(0.621288\pi\)
\(992\) 46328.7 1.48280
\(993\) −14348.6 −0.458548
\(994\) 7950.18 0.253687
\(995\) 2895.33 0.0922495
\(996\) −35557.6 −1.13121
\(997\) 10323.0 0.327916 0.163958 0.986467i \(-0.447574\pi\)
0.163958 + 0.986467i \(0.447574\pi\)
\(998\) 52512.0 1.66557
\(999\) −13690.6 −0.433584
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.1.40 yes 50
43.42 odd 2 1849.4.a.i.1.11 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.11 50 43.42 odd 2
1849.4.a.j.1.40 yes 50 1.1 even 1 trivial