Properties

Label 1849.4.a.g.1.16
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $30$
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: \(30\)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.188737 q^{2} +1.07307 q^{3} -7.96438 q^{4} -16.0623 q^{5} +0.202528 q^{6} -29.7402 q^{7} -3.01306 q^{8} -25.8485 q^{9} +O(q^{10})\) \(q+0.188737 q^{2} +1.07307 q^{3} -7.96438 q^{4} -16.0623 q^{5} +0.202528 q^{6} -29.7402 q^{7} -3.01306 q^{8} -25.8485 q^{9} -3.03154 q^{10} +12.2621 q^{11} -8.54636 q^{12} +37.3046 q^{13} -5.61307 q^{14} -17.2360 q^{15} +63.1464 q^{16} +35.5003 q^{17} -4.87856 q^{18} -95.8018 q^{19} +127.926 q^{20} -31.9135 q^{21} +2.31431 q^{22} +123.383 q^{23} -3.23324 q^{24} +132.997 q^{25} +7.04074 q^{26} -56.7103 q^{27} +236.863 q^{28} +194.724 q^{29} -3.25306 q^{30} -64.0494 q^{31} +36.0225 q^{32} +13.1581 q^{33} +6.70021 q^{34} +477.696 q^{35} +205.867 q^{36} -286.712 q^{37} -18.0813 q^{38} +40.0306 q^{39} +48.3966 q^{40} +442.065 q^{41} -6.02324 q^{42} -97.6600 q^{44} +415.186 q^{45} +23.2869 q^{46} -463.616 q^{47} +67.7607 q^{48} +541.482 q^{49} +25.1013 q^{50} +38.0945 q^{51} -297.108 q^{52} -142.238 q^{53} -10.7033 q^{54} -196.957 q^{55} +89.6092 q^{56} -102.802 q^{57} +36.7516 q^{58} +496.417 q^{59} +137.274 q^{60} -144.960 q^{61} -12.0885 q^{62} +768.741 q^{63} -498.372 q^{64} -599.196 q^{65} +2.48342 q^{66} +713.903 q^{67} -282.738 q^{68} +132.399 q^{69} +90.1587 q^{70} +548.984 q^{71} +77.8832 q^{72} +514.562 q^{73} -54.1131 q^{74} +142.715 q^{75} +763.002 q^{76} -364.678 q^{77} +7.55523 q^{78} -1074.57 q^{79} -1014.27 q^{80} +637.056 q^{81} +83.4338 q^{82} +126.403 q^{83} +254.171 q^{84} -570.216 q^{85} +208.953 q^{87} -36.9464 q^{88} -77.2915 q^{89} +78.3608 q^{90} -1109.45 q^{91} -982.671 q^{92} -68.7297 q^{93} -87.5013 q^{94} +1538.79 q^{95} +38.6548 q^{96} -200.732 q^{97} +102.197 q^{98} -316.957 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 6q^{2} - 2q^{3} + 114q^{4} - 27q^{5} + 8q^{6} - 48q^{7} - 90q^{8} + 216q^{9} + O(q^{10}) \) \( 30q - 6q^{2} - 2q^{3} + 114q^{4} - 27q^{5} + 8q^{6} - 48q^{7} - 90q^{8} + 216q^{9} - 27q^{10} + 80q^{11} + 36q^{12} - 13q^{13} + 36q^{14} + 16q^{15} + 318q^{16} + 66q^{17} - 80q^{18} - 254q^{19} - 312q^{20} - 548q^{21} - 305q^{22} - 105q^{23} + 123q^{24} + 523q^{25} - 549q^{26} + 10q^{27} - 578q^{28} - 793q^{29} - 1560q^{30} - 359q^{31} - 676q^{32} - 208q^{33} - 1007q^{34} - 514q^{35} + 776q^{36} - 510q^{37} - 2066q^{38} - 898q^{39} - 1248q^{40} - 270q^{41} + 915q^{42} + 3256q^{44} - 807q^{45} - 1960q^{46} + 1421q^{47} + 632q^{48} + 386q^{49} + 141q^{50} - 209q^{51} + 2825q^{52} - 21q^{53} + 2368q^{54} - 2258q^{55} + 2521q^{56} - 1723q^{57} - 347q^{58} + 1752q^{59} + 2711q^{60} - 1759q^{61} - 395q^{62} - 2204q^{63} + 222q^{64} - 1151q^{65} + 160q^{66} - 3001q^{67} + 1921q^{68} - 1660q^{69} - 1597q^{70} - 727q^{71} - 9100q^{72} - 4623q^{73} - 2649q^{74} - 1027q^{75} - 874q^{76} - 3556q^{77} - 4979q^{78} + 546q^{79} - 5809q^{80} - 410q^{81} + 4397q^{82} - 492q^{83} - 10611q^{84} + 1723q^{85} + 5937q^{87} - 3974q^{88} - 5218q^{89} + 10492q^{90} - 1104q^{91} + 1060q^{92} - 1997q^{93} + 2134q^{94} + 6346q^{95} - 11984q^{96} + 2590q^{97} - 6270q^{98} - 2693q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.188737 0.0667285 0.0333642 0.999443i \(-0.489378\pi\)
0.0333642 + 0.999443i \(0.489378\pi\)
\(3\) 1.07307 0.206513 0.103257 0.994655i \(-0.467074\pi\)
0.103257 + 0.994655i \(0.467074\pi\)
\(4\) −7.96438 −0.995547
\(5\) −16.0623 −1.43665 −0.718327 0.695706i \(-0.755092\pi\)
−0.718327 + 0.695706i \(0.755092\pi\)
\(6\) 0.202528 0.0137803
\(7\) −29.7402 −1.60582 −0.802911 0.596099i \(-0.796717\pi\)
−0.802911 + 0.596099i \(0.796717\pi\)
\(8\) −3.01306 −0.133160
\(9\) −25.8485 −0.957352
\(10\) −3.03154 −0.0958657
\(11\) 12.2621 0.336105 0.168053 0.985778i \(-0.446252\pi\)
0.168053 + 0.985778i \(0.446252\pi\)
\(12\) −8.54636 −0.205594
\(13\) 37.3046 0.795879 0.397940 0.917412i \(-0.369725\pi\)
0.397940 + 0.917412i \(0.369725\pi\)
\(14\) −5.61307 −0.107154
\(15\) −17.2360 −0.296688
\(16\) 63.1464 0.986662
\(17\) 35.5003 0.506476 0.253238 0.967404i \(-0.418504\pi\)
0.253238 + 0.967404i \(0.418504\pi\)
\(18\) −4.87856 −0.0638826
\(19\) −95.8018 −1.15676 −0.578380 0.815767i \(-0.696315\pi\)
−0.578380 + 0.815767i \(0.696315\pi\)
\(20\) 127.926 1.43026
\(21\) −31.9135 −0.331623
\(22\) 2.31431 0.0224278
\(23\) 123.383 1.11857 0.559287 0.828974i \(-0.311075\pi\)
0.559287 + 0.828974i \(0.311075\pi\)
\(24\) −3.23324 −0.0274992
\(25\) 132.997 1.06397
\(26\) 7.04074 0.0531078
\(27\) −56.7103 −0.404219
\(28\) 236.863 1.59867
\(29\) 194.724 1.24687 0.623437 0.781873i \(-0.285736\pi\)
0.623437 + 0.781873i \(0.285736\pi\)
\(30\) −3.25306 −0.0197975
\(31\) −64.0494 −0.371084 −0.185542 0.982636i \(-0.559404\pi\)
−0.185542 + 0.982636i \(0.559404\pi\)
\(32\) 36.0225 0.198998
\(33\) 13.1581 0.0694102
\(34\) 6.70021 0.0337964
\(35\) 477.696 2.30701
\(36\) 205.867 0.953090
\(37\) −286.712 −1.27392 −0.636962 0.770895i \(-0.719809\pi\)
−0.636962 + 0.770895i \(0.719809\pi\)
\(38\) −18.0813 −0.0771888
\(39\) 40.0306 0.164359
\(40\) 48.3966 0.191304
\(41\) 442.065 1.68388 0.841939 0.539573i \(-0.181414\pi\)
0.841939 + 0.539573i \(0.181414\pi\)
\(42\) −6.02324 −0.0221287
\(43\) 0 0
\(44\) −97.6600 −0.334609
\(45\) 415.186 1.37538
\(46\) 23.2869 0.0746407
\(47\) −463.616 −1.43884 −0.719418 0.694577i \(-0.755592\pi\)
−0.719418 + 0.694577i \(0.755592\pi\)
\(48\) 67.7607 0.203759
\(49\) 541.482 1.57866
\(50\) 25.1013 0.0709973
\(51\) 38.0945 0.104594
\(52\) −297.108 −0.792335
\(53\) −142.238 −0.368640 −0.184320 0.982866i \(-0.559008\pi\)
−0.184320 + 0.982866i \(0.559008\pi\)
\(54\) −10.7033 −0.0269729
\(55\) −196.957 −0.482867
\(56\) 89.6092 0.213831
\(57\) −102.802 −0.238886
\(58\) 36.7516 0.0832020
\(59\) 496.417 1.09539 0.547695 0.836678i \(-0.315505\pi\)
0.547695 + 0.836678i \(0.315505\pi\)
\(60\) 137.274 0.295367
\(61\) −144.960 −0.304267 −0.152134 0.988360i \(-0.548614\pi\)
−0.152134 + 0.988360i \(0.548614\pi\)
\(62\) −12.0885 −0.0247619
\(63\) 768.741 1.53734
\(64\) −498.372 −0.973383
\(65\) −599.196 −1.14340
\(66\) 2.48342 0.00463163
\(67\) 713.903 1.30175 0.650874 0.759186i \(-0.274403\pi\)
0.650874 + 0.759186i \(0.274403\pi\)
\(68\) −282.738 −0.504221
\(69\) 132.399 0.231000
\(70\) 90.1587 0.153943
\(71\) 548.984 0.917640 0.458820 0.888529i \(-0.348272\pi\)
0.458820 + 0.888529i \(0.348272\pi\)
\(72\) 77.8832 0.127481
\(73\) 514.562 0.824999 0.412499 0.910958i \(-0.364656\pi\)
0.412499 + 0.910958i \(0.364656\pi\)
\(74\) −54.1131 −0.0850070
\(75\) 142.715 0.219724
\(76\) 763.002 1.15161
\(77\) −364.678 −0.539726
\(78\) 7.55523 0.0109675
\(79\) −1074.57 −1.53036 −0.765180 0.643817i \(-0.777350\pi\)
−0.765180 + 0.643817i \(0.777350\pi\)
\(80\) −1014.27 −1.41749
\(81\) 637.056 0.873876
\(82\) 83.4338 0.112363
\(83\) 126.403 0.167162 0.0835812 0.996501i \(-0.473364\pi\)
0.0835812 + 0.996501i \(0.473364\pi\)
\(84\) 254.171 0.330147
\(85\) −570.216 −0.727631
\(86\) 0 0
\(87\) 208.953 0.257496
\(88\) −36.9464 −0.0447557
\(89\) −77.2915 −0.0920548 −0.0460274 0.998940i \(-0.514656\pi\)
−0.0460274 + 0.998940i \(0.514656\pi\)
\(90\) 78.3608 0.0917772
\(91\) −1109.45 −1.27804
\(92\) −982.671 −1.11359
\(93\) −68.7297 −0.0766338
\(94\) −87.5013 −0.0960114
\(95\) 1538.79 1.66186
\(96\) 38.6548 0.0410957
\(97\) −200.732 −0.210116 −0.105058 0.994466i \(-0.533503\pi\)
−0.105058 + 0.994466i \(0.533503\pi\)
\(98\) 102.197 0.105342
\(99\) −316.957 −0.321771
\(100\) −1059.24 −1.05924
\(101\) 1093.85 1.07765 0.538825 0.842418i \(-0.318868\pi\)
0.538825 + 0.842418i \(0.318868\pi\)
\(102\) 7.18982 0.00697940
\(103\) −680.319 −0.650813 −0.325407 0.945574i \(-0.605501\pi\)
−0.325407 + 0.945574i \(0.605501\pi\)
\(104\) −112.401 −0.105979
\(105\) 512.603 0.476428
\(106\) −26.8455 −0.0245987
\(107\) 510.574 0.461299 0.230650 0.973037i \(-0.425915\pi\)
0.230650 + 0.973037i \(0.425915\pi\)
\(108\) 451.663 0.402419
\(109\) −1738.31 −1.52752 −0.763761 0.645499i \(-0.776649\pi\)
−0.763761 + 0.645499i \(0.776649\pi\)
\(110\) −37.1730 −0.0322210
\(111\) −307.663 −0.263082
\(112\) −1877.99 −1.58440
\(113\) 842.602 0.701463 0.350731 0.936476i \(-0.385933\pi\)
0.350731 + 0.936476i \(0.385933\pi\)
\(114\) −19.4026 −0.0159405
\(115\) −1981.81 −1.60700
\(116\) −1550.86 −1.24132
\(117\) −964.268 −0.761937
\(118\) 93.6921 0.0730937
\(119\) −1055.79 −0.813311
\(120\) 51.9331 0.0395069
\(121\) −1180.64 −0.887033
\(122\) −27.3593 −0.0203033
\(123\) 474.368 0.347743
\(124\) 510.114 0.369432
\(125\) −128.443 −0.0919065
\(126\) 145.090 0.102584
\(127\) −665.523 −0.465005 −0.232502 0.972596i \(-0.574691\pi\)
−0.232502 + 0.972596i \(0.574691\pi\)
\(128\) −382.241 −0.263951
\(129\) 0 0
\(130\) −113.090 −0.0762975
\(131\) −393.649 −0.262544 −0.131272 0.991346i \(-0.541906\pi\)
−0.131272 + 0.991346i \(0.541906\pi\)
\(132\) −104.796 −0.0691011
\(133\) 2849.17 1.85755
\(134\) 134.740 0.0868636
\(135\) 910.897 0.580722
\(136\) −106.965 −0.0674423
\(137\) 3056.76 1.90625 0.953127 0.302570i \(-0.0978446\pi\)
0.953127 + 0.302570i \(0.0978446\pi\)
\(138\) 24.9886 0.0154143
\(139\) −2297.91 −1.40220 −0.701102 0.713061i \(-0.747308\pi\)
−0.701102 + 0.713061i \(0.747308\pi\)
\(140\) −3804.55 −2.29674
\(141\) −497.494 −0.297139
\(142\) 103.613 0.0612327
\(143\) 457.432 0.267499
\(144\) −1632.24 −0.944583
\(145\) −3127.71 −1.79133
\(146\) 97.1167 0.0550509
\(147\) 581.050 0.326015
\(148\) 2283.48 1.26825
\(149\) −862.754 −0.474359 −0.237180 0.971466i \(-0.576223\pi\)
−0.237180 + 0.971466i \(0.576223\pi\)
\(150\) 26.9356 0.0146619
\(151\) −1100.95 −0.593336 −0.296668 0.954981i \(-0.595875\pi\)
−0.296668 + 0.954981i \(0.595875\pi\)
\(152\) 288.657 0.154034
\(153\) −917.631 −0.484876
\(154\) −68.8280 −0.0360151
\(155\) 1028.78 0.533119
\(156\) −318.819 −0.163628
\(157\) 567.708 0.288586 0.144293 0.989535i \(-0.453909\pi\)
0.144293 + 0.989535i \(0.453909\pi\)
\(158\) −202.810 −0.102118
\(159\) −152.632 −0.0761289
\(160\) −578.604 −0.285891
\(161\) −3669.45 −1.79623
\(162\) 120.236 0.0583124
\(163\) −1560.44 −0.749836 −0.374918 0.927058i \(-0.622329\pi\)
−0.374918 + 0.927058i \(0.622329\pi\)
\(164\) −3520.77 −1.67638
\(165\) −211.349 −0.0997184
\(166\) 23.8568 0.0111545
\(167\) −2095.15 −0.970822 −0.485411 0.874286i \(-0.661330\pi\)
−0.485411 + 0.874286i \(0.661330\pi\)
\(168\) 96.1573 0.0441589
\(169\) −805.368 −0.366576
\(170\) −107.621 −0.0485537
\(171\) 2476.33 1.10743
\(172\) 0 0
\(173\) 832.450 0.365838 0.182919 0.983128i \(-0.441445\pi\)
0.182919 + 0.983128i \(0.441445\pi\)
\(174\) 39.4371 0.0171823
\(175\) −3955.35 −1.70855
\(176\) 774.307 0.331622
\(177\) 532.692 0.226212
\(178\) −14.5877 −0.00614268
\(179\) −2978.97 −1.24390 −0.621951 0.783056i \(-0.713660\pi\)
−0.621951 + 0.783056i \(0.713660\pi\)
\(180\) −3306.70 −1.36926
\(181\) 4250.39 1.74546 0.872732 0.488200i \(-0.162346\pi\)
0.872732 + 0.488200i \(0.162346\pi\)
\(182\) −209.393 −0.0852817
\(183\) −155.553 −0.0628351
\(184\) −371.761 −0.148949
\(185\) 4605.25 1.83019
\(186\) −12.9718 −0.00511365
\(187\) 435.309 0.170230
\(188\) 3692.41 1.43243
\(189\) 1686.58 0.649104
\(190\) 290.427 0.110894
\(191\) 1087.10 0.411831 0.205916 0.978570i \(-0.433983\pi\)
0.205916 + 0.978570i \(0.433983\pi\)
\(192\) −534.790 −0.201016
\(193\) 3796.24 1.41585 0.707926 0.706287i \(-0.249631\pi\)
0.707926 + 0.706287i \(0.249631\pi\)
\(194\) −37.8855 −0.0140207
\(195\) −642.982 −0.236128
\(196\) −4312.57 −1.57164
\(197\) 4410.07 1.59495 0.797473 0.603355i \(-0.206170\pi\)
0.797473 + 0.603355i \(0.206170\pi\)
\(198\) −59.8214 −0.0214713
\(199\) −939.475 −0.334661 −0.167331 0.985901i \(-0.553515\pi\)
−0.167331 + 0.985901i \(0.553515\pi\)
\(200\) −400.727 −0.141678
\(201\) 766.070 0.268828
\(202\) 206.450 0.0719099
\(203\) −5791.14 −2.00226
\(204\) −303.399 −0.104128
\(205\) −7100.57 −2.41915
\(206\) −128.401 −0.0434278
\(207\) −3189.27 −1.07087
\(208\) 2355.65 0.785264
\(209\) −1174.73 −0.388793
\(210\) 96.7469 0.0317913
\(211\) 4083.91 1.33246 0.666228 0.745748i \(-0.267908\pi\)
0.666228 + 0.745748i \(0.267908\pi\)
\(212\) 1132.84 0.366998
\(213\) 589.100 0.189505
\(214\) 96.3639 0.0307818
\(215\) 0 0
\(216\) 170.872 0.0538257
\(217\) 1904.84 0.595895
\(218\) −328.083 −0.101929
\(219\) 552.163 0.170373
\(220\) 1568.64 0.480717
\(221\) 1324.33 0.403094
\(222\) −58.0673 −0.0175551
\(223\) 357.375 0.107317 0.0536583 0.998559i \(-0.482912\pi\)
0.0536583 + 0.998559i \(0.482912\pi\)
\(224\) −1071.32 −0.319556
\(225\) −3437.76 −1.01860
\(226\) 159.030 0.0468075
\(227\) −4410.09 −1.28946 −0.644731 0.764410i \(-0.723031\pi\)
−0.644731 + 0.764410i \(0.723031\pi\)
\(228\) 818.757 0.237822
\(229\) 2520.88 0.727444 0.363722 0.931508i \(-0.381506\pi\)
0.363722 + 0.931508i \(0.381506\pi\)
\(230\) −374.041 −0.107233
\(231\) −391.326 −0.111460
\(232\) −586.716 −0.166034
\(233\) −3707.94 −1.04255 −0.521277 0.853388i \(-0.674544\pi\)
−0.521277 + 0.853388i \(0.674544\pi\)
\(234\) −181.993 −0.0508429
\(235\) 7446.73 2.06711
\(236\) −3953.65 −1.09051
\(237\) −1153.09 −0.316039
\(238\) −199.266 −0.0542710
\(239\) 1160.46 0.314076 0.157038 0.987593i \(-0.449806\pi\)
0.157038 + 0.987593i \(0.449806\pi\)
\(240\) −1088.39 −0.292730
\(241\) 989.096 0.264370 0.132185 0.991225i \(-0.457801\pi\)
0.132185 + 0.991225i \(0.457801\pi\)
\(242\) −222.830 −0.0591903
\(243\) 2214.79 0.584686
\(244\) 1154.52 0.302912
\(245\) −8697.43 −2.26799
\(246\) 89.5306 0.0232043
\(247\) −3573.85 −0.920641
\(248\) 192.985 0.0494135
\(249\) 135.639 0.0345212
\(250\) −24.2419 −0.00613278
\(251\) 335.320 0.0843235 0.0421617 0.999111i \(-0.486576\pi\)
0.0421617 + 0.999111i \(0.486576\pi\)
\(252\) −6122.54 −1.53049
\(253\) 1512.94 0.375959
\(254\) −125.609 −0.0310291
\(255\) −611.884 −0.150265
\(256\) 3914.83 0.955770
\(257\) −938.359 −0.227756 −0.113878 0.993495i \(-0.536327\pi\)
−0.113878 + 0.993495i \(0.536327\pi\)
\(258\) 0 0
\(259\) 8526.89 2.04570
\(260\) 4772.23 1.13831
\(261\) −5033.33 −1.19370
\(262\) −74.2959 −0.0175191
\(263\) 1594.82 0.373919 0.186960 0.982368i \(-0.440137\pi\)
0.186960 + 0.982368i \(0.440137\pi\)
\(264\) −39.6463 −0.00924265
\(265\) 2284.67 0.529607
\(266\) 537.742 0.123951
\(267\) −82.9394 −0.0190105
\(268\) −5685.79 −1.29595
\(269\) −1135.45 −0.257359 −0.128680 0.991686i \(-0.541074\pi\)
−0.128680 + 0.991686i \(0.541074\pi\)
\(270\) 171.920 0.0387507
\(271\) 3828.46 0.858163 0.429081 0.903266i \(-0.358837\pi\)
0.429081 + 0.903266i \(0.358837\pi\)
\(272\) 2241.72 0.499721
\(273\) −1190.52 −0.263932
\(274\) 576.923 0.127201
\(275\) 1630.82 0.357607
\(276\) −1054.48 −0.229971
\(277\) −4491.44 −0.974240 −0.487120 0.873335i \(-0.661953\pi\)
−0.487120 + 0.873335i \(0.661953\pi\)
\(278\) −433.700 −0.0935668
\(279\) 1655.58 0.355258
\(280\) −1439.33 −0.307201
\(281\) 3495.10 0.741993 0.370997 0.928634i \(-0.379016\pi\)
0.370997 + 0.928634i \(0.379016\pi\)
\(282\) −93.8953 −0.0198276
\(283\) 61.5992 0.0129388 0.00646942 0.999979i \(-0.497941\pi\)
0.00646942 + 0.999979i \(0.497941\pi\)
\(284\) −4372.32 −0.913554
\(285\) 1651.24 0.343196
\(286\) 86.3342 0.0178498
\(287\) −13147.1 −2.70401
\(288\) −931.129 −0.190511
\(289\) −3652.73 −0.743482
\(290\) −590.314 −0.119532
\(291\) −215.400 −0.0433917
\(292\) −4098.17 −0.821325
\(293\) 148.216 0.0295525 0.0147763 0.999891i \(-0.495296\pi\)
0.0147763 + 0.999891i \(0.495296\pi\)
\(294\) 109.665 0.0217545
\(295\) −7973.59 −1.57370
\(296\) 863.882 0.169635
\(297\) −695.387 −0.135860
\(298\) −162.833 −0.0316533
\(299\) 4602.76 0.890249
\(300\) −1136.64 −0.218746
\(301\) 0 0
\(302\) −207.789 −0.0395924
\(303\) 1173.79 0.222549
\(304\) −6049.53 −1.14133
\(305\) 2328.39 0.437126
\(306\) −173.191 −0.0323551
\(307\) 5885.87 1.09422 0.547108 0.837062i \(-0.315729\pi\)
0.547108 + 0.837062i \(0.315729\pi\)
\(308\) 2904.43 0.537322
\(309\) −730.032 −0.134402
\(310\) 194.168 0.0355742
\(311\) 6292.08 1.14724 0.573619 0.819122i \(-0.305539\pi\)
0.573619 + 0.819122i \(0.305539\pi\)
\(312\) −120.615 −0.0218861
\(313\) −4401.88 −0.794917 −0.397459 0.917620i \(-0.630108\pi\)
−0.397459 + 0.917620i \(0.630108\pi\)
\(314\) 107.147 0.0192569
\(315\) −12347.7 −2.20862
\(316\) 8558.27 1.52354
\(317\) 9513.95 1.68567 0.842834 0.538173i \(-0.180885\pi\)
0.842834 + 0.538173i \(0.180885\pi\)
\(318\) −28.8072 −0.00507996
\(319\) 2387.73 0.419081
\(320\) 8004.99 1.39841
\(321\) 547.883 0.0952643
\(322\) −692.559 −0.119860
\(323\) −3401.00 −0.585872
\(324\) −5073.75 −0.869985
\(325\) 4961.38 0.846794
\(326\) −294.512 −0.0500354
\(327\) −1865.33 −0.315453
\(328\) −1331.97 −0.224225
\(329\) 13788.1 2.31052
\(330\) −39.8894 −0.00665405
\(331\) 1929.53 0.320412 0.160206 0.987084i \(-0.448784\pi\)
0.160206 + 0.987084i \(0.448784\pi\)
\(332\) −1006.72 −0.166418
\(333\) 7411.08 1.21959
\(334\) −395.431 −0.0647815
\(335\) −11466.9 −1.87016
\(336\) −2015.22 −0.327200
\(337\) −6554.82 −1.05954 −0.529768 0.848142i \(-0.677721\pi\)
−0.529768 + 0.848142i \(0.677721\pi\)
\(338\) −152.002 −0.0244611
\(339\) 904.173 0.144861
\(340\) 4541.42 0.724391
\(341\) −785.380 −0.124723
\(342\) 467.375 0.0738969
\(343\) −5902.90 −0.929233
\(344\) 0 0
\(345\) −2126.63 −0.331867
\(346\) 157.114 0.0244118
\(347\) 3250.25 0.502832 0.251416 0.967879i \(-0.419104\pi\)
0.251416 + 0.967879i \(0.419104\pi\)
\(348\) −1664.18 −0.256349
\(349\) −11946.5 −1.83232 −0.916160 0.400814i \(-0.868727\pi\)
−0.916160 + 0.400814i \(0.868727\pi\)
\(350\) −746.519 −0.114009
\(351\) −2115.56 −0.321709
\(352\) 441.712 0.0668844
\(353\) 11585.6 1.74685 0.873427 0.486956i \(-0.161893\pi\)
0.873427 + 0.486956i \(0.161893\pi\)
\(354\) 100.538 0.0150948
\(355\) −8817.93 −1.31833
\(356\) 615.579 0.0916450
\(357\) −1132.94 −0.167959
\(358\) −562.240 −0.0830036
\(359\) −1265.03 −0.185977 −0.0929886 0.995667i \(-0.529642\pi\)
−0.0929886 + 0.995667i \(0.529642\pi\)
\(360\) −1250.98 −0.183146
\(361\) 2318.99 0.338094
\(362\) 802.204 0.116472
\(363\) −1266.91 −0.183184
\(364\) 8836.06 1.27235
\(365\) −8265.03 −1.18524
\(366\) −29.3586 −0.00419289
\(367\) −1501.45 −0.213556 −0.106778 0.994283i \(-0.534053\pi\)
−0.106778 + 0.994283i \(0.534053\pi\)
\(368\) 7791.20 1.10365
\(369\) −11426.7 −1.61206
\(370\) 869.179 0.122126
\(371\) 4230.19 0.591970
\(372\) 547.390 0.0762925
\(373\) 1196.30 0.166065 0.0830325 0.996547i \(-0.473539\pi\)
0.0830325 + 0.996547i \(0.473539\pi\)
\(374\) 82.1587 0.0113592
\(375\) −137.829 −0.0189799
\(376\) 1396.90 0.191595
\(377\) 7264.10 0.992361
\(378\) 318.319 0.0433137
\(379\) −1359.57 −0.184265 −0.0921326 0.995747i \(-0.529368\pi\)
−0.0921326 + 0.995747i \(0.529368\pi\)
\(380\) −12255.5 −1.65446
\(381\) −714.155 −0.0960296
\(382\) 205.175 0.0274809
\(383\) 10767.3 1.43651 0.718257 0.695778i \(-0.244940\pi\)
0.718257 + 0.695778i \(0.244940\pi\)
\(384\) −410.173 −0.0545092
\(385\) 5857.55 0.775399
\(386\) 716.489 0.0944776
\(387\) 0 0
\(388\) 1598.71 0.209181
\(389\) 6353.89 0.828161 0.414081 0.910240i \(-0.364103\pi\)
0.414081 + 0.910240i \(0.364103\pi\)
\(390\) −121.354 −0.0157564
\(391\) 4380.15 0.566531
\(392\) −1631.52 −0.210215
\(393\) −422.414 −0.0542187
\(394\) 832.341 0.106428
\(395\) 17260.0 2.19860
\(396\) 2524.36 0.320339
\(397\) −14439.9 −1.82548 −0.912741 0.408538i \(-0.866039\pi\)
−0.912741 + 0.408538i \(0.866039\pi\)
\(398\) −177.313 −0.0223314
\(399\) 3057.37 0.383609
\(400\) 8398.25 1.04978
\(401\) −4528.96 −0.564004 −0.282002 0.959414i \(-0.590998\pi\)
−0.282002 + 0.959414i \(0.590998\pi\)
\(402\) 144.585 0.0179385
\(403\) −2389.34 −0.295338
\(404\) −8711.87 −1.07285
\(405\) −10232.6 −1.25546
\(406\) −1093.00 −0.133608
\(407\) −3515.69 −0.428173
\(408\) −114.781 −0.0139277
\(409\) −1012.63 −0.122424 −0.0612120 0.998125i \(-0.519497\pi\)
−0.0612120 + 0.998125i \(0.519497\pi\)
\(410\) −1340.14 −0.161426
\(411\) 3280.13 0.393666
\(412\) 5418.32 0.647916
\(413\) −14763.6 −1.75900
\(414\) −601.932 −0.0714574
\(415\) −2030.31 −0.240154
\(416\) 1343.81 0.158379
\(417\) −2465.83 −0.289573
\(418\) −221.715 −0.0259436
\(419\) 2898.28 0.337924 0.168962 0.985623i \(-0.445958\pi\)
0.168962 + 0.985623i \(0.445958\pi\)
\(420\) −4082.56 −0.474306
\(421\) 3294.97 0.381442 0.190721 0.981644i \(-0.438917\pi\)
0.190721 + 0.981644i \(0.438917\pi\)
\(422\) 770.784 0.0889127
\(423\) 11983.8 1.37747
\(424\) 428.572 0.0490880
\(425\) 4721.42 0.538877
\(426\) 111.185 0.0126453
\(427\) 4311.16 0.488599
\(428\) −4066.40 −0.459245
\(429\) 490.858 0.0552421
\(430\) 0 0
\(431\) −10692.3 −1.19496 −0.597480 0.801884i \(-0.703831\pi\)
−0.597480 + 0.801884i \(0.703831\pi\)
\(432\) −3581.05 −0.398827
\(433\) −8088.13 −0.897669 −0.448835 0.893615i \(-0.648161\pi\)
−0.448835 + 0.893615i \(0.648161\pi\)
\(434\) 359.514 0.0397632
\(435\) −3356.26 −0.369932
\(436\) 13844.6 1.52072
\(437\) −11820.3 −1.29392
\(438\) 104.213 0.0113687
\(439\) 1011.15 0.109930 0.0549651 0.998488i \(-0.482495\pi\)
0.0549651 + 0.998488i \(0.482495\pi\)
\(440\) 593.444 0.0642985
\(441\) −13996.5 −1.51134
\(442\) 249.949 0.0268978
\(443\) −10329.4 −1.10783 −0.553913 0.832575i \(-0.686866\pi\)
−0.553913 + 0.832575i \(0.686866\pi\)
\(444\) 2450.35 0.261911
\(445\) 1241.48 0.132251
\(446\) 67.4498 0.00716108
\(447\) −925.798 −0.0979614
\(448\) 14821.7 1.56308
\(449\) 18981.4 1.99508 0.997539 0.0701154i \(-0.0223367\pi\)
0.997539 + 0.0701154i \(0.0223367\pi\)
\(450\) −648.832 −0.0679694
\(451\) 5420.64 0.565960
\(452\) −6710.80 −0.698339
\(453\) −1181.40 −0.122532
\(454\) −832.345 −0.0860438
\(455\) 17820.2 1.83610
\(456\) 309.750 0.0318100
\(457\) 1631.23 0.166971 0.0834857 0.996509i \(-0.473395\pi\)
0.0834857 + 0.996509i \(0.473395\pi\)
\(458\) 475.783 0.0485412
\(459\) −2013.24 −0.204727
\(460\) 15783.9 1.59985
\(461\) −11466.6 −1.15847 −0.579235 0.815160i \(-0.696649\pi\)
−0.579235 + 0.815160i \(0.696649\pi\)
\(462\) −73.8575 −0.00743758
\(463\) 160.216 0.0160818 0.00804090 0.999968i \(-0.497440\pi\)
0.00804090 + 0.999968i \(0.497440\pi\)
\(464\) 12296.1 1.23024
\(465\) 1103.96 0.110096
\(466\) −699.823 −0.0695680
\(467\) −11139.9 −1.10384 −0.551920 0.833897i \(-0.686105\pi\)
−0.551920 + 0.833897i \(0.686105\pi\)
\(468\) 7679.80 0.758544
\(469\) −21231.6 −2.09038
\(470\) 1405.47 0.137935
\(471\) 609.192 0.0595968
\(472\) −1495.74 −0.145862
\(473\) 0 0
\(474\) −217.630 −0.0210888
\(475\) −12741.3 −1.23076
\(476\) 8408.70 0.809690
\(477\) 3676.64 0.352918
\(478\) 219.022 0.0209578
\(479\) −13531.5 −1.29075 −0.645377 0.763864i \(-0.723300\pi\)
−0.645377 + 0.763864i \(0.723300\pi\)
\(480\) −620.884 −0.0590403
\(481\) −10695.7 −1.01389
\(482\) 186.679 0.0176410
\(483\) −3937.59 −0.370945
\(484\) 9403.07 0.883083
\(485\) 3224.21 0.301864
\(486\) 418.011 0.0390152
\(487\) 3215.48 0.299194 0.149597 0.988747i \(-0.452202\pi\)
0.149597 + 0.988747i \(0.452202\pi\)
\(488\) 436.775 0.0405161
\(489\) −1674.47 −0.154851
\(490\) −1641.52 −0.151340
\(491\) 6495.70 0.597040 0.298520 0.954403i \(-0.403507\pi\)
0.298520 + 0.954403i \(0.403507\pi\)
\(492\) −3778.05 −0.346194
\(493\) 6912.77 0.631512
\(494\) −674.515 −0.0614330
\(495\) 5091.05 0.462274
\(496\) −4044.49 −0.366135
\(497\) −16326.9 −1.47357
\(498\) 25.6001 0.00230355
\(499\) 17673.8 1.58555 0.792775 0.609514i \(-0.208635\pi\)
0.792775 + 0.609514i \(0.208635\pi\)
\(500\) 1022.97 0.0914973
\(501\) −2248.25 −0.200488
\(502\) 63.2871 0.00562678
\(503\) −16367.1 −1.45084 −0.725420 0.688306i \(-0.758355\pi\)
−0.725420 + 0.688306i \(0.758355\pi\)
\(504\) −2316.26 −0.204712
\(505\) −17569.8 −1.54821
\(506\) 285.546 0.0250871
\(507\) −864.219 −0.0757028
\(508\) 5300.48 0.462934
\(509\) 5525.13 0.481134 0.240567 0.970633i \(-0.422667\pi\)
0.240567 + 0.970633i \(0.422667\pi\)
\(510\) −115.485 −0.0100270
\(511\) −15303.2 −1.32480
\(512\) 3796.80 0.327728
\(513\) 5432.95 0.467584
\(514\) −177.103 −0.0151978
\(515\) 10927.5 0.934993
\(516\) 0 0
\(517\) −5684.90 −0.483601
\(518\) 1609.34 0.136506
\(519\) 893.281 0.0755504
\(520\) 1805.42 0.152255
\(521\) 18014.7 1.51485 0.757425 0.652922i \(-0.226457\pi\)
0.757425 + 0.652922i \(0.226457\pi\)
\(522\) −949.973 −0.0796536
\(523\) −2817.84 −0.235594 −0.117797 0.993038i \(-0.537583\pi\)
−0.117797 + 0.993038i \(0.537583\pi\)
\(524\) 3135.17 0.261375
\(525\) −4244.38 −0.352838
\(526\) 301.001 0.0249510
\(527\) −2273.78 −0.187945
\(528\) 830.888 0.0684844
\(529\) 3056.42 0.251206
\(530\) 431.200 0.0353399
\(531\) −12831.6 −1.04867
\(532\) −22691.9 −1.84928
\(533\) 16491.1 1.34016
\(534\) −15.6537 −0.00126854
\(535\) −8200.97 −0.662727
\(536\) −2151.03 −0.173340
\(537\) −3196.65 −0.256882
\(538\) −214.301 −0.0171732
\(539\) 6639.70 0.530598
\(540\) −7254.73 −0.578137
\(541\) −5662.83 −0.450026 −0.225013 0.974356i \(-0.572242\pi\)
−0.225013 + 0.974356i \(0.572242\pi\)
\(542\) 722.570 0.0572639
\(543\) 4560.98 0.360461
\(544\) 1278.81 0.100788
\(545\) 27921.2 2.19452
\(546\) −224.694 −0.0176118
\(547\) 8372.85 0.654474 0.327237 0.944942i \(-0.393882\pi\)
0.327237 + 0.944942i \(0.393882\pi\)
\(548\) −24345.2 −1.89777
\(549\) 3747.01 0.291291
\(550\) 307.795 0.0238626
\(551\) −18654.9 −1.44233
\(552\) −398.927 −0.0307599
\(553\) 31957.9 2.45748
\(554\) −847.699 −0.0650095
\(555\) 4941.77 0.377958
\(556\) 18301.4 1.39596
\(557\) −9315.08 −0.708604 −0.354302 0.935131i \(-0.615282\pi\)
−0.354302 + 0.935131i \(0.615282\pi\)
\(558\) 312.469 0.0237058
\(559\) 0 0
\(560\) 30164.8 2.27624
\(561\) 467.118 0.0351546
\(562\) 659.653 0.0495121
\(563\) −13652.0 −1.02196 −0.510980 0.859593i \(-0.670717\pi\)
−0.510980 + 0.859593i \(0.670717\pi\)
\(564\) 3962.23 0.295816
\(565\) −13534.1 −1.00776
\(566\) 11.6260 0.000863389 0
\(567\) −18946.2 −1.40329
\(568\) −1654.12 −0.122193
\(569\) 11683.5 0.860808 0.430404 0.902636i \(-0.358371\pi\)
0.430404 + 0.902636i \(0.358371\pi\)
\(570\) 311.649 0.0229010
\(571\) −13157.5 −0.964313 −0.482156 0.876085i \(-0.660146\pi\)
−0.482156 + 0.876085i \(0.660146\pi\)
\(572\) −3643.16 −0.266308
\(573\) 1166.54 0.0850485
\(574\) −2481.34 −0.180434
\(575\) 16409.5 1.19013
\(576\) 12882.2 0.931870
\(577\) −11315.2 −0.816395 −0.408198 0.912894i \(-0.633843\pi\)
−0.408198 + 0.912894i \(0.633843\pi\)
\(578\) −689.403 −0.0496114
\(579\) 4073.64 0.292392
\(580\) 24910.3 1.78335
\(581\) −3759.24 −0.268433
\(582\) −40.6539 −0.00289546
\(583\) −1744.14 −0.123902
\(584\) −1550.41 −0.109857
\(585\) 15488.3 1.09464
\(586\) 27.9739 0.00197200
\(587\) −24594.5 −1.72934 −0.864669 0.502342i \(-0.832472\pi\)
−0.864669 + 0.502342i \(0.832472\pi\)
\(588\) −4627.70 −0.324563
\(589\) 6136.05 0.429255
\(590\) −1504.91 −0.105010
\(591\) 4732.33 0.329377
\(592\) −18104.8 −1.25693
\(593\) 212.239 0.0146975 0.00734874 0.999973i \(-0.497661\pi\)
0.00734874 + 0.999973i \(0.497661\pi\)
\(594\) −131.245 −0.00906574
\(595\) 16958.4 1.16845
\(596\) 6871.30 0.472247
\(597\) −1008.13 −0.0691119
\(598\) 868.709 0.0594049
\(599\) −12278.6 −0.837546 −0.418773 0.908091i \(-0.637540\pi\)
−0.418773 + 0.908091i \(0.637540\pi\)
\(600\) −430.009 −0.0292584
\(601\) −23050.4 −1.56447 −0.782235 0.622983i \(-0.785921\pi\)
−0.782235 + 0.622983i \(0.785921\pi\)
\(602\) 0 0
\(603\) −18453.3 −1.24623
\(604\) 8768.35 0.590694
\(605\) 18963.8 1.27436
\(606\) 221.536 0.0148503
\(607\) 3484.20 0.232981 0.116490 0.993192i \(-0.462836\pi\)
0.116490 + 0.993192i \(0.462836\pi\)
\(608\) −3451.02 −0.230193
\(609\) −6214.32 −0.413493
\(610\) 439.453 0.0291688
\(611\) −17295.0 −1.14514
\(612\) 7308.36 0.482717
\(613\) 15811.8 1.04182 0.520908 0.853613i \(-0.325593\pi\)
0.520908 + 0.853613i \(0.325593\pi\)
\(614\) 1110.88 0.0730154
\(615\) −7619.43 −0.499586
\(616\) 1098.80 0.0718698
\(617\) −6781.94 −0.442513 −0.221257 0.975216i \(-0.571016\pi\)
−0.221257 + 0.975216i \(0.571016\pi\)
\(618\) −137.784 −0.00896840
\(619\) −25032.1 −1.62540 −0.812702 0.582679i \(-0.802004\pi\)
−0.812702 + 0.582679i \(0.802004\pi\)
\(620\) −8193.59 −0.530746
\(621\) −6997.10 −0.452148
\(622\) 1187.55 0.0765534
\(623\) 2298.67 0.147824
\(624\) 2527.78 0.162167
\(625\) −14561.5 −0.931935
\(626\) −830.796 −0.0530436
\(627\) −1260.57 −0.0802909
\(628\) −4521.44 −0.287301
\(629\) −10178.4 −0.645212
\(630\) −2330.47 −0.147378
\(631\) −13157.5 −0.830096 −0.415048 0.909800i \(-0.636235\pi\)
−0.415048 + 0.909800i \(0.636235\pi\)
\(632\) 3237.74 0.203782
\(633\) 4382.34 0.275170
\(634\) 1795.63 0.112482
\(635\) 10689.8 0.668051
\(636\) 1215.62 0.0757899
\(637\) 20199.8 1.25643
\(638\) 450.651 0.0279647
\(639\) −14190.4 −0.878505
\(640\) 6139.66 0.379205
\(641\) −17066.7 −1.05163 −0.525815 0.850599i \(-0.676240\pi\)
−0.525815 + 0.850599i \(0.676240\pi\)
\(642\) 103.406 0.00635684
\(643\) −7417.34 −0.454916 −0.227458 0.973788i \(-0.573042\pi\)
−0.227458 + 0.973788i \(0.573042\pi\)
\(644\) 29224.9 1.78823
\(645\) 0 0
\(646\) −641.893 −0.0390943
\(647\) −18527.2 −1.12578 −0.562890 0.826532i \(-0.690310\pi\)
−0.562890 + 0.826532i \(0.690310\pi\)
\(648\) −1919.49 −0.116365
\(649\) 6087.11 0.368167
\(650\) 936.394 0.0565052
\(651\) 2044.04 0.123060
\(652\) 12427.9 0.746497
\(653\) −3103.90 −0.186011 −0.0930053 0.995666i \(-0.529647\pi\)
−0.0930053 + 0.995666i \(0.529647\pi\)
\(654\) −352.057 −0.0210497
\(655\) 6322.89 0.377184
\(656\) 27914.8 1.66142
\(657\) −13300.7 −0.789815
\(658\) 2602.31 0.154177
\(659\) 27085.9 1.60109 0.800545 0.599273i \(-0.204544\pi\)
0.800545 + 0.599273i \(0.204544\pi\)
\(660\) 1683.27 0.0992744
\(661\) 1700.11 0.100040 0.0500202 0.998748i \(-0.484071\pi\)
0.0500202 + 0.998748i \(0.484071\pi\)
\(662\) 364.172 0.0213806
\(663\) 1421.10 0.0832442
\(664\) −380.859 −0.0222593
\(665\) −45764.1 −2.66866
\(666\) 1398.74 0.0813816
\(667\) 24025.7 1.39472
\(668\) 16686.5 0.966500
\(669\) 383.490 0.0221623
\(670\) −2164.22 −0.124793
\(671\) −1777.52 −0.102266
\(672\) −1149.60 −0.0659924
\(673\) −21221.0 −1.21547 −0.607733 0.794141i \(-0.707921\pi\)
−0.607733 + 0.794141i \(0.707921\pi\)
\(674\) −1237.13 −0.0707012
\(675\) −7542.28 −0.430078
\(676\) 6414.26 0.364944
\(677\) 15266.7 0.866688 0.433344 0.901229i \(-0.357333\pi\)
0.433344 + 0.901229i \(0.357333\pi\)
\(678\) 170.651 0.00966637
\(679\) 5969.82 0.337409
\(680\) 1718.10 0.0968912
\(681\) −4732.35 −0.266291
\(682\) −148.230 −0.00832260
\(683\) −6070.04 −0.340064 −0.170032 0.985439i \(-0.554387\pi\)
−0.170032 + 0.985439i \(0.554387\pi\)
\(684\) −19722.5 −1.10250
\(685\) −49098.6 −2.73863
\(686\) −1114.09 −0.0620063
\(687\) 2705.09 0.150227
\(688\) 0 0
\(689\) −5306.13 −0.293393
\(690\) −401.373 −0.0221450
\(691\) −13752.5 −0.757119 −0.378560 0.925577i \(-0.623580\pi\)
−0.378560 + 0.925577i \(0.623580\pi\)
\(692\) −6629.95 −0.364209
\(693\) 9426.37 0.516708
\(694\) 613.441 0.0335532
\(695\) 36909.7 2.01448
\(696\) −629.589 −0.0342881
\(697\) 15693.5 0.852844
\(698\) −2254.73 −0.122268
\(699\) −3978.89 −0.215301
\(700\) 31501.9 1.70094
\(701\) −2208.71 −0.119004 −0.0595021 0.998228i \(-0.518951\pi\)
−0.0595021 + 0.998228i \(0.518951\pi\)
\(702\) −399.283 −0.0214672
\(703\) 27467.5 1.47362
\(704\) −6111.08 −0.327159
\(705\) 7990.88 0.426885
\(706\) 2186.63 0.116565
\(707\) −32531.5 −1.73051
\(708\) −4242.56 −0.225205
\(709\) −12431.5 −0.658498 −0.329249 0.944243i \(-0.606796\pi\)
−0.329249 + 0.944243i \(0.606796\pi\)
\(710\) −1664.27 −0.0879701
\(711\) 27776.0 1.46509
\(712\) 232.884 0.0122580
\(713\) −7902.62 −0.415085
\(714\) −213.827 −0.0112077
\(715\) −7347.40 −0.384304
\(716\) 23725.6 1.23836
\(717\) 1245.26 0.0648608
\(718\) −238.758 −0.0124100
\(719\) 31040.8 1.61005 0.805025 0.593241i \(-0.202152\pi\)
0.805025 + 0.593241i \(0.202152\pi\)
\(720\) 26217.5 1.35704
\(721\) 20232.8 1.04509
\(722\) 437.677 0.0225605
\(723\) 1061.37 0.0545960
\(724\) −33851.7 −1.73769
\(725\) 25897.6 1.32664
\(726\) −239.113 −0.0122236
\(727\) 27301.9 1.39281 0.696405 0.717649i \(-0.254782\pi\)
0.696405 + 0.717649i \(0.254782\pi\)
\(728\) 3342.83 0.170184
\(729\) −14823.9 −0.753131
\(730\) −1559.91 −0.0790891
\(731\) 0 0
\(732\) 1238.88 0.0625553
\(733\) 4837.03 0.243738 0.121869 0.992546i \(-0.461111\pi\)
0.121869 + 0.992546i \(0.461111\pi\)
\(734\) −283.378 −0.0142502
\(735\) −9332.98 −0.468370
\(736\) 4444.58 0.222594
\(737\) 8753.94 0.437525
\(738\) −2156.64 −0.107571
\(739\) 7814.86 0.389005 0.194502 0.980902i \(-0.437691\pi\)
0.194502 + 0.980902i \(0.437691\pi\)
\(740\) −36677.9 −1.82204
\(741\) −3835.00 −0.190124
\(742\) 798.392 0.0395012
\(743\) 21269.6 1.05021 0.525106 0.851037i \(-0.324026\pi\)
0.525106 + 0.851037i \(0.324026\pi\)
\(744\) 207.087 0.0102045
\(745\) 13857.8 0.681490
\(746\) 225.786 0.0110813
\(747\) −3267.32 −0.160033
\(748\) −3466.96 −0.169472
\(749\) −15184.6 −0.740765
\(750\) −26.0134 −0.00126650
\(751\) −14443.0 −0.701773 −0.350887 0.936418i \(-0.614120\pi\)
−0.350887 + 0.936418i \(0.614120\pi\)
\(752\) −29275.7 −1.41965
\(753\) 359.823 0.0174139
\(754\) 1371.00 0.0662187
\(755\) 17683.7 0.852417
\(756\) −13432.6 −0.646213
\(757\) −24206.1 −1.16220 −0.581100 0.813832i \(-0.697378\pi\)
−0.581100 + 0.813832i \(0.697378\pi\)
\(758\) −256.601 −0.0122957
\(759\) 1623.49 0.0776404
\(760\) −4636.48 −0.221293
\(761\) 28668.2 1.36560 0.682801 0.730604i \(-0.260762\pi\)
0.682801 + 0.730604i \(0.260762\pi\)
\(762\) −134.787 −0.00640791
\(763\) 51697.7 2.45293
\(764\) −8658.07 −0.409997
\(765\) 14739.2 0.696599
\(766\) 2032.19 0.0958563
\(767\) 18518.6 0.871798
\(768\) 4200.90 0.197379
\(769\) −26609.6 −1.24781 −0.623904 0.781501i \(-0.714455\pi\)
−0.623904 + 0.781501i \(0.714455\pi\)
\(770\) 1105.53 0.0517412
\(771\) −1006.93 −0.0470346
\(772\) −30234.7 −1.40955
\(773\) −9132.09 −0.424914 −0.212457 0.977170i \(-0.568147\pi\)
−0.212457 + 0.977170i \(0.568147\pi\)
\(774\) 0 0
\(775\) −8518.35 −0.394824
\(776\) 604.818 0.0279790
\(777\) 9149.98 0.422463
\(778\) 1199.21 0.0552619
\(779\) −42350.6 −1.94784
\(780\) 5120.95 0.235076
\(781\) 6731.69 0.308424
\(782\) 826.694 0.0378037
\(783\) −11042.9 −0.504010
\(784\) 34192.6 1.55761
\(785\) −9118.67 −0.414598
\(786\) −79.7249 −0.00361793
\(787\) −1116.17 −0.0505557 −0.0252779 0.999680i \(-0.508047\pi\)
−0.0252779 + 0.999680i \(0.508047\pi\)
\(788\) −35123.5 −1.58784
\(789\) 1711.36 0.0772192
\(790\) 3257.59 0.146709
\(791\) −25059.2 −1.12642
\(792\) 955.011 0.0428470
\(793\) −5407.69 −0.242160
\(794\) −2725.33 −0.121812
\(795\) 2451.61 0.109371
\(796\) 7482.33 0.333171
\(797\) −21836.4 −0.970498 −0.485249 0.874376i \(-0.661271\pi\)
−0.485249 + 0.874376i \(0.661271\pi\)
\(798\) 577.037 0.0255976
\(799\) −16458.5 −0.728737
\(800\) 4790.87 0.211729
\(801\) 1997.87 0.0881289
\(802\) −854.780 −0.0376351
\(803\) 6309.61 0.277287
\(804\) −6101.27 −0.267631
\(805\) 58939.7 2.58056
\(806\) −450.955 −0.0197075
\(807\) −1218.42 −0.0531481
\(808\) −3295.85 −0.143500
\(809\) 27327.4 1.18761 0.593807 0.804607i \(-0.297624\pi\)
0.593807 + 0.804607i \(0.297624\pi\)
\(810\) −1931.26 −0.0837747
\(811\) 29154.8 1.26235 0.631174 0.775641i \(-0.282573\pi\)
0.631174 + 0.775641i \(0.282573\pi\)
\(812\) 46122.8 1.99334
\(813\) 4108.21 0.177222
\(814\) −663.540 −0.0285713
\(815\) 25064.2 1.07725
\(816\) 2405.53 0.103199
\(817\) 0 0
\(818\) −191.121 −0.00816916
\(819\) 28677.6 1.22354
\(820\) 56551.6 2.40838
\(821\) −30897.8 −1.31345 −0.656724 0.754131i \(-0.728058\pi\)
−0.656724 + 0.754131i \(0.728058\pi\)
\(822\) 619.081 0.0262688
\(823\) −4597.16 −0.194711 −0.0973554 0.995250i \(-0.531038\pi\)
−0.0973554 + 0.995250i \(0.531038\pi\)
\(824\) 2049.84 0.0866622
\(825\) 1749.99 0.0738505
\(826\) −2786.42 −0.117375
\(827\) 40709.2 1.71172 0.855862 0.517204i \(-0.173027\pi\)
0.855862 + 0.517204i \(0.173027\pi\)
\(828\) 25400.6 1.06610
\(829\) 6460.64 0.270672 0.135336 0.990800i \(-0.456789\pi\)
0.135336 + 0.990800i \(0.456789\pi\)
\(830\) −383.194 −0.0160251
\(831\) −4819.64 −0.201193
\(832\) −18591.6 −0.774695
\(833\) 19222.8 0.799556
\(834\) −465.392 −0.0193228
\(835\) 33652.8 1.39474
\(836\) 9356.00 0.387062
\(837\) 3632.26 0.149999
\(838\) 547.012 0.0225492
\(839\) 42238.9 1.73808 0.869039 0.494744i \(-0.164738\pi\)
0.869039 + 0.494744i \(0.164738\pi\)
\(840\) −1544.50 −0.0634410
\(841\) 13528.5 0.554696
\(842\) 621.882 0.0254530
\(843\) 3750.50 0.153231
\(844\) −32525.8 −1.32652
\(845\) 12936.0 0.526643
\(846\) 2261.78 0.0919167
\(847\) 35112.6 1.42442
\(848\) −8981.81 −0.363723
\(849\) 66.1004 0.00267204
\(850\) 891.106 0.0359584
\(851\) −35375.5 −1.42498
\(852\) −4691.82 −0.188661
\(853\) −5629.01 −0.225948 −0.112974 0.993598i \(-0.536038\pi\)
−0.112974 + 0.993598i \(0.536038\pi\)
\(854\) 813.674 0.0326034
\(855\) −39775.6 −1.59099
\(856\) −1538.39 −0.0614265
\(857\) −26651.2 −1.06229 −0.531147 0.847280i \(-0.678239\pi\)
−0.531147 + 0.847280i \(0.678239\pi\)
\(858\) 92.6429 0.00368622
\(859\) 2148.00 0.0853187 0.0426593 0.999090i \(-0.486417\pi\)
0.0426593 + 0.999090i \(0.486417\pi\)
\(860\) 0 0
\(861\) −14107.8 −0.558413
\(862\) −2018.02 −0.0797378
\(863\) −14989.5 −0.591251 −0.295625 0.955304i \(-0.595528\pi\)
−0.295625 + 0.955304i \(0.595528\pi\)
\(864\) −2042.85 −0.0804388
\(865\) −13371.0 −0.525583
\(866\) −1526.53 −0.0599001
\(867\) −3919.64 −0.153539
\(868\) −15170.9 −0.593242
\(869\) −13176.5 −0.514362
\(870\) −633.450 −0.0246850
\(871\) 26631.8 1.03603
\(872\) 5237.63 0.203404
\(873\) 5188.63 0.201155
\(874\) −2230.93 −0.0863413
\(875\) 3819.93 0.147586
\(876\) −4397.63 −0.169614
\(877\) 26925.9 1.03674 0.518370 0.855156i \(-0.326539\pi\)
0.518370 + 0.855156i \(0.326539\pi\)
\(878\) 190.840 0.00733548
\(879\) 159.047 0.00610299
\(880\) −12437.1 −0.476426
\(881\) 14099.7 0.539197 0.269598 0.962973i \(-0.413109\pi\)
0.269598 + 0.962973i \(0.413109\pi\)
\(882\) −2641.65 −0.100849
\(883\) 48023.0 1.83024 0.915120 0.403181i \(-0.132095\pi\)
0.915120 + 0.403181i \(0.132095\pi\)
\(884\) −10547.4 −0.401299
\(885\) −8556.24 −0.324989
\(886\) −1949.54 −0.0739235
\(887\) −9693.92 −0.366956 −0.183478 0.983024i \(-0.558736\pi\)
−0.183478 + 0.983024i \(0.558736\pi\)
\(888\) 927.008 0.0350319
\(889\) 19792.8 0.746715
\(890\) 234.312 0.00882490
\(891\) 7811.63 0.293714
\(892\) −2846.27 −0.106839
\(893\) 44415.2 1.66439
\(894\) −174.732 −0.00653681
\(895\) 47849.0 1.78705
\(896\) 11367.9 0.423858
\(897\) 4939.10 0.183848
\(898\) 3582.49 0.133128
\(899\) −12472.0 −0.462696
\(900\) 27379.7 1.01406
\(901\) −5049.50 −0.186707
\(902\) 1023.07 0.0377657
\(903\) 0 0
\(904\) −2538.81 −0.0934066
\(905\) −68270.9 −2.50763
\(906\) −222.973 −0.00817634
\(907\) 18966.2 0.694334 0.347167 0.937803i \(-0.387144\pi\)
0.347167 + 0.937803i \(0.387144\pi\)
\(908\) 35123.6 1.28372
\(909\) −28274.5 −1.03169
\(910\) 3363.33 0.122520
\(911\) 12247.3 0.445414 0.222707 0.974885i \(-0.428511\pi\)
0.222707 + 0.974885i \(0.428511\pi\)
\(912\) −6491.59 −0.235700
\(913\) 1549.96 0.0561842
\(914\) 307.874 0.0111417
\(915\) 2498.54 0.0902723
\(916\) −20077.3 −0.724205
\(917\) 11707.2 0.421599
\(918\) −379.971 −0.0136611
\(919\) −23177.0 −0.831926 −0.415963 0.909382i \(-0.636555\pi\)
−0.415963 + 0.909382i \(0.636555\pi\)
\(920\) 5971.33 0.213988
\(921\) 6315.97 0.225970
\(922\) −2164.18 −0.0773029
\(923\) 20479.6 0.730330
\(924\) 3116.67 0.110964
\(925\) −38131.7 −1.35542
\(926\) 30.2386 0.00107311
\(927\) 17585.2 0.623058
\(928\) 7014.45 0.248126
\(929\) 39323.8 1.38878 0.694388 0.719601i \(-0.255675\pi\)
0.694388 + 0.719601i \(0.255675\pi\)
\(930\) 208.357 0.00734655
\(931\) −51875.0 −1.82614
\(932\) 29531.4 1.03791
\(933\) 6751.86 0.236920
\(934\) −2102.51 −0.0736575
\(935\) −6992.04 −0.244561
\(936\) 2905.40 0.101459
\(937\) 43289.9 1.50931 0.754653 0.656124i \(-0.227805\pi\)
0.754653 + 0.656124i \(0.227805\pi\)
\(938\) −4007.19 −0.139488
\(939\) −4723.54 −0.164161
\(940\) −59308.5 −2.05791
\(941\) 28422.3 0.984635 0.492318 0.870416i \(-0.336150\pi\)
0.492318 + 0.870416i \(0.336150\pi\)
\(942\) 114.977 0.00397680
\(943\) 54543.4 1.88354
\(944\) 31346.9 1.08078
\(945\) −27090.3 −0.932537
\(946\) 0 0
\(947\) 2201.51 0.0755431 0.0377716 0.999286i \(-0.487974\pi\)
0.0377716 + 0.999286i \(0.487974\pi\)
\(948\) 9183.65 0.314632
\(949\) 19195.5 0.656599
\(950\) −2404.75 −0.0821268
\(951\) 10209.2 0.348113
\(952\) 3181.16 0.108300
\(953\) −10044.5 −0.341420 −0.170710 0.985321i \(-0.554606\pi\)
−0.170710 + 0.985321i \(0.554606\pi\)
\(954\) 693.917 0.0235497
\(955\) −17461.3 −0.591659
\(956\) −9242.37 −0.312677
\(957\) 2562.20 0.0865458
\(958\) −2553.89 −0.0861300
\(959\) −90908.9 −3.06111
\(960\) 8589.94 0.288791
\(961\) −25688.7 −0.862296
\(962\) −2018.67 −0.0676553
\(963\) −13197.6 −0.441626
\(964\) −7877.54 −0.263193
\(965\) −60976.2 −2.03409
\(966\) −743.167 −0.0247526
\(967\) −28057.6 −0.933062 −0.466531 0.884505i \(-0.654496\pi\)
−0.466531 + 0.884505i \(0.654496\pi\)
\(968\) 3557.34 0.118117
\(969\) −3649.52 −0.120990
\(970\) 608.527 0.0201429
\(971\) 38662.6 1.27780 0.638899 0.769290i \(-0.279390\pi\)
0.638899 + 0.769290i \(0.279390\pi\)
\(972\) −17639.4 −0.582082
\(973\) 68340.4 2.25169
\(974\) 606.879 0.0199647
\(975\) 5323.93 0.174874
\(976\) −9153.73 −0.300209
\(977\) 1575.15 0.0515798 0.0257899 0.999667i \(-0.491790\pi\)
0.0257899 + 0.999667i \(0.491790\pi\)
\(978\) −316.033 −0.0103330
\(979\) −947.755 −0.0309401
\(980\) 69269.6 2.25790
\(981\) 44932.7 1.46238
\(982\) 1225.98 0.0398396
\(983\) 51323.9 1.66529 0.832644 0.553809i \(-0.186826\pi\)
0.832644 + 0.553809i \(0.186826\pi\)
\(984\) −1429.30 −0.0463053
\(985\) −70835.7 −2.29138
\(986\) 1304.69 0.0421399
\(987\) 14795.6 0.477152
\(988\) 28463.5 0.916542
\(989\) 0 0
\(990\) 960.867 0.0308468
\(991\) −17395.6 −0.557609 −0.278804 0.960348i \(-0.589938\pi\)
−0.278804 + 0.960348i \(0.589938\pi\)
\(992\) −2307.22 −0.0738451
\(993\) 2070.52 0.0661693
\(994\) −3081.49 −0.0983288
\(995\) 15090.1 0.480792
\(996\) −1080.28 −0.0343675
\(997\) −9953.86 −0.316190 −0.158095 0.987424i \(-0.550535\pi\)
−0.158095 + 0.987424i \(0.550535\pi\)
\(998\) 3335.70 0.105801
\(999\) 16259.5 0.514944
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.g.1.16 30
43.8 odd 14 43.4.e.a.21.6 60
43.27 odd 14 43.4.e.a.41.6 yes 60
43.42 odd 2 1849.4.a.h.1.15 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.e.a.21.6 60 43.8 odd 14
43.4.e.a.41.6 yes 60 43.27 odd 14
1849.4.a.g.1.16 30 1.1 even 1 trivial
1849.4.a.h.1.15 30 43.42 odd 2