Properties

Label 1849.4.a.i.1.4
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 1.4
Character \(\chi\) \(=\) 1849.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.05256 q^{2} +9.36203 q^{3} +17.5283 q^{4} +14.1438 q^{5} -47.3022 q^{6} -13.7151 q^{7} -48.1425 q^{8} +60.6475 q^{9} +O(q^{10})\) \(q-5.05256 q^{2} +9.36203 q^{3} +17.5283 q^{4} +14.1438 q^{5} -47.3022 q^{6} -13.7151 q^{7} -48.1425 q^{8} +60.6475 q^{9} -71.4625 q^{10} +10.3705 q^{11} +164.101 q^{12} -61.4205 q^{13} +69.2963 q^{14} +132.415 q^{15} +103.016 q^{16} -24.4390 q^{17} -306.425 q^{18} -65.5106 q^{19} +247.918 q^{20} -128.401 q^{21} -52.3977 q^{22} +23.4730 q^{23} -450.711 q^{24} +75.0480 q^{25} +310.331 q^{26} +315.009 q^{27} -240.403 q^{28} -236.538 q^{29} -669.034 q^{30} -210.270 q^{31} -135.354 q^{32} +97.0891 q^{33} +123.479 q^{34} -193.984 q^{35} +1063.05 q^{36} -316.642 q^{37} +330.996 q^{38} -575.020 q^{39} -680.919 q^{40} +13.2054 q^{41} +648.754 q^{42} +181.778 q^{44} +857.789 q^{45} -118.599 q^{46} +450.216 q^{47} +964.439 q^{48} -154.896 q^{49} -379.185 q^{50} -228.798 q^{51} -1076.60 q^{52} -205.541 q^{53} -1591.60 q^{54} +146.679 q^{55} +660.279 q^{56} -613.312 q^{57} +1195.12 q^{58} +334.558 q^{59} +2321.01 q^{60} +811.774 q^{61} +1062.40 q^{62} -831.787 q^{63} -140.242 q^{64} -868.722 q^{65} -490.548 q^{66} -113.497 q^{67} -428.375 q^{68} +219.755 q^{69} +980.116 q^{70} -53.8087 q^{71} -2919.72 q^{72} -108.423 q^{73} +1599.85 q^{74} +702.602 q^{75} -1148.29 q^{76} -142.233 q^{77} +2905.32 q^{78} -723.417 q^{79} +1457.04 q^{80} +1311.64 q^{81} -66.7209 q^{82} +191.269 q^{83} -2250.66 q^{84} -345.661 q^{85} -2214.47 q^{87} -499.263 q^{88} +419.159 q^{89} -4334.03 q^{90} +842.389 q^{91} +411.443 q^{92} -1968.55 q^{93} -2274.74 q^{94} -926.571 q^{95} -1267.19 q^{96} -953.469 q^{97} +782.621 q^{98} +628.947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.05256 −1.78635 −0.893174 0.449710i \(-0.851527\pi\)
−0.893174 + 0.449710i \(0.851527\pi\)
\(3\) 9.36203 1.80172 0.900861 0.434107i \(-0.142936\pi\)
0.900861 + 0.434107i \(0.142936\pi\)
\(4\) 17.5283 2.19104
\(5\) 14.1438 1.26506 0.632531 0.774535i \(-0.282016\pi\)
0.632531 + 0.774535i \(0.282016\pi\)
\(6\) −47.3022 −3.21851
\(7\) −13.7151 −0.740546 −0.370273 0.928923i \(-0.620736\pi\)
−0.370273 + 0.928923i \(0.620736\pi\)
\(8\) −48.1425 −2.12762
\(9\) 60.6475 2.24620
\(10\) −71.4625 −2.25984
\(11\) 10.3705 0.284257 0.142129 0.989848i \(-0.454605\pi\)
0.142129 + 0.989848i \(0.454605\pi\)
\(12\) 164.101 3.94765
\(13\) −61.4205 −1.31038 −0.655192 0.755463i \(-0.727412\pi\)
−0.655192 + 0.755463i \(0.727412\pi\)
\(14\) 69.2963 1.32287
\(15\) 132.415 2.27929
\(16\) 103.016 1.60963
\(17\) −24.4390 −0.348666 −0.174333 0.984687i \(-0.555777\pi\)
−0.174333 + 0.984687i \(0.555777\pi\)
\(18\) −306.425 −4.01251
\(19\) −65.5106 −0.791008 −0.395504 0.918464i \(-0.629430\pi\)
−0.395504 + 0.918464i \(0.629430\pi\)
\(20\) 247.918 2.77181
\(21\) −128.401 −1.33426
\(22\) −52.3977 −0.507783
\(23\) 23.4730 0.212803 0.106401 0.994323i \(-0.466067\pi\)
0.106401 + 0.994323i \(0.466067\pi\)
\(24\) −450.711 −3.83338
\(25\) 75.0480 0.600384
\(26\) 310.331 2.34080
\(27\) 315.009 2.24532
\(28\) −240.403 −1.62257
\(29\) −236.538 −1.51462 −0.757310 0.653055i \(-0.773487\pi\)
−0.757310 + 0.653055i \(0.773487\pi\)
\(30\) −669.034 −4.07161
\(31\) −210.270 −1.21824 −0.609122 0.793076i \(-0.708478\pi\)
−0.609122 + 0.793076i \(0.708478\pi\)
\(32\) −135.354 −0.747735
\(33\) 97.0891 0.512153
\(34\) 123.479 0.622840
\(35\) −193.984 −0.936837
\(36\) 1063.05 4.92153
\(37\) −316.642 −1.40691 −0.703455 0.710740i \(-0.748360\pi\)
−0.703455 + 0.710740i \(0.748360\pi\)
\(38\) 330.996 1.41302
\(39\) −575.020 −2.36095
\(40\) −680.919 −2.69157
\(41\) 13.2054 0.0503008 0.0251504 0.999684i \(-0.491994\pi\)
0.0251504 + 0.999684i \(0.491994\pi\)
\(42\) 648.754 2.38345
\(43\) 0 0
\(44\) 181.778 0.622820
\(45\) 857.789 2.84159
\(46\) −118.599 −0.380140
\(47\) 450.216 1.39725 0.698625 0.715488i \(-0.253796\pi\)
0.698625 + 0.715488i \(0.253796\pi\)
\(48\) 964.439 2.90010
\(49\) −154.896 −0.451592
\(50\) −379.185 −1.07250
\(51\) −228.798 −0.628200
\(52\) −1076.60 −2.87111
\(53\) −205.541 −0.532701 −0.266351 0.963876i \(-0.585818\pi\)
−0.266351 + 0.963876i \(0.585818\pi\)
\(54\) −1591.60 −4.01092
\(55\) 146.679 0.359603
\(56\) 660.279 1.57560
\(57\) −613.312 −1.42518
\(58\) 1195.12 2.70564
\(59\) 334.558 0.738232 0.369116 0.929383i \(-0.379661\pi\)
0.369116 + 0.929383i \(0.379661\pi\)
\(60\) 2321.01 4.99403
\(61\) 811.774 1.70389 0.851943 0.523634i \(-0.175424\pi\)
0.851943 + 0.523634i \(0.175424\pi\)
\(62\) 1062.40 2.17621
\(63\) −831.787 −1.66342
\(64\) −140.242 −0.273910
\(65\) −868.722 −1.65772
\(66\) −490.548 −0.914884
\(67\) −113.497 −0.206952 −0.103476 0.994632i \(-0.532997\pi\)
−0.103476 + 0.994632i \(0.532997\pi\)
\(68\) −428.375 −0.763943
\(69\) 219.755 0.383411
\(70\) 980.116 1.67352
\(71\) −53.8087 −0.0899425 −0.0449712 0.998988i \(-0.514320\pi\)
−0.0449712 + 0.998988i \(0.514320\pi\)
\(72\) −2919.72 −4.77907
\(73\) −108.423 −0.173835 −0.0869174 0.996216i \(-0.527702\pi\)
−0.0869174 + 0.996216i \(0.527702\pi\)
\(74\) 1599.85 2.51323
\(75\) 702.602 1.08173
\(76\) −1148.29 −1.73313
\(77\) −142.233 −0.210506
\(78\) 2905.32 4.21748
\(79\) −723.417 −1.03026 −0.515132 0.857111i \(-0.672257\pi\)
−0.515132 + 0.857111i \(0.672257\pi\)
\(80\) 1457.04 2.03628
\(81\) 1311.64 1.79923
\(82\) −66.7209 −0.0898548
\(83\) 191.269 0.252945 0.126473 0.991970i \(-0.459634\pi\)
0.126473 + 0.991970i \(0.459634\pi\)
\(84\) −2250.66 −2.92342
\(85\) −345.661 −0.441085
\(86\) 0 0
\(87\) −2214.47 −2.72893
\(88\) −499.263 −0.604791
\(89\) 419.159 0.499221 0.249611 0.968346i \(-0.419697\pi\)
0.249611 + 0.968346i \(0.419697\pi\)
\(90\) −4334.03 −5.07607
\(91\) 842.389 0.970399
\(92\) 411.443 0.466260
\(93\) −1968.55 −2.19494
\(94\) −2274.74 −2.49598
\(95\) −926.571 −1.00068
\(96\) −1267.19 −1.34721
\(97\) −953.469 −0.998043 −0.499021 0.866590i \(-0.666307\pi\)
−0.499021 + 0.866590i \(0.666307\pi\)
\(98\) 782.621 0.806701
\(99\) 628.947 0.638500
\(100\) 1315.47 1.31547
\(101\) −1393.87 −1.37322 −0.686612 0.727024i \(-0.740903\pi\)
−0.686612 + 0.727024i \(0.740903\pi\)
\(102\) 1156.02 1.12218
\(103\) −1470.15 −1.40639 −0.703197 0.710995i \(-0.748245\pi\)
−0.703197 + 0.710995i \(0.748245\pi\)
\(104\) 2956.94 2.78800
\(105\) −1816.08 −1.68792
\(106\) 1038.51 0.951590
\(107\) −1071.54 −0.968124 −0.484062 0.875034i \(-0.660839\pi\)
−0.484062 + 0.875034i \(0.660839\pi\)
\(108\) 5521.59 4.91958
\(109\) −1637.65 −1.43907 −0.719536 0.694455i \(-0.755645\pi\)
−0.719536 + 0.694455i \(0.755645\pi\)
\(110\) −741.104 −0.642377
\(111\) −2964.41 −2.53486
\(112\) −1412.88 −1.19200
\(113\) 1051.03 0.874980 0.437490 0.899223i \(-0.355868\pi\)
0.437490 + 0.899223i \(0.355868\pi\)
\(114\) 3098.79 2.54586
\(115\) 331.998 0.269209
\(116\) −4146.12 −3.31860
\(117\) −3725.00 −2.94339
\(118\) −1690.37 −1.31874
\(119\) 335.183 0.258203
\(120\) −6374.79 −4.84946
\(121\) −1223.45 −0.919198
\(122\) −4101.54 −3.04374
\(123\) 123.629 0.0906281
\(124\) −3685.68 −2.66923
\(125\) −706.512 −0.505539
\(126\) 4202.65 2.97144
\(127\) 316.221 0.220946 0.110473 0.993879i \(-0.464763\pi\)
0.110473 + 0.993879i \(0.464763\pi\)
\(128\) 1791.42 1.23703
\(129\) 0 0
\(130\) 4389.27 2.96126
\(131\) −1798.72 −1.19965 −0.599826 0.800130i \(-0.704764\pi\)
−0.599826 + 0.800130i \(0.704764\pi\)
\(132\) 1701.81 1.12215
\(133\) 898.484 0.585778
\(134\) 573.448 0.369689
\(135\) 4455.44 2.84047
\(136\) 1176.55 0.741829
\(137\) 2412.04 1.50419 0.752096 0.659054i \(-0.229043\pi\)
0.752096 + 0.659054i \(0.229043\pi\)
\(138\) −1110.32 −0.684907
\(139\) 2424.03 1.47916 0.739582 0.673066i \(-0.235023\pi\)
0.739582 + 0.673066i \(0.235023\pi\)
\(140\) −3400.22 −2.05265
\(141\) 4214.93 2.51746
\(142\) 271.871 0.160669
\(143\) −636.963 −0.372486
\(144\) 6247.67 3.61555
\(145\) −3345.55 −1.91609
\(146\) 547.813 0.310530
\(147\) −1450.14 −0.813643
\(148\) −5550.21 −3.08260
\(149\) −263.130 −0.144674 −0.0723372 0.997380i \(-0.523046\pi\)
−0.0723372 + 0.997380i \(0.523046\pi\)
\(150\) −3549.94 −1.93234
\(151\) 1149.48 0.619493 0.309746 0.950819i \(-0.399756\pi\)
0.309746 + 0.950819i \(0.399756\pi\)
\(152\) 3153.84 1.68296
\(153\) −1482.16 −0.783176
\(154\) 718.639 0.376036
\(155\) −2974.02 −1.54116
\(156\) −10079.2 −5.17294
\(157\) −945.081 −0.480418 −0.240209 0.970721i \(-0.577216\pi\)
−0.240209 + 0.970721i \(0.577216\pi\)
\(158\) 3655.11 1.84041
\(159\) −1924.28 −0.959780
\(160\) −1914.43 −0.945932
\(161\) −321.935 −0.157590
\(162\) −6627.13 −3.21405
\(163\) −1316.21 −0.632476 −0.316238 0.948680i \(-0.602420\pi\)
−0.316238 + 0.948680i \(0.602420\pi\)
\(164\) 231.468 0.110211
\(165\) 1373.21 0.647906
\(166\) −966.396 −0.451849
\(167\) −1745.74 −0.808917 −0.404459 0.914556i \(-0.632540\pi\)
−0.404459 + 0.914556i \(0.632540\pi\)
\(168\) 6181.55 2.83879
\(169\) 1575.48 0.717105
\(170\) 1746.47 0.787931
\(171\) −3973.05 −1.77677
\(172\) 0 0
\(173\) 1020.88 0.448646 0.224323 0.974515i \(-0.427983\pi\)
0.224323 + 0.974515i \(0.427983\pi\)
\(174\) 11188.8 4.87482
\(175\) −1029.29 −0.444612
\(176\) 1068.33 0.457548
\(177\) 3132.14 1.33009
\(178\) −2117.82 −0.891784
\(179\) 1448.99 0.605043 0.302521 0.953143i \(-0.402172\pi\)
0.302521 + 0.953143i \(0.402172\pi\)
\(180\) 15035.6 6.22605
\(181\) −1207.52 −0.495882 −0.247941 0.968775i \(-0.579754\pi\)
−0.247941 + 0.968775i \(0.579754\pi\)
\(182\) −4256.22 −1.73347
\(183\) 7599.85 3.06993
\(184\) −1130.05 −0.452763
\(185\) −4478.53 −1.77983
\(186\) 9946.23 3.92093
\(187\) −253.445 −0.0991109
\(188\) 7891.54 3.06143
\(189\) −4320.38 −1.66276
\(190\) 4681.55 1.78756
\(191\) 4420.48 1.67463 0.837316 0.546719i \(-0.184123\pi\)
0.837316 + 0.546719i \(0.184123\pi\)
\(192\) −1312.95 −0.493510
\(193\) 3256.05 1.21438 0.607192 0.794556i \(-0.292296\pi\)
0.607192 + 0.794556i \(0.292296\pi\)
\(194\) 4817.46 1.78285
\(195\) −8132.99 −2.98675
\(196\) −2715.07 −0.989457
\(197\) −4223.73 −1.52755 −0.763777 0.645480i \(-0.776657\pi\)
−0.763777 + 0.645480i \(0.776657\pi\)
\(198\) −3177.79 −1.14058
\(199\) 4105.07 1.46232 0.731158 0.682208i \(-0.238980\pi\)
0.731158 + 0.682208i \(0.238980\pi\)
\(200\) −3613.00 −1.27739
\(201\) −1062.56 −0.372871
\(202\) 7042.63 2.45306
\(203\) 3244.14 1.12165
\(204\) −4010.46 −1.37641
\(205\) 186.775 0.0636337
\(206\) 7428.04 2.51231
\(207\) 1423.58 0.477998
\(208\) −6327.30 −2.10923
\(209\) −679.379 −0.224850
\(210\) 9175.87 3.01522
\(211\) −4020.06 −1.31162 −0.655811 0.754925i \(-0.727673\pi\)
−0.655811 + 0.754925i \(0.727673\pi\)
\(212\) −3602.78 −1.16717
\(213\) −503.758 −0.162051
\(214\) 5413.99 1.72941
\(215\) 0 0
\(216\) −15165.3 −4.77717
\(217\) 2883.87 0.902166
\(218\) 8274.34 2.57068
\(219\) −1015.06 −0.313202
\(220\) 2571.04 0.787906
\(221\) 1501.06 0.456887
\(222\) 14977.9 4.52815
\(223\) 924.761 0.277698 0.138849 0.990314i \(-0.455660\pi\)
0.138849 + 0.990314i \(0.455660\pi\)
\(224\) 1856.40 0.553732
\(225\) 4551.48 1.34859
\(226\) −5310.40 −1.56302
\(227\) 3472.29 1.01526 0.507630 0.861575i \(-0.330522\pi\)
0.507630 + 0.861575i \(0.330522\pi\)
\(228\) −10750.3 −3.12263
\(229\) 2118.36 0.611289 0.305644 0.952146i \(-0.401128\pi\)
0.305644 + 0.952146i \(0.401128\pi\)
\(230\) −1677.44 −0.480901
\(231\) −1331.59 −0.379273
\(232\) 11387.5 3.22253
\(233\) −3691.16 −1.03784 −0.518919 0.854824i \(-0.673665\pi\)
−0.518919 + 0.854824i \(0.673665\pi\)
\(234\) 18820.8 5.25792
\(235\) 6367.78 1.76761
\(236\) 5864.24 1.61750
\(237\) −6772.65 −1.85625
\(238\) −1693.53 −0.461241
\(239\) 4854.95 1.31398 0.656988 0.753901i \(-0.271830\pi\)
0.656988 + 0.753901i \(0.271830\pi\)
\(240\) 13640.9 3.66881
\(241\) 2585.98 0.691193 0.345597 0.938383i \(-0.387677\pi\)
0.345597 + 0.938383i \(0.387677\pi\)
\(242\) 6181.56 1.64201
\(243\) 3774.36 0.996400
\(244\) 14229.1 3.73329
\(245\) −2190.82 −0.571292
\(246\) −624.643 −0.161893
\(247\) 4023.69 1.03652
\(248\) 10122.9 2.59196
\(249\) 1790.66 0.455737
\(250\) 3569.69 0.903069
\(251\) −2636.94 −0.663116 −0.331558 0.943435i \(-0.607574\pi\)
−0.331558 + 0.943435i \(0.607574\pi\)
\(252\) −14579.8 −3.64462
\(253\) 243.427 0.0604907
\(254\) −1597.73 −0.394686
\(255\) −3236.09 −0.794712
\(256\) −7929.30 −1.93586
\(257\) −7352.59 −1.78460 −0.892299 0.451444i \(-0.850909\pi\)
−0.892299 + 0.451444i \(0.850909\pi\)
\(258\) 0 0
\(259\) 4342.78 1.04188
\(260\) −15227.2 −3.63213
\(261\) −14345.4 −3.40215
\(262\) 9088.11 2.14300
\(263\) −298.863 −0.0700710 −0.0350355 0.999386i \(-0.511154\pi\)
−0.0350355 + 0.999386i \(0.511154\pi\)
\(264\) −4674.11 −1.08967
\(265\) −2907.13 −0.673901
\(266\) −4539.64 −1.04640
\(267\) 3924.17 0.899459
\(268\) −1989.41 −0.453442
\(269\) −3228.02 −0.731657 −0.365828 0.930682i \(-0.619214\pi\)
−0.365828 + 0.930682i \(0.619214\pi\)
\(270\) −22511.3 −5.07406
\(271\) −5962.95 −1.33662 −0.668309 0.743883i \(-0.732982\pi\)
−0.668309 + 0.743883i \(0.732982\pi\)
\(272\) −2517.61 −0.561222
\(273\) 7886.46 1.74839
\(274\) −12187.0 −2.68701
\(275\) 778.287 0.170664
\(276\) 3851.94 0.840071
\(277\) 1771.14 0.384179 0.192089 0.981377i \(-0.438474\pi\)
0.192089 + 0.981377i \(0.438474\pi\)
\(278\) −12247.6 −2.64230
\(279\) −12752.4 −2.73643
\(280\) 9338.88 1.99323
\(281\) −981.025 −0.208267 −0.104134 0.994563i \(-0.533207\pi\)
−0.104134 + 0.994563i \(0.533207\pi\)
\(282\) −21296.2 −4.49706
\(283\) 8076.55 1.69647 0.848235 0.529620i \(-0.177666\pi\)
0.848235 + 0.529620i \(0.177666\pi\)
\(284\) −943.177 −0.197068
\(285\) −8674.58 −1.80294
\(286\) 3218.29 0.665390
\(287\) −181.113 −0.0372501
\(288\) −8208.91 −1.67957
\(289\) −4315.74 −0.878432
\(290\) 16903.6 3.42281
\(291\) −8926.41 −1.79820
\(292\) −1900.47 −0.380879
\(293\) −4573.34 −0.911869 −0.455934 0.890013i \(-0.650695\pi\)
−0.455934 + 0.890013i \(0.650695\pi\)
\(294\) 7326.92 1.45345
\(295\) 4731.93 0.933910
\(296\) 15243.9 2.99337
\(297\) 3266.81 0.638247
\(298\) 1329.48 0.258439
\(299\) −1441.72 −0.278853
\(300\) 12315.4 2.37011
\(301\) 0 0
\(302\) −5807.82 −1.10663
\(303\) −13049.5 −2.47417
\(304\) −6748.64 −1.27323
\(305\) 11481.6 2.15552
\(306\) 7488.72 1.39903
\(307\) 4509.23 0.838290 0.419145 0.907919i \(-0.362330\pi\)
0.419145 + 0.907919i \(0.362330\pi\)
\(308\) −2493.10 −0.461227
\(309\) −13763.6 −2.53393
\(310\) 15026.4 2.75304
\(311\) −720.198 −0.131314 −0.0656571 0.997842i \(-0.520914\pi\)
−0.0656571 + 0.997842i \(0.520914\pi\)
\(312\) 27682.9 5.02320
\(313\) 8593.59 1.55188 0.775940 0.630807i \(-0.217276\pi\)
0.775940 + 0.630807i \(0.217276\pi\)
\(314\) 4775.08 0.858195
\(315\) −11764.7 −2.10433
\(316\) −12680.3 −2.25735
\(317\) −57.3605 −0.0101630 −0.00508152 0.999987i \(-0.501618\pi\)
−0.00508152 + 0.999987i \(0.501618\pi\)
\(318\) 9722.51 1.71450
\(319\) −2453.02 −0.430542
\(320\) −1983.56 −0.346514
\(321\) −10031.7 −1.74429
\(322\) 1626.59 0.281511
\(323\) 1601.01 0.275798
\(324\) 22990.9 3.94219
\(325\) −4609.49 −0.786734
\(326\) 6650.24 1.12982
\(327\) −15331.8 −2.59281
\(328\) −635.740 −0.107021
\(329\) −6174.76 −1.03473
\(330\) −6938.23 −1.15739
\(331\) −3284.93 −0.545487 −0.272743 0.962087i \(-0.587931\pi\)
−0.272743 + 0.962087i \(0.587931\pi\)
\(332\) 3352.62 0.554214
\(333\) −19203.6 −3.16021
\(334\) 8820.43 1.44501
\(335\) −1605.28 −0.261808
\(336\) −13227.4 −2.14766
\(337\) 4713.15 0.761844 0.380922 0.924607i \(-0.375607\pi\)
0.380922 + 0.924607i \(0.375607\pi\)
\(338\) −7960.20 −1.28100
\(339\) 9839.78 1.57647
\(340\) −6058.86 −0.966436
\(341\) −2180.61 −0.346295
\(342\) 20074.1 3.17393
\(343\) 6828.69 1.07497
\(344\) 0 0
\(345\) 3108.18 0.485040
\(346\) −5158.03 −0.801438
\(347\) −75.9955 −0.0117569 −0.00587846 0.999983i \(-0.501871\pi\)
−0.00587846 + 0.999983i \(0.501871\pi\)
\(348\) −38816.1 −5.97920
\(349\) −8798.79 −1.34954 −0.674769 0.738029i \(-0.735757\pi\)
−0.674769 + 0.738029i \(0.735757\pi\)
\(350\) 5200.55 0.794232
\(351\) −19348.0 −2.94222
\(352\) −1403.70 −0.212549
\(353\) 2914.96 0.439511 0.219756 0.975555i \(-0.429474\pi\)
0.219756 + 0.975555i \(0.429474\pi\)
\(354\) −15825.3 −2.37600
\(355\) −761.061 −0.113783
\(356\) 7347.15 1.09382
\(357\) 3137.99 0.465211
\(358\) −7321.11 −1.08082
\(359\) 4644.90 0.682864 0.341432 0.939906i \(-0.389088\pi\)
0.341432 + 0.939906i \(0.389088\pi\)
\(360\) −41296.1 −6.04582
\(361\) −2567.36 −0.374306
\(362\) 6101.09 0.885818
\(363\) −11454.0 −1.65614
\(364\) 14765.7 2.12619
\(365\) −1533.52 −0.219912
\(366\) −38398.7 −5.48397
\(367\) 285.848 0.0406571 0.0203285 0.999793i \(-0.493529\pi\)
0.0203285 + 0.999793i \(0.493529\pi\)
\(368\) 2418.10 0.342533
\(369\) 800.873 0.112986
\(370\) 22628.1 3.17940
\(371\) 2819.01 0.394490
\(372\) −34505.5 −4.80921
\(373\) 10360.3 1.43816 0.719080 0.694927i \(-0.244563\pi\)
0.719080 + 0.694927i \(0.244563\pi\)
\(374\) 1280.55 0.177047
\(375\) −6614.39 −0.910841
\(376\) −21674.5 −2.97281
\(377\) 14528.3 1.98473
\(378\) 21829.0 2.97027
\(379\) 3278.07 0.444283 0.222141 0.975014i \(-0.428695\pi\)
0.222141 + 0.975014i \(0.428695\pi\)
\(380\) −16241.2 −2.19252
\(381\) 2960.47 0.398083
\(382\) −22334.7 −2.99148
\(383\) 8473.04 1.13042 0.565212 0.824946i \(-0.308794\pi\)
0.565212 + 0.824946i \(0.308794\pi\)
\(384\) 16771.3 2.22879
\(385\) −2011.72 −0.266303
\(386\) −16451.4 −2.16931
\(387\) 0 0
\(388\) −16712.7 −2.18675
\(389\) 4236.19 0.552142 0.276071 0.961137i \(-0.410967\pi\)
0.276071 + 0.961137i \(0.410967\pi\)
\(390\) 41092.4 5.33537
\(391\) −573.657 −0.0741971
\(392\) 7457.08 0.960815
\(393\) −16839.6 −2.16144
\(394\) 21340.6 2.72874
\(395\) −10231.9 −1.30335
\(396\) 11024.4 1.39898
\(397\) 11874.3 1.50114 0.750571 0.660789i \(-0.229778\pi\)
0.750571 + 0.660789i \(0.229778\pi\)
\(398\) −20741.1 −2.61221
\(399\) 8411.63 1.05541
\(400\) 7731.15 0.966394
\(401\) 2340.65 0.291487 0.145744 0.989322i \(-0.453443\pi\)
0.145744 + 0.989322i \(0.453443\pi\)
\(402\) 5368.64 0.666078
\(403\) 12914.9 1.59637
\(404\) −24432.3 −3.00879
\(405\) 18551.6 2.27614
\(406\) −16391.2 −2.00365
\(407\) −3283.74 −0.399924
\(408\) 11014.9 1.33657
\(409\) 7241.71 0.875501 0.437750 0.899097i \(-0.355775\pi\)
0.437750 + 0.899097i \(0.355775\pi\)
\(410\) −943.690 −0.113672
\(411\) 22581.6 2.71014
\(412\) −25769.4 −3.08147
\(413\) −4588.49 −0.546695
\(414\) −7192.72 −0.853872
\(415\) 2705.27 0.319992
\(416\) 8313.54 0.979819
\(417\) 22693.9 2.66505
\(418\) 3432.60 0.401660
\(419\) −7303.95 −0.851602 −0.425801 0.904817i \(-0.640008\pi\)
−0.425801 + 0.904817i \(0.640008\pi\)
\(420\) −31832.9 −3.69831
\(421\) −13018.6 −1.50710 −0.753551 0.657390i \(-0.771661\pi\)
−0.753551 + 0.657390i \(0.771661\pi\)
\(422\) 20311.6 2.34302
\(423\) 27304.5 3.13851
\(424\) 9895.23 1.13338
\(425\) −1834.10 −0.209334
\(426\) 2545.27 0.289480
\(427\) −11133.6 −1.26181
\(428\) −18782.2 −2.12120
\(429\) −5963.26 −0.671117
\(430\) 0 0
\(431\) −6513.96 −0.727996 −0.363998 0.931400i \(-0.618589\pi\)
−0.363998 + 0.931400i \(0.618589\pi\)
\(432\) 32451.0 3.61412
\(433\) −3136.65 −0.348124 −0.174062 0.984735i \(-0.555689\pi\)
−0.174062 + 0.984735i \(0.555689\pi\)
\(434\) −14570.9 −1.61158
\(435\) −31321.2 −3.45226
\(436\) −28705.4 −3.15307
\(437\) −1537.73 −0.168329
\(438\) 5128.64 0.559488
\(439\) 670.745 0.0729223 0.0364612 0.999335i \(-0.488391\pi\)
0.0364612 + 0.999335i \(0.488391\pi\)
\(440\) −7061.49 −0.765099
\(441\) −9394.06 −1.01437
\(442\) −7584.17 −0.816159
\(443\) 3012.53 0.323091 0.161546 0.986865i \(-0.448352\pi\)
0.161546 + 0.986865i \(0.448352\pi\)
\(444\) −51961.2 −5.55399
\(445\) 5928.51 0.631547
\(446\) −4672.41 −0.496065
\(447\) −2463.43 −0.260663
\(448\) 1923.43 0.202843
\(449\) 12542.4 1.31829 0.659147 0.752014i \(-0.270917\pi\)
0.659147 + 0.752014i \(0.270917\pi\)
\(450\) −22996.6 −2.40905
\(451\) 136.947 0.0142984
\(452\) 18422.8 1.91712
\(453\) 10761.5 1.11615
\(454\) −17544.0 −1.81361
\(455\) 11914.6 1.22762
\(456\) 29526.4 3.03223
\(457\) 9096.37 0.931094 0.465547 0.885023i \(-0.345858\pi\)
0.465547 + 0.885023i \(0.345858\pi\)
\(458\) −10703.1 −1.09197
\(459\) −7698.50 −0.782866
\(460\) 5819.38 0.589848
\(461\) 13699.3 1.38403 0.692016 0.721882i \(-0.256723\pi\)
0.692016 + 0.721882i \(0.256723\pi\)
\(462\) 6727.92 0.677513
\(463\) −18592.6 −1.86625 −0.933124 0.359555i \(-0.882928\pi\)
−0.933124 + 0.359555i \(0.882928\pi\)
\(464\) −24367.2 −2.43797
\(465\) −27842.9 −2.77674
\(466\) 18649.8 1.85394
\(467\) −1536.60 −0.152260 −0.0761299 0.997098i \(-0.524256\pi\)
−0.0761299 + 0.997098i \(0.524256\pi\)
\(468\) −65293.1 −6.44909
\(469\) 1556.62 0.153258
\(470\) −32173.6 −3.15757
\(471\) −8847.87 −0.865581
\(472\) −16106.4 −1.57068
\(473\) 0 0
\(474\) 34219.2 3.31591
\(475\) −4916.44 −0.474909
\(476\) 5875.21 0.565735
\(477\) −12465.5 −1.19656
\(478\) −24529.9 −2.34722
\(479\) −11184.2 −1.06685 −0.533424 0.845848i \(-0.679095\pi\)
−0.533424 + 0.845848i \(0.679095\pi\)
\(480\) −17923.0 −1.70431
\(481\) 19448.3 1.84359
\(482\) −13065.8 −1.23471
\(483\) −3013.96 −0.283934
\(484\) −21445.1 −2.01400
\(485\) −13485.7 −1.26259
\(486\) −19070.2 −1.77992
\(487\) 5611.36 0.522125 0.261063 0.965322i \(-0.415927\pi\)
0.261063 + 0.965322i \(0.415927\pi\)
\(488\) −39080.8 −3.62522
\(489\) −12322.4 −1.13955
\(490\) 11069.3 1.02053
\(491\) 6705.50 0.616324 0.308162 0.951334i \(-0.400286\pi\)
0.308162 + 0.951334i \(0.400286\pi\)
\(492\) 2167.01 0.198570
\(493\) 5780.75 0.528097
\(494\) −20329.9 −1.85159
\(495\) 8895.72 0.807743
\(496\) −21661.2 −1.96092
\(497\) 737.991 0.0666065
\(498\) −9047.42 −0.814106
\(499\) 1528.07 0.137086 0.0685430 0.997648i \(-0.478165\pi\)
0.0685430 + 0.997648i \(0.478165\pi\)
\(500\) −12384.0 −1.10766
\(501\) −16343.6 −1.45744
\(502\) 13323.3 1.18456
\(503\) −16420.3 −1.45556 −0.727779 0.685812i \(-0.759447\pi\)
−0.727779 + 0.685812i \(0.759447\pi\)
\(504\) 40044.3 3.53912
\(505\) −19714.7 −1.73722
\(506\) −1229.93 −0.108058
\(507\) 14749.7 1.29202
\(508\) 5542.83 0.484101
\(509\) −13005.9 −1.13257 −0.566284 0.824210i \(-0.691620\pi\)
−0.566284 + 0.824210i \(0.691620\pi\)
\(510\) 16350.5 1.41963
\(511\) 1487.03 0.128733
\(512\) 25731.9 2.22109
\(513\) −20636.4 −1.77606
\(514\) 37149.4 3.18792
\(515\) −20793.6 −1.77918
\(516\) 0 0
\(517\) 4668.97 0.397178
\(518\) −21942.1 −1.86116
\(519\) 9557.47 0.808336
\(520\) 41822.4 3.52699
\(521\) −3433.05 −0.288685 −0.144342 0.989528i \(-0.546107\pi\)
−0.144342 + 0.989528i \(0.546107\pi\)
\(522\) 72481.2 6.07742
\(523\) 14300.7 1.19565 0.597826 0.801626i \(-0.296031\pi\)
0.597826 + 0.801626i \(0.296031\pi\)
\(524\) −31528.5 −2.62849
\(525\) −9636.25 −0.801068
\(526\) 1510.02 0.125171
\(527\) 5138.79 0.424761
\(528\) 10001.7 0.824374
\(529\) −11616.0 −0.954715
\(530\) 14688.4 1.20382
\(531\) 20290.1 1.65822
\(532\) 15748.9 1.28346
\(533\) −811.081 −0.0659134
\(534\) −19827.1 −1.60675
\(535\) −15155.6 −1.22474
\(536\) 5464.01 0.440316
\(537\) 13565.5 1.09012
\(538\) 16309.7 1.30699
\(539\) −1606.35 −0.128368
\(540\) 78096.4 6.22358
\(541\) 2506.39 0.199184 0.0995918 0.995028i \(-0.468246\pi\)
0.0995918 + 0.995028i \(0.468246\pi\)
\(542\) 30128.2 2.38767
\(543\) −11304.9 −0.893441
\(544\) 3307.93 0.260710
\(545\) −23162.7 −1.82052
\(546\) −39846.8 −3.12323
\(547\) 3120.71 0.243934 0.121967 0.992534i \(-0.461080\pi\)
0.121967 + 0.992534i \(0.461080\pi\)
\(548\) 42279.0 3.29575
\(549\) 49232.1 3.82728
\(550\) −3932.34 −0.304865
\(551\) 15495.7 1.19808
\(552\) −10579.6 −0.815753
\(553\) 9921.74 0.762957
\(554\) −8948.79 −0.686277
\(555\) −41928.2 −3.20676
\(556\) 42489.3 3.24091
\(557\) 4921.10 0.374351 0.187176 0.982326i \(-0.440067\pi\)
0.187176 + 0.982326i \(0.440067\pi\)
\(558\) 64432.0 4.88821
\(559\) 0 0
\(560\) −19983.5 −1.50796
\(561\) −2372.76 −0.178570
\(562\) 4956.69 0.372038
\(563\) −13911.2 −1.04136 −0.520680 0.853752i \(-0.674321\pi\)
−0.520680 + 0.853752i \(0.674321\pi\)
\(564\) 73880.8 5.51586
\(565\) 14865.6 1.10690
\(566\) −40807.2 −3.03049
\(567\) −17989.3 −1.33241
\(568\) 2590.48 0.191363
\(569\) −2045.35 −0.150695 −0.0753476 0.997157i \(-0.524007\pi\)
−0.0753476 + 0.997157i \(0.524007\pi\)
\(570\) 43828.8 3.22068
\(571\) −19012.8 −1.39345 −0.696725 0.717339i \(-0.745360\pi\)
−0.696725 + 0.717339i \(0.745360\pi\)
\(572\) −11164.9 −0.816133
\(573\) 41384.7 3.01722
\(574\) 915.084 0.0665416
\(575\) 1761.60 0.127763
\(576\) −8505.33 −0.615258
\(577\) −4056.31 −0.292663 −0.146331 0.989236i \(-0.546747\pi\)
−0.146331 + 0.989236i \(0.546747\pi\)
\(578\) 21805.5 1.56919
\(579\) 30483.3 2.18798
\(580\) −58642.0 −4.19824
\(581\) −2623.27 −0.187318
\(582\) 45101.2 3.21221
\(583\) −2131.56 −0.151424
\(584\) 5219.75 0.369854
\(585\) −52685.8 −3.72357
\(586\) 23107.1 1.62892
\(587\) 19491.1 1.37050 0.685249 0.728309i \(-0.259693\pi\)
0.685249 + 0.728309i \(0.259693\pi\)
\(588\) −25418.6 −1.78273
\(589\) 13774.9 0.963642
\(590\) −23908.3 −1.66829
\(591\) −39542.6 −2.75223
\(592\) −32619.2 −2.26460
\(593\) 5465.18 0.378462 0.189231 0.981933i \(-0.439400\pi\)
0.189231 + 0.981933i \(0.439400\pi\)
\(594\) −16505.7 −1.14013
\(595\) 4740.78 0.326643
\(596\) −4612.24 −0.316988
\(597\) 38431.8 2.63469
\(598\) 7284.40 0.498129
\(599\) −25500.9 −1.73946 −0.869731 0.493526i \(-0.835708\pi\)
−0.869731 + 0.493526i \(0.835708\pi\)
\(600\) −33825.0 −2.30150
\(601\) −24308.3 −1.64985 −0.824923 0.565245i \(-0.808781\pi\)
−0.824923 + 0.565245i \(0.808781\pi\)
\(602\) 0 0
\(603\) −6883.29 −0.464858
\(604\) 20148.5 1.35733
\(605\) −17304.3 −1.16284
\(606\) 65933.3 4.41973
\(607\) −2862.31 −0.191397 −0.0956983 0.995410i \(-0.530508\pi\)
−0.0956983 + 0.995410i \(0.530508\pi\)
\(608\) 8867.15 0.591464
\(609\) 30371.7 2.02090
\(610\) −58011.5 −3.85052
\(611\) −27652.5 −1.83093
\(612\) −25979.9 −1.71597
\(613\) 20771.8 1.36862 0.684312 0.729189i \(-0.260103\pi\)
0.684312 + 0.729189i \(0.260103\pi\)
\(614\) −22783.1 −1.49748
\(615\) 1748.59 0.114650
\(616\) 6847.44 0.447875
\(617\) −18855.6 −1.23030 −0.615152 0.788408i \(-0.710905\pi\)
−0.615152 + 0.788408i \(0.710905\pi\)
\(618\) 69541.5 4.52649
\(619\) −5019.16 −0.325908 −0.162954 0.986634i \(-0.552102\pi\)
−0.162954 + 0.986634i \(0.552102\pi\)
\(620\) −52129.7 −3.37674
\(621\) 7394.21 0.477809
\(622\) 3638.84 0.234573
\(623\) −5748.80 −0.369696
\(624\) −59236.3 −3.80024
\(625\) −19373.8 −1.23992
\(626\) −43419.6 −2.77220
\(627\) −6360.36 −0.405117
\(628\) −16565.7 −1.05262
\(629\) 7738.42 0.490542
\(630\) 59441.6 3.75906
\(631\) 7678.40 0.484425 0.242213 0.970223i \(-0.422127\pi\)
0.242213 + 0.970223i \(0.422127\pi\)
\(632\) 34827.1 2.19201
\(633\) −37635.9 −2.36318
\(634\) 289.817 0.0181547
\(635\) 4472.58 0.279510
\(636\) −33729.4 −2.10292
\(637\) 9513.79 0.591759
\(638\) 12394.0 0.769098
\(639\) −3263.36 −0.202029
\(640\) 25337.5 1.56493
\(641\) 30358.4 1.87065 0.935324 0.353792i \(-0.115108\pi\)
0.935324 + 0.353792i \(0.115108\pi\)
\(642\) 50686.0 3.11591
\(643\) 1310.34 0.0803654 0.0401827 0.999192i \(-0.487206\pi\)
0.0401827 + 0.999192i \(0.487206\pi\)
\(644\) −5642.98 −0.345287
\(645\) 0 0
\(646\) −8089.21 −0.492671
\(647\) −16438.0 −0.998834 −0.499417 0.866362i \(-0.666452\pi\)
−0.499417 + 0.866362i \(0.666452\pi\)
\(648\) −63145.6 −3.82808
\(649\) 3469.54 0.209848
\(650\) 23289.7 1.40538
\(651\) 26998.9 1.62545
\(652\) −23071.0 −1.38578
\(653\) 8211.20 0.492081 0.246041 0.969260i \(-0.420870\pi\)
0.246041 + 0.969260i \(0.420870\pi\)
\(654\) 77464.6 4.63166
\(655\) −25440.7 −1.51764
\(656\) 1360.37 0.0809655
\(657\) −6575.58 −0.390469
\(658\) 31198.3 1.84838
\(659\) −18816.5 −1.11227 −0.556136 0.831091i \(-0.687717\pi\)
−0.556136 + 0.831091i \(0.687717\pi\)
\(660\) 24070.1 1.41959
\(661\) 10768.9 0.633677 0.316838 0.948480i \(-0.397379\pi\)
0.316838 + 0.948480i \(0.397379\pi\)
\(662\) 16597.3 0.974430
\(663\) 14052.9 0.823183
\(664\) −9208.15 −0.538171
\(665\) 12708.0 0.741046
\(666\) 97027.1 5.64523
\(667\) −5552.26 −0.322315
\(668\) −30599.9 −1.77237
\(669\) 8657.63 0.500334
\(670\) 8110.76 0.467680
\(671\) 8418.52 0.484342
\(672\) 17379.7 0.997671
\(673\) −24154.4 −1.38348 −0.691740 0.722146i \(-0.743156\pi\)
−0.691740 + 0.722146i \(0.743156\pi\)
\(674\) −23813.4 −1.36092
\(675\) 23640.8 1.34805
\(676\) 27615.6 1.57121
\(677\) 926.147 0.0525771 0.0262886 0.999654i \(-0.491631\pi\)
0.0262886 + 0.999654i \(0.491631\pi\)
\(678\) −49716.1 −2.81613
\(679\) 13076.9 0.739096
\(680\) 16641.0 0.938460
\(681\) 32507.7 1.82922
\(682\) 11017.7 0.618604
\(683\) −14605.3 −0.818237 −0.409119 0.912481i \(-0.634164\pi\)
−0.409119 + 0.912481i \(0.634164\pi\)
\(684\) −69641.1 −3.89297
\(685\) 34115.5 1.90290
\(686\) −34502.4 −1.92027
\(687\) 19832.1 1.10137
\(688\) 0 0
\(689\) 12624.4 0.698043
\(690\) −15704.2 −0.866450
\(691\) −14706.2 −0.809627 −0.404813 0.914399i \(-0.632664\pi\)
−0.404813 + 0.914399i \(0.632664\pi\)
\(692\) 17894.3 0.983003
\(693\) −8626.06 −0.472839
\(694\) 383.972 0.0210020
\(695\) 34285.1 1.87124
\(696\) 106610. 5.80611
\(697\) −322.726 −0.0175382
\(698\) 44456.4 2.41075
\(699\) −34556.8 −1.86990
\(700\) −18041.8 −0.974164
\(701\) −6588.69 −0.354995 −0.177497 0.984121i \(-0.556800\pi\)
−0.177497 + 0.984121i \(0.556800\pi\)
\(702\) 97757.0 5.25584
\(703\) 20743.4 1.11288
\(704\) −1454.38 −0.0778610
\(705\) 59615.3 3.18474
\(706\) −14728.0 −0.785121
\(707\) 19117.1 1.01694
\(708\) 54901.2 2.91428
\(709\) −7624.16 −0.403852 −0.201926 0.979401i \(-0.564720\pi\)
−0.201926 + 0.979401i \(0.564720\pi\)
\(710\) 3845.30 0.203256
\(711\) −43873.5 −2.31418
\(712\) −20179.3 −1.06215
\(713\) −4935.67 −0.259246
\(714\) −15854.9 −0.831029
\(715\) −9009.10 −0.471218
\(716\) 25398.4 1.32567
\(717\) 45452.1 2.36742
\(718\) −23468.6 −1.21983
\(719\) −31629.6 −1.64059 −0.820296 0.571939i \(-0.806192\pi\)
−0.820296 + 0.571939i \(0.806192\pi\)
\(720\) 88366.0 4.57390
\(721\) 20163.3 1.04150
\(722\) 12971.8 0.668641
\(723\) 24210.0 1.24534
\(724\) −21165.9 −1.08650
\(725\) −17751.7 −0.909355
\(726\) 57872.0 2.95844
\(727\) 23784.0 1.21334 0.606670 0.794954i \(-0.292505\pi\)
0.606670 + 0.794954i \(0.292505\pi\)
\(728\) −40554.7 −2.06464
\(729\) −78.6220 −0.00399441
\(730\) 7748.18 0.392840
\(731\) 0 0
\(732\) 133213. 6.72635
\(733\) −13440.2 −0.677252 −0.338626 0.940921i \(-0.609962\pi\)
−0.338626 + 0.940921i \(0.609962\pi\)
\(734\) −1444.26 −0.0726277
\(735\) −20510.5 −1.02931
\(736\) −3177.18 −0.159120
\(737\) −1177.02 −0.0588278
\(738\) −4046.46 −0.201832
\(739\) 28469.7 1.41715 0.708575 0.705636i \(-0.249338\pi\)
0.708575 + 0.705636i \(0.249338\pi\)
\(740\) −78501.3 −3.89968
\(741\) 37669.9 1.86753
\(742\) −14243.2 −0.704696
\(743\) −3370.81 −0.166437 −0.0832187 0.996531i \(-0.526520\pi\)
−0.0832187 + 0.996531i \(0.526520\pi\)
\(744\) 94771.0 4.66999
\(745\) −3721.67 −0.183022
\(746\) −52345.8 −2.56906
\(747\) 11600.0 0.568167
\(748\) −4442.47 −0.217156
\(749\) 14696.2 0.716940
\(750\) 33419.6 1.62708
\(751\) −2003.54 −0.0973505 −0.0486752 0.998815i \(-0.515500\pi\)
−0.0486752 + 0.998815i \(0.515500\pi\)
\(752\) 46379.5 2.24905
\(753\) −24687.1 −1.19475
\(754\) −73405.0 −3.54543
\(755\) 16258.1 0.783697
\(756\) −75729.1 −3.64318
\(757\) −4412.38 −0.211850 −0.105925 0.994374i \(-0.533780\pi\)
−0.105925 + 0.994374i \(0.533780\pi\)
\(758\) −16562.6 −0.793644
\(759\) 2278.97 0.108988
\(760\) 44607.4 2.12905
\(761\) 10159.0 0.483921 0.241961 0.970286i \(-0.422210\pi\)
0.241961 + 0.970286i \(0.422210\pi\)
\(762\) −14957.9 −0.711115
\(763\) 22460.6 1.06570
\(764\) 77483.7 3.66919
\(765\) −20963.5 −0.990767
\(766\) −42810.5 −2.01933
\(767\) −20548.7 −0.967367
\(768\) −74234.3 −3.48789
\(769\) 17334.7 0.812881 0.406440 0.913677i \(-0.366770\pi\)
0.406440 + 0.913677i \(0.366770\pi\)
\(770\) 10164.3 0.475710
\(771\) −68835.1 −3.21535
\(772\) 57073.2 2.66076
\(773\) 11330.7 0.527213 0.263607 0.964630i \(-0.415088\pi\)
0.263607 + 0.964630i \(0.415088\pi\)
\(774\) 0 0
\(775\) −15780.3 −0.731415
\(776\) 45902.4 2.12345
\(777\) 40657.2 1.87718
\(778\) −21403.6 −0.986319
\(779\) −865.092 −0.0397884
\(780\) −142558. −6.54409
\(781\) −558.024 −0.0255668
\(782\) 2898.43 0.132542
\(783\) −74511.6 −3.40080
\(784\) −15956.8 −0.726894
\(785\) −13367.1 −0.607759
\(786\) 85083.1 3.86109
\(787\) 14755.8 0.668343 0.334172 0.942512i \(-0.391543\pi\)
0.334172 + 0.942512i \(0.391543\pi\)
\(788\) −74034.9 −3.34694
\(789\) −2797.96 −0.126249
\(790\) 51697.3 2.32824
\(791\) −14415.0 −0.647962
\(792\) −30279.1 −1.35848
\(793\) −49859.6 −2.23274
\(794\) −59995.6 −2.68156
\(795\) −27216.6 −1.21418
\(796\) 71955.1 3.20400
\(797\) 21567.4 0.958538 0.479269 0.877668i \(-0.340902\pi\)
0.479269 + 0.877668i \(0.340902\pi\)
\(798\) −42500.3 −1.88533
\(799\) −11002.8 −0.487174
\(800\) −10158.1 −0.448928
\(801\) 25420.9 1.12135
\(802\) −11826.3 −0.520698
\(803\) −1124.40 −0.0494138
\(804\) −18624.9 −0.816976
\(805\) −4553.39 −0.199361
\(806\) −65253.2 −2.85167
\(807\) −30220.8 −1.31824
\(808\) 67104.6 2.92170
\(809\) 27638.2 1.20112 0.600561 0.799579i \(-0.294944\pi\)
0.600561 + 0.799579i \(0.294944\pi\)
\(810\) −93733.1 −4.06598
\(811\) 5477.83 0.237180 0.118590 0.992943i \(-0.462163\pi\)
0.118590 + 0.992943i \(0.462163\pi\)
\(812\) 56864.4 2.45757
\(813\) −55825.3 −2.40822
\(814\) 16591.3 0.714404
\(815\) −18616.3 −0.800122
\(816\) −23569.9 −1.01117
\(817\) 0 0
\(818\) −36589.2 −1.56395
\(819\) 51088.8 2.17972
\(820\) 3273.85 0.139424
\(821\) −3043.53 −0.129379 −0.0646894 0.997905i \(-0.520606\pi\)
−0.0646894 + 0.997905i \(0.520606\pi\)
\(822\) −114095. −4.84125
\(823\) 22867.8 0.968556 0.484278 0.874914i \(-0.339082\pi\)
0.484278 + 0.874914i \(0.339082\pi\)
\(824\) 70776.9 2.99227
\(825\) 7286.35 0.307489
\(826\) 23183.6 0.976587
\(827\) −13967.0 −0.587281 −0.293640 0.955916i \(-0.594867\pi\)
−0.293640 + 0.955916i \(0.594867\pi\)
\(828\) 24953.0 1.04732
\(829\) −4419.68 −0.185165 −0.0925825 0.995705i \(-0.529512\pi\)
−0.0925825 + 0.995705i \(0.529512\pi\)
\(830\) −13668.5 −0.571617
\(831\) 16581.5 0.692183
\(832\) 8613.74 0.358927
\(833\) 3785.50 0.157455
\(834\) −114662. −4.76070
\(835\) −24691.4 −1.02333
\(836\) −11908.4 −0.492656
\(837\) −66236.9 −2.73534
\(838\) 36903.6 1.52126
\(839\) −16617.7 −0.683797 −0.341898 0.939737i \(-0.611070\pi\)
−0.341898 + 0.939737i \(0.611070\pi\)
\(840\) 87430.8 3.59125
\(841\) 31561.2 1.29408
\(842\) 65777.4 2.69221
\(843\) −9184.38 −0.375240
\(844\) −70465.0 −2.87382
\(845\) 22283.3 0.907183
\(846\) −137957. −5.60647
\(847\) 16779.8 0.680708
\(848\) −21174.0 −0.857449
\(849\) 75612.8 3.05657
\(850\) 9266.89 0.373943
\(851\) −7432.55 −0.299394
\(852\) −8830.04 −0.355061
\(853\) −12302.6 −0.493825 −0.246912 0.969038i \(-0.579416\pi\)
−0.246912 + 0.969038i \(0.579416\pi\)
\(854\) 56253.0 2.25403
\(855\) −56194.2 −2.24772
\(856\) 51586.4 2.05980
\(857\) 39311.0 1.56690 0.783452 0.621452i \(-0.213457\pi\)
0.783452 + 0.621452i \(0.213457\pi\)
\(858\) 30129.7 1.19885
\(859\) 3412.44 0.135542 0.0677712 0.997701i \(-0.478411\pi\)
0.0677712 + 0.997701i \(0.478411\pi\)
\(860\) 0 0
\(861\) −1695.58 −0.0671143
\(862\) 32912.1 1.30045
\(863\) −19362.2 −0.763727 −0.381863 0.924219i \(-0.624718\pi\)
−0.381863 + 0.924219i \(0.624718\pi\)
\(864\) −42637.9 −1.67890
\(865\) 14439.1 0.567565
\(866\) 15848.1 0.621872
\(867\) −40404.0 −1.58269
\(868\) 50549.5 1.97668
\(869\) −7502.22 −0.292860
\(870\) 158252. 6.16695
\(871\) 6971.02 0.271187
\(872\) 78840.8 3.06179
\(873\) −57825.6 −2.24181
\(874\) 7769.47 0.300694
\(875\) 9689.89 0.374375
\(876\) −17792.3 −0.686239
\(877\) −16784.7 −0.646272 −0.323136 0.946353i \(-0.604737\pi\)
−0.323136 + 0.946353i \(0.604737\pi\)
\(878\) −3388.98 −0.130265
\(879\) −42815.7 −1.64293
\(880\) 15110.3 0.578827
\(881\) −21039.3 −0.804578 −0.402289 0.915513i \(-0.631785\pi\)
−0.402289 + 0.915513i \(0.631785\pi\)
\(882\) 47464.0 1.81202
\(883\) 20024.2 0.763157 0.381579 0.924336i \(-0.375381\pi\)
0.381579 + 0.924336i \(0.375381\pi\)
\(884\) 26311.0 1.00106
\(885\) 44300.4 1.68265
\(886\) −15221.0 −0.577154
\(887\) 16204.3 0.613401 0.306700 0.951806i \(-0.400775\pi\)
0.306700 + 0.951806i \(0.400775\pi\)
\(888\) 142714. 5.39322
\(889\) −4337.00 −0.163620
\(890\) −29954.1 −1.12816
\(891\) 13602.4 0.511445
\(892\) 16209.5 0.608447
\(893\) −29493.9 −1.10524
\(894\) 12446.6 0.465635
\(895\) 20494.3 0.765417
\(896\) −24569.5 −0.916080
\(897\) −13497.5 −0.502416
\(898\) −63371.4 −2.35493
\(899\) 49736.8 1.84518
\(900\) 79779.9 2.95481
\(901\) 5023.20 0.185735
\(902\) −691.931 −0.0255419
\(903\) 0 0
\(904\) −50599.3 −1.86162
\(905\) −17079.0 −0.627322
\(906\) −54372.9 −1.99384
\(907\) −13786.2 −0.504699 −0.252350 0.967636i \(-0.581203\pi\)
−0.252350 + 0.967636i \(0.581203\pi\)
\(908\) 60863.5 2.22448
\(909\) −84535.0 −3.08454
\(910\) −60199.2 −2.19295
\(911\) −23933.3 −0.870412 −0.435206 0.900331i \(-0.643324\pi\)
−0.435206 + 0.900331i \(0.643324\pi\)
\(912\) −63180.9 −2.29400
\(913\) 1983.56 0.0719015
\(914\) −45959.9 −1.66326
\(915\) 107491. 3.88366
\(916\) 37131.3 1.33936
\(917\) 24669.6 0.888398
\(918\) 38897.1 1.39847
\(919\) −31897.7 −1.14495 −0.572475 0.819922i \(-0.694017\pi\)
−0.572475 + 0.819922i \(0.694017\pi\)
\(920\) −15983.2 −0.572774
\(921\) 42215.5 1.51037
\(922\) −69216.4 −2.47236
\(923\) 3304.96 0.117859
\(924\) −23340.5 −0.831002
\(925\) −23763.4 −0.844686
\(926\) 93940.3 3.33377
\(927\) −89161.2 −3.15905
\(928\) 32016.5 1.13253
\(929\) −42084.6 −1.48628 −0.743138 0.669138i \(-0.766663\pi\)
−0.743138 + 0.669138i \(0.766663\pi\)
\(930\) 140678. 4.96022
\(931\) 10147.3 0.357213
\(932\) −64700.0 −2.27395
\(933\) −6742.51 −0.236592
\(934\) 7763.75 0.271989
\(935\) −3584.69 −0.125382
\(936\) 179331. 6.26241
\(937\) −6000.64 −0.209213 −0.104606 0.994514i \(-0.533358\pi\)
−0.104606 + 0.994514i \(0.533358\pi\)
\(938\) −7864.90 −0.273772
\(939\) 80453.4 2.79606
\(940\) 111617. 3.87291
\(941\) −17755.8 −0.615114 −0.307557 0.951530i \(-0.599511\pi\)
−0.307557 + 0.951530i \(0.599511\pi\)
\(942\) 44704.4 1.54623
\(943\) 309.970 0.0107041
\(944\) 34464.8 1.18828
\(945\) −61106.7 −2.10349
\(946\) 0 0
\(947\) 28692.8 0.984572 0.492286 0.870434i \(-0.336161\pi\)
0.492286 + 0.870434i \(0.336161\pi\)
\(948\) −118713. −4.06712
\(949\) 6659.39 0.227790
\(950\) 24840.6 0.848353
\(951\) −537.010 −0.0183110
\(952\) −16136.6 −0.549358
\(953\) −20739.6 −0.704956 −0.352478 0.935820i \(-0.614661\pi\)
−0.352478 + 0.935820i \(0.614661\pi\)
\(954\) 62982.8 2.13747
\(955\) 62522.6 2.11852
\(956\) 85099.2 2.87898
\(957\) −22965.3 −0.775717
\(958\) 56508.9 1.90576
\(959\) −33081.3 −1.11392
\(960\) −18570.1 −0.624321
\(961\) 14422.4 0.484121
\(962\) −98263.8 −3.29330
\(963\) −64986.0 −2.17460
\(964\) 45327.9 1.51443
\(965\) 46053.1 1.53627
\(966\) 15228.2 0.507205
\(967\) −35018.1 −1.16454 −0.582268 0.812997i \(-0.697835\pi\)
−0.582268 + 0.812997i \(0.697835\pi\)
\(968\) 58900.0 1.95570
\(969\) 14988.7 0.496911
\(970\) 68137.4 2.25542
\(971\) −52435.4 −1.73299 −0.866495 0.499186i \(-0.833633\pi\)
−0.866495 + 0.499186i \(0.833633\pi\)
\(972\) 66158.2 2.18316
\(973\) −33245.9 −1.09539
\(974\) −28351.7 −0.932697
\(975\) −43154.2 −1.41748
\(976\) 83625.8 2.74262
\(977\) 10021.8 0.328173 0.164086 0.986446i \(-0.447532\pi\)
0.164086 + 0.986446i \(0.447532\pi\)
\(978\) 62259.7 2.03563
\(979\) 4346.89 0.141907
\(980\) −38401.5 −1.25173
\(981\) −99319.7 −3.23245
\(982\) −33879.9 −1.10097
\(983\) −54750.4 −1.77647 −0.888233 0.459394i \(-0.848067\pi\)
−0.888233 + 0.459394i \(0.848067\pi\)
\(984\) −5951.81 −0.192822
\(985\) −59739.7 −1.93245
\(986\) −29207.6 −0.943366
\(987\) −57808.2 −1.86429
\(988\) 70528.7 2.27107
\(989\) 0 0
\(990\) −44946.1 −1.44291
\(991\) 49955.3 1.60130 0.800648 0.599135i \(-0.204489\pi\)
0.800648 + 0.599135i \(0.204489\pi\)
\(992\) 28461.0 0.910924
\(993\) −30753.6 −0.982816
\(994\) −3728.74 −0.118982
\(995\) 58061.5 1.84992
\(996\) 31387.3 0.998540
\(997\) −42986.1 −1.36548 −0.682740 0.730661i \(-0.739212\pi\)
−0.682740 + 0.730661i \(0.739212\pi\)
\(998\) −7720.68 −0.244884
\(999\) −99745.1 −3.15896
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.1.4 50
43.42 odd 2 1849.4.a.j.1.47 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.i.1.4 50 1.1 even 1 trivial
1849.4.a.j.1.47 yes 50 43.42 odd 2