Properties

Label 2151.4.a.h.1.13
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $59$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(59\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.13470 q^{2} +1.82636 q^{4} -4.91209 q^{5} +36.3874 q^{7} +19.3525 q^{8} +O(q^{10})\) \(q-3.13470 q^{2} +1.82636 q^{4} -4.91209 q^{5} +36.3874 q^{7} +19.3525 q^{8} +15.3979 q^{10} +0.654849 q^{11} -42.3822 q^{13} -114.064 q^{14} -75.2753 q^{16} -41.8110 q^{17} -79.2470 q^{19} -8.97125 q^{20} -2.05276 q^{22} +103.434 q^{23} -100.871 q^{25} +132.855 q^{26} +66.4566 q^{28} +150.719 q^{29} -43.3756 q^{31} +81.1455 q^{32} +131.065 q^{34} -178.738 q^{35} -328.704 q^{37} +248.416 q^{38} -95.0614 q^{40} +227.006 q^{41} -88.1867 q^{43} +1.19599 q^{44} -324.234 q^{46} +161.362 q^{47} +981.045 q^{49} +316.202 q^{50} -77.4051 q^{52} +206.317 q^{53} -3.21668 q^{55} +704.189 q^{56} -472.461 q^{58} -427.414 q^{59} -38.0290 q^{61} +135.970 q^{62} +347.835 q^{64} +208.185 q^{65} +594.441 q^{67} -76.3620 q^{68} +560.292 q^{70} +905.766 q^{71} +155.597 q^{73} +1030.39 q^{74} -144.734 q^{76} +23.8283 q^{77} +63.7719 q^{79} +369.759 q^{80} -711.597 q^{82} -834.746 q^{83} +205.379 q^{85} +276.439 q^{86} +12.6730 q^{88} -601.888 q^{89} -1542.18 q^{91} +188.907 q^{92} -505.820 q^{94} +389.268 q^{95} -495.710 q^{97} -3075.29 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.13470 −1.10828 −0.554142 0.832422i \(-0.686954\pi\)
−0.554142 + 0.832422i \(0.686954\pi\)
\(3\) 0 0
\(4\) 1.82636 0.228295
\(5\) −4.91209 −0.439351 −0.219675 0.975573i \(-0.570500\pi\)
−0.219675 + 0.975573i \(0.570500\pi\)
\(6\) 0 0
\(7\) 36.3874 1.96474 0.982368 0.186956i \(-0.0598621\pi\)
0.982368 + 0.186956i \(0.0598621\pi\)
\(8\) 19.3525 0.855269
\(9\) 0 0
\(10\) 15.3979 0.486926
\(11\) 0.654849 0.0179495 0.00897475 0.999960i \(-0.497143\pi\)
0.00897475 + 0.999960i \(0.497143\pi\)
\(12\) 0 0
\(13\) −42.3822 −0.904207 −0.452104 0.891965i \(-0.649326\pi\)
−0.452104 + 0.891965i \(0.649326\pi\)
\(14\) −114.064 −2.17749
\(15\) 0 0
\(16\) −75.2753 −1.17618
\(17\) −41.8110 −0.596509 −0.298255 0.954486i \(-0.596404\pi\)
−0.298255 + 0.954486i \(0.596404\pi\)
\(18\) 0 0
\(19\) −79.2470 −0.956869 −0.478434 0.878123i \(-0.658796\pi\)
−0.478434 + 0.878123i \(0.658796\pi\)
\(20\) −8.97125 −0.100302
\(21\) 0 0
\(22\) −2.05276 −0.0198932
\(23\) 103.434 0.937715 0.468857 0.883274i \(-0.344666\pi\)
0.468857 + 0.883274i \(0.344666\pi\)
\(24\) 0 0
\(25\) −100.871 −0.806971
\(26\) 132.855 1.00212
\(27\) 0 0
\(28\) 66.4566 0.448540
\(29\) 150.719 0.965100 0.482550 0.875868i \(-0.339711\pi\)
0.482550 + 0.875868i \(0.339711\pi\)
\(30\) 0 0
\(31\) −43.3756 −0.251306 −0.125653 0.992074i \(-0.540103\pi\)
−0.125653 + 0.992074i \(0.540103\pi\)
\(32\) 81.1455 0.448270
\(33\) 0 0
\(34\) 131.065 0.661102
\(35\) −178.738 −0.863209
\(36\) 0 0
\(37\) −328.704 −1.46050 −0.730252 0.683178i \(-0.760597\pi\)
−0.730252 + 0.683178i \(0.760597\pi\)
\(38\) 248.416 1.06048
\(39\) 0 0
\(40\) −95.0614 −0.375763
\(41\) 227.006 0.864693 0.432346 0.901708i \(-0.357686\pi\)
0.432346 + 0.901708i \(0.357686\pi\)
\(42\) 0 0
\(43\) −88.1867 −0.312752 −0.156376 0.987698i \(-0.549981\pi\)
−0.156376 + 0.987698i \(0.549981\pi\)
\(44\) 1.19599 0.00409778
\(45\) 0 0
\(46\) −324.234 −1.03925
\(47\) 161.362 0.500787 0.250394 0.968144i \(-0.419440\pi\)
0.250394 + 0.968144i \(0.419440\pi\)
\(48\) 0 0
\(49\) 981.045 2.86019
\(50\) 316.202 0.894354
\(51\) 0 0
\(52\) −77.4051 −0.206426
\(53\) 206.317 0.534714 0.267357 0.963598i \(-0.413850\pi\)
0.267357 + 0.963598i \(0.413850\pi\)
\(54\) 0 0
\(55\) −3.21668 −0.00788613
\(56\) 704.189 1.68038
\(57\) 0 0
\(58\) −472.461 −1.06961
\(59\) −427.414 −0.943128 −0.471564 0.881832i \(-0.656310\pi\)
−0.471564 + 0.881832i \(0.656310\pi\)
\(60\) 0 0
\(61\) −38.0290 −0.0798215 −0.0399108 0.999203i \(-0.512707\pi\)
−0.0399108 + 0.999203i \(0.512707\pi\)
\(62\) 135.970 0.278519
\(63\) 0 0
\(64\) 347.835 0.679366
\(65\) 208.185 0.397264
\(66\) 0 0
\(67\) 594.441 1.08392 0.541959 0.840405i \(-0.317683\pi\)
0.541959 + 0.840405i \(0.317683\pi\)
\(68\) −76.3620 −0.136180
\(69\) 0 0
\(70\) 560.292 0.956681
\(71\) 905.766 1.51401 0.757004 0.653410i \(-0.226662\pi\)
0.757004 + 0.653410i \(0.226662\pi\)
\(72\) 0 0
\(73\) 155.597 0.249469 0.124735 0.992190i \(-0.460192\pi\)
0.124735 + 0.992190i \(0.460192\pi\)
\(74\) 1030.39 1.61865
\(75\) 0 0
\(76\) −144.734 −0.218448
\(77\) 23.8283 0.0352660
\(78\) 0 0
\(79\) 63.7719 0.0908216 0.0454108 0.998968i \(-0.485540\pi\)
0.0454108 + 0.998968i \(0.485540\pi\)
\(80\) 369.759 0.516754
\(81\) 0 0
\(82\) −711.597 −0.958326
\(83\) −834.746 −1.10392 −0.551960 0.833871i \(-0.686120\pi\)
−0.551960 + 0.833871i \(0.686120\pi\)
\(84\) 0 0
\(85\) 205.379 0.262077
\(86\) 276.439 0.346619
\(87\) 0 0
\(88\) 12.6730 0.0153516
\(89\) −601.888 −0.716855 −0.358427 0.933558i \(-0.616687\pi\)
−0.358427 + 0.933558i \(0.616687\pi\)
\(90\) 0 0
\(91\) −1542.18 −1.77653
\(92\) 188.907 0.214076
\(93\) 0 0
\(94\) −505.820 −0.555015
\(95\) 389.268 0.420401
\(96\) 0 0
\(97\) −495.710 −0.518883 −0.259442 0.965759i \(-0.583539\pi\)
−0.259442 + 0.965759i \(0.583539\pi\)
\(98\) −3075.29 −3.16991
\(99\) 0 0
\(100\) −184.228 −0.184228
\(101\) −149.594 −0.147378 −0.0736891 0.997281i \(-0.523477\pi\)
−0.0736891 + 0.997281i \(0.523477\pi\)
\(102\) 0 0
\(103\) 564.393 0.539915 0.269958 0.962872i \(-0.412990\pi\)
0.269958 + 0.962872i \(0.412990\pi\)
\(104\) −820.202 −0.773340
\(105\) 0 0
\(106\) −646.742 −0.592615
\(107\) 2111.34 1.90758 0.953788 0.300480i \(-0.0971468\pi\)
0.953788 + 0.300480i \(0.0971468\pi\)
\(108\) 0 0
\(109\) 240.393 0.211243 0.105621 0.994406i \(-0.466317\pi\)
0.105621 + 0.994406i \(0.466317\pi\)
\(110\) 10.0833 0.00874008
\(111\) 0 0
\(112\) −2739.07 −2.31088
\(113\) −548.514 −0.456636 −0.228318 0.973587i \(-0.573323\pi\)
−0.228318 + 0.973587i \(0.573323\pi\)
\(114\) 0 0
\(115\) −508.076 −0.411986
\(116\) 275.268 0.220328
\(117\) 0 0
\(118\) 1339.82 1.04525
\(119\) −1521.39 −1.17198
\(120\) 0 0
\(121\) −1330.57 −0.999678
\(122\) 119.210 0.0884650
\(123\) 0 0
\(124\) −79.2195 −0.0573719
\(125\) 1109.50 0.793894
\(126\) 0 0
\(127\) −2477.98 −1.73138 −0.865690 0.500581i \(-0.833120\pi\)
−0.865690 + 0.500581i \(0.833120\pi\)
\(128\) −1739.52 −1.20120
\(129\) 0 0
\(130\) −652.598 −0.440282
\(131\) −240.252 −0.160236 −0.0801180 0.996785i \(-0.525530\pi\)
−0.0801180 + 0.996785i \(0.525530\pi\)
\(132\) 0 0
\(133\) −2883.59 −1.87999
\(134\) −1863.39 −1.20129
\(135\) 0 0
\(136\) −809.148 −0.510176
\(137\) −143.473 −0.0894728 −0.0447364 0.998999i \(-0.514245\pi\)
−0.0447364 + 0.998999i \(0.514245\pi\)
\(138\) 0 0
\(139\) −340.457 −0.207750 −0.103875 0.994590i \(-0.533124\pi\)
−0.103875 + 0.994590i \(0.533124\pi\)
\(140\) −326.441 −0.197066
\(141\) 0 0
\(142\) −2839.31 −1.67795
\(143\) −27.7539 −0.0162301
\(144\) 0 0
\(145\) −740.348 −0.424017
\(146\) −487.750 −0.276483
\(147\) 0 0
\(148\) −600.333 −0.333426
\(149\) 1418.37 0.779847 0.389923 0.920847i \(-0.372501\pi\)
0.389923 + 0.920847i \(0.372501\pi\)
\(150\) 0 0
\(151\) 335.359 0.180736 0.0903679 0.995908i \(-0.471196\pi\)
0.0903679 + 0.995908i \(0.471196\pi\)
\(152\) −1533.63 −0.818380
\(153\) 0 0
\(154\) −74.6946 −0.0390848
\(155\) 213.065 0.110411
\(156\) 0 0
\(157\) 2823.71 1.43539 0.717697 0.696355i \(-0.245196\pi\)
0.717697 + 0.696355i \(0.245196\pi\)
\(158\) −199.906 −0.100656
\(159\) 0 0
\(160\) −398.594 −0.196948
\(161\) 3763.69 1.84236
\(162\) 0 0
\(163\) 1947.03 0.935603 0.467802 0.883833i \(-0.345046\pi\)
0.467802 + 0.883833i \(0.345046\pi\)
\(164\) 414.595 0.197405
\(165\) 0 0
\(166\) 2616.68 1.22346
\(167\) 2376.81 1.10134 0.550669 0.834724i \(-0.314373\pi\)
0.550669 + 0.834724i \(0.314373\pi\)
\(168\) 0 0
\(169\) −400.753 −0.182409
\(170\) −643.803 −0.290456
\(171\) 0 0
\(172\) −161.061 −0.0713999
\(173\) −820.399 −0.360542 −0.180271 0.983617i \(-0.557697\pi\)
−0.180271 + 0.983617i \(0.557697\pi\)
\(174\) 0 0
\(175\) −3670.45 −1.58549
\(176\) −49.2940 −0.0211118
\(177\) 0 0
\(178\) 1886.74 0.794479
\(179\) 2688.77 1.12273 0.561364 0.827569i \(-0.310277\pi\)
0.561364 + 0.827569i \(0.310277\pi\)
\(180\) 0 0
\(181\) 2543.72 1.04460 0.522301 0.852761i \(-0.325074\pi\)
0.522301 + 0.852761i \(0.325074\pi\)
\(182\) 4834.27 1.96890
\(183\) 0 0
\(184\) 2001.70 0.801998
\(185\) 1614.62 0.641673
\(186\) 0 0
\(187\) −27.3799 −0.0107070
\(188\) 294.704 0.114327
\(189\) 0 0
\(190\) −1220.24 −0.465924
\(191\) −2251.64 −0.852999 −0.426499 0.904488i \(-0.640253\pi\)
−0.426499 + 0.904488i \(0.640253\pi\)
\(192\) 0 0
\(193\) 889.559 0.331771 0.165886 0.986145i \(-0.446952\pi\)
0.165886 + 0.986145i \(0.446952\pi\)
\(194\) 1553.90 0.575071
\(195\) 0 0
\(196\) 1791.74 0.652968
\(197\) −3780.75 −1.36735 −0.683673 0.729788i \(-0.739619\pi\)
−0.683673 + 0.729788i \(0.739619\pi\)
\(198\) 0 0
\(199\) −118.565 −0.0422355 −0.0211178 0.999777i \(-0.506722\pi\)
−0.0211178 + 0.999777i \(0.506722\pi\)
\(200\) −1952.12 −0.690177
\(201\) 0 0
\(202\) 468.934 0.163337
\(203\) 5484.29 1.89617
\(204\) 0 0
\(205\) −1115.07 −0.379903
\(206\) −1769.20 −0.598380
\(207\) 0 0
\(208\) 3190.33 1.06351
\(209\) −51.8948 −0.0171753
\(210\) 0 0
\(211\) −919.251 −0.299924 −0.149962 0.988692i \(-0.547915\pi\)
−0.149962 + 0.988692i \(0.547915\pi\)
\(212\) 376.809 0.122073
\(213\) 0 0
\(214\) −6618.41 −2.11414
\(215\) 433.181 0.137408
\(216\) 0 0
\(217\) −1578.33 −0.493750
\(218\) −753.561 −0.234117
\(219\) 0 0
\(220\) −5.87482 −0.00180037
\(221\) 1772.04 0.539368
\(222\) 0 0
\(223\) 1530.63 0.459635 0.229817 0.973234i \(-0.426187\pi\)
0.229817 + 0.973234i \(0.426187\pi\)
\(224\) 2952.68 0.880732
\(225\) 0 0
\(226\) 1719.43 0.506082
\(227\) 3079.49 0.900411 0.450205 0.892925i \(-0.351351\pi\)
0.450205 + 0.892925i \(0.351351\pi\)
\(228\) 0 0
\(229\) 1241.32 0.358205 0.179103 0.983830i \(-0.442681\pi\)
0.179103 + 0.983830i \(0.442681\pi\)
\(230\) 1592.67 0.456597
\(231\) 0 0
\(232\) 2916.80 0.825420
\(233\) −421.662 −0.118558 −0.0592789 0.998241i \(-0.518880\pi\)
−0.0592789 + 0.998241i \(0.518880\pi\)
\(234\) 0 0
\(235\) −792.623 −0.220021
\(236\) −780.612 −0.215312
\(237\) 0 0
\(238\) 4769.12 1.29889
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −990.944 −0.264864 −0.132432 0.991192i \(-0.542279\pi\)
−0.132432 + 0.991192i \(0.542279\pi\)
\(242\) 4170.95 1.10793
\(243\) 0 0
\(244\) −69.4547 −0.0182229
\(245\) −4818.98 −1.25663
\(246\) 0 0
\(247\) 3358.66 0.865208
\(248\) −839.427 −0.214934
\(249\) 0 0
\(250\) −3477.95 −0.879861
\(251\) 745.327 0.187429 0.0937144 0.995599i \(-0.470126\pi\)
0.0937144 + 0.995599i \(0.470126\pi\)
\(252\) 0 0
\(253\) 67.7336 0.0168315
\(254\) 7767.73 1.91886
\(255\) 0 0
\(256\) 2670.21 0.651906
\(257\) 1146.21 0.278205 0.139102 0.990278i \(-0.455578\pi\)
0.139102 + 0.990278i \(0.455578\pi\)
\(258\) 0 0
\(259\) −11960.7 −2.86951
\(260\) 380.221 0.0906935
\(261\) 0 0
\(262\) 753.119 0.177587
\(263\) 6051.57 1.41884 0.709421 0.704785i \(-0.248956\pi\)
0.709421 + 0.704785i \(0.248956\pi\)
\(264\) 0 0
\(265\) −1013.45 −0.234927
\(266\) 9039.21 2.08357
\(267\) 0 0
\(268\) 1085.66 0.247453
\(269\) 4009.38 0.908758 0.454379 0.890808i \(-0.349861\pi\)
0.454379 + 0.890808i \(0.349861\pi\)
\(270\) 0 0
\(271\) 6262.91 1.40386 0.701928 0.712248i \(-0.252323\pi\)
0.701928 + 0.712248i \(0.252323\pi\)
\(272\) 3147.33 0.701600
\(273\) 0 0
\(274\) 449.747 0.0991613
\(275\) −66.0556 −0.0144847
\(276\) 0 0
\(277\) −6892.58 −1.49507 −0.747536 0.664222i \(-0.768763\pi\)
−0.747536 + 0.664222i \(0.768763\pi\)
\(278\) 1067.23 0.230246
\(279\) 0 0
\(280\) −3459.04 −0.738275
\(281\) 1312.21 0.278577 0.139288 0.990252i \(-0.455518\pi\)
0.139288 + 0.990252i \(0.455518\pi\)
\(282\) 0 0
\(283\) 5425.57 1.13963 0.569817 0.821771i \(-0.307014\pi\)
0.569817 + 0.821771i \(0.307014\pi\)
\(284\) 1654.26 0.345641
\(285\) 0 0
\(286\) 87.0003 0.0179875
\(287\) 8260.17 1.69889
\(288\) 0 0
\(289\) −3164.84 −0.644177
\(290\) 2320.77 0.469932
\(291\) 0 0
\(292\) 284.176 0.0569526
\(293\) −7531.35 −1.50166 −0.750830 0.660496i \(-0.770346\pi\)
−0.750830 + 0.660496i \(0.770346\pi\)
\(294\) 0 0
\(295\) 2099.50 0.414364
\(296\) −6361.26 −1.24912
\(297\) 0 0
\(298\) −4446.16 −0.864292
\(299\) −4383.75 −0.847888
\(300\) 0 0
\(301\) −3208.89 −0.614476
\(302\) −1051.25 −0.200307
\(303\) 0 0
\(304\) 5965.34 1.12545
\(305\) 186.802 0.0350697
\(306\) 0 0
\(307\) 591.840 0.110026 0.0550132 0.998486i \(-0.482480\pi\)
0.0550132 + 0.998486i \(0.482480\pi\)
\(308\) 43.5191 0.00805107
\(309\) 0 0
\(310\) −667.895 −0.122367
\(311\) 9484.96 1.72940 0.864699 0.502290i \(-0.167509\pi\)
0.864699 + 0.502290i \(0.167509\pi\)
\(312\) 0 0
\(313\) −4919.24 −0.888344 −0.444172 0.895942i \(-0.646502\pi\)
−0.444172 + 0.895942i \(0.646502\pi\)
\(314\) −8851.51 −1.59083
\(315\) 0 0
\(316\) 116.471 0.0207341
\(317\) −496.312 −0.0879358 −0.0439679 0.999033i \(-0.514000\pi\)
−0.0439679 + 0.999033i \(0.514000\pi\)
\(318\) 0 0
\(319\) 98.6986 0.0173231
\(320\) −1708.60 −0.298480
\(321\) 0 0
\(322\) −11798.1 −2.04186
\(323\) 3313.39 0.570781
\(324\) 0 0
\(325\) 4275.15 0.729669
\(326\) −6103.37 −1.03691
\(327\) 0 0
\(328\) 4393.14 0.739545
\(329\) 5871.53 0.983915
\(330\) 0 0
\(331\) −2231.61 −0.370575 −0.185287 0.982684i \(-0.559322\pi\)
−0.185287 + 0.982684i \(0.559322\pi\)
\(332\) −1524.55 −0.252019
\(333\) 0 0
\(334\) −7450.61 −1.22060
\(335\) −2919.95 −0.476220
\(336\) 0 0
\(337\) −3569.71 −0.577016 −0.288508 0.957478i \(-0.593159\pi\)
−0.288508 + 0.957478i \(0.593159\pi\)
\(338\) 1256.24 0.202161
\(339\) 0 0
\(340\) 375.097 0.0598308
\(341\) −28.4045 −0.00451082
\(342\) 0 0
\(343\) 23216.8 3.65478
\(344\) −1706.64 −0.267487
\(345\) 0 0
\(346\) 2571.71 0.399583
\(347\) −5048.57 −0.781042 −0.390521 0.920594i \(-0.627705\pi\)
−0.390521 + 0.920594i \(0.627705\pi\)
\(348\) 0 0
\(349\) 1860.49 0.285358 0.142679 0.989769i \(-0.454428\pi\)
0.142679 + 0.989769i \(0.454428\pi\)
\(350\) 11505.8 1.75717
\(351\) 0 0
\(352\) 53.1381 0.00804622
\(353\) 11335.4 1.70912 0.854562 0.519349i \(-0.173825\pi\)
0.854562 + 0.519349i \(0.173825\pi\)
\(354\) 0 0
\(355\) −4449.20 −0.665181
\(356\) −1099.27 −0.163654
\(357\) 0 0
\(358\) −8428.50 −1.24430
\(359\) 3148.65 0.462895 0.231447 0.972847i \(-0.425654\pi\)
0.231447 + 0.972847i \(0.425654\pi\)
\(360\) 0 0
\(361\) −578.917 −0.0844025
\(362\) −7973.80 −1.15772
\(363\) 0 0
\(364\) −2816.57 −0.405573
\(365\) −764.307 −0.109604
\(366\) 0 0
\(367\) 6448.54 0.917197 0.458598 0.888644i \(-0.348352\pi\)
0.458598 + 0.888644i \(0.348352\pi\)
\(368\) −7786.01 −1.10292
\(369\) 0 0
\(370\) −5061.37 −0.711157
\(371\) 7507.35 1.05057
\(372\) 0 0
\(373\) −1545.86 −0.214588 −0.107294 0.994227i \(-0.534219\pi\)
−0.107294 + 0.994227i \(0.534219\pi\)
\(374\) 85.8279 0.0118665
\(375\) 0 0
\(376\) 3122.75 0.428308
\(377\) −6387.82 −0.872651
\(378\) 0 0
\(379\) −6544.96 −0.887050 −0.443525 0.896262i \(-0.646272\pi\)
−0.443525 + 0.896262i \(0.646272\pi\)
\(380\) 710.945 0.0959755
\(381\) 0 0
\(382\) 7058.21 0.945366
\(383\) 14067.3 1.87677 0.938386 0.345590i \(-0.112321\pi\)
0.938386 + 0.345590i \(0.112321\pi\)
\(384\) 0 0
\(385\) −117.047 −0.0154942
\(386\) −2788.50 −0.367697
\(387\) 0 0
\(388\) −905.345 −0.118459
\(389\) 7313.15 0.953191 0.476595 0.879123i \(-0.341871\pi\)
0.476595 + 0.879123i \(0.341871\pi\)
\(390\) 0 0
\(391\) −4324.67 −0.559355
\(392\) 18985.7 2.44623
\(393\) 0 0
\(394\) 11851.5 1.51541
\(395\) −313.254 −0.0399025
\(396\) 0 0
\(397\) 3707.91 0.468752 0.234376 0.972146i \(-0.424695\pi\)
0.234376 + 0.972146i \(0.424695\pi\)
\(398\) 371.667 0.0468090
\(399\) 0 0
\(400\) 7593.12 0.949140
\(401\) 6435.24 0.801398 0.400699 0.916210i \(-0.368767\pi\)
0.400699 + 0.916210i \(0.368767\pi\)
\(402\) 0 0
\(403\) 1838.35 0.227233
\(404\) −273.213 −0.0336457
\(405\) 0 0
\(406\) −17191.6 −2.10149
\(407\) −215.252 −0.0262153
\(408\) 0 0
\(409\) −9429.39 −1.13998 −0.569992 0.821650i \(-0.693054\pi\)
−0.569992 + 0.821650i \(0.693054\pi\)
\(410\) 3495.43 0.421041
\(411\) 0 0
\(412\) 1030.78 0.123260
\(413\) −15552.5 −1.85300
\(414\) 0 0
\(415\) 4100.35 0.485008
\(416\) −3439.12 −0.405329
\(417\) 0 0
\(418\) 162.675 0.0190351
\(419\) −8421.77 −0.981934 −0.490967 0.871178i \(-0.663356\pi\)
−0.490967 + 0.871178i \(0.663356\pi\)
\(420\) 0 0
\(421\) −8329.85 −0.964304 −0.482152 0.876088i \(-0.660145\pi\)
−0.482152 + 0.876088i \(0.660145\pi\)
\(422\) 2881.58 0.332401
\(423\) 0 0
\(424\) 3992.75 0.457324
\(425\) 4217.53 0.481365
\(426\) 0 0
\(427\) −1383.78 −0.156828
\(428\) 3856.06 0.435490
\(429\) 0 0
\(430\) −1357.89 −0.152287
\(431\) −5846.23 −0.653372 −0.326686 0.945133i \(-0.605932\pi\)
−0.326686 + 0.945133i \(0.605932\pi\)
\(432\) 0 0
\(433\) 11619.0 1.28954 0.644772 0.764375i \(-0.276952\pi\)
0.644772 + 0.764375i \(0.276952\pi\)
\(434\) 4947.58 0.547216
\(435\) 0 0
\(436\) 439.044 0.0482257
\(437\) −8196.82 −0.897270
\(438\) 0 0
\(439\) 10508.6 1.14248 0.571240 0.820783i \(-0.306463\pi\)
0.571240 + 0.820783i \(0.306463\pi\)
\(440\) −62.2509 −0.00674476
\(441\) 0 0
\(442\) −5554.82 −0.597773
\(443\) 11819.1 1.26759 0.633793 0.773503i \(-0.281497\pi\)
0.633793 + 0.773503i \(0.281497\pi\)
\(444\) 0 0
\(445\) 2956.53 0.314951
\(446\) −4798.07 −0.509406
\(447\) 0 0
\(448\) 12656.8 1.33478
\(449\) −9424.13 −0.990539 −0.495269 0.868739i \(-0.664931\pi\)
−0.495269 + 0.868739i \(0.664931\pi\)
\(450\) 0 0
\(451\) 148.655 0.0155208
\(452\) −1001.78 −0.104248
\(453\) 0 0
\(454\) −9653.30 −0.997912
\(455\) 7575.32 0.780520
\(456\) 0 0
\(457\) 8426.48 0.862526 0.431263 0.902226i \(-0.358068\pi\)
0.431263 + 0.902226i \(0.358068\pi\)
\(458\) −3891.18 −0.396993
\(459\) 0 0
\(460\) −927.931 −0.0940543
\(461\) −11913.7 −1.20363 −0.601817 0.798634i \(-0.705557\pi\)
−0.601817 + 0.798634i \(0.705557\pi\)
\(462\) 0 0
\(463\) 10300.0 1.03386 0.516932 0.856026i \(-0.327074\pi\)
0.516932 + 0.856026i \(0.327074\pi\)
\(464\) −11345.5 −1.13513
\(465\) 0 0
\(466\) 1321.78 0.131396
\(467\) −1463.70 −0.145036 −0.0725179 0.997367i \(-0.523103\pi\)
−0.0725179 + 0.997367i \(0.523103\pi\)
\(468\) 0 0
\(469\) 21630.2 2.12961
\(470\) 2484.64 0.243846
\(471\) 0 0
\(472\) −8271.54 −0.806628
\(473\) −57.7490 −0.00561375
\(474\) 0 0
\(475\) 7993.75 0.772165
\(476\) −2778.62 −0.267558
\(477\) 0 0
\(478\) 749.194 0.0716890
\(479\) 400.076 0.0381627 0.0190813 0.999818i \(-0.493926\pi\)
0.0190813 + 0.999818i \(0.493926\pi\)
\(480\) 0 0
\(481\) 13931.2 1.32060
\(482\) 3106.32 0.293545
\(483\) 0 0
\(484\) −2430.10 −0.228222
\(485\) 2434.97 0.227972
\(486\) 0 0
\(487\) 14121.7 1.31400 0.656999 0.753891i \(-0.271825\pi\)
0.656999 + 0.753891i \(0.271825\pi\)
\(488\) −735.957 −0.0682689
\(489\) 0 0
\(490\) 15106.1 1.39270
\(491\) −11270.3 −1.03589 −0.517945 0.855414i \(-0.673303\pi\)
−0.517945 + 0.855414i \(0.673303\pi\)
\(492\) 0 0
\(493\) −6301.73 −0.575691
\(494\) −10528.4 −0.958896
\(495\) 0 0
\(496\) 3265.11 0.295580
\(497\) 32958.5 2.97463
\(498\) 0 0
\(499\) 11360.2 1.01915 0.509573 0.860428i \(-0.329803\pi\)
0.509573 + 0.860428i \(0.329803\pi\)
\(500\) 2026.35 0.181242
\(501\) 0 0
\(502\) −2336.38 −0.207724
\(503\) 16393.5 1.45318 0.726589 0.687073i \(-0.241105\pi\)
0.726589 + 0.687073i \(0.241105\pi\)
\(504\) 0 0
\(505\) 734.821 0.0647507
\(506\) −212.325 −0.0186541
\(507\) 0 0
\(508\) −4525.69 −0.395265
\(509\) −9306.18 −0.810391 −0.405196 0.914230i \(-0.632797\pi\)
−0.405196 + 0.914230i \(0.632797\pi\)
\(510\) 0 0
\(511\) 5661.77 0.490141
\(512\) 5545.88 0.478703
\(513\) 0 0
\(514\) −3593.03 −0.308330
\(515\) −2772.35 −0.237212
\(516\) 0 0
\(517\) 105.668 0.00898888
\(518\) 37493.2 3.18023
\(519\) 0 0
\(520\) 4028.91 0.339768
\(521\) −19266.7 −1.62014 −0.810068 0.586337i \(-0.800570\pi\)
−0.810068 + 0.586337i \(0.800570\pi\)
\(522\) 0 0
\(523\) −11768.3 −0.983920 −0.491960 0.870618i \(-0.663719\pi\)
−0.491960 + 0.870618i \(0.663719\pi\)
\(524\) −438.787 −0.0365811
\(525\) 0 0
\(526\) −18969.9 −1.57248
\(527\) 1813.58 0.149906
\(528\) 0 0
\(529\) −1468.45 −0.120691
\(530\) 3176.86 0.260366
\(531\) 0 0
\(532\) −5266.48 −0.429194
\(533\) −9621.01 −0.781861
\(534\) 0 0
\(535\) −10371.1 −0.838095
\(536\) 11503.9 0.927041
\(537\) 0 0
\(538\) −12568.2 −1.00716
\(539\) 642.437 0.0513390
\(540\) 0 0
\(541\) 17595.6 1.39833 0.699164 0.714962i \(-0.253556\pi\)
0.699164 + 0.714962i \(0.253556\pi\)
\(542\) −19632.4 −1.55587
\(543\) 0 0
\(544\) −3392.77 −0.267397
\(545\) −1180.83 −0.0928097
\(546\) 0 0
\(547\) 15293.3 1.19542 0.597710 0.801713i \(-0.296077\pi\)
0.597710 + 0.801713i \(0.296077\pi\)
\(548\) −262.034 −0.0204262
\(549\) 0 0
\(550\) 207.065 0.0160532
\(551\) −11944.1 −0.923474
\(552\) 0 0
\(553\) 2320.50 0.178440
\(554\) 21606.2 1.65696
\(555\) 0 0
\(556\) −621.798 −0.0474283
\(557\) 7410.55 0.563725 0.281863 0.959455i \(-0.409048\pi\)
0.281863 + 0.959455i \(0.409048\pi\)
\(558\) 0 0
\(559\) 3737.54 0.282793
\(560\) 13454.6 1.01529
\(561\) 0 0
\(562\) −4113.40 −0.308743
\(563\) 12331.7 0.923128 0.461564 0.887107i \(-0.347288\pi\)
0.461564 + 0.887107i \(0.347288\pi\)
\(564\) 0 0
\(565\) 2694.35 0.200623
\(566\) −17007.6 −1.26304
\(567\) 0 0
\(568\) 17528.9 1.29488
\(569\) −5561.27 −0.409738 −0.204869 0.978789i \(-0.565677\pi\)
−0.204869 + 0.978789i \(0.565677\pi\)
\(570\) 0 0
\(571\) −24919.9 −1.82638 −0.913192 0.407529i \(-0.866390\pi\)
−0.913192 + 0.407529i \(0.866390\pi\)
\(572\) −50.6887 −0.00370525
\(573\) 0 0
\(574\) −25893.2 −1.88286
\(575\) −10433.5 −0.756708
\(576\) 0 0
\(577\) 1269.21 0.0915733 0.0457866 0.998951i \(-0.485421\pi\)
0.0457866 + 0.998951i \(0.485421\pi\)
\(578\) 9920.84 0.713931
\(579\) 0 0
\(580\) −1352.14 −0.0968011
\(581\) −30374.3 −2.16891
\(582\) 0 0
\(583\) 135.107 0.00959784
\(584\) 3011.19 0.213363
\(585\) 0 0
\(586\) 23608.5 1.66427
\(587\) −3024.29 −0.212651 −0.106325 0.994331i \(-0.533908\pi\)
−0.106325 + 0.994331i \(0.533908\pi\)
\(588\) 0 0
\(589\) 3437.38 0.240467
\(590\) −6581.30 −0.459234
\(591\) 0 0
\(592\) 24743.3 1.71781
\(593\) −7958.20 −0.551103 −0.275552 0.961286i \(-0.588860\pi\)
−0.275552 + 0.961286i \(0.588860\pi\)
\(594\) 0 0
\(595\) 7473.23 0.514912
\(596\) 2590.45 0.178035
\(597\) 0 0
\(598\) 13741.7 0.939702
\(599\) 15551.4 1.06079 0.530395 0.847751i \(-0.322044\pi\)
0.530395 + 0.847751i \(0.322044\pi\)
\(600\) 0 0
\(601\) 12402.8 0.841798 0.420899 0.907108i \(-0.361715\pi\)
0.420899 + 0.907108i \(0.361715\pi\)
\(602\) 10058.9 0.681015
\(603\) 0 0
\(604\) 612.486 0.0412611
\(605\) 6535.89 0.439209
\(606\) 0 0
\(607\) −7545.59 −0.504557 −0.252278 0.967655i \(-0.581180\pi\)
−0.252278 + 0.967655i \(0.581180\pi\)
\(608\) −6430.53 −0.428935
\(609\) 0 0
\(610\) −585.568 −0.0388672
\(611\) −6838.85 −0.452815
\(612\) 0 0
\(613\) 3744.35 0.246710 0.123355 0.992363i \(-0.460635\pi\)
0.123355 + 0.992363i \(0.460635\pi\)
\(614\) −1855.24 −0.121940
\(615\) 0 0
\(616\) 461.138 0.0301619
\(617\) 19319.9 1.26060 0.630300 0.776352i \(-0.282932\pi\)
0.630300 + 0.776352i \(0.282932\pi\)
\(618\) 0 0
\(619\) −4231.21 −0.274744 −0.137372 0.990520i \(-0.543866\pi\)
−0.137372 + 0.990520i \(0.543866\pi\)
\(620\) 389.133 0.0252064
\(621\) 0 0
\(622\) −29732.5 −1.91667
\(623\) −21901.2 −1.40843
\(624\) 0 0
\(625\) 7158.95 0.458173
\(626\) 15420.3 0.984538
\(627\) 0 0
\(628\) 5157.12 0.327694
\(629\) 13743.4 0.871204
\(630\) 0 0
\(631\) 19238.3 1.21373 0.606866 0.794804i \(-0.292426\pi\)
0.606866 + 0.794804i \(0.292426\pi\)
\(632\) 1234.15 0.0776769
\(633\) 0 0
\(634\) 1555.79 0.0974579
\(635\) 12172.1 0.760683
\(636\) 0 0
\(637\) −41578.8 −2.58620
\(638\) −309.391 −0.0191989
\(639\) 0 0
\(640\) 8544.70 0.527748
\(641\) 2485.24 0.153138 0.0765688 0.997064i \(-0.475604\pi\)
0.0765688 + 0.997064i \(0.475604\pi\)
\(642\) 0 0
\(643\) 26682.8 1.63649 0.818247 0.574867i \(-0.194946\pi\)
0.818247 + 0.574867i \(0.194946\pi\)
\(644\) 6873.86 0.420602
\(645\) 0 0
\(646\) −10386.5 −0.632588
\(647\) 27899.1 1.69525 0.847624 0.530598i \(-0.178033\pi\)
0.847624 + 0.530598i \(0.178033\pi\)
\(648\) 0 0
\(649\) −279.892 −0.0169287
\(650\) −13401.3 −0.808681
\(651\) 0 0
\(652\) 3555.98 0.213594
\(653\) −2943.64 −0.176406 −0.0882032 0.996103i \(-0.528112\pi\)
−0.0882032 + 0.996103i \(0.528112\pi\)
\(654\) 0 0
\(655\) 1180.14 0.0703998
\(656\) −17088.0 −1.01703
\(657\) 0 0
\(658\) −18405.5 −1.09046
\(659\) 23688.2 1.40025 0.700124 0.714021i \(-0.253128\pi\)
0.700124 + 0.714021i \(0.253128\pi\)
\(660\) 0 0
\(661\) 23515.5 1.38373 0.691867 0.722025i \(-0.256788\pi\)
0.691867 + 0.722025i \(0.256788\pi\)
\(662\) 6995.43 0.410702
\(663\) 0 0
\(664\) −16154.4 −0.944148
\(665\) 14164.5 0.825977
\(666\) 0 0
\(667\) 15589.5 0.904989
\(668\) 4340.92 0.251430
\(669\) 0 0
\(670\) 9153.17 0.527788
\(671\) −24.9033 −0.00143276
\(672\) 0 0
\(673\) 6923.43 0.396551 0.198275 0.980146i \(-0.436466\pi\)
0.198275 + 0.980146i \(0.436466\pi\)
\(674\) 11190.0 0.639498
\(675\) 0 0
\(676\) −731.920 −0.0416431
\(677\) −22544.6 −1.27985 −0.639925 0.768437i \(-0.721035\pi\)
−0.639925 + 0.768437i \(0.721035\pi\)
\(678\) 0 0
\(679\) −18037.6 −1.01947
\(680\) 3974.61 0.224146
\(681\) 0 0
\(682\) 89.0396 0.00499927
\(683\) 18136.0 1.01604 0.508020 0.861345i \(-0.330377\pi\)
0.508020 + 0.861345i \(0.330377\pi\)
\(684\) 0 0
\(685\) 704.755 0.0393099
\(686\) −72777.8 −4.05054
\(687\) 0 0
\(688\) 6638.28 0.367852
\(689\) −8744.16 −0.483492
\(690\) 0 0
\(691\) −16072.8 −0.884858 −0.442429 0.896803i \(-0.645883\pi\)
−0.442429 + 0.896803i \(0.645883\pi\)
\(692\) −1498.34 −0.0823100
\(693\) 0 0
\(694\) 15825.8 0.865617
\(695\) 1672.36 0.0912750
\(696\) 0 0
\(697\) −9491.35 −0.515797
\(698\) −5832.10 −0.316258
\(699\) 0 0
\(700\) −6703.57 −0.361959
\(701\) 10999.4 0.592640 0.296320 0.955089i \(-0.404240\pi\)
0.296320 + 0.955089i \(0.404240\pi\)
\(702\) 0 0
\(703\) 26048.8 1.39751
\(704\) 227.780 0.0121943
\(705\) 0 0
\(706\) −35533.0 −1.89420
\(707\) −5443.36 −0.289559
\(708\) 0 0
\(709\) 9279.33 0.491527 0.245763 0.969330i \(-0.420961\pi\)
0.245763 + 0.969330i \(0.420961\pi\)
\(710\) 13946.9 0.737210
\(711\) 0 0
\(712\) −11648.1 −0.613103
\(713\) −4486.50 −0.235653
\(714\) 0 0
\(715\) 136.330 0.00713070
\(716\) 4910.67 0.256313
\(717\) 0 0
\(718\) −9870.07 −0.513019
\(719\) −4475.10 −0.232119 −0.116059 0.993242i \(-0.537026\pi\)
−0.116059 + 0.993242i \(0.537026\pi\)
\(720\) 0 0
\(721\) 20536.8 1.06079
\(722\) 1814.73 0.0935421
\(723\) 0 0
\(724\) 4645.75 0.238478
\(725\) −15203.3 −0.778808
\(726\) 0 0
\(727\) 24722.2 1.26120 0.630601 0.776107i \(-0.282808\pi\)
0.630601 + 0.776107i \(0.282808\pi\)
\(728\) −29845.0 −1.51941
\(729\) 0 0
\(730\) 2395.87 0.121473
\(731\) 3687.18 0.186560
\(732\) 0 0
\(733\) 2743.32 0.138236 0.0691180 0.997608i \(-0.477982\pi\)
0.0691180 + 0.997608i \(0.477982\pi\)
\(734\) −20214.3 −1.01652
\(735\) 0 0
\(736\) 8393.19 0.420349
\(737\) 389.269 0.0194558
\(738\) 0 0
\(739\) 19302.2 0.960814 0.480407 0.877046i \(-0.340489\pi\)
0.480407 + 0.877046i \(0.340489\pi\)
\(740\) 2948.89 0.146491
\(741\) 0 0
\(742\) −23533.3 −1.16433
\(743\) −33863.2 −1.67203 −0.836017 0.548704i \(-0.815121\pi\)
−0.836017 + 0.548704i \(0.815121\pi\)
\(744\) 0 0
\(745\) −6967.15 −0.342626
\(746\) 4845.80 0.237825
\(747\) 0 0
\(748\) −50.0056 −0.00244437
\(749\) 76826.1 3.74789
\(750\) 0 0
\(751\) −30272.2 −1.47090 −0.735451 0.677578i \(-0.763029\pi\)
−0.735451 + 0.677578i \(0.763029\pi\)
\(752\) −12146.5 −0.589014
\(753\) 0 0
\(754\) 20023.9 0.967145
\(755\) −1647.31 −0.0794064
\(756\) 0 0
\(757\) −2202.96 −0.105770 −0.0528849 0.998601i \(-0.516842\pi\)
−0.0528849 + 0.998601i \(0.516842\pi\)
\(758\) 20516.5 0.983104
\(759\) 0 0
\(760\) 7533.32 0.359556
\(761\) −4867.98 −0.231885 −0.115942 0.993256i \(-0.536989\pi\)
−0.115942 + 0.993256i \(0.536989\pi\)
\(762\) 0 0
\(763\) 8747.28 0.415037
\(764\) −4112.30 −0.194736
\(765\) 0 0
\(766\) −44096.7 −2.08000
\(767\) 18114.7 0.852784
\(768\) 0 0
\(769\) −1744.23 −0.0817928 −0.0408964 0.999163i \(-0.513021\pi\)
−0.0408964 + 0.999163i \(0.513021\pi\)
\(770\) 366.907 0.0171719
\(771\) 0 0
\(772\) 1624.66 0.0757418
\(773\) −31838.9 −1.48145 −0.740727 0.671806i \(-0.765519\pi\)
−0.740727 + 0.671806i \(0.765519\pi\)
\(774\) 0 0
\(775\) 4375.35 0.202797
\(776\) −9593.23 −0.443785
\(777\) 0 0
\(778\) −22924.5 −1.05641
\(779\) −17989.5 −0.827397
\(780\) 0 0
\(781\) 593.140 0.0271757
\(782\) 13556.6 0.619925
\(783\) 0 0
\(784\) −73848.5 −3.36409
\(785\) −13870.3 −0.630642
\(786\) 0 0
\(787\) −6132.91 −0.277782 −0.138891 0.990308i \(-0.544354\pi\)
−0.138891 + 0.990308i \(0.544354\pi\)
\(788\) −6905.02 −0.312159
\(789\) 0 0
\(790\) 981.957 0.0442234
\(791\) −19959.0 −0.897169
\(792\) 0 0
\(793\) 1611.75 0.0721752
\(794\) −11623.2 −0.519510
\(795\) 0 0
\(796\) −216.543 −0.00964217
\(797\) −40316.5 −1.79182 −0.895911 0.444233i \(-0.853476\pi\)
−0.895911 + 0.444233i \(0.853476\pi\)
\(798\) 0 0
\(799\) −6746.68 −0.298724
\(800\) −8185.26 −0.361741
\(801\) 0 0
\(802\) −20172.6 −0.888178
\(803\) 101.893 0.00447785
\(804\) 0 0
\(805\) −18487.6 −0.809443
\(806\) −5762.68 −0.251838
\(807\) 0 0
\(808\) −2895.03 −0.126048
\(809\) 1070.47 0.0465211 0.0232605 0.999729i \(-0.492595\pi\)
0.0232605 + 0.999729i \(0.492595\pi\)
\(810\) 0 0
\(811\) 31220.1 1.35177 0.675885 0.737007i \(-0.263761\pi\)
0.675885 + 0.737007i \(0.263761\pi\)
\(812\) 10016.3 0.432886
\(813\) 0 0
\(814\) 674.750 0.0290540
\(815\) −9564.00 −0.411058
\(816\) 0 0
\(817\) 6988.53 0.299263
\(818\) 29558.4 1.26343
\(819\) 0 0
\(820\) −2036.53 −0.0867301
\(821\) −42159.9 −1.79219 −0.896096 0.443860i \(-0.853609\pi\)
−0.896096 + 0.443860i \(0.853609\pi\)
\(822\) 0 0
\(823\) 1888.54 0.0799884 0.0399942 0.999200i \(-0.487266\pi\)
0.0399942 + 0.999200i \(0.487266\pi\)
\(824\) 10922.4 0.461773
\(825\) 0 0
\(826\) 48752.5 2.05365
\(827\) −8491.02 −0.357027 −0.178514 0.983937i \(-0.557129\pi\)
−0.178514 + 0.983937i \(0.557129\pi\)
\(828\) 0 0
\(829\) 30959.9 1.29708 0.648541 0.761180i \(-0.275380\pi\)
0.648541 + 0.761180i \(0.275380\pi\)
\(830\) −12853.4 −0.537527
\(831\) 0 0
\(832\) −14742.0 −0.614288
\(833\) −41018.5 −1.70613
\(834\) 0 0
\(835\) −11675.1 −0.483874
\(836\) −94.7787 −0.00392104
\(837\) 0 0
\(838\) 26399.7 1.08826
\(839\) 40700.5 1.67478 0.837389 0.546608i \(-0.184081\pi\)
0.837389 + 0.546608i \(0.184081\pi\)
\(840\) 0 0
\(841\) −1672.64 −0.0685818
\(842\) 26111.6 1.06872
\(843\) 0 0
\(844\) −1678.88 −0.0684711
\(845\) 1968.54 0.0801416
\(846\) 0 0
\(847\) −48416.1 −1.96410
\(848\) −15530.6 −0.628918
\(849\) 0 0
\(850\) −13220.7 −0.533490
\(851\) −33999.1 −1.36954
\(852\) 0 0
\(853\) 38855.2 1.55964 0.779822 0.626001i \(-0.215309\pi\)
0.779822 + 0.626001i \(0.215309\pi\)
\(854\) 4337.73 0.173810
\(855\) 0 0
\(856\) 40859.7 1.63149
\(857\) 44433.6 1.77109 0.885544 0.464555i \(-0.153786\pi\)
0.885544 + 0.464555i \(0.153786\pi\)
\(858\) 0 0
\(859\) −7511.88 −0.298372 −0.149186 0.988809i \(-0.547665\pi\)
−0.149186 + 0.988809i \(0.547665\pi\)
\(860\) 791.146 0.0313696
\(861\) 0 0
\(862\) 18326.2 0.724122
\(863\) 8869.88 0.349866 0.174933 0.984580i \(-0.444029\pi\)
0.174933 + 0.984580i \(0.444029\pi\)
\(864\) 0 0
\(865\) 4029.87 0.158404
\(866\) −36422.0 −1.42918
\(867\) 0 0
\(868\) −2882.59 −0.112721
\(869\) 41.7610 0.00163020
\(870\) 0 0
\(871\) −25193.7 −0.980086
\(872\) 4652.21 0.180669
\(873\) 0 0
\(874\) 25694.6 0.994430
\(875\) 40371.9 1.55979
\(876\) 0 0
\(877\) −42946.9 −1.65361 −0.826804 0.562491i \(-0.809843\pi\)
−0.826804 + 0.562491i \(0.809843\pi\)
\(878\) −32941.4 −1.26619
\(879\) 0 0
\(880\) 242.137 0.00927548
\(881\) −10522.8 −0.402409 −0.201205 0.979549i \(-0.564486\pi\)
−0.201205 + 0.979549i \(0.564486\pi\)
\(882\) 0 0
\(883\) −33736.0 −1.28574 −0.642870 0.765975i \(-0.722256\pi\)
−0.642870 + 0.765975i \(0.722256\pi\)
\(884\) 3236.38 0.123135
\(885\) 0 0
\(886\) −37049.3 −1.40485
\(887\) 13266.6 0.502196 0.251098 0.967962i \(-0.419208\pi\)
0.251098 + 0.967962i \(0.419208\pi\)
\(888\) 0 0
\(889\) −90167.3 −3.40170
\(890\) −9267.85 −0.349055
\(891\) 0 0
\(892\) 2795.48 0.104932
\(893\) −12787.4 −0.479187
\(894\) 0 0
\(895\) −13207.5 −0.493271
\(896\) −63296.8 −2.36004
\(897\) 0 0
\(898\) 29541.8 1.09780
\(899\) −6537.54 −0.242535
\(900\) 0 0
\(901\) −8626.32 −0.318961
\(902\) −465.989 −0.0172015
\(903\) 0 0
\(904\) −10615.1 −0.390546
\(905\) −12495.0 −0.458947
\(906\) 0 0
\(907\) −39503.9 −1.44620 −0.723100 0.690743i \(-0.757284\pi\)
−0.723100 + 0.690743i \(0.757284\pi\)
\(908\) 5624.27 0.205559
\(909\) 0 0
\(910\) −23746.4 −0.865038
\(911\) 45573.3 1.65742 0.828711 0.559676i \(-0.189075\pi\)
0.828711 + 0.559676i \(0.189075\pi\)
\(912\) 0 0
\(913\) −546.633 −0.0198148
\(914\) −26414.5 −0.955924
\(915\) 0 0
\(916\) 2267.10 0.0817765
\(917\) −8742.16 −0.314822
\(918\) 0 0
\(919\) −43624.1 −1.56586 −0.782930 0.622110i \(-0.786276\pi\)
−0.782930 + 0.622110i \(0.786276\pi\)
\(920\) −9832.56 −0.352358
\(921\) 0 0
\(922\) 37345.9 1.33397
\(923\) −38388.3 −1.36898
\(924\) 0 0
\(925\) 33156.8 1.17858
\(926\) −32287.3 −1.14582
\(927\) 0 0
\(928\) 12230.2 0.432625
\(929\) −40824.6 −1.44178 −0.720889 0.693050i \(-0.756266\pi\)
−0.720889 + 0.693050i \(0.756266\pi\)
\(930\) 0 0
\(931\) −77744.9 −2.73683
\(932\) −770.107 −0.0270662
\(933\) 0 0
\(934\) 4588.25 0.160741
\(935\) 134.493 0.00470415
\(936\) 0 0
\(937\) 2247.16 0.0783474 0.0391737 0.999232i \(-0.487527\pi\)
0.0391737 + 0.999232i \(0.487527\pi\)
\(938\) −67804.2 −2.36022
\(939\) 0 0
\(940\) −1447.62 −0.0502298
\(941\) 52797.3 1.82906 0.914528 0.404522i \(-0.132562\pi\)
0.914528 + 0.404522i \(0.132562\pi\)
\(942\) 0 0
\(943\) 23480.1 0.810835
\(944\) 32173.7 1.10929
\(945\) 0 0
\(946\) 181.026 0.00622163
\(947\) 8350.80 0.286552 0.143276 0.989683i \(-0.454236\pi\)
0.143276 + 0.989683i \(0.454236\pi\)
\(948\) 0 0
\(949\) −6594.53 −0.225572
\(950\) −25058.0 −0.855779
\(951\) 0 0
\(952\) −29442.8 −1.00236
\(953\) −18670.3 −0.634616 −0.317308 0.948323i \(-0.602779\pi\)
−0.317308 + 0.948323i \(0.602779\pi\)
\(954\) 0 0
\(955\) 11060.2 0.374766
\(956\) −436.500 −0.0147672
\(957\) 0 0
\(958\) −1254.12 −0.0422951
\(959\) −5220.63 −0.175790
\(960\) 0 0
\(961\) −27909.6 −0.936845
\(962\) −43670.1 −1.46360
\(963\) 0 0
\(964\) −1809.82 −0.0604673
\(965\) −4369.60 −0.145764
\(966\) 0 0
\(967\) 34012.8 1.13110 0.565551 0.824713i \(-0.308663\pi\)
0.565551 + 0.824713i \(0.308663\pi\)
\(968\) −25749.9 −0.854993
\(969\) 0 0
\(970\) −7632.91 −0.252658
\(971\) 45188.5 1.49348 0.746739 0.665117i \(-0.231619\pi\)
0.746739 + 0.665117i \(0.231619\pi\)
\(972\) 0 0
\(973\) −12388.4 −0.408174
\(974\) −44267.5 −1.45628
\(975\) 0 0
\(976\) 2862.64 0.0938842
\(977\) −21244.1 −0.695658 −0.347829 0.937558i \(-0.613081\pi\)
−0.347829 + 0.937558i \(0.613081\pi\)
\(978\) 0 0
\(979\) −394.146 −0.0128672
\(980\) −8801.20 −0.286882
\(981\) 0 0
\(982\) 35329.1 1.14806
\(983\) 35357.8 1.14724 0.573621 0.819121i \(-0.305538\pi\)
0.573621 + 0.819121i \(0.305538\pi\)
\(984\) 0 0
\(985\) 18571.4 0.600745
\(986\) 19754.0 0.638030
\(987\) 0 0
\(988\) 6134.12 0.197523
\(989\) −9121.49 −0.293273
\(990\) 0 0
\(991\) 21457.7 0.687815 0.343908 0.939003i \(-0.388249\pi\)
0.343908 + 0.939003i \(0.388249\pi\)
\(992\) −3519.73 −0.112653
\(993\) 0 0
\(994\) −103315. −3.29674
\(995\) 582.404 0.0185562
\(996\) 0 0
\(997\) −26463.2 −0.840621 −0.420310 0.907380i \(-0.638079\pi\)
−0.420310 + 0.907380i \(0.638079\pi\)
\(998\) −35610.9 −1.12950
\(999\) 0 0
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 2151.4.a.h.1.13 yes 59
3.2 odd 2 2151.4.a.g.1.47 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.47 59 3.2 odd 2
2151.4.a.h.1.13 yes 59 1.1 even 1 trivial