Properties

Label 2151.4.a.h.1.16
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $59$
CM no
Inner twists $1$

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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 1.16
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.96328 q^{2} +0.781040 q^{4} +9.17370 q^{5} +2.35613 q^{7} +21.3918 q^{8} +O(q^{10})\) \(q-2.96328 q^{2} +0.781040 q^{4} +9.17370 q^{5} +2.35613 q^{7} +21.3918 q^{8} -27.1843 q^{10} -14.3796 q^{11} +15.1470 q^{13} -6.98188 q^{14} -69.6383 q^{16} -57.8861 q^{17} +103.148 q^{19} +7.16503 q^{20} +42.6109 q^{22} +82.7139 q^{23} -40.8433 q^{25} -44.8848 q^{26} +1.84023 q^{28} -82.2294 q^{29} -156.009 q^{31} +35.2234 q^{32} +171.533 q^{34} +21.6144 q^{35} +202.052 q^{37} -305.656 q^{38} +196.242 q^{40} -3.54593 q^{41} +357.565 q^{43} -11.2311 q^{44} -245.105 q^{46} +147.712 q^{47} -337.449 q^{49} +121.030 q^{50} +11.8304 q^{52} +160.081 q^{53} -131.915 q^{55} +50.4019 q^{56} +243.669 q^{58} -45.9350 q^{59} -743.891 q^{61} +462.299 q^{62} +452.730 q^{64} +138.954 q^{65} +165.554 q^{67} -45.2114 q^{68} -64.0497 q^{70} +747.149 q^{71} +962.660 q^{73} -598.738 q^{74} +80.5627 q^{76} -33.8803 q^{77} +803.730 q^{79} -638.841 q^{80} +10.5076 q^{82} +588.954 q^{83} -531.030 q^{85} -1059.57 q^{86} -307.607 q^{88} -764.364 q^{89} +35.6883 q^{91} +64.6029 q^{92} -437.713 q^{94} +946.248 q^{95} -135.843 q^{97} +999.955 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.96328 −1.04768 −0.523839 0.851817i \(-0.675501\pi\)
−0.523839 + 0.851817i \(0.675501\pi\)
\(3\) 0 0
\(4\) 0.781040 0.0976300
\(5\) 9.17370 0.820521 0.410260 0.911968i \(-0.365438\pi\)
0.410260 + 0.911968i \(0.365438\pi\)
\(6\) 0 0
\(7\) 2.35613 0.127219 0.0636096 0.997975i \(-0.479739\pi\)
0.0636096 + 0.997975i \(0.479739\pi\)
\(8\) 21.3918 0.945394
\(9\) 0 0
\(10\) −27.1843 −0.859642
\(11\) −14.3796 −0.394148 −0.197074 0.980389i \(-0.563144\pi\)
−0.197074 + 0.980389i \(0.563144\pi\)
\(12\) 0 0
\(13\) 15.1470 0.323155 0.161578 0.986860i \(-0.448342\pi\)
0.161578 + 0.986860i \(0.448342\pi\)
\(14\) −6.98188 −0.133285
\(15\) 0 0
\(16\) −69.6383 −1.08810
\(17\) −57.8861 −0.825849 −0.412925 0.910765i \(-0.635493\pi\)
−0.412925 + 0.910765i \(0.635493\pi\)
\(18\) 0 0
\(19\) 103.148 1.24546 0.622730 0.782436i \(-0.286023\pi\)
0.622730 + 0.782436i \(0.286023\pi\)
\(20\) 7.16503 0.0801074
\(21\) 0 0
\(22\) 42.6109 0.412940
\(23\) 82.7139 0.749872 0.374936 0.927051i \(-0.377665\pi\)
0.374936 + 0.927051i \(0.377665\pi\)
\(24\) 0 0
\(25\) −40.8433 −0.326746
\(26\) −44.8848 −0.338563
\(27\) 0 0
\(28\) 1.84023 0.0124204
\(29\) −82.2294 −0.526538 −0.263269 0.964722i \(-0.584801\pi\)
−0.263269 + 0.964722i \(0.584801\pi\)
\(30\) 0 0
\(31\) −156.009 −0.903874 −0.451937 0.892050i \(-0.649267\pi\)
−0.451937 + 0.892050i \(0.649267\pi\)
\(32\) 35.2234 0.194584
\(33\) 0 0
\(34\) 171.533 0.865225
\(35\) 21.6144 0.104386
\(36\) 0 0
\(37\) 202.052 0.897762 0.448881 0.893591i \(-0.351823\pi\)
0.448881 + 0.893591i \(0.351823\pi\)
\(38\) −305.656 −1.30484
\(39\) 0 0
\(40\) 196.242 0.775715
\(41\) −3.54593 −0.0135069 −0.00675344 0.999977i \(-0.502150\pi\)
−0.00675344 + 0.999977i \(0.502150\pi\)
\(42\) 0 0
\(43\) 357.565 1.26810 0.634048 0.773293i \(-0.281392\pi\)
0.634048 + 0.773293i \(0.281392\pi\)
\(44\) −11.2311 −0.0384807
\(45\) 0 0
\(46\) −245.105 −0.785624
\(47\) 147.712 0.458426 0.229213 0.973376i \(-0.426385\pi\)
0.229213 + 0.973376i \(0.426385\pi\)
\(48\) 0 0
\(49\) −337.449 −0.983815
\(50\) 121.030 0.342325
\(51\) 0 0
\(52\) 11.8304 0.0315496
\(53\) 160.081 0.414885 0.207442 0.978247i \(-0.433486\pi\)
0.207442 + 0.978247i \(0.433486\pi\)
\(54\) 0 0
\(55\) −131.915 −0.323406
\(56\) 50.4019 0.120272
\(57\) 0 0
\(58\) 243.669 0.551643
\(59\) −45.9350 −0.101360 −0.0506799 0.998715i \(-0.516139\pi\)
−0.0506799 + 0.998715i \(0.516139\pi\)
\(60\) 0 0
\(61\) −743.891 −1.56140 −0.780701 0.624905i \(-0.785138\pi\)
−0.780701 + 0.624905i \(0.785138\pi\)
\(62\) 462.299 0.946969
\(63\) 0 0
\(64\) 452.730 0.884237
\(65\) 138.954 0.265155
\(66\) 0 0
\(67\) 165.554 0.301876 0.150938 0.988543i \(-0.451771\pi\)
0.150938 + 0.988543i \(0.451771\pi\)
\(68\) −45.2114 −0.0806277
\(69\) 0 0
\(70\) −64.0497 −0.109363
\(71\) 747.149 1.24888 0.624439 0.781074i \(-0.285328\pi\)
0.624439 + 0.781074i \(0.285328\pi\)
\(72\) 0 0
\(73\) 962.660 1.54344 0.771718 0.635965i \(-0.219398\pi\)
0.771718 + 0.635965i \(0.219398\pi\)
\(74\) −598.738 −0.940566
\(75\) 0 0
\(76\) 80.5627 0.121594
\(77\) −33.8803 −0.0501432
\(78\) 0 0
\(79\) 803.730 1.14464 0.572321 0.820030i \(-0.306043\pi\)
0.572321 + 0.820030i \(0.306043\pi\)
\(80\) −638.841 −0.892807
\(81\) 0 0
\(82\) 10.5076 0.0141509
\(83\) 588.954 0.778869 0.389435 0.921054i \(-0.372670\pi\)
0.389435 + 0.921054i \(0.372670\pi\)
\(84\) 0 0
\(85\) −531.030 −0.677626
\(86\) −1059.57 −1.32856
\(87\) 0 0
\(88\) −307.607 −0.372625
\(89\) −764.364 −0.910365 −0.455182 0.890398i \(-0.650426\pi\)
−0.455182 + 0.890398i \(0.650426\pi\)
\(90\) 0 0
\(91\) 35.6883 0.0411115
\(92\) 64.6029 0.0732100
\(93\) 0 0
\(94\) −437.713 −0.480283
\(95\) 946.248 1.02193
\(96\) 0 0
\(97\) −135.843 −0.142193 −0.0710966 0.997469i \(-0.522650\pi\)
−0.0710966 + 0.997469i \(0.522650\pi\)
\(98\) 999.955 1.03072
\(99\) 0 0
\(100\) −31.9002 −0.0319002
\(101\) 1641.69 1.61737 0.808685 0.588241i \(-0.200179\pi\)
0.808685 + 0.588241i \(0.200179\pi\)
\(102\) 0 0
\(103\) −1733.25 −1.65808 −0.829041 0.559188i \(-0.811113\pi\)
−0.829041 + 0.559188i \(0.811113\pi\)
\(104\) 324.021 0.305509
\(105\) 0 0
\(106\) −474.367 −0.434666
\(107\) 1549.33 1.39981 0.699903 0.714238i \(-0.253227\pi\)
0.699903 + 0.714238i \(0.253227\pi\)
\(108\) 0 0
\(109\) −1886.61 −1.65784 −0.828920 0.559368i \(-0.811044\pi\)
−0.828920 + 0.559368i \(0.811044\pi\)
\(110\) 390.900 0.338826
\(111\) 0 0
\(112\) −164.077 −0.138427
\(113\) 177.382 0.147670 0.0738348 0.997270i \(-0.476476\pi\)
0.0738348 + 0.997270i \(0.476476\pi\)
\(114\) 0 0
\(115\) 758.793 0.615285
\(116\) −64.2244 −0.0514059
\(117\) 0 0
\(118\) 136.118 0.106192
\(119\) −136.387 −0.105064
\(120\) 0 0
\(121\) −1124.23 −0.844648
\(122\) 2204.36 1.63585
\(123\) 0 0
\(124\) −121.849 −0.0882452
\(125\) −1521.40 −1.08862
\(126\) 0 0
\(127\) 465.031 0.324920 0.162460 0.986715i \(-0.448057\pi\)
0.162460 + 0.986715i \(0.448057\pi\)
\(128\) −1623.35 −1.12098
\(129\) 0 0
\(130\) −411.759 −0.277798
\(131\) 91.2048 0.0608290 0.0304145 0.999537i \(-0.490317\pi\)
0.0304145 + 0.999537i \(0.490317\pi\)
\(132\) 0 0
\(133\) 243.030 0.158446
\(134\) −490.584 −0.316268
\(135\) 0 0
\(136\) −1238.29 −0.780753
\(137\) 2813.92 1.75481 0.877406 0.479748i \(-0.159272\pi\)
0.877406 + 0.479748i \(0.159272\pi\)
\(138\) 0 0
\(139\) −2029.26 −1.23827 −0.619136 0.785284i \(-0.712517\pi\)
−0.619136 + 0.785284i \(0.712517\pi\)
\(140\) 16.8817 0.0101912
\(141\) 0 0
\(142\) −2214.01 −1.30842
\(143\) −217.808 −0.127371
\(144\) 0 0
\(145\) −754.347 −0.432035
\(146\) −2852.63 −1.61703
\(147\) 0 0
\(148\) 157.811 0.0876485
\(149\) −833.802 −0.458441 −0.229221 0.973375i \(-0.573618\pi\)
−0.229221 + 0.973375i \(0.573618\pi\)
\(150\) 0 0
\(151\) 1231.99 0.663957 0.331979 0.943287i \(-0.392284\pi\)
0.331979 + 0.943287i \(0.392284\pi\)
\(152\) 2206.52 1.17745
\(153\) 0 0
\(154\) 100.397 0.0525339
\(155\) −1431.18 −0.741647
\(156\) 0 0
\(157\) −1856.39 −0.943670 −0.471835 0.881687i \(-0.656408\pi\)
−0.471835 + 0.881687i \(0.656408\pi\)
\(158\) −2381.68 −1.19922
\(159\) 0 0
\(160\) 323.129 0.159660
\(161\) 194.885 0.0953981
\(162\) 0 0
\(163\) −3384.37 −1.62629 −0.813143 0.582064i \(-0.802245\pi\)
−0.813143 + 0.582064i \(0.802245\pi\)
\(164\) −2.76952 −0.00131868
\(165\) 0 0
\(166\) −1745.24 −0.816005
\(167\) −1594.39 −0.738789 −0.369394 0.929273i \(-0.620435\pi\)
−0.369394 + 0.929273i \(0.620435\pi\)
\(168\) 0 0
\(169\) −1967.57 −0.895571
\(170\) 1573.59 0.709934
\(171\) 0 0
\(172\) 279.273 0.123804
\(173\) 1538.64 0.676191 0.338095 0.941112i \(-0.390217\pi\)
0.338095 + 0.941112i \(0.390217\pi\)
\(174\) 0 0
\(175\) −96.2321 −0.0415684
\(176\) 1001.37 0.428872
\(177\) 0 0
\(178\) 2265.03 0.953769
\(179\) −418.587 −0.174786 −0.0873929 0.996174i \(-0.527854\pi\)
−0.0873929 + 0.996174i \(0.527854\pi\)
\(180\) 0 0
\(181\) 1821.82 0.748149 0.374074 0.927399i \(-0.377960\pi\)
0.374074 + 0.927399i \(0.377960\pi\)
\(182\) −105.754 −0.0430717
\(183\) 0 0
\(184\) 1769.40 0.708924
\(185\) 1853.57 0.736632
\(186\) 0 0
\(187\) 832.381 0.325507
\(188\) 115.369 0.0447561
\(189\) 0 0
\(190\) −2804.00 −1.07065
\(191\) 1876.74 0.710974 0.355487 0.934681i \(-0.384315\pi\)
0.355487 + 0.934681i \(0.384315\pi\)
\(192\) 0 0
\(193\) 3743.99 1.39637 0.698183 0.715919i \(-0.253992\pi\)
0.698183 + 0.715919i \(0.253992\pi\)
\(194\) 402.540 0.148973
\(195\) 0 0
\(196\) −263.561 −0.0960499
\(197\) −22.9050 −0.00828384 −0.00414192 0.999991i \(-0.501318\pi\)
−0.00414192 + 0.999991i \(0.501318\pi\)
\(198\) 0 0
\(199\) 1922.67 0.684897 0.342448 0.939537i \(-0.388744\pi\)
0.342448 + 0.939537i \(0.388744\pi\)
\(200\) −873.711 −0.308904
\(201\) 0 0
\(202\) −4864.80 −1.69448
\(203\) −193.743 −0.0669858
\(204\) 0 0
\(205\) −32.5293 −0.0110827
\(206\) 5136.11 1.73714
\(207\) 0 0
\(208\) −1054.81 −0.351624
\(209\) −1483.23 −0.490896
\(210\) 0 0
\(211\) −1483.21 −0.483924 −0.241962 0.970286i \(-0.577791\pi\)
−0.241962 + 0.970286i \(0.577791\pi\)
\(212\) 125.030 0.0405052
\(213\) 0 0
\(214\) −4591.10 −1.46655
\(215\) 3280.19 1.04050
\(216\) 0 0
\(217\) −367.578 −0.114990
\(218\) 5590.56 1.73688
\(219\) 0 0
\(220\) −103.031 −0.0315742
\(221\) −876.799 −0.266877
\(222\) 0 0
\(223\) −2208.44 −0.663176 −0.331588 0.943424i \(-0.607584\pi\)
−0.331588 + 0.943424i \(0.607584\pi\)
\(224\) 82.9910 0.0247548
\(225\) 0 0
\(226\) −525.632 −0.154710
\(227\) 5649.03 1.65172 0.825858 0.563879i \(-0.190691\pi\)
0.825858 + 0.563879i \(0.190691\pi\)
\(228\) 0 0
\(229\) 5161.69 1.48949 0.744747 0.667347i \(-0.232570\pi\)
0.744747 + 0.667347i \(0.232570\pi\)
\(230\) −2248.52 −0.644621
\(231\) 0 0
\(232\) −1759.04 −0.497786
\(233\) 1290.84 0.362943 0.181472 0.983396i \(-0.441914\pi\)
0.181472 + 0.983396i \(0.441914\pi\)
\(234\) 0 0
\(235\) 1355.07 0.376148
\(236\) −35.8771 −0.00989575
\(237\) 0 0
\(238\) 404.154 0.110073
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −2953.77 −0.789497 −0.394749 0.918789i \(-0.629168\pi\)
−0.394749 + 0.918789i \(0.629168\pi\)
\(242\) 3331.40 0.884919
\(243\) 0 0
\(244\) −581.009 −0.152440
\(245\) −3095.65 −0.807241
\(246\) 0 0
\(247\) 1562.38 0.402477
\(248\) −3337.32 −0.854516
\(249\) 0 0
\(250\) 4508.33 1.14053
\(251\) 3409.90 0.857495 0.428747 0.903424i \(-0.358955\pi\)
0.428747 + 0.903424i \(0.358955\pi\)
\(252\) 0 0
\(253\) −1189.40 −0.295560
\(254\) −1378.02 −0.340412
\(255\) 0 0
\(256\) 1188.61 0.290189
\(257\) 6809.80 1.65286 0.826428 0.563043i \(-0.190369\pi\)
0.826428 + 0.563043i \(0.190369\pi\)
\(258\) 0 0
\(259\) 476.062 0.114213
\(260\) 108.528 0.0258871
\(261\) 0 0
\(262\) −270.265 −0.0637292
\(263\) −6686.40 −1.56768 −0.783842 0.620960i \(-0.786743\pi\)
−0.783842 + 0.620960i \(0.786743\pi\)
\(264\) 0 0
\(265\) 1468.54 0.340421
\(266\) −720.167 −0.166001
\(267\) 0 0
\(268\) 129.304 0.0294721
\(269\) −7028.75 −1.59312 −0.796562 0.604557i \(-0.793350\pi\)
−0.796562 + 0.604557i \(0.793350\pi\)
\(270\) 0 0
\(271\) 6307.26 1.41380 0.706898 0.707316i \(-0.250094\pi\)
0.706898 + 0.707316i \(0.250094\pi\)
\(272\) 4031.09 0.898605
\(273\) 0 0
\(274\) −8338.43 −1.83848
\(275\) 587.311 0.128786
\(276\) 0 0
\(277\) 997.811 0.216436 0.108218 0.994127i \(-0.465486\pi\)
0.108218 + 0.994127i \(0.465486\pi\)
\(278\) 6013.28 1.29731
\(279\) 0 0
\(280\) 462.372 0.0986858
\(281\) 4367.88 0.927281 0.463640 0.886024i \(-0.346543\pi\)
0.463640 + 0.886024i \(0.346543\pi\)
\(282\) 0 0
\(283\) −4659.41 −0.978705 −0.489352 0.872086i \(-0.662767\pi\)
−0.489352 + 0.872086i \(0.662767\pi\)
\(284\) 583.553 0.121928
\(285\) 0 0
\(286\) 645.427 0.133444
\(287\) −8.35469 −0.00171833
\(288\) 0 0
\(289\) −1562.20 −0.317973
\(290\) 2235.34 0.452634
\(291\) 0 0
\(292\) 751.876 0.150686
\(293\) −1873.11 −0.373476 −0.186738 0.982410i \(-0.559791\pi\)
−0.186738 + 0.982410i \(0.559791\pi\)
\(294\) 0 0
\(295\) −421.394 −0.0831677
\(296\) 4322.27 0.848739
\(297\) 0 0
\(298\) 2470.79 0.480299
\(299\) 1252.87 0.242325
\(300\) 0 0
\(301\) 842.471 0.161326
\(302\) −3650.72 −0.695614
\(303\) 0 0
\(304\) −7183.05 −1.35518
\(305\) −6824.23 −1.28116
\(306\) 0 0
\(307\) 9380.18 1.74383 0.871914 0.489659i \(-0.162879\pi\)
0.871914 + 0.489659i \(0.162879\pi\)
\(308\) −26.4619 −0.00489548
\(309\) 0 0
\(310\) 4241.00 0.777008
\(311\) −9990.35 −1.82155 −0.910773 0.412908i \(-0.864513\pi\)
−0.910773 + 0.412908i \(0.864513\pi\)
\(312\) 0 0
\(313\) −8829.71 −1.59452 −0.797260 0.603636i \(-0.793718\pi\)
−0.797260 + 0.603636i \(0.793718\pi\)
\(314\) 5501.01 0.988663
\(315\) 0 0
\(316\) 627.745 0.111751
\(317\) 4211.98 0.746273 0.373136 0.927776i \(-0.378282\pi\)
0.373136 + 0.927776i \(0.378282\pi\)
\(318\) 0 0
\(319\) 1182.43 0.207534
\(320\) 4153.20 0.725535
\(321\) 0 0
\(322\) −577.499 −0.0999465
\(323\) −5970.83 −1.02856
\(324\) 0 0
\(325\) −618.652 −0.105590
\(326\) 10028.8 1.70382
\(327\) 0 0
\(328\) −75.8539 −0.0127693
\(329\) 348.029 0.0583206
\(330\) 0 0
\(331\) 6313.47 1.04840 0.524199 0.851596i \(-0.324365\pi\)
0.524199 + 0.851596i \(0.324365\pi\)
\(332\) 459.997 0.0760410
\(333\) 0 0
\(334\) 4724.63 0.774013
\(335\) 1518.74 0.247695
\(336\) 0 0
\(337\) −7036.97 −1.13747 −0.568736 0.822520i \(-0.692567\pi\)
−0.568736 + 0.822520i \(0.692567\pi\)
\(338\) 5830.46 0.938270
\(339\) 0 0
\(340\) −414.755 −0.0661567
\(341\) 2243.36 0.356260
\(342\) 0 0
\(343\) −1603.23 −0.252379
\(344\) 7648.96 1.19885
\(345\) 0 0
\(346\) −4559.44 −0.708430
\(347\) 10927.9 1.69061 0.845306 0.534282i \(-0.179418\pi\)
0.845306 + 0.534282i \(0.179418\pi\)
\(348\) 0 0
\(349\) 4966.40 0.761734 0.380867 0.924630i \(-0.375626\pi\)
0.380867 + 0.924630i \(0.375626\pi\)
\(350\) 285.163 0.0435503
\(351\) 0 0
\(352\) −506.500 −0.0766947
\(353\) 7853.14 1.18408 0.592040 0.805908i \(-0.298323\pi\)
0.592040 + 0.805908i \(0.298323\pi\)
\(354\) 0 0
\(355\) 6854.12 1.02473
\(356\) −596.999 −0.0888789
\(357\) 0 0
\(358\) 1240.39 0.183119
\(359\) 4725.95 0.694781 0.347390 0.937721i \(-0.387068\pi\)
0.347390 + 0.937721i \(0.387068\pi\)
\(360\) 0 0
\(361\) 3780.49 0.551173
\(362\) −5398.57 −0.783819
\(363\) 0 0
\(364\) 27.8740 0.00401372
\(365\) 8831.16 1.26642
\(366\) 0 0
\(367\) 11340.8 1.61304 0.806522 0.591204i \(-0.201347\pi\)
0.806522 + 0.591204i \(0.201347\pi\)
\(368\) −5760.06 −0.815934
\(369\) 0 0
\(370\) −5492.64 −0.771754
\(371\) 377.173 0.0527813
\(372\) 0 0
\(373\) 9963.63 1.38310 0.691551 0.722328i \(-0.256928\pi\)
0.691551 + 0.722328i \(0.256928\pi\)
\(374\) −2466.58 −0.341026
\(375\) 0 0
\(376\) 3159.83 0.433393
\(377\) −1245.53 −0.170154
\(378\) 0 0
\(379\) −3903.68 −0.529073 −0.264536 0.964376i \(-0.585219\pi\)
−0.264536 + 0.964376i \(0.585219\pi\)
\(380\) 739.058 0.0997707
\(381\) 0 0
\(382\) −5561.31 −0.744872
\(383\) 7011.53 0.935438 0.467719 0.883877i \(-0.345076\pi\)
0.467719 + 0.883877i \(0.345076\pi\)
\(384\) 0 0
\(385\) −310.808 −0.0411435
\(386\) −11094.5 −1.46294
\(387\) 0 0
\(388\) −106.099 −0.0138823
\(389\) 6380.67 0.831652 0.415826 0.909444i \(-0.363493\pi\)
0.415826 + 0.909444i \(0.363493\pi\)
\(390\) 0 0
\(391\) −4787.99 −0.619281
\(392\) −7218.64 −0.930093
\(393\) 0 0
\(394\) 67.8741 0.00867880
\(395\) 7373.18 0.939202
\(396\) 0 0
\(397\) 13753.7 1.73874 0.869370 0.494162i \(-0.164525\pi\)
0.869370 + 0.494162i \(0.164525\pi\)
\(398\) −5697.41 −0.717552
\(399\) 0 0
\(400\) 2844.25 0.355532
\(401\) −2550.97 −0.317679 −0.158840 0.987304i \(-0.550775\pi\)
−0.158840 + 0.987304i \(0.550775\pi\)
\(402\) 0 0
\(403\) −2363.07 −0.292091
\(404\) 1282.23 0.157904
\(405\) 0 0
\(406\) 574.116 0.0701795
\(407\) −2905.44 −0.353851
\(408\) 0 0
\(409\) 10406.3 1.25809 0.629047 0.777367i \(-0.283445\pi\)
0.629047 + 0.777367i \(0.283445\pi\)
\(410\) 96.3936 0.0116111
\(411\) 0 0
\(412\) −1353.74 −0.161879
\(413\) −108.229 −0.0128949
\(414\) 0 0
\(415\) 5402.89 0.639078
\(416\) 533.528 0.0628807
\(417\) 0 0
\(418\) 4395.23 0.514301
\(419\) 15119.5 1.76286 0.881429 0.472317i \(-0.156582\pi\)
0.881429 + 0.472317i \(0.156582\pi\)
\(420\) 0 0
\(421\) −8421.52 −0.974917 −0.487458 0.873146i \(-0.662076\pi\)
−0.487458 + 0.873146i \(0.662076\pi\)
\(422\) 4395.16 0.506997
\(423\) 0 0
\(424\) 3424.43 0.392229
\(425\) 2364.26 0.269843
\(426\) 0 0
\(427\) −1752.71 −0.198640
\(428\) 1210.09 0.136663
\(429\) 0 0
\(430\) −9720.14 −1.09011
\(431\) −14275.6 −1.59544 −0.797719 0.603030i \(-0.793960\pi\)
−0.797719 + 0.603030i \(0.793960\pi\)
\(432\) 0 0
\(433\) 13380.4 1.48504 0.742518 0.669826i \(-0.233632\pi\)
0.742518 + 0.669826i \(0.233632\pi\)
\(434\) 1089.24 0.120473
\(435\) 0 0
\(436\) −1473.52 −0.161855
\(437\) 8531.77 0.933936
\(438\) 0 0
\(439\) 5354.50 0.582133 0.291067 0.956703i \(-0.405990\pi\)
0.291067 + 0.956703i \(0.405990\pi\)
\(440\) −2821.89 −0.305746
\(441\) 0 0
\(442\) 2598.20 0.279602
\(443\) 17239.1 1.84889 0.924443 0.381321i \(-0.124531\pi\)
0.924443 + 0.381321i \(0.124531\pi\)
\(444\) 0 0
\(445\) −7012.05 −0.746973
\(446\) 6544.24 0.694795
\(447\) 0 0
\(448\) 1066.69 0.112492
\(449\) −12372.6 −1.30044 −0.650220 0.759746i \(-0.725323\pi\)
−0.650220 + 0.759746i \(0.725323\pi\)
\(450\) 0 0
\(451\) 50.9893 0.00532370
\(452\) 138.542 0.0144170
\(453\) 0 0
\(454\) −16739.7 −1.73047
\(455\) 327.394 0.0337328
\(456\) 0 0
\(457\) 10218.6 1.04596 0.522982 0.852343i \(-0.324819\pi\)
0.522982 + 0.852343i \(0.324819\pi\)
\(458\) −15295.5 −1.56051
\(459\) 0 0
\(460\) 592.648 0.0600703
\(461\) 10295.4 1.04014 0.520069 0.854124i \(-0.325906\pi\)
0.520069 + 0.854124i \(0.325906\pi\)
\(462\) 0 0
\(463\) 624.733 0.0627080 0.0313540 0.999508i \(-0.490018\pi\)
0.0313540 + 0.999508i \(0.490018\pi\)
\(464\) 5726.31 0.572925
\(465\) 0 0
\(466\) −3825.12 −0.380248
\(467\) 3096.27 0.306805 0.153403 0.988164i \(-0.450977\pi\)
0.153403 + 0.988164i \(0.450977\pi\)
\(468\) 0 0
\(469\) 390.067 0.0384044
\(470\) −4015.44 −0.394082
\(471\) 0 0
\(472\) −982.632 −0.0958248
\(473\) −5141.66 −0.499817
\(474\) 0 0
\(475\) −4212.90 −0.406949
\(476\) −106.524 −0.0102574
\(477\) 0 0
\(478\) 708.224 0.0677687
\(479\) 3505.65 0.334399 0.167200 0.985923i \(-0.446528\pi\)
0.167200 + 0.985923i \(0.446528\pi\)
\(480\) 0 0
\(481\) 3060.48 0.290116
\(482\) 8752.84 0.827139
\(483\) 0 0
\(484\) −878.065 −0.0824629
\(485\) −1246.18 −0.116672
\(486\) 0 0
\(487\) −5020.73 −0.467168 −0.233584 0.972337i \(-0.575045\pi\)
−0.233584 + 0.972337i \(0.575045\pi\)
\(488\) −15913.2 −1.47614
\(489\) 0 0
\(490\) 9173.29 0.845729
\(491\) 7985.83 0.734003 0.367002 0.930220i \(-0.380384\pi\)
0.367002 + 0.930220i \(0.380384\pi\)
\(492\) 0 0
\(493\) 4759.94 0.434841
\(494\) −4629.77 −0.421666
\(495\) 0 0
\(496\) 10864.2 0.983504
\(497\) 1760.38 0.158881
\(498\) 0 0
\(499\) −19646.0 −1.76248 −0.881240 0.472669i \(-0.843291\pi\)
−0.881240 + 0.472669i \(0.843291\pi\)
\(500\) −1188.27 −0.106282
\(501\) 0 0
\(502\) −10104.5 −0.898379
\(503\) −8830.82 −0.782797 −0.391398 0.920221i \(-0.628009\pi\)
−0.391398 + 0.920221i \(0.628009\pi\)
\(504\) 0 0
\(505\) 15060.4 1.32709
\(506\) 3524.52 0.309652
\(507\) 0 0
\(508\) 363.208 0.0317220
\(509\) −11339.0 −0.987413 −0.493707 0.869628i \(-0.664358\pi\)
−0.493707 + 0.869628i \(0.664358\pi\)
\(510\) 0 0
\(511\) 2268.16 0.196355
\(512\) 9464.62 0.816955
\(513\) 0 0
\(514\) −20179.4 −1.73166
\(515\) −15900.3 −1.36049
\(516\) 0 0
\(517\) −2124.05 −0.180688
\(518\) −1410.71 −0.119658
\(519\) 0 0
\(520\) 2972.47 0.250676
\(521\) 10393.5 0.873985 0.436992 0.899465i \(-0.356044\pi\)
0.436992 + 0.899465i \(0.356044\pi\)
\(522\) 0 0
\(523\) 4010.67 0.335324 0.167662 0.985845i \(-0.446378\pi\)
0.167662 + 0.985845i \(0.446378\pi\)
\(524\) 71.2346 0.00593874
\(525\) 0 0
\(526\) 19813.7 1.64243
\(527\) 9030.77 0.746464
\(528\) 0 0
\(529\) −5325.40 −0.437692
\(530\) −4351.70 −0.356652
\(531\) 0 0
\(532\) 189.816 0.0154691
\(533\) −53.7102 −0.00436481
\(534\) 0 0
\(535\) 14213.1 1.14857
\(536\) 3541.50 0.285391
\(537\) 0 0
\(538\) 20828.2 1.66908
\(539\) 4852.39 0.387769
\(540\) 0 0
\(541\) 23915.0 1.90053 0.950264 0.311445i \(-0.100813\pi\)
0.950264 + 0.311445i \(0.100813\pi\)
\(542\) −18690.2 −1.48120
\(543\) 0 0
\(544\) −2038.94 −0.160697
\(545\) −17307.2 −1.36029
\(546\) 0 0
\(547\) 569.608 0.0445241 0.0222621 0.999752i \(-0.492913\pi\)
0.0222621 + 0.999752i \(0.492913\pi\)
\(548\) 2197.78 0.171322
\(549\) 0 0
\(550\) −1740.37 −0.134927
\(551\) −8481.79 −0.655783
\(552\) 0 0
\(553\) 1893.69 0.145620
\(554\) −2956.79 −0.226755
\(555\) 0 0
\(556\) −1584.94 −0.120893
\(557\) 4270.83 0.324885 0.162442 0.986718i \(-0.448063\pi\)
0.162442 + 0.986718i \(0.448063\pi\)
\(558\) 0 0
\(559\) 5416.03 0.409792
\(560\) −1505.19 −0.113582
\(561\) 0 0
\(562\) −12943.3 −0.971492
\(563\) −13696.2 −1.02527 −0.512633 0.858608i \(-0.671330\pi\)
−0.512633 + 0.858608i \(0.671330\pi\)
\(564\) 0 0
\(565\) 1627.25 0.121166
\(566\) 13807.2 1.02537
\(567\) 0 0
\(568\) 15982.9 1.18068
\(569\) 5737.72 0.422738 0.211369 0.977406i \(-0.432208\pi\)
0.211369 + 0.977406i \(0.432208\pi\)
\(570\) 0 0
\(571\) 9931.62 0.727890 0.363945 0.931420i \(-0.381430\pi\)
0.363945 + 0.931420i \(0.381430\pi\)
\(572\) −170.117 −0.0124352
\(573\) 0 0
\(574\) 24.7573 0.00180026
\(575\) −3378.31 −0.245018
\(576\) 0 0
\(577\) 1313.36 0.0947591 0.0473796 0.998877i \(-0.484913\pi\)
0.0473796 + 0.998877i \(0.484913\pi\)
\(578\) 4629.24 0.333133
\(579\) 0 0
\(580\) −589.176 −0.0421796
\(581\) 1387.65 0.0990871
\(582\) 0 0
\(583\) −2301.91 −0.163526
\(584\) 20593.1 1.45915
\(585\) 0 0
\(586\) 5550.56 0.391282
\(587\) 14304.2 1.00579 0.502894 0.864348i \(-0.332268\pi\)
0.502894 + 0.864348i \(0.332268\pi\)
\(588\) 0 0
\(589\) −16092.0 −1.12574
\(590\) 1248.71 0.0871331
\(591\) 0 0
\(592\) −14070.6 −0.976854
\(593\) 4557.38 0.315597 0.157799 0.987471i \(-0.449560\pi\)
0.157799 + 0.987471i \(0.449560\pi\)
\(594\) 0 0
\(595\) −1251.18 −0.0862071
\(596\) −651.233 −0.0447576
\(597\) 0 0
\(598\) −3712.60 −0.253878
\(599\) 26296.5 1.79373 0.896867 0.442300i \(-0.145837\pi\)
0.896867 + 0.442300i \(0.145837\pi\)
\(600\) 0 0
\(601\) 19846.9 1.34704 0.673520 0.739169i \(-0.264781\pi\)
0.673520 + 0.739169i \(0.264781\pi\)
\(602\) −2496.48 −0.169018
\(603\) 0 0
\(604\) 962.230 0.0648222
\(605\) −10313.3 −0.693051
\(606\) 0 0
\(607\) −18072.3 −1.20846 −0.604228 0.796812i \(-0.706518\pi\)
−0.604228 + 0.796812i \(0.706518\pi\)
\(608\) 3633.22 0.242346
\(609\) 0 0
\(610\) 20222.1 1.34225
\(611\) 2237.39 0.148143
\(612\) 0 0
\(613\) 12103.1 0.797457 0.398729 0.917069i \(-0.369451\pi\)
0.398729 + 0.917069i \(0.369451\pi\)
\(614\) −27796.1 −1.82697
\(615\) 0 0
\(616\) −724.762 −0.0474050
\(617\) −20613.6 −1.34502 −0.672508 0.740090i \(-0.734783\pi\)
−0.672508 + 0.740090i \(0.734783\pi\)
\(618\) 0 0
\(619\) −1056.49 −0.0686007 −0.0343004 0.999412i \(-0.510920\pi\)
−0.0343004 + 0.999412i \(0.510920\pi\)
\(620\) −1117.81 −0.0724070
\(621\) 0 0
\(622\) 29604.2 1.90839
\(623\) −1800.94 −0.115816
\(624\) 0 0
\(625\) −8851.42 −0.566491
\(626\) 26164.9 1.67054
\(627\) 0 0
\(628\) −1449.92 −0.0921305
\(629\) −11696.0 −0.741416
\(630\) 0 0
\(631\) −8013.19 −0.505547 −0.252773 0.967526i \(-0.581343\pi\)
−0.252773 + 0.967526i \(0.581343\pi\)
\(632\) 17193.2 1.08214
\(633\) 0 0
\(634\) −12481.3 −0.781854
\(635\) 4266.06 0.266604
\(636\) 0 0
\(637\) −5111.33 −0.317925
\(638\) −3503.87 −0.217429
\(639\) 0 0
\(640\) −14892.1 −0.919787
\(641\) 21822.2 1.34466 0.672328 0.740254i \(-0.265295\pi\)
0.672328 + 0.740254i \(0.265295\pi\)
\(642\) 0 0
\(643\) −6406.87 −0.392943 −0.196472 0.980510i \(-0.562948\pi\)
−0.196472 + 0.980510i \(0.562948\pi\)
\(644\) 152.213 0.00931371
\(645\) 0 0
\(646\) 17693.3 1.07760
\(647\) −13195.9 −0.801830 −0.400915 0.916115i \(-0.631308\pi\)
−0.400915 + 0.916115i \(0.631308\pi\)
\(648\) 0 0
\(649\) 660.529 0.0399507
\(650\) 1833.24 0.110624
\(651\) 0 0
\(652\) −2643.33 −0.158774
\(653\) 21736.7 1.30264 0.651319 0.758804i \(-0.274216\pi\)
0.651319 + 0.758804i \(0.274216\pi\)
\(654\) 0 0
\(655\) 836.685 0.0499114
\(656\) 246.933 0.0146968
\(657\) 0 0
\(658\) −1031.31 −0.0611012
\(659\) −16114.2 −0.952534 −0.476267 0.879301i \(-0.658010\pi\)
−0.476267 + 0.879301i \(0.658010\pi\)
\(660\) 0 0
\(661\) 3118.43 0.183499 0.0917496 0.995782i \(-0.470754\pi\)
0.0917496 + 0.995782i \(0.470754\pi\)
\(662\) −18708.6 −1.09838
\(663\) 0 0
\(664\) 12598.8 0.736338
\(665\) 2229.49 0.130009
\(666\) 0 0
\(667\) −6801.51 −0.394836
\(668\) −1245.28 −0.0721279
\(669\) 0 0
\(670\) −4500.47 −0.259505
\(671\) 10696.9 0.615423
\(672\) 0 0
\(673\) −7726.86 −0.442569 −0.221284 0.975209i \(-0.571025\pi\)
−0.221284 + 0.975209i \(0.571025\pi\)
\(674\) 20852.5 1.19171
\(675\) 0 0
\(676\) −1536.75 −0.0874346
\(677\) 32338.1 1.83583 0.917914 0.396780i \(-0.129873\pi\)
0.917914 + 0.396780i \(0.129873\pi\)
\(678\) 0 0
\(679\) −320.063 −0.0180897
\(680\) −11359.7 −0.640624
\(681\) 0 0
\(682\) −6647.70 −0.373246
\(683\) 31880.4 1.78604 0.893022 0.450013i \(-0.148581\pi\)
0.893022 + 0.450013i \(0.148581\pi\)
\(684\) 0 0
\(685\) 25814.0 1.43986
\(686\) 4750.81 0.264412
\(687\) 0 0
\(688\) −24900.2 −1.37981
\(689\) 2424.75 0.134072
\(690\) 0 0
\(691\) −11724.0 −0.645447 −0.322723 0.946493i \(-0.604598\pi\)
−0.322723 + 0.946493i \(0.604598\pi\)
\(692\) 1201.74 0.0660165
\(693\) 0 0
\(694\) −32382.6 −1.77122
\(695\) −18615.8 −1.01603
\(696\) 0 0
\(697\) 205.260 0.0111546
\(698\) −14716.8 −0.798052
\(699\) 0 0
\(700\) −75.1611 −0.00405832
\(701\) −14029.1 −0.755880 −0.377940 0.925830i \(-0.623367\pi\)
−0.377940 + 0.925830i \(0.623367\pi\)
\(702\) 0 0
\(703\) 20841.3 1.11813
\(704\) −6510.09 −0.348520
\(705\) 0 0
\(706\) −23271.1 −1.24054
\(707\) 3868.04 0.205761
\(708\) 0 0
\(709\) −15232.8 −0.806881 −0.403440 0.915006i \(-0.632186\pi\)
−0.403440 + 0.915006i \(0.632186\pi\)
\(710\) −20310.7 −1.07359
\(711\) 0 0
\(712\) −16351.1 −0.860653
\(713\) −12904.1 −0.677789
\(714\) 0 0
\(715\) −1998.11 −0.104510
\(716\) −326.933 −0.0170643
\(717\) 0 0
\(718\) −14004.3 −0.727907
\(719\) 33270.0 1.72568 0.862838 0.505481i \(-0.168685\pi\)
0.862838 + 0.505481i \(0.168685\pi\)
\(720\) 0 0
\(721\) −4083.77 −0.210940
\(722\) −11202.7 −0.577452
\(723\) 0 0
\(724\) 1422.92 0.0730418
\(725\) 3358.51 0.172044
\(726\) 0 0
\(727\) −16319.6 −0.832543 −0.416272 0.909240i \(-0.636663\pi\)
−0.416272 + 0.909240i \(0.636663\pi\)
\(728\) 763.437 0.0388666
\(729\) 0 0
\(730\) −26169.2 −1.32680
\(731\) −20698.0 −1.04726
\(732\) 0 0
\(733\) 32024.7 1.61372 0.806862 0.590741i \(-0.201164\pi\)
0.806862 + 0.590741i \(0.201164\pi\)
\(734\) −33606.1 −1.68995
\(735\) 0 0
\(736\) 2913.47 0.145913
\(737\) −2380.61 −0.118984
\(738\) 0 0
\(739\) −9196.88 −0.457798 −0.228899 0.973450i \(-0.573513\pi\)
−0.228899 + 0.973450i \(0.573513\pi\)
\(740\) 1447.71 0.0719174
\(741\) 0 0
\(742\) −1117.67 −0.0552978
\(743\) −33744.1 −1.66615 −0.833075 0.553160i \(-0.813422\pi\)
−0.833075 + 0.553160i \(0.813422\pi\)
\(744\) 0 0
\(745\) −7649.05 −0.376160
\(746\) −29525.0 −1.44905
\(747\) 0 0
\(748\) 650.123 0.0317792
\(749\) 3650.42 0.178082
\(750\) 0 0
\(751\) 11732.9 0.570091 0.285046 0.958514i \(-0.407991\pi\)
0.285046 + 0.958514i \(0.407991\pi\)
\(752\) −10286.4 −0.498813
\(753\) 0 0
\(754\) 3690.85 0.178266
\(755\) 11301.9 0.544791
\(756\) 0 0
\(757\) 15986.7 0.767563 0.383781 0.923424i \(-0.374622\pi\)
0.383781 + 0.923424i \(0.374622\pi\)
\(758\) 11567.7 0.554298
\(759\) 0 0
\(760\) 20242.0 0.966122
\(761\) −19860.3 −0.946039 −0.473019 0.881052i \(-0.656836\pi\)
−0.473019 + 0.881052i \(0.656836\pi\)
\(762\) 0 0
\(763\) −4445.10 −0.210909
\(764\) 1465.81 0.0694124
\(765\) 0 0
\(766\) −20777.2 −0.980038
\(767\) −695.776 −0.0327549
\(768\) 0 0
\(769\) 11902.2 0.558133 0.279067 0.960272i \(-0.409975\pi\)
0.279067 + 0.960272i \(0.409975\pi\)
\(770\) 921.012 0.0431051
\(771\) 0 0
\(772\) 2924.21 0.136327
\(773\) 36404.0 1.69387 0.846935 0.531696i \(-0.178445\pi\)
0.846935 + 0.531696i \(0.178445\pi\)
\(774\) 0 0
\(775\) 6371.93 0.295337
\(776\) −2905.92 −0.134428
\(777\) 0 0
\(778\) −18907.7 −0.871304
\(779\) −365.756 −0.0168223
\(780\) 0 0
\(781\) −10743.7 −0.492242
\(782\) 14188.2 0.648807
\(783\) 0 0
\(784\) 23499.3 1.07049
\(785\) −17030.0 −0.774301
\(786\) 0 0
\(787\) −14540.7 −0.658603 −0.329301 0.944225i \(-0.606813\pi\)
−0.329301 + 0.944225i \(0.606813\pi\)
\(788\) −17.8898 −0.000808752 0
\(789\) 0 0
\(790\) −21848.8 −0.983982
\(791\) 417.935 0.0187864
\(792\) 0 0
\(793\) −11267.7 −0.504575
\(794\) −40756.2 −1.82164
\(795\) 0 0
\(796\) 1501.68 0.0668665
\(797\) 25877.1 1.15008 0.575040 0.818125i \(-0.304986\pi\)
0.575040 + 0.818125i \(0.304986\pi\)
\(798\) 0 0
\(799\) −8550.48 −0.378591
\(800\) −1438.64 −0.0635794
\(801\) 0 0
\(802\) 7559.25 0.332826
\(803\) −13842.7 −0.608342
\(804\) 0 0
\(805\) 1787.82 0.0782761
\(806\) 7002.44 0.306018
\(807\) 0 0
\(808\) 35118.8 1.52905
\(809\) −7017.33 −0.304965 −0.152482 0.988306i \(-0.548727\pi\)
−0.152482 + 0.988306i \(0.548727\pi\)
\(810\) 0 0
\(811\) −9683.99 −0.419298 −0.209649 0.977777i \(-0.567232\pi\)
−0.209649 + 0.977777i \(0.567232\pi\)
\(812\) −151.321 −0.00653982
\(813\) 0 0
\(814\) 8609.64 0.370722
\(815\) −31047.2 −1.33440
\(816\) 0 0
\(817\) 36882.1 1.57936
\(818\) −30836.9 −1.31808
\(819\) 0 0
\(820\) −25.4067 −0.00108200
\(821\) 27788.1 1.18125 0.590627 0.806944i \(-0.298880\pi\)
0.590627 + 0.806944i \(0.298880\pi\)
\(822\) 0 0
\(823\) −33251.1 −1.40834 −0.704168 0.710034i \(-0.748680\pi\)
−0.704168 + 0.710034i \(0.748680\pi\)
\(824\) −37077.4 −1.56754
\(825\) 0 0
\(826\) 320.713 0.0135097
\(827\) −44335.1 −1.86419 −0.932093 0.362218i \(-0.882020\pi\)
−0.932093 + 0.362218i \(0.882020\pi\)
\(828\) 0 0
\(829\) −37480.4 −1.57026 −0.785132 0.619328i \(-0.787405\pi\)
−0.785132 + 0.619328i \(0.787405\pi\)
\(830\) −16010.3 −0.669548
\(831\) 0 0
\(832\) 6857.48 0.285746
\(833\) 19533.6 0.812483
\(834\) 0 0
\(835\) −14626.5 −0.606191
\(836\) −1158.46 −0.0479261
\(837\) 0 0
\(838\) −44803.4 −1.84691
\(839\) −28545.7 −1.17462 −0.587310 0.809362i \(-0.699813\pi\)
−0.587310 + 0.809362i \(0.699813\pi\)
\(840\) 0 0
\(841\) −17627.3 −0.722757
\(842\) 24955.3 1.02140
\(843\) 0 0
\(844\) −1158.44 −0.0472456
\(845\) −18049.9 −0.734834
\(846\) 0 0
\(847\) −2648.82 −0.107455
\(848\) −11147.8 −0.451435
\(849\) 0 0
\(850\) −7005.96 −0.282709
\(851\) 16712.5 0.673206
\(852\) 0 0
\(853\) 10701.2 0.429546 0.214773 0.976664i \(-0.431099\pi\)
0.214773 + 0.976664i \(0.431099\pi\)
\(854\) 5193.76 0.208111
\(855\) 0 0
\(856\) 33142.9 1.32337
\(857\) −31267.6 −1.24630 −0.623152 0.782101i \(-0.714148\pi\)
−0.623152 + 0.782101i \(0.714148\pi\)
\(858\) 0 0
\(859\) −35.6688 −0.00141677 −0.000708385 1.00000i \(-0.500225\pi\)
−0.000708385 1.00000i \(0.500225\pi\)
\(860\) 2561.96 0.101584
\(861\) 0 0
\(862\) 42302.8 1.67151
\(863\) −6916.71 −0.272825 −0.136412 0.990652i \(-0.543557\pi\)
−0.136412 + 0.990652i \(0.543557\pi\)
\(864\) 0 0
\(865\) 14115.1 0.554828
\(866\) −39649.9 −1.55584
\(867\) 0 0
\(868\) −287.093 −0.0112265
\(869\) −11557.4 −0.451158
\(870\) 0 0
\(871\) 2507.65 0.0975526
\(872\) −40358.0 −1.56731
\(873\) 0 0
\(874\) −25282.0 −0.978464
\(875\) −3584.61 −0.138494
\(876\) 0 0
\(877\) 2327.68 0.0896239 0.0448120 0.998995i \(-0.485731\pi\)
0.0448120 + 0.998995i \(0.485731\pi\)
\(878\) −15866.9 −0.609888
\(879\) 0 0
\(880\) 9186.30 0.351898
\(881\) −2343.54 −0.0896205 −0.0448103 0.998996i \(-0.514268\pi\)
−0.0448103 + 0.998996i \(0.514268\pi\)
\(882\) 0 0
\(883\) −19558.9 −0.745424 −0.372712 0.927947i \(-0.621572\pi\)
−0.372712 + 0.927947i \(0.621572\pi\)
\(884\) −684.815 −0.0260552
\(885\) 0 0
\(886\) −51084.4 −1.93704
\(887\) −10331.5 −0.391091 −0.195546 0.980695i \(-0.562648\pi\)
−0.195546 + 0.980695i \(0.562648\pi\)
\(888\) 0 0
\(889\) 1095.68 0.0413361
\(890\) 20778.7 0.782587
\(891\) 0 0
\(892\) −1724.88 −0.0647459
\(893\) 15236.2 0.570952
\(894\) 0 0
\(895\) −3839.99 −0.143415
\(896\) −3824.83 −0.142610
\(897\) 0 0
\(898\) 36663.4 1.36244
\(899\) 12828.5 0.475924
\(900\) 0 0
\(901\) −9266.49 −0.342632
\(902\) −151.096 −0.00557753
\(903\) 0 0
\(904\) 3794.52 0.139606
\(905\) 16712.8 0.613871
\(906\) 0 0
\(907\) 52052.2 1.90559 0.952793 0.303621i \(-0.0981957\pi\)
0.952793 + 0.303621i \(0.0981957\pi\)
\(908\) 4412.12 0.161257
\(909\) 0 0
\(910\) −970.159 −0.0353412
\(911\) −10108.8 −0.367639 −0.183820 0.982960i \(-0.558846\pi\)
−0.183820 + 0.982960i \(0.558846\pi\)
\(912\) 0 0
\(913\) −8468.95 −0.306990
\(914\) −30280.6 −1.09583
\(915\) 0 0
\(916\) 4031.48 0.145419
\(917\) 214.890 0.00773861
\(918\) 0 0
\(919\) 34840.7 1.25059 0.625293 0.780390i \(-0.284979\pi\)
0.625293 + 0.780390i \(0.284979\pi\)
\(920\) 16232.0 0.581687
\(921\) 0 0
\(922\) −30508.1 −1.08973
\(923\) 11317.0 0.403581
\(924\) 0 0
\(925\) −8252.48 −0.293340
\(926\) −1851.26 −0.0656978
\(927\) 0 0
\(928\) −2896.40 −0.102456
\(929\) −39014.1 −1.37784 −0.688919 0.724838i \(-0.741915\pi\)
−0.688919 + 0.724838i \(0.741915\pi\)
\(930\) 0 0
\(931\) −34807.1 −1.22530
\(932\) 1008.20 0.0354342
\(933\) 0 0
\(934\) −9175.11 −0.321433
\(935\) 7636.02 0.267085
\(936\) 0 0
\(937\) −23368.1 −0.814729 −0.407364 0.913266i \(-0.633552\pi\)
−0.407364 + 0.913266i \(0.633552\pi\)
\(938\) −1155.88 −0.0402354
\(939\) 0 0
\(940\) 1058.36 0.0367233
\(941\) −6990.35 −0.242167 −0.121083 0.992642i \(-0.538637\pi\)
−0.121083 + 0.992642i \(0.538637\pi\)
\(942\) 0 0
\(943\) −293.298 −0.0101284
\(944\) 3198.83 0.110289
\(945\) 0 0
\(946\) 15236.2 0.523648
\(947\) 34940.9 1.19897 0.599486 0.800385i \(-0.295372\pi\)
0.599486 + 0.800385i \(0.295372\pi\)
\(948\) 0 0
\(949\) 14581.4 0.498769
\(950\) 12484.0 0.426352
\(951\) 0 0
\(952\) −2917.57 −0.0993267
\(953\) 49498.4 1.68249 0.841244 0.540655i \(-0.181824\pi\)
0.841244 + 0.540655i \(0.181824\pi\)
\(954\) 0 0
\(955\) 17216.6 0.583369
\(956\) −186.669 −0.00631516
\(957\) 0 0
\(958\) −10388.2 −0.350343
\(959\) 6629.96 0.223246
\(960\) 0 0
\(961\) −5452.12 −0.183012
\(962\) −9069.07 −0.303949
\(963\) 0 0
\(964\) −2307.01 −0.0770786
\(965\) 34346.3 1.14575
\(966\) 0 0
\(967\) −22271.8 −0.740655 −0.370328 0.928901i \(-0.620755\pi\)
−0.370328 + 0.928901i \(0.620755\pi\)
\(968\) −24049.2 −0.798524
\(969\) 0 0
\(970\) 3692.78 0.122235
\(971\) −16361.7 −0.540753 −0.270376 0.962755i \(-0.587148\pi\)
−0.270376 + 0.962755i \(0.587148\pi\)
\(972\) 0 0
\(973\) −4781.21 −0.157532
\(974\) 14877.8 0.489442
\(975\) 0 0
\(976\) 51803.3 1.69896
\(977\) −13731.6 −0.449654 −0.224827 0.974399i \(-0.572182\pi\)
−0.224827 + 0.974399i \(0.572182\pi\)
\(978\) 0 0
\(979\) 10991.3 0.358818
\(980\) −2417.83 −0.0788109
\(981\) 0 0
\(982\) −23664.3 −0.768999
\(983\) −41619.1 −1.35040 −0.675200 0.737634i \(-0.735943\pi\)
−0.675200 + 0.737634i \(0.735943\pi\)
\(984\) 0 0
\(985\) −210.124 −0.00679706
\(986\) −14105.0 −0.455574
\(987\) 0 0
\(988\) 1220.28 0.0392938
\(989\) 29575.6 0.950910
\(990\) 0 0
\(991\) 15749.0 0.504827 0.252413 0.967619i \(-0.418776\pi\)
0.252413 + 0.967619i \(0.418776\pi\)
\(992\) −5495.18 −0.175879
\(993\) 0 0
\(994\) −5216.51 −0.166456
\(995\) 17638.0 0.561972
\(996\) 0 0
\(997\) −16722.9 −0.531212 −0.265606 0.964082i \(-0.585572\pi\)
−0.265606 + 0.964082i \(0.585572\pi\)
\(998\) 58216.8 1.84651
\(999\) 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.1.16 yes 59
3.2 odd 2 2151.4.a.g.1.44 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.44 59 3.2 odd 2
2151.4.a.h.1.16 yes 59 1.1 even 1 trivial