Properties

Label 2070.4.a.bj.1.2
Level $2070$
Weight $4$
Character 2070.1
Self dual yes
Analytic conductor $122.134$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2070.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(122.133953712\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \( x^{4} - 68x^{2} - 111x + 342 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.58997\) of defining polynomial
Character \(\chi\) \(=\) 2070.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -18.5077 q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -18.5077 q^{7} +8.00000 q^{8} +10.0000 q^{10} -47.9296 q^{11} +42.3717 q^{13} -37.0155 q^{14} +16.0000 q^{16} -1.70534 q^{17} +21.4208 q^{19} +20.0000 q^{20} -95.8592 q^{22} +23.0000 q^{23} +25.0000 q^{25} +84.7434 q^{26} -74.0310 q^{28} -57.6332 q^{29} +295.699 q^{31} +32.0000 q^{32} -3.41069 q^{34} -92.5387 q^{35} -7.85184 q^{37} +42.8416 q^{38} +40.0000 q^{40} -465.929 q^{41} +182.374 q^{43} -191.718 q^{44} +46.0000 q^{46} -449.193 q^{47} -0.463605 q^{49} +50.0000 q^{50} +169.487 q^{52} +368.316 q^{53} -239.648 q^{55} -148.062 q^{56} -115.266 q^{58} +377.032 q^{59} +849.042 q^{61} +591.398 q^{62} +64.0000 q^{64} +211.858 q^{65} +92.3424 q^{67} -6.82138 q^{68} -185.077 q^{70} +626.854 q^{71} +439.227 q^{73} -15.7037 q^{74} +85.6831 q^{76} +887.068 q^{77} +641.707 q^{79} +80.0000 q^{80} -931.859 q^{82} +609.932 q^{83} -8.52672 q^{85} +364.747 q^{86} -383.437 q^{88} -1122.87 q^{89} -784.204 q^{91} +92.0000 q^{92} -898.386 q^{94} +107.104 q^{95} -1428.80 q^{97} -0.927209 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{2} + 16 q^{4} + 20 q^{5} - q^{7} + 32 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{2} + 16 q^{4} + 20 q^{5} - q^{7} + 32 q^{8} + 40 q^{10} + 39 q^{11} - 20 q^{13} - 2 q^{14} + 64 q^{16} + 23 q^{17} + 53 q^{19} + 80 q^{20} + 78 q^{22} + 92 q^{23} + 100 q^{25} - 40 q^{26} - 4 q^{28} - 161 q^{29} + 388 q^{31} + 128 q^{32} + 46 q^{34} - 5 q^{35} + 466 q^{37} + 106 q^{38} + 160 q^{40} - 484 q^{41} + 894 q^{43} + 156 q^{44} + 184 q^{46} + 265 q^{47} + 1643 q^{49} + 200 q^{50} - 80 q^{52} - 576 q^{53} + 195 q^{55} - 8 q^{56} - 322 q^{58} + 94 q^{59} + 1153 q^{61} + 776 q^{62} + 256 q^{64} - 100 q^{65} - 1472 q^{67} + 92 q^{68} - 10 q^{70} - 200 q^{71} + 1147 q^{73} + 932 q^{74} + 212 q^{76} + 2176 q^{77} - 908 q^{79} + 320 q^{80} - 968 q^{82} + 1048 q^{83} + 115 q^{85} + 1788 q^{86} + 312 q^{88} + 1784 q^{89} + 2329 q^{91} + 368 q^{92} + 530 q^{94} + 265 q^{95} - 2047 q^{97} + 3286 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 0 0
\(4\) 4.00000 0.500000
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −18.5077 −0.999324 −0.499662 0.866220i \(-0.666542\pi\)
−0.499662 + 0.866220i \(0.666542\pi\)
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 10.0000 0.316228
\(11\) −47.9296 −1.31376 −0.656878 0.753997i \(-0.728123\pi\)
−0.656878 + 0.753997i \(0.728123\pi\)
\(12\) 0 0
\(13\) 42.3717 0.903984 0.451992 0.892022i \(-0.350714\pi\)
0.451992 + 0.892022i \(0.350714\pi\)
\(14\) −37.0155 −0.706629
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −1.70534 −0.0243298 −0.0121649 0.999926i \(-0.503872\pi\)
−0.0121649 + 0.999926i \(0.503872\pi\)
\(18\) 0 0
\(19\) 21.4208 0.258645 0.129323 0.991603i \(-0.458720\pi\)
0.129323 + 0.991603i \(0.458720\pi\)
\(20\) 20.0000 0.223607
\(21\) 0 0
\(22\) −95.8592 −0.928966
\(23\) 23.0000 0.208514
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 84.7434 0.639213
\(27\) 0 0
\(28\) −74.0310 −0.499662
\(29\) −57.6332 −0.369042 −0.184521 0.982829i \(-0.559073\pi\)
−0.184521 + 0.982829i \(0.559073\pi\)
\(30\) 0 0
\(31\) 295.699 1.71320 0.856599 0.515983i \(-0.172573\pi\)
0.856599 + 0.515983i \(0.172573\pi\)
\(32\) 32.0000 0.176777
\(33\) 0 0
\(34\) −3.41069 −0.0172038
\(35\) −92.5387 −0.446911
\(36\) 0 0
\(37\) −7.85184 −0.0348874 −0.0174437 0.999848i \(-0.505553\pi\)
−0.0174437 + 0.999848i \(0.505553\pi\)
\(38\) 42.8416 0.182890
\(39\) 0 0
\(40\) 40.0000 0.158114
\(41\) −465.929 −1.77478 −0.887390 0.461020i \(-0.847484\pi\)
−0.887390 + 0.461020i \(0.847484\pi\)
\(42\) 0 0
\(43\) 182.374 0.646784 0.323392 0.946265i \(-0.395177\pi\)
0.323392 + 0.946265i \(0.395177\pi\)
\(44\) −191.718 −0.656878
\(45\) 0 0
\(46\) 46.0000 0.147442
\(47\) −449.193 −1.39408 −0.697038 0.717035i \(-0.745499\pi\)
−0.697038 + 0.717035i \(0.745499\pi\)
\(48\) 0 0
\(49\) −0.463605 −0.00135162
\(50\) 50.0000 0.141421
\(51\) 0 0
\(52\) 169.487 0.451992
\(53\) 368.316 0.954567 0.477283 0.878749i \(-0.341621\pi\)
0.477283 + 0.878749i \(0.341621\pi\)
\(54\) 0 0
\(55\) −239.648 −0.587529
\(56\) −148.062 −0.353314
\(57\) 0 0
\(58\) −115.266 −0.260952
\(59\) 377.032 0.831955 0.415977 0.909375i \(-0.363440\pi\)
0.415977 + 0.909375i \(0.363440\pi\)
\(60\) 0 0
\(61\) 849.042 1.78211 0.891055 0.453896i \(-0.149966\pi\)
0.891055 + 0.453896i \(0.149966\pi\)
\(62\) 591.398 1.21141
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 211.858 0.404274
\(66\) 0 0
\(67\) 92.3424 0.168379 0.0841897 0.996450i \(-0.473170\pi\)
0.0841897 + 0.996450i \(0.473170\pi\)
\(68\) −6.82138 −0.0121649
\(69\) 0 0
\(70\) −185.077 −0.316014
\(71\) 626.854 1.04780 0.523901 0.851779i \(-0.324476\pi\)
0.523901 + 0.851779i \(0.324476\pi\)
\(72\) 0 0
\(73\) 439.227 0.704214 0.352107 0.935960i \(-0.385465\pi\)
0.352107 + 0.935960i \(0.385465\pi\)
\(74\) −15.7037 −0.0246691
\(75\) 0 0
\(76\) 85.6831 0.129323
\(77\) 887.068 1.31287
\(78\) 0 0
\(79\) 641.707 0.913894 0.456947 0.889494i \(-0.348943\pi\)
0.456947 + 0.889494i \(0.348943\pi\)
\(80\) 80.0000 0.111803
\(81\) 0 0
\(82\) −931.859 −1.25496
\(83\) 609.932 0.806611 0.403306 0.915065i \(-0.367861\pi\)
0.403306 + 0.915065i \(0.367861\pi\)
\(84\) 0 0
\(85\) −8.52672 −0.0108806
\(86\) 364.747 0.457346
\(87\) 0 0
\(88\) −383.437 −0.464483
\(89\) −1122.87 −1.33735 −0.668673 0.743557i \(-0.733137\pi\)
−0.668673 + 0.743557i \(0.733137\pi\)
\(90\) 0 0
\(91\) −784.204 −0.903373
\(92\) 92.0000 0.104257
\(93\) 0 0
\(94\) −898.386 −0.985760
\(95\) 107.104 0.115670
\(96\) 0 0
\(97\) −1428.80 −1.49559 −0.747795 0.663930i \(-0.768887\pi\)
−0.747795 + 0.663930i \(0.768887\pi\)
\(98\) −0.927209 −0.000955737 0
\(99\) 0 0
\(100\) 100.000 0.100000
\(101\) 1512.15 1.48975 0.744875 0.667204i \(-0.232509\pi\)
0.744875 + 0.667204i \(0.232509\pi\)
\(102\) 0 0
\(103\) 957.279 0.915762 0.457881 0.889013i \(-0.348609\pi\)
0.457881 + 0.889013i \(0.348609\pi\)
\(104\) 338.974 0.319607
\(105\) 0 0
\(106\) 736.631 0.674981
\(107\) 1742.16 1.57403 0.787013 0.616936i \(-0.211626\pi\)
0.787013 + 0.616936i \(0.211626\pi\)
\(108\) 0 0
\(109\) 1166.77 1.02529 0.512644 0.858601i \(-0.328666\pi\)
0.512644 + 0.858601i \(0.328666\pi\)
\(110\) −479.296 −0.415446
\(111\) 0 0
\(112\) −296.124 −0.249831
\(113\) 393.287 0.327410 0.163705 0.986509i \(-0.447655\pi\)
0.163705 + 0.986509i \(0.447655\pi\)
\(114\) 0 0
\(115\) 115.000 0.0932505
\(116\) −230.533 −0.184521
\(117\) 0 0
\(118\) 754.063 0.588281
\(119\) 31.5621 0.0243134
\(120\) 0 0
\(121\) 966.245 0.725954
\(122\) 1698.08 1.26014
\(123\) 0 0
\(124\) 1182.80 0.856599
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1067.87 −0.746127 −0.373063 0.927806i \(-0.621693\pi\)
−0.373063 + 0.927806i \(0.621693\pi\)
\(128\) 128.000 0.0883883
\(129\) 0 0
\(130\) 423.717 0.285865
\(131\) 175.497 0.117047 0.0585237 0.998286i \(-0.481361\pi\)
0.0585237 + 0.998286i \(0.481361\pi\)
\(132\) 0 0
\(133\) −396.450 −0.258471
\(134\) 184.685 0.119062
\(135\) 0 0
\(136\) −13.6428 −0.00860189
\(137\) −475.898 −0.296779 −0.148389 0.988929i \(-0.547409\pi\)
−0.148389 + 0.988929i \(0.547409\pi\)
\(138\) 0 0
\(139\) 153.167 0.0934638 0.0467319 0.998907i \(-0.485119\pi\)
0.0467319 + 0.998907i \(0.485119\pi\)
\(140\) −370.155 −0.223456
\(141\) 0 0
\(142\) 1253.71 0.740907
\(143\) −2030.86 −1.18761
\(144\) 0 0
\(145\) −288.166 −0.165041
\(146\) 878.454 0.497954
\(147\) 0 0
\(148\) −31.4074 −0.0174437
\(149\) −506.906 −0.278707 −0.139353 0.990243i \(-0.544502\pi\)
−0.139353 + 0.990243i \(0.544502\pi\)
\(150\) 0 0
\(151\) 2437.84 1.31383 0.656916 0.753964i \(-0.271861\pi\)
0.656916 + 0.753964i \(0.271861\pi\)
\(152\) 171.366 0.0914450
\(153\) 0 0
\(154\) 1774.14 0.928338
\(155\) 1478.50 0.766166
\(156\) 0 0
\(157\) 255.966 0.130117 0.0650584 0.997881i \(-0.479277\pi\)
0.0650584 + 0.997881i \(0.479277\pi\)
\(158\) 1283.41 0.646221
\(159\) 0 0
\(160\) 160.000 0.0790569
\(161\) −425.678 −0.208373
\(162\) 0 0
\(163\) 321.632 0.154553 0.0772767 0.997010i \(-0.475378\pi\)
0.0772767 + 0.997010i \(0.475378\pi\)
\(164\) −1863.72 −0.887390
\(165\) 0 0
\(166\) 1219.86 0.570360
\(167\) 2926.22 1.35591 0.677957 0.735102i \(-0.262866\pi\)
0.677957 + 0.735102i \(0.262866\pi\)
\(168\) 0 0
\(169\) −401.640 −0.182813
\(170\) −17.0534 −0.00769376
\(171\) 0 0
\(172\) 729.495 0.323392
\(173\) −1811.84 −0.796254 −0.398127 0.917330i \(-0.630340\pi\)
−0.398127 + 0.917330i \(0.630340\pi\)
\(174\) 0 0
\(175\) −462.693 −0.199865
\(176\) −766.873 −0.328439
\(177\) 0 0
\(178\) −2245.74 −0.945646
\(179\) −912.664 −0.381093 −0.190547 0.981678i \(-0.561026\pi\)
−0.190547 + 0.981678i \(0.561026\pi\)
\(180\) 0 0
\(181\) 3670.55 1.50735 0.753673 0.657249i \(-0.228280\pi\)
0.753673 + 0.657249i \(0.228280\pi\)
\(182\) −1568.41 −0.638781
\(183\) 0 0
\(184\) 184.000 0.0737210
\(185\) −39.2592 −0.0156021
\(186\) 0 0
\(187\) 81.7364 0.0319634
\(188\) −1796.77 −0.697038
\(189\) 0 0
\(190\) 214.208 0.0817909
\(191\) 1840.96 0.697419 0.348710 0.937231i \(-0.386620\pi\)
0.348710 + 0.937231i \(0.386620\pi\)
\(192\) 0 0
\(193\) −611.817 −0.228184 −0.114092 0.993470i \(-0.536396\pi\)
−0.114092 + 0.993470i \(0.536396\pi\)
\(194\) −2857.59 −1.05754
\(195\) 0 0
\(196\) −1.85442 −0.000675808 0
\(197\) −2830.26 −1.02359 −0.511796 0.859107i \(-0.671020\pi\)
−0.511796 + 0.859107i \(0.671020\pi\)
\(198\) 0 0
\(199\) −1162.74 −0.414195 −0.207097 0.978320i \(-0.566402\pi\)
−0.207097 + 0.978320i \(0.566402\pi\)
\(200\) 200.000 0.0707107
\(201\) 0 0
\(202\) 3024.31 1.05341
\(203\) 1066.66 0.368792
\(204\) 0 0
\(205\) −2329.65 −0.793705
\(206\) 1914.56 0.647542
\(207\) 0 0
\(208\) 677.947 0.225996
\(209\) −1026.69 −0.339797
\(210\) 0 0
\(211\) 1399.58 0.456641 0.228320 0.973586i \(-0.426677\pi\)
0.228320 + 0.973586i \(0.426677\pi\)
\(212\) 1473.26 0.477283
\(213\) 0 0
\(214\) 3484.32 1.11300
\(215\) 911.869 0.289251
\(216\) 0 0
\(217\) −5472.72 −1.71204
\(218\) 2333.54 0.724988
\(219\) 0 0
\(220\) −958.592 −0.293765
\(221\) −72.2583 −0.0219938
\(222\) 0 0
\(223\) 4257.98 1.27863 0.639317 0.768943i \(-0.279217\pi\)
0.639317 + 0.768943i \(0.279217\pi\)
\(224\) −592.248 −0.176657
\(225\) 0 0
\(226\) 786.574 0.231514
\(227\) 4025.03 1.17688 0.588438 0.808542i \(-0.299743\pi\)
0.588438 + 0.808542i \(0.299743\pi\)
\(228\) 0 0
\(229\) 3623.04 1.04549 0.522745 0.852489i \(-0.324908\pi\)
0.522745 + 0.852489i \(0.324908\pi\)
\(230\) 230.000 0.0659380
\(231\) 0 0
\(232\) −461.066 −0.130476
\(233\) −6502.81 −1.82838 −0.914192 0.405282i \(-0.867173\pi\)
−0.914192 + 0.405282i \(0.867173\pi\)
\(234\) 0 0
\(235\) −2245.96 −0.623449
\(236\) 1508.13 0.415977
\(237\) 0 0
\(238\) 63.1241 0.0171921
\(239\) 2690.07 0.728059 0.364030 0.931387i \(-0.381401\pi\)
0.364030 + 0.931387i \(0.381401\pi\)
\(240\) 0 0
\(241\) −44.6958 −0.0119465 −0.00597326 0.999982i \(-0.501901\pi\)
−0.00597326 + 0.999982i \(0.501901\pi\)
\(242\) 1932.49 0.513327
\(243\) 0 0
\(244\) 3396.17 0.891055
\(245\) −2.31802 −0.000604461 0
\(246\) 0 0
\(247\) 907.635 0.233811
\(248\) 2365.59 0.605707
\(249\) 0 0
\(250\) 250.000 0.0632456
\(251\) 6801.41 1.71036 0.855181 0.518329i \(-0.173446\pi\)
0.855181 + 0.518329i \(0.173446\pi\)
\(252\) 0 0
\(253\) −1102.38 −0.273937
\(254\) −2135.74 −0.527591
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) −5576.00 −1.35339 −0.676695 0.736263i \(-0.736589\pi\)
−0.676695 + 0.736263i \(0.736589\pi\)
\(258\) 0 0
\(259\) 145.320 0.0348638
\(260\) 847.434 0.202137
\(261\) 0 0
\(262\) 350.993 0.0827651
\(263\) 5669.58 1.32928 0.664641 0.747163i \(-0.268585\pi\)
0.664641 + 0.747163i \(0.268585\pi\)
\(264\) 0 0
\(265\) 1841.58 0.426895
\(266\) −792.900 −0.182766
\(267\) 0 0
\(268\) 369.370 0.0841897
\(269\) −6040.21 −1.36906 −0.684532 0.728983i \(-0.739994\pi\)
−0.684532 + 0.728983i \(0.739994\pi\)
\(270\) 0 0
\(271\) −6899.26 −1.54650 −0.773248 0.634104i \(-0.781369\pi\)
−0.773248 + 0.634104i \(0.781369\pi\)
\(272\) −27.2855 −0.00608245
\(273\) 0 0
\(274\) −951.795 −0.209854
\(275\) −1198.24 −0.262751
\(276\) 0 0
\(277\) 5617.68 1.21853 0.609267 0.792965i \(-0.291464\pi\)
0.609267 + 0.792965i \(0.291464\pi\)
\(278\) 306.334 0.0660889
\(279\) 0 0
\(280\) −740.310 −0.158007
\(281\) −3069.89 −0.651723 −0.325861 0.945418i \(-0.605654\pi\)
−0.325861 + 0.945418i \(0.605654\pi\)
\(282\) 0 0
\(283\) 1404.86 0.295089 0.147544 0.989055i \(-0.452863\pi\)
0.147544 + 0.989055i \(0.452863\pi\)
\(284\) 2507.42 0.523901
\(285\) 0 0
\(286\) −4061.72 −0.839770
\(287\) 8623.30 1.77358
\(288\) 0 0
\(289\) −4910.09 −0.999408
\(290\) −576.332 −0.116701
\(291\) 0 0
\(292\) 1756.91 0.352107
\(293\) 2407.05 0.479936 0.239968 0.970781i \(-0.422863\pi\)
0.239968 + 0.970781i \(0.422863\pi\)
\(294\) 0 0
\(295\) 1885.16 0.372062
\(296\) −62.8147 −0.0123346
\(297\) 0 0
\(298\) −1013.81 −0.197076
\(299\) 974.549 0.188494
\(300\) 0 0
\(301\) −3375.33 −0.646347
\(302\) 4875.68 0.929020
\(303\) 0 0
\(304\) 342.732 0.0646614
\(305\) 4245.21 0.796984
\(306\) 0 0
\(307\) −459.743 −0.0854689 −0.0427344 0.999086i \(-0.513607\pi\)
−0.0427344 + 0.999086i \(0.513607\pi\)
\(308\) 3548.27 0.656434
\(309\) 0 0
\(310\) 2956.99 0.541761
\(311\) −4119.48 −0.751107 −0.375553 0.926801i \(-0.622547\pi\)
−0.375553 + 0.926801i \(0.622547\pi\)
\(312\) 0 0
\(313\) 1684.15 0.304133 0.152066 0.988370i \(-0.451407\pi\)
0.152066 + 0.988370i \(0.451407\pi\)
\(314\) 511.933 0.0920065
\(315\) 0 0
\(316\) 2566.83 0.456947
\(317\) −8686.47 −1.53906 −0.769528 0.638613i \(-0.779508\pi\)
−0.769528 + 0.638613i \(0.779508\pi\)
\(318\) 0 0
\(319\) 2762.34 0.484831
\(320\) 320.000 0.0559017
\(321\) 0 0
\(322\) −851.356 −0.147342
\(323\) −36.5298 −0.00629279
\(324\) 0 0
\(325\) 1059.29 0.180797
\(326\) 643.265 0.109286
\(327\) 0 0
\(328\) −3727.44 −0.627479
\(329\) 8313.55 1.39313
\(330\) 0 0
\(331\) 4307.91 0.715359 0.357680 0.933844i \(-0.383568\pi\)
0.357680 + 0.933844i \(0.383568\pi\)
\(332\) 2439.73 0.403306
\(333\) 0 0
\(334\) 5852.44 0.958776
\(335\) 461.712 0.0753015
\(336\) 0 0
\(337\) −290.156 −0.0469015 −0.0234507 0.999725i \(-0.507465\pi\)
−0.0234507 + 0.999725i \(0.507465\pi\)
\(338\) −803.280 −0.129268
\(339\) 0 0
\(340\) −34.1069 −0.00544031
\(341\) −14172.7 −2.25072
\(342\) 0 0
\(343\) 6356.73 1.00067
\(344\) 1458.99 0.228673
\(345\) 0 0
\(346\) −3623.69 −0.563037
\(347\) −1042.94 −0.161349 −0.0806743 0.996741i \(-0.525707\pi\)
−0.0806743 + 0.996741i \(0.525707\pi\)
\(348\) 0 0
\(349\) −1819.56 −0.279080 −0.139540 0.990216i \(-0.544562\pi\)
−0.139540 + 0.990216i \(0.544562\pi\)
\(350\) −925.387 −0.141326
\(351\) 0 0
\(352\) −1533.75 −0.232241
\(353\) 4514.29 0.680656 0.340328 0.940307i \(-0.389462\pi\)
0.340328 + 0.940307i \(0.389462\pi\)
\(354\) 0 0
\(355\) 3134.27 0.468591
\(356\) −4491.47 −0.668673
\(357\) 0 0
\(358\) −1825.33 −0.269474
\(359\) −11527.9 −1.69476 −0.847379 0.530988i \(-0.821821\pi\)
−0.847379 + 0.530988i \(0.821821\pi\)
\(360\) 0 0
\(361\) −6400.15 −0.933103
\(362\) 7341.10 1.06585
\(363\) 0 0
\(364\) −3136.82 −0.451686
\(365\) 2196.13 0.314934
\(366\) 0 0
\(367\) 6894.09 0.980568 0.490284 0.871563i \(-0.336893\pi\)
0.490284 + 0.871563i \(0.336893\pi\)
\(368\) 368.000 0.0521286
\(369\) 0 0
\(370\) −78.5184 −0.0110324
\(371\) −6816.69 −0.953922
\(372\) 0 0
\(373\) 7733.25 1.07349 0.536746 0.843744i \(-0.319653\pi\)
0.536746 + 0.843744i \(0.319653\pi\)
\(374\) 163.473 0.0226016
\(375\) 0 0
\(376\) −3593.54 −0.492880
\(377\) −2442.02 −0.333608
\(378\) 0 0
\(379\) −9495.72 −1.28697 −0.643486 0.765458i \(-0.722512\pi\)
−0.643486 + 0.765458i \(0.722512\pi\)
\(380\) 428.416 0.0578349
\(381\) 0 0
\(382\) 3681.92 0.493150
\(383\) 12877.0 1.71797 0.858987 0.511998i \(-0.171094\pi\)
0.858987 + 0.511998i \(0.171094\pi\)
\(384\) 0 0
\(385\) 4435.34 0.587132
\(386\) −1223.63 −0.161351
\(387\) 0 0
\(388\) −5715.18 −0.747795
\(389\) 8200.40 1.06884 0.534418 0.845221i \(-0.320531\pi\)
0.534418 + 0.845221i \(0.320531\pi\)
\(390\) 0 0
\(391\) −39.2229 −0.00507312
\(392\) −3.70884 −0.000477869 0
\(393\) 0 0
\(394\) −5660.52 −0.723789
\(395\) 3208.53 0.408706
\(396\) 0 0
\(397\) 7842.68 0.991468 0.495734 0.868475i \(-0.334899\pi\)
0.495734 + 0.868475i \(0.334899\pi\)
\(398\) −2325.49 −0.292880
\(399\) 0 0
\(400\) 400.000 0.0500000
\(401\) 14534.2 1.80999 0.904993 0.425427i \(-0.139876\pi\)
0.904993 + 0.425427i \(0.139876\pi\)
\(402\) 0 0
\(403\) 12529.3 1.54870
\(404\) 6048.61 0.744875
\(405\) 0 0
\(406\) 2133.32 0.260776
\(407\) 376.335 0.0458335
\(408\) 0 0
\(409\) 13388.0 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(410\) −4659.29 −0.561234
\(411\) 0 0
\(412\) 3829.12 0.457881
\(413\) −6978.00 −0.831393
\(414\) 0 0
\(415\) 3049.66 0.360727
\(416\) 1355.89 0.159803
\(417\) 0 0
\(418\) −2053.38 −0.240273
\(419\) 3103.10 0.361805 0.180903 0.983501i \(-0.442098\pi\)
0.180903 + 0.983501i \(0.442098\pi\)
\(420\) 0 0
\(421\) −6075.82 −0.703367 −0.351684 0.936119i \(-0.614391\pi\)
−0.351684 + 0.936119i \(0.614391\pi\)
\(422\) 2799.16 0.322894
\(423\) 0 0
\(424\) 2946.53 0.337490
\(425\) −42.6336 −0.00486596
\(426\) 0 0
\(427\) −15713.8 −1.78090
\(428\) 6968.63 0.787013
\(429\) 0 0
\(430\) 1823.74 0.204531
\(431\) −14120.3 −1.57808 −0.789040 0.614341i \(-0.789422\pi\)
−0.789040 + 0.614341i \(0.789422\pi\)
\(432\) 0 0
\(433\) 8555.96 0.949592 0.474796 0.880096i \(-0.342522\pi\)
0.474796 + 0.880096i \(0.342522\pi\)
\(434\) −10945.4 −1.21060
\(435\) 0 0
\(436\) 4667.09 0.512644
\(437\) 492.678 0.0539313
\(438\) 0 0
\(439\) −10894.1 −1.18439 −0.592194 0.805796i \(-0.701738\pi\)
−0.592194 + 0.805796i \(0.701738\pi\)
\(440\) −1917.18 −0.207723
\(441\) 0 0
\(442\) −144.517 −0.0155519
\(443\) −16120.5 −1.72891 −0.864456 0.502708i \(-0.832337\pi\)
−0.864456 + 0.502708i \(0.832337\pi\)
\(444\) 0 0
\(445\) −5614.34 −0.598079
\(446\) 8515.96 0.904130
\(447\) 0 0
\(448\) −1184.50 −0.124915
\(449\) −4811.29 −0.505699 −0.252849 0.967506i \(-0.581368\pi\)
−0.252849 + 0.967506i \(0.581368\pi\)
\(450\) 0 0
\(451\) 22331.8 2.33163
\(452\) 1573.15 0.163705
\(453\) 0 0
\(454\) 8050.06 0.832177
\(455\) −3921.02 −0.404001
\(456\) 0 0
\(457\) −226.329 −0.0231667 −0.0115834 0.999933i \(-0.503687\pi\)
−0.0115834 + 0.999933i \(0.503687\pi\)
\(458\) 7246.08 0.739273
\(459\) 0 0
\(460\) 460.000 0.0466252
\(461\) 4349.17 0.439395 0.219697 0.975568i \(-0.429493\pi\)
0.219697 + 0.975568i \(0.429493\pi\)
\(462\) 0 0
\(463\) −989.313 −0.0993030 −0.0496515 0.998767i \(-0.515811\pi\)
−0.0496515 + 0.998767i \(0.515811\pi\)
\(464\) −922.131 −0.0922605
\(465\) 0 0
\(466\) −13005.6 −1.29286
\(467\) −8512.91 −0.843535 −0.421767 0.906704i \(-0.638590\pi\)
−0.421767 + 0.906704i \(0.638590\pi\)
\(468\) 0 0
\(469\) −1709.05 −0.168266
\(470\) −4491.93 −0.440845
\(471\) 0 0
\(472\) 3016.25 0.294140
\(473\) −8741.10 −0.849717
\(474\) 0 0
\(475\) 535.519 0.0517291
\(476\) 126.248 0.0121567
\(477\) 0 0
\(478\) 5380.14 0.514816
\(479\) 12058.6 1.15025 0.575125 0.818065i \(-0.304953\pi\)
0.575125 + 0.818065i \(0.304953\pi\)
\(480\) 0 0
\(481\) −332.696 −0.0315377
\(482\) −89.3916 −0.00844746
\(483\) 0 0
\(484\) 3864.98 0.362977
\(485\) −7143.98 −0.668848
\(486\) 0 0
\(487\) 11605.3 1.07985 0.539924 0.841714i \(-0.318453\pi\)
0.539924 + 0.841714i \(0.318453\pi\)
\(488\) 6792.34 0.630071
\(489\) 0 0
\(490\) −4.63605 −0.000427419 0
\(491\) 4651.88 0.427569 0.213785 0.976881i \(-0.431421\pi\)
0.213785 + 0.976881i \(0.431421\pi\)
\(492\) 0 0
\(493\) 98.2845 0.00897872
\(494\) 1815.27 0.165330
\(495\) 0 0
\(496\) 4731.19 0.428300
\(497\) −11601.6 −1.04709
\(498\) 0 0
\(499\) −7953.03 −0.713480 −0.356740 0.934204i \(-0.616112\pi\)
−0.356740 + 0.934204i \(0.616112\pi\)
\(500\) 500.000 0.0447214
\(501\) 0 0
\(502\) 13602.8 1.20941
\(503\) 11805.6 1.04649 0.523245 0.852182i \(-0.324721\pi\)
0.523245 + 0.852182i \(0.324721\pi\)
\(504\) 0 0
\(505\) 7560.76 0.666237
\(506\) −2204.76 −0.193703
\(507\) 0 0
\(508\) −4271.48 −0.373063
\(509\) 2732.89 0.237983 0.118991 0.992895i \(-0.462034\pi\)
0.118991 + 0.992895i \(0.462034\pi\)
\(510\) 0 0
\(511\) −8129.09 −0.703738
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −11152.0 −0.956992
\(515\) 4786.40 0.409541
\(516\) 0 0
\(517\) 21529.6 1.83147
\(518\) 290.640 0.0246525
\(519\) 0 0
\(520\) 1694.87 0.142932
\(521\) −14710.9 −1.23704 −0.618518 0.785771i \(-0.712267\pi\)
−0.618518 + 0.785771i \(0.712267\pi\)
\(522\) 0 0
\(523\) −7034.35 −0.588127 −0.294064 0.955786i \(-0.595008\pi\)
−0.294064 + 0.955786i \(0.595008\pi\)
\(524\) 701.987 0.0585237
\(525\) 0 0
\(526\) 11339.2 0.939944
\(527\) −504.269 −0.0416818
\(528\) 0 0
\(529\) 529.000 0.0434783
\(530\) 3683.16 0.301861
\(531\) 0 0
\(532\) −1585.80 −0.129235
\(533\) −19742.2 −1.60437
\(534\) 0 0
\(535\) 8710.79 0.703926
\(536\) 738.739 0.0595311
\(537\) 0 0
\(538\) −12080.4 −0.968075
\(539\) 22.2204 0.00177569
\(540\) 0 0
\(541\) 1552.90 0.123409 0.0617045 0.998094i \(-0.480346\pi\)
0.0617045 + 0.998094i \(0.480346\pi\)
\(542\) −13798.5 −1.09354
\(543\) 0 0
\(544\) −54.5710 −0.00430094
\(545\) 5833.86 0.458523
\(546\) 0 0
\(547\) 174.657 0.0136523 0.00682614 0.999977i \(-0.497827\pi\)
0.00682614 + 0.999977i \(0.497827\pi\)
\(548\) −1903.59 −0.148389
\(549\) 0 0
\(550\) −2396.48 −0.185793
\(551\) −1234.55 −0.0954510
\(552\) 0 0
\(553\) −11876.5 −0.913276
\(554\) 11235.4 0.861633
\(555\) 0 0
\(556\) 612.669 0.0467319
\(557\) 1990.63 0.151429 0.0757143 0.997130i \(-0.475876\pi\)
0.0757143 + 0.997130i \(0.475876\pi\)
\(558\) 0 0
\(559\) 7727.48 0.584683
\(560\) −1480.62 −0.111728
\(561\) 0 0
\(562\) −6139.78 −0.460838
\(563\) −208.006 −0.0155709 −0.00778543 0.999970i \(-0.502478\pi\)
−0.00778543 + 0.999970i \(0.502478\pi\)
\(564\) 0 0
\(565\) 1966.44 0.146422
\(566\) 2809.71 0.208659
\(567\) 0 0
\(568\) 5014.83 0.370454
\(569\) 3003.05 0.221256 0.110628 0.993862i \(-0.464714\pi\)
0.110628 + 0.993862i \(0.464714\pi\)
\(570\) 0 0
\(571\) −10796.1 −0.791249 −0.395624 0.918412i \(-0.629472\pi\)
−0.395624 + 0.918412i \(0.629472\pi\)
\(572\) −8123.43 −0.593807
\(573\) 0 0
\(574\) 17246.6 1.25411
\(575\) 575.000 0.0417029
\(576\) 0 0
\(577\) −26011.3 −1.87671 −0.938357 0.345667i \(-0.887653\pi\)
−0.938357 + 0.345667i \(0.887653\pi\)
\(578\) −9820.18 −0.706688
\(579\) 0 0
\(580\) −1152.66 −0.0825203
\(581\) −11288.5 −0.806066
\(582\) 0 0
\(583\) −17653.2 −1.25407
\(584\) 3513.81 0.248977
\(585\) 0 0
\(586\) 4814.09 0.339366
\(587\) 2774.97 0.195120 0.0975598 0.995230i \(-0.468896\pi\)
0.0975598 + 0.995230i \(0.468896\pi\)
\(588\) 0 0
\(589\) 6334.11 0.443111
\(590\) 3770.32 0.263087
\(591\) 0 0
\(592\) −125.629 −0.00872185
\(593\) 2384.07 0.165096 0.0825481 0.996587i \(-0.473694\pi\)
0.0825481 + 0.996587i \(0.473694\pi\)
\(594\) 0 0
\(595\) 157.810 0.0108733
\(596\) −2027.62 −0.139353
\(597\) 0 0
\(598\) 1949.10 0.133285
\(599\) 1090.87 0.0744102 0.0372051 0.999308i \(-0.488155\pi\)
0.0372051 + 0.999308i \(0.488155\pi\)
\(600\) 0 0
\(601\) −5192.37 −0.352414 −0.176207 0.984353i \(-0.556383\pi\)
−0.176207 + 0.984353i \(0.556383\pi\)
\(602\) −6750.65 −0.457036
\(603\) 0 0
\(604\) 9751.36 0.656916
\(605\) 4831.22 0.324657
\(606\) 0 0
\(607\) 1205.44 0.0806054 0.0403027 0.999188i \(-0.487168\pi\)
0.0403027 + 0.999188i \(0.487168\pi\)
\(608\) 685.465 0.0457225
\(609\) 0 0
\(610\) 8490.42 0.563553
\(611\) −19033.1 −1.26022
\(612\) 0 0
\(613\) −14243.2 −0.938466 −0.469233 0.883075i \(-0.655469\pi\)
−0.469233 + 0.883075i \(0.655469\pi\)
\(614\) −919.487 −0.0604356
\(615\) 0 0
\(616\) 7096.55 0.464169
\(617\) 422.492 0.0275671 0.0137835 0.999905i \(-0.495612\pi\)
0.0137835 + 0.999905i \(0.495612\pi\)
\(618\) 0 0
\(619\) −8826.35 −0.573119 −0.286560 0.958062i \(-0.592512\pi\)
−0.286560 + 0.958062i \(0.592512\pi\)
\(620\) 5913.98 0.383083
\(621\) 0 0
\(622\) −8238.96 −0.531113
\(623\) 20781.7 1.33644
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 3368.29 0.215054
\(627\) 0 0
\(628\) 1023.87 0.0650584
\(629\) 13.3901 0.000848804 0
\(630\) 0 0
\(631\) −19684.1 −1.24186 −0.620929 0.783867i \(-0.713244\pi\)
−0.620929 + 0.783867i \(0.713244\pi\)
\(632\) 5133.65 0.323110
\(633\) 0 0
\(634\) −17372.9 −1.08828
\(635\) −5339.35 −0.333678
\(636\) 0 0
\(637\) −19.6437 −0.00122184
\(638\) 5524.67 0.342827
\(639\) 0 0
\(640\) 640.000 0.0395285
\(641\) −15113.1 −0.931253 −0.465626 0.884981i \(-0.654171\pi\)
−0.465626 + 0.884981i \(0.654171\pi\)
\(642\) 0 0
\(643\) −16917.8 −1.03760 −0.518798 0.854897i \(-0.673620\pi\)
−0.518798 + 0.854897i \(0.673620\pi\)
\(644\) −1702.71 −0.104187
\(645\) 0 0
\(646\) −73.0596 −0.00444968
\(647\) −19564.5 −1.18881 −0.594405 0.804166i \(-0.702612\pi\)
−0.594405 + 0.804166i \(0.702612\pi\)
\(648\) 0 0
\(649\) −18071.0 −1.09299
\(650\) 2118.58 0.127843
\(651\) 0 0
\(652\) 1286.53 0.0772767
\(653\) 22735.0 1.36247 0.681233 0.732067i \(-0.261444\pi\)
0.681233 + 0.732067i \(0.261444\pi\)
\(654\) 0 0
\(655\) 877.483 0.0523452
\(656\) −7454.87 −0.443695
\(657\) 0 0
\(658\) 16627.1 0.985094
\(659\) 30730.7 1.81654 0.908269 0.418388i \(-0.137405\pi\)
0.908269 + 0.418388i \(0.137405\pi\)
\(660\) 0 0
\(661\) −29204.3 −1.71848 −0.859240 0.511573i \(-0.829063\pi\)
−0.859240 + 0.511573i \(0.829063\pi\)
\(662\) 8615.81 0.505835
\(663\) 0 0
\(664\) 4879.45 0.285180
\(665\) −1982.25 −0.115592
\(666\) 0 0
\(667\) −1325.56 −0.0769506
\(668\) 11704.9 0.677957
\(669\) 0 0
\(670\) 923.424 0.0532462
\(671\) −40694.2 −2.34126
\(672\) 0 0
\(673\) −17530.1 −1.00406 −0.502032 0.864849i \(-0.667414\pi\)
−0.502032 + 0.864849i \(0.667414\pi\)
\(674\) −580.312 −0.0331644
\(675\) 0 0
\(676\) −1606.56 −0.0914064
\(677\) 20553.4 1.16681 0.583407 0.812180i \(-0.301719\pi\)
0.583407 + 0.812180i \(0.301719\pi\)
\(678\) 0 0
\(679\) 26443.8 1.49458
\(680\) −68.2138 −0.00384688
\(681\) 0 0
\(682\) −28345.5 −1.59150
\(683\) −13174.8 −0.738098 −0.369049 0.929410i \(-0.620316\pi\)
−0.369049 + 0.929410i \(0.620316\pi\)
\(684\) 0 0
\(685\) −2379.49 −0.132723
\(686\) 12713.5 0.707584
\(687\) 0 0
\(688\) 2917.98 0.161696
\(689\) 15606.2 0.862913
\(690\) 0 0
\(691\) −14800.8 −0.814831 −0.407415 0.913243i \(-0.633570\pi\)
−0.407415 + 0.913243i \(0.633570\pi\)
\(692\) −7247.38 −0.398127
\(693\) 0 0
\(694\) −2085.88 −0.114091
\(695\) 765.836 0.0417983
\(696\) 0 0
\(697\) 794.570 0.0431800
\(698\) −3639.13 −0.197339
\(699\) 0 0
\(700\) −1850.77 −0.0999324
\(701\) 12311.5 0.663336 0.331668 0.943396i \(-0.392389\pi\)
0.331668 + 0.943396i \(0.392389\pi\)
\(702\) 0 0
\(703\) −168.192 −0.00902347
\(704\) −3067.49 −0.164219
\(705\) 0 0
\(706\) 9028.59 0.481297
\(707\) −27986.5 −1.48874
\(708\) 0 0
\(709\) 3893.89 0.206260 0.103130 0.994668i \(-0.467114\pi\)
0.103130 + 0.994668i \(0.467114\pi\)
\(710\) 6268.54 0.331344
\(711\) 0 0
\(712\) −8982.94 −0.472823
\(713\) 6801.08 0.357227
\(714\) 0 0
\(715\) −10154.3 −0.531117
\(716\) −3650.65 −0.190547
\(717\) 0 0
\(718\) −23055.8 −1.19838
\(719\) 19942.5 1.03440 0.517198 0.855866i \(-0.326975\pi\)
0.517198 + 0.855866i \(0.326975\pi\)
\(720\) 0 0
\(721\) −17717.1 −0.915143
\(722\) −12800.3 −0.659803
\(723\) 0 0
\(724\) 14682.2 0.753673
\(725\) −1440.83 −0.0738084
\(726\) 0 0
\(727\) 36167.0 1.84506 0.922530 0.385926i \(-0.126118\pi\)
0.922530 + 0.385926i \(0.126118\pi\)
\(728\) −6273.63 −0.319391
\(729\) 0 0
\(730\) 4392.27 0.222692
\(731\) −311.010 −0.0157361
\(732\) 0 0
\(733\) −11669.5 −0.588025 −0.294013 0.955802i \(-0.594991\pi\)
−0.294013 + 0.955802i \(0.594991\pi\)
\(734\) 13788.2 0.693366
\(735\) 0 0
\(736\) 736.000 0.0368605
\(737\) −4425.93 −0.221209
\(738\) 0 0
\(739\) 75.0536 0.00373598 0.00186799 0.999998i \(-0.499405\pi\)
0.00186799 + 0.999998i \(0.499405\pi\)
\(740\) −157.037 −0.00780106
\(741\) 0 0
\(742\) −13633.4 −0.674524
\(743\) −28279.8 −1.39635 −0.698173 0.715929i \(-0.746003\pi\)
−0.698173 + 0.715929i \(0.746003\pi\)
\(744\) 0 0
\(745\) −2534.53 −0.124641
\(746\) 15466.5 0.759074
\(747\) 0 0
\(748\) 326.946 0.0159817
\(749\) −32243.4 −1.57296
\(750\) 0 0
\(751\) −17268.1 −0.839044 −0.419522 0.907745i \(-0.637802\pi\)
−0.419522 + 0.907745i \(0.637802\pi\)
\(752\) −7187.09 −0.348519
\(753\) 0 0
\(754\) −4884.03 −0.235897
\(755\) 12189.2 0.587564
\(756\) 0 0
\(757\) −12525.8 −0.601400 −0.300700 0.953719i \(-0.597220\pi\)
−0.300700 + 0.953719i \(0.597220\pi\)
\(758\) −18991.4 −0.910026
\(759\) 0 0
\(760\) 856.831 0.0408954
\(761\) 18670.1 0.889343 0.444672 0.895694i \(-0.353320\pi\)
0.444672 + 0.895694i \(0.353320\pi\)
\(762\) 0 0
\(763\) −21594.3 −1.02460
\(764\) 7363.83 0.348710
\(765\) 0 0
\(766\) 25754.0 1.21479
\(767\) 15975.5 0.752074
\(768\) 0 0
\(769\) −32969.6 −1.54605 −0.773027 0.634373i \(-0.781258\pi\)
−0.773027 + 0.634373i \(0.781258\pi\)
\(770\) 8870.68 0.415165
\(771\) 0 0
\(772\) −2447.27 −0.114092
\(773\) 23251.3 1.08188 0.540938 0.841062i \(-0.318069\pi\)
0.540938 + 0.841062i \(0.318069\pi\)
\(774\) 0 0
\(775\) 7392.48 0.342640
\(776\) −11430.4 −0.528771
\(777\) 0 0
\(778\) 16400.8 0.755781
\(779\) −9980.57 −0.459039
\(780\) 0 0
\(781\) −30044.8 −1.37655
\(782\) −78.4458 −0.00358723
\(783\) 0 0
\(784\) −7.41767 −0.000337904 0
\(785\) 1279.83 0.0581900
\(786\) 0 0
\(787\) −29782.8 −1.34897 −0.674486 0.738288i \(-0.735635\pi\)
−0.674486 + 0.738288i \(0.735635\pi\)
\(788\) −11321.0 −0.511796
\(789\) 0 0
\(790\) 6417.07 0.288999
\(791\) −7278.86 −0.327189
\(792\) 0 0
\(793\) 35975.3 1.61100
\(794\) 15685.4 0.701073
\(795\) 0 0
\(796\) −4650.98 −0.207097
\(797\) −35307.2 −1.56919 −0.784596 0.620008i \(-0.787129\pi\)
−0.784596 + 0.620008i \(0.787129\pi\)
\(798\) 0 0
\(799\) 766.029 0.0339176
\(800\) 800.000 0.0353553
\(801\) 0 0
\(802\) 29068.4 1.27985
\(803\) −21052.0 −0.925165
\(804\) 0 0
\(805\) −2128.39 −0.0931874
\(806\) 25058.5 1.09510
\(807\) 0 0
\(808\) 12097.2 0.526706
\(809\) −7752.46 −0.336912 −0.168456 0.985709i \(-0.553878\pi\)
−0.168456 + 0.985709i \(0.553878\pi\)
\(810\) 0 0
\(811\) 23471.6 1.01627 0.508137 0.861276i \(-0.330334\pi\)
0.508137 + 0.861276i \(0.330334\pi\)
\(812\) 4266.64 0.184396
\(813\) 0 0
\(814\) 752.671 0.0324092
\(815\) 1608.16 0.0691184
\(816\) 0 0
\(817\) 3906.59 0.167288
\(818\) 26776.0 1.14450
\(819\) 0 0
\(820\) −9318.59 −0.396853
\(821\) −2467.55 −0.104894 −0.0524470 0.998624i \(-0.516702\pi\)
−0.0524470 + 0.998624i \(0.516702\pi\)
\(822\) 0 0
\(823\) 21984.5 0.931144 0.465572 0.885010i \(-0.345849\pi\)
0.465572 + 0.885010i \(0.345849\pi\)
\(824\) 7658.23 0.323771
\(825\) 0 0
\(826\) −13956.0 −0.587883
\(827\) 587.293 0.0246943 0.0123472 0.999924i \(-0.496070\pi\)
0.0123472 + 0.999924i \(0.496070\pi\)
\(828\) 0 0
\(829\) 41822.8 1.75219 0.876096 0.482137i \(-0.160139\pi\)
0.876096 + 0.482137i \(0.160139\pi\)
\(830\) 6099.32 0.255073
\(831\) 0 0
\(832\) 2711.79 0.112998
\(833\) 0.790605 3.28846e−5 0
\(834\) 0 0
\(835\) 14631.1 0.606383
\(836\) −4106.76 −0.169898
\(837\) 0 0
\(838\) 6206.20 0.255835
\(839\) 10126.5 0.416693 0.208346 0.978055i \(-0.433192\pi\)
0.208346 + 0.978055i \(0.433192\pi\)
\(840\) 0 0
\(841\) −21067.4 −0.863808
\(842\) −12151.6 −0.497356
\(843\) 0 0
\(844\) 5598.33 0.228320
\(845\) −2008.20 −0.0817564
\(846\) 0 0
\(847\) −17883.0 −0.725463
\(848\) 5893.05 0.238642
\(849\) 0 0
\(850\) −85.2672 −0.00344075
\(851\) −180.592 −0.00727453
\(852\) 0 0
\(853\) 11584.4 0.464995 0.232498 0.972597i \(-0.425310\pi\)
0.232498 + 0.972597i \(0.425310\pi\)
\(854\) −31427.7 −1.25929
\(855\) 0 0
\(856\) 13937.3 0.556502
\(857\) 9221.47 0.367561 0.183780 0.982967i \(-0.441166\pi\)
0.183780 + 0.982967i \(0.441166\pi\)
\(858\) 0 0
\(859\) 34654.2 1.37647 0.688235 0.725488i \(-0.258386\pi\)
0.688235 + 0.725488i \(0.258386\pi\)
\(860\) 3647.47 0.144625
\(861\) 0 0
\(862\) −28240.7 −1.11587
\(863\) −42887.7 −1.69167 −0.845837 0.533441i \(-0.820899\pi\)
−0.845837 + 0.533441i \(0.820899\pi\)
\(864\) 0 0
\(865\) −9059.22 −0.356096
\(866\) 17111.9 0.671463
\(867\) 0 0
\(868\) −21890.9 −0.856020
\(869\) −30756.7 −1.20063
\(870\) 0 0
\(871\) 3912.70 0.152212
\(872\) 9334.17 0.362494
\(873\) 0 0
\(874\) 985.356 0.0381352
\(875\) −2313.47 −0.0893823
\(876\) 0 0
\(877\) 45935.5 1.76868 0.884339 0.466846i \(-0.154610\pi\)
0.884339 + 0.466846i \(0.154610\pi\)
\(878\) −21788.2 −0.837488
\(879\) 0 0
\(880\) −3834.37 −0.146882
\(881\) 71.9309 0.00275075 0.00137538 0.999999i \(-0.499562\pi\)
0.00137538 + 0.999999i \(0.499562\pi\)
\(882\) 0 0
\(883\) 20003.8 0.762379 0.381189 0.924497i \(-0.375515\pi\)
0.381189 + 0.924497i \(0.375515\pi\)
\(884\) −289.033 −0.0109969
\(885\) 0 0
\(886\) −32241.0 −1.22253
\(887\) −26357.3 −0.997737 −0.498869 0.866678i \(-0.666251\pi\)
−0.498869 + 0.866678i \(0.666251\pi\)
\(888\) 0 0
\(889\) 19763.9 0.745623
\(890\) −11228.7 −0.422906
\(891\) 0 0
\(892\) 17031.9 0.639317
\(893\) −9622.06 −0.360571
\(894\) 0 0
\(895\) −4563.32 −0.170430
\(896\) −2368.99 −0.0883286
\(897\) 0 0
\(898\) −9622.57 −0.357583
\(899\) −17042.1 −0.632242
\(900\) 0 0
\(901\) −628.105 −0.0232244
\(902\) 44663.6 1.64871
\(903\) 0 0
\(904\) 3146.30 0.115757
\(905\) 18352.7 0.674106
\(906\) 0 0
\(907\) −39300.4 −1.43875 −0.719377 0.694620i \(-0.755572\pi\)
−0.719377 + 0.694620i \(0.755572\pi\)
\(908\) 16100.1 0.588438
\(909\) 0 0
\(910\) −7842.04 −0.285672
\(911\) −31099.2 −1.13103 −0.565513 0.824740i \(-0.691322\pi\)
−0.565513 + 0.824740i \(0.691322\pi\)
\(912\) 0 0
\(913\) −29233.8 −1.05969
\(914\) −452.657 −0.0163814
\(915\) 0 0
\(916\) 14492.2 0.522745
\(917\) −3248.05 −0.116968
\(918\) 0 0
\(919\) 18935.8 0.679690 0.339845 0.940481i \(-0.389625\pi\)
0.339845 + 0.940481i \(0.389625\pi\)
\(920\) 920.000 0.0329690
\(921\) 0 0
\(922\) 8698.33 0.310699
\(923\) 26560.9 0.947195
\(924\) 0 0
\(925\) −196.296 −0.00697748
\(926\) −1978.63 −0.0702178
\(927\) 0 0
\(928\) −1844.26 −0.0652380
\(929\) −40156.1 −1.41817 −0.709085 0.705123i \(-0.750892\pi\)
−0.709085 + 0.705123i \(0.750892\pi\)
\(930\) 0 0
\(931\) −9.93077 −0.000349590 0
\(932\) −26011.2 −0.914192
\(933\) 0 0
\(934\) −17025.8 −0.596469
\(935\) 408.682 0.0142945
\(936\) 0 0
\(937\) 126.898 0.00442432 0.00221216 0.999998i \(-0.499296\pi\)
0.00221216 + 0.999998i \(0.499296\pi\)
\(938\) −3418.10 −0.118982
\(939\) 0 0
\(940\) −8983.86 −0.311725
\(941\) 19266.6 0.667452 0.333726 0.942670i \(-0.391694\pi\)
0.333726 + 0.942670i \(0.391694\pi\)
\(942\) 0 0
\(943\) −10716.4 −0.370067
\(944\) 6032.51 0.207989
\(945\) 0 0
\(946\) −17482.2 −0.600840
\(947\) 54560.4 1.87220 0.936101 0.351732i \(-0.114407\pi\)
0.936101 + 0.351732i \(0.114407\pi\)
\(948\) 0 0
\(949\) 18610.8 0.636598
\(950\) 1071.04 0.0365780
\(951\) 0 0
\(952\) 252.497 0.00859607
\(953\) 44976.2 1.52877 0.764387 0.644758i \(-0.223042\pi\)
0.764387 + 0.644758i \(0.223042\pi\)
\(954\) 0 0
\(955\) 9204.79 0.311895
\(956\) 10760.3 0.364030
\(957\) 0 0
\(958\) 24117.1 0.813350
\(959\) 8807.79 0.296578
\(960\) 0 0
\(961\) 57647.0 1.93505
\(962\) −665.391 −0.0223005
\(963\) 0 0
\(964\) −178.783 −0.00597326
\(965\) −3059.08 −0.102047
\(966\) 0 0
\(967\) −39431.7 −1.31131 −0.655656 0.755059i \(-0.727608\pi\)
−0.655656 + 0.755059i \(0.727608\pi\)
\(968\) 7729.96 0.256664
\(969\) 0 0
\(970\) −14288.0 −0.472947
\(971\) −20249.9 −0.669258 −0.334629 0.942350i \(-0.608611\pi\)
−0.334629 + 0.942350i \(0.608611\pi\)
\(972\) 0 0
\(973\) −2834.78 −0.0934006
\(974\) 23210.6 0.763567
\(975\) 0 0
\(976\) 13584.7 0.445527
\(977\) 9673.55 0.316770 0.158385 0.987377i \(-0.449371\pi\)
0.158385 + 0.987377i \(0.449371\pi\)
\(978\) 0 0
\(979\) 53818.6 1.75695
\(980\) −9.27209 −0.000302231 0
\(981\) 0 0
\(982\) 9303.77 0.302337
\(983\) 17264.3 0.560168 0.280084 0.959975i \(-0.409638\pi\)
0.280084 + 0.959975i \(0.409638\pi\)
\(984\) 0 0
\(985\) −14151.3 −0.457764
\(986\) 196.569 0.00634891
\(987\) 0 0
\(988\) 3630.54 0.116906
\(989\) 4194.60 0.134864
\(990\) 0 0
\(991\) 23892.9 0.765876 0.382938 0.923774i \(-0.374912\pi\)
0.382938 + 0.923774i \(0.374912\pi\)
\(992\) 9462.37 0.302854
\(993\) 0 0
\(994\) −23203.3 −0.740406
\(995\) −5813.72 −0.185234
\(996\) 0 0
\(997\) −35830.2 −1.13817 −0.569083 0.822280i \(-0.692702\pi\)
−0.569083 + 0.822280i \(0.692702\pi\)
\(998\) −15906.1 −0.504507
\(999\) 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 2070.4.a.bj.1.2 4
3.2 odd 2 230.4.a.h.1.3 4
12.11 even 2 1840.4.a.m.1.2 4
15.2 even 4 1150.4.b.n.599.2 8
15.8 even 4 1150.4.b.n.599.7 8
15.14 odd 2 1150.4.a.p.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.a.h.1.3 4 3.2 odd 2
1150.4.a.p.1.2 4 15.14 odd 2
1150.4.b.n.599.2 8 15.2 even 4
1150.4.b.n.599.7 8 15.8 even 4
1840.4.a.m.1.2 4 12.11 even 2
2070.4.a.bj.1.2 4 1.1 even 1 trivial