Properties

Label 1815.4.a.l.1.1
Level $1815$
Weight $4$
Character 1815.1
Self dual yes
Analytic conductor $107.088$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(107.088466660\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
Defining polynomial: \(x^{2} - 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 1815.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.46410 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -10.3923 q^{6} -31.1769 q^{7} +13.8564 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-3.46410 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -10.3923 q^{6} -31.1769 q^{7} +13.8564 q^{8} +9.00000 q^{9} -17.3205 q^{10} +12.0000 q^{12} +76.2102 q^{13} +108.000 q^{14} +15.0000 q^{15} -80.0000 q^{16} -46.7654 q^{17} -31.1769 q^{18} +31.1769 q^{19} +20.0000 q^{20} -93.5307 q^{21} +195.000 q^{23} +41.5692 q^{24} +25.0000 q^{25} -264.000 q^{26} +27.0000 q^{27} -124.708 q^{28} -34.6410 q^{29} -51.9615 q^{30} +97.0000 q^{31} +166.277 q^{32} +162.000 q^{34} -155.885 q^{35} +36.0000 q^{36} +274.000 q^{37} -108.000 q^{38} +228.631 q^{39} +69.2820 q^{40} -384.515 q^{41} +324.000 q^{42} -415.692 q^{43} +45.0000 q^{45} -675.500 q^{46} +3.00000 q^{47} -240.000 q^{48} +629.000 q^{49} -86.6025 q^{50} -140.296 q^{51} +304.841 q^{52} +3.00000 q^{53} -93.5307 q^{54} -432.000 q^{56} +93.5307 q^{57} +120.000 q^{58} -648.000 q^{59} +60.0000 q^{60} +458.993 q^{61} -336.018 q^{62} -280.592 q^{63} +64.0000 q^{64} +381.051 q^{65} +70.0000 q^{67} -187.061 q^{68} +585.000 q^{69} +540.000 q^{70} -372.000 q^{71} +124.708 q^{72} -935.307 q^{73} -949.164 q^{74} +75.0000 q^{75} +124.708 q^{76} -792.000 q^{78} -521.347 q^{79} -400.000 q^{80} +81.0000 q^{81} +1332.00 q^{82} -45.0333 q^{83} -374.123 q^{84} -233.827 q^{85} +1440.00 q^{86} -103.923 q^{87} +1122.00 q^{89} -155.885 q^{90} -2376.00 q^{91} +780.000 q^{92} +291.000 q^{93} -10.3923 q^{94} +155.885 q^{95} +498.831 q^{96} +470.000 q^{97} -2178.92 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 6q^{3} + 8q^{4} + 10q^{5} + 18q^{9} + O(q^{10}) \) \( 2q + 6q^{3} + 8q^{4} + 10q^{5} + 18q^{9} + 24q^{12} + 216q^{14} + 30q^{15} - 160q^{16} + 40q^{20} + 390q^{23} + 50q^{25} - 528q^{26} + 54q^{27} + 194q^{31} + 324q^{34} + 72q^{36} + 548q^{37} - 216q^{38} + 648q^{42} + 90q^{45} + 6q^{47} - 480q^{48} + 1258q^{49} + 6q^{53} - 864q^{56} + 240q^{58} - 1296q^{59} + 120q^{60} + 128q^{64} + 140q^{67} + 1170q^{69} + 1080q^{70} - 744q^{71} + 150q^{75} - 1584q^{78} - 800q^{80} + 162q^{81} + 2664q^{82} + 2880q^{86} + 2244q^{89} - 4752q^{91} + 1560q^{92} + 582q^{93} + 940q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.46410 −1.22474 −0.612372 0.790569i \(-0.709785\pi\)
−0.612372 + 0.790569i \(0.709785\pi\)
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) 5.00000 0.447214
\(6\) −10.3923 −0.707107
\(7\) −31.1769 −1.68340 −0.841698 0.539949i \(-0.818443\pi\)
−0.841698 + 0.539949i \(0.818443\pi\)
\(8\) 13.8564 0.612372
\(9\) 9.00000 0.333333
\(10\) −17.3205 −0.547723
\(11\) 0 0
\(12\) 12.0000 0.288675
\(13\) 76.2102 1.62592 0.812958 0.582322i \(-0.197856\pi\)
0.812958 + 0.582322i \(0.197856\pi\)
\(14\) 108.000 2.06173
\(15\) 15.0000 0.258199
\(16\) −80.0000 −1.25000
\(17\) −46.7654 −0.667192 −0.333596 0.942716i \(-0.608262\pi\)
−0.333596 + 0.942716i \(0.608262\pi\)
\(18\) −31.1769 −0.408248
\(19\) 31.1769 0.376446 0.188223 0.982126i \(-0.439727\pi\)
0.188223 + 0.982126i \(0.439727\pi\)
\(20\) 20.0000 0.223607
\(21\) −93.5307 −0.971909
\(22\) 0 0
\(23\) 195.000 1.76784 0.883920 0.467639i \(-0.154895\pi\)
0.883920 + 0.467639i \(0.154895\pi\)
\(24\) 41.5692 0.353553
\(25\) 25.0000 0.200000
\(26\) −264.000 −1.99133
\(27\) 27.0000 0.192450
\(28\) −124.708 −0.841698
\(29\) −34.6410 −0.221816 −0.110908 0.993831i \(-0.535376\pi\)
−0.110908 + 0.993831i \(0.535376\pi\)
\(30\) −51.9615 −0.316228
\(31\) 97.0000 0.561991 0.280995 0.959709i \(-0.409335\pi\)
0.280995 + 0.959709i \(0.409335\pi\)
\(32\) 166.277 0.918559
\(33\) 0 0
\(34\) 162.000 0.817140
\(35\) −155.885 −0.752837
\(36\) 36.0000 0.166667
\(37\) 274.000 1.21744 0.608721 0.793385i \(-0.291683\pi\)
0.608721 + 0.793385i \(0.291683\pi\)
\(38\) −108.000 −0.461050
\(39\) 228.631 0.938723
\(40\) 69.2820 0.273861
\(41\) −384.515 −1.46466 −0.732332 0.680948i \(-0.761568\pi\)
−0.732332 + 0.680948i \(0.761568\pi\)
\(42\) 324.000 1.19034
\(43\) −415.692 −1.47424 −0.737122 0.675760i \(-0.763816\pi\)
−0.737122 + 0.675760i \(0.763816\pi\)
\(44\) 0 0
\(45\) 45.0000 0.149071
\(46\) −675.500 −2.16515
\(47\) 3.00000 0.00931053 0.00465527 0.999989i \(-0.498518\pi\)
0.00465527 + 0.999989i \(0.498518\pi\)
\(48\) −240.000 −0.721688
\(49\) 629.000 1.83382
\(50\) −86.6025 −0.244949
\(51\) −140.296 −0.385204
\(52\) 304.841 0.812958
\(53\) 3.00000 0.00777513 0.00388756 0.999992i \(-0.498763\pi\)
0.00388756 + 0.999992i \(0.498763\pi\)
\(54\) −93.5307 −0.235702
\(55\) 0 0
\(56\) −432.000 −1.03086
\(57\) 93.5307 0.217341
\(58\) 120.000 0.271668
\(59\) −648.000 −1.42987 −0.714936 0.699190i \(-0.753544\pi\)
−0.714936 + 0.699190i \(0.753544\pi\)
\(60\) 60.0000 0.129099
\(61\) 458.993 0.963411 0.481706 0.876333i \(-0.340017\pi\)
0.481706 + 0.876333i \(0.340017\pi\)
\(62\) −336.018 −0.688295
\(63\) −280.592 −0.561132
\(64\) 64.0000 0.125000
\(65\) 381.051 0.727132
\(66\) 0 0
\(67\) 70.0000 0.127640 0.0638199 0.997961i \(-0.479672\pi\)
0.0638199 + 0.997961i \(0.479672\pi\)
\(68\) −187.061 −0.333596
\(69\) 585.000 1.02066
\(70\) 540.000 0.922033
\(71\) −372.000 −0.621807 −0.310903 0.950442i \(-0.600632\pi\)
−0.310903 + 0.950442i \(0.600632\pi\)
\(72\) 124.708 0.204124
\(73\) −935.307 −1.49958 −0.749791 0.661675i \(-0.769846\pi\)
−0.749791 + 0.661675i \(0.769846\pi\)
\(74\) −949.164 −1.49105
\(75\) 75.0000 0.115470
\(76\) 124.708 0.188223
\(77\) 0 0
\(78\) −792.000 −1.14970
\(79\) −521.347 −0.742483 −0.371241 0.928536i \(-0.621068\pi\)
−0.371241 + 0.928536i \(0.621068\pi\)
\(80\) −400.000 −0.559017
\(81\) 81.0000 0.111111
\(82\) 1332.00 1.79384
\(83\) −45.0333 −0.0595548 −0.0297774 0.999557i \(-0.509480\pi\)
−0.0297774 + 0.999557i \(0.509480\pi\)
\(84\) −374.123 −0.485954
\(85\) −233.827 −0.298377
\(86\) 1440.00 1.80557
\(87\) −103.923 −0.128066
\(88\) 0 0
\(89\) 1122.00 1.33631 0.668156 0.744021i \(-0.267084\pi\)
0.668156 + 0.744021i \(0.267084\pi\)
\(90\) −155.885 −0.182574
\(91\) −2376.00 −2.73706
\(92\) 780.000 0.883920
\(93\) 291.000 0.324466
\(94\) −10.3923 −0.0114030
\(95\) 155.885 0.168352
\(96\) 498.831 0.530330
\(97\) 470.000 0.491972 0.245986 0.969273i \(-0.420888\pi\)
0.245986 + 0.969273i \(0.420888\pi\)
\(98\) −2178.92 −2.24596
\(99\) 0 0
\(100\) 100.000 0.100000
\(101\) 1932.97 1.90433 0.952166 0.305581i \(-0.0988505\pi\)
0.952166 + 0.305581i \(0.0988505\pi\)
\(102\) 486.000 0.471776
\(103\) 968.000 0.926018 0.463009 0.886354i \(-0.346770\pi\)
0.463009 + 0.886354i \(0.346770\pi\)
\(104\) 1056.00 0.995667
\(105\) −467.654 −0.434651
\(106\) −10.3923 −0.00952255
\(107\) 161.081 0.145535 0.0727676 0.997349i \(-0.476817\pi\)
0.0727676 + 0.997349i \(0.476817\pi\)
\(108\) 108.000 0.0962250
\(109\) 235.559 0.206995 0.103497 0.994630i \(-0.466997\pi\)
0.103497 + 0.994630i \(0.466997\pi\)
\(110\) 0 0
\(111\) 822.000 0.702890
\(112\) 2494.15 2.10424
\(113\) −1653.00 −1.37612 −0.688058 0.725655i \(-0.741537\pi\)
−0.688058 + 0.725655i \(0.741537\pi\)
\(114\) −324.000 −0.266188
\(115\) 975.000 0.790602
\(116\) −138.564 −0.110908
\(117\) 685.892 0.541972
\(118\) 2244.74 1.75123
\(119\) 1458.00 1.12315
\(120\) 207.846 0.158114
\(121\) 0 0
\(122\) −1590.00 −1.17993
\(123\) −1153.55 −0.845624
\(124\) 388.000 0.280995
\(125\) 125.000 0.0894427
\(126\) 972.000 0.687243
\(127\) 2057.68 1.43771 0.718855 0.695160i \(-0.244666\pi\)
0.718855 + 0.695160i \(0.244666\pi\)
\(128\) −1551.92 −1.07165
\(129\) −1247.08 −0.851155
\(130\) −1320.00 −0.890551
\(131\) 2151.21 1.43475 0.717373 0.696689i \(-0.245344\pi\)
0.717373 + 0.696689i \(0.245344\pi\)
\(132\) 0 0
\(133\) −972.000 −0.633707
\(134\) −242.487 −0.156326
\(135\) 135.000 0.0860663
\(136\) −648.000 −0.408570
\(137\) 921.000 0.574353 0.287176 0.957878i \(-0.407283\pi\)
0.287176 + 0.957878i \(0.407283\pi\)
\(138\) −2026.50 −1.25005
\(139\) −1726.85 −1.05374 −0.526870 0.849946i \(-0.676635\pi\)
−0.526870 + 0.849946i \(0.676635\pi\)
\(140\) −623.538 −0.376419
\(141\) 9.00000 0.00537544
\(142\) 1288.65 0.761555
\(143\) 0 0
\(144\) −720.000 −0.416667
\(145\) −173.205 −0.0991993
\(146\) 3240.00 1.83660
\(147\) 1887.00 1.05876
\(148\) 1096.00 0.608721
\(149\) 2016.11 1.10850 0.554248 0.832352i \(-0.313006\pi\)
0.554248 + 0.832352i \(0.313006\pi\)
\(150\) −259.808 −0.141421
\(151\) 774.227 0.417256 0.208628 0.977995i \(-0.433100\pi\)
0.208628 + 0.977995i \(0.433100\pi\)
\(152\) 432.000 0.230525
\(153\) −420.888 −0.222397
\(154\) 0 0
\(155\) 485.000 0.251330
\(156\) 914.523 0.469362
\(157\) −3602.00 −1.83102 −0.915512 0.402290i \(-0.868214\pi\)
−0.915512 + 0.402290i \(0.868214\pi\)
\(158\) 1806.00 0.909352
\(159\) 9.00000 0.00448897
\(160\) 831.384 0.410792
\(161\) −6079.50 −2.97597
\(162\) −280.592 −0.136083
\(163\) −1672.00 −0.803443 −0.401721 0.915762i \(-0.631588\pi\)
−0.401721 + 0.915762i \(0.631588\pi\)
\(164\) −1538.06 −0.732332
\(165\) 0 0
\(166\) 156.000 0.0729394
\(167\) −2527.06 −1.17096 −0.585479 0.810688i \(-0.699093\pi\)
−0.585479 + 0.810688i \(0.699093\pi\)
\(168\) −1296.00 −0.595170
\(169\) 3611.00 1.64360
\(170\) 810.000 0.365436
\(171\) 280.592 0.125482
\(172\) −1662.77 −0.737122
\(173\) −1745.91 −0.767277 −0.383638 0.923483i \(-0.625329\pi\)
−0.383638 + 0.923483i \(0.625329\pi\)
\(174\) 360.000 0.156848
\(175\) −779.423 −0.336679
\(176\) 0 0
\(177\) −1944.00 −0.825537
\(178\) −3886.72 −1.63664
\(179\) 1998.00 0.834288 0.417144 0.908840i \(-0.363031\pi\)
0.417144 + 0.908840i \(0.363031\pi\)
\(180\) 180.000 0.0745356
\(181\) −4534.00 −1.86193 −0.930966 0.365107i \(-0.881032\pi\)
−0.930966 + 0.365107i \(0.881032\pi\)
\(182\) 8230.71 3.35220
\(183\) 1376.98 0.556226
\(184\) 2702.00 1.08258
\(185\) 1370.00 0.544456
\(186\) −1008.05 −0.397387
\(187\) 0 0
\(188\) 12.0000 0.00465527
\(189\) −841.777 −0.323970
\(190\) −540.000 −0.206188
\(191\) 2754.00 1.04331 0.521656 0.853156i \(-0.325315\pi\)
0.521656 + 0.853156i \(0.325315\pi\)
\(192\) 192.000 0.0721688
\(193\) 772.495 0.288111 0.144055 0.989570i \(-0.453986\pi\)
0.144055 + 0.989570i \(0.453986\pi\)
\(194\) −1628.13 −0.602540
\(195\) 1143.15 0.419810
\(196\) 2516.00 0.916910
\(197\) 2757.42 0.997251 0.498625 0.866818i \(-0.333838\pi\)
0.498625 + 0.866818i \(0.333838\pi\)
\(198\) 0 0
\(199\) −731.000 −0.260398 −0.130199 0.991488i \(-0.541562\pi\)
−0.130199 + 0.991488i \(0.541562\pi\)
\(200\) 346.410 0.122474
\(201\) 210.000 0.0736928
\(202\) −6696.00 −2.33232
\(203\) 1080.00 0.373405
\(204\) −561.184 −0.192602
\(205\) −1922.58 −0.655017
\(206\) −3353.25 −1.13414
\(207\) 1755.00 0.589280
\(208\) −6096.82 −2.03240
\(209\) 0 0
\(210\) 1620.00 0.532336
\(211\) −2069.80 −0.675313 −0.337656 0.941269i \(-0.609634\pi\)
−0.337656 + 0.941269i \(0.609634\pi\)
\(212\) 12.0000 0.00388756
\(213\) −1116.00 −0.359000
\(214\) −558.000 −0.178243
\(215\) −2078.46 −0.659302
\(216\) 374.123 0.117851
\(217\) −3024.16 −0.946053
\(218\) −816.000 −0.253516
\(219\) −2805.92 −0.865784
\(220\) 0 0
\(221\) −3564.00 −1.08480
\(222\) −2847.49 −0.860861
\(223\) 5438.00 1.63298 0.816492 0.577357i \(-0.195916\pi\)
0.816492 + 0.577357i \(0.195916\pi\)
\(224\) −5184.00 −1.54630
\(225\) 225.000 0.0666667
\(226\) 5726.16 1.68539
\(227\) −2177.19 −0.636586 −0.318293 0.947992i \(-0.603110\pi\)
−0.318293 + 0.947992i \(0.603110\pi\)
\(228\) 374.123 0.108671
\(229\) 6073.00 1.75247 0.876234 0.481886i \(-0.160048\pi\)
0.876234 + 0.481886i \(0.160048\pi\)
\(230\) −3377.50 −0.968286
\(231\) 0 0
\(232\) −480.000 −0.135834
\(233\) −1574.43 −0.442681 −0.221340 0.975197i \(-0.571043\pi\)
−0.221340 + 0.975197i \(0.571043\pi\)
\(234\) −2376.00 −0.663778
\(235\) 15.0000 0.00416380
\(236\) −2592.00 −0.714936
\(237\) −1564.04 −0.428673
\(238\) −5050.66 −1.37557
\(239\) 6290.81 1.70259 0.851294 0.524689i \(-0.175818\pi\)
0.851294 + 0.524689i \(0.175818\pi\)
\(240\) −1200.00 −0.322749
\(241\) 3257.99 0.870811 0.435405 0.900234i \(-0.356605\pi\)
0.435405 + 0.900234i \(0.356605\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 1835.97 0.481706
\(245\) 3145.00 0.820109
\(246\) 3996.00 1.03567
\(247\) 2376.00 0.612070
\(248\) 1344.07 0.344148
\(249\) −135.100 −0.0343840
\(250\) −433.013 −0.109545
\(251\) 660.000 0.165971 0.0829857 0.996551i \(-0.473554\pi\)
0.0829857 + 0.996551i \(0.473554\pi\)
\(252\) −1122.37 −0.280566
\(253\) 0 0
\(254\) −7128.00 −1.76083
\(255\) −701.481 −0.172268
\(256\) 4864.00 1.18750
\(257\) −1641.00 −0.398299 −0.199149 0.979969i \(-0.563818\pi\)
−0.199149 + 0.979969i \(0.563818\pi\)
\(258\) 4320.00 1.04245
\(259\) −8542.47 −2.04943
\(260\) 1524.20 0.363566
\(261\) −311.769 −0.0739388
\(262\) −7452.00 −1.75720
\(263\) −2558.24 −0.599801 −0.299901 0.953970i \(-0.596954\pi\)
−0.299901 + 0.953970i \(0.596954\pi\)
\(264\) 0 0
\(265\) 15.0000 0.00347714
\(266\) 3367.11 0.776130
\(267\) 3366.00 0.771520
\(268\) 280.000 0.0638199
\(269\) 60.0000 0.0135995 0.00679975 0.999977i \(-0.497836\pi\)
0.00679975 + 0.999977i \(0.497836\pi\)
\(270\) −467.654 −0.105409
\(271\) −2818.05 −0.631676 −0.315838 0.948813i \(-0.602286\pi\)
−0.315838 + 0.948813i \(0.602286\pi\)
\(272\) 3741.23 0.833990
\(273\) −7128.00 −1.58024
\(274\) −3190.44 −0.703436
\(275\) 0 0
\(276\) 2340.00 0.510331
\(277\) 4205.42 0.912199 0.456100 0.889929i \(-0.349246\pi\)
0.456100 + 0.889929i \(0.349246\pi\)
\(278\) 5982.00 1.29056
\(279\) 873.000 0.187330
\(280\) −2160.00 −0.461017
\(281\) 5220.40 1.10827 0.554133 0.832428i \(-0.313050\pi\)
0.554133 + 0.832428i \(0.313050\pi\)
\(282\) −31.1769 −0.00658354
\(283\) 4077.25 0.856421 0.428211 0.903679i \(-0.359144\pi\)
0.428211 + 0.903679i \(0.359144\pi\)
\(284\) −1488.00 −0.310903
\(285\) 467.654 0.0971979
\(286\) 0 0
\(287\) 11988.0 2.46561
\(288\) 1496.49 0.306186
\(289\) −2726.00 −0.554854
\(290\) 600.000 0.121494
\(291\) 1410.00 0.284040
\(292\) −3741.23 −0.749791
\(293\) 6576.60 1.31129 0.655647 0.755068i \(-0.272396\pi\)
0.655647 + 0.755068i \(0.272396\pi\)
\(294\) −6536.76 −1.29671
\(295\) −3240.00 −0.639458
\(296\) 3796.66 0.745527
\(297\) 0 0
\(298\) −6984.00 −1.35763
\(299\) 14861.0 2.87436
\(300\) 300.000 0.0577350
\(301\) 12960.0 2.48173
\(302\) −2682.00 −0.511032
\(303\) 5798.91 1.09947
\(304\) −2494.15 −0.470558
\(305\) 2294.97 0.430851
\(306\) 1458.00 0.272380
\(307\) −6786.18 −1.26159 −0.630794 0.775950i \(-0.717271\pi\)
−0.630794 + 0.775950i \(0.717271\pi\)
\(308\) 0 0
\(309\) 2904.00 0.534637
\(310\) −1680.09 −0.307815
\(311\) 2934.00 0.534958 0.267479 0.963564i \(-0.413809\pi\)
0.267479 + 0.963564i \(0.413809\pi\)
\(312\) 3168.00 0.574848
\(313\) 7180.00 1.29661 0.648303 0.761383i \(-0.275479\pi\)
0.648303 + 0.761383i \(0.275479\pi\)
\(314\) 12477.7 2.24254
\(315\) −1402.96 −0.250946
\(316\) −2085.39 −0.371241
\(317\) 7713.00 1.36658 0.683289 0.730148i \(-0.260549\pi\)
0.683289 + 0.730148i \(0.260549\pi\)
\(318\) −31.1769 −0.00549784
\(319\) 0 0
\(320\) 320.000 0.0559017
\(321\) 483.242 0.0840248
\(322\) 21060.0 3.64481
\(323\) −1458.00 −0.251162
\(324\) 324.000 0.0555556
\(325\) 1905.26 0.325183
\(326\) 5791.98 0.984012
\(327\) 706.677 0.119509
\(328\) −5328.00 −0.896919
\(329\) −93.5307 −0.0156733
\(330\) 0 0
\(331\) −9349.00 −1.55247 −0.776235 0.630444i \(-0.782873\pi\)
−0.776235 + 0.630444i \(0.782873\pi\)
\(332\) −180.133 −0.0297774
\(333\) 2466.00 0.405814
\(334\) 8754.00 1.43412
\(335\) 350.000 0.0570822
\(336\) 7482.46 1.21489
\(337\) 3183.51 0.514590 0.257295 0.966333i \(-0.417169\pi\)
0.257295 + 0.966333i \(0.417169\pi\)
\(338\) −12508.9 −2.01300
\(339\) −4959.00 −0.794501
\(340\) −935.307 −0.149189
\(341\) 0 0
\(342\) −972.000 −0.153683
\(343\) −8916.60 −1.40365
\(344\) −5760.00 −0.902786
\(345\) 2925.00 0.456454
\(346\) 6048.00 0.939718
\(347\) 1470.51 0.227496 0.113748 0.993510i \(-0.463714\pi\)
0.113748 + 0.993510i \(0.463714\pi\)
\(348\) −415.692 −0.0640329
\(349\) 5326.06 0.816898 0.408449 0.912781i \(-0.366070\pi\)
0.408449 + 0.912781i \(0.366070\pi\)
\(350\) 2700.00 0.412346
\(351\) 2057.68 0.312908
\(352\) 0 0
\(353\) 11547.0 1.74103 0.870517 0.492139i \(-0.163785\pi\)
0.870517 + 0.492139i \(0.163785\pi\)
\(354\) 6734.21 1.01107
\(355\) −1860.00 −0.278080
\(356\) 4488.00 0.668156
\(357\) 4374.00 0.648450
\(358\) −6921.28 −1.02179
\(359\) 3547.24 0.521494 0.260747 0.965407i \(-0.416031\pi\)
0.260747 + 0.965407i \(0.416031\pi\)
\(360\) 623.538 0.0912871
\(361\) −5887.00 −0.858288
\(362\) 15706.2 2.28039
\(363\) 0 0
\(364\) −9504.00 −1.36853
\(365\) −4676.54 −0.670633
\(366\) −4770.00 −0.681235
\(367\) 5894.00 0.838322 0.419161 0.907912i \(-0.362324\pi\)
0.419161 + 0.907912i \(0.362324\pi\)
\(368\) −15600.0 −2.20980
\(369\) −3460.64 −0.488221
\(370\) −4745.82 −0.666820
\(371\) −93.5307 −0.0130886
\(372\) 1164.00 0.162233
\(373\) −3838.22 −0.532804 −0.266402 0.963862i \(-0.585835\pi\)
−0.266402 + 0.963862i \(0.585835\pi\)
\(374\) 0 0
\(375\) 375.000 0.0516398
\(376\) 41.5692 0.00570151
\(377\) −2640.00 −0.360655
\(378\) 2916.00 0.396780
\(379\) −5431.00 −0.736073 −0.368037 0.929811i \(-0.619970\pi\)
−0.368037 + 0.929811i \(0.619970\pi\)
\(380\) 623.538 0.0841759
\(381\) 6173.03 0.830063
\(382\) −9540.14 −1.27779
\(383\) 312.000 0.0416252 0.0208126 0.999783i \(-0.493375\pi\)
0.0208126 + 0.999783i \(0.493375\pi\)
\(384\) −4655.75 −0.618718
\(385\) 0 0
\(386\) −2676.00 −0.352862
\(387\) −3741.23 −0.491414
\(388\) 1880.00 0.245986
\(389\) 1512.00 0.197073 0.0985366 0.995133i \(-0.468584\pi\)
0.0985366 + 0.995133i \(0.468584\pi\)
\(390\) −3960.00 −0.514160
\(391\) −9119.25 −1.17949
\(392\) 8715.68 1.12298
\(393\) 6453.62 0.828351
\(394\) −9552.00 −1.22138
\(395\) −2606.74 −0.332048
\(396\) 0 0
\(397\) −10210.0 −1.29074 −0.645372 0.763869i \(-0.723298\pi\)
−0.645372 + 0.763869i \(0.723298\pi\)
\(398\) 2532.26 0.318921
\(399\) −2916.00 −0.365871
\(400\) −2000.00 −0.250000
\(401\) −10368.0 −1.29116 −0.645578 0.763695i \(-0.723383\pi\)
−0.645578 + 0.763695i \(0.723383\pi\)
\(402\) −727.461 −0.0902549
\(403\) 7392.39 0.913750
\(404\) 7731.87 0.952166
\(405\) 405.000 0.0496904
\(406\) −3741.23 −0.457325
\(407\) 0 0
\(408\) −1944.00 −0.235888
\(409\) 15611.0 1.88732 0.943659 0.330920i \(-0.107359\pi\)
0.943659 + 0.330920i \(0.107359\pi\)
\(410\) 6660.00 0.802229
\(411\) 2763.00 0.331603
\(412\) 3872.00 0.463009
\(413\) 20202.6 2.40704
\(414\) −6079.50 −0.721717
\(415\) −225.167 −0.0266337
\(416\) 12672.0 1.49350
\(417\) −5180.56 −0.608377
\(418\) 0 0
\(419\) 8802.00 1.02627 0.513133 0.858309i \(-0.328485\pi\)
0.513133 + 0.858309i \(0.328485\pi\)
\(420\) −1870.61 −0.217325
\(421\) −2537.00 −0.293696 −0.146848 0.989159i \(-0.546913\pi\)
−0.146848 + 0.989159i \(0.546913\pi\)
\(422\) 7170.00 0.827086
\(423\) 27.0000 0.00310351
\(424\) 41.5692 0.00476127
\(425\) −1169.13 −0.133438
\(426\) 3865.94 0.439684
\(427\) −14310.0 −1.62180
\(428\) 644.323 0.0727676
\(429\) 0 0
\(430\) 7200.00 0.807476
\(431\) 3824.37 0.427409 0.213705 0.976898i \(-0.431447\pi\)
0.213705 + 0.976898i \(0.431447\pi\)
\(432\) −2160.00 −0.240563
\(433\) −12004.0 −1.33228 −0.666138 0.745829i \(-0.732054\pi\)
−0.666138 + 0.745829i \(0.732054\pi\)
\(434\) 10476.0 1.15867
\(435\) −519.615 −0.0572727
\(436\) 942.236 0.103497
\(437\) 6079.50 0.665496
\(438\) 9720.00 1.06036
\(439\) 13127.2 1.42717 0.713585 0.700569i \(-0.247070\pi\)
0.713585 + 0.700569i \(0.247070\pi\)
\(440\) 0 0
\(441\) 5661.00 0.611273
\(442\) 12346.1 1.32860
\(443\) 1560.00 0.167309 0.0836544 0.996495i \(-0.473341\pi\)
0.0836544 + 0.996495i \(0.473341\pi\)
\(444\) 3288.00 0.351445
\(445\) 5610.00 0.597617
\(446\) −18837.8 −1.99999
\(447\) 6048.32 0.639991
\(448\) −1995.32 −0.210424
\(449\) 10890.0 1.14461 0.572306 0.820040i \(-0.306049\pi\)
0.572306 + 0.820040i \(0.306049\pi\)
\(450\) −779.423 −0.0816497
\(451\) 0 0
\(452\) −6612.00 −0.688058
\(453\) 2322.68 0.240903
\(454\) 7542.00 0.779656
\(455\) −11880.0 −1.22405
\(456\) 1296.00 0.133094
\(457\) 17746.6 1.81652 0.908261 0.418404i \(-0.137410\pi\)
0.908261 + 0.418404i \(0.137410\pi\)
\(458\) −21037.5 −2.14633
\(459\) −1262.67 −0.128401
\(460\) 3900.00 0.395301
\(461\) 10274.5 1.03803 0.519016 0.854765i \(-0.326299\pi\)
0.519016 + 0.854765i \(0.326299\pi\)
\(462\) 0 0
\(463\) 8978.00 0.901173 0.450586 0.892733i \(-0.351215\pi\)
0.450586 + 0.892733i \(0.351215\pi\)
\(464\) 2771.28 0.277270
\(465\) 1455.00 0.145105
\(466\) 5454.00 0.542171
\(467\) 9111.00 0.902798 0.451399 0.892322i \(-0.350925\pi\)
0.451399 + 0.892322i \(0.350925\pi\)
\(468\) 2743.57 0.270986
\(469\) −2182.38 −0.214868
\(470\) −51.9615 −0.00509959
\(471\) −10806.0 −1.05714
\(472\) −8978.95 −0.875614
\(473\) 0 0
\(474\) 5418.00 0.525015
\(475\) 779.423 0.0752892
\(476\) 5832.00 0.561574
\(477\) 27.0000 0.00259171
\(478\) −21792.0 −2.08524
\(479\) 13225.9 1.26160 0.630802 0.775944i \(-0.282726\pi\)
0.630802 + 0.775944i \(0.282726\pi\)
\(480\) 2494.15 0.237171
\(481\) 20881.6 1.97946
\(482\) −11286.0 −1.06652
\(483\) −18238.5 −1.71818
\(484\) 0 0
\(485\) 2350.00 0.220017
\(486\) −841.777 −0.0785674
\(487\) −9200.00 −0.856041 −0.428020 0.903769i \(-0.640789\pi\)
−0.428020 + 0.903769i \(0.640789\pi\)
\(488\) 6360.00 0.589967
\(489\) −5016.00 −0.463868
\(490\) −10894.6 −1.00442
\(491\) 1170.87 0.107618 0.0538090 0.998551i \(-0.482864\pi\)
0.0538090 + 0.998551i \(0.482864\pi\)
\(492\) −4614.18 −0.422812
\(493\) 1620.00 0.147994
\(494\) −8230.71 −0.749629
\(495\) 0 0
\(496\) −7760.00 −0.702488
\(497\) 11597.8 1.04675
\(498\) 468.000 0.0421116
\(499\) −3872.00 −0.347364 −0.173682 0.984802i \(-0.555566\pi\)
−0.173682 + 0.984802i \(0.555566\pi\)
\(500\) 500.000 0.0447214
\(501\) −7581.19 −0.676053
\(502\) −2286.31 −0.203273
\(503\) 19476.9 1.72651 0.863253 0.504771i \(-0.168423\pi\)
0.863253 + 0.504771i \(0.168423\pi\)
\(504\) −3888.00 −0.343622
\(505\) 9664.84 0.851643
\(506\) 0 0
\(507\) 10833.0 0.948936
\(508\) 8230.71 0.718855
\(509\) 14010.0 1.22000 0.610002 0.792400i \(-0.291169\pi\)
0.610002 + 0.792400i \(0.291169\pi\)
\(510\) 2430.00 0.210985
\(511\) 29160.0 2.52439
\(512\) −4434.05 −0.382733
\(513\) 841.777 0.0724471
\(514\) 5684.59 0.487814
\(515\) 4840.00 0.414128
\(516\) −4988.31 −0.425577
\(517\) 0 0
\(518\) 29592.0 2.51003
\(519\) −5237.72 −0.442987
\(520\) 5280.00 0.445276
\(521\) 9900.00 0.832489 0.416245 0.909253i \(-0.363346\pi\)
0.416245 + 0.909253i \(0.363346\pi\)
\(522\) 1080.00 0.0905562
\(523\) −16090.8 −1.34531 −0.672657 0.739954i \(-0.734847\pi\)
−0.672657 + 0.739954i \(0.734847\pi\)
\(524\) 8604.83 0.717373
\(525\) −2338.27 −0.194382
\(526\) 8862.00 0.734604
\(527\) −4536.24 −0.374956
\(528\) 0 0
\(529\) 25858.0 2.12526
\(530\) −51.9615 −0.00425861
\(531\) −5832.00 −0.476624
\(532\) −3888.00 −0.316854
\(533\) −29304.0 −2.38142
\(534\) −11660.2 −0.944915
\(535\) 805.404 0.0650853
\(536\) 969.948 0.0781630
\(537\) 5994.00 0.481676
\(538\) −207.846 −0.0166559
\(539\) 0 0
\(540\) 540.000 0.0430331
\(541\) 15013.4 1.19312 0.596559 0.802569i \(-0.296534\pi\)
0.596559 + 0.802569i \(0.296534\pi\)
\(542\) 9762.00 0.773642
\(543\) −13602.0 −1.07499
\(544\) −7776.00 −0.612855
\(545\) 1177.79 0.0925710
\(546\) 24692.1 1.93539
\(547\) −15429.1 −1.20603 −0.603017 0.797728i \(-0.706035\pi\)
−0.603017 + 0.797728i \(0.706035\pi\)
\(548\) 3684.00 0.287176
\(549\) 4130.94 0.321137
\(550\) 0 0
\(551\) −1080.00 −0.0835019
\(552\) 8106.00 0.625026
\(553\) 16254.0 1.24989
\(554\) −14568.0 −1.11721
\(555\) 4110.00 0.314342
\(556\) −6907.42 −0.526870
\(557\) −8395.25 −0.638632 −0.319316 0.947648i \(-0.603453\pi\)
−0.319316 + 0.947648i \(0.603453\pi\)
\(558\) −3024.16 −0.229432
\(559\) −31680.0 −2.39700
\(560\) 12470.8 0.941046
\(561\) 0 0
\(562\) −18084.0 −1.35734
\(563\) −7271.15 −0.544303 −0.272151 0.962254i \(-0.587735\pi\)
−0.272151 + 0.962254i \(0.587735\pi\)
\(564\) 36.0000 0.00268772
\(565\) −8265.00 −0.615418
\(566\) −14124.0 −1.04890
\(567\) −2525.33 −0.187044
\(568\) −5154.58 −0.380777
\(569\) 8182.21 0.602840 0.301420 0.953491i \(-0.402539\pi\)
0.301420 + 0.953491i \(0.402539\pi\)
\(570\) −1620.00 −0.119043
\(571\) 16414.6 1.20303 0.601516 0.798861i \(-0.294564\pi\)
0.601516 + 0.798861i \(0.294564\pi\)
\(572\) 0 0
\(573\) 8262.00 0.602356
\(574\) −41527.7 −3.01974
\(575\) 4875.00 0.353568
\(576\) 576.000 0.0416667
\(577\) 7300.00 0.526695 0.263347 0.964701i \(-0.415173\pi\)
0.263347 + 0.964701i \(0.415173\pi\)
\(578\) 9443.14 0.679555
\(579\) 2317.48 0.166341
\(580\) −692.820 −0.0495997
\(581\) 1404.00 0.100254
\(582\) −4884.38 −0.347877
\(583\) 0 0
\(584\) −12960.0 −0.918302
\(585\) 3429.46 0.242377
\(586\) −22782.0 −1.60600
\(587\) −5703.00 −0.401002 −0.200501 0.979694i \(-0.564257\pi\)
−0.200501 + 0.979694i \(0.564257\pi\)
\(588\) 7548.00 0.529378
\(589\) 3024.16 0.211559
\(590\) 11223.7 0.783173
\(591\) 8272.27 0.575763
\(592\) −21920.0 −1.52180
\(593\) −16717.8 −1.15770 −0.578850 0.815434i \(-0.696498\pi\)
−0.578850 + 0.815434i \(0.696498\pi\)
\(594\) 0 0
\(595\) 7290.00 0.502287
\(596\) 8064.43 0.554248
\(597\) −2193.00 −0.150341
\(598\) −51480.0 −3.52036
\(599\) 12630.0 0.861516 0.430758 0.902468i \(-0.358246\pi\)
0.430758 + 0.902468i \(0.358246\pi\)
\(600\) 1039.23 0.0707107
\(601\) −2757.42 −0.187151 −0.0935755 0.995612i \(-0.529830\pi\)
−0.0935755 + 0.995612i \(0.529830\pi\)
\(602\) −44894.8 −3.03949
\(603\) 630.000 0.0425466
\(604\) 3096.91 0.208628
\(605\) 0 0
\(606\) −20088.0 −1.34657
\(607\) −13035.4 −0.871649 −0.435825 0.900032i \(-0.643543\pi\)
−0.435825 + 0.900032i \(0.643543\pi\)
\(608\) 5184.00 0.345788
\(609\) 3240.00 0.215585
\(610\) −7950.00 −0.527682
\(611\) 228.631 0.0151381
\(612\) −1683.55 −0.111199
\(613\) 28142.4 1.85426 0.927128 0.374744i \(-0.122269\pi\)
0.927128 + 0.374744i \(0.122269\pi\)
\(614\) 23508.0 1.54512
\(615\) −5767.73 −0.378174
\(616\) 0 0
\(617\) −6942.00 −0.452957 −0.226478 0.974016i \(-0.572721\pi\)
−0.226478 + 0.974016i \(0.572721\pi\)
\(618\) −10059.8 −0.654794
\(619\) −9220.00 −0.598680 −0.299340 0.954146i \(-0.596767\pi\)
−0.299340 + 0.954146i \(0.596767\pi\)
\(620\) 1940.00 0.125665
\(621\) 5265.00 0.340221
\(622\) −10163.7 −0.655187
\(623\) −34980.5 −2.24954
\(624\) −18290.5 −1.17340
\(625\) 625.000 0.0400000
\(626\) −24872.2 −1.58801
\(627\) 0 0
\(628\) −14408.0 −0.915512
\(629\) −12813.7 −0.812267
\(630\) 4860.00 0.307344
\(631\) 7393.00 0.466419 0.233210 0.972426i \(-0.425077\pi\)
0.233210 + 0.972426i \(0.425077\pi\)
\(632\) −7224.00 −0.454676
\(633\) −6209.40 −0.389892
\(634\) −26718.6 −1.67371
\(635\) 10288.4 0.642964
\(636\) 36.0000 0.00224449
\(637\) 47936.2 2.98164
\(638\) 0 0
\(639\) −3348.00 −0.207269
\(640\) −7759.59 −0.479257
\(641\) −15390.0 −0.948313 −0.474156 0.880441i \(-0.657247\pi\)
−0.474156 + 0.880441i \(0.657247\pi\)
\(642\) −1674.00 −0.102909
\(643\) −12598.0 −0.772654 −0.386327 0.922362i \(-0.626256\pi\)
−0.386327 + 0.922362i \(0.626256\pi\)
\(644\) −24318.0 −1.48799
\(645\) −6235.38 −0.380648
\(646\) 5050.66 0.307609
\(647\) 7131.00 0.433305 0.216653 0.976249i \(-0.430486\pi\)
0.216653 + 0.976249i \(0.430486\pi\)
\(648\) 1122.37 0.0680414
\(649\) 0 0
\(650\) −6600.00 −0.398267
\(651\) −9072.48 −0.546204
\(652\) −6688.00 −0.401721
\(653\) −4890.00 −0.293048 −0.146524 0.989207i \(-0.546809\pi\)
−0.146524 + 0.989207i \(0.546809\pi\)
\(654\) −2448.00 −0.146368
\(655\) 10756.0 0.641638
\(656\) 30761.2 1.83083
\(657\) −8417.77 −0.499861
\(658\) 324.000 0.0191958
\(659\) −4569.15 −0.270089 −0.135045 0.990840i \(-0.543118\pi\)
−0.135045 + 0.990840i \(0.543118\pi\)
\(660\) 0 0
\(661\) −14438.0 −0.849581 −0.424791 0.905292i \(-0.639652\pi\)
−0.424791 + 0.905292i \(0.639652\pi\)
\(662\) 32385.9 1.90138
\(663\) −10692.0 −0.626309
\(664\) −624.000 −0.0364697
\(665\) −4860.00 −0.283403
\(666\) −8542.47 −0.497018
\(667\) −6755.00 −0.392136
\(668\) −10108.2 −0.585479
\(669\) 16314.0 0.942804
\(670\) −1212.44 −0.0699112
\(671\) 0 0
\(672\) −15552.0 −0.892755
\(673\) −10728.3 −0.614482 −0.307241 0.951632i \(-0.599406\pi\)
−0.307241 + 0.951632i \(0.599406\pi\)
\(674\) −11028.0 −0.630241
\(675\) 675.000 0.0384900
\(676\) 14444.0 0.821802
\(677\) −13461.5 −0.764206 −0.382103 0.924120i \(-0.624800\pi\)
−0.382103 + 0.924120i \(0.624800\pi\)
\(678\) 17178.5 0.973061
\(679\) −14653.1 −0.828183
\(680\) −3240.00 −0.182718
\(681\) −6531.56 −0.367533
\(682\) 0 0
\(683\) −4068.00 −0.227903 −0.113951 0.993486i \(-0.536351\pi\)
−0.113951 + 0.993486i \(0.536351\pi\)
\(684\) 1122.37 0.0627410
\(685\) 4605.00 0.256858
\(686\) 30888.0 1.71911
\(687\) 18219.0 1.01179
\(688\) 33255.4 1.84280
\(689\) 228.631 0.0126417
\(690\) −10132.5 −0.559040
\(691\) 3065.00 0.168738 0.0843691 0.996435i \(-0.473113\pi\)
0.0843691 + 0.996435i \(0.473113\pi\)
\(692\) −6983.63 −0.383638
\(693\) 0 0
\(694\) −5094.00 −0.278625
\(695\) −8634.27 −0.471247
\(696\) −1440.00 −0.0784239
\(697\) 17982.0 0.977212
\(698\) −18450.0 −1.00049
\(699\) −4723.30 −0.255582
\(700\) −3117.69 −0.168340
\(701\) −2303.63 −0.124118 −0.0620591 0.998072i \(-0.519767\pi\)
−0.0620591 + 0.998072i \(0.519767\pi\)
\(702\) −7128.00 −0.383232
\(703\) 8542.47 0.458301
\(704\) 0 0
\(705\) 45.0000 0.00240397
\(706\) −40000.0 −2.13232
\(707\) −60264.0 −3.20574
\(708\) −7776.00 −0.412768
\(709\) 13795.0 0.730722 0.365361 0.930866i \(-0.380946\pi\)
0.365361 + 0.930866i \(0.380946\pi\)
\(710\) 6443.23 0.340578
\(711\) −4692.13 −0.247494
\(712\) 15546.9 0.818321
\(713\) 18915.0 0.993510
\(714\) −15152.0 −0.794186
\(715\) 0 0
\(716\) 7992.00 0.417144
\(717\) 18872.4 0.982990
\(718\) −12288.0 −0.638697
\(719\) −23406.0 −1.21404 −0.607021 0.794686i \(-0.707636\pi\)
−0.607021 + 0.794686i \(0.707636\pi\)
\(720\) −3600.00 −0.186339
\(721\) −30179.3 −1.55885
\(722\) 20393.2 1.05118
\(723\) 9773.96 0.502763
\(724\) −18136.0 −0.930966
\(725\) −866.025 −0.0443633
\(726\) 0 0
\(727\) −6518.00 −0.332516 −0.166258 0.986082i \(-0.553168\pi\)
−0.166258 + 0.986082i \(0.553168\pi\)
\(728\) −32922.8 −1.67610
\(729\) 729.000 0.0370370
\(730\) 16200.0 0.821355
\(731\) 19440.0 0.983604
\(732\) 5507.92 0.278113
\(733\) −266.736 −0.0134408 −0.00672040 0.999977i \(-0.502139\pi\)
−0.00672040 + 0.999977i \(0.502139\pi\)
\(734\) −20417.4 −1.02673
\(735\) 9435.00 0.473490
\(736\) 32424.0 1.62386
\(737\) 0 0
\(738\) 11988.0 0.597946
\(739\) 33388.7 1.66201 0.831005 0.556266i \(-0.187766\pi\)
0.831005 + 0.556266i \(0.187766\pi\)
\(740\) 5480.00 0.272228
\(741\) 7128.00 0.353379
\(742\) 324.000 0.0160302
\(743\) −34362.2 −1.69667 −0.848335 0.529460i \(-0.822394\pi\)
−0.848335 + 0.529460i \(0.822394\pi\)
\(744\) 4032.21 0.198694
\(745\) 10080.5 0.495735
\(746\) 13296.0 0.652548
\(747\) −405.300 −0.0198516
\(748\) 0 0
\(749\) −5022.00 −0.244993
\(750\) −1299.04 −0.0632456
\(751\) 6301.00 0.306161 0.153080 0.988214i \(-0.451081\pi\)
0.153080 + 0.988214i \(0.451081\pi\)
\(752\) −240.000 −0.0116382
\(753\) 1980.00 0.0958237
\(754\) 9145.23 0.441710
\(755\) 3871.13 0.186603
\(756\) −3367.11 −0.161985
\(757\) 17026.0 0.817464 0.408732 0.912654i \(-0.365971\pi\)
0.408732 + 0.912654i \(0.365971\pi\)
\(758\) 18813.5 0.901502
\(759\) 0 0
\(760\) 2160.00 0.103094
\(761\) −12574.7 −0.598991 −0.299495 0.954098i \(-0.596818\pi\)
−0.299495 + 0.954098i \(0.596818\pi\)
\(762\) −21384.0 −1.01661
\(763\) −7344.00 −0.348454
\(764\) 11016.0 0.521656
\(765\) −2104.44 −0.0994592
\(766\) −1080.80 −0.0509803
\(767\) −49384.2 −2.32485
\(768\) 14592.0 0.685603
\(769\) 13702.3 0.642543 0.321272 0.946987i \(-0.395890\pi\)
0.321272 + 0.946987i \(0.395890\pi\)
\(770\) 0 0
\(771\) −4923.00 −0.229958
\(772\) 3089.98 0.144055
\(773\) −10155.0 −0.472510 −0.236255 0.971691i \(-0.575920\pi\)
−0.236255 + 0.971691i \(0.575920\pi\)
\(774\) 12960.0 0.601857
\(775\) 2425.00 0.112398
\(776\) 6512.51 0.301270
\(777\) −25627.4 −1.18324
\(778\) −5237.72 −0.241364
\(779\) −11988.0 −0.551367
\(780\) 4572.61 0.209905
\(781\) 0 0
\(782\) 31590.0 1.44457
\(783\) −935.307 −0.0426886
\(784\) −50320.0 −2.29227
\(785\) −18010.0 −0.818859
\(786\) −22356.0 −1.01452
\(787\) −33671.1 −1.52509 −0.762544 0.646937i \(-0.776050\pi\)
−0.762544 + 0.646937i \(0.776050\pi\)
\(788\) 11029.7 0.498625
\(789\) −7674.72 −0.346296
\(790\) 9030.00 0.406675
\(791\) 51535.4 2.31655
\(792\) 0 0
\(793\) 34980.0 1.56643
\(794\) 35368.5 1.58083
\(795\) 45.0000 0.00200753
\(796\) −2924.00 −0.130199
\(797\) 14106.0 0.626926 0.313463 0.949600i \(-0.398511\pi\)
0.313463 + 0.949600i \(0.398511\pi\)
\(798\) 10101.3 0.448099
\(799\) −140.296 −0.00621191
\(800\) 4156.92 0.183712
\(801\) 10098.0 0.445437
\(802\) 35915.8 1.58134
\(803\) 0 0
\(804\) 840.000 0.0368464
\(805\) −30397.5 −1.33090
\(806\) −25608.0 −1.11911
\(807\) 180.000 0.00785167
\(808\) 26784.0 1.16616
\(809\) −533.472 −0.0231840 −0.0115920 0.999933i \(-0.503690\pi\)
−0.0115920 + 0.999933i \(0.503690\pi\)
\(810\) −1402.96 −0.0608581
\(811\) 12870.9 0.557284 0.278642 0.960395i \(-0.410116\pi\)
0.278642 + 0.960395i \(0.410116\pi\)
\(812\) 4320.00 0.186702
\(813\) −8454.14 −0.364698
\(814\) 0 0
\(815\) −8360.00 −0.359310
\(816\) 11223.7 0.481505
\(817\) −12960.0 −0.554973
\(818\) −54078.0 −2.31148
\(819\) −21384.0 −0.912353
\(820\) −7690.31 −0.327509
\(821\) 2975.66 0.126494 0.0632469 0.997998i \(-0.479854\pi\)
0.0632469 + 0.997998i \(0.479854\pi\)
\(822\) −9571.31 −0.406129
\(823\) −3664.00 −0.155187 −0.0775936 0.996985i \(-0.524724\pi\)
−0.0775936 + 0.996985i \(0.524724\pi\)
\(824\) 13413.0 0.567068
\(825\) 0 0
\(826\) −69984.0 −2.94801
\(827\) −31547.6 −1.32650 −0.663251 0.748397i \(-0.730824\pi\)
−0.663251 + 0.748397i \(0.730824\pi\)
\(828\) 7020.00 0.294640
\(829\) −24829.0 −1.04023 −0.520113 0.854098i \(-0.674110\pi\)
−0.520113 + 0.854098i \(0.674110\pi\)
\(830\) 780.000 0.0326195
\(831\) 12616.3 0.526658
\(832\) 4877.46 0.203240
\(833\) −29415.4 −1.22351
\(834\) 17946.0 0.745107
\(835\) −12635.3 −0.523668
\(836\) 0 0
\(837\) 2619.00 0.108155
\(838\) −30491.0 −1.25692
\(839\) −6048.00 −0.248868 −0.124434 0.992228i \(-0.539711\pi\)
−0.124434 + 0.992228i \(0.539711\pi\)
\(840\) −6480.00 −0.266168
\(841\) −23189.0 −0.950797
\(842\) 8788.43 0.359702
\(843\) 15661.2 0.639858
\(844\) −8279.20 −0.337656
\(845\) 18055.0 0.735042
\(846\) −93.5307 −0.00380101
\(847\) 0 0
\(848\) −240.000 −0.00971891
\(849\) 12231.7 0.494455
\(850\) 4050.00 0.163428
\(851\) 53430.0 2.15224
\(852\) −4464.00 −0.179500
\(853\) −11656.7 −0.467899 −0.233950 0.972249i \(-0.575165\pi\)
−0.233950 + 0.972249i \(0.575165\pi\)
\(854\) 49571.3 1.98629
\(855\) 1402.96 0.0561173
\(856\) 2232.00 0.0891217
\(857\) 33198.2 1.32325 0.661627 0.749833i \(-0.269866\pi\)
0.661627 + 0.749833i \(0.269866\pi\)
\(858\) 0 0
\(859\) 16196.0 0.643307 0.321653 0.946858i \(-0.395761\pi\)
0.321653 + 0.946858i \(0.395761\pi\)
\(860\) −8313.84 −0.329651
\(861\) 35964.0 1.42352
\(862\) −13248.0 −0.523467
\(863\) 10728.0 0.423158 0.211579 0.977361i \(-0.432139\pi\)
0.211579 + 0.977361i \(0.432139\pi\)
\(864\) 4489.48 0.176777
\(865\) −8729.54 −0.343137
\(866\) 41583.1 1.63170
\(867\) −8178.00 −0.320345
\(868\) −12096.6 −0.473026
\(869\) 0 0
\(870\) 1800.00 0.0701445
\(871\) 5334.72 0.207532
\(872\) 3264.00 0.126758
\(873\) 4230.00 0.163991
\(874\) −21060.0 −0.815063
\(875\) −3897.11 −0.150567
\(876\) −11223.7 −0.432892
\(877\) 47392.4 1.82477 0.912387 0.409329i \(-0.134237\pi\)
0.912387 + 0.409329i \(0.134237\pi\)
\(878\) −45474.0 −1.74792
\(879\) 19729.8 0.757075
\(880\) 0 0
\(881\) 20664.0 0.790225 0.395112 0.918633i \(-0.370706\pi\)
0.395112 + 0.918633i \(0.370706\pi\)
\(882\) −19610.3 −0.748654
\(883\) 27532.0 1.04929 0.524646 0.851320i \(-0.324198\pi\)
0.524646 + 0.851320i \(0.324198\pi\)
\(884\) −14256.0 −0.542400
\(885\) −9720.00 −0.369191
\(886\) −5404.00 −0.204911
\(887\) 29822.5 1.12891 0.564453 0.825465i \(-0.309087\pi\)
0.564453 + 0.825465i \(0.309087\pi\)
\(888\) 11390.0 0.430430
\(889\) −64152.0 −2.42024
\(890\) −19433.6 −0.731928
\(891\) 0 0
\(892\) 21752.0 0.816492
\(893\) 93.5307 0.00350491
\(894\) −20952.0 −0.783825
\(895\) 9990.00 0.373105
\(896\) 48384.0 1.80401
\(897\) 44583.0 1.65951
\(898\) −37724.1 −1.40186
\(899\) −3360.18 −0.124659
\(900\) 900.000 0.0333333
\(901\) −140.296 −0.00518750
\(902\) 0 0
\(903\) 38880.0 1.43283
\(904\) −22904.6 −0.842696
\(905\) −22670.0 −0.832681
\(906\) −8046.00 −0.295045
\(907\) −6406.00 −0.234518 −0.117259 0.993101i \(-0.537411\pi\)
−0.117259 + 0.993101i \(0.537411\pi\)
\(908\) −8708.75 −0.318293
\(909\) 17396.7 0.634777
\(910\) 41153.5 1.49915
\(911\) 35046.0 1.27456 0.637281 0.770632i \(-0.280059\pi\)
0.637281 + 0.770632i \(0.280059\pi\)
\(912\) −7482.46 −0.271677
\(913\) 0 0
\(914\) −61476.0 −2.22478
\(915\) 6884.90 0.248752
\(916\) 24292.0 0.876234
\(917\) −67068.0 −2.41525
\(918\) 4374.00 0.157259
\(919\) 23801.8 0.854353 0.427176 0.904168i \(-0.359508\pi\)
0.427176 + 0.904168i \(0.359508\pi\)
\(920\) 13510.0 0.484143
\(921\) −20358.5 −0.728378
\(922\) −35592.0 −1.27132
\(923\) −28350.2 −1.01101
\(924\) 0 0
\(925\) 6850.00 0.243488
\(926\) −31100.7 −1.10371
\(927\) 8712.00 0.308673
\(928\) −5760.00 −0.203751
\(929\) −42558.0 −1.50300 −0.751498 0.659736i \(-0.770668\pi\)
−0.751498 + 0.659736i \(0.770668\pi\)
\(930\) −5040.27 −0.177717
\(931\) 19610.3 0.690334
\(932\) −6297.74 −0.221340
\(933\) 8802.00 0.308858
\(934\) −31561.4 −1.10570
\(935\) 0 0
\(936\) 9504.00 0.331889
\(937\) −10049.4 −0.350372 −0.175186 0.984535i \(-0.556053\pi\)
−0.175186 + 0.984535i \(0.556053\pi\)
\(938\) 7560.00 0.263159
\(939\) 21540.0 0.748596
\(940\) 60.0000 0.00208190
\(941\) 13343.7 0.462267 0.231133 0.972922i \(-0.425757\pi\)
0.231133 + 0.972922i \(0.425757\pi\)
\(942\) 37433.1 1.29473
\(943\) −74980.5 −2.58929
\(944\) 51840.0 1.78734
\(945\) −4208.88 −0.144884
\(946\) 0 0
\(947\) −1899.00 −0.0651628 −0.0325814 0.999469i \(-0.510373\pi\)
−0.0325814 + 0.999469i \(0.510373\pi\)
\(948\) −6256.17 −0.214336
\(949\) −71280.0 −2.43819
\(950\) −2700.00 −0.0922101
\(951\) 23139.0 0.788994
\(952\) 20202.6 0.687785
\(953\) −25766.0 −0.875805 −0.437903 0.899022i \(-0.644279\pi\)
−0.437903 + 0.899022i \(0.644279\pi\)
\(954\) −93.5307 −0.00317418
\(955\) 13770.0 0.466583
\(956\) 25163.2 0.851294
\(957\) 0 0
\(958\) −45816.0 −1.54514
\(959\) −28713.9 −0.966863
\(960\) 960.000 0.0322749
\(961\) −20382.0 −0.684166
\(962\) −72336.0 −2.42433
\(963\) 1449.73 0.0485117
\(964\) 13032.0 0.435405
\(965\) 3862.47 0.128847
\(966\) 63180.0 2.10433
\(967\) −45005.6 −1.49667 −0.748336 0.663319i \(-0.769147\pi\)
−0.748336 + 0.663319i \(0.769147\pi\)
\(968\) 0 0
\(969\) −4374.00 −0.145008
\(970\) −8140.64 −0.269464
\(971\) −51840.0 −1.71331 −0.856655 0.515889i \(-0.827462\pi\)
−0.856655 + 0.515889i \(0.827462\pi\)
\(972\) 972.000 0.0320750
\(973\) 53838.0 1.77386
\(974\) 31869.7 1.04843
\(975\) 5715.77 0.187745
\(976\) −36719.5 −1.20426
\(977\) −17133.0 −0.561037 −0.280519 0.959849i \(-0.590506\pi\)
−0.280519 + 0.959849i \(0.590506\pi\)
\(978\) 17375.9 0.568120
\(979\) 0 0
\(980\) 12580.0 0.410054
\(981\) 2120.03 0.0689983
\(982\) −4056.00 −0.131805
\(983\) 11241.0 0.364733 0.182366 0.983231i \(-0.441624\pi\)
0.182366 + 0.983231i \(0.441624\pi\)
\(984\) −15984.0 −0.517837
\(985\) 13787.1 0.445984
\(986\) −5611.84 −0.181255
\(987\) −280.592 −0.00904899
\(988\) 9504.00 0.306035
\(989\) −81060.0 −2.60623
\(990\) 0 0
\(991\) −14567.0 −0.466938 −0.233469 0.972364i \(-0.575008\pi\)
−0.233469 + 0.972364i \(0.575008\pi\)
\(992\) 16128.9 0.516221
\(993\) −28047.0 −0.896319
\(994\) −40176.0 −1.28200
\(995\) −3655.00 −0.116454
\(996\) −540.400 −0.0171920
\(997\) −29874.4 −0.948979 −0.474490 0.880261i \(-0.657367\pi\)
−0.474490 + 0.880261i \(0.657367\pi\)
\(998\) 13413.0 0.425432
\(999\) 7398.00 0.234297
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 1815.4.a.l.1.1 2
11.10 odd 2 inner 1815.4.a.l.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1815.4.a.l.1.1 2 1.1 even 1 trivial
1815.4.a.l.1.2 yes 2 11.10 odd 2 inner