Properties

Label 320.6.a.x.1.2
Level 320
Weight 6
Character 320.1
Self dual yes
Analytic conductor 51.323
Analytic rank 0
Dimension 3
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.3228223402\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.39180.1
Defining polynomial: \(x^{3} - x^{2} - 36 x - 24\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 160)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.688934\) of defining polynomial
Character \(\chi\) \(=\) 320.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.755735 q^{3} +25.0000 q^{5} -172.424 q^{7} -242.429 q^{9} +O(q^{10})\) \(q+0.755735 q^{3} +25.0000 q^{5} -172.424 q^{7} -242.429 q^{9} -391.540 q^{11} -149.245 q^{13} +18.8934 q^{15} +1187.74 q^{17} -685.033 q^{19} -130.307 q^{21} +996.236 q^{23} +625.000 q^{25} -366.856 q^{27} +8769.13 q^{29} +9525.61 q^{31} -295.901 q^{33} -4310.61 q^{35} -10226.8 q^{37} -112.790 q^{39} +32.6496 q^{41} -10321.5 q^{43} -6060.72 q^{45} +16931.7 q^{47} +12923.1 q^{49} +897.614 q^{51} +22287.0 q^{53} -9788.50 q^{55} -517.704 q^{57} -44251.2 q^{59} +21743.1 q^{61} +41800.6 q^{63} -3731.13 q^{65} -20709.0 q^{67} +752.891 q^{69} +15379.5 q^{71} +57995.4 q^{73} +472.335 q^{75} +67511.0 q^{77} -62466.5 q^{79} +58633.0 q^{81} +43578.7 q^{83} +29693.4 q^{85} +6627.14 q^{87} +66297.9 q^{89} +25733.5 q^{91} +7198.84 q^{93} -17125.8 q^{95} -12264.3 q^{97} +94920.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 10q^{3} + 75q^{5} - 6q^{7} + 467q^{9} + O(q^{10}) \) \( 3q - 10q^{3} + 75q^{5} - 6q^{7} + 467q^{9} + 396q^{11} + 354q^{13} - 250q^{15} + 1158q^{17} - 3192q^{19} + 820q^{21} + 6126q^{23} + 1875q^{25} - 13804q^{27} - 426q^{29} + 3276q^{31} - 2408q^{33} - 150q^{35} + 11562q^{37} + 21348q^{39} + 12450q^{41} - 26346q^{43} + 11675q^{45} + 36762q^{47} - 3849q^{49} - 71444q^{51} + 21162q^{53} + 9900q^{55} + 69136q^{57} - 35040q^{59} + 24138q^{61} + 80986q^{63} + 8850q^{65} + 9570q^{67} + 27036q^{69} + 88092q^{71} + 66750q^{73} - 6250q^{75} + 136488q^{77} - 92952q^{79} + 151391q^{81} - 30258q^{83} + 28950q^{85} - 26228q^{87} + 172686q^{89} + 106812q^{91} + 318232q^{93} - 79800q^{95} + 170910q^{97} + 351436q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.755735 0.0484804 0.0242402 0.999706i \(-0.492283\pi\)
0.0242402 + 0.999706i \(0.492283\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) −172.424 −1.33001 −0.665003 0.746841i \(-0.731570\pi\)
−0.665003 + 0.746841i \(0.731570\pi\)
\(8\) 0 0
\(9\) −242.429 −0.997650
\(10\) 0 0
\(11\) −391.540 −0.975651 −0.487825 0.872941i \(-0.662210\pi\)
−0.487825 + 0.872941i \(0.662210\pi\)
\(12\) 0 0
\(13\) −149.245 −0.244930 −0.122465 0.992473i \(-0.539080\pi\)
−0.122465 + 0.992473i \(0.539080\pi\)
\(14\) 0 0
\(15\) 18.8934 0.0216811
\(16\) 0 0
\(17\) 1187.74 0.996776 0.498388 0.866954i \(-0.333925\pi\)
0.498388 + 0.866954i \(0.333925\pi\)
\(18\) 0 0
\(19\) −685.033 −0.435339 −0.217670 0.976023i \(-0.569845\pi\)
−0.217670 + 0.976023i \(0.569845\pi\)
\(20\) 0 0
\(21\) −130.307 −0.0644792
\(22\) 0 0
\(23\) 996.236 0.392684 0.196342 0.980536i \(-0.437094\pi\)
0.196342 + 0.980536i \(0.437094\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) −366.856 −0.0968469
\(28\) 0 0
\(29\) 8769.13 1.93625 0.968125 0.250466i \(-0.0805839\pi\)
0.968125 + 0.250466i \(0.0805839\pi\)
\(30\) 0 0
\(31\) 9525.61 1.78028 0.890140 0.455686i \(-0.150606\pi\)
0.890140 + 0.455686i \(0.150606\pi\)
\(32\) 0 0
\(33\) −295.901 −0.0473000
\(34\) 0 0
\(35\) −4310.61 −0.594796
\(36\) 0 0
\(37\) −10226.8 −1.22811 −0.614054 0.789264i \(-0.710462\pi\)
−0.614054 + 0.789264i \(0.710462\pi\)
\(38\) 0 0
\(39\) −112.790 −0.0118743
\(40\) 0 0
\(41\) 32.6496 0.00303332 0.00151666 0.999999i \(-0.499517\pi\)
0.00151666 + 0.999999i \(0.499517\pi\)
\(42\) 0 0
\(43\) −10321.5 −0.851279 −0.425639 0.904893i \(-0.639951\pi\)
−0.425639 + 0.904893i \(0.639951\pi\)
\(44\) 0 0
\(45\) −6060.72 −0.446162
\(46\) 0 0
\(47\) 16931.7 1.11804 0.559018 0.829156i \(-0.311178\pi\)
0.559018 + 0.829156i \(0.311178\pi\)
\(48\) 0 0
\(49\) 12923.1 0.768914
\(50\) 0 0
\(51\) 897.614 0.0483242
\(52\) 0 0
\(53\) 22287.0 1.08984 0.544919 0.838489i \(-0.316561\pi\)
0.544919 + 0.838489i \(0.316561\pi\)
\(54\) 0 0
\(55\) −9788.50 −0.436324
\(56\) 0 0
\(57\) −517.704 −0.0211054
\(58\) 0 0
\(59\) −44251.2 −1.65499 −0.827494 0.561474i \(-0.810234\pi\)
−0.827494 + 0.561474i \(0.810234\pi\)
\(60\) 0 0
\(61\) 21743.1 0.748165 0.374083 0.927395i \(-0.377958\pi\)
0.374083 + 0.927395i \(0.377958\pi\)
\(62\) 0 0
\(63\) 41800.6 1.32688
\(64\) 0 0
\(65\) −3731.13 −0.109536
\(66\) 0 0
\(67\) −20709.0 −0.563600 −0.281800 0.959473i \(-0.590932\pi\)
−0.281800 + 0.959473i \(0.590932\pi\)
\(68\) 0 0
\(69\) 752.891 0.0190375
\(70\) 0 0
\(71\) 15379.5 0.362073 0.181037 0.983476i \(-0.442055\pi\)
0.181037 + 0.983476i \(0.442055\pi\)
\(72\) 0 0
\(73\) 57995.4 1.27376 0.636878 0.770964i \(-0.280225\pi\)
0.636878 + 0.770964i \(0.280225\pi\)
\(74\) 0 0
\(75\) 472.335 0.00969609
\(76\) 0 0
\(77\) 67511.0 1.29762
\(78\) 0 0
\(79\) −62466.5 −1.12611 −0.563054 0.826420i \(-0.690374\pi\)
−0.563054 + 0.826420i \(0.690374\pi\)
\(80\) 0 0
\(81\) 58633.0 0.992954
\(82\) 0 0
\(83\) 43578.7 0.694351 0.347175 0.937800i \(-0.387141\pi\)
0.347175 + 0.937800i \(0.387141\pi\)
\(84\) 0 0
\(85\) 29693.4 0.445772
\(86\) 0 0
\(87\) 6627.14 0.0938703
\(88\) 0 0
\(89\) 66297.9 0.887207 0.443603 0.896223i \(-0.353700\pi\)
0.443603 + 0.896223i \(0.353700\pi\)
\(90\) 0 0
\(91\) 25733.5 0.325758
\(92\) 0 0
\(93\) 7198.84 0.0863088
\(94\) 0 0
\(95\) −17125.8 −0.194690
\(96\) 0 0
\(97\) −12264.3 −0.132346 −0.0661732 0.997808i \(-0.521079\pi\)
−0.0661732 + 0.997808i \(0.521079\pi\)
\(98\) 0 0
\(99\) 94920.6 0.973358
\(100\) 0 0
\(101\) 37376.8 0.364584 0.182292 0.983244i \(-0.441648\pi\)
0.182292 + 0.983244i \(0.441648\pi\)
\(102\) 0 0
\(103\) 41642.9 0.386765 0.193383 0.981123i \(-0.438054\pi\)
0.193383 + 0.981123i \(0.438054\pi\)
\(104\) 0 0
\(105\) −3257.68 −0.0288360
\(106\) 0 0
\(107\) 69664.7 0.588239 0.294119 0.955769i \(-0.404974\pi\)
0.294119 + 0.955769i \(0.404974\pi\)
\(108\) 0 0
\(109\) 88554.2 0.713909 0.356954 0.934122i \(-0.383815\pi\)
0.356954 + 0.934122i \(0.383815\pi\)
\(110\) 0 0
\(111\) −7728.78 −0.0595392
\(112\) 0 0
\(113\) 77809.3 0.573239 0.286619 0.958045i \(-0.407469\pi\)
0.286619 + 0.958045i \(0.407469\pi\)
\(114\) 0 0
\(115\) 24905.9 0.175613
\(116\) 0 0
\(117\) 36181.4 0.244355
\(118\) 0 0
\(119\) −204795. −1.32572
\(120\) 0 0
\(121\) −7747.38 −0.0481051
\(122\) 0 0
\(123\) 24.6744 0.000147057 0
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −294580. −1.62067 −0.810333 0.585970i \(-0.800714\pi\)
−0.810333 + 0.585970i \(0.800714\pi\)
\(128\) 0 0
\(129\) −7800.32 −0.0412704
\(130\) 0 0
\(131\) −173565. −0.883658 −0.441829 0.897099i \(-0.645670\pi\)
−0.441829 + 0.897099i \(0.645670\pi\)
\(132\) 0 0
\(133\) 118116. 0.579003
\(134\) 0 0
\(135\) −9171.39 −0.0433113
\(136\) 0 0
\(137\) 346072. 1.57531 0.787653 0.616119i \(-0.211296\pi\)
0.787653 + 0.616119i \(0.211296\pi\)
\(138\) 0 0
\(139\) 329344. 1.44581 0.722907 0.690945i \(-0.242805\pi\)
0.722907 + 0.690945i \(0.242805\pi\)
\(140\) 0 0
\(141\) 12795.9 0.0542029
\(142\) 0 0
\(143\) 58435.5 0.238966
\(144\) 0 0
\(145\) 219228. 0.865918
\(146\) 0 0
\(147\) 9766.47 0.0372773
\(148\) 0 0
\(149\) −83495.2 −0.308103 −0.154052 0.988063i \(-0.549232\pi\)
−0.154052 + 0.988063i \(0.549232\pi\)
\(150\) 0 0
\(151\) −155105. −0.553585 −0.276792 0.960930i \(-0.589271\pi\)
−0.276792 + 0.960930i \(0.589271\pi\)
\(152\) 0 0
\(153\) −287941. −0.994433
\(154\) 0 0
\(155\) 238140. 0.796166
\(156\) 0 0
\(157\) 60634.6 0.196323 0.0981615 0.995170i \(-0.468704\pi\)
0.0981615 + 0.995170i \(0.468704\pi\)
\(158\) 0 0
\(159\) 16843.1 0.0528358
\(160\) 0 0
\(161\) −171775. −0.522271
\(162\) 0 0
\(163\) −528292. −1.55742 −0.778708 0.627387i \(-0.784125\pi\)
−0.778708 + 0.627387i \(0.784125\pi\)
\(164\) 0 0
\(165\) −7397.52 −0.0211532
\(166\) 0 0
\(167\) 681927. 1.89211 0.946056 0.324002i \(-0.105029\pi\)
0.946056 + 0.324002i \(0.105029\pi\)
\(168\) 0 0
\(169\) −349019. −0.940009
\(170\) 0 0
\(171\) 166072. 0.434316
\(172\) 0 0
\(173\) 148111. 0.376245 0.188122 0.982146i \(-0.439760\pi\)
0.188122 + 0.982146i \(0.439760\pi\)
\(174\) 0 0
\(175\) −107765. −0.266001
\(176\) 0 0
\(177\) −33442.2 −0.0802346
\(178\) 0 0
\(179\) 650289. 1.51696 0.758480 0.651697i \(-0.225942\pi\)
0.758480 + 0.651697i \(0.225942\pi\)
\(180\) 0 0
\(181\) −315052. −0.714803 −0.357401 0.933951i \(-0.616337\pi\)
−0.357401 + 0.933951i \(0.616337\pi\)
\(182\) 0 0
\(183\) 16432.1 0.0362714
\(184\) 0 0
\(185\) −255671. −0.549227
\(186\) 0 0
\(187\) −465046. −0.972506
\(188\) 0 0
\(189\) 63254.8 0.128807
\(190\) 0 0
\(191\) 851610. 1.68911 0.844554 0.535471i \(-0.179866\pi\)
0.844554 + 0.535471i \(0.179866\pi\)
\(192\) 0 0
\(193\) 916910. 1.77188 0.885938 0.463804i \(-0.153516\pi\)
0.885938 + 0.463804i \(0.153516\pi\)
\(194\) 0 0
\(195\) −2819.75 −0.00531036
\(196\) 0 0
\(197\) −595345. −1.09296 −0.546479 0.837473i \(-0.684032\pi\)
−0.546479 + 0.837473i \(0.684032\pi\)
\(198\) 0 0
\(199\) −159504. −0.285522 −0.142761 0.989757i \(-0.545598\pi\)
−0.142761 + 0.989757i \(0.545598\pi\)
\(200\) 0 0
\(201\) −15650.5 −0.0273236
\(202\) 0 0
\(203\) −1.51201e6 −2.57522
\(204\) 0 0
\(205\) 816.239 0.00135654
\(206\) 0 0
\(207\) −241516. −0.391761
\(208\) 0 0
\(209\) 268218. 0.424739
\(210\) 0 0
\(211\) −776648. −1.20093 −0.600466 0.799650i \(-0.705018\pi\)
−0.600466 + 0.799650i \(0.705018\pi\)
\(212\) 0 0
\(213\) 11622.8 0.0175535
\(214\) 0 0
\(215\) −258038. −0.380703
\(216\) 0 0
\(217\) −1.64245e6 −2.36778
\(218\) 0 0
\(219\) 43829.2 0.0617523
\(220\) 0 0
\(221\) −177264. −0.244141
\(222\) 0 0
\(223\) 969846. 1.30599 0.652996 0.757361i \(-0.273512\pi\)
0.652996 + 0.757361i \(0.273512\pi\)
\(224\) 0 0
\(225\) −151518. −0.199530
\(226\) 0 0
\(227\) −32926.6 −0.0424113 −0.0212057 0.999775i \(-0.506750\pi\)
−0.0212057 + 0.999775i \(0.506750\pi\)
\(228\) 0 0
\(229\) −730255. −0.920208 −0.460104 0.887865i \(-0.652188\pi\)
−0.460104 + 0.887865i \(0.652188\pi\)
\(230\) 0 0
\(231\) 51020.5 0.0629092
\(232\) 0 0
\(233\) −550888. −0.664774 −0.332387 0.943143i \(-0.607854\pi\)
−0.332387 + 0.943143i \(0.607854\pi\)
\(234\) 0 0
\(235\) 423292. 0.500001
\(236\) 0 0
\(237\) −47208.2 −0.0545942
\(238\) 0 0
\(239\) −996266. −1.12819 −0.564093 0.825711i \(-0.690774\pi\)
−0.564093 + 0.825711i \(0.690774\pi\)
\(240\) 0 0
\(241\) −953235. −1.05720 −0.528600 0.848871i \(-0.677283\pi\)
−0.528600 + 0.848871i \(0.677283\pi\)
\(242\) 0 0
\(243\) 133457. 0.144986
\(244\) 0 0
\(245\) 323078. 0.343869
\(246\) 0 0
\(247\) 102238. 0.106628
\(248\) 0 0
\(249\) 32933.9 0.0336624
\(250\) 0 0
\(251\) −780609. −0.782077 −0.391038 0.920374i \(-0.627884\pi\)
−0.391038 + 0.920374i \(0.627884\pi\)
\(252\) 0 0
\(253\) −390066. −0.383122
\(254\) 0 0
\(255\) 22440.4 0.0216112
\(256\) 0 0
\(257\) −340539. −0.321614 −0.160807 0.986986i \(-0.551410\pi\)
−0.160807 + 0.986986i \(0.551410\pi\)
\(258\) 0 0
\(259\) 1.76335e6 1.63339
\(260\) 0 0
\(261\) −2.12589e6 −1.93170
\(262\) 0 0
\(263\) 2.05298e6 1.83018 0.915092 0.403246i \(-0.132118\pi\)
0.915092 + 0.403246i \(0.132118\pi\)
\(264\) 0 0
\(265\) 557175. 0.487390
\(266\) 0 0
\(267\) 50103.7 0.0430122
\(268\) 0 0
\(269\) −98629.8 −0.0831050 −0.0415525 0.999136i \(-0.513230\pi\)
−0.0415525 + 0.999136i \(0.513230\pi\)
\(270\) 0 0
\(271\) 1.17220e6 0.969565 0.484783 0.874635i \(-0.338899\pi\)
0.484783 + 0.874635i \(0.338899\pi\)
\(272\) 0 0
\(273\) 19447.7 0.0157929
\(274\) 0 0
\(275\) −244713. −0.195130
\(276\) 0 0
\(277\) −1.13901e6 −0.891923 −0.445962 0.895052i \(-0.647138\pi\)
−0.445962 + 0.895052i \(0.647138\pi\)
\(278\) 0 0
\(279\) −2.30928e6 −1.77610
\(280\) 0 0
\(281\) −1.33128e6 −1.00578 −0.502889 0.864351i \(-0.667730\pi\)
−0.502889 + 0.864351i \(0.667730\pi\)
\(282\) 0 0
\(283\) 921840. 0.684210 0.342105 0.939662i \(-0.388860\pi\)
0.342105 + 0.939662i \(0.388860\pi\)
\(284\) 0 0
\(285\) −12942.6 −0.00943864
\(286\) 0 0
\(287\) −5629.58 −0.00403433
\(288\) 0 0
\(289\) −9140.20 −0.00643741
\(290\) 0 0
\(291\) −9268.54 −0.00641621
\(292\) 0 0
\(293\) 1.64240e6 1.11766 0.558831 0.829281i \(-0.311250\pi\)
0.558831 + 0.829281i \(0.311250\pi\)
\(294\) 0 0
\(295\) −1.10628e6 −0.740134
\(296\) 0 0
\(297\) 143639. 0.0944888
\(298\) 0 0
\(299\) −148684. −0.0961801
\(300\) 0 0
\(301\) 1.77968e6 1.13221
\(302\) 0 0
\(303\) 28246.9 0.0176752
\(304\) 0 0
\(305\) 543578. 0.334590
\(306\) 0 0
\(307\) 810866. 0.491025 0.245512 0.969393i \(-0.421044\pi\)
0.245512 + 0.969393i \(0.421044\pi\)
\(308\) 0 0
\(309\) 31471.0 0.0187506
\(310\) 0 0
\(311\) −1.67678e6 −0.983050 −0.491525 0.870864i \(-0.663560\pi\)
−0.491525 + 0.870864i \(0.663560\pi\)
\(312\) 0 0
\(313\) 1.43902e6 0.830242 0.415121 0.909766i \(-0.363739\pi\)
0.415121 + 0.909766i \(0.363739\pi\)
\(314\) 0 0
\(315\) 1.04502e6 0.593398
\(316\) 0 0
\(317\) −783839. −0.438105 −0.219053 0.975713i \(-0.570297\pi\)
−0.219053 + 0.975713i \(0.570297\pi\)
\(318\) 0 0
\(319\) −3.43347e6 −1.88910
\(320\) 0 0
\(321\) 52648.1 0.0285181
\(322\) 0 0
\(323\) −813639. −0.433936
\(324\) 0 0
\(325\) −93278.3 −0.0489860
\(326\) 0 0
\(327\) 66923.5 0.0346106
\(328\) 0 0
\(329\) −2.91943e6 −1.48699
\(330\) 0 0
\(331\) 3.30343e6 1.65728 0.828638 0.559785i \(-0.189116\pi\)
0.828638 + 0.559785i \(0.189116\pi\)
\(332\) 0 0
\(333\) 2.47928e6 1.22522
\(334\) 0 0
\(335\) −517724. −0.252050
\(336\) 0 0
\(337\) 2.17037e6 1.04102 0.520510 0.853856i \(-0.325742\pi\)
0.520510 + 0.853856i \(0.325742\pi\)
\(338\) 0 0
\(339\) 58803.2 0.0277909
\(340\) 0 0
\(341\) −3.72966e6 −1.73693
\(342\) 0 0
\(343\) 669673. 0.307346
\(344\) 0 0
\(345\) 18822.3 0.00851382
\(346\) 0 0
\(347\) −1.26327e6 −0.563215 −0.281607 0.959530i \(-0.590868\pi\)
−0.281607 + 0.959530i \(0.590868\pi\)
\(348\) 0 0
\(349\) 1.84682e6 0.811636 0.405818 0.913954i \(-0.366987\pi\)
0.405818 + 0.913954i \(0.366987\pi\)
\(350\) 0 0
\(351\) 54751.5 0.0237207
\(352\) 0 0
\(353\) 3.82123e6 1.63217 0.816087 0.577929i \(-0.196139\pi\)
0.816087 + 0.577929i \(0.196139\pi\)
\(354\) 0 0
\(355\) 384488. 0.161924
\(356\) 0 0
\(357\) −154770. −0.0642714
\(358\) 0 0
\(359\) 1.71131e6 0.700798 0.350399 0.936600i \(-0.386046\pi\)
0.350399 + 0.936600i \(0.386046\pi\)
\(360\) 0 0
\(361\) −2.00683e6 −0.810480
\(362\) 0 0
\(363\) −5854.97 −0.00233216
\(364\) 0 0
\(365\) 1.44989e6 0.569641
\(366\) 0 0
\(367\) −1.72599e6 −0.668919 −0.334460 0.942410i \(-0.608554\pi\)
−0.334460 + 0.942410i \(0.608554\pi\)
\(368\) 0 0
\(369\) −7915.20 −0.00302619
\(370\) 0 0
\(371\) −3.84282e6 −1.44949
\(372\) 0 0
\(373\) −732009. −0.272423 −0.136212 0.990680i \(-0.543493\pi\)
−0.136212 + 0.990680i \(0.543493\pi\)
\(374\) 0 0
\(375\) 11808.4 0.00433622
\(376\) 0 0
\(377\) −1.30875e6 −0.474246
\(378\) 0 0
\(379\) 3.07751e6 1.10053 0.550264 0.834991i \(-0.314527\pi\)
0.550264 + 0.834991i \(0.314527\pi\)
\(380\) 0 0
\(381\) −222624. −0.0785706
\(382\) 0 0
\(383\) 1.26468e6 0.440540 0.220270 0.975439i \(-0.429306\pi\)
0.220270 + 0.975439i \(0.429306\pi\)
\(384\) 0 0
\(385\) 1.68778e6 0.580314
\(386\) 0 0
\(387\) 2.50223e6 0.849278
\(388\) 0 0
\(389\) −3.65533e6 −1.22476 −0.612382 0.790562i \(-0.709788\pi\)
−0.612382 + 0.790562i \(0.709788\pi\)
\(390\) 0 0
\(391\) 1.18327e6 0.391418
\(392\) 0 0
\(393\) −131169. −0.0428401
\(394\) 0 0
\(395\) −1.56166e6 −0.503610
\(396\) 0 0
\(397\) 4.99465e6 1.59048 0.795241 0.606294i \(-0.207345\pi\)
0.795241 + 0.606294i \(0.207345\pi\)
\(398\) 0 0
\(399\) 89264.7 0.0280703
\(400\) 0 0
\(401\) 298037. 0.0925570 0.0462785 0.998929i \(-0.485264\pi\)
0.0462785 + 0.998929i \(0.485264\pi\)
\(402\) 0 0
\(403\) −1.42165e6 −0.436045
\(404\) 0 0
\(405\) 1.46582e6 0.444063
\(406\) 0 0
\(407\) 4.00421e6 1.19821
\(408\) 0 0
\(409\) 3.26110e6 0.963954 0.481977 0.876184i \(-0.339919\pi\)
0.481977 + 0.876184i \(0.339919\pi\)
\(410\) 0 0
\(411\) 261539. 0.0763715
\(412\) 0 0
\(413\) 7.62998e6 2.20114
\(414\) 0 0
\(415\) 1.08947e6 0.310523
\(416\) 0 0
\(417\) 248897. 0.0700937
\(418\) 0 0
\(419\) −1.24623e6 −0.346786 −0.173393 0.984853i \(-0.555473\pi\)
−0.173393 + 0.984853i \(0.555473\pi\)
\(420\) 0 0
\(421\) 1.88625e6 0.518674 0.259337 0.965787i \(-0.416496\pi\)
0.259337 + 0.965787i \(0.416496\pi\)
\(422\) 0 0
\(423\) −4.10473e6 −1.11541
\(424\) 0 0
\(425\) 742335. 0.199355
\(426\) 0 0
\(427\) −3.74905e6 −0.995064
\(428\) 0 0
\(429\) 44161.8 0.0115852
\(430\) 0 0
\(431\) 3.30534e6 0.857082 0.428541 0.903522i \(-0.359028\pi\)
0.428541 + 0.903522i \(0.359028\pi\)
\(432\) 0 0
\(433\) 7.61270e6 1.95128 0.975639 0.219384i \(-0.0704048\pi\)
0.975639 + 0.219384i \(0.0704048\pi\)
\(434\) 0 0
\(435\) 165679. 0.0419801
\(436\) 0 0
\(437\) −682455. −0.170951
\(438\) 0 0
\(439\) 5.45916e6 1.35196 0.675982 0.736918i \(-0.263720\pi\)
0.675982 + 0.736918i \(0.263720\pi\)
\(440\) 0 0
\(441\) −3.13294e6 −0.767107
\(442\) 0 0
\(443\) −5.09261e6 −1.23291 −0.616454 0.787391i \(-0.711431\pi\)
−0.616454 + 0.787391i \(0.711431\pi\)
\(444\) 0 0
\(445\) 1.65745e6 0.396771
\(446\) 0 0
\(447\) −63100.3 −0.0149370
\(448\) 0 0
\(449\) 5.83842e6 1.36672 0.683360 0.730082i \(-0.260518\pi\)
0.683360 + 0.730082i \(0.260518\pi\)
\(450\) 0 0
\(451\) −12783.6 −0.00295946
\(452\) 0 0
\(453\) −117219. −0.0268380
\(454\) 0 0
\(455\) 643338. 0.145684
\(456\) 0 0
\(457\) −5.06917e6 −1.13539 −0.567697 0.823238i \(-0.692165\pi\)
−0.567697 + 0.823238i \(0.692165\pi\)
\(458\) 0 0
\(459\) −435728. −0.0965347
\(460\) 0 0
\(461\) −6.10777e6 −1.33854 −0.669269 0.743021i \(-0.733392\pi\)
−0.669269 + 0.743021i \(0.733392\pi\)
\(462\) 0 0
\(463\) −4.29238e6 −0.930563 −0.465282 0.885163i \(-0.654047\pi\)
−0.465282 + 0.885163i \(0.654047\pi\)
\(464\) 0 0
\(465\) 179971. 0.0385985
\(466\) 0 0
\(467\) 1.64461e6 0.348957 0.174478 0.984661i \(-0.444176\pi\)
0.174478 + 0.984661i \(0.444176\pi\)
\(468\) 0 0
\(469\) 3.57073e6 0.749591
\(470\) 0 0
\(471\) 45823.7 0.00951783
\(472\) 0 0
\(473\) 4.04128e6 0.830551
\(474\) 0 0
\(475\) −428146. −0.0870678
\(476\) 0 0
\(477\) −5.40301e6 −1.08728
\(478\) 0 0
\(479\) 8.11578e6 1.61619 0.808093 0.589055i \(-0.200500\pi\)
0.808093 + 0.589055i \(0.200500\pi\)
\(480\) 0 0
\(481\) 1.52631e6 0.300801
\(482\) 0 0
\(483\) −129817. −0.0253199
\(484\) 0 0
\(485\) −306607. −0.0591871
\(486\) 0 0
\(487\) −6.11681e6 −1.16870 −0.584350 0.811502i \(-0.698650\pi\)
−0.584350 + 0.811502i \(0.698650\pi\)
\(488\) 0 0
\(489\) −399249. −0.0755042
\(490\) 0 0
\(491\) −6.78707e6 −1.27051 −0.635256 0.772301i \(-0.719105\pi\)
−0.635256 + 0.772301i \(0.719105\pi\)
\(492\) 0 0
\(493\) 1.04154e7 1.93001
\(494\) 0 0
\(495\) 2.37302e6 0.435299
\(496\) 0 0
\(497\) −2.65180e6 −0.481560
\(498\) 0 0
\(499\) −6.07689e6 −1.09252 −0.546260 0.837615i \(-0.683949\pi\)
−0.546260 + 0.837615i \(0.683949\pi\)
\(500\) 0 0
\(501\) 515357. 0.0917305
\(502\) 0 0
\(503\) 1.89757e6 0.334410 0.167205 0.985922i \(-0.446526\pi\)
0.167205 + 0.985922i \(0.446526\pi\)
\(504\) 0 0
\(505\) 934419. 0.163047
\(506\) 0 0
\(507\) −263766. −0.0455721
\(508\) 0 0
\(509\) 7.07101e6 1.20973 0.604863 0.796330i \(-0.293228\pi\)
0.604863 + 0.796330i \(0.293228\pi\)
\(510\) 0 0
\(511\) −9.99982e6 −1.69410
\(512\) 0 0
\(513\) 251308. 0.0421613
\(514\) 0 0
\(515\) 1.04107e6 0.172967
\(516\) 0 0
\(517\) −6.62944e6 −1.09081
\(518\) 0 0
\(519\) 111932. 0.0182405
\(520\) 0 0
\(521\) −7.99273e6 −1.29003 −0.645017 0.764169i \(-0.723150\pi\)
−0.645017 + 0.764169i \(0.723150\pi\)
\(522\) 0 0
\(523\) 1.04897e7 1.67691 0.838453 0.544974i \(-0.183460\pi\)
0.838453 + 0.544974i \(0.183460\pi\)
\(524\) 0 0
\(525\) −81442.0 −0.0128958
\(526\) 0 0
\(527\) 1.13139e7 1.77454
\(528\) 0 0
\(529\) −5.44386e6 −0.845800
\(530\) 0 0
\(531\) 1.07278e7 1.65110
\(532\) 0 0
\(533\) −4872.79 −0.000742951 0
\(534\) 0 0
\(535\) 1.74162e6 0.263068
\(536\) 0 0
\(537\) 491447. 0.0735429
\(538\) 0 0
\(539\) −5.05992e6 −0.750191
\(540\) 0 0
\(541\) −6.56741e6 −0.964719 −0.482359 0.875973i \(-0.660220\pi\)
−0.482359 + 0.875973i \(0.660220\pi\)
\(542\) 0 0
\(543\) −238096. −0.0346540
\(544\) 0 0
\(545\) 2.21385e6 0.319270
\(546\) 0 0
\(547\) −5.90324e6 −0.843573 −0.421786 0.906695i \(-0.638597\pi\)
−0.421786 + 0.906695i \(0.638597\pi\)
\(548\) 0 0
\(549\) −5.27116e6 −0.746407
\(550\) 0 0
\(551\) −6.00715e6 −0.842926
\(552\) 0 0
\(553\) 1.07707e7 1.49773
\(554\) 0 0
\(555\) −193219. −0.0266268
\(556\) 0 0
\(557\) −3.34903e6 −0.457384 −0.228692 0.973499i \(-0.573445\pi\)
−0.228692 + 0.973499i \(0.573445\pi\)
\(558\) 0 0
\(559\) 1.54044e6 0.208504
\(560\) 0 0
\(561\) −351452. −0.0471475
\(562\) 0 0
\(563\) 1.34193e7 1.78426 0.892132 0.451774i \(-0.149209\pi\)
0.892132 + 0.451774i \(0.149209\pi\)
\(564\) 0 0
\(565\) 1.94523e6 0.256360
\(566\) 0 0
\(567\) −1.01097e7 −1.32063
\(568\) 0 0
\(569\) −1.38493e7 −1.79327 −0.896635 0.442770i \(-0.853996\pi\)
−0.896635 + 0.442770i \(0.853996\pi\)
\(570\) 0 0
\(571\) 8.24337e6 1.05807 0.529035 0.848600i \(-0.322554\pi\)
0.529035 + 0.848600i \(0.322554\pi\)
\(572\) 0 0
\(573\) 643592. 0.0818887
\(574\) 0 0
\(575\) 622648. 0.0785367
\(576\) 0 0
\(577\) 9.90608e6 1.23869 0.619345 0.785119i \(-0.287398\pi\)
0.619345 + 0.785119i \(0.287398\pi\)
\(578\) 0 0
\(579\) 692941. 0.0859013
\(580\) 0 0
\(581\) −7.51402e6 −0.923490
\(582\) 0 0
\(583\) −8.72625e6 −1.06330
\(584\) 0 0
\(585\) 904534. 0.109279
\(586\) 0 0
\(587\) 1.29572e7 1.55209 0.776044 0.630679i \(-0.217224\pi\)
0.776044 + 0.630679i \(0.217224\pi\)
\(588\) 0 0
\(589\) −6.52536e6 −0.775026
\(590\) 0 0
\(591\) −449923. −0.0529871
\(592\) 0 0
\(593\) −5.95284e6 −0.695164 −0.347582 0.937650i \(-0.612997\pi\)
−0.347582 + 0.937650i \(0.612997\pi\)
\(594\) 0 0
\(595\) −5.11986e6 −0.592879
\(596\) 0 0
\(597\) −120543. −0.0138423
\(598\) 0 0
\(599\) 2.48855e6 0.283387 0.141694 0.989911i \(-0.454745\pi\)
0.141694 + 0.989911i \(0.454745\pi\)
\(600\) 0 0
\(601\) −1.34152e7 −1.51499 −0.757497 0.652838i \(-0.773578\pi\)
−0.757497 + 0.652838i \(0.773578\pi\)
\(602\) 0 0
\(603\) 5.02045e6 0.562276
\(604\) 0 0
\(605\) −193685. −0.0215133
\(606\) 0 0
\(607\) −8.49423e6 −0.935734 −0.467867 0.883799i \(-0.654977\pi\)
−0.467867 + 0.883799i \(0.654977\pi\)
\(608\) 0 0
\(609\) −1.14268e6 −0.124848
\(610\) 0 0
\(611\) −2.52698e6 −0.273841
\(612\) 0 0
\(613\) 1.36612e7 1.46837 0.734187 0.678948i \(-0.237564\pi\)
0.734187 + 0.678948i \(0.237564\pi\)
\(614\) 0 0
\(615\) 616.861 6.57657e−5 0
\(616\) 0 0
\(617\) −1.43013e7 −1.51238 −0.756191 0.654351i \(-0.772942\pi\)
−0.756191 + 0.654351i \(0.772942\pi\)
\(618\) 0 0
\(619\) −1.03774e7 −1.08858 −0.544292 0.838896i \(-0.683202\pi\)
−0.544292 + 0.838896i \(0.683202\pi\)
\(620\) 0 0
\(621\) −365475. −0.0380302
\(622\) 0 0
\(623\) −1.14314e7 −1.17999
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 202702. 0.0205915
\(628\) 0 0
\(629\) −1.21468e7 −1.22415
\(630\) 0 0
\(631\) 7.91347e6 0.791214 0.395607 0.918420i \(-0.370534\pi\)
0.395607 + 0.918420i \(0.370534\pi\)
\(632\) 0 0
\(633\) −586941. −0.0582217
\(634\) 0 0
\(635\) −7.36449e6 −0.724784
\(636\) 0 0
\(637\) −1.92872e6 −0.188330
\(638\) 0 0
\(639\) −3.72844e6 −0.361222
\(640\) 0 0
\(641\) −5.70174e6 −0.548103 −0.274052 0.961715i \(-0.588364\pi\)
−0.274052 + 0.961715i \(0.588364\pi\)
\(642\) 0 0
\(643\) 3.06376e6 0.292232 0.146116 0.989267i \(-0.453323\pi\)
0.146116 + 0.989267i \(0.453323\pi\)
\(644\) 0 0
\(645\) −195008. −0.0184567
\(646\) 0 0
\(647\) 1.36482e6 0.128178 0.0640890 0.997944i \(-0.479586\pi\)
0.0640890 + 0.997944i \(0.479586\pi\)
\(648\) 0 0
\(649\) 1.73261e7 1.61469
\(650\) 0 0
\(651\) −1.24125e6 −0.114791
\(652\) 0 0
\(653\) −8.58212e6 −0.787610 −0.393805 0.919194i \(-0.628842\pi\)
−0.393805 + 0.919194i \(0.628842\pi\)
\(654\) 0 0
\(655\) −4.33913e6 −0.395184
\(656\) 0 0
\(657\) −1.40598e7 −1.27076
\(658\) 0 0
\(659\) −1.84222e7 −1.65245 −0.826224 0.563342i \(-0.809515\pi\)
−0.826224 + 0.563342i \(0.809515\pi\)
\(660\) 0 0
\(661\) −1.69479e7 −1.50873 −0.754367 0.656453i \(-0.772056\pi\)
−0.754367 + 0.656453i \(0.772056\pi\)
\(662\) 0 0
\(663\) −133965. −0.0118360
\(664\) 0 0
\(665\) 2.95291e6 0.258938
\(666\) 0 0
\(667\) 8.73613e6 0.760334
\(668\) 0 0
\(669\) 732947. 0.0633151
\(670\) 0 0
\(671\) −8.51331e6 −0.729948
\(672\) 0 0
\(673\) 1.18245e6 0.100634 0.0503172 0.998733i \(-0.483977\pi\)
0.0503172 + 0.998733i \(0.483977\pi\)
\(674\) 0 0
\(675\) −229285. −0.0193694
\(676\) 0 0
\(677\) 4.34424e6 0.364285 0.182143 0.983272i \(-0.441697\pi\)
0.182143 + 0.983272i \(0.441697\pi\)
\(678\) 0 0
\(679\) 2.11466e6 0.176021
\(680\) 0 0
\(681\) −24883.8 −0.00205612
\(682\) 0 0
\(683\) 1.03260e7 0.846991 0.423495 0.905898i \(-0.360803\pi\)
0.423495 + 0.905898i \(0.360803\pi\)
\(684\) 0 0
\(685\) 8.65180e6 0.704498
\(686\) 0 0
\(687\) −551880. −0.0446121
\(688\) 0 0
\(689\) −3.32623e6 −0.266934
\(690\) 0 0
\(691\) 2.07013e7 1.64931 0.824656 0.565635i \(-0.191369\pi\)
0.824656 + 0.565635i \(0.191369\pi\)
\(692\) 0 0
\(693\) −1.63666e7 −1.29457
\(694\) 0 0
\(695\) 8.23360e6 0.646588
\(696\) 0 0
\(697\) 38779.1 0.00302354
\(698\) 0 0
\(699\) −416326. −0.0322285
\(700\) 0 0
\(701\) 2.75116e6 0.211457 0.105728 0.994395i \(-0.466283\pi\)
0.105728 + 0.994395i \(0.466283\pi\)
\(702\) 0 0
\(703\) 7.00572e6 0.534643
\(704\) 0 0
\(705\) 319897. 0.0242403
\(706\) 0 0
\(707\) −6.44466e6 −0.484899
\(708\) 0 0
\(709\) 4.07210e6 0.304230 0.152115 0.988363i \(-0.451392\pi\)
0.152115 + 0.988363i \(0.451392\pi\)
\(710\) 0 0
\(711\) 1.51437e7 1.12346
\(712\) 0 0
\(713\) 9.48976e6 0.699087
\(714\) 0 0
\(715\) 1.46089e6 0.106869
\(716\) 0 0
\(717\) −752914. −0.0546950
\(718\) 0 0
\(719\) 1.75553e7 1.26645 0.633223 0.773970i \(-0.281732\pi\)
0.633223 + 0.773970i \(0.281732\pi\)
\(720\) 0 0
\(721\) −7.18024e6 −0.514400
\(722\) 0 0
\(723\) −720394. −0.0512536
\(724\) 0 0
\(725\) 5.48071e6 0.387250
\(726\) 0 0
\(727\) 1.46241e7 1.02620 0.513101 0.858328i \(-0.328496\pi\)
0.513101 + 0.858328i \(0.328496\pi\)
\(728\) 0 0
\(729\) −1.41470e7 −0.985925
\(730\) 0 0
\(731\) −1.22592e7 −0.848534
\(732\) 0 0
\(733\) 1.54961e7 1.06528 0.532639 0.846342i \(-0.321200\pi\)
0.532639 + 0.846342i \(0.321200\pi\)
\(734\) 0 0
\(735\) 244162. 0.0166709
\(736\) 0 0
\(737\) 8.10839e6 0.549877
\(738\) 0 0
\(739\) −3.39408e6 −0.228619 −0.114309 0.993445i \(-0.536465\pi\)
−0.114309 + 0.993445i \(0.536465\pi\)
\(740\) 0 0
\(741\) 77264.9 0.00516936
\(742\) 0 0
\(743\) −3.94591e6 −0.262225 −0.131113 0.991367i \(-0.541855\pi\)
−0.131113 + 0.991367i \(0.541855\pi\)
\(744\) 0 0
\(745\) −2.08738e6 −0.137788
\(746\) 0 0
\(747\) −1.05647e7 −0.692719
\(748\) 0 0
\(749\) −1.20119e7 −0.782360
\(750\) 0 0
\(751\) −824656. −0.0533547 −0.0266774 0.999644i \(-0.508493\pi\)
−0.0266774 + 0.999644i \(0.508493\pi\)
\(752\) 0 0
\(753\) −589934. −0.0379154
\(754\) 0 0
\(755\) −3.87763e6 −0.247571
\(756\) 0 0
\(757\) 1.53800e7 0.975474 0.487737 0.872991i \(-0.337823\pi\)
0.487737 + 0.872991i \(0.337823\pi\)
\(758\) 0 0
\(759\) −294787. −0.0185739
\(760\) 0 0
\(761\) 8.06295e6 0.504699 0.252349 0.967636i \(-0.418797\pi\)
0.252349 + 0.967636i \(0.418797\pi\)
\(762\) 0 0
\(763\) −1.52689e7 −0.949502
\(764\) 0 0
\(765\) −7.19854e6 −0.444724
\(766\) 0 0
\(767\) 6.60429e6 0.405357
\(768\) 0 0
\(769\) −1.12351e7 −0.685110 −0.342555 0.939498i \(-0.611292\pi\)
−0.342555 + 0.939498i \(0.611292\pi\)
\(770\) 0 0
\(771\) −257358. −0.0155920
\(772\) 0 0
\(773\) −554517. −0.0333784 −0.0166892 0.999861i \(-0.505313\pi\)
−0.0166892 + 0.999861i \(0.505313\pi\)
\(774\) 0 0
\(775\) 5.95351e6 0.356056
\(776\) 0 0
\(777\) 1.33263e6 0.0791875
\(778\) 0 0
\(779\) −22366.0 −0.00132052
\(780\) 0 0
\(781\) −6.02169e6 −0.353257
\(782\) 0 0
\(783\) −3.21701e6 −0.187520
\(784\) 0 0
\(785\) 1.51586e6 0.0877983
\(786\) 0 0
\(787\) −1.56812e7 −0.902492 −0.451246 0.892400i \(-0.649020\pi\)
−0.451246 + 0.892400i \(0.649020\pi\)
\(788\) 0 0
\(789\) 1.55151e6 0.0887281
\(790\) 0 0
\(791\) −1.34162e7 −0.762410
\(792\) 0 0
\(793\) −3.24506e6 −0.183248
\(794\) 0 0
\(795\) 421077. 0.0236289
\(796\) 0 0
\(797\) −3.44267e7 −1.91977 −0.959885 0.280393i \(-0.909535\pi\)
−0.959885 + 0.280393i \(0.909535\pi\)
\(798\) 0 0
\(799\) 2.01104e7 1.11443
\(800\) 0 0
\(801\) −1.60725e7 −0.885122
\(802\) 0 0
\(803\) −2.27075e7 −1.24274
\(804\) 0 0
\(805\) −4.29438e6 −0.233567
\(806\) 0 0
\(807\) −74538.0 −0.00402897
\(808\) 0 0
\(809\) 1.20856e7 0.649230 0.324615 0.945846i \(-0.394765\pi\)
0.324615 + 0.945846i \(0.394765\pi\)
\(810\) 0 0
\(811\) −6.20419e6 −0.331232 −0.165616 0.986190i \(-0.552961\pi\)
−0.165616 + 0.986190i \(0.552961\pi\)
\(812\) 0 0
\(813\) 885870. 0.0470050
\(814\) 0 0
\(815\) −1.32073e7 −0.696498
\(816\) 0 0
\(817\) 7.07057e6 0.370595
\(818\) 0 0
\(819\) −6.23855e6 −0.324993
\(820\) 0 0
\(821\) 2.59426e7 1.34325 0.671624 0.740892i \(-0.265597\pi\)
0.671624 + 0.740892i \(0.265597\pi\)
\(822\) 0 0
\(823\) −7.30743e6 −0.376067 −0.188034 0.982163i \(-0.560211\pi\)
−0.188034 + 0.982163i \(0.560211\pi\)
\(824\) 0 0
\(825\) −184938. −0.00946000
\(826\) 0 0
\(827\) 1.22800e7 0.624357 0.312179 0.950023i \(-0.398941\pi\)
0.312179 + 0.950023i \(0.398941\pi\)
\(828\) 0 0
\(829\) 3.21244e7 1.62349 0.811743 0.584014i \(-0.198519\pi\)
0.811743 + 0.584014i \(0.198519\pi\)
\(830\) 0 0
\(831\) −860789. −0.0432408
\(832\) 0 0
\(833\) 1.53493e7 0.766435
\(834\) 0 0
\(835\) 1.70482e7 0.846178
\(836\) 0 0
\(837\) −3.49452e6 −0.172415
\(838\) 0 0
\(839\) −6.36956e6 −0.312395 −0.156198 0.987726i \(-0.549924\pi\)
−0.156198 + 0.987726i \(0.549924\pi\)
\(840\) 0 0
\(841\) 5.63865e7 2.74907
\(842\) 0 0
\(843\) −1.00609e6 −0.0487606
\(844\) 0 0
\(845\) −8.72547e6 −0.420385
\(846\) 0 0
\(847\) 1.33584e6 0.0639801
\(848\) 0 0
\(849\) 696667. 0.0331708
\(850\) 0 0
\(851\) −1.01883e7 −0.482258
\(852\) 0 0
\(853\) 4.05840e7 1.90978 0.954889 0.296964i \(-0.0959743\pi\)
0.954889 + 0.296964i \(0.0959743\pi\)
\(854\) 0 0
\(855\) 4.15180e6 0.194232
\(856\) 0 0
\(857\) 3.30412e6 0.153675 0.0768376 0.997044i \(-0.475518\pi\)
0.0768376 + 0.997044i \(0.475518\pi\)
\(858\) 0 0
\(859\) 1.45392e7 0.672292 0.336146 0.941810i \(-0.390876\pi\)
0.336146 + 0.941810i \(0.390876\pi\)
\(860\) 0 0
\(861\) −4254.47 −0.000195586 0
\(862\) 0 0
\(863\) 2.28020e7 1.04219 0.521094 0.853499i \(-0.325524\pi\)
0.521094 + 0.853499i \(0.325524\pi\)
\(864\) 0 0
\(865\) 3.70276e6 0.168262
\(866\) 0 0
\(867\) −6907.58 −0.000312089 0
\(868\) 0 0
\(869\) 2.44582e7 1.09869
\(870\) 0 0
\(871\) 3.09072e6 0.138043
\(872\) 0 0
\(873\) 2.97321e6 0.132035
\(874\) 0 0
\(875\) −2.69413e6 −0.118959
\(876\) 0 0
\(877\) 7.93150e6 0.348222 0.174111 0.984726i \(-0.444295\pi\)
0.174111 + 0.984726i \(0.444295\pi\)
\(878\) 0 0
\(879\) 1.24122e6 0.0541848
\(880\) 0 0
\(881\) −3.31349e7 −1.43829 −0.719144 0.694861i \(-0.755466\pi\)
−0.719144 + 0.694861i \(0.755466\pi\)
\(882\) 0 0
\(883\) 2.25079e7 0.971479 0.485740 0.874104i \(-0.338550\pi\)
0.485740 + 0.874104i \(0.338550\pi\)
\(884\) 0 0
\(885\) −836055. −0.0358820
\(886\) 0 0
\(887\) −3.66717e7 −1.56503 −0.782515 0.622632i \(-0.786063\pi\)
−0.782515 + 0.622632i \(0.786063\pi\)
\(888\) 0 0
\(889\) 5.07927e7 2.15549
\(890\) 0 0
\(891\) −2.29572e7 −0.968777
\(892\) 0 0
\(893\) −1.15988e7 −0.486725
\(894\) 0 0
\(895\) 1.62572e7 0.678405
\(896\) 0 0
\(897\) −112365. −0.00466285
\(898\) 0 0
\(899\) 8.35313e7 3.44707
\(900\) 0 0
\(901\) 2.64711e7 1.08632
\(902\) 0 0
\(903\) 1.34497e6 0.0548898
\(904\) 0 0
\(905\) −7.87631e6 −0.319670
\(906\) 0 0
\(907\) 2.40388e6 0.0970274 0.0485137 0.998823i \(-0.484552\pi\)
0.0485137 + 0.998823i \(0.484552\pi\)
\(908\) 0 0
\(909\) −9.06120e6 −0.363728
\(910\) 0 0
\(911\) 467873. 0.0186781 0.00933904 0.999956i \(-0.497027\pi\)
0.00933904 + 0.999956i \(0.497027\pi\)
\(912\) 0 0
\(913\) −1.70628e7 −0.677444
\(914\) 0 0
\(915\) 410801. 0.0162211
\(916\) 0 0
\(917\) 2.99268e7 1.17527
\(918\) 0 0
\(919\) −2.59601e7 −1.01395 −0.506976 0.861960i \(-0.669237\pi\)
−0.506976 + 0.861960i \(0.669237\pi\)
\(920\) 0 0
\(921\) 612800. 0.0238051
\(922\) 0 0
\(923\) −2.29532e6 −0.0886827
\(924\) 0 0
\(925\) −6.39177e6 −0.245622
\(926\) 0 0
\(927\) −1.00954e7 −0.385856
\(928\) 0 0
\(929\) −4.52441e6 −0.171998 −0.0859989 0.996295i \(-0.527408\pi\)
−0.0859989 + 0.996295i \(0.527408\pi\)
\(930\) 0 0
\(931\) −8.85278e6 −0.334738
\(932\) 0 0
\(933\) −1.26720e6 −0.0476587
\(934\) 0 0
\(935\) −1.16262e7 −0.434918
\(936\) 0 0
\(937\) 2.69269e7 1.00193 0.500964 0.865468i \(-0.332979\pi\)
0.500964 + 0.865468i \(0.332979\pi\)
\(938\) 0 0
\(939\) 1.08751e6 0.0402505
\(940\) 0 0
\(941\) 1.38789e6 0.0510953 0.0255477 0.999674i \(-0.491867\pi\)
0.0255477 + 0.999674i \(0.491867\pi\)
\(942\) 0 0
\(943\) 32526.7 0.00119113
\(944\) 0 0
\(945\) 1.58137e6 0.0576042
\(946\) 0 0
\(947\) 1.10208e7 0.399335 0.199667 0.979864i \(-0.436014\pi\)
0.199667 + 0.979864i \(0.436014\pi\)
\(948\) 0 0
\(949\) −8.65555e6 −0.311982
\(950\) 0 0
\(951\) −592375. −0.0212396
\(952\) 0 0
\(953\) −1.09536e7 −0.390683 −0.195342 0.980735i \(-0.562582\pi\)
−0.195342 + 0.980735i \(0.562582\pi\)
\(954\) 0 0
\(955\) 2.12902e7 0.755392
\(956\) 0 0
\(957\) −2.59479e6 −0.0915847
\(958\) 0 0
\(959\) −5.96712e7 −2.09517
\(960\) 0 0
\(961\) 6.21081e7 2.16940
\(962\) 0 0
\(963\) −1.68887e7 −0.586856
\(964\) 0 0
\(965\) 2.29227e7 0.792407
\(966\) 0 0
\(967\) 3.52685e7 1.21289 0.606443 0.795127i \(-0.292596\pi\)
0.606443 + 0.795127i \(0.292596\pi\)
\(968\) 0 0
\(969\) −614895. −0.0210374
\(970\) 0 0
\(971\) 3.58480e7 1.22016 0.610079 0.792340i \(-0.291138\pi\)
0.610079 + 0.792340i \(0.291138\pi\)
\(972\) 0 0
\(973\) −5.67869e7 −1.92294
\(974\) 0 0
\(975\) −70493.7 −0.00237487
\(976\) 0 0
\(977\) −8.95941e6 −0.300292 −0.150146 0.988664i \(-0.547974\pi\)
−0.150146 + 0.988664i \(0.547974\pi\)
\(978\) 0 0
\(979\) −2.59583e7 −0.865604
\(980\) 0 0
\(981\) −2.14681e7 −0.712231
\(982\) 0 0
\(983\) 6.94666e6 0.229294 0.114647 0.993406i \(-0.463426\pi\)
0.114647 + 0.993406i \(0.463426\pi\)
\(984\) 0 0
\(985\) −1.48836e7 −0.488785
\(986\) 0 0
\(987\) −2.20632e6 −0.0720901
\(988\) 0 0
\(989\) −1.02827e7 −0.334283
\(990\) 0 0
\(991\) −7.72743e6 −0.249949 −0.124974 0.992160i \(-0.539885\pi\)
−0.124974 + 0.992160i \(0.539885\pi\)
\(992\) 0 0
\(993\) 2.49652e6 0.0803455
\(994\) 0 0
\(995\) −3.98761e6 −0.127690
\(996\) 0 0
\(997\) 4.32625e7 1.37840 0.689198 0.724573i \(-0.257963\pi\)
0.689198 + 0.724573i \(0.257963\pi\)
\(998\) 0 0
\(999\) 3.75177e6 0.118939
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 320.6.a.x.1.2 3
4.3 odd 2 320.6.a.y.1.2 3
8.3 odd 2 160.6.a.f.1.2 3
8.5 even 2 160.6.a.g.1.2 yes 3
40.3 even 4 800.6.c.k.449.4 6
40.13 odd 4 800.6.c.j.449.3 6
40.19 odd 2 800.6.a.o.1.2 3
40.27 even 4 800.6.c.k.449.3 6
40.29 even 2 800.6.a.n.1.2 3
40.37 odd 4 800.6.c.j.449.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.6.a.f.1.2 3 8.3 odd 2
160.6.a.g.1.2 yes 3 8.5 even 2
320.6.a.x.1.2 3 1.1 even 1 trivial
320.6.a.y.1.2 3 4.3 odd 2
800.6.a.n.1.2 3 40.29 even 2
800.6.a.o.1.2 3 40.19 odd 2
800.6.c.j.449.3 6 40.13 odd 4
800.6.c.j.449.4 6 40.37 odd 4
800.6.c.k.449.3 6 40.27 even 4
800.6.c.k.449.4 6 40.3 even 4