Properties

Label 280.6.a.b.1.1
Level $280$
Weight $6$
Character 280.1
Self dual yes
Analytic conductor $44.907$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.9074695476\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 280.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{3} +25.0000 q^{5} -49.0000 q^{7} -227.000 q^{9} +O(q^{10})\) \(q+4.00000 q^{3} +25.0000 q^{5} -49.0000 q^{7} -227.000 q^{9} +124.000 q^{11} +766.000 q^{13} +100.000 q^{15} -1102.00 q^{17} -764.000 q^{19} -196.000 q^{21} +168.000 q^{23} +625.000 q^{25} -1880.00 q^{27} -6866.00 q^{29} -4096.00 q^{31} +496.000 q^{33} -1225.00 q^{35} -4682.00 q^{37} +3064.00 q^{39} +13130.0 q^{41} +18220.0 q^{43} -5675.00 q^{45} -7104.00 q^{47} +2401.00 q^{49} -4408.00 q^{51} -20026.0 q^{53} +3100.00 q^{55} -3056.00 q^{57} -38964.0 q^{59} -56274.0 q^{61} +11123.0 q^{63} +19150.0 q^{65} -24060.0 q^{67} +672.000 q^{69} -31896.0 q^{71} -23670.0 q^{73} +2500.00 q^{75} -6076.00 q^{77} +37744.0 q^{79} +47641.0 q^{81} -68204.0 q^{83} -27550.0 q^{85} -27464.0 q^{87} -19078.0 q^{89} -37534.0 q^{91} -16384.0 q^{93} -19100.0 q^{95} -115646. q^{97} -28148.0 q^{99} +O(q^{100})\)

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
\(3\) 4.00000 0.256600 0.128300 0.991735i \(-0.459048\pi\)
0.128300 + 0.991735i \(0.459048\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) −227.000 −0.934156
\(10\) 0 0
\(11\) 124.000 0.308987 0.154493 0.987994i \(-0.450625\pi\)
0.154493 + 0.987994i \(0.450625\pi\)
\(12\) 0 0
\(13\) 766.000 1.25710 0.628551 0.777769i \(-0.283648\pi\)
0.628551 + 0.777769i \(0.283648\pi\)
\(14\) 0 0
\(15\) 100.000 0.114755
\(16\) 0 0
\(17\) −1102.00 −0.924824 −0.462412 0.886665i \(-0.653016\pi\)
−0.462412 + 0.886665i \(0.653016\pi\)
\(18\) 0 0
\(19\) −764.000 −0.485522 −0.242761 0.970086i \(-0.578053\pi\)
−0.242761 + 0.970086i \(0.578053\pi\)
\(20\) 0 0
\(21\) −196.000 −0.0969857
\(22\) 0 0
\(23\) 168.000 0.0662201 0.0331100 0.999452i \(-0.489459\pi\)
0.0331100 + 0.999452i \(0.489459\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) −1880.00 −0.496305
\(28\) 0 0
\(29\) −6866.00 −1.51603 −0.758017 0.652235i \(-0.773832\pi\)
−0.758017 + 0.652235i \(0.773832\pi\)
\(30\) 0 0
\(31\) −4096.00 −0.765519 −0.382759 0.923848i \(-0.625026\pi\)
−0.382759 + 0.923848i \(0.625026\pi\)
\(32\) 0 0
\(33\) 496.000 0.0792861
\(34\) 0 0
\(35\) −1225.00 −0.169031
\(36\) 0 0
\(37\) −4682.00 −0.562247 −0.281123 0.959672i \(-0.590707\pi\)
−0.281123 + 0.959672i \(0.590707\pi\)
\(38\) 0 0
\(39\) 3064.00 0.322572
\(40\) 0 0
\(41\) 13130.0 1.21985 0.609923 0.792461i \(-0.291200\pi\)
0.609923 + 0.792461i \(0.291200\pi\)
\(42\) 0 0
\(43\) 18220.0 1.50272 0.751359 0.659894i \(-0.229399\pi\)
0.751359 + 0.659894i \(0.229399\pi\)
\(44\) 0 0
\(45\) −5675.00 −0.417767
\(46\) 0 0
\(47\) −7104.00 −0.469092 −0.234546 0.972105i \(-0.575360\pi\)
−0.234546 + 0.972105i \(0.575360\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) −4408.00 −0.237310
\(52\) 0 0
\(53\) −20026.0 −0.979275 −0.489637 0.871926i \(-0.662871\pi\)
−0.489637 + 0.871926i \(0.662871\pi\)
\(54\) 0 0
\(55\) 3100.00 0.138183
\(56\) 0 0
\(57\) −3056.00 −0.124585
\(58\) 0 0
\(59\) −38964.0 −1.45725 −0.728624 0.684914i \(-0.759840\pi\)
−0.728624 + 0.684914i \(0.759840\pi\)
\(60\) 0 0
\(61\) −56274.0 −1.93635 −0.968174 0.250280i \(-0.919477\pi\)
−0.968174 + 0.250280i \(0.919477\pi\)
\(62\) 0 0
\(63\) 11123.0 0.353078
\(64\) 0 0
\(65\) 19150.0 0.562193
\(66\) 0 0
\(67\) −24060.0 −0.654800 −0.327400 0.944886i \(-0.606172\pi\)
−0.327400 + 0.944886i \(0.606172\pi\)
\(68\) 0 0
\(69\) 672.000 0.0169921
\(70\) 0 0
\(71\) −31896.0 −0.750914 −0.375457 0.926840i \(-0.622514\pi\)
−0.375457 + 0.926840i \(0.622514\pi\)
\(72\) 0 0
\(73\) −23670.0 −0.519866 −0.259933 0.965627i \(-0.583700\pi\)
−0.259933 + 0.965627i \(0.583700\pi\)
\(74\) 0 0
\(75\) 2500.00 0.0513200
\(76\) 0 0
\(77\) −6076.00 −0.116786
\(78\) 0 0
\(79\) 37744.0 0.680425 0.340212 0.940349i \(-0.389501\pi\)
0.340212 + 0.940349i \(0.389501\pi\)
\(80\) 0 0
\(81\) 47641.0 0.806805
\(82\) 0 0
\(83\) −68204.0 −1.08671 −0.543356 0.839502i \(-0.682847\pi\)
−0.543356 + 0.839502i \(0.682847\pi\)
\(84\) 0 0
\(85\) −27550.0 −0.413594
\(86\) 0 0
\(87\) −27464.0 −0.389014
\(88\) 0 0
\(89\) −19078.0 −0.255304 −0.127652 0.991819i \(-0.540744\pi\)
−0.127652 + 0.991819i \(0.540744\pi\)
\(90\) 0 0
\(91\) −37534.0 −0.475140
\(92\) 0 0
\(93\) −16384.0 −0.196432
\(94\) 0 0
\(95\) −19100.0 −0.217132
\(96\) 0 0
\(97\) −115646. −1.24796 −0.623981 0.781440i \(-0.714486\pi\)
−0.623981 + 0.781440i \(0.714486\pi\)
\(98\) 0 0
\(99\) −28148.0 −0.288642
\(100\) 0 0
\(101\) 100790. 0.983137 0.491568 0.870839i \(-0.336424\pi\)
0.491568 + 0.870839i \(0.336424\pi\)
\(102\) 0 0
\(103\) 13304.0 0.123563 0.0617816 0.998090i \(-0.480322\pi\)
0.0617816 + 0.998090i \(0.480322\pi\)
\(104\) 0 0
\(105\) −4900.00 −0.0433733
\(106\) 0 0
\(107\) 128204. 1.08254 0.541268 0.840850i \(-0.317945\pi\)
0.541268 + 0.840850i \(0.317945\pi\)
\(108\) 0 0
\(109\) −176450. −1.42251 −0.711255 0.702934i \(-0.751873\pi\)
−0.711255 + 0.702934i \(0.751873\pi\)
\(110\) 0 0
\(111\) −18728.0 −0.144273
\(112\) 0 0
\(113\) −166734. −1.22837 −0.614183 0.789163i \(-0.710514\pi\)
−0.614183 + 0.789163i \(0.710514\pi\)
\(114\) 0 0
\(115\) 4200.00 0.0296145
\(116\) 0 0
\(117\) −173882. −1.17433
\(118\) 0 0
\(119\) 53998.0 0.349551
\(120\) 0 0
\(121\) −145675. −0.904527
\(122\) 0 0
\(123\) 52520.0 0.313013
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) 228112. 1.25499 0.627493 0.778622i \(-0.284081\pi\)
0.627493 + 0.778622i \(0.284081\pi\)
\(128\) 0 0
\(129\) 72880.0 0.385597
\(130\) 0 0
\(131\) 131796. 0.671002 0.335501 0.942040i \(-0.391094\pi\)
0.335501 + 0.942040i \(0.391094\pi\)
\(132\) 0 0
\(133\) 37436.0 0.183510
\(134\) 0 0
\(135\) −47000.0 −0.221954
\(136\) 0 0
\(137\) −187862. −0.855141 −0.427570 0.903982i \(-0.640630\pi\)
−0.427570 + 0.903982i \(0.640630\pi\)
\(138\) 0 0
\(139\) −106404. −0.467112 −0.233556 0.972343i \(-0.575036\pi\)
−0.233556 + 0.972343i \(0.575036\pi\)
\(140\) 0 0
\(141\) −28416.0 −0.120369
\(142\) 0 0
\(143\) 94984.0 0.388428
\(144\) 0 0
\(145\) −171650. −0.677991
\(146\) 0 0
\(147\) 9604.00 0.0366572
\(148\) 0 0
\(149\) −177466. −0.654862 −0.327431 0.944875i \(-0.606183\pi\)
−0.327431 + 0.944875i \(0.606183\pi\)
\(150\) 0 0
\(151\) 117048. 0.417755 0.208877 0.977942i \(-0.433019\pi\)
0.208877 + 0.977942i \(0.433019\pi\)
\(152\) 0 0
\(153\) 250154. 0.863931
\(154\) 0 0
\(155\) −102400. −0.342350
\(156\) 0 0
\(157\) −31986.0 −0.103564 −0.0517822 0.998658i \(-0.516490\pi\)
−0.0517822 + 0.998658i \(0.516490\pi\)
\(158\) 0 0
\(159\) −80104.0 −0.251282
\(160\) 0 0
\(161\) −8232.00 −0.0250288
\(162\) 0 0
\(163\) 37060.0 0.109254 0.0546269 0.998507i \(-0.482603\pi\)
0.0546269 + 0.998507i \(0.482603\pi\)
\(164\) 0 0
\(165\) 12400.0 0.0354578
\(166\) 0 0
\(167\) 185880. 0.515753 0.257876 0.966178i \(-0.416977\pi\)
0.257876 + 0.966178i \(0.416977\pi\)
\(168\) 0 0
\(169\) 215463. 0.580305
\(170\) 0 0
\(171\) 173428. 0.453554
\(172\) 0 0
\(173\) 464990. 1.18121 0.590607 0.806960i \(-0.298888\pi\)
0.590607 + 0.806960i \(0.298888\pi\)
\(174\) 0 0
\(175\) −30625.0 −0.0755929
\(176\) 0 0
\(177\) −155856. −0.373930
\(178\) 0 0
\(179\) 835300. 1.94854 0.974271 0.225378i \(-0.0723618\pi\)
0.974271 + 0.225378i \(0.0723618\pi\)
\(180\) 0 0
\(181\) −498682. −1.13143 −0.565714 0.824601i \(-0.691400\pi\)
−0.565714 + 0.824601i \(0.691400\pi\)
\(182\) 0 0
\(183\) −225096. −0.496867
\(184\) 0 0
\(185\) −117050. −0.251444
\(186\) 0 0
\(187\) −136648. −0.285759
\(188\) 0 0
\(189\) 92120.0 0.187586
\(190\) 0 0
\(191\) 295168. 0.585445 0.292722 0.956197i \(-0.405439\pi\)
0.292722 + 0.956197i \(0.405439\pi\)
\(192\) 0 0
\(193\) 77506.0 0.149776 0.0748880 0.997192i \(-0.476140\pi\)
0.0748880 + 0.997192i \(0.476140\pi\)
\(194\) 0 0
\(195\) 76600.0 0.144259
\(196\) 0 0
\(197\) 310486. 0.570002 0.285001 0.958527i \(-0.408006\pi\)
0.285001 + 0.958527i \(0.408006\pi\)
\(198\) 0 0
\(199\) 639080. 1.14399 0.571995 0.820257i \(-0.306170\pi\)
0.571995 + 0.820257i \(0.306170\pi\)
\(200\) 0 0
\(201\) −96240.0 −0.168022
\(202\) 0 0
\(203\) 336434. 0.573007
\(204\) 0 0
\(205\) 328250. 0.545532
\(206\) 0 0
\(207\) −38136.0 −0.0618599
\(208\) 0 0
\(209\) −94736.0 −0.150020
\(210\) 0 0
\(211\) 985636. 1.52409 0.762045 0.647524i \(-0.224196\pi\)
0.762045 + 0.647524i \(0.224196\pi\)
\(212\) 0 0
\(213\) −127584. −0.192685
\(214\) 0 0
\(215\) 455500. 0.672036
\(216\) 0 0
\(217\) 200704. 0.289339
\(218\) 0 0
\(219\) −94680.0 −0.133398
\(220\) 0 0
\(221\) −844132. −1.16260
\(222\) 0 0
\(223\) 1.26920e6 1.70910 0.854551 0.519368i \(-0.173833\pi\)
0.854551 + 0.519368i \(0.173833\pi\)
\(224\) 0 0
\(225\) −141875. −0.186831
\(226\) 0 0
\(227\) −1.01843e6 −1.31179 −0.655897 0.754850i \(-0.727709\pi\)
−0.655897 + 0.754850i \(0.727709\pi\)
\(228\) 0 0
\(229\) 442358. 0.557423 0.278712 0.960375i \(-0.410093\pi\)
0.278712 + 0.960375i \(0.410093\pi\)
\(230\) 0 0
\(231\) −24304.0 −0.0299673
\(232\) 0 0
\(233\) 396810. 0.478843 0.239421 0.970916i \(-0.423042\pi\)
0.239421 + 0.970916i \(0.423042\pi\)
\(234\) 0 0
\(235\) −177600. −0.209784
\(236\) 0 0
\(237\) 150976. 0.174597
\(238\) 0 0
\(239\) 649872. 0.735924 0.367962 0.929841i \(-0.380056\pi\)
0.367962 + 0.929841i \(0.380056\pi\)
\(240\) 0 0
\(241\) 716082. 0.794182 0.397091 0.917779i \(-0.370020\pi\)
0.397091 + 0.917779i \(0.370020\pi\)
\(242\) 0 0
\(243\) 647404. 0.703331
\(244\) 0 0
\(245\) 60025.0 0.0638877
\(246\) 0 0
\(247\) −585224. −0.610351
\(248\) 0 0
\(249\) −272816. −0.278851
\(250\) 0 0
\(251\) −411860. −0.412634 −0.206317 0.978485i \(-0.566148\pi\)
−0.206317 + 0.978485i \(0.566148\pi\)
\(252\) 0 0
\(253\) 20832.0 0.0204611
\(254\) 0 0
\(255\) −110200. −0.106128
\(256\) 0 0
\(257\) −1.51856e6 −1.43416 −0.717082 0.696989i \(-0.754523\pi\)
−0.717082 + 0.696989i \(0.754523\pi\)
\(258\) 0 0
\(259\) 229418. 0.212509
\(260\) 0 0
\(261\) 1.55858e6 1.41621
\(262\) 0 0
\(263\) −1.77546e6 −1.58279 −0.791394 0.611307i \(-0.790644\pi\)
−0.791394 + 0.611307i \(0.790644\pi\)
\(264\) 0 0
\(265\) −500650. −0.437945
\(266\) 0 0
\(267\) −76312.0 −0.0655111
\(268\) 0 0
\(269\) 550014. 0.463439 0.231720 0.972783i \(-0.425565\pi\)
0.231720 + 0.972783i \(0.425565\pi\)
\(270\) 0 0
\(271\) −64144.0 −0.0530558 −0.0265279 0.999648i \(-0.508445\pi\)
−0.0265279 + 0.999648i \(0.508445\pi\)
\(272\) 0 0
\(273\) −150136. −0.121921
\(274\) 0 0
\(275\) 77500.0 0.0617974
\(276\) 0 0
\(277\) 112998. 0.0884853 0.0442427 0.999021i \(-0.485913\pi\)
0.0442427 + 0.999021i \(0.485913\pi\)
\(278\) 0 0
\(279\) 929792. 0.715114
\(280\) 0 0
\(281\) 606330. 0.458082 0.229041 0.973417i \(-0.426441\pi\)
0.229041 + 0.973417i \(0.426441\pi\)
\(282\) 0 0
\(283\) −565444. −0.419685 −0.209843 0.977735i \(-0.567295\pi\)
−0.209843 + 0.977735i \(0.567295\pi\)
\(284\) 0 0
\(285\) −76400.0 −0.0557162
\(286\) 0 0
\(287\) −643370. −0.461059
\(288\) 0 0
\(289\) −205453. −0.144700
\(290\) 0 0
\(291\) −462584. −0.320227
\(292\) 0 0
\(293\) −726474. −0.494369 −0.247184 0.968968i \(-0.579505\pi\)
−0.247184 + 0.968968i \(0.579505\pi\)
\(294\) 0 0
\(295\) −974100. −0.651701
\(296\) 0 0
\(297\) −233120. −0.153352
\(298\) 0 0
\(299\) 128688. 0.0832454
\(300\) 0 0
\(301\) −892780. −0.567974
\(302\) 0 0
\(303\) 403160. 0.252273
\(304\) 0 0
\(305\) −1.40685e6 −0.865961
\(306\) 0 0
\(307\) 1.69346e6 1.02548 0.512742 0.858543i \(-0.328630\pi\)
0.512742 + 0.858543i \(0.328630\pi\)
\(308\) 0 0
\(309\) 53216.0 0.0317063
\(310\) 0 0
\(311\) 2.52684e6 1.48142 0.740708 0.671828i \(-0.234490\pi\)
0.740708 + 0.671828i \(0.234490\pi\)
\(312\) 0 0
\(313\) 1.00966e6 0.582523 0.291262 0.956643i \(-0.405925\pi\)
0.291262 + 0.956643i \(0.405925\pi\)
\(314\) 0 0
\(315\) 278075. 0.157901
\(316\) 0 0
\(317\) −1.14792e6 −0.641600 −0.320800 0.947147i \(-0.603952\pi\)
−0.320800 + 0.947147i \(0.603952\pi\)
\(318\) 0 0
\(319\) −851384. −0.468434
\(320\) 0 0
\(321\) 512816. 0.277779
\(322\) 0 0
\(323\) 841928. 0.449023
\(324\) 0 0
\(325\) 478750. 0.251420
\(326\) 0 0
\(327\) −705800. −0.365016
\(328\) 0 0
\(329\) 348096. 0.177300
\(330\) 0 0
\(331\) −3.02349e6 −1.51684 −0.758418 0.651768i \(-0.774028\pi\)
−0.758418 + 0.651768i \(0.774028\pi\)
\(332\) 0 0
\(333\) 1.06281e6 0.525227
\(334\) 0 0
\(335\) −601500. −0.292835
\(336\) 0 0
\(337\) −763054. −0.366000 −0.183000 0.983113i \(-0.558581\pi\)
−0.183000 + 0.983113i \(0.558581\pi\)
\(338\) 0 0
\(339\) −666936. −0.315199
\(340\) 0 0
\(341\) −507904. −0.236535
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 16800.0 0.00759909
\(346\) 0 0
\(347\) −3.93575e6 −1.75470 −0.877351 0.479848i \(-0.840692\pi\)
−0.877351 + 0.479848i \(0.840692\pi\)
\(348\) 0 0
\(349\) 4.28424e6 1.88283 0.941413 0.337257i \(-0.109499\pi\)
0.941413 + 0.337257i \(0.109499\pi\)
\(350\) 0 0
\(351\) −1.44008e6 −0.623906
\(352\) 0 0
\(353\) 603906. 0.257948 0.128974 0.991648i \(-0.458832\pi\)
0.128974 + 0.991648i \(0.458832\pi\)
\(354\) 0 0
\(355\) −797400. −0.335819
\(356\) 0 0
\(357\) 215992. 0.0896948
\(358\) 0 0
\(359\) 2.78858e6 1.14195 0.570976 0.820967i \(-0.306565\pi\)
0.570976 + 0.820967i \(0.306565\pi\)
\(360\) 0 0
\(361\) −1.89240e6 −0.764268
\(362\) 0 0
\(363\) −582700. −0.232102
\(364\) 0 0
\(365\) −591750. −0.232491
\(366\) 0 0
\(367\) −3.04883e6 −1.18159 −0.590797 0.806820i \(-0.701187\pi\)
−0.590797 + 0.806820i \(0.701187\pi\)
\(368\) 0 0
\(369\) −2.98051e6 −1.13953
\(370\) 0 0
\(371\) 981274. 0.370131
\(372\) 0 0
\(373\) −1.57465e6 −0.586019 −0.293010 0.956109i \(-0.594657\pi\)
−0.293010 + 0.956109i \(0.594657\pi\)
\(374\) 0 0
\(375\) 62500.0 0.0229510
\(376\) 0 0
\(377\) −5.25936e6 −1.90581
\(378\) 0 0
\(379\) 4.00929e6 1.43374 0.716869 0.697208i \(-0.245575\pi\)
0.716869 + 0.697208i \(0.245575\pi\)
\(380\) 0 0
\(381\) 912448. 0.322030
\(382\) 0 0
\(383\) −3.44590e6 −1.20035 −0.600173 0.799870i \(-0.704901\pi\)
−0.600173 + 0.799870i \(0.704901\pi\)
\(384\) 0 0
\(385\) −151900. −0.0522283
\(386\) 0 0
\(387\) −4.13594e6 −1.40377
\(388\) 0 0
\(389\) 1.09125e6 0.365638 0.182819 0.983147i \(-0.441478\pi\)
0.182819 + 0.983147i \(0.441478\pi\)
\(390\) 0 0
\(391\) −185136. −0.0612419
\(392\) 0 0
\(393\) 527184. 0.172179
\(394\) 0 0
\(395\) 943600. 0.304295
\(396\) 0 0
\(397\) 68990.0 0.0219690 0.0109845 0.999940i \(-0.496503\pi\)
0.0109845 + 0.999940i \(0.496503\pi\)
\(398\) 0 0
\(399\) 149744. 0.0470888
\(400\) 0 0
\(401\) 249938. 0.0776196 0.0388098 0.999247i \(-0.487643\pi\)
0.0388098 + 0.999247i \(0.487643\pi\)
\(402\) 0 0
\(403\) −3.13754e6 −0.962335
\(404\) 0 0
\(405\) 1.19102e6 0.360814
\(406\) 0 0
\(407\) −580568. −0.173727
\(408\) 0 0
\(409\) 1.21836e6 0.360137 0.180069 0.983654i \(-0.442368\pi\)
0.180069 + 0.983654i \(0.442368\pi\)
\(410\) 0 0
\(411\) −751448. −0.219429
\(412\) 0 0
\(413\) 1.90924e6 0.550788
\(414\) 0 0
\(415\) −1.70510e6 −0.485993
\(416\) 0 0
\(417\) −425616. −0.119861
\(418\) 0 0
\(419\) −1.21502e6 −0.338102 −0.169051 0.985607i \(-0.554070\pi\)
−0.169051 + 0.985607i \(0.554070\pi\)
\(420\) 0 0
\(421\) 882646. 0.242706 0.121353 0.992609i \(-0.461277\pi\)
0.121353 + 0.992609i \(0.461277\pi\)
\(422\) 0 0
\(423\) 1.61261e6 0.438206
\(424\) 0 0
\(425\) −688750. −0.184965
\(426\) 0 0
\(427\) 2.75743e6 0.731870
\(428\) 0 0
\(429\) 379936. 0.0996706
\(430\) 0 0
\(431\) −6.95086e6 −1.80238 −0.901188 0.433427i \(-0.857304\pi\)
−0.901188 + 0.433427i \(0.857304\pi\)
\(432\) 0 0
\(433\) 7.09723e6 1.81915 0.909577 0.415536i \(-0.136406\pi\)
0.909577 + 0.415536i \(0.136406\pi\)
\(434\) 0 0
\(435\) −686600. −0.173973
\(436\) 0 0
\(437\) −128352. −0.0321513
\(438\) 0 0
\(439\) 4.40444e6 1.09076 0.545380 0.838189i \(-0.316385\pi\)
0.545380 + 0.838189i \(0.316385\pi\)
\(440\) 0 0
\(441\) −545027. −0.133451
\(442\) 0 0
\(443\) −2.59066e6 −0.627193 −0.313596 0.949556i \(-0.601534\pi\)
−0.313596 + 0.949556i \(0.601534\pi\)
\(444\) 0 0
\(445\) −476950. −0.114175
\(446\) 0 0
\(447\) −709864. −0.168038
\(448\) 0 0
\(449\) 1.61888e6 0.378965 0.189483 0.981884i \(-0.439319\pi\)
0.189483 + 0.981884i \(0.439319\pi\)
\(450\) 0 0
\(451\) 1.62812e6 0.376916
\(452\) 0 0
\(453\) 468192. 0.107196
\(454\) 0 0
\(455\) −938350. −0.212489
\(456\) 0 0
\(457\) −7.32412e6 −1.64046 −0.820228 0.572036i \(-0.806154\pi\)
−0.820228 + 0.572036i \(0.806154\pi\)
\(458\) 0 0
\(459\) 2.07176e6 0.458995
\(460\) 0 0
\(461\) 5.86086e6 1.28443 0.642213 0.766526i \(-0.278016\pi\)
0.642213 + 0.766526i \(0.278016\pi\)
\(462\) 0 0
\(463\) −1.15974e6 −0.251426 −0.125713 0.992067i \(-0.540122\pi\)
−0.125713 + 0.992067i \(0.540122\pi\)
\(464\) 0 0
\(465\) −409600. −0.0878471
\(466\) 0 0
\(467\) −6.37889e6 −1.35348 −0.676742 0.736220i \(-0.736609\pi\)
−0.676742 + 0.736220i \(0.736609\pi\)
\(468\) 0 0
\(469\) 1.17894e6 0.247491
\(470\) 0 0
\(471\) −127944. −0.0265747
\(472\) 0 0
\(473\) 2.25928e6 0.464320
\(474\) 0 0
\(475\) −477500. −0.0971045
\(476\) 0 0
\(477\) 4.54590e6 0.914796
\(478\) 0 0
\(479\) −2.52893e6 −0.503614 −0.251807 0.967777i \(-0.581025\pi\)
−0.251807 + 0.967777i \(0.581025\pi\)
\(480\) 0 0
\(481\) −3.58641e6 −0.706802
\(482\) 0 0
\(483\) −32928.0 −0.00642240
\(484\) 0 0
\(485\) −2.89115e6 −0.558105
\(486\) 0 0
\(487\) −991272. −0.189396 −0.0946979 0.995506i \(-0.530189\pi\)
−0.0946979 + 0.995506i \(0.530189\pi\)
\(488\) 0 0
\(489\) 148240. 0.0280345
\(490\) 0 0
\(491\) −6.58506e6 −1.23270 −0.616348 0.787474i \(-0.711389\pi\)
−0.616348 + 0.787474i \(0.711389\pi\)
\(492\) 0 0
\(493\) 7.56633e6 1.40206
\(494\) 0 0
\(495\) −703700. −0.129085
\(496\) 0 0
\(497\) 1.56290e6 0.283819
\(498\) 0 0
\(499\) 6.39831e6 1.15031 0.575154 0.818045i \(-0.304942\pi\)
0.575154 + 0.818045i \(0.304942\pi\)
\(500\) 0 0
\(501\) 743520. 0.132342
\(502\) 0 0
\(503\) 1.91546e6 0.337562 0.168781 0.985654i \(-0.446017\pi\)
0.168781 + 0.985654i \(0.446017\pi\)
\(504\) 0 0
\(505\) 2.51975e6 0.439672
\(506\) 0 0
\(507\) 861852. 0.148906
\(508\) 0 0
\(509\) −2.72437e6 −0.466092 −0.233046 0.972466i \(-0.574869\pi\)
−0.233046 + 0.972466i \(0.574869\pi\)
\(510\) 0 0
\(511\) 1.15983e6 0.196491
\(512\) 0 0
\(513\) 1.43632e6 0.240967
\(514\) 0 0
\(515\) 332600. 0.0552591
\(516\) 0 0
\(517\) −880896. −0.144943
\(518\) 0 0
\(519\) 1.85996e6 0.303099
\(520\) 0 0
\(521\) 4.28260e6 0.691215 0.345608 0.938379i \(-0.387673\pi\)
0.345608 + 0.938379i \(0.387673\pi\)
\(522\) 0 0
\(523\) 3.61035e6 0.577158 0.288579 0.957456i \(-0.406817\pi\)
0.288579 + 0.957456i \(0.406817\pi\)
\(524\) 0 0
\(525\) −122500. −0.0193971
\(526\) 0 0
\(527\) 4.51379e6 0.707970
\(528\) 0 0
\(529\) −6.40812e6 −0.995615
\(530\) 0 0
\(531\) 8.84483e6 1.36130
\(532\) 0 0
\(533\) 1.00576e7 1.53347
\(534\) 0 0
\(535\) 3.20510e6 0.484125
\(536\) 0 0
\(537\) 3.34120e6 0.499996
\(538\) 0 0
\(539\) 297724. 0.0441410
\(540\) 0 0
\(541\) 1.17755e7 1.72977 0.864883 0.501973i \(-0.167392\pi\)
0.864883 + 0.501973i \(0.167392\pi\)
\(542\) 0 0
\(543\) −1.99473e6 −0.290325
\(544\) 0 0
\(545\) −4.41125e6 −0.636166
\(546\) 0 0
\(547\) −1.07968e7 −1.54286 −0.771428 0.636317i \(-0.780457\pi\)
−0.771428 + 0.636317i \(0.780457\pi\)
\(548\) 0 0
\(549\) 1.27742e7 1.80885
\(550\) 0 0
\(551\) 5.24562e6 0.736068
\(552\) 0 0
\(553\) −1.84946e6 −0.257176
\(554\) 0 0
\(555\) −468200. −0.0645207
\(556\) 0 0
\(557\) −1.11383e7 −1.52118 −0.760589 0.649234i \(-0.775090\pi\)
−0.760589 + 0.649234i \(0.775090\pi\)
\(558\) 0 0
\(559\) 1.39565e7 1.88907
\(560\) 0 0
\(561\) −546592. −0.0733257
\(562\) 0 0
\(563\) 4.49836e6 0.598112 0.299056 0.954235i \(-0.403328\pi\)
0.299056 + 0.954235i \(0.403328\pi\)
\(564\) 0 0
\(565\) −4.16835e6 −0.549342
\(566\) 0 0
\(567\) −2.33441e6 −0.304943
\(568\) 0 0
\(569\) −5.14929e6 −0.666755 −0.333378 0.942793i \(-0.608188\pi\)
−0.333378 + 0.942793i \(0.608188\pi\)
\(570\) 0 0
\(571\) 1.95544e6 0.250988 0.125494 0.992094i \(-0.459948\pi\)
0.125494 + 0.992094i \(0.459948\pi\)
\(572\) 0 0
\(573\) 1.18067e6 0.150225
\(574\) 0 0
\(575\) 105000. 0.0132440
\(576\) 0 0
\(577\) 2.50179e6 0.312833 0.156416 0.987691i \(-0.450006\pi\)
0.156416 + 0.987691i \(0.450006\pi\)
\(578\) 0 0
\(579\) 310024. 0.0384325
\(580\) 0 0
\(581\) 3.34200e6 0.410739
\(582\) 0 0
\(583\) −2.48322e6 −0.302583
\(584\) 0 0
\(585\) −4.34705e6 −0.525176
\(586\) 0 0
\(587\) 1.31352e7 1.57341 0.786703 0.617332i \(-0.211786\pi\)
0.786703 + 0.617332i \(0.211786\pi\)
\(588\) 0 0
\(589\) 3.12934e6 0.371676
\(590\) 0 0
\(591\) 1.24194e6 0.146263
\(592\) 0 0
\(593\) −1.61671e7 −1.88797 −0.943983 0.329994i \(-0.892953\pi\)
−0.943983 + 0.329994i \(0.892953\pi\)
\(594\) 0 0
\(595\) 1.34995e6 0.156324
\(596\) 0 0
\(597\) 2.55632e6 0.293548
\(598\) 0 0
\(599\) −1.39864e7 −1.59272 −0.796359 0.604824i \(-0.793244\pi\)
−0.796359 + 0.604824i \(0.793244\pi\)
\(600\) 0 0
\(601\) 5.95609e6 0.672628 0.336314 0.941750i \(-0.390820\pi\)
0.336314 + 0.941750i \(0.390820\pi\)
\(602\) 0 0
\(603\) 5.46162e6 0.611686
\(604\) 0 0
\(605\) −3.64188e6 −0.404517
\(606\) 0 0
\(607\) −1.44142e7 −1.58789 −0.793943 0.607992i \(-0.791975\pi\)
−0.793943 + 0.607992i \(0.791975\pi\)
\(608\) 0 0
\(609\) 1.34574e6 0.147034
\(610\) 0 0
\(611\) −5.44166e6 −0.589697
\(612\) 0 0
\(613\) −1.08923e6 −0.117076 −0.0585379 0.998285i \(-0.518644\pi\)
−0.0585379 + 0.998285i \(0.518644\pi\)
\(614\) 0 0
\(615\) 1.31300e6 0.139984
\(616\) 0 0
\(617\) −983542. −0.104011 −0.0520056 0.998647i \(-0.516561\pi\)
−0.0520056 + 0.998647i \(0.516561\pi\)
\(618\) 0 0
\(619\) 1.30483e7 1.36875 0.684377 0.729128i \(-0.260074\pi\)
0.684377 + 0.729128i \(0.260074\pi\)
\(620\) 0 0
\(621\) −315840. −0.0328653
\(622\) 0 0
\(623\) 934822. 0.0964959
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) −378944. −0.0384952
\(628\) 0 0
\(629\) 5.15956e6 0.519980
\(630\) 0 0
\(631\) 8.59951e6 0.859806 0.429903 0.902875i \(-0.358548\pi\)
0.429903 + 0.902875i \(0.358548\pi\)
\(632\) 0 0
\(633\) 3.94254e6 0.391082
\(634\) 0 0
\(635\) 5.70280e6 0.561247
\(636\) 0 0
\(637\) 1.83917e6 0.179586
\(638\) 0 0
\(639\) 7.24039e6 0.701471
\(640\) 0 0
\(641\) −7.40288e6 −0.711632 −0.355816 0.934556i \(-0.615797\pi\)
−0.355816 + 0.934556i \(0.615797\pi\)
\(642\) 0 0
\(643\) −7.68038e6 −0.732580 −0.366290 0.930501i \(-0.619372\pi\)
−0.366290 + 0.930501i \(0.619372\pi\)
\(644\) 0 0
\(645\) 1.82200e6 0.172444
\(646\) 0 0
\(647\) −2.00321e6 −0.188133 −0.0940666 0.995566i \(-0.529987\pi\)
−0.0940666 + 0.995566i \(0.529987\pi\)
\(648\) 0 0
\(649\) −4.83154e6 −0.450270
\(650\) 0 0
\(651\) 802816. 0.0742444
\(652\) 0 0
\(653\) 3.64089e6 0.334137 0.167069 0.985945i \(-0.446570\pi\)
0.167069 + 0.985945i \(0.446570\pi\)
\(654\) 0 0
\(655\) 3.29490e6 0.300081
\(656\) 0 0
\(657\) 5.37309e6 0.485636
\(658\) 0 0
\(659\) 3.02720e6 0.271536 0.135768 0.990741i \(-0.456650\pi\)
0.135768 + 0.990741i \(0.456650\pi\)
\(660\) 0 0
\(661\) −5.76758e6 −0.513440 −0.256720 0.966486i \(-0.582642\pi\)
−0.256720 + 0.966486i \(0.582642\pi\)
\(662\) 0 0
\(663\) −3.37653e6 −0.298323
\(664\) 0 0
\(665\) 935900. 0.0820683
\(666\) 0 0
\(667\) −1.15349e6 −0.100392
\(668\) 0 0
\(669\) 5.07680e6 0.438556
\(670\) 0 0
\(671\) −6.97798e6 −0.598306
\(672\) 0 0
\(673\) 1.43872e7 1.22444 0.612220 0.790687i \(-0.290277\pi\)
0.612220 + 0.790687i \(0.290277\pi\)
\(674\) 0 0
\(675\) −1.17500e6 −0.0992610
\(676\) 0 0
\(677\) −4.13262e6 −0.346540 −0.173270 0.984874i \(-0.555433\pi\)
−0.173270 + 0.984874i \(0.555433\pi\)
\(678\) 0 0
\(679\) 5.66665e6 0.471685
\(680\) 0 0
\(681\) −4.07371e6 −0.336607
\(682\) 0 0
\(683\) −5.15356e6 −0.422722 −0.211361 0.977408i \(-0.567790\pi\)
−0.211361 + 0.977408i \(0.567790\pi\)
\(684\) 0 0
\(685\) −4.69655e6 −0.382431
\(686\) 0 0
\(687\) 1.76943e6 0.143035
\(688\) 0 0
\(689\) −1.53399e7 −1.23105
\(690\) 0 0
\(691\) −1.01299e6 −0.0807066 −0.0403533 0.999185i \(-0.512848\pi\)
−0.0403533 + 0.999185i \(0.512848\pi\)
\(692\) 0 0
\(693\) 1.37925e6 0.109096
\(694\) 0 0
\(695\) −2.66010e6 −0.208899
\(696\) 0 0
\(697\) −1.44693e7 −1.12814
\(698\) 0 0
\(699\) 1.58724e6 0.122871
\(700\) 0 0
\(701\) 7.19041e6 0.552661 0.276331 0.961063i \(-0.410882\pi\)
0.276331 + 0.961063i \(0.410882\pi\)
\(702\) 0 0
\(703\) 3.57705e6 0.272984
\(704\) 0 0
\(705\) −710400. −0.0538307
\(706\) 0 0
\(707\) −4.93871e6 −0.371591
\(708\) 0 0
\(709\) −2.41861e7 −1.80697 −0.903484 0.428621i \(-0.859000\pi\)
−0.903484 + 0.428621i \(0.859000\pi\)
\(710\) 0 0
\(711\) −8.56789e6 −0.635623
\(712\) 0 0
\(713\) −688128. −0.0506927
\(714\) 0 0
\(715\) 2.37460e6 0.173710
\(716\) 0 0
\(717\) 2.59949e6 0.188838
\(718\) 0 0
\(719\) 1.88305e7 1.35844 0.679218 0.733937i \(-0.262319\pi\)
0.679218 + 0.733937i \(0.262319\pi\)
\(720\) 0 0
\(721\) −651896. −0.0467025
\(722\) 0 0
\(723\) 2.86433e6 0.203787
\(724\) 0 0
\(725\) −4.29125e6 −0.303207
\(726\) 0 0
\(727\) 1.42513e7 1.00005 0.500023 0.866012i \(-0.333325\pi\)
0.500023 + 0.866012i \(0.333325\pi\)
\(728\) 0 0
\(729\) −8.98715e6 −0.626330
\(730\) 0 0
\(731\) −2.00784e7 −1.38975
\(732\) 0 0
\(733\) −945586. −0.0650042 −0.0325021 0.999472i \(-0.510348\pi\)
−0.0325021 + 0.999472i \(0.510348\pi\)
\(734\) 0 0
\(735\) 240100. 0.0163936
\(736\) 0 0
\(737\) −2.98344e6 −0.202325
\(738\) 0 0
\(739\) −2.01534e6 −0.135749 −0.0678746 0.997694i \(-0.521622\pi\)
−0.0678746 + 0.997694i \(0.521622\pi\)
\(740\) 0 0
\(741\) −2.34090e6 −0.156616
\(742\) 0 0
\(743\) −1.22830e7 −0.816264 −0.408132 0.912923i \(-0.633820\pi\)
−0.408132 + 0.912923i \(0.633820\pi\)
\(744\) 0 0
\(745\) −4.43665e6 −0.292863
\(746\) 0 0
\(747\) 1.54823e7 1.01516
\(748\) 0 0
\(749\) −6.28200e6 −0.409160
\(750\) 0 0
\(751\) 6.43979e6 0.416651 0.208325 0.978060i \(-0.433199\pi\)
0.208325 + 0.978060i \(0.433199\pi\)
\(752\) 0 0
\(753\) −1.64744e6 −0.105882
\(754\) 0 0
\(755\) 2.92620e6 0.186826
\(756\) 0 0
\(757\) 1.08870e7 0.690507 0.345253 0.938510i \(-0.387793\pi\)
0.345253 + 0.938510i \(0.387793\pi\)
\(758\) 0 0
\(759\) 83328.0 0.00525033
\(760\) 0 0
\(761\) −2.57412e7 −1.61126 −0.805632 0.592417i \(-0.798174\pi\)
−0.805632 + 0.592417i \(0.798174\pi\)
\(762\) 0 0
\(763\) 8.64605e6 0.537658
\(764\) 0 0
\(765\) 6.25385e6 0.386362
\(766\) 0 0
\(767\) −2.98464e7 −1.83191
\(768\) 0 0
\(769\) −2.38746e7 −1.45586 −0.727930 0.685652i \(-0.759517\pi\)
−0.727930 + 0.685652i \(0.759517\pi\)
\(770\) 0 0
\(771\) −6.07423e6 −0.368006
\(772\) 0 0
\(773\) 1.70534e7 1.02651 0.513254 0.858237i \(-0.328440\pi\)
0.513254 + 0.858237i \(0.328440\pi\)
\(774\) 0 0
\(775\) −2.56000e6 −0.153104
\(776\) 0 0
\(777\) 917672. 0.0545299
\(778\) 0 0
\(779\) −1.00313e7 −0.592263
\(780\) 0 0
\(781\) −3.95510e6 −0.232023
\(782\) 0 0
\(783\) 1.29081e7 0.752415
\(784\) 0 0
\(785\) −799650. −0.0463154
\(786\) 0 0
\(787\) 2.15326e7 1.23925 0.619626 0.784897i \(-0.287284\pi\)
0.619626 + 0.784897i \(0.287284\pi\)
\(788\) 0 0
\(789\) −7.10186e6 −0.406143
\(790\) 0 0
\(791\) 8.16997e6 0.464279
\(792\) 0 0
\(793\) −4.31059e7 −2.43419
\(794\) 0 0
\(795\) −2.00260e6 −0.112377
\(796\) 0 0
\(797\) −7.38450e6 −0.411789 −0.205895 0.978574i \(-0.566010\pi\)
−0.205895 + 0.978574i \(0.566010\pi\)
\(798\) 0 0
\(799\) 7.82861e6 0.433828
\(800\) 0 0
\(801\) 4.33071e6 0.238494
\(802\) 0 0
\(803\) −2.93508e6 −0.160632
\(804\) 0 0
\(805\) −205800. −0.0111932
\(806\) 0 0
\(807\) 2.20006e6 0.118919
\(808\) 0 0
\(809\) −2.80415e7 −1.50637 −0.753183 0.657811i \(-0.771482\pi\)
−0.753183 + 0.657811i \(0.771482\pi\)
\(810\) 0 0
\(811\) 1.07165e7 0.572138 0.286069 0.958209i \(-0.407651\pi\)
0.286069 + 0.958209i \(0.407651\pi\)
\(812\) 0 0
\(813\) −256576. −0.0136141
\(814\) 0 0
\(815\) 926500. 0.0488598
\(816\) 0 0
\(817\) −1.39201e7 −0.729603
\(818\) 0 0
\(819\) 8.52022e6 0.443855
\(820\) 0 0
\(821\) −2.28481e7 −1.18302 −0.591510 0.806298i \(-0.701468\pi\)
−0.591510 + 0.806298i \(0.701468\pi\)
\(822\) 0 0
\(823\) −1.36644e7 −0.703222 −0.351611 0.936146i \(-0.614366\pi\)
−0.351611 + 0.936146i \(0.614366\pi\)
\(824\) 0 0
\(825\) 310000. 0.0158572
\(826\) 0 0
\(827\) −1.59497e7 −0.810938 −0.405469 0.914109i \(-0.632892\pi\)
−0.405469 + 0.914109i \(0.632892\pi\)
\(828\) 0 0
\(829\) −615250. −0.0310932 −0.0155466 0.999879i \(-0.504949\pi\)
−0.0155466 + 0.999879i \(0.504949\pi\)
\(830\) 0 0
\(831\) 451992. 0.0227053
\(832\) 0 0
\(833\) −2.64590e6 −0.132118
\(834\) 0 0
\(835\) 4.64700e6 0.230652
\(836\) 0 0
\(837\) 7.70048e6 0.379930
\(838\) 0 0
\(839\) −5.07702e6 −0.249002 −0.124501 0.992219i \(-0.539733\pi\)
−0.124501 + 0.992219i \(0.539733\pi\)
\(840\) 0 0
\(841\) 2.66308e7 1.29836
\(842\) 0 0
\(843\) 2.42532e6 0.117544
\(844\) 0 0
\(845\) 5.38658e6 0.259520
\(846\) 0 0
\(847\) 7.13808e6 0.341879
\(848\) 0 0
\(849\) −2.26178e6 −0.107691
\(850\) 0 0
\(851\) −786576. −0.0372320
\(852\) 0 0
\(853\) 2.28325e7 1.07444 0.537218 0.843443i \(-0.319475\pi\)
0.537218 + 0.843443i \(0.319475\pi\)
\(854\) 0 0
\(855\) 4.33570e6 0.202835
\(856\) 0 0
\(857\) 1.03857e7 0.483040 0.241520 0.970396i \(-0.422354\pi\)
0.241520 + 0.970396i \(0.422354\pi\)
\(858\) 0 0
\(859\) −9.66607e6 −0.446958 −0.223479 0.974709i \(-0.571741\pi\)
−0.223479 + 0.974709i \(0.571741\pi\)
\(860\) 0 0
\(861\) −2.57348e6 −0.118308
\(862\) 0 0
\(863\) −2.47160e7 −1.12967 −0.564835 0.825204i \(-0.691060\pi\)
−0.564835 + 0.825204i \(0.691060\pi\)
\(864\) 0 0
\(865\) 1.16248e7 0.528255
\(866\) 0 0
\(867\) −821812. −0.0371300
\(868\) 0 0
\(869\) 4.68026e6 0.210242
\(870\) 0 0
\(871\) −1.84300e7 −0.823150
\(872\) 0 0
\(873\) 2.62516e7 1.16579
\(874\) 0 0
\(875\) −765625. −0.0338062
\(876\) 0 0
\(877\) 3.87672e7 1.70202 0.851012 0.525147i \(-0.175990\pi\)
0.851012 + 0.525147i \(0.175990\pi\)
\(878\) 0 0
\(879\) −2.90590e6 −0.126855
\(880\) 0 0
\(881\) 1.21677e7 0.528162 0.264081 0.964500i \(-0.414931\pi\)
0.264081 + 0.964500i \(0.414931\pi\)
\(882\) 0 0
\(883\) −4.54978e7 −1.96376 −0.981881 0.189497i \(-0.939314\pi\)
−0.981881 + 0.189497i \(0.939314\pi\)
\(884\) 0 0
\(885\) −3.89640e6 −0.167227
\(886\) 0 0
\(887\) 1.30952e7 0.558860 0.279430 0.960166i \(-0.409854\pi\)
0.279430 + 0.960166i \(0.409854\pi\)
\(888\) 0 0
\(889\) −1.11775e7 −0.474340
\(890\) 0 0
\(891\) 5.90748e6 0.249292
\(892\) 0 0
\(893\) 5.42746e6 0.227755
\(894\) 0 0
\(895\) 2.08825e7 0.871415
\(896\) 0 0
\(897\) 514752. 0.0213608
\(898\) 0 0
\(899\) 2.81231e7 1.16055
\(900\) 0 0
\(901\) 2.20687e7 0.905657
\(902\) 0 0
\(903\) −3.57112e6 −0.145742
\(904\) 0 0
\(905\) −1.24670e7 −0.505990
\(906\) 0 0
\(907\) 9.98552e6 0.403044 0.201522 0.979484i \(-0.435411\pi\)
0.201522 + 0.979484i \(0.435411\pi\)
\(908\) 0 0
\(909\) −2.28793e7 −0.918404
\(910\) 0 0
\(911\) −1.58347e7 −0.632140 −0.316070 0.948736i \(-0.602363\pi\)
−0.316070 + 0.948736i \(0.602363\pi\)
\(912\) 0 0
\(913\) −8.45730e6 −0.335780
\(914\) 0 0
\(915\) −5.62740e6 −0.222206
\(916\) 0 0
\(917\) −6.45800e6 −0.253615
\(918\) 0 0
\(919\) 4.40462e7 1.72036 0.860180 0.509991i \(-0.170351\pi\)
0.860180 + 0.509991i \(0.170351\pi\)
\(920\) 0 0
\(921\) 6.77384e6 0.263139
\(922\) 0 0
\(923\) −2.44323e7 −0.943976
\(924\) 0 0
\(925\) −2.92625e6 −0.112449
\(926\) 0 0
\(927\) −3.02001e6 −0.115427
\(928\) 0 0
\(929\) −1.33648e7 −0.508068 −0.254034 0.967195i \(-0.581758\pi\)
−0.254034 + 0.967195i \(0.581758\pi\)
\(930\) 0 0
\(931\) −1.83436e6 −0.0693604
\(932\) 0 0
\(933\) 1.01074e7 0.380131
\(934\) 0 0
\(935\) −3.41620e6 −0.127795
\(936\) 0 0
\(937\) −2.72180e7 −1.01276 −0.506381 0.862310i \(-0.669017\pi\)
−0.506381 + 0.862310i \(0.669017\pi\)
\(938\) 0 0
\(939\) 4.03863e6 0.149476
\(940\) 0 0
\(941\) 3.09420e7 1.13913 0.569566 0.821946i \(-0.307111\pi\)
0.569566 + 0.821946i \(0.307111\pi\)
\(942\) 0 0
\(943\) 2.20584e6 0.0807783
\(944\) 0 0
\(945\) 2.30300e6 0.0838908
\(946\) 0 0
\(947\) 6.39058e6 0.231561 0.115780 0.993275i \(-0.463063\pi\)
0.115780 + 0.993275i \(0.463063\pi\)
\(948\) 0 0
\(949\) −1.81312e7 −0.653524
\(950\) 0 0
\(951\) −4.59169e6 −0.164635
\(952\) 0 0
\(953\) −3.72447e7 −1.32841 −0.664205 0.747550i \(-0.731230\pi\)
−0.664205 + 0.747550i \(0.731230\pi\)
\(954\) 0 0
\(955\) 7.37920e6 0.261819
\(956\) 0 0
\(957\) −3.40554e6 −0.120200
\(958\) 0 0
\(959\) 9.20524e6 0.323213
\(960\) 0 0
\(961\) −1.18519e7 −0.413981
\(962\) 0 0
\(963\) −2.91023e7 −1.01126
\(964\) 0 0
\(965\) 1.93765e6 0.0669818
\(966\) 0 0
\(967\) 4.34627e7 1.49469 0.747344 0.664437i \(-0.231329\pi\)
0.747344 + 0.664437i \(0.231329\pi\)
\(968\) 0 0
\(969\) 3.36771e6 0.115219
\(970\) 0 0
\(971\) −4.88474e7 −1.66262 −0.831311 0.555807i \(-0.812409\pi\)
−0.831311 + 0.555807i \(0.812409\pi\)
\(972\) 0 0
\(973\) 5.21380e6 0.176552
\(974\) 0 0
\(975\) 1.91500e6 0.0645145
\(976\) 0 0
\(977\) 1.46440e7 0.490823 0.245411 0.969419i \(-0.421077\pi\)
0.245411 + 0.969419i \(0.421077\pi\)
\(978\) 0 0
\(979\) −2.36567e6 −0.0788856
\(980\) 0 0
\(981\) 4.00542e7 1.32885
\(982\) 0 0
\(983\) −4.58487e7 −1.51336 −0.756681 0.653784i \(-0.773180\pi\)
−0.756681 + 0.653784i \(0.773180\pi\)
\(984\) 0 0
\(985\) 7.76215e6 0.254913
\(986\) 0 0
\(987\) 1.39238e6 0.0454953
\(988\) 0 0
\(989\) 3.06096e6 0.0995100
\(990\) 0 0
\(991\) 1.86037e7 0.601748 0.300874 0.953664i \(-0.402722\pi\)
0.300874 + 0.953664i \(0.402722\pi\)
\(992\) 0 0
\(993\) −1.20940e7 −0.389220
\(994\) 0 0
\(995\) 1.59770e7 0.511608
\(996\) 0 0
\(997\) 3.26338e7 1.03975 0.519876 0.854242i \(-0.325978\pi\)
0.519876 + 0.854242i \(0.325978\pi\)
\(998\) 0 0
\(999\) 8.80216e6 0.279046
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 280.6.a.b.1.1 1
4.3 odd 2 560.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.6.a.b.1.1 1 1.1 even 1 trivial
560.6.a.b.1.1 1 4.3 odd 2