Properties

Label 320.6.a.w.1.2
Level $320$
Weight $6$
Character 320.1
Self dual yes
Analytic conductor $51.323$
Analytic rank $1$
Dimension $2$
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: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{129}) \)
Defining polynomial: \(x^{2} - x - 32\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(6.17891\) of defining polynomial
Character \(\chi\) \(=\) 320.1

$q$-expansion

\(f(q)\) \(=\) \(q+28.7156 q^{3} -25.0000 q^{5} -42.1469 q^{7} +581.588 q^{9} +O(q^{10})\) \(q+28.7156 q^{3} -25.0000 q^{5} -42.1469 q^{7} +581.588 q^{9} -416.294 q^{11} -966.588 q^{13} -717.891 q^{15} -1834.11 q^{17} -317.763 q^{19} -1210.27 q^{21} +1568.02 q^{23} +625.000 q^{25} +9722.76 q^{27} -7757.28 q^{29} +102.644 q^{31} -11954.1 q^{33} +1053.67 q^{35} -1936.58 q^{37} -27756.2 q^{39} +7994.36 q^{41} -16542.6 q^{43} -14539.7 q^{45} +18649.3 q^{47} -15030.6 q^{49} -52667.7 q^{51} +14972.4 q^{53} +10407.3 q^{55} -9124.76 q^{57} -19843.3 q^{59} +18024.1 q^{61} -24512.1 q^{63} +24164.7 q^{65} +55040.6 q^{67} +45026.8 q^{69} +11201.3 q^{71} -4013.95 q^{73} +17947.3 q^{75} +17545.5 q^{77} +24018.8 q^{79} +137869. q^{81} -70512.8 q^{83} +45852.8 q^{85} -222755. q^{87} -60765.7 q^{89} +40738.7 q^{91} +2947.49 q^{93} +7944.07 q^{95} -31112.2 q^{97} -242111. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 12q^{3} - 50q^{5} + 52q^{7} + 618q^{9} + O(q^{10}) \) \( 2q + 12q^{3} - 50q^{5} + 52q^{7} + 618q^{9} - 560q^{11} - 1388q^{13} - 300q^{15} + 148q^{17} + 1000q^{19} - 2784q^{21} - 2452q^{23} + 1250q^{25} + 13176q^{27} - 1340q^{29} - 2248q^{31} - 9552q^{33} - 1300q^{35} + 5940q^{37} - 20712q^{39} + 23076q^{41} - 17684q^{43} - 15450q^{45} - 2908q^{47} - 22974q^{49} - 85800q^{51} + 5412q^{53} + 14000q^{55} - 31152q^{57} - 62584q^{59} - 14108q^{61} - 21084q^{63} + 34700q^{65} + 85412q^{67} + 112224q^{69} + 47208q^{71} - 67452q^{73} + 7500q^{75} + 4016q^{77} - 65904q^{79} + 71298q^{81} - 108724q^{83} - 3700q^{85} - 330024q^{87} - 55020q^{89} + 1064q^{91} + 42240q^{93} - 25000q^{95} + 147668q^{97} - 247344q^{99} + O(q^{100}) \)

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
\(3\) 28.7156 1.84211 0.921054 0.389434i \(-0.127329\pi\)
0.921054 + 0.389434i \(0.127329\pi\)
\(4\) 0 0
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) −42.1469 −0.325103 −0.162551 0.986700i \(-0.551972\pi\)
−0.162551 + 0.986700i \(0.551972\pi\)
\(8\) 0 0
\(9\) 581.588 2.39336
\(10\) 0 0
\(11\) −416.294 −1.03733 −0.518667 0.854977i \(-0.673571\pi\)
−0.518667 + 0.854977i \(0.673571\pi\)
\(12\) 0 0
\(13\) −966.588 −1.58629 −0.793145 0.609032i \(-0.791558\pi\)
−0.793145 + 0.609032i \(0.791558\pi\)
\(14\) 0 0
\(15\) −717.891 −0.823816
\(16\) 0 0
\(17\) −1834.11 −1.53923 −0.769616 0.638508i \(-0.779552\pi\)
−0.769616 + 0.638508i \(0.779552\pi\)
\(18\) 0 0
\(19\) −317.763 −0.201938 −0.100969 0.994890i \(-0.532194\pi\)
−0.100969 + 0.994890i \(0.532194\pi\)
\(20\) 0 0
\(21\) −1210.27 −0.598874
\(22\) 0 0
\(23\) 1568.02 0.618063 0.309032 0.951052i \(-0.399995\pi\)
0.309032 + 0.951052i \(0.399995\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 9722.76 2.56673
\(28\) 0 0
\(29\) −7757.28 −1.71283 −0.856415 0.516288i \(-0.827313\pi\)
−0.856415 + 0.516288i \(0.827313\pi\)
\(30\) 0 0
\(31\) 102.644 0.0191836 0.00959180 0.999954i \(-0.496947\pi\)
0.00959180 + 0.999954i \(0.496947\pi\)
\(32\) 0 0
\(33\) −11954.1 −1.91088
\(34\) 0 0
\(35\) 1053.67 0.145390
\(36\) 0 0
\(37\) −1936.58 −0.232558 −0.116279 0.993217i \(-0.537097\pi\)
−0.116279 + 0.993217i \(0.537097\pi\)
\(38\) 0 0
\(39\) −27756.2 −2.92212
\(40\) 0 0
\(41\) 7994.36 0.742718 0.371359 0.928489i \(-0.378892\pi\)
0.371359 + 0.928489i \(0.378892\pi\)
\(42\) 0 0
\(43\) −16542.6 −1.36437 −0.682186 0.731179i \(-0.738970\pi\)
−0.682186 + 0.731179i \(0.738970\pi\)
\(44\) 0 0
\(45\) −14539.7 −1.07035
\(46\) 0 0
\(47\) 18649.3 1.23146 0.615728 0.787959i \(-0.288862\pi\)
0.615728 + 0.787959i \(0.288862\pi\)
\(48\) 0 0
\(49\) −15030.6 −0.894308
\(50\) 0 0
\(51\) −52667.7 −2.83543
\(52\) 0 0
\(53\) 14972.4 0.732155 0.366077 0.930584i \(-0.380701\pi\)
0.366077 + 0.930584i \(0.380701\pi\)
\(54\) 0 0
\(55\) 10407.3 0.463909
\(56\) 0 0
\(57\) −9124.76 −0.371993
\(58\) 0 0
\(59\) −19843.3 −0.742137 −0.371069 0.928605i \(-0.621009\pi\)
−0.371069 + 0.928605i \(0.621009\pi\)
\(60\) 0 0
\(61\) 18024.1 0.620195 0.310097 0.950705i \(-0.399638\pi\)
0.310097 + 0.950705i \(0.399638\pi\)
\(62\) 0 0
\(63\) −24512.1 −0.778089
\(64\) 0 0
\(65\) 24164.7 0.709411
\(66\) 0 0
\(67\) 55040.6 1.49795 0.748973 0.662601i \(-0.230547\pi\)
0.748973 + 0.662601i \(0.230547\pi\)
\(68\) 0 0
\(69\) 45026.8 1.13854
\(70\) 0 0
\(71\) 11201.3 0.263707 0.131853 0.991269i \(-0.457907\pi\)
0.131853 + 0.991269i \(0.457907\pi\)
\(72\) 0 0
\(73\) −4013.95 −0.0881587 −0.0440793 0.999028i \(-0.514035\pi\)
−0.0440793 + 0.999028i \(0.514035\pi\)
\(74\) 0 0
\(75\) 17947.3 0.368422
\(76\) 0 0
\(77\) 17545.5 0.337240
\(78\) 0 0
\(79\) 24018.8 0.432996 0.216498 0.976283i \(-0.430537\pi\)
0.216498 + 0.976283i \(0.430537\pi\)
\(80\) 0 0
\(81\) 137869. 2.33483
\(82\) 0 0
\(83\) −70512.8 −1.12350 −0.561750 0.827307i \(-0.689872\pi\)
−0.561750 + 0.827307i \(0.689872\pi\)
\(84\) 0 0
\(85\) 45852.8 0.688365
\(86\) 0 0
\(87\) −222755. −3.15522
\(88\) 0 0
\(89\) −60765.7 −0.813174 −0.406587 0.913612i \(-0.633281\pi\)
−0.406587 + 0.913612i \(0.633281\pi\)
\(90\) 0 0
\(91\) 40738.7 0.515707
\(92\) 0 0
\(93\) 2947.49 0.0353383
\(94\) 0 0
\(95\) 7944.07 0.0903096
\(96\) 0 0
\(97\) −31112.2 −0.335739 −0.167869 0.985809i \(-0.553689\pi\)
−0.167869 + 0.985809i \(0.553689\pi\)
\(98\) 0 0
\(99\) −242111. −2.48272
\(100\) 0 0
\(101\) 49491.4 0.482755 0.241377 0.970431i \(-0.422401\pi\)
0.241377 + 0.970431i \(0.422401\pi\)
\(102\) 0 0
\(103\) −95117.9 −0.883424 −0.441712 0.897157i \(-0.645629\pi\)
−0.441712 + 0.897157i \(0.645629\pi\)
\(104\) 0 0
\(105\) 30256.9 0.267825
\(106\) 0 0
\(107\) −88429.8 −0.746688 −0.373344 0.927693i \(-0.621789\pi\)
−0.373344 + 0.927693i \(0.621789\pi\)
\(108\) 0 0
\(109\) 10598.9 0.0854464 0.0427232 0.999087i \(-0.486397\pi\)
0.0427232 + 0.999087i \(0.486397\pi\)
\(110\) 0 0
\(111\) −55610.0 −0.428396
\(112\) 0 0
\(113\) 235124. 1.73221 0.866107 0.499859i \(-0.166615\pi\)
0.866107 + 0.499859i \(0.166615\pi\)
\(114\) 0 0
\(115\) −39200.6 −0.276406
\(116\) 0 0
\(117\) −562155. −3.79657
\(118\) 0 0
\(119\) 77302.2 0.500408
\(120\) 0 0
\(121\) 12249.5 0.0760599
\(122\) 0 0
\(123\) 229563. 1.36817
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) −102533. −0.564098 −0.282049 0.959400i \(-0.591014\pi\)
−0.282049 + 0.959400i \(0.591014\pi\)
\(128\) 0 0
\(129\) −475031. −2.51332
\(130\) 0 0
\(131\) −50603.0 −0.257631 −0.128815 0.991669i \(-0.541117\pi\)
−0.128815 + 0.991669i \(0.541117\pi\)
\(132\) 0 0
\(133\) 13392.7 0.0656507
\(134\) 0 0
\(135\) −243069. −1.14788
\(136\) 0 0
\(137\) 47811.7 0.217637 0.108818 0.994062i \(-0.465293\pi\)
0.108818 + 0.994062i \(0.465293\pi\)
\(138\) 0 0
\(139\) 220190. 0.966629 0.483314 0.875447i \(-0.339433\pi\)
0.483314 + 0.875447i \(0.339433\pi\)
\(140\) 0 0
\(141\) 535527. 2.26847
\(142\) 0 0
\(143\) 402384. 1.64551
\(144\) 0 0
\(145\) 193932. 0.766001
\(146\) 0 0
\(147\) −431614. −1.64741
\(148\) 0 0
\(149\) −154533. −0.570236 −0.285118 0.958492i \(-0.592033\pi\)
−0.285118 + 0.958492i \(0.592033\pi\)
\(150\) 0 0
\(151\) −455395. −1.62534 −0.812672 0.582721i \(-0.801988\pi\)
−0.812672 + 0.582721i \(0.801988\pi\)
\(152\) 0 0
\(153\) −1.06670e6 −3.68394
\(154\) 0 0
\(155\) −2566.11 −0.00857917
\(156\) 0 0
\(157\) −361690. −1.17108 −0.585541 0.810643i \(-0.699118\pi\)
−0.585541 + 0.810643i \(0.699118\pi\)
\(158\) 0 0
\(159\) 429943. 1.34871
\(160\) 0 0
\(161\) −66087.3 −0.200934
\(162\) 0 0
\(163\) −490843. −1.44702 −0.723508 0.690316i \(-0.757472\pi\)
−0.723508 + 0.690316i \(0.757472\pi\)
\(164\) 0 0
\(165\) 298854. 0.854572
\(166\) 0 0
\(167\) −196273. −0.544591 −0.272295 0.962214i \(-0.587783\pi\)
−0.272295 + 0.962214i \(0.587783\pi\)
\(168\) 0 0
\(169\) 562999. 1.51632
\(170\) 0 0
\(171\) −184807. −0.483312
\(172\) 0 0
\(173\) −183395. −0.465877 −0.232938 0.972491i \(-0.574834\pi\)
−0.232938 + 0.972491i \(0.574834\pi\)
\(174\) 0 0
\(175\) −26341.8 −0.0650205
\(176\) 0 0
\(177\) −569814. −1.36710
\(178\) 0 0
\(179\) 38660.0 0.0901839 0.0450920 0.998983i \(-0.485642\pi\)
0.0450920 + 0.998983i \(0.485642\pi\)
\(180\) 0 0
\(181\) 561287. 1.27347 0.636735 0.771083i \(-0.280285\pi\)
0.636735 + 0.771083i \(0.280285\pi\)
\(182\) 0 0
\(183\) 517572. 1.14247
\(184\) 0 0
\(185\) 48414.4 0.104003
\(186\) 0 0
\(187\) 763530. 1.59670
\(188\) 0 0
\(189\) −409784. −0.834450
\(190\) 0 0
\(191\) 265393. 0.526387 0.263194 0.964743i \(-0.415224\pi\)
0.263194 + 0.964743i \(0.415224\pi\)
\(192\) 0 0
\(193\) 863148. 1.66798 0.833992 0.551776i \(-0.186050\pi\)
0.833992 + 0.551776i \(0.186050\pi\)
\(194\) 0 0
\(195\) 693904. 1.30681
\(196\) 0 0
\(197\) −281871. −0.517469 −0.258734 0.965949i \(-0.583305\pi\)
−0.258734 + 0.965949i \(0.583305\pi\)
\(198\) 0 0
\(199\) −192798. −0.345120 −0.172560 0.984999i \(-0.555204\pi\)
−0.172560 + 0.984999i \(0.555204\pi\)
\(200\) 0 0
\(201\) 1.58053e6 2.75938
\(202\) 0 0
\(203\) 326945. 0.556846
\(204\) 0 0
\(205\) −199859. −0.332154
\(206\) 0 0
\(207\) 911943. 1.47925
\(208\) 0 0
\(209\) 132283. 0.209477
\(210\) 0 0
\(211\) −44631.4 −0.0690136 −0.0345068 0.999404i \(-0.510986\pi\)
−0.0345068 + 0.999404i \(0.510986\pi\)
\(212\) 0 0
\(213\) 321651. 0.485776
\(214\) 0 0
\(215\) 413565. 0.610165
\(216\) 0 0
\(217\) −4326.13 −0.00623664
\(218\) 0 0
\(219\) −115263. −0.162398
\(220\) 0 0
\(221\) 1.77283e6 2.44167
\(222\) 0 0
\(223\) −904469. −1.21796 −0.608978 0.793187i \(-0.708420\pi\)
−0.608978 + 0.793187i \(0.708420\pi\)
\(224\) 0 0
\(225\) 363492. 0.478673
\(226\) 0 0
\(227\) 1.02684e6 1.32263 0.661314 0.750109i \(-0.269999\pi\)
0.661314 + 0.750109i \(0.269999\pi\)
\(228\) 0 0
\(229\) 101521. 0.127928 0.0639641 0.997952i \(-0.479626\pi\)
0.0639641 + 0.997952i \(0.479626\pi\)
\(230\) 0 0
\(231\) 503830. 0.621232
\(232\) 0 0
\(233\) −313713. −0.378567 −0.189283 0.981923i \(-0.560616\pi\)
−0.189283 + 0.981923i \(0.560616\pi\)
\(234\) 0 0
\(235\) −466233. −0.550724
\(236\) 0 0
\(237\) 689715. 0.797625
\(238\) 0 0
\(239\) −1.53093e6 −1.73365 −0.866825 0.498612i \(-0.833843\pi\)
−0.866825 + 0.498612i \(0.833843\pi\)
\(240\) 0 0
\(241\) 506999. 0.562296 0.281148 0.959664i \(-0.409285\pi\)
0.281148 + 0.959664i \(0.409285\pi\)
\(242\) 0 0
\(243\) 1.59638e6 1.73428
\(244\) 0 0
\(245\) 375766. 0.399947
\(246\) 0 0
\(247\) 307146. 0.320333
\(248\) 0 0
\(249\) −2.02482e6 −2.06961
\(250\) 0 0
\(251\) 511659. 0.512621 0.256311 0.966594i \(-0.417493\pi\)
0.256311 + 0.966594i \(0.417493\pi\)
\(252\) 0 0
\(253\) −652758. −0.641137
\(254\) 0 0
\(255\) 1.31669e6 1.26804
\(256\) 0 0
\(257\) −256082. −0.241850 −0.120925 0.992662i \(-0.538586\pi\)
−0.120925 + 0.992662i \(0.538586\pi\)
\(258\) 0 0
\(259\) 81620.7 0.0756051
\(260\) 0 0
\(261\) −4.51154e6 −4.09943
\(262\) 0 0
\(263\) 1.32451e6 1.18077 0.590386 0.807121i \(-0.298976\pi\)
0.590386 + 0.807121i \(0.298976\pi\)
\(264\) 0 0
\(265\) −374311. −0.327430
\(266\) 0 0
\(267\) −1.74493e6 −1.49795
\(268\) 0 0
\(269\) 1.42989e6 1.20482 0.602410 0.798187i \(-0.294207\pi\)
0.602410 + 0.798187i \(0.294207\pi\)
\(270\) 0 0
\(271\) −706426. −0.584310 −0.292155 0.956371i \(-0.594372\pi\)
−0.292155 + 0.956371i \(0.594372\pi\)
\(272\) 0 0
\(273\) 1.16984e6 0.949989
\(274\) 0 0
\(275\) −260184. −0.207467
\(276\) 0 0
\(277\) −314677. −0.246414 −0.123207 0.992381i \(-0.539318\pi\)
−0.123207 + 0.992381i \(0.539318\pi\)
\(278\) 0 0
\(279\) 59696.6 0.0459134
\(280\) 0 0
\(281\) −437793. −0.330752 −0.165376 0.986231i \(-0.552884\pi\)
−0.165376 + 0.986231i \(0.552884\pi\)
\(282\) 0 0
\(283\) 2.08248e6 1.54566 0.772831 0.634612i \(-0.218840\pi\)
0.772831 + 0.634612i \(0.218840\pi\)
\(284\) 0 0
\(285\) 228119. 0.166360
\(286\) 0 0
\(287\) −336938. −0.241460
\(288\) 0 0
\(289\) 1.94411e6 1.36923
\(290\) 0 0
\(291\) −893407. −0.618468
\(292\) 0 0
\(293\) −90716.3 −0.0617329 −0.0308664 0.999524i \(-0.509827\pi\)
−0.0308664 + 0.999524i \(0.509827\pi\)
\(294\) 0 0
\(295\) 496083. 0.331894
\(296\) 0 0
\(297\) −4.04752e6 −2.66255
\(298\) 0 0
\(299\) −1.51563e6 −0.980428
\(300\) 0 0
\(301\) 697219. 0.443561
\(302\) 0 0
\(303\) 1.42118e6 0.889286
\(304\) 0 0
\(305\) −450601. −0.277359
\(306\) 0 0
\(307\) 571699. 0.346196 0.173098 0.984905i \(-0.444622\pi\)
0.173098 + 0.984905i \(0.444622\pi\)
\(308\) 0 0
\(309\) −2.73137e6 −1.62736
\(310\) 0 0
\(311\) 2.59515e6 1.52147 0.760733 0.649065i \(-0.224840\pi\)
0.760733 + 0.649065i \(0.224840\pi\)
\(312\) 0 0
\(313\) −510659. −0.294625 −0.147313 0.989090i \(-0.547062\pi\)
−0.147313 + 0.989090i \(0.547062\pi\)
\(314\) 0 0
\(315\) 612803. 0.347972
\(316\) 0 0
\(317\) 3.37030e6 1.88374 0.941868 0.335984i \(-0.109069\pi\)
0.941868 + 0.335984i \(0.109069\pi\)
\(318\) 0 0
\(319\) 3.22931e6 1.77678
\(320\) 0 0
\(321\) −2.53932e6 −1.37548
\(322\) 0 0
\(323\) 582813. 0.310830
\(324\) 0 0
\(325\) −604117. −0.317258
\(326\) 0 0
\(327\) 304354. 0.157402
\(328\) 0 0
\(329\) −786012. −0.400349
\(330\) 0 0
\(331\) −3.80172e6 −1.90726 −0.953632 0.300976i \(-0.902688\pi\)
−0.953632 + 0.300976i \(0.902688\pi\)
\(332\) 0 0
\(333\) −1.12629e6 −0.556595
\(334\) 0 0
\(335\) −1.37601e6 −0.669902
\(336\) 0 0
\(337\) 2.06627e6 0.991088 0.495544 0.868583i \(-0.334969\pi\)
0.495544 + 0.868583i \(0.334969\pi\)
\(338\) 0 0
\(339\) 6.75174e6 3.19093
\(340\) 0 0
\(341\) −42730.1 −0.0198998
\(342\) 0 0
\(343\) 1.34186e6 0.615845
\(344\) 0 0
\(345\) −1.12567e6 −0.509170
\(346\) 0 0
\(347\) −2.35066e6 −1.04801 −0.524005 0.851715i \(-0.675563\pi\)
−0.524005 + 0.851715i \(0.675563\pi\)
\(348\) 0 0
\(349\) −1.67220e6 −0.734896 −0.367448 0.930044i \(-0.619768\pi\)
−0.367448 + 0.930044i \(0.619768\pi\)
\(350\) 0 0
\(351\) −9.39790e6 −4.07158
\(352\) 0 0
\(353\) 1.71355e6 0.731914 0.365957 0.930632i \(-0.380742\pi\)
0.365957 + 0.930632i \(0.380742\pi\)
\(354\) 0 0
\(355\) −280032. −0.117933
\(356\) 0 0
\(357\) 2.21978e6 0.921806
\(358\) 0 0
\(359\) −3.85773e6 −1.57978 −0.789888 0.613251i \(-0.789861\pi\)
−0.789888 + 0.613251i \(0.789861\pi\)
\(360\) 0 0
\(361\) −2.37513e6 −0.959221
\(362\) 0 0
\(363\) 351753. 0.140111
\(364\) 0 0
\(365\) 100349. 0.0394258
\(366\) 0 0
\(367\) −3.18109e6 −1.23285 −0.616427 0.787412i \(-0.711420\pi\)
−0.616427 + 0.787412i \(0.711420\pi\)
\(368\) 0 0
\(369\) 4.64942e6 1.77760
\(370\) 0 0
\(371\) −631042. −0.238026
\(372\) 0 0
\(373\) 4.79295e6 1.78374 0.891868 0.452295i \(-0.149395\pi\)
0.891868 + 0.452295i \(0.149395\pi\)
\(374\) 0 0
\(375\) −448682. −0.164763
\(376\) 0 0
\(377\) 7.49809e6 2.71705
\(378\) 0 0
\(379\) −7018.36 −0.00250979 −0.00125490 0.999999i \(-0.500399\pi\)
−0.00125490 + 0.999999i \(0.500399\pi\)
\(380\) 0 0
\(381\) −2.94430e6 −1.03913
\(382\) 0 0
\(383\) −694105. −0.241784 −0.120892 0.992666i \(-0.538576\pi\)
−0.120892 + 0.992666i \(0.538576\pi\)
\(384\) 0 0
\(385\) −438637. −0.150818
\(386\) 0 0
\(387\) −9.62097e6 −3.26544
\(388\) 0 0
\(389\) 53514.1 0.0179306 0.00896529 0.999960i \(-0.497146\pi\)
0.00896529 + 0.999960i \(0.497146\pi\)
\(390\) 0 0
\(391\) −2.87593e6 −0.951342
\(392\) 0 0
\(393\) −1.45310e6 −0.474584
\(394\) 0 0
\(395\) −600470. −0.193642
\(396\) 0 0
\(397\) −907937. −0.289121 −0.144560 0.989496i \(-0.546177\pi\)
−0.144560 + 0.989496i \(0.546177\pi\)
\(398\) 0 0
\(399\) 384580. 0.120936
\(400\) 0 0
\(401\) −514404. −0.159751 −0.0798755 0.996805i \(-0.525452\pi\)
−0.0798755 + 0.996805i \(0.525452\pi\)
\(402\) 0 0
\(403\) −99214.6 −0.0304308
\(404\) 0 0
\(405\) −3.44673e6 −1.04417
\(406\) 0 0
\(407\) 806185. 0.241240
\(408\) 0 0
\(409\) 5.61814e6 1.66067 0.830337 0.557262i \(-0.188148\pi\)
0.830337 + 0.557262i \(0.188148\pi\)
\(410\) 0 0
\(411\) 1.37294e6 0.400911
\(412\) 0 0
\(413\) 836334. 0.241271
\(414\) 0 0
\(415\) 1.76282e6 0.502444
\(416\) 0 0
\(417\) 6.32288e6 1.78064
\(418\) 0 0
\(419\) −708382. −0.197121 −0.0985605 0.995131i \(-0.531424\pi\)
−0.0985605 + 0.995131i \(0.531424\pi\)
\(420\) 0 0
\(421\) 3.91741e6 1.07719 0.538597 0.842563i \(-0.318954\pi\)
0.538597 + 0.842563i \(0.318954\pi\)
\(422\) 0 0
\(423\) 1.08462e7 2.94732
\(424\) 0 0
\(425\) −1.14632e6 −0.307846
\(426\) 0 0
\(427\) −759658. −0.201627
\(428\) 0 0
\(429\) 1.15547e7 3.03121
\(430\) 0 0
\(431\) 4.42095e6 1.14636 0.573181 0.819429i \(-0.305709\pi\)
0.573181 + 0.819429i \(0.305709\pi\)
\(432\) 0 0
\(433\) −4.01914e6 −1.03018 −0.515090 0.857136i \(-0.672242\pi\)
−0.515090 + 0.857136i \(0.672242\pi\)
\(434\) 0 0
\(435\) 5.56888e6 1.41106
\(436\) 0 0
\(437\) −498259. −0.124811
\(438\) 0 0
\(439\) −5.41795e6 −1.34176 −0.670879 0.741567i \(-0.734083\pi\)
−0.670879 + 0.741567i \(0.734083\pi\)
\(440\) 0 0
\(441\) −8.74163e6 −2.14041
\(442\) 0 0
\(443\) 7.21518e6 1.74678 0.873389 0.487023i \(-0.161917\pi\)
0.873389 + 0.487023i \(0.161917\pi\)
\(444\) 0 0
\(445\) 1.51914e6 0.363662
\(446\) 0 0
\(447\) −4.43751e6 −1.05044
\(448\) 0 0
\(449\) −203792. −0.0477057 −0.0238529 0.999715i \(-0.507593\pi\)
−0.0238529 + 0.999715i \(0.507593\pi\)
\(450\) 0 0
\(451\) −3.32800e6 −0.770446
\(452\) 0 0
\(453\) −1.30769e7 −2.99406
\(454\) 0 0
\(455\) −1.01847e6 −0.230631
\(456\) 0 0
\(457\) −3.45642e6 −0.774169 −0.387085 0.922044i \(-0.626518\pi\)
−0.387085 + 0.922044i \(0.626518\pi\)
\(458\) 0 0
\(459\) −1.78326e7 −3.95079
\(460\) 0 0
\(461\) −6.40596e6 −1.40389 −0.701944 0.712233i \(-0.747684\pi\)
−0.701944 + 0.712233i \(0.747684\pi\)
\(462\) 0 0
\(463\) −7.59550e6 −1.64666 −0.823330 0.567563i \(-0.807887\pi\)
−0.823330 + 0.567563i \(0.807887\pi\)
\(464\) 0 0
\(465\) −73687.3 −0.0158038
\(466\) 0 0
\(467\) 4.58166e6 0.972145 0.486072 0.873919i \(-0.338429\pi\)
0.486072 + 0.873919i \(0.338429\pi\)
\(468\) 0 0
\(469\) −2.31979e6 −0.486986
\(470\) 0 0
\(471\) −1.03862e7 −2.15726
\(472\) 0 0
\(473\) 6.88658e6 1.41531
\(474\) 0 0
\(475\) −198602. −0.0403877
\(476\) 0 0
\(477\) 8.70779e6 1.75231
\(478\) 0 0
\(479\) 5.01195e6 0.998085 0.499043 0.866577i \(-0.333685\pi\)
0.499043 + 0.866577i \(0.333685\pi\)
\(480\) 0 0
\(481\) 1.87187e6 0.368904
\(482\) 0 0
\(483\) −1.89774e6 −0.370142
\(484\) 0 0
\(485\) 777806. 0.150147
\(486\) 0 0
\(487\) −2.10670e6 −0.402514 −0.201257 0.979539i \(-0.564503\pi\)
−0.201257 + 0.979539i \(0.564503\pi\)
\(488\) 0 0
\(489\) −1.40949e7 −2.66556
\(490\) 0 0
\(491\) −5.43322e6 −1.01708 −0.508538 0.861040i \(-0.669814\pi\)
−0.508538 + 0.861040i \(0.669814\pi\)
\(492\) 0 0
\(493\) 1.42277e7 2.63644
\(494\) 0 0
\(495\) 6.05278e6 1.11030
\(496\) 0 0
\(497\) −472099. −0.0857318
\(498\) 0 0
\(499\) −9.65183e6 −1.73523 −0.867617 0.497233i \(-0.834350\pi\)
−0.867617 + 0.497233i \(0.834350\pi\)
\(500\) 0 0
\(501\) −5.63611e6 −1.00319
\(502\) 0 0
\(503\) 1.33954e6 0.236067 0.118034 0.993010i \(-0.462341\pi\)
0.118034 + 0.993010i \(0.462341\pi\)
\(504\) 0 0
\(505\) −1.23729e6 −0.215894
\(506\) 0 0
\(507\) 1.61669e7 2.79322
\(508\) 0 0
\(509\) −4.60771e6 −0.788299 −0.394150 0.919046i \(-0.628961\pi\)
−0.394150 + 0.919046i \(0.628961\pi\)
\(510\) 0 0
\(511\) 169176. 0.0286606
\(512\) 0 0
\(513\) −3.08953e6 −0.518321
\(514\) 0 0
\(515\) 2.37795e6 0.395079
\(516\) 0 0
\(517\) −7.76360e6 −1.27743
\(518\) 0 0
\(519\) −5.26629e6 −0.858196
\(520\) 0 0
\(521\) −5.80941e6 −0.937644 −0.468822 0.883293i \(-0.655321\pi\)
−0.468822 + 0.883293i \(0.655321\pi\)
\(522\) 0 0
\(523\) 3.83877e6 0.613674 0.306837 0.951762i \(-0.400729\pi\)
0.306837 + 0.951762i \(0.400729\pi\)
\(524\) 0 0
\(525\) −756422. −0.119775
\(526\) 0 0
\(527\) −188261. −0.0295280
\(528\) 0 0
\(529\) −3.97765e6 −0.617998
\(530\) 0 0
\(531\) −1.15406e7 −1.77621
\(532\) 0 0
\(533\) −7.72725e6 −1.17817
\(534\) 0 0
\(535\) 2.21075e6 0.333929
\(536\) 0 0
\(537\) 1.11015e6 0.166129
\(538\) 0 0
\(539\) 6.25716e6 0.927696
\(540\) 0 0
\(541\) −6.28830e6 −0.923720 −0.461860 0.886953i \(-0.652818\pi\)
−0.461860 + 0.886953i \(0.652818\pi\)
\(542\) 0 0
\(543\) 1.61177e7 2.34587
\(544\) 0 0
\(545\) −264972. −0.0382128
\(546\) 0 0
\(547\) −4.54365e6 −0.649287 −0.324644 0.945836i \(-0.605244\pi\)
−0.324644 + 0.945836i \(0.605244\pi\)
\(548\) 0 0
\(549\) 1.04826e7 1.48435
\(550\) 0 0
\(551\) 2.46497e6 0.345886
\(552\) 0 0
\(553\) −1.01232e6 −0.140768
\(554\) 0 0
\(555\) 1.39025e6 0.191585
\(556\) 0 0
\(557\) −1.20198e7 −1.64157 −0.820783 0.571239i \(-0.806463\pi\)
−0.820783 + 0.571239i \(0.806463\pi\)
\(558\) 0 0
\(559\) 1.59899e7 2.16429
\(560\) 0 0
\(561\) 2.19252e7 2.94129
\(562\) 0 0
\(563\) −3.65741e6 −0.486298 −0.243149 0.969989i \(-0.578180\pi\)
−0.243149 + 0.969989i \(0.578180\pi\)
\(564\) 0 0
\(565\) −5.87811e6 −0.774670
\(566\) 0 0
\(567\) −5.81077e6 −0.759059
\(568\) 0 0
\(569\) −2.80214e6 −0.362835 −0.181418 0.983406i \(-0.558069\pi\)
−0.181418 + 0.983406i \(0.558069\pi\)
\(570\) 0 0
\(571\) 6.78472e6 0.870846 0.435423 0.900226i \(-0.356599\pi\)
0.435423 + 0.900226i \(0.356599\pi\)
\(572\) 0 0
\(573\) 7.62091e6 0.969662
\(574\) 0 0
\(575\) 980014. 0.123613
\(576\) 0 0
\(577\) −1.25416e6 −0.156825 −0.0784123 0.996921i \(-0.524985\pi\)
−0.0784123 + 0.996921i \(0.524985\pi\)
\(578\) 0 0
\(579\) 2.47858e7 3.07261
\(580\) 0 0
\(581\) 2.97190e6 0.365253
\(582\) 0 0
\(583\) −6.23293e6 −0.759488
\(584\) 0 0
\(585\) 1.40539e7 1.69788
\(586\) 0 0
\(587\) −726476. −0.0870213 −0.0435107 0.999053i \(-0.513854\pi\)
−0.0435107 + 0.999053i \(0.513854\pi\)
\(588\) 0 0
\(589\) −32616.5 −0.00387391
\(590\) 0 0
\(591\) −8.09409e6 −0.953234
\(592\) 0 0
\(593\) 933494. 0.109012 0.0545060 0.998513i \(-0.482642\pi\)
0.0545060 + 0.998513i \(0.482642\pi\)
\(594\) 0 0
\(595\) −1.93255e6 −0.223789
\(596\) 0 0
\(597\) −5.53632e6 −0.635749
\(598\) 0 0
\(599\) −1.27354e7 −1.45025 −0.725127 0.688615i \(-0.758219\pi\)
−0.725127 + 0.688615i \(0.758219\pi\)
\(600\) 0 0
\(601\) −6.87190e6 −0.776052 −0.388026 0.921648i \(-0.626843\pi\)
−0.388026 + 0.921648i \(0.626843\pi\)
\(602\) 0 0
\(603\) 3.20109e7 3.58513
\(604\) 0 0
\(605\) −306238. −0.0340150
\(606\) 0 0
\(607\) −3.87130e6 −0.426467 −0.213233 0.977001i \(-0.568399\pi\)
−0.213233 + 0.977001i \(0.568399\pi\)
\(608\) 0 0
\(609\) 9.38844e6 1.02577
\(610\) 0 0
\(611\) −1.80262e7 −1.95345
\(612\) 0 0
\(613\) 2.38824e6 0.256701 0.128350 0.991729i \(-0.459032\pi\)
0.128350 + 0.991729i \(0.459032\pi\)
\(614\) 0 0
\(615\) −5.73908e6 −0.611863
\(616\) 0 0
\(617\) −3.07299e6 −0.324974 −0.162487 0.986711i \(-0.551952\pi\)
−0.162487 + 0.986711i \(0.551952\pi\)
\(618\) 0 0
\(619\) −8.52257e6 −0.894013 −0.447007 0.894531i \(-0.647510\pi\)
−0.447007 + 0.894531i \(0.647510\pi\)
\(620\) 0 0
\(621\) 1.52455e7 1.58640
\(622\) 0 0
\(623\) 2.56109e6 0.264365
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 3.79858e6 0.385880
\(628\) 0 0
\(629\) 3.55190e6 0.357960
\(630\) 0 0
\(631\) 8.54170e6 0.854026 0.427013 0.904246i \(-0.359566\pi\)
0.427013 + 0.904246i \(0.359566\pi\)
\(632\) 0 0
\(633\) −1.28162e6 −0.127131
\(634\) 0 0
\(635\) 2.56333e6 0.252272
\(636\) 0 0
\(637\) 1.45284e7 1.41863
\(638\) 0 0
\(639\) 6.51452e6 0.631146
\(640\) 0 0
\(641\) 3.81006e6 0.366257 0.183129 0.983089i \(-0.441377\pi\)
0.183129 + 0.983089i \(0.441377\pi\)
\(642\) 0 0
\(643\) −1.40516e7 −1.34029 −0.670144 0.742231i \(-0.733768\pi\)
−0.670144 + 0.742231i \(0.733768\pi\)
\(644\) 0 0
\(645\) 1.18758e7 1.12399
\(646\) 0 0
\(647\) 962366. 0.0903815 0.0451908 0.998978i \(-0.485610\pi\)
0.0451908 + 0.998978i \(0.485610\pi\)
\(648\) 0 0
\(649\) 8.26065e6 0.769844
\(650\) 0 0
\(651\) −124228. −0.0114886
\(652\) 0 0
\(653\) 413989. 0.0379932 0.0189966 0.999820i \(-0.493953\pi\)
0.0189966 + 0.999820i \(0.493953\pi\)
\(654\) 0 0
\(655\) 1.26508e6 0.115216
\(656\) 0 0
\(657\) −2.33446e6 −0.210996
\(658\) 0 0
\(659\) 1.92401e7 1.72581 0.862905 0.505367i \(-0.168643\pi\)
0.862905 + 0.505367i \(0.168643\pi\)
\(660\) 0 0
\(661\) 2.04652e7 1.82185 0.910924 0.412574i \(-0.135370\pi\)
0.910924 + 0.412574i \(0.135370\pi\)
\(662\) 0 0
\(663\) 5.09080e7 4.49782
\(664\) 0 0
\(665\) −334818. −0.0293599
\(666\) 0 0
\(667\) −1.21636e7 −1.05864
\(668\) 0 0
\(669\) −2.59724e7 −2.24361
\(670\) 0 0
\(671\) −7.50330e6 −0.643348
\(672\) 0 0
\(673\) −9.12086e6 −0.776244 −0.388122 0.921608i \(-0.626876\pi\)
−0.388122 + 0.921608i \(0.626876\pi\)
\(674\) 0 0
\(675\) 6.07672e6 0.513346
\(676\) 0 0
\(677\) 1.29457e7 1.08556 0.542778 0.839876i \(-0.317372\pi\)
0.542778 + 0.839876i \(0.317372\pi\)
\(678\) 0 0
\(679\) 1.31128e6 0.109150
\(680\) 0 0
\(681\) 2.94863e7 2.43642
\(682\) 0 0
\(683\) 8.56637e6 0.702660 0.351330 0.936252i \(-0.385730\pi\)
0.351330 + 0.936252i \(0.385730\pi\)
\(684\) 0 0
\(685\) −1.19529e6 −0.0973302
\(686\) 0 0
\(687\) 2.91523e6 0.235658
\(688\) 0 0
\(689\) −1.44722e7 −1.16141
\(690\) 0 0
\(691\) 1.01163e7 0.805984 0.402992 0.915204i \(-0.367970\pi\)
0.402992 + 0.915204i \(0.367970\pi\)
\(692\) 0 0
\(693\) 1.02042e7 0.807138
\(694\) 0 0
\(695\) −5.50474e6 −0.432289
\(696\) 0 0
\(697\) −1.46626e7 −1.14322
\(698\) 0 0
\(699\) −9.00846e6 −0.697361
\(700\) 0 0
\(701\) 1.95732e7 1.50441 0.752207 0.658927i \(-0.228989\pi\)
0.752207 + 0.658927i \(0.228989\pi\)
\(702\) 0 0
\(703\) 615372. 0.0469623
\(704\) 0 0
\(705\) −1.33882e7 −1.01449
\(706\) 0 0
\(707\) −2.08591e6 −0.156945
\(708\) 0 0
\(709\) −2.36252e7 −1.76506 −0.882531 0.470254i \(-0.844162\pi\)
−0.882531 + 0.470254i \(0.844162\pi\)
\(710\) 0 0
\(711\) 1.39690e7 1.03632
\(712\) 0 0
\(713\) 160948. 0.0118567
\(714\) 0 0
\(715\) −1.00596e7 −0.735895
\(716\) 0 0
\(717\) −4.39617e7 −3.19357
\(718\) 0 0
\(719\) 2.44994e7 1.76740 0.883698 0.468058i \(-0.155046\pi\)
0.883698 + 0.468058i \(0.155046\pi\)
\(720\) 0 0
\(721\) 4.00892e6 0.287204
\(722\) 0 0
\(723\) 1.45588e7 1.03581
\(724\) 0 0
\(725\) −4.84830e6 −0.342566
\(726\) 0 0
\(727\) −1.75199e7 −1.22941 −0.614703 0.788759i \(-0.710724\pi\)
−0.614703 + 0.788759i \(0.710724\pi\)
\(728\) 0 0
\(729\) 1.23387e7 0.859904
\(730\) 0 0
\(731\) 3.03410e7 2.10008
\(732\) 0 0
\(733\) −2.29025e7 −1.57443 −0.787215 0.616679i \(-0.788478\pi\)
−0.787215 + 0.616679i \(0.788478\pi\)
\(734\) 0 0
\(735\) 1.07904e7 0.736746
\(736\) 0 0
\(737\) −2.29131e7 −1.55387
\(738\) 0 0
\(739\) −1.31983e7 −0.889010 −0.444505 0.895776i \(-0.646620\pi\)
−0.444505 + 0.895776i \(0.646620\pi\)
\(740\) 0 0
\(741\) 8.81988e6 0.590089
\(742\) 0 0
\(743\) −1.89399e6 −0.125865 −0.0629326 0.998018i \(-0.520045\pi\)
−0.0629326 + 0.998018i \(0.520045\pi\)
\(744\) 0 0
\(745\) 3.86332e6 0.255017
\(746\) 0 0
\(747\) −4.10094e7 −2.68894
\(748\) 0 0
\(749\) 3.72704e6 0.242750
\(750\) 0 0
\(751\) −1.71988e7 −1.11275 −0.556376 0.830930i \(-0.687809\pi\)
−0.556376 + 0.830930i \(0.687809\pi\)
\(752\) 0 0
\(753\) 1.46926e7 0.944304
\(754\) 0 0
\(755\) 1.13849e7 0.726876
\(756\) 0 0
\(757\) −2.02697e7 −1.28561 −0.642804 0.766031i \(-0.722229\pi\)
−0.642804 + 0.766031i \(0.722229\pi\)
\(758\) 0 0
\(759\) −1.87444e7 −1.18104
\(760\) 0 0
\(761\) −6.54894e6 −0.409929 −0.204965 0.978769i \(-0.565708\pi\)
−0.204965 + 0.978769i \(0.565708\pi\)
\(762\) 0 0
\(763\) −446710. −0.0277789
\(764\) 0 0
\(765\) 2.66674e7 1.64751
\(766\) 0 0
\(767\) 1.91803e7 1.17725
\(768\) 0 0
\(769\) −2.48043e7 −1.51256 −0.756278 0.654251i \(-0.772984\pi\)
−0.756278 + 0.654251i \(0.772984\pi\)
\(770\) 0 0
\(771\) −7.35357e6 −0.445515
\(772\) 0 0
\(773\) −2.27616e7 −1.37010 −0.685052 0.728495i \(-0.740220\pi\)
−0.685052 + 0.728495i \(0.740220\pi\)
\(774\) 0 0
\(775\) 64152.6 0.00383672
\(776\) 0 0
\(777\) 2.34379e6 0.139273
\(778\) 0 0
\(779\) −2.54031e6 −0.149983
\(780\) 0 0
\(781\) −4.66302e6 −0.273552
\(782\) 0 0
\(783\) −7.54221e7 −4.39637
\(784\) 0 0
\(785\) 9.04225e6 0.523724
\(786\) 0 0
\(787\) −1.56494e7 −0.900658 −0.450329 0.892863i \(-0.648693\pi\)
−0.450329 + 0.892863i \(0.648693\pi\)
\(788\) 0 0
\(789\) 3.80341e7 2.17511
\(790\) 0 0
\(791\) −9.90976e6 −0.563147
\(792\) 0 0
\(793\) −1.74218e7 −0.983809
\(794\) 0 0
\(795\) −1.07486e7 −0.603161
\(796\) 0 0
\(797\) 2.26205e7 1.26141 0.630704 0.776023i \(-0.282766\pi\)
0.630704 + 0.776023i \(0.282766\pi\)
\(798\) 0 0
\(799\) −3.42050e7 −1.89549
\(800\) 0 0
\(801\) −3.53406e7 −1.94622
\(802\) 0 0
\(803\) 1.67098e6 0.0914499
\(804\) 0 0
\(805\) 1.65218e6 0.0898604
\(806\) 0 0
\(807\) 4.10602e7 2.21941
\(808\) 0 0
\(809\) −2.25367e7 −1.21065 −0.605326 0.795977i \(-0.706957\pi\)
−0.605326 + 0.795977i \(0.706957\pi\)
\(810\) 0 0
\(811\) 410196. 0.0218997 0.0109499 0.999940i \(-0.496514\pi\)
0.0109499 + 0.999940i \(0.496514\pi\)
\(812\) 0 0
\(813\) −2.02855e7 −1.07636
\(814\) 0 0
\(815\) 1.22711e7 0.647126
\(816\) 0 0
\(817\) 5.25662e6 0.275519
\(818\) 0 0
\(819\) 2.36931e7 1.23428
\(820\) 0 0
\(821\) −1.62749e7 −0.842678 −0.421339 0.906903i \(-0.638440\pi\)
−0.421339 + 0.906903i \(0.638440\pi\)
\(822\) 0 0
\(823\) −628881. −0.0323645 −0.0161823 0.999869i \(-0.505151\pi\)
−0.0161823 + 0.999869i \(0.505151\pi\)
\(824\) 0 0
\(825\) −7.47134e6 −0.382176
\(826\) 0 0
\(827\) 1.94403e7 0.988417 0.494209 0.869343i \(-0.335458\pi\)
0.494209 + 0.869343i \(0.335458\pi\)
\(828\) 0 0
\(829\) −3.39088e7 −1.71366 −0.856832 0.515595i \(-0.827571\pi\)
−0.856832 + 0.515595i \(0.827571\pi\)
\(830\) 0 0
\(831\) −9.03614e6 −0.453921
\(832\) 0 0
\(833\) 2.75679e7 1.37655
\(834\) 0 0
\(835\) 4.90683e6 0.243548
\(836\) 0 0
\(837\) 997985. 0.0492391
\(838\) 0 0
\(839\) 6.84583e6 0.335754 0.167877 0.985808i \(-0.446309\pi\)
0.167877 + 0.985808i \(0.446309\pi\)
\(840\) 0 0
\(841\) 3.96642e7 1.93379
\(842\) 0 0
\(843\) −1.25715e7 −0.609282
\(844\) 0 0
\(845\) −1.40750e7 −0.678118
\(846\) 0 0
\(847\) −516280. −0.0247273
\(848\) 0 0
\(849\) 5.97997e7 2.84728
\(850\) 0 0
\(851\) −3.03660e6 −0.143735
\(852\) 0 0
\(853\) 2.67852e7 1.26044 0.630221 0.776416i \(-0.282964\pi\)
0.630221 + 0.776416i \(0.282964\pi\)
\(854\) 0 0
\(855\) 4.62017e6 0.216144
\(856\) 0 0
\(857\) 9.32339e6 0.433632 0.216816 0.976212i \(-0.430433\pi\)
0.216816 + 0.976212i \(0.430433\pi\)
\(858\) 0 0
\(859\) −3.73055e7 −1.72500 −0.862502 0.506054i \(-0.831104\pi\)
−0.862502 + 0.506054i \(0.831104\pi\)
\(860\) 0 0
\(861\) −9.67537e6 −0.444795
\(862\) 0 0
\(863\) −5.18636e6 −0.237048 −0.118524 0.992951i \(-0.537816\pi\)
−0.118524 + 0.992951i \(0.537816\pi\)
\(864\) 0 0
\(865\) 4.58486e6 0.208346
\(866\) 0 0
\(867\) 5.58265e7 2.52228
\(868\) 0 0
\(869\) −9.99888e6 −0.449161
\(870\) 0 0
\(871\) −5.32016e7 −2.37618
\(872\) 0 0
\(873\) −1.80945e7 −0.803546
\(874\) 0 0
\(875\) 658545. 0.0290781
\(876\) 0 0
\(877\) 5.63396e6 0.247352 0.123676 0.992323i \(-0.460532\pi\)
0.123676 + 0.992323i \(0.460532\pi\)
\(878\) 0 0
\(879\) −2.60498e6 −0.113719
\(880\) 0 0
\(881\) −5.76880e6 −0.250407 −0.125203 0.992131i \(-0.539958\pi\)
−0.125203 + 0.992131i \(0.539958\pi\)
\(882\) 0 0
\(883\) −2.60630e7 −1.12492 −0.562462 0.826823i \(-0.690146\pi\)
−0.562462 + 0.826823i \(0.690146\pi\)
\(884\) 0 0
\(885\) 1.42453e7 0.611385
\(886\) 0 0
\(887\) 3.24889e7 1.38652 0.693259 0.720688i \(-0.256174\pi\)
0.693259 + 0.720688i \(0.256174\pi\)
\(888\) 0 0
\(889\) 4.32145e6 0.183390
\(890\) 0 0
\(891\) −5.73942e7 −2.42200
\(892\) 0 0
\(893\) −5.92607e6 −0.248678
\(894\) 0 0
\(895\) −966499. −0.0403315
\(896\) 0 0
\(897\) −4.35223e7 −1.80605
\(898\) 0 0
\(899\) −796240. −0.0328583
\(900\) 0 0
\(901\) −2.74612e7 −1.12696
\(902\) 0 0
\(903\) 2.00211e7 0.817087
\(904\) 0 0
\(905\) −1.40322e7 −0.569513
\(906\) 0 0
\(907\) 3.11745e7 1.25829 0.629145 0.777288i \(-0.283405\pi\)
0.629145 + 0.777288i \(0.283405\pi\)
\(908\) 0 0
\(909\) 2.87836e7 1.15541
\(910\) 0 0
\(911\) 3.58254e7 1.43019 0.715097 0.699025i \(-0.246382\pi\)
0.715097 + 0.699025i \(0.246382\pi\)
\(912\) 0 0
\(913\) 2.93540e7 1.16544
\(914\) 0 0
\(915\) −1.29393e7 −0.510926
\(916\) 0 0
\(917\) 2.13276e6 0.0837565
\(918\) 0 0
\(919\) −3.14710e7 −1.22920 −0.614598 0.788840i \(-0.710682\pi\)
−0.614598 + 0.788840i \(0.710682\pi\)
\(920\) 0 0
\(921\) 1.64167e7 0.637730
\(922\) 0 0
\(923\) −1.08270e7 −0.418316
\(924\) 0 0
\(925\) −1.21036e6 −0.0465115
\(926\) 0 0
\(927\) −5.53194e7 −2.11436
\(928\) 0 0
\(929\) 532600. 0.0202471 0.0101235 0.999949i \(-0.496778\pi\)
0.0101235 + 0.999949i \(0.496778\pi\)
\(930\) 0 0
\(931\) 4.77618e6 0.180595
\(932\) 0 0
\(933\) 7.45215e7 2.80270
\(934\) 0 0
\(935\) −1.90882e7 −0.714064
\(936\) 0 0
\(937\) 1.97320e7 0.734214 0.367107 0.930179i \(-0.380348\pi\)
0.367107 + 0.930179i \(0.380348\pi\)
\(938\) 0 0
\(939\) −1.46639e7 −0.542732
\(940\) 0 0
\(941\) 2.12060e7 0.780702 0.390351 0.920666i \(-0.372354\pi\)
0.390351 + 0.920666i \(0.372354\pi\)
\(942\) 0 0
\(943\) 1.25353e7 0.459047
\(944\) 0 0
\(945\) 1.02446e7 0.373178
\(946\) 0 0
\(947\) −4.60224e7 −1.66761 −0.833804 0.552060i \(-0.813842\pi\)
−0.833804 + 0.552060i \(0.813842\pi\)
\(948\) 0 0
\(949\) 3.87984e6 0.139845
\(950\) 0 0
\(951\) 9.67802e7 3.47004
\(952\) 0 0
\(953\) 4.76525e7 1.69963 0.849813 0.527085i \(-0.176715\pi\)
0.849813 + 0.527085i \(0.176715\pi\)
\(954\) 0 0
\(955\) −6.63481e6 −0.235407
\(956\) 0 0
\(957\) 9.27316e7 3.27301
\(958\) 0 0
\(959\) −2.01511e6 −0.0707543
\(960\) 0 0
\(961\) −2.86186e7 −0.999632
\(962\) 0 0
\(963\) −5.14297e7 −1.78710
\(964\) 0 0
\(965\) −2.15787e7 −0.745946
\(966\) 0 0
\(967\) −2.29686e7 −0.789893 −0.394946 0.918704i \(-0.629237\pi\)
−0.394946 + 0.918704i \(0.629237\pi\)
\(968\) 0 0
\(969\) 1.67358e7 0.572583
\(970\) 0 0
\(971\) −2.22231e7 −0.756408 −0.378204 0.925722i \(-0.623458\pi\)
−0.378204 + 0.925722i \(0.623458\pi\)
\(972\) 0 0
\(973\) −9.28031e6 −0.314254
\(974\) 0 0
\(975\) −1.73476e7 −0.584424
\(976\) 0 0
\(977\) −3.68581e7 −1.23537 −0.617684 0.786426i \(-0.711929\pi\)
−0.617684 + 0.786426i \(0.711929\pi\)
\(978\) 0 0
\(979\) 2.52964e7 0.843532
\(980\) 0 0
\(981\) 6.16418e6 0.204504
\(982\) 0 0
\(983\) −4.53136e7 −1.49570 −0.747850 0.663868i \(-0.768914\pi\)
−0.747850 + 0.663868i \(0.768914\pi\)
\(984\) 0 0
\(985\) 7.04676e6 0.231419
\(986\) 0 0
\(987\) −2.25708e7 −0.737487
\(988\) 0 0
\(989\) −2.59392e7 −0.843268
\(990\) 0 0
\(991\) −3.68582e7 −1.19220 −0.596102 0.802909i \(-0.703284\pi\)
−0.596102 + 0.802909i \(0.703284\pi\)
\(992\) 0 0
\(993\) −1.09169e8 −3.51339
\(994\) 0 0
\(995\) 4.81995e6 0.154342
\(996\) 0 0
\(997\) 4.19245e7 1.33577 0.667883 0.744266i \(-0.267201\pi\)
0.667883 + 0.744266i \(0.267201\pi\)
\(998\) 0 0
\(999\) −1.88289e7 −0.596912
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.w.1.2 2
4.3 odd 2 320.6.a.q.1.1 2
8.3 odd 2 80.6.a.i.1.2 2
8.5 even 2 40.6.a.d.1.1 2
24.5 odd 2 360.6.a.l.1.1 2
24.11 even 2 720.6.a.z.1.2 2
40.3 even 4 400.6.c.l.49.4 4
40.13 odd 4 200.6.c.e.49.1 4
40.19 odd 2 400.6.a.q.1.1 2
40.27 even 4 400.6.c.l.49.1 4
40.29 even 2 200.6.a.g.1.2 2
40.37 odd 4 200.6.c.e.49.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.a.d.1.1 2 8.5 even 2
80.6.a.i.1.2 2 8.3 odd 2
200.6.a.g.1.2 2 40.29 even 2
200.6.c.e.49.1 4 40.13 odd 4
200.6.c.e.49.4 4 40.37 odd 4
320.6.a.q.1.1 2 4.3 odd 2
320.6.a.w.1.2 2 1.1 even 1 trivial
360.6.a.l.1.1 2 24.5 odd 2
400.6.a.q.1.1 2 40.19 odd 2
400.6.c.l.49.1 4 40.27 even 4
400.6.c.l.49.4 4 40.3 even 4
720.6.a.z.1.2 2 24.11 even 2