Properties

Label 912.6.a.y.1.6
Level $912$
Weight $6$
Character 912.1
Self dual yes
Analytic conductor $146.270$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 912.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(146.270043669\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \(x^{6} - 2 x^{5} - 4725 x^{4} + 92430 x^{3} + 1610577 x^{2} - 16081740 x - 24661341\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: no (minimal twist has level 456)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(9.09727\) of defining polynomial
Character \(\chi\) \(=\) 912.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.00000 q^{3} +68.0602 q^{5} +181.508 q^{7} +81.0000 q^{9} +O(q^{10})\) \(q+9.00000 q^{3} +68.0602 q^{5} +181.508 q^{7} +81.0000 q^{9} -56.2292 q^{11} -183.089 q^{13} +612.542 q^{15} +2031.56 q^{17} -361.000 q^{19} +1633.57 q^{21} +4003.43 q^{23} +1507.19 q^{25} +729.000 q^{27} -4073.95 q^{29} -6141.15 q^{31} -506.063 q^{33} +12353.4 q^{35} +3425.06 q^{37} -1647.80 q^{39} -6813.12 q^{41} +2183.21 q^{43} +5512.87 q^{45} +8348.99 q^{47} +16138.0 q^{49} +18284.0 q^{51} +39002.6 q^{53} -3826.97 q^{55} -3249.00 q^{57} +30218.1 q^{59} +12329.1 q^{61} +14702.1 q^{63} -12461.0 q^{65} +8132.92 q^{67} +36030.9 q^{69} +11559.2 q^{71} -28897.5 q^{73} +13564.7 q^{75} -10206.0 q^{77} -164.115 q^{79} +6561.00 q^{81} -13470.3 q^{83} +138268. q^{85} -36665.5 q^{87} -103567. q^{89} -33232.0 q^{91} -55270.3 q^{93} -24569.7 q^{95} -34490.7 q^{97} -4554.57 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 54 q^{3} - 65 q^{5} + 149 q^{7} + 486 q^{9} + O(q^{10}) \) \( 6 q + 54 q^{3} - 65 q^{5} + 149 q^{7} + 486 q^{9} + 203 q^{11} - 298 q^{13} - 585 q^{15} + 1319 q^{17} - 2166 q^{19} + 1341 q^{21} - 1234 q^{23} + 4589 q^{25} + 4374 q^{27} + 7356 q^{29} - 1632 q^{31} + 1827 q^{33} - 4383 q^{35} + 14204 q^{37} - 2682 q^{39} + 14734 q^{41} + 4693 q^{43} - 5265 q^{45} + 10955 q^{47} + 38561 q^{49} + 11871 q^{51} + 47500 q^{53} - 769 q^{55} - 19494 q^{57} + 61744 q^{59} - 81581 q^{61} + 12069 q^{63} - 59686 q^{65} + 45756 q^{67} - 11106 q^{69} + 10416 q^{71} - 54615 q^{73} + 41301 q^{75} - 29515 q^{77} + 145594 q^{79} + 39366 q^{81} + 160548 q^{83} - 53947 q^{85} + 66204 q^{87} - 97728 q^{89} + 418294 q^{91} - 14688 q^{93} + 23465 q^{95} - 760 q^{97} + 16443 q^{99} + O(q^{100}) \)

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
\(3\) 9.00000 0.577350
\(4\) 0 0
\(5\) 68.0602 1.21750 0.608749 0.793363i \(-0.291672\pi\)
0.608749 + 0.793363i \(0.291672\pi\)
\(6\) 0 0
\(7\) 181.508 1.40007 0.700035 0.714108i \(-0.253168\pi\)
0.700035 + 0.714108i \(0.253168\pi\)
\(8\) 0 0
\(9\) 81.0000 0.333333
\(10\) 0 0
\(11\) −56.2292 −0.140114 −0.0700568 0.997543i \(-0.522318\pi\)
−0.0700568 + 0.997543i \(0.522318\pi\)
\(12\) 0 0
\(13\) −183.089 −0.300471 −0.150236 0.988650i \(-0.548003\pi\)
−0.150236 + 0.988650i \(0.548003\pi\)
\(14\) 0 0
\(15\) 612.542 0.702922
\(16\) 0 0
\(17\) 2031.56 1.70493 0.852465 0.522785i \(-0.175107\pi\)
0.852465 + 0.522785i \(0.175107\pi\)
\(18\) 0 0
\(19\) −361.000 −0.229416
\(20\) 0 0
\(21\) 1633.57 0.808331
\(22\) 0 0
\(23\) 4003.43 1.57802 0.789010 0.614380i \(-0.210594\pi\)
0.789010 + 0.614380i \(0.210594\pi\)
\(24\) 0 0
\(25\) 1507.19 0.482300
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −4073.95 −0.899540 −0.449770 0.893144i \(-0.648494\pi\)
−0.449770 + 0.893144i \(0.648494\pi\)
\(30\) 0 0
\(31\) −6141.15 −1.14774 −0.573872 0.818945i \(-0.694559\pi\)
−0.573872 + 0.818945i \(0.694559\pi\)
\(32\) 0 0
\(33\) −506.063 −0.0808947
\(34\) 0 0
\(35\) 12353.4 1.70458
\(36\) 0 0
\(37\) 3425.06 0.411305 0.205653 0.978625i \(-0.434068\pi\)
0.205653 + 0.978625i \(0.434068\pi\)
\(38\) 0 0
\(39\) −1647.80 −0.173477
\(40\) 0 0
\(41\) −6813.12 −0.632974 −0.316487 0.948597i \(-0.602503\pi\)
−0.316487 + 0.948597i \(0.602503\pi\)
\(42\) 0 0
\(43\) 2183.21 0.180063 0.0900315 0.995939i \(-0.471303\pi\)
0.0900315 + 0.995939i \(0.471303\pi\)
\(44\) 0 0
\(45\) 5512.87 0.405832
\(46\) 0 0
\(47\) 8348.99 0.551302 0.275651 0.961258i \(-0.411107\pi\)
0.275651 + 0.961258i \(0.411107\pi\)
\(48\) 0 0
\(49\) 16138.0 0.960198
\(50\) 0 0
\(51\) 18284.0 0.984341
\(52\) 0 0
\(53\) 39002.6 1.90723 0.953616 0.301027i \(-0.0973293\pi\)
0.953616 + 0.301027i \(0.0973293\pi\)
\(54\) 0 0
\(55\) −3826.97 −0.170588
\(56\) 0 0
\(57\) −3249.00 −0.132453
\(58\) 0 0
\(59\) 30218.1 1.13015 0.565076 0.825039i \(-0.308847\pi\)
0.565076 + 0.825039i \(0.308847\pi\)
\(60\) 0 0
\(61\) 12329.1 0.424237 0.212118 0.977244i \(-0.431964\pi\)
0.212118 + 0.977244i \(0.431964\pi\)
\(62\) 0 0
\(63\) 14702.1 0.466690
\(64\) 0 0
\(65\) −12461.0 −0.365823
\(66\) 0 0
\(67\) 8132.92 0.221340 0.110670 0.993857i \(-0.464700\pi\)
0.110670 + 0.993857i \(0.464700\pi\)
\(68\) 0 0
\(69\) 36030.9 0.911071
\(70\) 0 0
\(71\) 11559.2 0.272134 0.136067 0.990700i \(-0.456554\pi\)
0.136067 + 0.990700i \(0.456554\pi\)
\(72\) 0 0
\(73\) −28897.5 −0.634677 −0.317338 0.948312i \(-0.602789\pi\)
−0.317338 + 0.948312i \(0.602789\pi\)
\(74\) 0 0
\(75\) 13564.7 0.278456
\(76\) 0 0
\(77\) −10206.0 −0.196169
\(78\) 0 0
\(79\) −164.115 −0.00295856 −0.00147928 0.999999i \(-0.500471\pi\)
−0.00147928 + 0.999999i \(0.500471\pi\)
\(80\) 0 0
\(81\) 6561.00 0.111111
\(82\) 0 0
\(83\) −13470.3 −0.214625 −0.107313 0.994225i \(-0.534225\pi\)
−0.107313 + 0.994225i \(0.534225\pi\)
\(84\) 0 0
\(85\) 138268. 2.07575
\(86\) 0 0
\(87\) −36665.5 −0.519350
\(88\) 0 0
\(89\) −103567. −1.38595 −0.692975 0.720961i \(-0.743700\pi\)
−0.692975 + 0.720961i \(0.743700\pi\)
\(90\) 0 0
\(91\) −33232.0 −0.420681
\(92\) 0 0
\(93\) −55270.3 −0.662651
\(94\) 0 0
\(95\) −24569.7 −0.279313
\(96\) 0 0
\(97\) −34490.7 −0.372197 −0.186099 0.982531i \(-0.559584\pi\)
−0.186099 + 0.982531i \(0.559584\pi\)
\(98\) 0 0
\(99\) −4554.57 −0.0467046
\(100\) 0 0
\(101\) −72989.7 −0.711964 −0.355982 0.934493i \(-0.615854\pi\)
−0.355982 + 0.934493i \(0.615854\pi\)
\(102\) 0 0
\(103\) 15482.1 0.143793 0.0718964 0.997412i \(-0.477095\pi\)
0.0718964 + 0.997412i \(0.477095\pi\)
\(104\) 0 0
\(105\) 111181. 0.984141
\(106\) 0 0
\(107\) 48215.9 0.407128 0.203564 0.979062i \(-0.434748\pi\)
0.203564 + 0.979062i \(0.434748\pi\)
\(108\) 0 0
\(109\) −151242. −1.21929 −0.609643 0.792676i \(-0.708687\pi\)
−0.609643 + 0.792676i \(0.708687\pi\)
\(110\) 0 0
\(111\) 30825.6 0.237467
\(112\) 0 0
\(113\) −233254. −1.71843 −0.859217 0.511612i \(-0.829049\pi\)
−0.859217 + 0.511612i \(0.829049\pi\)
\(114\) 0 0
\(115\) 272474. 1.92124
\(116\) 0 0
\(117\) −14830.2 −0.100157
\(118\) 0 0
\(119\) 368743. 2.38702
\(120\) 0 0
\(121\) −157889. −0.980368
\(122\) 0 0
\(123\) −61318.0 −0.365448
\(124\) 0 0
\(125\) −110109. −0.630299
\(126\) 0 0
\(127\) 200268. 1.10180 0.550900 0.834571i \(-0.314285\pi\)
0.550900 + 0.834571i \(0.314285\pi\)
\(128\) 0 0
\(129\) 19648.9 0.103959
\(130\) 0 0
\(131\) 4663.95 0.0237452 0.0118726 0.999930i \(-0.496221\pi\)
0.0118726 + 0.999930i \(0.496221\pi\)
\(132\) 0 0
\(133\) −65524.3 −0.321198
\(134\) 0 0
\(135\) 49615.9 0.234307
\(136\) 0 0
\(137\) −25589.9 −0.116484 −0.0582421 0.998302i \(-0.518550\pi\)
−0.0582421 + 0.998302i \(0.518550\pi\)
\(138\) 0 0
\(139\) 67288.8 0.295397 0.147698 0.989032i \(-0.452813\pi\)
0.147698 + 0.989032i \(0.452813\pi\)
\(140\) 0 0
\(141\) 75140.9 0.318294
\(142\) 0 0
\(143\) 10294.9 0.0421002
\(144\) 0 0
\(145\) −277274. −1.09519
\(146\) 0 0
\(147\) 145242. 0.554370
\(148\) 0 0
\(149\) −236573. −0.872969 −0.436485 0.899712i \(-0.643777\pi\)
−0.436485 + 0.899712i \(0.643777\pi\)
\(150\) 0 0
\(151\) 96930.5 0.345954 0.172977 0.984926i \(-0.444661\pi\)
0.172977 + 0.984926i \(0.444661\pi\)
\(152\) 0 0
\(153\) 164556. 0.568310
\(154\) 0 0
\(155\) −417968. −1.39738
\(156\) 0 0
\(157\) −51875.0 −0.167961 −0.0839806 0.996467i \(-0.526763\pi\)
−0.0839806 + 0.996467i \(0.526763\pi\)
\(158\) 0 0
\(159\) 351023. 1.10114
\(160\) 0 0
\(161\) 726653. 2.20934
\(162\) 0 0
\(163\) 194876. 0.574499 0.287250 0.957856i \(-0.407259\pi\)
0.287250 + 0.957856i \(0.407259\pi\)
\(164\) 0 0
\(165\) −34442.8 −0.0984891
\(166\) 0 0
\(167\) −512937. −1.42322 −0.711611 0.702573i \(-0.752034\pi\)
−0.711611 + 0.702573i \(0.752034\pi\)
\(168\) 0 0
\(169\) −337772. −0.909717
\(170\) 0 0
\(171\) −29241.0 −0.0764719
\(172\) 0 0
\(173\) 344170. 0.874295 0.437148 0.899390i \(-0.355989\pi\)
0.437148 + 0.899390i \(0.355989\pi\)
\(174\) 0 0
\(175\) 273566. 0.675254
\(176\) 0 0
\(177\) 271963. 0.652494
\(178\) 0 0
\(179\) 535947. 1.25023 0.625114 0.780534i \(-0.285053\pi\)
0.625114 + 0.780534i \(0.285053\pi\)
\(180\) 0 0
\(181\) 717175. 1.62715 0.813577 0.581457i \(-0.197517\pi\)
0.813577 + 0.581457i \(0.197517\pi\)
\(182\) 0 0
\(183\) 110962. 0.244933
\(184\) 0 0
\(185\) 233110. 0.500763
\(186\) 0 0
\(187\) −114233. −0.238884
\(188\) 0 0
\(189\) 132319. 0.269444
\(190\) 0 0
\(191\) 616524. 1.22283 0.611416 0.791310i \(-0.290600\pi\)
0.611416 + 0.791310i \(0.290600\pi\)
\(192\) 0 0
\(193\) −297746. −0.575377 −0.287688 0.957724i \(-0.592887\pi\)
−0.287688 + 0.957724i \(0.592887\pi\)
\(194\) 0 0
\(195\) −112149. −0.211208
\(196\) 0 0
\(197\) 750295. 1.37742 0.688710 0.725037i \(-0.258177\pi\)
0.688710 + 0.725037i \(0.258177\pi\)
\(198\) 0 0
\(199\) 447059. 0.800262 0.400131 0.916458i \(-0.368965\pi\)
0.400131 + 0.916458i \(0.368965\pi\)
\(200\) 0 0
\(201\) 73196.3 0.127791
\(202\) 0 0
\(203\) −739453. −1.25942
\(204\) 0 0
\(205\) −463702. −0.770645
\(206\) 0 0
\(207\) 324278. 0.526007
\(208\) 0 0
\(209\) 20298.8 0.0321443
\(210\) 0 0
\(211\) −765080. −1.18304 −0.591522 0.806289i \(-0.701473\pi\)
−0.591522 + 0.806289i \(0.701473\pi\)
\(212\) 0 0
\(213\) 104033. 0.157117
\(214\) 0 0
\(215\) 148590. 0.219226
\(216\) 0 0
\(217\) −1.11467e6 −1.60692
\(218\) 0 0
\(219\) −260077. −0.366431
\(220\) 0 0
\(221\) −371955. −0.512283
\(222\) 0 0
\(223\) −624803. −0.841358 −0.420679 0.907210i \(-0.638208\pi\)
−0.420679 + 0.907210i \(0.638208\pi\)
\(224\) 0 0
\(225\) 122082. 0.160767
\(226\) 0 0
\(227\) 8488.97 0.0109343 0.00546714 0.999985i \(-0.498260\pi\)
0.00546714 + 0.999985i \(0.498260\pi\)
\(228\) 0 0
\(229\) 502157. 0.632777 0.316388 0.948630i \(-0.397530\pi\)
0.316388 + 0.948630i \(0.397530\pi\)
\(230\) 0 0
\(231\) −91854.4 −0.113258
\(232\) 0 0
\(233\) −319233. −0.385228 −0.192614 0.981275i \(-0.561696\pi\)
−0.192614 + 0.981275i \(0.561696\pi\)
\(234\) 0 0
\(235\) 568234. 0.671209
\(236\) 0 0
\(237\) −1477.04 −0.00170813
\(238\) 0 0
\(239\) 756618. 0.856805 0.428402 0.903588i \(-0.359077\pi\)
0.428402 + 0.903588i \(0.359077\pi\)
\(240\) 0 0
\(241\) −645205. −0.715575 −0.357788 0.933803i \(-0.616469\pi\)
−0.357788 + 0.933803i \(0.616469\pi\)
\(242\) 0 0
\(243\) 59049.0 0.0641500
\(244\) 0 0
\(245\) 1.09836e6 1.16904
\(246\) 0 0
\(247\) 66095.0 0.0689329
\(248\) 0 0
\(249\) −121232. −0.123914
\(250\) 0 0
\(251\) 1.69048e6 1.69366 0.846829 0.531866i \(-0.178509\pi\)
0.846829 + 0.531866i \(0.178509\pi\)
\(252\) 0 0
\(253\) −225110. −0.221102
\(254\) 0 0
\(255\) 1.24441e6 1.19843
\(256\) 0 0
\(257\) −200205. −0.189079 −0.0945393 0.995521i \(-0.530138\pi\)
−0.0945393 + 0.995521i \(0.530138\pi\)
\(258\) 0 0
\(259\) 621675. 0.575857
\(260\) 0 0
\(261\) −329990. −0.299847
\(262\) 0 0
\(263\) 791636. 0.705726 0.352863 0.935675i \(-0.385208\pi\)
0.352863 + 0.935675i \(0.385208\pi\)
\(264\) 0 0
\(265\) 2.65452e6 2.32205
\(266\) 0 0
\(267\) −932106. −0.800179
\(268\) 0 0
\(269\) 679190. 0.572283 0.286141 0.958187i \(-0.407627\pi\)
0.286141 + 0.958187i \(0.407627\pi\)
\(270\) 0 0
\(271\) 1.62480e6 1.34393 0.671965 0.740583i \(-0.265451\pi\)
0.671965 + 0.740583i \(0.265451\pi\)
\(272\) 0 0
\(273\) −299088. −0.242880
\(274\) 0 0
\(275\) −84748.0 −0.0675768
\(276\) 0 0
\(277\) −2.46645e6 −1.93141 −0.965703 0.259651i \(-0.916392\pi\)
−0.965703 + 0.259651i \(0.916392\pi\)
\(278\) 0 0
\(279\) −497433. −0.382582
\(280\) 0 0
\(281\) 955572. 0.721934 0.360967 0.932579i \(-0.382447\pi\)
0.360967 + 0.932579i \(0.382447\pi\)
\(282\) 0 0
\(283\) 152472. 0.113168 0.0565841 0.998398i \(-0.481979\pi\)
0.0565841 + 0.998398i \(0.481979\pi\)
\(284\) 0 0
\(285\) −221127. −0.161261
\(286\) 0 0
\(287\) −1.23663e6 −0.886209
\(288\) 0 0
\(289\) 2.70736e6 1.90678
\(290\) 0 0
\(291\) −310417. −0.214888
\(292\) 0 0
\(293\) 2.54402e6 1.73121 0.865607 0.500724i \(-0.166933\pi\)
0.865607 + 0.500724i \(0.166933\pi\)
\(294\) 0 0
\(295\) 2.05665e6 1.37596
\(296\) 0 0
\(297\) −40991.1 −0.0269649
\(298\) 0 0
\(299\) −732983. −0.474150
\(300\) 0 0
\(301\) 396270. 0.252101
\(302\) 0 0
\(303\) −656907. −0.411053
\(304\) 0 0
\(305\) 839124. 0.516507
\(306\) 0 0
\(307\) −1.13060e6 −0.684644 −0.342322 0.939583i \(-0.611213\pi\)
−0.342322 + 0.939583i \(0.611213\pi\)
\(308\) 0 0
\(309\) 139339. 0.0830188
\(310\) 0 0
\(311\) −3.39201e6 −1.98864 −0.994320 0.106428i \(-0.966058\pi\)
−0.994320 + 0.106428i \(0.966058\pi\)
\(312\) 0 0
\(313\) 430684. 0.248484 0.124242 0.992252i \(-0.460350\pi\)
0.124242 + 0.992252i \(0.460350\pi\)
\(314\) 0 0
\(315\) 1.00063e6 0.568194
\(316\) 0 0
\(317\) −3.42810e6 −1.91604 −0.958022 0.286695i \(-0.907443\pi\)
−0.958022 + 0.286695i \(0.907443\pi\)
\(318\) 0 0
\(319\) 229075. 0.126038
\(320\) 0 0
\(321\) 433943. 0.235055
\(322\) 0 0
\(323\) −733392. −0.391138
\(324\) 0 0
\(325\) −275949. −0.144917
\(326\) 0 0
\(327\) −1.36118e6 −0.703955
\(328\) 0 0
\(329\) 1.51541e6 0.771862
\(330\) 0 0
\(331\) 21956.4 0.0110152 0.00550758 0.999985i \(-0.498247\pi\)
0.00550758 + 0.999985i \(0.498247\pi\)
\(332\) 0 0
\(333\) 277430. 0.137102
\(334\) 0 0
\(335\) 553528. 0.269481
\(336\) 0 0
\(337\) 2.54253e6 1.21953 0.609764 0.792583i \(-0.291264\pi\)
0.609764 + 0.792583i \(0.291264\pi\)
\(338\) 0 0
\(339\) −2.09928e6 −0.992138
\(340\) 0 0
\(341\) 345312. 0.160815
\(342\) 0 0
\(343\) −121421. −0.0557262
\(344\) 0 0
\(345\) 2.45227e6 1.10923
\(346\) 0 0
\(347\) 1.25363e6 0.558914 0.279457 0.960158i \(-0.409846\pi\)
0.279457 + 0.960158i \(0.409846\pi\)
\(348\) 0 0
\(349\) 1.36606e6 0.600352 0.300176 0.953884i \(-0.402955\pi\)
0.300176 + 0.953884i \(0.402955\pi\)
\(350\) 0 0
\(351\) −133472. −0.0578258
\(352\) 0 0
\(353\) 3.16721e6 1.35282 0.676411 0.736525i \(-0.263534\pi\)
0.676411 + 0.736525i \(0.263534\pi\)
\(354\) 0 0
\(355\) 786723. 0.331322
\(356\) 0 0
\(357\) 3.31869e6 1.37815
\(358\) 0 0
\(359\) −2.40859e6 −0.986342 −0.493171 0.869932i \(-0.664162\pi\)
−0.493171 + 0.869932i \(0.664162\pi\)
\(360\) 0 0
\(361\) 130321. 0.0526316
\(362\) 0 0
\(363\) −1.42100e6 −0.566016
\(364\) 0 0
\(365\) −1.96677e6 −0.772717
\(366\) 0 0
\(367\) −2.29575e6 −0.889734 −0.444867 0.895597i \(-0.646749\pi\)
−0.444867 + 0.895597i \(0.646749\pi\)
\(368\) 0 0
\(369\) −551862. −0.210991
\(370\) 0 0
\(371\) 7.07926e6 2.67026
\(372\) 0 0
\(373\) −4.59398e6 −1.70969 −0.854844 0.518885i \(-0.826347\pi\)
−0.854844 + 0.518885i \(0.826347\pi\)
\(374\) 0 0
\(375\) −990978. −0.363903
\(376\) 0 0
\(377\) 745894. 0.270286
\(378\) 0 0
\(379\) 1.51884e6 0.543143 0.271572 0.962418i \(-0.412457\pi\)
0.271572 + 0.962418i \(0.412457\pi\)
\(380\) 0 0
\(381\) 1.80241e6 0.636125
\(382\) 0 0
\(383\) −796963. −0.277614 −0.138807 0.990319i \(-0.544327\pi\)
−0.138807 + 0.990319i \(0.544327\pi\)
\(384\) 0 0
\(385\) −694625. −0.238835
\(386\) 0 0
\(387\) 176840. 0.0600210
\(388\) 0 0
\(389\) 1.08768e6 0.364440 0.182220 0.983258i \(-0.441672\pi\)
0.182220 + 0.983258i \(0.441672\pi\)
\(390\) 0 0
\(391\) 8.13319e6 2.69041
\(392\) 0 0
\(393\) 41975.5 0.0137093
\(394\) 0 0
\(395\) −11169.7 −0.00360204
\(396\) 0 0
\(397\) −90856.2 −0.0289320 −0.0144660 0.999895i \(-0.504605\pi\)
−0.0144660 + 0.999895i \(0.504605\pi\)
\(398\) 0 0
\(399\) −589718. −0.185444
\(400\) 0 0
\(401\) −3.42123e6 −1.06248 −0.531241 0.847221i \(-0.678274\pi\)
−0.531241 + 0.847221i \(0.678274\pi\)
\(402\) 0 0
\(403\) 1.12437e6 0.344864
\(404\) 0 0
\(405\) 446543. 0.135277
\(406\) 0 0
\(407\) −192589. −0.0576295
\(408\) 0 0
\(409\) −1.71976e6 −0.508346 −0.254173 0.967159i \(-0.581803\pi\)
−0.254173 + 0.967159i \(0.581803\pi\)
\(410\) 0 0
\(411\) −230309. −0.0672522
\(412\) 0 0
\(413\) 5.48481e6 1.58229
\(414\) 0 0
\(415\) −916789. −0.261306
\(416\) 0 0
\(417\) 605599. 0.170547
\(418\) 0 0
\(419\) −6.64727e6 −1.84973 −0.924864 0.380297i \(-0.875822\pi\)
−0.924864 + 0.380297i \(0.875822\pi\)
\(420\) 0 0
\(421\) 4.48576e6 1.23348 0.616739 0.787168i \(-0.288454\pi\)
0.616739 + 0.787168i \(0.288454\pi\)
\(422\) 0 0
\(423\) 676268. 0.183767
\(424\) 0 0
\(425\) 3.06193e6 0.822287
\(426\) 0 0
\(427\) 2.23783e6 0.593961
\(428\) 0 0
\(429\) 92654.5 0.0243065
\(430\) 0 0
\(431\) −4.50573e6 −1.16835 −0.584174 0.811629i \(-0.698581\pi\)
−0.584174 + 0.811629i \(0.698581\pi\)
\(432\) 0 0
\(433\) 6.74569e6 1.72905 0.864524 0.502592i \(-0.167620\pi\)
0.864524 + 0.502592i \(0.167620\pi\)
\(434\) 0 0
\(435\) −2.49546e6 −0.632307
\(436\) 0 0
\(437\) −1.44524e6 −0.362023
\(438\) 0 0
\(439\) 5.54556e6 1.37336 0.686679 0.726960i \(-0.259068\pi\)
0.686679 + 0.726960i \(0.259068\pi\)
\(440\) 0 0
\(441\) 1.30718e6 0.320066
\(442\) 0 0
\(443\) −1.36139e6 −0.329589 −0.164795 0.986328i \(-0.552696\pi\)
−0.164795 + 0.986328i \(0.552696\pi\)
\(444\) 0 0
\(445\) −7.04881e6 −1.68739
\(446\) 0 0
\(447\) −2.12915e6 −0.504009
\(448\) 0 0
\(449\) −577806. −0.135259 −0.0676295 0.997711i \(-0.521544\pi\)
−0.0676295 + 0.997711i \(0.521544\pi\)
\(450\) 0 0
\(451\) 383096. 0.0886884
\(452\) 0 0
\(453\) 872375. 0.199737
\(454\) 0 0
\(455\) −2.26178e6 −0.512178
\(456\) 0 0
\(457\) 4.53412e6 1.01555 0.507777 0.861489i \(-0.330468\pi\)
0.507777 + 0.861489i \(0.330468\pi\)
\(458\) 0 0
\(459\) 1.48100e6 0.328114
\(460\) 0 0
\(461\) −7.58278e6 −1.66179 −0.830895 0.556429i \(-0.812171\pi\)
−0.830895 + 0.556429i \(0.812171\pi\)
\(462\) 0 0
\(463\) 8.74510e6 1.89589 0.947943 0.318440i \(-0.103159\pi\)
0.947943 + 0.318440i \(0.103159\pi\)
\(464\) 0 0
\(465\) −3.76171e6 −0.806775
\(466\) 0 0
\(467\) −3.25842e6 −0.691378 −0.345689 0.938349i \(-0.612355\pi\)
−0.345689 + 0.938349i \(0.612355\pi\)
\(468\) 0 0
\(469\) 1.47619e6 0.309891
\(470\) 0 0
\(471\) −466875. −0.0969724
\(472\) 0 0
\(473\) −122760. −0.0252293
\(474\) 0 0
\(475\) −544095. −0.110647
\(476\) 0 0
\(477\) 3.15921e6 0.635744
\(478\) 0 0
\(479\) 481496. 0.0958857 0.0479429 0.998850i \(-0.484733\pi\)
0.0479429 + 0.998850i \(0.484733\pi\)
\(480\) 0 0
\(481\) −627091. −0.123586
\(482\) 0 0
\(483\) 6.53988e6 1.27556
\(484\) 0 0
\(485\) −2.34745e6 −0.453149
\(486\) 0 0
\(487\) −4.42000e6 −0.844500 −0.422250 0.906479i \(-0.638760\pi\)
−0.422250 + 0.906479i \(0.638760\pi\)
\(488\) 0 0
\(489\) 1.75388e6 0.331687
\(490\) 0 0
\(491\) 257981. 0.0482930 0.0241465 0.999708i \(-0.492313\pi\)
0.0241465 + 0.999708i \(0.492313\pi\)
\(492\) 0 0
\(493\) −8.27645e6 −1.53365
\(494\) 0 0
\(495\) −309985. −0.0568627
\(496\) 0 0
\(497\) 2.09809e6 0.381007
\(498\) 0 0
\(499\) 1.08106e7 1.94356 0.971782 0.235882i \(-0.0757978\pi\)
0.971782 + 0.235882i \(0.0757978\pi\)
\(500\) 0 0
\(501\) −4.61643e6 −0.821698
\(502\) 0 0
\(503\) −1.13024e7 −1.99183 −0.995915 0.0902925i \(-0.971220\pi\)
−0.995915 + 0.0902925i \(0.971220\pi\)
\(504\) 0 0
\(505\) −4.96769e6 −0.866814
\(506\) 0 0
\(507\) −3.03994e6 −0.525225
\(508\) 0 0
\(509\) 5.04265e6 0.862708 0.431354 0.902183i \(-0.358036\pi\)
0.431354 + 0.902183i \(0.358036\pi\)
\(510\) 0 0
\(511\) −5.24511e6 −0.888592
\(512\) 0 0
\(513\) −263169. −0.0441511
\(514\) 0 0
\(515\) 1.05372e6 0.175067
\(516\) 0 0
\(517\) −469458. −0.0772449
\(518\) 0 0
\(519\) 3.09753e6 0.504775
\(520\) 0 0
\(521\) −5.51864e6 −0.890713 −0.445357 0.895353i \(-0.646923\pi\)
−0.445357 + 0.895353i \(0.646923\pi\)
\(522\) 0 0
\(523\) −5.84641e6 −0.934621 −0.467310 0.884093i \(-0.654777\pi\)
−0.467310 + 0.884093i \(0.654777\pi\)
\(524\) 0 0
\(525\) 2.46209e6 0.389858
\(526\) 0 0
\(527\) −1.24761e7 −1.95682
\(528\) 0 0
\(529\) 9.59111e6 1.49015
\(530\) 0 0
\(531\) 2.44766e6 0.376717
\(532\) 0 0
\(533\) 1.24740e6 0.190191
\(534\) 0 0
\(535\) 3.28158e6 0.495677
\(536\) 0 0
\(537\) 4.82352e6 0.721819
\(538\) 0 0
\(539\) −907430. −0.134537
\(540\) 0 0
\(541\) −2.21955e6 −0.326041 −0.163020 0.986623i \(-0.552124\pi\)
−0.163020 + 0.986623i \(0.552124\pi\)
\(542\) 0 0
\(543\) 6.45458e6 0.939438
\(544\) 0 0
\(545\) −1.02935e7 −1.48448
\(546\) 0 0
\(547\) 1.37703e6 0.196777 0.0983883 0.995148i \(-0.468631\pi\)
0.0983883 + 0.995148i \(0.468631\pi\)
\(548\) 0 0
\(549\) 998661. 0.141412
\(550\) 0 0
\(551\) 1.47070e6 0.206369
\(552\) 0 0
\(553\) −29788.2 −0.00414220
\(554\) 0 0
\(555\) 2.09799e6 0.289116
\(556\) 0 0
\(557\) −4.61215e6 −0.629891 −0.314946 0.949110i \(-0.601986\pi\)
−0.314946 + 0.949110i \(0.601986\pi\)
\(558\) 0 0
\(559\) −399721. −0.0541038
\(560\) 0 0
\(561\) −1.02810e6 −0.137920
\(562\) 0 0
\(563\) 1.39621e7 1.85643 0.928214 0.372046i \(-0.121343\pi\)
0.928214 + 0.372046i \(0.121343\pi\)
\(564\) 0 0
\(565\) −1.58753e7 −2.09219
\(566\) 0 0
\(567\) 1.19087e6 0.155563
\(568\) 0 0
\(569\) −1.25243e7 −1.62170 −0.810852 0.585251i \(-0.800996\pi\)
−0.810852 + 0.585251i \(0.800996\pi\)
\(570\) 0 0
\(571\) 8.03755e6 1.03165 0.515826 0.856693i \(-0.327485\pi\)
0.515826 + 0.856693i \(0.327485\pi\)
\(572\) 0 0
\(573\) 5.54872e6 0.706002
\(574\) 0 0
\(575\) 6.03392e6 0.761079
\(576\) 0 0
\(577\) 1.33502e7 1.66935 0.834674 0.550744i \(-0.185656\pi\)
0.834674 + 0.550744i \(0.185656\pi\)
\(578\) 0 0
\(579\) −2.67971e6 −0.332194
\(580\) 0 0
\(581\) −2.44496e6 −0.300491
\(582\) 0 0
\(583\) −2.19308e6 −0.267229
\(584\) 0 0
\(585\) −1.00934e6 −0.121941
\(586\) 0 0
\(587\) 4.01353e6 0.480763 0.240382 0.970678i \(-0.422727\pi\)
0.240382 + 0.970678i \(0.422727\pi\)
\(588\) 0 0
\(589\) 2.21695e6 0.263311
\(590\) 0 0
\(591\) 6.75265e6 0.795254
\(592\) 0 0
\(593\) 8.78650e6 1.02608 0.513038 0.858366i \(-0.328520\pi\)
0.513038 + 0.858366i \(0.328520\pi\)
\(594\) 0 0
\(595\) 2.50967e7 2.90619
\(596\) 0 0
\(597\) 4.02353e6 0.462031
\(598\) 0 0
\(599\) −1.36952e7 −1.55955 −0.779777 0.626058i \(-0.784667\pi\)
−0.779777 + 0.626058i \(0.784667\pi\)
\(600\) 0 0
\(601\) −1.47348e7 −1.66402 −0.832010 0.554760i \(-0.812810\pi\)
−0.832010 + 0.554760i \(0.812810\pi\)
\(602\) 0 0
\(603\) 658767. 0.0737800
\(604\) 0 0
\(605\) −1.07460e7 −1.19360
\(606\) 0 0
\(607\) −7.98391e6 −0.879516 −0.439758 0.898116i \(-0.644936\pi\)
−0.439758 + 0.898116i \(0.644936\pi\)
\(608\) 0 0
\(609\) −6.65508e6 −0.727126
\(610\) 0 0
\(611\) −1.52861e6 −0.165650
\(612\) 0 0
\(613\) −1.43938e7 −1.54712 −0.773558 0.633725i \(-0.781525\pi\)
−0.773558 + 0.633725i \(0.781525\pi\)
\(614\) 0 0
\(615\) −4.17332e6 −0.444932
\(616\) 0 0
\(617\) −1.35120e7 −1.42892 −0.714459 0.699677i \(-0.753327\pi\)
−0.714459 + 0.699677i \(0.753327\pi\)
\(618\) 0 0
\(619\) −1.80703e6 −0.189557 −0.0947783 0.995498i \(-0.530214\pi\)
−0.0947783 + 0.995498i \(0.530214\pi\)
\(620\) 0 0
\(621\) 2.91850e6 0.303690
\(622\) 0 0
\(623\) −1.87983e7 −1.94043
\(624\) 0 0
\(625\) −1.22040e7 −1.24969
\(626\) 0 0
\(627\) 182689. 0.0185585
\(628\) 0 0
\(629\) 6.95821e6 0.701247
\(630\) 0 0
\(631\) −1.73492e7 −1.73463 −0.867313 0.497762i \(-0.834155\pi\)
−0.867313 + 0.497762i \(0.834155\pi\)
\(632\) 0 0
\(633\) −6.88572e6 −0.683030
\(634\) 0 0
\(635\) 1.36303e7 1.34144
\(636\) 0 0
\(637\) −2.95469e6 −0.288512
\(638\) 0 0
\(639\) 936297. 0.0907113
\(640\) 0 0
\(641\) −5.83239e6 −0.560662 −0.280331 0.959903i \(-0.590444\pi\)
−0.280331 + 0.959903i \(0.590444\pi\)
\(642\) 0 0
\(643\) 1.08231e7 1.03235 0.516173 0.856484i \(-0.327356\pi\)
0.516173 + 0.856484i \(0.327356\pi\)
\(644\) 0 0
\(645\) 1.33731e6 0.126570
\(646\) 0 0
\(647\) −1.06311e7 −0.998433 −0.499217 0.866477i \(-0.666379\pi\)
−0.499217 + 0.866477i \(0.666379\pi\)
\(648\) 0 0
\(649\) −1.69914e6 −0.158350
\(650\) 0 0
\(651\) −1.00320e7 −0.927758
\(652\) 0 0
\(653\) 1.53877e7 1.41219 0.706093 0.708119i \(-0.250456\pi\)
0.706093 + 0.708119i \(0.250456\pi\)
\(654\) 0 0
\(655\) 317429. 0.0289097
\(656\) 0 0
\(657\) −2.34070e6 −0.211559
\(658\) 0 0
\(659\) −1.66297e6 −0.149166 −0.0745832 0.997215i \(-0.523763\pi\)
−0.0745832 + 0.997215i \(0.523763\pi\)
\(660\) 0 0
\(661\) 3.97953e6 0.354265 0.177133 0.984187i \(-0.443318\pi\)
0.177133 + 0.984187i \(0.443318\pi\)
\(662\) 0 0
\(663\) −3.34759e6 −0.295766
\(664\) 0 0
\(665\) −4.45959e6 −0.391058
\(666\) 0 0
\(667\) −1.63098e7 −1.41949
\(668\) 0 0
\(669\) −5.62323e6 −0.485758
\(670\) 0 0
\(671\) −693259. −0.0594414
\(672\) 0 0
\(673\) 7.83424e6 0.666744 0.333372 0.942795i \(-0.391814\pi\)
0.333372 + 0.942795i \(0.391814\pi\)
\(674\) 0 0
\(675\) 1.09874e6 0.0928186
\(676\) 0 0
\(677\) −7.68877e6 −0.644741 −0.322370 0.946614i \(-0.604480\pi\)
−0.322370 + 0.946614i \(0.604480\pi\)
\(678\) 0 0
\(679\) −6.26033e6 −0.521102
\(680\) 0 0
\(681\) 76400.7 0.00631291
\(682\) 0 0
\(683\) −1.48293e7 −1.21638 −0.608190 0.793792i \(-0.708104\pi\)
−0.608190 + 0.793792i \(0.708104\pi\)
\(684\) 0 0
\(685\) −1.74165e6 −0.141819
\(686\) 0 0
\(687\) 4.51941e6 0.365334
\(688\) 0 0
\(689\) −7.14093e6 −0.573069
\(690\) 0 0
\(691\) 2.34870e7 1.87125 0.935626 0.352992i \(-0.114836\pi\)
0.935626 + 0.352992i \(0.114836\pi\)
\(692\) 0 0
\(693\) −826689. −0.0653897
\(694\) 0 0
\(695\) 4.57969e6 0.359645
\(696\) 0 0
\(697\) −1.38412e7 −1.07918
\(698\) 0 0
\(699\) −2.87309e6 −0.222411
\(700\) 0 0
\(701\) −3.22661e6 −0.248000 −0.124000 0.992282i \(-0.539572\pi\)
−0.124000 + 0.992282i \(0.539572\pi\)
\(702\) 0 0
\(703\) −1.23645e6 −0.0943599
\(704\) 0 0
\(705\) 5.11411e6 0.387522
\(706\) 0 0
\(707\) −1.32482e7 −0.996800
\(708\) 0 0
\(709\) 2.35520e6 0.175959 0.0879796 0.996122i \(-0.471959\pi\)
0.0879796 + 0.996122i \(0.471959\pi\)
\(710\) 0 0
\(711\) −13293.3 −0.000986188 0
\(712\) 0 0
\(713\) −2.45857e7 −1.81116
\(714\) 0 0
\(715\) 700675. 0.0512568
\(716\) 0 0
\(717\) 6.80956e6 0.494677
\(718\) 0 0
\(719\) 2.13336e7 1.53901 0.769507 0.638638i \(-0.220502\pi\)
0.769507 + 0.638638i \(0.220502\pi\)
\(720\) 0 0
\(721\) 2.81012e6 0.201320
\(722\) 0 0
\(723\) −5.80685e6 −0.413138
\(724\) 0 0
\(725\) −6.14020e6 −0.433848
\(726\) 0 0
\(727\) −1.88770e6 −0.132464 −0.0662319 0.997804i \(-0.521098\pi\)
−0.0662319 + 0.997804i \(0.521098\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) 4.43531e6 0.306995
\(732\) 0 0
\(733\) −899424. −0.0618308 −0.0309154 0.999522i \(-0.509842\pi\)
−0.0309154 + 0.999522i \(0.509842\pi\)
\(734\) 0 0
\(735\) 9.88522e6 0.674944
\(736\) 0 0
\(737\) −457308. −0.0310127
\(738\) 0 0
\(739\) 157022. 0.0105767 0.00528833 0.999986i \(-0.498317\pi\)
0.00528833 + 0.999986i \(0.498317\pi\)
\(740\) 0 0
\(741\) 594855. 0.0397984
\(742\) 0 0
\(743\) −1.95058e7 −1.29626 −0.648128 0.761531i \(-0.724448\pi\)
−0.648128 + 0.761531i \(0.724448\pi\)
\(744\) 0 0
\(745\) −1.61012e7 −1.06284
\(746\) 0 0
\(747\) −1.09109e6 −0.0715418
\(748\) 0 0
\(749\) 8.75156e6 0.570008
\(750\) 0 0
\(751\) −1.45467e7 −0.941163 −0.470582 0.882356i \(-0.655956\pi\)
−0.470582 + 0.882356i \(0.655956\pi\)
\(752\) 0 0
\(753\) 1.52143e7 0.977834
\(754\) 0 0
\(755\) 6.59711e6 0.421198
\(756\) 0 0
\(757\) −1.20959e7 −0.767183 −0.383592 0.923503i \(-0.625313\pi\)
−0.383592 + 0.923503i \(0.625313\pi\)
\(758\) 0 0
\(759\) −2.02599e6 −0.127653
\(760\) 0 0
\(761\) −1.04786e7 −0.655905 −0.327952 0.944694i \(-0.606359\pi\)
−0.327952 + 0.944694i \(0.606359\pi\)
\(762\) 0 0
\(763\) −2.74515e7 −1.70709
\(764\) 0 0
\(765\) 1.11997e7 0.691916
\(766\) 0 0
\(767\) −5.53259e6 −0.339578
\(768\) 0 0
\(769\) −1.61815e6 −0.0986739 −0.0493370 0.998782i \(-0.515711\pi\)
−0.0493370 + 0.998782i \(0.515711\pi\)
\(770\) 0 0
\(771\) −1.80185e6 −0.109165
\(772\) 0 0
\(773\) 2.19651e7 1.32216 0.661080 0.750315i \(-0.270098\pi\)
0.661080 + 0.750315i \(0.270098\pi\)
\(774\) 0 0
\(775\) −9.25586e6 −0.553557
\(776\) 0 0
\(777\) 5.59508e6 0.332471
\(778\) 0 0
\(779\) 2.45953e6 0.145214
\(780\) 0 0
\(781\) −649966. −0.0381297
\(782\) 0 0
\(783\) −2.96991e6 −0.173117
\(784\) 0 0
\(785\) −3.53062e6 −0.204492
\(786\) 0 0
\(787\) −1.02291e7 −0.588707 −0.294354 0.955697i \(-0.595104\pi\)
−0.294354 + 0.955697i \(0.595104\pi\)
\(788\) 0 0
\(789\) 7.12472e6 0.407451
\(790\) 0 0
\(791\) −4.23374e7 −2.40593
\(792\) 0 0
\(793\) −2.25733e6 −0.127471
\(794\) 0 0
\(795\) 2.38907e7 1.34064
\(796\) 0 0
\(797\) −2.15124e7 −1.19962 −0.599808 0.800144i \(-0.704756\pi\)
−0.599808 + 0.800144i \(0.704756\pi\)
\(798\) 0 0
\(799\) 1.69614e7 0.939931
\(800\) 0 0
\(801\) −8.38895e6 −0.461983
\(802\) 0 0
\(803\) 1.62488e6 0.0889269
\(804\) 0 0
\(805\) 4.94562e7 2.68987
\(806\) 0 0
\(807\) 6.11271e6 0.330408
\(808\) 0 0
\(809\) −5.72326e6 −0.307448 −0.153724 0.988114i \(-0.549127\pi\)
−0.153724 + 0.988114i \(0.549127\pi\)
\(810\) 0 0
\(811\) −2.78783e7 −1.48838 −0.744191 0.667967i \(-0.767165\pi\)
−0.744191 + 0.667967i \(0.767165\pi\)
\(812\) 0 0
\(813\) 1.46232e7 0.775918
\(814\) 0 0
\(815\) 1.32633e7 0.699451
\(816\) 0 0
\(817\) −788139. −0.0413093
\(818\) 0 0
\(819\) −2.69179e6 −0.140227
\(820\) 0 0
\(821\) 6.54662e6 0.338969 0.169484 0.985533i \(-0.445790\pi\)
0.169484 + 0.985533i \(0.445790\pi\)
\(822\) 0 0
\(823\) 1.03390e7 0.532082 0.266041 0.963962i \(-0.414284\pi\)
0.266041 + 0.963962i \(0.414284\pi\)
\(824\) 0 0
\(825\) −762732. −0.0390155
\(826\) 0 0
\(827\) 1.19751e7 0.608858 0.304429 0.952535i \(-0.401534\pi\)
0.304429 + 0.952535i \(0.401534\pi\)
\(828\) 0 0
\(829\) −1.39945e7 −0.707249 −0.353625 0.935387i \(-0.615051\pi\)
−0.353625 + 0.935387i \(0.615051\pi\)
\(830\) 0 0
\(831\) −2.21981e7 −1.11510
\(832\) 0 0
\(833\) 3.27853e7 1.63707
\(834\) 0 0
\(835\) −3.49106e7 −1.73277
\(836\) 0 0
\(837\) −4.47690e6 −0.220884
\(838\) 0 0
\(839\) 2.12669e7 1.04303 0.521517 0.853241i \(-0.325366\pi\)
0.521517 + 0.853241i \(0.325366\pi\)
\(840\) 0 0
\(841\) −3.91410e6 −0.190828
\(842\) 0 0
\(843\) 8.60015e6 0.416809
\(844\) 0 0
\(845\) −2.29888e7 −1.10758
\(846\) 0 0
\(847\) −2.86581e7 −1.37258
\(848\) 0 0
\(849\) 1.37225e6 0.0653377
\(850\) 0 0
\(851\) 1.37120e7 0.649048
\(852\) 0 0
\(853\) −4.31526e6 −0.203065 −0.101532 0.994832i \(-0.532375\pi\)
−0.101532 + 0.994832i \(0.532375\pi\)
\(854\) 0 0
\(855\) −1.99015e6 −0.0931044
\(856\) 0 0
\(857\) 1.59971e6 0.0744029 0.0372015 0.999308i \(-0.488156\pi\)
0.0372015 + 0.999308i \(0.488156\pi\)
\(858\) 0 0
\(859\) −2.97990e7 −1.37790 −0.688951 0.724808i \(-0.741928\pi\)
−0.688951 + 0.724808i \(0.741928\pi\)
\(860\) 0 0
\(861\) −1.11297e7 −0.511653
\(862\) 0 0
\(863\) 1.17818e7 0.538498 0.269249 0.963071i \(-0.413225\pi\)
0.269249 + 0.963071i \(0.413225\pi\)
\(864\) 0 0
\(865\) 2.34243e7 1.06445
\(866\) 0 0
\(867\) 2.43662e7 1.10088
\(868\) 0 0
\(869\) 9228.07 0.000414535 0
\(870\) 0 0
\(871\) −1.48905e6 −0.0665063
\(872\) 0 0
\(873\) −2.79375e6 −0.124066
\(874\) 0 0
\(875\) −1.99856e7 −0.882462
\(876\) 0 0
\(877\) −1.60831e7 −0.706108 −0.353054 0.935603i \(-0.614857\pi\)
−0.353054 + 0.935603i \(0.614857\pi\)
\(878\) 0 0
\(879\) 2.28961e7 0.999517
\(880\) 0 0
\(881\) −2.06461e7 −0.896187 −0.448093 0.893987i \(-0.647897\pi\)
−0.448093 + 0.893987i \(0.647897\pi\)
\(882\) 0 0
\(883\) 2.44612e7 1.05579 0.527894 0.849310i \(-0.322982\pi\)
0.527894 + 0.849310i \(0.322982\pi\)
\(884\) 0 0
\(885\) 1.85098e7 0.794409
\(886\) 0 0
\(887\) −2.49921e7 −1.06658 −0.533290 0.845932i \(-0.679045\pi\)
−0.533290 + 0.845932i \(0.679045\pi\)
\(888\) 0 0
\(889\) 3.63502e7 1.54260
\(890\) 0 0
\(891\) −368920. −0.0155682
\(892\) 0 0
\(893\) −3.01399e6 −0.126477
\(894\) 0 0
\(895\) 3.64766e7 1.52215
\(896\) 0 0
\(897\) −6.59685e6 −0.273751
\(898\) 0 0
\(899\) 2.50187e7 1.03244
\(900\) 0 0
\(901\) 7.92359e7 3.25169
\(902\) 0 0
\(903\) 3.56643e6 0.145551
\(904\) 0 0
\(905\) 4.88111e7 1.98106
\(906\) 0 0
\(907\) −1.33799e6 −0.0540051 −0.0270026 0.999635i \(-0.508596\pi\)
−0.0270026 + 0.999635i \(0.508596\pi\)
\(908\) 0 0
\(909\) −5.91216e6 −0.237321
\(910\) 0 0
\(911\) 4.41172e6 0.176121 0.0880606 0.996115i \(-0.471933\pi\)
0.0880606 + 0.996115i \(0.471933\pi\)
\(912\) 0 0
\(913\) 757423. 0.0300719
\(914\) 0 0
\(915\) 7.55211e6 0.298206
\(916\) 0 0
\(917\) 846542. 0.0332449
\(918\) 0 0
\(919\) 1.72978e7 0.675619 0.337810 0.941214i \(-0.390314\pi\)
0.337810 + 0.941214i \(0.390314\pi\)
\(920\) 0 0
\(921\) −1.01754e7 −0.395279
\(922\) 0 0
\(923\) −2.11636e6 −0.0817685
\(924\) 0 0
\(925\) 5.16221e6 0.198373
\(926\) 0 0
\(927\) 1.25405e6 0.0479309
\(928\) 0 0
\(929\) −1.09081e7 −0.414676 −0.207338 0.978269i \(-0.566480\pi\)
−0.207338 + 0.978269i \(0.566480\pi\)
\(930\) 0 0
\(931\) −5.82583e6 −0.220284
\(932\) 0 0
\(933\) −3.05281e7 −1.14814
\(934\) 0 0
\(935\) −7.77471e6 −0.290841
\(936\) 0 0
\(937\) 3.85474e7 1.43432 0.717159 0.696909i \(-0.245442\pi\)
0.717159 + 0.696909i \(0.245442\pi\)
\(938\) 0 0
\(939\) 3.87616e6 0.143462
\(940\) 0 0
\(941\) 2.02392e6 0.0745110 0.0372555 0.999306i \(-0.488138\pi\)
0.0372555 + 0.999306i \(0.488138\pi\)
\(942\) 0 0
\(943\) −2.72758e7 −0.998847
\(944\) 0 0
\(945\) 9.00566e6 0.328047
\(946\) 0 0
\(947\) −1.58028e7 −0.572611 −0.286306 0.958138i \(-0.592427\pi\)
−0.286306 + 0.958138i \(0.592427\pi\)
\(948\) 0 0
\(949\) 5.29080e6 0.190702
\(950\) 0 0
\(951\) −3.08529e7 −1.10623
\(952\) 0 0
\(953\) −4.55765e7 −1.62558 −0.812791 0.582555i \(-0.802053\pi\)
−0.812791 + 0.582555i \(0.802053\pi\)
\(954\) 0 0
\(955\) 4.19607e7 1.48879
\(956\) 0 0
\(957\) 2.06168e6 0.0727680
\(958\) 0 0
\(959\) −4.64477e6 −0.163086
\(960\) 0 0
\(961\) 9.08453e6 0.317318
\(962\) 0 0
\(963\) 3.90549e6 0.135709
\(964\) 0 0
\(965\) −2.02646e7 −0.700520
\(966\) 0 0
\(967\) 4.49937e7 1.54734 0.773669 0.633589i \(-0.218419\pi\)
0.773669 + 0.633589i \(0.218419\pi\)
\(968\) 0 0
\(969\) −6.60052e6 −0.225823
\(970\) 0 0
\(971\) −4.31949e7 −1.47023 −0.735114 0.677944i \(-0.762871\pi\)
−0.735114 + 0.677944i \(0.762871\pi\)
\(972\) 0 0
\(973\) 1.22134e7 0.413577
\(974\) 0 0
\(975\) −2.48354e6 −0.0836681
\(976\) 0 0
\(977\) 8.76839e6 0.293889 0.146945 0.989145i \(-0.453056\pi\)
0.146945 + 0.989145i \(0.453056\pi\)
\(978\) 0 0
\(979\) 5.82351e6 0.194191
\(980\) 0 0
\(981\) −1.22506e7 −0.406428
\(982\) 0 0
\(983\) 4.18236e7 1.38051 0.690253 0.723568i \(-0.257499\pi\)
0.690253 + 0.723568i \(0.257499\pi\)
\(984\) 0 0
\(985\) 5.10652e7 1.67700
\(986\) 0 0
\(987\) 1.36387e7 0.445634
\(988\) 0 0
\(989\) 8.74033e6 0.284143
\(990\) 0 0
\(991\) −2.87743e7 −0.930723 −0.465362 0.885121i \(-0.654076\pi\)
−0.465362 + 0.885121i \(0.654076\pi\)
\(992\) 0 0
\(993\) 197607. 0.00635960
\(994\) 0 0
\(995\) 3.04269e7 0.974317
\(996\) 0 0
\(997\) −9.50959e6 −0.302987 −0.151493 0.988458i \(-0.548408\pi\)
−0.151493 + 0.988458i \(0.548408\pi\)
\(998\) 0 0
\(999\) 2.49687e6 0.0791558
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 912.6.a.y.1.6 6
4.3 odd 2 456.6.a.f.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.6.a.f.1.6 6 4.3 odd 2
912.6.a.y.1.6 6 1.1 even 1 trivial