Properties

Label 441.6.a.g.1.1
Level $441$
Weight $6$
Character 441.1
Self dual yes
Analytic conductor $70.729$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(70.7292645375\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 441.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -28.0000 q^{4} -11.0000 q^{5} -120.000 q^{8} +O(q^{10})\) \(q+2.00000 q^{2} -28.0000 q^{4} -11.0000 q^{5} -120.000 q^{8} -22.0000 q^{10} -269.000 q^{11} -308.000 q^{13} +656.000 q^{16} -1896.00 q^{17} -164.000 q^{19} +308.000 q^{20} -538.000 q^{22} +3264.00 q^{23} -3004.00 q^{25} -616.000 q^{26} -2417.00 q^{29} +2841.00 q^{31} +5152.00 q^{32} -3792.00 q^{34} -11328.0 q^{37} -328.000 q^{38} +1320.00 q^{40} +16856.0 q^{41} -7894.00 q^{43} +7532.00 q^{44} +6528.00 q^{46} -21102.0 q^{47} -6008.00 q^{50} +8624.00 q^{52} +29691.0 q^{53} +2959.00 q^{55} -4834.00 q^{58} +8163.00 q^{59} +15166.0 q^{61} +5682.00 q^{62} -10688.0 q^{64} +3388.00 q^{65} -32078.0 q^{67} +53088.0 q^{68} +38274.0 q^{71} +34866.0 q^{73} -22656.0 q^{74} +4592.00 q^{76} +13529.0 q^{79} -7216.00 q^{80} +33712.0 q^{82} +68103.0 q^{83} +20856.0 q^{85} -15788.0 q^{86} +32280.0 q^{88} +114922. q^{89} -91392.0 q^{92} -42204.0 q^{94} +1804.00 q^{95} +154959. q^{97} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.353553 0.176777 0.984251i \(-0.443433\pi\)
0.176777 + 0.984251i \(0.443433\pi\)
\(3\) 0 0
\(4\) −28.0000 −0.875000
\(5\) −11.0000 −0.196774 −0.0983870 0.995148i \(-0.531368\pi\)
−0.0983870 + 0.995148i \(0.531368\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −120.000 −0.662913
\(9\) 0 0
\(10\) −22.0000 −0.0695701
\(11\) −269.000 −0.670302 −0.335151 0.942164i \(-0.608787\pi\)
−0.335151 + 0.942164i \(0.608787\pi\)
\(12\) 0 0
\(13\) −308.000 −0.505466 −0.252733 0.967536i \(-0.581329\pi\)
−0.252733 + 0.967536i \(0.581329\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 656.000 0.640625
\(17\) −1896.00 −1.59117 −0.795584 0.605843i \(-0.792836\pi\)
−0.795584 + 0.605843i \(0.792836\pi\)
\(18\) 0 0
\(19\) −164.000 −0.104222 −0.0521111 0.998641i \(-0.516595\pi\)
−0.0521111 + 0.998641i \(0.516595\pi\)
\(20\) 308.000 0.172177
\(21\) 0 0
\(22\) −538.000 −0.236988
\(23\) 3264.00 1.28656 0.643281 0.765630i \(-0.277573\pi\)
0.643281 + 0.765630i \(0.277573\pi\)
\(24\) 0 0
\(25\) −3004.00 −0.961280
\(26\) −616.000 −0.178709
\(27\) 0 0
\(28\) 0 0
\(29\) −2417.00 −0.533681 −0.266840 0.963741i \(-0.585980\pi\)
−0.266840 + 0.963741i \(0.585980\pi\)
\(30\) 0 0
\(31\) 2841.00 0.530966 0.265483 0.964115i \(-0.414469\pi\)
0.265483 + 0.964115i \(0.414469\pi\)
\(32\) 5152.00 0.889408
\(33\) 0 0
\(34\) −3792.00 −0.562563
\(35\) 0 0
\(36\) 0 0
\(37\) −11328.0 −1.36034 −0.680172 0.733052i \(-0.738095\pi\)
−0.680172 + 0.733052i \(0.738095\pi\)
\(38\) −328.000 −0.0368481
\(39\) 0 0
\(40\) 1320.00 0.130444
\(41\) 16856.0 1.56601 0.783006 0.622015i \(-0.213686\pi\)
0.783006 + 0.622015i \(0.213686\pi\)
\(42\) 0 0
\(43\) −7894.00 −0.651067 −0.325534 0.945530i \(-0.605544\pi\)
−0.325534 + 0.945530i \(0.605544\pi\)
\(44\) 7532.00 0.586514
\(45\) 0 0
\(46\) 6528.00 0.454868
\(47\) −21102.0 −1.39341 −0.696705 0.717358i \(-0.745351\pi\)
−0.696705 + 0.717358i \(0.745351\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −6008.00 −0.339864
\(51\) 0 0
\(52\) 8624.00 0.442283
\(53\) 29691.0 1.45189 0.725947 0.687750i \(-0.241402\pi\)
0.725947 + 0.687750i \(0.241402\pi\)
\(54\) 0 0
\(55\) 2959.00 0.131898
\(56\) 0 0
\(57\) 0 0
\(58\) −4834.00 −0.188685
\(59\) 8163.00 0.305295 0.152648 0.988281i \(-0.451220\pi\)
0.152648 + 0.988281i \(0.451220\pi\)
\(60\) 0 0
\(61\) 15166.0 0.521851 0.260925 0.965359i \(-0.415972\pi\)
0.260925 + 0.965359i \(0.415972\pi\)
\(62\) 5682.00 0.187725
\(63\) 0 0
\(64\) −10688.0 −0.326172
\(65\) 3388.00 0.0994626
\(66\) 0 0
\(67\) −32078.0 −0.873012 −0.436506 0.899701i \(-0.643784\pi\)
−0.436506 + 0.899701i \(0.643784\pi\)
\(68\) 53088.0 1.39227
\(69\) 0 0
\(70\) 0 0
\(71\) 38274.0 0.901069 0.450534 0.892759i \(-0.351233\pi\)
0.450534 + 0.892759i \(0.351233\pi\)
\(72\) 0 0
\(73\) 34866.0 0.765764 0.382882 0.923797i \(-0.374932\pi\)
0.382882 + 0.923797i \(0.374932\pi\)
\(74\) −22656.0 −0.480954
\(75\) 0 0
\(76\) 4592.00 0.0911943
\(77\) 0 0
\(78\) 0 0
\(79\) 13529.0 0.243892 0.121946 0.992537i \(-0.461086\pi\)
0.121946 + 0.992537i \(0.461086\pi\)
\(80\) −7216.00 −0.126058
\(81\) 0 0
\(82\) 33712.0 0.553669
\(83\) 68103.0 1.08510 0.542552 0.840023i \(-0.317458\pi\)
0.542552 + 0.840023i \(0.317458\pi\)
\(84\) 0 0
\(85\) 20856.0 0.313100
\(86\) −15788.0 −0.230187
\(87\) 0 0
\(88\) 32280.0 0.444352
\(89\) 114922. 1.53790 0.768950 0.639309i \(-0.220779\pi\)
0.768950 + 0.639309i \(0.220779\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −91392.0 −1.12574
\(93\) 0 0
\(94\) −42204.0 −0.492645
\(95\) 1804.00 0.0205082
\(96\) 0 0
\(97\) 154959. 1.67220 0.836099 0.548579i \(-0.184831\pi\)
0.836099 + 0.548579i \(0.184831\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 84112.0 0.841120
\(101\) 107570. 1.04927 0.524636 0.851327i \(-0.324202\pi\)
0.524636 + 0.851327i \(0.324202\pi\)
\(102\) 0 0
\(103\) 8936.00 0.0829947 0.0414973 0.999139i \(-0.486787\pi\)
0.0414973 + 0.999139i \(0.486787\pi\)
\(104\) 36960.0 0.335080
\(105\) 0 0
\(106\) 59382.0 0.513322
\(107\) −193667. −1.63530 −0.817648 0.575719i \(-0.804722\pi\)
−0.817648 + 0.575719i \(0.804722\pi\)
\(108\) 0 0
\(109\) 205110. 1.65356 0.826781 0.562524i \(-0.190169\pi\)
0.826781 + 0.562524i \(0.190169\pi\)
\(110\) 5918.00 0.0466330
\(111\) 0 0
\(112\) 0 0
\(113\) −46664.0 −0.343784 −0.171892 0.985116i \(-0.554988\pi\)
−0.171892 + 0.985116i \(0.554988\pi\)
\(114\) 0 0
\(115\) −35904.0 −0.253162
\(116\) 67676.0 0.466971
\(117\) 0 0
\(118\) 16326.0 0.107938
\(119\) 0 0
\(120\) 0 0
\(121\) −88690.0 −0.550695
\(122\) 30332.0 0.184502
\(123\) 0 0
\(124\) −79548.0 −0.464596
\(125\) 67419.0 0.385929
\(126\) 0 0
\(127\) −304365. −1.67450 −0.837250 0.546820i \(-0.815838\pi\)
−0.837250 + 0.546820i \(0.815838\pi\)
\(128\) −186240. −1.00473
\(129\) 0 0
\(130\) 6776.00 0.0351654
\(131\) 13303.0 0.0677285 0.0338642 0.999426i \(-0.489219\pi\)
0.0338642 + 0.999426i \(0.489219\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −64156.0 −0.308656
\(135\) 0 0
\(136\) 227520. 1.05481
\(137\) 398262. 1.81287 0.906437 0.422342i \(-0.138792\pi\)
0.906437 + 0.422342i \(0.138792\pi\)
\(138\) 0 0
\(139\) 230286. 1.01095 0.505476 0.862841i \(-0.331317\pi\)
0.505476 + 0.862841i \(0.331317\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 76548.0 0.318576
\(143\) 82852.0 0.338815
\(144\) 0 0
\(145\) 26587.0 0.105015
\(146\) 69732.0 0.270738
\(147\) 0 0
\(148\) 317184. 1.19030
\(149\) 97134.0 0.358431 0.179216 0.983810i \(-0.442644\pi\)
0.179216 + 0.983810i \(0.442644\pi\)
\(150\) 0 0
\(151\) −29047.0 −0.103671 −0.0518357 0.998656i \(-0.516507\pi\)
−0.0518357 + 0.998656i \(0.516507\pi\)
\(152\) 19680.0 0.0690901
\(153\) 0 0
\(154\) 0 0
\(155\) −31251.0 −0.104480
\(156\) 0 0
\(157\) −576500. −1.86660 −0.933298 0.359104i \(-0.883082\pi\)
−0.933298 + 0.359104i \(0.883082\pi\)
\(158\) 27058.0 0.0862289
\(159\) 0 0
\(160\) −56672.0 −0.175012
\(161\) 0 0
\(162\) 0 0
\(163\) −265232. −0.781910 −0.390955 0.920410i \(-0.627855\pi\)
−0.390955 + 0.920410i \(0.627855\pi\)
\(164\) −471968. −1.37026
\(165\) 0 0
\(166\) 136206. 0.383642
\(167\) 363790. 1.00939 0.504696 0.863297i \(-0.331605\pi\)
0.504696 + 0.863297i \(0.331605\pi\)
\(168\) 0 0
\(169\) −276429. −0.744504
\(170\) 41712.0 0.110698
\(171\) 0 0
\(172\) 221032. 0.569684
\(173\) 164846. 0.418758 0.209379 0.977835i \(-0.432856\pi\)
0.209379 + 0.977835i \(0.432856\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −176464. −0.429412
\(177\) 0 0
\(178\) 229844. 0.543730
\(179\) −30628.0 −0.0714473 −0.0357237 0.999362i \(-0.511374\pi\)
−0.0357237 + 0.999362i \(0.511374\pi\)
\(180\) 0 0
\(181\) −651392. −1.47790 −0.738952 0.673759i \(-0.764679\pi\)
−0.738952 + 0.673759i \(0.764679\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −391680. −0.852878
\(185\) 124608. 0.267680
\(186\) 0 0
\(187\) 510024. 1.06656
\(188\) 590856. 1.21923
\(189\) 0 0
\(190\) 3608.00 0.00725074
\(191\) 757360. 1.50217 0.751085 0.660206i \(-0.229531\pi\)
0.751085 + 0.660206i \(0.229531\pi\)
\(192\) 0 0
\(193\) −160339. −0.309846 −0.154923 0.987927i \(-0.549513\pi\)
−0.154923 + 0.987927i \(0.549513\pi\)
\(194\) 309918. 0.591211
\(195\) 0 0
\(196\) 0 0
\(197\) 61738.0 0.113341 0.0566705 0.998393i \(-0.481952\pi\)
0.0566705 + 0.998393i \(0.481952\pi\)
\(198\) 0 0
\(199\) 370908. 0.663947 0.331974 0.943289i \(-0.392286\pi\)
0.331974 + 0.943289i \(0.392286\pi\)
\(200\) 360480. 0.637245
\(201\) 0 0
\(202\) 215140. 0.370973
\(203\) 0 0
\(204\) 0 0
\(205\) −185416. −0.308150
\(206\) 17872.0 0.0293430
\(207\) 0 0
\(208\) −202048. −0.323814
\(209\) 44116.0 0.0698603
\(210\) 0 0
\(211\) 217450. 0.336243 0.168122 0.985766i \(-0.446230\pi\)
0.168122 + 0.985766i \(0.446230\pi\)
\(212\) −831348. −1.27041
\(213\) 0 0
\(214\) −387334. −0.578164
\(215\) 86834.0 0.128113
\(216\) 0 0
\(217\) 0 0
\(218\) 410220. 0.584623
\(219\) 0 0
\(220\) −82852.0 −0.115411
\(221\) 583968. 0.804282
\(222\) 0 0
\(223\) 589771. 0.794184 0.397092 0.917779i \(-0.370019\pi\)
0.397092 + 0.917779i \(0.370019\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −93328.0 −0.121546
\(227\) 387045. 0.498536 0.249268 0.968434i \(-0.419810\pi\)
0.249268 + 0.968434i \(0.419810\pi\)
\(228\) 0 0
\(229\) −232732. −0.293270 −0.146635 0.989191i \(-0.546844\pi\)
−0.146635 + 0.989191i \(0.546844\pi\)
\(230\) −71808.0 −0.0895062
\(231\) 0 0
\(232\) 290040. 0.353784
\(233\) −42096.0 −0.0507985 −0.0253993 0.999677i \(-0.508086\pi\)
−0.0253993 + 0.999677i \(0.508086\pi\)
\(234\) 0 0
\(235\) 232122. 0.274187
\(236\) −228564. −0.267133
\(237\) 0 0
\(238\) 0 0
\(239\) 313416. 0.354917 0.177458 0.984128i \(-0.443212\pi\)
0.177458 + 0.984128i \(0.443212\pi\)
\(240\) 0 0
\(241\) 857807. 0.951365 0.475682 0.879617i \(-0.342201\pi\)
0.475682 + 0.879617i \(0.342201\pi\)
\(242\) −177380. −0.194700
\(243\) 0 0
\(244\) −424648. −0.456620
\(245\) 0 0
\(246\) 0 0
\(247\) 50512.0 0.0526808
\(248\) −340920. −0.351984
\(249\) 0 0
\(250\) 134838. 0.136446
\(251\) −454517. −0.455371 −0.227686 0.973735i \(-0.573116\pi\)
−0.227686 + 0.973735i \(0.573116\pi\)
\(252\) 0 0
\(253\) −878016. −0.862385
\(254\) −608730. −0.592026
\(255\) 0 0
\(256\) −30464.0 −0.0290527
\(257\) −878182. −0.829376 −0.414688 0.909964i \(-0.636109\pi\)
−0.414688 + 0.909964i \(0.636109\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −94864.0 −0.0870298
\(261\) 0 0
\(262\) 26606.0 0.0239456
\(263\) −1.96093e6 −1.74813 −0.874065 0.485809i \(-0.838525\pi\)
−0.874065 + 0.485809i \(0.838525\pi\)
\(264\) 0 0
\(265\) −326601. −0.285695
\(266\) 0 0
\(267\) 0 0
\(268\) 898184. 0.763886
\(269\) 1.05380e6 0.887923 0.443962 0.896046i \(-0.353573\pi\)
0.443962 + 0.896046i \(0.353573\pi\)
\(270\) 0 0
\(271\) −105059. −0.0868981 −0.0434490 0.999056i \(-0.513835\pi\)
−0.0434490 + 0.999056i \(0.513835\pi\)
\(272\) −1.24378e6 −1.01934
\(273\) 0 0
\(274\) 796524. 0.640948
\(275\) 808076. 0.644348
\(276\) 0 0
\(277\) −427592. −0.334834 −0.167417 0.985886i \(-0.553543\pi\)
−0.167417 + 0.985886i \(0.553543\pi\)
\(278\) 460572. 0.357426
\(279\) 0 0
\(280\) 0 0
\(281\) −638878. −0.482672 −0.241336 0.970442i \(-0.577586\pi\)
−0.241336 + 0.970442i \(0.577586\pi\)
\(282\) 0 0
\(283\) −2.45142e6 −1.81950 −0.909750 0.415157i \(-0.863727\pi\)
−0.909750 + 0.415157i \(0.863727\pi\)
\(284\) −1.07167e6 −0.788435
\(285\) 0 0
\(286\) 165704. 0.119789
\(287\) 0 0
\(288\) 0 0
\(289\) 2.17496e6 1.53182
\(290\) 53174.0 0.0371282
\(291\) 0 0
\(292\) −976248. −0.670044
\(293\) −1.71617e6 −1.16786 −0.583930 0.811804i \(-0.698486\pi\)
−0.583930 + 0.811804i \(0.698486\pi\)
\(294\) 0 0
\(295\) −89793.0 −0.0600741
\(296\) 1.35936e6 0.901790
\(297\) 0 0
\(298\) 194268. 0.126725
\(299\) −1.00531e6 −0.650314
\(300\) 0 0
\(301\) 0 0
\(302\) −58094.0 −0.0366534
\(303\) 0 0
\(304\) −107584. −0.0667673
\(305\) −166826. −0.102687
\(306\) 0 0
\(307\) 1.80897e6 1.09543 0.547715 0.836665i \(-0.315498\pi\)
0.547715 + 0.836665i \(0.315498\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −62502.0 −0.0369394
\(311\) −1.52146e6 −0.891987 −0.445993 0.895036i \(-0.647150\pi\)
−0.445993 + 0.895036i \(0.647150\pi\)
\(312\) 0 0
\(313\) −1.34840e6 −0.777961 −0.388980 0.921246i \(-0.627173\pi\)
−0.388980 + 0.921246i \(0.627173\pi\)
\(314\) −1.15300e6 −0.659941
\(315\) 0 0
\(316\) −378812. −0.213406
\(317\) 49695.0 0.0277757 0.0138878 0.999904i \(-0.495579\pi\)
0.0138878 + 0.999904i \(0.495579\pi\)
\(318\) 0 0
\(319\) 650173. 0.357727
\(320\) 117568. 0.0641821
\(321\) 0 0
\(322\) 0 0
\(323\) 310944. 0.165835
\(324\) 0 0
\(325\) 925232. 0.485895
\(326\) −530464. −0.276447
\(327\) 0 0
\(328\) −2.02272e6 −1.03813
\(329\) 0 0
\(330\) 0 0
\(331\) 1.58784e6 0.796591 0.398296 0.917257i \(-0.369602\pi\)
0.398296 + 0.917257i \(0.369602\pi\)
\(332\) −1.90688e6 −0.949465
\(333\) 0 0
\(334\) 727580. 0.356874
\(335\) 352858. 0.171786
\(336\) 0 0
\(337\) 214825. 0.103041 0.0515205 0.998672i \(-0.483593\pi\)
0.0515205 + 0.998672i \(0.483593\pi\)
\(338\) −552858. −0.263222
\(339\) 0 0
\(340\) −583968. −0.273963
\(341\) −764229. −0.355908
\(342\) 0 0
\(343\) 0 0
\(344\) 947280. 0.431601
\(345\) 0 0
\(346\) 329692. 0.148053
\(347\) −2.58860e6 −1.15409 −0.577046 0.816711i \(-0.695795\pi\)
−0.577046 + 0.816711i \(0.695795\pi\)
\(348\) 0 0
\(349\) −24878.0 −0.0109333 −0.00546666 0.999985i \(-0.501740\pi\)
−0.00546666 + 0.999985i \(0.501740\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.38589e6 −0.596172
\(353\) 1.73601e6 0.741506 0.370753 0.928731i \(-0.379100\pi\)
0.370753 + 0.928731i \(0.379100\pi\)
\(354\) 0 0
\(355\) −421014. −0.177307
\(356\) −3.21782e6 −1.34566
\(357\) 0 0
\(358\) −61256.0 −0.0252604
\(359\) −862426. −0.353172 −0.176586 0.984285i \(-0.556505\pi\)
−0.176586 + 0.984285i \(0.556505\pi\)
\(360\) 0 0
\(361\) −2.44920e6 −0.989138
\(362\) −1.30278e6 −0.522518
\(363\) 0 0
\(364\) 0 0
\(365\) −383526. −0.150682
\(366\) 0 0
\(367\) 3.11542e6 1.20740 0.603700 0.797211i \(-0.293692\pi\)
0.603700 + 0.797211i \(0.293692\pi\)
\(368\) 2.14118e6 0.824203
\(369\) 0 0
\(370\) 249216. 0.0946393
\(371\) 0 0
\(372\) 0 0
\(373\) −1.79694e6 −0.668748 −0.334374 0.942440i \(-0.608525\pi\)
−0.334374 + 0.942440i \(0.608525\pi\)
\(374\) 1.02005e6 0.377087
\(375\) 0 0
\(376\) 2.53224e6 0.923709
\(377\) 744436. 0.269758
\(378\) 0 0
\(379\) 3.45466e6 1.23540 0.617699 0.786415i \(-0.288065\pi\)
0.617699 + 0.786415i \(0.288065\pi\)
\(380\) −50512.0 −0.0179447
\(381\) 0 0
\(382\) 1.51472e6 0.531097
\(383\) −2.15504e6 −0.750685 −0.375343 0.926886i \(-0.622475\pi\)
−0.375343 + 0.926886i \(0.622475\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −320678. −0.109547
\(387\) 0 0
\(388\) −4.33885e6 −1.46317
\(389\) 462774. 0.155058 0.0775291 0.996990i \(-0.475297\pi\)
0.0775291 + 0.996990i \(0.475297\pi\)
\(390\) 0 0
\(391\) −6.18854e6 −2.04714
\(392\) 0 0
\(393\) 0 0
\(394\) 123476. 0.0400721
\(395\) −148819. −0.0479916
\(396\) 0 0
\(397\) −4.06621e6 −1.29483 −0.647416 0.762136i \(-0.724151\pi\)
−0.647416 + 0.762136i \(0.724151\pi\)
\(398\) 741816. 0.234741
\(399\) 0 0
\(400\) −1.97062e6 −0.615820
\(401\) 5.06863e6 1.57409 0.787045 0.616895i \(-0.211610\pi\)
0.787045 + 0.616895i \(0.211610\pi\)
\(402\) 0 0
\(403\) −875028. −0.268386
\(404\) −3.01196e6 −0.918112
\(405\) 0 0
\(406\) 0 0
\(407\) 3.04723e6 0.911842
\(408\) 0 0
\(409\) 2.87734e6 0.850515 0.425258 0.905072i \(-0.360183\pi\)
0.425258 + 0.905072i \(0.360183\pi\)
\(410\) −370832. −0.108948
\(411\) 0 0
\(412\) −250208. −0.0726203
\(413\) 0 0
\(414\) 0 0
\(415\) −749133. −0.213520
\(416\) −1.58682e6 −0.449566
\(417\) 0 0
\(418\) 88232.0 0.0246993
\(419\) 3.41342e6 0.949850 0.474925 0.880026i \(-0.342475\pi\)
0.474925 + 0.880026i \(0.342475\pi\)
\(420\) 0 0
\(421\) −1.30737e6 −0.359496 −0.179748 0.983713i \(-0.557528\pi\)
−0.179748 + 0.983713i \(0.557528\pi\)
\(422\) 434900. 0.118880
\(423\) 0 0
\(424\) −3.56292e6 −0.962479
\(425\) 5.69558e6 1.52956
\(426\) 0 0
\(427\) 0 0
\(428\) 5.42268e6 1.43088
\(429\) 0 0
\(430\) 173668. 0.0452948
\(431\) −1.93547e6 −0.501872 −0.250936 0.968004i \(-0.580738\pi\)
−0.250936 + 0.968004i \(0.580738\pi\)
\(432\) 0 0
\(433\) 516670. 0.132432 0.0662161 0.997805i \(-0.478907\pi\)
0.0662161 + 0.997805i \(0.478907\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −5.74308e6 −1.44687
\(437\) −535296. −0.134088
\(438\) 0 0
\(439\) 2.91530e6 0.721975 0.360987 0.932571i \(-0.382440\pi\)
0.360987 + 0.932571i \(0.382440\pi\)
\(440\) −355080. −0.0874369
\(441\) 0 0
\(442\) 1.16794e6 0.284357
\(443\) 1.78379e6 0.431852 0.215926 0.976410i \(-0.430723\pi\)
0.215926 + 0.976410i \(0.430723\pi\)
\(444\) 0 0
\(445\) −1.26414e6 −0.302619
\(446\) 1.17954e6 0.280787
\(447\) 0 0
\(448\) 0 0
\(449\) −4.00158e6 −0.936733 −0.468366 0.883534i \(-0.655157\pi\)
−0.468366 + 0.883534i \(0.655157\pi\)
\(450\) 0 0
\(451\) −4.53426e6 −1.04970
\(452\) 1.30659e6 0.300811
\(453\) 0 0
\(454\) 774090. 0.176259
\(455\) 0 0
\(456\) 0 0
\(457\) −1.16766e6 −0.261534 −0.130767 0.991413i \(-0.541744\pi\)
−0.130767 + 0.991413i \(0.541744\pi\)
\(458\) −465464. −0.103687
\(459\) 0 0
\(460\) 1.00531e6 0.221517
\(461\) −3.61358e6 −0.791928 −0.395964 0.918266i \(-0.629589\pi\)
−0.395964 + 0.918266i \(0.629589\pi\)
\(462\) 0 0
\(463\) −1.80111e6 −0.390471 −0.195235 0.980756i \(-0.562547\pi\)
−0.195235 + 0.980756i \(0.562547\pi\)
\(464\) −1.58555e6 −0.341889
\(465\) 0 0
\(466\) −84192.0 −0.0179600
\(467\) 2.36975e6 0.502817 0.251409 0.967881i \(-0.419106\pi\)
0.251409 + 0.967881i \(0.419106\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 464244. 0.0969397
\(471\) 0 0
\(472\) −979560. −0.202384
\(473\) 2.12349e6 0.436412
\(474\) 0 0
\(475\) 492656. 0.100187
\(476\) 0 0
\(477\) 0 0
\(478\) 626832. 0.125482
\(479\) −518146. −0.103184 −0.0515921 0.998668i \(-0.516430\pi\)
−0.0515921 + 0.998668i \(0.516430\pi\)
\(480\) 0 0
\(481\) 3.48902e6 0.687609
\(482\) 1.71561e6 0.336358
\(483\) 0 0
\(484\) 2.48332e6 0.481858
\(485\) −1.70455e6 −0.329045
\(486\) 0 0
\(487\) 2.82613e6 0.539970 0.269985 0.962865i \(-0.412981\pi\)
0.269985 + 0.962865i \(0.412981\pi\)
\(488\) −1.81992e6 −0.345942
\(489\) 0 0
\(490\) 0 0
\(491\) −9.34747e6 −1.74981 −0.874904 0.484296i \(-0.839076\pi\)
−0.874904 + 0.484296i \(0.839076\pi\)
\(492\) 0 0
\(493\) 4.58263e6 0.849176
\(494\) 101024. 0.0186255
\(495\) 0 0
\(496\) 1.86370e6 0.340150
\(497\) 0 0
\(498\) 0 0
\(499\) 8.17185e6 1.46916 0.734580 0.678522i \(-0.237379\pi\)
0.734580 + 0.678522i \(0.237379\pi\)
\(500\) −1.88773e6 −0.337688
\(501\) 0 0
\(502\) −909034. −0.160998
\(503\) 7.37713e6 1.30007 0.650036 0.759903i \(-0.274754\pi\)
0.650036 + 0.759903i \(0.274754\pi\)
\(504\) 0 0
\(505\) −1.18327e6 −0.206469
\(506\) −1.75603e6 −0.304899
\(507\) 0 0
\(508\) 8.52222e6 1.46519
\(509\) 326315. 0.0558268 0.0279134 0.999610i \(-0.491114\pi\)
0.0279134 + 0.999610i \(0.491114\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 5.89875e6 0.994455
\(513\) 0 0
\(514\) −1.75636e6 −0.293229
\(515\) −98296.0 −0.0163312
\(516\) 0 0
\(517\) 5.67644e6 0.934006
\(518\) 0 0
\(519\) 0 0
\(520\) −406560. −0.0659350
\(521\) 2.16703e6 0.349760 0.174880 0.984590i \(-0.444046\pi\)
0.174880 + 0.984590i \(0.444046\pi\)
\(522\) 0 0
\(523\) −723404. −0.115645 −0.0578225 0.998327i \(-0.518416\pi\)
−0.0578225 + 0.998327i \(0.518416\pi\)
\(524\) −372484. −0.0592624
\(525\) 0 0
\(526\) −3.92187e6 −0.618057
\(527\) −5.38654e6 −0.844857
\(528\) 0 0
\(529\) 4.21735e6 0.655241
\(530\) −653202. −0.101008
\(531\) 0 0
\(532\) 0 0
\(533\) −5.19165e6 −0.791566
\(534\) 0 0
\(535\) 2.13034e6 0.321784
\(536\) 3.84936e6 0.578731
\(537\) 0 0
\(538\) 2.10759e6 0.313928
\(539\) 0 0
\(540\) 0 0
\(541\) 5.99964e6 0.881317 0.440659 0.897675i \(-0.354745\pi\)
0.440659 + 0.897675i \(0.354745\pi\)
\(542\) −210118. −0.0307231
\(543\) 0 0
\(544\) −9.76819e6 −1.41520
\(545\) −2.25621e6 −0.325378
\(546\) 0 0
\(547\) 7.01570e6 1.00254 0.501271 0.865290i \(-0.332866\pi\)
0.501271 + 0.865290i \(0.332866\pi\)
\(548\) −1.11513e7 −1.58626
\(549\) 0 0
\(550\) 1.61615e6 0.227811
\(551\) 396388. 0.0556213
\(552\) 0 0
\(553\) 0 0
\(554\) −855184. −0.118382
\(555\) 0 0
\(556\) −6.44801e6 −0.884583
\(557\) 8.91872e6 1.21805 0.609025 0.793151i \(-0.291561\pi\)
0.609025 + 0.793151i \(0.291561\pi\)
\(558\) 0 0
\(559\) 2.43135e6 0.329093
\(560\) 0 0
\(561\) 0 0
\(562\) −1.27776e6 −0.170650
\(563\) 1.33482e7 1.77481 0.887407 0.460987i \(-0.152505\pi\)
0.887407 + 0.460987i \(0.152505\pi\)
\(564\) 0 0
\(565\) 513304. 0.0676478
\(566\) −4.90284e6 −0.643290
\(567\) 0 0
\(568\) −4.59288e6 −0.597330
\(569\) −1.10215e6 −0.142712 −0.0713558 0.997451i \(-0.522733\pi\)
−0.0713558 + 0.997451i \(0.522733\pi\)
\(570\) 0 0
\(571\) 1.89348e6 0.243036 0.121518 0.992589i \(-0.461224\pi\)
0.121518 + 0.992589i \(0.461224\pi\)
\(572\) −2.31986e6 −0.296463
\(573\) 0 0
\(574\) 0 0
\(575\) −9.80506e6 −1.23675
\(576\) 0 0
\(577\) 2.82951e6 0.353811 0.176906 0.984228i \(-0.443391\pi\)
0.176906 + 0.984228i \(0.443391\pi\)
\(578\) 4.34992e6 0.541579
\(579\) 0 0
\(580\) −744436. −0.0918877
\(581\) 0 0
\(582\) 0 0
\(583\) −7.98688e6 −0.973208
\(584\) −4.18392e6 −0.507635
\(585\) 0 0
\(586\) −3.43234e6 −0.412901
\(587\) 1.06799e7 1.27930 0.639649 0.768667i \(-0.279080\pi\)
0.639649 + 0.768667i \(0.279080\pi\)
\(588\) 0 0
\(589\) −465924. −0.0553384
\(590\) −179586. −0.0212394
\(591\) 0 0
\(592\) −7.43117e6 −0.871471
\(593\) 1.46997e7 1.71661 0.858304 0.513141i \(-0.171518\pi\)
0.858304 + 0.513141i \(0.171518\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2.71975e6 −0.313627
\(597\) 0 0
\(598\) −2.01062e6 −0.229921
\(599\) −8.49163e6 −0.966994 −0.483497 0.875346i \(-0.660634\pi\)
−0.483497 + 0.875346i \(0.660634\pi\)
\(600\) 0 0
\(601\) 8.62947e6 0.974536 0.487268 0.873253i \(-0.337994\pi\)
0.487268 + 0.873253i \(0.337994\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 813316. 0.0907125
\(605\) 975590. 0.108362
\(606\) 0 0
\(607\) 1.05807e7 1.16559 0.582793 0.812621i \(-0.301960\pi\)
0.582793 + 0.812621i \(0.301960\pi\)
\(608\) −844928. −0.0926959
\(609\) 0 0
\(610\) −333652. −0.0363052
\(611\) 6.49942e6 0.704322
\(612\) 0 0
\(613\) 3.84784e6 0.413586 0.206793 0.978385i \(-0.433697\pi\)
0.206793 + 0.978385i \(0.433697\pi\)
\(614\) 3.61794e6 0.387293
\(615\) 0 0
\(616\) 0 0
\(617\) 1.51001e7 1.59686 0.798428 0.602090i \(-0.205665\pi\)
0.798428 + 0.602090i \(0.205665\pi\)
\(618\) 0 0
\(619\) 9.93102e6 1.04176 0.520879 0.853630i \(-0.325604\pi\)
0.520879 + 0.853630i \(0.325604\pi\)
\(620\) 875028. 0.0914203
\(621\) 0 0
\(622\) −3.04291e6 −0.315365
\(623\) 0 0
\(624\) 0 0
\(625\) 8.64589e6 0.885339
\(626\) −2.69680e6 −0.275051
\(627\) 0 0
\(628\) 1.61420e7 1.63327
\(629\) 2.14779e7 2.16454
\(630\) 0 0
\(631\) −9.25224e6 −0.925068 −0.462534 0.886602i \(-0.653060\pi\)
−0.462534 + 0.886602i \(0.653060\pi\)
\(632\) −1.62348e6 −0.161679
\(633\) 0 0
\(634\) 99390.0 0.00982018
\(635\) 3.34802e6 0.329498
\(636\) 0 0
\(637\) 0 0
\(638\) 1.30035e6 0.126476
\(639\) 0 0
\(640\) 2.04864e6 0.197704
\(641\) −5.00428e6 −0.481057 −0.240529 0.970642i \(-0.577321\pi\)
−0.240529 + 0.970642i \(0.577321\pi\)
\(642\) 0 0
\(643\) 1.26137e7 1.20314 0.601569 0.798821i \(-0.294543\pi\)
0.601569 + 0.798821i \(0.294543\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 621888. 0.0586315
\(647\) 1.25383e7 1.17755 0.588774 0.808298i \(-0.299611\pi\)
0.588774 + 0.808298i \(0.299611\pi\)
\(648\) 0 0
\(649\) −2.19585e6 −0.204640
\(650\) 1.85046e6 0.171790
\(651\) 0 0
\(652\) 7.42650e6 0.684171
\(653\) 8.66066e6 0.794819 0.397409 0.917641i \(-0.369909\pi\)
0.397409 + 0.917641i \(0.369909\pi\)
\(654\) 0 0
\(655\) −146333. −0.0133272
\(656\) 1.10575e7 1.00323
\(657\) 0 0
\(658\) 0 0
\(659\) −7.94177e6 −0.712367 −0.356183 0.934416i \(-0.615922\pi\)
−0.356183 + 0.934416i \(0.615922\pi\)
\(660\) 0 0
\(661\) −2.11416e6 −0.188206 −0.0941032 0.995562i \(-0.529998\pi\)
−0.0941032 + 0.995562i \(0.529998\pi\)
\(662\) 3.17567e6 0.281638
\(663\) 0 0
\(664\) −8.17236e6 −0.719329
\(665\) 0 0
\(666\) 0 0
\(667\) −7.88909e6 −0.686613
\(668\) −1.01861e7 −0.883217
\(669\) 0 0
\(670\) 705716. 0.0607355
\(671\) −4.07965e6 −0.349798
\(672\) 0 0
\(673\) −442307. −0.0376432 −0.0188216 0.999823i \(-0.505991\pi\)
−0.0188216 + 0.999823i \(0.505991\pi\)
\(674\) 429650. 0.0364305
\(675\) 0 0
\(676\) 7.74001e6 0.651441
\(677\) −1.07561e7 −0.901949 −0.450975 0.892537i \(-0.648923\pi\)
−0.450975 + 0.892537i \(0.648923\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2.50272e6 −0.207558
\(681\) 0 0
\(682\) −1.52846e6 −0.125832
\(683\) 1.14886e7 0.942356 0.471178 0.882038i \(-0.343829\pi\)
0.471178 + 0.882038i \(0.343829\pi\)
\(684\) 0 0
\(685\) −4.38088e6 −0.356726
\(686\) 0 0
\(687\) 0 0
\(688\) −5.17846e6 −0.417090
\(689\) −9.14483e6 −0.733884
\(690\) 0 0
\(691\) 1.01388e7 0.807779 0.403890 0.914808i \(-0.367658\pi\)
0.403890 + 0.914808i \(0.367658\pi\)
\(692\) −4.61569e6 −0.366413
\(693\) 0 0
\(694\) −5.17719e6 −0.408033
\(695\) −2.53315e6 −0.198929
\(696\) 0 0
\(697\) −3.19590e7 −2.49179
\(698\) −49756.0 −0.00386551
\(699\) 0 0
\(700\) 0 0
\(701\) 1.96839e7 1.51292 0.756459 0.654041i \(-0.226927\pi\)
0.756459 + 0.654041i \(0.226927\pi\)
\(702\) 0 0
\(703\) 1.85779e6 0.141778
\(704\) 2.87507e6 0.218634
\(705\) 0 0
\(706\) 3.47202e6 0.262162
\(707\) 0 0
\(708\) 0 0
\(709\) −2.01717e7 −1.50705 −0.753524 0.657420i \(-0.771648\pi\)
−0.753524 + 0.657420i \(0.771648\pi\)
\(710\) −842028. −0.0626875
\(711\) 0 0
\(712\) −1.37906e7 −1.01949
\(713\) 9.27302e6 0.683121
\(714\) 0 0
\(715\) −911372. −0.0666700
\(716\) 857584. 0.0625164
\(717\) 0 0
\(718\) −1.72485e6 −0.124865
\(719\) −4.15735e6 −0.299912 −0.149956 0.988693i \(-0.547913\pi\)
−0.149956 + 0.988693i \(0.547913\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −4.89841e6 −0.349713
\(723\) 0 0
\(724\) 1.82390e7 1.29317
\(725\) 7.26067e6 0.513017
\(726\) 0 0
\(727\) −1.54433e7 −1.08369 −0.541845 0.840479i \(-0.682274\pi\)
−0.541845 + 0.840479i \(0.682274\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −767052. −0.0532743
\(731\) 1.49670e7 1.03596
\(732\) 0 0
\(733\) −6.20414e6 −0.426502 −0.213251 0.976997i \(-0.568405\pi\)
−0.213251 + 0.976997i \(0.568405\pi\)
\(734\) 6.23084e6 0.426880
\(735\) 0 0
\(736\) 1.68161e7 1.14428
\(737\) 8.62898e6 0.585182
\(738\) 0 0
\(739\) 2.18984e7 1.47503 0.737517 0.675328i \(-0.235998\pi\)
0.737517 + 0.675328i \(0.235998\pi\)
\(740\) −3.48902e6 −0.234220
\(741\) 0 0
\(742\) 0 0
\(743\) 2.75483e6 0.183073 0.0915363 0.995802i \(-0.470822\pi\)
0.0915363 + 0.995802i \(0.470822\pi\)
\(744\) 0 0
\(745\) −1.06847e6 −0.0705299
\(746\) −3.59389e6 −0.236438
\(747\) 0 0
\(748\) −1.42807e7 −0.933243
\(749\) 0 0
\(750\) 0 0
\(751\) 1.29121e7 0.835404 0.417702 0.908584i \(-0.362836\pi\)
0.417702 + 0.908584i \(0.362836\pi\)
\(752\) −1.38429e7 −0.892653
\(753\) 0 0
\(754\) 1.48887e6 0.0953738
\(755\) 319517. 0.0203998
\(756\) 0 0
\(757\) −2.64315e7 −1.67642 −0.838209 0.545349i \(-0.816397\pi\)
−0.838209 + 0.545349i \(0.816397\pi\)
\(758\) 6.90931e6 0.436779
\(759\) 0 0
\(760\) −216480. −0.0135951
\(761\) −1.22214e7 −0.764996 −0.382498 0.923956i \(-0.624936\pi\)
−0.382498 + 0.923956i \(0.624936\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2.12061e7 −1.31440
\(765\) 0 0
\(766\) −4.31008e6 −0.265407
\(767\) −2.51420e6 −0.154316
\(768\) 0 0
\(769\) 6.10654e6 0.372374 0.186187 0.982514i \(-0.440387\pi\)
0.186187 + 0.982514i \(0.440387\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.48949e6 0.271115
\(773\) 3.02220e6 0.181918 0.0909588 0.995855i \(-0.471007\pi\)
0.0909588 + 0.995855i \(0.471007\pi\)
\(774\) 0 0
\(775\) −8.53436e6 −0.510407
\(776\) −1.85951e7 −1.10852
\(777\) 0 0
\(778\) 925548. 0.0548214
\(779\) −2.76438e6 −0.163213
\(780\) 0 0
\(781\) −1.02957e7 −0.603988
\(782\) −1.23771e7 −0.723772
\(783\) 0 0
\(784\) 0 0
\(785\) 6.34150e6 0.367297
\(786\) 0 0
\(787\) −2.08285e7 −1.19873 −0.599365 0.800476i \(-0.704580\pi\)
−0.599365 + 0.800476i \(0.704580\pi\)
\(788\) −1.72866e6 −0.0991734
\(789\) 0 0
\(790\) −297638. −0.0169676
\(791\) 0 0
\(792\) 0 0
\(793\) −4.67113e6 −0.263778
\(794\) −8.13242e6 −0.457793
\(795\) 0 0
\(796\) −1.03854e7 −0.580954
\(797\) −2.32328e7 −1.29556 −0.647778 0.761829i \(-0.724302\pi\)
−0.647778 + 0.761829i \(0.724302\pi\)
\(798\) 0 0
\(799\) 4.00094e7 2.21715
\(800\) −1.54766e7 −0.854970
\(801\) 0 0
\(802\) 1.01373e7 0.556525
\(803\) −9.37895e6 −0.513293
\(804\) 0 0
\(805\) 0 0
\(806\) −1.75006e6 −0.0948887
\(807\) 0 0
\(808\) −1.29084e7 −0.695575
\(809\) −1.08668e7 −0.583753 −0.291876 0.956456i \(-0.594280\pi\)
−0.291876 + 0.956456i \(0.594280\pi\)
\(810\) 0 0
\(811\) −2.22632e7 −1.18860 −0.594299 0.804244i \(-0.702570\pi\)
−0.594299 + 0.804244i \(0.702570\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 6.09446e6 0.322385
\(815\) 2.91755e6 0.153860
\(816\) 0 0
\(817\) 1.29462e6 0.0678556
\(818\) 5.75467e6 0.300703
\(819\) 0 0
\(820\) 5.19165e6 0.269631
\(821\) 1.23881e7 0.641426 0.320713 0.947176i \(-0.396078\pi\)
0.320713 + 0.947176i \(0.396078\pi\)
\(822\) 0 0
\(823\) 1.69481e6 0.0872210 0.0436105 0.999049i \(-0.486114\pi\)
0.0436105 + 0.999049i \(0.486114\pi\)
\(824\) −1.07232e6 −0.0550182
\(825\) 0 0
\(826\) 0 0
\(827\) 378495. 0.0192440 0.00962202 0.999954i \(-0.496937\pi\)
0.00962202 + 0.999954i \(0.496937\pi\)
\(828\) 0 0
\(829\) −1.04287e7 −0.527043 −0.263521 0.964654i \(-0.584884\pi\)
−0.263521 + 0.964654i \(0.584884\pi\)
\(830\) −1.49827e6 −0.0754907
\(831\) 0 0
\(832\) 3.29190e6 0.164869
\(833\) 0 0
\(834\) 0 0
\(835\) −4.00169e6 −0.198622
\(836\) −1.23525e6 −0.0611278
\(837\) 0 0
\(838\) 6.82685e6 0.335823
\(839\) −3.04082e7 −1.49137 −0.745686 0.666297i \(-0.767878\pi\)
−0.745686 + 0.666297i \(0.767878\pi\)
\(840\) 0 0
\(841\) −1.46693e7 −0.715185
\(842\) −2.61475e6 −0.127101
\(843\) 0 0
\(844\) −6.08860e6 −0.294213
\(845\) 3.04072e6 0.146499
\(846\) 0 0
\(847\) 0 0
\(848\) 1.94773e7 0.930120
\(849\) 0 0
\(850\) 1.13912e7 0.540780
\(851\) −3.69746e7 −1.75017
\(852\) 0 0
\(853\) 2.80315e7 1.31909 0.659544 0.751666i \(-0.270750\pi\)
0.659544 + 0.751666i \(0.270750\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 2.32400e7 1.08406
\(857\) −1.88030e7 −0.874529 −0.437264 0.899333i \(-0.644053\pi\)
−0.437264 + 0.899333i \(0.644053\pi\)
\(858\) 0 0
\(859\) 7.86323e6 0.363595 0.181798 0.983336i \(-0.441808\pi\)
0.181798 + 0.983336i \(0.441808\pi\)
\(860\) −2.43135e6 −0.112099
\(861\) 0 0
\(862\) −3.87094e6 −0.177438
\(863\) 1.12858e7 0.515827 0.257913 0.966168i \(-0.416965\pi\)
0.257913 + 0.966168i \(0.416965\pi\)
\(864\) 0 0
\(865\) −1.81331e6 −0.0824007
\(866\) 1.03334e6 0.0468218
\(867\) 0 0
\(868\) 0 0
\(869\) −3.63930e6 −0.163481
\(870\) 0 0
\(871\) 9.88002e6 0.441278
\(872\) −2.46132e7 −1.09617
\(873\) 0 0
\(874\) −1.07059e6 −0.0474073
\(875\) 0 0
\(876\) 0 0
\(877\) 1.34150e7 0.588968 0.294484 0.955656i \(-0.404852\pi\)
0.294484 + 0.955656i \(0.404852\pi\)
\(878\) 5.83060e6 0.255257
\(879\) 0 0
\(880\) 1.94110e6 0.0844972
\(881\) −3.18547e7 −1.38272 −0.691359 0.722511i \(-0.742988\pi\)
−0.691359 + 0.722511i \(0.742988\pi\)
\(882\) 0 0
\(883\) −3.05922e7 −1.32041 −0.660205 0.751086i \(-0.729530\pi\)
−0.660205 + 0.751086i \(0.729530\pi\)
\(884\) −1.63511e7 −0.703747
\(885\) 0 0
\(886\) 3.56758e6 0.152683
\(887\) 4.63772e6 0.197923 0.0989613 0.995091i \(-0.468448\pi\)
0.0989613 + 0.995091i \(0.468448\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −2.52828e6 −0.106992
\(891\) 0 0
\(892\) −1.65136e7 −0.694911
\(893\) 3.46073e6 0.145224
\(894\) 0 0
\(895\) 336908. 0.0140590
\(896\) 0 0
\(897\) 0 0
\(898\) −8.00316e6 −0.331185
\(899\) −6.86670e6 −0.283367
\(900\) 0 0
\(901\) −5.62941e7 −2.31021
\(902\) −9.06853e6 −0.371125
\(903\) 0 0
\(904\) 5.59968e6 0.227899
\(905\) 7.16531e6 0.290813
\(906\) 0 0
\(907\) 604376. 0.0243943 0.0121972 0.999926i \(-0.496117\pi\)
0.0121972 + 0.999926i \(0.496117\pi\)
\(908\) −1.08373e7 −0.436219
\(909\) 0 0
\(910\) 0 0
\(911\) 2.44059e7 0.974315 0.487157 0.873314i \(-0.338034\pi\)
0.487157 + 0.873314i \(0.338034\pi\)
\(912\) 0 0
\(913\) −1.83197e7 −0.727347
\(914\) −2.33533e6 −0.0924661
\(915\) 0 0
\(916\) 6.51650e6 0.256611
\(917\) 0 0
\(918\) 0 0
\(919\) 3.67095e7 1.43380 0.716902 0.697174i \(-0.245560\pi\)
0.716902 + 0.697174i \(0.245560\pi\)
\(920\) 4.30848e6 0.167824
\(921\) 0 0
\(922\) −7.22716e6 −0.279989
\(923\) −1.17884e7 −0.455460
\(924\) 0 0
\(925\) 3.40293e7 1.30767
\(926\) −3.60222e6 −0.138052
\(927\) 0 0
\(928\) −1.24524e7 −0.474660
\(929\) 2.29089e7 0.870892 0.435446 0.900215i \(-0.356591\pi\)
0.435446 + 0.900215i \(0.356591\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.17869e6 0.0444487
\(933\) 0 0
\(934\) 4.73950e6 0.177773
\(935\) −5.61026e6 −0.209872
\(936\) 0 0
\(937\) −5.99611e6 −0.223111 −0.111555 0.993758i \(-0.535583\pi\)
−0.111555 + 0.993758i \(0.535583\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −6.49942e6 −0.239914
\(941\) 1.16516e7 0.428954 0.214477 0.976729i \(-0.431195\pi\)
0.214477 + 0.976729i \(0.431195\pi\)
\(942\) 0 0
\(943\) 5.50180e7 2.01477
\(944\) 5.35493e6 0.195580
\(945\) 0 0
\(946\) 4.24697e6 0.154295
\(947\) 1.10926e6 0.0401939 0.0200969 0.999798i \(-0.493603\pi\)
0.0200969 + 0.999798i \(0.493603\pi\)
\(948\) 0 0
\(949\) −1.07387e7 −0.387068
\(950\) 985312. 0.0354213
\(951\) 0 0
\(952\) 0 0
\(953\) −1.05743e7 −0.377155 −0.188578 0.982058i \(-0.560388\pi\)
−0.188578 + 0.982058i \(0.560388\pi\)
\(954\) 0 0
\(955\) −8.33096e6 −0.295588
\(956\) −8.77565e6 −0.310552
\(957\) 0 0
\(958\) −1.03629e6 −0.0364811
\(959\) 0 0
\(960\) 0 0
\(961\) −2.05579e7 −0.718075
\(962\) 6.97805e6 0.243106
\(963\) 0 0
\(964\) −2.40186e7 −0.832444
\(965\) 1.76373e6 0.0609696
\(966\) 0 0
\(967\) 6.32666e6 0.217575 0.108787 0.994065i \(-0.465303\pi\)
0.108787 + 0.994065i \(0.465303\pi\)
\(968\) 1.06428e7 0.365063
\(969\) 0 0
\(970\) −3.40910e6 −0.116335
\(971\) −3.92395e7 −1.33560 −0.667798 0.744343i \(-0.732763\pi\)
−0.667798 + 0.744343i \(0.732763\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 5.65225e6 0.190908
\(975\) 0 0
\(976\) 9.94890e6 0.334311
\(977\) 1.55074e6 0.0519760 0.0259880 0.999662i \(-0.491727\pi\)
0.0259880 + 0.999662i \(0.491727\pi\)
\(978\) 0 0
\(979\) −3.09140e7 −1.03086
\(980\) 0 0
\(981\) 0 0
\(982\) −1.86949e7 −0.618651
\(983\) 4.87484e7 1.60908 0.804538 0.593901i \(-0.202413\pi\)
0.804538 + 0.593901i \(0.202413\pi\)
\(984\) 0 0
\(985\) −679118. −0.0223026
\(986\) 9.16526e6 0.300229
\(987\) 0 0
\(988\) −1.41434e6 −0.0460957
\(989\) −2.57660e7 −0.837638
\(990\) 0 0
\(991\) −1.92552e6 −0.0622820 −0.0311410 0.999515i \(-0.509914\pi\)
−0.0311410 + 0.999515i \(0.509914\pi\)
\(992\) 1.46368e7 0.472246
\(993\) 0 0
\(994\) 0 0
\(995\) −4.07999e6 −0.130648
\(996\) 0 0
\(997\) 5.42564e7 1.72867 0.864337 0.502913i \(-0.167739\pi\)
0.864337 + 0.502913i \(0.167739\pi\)
\(998\) 1.63437e7 0.519427
\(999\) 0 0
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 441.6.a.g.1.1 1
3.2 odd 2 147.6.a.c.1.1 1
7.2 even 3 63.6.e.a.46.1 2
7.4 even 3 63.6.e.a.37.1 2
7.6 odd 2 441.6.a.h.1.1 1
21.2 odd 6 21.6.e.a.4.1 2
21.5 even 6 147.6.e.g.67.1 2
21.11 odd 6 21.6.e.a.16.1 yes 2
21.17 even 6 147.6.e.g.79.1 2
21.20 even 2 147.6.a.d.1.1 1
84.11 even 6 336.6.q.b.289.1 2
84.23 even 6 336.6.q.b.193.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.e.a.4.1 2 21.2 odd 6
21.6.e.a.16.1 yes 2 21.11 odd 6
63.6.e.a.37.1 2 7.4 even 3
63.6.e.a.46.1 2 7.2 even 3
147.6.a.c.1.1 1 3.2 odd 2
147.6.a.d.1.1 1 21.20 even 2
147.6.e.g.67.1 2 21.5 even 6
147.6.e.g.79.1 2 21.17 even 6
336.6.q.b.193.1 2 84.23 even 6
336.6.q.b.289.1 2 84.11 even 6
441.6.a.g.1.1 1 1.1 even 1 trivial
441.6.a.h.1.1 1 7.6 odd 2