Properties

Label 72.6.a.e.1.1
Level $72$
Weight $6$
Character 72.1
Self dual yes
Analytic conductor $11.548$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 72.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5476350265\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 24)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 72.1

$q$-expansion

\(f(q)\) \(=\) \(q+34.0000 q^{5} -240.000 q^{7} +O(q^{10})\) \(q+34.0000 q^{5} -240.000 q^{7} +124.000 q^{11} +46.0000 q^{13} -1954.00 q^{17} -1924.00 q^{19} -2840.00 q^{23} -1969.00 q^{25} +8922.00 q^{29} -4648.00 q^{31} -8160.00 q^{35} -4362.00 q^{37} +2886.00 q^{41} +11332.0 q^{43} -7008.00 q^{47} +40793.0 q^{49} +22594.0 q^{53} +4216.00 q^{55} +28.0000 q^{59} -6386.00 q^{61} +1564.00 q^{65} -39076.0 q^{67} +54872.0 q^{71} +21034.0 q^{73} -29760.0 q^{77} +26632.0 q^{79} -56188.0 q^{83} -66436.0 q^{85} -64410.0 q^{89} -11040.0 q^{91} -65416.0 q^{95} -116158. q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 34.0000 0.608210 0.304105 0.952638i \(-0.401643\pi\)
0.304105 + 0.952638i \(0.401643\pi\)
\(6\) 0 0
\(7\) −240.000 −1.85125 −0.925627 0.378436i \(-0.876462\pi\)
−0.925627 + 0.378436i \(0.876462\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 124.000 0.308987 0.154493 0.987994i \(-0.450625\pi\)
0.154493 + 0.987994i \(0.450625\pi\)
\(12\) 0 0
\(13\) 46.0000 0.0754917 0.0377459 0.999287i \(-0.487982\pi\)
0.0377459 + 0.999287i \(0.487982\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1954.00 −1.63984 −0.819921 0.572476i \(-0.805983\pi\)
−0.819921 + 0.572476i \(0.805983\pi\)
\(18\) 0 0
\(19\) −1924.00 −1.22270 −0.611352 0.791359i \(-0.709374\pi\)
−0.611352 + 0.791359i \(0.709374\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2840.00 −1.11943 −0.559717 0.828684i \(-0.689090\pi\)
−0.559717 + 0.828684i \(0.689090\pi\)
\(24\) 0 0
\(25\) −1969.00 −0.630080
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8922.00 1.97000 0.985002 0.172541i \(-0.0551979\pi\)
0.985002 + 0.172541i \(0.0551979\pi\)
\(30\) 0 0
\(31\) −4648.00 −0.868684 −0.434342 0.900748i \(-0.643019\pi\)
−0.434342 + 0.900748i \(0.643019\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −8160.00 −1.12595
\(36\) 0 0
\(37\) −4362.00 −0.523819 −0.261910 0.965092i \(-0.584352\pi\)
−0.261910 + 0.965092i \(0.584352\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2886.00 0.268125 0.134062 0.990973i \(-0.457198\pi\)
0.134062 + 0.990973i \(0.457198\pi\)
\(42\) 0 0
\(43\) 11332.0 0.934621 0.467310 0.884093i \(-0.345223\pi\)
0.467310 + 0.884093i \(0.345223\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7008.00 −0.462753 −0.231377 0.972864i \(-0.574323\pi\)
−0.231377 + 0.972864i \(0.574323\pi\)
\(48\) 0 0
\(49\) 40793.0 2.42714
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 22594.0 1.10485 0.552425 0.833562i \(-0.313703\pi\)
0.552425 + 0.833562i \(0.313703\pi\)
\(54\) 0 0
\(55\) 4216.00 0.187929
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 28.0000 0.00104720 0.000523598 1.00000i \(-0.499833\pi\)
0.000523598 1.00000i \(0.499833\pi\)
\(60\) 0 0
\(61\) −6386.00 −0.219738 −0.109869 0.993946i \(-0.535043\pi\)
−0.109869 + 0.993946i \(0.535043\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1564.00 0.0459149
\(66\) 0 0
\(67\) −39076.0 −1.06346 −0.531732 0.846912i \(-0.678459\pi\)
−0.531732 + 0.846912i \(0.678459\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 54872.0 1.29183 0.645914 0.763410i \(-0.276476\pi\)
0.645914 + 0.763410i \(0.276476\pi\)
\(72\) 0 0
\(73\) 21034.0 0.461971 0.230986 0.972957i \(-0.425805\pi\)
0.230986 + 0.972957i \(0.425805\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −29760.0 −0.572013
\(78\) 0 0
\(79\) 26632.0 0.480105 0.240052 0.970760i \(-0.422835\pi\)
0.240052 + 0.970760i \(0.422835\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −56188.0 −0.895258 −0.447629 0.894219i \(-0.647732\pi\)
−0.447629 + 0.894219i \(0.647732\pi\)
\(84\) 0 0
\(85\) −66436.0 −0.997370
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −64410.0 −0.861942 −0.430971 0.902366i \(-0.641829\pi\)
−0.430971 + 0.902366i \(0.641829\pi\)
\(90\) 0 0
\(91\) −11040.0 −0.139754
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −65416.0 −0.743661
\(96\) 0 0
\(97\) −116158. −1.25349 −0.626743 0.779226i \(-0.715613\pi\)
−0.626743 + 0.779226i \(0.715613\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 66834.0 0.651920 0.325960 0.945384i \(-0.394313\pi\)
0.325960 + 0.945384i \(0.394313\pi\)
\(102\) 0 0
\(103\) 64000.0 0.594411 0.297206 0.954814i \(-0.403945\pi\)
0.297206 + 0.954814i \(0.403945\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15084.0 0.127367 0.0636835 0.997970i \(-0.479715\pi\)
0.0636835 + 0.997970i \(0.479715\pi\)
\(108\) 0 0
\(109\) −39698.0 −0.320039 −0.160019 0.987114i \(-0.551156\pi\)
−0.160019 + 0.987114i \(0.551156\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −155154. −1.14305 −0.571527 0.820583i \(-0.693649\pi\)
−0.571527 + 0.820583i \(0.693649\pi\)
\(114\) 0 0
\(115\) −96560.0 −0.680852
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 468960. 3.03577
\(120\) 0 0
\(121\) −145675. −0.904527
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −173196. −0.991432
\(126\) 0 0
\(127\) 52072.0 0.286480 0.143240 0.989688i \(-0.454248\pi\)
0.143240 + 0.989688i \(0.454248\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −159964. −0.814412 −0.407206 0.913336i \(-0.633497\pi\)
−0.407206 + 0.913336i \(0.633497\pi\)
\(132\) 0 0
\(133\) 461760. 2.26353
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 262278. 1.19388 0.596940 0.802286i \(-0.296383\pi\)
0.596940 + 0.802286i \(0.296383\pi\)
\(138\) 0 0
\(139\) 253524. 1.11297 0.556483 0.830859i \(-0.312150\pi\)
0.556483 + 0.830859i \(0.312150\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5704.00 0.0233260
\(144\) 0 0
\(145\) 303348. 1.19818
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −355630. −1.31230 −0.656149 0.754631i \(-0.727816\pi\)
−0.656149 + 0.754631i \(0.727816\pi\)
\(150\) 0 0
\(151\) −1024.00 −0.00365475 −0.00182737 0.999998i \(-0.500582\pi\)
−0.00182737 + 0.999998i \(0.500582\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −158032. −0.528343
\(156\) 0 0
\(157\) −59954.0 −0.194119 −0.0970597 0.995279i \(-0.530944\pi\)
−0.0970597 + 0.995279i \(0.530944\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 681600. 2.07236
\(162\) 0 0
\(163\) −341556. −1.00692 −0.503458 0.864020i \(-0.667939\pi\)
−0.503458 + 0.864020i \(0.667939\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5016.00 −0.0139177 −0.00695883 0.999976i \(-0.502215\pi\)
−0.00695883 + 0.999976i \(0.502215\pi\)
\(168\) 0 0
\(169\) −369177. −0.994301
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 228666. 0.580880 0.290440 0.956893i \(-0.406198\pi\)
0.290440 + 0.956893i \(0.406198\pi\)
\(174\) 0 0
\(175\) 472560. 1.16644
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −161388. −0.376477 −0.188239 0.982123i \(-0.560278\pi\)
−0.188239 + 0.982123i \(0.560278\pi\)
\(180\) 0 0
\(181\) −291690. −0.661797 −0.330899 0.943666i \(-0.607352\pi\)
−0.330899 + 0.943666i \(0.607352\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −148308. −0.318592
\(186\) 0 0
\(187\) −242296. −0.506690
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 55680.0 0.110437 0.0552187 0.998474i \(-0.482414\pi\)
0.0552187 + 0.998474i \(0.482414\pi\)
\(192\) 0 0
\(193\) −176254. −0.340601 −0.170300 0.985392i \(-0.554474\pi\)
−0.170300 + 0.985392i \(0.554474\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 374610. 0.687723 0.343862 0.939020i \(-0.388265\pi\)
0.343862 + 0.939020i \(0.388265\pi\)
\(198\) 0 0
\(199\) −637760. −1.14163 −0.570814 0.821079i \(-0.693372\pi\)
−0.570814 + 0.821079i \(0.693372\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.14128e6 −3.64698
\(204\) 0 0
\(205\) 98124.0 0.163076
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −238576. −0.377799
\(210\) 0 0
\(211\) −904628. −1.39883 −0.699413 0.714717i \(-0.746555\pi\)
−0.699413 + 0.714717i \(0.746555\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 385288. 0.568446
\(216\) 0 0
\(217\) 1.11552e6 1.60816
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −89884.0 −0.123795
\(222\) 0 0
\(223\) 619048. 0.833609 0.416804 0.908996i \(-0.363150\pi\)
0.416804 + 0.908996i \(0.363150\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.46975e6 1.89312 0.946560 0.322527i \(-0.104532\pi\)
0.946560 + 0.322527i \(0.104532\pi\)
\(228\) 0 0
\(229\) −3290.00 −0.00414579 −0.00207289 0.999998i \(-0.500660\pi\)
−0.00207289 + 0.999998i \(0.500660\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −935402. −1.12878 −0.564389 0.825509i \(-0.690888\pi\)
−0.564389 + 0.825509i \(0.690888\pi\)
\(234\) 0 0
\(235\) −238272. −0.281451
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 875600. 0.991542 0.495771 0.868453i \(-0.334886\pi\)
0.495771 + 0.868453i \(0.334886\pi\)
\(240\) 0 0
\(241\) −959214. −1.06383 −0.531916 0.846797i \(-0.678528\pi\)
−0.531916 + 0.846797i \(0.678528\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.38696e6 1.47621
\(246\) 0 0
\(247\) −88504.0 −0.0923040
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −318868. −0.319467 −0.159734 0.987160i \(-0.551064\pi\)
−0.159734 + 0.987160i \(0.551064\pi\)
\(252\) 0 0
\(253\) −352160. −0.345891
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.71469e6 −1.61940 −0.809698 0.586847i \(-0.800369\pi\)
−0.809698 + 0.586847i \(0.800369\pi\)
\(258\) 0 0
\(259\) 1.04688e6 0.969723
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.11028e6 0.989790 0.494895 0.868953i \(-0.335206\pi\)
0.494895 + 0.868953i \(0.335206\pi\)
\(264\) 0 0
\(265\) 768196. 0.671982
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 398378. 0.335672 0.167836 0.985815i \(-0.446322\pi\)
0.167836 + 0.985815i \(0.446322\pi\)
\(270\) 0 0
\(271\) 1.44198e6 1.19271 0.596355 0.802721i \(-0.296615\pi\)
0.596355 + 0.802721i \(0.296615\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −244156. −0.194686
\(276\) 0 0
\(277\) 117238. 0.0918056 0.0459028 0.998946i \(-0.485384\pi\)
0.0459028 + 0.998946i \(0.485384\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.67514e6 1.26557 0.632784 0.774328i \(-0.281912\pi\)
0.632784 + 0.774328i \(0.281912\pi\)
\(282\) 0 0
\(283\) 1.92468e6 1.42854 0.714269 0.699872i \(-0.246760\pi\)
0.714269 + 0.699872i \(0.246760\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −692640. −0.496367
\(288\) 0 0
\(289\) 2.39826e6 1.68908
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.28062e6 −0.871469 −0.435734 0.900075i \(-0.643511\pi\)
−0.435734 + 0.900075i \(0.643511\pi\)
\(294\) 0 0
\(295\) 952.000 0.000636916 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −130640. −0.0845081
\(300\) 0 0
\(301\) −2.71968e6 −1.73022
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −217124. −0.133647
\(306\) 0 0
\(307\) −2.26319e6 −1.37049 −0.685243 0.728314i \(-0.740304\pi\)
−0.685243 + 0.728314i \(0.740304\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −247848. −0.145306 −0.0726532 0.997357i \(-0.523147\pi\)
−0.0726532 + 0.997357i \(0.523147\pi\)
\(312\) 0 0
\(313\) −1.82391e6 −1.05231 −0.526154 0.850390i \(-0.676366\pi\)
−0.526154 + 0.850390i \(0.676366\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.85629e6 −1.59645 −0.798224 0.602361i \(-0.794227\pi\)
−0.798224 + 0.602361i \(0.794227\pi\)
\(318\) 0 0
\(319\) 1.10633e6 0.608705
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.75950e6 2.00504
\(324\) 0 0
\(325\) −90574.0 −0.0475658
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.68192e6 0.856674
\(330\) 0 0
\(331\) −147148. −0.0738218 −0.0369109 0.999319i \(-0.511752\pi\)
−0.0369109 + 0.999319i \(0.511752\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.32858e6 −0.646810
\(336\) 0 0
\(337\) −3.24728e6 −1.55756 −0.778780 0.627297i \(-0.784161\pi\)
−0.778780 + 0.627297i \(0.784161\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −576352. −0.268412
\(342\) 0 0
\(343\) −5.75664e6 −2.64201
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.55675e6 0.694056 0.347028 0.937855i \(-0.387191\pi\)
0.347028 + 0.937855i \(0.387191\pi\)
\(348\) 0 0
\(349\) 4.03217e6 1.77205 0.886024 0.463639i \(-0.153456\pi\)
0.886024 + 0.463639i \(0.153456\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.79399e6 −0.766271 −0.383135 0.923692i \(-0.625156\pi\)
−0.383135 + 0.923692i \(0.625156\pi\)
\(354\) 0 0
\(355\) 1.86565e6 0.785704
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.55278e6 −0.635876 −0.317938 0.948111i \(-0.602990\pi\)
−0.317938 + 0.948111i \(0.602990\pi\)
\(360\) 0 0
\(361\) 1.22568e6 0.495003
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 715156. 0.280976
\(366\) 0 0
\(367\) −3.11545e6 −1.20741 −0.603706 0.797207i \(-0.706310\pi\)
−0.603706 + 0.797207i \(0.706310\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5.42256e6 −2.04536
\(372\) 0 0
\(373\) −630682. −0.234714 −0.117357 0.993090i \(-0.537442\pi\)
−0.117357 + 0.993090i \(0.537442\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 410412. 0.148719
\(378\) 0 0
\(379\) 48404.0 0.0173094 0.00865472 0.999963i \(-0.497245\pi\)
0.00865472 + 0.999963i \(0.497245\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.74182e6 −0.606747 −0.303373 0.952872i \(-0.598113\pi\)
−0.303373 + 0.952872i \(0.598113\pi\)
\(384\) 0 0
\(385\) −1.01184e6 −0.347904
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.06819e6 1.02804 0.514019 0.857779i \(-0.328156\pi\)
0.514019 + 0.857779i \(0.328156\pi\)
\(390\) 0 0
\(391\) 5.54936e6 1.83570
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 905488. 0.292005
\(396\) 0 0
\(397\) 5.35984e6 1.70677 0.853386 0.521280i \(-0.174545\pi\)
0.853386 + 0.521280i \(0.174545\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.76473e6 0.858603 0.429302 0.903161i \(-0.358760\pi\)
0.429302 + 0.903161i \(0.358760\pi\)
\(402\) 0 0
\(403\) −213808. −0.0655785
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −540888. −0.161853
\(408\) 0 0
\(409\) −1.20893e6 −0.357350 −0.178675 0.983908i \(-0.557181\pi\)
−0.178675 + 0.983908i \(0.557181\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6720.00 −0.00193863
\(414\) 0 0
\(415\) −1.91039e6 −0.544505
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.38008e6 1.21884 0.609421 0.792847i \(-0.291402\pi\)
0.609421 + 0.792847i \(0.291402\pi\)
\(420\) 0 0
\(421\) −922810. −0.253751 −0.126875 0.991919i \(-0.540495\pi\)
−0.126875 + 0.991919i \(0.540495\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.84743e6 1.03323
\(426\) 0 0
\(427\) 1.53264e6 0.406790
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.12678e6 −1.58869 −0.794345 0.607466i \(-0.792186\pi\)
−0.794345 + 0.607466i \(0.792186\pi\)
\(432\) 0 0
\(433\) −1.76315e6 −0.451928 −0.225964 0.974136i \(-0.572553\pi\)
−0.225964 + 0.974136i \(0.572553\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.46416e6 1.36874
\(438\) 0 0
\(439\) 3.85906e6 0.955696 0.477848 0.878443i \(-0.341417\pi\)
0.477848 + 0.878443i \(0.341417\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.39396e6 1.06377 0.531884 0.846817i \(-0.321484\pi\)
0.531884 + 0.846817i \(0.321484\pi\)
\(444\) 0 0
\(445\) −2.18994e6 −0.524242
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 793390. 0.185725 0.0928626 0.995679i \(-0.470398\pi\)
0.0928626 + 0.995679i \(0.470398\pi\)
\(450\) 0 0
\(451\) 357864. 0.0828470
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −375360. −0.0850001
\(456\) 0 0
\(457\) 7.04302e6 1.57750 0.788748 0.614717i \(-0.210730\pi\)
0.788748 + 0.614717i \(0.210730\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.43005e6 −1.62832 −0.814160 0.580641i \(-0.802802\pi\)
−0.814160 + 0.580641i \(0.802802\pi\)
\(462\) 0 0
\(463\) −4.10567e6 −0.890086 −0.445043 0.895509i \(-0.646812\pi\)
−0.445043 + 0.895509i \(0.646812\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.39817e6 −0.721030 −0.360515 0.932753i \(-0.617399\pi\)
−0.360515 + 0.932753i \(0.617399\pi\)
\(468\) 0 0
\(469\) 9.37824e6 1.96874
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.40517e6 0.288786
\(474\) 0 0
\(475\) 3.78836e6 0.770401
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.78133e6 −0.553877 −0.276939 0.960888i \(-0.589320\pi\)
−0.276939 + 0.960888i \(0.589320\pi\)
\(480\) 0 0
\(481\) −200652. −0.0395440
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.94937e6 −0.762384
\(486\) 0 0
\(487\) −2.06734e6 −0.394994 −0.197497 0.980304i \(-0.563281\pi\)
−0.197497 + 0.980304i \(0.563281\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.65976e6 1.43387 0.716937 0.697138i \(-0.245543\pi\)
0.716937 + 0.697138i \(0.245543\pi\)
\(492\) 0 0
\(493\) −1.74336e7 −3.23050
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.31693e7 −2.39150
\(498\) 0 0
\(499\) −386580. −0.0695005 −0.0347503 0.999396i \(-0.511064\pi\)
−0.0347503 + 0.999396i \(0.511064\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2.57326e6 0.453485 0.226743 0.973955i \(-0.427192\pi\)
0.226743 + 0.973955i \(0.427192\pi\)
\(504\) 0 0
\(505\) 2.27236e6 0.396504
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −360678. −0.0617057 −0.0308528 0.999524i \(-0.509822\pi\)
−0.0308528 + 0.999524i \(0.509822\pi\)
\(510\) 0 0
\(511\) −5.04816e6 −0.855226
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.17600e6 0.361527
\(516\) 0 0
\(517\) −868992. −0.142985
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.55908e6 0.251636 0.125818 0.992053i \(-0.459844\pi\)
0.125818 + 0.992053i \(0.459844\pi\)
\(522\) 0 0
\(523\) −9.18220e6 −1.46789 −0.733944 0.679210i \(-0.762322\pi\)
−0.733944 + 0.679210i \(0.762322\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.08219e6 1.42451
\(528\) 0 0
\(529\) 1.62926e6 0.253134
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 132756. 0.0202412
\(534\) 0 0
\(535\) 512856. 0.0774660
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5.05833e6 0.749955
\(540\) 0 0
\(541\) −6.67773e6 −0.980925 −0.490462 0.871462i \(-0.663172\pi\)
−0.490462 + 0.871462i \(0.663172\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.34973e6 −0.194651
\(546\) 0 0
\(547\) 8.89656e6 1.27132 0.635658 0.771971i \(-0.280729\pi\)
0.635658 + 0.771971i \(0.280729\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.71659e7 −2.40873
\(552\) 0 0
\(553\) −6.39168e6 −0.888796
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.46070e6 0.609207 0.304603 0.952479i \(-0.401476\pi\)
0.304603 + 0.952479i \(0.401476\pi\)
\(558\) 0 0
\(559\) 521272. 0.0705562
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6.37660e6 −0.847849 −0.423924 0.905698i \(-0.639348\pi\)
−0.423924 + 0.905698i \(0.639348\pi\)
\(564\) 0 0
\(565\) −5.27524e6 −0.695218
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.51143e6 −0.713648 −0.356824 0.934172i \(-0.616140\pi\)
−0.356824 + 0.934172i \(0.616140\pi\)
\(570\) 0 0
\(571\) 1.35431e6 0.173831 0.0869155 0.996216i \(-0.472299\pi\)
0.0869155 + 0.996216i \(0.472299\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.59196e6 0.705333
\(576\) 0 0
\(577\) −5.00736e6 −0.626137 −0.313068 0.949731i \(-0.601357\pi\)
−0.313068 + 0.949731i \(0.601357\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.34851e7 1.65735
\(582\) 0 0
\(583\) 2.80166e6 0.341384
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.69964e6 −0.323378 −0.161689 0.986842i \(-0.551694\pi\)
−0.161689 + 0.986842i \(0.551694\pi\)
\(588\) 0 0
\(589\) 8.94275e6 1.06214
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.31035e7 −1.53021 −0.765103 0.643908i \(-0.777312\pi\)
−0.765103 + 0.643908i \(0.777312\pi\)
\(594\) 0 0
\(595\) 1.59446e7 1.84639
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.22804e6 0.595349 0.297675 0.954667i \(-0.403789\pi\)
0.297675 + 0.954667i \(0.403789\pi\)
\(600\) 0 0
\(601\) 1.02248e7 1.15470 0.577351 0.816496i \(-0.304087\pi\)
0.577351 + 0.816496i \(0.304087\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.95295e6 −0.550143
\(606\) 0 0
\(607\) 8.81684e6 0.971273 0.485636 0.874161i \(-0.338588\pi\)
0.485636 + 0.874161i \(0.338588\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −322368. −0.0349340
\(612\) 0 0
\(613\) 1.13600e7 1.22103 0.610514 0.792006i \(-0.290963\pi\)
0.610514 + 0.792006i \(0.290963\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.77356e6 0.504812 0.252406 0.967621i \(-0.418778\pi\)
0.252406 + 0.967621i \(0.418778\pi\)
\(618\) 0 0
\(619\) −2.55931e6 −0.268470 −0.134235 0.990950i \(-0.542858\pi\)
−0.134235 + 0.990950i \(0.542858\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.54584e7 1.59567
\(624\) 0 0
\(625\) 264461. 0.0270808
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 8.52335e6 0.858981
\(630\) 0 0
\(631\) −8.41981e6 −0.841839 −0.420919 0.907098i \(-0.638292\pi\)
−0.420919 + 0.907098i \(0.638292\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.77045e6 0.174240
\(636\) 0 0
\(637\) 1.87648e6 0.183229
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.21494e7 1.16791 0.583957 0.811785i \(-0.301504\pi\)
0.583957 + 0.811785i \(0.301504\pi\)
\(642\) 0 0
\(643\) −1.08968e7 −1.03937 −0.519685 0.854358i \(-0.673951\pi\)
−0.519685 + 0.854358i \(0.673951\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.32166e7 −1.24124 −0.620622 0.784110i \(-0.713120\pi\)
−0.620622 + 0.784110i \(0.713120\pi\)
\(648\) 0 0
\(649\) 3472.00 0.000323570 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.65915e7 −1.52266 −0.761329 0.648365i \(-0.775453\pi\)
−0.761329 + 0.648365i \(0.775453\pi\)
\(654\) 0 0
\(655\) −5.43878e6 −0.495334
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.29372e6 0.205743 0.102872 0.994695i \(-0.467197\pi\)
0.102872 + 0.994695i \(0.467197\pi\)
\(660\) 0 0
\(661\) −719194. −0.0640239 −0.0320120 0.999487i \(-0.510191\pi\)
−0.0320120 + 0.999487i \(0.510191\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.56998e7 1.37671
\(666\) 0 0
\(667\) −2.53385e7 −2.20529
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −791864. −0.0678960
\(672\) 0 0
\(673\) 8.64695e6 0.735911 0.367955 0.929843i \(-0.380058\pi\)
0.367955 + 0.929843i \(0.380058\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.69592e7 1.42211 0.711056 0.703135i \(-0.248217\pi\)
0.711056 + 0.703135i \(0.248217\pi\)
\(678\) 0 0
\(679\) 2.78779e7 2.32052
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.87105e7 −1.53473 −0.767367 0.641209i \(-0.778433\pi\)
−0.767367 + 0.641209i \(0.778433\pi\)
\(684\) 0 0
\(685\) 8.91745e6 0.726130
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.03932e6 0.0834071
\(690\) 0 0
\(691\) −1.16204e7 −0.925820 −0.462910 0.886405i \(-0.653195\pi\)
−0.462910 + 0.886405i \(0.653195\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 8.61982e6 0.676918
\(696\) 0 0
\(697\) −5.63924e6 −0.439682
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.23497e7 −1.71781 −0.858907 0.512132i \(-0.828856\pi\)
−0.858907 + 0.512132i \(0.828856\pi\)
\(702\) 0 0
\(703\) 8.39249e6 0.640475
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.60402e7 −1.20687
\(708\) 0 0
\(709\) 1.02353e7 0.764687 0.382344 0.924020i \(-0.375117\pi\)
0.382344 + 0.924020i \(0.375117\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.32003e7 0.972435
\(714\) 0 0
\(715\) 193936. 0.0141871
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.70339e7 1.22883 0.614416 0.788982i \(-0.289392\pi\)
0.614416 + 0.788982i \(0.289392\pi\)
\(720\) 0 0
\(721\) −1.53600e7 −1.10041
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.75674e7 −1.24126
\(726\) 0 0
\(727\) −1.62280e7 −1.13875 −0.569377 0.822077i \(-0.692815\pi\)
−0.569377 + 0.822077i \(0.692815\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.21427e7 −1.53263
\(732\) 0 0
\(733\) −2.17495e7 −1.49517 −0.747583 0.664168i \(-0.768786\pi\)
−0.747583 + 0.664168i \(0.768786\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.84542e6 −0.328597
\(738\) 0 0
\(739\) 1.96200e7 1.32156 0.660781 0.750578i \(-0.270225\pi\)
0.660781 + 0.750578i \(0.270225\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.74018e7 −1.15644 −0.578218 0.815882i \(-0.696252\pi\)
−0.578218 + 0.815882i \(0.696252\pi\)
\(744\) 0 0
\(745\) −1.20914e7 −0.798154
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.62016e6 −0.235789
\(750\) 0 0
\(751\) −2.62693e7 −1.69961 −0.849803 0.527101i \(-0.823279\pi\)
−0.849803 + 0.527101i \(0.823279\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −34816.0 −0.00222286
\(756\) 0 0
\(757\) −5.70356e6 −0.361748 −0.180874 0.983506i \(-0.557893\pi\)
−0.180874 + 0.983506i \(0.557893\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.13762e7 1.33804 0.669020 0.743244i \(-0.266714\pi\)
0.669020 + 0.743244i \(0.266714\pi\)
\(762\) 0 0
\(763\) 9.52752e6 0.592473
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1288.00 7.90547e−5 0
\(768\) 0 0
\(769\) −2.01523e6 −0.122888 −0.0614439 0.998111i \(-0.519571\pi\)
−0.0614439 + 0.998111i \(0.519571\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.27674e7 0.768520 0.384260 0.923225i \(-0.374457\pi\)
0.384260 + 0.923225i \(0.374457\pi\)
\(774\) 0 0
\(775\) 9.15191e6 0.547340
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.55266e6 −0.327837
\(780\) 0 0
\(781\) 6.80413e6 0.399158
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.03844e6 −0.118065
\(786\) 0 0
\(787\) −2.72384e7 −1.56764 −0.783818 0.620990i \(-0.786731\pi\)
−0.783818 + 0.620990i \(0.786731\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.72370e7 2.11608
\(792\) 0 0
\(793\) −293756. −0.0165884
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.66724e6 0.427556 0.213778 0.976882i \(-0.431423\pi\)
0.213778 + 0.976882i \(0.431423\pi\)
\(798\) 0 0
\(799\) 1.36936e7 0.758843
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.60822e6 0.142743
\(804\) 0 0
\(805\) 2.31744e7 1.26043
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.05541e7 0.566956 0.283478 0.958979i \(-0.408512\pi\)
0.283478 + 0.958979i \(0.408512\pi\)
\(810\) 0 0
\(811\) −1.32883e6 −0.0709442 −0.0354721 0.999371i \(-0.511293\pi\)
−0.0354721 + 0.999371i \(0.511293\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.16129e7 −0.612416
\(816\) 0 0
\(817\) −2.18028e7 −1.14276
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 6.15933e6 0.318915 0.159458 0.987205i \(-0.449025\pi\)
0.159458 + 0.987205i \(0.449025\pi\)
\(822\) 0 0
\(823\) 1.00734e7 0.518414 0.259207 0.965822i \(-0.416539\pi\)
0.259207 + 0.965822i \(0.416539\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 6.49152e6 0.330052 0.165026 0.986289i \(-0.447229\pi\)
0.165026 + 0.986289i \(0.447229\pi\)
\(828\) 0 0
\(829\) −1.93536e7 −0.978082 −0.489041 0.872261i \(-0.662653\pi\)
−0.489041 + 0.872261i \(0.662653\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −7.97095e7 −3.98013
\(834\) 0 0
\(835\) −170544. −0.00846487
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.78622e7 1.36650 0.683251 0.730183i \(-0.260565\pi\)
0.683251 + 0.730183i \(0.260565\pi\)
\(840\) 0 0
\(841\) 5.90909e7 2.88092
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.25520e7 −0.604744
\(846\) 0 0
\(847\) 3.49620e7 1.67451
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.23881e7 0.586381
\(852\) 0 0
\(853\) 1.07651e7 0.506577 0.253288 0.967391i \(-0.418488\pi\)
0.253288 + 0.967391i \(0.418488\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.22439e7 −0.569465 −0.284733 0.958607i \(-0.591905\pi\)
−0.284733 + 0.958607i \(0.591905\pi\)
\(858\) 0 0
\(859\) −1.38664e6 −0.0641179 −0.0320590 0.999486i \(-0.510206\pi\)
−0.0320590 + 0.999486i \(0.510206\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.09856e7 0.502109 0.251055 0.967973i \(-0.419223\pi\)
0.251055 + 0.967973i \(0.419223\pi\)
\(864\) 0 0
\(865\) 7.77464e6 0.353297
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3.30237e6 0.148346
\(870\) 0 0
\(871\) −1.79750e6 −0.0802828
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 4.15670e7 1.83539
\(876\) 0 0
\(877\) 8.17798e6 0.359044 0.179522 0.983754i \(-0.442545\pi\)
0.179522 + 0.983754i \(0.442545\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −4.66520e6 −0.202503 −0.101251 0.994861i \(-0.532285\pi\)
−0.101251 + 0.994861i \(0.532285\pi\)
\(882\) 0 0
\(883\) 3.82201e7 1.64964 0.824822 0.565393i \(-0.191276\pi\)
0.824822 + 0.565393i \(0.191276\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 7.72172e6 0.329538 0.164769 0.986332i \(-0.447312\pi\)
0.164769 + 0.986332i \(0.447312\pi\)
\(888\) 0 0
\(889\) −1.24973e7 −0.530348
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.34834e7 0.565810
\(894\) 0 0
\(895\) −5.48719e6 −0.228977
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4.14695e7 −1.71131
\(900\) 0 0
\(901\) −4.41487e7 −1.81178
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −9.91746e6 −0.402512
\(906\) 0 0
\(907\) 4.33137e7 1.74826 0.874131 0.485689i \(-0.161431\pi\)
0.874131 + 0.485689i \(0.161431\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −3.44456e6 −0.137511 −0.0687556 0.997634i \(-0.521903\pi\)
−0.0687556 + 0.997634i \(0.521903\pi\)
\(912\) 0 0
\(913\) −6.96731e6 −0.276623
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.83914e7 1.50768
\(918\) 0 0
\(919\) −4.37073e7 −1.70712 −0.853562 0.520991i \(-0.825563\pi\)
−0.853562 + 0.520991i \(0.825563\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.52411e6 0.0975224
\(924\) 0 0
\(925\) 8.58878e6 0.330048
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.13022e7 1.57012 0.785062 0.619418i \(-0.212631\pi\)
0.785062 + 0.619418i \(0.212631\pi\)
\(930\) 0 0
\(931\) −7.84857e7 −2.96768
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −8.23806e6 −0.308174
\(936\) 0 0
\(937\) 9.57460e6 0.356264 0.178132 0.984007i \(-0.442995\pi\)
0.178132 + 0.984007i \(0.442995\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −8.71623e6 −0.320889 −0.160444 0.987045i \(-0.551293\pi\)
−0.160444 + 0.987045i \(0.551293\pi\)
\(942\) 0 0
\(943\) −8.19624e6 −0.300148
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.30605e7 0.473244 0.236622 0.971602i \(-0.423960\pi\)
0.236622 + 0.971602i \(0.423960\pi\)
\(948\) 0 0
\(949\) 967564. 0.0348750
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.13875e7 −0.406158 −0.203079 0.979162i \(-0.565095\pi\)
−0.203079 + 0.979162i \(0.565095\pi\)
\(954\) 0 0
\(955\) 1.89312e6 0.0671691
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6.29467e7 −2.21017
\(960\) 0 0
\(961\) −7.02525e6 −0.245388
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −5.99264e6 −0.207157
\(966\) 0 0
\(967\) 4.62711e7 1.59127 0.795634 0.605778i \(-0.207138\pi\)
0.795634 + 0.605778i \(0.207138\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.63206e7 −0.555506 −0.277753 0.960653i \(-0.589590\pi\)
−0.277753 + 0.960653i \(0.589590\pi\)
\(972\) 0 0
\(973\) −6.08458e7 −2.06038
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.95213e7 0.654294 0.327147 0.944973i \(-0.393913\pi\)
0.327147 + 0.944973i \(0.393913\pi\)
\(978\) 0 0
\(979\) −7.98684e6 −0.266329
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 4.33962e7 1.43241 0.716207 0.697888i \(-0.245877\pi\)
0.716207 + 0.697888i \(0.245877\pi\)
\(984\) 0 0
\(985\) 1.27367e7 0.418281
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3.21829e7 −1.04625
\(990\) 0 0
\(991\) 3.83518e7 1.24051 0.620257 0.784399i \(-0.287028\pi\)
0.620257 + 0.784399i \(0.287028\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −2.16838e7 −0.694350
\(996\) 0 0
\(997\) −7.82206e6 −0.249220 −0.124610 0.992206i \(-0.539768\pi\)
−0.124610 + 0.992206i \(0.539768\pi\)
\(998\) 0 0
\(999\) 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 72.6.a.e.1.1 1
3.2 odd 2 24.6.a.a.1.1 1
4.3 odd 2 144.6.a.i.1.1 1
8.3 odd 2 576.6.a.l.1.1 1
8.5 even 2 576.6.a.k.1.1 1
12.11 even 2 48.6.a.d.1.1 1
15.2 even 4 600.6.f.f.49.2 2
15.8 even 4 600.6.f.f.49.1 2
15.14 odd 2 600.6.a.i.1.1 1
24.5 odd 2 192.6.a.n.1.1 1
24.11 even 2 192.6.a.f.1.1 1
48.5 odd 4 768.6.d.r.385.2 2
48.11 even 4 768.6.d.a.385.1 2
48.29 odd 4 768.6.d.r.385.1 2
48.35 even 4 768.6.d.a.385.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
24.6.a.a.1.1 1 3.2 odd 2
48.6.a.d.1.1 1 12.11 even 2
72.6.a.e.1.1 1 1.1 even 1 trivial
144.6.a.i.1.1 1 4.3 odd 2
192.6.a.f.1.1 1 24.11 even 2
192.6.a.n.1.1 1 24.5 odd 2
576.6.a.k.1.1 1 8.5 even 2
576.6.a.l.1.1 1 8.3 odd 2
600.6.a.i.1.1 1 15.14 odd 2
600.6.f.f.49.1 2 15.8 even 4
600.6.f.f.49.2 2 15.2 even 4
768.6.d.a.385.1 2 48.11 even 4
768.6.d.a.385.2 2 48.35 even 4
768.6.d.r.385.1 2 48.29 odd 4
768.6.d.r.385.2 2 48.5 odd 4