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Properties

Label 504.6.a.b.1.1
Level $504$
Weight $6$
Character 504.1
Self dual yes
Analytic conductor $80.833$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,6,Mod(1,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 504.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(80.8334451857\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 504.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-32.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-32.0000 q^{5} +49.0000 q^{7} +624.000 q^{11} -708.000 q^{13} -934.000 q^{17} +1858.00 q^{19} +1120.00 q^{23} -2101.00 q^{25} +1174.00 q^{29} +2908.00 q^{31} -1568.00 q^{35} -12462.0 q^{37} -2662.00 q^{41} -7144.00 q^{43} +7468.00 q^{47} +2401.00 q^{49} +27274.0 q^{53} -19968.0 q^{55} -2490.00 q^{59} -11096.0 q^{61} +22656.0 q^{65} +39756.0 q^{67} +69888.0 q^{71} +16450.0 q^{73} +30576.0 q^{77} +78376.0 q^{79} -109818. q^{83} +29888.0 q^{85} +56966.0 q^{89} -34692.0 q^{91} -59456.0 q^{95} -115946. q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(5\) −32.0000 −0.572433 −0.286217 − 0.958165i \(-0.592398\pi\)
−0.286217 + 0.958165i \(0.592398\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 624.000 1.55490 0.777451 − 0.628944i \(-0.216512\pi\)
0.777451 + 0.628944i \(0.216512\pi\)
\(12\) 0 0
\(13\) −708.000 −1.16192 −0.580958 − 0.813933i \(-0.697322\pi\)
−0.580958 + 0.813933i \(0.697322\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −934.000 −0.783835 −0.391917 − 0.920000i \(-0.628188\pi\)
−0.391917 + 0.920000i \(0.628188\pi\)
\(18\) 0 0
\(19\) 1858.00 1.18076 0.590380 − 0.807125i \(-0.298978\pi\)
0.590380 + 0.807125i \(0.298978\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1120.00 0.441467 0.220734 − 0.975334i \(-0.429155\pi\)
0.220734 + 0.975334i \(0.429155\pi\)
\(24\) 0 0
\(25\) −2101.00 −0.672320
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1174.00 0.259223 0.129611 − 0.991565i \(-0.458627\pi\)
0.129611 + 0.991565i \(0.458627\pi\)
\(30\) 0 0
\(31\) 2908.00 0.543488 0.271744 − 0.962370i \(-0.412400\pi\)
0.271744 + 0.962370i \(0.412400\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1568.00 −0.216359
\(36\) 0 0
\(37\) −12462.0 −1.49652 −0.748262 − 0.663404i \(-0.769111\pi\)
−0.748262 + 0.663404i \(0.769111\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2662.00 −0.247314 −0.123657 − 0.992325i \(-0.539462\pi\)
−0.123657 + 0.992325i \(0.539462\pi\)
\(42\) 0 0
\(43\) −7144.00 −0.589210 −0.294605 − 0.955619i \(-0.595188\pi\)
−0.294605 + 0.955619i \(0.595188\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7468.00 0.493128 0.246564 − 0.969127i \(-0.420698\pi\)
0.246564 + 0.969127i \(0.420698\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 27274.0 1.33370 0.666852 − 0.745191i \(-0.267642\pi\)
0.666852 + 0.745191i \(0.267642\pi\)
\(54\) 0 0
\(55\) −19968.0 −0.890078
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2490.00 −0.0931257 −0.0465628 − 0.998915i \(-0.514827\pi\)
−0.0465628 + 0.998915i \(0.514827\pi\)
\(60\) 0 0
\(61\) −11096.0 −0.381805 −0.190903 − 0.981609i \(-0.561141\pi\)
−0.190903 + 0.981609i \(0.561141\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 22656.0 0.665120
\(66\) 0 0
\(67\) 39756.0 1.08197 0.540986 − 0.841032i \(-0.318051\pi\)
0.540986 + 0.841032i \(0.318051\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 69888.0 1.64534 0.822672 − 0.568516i \(-0.192482\pi\)
0.822672 + 0.568516i \(0.192482\pi\)
\(72\) 0 0
\(73\) 16450.0 0.361292 0.180646 − 0.983548i \(-0.442181\pi\)
0.180646 + 0.983548i \(0.442181\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 30576.0 0.587698
\(78\) 0 0
\(79\) 78376.0 1.41291 0.706456 − 0.707757i \(-0.250293\pi\)
0.706456 + 0.707757i \(0.250293\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −109818. −1.74976 −0.874880 − 0.484340i \(-0.839060\pi\)
−0.874880 + 0.484340i \(0.839060\pi\)
\(84\) 0 0
\(85\) 29888.0 0.448693
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 56966.0 0.762326 0.381163 − 0.924508i \(-0.375524\pi\)
0.381163 + 0.924508i \(0.375524\pi\)
\(90\) 0 0
\(91\) −34692.0 −0.439163
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −59456.0 −0.675907
\(96\) 0 0
\(97\) −115946. −1.25120 −0.625600 − 0.780144i \(-0.715146\pi\)
−0.625600 + 0.780144i \(0.715146\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8352.00 −0.0814680 −0.0407340 − 0.999170i \(-0.512970\pi\)
−0.0407340 + 0.999170i \(0.512970\pi\)
\(102\) 0 0
\(103\) 179484. 1.66699 0.833494 − 0.552528i \(-0.186337\pi\)
0.833494 + 0.552528i \(0.186337\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 53892.0 0.455056 0.227528 − 0.973772i \(-0.426936\pi\)
0.227528 + 0.973772i \(0.426936\pi\)
\(108\) 0 0
\(109\) 105970. 0.854312 0.427156 − 0.904178i \(-0.359515\pi\)
0.427156 + 0.904178i \(0.359515\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2502.00 −0.0184328 −0.00921640 − 0.999958i \(-0.502934\pi\)
−0.00921640 + 0.999958i \(0.502934\pi\)
\(114\) 0 0
\(115\) −35840.0 −0.252711
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −45766.0 −0.296262
\(120\) 0 0
\(121\) 228325. 1.41772
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 167232. 0.957292
\(126\) 0 0
\(127\) 287792. 1.58332 0.791661 − 0.610960i \(-0.209216\pi\)
0.791661 + 0.610960i \(0.209216\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 47662.0 0.242658 0.121329 − 0.992612i \(-0.461284\pi\)
0.121329 + 0.992612i \(0.461284\pi\)
\(132\) 0 0
\(133\) 91042.0 0.446285
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −223154. −1.01579 −0.507894 − 0.861419i \(-0.669576\pi\)
−0.507894 + 0.861419i \(0.669576\pi\)
\(138\) 0 0
\(139\) 250542. 1.09988 0.549938 − 0.835206i \(-0.314651\pi\)
0.549938 + 0.835206i \(0.314651\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −441792. −1.80667
\(144\) 0 0
\(145\) −37568.0 −0.148388
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 487394. 1.79852 0.899258 − 0.437418i \(-0.144107\pi\)
0.899258 + 0.437418i \(0.144107\pi\)
\(150\) 0 0
\(151\) −54680.0 −0.195158 −0.0975790 − 0.995228i \(-0.531110\pi\)
−0.0975790 + 0.995228i \(0.531110\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −93056.0 −0.311111
\(156\) 0 0
\(157\) 211068. 0.683397 0.341699 − 0.939810i \(-0.388998\pi\)
0.341699 + 0.939810i \(0.388998\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 54880.0 0.166859
\(162\) 0 0
\(163\) −20192.0 −0.0595265 −0.0297632 − 0.999557i \(-0.509475\pi\)
−0.0297632 + 0.999557i \(0.509475\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4524.00 0.0125525 0.00627627 − 0.999980i \(-0.498002\pi\)
0.00627627 + 0.999980i \(0.498002\pi\)
\(168\) 0 0
\(169\) 129971. 0.350050
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 104332. 0.265034 0.132517 − 0.991181i \(-0.457694\pi\)
0.132517 + 0.991181i \(0.457694\pi\)
\(174\) 0 0
\(175\) −102949. −0.254113
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 201724. 0.470571 0.235285 − 0.971926i \(-0.424398\pi\)
0.235285 + 0.971926i \(0.424398\pi\)
\(180\) 0 0
\(181\) 655700. 1.48768 0.743839 − 0.668359i \(-0.233003\pi\)
0.743839 + 0.668359i \(0.233003\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 398784. 0.856660
\(186\) 0 0
\(187\) −582816. −1.21879
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 151496. 0.300482 0.150241 − 0.988649i \(-0.451995\pi\)
0.150241 + 0.988649i \(0.451995\pi\)
\(192\) 0 0
\(193\) 229326. 0.443159 0.221580 − 0.975142i \(-0.428879\pi\)
0.221580 + 0.975142i \(0.428879\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −421086. −0.773046 −0.386523 − 0.922280i \(-0.626324\pi\)
−0.386523 + 0.922280i \(0.626324\pi\)
\(198\) 0 0
\(199\) 197300. 0.353179 0.176589 − 0.984285i \(-0.443494\pi\)
0.176589 + 0.984285i \(0.443494\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 57526.0 0.0979770
\(204\) 0 0
\(205\) 85184.0 0.141571
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.15939e6 1.83597
\(210\) 0 0
\(211\) 679052. 1.05002 0.525009 − 0.851097i \(-0.324062\pi\)
0.525009 + 0.851097i \(0.324062\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 228608. 0.337284
\(216\) 0 0
\(217\) 142492. 0.205419
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 661272. 0.910751
\(222\) 0 0
\(223\) −184440. −0.248366 −0.124183 − 0.992259i \(-0.539631\pi\)
−0.124183 + 0.992259i \(0.539631\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 868078. 1.11813 0.559067 − 0.829122i \(-0.311159\pi\)
0.559067 + 0.829122i \(0.311159\pi\)
\(228\) 0 0
\(229\) −593860. −0.748334 −0.374167 − 0.927361i \(-0.622071\pi\)
−0.374167 + 0.927361i \(0.622071\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −48218.0 −0.0581861 −0.0290931 − 0.999577i \(-0.509262\pi\)
−0.0290931 + 0.999577i \(0.509262\pi\)
\(234\) 0 0
\(235\) −238976. −0.282283
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −241688. −0.273691 −0.136845 − 0.990592i \(-0.543696\pi\)
−0.136845 + 0.990592i \(0.543696\pi\)
\(240\) 0 0
\(241\) 565270. 0.626922 0.313461 − 0.949601i \(-0.398512\pi\)
0.313461 + 0.949601i \(0.398512\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −76832.0 −0.0817762
\(246\) 0 0
\(247\) −1.31546e6 −1.37194
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.43775e6 1.44045 0.720224 − 0.693741i \(-0.244039\pi\)
0.720224 + 0.693741i \(0.244039\pi\)
\(252\) 0 0
\(253\) 698880. 0.686438
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −494802. −0.467303 −0.233652 − 0.972320i \(-0.575067\pi\)
−0.233652 + 0.972320i \(0.575067\pi\)
\(258\) 0 0
\(259\) −610638. −0.565633
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.55654e6 −1.38762 −0.693812 − 0.720156i \(-0.744070\pi\)
−0.693812 + 0.720156i \(0.744070\pi\)
\(264\) 0 0
\(265\) −872768. −0.763456
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.36204e6 −1.14765 −0.573823 − 0.818979i \(-0.694540\pi\)
−0.573823 + 0.818979i \(0.694540\pi\)
\(270\) 0 0
\(271\) 558320. 0.461806 0.230903 − 0.972977i \(-0.425832\pi\)
0.230903 + 0.972977i \(0.425832\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.31102e6 −1.04539
\(276\) 0 0
\(277\) 586342. 0.459147 0.229573 − 0.973291i \(-0.426267\pi\)
0.229573 + 0.973291i \(0.426267\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −606234. −0.458010 −0.229005 − 0.973425i \(-0.573547\pi\)
−0.229005 + 0.973425i \(0.573547\pi\)
\(282\) 0 0
\(283\) −865174. −0.642151 −0.321076 − 0.947054i \(-0.604044\pi\)
−0.321076 + 0.947054i \(0.604044\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −130438. −0.0934758
\(288\) 0 0
\(289\) −547501. −0.385603
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 353352. 0.240458 0.120229 − 0.992746i \(-0.461637\pi\)
0.120229 + 0.992746i \(0.461637\pi\)
\(294\) 0 0
\(295\) 79680.0 0.0533082
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −792960. −0.512948
\(300\) 0 0
\(301\) −350056. −0.222701
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 355072. 0.218558
\(306\) 0 0
\(307\) −1.95904e6 −1.18631 −0.593153 − 0.805090i \(-0.702117\pi\)
−0.593153 + 0.805090i \(0.702117\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.06257e6 −1.79550 −0.897749 − 0.440508i \(-0.854798\pi\)
−0.897749 + 0.440508i \(0.854798\pi\)
\(312\) 0 0
\(313\) −582634. −0.336151 −0.168076 − 0.985774i \(-0.553755\pi\)
−0.168076 + 0.985774i \(0.553755\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.09585e6 1.73034 0.865171 − 0.501478i \(-0.167210\pi\)
0.865171 + 0.501478i \(0.167210\pi\)
\(318\) 0 0
\(319\) 732576. 0.403066
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.73537e6 −0.925521
\(324\) 0 0
\(325\) 1.48751e6 0.781180
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 365932. 0.186385
\(330\) 0 0
\(331\) 625496. 0.313801 0.156901 − 0.987614i \(-0.449850\pi\)
0.156901 + 0.987614i \(0.449850\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.27219e6 −0.619356
\(336\) 0 0
\(337\) 2.32494e6 1.11516 0.557580 − 0.830123i \(-0.311730\pi\)
0.557580 + 0.830123i \(0.311730\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.81459e6 0.845071
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 781128. 0.348256 0.174128 − 0.984723i \(-0.444289\pi\)
0.174128 + 0.984723i \(0.444289\pi\)
\(348\) 0 0
\(349\) 1.48586e6 0.653002 0.326501 − 0.945197i \(-0.394130\pi\)
0.326501 + 0.945197i \(0.394130\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.44463e6 −0.617048 −0.308524 − 0.951217i \(-0.599835\pi\)
−0.308524 + 0.951217i \(0.599835\pi\)
\(354\) 0 0
\(355\) −2.23642e6 −0.941850
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −404040. −0.165458 −0.0827291 − 0.996572i \(-0.526364\pi\)
−0.0827291 + 0.996572i \(0.526364\pi\)
\(360\) 0 0
\(361\) 976065. 0.394195
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −526400. −0.206816
\(366\) 0 0
\(367\) −2.71698e6 −1.05298 −0.526492 − 0.850180i \(-0.676493\pi\)
−0.526492 + 0.850180i \(0.676493\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.33643e6 0.504092
\(372\) 0 0
\(373\) −1.79399e6 −0.667647 −0.333824 − 0.942636i \(-0.608339\pi\)
−0.333824 + 0.942636i \(0.608339\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −831192. −0.301195
\(378\) 0 0
\(379\) −18624.0 −0.00666001 −0.00333001 − 0.999994i \(-0.501060\pi\)
−0.00333001 + 0.999994i \(0.501060\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.33004e6 0.463307 0.231654 − 0.972798i \(-0.425586\pi\)
0.231654 + 0.972798i \(0.425586\pi\)
\(384\) 0 0
\(385\) −978432. −0.336418
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.26506e6 −0.758936 −0.379468 − 0.925205i \(-0.623893\pi\)
−0.379468 + 0.925205i \(0.623893\pi\)
\(390\) 0 0
\(391\) −1.04608e6 −0.346037
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.50803e6 −0.808798
\(396\) 0 0
\(397\) −4.48900e6 −1.42947 −0.714733 − 0.699398i \(-0.753452\pi\)
−0.714733 + 0.699398i \(0.753452\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 95442.0 0.0296400 0.0148200 − 0.999890i \(-0.495282\pi\)
0.0148200 + 0.999890i \(0.495282\pi\)
\(402\) 0 0
\(403\) −2.05886e6 −0.631488
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.77629e6 −2.32695
\(408\) 0 0
\(409\) −2.99003e6 −0.883828 −0.441914 − 0.897057i \(-0.645700\pi\)
−0.441914 + 0.897057i \(0.645700\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −122010. −0.0351982
\(414\) 0 0
\(415\) 3.51418e6 1.00162
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.39037e6 −0.943436 −0.471718 − 0.881749i \(-0.656366\pi\)
−0.471718 + 0.881749i \(0.656366\pi\)
\(420\) 0 0
\(421\) 3.38397e6 0.930512 0.465256 − 0.885176i \(-0.345962\pi\)
0.465256 + 0.885176i \(0.345962\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.96233e6 0.526988
\(426\) 0 0
\(427\) −543704. −0.144309
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.98353e6 0.514334 0.257167 − 0.966367i \(-0.417211\pi\)
0.257167 + 0.966367i \(0.417211\pi\)
\(432\) 0 0
\(433\) −7.17581e6 −1.83929 −0.919647 − 0.392746i \(-0.871525\pi\)
−0.919647 + 0.392746i \(0.871525\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.08096e6 0.521267
\(438\) 0 0
\(439\) −2.44390e6 −0.605231 −0.302616 − 0.953113i \(-0.597860\pi\)
−0.302616 + 0.953113i \(0.597860\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −231716. −0.0560979 −0.0280490 − 0.999607i \(-0.508929\pi\)
−0.0280490 + 0.999607i \(0.508929\pi\)
\(444\) 0 0
\(445\) −1.82291e6 −0.436381
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.73637e6 1.10874 0.554370 − 0.832271i \(-0.312959\pi\)
0.554370 + 0.832271i \(0.312959\pi\)
\(450\) 0 0
\(451\) −1.66109e6 −0.384549
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.11014e6 0.251392
\(456\) 0 0
\(457\) −7.87486e6 −1.76381 −0.881906 − 0.471426i \(-0.843740\pi\)
−0.881906 + 0.471426i \(0.843740\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8.23218e6 1.80411 0.902054 − 0.431623i \(-0.142059\pi\)
0.902054 + 0.431623i \(0.142059\pi\)
\(462\) 0 0
\(463\) 2.36038e6 0.511717 0.255859 − 0.966714i \(-0.417642\pi\)
0.255859 + 0.966714i \(0.417642\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.31700e6 1.34035 0.670175 − 0.742203i \(-0.266219\pi\)
0.670175 + 0.742203i \(0.266219\pi\)
\(468\) 0 0
\(469\) 1.94804e6 0.408947
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.45786e6 −0.916164
\(474\) 0 0
\(475\) −3.90366e6 −0.793849
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.45856e6 −0.290459 −0.145229 − 0.989398i \(-0.546392\pi\)
−0.145229 + 0.989398i \(0.546392\pi\)
\(480\) 0 0
\(481\) 8.82310e6 1.73883
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.71027e6 0.716228
\(486\) 0 0
\(487\) 9.28782e6 1.77456 0.887282 − 0.461228i \(-0.152591\pi\)
0.887282 + 0.461228i \(0.152591\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 234972. 0.0439858 0.0219929 − 0.999758i \(-0.492999\pi\)
0.0219929 + 0.999758i \(0.492999\pi\)
\(492\) 0 0
\(493\) −1.09652e6 −0.203188
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.42451e6 0.621882
\(498\) 0 0
\(499\) −7.00792e6 −1.25991 −0.629953 − 0.776633i \(-0.716926\pi\)
−0.629953 + 0.776633i \(0.716926\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.94752e6 −0.871902 −0.435951 − 0.899970i \(-0.643588\pi\)
−0.435951 + 0.899970i \(0.643588\pi\)
\(504\) 0 0
\(505\) 267264. 0.0466350
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.50640e6 −0.942049 −0.471025 − 0.882120i \(-0.656116\pi\)
−0.471025 + 0.882120i \(0.656116\pi\)
\(510\) 0 0
\(511\) 806050. 0.136556
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5.74349e6 −0.954240
\(516\) 0 0
\(517\) 4.66003e6 0.766765
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.63076e6 −0.263206 −0.131603 − 0.991303i \(-0.542012\pi\)
−0.131603 + 0.991303i \(0.542012\pi\)
\(522\) 0 0
\(523\) −1.00765e7 −1.61086 −0.805429 − 0.592692i \(-0.798065\pi\)
−0.805429 + 0.592692i \(0.798065\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.71607e6 −0.426005
\(528\) 0 0
\(529\) −5.18194e6 −0.805107
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.88470e6 0.287358
\(534\) 0 0
\(535\) −1.72454e6 −0.260489
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.49822e6 0.222129
\(540\) 0 0
\(541\) −1.25225e7 −1.83949 −0.919746 − 0.392513i \(-0.871606\pi\)
−0.919746 + 0.392513i \(0.871606\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.39104e6 −0.489037
\(546\) 0 0
\(547\) 6.67430e6 0.953756 0.476878 − 0.878970i \(-0.341768\pi\)
0.476878 + 0.878970i \(0.341768\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.18129e6 0.306080
\(552\) 0 0
\(553\) 3.84042e6 0.534031
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.61643e6 0.630475 0.315238 − 0.949013i \(-0.397916\pi\)
0.315238 + 0.949013i \(0.397916\pi\)
\(558\) 0 0
\(559\) 5.05795e6 0.684613
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 8.84218e6 1.17568 0.587839 − 0.808978i \(-0.299979\pi\)
0.587839 + 0.808978i \(0.299979\pi\)
\(564\) 0 0
\(565\) 80064.0 0.0105515
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.15771e7 −1.49906 −0.749532 − 0.661968i \(-0.769721\pi\)
−0.749532 + 0.661968i \(0.769721\pi\)
\(570\) 0 0
\(571\) 4.48069e6 0.575115 0.287557 − 0.957763i \(-0.407157\pi\)
0.287557 + 0.957763i \(0.407157\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2.35312e6 −0.296807
\(576\) 0 0
\(577\) 1.32788e7 1.66042 0.830212 − 0.557448i \(-0.188220\pi\)
0.830212 + 0.557448i \(0.188220\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.38108e6 −0.661347
\(582\) 0 0
\(583\) 1.70190e7 2.07378
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.11188e7 1.33187 0.665936 − 0.746009i \(-0.268032\pi\)
0.665936 + 0.746009i \(0.268032\pi\)
\(588\) 0 0
\(589\) 5.40306e6 0.641729
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.92737e6 0.458632 0.229316 − 0.973352i \(-0.426351\pi\)
0.229316 + 0.973352i \(0.426351\pi\)
\(594\) 0 0
\(595\) 1.46451e6 0.169590
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.74099e7 1.98258 0.991289 − 0.131704i \(-0.0420449\pi\)
0.991289 + 0.131704i \(0.0420449\pi\)
\(600\) 0 0
\(601\) 7.46243e6 0.842740 0.421370 − 0.906889i \(-0.361549\pi\)
0.421370 + 0.906889i \(0.361549\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.30640e6 −0.811549
\(606\) 0 0
\(607\) 701152. 0.0772397 0.0386198 − 0.999254i \(-0.487704\pi\)
0.0386198 + 0.999254i \(0.487704\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.28734e6 −0.572974
\(612\) 0 0
\(613\) 1.09575e7 1.17777 0.588886 − 0.808216i \(-0.299567\pi\)
0.588886 + 0.808216i \(0.299567\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.90666e6 −0.201633 −0.100816 − 0.994905i \(-0.532145\pi\)
−0.100816 + 0.994905i \(0.532145\pi\)
\(618\) 0 0
\(619\) −2.22346e6 −0.233240 −0.116620 − 0.993177i \(-0.537206\pi\)
−0.116620 + 0.993177i \(0.537206\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.79133e6 0.288132
\(624\) 0 0
\(625\) 1.21420e6 0.124334
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.16395e7 1.17303
\(630\) 0 0
\(631\) 752624. 0.0752497 0.0376248 − 0.999292i \(-0.488021\pi\)
0.0376248 + 0.999292i \(0.488021\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.20934e6 −0.906347
\(636\) 0 0
\(637\) −1.69991e6 −0.165988
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.45429e6 0.235929 0.117964 − 0.993018i \(-0.462363\pi\)
0.117964 + 0.993018i \(0.462363\pi\)
\(642\) 0 0
\(643\) 1.58237e7 1.50932 0.754660 − 0.656116i \(-0.227802\pi\)
0.754660 + 0.656116i \(0.227802\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.65489e6 0.249337 0.124668 − 0.992198i \(-0.460213\pi\)
0.124668 + 0.992198i \(0.460213\pi\)
\(648\) 0 0
\(649\) −1.55376e6 −0.144801
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.26899e6 −0.850648 −0.425324 − 0.905041i \(-0.639840\pi\)
−0.425324 + 0.905041i \(0.639840\pi\)
\(654\) 0 0
\(655\) −1.52518e6 −0.138905
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.68242e7 1.50911 0.754556 − 0.656235i \(-0.227852\pi\)
0.754556 + 0.656235i \(0.227852\pi\)
\(660\) 0 0
\(661\) −6.77217e6 −0.602871 −0.301435 − 0.953487i \(-0.597466\pi\)
−0.301435 + 0.953487i \(0.597466\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.91334e6 −0.255469
\(666\) 0 0
\(667\) 1.31488e6 0.114438
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −6.92390e6 −0.593669
\(672\) 0 0
\(673\) 7.61315e6 0.647928 0.323964 − 0.946069i \(-0.394984\pi\)
0.323964 + 0.946069i \(0.394984\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.11672e6 −0.512917 −0.256459 − 0.966555i \(-0.582556\pi\)
−0.256459 + 0.966555i \(0.582556\pi\)
\(678\) 0 0
\(679\) −5.68135e6 −0.472909
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.12588e7 0.923511 0.461755 − 0.887007i \(-0.347220\pi\)
0.461755 + 0.887007i \(0.347220\pi\)
\(684\) 0 0
\(685\) 7.14093e6 0.581471
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.93100e7 −1.54965
\(690\) 0 0
\(691\) 9.50952e6 0.757641 0.378821 − 0.925470i \(-0.376330\pi\)
0.378821 + 0.925470i \(0.376330\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.01734e6 −0.629605
\(696\) 0 0
\(697\) 2.48631e6 0.193853
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.53868e7 −1.18264 −0.591322 − 0.806436i \(-0.701394\pi\)
−0.591322 + 0.806436i \(0.701394\pi\)
\(702\) 0 0
\(703\) −2.31544e7 −1.76703
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −409248. −0.0307920
\(708\) 0 0
\(709\) −1.21379e6 −0.0906834 −0.0453417 − 0.998972i \(-0.514438\pi\)
−0.0453417 + 0.998972i \(0.514438\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.25696e6 0.239932
\(714\) 0 0
\(715\) 1.41373e7 1.03420
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.00002e7 0.721418 0.360709 − 0.932678i \(-0.382535\pi\)
0.360709 + 0.932678i \(0.382535\pi\)
\(720\) 0 0
\(721\) 8.79472e6 0.630063
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.46657e6 −0.174281
\(726\) 0 0
\(727\) 1.33745e7 0.938514 0.469257 − 0.883062i \(-0.344522\pi\)
0.469257 + 0.883062i \(0.344522\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 6.67250e6 0.461844
\(732\) 0 0
\(733\) 1.61380e7 1.10940 0.554701 − 0.832050i \(-0.312833\pi\)
0.554701 + 0.832050i \(0.312833\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.48077e7 1.68236
\(738\) 0 0
\(739\) 8.61059e6 0.579992 0.289996 − 0.957028i \(-0.406346\pi\)
0.289996 + 0.957028i \(0.406346\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.85027e7 1.89415 0.947075 − 0.321012i \(-0.104023\pi\)
0.947075 + 0.321012i \(0.104023\pi\)
\(744\) 0 0
\(745\) −1.55966e7 −1.02953
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.64071e6 0.171995
\(750\) 0 0
\(751\) −7.28721e6 −0.471478 −0.235739 − 0.971816i \(-0.575751\pi\)
−0.235739 + 0.971816i \(0.575751\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.74976e6 0.111715
\(756\) 0 0
\(757\) −2.77165e7 −1.75792 −0.878958 − 0.476899i \(-0.841761\pi\)
−0.878958 + 0.476899i \(0.841761\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.07625e7 −1.92557 −0.962787 − 0.270262i \(-0.912890\pi\)
−0.962787 + 0.270262i \(0.912890\pi\)
\(762\) 0 0
\(763\) 5.19253e6 0.322900
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.76292e6 0.108204
\(768\) 0 0
\(769\) −1.83665e7 −1.11998 −0.559990 − 0.828499i \(-0.689195\pi\)
−0.559990 + 0.828499i \(0.689195\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.01397e7 0.610348 0.305174 − 0.952297i \(-0.401285\pi\)
0.305174 + 0.952297i \(0.401285\pi\)
\(774\) 0 0
\(775\) −6.10971e6 −0.365398
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.94600e6 −0.292018
\(780\) 0 0
\(781\) 4.36101e7 2.55835
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.75418e6 −0.391199
\(786\) 0 0
\(787\) −1.89442e7 −1.09028 −0.545140 − 0.838345i \(-0.683524\pi\)
−0.545140 + 0.838345i \(0.683524\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −122598. −0.00696694
\(792\) 0 0
\(793\) 7.85597e6 0.443626
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.19835e7 0.668248 0.334124 − 0.942529i \(-0.391560\pi\)
0.334124 + 0.942529i \(0.391560\pi\)
\(798\) 0 0
\(799\) −6.97511e6 −0.386531
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.02648e7 0.561774
\(804\) 0 0
\(805\) −1.75616e6 −0.0955156
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 6.31823e6 0.339410 0.169705 − 0.985495i \(-0.445719\pi\)
0.169705 + 0.985495i \(0.445719\pi\)
\(810\) 0 0
\(811\) 1.47079e6 0.0785231 0.0392615 − 0.999229i \(-0.487499\pi\)
0.0392615 + 0.999229i \(0.487499\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 646144. 0.0340750
\(816\) 0 0
\(817\) −1.32736e7 −0.695716
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.10138e7 1.08804 0.544022 − 0.839071i \(-0.316901\pi\)
0.544022 + 0.839071i \(0.316901\pi\)
\(822\) 0 0
\(823\) −1.35856e7 −0.699163 −0.349582 − 0.936906i \(-0.613676\pi\)
−0.349582 + 0.936906i \(0.613676\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.62070e7 1.33246 0.666230 − 0.745747i \(-0.267907\pi\)
0.666230 + 0.745747i \(0.267907\pi\)
\(828\) 0 0
\(829\) −1.17710e7 −0.594876 −0.297438 − 0.954741i \(-0.596132\pi\)
−0.297438 + 0.954741i \(0.596132\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.24253e6 −0.111976
\(834\) 0 0
\(835\) −144768. −0.00718549
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.44898e7 −0.710651 −0.355326 − 0.934743i \(-0.615630\pi\)
−0.355326 + 0.934743i \(0.615630\pi\)
\(840\) 0 0
\(841\) −1.91329e7 −0.932804
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.15907e6 −0.200380
\(846\) 0 0
\(847\) 1.11879e7 0.535847
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.39574e7 −0.660666
\(852\) 0 0
\(853\) 1.77865e7 0.836984 0.418492 − 0.908220i \(-0.362559\pi\)
0.418492 + 0.908220i \(0.362559\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.79124e7 −1.76331 −0.881656 − 0.471893i \(-0.843571\pi\)
−0.881656 + 0.471893i \(0.843571\pi\)
\(858\) 0 0
\(859\) 3.32376e7 1.53690 0.768451 − 0.639909i \(-0.221028\pi\)
0.768451 + 0.639909i \(0.221028\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.33166e6 −0.106571 −0.0532853 − 0.998579i \(-0.516969\pi\)
−0.0532853 + 0.998579i \(0.516969\pi\)
\(864\) 0 0
\(865\) −3.33862e6 −0.151715
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.89066e7 2.19694
\(870\) 0 0
\(871\) −2.81472e7 −1.25716
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8.19437e6 0.361822
\(876\) 0 0
\(877\) −3.38189e7 −1.48477 −0.742386 − 0.669972i \(-0.766306\pi\)
−0.742386 + 0.669972i \(0.766306\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.65707e7 −1.15336 −0.576678 − 0.816972i \(-0.695651\pi\)
−0.576678 + 0.816972i \(0.695651\pi\)
\(882\) 0 0
\(883\) 1.74913e7 0.754954 0.377477 − 0.926019i \(-0.376792\pi\)
0.377477 + 0.926019i \(0.376792\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.77452e7 0.757305 0.378652 − 0.925539i \(-0.376388\pi\)
0.378652 + 0.925539i \(0.376388\pi\)
\(888\) 0 0
\(889\) 1.41018e7 0.598440
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.38755e7 0.582266
\(894\) 0 0
\(895\) −6.45517e6 −0.269370
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.41399e6 0.140885
\(900\) 0 0
\(901\) −2.54739e7 −1.04540
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.09824e7 −0.851596
\(906\) 0 0
\(907\) −2.82335e7 −1.13958 −0.569792 − 0.821789i \(-0.692976\pi\)
−0.569792 + 0.821789i \(0.692976\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.71757e7 −0.685674 −0.342837 − 0.939395i \(-0.611388\pi\)
−0.342837 + 0.939395i \(0.611388\pi\)
\(912\) 0 0
\(913\) −6.85264e7 −2.72070
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.33544e6 0.0917160
\(918\) 0 0
\(919\) 2.42273e7 0.946273 0.473137 − 0.880989i \(-0.343122\pi\)
0.473137 + 0.880989i \(0.343122\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −4.94807e7 −1.91175
\(924\) 0 0
\(925\) 2.61827e7 1.00614
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.45919e7 −0.934874 −0.467437 − 0.884026i \(-0.654822\pi\)
−0.467437 + 0.884026i \(0.654822\pi\)
\(930\) 0 0
\(931\) 4.46106e6 0.168680
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.86501e7 0.697674
\(936\) 0 0
\(937\) −1.31199e7 −0.488181 −0.244090 − 0.969753i \(-0.578489\pi\)
−0.244090 + 0.969753i \(0.578489\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −640776. −0.0235902 −0.0117951 − 0.999930i \(-0.503755\pi\)
−0.0117951 + 0.999930i \(0.503755\pi\)
\(942\) 0 0
\(943\) −2.98144e6 −0.109181
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.01502e7 −0.730135 −0.365068 − 0.930981i \(-0.618954\pi\)
−0.365068 + 0.930981i \(0.618954\pi\)
\(948\) 0 0
\(949\) −1.16466e7 −0.419791
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3.33217e7 1.18849 0.594244 − 0.804285i \(-0.297451\pi\)
0.594244 + 0.804285i \(0.297451\pi\)
\(954\) 0 0
\(955\) −4.84787e6 −0.172006
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.09345e7 −0.383932
\(960\) 0 0
\(961\) −2.01727e7 −0.704621
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −7.33843e6 −0.253679
\(966\) 0 0
\(967\) 4.51857e7 1.55394 0.776970 − 0.629537i \(-0.216755\pi\)
0.776970 + 0.629537i \(0.216755\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2.62935e7 −0.894953 −0.447477 − 0.894296i \(-0.647677\pi\)
−0.447477 + 0.894296i \(0.647677\pi\)
\(972\) 0 0
\(973\) 1.22766e7 0.415714
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.02548e7 −0.678879 −0.339440 − 0.940628i \(-0.610237\pi\)
−0.339440 + 0.940628i \(0.610237\pi\)
\(978\) 0 0
\(979\) 3.55468e7 1.18534
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −9.43782e6 −0.311521 −0.155761 − 0.987795i \(-0.549783\pi\)
−0.155761 + 0.987795i \(0.549783\pi\)
\(984\) 0 0
\(985\) 1.34748e7 0.442517
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.00128e6 −0.260117
\(990\) 0 0
\(991\) 1.53265e7 0.495747 0.247874 − 0.968792i \(-0.420268\pi\)
0.247874 + 0.968792i \(0.420268\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −6.31360e6 −0.202171
\(996\) 0 0
\(997\) −2.16514e6 −0.0689841 −0.0344920 − 0.999405i \(-0.510981\pi\)
−0.0344920 + 0.999405i \(0.510981\pi\)
\(998\) 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 504.6.a.b.1.1 1
3.2 odd 2 56.6.a.b.1.1 ✓ 1
4.3 odd 2 1008.6.a.h.1.1 1
12.11 even 2 112.6.a.a.1.1 1
21.2 odd 6 392.6.i.a.361.1 2
21.5 even 6 392.6.i.f.361.1 2
21.11 odd 6 392.6.i.a.177.1 2
21.17 even 6 392.6.i.f.177.1 2
21.20 even 2 392.6.a.a.1.1 1
24.5 odd 2 448.6.a.a.1.1 1
24.11 even 2 448.6.a.p.1.1 1
84.83 odd 2 784.6.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.6.a.b.1.1 ✓ 1 3.2 odd 2
112.6.a.a.1.1 1 12.11 even 2
392.6.a.a.1.1 1 21.20 even 2
392.6.i.a.177.1 2 21.11 odd 6
392.6.i.a.361.1 2 21.2 odd 6
392.6.i.f.177.1 2 21.17 even 6
392.6.i.f.361.1 2 21.5 even 6
448.6.a.a.1.1 1 24.5 odd 2
448.6.a.p.1.1 1 24.11 even 2
504.6.a.b.1.1 1 1.1 even 1 trivial
784.6.a.n.1.1 1 84.83 odd 2
1008.6.a.h.1.1 1 4.3 odd 2