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Properties

Label 252.6.a.c.1.1
Level $252$
Weight $6$
Character 252.1
Self dual yes
Analytic conductor $40.417$
Analytic rank $1$
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] = [252,6,Mod(1,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("252.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 252.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: \(40.4167225929\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 252.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+34.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+34.0000 q^{5} -49.0000 q^{7} +332.000 q^{11} -1026.00 q^{13} -922.000 q^{17} +452.000 q^{19} +3776.00 q^{23} -1969.00 q^{25} -1166.00 q^{29} -9792.00 q^{31} -1666.00 q^{35} +2390.00 q^{37} +7230.00 q^{41} +4652.00 q^{43} -24672.0 q^{47} +2401.00 q^{49} -1110.00 q^{53} +11288.0 q^{55} -46892.0 q^{59} -9762.00 q^{61} -34884.0 q^{65} -26252.0 q^{67} -65440.0 q^{71} -5606.00 q^{73} -16268.0 q^{77} -9840.00 q^{79} -61108.0 q^{83} -31348.0 q^{85} +62958.0 q^{89} +50274.0 q^{91} +15368.0 q^{95} -37838.0 q^{97} +O(q^{100})\)

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
\(5\) 34.0000 0.608210 0.304105 − 0.952638i \(-0.401643\pi\)
0.304105 + 0.952638i \(0.401643\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 332.000 0.827287 0.413644 − 0.910439i \(-0.364256\pi\)
0.413644 + 0.910439i \(0.364256\pi\)
\(12\) 0 0
\(13\) −1026.00 −1.68379 −0.841897 − 0.539638i \(-0.818561\pi\)
−0.841897 + 0.539638i \(0.818561\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −922.000 −0.773764 −0.386882 − 0.922129i \(-0.626448\pi\)
−0.386882 + 0.922129i \(0.626448\pi\)
\(18\) 0 0
\(19\) 452.000 0.287246 0.143623 − 0.989632i \(-0.454125\pi\)
0.143623 + 0.989632i \(0.454125\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3776.00 1.48838 0.744188 − 0.667971i \(-0.232837\pi\)
0.744188 + 0.667971i \(0.232837\pi\)
\(24\) 0 0
\(25\) −1969.00 −0.630080
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1166.00 −0.257456 −0.128728 − 0.991680i \(-0.541089\pi\)
−0.128728 + 0.991680i \(0.541089\pi\)
\(30\) 0 0
\(31\) −9792.00 −1.83007 −0.915034 − 0.403377i \(-0.867836\pi\)
−0.915034 + 0.403377i \(0.867836\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1666.00 −0.229882
\(36\) 0 0
\(37\) 2390.00 0.287008 0.143504 − 0.989650i \(-0.454163\pi\)
0.143504 + 0.989650i \(0.454163\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7230.00 0.671705 0.335853 − 0.941915i \(-0.390976\pi\)
0.335853 + 0.941915i \(0.390976\pi\)
\(42\) 0 0
\(43\) 4652.00 0.383679 0.191840 − 0.981426i \(-0.438555\pi\)
0.191840 + 0.981426i \(0.438555\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −24672.0 −1.62914 −0.814572 − 0.580062i \(-0.803028\pi\)
−0.814572 + 0.580062i \(0.803028\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1110.00 −0.0542792 −0.0271396 − 0.999632i \(-0.508640\pi\)
−0.0271396 + 0.999632i \(0.508640\pi\)
\(54\) 0 0
\(55\) 11288.0 0.503165
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −46892.0 −1.75375 −0.876877 − 0.480715i \(-0.840377\pi\)
−0.876877 + 0.480715i \(0.840377\pi\)
\(60\) 0 0
\(61\) −9762.00 −0.335903 −0.167952 − 0.985795i \(-0.553715\pi\)
−0.167952 + 0.985795i \(0.553715\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −34884.0 −1.02410
\(66\) 0 0
\(67\) −26252.0 −0.714456 −0.357228 − 0.934017i \(-0.616278\pi\)
−0.357228 + 0.934017i \(0.616278\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −65440.0 −1.54063 −0.770313 − 0.637666i \(-0.779900\pi\)
−0.770313 + 0.637666i \(0.779900\pi\)
\(72\) 0 0
\(73\) −5606.00 −0.123125 −0.0615625 − 0.998103i \(-0.519608\pi\)
−0.0615625 + 0.998103i \(0.519608\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −16268.0 −0.312685
\(78\) 0 0
\(79\) −9840.00 −0.177389 −0.0886946 − 0.996059i \(-0.528270\pi\)
−0.0886946 + 0.996059i \(0.528270\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −61108.0 −0.973650 −0.486825 − 0.873500i \(-0.661845\pi\)
−0.486825 + 0.873500i \(0.661845\pi\)
\(84\) 0 0
\(85\) −31348.0 −0.470611
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 62958.0 0.842512 0.421256 − 0.906942i \(-0.361589\pi\)
0.421256 + 0.906942i \(0.361589\pi\)
\(90\) 0 0
\(91\) 50274.0 0.636414
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 15368.0 0.174706
\(96\) 0 0
\(97\) −37838.0 −0.408318 −0.204159 − 0.978938i \(-0.565446\pi\)
−0.204159 + 0.978938i \(0.565446\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 56146.0 0.547666 0.273833 − 0.961777i \(-0.411709\pi\)
0.273833 + 0.961777i \(0.411709\pi\)
\(102\) 0 0
\(103\) −26392.0 −0.245120 −0.122560 − 0.992461i \(-0.539110\pi\)
−0.122560 + 0.992461i \(0.539110\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −47124.0 −0.397908 −0.198954 − 0.980009i \(-0.563754\pi\)
−0.198954 + 0.980009i \(0.563754\pi\)
\(108\) 0 0
\(109\) −221474. −1.78549 −0.892743 − 0.450566i \(-0.851222\pi\)
−0.892743 + 0.450566i \(0.851222\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −54194.0 −0.399259 −0.199630 − 0.979871i \(-0.563974\pi\)
−0.199630 + 0.979871i \(0.563974\pi\)
\(114\) 0 0
\(115\) 128384. 0.905245
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 45178.0 0.292455
\(120\) 0 0
\(121\) −50827.0 −0.315596
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −173196. −0.991432
\(126\) 0 0
\(127\) −245760. −1.35208 −0.676039 − 0.736866i \(-0.736305\pi\)
−0.676039 + 0.736866i \(0.736305\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 150268. 0.765047 0.382524 − 0.923946i \(-0.375055\pi\)
0.382524 + 0.923946i \(0.375055\pi\)
\(132\) 0 0
\(133\) −22148.0 −0.108569
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 401638. 1.82824 0.914120 − 0.405443i \(-0.132883\pi\)
0.914120 + 0.405443i \(0.132883\pi\)
\(138\) 0 0
\(139\) 374092. 1.64226 0.821129 − 0.570743i \(-0.193345\pi\)
0.821129 + 0.570743i \(0.193345\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −340632. −1.39298
\(144\) 0 0
\(145\) −39644.0 −0.156588
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 456042. 1.68283 0.841413 − 0.540393i \(-0.181724\pi\)
0.841413 + 0.540393i \(0.181724\pi\)
\(150\) 0 0
\(151\) −8024.00 −0.0286384 −0.0143192 − 0.999897i \(-0.504558\pi\)
−0.0143192 + 0.999897i \(0.504558\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −332928. −1.11307
\(156\) 0 0
\(157\) 110078. 0.356411 0.178206 − 0.983993i \(-0.442971\pi\)
0.178206 + 0.983993i \(0.442971\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −185024. −0.562553
\(162\) 0 0
\(163\) −3628.00 −0.0106954 −0.00534772 − 0.999986i \(-0.501702\pi\)
−0.00534772 + 0.999986i \(0.501702\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −192824. −0.535020 −0.267510 − 0.963555i \(-0.586201\pi\)
−0.267510 + 0.963555i \(0.586201\pi\)
\(168\) 0 0
\(169\) 681383. 1.83516
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −157142. −0.399188 −0.199594 − 0.979879i \(-0.563962\pi\)
−0.199594 + 0.979879i \(0.563962\pi\)
\(174\) 0 0
\(175\) 96481.0 0.238148
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 446868. 1.04243 0.521215 − 0.853426i \(-0.325479\pi\)
0.521215 + 0.853426i \(0.325479\pi\)
\(180\) 0 0
\(181\) 805638. 1.82786 0.913931 − 0.405869i \(-0.133031\pi\)
0.913931 + 0.405869i \(0.133031\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 81260.0 0.174561
\(186\) 0 0
\(187\) −306104. −0.640125
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 747912. 1.48343 0.741715 − 0.670715i \(-0.234013\pi\)
0.741715 + 0.670715i \(0.234013\pi\)
\(192\) 0 0
\(193\) −577534. −1.11605 −0.558026 − 0.829824i \(-0.688441\pi\)
−0.558026 + 0.829824i \(0.688441\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 771098. 1.41561 0.707806 − 0.706407i \(-0.249685\pi\)
0.707806 + 0.706407i \(0.249685\pi\)
\(198\) 0 0
\(199\) 557240. 0.997492 0.498746 − 0.866748i \(-0.333794\pi\)
0.498746 + 0.866748i \(0.333794\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 57134.0 0.0973093
\(204\) 0 0
\(205\) 245820. 0.408538
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 150064. 0.237635
\(210\) 0 0
\(211\) −19660.0 −0.0304003 −0.0152001 − 0.999884i \(-0.504839\pi\)
−0.0152001 + 0.999884i \(0.504839\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 158168. 0.233358
\(216\) 0 0
\(217\) 479808. 0.691701
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 945972. 1.30286
\(222\) 0 0
\(223\) −896848. −1.20769 −0.603847 − 0.797100i \(-0.706366\pi\)
−0.603847 + 0.797100i \(0.706366\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −234228. −0.301699 −0.150850 − 0.988557i \(-0.548201\pi\)
−0.150850 + 0.988557i \(0.548201\pi\)
\(228\) 0 0
\(229\) −1.03563e6 −1.30501 −0.652506 − 0.757784i \(-0.726282\pi\)
−0.652506 + 0.757784i \(0.726282\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −457114. −0.551613 −0.275807 − 0.961213i \(-0.588945\pi\)
−0.275807 + 0.961213i \(0.588945\pi\)
\(234\) 0 0
\(235\) −838848. −0.990863
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −676344. −0.765901 −0.382951 − 0.923769i \(-0.625092\pi\)
−0.382951 + 0.923769i \(0.625092\pi\)
\(240\) 0 0
\(241\) −96670.0 −0.107213 −0.0536067 − 0.998562i \(-0.517072\pi\)
−0.0536067 + 0.998562i \(0.517072\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 81634.0 0.0868872
\(246\) 0 0
\(247\) −463752. −0.483664
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −288876. −0.289419 −0.144710 − 0.989474i \(-0.546225\pi\)
−0.144710 + 0.989474i \(0.546225\pi\)
\(252\) 0 0
\(253\) 1.25363e6 1.23131
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 711846. 0.672285 0.336142 − 0.941811i \(-0.390878\pi\)
0.336142 + 0.941811i \(0.390878\pi\)
\(258\) 0 0
\(259\) −117110. −0.108479
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.87368e6 1.67034 0.835172 − 0.549988i \(-0.185368\pi\)
0.835172 + 0.549988i \(0.185368\pi\)
\(264\) 0 0
\(265\) −37740.0 −0.0330132
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.37660e6 1.15992 0.579960 − 0.814645i \(-0.303068\pi\)
0.579960 + 0.814645i \(0.303068\pi\)
\(270\) 0 0
\(271\) −781776. −0.646635 −0.323317 − 0.946291i \(-0.604798\pi\)
−0.323317 + 0.946291i \(0.604798\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −653708. −0.521257
\(276\) 0 0
\(277\) 2.06932e6 1.62042 0.810210 − 0.586139i \(-0.199353\pi\)
0.810210 + 0.586139i \(0.199353\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.87911e6 −1.41967 −0.709835 − 0.704368i \(-0.751230\pi\)
−0.709835 + 0.704368i \(0.751230\pi\)
\(282\) 0 0
\(283\) 670156. 0.497405 0.248702 − 0.968580i \(-0.419996\pi\)
0.248702 + 0.968580i \(0.419996\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −354270. −0.253881
\(288\) 0 0
\(289\) −569773. −0.401289
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.69611e6 −1.15421 −0.577105 − 0.816670i \(-0.695818\pi\)
−0.577105 + 0.816670i \(0.695818\pi\)
\(294\) 0 0
\(295\) −1.59433e6 −1.06665
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.87418e6 −2.50612
\(300\) 0 0
\(301\) −227948. −0.145017
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −331908. −0.204300
\(306\) 0 0
\(307\) −1.09459e6 −0.662834 −0.331417 − 0.943484i \(-0.607527\pi\)
−0.331417 + 0.943484i \(0.607527\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.21249e6 −0.710848 −0.355424 − 0.934705i \(-0.615663\pi\)
−0.355424 + 0.934705i \(0.615663\pi\)
\(312\) 0 0
\(313\) 1.69436e6 0.977564 0.488782 − 0.872406i \(-0.337441\pi\)
0.488782 + 0.872406i \(0.337441\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −333342. −0.186312 −0.0931562 − 0.995652i \(-0.529696\pi\)
−0.0931562 + 0.995652i \(0.529696\pi\)
\(318\) 0 0
\(319\) −387112. −0.212990
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −416744. −0.222261
\(324\) 0 0
\(325\) 2.02019e6 1.06092
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.20893e6 0.615759
\(330\) 0 0
\(331\) 1.83614e6 0.921162 0.460581 − 0.887618i \(-0.347641\pi\)
0.460581 + 0.887618i \(0.347641\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −892568. −0.434540
\(336\) 0 0
\(337\) −973518. −0.466949 −0.233474 − 0.972363i \(-0.575009\pi\)
−0.233474 + 0.972363i \(0.575009\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.25094e6 −1.51399
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.39810e6 −1.51500 −0.757500 − 0.652835i \(-0.773579\pi\)
−0.757500 + 0.652835i \(0.773579\pi\)
\(348\) 0 0
\(349\) −34370.0 −0.0151048 −0.00755242 − 0.999971i \(-0.502404\pi\)
−0.00755242 + 0.999971i \(0.502404\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.50239e6 1.06885 0.534427 − 0.845215i \(-0.320528\pi\)
0.534427 + 0.845215i \(0.320528\pi\)
\(354\) 0 0
\(355\) −2.22496e6 −0.937025
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.02800e6 1.23999 0.619997 − 0.784604i \(-0.287134\pi\)
0.619997 + 0.784604i \(0.287134\pi\)
\(360\) 0 0
\(361\) −2.27180e6 −0.917490
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −190604. −0.0748859
\(366\) 0 0
\(367\) −3.20944e6 −1.24384 −0.621919 − 0.783081i \(-0.713647\pi\)
−0.621919 + 0.783081i \(0.713647\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 54390.0 0.0205156
\(372\) 0 0
\(373\) 1.51505e6 0.563837 0.281919 − 0.959438i \(-0.409029\pi\)
0.281919 + 0.959438i \(0.409029\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.19632e6 0.433503
\(378\) 0 0
\(379\) 643516. 0.230124 0.115062 − 0.993358i \(-0.463293\pi\)
0.115062 + 0.993358i \(0.463293\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.75082e6 −1.65490 −0.827449 − 0.561541i \(-0.810209\pi\)
−0.827449 + 0.561541i \(0.810209\pi\)
\(384\) 0 0
\(385\) −553112. −0.190178
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −379574. −0.127181 −0.0635905 − 0.997976i \(-0.520255\pi\)
−0.0635905 + 0.997976i \(0.520255\pi\)
\(390\) 0 0
\(391\) −3.48147e6 −1.15165
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −334560. −0.107890
\(396\) 0 0
\(397\) −5.42133e6 −1.72635 −0.863176 − 0.504902i \(-0.831528\pi\)
−0.863176 + 0.504902i \(0.831528\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.20643e6 1.92744 0.963720 − 0.266915i \(-0.0860042\pi\)
0.963720 + 0.266915i \(0.0860042\pi\)
\(402\) 0 0
\(403\) 1.00466e7 3.08146
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 793480. 0.237438
\(408\) 0 0
\(409\) −4.25397e6 −1.25744 −0.628719 − 0.777633i \(-0.716420\pi\)
−0.628719 + 0.777633i \(0.716420\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.29771e6 0.662857
\(414\) 0 0
\(415\) −2.07767e6 −0.592184
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 725484. 0.201880 0.100940 − 0.994893i \(-0.467815\pi\)
0.100940 + 0.994893i \(0.467815\pi\)
\(420\) 0 0
\(421\) −6.49867e6 −1.78698 −0.893489 − 0.449086i \(-0.851750\pi\)
−0.893489 + 0.449086i \(0.851750\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.81542e6 0.487533
\(426\) 0 0
\(427\) 478338. 0.126959
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.96524e6 0.509592 0.254796 − 0.966995i \(-0.417992\pi\)
0.254796 + 0.966995i \(0.417992\pi\)
\(432\) 0 0
\(433\) 4.33531e6 1.11122 0.555611 − 0.831442i \(-0.312484\pi\)
0.555611 + 0.831442i \(0.312484\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.70675e6 0.427530
\(438\) 0 0
\(439\) 6.47748e6 1.60415 0.802075 − 0.597224i \(-0.203730\pi\)
0.802075 + 0.597224i \(0.203730\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.32696e6 −1.04755 −0.523774 − 0.851857i \(-0.675476\pi\)
−0.523774 + 0.851857i \(0.675476\pi\)
\(444\) 0 0
\(445\) 2.14057e6 0.512424
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −482210. −0.112881 −0.0564404 − 0.998406i \(-0.517975\pi\)
−0.0564404 + 0.998406i \(0.517975\pi\)
\(450\) 0 0
\(451\) 2.40036e6 0.555693
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.70932e6 0.387074
\(456\) 0 0
\(457\) 8.52164e6 1.90868 0.954339 − 0.298725i \(-0.0965613\pi\)
0.954339 + 0.298725i \(0.0965613\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.99857e6 1.31461 0.657303 − 0.753627i \(-0.271697\pi\)
0.657303 + 0.753627i \(0.271697\pi\)
\(462\) 0 0
\(463\) −4.59483e6 −0.996133 −0.498066 − 0.867139i \(-0.665956\pi\)
−0.498066 + 0.867139i \(0.665956\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.84330e6 −1.87639 −0.938193 − 0.346113i \(-0.887501\pi\)
−0.938193 + 0.346113i \(0.887501\pi\)
\(468\) 0 0
\(469\) 1.28635e6 0.270039
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.54446e6 0.317413
\(474\) 0 0
\(475\) −889988. −0.180988
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.56062e6 1.30649 0.653245 − 0.757146i \(-0.273407\pi\)
0.653245 + 0.757146i \(0.273407\pi\)
\(480\) 0 0
\(481\) −2.45214e6 −0.483262
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.28649e6 −0.248343
\(486\) 0 0
\(487\) 7.87772e6 1.50514 0.752572 − 0.658510i \(-0.228813\pi\)
0.752572 + 0.658510i \(0.228813\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −637860. −0.119405 −0.0597024 − 0.998216i \(-0.519015\pi\)
−0.0597024 + 0.998216i \(0.519015\pi\)
\(492\) 0 0
\(493\) 1.07505e6 0.199210
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.20656e6 0.582302
\(498\) 0 0
\(499\) −4.93646e6 −0.887492 −0.443746 − 0.896153i \(-0.646351\pi\)
−0.443746 + 0.896153i \(0.646351\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −226872. −0.0399817 −0.0199908 − 0.999800i \(-0.506364\pi\)
−0.0199908 + 0.999800i \(0.506364\pi\)
\(504\) 0 0
\(505\) 1.90896e6 0.333096
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.37404e6 −0.919404 −0.459702 − 0.888073i \(-0.652044\pi\)
−0.459702 + 0.888073i \(0.652044\pi\)
\(510\) 0 0
\(511\) 274694. 0.0465368
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −897328. −0.149085
\(516\) 0 0
\(517\) −8.19110e6 −1.34777
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9.61419e6 1.55174 0.775869 − 0.630894i \(-0.217312\pi\)
0.775869 + 0.630894i \(0.217312\pi\)
\(522\) 0 0
\(523\) 4.96430e6 0.793604 0.396802 − 0.917904i \(-0.370120\pi\)
0.396802 + 0.917904i \(0.370120\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.02822e6 1.41604
\(528\) 0 0
\(529\) 7.82183e6 1.21526
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −7.41798e6 −1.13101
\(534\) 0 0
\(535\) −1.60222e6 −0.242012
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 797132. 0.118184
\(540\) 0 0
\(541\) 1.20449e7 1.76934 0.884668 − 0.466221i \(-0.154385\pi\)
0.884668 + 0.466221i \(0.154385\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.53012e6 −1.08595
\(546\) 0 0
\(547\) 4.23695e6 0.605459 0.302730 − 0.953077i \(-0.402102\pi\)
0.302730 + 0.953077i \(0.402102\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −527032. −0.0739534
\(552\) 0 0
\(553\) 482160. 0.0670468
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.02575e7 1.40089 0.700444 − 0.713708i \(-0.252986\pi\)
0.700444 + 0.713708i \(0.252986\pi\)
\(558\) 0 0
\(559\) −4.77295e6 −0.646037
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.40777e6 0.719031 0.359515 − 0.933139i \(-0.382942\pi\)
0.359515 + 0.933139i \(0.382942\pi\)
\(564\) 0 0
\(565\) −1.84260e6 −0.242834
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.38967e6 −0.697882 −0.348941 − 0.937145i \(-0.613459\pi\)
−0.348941 + 0.937145i \(0.613459\pi\)
\(570\) 0 0
\(571\) −8.24552e6 −1.05835 −0.529173 − 0.848514i \(-0.677498\pi\)
−0.529173 + 0.848514i \(0.677498\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −7.43494e6 −0.937795
\(576\) 0 0
\(577\) −1.15408e6 −0.144310 −0.0721549 − 0.997393i \(-0.522988\pi\)
−0.0721549 + 0.997393i \(0.522988\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.99429e6 0.368005
\(582\) 0 0
\(583\) −368520. −0.0449045
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.16464e6 0.858221 0.429111 − 0.903252i \(-0.358827\pi\)
0.429111 + 0.903252i \(0.358827\pi\)
\(588\) 0 0
\(589\) −4.42598e6 −0.525680
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.45534e7 −1.69953 −0.849763 − 0.527165i \(-0.823255\pi\)
−0.849763 + 0.527165i \(0.823255\pi\)
\(594\) 0 0
\(595\) 1.53605e6 0.177874
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.04320e7 1.18795 0.593977 − 0.804482i \(-0.297557\pi\)
0.593977 + 0.804482i \(0.297557\pi\)
\(600\) 0 0
\(601\) 416858. 0.0470763 0.0235381 − 0.999723i \(-0.492507\pi\)
0.0235381 + 0.999723i \(0.492507\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.72812e6 −0.191949
\(606\) 0 0
\(607\) −7.90834e6 −0.871191 −0.435596 − 0.900143i \(-0.643462\pi\)
−0.435596 + 0.900143i \(0.643462\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.53135e7 2.74314
\(612\) 0 0
\(613\) −1.13761e7 −1.22277 −0.611383 − 0.791335i \(-0.709387\pi\)
−0.611383 + 0.791335i \(0.709387\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.77271e6 0.927728 0.463864 − 0.885906i \(-0.346463\pi\)
0.463864 + 0.885906i \(0.346463\pi\)
\(618\) 0 0
\(619\) 1.44110e7 1.51171 0.755854 − 0.654740i \(-0.227222\pi\)
0.755854 + 0.654740i \(0.227222\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.08494e6 −0.318439
\(624\) 0 0
\(625\) 264461. 0.0270808
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.20358e6 −0.222076
\(630\) 0 0
\(631\) −1.29466e7 −1.29444 −0.647221 − 0.762303i \(-0.724069\pi\)
−0.647221 + 0.762303i \(0.724069\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.35584e6 −0.822348
\(636\) 0 0
\(637\) −2.46343e6 −0.240542
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.89035e6 0.470105 0.235052 − 0.971983i \(-0.424474\pi\)
0.235052 + 0.971983i \(0.424474\pi\)
\(642\) 0 0
\(643\) 1.22604e6 0.116943 0.0584717 − 0.998289i \(-0.481377\pi\)
0.0584717 + 0.998289i \(0.481377\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.21098e7 −1.13731 −0.568654 − 0.822577i \(-0.692536\pi\)
−0.568654 + 0.822577i \(0.692536\pi\)
\(648\) 0 0
\(649\) −1.55681e7 −1.45086
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.28697e6 −0.852298 −0.426149 − 0.904653i \(-0.640130\pi\)
−0.426149 + 0.904653i \(0.640130\pi\)
\(654\) 0 0
\(655\) 5.10911e6 0.465310
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −451612. −0.0405090 −0.0202545 − 0.999795i \(-0.506448\pi\)
−0.0202545 + 0.999795i \(0.506448\pi\)
\(660\) 0 0
\(661\) −1.85508e6 −0.165143 −0.0825714 − 0.996585i \(-0.526313\pi\)
−0.0825714 + 0.996585i \(0.526313\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −753032. −0.0660327
\(666\) 0 0
\(667\) −4.40282e6 −0.383192
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.24098e6 −0.277889
\(672\) 0 0
\(673\) 2.14534e7 1.82582 0.912911 − 0.408158i \(-0.133829\pi\)
0.912911 + 0.408158i \(0.133829\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.56987e7 −1.31641 −0.658205 − 0.752839i \(-0.728684\pi\)
−0.658205 + 0.752839i \(0.728684\pi\)
\(678\) 0 0
\(679\) 1.85406e6 0.154330
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.40250e7 −1.15040 −0.575201 − 0.818012i \(-0.695076\pi\)
−0.575201 + 0.818012i \(0.695076\pi\)
\(684\) 0 0
\(685\) 1.36557e7 1.11196
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.13886e6 0.0913950
\(690\) 0 0
\(691\) −1.89819e7 −1.51232 −0.756160 − 0.654387i \(-0.772927\pi\)
−0.756160 + 0.654387i \(0.772927\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.27191e7 0.998839
\(696\) 0 0
\(697\) −6.66606e6 −0.519741
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.22806e7 −1.71250 −0.856251 − 0.516560i \(-0.827212\pi\)
−0.856251 + 0.516560i \(0.827212\pi\)
\(702\) 0 0
\(703\) 1.08028e6 0.0824419
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.75115e6 −0.206998
\(708\) 0 0
\(709\) −476266. −0.0355823 −0.0177911 − 0.999842i \(-0.505663\pi\)
−0.0177911 + 0.999842i \(0.505663\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.69746e7 −2.72383
\(714\) 0 0
\(715\) −1.15815e7 −0.847226
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 263568. 0.0190139 0.00950693 − 0.999955i \(-0.496974\pi\)
0.00950693 + 0.999955i \(0.496974\pi\)
\(720\) 0 0
\(721\) 1.29321e6 0.0926468
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.29585e6 0.162218
\(726\) 0 0
\(727\) 9.28319e6 0.651420 0.325710 − 0.945470i \(-0.394397\pi\)
0.325710 + 0.945470i \(0.394397\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.28914e6 −0.296877
\(732\) 0 0
\(733\) −1.89547e7 −1.30304 −0.651520 − 0.758631i \(-0.725868\pi\)
−0.651520 + 0.758631i \(0.725868\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8.71566e6 −0.591060
\(738\) 0 0
\(739\) 1.95454e7 1.31654 0.658269 − 0.752783i \(-0.271289\pi\)
0.658269 + 0.752783i \(0.271289\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.54683e7 −1.02795 −0.513973 − 0.857806i \(-0.671827\pi\)
−0.513973 + 0.857806i \(0.671827\pi\)
\(744\) 0 0
\(745\) 1.55054e7 1.02351
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.30908e6 0.150395
\(750\) 0 0
\(751\) −1.45188e7 −0.939354 −0.469677 − 0.882838i \(-0.655630\pi\)
−0.469677 + 0.882838i \(0.655630\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −272816. −0.0174182
\(756\) 0 0
\(757\) 8.54477e6 0.541952 0.270976 − 0.962586i \(-0.412654\pi\)
0.270976 + 0.962586i \(0.412654\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8.50398e6 0.532305 0.266153 − 0.963931i \(-0.414247\pi\)
0.266153 + 0.963931i \(0.414247\pi\)
\(762\) 0 0
\(763\) 1.08522e7 0.674850
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.81112e7 2.95296
\(768\) 0 0
\(769\) −1.66581e7 −1.01580 −0.507901 − 0.861415i \(-0.669578\pi\)
−0.507901 + 0.861415i \(0.669578\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.17326e7 −1.30817 −0.654083 − 0.756423i \(-0.726945\pi\)
−0.654083 + 0.756423i \(0.726945\pi\)
\(774\) 0 0
\(775\) 1.92804e7 1.15309
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.26796e6 0.192945
\(780\) 0 0
\(781\) −2.17261e7 −1.27454
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.74265e6 0.216773
\(786\) 0 0
\(787\) 2.05602e6 0.118329 0.0591644 − 0.998248i \(-0.481156\pi\)
0.0591644 + 0.998248i \(0.481156\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.65551e6 0.150906
\(792\) 0 0
\(793\) 1.00158e7 0.565592
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.17641e7 −1.77129 −0.885647 − 0.464359i \(-0.846285\pi\)
−0.885647 + 0.464359i \(0.846285\pi\)
\(798\) 0 0
\(799\) 2.27476e7 1.26057
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.86119e6 −0.101860
\(804\) 0 0
\(805\) −6.29082e6 −0.342151
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.14050e7 1.14986 0.574930 − 0.818203i \(-0.305029\pi\)
0.574930 + 0.818203i \(0.305029\pi\)
\(810\) 0 0
\(811\) −6.61432e6 −0.353129 −0.176564 − 0.984289i \(-0.556498\pi\)
−0.176564 + 0.984289i \(0.556498\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −123352. −0.00650507
\(816\) 0 0
\(817\) 2.10270e6 0.110211
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.78006e7 −0.921674 −0.460837 − 0.887485i \(-0.652451\pi\)
−0.460837 + 0.887485i \(0.652451\pi\)
\(822\) 0 0
\(823\) −1.23818e7 −0.637212 −0.318606 − 0.947887i \(-0.603215\pi\)
−0.318606 + 0.947887i \(0.603215\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.17279e7 1.10473 0.552363 − 0.833604i \(-0.313726\pi\)
0.552363 + 0.833604i \(0.313726\pi\)
\(828\) 0 0
\(829\) −1.35893e7 −0.686771 −0.343385 − 0.939195i \(-0.611574\pi\)
−0.343385 + 0.939195i \(0.611574\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.21372e6 −0.110538
\(834\) 0 0
\(835\) −6.55602e6 −0.325405
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 171272. 0.00840004 0.00420002 − 0.999991i \(-0.498663\pi\)
0.00420002 + 0.999991i \(0.498663\pi\)
\(840\) 0 0
\(841\) −1.91516e7 −0.933716
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.31670e7 1.11617
\(846\) 0 0
\(847\) 2.49052e6 0.119284
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 9.02464e6 0.427175
\(852\) 0 0
\(853\) 2.90172e7 1.36547 0.682737 − 0.730664i \(-0.260789\pi\)
0.682737 + 0.730664i \(0.260789\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.84967e7 1.79049 0.895243 − 0.445578i \(-0.147002\pi\)
0.895243 + 0.445578i \(0.147002\pi\)
\(858\) 0 0
\(859\) −1.98458e7 −0.917670 −0.458835 − 0.888521i \(-0.651733\pi\)
−0.458835 + 0.888521i \(0.651733\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.70833e7 0.780808 0.390404 − 0.920644i \(-0.372335\pi\)
0.390404 + 0.920644i \(0.372335\pi\)
\(864\) 0 0
\(865\) −5.34283e6 −0.242790
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −3.26688e6 −0.146752
\(870\) 0 0
\(871\) 2.69346e7 1.20300
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8.48660e6 0.374726
\(876\) 0 0
\(877\) −2.53810e7 −1.11432 −0.557159 − 0.830406i \(-0.688109\pi\)
−0.557159 + 0.830406i \(0.688109\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.59580e7 1.12676 0.563381 − 0.826198i \(-0.309501\pi\)
0.563381 + 0.826198i \(0.309501\pi\)
\(882\) 0 0
\(883\) 4.37666e6 0.188904 0.0944520 − 0.995529i \(-0.469890\pi\)
0.0944520 + 0.995529i \(0.469890\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −3.23310e7 −1.37978 −0.689889 − 0.723915i \(-0.742341\pi\)
−0.689889 + 0.723915i \(0.742341\pi\)
\(888\) 0 0
\(889\) 1.20422e7 0.511038
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.11517e7 −0.467966
\(894\) 0 0
\(895\) 1.51935e7 0.634017
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1.14175e7 0.471163
\(900\) 0 0
\(901\) 1.02342e6 0.0419993
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.73917e7 1.11173
\(906\) 0 0
\(907\) −3.67108e7 −1.48175 −0.740876 − 0.671642i \(-0.765589\pi\)
−0.740876 + 0.671642i \(0.765589\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −3.52261e7 −1.40627 −0.703135 − 0.711056i \(-0.748217\pi\)
−0.703135 + 0.711056i \(0.748217\pi\)
\(912\) 0 0
\(913\) −2.02879e7 −0.805488
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7.36313e6 −0.289161
\(918\) 0 0
\(919\) −3.16978e6 −0.123806 −0.0619029 − 0.998082i \(-0.519717\pi\)
−0.0619029 + 0.998082i \(0.519717\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 6.71414e7 2.59410
\(924\) 0 0
\(925\) −4.70591e6 −0.180838
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.98030e7 1.13298 0.566488 − 0.824070i \(-0.308302\pi\)
0.566488 + 0.824070i \(0.308302\pi\)
\(930\) 0 0
\(931\) 1.08525e6 0.0410352
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.04075e7 −0.389331
\(936\) 0 0
\(937\) −1.62312e7 −0.603952 −0.301976 − 0.953316i \(-0.597646\pi\)
−0.301976 + 0.953316i \(0.597646\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.09759e7 −0.404079 −0.202040 − 0.979377i \(-0.564757\pi\)
−0.202040 + 0.979377i \(0.564757\pi\)
\(942\) 0 0
\(943\) 2.73005e7 0.999749
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.50304e6 −0.126932 −0.0634658 − 0.997984i \(-0.520215\pi\)
−0.0634658 + 0.997984i \(0.520215\pi\)
\(948\) 0 0
\(949\) 5.75176e6 0.207317
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.00120e7 0.357098 0.178549 − 0.983931i \(-0.442860\pi\)
0.178549 + 0.983931i \(0.442860\pi\)
\(954\) 0 0
\(955\) 2.54290e7 0.902238
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.96803e7 −0.691010
\(960\) 0 0
\(961\) 6.72541e7 2.34915
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.96362e7 −0.678794
\(966\) 0 0
\(967\) −652984. −0.0224562 −0.0112281 − 0.999937i \(-0.503574\pi\)
−0.0112281 + 0.999937i \(0.503574\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.24897e7 0.425112 0.212556 − 0.977149i \(-0.431821\pi\)
0.212556 + 0.977149i \(0.431821\pi\)
\(972\) 0 0
\(973\) −1.83305e7 −0.620715
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 7.43408e6 0.249167 0.124584 − 0.992209i \(-0.460241\pi\)
0.124584 + 0.992209i \(0.460241\pi\)
\(978\) 0 0
\(979\) 2.09021e7 0.696999
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.44904e7 −0.808373 −0.404187 − 0.914677i \(-0.632445\pi\)
−0.404187 + 0.914677i \(0.632445\pi\)
\(984\) 0 0
\(985\) 2.62173e7 0.860990
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.75660e7 0.571059
\(990\) 0 0
\(991\) 4.87464e7 1.57673 0.788367 − 0.615206i \(-0.210927\pi\)
0.788367 + 0.615206i \(0.210927\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.89462e7 0.606685
\(996\) 0 0
\(997\) 2.35242e6 0.0749510 0.0374755 − 0.999298i \(-0.488068\pi\)
0.0374755 + 0.999298i \(0.488068\pi\)
\(998\) 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 252.6.a.c.1.1 1
3.2 odd 2 84.6.a.b.1.1 ✓ 1
4.3 odd 2 1008.6.a.u.1.1 1
12.11 even 2 336.6.a.e.1.1 1
21.2 odd 6 588.6.i.c.361.1 2
21.5 even 6 588.6.i.e.361.1 2
21.11 odd 6 588.6.i.c.373.1 2
21.17 even 6 588.6.i.e.373.1 2
21.20 even 2 588.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.a.b.1.1 ✓ 1 3.2 odd 2
252.6.a.c.1.1 1 1.1 even 1 trivial
336.6.a.e.1.1 1 12.11 even 2
588.6.a.b.1.1 1 21.20 even 2
588.6.i.c.361.1 2 21.2 odd 6
588.6.i.c.373.1 2 21.11 odd 6
588.6.i.e.361.1 2 21.5 even 6
588.6.i.e.373.1 2 21.17 even 6
1008.6.a.u.1.1 1 4.3 odd 2