↑

Properties

Label 784.6.a.i.1.1
Level $784$
Weight $6$
Character 784.1
Self dual yes
Analytic conductor $125.741$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,6,Mod(1,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, 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("784.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 784.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: \(125.740914733\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 784.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+10.0000 q^{3} -84.0000 q^{5} -143.000 q^{9} +336.000 q^{11} -584.000 q^{13} -840.000 q^{15} +1458.00 q^{17} +470.000 q^{19} +4200.00 q^{23} +3931.00 q^{25} -3860.00 q^{27} +4866.00 q^{29} -7372.00 q^{31} +3360.00 q^{33} +14330.0 q^{37} -5840.00 q^{39} -6222.00 q^{41} -3704.00 q^{43} +12012.0 q^{45} -1812.00 q^{47} +14580.0 q^{51} -37242.0 q^{53} -28224.0 q^{55} +4700.00 q^{57} +34302.0 q^{59} -24476.0 q^{61} +49056.0 q^{65} +17452.0 q^{67} +42000.0 q^{69} -28224.0 q^{71} -3602.00 q^{73} +39310.0 q^{75} -42872.0 q^{79} -3851.00 q^{81} -35202.0 q^{83} -122472. q^{85} +48660.0 q^{87} -26730.0 q^{89} -73720.0 q^{93} -39480.0 q^{95} +16978.0 q^{97} -48048.0 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 10.0000 0.641500 0.320750 − 0.947164i \(-0.396065\pi\)
0.320750 + 0.947164i \(0.396065\pi\)
\(4\) 0 0
\(5\) −84.0000 −1.50264 −0.751319 − 0.659939i \(-0.770582\pi\)
−0.751319 + 0.659939i \(0.770582\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −143.000 −0.588477
\(10\) 0 0
\(11\) 336.000 0.837255 0.418627 − 0.908158i \(-0.362511\pi\)
0.418627 + 0.908158i \(0.362511\pi\)
\(12\) 0 0
\(13\) −584.000 −0.958417 −0.479208 − 0.877701i \(-0.659076\pi\)
−0.479208 + 0.877701i \(0.659076\pi\)
\(14\) 0 0
\(15\) −840.000 −0.963943
\(16\) 0 0
\(17\) 1458.00 1.22359 0.611794 − 0.791017i \(-0.290448\pi\)
0.611794 + 0.791017i \(0.290448\pi\)
\(18\) 0 0
\(19\) 470.000 0.298685 0.149343 − 0.988786i \(-0.452284\pi\)
0.149343 + 0.988786i \(0.452284\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4200.00 1.65550 0.827751 − 0.561096i \(-0.189620\pi\)
0.827751 + 0.561096i \(0.189620\pi\)
\(24\) 0 0
\(25\) 3931.00 1.25792
\(26\) 0 0
\(27\) −3860.00 −1.01901
\(28\) 0 0
\(29\) 4866.00 1.07443 0.537214 − 0.843446i \(-0.319477\pi\)
0.537214 + 0.843446i \(0.319477\pi\)
\(30\) 0 0
\(31\) −7372.00 −1.37778 −0.688892 − 0.724864i \(-0.741903\pi\)
−0.688892 + 0.724864i \(0.741903\pi\)
\(32\) 0 0
\(33\) 3360.00 0.537099
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 14330.0 1.72085 0.860423 − 0.509581i \(-0.170200\pi\)
0.860423 + 0.509581i \(0.170200\pi\)
\(38\) 0 0
\(39\) −5840.00 −0.614825
\(40\) 0 0
\(41\) −6222.00 −0.578057 −0.289028 − 0.957321i \(-0.593332\pi\)
−0.289028 + 0.957321i \(0.593332\pi\)
\(42\) 0 0
\(43\) −3704.00 −0.305492 −0.152746 − 0.988265i \(-0.548812\pi\)
−0.152746 + 0.988265i \(0.548812\pi\)
\(44\) 0 0
\(45\) 12012.0 0.884268
\(46\) 0 0
\(47\) −1812.00 −0.119650 −0.0598251 − 0.998209i \(-0.519054\pi\)
−0.0598251 + 0.998209i \(0.519054\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 14580.0 0.784932
\(52\) 0 0
\(53\) −37242.0 −1.82114 −0.910570 − 0.413355i \(-0.864357\pi\)
−0.910570 + 0.413355i \(0.864357\pi\)
\(54\) 0 0
\(55\) −28224.0 −1.25809
\(56\) 0 0
\(57\) 4700.00 0.191607
\(58\) 0 0
\(59\) 34302.0 1.28289 0.641445 − 0.767169i \(-0.278335\pi\)
0.641445 + 0.767169i \(0.278335\pi\)
\(60\) 0 0
\(61\) −24476.0 −0.842201 −0.421101 − 0.907014i \(-0.638356\pi\)
−0.421101 + 0.907014i \(0.638356\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 49056.0 1.44015
\(66\) 0 0
\(67\) 17452.0 0.474961 0.237481 − 0.971392i \(-0.423678\pi\)
0.237481 + 0.971392i \(0.423678\pi\)
\(68\) 0 0
\(69\) 42000.0 1.06201
\(70\) 0 0
\(71\) −28224.0 −0.664466 −0.332233 − 0.943197i \(-0.607802\pi\)
−0.332233 + 0.943197i \(0.607802\pi\)
\(72\) 0 0
\(73\) −3602.00 −0.0791109 −0.0395555 − 0.999217i \(-0.512594\pi\)
−0.0395555 + 0.999217i \(0.512594\pi\)
\(74\) 0 0
\(75\) 39310.0 0.806956
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −42872.0 −0.772869 −0.386435 − 0.922317i \(-0.626294\pi\)
−0.386435 + 0.922317i \(0.626294\pi\)
\(80\) 0 0
\(81\) −3851.00 −0.0652170
\(82\) 0 0
\(83\) −35202.0 −0.560883 −0.280441 − 0.959871i \(-0.590481\pi\)
−0.280441 + 0.959871i \(0.590481\pi\)
\(84\) 0 0
\(85\) −122472. −1.83861
\(86\) 0 0
\(87\) 48660.0 0.689246
\(88\) 0 0
\(89\) −26730.0 −0.357704 −0.178852 − 0.983876i \(-0.557238\pi\)
−0.178852 + 0.983876i \(0.557238\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −73720.0 −0.883849
\(94\) 0 0
\(95\) −39480.0 −0.448816
\(96\) 0 0
\(97\) 16978.0 0.183213 0.0916067 − 0.995795i \(-0.470800\pi\)
0.0916067 + 0.995795i \(0.470800\pi\)
\(98\) 0 0
\(99\) −48048.0 −0.492705
\(100\) 0 0
\(101\) −99204.0 −0.967667 −0.483833 − 0.875160i \(-0.660756\pi\)
−0.483833 + 0.875160i \(0.660756\pi\)
\(102\) 0 0
\(103\) −131644. −1.22267 −0.611333 − 0.791373i \(-0.709366\pi\)
−0.611333 + 0.791373i \(0.709366\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −48852.0 −0.412499 −0.206250 − 0.978499i \(-0.566126\pi\)
−0.206250 + 0.978499i \(0.566126\pi\)
\(108\) 0 0
\(109\) −56374.0 −0.454478 −0.227239 − 0.973839i \(-0.572970\pi\)
−0.227239 + 0.973839i \(0.572970\pi\)
\(110\) 0 0
\(111\) 143300. 1.10392
\(112\) 0 0
\(113\) 8742.00 0.0644043 0.0322021 − 0.999481i \(-0.489748\pi\)
0.0322021 + 0.999481i \(0.489748\pi\)
\(114\) 0 0
\(115\) −352800. −2.48762
\(116\) 0 0
\(117\) 83512.0 0.564007
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −48155.0 −0.299005
\(122\) 0 0
\(123\) −62220.0 −0.370823
\(124\) 0 0
\(125\) −67704.0 −0.387560
\(126\) 0 0
\(127\) −315992. −1.73847 −0.869234 − 0.494401i \(-0.835388\pi\)
−0.869234 + 0.494401i \(0.835388\pi\)
\(128\) 0 0
\(129\) −37040.0 −0.195973
\(130\) 0 0
\(131\) −24666.0 −0.125580 −0.0627900 − 0.998027i \(-0.520000\pi\)
−0.0627900 + 0.998027i \(0.520000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 324240. 1.53120
\(136\) 0 0
\(137\) 303234. 1.38031 0.690155 − 0.723662i \(-0.257542\pi\)
0.690155 + 0.723662i \(0.257542\pi\)
\(138\) 0 0
\(139\) 250586. 1.10007 0.550034 − 0.835142i \(-0.314615\pi\)
0.550034 + 0.835142i \(0.314615\pi\)
\(140\) 0 0
\(141\) −18120.0 −0.0767557
\(142\) 0 0
\(143\) −196224. −0.802439
\(144\) 0 0
\(145\) −408744. −1.61448
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −60594.0 −0.223596 −0.111798 − 0.993731i \(-0.535661\pi\)
−0.111798 + 0.993731i \(0.535661\pi\)
\(150\) 0 0
\(151\) −124448. −0.444166 −0.222083 − 0.975028i \(-0.571286\pi\)
−0.222083 + 0.975028i \(0.571286\pi\)
\(152\) 0 0
\(153\) −208494. −0.720054
\(154\) 0 0
\(155\) 619248. 2.07031
\(156\) 0 0
\(157\) −76040.0 −0.246203 −0.123101 − 0.992394i \(-0.539284\pi\)
−0.123101 + 0.992394i \(0.539284\pi\)
\(158\) 0 0
\(159\) −372420. −1.16826
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −124256. −0.366310 −0.183155 − 0.983084i \(-0.558631\pi\)
−0.183155 + 0.983084i \(0.558631\pi\)
\(164\) 0 0
\(165\) −282240. −0.807065
\(166\) 0 0
\(167\) −72420.0 −0.200940 −0.100470 − 0.994940i \(-0.532035\pi\)
−0.100470 + 0.994940i \(0.532035\pi\)
\(168\) 0 0
\(169\) −30237.0 −0.0814370
\(170\) 0 0
\(171\) −67210.0 −0.175770
\(172\) 0 0
\(173\) 441552. 1.12167 0.560837 − 0.827926i \(-0.310479\pi\)
0.560837 + 0.827926i \(0.310479\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 343020. 0.822974
\(178\) 0 0
\(179\) 10692.0 0.0249417 0.0124709 − 0.999922i \(-0.496030\pi\)
0.0124709 + 0.999922i \(0.496030\pi\)
\(180\) 0 0
\(181\) 546064. 1.23893 0.619465 − 0.785024i \(-0.287349\pi\)
0.619465 + 0.785024i \(0.287349\pi\)
\(182\) 0 0
\(183\) −244760. −0.540272
\(184\) 0 0
\(185\) −1.20372e6 −2.58581
\(186\) 0 0
\(187\) 489888. 1.02445
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 575976. 1.14241 0.571204 − 0.820808i \(-0.306477\pi\)
0.571204 + 0.820808i \(0.306477\pi\)
\(192\) 0 0
\(193\) −413938. −0.799912 −0.399956 − 0.916534i \(-0.630975\pi\)
−0.399956 + 0.916534i \(0.630975\pi\)
\(194\) 0 0
\(195\) 490560. 0.923859
\(196\) 0 0
\(197\) −494946. −0.908641 −0.454320 − 0.890838i \(-0.650118\pi\)
−0.454320 + 0.890838i \(0.650118\pi\)
\(198\) 0 0
\(199\) 520364. 0.931482 0.465741 − 0.884921i \(-0.345788\pi\)
0.465741 + 0.884921i \(0.345788\pi\)
\(200\) 0 0
\(201\) 174520. 0.304688
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 522648. 0.868610
\(206\) 0 0
\(207\) −600600. −0.974225
\(208\) 0 0
\(209\) 157920. 0.250076
\(210\) 0 0
\(211\) −183284. −0.283412 −0.141706 − 0.989909i \(-0.545259\pi\)
−0.141706 + 0.989909i \(0.545259\pi\)
\(212\) 0 0
\(213\) −282240. −0.426255
\(214\) 0 0
\(215\) 311136. 0.459044
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −36020.0 −0.0507497
\(220\) 0 0
\(221\) −851472. −1.17271
\(222\) 0 0
\(223\) −1.27746e6 −1.72023 −0.860115 − 0.510100i \(-0.829608\pi\)
−0.860115 + 0.510100i \(0.829608\pi\)
\(224\) 0 0
\(225\) −562133. −0.740257
\(226\) 0 0
\(227\) −1.28764e6 −1.65856 −0.829279 − 0.558835i \(-0.811248\pi\)
−0.829279 + 0.558835i \(0.811248\pi\)
\(228\) 0 0
\(229\) −350936. −0.442221 −0.221110 − 0.975249i \(-0.570968\pi\)
−0.221110 + 0.975249i \(0.570968\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 836154. 1.00901 0.504506 − 0.863408i \(-0.331675\pi\)
0.504506 + 0.863408i \(0.331675\pi\)
\(234\) 0 0
\(235\) 152208. 0.179791
\(236\) 0 0
\(237\) −428720. −0.495796
\(238\) 0 0
\(239\) −774336. −0.876869 −0.438434 − 0.898763i \(-0.644467\pi\)
−0.438434 + 0.898763i \(0.644467\pi\)
\(240\) 0 0
\(241\) 1.15285e6 1.27859 0.639293 − 0.768963i \(-0.279227\pi\)
0.639293 + 0.768963i \(0.279227\pi\)
\(242\) 0 0
\(243\) 899470. 0.977172
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −274480. −0.286265
\(248\) 0 0
\(249\) −352020. −0.359806
\(250\) 0 0
\(251\) 1.35801e6 1.36056 0.680282 − 0.732951i \(-0.261858\pi\)
0.680282 + 0.732951i \(0.261858\pi\)
\(252\) 0 0
\(253\) 1.41120e6 1.38608
\(254\) 0 0
\(255\) −1.22472e6 −1.17947
\(256\) 0 0
\(257\) 317742. 0.300083 0.150042 − 0.988680i \(-0.452059\pi\)
0.150042 + 0.988680i \(0.452059\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −695838. −0.632276
\(262\) 0 0
\(263\) −1.05101e6 −0.936951 −0.468475 − 0.883477i \(-0.655196\pi\)
−0.468475 + 0.883477i \(0.655196\pi\)
\(264\) 0 0
\(265\) 3.12833e6 2.73651
\(266\) 0 0
\(267\) −267300. −0.229467
\(268\) 0 0
\(269\) −1.18958e6 −1.00234 −0.501169 − 0.865349i \(-0.667097\pi\)
−0.501169 + 0.865349i \(0.667097\pi\)
\(270\) 0 0
\(271\) −1.43008e6 −1.18287 −0.591435 − 0.806353i \(-0.701438\pi\)
−0.591435 + 0.806353i \(0.701438\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.32082e6 1.05320
\(276\) 0 0
\(277\) 63302.0 0.0495699 0.0247849 − 0.999693i \(-0.492110\pi\)
0.0247849 + 0.999693i \(0.492110\pi\)
\(278\) 0 0
\(279\) 1.05420e6 0.810795
\(280\) 0 0
\(281\) −496614. −0.375192 −0.187596 − 0.982246i \(-0.560070\pi\)
−0.187596 + 0.982246i \(0.560070\pi\)
\(282\) 0 0
\(283\) −1.15842e6 −0.859803 −0.429902 − 0.902876i \(-0.641452\pi\)
−0.429902 + 0.902876i \(0.641452\pi\)
\(284\) 0 0
\(285\) −394800. −0.287915
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 705907. 0.497168
\(290\) 0 0
\(291\) 169780. 0.117531
\(292\) 0 0
\(293\) −1.43886e6 −0.979151 −0.489575 − 0.871961i \(-0.662848\pi\)
−0.489575 + 0.871961i \(0.662848\pi\)
\(294\) 0 0
\(295\) −2.88137e6 −1.92772
\(296\) 0 0
\(297\) −1.29696e6 −0.853170
\(298\) 0 0
\(299\) −2.45280e6 −1.58666
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −992040. −0.620758
\(304\) 0 0
\(305\) 2.05598e6 1.26552
\(306\) 0 0
\(307\) −989098. −0.598954 −0.299477 − 0.954104i \(-0.596812\pi\)
−0.299477 + 0.954104i \(0.596812\pi\)
\(308\) 0 0
\(309\) −1.31644e6 −0.784341
\(310\) 0 0
\(311\) −2.22050e6 −1.30182 −0.650909 − 0.759155i \(-0.725612\pi\)
−0.650909 + 0.759155i \(0.725612\pi\)
\(312\) 0 0
\(313\) −2.33008e6 −1.34434 −0.672171 − 0.740396i \(-0.734638\pi\)
−0.672171 + 0.740396i \(0.734638\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 427542. 0.238963 0.119481 − 0.992836i \(-0.461877\pi\)
0.119481 + 0.992836i \(0.461877\pi\)
\(318\) 0 0
\(319\) 1.63498e6 0.899569
\(320\) 0 0
\(321\) −488520. −0.264618
\(322\) 0 0
\(323\) 685260. 0.365468
\(324\) 0 0
\(325\) −2.29570e6 −1.20561
\(326\) 0 0
\(327\) −563740. −0.291548
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 396616. 0.198976 0.0994879 − 0.995039i \(-0.468280\pi\)
0.0994879 + 0.995039i \(0.468280\pi\)
\(332\) 0 0
\(333\) −2.04919e6 −1.01268
\(334\) 0 0
\(335\) −1.46597e6 −0.713695
\(336\) 0 0
\(337\) −3.21819e6 −1.54361 −0.771805 − 0.635860i \(-0.780646\pi\)
−0.771805 + 0.635860i \(0.780646\pi\)
\(338\) 0 0
\(339\) 87420.0 0.0413154
\(340\) 0 0
\(341\) −2.47699e6 −1.15356
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −3.52800e6 −1.59581
\(346\) 0 0
\(347\) −2.78018e6 −1.23951 −0.619755 − 0.784796i \(-0.712768\pi\)
−0.619755 + 0.784796i \(0.712768\pi\)
\(348\) 0 0
\(349\) 338800. 0.148895 0.0744475 − 0.997225i \(-0.476281\pi\)
0.0744475 + 0.997225i \(0.476281\pi\)
\(350\) 0 0
\(351\) 2.25424e6 0.976635
\(352\) 0 0
\(353\) 362046. 0.154642 0.0773209 − 0.997006i \(-0.475363\pi\)
0.0773209 + 0.997006i \(0.475363\pi\)
\(354\) 0 0
\(355\) 2.37082e6 0.998451
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −876528. −0.358946 −0.179473 − 0.983763i \(-0.557439\pi\)
−0.179473 + 0.983763i \(0.557439\pi\)
\(360\) 0 0
\(361\) −2.25520e6 −0.910787
\(362\) 0 0
\(363\) −481550. −0.191812
\(364\) 0 0
\(365\) 302568. 0.118875
\(366\) 0 0
\(367\) 2.98062e6 1.15516 0.577578 − 0.816335i \(-0.303998\pi\)
0.577578 + 0.816335i \(0.303998\pi\)
\(368\) 0 0
\(369\) 889746. 0.340173
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 3.91441e6 1.45678 0.728391 − 0.685162i \(-0.240268\pi\)
0.728391 + 0.685162i \(0.240268\pi\)
\(374\) 0 0
\(375\) −677040. −0.248620
\(376\) 0 0
\(377\) −2.84174e6 −1.02975
\(378\) 0 0
\(379\) −3.60661e6 −1.28974 −0.644868 − 0.764294i \(-0.723088\pi\)
−0.644868 + 0.764294i \(0.723088\pi\)
\(380\) 0 0
\(381\) −3.15992e6 −1.11523
\(382\) 0 0
\(383\) −2.66644e6 −0.928826 −0.464413 − 0.885619i \(-0.653735\pi\)
−0.464413 + 0.885619i \(0.653735\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 529672. 0.179775
\(388\) 0 0
\(389\) −213366. −0.0714910 −0.0357455 − 0.999361i \(-0.511381\pi\)
−0.0357455 + 0.999361i \(0.511381\pi\)
\(390\) 0 0
\(391\) 6.12360e6 2.02565
\(392\) 0 0
\(393\) −246660. −0.0805596
\(394\) 0 0
\(395\) 3.60125e6 1.16134
\(396\) 0 0
\(397\) 4.09408e6 1.30371 0.651854 − 0.758345i \(-0.273992\pi\)
0.651854 + 0.758345i \(0.273992\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 942366. 0.292657 0.146328 − 0.989236i \(-0.453254\pi\)
0.146328 + 0.989236i \(0.453254\pi\)
\(402\) 0 0
\(403\) 4.30525e6 1.32049
\(404\) 0 0
\(405\) 323484. 0.0979976
\(406\) 0 0
\(407\) 4.81488e6 1.44079
\(408\) 0 0
\(409\) 4.84561e6 1.43232 0.716160 − 0.697936i \(-0.245898\pi\)
0.716160 + 0.697936i \(0.245898\pi\)
\(410\) 0 0
\(411\) 3.03234e6 0.885469
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 2.95697e6 0.842804
\(416\) 0 0
\(417\) 2.50586e6 0.705694
\(418\) 0 0
\(419\) −1.73485e6 −0.482754 −0.241377 − 0.970431i \(-0.577599\pi\)
−0.241377 + 0.970431i \(0.577599\pi\)
\(420\) 0 0
\(421\) −1.65145e6 −0.454109 −0.227055 − 0.973882i \(-0.572910\pi\)
−0.227055 + 0.973882i \(0.572910\pi\)
\(422\) 0 0
\(423\) 259116. 0.0704115
\(424\) 0 0
\(425\) 5.73140e6 1.53918
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.96224e6 −0.514765
\(430\) 0 0
\(431\) −4.14360e6 −1.07445 −0.537223 − 0.843440i \(-0.680527\pi\)
−0.537223 + 0.843440i \(0.680527\pi\)
\(432\) 0 0
\(433\) 3.03966e6 0.779121 0.389561 − 0.921001i \(-0.372627\pi\)
0.389561 + 0.921001i \(0.372627\pi\)
\(434\) 0 0
\(435\) −4.08744e6 −1.03569
\(436\) 0 0
\(437\) 1.97400e6 0.494474
\(438\) 0 0
\(439\) 2.54271e6 0.629703 0.314852 − 0.949141i \(-0.398045\pi\)
0.314852 + 0.949141i \(0.398045\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.43210e6 0.588806 0.294403 − 0.955681i \(-0.404879\pi\)
0.294403 + 0.955681i \(0.404879\pi\)
\(444\) 0 0
\(445\) 2.24532e6 0.537500
\(446\) 0 0
\(447\) −605940. −0.143437
\(448\) 0 0
\(449\) 1.82853e6 0.428042 0.214021 − 0.976829i \(-0.431344\pi\)
0.214021 + 0.976829i \(0.431344\pi\)
\(450\) 0 0
\(451\) −2.09059e6 −0.483981
\(452\) 0 0
\(453\) −1.24448e6 −0.284933
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.58063e6 0.354030 0.177015 − 0.984208i \(-0.443356\pi\)
0.177015 + 0.984208i \(0.443356\pi\)
\(458\) 0 0
\(459\) −5.62788e6 −1.24685
\(460\) 0 0
\(461\) −5.09604e6 −1.11681 −0.558407 − 0.829567i \(-0.688587\pi\)
−0.558407 + 0.829567i \(0.688587\pi\)
\(462\) 0 0
\(463\) 7.02338e6 1.52263 0.761313 − 0.648384i \(-0.224555\pi\)
0.761313 + 0.648384i \(0.224555\pi\)
\(464\) 0 0
\(465\) 6.19248e6 1.32810
\(466\) 0 0
\(467\) −4.24845e6 −0.901443 −0.450722 − 0.892665i \(-0.648833\pi\)
−0.450722 + 0.892665i \(0.648833\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −760400. −0.157939
\(472\) 0 0
\(473\) −1.24454e6 −0.255775
\(474\) 0 0
\(475\) 1.84757e6 0.375722
\(476\) 0 0
\(477\) 5.32561e6 1.07170
\(478\) 0 0
\(479\) 559284. 0.111377 0.0556883 − 0.998448i \(-0.482265\pi\)
0.0556883 + 0.998448i \(0.482265\pi\)
\(480\) 0 0
\(481\) −8.36872e6 −1.64929
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.42615e6 −0.275303
\(486\) 0 0
\(487\) 1.32057e6 0.252312 0.126156 − 0.992010i \(-0.459736\pi\)
0.126156 + 0.992010i \(0.459736\pi\)
\(488\) 0 0
\(489\) −1.24256e6 −0.234988
\(490\) 0 0
\(491\) −6.27193e6 −1.17408 −0.587040 − 0.809558i \(-0.699707\pi\)
−0.587040 + 0.809558i \(0.699707\pi\)
\(492\) 0 0
\(493\) 7.09463e6 1.31466
\(494\) 0 0
\(495\) 4.03603e6 0.740358
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.93785e6 0.707959 0.353979 − 0.935253i \(-0.384828\pi\)
0.353979 + 0.935253i \(0.384828\pi\)
\(500\) 0 0
\(501\) −724200. −0.128903
\(502\) 0 0
\(503\) −7.59830e6 −1.33905 −0.669525 − 0.742790i \(-0.733502\pi\)
−0.669525 + 0.742790i \(0.733502\pi\)
\(504\) 0 0
\(505\) 8.33314e6 1.45405
\(506\) 0 0
\(507\) −302370. −0.0522419
\(508\) 0 0
\(509\) 7.82664e6 1.33900 0.669501 − 0.742812i \(-0.266508\pi\)
0.669501 + 0.742812i \(0.266508\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1.81420e6 −0.304363
\(514\) 0 0
\(515\) 1.10581e7 1.83722
\(516\) 0 0
\(517\) −608832. −0.100178
\(518\) 0 0
\(519\) 4.41552e6 0.719554
\(520\) 0 0
\(521\) −8.94454e6 −1.44366 −0.721828 − 0.692072i \(-0.756698\pi\)
−0.721828 + 0.692072i \(0.756698\pi\)
\(522\) 0 0
\(523\) 4.07481e6 0.651407 0.325704 − 0.945472i \(-0.394399\pi\)
0.325704 + 0.945472i \(0.394399\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.07484e7 −1.68584
\(528\) 0 0
\(529\) 1.12037e7 1.74069
\(530\) 0 0
\(531\) −4.90519e6 −0.754952
\(532\) 0 0
\(533\) 3.63365e6 0.554019
\(534\) 0 0
\(535\) 4.10357e6 0.619837
\(536\) 0 0
\(537\) 106920. 0.0160001
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.18676e7 −1.74329 −0.871644 − 0.490140i \(-0.836946\pi\)
−0.871644 + 0.490140i \(0.836946\pi\)
\(542\) 0 0
\(543\) 5.46064e6 0.794775
\(544\) 0 0
\(545\) 4.73542e6 0.682915
\(546\) 0 0
\(547\) 5.37801e6 0.768516 0.384258 − 0.923226i \(-0.374457\pi\)
0.384258 + 0.923226i \(0.374457\pi\)
\(548\) 0 0
\(549\) 3.50007e6 0.495616
\(550\) 0 0
\(551\) 2.28702e6 0.320916
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1.20372e7 −1.65880
\(556\) 0 0
\(557\) −5.64878e6 −0.771466 −0.385733 − 0.922611i \(-0.626051\pi\)
−0.385733 + 0.922611i \(0.626051\pi\)
\(558\) 0 0
\(559\) 2.16314e6 0.292789
\(560\) 0 0
\(561\) 4.89888e6 0.657188
\(562\) 0 0
\(563\) 4.56407e6 0.606850 0.303425 − 0.952855i \(-0.401870\pi\)
0.303425 + 0.952855i \(0.401870\pi\)
\(564\) 0 0
\(565\) −734328. −0.0967763
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.00165e6 1.03609 0.518047 − 0.855352i \(-0.326659\pi\)
0.518047 + 0.855352i \(0.326659\pi\)
\(570\) 0 0
\(571\) 1.37164e7 1.76055 0.880275 − 0.474464i \(-0.157358\pi\)
0.880275 + 0.474464i \(0.157358\pi\)
\(572\) 0 0
\(573\) 5.75976e6 0.732855
\(574\) 0 0
\(575\) 1.65102e7 2.08249
\(576\) 0 0
\(577\) −6.09797e6 −0.762510 −0.381255 − 0.924470i \(-0.624508\pi\)
−0.381255 + 0.924470i \(0.624508\pi\)
\(578\) 0 0
\(579\) −4.13938e6 −0.513144
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.25133e7 −1.52476
\(584\) 0 0
\(585\) −7.01501e6 −0.847498
\(586\) 0 0
\(587\) −8.08462e6 −0.968422 −0.484211 − 0.874951i \(-0.660893\pi\)
−0.484211 + 0.874951i \(0.660893\pi\)
\(588\) 0 0
\(589\) −3.46484e6 −0.411524
\(590\) 0 0
\(591\) −4.94946e6 −0.582893
\(592\) 0 0
\(593\) −1.41575e6 −0.165330 −0.0826649 − 0.996577i \(-0.526343\pi\)
−0.0826649 + 0.996577i \(0.526343\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5.20364e6 0.597546
\(598\) 0 0
\(599\) −8.75460e6 −0.996941 −0.498470 − 0.866907i \(-0.666105\pi\)
−0.498470 + 0.866907i \(0.666105\pi\)
\(600\) 0 0
\(601\) −8.70276e6 −0.982813 −0.491407 − 0.870930i \(-0.663517\pi\)
−0.491407 + 0.870930i \(0.663517\pi\)
\(602\) 0 0
\(603\) −2.49564e6 −0.279504
\(604\) 0 0
\(605\) 4.04502e6 0.449296
\(606\) 0 0
\(607\) −1.69578e7 −1.86809 −0.934045 − 0.357157i \(-0.883746\pi\)
−0.934045 + 0.357157i \(0.883746\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.05821e6 0.114675
\(612\) 0 0
\(613\) 1.76743e7 1.89973 0.949866 − 0.312658i \(-0.101220\pi\)
0.949866 + 0.312658i \(0.101220\pi\)
\(614\) 0 0
\(615\) 5.22648e6 0.557213
\(616\) 0 0
\(617\) −9.70636e6 −1.02646 −0.513232 − 0.858250i \(-0.671552\pi\)
−0.513232 + 0.858250i \(0.671552\pi\)
\(618\) 0 0
\(619\) 1.48739e7 1.56027 0.780133 − 0.625613i \(-0.215151\pi\)
0.780133 + 0.625613i \(0.215151\pi\)
\(620\) 0 0
\(621\) −1.62120e7 −1.68697
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −6.59724e6 −0.675557
\(626\) 0 0
\(627\) 1.57920e6 0.160424
\(628\) 0 0
\(629\) 2.08931e7 2.10561
\(630\) 0 0
\(631\) −1.26353e7 −1.26331 −0.631656 − 0.775248i \(-0.717625\pi\)
−0.631656 + 0.775248i \(0.717625\pi\)
\(632\) 0 0
\(633\) −1.83284e6 −0.181809
\(634\) 0 0
\(635\) 2.65433e7 2.61229
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 4.03603e6 0.391023
\(640\) 0 0
\(641\) 6.23398e6 0.599267 0.299634 − 0.954054i \(-0.403136\pi\)
0.299634 + 0.954054i \(0.403136\pi\)
\(642\) 0 0
\(643\) 1.06874e7 1.01940 0.509701 − 0.860352i \(-0.329756\pi\)
0.509701 + 0.860352i \(0.329756\pi\)
\(644\) 0 0
\(645\) 3.11136e6 0.294477
\(646\) 0 0
\(647\) 1.83258e7 1.72109 0.860544 − 0.509376i \(-0.170124\pi\)
0.860544 + 0.509376i \(0.170124\pi\)
\(648\) 0 0
\(649\) 1.15255e7 1.07411
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.28857e6 −0.668897 −0.334448 − 0.942414i \(-0.608550\pi\)
−0.334448 + 0.942414i \(0.608550\pi\)
\(654\) 0 0
\(655\) 2.07194e6 0.188701
\(656\) 0 0
\(657\) 515086. 0.0465550
\(658\) 0 0
\(659\) −4.54337e6 −0.407534 −0.203767 − 0.979019i \(-0.565319\pi\)
−0.203767 + 0.979019i \(0.565319\pi\)
\(660\) 0 0
\(661\) 2.10021e7 1.86964 0.934821 − 0.355120i \(-0.115560\pi\)
0.934821 + 0.355120i \(0.115560\pi\)
\(662\) 0 0
\(663\) −8.51472e6 −0.752292
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 2.04372e7 1.77872
\(668\) 0 0
\(669\) −1.27746e7 −1.10353
\(670\) 0 0
\(671\) −8.22394e6 −0.705137
\(672\) 0 0
\(673\) 3.46923e6 0.295253 0.147627 − 0.989043i \(-0.452837\pi\)
0.147627 + 0.989043i \(0.452837\pi\)
\(674\) 0 0
\(675\) −1.51737e7 −1.28183
\(676\) 0 0
\(677\) 1.80916e7 1.51707 0.758536 − 0.651631i \(-0.225915\pi\)
0.758536 + 0.651631i \(0.225915\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.28764e7 −1.06397
\(682\) 0 0
\(683\) −4.67752e6 −0.383675 −0.191838 − 0.981427i \(-0.561445\pi\)
−0.191838 + 0.981427i \(0.561445\pi\)
\(684\) 0 0
\(685\) −2.54717e7 −2.07411
\(686\) 0 0
\(687\) −3.50936e6 −0.283685
\(688\) 0 0
\(689\) 2.17493e7 1.74541
\(690\) 0 0
\(691\) 1.68960e7 1.34614 0.673069 − 0.739579i \(-0.264976\pi\)
0.673069 + 0.739579i \(0.264976\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.10492e7 −1.65300
\(696\) 0 0
\(697\) −9.07168e6 −0.707303
\(698\) 0 0
\(699\) 8.36154e6 0.647282
\(700\) 0 0
\(701\) 2.40964e6 0.185207 0.0926035 − 0.995703i \(-0.470481\pi\)
0.0926035 + 0.995703i \(0.470481\pi\)
\(702\) 0 0
\(703\) 6.73510e6 0.513991
\(704\) 0 0
\(705\) 1.52208e6 0.115336
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −5.77010e6 −0.431090 −0.215545 − 0.976494i \(-0.569153\pi\)
−0.215545 + 0.976494i \(0.569153\pi\)
\(710\) 0 0
\(711\) 6.13070e6 0.454816
\(712\) 0 0
\(713\) −3.09624e7 −2.28092
\(714\) 0 0
\(715\) 1.64828e7 1.20578
\(716\) 0 0
\(717\) −7.74336e6 −0.562512
\(718\) 0 0
\(719\) −1.43716e7 −1.03677 −0.518385 − 0.855147i \(-0.673467\pi\)
−0.518385 + 0.855147i \(0.673467\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1.15285e7 0.820214
\(724\) 0 0
\(725\) 1.91282e7 1.35154
\(726\) 0 0
\(727\) −1.40705e7 −0.987353 −0.493676 − 0.869646i \(-0.664347\pi\)
−0.493676 + 0.869646i \(0.664347\pi\)
\(728\) 0 0
\(729\) 9.93049e6 0.692073
\(730\) 0 0
\(731\) −5.40043e6 −0.373796
\(732\) 0 0
\(733\) 3.75000e6 0.257793 0.128897 − 0.991658i \(-0.458856\pi\)
0.128897 + 0.991658i \(0.458856\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.86387e6 0.397664
\(738\) 0 0
\(739\) −2.61318e7 −1.76019 −0.880093 − 0.474802i \(-0.842520\pi\)
−0.880093 + 0.474802i \(0.842520\pi\)
\(740\) 0 0
\(741\) −2.74480e6 −0.183639
\(742\) 0 0
\(743\) 159072. 0.0105711 0.00528557 − 0.999986i \(-0.498318\pi\)
0.00528557 + 0.999986i \(0.498318\pi\)
\(744\) 0 0
\(745\) 5.08990e6 0.335984
\(746\) 0 0
\(747\) 5.03389e6 0.330067
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 2.65311e7 1.71654 0.858272 − 0.513196i \(-0.171539\pi\)
0.858272 + 0.513196i \(0.171539\pi\)
\(752\) 0 0
\(753\) 1.35801e7 0.872802
\(754\) 0 0
\(755\) 1.04536e7 0.667421
\(756\) 0 0
\(757\) −1.52032e7 −0.964260 −0.482130 − 0.876100i \(-0.660137\pi\)
−0.482130 + 0.876100i \(0.660137\pi\)
\(758\) 0 0
\(759\) 1.41120e7 0.889169
\(760\) 0 0
\(761\) −4.71380e6 −0.295059 −0.147530 − 0.989058i \(-0.547132\pi\)
−0.147530 + 0.989058i \(0.547132\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 1.75135e7 1.08198
\(766\) 0 0
\(767\) −2.00324e7 −1.22954
\(768\) 0 0
\(769\) 1.58977e6 0.0969434 0.0484717 − 0.998825i \(-0.484565\pi\)
0.0484717 + 0.998825i \(0.484565\pi\)
\(770\) 0 0
\(771\) 3.17742e6 0.192504
\(772\) 0 0
\(773\) 9.69095e6 0.583334 0.291667 − 0.956520i \(-0.405790\pi\)
0.291667 + 0.956520i \(0.405790\pi\)
\(774\) 0 0
\(775\) −2.89793e7 −1.73314
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.92434e6 −0.172657
\(780\) 0 0
\(781\) −9.48326e6 −0.556327
\(782\) 0 0
\(783\) −1.87828e7 −1.09485
\(784\) 0 0
\(785\) 6.38736e6 0.369954
\(786\) 0 0
\(787\) −1.57170e6 −0.0904549 −0.0452275 − 0.998977i \(-0.514401\pi\)
−0.0452275 + 0.998977i \(0.514401\pi\)
\(788\) 0 0
\(789\) −1.05101e7 −0.601054
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1.42940e7 0.807180
\(794\) 0 0
\(795\) 3.12833e7 1.75547
\(796\) 0 0
\(797\) 2.25298e6 0.125635 0.0628175 − 0.998025i \(-0.479991\pi\)
0.0628175 + 0.998025i \(0.479991\pi\)
\(798\) 0 0
\(799\) −2.64190e6 −0.146403
\(800\) 0 0
\(801\) 3.82239e6 0.210501
\(802\) 0 0
\(803\) −1.21027e6 −0.0662360
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.18958e7 −0.643000
\(808\) 0 0
\(809\) −2.37938e7 −1.27818 −0.639090 − 0.769132i \(-0.720689\pi\)
−0.639090 + 0.769132i \(0.720689\pi\)
\(810\) 0 0
\(811\) 5.32300e6 0.284187 0.142093 − 0.989853i \(-0.454617\pi\)
0.142093 + 0.989853i \(0.454617\pi\)
\(812\) 0 0
\(813\) −1.43008e7 −0.758812
\(814\) 0 0
\(815\) 1.04375e7 0.550431
\(816\) 0 0
\(817\) −1.74088e6 −0.0912460
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.48802e7 0.770464 0.385232 − 0.922820i \(-0.374121\pi\)
0.385232 + 0.922820i \(0.374121\pi\)
\(822\) 0 0
\(823\) −2.00601e7 −1.03236 −0.516182 − 0.856479i \(-0.672647\pi\)
−0.516182 + 0.856479i \(0.672647\pi\)
\(824\) 0 0
\(825\) 1.32082e7 0.675628
\(826\) 0 0
\(827\) −1.21539e7 −0.617949 −0.308975 − 0.951070i \(-0.599986\pi\)
−0.308975 + 0.951070i \(0.599986\pi\)
\(828\) 0 0
\(829\) −3.21197e7 −1.62325 −0.811625 − 0.584179i \(-0.801417\pi\)
−0.811625 + 0.584179i \(0.801417\pi\)
\(830\) 0 0
\(831\) 633020. 0.0317991
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 6.08328e6 0.301941
\(836\) 0 0
\(837\) 2.84559e7 1.40397
\(838\) 0 0
\(839\) −1.01320e6 −0.0496922 −0.0248461 − 0.999691i \(-0.507910\pi\)
−0.0248461 + 0.999691i \(0.507910\pi\)
\(840\) 0 0
\(841\) 3.16681e6 0.154394
\(842\) 0 0
\(843\) −4.96614e6 −0.240686
\(844\) 0 0
\(845\) 2.53991e6 0.122370
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −1.15842e7 −0.551564
\(850\) 0 0
\(851\) 6.01860e7 2.84886
\(852\) 0 0
\(853\) −234824. −0.0110502 −0.00552510 − 0.999985i \(-0.501759\pi\)
−0.00552510 + 0.999985i \(0.501759\pi\)
\(854\) 0 0
\(855\) 5.64564e6 0.264118
\(856\) 0 0
\(857\) −2.83802e7 −1.31997 −0.659985 − 0.751279i \(-0.729437\pi\)
−0.659985 + 0.751279i \(0.729437\pi\)
\(858\) 0 0
\(859\) 4.00081e7 1.84997 0.924986 − 0.380001i \(-0.124076\pi\)
0.924986 + 0.380001i \(0.124076\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.08030e7 0.950823 0.475411 − 0.879764i \(-0.342299\pi\)
0.475411 + 0.879764i \(0.342299\pi\)
\(864\) 0 0
\(865\) −3.70904e7 −1.68547
\(866\) 0 0
\(867\) 7.05907e6 0.318933
\(868\) 0 0
\(869\) −1.44050e7 −0.647088
\(870\) 0 0
\(871\) −1.01920e7 −0.455211
\(872\) 0 0
\(873\) −2.42785e6 −0.107817
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 3.03559e7 1.33273 0.666367 − 0.745624i \(-0.267848\pi\)
0.666367 + 0.745624i \(0.267848\pi\)
\(878\) 0 0
\(879\) −1.43886e7 −0.628125
\(880\) 0 0
\(881\) 2.58936e7 1.12396 0.561981 − 0.827150i \(-0.310039\pi\)
0.561981 + 0.827150i \(0.310039\pi\)
\(882\) 0 0
\(883\) 1.88813e7 0.814950 0.407475 − 0.913216i \(-0.366409\pi\)
0.407475 + 0.913216i \(0.366409\pi\)
\(884\) 0 0
\(885\) −2.88137e7 −1.23663
\(886\) 0 0
\(887\) −2.34431e7 −1.00048 −0.500238 − 0.865888i \(-0.666754\pi\)
−0.500238 + 0.865888i \(0.666754\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.29394e6 −0.0546033
\(892\) 0 0
\(893\) −851640. −0.0357378
\(894\) 0 0
\(895\) −898128. −0.0374784
\(896\) 0 0
\(897\) −2.45280e7 −1.01784
\(898\) 0 0
\(899\) −3.58722e7 −1.48033
\(900\) 0 0
\(901\) −5.42988e7 −2.22833
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4.58694e7 −1.86166
\(906\) 0 0
\(907\) 5.60873e6 0.226384 0.113192 − 0.993573i \(-0.463892\pi\)
0.113192 + 0.993573i \(0.463892\pi\)
\(908\) 0 0
\(909\) 1.41862e7 0.569450
\(910\) 0 0
\(911\) −2.16215e7 −0.863156 −0.431578 − 0.902076i \(-0.642043\pi\)
−0.431578 + 0.902076i \(0.642043\pi\)
\(912\) 0 0
\(913\) −1.18279e7 −0.469602
\(914\) 0 0
\(915\) 2.05598e7 0.811834
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −4.51695e7 −1.76424 −0.882119 − 0.471028i \(-0.843883\pi\)
−0.882119 + 0.471028i \(0.843883\pi\)
\(920\) 0 0
\(921\) −9.89098e6 −0.384229
\(922\) 0 0
\(923\) 1.64828e7 0.636835
\(924\) 0 0
\(925\) 5.63312e7 2.16469
\(926\) 0 0
\(927\) 1.88251e7 0.719512
\(928\) 0 0
\(929\) 2.28729e7 0.869524 0.434762 − 0.900545i \(-0.356832\pi\)
0.434762 + 0.900545i \(0.356832\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −2.22050e7 −0.835117
\(934\) 0 0
\(935\) −4.11506e7 −1.53938
\(936\) 0 0
\(937\) 1.79616e7 0.668336 0.334168 − 0.942514i \(-0.391545\pi\)
0.334168 + 0.942514i \(0.391545\pi\)
\(938\) 0 0
\(939\) −2.33008e7 −0.862395
\(940\) 0 0
\(941\) 1.79697e7 0.661558 0.330779 − 0.943708i \(-0.392689\pi\)
0.330779 + 0.943708i \(0.392689\pi\)
\(942\) 0 0
\(943\) −2.61324e7 −0.956974
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.32115e7 −1.56576 −0.782879 − 0.622174i \(-0.786250\pi\)
−0.782879 + 0.622174i \(0.786250\pi\)
\(948\) 0 0
\(949\) 2.10357e6 0.0758213
\(950\) 0 0
\(951\) 4.27542e6 0.153295
\(952\) 0 0
\(953\) −7.50965e6 −0.267848 −0.133924 − 0.990992i \(-0.542758\pi\)
−0.133924 + 0.990992i \(0.542758\pi\)
\(954\) 0 0
\(955\) −4.83820e7 −1.71662
\(956\) 0 0
\(957\) 1.63498e7 0.577074
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 2.57172e7 0.898288
\(962\) 0 0
\(963\) 6.98584e6 0.242746
\(964\) 0 0
\(965\) 3.47708e7 1.20198
\(966\) 0 0
\(967\) 1.69305e7 0.582242 0.291121 − 0.956686i \(-0.405972\pi\)
0.291121 + 0.956686i \(0.405972\pi\)
\(968\) 0 0
\(969\) 6.85260e6 0.234448
\(970\) 0 0
\(971\) 2.86144e7 0.973949 0.486974 − 0.873416i \(-0.338101\pi\)
0.486974 + 0.873416i \(0.338101\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −2.29570e7 −0.773400
\(976\) 0 0
\(977\) 3.69445e7 1.23826 0.619132 − 0.785287i \(-0.287485\pi\)
0.619132 + 0.785287i \(0.287485\pi\)
\(978\) 0 0
\(979\) −8.98128e6 −0.299489
\(980\) 0 0
\(981\) 8.06148e6 0.267450
\(982\) 0 0
\(983\) −3.88787e7 −1.28330 −0.641650 − 0.766998i \(-0.721750\pi\)
−0.641650 + 0.766998i \(0.721750\pi\)
\(984\) 0 0
\(985\) 4.15755e7 1.36536
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.55568e7 −0.505743
\(990\) 0 0
\(991\) −2.49212e7 −0.806092 −0.403046 − 0.915180i \(-0.632049\pi\)
−0.403046 + 0.915180i \(0.632049\pi\)
\(992\) 0 0
\(993\) 3.96616e6 0.127643
\(994\) 0 0
\(995\) −4.37106e7 −1.39968
\(996\) 0 0
\(997\) −1.01956e7 −0.324845 −0.162422 − 0.986721i \(-0.551931\pi\)
−0.162422 + 0.986721i \(0.551931\pi\)
\(998\) 0 0
\(999\) −5.53138e7 −1.75356
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 784.6.a.i.1.1 1
4.3 odd 2 98.6.a.a.1.1 1
7.6 odd 2 112.6.a.c.1.1 1
12.11 even 2 882.6.a.x.1.1 1
21.20 even 2 1008.6.a.b.1.1 1
28.3 even 6 98.6.c.c.79.1 2
28.11 odd 6 98.6.c.d.79.1 2
28.19 even 6 98.6.c.c.67.1 2
28.23 odd 6 98.6.c.d.67.1 2
28.27 even 2 14.6.a.a.1.1 ✓ 1
56.13 odd 2 448.6.a.l.1.1 1
56.27 even 2 448.6.a.e.1.1 1
84.83 odd 2 126.6.a.f.1.1 1
140.27 odd 4 350.6.c.d.99.1 2
140.83 odd 4 350.6.c.d.99.2 2
140.139 even 2 350.6.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.6.a.a.1.1 ✓ 1 28.27 even 2
98.6.a.a.1.1 1 4.3 odd 2
98.6.c.c.67.1 2 28.19 even 6
98.6.c.c.79.1 2 28.3 even 6
98.6.c.d.67.1 2 28.23 odd 6
98.6.c.d.79.1 2 28.11 odd 6
112.6.a.c.1.1 1 7.6 odd 2
126.6.a.f.1.1 1 84.83 odd 2
350.6.a.i.1.1 1 140.139 even 2
350.6.c.d.99.1 2 140.27 odd 4
350.6.c.d.99.2 2 140.83 odd 4
448.6.a.e.1.1 1 56.27 even 2
448.6.a.l.1.1 1 56.13 odd 2
784.6.a.i.1.1 1 1.1 even 1 trivial
882.6.a.x.1.1 1 12.11 even 2
1008.6.a.b.1.1 1 21.20 even 2