Properties

Label 1008.6.a.bv.1.2
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
Dimension $2$
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] = [1008,6,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, 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("1008.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(161.666890371\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{106}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 106 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 504)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(10.2956\) of defining polynomial
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+99.7738 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+99.7738 q^{5} -49.0000 q^{7} +26.8689 q^{11} +10.9049 q^{13} -593.964 q^{17} -1427.10 q^{19} -1514.73 q^{23} +6829.81 q^{25} +2924.52 q^{29} -2049.00 q^{31} -4888.92 q^{35} +2476.43 q^{37} -20188.3 q^{41} -9587.24 q^{43} -20069.8 q^{47} +2401.00 q^{49} -6554.12 q^{53} +2680.81 q^{55} -18212.8 q^{59} -35155.6 q^{61} +1088.02 q^{65} +28813.0 q^{67} -17116.0 q^{71} +21872.2 q^{73} -1316.58 q^{77} +87602.0 q^{79} -71085.9 q^{83} -59262.0 q^{85} +3299.03 q^{89} -534.339 q^{91} -142387. q^{95} -117193. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 76 q^{5} - 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 76 q^{5} - 98 q^{7} - 564 q^{11} + 516 q^{13} - 76 q^{17} - 2360 q^{19} + 2036 q^{23} + 4270 q^{25} + 8320 q^{29} + 6280 q^{31} - 3724 q^{35} - 2460 q^{37} - 14308 q^{41} - 23128 q^{43} - 12712 q^{47} + 4802 q^{49} - 9896 q^{53} + 16728 q^{55} - 60888 q^{59} + 16172 q^{61} - 10920 q^{65} + 62568 q^{67} + 732 q^{71} + 1244 q^{73} + 27636 q^{77} - 11600 q^{79} - 132288 q^{83} - 71576 q^{85} + 93452 q^{89} - 25284 q^{91} - 120208 q^{95} - 272932 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) 99.7738 1.78481 0.892404 0.451238i \(-0.149017\pi\)
0.892404 + 0.451238i \(0.149017\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 26.8689 0.0669527 0.0334764 0.999440i \(-0.489342\pi\)
0.0334764 + 0.999440i \(0.489342\pi\)
\(12\) 0 0
\(13\) 10.9049 0.0178963 0.00894813 0.999960i \(-0.497152\pi\)
0.00894813 + 0.999960i \(0.497152\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −593.964 −0.498469 −0.249234 0.968443i \(-0.580179\pi\)
−0.249234 + 0.968443i \(0.580179\pi\)
\(18\) 0 0
\(19\) −1427.10 −0.906920 −0.453460 0.891277i \(-0.649810\pi\)
−0.453460 + 0.891277i \(0.649810\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1514.73 −0.597055 −0.298527 0.954401i \(-0.596495\pi\)
−0.298527 + 0.954401i \(0.596495\pi\)
\(24\) 0 0
\(25\) 6829.81 2.18554
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2924.52 0.645744 0.322872 0.946443i \(-0.395352\pi\)
0.322872 + 0.946443i \(0.395352\pi\)
\(30\) 0 0
\(31\) −2049.00 −0.382946 −0.191473 0.981498i \(-0.561326\pi\)
−0.191473 + 0.981498i \(0.561326\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4888.92 −0.674594
\(36\) 0 0
\(37\) 2476.43 0.297386 0.148693 0.988883i \(-0.452493\pi\)
0.148693 + 0.988883i \(0.452493\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −20188.3 −1.87560 −0.937798 0.347181i \(-0.887139\pi\)
−0.937798 + 0.347181i \(0.887139\pi\)
\(42\) 0 0
\(43\) −9587.24 −0.790719 −0.395360 0.918526i \(-0.629380\pi\)
−0.395360 + 0.918526i \(0.629380\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −20069.8 −1.32525 −0.662625 0.748951i \(-0.730558\pi\)
−0.662625 + 0.748951i \(0.730558\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6554.12 −0.320497 −0.160249 0.987077i \(-0.551230\pi\)
−0.160249 + 0.987077i \(0.551230\pi\)
\(54\) 0 0
\(55\) 2680.81 0.119498
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −18212.8 −0.681156 −0.340578 0.940216i \(-0.610623\pi\)
−0.340578 + 0.940216i \(0.610623\pi\)
\(60\) 0 0
\(61\) −35155.6 −1.20968 −0.604840 0.796347i \(-0.706763\pi\)
−0.604840 + 0.796347i \(0.706763\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1088.02 0.0319414
\(66\) 0 0
\(67\) 28813.0 0.784156 0.392078 0.919932i \(-0.371756\pi\)
0.392078 + 0.919932i \(0.371756\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −17116.0 −0.402954 −0.201477 0.979493i \(-0.564574\pi\)
−0.201477 + 0.979493i \(0.564574\pi\)
\(72\) 0 0
\(73\) 21872.2 0.480380 0.240190 0.970726i \(-0.422790\pi\)
0.240190 + 0.970726i \(0.422790\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1316.58 −0.0253058
\(78\) 0 0
\(79\) 87602.0 1.57923 0.789616 0.613601i \(-0.210280\pi\)
0.789616 + 0.613601i \(0.210280\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −71085.9 −1.13263 −0.566315 0.824189i \(-0.691632\pi\)
−0.566315 + 0.824189i \(0.691632\pi\)
\(84\) 0 0
\(85\) −59262.0 −0.889671
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3299.03 0.0441480 0.0220740 0.999756i \(-0.492973\pi\)
0.0220740 + 0.999756i \(0.492973\pi\)
\(90\) 0 0
\(91\) −534.339 −0.00676415
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −142387. −1.61868
\(96\) 0 0
\(97\) −117193. −1.26465 −0.632326 0.774703i \(-0.717900\pi\)
−0.632326 + 0.774703i \(0.717900\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 87975.0 0.858135 0.429068 0.903272i \(-0.358842\pi\)
0.429068 + 0.903272i \(0.358842\pi\)
\(102\) 0 0
\(103\) −185294. −1.72095 −0.860474 0.509494i \(-0.829833\pi\)
−0.860474 + 0.509494i \(0.829833\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15850.6 0.133840 0.0669200 0.997758i \(-0.478683\pi\)
0.0669200 + 0.997758i \(0.478683\pi\)
\(108\) 0 0
\(109\) 154617. 1.24649 0.623247 0.782025i \(-0.285813\pi\)
0.623247 + 0.782025i \(0.285813\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 43252.8 0.318653 0.159327 0.987226i \(-0.449068\pi\)
0.159327 + 0.987226i \(0.449068\pi\)
\(114\) 0 0
\(115\) −151130. −1.06563
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 29104.2 0.188403
\(120\) 0 0
\(121\) −160329. −0.995517
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 369643. 2.11596
\(126\) 0 0
\(127\) −68236.6 −0.375412 −0.187706 0.982225i \(-0.560105\pi\)
−0.187706 + 0.982225i \(0.560105\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −59398.9 −0.302413 −0.151206 0.988502i \(-0.548316\pi\)
−0.151206 + 0.988502i \(0.548316\pi\)
\(132\) 0 0
\(133\) 69927.7 0.342783
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 32603.1 0.148408 0.0742040 0.997243i \(-0.476358\pi\)
0.0742040 + 0.997243i \(0.476358\pi\)
\(138\) 0 0
\(139\) −126248. −0.554225 −0.277113 0.960837i \(-0.589378\pi\)
−0.277113 + 0.960837i \(0.589378\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 293.002 0.00119820
\(144\) 0 0
\(145\) 291791. 1.15253
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 522092. 1.92655 0.963277 0.268509i \(-0.0865309\pi\)
0.963277 + 0.268509i \(0.0865309\pi\)
\(150\) 0 0
\(151\) −144406. −0.515397 −0.257698 0.966225i \(-0.582964\pi\)
−0.257698 + 0.966225i \(0.582964\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −204436. −0.683484
\(156\) 0 0
\(157\) 131612. 0.426133 0.213067 0.977038i \(-0.431655\pi\)
0.213067 + 0.977038i \(0.431655\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 74221.5 0.225666
\(162\) 0 0
\(163\) 464116. 1.36823 0.684113 0.729376i \(-0.260189\pi\)
0.684113 + 0.729376i \(0.260189\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 321971. 0.893358 0.446679 0.894694i \(-0.352607\pi\)
0.446679 + 0.894694i \(0.352607\pi\)
\(168\) 0 0
\(169\) −371174. −0.999680
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 296228. 0.752508 0.376254 0.926517i \(-0.377212\pi\)
0.376254 + 0.926517i \(0.377212\pi\)
\(174\) 0 0
\(175\) −334661. −0.826056
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −114025. −0.265991 −0.132995 0.991117i \(-0.542460\pi\)
−0.132995 + 0.991117i \(0.542460\pi\)
\(180\) 0 0
\(181\) −498098. −1.13010 −0.565051 0.825056i \(-0.691144\pi\)
−0.565051 + 0.825056i \(0.691144\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 247082. 0.530778
\(186\) 0 0
\(187\) −15959.2 −0.0333738
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −525214. −1.04173 −0.520863 0.853640i \(-0.674390\pi\)
−0.520863 + 0.853640i \(0.674390\pi\)
\(192\) 0 0
\(193\) −230768. −0.445946 −0.222973 0.974825i \(-0.571576\pi\)
−0.222973 + 0.974825i \(0.571576\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 896175. 1.64523 0.822617 0.568596i \(-0.192513\pi\)
0.822617 + 0.568596i \(0.192513\pi\)
\(198\) 0 0
\(199\) −904772. −1.61959 −0.809797 0.586710i \(-0.800423\pi\)
−0.809797 + 0.586710i \(0.800423\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −143302. −0.244068
\(204\) 0 0
\(205\) −2.01426e6 −3.34758
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −38344.5 −0.0607208
\(210\) 0 0
\(211\) 652886. 1.00956 0.504779 0.863249i \(-0.331574\pi\)
0.504779 + 0.863249i \(0.331574\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −956555. −1.41128
\(216\) 0 0
\(217\) 100401. 0.144740
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6477.10 −0.00892073
\(222\) 0 0
\(223\) 1.35439e6 1.82382 0.911910 0.410391i \(-0.134608\pi\)
0.911910 + 0.410391i \(0.134608\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 51188.1 0.0659333 0.0329666 0.999456i \(-0.489504\pi\)
0.0329666 + 0.999456i \(0.489504\pi\)
\(228\) 0 0
\(229\) 727407. 0.916619 0.458309 0.888793i \(-0.348455\pi\)
0.458309 + 0.888793i \(0.348455\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.44907e6 −1.74863 −0.874317 0.485355i \(-0.838690\pi\)
−0.874317 + 0.485355i \(0.838690\pi\)
\(234\) 0 0
\(235\) −2.00244e6 −2.36532
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 522404. 0.591578 0.295789 0.955253i \(-0.404417\pi\)
0.295789 + 0.955253i \(0.404417\pi\)
\(240\) 0 0
\(241\) 437082. 0.484753 0.242377 0.970182i \(-0.422073\pi\)
0.242377 + 0.970182i \(0.422073\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 239557. 0.254973
\(246\) 0 0
\(247\) −15562.3 −0.0162305
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −528351. −0.529344 −0.264672 0.964338i \(-0.585264\pi\)
−0.264672 + 0.964338i \(0.585264\pi\)
\(252\) 0 0
\(253\) −40699.0 −0.0399744
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.79360e6 −1.69392 −0.846962 0.531653i \(-0.821571\pi\)
−0.846962 + 0.531653i \(0.821571\pi\)
\(258\) 0 0
\(259\) −121345. −0.112402
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.22568e6 −1.98415 −0.992074 0.125654i \(-0.959897\pi\)
−0.992074 + 0.125654i \(0.959897\pi\)
\(264\) 0 0
\(265\) −653929. −0.572026
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 520438. 0.438519 0.219259 0.975667i \(-0.429636\pi\)
0.219259 + 0.975667i \(0.429636\pi\)
\(270\) 0 0
\(271\) −2.15215e6 −1.78012 −0.890061 0.455841i \(-0.849339\pi\)
−0.890061 + 0.455841i \(0.849339\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 183509. 0.146328
\(276\) 0 0
\(277\) −656005. −0.513698 −0.256849 0.966452i \(-0.582684\pi\)
−0.256849 + 0.966452i \(0.582684\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.05359e6 −0.795985 −0.397992 0.917389i \(-0.630293\pi\)
−0.397992 + 0.917389i \(0.630293\pi\)
\(282\) 0 0
\(283\) −1.98071e6 −1.47013 −0.735064 0.677997i \(-0.762848\pi\)
−0.735064 + 0.677997i \(0.762848\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 989225. 0.708909
\(288\) 0 0
\(289\) −1.06706e6 −0.751529
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.66438e6 1.13262 0.566310 0.824192i \(-0.308370\pi\)
0.566310 + 0.824192i \(0.308370\pi\)
\(294\) 0 0
\(295\) −1.81716e6 −1.21573
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −16517.9 −0.0106851
\(300\) 0 0
\(301\) 469775. 0.298864
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.50761e6 −2.15905
\(306\) 0 0
\(307\) −2.45524e6 −1.48678 −0.743392 0.668856i \(-0.766784\pi\)
−0.743392 + 0.668856i \(0.766784\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.91960e6 1.12541 0.562704 0.826658i \(-0.309761\pi\)
0.562704 + 0.826658i \(0.309761\pi\)
\(312\) 0 0
\(313\) −1.62377e6 −0.936836 −0.468418 0.883507i \(-0.655176\pi\)
−0.468418 + 0.883507i \(0.655176\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.22066e6 −0.682255 −0.341128 0.940017i \(-0.610809\pi\)
−0.341128 + 0.940017i \(0.610809\pi\)
\(318\) 0 0
\(319\) 78578.8 0.0432343
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 847643. 0.452071
\(324\) 0 0
\(325\) 74478.2 0.0391130
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 983419. 0.500898
\(330\) 0 0
\(331\) 2.83639e6 1.42297 0.711487 0.702700i \(-0.248022\pi\)
0.711487 + 0.702700i \(0.248022\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.87479e6 1.39957
\(336\) 0 0
\(337\) −1.42332e6 −0.682697 −0.341349 0.939937i \(-0.610884\pi\)
−0.341349 + 0.939937i \(0.610884\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −55054.3 −0.0256393
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.09903e6 −0.935825 −0.467912 0.883775i \(-0.654994\pi\)
−0.467912 + 0.883775i \(0.654994\pi\)
\(348\) 0 0
\(349\) −2.82234e6 −1.24035 −0.620177 0.784462i \(-0.712939\pi\)
−0.620177 + 0.784462i \(0.712939\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.24004e6 −0.529663 −0.264831 0.964295i \(-0.585316\pi\)
−0.264831 + 0.964295i \(0.585316\pi\)
\(354\) 0 0
\(355\) −1.70773e6 −0.719196
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 234371. 0.0959770 0.0479885 0.998848i \(-0.484719\pi\)
0.0479885 + 0.998848i \(0.484719\pi\)
\(360\) 0 0
\(361\) −439499. −0.177496
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.18227e6 0.857386
\(366\) 0 0
\(367\) 2.45074e6 0.949800 0.474900 0.880040i \(-0.342484\pi\)
0.474900 + 0.880040i \(0.342484\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 321152. 0.121137
\(372\) 0 0
\(373\) 4924.89 0.00183284 0.000916420 1.00000i \(-0.499708\pi\)
0.000916420 1.00000i \(0.499708\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 31891.6 0.0115564
\(378\) 0 0
\(379\) 540900. 0.193428 0.0967140 0.995312i \(-0.469167\pi\)
0.0967140 + 0.995312i \(0.469167\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.04844e6 1.06189 0.530947 0.847405i \(-0.321836\pi\)
0.530947 + 0.847405i \(0.321836\pi\)
\(384\) 0 0
\(385\) −131360. −0.0451659
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.46106e6 −1.49473 −0.747366 0.664412i \(-0.768682\pi\)
−0.747366 + 0.664412i \(0.768682\pi\)
\(390\) 0 0
\(391\) 899692. 0.297613
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.74038e6 2.81863
\(396\) 0 0
\(397\) −3.74992e6 −1.19411 −0.597057 0.802199i \(-0.703663\pi\)
−0.597057 + 0.802199i \(0.703663\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.73486e6 0.538770 0.269385 0.963033i \(-0.413180\pi\)
0.269385 + 0.963033i \(0.413180\pi\)
\(402\) 0 0
\(403\) −22344.1 −0.00685330
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 66538.9 0.0199108
\(408\) 0 0
\(409\) −3.38651e6 −1.00102 −0.500512 0.865730i \(-0.666855\pi\)
−0.500512 + 0.865730i \(0.666855\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 892427. 0.257453
\(414\) 0 0
\(415\) −7.09251e6 −2.02153
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.92994e6 1.65012 0.825060 0.565045i \(-0.191141\pi\)
0.825060 + 0.565045i \(0.191141\pi\)
\(420\) 0 0
\(421\) −3.61340e6 −0.993598 −0.496799 0.867866i \(-0.665491\pi\)
−0.496799 + 0.867866i \(0.665491\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.05666e6 −1.08942
\(426\) 0 0
\(427\) 1.72263e6 0.457216
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 46574.4 0.0120769 0.00603843 0.999982i \(-0.498078\pi\)
0.00603843 + 0.999982i \(0.498078\pi\)
\(432\) 0 0
\(433\) 3.55113e6 0.910222 0.455111 0.890435i \(-0.349600\pi\)
0.455111 + 0.890435i \(0.349600\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.16166e6 0.541481
\(438\) 0 0
\(439\) 991127. 0.245453 0.122726 0.992441i \(-0.460836\pi\)
0.122726 + 0.992441i \(0.460836\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.23482e6 0.298948 0.149474 0.988766i \(-0.452242\pi\)
0.149474 + 0.988766i \(0.452242\pi\)
\(444\) 0 0
\(445\) 329157. 0.0787958
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.84247e6 0.899485 0.449743 0.893158i \(-0.351516\pi\)
0.449743 + 0.893158i \(0.351516\pi\)
\(450\) 0 0
\(451\) −542437. −0.125576
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −53313.0 −0.0120727
\(456\) 0 0
\(457\) 8.81800e6 1.97506 0.987528 0.157443i \(-0.0503250\pi\)
0.987528 + 0.157443i \(0.0503250\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.76947e6 0.606938 0.303469 0.952841i \(-0.401855\pi\)
0.303469 + 0.952841i \(0.401855\pi\)
\(462\) 0 0
\(463\) −3.54086e6 −0.767638 −0.383819 0.923408i \(-0.625391\pi\)
−0.383819 + 0.923408i \(0.625391\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.07387e6 −1.28876 −0.644382 0.764704i \(-0.722885\pi\)
−0.644382 + 0.764704i \(0.722885\pi\)
\(468\) 0 0
\(469\) −1.41184e6 −0.296383
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −257599. −0.0529408
\(474\) 0 0
\(475\) −9.74678e6 −1.98211
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.31185e6 0.659526 0.329763 0.944064i \(-0.393031\pi\)
0.329763 + 0.944064i \(0.393031\pi\)
\(480\) 0 0
\(481\) 27005.1 0.00532211
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.16927e7 −2.25716
\(486\) 0 0
\(487\) 5.06263e6 0.967284 0.483642 0.875266i \(-0.339314\pi\)
0.483642 + 0.875266i \(0.339314\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.68987e6 1.25232 0.626158 0.779696i \(-0.284627\pi\)
0.626158 + 0.779696i \(0.284627\pi\)
\(492\) 0 0
\(493\) −1.73706e6 −0.321883
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 838683. 0.152302
\(498\) 0 0
\(499\) −7.59272e6 −1.36504 −0.682521 0.730866i \(-0.739116\pi\)
−0.682521 + 0.730866i \(0.739116\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.61812e6 −0.637621 −0.318811 0.947818i \(-0.603283\pi\)
−0.318811 + 0.947818i \(0.603283\pi\)
\(504\) 0 0
\(505\) 8.77759e6 1.53161
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6.94370e6 −1.18795 −0.593973 0.804485i \(-0.702441\pi\)
−0.593973 + 0.804485i \(0.702441\pi\)
\(510\) 0 0
\(511\) −1.07174e6 −0.181567
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.84875e7 −3.07156
\(516\) 0 0
\(517\) −539253. −0.0887291
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.41143e6 0.227807 0.113903 0.993492i \(-0.463665\pi\)
0.113903 + 0.993492i \(0.463665\pi\)
\(522\) 0 0
\(523\) 1.13103e7 1.80808 0.904042 0.427443i \(-0.140586\pi\)
0.904042 + 0.427443i \(0.140586\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.21703e6 0.190886
\(528\) 0 0
\(529\) −4.14195e6 −0.643526
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −220151. −0.0335662
\(534\) 0 0
\(535\) 1.58147e6 0.238879
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 64512.2 0.00956467
\(540\) 0 0
\(541\) −190192. −0.0279382 −0.0139691 0.999902i \(-0.504447\pi\)
−0.0139691 + 0.999902i \(0.504447\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.54267e7 2.22475
\(546\) 0 0
\(547\) −1.06805e6 −0.152625 −0.0763123 0.997084i \(-0.524315\pi\)
−0.0763123 + 0.997084i \(0.524315\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4.17357e6 −0.585638
\(552\) 0 0
\(553\) −4.29250e6 −0.596894
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.25567e6 −1.12749 −0.563747 0.825947i \(-0.690641\pi\)
−0.563747 + 0.825947i \(0.690641\pi\)
\(558\) 0 0
\(559\) −104548. −0.0141509
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −436297. −0.0580111 −0.0290055 0.999579i \(-0.509234\pi\)
−0.0290055 + 0.999579i \(0.509234\pi\)
\(564\) 0 0
\(565\) 4.31550e6 0.568735
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.17645e6 −0.152332 −0.0761660 0.997095i \(-0.524268\pi\)
−0.0761660 + 0.997095i \(0.524268\pi\)
\(570\) 0 0
\(571\) 398202. 0.0511109 0.0255554 0.999673i \(-0.491865\pi\)
0.0255554 + 0.999673i \(0.491865\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.03453e7 −1.30489
\(576\) 0 0
\(577\) −1.36513e7 −1.70700 −0.853502 0.521089i \(-0.825526\pi\)
−0.853502 + 0.521089i \(0.825526\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.48321e6 0.428094
\(582\) 0 0
\(583\) −176102. −0.0214582
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 423932. 0.0507810 0.0253905 0.999678i \(-0.491917\pi\)
0.0253905 + 0.999678i \(0.491917\pi\)
\(588\) 0 0
\(589\) 2.92411e6 0.347301
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.05447e6 −0.123140 −0.0615698 0.998103i \(-0.519611\pi\)
−0.0615698 + 0.998103i \(0.519611\pi\)
\(594\) 0 0
\(595\) 2.90384e6 0.336264
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.26516e7 −1.44072 −0.720359 0.693601i \(-0.756023\pi\)
−0.720359 + 0.693601i \(0.756023\pi\)
\(600\) 0 0
\(601\) 4.90694e6 0.554147 0.277073 0.960849i \(-0.410635\pi\)
0.277073 + 0.960849i \(0.410635\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.59966e7 −1.77681
\(606\) 0 0
\(607\) 1.25925e7 1.38720 0.693600 0.720360i \(-0.256023\pi\)
0.693600 + 0.720360i \(0.256023\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −218858. −0.0237170
\(612\) 0 0
\(613\) −8.84587e6 −0.950801 −0.475400 0.879770i \(-0.657697\pi\)
−0.475400 + 0.879770i \(0.657697\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.69655e7 1.79413 0.897066 0.441896i \(-0.145694\pi\)
0.897066 + 0.441896i \(0.145694\pi\)
\(618\) 0 0
\(619\) 1.15237e7 1.20884 0.604418 0.796668i \(-0.293406\pi\)
0.604418 + 0.796668i \(0.293406\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −161653. −0.0166864
\(624\) 0 0
\(625\) 1.55375e7 1.59104
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.47091e6 −0.148238
\(630\) 0 0
\(631\) 1.10729e7 1.10711 0.553553 0.832814i \(-0.313272\pi\)
0.553553 + 0.832814i \(0.313272\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.80822e6 −0.670038
\(636\) 0 0
\(637\) 26182.6 0.00255661
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6.37605e6 0.612924 0.306462 0.951883i \(-0.400855\pi\)
0.306462 + 0.951883i \(0.400855\pi\)
\(642\) 0 0
\(643\) 9.80768e6 0.935489 0.467745 0.883864i \(-0.345067\pi\)
0.467745 + 0.883864i \(0.345067\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.05994e7 0.995455 0.497728 0.867333i \(-0.334168\pi\)
0.497728 + 0.867333i \(0.334168\pi\)
\(648\) 0 0
\(649\) −489358. −0.0456052
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.16241e7 1.06679 0.533393 0.845868i \(-0.320917\pi\)
0.533393 + 0.845868i \(0.320917\pi\)
\(654\) 0 0
\(655\) −5.92645e6 −0.539748
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.23526e7 −1.10801 −0.554005 0.832514i \(-0.686901\pi\)
−0.554005 + 0.832514i \(0.686901\pi\)
\(660\) 0 0
\(661\) −677746. −0.0603341 −0.0301671 0.999545i \(-0.509604\pi\)
−0.0301671 + 0.999545i \(0.509604\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6.97695e6 0.611803
\(666\) 0 0
\(667\) −4.42985e6 −0.385544
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −944594. −0.0809914
\(672\) 0 0
\(673\) 1.33598e7 1.13701 0.568504 0.822680i \(-0.307522\pi\)
0.568504 + 0.822680i \(0.307522\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 5.11219e6 0.428682 0.214341 0.976759i \(-0.431240\pi\)
0.214341 + 0.976759i \(0.431240\pi\)
\(678\) 0 0
\(679\) 5.74244e6 0.477993
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 3.13650e6 0.257273 0.128636 0.991692i \(-0.458940\pi\)
0.128636 + 0.991692i \(0.458940\pi\)
\(684\) 0 0
\(685\) 3.25293e6 0.264880
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −71471.9 −0.00573571
\(690\) 0 0
\(691\) −6.46277e6 −0.514901 −0.257450 0.966291i \(-0.582882\pi\)
−0.257450 + 0.966291i \(0.582882\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.25962e7 −0.989185
\(696\) 0 0
\(697\) 1.19911e7 0.934926
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 9.52280e6 0.731930 0.365965 0.930629i \(-0.380739\pi\)
0.365965 + 0.930629i \(0.380739\pi\)
\(702\) 0 0
\(703\) −3.53410e6 −0.269706
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.31077e6 −0.324345
\(708\) 0 0
\(709\) 6.51985e6 0.487105 0.243552 0.969888i \(-0.421687\pi\)
0.243552 + 0.969888i \(0.421687\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.10367e6 0.228640
\(714\) 0 0
\(715\) 29233.9 0.00213856
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.18789e7 1.57835 0.789175 0.614168i \(-0.210508\pi\)
0.789175 + 0.614168i \(0.210508\pi\)
\(720\) 0 0
\(721\) 9.07940e6 0.650457
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.99739e7 1.41130
\(726\) 0 0
\(727\) −1.72693e7 −1.21182 −0.605911 0.795533i \(-0.707191\pi\)
−0.605911 + 0.795533i \(0.707191\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.69448e6 0.394149
\(732\) 0 0
\(733\) −3.05461e6 −0.209988 −0.104994 0.994473i \(-0.533482\pi\)
−0.104994 + 0.994473i \(0.533482\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 774175. 0.0525013
\(738\) 0 0
\(739\) 1.41503e7 0.953136 0.476568 0.879138i \(-0.341881\pi\)
0.476568 + 0.879138i \(0.341881\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.65710e7 −1.10122 −0.550612 0.834761i \(-0.685606\pi\)
−0.550612 + 0.834761i \(0.685606\pi\)
\(744\) 0 0
\(745\) 5.20911e7 3.43853
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −776679. −0.0505868
\(750\) 0 0
\(751\) 2.51204e7 1.62527 0.812637 0.582771i \(-0.198031\pi\)
0.812637 + 0.582771i \(0.198031\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.44079e7 −0.919884
\(756\) 0 0
\(757\) −8.12854e6 −0.515553 −0.257776 0.966205i \(-0.582990\pi\)
−0.257776 + 0.966205i \(0.582990\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.77695e7 1.11228 0.556139 0.831089i \(-0.312282\pi\)
0.556139 + 0.831089i \(0.312282\pi\)
\(762\) 0 0
\(763\) −7.57622e6 −0.471130
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −198608. −0.0121901
\(768\) 0 0
\(769\) 2.76525e6 0.168624 0.0843119 0.996439i \(-0.473131\pi\)
0.0843119 + 0.996439i \(0.473131\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.27256e7 −0.765999 −0.382999 0.923749i \(-0.625109\pi\)
−0.382999 + 0.923749i \(0.625109\pi\)
\(774\) 0 0
\(775\) −1.39943e7 −0.836943
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.88106e7 1.70102
\(780\) 0 0
\(781\) −459888. −0.0269789
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.31314e7 0.760566
\(786\) 0 0
\(787\) 8.99512e6 0.517691 0.258845 0.965919i \(-0.416658\pi\)
0.258845 + 0.965919i \(0.416658\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.11939e6 −0.120440
\(792\) 0 0
\(793\) −383368. −0.0216488
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.16172e7 1.20546 0.602731 0.797944i \(-0.294079\pi\)
0.602731 + 0.797944i \(0.294079\pi\)
\(798\) 0 0
\(799\) 1.19207e7 0.660596
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 587682. 0.0321628
\(804\) 0 0
\(805\) 7.40536e6 0.402770
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.63701e7 1.41658 0.708289 0.705923i \(-0.249467\pi\)
0.708289 + 0.705923i \(0.249467\pi\)
\(810\) 0 0
\(811\) 3.10910e7 1.65990 0.829952 0.557835i \(-0.188368\pi\)
0.829952 + 0.557835i \(0.188368\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 4.63066e7 2.44202
\(816\) 0 0
\(817\) 1.36819e7 0.717119
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.17372e7 −1.12550 −0.562751 0.826627i \(-0.690257\pi\)
−0.562751 + 0.826627i \(0.690257\pi\)
\(822\) 0 0
\(823\) −1.33966e7 −0.689436 −0.344718 0.938706i \(-0.612026\pi\)
−0.344718 + 0.938706i \(0.612026\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.67048e7 0.849334 0.424667 0.905350i \(-0.360391\pi\)
0.424667 + 0.905350i \(0.360391\pi\)
\(828\) 0 0
\(829\) −1.99150e7 −1.00646 −0.503228 0.864154i \(-0.667855\pi\)
−0.503228 + 0.864154i \(0.667855\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.42611e6 −0.0712098
\(834\) 0 0
\(835\) 3.21243e7 1.59447
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.56979e7 −1.75081 −0.875404 0.483393i \(-0.839404\pi\)
−0.875404 + 0.483393i \(0.839404\pi\)
\(840\) 0 0
\(841\) −1.19583e7 −0.583015
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.70334e7 −1.78424
\(846\) 0 0
\(847\) 7.85612e6 0.376270
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3.75111e6 −0.177556
\(852\) 0 0
\(853\) −2.85813e7 −1.34496 −0.672480 0.740115i \(-0.734771\pi\)
−0.672480 + 0.740115i \(0.734771\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.35988e7 −1.09759 −0.548793 0.835958i \(-0.684913\pi\)
−0.548793 + 0.835958i \(0.684913\pi\)
\(858\) 0 0
\(859\) −1.57178e7 −0.726789 −0.363395 0.931635i \(-0.618382\pi\)
−0.363395 + 0.931635i \(0.618382\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.57903e7 0.721712 0.360856 0.932622i \(-0.382485\pi\)
0.360856 + 0.932622i \(0.382485\pi\)
\(864\) 0 0
\(865\) 2.95558e7 1.34308
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2.35377e6 0.105734
\(870\) 0 0
\(871\) 314203. 0.0140335
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.81125e7 −0.799757
\(876\) 0 0
\(877\) −2.98385e7 −1.31002 −0.655010 0.755620i \(-0.727336\pi\)
−0.655010 + 0.755620i \(0.727336\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.42418e7 −1.05227 −0.526133 0.850402i \(-0.676359\pi\)
−0.526133 + 0.850402i \(0.676359\pi\)
\(882\) 0 0
\(883\) 1.08649e7 0.468946 0.234473 0.972123i \(-0.424664\pi\)
0.234473 + 0.972123i \(0.424664\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −620748. −0.0264915 −0.0132457 0.999912i \(-0.504216\pi\)
−0.0132457 + 0.999912i \(0.504216\pi\)
\(888\) 0 0
\(889\) 3.34359e6 0.141892
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.86415e7 1.20190
\(894\) 0 0
\(895\) −1.13767e7 −0.474743
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5.99234e6 −0.247285
\(900\) 0 0
\(901\) 3.89291e6 0.159758
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4.96971e7 −2.01702
\(906\) 0 0
\(907\) 9.31727e6 0.376071 0.188036 0.982162i \(-0.439788\pi\)
0.188036 + 0.982162i \(0.439788\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.48642e7 −0.992608 −0.496304 0.868149i \(-0.665310\pi\)
−0.496304 + 0.868149i \(0.665310\pi\)
\(912\) 0 0
\(913\) −1.91000e6 −0.0758327
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.91054e6 0.114301
\(918\) 0 0
\(919\) 4.09652e7 1.60003 0.800013 0.599983i \(-0.204826\pi\)
0.800013 + 0.599983i \(0.204826\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −186648. −0.00721138
\(924\) 0 0
\(925\) 1.69135e7 0.649950
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.84805e6 −0.0702544 −0.0351272 0.999383i \(-0.511184\pi\)
−0.0351272 + 0.999383i \(0.511184\pi\)
\(930\) 0 0
\(931\) −3.42646e6 −0.129560
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.59231e6 −0.0595659
\(936\) 0 0
\(937\) −1.60973e7 −0.598968 −0.299484 0.954101i \(-0.596815\pi\)
−0.299484 + 0.954101i \(0.596815\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.47172e7 −1.27812 −0.639059 0.769158i \(-0.720676\pi\)
−0.639059 + 0.769158i \(0.720676\pi\)
\(942\) 0 0
\(943\) 3.05797e7 1.11983
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.93018e7 1.42409 0.712046 0.702133i \(-0.247769\pi\)
0.712046 + 0.702133i \(0.247769\pi\)
\(948\) 0 0
\(949\) 238513. 0.00859701
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −3.99314e7 −1.42424 −0.712118 0.702060i \(-0.752264\pi\)
−0.712118 + 0.702060i \(0.752264\pi\)
\(954\) 0 0
\(955\) −5.24026e7 −1.85928
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.59755e6 −0.0560929
\(960\) 0 0
\(961\) −2.44308e7 −0.853353
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2.30246e7 −0.795927
\(966\) 0 0
\(967\) 2.42085e7 0.832534 0.416267 0.909242i \(-0.363338\pi\)
0.416267 + 0.909242i \(0.363338\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.00227e7 1.36226 0.681128 0.732164i \(-0.261490\pi\)
0.681128 + 0.732164i \(0.261490\pi\)
\(972\) 0 0
\(973\) 6.18614e6 0.209477
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −6.69145e6 −0.224277 −0.112138 0.993693i \(-0.535770\pi\)
−0.112138 + 0.993693i \(0.535770\pi\)
\(978\) 0 0
\(979\) 88641.4 0.00295583
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3.41067e7 1.12579 0.562894 0.826529i \(-0.309688\pi\)
0.562894 + 0.826529i \(0.309688\pi\)
\(984\) 0 0
\(985\) 8.94148e7 2.93642
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.45220e7 0.472103
\(990\) 0 0
\(991\) −2.75297e7 −0.890465 −0.445232 0.895415i \(-0.646879\pi\)
−0.445232 + 0.895415i \(0.646879\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −9.02725e7 −2.89066
\(996\) 0 0
\(997\) 3.40958e7 1.08633 0.543166 0.839625i \(-0.317226\pi\)
0.543166 + 0.839625i \(0.317226\pi\)
\(998\) 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 1008.6.a.bv.1.2 2
3.2 odd 2 1008.6.a.bg.1.1 2
4.3 odd 2 504.6.a.u.1.2 yes 2
12.11 even 2 504.6.a.k.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.k.1.1 2 12.11 even 2
504.6.a.u.1.2 yes 2 4.3 odd 2
1008.6.a.bg.1.1 2 3.2 odd 2
1008.6.a.bv.1.2 2 1.1 even 1 trivial