Properties

Label 495.6.a.a.1.1
Level $495$
Weight $6$
Character 495.1
Self dual yes
Analytic conductor $79.390$
Analytic rank $1$
Dimension $3$
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] = [495,6,Mod(1,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, 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("495.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 495.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: \(79.3899908074\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.307532.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 76x + 168 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(7.91848\) of defining polynomial
Character \(\chi\) \(=\) 495.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-9.91848 q^{2} +66.3762 q^{4} +25.0000 q^{5} +92.6461 q^{7} -340.959 q^{8} +O(q^{10})\) \(q-9.91848 q^{2} +66.3762 q^{4} +25.0000 q^{5} +92.6461 q^{7} -340.959 q^{8} -247.962 q^{10} -121.000 q^{11} +800.249 q^{13} -918.908 q^{14} +1257.76 q^{16} +117.742 q^{17} +831.422 q^{19} +1659.40 q^{20} +1200.14 q^{22} -2952.23 q^{23} +625.000 q^{25} -7937.25 q^{26} +6149.49 q^{28} -5765.87 q^{29} -61.7803 q^{31} -1564.36 q^{32} -1167.83 q^{34} +2316.15 q^{35} -10236.6 q^{37} -8246.44 q^{38} -8523.98 q^{40} -9599.21 q^{41} -17473.2 q^{43} -8031.52 q^{44} +29281.7 q^{46} -18748.3 q^{47} -8223.71 q^{49} -6199.05 q^{50} +53117.5 q^{52} +9703.45 q^{53} -3025.00 q^{55} -31588.5 q^{56} +57188.6 q^{58} +24401.4 q^{59} +33910.3 q^{61} +612.766 q^{62} -24732.2 q^{64} +20006.2 q^{65} -4989.24 q^{67} +7815.29 q^{68} -22972.7 q^{70} +62961.6 q^{71} -54232.5 q^{73} +101531. q^{74} +55186.6 q^{76} -11210.2 q^{77} -56996.4 q^{79} +31444.0 q^{80} +95209.6 q^{82} -49685.9 q^{83} +2943.56 q^{85} +173308. q^{86} +41256.1 q^{88} +87990.1 q^{89} +74139.9 q^{91} -195958. q^{92} +185954. q^{94} +20785.5 q^{95} -44817.9 q^{97} +81566.7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 7 q^{2} + 73 q^{4} + 75 q^{5} + 92 q^{7} - 231 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 7 q^{2} + 73 q^{4} + 75 q^{5} + 92 q^{7} - 231 q^{8} - 175 q^{10} - 363 q^{11} - 90 q^{13} + 784 q^{14} - 415 q^{16} - 1934 q^{17} + 2084 q^{19} + 1825 q^{20} + 847 q^{22} - 1220 q^{23} + 1875 q^{25} - 17062 q^{26} + 11120 q^{28} - 4402 q^{29} - 10688 q^{31} - 12439 q^{32} - 4094 q^{34} + 2300 q^{35} - 8190 q^{37} - 13792 q^{38} - 5775 q^{40} - 5974 q^{41} + 18868 q^{43} - 8833 q^{44} + 46220 q^{46} - 55500 q^{47} + 1907 q^{49} - 4375 q^{50} + 27330 q^{52} - 9206 q^{53} - 9075 q^{55} - 73248 q^{56} + 15366 q^{58} + 59196 q^{59} + 79902 q^{61} - 64616 q^{62} + 2129 q^{64} - 2250 q^{65} + 4468 q^{67} + 1218 q^{68} + 19600 q^{70} + 75164 q^{71} - 61290 q^{73} + 56766 q^{74} + 37816 q^{76} - 11132 q^{77} - 83564 q^{79} - 10375 q^{80} + 147410 q^{82} - 74764 q^{83} - 48350 q^{85} + 253432 q^{86} + 27951 q^{88} - 37342 q^{89} - 126488 q^{91} - 148164 q^{92} + 59252 q^{94} + 52100 q^{95} + 33486 q^{97} + 95249 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.91848 −1.75336 −0.876678 0.481078i \(-0.840245\pi\)
−0.876678 + 0.481078i \(0.840245\pi\)
\(3\) 0 0
\(4\) 66.3762 2.07426
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 92.6461 0.714631 0.357315 0.933984i \(-0.383692\pi\)
0.357315 + 0.933984i \(0.383692\pi\)
\(8\) −340.959 −1.88355
\(9\) 0 0
\(10\) −247.962 −0.784124
\(11\) −121.000 −0.301511
\(12\) 0 0
\(13\) 800.249 1.31331 0.656654 0.754192i \(-0.271971\pi\)
0.656654 + 0.754192i \(0.271971\pi\)
\(14\) −918.908 −1.25300
\(15\) 0 0
\(16\) 1257.76 1.22828
\(17\) 117.742 0.0988122 0.0494061 0.998779i \(-0.484267\pi\)
0.0494061 + 0.998779i \(0.484267\pi\)
\(18\) 0 0
\(19\) 831.422 0.528369 0.264185 0.964472i \(-0.414897\pi\)
0.264185 + 0.964472i \(0.414897\pi\)
\(20\) 1659.40 0.927635
\(21\) 0 0
\(22\) 1200.14 0.528657
\(23\) −2952.23 −1.16367 −0.581837 0.813306i \(-0.697666\pi\)
−0.581837 + 0.813306i \(0.697666\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) −7937.25 −2.30270
\(27\) 0 0
\(28\) 6149.49 1.48233
\(29\) −5765.87 −1.27312 −0.636560 0.771227i \(-0.719643\pi\)
−0.636560 + 0.771227i \(0.719643\pi\)
\(30\) 0 0
\(31\) −61.7803 −0.0115464 −0.00577319 0.999983i \(-0.501838\pi\)
−0.00577319 + 0.999983i \(0.501838\pi\)
\(32\) −1564.36 −0.270061
\(33\) 0 0
\(34\) −1167.83 −0.173253
\(35\) 2316.15 0.319593
\(36\) 0 0
\(37\) −10236.6 −1.22928 −0.614640 0.788808i \(-0.710699\pi\)
−0.614640 + 0.788808i \(0.710699\pi\)
\(38\) −8246.44 −0.926419
\(39\) 0 0
\(40\) −8523.98 −0.842350
\(41\) −9599.21 −0.891818 −0.445909 0.895078i \(-0.647119\pi\)
−0.445909 + 0.895078i \(0.647119\pi\)
\(42\) 0 0
\(43\) −17473.2 −1.44113 −0.720563 0.693389i \(-0.756117\pi\)
−0.720563 + 0.693389i \(0.756117\pi\)
\(44\) −8031.52 −0.625412
\(45\) 0 0
\(46\) 29281.7 2.04033
\(47\) −18748.3 −1.23799 −0.618995 0.785395i \(-0.712460\pi\)
−0.618995 + 0.785395i \(0.712460\pi\)
\(48\) 0 0
\(49\) −8223.71 −0.489303
\(50\) −6199.05 −0.350671
\(51\) 0 0
\(52\) 53117.5 2.72414
\(53\) 9703.45 0.474500 0.237250 0.971449i \(-0.423754\pi\)
0.237250 + 0.971449i \(0.423754\pi\)
\(54\) 0 0
\(55\) −3025.00 −0.134840
\(56\) −31588.5 −1.34604
\(57\) 0 0
\(58\) 57188.6 2.23223
\(59\) 24401.4 0.912609 0.456305 0.889824i \(-0.349173\pi\)
0.456305 + 0.889824i \(0.349173\pi\)
\(60\) 0 0
\(61\) 33910.3 1.16683 0.583413 0.812175i \(-0.301717\pi\)
0.583413 + 0.812175i \(0.301717\pi\)
\(62\) 612.766 0.0202449
\(63\) 0 0
\(64\) −24732.2 −0.754768
\(65\) 20006.2 0.587329
\(66\) 0 0
\(67\) −4989.24 −0.135784 −0.0678918 0.997693i \(-0.521627\pi\)
−0.0678918 + 0.997693i \(0.521627\pi\)
\(68\) 7815.29 0.204962
\(69\) 0 0
\(70\) −22972.7 −0.560360
\(71\) 62961.6 1.48228 0.741140 0.671351i \(-0.234286\pi\)
0.741140 + 0.671351i \(0.234286\pi\)
\(72\) 0 0
\(73\) −54232.5 −1.19111 −0.595556 0.803314i \(-0.703068\pi\)
−0.595556 + 0.803314i \(0.703068\pi\)
\(74\) 101531. 2.15537
\(75\) 0 0
\(76\) 55186.6 1.09597
\(77\) −11210.2 −0.215469
\(78\) 0 0
\(79\) −56996.4 −1.02750 −0.513748 0.857941i \(-0.671743\pi\)
−0.513748 + 0.857941i \(0.671743\pi\)
\(80\) 31444.0 0.549304
\(81\) 0 0
\(82\) 95209.6 1.56367
\(83\) −49685.9 −0.791659 −0.395830 0.918324i \(-0.629543\pi\)
−0.395830 + 0.918324i \(0.629543\pi\)
\(84\) 0 0
\(85\) 2943.56 0.0441902
\(86\) 173308. 2.52681
\(87\) 0 0
\(88\) 41256.1 0.567912
\(89\) 87990.1 1.17749 0.588747 0.808317i \(-0.299621\pi\)
0.588747 + 0.808317i \(0.299621\pi\)
\(90\) 0 0
\(91\) 74139.9 0.938531
\(92\) −195958. −2.41376
\(93\) 0 0
\(94\) 185954. 2.17064
\(95\) 20785.5 0.236294
\(96\) 0 0
\(97\) −44817.9 −0.483640 −0.241820 0.970321i \(-0.577744\pi\)
−0.241820 + 0.970321i \(0.577744\pi\)
\(98\) 81566.7 0.857921
\(99\) 0 0
\(100\) 41485.1 0.414851
\(101\) −82871.7 −0.808356 −0.404178 0.914680i \(-0.632442\pi\)
−0.404178 + 0.914680i \(0.632442\pi\)
\(102\) 0 0
\(103\) 153697. 1.42749 0.713744 0.700406i \(-0.246998\pi\)
0.713744 + 0.700406i \(0.246998\pi\)
\(104\) −272852. −2.47368
\(105\) 0 0
\(106\) −96243.5 −0.831968
\(107\) −41662.3 −0.351790 −0.175895 0.984409i \(-0.556282\pi\)
−0.175895 + 0.984409i \(0.556282\pi\)
\(108\) 0 0
\(109\) 39745.0 0.320417 0.160209 0.987083i \(-0.448783\pi\)
0.160209 + 0.987083i \(0.448783\pi\)
\(110\) 30003.4 0.236422
\(111\) 0 0
\(112\) 116526. 0.877768
\(113\) 191157. 1.40829 0.704147 0.710054i \(-0.251329\pi\)
0.704147 + 0.710054i \(0.251329\pi\)
\(114\) 0 0
\(115\) −73805.8 −0.520411
\(116\) −382716. −2.64078
\(117\) 0 0
\(118\) −242025. −1.60013
\(119\) 10908.4 0.0706143
\(120\) 0 0
\(121\) 14641.0 0.0909091
\(122\) −336338. −2.04586
\(123\) 0 0
\(124\) −4100.74 −0.0239501
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −212879. −1.17118 −0.585590 0.810608i \(-0.699137\pi\)
−0.585590 + 0.810608i \(0.699137\pi\)
\(128\) 295366. 1.59344
\(129\) 0 0
\(130\) −198431. −1.02980
\(131\) 146592. 0.746333 0.373166 0.927764i \(-0.378272\pi\)
0.373166 + 0.927764i \(0.378272\pi\)
\(132\) 0 0
\(133\) 77027.9 0.377589
\(134\) 49485.7 0.238077
\(135\) 0 0
\(136\) −40145.4 −0.186118
\(137\) −335075. −1.52525 −0.762623 0.646843i \(-0.776089\pi\)
−0.762623 + 0.646843i \(0.776089\pi\)
\(138\) 0 0
\(139\) 30053.6 0.131935 0.0659674 0.997822i \(-0.478987\pi\)
0.0659674 + 0.997822i \(0.478987\pi\)
\(140\) 153737. 0.662917
\(141\) 0 0
\(142\) −624483. −2.59896
\(143\) −96830.1 −0.395977
\(144\) 0 0
\(145\) −144147. −0.569357
\(146\) 537904. 2.08844
\(147\) 0 0
\(148\) −679466. −2.54984
\(149\) −240256. −0.886559 −0.443280 0.896383i \(-0.646185\pi\)
−0.443280 + 0.896383i \(0.646185\pi\)
\(150\) 0 0
\(151\) 37997.8 0.135617 0.0678087 0.997698i \(-0.478399\pi\)
0.0678087 + 0.997698i \(0.478399\pi\)
\(152\) −283481. −0.995211
\(153\) 0 0
\(154\) 111188. 0.377794
\(155\) −1544.51 −0.00516369
\(156\) 0 0
\(157\) −260511. −0.843483 −0.421742 0.906716i \(-0.638581\pi\)
−0.421742 + 0.906716i \(0.638581\pi\)
\(158\) 565318. 1.80157
\(159\) 0 0
\(160\) −39109.0 −0.120775
\(161\) −273513. −0.831597
\(162\) 0 0
\(163\) −364741. −1.07527 −0.537633 0.843179i \(-0.680681\pi\)
−0.537633 + 0.843179i \(0.680681\pi\)
\(164\) −637159. −1.84986
\(165\) 0 0
\(166\) 492809. 1.38806
\(167\) −70995.9 −0.196989 −0.0984945 0.995138i \(-0.531403\pi\)
−0.0984945 + 0.995138i \(0.531403\pi\)
\(168\) 0 0
\(169\) 269105. 0.724778
\(170\) −29195.6 −0.0774811
\(171\) 0 0
\(172\) −1.15981e6 −2.98927
\(173\) −295710. −0.751192 −0.375596 0.926783i \(-0.622562\pi\)
−0.375596 + 0.926783i \(0.622562\pi\)
\(174\) 0 0
\(175\) 57903.8 0.142926
\(176\) −152189. −0.370341
\(177\) 0 0
\(178\) −872727. −2.06457
\(179\) 567691. 1.32428 0.662139 0.749381i \(-0.269649\pi\)
0.662139 + 0.749381i \(0.269649\pi\)
\(180\) 0 0
\(181\) −361118. −0.819319 −0.409660 0.912239i \(-0.634352\pi\)
−0.409660 + 0.912239i \(0.634352\pi\)
\(182\) −735355. −1.64558
\(183\) 0 0
\(184\) 1.00659e6 2.19184
\(185\) −255915. −0.549751
\(186\) 0 0
\(187\) −14246.8 −0.0297930
\(188\) −1.24444e6 −2.56791
\(189\) 0 0
\(190\) −206161. −0.414307
\(191\) −334871. −0.664193 −0.332096 0.943245i \(-0.607756\pi\)
−0.332096 + 0.943245i \(0.607756\pi\)
\(192\) 0 0
\(193\) −286645. −0.553926 −0.276963 0.960881i \(-0.589328\pi\)
−0.276963 + 0.960881i \(0.589328\pi\)
\(194\) 444525. 0.847992
\(195\) 0 0
\(196\) −545858. −1.01494
\(197\) −402554. −0.739024 −0.369512 0.929226i \(-0.620475\pi\)
−0.369512 + 0.929226i \(0.620475\pi\)
\(198\) 0 0
\(199\) 506857. 0.907304 0.453652 0.891179i \(-0.350121\pi\)
0.453652 + 0.891179i \(0.350121\pi\)
\(200\) −213100. −0.376710
\(201\) 0 0
\(202\) 821961. 1.41734
\(203\) −534185. −0.909812
\(204\) 0 0
\(205\) −239980. −0.398833
\(206\) −1.52444e6 −2.50289
\(207\) 0 0
\(208\) 1.00652e6 1.61311
\(209\) −100602. −0.159309
\(210\) 0 0
\(211\) 166764. 0.257867 0.128934 0.991653i \(-0.458845\pi\)
0.128934 + 0.991653i \(0.458845\pi\)
\(212\) 644078. 0.984235
\(213\) 0 0
\(214\) 413227. 0.616813
\(215\) −436831. −0.644492
\(216\) 0 0
\(217\) −5723.70 −0.00825140
\(218\) −394209. −0.561805
\(219\) 0 0
\(220\) −200788. −0.279693
\(221\) 94223.2 0.129771
\(222\) 0 0
\(223\) 556053. 0.748780 0.374390 0.927271i \(-0.377852\pi\)
0.374390 + 0.927271i \(0.377852\pi\)
\(224\) −144932. −0.192994
\(225\) 0 0
\(226\) −1.89598e6 −2.46924
\(227\) −507849. −0.654139 −0.327069 0.945000i \(-0.606061\pi\)
−0.327069 + 0.945000i \(0.606061\pi\)
\(228\) 0 0
\(229\) −627193. −0.790337 −0.395169 0.918609i \(-0.629314\pi\)
−0.395169 + 0.918609i \(0.629314\pi\)
\(230\) 732042. 0.912465
\(231\) 0 0
\(232\) 1.96593e6 2.39799
\(233\) −955870. −1.15348 −0.576738 0.816929i \(-0.695675\pi\)
−0.576738 + 0.816929i \(0.695675\pi\)
\(234\) 0 0
\(235\) −468707. −0.553646
\(236\) 1.61967e6 1.89298
\(237\) 0 0
\(238\) −108194. −0.123812
\(239\) 509255. 0.576687 0.288344 0.957527i \(-0.406895\pi\)
0.288344 + 0.957527i \(0.406895\pi\)
\(240\) 0 0
\(241\) −666125. −0.738776 −0.369388 0.929275i \(-0.620433\pi\)
−0.369388 + 0.929275i \(0.620433\pi\)
\(242\) −145216. −0.159396
\(243\) 0 0
\(244\) 2.25083e6 2.42030
\(245\) −205593. −0.218823
\(246\) 0 0
\(247\) 665344. 0.693911
\(248\) 21064.6 0.0217482
\(249\) 0 0
\(250\) −154976. −0.156825
\(251\) −505010. −0.505960 −0.252980 0.967472i \(-0.581411\pi\)
−0.252980 + 0.967472i \(0.581411\pi\)
\(252\) 0 0
\(253\) 357220. 0.350861
\(254\) 2.11144e6 2.05349
\(255\) 0 0
\(256\) −2.13815e6 −2.03909
\(257\) 2.02669e6 1.91405 0.957027 0.290000i \(-0.0936552\pi\)
0.957027 + 0.290000i \(0.0936552\pi\)
\(258\) 0 0
\(259\) −948379. −0.878482
\(260\) 1.32794e6 1.21827
\(261\) 0 0
\(262\) −1.45397e6 −1.30859
\(263\) −1.57349e6 −1.40273 −0.701366 0.712801i \(-0.747426\pi\)
−0.701366 + 0.712801i \(0.747426\pi\)
\(264\) 0 0
\(265\) 242586. 0.212203
\(266\) −764000. −0.662048
\(267\) 0 0
\(268\) −331167. −0.281650
\(269\) 1.55958e6 1.31409 0.657046 0.753850i \(-0.271806\pi\)
0.657046 + 0.753850i \(0.271806\pi\)
\(270\) 0 0
\(271\) 1.35274e6 1.11890 0.559451 0.828864i \(-0.311012\pi\)
0.559451 + 0.828864i \(0.311012\pi\)
\(272\) 148092. 0.121369
\(273\) 0 0
\(274\) 3.32343e6 2.67430
\(275\) −75625.0 −0.0603023
\(276\) 0 0
\(277\) 2.47205e6 1.93579 0.967895 0.251353i \(-0.0808755\pi\)
0.967895 + 0.251353i \(0.0808755\pi\)
\(278\) −298086. −0.231328
\(279\) 0 0
\(280\) −789714. −0.601970
\(281\) −769611. −0.581441 −0.290721 0.956808i \(-0.593895\pi\)
−0.290721 + 0.956808i \(0.593895\pi\)
\(282\) 0 0
\(283\) 2.52887e6 1.87698 0.938490 0.345305i \(-0.112225\pi\)
0.938490 + 0.345305i \(0.112225\pi\)
\(284\) 4.17915e6 3.07463
\(285\) 0 0
\(286\) 960407. 0.694289
\(287\) −889329. −0.637320
\(288\) 0 0
\(289\) −1.40599e6 −0.990236
\(290\) 1.42972e6 0.998285
\(291\) 0 0
\(292\) −3.59975e6 −2.47067
\(293\) −2.06542e6 −1.40553 −0.702764 0.711423i \(-0.748051\pi\)
−0.702764 + 0.711423i \(0.748051\pi\)
\(294\) 0 0
\(295\) 610035. 0.408131
\(296\) 3.49026e6 2.31541
\(297\) 0 0
\(298\) 2.38297e6 1.55445
\(299\) −2.36252e6 −1.52826
\(300\) 0 0
\(301\) −1.61883e6 −1.02987
\(302\) −376880. −0.237786
\(303\) 0 0
\(304\) 1.04573e6 0.648986
\(305\) 847756. 0.521821
\(306\) 0 0
\(307\) −2.17085e6 −1.31457 −0.657286 0.753641i \(-0.728296\pi\)
−0.657286 + 0.753641i \(0.728296\pi\)
\(308\) −744088. −0.446939
\(309\) 0 0
\(310\) 15319.2 0.00905379
\(311\) 198576. 0.116420 0.0582098 0.998304i \(-0.481461\pi\)
0.0582098 + 0.998304i \(0.481461\pi\)
\(312\) 0 0
\(313\) −483762. −0.279107 −0.139554 0.990215i \(-0.544567\pi\)
−0.139554 + 0.990215i \(0.544567\pi\)
\(314\) 2.58387e6 1.47893
\(315\) 0 0
\(316\) −3.78321e6 −2.13129
\(317\) 1.68099e6 0.939542 0.469771 0.882788i \(-0.344336\pi\)
0.469771 + 0.882788i \(0.344336\pi\)
\(318\) 0 0
\(319\) 697670. 0.383860
\(320\) −618306. −0.337542
\(321\) 0 0
\(322\) 2.71283e6 1.45809
\(323\) 97893.6 0.0522093
\(324\) 0 0
\(325\) 500155. 0.262662
\(326\) 3.61768e6 1.88532
\(327\) 0 0
\(328\) 3.27294e6 1.67979
\(329\) −1.73696e6 −0.884706
\(330\) 0 0
\(331\) −1.18881e6 −0.596407 −0.298204 0.954502i \(-0.596387\pi\)
−0.298204 + 0.954502i \(0.596387\pi\)
\(332\) −3.29796e6 −1.64210
\(333\) 0 0
\(334\) 704171. 0.345392
\(335\) −124731. −0.0607243
\(336\) 0 0
\(337\) 1.78561e6 0.856470 0.428235 0.903667i \(-0.359135\pi\)
0.428235 + 0.903667i \(0.359135\pi\)
\(338\) −2.66911e6 −1.27079
\(339\) 0 0
\(340\) 195382. 0.0916617
\(341\) 7475.41 0.00348136
\(342\) 0 0
\(343\) −2.31900e6 −1.06430
\(344\) 5.95766e6 2.71444
\(345\) 0 0
\(346\) 2.93299e6 1.31711
\(347\) −2.71689e6 −1.21129 −0.605645 0.795735i \(-0.707085\pi\)
−0.605645 + 0.795735i \(0.707085\pi\)
\(348\) 0 0
\(349\) −1.87050e6 −0.822044 −0.411022 0.911626i \(-0.634828\pi\)
−0.411022 + 0.911626i \(0.634828\pi\)
\(350\) −574317. −0.250600
\(351\) 0 0
\(352\) 189288. 0.0814265
\(353\) 4.27952e6 1.82793 0.913963 0.405798i \(-0.133006\pi\)
0.913963 + 0.405798i \(0.133006\pi\)
\(354\) 0 0
\(355\) 1.57404e6 0.662896
\(356\) 5.84045e6 2.44242
\(357\) 0 0
\(358\) −5.63063e6 −2.32193
\(359\) 1.39681e6 0.572007 0.286003 0.958229i \(-0.407673\pi\)
0.286003 + 0.958229i \(0.407673\pi\)
\(360\) 0 0
\(361\) −1.78484e6 −0.720826
\(362\) 3.58174e6 1.43656
\(363\) 0 0
\(364\) 4.92112e6 1.94675
\(365\) −1.35581e6 −0.532681
\(366\) 0 0
\(367\) −5.05674e6 −1.95977 −0.979885 0.199561i \(-0.936049\pi\)
−0.979885 + 0.199561i \(0.936049\pi\)
\(368\) −3.71320e6 −1.42932
\(369\) 0 0
\(370\) 2.53828e6 0.963909
\(371\) 898987. 0.339093
\(372\) 0 0
\(373\) −4.68117e6 −1.74214 −0.871069 0.491161i \(-0.836573\pi\)
−0.871069 + 0.491161i \(0.836573\pi\)
\(374\) 141307. 0.0522377
\(375\) 0 0
\(376\) 6.39241e6 2.33182
\(377\) −4.61413e6 −1.67200
\(378\) 0 0
\(379\) −3.76641e6 −1.34688 −0.673442 0.739240i \(-0.735185\pi\)
−0.673442 + 0.739240i \(0.735185\pi\)
\(380\) 1.37966e6 0.490134
\(381\) 0 0
\(382\) 3.32141e6 1.16457
\(383\) −4.17276e6 −1.45354 −0.726770 0.686881i \(-0.758979\pi\)
−0.726770 + 0.686881i \(0.758979\pi\)
\(384\) 0 0
\(385\) −280254. −0.0963608
\(386\) 2.84308e6 0.971228
\(387\) 0 0
\(388\) −2.97484e6 −1.00319
\(389\) 3.73222e6 1.25053 0.625265 0.780413i \(-0.284991\pi\)
0.625265 + 0.780413i \(0.284991\pi\)
\(390\) 0 0
\(391\) −347603. −0.114985
\(392\) 2.80395e6 0.921627
\(393\) 0 0
\(394\) 3.99272e6 1.29577
\(395\) −1.42491e6 −0.459510
\(396\) 0 0
\(397\) 5.71418e6 1.81961 0.909804 0.415038i \(-0.136232\pi\)
0.909804 + 0.415038i \(0.136232\pi\)
\(398\) −5.02725e6 −1.59083
\(399\) 0 0
\(400\) 786100. 0.245656
\(401\) −3.60785e6 −1.12044 −0.560219 0.828345i \(-0.689283\pi\)
−0.560219 + 0.828345i \(0.689283\pi\)
\(402\) 0 0
\(403\) −49439.6 −0.0151639
\(404\) −5.50070e6 −1.67674
\(405\) 0 0
\(406\) 5.29830e6 1.59522
\(407\) 1.23863e6 0.370642
\(408\) 0 0
\(409\) −4.59452e6 −1.35810 −0.679050 0.734092i \(-0.737608\pi\)
−0.679050 + 0.734092i \(0.737608\pi\)
\(410\) 2.38024e6 0.699296
\(411\) 0 0
\(412\) 1.02018e7 2.96098
\(413\) 2.26069e6 0.652179
\(414\) 0 0
\(415\) −1.24215e6 −0.354041
\(416\) −1.25188e6 −0.354673
\(417\) 0 0
\(418\) 997819. 0.279326
\(419\) −1.92383e6 −0.535343 −0.267671 0.963510i \(-0.586254\pi\)
−0.267671 + 0.963510i \(0.586254\pi\)
\(420\) 0 0
\(421\) −4.28936e6 −1.17947 −0.589736 0.807596i \(-0.700768\pi\)
−0.589736 + 0.807596i \(0.700768\pi\)
\(422\) −1.65404e6 −0.452133
\(423\) 0 0
\(424\) −3.30848e6 −0.893746
\(425\) 73589.0 0.0197624
\(426\) 0 0
\(427\) 3.14165e6 0.833851
\(428\) −2.76538e6 −0.729703
\(429\) 0 0
\(430\) 4.33270e6 1.13002
\(431\) −477444. −0.123802 −0.0619012 0.998082i \(-0.519716\pi\)
−0.0619012 + 0.998082i \(0.519716\pi\)
\(432\) 0 0
\(433\) −6.24919e6 −1.60178 −0.800892 0.598808i \(-0.795641\pi\)
−0.800892 + 0.598808i \(0.795641\pi\)
\(434\) 56770.4 0.0144676
\(435\) 0 0
\(436\) 2.63812e6 0.664627
\(437\) −2.45455e6 −0.614849
\(438\) 0 0
\(439\) 5.45632e6 1.35126 0.675629 0.737241i \(-0.263872\pi\)
0.675629 + 0.737241i \(0.263872\pi\)
\(440\) 1.03140e6 0.253978
\(441\) 0 0
\(442\) −934551. −0.227534
\(443\) 3.75783e6 0.909762 0.454881 0.890552i \(-0.349682\pi\)
0.454881 + 0.890552i \(0.349682\pi\)
\(444\) 0 0
\(445\) 2.19975e6 0.526591
\(446\) −5.51520e6 −1.31288
\(447\) 0 0
\(448\) −2.29134e6 −0.539380
\(449\) 7.17310e6 1.67916 0.839578 0.543239i \(-0.182802\pi\)
0.839578 + 0.543239i \(0.182802\pi\)
\(450\) 0 0
\(451\) 1.16150e6 0.268893
\(452\) 1.26883e7 2.92116
\(453\) 0 0
\(454\) 5.03709e6 1.14694
\(455\) 1.85350e6 0.419724
\(456\) 0 0
\(457\) −3.21240e6 −0.719513 −0.359757 0.933046i \(-0.617140\pi\)
−0.359757 + 0.933046i \(0.617140\pi\)
\(458\) 6.22080e6 1.38574
\(459\) 0 0
\(460\) −4.89895e6 −1.07946
\(461\) 5.17808e6 1.13479 0.567396 0.823445i \(-0.307951\pi\)
0.567396 + 0.823445i \(0.307951\pi\)
\(462\) 0 0
\(463\) 2.95142e6 0.639851 0.319926 0.947443i \(-0.396342\pi\)
0.319926 + 0.947443i \(0.396342\pi\)
\(464\) −7.25208e6 −1.56375
\(465\) 0 0
\(466\) 9.48077e6 2.02245
\(467\) −7.26608e6 −1.54173 −0.770865 0.636999i \(-0.780175\pi\)
−0.770865 + 0.636999i \(0.780175\pi\)
\(468\) 0 0
\(469\) −462234. −0.0970352
\(470\) 4.64886e6 0.970738
\(471\) 0 0
\(472\) −8.31989e6 −1.71895
\(473\) 2.11426e6 0.434516
\(474\) 0 0
\(475\) 519639. 0.105674
\(476\) 724056. 0.146472
\(477\) 0 0
\(478\) −5.05103e6 −1.01114
\(479\) 4.09584e6 0.815651 0.407826 0.913060i \(-0.366287\pi\)
0.407826 + 0.913060i \(0.366287\pi\)
\(480\) 0 0
\(481\) −8.19181e6 −1.61442
\(482\) 6.60694e6 1.29534
\(483\) 0 0
\(484\) 971814. 0.188569
\(485\) −1.12045e6 −0.216290
\(486\) 0 0
\(487\) 218477. 0.0417429 0.0208715 0.999782i \(-0.493356\pi\)
0.0208715 + 0.999782i \(0.493356\pi\)
\(488\) −1.15620e7 −2.19778
\(489\) 0 0
\(490\) 2.03917e6 0.383674
\(491\) 3.49848e6 0.654901 0.327451 0.944868i \(-0.393810\pi\)
0.327451 + 0.944868i \(0.393810\pi\)
\(492\) 0 0
\(493\) −678887. −0.125800
\(494\) −6.59920e6 −1.21667
\(495\) 0 0
\(496\) −77704.7 −0.0141822
\(497\) 5.83315e6 1.05928
\(498\) 0 0
\(499\) −3.62715e6 −0.652100 −0.326050 0.945353i \(-0.605718\pi\)
−0.326050 + 0.945353i \(0.605718\pi\)
\(500\) 1.03713e6 0.185527
\(501\) 0 0
\(502\) 5.00893e6 0.887127
\(503\) −6.00845e6 −1.05887 −0.529435 0.848351i \(-0.677596\pi\)
−0.529435 + 0.848351i \(0.677596\pi\)
\(504\) 0 0
\(505\) −2.07179e6 −0.361508
\(506\) −3.54308e6 −0.615184
\(507\) 0 0
\(508\) −1.41301e7 −2.42933
\(509\) −4.28786e6 −0.733578 −0.366789 0.930304i \(-0.619543\pi\)
−0.366789 + 0.930304i \(0.619543\pi\)
\(510\) 0 0
\(511\) −5.02443e6 −0.851205
\(512\) 1.17554e7 1.98182
\(513\) 0 0
\(514\) −2.01017e7 −3.35602
\(515\) 3.84243e6 0.638392
\(516\) 0 0
\(517\) 2.26854e6 0.373268
\(518\) 9.40648e6 1.54029
\(519\) 0 0
\(520\) −6.82131e6 −1.10627
\(521\) −1.06243e7 −1.71477 −0.857386 0.514673i \(-0.827913\pi\)
−0.857386 + 0.514673i \(0.827913\pi\)
\(522\) 0 0
\(523\) 123402. 0.0197273 0.00986367 0.999951i \(-0.496860\pi\)
0.00986367 + 0.999951i \(0.496860\pi\)
\(524\) 9.73023e6 1.54809
\(525\) 0 0
\(526\) 1.56066e7 2.45949
\(527\) −7274.16 −0.00114092
\(528\) 0 0
\(529\) 2.27934e6 0.354136
\(530\) −2.40609e6 −0.372067
\(531\) 0 0
\(532\) 5.11282e6 0.783216
\(533\) −7.68176e6 −1.17123
\(534\) 0 0
\(535\) −1.04156e6 −0.157325
\(536\) 1.70113e6 0.255756
\(537\) 0 0
\(538\) −1.54686e7 −2.30407
\(539\) 995069. 0.147530
\(540\) 0 0
\(541\) −5.60908e6 −0.823946 −0.411973 0.911196i \(-0.635160\pi\)
−0.411973 + 0.911196i \(0.635160\pi\)
\(542\) −1.34171e7 −1.96183
\(543\) 0 0
\(544\) −184192. −0.0266853
\(545\) 993624. 0.143295
\(546\) 0 0
\(547\) 2.72729e6 0.389729 0.194864 0.980830i \(-0.437573\pi\)
0.194864 + 0.980830i \(0.437573\pi\)
\(548\) −2.22410e7 −3.16375
\(549\) 0 0
\(550\) 750085. 0.105731
\(551\) −4.79387e6 −0.672678
\(552\) 0 0
\(553\) −5.28050e6 −0.734280
\(554\) −2.45190e7 −3.39413
\(555\) 0 0
\(556\) 1.99484e6 0.273666
\(557\) −3.50042e6 −0.478059 −0.239030 0.971012i \(-0.576829\pi\)
−0.239030 + 0.971012i \(0.576829\pi\)
\(558\) 0 0
\(559\) −1.39829e7 −1.89264
\(560\) 2.91316e6 0.392550
\(561\) 0 0
\(562\) 7.63337e6 1.01947
\(563\) −1.03320e7 −1.37377 −0.686886 0.726766i \(-0.741023\pi\)
−0.686886 + 0.726766i \(0.741023\pi\)
\(564\) 0 0
\(565\) 4.77892e6 0.629809
\(566\) −2.50825e7 −3.29101
\(567\) 0 0
\(568\) −2.14674e7 −2.79195
\(569\) 1.31943e7 1.70846 0.854229 0.519897i \(-0.174030\pi\)
0.854229 + 0.519897i \(0.174030\pi\)
\(570\) 0 0
\(571\) −5.98575e6 −0.768295 −0.384148 0.923272i \(-0.625505\pi\)
−0.384148 + 0.923272i \(0.625505\pi\)
\(572\) −6.42721e6 −0.821358
\(573\) 0 0
\(574\) 8.82079e6 1.11745
\(575\) −1.84515e6 −0.232735
\(576\) 0 0
\(577\) 7.74177e6 0.968056 0.484028 0.875052i \(-0.339173\pi\)
0.484028 + 0.875052i \(0.339173\pi\)
\(578\) 1.39453e7 1.73624
\(579\) 0 0
\(580\) −9.56791e6 −1.18099
\(581\) −4.60321e6 −0.565744
\(582\) 0 0
\(583\) −1.17412e6 −0.143067
\(584\) 1.84911e7 2.24352
\(585\) 0 0
\(586\) 2.04858e7 2.46439
\(587\) −1.19577e7 −1.43236 −0.716181 0.697915i \(-0.754111\pi\)
−0.716181 + 0.697915i \(0.754111\pi\)
\(588\) 0 0
\(589\) −51365.5 −0.00610075
\(590\) −6.05062e6 −0.715599
\(591\) 0 0
\(592\) −1.28752e7 −1.50990
\(593\) 1.08502e7 1.26707 0.633536 0.773713i \(-0.281603\pi\)
0.633536 + 0.773713i \(0.281603\pi\)
\(594\) 0 0
\(595\) 272709. 0.0315797
\(596\) −1.59472e7 −1.83895
\(597\) 0 0
\(598\) 2.34326e7 2.67959
\(599\) 1.23306e7 1.40416 0.702082 0.712096i \(-0.252254\pi\)
0.702082 + 0.712096i \(0.252254\pi\)
\(600\) 0 0
\(601\) 1.17382e7 1.32561 0.662807 0.748790i \(-0.269365\pi\)
0.662807 + 0.748790i \(0.269365\pi\)
\(602\) 1.60563e7 1.80574
\(603\) 0 0
\(604\) 2.52215e6 0.281305
\(605\) 366025. 0.0406558
\(606\) 0 0
\(607\) 9.20559e6 1.01410 0.507049 0.861917i \(-0.330736\pi\)
0.507049 + 0.861917i \(0.330736\pi\)
\(608\) −1.30064e6 −0.142692
\(609\) 0 0
\(610\) −8.40845e6 −0.914938
\(611\) −1.50033e7 −1.62586
\(612\) 0 0
\(613\) 5.83164e6 0.626815 0.313408 0.949619i \(-0.398529\pi\)
0.313408 + 0.949619i \(0.398529\pi\)
\(614\) 2.15316e7 2.30491
\(615\) 0 0
\(616\) 3.82221e6 0.405848
\(617\) 9.28462e6 0.981863 0.490932 0.871198i \(-0.336656\pi\)
0.490932 + 0.871198i \(0.336656\pi\)
\(618\) 0 0
\(619\) 2.47650e6 0.259784 0.129892 0.991528i \(-0.458537\pi\)
0.129892 + 0.991528i \(0.458537\pi\)
\(620\) −102518. −0.0107108
\(621\) 0 0
\(622\) −1.96957e6 −0.204125
\(623\) 8.15193e6 0.841474
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 4.79819e6 0.489374
\(627\) 0 0
\(628\) −1.72917e7 −1.74960
\(629\) −1.20528e6 −0.121468
\(630\) 0 0
\(631\) 8.58315e6 0.858170 0.429085 0.903264i \(-0.358836\pi\)
0.429085 + 0.903264i \(0.358836\pi\)
\(632\) 1.94335e7 1.93534
\(633\) 0 0
\(634\) −1.66728e7 −1.64735
\(635\) −5.32197e6 −0.523767
\(636\) 0 0
\(637\) −6.58101e6 −0.642605
\(638\) −6.91982e6 −0.673044
\(639\) 0 0
\(640\) 7.38414e6 0.712607
\(641\) −4.59033e6 −0.441264 −0.220632 0.975357i \(-0.570812\pi\)
−0.220632 + 0.975357i \(0.570812\pi\)
\(642\) 0 0
\(643\) 9.70391e6 0.925592 0.462796 0.886465i \(-0.346846\pi\)
0.462796 + 0.886465i \(0.346846\pi\)
\(644\) −1.81547e7 −1.72494
\(645\) 0 0
\(646\) −970955. −0.0915415
\(647\) 9.01887e6 0.847015 0.423508 0.905892i \(-0.360799\pi\)
0.423508 + 0.905892i \(0.360799\pi\)
\(648\) 0 0
\(649\) −2.95257e6 −0.275162
\(650\) −4.96078e6 −0.460539
\(651\) 0 0
\(652\) −2.42101e7 −2.23038
\(653\) −1.94337e6 −0.178349 −0.0891747 0.996016i \(-0.528423\pi\)
−0.0891747 + 0.996016i \(0.528423\pi\)
\(654\) 0 0
\(655\) 3.66481e6 0.333770
\(656\) −1.20735e7 −1.09540
\(657\) 0 0
\(658\) 1.72279e7 1.55120
\(659\) 6.36990e6 0.571372 0.285686 0.958323i \(-0.407779\pi\)
0.285686 + 0.958323i \(0.407779\pi\)
\(660\) 0 0
\(661\) −7.88417e6 −0.701863 −0.350931 0.936401i \(-0.614135\pi\)
−0.350931 + 0.936401i \(0.614135\pi\)
\(662\) 1.17912e7 1.04571
\(663\) 0 0
\(664\) 1.69409e7 1.49113
\(665\) 1.92570e6 0.168863
\(666\) 0 0
\(667\) 1.70222e7 1.48150
\(668\) −4.71244e6 −0.408606
\(669\) 0 0
\(670\) 1.23714e6 0.106471
\(671\) −4.10314e6 −0.351812
\(672\) 0 0
\(673\) −4.51895e6 −0.384592 −0.192296 0.981337i \(-0.561593\pi\)
−0.192296 + 0.981337i \(0.561593\pi\)
\(674\) −1.77106e7 −1.50170
\(675\) 0 0
\(676\) 1.78622e7 1.50337
\(677\) −1.17659e7 −0.986624 −0.493312 0.869852i \(-0.664214\pi\)
−0.493312 + 0.869852i \(0.664214\pi\)
\(678\) 0 0
\(679\) −4.15220e6 −0.345624
\(680\) −1.00363e6 −0.0832345
\(681\) 0 0
\(682\) −74144.7 −0.00610407
\(683\) 1.27636e7 1.04694 0.523470 0.852044i \(-0.324637\pi\)
0.523470 + 0.852044i \(0.324637\pi\)
\(684\) 0 0
\(685\) −8.37686e6 −0.682111
\(686\) 2.30009e7 1.86610
\(687\) 0 0
\(688\) −2.19771e7 −1.77011
\(689\) 7.76518e6 0.623165
\(690\) 0 0
\(691\) 1.94008e7 1.54570 0.772849 0.634590i \(-0.218831\pi\)
0.772849 + 0.634590i \(0.218831\pi\)
\(692\) −1.96281e7 −1.55816
\(693\) 0 0
\(694\) 2.69474e7 2.12382
\(695\) 751339. 0.0590030
\(696\) 0 0
\(697\) −1.13023e6 −0.0881225
\(698\) 1.85525e7 1.44133
\(699\) 0 0
\(700\) 3.84343e6 0.296465
\(701\) −1.81026e7 −1.39138 −0.695690 0.718342i \(-0.744901\pi\)
−0.695690 + 0.718342i \(0.744901\pi\)
\(702\) 0 0
\(703\) −8.51092e6 −0.649514
\(704\) 2.99260e6 0.227571
\(705\) 0 0
\(706\) −4.24463e7 −3.20500
\(707\) −7.67773e6 −0.577676
\(708\) 0 0
\(709\) 1.55411e7 1.16109 0.580547 0.814227i \(-0.302839\pi\)
0.580547 + 0.814227i \(0.302839\pi\)
\(710\) −1.56121e7 −1.16229
\(711\) 0 0
\(712\) −3.00010e7 −2.21787
\(713\) 182390. 0.0134362
\(714\) 0 0
\(715\) −2.42075e6 −0.177086
\(716\) 3.76812e7 2.74689
\(717\) 0 0
\(718\) −1.38542e7 −1.00293
\(719\) −8.88792e6 −0.641177 −0.320589 0.947219i \(-0.603881\pi\)
−0.320589 + 0.947219i \(0.603881\pi\)
\(720\) 0 0
\(721\) 1.42394e7 1.02013
\(722\) 1.77029e7 1.26386
\(723\) 0 0
\(724\) −2.39697e7 −1.69948
\(725\) −3.60367e6 −0.254624
\(726\) 0 0
\(727\) −5.73697e6 −0.402575 −0.201287 0.979532i \(-0.564513\pi\)
−0.201287 + 0.979532i \(0.564513\pi\)
\(728\) −2.52787e7 −1.76777
\(729\) 0 0
\(730\) 1.34476e7 0.933980
\(731\) −2.05734e6 −0.142401
\(732\) 0 0
\(733\) 1.77002e6 0.121680 0.0608399 0.998148i \(-0.480622\pi\)
0.0608399 + 0.998148i \(0.480622\pi\)
\(734\) 5.01551e7 3.43618
\(735\) 0 0
\(736\) 4.61836e6 0.314263
\(737\) 603698. 0.0409403
\(738\) 0 0
\(739\) 1.53957e7 1.03702 0.518512 0.855070i \(-0.326486\pi\)
0.518512 + 0.855070i \(0.326486\pi\)
\(740\) −1.69866e7 −1.14032
\(741\) 0 0
\(742\) −8.91658e6 −0.594550
\(743\) −1.65861e7 −1.10223 −0.551115 0.834429i \(-0.685798\pi\)
−0.551115 + 0.834429i \(0.685798\pi\)
\(744\) 0 0
\(745\) −6.00639e6 −0.396481
\(746\) 4.64301e7 3.05459
\(747\) 0 0
\(748\) −945650. −0.0617983
\(749\) −3.85985e6 −0.251400
\(750\) 0 0
\(751\) 9.40157e6 0.608276 0.304138 0.952628i \(-0.401632\pi\)
0.304138 + 0.952628i \(0.401632\pi\)
\(752\) −2.35808e7 −1.52060
\(753\) 0 0
\(754\) 4.57651e7 2.93161
\(755\) 949944. 0.0606500
\(756\) 0 0
\(757\) 1.22686e7 0.778134 0.389067 0.921209i \(-0.372797\pi\)
0.389067 + 0.921209i \(0.372797\pi\)
\(758\) 3.73571e7 2.36157
\(759\) 0 0
\(760\) −7.08703e6 −0.445072
\(761\) 2.14104e7 1.34018 0.670090 0.742280i \(-0.266256\pi\)
0.670090 + 0.742280i \(0.266256\pi\)
\(762\) 0 0
\(763\) 3.68221e6 0.228980
\(764\) −2.22275e7 −1.37771
\(765\) 0 0
\(766\) 4.13875e7 2.54857
\(767\) 1.95272e7 1.19854
\(768\) 0 0
\(769\) 8.34064e6 0.508609 0.254304 0.967124i \(-0.418154\pi\)
0.254304 + 0.967124i \(0.418154\pi\)
\(770\) 2.77970e6 0.168955
\(771\) 0 0
\(772\) −1.90264e7 −1.14898
\(773\) −3.00417e7 −1.80832 −0.904162 0.427191i \(-0.859503\pi\)
−0.904162 + 0.427191i \(0.859503\pi\)
\(774\) 0 0
\(775\) −38612.7 −0.00230927
\(776\) 1.52811e7 0.910960
\(777\) 0 0
\(778\) −3.70180e7 −2.19262
\(779\) −7.98099e6 −0.471209
\(780\) 0 0
\(781\) −7.61836e6 −0.446924
\(782\) 3.44769e6 0.201610
\(783\) 0 0
\(784\) −1.03434e7 −0.601001
\(785\) −6.51277e6 −0.377217
\(786\) 0 0
\(787\) −1.55411e7 −0.894427 −0.447213 0.894427i \(-0.647584\pi\)
−0.447213 + 0.894427i \(0.647584\pi\)
\(788\) −2.67200e7 −1.53292
\(789\) 0 0
\(790\) 1.41329e7 0.805684
\(791\) 1.77099e7 1.00641
\(792\) 0 0
\(793\) 2.71366e7 1.53240
\(794\) −5.66760e7 −3.19042
\(795\) 0 0
\(796\) 3.36432e7 1.88198
\(797\) 2.13571e7 1.19096 0.595478 0.803371i \(-0.296963\pi\)
0.595478 + 0.803371i \(0.296963\pi\)
\(798\) 0 0
\(799\) −2.20747e6 −0.122328
\(800\) −977726. −0.0540122
\(801\) 0 0
\(802\) 3.57844e7 1.96453
\(803\) 6.56213e6 0.359134
\(804\) 0 0
\(805\) −6.83782e6 −0.371902
\(806\) 490365. 0.0265878
\(807\) 0 0
\(808\) 2.82559e7 1.52258
\(809\) −9.58699e6 −0.515004 −0.257502 0.966278i \(-0.582899\pi\)
−0.257502 + 0.966278i \(0.582899\pi\)
\(810\) 0 0
\(811\) 2.27762e6 0.121599 0.0607995 0.998150i \(-0.480635\pi\)
0.0607995 + 0.998150i \(0.480635\pi\)
\(812\) −3.54572e7 −1.88718
\(813\) 0 0
\(814\) −1.22853e7 −0.649867
\(815\) −9.11853e6 −0.480874
\(816\) 0 0
\(817\) −1.45276e7 −0.761447
\(818\) 4.55706e7 2.38123
\(819\) 0 0
\(820\) −1.59290e7 −0.827282
\(821\) −2.31851e7 −1.20047 −0.600234 0.799824i \(-0.704926\pi\)
−0.600234 + 0.799824i \(0.704926\pi\)
\(822\) 0 0
\(823\) 3.30629e7 1.70153 0.850767 0.525542i \(-0.176138\pi\)
0.850767 + 0.525542i \(0.176138\pi\)
\(824\) −5.24045e7 −2.68875
\(825\) 0 0
\(826\) −2.24226e7 −1.14350
\(827\) −2.84571e7 −1.44686 −0.723431 0.690396i \(-0.757436\pi\)
−0.723431 + 0.690396i \(0.757436\pi\)
\(828\) 0 0
\(829\) −3.34334e7 −1.68964 −0.844821 0.535050i \(-0.820293\pi\)
−0.844821 + 0.535050i \(0.820293\pi\)
\(830\) 1.23202e7 0.620759
\(831\) 0 0
\(832\) −1.97919e7 −0.991243
\(833\) −968279. −0.0483491
\(834\) 0 0
\(835\) −1.77490e6 −0.0880962
\(836\) −6.67758e6 −0.330448
\(837\) 0 0
\(838\) 1.90815e7 0.938646
\(839\) 1.79019e7 0.877999 0.438999 0.898487i \(-0.355333\pi\)
0.438999 + 0.898487i \(0.355333\pi\)
\(840\) 0 0
\(841\) 1.27341e7 0.620837
\(842\) 4.25440e7 2.06803
\(843\) 0 0
\(844\) 1.10691e7 0.534882
\(845\) 6.72762e6 0.324130
\(846\) 0 0
\(847\) 1.35643e6 0.0649665
\(848\) 1.22046e7 0.582820
\(849\) 0 0
\(850\) −729891. −0.0346506
\(851\) 3.02208e7 1.43048
\(852\) 0 0
\(853\) −2.79631e7 −1.31587 −0.657934 0.753076i \(-0.728569\pi\)
−0.657934 + 0.753076i \(0.728569\pi\)
\(854\) −3.11604e7 −1.46204
\(855\) 0 0
\(856\) 1.42052e7 0.662615
\(857\) −9.24668e6 −0.430065 −0.215032 0.976607i \(-0.568986\pi\)
−0.215032 + 0.976607i \(0.568986\pi\)
\(858\) 0 0
\(859\) 1.46860e7 0.679081 0.339540 0.940591i \(-0.389728\pi\)
0.339540 + 0.940591i \(0.389728\pi\)
\(860\) −2.89952e7 −1.33684
\(861\) 0 0
\(862\) 4.73551e6 0.217070
\(863\) −1.14915e7 −0.525231 −0.262615 0.964901i \(-0.584585\pi\)
−0.262615 + 0.964901i \(0.584585\pi\)
\(864\) 0 0
\(865\) −7.39275e6 −0.335943
\(866\) 6.19825e7 2.80850
\(867\) 0 0
\(868\) −379917. −0.0171155
\(869\) 6.89657e6 0.309802
\(870\) 0 0
\(871\) −3.99263e6 −0.178326
\(872\) −1.35514e7 −0.603523
\(873\) 0 0
\(874\) 2.43454e7 1.07805
\(875\) 1.44759e6 0.0639185
\(876\) 0 0
\(877\) 2.92652e7 1.28485 0.642426 0.766348i \(-0.277928\pi\)
0.642426 + 0.766348i \(0.277928\pi\)
\(878\) −5.41184e7 −2.36924
\(879\) 0 0
\(880\) −3.80472e6 −0.165621
\(881\) 6.92950e6 0.300789 0.150395 0.988626i \(-0.451946\pi\)
0.150395 + 0.988626i \(0.451946\pi\)
\(882\) 0 0
\(883\) 4.40887e7 1.90294 0.951470 0.307740i \(-0.0995727\pi\)
0.951470 + 0.307740i \(0.0995727\pi\)
\(884\) 6.25418e6 0.269178
\(885\) 0 0
\(886\) −3.72719e7 −1.59514
\(887\) −4.26047e7 −1.81823 −0.909115 0.416545i \(-0.863241\pi\)
−0.909115 + 0.416545i \(0.863241\pi\)
\(888\) 0 0
\(889\) −1.97224e7 −0.836961
\(890\) −2.18182e7 −0.923302
\(891\) 0 0
\(892\) 3.69087e7 1.55316
\(893\) −1.55877e7 −0.654115
\(894\) 0 0
\(895\) 1.41923e7 0.592236
\(896\) 2.73645e7 1.13872
\(897\) 0 0
\(898\) −7.11462e7 −2.94416
\(899\) 356217. 0.0146999
\(900\) 0 0
\(901\) 1.14251e6 0.0468864
\(902\) −1.15204e7 −0.471465
\(903\) 0 0
\(904\) −6.51767e7 −2.65260
\(905\) −9.02796e6 −0.366411
\(906\) 0 0
\(907\) 2.03750e7 0.822392 0.411196 0.911547i \(-0.365111\pi\)
0.411196 + 0.911547i \(0.365111\pi\)
\(908\) −3.37091e7 −1.35685
\(909\) 0 0
\(910\) −1.83839e7 −0.735925
\(911\) −1.25015e7 −0.499077 −0.249538 0.968365i \(-0.580279\pi\)
−0.249538 + 0.968365i \(0.580279\pi\)
\(912\) 0 0
\(913\) 6.01200e6 0.238694
\(914\) 3.18621e7 1.26156
\(915\) 0 0
\(916\) −4.16307e7 −1.63936
\(917\) 1.35812e7 0.533353
\(918\) 0 0
\(919\) 2.12364e7 0.829455 0.414728 0.909946i \(-0.363877\pi\)
0.414728 + 0.909946i \(0.363877\pi\)
\(920\) 2.51648e7 0.980221
\(921\) 0 0
\(922\) −5.13586e7 −1.98969
\(923\) 5.03850e7 1.94669
\(924\) 0 0
\(925\) −6.39787e6 −0.245856
\(926\) −2.92736e7 −1.12189
\(927\) 0 0
\(928\) 9.01990e6 0.343821
\(929\) −2.38747e7 −0.907608 −0.453804 0.891102i \(-0.649933\pi\)
−0.453804 + 0.891102i \(0.649933\pi\)
\(930\) 0 0
\(931\) −6.83737e6 −0.258532
\(932\) −6.34470e7 −2.39261
\(933\) 0 0
\(934\) 7.20685e7 2.70320
\(935\) −356171. −0.0133238
\(936\) 0 0
\(937\) −1.33814e7 −0.497914 −0.248957 0.968515i \(-0.580088\pi\)
−0.248957 + 0.968515i \(0.580088\pi\)
\(938\) 4.58465e6 0.170137
\(939\) 0 0
\(940\) −3.11110e7 −1.14840
\(941\) −5.91644e6 −0.217814 −0.108907 0.994052i \(-0.534735\pi\)
−0.108907 + 0.994052i \(0.534735\pi\)
\(942\) 0 0
\(943\) 2.83391e7 1.03778
\(944\) 3.06911e7 1.12094
\(945\) 0 0
\(946\) −2.09703e7 −0.761861
\(947\) 4.78035e7 1.73215 0.866074 0.499916i \(-0.166636\pi\)
0.866074 + 0.499916i \(0.166636\pi\)
\(948\) 0 0
\(949\) −4.33995e7 −1.56430
\(950\) −5.15402e6 −0.185284
\(951\) 0 0
\(952\) −3.71931e6 −0.133006
\(953\) 3.75680e7 1.33994 0.669971 0.742387i \(-0.266306\pi\)
0.669971 + 0.742387i \(0.266306\pi\)
\(954\) 0 0
\(955\) −8.37177e6 −0.297036
\(956\) 3.38024e7 1.19620
\(957\) 0 0
\(958\) −4.06245e7 −1.43013
\(959\) −3.10433e7 −1.08999
\(960\) 0 0
\(961\) −2.86253e7 −0.999867
\(962\) 8.12503e7 2.83066
\(963\) 0 0
\(964\) −4.42148e7 −1.53241
\(965\) −7.16613e6 −0.247723
\(966\) 0 0
\(967\) −2.07684e7 −0.714228 −0.357114 0.934061i \(-0.616239\pi\)
−0.357114 + 0.934061i \(0.616239\pi\)
\(968\) −4.99199e6 −0.171232
\(969\) 0 0
\(970\) 1.11131e7 0.379234
\(971\) −1.39451e7 −0.474650 −0.237325 0.971430i \(-0.576271\pi\)
−0.237325 + 0.971430i \(0.576271\pi\)
\(972\) 0 0
\(973\) 2.78434e6 0.0942846
\(974\) −2.16696e6 −0.0731902
\(975\) 0 0
\(976\) 4.26510e7 1.43319
\(977\) −2.07797e7 −0.696471 −0.348236 0.937407i \(-0.613219\pi\)
−0.348236 + 0.937407i \(0.613219\pi\)
\(978\) 0 0
\(979\) −1.06468e7 −0.355028
\(980\) −1.36465e7 −0.453894
\(981\) 0 0
\(982\) −3.46996e7 −1.14828
\(983\) −1.16598e7 −0.384864 −0.192432 0.981310i \(-0.561637\pi\)
−0.192432 + 0.981310i \(0.561637\pi\)
\(984\) 0 0
\(985\) −1.00638e7 −0.330501
\(986\) 6.73353e6 0.220572
\(987\) 0 0
\(988\) 4.41630e7 1.43935
\(989\) 5.15851e7 1.67700
\(990\) 0 0
\(991\) −2.35287e7 −0.761050 −0.380525 0.924771i \(-0.624257\pi\)
−0.380525 + 0.924771i \(0.624257\pi\)
\(992\) 96646.7 0.00311823
\(993\) 0 0
\(994\) −5.78559e7 −1.85730
\(995\) 1.26714e7 0.405759
\(996\) 0 0
\(997\) −4.85989e7 −1.54842 −0.774210 0.632929i \(-0.781853\pi\)
−0.774210 + 0.632929i \(0.781853\pi\)
\(998\) 3.59758e7 1.14336
\(999\) 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 495.6.a.a.1.1 3
3.2 odd 2 165.6.a.e.1.3 3
15.14 odd 2 825.6.a.f.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.6.a.e.1.3 3 3.2 odd 2
495.6.a.a.1.1 3 1.1 even 1 trivial
825.6.a.f.1.1 3 15.14 odd 2