Properties

Label 588.6.a.p.1.4
Level $588$
Weight $6$
Character 588.1
Self dual yes
Analytic conductor $94.306$
Analytic rank $0$
Dimension $4$
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] = [588,6,Mod(1,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, 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("588.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 588.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: \(94.3056860500\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 699x^{2} - 686x + 59664 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3}\cdot 3^{2}\cdot 7 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-22.4831\) of defining polynomial
Character \(\chi\) \(=\) 588.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+9.00000 q^{3} +92.8255 q^{5} +81.0000 q^{9} +O(q^{10})\) \(q+9.00000 q^{3} +92.8255 q^{5} +81.0000 q^{9} +140.762 q^{11} +1111.24 q^{13} +835.430 q^{15} -54.8869 q^{17} +1711.86 q^{19} -3287.91 q^{23} +5491.58 q^{25} +729.000 q^{27} -3790.72 q^{29} +4847.32 q^{31} +1266.86 q^{33} -11366.7 q^{37} +10001.2 q^{39} +10385.6 q^{41} +7137.16 q^{43} +7518.87 q^{45} +16415.1 q^{47} -493.983 q^{51} -20974.3 q^{53} +13066.3 q^{55} +15406.7 q^{57} +36211.9 q^{59} -4948.70 q^{61} +103152. q^{65} -22965.6 q^{67} -29591.2 q^{69} -26341.8 q^{71} -55387.4 q^{73} +49424.2 q^{75} -49956.6 q^{79} +6561.00 q^{81} -44858.9 q^{83} -5094.91 q^{85} -34116.5 q^{87} -127945. q^{89} +43625.9 q^{93} +158904. q^{95} +65685.9 q^{97} +11401.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 36 q^{3} + 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 36 q^{3} + 324 q^{9} + 462 q^{11} + 602 q^{13} + 228 q^{17} + 358 q^{19} + 2148 q^{23} + 5454 q^{25} + 2916 q^{27} - 5532 q^{29} + 830 q^{31} + 4158 q^{33} + 3914 q^{37} + 5418 q^{39} + 8316 q^{41} - 14518 q^{43} + 41700 q^{47} + 2052 q^{51} - 22164 q^{53} - 3892 q^{55} + 3222 q^{57} + 32886 q^{59} + 83732 q^{61} + 93192 q^{65} + 80034 q^{67} + 19332 q^{69} + 44772 q^{71} - 22470 q^{73} + 49086 q^{75} + 75286 q^{79} + 26244 q^{81} + 17418 q^{83} + 139252 q^{85} - 49788 q^{87} + 28944 q^{89} + 7470 q^{93} + 144120 q^{95} + 216678 q^{97} + 37422 q^{99}+O(q^{100}) \) 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
\(3\) 9.00000 0.577350
\(4\) 0 0
\(5\) 92.8255 1.66051 0.830257 0.557381i \(-0.188194\pi\)
0.830257 + 0.557381i \(0.188194\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 81.0000 0.333333
\(10\) 0 0
\(11\) 140.762 0.350756 0.175378 0.984501i \(-0.443885\pi\)
0.175378 + 0.984501i \(0.443885\pi\)
\(12\) 0 0
\(13\) 1111.24 1.82369 0.911844 0.410537i \(-0.134659\pi\)
0.911844 + 0.410537i \(0.134659\pi\)
\(14\) 0 0
\(15\) 835.430 0.958698
\(16\) 0 0
\(17\) −54.8869 −0.0460624 −0.0230312 0.999735i \(-0.507332\pi\)
−0.0230312 + 0.999735i \(0.507332\pi\)
\(18\) 0 0
\(19\) 1711.86 1.08789 0.543943 0.839122i \(-0.316931\pi\)
0.543943 + 0.839122i \(0.316931\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3287.91 −1.29599 −0.647993 0.761646i \(-0.724391\pi\)
−0.647993 + 0.761646i \(0.724391\pi\)
\(24\) 0 0
\(25\) 5491.58 1.75731
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −3790.72 −0.837003 −0.418501 0.908216i \(-0.637445\pi\)
−0.418501 + 0.908216i \(0.637445\pi\)
\(30\) 0 0
\(31\) 4847.32 0.905936 0.452968 0.891527i \(-0.350365\pi\)
0.452968 + 0.891527i \(0.350365\pi\)
\(32\) 0 0
\(33\) 1266.86 0.202509
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −11366.7 −1.36499 −0.682496 0.730889i \(-0.739106\pi\)
−0.682496 + 0.730889i \(0.739106\pi\)
\(38\) 0 0
\(39\) 10001.2 1.05291
\(40\) 0 0
\(41\) 10385.6 0.964881 0.482440 0.875929i \(-0.339751\pi\)
0.482440 + 0.875929i \(0.339751\pi\)
\(42\) 0 0
\(43\) 7137.16 0.588646 0.294323 0.955706i \(-0.404906\pi\)
0.294323 + 0.955706i \(0.404906\pi\)
\(44\) 0 0
\(45\) 7518.87 0.553505
\(46\) 0 0
\(47\) 16415.1 1.08392 0.541961 0.840404i \(-0.317682\pi\)
0.541961 + 0.840404i \(0.317682\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −493.983 −0.0265942
\(52\) 0 0
\(53\) −20974.3 −1.02565 −0.512824 0.858494i \(-0.671401\pi\)
−0.512824 + 0.858494i \(0.671401\pi\)
\(54\) 0 0
\(55\) 13066.3 0.582435
\(56\) 0 0
\(57\) 15406.7 0.628092
\(58\) 0 0
\(59\) 36211.9 1.35432 0.677161 0.735835i \(-0.263210\pi\)
0.677161 + 0.735835i \(0.263210\pi\)
\(60\) 0 0
\(61\) −4948.70 −0.170281 −0.0851405 0.996369i \(-0.527134\pi\)
−0.0851405 + 0.996369i \(0.527134\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 103152. 3.02826
\(66\) 0 0
\(67\) −22965.6 −0.625015 −0.312507 0.949915i \(-0.601169\pi\)
−0.312507 + 0.949915i \(0.601169\pi\)
\(68\) 0 0
\(69\) −29591.2 −0.748238
\(70\) 0 0
\(71\) −26341.8 −0.620154 −0.310077 0.950711i \(-0.600355\pi\)
−0.310077 + 0.950711i \(0.600355\pi\)
\(72\) 0 0
\(73\) −55387.4 −1.21648 −0.608238 0.793755i \(-0.708123\pi\)
−0.608238 + 0.793755i \(0.708123\pi\)
\(74\) 0 0
\(75\) 49424.2 1.01458
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −49956.6 −0.900586 −0.450293 0.892881i \(-0.648680\pi\)
−0.450293 + 0.892881i \(0.648680\pi\)
\(80\) 0 0
\(81\) 6561.00 0.111111
\(82\) 0 0
\(83\) −44858.9 −0.714749 −0.357374 0.933961i \(-0.616328\pi\)
−0.357374 + 0.933961i \(0.616328\pi\)
\(84\) 0 0
\(85\) −5094.91 −0.0764873
\(86\) 0 0
\(87\) −34116.5 −0.483244
\(88\) 0 0
\(89\) −127945. −1.71217 −0.856087 0.516831i \(-0.827111\pi\)
−0.856087 + 0.516831i \(0.827111\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 43625.9 0.523042
\(94\) 0 0
\(95\) 158904. 1.80645
\(96\) 0 0
\(97\) 65685.9 0.708831 0.354415 0.935088i \(-0.384680\pi\)
0.354415 + 0.935088i \(0.384680\pi\)
\(98\) 0 0
\(99\) 11401.8 0.116919
\(100\) 0 0
\(101\) −175783. −1.71464 −0.857320 0.514784i \(-0.827872\pi\)
−0.857320 + 0.514784i \(0.827872\pi\)
\(102\) 0 0
\(103\) 154109. 1.43132 0.715659 0.698450i \(-0.246127\pi\)
0.715659 + 0.698450i \(0.246127\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 183362. 1.54828 0.774141 0.633013i \(-0.218182\pi\)
0.774141 + 0.633013i \(0.218182\pi\)
\(108\) 0 0
\(109\) −134645. −1.08548 −0.542741 0.839900i \(-0.682613\pi\)
−0.542741 + 0.839900i \(0.682613\pi\)
\(110\) 0 0
\(111\) −102300. −0.788079
\(112\) 0 0
\(113\) 176955. 1.30367 0.651833 0.758362i \(-0.274000\pi\)
0.651833 + 0.758362i \(0.274000\pi\)
\(114\) 0 0
\(115\) −305202. −2.15200
\(116\) 0 0
\(117\) 90010.7 0.607896
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −141237. −0.876970
\(122\) 0 0
\(123\) 93470.8 0.557074
\(124\) 0 0
\(125\) 219679. 1.25752
\(126\) 0 0
\(127\) 144432. 0.794608 0.397304 0.917687i \(-0.369946\pi\)
0.397304 + 0.917687i \(0.369946\pi\)
\(128\) 0 0
\(129\) 64234.4 0.339855
\(130\) 0 0
\(131\) 237508. 1.20920 0.604602 0.796527i \(-0.293332\pi\)
0.604602 + 0.796527i \(0.293332\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 67669.8 0.319566
\(136\) 0 0
\(137\) −96203.3 −0.437914 −0.218957 0.975735i \(-0.570265\pi\)
−0.218957 + 0.975735i \(0.570265\pi\)
\(138\) 0 0
\(139\) 391373. 1.71812 0.859060 0.511874i \(-0.171049\pi\)
0.859060 + 0.511874i \(0.171049\pi\)
\(140\) 0 0
\(141\) 147736. 0.625802
\(142\) 0 0
\(143\) 156421. 0.639669
\(144\) 0 0
\(145\) −351876. −1.38985
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −80678.8 −0.297710 −0.148855 0.988859i \(-0.547559\pi\)
−0.148855 + 0.988859i \(0.547559\pi\)
\(150\) 0 0
\(151\) 95682.6 0.341500 0.170750 0.985314i \(-0.445381\pi\)
0.170750 + 0.985314i \(0.445381\pi\)
\(152\) 0 0
\(153\) −4445.84 −0.0153541
\(154\) 0 0
\(155\) 449955. 1.50432
\(156\) 0 0
\(157\) 195625. 0.633397 0.316699 0.948526i \(-0.397426\pi\)
0.316699 + 0.948526i \(0.397426\pi\)
\(158\) 0 0
\(159\) −188769. −0.592158
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 37645.7 0.110980 0.0554902 0.998459i \(-0.482328\pi\)
0.0554902 + 0.998459i \(0.482328\pi\)
\(164\) 0 0
\(165\) 117597. 0.336269
\(166\) 0 0
\(167\) −646778. −1.79458 −0.897292 0.441437i \(-0.854469\pi\)
−0.897292 + 0.441437i \(0.854469\pi\)
\(168\) 0 0
\(169\) 863568. 2.32584
\(170\) 0 0
\(171\) 138661. 0.362629
\(172\) 0 0
\(173\) 386908. 0.982863 0.491431 0.870916i \(-0.336474\pi\)
0.491431 + 0.870916i \(0.336474\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 325907. 0.781918
\(178\) 0 0
\(179\) 27410.5 0.0639418 0.0319709 0.999489i \(-0.489822\pi\)
0.0319709 + 0.999489i \(0.489822\pi\)
\(180\) 0 0
\(181\) 196155. 0.445044 0.222522 0.974928i \(-0.428571\pi\)
0.222522 + 0.974928i \(0.428571\pi\)
\(182\) 0 0
\(183\) −44538.3 −0.0983118
\(184\) 0 0
\(185\) −1.05512e6 −2.26659
\(186\) 0 0
\(187\) −7726.02 −0.0161567
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 266982. 0.529540 0.264770 0.964312i \(-0.414704\pi\)
0.264770 + 0.964312i \(0.414704\pi\)
\(192\) 0 0
\(193\) −101364. −0.195880 −0.0979398 0.995192i \(-0.531225\pi\)
−0.0979398 + 0.995192i \(0.531225\pi\)
\(194\) 0 0
\(195\) 928366. 1.74837
\(196\) 0 0
\(197\) 362366. 0.665245 0.332623 0.943060i \(-0.392066\pi\)
0.332623 + 0.943060i \(0.392066\pi\)
\(198\) 0 0
\(199\) −225413. −0.403502 −0.201751 0.979437i \(-0.564663\pi\)
−0.201751 + 0.979437i \(0.564663\pi\)
\(200\) 0 0
\(201\) −206690. −0.360852
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 964053. 1.60220
\(206\) 0 0
\(207\) −266321. −0.431995
\(208\) 0 0
\(209\) 240965. 0.381583
\(210\) 0 0
\(211\) −327801. −0.506878 −0.253439 0.967351i \(-0.581562\pi\)
−0.253439 + 0.967351i \(0.581562\pi\)
\(212\) 0 0
\(213\) −237076. −0.358046
\(214\) 0 0
\(215\) 662511. 0.977455
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −498486. −0.702333
\(220\) 0 0
\(221\) −60992.7 −0.0840035
\(222\) 0 0
\(223\) −109690. −0.147708 −0.0738538 0.997269i \(-0.523530\pi\)
−0.0738538 + 0.997269i \(0.523530\pi\)
\(224\) 0 0
\(225\) 444818. 0.585769
\(226\) 0 0
\(227\) −1.21747e6 −1.56817 −0.784083 0.620656i \(-0.786866\pi\)
−0.784083 + 0.620656i \(0.786866\pi\)
\(228\) 0 0
\(229\) 1.33603e6 1.68355 0.841776 0.539827i \(-0.181510\pi\)
0.841776 + 0.539827i \(0.181510\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 46788.4 0.0564610 0.0282305 0.999601i \(-0.491013\pi\)
0.0282305 + 0.999601i \(0.491013\pi\)
\(234\) 0 0
\(235\) 1.52374e6 1.79987
\(236\) 0 0
\(237\) −449609. −0.519954
\(238\) 0 0
\(239\) 86350.2 0.0977841 0.0488921 0.998804i \(-0.484431\pi\)
0.0488921 + 0.998804i \(0.484431\pi\)
\(240\) 0 0
\(241\) −825299. −0.915311 −0.457655 0.889130i \(-0.651311\pi\)
−0.457655 + 0.889130i \(0.651311\pi\)
\(242\) 0 0
\(243\) 59049.0 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.90229e6 1.98397
\(248\) 0 0
\(249\) −403730. −0.412660
\(250\) 0 0
\(251\) 130188. 0.130432 0.0652162 0.997871i \(-0.479226\pi\)
0.0652162 + 0.997871i \(0.479226\pi\)
\(252\) 0 0
\(253\) −462814. −0.454574
\(254\) 0 0
\(255\) −45854.2 −0.0441600
\(256\) 0 0
\(257\) −102790. −0.0970775 −0.0485388 0.998821i \(-0.515456\pi\)
−0.0485388 + 0.998821i \(0.515456\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −307048. −0.279001
\(262\) 0 0
\(263\) −35500.7 −0.0316481 −0.0158241 0.999875i \(-0.505037\pi\)
−0.0158241 + 0.999875i \(0.505037\pi\)
\(264\) 0 0
\(265\) −1.94695e6 −1.70310
\(266\) 0 0
\(267\) −1.15150e6 −0.988524
\(268\) 0 0
\(269\) −1.04634e6 −0.881643 −0.440821 0.897595i \(-0.645313\pi\)
−0.440821 + 0.897595i \(0.645313\pi\)
\(270\) 0 0
\(271\) −177278. −0.146633 −0.0733167 0.997309i \(-0.523358\pi\)
−0.0733167 + 0.997309i \(0.523358\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 773008. 0.616385
\(276\) 0 0
\(277\) 145586. 0.114004 0.0570020 0.998374i \(-0.481846\pi\)
0.0570020 + 0.998374i \(0.481846\pi\)
\(278\) 0 0
\(279\) 392633. 0.301979
\(280\) 0 0
\(281\) −1.03073e6 −0.778714 −0.389357 0.921087i \(-0.627303\pi\)
−0.389357 + 0.921087i \(0.627303\pi\)
\(282\) 0 0
\(283\) 1.11726e6 0.829257 0.414628 0.909991i \(-0.363912\pi\)
0.414628 + 0.909991i \(0.363912\pi\)
\(284\) 0 0
\(285\) 1.43014e6 1.04296
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.41684e6 −0.997878
\(290\) 0 0
\(291\) 591173. 0.409244
\(292\) 0 0
\(293\) 2.02032e6 1.37484 0.687418 0.726262i \(-0.258744\pi\)
0.687418 + 0.726262i \(0.258744\pi\)
\(294\) 0 0
\(295\) 3.36139e6 2.24887
\(296\) 0 0
\(297\) 102616. 0.0675030
\(298\) 0 0
\(299\) −3.65367e6 −2.36347
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −1.58204e6 −0.989948
\(304\) 0 0
\(305\) −459366. −0.282754
\(306\) 0 0
\(307\) 535150. 0.324063 0.162031 0.986786i \(-0.448195\pi\)
0.162031 + 0.986786i \(0.448195\pi\)
\(308\) 0 0
\(309\) 1.38698e6 0.826372
\(310\) 0 0
\(311\) 2.30019e6 1.34854 0.674268 0.738487i \(-0.264459\pi\)
0.674268 + 0.738487i \(0.264459\pi\)
\(312\) 0 0
\(313\) 2.75727e6 1.59081 0.795404 0.606079i \(-0.207258\pi\)
0.795404 + 0.606079i \(0.207258\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.54809e6 1.42418 0.712092 0.702086i \(-0.247748\pi\)
0.712092 + 0.702086i \(0.247748\pi\)
\(318\) 0 0
\(319\) −533591. −0.293584
\(320\) 0 0
\(321\) 1.65026e6 0.893901
\(322\) 0 0
\(323\) −93958.7 −0.0501107
\(324\) 0 0
\(325\) 6.10248e6 3.20478
\(326\) 0 0
\(327\) −1.21180e6 −0.626703
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −489335. −0.245491 −0.122746 0.992438i \(-0.539170\pi\)
−0.122746 + 0.992438i \(0.539170\pi\)
\(332\) 0 0
\(333\) −920703. −0.454998
\(334\) 0 0
\(335\) −2.13179e6 −1.03785
\(336\) 0 0
\(337\) −1.47140e6 −0.705757 −0.352878 0.935669i \(-0.614797\pi\)
−0.352878 + 0.935669i \(0.614797\pi\)
\(338\) 0 0
\(339\) 1.59259e6 0.752672
\(340\) 0 0
\(341\) 682320. 0.317762
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −2.74682e6 −1.24246
\(346\) 0 0
\(347\) −2.41925e6 −1.07859 −0.539296 0.842116i \(-0.681310\pi\)
−0.539296 + 0.842116i \(0.681310\pi\)
\(348\) 0 0
\(349\) 2.58571e6 1.13636 0.568180 0.822905i \(-0.307648\pi\)
0.568180 + 0.822905i \(0.307648\pi\)
\(350\) 0 0
\(351\) 810096. 0.350969
\(352\) 0 0
\(353\) −1.00440e6 −0.429010 −0.214505 0.976723i \(-0.568814\pi\)
−0.214505 + 0.976723i \(0.568814\pi\)
\(354\) 0 0
\(355\) −2.44519e6 −1.02977
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.26765e6 −0.928625 −0.464313 0.885671i \(-0.653699\pi\)
−0.464313 + 0.885671i \(0.653699\pi\)
\(360\) 0 0
\(361\) 454359. 0.183498
\(362\) 0 0
\(363\) −1.27113e6 −0.506319
\(364\) 0 0
\(365\) −5.14136e6 −2.01998
\(366\) 0 0
\(367\) −4.78623e6 −1.85493 −0.927467 0.373905i \(-0.878019\pi\)
−0.927467 + 0.373905i \(0.878019\pi\)
\(368\) 0 0
\(369\) 841237. 0.321627
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −4.62701e6 −1.72198 −0.860991 0.508619i \(-0.830156\pi\)
−0.860991 + 0.508619i \(0.830156\pi\)
\(374\) 0 0
\(375\) 1.97711e6 0.726028
\(376\) 0 0
\(377\) −4.21241e6 −1.52643
\(378\) 0 0
\(379\) −497760. −0.178001 −0.0890004 0.996032i \(-0.528367\pi\)
−0.0890004 + 0.996032i \(0.528367\pi\)
\(380\) 0 0
\(381\) 1.29988e6 0.458767
\(382\) 0 0
\(383\) −1.38749e6 −0.483318 −0.241659 0.970361i \(-0.577692\pi\)
−0.241659 + 0.970361i \(0.577692\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 578110. 0.196215
\(388\) 0 0
\(389\) −586055. −0.196365 −0.0981826 0.995168i \(-0.531303\pi\)
−0.0981826 + 0.995168i \(0.531303\pi\)
\(390\) 0 0
\(391\) 180463. 0.0596962
\(392\) 0 0
\(393\) 2.13757e6 0.698135
\(394\) 0 0
\(395\) −4.63725e6 −1.49544
\(396\) 0 0
\(397\) −3.05336e6 −0.972302 −0.486151 0.873875i \(-0.661600\pi\)
−0.486151 + 0.873875i \(0.661600\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.52316e6 1.71525 0.857624 0.514278i \(-0.171940\pi\)
0.857624 + 0.514278i \(0.171940\pi\)
\(402\) 0 0
\(403\) 5.38655e6 1.65214
\(404\) 0 0
\(405\) 609028. 0.184502
\(406\) 0 0
\(407\) −1.60000e6 −0.478779
\(408\) 0 0
\(409\) 3.34927e6 0.990016 0.495008 0.868888i \(-0.335165\pi\)
0.495008 + 0.868888i \(0.335165\pi\)
\(410\) 0 0
\(411\) −865829. −0.252830
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −4.16405e6 −1.18685
\(416\) 0 0
\(417\) 3.52236e6 0.991957
\(418\) 0 0
\(419\) −2.97012e6 −0.826493 −0.413247 0.910619i \(-0.635605\pi\)
−0.413247 + 0.910619i \(0.635605\pi\)
\(420\) 0 0
\(421\) −5.41478e6 −1.48894 −0.744468 0.667658i \(-0.767297\pi\)
−0.744468 + 0.667658i \(0.767297\pi\)
\(422\) 0 0
\(423\) 1.32962e6 0.361307
\(424\) 0 0
\(425\) −301416. −0.0809458
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 1.40779e6 0.369313
\(430\) 0 0
\(431\) −5.05950e6 −1.31194 −0.655970 0.754787i \(-0.727740\pi\)
−0.655970 + 0.754787i \(0.727740\pi\)
\(432\) 0 0
\(433\) −3.84174e6 −0.984711 −0.492355 0.870394i \(-0.663864\pi\)
−0.492355 + 0.870394i \(0.663864\pi\)
\(434\) 0 0
\(435\) −3.16688e6 −0.802433
\(436\) 0 0
\(437\) −5.62843e6 −1.40989
\(438\) 0 0
\(439\) 1.52572e6 0.377844 0.188922 0.981992i \(-0.439501\pi\)
0.188922 + 0.981992i \(0.439501\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.47014e6 −0.355916 −0.177958 0.984038i \(-0.556949\pi\)
−0.177958 + 0.984038i \(0.556949\pi\)
\(444\) 0 0
\(445\) −1.18766e7 −2.84309
\(446\) 0 0
\(447\) −726110. −0.171883
\(448\) 0 0
\(449\) −6.05071e6 −1.41641 −0.708207 0.706004i \(-0.750496\pi\)
−0.708207 + 0.706004i \(0.750496\pi\)
\(450\) 0 0
\(451\) 1.46191e6 0.338437
\(452\) 0 0
\(453\) 861144. 0.197165
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.75420e6 −1.28883 −0.644413 0.764678i \(-0.722898\pi\)
−0.644413 + 0.764678i \(0.722898\pi\)
\(458\) 0 0
\(459\) −40012.6 −0.00886472
\(460\) 0 0
\(461\) −2.83684e6 −0.621703 −0.310851 0.950458i \(-0.600614\pi\)
−0.310851 + 0.950458i \(0.600614\pi\)
\(462\) 0 0
\(463\) 5.19089e6 1.12535 0.562677 0.826677i \(-0.309771\pi\)
0.562677 + 0.826677i \(0.309771\pi\)
\(464\) 0 0
\(465\) 4.04960e6 0.868519
\(466\) 0 0
\(467\) −1.08904e6 −0.231074 −0.115537 0.993303i \(-0.536859\pi\)
−0.115537 + 0.993303i \(0.536859\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1.76063e6 0.365692
\(472\) 0 0
\(473\) 1.00464e6 0.206471
\(474\) 0 0
\(475\) 9.40081e6 1.91175
\(476\) 0 0
\(477\) −1.69892e6 −0.341883
\(478\) 0 0
\(479\) 5.69411e6 1.13393 0.566966 0.823741i \(-0.308117\pi\)
0.566966 + 0.823741i \(0.308117\pi\)
\(480\) 0 0
\(481\) −1.26312e7 −2.48932
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6.09733e6 1.17702
\(486\) 0 0
\(487\) −4.11425e6 −0.786083 −0.393042 0.919521i \(-0.628577\pi\)
−0.393042 + 0.919521i \(0.628577\pi\)
\(488\) 0 0
\(489\) 338811. 0.0640745
\(490\) 0 0
\(491\) −609530. −0.114101 −0.0570507 0.998371i \(-0.518170\pi\)
−0.0570507 + 0.998371i \(0.518170\pi\)
\(492\) 0 0
\(493\) 208061. 0.0385544
\(494\) 0 0
\(495\) 1.05837e6 0.194145
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 995793. 0.179027 0.0895133 0.995986i \(-0.471469\pi\)
0.0895133 + 0.995986i \(0.471469\pi\)
\(500\) 0 0
\(501\) −5.82100e6 −1.03610
\(502\) 0 0
\(503\) −1.02730e7 −1.81042 −0.905209 0.424966i \(-0.860286\pi\)
−0.905209 + 0.424966i \(0.860286\pi\)
\(504\) 0 0
\(505\) −1.63171e7 −2.84718
\(506\) 0 0
\(507\) 7.77211e6 1.34282
\(508\) 0 0
\(509\) 2.78427e6 0.476339 0.238170 0.971224i \(-0.423453\pi\)
0.238170 + 0.971224i \(0.423453\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1.24794e6 0.209364
\(514\) 0 0
\(515\) 1.43053e7 2.37672
\(516\) 0 0
\(517\) 2.31062e6 0.380192
\(518\) 0 0
\(519\) 3.48218e6 0.567456
\(520\) 0 0
\(521\) −1.04536e6 −0.168721 −0.0843607 0.996435i \(-0.526885\pi\)
−0.0843607 + 0.996435i \(0.526885\pi\)
\(522\) 0 0
\(523\) 3.63156e6 0.580550 0.290275 0.956943i \(-0.406253\pi\)
0.290275 + 0.956943i \(0.406253\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −266055. −0.0417296
\(528\) 0 0
\(529\) 4.37400e6 0.679579
\(530\) 0 0
\(531\) 2.93317e6 0.451440
\(532\) 0 0
\(533\) 1.15410e7 1.75964
\(534\) 0 0
\(535\) 1.70207e7 2.57094
\(536\) 0 0
\(537\) 246695. 0.0369168
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −9.44884e6 −1.38799 −0.693994 0.719981i \(-0.744150\pi\)
−0.693994 + 0.719981i \(0.744150\pi\)
\(542\) 0 0
\(543\) 1.76540e6 0.256946
\(544\) 0 0
\(545\) −1.24985e7 −1.80246
\(546\) 0 0
\(547\) 2.69014e6 0.384421 0.192210 0.981354i \(-0.438434\pi\)
0.192210 + 0.981354i \(0.438434\pi\)
\(548\) 0 0
\(549\) −400845. −0.0567604
\(550\) 0 0
\(551\) −6.48918e6 −0.910564
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −9.49609e6 −1.30862
\(556\) 0 0
\(557\) −8.88981e6 −1.21410 −0.607050 0.794664i \(-0.707647\pi\)
−0.607050 + 0.794664i \(0.707647\pi\)
\(558\) 0 0
\(559\) 7.93112e6 1.07351
\(560\) 0 0
\(561\) −69534.1 −0.00932805
\(562\) 0 0
\(563\) −1.25993e6 −0.167523 −0.0837615 0.996486i \(-0.526693\pi\)
−0.0837615 + 0.996486i \(0.526693\pi\)
\(564\) 0 0
\(565\) 1.64259e7 2.16476
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.82038e6 −0.753651 −0.376826 0.926284i \(-0.622984\pi\)
−0.376826 + 0.926284i \(0.622984\pi\)
\(570\) 0 0
\(571\) 4.65961e6 0.598080 0.299040 0.954241i \(-0.403334\pi\)
0.299040 + 0.954241i \(0.403334\pi\)
\(572\) 0 0
\(573\) 2.40284e6 0.305730
\(574\) 0 0
\(575\) −1.80558e7 −2.27744
\(576\) 0 0
\(577\) 1.52478e6 0.190664 0.0953319 0.995446i \(-0.469609\pi\)
0.0953319 + 0.995446i \(0.469609\pi\)
\(578\) 0 0
\(579\) −912273. −0.113091
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2.95240e6 −0.359752
\(584\) 0 0
\(585\) 8.35529e6 1.00942
\(586\) 0 0
\(587\) 1.50087e7 1.79783 0.898914 0.438124i \(-0.144357\pi\)
0.898914 + 0.438124i \(0.144357\pi\)
\(588\) 0 0
\(589\) 8.29792e6 0.985556
\(590\) 0 0
\(591\) 3.26129e6 0.384079
\(592\) 0 0
\(593\) 7.07946e6 0.826729 0.413364 0.910566i \(-0.364354\pi\)
0.413364 + 0.910566i \(0.364354\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.02871e6 −0.232962
\(598\) 0 0
\(599\) −2.17521e6 −0.247705 −0.123853 0.992301i \(-0.539525\pi\)
−0.123853 + 0.992301i \(0.539525\pi\)
\(600\) 0 0
\(601\) −2.69785e6 −0.304671 −0.152336 0.988329i \(-0.548679\pi\)
−0.152336 + 0.988329i \(0.548679\pi\)
\(602\) 0 0
\(603\) −1.86021e6 −0.208338
\(604\) 0 0
\(605\) −1.31104e7 −1.45622
\(606\) 0 0
\(607\) −4.98834e6 −0.549521 −0.274760 0.961513i \(-0.588598\pi\)
−0.274760 + 0.961513i \(0.588598\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.82411e7 1.97673
\(612\) 0 0
\(613\) 1.11364e6 0.119700 0.0598500 0.998207i \(-0.480938\pi\)
0.0598500 + 0.998207i \(0.480938\pi\)
\(614\) 0 0
\(615\) 8.67647e6 0.925029
\(616\) 0 0
\(617\) −5.14757e6 −0.544364 −0.272182 0.962246i \(-0.587745\pi\)
−0.272182 + 0.962246i \(0.587745\pi\)
\(618\) 0 0
\(619\) −243176. −0.0255091 −0.0127545 0.999919i \(-0.504060\pi\)
−0.0127545 + 0.999919i \(0.504060\pi\)
\(620\) 0 0
\(621\) −2.39689e6 −0.249413
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 3.23066e6 0.330819
\(626\) 0 0
\(627\) 2.16869e6 0.220307
\(628\) 0 0
\(629\) 623884. 0.0628749
\(630\) 0 0
\(631\) 9.94255e6 0.994087 0.497044 0.867726i \(-0.334419\pi\)
0.497044 + 0.867726i \(0.334419\pi\)
\(632\) 0 0
\(633\) −2.95021e6 −0.292646
\(634\) 0 0
\(635\) 1.34069e7 1.31946
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −2.13369e6 −0.206718
\(640\) 0 0
\(641\) −1.15553e7 −1.11080 −0.555402 0.831582i \(-0.687436\pi\)
−0.555402 + 0.831582i \(0.687436\pi\)
\(642\) 0 0
\(643\) −1.35139e6 −0.128900 −0.0644500 0.997921i \(-0.520529\pi\)
−0.0644500 + 0.997921i \(0.520529\pi\)
\(644\) 0 0
\(645\) 5.96260e6 0.564334
\(646\) 0 0
\(647\) −1.75536e7 −1.64856 −0.824279 0.566183i \(-0.808419\pi\)
−0.824279 + 0.566183i \(0.808419\pi\)
\(648\) 0 0
\(649\) 5.09728e6 0.475036
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.99873e6 −0.734071 −0.367035 0.930207i \(-0.619627\pi\)
−0.367035 + 0.930207i \(0.619627\pi\)
\(654\) 0 0
\(655\) 2.20468e7 2.00790
\(656\) 0 0
\(657\) −4.48638e6 −0.405492
\(658\) 0 0
\(659\) 229419. 0.0205786 0.0102893 0.999947i \(-0.496725\pi\)
0.0102893 + 0.999947i \(0.496725\pi\)
\(660\) 0 0
\(661\) 3.28557e6 0.292488 0.146244 0.989249i \(-0.453282\pi\)
0.146244 + 0.989249i \(0.453282\pi\)
\(662\) 0 0
\(663\) −548935. −0.0484994
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.24635e7 1.08474
\(668\) 0 0
\(669\) −987206. −0.0852791
\(670\) 0 0
\(671\) −696590. −0.0597271
\(672\) 0 0
\(673\) 8.22188e6 0.699734 0.349867 0.936799i \(-0.386227\pi\)
0.349867 + 0.936799i \(0.386227\pi\)
\(674\) 0 0
\(675\) 4.00336e6 0.338194
\(676\) 0 0
\(677\) −2.15405e7 −1.80628 −0.903138 0.429351i \(-0.858742\pi\)
−0.903138 + 0.429351i \(0.858742\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.09572e7 −0.905381
\(682\) 0 0
\(683\) −1.61741e7 −1.32669 −0.663344 0.748314i \(-0.730863\pi\)
−0.663344 + 0.748314i \(0.730863\pi\)
\(684\) 0 0
\(685\) −8.93012e6 −0.727162
\(686\) 0 0
\(687\) 1.20242e7 0.971999
\(688\) 0 0
\(689\) −2.33076e7 −1.87046
\(690\) 0 0
\(691\) −1.06464e7 −0.848215 −0.424108 0.905612i \(-0.639412\pi\)
−0.424108 + 0.905612i \(0.639412\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.63294e7 2.85296
\(696\) 0 0
\(697\) −570036. −0.0444447
\(698\) 0 0
\(699\) 421096. 0.0325978
\(700\) 0 0
\(701\) −4.55461e6 −0.350071 −0.175035 0.984562i \(-0.556004\pi\)
−0.175035 + 0.984562i \(0.556004\pi\)
\(702\) 0 0
\(703\) −1.94582e7 −1.48496
\(704\) 0 0
\(705\) 1.37136e7 1.03915
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.31035e7 0.978974 0.489487 0.872011i \(-0.337184\pi\)
0.489487 + 0.872011i \(0.337184\pi\)
\(710\) 0 0
\(711\) −4.04649e6 −0.300195
\(712\) 0 0
\(713\) −1.59375e7 −1.17408
\(714\) 0 0
\(715\) 1.45199e7 1.06218
\(716\) 0 0
\(717\) 777151. 0.0564557
\(718\) 0 0
\(719\) −1.79188e7 −1.29267 −0.646335 0.763054i \(-0.723699\pi\)
−0.646335 + 0.763054i \(0.723699\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −7.42769e6 −0.528455
\(724\) 0 0
\(725\) −2.08171e7 −1.47087
\(726\) 0 0
\(727\) −1.41466e7 −0.992693 −0.496347 0.868125i \(-0.665325\pi\)
−0.496347 + 0.868125i \(0.665325\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) −391737. −0.0271145
\(732\) 0 0
\(733\) 1.24448e7 0.855517 0.427758 0.903893i \(-0.359303\pi\)
0.427758 + 0.903893i \(0.359303\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.23269e6 −0.219228
\(738\) 0 0
\(739\) −1.76664e6 −0.118998 −0.0594988 0.998228i \(-0.518950\pi\)
−0.0594988 + 0.998228i \(0.518950\pi\)
\(740\) 0 0
\(741\) 1.71206e7 1.14544
\(742\) 0 0
\(743\) 5.73250e6 0.380953 0.190477 0.981692i \(-0.438997\pi\)
0.190477 + 0.981692i \(0.438997\pi\)
\(744\) 0 0
\(745\) −7.48906e6 −0.494352
\(746\) 0 0
\(747\) −3.63357e6 −0.238250
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 2.63132e7 1.70245 0.851224 0.524803i \(-0.175861\pi\)
0.851224 + 0.524803i \(0.175861\pi\)
\(752\) 0 0
\(753\) 1.17169e6 0.0753052
\(754\) 0 0
\(755\) 8.88179e6 0.567066
\(756\) 0 0
\(757\) 1.63104e7 1.03449 0.517245 0.855838i \(-0.326958\pi\)
0.517245 + 0.855838i \(0.326958\pi\)
\(758\) 0 0
\(759\) −4.16532e6 −0.262449
\(760\) 0 0
\(761\) −1.68416e7 −1.05420 −0.527098 0.849804i \(-0.676720\pi\)
−0.527098 + 0.849804i \(0.676720\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −412688. −0.0254958
\(766\) 0 0
\(767\) 4.02402e7 2.46986
\(768\) 0 0
\(769\) −1.19890e7 −0.731084 −0.365542 0.930795i \(-0.619116\pi\)
−0.365542 + 0.930795i \(0.619116\pi\)
\(770\) 0 0
\(771\) −925112. −0.0560477
\(772\) 0 0
\(773\) −1.69774e7 −1.02193 −0.510965 0.859601i \(-0.670712\pi\)
−0.510965 + 0.859601i \(0.670712\pi\)
\(774\) 0 0
\(775\) 2.66195e7 1.59201
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.77787e7 1.04968
\(780\) 0 0
\(781\) −3.70793e6 −0.217523
\(782\) 0 0
\(783\) −2.76344e6 −0.161081
\(784\) 0 0
\(785\) 1.81590e7 1.05177
\(786\) 0 0
\(787\) 3.19500e7 1.83880 0.919400 0.393323i \(-0.128675\pi\)
0.919400 + 0.393323i \(0.128675\pi\)
\(788\) 0 0
\(789\) −319507. −0.0182720
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −5.49921e6 −0.310540
\(794\) 0 0
\(795\) −1.75226e7 −0.983287
\(796\) 0 0
\(797\) 1.63006e7 0.908988 0.454494 0.890750i \(-0.349820\pi\)
0.454494 + 0.890750i \(0.349820\pi\)
\(798\) 0 0
\(799\) −900972. −0.0499280
\(800\) 0 0
\(801\) −1.03635e7 −0.570725
\(802\) 0 0
\(803\) −7.79646e6 −0.426686
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −9.41707e6 −0.509017
\(808\) 0 0
\(809\) −2.51398e7 −1.35049 −0.675244 0.737594i \(-0.735962\pi\)
−0.675244 + 0.737594i \(0.735962\pi\)
\(810\) 0 0
\(811\) 2.27245e7 1.21323 0.606613 0.794997i \(-0.292528\pi\)
0.606613 + 0.794997i \(0.292528\pi\)
\(812\) 0 0
\(813\) −1.59551e6 −0.0846588
\(814\) 0 0
\(815\) 3.49448e6 0.184284
\(816\) 0 0
\(817\) 1.22178e7 0.640380
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.10488e7 0.572080 0.286040 0.958218i \(-0.407661\pi\)
0.286040 + 0.958218i \(0.407661\pi\)
\(822\) 0 0
\(823\) −7.30479e6 −0.375931 −0.187966 0.982176i \(-0.560189\pi\)
−0.187966 + 0.982176i \(0.560189\pi\)
\(824\) 0 0
\(825\) 6.95707e6 0.355870
\(826\) 0 0
\(827\) 3.01208e7 1.53145 0.765724 0.643170i \(-0.222381\pi\)
0.765724 + 0.643170i \(0.222381\pi\)
\(828\) 0 0
\(829\) −1.35804e7 −0.686318 −0.343159 0.939277i \(-0.611497\pi\)
−0.343159 + 0.939277i \(0.611497\pi\)
\(830\) 0 0
\(831\) 1.31027e6 0.0658203
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −6.00375e7 −2.97993
\(836\) 0 0
\(837\) 3.53370e6 0.174347
\(838\) 0 0
\(839\) 3.78208e7 1.85492 0.927460 0.373922i \(-0.121987\pi\)
0.927460 + 0.373922i \(0.121987\pi\)
\(840\) 0 0
\(841\) −6.14158e6 −0.299426
\(842\) 0 0
\(843\) −9.27654e6 −0.449591
\(844\) 0 0
\(845\) 8.01611e7 3.86209
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 1.00554e7 0.478772
\(850\) 0 0
\(851\) 3.73727e7 1.76901
\(852\) 0 0
\(853\) 3.36325e7 1.58265 0.791327 0.611393i \(-0.209391\pi\)
0.791327 + 0.611393i \(0.209391\pi\)
\(854\) 0 0
\(855\) 1.28712e7 0.602150
\(856\) 0 0
\(857\) 1.71796e7 0.799028 0.399514 0.916727i \(-0.369179\pi\)
0.399514 + 0.916727i \(0.369179\pi\)
\(858\) 0 0
\(859\) −2.49154e7 −1.15209 −0.576043 0.817420i \(-0.695404\pi\)
−0.576043 + 0.817420i \(0.695404\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −3.70839e7 −1.69495 −0.847477 0.530832i \(-0.821880\pi\)
−0.847477 + 0.530832i \(0.821880\pi\)
\(864\) 0 0
\(865\) 3.59150e7 1.63206
\(866\) 0 0
\(867\) −1.27516e7 −0.576125
\(868\) 0 0
\(869\) −7.03201e6 −0.315886
\(870\) 0 0
\(871\) −2.55203e7 −1.13983
\(872\) 0 0
\(873\) 5.32055e6 0.236277
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 2.35684e7 1.03474 0.517370 0.855762i \(-0.326911\pi\)
0.517370 + 0.855762i \(0.326911\pi\)
\(878\) 0 0
\(879\) 1.81829e7 0.793762
\(880\) 0 0
\(881\) −3.52124e7 −1.52847 −0.764234 0.644939i \(-0.776883\pi\)
−0.764234 + 0.644939i \(0.776883\pi\)
\(882\) 0 0
\(883\) 4.08063e7 1.76127 0.880634 0.473796i \(-0.157117\pi\)
0.880634 + 0.473796i \(0.157117\pi\)
\(884\) 0 0
\(885\) 3.02525e7 1.29839
\(886\) 0 0
\(887\) −6.02857e6 −0.257280 −0.128640 0.991691i \(-0.541061\pi\)
−0.128640 + 0.991691i \(0.541061\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 923542. 0.0389729
\(892\) 0 0
\(893\) 2.81003e7 1.17918
\(894\) 0 0
\(895\) 2.54440e6 0.106176
\(896\) 0 0
\(897\) −3.28830e7 −1.36455
\(898\) 0 0
\(899\) −1.83748e7 −0.758271
\(900\) 0 0
\(901\) 1.15122e6 0.0472438
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.82082e7 0.739002
\(906\) 0 0
\(907\) 1.42799e7 0.576377 0.288188 0.957574i \(-0.406947\pi\)
0.288188 + 0.957574i \(0.406947\pi\)
\(908\) 0 0
\(909\) −1.42384e7 −0.571546
\(910\) 0 0
\(911\) 2.11130e7 0.842855 0.421428 0.906862i \(-0.361529\pi\)
0.421428 + 0.906862i \(0.361529\pi\)
\(912\) 0 0
\(913\) −6.31445e6 −0.250702
\(914\) 0 0
\(915\) −4.13429e6 −0.163248
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.65736e7 0.647334 0.323667 0.946171i \(-0.395084\pi\)
0.323667 + 0.946171i \(0.395084\pi\)
\(920\) 0 0
\(921\) 4.81635e6 0.187098
\(922\) 0 0
\(923\) −2.92721e7 −1.13097
\(924\) 0 0
\(925\) −6.24212e7 −2.39871
\(926\) 0 0
\(927\) 1.24829e7 0.477106
\(928\) 0 0
\(929\) −1.63934e7 −0.623203 −0.311601 0.950213i \(-0.600865\pi\)
−0.311601 + 0.950213i \(0.600865\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 2.07017e7 0.778577
\(934\) 0 0
\(935\) −717172. −0.0268284
\(936\) 0 0
\(937\) 2.68057e7 0.997420 0.498710 0.866769i \(-0.333807\pi\)
0.498710 + 0.866769i \(0.333807\pi\)
\(938\) 0 0
\(939\) 2.48154e7 0.918454
\(940\) 0 0
\(941\) 5.62875e6 0.207223 0.103611 0.994618i \(-0.466960\pi\)
0.103611 + 0.994618i \(0.466960\pi\)
\(942\) 0 0
\(943\) −3.41470e7 −1.25047
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.76782e7 −1.00291 −0.501456 0.865183i \(-0.667202\pi\)
−0.501456 + 0.865183i \(0.667202\pi\)
\(948\) 0 0
\(949\) −6.15488e7 −2.21847
\(950\) 0 0
\(951\) 2.29328e7 0.822253
\(952\) 0 0
\(953\) −2.40114e7 −0.856416 −0.428208 0.903680i \(-0.640855\pi\)
−0.428208 + 0.903680i \(0.640855\pi\)
\(954\) 0 0
\(955\) 2.47828e7 0.879309
\(956\) 0 0
\(957\) −4.80232e6 −0.169501
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −5.13264e6 −0.179280
\(962\) 0 0
\(963\) 1.48523e7 0.516094
\(964\) 0 0
\(965\) −9.40914e6 −0.325261
\(966\) 0 0
\(967\) −1.43801e7 −0.494535 −0.247267 0.968947i \(-0.579533\pi\)
−0.247267 + 0.968947i \(0.579533\pi\)
\(968\) 0 0
\(969\) −845628. −0.0289314
\(970\) 0 0
\(971\) 4.87782e7 1.66027 0.830133 0.557566i \(-0.188265\pi\)
0.830133 + 0.557566i \(0.188265\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 5.49223e7 1.85028
\(976\) 0 0
\(977\) −4.70305e7 −1.57632 −0.788158 0.615472i \(-0.788965\pi\)
−0.788158 + 0.615472i \(0.788965\pi\)
\(978\) 0 0
\(979\) −1.80098e7 −0.600555
\(980\) 0 0
\(981\) −1.09062e7 −0.361827
\(982\) 0 0
\(983\) −7.44416e6 −0.245715 −0.122858 0.992424i \(-0.539206\pi\)
−0.122858 + 0.992424i \(0.539206\pi\)
\(984\) 0 0
\(985\) 3.36368e7 1.10465
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2.34663e7 −0.762877
\(990\) 0 0
\(991\) −4.62294e7 −1.49532 −0.747659 0.664082i \(-0.768822\pi\)
−0.747659 + 0.664082i \(0.768822\pi\)
\(992\) 0 0
\(993\) −4.40401e6 −0.141734
\(994\) 0 0
\(995\) −2.09241e7 −0.670021
\(996\) 0 0
\(997\) 6.18781e6 0.197151 0.0985755 0.995130i \(-0.468571\pi\)
0.0985755 + 0.995130i \(0.468571\pi\)
\(998\) 0 0
\(999\) −8.28633e6 −0.262693
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 588.6.a.p.1.4 4
7.2 even 3 588.6.i.o.361.1 8
7.3 odd 6 84.6.i.c.37.4 yes 8
7.4 even 3 588.6.i.o.373.1 8
7.5 odd 6 84.6.i.c.25.4 8
7.6 odd 2 588.6.a.n.1.1 4
21.5 even 6 252.6.k.f.109.1 8
21.17 even 6 252.6.k.f.37.1 8
28.3 even 6 336.6.q.i.289.4 8
28.19 even 6 336.6.q.i.193.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.i.c.25.4 8 7.5 odd 6
84.6.i.c.37.4 yes 8 7.3 odd 6
252.6.k.f.37.1 8 21.17 even 6
252.6.k.f.109.1 8 21.5 even 6
336.6.q.i.193.4 8 28.19 even 6
336.6.q.i.289.4 8 28.3 even 6
588.6.a.n.1.1 4 7.6 odd 2
588.6.a.p.1.4 4 1.1 even 1 trivial
588.6.i.o.361.1 8 7.2 even 3
588.6.i.o.373.1 8 7.4 even 3