Properties

Label 70.6.a.e.1.1
Level $70$
Weight $6$
Character 70.1
Self dual yes
Analytic conductor $11.227$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [70,6,Mod(1,70)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(70, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("70.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 70.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: \(11.2268673869\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 70.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} -17.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -68.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +46.0000 q^{9} +100.000 q^{10} -715.000 q^{11} -272.000 q^{12} +331.000 q^{13} -196.000 q^{14} -425.000 q^{15} +256.000 q^{16} -1699.00 q^{17} +184.000 q^{18} -1718.00 q^{19} +400.000 q^{20} +833.000 q^{21} -2860.00 q^{22} -3950.00 q^{23} -1088.00 q^{24} +625.000 q^{25} +1324.00 q^{26} +3349.00 q^{27} -784.000 q^{28} +4579.00 q^{29} -1700.00 q^{30} +6756.00 q^{31} +1024.00 q^{32} +12155.0 q^{33} -6796.00 q^{34} -1225.00 q^{35} +736.000 q^{36} -16518.0 q^{37} -6872.00 q^{38} -5627.00 q^{39} +1600.00 q^{40} +18876.0 q^{41} +3332.00 q^{42} +2258.00 q^{43} -11440.0 q^{44} +1150.00 q^{45} -15800.0 q^{46} -537.000 q^{47} -4352.00 q^{48} +2401.00 q^{49} +2500.00 q^{50} +28883.0 q^{51} +5296.00 q^{52} -10984.0 q^{53} +13396.0 q^{54} -17875.0 q^{55} -3136.00 q^{56} +29206.0 q^{57} +18316.0 q^{58} -25956.0 q^{59} -6800.00 q^{60} +39188.0 q^{61} +27024.0 q^{62} -2254.00 q^{63} +4096.00 q^{64} +8275.00 q^{65} +48620.0 q^{66} +4416.00 q^{67} -27184.0 q^{68} +67150.0 q^{69} -4900.00 q^{70} -31880.0 q^{71} +2944.00 q^{72} -5018.00 q^{73} -66072.0 q^{74} -10625.0 q^{75} -27488.0 q^{76} +35035.0 q^{77} -22508.0 q^{78} -27977.0 q^{79} +6400.00 q^{80} -68111.0 q^{81} +75504.0 q^{82} +37644.0 q^{83} +13328.0 q^{84} -42475.0 q^{85} +9032.00 q^{86} -77843.0 q^{87} -45760.0 q^{88} -17216.0 q^{89} +4600.00 q^{90} -16219.0 q^{91} -63200.0 q^{92} -114852. q^{93} -2148.00 q^{94} -42950.0 q^{95} -17408.0 q^{96} -63175.0 q^{97} +9604.00 q^{98} -32890.0 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) −17.0000 −1.09055 −0.545275 0.838257i \(-0.683575\pi\)
−0.545275 + 0.838257i \(0.683575\pi\)
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) −68.0000 −0.771136
\(7\) −49.0000 −0.377964
\(8\) 64.0000 0.353553
\(9\) 46.0000 0.189300
\(10\) 100.000 0.316228
\(11\) −715.000 −1.78166 −0.890829 0.454339i \(-0.849876\pi\)
−0.890829 + 0.454339i \(0.849876\pi\)
\(12\) −272.000 −0.545275
\(13\) 331.000 0.543212 0.271606 0.962408i \(-0.412445\pi\)
0.271606 + 0.962408i \(0.412445\pi\)
\(14\) −196.000 −0.267261
\(15\) −425.000 −0.487709
\(16\) 256.000 0.250000
\(17\) −1699.00 −1.42584 −0.712920 0.701245i \(-0.752628\pi\)
−0.712920 + 0.701245i \(0.752628\pi\)
\(18\) 184.000 0.133856
\(19\) −1718.00 −1.09179 −0.545895 0.837854i \(-0.683810\pi\)
−0.545895 + 0.837854i \(0.683810\pi\)
\(20\) 400.000 0.223607
\(21\) 833.000 0.412189
\(22\) −2860.00 −1.25982
\(23\) −3950.00 −1.55696 −0.778480 0.627669i \(-0.784009\pi\)
−0.778480 + 0.627669i \(0.784009\pi\)
\(24\) −1088.00 −0.385568
\(25\) 625.000 0.200000
\(26\) 1324.00 0.384109
\(27\) 3349.00 0.884109
\(28\) −784.000 −0.188982
\(29\) 4579.00 1.01106 0.505529 0.862810i \(-0.331298\pi\)
0.505529 + 0.862810i \(0.331298\pi\)
\(30\) −1700.00 −0.344862
\(31\) 6756.00 1.26266 0.631329 0.775516i \(-0.282510\pi\)
0.631329 + 0.775516i \(0.282510\pi\)
\(32\) 1024.00 0.176777
\(33\) 12155.0 1.94299
\(34\) −6796.00 −1.00822
\(35\) −1225.00 −0.169031
\(36\) 736.000 0.0946502
\(37\) −16518.0 −1.98360 −0.991798 0.127816i \(-0.959203\pi\)
−0.991798 + 0.127816i \(0.959203\pi\)
\(38\) −6872.00 −0.772012
\(39\) −5627.00 −0.592400
\(40\) 1600.00 0.158114
\(41\) 18876.0 1.75368 0.876840 0.480782i \(-0.159647\pi\)
0.876840 + 0.480782i \(0.159647\pi\)
\(42\) 3332.00 0.291462
\(43\) 2258.00 0.186231 0.0931157 0.995655i \(-0.470317\pi\)
0.0931157 + 0.995655i \(0.470317\pi\)
\(44\) −11440.0 −0.890829
\(45\) 1150.00 0.0846577
\(46\) −15800.0 −1.10094
\(47\) −537.000 −0.0354593 −0.0177296 0.999843i \(-0.505644\pi\)
−0.0177296 + 0.999843i \(0.505644\pi\)
\(48\) −4352.00 −0.272638
\(49\) 2401.00 0.142857
\(50\) 2500.00 0.141421
\(51\) 28883.0 1.55495
\(52\) 5296.00 0.271606
\(53\) −10984.0 −0.537119 −0.268560 0.963263i \(-0.586548\pi\)
−0.268560 + 0.963263i \(0.586548\pi\)
\(54\) 13396.0 0.625159
\(55\) −17875.0 −0.796782
\(56\) −3136.00 −0.133631
\(57\) 29206.0 1.19065
\(58\) 18316.0 0.714925
\(59\) −25956.0 −0.970751 −0.485375 0.874306i \(-0.661317\pi\)
−0.485375 + 0.874306i \(0.661317\pi\)
\(60\) −6800.00 −0.243855
\(61\) 39188.0 1.34843 0.674215 0.738535i \(-0.264482\pi\)
0.674215 + 0.738535i \(0.264482\pi\)
\(62\) 27024.0 0.892833
\(63\) −2254.00 −0.0715488
\(64\) 4096.00 0.125000
\(65\) 8275.00 0.242932
\(66\) 48620.0 1.37390
\(67\) 4416.00 0.120183 0.0600914 0.998193i \(-0.480861\pi\)
0.0600914 + 0.998193i \(0.480861\pi\)
\(68\) −27184.0 −0.712920
\(69\) 67150.0 1.69794
\(70\) −4900.00 −0.119523
\(71\) −31880.0 −0.750538 −0.375269 0.926916i \(-0.622450\pi\)
−0.375269 + 0.926916i \(0.622450\pi\)
\(72\) 2944.00 0.0669278
\(73\) −5018.00 −0.110211 −0.0551053 0.998481i \(-0.517549\pi\)
−0.0551053 + 0.998481i \(0.517549\pi\)
\(74\) −66072.0 −1.40261
\(75\) −10625.0 −0.218110
\(76\) −27488.0 −0.545895
\(77\) 35035.0 0.673403
\(78\) −22508.0 −0.418890
\(79\) −27977.0 −0.504352 −0.252176 0.967681i \(-0.581146\pi\)
−0.252176 + 0.967681i \(0.581146\pi\)
\(80\) 6400.00 0.111803
\(81\) −68111.0 −1.15347
\(82\) 75504.0 1.24004
\(83\) 37644.0 0.599792 0.299896 0.953972i \(-0.403048\pi\)
0.299896 + 0.953972i \(0.403048\pi\)
\(84\) 13328.0 0.206095
\(85\) −42475.0 −0.637655
\(86\) 9032.00 0.131685
\(87\) −77843.0 −1.10261
\(88\) −45760.0 −0.629911
\(89\) −17216.0 −0.230387 −0.115193 0.993343i \(-0.536749\pi\)
−0.115193 + 0.993343i \(0.536749\pi\)
\(90\) 4600.00 0.0598620
\(91\) −16219.0 −0.205315
\(92\) −63200.0 −0.778480
\(93\) −114852. −1.37699
\(94\) −2148.00 −0.0250735
\(95\) −42950.0 −0.488263
\(96\) −17408.0 −0.192784
\(97\) −63175.0 −0.681736 −0.340868 0.940111i \(-0.610721\pi\)
−0.340868 + 0.940111i \(0.610721\pi\)
\(98\) 9604.00 0.101015
\(99\) −32890.0 −0.337269
\(100\) 10000.0 0.100000
\(101\) −29250.0 −0.285314 −0.142657 0.989772i \(-0.545565\pi\)
−0.142657 + 0.989772i \(0.545565\pi\)
\(102\) 115532. 1.09952
\(103\) −149189. −1.38562 −0.692809 0.721121i \(-0.743627\pi\)
−0.692809 + 0.721121i \(0.743627\pi\)
\(104\) 21184.0 0.192055
\(105\) 20825.0 0.184337
\(106\) −43936.0 −0.379801
\(107\) 83742.0 0.707105 0.353552 0.935415i \(-0.384974\pi\)
0.353552 + 0.935415i \(0.384974\pi\)
\(108\) 53584.0 0.442054
\(109\) 105377. 0.849532 0.424766 0.905303i \(-0.360356\pi\)
0.424766 + 0.905303i \(0.360356\pi\)
\(110\) −71500.0 −0.563410
\(111\) 280806. 2.16321
\(112\) −12544.0 −0.0944911
\(113\) −122754. −0.904356 −0.452178 0.891928i \(-0.649353\pi\)
−0.452178 + 0.891928i \(0.649353\pi\)
\(114\) 116824. 0.841918
\(115\) −98750.0 −0.696294
\(116\) 73264.0 0.505529
\(117\) 15226.0 0.102830
\(118\) −103824. −0.686424
\(119\) 83251.0 0.538917
\(120\) −27200.0 −0.172431
\(121\) 350174. 2.17431
\(122\) 156752. 0.953484
\(123\) −320892. −1.91248
\(124\) 108096. 0.631329
\(125\) 15625.0 0.0894427
\(126\) −9016.00 −0.0505927
\(127\) −219196. −1.20593 −0.602967 0.797766i \(-0.706015\pi\)
−0.602967 + 0.797766i \(0.706015\pi\)
\(128\) 16384.0 0.0883883
\(129\) −38386.0 −0.203095
\(130\) 33100.0 0.171779
\(131\) −96682.0 −0.492229 −0.246115 0.969241i \(-0.579154\pi\)
−0.246115 + 0.969241i \(0.579154\pi\)
\(132\) 194480. 0.971494
\(133\) 84182.0 0.412658
\(134\) 17664.0 0.0849820
\(135\) 83725.0 0.395385
\(136\) −108736. −0.504111
\(137\) 187288. 0.852528 0.426264 0.904599i \(-0.359830\pi\)
0.426264 + 0.904599i \(0.359830\pi\)
\(138\) 268600. 1.20063
\(139\) 176894. 0.776562 0.388281 0.921541i \(-0.373069\pi\)
0.388281 + 0.921541i \(0.373069\pi\)
\(140\) −19600.0 −0.0845154
\(141\) 9129.00 0.0386701
\(142\) −127520. −0.530710
\(143\) −236665. −0.967819
\(144\) 11776.0 0.0473251
\(145\) 114475. 0.452158
\(146\) −20072.0 −0.0779307
\(147\) −40817.0 −0.155793
\(148\) −264288. −0.991798
\(149\) −199078. −0.734611 −0.367306 0.930100i \(-0.619720\pi\)
−0.367306 + 0.930100i \(0.619720\pi\)
\(150\) −42500.0 −0.154227
\(151\) 471583. 1.68312 0.841561 0.540162i \(-0.181637\pi\)
0.841561 + 0.540162i \(0.181637\pi\)
\(152\) −109952. −0.386006
\(153\) −78154.0 −0.269912
\(154\) 140140. 0.476168
\(155\) 168900. 0.564677
\(156\) −90032.0 −0.296200
\(157\) −72054.0 −0.233297 −0.116648 0.993173i \(-0.537215\pi\)
−0.116648 + 0.993173i \(0.537215\pi\)
\(158\) −111908. −0.356630
\(159\) 186728. 0.585756
\(160\) 25600.0 0.0790569
\(161\) 193550. 0.588476
\(162\) −272444. −0.815623
\(163\) 385334. 1.13597 0.567987 0.823038i \(-0.307722\pi\)
0.567987 + 0.823038i \(0.307722\pi\)
\(164\) 302016. 0.876840
\(165\) 303875. 0.868931
\(166\) 150576. 0.424117
\(167\) −542957. −1.50652 −0.753259 0.657724i \(-0.771519\pi\)
−0.753259 + 0.657724i \(0.771519\pi\)
\(168\) 53312.0 0.145731
\(169\) −261732. −0.704920
\(170\) −169900. −0.450890
\(171\) −79028.0 −0.206676
\(172\) 36128.0 0.0931157
\(173\) 370953. 0.942331 0.471166 0.882045i \(-0.343833\pi\)
0.471166 + 0.882045i \(0.343833\pi\)
\(174\) −311372. −0.779662
\(175\) −30625.0 −0.0755929
\(176\) −183040. −0.445414
\(177\) 441252. 1.05865
\(178\) −68864.0 −0.162908
\(179\) −754172. −1.75929 −0.879646 0.475629i \(-0.842220\pi\)
−0.879646 + 0.475629i \(0.842220\pi\)
\(180\) 18400.0 0.0423289
\(181\) 303840. 0.689364 0.344682 0.938720i \(-0.387987\pi\)
0.344682 + 0.938720i \(0.387987\pi\)
\(182\) −64876.0 −0.145180
\(183\) −666196. −1.47053
\(184\) −252800. −0.550469
\(185\) −412950. −0.887091
\(186\) −459408. −0.973680
\(187\) 1.21478e6 2.54036
\(188\) −8592.00 −0.0177296
\(189\) −164101. −0.334162
\(190\) −171800. −0.345254
\(191\) −186271. −0.369455 −0.184728 0.982790i \(-0.559140\pi\)
−0.184728 + 0.982790i \(0.559140\pi\)
\(192\) −69632.0 −0.136319
\(193\) 92504.0 0.178759 0.0893794 0.995998i \(-0.471512\pi\)
0.0893794 + 0.995998i \(0.471512\pi\)
\(194\) −252700. −0.482060
\(195\) −140675. −0.264930
\(196\) 38416.0 0.0714286
\(197\) −736368. −1.35185 −0.675926 0.736969i \(-0.736256\pi\)
−0.675926 + 0.736969i \(0.736256\pi\)
\(198\) −131560. −0.238485
\(199\) −481620. −0.862128 −0.431064 0.902321i \(-0.641862\pi\)
−0.431064 + 0.902321i \(0.641862\pi\)
\(200\) 40000.0 0.0707107
\(201\) −75072.0 −0.131065
\(202\) −117000. −0.201747
\(203\) −224371. −0.382144
\(204\) 462128. 0.777476
\(205\) 471900. 0.784269
\(206\) −596756. −0.979780
\(207\) −181700. −0.294733
\(208\) 84736.0 0.135803
\(209\) 1.22837e6 1.94520
\(210\) 83300.0 0.130346
\(211\) 189531. 0.293072 0.146536 0.989205i \(-0.453188\pi\)
0.146536 + 0.989205i \(0.453188\pi\)
\(212\) −175744. −0.268560
\(213\) 541960. 0.818499
\(214\) 334968. 0.499999
\(215\) 56450.0 0.0832852
\(216\) 214336. 0.312580
\(217\) −331044. −0.477240
\(218\) 421508. 0.600710
\(219\) 85306.0 0.120190
\(220\) −286000. −0.398391
\(221\) −562369. −0.774534
\(222\) 1.12322e6 1.52962
\(223\) −22597.0 −0.0304291 −0.0152145 0.999884i \(-0.504843\pi\)
−0.0152145 + 0.999884i \(0.504843\pi\)
\(224\) −50176.0 −0.0668153
\(225\) 28750.0 0.0378601
\(226\) −491016. −0.639476
\(227\) −998117. −1.28563 −0.642816 0.766020i \(-0.722234\pi\)
−0.642816 + 0.766020i \(0.722234\pi\)
\(228\) 467296. 0.595326
\(229\) −854644. −1.07695 −0.538476 0.842641i \(-0.681000\pi\)
−0.538476 + 0.842641i \(0.681000\pi\)
\(230\) −395000. −0.492354
\(231\) −595595. −0.734380
\(232\) 293056. 0.357463
\(233\) 1.25818e6 1.51829 0.759144 0.650922i \(-0.225618\pi\)
0.759144 + 0.650922i \(0.225618\pi\)
\(234\) 60904.0 0.0727120
\(235\) −13425.0 −0.0158579
\(236\) −415296. −0.485375
\(237\) 475609. 0.550021
\(238\) 333004. 0.381072
\(239\) −706581. −0.800142 −0.400071 0.916484i \(-0.631015\pi\)
−0.400071 + 0.916484i \(0.631015\pi\)
\(240\) −108800. −0.121927
\(241\) 616330. 0.683551 0.341775 0.939782i \(-0.388972\pi\)
0.341775 + 0.939782i \(0.388972\pi\)
\(242\) 1.40070e6 1.53747
\(243\) 344080. 0.373804
\(244\) 627008. 0.674215
\(245\) 60025.0 0.0638877
\(246\) −1.28357e6 −1.35233
\(247\) −568658. −0.593074
\(248\) 432384. 0.446417
\(249\) −639948. −0.654103
\(250\) 62500.0 0.0632456
\(251\) 190842. 0.191201 0.0956004 0.995420i \(-0.469523\pi\)
0.0956004 + 0.995420i \(0.469523\pi\)
\(252\) −36064.0 −0.0357744
\(253\) 2.82425e6 2.77397
\(254\) −876784. −0.852724
\(255\) 722075. 0.695395
\(256\) 65536.0 0.0625000
\(257\) −1.13094e6 −1.06809 −0.534045 0.845456i \(-0.679329\pi\)
−0.534045 + 0.845456i \(0.679329\pi\)
\(258\) −153544. −0.143610
\(259\) 809382. 0.749729
\(260\) 132400. 0.121466
\(261\) 210634. 0.191394
\(262\) −386728. −0.348059
\(263\) −1.67377e6 −1.49213 −0.746065 0.665874i \(-0.768059\pi\)
−0.746065 + 0.665874i \(0.768059\pi\)
\(264\) 777920. 0.686950
\(265\) −274600. −0.240207
\(266\) 336728. 0.291793
\(267\) 292672. 0.251248
\(268\) 70656.0 0.0600914
\(269\) −630942. −0.531629 −0.265815 0.964024i \(-0.585641\pi\)
−0.265815 + 0.964024i \(0.585641\pi\)
\(270\) 334900. 0.279580
\(271\) −372476. −0.308088 −0.154044 0.988064i \(-0.549230\pi\)
−0.154044 + 0.988064i \(0.549230\pi\)
\(272\) −434944. −0.356460
\(273\) 275723. 0.223906
\(274\) 749152. 0.602828
\(275\) −446875. −0.356332
\(276\) 1.07440e6 0.848972
\(277\) 867010. 0.678930 0.339465 0.940619i \(-0.389754\pi\)
0.339465 + 0.940619i \(0.389754\pi\)
\(278\) 707576. 0.549112
\(279\) 310776. 0.239021
\(280\) −78400.0 −0.0597614
\(281\) −1.94498e6 −1.46943 −0.734716 0.678375i \(-0.762685\pi\)
−0.734716 + 0.678375i \(0.762685\pi\)
\(282\) 36516.0 0.0273439
\(283\) 1.18501e6 0.879543 0.439771 0.898110i \(-0.355059\pi\)
0.439771 + 0.898110i \(0.355059\pi\)
\(284\) −510080. −0.375269
\(285\) 730150. 0.532476
\(286\) −946660. −0.684351
\(287\) −924924. −0.662829
\(288\) 47104.0 0.0334639
\(289\) 1.46674e6 1.03302
\(290\) 457900. 0.319724
\(291\) 1.07398e6 0.743467
\(292\) −80288.0 −0.0551053
\(293\) 33669.0 0.0229119 0.0114560 0.999934i \(-0.496353\pi\)
0.0114560 + 0.999934i \(0.496353\pi\)
\(294\) −163268. −0.110162
\(295\) −648900. −0.434133
\(296\) −1.05715e6 −0.701307
\(297\) −2.39454e6 −1.57518
\(298\) −796312. −0.519449
\(299\) −1.30745e6 −0.845760
\(300\) −170000. −0.109055
\(301\) −110642. −0.0703888
\(302\) 1.88633e6 1.19015
\(303\) 497250. 0.311149
\(304\) −439808. −0.272948
\(305\) 979700. 0.603036
\(306\) −312616. −0.190857
\(307\) −27043.0 −0.0163760 −0.00818802 0.999966i \(-0.502606\pi\)
−0.00818802 + 0.999966i \(0.502606\pi\)
\(308\) 560560. 0.336702
\(309\) 2.53621e6 1.51109
\(310\) 675600. 0.399287
\(311\) 2.14919e6 1.26001 0.630004 0.776592i \(-0.283053\pi\)
0.630004 + 0.776592i \(0.283053\pi\)
\(312\) −360128. −0.209445
\(313\) −2.67052e6 −1.54076 −0.770381 0.637583i \(-0.779934\pi\)
−0.770381 + 0.637583i \(0.779934\pi\)
\(314\) −288216. −0.164966
\(315\) −56350.0 −0.0319976
\(316\) −447632. −0.252176
\(317\) −250514. −0.140018 −0.0700090 0.997546i \(-0.522303\pi\)
−0.0700090 + 0.997546i \(0.522303\pi\)
\(318\) 746912. 0.414192
\(319\) −3.27398e6 −1.80136
\(320\) 102400. 0.0559017
\(321\) −1.42361e6 −0.771134
\(322\) 774200. 0.416115
\(323\) 2.91888e6 1.55672
\(324\) −1.08978e6 −0.576733
\(325\) 206875. 0.108642
\(326\) 1.54134e6 0.803255
\(327\) −1.79141e6 −0.926457
\(328\) 1.20806e6 0.620019
\(329\) 26313.0 0.0134023
\(330\) 1.21550e6 0.614427
\(331\) 1.05899e6 0.531277 0.265639 0.964073i \(-0.414417\pi\)
0.265639 + 0.964073i \(0.414417\pi\)
\(332\) 602304. 0.299896
\(333\) −759828. −0.375495
\(334\) −2.17183e6 −1.06527
\(335\) 110400. 0.0537473
\(336\) 213248. 0.103047
\(337\) −2.85025e6 −1.36712 −0.683562 0.729893i \(-0.739570\pi\)
−0.683562 + 0.729893i \(0.739570\pi\)
\(338\) −1.04693e6 −0.498454
\(339\) 2.08682e6 0.986246
\(340\) −679600. −0.318828
\(341\) −4.83054e6 −2.24962
\(342\) −316112. −0.146142
\(343\) −117649. −0.0539949
\(344\) 144512. 0.0658427
\(345\) 1.67875e6 0.759344
\(346\) 1.48381e6 0.666329
\(347\) 1.89141e6 0.843259 0.421630 0.906768i \(-0.361458\pi\)
0.421630 + 0.906768i \(0.361458\pi\)
\(348\) −1.24549e6 −0.551304
\(349\) −1.04232e6 −0.458075 −0.229038 0.973418i \(-0.573558\pi\)
−0.229038 + 0.973418i \(0.573558\pi\)
\(350\) −122500. −0.0534522
\(351\) 1.10852e6 0.480259
\(352\) −732160. −0.314956
\(353\) −2.30309e6 −0.983725 −0.491862 0.870673i \(-0.663684\pi\)
−0.491862 + 0.870673i \(0.663684\pi\)
\(354\) 1.76501e6 0.748581
\(355\) −797000. −0.335651
\(356\) −275456. −0.115193
\(357\) −1.41527e6 −0.587716
\(358\) −3.01669e6 −1.24401
\(359\) −1.67594e6 −0.686315 −0.343157 0.939278i \(-0.611496\pi\)
−0.343157 + 0.939278i \(0.611496\pi\)
\(360\) 73600.0 0.0299310
\(361\) 475425. 0.192006
\(362\) 1.21536e6 0.487454
\(363\) −5.95296e6 −2.37119
\(364\) −259504. −0.102657
\(365\) −125450. −0.0492877
\(366\) −2.66478e6 −1.03982
\(367\) 94663.0 0.0366872 0.0183436 0.999832i \(-0.494161\pi\)
0.0183436 + 0.999832i \(0.494161\pi\)
\(368\) −1.01120e6 −0.389240
\(369\) 868296. 0.331972
\(370\) −1.65180e6 −0.627268
\(371\) 538216. 0.203012
\(372\) −1.83763e6 −0.688496
\(373\) −953536. −0.354867 −0.177433 0.984133i \(-0.556779\pi\)
−0.177433 + 0.984133i \(0.556779\pi\)
\(374\) 4.85914e6 1.79631
\(375\) −265625. −0.0975418
\(376\) −34368.0 −0.0125367
\(377\) 1.51565e6 0.549219
\(378\) −656404. −0.236288
\(379\) 3.88824e6 1.39045 0.695225 0.718792i \(-0.255305\pi\)
0.695225 + 0.718792i \(0.255305\pi\)
\(380\) −687200. −0.244132
\(381\) 3.72633e6 1.31513
\(382\) −745084. −0.261244
\(383\) 2.93636e6 1.02285 0.511425 0.859328i \(-0.329118\pi\)
0.511425 + 0.859328i \(0.329118\pi\)
\(384\) −278528. −0.0963920
\(385\) 875875. 0.301155
\(386\) 370016. 0.126402
\(387\) 103868. 0.0352537
\(388\) −1.01080e6 −0.340868
\(389\) 1.70377e6 0.570871 0.285435 0.958398i \(-0.407862\pi\)
0.285435 + 0.958398i \(0.407862\pi\)
\(390\) −562700. −0.187333
\(391\) 6.71105e6 2.21998
\(392\) 153664. 0.0505076
\(393\) 1.64359e6 0.536801
\(394\) −2.94547e6 −0.955904
\(395\) −699425. −0.225553
\(396\) −526240. −0.168634
\(397\) 1.19110e6 0.379292 0.189646 0.981853i \(-0.439266\pi\)
0.189646 + 0.981853i \(0.439266\pi\)
\(398\) −1.92648e6 −0.609617
\(399\) −1.43109e6 −0.450024
\(400\) 160000. 0.0500000
\(401\) −3.38330e6 −1.05070 −0.525351 0.850885i \(-0.676066\pi\)
−0.525351 + 0.850885i \(0.676066\pi\)
\(402\) −300288. −0.0926772
\(403\) 2.23624e6 0.685891
\(404\) −468000. −0.142657
\(405\) −1.70278e6 −0.515846
\(406\) −897484. −0.270216
\(407\) 1.18104e7 3.53409
\(408\) 1.84851e6 0.549758
\(409\) −1.33185e6 −0.393682 −0.196841 0.980435i \(-0.563068\pi\)
−0.196841 + 0.980435i \(0.563068\pi\)
\(410\) 1.88760e6 0.554562
\(411\) −3.18390e6 −0.929725
\(412\) −2.38702e6 −0.692809
\(413\) 1.27184e6 0.366909
\(414\) −726800. −0.208408
\(415\) 941100. 0.268235
\(416\) 338944. 0.0960273
\(417\) −3.00720e6 −0.846880
\(418\) 4.91348e6 1.37546
\(419\) 5.82786e6 1.62171 0.810856 0.585246i \(-0.199002\pi\)
0.810856 + 0.585246i \(0.199002\pi\)
\(420\) 333200. 0.0921683
\(421\) 2.47430e6 0.680374 0.340187 0.940358i \(-0.389510\pi\)
0.340187 + 0.940358i \(0.389510\pi\)
\(422\) 758124. 0.207233
\(423\) −24702.0 −0.00671245
\(424\) −702976. −0.189900
\(425\) −1.06188e6 −0.285168
\(426\) 2.16784e6 0.578766
\(427\) −1.92021e6 −0.509659
\(428\) 1.33987e6 0.353552
\(429\) 4.02331e6 1.05546
\(430\) 225800. 0.0588915
\(431\) 4.61851e6 1.19759 0.598796 0.800902i \(-0.295646\pi\)
0.598796 + 0.800902i \(0.295646\pi\)
\(432\) 857344. 0.221027
\(433\) 58606.0 0.0150218 0.00751091 0.999972i \(-0.497609\pi\)
0.00751091 + 0.999972i \(0.497609\pi\)
\(434\) −1.32418e6 −0.337459
\(435\) −1.94608e6 −0.493102
\(436\) 1.68603e6 0.424766
\(437\) 6.78610e6 1.69987
\(438\) 341224. 0.0849874
\(439\) 7.04298e6 1.74419 0.872097 0.489332i \(-0.162759\pi\)
0.872097 + 0.489332i \(0.162759\pi\)
\(440\) −1.14400e6 −0.281705
\(441\) 110446. 0.0270429
\(442\) −2.24948e6 −0.547678
\(443\) 1.46894e6 0.355627 0.177813 0.984064i \(-0.443098\pi\)
0.177813 + 0.984064i \(0.443098\pi\)
\(444\) 4.49290e6 1.08161
\(445\) −430400. −0.103032
\(446\) −90388.0 −0.0215166
\(447\) 3.38433e6 0.801131
\(448\) −200704. −0.0472456
\(449\) −7.48414e6 −1.75197 −0.875983 0.482341i \(-0.839787\pi\)
−0.875983 + 0.482341i \(0.839787\pi\)
\(450\) 115000. 0.0267711
\(451\) −1.34963e7 −3.12446
\(452\) −1.96406e6 −0.452178
\(453\) −8.01691e6 −1.83553
\(454\) −3.99247e6 −0.909079
\(455\) −405475. −0.0918196
\(456\) 1.86918e6 0.420959
\(457\) 170320. 0.0381483 0.0190741 0.999818i \(-0.493928\pi\)
0.0190741 + 0.999818i \(0.493928\pi\)
\(458\) −3.41858e6 −0.761520
\(459\) −5.68995e6 −1.26060
\(460\) −1.58000e6 −0.348147
\(461\) −4.28685e6 −0.939476 −0.469738 0.882806i \(-0.655652\pi\)
−0.469738 + 0.882806i \(0.655652\pi\)
\(462\) −2.38238e6 −0.519285
\(463\) 3.38317e6 0.733452 0.366726 0.930329i \(-0.380479\pi\)
0.366726 + 0.930329i \(0.380479\pi\)
\(464\) 1.17222e6 0.252764
\(465\) −2.87130e6 −0.615809
\(466\) 5.03274e6 1.07359
\(467\) 5.18029e6 1.09916 0.549581 0.835440i \(-0.314787\pi\)
0.549581 + 0.835440i \(0.314787\pi\)
\(468\) 243616. 0.0514152
\(469\) −216384. −0.0454248
\(470\) −53700.0 −0.0112132
\(471\) 1.22492e6 0.254422
\(472\) −1.66118e6 −0.343212
\(473\) −1.61447e6 −0.331801
\(474\) 1.90244e6 0.388924
\(475\) −1.07375e6 −0.218358
\(476\) 1.33202e6 0.269459
\(477\) −505264. −0.101677
\(478\) −2.82632e6 −0.565786
\(479\) −8.76779e6 −1.74603 −0.873014 0.487695i \(-0.837838\pi\)
−0.873014 + 0.487695i \(0.837838\pi\)
\(480\) −435200. −0.0862156
\(481\) −5.46746e6 −1.07751
\(482\) 2.46532e6 0.483343
\(483\) −3.29035e6 −0.641762
\(484\) 5.60278e6 1.08715
\(485\) −1.57938e6 −0.304881
\(486\) 1.37632e6 0.264319
\(487\) 270154. 0.0516166 0.0258083 0.999667i \(-0.491784\pi\)
0.0258083 + 0.999667i \(0.491784\pi\)
\(488\) 2.50803e6 0.476742
\(489\) −6.55068e6 −1.23884
\(490\) 240100. 0.0451754
\(491\) 4.85550e6 0.908930 0.454465 0.890765i \(-0.349830\pi\)
0.454465 + 0.890765i \(0.349830\pi\)
\(492\) −5.13427e6 −0.956238
\(493\) −7.77972e6 −1.44161
\(494\) −2.27463e6 −0.419367
\(495\) −822250. −0.150831
\(496\) 1.72954e6 0.315664
\(497\) 1.56212e6 0.283677
\(498\) −2.55979e6 −0.462521
\(499\) −2.98576e6 −0.536789 −0.268394 0.963309i \(-0.586493\pi\)
−0.268394 + 0.963309i \(0.586493\pi\)
\(500\) 250000. 0.0447214
\(501\) 9.23027e6 1.64293
\(502\) 763368. 0.135199
\(503\) −8.28783e6 −1.46057 −0.730283 0.683145i \(-0.760612\pi\)
−0.730283 + 0.683145i \(0.760612\pi\)
\(504\) −144256. −0.0252963
\(505\) −731250. −0.127596
\(506\) 1.12970e7 1.96149
\(507\) 4.44944e6 0.768751
\(508\) −3.50714e6 −0.602967
\(509\) 6.24307e6 1.06808 0.534040 0.845459i \(-0.320673\pi\)
0.534040 + 0.845459i \(0.320673\pi\)
\(510\) 2.88830e6 0.491719
\(511\) 245882. 0.0416557
\(512\) 262144. 0.0441942
\(513\) −5.75358e6 −0.965261
\(514\) −4.52377e6 −0.755253
\(515\) −3.72972e6 −0.619668
\(516\) −614176. −0.101547
\(517\) 383955. 0.0631763
\(518\) 3.23753e6 0.530138
\(519\) −6.30620e6 −1.02766
\(520\) 529600. 0.0858894
\(521\) 7.49509e6 1.20971 0.604856 0.796335i \(-0.293230\pi\)
0.604856 + 0.796335i \(0.293230\pi\)
\(522\) 842536. 0.135336
\(523\) 3.80957e6 0.609007 0.304503 0.952511i \(-0.401510\pi\)
0.304503 + 0.952511i \(0.401510\pi\)
\(524\) −1.54691e6 −0.246115
\(525\) 520625. 0.0824379
\(526\) −6.69508e6 −1.05509
\(527\) −1.14784e7 −1.80035
\(528\) 3.11168e6 0.485747
\(529\) 9.16616e6 1.42413
\(530\) −1.09840e6 −0.169852
\(531\) −1.19398e6 −0.183764
\(532\) 1.34691e6 0.206329
\(533\) 6.24796e6 0.952621
\(534\) 1.17069e6 0.177659
\(535\) 2.09355e6 0.316227
\(536\) 282624. 0.0424910
\(537\) 1.28209e7 1.91860
\(538\) −2.52377e6 −0.375919
\(539\) −1.71672e6 −0.254523
\(540\) 1.33960e6 0.197693
\(541\) 7.67156e6 1.12691 0.563457 0.826145i \(-0.309471\pi\)
0.563457 + 0.826145i \(0.309471\pi\)
\(542\) −1.48990e6 −0.217851
\(543\) −5.16528e6 −0.751786
\(544\) −1.73978e6 −0.252055
\(545\) 2.63442e6 0.379922
\(546\) 1.10289e6 0.158326
\(547\) −9.53845e6 −1.36304 −0.681522 0.731798i \(-0.738681\pi\)
−0.681522 + 0.731798i \(0.738681\pi\)
\(548\) 2.99661e6 0.426264
\(549\) 1.80265e6 0.255258
\(550\) −1.78750e6 −0.251964
\(551\) −7.86672e6 −1.10386
\(552\) 4.29760e6 0.600314
\(553\) 1.37087e6 0.190627
\(554\) 3.46804e6 0.480076
\(555\) 7.02015e6 0.967417
\(556\) 2.83030e6 0.388281
\(557\) −7.45022e6 −1.01749 −0.508746 0.860916i \(-0.669891\pi\)
−0.508746 + 0.860916i \(0.669891\pi\)
\(558\) 1.24310e6 0.169014
\(559\) 747398. 0.101163
\(560\) −313600. −0.0422577
\(561\) −2.06513e7 −2.77039
\(562\) −7.77992e6 −1.03905
\(563\) 3.36698e6 0.447682 0.223841 0.974626i \(-0.428140\pi\)
0.223841 + 0.974626i \(0.428140\pi\)
\(564\) 146064. 0.0193351
\(565\) −3.06885e6 −0.404440
\(566\) 4.74005e6 0.621931
\(567\) 3.33744e6 0.435969
\(568\) −2.04032e6 −0.265355
\(569\) −4.05501e6 −0.525063 −0.262532 0.964923i \(-0.584557\pi\)
−0.262532 + 0.964923i \(0.584557\pi\)
\(570\) 2.92060e6 0.376517
\(571\) 7.31585e6 0.939020 0.469510 0.882927i \(-0.344431\pi\)
0.469510 + 0.882927i \(0.344431\pi\)
\(572\) −3.78664e6 −0.483909
\(573\) 3.16661e6 0.402910
\(574\) −3.69970e6 −0.468691
\(575\) −2.46875e6 −0.311392
\(576\) 188416. 0.0236626
\(577\) −9.76895e6 −1.22154 −0.610771 0.791807i \(-0.709140\pi\)
−0.610771 + 0.791807i \(0.709140\pi\)
\(578\) 5.86698e6 0.730457
\(579\) −1.57257e6 −0.194945
\(580\) 1.83160e6 0.226079
\(581\) −1.84456e6 −0.226700
\(582\) 4.29590e6 0.525711
\(583\) 7.85356e6 0.956963
\(584\) −321152. −0.0389653
\(585\) 380650. 0.0459871
\(586\) 134676. 0.0162012
\(587\) 3.75689e6 0.450021 0.225011 0.974356i \(-0.427758\pi\)
0.225011 + 0.974356i \(0.427758\pi\)
\(588\) −653072. −0.0778965
\(589\) −1.16068e7 −1.37856
\(590\) −2.59560e6 −0.306978
\(591\) 1.25183e7 1.47426
\(592\) −4.22861e6 −0.495899
\(593\) 2.89048e6 0.337546 0.168773 0.985655i \(-0.446020\pi\)
0.168773 + 0.985655i \(0.446020\pi\)
\(594\) −9.57814e6 −1.11382
\(595\) 2.08128e6 0.241011
\(596\) −3.18525e6 −0.367306
\(597\) 8.18754e6 0.940194
\(598\) −5.22980e6 −0.598043
\(599\) 1.32233e7 1.50582 0.752910 0.658124i \(-0.228650\pi\)
0.752910 + 0.658124i \(0.228650\pi\)
\(600\) −680000. −0.0771136
\(601\) 3.47399e6 0.392321 0.196161 0.980572i \(-0.437153\pi\)
0.196161 + 0.980572i \(0.437153\pi\)
\(602\) −442568. −0.0497724
\(603\) 203136. 0.0227506
\(604\) 7.54533e6 0.841561
\(605\) 8.75435e6 0.972379
\(606\) 1.98900e6 0.220015
\(607\) 6.45088e6 0.710636 0.355318 0.934746i \(-0.384373\pi\)
0.355318 + 0.934746i \(0.384373\pi\)
\(608\) −1.75923e6 −0.193003
\(609\) 3.81431e6 0.416747
\(610\) 3.91880e6 0.426411
\(611\) −177747. −0.0192619
\(612\) −1.25046e6 −0.134956
\(613\) 8.43820e6 0.906982 0.453491 0.891261i \(-0.350178\pi\)
0.453491 + 0.891261i \(0.350178\pi\)
\(614\) −108172. −0.0115796
\(615\) −8.02230e6 −0.855285
\(616\) 2.24224e6 0.238084
\(617\) 9.45501e6 0.999882 0.499941 0.866059i \(-0.333355\pi\)
0.499941 + 0.866059i \(0.333355\pi\)
\(618\) 1.01449e7 1.06850
\(619\) 1.43145e6 0.150158 0.0750790 0.997178i \(-0.476079\pi\)
0.0750790 + 0.997178i \(0.476079\pi\)
\(620\) 2.70240e6 0.282339
\(621\) −1.32286e7 −1.37652
\(622\) 8.59674e6 0.890960
\(623\) 843584. 0.0870780
\(624\) −1.44051e6 −0.148100
\(625\) 390625. 0.0400000
\(626\) −1.06821e7 −1.08948
\(627\) −2.08823e7 −2.12134
\(628\) −1.15286e6 −0.116648
\(629\) 2.80641e7 2.82829
\(630\) −225400. −0.0226257
\(631\) −1.01813e7 −1.01795 −0.508977 0.860780i \(-0.669976\pi\)
−0.508977 + 0.860780i \(0.669976\pi\)
\(632\) −1.79053e6 −0.178315
\(633\) −3.22203e6 −0.319610
\(634\) −1.00206e6 −0.0990077
\(635\) −5.47990e6 −0.539310
\(636\) 2.98765e6 0.292878
\(637\) 794731. 0.0776018
\(638\) −1.30959e7 −1.27375
\(639\) −1.46648e6 −0.142077
\(640\) 409600. 0.0395285
\(641\) −1.76908e7 −1.70060 −0.850300 0.526298i \(-0.823580\pi\)
−0.850300 + 0.526298i \(0.823580\pi\)
\(642\) −5.69446e6 −0.545274
\(643\) 1.82748e7 1.74311 0.871556 0.490296i \(-0.163111\pi\)
0.871556 + 0.490296i \(0.163111\pi\)
\(644\) 3.09680e6 0.294238
\(645\) −959650. −0.0908267
\(646\) 1.16755e7 1.10077
\(647\) 1.52897e6 0.143594 0.0717972 0.997419i \(-0.477127\pi\)
0.0717972 + 0.997419i \(0.477127\pi\)
\(648\) −4.35910e6 −0.407812
\(649\) 1.85585e7 1.72955
\(650\) 827500. 0.0768218
\(651\) 5.62775e6 0.520454
\(652\) 6.16534e6 0.567987
\(653\) −9.10088e6 −0.835219 −0.417610 0.908627i \(-0.637132\pi\)
−0.417610 + 0.908627i \(0.637132\pi\)
\(654\) −7.16564e6 −0.655104
\(655\) −2.41705e6 −0.220132
\(656\) 4.83226e6 0.438420
\(657\) −230828. −0.0208629
\(658\) 105252. 0.00947689
\(659\) −430119. −0.0385811 −0.0192906 0.999814i \(-0.506141\pi\)
−0.0192906 + 0.999814i \(0.506141\pi\)
\(660\) 4.86200e6 0.434465
\(661\) 7.65248e6 0.681238 0.340619 0.940202i \(-0.389363\pi\)
0.340619 + 0.940202i \(0.389363\pi\)
\(662\) 4.23595e6 0.375670
\(663\) 9.56027e6 0.844669
\(664\) 2.40922e6 0.212058
\(665\) 2.10455e6 0.184546
\(666\) −3.03931e6 −0.265515
\(667\) −1.80870e7 −1.57418
\(668\) −8.68731e6 −0.753259
\(669\) 384149. 0.0331844
\(670\) 441600. 0.0380051
\(671\) −2.80194e7 −2.40244
\(672\) 852992. 0.0728655
\(673\) −2.18404e7 −1.85876 −0.929378 0.369128i \(-0.879656\pi\)
−0.929378 + 0.369128i \(0.879656\pi\)
\(674\) −1.14010e7 −0.966702
\(675\) 2.09312e6 0.176822
\(676\) −4.18771e6 −0.352460
\(677\) 1.39504e7 1.16981 0.584905 0.811102i \(-0.301132\pi\)
0.584905 + 0.811102i \(0.301132\pi\)
\(678\) 8.34727e6 0.697381
\(679\) 3.09558e6 0.257672
\(680\) −2.71840e6 −0.225445
\(681\) 1.69680e7 1.40205
\(682\) −1.93222e7 −1.59072
\(683\) 2.29121e7 1.87937 0.939686 0.342040i \(-0.111118\pi\)
0.939686 + 0.342040i \(0.111118\pi\)
\(684\) −1.26445e6 −0.103338
\(685\) 4.68220e6 0.381262
\(686\) −470596. −0.0381802
\(687\) 1.45289e7 1.17447
\(688\) 578048. 0.0465578
\(689\) −3.63570e6 −0.291770
\(690\) 6.71500e6 0.536937
\(691\) −1.69127e7 −1.34747 −0.673734 0.738974i \(-0.735310\pi\)
−0.673734 + 0.738974i \(0.735310\pi\)
\(692\) 5.93525e6 0.471166
\(693\) 1.61161e6 0.127476
\(694\) 7.56562e6 0.596274
\(695\) 4.42235e6 0.347289
\(696\) −4.98195e6 −0.389831
\(697\) −3.20703e7 −2.50047
\(698\) −4.16927e6 −0.323908
\(699\) −2.13891e7 −1.65577
\(700\) −490000. −0.0377964
\(701\) −1.90087e7 −1.46102 −0.730510 0.682902i \(-0.760718\pi\)
−0.730510 + 0.682902i \(0.760718\pi\)
\(702\) 4.43408e6 0.339594
\(703\) 2.83779e7 2.16567
\(704\) −2.92864e6 −0.222707
\(705\) 228225. 0.0172938
\(706\) −9.21235e6 −0.695598
\(707\) 1.43325e6 0.107838
\(708\) 7.06003e6 0.529326
\(709\) 1.66079e7 1.24079 0.620396 0.784289i \(-0.286972\pi\)
0.620396 + 0.784289i \(0.286972\pi\)
\(710\) −3.18800e6 −0.237341
\(711\) −1.28694e6 −0.0954740
\(712\) −1.10182e6 −0.0814540
\(713\) −2.66862e7 −1.96591
\(714\) −5.66107e6 −0.415578
\(715\) −5.91662e6 −0.432822
\(716\) −1.20668e7 −0.879646
\(717\) 1.20119e7 0.872596
\(718\) −6.70378e6 −0.485298
\(719\) 5.93610e6 0.428232 0.214116 0.976808i \(-0.431313\pi\)
0.214116 + 0.976808i \(0.431313\pi\)
\(720\) 294400. 0.0211644
\(721\) 7.31026e6 0.523715
\(722\) 1.90170e6 0.135768
\(723\) −1.04776e7 −0.745447
\(724\) 4.86144e6 0.344682
\(725\) 2.86188e6 0.202211
\(726\) −2.38118e7 −1.67668
\(727\) 1.73276e7 1.21591 0.607957 0.793970i \(-0.291989\pi\)
0.607957 + 0.793970i \(0.291989\pi\)
\(728\) −1.03802e6 −0.0725898
\(729\) 1.07016e7 0.745814
\(730\) −501800. −0.0348517
\(731\) −3.83634e6 −0.265536
\(732\) −1.06591e7 −0.735266
\(733\) 1.39829e7 0.961255 0.480627 0.876925i \(-0.340409\pi\)
0.480627 + 0.876925i \(0.340409\pi\)
\(734\) 378652. 0.0259418
\(735\) −1.02042e6 −0.0696727
\(736\) −4.04480e6 −0.275234
\(737\) −3.15744e6 −0.214125
\(738\) 3.47318e6 0.234740
\(739\) −1.14263e7 −0.769649 −0.384824 0.922990i \(-0.625738\pi\)
−0.384824 + 0.922990i \(0.625738\pi\)
\(740\) −6.60720e6 −0.443545
\(741\) 9.66719e6 0.646777
\(742\) 2.15286e6 0.143551
\(743\) 1.23126e7 0.818236 0.409118 0.912481i \(-0.365836\pi\)
0.409118 + 0.912481i \(0.365836\pi\)
\(744\) −7.35053e6 −0.486840
\(745\) −4.97695e6 −0.328528
\(746\) −3.81414e6 −0.250929
\(747\) 1.73162e6 0.113541
\(748\) 1.94366e7 1.27018
\(749\) −4.10336e6 −0.267261
\(750\) −1.06250e6 −0.0689725
\(751\) −1.43093e7 −0.925806 −0.462903 0.886409i \(-0.653192\pi\)
−0.462903 + 0.886409i \(0.653192\pi\)
\(752\) −137472. −0.00886481
\(753\) −3.24431e6 −0.208514
\(754\) 6.06260e6 0.388356
\(755\) 1.17896e7 0.752715
\(756\) −2.62562e6 −0.167081
\(757\) −5.34505e6 −0.339010 −0.169505 0.985529i \(-0.554217\pi\)
−0.169505 + 0.985529i \(0.554217\pi\)
\(758\) 1.55530e7 0.983197
\(759\) −4.80122e7 −3.02515
\(760\) −2.74880e6 −0.172627
\(761\) 6.22568e6 0.389695 0.194848 0.980834i \(-0.437579\pi\)
0.194848 + 0.980834i \(0.437579\pi\)
\(762\) 1.49053e7 0.929938
\(763\) −5.16347e6 −0.321093
\(764\) −2.98034e6 −0.184728
\(765\) −1.95385e6 −0.120708
\(766\) 1.17454e7 0.723264
\(767\) −8.59144e6 −0.527324
\(768\) −1.11411e6 −0.0681594
\(769\) 1.57888e7 0.962793 0.481397 0.876503i \(-0.340130\pi\)
0.481397 + 0.876503i \(0.340130\pi\)
\(770\) 3.50350e6 0.212949
\(771\) 1.92260e7 1.16481
\(772\) 1.48006e6 0.0893794
\(773\) −2.50453e7 −1.50757 −0.753785 0.657121i \(-0.771774\pi\)
−0.753785 + 0.657121i \(0.771774\pi\)
\(774\) 415472. 0.0249281
\(775\) 4.22250e6 0.252531
\(776\) −4.04320e6 −0.241030
\(777\) −1.37595e7 −0.817617
\(778\) 6.81509e6 0.403667
\(779\) −3.24290e7 −1.91465
\(780\) −2.25080e6 −0.132465
\(781\) 2.27942e7 1.33720
\(782\) 2.68442e7 1.56976
\(783\) 1.53351e7 0.893884
\(784\) 614656. 0.0357143
\(785\) −1.80135e6 −0.104334
\(786\) 6.57438e6 0.379576
\(787\) −1.28020e6 −0.0736784 −0.0368392 0.999321i \(-0.511729\pi\)
−0.0368392 + 0.999321i \(0.511729\pi\)
\(788\) −1.17819e7 −0.675926
\(789\) 2.84541e7 1.62724
\(790\) −2.79770e6 −0.159490
\(791\) 6.01495e6 0.341815
\(792\) −2.10496e6 −0.119242
\(793\) 1.29712e7 0.732484
\(794\) 4.76442e6 0.268200
\(795\) 4.66820e6 0.261958
\(796\) −7.70592e6 −0.431064
\(797\) −1.13798e7 −0.634584 −0.317292 0.948328i \(-0.602774\pi\)
−0.317292 + 0.948328i \(0.602774\pi\)
\(798\) −5.72438e6 −0.318215
\(799\) 912363. 0.0505593
\(800\) 640000. 0.0353553
\(801\) −791936. −0.0436123
\(802\) −1.35332e7 −0.742959
\(803\) 3.58787e6 0.196358
\(804\) −1.20115e6 −0.0655327
\(805\) 4.83875e6 0.263174
\(806\) 8.94494e6 0.484998
\(807\) 1.07260e7 0.579768
\(808\) −1.87200e6 −0.100874
\(809\) −1.70542e7 −0.916138 −0.458069 0.888917i \(-0.651459\pi\)
−0.458069 + 0.888917i \(0.651459\pi\)
\(810\) −6.81110e6 −0.364758
\(811\) −2.21494e7 −1.18252 −0.591262 0.806480i \(-0.701370\pi\)
−0.591262 + 0.806480i \(0.701370\pi\)
\(812\) −3.58994e6 −0.191072
\(813\) 6.33209e6 0.335986
\(814\) 4.72415e7 2.49898
\(815\) 9.63335e6 0.508023
\(816\) 7.39405e6 0.388738
\(817\) −3.87924e6 −0.203326
\(818\) −5.32738e6 −0.278375
\(819\) −746074. −0.0388662
\(820\) 7.55040e6 0.392135
\(821\) −1.01068e7 −0.523307 −0.261654 0.965162i \(-0.584268\pi\)
−0.261654 + 0.965162i \(0.584268\pi\)
\(822\) −1.27356e7 −0.657415
\(823\) −1.83993e7 −0.946895 −0.473447 0.880822i \(-0.656991\pi\)
−0.473447 + 0.880822i \(0.656991\pi\)
\(824\) −9.54810e6 −0.489890
\(825\) 7.59688e6 0.388598
\(826\) 5.08738e6 0.259444
\(827\) −2.48056e7 −1.26121 −0.630604 0.776105i \(-0.717193\pi\)
−0.630604 + 0.776105i \(0.717193\pi\)
\(828\) −2.90720e6 −0.147367
\(829\) −1.19708e6 −0.0604976 −0.0302488 0.999542i \(-0.509630\pi\)
−0.0302488 + 0.999542i \(0.509630\pi\)
\(830\) 3.76440e6 0.189671
\(831\) −1.47392e7 −0.740407
\(832\) 1.35578e6 0.0679015
\(833\) −4.07930e6 −0.203692
\(834\) −1.20288e7 −0.598835
\(835\) −1.35739e7 −0.673735
\(836\) 1.96539e7 0.972598
\(837\) 2.26258e7 1.11633
\(838\) 2.33114e7 1.14672
\(839\) −3.17171e7 −1.55557 −0.777783 0.628533i \(-0.783656\pi\)
−0.777783 + 0.628533i \(0.783656\pi\)
\(840\) 1.33280e6 0.0651729
\(841\) 456092. 0.0222363
\(842\) 9.89722e6 0.481097
\(843\) 3.30647e7 1.60249
\(844\) 3.03250e6 0.146536
\(845\) −6.54330e6 −0.315250
\(846\) −98808.0 −0.00474642
\(847\) −1.71585e7 −0.821810
\(848\) −2.81190e6 −0.134280
\(849\) −2.01452e7 −0.959186
\(850\) −4.24750e6 −0.201644
\(851\) 6.52461e7 3.08838
\(852\) 8.67136e6 0.409250
\(853\) 3.18237e7 1.49754 0.748769 0.662831i \(-0.230645\pi\)
0.748769 + 0.662831i \(0.230645\pi\)
\(854\) −7.68085e6 −0.360383
\(855\) −1.97570e6 −0.0924285
\(856\) 5.35949e6 0.249999
\(857\) 2.27853e7 1.05975 0.529874 0.848076i \(-0.322239\pi\)
0.529874 + 0.848076i \(0.322239\pi\)
\(858\) 1.60932e7 0.746319
\(859\) −1.85966e7 −0.859907 −0.429953 0.902851i \(-0.641470\pi\)
−0.429953 + 0.902851i \(0.641470\pi\)
\(860\) 903200. 0.0416426
\(861\) 1.57237e7 0.722848
\(862\) 1.84740e7 0.846825
\(863\) −2.77046e7 −1.26627 −0.633133 0.774043i \(-0.718231\pi\)
−0.633133 + 0.774043i \(0.718231\pi\)
\(864\) 3.42938e6 0.156290
\(865\) 9.27382e6 0.421423
\(866\) 234424. 0.0106220
\(867\) −2.49346e7 −1.12656
\(868\) −5.29670e6 −0.238620
\(869\) 2.00036e7 0.898582
\(870\) −7.78430e6 −0.348676
\(871\) 1.46170e6 0.0652847
\(872\) 6.74413e6 0.300355
\(873\) −2.90605e6 −0.129053
\(874\) 2.71444e7 1.20199
\(875\) −765625. −0.0338062
\(876\) 1.36490e6 0.0600951
\(877\) −2.41150e7 −1.05874 −0.529370 0.848391i \(-0.677572\pi\)
−0.529370 + 0.848391i \(0.677572\pi\)
\(878\) 2.81719e7 1.23333
\(879\) −572373. −0.0249866
\(880\) −4.57600e6 −0.199195
\(881\) −1.26207e7 −0.547827 −0.273914 0.961754i \(-0.588318\pi\)
−0.273914 + 0.961754i \(0.588318\pi\)
\(882\) 441784. 0.0191222
\(883\) −6.01876e6 −0.259780 −0.129890 0.991528i \(-0.541462\pi\)
−0.129890 + 0.991528i \(0.541462\pi\)
\(884\) −8.99790e6 −0.387267
\(885\) 1.10313e7 0.473444
\(886\) 5.87575e6 0.251466
\(887\) 2.36901e7 1.01102 0.505509 0.862821i \(-0.331305\pi\)
0.505509 + 0.862821i \(0.331305\pi\)
\(888\) 1.79716e7 0.764811
\(889\) 1.07406e7 0.455800
\(890\) −1.72160e6 −0.0728546
\(891\) 4.86994e7 2.05508
\(892\) −361552. −0.0152145
\(893\) 922566. 0.0387141
\(894\) 1.35373e7 0.566485
\(895\) −1.88543e7 −0.786779
\(896\) −802816. −0.0334077
\(897\) 2.22266e7 0.922344
\(898\) −2.99365e7 −1.23883
\(899\) 3.09357e7 1.27662
\(900\) 460000. 0.0189300
\(901\) 1.86618e7 0.765847
\(902\) −5.39854e7 −2.20933
\(903\) 1.88091e6 0.0767626
\(904\) −7.85626e6 −0.319738
\(905\) 7.59600e6 0.308293
\(906\) −3.20676e7 −1.29792
\(907\) −1.10583e7 −0.446346 −0.223173 0.974779i \(-0.571641\pi\)
−0.223173 + 0.974779i \(0.571641\pi\)
\(908\) −1.59699e7 −0.642816
\(909\) −1.34550e6 −0.0540100
\(910\) −1.62190e6 −0.0649263
\(911\) 3.07573e6 0.122787 0.0613934 0.998114i \(-0.480446\pi\)
0.0613934 + 0.998114i \(0.480446\pi\)
\(912\) 7.47674e6 0.297663
\(913\) −2.69155e7 −1.06862
\(914\) 681280. 0.0269749
\(915\) −1.66549e7 −0.657642
\(916\) −1.36743e7 −0.538476
\(917\) 4.73742e6 0.186045
\(918\) −2.27598e7 −0.891378
\(919\) −1.89018e7 −0.738270 −0.369135 0.929376i \(-0.620346\pi\)
−0.369135 + 0.929376i \(0.620346\pi\)
\(920\) −6.32000e6 −0.246177
\(921\) 459731. 0.0178589
\(922\) −1.71474e7 −0.664310
\(923\) −1.05523e7 −0.407701
\(924\) −9.52952e6 −0.367190
\(925\) −1.03238e7 −0.396719
\(926\) 1.35327e7 0.518629
\(927\) −6.86269e6 −0.262298
\(928\) 4.68890e6 0.178731
\(929\) −1.81458e7 −0.689821 −0.344911 0.938636i \(-0.612091\pi\)
−0.344911 + 0.938636i \(0.612091\pi\)
\(930\) −1.14852e7 −0.435443
\(931\) −4.12492e6 −0.155970
\(932\) 2.01309e7 0.759144
\(933\) −3.65362e7 −1.37410
\(934\) 2.07212e7 0.777225
\(935\) 3.03696e7 1.13608
\(936\) 974464. 0.0363560
\(937\) −2.17350e7 −0.808744 −0.404372 0.914595i \(-0.632510\pi\)
−0.404372 + 0.914595i \(0.632510\pi\)
\(938\) −865536. −0.0321202
\(939\) 4.53989e7 1.68028
\(940\) −214800. −0.00792893
\(941\) 1.86808e7 0.687735 0.343868 0.939018i \(-0.388263\pi\)
0.343868 + 0.939018i \(0.388263\pi\)
\(942\) 4.89967e6 0.179904
\(943\) −7.45602e7 −2.73041
\(944\) −6.64474e6 −0.242688
\(945\) −4.10252e6 −0.149442
\(946\) −6.45788e6 −0.234618
\(947\) −2.24778e6 −0.0814476 −0.0407238 0.999170i \(-0.512966\pi\)
−0.0407238 + 0.999170i \(0.512966\pi\)
\(948\) 7.60974e6 0.275010
\(949\) −1.66096e6 −0.0598678
\(950\) −4.29500e6 −0.154402
\(951\) 4.25874e6 0.152697
\(952\) 5.32806e6 0.190536
\(953\) −3.73293e7 −1.33143 −0.665714 0.746207i \(-0.731873\pi\)
−0.665714 + 0.746207i \(0.731873\pi\)
\(954\) −2.02106e6 −0.0718964
\(955\) −4.65678e6 −0.165225
\(956\) −1.13053e7 −0.400071
\(957\) 5.56577e7 1.96447
\(958\) −3.50711e7 −1.23463
\(959\) −9.17711e6 −0.322225
\(960\) −1.74080e6 −0.0609636
\(961\) 1.70144e7 0.594303
\(962\) −2.18698e7 −0.761917
\(963\) 3.85213e6 0.133855
\(964\) 9.86128e6 0.341775
\(965\) 2.31260e6 0.0799433
\(966\) −1.31614e7 −0.453795
\(967\) 2.61870e7 0.900573 0.450287 0.892884i \(-0.351322\pi\)
0.450287 + 0.892884i \(0.351322\pi\)
\(968\) 2.24111e7 0.768733
\(969\) −4.96210e7 −1.69768
\(970\) −6.31750e6 −0.215584
\(971\) −3.91957e7 −1.33410 −0.667052 0.745011i \(-0.732444\pi\)
−0.667052 + 0.745011i \(0.732444\pi\)
\(972\) 5.50528e6 0.186902
\(973\) −8.66781e6 −0.293513
\(974\) 1.08062e6 0.0364984
\(975\) −3.51688e6 −0.118480
\(976\) 1.00321e7 0.337108
\(977\) 3.03935e6 0.101870 0.0509348 0.998702i \(-0.483780\pi\)
0.0509348 + 0.998702i \(0.483780\pi\)
\(978\) −2.62027e7 −0.875990
\(979\) 1.23094e7 0.410470
\(980\) 960400. 0.0319438
\(981\) 4.84734e6 0.160817
\(982\) 1.94220e7 0.642711
\(983\) −1.59937e7 −0.527915 −0.263957 0.964534i \(-0.585028\pi\)
−0.263957 + 0.964534i \(0.585028\pi\)
\(984\) −2.05371e7 −0.676163
\(985\) −1.84092e7 −0.604567
\(986\) −3.11189e7 −1.01937
\(987\) −447321. −0.0146159
\(988\) −9.09853e6 −0.296537
\(989\) −8.91910e6 −0.289955
\(990\) −3.28900e6 −0.106654
\(991\) 3.63186e6 0.117475 0.0587375 0.998273i \(-0.481293\pi\)
0.0587375 + 0.998273i \(0.481293\pi\)
\(992\) 6.91814e6 0.223208
\(993\) −1.80028e7 −0.579384
\(994\) 6.24848e6 0.200590
\(995\) −1.20405e7 −0.385555
\(996\) −1.02392e7 −0.327052
\(997\) −4.33287e7 −1.38051 −0.690253 0.723568i \(-0.742501\pi\)
−0.690253 + 0.723568i \(0.742501\pi\)
\(998\) −1.19430e7 −0.379567
\(999\) −5.53188e7 −1.75371
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 70.6.a.e.1.1 1
3.2 odd 2 630.6.a.b.1.1 1
4.3 odd 2 560.6.a.h.1.1 1
5.2 odd 4 350.6.c.a.99.2 2
5.3 odd 4 350.6.c.a.99.1 2
5.4 even 2 350.6.a.e.1.1 1
7.6 odd 2 490.6.a.m.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.6.a.e.1.1 1 1.1 even 1 trivial
350.6.a.e.1.1 1 5.4 even 2
350.6.c.a.99.1 2 5.3 odd 4
350.6.c.a.99.2 2 5.2 odd 4
490.6.a.m.1.1 1 7.6 odd 2
560.6.a.h.1.1 1 4.3 odd 2
630.6.a.b.1.1 1 3.2 odd 2