Properties

Label 126.6.a.i.1.1
Level $126$
Weight $6$
Character 126.1
Self dual yes
Analytic conductor $20.208$
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] = [126,6,Mod(1,126)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(126, 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("126.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 126.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: \(20.2083612964\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 126.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} +16.0000 q^{4} -26.0000 q^{5} -49.0000 q^{7} +64.0000 q^{8} +O(q^{10})\) \(q+4.00000 q^{2} +16.0000 q^{4} -26.0000 q^{5} -49.0000 q^{7} +64.0000 q^{8} -104.000 q^{10} -664.000 q^{11} +318.000 q^{13} -196.000 q^{14} +256.000 q^{16} -1582.00 q^{17} +236.000 q^{19} -416.000 q^{20} -2656.00 q^{22} -2212.00 q^{23} -2449.00 q^{25} +1272.00 q^{26} -784.000 q^{28} +4954.00 q^{29} -7128.00 q^{31} +1024.00 q^{32} -6328.00 q^{34} +1274.00 q^{35} +4358.00 q^{37} +944.000 q^{38} -1664.00 q^{40} -10542.0 q^{41} -8452.00 q^{43} -10624.0 q^{44} -8848.00 q^{46} -5352.00 q^{47} +2401.00 q^{49} -9796.00 q^{50} +5088.00 q^{52} +33354.0 q^{53} +17264.0 q^{55} -3136.00 q^{56} +19816.0 q^{58} +15436.0 q^{59} -36762.0 q^{61} -28512.0 q^{62} +4096.00 q^{64} -8268.00 q^{65} +40972.0 q^{67} -25312.0 q^{68} +5096.00 q^{70} +9092.00 q^{71} -73454.0 q^{73} +17432.0 q^{74} +3776.00 q^{76} +32536.0 q^{77} +89400.0 q^{79} -6656.00 q^{80} -42168.0 q^{82} +6428.00 q^{83} +41132.0 q^{85} -33808.0 q^{86} -42496.0 q^{88} +122658. q^{89} -15582.0 q^{91} -35392.0 q^{92} -21408.0 q^{94} -6136.00 q^{95} +21370.0 q^{97} +9604.00 q^{98} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 16.0000 0.500000
\(5\) −26.0000 −0.465102 −0.232551 0.972584i \(-0.574707\pi\)
−0.232551 + 0.972584i \(0.574707\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 64.0000 0.353553
\(9\) 0 0
\(10\) −104.000 −0.328877
\(11\) −664.000 −1.65457 −0.827287 0.561779i \(-0.810117\pi\)
−0.827287 + 0.561779i \(0.810117\pi\)
\(12\) 0 0
\(13\) 318.000 0.521878 0.260939 0.965355i \(-0.415968\pi\)
0.260939 + 0.965355i \(0.415968\pi\)
\(14\) −196.000 −0.267261
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) −1582.00 −1.32765 −0.663826 0.747887i \(-0.731068\pi\)
−0.663826 + 0.747887i \(0.731068\pi\)
\(18\) 0 0
\(19\) 236.000 0.149978 0.0749891 0.997184i \(-0.476108\pi\)
0.0749891 + 0.997184i \(0.476108\pi\)
\(20\) −416.000 −0.232551
\(21\) 0 0
\(22\) −2656.00 −1.16996
\(23\) −2212.00 −0.871898 −0.435949 0.899971i \(-0.643587\pi\)
−0.435949 + 0.899971i \(0.643587\pi\)
\(24\) 0 0
\(25\) −2449.00 −0.783680
\(26\) 1272.00 0.369023
\(27\) 0 0
\(28\) −784.000 −0.188982
\(29\) 4954.00 1.09386 0.546929 0.837179i \(-0.315797\pi\)
0.546929 + 0.837179i \(0.315797\pi\)
\(30\) 0 0
\(31\) −7128.00 −1.33218 −0.666091 0.745871i \(-0.732034\pi\)
−0.666091 + 0.745871i \(0.732034\pi\)
\(32\) 1024.00 0.176777
\(33\) 0 0
\(34\) −6328.00 −0.938792
\(35\) 1274.00 0.175792
\(36\) 0 0
\(37\) 4358.00 0.523339 0.261669 0.965158i \(-0.415727\pi\)
0.261669 + 0.965158i \(0.415727\pi\)
\(38\) 944.000 0.106051
\(39\) 0 0
\(40\) −1664.00 −0.164438
\(41\) −10542.0 −0.979407 −0.489704 0.871889i \(-0.662895\pi\)
−0.489704 + 0.871889i \(0.662895\pi\)
\(42\) 0 0
\(43\) −8452.00 −0.697089 −0.348545 0.937292i \(-0.613324\pi\)
−0.348545 + 0.937292i \(0.613324\pi\)
\(44\) −10624.0 −0.827287
\(45\) 0 0
\(46\) −8848.00 −0.616525
\(47\) −5352.00 −0.353404 −0.176702 0.984264i \(-0.556543\pi\)
−0.176702 + 0.984264i \(0.556543\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) −9796.00 −0.554145
\(51\) 0 0
\(52\) 5088.00 0.260939
\(53\) 33354.0 1.63102 0.815508 0.578746i \(-0.196458\pi\)
0.815508 + 0.578746i \(0.196458\pi\)
\(54\) 0 0
\(55\) 17264.0 0.769546
\(56\) −3136.00 −0.133631
\(57\) 0 0
\(58\) 19816.0 0.773475
\(59\) 15436.0 0.577304 0.288652 0.957434i \(-0.406793\pi\)
0.288652 + 0.957434i \(0.406793\pi\)
\(60\) 0 0
\(61\) −36762.0 −1.26495 −0.632477 0.774579i \(-0.717962\pi\)
−0.632477 + 0.774579i \(0.717962\pi\)
\(62\) −28512.0 −0.941995
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −8268.00 −0.242726
\(66\) 0 0
\(67\) 40972.0 1.11506 0.557532 0.830155i \(-0.311748\pi\)
0.557532 + 0.830155i \(0.311748\pi\)
\(68\) −25312.0 −0.663826
\(69\) 0 0
\(70\) 5096.00 0.124304
\(71\) 9092.00 0.214049 0.107025 0.994256i \(-0.465868\pi\)
0.107025 + 0.994256i \(0.465868\pi\)
\(72\) 0 0
\(73\) −73454.0 −1.61327 −0.806637 0.591047i \(-0.798715\pi\)
−0.806637 + 0.591047i \(0.798715\pi\)
\(74\) 17432.0 0.370056
\(75\) 0 0
\(76\) 3776.00 0.0749891
\(77\) 32536.0 0.625370
\(78\) 0 0
\(79\) 89400.0 1.61165 0.805823 0.592156i \(-0.201723\pi\)
0.805823 + 0.592156i \(0.201723\pi\)
\(80\) −6656.00 −0.116276
\(81\) 0 0
\(82\) −42168.0 −0.692546
\(83\) 6428.00 0.102419 0.0512095 0.998688i \(-0.483692\pi\)
0.0512095 + 0.998688i \(0.483692\pi\)
\(84\) 0 0
\(85\) 41132.0 0.617494
\(86\) −33808.0 −0.492916
\(87\) 0 0
\(88\) −42496.0 −0.584980
\(89\) 122658. 1.64142 0.820712 0.571342i \(-0.193577\pi\)
0.820712 + 0.571342i \(0.193577\pi\)
\(90\) 0 0
\(91\) −15582.0 −0.197251
\(92\) −35392.0 −0.435949
\(93\) 0 0
\(94\) −21408.0 −0.249894
\(95\) −6136.00 −0.0697552
\(96\) 0 0
\(97\) 21370.0 0.230608 0.115304 0.993330i \(-0.463216\pi\)
0.115304 + 0.993330i \(0.463216\pi\)
\(98\) 9604.00 0.101015
\(99\) 0 0
\(100\) −39184.0 −0.391840
\(101\) 36814.0 0.359095 0.179548 0.983749i \(-0.442537\pi\)
0.179548 + 0.983749i \(0.442537\pi\)
\(102\) 0 0
\(103\) 104528. 0.970822 0.485411 0.874286i \(-0.338670\pi\)
0.485411 + 0.874286i \(0.338670\pi\)
\(104\) 20352.0 0.184512
\(105\) 0 0
\(106\) 133416. 1.15330
\(107\) −214440. −1.81070 −0.905350 0.424667i \(-0.860391\pi\)
−0.905350 + 0.424667i \(0.860391\pi\)
\(108\) 0 0
\(109\) 28798.0 0.232165 0.116082 0.993240i \(-0.462966\pi\)
0.116082 + 0.993240i \(0.462966\pi\)
\(110\) 69056.0 0.544151
\(111\) 0 0
\(112\) −12544.0 −0.0944911
\(113\) 56014.0 0.412668 0.206334 0.978482i \(-0.433847\pi\)
0.206334 + 0.978482i \(0.433847\pi\)
\(114\) 0 0
\(115\) 57512.0 0.405521
\(116\) 79264.0 0.546929
\(117\) 0 0
\(118\) 61744.0 0.408216
\(119\) 77518.0 0.501805
\(120\) 0 0
\(121\) 279845. 1.73762
\(122\) −147048. −0.894457
\(123\) 0 0
\(124\) −114048. −0.666091
\(125\) 144924. 0.829593
\(126\) 0 0
\(127\) 185400. 1.02000 0.510000 0.860174i \(-0.329645\pi\)
0.510000 + 0.860174i \(0.329645\pi\)
\(128\) 16384.0 0.0883883
\(129\) 0 0
\(130\) −33072.0 −0.171634
\(131\) −64532.0 −0.328547 −0.164273 0.986415i \(-0.552528\pi\)
−0.164273 + 0.986415i \(0.552528\pi\)
\(132\) 0 0
\(133\) −11564.0 −0.0566864
\(134\) 163888. 0.788470
\(135\) 0 0
\(136\) −101248. −0.469396
\(137\) −152930. −0.696131 −0.348066 0.937470i \(-0.613161\pi\)
−0.348066 + 0.937470i \(0.613161\pi\)
\(138\) 0 0
\(139\) −343460. −1.50778 −0.753892 0.656998i \(-0.771826\pi\)
−0.753892 + 0.656998i \(0.771826\pi\)
\(140\) 20384.0 0.0878960
\(141\) 0 0
\(142\) 36368.0 0.151356
\(143\) −211152. −0.863486
\(144\) 0 0
\(145\) −128804. −0.508756
\(146\) −293816. −1.14076
\(147\) 0 0
\(148\) 69728.0 0.261669
\(149\) 174858. 0.645238 0.322619 0.946529i \(-0.395437\pi\)
0.322619 + 0.946529i \(0.395437\pi\)
\(150\) 0 0
\(151\) −452552. −1.61520 −0.807600 0.589731i \(-0.799234\pi\)
−0.807600 + 0.589731i \(0.799234\pi\)
\(152\) 15104.0 0.0530253
\(153\) 0 0
\(154\) 130144. 0.442204
\(155\) 185328. 0.619601
\(156\) 0 0
\(157\) −499066. −1.61588 −0.807940 0.589265i \(-0.799417\pi\)
−0.807940 + 0.589265i \(0.799417\pi\)
\(158\) 357600. 1.13961
\(159\) 0 0
\(160\) −26624.0 −0.0822192
\(161\) 108388. 0.329546
\(162\) 0 0
\(163\) −475588. −1.40204 −0.701022 0.713139i \(-0.747273\pi\)
−0.701022 + 0.713139i \(0.747273\pi\)
\(164\) −168672. −0.489704
\(165\) 0 0
\(166\) 25712.0 0.0724212
\(167\) −120224. −0.333580 −0.166790 0.985992i \(-0.553340\pi\)
−0.166790 + 0.985992i \(0.553340\pi\)
\(168\) 0 0
\(169\) −270169. −0.727644
\(170\) 164528. 0.436634
\(171\) 0 0
\(172\) −135232. −0.348545
\(173\) −508874. −1.29269 −0.646346 0.763045i \(-0.723704\pi\)
−0.646346 + 0.763045i \(0.723704\pi\)
\(174\) 0 0
\(175\) 120001. 0.296203
\(176\) −169984. −0.413644
\(177\) 0 0
\(178\) 490632. 1.16066
\(179\) −487560. −1.13735 −0.568677 0.822561i \(-0.692544\pi\)
−0.568677 + 0.822561i \(0.692544\pi\)
\(180\) 0 0
\(181\) −544410. −1.23518 −0.617589 0.786501i \(-0.711891\pi\)
−0.617589 + 0.786501i \(0.711891\pi\)
\(182\) −62328.0 −0.139478
\(183\) 0 0
\(184\) −141568. −0.308262
\(185\) −113308. −0.243406
\(186\) 0 0
\(187\) 1.05045e6 2.19670
\(188\) −85632.0 −0.176702
\(189\) 0 0
\(190\) −24544.0 −0.0493243
\(191\) −376404. −0.746570 −0.373285 0.927717i \(-0.621769\pi\)
−0.373285 + 0.927717i \(0.621769\pi\)
\(192\) 0 0
\(193\) 844946. 1.63281 0.816405 0.577480i \(-0.195964\pi\)
0.816405 + 0.577480i \(0.195964\pi\)
\(194\) 85480.0 0.163065
\(195\) 0 0
\(196\) 38416.0 0.0714286
\(197\) 492794. 0.904690 0.452345 0.891843i \(-0.350588\pi\)
0.452345 + 0.891843i \(0.350588\pi\)
\(198\) 0 0
\(199\) −914776. −1.63750 −0.818751 0.574148i \(-0.805333\pi\)
−0.818751 + 0.574148i \(0.805333\pi\)
\(200\) −156736. −0.277073
\(201\) 0 0
\(202\) 147256. 0.253919
\(203\) −242746. −0.413440
\(204\) 0 0
\(205\) 274092. 0.455524
\(206\) 418112. 0.686475
\(207\) 0 0
\(208\) 81408.0 0.130469
\(209\) −156704. −0.248150
\(210\) 0 0
\(211\) 311780. 0.482106 0.241053 0.970512i \(-0.422507\pi\)
0.241053 + 0.970512i \(0.422507\pi\)
\(212\) 533664. 0.815508
\(213\) 0 0
\(214\) −857760. −1.28036
\(215\) 219752. 0.324218
\(216\) 0 0
\(217\) 349272. 0.503517
\(218\) 115192. 0.164165
\(219\) 0 0
\(220\) 276224. 0.384773
\(221\) −503076. −0.692872
\(222\) 0 0
\(223\) −1.28776e6 −1.73409 −0.867047 0.498226i \(-0.833985\pi\)
−0.867047 + 0.498226i \(0.833985\pi\)
\(224\) −50176.0 −0.0668153
\(225\) 0 0
\(226\) 224056. 0.291800
\(227\) −1.28905e6 −1.66037 −0.830187 0.557485i \(-0.811766\pi\)
−0.830187 + 0.557485i \(0.811766\pi\)
\(228\) 0 0
\(229\) 678214. 0.854630 0.427315 0.904103i \(-0.359460\pi\)
0.427315 + 0.904103i \(0.359460\pi\)
\(230\) 230048. 0.286747
\(231\) 0 0
\(232\) 317056. 0.386737
\(233\) 1.11731e6 1.34829 0.674146 0.738598i \(-0.264512\pi\)
0.674146 + 0.738598i \(0.264512\pi\)
\(234\) 0 0
\(235\) 139152. 0.164369
\(236\) 246976. 0.288652
\(237\) 0 0
\(238\) 310072. 0.354830
\(239\) 1.26196e6 1.42906 0.714528 0.699606i \(-0.246641\pi\)
0.714528 + 0.699606i \(0.246641\pi\)
\(240\) 0 0
\(241\) 948218. 1.05164 0.525818 0.850597i \(-0.323759\pi\)
0.525818 + 0.850597i \(0.323759\pi\)
\(242\) 1.11938e6 1.22868
\(243\) 0 0
\(244\) −588192. −0.632477
\(245\) −62426.0 −0.0664432
\(246\) 0 0
\(247\) 75048.0 0.0782703
\(248\) −456192. −0.470997
\(249\) 0 0
\(250\) 579696. 0.586611
\(251\) 486396. 0.487310 0.243655 0.969862i \(-0.421653\pi\)
0.243655 + 0.969862i \(0.421653\pi\)
\(252\) 0 0
\(253\) 1.46877e6 1.44262
\(254\) 741600. 0.721249
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) 1.03910e6 0.981349 0.490675 0.871343i \(-0.336750\pi\)
0.490675 + 0.871343i \(0.336750\pi\)
\(258\) 0 0
\(259\) −213542. −0.197803
\(260\) −132288. −0.121363
\(261\) 0 0
\(262\) −258128. −0.232317
\(263\) −1.35104e6 −1.20443 −0.602213 0.798335i \(-0.705714\pi\)
−0.602213 + 0.798335i \(0.705714\pi\)
\(264\) 0 0
\(265\) −867204. −0.758589
\(266\) −46256.0 −0.0400833
\(267\) 0 0
\(268\) 655552. 0.557532
\(269\) 1.11811e6 0.942115 0.471057 0.882103i \(-0.343872\pi\)
0.471057 + 0.882103i \(0.343872\pi\)
\(270\) 0 0
\(271\) −190104. −0.157242 −0.0786209 0.996905i \(-0.525052\pi\)
−0.0786209 + 0.996905i \(0.525052\pi\)
\(272\) −404992. −0.331913
\(273\) 0 0
\(274\) −611720. −0.492239
\(275\) 1.62614e6 1.29666
\(276\) 0 0
\(277\) −200506. −0.157010 −0.0785051 0.996914i \(-0.525015\pi\)
−0.0785051 + 0.996914i \(0.525015\pi\)
\(278\) −1.37384e6 −1.06616
\(279\) 0 0
\(280\) 81536.0 0.0621519
\(281\) −1.09237e6 −0.825285 −0.412643 0.910893i \(-0.635394\pi\)
−0.412643 + 0.910893i \(0.635394\pi\)
\(282\) 0 0
\(283\) 1.81258e6 1.34534 0.672669 0.739944i \(-0.265148\pi\)
0.672669 + 0.739944i \(0.265148\pi\)
\(284\) 145472. 0.107025
\(285\) 0 0
\(286\) −844608. −0.610577
\(287\) 516558. 0.370181
\(288\) 0 0
\(289\) 1.08287e6 0.762659
\(290\) −515216. −0.359745
\(291\) 0 0
\(292\) −1.17526e6 −0.806637
\(293\) −2.10031e6 −1.42927 −0.714634 0.699499i \(-0.753407\pi\)
−0.714634 + 0.699499i \(0.753407\pi\)
\(294\) 0 0
\(295\) −401336. −0.268505
\(296\) 278912. 0.185028
\(297\) 0 0
\(298\) 699432. 0.456252
\(299\) −703416. −0.455024
\(300\) 0 0
\(301\) 414148. 0.263475
\(302\) −1.81021e6 −1.14212
\(303\) 0 0
\(304\) 60416.0 0.0374945
\(305\) 955812. 0.588333
\(306\) 0 0
\(307\) −1.64104e6 −0.993743 −0.496872 0.867824i \(-0.665518\pi\)
−0.496872 + 0.867824i \(0.665518\pi\)
\(308\) 520576. 0.312685
\(309\) 0 0
\(310\) 741312. 0.438124
\(311\) 945232. 0.554163 0.277081 0.960846i \(-0.410633\pi\)
0.277081 + 0.960846i \(0.410633\pi\)
\(312\) 0 0
\(313\) 415354. 0.239639 0.119820 0.992796i \(-0.461768\pi\)
0.119820 + 0.992796i \(0.461768\pi\)
\(314\) −1.99626e6 −1.14260
\(315\) 0 0
\(316\) 1.43040e6 0.805823
\(317\) −1.18481e6 −0.662220 −0.331110 0.943592i \(-0.607423\pi\)
−0.331110 + 0.943592i \(0.607423\pi\)
\(318\) 0 0
\(319\) −3.28946e6 −1.80987
\(320\) −106496. −0.0581378
\(321\) 0 0
\(322\) 433552. 0.233024
\(323\) −373352. −0.199119
\(324\) 0 0
\(325\) −778782. −0.408985
\(326\) −1.90235e6 −0.991395
\(327\) 0 0
\(328\) −674688. −0.346273
\(329\) 262248. 0.133574
\(330\) 0 0
\(331\) 1.37155e6 0.688083 0.344042 0.938954i \(-0.388204\pi\)
0.344042 + 0.938954i \(0.388204\pi\)
\(332\) 102848. 0.0512095
\(333\) 0 0
\(334\) −480896. −0.235877
\(335\) −1.06527e6 −0.518619
\(336\) 0 0
\(337\) 963522. 0.462154 0.231077 0.972935i \(-0.425775\pi\)
0.231077 + 0.972935i \(0.425775\pi\)
\(338\) −1.08068e6 −0.514522
\(339\) 0 0
\(340\) 658112. 0.308747
\(341\) 4.73299e6 2.20419
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) −540928. −0.246458
\(345\) 0 0
\(346\) −2.03550e6 −0.914071
\(347\) −2.57731e6 −1.14906 −0.574531 0.818483i \(-0.694815\pi\)
−0.574531 + 0.818483i \(0.694815\pi\)
\(348\) 0 0
\(349\) −3.06751e6 −1.34810 −0.674051 0.738684i \(-0.735447\pi\)
−0.674051 + 0.738684i \(0.735447\pi\)
\(350\) 480004. 0.209447
\(351\) 0 0
\(352\) −679936. −0.292490
\(353\) 3.10144e6 1.32473 0.662364 0.749182i \(-0.269553\pi\)
0.662364 + 0.749182i \(0.269553\pi\)
\(354\) 0 0
\(355\) −236392. −0.0995547
\(356\) 1.96253e6 0.820712
\(357\) 0 0
\(358\) −1.95024e6 −0.804230
\(359\) 327508. 0.134118 0.0670588 0.997749i \(-0.478638\pi\)
0.0670588 + 0.997749i \(0.478638\pi\)
\(360\) 0 0
\(361\) −2.42040e6 −0.977507
\(362\) −2.17764e6 −0.873403
\(363\) 0 0
\(364\) −249312. −0.0986256
\(365\) 1.90980e6 0.750337
\(366\) 0 0
\(367\) −2.86739e6 −1.11128 −0.555638 0.831424i \(-0.687526\pi\)
−0.555638 + 0.831424i \(0.687526\pi\)
\(368\) −566272. −0.217974
\(369\) 0 0
\(370\) −453232. −0.172114
\(371\) −1.63435e6 −0.616466
\(372\) 0 0
\(373\) 3.58029e6 1.33244 0.666218 0.745757i \(-0.267912\pi\)
0.666218 + 0.745757i \(0.267912\pi\)
\(374\) 4.20179e6 1.55330
\(375\) 0 0
\(376\) −342528. −0.124947
\(377\) 1.57537e6 0.570860
\(378\) 0 0
\(379\) 1.64235e6 0.587310 0.293655 0.955912i \(-0.405128\pi\)
0.293655 + 0.955912i \(0.405128\pi\)
\(380\) −98176.0 −0.0348776
\(381\) 0 0
\(382\) −1.50562e6 −0.527905
\(383\) 2.05698e6 0.716527 0.358263 0.933621i \(-0.383369\pi\)
0.358263 + 0.933621i \(0.383369\pi\)
\(384\) 0 0
\(385\) −845936. −0.290861
\(386\) 3.37978e6 1.15457
\(387\) 0 0
\(388\) 341920. 0.115304
\(389\) −616142. −0.206446 −0.103223 0.994658i \(-0.532916\pi\)
−0.103223 + 0.994658i \(0.532916\pi\)
\(390\) 0 0
\(391\) 3.49938e6 1.15758
\(392\) 153664. 0.0505076
\(393\) 0 0
\(394\) 1.97118e6 0.639713
\(395\) −2.32440e6 −0.749580
\(396\) 0 0
\(397\) 2.19212e6 0.698052 0.349026 0.937113i \(-0.386513\pi\)
0.349026 + 0.937113i \(0.386513\pi\)
\(398\) −3.65910e6 −1.15789
\(399\) 0 0
\(400\) −626944. −0.195920
\(401\) −3.28454e6 −1.02003 −0.510015 0.860165i \(-0.670360\pi\)
−0.510015 + 0.860165i \(0.670360\pi\)
\(402\) 0 0
\(403\) −2.26670e6 −0.695236
\(404\) 589024. 0.179548
\(405\) 0 0
\(406\) −970984. −0.292346
\(407\) −2.89371e6 −0.865903
\(408\) 0 0
\(409\) −3.61219e6 −1.06773 −0.533866 0.845569i \(-0.679261\pi\)
−0.533866 + 0.845569i \(0.679261\pi\)
\(410\) 1.09637e6 0.322104
\(411\) 0 0
\(412\) 1.67245e6 0.485411
\(413\) −756364. −0.218200
\(414\) 0 0
\(415\) −167128. −0.0476353
\(416\) 325632. 0.0922558
\(417\) 0 0
\(418\) −626816. −0.175469
\(419\) −5.41489e6 −1.50680 −0.753398 0.657564i \(-0.771587\pi\)
−0.753398 + 0.657564i \(0.771587\pi\)
\(420\) 0 0
\(421\) 3.60629e6 0.991644 0.495822 0.868424i \(-0.334867\pi\)
0.495822 + 0.868424i \(0.334867\pi\)
\(422\) 1.24712e6 0.340900
\(423\) 0 0
\(424\) 2.13466e6 0.576651
\(425\) 3.87432e6 1.04045
\(426\) 0 0
\(427\) 1.80134e6 0.478107
\(428\) −3.43104e6 −0.905350
\(429\) 0 0
\(430\) 879008. 0.229257
\(431\) 2.78214e6 0.721416 0.360708 0.932679i \(-0.382535\pi\)
0.360708 + 0.932679i \(0.382535\pi\)
\(432\) 0 0
\(433\) 6.27619e6 1.60871 0.804353 0.594152i \(-0.202512\pi\)
0.804353 + 0.594152i \(0.202512\pi\)
\(434\) 1.39709e6 0.356041
\(435\) 0 0
\(436\) 460768. 0.116082
\(437\) −522032. −0.130766
\(438\) 0 0
\(439\) 641592. 0.158890 0.0794452 0.996839i \(-0.474685\pi\)
0.0794452 + 0.996839i \(0.474685\pi\)
\(440\) 1.10490e6 0.272076
\(441\) 0 0
\(442\) −2.01230e6 −0.489934
\(443\) −6.05546e6 −1.46601 −0.733006 0.680222i \(-0.761883\pi\)
−0.733006 + 0.680222i \(0.761883\pi\)
\(444\) 0 0
\(445\) −3.18911e6 −0.763430
\(446\) −5.15104e6 −1.22619
\(447\) 0 0
\(448\) −200704. −0.0472456
\(449\) 5.16681e6 1.20950 0.604752 0.796414i \(-0.293272\pi\)
0.604752 + 0.796414i \(0.293272\pi\)
\(450\) 0 0
\(451\) 6.99989e6 1.62050
\(452\) 896224. 0.206334
\(453\) 0 0
\(454\) −5.15621e6 −1.17406
\(455\) 405132. 0.0917420
\(456\) 0 0
\(457\) −227798. −0.0510222 −0.0255111 0.999675i \(-0.508121\pi\)
−0.0255111 + 0.999675i \(0.508121\pi\)
\(458\) 2.71286e6 0.604315
\(459\) 0 0
\(460\) 920192. 0.202761
\(461\) −585146. −0.128237 −0.0641183 0.997942i \(-0.520423\pi\)
−0.0641183 + 0.997942i \(0.520423\pi\)
\(462\) 0 0
\(463\) −3.41454e6 −0.740251 −0.370126 0.928982i \(-0.620685\pi\)
−0.370126 + 0.928982i \(0.620685\pi\)
\(464\) 1.26822e6 0.273465
\(465\) 0 0
\(466\) 4.46924e6 0.953386
\(467\) −716300. −0.151986 −0.0759929 0.997108i \(-0.524213\pi\)
−0.0759929 + 0.997108i \(0.524213\pi\)
\(468\) 0 0
\(469\) −2.00763e6 −0.421455
\(470\) 556608. 0.116226
\(471\) 0 0
\(472\) 987904. 0.204108
\(473\) 5.61213e6 1.15339
\(474\) 0 0
\(475\) −577964. −0.117535
\(476\) 1.24029e6 0.250903
\(477\) 0 0
\(478\) 5.04782e6 1.01050
\(479\) −5.24092e6 −1.04368 −0.521842 0.853042i \(-0.674755\pi\)
−0.521842 + 0.853042i \(0.674755\pi\)
\(480\) 0 0
\(481\) 1.38584e6 0.273119
\(482\) 3.79287e6 0.743619
\(483\) 0 0
\(484\) 4.47752e6 0.868809
\(485\) −555620. −0.107256
\(486\) 0 0
\(487\) 1.11702e6 0.213421 0.106710 0.994290i \(-0.465968\pi\)
0.106710 + 0.994290i \(0.465968\pi\)
\(488\) −2.35277e6 −0.447229
\(489\) 0 0
\(490\) −249704. −0.0469824
\(491\) −1.34458e6 −0.251699 −0.125850 0.992049i \(-0.540166\pi\)
−0.125850 + 0.992049i \(0.540166\pi\)
\(492\) 0 0
\(493\) −7.83723e6 −1.45226
\(494\) 300192. 0.0553454
\(495\) 0 0
\(496\) −1.82477e6 −0.333045
\(497\) −445508. −0.0809030
\(498\) 0 0
\(499\) −6.54648e6 −1.17695 −0.588473 0.808517i \(-0.700271\pi\)
−0.588473 + 0.808517i \(0.700271\pi\)
\(500\) 2.31878e6 0.414797
\(501\) 0 0
\(502\) 1.94558e6 0.344580
\(503\) 8.22050e6 1.44870 0.724350 0.689432i \(-0.242140\pi\)
0.724350 + 0.689432i \(0.242140\pi\)
\(504\) 0 0
\(505\) −957164. −0.167016
\(506\) 5.87507e6 1.02009
\(507\) 0 0
\(508\) 2.96640e6 0.510000
\(509\) 5.11045e6 0.874308 0.437154 0.899387i \(-0.355987\pi\)
0.437154 + 0.899387i \(0.355987\pi\)
\(510\) 0 0
\(511\) 3.59925e6 0.609760
\(512\) 262144. 0.0441942
\(513\) 0 0
\(514\) 4.15639e6 0.693919
\(515\) −2.71773e6 −0.451531
\(516\) 0 0
\(517\) 3.55373e6 0.584733
\(518\) −854168. −0.139868
\(519\) 0 0
\(520\) −529152. −0.0858168
\(521\) −9.69999e6 −1.56559 −0.782793 0.622282i \(-0.786206\pi\)
−0.782793 + 0.622282i \(0.786206\pi\)
\(522\) 0 0
\(523\) −3.17295e6 −0.507234 −0.253617 0.967305i \(-0.581620\pi\)
−0.253617 + 0.967305i \(0.581620\pi\)
\(524\) −1.03251e6 −0.164273
\(525\) 0 0
\(526\) −5.40418e6 −0.851658
\(527\) 1.12765e7 1.76867
\(528\) 0 0
\(529\) −1.54340e6 −0.239794
\(530\) −3.46882e6 −0.536403
\(531\) 0 0
\(532\) −185024. −0.0283432
\(533\) −3.35236e6 −0.511131
\(534\) 0 0
\(535\) 5.57544e6 0.842160
\(536\) 2.62221e6 0.394235
\(537\) 0 0
\(538\) 4.47244e6 0.666176
\(539\) −1.59426e6 −0.236368
\(540\) 0 0
\(541\) −6.62575e6 −0.973289 −0.486644 0.873600i \(-0.661779\pi\)
−0.486644 + 0.873600i \(0.661779\pi\)
\(542\) −760416. −0.111187
\(543\) 0 0
\(544\) −1.61997e6 −0.234698
\(545\) −748748. −0.107980
\(546\) 0 0
\(547\) 3.84707e6 0.549745 0.274873 0.961481i \(-0.411364\pi\)
0.274873 + 0.961481i \(0.411364\pi\)
\(548\) −2.44688e6 −0.348066
\(549\) 0 0
\(550\) 6.50454e6 0.916875
\(551\) 1.16914e6 0.164055
\(552\) 0 0
\(553\) −4.38060e6 −0.609145
\(554\) −802024. −0.111023
\(555\) 0 0
\(556\) −5.49536e6 −0.753892
\(557\) −5.00176e6 −0.683101 −0.341550 0.939863i \(-0.610952\pi\)
−0.341550 + 0.939863i \(0.610952\pi\)
\(558\) 0 0
\(559\) −2.68774e6 −0.363795
\(560\) 326144. 0.0439480
\(561\) 0 0
\(562\) −4.36948e6 −0.583565
\(563\) −2.27772e6 −0.302852 −0.151426 0.988469i \(-0.548386\pi\)
−0.151426 + 0.988469i \(0.548386\pi\)
\(564\) 0 0
\(565\) −1.45636e6 −0.191933
\(566\) 7.25032e6 0.951297
\(567\) 0 0
\(568\) 581888. 0.0756778
\(569\) −8.86979e6 −1.14850 −0.574252 0.818678i \(-0.694707\pi\)
−0.574252 + 0.818678i \(0.694707\pi\)
\(570\) 0 0
\(571\) 1.40102e7 1.79826 0.899132 0.437678i \(-0.144199\pi\)
0.899132 + 0.437678i \(0.144199\pi\)
\(572\) −3.37843e6 −0.431743
\(573\) 0 0
\(574\) 2.06623e6 0.261758
\(575\) 5.41719e6 0.683289
\(576\) 0 0
\(577\) 8.75327e6 1.09454 0.547269 0.836957i \(-0.315668\pi\)
0.547269 + 0.836957i \(0.315668\pi\)
\(578\) 4.33147e6 0.539281
\(579\) 0 0
\(580\) −2.06086e6 −0.254378
\(581\) −314972. −0.0387108
\(582\) 0 0
\(583\) −2.21471e7 −2.69864
\(584\) −4.70106e6 −0.570379
\(585\) 0 0
\(586\) −8.40122e6 −1.01064
\(587\) 1.06117e7 1.27113 0.635564 0.772048i \(-0.280768\pi\)
0.635564 + 0.772048i \(0.280768\pi\)
\(588\) 0 0
\(589\) −1.68221e6 −0.199798
\(590\) −1.60534e6 −0.189862
\(591\) 0 0
\(592\) 1.11565e6 0.130835
\(593\) −1.88552e6 −0.220188 −0.110094 0.993921i \(-0.535115\pi\)
−0.110094 + 0.993921i \(0.535115\pi\)
\(594\) 0 0
\(595\) −2.01547e6 −0.233391
\(596\) 2.79773e6 0.322619
\(597\) 0 0
\(598\) −2.81366e6 −0.321751
\(599\) −1.27256e7 −1.44915 −0.724573 0.689198i \(-0.757963\pi\)
−0.724573 + 0.689198i \(0.757963\pi\)
\(600\) 0 0
\(601\) 7.18846e6 0.811801 0.405900 0.913917i \(-0.366958\pi\)
0.405900 + 0.913917i \(0.366958\pi\)
\(602\) 1.65659e6 0.186305
\(603\) 0 0
\(604\) −7.24083e6 −0.807600
\(605\) −7.27597e6 −0.808170
\(606\) 0 0
\(607\) 1.08494e7 1.19519 0.597593 0.801800i \(-0.296124\pi\)
0.597593 + 0.801800i \(0.296124\pi\)
\(608\) 241664. 0.0265126
\(609\) 0 0
\(610\) 3.82325e6 0.416014
\(611\) −1.70194e6 −0.184434
\(612\) 0 0
\(613\) −4.90511e6 −0.527227 −0.263614 0.964628i \(-0.584914\pi\)
−0.263614 + 0.964628i \(0.584914\pi\)
\(614\) −6.56418e6 −0.702683
\(615\) 0 0
\(616\) 2.08230e6 0.221102
\(617\) −2.58445e6 −0.273310 −0.136655 0.990619i \(-0.543635\pi\)
−0.136655 + 0.990619i \(0.543635\pi\)
\(618\) 0 0
\(619\) −4.99336e6 −0.523801 −0.261901 0.965095i \(-0.584349\pi\)
−0.261901 + 0.965095i \(0.584349\pi\)
\(620\) 2.96525e6 0.309800
\(621\) 0 0
\(622\) 3.78093e6 0.391852
\(623\) −6.01024e6 −0.620400
\(624\) 0 0
\(625\) 3.88510e6 0.397834
\(626\) 1.66142e6 0.169450
\(627\) 0 0
\(628\) −7.98506e6 −0.807940
\(629\) −6.89436e6 −0.694812
\(630\) 0 0
\(631\) −1.18219e7 −1.18199 −0.590997 0.806674i \(-0.701265\pi\)
−0.590997 + 0.806674i \(0.701265\pi\)
\(632\) 5.72160e6 0.569803
\(633\) 0 0
\(634\) −4.73926e6 −0.468260
\(635\) −4.82040e6 −0.474404
\(636\) 0 0
\(637\) 763518. 0.0745540
\(638\) −1.31578e7 −1.27977
\(639\) 0 0
\(640\) −425984. −0.0411096
\(641\) 5.47007e6 0.525833 0.262916 0.964819i \(-0.415316\pi\)
0.262916 + 0.964819i \(0.415316\pi\)
\(642\) 0 0
\(643\) 9.64934e6 0.920386 0.460193 0.887819i \(-0.347780\pi\)
0.460193 + 0.887819i \(0.347780\pi\)
\(644\) 1.73421e6 0.164773
\(645\) 0 0
\(646\) −1.49341e6 −0.140798
\(647\) −292368. −0.0274580 −0.0137290 0.999906i \(-0.504370\pi\)
−0.0137290 + 0.999906i \(0.504370\pi\)
\(648\) 0 0
\(649\) −1.02495e7 −0.955193
\(650\) −3.11513e6 −0.289196
\(651\) 0 0
\(652\) −7.60941e6 −0.701022
\(653\) −6.94081e6 −0.636982 −0.318491 0.947926i \(-0.603176\pi\)
−0.318491 + 0.947926i \(0.603176\pi\)
\(654\) 0 0
\(655\) 1.67783e6 0.152808
\(656\) −2.69875e6 −0.244852
\(657\) 0 0
\(658\) 1.04899e6 0.0944512
\(659\) 1.32912e7 1.19221 0.596104 0.802908i \(-0.296715\pi\)
0.596104 + 0.802908i \(0.296715\pi\)
\(660\) 0 0
\(661\) 2.05219e6 0.182690 0.0913448 0.995819i \(-0.470883\pi\)
0.0913448 + 0.995819i \(0.470883\pi\)
\(662\) 5.48619e6 0.486548
\(663\) 0 0
\(664\) 411392. 0.0362106
\(665\) 300664. 0.0263650
\(666\) 0 0
\(667\) −1.09582e7 −0.953732
\(668\) −1.92358e6 −0.166790
\(669\) 0 0
\(670\) −4.26109e6 −0.366719
\(671\) 2.44100e7 2.09296
\(672\) 0 0
\(673\) −1.57039e7 −1.33650 −0.668252 0.743935i \(-0.732957\pi\)
−0.668252 + 0.743935i \(0.732957\pi\)
\(674\) 3.85409e6 0.326792
\(675\) 0 0
\(676\) −4.32270e6 −0.363822
\(677\) 969534. 0.0813002 0.0406501 0.999173i \(-0.487057\pi\)
0.0406501 + 0.999173i \(0.487057\pi\)
\(678\) 0 0
\(679\) −1.04713e6 −0.0871618
\(680\) 2.63245e6 0.218317
\(681\) 0 0
\(682\) 1.89320e7 1.55860
\(683\) 1.49908e7 1.22962 0.614812 0.788673i \(-0.289232\pi\)
0.614812 + 0.788673i \(0.289232\pi\)
\(684\) 0 0
\(685\) 3.97618e6 0.323772
\(686\) −470596. −0.0381802
\(687\) 0 0
\(688\) −2.16371e6 −0.174272
\(689\) 1.06066e7 0.851191
\(690\) 0 0
\(691\) −7.16038e6 −0.570481 −0.285240 0.958456i \(-0.592073\pi\)
−0.285240 + 0.958456i \(0.592073\pi\)
\(692\) −8.14198e6 −0.646346
\(693\) 0 0
\(694\) −1.03092e7 −0.812509
\(695\) 8.92996e6 0.701274
\(696\) 0 0
\(697\) 1.66774e7 1.30031
\(698\) −1.22701e7 −0.953253
\(699\) 0 0
\(700\) 1.92002e6 0.148102
\(701\) 91834.0 0.00705844 0.00352922 0.999994i \(-0.498877\pi\)
0.00352922 + 0.999994i \(0.498877\pi\)
\(702\) 0 0
\(703\) 1.02849e6 0.0784894
\(704\) −2.71974e6 −0.206822
\(705\) 0 0
\(706\) 1.24058e7 0.936725
\(707\) −1.80389e6 −0.135725
\(708\) 0 0
\(709\) 2.20981e7 1.65097 0.825487 0.564422i \(-0.190901\pi\)
0.825487 + 0.564422i \(0.190901\pi\)
\(710\) −945568. −0.0703958
\(711\) 0 0
\(712\) 7.85011e6 0.580331
\(713\) 1.57671e7 1.16153
\(714\) 0 0
\(715\) 5.48995e6 0.401609
\(716\) −7.80096e6 −0.568677
\(717\) 0 0
\(718\) 1.31003e6 0.0948355
\(719\) −1.58388e7 −1.14262 −0.571308 0.820736i \(-0.693564\pi\)
−0.571308 + 0.820736i \(0.693564\pi\)
\(720\) 0 0
\(721\) −5.12187e6 −0.366936
\(722\) −9.68161e6 −0.691202
\(723\) 0 0
\(724\) −8.71056e6 −0.617589
\(725\) −1.21323e7 −0.857235
\(726\) 0 0
\(727\) 6.31418e6 0.443078 0.221539 0.975151i \(-0.428892\pi\)
0.221539 + 0.975151i \(0.428892\pi\)
\(728\) −997248. −0.0697388
\(729\) 0 0
\(730\) 7.63922e6 0.530569
\(731\) 1.33711e7 0.925492
\(732\) 0 0
\(733\) 6.93003e6 0.476404 0.238202 0.971216i \(-0.423442\pi\)
0.238202 + 0.971216i \(0.423442\pi\)
\(734\) −1.14696e7 −0.785791
\(735\) 0 0
\(736\) −2.26509e6 −0.154131
\(737\) −2.72054e7 −1.84496
\(738\) 0 0
\(739\) 1.42331e7 0.958714 0.479357 0.877620i \(-0.340870\pi\)
0.479357 + 0.877620i \(0.340870\pi\)
\(740\) −1.81293e6 −0.121703
\(741\) 0 0
\(742\) −6.53738e6 −0.435907
\(743\) 5.94460e6 0.395048 0.197524 0.980298i \(-0.436710\pi\)
0.197524 + 0.980298i \(0.436710\pi\)
\(744\) 0 0
\(745\) −4.54631e6 −0.300102
\(746\) 1.43212e7 0.942175
\(747\) 0 0
\(748\) 1.68072e7 1.09835
\(749\) 1.05076e7 0.684380
\(750\) 0 0
\(751\) −682752. −0.0441736 −0.0220868 0.999756i \(-0.507031\pi\)
−0.0220868 + 0.999756i \(0.507031\pi\)
\(752\) −1.37011e6 −0.0883510
\(753\) 0 0
\(754\) 6.30149e6 0.403659
\(755\) 1.17664e7 0.751233
\(756\) 0 0
\(757\) 1.46333e7 0.928116 0.464058 0.885805i \(-0.346393\pi\)
0.464058 + 0.885805i \(0.346393\pi\)
\(758\) 6.56939e6 0.415291
\(759\) 0 0
\(760\) −392704. −0.0246622
\(761\) 1.16367e7 0.728399 0.364200 0.931321i \(-0.381343\pi\)
0.364200 + 0.931321i \(0.381343\pi\)
\(762\) 0 0
\(763\) −1.41110e6 −0.0877500
\(764\) −6.02246e6 −0.373285
\(765\) 0 0
\(766\) 8.22790e6 0.506661
\(767\) 4.90865e6 0.301282
\(768\) 0 0
\(769\) 1.91472e7 1.16759 0.583793 0.811902i \(-0.301568\pi\)
0.583793 + 0.811902i \(0.301568\pi\)
\(770\) −3.38374e6 −0.205670
\(771\) 0 0
\(772\) 1.35191e7 0.816405
\(773\) 5.39261e6 0.324601 0.162301 0.986741i \(-0.448109\pi\)
0.162301 + 0.986741i \(0.448109\pi\)
\(774\) 0 0
\(775\) 1.74565e7 1.04400
\(776\) 1.36768e6 0.0815324
\(777\) 0 0
\(778\) −2.46457e6 −0.145979
\(779\) −2.48791e6 −0.146890
\(780\) 0 0
\(781\) −6.03709e6 −0.354160
\(782\) 1.39975e7 0.818530
\(783\) 0 0
\(784\) 614656. 0.0357143
\(785\) 1.29757e7 0.751549
\(786\) 0 0
\(787\) 3.04348e6 0.175159 0.0875796 0.996158i \(-0.472087\pi\)
0.0875796 + 0.996158i \(0.472087\pi\)
\(788\) 7.88470e6 0.452345
\(789\) 0 0
\(790\) −9.29760e6 −0.530033
\(791\) −2.74469e6 −0.155974
\(792\) 0 0
\(793\) −1.16903e7 −0.660151
\(794\) 8.76847e6 0.493597
\(795\) 0 0
\(796\) −1.46364e7 −0.818751
\(797\) −2.29652e7 −1.28063 −0.640316 0.768111i \(-0.721197\pi\)
−0.640316 + 0.768111i \(0.721197\pi\)
\(798\) 0 0
\(799\) 8.46686e6 0.469197
\(800\) −2.50778e6 −0.138536
\(801\) 0 0
\(802\) −1.31382e7 −0.721271
\(803\) 4.87735e7 2.66928
\(804\) 0 0
\(805\) −2.81809e6 −0.153273
\(806\) −9.06682e6 −0.491606
\(807\) 0 0
\(808\) 2.35610e6 0.126959
\(809\) −1.90787e7 −1.02489 −0.512445 0.858720i \(-0.671260\pi\)
−0.512445 + 0.858720i \(0.671260\pi\)
\(810\) 0 0
\(811\) 1.09414e7 0.584147 0.292074 0.956396i \(-0.405655\pi\)
0.292074 + 0.956396i \(0.405655\pi\)
\(812\) −3.88394e6 −0.206720
\(813\) 0 0
\(814\) −1.15748e7 −0.612286
\(815\) 1.23653e7 0.652094
\(816\) 0 0
\(817\) −1.99467e6 −0.104548
\(818\) −1.44488e7 −0.755001
\(819\) 0 0
\(820\) 4.38547e6 0.227762
\(821\) −2.12594e7 −1.10076 −0.550380 0.834914i \(-0.685517\pi\)
−0.550380 + 0.834914i \(0.685517\pi\)
\(822\) 0 0
\(823\) −1.42256e7 −0.732103 −0.366052 0.930595i \(-0.619291\pi\)
−0.366052 + 0.930595i \(0.619291\pi\)
\(824\) 6.68979e6 0.343237
\(825\) 0 0
\(826\) −3.02546e6 −0.154291
\(827\) −2.76103e6 −0.140381 −0.0701904 0.997534i \(-0.522361\pi\)
−0.0701904 + 0.997534i \(0.522361\pi\)
\(828\) 0 0
\(829\) −3.82147e7 −1.93127 −0.965637 0.259895i \(-0.916312\pi\)
−0.965637 + 0.259895i \(0.916312\pi\)
\(830\) −668512. −0.0336832
\(831\) 0 0
\(832\) 1.30253e6 0.0652347
\(833\) −3.79838e6 −0.189665
\(834\) 0 0
\(835\) 3.12582e6 0.155149
\(836\) −2.50726e6 −0.124075
\(837\) 0 0
\(838\) −2.16596e7 −1.06547
\(839\) −1.06044e7 −0.520094 −0.260047 0.965596i \(-0.583738\pi\)
−0.260047 + 0.965596i \(0.583738\pi\)
\(840\) 0 0
\(841\) 4.03097e6 0.196526
\(842\) 1.44252e7 0.701198
\(843\) 0 0
\(844\) 4.98848e6 0.241053
\(845\) 7.02439e6 0.338429
\(846\) 0 0
\(847\) −1.37124e7 −0.656758
\(848\) 8.53862e6 0.407754
\(849\) 0 0
\(850\) 1.54973e7 0.735712
\(851\) −9.63990e6 −0.456298
\(852\) 0 0
\(853\) −4.07009e7 −1.91527 −0.957637 0.287977i \(-0.907017\pi\)
−0.957637 + 0.287977i \(0.907017\pi\)
\(854\) 7.20535e6 0.338073
\(855\) 0 0
\(856\) −1.37242e7 −0.640179
\(857\) 3.10120e7 1.44237 0.721187 0.692741i \(-0.243597\pi\)
0.721187 + 0.692741i \(0.243597\pi\)
\(858\) 0 0
\(859\) 1.09104e7 0.504495 0.252247 0.967663i \(-0.418830\pi\)
0.252247 + 0.967663i \(0.418830\pi\)
\(860\) 3.51603e6 0.162109
\(861\) 0 0
\(862\) 1.11286e7 0.510118
\(863\) −1.04089e7 −0.475751 −0.237875 0.971296i \(-0.576451\pi\)
−0.237875 + 0.971296i \(0.576451\pi\)
\(864\) 0 0
\(865\) 1.32307e7 0.601234
\(866\) 2.51048e7 1.13753
\(867\) 0 0
\(868\) 5.58835e6 0.251759
\(869\) −5.93616e7 −2.66659
\(870\) 0 0
\(871\) 1.30291e7 0.581928
\(872\) 1.84307e6 0.0820826
\(873\) 0 0
\(874\) −2.08813e6 −0.0924652
\(875\) −7.10128e6 −0.313557
\(876\) 0 0
\(877\) 1.64064e7 0.720299 0.360150 0.932895i \(-0.382726\pi\)
0.360150 + 0.932895i \(0.382726\pi\)
\(878\) 2.56637e6 0.112352
\(879\) 0 0
\(880\) 4.41958e6 0.192387
\(881\) −1.48577e7 −0.644927 −0.322464 0.946582i \(-0.604511\pi\)
−0.322464 + 0.946582i \(0.604511\pi\)
\(882\) 0 0
\(883\) −2.72018e7 −1.17407 −0.587037 0.809560i \(-0.699706\pi\)
−0.587037 + 0.809560i \(0.699706\pi\)
\(884\) −8.04922e6 −0.346436
\(885\) 0 0
\(886\) −2.42218e7 −1.03663
\(887\) −2.71242e7 −1.15757 −0.578785 0.815480i \(-0.696473\pi\)
−0.578785 + 0.815480i \(0.696473\pi\)
\(888\) 0 0
\(889\) −9.08460e6 −0.385524
\(890\) −1.27564e7 −0.539827
\(891\) 0 0
\(892\) −2.06042e7 −0.867047
\(893\) −1.26307e6 −0.0530029
\(894\) 0 0
\(895\) 1.26766e7 0.528986
\(896\) −802816. −0.0334077
\(897\) 0 0
\(898\) 2.06673e7 0.855248
\(899\) −3.53121e7 −1.45722
\(900\) 0 0
\(901\) −5.27660e7 −2.16542
\(902\) 2.79996e7 1.14587
\(903\) 0 0
\(904\) 3.58490e6 0.145900
\(905\) 1.41547e7 0.574484
\(906\) 0 0
\(907\) −8.42269e6 −0.339964 −0.169982 0.985447i \(-0.554371\pi\)
−0.169982 + 0.985447i \(0.554371\pi\)
\(908\) −2.06248e7 −0.830187
\(909\) 0 0
\(910\) 1.62053e6 0.0648714
\(911\) −3.08637e7 −1.23212 −0.616060 0.787700i \(-0.711272\pi\)
−0.616060 + 0.787700i \(0.711272\pi\)
\(912\) 0 0
\(913\) −4.26819e6 −0.169460
\(914\) −911192. −0.0360782
\(915\) 0 0
\(916\) 1.08514e7 0.427315
\(917\) 3.16207e6 0.124179
\(918\) 0 0
\(919\) 4.93895e6 0.192906 0.0964531 0.995338i \(-0.469250\pi\)
0.0964531 + 0.995338i \(0.469250\pi\)
\(920\) 3.68077e6 0.143373
\(921\) 0 0
\(922\) −2.34058e6 −0.0906770
\(923\) 2.89126e6 0.111707
\(924\) 0 0
\(925\) −1.06727e7 −0.410130
\(926\) −1.36581e7 −0.523437
\(927\) 0 0
\(928\) 5.07290e6 0.193369
\(929\) −5.62575e6 −0.213866 −0.106933 0.994266i \(-0.534103\pi\)
−0.106933 + 0.994266i \(0.534103\pi\)
\(930\) 0 0
\(931\) 566636. 0.0214255
\(932\) 1.78770e7 0.674146
\(933\) 0 0
\(934\) −2.86520e6 −0.107470
\(935\) −2.73116e7 −1.02169
\(936\) 0 0
\(937\) 2.60073e7 0.967714 0.483857 0.875147i \(-0.339236\pi\)
0.483857 + 0.875147i \(0.339236\pi\)
\(938\) −8.03051e6 −0.298014
\(939\) 0 0
\(940\) 2.22643e6 0.0821845
\(941\) −3.02160e6 −0.111241 −0.0556203 0.998452i \(-0.517714\pi\)
−0.0556203 + 0.998452i \(0.517714\pi\)
\(942\) 0 0
\(943\) 2.33189e7 0.853943
\(944\) 3.95162e6 0.144326
\(945\) 0 0
\(946\) 2.24485e7 0.815567
\(947\) 3.48282e7 1.26199 0.630995 0.775787i \(-0.282647\pi\)
0.630995 + 0.775787i \(0.282647\pi\)
\(948\) 0 0
\(949\) −2.33584e7 −0.841932
\(950\) −2.31186e6 −0.0831097
\(951\) 0 0
\(952\) 4.96115e6 0.177415
\(953\) 9.39009e6 0.334917 0.167459 0.985879i \(-0.446444\pi\)
0.167459 + 0.985879i \(0.446444\pi\)
\(954\) 0 0
\(955\) 9.78650e6 0.347232
\(956\) 2.01913e7 0.714528
\(957\) 0 0
\(958\) −2.09637e7 −0.737996
\(959\) 7.49357e6 0.263113
\(960\) 0 0
\(961\) 2.21792e7 0.774708
\(962\) 5.54338e6 0.193124
\(963\) 0 0
\(964\) 1.51715e7 0.525818
\(965\) −2.19686e7 −0.759423
\(966\) 0 0
\(967\) 1.44768e7 0.497860 0.248930 0.968521i \(-0.419921\pi\)
0.248930 + 0.968521i \(0.419921\pi\)
\(968\) 1.79101e7 0.614340
\(969\) 0 0
\(970\) −2.22248e6 −0.0758418
\(971\) −9.24976e6 −0.314834 −0.157417 0.987532i \(-0.550317\pi\)
−0.157417 + 0.987532i \(0.550317\pi\)
\(972\) 0 0
\(973\) 1.68295e7 0.569889
\(974\) 4.46806e6 0.150911
\(975\) 0 0
\(976\) −9.41107e6 −0.316238
\(977\) 4.97780e7 1.66840 0.834202 0.551459i \(-0.185929\pi\)
0.834202 + 0.551459i \(0.185929\pi\)
\(978\) 0 0
\(979\) −8.14449e7 −2.71586
\(980\) −998816. −0.0332216
\(981\) 0 0
\(982\) −5.37830e6 −0.177978
\(983\) 8.95601e6 0.295618 0.147809 0.989016i \(-0.452778\pi\)
0.147809 + 0.989016i \(0.452778\pi\)
\(984\) 0 0
\(985\) −1.28126e7 −0.420773
\(986\) −3.13489e7 −1.02690
\(987\) 0 0
\(988\) 1.20077e6 0.0391351
\(989\) 1.86958e7 0.607790
\(990\) 0 0
\(991\) 2.62400e7 0.848751 0.424376 0.905486i \(-0.360494\pi\)
0.424376 + 0.905486i \(0.360494\pi\)
\(992\) −7.29907e6 −0.235499
\(993\) 0 0
\(994\) −1.78203e6 −0.0572070
\(995\) 2.37842e7 0.761606
\(996\) 0 0
\(997\) 2.80506e7 0.893727 0.446863 0.894602i \(-0.352541\pi\)
0.446863 + 0.894602i \(0.352541\pi\)
\(998\) −2.61859e7 −0.832226
\(999\) 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 126.6.a.i.1.1 1
3.2 odd 2 42.6.a.d.1.1 1
4.3 odd 2 1008.6.a.j.1.1 1
7.6 odd 2 882.6.a.s.1.1 1
12.11 even 2 336.6.a.h.1.1 1
15.2 even 4 1050.6.g.i.799.1 2
15.8 even 4 1050.6.g.i.799.2 2
15.14 odd 2 1050.6.a.k.1.1 1
21.2 odd 6 294.6.e.i.67.1 2
21.5 even 6 294.6.e.p.67.1 2
21.11 odd 6 294.6.e.i.79.1 2
21.17 even 6 294.6.e.p.79.1 2
21.20 even 2 294.6.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.d.1.1 1 3.2 odd 2
126.6.a.i.1.1 1 1.1 even 1 trivial
294.6.a.b.1.1 1 21.20 even 2
294.6.e.i.67.1 2 21.2 odd 6
294.6.e.i.79.1 2 21.11 odd 6
294.6.e.p.67.1 2 21.5 even 6
294.6.e.p.79.1 2 21.17 even 6
336.6.a.h.1.1 1 12.11 even 2
882.6.a.s.1.1 1 7.6 odd 2
1008.6.a.j.1.1 1 4.3 odd 2
1050.6.a.k.1.1 1 15.14 odd 2
1050.6.g.i.799.1 2 15.2 even 4
1050.6.g.i.799.2 2 15.8 even 4