Properties

Label 338.6.a.d.1.1
Level $338$
Weight $6$
Character 338.1
Self dual yes
Analytic conductor $54.210$
Analytic rank $0$
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] = [338,6,Mod(1,338)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(338, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("338.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 338.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: \(54.2097310968\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 338.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.00000 q^{2} +16.0000 q^{4} +14.0000 q^{5} +170.000 q^{7} +64.0000 q^{8} -243.000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} +16.0000 q^{4} +14.0000 q^{5} +170.000 q^{7} +64.0000 q^{8} -243.000 q^{9} +56.0000 q^{10} +250.000 q^{11} +680.000 q^{14} +256.000 q^{16} +1062.00 q^{17} -972.000 q^{18} +78.0000 q^{19} +224.000 q^{20} +1000.00 q^{22} +1576.00 q^{23} -2929.00 q^{25} +2720.00 q^{28} +2578.00 q^{29} +8654.00 q^{31} +1024.00 q^{32} +4248.00 q^{34} +2380.00 q^{35} -3888.00 q^{36} -10986.0 q^{37} +312.000 q^{38} +896.000 q^{40} -1050.00 q^{41} -5900.00 q^{43} +4000.00 q^{44} -3402.00 q^{45} +6304.00 q^{46} +5962.00 q^{47} +12093.0 q^{49} -11716.0 q^{50} +29046.0 q^{53} +3500.00 q^{55} +10880.0 q^{56} +10312.0 q^{58} +13922.0 q^{59} -32882.0 q^{61} +34616.0 q^{62} -41310.0 q^{63} +4096.00 q^{64} +69566.0 q^{67} +16992.0 q^{68} +9520.00 q^{70} +50542.0 q^{71} -15552.0 q^{72} +46750.0 q^{73} -43944.0 q^{74} +1248.00 q^{76} +42500.0 q^{77} -19348.0 q^{79} +3584.00 q^{80} +59049.0 q^{81} -4200.00 q^{82} +87438.0 q^{83} +14868.0 q^{85} -23600.0 q^{86} +16000.0 q^{88} -94170.0 q^{89} -13608.0 q^{90} +25216.0 q^{92} +23848.0 q^{94} +1092.00 q^{95} -182786. q^{97} +48372.0 q^{98} -60750.0 q^{99} +O(q^{100})\)

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
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 16.0000 0.500000
\(5\) 14.0000 0.250440 0.125220 0.992129i \(-0.460036\pi\)
0.125220 + 0.992129i \(0.460036\pi\)
\(6\) 0 0
\(7\) 170.000 1.31131 0.655653 0.755063i \(-0.272394\pi\)
0.655653 + 0.755063i \(0.272394\pi\)
\(8\) 64.0000 0.353553
\(9\) −243.000 −1.00000
\(10\) 56.0000 0.177088
\(11\) 250.000 0.622957 0.311479 0.950253i \(-0.399176\pi\)
0.311479 + 0.950253i \(0.399176\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 680.000 0.927233
\(15\) 0 0
\(16\) 256.000 0.250000
\(17\) 1062.00 0.891255 0.445628 0.895218i \(-0.352981\pi\)
0.445628 + 0.895218i \(0.352981\pi\)
\(18\) −972.000 −0.707107
\(19\) 78.0000 0.0495691 0.0247845 0.999693i \(-0.492110\pi\)
0.0247845 + 0.999693i \(0.492110\pi\)
\(20\) 224.000 0.125220
\(21\) 0 0
\(22\) 1000.00 0.440497
\(23\) 1576.00 0.621207 0.310604 0.950539i \(-0.399469\pi\)
0.310604 + 0.950539i \(0.399469\pi\)
\(24\) 0 0
\(25\) −2929.00 −0.937280
\(26\) 0 0
\(27\) 0 0
\(28\) 2720.00 0.655653
\(29\) 2578.00 0.569230 0.284615 0.958642i \(-0.408134\pi\)
0.284615 + 0.958642i \(0.408134\pi\)
\(30\) 0 0
\(31\) 8654.00 1.61738 0.808691 0.588234i \(-0.200176\pi\)
0.808691 + 0.588234i \(0.200176\pi\)
\(32\) 1024.00 0.176777
\(33\) 0 0
\(34\) 4248.00 0.630213
\(35\) 2380.00 0.328403
\(36\) −3888.00 −0.500000
\(37\) −10986.0 −1.31927 −0.659637 0.751584i \(-0.729290\pi\)
−0.659637 + 0.751584i \(0.729290\pi\)
\(38\) 312.000 0.0350506
\(39\) 0 0
\(40\) 896.000 0.0885438
\(41\) −1050.00 −0.0975505 −0.0487753 0.998810i \(-0.515532\pi\)
−0.0487753 + 0.998810i \(0.515532\pi\)
\(42\) 0 0
\(43\) −5900.00 −0.486610 −0.243305 0.969950i \(-0.578232\pi\)
−0.243305 + 0.969950i \(0.578232\pi\)
\(44\) 4000.00 0.311479
\(45\) −3402.00 −0.250440
\(46\) 6304.00 0.439260
\(47\) 5962.00 0.393684 0.196842 0.980435i \(-0.436931\pi\)
0.196842 + 0.980435i \(0.436931\pi\)
\(48\) 0 0
\(49\) 12093.0 0.719522
\(50\) −11716.0 −0.662757
\(51\) 0 0
\(52\) 0 0
\(53\) 29046.0 1.42035 0.710177 0.704023i \(-0.248615\pi\)
0.710177 + 0.704023i \(0.248615\pi\)
\(54\) 0 0
\(55\) 3500.00 0.156013
\(56\) 10880.0 0.463616
\(57\) 0 0
\(58\) 10312.0 0.402507
\(59\) 13922.0 0.520681 0.260340 0.965517i \(-0.416165\pi\)
0.260340 + 0.965517i \(0.416165\pi\)
\(60\) 0 0
\(61\) −32882.0 −1.13145 −0.565723 0.824596i \(-0.691403\pi\)
−0.565723 + 0.824596i \(0.691403\pi\)
\(62\) 34616.0 1.14366
\(63\) −41310.0 −1.31131
\(64\) 4096.00 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 69566.0 1.89326 0.946629 0.322324i \(-0.104464\pi\)
0.946629 + 0.322324i \(0.104464\pi\)
\(68\) 16992.0 0.445628
\(69\) 0 0
\(70\) 9520.00 0.232216
\(71\) 50542.0 1.18989 0.594945 0.803767i \(-0.297174\pi\)
0.594945 + 0.803767i \(0.297174\pi\)
\(72\) −15552.0 −0.353553
\(73\) 46750.0 1.02677 0.513387 0.858157i \(-0.328391\pi\)
0.513387 + 0.858157i \(0.328391\pi\)
\(74\) −43944.0 −0.932868
\(75\) 0 0
\(76\) 1248.00 0.0247845
\(77\) 42500.0 0.816887
\(78\) 0 0
\(79\) −19348.0 −0.348793 −0.174397 0.984675i \(-0.555798\pi\)
−0.174397 + 0.984675i \(0.555798\pi\)
\(80\) 3584.00 0.0626099
\(81\) 59049.0 1.00000
\(82\) −4200.00 −0.0689786
\(83\) 87438.0 1.39317 0.696586 0.717473i \(-0.254701\pi\)
0.696586 + 0.717473i \(0.254701\pi\)
\(84\) 0 0
\(85\) 14868.0 0.223206
\(86\) −23600.0 −0.344085
\(87\) 0 0
\(88\) 16000.0 0.220249
\(89\) −94170.0 −1.26019 −0.630097 0.776516i \(-0.716985\pi\)
−0.630097 + 0.776516i \(0.716985\pi\)
\(90\) −13608.0 −0.177088
\(91\) 0 0
\(92\) 25216.0 0.310604
\(93\) 0 0
\(94\) 23848.0 0.278376
\(95\) 1092.00 0.0124141
\(96\) 0 0
\(97\) −182786. −1.97248 −0.986242 0.165307i \(-0.947139\pi\)
−0.986242 + 0.165307i \(0.947139\pi\)
\(98\) 48372.0 0.508779
\(99\) −60750.0 −0.622957
\(100\) −46864.0 −0.468640
\(101\) −18514.0 −0.180591 −0.0902957 0.995915i \(-0.528781\pi\)
−0.0902957 + 0.995915i \(0.528781\pi\)
\(102\) 0 0
\(103\) 116056. 1.07789 0.538945 0.842341i \(-0.318823\pi\)
0.538945 + 0.842341i \(0.318823\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 116184. 1.00434
\(107\) 153520. 1.29630 0.648150 0.761513i \(-0.275543\pi\)
0.648150 + 0.761513i \(0.275543\pi\)
\(108\) 0 0
\(109\) 178622. 1.44002 0.720010 0.693963i \(-0.244137\pi\)
0.720010 + 0.693963i \(0.244137\pi\)
\(110\) 14000.0 0.110318
\(111\) 0 0
\(112\) 43520.0 0.327826
\(113\) −244754. −1.80316 −0.901579 0.432615i \(-0.857591\pi\)
−0.901579 + 0.432615i \(0.857591\pi\)
\(114\) 0 0
\(115\) 22064.0 0.155575
\(116\) 41248.0 0.284615
\(117\) 0 0
\(118\) 55688.0 0.368177
\(119\) 180540. 1.16871
\(120\) 0 0
\(121\) −98551.0 −0.611924
\(122\) −131528. −0.800053
\(123\) 0 0
\(124\) 138464. 0.808691
\(125\) −84756.0 −0.485172
\(126\) −165240. −0.927233
\(127\) 256600. 1.41172 0.705858 0.708353i \(-0.250562\pi\)
0.705858 + 0.708353i \(0.250562\pi\)
\(128\) 16384.0 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −262736. −1.33765 −0.668823 0.743421i \(-0.733202\pi\)
−0.668823 + 0.743421i \(0.733202\pi\)
\(132\) 0 0
\(133\) 13260.0 0.0650002
\(134\) 278264. 1.33874
\(135\) 0 0
\(136\) 67968.0 0.315106
\(137\) 38286.0 0.174276 0.0871382 0.996196i \(-0.472228\pi\)
0.0871382 + 0.996196i \(0.472228\pi\)
\(138\) 0 0
\(139\) −57776.0 −0.253636 −0.126818 0.991926i \(-0.540476\pi\)
−0.126818 + 0.991926i \(0.540476\pi\)
\(140\) 38080.0 0.164201
\(141\) 0 0
\(142\) 202168. 0.841379
\(143\) 0 0
\(144\) −62208.0 −0.250000
\(145\) 36092.0 0.142558
\(146\) 187000. 0.726038
\(147\) 0 0
\(148\) −175776. −0.659637
\(149\) −28866.0 −0.106517 −0.0532587 0.998581i \(-0.516961\pi\)
−0.0532587 + 0.998581i \(0.516961\pi\)
\(150\) 0 0
\(151\) −39870.0 −0.142300 −0.0711498 0.997466i \(-0.522667\pi\)
−0.0711498 + 0.997466i \(0.522667\pi\)
\(152\) 4992.00 0.0175253
\(153\) −258066. −0.891255
\(154\) 170000. 0.577627
\(155\) 121156. 0.405057
\(156\) 0 0
\(157\) 161042. 0.521423 0.260711 0.965417i \(-0.416043\pi\)
0.260711 + 0.965417i \(0.416043\pi\)
\(158\) −77392.0 −0.246634
\(159\) 0 0
\(160\) 14336.0 0.0442719
\(161\) 267920. 0.814593
\(162\) 236196. 0.707107
\(163\) −312830. −0.922230 −0.461115 0.887340i \(-0.652550\pi\)
−0.461115 + 0.887340i \(0.652550\pi\)
\(164\) −16800.0 −0.0487753
\(165\) 0 0
\(166\) 349752. 0.985122
\(167\) −532926. −1.47869 −0.739343 0.673329i \(-0.764864\pi\)
−0.739343 + 0.673329i \(0.764864\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 59472.0 0.157830
\(171\) −18954.0 −0.0495691
\(172\) −94400.0 −0.243305
\(173\) −630458. −1.60155 −0.800776 0.598964i \(-0.795579\pi\)
−0.800776 + 0.598964i \(0.795579\pi\)
\(174\) 0 0
\(175\) −497930. −1.22906
\(176\) 64000.0 0.155739
\(177\) 0 0
\(178\) −376680. −0.891092
\(179\) −674916. −1.57441 −0.787204 0.616693i \(-0.788472\pi\)
−0.787204 + 0.616693i \(0.788472\pi\)
\(180\) −54432.0 −0.125220
\(181\) 186282. 0.422644 0.211322 0.977417i \(-0.432223\pi\)
0.211322 + 0.977417i \(0.432223\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 100864. 0.219630
\(185\) −153804. −0.330399
\(186\) 0 0
\(187\) 265500. 0.555214
\(188\) 95392.0 0.196842
\(189\) 0 0
\(190\) 4368.00 0.00877806
\(191\) 812180. 1.61090 0.805451 0.592663i \(-0.201923\pi\)
0.805451 + 0.592663i \(0.201923\pi\)
\(192\) 0 0
\(193\) 150142. 0.290141 0.145070 0.989421i \(-0.453659\pi\)
0.145070 + 0.989421i \(0.453659\pi\)
\(194\) −731144. −1.39476
\(195\) 0 0
\(196\) 193488. 0.359761
\(197\) −236394. −0.433981 −0.216991 0.976174i \(-0.569624\pi\)
−0.216991 + 0.976174i \(0.569624\pi\)
\(198\) −243000. −0.440497
\(199\) −39376.0 −0.0704854 −0.0352427 0.999379i \(-0.511220\pi\)
−0.0352427 + 0.999379i \(0.511220\pi\)
\(200\) −187456. −0.331379
\(201\) 0 0
\(202\) −74056.0 −0.127697
\(203\) 438260. 0.746435
\(204\) 0 0
\(205\) −14700.0 −0.0244305
\(206\) 464224. 0.762183
\(207\) −382968. −0.621207
\(208\) 0 0
\(209\) 19500.0 0.0308794
\(210\) 0 0
\(211\) −410776. −0.635183 −0.317592 0.948228i \(-0.602874\pi\)
−0.317592 + 0.948228i \(0.602874\pi\)
\(212\) 464736. 0.710177
\(213\) 0 0
\(214\) 614080. 0.916623
\(215\) −82600.0 −0.121866
\(216\) 0 0
\(217\) 1.47118e6 2.12088
\(218\) 714488. 1.01825
\(219\) 0 0
\(220\) 56000.0 0.0780066
\(221\) 0 0
\(222\) 0 0
\(223\) −1.08688e6 −1.46359 −0.731796 0.681523i \(-0.761318\pi\)
−0.731796 + 0.681523i \(0.761318\pi\)
\(224\) 174080. 0.231808
\(225\) 711747. 0.937280
\(226\) −979016. −1.27502
\(227\) 256470. 0.330348 0.165174 0.986264i \(-0.447181\pi\)
0.165174 + 0.986264i \(0.447181\pi\)
\(228\) 0 0
\(229\) 298110. 0.375654 0.187827 0.982202i \(-0.439856\pi\)
0.187827 + 0.982202i \(0.439856\pi\)
\(230\) 88256.0 0.110008
\(231\) 0 0
\(232\) 164992. 0.201253
\(233\) −611926. −0.738430 −0.369215 0.929344i \(-0.620373\pi\)
−0.369215 + 0.929344i \(0.620373\pi\)
\(234\) 0 0
\(235\) 83468.0 0.0985940
\(236\) 222752. 0.260340
\(237\) 0 0
\(238\) 722160. 0.826401
\(239\) −36570.0 −0.0414124 −0.0207062 0.999786i \(-0.506591\pi\)
−0.0207062 + 0.999786i \(0.506591\pi\)
\(240\) 0 0
\(241\) −380922. −0.422468 −0.211234 0.977436i \(-0.567748\pi\)
−0.211234 + 0.977436i \(0.567748\pi\)
\(242\) −394204. −0.432696
\(243\) 0 0
\(244\) −526112. −0.565723
\(245\) 169302. 0.180197
\(246\) 0 0
\(247\) 0 0
\(248\) 553856. 0.571831
\(249\) 0 0
\(250\) −339024. −0.343068
\(251\) −1.22807e6 −1.23038 −0.615188 0.788380i \(-0.710920\pi\)
−0.615188 + 0.788380i \(0.710920\pi\)
\(252\) −660960. −0.655653
\(253\) 394000. 0.386986
\(254\) 1.02640e6 0.998234
\(255\) 0 0
\(256\) 65536.0 0.0625000
\(257\) −439278. −0.414865 −0.207432 0.978249i \(-0.566511\pi\)
−0.207432 + 0.978249i \(0.566511\pi\)
\(258\) 0 0
\(259\) −1.86762e6 −1.72997
\(260\) 0 0
\(261\) −626454. −0.569230
\(262\) −1.05094e6 −0.945859
\(263\) −1.67987e6 −1.49757 −0.748783 0.662816i \(-0.769361\pi\)
−0.748783 + 0.662816i \(0.769361\pi\)
\(264\) 0 0
\(265\) 406644. 0.355713
\(266\) 53040.0 0.0459621
\(267\) 0 0
\(268\) 1.11306e6 0.946629
\(269\) 1.93840e6 1.63329 0.816645 0.577141i \(-0.195832\pi\)
0.816645 + 0.577141i \(0.195832\pi\)
\(270\) 0 0
\(271\) 695498. 0.575271 0.287636 0.957740i \(-0.407131\pi\)
0.287636 + 0.957740i \(0.407131\pi\)
\(272\) 271872. 0.222814
\(273\) 0 0
\(274\) 153144. 0.123232
\(275\) −732250. −0.583885
\(276\) 0 0
\(277\) −1.13138e6 −0.885948 −0.442974 0.896534i \(-0.646077\pi\)
−0.442974 + 0.896534i \(0.646077\pi\)
\(278\) −231104. −0.179348
\(279\) −2.10292e6 −1.61738
\(280\) 152320. 0.116108
\(281\) −1.73122e6 −1.30793 −0.653967 0.756523i \(-0.726897\pi\)
−0.653967 + 0.756523i \(0.726897\pi\)
\(282\) 0 0
\(283\) −1.47124e6 −1.09199 −0.545995 0.837788i \(-0.683848\pi\)
−0.545995 + 0.837788i \(0.683848\pi\)
\(284\) 808672. 0.594945
\(285\) 0 0
\(286\) 0 0
\(287\) −178500. −0.127919
\(288\) −248832. −0.176777
\(289\) −292013. −0.205664
\(290\) 144368. 0.100804
\(291\) 0 0
\(292\) 748000. 0.513387
\(293\) −2.88855e6 −1.96567 −0.982834 0.184491i \(-0.940936\pi\)
−0.982834 + 0.184491i \(0.940936\pi\)
\(294\) 0 0
\(295\) 194908. 0.130399
\(296\) −703104. −0.466434
\(297\) 0 0
\(298\) −115464. −0.0753192
\(299\) 0 0
\(300\) 0 0
\(301\) −1.00300e6 −0.638094
\(302\) −159480. −0.100621
\(303\) 0 0
\(304\) 19968.0 0.0123923
\(305\) −460348. −0.283359
\(306\) −1.03226e6 −0.630213
\(307\) −874118. −0.529327 −0.264664 0.964341i \(-0.585261\pi\)
−0.264664 + 0.964341i \(0.585261\pi\)
\(308\) 680000. 0.408444
\(309\) 0 0
\(310\) 484624. 0.286418
\(311\) 2.68224e6 1.57252 0.786261 0.617895i \(-0.212014\pi\)
0.786261 + 0.617895i \(0.212014\pi\)
\(312\) 0 0
\(313\) −1.34459e6 −0.775761 −0.387880 0.921710i \(-0.626793\pi\)
−0.387880 + 0.921710i \(0.626793\pi\)
\(314\) 644168. 0.368702
\(315\) −578340. −0.328403
\(316\) −309568. −0.174397
\(317\) −1.32074e6 −0.738191 −0.369095 0.929392i \(-0.620332\pi\)
−0.369095 + 0.929392i \(0.620332\pi\)
\(318\) 0 0
\(319\) 644500. 0.354606
\(320\) 57344.0 0.0313050
\(321\) 0 0
\(322\) 1.07168e6 0.576004
\(323\) 82836.0 0.0441787
\(324\) 944784. 0.500000
\(325\) 0 0
\(326\) −1.25132e6 −0.652115
\(327\) 0 0
\(328\) −67200.0 −0.0344893
\(329\) 1.01354e6 0.516239
\(330\) 0 0
\(331\) 2.05728e6 1.03210 0.516051 0.856558i \(-0.327401\pi\)
0.516051 + 0.856558i \(0.327401\pi\)
\(332\) 1.39901e6 0.696586
\(333\) 2.66960e6 1.31927
\(334\) −2.13170e6 −1.04559
\(335\) 973924. 0.474147
\(336\) 0 0
\(337\) 453398. 0.217473 0.108736 0.994071i \(-0.465320\pi\)
0.108736 + 0.994071i \(0.465320\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 237888. 0.111603
\(341\) 2.16350e6 1.00756
\(342\) −75816.0 −0.0350506
\(343\) −801380. −0.367793
\(344\) −377600. −0.172043
\(345\) 0 0
\(346\) −2.52183e6 −1.13247
\(347\) −1.23065e6 −0.548669 −0.274334 0.961634i \(-0.588457\pi\)
−0.274334 + 0.961634i \(0.588457\pi\)
\(348\) 0 0
\(349\) 2.43825e6 1.07155 0.535777 0.844360i \(-0.320019\pi\)
0.535777 + 0.844360i \(0.320019\pi\)
\(350\) −1.99172e6 −0.869077
\(351\) 0 0
\(352\) 256000. 0.110124
\(353\) 2.68315e6 1.14606 0.573031 0.819534i \(-0.305767\pi\)
0.573031 + 0.819534i \(0.305767\pi\)
\(354\) 0 0
\(355\) 707588. 0.297995
\(356\) −1.50672e6 −0.630097
\(357\) 0 0
\(358\) −2.69966e6 −1.11327
\(359\) −1.58693e6 −0.649864 −0.324932 0.945737i \(-0.605341\pi\)
−0.324932 + 0.945737i \(0.605341\pi\)
\(360\) −217728. −0.0885438
\(361\) −2.47002e6 −0.997543
\(362\) 745128. 0.298854
\(363\) 0 0
\(364\) 0 0
\(365\) 654500. 0.257145
\(366\) 0 0
\(367\) −60052.0 −0.0232735 −0.0116368 0.999932i \(-0.503704\pi\)
−0.0116368 + 0.999932i \(0.503704\pi\)
\(368\) 403456. 0.155302
\(369\) 255150. 0.0975505
\(370\) −615216. −0.233627
\(371\) 4.93782e6 1.86252
\(372\) 0 0
\(373\) −4.01853e6 −1.49553 −0.747766 0.663963i \(-0.768873\pi\)
−0.747766 + 0.663963i \(0.768873\pi\)
\(374\) 1.06200e6 0.392596
\(375\) 0 0
\(376\) 381568. 0.139188
\(377\) 0 0
\(378\) 0 0
\(379\) −1.67581e6 −0.599276 −0.299638 0.954053i \(-0.596866\pi\)
−0.299638 + 0.954053i \(0.596866\pi\)
\(380\) 17472.0 0.00620703
\(381\) 0 0
\(382\) 3.24872e6 1.13908
\(383\) −687258. −0.239399 −0.119700 0.992810i \(-0.538193\pi\)
−0.119700 + 0.992810i \(0.538193\pi\)
\(384\) 0 0
\(385\) 595000. 0.204581
\(386\) 600568. 0.205161
\(387\) 1.43370e6 0.486610
\(388\) −2.92458e6 −0.986242
\(389\) 1.37611e6 0.461082 0.230541 0.973063i \(-0.425950\pi\)
0.230541 + 0.973063i \(0.425950\pi\)
\(390\) 0 0
\(391\) 1.67371e6 0.553655
\(392\) 773952. 0.254389
\(393\) 0 0
\(394\) −945576. −0.306871
\(395\) −270872. −0.0873517
\(396\) −972000. −0.311479
\(397\) 721198. 0.229656 0.114828 0.993385i \(-0.463368\pi\)
0.114828 + 0.993385i \(0.463368\pi\)
\(398\) −157504. −0.0498407
\(399\) 0 0
\(400\) −749824. −0.234320
\(401\) −2.22681e6 −0.691548 −0.345774 0.938318i \(-0.612384\pi\)
−0.345774 + 0.938318i \(0.612384\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −296224. −0.0902957
\(405\) 826686. 0.250440
\(406\) 1.75304e6 0.527809
\(407\) −2.74650e6 −0.821852
\(408\) 0 0
\(409\) −2.00783e6 −0.593496 −0.296748 0.954956i \(-0.595902\pi\)
−0.296748 + 0.954956i \(0.595902\pi\)
\(410\) −58800.0 −0.0172750
\(411\) 0 0
\(412\) 1.85690e6 0.538945
\(413\) 2.36674e6 0.682772
\(414\) −1.53187e6 −0.439260
\(415\) 1.22413e6 0.348906
\(416\) 0 0
\(417\) 0 0
\(418\) 78000.0 0.0218350
\(419\) 5.99378e6 1.66788 0.833942 0.551852i \(-0.186079\pi\)
0.833942 + 0.551852i \(0.186079\pi\)
\(420\) 0 0
\(421\) 5.32737e6 1.46490 0.732449 0.680822i \(-0.238377\pi\)
0.732449 + 0.680822i \(0.238377\pi\)
\(422\) −1.64310e6 −0.449142
\(423\) −1.44877e6 −0.393684
\(424\) 1.85894e6 0.502171
\(425\) −3.11060e6 −0.835356
\(426\) 0 0
\(427\) −5.58994e6 −1.48367
\(428\) 2.45632e6 0.648150
\(429\) 0 0
\(430\) −330400. −0.0861725
\(431\) 5.42972e6 1.40794 0.703970 0.710230i \(-0.251409\pi\)
0.703970 + 0.710230i \(0.251409\pi\)
\(432\) 0 0
\(433\) 7.43979e6 1.90696 0.953479 0.301459i \(-0.0974737\pi\)
0.953479 + 0.301459i \(0.0974737\pi\)
\(434\) 5.88472e6 1.49969
\(435\) 0 0
\(436\) 2.85795e6 0.720010
\(437\) 122928. 0.0307927
\(438\) 0 0
\(439\) 6.86418e6 1.69991 0.849957 0.526852i \(-0.176628\pi\)
0.849957 + 0.526852i \(0.176628\pi\)
\(440\) 224000. 0.0551590
\(441\) −2.93860e6 −0.719522
\(442\) 0 0
\(443\) −3.46630e6 −0.839182 −0.419591 0.907713i \(-0.637827\pi\)
−0.419591 + 0.907713i \(0.637827\pi\)
\(444\) 0 0
\(445\) −1.31838e6 −0.315603
\(446\) −4.34753e6 −1.03492
\(447\) 0 0
\(448\) 696320. 0.163913
\(449\) 1.40426e6 0.328725 0.164362 0.986400i \(-0.447443\pi\)
0.164362 + 0.986400i \(0.447443\pi\)
\(450\) 2.84699e6 0.662757
\(451\) −262500. −0.0607698
\(452\) −3.91606e6 −0.901579
\(453\) 0 0
\(454\) 1.02588e6 0.233591
\(455\) 0 0
\(456\) 0 0
\(457\) 5.95072e6 1.33284 0.666421 0.745575i \(-0.267825\pi\)
0.666421 + 0.745575i \(0.267825\pi\)
\(458\) 1.19244e6 0.265627
\(459\) 0 0
\(460\) 353024. 0.0777875
\(461\) 6.25465e6 1.37073 0.685363 0.728202i \(-0.259644\pi\)
0.685363 + 0.728202i \(0.259644\pi\)
\(462\) 0 0
\(463\) 1.55055e6 0.336149 0.168075 0.985774i \(-0.446245\pi\)
0.168075 + 0.985774i \(0.446245\pi\)
\(464\) 659968. 0.142308
\(465\) 0 0
\(466\) −2.44770e6 −0.522149
\(467\) −1.80480e6 −0.382945 −0.191472 0.981498i \(-0.561326\pi\)
−0.191472 + 0.981498i \(0.561326\pi\)
\(468\) 0 0
\(469\) 1.18262e7 2.48264
\(470\) 333872. 0.0697165
\(471\) 0 0
\(472\) 891008. 0.184088
\(473\) −1.47500e6 −0.303137
\(474\) 0 0
\(475\) −228462. −0.0464601
\(476\) 2.88864e6 0.584354
\(477\) −7.05818e6 −1.42035
\(478\) −146280. −0.0292830
\(479\) −2.21809e6 −0.441712 −0.220856 0.975306i \(-0.570885\pi\)
−0.220856 + 0.975306i \(0.570885\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.52369e6 −0.298730
\(483\) 0 0
\(484\) −1.57682e6 −0.305962
\(485\) −2.55900e6 −0.493988
\(486\) 0 0
\(487\) 6.14268e6 1.17364 0.586821 0.809717i \(-0.300379\pi\)
0.586821 + 0.809717i \(0.300379\pi\)
\(488\) −2.10445e6 −0.400026
\(489\) 0 0
\(490\) 677208. 0.127418
\(491\) 6.44486e6 1.20645 0.603226 0.797571i \(-0.293882\pi\)
0.603226 + 0.797571i \(0.293882\pi\)
\(492\) 0 0
\(493\) 2.73784e6 0.507330
\(494\) 0 0
\(495\) −850500. −0.156013
\(496\) 2.21542e6 0.404346
\(497\) 8.59214e6 1.56031
\(498\) 0 0
\(499\) −4.25838e6 −0.765584 −0.382792 0.923835i \(-0.625037\pi\)
−0.382792 + 0.923835i \(0.625037\pi\)
\(500\) −1.35610e6 −0.242586
\(501\) 0 0
\(502\) −4.91227e6 −0.870008
\(503\) −3.56242e6 −0.627806 −0.313903 0.949455i \(-0.601637\pi\)
−0.313903 + 0.949455i \(0.601637\pi\)
\(504\) −2.64384e6 −0.463616
\(505\) −259196. −0.0452272
\(506\) 1.57600e6 0.273640
\(507\) 0 0
\(508\) 4.10560e6 0.705858
\(509\) −4.23936e6 −0.725281 −0.362640 0.931929i \(-0.618125\pi\)
−0.362640 + 0.931929i \(0.618125\pi\)
\(510\) 0 0
\(511\) 7.94750e6 1.34641
\(512\) 262144. 0.0441942
\(513\) 0 0
\(514\) −1.75711e6 −0.293354
\(515\) 1.62478e6 0.269946
\(516\) 0 0
\(517\) 1.49050e6 0.245248
\(518\) −7.47048e6 −1.22328
\(519\) 0 0
\(520\) 0 0
\(521\) 2.38657e6 0.385194 0.192597 0.981278i \(-0.438309\pi\)
0.192597 + 0.981278i \(0.438309\pi\)
\(522\) −2.50582e6 −0.402507
\(523\) −8.84129e6 −1.41339 −0.706694 0.707519i \(-0.749814\pi\)
−0.706694 + 0.707519i \(0.749814\pi\)
\(524\) −4.20378e6 −0.668823
\(525\) 0 0
\(526\) −6.71947e6 −1.05894
\(527\) 9.19055e6 1.44150
\(528\) 0 0
\(529\) −3.95257e6 −0.614101
\(530\) 1.62658e6 0.251527
\(531\) −3.38305e6 −0.520681
\(532\) 212160. 0.0325001
\(533\) 0 0
\(534\) 0 0
\(535\) 2.14928e6 0.324645
\(536\) 4.45222e6 0.669368
\(537\) 0 0
\(538\) 7.75361e6 1.15491
\(539\) 3.02325e6 0.448231
\(540\) 0 0
\(541\) −70058.0 −0.0102912 −0.00514558 0.999987i \(-0.501638\pi\)
−0.00514558 + 0.999987i \(0.501638\pi\)
\(542\) 2.78199e6 0.406778
\(543\) 0 0
\(544\) 1.08749e6 0.157553
\(545\) 2.50071e6 0.360638
\(546\) 0 0
\(547\) −6.60752e6 −0.944213 −0.472107 0.881541i \(-0.656506\pi\)
−0.472107 + 0.881541i \(0.656506\pi\)
\(548\) 612576. 0.0871382
\(549\) 7.99033e6 1.13145
\(550\) −2.92900e6 −0.412869
\(551\) 201084. 0.0282162
\(552\) 0 0
\(553\) −3.28916e6 −0.457375
\(554\) −4.52551e6 −0.626460
\(555\) 0 0
\(556\) −924416. −0.126818
\(557\) 1.10726e7 1.51221 0.756107 0.654448i \(-0.227099\pi\)
0.756107 + 0.654448i \(0.227099\pi\)
\(558\) −8.41169e6 −1.14366
\(559\) 0 0
\(560\) 609280. 0.0821007
\(561\) 0 0
\(562\) −6.92487e6 −0.924849
\(563\) −1.43532e6 −0.190843 −0.0954216 0.995437i \(-0.530420\pi\)
−0.0954216 + 0.995437i \(0.530420\pi\)
\(564\) 0 0
\(565\) −3.42656e6 −0.451582
\(566\) −5.88498e6 −0.772153
\(567\) 1.00383e7 1.31131
\(568\) 3.23469e6 0.420689
\(569\) −1.17051e7 −1.51564 −0.757818 0.652466i \(-0.773734\pi\)
−0.757818 + 0.652466i \(0.773734\pi\)
\(570\) 0 0
\(571\) 4.81885e6 0.618519 0.309260 0.950978i \(-0.399919\pi\)
0.309260 + 0.950978i \(0.399919\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −714000. −0.0904521
\(575\) −4.61610e6 −0.582245
\(576\) −995328. −0.125000
\(577\) 1.35572e6 0.169523 0.0847617 0.996401i \(-0.472987\pi\)
0.0847617 + 0.996401i \(0.472987\pi\)
\(578\) −1.16805e6 −0.145426
\(579\) 0 0
\(580\) 577472. 0.0712789
\(581\) 1.48645e7 1.82687
\(582\) 0 0
\(583\) 7.26150e6 0.884820
\(584\) 2.99200e6 0.363019
\(585\) 0 0
\(586\) −1.15542e7 −1.38994
\(587\) −5.03941e6 −0.603649 −0.301824 0.953364i \(-0.597596\pi\)
−0.301824 + 0.953364i \(0.597596\pi\)
\(588\) 0 0
\(589\) 675012. 0.0801721
\(590\) 779632. 0.0922061
\(591\) 0 0
\(592\) −2.81242e6 −0.329819
\(593\) −9.16124e6 −1.06984 −0.534919 0.844904i \(-0.679658\pi\)
−0.534919 + 0.844904i \(0.679658\pi\)
\(594\) 0 0
\(595\) 2.52756e6 0.292691
\(596\) −461856. −0.0532587
\(597\) 0 0
\(598\) 0 0
\(599\) −6.46635e6 −0.736363 −0.368182 0.929754i \(-0.620020\pi\)
−0.368182 + 0.929754i \(0.620020\pi\)
\(600\) 0 0
\(601\) −1.18021e7 −1.33282 −0.666411 0.745585i \(-0.732170\pi\)
−0.666411 + 0.745585i \(0.732170\pi\)
\(602\) −4.01200e6 −0.451201
\(603\) −1.69045e7 −1.89326
\(604\) −637920. −0.0711498
\(605\) −1.37971e6 −0.153250
\(606\) 0 0
\(607\) 2.25748e6 0.248686 0.124343 0.992239i \(-0.460318\pi\)
0.124343 + 0.992239i \(0.460318\pi\)
\(608\) 79872.0 0.00876265
\(609\) 0 0
\(610\) −1.84139e6 −0.200365
\(611\) 0 0
\(612\) −4.12906e6 −0.445628
\(613\) 2.75378e6 0.295991 0.147995 0.988988i \(-0.452718\pi\)
0.147995 + 0.988988i \(0.452718\pi\)
\(614\) −3.49647e6 −0.374291
\(615\) 0 0
\(616\) 2.72000e6 0.288813
\(617\) −3.41607e6 −0.361255 −0.180627 0.983552i \(-0.557813\pi\)
−0.180627 + 0.983552i \(0.557813\pi\)
\(618\) 0 0
\(619\) −9.43169e6 −0.989379 −0.494690 0.869070i \(-0.664718\pi\)
−0.494690 + 0.869070i \(0.664718\pi\)
\(620\) 1.93850e6 0.202528
\(621\) 0 0
\(622\) 1.07290e7 1.11194
\(623\) −1.60089e7 −1.65250
\(624\) 0 0
\(625\) 7.96654e6 0.815774
\(626\) −5.37834e6 −0.548546
\(627\) 0 0
\(628\) 2.57667e6 0.260711
\(629\) −1.16671e7 −1.17581
\(630\) −2.31336e6 −0.232216
\(631\) 4.87474e6 0.487391 0.243696 0.969852i \(-0.421640\pi\)
0.243696 + 0.969852i \(0.421640\pi\)
\(632\) −1.23827e6 −0.123317
\(633\) 0 0
\(634\) −5.28295e6 −0.521980
\(635\) 3.59240e6 0.353550
\(636\) 0 0
\(637\) 0 0
\(638\) 2.57800e6 0.250744
\(639\) −1.22817e7 −1.18989
\(640\) 229376. 0.0221359
\(641\) 9.74279e6 0.936566 0.468283 0.883579i \(-0.344873\pi\)
0.468283 + 0.883579i \(0.344873\pi\)
\(642\) 0 0
\(643\) −1.63894e6 −0.156327 −0.0781637 0.996941i \(-0.524906\pi\)
−0.0781637 + 0.996941i \(0.524906\pi\)
\(644\) 4.28672e6 0.407296
\(645\) 0 0
\(646\) 331344. 0.0312390
\(647\) −1.59069e6 −0.149391 −0.0746955 0.997206i \(-0.523798\pi\)
−0.0746955 + 0.997206i \(0.523798\pi\)
\(648\) 3.77914e6 0.353553
\(649\) 3.48050e6 0.324362
\(650\) 0 0
\(651\) 0 0
\(652\) −5.00528e6 −0.461115
\(653\) 1.59778e7 1.46634 0.733170 0.680045i \(-0.238040\pi\)
0.733170 + 0.680045i \(0.238040\pi\)
\(654\) 0 0
\(655\) −3.67830e6 −0.335000
\(656\) −268800. −0.0243876
\(657\) −1.13602e7 −1.02677
\(658\) 4.05416e6 0.365036
\(659\) −6.02458e6 −0.540397 −0.270199 0.962805i \(-0.587089\pi\)
−0.270199 + 0.962805i \(0.587089\pi\)
\(660\) 0 0
\(661\) 2.00705e7 1.78671 0.893355 0.449352i \(-0.148345\pi\)
0.893355 + 0.449352i \(0.148345\pi\)
\(662\) 8.22911e6 0.729807
\(663\) 0 0
\(664\) 5.59603e6 0.492561
\(665\) 185640. 0.0162786
\(666\) 1.06784e7 0.932868
\(667\) 4.06293e6 0.353610
\(668\) −8.52682e6 −0.739343
\(669\) 0 0
\(670\) 3.89570e6 0.335273
\(671\) −8.22050e6 −0.704842
\(672\) 0 0
\(673\) −5.48575e6 −0.466873 −0.233436 0.972372i \(-0.574997\pi\)
−0.233436 + 0.972372i \(0.574997\pi\)
\(674\) 1.81359e6 0.153776
\(675\) 0 0
\(676\) 0 0
\(677\) −4.74926e6 −0.398248 −0.199124 0.979974i \(-0.563810\pi\)
−0.199124 + 0.979974i \(0.563810\pi\)
\(678\) 0 0
\(679\) −3.10736e7 −2.58653
\(680\) 951552. 0.0789151
\(681\) 0 0
\(682\) 8.65400e6 0.712453
\(683\) 6.13964e6 0.503606 0.251803 0.967778i \(-0.418976\pi\)
0.251803 + 0.967778i \(0.418976\pi\)
\(684\) −303264. −0.0247845
\(685\) 536004. 0.0436457
\(686\) −3.20552e6 −0.260069
\(687\) 0 0
\(688\) −1.51040e6 −0.121652
\(689\) 0 0
\(690\) 0 0
\(691\) −1.57617e7 −1.25577 −0.627883 0.778308i \(-0.716078\pi\)
−0.627883 + 0.778308i \(0.716078\pi\)
\(692\) −1.00873e7 −0.800776
\(693\) −1.03275e7 −0.816887
\(694\) −4.92259e6 −0.387967
\(695\) −808864. −0.0635204
\(696\) 0 0
\(697\) −1.11510e6 −0.0869424
\(698\) 9.75298e6 0.757703
\(699\) 0 0
\(700\) −7.96688e6 −0.614530
\(701\) −1.42036e7 −1.09170 −0.545851 0.837882i \(-0.683793\pi\)
−0.545851 + 0.837882i \(0.683793\pi\)
\(702\) 0 0
\(703\) −856908. −0.0653952
\(704\) 1.02400e6 0.0778697
\(705\) 0 0
\(706\) 1.07326e7 0.810388
\(707\) −3.14738e6 −0.236810
\(708\) 0 0
\(709\) −1.60718e7 −1.20074 −0.600369 0.799723i \(-0.704980\pi\)
−0.600369 + 0.799723i \(0.704980\pi\)
\(710\) 2.83035e6 0.210715
\(711\) 4.70156e6 0.348793
\(712\) −6.02688e6 −0.445546
\(713\) 1.36387e7 1.00473
\(714\) 0 0
\(715\) 0 0
\(716\) −1.07987e7 −0.787204
\(717\) 0 0
\(718\) −6.34774e6 −0.459524
\(719\) −2.07078e7 −1.49387 −0.746933 0.664900i \(-0.768474\pi\)
−0.746933 + 0.664900i \(0.768474\pi\)
\(720\) −870912. −0.0626099
\(721\) 1.97295e7 1.41344
\(722\) −9.88006e6 −0.705369
\(723\) 0 0
\(724\) 2.98051e6 0.211322
\(725\) −7.55096e6 −0.533528
\(726\) 0 0
\(727\) 5.04803e6 0.354231 0.177115 0.984190i \(-0.443323\pi\)
0.177115 + 0.984190i \(0.443323\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −1.00000
\(730\) 2.61800e6 0.181829
\(731\) −6.26580e6 −0.433694
\(732\) 0 0
\(733\) 2.10377e7 1.44623 0.723115 0.690728i \(-0.242710\pi\)
0.723115 + 0.690728i \(0.242710\pi\)
\(734\) −240208. −0.0164569
\(735\) 0 0
\(736\) 1.61382e6 0.109815
\(737\) 1.73915e7 1.17942
\(738\) 1.02060e6 0.0689786
\(739\) −1.38992e7 −0.936218 −0.468109 0.883671i \(-0.655065\pi\)
−0.468109 + 0.883671i \(0.655065\pi\)
\(740\) −2.46086e6 −0.165199
\(741\) 0 0
\(742\) 1.97513e7 1.31700
\(743\) −1.23267e6 −0.0819169 −0.0409584 0.999161i \(-0.513041\pi\)
−0.0409584 + 0.999161i \(0.513041\pi\)
\(744\) 0 0
\(745\) −404124. −0.0266762
\(746\) −1.60741e7 −1.05750
\(747\) −2.12474e7 −1.39317
\(748\) 4.24800e6 0.277607
\(749\) 2.60984e7 1.69985
\(750\) 0 0
\(751\) −1.62624e6 −0.105217 −0.0526084 0.998615i \(-0.516753\pi\)
−0.0526084 + 0.998615i \(0.516753\pi\)
\(752\) 1.52627e6 0.0984209
\(753\) 0 0
\(754\) 0 0
\(755\) −558180. −0.0356375
\(756\) 0 0
\(757\) 3.49882e6 0.221913 0.110956 0.993825i \(-0.464609\pi\)
0.110956 + 0.993825i \(0.464609\pi\)
\(758\) −6.70324e6 −0.423752
\(759\) 0 0
\(760\) 69888.0 0.00438903
\(761\) −2.21713e7 −1.38781 −0.693905 0.720067i \(-0.744111\pi\)
−0.693905 + 0.720067i \(0.744111\pi\)
\(762\) 0 0
\(763\) 3.03657e7 1.88831
\(764\) 1.29949e7 0.805451
\(765\) −3.61292e6 −0.223206
\(766\) −2.74903e6 −0.169281
\(767\) 0 0
\(768\) 0 0
\(769\) −1.08955e6 −0.0664400 −0.0332200 0.999448i \(-0.510576\pi\)
−0.0332200 + 0.999448i \(0.510576\pi\)
\(770\) 2.38000e6 0.144661
\(771\) 0 0
\(772\) 2.40227e6 0.145070
\(773\) −1.95219e6 −0.117510 −0.0587549 0.998272i \(-0.518713\pi\)
−0.0587549 + 0.998272i \(0.518713\pi\)
\(774\) 5.73480e6 0.344085
\(775\) −2.53476e7 −1.51594
\(776\) −1.16983e7 −0.697379
\(777\) 0 0
\(778\) 5.50442e6 0.326034
\(779\) −81900.0 −0.00483549
\(780\) 0 0
\(781\) 1.26355e7 0.741250
\(782\) 6.69485e6 0.391493
\(783\) 0 0
\(784\) 3.09581e6 0.179880
\(785\) 2.25459e6 0.130585
\(786\) 0 0
\(787\) 1.44531e7 0.831809 0.415904 0.909408i \(-0.363465\pi\)
0.415904 + 0.909408i \(0.363465\pi\)
\(788\) −3.78230e6 −0.216991
\(789\) 0 0
\(790\) −1.08349e6 −0.0617670
\(791\) −4.16082e7 −2.36449
\(792\) −3.88800e6 −0.220249
\(793\) 0 0
\(794\) 2.88479e6 0.162391
\(795\) 0 0
\(796\) −630016. −0.0352427
\(797\) 1.23500e7 0.688685 0.344343 0.938844i \(-0.388102\pi\)
0.344343 + 0.938844i \(0.388102\pi\)
\(798\) 0 0
\(799\) 6.33164e6 0.350873
\(800\) −2.99930e6 −0.165689
\(801\) 2.28833e7 1.26019
\(802\) −8.90724e6 −0.488998
\(803\) 1.16875e7 0.639636
\(804\) 0 0
\(805\) 3.75088e6 0.204006
\(806\) 0 0
\(807\) 0 0
\(808\) −1.18490e6 −0.0638487
\(809\) 1.15968e7 0.622970 0.311485 0.950251i \(-0.399174\pi\)
0.311485 + 0.950251i \(0.399174\pi\)
\(810\) 3.30674e6 0.177088
\(811\) 2.47534e7 1.32155 0.660774 0.750585i \(-0.270228\pi\)
0.660774 + 0.750585i \(0.270228\pi\)
\(812\) 7.01216e6 0.373217
\(813\) 0 0
\(814\) −1.09860e7 −0.581137
\(815\) −4.37962e6 −0.230963
\(816\) 0 0
\(817\) −460200. −0.0241208
\(818\) −8.03130e6 −0.419665
\(819\) 0 0
\(820\) −235200. −0.0122153
\(821\) 2.47470e6 0.128134 0.0640671 0.997946i \(-0.479593\pi\)
0.0640671 + 0.997946i \(0.479593\pi\)
\(822\) 0 0
\(823\) −7.84754e6 −0.403863 −0.201932 0.979400i \(-0.564722\pi\)
−0.201932 + 0.979400i \(0.564722\pi\)
\(824\) 7.42758e6 0.381092
\(825\) 0 0
\(826\) 9.46696e6 0.482792
\(827\) 2.26192e7 1.15004 0.575020 0.818140i \(-0.304994\pi\)
0.575020 + 0.818140i \(0.304994\pi\)
\(828\) −6.12749e6 −0.310604
\(829\) −1.73912e7 −0.878907 −0.439454 0.898265i \(-0.644828\pi\)
−0.439454 + 0.898265i \(0.644828\pi\)
\(830\) 4.89653e6 0.246714
\(831\) 0 0
\(832\) 0 0
\(833\) 1.28428e7 0.641278
\(834\) 0 0
\(835\) −7.46096e6 −0.370321
\(836\) 312000. 0.0154397
\(837\) 0 0
\(838\) 2.39751e7 1.17937
\(839\) 3.43825e7 1.68629 0.843147 0.537684i \(-0.180701\pi\)
0.843147 + 0.537684i \(0.180701\pi\)
\(840\) 0 0
\(841\) −1.38651e7 −0.675977
\(842\) 2.13095e7 1.03584
\(843\) 0 0
\(844\) −6.57242e6 −0.317592
\(845\) 0 0
\(846\) −5.79506e6 −0.278376
\(847\) −1.67537e7 −0.802419
\(848\) 7.43578e6 0.355089
\(849\) 0 0
\(850\) −1.24424e7 −0.590686
\(851\) −1.73139e7 −0.819543
\(852\) 0 0
\(853\) −2.31007e7 −1.08706 −0.543528 0.839391i \(-0.682912\pi\)
−0.543528 + 0.839391i \(0.682912\pi\)
\(854\) −2.23598e7 −1.04911
\(855\) −265356. −0.0124141
\(856\) 9.82528e6 0.458311
\(857\) −7.02305e6 −0.326643 −0.163322 0.986573i \(-0.552221\pi\)
−0.163322 + 0.986573i \(0.552221\pi\)
\(858\) 0 0
\(859\) 8.82135e6 0.407899 0.203949 0.978981i \(-0.434622\pi\)
0.203949 + 0.978981i \(0.434622\pi\)
\(860\) −1.32160e6 −0.0609332
\(861\) 0 0
\(862\) 2.17189e7 0.995564
\(863\) −2.39560e7 −1.09493 −0.547466 0.836828i \(-0.684408\pi\)
−0.547466 + 0.836828i \(0.684408\pi\)
\(864\) 0 0
\(865\) −8.82641e6 −0.401092
\(866\) 2.97592e7 1.34842
\(867\) 0 0
\(868\) 2.35389e7 1.06044
\(869\) −4.83700e6 −0.217283
\(870\) 0 0
\(871\) 0 0
\(872\) 1.14318e7 0.509124
\(873\) 4.44170e7 1.97248
\(874\) 491712. 0.0217737
\(875\) −1.44085e7 −0.636208
\(876\) 0 0
\(877\) 5.79805e6 0.254556 0.127278 0.991867i \(-0.459376\pi\)
0.127278 + 0.991867i \(0.459376\pi\)
\(878\) 2.74567e7 1.20202
\(879\) 0 0
\(880\) 896000. 0.0390033
\(881\) −1.30527e7 −0.566580 −0.283290 0.959034i \(-0.591426\pi\)
−0.283290 + 0.959034i \(0.591426\pi\)
\(882\) −1.17544e7 −0.508779
\(883\) 4.73009e6 0.204159 0.102079 0.994776i \(-0.467450\pi\)
0.102079 + 0.994776i \(0.467450\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.38652e7 −0.593392
\(887\) 2.80737e7 1.19809 0.599046 0.800714i \(-0.295547\pi\)
0.599046 + 0.800714i \(0.295547\pi\)
\(888\) 0 0
\(889\) 4.36220e7 1.85119
\(890\) −5.27352e6 −0.223165
\(891\) 1.47622e7 0.622957
\(892\) −1.73901e7 −0.731796
\(893\) 465036. 0.0195145
\(894\) 0 0
\(895\) −9.44882e6 −0.394294
\(896\) 2.78528e6 0.115904
\(897\) 0 0
\(898\) 5.61705e6 0.232443
\(899\) 2.23100e7 0.920663
\(900\) 1.13880e7 0.468640
\(901\) 3.08469e7 1.26590
\(902\) −1.05000e6 −0.0429708
\(903\) 0 0
\(904\) −1.56643e7 −0.637512
\(905\) 2.60795e6 0.105847
\(906\) 0 0
\(907\) 2.28552e7 0.922500 0.461250 0.887270i \(-0.347401\pi\)
0.461250 + 0.887270i \(0.347401\pi\)
\(908\) 4.10352e6 0.165174
\(909\) 4.49890e6 0.180591
\(910\) 0 0
\(911\) −3.27335e7 −1.30676 −0.653381 0.757029i \(-0.726650\pi\)
−0.653381 + 0.757029i \(0.726650\pi\)
\(912\) 0 0
\(913\) 2.18595e7 0.867887
\(914\) 2.38029e7 0.942462
\(915\) 0 0
\(916\) 4.76976e6 0.187827
\(917\) −4.46651e7 −1.75406
\(918\) 0 0
\(919\) −1.27717e7 −0.498839 −0.249419 0.968396i \(-0.580240\pi\)
−0.249419 + 0.968396i \(0.580240\pi\)
\(920\) 1.41210e6 0.0550040
\(921\) 0 0
\(922\) 2.50186e7 0.969249
\(923\) 0 0
\(924\) 0 0
\(925\) 3.21780e7 1.23653
\(926\) 6.20218e6 0.237693
\(927\) −2.82016e7 −1.07789
\(928\) 2.63987e6 0.100627
\(929\) −3.48297e7 −1.32407 −0.662034 0.749473i \(-0.730307\pi\)
−0.662034 + 0.749473i \(0.730307\pi\)
\(930\) 0 0
\(931\) 943254. 0.0356660
\(932\) −9.79082e6 −0.369215
\(933\) 0 0
\(934\) −7.21918e6 −0.270783
\(935\) 3.71700e6 0.139048
\(936\) 0 0
\(937\) 3.00172e7 1.11692 0.558459 0.829532i \(-0.311393\pi\)
0.558459 + 0.829532i \(0.311393\pi\)
\(938\) 4.73049e7 1.75549
\(939\) 0 0
\(940\) 1.33549e6 0.0492970
\(941\) 4.50649e7 1.65907 0.829534 0.558457i \(-0.188606\pi\)
0.829534 + 0.558457i \(0.188606\pi\)
\(942\) 0 0
\(943\) −1.65480e6 −0.0605991
\(944\) 3.56403e6 0.130170
\(945\) 0 0
\(946\) −5.90000e6 −0.214350
\(947\) −2.99276e7 −1.08442 −0.542210 0.840243i \(-0.682412\pi\)
−0.542210 + 0.840243i \(0.682412\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −913848. −0.0328522
\(951\) 0 0
\(952\) 1.15546e7 0.413201
\(953\) −4.25147e7 −1.51638 −0.758188 0.652036i \(-0.773915\pi\)
−0.758188 + 0.652036i \(0.773915\pi\)
\(954\) −2.82327e7 −1.00434
\(955\) 1.13705e7 0.403433
\(956\) −585120. −0.0207062
\(957\) 0 0
\(958\) −8.87234e6 −0.312338
\(959\) 6.50862e6 0.228530
\(960\) 0 0
\(961\) 4.62626e7 1.61593
\(962\) 0 0
\(963\) −3.73054e7 −1.29630
\(964\) −6.09475e6 −0.211234
\(965\) 2.10199e6 0.0726628
\(966\) 0 0
\(967\) 3.00251e7 1.03257 0.516284 0.856417i \(-0.327315\pi\)
0.516284 + 0.856417i \(0.327315\pi\)
\(968\) −6.30726e6 −0.216348
\(969\) 0 0
\(970\) −1.02360e7 −0.349302
\(971\) −4.00864e7 −1.36442 −0.682211 0.731155i \(-0.738982\pi\)
−0.682211 + 0.731155i \(0.738982\pi\)
\(972\) 0 0
\(973\) −9.82192e6 −0.332594
\(974\) 2.45707e7 0.829890
\(975\) 0 0
\(976\) −8.41779e6 −0.282861
\(977\) −5.12151e7 −1.71657 −0.858284 0.513174i \(-0.828469\pi\)
−0.858284 + 0.513174i \(0.828469\pi\)
\(978\) 0 0
\(979\) −2.35425e7 −0.785047
\(980\) 2.70883e6 0.0900984
\(981\) −4.34051e7 −1.44002
\(982\) 2.57794e7 0.853090
\(983\) −1.82382e7 −0.602004 −0.301002 0.953624i \(-0.597321\pi\)
−0.301002 + 0.953624i \(0.597321\pi\)
\(984\) 0 0
\(985\) −3.30952e6 −0.108686
\(986\) 1.09513e7 0.358736
\(987\) 0 0
\(988\) 0 0
\(989\) −9.29840e6 −0.302286
\(990\) −3.40200e6 −0.110318
\(991\) −3.24103e7 −1.04833 −0.524166 0.851616i \(-0.675623\pi\)
−0.524166 + 0.851616i \(0.675623\pi\)
\(992\) 8.86170e6 0.285915
\(993\) 0 0
\(994\) 3.43686e7 1.10330
\(995\) −551264. −0.0176523
\(996\) 0 0
\(997\) −2.07867e7 −0.662289 −0.331145 0.943580i \(-0.607435\pi\)
−0.331145 + 0.943580i \(0.607435\pi\)
\(998\) −1.70335e7 −0.541350
\(999\) 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 338.6.a.d.1.1 1
13.5 odd 4 338.6.b.a.337.1 2
13.8 odd 4 338.6.b.a.337.2 2
13.12 even 2 26.6.a.a.1.1 1
39.38 odd 2 234.6.a.g.1.1 1
52.51 odd 2 208.6.a.b.1.1 1
65.12 odd 4 650.6.b.a.599.1 2
65.38 odd 4 650.6.b.a.599.2 2
65.64 even 2 650.6.a.a.1.1 1
104.51 odd 2 832.6.a.e.1.1 1
104.77 even 2 832.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
26.6.a.a.1.1 1 13.12 even 2
208.6.a.b.1.1 1 52.51 odd 2
234.6.a.g.1.1 1 39.38 odd 2
338.6.a.d.1.1 1 1.1 even 1 trivial
338.6.b.a.337.1 2 13.5 odd 4
338.6.b.a.337.2 2 13.8 odd 4
650.6.a.a.1.1 1 65.64 even 2
650.6.b.a.599.1 2 65.12 odd 4
650.6.b.a.599.2 2 65.38 odd 4
832.6.a.d.1.1 1 104.77 even 2
832.6.a.e.1.1 1 104.51 odd 2