Properties

Label 26.6.a.a.1.1
Level $26$
Weight $6$
Character 26.1
Self dual yes
Analytic conductor $4.170$
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] = [26,6,Mod(1,26)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(26, 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("26.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 26.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: \(4.16997931514\)
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 \(\chi\) \(=\) 26.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{2} +16.0000 q^{4} -14.0000 q^{5} -170.000 q^{7} -64.0000 q^{8} -243.000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +16.0000 q^{4} -14.0000 q^{5} -170.000 q^{7} -64.0000 q^{8} -243.000 q^{9} +56.0000 q^{10} -250.000 q^{11} -169.000 q^{13} +680.000 q^{14} +256.000 q^{16} +1062.00 q^{17} +972.000 q^{18} -78.0000 q^{19} -224.000 q^{20} +1000.00 q^{22} +1576.00 q^{23} -2929.00 q^{25} +676.000 q^{26} -2720.00 q^{28} +2578.00 q^{29} -8654.00 q^{31} -1024.00 q^{32} -4248.00 q^{34} +2380.00 q^{35} -3888.00 q^{36} +10986.0 q^{37} +312.000 q^{38} +896.000 q^{40} +1050.00 q^{41} -5900.00 q^{43} -4000.00 q^{44} +3402.00 q^{45} -6304.00 q^{46} -5962.00 q^{47} +12093.0 q^{49} +11716.0 q^{50} -2704.00 q^{52} +29046.0 q^{53} +3500.00 q^{55} +10880.0 q^{56} -10312.0 q^{58} -13922.0 q^{59} -32882.0 q^{61} +34616.0 q^{62} +41310.0 q^{63} +4096.00 q^{64} +2366.00 q^{65} -69566.0 q^{67} +16992.0 q^{68} -9520.00 q^{70} -50542.0 q^{71} +15552.0 q^{72} -46750.0 q^{73} -43944.0 q^{74} -1248.00 q^{76} +42500.0 q^{77} -19348.0 q^{79} -3584.00 q^{80} +59049.0 q^{81} -4200.00 q^{82} -87438.0 q^{83} -14868.0 q^{85} +23600.0 q^{86} +16000.0 q^{88} +94170.0 q^{89} -13608.0 q^{90} +28730.0 q^{91} +25216.0 q^{92} +23848.0 q^{94} +1092.00 q^{95} +182786. q^{97} -48372.0 q^{98} +60750.0 q^{99} +O(q^{100})\)

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 \(-0.539964\pi\)
−0.125220 + 0.992129i \(0.539964\pi\)
\(6\) 0 0
\(7\) −170.000 −1.31131 −0.655653 0.755063i \(-0.727606\pi\)
−0.655653 + 0.755063i \(0.727606\pi\)
\(8\) −64.0000 −0.353553
\(9\) −243.000 −1.00000
\(10\) 56.0000 0.177088
\(11\) −250.000 −0.622957 −0.311479 0.950253i \(-0.600824\pi\)
−0.311479 + 0.950253i \(0.600824\pi\)
\(12\) 0 0
\(13\) −169.000 −0.277350
\(14\) 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 \(-0.507890\pi\)
−0.0247845 + 0.999693i \(0.507890\pi\)
\(20\) −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
\(26\) 676.000 0.196116
\(27\) 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 \(-0.799824\pi\)
−0.808691 + 0.588234i \(0.799824\pi\)
\(32\) −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 \(-0.270710\pi\)
0.659637 + 0.751584i \(0.270710\pi\)
\(38\) 312.000 0.0350506
\(39\) 0 0
\(40\) 896.000 0.0885438
\(41\) 1050.00 0.0975505 0.0487753 0.998810i \(-0.484468\pi\)
0.0487753 + 0.998810i \(0.484468\pi\)
\(42\) 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 \(-0.563069\pi\)
−0.196842 + 0.980435i \(0.563069\pi\)
\(48\) 0 0
\(49\) 12093.0 0.719522
\(50\) 11716.0 0.662757
\(51\) 0 0
\(52\) −2704.00 −0.138675
\(53\) 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 \(-0.583835\pi\)
−0.260340 + 0.965517i \(0.583835\pi\)
\(60\) 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
\(65\) 2366.00 0.0694595
\(66\) 0 0
\(67\) −69566.0 −1.89326 −0.946629 0.322324i \(-0.895536\pi\)
−0.946629 + 0.322324i \(0.895536\pi\)
\(68\) 16992.0 0.445628
\(69\) 0 0
\(70\) −9520.00 −0.232216
\(71\) −50542.0 −1.18989 −0.594945 0.803767i \(-0.702826\pi\)
−0.594945 + 0.803767i \(0.702826\pi\)
\(72\) 15552.0 0.353553
\(73\) −46750.0 −1.02677 −0.513387 0.858157i \(-0.671609\pi\)
−0.513387 + 0.858157i \(0.671609\pi\)
\(74\) −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 \(-0.745299\pi\)
−0.696586 + 0.717473i \(0.745299\pi\)
\(84\) 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 \(-0.283015\pi\)
0.630097 + 0.776516i \(0.283015\pi\)
\(90\) −13608.0 −0.177088
\(91\) 28730.0 0.363691
\(92\) 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 \(-0.0528613\pi\)
0.986242 + 0.165307i \(0.0528613\pi\)
\(98\) −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 \(0.318823\pi\)
\(104\) 10816.0 0.0980581
\(105\) 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 \(-0.755863\pi\)
−0.720010 + 0.693963i \(0.755863\pi\)
\(110\) −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
\(117\) 41067.0 0.277350
\(118\) 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
\(130\) −9464.00 −0.0491152
\(131\) −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 \(-0.527772\pi\)
−0.0871382 + 0.996196i \(0.527772\pi\)
\(138\) 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
\(143\) 42250.0 0.172777
\(144\) −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 \(-0.483039\pi\)
0.0532587 + 0.998581i \(0.483039\pi\)
\(150\) 0 0
\(151\) 39870.0 0.142300 0.0711498 0.997466i \(-0.477333\pi\)
0.0711498 + 0.997466i \(0.477333\pi\)
\(152\) 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 \(-0.347450\pi\)
0.461115 + 0.887340i \(0.347450\pi\)
\(164\) 16800.0 0.0487753
\(165\) 0 0
\(166\) 349752. 0.985122
\(167\) 532926. 1.47869 0.739343 0.673329i \(-0.235136\pi\)
0.739343 + 0.673329i \(0.235136\pi\)
\(168\) 0 0
\(169\) 28561.0 0.0769231
\(170\) 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 \(0.432223\pi\)
\(182\) −114920. −0.257168
\(183\) 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 \(-0.546341\pi\)
−0.145070 + 0.989421i \(0.546341\pi\)
\(194\) −731144. −1.39476
\(195\) 0 0
\(196\) 193488. 0.359761
\(197\) 236394. 0.433981 0.216991 0.976174i \(-0.430376\pi\)
0.216991 + 0.976174i \(0.430376\pi\)
\(198\) −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
\(208\) −43264.0 −0.0693375
\(209\) 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
\(221\) −179478. −0.247190
\(222\) 0 0
\(223\) 1.08688e6 1.46359 0.731796 0.681523i \(-0.238682\pi\)
0.731796 + 0.681523i \(0.238682\pi\)
\(224\) 174080. 0.231808
\(225\) 711747. 0.937280
\(226\) 979016. 1.27502
\(227\) −256470. −0.330348 −0.165174 0.986264i \(-0.552819\pi\)
−0.165174 + 0.986264i \(0.552819\pi\)
\(228\) 0 0
\(229\) −298110. −0.375654 −0.187827 0.982202i \(-0.560144\pi\)
−0.187827 + 0.982202i \(0.560144\pi\)
\(230\) 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 \(0.620373\pi\)
\(234\) −164268. −0.196116
\(235\) 83468.0 0.0985940
\(236\) −222752. −0.260340
\(237\) 0 0
\(238\) 722160. 0.826401
\(239\) 36570.0 0.0414124 0.0207062 0.999786i \(-0.493409\pi\)
0.0207062 + 0.999786i \(0.493409\pi\)
\(240\) 0 0
\(241\) 380922. 0.422468 0.211234 0.977436i \(-0.432252\pi\)
0.211234 + 0.977436i \(0.432252\pi\)
\(242\) 394204. 0.432696
\(243\) 0 0
\(244\) −526112. −0.565723
\(245\) −169302. −0.180197
\(246\) 0 0
\(247\) 13182.0 0.0137480
\(248\) 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
\(260\) 37856.0 0.0347297
\(261\) −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 \(-0.592869\pi\)
−0.287636 + 0.957740i \(0.592869\pi\)
\(272\) 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 \(-0.273103\pi\)
0.653967 + 0.756523i \(0.273103\pi\)
\(282\) 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
\(286\) −169000. −0.122172
\(287\) −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 \(-0.0590637\pi\)
0.982834 + 0.184491i \(0.0590637\pi\)
\(294\) 0 0
\(295\) 194908. 0.130399
\(296\) −703104. −0.466434
\(297\) 0 0
\(298\) −115464. −0.0753192
\(299\) −266344. −0.172292
\(300\) 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 \(-0.414739\pi\)
0.264664 + 0.964341i \(0.414739\pi\)
\(308\) 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 \(-0.379668\pi\)
0.369095 + 0.929392i \(0.379668\pi\)
\(318\) 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
\(325\) 495001. 0.259955
\(326\) −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 \(-0.672599\pi\)
−0.516051 + 0.856558i \(0.672599\pi\)
\(332\) −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 \(0.465320\pi\)
\(338\) −114244. −0.0543928
\(339\) 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 \(-0.679981\pi\)
−0.535777 + 0.844360i \(0.679981\pi\)
\(350\) −1.99172e6 −0.869077
\(351\) 0 0
\(352\) 256000. 0.110124
\(353\) −2.68315e6 −1.14606 −0.573031 0.819534i \(-0.694233\pi\)
−0.573031 + 0.819534i \(0.694233\pi\)
\(354\) 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 \(-0.394659\pi\)
0.324932 + 0.945737i \(0.394659\pi\)
\(360\) −217728. −0.0885438
\(361\) −2.47002e6 −0.997543
\(362\) −745128. −0.298854
\(363\) 0 0
\(364\) 459680. 0.181845
\(365\) 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
\(377\) −435682. −0.157876
\(378\) 0 0
\(379\) 1.67581e6 0.599276 0.299638 0.954053i \(-0.403134\pi\)
0.299638 + 0.954053i \(0.403134\pi\)
\(380\) 17472.0 0.00620703
\(381\) 0 0
\(382\) −3.24872e6 −1.13908
\(383\) 687258. 0.239399 0.119700 0.992810i \(-0.461807\pi\)
0.119700 + 0.992810i \(0.461807\pi\)
\(384\) 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 \(-0.536632\pi\)
−0.114828 + 0.993385i \(0.536632\pi\)
\(398\) 157504. 0.0498407
\(399\) 0 0
\(400\) −749824. −0.234320
\(401\) 2.22681e6 0.691548 0.345774 0.938318i \(-0.387616\pi\)
0.345774 + 0.938318i \(0.387616\pi\)
\(402\) 0 0
\(403\) 1.46253e6 0.448581
\(404\) −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 \(-0.404098\pi\)
0.296748 + 0.954956i \(0.404098\pi\)
\(410\) 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
\(416\) 173056. 0.0490290
\(417\) 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 \(-0.761623\pi\)
−0.732449 + 0.680822i \(0.761623\pi\)
\(422\) 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 \(-0.748591\pi\)
−0.703970 + 0.710230i \(0.748591\pi\)
\(432\) 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
\(442\) 717912. 0.174790
\(443\) −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 \(-0.552557\pi\)
−0.164362 + 0.986400i \(0.552557\pi\)
\(450\) −2.84699e6 −0.662757
\(451\) −262500. −0.0607698
\(452\) −3.91606e6 −0.901579
\(453\) 0 0
\(454\) 1.02588e6 0.233591
\(455\) −402220. −0.0910825
\(456\) 0 0
\(457\) −5.95072e6 −1.33284 −0.666421 0.745575i \(-0.732175\pi\)
−0.666421 + 0.745575i \(0.732175\pi\)
\(458\) 1.19244e6 0.265627
\(459\) 0 0
\(460\) −353024. −0.0777875
\(461\) −6.25465e6 −1.37073 −0.685363 0.728202i \(-0.740356\pi\)
−0.685363 + 0.728202i \(0.740356\pi\)
\(462\) 0 0
\(463\) −1.55055e6 −0.336149 −0.168075 0.985774i \(-0.553755\pi\)
−0.168075 + 0.985774i \(0.553755\pi\)
\(464\) 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 \(0.561326\pi\)
\(468\) 657072. 0.138675
\(469\) 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 \(-0.429115\pi\)
0.220856 + 0.975306i \(0.429115\pi\)
\(480\) 0 0
\(481\) −1.85663e6 −0.365901
\(482\) −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 \(-0.699621\pi\)
−0.586821 + 0.809717i \(0.699621\pi\)
\(488\) 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
\(494\) −52728.0 −0.00972129
\(495\) −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 \(-0.374963\pi\)
0.382792 + 0.923835i \(0.374963\pi\)
\(500\) 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 \(-0.381875\pi\)
0.362640 + 0.931929i \(0.381875\pi\)
\(510\) 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
\(520\) −151424. −0.0245576
\(521\) 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
\(533\) −177450. −0.0270557
\(534\) 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 \(-0.498362\pi\)
0.00514558 + 0.999987i \(0.498362\pi\)
\(542\) 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 \(-0.772901\pi\)
−0.756107 + 0.654448i \(0.772901\pi\)
\(558\) −8.41169e6 −1.14366
\(559\) 997100. 0.134961
\(560\) 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 \(0.399919\pi\)
\(572\) 676000. 0.0863886
\(573\) 0 0
\(574\) 714000. 0.0904521
\(575\) −4.61610e6 −0.582245
\(576\) −995328. −0.125000
\(577\) −1.35572e6 −0.169523 −0.0847617 0.996401i \(-0.527013\pi\)
−0.0847617 + 0.996401i \(0.527013\pi\)
\(578\) 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
\(585\) −574938. −0.0694595
\(586\) −1.15542e7 −1.38994
\(587\) 5.03941e6 0.603649 0.301824 0.953364i \(-0.402404\pi\)
0.301824 + 0.953364i \(0.402404\pi\)
\(588\) 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 \(-0.320342\pi\)
0.534919 + 0.844904i \(0.320342\pi\)
\(594\) 0 0
\(595\) 2.52756e6 0.292691
\(596\) 461856. 0.0532587
\(597\) 0 0
\(598\) 1.06538e6 0.121829
\(599\) −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
\(611\) 1.00758e6 0.109188
\(612\) −4.12906e6 −0.445628
\(613\) −2.75378e6 −0.295991 −0.147995 0.988988i \(-0.547282\pi\)
−0.147995 + 0.988988i \(0.547282\pi\)
\(614\) −3.49647e6 −0.374291
\(615\) 0 0
\(616\) −2.72000e6 −0.288813
\(617\) 3.41607e6 0.361255 0.180627 0.983552i \(-0.442187\pi\)
0.180627 + 0.983552i \(0.442187\pi\)
\(618\) 0 0
\(619\) 9.43169e6 0.989379 0.494690 0.869070i \(-0.335282\pi\)
0.494690 + 0.869070i \(0.335282\pi\)
\(620\) 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 \(-0.578360\pi\)
−0.243696 + 0.969852i \(0.578360\pi\)
\(632\) 1.23827e6 0.123317
\(633\) 0 0
\(634\) −5.28295e6 −0.521980
\(635\) −3.59240e6 −0.353550
\(636\) 0 0
\(637\) −2.04372e6 −0.199559
\(638\) 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 \(-0.475094\pi\)
0.0781637 + 0.996941i \(0.475094\pi\)
\(644\) −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
\(650\) −1.98000e6 −0.183816
\(651\) 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 \(-0.851655\pi\)
−0.893355 + 0.449352i \(0.851655\pi\)
\(662\) 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
\(676\) 456976. 0.0384615
\(677\) −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 \(-0.581024\pi\)
−0.251803 + 0.967778i \(0.581024\pi\)
\(684\) 303264. 0.0247845
\(685\) 536004. 0.0436457
\(686\) −3.20552e6 −0.260069
\(687\) 0 0
\(688\) −1.51040e6 −0.121652
\(689\) −4.90877e6 −0.393935
\(690\) 0 0
\(691\) 1.57617e7 1.25577 0.627883 0.778308i \(-0.283922\pi\)
0.627883 + 0.778308i \(0.283922\pi\)
\(692\) −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 \(-0.295020\pi\)
0.600369 + 0.799723i \(0.295020\pi\)
\(710\) −2.83035e6 −0.210715
\(711\) 4.70156e6 0.348793
\(712\) −6.02688e6 −0.445546
\(713\) −1.36387e7 −1.00473
\(714\) 0 0
\(715\) −591500. −0.0432703
\(716\) −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 \(0.443323\pi\)
\(728\) −1.83872e6 −0.128584
\(729\) −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 \(-0.757290\pi\)
−0.723115 + 0.690728i \(0.757290\pi\)
\(734\) 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 \(-0.344935\pi\)
0.468109 + 0.883671i \(0.344935\pi\)
\(740\) −2.46086e6 −0.165199
\(741\) 0 0
\(742\) 1.97513e7 1.31700
\(743\) 1.23267e6 0.0819169 0.0409584 0.999161i \(-0.486959\pi\)
0.0409584 + 0.999161i \(0.486959\pi\)
\(744\) 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
\(754\) 1.74273e6 0.111635
\(755\) −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 \(-0.255889\pi\)
0.693905 + 0.720067i \(0.255889\pi\)
\(762\) 0 0
\(763\) 3.03657e7 1.88831
\(764\) 1.29949e7 0.805451
\(765\) 3.61292e6 0.223206
\(766\) −2.74903e6 −0.169281
\(767\) 2.35282e6 0.144411
\(768\) 0 0
\(769\) 1.08955e6 0.0664400 0.0332200 0.999448i \(-0.489424\pi\)
0.0332200 + 0.999448i \(0.489424\pi\)
\(770\) 2.38000e6 0.144661
\(771\) 0 0
\(772\) −2.40227e6 −0.145070
\(773\) 1.95219e6 0.117510 0.0587549 0.998272i \(-0.481287\pi\)
0.0587549 + 0.998272i \(0.481287\pi\)
\(774\) −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 \(-0.636535\pi\)
−0.415904 + 0.909408i \(0.636535\pi\)
\(788\) 3.78230e6 0.216991
\(789\) 0 0
\(790\) −1.08349e6 −0.0617670
\(791\) 4.16082e7 2.36449
\(792\) −3.88800e6 −0.220249
\(793\) 5.55706e6 0.313807
\(794\) 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
\(806\) −5.85010e6 −0.317195
\(807\) 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 \(-0.729772\pi\)
−0.660774 + 0.750585i \(0.729772\pi\)
\(812\) −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
\(819\) −6.98139e6 −0.363691
\(820\) −235200. −0.0122153
\(821\) −2.47470e6 −0.128134 −0.0640671 0.997946i \(-0.520407\pi\)
−0.0640671 + 0.997946i \(0.520407\pi\)
\(822\) 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 \(-0.695006\pi\)
−0.575020 + 0.818140i \(0.695006\pi\)
\(828\) −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
\(832\) −692224. −0.0346688
\(833\) 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 \(-0.819299\pi\)
−0.843147 + 0.537684i \(0.819299\pi\)
\(840\) 0 0
\(841\) −1.38651e7 −0.675977
\(842\) 2.13095e7 1.03584
\(843\) 0 0
\(844\) −6.57242e6 −0.317592
\(845\) −399854. −0.0192646
\(846\) −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 \(-0.317088\pi\)
0.543528 + 0.839391i \(0.317088\pi\)
\(854\) −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 \(-0.315592\pi\)
0.547466 + 0.836828i \(0.315592\pi\)
\(864\) 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
\(871\) 1.17567e7 0.525096
\(872\) 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 \(-0.540624\pi\)
−0.127278 + 0.991867i \(0.540624\pi\)
\(878\) −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 \(0.467450\pi\)
\(884\) −2.87165e6 −0.123595
\(885\) 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
\(910\) 1.60888e6 0.0644051
\(911\) −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
\(923\) 8.54160e6 0.330016
\(924\) 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 \(-0.269693\pi\)
0.662034 + 0.749473i \(0.269693\pi\)
\(930\) 0 0
\(931\) −943254. −0.0356660
\(932\) −9.79082e6 −0.369215
\(933\) 0 0
\(934\) 7.21918e6 0.270783
\(935\) 3.71700e6 0.139048
\(936\) −2.62829e6 −0.0980581
\(937\) 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 \(-0.811394\pi\)
−0.829534 + 0.558457i \(0.811394\pi\)
\(942\) 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 \(-0.317588\pi\)
0.542210 + 0.840243i \(0.317588\pi\)
\(948\) 0 0
\(949\) 7.90075e6 0.284776
\(950\) −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
\(962\) 7.42654e6 0.258731
\(963\) −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 \(-0.672685\pi\)
−0.516284 + 0.856417i \(0.672685\pi\)
\(968\) 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 \(-0.171531\pi\)
0.858284 + 0.513174i \(0.171531\pi\)
\(978\) 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 \(-0.402679\pi\)
0.301002 + 0.953624i \(0.402679\pi\)
\(984\) 0 0
\(985\) −3.30952e6 −0.108686
\(986\) −1.09513e7 −0.358736
\(987\) 0 0
\(988\) 210912. 0.00687399
\(989\) −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 26.6.a.a.1.1 1
3.2 odd 2 234.6.a.g.1.1 1
4.3 odd 2 208.6.a.b.1.1 1
5.2 odd 4 650.6.b.a.599.1 2
5.3 odd 4 650.6.b.a.599.2 2
5.4 even 2 650.6.a.a.1.1 1
8.3 odd 2 832.6.a.e.1.1 1
8.5 even 2 832.6.a.d.1.1 1
13.5 odd 4 338.6.b.a.337.2 2
13.8 odd 4 338.6.b.a.337.1 2
13.12 even 2 338.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
26.6.a.a.1.1 1 1.1 even 1 trivial
208.6.a.b.1.1 1 4.3 odd 2
234.6.a.g.1.1 1 3.2 odd 2
338.6.a.d.1.1 1 13.12 even 2
338.6.b.a.337.1 2 13.8 odd 4
338.6.b.a.337.2 2 13.5 odd 4
650.6.a.a.1.1 1 5.4 even 2
650.6.b.a.599.1 2 5.2 odd 4
650.6.b.a.599.2 2 5.3 odd 4
832.6.a.d.1.1 1 8.5 even 2
832.6.a.e.1.1 1 8.3 odd 2