Properties

Label 29.12.a.a.1.7
Level $29$
Weight $12$
Character 29.1
Self dual yes
Analytic conductor $22.282$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.2819522362\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} - 388180519304 x^{4} + 193065378004825 x^{3} + 1279291654973975 x^{2} - 65244901875230266 x - 758324542468966858\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(30.4581\) of defining polynomial
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q+27.4581 q^{2} -457.582 q^{3} -1294.05 q^{4} +9990.24 q^{5} -12564.3 q^{6} +28164.0 q^{7} -91766.4 q^{8} +32234.4 q^{9} +O(q^{10})\) \(q+27.4581 q^{2} -457.582 q^{3} -1294.05 q^{4} +9990.24 q^{5} -12564.3 q^{6} +28164.0 q^{7} -91766.4 q^{8} +32234.4 q^{9} +274313. q^{10} +820236. q^{11} +592135. q^{12} -2.01616e6 q^{13} +773331. q^{14} -4.57136e6 q^{15} +130485. q^{16} -4.16146e6 q^{17} +885095. q^{18} -1.10989e7 q^{19} -1.29279e7 q^{20} -1.28873e7 q^{21} +2.25221e7 q^{22} -5.64014e7 q^{23} +4.19907e7 q^{24} +5.09768e7 q^{25} -5.53600e7 q^{26} +6.63094e7 q^{27} -3.64457e7 q^{28} +2.05111e7 q^{29} -1.25521e8 q^{30} -2.38256e8 q^{31} +1.91521e8 q^{32} -3.75325e8 q^{33} -1.14266e8 q^{34} +2.81365e8 q^{35} -4.17130e7 q^{36} -2.44550e8 q^{37} -3.04756e8 q^{38} +9.22560e8 q^{39} -9.16769e8 q^{40} -4.55274e8 q^{41} -3.53862e8 q^{42} +1.01485e9 q^{43} -1.06143e9 q^{44} +3.22029e8 q^{45} -1.54867e9 q^{46} -1.80353e9 q^{47} -5.97074e7 q^{48} -1.18412e9 q^{49} +1.39973e9 q^{50} +1.90421e9 q^{51} +2.60902e9 q^{52} +4.71738e9 q^{53} +1.82073e9 q^{54} +8.19436e9 q^{55} -2.58451e9 q^{56} +5.07868e9 q^{57} +5.63197e8 q^{58} -4.22188e9 q^{59} +5.91557e9 q^{60} -2.28265e9 q^{61} -6.54205e9 q^{62} +9.07849e8 q^{63} +4.99156e9 q^{64} -2.01420e10 q^{65} -1.03057e10 q^{66} +1.31932e10 q^{67} +5.38514e9 q^{68} +2.58083e10 q^{69} +7.72576e9 q^{70} -2.42493e10 q^{71} -2.95803e9 q^{72} +2.85298e9 q^{73} -6.71487e9 q^{74} -2.33261e10 q^{75} +1.43626e10 q^{76} +2.31011e10 q^{77} +2.53318e10 q^{78} +3.05806e9 q^{79} +1.30357e9 q^{80} -3.60522e10 q^{81} -1.25010e10 q^{82} -6.23364e10 q^{83} +1.66769e10 q^{84} -4.15739e10 q^{85} +2.78658e10 q^{86} -9.38553e9 q^{87} -7.52702e10 q^{88} +8.45655e9 q^{89} +8.84232e9 q^{90} -5.67832e10 q^{91} +7.29863e10 q^{92} +1.09022e11 q^{93} -4.95215e10 q^{94} -1.10881e11 q^{95} -8.76364e10 q^{96} +6.21636e10 q^{97} -3.25136e10 q^{98} +2.64398e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} + O(q^{10}) \) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} - 685834q^{10} - 612246q^{11} + 2578538q^{12} + 1510364q^{13} + 3955400q^{14} - 2462818q^{15} + 3024818q^{16} - 3291098q^{17} - 27885614q^{18} - 44121388q^{19} - 49472662q^{20} - 46916800q^{21} - 43435618q^{22} - 88684076q^{23} - 224700678q^{24} - 44195521q^{25} - 324999762q^{26} - 236304286q^{27} - 391274848q^{28} + 225622639q^{29} - 494910382q^{30} - 292235934q^{31} - 632542514q^{32} - 1079766410q^{33} - 1113307936q^{34} - 1312820120q^{35} - 2236726492q^{36} - 1380429338q^{37} - 1222857284q^{38} - 1186931090q^{39} - 2713154106q^{40} - 1062067494q^{41} + 205598960q^{42} + 74588594q^{43} + 52891466q^{44} + 4527996830q^{45} - 87670324q^{46} - 1821239394q^{47} + 2666035542q^{48} + 4692522003q^{49} + 9494259926q^{50} + 8768158380q^{51} + 3266669866q^{52} + 7818635688q^{53} + 17402728558q^{54} - 191002682q^{55} + 11263587512q^{56} + 15495358340q^{57} - 656356768q^{58} + 1230002712q^{59} + 31834046430q^{60} - 18602654230q^{61} + 22075953162q^{62} - 9964531456q^{63} + 11813658086q^{64} + 32245789334q^{65} + 42677188354q^{66} + 27481284652q^{67} + 29588811820q^{68} - 20565315068q^{69} + 42862666712q^{70} - 20347168516q^{71} + 47061083616q^{72} - 57740010478q^{73} - 2640709564q^{74} - 23544691000q^{75} - 33350650772q^{76} + 871959792q^{77} - 15384525342q^{78} - 120245016462q^{79} - 84319695274q^{80} - 48880047865q^{81} - 111495532412q^{82} - 142463983824q^{83} - 134146226376q^{84} - 181628566552q^{85} + 47870165542q^{86} - 20141948318q^{87} - 180608014462q^{88} - 96700717270q^{89} - 25522461244q^{90} - 355162031176q^{91} - 22429477796q^{92} - 172582115142q^{93} + 172608565078q^{94} - 195922150708q^{95} + 226391047758q^{96} - 303190852014q^{97} - 123776497136q^{98} - 139125462440q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 27.4581 0.606744 0.303372 0.952872i \(-0.401887\pi\)
0.303372 + 0.952872i \(0.401887\pi\)
\(3\) −457.582 −1.08718 −0.543591 0.839350i \(-0.682936\pi\)
−0.543591 + 0.839350i \(0.682936\pi\)
\(4\) −1294.05 −0.631861
\(5\) 9990.24 1.42969 0.714844 0.699284i \(-0.246498\pi\)
0.714844 + 0.699284i \(0.246498\pi\)
\(6\) −12564.3 −0.659641
\(7\) 28164.0 0.633367 0.316683 0.948531i \(-0.397431\pi\)
0.316683 + 0.948531i \(0.397431\pi\)
\(8\) −91766.4 −0.990123
\(9\) 32234.4 0.181964
\(10\) 274313. 0.867455
\(11\) 820236. 1.53560 0.767802 0.640687i \(-0.221350\pi\)
0.767802 + 0.640687i \(0.221350\pi\)
\(12\) 592135. 0.686948
\(13\) −2.01616e6 −1.50604 −0.753021 0.657997i \(-0.771404\pi\)
−0.753021 + 0.657997i \(0.771404\pi\)
\(14\) 773331. 0.384292
\(15\) −4.57136e6 −1.55433
\(16\) 130485. 0.0311100
\(17\) −4.16146e6 −0.710847 −0.355424 0.934705i \(-0.615663\pi\)
−0.355424 + 0.934705i \(0.615663\pi\)
\(18\) 885095. 0.110406
\(19\) −1.10989e7 −1.02834 −0.514170 0.857688i \(-0.671900\pi\)
−0.514170 + 0.857688i \(0.671900\pi\)
\(20\) −1.29279e7 −0.903364
\(21\) −1.28873e7 −0.688585
\(22\) 2.25221e7 0.931719
\(23\) −5.64014e7 −1.82720 −0.913601 0.406612i \(-0.866710\pi\)
−0.913601 + 0.406612i \(0.866710\pi\)
\(24\) 4.19907e7 1.07644
\(25\) 5.09768e7 1.04401
\(26\) −5.53600e7 −0.913782
\(27\) 6.63094e7 0.889354
\(28\) −3.64457e7 −0.400200
\(29\) 2.05111e7 0.185695
\(30\) −1.25521e8 −0.943081
\(31\) −2.38256e8 −1.49470 −0.747350 0.664430i \(-0.768674\pi\)
−0.747350 + 0.664430i \(0.768674\pi\)
\(32\) 1.91521e8 1.00900
\(33\) −3.75325e8 −1.66948
\(34\) −1.14266e8 −0.431302
\(35\) 2.81365e8 0.905516
\(36\) −4.17130e7 −0.114976
\(37\) −2.44550e8 −0.579772 −0.289886 0.957061i \(-0.593617\pi\)
−0.289886 + 0.957061i \(0.593617\pi\)
\(38\) −3.04756e8 −0.623940
\(39\) 9.22560e8 1.63734
\(40\) −9.16769e8 −1.41557
\(41\) −4.55274e8 −0.613707 −0.306854 0.951757i \(-0.599276\pi\)
−0.306854 + 0.951757i \(0.599276\pi\)
\(42\) −3.53862e8 −0.417795
\(43\) 1.01485e9 1.05275 0.526374 0.850253i \(-0.323551\pi\)
0.526374 + 0.850253i \(0.323551\pi\)
\(44\) −1.06143e9 −0.970289
\(45\) 3.22029e8 0.260152
\(46\) −1.54867e9 −1.10864
\(47\) −1.80353e9 −1.14706 −0.573529 0.819185i \(-0.694426\pi\)
−0.573529 + 0.819185i \(0.694426\pi\)
\(48\) −5.97074e7 −0.0338222
\(49\) −1.18412e9 −0.598847
\(50\) 1.39973e9 0.633444
\(51\) 1.90421e9 0.772820
\(52\) 2.60902e9 0.951610
\(53\) 4.71738e9 1.54947 0.774735 0.632286i \(-0.217883\pi\)
0.774735 + 0.632286i \(0.217883\pi\)
\(54\) 1.82073e9 0.539610
\(55\) 8.19436e9 2.19543
\(56\) −2.58451e9 −0.627111
\(57\) 5.07868e9 1.11799
\(58\) 5.63197e8 0.112670
\(59\) −4.22188e9 −0.768812 −0.384406 0.923164i \(-0.625594\pi\)
−0.384406 + 0.923164i \(0.625594\pi\)
\(60\) 5.91557e9 0.982121
\(61\) −2.28265e9 −0.346039 −0.173020 0.984918i \(-0.555352\pi\)
−0.173020 + 0.984918i \(0.555352\pi\)
\(62\) −6.54205e9 −0.906901
\(63\) 9.07849e8 0.115250
\(64\) 4.99156e9 0.581094
\(65\) −2.01420e10 −2.15317
\(66\) −1.03057e10 −1.01295
\(67\) 1.31932e10 1.19382 0.596909 0.802309i \(-0.296395\pi\)
0.596909 + 0.802309i \(0.296395\pi\)
\(68\) 5.38514e9 0.449157
\(69\) 2.58083e10 1.98650
\(70\) 7.72576e9 0.549417
\(71\) −2.42493e10 −1.59506 −0.797532 0.603276i \(-0.793862\pi\)
−0.797532 + 0.603276i \(0.793862\pi\)
\(72\) −2.95803e9 −0.180167
\(73\) 2.85298e9 0.161073 0.0805365 0.996752i \(-0.474337\pi\)
0.0805365 + 0.996752i \(0.474337\pi\)
\(74\) −6.71487e9 −0.351774
\(75\) −2.33261e10 −1.13502
\(76\) 1.43626e10 0.649769
\(77\) 2.31011e10 0.972600
\(78\) 2.53318e10 0.993448
\(79\) 3.05806e9 0.111814 0.0559070 0.998436i \(-0.482195\pi\)
0.0559070 + 0.998436i \(0.482195\pi\)
\(80\) 1.30357e9 0.0444775
\(81\) −3.60522e10 −1.14885
\(82\) −1.25010e10 −0.372363
\(83\) −6.23364e10 −1.73705 −0.868525 0.495646i \(-0.834931\pi\)
−0.868525 + 0.495646i \(0.834931\pi\)
\(84\) 1.66769e10 0.435090
\(85\) −4.15739e10 −1.01629
\(86\) 2.78658e10 0.638749
\(87\) −9.38553e9 −0.201885
\(88\) −7.52702e10 −1.52044
\(89\) 8.45655e9 0.160527 0.0802635 0.996774i \(-0.474424\pi\)
0.0802635 + 0.996774i \(0.474424\pi\)
\(90\) 8.84232e9 0.157846
\(91\) −5.67832e10 −0.953877
\(92\) 7.29863e10 1.15454
\(93\) 1.09022e11 1.62501
\(94\) −4.95215e10 −0.695971
\(95\) −1.10881e11 −1.47021
\(96\) −8.76364e10 −1.09696
\(97\) 6.21636e10 0.735008 0.367504 0.930022i \(-0.380212\pi\)
0.367504 + 0.930022i \(0.380212\pi\)
\(98\) −3.25136e10 −0.363347
\(99\) 2.64398e10 0.279425
\(100\) −6.59666e10 −0.659666
\(101\) 8.08638e9 0.0765573 0.0382786 0.999267i \(-0.487813\pi\)
0.0382786 + 0.999267i \(0.487813\pi\)
\(102\) 5.22860e10 0.468904
\(103\) 1.33741e11 1.13674 0.568370 0.822773i \(-0.307574\pi\)
0.568370 + 0.822773i \(0.307574\pi\)
\(104\) 1.85016e11 1.49117
\(105\) −1.28748e11 −0.984461
\(106\) 1.29530e11 0.940133
\(107\) −6.78355e10 −0.467570 −0.233785 0.972288i \(-0.575111\pi\)
−0.233785 + 0.972288i \(0.575111\pi\)
\(108\) −8.58078e10 −0.561948
\(109\) 1.42660e11 0.888090 0.444045 0.896004i \(-0.353543\pi\)
0.444045 + 0.896004i \(0.353543\pi\)
\(110\) 2.25002e11 1.33207
\(111\) 1.11902e11 0.630318
\(112\) 3.67497e9 0.0197040
\(113\) −4.60648e10 −0.235200 −0.117600 0.993061i \(-0.537520\pi\)
−0.117600 + 0.993061i \(0.537520\pi\)
\(114\) 1.39451e11 0.678336
\(115\) −5.63463e11 −2.61233
\(116\) −2.65425e10 −0.117334
\(117\) −6.49897e10 −0.274045
\(118\) −1.15925e11 −0.466472
\(119\) −1.17203e11 −0.450227
\(120\) 4.19497e11 1.53898
\(121\) 3.87476e11 1.35808
\(122\) −6.26773e10 −0.209957
\(123\) 2.08325e11 0.667211
\(124\) 3.08315e11 0.944443
\(125\) 2.14660e10 0.0629137
\(126\) 2.49278e10 0.0699272
\(127\) −2.44240e11 −0.655990 −0.327995 0.944679i \(-0.606373\pi\)
−0.327995 + 0.944679i \(0.606373\pi\)
\(128\) −2.55175e11 −0.656423
\(129\) −4.64376e11 −1.14453
\(130\) −5.53060e11 −1.30642
\(131\) 6.47988e10 0.146749 0.0733744 0.997304i \(-0.476623\pi\)
0.0733744 + 0.997304i \(0.476623\pi\)
\(132\) 4.85691e11 1.05488
\(133\) −3.12591e11 −0.651317
\(134\) 3.62260e11 0.724343
\(135\) 6.62447e11 1.27150
\(136\) 3.81882e11 0.703826
\(137\) −2.29352e11 −0.406012 −0.203006 0.979177i \(-0.565071\pi\)
−0.203006 + 0.979177i \(0.565071\pi\)
\(138\) 7.08646e11 1.20530
\(139\) −2.93273e11 −0.479393 −0.239696 0.970848i \(-0.577048\pi\)
−0.239696 + 0.970848i \(0.577048\pi\)
\(140\) −3.64101e11 −0.572161
\(141\) 8.25263e11 1.24706
\(142\) −6.65840e11 −0.967796
\(143\) −1.65373e12 −2.31268
\(144\) 4.20609e9 0.00566089
\(145\) 2.04911e11 0.265486
\(146\) 7.83374e10 0.0977301
\(147\) 5.41830e11 0.651055
\(148\) 3.16460e11 0.366336
\(149\) 3.93354e11 0.438793 0.219396 0.975636i \(-0.429591\pi\)
0.219396 + 0.975636i \(0.429591\pi\)
\(150\) −6.40490e11 −0.688669
\(151\) −3.87179e11 −0.401364 −0.200682 0.979656i \(-0.564316\pi\)
−0.200682 + 0.979656i \(0.564316\pi\)
\(152\) 1.01851e12 1.01818
\(153\) −1.34142e11 −0.129349
\(154\) 6.34314e11 0.590120
\(155\) −2.38023e12 −2.13695
\(156\) −1.19384e12 −1.03457
\(157\) 1.94053e12 1.62357 0.811786 0.583955i \(-0.198496\pi\)
0.811786 + 0.583955i \(0.198496\pi\)
\(158\) 8.39684e10 0.0678425
\(159\) −2.15859e12 −1.68456
\(160\) 1.91334e12 1.44255
\(161\) −1.58849e12 −1.15729
\(162\) −9.89926e11 −0.697060
\(163\) −2.38982e12 −1.62680 −0.813399 0.581707i \(-0.802385\pi\)
−0.813399 + 0.581707i \(0.802385\pi\)
\(164\) 5.89148e11 0.387778
\(165\) −3.74959e12 −2.38683
\(166\) −1.71164e12 −1.05395
\(167\) 1.58906e12 0.946675 0.473337 0.880881i \(-0.343049\pi\)
0.473337 + 0.880881i \(0.343049\pi\)
\(168\) 1.18263e12 0.681783
\(169\) 2.27275e12 1.26816
\(170\) −1.14154e12 −0.616628
\(171\) −3.57768e11 −0.187121
\(172\) −1.31327e12 −0.665191
\(173\) 2.24583e12 1.10185 0.550926 0.834554i \(-0.314275\pi\)
0.550926 + 0.834554i \(0.314275\pi\)
\(174\) −2.57709e11 −0.122492
\(175\) 1.43571e12 0.661238
\(176\) 1.07028e11 0.0477726
\(177\) 1.93186e12 0.835838
\(178\) 2.32201e11 0.0973988
\(179\) 4.01047e12 1.63118 0.815592 0.578627i \(-0.196411\pi\)
0.815592 + 0.578627i \(0.196411\pi\)
\(180\) −4.16723e11 −0.164380
\(181\) 1.24801e12 0.477512 0.238756 0.971080i \(-0.423260\pi\)
0.238756 + 0.971080i \(0.423260\pi\)
\(182\) −1.55916e12 −0.578759
\(183\) 1.04450e12 0.376208
\(184\) 5.17575e12 1.80915
\(185\) −2.44311e12 −0.828893
\(186\) 2.99353e12 0.985966
\(187\) −3.41338e12 −1.09158
\(188\) 2.33386e12 0.724781
\(189\) 1.86754e12 0.563287
\(190\) −3.04459e12 −0.892039
\(191\) 2.13213e12 0.606917 0.303458 0.952845i \(-0.401859\pi\)
0.303458 + 0.952845i \(0.401859\pi\)
\(192\) −2.28405e12 −0.631755
\(193\) −4.63056e11 −0.124471 −0.0622355 0.998061i \(-0.519823\pi\)
−0.0622355 + 0.998061i \(0.519823\pi\)
\(194\) 1.70690e12 0.445962
\(195\) 9.21660e12 2.34089
\(196\) 1.53231e12 0.378388
\(197\) 4.04928e12 0.972330 0.486165 0.873867i \(-0.338395\pi\)
0.486165 + 0.873867i \(0.338395\pi\)
\(198\) 7.25987e11 0.169539
\(199\) 2.92500e11 0.0664407 0.0332204 0.999448i \(-0.489424\pi\)
0.0332204 + 0.999448i \(0.489424\pi\)
\(200\) −4.67796e12 −1.03369
\(201\) −6.03697e12 −1.29790
\(202\) 2.22037e11 0.0464507
\(203\) 5.77676e11 0.117613
\(204\) −2.46414e12 −0.488315
\(205\) −4.54829e12 −0.877410
\(206\) 3.67229e12 0.689710
\(207\) −1.81806e12 −0.332485
\(208\) −2.63078e11 −0.0468529
\(209\) −9.10376e12 −1.57912
\(210\) −3.53517e12 −0.597316
\(211\) −8.54356e11 −0.140632 −0.0703162 0.997525i \(-0.522401\pi\)
−0.0703162 + 0.997525i \(0.522401\pi\)
\(212\) −6.10453e12 −0.979051
\(213\) 1.10960e13 1.73412
\(214\) −1.86264e12 −0.283695
\(215\) 1.01386e13 1.50510
\(216\) −6.08498e12 −0.880569
\(217\) −6.71024e12 −0.946693
\(218\) 3.91718e12 0.538844
\(219\) −1.30547e12 −0.175116
\(220\) −1.06039e13 −1.38721
\(221\) 8.39017e12 1.07057
\(222\) 3.07261e12 0.382442
\(223\) 4.19005e12 0.508794 0.254397 0.967100i \(-0.418123\pi\)
0.254397 + 0.967100i \(0.418123\pi\)
\(224\) 5.39399e12 0.639066
\(225\) 1.64321e12 0.189971
\(226\) −1.26485e12 −0.142706
\(227\) −1.79772e12 −0.197961 −0.0989806 0.995089i \(-0.531558\pi\)
−0.0989806 + 0.995089i \(0.531558\pi\)
\(228\) −6.57207e12 −0.706416
\(229\) 5.90495e12 0.619614 0.309807 0.950800i \(-0.399736\pi\)
0.309807 + 0.950800i \(0.399736\pi\)
\(230\) −1.54716e13 −1.58501
\(231\) −1.05707e13 −1.05739
\(232\) −1.88224e12 −0.183861
\(233\) 1.96123e13 1.87099 0.935496 0.353337i \(-0.114953\pi\)
0.935496 + 0.353337i \(0.114953\pi\)
\(234\) −1.78450e12 −0.166276
\(235\) −1.80177e13 −1.63993
\(236\) 5.46334e12 0.485783
\(237\) −1.39931e12 −0.121562
\(238\) −3.21818e12 −0.273173
\(239\) −1.70534e13 −1.41456 −0.707280 0.706933i \(-0.750078\pi\)
−0.707280 + 0.706933i \(0.750078\pi\)
\(240\) −5.96492e11 −0.0483551
\(241\) −1.68533e13 −1.33534 −0.667668 0.744459i \(-0.732707\pi\)
−0.667668 + 0.744459i \(0.732707\pi\)
\(242\) 1.06394e13 0.824007
\(243\) 4.75034e12 0.359658
\(244\) 2.95387e12 0.218649
\(245\) −1.18296e13 −0.856163
\(246\) 5.72021e12 0.404827
\(247\) 2.23773e13 1.54872
\(248\) 2.18639e13 1.47994
\(249\) 2.85240e13 1.88849
\(250\) 5.89415e11 0.0381726
\(251\) −1.41324e13 −0.895383 −0.447692 0.894188i \(-0.647754\pi\)
−0.447692 + 0.894188i \(0.647754\pi\)
\(252\) −1.17480e12 −0.0728220
\(253\) −4.62624e13 −2.80586
\(254\) −6.70638e12 −0.398018
\(255\) 1.90235e13 1.10489
\(256\) −1.72293e13 −0.979375
\(257\) 2.09702e13 1.16673 0.583364 0.812211i \(-0.301736\pi\)
0.583364 + 0.812211i \(0.301736\pi\)
\(258\) −1.27509e13 −0.694436
\(259\) −6.88750e12 −0.367209
\(260\) 2.60647e13 1.36050
\(261\) 6.61164e11 0.0337899
\(262\) 1.77925e12 0.0890390
\(263\) −3.33053e13 −1.63214 −0.816070 0.577953i \(-0.803852\pi\)
−0.816070 + 0.577953i \(0.803852\pi\)
\(264\) 3.44423e13 1.65299
\(265\) 4.71277e13 2.21526
\(266\) −8.58315e12 −0.395183
\(267\) −3.86956e12 −0.174522
\(268\) −1.70727e13 −0.754328
\(269\) −1.52686e13 −0.660938 −0.330469 0.943817i \(-0.607207\pi\)
−0.330469 + 0.943817i \(0.607207\pi\)
\(270\) 1.81896e13 0.771474
\(271\) −1.62843e13 −0.676766 −0.338383 0.941009i \(-0.609880\pi\)
−0.338383 + 0.941009i \(0.609880\pi\)
\(272\) −5.43006e11 −0.0221144
\(273\) 2.59830e13 1.03704
\(274\) −6.29757e12 −0.246346
\(275\) 4.18130e13 1.60318
\(276\) −3.33972e13 −1.25519
\(277\) 7.21098e12 0.265678 0.132839 0.991138i \(-0.457591\pi\)
0.132839 + 0.991138i \(0.457591\pi\)
\(278\) −8.05274e12 −0.290869
\(279\) −7.68003e12 −0.271982
\(280\) −2.58199e13 −0.896572
\(281\) −2.36856e12 −0.0806490 −0.0403245 0.999187i \(-0.512839\pi\)
−0.0403245 + 0.999187i \(0.512839\pi\)
\(282\) 2.26602e13 0.756647
\(283\) 1.01047e13 0.330902 0.165451 0.986218i \(-0.447092\pi\)
0.165451 + 0.986218i \(0.447092\pi\)
\(284\) 3.13798e13 1.00786
\(285\) 5.07372e13 1.59838
\(286\) −4.54083e13 −1.40321
\(287\) −1.28223e13 −0.388702
\(288\) 6.17355e12 0.183601
\(289\) −1.69542e13 −0.494696
\(290\) 5.62648e12 0.161082
\(291\) −2.84450e13 −0.799087
\(292\) −3.69190e12 −0.101776
\(293\) −4.22814e12 −0.114387 −0.0571936 0.998363i \(-0.518215\pi\)
−0.0571936 + 0.998363i \(0.518215\pi\)
\(294\) 1.48776e13 0.395024
\(295\) −4.21776e13 −1.09916
\(296\) 2.24415e13 0.574046
\(297\) 5.43894e13 1.36570
\(298\) 1.08008e13 0.266235
\(299\) 1.13714e14 2.75184
\(300\) 3.01852e13 0.717177
\(301\) 2.85822e13 0.666775
\(302\) −1.06312e13 −0.243525
\(303\) −3.70018e12 −0.0832317
\(304\) −1.44824e12 −0.0319916
\(305\) −2.28042e13 −0.494728
\(306\) −3.68328e12 −0.0784815
\(307\) 4.10121e13 0.858323 0.429162 0.903228i \(-0.358809\pi\)
0.429162 + 0.903228i \(0.358809\pi\)
\(308\) −2.98941e13 −0.614549
\(309\) −6.11976e13 −1.23584
\(310\) −6.53567e13 −1.29658
\(311\) −9.97319e13 −1.94380 −0.971900 0.235393i \(-0.924362\pi\)
−0.971900 + 0.235393i \(0.924362\pi\)
\(312\) −8.46600e13 −1.62117
\(313\) −5.66854e13 −1.06654 −0.533270 0.845945i \(-0.679037\pi\)
−0.533270 + 0.845945i \(0.679037\pi\)
\(314\) 5.32832e13 0.985093
\(315\) 9.06963e12 0.164771
\(316\) −3.95728e12 −0.0706510
\(317\) 2.09336e13 0.367297 0.183649 0.982992i \(-0.441209\pi\)
0.183649 + 0.982992i \(0.441209\pi\)
\(318\) −5.92708e13 −1.02210
\(319\) 1.68240e13 0.285155
\(320\) 4.98669e13 0.830783
\(321\) 3.10403e13 0.508333
\(322\) −4.36169e13 −0.702178
\(323\) 4.61878e13 0.730993
\(324\) 4.66535e13 0.725916
\(325\) −1.02778e14 −1.57232
\(326\) −6.56200e13 −0.987050
\(327\) −6.52788e13 −0.965515
\(328\) 4.17788e13 0.607646
\(329\) −5.07946e13 −0.726508
\(330\) −1.02957e14 −1.44820
\(331\) 7.24918e13 1.00285 0.501424 0.865202i \(-0.332810\pi\)
0.501424 + 0.865202i \(0.332810\pi\)
\(332\) 8.06665e13 1.09757
\(333\) −7.88290e12 −0.105498
\(334\) 4.36327e13 0.574390
\(335\) 1.31803e14 1.70679
\(336\) −1.68160e12 −0.0214218
\(337\) −1.03678e14 −1.29934 −0.649670 0.760217i \(-0.725093\pi\)
−0.649670 + 0.760217i \(0.725093\pi\)
\(338\) 6.24054e13 0.769450
\(339\) 2.10784e13 0.255705
\(340\) 5.37988e13 0.642154
\(341\) −1.95426e14 −2.29527
\(342\) −9.82362e12 −0.113535
\(343\) −8.90389e13 −1.01266
\(344\) −9.31290e13 −1.04235
\(345\) 2.57831e14 2.84007
\(346\) 6.16663e13 0.668543
\(347\) 1.05495e14 1.12569 0.562844 0.826563i \(-0.309707\pi\)
0.562844 + 0.826563i \(0.309707\pi\)
\(348\) 1.21454e13 0.127563
\(349\) −6.55800e13 −0.678003 −0.339001 0.940786i \(-0.610089\pi\)
−0.339001 + 0.940786i \(0.610089\pi\)
\(350\) 3.94219e13 0.401203
\(351\) −1.33691e14 −1.33940
\(352\) 1.57092e14 1.54942
\(353\) −2.34111e13 −0.227332 −0.113666 0.993519i \(-0.536259\pi\)
−0.113666 + 0.993519i \(0.536259\pi\)
\(354\) 5.30452e13 0.507140
\(355\) −2.42256e14 −2.28044
\(356\) −1.09432e13 −0.101431
\(357\) 5.36301e13 0.489478
\(358\) 1.10120e14 0.989712
\(359\) −7.84584e13 −0.694416 −0.347208 0.937788i \(-0.612870\pi\)
−0.347208 + 0.937788i \(0.612870\pi\)
\(360\) −2.95515e13 −0.257582
\(361\) 6.69634e12 0.0574841
\(362\) 3.42679e13 0.289728
\(363\) −1.77302e14 −1.47648
\(364\) 7.34804e13 0.602718
\(365\) 2.85019e13 0.230284
\(366\) 2.86800e13 0.228262
\(367\) −1.84739e13 −0.144842 −0.0724212 0.997374i \(-0.523073\pi\)
−0.0724212 + 0.997374i \(0.523073\pi\)
\(368\) −7.35951e12 −0.0568441
\(369\) −1.46755e13 −0.111673
\(370\) −6.70832e13 −0.502926
\(371\) 1.32860e14 0.981383
\(372\) −1.41080e14 −1.02678
\(373\) −1.14087e14 −0.818158 −0.409079 0.912499i \(-0.634150\pi\)
−0.409079 + 0.912499i \(0.634150\pi\)
\(374\) −9.37249e13 −0.662310
\(375\) −9.82245e12 −0.0683987
\(376\) 1.65504e14 1.13573
\(377\) −4.13538e13 −0.279665
\(378\) 5.12791e13 0.341771
\(379\) −1.39087e14 −0.913630 −0.456815 0.889562i \(-0.651010\pi\)
−0.456815 + 0.889562i \(0.651010\pi\)
\(380\) 1.43486e14 0.928966
\(381\) 1.11760e14 0.713180
\(382\) 5.85441e13 0.368243
\(383\) 1.07589e14 0.667078 0.333539 0.942736i \(-0.391757\pi\)
0.333539 + 0.942736i \(0.391757\pi\)
\(384\) 1.16764e14 0.713651
\(385\) 2.30786e14 1.39051
\(386\) −1.27146e13 −0.0755221
\(387\) 3.27130e13 0.191562
\(388\) −8.04430e13 −0.464423
\(389\) 1.72334e14 0.980953 0.490476 0.871454i \(-0.336823\pi\)
0.490476 + 0.871454i \(0.336823\pi\)
\(390\) 2.53070e14 1.42032
\(391\) 2.34712e14 1.29886
\(392\) 1.08662e14 0.592932
\(393\) −2.96508e13 −0.159543
\(394\) 1.11186e14 0.589956
\(395\) 3.05507e13 0.159859
\(396\) −3.42145e13 −0.176558
\(397\) −8.40997e13 −0.428003 −0.214002 0.976833i \(-0.568650\pi\)
−0.214002 + 0.976833i \(0.568650\pi\)
\(398\) 8.03151e12 0.0403125
\(399\) 1.43036e14 0.708099
\(400\) 6.65169e12 0.0324790
\(401\) 1.63151e13 0.0785768 0.0392884 0.999228i \(-0.487491\pi\)
0.0392884 + 0.999228i \(0.487491\pi\)
\(402\) −1.65764e14 −0.787492
\(403\) 4.80362e14 2.25108
\(404\) −1.04642e13 −0.0483736
\(405\) −3.60170e14 −1.64250
\(406\) 1.58619e13 0.0713612
\(407\) −2.00588e14 −0.890301
\(408\) −1.74742e14 −0.765187
\(409\) −9.98435e13 −0.431362 −0.215681 0.976464i \(-0.569197\pi\)
−0.215681 + 0.976464i \(0.569197\pi\)
\(410\) −1.24888e14 −0.532363
\(411\) 1.04947e14 0.441409
\(412\) −1.73068e14 −0.718262
\(413\) −1.18905e14 −0.486940
\(414\) −4.99206e13 −0.201733
\(415\) −6.22756e14 −2.48344
\(416\) −3.86137e14 −1.51959
\(417\) 1.34197e14 0.521187
\(418\) −2.49972e14 −0.958124
\(419\) −2.11256e14 −0.799157 −0.399578 0.916699i \(-0.630843\pi\)
−0.399578 + 0.916699i \(0.630843\pi\)
\(420\) 1.66606e14 0.622043
\(421\) 1.98202e14 0.730394 0.365197 0.930930i \(-0.381002\pi\)
0.365197 + 0.930930i \(0.381002\pi\)
\(422\) −2.34590e13 −0.0853279
\(423\) −5.81357e13 −0.208723
\(424\) −4.32897e14 −1.53417
\(425\) −2.12138e14 −0.742128
\(426\) 3.04676e14 1.05217
\(427\) −6.42886e13 −0.219170
\(428\) 8.77827e13 0.295439
\(429\) 7.56717e14 2.51431
\(430\) 2.78386e14 0.913211
\(431\) −1.18759e14 −0.384627 −0.192314 0.981333i \(-0.561599\pi\)
−0.192314 + 0.981333i \(0.561599\pi\)
\(432\) 8.65236e12 0.0276678
\(433\) −3.54607e14 −1.11960 −0.559801 0.828627i \(-0.689122\pi\)
−0.559801 + 0.828627i \(0.689122\pi\)
\(434\) −1.84250e14 −0.574401
\(435\) −9.37638e13 −0.288632
\(436\) −1.84610e14 −0.561150
\(437\) 6.25996e14 1.87899
\(438\) −3.58458e13 −0.106250
\(439\) 1.85936e14 0.544262 0.272131 0.962260i \(-0.412272\pi\)
0.272131 + 0.962260i \(0.412272\pi\)
\(440\) −7.51967e14 −2.17375
\(441\) −3.81692e13 −0.108969
\(442\) 2.30378e14 0.649560
\(443\) −5.43269e14 −1.51284 −0.756422 0.654084i \(-0.773054\pi\)
−0.756422 + 0.654084i \(0.773054\pi\)
\(444\) −1.44806e14 −0.398273
\(445\) 8.44829e13 0.229503
\(446\) 1.15051e14 0.308708
\(447\) −1.79992e14 −0.477048
\(448\) 1.40582e14 0.368046
\(449\) 1.39738e14 0.361375 0.180688 0.983541i \(-0.442168\pi\)
0.180688 + 0.983541i \(0.442168\pi\)
\(450\) 4.51193e13 0.115264
\(451\) −3.73432e14 −0.942412
\(452\) 5.96102e13 0.148614
\(453\) 1.77166e14 0.436355
\(454\) −4.93620e13 −0.120112
\(455\) −5.67278e14 −1.36375
\(456\) −4.66052e14 −1.10695
\(457\) 2.73468e14 0.641752 0.320876 0.947121i \(-0.396023\pi\)
0.320876 + 0.947121i \(0.396023\pi\)
\(458\) 1.62139e14 0.375947
\(459\) −2.75944e14 −0.632195
\(460\) 7.29151e14 1.65063
\(461\) 2.67401e14 0.598148 0.299074 0.954230i \(-0.403322\pi\)
0.299074 + 0.954230i \(0.403322\pi\)
\(462\) −2.90251e14 −0.641567
\(463\) 5.18177e14 1.13183 0.565917 0.824462i \(-0.308522\pi\)
0.565917 + 0.824462i \(0.308522\pi\)
\(464\) 2.67639e12 0.00577697
\(465\) 1.08915e15 2.32326
\(466\) 5.38518e14 1.13521
\(467\) 2.97457e14 0.619700 0.309850 0.950785i \(-0.399721\pi\)
0.309850 + 0.950785i \(0.399721\pi\)
\(468\) 8.41001e13 0.173159
\(469\) 3.71573e14 0.756125
\(470\) −4.94732e14 −0.995020
\(471\) −8.87950e14 −1.76512
\(472\) 3.87427e14 0.761218
\(473\) 8.32415e14 1.61660
\(474\) −3.84225e13 −0.0737572
\(475\) −5.65789e14 −1.07359
\(476\) 1.51667e14 0.284481
\(477\) 1.52062e14 0.281948
\(478\) −4.68253e14 −0.858277
\(479\) 2.72110e13 0.0493060 0.0246530 0.999696i \(-0.492152\pi\)
0.0246530 + 0.999696i \(0.492152\pi\)
\(480\) −8.75509e14 −1.56832
\(481\) 4.93052e14 0.873162
\(482\) −4.62759e14 −0.810207
\(483\) 7.26864e14 1.25818
\(484\) −5.01414e14 −0.858118
\(485\) 6.21030e14 1.05083
\(486\) 1.30435e14 0.218221
\(487\) −4.35591e14 −0.720560 −0.360280 0.932844i \(-0.617319\pi\)
−0.360280 + 0.932844i \(0.617319\pi\)
\(488\) 2.09471e14 0.342621
\(489\) 1.09354e15 1.76862
\(490\) −3.24819e14 −0.519472
\(491\) 2.56952e14 0.406354 0.203177 0.979142i \(-0.434873\pi\)
0.203177 + 0.979142i \(0.434873\pi\)
\(492\) −2.69583e14 −0.421585
\(493\) −8.53562e13 −0.132001
\(494\) 6.14438e14 0.939679
\(495\) 2.64140e14 0.399490
\(496\) −3.10887e13 −0.0465000
\(497\) −6.82957e14 −1.01026
\(498\) 7.83216e14 1.14583
\(499\) 1.66560e14 0.241000 0.120500 0.992713i \(-0.461550\pi\)
0.120500 + 0.992713i \(0.461550\pi\)
\(500\) −2.77781e13 −0.0397528
\(501\) −7.27127e14 −1.02921
\(502\) −3.88048e14 −0.543269
\(503\) −4.75170e14 −0.657998 −0.328999 0.944330i \(-0.606711\pi\)
−0.328999 + 0.944330i \(0.606711\pi\)
\(504\) −8.33101e13 −0.114112
\(505\) 8.07849e13 0.109453
\(506\) −1.27028e15 −1.70244
\(507\) −1.03997e15 −1.37872
\(508\) 3.16060e14 0.414495
\(509\) 2.49704e14 0.323950 0.161975 0.986795i \(-0.448214\pi\)
0.161975 + 0.986795i \(0.448214\pi\)
\(510\) 5.22349e14 0.670386
\(511\) 8.03513e13 0.102018
\(512\) 4.95135e13 0.0621926
\(513\) −7.35965e14 −0.914558
\(514\) 5.75802e14 0.707906
\(515\) 1.33611e15 1.62518
\(516\) 6.00927e14 0.723183
\(517\) −1.47932e15 −1.76143
\(518\) −1.89118e14 −0.222802
\(519\) −1.02765e15 −1.19791
\(520\) 1.84836e15 2.13190
\(521\) 5.63704e14 0.643344 0.321672 0.946851i \(-0.395755\pi\)
0.321672 + 0.946851i \(0.395755\pi\)
\(522\) 1.81543e13 0.0205018
\(523\) 3.19146e14 0.356640 0.178320 0.983973i \(-0.442934\pi\)
0.178320 + 0.983973i \(0.442934\pi\)
\(524\) −8.38530e13 −0.0927249
\(525\) −6.56956e14 −0.718886
\(526\) −9.14502e14 −0.990292
\(527\) 9.91491e14 1.06250
\(528\) −4.89742e13 −0.0519375
\(529\) 2.22830e15 2.33867
\(530\) 1.29404e15 1.34410
\(531\) −1.36090e14 −0.139896
\(532\) 4.04509e14 0.411542
\(533\) 9.17906e14 0.924269
\(534\) −1.06251e14 −0.105890
\(535\) −6.77693e14 −0.668478
\(536\) −1.21069e15 −1.18203
\(537\) −1.83512e15 −1.77339
\(538\) −4.19246e14 −0.401021
\(539\) −9.71255e14 −0.919591
\(540\) −8.57241e14 −0.803410
\(541\) 6.42697e14 0.596240 0.298120 0.954528i \(-0.403640\pi\)
0.298120 + 0.954528i \(0.403640\pi\)
\(542\) −4.47137e14 −0.410624
\(543\) −5.71065e14 −0.519142
\(544\) −7.97004e14 −0.717244
\(545\) 1.42521e15 1.26969
\(546\) 7.13444e14 0.629217
\(547\) 8.80101e14 0.768426 0.384213 0.923244i \(-0.374473\pi\)
0.384213 + 0.923244i \(0.374473\pi\)
\(548\) 2.96793e14 0.256543
\(549\) −7.35798e13 −0.0629667
\(550\) 1.14811e15 0.972720
\(551\) −2.27652e14 −0.190958
\(552\) −2.36833e15 −1.96688
\(553\) 8.61271e13 0.0708193
\(554\) 1.98000e14 0.161199
\(555\) 1.11792e15 0.901157
\(556\) 3.79511e14 0.302910
\(557\) −1.66295e15 −1.31424 −0.657122 0.753784i \(-0.728227\pi\)
−0.657122 + 0.753784i \(0.728227\pi\)
\(558\) −2.10879e14 −0.165023
\(559\) −2.04610e15 −1.58548
\(560\) 3.67138e13 0.0281706
\(561\) 1.56190e15 1.18675
\(562\) −6.50361e13 −0.0489334
\(563\) −2.59049e15 −1.93012 −0.965062 0.262023i \(-0.915610\pi\)
−0.965062 + 0.262023i \(0.915610\pi\)
\(564\) −1.06793e15 −0.787969
\(565\) −4.60198e14 −0.336263
\(566\) 2.77457e14 0.200773
\(567\) −1.01538e15 −0.727645
\(568\) 2.22527e15 1.57931
\(569\) −1.52748e15 −1.07364 −0.536820 0.843697i \(-0.680375\pi\)
−0.536820 + 0.843697i \(0.680375\pi\)
\(570\) 1.39315e15 0.969808
\(571\) 1.46536e15 1.01029 0.505145 0.863035i \(-0.331439\pi\)
0.505145 + 0.863035i \(0.331439\pi\)
\(572\) 2.14001e15 1.46130
\(573\) −9.75622e14 −0.659829
\(574\) −3.52077e14 −0.235843
\(575\) −2.87516e15 −1.90761
\(576\) 1.60900e14 0.105738
\(577\) −4.85756e14 −0.316192 −0.158096 0.987424i \(-0.550536\pi\)
−0.158096 + 0.987424i \(0.550536\pi\)
\(578\) −4.65530e14 −0.300154
\(579\) 2.11886e14 0.135323
\(580\) −2.65166e14 −0.167750
\(581\) −1.75564e15 −1.10019
\(582\) −7.81045e14 −0.484841
\(583\) 3.86936e15 2.37937
\(584\) −2.61808e14 −0.159482
\(585\) −6.49263e14 −0.391799
\(586\) −1.16097e14 −0.0694038
\(587\) −2.96859e15 −1.75809 −0.879045 0.476739i \(-0.841819\pi\)
−0.879045 + 0.476739i \(0.841819\pi\)
\(588\) −7.01156e14 −0.411377
\(589\) 2.64439e15 1.53706
\(590\) −1.15812e15 −0.666910
\(591\) −1.85288e15 −1.05710
\(592\) −3.19100e13 −0.0180367
\(593\) 1.54519e15 0.865331 0.432665 0.901555i \(-0.357573\pi\)
0.432665 + 0.901555i \(0.357573\pi\)
\(594\) 1.49343e15 0.828628
\(595\) −1.17089e15 −0.643684
\(596\) −5.09021e14 −0.277256
\(597\) −1.33843e14 −0.0722332
\(598\) 3.12238e15 1.66966
\(599\) −2.08623e13 −0.0110539 −0.00552694 0.999985i \(-0.501759\pi\)
−0.00552694 + 0.999985i \(0.501759\pi\)
\(600\) 2.14055e15 1.12381
\(601\) −1.73470e15 −0.902434 −0.451217 0.892414i \(-0.649010\pi\)
−0.451217 + 0.892414i \(0.649010\pi\)
\(602\) 7.84813e14 0.404562
\(603\) 4.25274e14 0.217232
\(604\) 5.01029e14 0.253606
\(605\) 3.87098e15 1.94163
\(606\) −1.01600e14 −0.0505003
\(607\) 2.55839e14 0.126017 0.0630085 0.998013i \(-0.479930\pi\)
0.0630085 + 0.998013i \(0.479930\pi\)
\(608\) −2.12568e15 −1.03759
\(609\) −2.64334e14 −0.127867
\(610\) −6.26161e14 −0.300173
\(611\) 3.63621e15 1.72752
\(612\) 1.73587e14 0.0817304
\(613\) 3.22844e15 1.50647 0.753235 0.657751i \(-0.228492\pi\)
0.753235 + 0.657751i \(0.228492\pi\)
\(614\) 1.12611e15 0.520783
\(615\) 2.08122e15 0.953904
\(616\) −2.11991e15 −0.962994
\(617\) 3.85111e15 1.73387 0.866937 0.498417i \(-0.166085\pi\)
0.866937 + 0.498417i \(0.166085\pi\)
\(618\) −1.68037e15 −0.749840
\(619\) −3.57668e15 −1.58191 −0.790954 0.611876i \(-0.790415\pi\)
−0.790954 + 0.611876i \(0.790415\pi\)
\(620\) 3.08014e15 1.35026
\(621\) −3.73994e15 −1.62503
\(622\) −2.73845e15 −1.17939
\(623\) 2.38170e14 0.101672
\(624\) 1.20380e14 0.0509376
\(625\) −2.27465e15 −0.954058
\(626\) −1.55647e15 −0.647117
\(627\) 4.16572e15 1.71679
\(628\) −2.51114e15 −1.02587
\(629\) 1.01768e15 0.412130
\(630\) 2.49035e14 0.0999741
\(631\) 2.99953e15 1.19369 0.596845 0.802357i \(-0.296421\pi\)
0.596845 + 0.802357i \(0.296421\pi\)
\(632\) −2.80627e14 −0.110710
\(633\) 3.90938e14 0.152893
\(634\) 5.74797e14 0.222856
\(635\) −2.44002e15 −0.937860
\(636\) 2.79332e15 1.06441
\(637\) 2.38737e15 0.901888
\(638\) 4.61955e14 0.173016
\(639\) −7.81661e14 −0.290244
\(640\) −2.54926e15 −0.938479
\(641\) −1.92000e15 −0.700779 −0.350390 0.936604i \(-0.613951\pi\)
−0.350390 + 0.936604i \(0.613951\pi\)
\(642\) 8.52308e14 0.308428
\(643\) −6.57468e14 −0.235893 −0.117946 0.993020i \(-0.537631\pi\)
−0.117946 + 0.993020i \(0.537631\pi\)
\(644\) 2.05559e15 0.731246
\(645\) −4.63923e15 −1.63632
\(646\) 1.26823e15 0.443526
\(647\) 3.89397e15 1.35026 0.675132 0.737697i \(-0.264087\pi\)
0.675132 + 0.737697i \(0.264087\pi\)
\(648\) 3.30838e15 1.13751
\(649\) −3.46294e15 −1.18059
\(650\) −2.82208e15 −0.953994
\(651\) 3.07048e15 1.02923
\(652\) 3.09255e15 1.02791
\(653\) 1.13595e15 0.374400 0.187200 0.982322i \(-0.440059\pi\)
0.187200 + 0.982322i \(0.440059\pi\)
\(654\) −1.79243e15 −0.585821
\(655\) 6.47356e14 0.209805
\(656\) −5.94062e13 −0.0190924
\(657\) 9.19640e13 0.0293095
\(658\) −1.39473e15 −0.440805
\(659\) 1.83420e15 0.574881 0.287440 0.957799i \(-0.407196\pi\)
0.287440 + 0.957799i \(0.407196\pi\)
\(660\) 4.85217e15 1.50815
\(661\) −6.16892e15 −1.90152 −0.950761 0.309925i \(-0.899696\pi\)
−0.950761 + 0.309925i \(0.899696\pi\)
\(662\) 1.99049e15 0.608472
\(663\) −3.83919e15 −1.16390
\(664\) 5.72039e15 1.71989
\(665\) −3.12286e15 −0.931179
\(666\) −2.16450e14 −0.0640101
\(667\) −1.15686e15 −0.339303
\(668\) −2.05633e15 −0.598167
\(669\) −1.91729e15 −0.553152
\(670\) 3.61907e15 1.03558
\(671\) −1.87231e15 −0.531379
\(672\) −2.46819e15 −0.694781
\(673\) 4.64828e15 1.29780 0.648902 0.760872i \(-0.275228\pi\)
0.648902 + 0.760872i \(0.275228\pi\)
\(674\) −2.84680e15 −0.788367
\(675\) 3.38024e15 0.928490
\(676\) −2.94106e15 −0.801303
\(677\) −4.11808e15 −1.11290 −0.556451 0.830881i \(-0.687837\pi\)
−0.556451 + 0.830881i \(0.687837\pi\)
\(678\) 5.78774e14 0.155148
\(679\) 1.75078e15 0.465529
\(680\) 3.81509e15 1.00625
\(681\) 8.22605e14 0.215220
\(682\) −5.36603e15 −1.39264
\(683\) −1.25755e14 −0.0323751 −0.0161876 0.999869i \(-0.505153\pi\)
−0.0161876 + 0.999869i \(0.505153\pi\)
\(684\) 4.62970e14 0.118234
\(685\) −2.29128e15 −0.580470
\(686\) −2.44484e15 −0.614423
\(687\) −2.70200e15 −0.673632
\(688\) 1.32422e14 0.0327509
\(689\) −9.51100e15 −2.33357
\(690\) 7.07954e15 1.72320
\(691\) −7.66811e14 −0.185165 −0.0925825 0.995705i \(-0.529512\pi\)
−0.0925825 + 0.995705i \(0.529512\pi\)
\(692\) −2.90622e15 −0.696218
\(693\) 7.44651e14 0.176978
\(694\) 2.89668e15 0.683005
\(695\) −2.92987e15 −0.685382
\(696\) 8.61277e14 0.199890
\(697\) 1.89460e15 0.436252
\(698\) −1.80070e15 −0.411374
\(699\) −8.97426e15 −2.03411
\(700\) −1.85789e15 −0.417811
\(701\) 1.21260e15 0.270563 0.135281 0.990807i \(-0.456806\pi\)
0.135281 + 0.990807i \(0.456806\pi\)
\(702\) −3.67089e15 −0.812676
\(703\) 2.71424e15 0.596203
\(704\) 4.09426e15 0.892331
\(705\) 8.24458e15 1.78291
\(706\) −6.42825e14 −0.137933
\(707\) 2.27745e14 0.0484888
\(708\) −2.49993e15 −0.528134
\(709\) −3.37885e15 −0.708296 −0.354148 0.935189i \(-0.615229\pi\)
−0.354148 + 0.935189i \(0.615229\pi\)
\(710\) −6.65190e15 −1.38365
\(711\) 9.85745e13 0.0203461
\(712\) −7.76027e14 −0.158941
\(713\) 1.34379e16 2.73112
\(714\) 1.47258e15 0.296988
\(715\) −1.65212e16 −3.30641
\(716\) −5.18975e15 −1.03068
\(717\) 7.80331e15 1.53788
\(718\) −2.15432e15 −0.421333
\(719\) −1.75792e15 −0.341185 −0.170592 0.985342i \(-0.554568\pi\)
−0.170592 + 0.985342i \(0.554568\pi\)
\(720\) 4.20199e13 0.00809330
\(721\) 3.76669e15 0.719973
\(722\) 1.83869e14 0.0348781
\(723\) 7.71175e15 1.45175
\(724\) −1.61498e15 −0.301721
\(725\) 1.04559e15 0.193867
\(726\) −4.86838e15 −0.895846
\(727\) 2.56923e15 0.469205 0.234603 0.972091i \(-0.424621\pi\)
0.234603 + 0.972091i \(0.424621\pi\)
\(728\) 5.21079e15 0.944455
\(729\) 4.21287e15 0.757839
\(730\) 7.82610e14 0.139723
\(731\) −4.22324e15 −0.748343
\(732\) −1.35164e15 −0.237711
\(733\) 7.65401e15 1.33603 0.668017 0.744146i \(-0.267143\pi\)
0.668017 + 0.744146i \(0.267143\pi\)
\(734\) −5.07259e14 −0.0878824
\(735\) 5.41301e15 0.930805
\(736\) −1.08020e16 −1.84364
\(737\) 1.08215e16 1.83323
\(738\) −4.02961e14 −0.0677568
\(739\) −1.10369e16 −1.84206 −0.921031 0.389490i \(-0.872651\pi\)
−0.921031 + 0.389490i \(0.872651\pi\)
\(740\) 3.16151e15 0.523745
\(741\) −1.02394e16 −1.68374
\(742\) 3.64809e15 0.595449
\(743\) 7.30257e15 1.18314 0.591572 0.806253i \(-0.298508\pi\)
0.591572 + 0.806253i \(0.298508\pi\)
\(744\) −1.00045e16 −1.60896
\(745\) 3.92971e15 0.627337
\(746\) −3.13261e15 −0.496413
\(747\) −2.00938e15 −0.316081
\(748\) 4.41709e15 0.689727
\(749\) −1.91052e15 −0.296143
\(750\) −2.69706e14 −0.0415005
\(751\) 7.71607e15 1.17863 0.589313 0.807905i \(-0.299398\pi\)
0.589313 + 0.807905i \(0.299398\pi\)
\(752\) −2.35333e14 −0.0356849
\(753\) 6.46671e15 0.973444
\(754\) −1.13550e15 −0.169685
\(755\) −3.86801e15 −0.573825
\(756\) −2.41669e15 −0.355919
\(757\) −1.00894e16 −1.47516 −0.737578 0.675262i \(-0.764031\pi\)
−0.737578 + 0.675262i \(0.764031\pi\)
\(758\) −3.81906e15 −0.554340
\(759\) 2.11689e16 3.05048
\(760\) 1.01752e16 1.45568
\(761\) −3.81428e15 −0.541748 −0.270874 0.962615i \(-0.587313\pi\)
−0.270874 + 0.962615i \(0.587313\pi\)
\(762\) 3.06872e15 0.432718
\(763\) 4.01788e15 0.562487
\(764\) −2.75908e15 −0.383487
\(765\) −1.34011e15 −0.184928
\(766\) 2.95420e15 0.404746
\(767\) 8.51200e15 1.15786
\(768\) 7.88384e15 1.06476
\(769\) 6.91913e15 0.927805 0.463903 0.885886i \(-0.346449\pi\)
0.463903 + 0.885886i \(0.346449\pi\)
\(770\) 6.33695e15 0.843687
\(771\) −9.59558e15 −1.26845
\(772\) 5.99218e14 0.0786484
\(773\) 4.63161e15 0.603593 0.301797 0.953372i \(-0.402414\pi\)
0.301797 + 0.953372i \(0.402414\pi\)
\(774\) 8.98237e14 0.116229
\(775\) −1.21455e16 −1.56047
\(776\) −5.70454e15 −0.727748
\(777\) 3.15160e15 0.399222
\(778\) 4.73197e15 0.595188
\(779\) 5.05306e15 0.631100
\(780\) −1.19268e16 −1.47911
\(781\) −1.98902e16 −2.44939
\(782\) 6.44474e15 0.788077
\(783\) 1.36008e15 0.165149
\(784\) −1.54509e14 −0.0186301
\(785\) 1.93863e16 2.32120
\(786\) −8.14154e14 −0.0968016
\(787\) 2.98178e15 0.352058 0.176029 0.984385i \(-0.443675\pi\)
0.176029 + 0.984385i \(0.443675\pi\)
\(788\) −5.23998e15 −0.614378
\(789\) 1.52399e16 1.77443
\(790\) 8.38865e14 0.0969936
\(791\) −1.29737e15 −0.148968
\(792\) −2.42629e15 −0.276665
\(793\) 4.60220e15 0.521150
\(794\) −2.30922e15 −0.259688
\(795\) −2.15648e16 −2.40839
\(796\) −3.78511e14 −0.0419813
\(797\) −5.13438e15 −0.565545 −0.282772 0.959187i \(-0.591254\pi\)
−0.282772 + 0.959187i \(0.591254\pi\)
\(798\) 3.92750e15 0.429635
\(799\) 7.50531e15 0.815383
\(800\) 9.76311e15 1.05340
\(801\) 2.72591e14 0.0292101
\(802\) 4.47981e14 0.0476760
\(803\) 2.34012e15 0.247344
\(804\) 7.81215e15 0.820091
\(805\) −1.58694e16 −1.65456
\(806\) 1.31898e16 1.36583
\(807\) 6.98663e15 0.718560
\(808\) −7.42058e14 −0.0758011
\(809\) −1.70412e16 −1.72896 −0.864478 0.502670i \(-0.832351\pi\)
−0.864478 + 0.502670i \(0.832351\pi\)
\(810\) −9.88960e15 −0.996578
\(811\) 1.29797e16 1.29913 0.649563 0.760308i \(-0.274952\pi\)
0.649563 + 0.760308i \(0.274952\pi\)
\(812\) −7.47543e14 −0.0743153
\(813\) 7.45141e15 0.735767
\(814\) −5.50778e15 −0.540185
\(815\) −2.38749e16 −2.32581
\(816\) 2.48470e14 0.0240424
\(817\) −1.12637e16 −1.08258
\(818\) −2.74152e15 −0.261726
\(819\) −1.83037e15 −0.173571
\(820\) 5.88573e15 0.554401
\(821\) 1.93401e15 0.180955 0.0904775 0.995899i \(-0.471161\pi\)
0.0904775 + 0.995899i \(0.471161\pi\)
\(822\) 2.88165e15 0.267822
\(823\) −4.38449e15 −0.404781 −0.202391 0.979305i \(-0.564871\pi\)
−0.202391 + 0.979305i \(0.564871\pi\)
\(824\) −1.22730e16 −1.12551
\(825\) −1.91329e16 −1.74295
\(826\) −3.26491e15 −0.295448
\(827\) 6.99123e15 0.628453 0.314227 0.949348i \(-0.398255\pi\)
0.314227 + 0.949348i \(0.398255\pi\)
\(828\) 2.35267e15 0.210084
\(829\) −1.75858e16 −1.55995 −0.779977 0.625808i \(-0.784770\pi\)
−0.779977 + 0.625808i \(0.784770\pi\)
\(830\) −1.70997e16 −1.50681
\(831\) −3.29962e15 −0.288840
\(832\) −1.00638e16 −0.875152
\(833\) 4.92764e15 0.425688
\(834\) 3.68479e15 0.316227
\(835\) 1.58751e16 1.35345
\(836\) 1.17807e16 0.997787
\(837\) −1.57986e16 −1.32932
\(838\) −5.80069e15 −0.484884
\(839\) −1.58820e16 −1.31890 −0.659452 0.751746i \(-0.729212\pi\)
−0.659452 + 0.751746i \(0.729212\pi\)
\(840\) 1.18147e16 0.974737
\(841\) 4.20707e14 0.0344828
\(842\) 5.44226e15 0.443162
\(843\) 1.08381e15 0.0876802
\(844\) 1.10558e15 0.0888602
\(845\) 2.27053e16 1.81308
\(846\) −1.59630e15 −0.126642
\(847\) 1.09129e16 0.860163
\(848\) 6.15545e14 0.0482040
\(849\) −4.62374e15 −0.359750
\(850\) −5.82490e15 −0.450282
\(851\) 1.37929e16 1.05936
\(852\) −1.43589e16 −1.09573
\(853\) −1.91284e16 −1.45031 −0.725153 0.688588i \(-0.758231\pi\)
−0.725153 + 0.688588i \(0.758231\pi\)
\(854\) −1.76524e15 −0.132980
\(855\) −3.57419e15 −0.267524
\(856\) 6.22502e15 0.462951
\(857\) 1.22456e16 0.904868 0.452434 0.891798i \(-0.350556\pi\)
0.452434 + 0.891798i \(0.350556\pi\)
\(858\) 2.07780e16 1.52554
\(859\) 1.71244e15 0.124926 0.0624630 0.998047i \(-0.480104\pi\)
0.0624630 + 0.998047i \(0.480104\pi\)
\(860\) −1.31198e16 −0.951014
\(861\) 5.86727e15 0.422589
\(862\) −3.26089e15 −0.233371
\(863\) 2.12302e16 1.50972 0.754858 0.655888i \(-0.227706\pi\)
0.754858 + 0.655888i \(0.227706\pi\)
\(864\) 1.26996e16 0.897357
\(865\) 2.24364e16 1.57530
\(866\) −9.73684e15 −0.679312
\(867\) 7.75793e15 0.537825
\(868\) 8.68339e15 0.598179
\(869\) 2.50833e15 0.171702
\(870\) −2.57458e15 −0.175126
\(871\) −2.65996e16 −1.79794
\(872\) −1.30914e16 −0.879318
\(873\) 2.00381e15 0.133745
\(874\) 1.71887e16 1.14006
\(875\) 6.04568e14 0.0398475
\(876\) 1.68935e15 0.110649
\(877\) −1.92397e16 −1.25228 −0.626140 0.779711i \(-0.715366\pi\)
−0.626140 + 0.779711i \(0.715366\pi\)
\(878\) 5.10544e15 0.330228
\(879\) 1.93472e15 0.124360
\(880\) 1.06924e15 0.0682998
\(881\) 1.96899e16 1.24990 0.624952 0.780663i \(-0.285119\pi\)
0.624952 + 0.780663i \(0.285119\pi\)
\(882\) −1.04805e15 −0.0661160
\(883\) −2.17436e16 −1.36316 −0.681582 0.731741i \(-0.738708\pi\)
−0.681582 + 0.731741i \(0.738708\pi\)
\(884\) −1.08573e16 −0.676449
\(885\) 1.92997e16 1.19499
\(886\) −1.49171e16 −0.917909
\(887\) 3.10400e16 1.89820 0.949100 0.314975i \(-0.101996\pi\)
0.949100 + 0.314975i \(0.101996\pi\)
\(888\) −1.02688e16 −0.624092
\(889\) −6.87879e15 −0.415482
\(890\) 2.31974e15 0.139250
\(891\) −2.95713e16 −1.76418
\(892\) −5.42214e15 −0.321488
\(893\) 2.00173e16 1.17957
\(894\) −4.94224e15 −0.289446
\(895\) 4.00655e16 2.33208
\(896\) −7.18676e15 −0.415756
\(897\) −5.20336e16 −2.99175
\(898\) 3.83693e15 0.219262
\(899\) −4.88690e15 −0.277559
\(900\) −2.12639e15 −0.120036
\(901\) −1.96312e16 −1.10144
\(902\) −1.02537e16 −0.571803
\(903\) −1.30787e16 −0.724906
\(904\) 4.22720e15 0.232877
\(905\) 1.24679e16 0.682693
\(906\) 4.86465e15 0.264756
\(907\) 3.65942e15 0.197958 0.0989788 0.995090i \(-0.468442\pi\)
0.0989788 + 0.995090i \(0.468442\pi\)
\(908\) 2.32634e15 0.125084
\(909\) 2.60659e14 0.0139307
\(910\) −1.55764e16 −0.827445
\(911\) −1.86890e16 −0.986815 −0.493407 0.869798i \(-0.664249\pi\)
−0.493407 + 0.869798i \(0.664249\pi\)
\(912\) 6.62689e14 0.0347807
\(913\) −5.11306e16 −2.66742
\(914\) 7.50892e15 0.389380
\(915\) 1.04348e16 0.537859
\(916\) −7.64131e15 −0.391510
\(917\) 1.82499e15 0.0929458
\(918\) −7.57689e15 −0.383580
\(919\) −8.05474e14 −0.0405337 −0.0202668 0.999795i \(-0.506452\pi\)
−0.0202668 + 0.999795i \(0.506452\pi\)
\(920\) 5.17070e16 2.58652
\(921\) −1.87664e16 −0.933153
\(922\) 7.34234e15 0.362923
\(923\) 4.88905e16 2.40223
\(924\) 1.36790e16 0.668126
\(925\) −1.24664e16 −0.605285
\(926\) 1.42282e16 0.686734
\(927\) 4.31107e15 0.206846
\(928\) 3.92831e15 0.187366
\(929\) 1.95360e15 0.0926297 0.0463148 0.998927i \(-0.485252\pi\)
0.0463148 + 0.998927i \(0.485252\pi\)
\(930\) 2.99061e16 1.40962
\(931\) 1.31424e16 0.615818
\(932\) −2.53794e16 −1.18221
\(933\) 4.56355e16 2.11326
\(934\) 8.16761e15 0.376000
\(935\) −3.41005e16 −1.56062
\(936\) 5.96388e15 0.271339
\(937\) −1.32425e16 −0.598964 −0.299482 0.954102i \(-0.596814\pi\)
−0.299482 + 0.954102i \(0.596814\pi\)
\(938\) 1.02027e16 0.458775
\(939\) 2.59382e16 1.15952
\(940\) 2.33158e16 1.03621
\(941\) 2.17167e16 0.959511 0.479756 0.877402i \(-0.340725\pi\)
0.479756 + 0.877402i \(0.340725\pi\)
\(942\) −2.43814e16 −1.07098
\(943\) 2.56781e16 1.12137
\(944\) −5.50891e14 −0.0239177
\(945\) 1.86572e16 0.805324
\(946\) 2.28565e16 0.980865
\(947\) −2.98709e16 −1.27445 −0.637225 0.770678i \(-0.719918\pi\)
−0.637225 + 0.770678i \(0.719918\pi\)
\(948\) 1.81078e15 0.0768104
\(949\) −5.75207e15 −0.242583
\(950\) −1.55355e16 −0.651396
\(951\) −9.57884e15 −0.399319
\(952\) 1.07553e16 0.445780
\(953\) −3.61993e16 −1.49173 −0.745863 0.666099i \(-0.767963\pi\)
−0.745863 + 0.666099i \(0.767963\pi\)
\(954\) 4.17533e15 0.171070
\(955\) 2.13004e16 0.867701
\(956\) 2.20679e16 0.893806
\(957\) −7.69836e15 −0.310015
\(958\) 7.47164e14 0.0299161
\(959\) −6.45947e15 −0.257155
\(960\) −2.28182e16 −0.903212
\(961\) 3.13573e16 1.23413
\(962\) 1.35383e16 0.529786
\(963\) −2.18664e15 −0.0850808
\(964\) 2.18090e16 0.843747
\(965\) −4.62604e15 −0.177955
\(966\) 1.99583e16 0.763395
\(967\) −3.95775e15 −0.150523 −0.0752616 0.997164i \(-0.523979\pi\)
−0.0752616 + 0.997164i \(0.523979\pi\)
\(968\) −3.55573e16 −1.34467
\(969\) −2.11347e16 −0.794722
\(970\) 1.70523e16 0.637586
\(971\) −3.84988e16 −1.43134 −0.715668 0.698441i \(-0.753878\pi\)
−0.715668 + 0.698441i \(0.753878\pi\)
\(972\) −6.14718e15 −0.227254
\(973\) −8.25976e15 −0.303631
\(974\) −1.19605e16 −0.437196
\(975\) 4.70292e16 1.70939
\(976\) −2.97851e14 −0.0107653
\(977\) −2.81728e16 −1.01254 −0.506268 0.862376i \(-0.668975\pi\)
−0.506268 + 0.862376i \(0.668975\pi\)
\(978\) 3.00265e16 1.07310
\(979\) 6.93637e15 0.246506
\(980\) 1.53081e16 0.540976
\(981\) 4.59856e15 0.161600
\(982\) 7.05543e15 0.246553
\(983\) −1.45405e16 −0.505282 −0.252641 0.967560i \(-0.581299\pi\)
−0.252641 + 0.967560i \(0.581299\pi\)
\(984\) −1.91173e16 −0.660621
\(985\) 4.04533e16 1.39013
\(986\) −2.34372e15 −0.0800909
\(987\) 2.32427e16 0.789846
\(988\) −2.89574e16 −0.978579
\(989\) −5.72388e16 −1.92358
\(990\) 7.25279e15 0.242388
\(991\) 4.13728e16 1.37502 0.687511 0.726174i \(-0.258703\pi\)
0.687511 + 0.726174i \(0.258703\pi\)
\(992\) −4.56309e16 −1.50815
\(993\) −3.31710e16 −1.09028
\(994\) −1.87527e16 −0.612970
\(995\) 2.92215e15 0.0949895
\(996\) −3.69116e16 −1.19326
\(997\) −5.41765e16 −1.74176 −0.870879 0.491498i \(-0.836450\pi\)
−0.870879 + 0.491498i \(0.836450\pi\)
\(998\) 4.57342e15 0.146225
\(999\) −1.62159e16 −0.515623
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 29.12.a.a.1.7 11
3.2 odd 2 261.12.a.a.1.5 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.12.a.a.1.7 11 1.1 even 1 trivial
261.12.a.a.1.5 11 3.2 odd 2