Properties

Label 177.14.a.c.1.5
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-121.100 q^{2} +729.000 q^{3} +6473.28 q^{4} -61050.1 q^{5} -88282.1 q^{6} +274195. q^{7} +208137. q^{8} +531441. q^{9} +O(q^{10})\) \(q-121.100 q^{2} +729.000 q^{3} +6473.28 q^{4} -61050.1 q^{5} -88282.1 q^{6} +274195. q^{7} +208137. q^{8} +531441. q^{9} +7.39319e6 q^{10} -3.07589e6 q^{11} +4.71902e6 q^{12} -2.44374e7 q^{13} -3.32051e7 q^{14} -4.45056e7 q^{15} -7.82346e7 q^{16} +3.05792e7 q^{17} -6.43577e7 q^{18} -2.42138e8 q^{19} -3.95195e8 q^{20} +1.99888e8 q^{21} +3.72491e8 q^{22} +1.25066e8 q^{23} +1.51732e8 q^{24} +2.50642e9 q^{25} +2.95938e9 q^{26} +3.87420e8 q^{27} +1.77494e9 q^{28} -1.37616e9 q^{29} +5.38964e9 q^{30} -3.28072e9 q^{31} +7.76917e9 q^{32} -2.24232e9 q^{33} -3.70315e9 q^{34} -1.67397e10 q^{35} +3.44017e9 q^{36} +9.54723e8 q^{37} +2.93229e10 q^{38} -1.78149e10 q^{39} -1.27068e10 q^{40} -2.77688e9 q^{41} -2.42065e10 q^{42} -1.07940e10 q^{43} -1.99111e10 q^{44} -3.24445e10 q^{45} -1.51456e10 q^{46} +4.60463e10 q^{47} -5.70330e10 q^{48} -2.17060e10 q^{49} -3.03528e11 q^{50} +2.22922e10 q^{51} -1.58190e11 q^{52} -8.57839e10 q^{53} -4.69167e10 q^{54} +1.87784e11 q^{55} +5.70702e10 q^{56} -1.76518e11 q^{57} +1.66653e11 q^{58} -4.21805e10 q^{59} -2.88097e11 q^{60} -8.82203e10 q^{61} +3.97296e11 q^{62} +1.45719e11 q^{63} -2.99952e11 q^{64} +1.49191e12 q^{65} +2.71546e11 q^{66} -3.21100e11 q^{67} +1.97948e11 q^{68} +9.11734e10 q^{69} +2.02718e12 q^{70} -3.12169e11 q^{71} +1.10613e11 q^{72} -1.78284e12 q^{73} -1.15617e11 q^{74} +1.82718e12 q^{75} -1.56743e12 q^{76} -8.43394e11 q^{77} +2.15739e12 q^{78} -3.29175e12 q^{79} +4.77623e12 q^{80} +2.82430e11 q^{81} +3.36281e11 q^{82} -2.11978e12 q^{83} +1.29393e12 q^{84} -1.86686e12 q^{85} +1.30716e12 q^{86} -1.00322e12 q^{87} -6.40207e11 q^{88} +5.49190e12 q^{89} +3.92904e12 q^{90} -6.70062e12 q^{91} +8.09590e11 q^{92} -2.39164e12 q^{93} -5.57622e12 q^{94} +1.47825e13 q^{95} +5.66373e12 q^{96} -1.88598e12 q^{97} +2.62860e12 q^{98} -1.63465e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −121.100 −1.33798 −0.668991 0.743271i \(-0.733274\pi\)
−0.668991 + 0.743271i \(0.733274\pi\)
\(3\) 729.000 0.577350
\(4\) 6473.28 0.790196
\(5\) −61050.1 −1.74736 −0.873678 0.486504i \(-0.838272\pi\)
−0.873678 + 0.486504i \(0.838272\pi\)
\(6\) −88282.1 −0.772484
\(7\) 274195. 0.880892 0.440446 0.897779i \(-0.354820\pi\)
0.440446 + 0.897779i \(0.354820\pi\)
\(8\) 208137. 0.280714
\(9\) 531441. 0.333333
\(10\) 7.39319e6 2.33793
\(11\) −3.07589e6 −0.523502 −0.261751 0.965135i \(-0.584300\pi\)
−0.261751 + 0.965135i \(0.584300\pi\)
\(12\) 4.71902e6 0.456220
\(13\) −2.44374e7 −1.40418 −0.702091 0.712087i \(-0.747750\pi\)
−0.702091 + 0.712087i \(0.747750\pi\)
\(14\) −3.32051e7 −1.17862
\(15\) −4.45056e7 −1.00884
\(16\) −7.82346e7 −1.16579
\(17\) 3.05792e7 0.307261 0.153631 0.988128i \(-0.450903\pi\)
0.153631 + 0.988128i \(0.450903\pi\)
\(18\) −6.43577e7 −0.445994
\(19\) −2.42138e8 −1.18077 −0.590383 0.807123i \(-0.701023\pi\)
−0.590383 + 0.807123i \(0.701023\pi\)
\(20\) −3.95195e8 −1.38075
\(21\) 1.99888e8 0.508583
\(22\) 3.72491e8 0.700436
\(23\) 1.25066e8 0.176161 0.0880805 0.996113i \(-0.471927\pi\)
0.0880805 + 0.996113i \(0.471927\pi\)
\(24\) 1.51732e8 0.162071
\(25\) 2.50642e9 2.05326
\(26\) 2.95938e9 1.87877
\(27\) 3.87420e8 0.192450
\(28\) 1.77494e9 0.696077
\(29\) −1.37616e9 −0.429616 −0.214808 0.976656i \(-0.568913\pi\)
−0.214808 + 0.976656i \(0.568913\pi\)
\(30\) 5.38964e9 1.34981
\(31\) −3.28072e9 −0.663924 −0.331962 0.943293i \(-0.607710\pi\)
−0.331962 + 0.943293i \(0.607710\pi\)
\(32\) 7.76917e9 1.27909
\(33\) −2.24232e9 −0.302244
\(34\) −3.70315e9 −0.411110
\(35\) −1.67397e10 −1.53923
\(36\) 3.44017e9 0.263399
\(37\) 9.54723e8 0.0611739 0.0305870 0.999532i \(-0.490262\pi\)
0.0305870 + 0.999532i \(0.490262\pi\)
\(38\) 2.93229e10 1.57984
\(39\) −1.78149e10 −0.810705
\(40\) −1.27068e10 −0.490508
\(41\) −2.77688e9 −0.0912981 −0.0456491 0.998958i \(-0.514536\pi\)
−0.0456491 + 0.998958i \(0.514536\pi\)
\(42\) −2.42065e10 −0.680475
\(43\) −1.07940e10 −0.260398 −0.130199 0.991488i \(-0.541562\pi\)
−0.130199 + 0.991488i \(0.541562\pi\)
\(44\) −1.99111e10 −0.413669
\(45\) −3.24445e10 −0.582452
\(46\) −1.51456e10 −0.235700
\(47\) 4.60463e10 0.623102 0.311551 0.950230i \(-0.399152\pi\)
0.311551 + 0.950230i \(0.399152\pi\)
\(48\) −5.70330e10 −0.673067
\(49\) −2.17060e10 −0.224029
\(50\) −3.03528e11 −2.74722
\(51\) 2.22922e10 0.177397
\(52\) −1.58190e11 −1.10958
\(53\) −8.57839e10 −0.531634 −0.265817 0.964024i \(-0.585642\pi\)
−0.265817 + 0.964024i \(0.585642\pi\)
\(54\) −4.69167e10 −0.257495
\(55\) 1.87784e11 0.914745
\(56\) 5.70702e10 0.247279
\(57\) −1.76518e11 −0.681715
\(58\) 1.66653e11 0.574819
\(59\) −4.21805e10 −0.130189
\(60\) −2.88097e11 −0.797179
\(61\) −8.82203e10 −0.219243 −0.109621 0.993973i \(-0.534964\pi\)
−0.109621 + 0.993973i \(0.534964\pi\)
\(62\) 3.97296e11 0.888318
\(63\) 1.45719e11 0.293631
\(64\) −2.99952e11 −0.545609
\(65\) 1.49191e12 2.45361
\(66\) 2.71546e11 0.404397
\(67\) −3.21100e11 −0.433664 −0.216832 0.976209i \(-0.569572\pi\)
−0.216832 + 0.976209i \(0.569572\pi\)
\(68\) 1.97948e11 0.242797
\(69\) 9.11734e10 0.101707
\(70\) 2.02718e12 2.05947
\(71\) −3.12169e11 −0.289208 −0.144604 0.989490i \(-0.546191\pi\)
−0.144604 + 0.989490i \(0.546191\pi\)
\(72\) 1.10613e11 0.0935715
\(73\) −1.78284e12 −1.37884 −0.689419 0.724363i \(-0.742134\pi\)
−0.689419 + 0.724363i \(0.742134\pi\)
\(74\) −1.15617e11 −0.0818496
\(75\) 1.82718e12 1.18545
\(76\) −1.56743e12 −0.933036
\(77\) −8.43394e11 −0.461149
\(78\) 2.15739e12 1.08471
\(79\) −3.29175e12 −1.52353 −0.761765 0.647853i \(-0.775667\pi\)
−0.761765 + 0.647853i \(0.775667\pi\)
\(80\) 4.77623e12 2.03705
\(81\) 2.82430e11 0.111111
\(82\) 3.36281e11 0.122155
\(83\) −2.11978e12 −0.711677 −0.355839 0.934547i \(-0.615805\pi\)
−0.355839 + 0.934547i \(0.615805\pi\)
\(84\) 1.29393e12 0.401880
\(85\) −1.86686e12 −0.536895
\(86\) 1.30716e12 0.348407
\(87\) −1.00322e12 −0.248039
\(88\) −6.40207e11 −0.146955
\(89\) 5.49190e12 1.17135 0.585676 0.810545i \(-0.300829\pi\)
0.585676 + 0.810545i \(0.300829\pi\)
\(90\) 3.92904e12 0.779311
\(91\) −6.70062e12 −1.23693
\(92\) 8.09590e11 0.139202
\(93\) −2.39164e12 −0.383316
\(94\) −5.57622e12 −0.833699
\(95\) 1.47825e13 2.06322
\(96\) 5.66373e12 0.738481
\(97\) −1.88598e12 −0.229890 −0.114945 0.993372i \(-0.536669\pi\)
−0.114945 + 0.993372i \(0.536669\pi\)
\(98\) 2.62860e12 0.299747
\(99\) −1.63465e12 −0.174501
\(100\) 1.62247e13 1.62247
\(101\) 9.71006e12 0.910192 0.455096 0.890442i \(-0.349605\pi\)
0.455096 + 0.890442i \(0.349605\pi\)
\(102\) −2.69960e12 −0.237355
\(103\) −8.58384e12 −0.708336 −0.354168 0.935182i \(-0.615236\pi\)
−0.354168 + 0.935182i \(0.615236\pi\)
\(104\) −5.08633e12 −0.394174
\(105\) −1.22032e13 −0.888676
\(106\) 1.03885e13 0.711316
\(107\) −1.17403e13 −0.756282 −0.378141 0.925748i \(-0.623437\pi\)
−0.378141 + 0.925748i \(0.623437\pi\)
\(108\) 2.50788e12 0.152073
\(109\) −2.63894e13 −1.50715 −0.753577 0.657359i \(-0.771673\pi\)
−0.753577 + 0.657359i \(0.771673\pi\)
\(110\) −2.27406e13 −1.22391
\(111\) 6.95993e11 0.0353188
\(112\) −2.14516e13 −1.02693
\(113\) −1.85358e13 −0.837530 −0.418765 0.908095i \(-0.637537\pi\)
−0.418765 + 0.908095i \(0.637537\pi\)
\(114\) 2.13764e13 0.912123
\(115\) −7.63532e12 −0.307816
\(116\) −8.90824e12 −0.339481
\(117\) −1.29870e13 −0.468061
\(118\) 5.10808e12 0.174190
\(119\) 8.38467e12 0.270664
\(120\) −9.26326e12 −0.283195
\(121\) −2.50616e13 −0.725946
\(122\) 1.06835e13 0.293343
\(123\) −2.02434e12 −0.0527110
\(124\) −2.12370e13 −0.524629
\(125\) −7.84930e13 −1.84041
\(126\) −1.76466e13 −0.392873
\(127\) 4.43860e13 0.938689 0.469345 0.883015i \(-0.344490\pi\)
0.469345 + 0.883015i \(0.344490\pi\)
\(128\) −2.73209e13 −0.549072
\(129\) −7.86882e12 −0.150341
\(130\) −1.80670e14 −3.28288
\(131\) −9.98618e11 −0.0172638 −0.00863189 0.999963i \(-0.502748\pi\)
−0.00863189 + 0.999963i \(0.502748\pi\)
\(132\) −1.45152e13 −0.238832
\(133\) −6.63930e13 −1.04013
\(134\) 3.88853e13 0.580235
\(135\) −2.36521e13 −0.336279
\(136\) 6.36467e12 0.0862527
\(137\) −3.21919e13 −0.415971 −0.207985 0.978132i \(-0.566691\pi\)
−0.207985 + 0.978132i \(0.566691\pi\)
\(138\) −1.10411e13 −0.136082
\(139\) −4.94997e13 −0.582111 −0.291056 0.956706i \(-0.594006\pi\)
−0.291056 + 0.956706i \(0.594006\pi\)
\(140\) −1.08361e14 −1.21630
\(141\) 3.35678e13 0.359748
\(142\) 3.78038e13 0.386956
\(143\) 7.51668e13 0.735092
\(144\) −4.15771e13 −0.388595
\(145\) 8.40145e13 0.750693
\(146\) 2.15902e14 1.84486
\(147\) −1.58237e13 −0.129343
\(148\) 6.18019e12 0.0483394
\(149\) −1.37835e14 −1.03193 −0.515964 0.856611i \(-0.672566\pi\)
−0.515964 + 0.856611i \(0.672566\pi\)
\(150\) −2.21272e14 −1.58611
\(151\) 4.68429e13 0.321583 0.160792 0.986988i \(-0.448595\pi\)
0.160792 + 0.986988i \(0.448595\pi\)
\(152\) −5.03978e13 −0.331458
\(153\) 1.62510e13 0.102420
\(154\) 1.02135e14 0.617009
\(155\) 2.00288e14 1.16011
\(156\) −1.15321e14 −0.640616
\(157\) −3.32582e14 −1.77236 −0.886179 0.463343i \(-0.846650\pi\)
−0.886179 + 0.463343i \(0.846650\pi\)
\(158\) 3.98632e14 2.03846
\(159\) −6.25364e13 −0.306939
\(160\) −4.74309e14 −2.23502
\(161\) 3.42926e13 0.155179
\(162\) −3.42023e13 −0.148665
\(163\) 1.44110e14 0.601829 0.300915 0.953651i \(-0.402708\pi\)
0.300915 + 0.953651i \(0.402708\pi\)
\(164\) −1.79755e13 −0.0721434
\(165\) 1.36894e14 0.528128
\(166\) 2.56706e14 0.952211
\(167\) 4.87703e14 1.73980 0.869898 0.493231i \(-0.164184\pi\)
0.869898 + 0.493231i \(0.164184\pi\)
\(168\) 4.16042e13 0.142767
\(169\) 2.94312e14 0.971729
\(170\) 2.26078e14 0.718356
\(171\) −1.28682e14 −0.393589
\(172\) −6.98726e13 −0.205765
\(173\) −1.07018e14 −0.303499 −0.151750 0.988419i \(-0.548491\pi\)
−0.151750 + 0.988419i \(0.548491\pi\)
\(174\) 1.21490e14 0.331872
\(175\) 6.87247e14 1.80870
\(176\) 2.40641e14 0.610292
\(177\) −3.07496e13 −0.0751646
\(178\) −6.65071e14 −1.56725
\(179\) 5.73790e13 0.130379 0.0651896 0.997873i \(-0.479235\pi\)
0.0651896 + 0.997873i \(0.479235\pi\)
\(180\) −2.10023e14 −0.460251
\(181\) 7.11425e14 1.50390 0.751949 0.659222i \(-0.229114\pi\)
0.751949 + 0.659222i \(0.229114\pi\)
\(182\) 8.11448e14 1.65499
\(183\) −6.43126e13 −0.126580
\(184\) 2.60310e13 0.0494509
\(185\) −5.82860e13 −0.106893
\(186\) 2.89629e14 0.512870
\(187\) −9.40582e13 −0.160852
\(188\) 2.98071e14 0.492372
\(189\) 1.06229e14 0.169528
\(190\) −1.79017e15 −2.76055
\(191\) −8.97598e13 −0.133772 −0.0668860 0.997761i \(-0.521306\pi\)
−0.0668860 + 0.997761i \(0.521306\pi\)
\(192\) −2.18665e14 −0.315007
\(193\) −7.79025e14 −1.08500 −0.542499 0.840056i \(-0.682522\pi\)
−0.542499 + 0.840056i \(0.682522\pi\)
\(194\) 2.28392e14 0.307588
\(195\) 1.08760e15 1.41659
\(196\) −1.40509e14 −0.177027
\(197\) −6.92027e14 −0.843514 −0.421757 0.906709i \(-0.638586\pi\)
−0.421757 + 0.906709i \(0.638586\pi\)
\(198\) 1.97957e14 0.233479
\(199\) −1.38580e15 −1.58181 −0.790906 0.611937i \(-0.790391\pi\)
−0.790906 + 0.611937i \(0.790391\pi\)
\(200\) 5.21678e14 0.576379
\(201\) −2.34082e14 −0.250376
\(202\) −1.17589e15 −1.21782
\(203\) −3.77335e14 −0.378445
\(204\) 1.44304e14 0.140179
\(205\) 1.69529e14 0.159530
\(206\) 1.03951e15 0.947741
\(207\) 6.64654e13 0.0587203
\(208\) 1.91185e15 1.63698
\(209\) 7.44789e14 0.618133
\(210\) 1.47781e15 1.18903
\(211\) 1.57225e15 1.22655 0.613276 0.789869i \(-0.289851\pi\)
0.613276 + 0.789869i \(0.289851\pi\)
\(212\) −5.55303e14 −0.420095
\(213\) −2.27571e14 −0.166975
\(214\) 1.42175e15 1.01189
\(215\) 6.58975e14 0.455008
\(216\) 8.06366e13 0.0540235
\(217\) −8.99558e14 −0.584845
\(218\) 3.19577e15 2.01655
\(219\) −1.29969e15 −0.796073
\(220\) 1.21558e15 0.722827
\(221\) −7.47277e14 −0.431451
\(222\) −8.42850e13 −0.0472559
\(223\) −6.96136e14 −0.379064 −0.189532 0.981875i \(-0.560697\pi\)
−0.189532 + 0.981875i \(0.560697\pi\)
\(224\) 2.13027e15 1.12674
\(225\) 1.33201e15 0.684419
\(226\) 2.24469e15 1.12060
\(227\) −8.89211e14 −0.431357 −0.215678 0.976464i \(-0.569196\pi\)
−0.215678 + 0.976464i \(0.569196\pi\)
\(228\) −1.14265e15 −0.538689
\(229\) 3.28787e15 1.50655 0.753275 0.657705i \(-0.228473\pi\)
0.753275 + 0.657705i \(0.228473\pi\)
\(230\) 9.24640e14 0.411852
\(231\) −6.14834e14 −0.266244
\(232\) −2.86429e14 −0.120599
\(233\) 2.67543e15 1.09542 0.547710 0.836668i \(-0.315500\pi\)
0.547710 + 0.836668i \(0.315500\pi\)
\(234\) 1.57274e15 0.626257
\(235\) −2.81113e15 −1.08878
\(236\) −2.73047e14 −0.102875
\(237\) −2.39969e15 −0.879611
\(238\) −1.01539e15 −0.362144
\(239\) 3.21727e15 1.11661 0.558304 0.829637i \(-0.311452\pi\)
0.558304 + 0.829637i \(0.311452\pi\)
\(240\) 3.48187e15 1.17609
\(241\) −1.52954e15 −0.502864 −0.251432 0.967875i \(-0.580902\pi\)
−0.251432 + 0.967875i \(0.580902\pi\)
\(242\) 3.03497e15 0.971302
\(243\) 2.05891e14 0.0641500
\(244\) −5.71075e14 −0.173244
\(245\) 1.32515e15 0.391459
\(246\) 2.45149e14 0.0705264
\(247\) 5.91722e15 1.65801
\(248\) −6.82840e14 −0.186373
\(249\) −1.54532e15 −0.410887
\(250\) 9.50552e15 2.46244
\(251\) 2.68892e15 0.678734 0.339367 0.940654i \(-0.389787\pi\)
0.339367 + 0.940654i \(0.389787\pi\)
\(252\) 9.43278e14 0.232026
\(253\) −3.84690e14 −0.0922206
\(254\) −5.37516e15 −1.25595
\(255\) −1.36094e15 −0.309977
\(256\) 5.76577e15 1.28026
\(257\) −7.56048e15 −1.63676 −0.818378 0.574681i \(-0.805126\pi\)
−0.818378 + 0.574681i \(0.805126\pi\)
\(258\) 9.52917e14 0.201153
\(259\) 2.61781e14 0.0538876
\(260\) 9.65754e15 1.93883
\(261\) −7.31345e14 −0.143205
\(262\) 1.20933e14 0.0230986
\(263\) 2.02110e15 0.376596 0.188298 0.982112i \(-0.439703\pi\)
0.188298 + 0.982112i \(0.439703\pi\)
\(264\) −4.66711e14 −0.0848442
\(265\) 5.23712e15 0.928954
\(266\) 8.04021e15 1.39167
\(267\) 4.00359e15 0.676280
\(268\) −2.07857e15 −0.342680
\(269\) −1.16386e16 −1.87288 −0.936440 0.350827i \(-0.885901\pi\)
−0.936440 + 0.350827i \(0.885901\pi\)
\(270\) 2.86427e15 0.449935
\(271\) 5.92073e15 0.907977 0.453989 0.891007i \(-0.350001\pi\)
0.453989 + 0.891007i \(0.350001\pi\)
\(272\) −2.39235e15 −0.358201
\(273\) −4.88475e15 −0.714144
\(274\) 3.89845e15 0.556561
\(275\) −7.70946e15 −1.07488
\(276\) 5.90191e14 0.0803681
\(277\) 5.31697e15 0.707206 0.353603 0.935396i \(-0.384956\pi\)
0.353603 + 0.935396i \(0.384956\pi\)
\(278\) 5.99442e15 0.778854
\(279\) −1.74351e15 −0.221308
\(280\) −3.48414e15 −0.432085
\(281\) 9.06497e15 1.09844 0.549219 0.835679i \(-0.314925\pi\)
0.549219 + 0.835679i \(0.314925\pi\)
\(282\) −4.06507e15 −0.481336
\(283\) 9.24656e15 1.06996 0.534981 0.844864i \(-0.320319\pi\)
0.534981 + 0.844864i \(0.320319\pi\)
\(284\) −2.02076e15 −0.228531
\(285\) 1.07765e16 1.19120
\(286\) −9.10272e15 −0.983540
\(287\) −7.61407e14 −0.0804238
\(288\) 4.12886e15 0.426362
\(289\) −8.96949e15 −0.905590
\(290\) −1.01742e16 −1.00441
\(291\) −1.37488e15 −0.132727
\(292\) −1.15408e16 −1.08955
\(293\) 4.36941e14 0.0403444 0.0201722 0.999797i \(-0.493579\pi\)
0.0201722 + 0.999797i \(0.493579\pi\)
\(294\) 1.91625e15 0.173059
\(295\) 2.57513e15 0.227487
\(296\) 1.98713e14 0.0171724
\(297\) −1.19166e15 −0.100748
\(298\) 1.66919e16 1.38070
\(299\) −3.05630e15 −0.247362
\(300\) 1.18278e16 0.936736
\(301\) −2.95966e15 −0.229382
\(302\) −5.67269e15 −0.430273
\(303\) 7.07863e15 0.525499
\(304\) 1.89435e16 1.37652
\(305\) 5.38586e15 0.383095
\(306\) −1.96801e15 −0.137037
\(307\) −7.47865e15 −0.509828 −0.254914 0.966964i \(-0.582047\pi\)
−0.254914 + 0.966964i \(0.582047\pi\)
\(308\) −5.45953e15 −0.364398
\(309\) −6.25762e15 −0.408958
\(310\) −2.42550e16 −1.55221
\(311\) 1.12353e16 0.704110 0.352055 0.935979i \(-0.385483\pi\)
0.352055 + 0.935979i \(0.385483\pi\)
\(312\) −3.70794e15 −0.227577
\(313\) 2.80446e16 1.68582 0.842911 0.538053i \(-0.180840\pi\)
0.842911 + 0.538053i \(0.180840\pi\)
\(314\) 4.02758e16 2.37138
\(315\) −8.89614e15 −0.513078
\(316\) −2.13085e16 −1.20389
\(317\) 2.90786e16 1.60949 0.804744 0.593622i \(-0.202302\pi\)
0.804744 + 0.593622i \(0.202302\pi\)
\(318\) 7.57318e15 0.410679
\(319\) 4.23290e15 0.224905
\(320\) 1.83121e16 0.953373
\(321\) −8.55866e15 −0.436639
\(322\) −4.15284e15 −0.207626
\(323\) −7.40437e15 −0.362804
\(324\) 1.82825e15 0.0877995
\(325\) −6.12504e16 −2.88315
\(326\) −1.74517e16 −0.805237
\(327\) −1.92379e16 −0.870156
\(328\) −5.77972e14 −0.0256287
\(329\) 1.26257e16 0.548885
\(330\) −1.65779e16 −0.706626
\(331\) −1.33097e16 −0.556271 −0.278136 0.960542i \(-0.589717\pi\)
−0.278136 + 0.960542i \(0.589717\pi\)
\(332\) −1.37219e16 −0.562364
\(333\) 5.07379e14 0.0203913
\(334\) −5.90610e16 −2.32782
\(335\) 1.96032e16 0.757766
\(336\) −1.56382e16 −0.592899
\(337\) −1.66329e16 −0.618547 −0.309274 0.950973i \(-0.600086\pi\)
−0.309274 + 0.950973i \(0.600086\pi\)
\(338\) −3.56413e16 −1.30016
\(339\) −1.35126e16 −0.483548
\(340\) −1.20847e16 −0.424252
\(341\) 1.00911e16 0.347565
\(342\) 1.55834e16 0.526614
\(343\) −3.25182e16 −1.07824
\(344\) −2.24663e15 −0.0730974
\(345\) −5.56615e15 −0.177718
\(346\) 1.29599e16 0.406076
\(347\) 1.41261e16 0.434391 0.217195 0.976128i \(-0.430309\pi\)
0.217195 + 0.976128i \(0.430309\pi\)
\(348\) −6.49411e15 −0.195999
\(349\) 4.64435e16 1.37581 0.687907 0.725799i \(-0.258530\pi\)
0.687907 + 0.725799i \(0.258530\pi\)
\(350\) −8.32259e16 −2.42000
\(351\) −9.46756e15 −0.270235
\(352\) −2.38971e16 −0.669605
\(353\) 6.70363e16 1.84406 0.922029 0.387121i \(-0.126530\pi\)
0.922029 + 0.387121i \(0.126530\pi\)
\(354\) 3.72379e15 0.100569
\(355\) 1.90580e16 0.505350
\(356\) 3.55506e16 0.925597
\(357\) 6.11242e15 0.156268
\(358\) −6.94862e15 −0.174445
\(359\) −8.02458e15 −0.197837 −0.0989187 0.995096i \(-0.531538\pi\)
−0.0989187 + 0.995096i \(0.531538\pi\)
\(360\) −6.75292e15 −0.163503
\(361\) 1.65776e16 0.394208
\(362\) −8.61537e16 −2.01219
\(363\) −1.82699e16 −0.419125
\(364\) −4.33750e16 −0.977419
\(365\) 1.08843e17 2.40932
\(366\) 7.78828e15 0.169361
\(367\) 7.02076e16 1.49987 0.749937 0.661509i \(-0.230084\pi\)
0.749937 + 0.661509i \(0.230084\pi\)
\(368\) −9.78452e15 −0.205366
\(369\) −1.47575e15 −0.0304327
\(370\) 7.05845e15 0.143020
\(371\) −2.35215e16 −0.468312
\(372\) −1.54818e16 −0.302895
\(373\) 3.05940e16 0.588205 0.294102 0.955774i \(-0.404979\pi\)
0.294102 + 0.955774i \(0.404979\pi\)
\(374\) 1.13905e16 0.215217
\(375\) −5.72214e16 −1.06256
\(376\) 9.58395e15 0.174914
\(377\) 3.36297e16 0.603259
\(378\) −1.28643e16 −0.226825
\(379\) 4.13153e16 0.716070 0.358035 0.933708i \(-0.383447\pi\)
0.358035 + 0.933708i \(0.383447\pi\)
\(380\) 9.56915e16 1.63035
\(381\) 3.23574e16 0.541952
\(382\) 1.08699e16 0.178984
\(383\) −1.92088e16 −0.310962 −0.155481 0.987839i \(-0.549693\pi\)
−0.155481 + 0.987839i \(0.549693\pi\)
\(384\) −1.99169e16 −0.317007
\(385\) 5.14893e16 0.805791
\(386\) 9.43402e16 1.45171
\(387\) −5.73637e15 −0.0867992
\(388\) −1.22085e16 −0.181658
\(389\) −5.74473e16 −0.840614 −0.420307 0.907382i \(-0.638078\pi\)
−0.420307 + 0.907382i \(0.638078\pi\)
\(390\) −1.31709e17 −1.89537
\(391\) 3.82443e15 0.0541275
\(392\) −4.51782e15 −0.0628883
\(393\) −7.27993e14 −0.00996725
\(394\) 8.38046e16 1.12861
\(395\) 2.00962e17 2.66215
\(396\) −1.05816e16 −0.137890
\(397\) −8.63214e16 −1.10657 −0.553287 0.832991i \(-0.686627\pi\)
−0.553287 + 0.832991i \(0.686627\pi\)
\(398\) 1.67821e17 2.11644
\(399\) −4.84005e16 −0.600518
\(400\) −1.96089e17 −2.39366
\(401\) 5.95325e16 0.715016 0.357508 0.933910i \(-0.383627\pi\)
0.357508 + 0.933910i \(0.383627\pi\)
\(402\) 2.83474e16 0.334999
\(403\) 8.01723e16 0.932270
\(404\) 6.28559e16 0.719229
\(405\) −1.72424e16 −0.194151
\(406\) 4.56954e16 0.506353
\(407\) −2.93662e15 −0.0320247
\(408\) 4.63984e15 0.0497980
\(409\) 1.70471e17 1.80073 0.900367 0.435131i \(-0.143298\pi\)
0.900367 + 0.435131i \(0.143298\pi\)
\(410\) −2.05300e16 −0.213449
\(411\) −2.34679e16 −0.240161
\(412\) −5.55656e16 −0.559724
\(413\) −1.15657e16 −0.114682
\(414\) −8.04898e15 −0.0785667
\(415\) 1.29413e17 1.24355
\(416\) −1.89859e17 −1.79607
\(417\) −3.60852e16 −0.336082
\(418\) −9.01941e16 −0.827051
\(419\) −7.73612e16 −0.698444 −0.349222 0.937040i \(-0.613554\pi\)
−0.349222 + 0.937040i \(0.613554\pi\)
\(420\) −7.89948e16 −0.702228
\(421\) −4.89260e16 −0.428259 −0.214129 0.976805i \(-0.568691\pi\)
−0.214129 + 0.976805i \(0.568691\pi\)
\(422\) −1.90400e17 −1.64111
\(423\) 2.44709e16 0.207701
\(424\) −1.78548e16 −0.149237
\(425\) 7.66442e16 0.630887
\(426\) 2.75590e16 0.223409
\(427\) −2.41896e16 −0.193129
\(428\) −7.59981e16 −0.597611
\(429\) 5.47966e16 0.424406
\(430\) −7.98020e16 −0.608792
\(431\) 1.40520e17 1.05593 0.527967 0.849265i \(-0.322954\pi\)
0.527967 + 0.849265i \(0.322954\pi\)
\(432\) −3.03097e16 −0.224356
\(433\) −1.11981e16 −0.0816533 −0.0408266 0.999166i \(-0.512999\pi\)
−0.0408266 + 0.999166i \(0.512999\pi\)
\(434\) 1.08937e17 0.782512
\(435\) 6.12466e16 0.433413
\(436\) −1.70826e17 −1.19095
\(437\) −3.02833e16 −0.208005
\(438\) 1.57393e17 1.06513
\(439\) −5.98073e16 −0.398781 −0.199391 0.979920i \(-0.563896\pi\)
−0.199391 + 0.979920i \(0.563896\pi\)
\(440\) 3.90847e16 0.256782
\(441\) −1.15354e16 −0.0746765
\(442\) 9.04954e16 0.577274
\(443\) −1.04301e17 −0.655635 −0.327818 0.944741i \(-0.606313\pi\)
−0.327818 + 0.944741i \(0.606313\pi\)
\(444\) 4.50536e15 0.0279087
\(445\) −3.35281e17 −2.04677
\(446\) 8.43023e16 0.507181
\(447\) −1.00482e17 −0.595783
\(448\) −8.22453e16 −0.480622
\(449\) 1.84771e17 1.06422 0.532112 0.846674i \(-0.321399\pi\)
0.532112 + 0.846674i \(0.321399\pi\)
\(450\) −1.61307e17 −0.915740
\(451\) 8.54137e15 0.0477947
\(452\) −1.19987e17 −0.661813
\(453\) 3.41485e16 0.185666
\(454\) 1.07684e17 0.577148
\(455\) 4.09074e17 2.16136
\(456\) −3.67400e16 −0.191367
\(457\) −1.40580e17 −0.721887 −0.360944 0.932588i \(-0.617545\pi\)
−0.360944 + 0.932588i \(0.617545\pi\)
\(458\) −3.98162e17 −2.01574
\(459\) 1.18470e16 0.0591325
\(460\) −4.94256e16 −0.243235
\(461\) 3.62232e17 1.75764 0.878821 0.477152i \(-0.158331\pi\)
0.878821 + 0.477152i \(0.158331\pi\)
\(462\) 7.44566e16 0.356230
\(463\) −8.62407e16 −0.406851 −0.203426 0.979090i \(-0.565208\pi\)
−0.203426 + 0.979090i \(0.565208\pi\)
\(464\) 1.07663e17 0.500841
\(465\) 1.46010e17 0.669791
\(466\) −3.23996e17 −1.46565
\(467\) 8.73900e16 0.389854 0.194927 0.980818i \(-0.437553\pi\)
0.194927 + 0.980818i \(0.437553\pi\)
\(468\) −8.40688e16 −0.369860
\(469\) −8.80440e16 −0.382011
\(470\) 3.40429e17 1.45677
\(471\) −2.42453e17 −1.02327
\(472\) −8.77934e15 −0.0365459
\(473\) 3.32011e16 0.136319
\(474\) 2.90603e17 1.17690
\(475\) −6.06898e17 −2.42442
\(476\) 5.42763e16 0.213878
\(477\) −4.55891e16 −0.177211
\(478\) −3.89612e17 −1.49400
\(479\) 4.14866e17 1.56937 0.784687 0.619892i \(-0.212824\pi\)
0.784687 + 0.619892i \(0.212824\pi\)
\(480\) −3.45771e17 −1.29039
\(481\) −2.33310e16 −0.0858993
\(482\) 1.85228e17 0.672823
\(483\) 2.49993e16 0.0895925
\(484\) −1.62231e17 −0.573639
\(485\) 1.15139e17 0.401700
\(486\) −2.49335e16 −0.0858316
\(487\) −3.38059e17 −1.14830 −0.574149 0.818751i \(-0.694667\pi\)
−0.574149 + 0.818751i \(0.694667\pi\)
\(488\) −1.83619e16 −0.0615445
\(489\) 1.05056e17 0.347466
\(490\) −1.60476e17 −0.523765
\(491\) −4.52509e17 −1.45746 −0.728731 0.684800i \(-0.759890\pi\)
−0.728731 + 0.684800i \(0.759890\pi\)
\(492\) −1.31042e16 −0.0416520
\(493\) −4.20817e16 −0.132004
\(494\) −7.16577e17 −2.21839
\(495\) 9.97959e16 0.304915
\(496\) 2.56666e17 0.773993
\(497\) −8.55953e16 −0.254761
\(498\) 1.87139e17 0.549759
\(499\) −3.07360e17 −0.891237 −0.445619 0.895223i \(-0.647016\pi\)
−0.445619 + 0.895223i \(0.647016\pi\)
\(500\) −5.08107e17 −1.45429
\(501\) 3.55536e17 1.00447
\(502\) −3.25629e17 −0.908133
\(503\) −1.76801e17 −0.486734 −0.243367 0.969934i \(-0.578252\pi\)
−0.243367 + 0.969934i \(0.578252\pi\)
\(504\) 3.03295e16 0.0824263
\(505\) −5.92800e17 −1.59043
\(506\) 4.65861e16 0.123390
\(507\) 2.14554e17 0.561028
\(508\) 2.87323e17 0.741748
\(509\) 6.95952e16 0.177384 0.0886919 0.996059i \(-0.471731\pi\)
0.0886919 + 0.996059i \(0.471731\pi\)
\(510\) 1.64811e17 0.414743
\(511\) −4.88846e17 −1.21461
\(512\) −4.74424e17 −1.16389
\(513\) −9.38091e16 −0.227238
\(514\) 9.15576e17 2.18995
\(515\) 5.24044e17 1.23772
\(516\) −5.09371e16 −0.118799
\(517\) −1.41633e17 −0.326195
\(518\) −3.17017e16 −0.0721006
\(519\) −7.80162e16 −0.175225
\(520\) 3.10521e17 0.688763
\(521\) −5.04741e17 −1.10566 −0.552832 0.833293i \(-0.686453\pi\)
−0.552832 + 0.833293i \(0.686453\pi\)
\(522\) 8.85662e16 0.191606
\(523\) −4.26871e16 −0.0912086 −0.0456043 0.998960i \(-0.514521\pi\)
−0.0456043 + 0.998960i \(0.514521\pi\)
\(524\) −6.46434e15 −0.0136418
\(525\) 5.01003e17 1.04425
\(526\) −2.44756e17 −0.503878
\(527\) −1.00322e17 −0.203998
\(528\) 1.75427e17 0.352352
\(529\) −4.88395e17 −0.968967
\(530\) −6.34216e17 −1.24292
\(531\) −2.24165e16 −0.0433963
\(532\) −4.29780e17 −0.821904
\(533\) 6.78598e16 0.128199
\(534\) −4.84836e17 −0.904851
\(535\) 7.16745e17 1.32149
\(536\) −6.68327e16 −0.121736
\(537\) 4.18293e16 0.0752745
\(538\) 1.40944e18 2.50588
\(539\) 6.67652e16 0.117280
\(540\) −1.53107e17 −0.265726
\(541\) 7.38366e16 0.126616 0.0633081 0.997994i \(-0.479835\pi\)
0.0633081 + 0.997994i \(0.479835\pi\)
\(542\) −7.17003e17 −1.21486
\(543\) 5.18628e17 0.868275
\(544\) 2.37575e17 0.393014
\(545\) 1.61108e18 2.63354
\(546\) 5.91545e17 0.955511
\(547\) 1.17777e18 1.87993 0.939966 0.341269i \(-0.110857\pi\)
0.939966 + 0.341269i \(0.110857\pi\)
\(548\) −2.08387e17 −0.328698
\(549\) −4.68839e16 −0.0730808
\(550\) 9.33618e17 1.43818
\(551\) 3.33219e17 0.507276
\(552\) 1.89766e16 0.0285505
\(553\) −9.02583e17 −1.34207
\(554\) −6.43887e17 −0.946229
\(555\) −4.24905e16 −0.0617145
\(556\) −3.20425e17 −0.459982
\(557\) −3.89846e17 −0.553139 −0.276569 0.960994i \(-0.589198\pi\)
−0.276569 + 0.960994i \(0.589198\pi\)
\(558\) 2.11139e17 0.296106
\(559\) 2.63777e17 0.365646
\(560\) 1.30962e18 1.79442
\(561\) −6.85685e16 −0.0928679
\(562\) −1.09777e18 −1.46969
\(563\) −1.00758e18 −1.33344 −0.666719 0.745309i \(-0.732302\pi\)
−0.666719 + 0.745309i \(0.732302\pi\)
\(564\) 2.17294e17 0.284271
\(565\) 1.13161e18 1.46346
\(566\) −1.11976e18 −1.43159
\(567\) 7.74408e16 0.0978769
\(568\) −6.49740e16 −0.0811849
\(569\) 1.46828e18 1.81376 0.906880 0.421389i \(-0.138457\pi\)
0.906880 + 0.421389i \(0.138457\pi\)
\(570\) −1.30503e18 −1.59380
\(571\) −4.20427e17 −0.507640 −0.253820 0.967252i \(-0.581687\pi\)
−0.253820 + 0.967252i \(0.581687\pi\)
\(572\) 4.86576e17 0.580867
\(573\) −6.54349e16 −0.0772333
\(574\) 9.22066e16 0.107606
\(575\) 3.13468e17 0.361704
\(576\) −1.59407e17 −0.181870
\(577\) −1.50538e18 −1.69826 −0.849131 0.528183i \(-0.822874\pi\)
−0.849131 + 0.528183i \(0.822874\pi\)
\(578\) 1.08621e18 1.21166
\(579\) −5.67909e17 −0.626424
\(580\) 5.43850e17 0.593194
\(581\) −5.81233e17 −0.626911
\(582\) 1.66498e17 0.177586
\(583\) 2.63862e17 0.278311
\(584\) −3.71075e17 −0.387060
\(585\) 7.92861e17 0.817869
\(586\) −5.29136e16 −0.0539800
\(587\) −5.11404e16 −0.0515960 −0.0257980 0.999667i \(-0.508213\pi\)
−0.0257980 + 0.999667i \(0.508213\pi\)
\(588\) −1.02431e17 −0.102207
\(589\) 7.94385e17 0.783938
\(590\) −3.11849e17 −0.304373
\(591\) −5.04487e17 −0.487003
\(592\) −7.46924e16 −0.0713157
\(593\) −1.67701e18 −1.58373 −0.791863 0.610699i \(-0.790889\pi\)
−0.791863 + 0.610699i \(0.790889\pi\)
\(594\) 1.44311e17 0.134799
\(595\) −5.11885e17 −0.472947
\(596\) −8.92245e17 −0.815424
\(597\) −1.01025e18 −0.913260
\(598\) 3.70119e17 0.330966
\(599\) −2.13441e18 −1.88801 −0.944004 0.329933i \(-0.892974\pi\)
−0.944004 + 0.329933i \(0.892974\pi\)
\(600\) 3.80304e17 0.332772
\(601\) 3.06273e17 0.265109 0.132555 0.991176i \(-0.457682\pi\)
0.132555 + 0.991176i \(0.457682\pi\)
\(602\) 3.58416e17 0.306909
\(603\) −1.70645e17 −0.144555
\(604\) 3.03227e17 0.254114
\(605\) 1.53002e18 1.26849
\(606\) −8.57224e17 −0.703109
\(607\) −1.44125e18 −1.16953 −0.584765 0.811203i \(-0.698813\pi\)
−0.584765 + 0.811203i \(0.698813\pi\)
\(608\) −1.88121e18 −1.51030
\(609\) −2.75077e17 −0.218496
\(610\) −6.52230e17 −0.512574
\(611\) −1.12525e18 −0.874948
\(612\) 1.05198e17 0.0809322
\(613\) −4.13566e17 −0.314812 −0.157406 0.987534i \(-0.550313\pi\)
−0.157406 + 0.987534i \(0.550313\pi\)
\(614\) 9.05667e17 0.682141
\(615\) 1.23587e17 0.0921049
\(616\) −1.75542e17 −0.129451
\(617\) 1.32421e18 0.966282 0.483141 0.875543i \(-0.339496\pi\)
0.483141 + 0.875543i \(0.339496\pi\)
\(618\) 7.57799e17 0.547179
\(619\) 7.43808e17 0.531461 0.265731 0.964047i \(-0.414387\pi\)
0.265731 + 0.964047i \(0.414387\pi\)
\(620\) 1.29652e18 0.916715
\(621\) 4.84533e16 0.0339022
\(622\) −1.36059e18 −0.942086
\(623\) 1.50585e18 1.03183
\(624\) 1.39374e18 0.945109
\(625\) 1.73242e18 1.16261
\(626\) −3.39621e18 −2.25560
\(627\) 5.42951e17 0.356879
\(628\) −2.15290e18 −1.40051
\(629\) 2.91947e16 0.0187964
\(630\) 1.07733e18 0.686489
\(631\) 1.03057e18 0.649960 0.324980 0.945721i \(-0.394642\pi\)
0.324980 + 0.945721i \(0.394642\pi\)
\(632\) −6.85136e17 −0.427677
\(633\) 1.14617e18 0.708150
\(634\) −3.52142e18 −2.15347
\(635\) −2.70977e18 −1.64023
\(636\) −4.04816e17 −0.242542
\(637\) 5.30438e17 0.314578
\(638\) −5.12606e17 −0.300919
\(639\) −1.65900e17 −0.0964028
\(640\) 1.66794e18 0.959425
\(641\) 1.80067e18 1.02531 0.512657 0.858594i \(-0.328661\pi\)
0.512657 + 0.858594i \(0.328661\pi\)
\(642\) 1.03646e18 0.584216
\(643\) 1.03269e18 0.576232 0.288116 0.957595i \(-0.406971\pi\)
0.288116 + 0.957595i \(0.406971\pi\)
\(644\) 2.21986e17 0.122622
\(645\) 4.80393e17 0.262699
\(646\) 8.96672e17 0.485425
\(647\) 2.70114e18 1.44767 0.723833 0.689975i \(-0.242378\pi\)
0.723833 + 0.689975i \(0.242378\pi\)
\(648\) 5.87841e16 0.0311905
\(649\) 1.29743e17 0.0681542
\(650\) 7.41744e18 3.85760
\(651\) −6.55777e17 −0.337660
\(652\) 9.32862e17 0.475563
\(653\) 2.27483e18 1.14819 0.574095 0.818789i \(-0.305354\pi\)
0.574095 + 0.818789i \(0.305354\pi\)
\(654\) 2.32971e18 1.16425
\(655\) 6.09658e16 0.0301660
\(656\) 2.17248e17 0.106434
\(657\) −9.47473e17 −0.459613
\(658\) −1.52897e18 −0.734398
\(659\) −2.42135e18 −1.15160 −0.575802 0.817589i \(-0.695310\pi\)
−0.575802 + 0.817589i \(0.695310\pi\)
\(660\) 8.86155e17 0.417325
\(661\) 2.49936e18 1.16552 0.582759 0.812645i \(-0.301973\pi\)
0.582759 + 0.812645i \(0.301973\pi\)
\(662\) 1.61181e18 0.744281
\(663\) −5.44765e17 −0.249098
\(664\) −4.41205e17 −0.199778
\(665\) 4.05330e18 1.81747
\(666\) −6.14437e16 −0.0272832
\(667\) −1.72111e17 −0.0756816
\(668\) 3.15704e18 1.37478
\(669\) −5.07483e17 −0.218853
\(670\) −2.37395e18 −1.01388
\(671\) 2.71356e17 0.114774
\(672\) 1.55297e18 0.650522
\(673\) 1.86948e18 0.775574 0.387787 0.921749i \(-0.373240\pi\)
0.387787 + 0.921749i \(0.373240\pi\)
\(674\) 2.01425e18 0.827605
\(675\) 9.71037e17 0.395149
\(676\) 1.90517e18 0.767856
\(677\) −2.48844e18 −0.993347 −0.496673 0.867938i \(-0.665445\pi\)
−0.496673 + 0.867938i \(0.665445\pi\)
\(678\) 1.63638e18 0.646979
\(679\) −5.17125e17 −0.202508
\(680\) −3.88564e17 −0.150714
\(681\) −6.48235e17 −0.249044
\(682\) −1.22204e18 −0.465036
\(683\) −3.32409e17 −0.125296 −0.0626482 0.998036i \(-0.519955\pi\)
−0.0626482 + 0.998036i \(0.519955\pi\)
\(684\) −8.32994e17 −0.311012
\(685\) 1.96532e18 0.726849
\(686\) 3.93796e18 1.44266
\(687\) 2.39686e18 0.869808
\(688\) 8.44464e17 0.303568
\(689\) 2.09634e18 0.746511
\(690\) 6.74062e17 0.237783
\(691\) 2.91763e18 1.01958 0.509791 0.860298i \(-0.329723\pi\)
0.509791 + 0.860298i \(0.329723\pi\)
\(692\) −6.92758e17 −0.239824
\(693\) −4.48214e17 −0.153716
\(694\) −1.71067e18 −0.581207
\(695\) 3.02196e18 1.01716
\(696\) −2.08807e17 −0.0696281
\(697\) −8.49147e16 −0.0280524
\(698\) −5.62432e18 −1.84081
\(699\) 1.95039e18 0.632441
\(700\) 4.44875e18 1.42922
\(701\) 5.23262e18 1.66553 0.832764 0.553629i \(-0.186757\pi\)
0.832764 + 0.553629i \(0.186757\pi\)
\(702\) 1.14652e18 0.361570
\(703\) −2.31174e17 −0.0722321
\(704\) 9.22618e17 0.285627
\(705\) −2.04932e18 −0.628608
\(706\) −8.11812e18 −2.46732
\(707\) 2.66245e18 0.801780
\(708\) −1.99051e17 −0.0593947
\(709\) 2.70447e18 0.799617 0.399809 0.916599i \(-0.369077\pi\)
0.399809 + 0.916599i \(0.369077\pi\)
\(710\) −2.30793e18 −0.676149
\(711\) −1.74937e18 −0.507844
\(712\) 1.14307e18 0.328815
\(713\) −4.10308e17 −0.116957
\(714\) −7.40216e17 −0.209084
\(715\) −4.58894e18 −1.28447
\(716\) 3.71431e17 0.103025
\(717\) 2.34539e18 0.644674
\(718\) 9.71779e17 0.264703
\(719\) −1.14317e18 −0.308585 −0.154292 0.988025i \(-0.549310\pi\)
−0.154292 + 0.988025i \(0.549310\pi\)
\(720\) 2.53829e18 0.679015
\(721\) −2.35365e18 −0.623968
\(722\) −2.00755e18 −0.527443
\(723\) −1.11504e18 −0.290329
\(724\) 4.60525e18 1.18837
\(725\) −3.44922e18 −0.882112
\(726\) 2.21249e18 0.560782
\(727\) 4.45771e18 1.11979 0.559897 0.828562i \(-0.310841\pi\)
0.559897 + 0.828562i \(0.310841\pi\)
\(728\) −1.39465e18 −0.347225
\(729\) 1.50095e17 0.0370370
\(730\) −1.31809e19 −3.22363
\(731\) −3.30072e17 −0.0800102
\(732\) −4.16314e17 −0.100023
\(733\) −2.25620e18 −0.537280 −0.268640 0.963241i \(-0.586574\pi\)
−0.268640 + 0.963241i \(0.586574\pi\)
\(734\) −8.50216e18 −2.00680
\(735\) 9.66037e17 0.226009
\(736\) 9.71663e17 0.225325
\(737\) 9.87667e17 0.227024
\(738\) 1.78713e17 0.0407184
\(739\) 1.89825e18 0.428710 0.214355 0.976756i \(-0.431235\pi\)
0.214355 + 0.976756i \(0.431235\pi\)
\(740\) −3.77302e17 −0.0844661
\(741\) 4.31365e18 0.957253
\(742\) 2.84846e18 0.626593
\(743\) 5.77525e18 1.25934 0.629671 0.776862i \(-0.283190\pi\)
0.629671 + 0.776862i \(0.283190\pi\)
\(744\) −4.97790e17 −0.107602
\(745\) 8.41485e18 1.80315
\(746\) −3.70494e18 −0.787007
\(747\) −1.12654e18 −0.237226
\(748\) −6.08866e17 −0.127105
\(749\) −3.21913e18 −0.666202
\(750\) 6.92953e18 1.42169
\(751\) 4.34729e18 0.884217 0.442109 0.896962i \(-0.354231\pi\)
0.442109 + 0.896962i \(0.354231\pi\)
\(752\) −3.60242e18 −0.726403
\(753\) 1.96023e18 0.391867
\(754\) −4.07257e18 −0.807150
\(755\) −2.85977e18 −0.561921
\(756\) 6.87649e17 0.133960
\(757\) 1.27677e18 0.246598 0.123299 0.992370i \(-0.460653\pi\)
0.123299 + 0.992370i \(0.460653\pi\)
\(758\) −5.00329e18 −0.958089
\(759\) −2.80439e17 −0.0532436
\(760\) 3.07679e18 0.579175
\(761\) 2.52588e18 0.471425 0.235713 0.971823i \(-0.424258\pi\)
0.235713 + 0.971823i \(0.424258\pi\)
\(762\) −3.91849e18 −0.725123
\(763\) −7.23586e18 −1.32764
\(764\) −5.81041e17 −0.105706
\(765\) −9.92128e17 −0.178965
\(766\) 2.32619e18 0.416062
\(767\) 1.03078e18 0.182809
\(768\) 4.20324e18 0.739157
\(769\) 4.70991e18 0.821280 0.410640 0.911797i \(-0.365305\pi\)
0.410640 + 0.911797i \(0.365305\pi\)
\(770\) −6.23538e18 −1.07813
\(771\) −5.51159e18 −0.944981
\(772\) −5.04285e18 −0.857361
\(773\) −1.03352e19 −1.74242 −0.871209 0.490912i \(-0.836664\pi\)
−0.871209 + 0.490912i \(0.836664\pi\)
\(774\) 6.94676e17 0.116136
\(775\) −8.22285e18 −1.36321
\(776\) −3.92542e17 −0.0645334
\(777\) 1.90838e17 0.0311120
\(778\) 6.95688e18 1.12473
\(779\) 6.72387e17 0.107802
\(780\) 7.04035e18 1.11938
\(781\) 9.60198e17 0.151401
\(782\) −4.63140e17 −0.0724216
\(783\) −5.33151e17 −0.0826797
\(784\) 1.69816e18 0.261170
\(785\) 2.03042e19 3.09694
\(786\) 8.81601e16 0.0133360
\(787\) −7.83829e18 −1.17594 −0.587971 0.808882i \(-0.700073\pi\)
−0.587971 + 0.808882i \(0.700073\pi\)
\(788\) −4.47968e18 −0.666541
\(789\) 1.47338e18 0.217428
\(790\) −2.43366e19 −3.56191
\(791\) −5.08242e18 −0.737774
\(792\) −3.40232e17 −0.0489848
\(793\) 2.15588e18 0.307857
\(794\) 1.04536e19 1.48058
\(795\) 3.81786e18 0.536332
\(796\) −8.97067e18 −1.24994
\(797\) 9.69196e18 1.33947 0.669734 0.742601i \(-0.266408\pi\)
0.669734 + 0.742601i \(0.266408\pi\)
\(798\) 5.86131e18 0.803482
\(799\) 1.40806e18 0.191455
\(800\) 1.94728e19 2.62629
\(801\) 2.91862e18 0.390451
\(802\) −7.20940e18 −0.956678
\(803\) 5.48381e18 0.721825
\(804\) −1.51528e18 −0.197846
\(805\) −2.09357e18 −0.271153
\(806\) −9.70889e18 −1.24736
\(807\) −8.48452e18 −1.08131
\(808\) 2.02102e18 0.255504
\(809\) −1.39322e18 −0.174725 −0.0873625 0.996177i \(-0.527844\pi\)
−0.0873625 + 0.996177i \(0.527844\pi\)
\(810\) 2.08806e18 0.259770
\(811\) −1.14333e19 −1.41102 −0.705512 0.708698i \(-0.749283\pi\)
−0.705512 + 0.708698i \(0.749283\pi\)
\(812\) −2.44260e18 −0.299046
\(813\) 4.31621e18 0.524221
\(814\) 3.55626e17 0.0428484
\(815\) −8.79791e18 −1.05161
\(816\) −1.74402e18 −0.206808
\(817\) 2.61363e18 0.307469
\(818\) −2.06441e19 −2.40935
\(819\) −3.56099e18 −0.412311
\(820\) 1.09741e18 0.126060
\(821\) −9.33974e18 −1.06440 −0.532200 0.846619i \(-0.678634\pi\)
−0.532200 + 0.846619i \(0.678634\pi\)
\(822\) 2.84197e18 0.321331
\(823\) −1.64755e19 −1.84816 −0.924082 0.382195i \(-0.875168\pi\)
−0.924082 + 0.382195i \(0.875168\pi\)
\(824\) −1.78662e18 −0.198840
\(825\) −5.62020e18 −0.620584
\(826\) 1.40061e18 0.153443
\(827\) −2.37125e18 −0.257746 −0.128873 0.991661i \(-0.541136\pi\)
−0.128873 + 0.991661i \(0.541136\pi\)
\(828\) 4.30249e17 0.0464005
\(829\) 1.47626e19 1.57964 0.789821 0.613338i \(-0.210174\pi\)
0.789821 + 0.613338i \(0.210174\pi\)
\(830\) −1.56719e19 −1.66385
\(831\) 3.87607e18 0.408305
\(832\) 7.33004e18 0.766134
\(833\) −6.63752e17 −0.0688356
\(834\) 4.36993e18 0.449672
\(835\) −2.97743e19 −3.04005
\(836\) 4.82123e18 0.488446
\(837\) −1.27102e18 −0.127772
\(838\) 9.36846e18 0.934506
\(839\) −1.80444e19 −1.78603 −0.893016 0.450025i \(-0.851415\pi\)
−0.893016 + 0.450025i \(0.851415\pi\)
\(840\) −2.53994e18 −0.249464
\(841\) −8.36682e18 −0.815430
\(842\) 5.92496e18 0.573003
\(843\) 6.60836e18 0.634183
\(844\) 1.01776e19 0.969216
\(845\) −1.79678e19 −1.69796
\(846\) −2.96343e18 −0.277900
\(847\) −6.87177e18 −0.639480
\(848\) 6.71127e18 0.619771
\(849\) 6.74075e18 0.617743
\(850\) −9.28164e18 −0.844115
\(851\) 1.19404e17 0.0107765
\(852\) −1.47313e18 −0.131943
\(853\) −2.51116e18 −0.223206 −0.111603 0.993753i \(-0.535599\pi\)
−0.111603 + 0.993753i \(0.535599\pi\)
\(854\) 2.92937e18 0.258403
\(855\) 7.85604e18 0.687740
\(856\) −2.44359e18 −0.212299
\(857\) 4.39477e18 0.378932 0.189466 0.981887i \(-0.439324\pi\)
0.189466 + 0.981887i \(0.439324\pi\)
\(858\) −6.63589e18 −0.567847
\(859\) −7.28347e17 −0.0618561 −0.0309280 0.999522i \(-0.509846\pi\)
−0.0309280 + 0.999522i \(0.509846\pi\)
\(860\) 4.26573e18 0.359545
\(861\) −5.55066e17 −0.0464327
\(862\) −1.70171e19 −1.41282
\(863\) 1.16775e19 0.962232 0.481116 0.876657i \(-0.340232\pi\)
0.481116 + 0.876657i \(0.340232\pi\)
\(864\) 3.00994e18 0.246160
\(865\) 6.53347e18 0.530321
\(866\) 1.35610e18 0.109251
\(867\) −6.53876e18 −0.522843
\(868\) −5.82309e18 −0.462142
\(869\) 1.01251e19 0.797571
\(870\) −7.41698e18 −0.579898
\(871\) 7.84685e18 0.608944
\(872\) −5.49262e18 −0.423080
\(873\) −1.00228e18 −0.0766299
\(874\) 3.66731e18 0.278307
\(875\) −2.15224e19 −1.62121
\(876\) −8.41325e18 −0.629053
\(877\) 1.82012e19 1.35084 0.675420 0.737434i \(-0.263962\pi\)
0.675420 + 0.737434i \(0.263962\pi\)
\(878\) 7.24268e18 0.533562
\(879\) 3.18530e17 0.0232928
\(880\) −1.46912e19 −1.06640
\(881\) 2.45990e18 0.177245 0.0886225 0.996065i \(-0.471754\pi\)
0.0886225 + 0.996065i \(0.471754\pi\)
\(882\) 1.39695e18 0.0999158
\(883\) −6.44851e18 −0.457841 −0.228921 0.973445i \(-0.573520\pi\)
−0.228921 + 0.973445i \(0.573520\pi\)
\(884\) −4.83733e18 −0.340931
\(885\) 1.87727e18 0.131339
\(886\) 1.26308e19 0.877228
\(887\) 5.94950e18 0.410183 0.205091 0.978743i \(-0.434251\pi\)
0.205091 + 0.978743i \(0.434251\pi\)
\(888\) 1.44862e17 0.00991449
\(889\) 1.21704e19 0.826884
\(890\) 4.06027e19 2.73854
\(891\) −8.68722e17 −0.0581669
\(892\) −4.50629e18 −0.299535
\(893\) −1.11495e19 −0.735737
\(894\) 1.21684e19 0.797147
\(895\) −3.50300e18 −0.227819
\(896\) −7.49125e18 −0.483673
\(897\) −2.22804e18 −0.142815
\(898\) −2.23758e19 −1.42391
\(899\) 4.51478e18 0.285232
\(900\) 8.62249e18 0.540825
\(901\) −2.62320e18 −0.163351
\(902\) −1.03436e18 −0.0639485
\(903\) −2.15759e18 −0.132434
\(904\) −3.85798e18 −0.235107
\(905\) −4.34326e19 −2.62785
\(906\) −4.13539e18 −0.248418
\(907\) −2.82484e19 −1.68479 −0.842396 0.538859i \(-0.818856\pi\)
−0.842396 + 0.538859i \(0.818856\pi\)
\(908\) −5.75611e18 −0.340856
\(909\) 5.16032e18 0.303397
\(910\) −4.95390e19 −2.89187
\(911\) 1.04031e19 0.602970 0.301485 0.953471i \(-0.402518\pi\)
0.301485 + 0.953471i \(0.402518\pi\)
\(912\) 1.38098e19 0.794735
\(913\) 6.52021e18 0.372564
\(914\) 1.70243e19 0.965872
\(915\) 3.92629e18 0.221180
\(916\) 2.12833e19 1.19047
\(917\) −2.73816e17 −0.0152075
\(918\) −1.43468e18 −0.0791182
\(919\) 1.98217e18 0.108540 0.0542699 0.998526i \(-0.482717\pi\)
0.0542699 + 0.998526i \(0.482717\pi\)
\(920\) −1.58919e18 −0.0864084
\(921\) −5.45193e18 −0.294349
\(922\) −4.38664e19 −2.35169
\(923\) 7.62861e18 0.406101
\(924\) −3.98000e18 −0.210385
\(925\) 2.39293e18 0.125606
\(926\) 1.04438e19 0.544360
\(927\) −4.56180e18 −0.236112
\(928\) −1.06916e19 −0.549516
\(929\) −2.39212e19 −1.22090 −0.610450 0.792055i \(-0.709011\pi\)
−0.610450 + 0.792055i \(0.709011\pi\)
\(930\) −1.76819e19 −0.896168
\(931\) 5.25583e18 0.264526
\(932\) 1.73188e19 0.865596
\(933\) 8.19050e18 0.406518
\(934\) −1.05830e19 −0.521618
\(935\) 5.74227e18 0.281066
\(936\) −2.70309e18 −0.131391
\(937\) −2.64946e19 −1.27894 −0.639470 0.768816i \(-0.720846\pi\)
−0.639470 + 0.768816i \(0.720846\pi\)
\(938\) 1.06622e19 0.511124
\(939\) 2.04445e19 0.973309
\(940\) −1.81973e19 −0.860350
\(941\) 1.00832e19 0.473440 0.236720 0.971578i \(-0.423928\pi\)
0.236720 + 0.971578i \(0.423928\pi\)
\(942\) 2.93611e19 1.36912
\(943\) −3.47294e17 −0.0160832
\(944\) 3.29998e18 0.151772
\(945\) −6.48529e18 −0.296225
\(946\) −4.02067e18 −0.182392
\(947\) −3.84959e18 −0.173436 −0.0867181 0.996233i \(-0.527638\pi\)
−0.0867181 + 0.996233i \(0.527638\pi\)
\(948\) −1.55339e19 −0.695065
\(949\) 4.35680e19 1.93614
\(950\) 7.34955e19 3.24382
\(951\) 2.11983e19 0.929239
\(952\) 1.74516e18 0.0759793
\(953\) 2.19742e19 0.950187 0.475093 0.879935i \(-0.342414\pi\)
0.475093 + 0.879935i \(0.342414\pi\)
\(954\) 5.52085e18 0.237105
\(955\) 5.47985e18 0.233747
\(956\) 2.08263e19 0.882339
\(957\) 3.08579e18 0.129849
\(958\) −5.02403e19 −2.09979
\(959\) −8.82686e18 −0.366425
\(960\) 1.33495e19 0.550430
\(961\) −1.36544e19 −0.559206
\(962\) 2.82539e18 0.114932
\(963\) −6.23926e18 −0.252094
\(964\) −9.90116e18 −0.397361
\(965\) 4.75596e19 1.89588
\(966\) −3.02742e18 −0.119873
\(967\) −2.51950e19 −0.990928 −0.495464 0.868628i \(-0.665002\pi\)
−0.495464 + 0.868628i \(0.665002\pi\)
\(968\) −5.21625e18 −0.203783
\(969\) −5.39779e18 −0.209465
\(970\) −1.39434e19 −0.537467
\(971\) −1.58447e19 −0.606680 −0.303340 0.952882i \(-0.598102\pi\)
−0.303340 + 0.952882i \(0.598102\pi\)
\(972\) 1.33279e18 0.0506911
\(973\) −1.35726e19 −0.512777
\(974\) 4.09391e19 1.53640
\(975\) −4.46515e19 −1.66459
\(976\) 6.90188e18 0.255590
\(977\) 3.10880e19 1.14361 0.571805 0.820389i \(-0.306243\pi\)
0.571805 + 0.820389i \(0.306243\pi\)
\(978\) −1.27223e19 −0.464904
\(979\) −1.68925e19 −0.613205
\(980\) 8.57809e18 0.309329
\(981\) −1.40244e19 −0.502385
\(982\) 5.47989e19 1.95006
\(983\) 1.32946e19 0.469979 0.234989 0.971998i \(-0.424494\pi\)
0.234989 + 0.971998i \(0.424494\pi\)
\(984\) −4.21341e17 −0.0147967
\(985\) 4.22483e19 1.47392
\(986\) 5.09611e18 0.176620
\(987\) 9.20412e18 0.316899
\(988\) 3.83038e19 1.31015
\(989\) −1.34997e18 −0.0458719
\(990\) −1.20853e19 −0.407971
\(991\) −3.07838e19 −1.03239 −0.516194 0.856472i \(-0.672652\pi\)
−0.516194 + 0.856472i \(0.672652\pi\)
\(992\) −2.54885e19 −0.849216
\(993\) −9.70278e18 −0.321163
\(994\) 1.03656e19 0.340866
\(995\) 8.46032e19 2.76399
\(996\) −1.00033e19 −0.324681
\(997\) 1.34236e19 0.432863 0.216431 0.976298i \(-0.430558\pi\)
0.216431 + 0.976298i \(0.430558\pi\)
\(998\) 3.72214e19 1.19246
\(999\) 3.69879e17 0.0117729
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 177.14.a.c.1.5 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.5 31 1.1 even 1 trivial