Properties

Label 289.10.a.h.1.31
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(148.845356651\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.31
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+35.6294 q^{2} +0.238037 q^{3} +757.456 q^{4} -2006.11 q^{5} +8.48114 q^{6} +3110.91 q^{7} +8745.46 q^{8} -19682.9 q^{9} +O(q^{10})\) \(q+35.6294 q^{2} +0.238037 q^{3} +757.456 q^{4} -2006.11 q^{5} +8.48114 q^{6} +3110.91 q^{7} +8745.46 q^{8} -19682.9 q^{9} -71476.4 q^{10} -21988.6 q^{11} +180.303 q^{12} -170282. q^{13} +110840. q^{14} -477.528 q^{15} -76221.9 q^{16} -701292. q^{18} +578915. q^{19} -1.51954e6 q^{20} +740.514 q^{21} -783440. q^{22} +1.14210e6 q^{23} +2081.75 q^{24} +2.07134e6 q^{25} -6.06707e6 q^{26} -9370.57 q^{27} +2.35638e6 q^{28} +2.04445e6 q^{29} -17014.1 q^{30} +6.36010e6 q^{31} -7.19342e6 q^{32} -5234.10 q^{33} -6.24082e6 q^{35} -1.49090e7 q^{36} +1.74773e7 q^{37} +2.06264e7 q^{38} -40533.6 q^{39} -1.75443e7 q^{40} +8.92910e6 q^{41} +26384.1 q^{42} +2.23811e7 q^{43} -1.66554e7 q^{44} +3.94861e7 q^{45} +4.06922e7 q^{46} +5.29083e7 q^{47} -18143.7 q^{48} -3.06758e7 q^{49} +7.38005e7 q^{50} -1.28981e8 q^{52} -4.96802e7 q^{53} -333868. q^{54} +4.41114e7 q^{55} +2.72064e7 q^{56} +137804. q^{57} +7.28426e7 q^{58} -1.25066e8 q^{59} -361707. q^{60} -7.55780e7 q^{61} +2.26607e8 q^{62} -6.12319e7 q^{63} -2.17272e8 q^{64} +3.41605e8 q^{65} -186488. q^{66} -5.66451e7 q^{67} +271862. q^{69} -2.22357e8 q^{70} -9.81048e6 q^{71} -1.72136e8 q^{72} -4.37401e8 q^{73} +6.22707e8 q^{74} +493056. q^{75} +4.38503e8 q^{76} -6.84045e7 q^{77} -1.44419e6 q^{78} +1.18121e8 q^{79} +1.52909e8 q^{80} +3.87417e8 q^{81} +3.18139e8 q^{82} +7.42977e8 q^{83} +560907. q^{84} +7.97425e8 q^{86} +486656. q^{87} -1.92300e8 q^{88} -6.40009e8 q^{89} +1.40687e9 q^{90} -5.29734e8 q^{91} +8.65088e8 q^{92} +1.51394e6 q^{93} +1.88509e9 q^{94} -1.16137e9 q^{95} -1.71230e6 q^{96} +1.49842e9 q^{97} -1.09296e9 q^{98} +4.32800e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 35.6294 1.57461 0.787307 0.616562i \(-0.211475\pi\)
0.787307 + 0.616562i \(0.211475\pi\)
\(3\) 0.238037 0.00169668 0.000848340 1.00000i \(-0.499730\pi\)
0.000848340 1.00000i \(0.499730\pi\)
\(4\) 757.456 1.47941
\(5\) −2006.11 −1.43545 −0.717726 0.696325i \(-0.754817\pi\)
−0.717726 + 0.696325i \(0.754817\pi\)
\(6\) 8.48114 0.00267161
\(7\) 3110.91 0.489719 0.244859 0.969559i \(-0.421258\pi\)
0.244859 + 0.969559i \(0.421258\pi\)
\(8\) 8745.46 0.754879
\(9\) −19682.9 −0.999997
\(10\) −71476.4 −2.26028
\(11\) −21988.6 −0.452824 −0.226412 0.974032i \(-0.572700\pi\)
−0.226412 + 0.974032i \(0.572700\pi\)
\(12\) 180.303 0.00251008
\(13\) −170282. −1.65358 −0.826789 0.562512i \(-0.809835\pi\)
−0.826789 + 0.562512i \(0.809835\pi\)
\(14\) 110840. 0.771118
\(15\) −477.528 −0.00243550
\(16\) −76221.9 −0.290763
\(17\) 0 0
\(18\) −701292. −1.57461
\(19\) 578915. 1.01912 0.509558 0.860436i \(-0.329809\pi\)
0.509558 + 0.860436i \(0.329809\pi\)
\(20\) −1.51954e6 −2.12362
\(21\) 740.514 0.000830896 0
\(22\) −783440. −0.713023
\(23\) 1.14210e6 0.850996 0.425498 0.904959i \(-0.360099\pi\)
0.425498 + 0.904959i \(0.360099\pi\)
\(24\) 2081.75 0.00128079
\(25\) 2.07134e6 1.06052
\(26\) −6.06707e6 −2.60375
\(27\) −9370.57 −0.00339335
\(28\) 2.35638e6 0.724493
\(29\) 2.04445e6 0.536767 0.268384 0.963312i \(-0.413511\pi\)
0.268384 + 0.963312i \(0.413511\pi\)
\(30\) −17014.1 −0.00383497
\(31\) 6.36010e6 1.23691 0.618453 0.785822i \(-0.287760\pi\)
0.618453 + 0.785822i \(0.287760\pi\)
\(32\) −7.19342e6 −1.21272
\(33\) −5234.10 −0.000768298 0
\(34\) 0 0
\(35\) −6.24082e6 −0.702968
\(36\) −1.49090e7 −1.47940
\(37\) 1.74773e7 1.53309 0.766544 0.642192i \(-0.221975\pi\)
0.766544 + 0.642192i \(0.221975\pi\)
\(38\) 2.06264e7 1.60471
\(39\) −40533.6 −0.00280559
\(40\) −1.75443e7 −1.08359
\(41\) 8.92910e6 0.493492 0.246746 0.969080i \(-0.420639\pi\)
0.246746 + 0.969080i \(0.420639\pi\)
\(42\) 26384.1 0.00130834
\(43\) 2.23811e7 0.998327 0.499163 0.866508i \(-0.333641\pi\)
0.499163 + 0.866508i \(0.333641\pi\)
\(44\) −1.66554e7 −0.669911
\(45\) 3.94861e7 1.43545
\(46\) 4.06922e7 1.33999
\(47\) 5.29083e7 1.58155 0.790776 0.612106i \(-0.209678\pi\)
0.790776 + 0.612106i \(0.209678\pi\)
\(48\) −18143.7 −0.000493332 0
\(49\) −3.06758e7 −0.760176
\(50\) 7.38005e7 1.66992
\(51\) 0 0
\(52\) −1.28981e8 −2.44631
\(53\) −4.96802e7 −0.864853 −0.432427 0.901669i \(-0.642343\pi\)
−0.432427 + 0.901669i \(0.642343\pi\)
\(54\) −333868. −0.00534322
\(55\) 4.41114e7 0.650008
\(56\) 2.72064e7 0.369679
\(57\) 137804. 0.00172911
\(58\) 7.28426e7 0.845201
\(59\) −1.25066e8 −1.34371 −0.671853 0.740684i \(-0.734501\pi\)
−0.671853 + 0.740684i \(0.734501\pi\)
\(60\) −361707. −0.00360310
\(61\) −7.55780e7 −0.698893 −0.349447 0.936956i \(-0.613630\pi\)
−0.349447 + 0.936956i \(0.613630\pi\)
\(62\) 2.26607e8 1.94765
\(63\) −6.12319e7 −0.489717
\(64\) −2.17272e8 −1.61880
\(65\) 3.41605e8 2.37363
\(66\) −186488. −0.00120977
\(67\) −5.66451e7 −0.343420 −0.171710 0.985148i \(-0.554929\pi\)
−0.171710 + 0.985148i \(0.554929\pi\)
\(68\) 0 0
\(69\) 271862. 0.00144387
\(70\) −2.22357e8 −1.10690
\(71\) −9.81048e6 −0.0458171 −0.0229085 0.999738i \(-0.507293\pi\)
−0.0229085 + 0.999738i \(0.507293\pi\)
\(72\) −1.72136e8 −0.754877
\(73\) −4.37401e8 −1.80271 −0.901357 0.433078i \(-0.857428\pi\)
−0.901357 + 0.433078i \(0.857428\pi\)
\(74\) 6.22707e8 2.41402
\(75\) 493056. 0.00179937
\(76\) 4.38503e8 1.50769
\(77\) −6.84045e7 −0.221757
\(78\) −1.44419e6 −0.00441772
\(79\) 1.18121e8 0.341196 0.170598 0.985341i \(-0.445430\pi\)
0.170598 + 0.985341i \(0.445430\pi\)
\(80\) 1.52909e8 0.417377
\(81\) 3.87417e8 0.999991
\(82\) 3.18139e8 0.777060
\(83\) 7.42977e8 1.71840 0.859199 0.511641i \(-0.170962\pi\)
0.859199 + 0.511641i \(0.170962\pi\)
\(84\) 560907. 0.00122923
\(85\) 0 0
\(86\) 7.97425e8 1.57198
\(87\) 486656. 0.000910722 0
\(88\) −1.92300e8 −0.341828
\(89\) −6.40009e8 −1.08126 −0.540631 0.841260i \(-0.681814\pi\)
−0.540631 + 0.841260i \(0.681814\pi\)
\(90\) 1.40687e9 2.26028
\(91\) −5.29734e8 −0.809788
\(92\) 8.65088e8 1.25897
\(93\) 1.51394e6 0.00209863
\(94\) 1.88509e9 2.49033
\(95\) −1.16137e9 −1.46289
\(96\) −1.71230e6 −0.00205760
\(97\) 1.49842e9 1.71855 0.859274 0.511516i \(-0.170916\pi\)
0.859274 + 0.511516i \(0.170916\pi\)
\(98\) −1.09296e9 −1.19698
\(99\) 4.32800e8 0.452823
\(100\) 1.56895e9 1.56895
\(101\) 1.10300e7 0.0105470 0.00527352 0.999986i \(-0.498321\pi\)
0.00527352 + 0.999986i \(0.498321\pi\)
\(102\) 0 0
\(103\) 2.12633e9 1.86150 0.930748 0.365660i \(-0.119157\pi\)
0.930748 + 0.365660i \(0.119157\pi\)
\(104\) −1.48920e9 −1.24825
\(105\) −1.48555e6 −0.00119271
\(106\) −1.77008e9 −1.36181
\(107\) 1.24966e9 0.921651 0.460825 0.887491i \(-0.347553\pi\)
0.460825 + 0.887491i \(0.347553\pi\)
\(108\) −7.09779e6 −0.00502015
\(109\) −2.38971e9 −1.62153 −0.810766 0.585371i \(-0.800949\pi\)
−0.810766 + 0.585371i \(0.800949\pi\)
\(110\) 1.57166e9 1.02351
\(111\) 4.16026e6 0.00260116
\(112\) −2.37120e8 −0.142392
\(113\) 1.78971e9 1.03260 0.516298 0.856409i \(-0.327310\pi\)
0.516298 + 0.856409i \(0.327310\pi\)
\(114\) 4.90986e6 0.00272268
\(115\) −2.29117e9 −1.22156
\(116\) 1.54858e9 0.794097
\(117\) 3.35166e9 1.65357
\(118\) −4.45602e9 −2.11582
\(119\) 0 0
\(120\) −4.17620e6 −0.00183851
\(121\) −1.87445e9 −0.794950
\(122\) −2.69280e9 −1.10049
\(123\) 2.12546e6 0.000837298 0
\(124\) 4.81750e9 1.82989
\(125\) −2.37144e8 −0.0868796
\(126\) −2.18166e9 −0.771115
\(127\) −1.30529e9 −0.445235 −0.222618 0.974906i \(-0.571460\pi\)
−0.222618 + 0.974906i \(0.571460\pi\)
\(128\) −4.05824e9 −1.33626
\(129\) 5.32753e6 0.00169384
\(130\) 1.21712e10 3.73755
\(131\) 6.34853e8 0.188344 0.0941722 0.995556i \(-0.469980\pi\)
0.0941722 + 0.995556i \(0.469980\pi\)
\(132\) −3.96460e6 −0.00113662
\(133\) 1.80096e9 0.499080
\(134\) −2.01823e9 −0.540754
\(135\) 1.87984e7 0.00487100
\(136\) 0 0
\(137\) 1.67526e9 0.406293 0.203147 0.979148i \(-0.434883\pi\)
0.203147 + 0.979148i \(0.434883\pi\)
\(138\) 9.68628e6 0.00227353
\(139\) −3.13923e8 −0.0713273 −0.0356637 0.999364i \(-0.511355\pi\)
−0.0356637 + 0.999364i \(0.511355\pi\)
\(140\) −4.72715e9 −1.03998
\(141\) 1.25942e7 0.00268338
\(142\) −3.49542e8 −0.0721442
\(143\) 3.74427e9 0.748781
\(144\) 1.50027e9 0.290763
\(145\) −4.10139e9 −0.770504
\(146\) −1.55843e10 −2.83858
\(147\) −7.30200e6 −0.00128977
\(148\) 1.32383e10 2.26806
\(149\) 1.88570e8 0.0313426 0.0156713 0.999877i \(-0.495011\pi\)
0.0156713 + 0.999877i \(0.495011\pi\)
\(150\) 1.75673e7 0.00283331
\(151\) 2.87194e9 0.449551 0.224775 0.974411i \(-0.427835\pi\)
0.224775 + 0.974411i \(0.427835\pi\)
\(152\) 5.06288e9 0.769310
\(153\) 0 0
\(154\) −2.43721e9 −0.349181
\(155\) −1.27590e10 −1.77552
\(156\) −3.07024e7 −0.00415061
\(157\) −1.23729e9 −0.162526 −0.0812630 0.996693i \(-0.525895\pi\)
−0.0812630 + 0.996693i \(0.525895\pi\)
\(158\) 4.20857e9 0.537251
\(159\) −1.18258e7 −0.00146738
\(160\) 1.44308e10 1.74080
\(161\) 3.55296e9 0.416749
\(162\) 1.38035e10 1.57460
\(163\) 1.52441e10 1.69144 0.845722 0.533624i \(-0.179170\pi\)
0.845722 + 0.533624i \(0.179170\pi\)
\(164\) 6.76340e9 0.730076
\(165\) 1.05002e7 0.00110285
\(166\) 2.64718e10 2.70581
\(167\) 7.98265e9 0.794187 0.397094 0.917778i \(-0.370019\pi\)
0.397094 + 0.917778i \(0.370019\pi\)
\(168\) 6.47613e6 0.000627226 0
\(169\) 1.83916e10 1.73432
\(170\) 0 0
\(171\) −1.13948e10 −1.01911
\(172\) 1.69527e10 1.47693
\(173\) 6.70354e9 0.568980 0.284490 0.958679i \(-0.408176\pi\)
0.284490 + 0.958679i \(0.408176\pi\)
\(174\) 1.73393e7 0.00143403
\(175\) 6.44375e9 0.519359
\(176\) 1.67601e9 0.131665
\(177\) −2.97703e7 −0.00227984
\(178\) −2.28031e10 −1.70257
\(179\) −6.50426e9 −0.473543 −0.236771 0.971565i \(-0.576089\pi\)
−0.236771 + 0.971565i \(0.576089\pi\)
\(180\) 2.99090e10 2.12361
\(181\) −1.61582e9 −0.111902 −0.0559510 0.998434i \(-0.517819\pi\)
−0.0559510 + 0.998434i \(0.517819\pi\)
\(182\) −1.88741e10 −1.27510
\(183\) −1.79904e7 −0.00118580
\(184\) 9.98816e9 0.642399
\(185\) −3.50614e10 −2.20068
\(186\) 5.39409e7 0.00330453
\(187\) 0 0
\(188\) 4.00757e10 2.33976
\(189\) −2.91510e7 −0.00166179
\(190\) −4.13788e10 −2.30349
\(191\) −3.04910e10 −1.65776 −0.828879 0.559428i \(-0.811021\pi\)
−0.828879 + 0.559428i \(0.811021\pi\)
\(192\) −5.17188e7 −0.00274658
\(193\) 2.89268e10 1.50070 0.750349 0.661042i \(-0.229886\pi\)
0.750349 + 0.661042i \(0.229886\pi\)
\(194\) 5.33879e10 2.70605
\(195\) 8.13147e7 0.00402729
\(196\) −2.32356e10 −1.12461
\(197\) −2.47919e9 −0.117277 −0.0586383 0.998279i \(-0.518676\pi\)
−0.0586383 + 0.998279i \(0.518676\pi\)
\(198\) 1.54204e10 0.713021
\(199\) −2.36696e10 −1.06992 −0.534960 0.844877i \(-0.679673\pi\)
−0.534960 + 0.844877i \(0.679673\pi\)
\(200\) 1.81148e10 0.800568
\(201\) −1.34837e7 −0.000582674 0
\(202\) 3.92994e8 0.0166075
\(203\) 6.36011e9 0.262865
\(204\) 0 0
\(205\) −1.79127e10 −0.708385
\(206\) 7.57598e10 2.93114
\(207\) −2.24798e10 −0.850994
\(208\) 1.29792e10 0.480800
\(209\) −1.27295e10 −0.461481
\(210\) −5.29293e7 −0.00187806
\(211\) −5.06744e10 −1.76002 −0.880009 0.474956i \(-0.842464\pi\)
−0.880009 + 0.474956i \(0.842464\pi\)
\(212\) −3.76306e10 −1.27947
\(213\) −2.33526e6 −7.77369e−5 0
\(214\) 4.45248e10 1.45124
\(215\) −4.48988e10 −1.43305
\(216\) −8.19499e7 −0.00256157
\(217\) 1.97857e10 0.605736
\(218\) −8.51439e10 −2.55328
\(219\) −1.04118e8 −0.00305863
\(220\) 3.34124e10 0.961626
\(221\) 0 0
\(222\) 1.48228e8 0.00409582
\(223\) 1.86341e10 0.504588 0.252294 0.967651i \(-0.418815\pi\)
0.252294 + 0.967651i \(0.418815\pi\)
\(224\) −2.23781e10 −0.593891
\(225\) −4.07700e10 −1.06052
\(226\) 6.37665e10 1.62594
\(227\) −6.75910e10 −1.68956 −0.844778 0.535118i \(-0.820267\pi\)
−0.844778 + 0.535118i \(0.820267\pi\)
\(228\) 1.04380e8 0.00255806
\(229\) −4.65557e9 −0.111870 −0.0559349 0.998434i \(-0.517814\pi\)
−0.0559349 + 0.998434i \(0.517814\pi\)
\(230\) −8.16330e10 −1.92349
\(231\) −1.62828e7 −0.000376250 0
\(232\) 1.78797e10 0.405194
\(233\) 3.07788e10 0.684148 0.342074 0.939673i \(-0.388871\pi\)
0.342074 + 0.939673i \(0.388871\pi\)
\(234\) 1.19418e11 2.60374
\(235\) −1.06140e11 −2.27024
\(236\) −9.47318e10 −1.98789
\(237\) 2.81171e7 0.000578900 0
\(238\) 0 0
\(239\) 7.55716e10 1.49819 0.749097 0.662460i \(-0.230487\pi\)
0.749097 + 0.662460i \(0.230487\pi\)
\(240\) 3.63981e7 0.000708155 0
\(241\) 2.68306e10 0.512335 0.256167 0.966632i \(-0.417540\pi\)
0.256167 + 0.966632i \(0.417540\pi\)
\(242\) −6.67856e10 −1.25174
\(243\) 2.76661e8 0.00509002
\(244\) −5.72470e10 −1.03395
\(245\) 6.15390e10 1.09120
\(246\) 7.57290e7 0.00131842
\(247\) −9.85791e10 −1.68519
\(248\) 5.56220e10 0.933714
\(249\) 1.76856e8 0.00291557
\(250\) −8.44932e9 −0.136802
\(251\) 4.14790e10 0.659624 0.329812 0.944047i \(-0.393015\pi\)
0.329812 + 0.944047i \(0.393015\pi\)
\(252\) −4.63805e10 −0.724491
\(253\) −2.51131e10 −0.385352
\(254\) −4.65066e10 −0.701073
\(255\) 0 0
\(256\) −3.33495e10 −0.485299
\(257\) 4.82861e10 0.690435 0.345217 0.938523i \(-0.387805\pi\)
0.345217 + 0.938523i \(0.387805\pi\)
\(258\) 1.89817e8 0.00266714
\(259\) 5.43704e10 0.750782
\(260\) 2.58750e11 3.51157
\(261\) −4.02408e10 −0.536766
\(262\) 2.26195e10 0.296569
\(263\) −2.55822e10 −0.329714 −0.164857 0.986317i \(-0.552716\pi\)
−0.164857 + 0.986317i \(0.552716\pi\)
\(264\) −4.57746e7 −0.000579972 0
\(265\) 9.96638e10 1.24146
\(266\) 6.41670e10 0.785859
\(267\) −1.52346e8 −0.00183455
\(268\) −4.29062e10 −0.508058
\(269\) 6.96548e10 0.811083 0.405542 0.914077i \(-0.367083\pi\)
0.405542 + 0.914077i \(0.367083\pi\)
\(270\) 6.69775e8 0.00766994
\(271\) −5.29874e10 −0.596775 −0.298387 0.954445i \(-0.596449\pi\)
−0.298387 + 0.954445i \(0.596449\pi\)
\(272\) 0 0
\(273\) −1.26097e8 −0.00137395
\(274\) 5.96886e10 0.639755
\(275\) −4.55457e10 −0.480231
\(276\) 2.05923e8 0.00213607
\(277\) −1.49045e11 −1.52110 −0.760552 0.649277i \(-0.775072\pi\)
−0.760552 + 0.649277i \(0.775072\pi\)
\(278\) −1.11849e10 −0.112313
\(279\) −1.25186e11 −1.23690
\(280\) −5.45788e10 −0.530656
\(281\) −2.16237e10 −0.206896 −0.103448 0.994635i \(-0.532987\pi\)
−0.103448 + 0.994635i \(0.532987\pi\)
\(282\) 4.48722e8 0.00422529
\(283\) 1.51427e11 1.40335 0.701675 0.712498i \(-0.252436\pi\)
0.701675 + 0.712498i \(0.252436\pi\)
\(284\) −7.43100e9 −0.0677821
\(285\) −2.76448e8 −0.00248206
\(286\) 1.33406e11 1.17904
\(287\) 2.77777e10 0.241673
\(288\) 1.41588e11 1.21272
\(289\) 0 0
\(290\) −1.46130e11 −1.21325
\(291\) 3.56681e8 0.00291582
\(292\) −3.31312e11 −2.66695
\(293\) 4.42128e10 0.350464 0.175232 0.984527i \(-0.443932\pi\)
0.175232 + 0.984527i \(0.443932\pi\)
\(294\) −2.60166e8 −0.00203089
\(295\) 2.50895e11 1.92883
\(296\) 1.52847e11 1.15730
\(297\) 2.06045e8 0.00153659
\(298\) 6.71865e9 0.0493525
\(299\) −1.94479e11 −1.40719
\(300\) 3.73468e8 0.00266200
\(301\) 6.96256e10 0.488899
\(302\) 1.02325e11 0.707868
\(303\) 2.62556e6 1.78950e−5 0
\(304\) −4.41260e10 −0.296322
\(305\) 1.51617e11 1.00323
\(306\) 0 0
\(307\) 2.29583e11 1.47509 0.737543 0.675300i \(-0.235986\pi\)
0.737543 + 0.675300i \(0.235986\pi\)
\(308\) −5.18134e10 −0.328068
\(309\) 5.06145e8 0.00315836
\(310\) −4.54597e11 −2.79576
\(311\) −4.73812e10 −0.287200 −0.143600 0.989636i \(-0.545868\pi\)
−0.143600 + 0.989636i \(0.545868\pi\)
\(312\) −3.54485e8 −0.00211788
\(313\) 2.62450e11 1.54560 0.772801 0.634648i \(-0.218855\pi\)
0.772801 + 0.634648i \(0.218855\pi\)
\(314\) −4.40839e10 −0.255916
\(315\) 1.22838e11 0.702966
\(316\) 8.94711e10 0.504767
\(317\) 9.07698e10 0.504864 0.252432 0.967615i \(-0.418770\pi\)
0.252432 + 0.967615i \(0.418770\pi\)
\(318\) −4.21345e8 −0.00231055
\(319\) −4.49546e10 −0.243061
\(320\) 4.35870e11 2.32371
\(321\) 2.97467e8 0.00156375
\(322\) 1.26590e11 0.656218
\(323\) 0 0
\(324\) 2.93451e11 1.47939
\(325\) −3.52712e11 −1.75366
\(326\) 5.43138e11 2.66337
\(327\) −5.68840e8 −0.00275122
\(328\) 7.80891e10 0.372527
\(329\) 1.64593e11 0.774515
\(330\) 3.74115e8 0.00173657
\(331\) 1.53040e11 0.700775 0.350387 0.936605i \(-0.386050\pi\)
0.350387 + 0.936605i \(0.386050\pi\)
\(332\) 5.62772e11 2.54221
\(333\) −3.44005e11 −1.53308
\(334\) 2.84417e11 1.25054
\(335\) 1.13636e11 0.492963
\(336\) −5.64434e7 −0.000241594 0
\(337\) 4.73479e10 0.199971 0.0999854 0.994989i \(-0.468120\pi\)
0.0999854 + 0.994989i \(0.468120\pi\)
\(338\) 6.55282e11 2.73088
\(339\) 4.26019e8 0.00175198
\(340\) 0 0
\(341\) −1.39850e11 −0.560101
\(342\) −4.05989e11 −1.60471
\(343\) −2.20966e11 −0.861991
\(344\) 1.95733e11 0.753616
\(345\) −5.45384e8 −0.00207260
\(346\) 2.38843e11 0.895923
\(347\) 1.71966e11 0.636736 0.318368 0.947967i \(-0.396865\pi\)
0.318368 + 0.947967i \(0.396865\pi\)
\(348\) 3.68621e8 0.00134733
\(349\) −9.37822e10 −0.338381 −0.169191 0.985583i \(-0.554115\pi\)
−0.169191 + 0.985583i \(0.554115\pi\)
\(350\) 2.29587e11 0.817789
\(351\) 1.59564e9 0.00561118
\(352\) 1.58173e11 0.549149
\(353\) 3.21525e11 1.10212 0.551059 0.834466i \(-0.314224\pi\)
0.551059 + 0.834466i \(0.314224\pi\)
\(354\) −1.06070e9 −0.00358986
\(355\) 1.96809e10 0.0657683
\(356\) −4.84778e11 −1.59963
\(357\) 0 0
\(358\) −2.31743e11 −0.745647
\(359\) −2.50132e10 −0.0794776 −0.0397388 0.999210i \(-0.512653\pi\)
−0.0397388 + 0.999210i \(0.512653\pi\)
\(360\) 3.45324e11 1.08359
\(361\) 1.24551e10 0.0385981
\(362\) −5.75706e10 −0.176202
\(363\) −4.46190e8 −0.00134878
\(364\) −4.01250e11 −1.19801
\(365\) 8.77472e11 2.58771
\(366\) −6.40987e8 −0.00186717
\(367\) −5.32399e11 −1.53193 −0.765967 0.642880i \(-0.777740\pi\)
−0.765967 + 0.642880i \(0.777740\pi\)
\(368\) −8.70528e10 −0.247439
\(369\) −1.75751e11 −0.493491
\(370\) −1.24922e12 −3.46521
\(371\) −1.54551e11 −0.423535
\(372\) 1.14675e9 0.00310473
\(373\) −3.56768e11 −0.954325 −0.477163 0.878815i \(-0.658335\pi\)
−0.477163 + 0.878815i \(0.658335\pi\)
\(374\) 0 0
\(375\) −5.64493e7 −0.000147407 0
\(376\) 4.62707e11 1.19388
\(377\) −3.48134e11 −0.887586
\(378\) −1.03863e9 −0.00261667
\(379\) 2.85881e11 0.711720 0.355860 0.934539i \(-0.384188\pi\)
0.355860 + 0.934539i \(0.384188\pi\)
\(380\) −8.79683e11 −2.16421
\(381\) −3.10707e8 −0.000755421 0
\(382\) −1.08638e12 −2.61033
\(383\) −3.68259e11 −0.874498 −0.437249 0.899340i \(-0.644047\pi\)
−0.437249 + 0.899340i \(0.644047\pi\)
\(384\) −9.66012e8 −0.00226721
\(385\) 1.37227e11 0.318321
\(386\) 1.03065e12 2.36302
\(387\) −4.40525e11 −0.998324
\(388\) 1.13499e12 2.54243
\(389\) 3.24891e11 0.719391 0.359696 0.933070i \(-0.382881\pi\)
0.359696 + 0.933070i \(0.382881\pi\)
\(390\) 2.89720e9 0.00634143
\(391\) 0 0
\(392\) −2.68274e11 −0.573841
\(393\) 1.51119e8 0.000319560 0
\(394\) −8.83321e10 −0.184665
\(395\) −2.36962e11 −0.489770
\(396\) 3.27827e11 0.669909
\(397\) 1.08653e11 0.219525 0.109763 0.993958i \(-0.464991\pi\)
0.109763 + 0.993958i \(0.464991\pi\)
\(398\) −8.43333e11 −1.68471
\(399\) 4.28695e8 0.000846779 0
\(400\) −1.57881e11 −0.308362
\(401\) −1.67993e11 −0.324446 −0.162223 0.986754i \(-0.551866\pi\)
−0.162223 + 0.986754i \(0.551866\pi\)
\(402\) −4.80415e8 −0.000917486 0
\(403\) −1.08301e12 −2.04532
\(404\) 8.35477e9 0.0156034
\(405\) −7.77200e11 −1.43544
\(406\) 2.26607e11 0.413911
\(407\) −3.84301e11 −0.694220
\(408\) 0 0
\(409\) 3.07465e11 0.543302 0.271651 0.962396i \(-0.412430\pi\)
0.271651 + 0.962396i \(0.412430\pi\)
\(410\) −6.38220e11 −1.11543
\(411\) 3.98775e8 0.000689349 0
\(412\) 1.61060e12 2.75391
\(413\) −3.89069e11 −0.658038
\(414\) −8.00943e11 −1.33999
\(415\) −1.49049e12 −2.46668
\(416\) 1.22491e12 2.00533
\(417\) −7.47254e7 −0.000121020 0
\(418\) −4.53545e11 −0.726654
\(419\) −4.23303e11 −0.670947 −0.335473 0.942050i \(-0.608896\pi\)
−0.335473 + 0.942050i \(0.608896\pi\)
\(420\) −1.12524e9 −0.00176450
\(421\) −1.49913e11 −0.232578 −0.116289 0.993215i \(-0.537100\pi\)
−0.116289 + 0.993215i \(0.537100\pi\)
\(422\) −1.80550e12 −2.77135
\(423\) −1.04139e12 −1.58155
\(424\) −4.34476e11 −0.652860
\(425\) 0 0
\(426\) −8.32040e7 −0.000122406 0
\(427\) −2.35116e11 −0.342261
\(428\) 9.46566e11 1.36350
\(429\) 8.91276e8 0.00127044
\(430\) −1.59972e12 −2.25650
\(431\) 1.13823e12 1.58885 0.794427 0.607360i \(-0.207771\pi\)
0.794427 + 0.607360i \(0.207771\pi\)
\(432\) 7.14243e8 0.000986663 0
\(433\) 9.00628e11 1.23126 0.615630 0.788035i \(-0.288902\pi\)
0.615630 + 0.788035i \(0.288902\pi\)
\(434\) 7.04954e11 0.953800
\(435\) −9.76284e8 −0.00130730
\(436\) −1.81010e12 −2.39890
\(437\) 6.61177e11 0.867264
\(438\) −3.70966e9 −0.00481615
\(439\) −2.15467e11 −0.276879 −0.138440 0.990371i \(-0.544209\pi\)
−0.138440 + 0.990371i \(0.544209\pi\)
\(440\) 3.85774e11 0.490678
\(441\) 6.03791e11 0.760173
\(442\) 0 0
\(443\) 3.47695e11 0.428925 0.214462 0.976732i \(-0.431200\pi\)
0.214462 + 0.976732i \(0.431200\pi\)
\(444\) 3.15121e9 0.00384817
\(445\) 1.28393e12 1.55210
\(446\) 6.63923e11 0.794531
\(447\) 4.48868e7 5.31783e−5 0
\(448\) −6.75913e11 −0.792757
\(449\) 1.08563e12 1.26059 0.630296 0.776355i \(-0.282934\pi\)
0.630296 + 0.776355i \(0.282934\pi\)
\(450\) −1.45261e12 −1.66991
\(451\) −1.96338e11 −0.223465
\(452\) 1.35563e12 1.52763
\(453\) 6.83629e8 0.000762743 0
\(454\) −2.40823e12 −2.66040
\(455\) 1.06270e12 1.16241
\(456\) 1.20515e9 0.00130527
\(457\) −8.91105e11 −0.955666 −0.477833 0.878451i \(-0.658578\pi\)
−0.477833 + 0.878451i \(0.658578\pi\)
\(458\) −1.65875e11 −0.176152
\(459\) 0 0
\(460\) −1.73546e12 −1.80719
\(461\) 7.21170e11 0.743675 0.371838 0.928298i \(-0.378728\pi\)
0.371838 + 0.928298i \(0.378728\pi\)
\(462\) −5.80148e8 −0.000592448 0
\(463\) 2.47341e11 0.250139 0.125069 0.992148i \(-0.460085\pi\)
0.125069 + 0.992148i \(0.460085\pi\)
\(464\) −1.55832e11 −0.156072
\(465\) −3.03713e9 −0.00301249
\(466\) 1.09663e12 1.07727
\(467\) 3.73549e10 0.0363431 0.0181715 0.999835i \(-0.494215\pi\)
0.0181715 + 0.999835i \(0.494215\pi\)
\(468\) 2.53873e12 2.44631
\(469\) −1.76218e11 −0.168179
\(470\) −3.78169e12 −3.57475
\(471\) −2.94521e8 −0.000275754 0
\(472\) −1.09376e12 −1.01434
\(473\) −4.92128e11 −0.452067
\(474\) 1.00180e9 0.000911543 0
\(475\) 1.19913e12 1.08080
\(476\) 0 0
\(477\) 9.77853e11 0.864851
\(478\) 2.69257e12 2.35908
\(479\) −1.56185e11 −0.135560 −0.0677798 0.997700i \(-0.521592\pi\)
−0.0677798 + 0.997700i \(0.521592\pi\)
\(480\) 3.43506e9 0.00295358
\(481\) −2.97608e12 −2.53508
\(482\) 9.55959e11 0.806729
\(483\) 8.45739e8 0.000707089 0
\(484\) −1.41981e12 −1.17605
\(485\) −3.00600e12 −2.46689
\(486\) 9.85726e9 0.00801481
\(487\) 7.04881e11 0.567853 0.283926 0.958846i \(-0.408363\pi\)
0.283926 + 0.958846i \(0.408363\pi\)
\(488\) −6.60964e11 −0.527580
\(489\) 3.62867e9 0.00286984
\(490\) 2.19260e12 1.71821
\(491\) 2.70124e11 0.209747 0.104874 0.994486i \(-0.466556\pi\)
0.104874 + 0.994486i \(0.466556\pi\)
\(492\) 1.60994e9 0.00123870
\(493\) 0 0
\(494\) −3.51232e12 −2.65352
\(495\) −8.68242e11 −0.650006
\(496\) −4.84779e11 −0.359647
\(497\) −3.05195e10 −0.0224375
\(498\) 6.30129e9 0.00459090
\(499\) 1.68888e12 1.21940 0.609699 0.792633i \(-0.291290\pi\)
0.609699 + 0.792633i \(0.291290\pi\)
\(500\) −1.79626e11 −0.128530
\(501\) 1.90017e9 0.00134748
\(502\) 1.47787e12 1.03865
\(503\) 4.85829e11 0.338398 0.169199 0.985582i \(-0.445882\pi\)
0.169199 + 0.985582i \(0.445882\pi\)
\(504\) −5.35501e11 −0.369678
\(505\) −2.21274e10 −0.0151398
\(506\) −8.94764e11 −0.606780
\(507\) 4.37789e9 0.00294259
\(508\) −9.88698e11 −0.658684
\(509\) 4.99864e11 0.330082 0.165041 0.986287i \(-0.447224\pi\)
0.165041 + 0.986287i \(0.447224\pi\)
\(510\) 0 0
\(511\) −1.36072e12 −0.882823
\(512\) 8.89593e11 0.572106
\(513\) −5.42477e9 −0.00345822
\(514\) 1.72040e12 1.08717
\(515\) −4.26563e12 −2.67209
\(516\) 4.03537e9 0.00250588
\(517\) −1.16338e12 −0.716165
\(518\) 1.93719e12 1.18219
\(519\) 1.59569e9 0.000965376 0
\(520\) 2.98749e12 1.79181
\(521\) −2.25253e12 −1.33937 −0.669687 0.742644i \(-0.733572\pi\)
−0.669687 + 0.742644i \(0.733572\pi\)
\(522\) −1.43376e12 −0.845198
\(523\) 1.33630e12 0.780990 0.390495 0.920605i \(-0.372304\pi\)
0.390495 + 0.920605i \(0.372304\pi\)
\(524\) 4.80873e11 0.278638
\(525\) 1.53385e9 0.000881185 0
\(526\) −9.11481e11 −0.519172
\(527\) 0 0
\(528\) 3.98953e8 0.000223393 0
\(529\) −4.96768e11 −0.275806
\(530\) 3.55097e12 1.95481
\(531\) 2.46166e12 1.34370
\(532\) 1.36414e12 0.738343
\(533\) −1.52047e12 −0.816028
\(534\) −5.42800e9 −0.00288871
\(535\) −2.50696e12 −1.32299
\(536\) −4.95387e11 −0.259241
\(537\) −1.54826e9 −0.000803451 0
\(538\) 2.48176e12 1.27714
\(539\) 6.74517e11 0.344226
\(540\) 1.42389e10 0.00720618
\(541\) −1.60577e12 −0.805928 −0.402964 0.915216i \(-0.632020\pi\)
−0.402964 + 0.915216i \(0.632020\pi\)
\(542\) −1.88791e12 −0.939689
\(543\) −3.84625e8 −0.000189862 0
\(544\) 0 0
\(545\) 4.79400e12 2.32763
\(546\) −4.49275e9 −0.00216344
\(547\) −2.50244e12 −1.19515 −0.597573 0.801815i \(-0.703868\pi\)
−0.597573 + 0.801815i \(0.703868\pi\)
\(548\) 1.26894e12 0.601073
\(549\) 1.48760e12 0.698891
\(550\) −1.62277e12 −0.756178
\(551\) 1.18356e12 0.547028
\(552\) 2.37756e9 0.00108995
\(553\) 3.67463e11 0.167090
\(554\) −5.31040e12 −2.39515
\(555\) −8.34592e9 −0.00373384
\(556\) −2.37783e11 −0.105522
\(557\) 3.78565e10 0.0166645 0.00833225 0.999965i \(-0.497348\pi\)
0.00833225 + 0.999965i \(0.497348\pi\)
\(558\) −4.46029e12 −1.94764
\(559\) −3.81110e12 −1.65081
\(560\) 4.75687e11 0.204397
\(561\) 0 0
\(562\) −7.70440e11 −0.325781
\(563\) −3.79841e12 −1.59336 −0.796681 0.604400i \(-0.793413\pi\)
−0.796681 + 0.604400i \(0.793413\pi\)
\(564\) 9.53952e9 0.00396982
\(565\) −3.59035e12 −1.48224
\(566\) 5.39527e12 2.20973
\(567\) 1.20522e12 0.489715
\(568\) −8.57971e10 −0.0345864
\(569\) 4.15125e12 1.66025 0.830126 0.557575i \(-0.188268\pi\)
0.830126 + 0.557575i \(0.188268\pi\)
\(570\) −9.84970e9 −0.00390828
\(571\) −2.49821e12 −0.983483 −0.491741 0.870741i \(-0.663639\pi\)
−0.491741 + 0.870741i \(0.663639\pi\)
\(572\) 2.83612e12 1.10775
\(573\) −7.25800e9 −0.00281268
\(574\) 9.89702e11 0.380541
\(575\) 2.36567e12 0.902502
\(576\) 4.27655e12 1.61880
\(577\) 9.96726e11 0.374356 0.187178 0.982326i \(-0.440066\pi\)
0.187178 + 0.982326i \(0.440066\pi\)
\(578\) 0 0
\(579\) 6.88567e9 0.00254620
\(580\) −3.10662e12 −1.13989
\(581\) 2.31134e12 0.841532
\(582\) 1.27083e10 0.00459129
\(583\) 1.09240e12 0.391627
\(584\) −3.82527e12 −1.36083
\(585\) −6.72378e12 −2.37363
\(586\) 1.57528e12 0.551845
\(587\) −3.55291e12 −1.23513 −0.617566 0.786519i \(-0.711881\pi\)
−0.617566 + 0.786519i \(0.711881\pi\)
\(588\) −5.53094e9 −0.00190810
\(589\) 3.68196e12 1.26055
\(590\) 8.93925e12 3.03716
\(591\) −5.90140e8 −0.000198981 0
\(592\) −1.33215e12 −0.445766
\(593\) 4.25252e12 1.41221 0.706107 0.708105i \(-0.250450\pi\)
0.706107 + 0.708105i \(0.250450\pi\)
\(594\) 7.34128e9 0.00241954
\(595\) 0 0
\(596\) 1.42834e11 0.0463684
\(597\) −5.63424e9 −0.00181531
\(598\) −6.92917e12 −2.21578
\(599\) −4.95143e12 −1.57149 −0.785743 0.618554i \(-0.787719\pi\)
−0.785743 + 0.618554i \(0.787719\pi\)
\(600\) 4.31200e9 0.00135831
\(601\) −1.76825e12 −0.552850 −0.276425 0.961035i \(-0.589150\pi\)
−0.276425 + 0.961035i \(0.589150\pi\)
\(602\) 2.48072e12 0.769827
\(603\) 1.11494e12 0.343419
\(604\) 2.17537e12 0.665068
\(605\) 3.76035e12 1.14111
\(606\) 9.35473e7 2.81776e−5 0
\(607\) 2.04371e11 0.0611042 0.0305521 0.999533i \(-0.490273\pi\)
0.0305521 + 0.999533i \(0.490273\pi\)
\(608\) −4.16438e12 −1.23590
\(609\) 1.51395e9 0.000445997 0
\(610\) 5.40204e12 1.57970
\(611\) −9.00935e12 −2.61522
\(612\) 0 0
\(613\) −1.76517e12 −0.504911 −0.252455 0.967609i \(-0.581238\pi\)
−0.252455 + 0.967609i \(0.581238\pi\)
\(614\) 8.17992e12 2.32269
\(615\) −4.26390e9 −0.00120190
\(616\) −5.98229e11 −0.167399
\(617\) 4.51327e12 1.25374 0.626872 0.779123i \(-0.284335\pi\)
0.626872 + 0.779123i \(0.284335\pi\)
\(618\) 1.80337e10 0.00497320
\(619\) −2.40683e10 −0.00658926 −0.00329463 0.999995i \(-0.501049\pi\)
−0.00329463 + 0.999995i \(0.501049\pi\)
\(620\) −9.66441e12 −2.62671
\(621\) −1.07021e10 −0.00288773
\(622\) −1.68816e12 −0.452228
\(623\) −1.99101e12 −0.529514
\(624\) 3.08955e9 0.000815764 0
\(625\) −3.56984e12 −0.935813
\(626\) 9.35096e12 2.43373
\(627\) −3.03010e9 −0.000782985 0
\(628\) −9.37192e11 −0.240442
\(629\) 0 0
\(630\) 4.37664e12 1.10690
\(631\) −5.35424e12 −1.34451 −0.672257 0.740318i \(-0.734675\pi\)
−0.672257 + 0.740318i \(0.734675\pi\)
\(632\) 1.03302e12 0.257562
\(633\) −1.20624e10 −0.00298619
\(634\) 3.23408e12 0.794966
\(635\) 2.61854e12 0.639114
\(636\) −8.95749e9 −0.00217085
\(637\) 5.22355e12 1.25701
\(638\) −1.60171e12 −0.382727
\(639\) 1.93099e11 0.0458170
\(640\) 8.14125e12 1.91814
\(641\) −6.68364e12 −1.56369 −0.781847 0.623470i \(-0.785722\pi\)
−0.781847 + 0.623470i \(0.785722\pi\)
\(642\) 1.05986e10 0.00246229
\(643\) 4.42198e12 1.02016 0.510079 0.860128i \(-0.329616\pi\)
0.510079 + 0.860128i \(0.329616\pi\)
\(644\) 2.69121e12 0.616541
\(645\) −1.06876e10 −0.00243143
\(646\) 0 0
\(647\) 7.65641e12 1.71773 0.858867 0.512198i \(-0.171169\pi\)
0.858867 + 0.512198i \(0.171169\pi\)
\(648\) 3.38814e12 0.754873
\(649\) 2.75002e12 0.608463
\(650\) −1.25669e13 −2.76134
\(651\) 4.70975e9 0.00102774
\(652\) 1.15467e13 2.50233
\(653\) 8.87094e12 1.90924 0.954620 0.297826i \(-0.0962617\pi\)
0.954620 + 0.297826i \(0.0962617\pi\)
\(654\) −2.02674e10 −0.00433210
\(655\) −1.27358e12 −0.270359
\(656\) −6.80593e11 −0.143490
\(657\) 8.60933e12 1.80271
\(658\) 5.86436e12 1.21956
\(659\) 2.06299e12 0.426101 0.213051 0.977041i \(-0.431660\pi\)
0.213051 + 0.977041i \(0.431660\pi\)
\(660\) 7.95341e9 0.00163157
\(661\) 1.41824e11 0.0288965 0.0144482 0.999896i \(-0.495401\pi\)
0.0144482 + 0.999896i \(0.495401\pi\)
\(662\) 5.45272e12 1.10345
\(663\) 0 0
\(664\) 6.49767e12 1.29718
\(665\) −3.61291e12 −0.716406
\(666\) −1.22567e13 −2.41401
\(667\) 2.33496e12 0.456787
\(668\) 6.04650e12 1.17493
\(669\) 4.43562e9 0.000856124 0
\(670\) 4.04879e12 0.776226
\(671\) 1.66185e12 0.316476
\(672\) −5.32683e9 −0.00100764
\(673\) 9.81683e11 0.184460 0.0922302 0.995738i \(-0.470600\pi\)
0.0922302 + 0.995738i \(0.470600\pi\)
\(674\) 1.68698e12 0.314877
\(675\) −1.94096e10 −0.00359873
\(676\) 1.39308e13 2.56577
\(677\) −2.20727e12 −0.403837 −0.201919 0.979402i \(-0.564718\pi\)
−0.201919 + 0.979402i \(0.564718\pi\)
\(678\) 1.51788e10 0.00275870
\(679\) 4.66146e12 0.841605
\(680\) 0 0
\(681\) −1.60892e10 −0.00286663
\(682\) −4.98276e12 −0.881942
\(683\) −3.00134e11 −0.0527742 −0.0263871 0.999652i \(-0.508400\pi\)
−0.0263871 + 0.999652i \(0.508400\pi\)
\(684\) −8.63103e12 −1.50768
\(685\) −3.36075e12 −0.583215
\(686\) −7.87291e12 −1.35730
\(687\) −1.10820e9 −0.000189807 0
\(688\) −1.70593e12 −0.290277
\(689\) 8.45967e12 1.43010
\(690\) −1.94317e10 −0.00326355
\(691\) −7.77169e10 −0.0129677 −0.00648387 0.999979i \(-0.502064\pi\)
−0.00648387 + 0.999979i \(0.502064\pi\)
\(692\) 5.07764e12 0.841752
\(693\) 1.34640e12 0.221756
\(694\) 6.12704e12 1.00261
\(695\) 6.29762e11 0.102387
\(696\) 4.25603e9 0.000687485 0
\(697\) 0 0
\(698\) −3.34141e12 −0.532819
\(699\) 7.32651e9 0.00116078
\(700\) 4.88086e12 0.768342
\(701\) 5.48906e12 0.858552 0.429276 0.903173i \(-0.358769\pi\)
0.429276 + 0.903173i \(0.358769\pi\)
\(702\) 5.68519e10 0.00883543
\(703\) 1.01179e13 1.56240
\(704\) 4.77749e12 0.733032
\(705\) −2.52652e10 −0.00385187
\(706\) 1.14557e13 1.73541
\(707\) 3.43135e10 0.00516509
\(708\) −2.25497e10 −0.00337281
\(709\) −2.18350e12 −0.324523 −0.162262 0.986748i \(-0.551879\pi\)
−0.162262 + 0.986748i \(0.551879\pi\)
\(710\) 7.01217e11 0.103560
\(711\) −2.32496e12 −0.341195
\(712\) −5.59717e12 −0.816222
\(713\) 7.26385e12 1.05260
\(714\) 0 0
\(715\) −7.51139e12 −1.07484
\(716\) −4.92669e12 −0.700562
\(717\) 1.79889e10 0.00254196
\(718\) −8.91207e11 −0.125146
\(719\) 6.20764e12 0.866257 0.433128 0.901332i \(-0.357410\pi\)
0.433128 + 0.901332i \(0.357410\pi\)
\(720\) −3.00970e12 −0.417376
\(721\) 6.61482e12 0.911610
\(722\) 4.43769e11 0.0607771
\(723\) 6.38669e9 0.000869267 0
\(724\) −1.22391e12 −0.165549
\(725\) 4.23475e12 0.569255
\(726\) −1.58975e10 −0.00212380
\(727\) 8.67792e12 1.15215 0.576077 0.817395i \(-0.304583\pi\)
0.576077 + 0.817395i \(0.304583\pi\)
\(728\) −4.63276e12 −0.611292
\(729\) −7.62547e12 −0.999983
\(730\) 3.12638e13 4.07464
\(731\) 0 0
\(732\) −1.36269e10 −0.00175428
\(733\) 6.34487e12 0.811811 0.405905 0.913915i \(-0.366956\pi\)
0.405905 + 0.913915i \(0.366956\pi\)
\(734\) −1.89691e13 −2.41220
\(735\) 1.46486e10 0.00185141
\(736\) −8.21558e12 −1.03202
\(737\) 1.24554e12 0.155509
\(738\) −6.26191e12 −0.777057
\(739\) −1.28807e13 −1.58869 −0.794344 0.607468i \(-0.792185\pi\)
−0.794344 + 0.607468i \(0.792185\pi\)
\(740\) −2.65574e13 −3.25569
\(741\) −2.34655e10 −0.00285922
\(742\) −5.50656e12 −0.666903
\(743\) 1.97478e12 0.237722 0.118861 0.992911i \(-0.462076\pi\)
0.118861 + 0.992911i \(0.462076\pi\)
\(744\) 1.32401e10 0.00158421
\(745\) −3.78292e11 −0.0449908
\(746\) −1.27114e13 −1.50269
\(747\) −1.46240e13 −1.71839
\(748\) 0 0
\(749\) 3.88760e12 0.451350
\(750\) −2.01125e9 −0.000232109 0
\(751\) 1.19872e13 1.37512 0.687558 0.726129i \(-0.258683\pi\)
0.687558 + 0.726129i \(0.258683\pi\)
\(752\) −4.03277e12 −0.459857
\(753\) 9.87356e9 0.00111917
\(754\) −1.24038e13 −1.39761
\(755\) −5.76141e12 −0.645309
\(756\) −2.20806e10 −0.00245846
\(757\) −9.64713e12 −1.06774 −0.533871 0.845566i \(-0.679263\pi\)
−0.533871 + 0.845566i \(0.679263\pi\)
\(758\) 1.01858e13 1.12068
\(759\) −5.97785e9 −0.000653818 0
\(760\) −1.01567e13 −1.10431
\(761\) −4.48077e12 −0.484308 −0.242154 0.970238i \(-0.577854\pi\)
−0.242154 + 0.970238i \(0.577854\pi\)
\(762\) −1.10703e10 −0.00118950
\(763\) −7.43417e12 −0.794094
\(764\) −2.30956e13 −2.45250
\(765\) 0 0
\(766\) −1.31209e13 −1.37700
\(767\) 2.12965e13 2.22192
\(768\) −7.93844e9 −0.000823397 0
\(769\) 1.58699e13 1.63646 0.818230 0.574891i \(-0.194956\pi\)
0.818230 + 0.574891i \(0.194956\pi\)
\(770\) 4.88931e12 0.501233
\(771\) 1.14939e10 0.00117145
\(772\) 2.19108e13 2.22014
\(773\) −1.21257e12 −0.122151 −0.0610755 0.998133i \(-0.519453\pi\)
−0.0610755 + 0.998133i \(0.519453\pi\)
\(774\) −1.56957e13 −1.57197
\(775\) 1.31739e13 1.31177
\(776\) 1.31044e13 1.29730
\(777\) 1.29422e10 0.00127384
\(778\) 1.15757e13 1.13276
\(779\) 5.16919e12 0.502926
\(780\) 6.15923e10 0.00595800
\(781\) 2.15718e11 0.0207471
\(782\) 0 0
\(783\) −1.91577e10 −0.00182144
\(784\) 2.33817e12 0.221031
\(785\) 2.48213e12 0.233298
\(786\) 5.38428e9 0.000503183 0
\(787\) 1.14356e13 1.06261 0.531304 0.847181i \(-0.321702\pi\)
0.531304 + 0.847181i \(0.321702\pi\)
\(788\) −1.87788e12 −0.173500
\(789\) −6.08953e9 −0.000559419 0
\(790\) −8.44283e12 −0.771199
\(791\) 5.56764e12 0.505682
\(792\) 3.78503e12 0.341827
\(793\) 1.28696e13 1.15567
\(794\) 3.87124e12 0.345667
\(795\) 2.37237e10 0.00210635
\(796\) −1.79286e13 −1.58285
\(797\) 1.15535e13 1.01427 0.507133 0.861868i \(-0.330705\pi\)
0.507133 + 0.861868i \(0.330705\pi\)
\(798\) 1.52742e10 0.00133335
\(799\) 0 0
\(800\) −1.49000e13 −1.28612
\(801\) 1.25973e13 1.08126
\(802\) −5.98550e12 −0.510876
\(803\) 9.61781e12 0.816313
\(804\) −1.02133e10 −0.000862011 0
\(805\) −7.12762e12 −0.598223
\(806\) −3.85872e13 −3.22059
\(807\) 1.65804e10 0.00137615
\(808\) 9.64627e10 0.00796175
\(809\) 1.64570e13 1.35077 0.675387 0.737464i \(-0.263977\pi\)
0.675387 + 0.737464i \(0.263977\pi\)
\(810\) −2.76912e13 −2.26026
\(811\) 4.72555e12 0.383582 0.191791 0.981436i \(-0.438570\pi\)
0.191791 + 0.981436i \(0.438570\pi\)
\(812\) 4.81751e12 0.388884
\(813\) −1.26130e10 −0.00101254
\(814\) −1.36924e13 −1.09313
\(815\) −3.05813e13 −2.42799
\(816\) 0 0
\(817\) 1.29567e13 1.01741
\(818\) 1.09548e13 0.855490
\(819\) 1.04267e13 0.809786
\(820\) −1.35681e13 −1.04799
\(821\) −1.56503e13 −1.20221 −0.601103 0.799172i \(-0.705272\pi\)
−0.601103 + 0.799172i \(0.705272\pi\)
\(822\) 1.42081e10 0.00108546
\(823\) 7.85441e12 0.596780 0.298390 0.954444i \(-0.403550\pi\)
0.298390 + 0.954444i \(0.403550\pi\)
\(824\) 1.85957e13 1.40521
\(825\) −1.08416e10 −0.000814798 0
\(826\) −1.38623e13 −1.03616
\(827\) −2.59264e13 −1.92738 −0.963689 0.267026i \(-0.913959\pi\)
−0.963689 + 0.267026i \(0.913959\pi\)
\(828\) −1.70275e13 −1.25897
\(829\) 8.15862e12 0.599959 0.299979 0.953946i \(-0.403020\pi\)
0.299979 + 0.953946i \(0.403020\pi\)
\(830\) −5.31053e13 −3.88407
\(831\) −3.54784e10 −0.00258083
\(832\) 3.69975e13 2.67681
\(833\) 0 0
\(834\) −2.66242e9 −0.000190559 0
\(835\) −1.60140e13 −1.14002
\(836\) −9.64205e12 −0.682717
\(837\) −5.95978e10 −0.00419726
\(838\) −1.50820e13 −1.05648
\(839\) −1.19352e13 −0.831576 −0.415788 0.909462i \(-0.636494\pi\)
−0.415788 + 0.909462i \(0.636494\pi\)
\(840\) −1.29918e10 −0.000900353 0
\(841\) −1.03274e13 −0.711881
\(842\) −5.34130e12 −0.366221
\(843\) −5.14725e9 −0.000351036 0
\(844\) −3.83836e13 −2.60378
\(845\) −3.68955e13 −2.48954
\(846\) −3.71041e13 −2.49032
\(847\) −5.83125e12 −0.389302
\(848\) 3.78672e12 0.251468
\(849\) 3.60454e10 0.00238103
\(850\) 0 0
\(851\) 1.99608e13 1.30465
\(852\) −1.76886e9 −0.000115004 0
\(853\) 1.88383e13 1.21835 0.609174 0.793037i \(-0.291501\pi\)
0.609174 + 0.793037i \(0.291501\pi\)
\(854\) −8.37706e12 −0.538929
\(855\) 2.28591e13 1.46289
\(856\) 1.09289e13 0.695735
\(857\) −1.23172e13 −0.780009 −0.390005 0.920813i \(-0.627527\pi\)
−0.390005 + 0.920813i \(0.627527\pi\)
\(858\) 3.17556e10 0.00200045
\(859\) 1.58752e13 0.994832 0.497416 0.867512i \(-0.334282\pi\)
0.497416 + 0.867512i \(0.334282\pi\)
\(860\) −3.40089e13 −2.12006
\(861\) 6.61213e9 0.000410041 0
\(862\) 4.05546e13 2.50183
\(863\) 2.03855e13 1.25104 0.625521 0.780207i \(-0.284886\pi\)
0.625521 + 0.780207i \(0.284886\pi\)
\(864\) 6.74064e10 0.00411518
\(865\) −1.34480e13 −0.816743
\(866\) 3.20889e13 1.93876
\(867\) 0 0
\(868\) 1.49868e13 0.896129
\(869\) −2.59730e12 −0.154502
\(870\) −3.47844e10 −0.00205849
\(871\) 9.64566e12 0.567872
\(872\) −2.08991e13 −1.22406
\(873\) −2.94934e13 −1.71854
\(874\) 2.35574e13 1.36561
\(875\) −7.37736e11 −0.0425466
\(876\) −7.88646e10 −0.00452495
\(877\) 2.26963e13 1.29556 0.647778 0.761829i \(-0.275698\pi\)
0.647778 + 0.761829i \(0.275698\pi\)
\(878\) −7.67696e12 −0.435977
\(879\) 1.05243e10 0.000594625 0
\(880\) −3.36225e12 −0.188999
\(881\) 5.12762e12 0.286764 0.143382 0.989667i \(-0.454202\pi\)
0.143382 + 0.989667i \(0.454202\pi\)
\(882\) 2.15127e13 1.19698
\(883\) −2.76572e13 −1.53104 −0.765518 0.643415i \(-0.777517\pi\)
−0.765518 + 0.643415i \(0.777517\pi\)
\(884\) 0 0
\(885\) 5.97224e10 0.00327260
\(886\) 1.23882e13 0.675391
\(887\) −2.27687e13 −1.23504 −0.617521 0.786554i \(-0.711863\pi\)
−0.617521 + 0.786554i \(0.711863\pi\)
\(888\) 3.63834e10 0.00196356
\(889\) −4.06064e12 −0.218040
\(890\) 4.57455e13 2.44396
\(891\) −8.51875e12 −0.452820
\(892\) 1.41145e13 0.746491
\(893\) 3.06294e13 1.61178
\(894\) 1.59929e9 8.37353e−5 0
\(895\) 1.30482e13 0.679748
\(896\) −1.26248e13 −0.654394
\(897\) −4.62933e10 −0.00238755
\(898\) 3.86805e13 1.98494
\(899\) 1.30029e13 0.663930
\(900\) −3.08815e13 −1.56894
\(901\) 0 0
\(902\) −6.99542e12 −0.351872
\(903\) 1.65735e10 0.000829505 0
\(904\) 1.56519e13 0.779485
\(905\) 3.24150e12 0.160630
\(906\) 2.43573e10 0.00120103
\(907\) 1.29915e13 0.637423 0.318711 0.947852i \(-0.396750\pi\)
0.318711 + 0.947852i \(0.396750\pi\)
\(908\) −5.11972e13 −2.49954
\(909\) −2.17104e11 −0.0105470
\(910\) 3.78635e13 1.83035
\(911\) 2.54247e13 1.22299 0.611496 0.791248i \(-0.290568\pi\)
0.611496 + 0.791248i \(0.290568\pi\)
\(912\) −1.05036e10 −0.000502763 0
\(913\) −1.63370e13 −0.778133
\(914\) −3.17496e13 −1.50480
\(915\) 3.60906e10 0.00170216
\(916\) −3.52639e12 −0.165501
\(917\) 1.97497e12 0.0922357
\(918\) 0 0
\(919\) −2.91533e13 −1.34824 −0.674121 0.738621i \(-0.735477\pi\)
−0.674121 + 0.738621i \(0.735477\pi\)
\(920\) −2.00373e13 −0.922134
\(921\) 5.46494e10 0.00250275
\(922\) 2.56949e13 1.17100
\(923\) 1.67055e12 0.0757621
\(924\) −1.23335e10 −0.000556626 0
\(925\) 3.62014e13 1.62588
\(926\) 8.81261e12 0.393872
\(927\) −4.18523e13 −1.86149
\(928\) −1.47066e13 −0.650948
\(929\) 3.16234e13 1.39296 0.696480 0.717576i \(-0.254749\pi\)
0.696480 + 0.717576i \(0.254749\pi\)
\(930\) −1.08211e11 −0.00474350
\(931\) −1.77587e13 −0.774707
\(932\) 2.33136e13 1.01213
\(933\) −1.12785e10 −0.000487286 0
\(934\) 1.33093e12 0.0572263
\(935\) 0 0
\(936\) 2.93118e13 1.24825
\(937\) −3.18028e13 −1.34784 −0.673918 0.738806i \(-0.735390\pi\)
−0.673918 + 0.738806i \(0.735390\pi\)
\(938\) −6.27855e12 −0.264817
\(939\) 6.24730e10 0.00262239
\(940\) −8.03961e13 −3.35861
\(941\) 2.16662e13 0.900803 0.450401 0.892826i \(-0.351281\pi\)
0.450401 + 0.892826i \(0.351281\pi\)
\(942\) −1.04936e10 −0.000434207 0
\(943\) 1.01979e13 0.419960
\(944\) 9.53275e12 0.390701
\(945\) 5.84801e10 0.00238542
\(946\) −1.75342e13 −0.711830
\(947\) −1.15699e13 −0.467470 −0.233735 0.972300i \(-0.575095\pi\)
−0.233735 + 0.972300i \(0.575095\pi\)
\(948\) 2.12975e10 0.000856428 0
\(949\) 7.44817e13 2.98093
\(950\) 4.27242e13 1.70184
\(951\) 2.16066e10 0.000856593 0
\(952\) 0 0
\(953\) −1.14361e13 −0.449118 −0.224559 0.974461i \(-0.572094\pi\)
−0.224559 + 0.974461i \(0.572094\pi\)
\(954\) 3.48404e13 1.36180
\(955\) 6.11681e13 2.37963
\(956\) 5.72422e13 2.21644
\(957\) −1.07009e10 −0.000412397 0
\(958\) −5.56479e12 −0.213454
\(959\) 5.21159e12 0.198969
\(960\) 1.03753e11 0.00394259
\(961\) 1.40113e13 0.529936
\(962\) −1.06036e14 −3.99177
\(963\) −2.45971e13 −0.921648
\(964\) 2.03230e13 0.757951
\(965\) −5.80303e13 −2.15418
\(966\) 3.01332e10 0.00111339
\(967\) −1.44349e13 −0.530879 −0.265439 0.964128i \(-0.585517\pi\)
−0.265439 + 0.964128i \(0.585517\pi\)
\(968\) −1.63929e13 −0.600091
\(969\) 0 0
\(970\) −1.07102e14 −3.88440
\(971\) −3.20825e13 −1.15819 −0.579097 0.815259i \(-0.696595\pi\)
−0.579097 + 0.815259i \(0.696595\pi\)
\(972\) 2.09558e11 0.00753020
\(973\) −9.76586e11 −0.0349303
\(974\) 2.51145e13 0.894148
\(975\) −8.39587e10 −0.00297540
\(976\) 5.76069e12 0.203213
\(977\) 1.42575e12 0.0500630 0.0250315 0.999687i \(-0.492031\pi\)
0.0250315 + 0.999687i \(0.492031\pi\)
\(978\) 1.29287e11 0.00451888
\(979\) 1.40729e13 0.489622
\(980\) 4.66130e13 1.61432
\(981\) 4.70365e13 1.62153
\(982\) 9.62436e12 0.330271
\(983\) 1.41784e13 0.484323 0.242161 0.970236i \(-0.422144\pi\)
0.242161 + 0.970236i \(0.422144\pi\)
\(984\) 1.85881e10 0.000632059 0
\(985\) 4.97352e12 0.168345
\(986\) 0 0
\(987\) 3.91793e10 0.00131410
\(988\) −7.46693e13 −2.49308
\(989\) 2.55613e13 0.849572
\(990\) −3.09350e13 −1.02351
\(991\) 2.24466e13 0.739296 0.369648 0.929172i \(-0.379478\pi\)
0.369648 + 0.929172i \(0.379478\pi\)
\(992\) −4.57509e13 −1.50002
\(993\) 3.64292e10 0.00118899
\(994\) −1.08739e12 −0.0353304
\(995\) 4.74836e13 1.53582
\(996\) 1.33961e11 0.00431331
\(997\) 1.92497e13 0.617015 0.308508 0.951222i \(-0.400170\pi\)
0.308508 + 0.951222i \(0.400170\pi\)
\(998\) 6.01737e13 1.92008
\(999\) −1.63773e11 −0.00520231
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 289.10.a.h.1.31 yes 36
17.16 even 2 289.10.a.g.1.31 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.31 36 17.16 even 2
289.10.a.h.1.31 yes 36 1.1 even 1 trivial