Properties

Label 177.12.a.b.1.3
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-78.8162 q^{2} +243.000 q^{3} +4163.99 q^{4} +6894.11 q^{5} -19152.3 q^{6} +41129.0 q^{7} -166774. q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-78.8162 q^{2} +243.000 q^{3} +4163.99 q^{4} +6894.11 q^{5} -19152.3 q^{6} +41129.0 q^{7} -166774. q^{8} +59049.0 q^{9} -543367. q^{10} -469594. q^{11} +1.01185e6 q^{12} +1.92887e6 q^{13} -3.24163e6 q^{14} +1.67527e6 q^{15} +4.61666e6 q^{16} -6.53047e6 q^{17} -4.65402e6 q^{18} +1.40980e7 q^{19} +2.87070e7 q^{20} +9.99434e6 q^{21} +3.70116e7 q^{22} +4.11538e6 q^{23} -4.05262e7 q^{24} -1.29943e6 q^{25} -1.52026e8 q^{26} +1.43489e7 q^{27} +1.71261e8 q^{28} -1.20032e8 q^{29} -1.32038e8 q^{30} -6.86675e7 q^{31} -2.23139e7 q^{32} -1.14111e8 q^{33} +5.14707e8 q^{34} +2.83548e8 q^{35} +2.45880e8 q^{36} -4.59827e8 q^{37} -1.11115e9 q^{38} +4.68715e8 q^{39} -1.14976e9 q^{40} -9.53500e8 q^{41} -7.87716e8 q^{42} -1.75893e9 q^{43} -1.95538e9 q^{44} +4.07090e8 q^{45} -3.24359e8 q^{46} -7.20564e8 q^{47} +1.12185e9 q^{48} -2.85733e8 q^{49} +1.02416e8 q^{50} -1.58690e9 q^{51} +8.03178e9 q^{52} -4.93630e9 q^{53} -1.13093e9 q^{54} -3.23743e9 q^{55} -6.85926e9 q^{56} +3.42580e9 q^{57} +9.46049e9 q^{58} -7.14924e8 q^{59} +6.97580e9 q^{60} -6.74509e9 q^{61} +5.41211e9 q^{62} +2.42863e9 q^{63} -7.69623e9 q^{64} +1.32978e10 q^{65} +8.99382e9 q^{66} -8.57249e9 q^{67} -2.71928e10 q^{68} +1.00004e9 q^{69} -2.23481e10 q^{70} +3.87295e8 q^{71} -9.84786e9 q^{72} -6.36342e9 q^{73} +3.62418e10 q^{74} -3.15762e8 q^{75} +5.87038e10 q^{76} -1.93139e10 q^{77} -3.69423e10 q^{78} +9.47459e9 q^{79} +3.18278e10 q^{80} +3.48678e9 q^{81} +7.51512e10 q^{82} +2.58868e10 q^{83} +4.16164e10 q^{84} -4.50217e10 q^{85} +1.38632e11 q^{86} -2.91679e10 q^{87} +7.83162e10 q^{88} -5.07898e10 q^{89} -3.20853e10 q^{90} +7.93323e10 q^{91} +1.71364e10 q^{92} -1.66862e10 q^{93} +5.67921e10 q^{94} +9.71928e10 q^{95} -5.42229e9 q^{96} +2.09497e10 q^{97} +2.25204e10 q^{98} -2.77291e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −78.8162 −1.74161 −0.870804 0.491630i \(-0.836401\pi\)
−0.870804 + 0.491630i \(0.836401\pi\)
\(3\) 243.000 0.577350
\(4\) 4163.99 2.03320
\(5\) 6894.11 0.986604 0.493302 0.869858i \(-0.335790\pi\)
0.493302 + 0.869858i \(0.335790\pi\)
\(6\) −19152.3 −1.00552
\(7\) 41129.0 0.924930 0.462465 0.886638i \(-0.346965\pi\)
0.462465 + 0.886638i \(0.346965\pi\)
\(8\) −166774. −1.79943
\(9\) 59049.0 0.333333
\(10\) −543367. −1.71828
\(11\) −469594. −0.879149 −0.439575 0.898206i \(-0.644871\pi\)
−0.439575 + 0.898206i \(0.644871\pi\)
\(12\) 1.01185e6 1.17387
\(13\) 1.92887e6 1.44083 0.720417 0.693541i \(-0.243951\pi\)
0.720417 + 0.693541i \(0.243951\pi\)
\(14\) −3.24163e6 −1.61087
\(15\) 1.67527e6 0.569616
\(16\) 4.61666e6 1.10070
\(17\) −6.53047e6 −1.11551 −0.557757 0.830004i \(-0.688338\pi\)
−0.557757 + 0.830004i \(0.688338\pi\)
\(18\) −4.65402e6 −0.580536
\(19\) 1.40980e7 1.30621 0.653103 0.757269i \(-0.273467\pi\)
0.653103 + 0.757269i \(0.273467\pi\)
\(20\) 2.87070e7 2.00596
\(21\) 9.99434e6 0.534008
\(22\) 3.70116e7 1.53113
\(23\) 4.11538e6 0.133324 0.0666618 0.997776i \(-0.478765\pi\)
0.0666618 + 0.997776i \(0.478765\pi\)
\(24\) −4.05262e7 −1.03890
\(25\) −1.29943e6 −0.0266124
\(26\) −1.52026e8 −2.50937
\(27\) 1.43489e7 0.192450
\(28\) 1.71261e8 1.88057
\(29\) −1.20032e8 −1.08670 −0.543350 0.839506i \(-0.682844\pi\)
−0.543350 + 0.839506i \(0.682844\pi\)
\(30\) −1.32038e8 −0.992048
\(31\) −6.86675e7 −0.430786 −0.215393 0.976527i \(-0.569103\pi\)
−0.215393 + 0.976527i \(0.569103\pi\)
\(32\) −2.23139e7 −0.117558
\(33\) −1.14111e8 −0.507577
\(34\) 5.14707e8 1.94279
\(35\) 2.83548e8 0.912539
\(36\) 2.45880e8 0.677733
\(37\) −4.59827e8 −1.09015 −0.545073 0.838388i \(-0.683498\pi\)
−0.545073 + 0.838388i \(0.683498\pi\)
\(38\) −1.11115e9 −2.27490
\(39\) 4.68715e8 0.831866
\(40\) −1.14976e9 −1.77532
\(41\) −9.53500e8 −1.28531 −0.642657 0.766154i \(-0.722168\pi\)
−0.642657 + 0.766154i \(0.722168\pi\)
\(42\) −7.87716e8 −0.930033
\(43\) −1.75893e9 −1.82461 −0.912307 0.409506i \(-0.865701\pi\)
−0.912307 + 0.409506i \(0.865701\pi\)
\(44\) −1.95538e9 −1.78749
\(45\) 4.07090e8 0.328868
\(46\) −3.24359e8 −0.232198
\(47\) −7.20564e8 −0.458284 −0.229142 0.973393i \(-0.573592\pi\)
−0.229142 + 0.973393i \(0.573592\pi\)
\(48\) 1.12185e9 0.635488
\(49\) −2.85733e8 −0.144505
\(50\) 1.02416e8 0.0463484
\(51\) −1.58690e9 −0.644043
\(52\) 8.03178e9 2.92950
\(53\) −4.93630e9 −1.62138 −0.810690 0.585476i \(-0.800908\pi\)
−0.810690 + 0.585476i \(0.800908\pi\)
\(54\) −1.13093e9 −0.335173
\(55\) −3.23743e9 −0.867372
\(56\) −6.85926e9 −1.66434
\(57\) 3.42580e9 0.754138
\(58\) 9.46049e9 1.89260
\(59\) −7.14924e8 −0.130189
\(60\) 6.97580e9 1.15814
\(61\) −6.74509e9 −1.02252 −0.511262 0.859425i \(-0.670822\pi\)
−0.511262 + 0.859425i \(0.670822\pi\)
\(62\) 5.41211e9 0.750261
\(63\) 2.42863e9 0.308310
\(64\) −7.69623e9 −0.895959
\(65\) 1.32978e10 1.42153
\(66\) 8.99382e9 0.884000
\(67\) −8.57249e9 −0.775703 −0.387851 0.921722i \(-0.626783\pi\)
−0.387851 + 0.921722i \(0.626783\pi\)
\(68\) −2.71928e10 −2.26806
\(69\) 1.00004e9 0.0769744
\(70\) −2.23481e10 −1.58929
\(71\) 3.87295e8 0.0254754 0.0127377 0.999919i \(-0.495945\pi\)
0.0127377 + 0.999919i \(0.495945\pi\)
\(72\) −9.84786e9 −0.599809
\(73\) −6.36342e9 −0.359265 −0.179633 0.983734i \(-0.557491\pi\)
−0.179633 + 0.983734i \(0.557491\pi\)
\(74\) 3.62418e10 1.89861
\(75\) −3.15762e8 −0.0153647
\(76\) 5.87038e10 2.65577
\(77\) −1.93139e10 −0.813151
\(78\) −3.69423e10 −1.44878
\(79\) 9.47459e9 0.346427 0.173213 0.984884i \(-0.444585\pi\)
0.173213 + 0.984884i \(0.444585\pi\)
\(80\) 3.18278e10 1.08595
\(81\) 3.48678e9 0.111111
\(82\) 7.51512e10 2.23851
\(83\) 2.58868e10 0.721355 0.360677 0.932691i \(-0.382546\pi\)
0.360677 + 0.932691i \(0.382546\pi\)
\(84\) 4.16164e10 1.08575
\(85\) −4.50217e10 −1.10057
\(86\) 1.38632e11 3.17776
\(87\) −2.91679e10 −0.627406
\(88\) 7.83162e10 1.58197
\(89\) −5.07898e10 −0.964120 −0.482060 0.876138i \(-0.660111\pi\)
−0.482060 + 0.876138i \(0.660111\pi\)
\(90\) −3.20853e10 −0.572759
\(91\) 7.93323e10 1.33267
\(92\) 1.71364e10 0.271073
\(93\) −1.66862e10 −0.248715
\(94\) 5.67921e10 0.798151
\(95\) 9.71928e10 1.28871
\(96\) −5.42229e9 −0.0678720
\(97\) 2.09497e10 0.247704 0.123852 0.992301i \(-0.460475\pi\)
0.123852 + 0.992301i \(0.460475\pi\)
\(98\) 2.25204e10 0.251671
\(99\) −2.77291e10 −0.293050
\(100\) −5.41083e9 −0.0541083
\(101\) −1.72710e11 −1.63513 −0.817563 0.575839i \(-0.804675\pi\)
−0.817563 + 0.575839i \(0.804675\pi\)
\(102\) 1.25074e11 1.12167
\(103\) 1.85002e11 1.57243 0.786216 0.617952i \(-0.212037\pi\)
0.786216 + 0.617952i \(0.212037\pi\)
\(104\) −3.21685e11 −2.59268
\(105\) 6.89021e10 0.526855
\(106\) 3.89061e11 2.82381
\(107\) 1.71381e11 1.18128 0.590638 0.806937i \(-0.298876\pi\)
0.590638 + 0.806937i \(0.298876\pi\)
\(108\) 5.97487e10 0.391289
\(109\) 4.45873e10 0.277566 0.138783 0.990323i \(-0.455681\pi\)
0.138783 + 0.990323i \(0.455681\pi\)
\(110\) 2.55162e11 1.51062
\(111\) −1.11738e11 −0.629397
\(112\) 1.89879e11 1.01807
\(113\) 4.97055e9 0.0253789 0.0126895 0.999919i \(-0.495961\pi\)
0.0126895 + 0.999919i \(0.495961\pi\)
\(114\) −2.70009e11 −1.31341
\(115\) 2.83719e10 0.131538
\(116\) −4.99814e11 −2.20948
\(117\) 1.13898e11 0.480278
\(118\) 5.63476e10 0.226738
\(119\) −2.68592e11 −1.03177
\(120\) −2.79392e11 −1.02498
\(121\) −6.47932e10 −0.227096
\(122\) 5.31622e11 1.78084
\(123\) −2.31700e11 −0.742077
\(124\) −2.85931e11 −0.875874
\(125\) −3.45585e11 −1.01286
\(126\) −1.91415e11 −0.536955
\(127\) −1.07878e11 −0.289742 −0.144871 0.989451i \(-0.546277\pi\)
−0.144871 + 0.989451i \(0.546277\pi\)
\(128\) 6.52286e11 1.67797
\(129\) −4.27419e11 −1.05344
\(130\) −1.04808e12 −2.47575
\(131\) −5.39694e10 −0.122224 −0.0611118 0.998131i \(-0.519465\pi\)
−0.0611118 + 0.998131i \(0.519465\pi\)
\(132\) −4.75159e11 −1.03201
\(133\) 5.79835e11 1.20815
\(134\) 6.75651e11 1.35097
\(135\) 9.89229e10 0.189872
\(136\) 1.08911e12 2.00729
\(137\) −6.06664e11 −1.07395 −0.536976 0.843598i \(-0.680433\pi\)
−0.536976 + 0.843598i \(0.680433\pi\)
\(138\) −7.88192e10 −0.134059
\(139\) 5.61474e11 0.917801 0.458900 0.888488i \(-0.348243\pi\)
0.458900 + 0.888488i \(0.348243\pi\)
\(140\) 1.18069e12 1.85537
\(141\) −1.75097e11 −0.264590
\(142\) −3.05251e10 −0.0443682
\(143\) −9.05784e11 −1.26671
\(144\) 2.72609e11 0.366899
\(145\) −8.27516e11 −1.07214
\(146\) 5.01541e11 0.625699
\(147\) −6.94332e10 −0.0834300
\(148\) −1.91472e12 −2.21649
\(149\) 2.28609e11 0.255016 0.127508 0.991838i \(-0.459302\pi\)
0.127508 + 0.991838i \(0.459302\pi\)
\(150\) 2.48872e10 0.0267592
\(151\) −1.57142e12 −1.62899 −0.814496 0.580169i \(-0.802986\pi\)
−0.814496 + 0.580169i \(0.802986\pi\)
\(152\) −2.35118e12 −2.35042
\(153\) −3.85618e11 −0.371838
\(154\) 1.52225e12 1.41619
\(155\) −4.73401e11 −0.425016
\(156\) 1.95172e12 1.69135
\(157\) 5.60897e10 0.0469283 0.0234641 0.999725i \(-0.492530\pi\)
0.0234641 + 0.999725i \(0.492530\pi\)
\(158\) −7.46751e11 −0.603340
\(159\) −1.19952e12 −0.936104
\(160\) −1.53835e11 −0.115983
\(161\) 1.69262e11 0.123315
\(162\) −2.74815e11 −0.193512
\(163\) 1.44082e12 0.980795 0.490398 0.871499i \(-0.336852\pi\)
0.490398 + 0.871499i \(0.336852\pi\)
\(164\) −3.97036e12 −2.61330
\(165\) −7.86695e11 −0.500778
\(166\) −2.04030e12 −1.25632
\(167\) 1.12221e12 0.668550 0.334275 0.942476i \(-0.391509\pi\)
0.334275 + 0.942476i \(0.391509\pi\)
\(168\) −1.66680e12 −0.960909
\(169\) 1.92837e12 1.07600
\(170\) 3.54844e12 1.91676
\(171\) 8.32470e11 0.435402
\(172\) −7.32415e12 −3.70980
\(173\) −3.67297e12 −1.80204 −0.901018 0.433781i \(-0.857179\pi\)
−0.901018 + 0.433781i \(0.857179\pi\)
\(174\) 2.29890e12 1.09270
\(175\) −5.34444e10 −0.0246146
\(176\) −2.16796e12 −0.967678
\(177\) −1.73727e11 −0.0751646
\(178\) 4.00305e12 1.67912
\(179\) 2.46501e10 0.0100260 0.00501300 0.999987i \(-0.498404\pi\)
0.00501300 + 0.999987i \(0.498404\pi\)
\(180\) 1.69512e12 0.668654
\(181\) 3.13928e12 1.20115 0.600577 0.799567i \(-0.294938\pi\)
0.600577 + 0.799567i \(0.294938\pi\)
\(182\) −6.25267e12 −2.32099
\(183\) −1.63906e12 −0.590354
\(184\) −6.86340e11 −0.239906
\(185\) −3.17010e12 −1.07554
\(186\) 1.31514e12 0.433164
\(187\) 3.06667e12 0.980704
\(188\) −3.00042e12 −0.931782
\(189\) 5.90156e11 0.178003
\(190\) −7.66037e12 −2.24442
\(191\) −1.65434e12 −0.470913 −0.235457 0.971885i \(-0.575659\pi\)
−0.235457 + 0.971885i \(0.575659\pi\)
\(192\) −1.87018e12 −0.517282
\(193\) 6.12757e12 1.64711 0.823556 0.567234i \(-0.191987\pi\)
0.823556 + 0.567234i \(0.191987\pi\)
\(194\) −1.65117e12 −0.431403
\(195\) 3.23137e12 0.820722
\(196\) −1.18979e12 −0.293807
\(197\) 7.65084e12 1.83715 0.918576 0.395245i \(-0.129340\pi\)
0.918576 + 0.395245i \(0.129340\pi\)
\(198\) 2.18550e12 0.510378
\(199\) −5.25431e12 −1.19350 −0.596752 0.802426i \(-0.703542\pi\)
−0.596752 + 0.802426i \(0.703542\pi\)
\(200\) 2.16712e11 0.0478871
\(201\) −2.08311e12 −0.447852
\(202\) 1.36124e13 2.84775
\(203\) −4.93681e12 −1.00512
\(204\) −6.60785e12 −1.30947
\(205\) −6.57353e12 −1.26810
\(206\) −1.45812e13 −2.73856
\(207\) 2.43009e11 0.0444412
\(208\) 8.90493e12 1.58592
\(209\) −6.62031e12 −1.14835
\(210\) −5.43060e12 −0.917575
\(211\) −3.17714e12 −0.522977 −0.261488 0.965207i \(-0.584213\pi\)
−0.261488 + 0.965207i \(0.584213\pi\)
\(212\) −2.05547e13 −3.29659
\(213\) 9.41127e10 0.0147082
\(214\) −1.35076e13 −2.05732
\(215\) −1.21262e13 −1.80017
\(216\) −2.39303e12 −0.346300
\(217\) −2.82423e12 −0.398447
\(218\) −3.51420e12 −0.483410
\(219\) −1.54631e12 −0.207422
\(220\) −1.34806e13 −1.76354
\(221\) −1.25964e13 −1.60727
\(222\) 8.80676e12 1.09616
\(223\) 4.88782e12 0.593524 0.296762 0.954951i \(-0.404093\pi\)
0.296762 + 0.954951i \(0.404093\pi\)
\(224\) −9.17750e11 −0.108733
\(225\) −7.67303e10 −0.00887080
\(226\) −3.91760e11 −0.0442001
\(227\) 1.40691e13 1.54926 0.774628 0.632417i \(-0.217937\pi\)
0.774628 + 0.632417i \(0.217937\pi\)
\(228\) 1.42650e13 1.53331
\(229\) 1.66346e13 1.74549 0.872747 0.488173i \(-0.162336\pi\)
0.872747 + 0.488173i \(0.162336\pi\)
\(230\) −2.23616e12 −0.229087
\(231\) −4.69328e12 −0.469473
\(232\) 2.00183e13 1.95544
\(233\) −1.03722e13 −0.989494 −0.494747 0.869037i \(-0.664739\pi\)
−0.494747 + 0.869037i \(0.664739\pi\)
\(234\) −8.97698e12 −0.836456
\(235\) −4.96765e12 −0.452145
\(236\) −2.97694e12 −0.264700
\(237\) 2.30233e12 0.200010
\(238\) 2.11694e13 1.79694
\(239\) 8.65379e12 0.717824 0.358912 0.933371i \(-0.383148\pi\)
0.358912 + 0.933371i \(0.383148\pi\)
\(240\) 7.73415e12 0.626976
\(241\) 1.61354e13 1.27846 0.639229 0.769017i \(-0.279254\pi\)
0.639229 + 0.769017i \(0.279254\pi\)
\(242\) 5.10675e12 0.395513
\(243\) 8.47289e11 0.0641500
\(244\) −2.80865e13 −2.07899
\(245\) −1.96988e12 −0.142569
\(246\) 1.82617e13 1.29241
\(247\) 2.71931e13 1.88202
\(248\) 1.14520e13 0.775169
\(249\) 6.29049e12 0.416474
\(250\) 2.72377e13 1.76401
\(251\) 1.02192e13 0.647460 0.323730 0.946150i \(-0.395063\pi\)
0.323730 + 0.946150i \(0.395063\pi\)
\(252\) 1.01128e13 0.626855
\(253\) −1.93256e12 −0.117211
\(254\) 8.50253e12 0.504618
\(255\) −1.09403e13 −0.635415
\(256\) −3.56488e13 −2.02640
\(257\) −2.69070e12 −0.149704 −0.0748520 0.997195i \(-0.523848\pi\)
−0.0748520 + 0.997195i \(0.523848\pi\)
\(258\) 3.36875e13 1.83468
\(259\) −1.89122e13 −1.00831
\(260\) 5.53720e13 2.89026
\(261\) −7.08779e12 −0.362233
\(262\) 4.25366e12 0.212866
\(263\) 2.08710e13 1.02279 0.511395 0.859346i \(-0.329129\pi\)
0.511395 + 0.859346i \(0.329129\pi\)
\(264\) 1.90308e13 0.913348
\(265\) −3.40314e13 −1.59966
\(266\) −4.57004e13 −2.10412
\(267\) −1.23419e13 −0.556635
\(268\) −3.56958e13 −1.57716
\(269\) −9.86757e12 −0.427142 −0.213571 0.976928i \(-0.568510\pi\)
−0.213571 + 0.976928i \(0.568510\pi\)
\(270\) −7.79672e12 −0.330683
\(271\) −3.66647e13 −1.52376 −0.761881 0.647717i \(-0.775724\pi\)
−0.761881 + 0.647717i \(0.775724\pi\)
\(272\) −3.01490e13 −1.22785
\(273\) 1.92778e13 0.769417
\(274\) 4.78149e13 1.87040
\(275\) 6.10206e11 0.0233963
\(276\) 4.16415e12 0.156504
\(277\) 4.73040e13 1.74285 0.871423 0.490532i \(-0.163198\pi\)
0.871423 + 0.490532i \(0.163198\pi\)
\(278\) −4.42533e13 −1.59845
\(279\) −4.05475e12 −0.143595
\(280\) −4.72885e13 −1.64205
\(281\) 1.44433e13 0.491792 0.245896 0.969296i \(-0.420918\pi\)
0.245896 + 0.969296i \(0.420918\pi\)
\(282\) 1.38005e13 0.460813
\(283\) −4.09853e13 −1.34215 −0.671077 0.741387i \(-0.734168\pi\)
−0.671077 + 0.741387i \(0.734168\pi\)
\(284\) 1.61269e12 0.0517966
\(285\) 2.36179e13 0.744035
\(286\) 7.13904e13 2.20611
\(287\) −3.92165e13 −1.18883
\(288\) −1.31762e12 −0.0391859
\(289\) 8.37514e12 0.244373
\(290\) 6.52216e13 1.86725
\(291\) 5.09077e12 0.143012
\(292\) −2.64972e13 −0.730457
\(293\) −2.69413e12 −0.0728863 −0.0364432 0.999336i \(-0.511603\pi\)
−0.0364432 + 0.999336i \(0.511603\pi\)
\(294\) 5.47246e12 0.145302
\(295\) −4.92876e12 −0.128445
\(296\) 7.66874e13 1.96164
\(297\) −6.73816e12 −0.169192
\(298\) −1.80181e13 −0.444139
\(299\) 7.93803e12 0.192097
\(300\) −1.31483e12 −0.0312394
\(301\) −7.23429e13 −1.68764
\(302\) 1.23853e14 2.83707
\(303\) −4.19686e13 −0.944040
\(304\) 6.50855e13 1.43774
\(305\) −4.65013e13 −1.00883
\(306\) 3.03929e13 0.647597
\(307\) −3.92324e13 −0.821077 −0.410538 0.911843i \(-0.634659\pi\)
−0.410538 + 0.911843i \(0.634659\pi\)
\(308\) −8.04230e13 −1.65330
\(309\) 4.49555e13 0.907844
\(310\) 3.73117e13 0.740211
\(311\) 8.66964e12 0.168974 0.0844868 0.996425i \(-0.473075\pi\)
0.0844868 + 0.996425i \(0.473075\pi\)
\(312\) −7.81696e13 −1.49688
\(313\) 1.16560e13 0.219308 0.109654 0.993970i \(-0.465026\pi\)
0.109654 + 0.993970i \(0.465026\pi\)
\(314\) −4.42077e12 −0.0817307
\(315\) 1.67432e13 0.304180
\(316\) 3.94521e13 0.704355
\(317\) 6.66638e13 1.16967 0.584836 0.811152i \(-0.301159\pi\)
0.584836 + 0.811152i \(0.301159\pi\)
\(318\) 9.45417e13 1.63033
\(319\) 5.63665e13 0.955371
\(320\) −5.30586e13 −0.883956
\(321\) 4.16455e13 0.682010
\(322\) −1.33405e13 −0.214766
\(323\) −9.20663e13 −1.45709
\(324\) 1.45189e13 0.225911
\(325\) −2.50643e12 −0.0383440
\(326\) −1.13560e14 −1.70816
\(327\) 1.08347e13 0.160253
\(328\) 1.59019e14 2.31283
\(329\) −2.96361e13 −0.423880
\(330\) 6.20043e13 0.872158
\(331\) 4.14677e13 0.573662 0.286831 0.957981i \(-0.407398\pi\)
0.286831 + 0.957981i \(0.407398\pi\)
\(332\) 1.07792e14 1.46666
\(333\) −2.71523e13 −0.363382
\(334\) −8.84484e13 −1.16435
\(335\) −5.90996e13 −0.765312
\(336\) 4.61405e13 0.587782
\(337\) 1.12179e14 1.40588 0.702939 0.711250i \(-0.251871\pi\)
0.702939 + 0.711250i \(0.251871\pi\)
\(338\) −1.51987e14 −1.87397
\(339\) 1.20784e12 0.0146525
\(340\) −1.87470e14 −2.23768
\(341\) 3.22459e13 0.378726
\(342\) −6.56121e13 −0.758299
\(343\) −9.30774e13 −1.05859
\(344\) 2.93344e14 3.28326
\(345\) 6.89437e12 0.0759433
\(346\) 2.89489e14 3.13844
\(347\) −1.50039e14 −1.60101 −0.800504 0.599328i \(-0.795435\pi\)
−0.800504 + 0.599328i \(0.795435\pi\)
\(348\) −1.21455e14 −1.27564
\(349\) 1.07318e14 1.10951 0.554757 0.832012i \(-0.312811\pi\)
0.554757 + 0.832012i \(0.312811\pi\)
\(350\) 4.21228e12 0.0428690
\(351\) 2.76771e13 0.277289
\(352\) 1.04785e13 0.103351
\(353\) −2.15659e13 −0.209414 −0.104707 0.994503i \(-0.533391\pi\)
−0.104707 + 0.994503i \(0.533391\pi\)
\(354\) 1.36925e13 0.130907
\(355\) 2.67005e12 0.0251341
\(356\) −2.11488e14 −1.96025
\(357\) −6.52678e13 −0.595694
\(358\) −1.94283e12 −0.0174614
\(359\) −1.95610e14 −1.73130 −0.865650 0.500650i \(-0.833095\pi\)
−0.865650 + 0.500650i \(0.833095\pi\)
\(360\) −6.78922e13 −0.591774
\(361\) 8.22621e13 0.706172
\(362\) −2.47426e14 −2.09194
\(363\) −1.57448e13 −0.131114
\(364\) 3.30339e14 2.70958
\(365\) −4.38701e13 −0.354452
\(366\) 1.29184e14 1.02817
\(367\) −1.86834e14 −1.46485 −0.732423 0.680849i \(-0.761611\pi\)
−0.732423 + 0.680849i \(0.761611\pi\)
\(368\) 1.89993e13 0.146749
\(369\) −5.63032e13 −0.428438
\(370\) 2.49855e14 1.87318
\(371\) −2.03025e14 −1.49966
\(372\) −6.94812e13 −0.505686
\(373\) −1.90329e14 −1.36492 −0.682458 0.730925i \(-0.739089\pi\)
−0.682458 + 0.730925i \(0.739089\pi\)
\(374\) −2.41703e14 −1.70800
\(375\) −8.39771e13 −0.584775
\(376\) 1.20172e14 0.824649
\(377\) −2.31526e14 −1.56575
\(378\) −4.65138e13 −0.310011
\(379\) 2.18200e14 1.43331 0.716653 0.697430i \(-0.245673\pi\)
0.716653 + 0.697430i \(0.245673\pi\)
\(380\) 4.04710e14 2.62020
\(381\) −2.62143e13 −0.167283
\(382\) 1.30389e14 0.820146
\(383\) 1.50934e14 0.935825 0.467913 0.883775i \(-0.345006\pi\)
0.467913 + 0.883775i \(0.345006\pi\)
\(384\) 1.58506e14 0.968774
\(385\) −1.33152e14 −0.802259
\(386\) −4.82952e14 −2.86862
\(387\) −1.03863e14 −0.608205
\(388\) 8.72342e13 0.503631
\(389\) −1.25855e14 −0.716389 −0.358195 0.933647i \(-0.616608\pi\)
−0.358195 + 0.933647i \(0.616608\pi\)
\(390\) −2.54684e14 −1.42938
\(391\) −2.68754e13 −0.148724
\(392\) 4.76530e13 0.260026
\(393\) −1.31146e13 −0.0705659
\(394\) −6.03010e14 −3.19960
\(395\) 6.53188e13 0.341786
\(396\) −1.15464e14 −0.595828
\(397\) −1.64721e14 −0.838306 −0.419153 0.907916i \(-0.637673\pi\)
−0.419153 + 0.907916i \(0.637673\pi\)
\(398\) 4.14125e14 2.07862
\(399\) 1.40900e14 0.697525
\(400\) −5.99905e12 −0.0292922
\(401\) −1.25477e14 −0.604323 −0.302162 0.953257i \(-0.597708\pi\)
−0.302162 + 0.953257i \(0.597708\pi\)
\(402\) 1.64183e14 0.779983
\(403\) −1.32451e14 −0.620692
\(404\) −7.19165e14 −3.32454
\(405\) 2.40383e13 0.109623
\(406\) 3.89100e14 1.75053
\(407\) 2.15932e14 0.958402
\(408\) 2.64655e14 1.15891
\(409\) −1.51053e14 −0.652607 −0.326304 0.945265i \(-0.605803\pi\)
−0.326304 + 0.945265i \(0.605803\pi\)
\(410\) 5.18100e14 2.20853
\(411\) −1.47419e14 −0.620046
\(412\) 7.70347e14 3.19707
\(413\) −2.94041e13 −0.120416
\(414\) −1.91531e13 −0.0773992
\(415\) 1.78466e14 0.711691
\(416\) −4.30406e13 −0.169381
\(417\) 1.36438e14 0.529893
\(418\) 5.21788e14 1.99997
\(419\) 1.26362e13 0.0478013 0.0239007 0.999714i \(-0.492391\pi\)
0.0239007 + 0.999714i \(0.492391\pi\)
\(420\) 2.86908e14 1.07120
\(421\) −2.87292e14 −1.05870 −0.529350 0.848404i \(-0.677564\pi\)
−0.529350 + 0.848404i \(0.677564\pi\)
\(422\) 2.50410e14 0.910820
\(423\) −4.25486e13 −0.152761
\(424\) 8.23249e14 2.91755
\(425\) 8.48591e12 0.0296865
\(426\) −7.41760e12 −0.0256160
\(427\) −2.77419e14 −0.945763
\(428\) 7.13628e14 2.40177
\(429\) −2.20106e14 −0.731334
\(430\) 9.55743e14 3.13519
\(431\) 3.33625e14 1.08052 0.540260 0.841498i \(-0.318326\pi\)
0.540260 + 0.841498i \(0.318326\pi\)
\(432\) 6.62441e13 0.211829
\(433\) −2.21538e14 −0.699463 −0.349732 0.936850i \(-0.613727\pi\)
−0.349732 + 0.936850i \(0.613727\pi\)
\(434\) 2.22595e14 0.693939
\(435\) −2.01086e14 −0.619001
\(436\) 1.85661e14 0.564346
\(437\) 5.80185e13 0.174148
\(438\) 1.21874e14 0.361247
\(439\) −1.01863e14 −0.298168 −0.149084 0.988825i \(-0.547632\pi\)
−0.149084 + 0.988825i \(0.547632\pi\)
\(440\) 5.39920e14 1.56077
\(441\) −1.68723e13 −0.0481683
\(442\) 9.92801e14 2.79924
\(443\) −1.00942e14 −0.281093 −0.140546 0.990074i \(-0.544886\pi\)
−0.140546 + 0.990074i \(0.544886\pi\)
\(444\) −4.65276e14 −1.27969
\(445\) −3.50150e14 −0.951205
\(446\) −3.85239e14 −1.03369
\(447\) 5.55519e13 0.147234
\(448\) −3.16538e14 −0.828699
\(449\) 2.46092e14 0.636417 0.318209 0.948021i \(-0.396919\pi\)
0.318209 + 0.948021i \(0.396919\pi\)
\(450\) 6.04759e12 0.0154495
\(451\) 4.47758e14 1.12998
\(452\) 2.06973e13 0.0516004
\(453\) −3.81855e14 −0.940499
\(454\) −1.10887e15 −2.69820
\(455\) 5.46925e14 1.31482
\(456\) −5.71336e14 −1.35702
\(457\) 6.75579e14 1.58539 0.792696 0.609617i \(-0.208677\pi\)
0.792696 + 0.609617i \(0.208677\pi\)
\(458\) −1.31108e15 −3.03997
\(459\) −9.37051e13 −0.214681
\(460\) 1.18140e14 0.267442
\(461\) 2.11996e14 0.474213 0.237107 0.971484i \(-0.423801\pi\)
0.237107 + 0.971484i \(0.423801\pi\)
\(462\) 3.69907e14 0.817638
\(463\) 3.43294e14 0.749844 0.374922 0.927056i \(-0.377669\pi\)
0.374922 + 0.927056i \(0.377669\pi\)
\(464\) −5.54149e14 −1.19613
\(465\) −1.15036e14 −0.245383
\(466\) 8.17497e14 1.72331
\(467\) −9.00452e13 −0.187594 −0.0937968 0.995591i \(-0.529900\pi\)
−0.0937968 + 0.995591i \(0.529900\pi\)
\(468\) 4.74269e14 0.976500
\(469\) −3.52578e14 −0.717471
\(470\) 3.91531e14 0.787459
\(471\) 1.36298e13 0.0270941
\(472\) 1.19231e14 0.234265
\(473\) 8.25981e14 1.60411
\(474\) −1.81461e14 −0.348338
\(475\) −1.83194e13 −0.0347613
\(476\) −1.11841e15 −2.09780
\(477\) −2.91484e14 −0.540460
\(478\) −6.82059e14 −1.25017
\(479\) 5.26598e14 0.954188 0.477094 0.878852i \(-0.341690\pi\)
0.477094 + 0.878852i \(0.341690\pi\)
\(480\) −3.73818e13 −0.0669628
\(481\) −8.86945e14 −1.57072
\(482\) −1.27173e15 −2.22657
\(483\) 4.11305e13 0.0711959
\(484\) −2.69798e14 −0.461732
\(485\) 1.44429e14 0.244386
\(486\) −6.67801e13 −0.111724
\(487\) −7.04142e14 −1.16480 −0.582400 0.812903i \(-0.697886\pi\)
−0.582400 + 0.812903i \(0.697886\pi\)
\(488\) 1.12491e15 1.83996
\(489\) 3.50120e14 0.566263
\(490\) 1.55258e14 0.248300
\(491\) 4.33955e14 0.686272 0.343136 0.939286i \(-0.388511\pi\)
0.343136 + 0.939286i \(0.388511\pi\)
\(492\) −9.64799e14 −1.50879
\(493\) 7.83868e14 1.21223
\(494\) −2.14325e15 −3.27775
\(495\) −1.91167e14 −0.289124
\(496\) −3.17015e14 −0.474166
\(497\) 1.59291e13 0.0235630
\(498\) −4.95792e14 −0.725335
\(499\) 3.20518e13 0.0463767 0.0231884 0.999731i \(-0.492618\pi\)
0.0231884 + 0.999731i \(0.492618\pi\)
\(500\) −1.43901e15 −2.05935
\(501\) 2.72697e14 0.385988
\(502\) −8.05441e14 −1.12762
\(503\) −1.28261e13 −0.0177611 −0.00888054 0.999961i \(-0.502827\pi\)
−0.00888054 + 0.999961i \(0.502827\pi\)
\(504\) −4.05032e14 −0.554781
\(505\) −1.19068e15 −1.61322
\(506\) 1.52317e14 0.204136
\(507\) 4.68593e14 0.621230
\(508\) −4.49203e14 −0.589104
\(509\) −2.01034e13 −0.0260808 −0.0130404 0.999915i \(-0.504151\pi\)
−0.0130404 + 0.999915i \(0.504151\pi\)
\(510\) 8.62272e14 1.10664
\(511\) −2.61721e14 −0.332295
\(512\) 1.47382e15 1.85123
\(513\) 2.02290e14 0.251379
\(514\) 2.12071e14 0.260726
\(515\) 1.27542e15 1.55137
\(516\) −1.77977e15 −2.14186
\(517\) 3.38373e14 0.402900
\(518\) 1.49059e15 1.75608
\(519\) −8.92531e14 −1.04041
\(520\) −2.21773e15 −2.55794
\(521\) −2.88358e14 −0.329097 −0.164549 0.986369i \(-0.552617\pi\)
−0.164549 + 0.986369i \(0.552617\pi\)
\(522\) 5.58633e14 0.630868
\(523\) −5.55798e14 −0.621094 −0.310547 0.950558i \(-0.600512\pi\)
−0.310547 + 0.950558i \(0.600512\pi\)
\(524\) −2.24728e14 −0.248505
\(525\) −1.29870e13 −0.0142112
\(526\) −1.64497e15 −1.78130
\(527\) 4.48431e14 0.480549
\(528\) −5.26814e14 −0.558689
\(529\) −9.35873e14 −0.982225
\(530\) 2.68223e15 2.78598
\(531\) −4.22156e13 −0.0433963
\(532\) 2.41443e15 2.45640
\(533\) −1.83917e15 −1.85192
\(534\) 9.72742e14 0.969440
\(535\) 1.18152e15 1.16545
\(536\) 1.42967e15 1.39582
\(537\) 5.98998e12 0.00578851
\(538\) 7.77724e14 0.743915
\(539\) 1.34179e14 0.127041
\(540\) 4.11914e14 0.386048
\(541\) −5.01411e14 −0.465167 −0.232584 0.972576i \(-0.574718\pi\)
−0.232584 + 0.972576i \(0.574718\pi\)
\(542\) 2.88977e15 2.65380
\(543\) 7.62846e14 0.693486
\(544\) 1.45721e14 0.131138
\(545\) 3.07390e14 0.273847
\(546\) −1.51940e15 −1.34002
\(547\) −2.59756e14 −0.226796 −0.113398 0.993550i \(-0.536174\pi\)
−0.113398 + 0.993550i \(0.536174\pi\)
\(548\) −2.52614e15 −2.18356
\(549\) −3.98291e14 −0.340841
\(550\) −4.80941e13 −0.0407471
\(551\) −1.69221e15 −1.41945
\(552\) −1.66781e14 −0.138510
\(553\) 3.89680e14 0.320421
\(554\) −3.72832e15 −3.03535
\(555\) −7.70333e14 −0.620965
\(556\) 2.33797e15 1.86607
\(557\) −1.04084e15 −0.822587 −0.411293 0.911503i \(-0.634923\pi\)
−0.411293 + 0.911503i \(0.634923\pi\)
\(558\) 3.19580e14 0.250087
\(559\) −3.39274e15 −2.62897
\(560\) 1.30904e15 1.00443
\(561\) 7.45201e14 0.566210
\(562\) −1.13836e15 −0.856509
\(563\) −8.78087e14 −0.654246 −0.327123 0.944982i \(-0.606079\pi\)
−0.327123 + 0.944982i \(0.606079\pi\)
\(564\) −7.29103e14 −0.537965
\(565\) 3.42675e13 0.0250389
\(566\) 3.23030e15 2.33751
\(567\) 1.43408e14 0.102770
\(568\) −6.45909e13 −0.0458411
\(569\) −2.14884e15 −1.51038 −0.755191 0.655505i \(-0.772456\pi\)
−0.755191 + 0.655505i \(0.772456\pi\)
\(570\) −1.86147e15 −1.29582
\(571\) 5.35406e14 0.369134 0.184567 0.982820i \(-0.440912\pi\)
0.184567 + 0.982820i \(0.440912\pi\)
\(572\) −3.77168e15 −2.57547
\(573\) −4.02004e14 −0.271882
\(574\) 3.09089e15 2.07047
\(575\) −5.34767e12 −0.00354806
\(576\) −4.54454e14 −0.298653
\(577\) 5.44577e14 0.354480 0.177240 0.984168i \(-0.443283\pi\)
0.177240 + 0.984168i \(0.443283\pi\)
\(578\) −6.60097e14 −0.425603
\(579\) 1.48900e15 0.950961
\(580\) −3.44577e15 −2.17988
\(581\) 1.06470e15 0.667202
\(582\) −4.01235e14 −0.249071
\(583\) 2.31806e15 1.42543
\(584\) 1.06126e15 0.646471
\(585\) 7.85222e14 0.473844
\(586\) 2.12341e14 0.126939
\(587\) 2.93282e15 1.73691 0.868453 0.495771i \(-0.165114\pi\)
0.868453 + 0.495771i \(0.165114\pi\)
\(588\) −2.89119e14 −0.169630
\(589\) −9.68072e14 −0.562695
\(590\) 3.88466e14 0.223701
\(591\) 1.85915e15 1.06068
\(592\) −2.12287e15 −1.19992
\(593\) −1.20511e15 −0.674877 −0.337438 0.941348i \(-0.609560\pi\)
−0.337438 + 0.941348i \(0.609560\pi\)
\(594\) 5.31076e14 0.294667
\(595\) −1.85170e15 −1.01795
\(596\) 9.51924e14 0.518499
\(597\) −1.27680e15 −0.689070
\(598\) −6.25645e14 −0.334558
\(599\) −1.80492e15 −0.956335 −0.478168 0.878269i \(-0.658699\pi\)
−0.478168 + 0.878269i \(0.658699\pi\)
\(600\) 5.26611e13 0.0276476
\(601\) 2.52227e15 1.31215 0.656074 0.754697i \(-0.272216\pi\)
0.656074 + 0.754697i \(0.272216\pi\)
\(602\) 5.70179e15 2.93921
\(603\) −5.06197e14 −0.258568
\(604\) −6.54338e15 −3.31206
\(605\) −4.46691e14 −0.224054
\(606\) 3.30781e15 1.64415
\(607\) −1.47629e15 −0.727167 −0.363583 0.931562i \(-0.618447\pi\)
−0.363583 + 0.931562i \(0.618447\pi\)
\(608\) −3.14581e14 −0.153555
\(609\) −1.19964e15 −0.580307
\(610\) 3.66506e15 1.75698
\(611\) −1.38987e15 −0.660311
\(612\) −1.60571e15 −0.756021
\(613\) −6.61911e14 −0.308864 −0.154432 0.988003i \(-0.549355\pi\)
−0.154432 + 0.988003i \(0.549355\pi\)
\(614\) 3.09215e15 1.42999
\(615\) −1.59737e15 −0.732136
\(616\) 3.22107e15 1.46321
\(617\) 3.35290e15 1.50957 0.754783 0.655974i \(-0.227742\pi\)
0.754783 + 0.655974i \(0.227742\pi\)
\(618\) −3.54322e15 −1.58111
\(619\) 1.77549e15 0.785270 0.392635 0.919694i \(-0.371564\pi\)
0.392635 + 0.919694i \(0.371564\pi\)
\(620\) −1.97124e15 −0.864141
\(621\) 5.90512e13 0.0256581
\(622\) −6.83308e14 −0.294286
\(623\) −2.08893e15 −0.891743
\(624\) 2.16390e15 0.915633
\(625\) −2.31905e15 −0.972679
\(626\) −9.18679e14 −0.381949
\(627\) −1.60874e15 −0.663000
\(628\) 2.33557e14 0.0954145
\(629\) 3.00289e15 1.21608
\(630\) −1.31964e15 −0.529762
\(631\) 3.54099e15 1.40917 0.704585 0.709620i \(-0.251133\pi\)
0.704585 + 0.709620i \(0.251133\pi\)
\(632\) −1.58012e15 −0.623370
\(633\) −7.72044e14 −0.301941
\(634\) −5.25419e15 −2.03711
\(635\) −7.43722e14 −0.285861
\(636\) −4.99480e15 −1.90329
\(637\) −5.51142e14 −0.208208
\(638\) −4.44259e15 −1.66388
\(639\) 2.28694e13 0.00849180
\(640\) 4.49693e15 1.65549
\(641\) 3.15496e15 1.15153 0.575765 0.817615i \(-0.304704\pi\)
0.575765 + 0.817615i \(0.304704\pi\)
\(642\) −3.28234e15 −1.18779
\(643\) −4.92157e15 −1.76581 −0.882904 0.469554i \(-0.844415\pi\)
−0.882904 + 0.469554i \(0.844415\pi\)
\(644\) 7.04803e14 0.250724
\(645\) −2.94667e15 −1.03933
\(646\) 7.25631e15 2.53768
\(647\) 4.06035e15 1.40796 0.703979 0.710221i \(-0.251405\pi\)
0.703979 + 0.710221i \(0.251405\pi\)
\(648\) −5.81506e14 −0.199936
\(649\) 3.35724e14 0.114456
\(650\) 1.97548e14 0.0667803
\(651\) −6.86287e14 −0.230044
\(652\) 5.99957e15 1.99415
\(653\) 1.19641e15 0.394328 0.197164 0.980371i \(-0.436827\pi\)
0.197164 + 0.980371i \(0.436827\pi\)
\(654\) −8.53951e14 −0.279097
\(655\) −3.72071e14 −0.120586
\(656\) −4.40199e15 −1.41474
\(657\) −3.75754e14 −0.119755
\(658\) 2.33580e15 0.738234
\(659\) −3.89731e15 −1.22150 −0.610752 0.791822i \(-0.709133\pi\)
−0.610752 + 0.791822i \(0.709133\pi\)
\(660\) −3.27579e15 −1.01818
\(661\) 6.16282e15 1.89964 0.949820 0.312797i \(-0.101266\pi\)
0.949820 + 0.312797i \(0.101266\pi\)
\(662\) −3.26832e15 −0.999094
\(663\) −3.06093e15 −0.927959
\(664\) −4.31725e15 −1.29802
\(665\) 3.99744e15 1.19196
\(666\) 2.14004e15 0.632870
\(667\) −4.93979e14 −0.144883
\(668\) 4.67288e15 1.35930
\(669\) 1.18774e15 0.342671
\(670\) 4.65801e15 1.33287
\(671\) 3.16745e15 0.898951
\(672\) −2.23013e14 −0.0627769
\(673\) −2.03701e14 −0.0568736 −0.0284368 0.999596i \(-0.509053\pi\)
−0.0284368 + 0.999596i \(0.509053\pi\)
\(674\) −8.84153e15 −2.44849
\(675\) −1.86455e13 −0.00512156
\(676\) 8.02970e15 2.18772
\(677\) 1.64809e15 0.445393 0.222697 0.974888i \(-0.428514\pi\)
0.222697 + 0.974888i \(0.428514\pi\)
\(678\) −9.51977e13 −0.0255190
\(679\) 8.61638e14 0.229109
\(680\) 7.50847e15 1.98040
\(681\) 3.41878e15 0.894464
\(682\) −2.54149e15 −0.659592
\(683\) −5.85577e15 −1.50755 −0.753773 0.657135i \(-0.771768\pi\)
−0.753773 + 0.657135i \(0.771768\pi\)
\(684\) 3.46640e15 0.885258
\(685\) −4.18240e15 −1.05957
\(686\) 7.33600e15 1.84364
\(687\) 4.04222e15 1.00776
\(688\) −8.12037e15 −2.00835
\(689\) −9.52147e15 −2.33614
\(690\) −5.43388e14 −0.132263
\(691\) 1.41036e15 0.340567 0.170283 0.985395i \(-0.445532\pi\)
0.170283 + 0.985395i \(0.445532\pi\)
\(692\) −1.52942e16 −3.66390
\(693\) −1.14047e15 −0.271050
\(694\) 1.18255e16 2.78833
\(695\) 3.87086e15 0.905506
\(696\) 4.86445e15 1.12897
\(697\) 6.22680e15 1.43379
\(698\) −8.45840e15 −1.93234
\(699\) −2.52044e15 −0.571284
\(700\) −2.22542e14 −0.0500464
\(701\) 4.55950e15 1.01734 0.508672 0.860960i \(-0.330136\pi\)
0.508672 + 0.860960i \(0.330136\pi\)
\(702\) −2.18141e15 −0.482928
\(703\) −6.48262e15 −1.42396
\(704\) 3.61410e15 0.787682
\(705\) −1.20714e15 −0.261046
\(706\) 1.69974e15 0.364718
\(707\) −7.10341e15 −1.51238
\(708\) −7.23396e14 −0.152825
\(709\) 8.37079e15 1.75474 0.877369 0.479816i \(-0.159297\pi\)
0.877369 + 0.479816i \(0.159297\pi\)
\(710\) −2.10443e14 −0.0437738
\(711\) 5.59465e14 0.115476
\(712\) 8.47043e15 1.73486
\(713\) −2.82593e14 −0.0574340
\(714\) 5.14416e15 1.03747
\(715\) −6.24457e15 −1.24974
\(716\) 1.02643e14 0.0203848
\(717\) 2.10287e15 0.414436
\(718\) 1.54173e16 3.01525
\(719\) −7.11696e15 −1.38129 −0.690646 0.723193i \(-0.742674\pi\)
−0.690646 + 0.723193i \(0.742674\pi\)
\(720\) 1.87940e15 0.361984
\(721\) 7.60894e15 1.45439
\(722\) −6.48359e15 −1.22987
\(723\) 3.92091e15 0.738118
\(724\) 1.30719e16 2.44218
\(725\) 1.55974e14 0.0289197
\(726\) 1.24094e15 0.228349
\(727\) 1.56846e15 0.286441 0.143221 0.989691i \(-0.454254\pi\)
0.143221 + 0.989691i \(0.454254\pi\)
\(728\) −1.32306e16 −2.39804
\(729\) 2.05891e14 0.0370370
\(730\) 3.45767e15 0.617317
\(731\) 1.14866e16 2.03538
\(732\) −6.82501e15 −1.20031
\(733\) −5.61723e14 −0.0980507 −0.0490253 0.998798i \(-0.515612\pi\)
−0.0490253 + 0.998798i \(0.515612\pi\)
\(734\) 1.47255e16 2.55119
\(735\) −4.78680e14 −0.0823123
\(736\) −9.18304e13 −0.0156732
\(737\) 4.02559e15 0.681959
\(738\) 4.43760e15 0.746171
\(739\) −9.25820e15 −1.54519 −0.772595 0.634899i \(-0.781042\pi\)
−0.772595 + 0.634899i \(0.781042\pi\)
\(740\) −1.32003e16 −2.18679
\(741\) 6.60792e15 1.08659
\(742\) 1.60017e16 2.61182
\(743\) 1.04514e16 1.69331 0.846653 0.532146i \(-0.178614\pi\)
0.846653 + 0.532146i \(0.178614\pi\)
\(744\) 2.78283e15 0.447544
\(745\) 1.57605e15 0.251600
\(746\) 1.50010e16 2.37715
\(747\) 1.52859e15 0.240452
\(748\) 1.27696e16 1.99397
\(749\) 7.04871e15 1.09260
\(750\) 6.61875e15 1.01845
\(751\) 7.19109e15 1.09844 0.549218 0.835679i \(-0.314926\pi\)
0.549218 + 0.835679i \(0.314926\pi\)
\(752\) −3.32660e15 −0.504432
\(753\) 2.48327e15 0.373811
\(754\) 1.82480e16 2.72693
\(755\) −1.08335e16 −1.60717
\(756\) 2.45740e15 0.361915
\(757\) −1.28041e16 −1.87207 −0.936035 0.351907i \(-0.885533\pi\)
−0.936035 + 0.351907i \(0.885533\pi\)
\(758\) −1.71977e16 −2.49626
\(759\) −4.69612e14 −0.0676720
\(760\) −1.62093e16 −2.31893
\(761\) −7.01690e15 −0.996621 −0.498310 0.866999i \(-0.666046\pi\)
−0.498310 + 0.866999i \(0.666046\pi\)
\(762\) 2.06611e15 0.291341
\(763\) 1.83383e15 0.256729
\(764\) −6.88865e15 −0.957460
\(765\) −2.65849e15 −0.366857
\(766\) −1.18961e16 −1.62984
\(767\) −1.37899e15 −0.187581
\(768\) −8.66267e15 −1.16994
\(769\) 9.89121e15 1.32634 0.663169 0.748469i \(-0.269211\pi\)
0.663169 + 0.748469i \(0.269211\pi\)
\(770\) 1.04945e16 1.39722
\(771\) −6.53840e14 −0.0864316
\(772\) 2.55152e16 3.34891
\(773\) 1.66297e15 0.216719 0.108359 0.994112i \(-0.465440\pi\)
0.108359 + 0.994112i \(0.465440\pi\)
\(774\) 8.18607e15 1.05925
\(775\) 8.92289e13 0.0114643
\(776\) −3.49387e15 −0.445725
\(777\) −4.59567e15 −0.582148
\(778\) 9.91944e15 1.24767
\(779\) −1.34424e16 −1.67888
\(780\) 1.34554e16 1.66869
\(781\) −1.81871e14 −0.0223967
\(782\) 2.11822e15 0.259020
\(783\) −1.72233e15 −0.209135
\(784\) −1.31914e15 −0.159056
\(785\) 3.86688e14 0.0462996
\(786\) 1.03364e15 0.122898
\(787\) −6.06654e14 −0.0716275 −0.0358138 0.999358i \(-0.511402\pi\)
−0.0358138 + 0.999358i \(0.511402\pi\)
\(788\) 3.18580e16 3.73529
\(789\) 5.07165e15 0.590508
\(790\) −5.14818e15 −0.595258
\(791\) 2.04434e14 0.0234737
\(792\) 4.62449e15 0.527322
\(793\) −1.30104e16 −1.47329
\(794\) 1.29827e16 1.46000
\(795\) −8.26963e15 −0.923564
\(796\) −2.18789e16 −2.42663
\(797\) −1.30937e15 −0.144225 −0.0721126 0.997396i \(-0.522974\pi\)
−0.0721126 + 0.997396i \(0.522974\pi\)
\(798\) −1.11052e16 −1.21481
\(799\) 4.70562e15 0.511223
\(800\) 2.89955e13 0.00312850
\(801\) −2.99908e15 −0.321373
\(802\) 9.88960e15 1.05249
\(803\) 2.98822e15 0.315848
\(804\) −8.67407e15 −0.910573
\(805\) 1.16691e15 0.121663
\(806\) 1.04392e16 1.08100
\(807\) −2.39782e15 −0.246611
\(808\) 2.88037e16 2.94229
\(809\) −2.48188e15 −0.251805 −0.125902 0.992043i \(-0.540183\pi\)
−0.125902 + 0.992043i \(0.540183\pi\)
\(810\) −1.89460e15 −0.190920
\(811\) −8.82367e15 −0.883150 −0.441575 0.897224i \(-0.645580\pi\)
−0.441575 + 0.897224i \(0.645580\pi\)
\(812\) −2.05568e16 −2.04361
\(813\) −8.90953e15 −0.879745
\(814\) −1.70189e16 −1.66916
\(815\) 9.93318e15 0.967657
\(816\) −7.32620e15 −0.708897
\(817\) −2.47973e16 −2.38332
\(818\) 1.19054e16 1.13659
\(819\) 4.68449e15 0.444223
\(820\) −2.73721e16 −2.57829
\(821\) −9.53702e15 −0.892329 −0.446165 0.894951i \(-0.647210\pi\)
−0.446165 + 0.894951i \(0.647210\pi\)
\(822\) 1.16190e16 1.07988
\(823\) −5.52313e15 −0.509902 −0.254951 0.966954i \(-0.582059\pi\)
−0.254951 + 0.966954i \(0.582059\pi\)
\(824\) −3.08536e16 −2.82948
\(825\) 1.48280e14 0.0135078
\(826\) 2.31752e15 0.209717
\(827\) −1.99655e16 −1.79473 −0.897365 0.441290i \(-0.854521\pi\)
−0.897365 + 0.441290i \(0.854521\pi\)
\(828\) 1.01189e15 0.0903578
\(829\) 1.15384e16 1.02352 0.511761 0.859128i \(-0.328993\pi\)
0.511761 + 0.859128i \(0.328993\pi\)
\(830\) −1.40660e16 −1.23949
\(831\) 1.14949e16 1.00623
\(832\) −1.48450e16 −1.29093
\(833\) 1.86597e15 0.161197
\(834\) −1.07535e16 −0.922865
\(835\) 7.73665e15 0.659595
\(836\) −2.75669e16 −2.33482
\(837\) −9.85304e14 −0.0829049
\(838\) −9.95938e14 −0.0832512
\(839\) 1.15818e16 0.961805 0.480903 0.876774i \(-0.340309\pi\)
0.480903 + 0.876774i \(0.340309\pi\)
\(840\) −1.14911e16 −0.948037
\(841\) 2.20726e15 0.180915
\(842\) 2.26433e16 1.84384
\(843\) 3.50972e15 0.283936
\(844\) −1.32296e16 −1.06332
\(845\) 1.32944e16 1.06159
\(846\) 3.35352e15 0.266050
\(847\) −2.66488e15 −0.210048
\(848\) −2.27893e16 −1.78465
\(849\) −9.95943e15 −0.774893
\(850\) −6.68827e14 −0.0517023
\(851\) −1.89236e15 −0.145342
\(852\) 3.91884e14 0.0299048
\(853\) 1.66923e15 0.126560 0.0632800 0.997996i \(-0.479844\pi\)
0.0632800 + 0.997996i \(0.479844\pi\)
\(854\) 2.18651e16 1.64715
\(855\) 5.73914e15 0.429569
\(856\) −2.85819e16 −2.12562
\(857\) −1.29440e16 −0.956478 −0.478239 0.878230i \(-0.658725\pi\)
−0.478239 + 0.878230i \(0.658725\pi\)
\(858\) 1.73479e16 1.27370
\(859\) 2.32871e15 0.169884 0.0849422 0.996386i \(-0.472929\pi\)
0.0849422 + 0.996386i \(0.472929\pi\)
\(860\) −5.04935e16 −3.66011
\(861\) −9.52960e15 −0.686369
\(862\) −2.62950e16 −1.88184
\(863\) 5.04983e15 0.359101 0.179551 0.983749i \(-0.442536\pi\)
0.179551 + 0.983749i \(0.442536\pi\)
\(864\) −3.20181e14 −0.0226240
\(865\) −2.53218e16 −1.77790
\(866\) 1.74608e16 1.21819
\(867\) 2.03516e15 0.141089
\(868\) −1.17600e16 −0.810122
\(869\) −4.44921e15 −0.304561
\(870\) 1.58489e16 1.07806
\(871\) −1.65352e16 −1.11766
\(872\) −7.43602e15 −0.499459
\(873\) 1.23706e15 0.0825679
\(874\) −4.57280e15 −0.303298
\(875\) −1.42135e16 −0.936824
\(876\) −6.43883e15 −0.421730
\(877\) 4.02349e15 0.261882 0.130941 0.991390i \(-0.458200\pi\)
0.130941 + 0.991390i \(0.458200\pi\)
\(878\) 8.02844e15 0.519292
\(879\) −6.54673e14 −0.0420809
\(880\) −1.49461e16 −0.954715
\(881\) −4.97677e15 −0.315922 −0.157961 0.987445i \(-0.550492\pi\)
−0.157961 + 0.987445i \(0.550492\pi\)
\(882\) 1.32981e15 0.0838903
\(883\) −7.93370e15 −0.497384 −0.248692 0.968583i \(-0.580001\pi\)
−0.248692 + 0.968583i \(0.580001\pi\)
\(884\) −5.24513e16 −3.26790
\(885\) −1.19769e15 −0.0741577
\(886\) 7.95583e15 0.489553
\(887\) 2.57465e16 1.57449 0.787243 0.616643i \(-0.211508\pi\)
0.787243 + 0.616643i \(0.211508\pi\)
\(888\) 1.86350e16 1.13255
\(889\) −4.43691e15 −0.267991
\(890\) 2.75975e16 1.65663
\(891\) −1.63737e15 −0.0976833
\(892\) 2.03528e16 1.20675
\(893\) −1.01585e16 −0.598613
\(894\) −4.37839e15 −0.256424
\(895\) 1.69941e14 0.00989169
\(896\) 2.68279e16 1.55200
\(897\) 1.92894e15 0.110907
\(898\) −1.93960e16 −1.10839
\(899\) 8.24233e15 0.468135
\(900\) −3.19504e14 −0.0180361
\(901\) 3.22364e16 1.80867
\(902\) −3.52906e16 −1.96799
\(903\) −1.75793e16 −0.974360
\(904\) −8.28960e14 −0.0456675
\(905\) 2.16425e16 1.18506
\(906\) 3.00963e16 1.63798
\(907\) −2.73038e15 −0.147701 −0.0738503 0.997269i \(-0.523529\pi\)
−0.0738503 + 0.997269i \(0.523529\pi\)
\(908\) 5.85835e16 3.14995
\(909\) −1.01984e16 −0.545042
\(910\) −4.31066e16 −2.28990
\(911\) 3.03460e16 1.60232 0.801161 0.598449i \(-0.204216\pi\)
0.801161 + 0.598449i \(0.204216\pi\)
\(912\) 1.58158e16 0.830078
\(913\) −1.21563e16 −0.634178
\(914\) −5.32465e16 −2.76113
\(915\) −1.12998e16 −0.582446
\(916\) 6.92665e16 3.54894
\(917\) −2.21971e15 −0.113048
\(918\) 7.38548e15 0.373890
\(919\) 8.32053e15 0.418712 0.209356 0.977839i \(-0.432863\pi\)
0.209356 + 0.977839i \(0.432863\pi\)
\(920\) −4.73170e15 −0.236692
\(921\) −9.53347e15 −0.474049
\(922\) −1.67088e16 −0.825893
\(923\) 7.47041e14 0.0367058
\(924\) −1.95428e16 −0.954532
\(925\) 5.97515e14 0.0290114
\(926\) −2.70571e16 −1.30593
\(927\) 1.09242e16 0.524144
\(928\) 2.67840e15 0.127750
\(929\) 9.21014e15 0.436697 0.218348 0.975871i \(-0.429933\pi\)
0.218348 + 0.975871i \(0.429933\pi\)
\(930\) 9.06674e15 0.427361
\(931\) −4.02826e15 −0.188753
\(932\) −4.31897e16 −2.01184
\(933\) 2.10672e15 0.0975570
\(934\) 7.09702e15 0.326714
\(935\) 2.11419e16 0.967567
\(936\) −1.89952e16 −0.864225
\(937\) 3.22835e15 0.146020 0.0730102 0.997331i \(-0.476739\pi\)
0.0730102 + 0.997331i \(0.476739\pi\)
\(938\) 2.77888e16 1.24955
\(939\) 2.83240e15 0.126618
\(940\) −2.06852e16 −0.919300
\(941\) −1.25668e16 −0.555240 −0.277620 0.960691i \(-0.589546\pi\)
−0.277620 + 0.960691i \(0.589546\pi\)
\(942\) −1.07425e15 −0.0471872
\(943\) −3.92402e15 −0.171363
\(944\) −3.30056e15 −0.143299
\(945\) 4.06860e15 0.175618
\(946\) −6.51007e16 −2.79373
\(947\) 2.63934e16 1.12609 0.563043 0.826428i \(-0.309631\pi\)
0.563043 + 0.826428i \(0.309631\pi\)
\(948\) 9.58687e15 0.406659
\(949\) −1.22742e16 −0.517641
\(950\) 1.44386e15 0.0605405
\(951\) 1.61993e16 0.675310
\(952\) 4.47942e16 1.85660
\(953\) −1.33878e16 −0.551696 −0.275848 0.961201i \(-0.588959\pi\)
−0.275848 + 0.961201i \(0.588959\pi\)
\(954\) 2.29736e16 0.941269
\(955\) −1.14052e16 −0.464605
\(956\) 3.60343e16 1.45948
\(957\) 1.36971e16 0.551584
\(958\) −4.15045e16 −1.66182
\(959\) −2.49515e16 −0.993330
\(960\) −1.28932e16 −0.510352
\(961\) −2.06932e16 −0.814423
\(962\) 6.99056e16 2.73558
\(963\) 1.01199e16 0.393758
\(964\) 6.71877e16 2.59936
\(965\) 4.22441e16 1.62505
\(966\) −3.24175e15 −0.123995
\(967\) 3.19970e15 0.121693 0.0608463 0.998147i \(-0.480620\pi\)
0.0608463 + 0.998147i \(0.480620\pi\)
\(968\) 1.08058e16 0.408643
\(969\) −2.23721e16 −0.841252
\(970\) −1.13834e16 −0.425624
\(971\) −2.83042e16 −1.05231 −0.526157 0.850387i \(-0.676368\pi\)
−0.526157 + 0.850387i \(0.676368\pi\)
\(972\) 3.52810e15 0.130430
\(973\) 2.30929e16 0.848901
\(974\) 5.54978e16 2.02862
\(975\) −6.09064e14 −0.0221379
\(976\) −3.11398e16 −1.12549
\(977\) −1.41657e16 −0.509118 −0.254559 0.967057i \(-0.581930\pi\)
−0.254559 + 0.967057i \(0.581930\pi\)
\(978\) −2.75951e16 −0.986207
\(979\) 2.38506e16 0.847605
\(980\) −8.20255e15 −0.289871
\(981\) 2.63284e15 0.0925219
\(982\) −3.42027e16 −1.19522
\(983\) −5.37875e16 −1.86912 −0.934559 0.355808i \(-0.884206\pi\)
−0.934559 + 0.355808i \(0.884206\pi\)
\(984\) 3.86417e16 1.33531
\(985\) 5.27457e16 1.81254
\(986\) −6.17815e16 −2.11123
\(987\) −7.20157e15 −0.244727
\(988\) 1.13232e17 3.82653
\(989\) −7.23866e15 −0.243264
\(990\) 1.50671e16 0.503541
\(991\) 5.04112e16 1.67541 0.837707 0.546120i \(-0.183896\pi\)
0.837707 + 0.546120i \(0.183896\pi\)
\(992\) 1.53224e15 0.0506423
\(993\) 1.00766e16 0.331204
\(994\) −1.25547e15 −0.0410374
\(995\) −3.62238e16 −1.17752
\(996\) 2.61935e16 0.846775
\(997\) −3.33872e16 −1.07339 −0.536694 0.843777i \(-0.680327\pi\)
−0.536694 + 0.843777i \(0.680327\pi\)
\(998\) −2.52620e15 −0.0807701
\(999\) −6.59802e15 −0.209799
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 177.12.a.b.1.3 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.b.1.3 27 1.1 even 1 trivial