Properties

Label 177.12.a.b.1.4
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $27$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-71.6191 q^{2} +243.000 q^{3} +3081.30 q^{4} -9710.01 q^{5} -17403.4 q^{6} +37645.0 q^{7} -74003.9 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-71.6191 q^{2} +243.000 q^{3} +3081.30 q^{4} -9710.01 q^{5} -17403.4 q^{6} +37645.0 q^{7} -74003.9 q^{8} +59049.0 q^{9} +695422. q^{10} +60655.0 q^{11} +748755. q^{12} +624964. q^{13} -2.69610e6 q^{14} -2.35953e6 q^{15} -1.01041e6 q^{16} +2.49028e6 q^{17} -4.22904e6 q^{18} -1.44054e7 q^{19} -2.99194e7 q^{20} +9.14772e6 q^{21} -4.34406e6 q^{22} +1.14743e7 q^{23} -1.79829e7 q^{24} +4.54562e7 q^{25} -4.47593e7 q^{26} +1.43489e7 q^{27} +1.15995e8 q^{28} -1.23449e8 q^{29} +1.68988e8 q^{30} +2.37452e8 q^{31} +2.23924e8 q^{32} +1.47392e7 q^{33} -1.78352e8 q^{34} -3.65533e8 q^{35} +1.81948e8 q^{36} -4.08733e8 q^{37} +1.03170e9 q^{38} +1.51866e8 q^{39} +7.18578e8 q^{40} -2.82822e8 q^{41} -6.55152e8 q^{42} +1.04999e9 q^{43} +1.86896e8 q^{44} -5.73366e8 q^{45} -8.21780e8 q^{46} -2.58355e9 q^{47} -2.45529e8 q^{48} -5.60184e8 q^{49} -3.25553e9 q^{50} +6.05138e8 q^{51} +1.92570e9 q^{52} -1.74096e9 q^{53} -1.02766e9 q^{54} -5.88961e8 q^{55} -2.78587e9 q^{56} -3.50052e9 q^{57} +8.84130e9 q^{58} -7.14924e8 q^{59} -7.27042e9 q^{60} +1.03848e10 q^{61} -1.70061e10 q^{62} +2.22290e9 q^{63} -1.39679e10 q^{64} -6.06840e9 q^{65} -1.05561e9 q^{66} +1.41202e10 q^{67} +7.67329e9 q^{68} +2.78826e9 q^{69} +2.61791e10 q^{70} -1.38159e10 q^{71} -4.36986e9 q^{72} +1.71356e10 q^{73} +2.92731e10 q^{74} +1.10459e10 q^{75} -4.43874e10 q^{76} +2.28336e9 q^{77} -1.08765e10 q^{78} +1.65750e10 q^{79} +9.81105e9 q^{80} +3.48678e9 q^{81} +2.02554e10 q^{82} +1.81884e10 q^{83} +2.81869e10 q^{84} -2.41806e10 q^{85} -7.51994e10 q^{86} -2.99981e10 q^{87} -4.48871e9 q^{88} -9.62794e10 q^{89} +4.10640e10 q^{90} +2.35267e10 q^{91} +3.53558e10 q^{92} +5.77008e10 q^{93} +1.85031e11 q^{94} +1.39877e11 q^{95} +5.44136e10 q^{96} +6.76303e10 q^{97} +4.01199e10 q^{98} +3.58162e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −71.6191 −1.58257 −0.791287 0.611445i \(-0.790589\pi\)
−0.791287 + 0.611445i \(0.790589\pi\)
\(3\) 243.000 0.577350
\(4\) 3081.30 1.50454
\(5\) −9710.01 −1.38958 −0.694792 0.719211i \(-0.744503\pi\)
−0.694792 + 0.719211i \(0.744503\pi\)
\(6\) −17403.4 −0.913699
\(7\) 37645.0 0.846579 0.423290 0.905994i \(-0.360875\pi\)
0.423290 + 0.905994i \(0.360875\pi\)
\(8\) −74003.9 −0.798472
\(9\) 59049.0 0.333333
\(10\) 695422. 2.19912
\(11\) 60655.0 0.113555 0.0567776 0.998387i \(-0.481917\pi\)
0.0567776 + 0.998387i \(0.481917\pi\)
\(12\) 748755. 0.868647
\(13\) 624964. 0.466838 0.233419 0.972376i \(-0.425009\pi\)
0.233419 + 0.972376i \(0.425009\pi\)
\(14\) −2.69610e6 −1.33977
\(15\) −2.35953e6 −0.802276
\(16\) −1.01041e6 −0.240899
\(17\) 2.49028e6 0.425382 0.212691 0.977120i \(-0.431777\pi\)
0.212691 + 0.977120i \(0.431777\pi\)
\(18\) −4.22904e6 −0.527525
\(19\) −1.44054e7 −1.33469 −0.667346 0.744748i \(-0.732570\pi\)
−0.667346 + 0.744748i \(0.732570\pi\)
\(20\) −2.99194e7 −2.09068
\(21\) 9.14772e6 0.488773
\(22\) −4.34406e6 −0.179709
\(23\) 1.14743e7 0.371727 0.185863 0.982576i \(-0.440492\pi\)
0.185863 + 0.982576i \(0.440492\pi\)
\(24\) −1.79829e7 −0.460998
\(25\) 4.54562e7 0.930942
\(26\) −4.47593e7 −0.738806
\(27\) 1.43489e7 0.192450
\(28\) 1.15995e8 1.27371
\(29\) −1.23449e8 −1.11763 −0.558815 0.829292i \(-0.688744\pi\)
−0.558815 + 0.829292i \(0.688744\pi\)
\(30\) 1.68988e8 1.26966
\(31\) 2.37452e8 1.48966 0.744828 0.667256i \(-0.232531\pi\)
0.744828 + 0.667256i \(0.232531\pi\)
\(32\) 2.23924e8 1.17971
\(33\) 1.47392e7 0.0655611
\(34\) −1.78352e8 −0.673198
\(35\) −3.65533e8 −1.17639
\(36\) 1.81948e8 0.501513
\(37\) −4.08733e8 −0.969015 −0.484507 0.874787i \(-0.661001\pi\)
−0.484507 + 0.874787i \(0.661001\pi\)
\(38\) 1.03170e9 2.11225
\(39\) 1.51866e8 0.269529
\(40\) 7.18578e8 1.10954
\(41\) −2.82822e8 −0.381243 −0.190621 0.981664i \(-0.561050\pi\)
−0.190621 + 0.981664i \(0.561050\pi\)
\(42\) −6.55152e8 −0.773519
\(43\) 1.04999e9 1.08920 0.544601 0.838695i \(-0.316681\pi\)
0.544601 + 0.838695i \(0.316681\pi\)
\(44\) 1.86896e8 0.170848
\(45\) −5.73366e8 −0.463195
\(46\) −8.21780e8 −0.588285
\(47\) −2.58355e9 −1.64315 −0.821577 0.570098i \(-0.806905\pi\)
−0.821577 + 0.570098i \(0.806905\pi\)
\(48\) −2.45529e8 −0.139083
\(49\) −5.60184e8 −0.283304
\(50\) −3.25553e9 −1.47329
\(51\) 6.05138e8 0.245594
\(52\) 1.92570e9 0.702376
\(53\) −1.74096e9 −0.571835 −0.285918 0.958254i \(-0.592298\pi\)
−0.285918 + 0.958254i \(0.592298\pi\)
\(54\) −1.02766e9 −0.304566
\(55\) −5.88961e8 −0.157794
\(56\) −2.78587e9 −0.675969
\(57\) −3.50052e9 −0.770585
\(58\) 8.84130e9 1.76873
\(59\) −7.14924e8 −0.130189
\(60\) −7.27042e9 −1.20706
\(61\) 1.03848e10 1.57429 0.787146 0.616766i \(-0.211558\pi\)
0.787146 + 0.616766i \(0.211558\pi\)
\(62\) −1.70061e10 −2.35749
\(63\) 2.22290e9 0.282193
\(64\) −1.39679e10 −1.62608
\(65\) −6.06840e9 −0.648710
\(66\) −1.05561e9 −0.103755
\(67\) 1.41202e10 1.27770 0.638850 0.769331i \(-0.279410\pi\)
0.638850 + 0.769331i \(0.279410\pi\)
\(68\) 7.67329e9 0.640004
\(69\) 2.78826e9 0.214616
\(70\) 2.61791e10 1.86173
\(71\) −1.38159e10 −0.908778 −0.454389 0.890803i \(-0.650142\pi\)
−0.454389 + 0.890803i \(0.650142\pi\)
\(72\) −4.36986e9 −0.266157
\(73\) 1.71356e10 0.967442 0.483721 0.875222i \(-0.339285\pi\)
0.483721 + 0.875222i \(0.339285\pi\)
\(74\) 2.92731e10 1.53354
\(75\) 1.10459e10 0.537480
\(76\) −4.43874e10 −2.00810
\(77\) 2.28336e9 0.0961334
\(78\) −1.08765e10 −0.426550
\(79\) 1.65750e10 0.606044 0.303022 0.952984i \(-0.402004\pi\)
0.303022 + 0.952984i \(0.402004\pi\)
\(80\) 9.81105e9 0.334750
\(81\) 3.48678e9 0.111111
\(82\) 2.02554e10 0.603345
\(83\) 1.81884e10 0.506834 0.253417 0.967357i \(-0.418446\pi\)
0.253417 + 0.967357i \(0.418446\pi\)
\(84\) 2.81869e10 0.735378
\(85\) −2.41806e10 −0.591104
\(86\) −7.51994e10 −1.72374
\(87\) −2.99981e10 −0.645264
\(88\) −4.48871e9 −0.0906706
\(89\) −9.62794e10 −1.82763 −0.913815 0.406131i \(-0.866878\pi\)
−0.913815 + 0.406131i \(0.866878\pi\)
\(90\) 4.10640e10 0.733040
\(91\) 2.35267e10 0.395215
\(92\) 3.53558e10 0.559278
\(93\) 5.77008e10 0.860053
\(94\) 1.85031e11 2.60041
\(95\) 1.39877e11 1.85467
\(96\) 5.44136e10 0.681108
\(97\) 6.76303e10 0.799644 0.399822 0.916593i \(-0.369072\pi\)
0.399822 + 0.916593i \(0.369072\pi\)
\(98\) 4.01199e10 0.448349
\(99\) 3.58162e9 0.0378517
\(100\) 1.40064e11 1.40064
\(101\) 9.72443e10 0.920654 0.460327 0.887749i \(-0.347732\pi\)
0.460327 + 0.887749i \(0.347732\pi\)
\(102\) −4.33395e10 −0.388671
\(103\) 1.68362e11 1.43100 0.715500 0.698613i \(-0.246199\pi\)
0.715500 + 0.698613i \(0.246199\pi\)
\(104\) −4.62497e10 −0.372757
\(105\) −8.88245e10 −0.679190
\(106\) 1.24686e11 0.904971
\(107\) 2.85563e10 0.196830 0.0984151 0.995145i \(-0.468623\pi\)
0.0984151 + 0.995145i \(0.468623\pi\)
\(108\) 4.42133e10 0.289549
\(109\) 1.07166e11 0.667134 0.333567 0.942726i \(-0.391748\pi\)
0.333567 + 0.942726i \(0.391748\pi\)
\(110\) 4.21809e10 0.249721
\(111\) −9.93222e10 −0.559461
\(112\) −3.80367e10 −0.203940
\(113\) 2.67933e11 1.36803 0.684015 0.729468i \(-0.260232\pi\)
0.684015 + 0.729468i \(0.260232\pi\)
\(114\) 2.50704e11 1.21951
\(115\) −1.11416e11 −0.516545
\(116\) −3.80383e11 −1.68152
\(117\) 3.69035e10 0.155613
\(118\) 5.12022e10 0.206034
\(119\) 9.37465e10 0.360120
\(120\) 1.74615e11 0.640595
\(121\) −2.81633e11 −0.987105
\(122\) −7.43753e11 −2.49143
\(123\) −6.87257e10 −0.220111
\(124\) 7.31659e11 2.24125
\(125\) 3.27417e10 0.0959613
\(126\) −1.59202e11 −0.446591
\(127\) −4.93391e11 −1.32517 −0.662583 0.748988i \(-0.730540\pi\)
−0.662583 + 0.748988i \(0.730540\pi\)
\(128\) 5.41775e11 1.39368
\(129\) 2.55148e11 0.628851
\(130\) 4.34614e11 1.02663
\(131\) −3.92825e11 −0.889625 −0.444813 0.895624i \(-0.646730\pi\)
−0.444813 + 0.895624i \(0.646730\pi\)
\(132\) 4.54158e10 0.0986393
\(133\) −5.42292e11 −1.12992
\(134\) −1.01127e12 −2.02205
\(135\) −1.39328e11 −0.267425
\(136\) −1.84290e11 −0.339656
\(137\) 1.35467e11 0.239811 0.119906 0.992785i \(-0.461741\pi\)
0.119906 + 0.992785i \(0.461741\pi\)
\(138\) −1.99693e11 −0.339646
\(139\) −3.25168e11 −0.531529 −0.265764 0.964038i \(-0.585624\pi\)
−0.265764 + 0.964038i \(0.585624\pi\)
\(140\) −1.12632e12 −1.76993
\(141\) −6.27802e11 −0.948675
\(142\) 9.89481e11 1.43821
\(143\) 3.79072e10 0.0530119
\(144\) −5.96634e10 −0.0802998
\(145\) 1.19869e12 1.55304
\(146\) −1.22724e12 −1.53105
\(147\) −1.36125e11 −0.163566
\(148\) −1.25943e12 −1.45792
\(149\) −8.60761e11 −0.960192 −0.480096 0.877216i \(-0.659398\pi\)
−0.480096 + 0.877216i \(0.659398\pi\)
\(150\) −7.91094e11 −0.850602
\(151\) −2.95852e11 −0.306691 −0.153346 0.988173i \(-0.549005\pi\)
−0.153346 + 0.988173i \(0.549005\pi\)
\(152\) 1.06606e12 1.06571
\(153\) 1.47049e11 0.141794
\(154\) −1.63532e11 −0.152138
\(155\) −2.30566e12 −2.07000
\(156\) 4.67945e11 0.405517
\(157\) 8.60052e11 0.719576 0.359788 0.933034i \(-0.382849\pi\)
0.359788 + 0.933034i \(0.382849\pi\)
\(158\) −1.18709e12 −0.959109
\(159\) −4.23053e11 −0.330149
\(160\) −2.17431e12 −1.63931
\(161\) 4.31950e11 0.314696
\(162\) −2.49720e11 −0.175842
\(163\) −4.52373e11 −0.307939 −0.153970 0.988076i \(-0.549206\pi\)
−0.153970 + 0.988076i \(0.549206\pi\)
\(164\) −8.71458e11 −0.573595
\(165\) −1.43117e11 −0.0911027
\(166\) −1.30264e12 −0.802102
\(167\) −3.57279e11 −0.212846 −0.106423 0.994321i \(-0.533940\pi\)
−0.106423 + 0.994321i \(0.533940\pi\)
\(168\) −6.76967e11 −0.390271
\(169\) −1.40158e12 −0.782062
\(170\) 1.73180e12 0.935466
\(171\) −8.50626e11 −0.444898
\(172\) 3.23533e12 1.63875
\(173\) 1.16482e12 0.571486 0.285743 0.958306i \(-0.407760\pi\)
0.285743 + 0.958306i \(0.407760\pi\)
\(174\) 2.14844e12 1.02118
\(175\) 1.71120e12 0.788116
\(176\) −6.12862e10 −0.0273554
\(177\) −1.73727e11 −0.0751646
\(178\) 6.89544e12 2.89236
\(179\) −5.99613e11 −0.243882 −0.121941 0.992537i \(-0.538912\pi\)
−0.121941 + 0.992537i \(0.538912\pi\)
\(180\) −1.76671e12 −0.696895
\(181\) 2.40799e11 0.0921347 0.0460673 0.998938i \(-0.485331\pi\)
0.0460673 + 0.998938i \(0.485331\pi\)
\(182\) −1.68496e12 −0.625457
\(183\) 2.52351e12 0.908918
\(184\) −8.49144e11 −0.296813
\(185\) 3.96880e12 1.34653
\(186\) −4.13248e12 −1.36110
\(187\) 1.51048e11 0.0483043
\(188\) −7.96068e12 −2.47219
\(189\) 5.40164e11 0.162924
\(190\) −1.00179e13 −2.93515
\(191\) −1.64656e12 −0.468699 −0.234350 0.972152i \(-0.575296\pi\)
−0.234350 + 0.972152i \(0.575296\pi\)
\(192\) −3.39421e12 −0.938820
\(193\) 1.54565e12 0.415476 0.207738 0.978185i \(-0.433390\pi\)
0.207738 + 0.978185i \(0.433390\pi\)
\(194\) −4.84362e12 −1.26550
\(195\) −1.47462e12 −0.374533
\(196\) −1.72609e12 −0.426242
\(197\) 1.38427e12 0.332397 0.166199 0.986092i \(-0.446851\pi\)
0.166199 + 0.986092i \(0.446851\pi\)
\(198\) −2.56512e11 −0.0599032
\(199\) −1.07613e12 −0.244441 −0.122221 0.992503i \(-0.539002\pi\)
−0.122221 + 0.992503i \(0.539002\pi\)
\(200\) −3.36393e12 −0.743331
\(201\) 3.43120e12 0.737680
\(202\) −6.96455e12 −1.45700
\(203\) −4.64723e12 −0.946163
\(204\) 1.86461e12 0.369507
\(205\) 2.74620e12 0.529769
\(206\) −1.20579e13 −2.26466
\(207\) 6.77547e11 0.123909
\(208\) −6.31467e11 −0.112461
\(209\) −8.73761e11 −0.151561
\(210\) 6.36153e12 1.07487
\(211\) −9.00351e12 −1.48204 −0.741018 0.671486i \(-0.765657\pi\)
−0.741018 + 0.671486i \(0.765657\pi\)
\(212\) −5.36441e12 −0.860349
\(213\) −3.35726e12 −0.524683
\(214\) −2.04518e12 −0.311498
\(215\) −1.01954e13 −1.51354
\(216\) −1.06187e12 −0.153666
\(217\) 8.93886e12 1.26111
\(218\) −7.67517e12 −1.05579
\(219\) 4.16396e12 0.558553
\(220\) −1.81476e12 −0.237408
\(221\) 1.55633e12 0.198585
\(222\) 7.11337e12 0.885388
\(223\) 2.56413e12 0.311360 0.155680 0.987808i \(-0.450243\pi\)
0.155680 + 0.987808i \(0.450243\pi\)
\(224\) 8.42962e12 0.998720
\(225\) 2.68414e12 0.310314
\(226\) −1.91892e13 −2.16501
\(227\) 4.72205e12 0.519982 0.259991 0.965611i \(-0.416280\pi\)
0.259991 + 0.965611i \(0.416280\pi\)
\(228\) −1.07861e13 −1.15938
\(229\) −1.74449e13 −1.83051 −0.915256 0.402873i \(-0.868012\pi\)
−0.915256 + 0.402873i \(0.868012\pi\)
\(230\) 7.97949e12 0.817471
\(231\) 5.54855e11 0.0555027
\(232\) 9.13570e12 0.892396
\(233\) 6.59376e11 0.0629036 0.0314518 0.999505i \(-0.489987\pi\)
0.0314518 + 0.999505i \(0.489987\pi\)
\(234\) −2.64299e12 −0.246269
\(235\) 2.50863e13 2.28330
\(236\) −2.20289e12 −0.195874
\(237\) 4.02772e12 0.349899
\(238\) −6.71404e12 −0.569916
\(239\) −9.06209e12 −0.751692 −0.375846 0.926682i \(-0.622648\pi\)
−0.375846 + 0.926682i \(0.622648\pi\)
\(240\) 2.38408e12 0.193268
\(241\) −2.24055e13 −1.77525 −0.887626 0.460565i \(-0.847647\pi\)
−0.887626 + 0.460565i \(0.847647\pi\)
\(242\) 2.01703e13 1.56217
\(243\) 8.47289e11 0.0641500
\(244\) 3.19988e13 2.36859
\(245\) 5.43940e12 0.393674
\(246\) 4.92207e12 0.348341
\(247\) −9.00287e12 −0.623085
\(248\) −1.75723e13 −1.18945
\(249\) 4.41979e12 0.292621
\(250\) −2.34493e12 −0.151866
\(251\) 1.13619e13 0.719857 0.359929 0.932980i \(-0.382801\pi\)
0.359929 + 0.932980i \(0.382801\pi\)
\(252\) 6.84941e12 0.424571
\(253\) 6.95975e11 0.0422115
\(254\) 3.53362e13 2.09717
\(255\) −5.87590e12 −0.341274
\(256\) −1.01951e13 −0.579525
\(257\) 1.61056e12 0.0896074 0.0448037 0.998996i \(-0.485734\pi\)
0.0448037 + 0.998996i \(0.485734\pi\)
\(258\) −1.82734e13 −0.995204
\(259\) −1.53867e13 −0.820348
\(260\) −1.86986e13 −0.976011
\(261\) −7.28953e12 −0.372544
\(262\) 2.81338e13 1.40790
\(263\) −1.14324e13 −0.560251 −0.280125 0.959963i \(-0.590376\pi\)
−0.280125 + 0.959963i \(0.590376\pi\)
\(264\) −1.09076e12 −0.0523487
\(265\) 1.69047e13 0.794613
\(266\) 3.88384e13 1.78819
\(267\) −2.33959e13 −1.05518
\(268\) 4.35085e13 1.92235
\(269\) −3.96300e13 −1.71548 −0.857742 0.514081i \(-0.828133\pi\)
−0.857742 + 0.514081i \(0.828133\pi\)
\(270\) 9.97855e12 0.423221
\(271\) 6.17718e12 0.256720 0.128360 0.991728i \(-0.459029\pi\)
0.128360 + 0.991728i \(0.459029\pi\)
\(272\) −2.51619e12 −0.102474
\(273\) 5.71699e12 0.228178
\(274\) −9.70201e12 −0.379519
\(275\) 2.75715e12 0.105713
\(276\) 8.59145e12 0.322899
\(277\) −5.13723e13 −1.89274 −0.946368 0.323090i \(-0.895278\pi\)
−0.946368 + 0.323090i \(0.895278\pi\)
\(278\) 2.32883e13 0.841184
\(279\) 1.40213e13 0.496552
\(280\) 2.70508e13 0.939316
\(281\) 1.65407e13 0.563210 0.281605 0.959530i \(-0.409133\pi\)
0.281605 + 0.959530i \(0.409133\pi\)
\(282\) 4.49626e13 1.50135
\(283\) 9.14231e12 0.299385 0.149693 0.988733i \(-0.452172\pi\)
0.149693 + 0.988733i \(0.452172\pi\)
\(284\) −4.25708e13 −1.36729
\(285\) 3.39901e13 1.07079
\(286\) −2.71488e12 −0.0838952
\(287\) −1.06468e13 −0.322752
\(288\) 1.32225e13 0.393238
\(289\) −2.80704e13 −0.819050
\(290\) −8.58491e13 −2.45780
\(291\) 1.64342e13 0.461675
\(292\) 5.28000e13 1.45555
\(293\) −1.46326e13 −0.395866 −0.197933 0.980216i \(-0.563423\pi\)
−0.197933 + 0.980216i \(0.563423\pi\)
\(294\) 9.74914e12 0.258855
\(295\) 6.94192e12 0.180908
\(296\) 3.02478e13 0.773731
\(297\) 8.70333e11 0.0218537
\(298\) 6.16470e13 1.51958
\(299\) 7.17103e12 0.173536
\(300\) 3.40356e13 0.808660
\(301\) 3.95268e13 0.922096
\(302\) 2.11887e13 0.485362
\(303\) 2.36304e13 0.531540
\(304\) 1.45553e13 0.321527
\(305\) −1.00837e14 −2.18761
\(306\) −1.05315e13 −0.224399
\(307\) 9.77088e12 0.204490 0.102245 0.994759i \(-0.467397\pi\)
0.102245 + 0.994759i \(0.467397\pi\)
\(308\) 7.03570e12 0.144637
\(309\) 4.09120e13 0.826188
\(310\) 1.65129e14 3.27593
\(311\) −3.39024e13 −0.660767 −0.330383 0.943847i \(-0.607178\pi\)
−0.330383 + 0.943847i \(0.607178\pi\)
\(312\) −1.12387e13 −0.215211
\(313\) −6.89569e13 −1.29743 −0.648714 0.761032i \(-0.724693\pi\)
−0.648714 + 0.761032i \(0.724693\pi\)
\(314\) −6.15962e13 −1.13878
\(315\) −2.15843e13 −0.392131
\(316\) 5.10724e13 0.911817
\(317\) −6.46132e13 −1.13369 −0.566847 0.823823i \(-0.691837\pi\)
−0.566847 + 0.823823i \(0.691837\pi\)
\(318\) 3.02987e13 0.522485
\(319\) −7.48780e12 −0.126913
\(320\) 1.35629e14 2.25958
\(321\) 6.93919e12 0.113640
\(322\) −3.09359e13 −0.498030
\(323\) −3.58735e13 −0.567754
\(324\) 1.07438e13 0.167171
\(325\) 2.84085e13 0.434599
\(326\) 3.23986e13 0.487337
\(327\) 2.60415e13 0.385170
\(328\) 2.09299e13 0.304412
\(329\) −9.72575e13 −1.39106
\(330\) 1.02499e13 0.144177
\(331\) −9.99966e13 −1.38335 −0.691674 0.722210i \(-0.743126\pi\)
−0.691674 + 0.722210i \(0.743126\pi\)
\(332\) 5.60439e13 0.762552
\(333\) −2.41353e13 −0.323005
\(334\) 2.55880e13 0.336845
\(335\) −1.37107e14 −1.77547
\(336\) −9.24291e12 −0.117745
\(337\) −1.23806e14 −1.55159 −0.775795 0.630985i \(-0.782651\pi\)
−0.775795 + 0.630985i \(0.782651\pi\)
\(338\) 1.00380e14 1.23767
\(339\) 6.51078e13 0.789832
\(340\) −7.45078e13 −0.889339
\(341\) 1.44026e13 0.169158
\(342\) 6.09211e13 0.704083
\(343\) −9.55245e13 −1.08642
\(344\) −7.77033e13 −0.869698
\(345\) −2.70740e13 −0.298227
\(346\) −8.34234e13 −0.904418
\(347\) 9.04500e13 0.965154 0.482577 0.875854i \(-0.339701\pi\)
0.482577 + 0.875854i \(0.339701\pi\)
\(348\) −9.24330e13 −0.970826
\(349\) −4.98058e12 −0.0514920 −0.0257460 0.999669i \(-0.508196\pi\)
−0.0257460 + 0.999669i \(0.508196\pi\)
\(350\) −1.22554e14 −1.24725
\(351\) 8.96754e12 0.0898430
\(352\) 1.35821e13 0.133963
\(353\) −9.99494e13 −0.970554 −0.485277 0.874361i \(-0.661281\pi\)
−0.485277 + 0.874361i \(0.661281\pi\)
\(354\) 1.24421e13 0.118954
\(355\) 1.34152e14 1.26282
\(356\) −2.96665e14 −2.74974
\(357\) 2.27804e13 0.207915
\(358\) 4.29437e13 0.385961
\(359\) 7.76199e13 0.686995 0.343498 0.939154i \(-0.388388\pi\)
0.343498 + 0.939154i \(0.388388\pi\)
\(360\) 4.24313e13 0.369848
\(361\) 9.10260e13 0.781404
\(362\) −1.72458e13 −0.145810
\(363\) −6.84367e13 −0.569905
\(364\) 7.24928e13 0.594617
\(365\) −1.66387e14 −1.34434
\(366\) −1.80732e14 −1.43843
\(367\) 1.26252e14 0.989861 0.494930 0.868933i \(-0.335194\pi\)
0.494930 + 0.868933i \(0.335194\pi\)
\(368\) −1.15937e13 −0.0895487
\(369\) −1.67003e13 −0.127081
\(370\) −2.84242e14 −2.13098
\(371\) −6.55383e13 −0.484104
\(372\) 1.77793e14 1.29398
\(373\) 2.49748e14 1.79103 0.895515 0.445031i \(-0.146807\pi\)
0.895515 + 0.445031i \(0.146807\pi\)
\(374\) −1.08179e13 −0.0764452
\(375\) 7.95623e12 0.0554033
\(376\) 1.91193e14 1.31201
\(377\) −7.71511e13 −0.521752
\(378\) −3.86861e13 −0.257840
\(379\) 5.89118e13 0.386978 0.193489 0.981102i \(-0.438020\pi\)
0.193489 + 0.981102i \(0.438020\pi\)
\(380\) 4.31002e14 2.79042
\(381\) −1.19894e14 −0.765085
\(382\) 1.17925e14 0.741752
\(383\) −1.30460e14 −0.808881 −0.404440 0.914564i \(-0.632534\pi\)
−0.404440 + 0.914564i \(0.632534\pi\)
\(384\) 1.31651e14 0.804644
\(385\) −2.21714e13 −0.133585
\(386\) −1.10698e14 −0.657521
\(387\) 6.20009e13 0.363068
\(388\) 2.08389e14 1.20310
\(389\) 1.05199e14 0.598807 0.299403 0.954127i \(-0.403212\pi\)
0.299403 + 0.954127i \(0.403212\pi\)
\(390\) 1.05611e14 0.592726
\(391\) 2.85743e13 0.158126
\(392\) 4.14558e13 0.226210
\(393\) −9.54565e13 −0.513625
\(394\) −9.91404e13 −0.526043
\(395\) −1.60943e14 −0.842148
\(396\) 1.10360e13 0.0569494
\(397\) −2.32327e14 −1.18237 −0.591184 0.806537i \(-0.701339\pi\)
−0.591184 + 0.806537i \(0.701339\pi\)
\(398\) 7.70718e13 0.386846
\(399\) −1.31777e14 −0.652361
\(400\) −4.59292e13 −0.224264
\(401\) −3.00084e14 −1.44527 −0.722635 0.691230i \(-0.757069\pi\)
−0.722635 + 0.691230i \(0.757069\pi\)
\(402\) −2.45740e14 −1.16743
\(403\) 1.48399e14 0.695428
\(404\) 2.99639e14 1.38516
\(405\) −3.38567e13 −0.154398
\(406\) 3.32830e14 1.49737
\(407\) −2.47917e13 −0.110037
\(408\) −4.47826e13 −0.196100
\(409\) 3.69758e14 1.59749 0.798747 0.601667i \(-0.205497\pi\)
0.798747 + 0.601667i \(0.205497\pi\)
\(410\) −1.96681e14 −0.838398
\(411\) 3.29184e13 0.138455
\(412\) 5.18774e14 2.15300
\(413\) −2.69133e13 −0.110215
\(414\) −4.85253e13 −0.196095
\(415\) −1.76610e14 −0.704288
\(416\) 1.39945e14 0.550735
\(417\) −7.90159e13 −0.306878
\(418\) 6.25780e13 0.239857
\(419\) 1.12710e14 0.426370 0.213185 0.977012i \(-0.431616\pi\)
0.213185 + 0.977012i \(0.431616\pi\)
\(420\) −2.73695e14 −1.02187
\(421\) 4.47083e14 1.64754 0.823772 0.566922i \(-0.191866\pi\)
0.823772 + 0.566922i \(0.191866\pi\)
\(422\) 6.44824e14 2.34543
\(423\) −1.52556e14 −0.547718
\(424\) 1.28838e14 0.456594
\(425\) 1.13199e14 0.396006
\(426\) 2.40444e14 0.830350
\(427\) 3.90937e14 1.33276
\(428\) 8.79906e13 0.296139
\(429\) 9.21144e12 0.0306064
\(430\) 7.30187e14 2.39529
\(431\) 2.16562e14 0.701386 0.350693 0.936490i \(-0.385946\pi\)
0.350693 + 0.936490i \(0.385946\pi\)
\(432\) −1.44982e13 −0.0463611
\(433\) −4.32371e14 −1.36513 −0.682563 0.730827i \(-0.739135\pi\)
−0.682563 + 0.730827i \(0.739135\pi\)
\(434\) −6.40193e14 −1.99580
\(435\) 2.91282e14 0.896649
\(436\) 3.30212e14 1.00373
\(437\) −1.65292e14 −0.496141
\(438\) −2.98219e14 −0.883951
\(439\) −3.18492e14 −0.932275 −0.466137 0.884712i \(-0.654355\pi\)
−0.466137 + 0.884712i \(0.654355\pi\)
\(440\) 4.35854e13 0.125994
\(441\) −3.30783e13 −0.0944346
\(442\) −1.11463e14 −0.314275
\(443\) 4.44114e14 1.23673 0.618364 0.785892i \(-0.287796\pi\)
0.618364 + 0.785892i \(0.287796\pi\)
\(444\) −3.06041e14 −0.841731
\(445\) 9.34874e14 2.53964
\(446\) −1.83641e14 −0.492751
\(447\) −2.09165e14 −0.554367
\(448\) −5.25823e14 −1.37661
\(449\) −1.82168e14 −0.471105 −0.235552 0.971862i \(-0.575690\pi\)
−0.235552 + 0.971862i \(0.575690\pi\)
\(450\) −1.92236e14 −0.491095
\(451\) −1.71546e13 −0.0432921
\(452\) 8.25583e14 2.05825
\(453\) −7.18921e13 −0.177068
\(454\) −3.38189e14 −0.822910
\(455\) −2.28445e14 −0.549185
\(456\) 2.59052e14 0.615290
\(457\) 1.57071e14 0.368602 0.184301 0.982870i \(-0.440998\pi\)
0.184301 + 0.982870i \(0.440998\pi\)
\(458\) 1.24939e15 2.89692
\(459\) 3.57328e13 0.0818648
\(460\) −3.43305e14 −0.777163
\(461\) −6.23903e14 −1.39560 −0.697801 0.716292i \(-0.745838\pi\)
−0.697801 + 0.716292i \(0.745838\pi\)
\(462\) −3.97382e13 −0.0878371
\(463\) −3.29305e14 −0.719288 −0.359644 0.933090i \(-0.617102\pi\)
−0.359644 + 0.933090i \(0.617102\pi\)
\(464\) 1.24733e14 0.269237
\(465\) −5.60275e14 −1.19512
\(466\) −4.72240e13 −0.0995497
\(467\) 7.60322e14 1.58400 0.791999 0.610522i \(-0.209040\pi\)
0.791999 + 0.610522i \(0.209040\pi\)
\(468\) 1.13711e14 0.234125
\(469\) 5.31554e14 1.08167
\(470\) −1.79666e15 −3.61349
\(471\) 2.08993e14 0.415447
\(472\) 5.29072e13 0.103952
\(473\) 6.36872e13 0.123685
\(474\) −2.88462e14 −0.553742
\(475\) −6.54815e14 −1.24252
\(476\) 2.88861e14 0.541814
\(477\) −1.02802e14 −0.190612
\(478\) 6.49019e14 1.18961
\(479\) −5.26864e13 −0.0954669 −0.0477335 0.998860i \(-0.515200\pi\)
−0.0477335 + 0.998860i \(0.515200\pi\)
\(480\) −5.28357e14 −0.946456
\(481\) −2.55443e14 −0.452373
\(482\) 1.60466e15 2.80947
\(483\) 1.04964e14 0.181690
\(484\) −8.67794e14 −1.48514
\(485\) −6.56691e14 −1.11117
\(486\) −6.06821e13 −0.101522
\(487\) −3.58994e14 −0.593851 −0.296926 0.954901i \(-0.595961\pi\)
−0.296926 + 0.954901i \(0.595961\pi\)
\(488\) −7.68518e14 −1.25703
\(489\) −1.09927e14 −0.177789
\(490\) −3.89565e14 −0.623019
\(491\) 8.18417e14 1.29427 0.647137 0.762373i \(-0.275966\pi\)
0.647137 + 0.762373i \(0.275966\pi\)
\(492\) −2.11764e14 −0.331165
\(493\) −3.07422e14 −0.475420
\(494\) 6.44777e14 0.986078
\(495\) −3.47775e13 −0.0525981
\(496\) −2.39923e14 −0.358857
\(497\) −5.20098e14 −0.769352
\(498\) −3.16541e14 −0.463094
\(499\) 1.37376e13 0.0198774 0.00993869 0.999951i \(-0.496836\pi\)
0.00993869 + 0.999951i \(0.496836\pi\)
\(500\) 1.00887e14 0.144378
\(501\) −8.68187e13 −0.122887
\(502\) −8.13731e14 −1.13923
\(503\) 5.86134e14 0.811658 0.405829 0.913949i \(-0.366983\pi\)
0.405829 + 0.913949i \(0.366983\pi\)
\(504\) −1.64503e14 −0.225323
\(505\) −9.44243e14 −1.27933
\(506\) −4.98451e13 −0.0668028
\(507\) −3.40584e14 −0.451524
\(508\) −1.52028e15 −1.99377
\(509\) −9.93752e14 −1.28923 −0.644615 0.764507i \(-0.722982\pi\)
−0.644615 + 0.764507i \(0.722982\pi\)
\(510\) 4.20827e14 0.540091
\(511\) 6.45071e14 0.819016
\(512\) −3.79391e14 −0.476544
\(513\) −2.06702e14 −0.256862
\(514\) −1.15347e14 −0.141810
\(515\) −1.63480e15 −1.98849
\(516\) 7.86186e14 0.946132
\(517\) −1.56705e14 −0.186589
\(518\) 1.10198e15 1.29826
\(519\) 2.83051e14 0.329947
\(520\) 4.49085e14 0.517977
\(521\) 8.59337e14 0.980745 0.490372 0.871513i \(-0.336861\pi\)
0.490372 + 0.871513i \(0.336861\pi\)
\(522\) 5.22070e14 0.589578
\(523\) 4.92525e13 0.0550388 0.0275194 0.999621i \(-0.491239\pi\)
0.0275194 + 0.999621i \(0.491239\pi\)
\(524\) −1.21041e15 −1.33848
\(525\) 4.15820e14 0.455019
\(526\) 8.18781e14 0.886638
\(527\) 5.91321e14 0.633673
\(528\) −1.48925e13 −0.0157936
\(529\) −8.21150e14 −0.861819
\(530\) −1.21070e15 −1.25753
\(531\) −4.22156e13 −0.0433963
\(532\) −1.67096e15 −1.70001
\(533\) −1.76753e14 −0.177979
\(534\) 1.67559e15 1.66990
\(535\) −2.77282e14 −0.273512
\(536\) −1.04495e15 −1.02021
\(537\) −1.45706e14 −0.140805
\(538\) 2.83827e15 2.71488
\(539\) −3.39780e13 −0.0321706
\(540\) −4.29311e14 −0.402352
\(541\) 4.94069e14 0.458356 0.229178 0.973385i \(-0.426396\pi\)
0.229178 + 0.973385i \(0.426396\pi\)
\(542\) −4.42404e14 −0.406278
\(543\) 5.85142e13 0.0531940
\(544\) 5.57634e14 0.501829
\(545\) −1.04059e15 −0.927039
\(546\) −4.09446e14 −0.361108
\(547\) 5.68865e12 0.00496682 0.00248341 0.999997i \(-0.499210\pi\)
0.00248341 + 0.999997i \(0.499210\pi\)
\(548\) 4.17413e14 0.360806
\(549\) 6.13214e14 0.524764
\(550\) −1.97464e14 −0.167299
\(551\) 1.77833e15 1.49169
\(552\) −2.06342e14 −0.171365
\(553\) 6.23964e14 0.513064
\(554\) 3.67924e15 2.99540
\(555\) 9.64419e14 0.777418
\(556\) −1.00194e15 −0.799706
\(557\) 2.04927e15 1.61956 0.809778 0.586737i \(-0.199588\pi\)
0.809778 + 0.586737i \(0.199588\pi\)
\(558\) −1.00419e15 −0.785830
\(559\) 6.56205e14 0.508481
\(560\) 3.69336e14 0.283392
\(561\) 3.67047e13 0.0278885
\(562\) −1.18463e15 −0.891321
\(563\) −1.25655e15 −0.936234 −0.468117 0.883667i \(-0.655067\pi\)
−0.468117 + 0.883667i \(0.655067\pi\)
\(564\) −1.93444e15 −1.42732
\(565\) −2.60164e15 −1.90099
\(566\) −6.54764e14 −0.473800
\(567\) 1.31260e14 0.0940643
\(568\) 1.02243e15 0.725633
\(569\) −2.63511e15 −1.85217 −0.926085 0.377316i \(-0.876847\pi\)
−0.926085 + 0.377316i \(0.876847\pi\)
\(570\) −2.43434e15 −1.69461
\(571\) 1.17266e15 0.808485 0.404242 0.914652i \(-0.367535\pi\)
0.404242 + 0.914652i \(0.367535\pi\)
\(572\) 1.16803e14 0.0797585
\(573\) −4.00114e14 −0.270604
\(574\) 7.62515e14 0.510779
\(575\) 5.21578e14 0.346056
\(576\) −8.24793e14 −0.542028
\(577\) −1.41481e15 −0.920938 −0.460469 0.887676i \(-0.652319\pi\)
−0.460469 + 0.887676i \(0.652319\pi\)
\(578\) 2.01038e15 1.29621
\(579\) 3.75593e14 0.239875
\(580\) 3.69352e15 2.33661
\(581\) 6.84702e14 0.429075
\(582\) −1.17700e15 −0.730635
\(583\) −1.05598e14 −0.0649349
\(584\) −1.26810e15 −0.772475
\(585\) −3.58333e14 −0.216237
\(586\) 1.04797e15 0.626487
\(587\) −7.67307e14 −0.454422 −0.227211 0.973846i \(-0.572961\pi\)
−0.227211 + 0.973846i \(0.572961\pi\)
\(588\) −4.19441e14 −0.246091
\(589\) −3.42059e15 −1.98823
\(590\) −4.97174e14 −0.286301
\(591\) 3.36378e14 0.191910
\(592\) 4.12986e14 0.233435
\(593\) 7.93935e14 0.444615 0.222307 0.974977i \(-0.428641\pi\)
0.222307 + 0.974977i \(0.428641\pi\)
\(594\) −6.23325e13 −0.0345851
\(595\) −9.10279e14 −0.500416
\(596\) −2.65226e15 −1.44465
\(597\) −2.61501e14 −0.141128
\(598\) −5.13583e14 −0.274634
\(599\) −7.13533e14 −0.378065 −0.189033 0.981971i \(-0.560535\pi\)
−0.189033 + 0.981971i \(0.560535\pi\)
\(600\) −8.17436e14 −0.429162
\(601\) 1.02257e15 0.531967 0.265984 0.963978i \(-0.414303\pi\)
0.265984 + 0.963978i \(0.414303\pi\)
\(602\) −2.83088e15 −1.45929
\(603\) 8.33783e14 0.425900
\(604\) −9.11608e14 −0.461429
\(605\) 2.73466e15 1.37167
\(606\) −1.69239e15 −0.841201
\(607\) −2.89132e14 −0.142416 −0.0712078 0.997462i \(-0.522685\pi\)
−0.0712078 + 0.997462i \(0.522685\pi\)
\(608\) −3.22572e15 −1.57455
\(609\) −1.12928e15 −0.546267
\(610\) 7.22185e15 3.46206
\(611\) −1.61462e15 −0.767087
\(612\) 4.53100e14 0.213335
\(613\) 1.49684e15 0.698463 0.349232 0.937036i \(-0.386443\pi\)
0.349232 + 0.937036i \(0.386443\pi\)
\(614\) −6.99782e14 −0.323621
\(615\) 6.67327e14 0.305862
\(616\) −1.68977e14 −0.0767598
\(617\) −3.99373e15 −1.79808 −0.899042 0.437863i \(-0.855736\pi\)
−0.899042 + 0.437863i \(0.855736\pi\)
\(618\) −2.93008e15 −1.30750
\(619\) −2.08009e15 −0.919989 −0.459995 0.887922i \(-0.652149\pi\)
−0.459995 + 0.887922i \(0.652149\pi\)
\(620\) −7.10442e15 −3.11440
\(621\) 1.64644e14 0.0715388
\(622\) 2.42806e15 1.04571
\(623\) −3.62443e15 −1.54723
\(624\) −1.53446e14 −0.0649294
\(625\) −2.53746e15 −1.06429
\(626\) 4.93863e15 2.05328
\(627\) −2.12324e14 −0.0875039
\(628\) 2.65008e15 1.08263
\(629\) −1.01786e15 −0.412202
\(630\) 1.54585e15 0.620576
\(631\) −3.76713e15 −1.49916 −0.749581 0.661912i \(-0.769745\pi\)
−0.749581 + 0.661912i \(0.769745\pi\)
\(632\) −1.22661e15 −0.483909
\(633\) −2.18785e15 −0.855653
\(634\) 4.62754e15 1.79415
\(635\) 4.79083e15 1.84143
\(636\) −1.30355e15 −0.496723
\(637\) −3.50095e14 −0.132257
\(638\) 5.36269e14 0.200849
\(639\) −8.15814e14 −0.302926
\(640\) −5.26064e15 −1.93664
\(641\) 3.19313e15 1.16546 0.582731 0.812665i \(-0.301984\pi\)
0.582731 + 0.812665i \(0.301984\pi\)
\(642\) −4.96979e14 −0.179844
\(643\) −1.62229e15 −0.582061 −0.291030 0.956714i \(-0.593998\pi\)
−0.291030 + 0.956714i \(0.593998\pi\)
\(644\) 1.33097e15 0.473473
\(645\) −2.47749e15 −0.873842
\(646\) 2.56923e15 0.898513
\(647\) 1.56046e15 0.541102 0.270551 0.962706i \(-0.412794\pi\)
0.270551 + 0.962706i \(0.412794\pi\)
\(648\) −2.58036e14 −0.0887191
\(649\) −4.33637e13 −0.0147836
\(650\) −2.03459e15 −0.687786
\(651\) 2.17214e15 0.728103
\(652\) −1.39390e15 −0.463307
\(653\) −3.73978e15 −1.23260 −0.616301 0.787511i \(-0.711370\pi\)
−0.616301 + 0.787511i \(0.711370\pi\)
\(654\) −1.86507e15 −0.609560
\(655\) 3.81434e15 1.23621
\(656\) 2.85765e14 0.0918412
\(657\) 1.01184e15 0.322481
\(658\) 6.96550e15 2.20145
\(659\) −8.52327e14 −0.267139 −0.133569 0.991039i \(-0.542644\pi\)
−0.133569 + 0.991039i \(0.542644\pi\)
\(660\) −4.40988e14 −0.137068
\(661\) 6.46071e14 0.199146 0.0995732 0.995030i \(-0.468252\pi\)
0.0995732 + 0.995030i \(0.468252\pi\)
\(662\) 7.16167e15 2.18925
\(663\) 3.78189e14 0.114653
\(664\) −1.34601e15 −0.404692
\(665\) 5.26566e15 1.57012
\(666\) 1.72855e15 0.511179
\(667\) −1.41649e15 −0.415453
\(668\) −1.10088e15 −0.320236
\(669\) 6.23084e14 0.179764
\(670\) 9.81949e15 2.80981
\(671\) 6.29892e14 0.178769
\(672\) 2.04840e15 0.576611
\(673\) −5.08949e15 −1.42099 −0.710495 0.703702i \(-0.751529\pi\)
−0.710495 + 0.703702i \(0.751529\pi\)
\(674\) 8.86687e15 2.45551
\(675\) 6.52246e14 0.179160
\(676\) −4.31869e15 −1.17664
\(677\) −3.90992e14 −0.105665 −0.0528324 0.998603i \(-0.516825\pi\)
−0.0528324 + 0.998603i \(0.516825\pi\)
\(678\) −4.66296e15 −1.24997
\(679\) 2.54594e15 0.676962
\(680\) 1.78946e15 0.471980
\(681\) 1.14746e15 0.300212
\(682\) −1.03150e15 −0.267705
\(683\) −1.81796e15 −0.468026 −0.234013 0.972233i \(-0.575186\pi\)
−0.234013 + 0.972233i \(0.575186\pi\)
\(684\) −2.62103e15 −0.669366
\(685\) −1.31538e15 −0.333238
\(686\) 6.84138e15 1.71934
\(687\) −4.23910e15 −1.05685
\(688\) −1.06092e15 −0.262388
\(689\) −1.08803e15 −0.266954
\(690\) 1.93902e15 0.471967
\(691\) 4.28858e15 1.03558 0.517791 0.855507i \(-0.326754\pi\)
0.517791 + 0.855507i \(0.326754\pi\)
\(692\) 3.58916e15 0.859823
\(693\) 1.34830e14 0.0320445
\(694\) −6.47795e15 −1.52743
\(695\) 3.15739e15 0.738604
\(696\) 2.21997e15 0.515225
\(697\) −7.04306e14 −0.162174
\(698\) 3.56705e14 0.0814899
\(699\) 1.60228e14 0.0363174
\(700\) 5.27270e15 1.18575
\(701\) 4.36940e15 0.974929 0.487464 0.873143i \(-0.337922\pi\)
0.487464 + 0.873143i \(0.337922\pi\)
\(702\) −6.42248e14 −0.142183
\(703\) 5.88798e15 1.29334
\(704\) −8.47226e14 −0.184650
\(705\) 6.09596e15 1.31826
\(706\) 7.15829e15 1.53597
\(707\) 3.66076e15 0.779407
\(708\) −5.35303e14 −0.113088
\(709\) −5.54169e14 −0.116168 −0.0580842 0.998312i \(-0.518499\pi\)
−0.0580842 + 0.998312i \(0.518499\pi\)
\(710\) −9.60787e15 −1.99851
\(711\) 9.78736e14 0.202015
\(712\) 7.12505e15 1.45931
\(713\) 2.72460e15 0.553745
\(714\) −1.63151e15 −0.329041
\(715\) −3.68079e14 −0.0736644
\(716\) −1.84759e15 −0.366930
\(717\) −2.20209e15 −0.433990
\(718\) −5.55907e15 −1.08722
\(719\) −1.11509e15 −0.216422 −0.108211 0.994128i \(-0.534512\pi\)
−0.108211 + 0.994128i \(0.534512\pi\)
\(720\) 5.79333e14 0.111583
\(721\) 6.33798e15 1.21145
\(722\) −6.51920e15 −1.23663
\(723\) −5.44453e15 −1.02494
\(724\) 7.41974e14 0.138620
\(725\) −5.61151e15 −1.04045
\(726\) 4.90138e15 0.901917
\(727\) 8.02340e15 1.46528 0.732638 0.680619i \(-0.238289\pi\)
0.732638 + 0.680619i \(0.238289\pi\)
\(728\) −1.74107e15 −0.315568
\(729\) 2.05891e14 0.0370370
\(730\) 1.19165e16 2.12752
\(731\) 2.61477e15 0.463327
\(732\) 7.77570e15 1.36750
\(733\) −9.57279e14 −0.167096 −0.0835481 0.996504i \(-0.526625\pi\)
−0.0835481 + 0.996504i \(0.526625\pi\)
\(734\) −9.04204e15 −1.56653
\(735\) 1.32177e15 0.227288
\(736\) 2.56938e15 0.438531
\(737\) 8.56460e14 0.145089
\(738\) 1.19606e15 0.201115
\(739\) −9.01924e14 −0.150531 −0.0752654 0.997164i \(-0.523980\pi\)
−0.0752654 + 0.997164i \(0.523980\pi\)
\(740\) 1.22291e16 2.02590
\(741\) −2.18770e15 −0.359738
\(742\) 4.69379e15 0.766130
\(743\) 2.27033e15 0.367833 0.183916 0.982942i \(-0.441122\pi\)
0.183916 + 0.982942i \(0.441122\pi\)
\(744\) −4.27008e15 −0.686728
\(745\) 8.35800e15 1.33427
\(746\) −1.78867e16 −2.83444
\(747\) 1.07401e15 0.168945
\(748\) 4.65424e14 0.0726758
\(749\) 1.07500e15 0.166632
\(750\) −5.69818e14 −0.0876798
\(751\) −3.58007e15 −0.546855 −0.273427 0.961893i \(-0.588157\pi\)
−0.273427 + 0.961893i \(0.588157\pi\)
\(752\) 2.61043e15 0.395835
\(753\) 2.76095e15 0.415610
\(754\) 5.52549e15 0.825712
\(755\) 2.87273e15 0.426173
\(756\) 1.66441e15 0.245126
\(757\) −9.09591e15 −1.32990 −0.664950 0.746888i \(-0.731547\pi\)
−0.664950 + 0.746888i \(0.731547\pi\)
\(758\) −4.21921e15 −0.612422
\(759\) 1.69122e14 0.0243708
\(760\) −1.03514e16 −1.48090
\(761\) −6.24456e15 −0.886924 −0.443462 0.896293i \(-0.646250\pi\)
−0.443462 + 0.896293i \(0.646250\pi\)
\(762\) 8.58670e15 1.21080
\(763\) 4.03428e15 0.564782
\(764\) −5.07355e15 −0.705177
\(765\) −1.42784e15 −0.197035
\(766\) 9.34344e15 1.28011
\(767\) −4.46802e14 −0.0607771
\(768\) −2.47741e15 −0.334589
\(769\) 9.24521e15 1.23972 0.619858 0.784714i \(-0.287190\pi\)
0.619858 + 0.784714i \(0.287190\pi\)
\(770\) 1.58790e15 0.211409
\(771\) 3.91365e14 0.0517349
\(772\) 4.76261e15 0.625100
\(773\) −1.06718e15 −0.139075 −0.0695376 0.997579i \(-0.522152\pi\)
−0.0695376 + 0.997579i \(0.522152\pi\)
\(774\) −4.44045e15 −0.574581
\(775\) 1.07936e16 1.38678
\(776\) −5.00491e15 −0.638493
\(777\) −3.73898e15 −0.473628
\(778\) −7.53422e15 −0.947656
\(779\) 4.07417e15 0.508842
\(780\) −4.54375e15 −0.563500
\(781\) −8.38002e14 −0.103196
\(782\) −2.04646e15 −0.250246
\(783\) −1.77136e15 −0.215088
\(784\) 5.66013e14 0.0682478
\(785\) −8.35111e15 −0.999911
\(786\) 6.83651e15 0.812850
\(787\) 1.31820e16 1.55640 0.778201 0.628016i \(-0.216133\pi\)
0.778201 + 0.628016i \(0.216133\pi\)
\(788\) 4.26536e15 0.500105
\(789\) −2.77808e15 −0.323461
\(790\) 1.15266e16 1.33276
\(791\) 1.00863e16 1.15815
\(792\) −2.65054e14 −0.0302235
\(793\) 6.49014e15 0.734940
\(794\) 1.66391e16 1.87119
\(795\) 4.10785e15 0.458770
\(796\) −3.31589e15 −0.367772
\(797\) 8.00193e14 0.0881401 0.0440701 0.999028i \(-0.485968\pi\)
0.0440701 + 0.999028i \(0.485968\pi\)
\(798\) 9.43774e15 1.03241
\(799\) −6.43376e15 −0.698968
\(800\) 1.01787e16 1.09824
\(801\) −5.68520e15 −0.609210
\(802\) 2.14918e16 2.28725
\(803\) 1.03936e15 0.109858
\(804\) 1.05726e16 1.10987
\(805\) −4.19424e15 −0.437296
\(806\) −1.06282e16 −1.10057
\(807\) −9.63009e15 −0.990435
\(808\) −7.19646e15 −0.735116
\(809\) −6.00294e15 −0.609042 −0.304521 0.952506i \(-0.598496\pi\)
−0.304521 + 0.952506i \(0.598496\pi\)
\(810\) 2.42479e15 0.244347
\(811\) −2.41855e15 −0.242070 −0.121035 0.992648i \(-0.538621\pi\)
−0.121035 + 0.992648i \(0.538621\pi\)
\(812\) −1.43195e16 −1.42354
\(813\) 1.50105e15 0.148217
\(814\) 1.77556e15 0.174141
\(815\) 4.39255e15 0.427907
\(816\) −6.11435e14 −0.0591636
\(817\) −1.51256e16 −1.45375
\(818\) −2.64817e16 −2.52815
\(819\) 1.38923e15 0.131738
\(820\) 8.46187e15 0.797058
\(821\) −1.95856e16 −1.83252 −0.916260 0.400584i \(-0.868807\pi\)
−0.916260 + 0.400584i \(0.868807\pi\)
\(822\) −2.35759e15 −0.219115
\(823\) −8.60498e15 −0.794421 −0.397211 0.917727i \(-0.630022\pi\)
−0.397211 + 0.917727i \(0.630022\pi\)
\(824\) −1.24595e16 −1.14261
\(825\) 6.69986e14 0.0610336
\(826\) 1.92751e15 0.174424
\(827\) −9.60942e15 −0.863807 −0.431904 0.901920i \(-0.642158\pi\)
−0.431904 + 0.901920i \(0.642158\pi\)
\(828\) 2.08772e15 0.186426
\(829\) −1.43126e16 −1.26960 −0.634800 0.772676i \(-0.718918\pi\)
−0.634800 + 0.772676i \(0.718918\pi\)
\(830\) 1.26486e16 1.11459
\(831\) −1.24835e16 −1.09277
\(832\) −8.72946e15 −0.759118
\(833\) −1.39502e15 −0.120512
\(834\) 5.65905e15 0.485658
\(835\) 3.46918e15 0.295768
\(836\) −2.69232e15 −0.228030
\(837\) 3.40717e15 0.286684
\(838\) −8.07222e15 −0.674763
\(839\) −4.75190e15 −0.394618 −0.197309 0.980341i \(-0.563220\pi\)
−0.197309 + 0.980341i \(0.563220\pi\)
\(840\) 6.57336e15 0.542314
\(841\) 3.03912e15 0.249098
\(842\) −3.20197e16 −2.60736
\(843\) 4.01940e15 0.325169
\(844\) −2.77425e16 −2.22978
\(845\) 1.36094e16 1.08674
\(846\) 1.09259e16 0.866804
\(847\) −1.06020e16 −0.835663
\(848\) 1.75907e15 0.137755
\(849\) 2.22158e15 0.172850
\(850\) −8.10718e15 −0.626709
\(851\) −4.68993e15 −0.360209
\(852\) −1.03447e16 −0.789406
\(853\) 3.78608e15 0.287058 0.143529 0.989646i \(-0.454155\pi\)
0.143529 + 0.989646i \(0.454155\pi\)
\(854\) −2.79985e16 −2.10920
\(855\) 8.25959e15 0.618222
\(856\) −2.11328e15 −0.157163
\(857\) 4.05160e15 0.299386 0.149693 0.988733i \(-0.452171\pi\)
0.149693 + 0.988733i \(0.452171\pi\)
\(858\) −6.59715e14 −0.0484369
\(859\) −1.59860e16 −1.16621 −0.583107 0.812395i \(-0.698163\pi\)
−0.583107 + 0.812395i \(0.698163\pi\)
\(860\) −3.14151e16 −2.27718
\(861\) −2.58718e15 −0.186341
\(862\) −1.55100e16 −1.11000
\(863\) 1.06600e16 0.758052 0.379026 0.925386i \(-0.376259\pi\)
0.379026 + 0.925386i \(0.376259\pi\)
\(864\) 3.21307e15 0.227036
\(865\) −1.13104e16 −0.794127
\(866\) 3.09660e16 2.16041
\(867\) −6.82111e15 −0.472879
\(868\) 2.75433e16 1.89739
\(869\) 1.00536e15 0.0688194
\(870\) −2.08613e16 −1.41901
\(871\) 8.82460e15 0.596479
\(872\) −7.93074e15 −0.532688
\(873\) 3.99350e15 0.266548
\(874\) 1.18381e16 0.785179
\(875\) 1.23256e15 0.0812388
\(876\) 1.28304e16 0.840365
\(877\) 5.94643e15 0.387043 0.193521 0.981096i \(-0.438009\pi\)
0.193521 + 0.981096i \(0.438009\pi\)
\(878\) 2.28101e16 1.47539
\(879\) −3.55571e15 −0.228553
\(880\) 5.95089e14 0.0380126
\(881\) 2.84161e16 1.80384 0.901918 0.431907i \(-0.142159\pi\)
0.901918 + 0.431907i \(0.142159\pi\)
\(882\) 2.36904e15 0.149450
\(883\) −8.18053e15 −0.512858 −0.256429 0.966563i \(-0.582546\pi\)
−0.256429 + 0.966563i \(0.582546\pi\)
\(884\) 4.79553e15 0.298778
\(885\) 1.68689e15 0.104447
\(886\) −3.18071e16 −1.95721
\(887\) −1.99589e16 −1.22055 −0.610277 0.792188i \(-0.708942\pi\)
−0.610277 + 0.792188i \(0.708942\pi\)
\(888\) 7.35023e15 0.446714
\(889\) −1.85737e16 −1.12186
\(890\) −6.69548e16 −4.01918
\(891\) 2.11491e14 0.0126172
\(892\) 7.90085e15 0.468454
\(893\) 3.72171e16 2.19311
\(894\) 1.49802e16 0.877327
\(895\) 5.82224e15 0.338894
\(896\) 2.03951e16 1.17986
\(897\) 1.74256e15 0.100191
\(898\) 1.30467e16 0.745558
\(899\) −2.93132e16 −1.66489
\(900\) 8.27064e15 0.466880
\(901\) −4.33547e15 −0.243248
\(902\) 1.22859e15 0.0685130
\(903\) 9.60502e15 0.532372
\(904\) −1.98281e16 −1.09233
\(905\) −2.33816e15 −0.128029
\(906\) 5.14885e15 0.280224
\(907\) −2.33057e16 −1.26073 −0.630366 0.776298i \(-0.717095\pi\)
−0.630366 + 0.776298i \(0.717095\pi\)
\(908\) 1.45500e16 0.782334
\(909\) 5.74218e15 0.306885
\(910\) 1.63610e16 0.869125
\(911\) −1.41043e16 −0.744731 −0.372366 0.928086i \(-0.621453\pi\)
−0.372366 + 0.928086i \(0.621453\pi\)
\(912\) 3.53694e15 0.185634
\(913\) 1.10322e15 0.0575536
\(914\) −1.12493e16 −0.583340
\(915\) −2.45034e16 −1.26302
\(916\) −5.37528e16 −2.75408
\(917\) −1.47879e16 −0.753138
\(918\) −2.55915e15 −0.129557
\(919\) −2.24983e16 −1.13218 −0.566088 0.824345i \(-0.691544\pi\)
−0.566088 + 0.824345i \(0.691544\pi\)
\(920\) 8.24519e15 0.412447
\(921\) 2.37432e15 0.118062
\(922\) 4.46833e16 2.20864
\(923\) −8.63442e15 −0.424252
\(924\) 1.70967e15 0.0835060
\(925\) −1.85794e16 −0.902097
\(926\) 2.35845e16 1.13833
\(927\) 9.94162e15 0.477000
\(928\) −2.76432e16 −1.31848
\(929\) −1.50141e16 −0.711888 −0.355944 0.934507i \(-0.615841\pi\)
−0.355944 + 0.934507i \(0.615841\pi\)
\(930\) 4.01264e16 1.89136
\(931\) 8.06969e15 0.378124
\(932\) 2.03173e15 0.0946410
\(933\) −8.23828e15 −0.381494
\(934\) −5.44536e16 −2.50679
\(935\) −1.46668e15 −0.0671229
\(936\) −2.73100e15 −0.124252
\(937\) −3.18844e15 −0.144215 −0.0721075 0.997397i \(-0.522972\pi\)
−0.0721075 + 0.997397i \(0.522972\pi\)
\(938\) −3.80694e16 −1.71183
\(939\) −1.67565e16 −0.749071
\(940\) 7.72983e16 3.43532
\(941\) 5.16849e15 0.228360 0.114180 0.993460i \(-0.463576\pi\)
0.114180 + 0.993460i \(0.463576\pi\)
\(942\) −1.49679e16 −0.657476
\(943\) −3.24519e15 −0.141718
\(944\) 7.22363e14 0.0313624
\(945\) −5.24500e15 −0.226397
\(946\) −4.56122e15 −0.195740
\(947\) 3.76798e16 1.60762 0.803811 0.594885i \(-0.202802\pi\)
0.803811 + 0.594885i \(0.202802\pi\)
\(948\) 1.24106e16 0.526438
\(949\) 1.07092e16 0.451639
\(950\) 4.68973e16 1.96638
\(951\) −1.57010e16 −0.654538
\(952\) −6.93760e15 −0.287545
\(953\) 2.04664e15 0.0843396 0.0421698 0.999110i \(-0.486573\pi\)
0.0421698 + 0.999110i \(0.486573\pi\)
\(954\) 7.36257e15 0.301657
\(955\) 1.59881e16 0.651297
\(956\) −2.79230e16 −1.13095
\(957\) −1.81953e15 −0.0732731
\(958\) 3.77335e15 0.151083
\(959\) 5.09964e15 0.203019
\(960\) 3.29578e16 1.30457
\(961\) 3.09748e16 1.21908
\(962\) 1.82946e16 0.715914
\(963\) 1.68622e15 0.0656101
\(964\) −6.90379e16 −2.67094
\(965\) −1.50083e16 −0.577339
\(966\) −7.51742e15 −0.287538
\(967\) −2.18214e16 −0.829923 −0.414961 0.909839i \(-0.636205\pi\)
−0.414961 + 0.909839i \(0.636205\pi\)
\(968\) 2.08419e16 0.788176
\(969\) −8.71727e15 −0.327793
\(970\) 4.70316e16 1.75851
\(971\) −7.42026e15 −0.275876 −0.137938 0.990441i \(-0.544047\pi\)
−0.137938 + 0.990441i \(0.544047\pi\)
\(972\) 2.61075e15 0.0965163
\(973\) −1.22409e16 −0.449981
\(974\) 2.57108e16 0.939813
\(975\) 6.90325e15 0.250916
\(976\) −1.04929e16 −0.379246
\(977\) −3.89311e16 −1.39919 −0.699595 0.714540i \(-0.746636\pi\)
−0.699595 + 0.714540i \(0.746636\pi\)
\(978\) 7.87285e15 0.281364
\(979\) −5.83983e15 −0.207537
\(980\) 1.67604e16 0.592299
\(981\) 6.32807e15 0.222378
\(982\) −5.86143e16 −2.04829
\(983\) 2.02760e16 0.704591 0.352295 0.935889i \(-0.385401\pi\)
0.352295 + 0.935889i \(0.385401\pi\)
\(984\) 5.08597e15 0.175752
\(985\) −1.34413e16 −0.461894
\(986\) 2.20173e16 0.752387
\(987\) −2.36336e16 −0.803129
\(988\) −2.77405e16 −0.937457
\(989\) 1.20479e16 0.404886
\(990\) 2.49074e15 0.0832404
\(991\) −1.25418e16 −0.416827 −0.208414 0.978041i \(-0.566830\pi\)
−0.208414 + 0.978041i \(0.566830\pi\)
\(992\) 5.31712e16 1.75737
\(993\) −2.42992e16 −0.798676
\(994\) 3.72490e16 1.21756
\(995\) 1.04493e16 0.339672
\(996\) 1.36187e16 0.440259
\(997\) 8.28428e15 0.266337 0.133169 0.991093i \(-0.457485\pi\)
0.133169 + 0.991093i \(0.457485\pi\)
\(998\) −9.83877e14 −0.0314574
\(999\) −5.86487e15 −0.186487
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.1.4 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.b.1.4 27 1.1 even 1 trivial