Properties

Label 177.14.a.c.1.19
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+66.7973 q^{2} +729.000 q^{3} -3730.11 q^{4} +36075.7 q^{5} +48695.3 q^{6} -269744. q^{7} -796366. q^{8} +531441. q^{9} +O(q^{10})\) \(q+66.7973 q^{2} +729.000 q^{3} -3730.11 q^{4} +36075.7 q^{5} +48695.3 q^{6} -269744. q^{7} -796366. q^{8} +531441. q^{9} +2.40976e6 q^{10} +1.04015e7 q^{11} -2.71925e6 q^{12} -7.55745e6 q^{13} -1.80182e7 q^{14} +2.62992e7 q^{15} -2.26380e7 q^{16} -1.33275e8 q^{17} +3.54989e7 q^{18} +2.81117e8 q^{19} -1.34567e8 q^{20} -1.96643e8 q^{21} +6.94792e8 q^{22} +2.81992e8 q^{23} -5.80551e8 q^{24} +8.07543e7 q^{25} -5.04818e8 q^{26} +3.87420e8 q^{27} +1.00618e9 q^{28} +3.19316e9 q^{29} +1.75672e9 q^{30} -5.46963e9 q^{31} +5.01167e9 q^{32} +7.58269e9 q^{33} -8.90243e9 q^{34} -9.73121e9 q^{35} -1.98234e9 q^{36} -7.12239e9 q^{37} +1.87779e10 q^{38} -5.50938e9 q^{39} -2.87295e10 q^{40} +2.84811e10 q^{41} -1.31353e10 q^{42} -4.95408e10 q^{43} -3.87988e10 q^{44} +1.91721e10 q^{45} +1.88363e10 q^{46} -1.09577e10 q^{47} -1.65031e10 q^{48} -2.41272e10 q^{49} +5.39418e9 q^{50} -9.71577e10 q^{51} +2.81902e10 q^{52} +2.87608e11 q^{53} +2.58787e10 q^{54} +3.75241e11 q^{55} +2.14815e11 q^{56} +2.04934e11 q^{57} +2.13295e11 q^{58} -4.21805e10 q^{59} -9.80990e10 q^{60} +1.11011e11 q^{61} -3.65357e11 q^{62} -1.43353e11 q^{63} +5.20217e11 q^{64} -2.72641e11 q^{65} +5.06504e11 q^{66} +9.50274e11 q^{67} +4.97132e11 q^{68} +2.05572e11 q^{69} -6.50019e11 q^{70} +2.78596e11 q^{71} -4.23221e11 q^{72} +5.64617e11 q^{73} -4.75757e11 q^{74} +5.88699e10 q^{75} -1.04860e12 q^{76} -2.80574e12 q^{77} -3.68012e11 q^{78} +1.36889e12 q^{79} -8.16683e11 q^{80} +2.82430e11 q^{81} +1.90246e12 q^{82} +2.62840e12 q^{83} +7.33502e11 q^{84} -4.80800e12 q^{85} -3.30920e12 q^{86} +2.32781e12 q^{87} -8.28339e12 q^{88} -7.86312e12 q^{89} +1.28065e12 q^{90} +2.03858e12 q^{91} -1.05186e12 q^{92} -3.98736e12 q^{93} -7.31947e11 q^{94} +1.01415e13 q^{95} +3.65351e12 q^{96} +8.83232e12 q^{97} -1.61163e12 q^{98} +5.52778e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 66.7973 0.738013 0.369007 0.929427i \(-0.379698\pi\)
0.369007 + 0.929427i \(0.379698\pi\)
\(3\) 729.000 0.577350
\(4\) −3730.11 −0.455336
\(5\) 36075.7 1.03255 0.516274 0.856424i \(-0.327319\pi\)
0.516274 + 0.856424i \(0.327319\pi\)
\(6\) 48695.3 0.426092
\(7\) −269744. −0.866592 −0.433296 0.901252i \(-0.642649\pi\)
−0.433296 + 0.901252i \(0.642649\pi\)
\(8\) −796366. −1.07406
\(9\) 531441. 0.333333
\(10\) 2.40976e6 0.762034
\(11\) 1.04015e7 1.77029 0.885143 0.465320i \(-0.154061\pi\)
0.885143 + 0.465320i \(0.154061\pi\)
\(12\) −2.71925e6 −0.262888
\(13\) −7.55745e6 −0.434254 −0.217127 0.976143i \(-0.569669\pi\)
−0.217127 + 0.976143i \(0.569669\pi\)
\(14\) −1.80182e7 −0.639556
\(15\) 2.62992e7 0.596141
\(16\) −2.26380e7 −0.337333
\(17\) −1.33275e8 −1.33916 −0.669579 0.742741i \(-0.733525\pi\)
−0.669579 + 0.742741i \(0.733525\pi\)
\(18\) 3.54989e7 0.246004
\(19\) 2.81117e8 1.37085 0.685423 0.728145i \(-0.259617\pi\)
0.685423 + 0.728145i \(0.259617\pi\)
\(20\) −1.34567e8 −0.470156
\(21\) −1.96643e8 −0.500327
\(22\) 6.94792e8 1.30649
\(23\) 2.81992e8 0.397197 0.198599 0.980081i \(-0.436361\pi\)
0.198599 + 0.980081i \(0.436361\pi\)
\(24\) −5.80551e8 −0.620107
\(25\) 8.07543e7 0.0661540
\(26\) −5.04818e8 −0.320485
\(27\) 3.87420e8 0.192450
\(28\) 1.00618e9 0.394590
\(29\) 3.19316e9 0.996858 0.498429 0.866930i \(-0.333910\pi\)
0.498429 + 0.866930i \(0.333910\pi\)
\(30\) 1.75672e9 0.439960
\(31\) −5.46963e9 −1.10690 −0.553449 0.832883i \(-0.686688\pi\)
−0.553449 + 0.832883i \(0.686688\pi\)
\(32\) 5.01167e9 0.825102
\(33\) 7.58269e9 1.02207
\(34\) −8.90243e9 −0.988316
\(35\) −9.73121e9 −0.894797
\(36\) −1.98234e9 −0.151779
\(37\) −7.12239e9 −0.456367 −0.228184 0.973618i \(-0.573279\pi\)
−0.228184 + 0.973618i \(0.573279\pi\)
\(38\) 1.87779e10 1.01170
\(39\) −5.50938e9 −0.250717
\(40\) −2.87295e10 −1.10902
\(41\) 2.84811e10 0.936400 0.468200 0.883622i \(-0.344903\pi\)
0.468200 + 0.883622i \(0.344903\pi\)
\(42\) −1.31353e10 −0.369248
\(43\) −4.95408e10 −1.19514 −0.597569 0.801817i \(-0.703867\pi\)
−0.597569 + 0.801817i \(0.703867\pi\)
\(44\) −3.87988e10 −0.806075
\(45\) 1.91721e10 0.344182
\(46\) 1.88363e10 0.293137
\(47\) −1.09577e10 −0.148281 −0.0741403 0.997248i \(-0.523621\pi\)
−0.0741403 + 0.997248i \(0.523621\pi\)
\(48\) −1.65031e10 −0.194759
\(49\) −2.41272e10 −0.249019
\(50\) 5.39418e9 0.0488225
\(51\) −9.71577e10 −0.773163
\(52\) 2.81902e10 0.197731
\(53\) 2.87608e11 1.78241 0.891205 0.453601i \(-0.149861\pi\)
0.891205 + 0.453601i \(0.149861\pi\)
\(54\) 2.58787e10 0.142031
\(55\) 3.75241e11 1.82790
\(56\) 2.14815e11 0.930769
\(57\) 2.04934e11 0.791458
\(58\) 2.13295e11 0.735695
\(59\) −4.21805e10 −0.130189
\(60\) −9.80990e10 −0.271445
\(61\) 1.11011e11 0.275882 0.137941 0.990440i \(-0.455952\pi\)
0.137941 + 0.990440i \(0.455952\pi\)
\(62\) −3.65357e11 −0.816905
\(63\) −1.43353e11 −0.288864
\(64\) 5.20217e11 0.946269
\(65\) −2.72641e11 −0.448388
\(66\) 5.06504e11 0.754305
\(67\) 9.50274e11 1.28340 0.641701 0.766955i \(-0.278229\pi\)
0.641701 + 0.766955i \(0.278229\pi\)
\(68\) 4.97132e11 0.609767
\(69\) 2.05572e11 0.229322
\(70\) −6.50019e11 −0.660372
\(71\) 2.78596e11 0.258104 0.129052 0.991638i \(-0.458807\pi\)
0.129052 + 0.991638i \(0.458807\pi\)
\(72\) −4.23221e11 −0.358019
\(73\) 5.64617e11 0.436672 0.218336 0.975874i \(-0.429937\pi\)
0.218336 + 0.975874i \(0.429937\pi\)
\(74\) −4.75757e11 −0.336805
\(75\) 5.88699e10 0.0381940
\(76\) −1.04860e12 −0.624196
\(77\) −2.80574e12 −1.53411
\(78\) −3.68012e11 −0.185032
\(79\) 1.36889e12 0.633565 0.316783 0.948498i \(-0.397397\pi\)
0.316783 + 0.948498i \(0.397397\pi\)
\(80\) −8.16683e11 −0.348312
\(81\) 2.82430e11 0.111111
\(82\) 1.90246e12 0.691076
\(83\) 2.62840e12 0.882437 0.441218 0.897400i \(-0.354546\pi\)
0.441218 + 0.897400i \(0.354546\pi\)
\(84\) 7.33502e11 0.227817
\(85\) −4.80800e12 −1.38274
\(86\) −3.30920e12 −0.882028
\(87\) 2.32781e12 0.575536
\(88\) −8.28339e12 −1.90139
\(89\) −7.86312e12 −1.67710 −0.838552 0.544822i \(-0.816597\pi\)
−0.838552 + 0.544822i \(0.816597\pi\)
\(90\) 1.28065e12 0.254011
\(91\) 2.03858e12 0.376321
\(92\) −1.05186e12 −0.180858
\(93\) −3.98736e12 −0.639067
\(94\) −7.31947e11 −0.109433
\(95\) 1.01415e13 1.41546
\(96\) 3.65351e12 0.476373
\(97\) 8.83232e12 1.07661 0.538305 0.842750i \(-0.319065\pi\)
0.538305 + 0.842750i \(0.319065\pi\)
\(98\) −1.61163e12 −0.183779
\(99\) 5.52778e12 0.590095
\(100\) −3.01223e11 −0.0301223
\(101\) 1.31591e13 1.23349 0.616746 0.787163i \(-0.288451\pi\)
0.616746 + 0.787163i \(0.288451\pi\)
\(102\) −6.48987e12 −0.570604
\(103\) 7.79654e12 0.643368 0.321684 0.946847i \(-0.395751\pi\)
0.321684 + 0.946847i \(0.395751\pi\)
\(104\) 6.01850e12 0.466414
\(105\) −7.09405e12 −0.516611
\(106\) 1.92114e13 1.31544
\(107\) 9.30476e12 0.599391 0.299696 0.954035i \(-0.403115\pi\)
0.299696 + 0.954035i \(0.403115\pi\)
\(108\) −1.44512e12 −0.0876295
\(109\) −1.22871e13 −0.701740 −0.350870 0.936424i \(-0.614114\pi\)
−0.350870 + 0.936424i \(0.614114\pi\)
\(110\) 2.50651e13 1.34902
\(111\) −5.19222e12 −0.263484
\(112\) 6.10647e12 0.292330
\(113\) 2.41725e13 1.09222 0.546112 0.837712i \(-0.316107\pi\)
0.546112 + 0.837712i \(0.316107\pi\)
\(114\) 1.36891e13 0.584107
\(115\) 1.01731e13 0.410125
\(116\) −1.19108e13 −0.453906
\(117\) −4.01634e12 −0.144751
\(118\) −2.81755e12 −0.0960812
\(119\) 3.59502e13 1.16050
\(120\) −2.09438e13 −0.640290
\(121\) 7.36684e13 2.13391
\(122\) 7.41527e12 0.203605
\(123\) 2.07627e13 0.540631
\(124\) 2.04024e13 0.504010
\(125\) −4.11245e13 −0.964240
\(126\) −9.57560e12 −0.213185
\(127\) 5.48079e13 1.15909 0.579547 0.814939i \(-0.303230\pi\)
0.579547 + 0.814939i \(0.303230\pi\)
\(128\) −6.30648e12 −0.126742
\(129\) −3.61153e13 −0.690014
\(130\) −1.82117e13 −0.330916
\(131\) −7.41441e13 −1.28178 −0.640889 0.767633i \(-0.721434\pi\)
−0.640889 + 0.767633i \(0.721434\pi\)
\(132\) −2.82843e13 −0.465388
\(133\) −7.58296e13 −1.18796
\(134\) 6.34758e13 0.947168
\(135\) 1.39765e13 0.198714
\(136\) 1.06136e14 1.43833
\(137\) 4.34145e13 0.560985 0.280493 0.959856i \(-0.409502\pi\)
0.280493 + 0.959856i \(0.409502\pi\)
\(138\) 1.37317e13 0.169243
\(139\) −6.68955e13 −0.786684 −0.393342 0.919392i \(-0.628681\pi\)
−0.393342 + 0.919392i \(0.628681\pi\)
\(140\) 3.62985e13 0.407433
\(141\) −7.98818e12 −0.0856098
\(142\) 1.86095e13 0.190484
\(143\) −7.86088e13 −0.768753
\(144\) −1.20308e13 −0.112444
\(145\) 1.15195e14 1.02930
\(146\) 3.77149e13 0.322270
\(147\) −1.75887e13 −0.143771
\(148\) 2.65673e13 0.207801
\(149\) 6.45815e13 0.483501 0.241751 0.970338i \(-0.422278\pi\)
0.241751 + 0.970338i \(0.422278\pi\)
\(150\) 3.93235e12 0.0281877
\(151\) 1.68635e14 1.15770 0.578852 0.815433i \(-0.303501\pi\)
0.578852 + 0.815433i \(0.303501\pi\)
\(152\) −2.23872e14 −1.47237
\(153\) −7.08279e13 −0.446386
\(154\) −1.87416e14 −1.13220
\(155\) −1.97321e14 −1.14292
\(156\) 2.05506e13 0.114160
\(157\) 2.08951e14 1.11352 0.556758 0.830674i \(-0.312045\pi\)
0.556758 + 0.830674i \(0.312045\pi\)
\(158\) 9.14380e13 0.467580
\(159\) 2.09666e14 1.02907
\(160\) 1.80800e14 0.851956
\(161\) −7.60657e13 −0.344208
\(162\) 1.88655e13 0.0820015
\(163\) 9.07004e13 0.378782 0.189391 0.981902i \(-0.439349\pi\)
0.189391 + 0.981902i \(0.439349\pi\)
\(164\) −1.06238e14 −0.426377
\(165\) 2.73551e14 1.05534
\(166\) 1.75570e14 0.651250
\(167\) −4.26672e14 −1.52208 −0.761040 0.648705i \(-0.775311\pi\)
−0.761040 + 0.648705i \(0.775311\pi\)
\(168\) 1.56600e14 0.537380
\(169\) −2.45760e14 −0.811424
\(170\) −3.21162e14 −1.02048
\(171\) 1.49397e14 0.456949
\(172\) 1.84793e14 0.544190
\(173\) −3.01561e14 −0.855214 −0.427607 0.903965i \(-0.640643\pi\)
−0.427607 + 0.903965i \(0.640643\pi\)
\(174\) 1.55492e14 0.424754
\(175\) −2.17830e13 −0.0573285
\(176\) −2.35469e14 −0.597175
\(177\) −3.07496e13 −0.0751646
\(178\) −5.25236e14 −1.23773
\(179\) 2.66888e14 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(180\) −7.15142e13 −0.156719
\(181\) 3.88509e14 0.821279 0.410640 0.911798i \(-0.365305\pi\)
0.410640 + 0.911798i \(0.365305\pi\)
\(182\) 1.36172e14 0.277730
\(183\) 8.09274e13 0.159281
\(184\) −2.24569e14 −0.426613
\(185\) −2.56945e14 −0.471221
\(186\) −2.66345e14 −0.471640
\(187\) −1.38626e15 −2.37069
\(188\) 4.08736e13 0.0675175
\(189\) −1.04504e14 −0.166776
\(190\) 6.77425e14 1.04463
\(191\) 3.48286e14 0.519062 0.259531 0.965735i \(-0.416432\pi\)
0.259531 + 0.965735i \(0.416432\pi\)
\(192\) 3.79238e14 0.546329
\(193\) 1.27197e15 1.77155 0.885777 0.464111i \(-0.153626\pi\)
0.885777 + 0.464111i \(0.153626\pi\)
\(194\) 5.89976e14 0.794553
\(195\) −1.98755e14 −0.258877
\(196\) 8.99973e13 0.113387
\(197\) 7.47060e14 0.910595 0.455297 0.890339i \(-0.349533\pi\)
0.455297 + 0.890339i \(0.349533\pi\)
\(198\) 3.69241e14 0.435498
\(199\) 6.97898e14 0.796612 0.398306 0.917253i \(-0.369598\pi\)
0.398306 + 0.917253i \(0.369598\pi\)
\(200\) −6.43100e13 −0.0710532
\(201\) 6.92750e14 0.740972
\(202\) 8.78991e14 0.910333
\(203\) −8.61335e14 −0.863869
\(204\) 3.62409e14 0.352049
\(205\) 1.02748e15 0.966877
\(206\) 5.20788e14 0.474815
\(207\) 1.49862e14 0.132399
\(208\) 1.71086e14 0.146488
\(209\) 2.92404e15 2.42679
\(210\) −4.73864e14 −0.381266
\(211\) −1.54920e15 −1.20857 −0.604286 0.796768i \(-0.706541\pi\)
−0.604286 + 0.796768i \(0.706541\pi\)
\(212\) −1.07281e15 −0.811596
\(213\) 2.03096e14 0.149017
\(214\) 6.21533e14 0.442359
\(215\) −1.78722e15 −1.23404
\(216\) −3.08528e14 −0.206702
\(217\) 1.47540e15 0.959228
\(218\) −8.20744e14 −0.517893
\(219\) 4.11606e14 0.252113
\(220\) −1.39969e15 −0.832311
\(221\) 1.00722e15 0.581534
\(222\) −3.46827e14 −0.194455
\(223\) −1.50741e15 −0.820823 −0.410412 0.911900i \(-0.634615\pi\)
−0.410412 + 0.911900i \(0.634615\pi\)
\(224\) −1.35187e15 −0.715026
\(225\) 4.29162e13 0.0220513
\(226\) 1.61466e15 0.806075
\(227\) 3.92080e15 1.90198 0.950990 0.309221i \(-0.100068\pi\)
0.950990 + 0.309221i \(0.100068\pi\)
\(228\) −7.64428e14 −0.360380
\(229\) 1.37291e15 0.629090 0.314545 0.949243i \(-0.398148\pi\)
0.314545 + 0.949243i \(0.398148\pi\)
\(230\) 6.79534e14 0.302678
\(231\) −2.04538e15 −0.885721
\(232\) −2.54292e15 −1.07068
\(233\) −3.53572e15 −1.44765 −0.723827 0.689982i \(-0.757618\pi\)
−0.723827 + 0.689982i \(0.757618\pi\)
\(234\) −2.68281e14 −0.106828
\(235\) −3.95308e14 −0.153107
\(236\) 1.57338e14 0.0592797
\(237\) 9.97918e14 0.365789
\(238\) 2.40138e15 0.856466
\(239\) 3.42983e15 1.19038 0.595191 0.803584i \(-0.297076\pi\)
0.595191 + 0.803584i \(0.297076\pi\)
\(240\) −5.95362e14 −0.201098
\(241\) 3.54669e15 1.16604 0.583019 0.812458i \(-0.301871\pi\)
0.583019 + 0.812458i \(0.301871\pi\)
\(242\) 4.92085e15 1.57485
\(243\) 2.05891e14 0.0641500
\(244\) −4.14085e14 −0.125619
\(245\) −8.70407e14 −0.257124
\(246\) 1.38689e15 0.398993
\(247\) −2.12453e15 −0.595295
\(248\) 4.35583e15 1.18887
\(249\) 1.91610e15 0.509475
\(250\) −2.74701e15 −0.711622
\(251\) 2.73465e15 0.690275 0.345137 0.938552i \(-0.387832\pi\)
0.345137 + 0.938552i \(0.387832\pi\)
\(252\) 5.34723e14 0.131530
\(253\) 2.93314e15 0.703153
\(254\) 3.66102e15 0.855427
\(255\) −3.50503e15 −0.798327
\(256\) −4.68287e15 −1.03981
\(257\) 6.15631e15 1.33277 0.666385 0.745608i \(-0.267841\pi\)
0.666385 + 0.745608i \(0.267841\pi\)
\(258\) −2.41240e15 −0.509239
\(259\) 1.92122e15 0.395484
\(260\) 1.01698e15 0.204167
\(261\) 1.69698e15 0.332286
\(262\) −4.95263e15 −0.945970
\(263\) −7.90796e15 −1.47351 −0.736753 0.676162i \(-0.763642\pi\)
−0.736753 + 0.676162i \(0.763642\pi\)
\(264\) −6.03859e15 −1.09777
\(265\) 1.03757e16 1.84042
\(266\) −5.06522e15 −0.876733
\(267\) −5.73222e15 −0.968276
\(268\) −3.54463e15 −0.584379
\(269\) 5.00304e15 0.805089 0.402544 0.915400i \(-0.368126\pi\)
0.402544 + 0.915400i \(0.368126\pi\)
\(270\) 9.33591e14 0.146653
\(271\) 6.11108e15 0.937168 0.468584 0.883419i \(-0.344764\pi\)
0.468584 + 0.883419i \(0.344764\pi\)
\(272\) 3.01709e15 0.451742
\(273\) 1.48612e15 0.217269
\(274\) 2.89998e15 0.414015
\(275\) 8.39966e14 0.117111
\(276\) −7.66808e14 −0.104419
\(277\) 1.15576e15 0.153727 0.0768634 0.997042i \(-0.475509\pi\)
0.0768634 + 0.997042i \(0.475509\pi\)
\(278\) −4.46844e15 −0.580584
\(279\) −2.90679e15 −0.368966
\(280\) 7.74960e15 0.961063
\(281\) −1.61496e16 −1.95691 −0.978453 0.206470i \(-0.933802\pi\)
−0.978453 + 0.206470i \(0.933802\pi\)
\(282\) −5.33589e14 −0.0631812
\(283\) 3.53645e15 0.409219 0.204609 0.978844i \(-0.434408\pi\)
0.204609 + 0.978844i \(0.434408\pi\)
\(284\) −1.03919e15 −0.117524
\(285\) 7.39315e15 0.817218
\(286\) −5.25086e15 −0.567350
\(287\) −7.68260e15 −0.811476
\(288\) 2.66341e15 0.275034
\(289\) 7.85772e15 0.793342
\(290\) 7.69475e15 0.759640
\(291\) 6.43876e15 0.621582
\(292\) −2.10609e15 −0.198833
\(293\) −9.99081e15 −0.922489 −0.461245 0.887273i \(-0.652597\pi\)
−0.461245 + 0.887273i \(0.652597\pi\)
\(294\) −1.17488e15 −0.106105
\(295\) −1.52169e15 −0.134426
\(296\) 5.67203e15 0.490165
\(297\) 4.02975e15 0.340692
\(298\) 4.31387e15 0.356830
\(299\) −2.13114e15 −0.172484
\(300\) −2.19592e14 −0.0173911
\(301\) 1.33633e16 1.03570
\(302\) 1.12644e16 0.854401
\(303\) 9.59296e15 0.712156
\(304\) −6.36393e15 −0.462431
\(305\) 4.00482e15 0.284862
\(306\) −4.73112e15 −0.329439
\(307\) −6.51657e15 −0.444242 −0.222121 0.975019i \(-0.571298\pi\)
−0.222121 + 0.975019i \(0.571298\pi\)
\(308\) 1.04657e16 0.698538
\(309\) 5.68368e15 0.371449
\(310\) −1.31805e16 −0.843493
\(311\) −8.66465e15 −0.543011 −0.271506 0.962437i \(-0.587522\pi\)
−0.271506 + 0.962437i \(0.587522\pi\)
\(312\) 4.38748e15 0.269284
\(313\) 3.17591e16 1.90911 0.954553 0.298040i \(-0.0963328\pi\)
0.954553 + 0.298040i \(0.0963328\pi\)
\(314\) 1.39574e16 0.821790
\(315\) −5.17156e15 −0.298266
\(316\) −5.10610e15 −0.288485
\(317\) −2.76487e15 −0.153035 −0.0765173 0.997068i \(-0.524380\pi\)
−0.0765173 + 0.997068i \(0.524380\pi\)
\(318\) 1.40051e16 0.759471
\(319\) 3.32136e16 1.76472
\(320\) 1.87672e16 0.977067
\(321\) 6.78317e15 0.346059
\(322\) −5.08099e15 −0.254030
\(323\) −3.74659e16 −1.83578
\(324\) −1.05349e15 −0.0505929
\(325\) −6.10297e14 −0.0287276
\(326\) 6.05855e15 0.279547
\(327\) −8.95727e15 −0.405150
\(328\) −2.26814e16 −1.00575
\(329\) 2.95578e15 0.128499
\(330\) 1.82725e16 0.778855
\(331\) 1.88942e16 0.789672 0.394836 0.918752i \(-0.370801\pi\)
0.394836 + 0.918752i \(0.370801\pi\)
\(332\) −9.80423e15 −0.401805
\(333\) −3.78513e15 −0.152122
\(334\) −2.85006e16 −1.12332
\(335\) 3.42818e16 1.32517
\(336\) 4.45162e15 0.168777
\(337\) 2.73402e15 0.101673 0.0508367 0.998707i \(-0.483811\pi\)
0.0508367 + 0.998707i \(0.483811\pi\)
\(338\) −1.64161e16 −0.598842
\(339\) 1.76217e16 0.630595
\(340\) 1.79344e16 0.629613
\(341\) −5.68924e16 −1.95952
\(342\) 9.97933e15 0.337234
\(343\) 3.26434e16 1.08239
\(344\) 3.94526e16 1.28365
\(345\) 7.41617e15 0.236786
\(346\) −2.01435e16 −0.631160
\(347\) 4.42948e16 1.36211 0.681053 0.732234i \(-0.261522\pi\)
0.681053 + 0.732234i \(0.261522\pi\)
\(348\) −8.68301e15 −0.262063
\(349\) −1.74421e16 −0.516695 −0.258348 0.966052i \(-0.583178\pi\)
−0.258348 + 0.966052i \(0.583178\pi\)
\(350\) −1.45505e15 −0.0423092
\(351\) −2.92791e15 −0.0835722
\(352\) 5.21288e16 1.46067
\(353\) 4.68774e16 1.28952 0.644760 0.764385i \(-0.276957\pi\)
0.644760 + 0.764385i \(0.276957\pi\)
\(354\) −2.05399e15 −0.0554725
\(355\) 1.00505e16 0.266505
\(356\) 2.93303e16 0.763646
\(357\) 2.62077e16 0.670016
\(358\) 1.78274e16 0.447557
\(359\) 4.02884e15 0.0993268 0.0496634 0.998766i \(-0.484185\pi\)
0.0496634 + 0.998766i \(0.484185\pi\)
\(360\) −1.52680e16 −0.369672
\(361\) 3.69738e16 0.879219
\(362\) 2.59514e16 0.606115
\(363\) 5.37042e16 1.23201
\(364\) −7.60413e15 −0.171352
\(365\) 2.03690e16 0.450885
\(366\) 5.40573e15 0.117551
\(367\) −1.29453e16 −0.276555 −0.138277 0.990394i \(-0.544157\pi\)
−0.138277 + 0.990394i \(0.544157\pi\)
\(368\) −6.38375e15 −0.133988
\(369\) 1.51360e16 0.312133
\(370\) −1.71633e16 −0.347767
\(371\) −7.75805e16 −1.54462
\(372\) 1.48733e16 0.290991
\(373\) −7.16111e16 −1.37681 −0.688403 0.725328i \(-0.741688\pi\)
−0.688403 + 0.725328i \(0.741688\pi\)
\(374\) −9.25986e16 −1.74960
\(375\) −2.99797e16 −0.556704
\(376\) 8.72635e15 0.159262
\(377\) −2.41321e16 −0.432890
\(378\) −6.98061e15 −0.123083
\(379\) −7.79312e16 −1.35069 −0.675347 0.737501i \(-0.736006\pi\)
−0.675347 + 0.737501i \(0.736006\pi\)
\(380\) −3.78289e16 −0.644512
\(381\) 3.99549e16 0.669203
\(382\) 2.32646e16 0.383075
\(383\) −2.34127e16 −0.379017 −0.189509 0.981879i \(-0.560690\pi\)
−0.189509 + 0.981879i \(0.560690\pi\)
\(384\) −4.59742e15 −0.0731748
\(385\) −1.01219e17 −1.58405
\(386\) 8.49642e16 1.30743
\(387\) −2.63280e16 −0.398380
\(388\) −3.29456e16 −0.490220
\(389\) −1.24503e17 −1.82182 −0.910911 0.412602i \(-0.864620\pi\)
−0.910911 + 0.412602i \(0.864620\pi\)
\(390\) −1.32763e16 −0.191054
\(391\) −3.75826e16 −0.531910
\(392\) 1.92141e16 0.267461
\(393\) −5.40510e16 −0.740035
\(394\) 4.99016e16 0.672031
\(395\) 4.93836e16 0.654186
\(396\) −2.06193e16 −0.268692
\(397\) 5.19525e16 0.665991 0.332996 0.942928i \(-0.391941\pi\)
0.332996 + 0.942928i \(0.391941\pi\)
\(398\) 4.66177e16 0.587910
\(399\) −5.52798e16 −0.685871
\(400\) −1.82812e15 −0.0223159
\(401\) −4.99087e16 −0.599429 −0.299715 0.954029i \(-0.596891\pi\)
−0.299715 + 0.954029i \(0.596891\pi\)
\(402\) 4.62738e16 0.546847
\(403\) 4.13365e16 0.480674
\(404\) −4.90848e16 −0.561653
\(405\) 1.01888e16 0.114727
\(406\) −5.75349e16 −0.637547
\(407\) −7.40835e16 −0.807900
\(408\) 7.73730e16 0.830421
\(409\) −1.76276e16 −0.186205 −0.0931027 0.995657i \(-0.529678\pi\)
−0.0931027 + 0.995657i \(0.529678\pi\)
\(410\) 6.86327e16 0.713569
\(411\) 3.16492e16 0.323885
\(412\) −2.90820e16 −0.292949
\(413\) 1.13779e16 0.112821
\(414\) 1.00104e16 0.0977123
\(415\) 9.48214e16 0.911158
\(416\) −3.78754e16 −0.358303
\(417\) −4.87668e16 −0.454192
\(418\) 1.95318e17 1.79100
\(419\) −1.36737e17 −1.23451 −0.617254 0.786764i \(-0.711755\pi\)
−0.617254 + 0.786764i \(0.711755\pi\)
\(420\) 2.64616e16 0.235232
\(421\) −1.16180e17 −1.01695 −0.508474 0.861077i \(-0.669790\pi\)
−0.508474 + 0.861077i \(0.669790\pi\)
\(422\) −1.03483e17 −0.891942
\(423\) −5.82338e15 −0.0494269
\(424\) −2.29041e17 −1.91441
\(425\) −1.07626e16 −0.0885905
\(426\) 1.35663e16 0.109976
\(427\) −2.99447e16 −0.239077
\(428\) −3.47078e16 −0.272925
\(429\) −5.73058e16 −0.443840
\(430\) −1.19382e17 −0.910736
\(431\) −2.00159e17 −1.50408 −0.752042 0.659116i \(-0.770931\pi\)
−0.752042 + 0.659116i \(0.770931\pi\)
\(432\) −8.77043e15 −0.0649197
\(433\) 1.95873e17 1.42825 0.714123 0.700020i \(-0.246826\pi\)
0.714123 + 0.700020i \(0.246826\pi\)
\(434\) 9.85529e16 0.707923
\(435\) 8.39775e16 0.594269
\(436\) 4.58322e16 0.319527
\(437\) 7.92728e16 0.544496
\(438\) 2.74942e16 0.186063
\(439\) −7.85789e16 −0.523946 −0.261973 0.965075i \(-0.584373\pi\)
−0.261973 + 0.965075i \(0.584373\pi\)
\(440\) −2.98829e17 −1.96327
\(441\) −1.28222e16 −0.0830064
\(442\) 6.72797e16 0.429180
\(443\) −1.51027e17 −0.949358 −0.474679 0.880159i \(-0.657436\pi\)
−0.474679 + 0.880159i \(0.657436\pi\)
\(444\) 1.93676e16 0.119974
\(445\) −2.83668e17 −1.73169
\(446\) −1.00691e17 −0.605779
\(447\) 4.70799e16 0.279150
\(448\) −1.40325e17 −0.820029
\(449\) −2.18212e17 −1.25683 −0.628416 0.777878i \(-0.716296\pi\)
−0.628416 + 0.777878i \(0.716296\pi\)
\(450\) 2.86669e15 0.0162742
\(451\) 2.96246e17 1.65770
\(452\) −9.01661e16 −0.497329
\(453\) 1.22935e17 0.668401
\(454\) 2.61899e17 1.40369
\(455\) 7.35431e16 0.388569
\(456\) −1.63203e17 −0.850072
\(457\) 1.89865e17 0.974969 0.487484 0.873132i \(-0.337915\pi\)
0.487484 + 0.873132i \(0.337915\pi\)
\(458\) 9.17071e16 0.464277
\(459\) −5.16336e16 −0.257721
\(460\) −3.79467e16 −0.186745
\(461\) 2.49093e17 1.20866 0.604331 0.796733i \(-0.293441\pi\)
0.604331 + 0.796733i \(0.293441\pi\)
\(462\) −1.36626e17 −0.653674
\(463\) −3.15470e17 −1.48827 −0.744135 0.668029i \(-0.767138\pi\)
−0.744135 + 0.668029i \(0.767138\pi\)
\(464\) −7.22868e16 −0.336273
\(465\) −1.43847e17 −0.659867
\(466\) −2.36177e17 −1.06839
\(467\) −2.61403e17 −1.16614 −0.583071 0.812421i \(-0.698149\pi\)
−0.583071 + 0.812421i \(0.698149\pi\)
\(468\) 1.49814e16 0.0659105
\(469\) −2.56331e17 −1.11219
\(470\) −2.64055e16 −0.112995
\(471\) 1.52325e17 0.642889
\(472\) 3.35911e16 0.139830
\(473\) −5.15299e17 −2.11574
\(474\) 6.66583e16 0.269957
\(475\) 2.27014e16 0.0906869
\(476\) −1.34098e17 −0.528419
\(477\) 1.52847e17 0.594137
\(478\) 2.29104e17 0.878518
\(479\) 1.91515e16 0.0724472 0.0362236 0.999344i \(-0.488467\pi\)
0.0362236 + 0.999344i \(0.488467\pi\)
\(480\) 1.31803e17 0.491877
\(481\) 5.38271e16 0.198179
\(482\) 2.36910e17 0.860552
\(483\) −5.54519e16 −0.198728
\(484\) −2.74791e17 −0.971647
\(485\) 3.18632e17 1.11165
\(486\) 1.37530e16 0.0473436
\(487\) 8.83888e15 0.0300233 0.0150117 0.999887i \(-0.495221\pi\)
0.0150117 + 0.999887i \(0.495221\pi\)
\(488\) −8.84057e16 −0.296314
\(489\) 6.61206e16 0.218690
\(490\) −5.81409e16 −0.189761
\(491\) 2.01895e17 0.650272 0.325136 0.945667i \(-0.394590\pi\)
0.325136 + 0.945667i \(0.394590\pi\)
\(492\) −7.74473e16 −0.246169
\(493\) −4.25569e17 −1.33495
\(494\) −1.41913e17 −0.439336
\(495\) 1.99419e17 0.609301
\(496\) 1.23822e17 0.373393
\(497\) −7.51495e16 −0.223671
\(498\) 1.27991e17 0.376000
\(499\) −2.92605e17 −0.848452 −0.424226 0.905556i \(-0.639454\pi\)
−0.424226 + 0.905556i \(0.639454\pi\)
\(500\) 1.53399e17 0.439053
\(501\) −3.11044e17 −0.878773
\(502\) 1.82667e17 0.509432
\(503\) 2.49375e17 0.686532 0.343266 0.939238i \(-0.388467\pi\)
0.343266 + 0.939238i \(0.388467\pi\)
\(504\) 1.14161e17 0.310256
\(505\) 4.74723e17 1.27364
\(506\) 1.95926e17 0.518936
\(507\) −1.79159e17 −0.468476
\(508\) −2.04440e17 −0.527777
\(509\) −3.19866e17 −0.815271 −0.407635 0.913145i \(-0.633647\pi\)
−0.407635 + 0.913145i \(0.633647\pi\)
\(510\) −2.34127e17 −0.589176
\(511\) −1.52302e17 −0.378417
\(512\) −2.61141e17 −0.640649
\(513\) 1.08910e17 0.263819
\(514\) 4.11225e17 0.983602
\(515\) 2.81266e17 0.664308
\(516\) 1.34714e17 0.314188
\(517\) −1.13977e17 −0.262499
\(518\) 1.28332e17 0.291873
\(519\) −2.19838e17 −0.493758
\(520\) 2.17122e17 0.481594
\(521\) 5.68272e15 0.0124483 0.00622416 0.999981i \(-0.498019\pi\)
0.00622416 + 0.999981i \(0.498019\pi\)
\(522\) 1.13353e17 0.245232
\(523\) −2.23120e17 −0.476735 −0.238367 0.971175i \(-0.576612\pi\)
−0.238367 + 0.971175i \(0.576612\pi\)
\(524\) 2.76566e17 0.583640
\(525\) −1.58798e16 −0.0330986
\(526\) −5.28231e17 −1.08747
\(527\) 7.28967e17 1.48231
\(528\) −1.71657e17 −0.344779
\(529\) −4.24517e17 −0.842234
\(530\) 6.93067e17 1.35826
\(531\) −2.24165e16 −0.0433963
\(532\) 2.82853e17 0.540923
\(533\) −2.15244e17 −0.406635
\(534\) −3.82897e17 −0.714601
\(535\) 3.35676e17 0.618900
\(536\) −7.56765e17 −1.37845
\(537\) 1.94561e17 0.350125
\(538\) 3.34190e17 0.594166
\(539\) −2.50959e17 −0.440835
\(540\) −5.21338e16 −0.0904816
\(541\) 6.72211e17 1.15272 0.576360 0.817196i \(-0.304473\pi\)
0.576360 + 0.817196i \(0.304473\pi\)
\(542\) 4.08204e17 0.691643
\(543\) 2.83223e17 0.474166
\(544\) −6.67931e17 −1.10494
\(545\) −4.43265e17 −0.724579
\(546\) 9.92691e16 0.160347
\(547\) −1.12671e18 −1.79844 −0.899218 0.437500i \(-0.855864\pi\)
−0.899218 + 0.437500i \(0.855864\pi\)
\(548\) −1.61941e17 −0.255437
\(549\) 5.89961e16 0.0919608
\(550\) 5.61075e16 0.0864298
\(551\) 8.97651e17 1.36654
\(552\) −1.63711e17 −0.246305
\(553\) −3.69249e17 −0.549042
\(554\) 7.72018e16 0.113452
\(555\) −1.87313e17 −0.272059
\(556\) 2.49528e17 0.358206
\(557\) 1.42157e17 0.201702 0.100851 0.994902i \(-0.467844\pi\)
0.100851 + 0.994902i \(0.467844\pi\)
\(558\) −1.94166e17 −0.272302
\(559\) 3.74402e17 0.518994
\(560\) 2.20295e17 0.301844
\(561\) −1.01058e18 −1.36872
\(562\) −1.07875e18 −1.44422
\(563\) −4.66727e17 −0.617673 −0.308836 0.951115i \(-0.599940\pi\)
−0.308836 + 0.951115i \(0.599940\pi\)
\(564\) 2.97968e16 0.0389813
\(565\) 8.72040e17 1.12777
\(566\) 2.36225e17 0.302009
\(567\) −7.61837e16 −0.0962879
\(568\) −2.21864e17 −0.277219
\(569\) 7.21466e17 0.891222 0.445611 0.895227i \(-0.352986\pi\)
0.445611 + 0.895227i \(0.352986\pi\)
\(570\) 4.93843e17 0.603118
\(571\) −2.19647e17 −0.265211 −0.132605 0.991169i \(-0.542334\pi\)
−0.132605 + 0.991169i \(0.542334\pi\)
\(572\) 2.93220e17 0.350041
\(573\) 2.53901e17 0.299681
\(574\) −5.13177e17 −0.598881
\(575\) 2.27721e16 0.0262762
\(576\) 2.76465e17 0.315423
\(577\) 6.19858e16 0.0699277 0.0349638 0.999389i \(-0.488868\pi\)
0.0349638 + 0.999389i \(0.488868\pi\)
\(578\) 5.24875e17 0.585497
\(579\) 9.27266e17 1.02281
\(580\) −4.29692e17 −0.468679
\(581\) −7.08995e17 −0.764712
\(582\) 4.30092e17 0.458736
\(583\) 2.99155e18 3.15537
\(584\) −4.49642e17 −0.469011
\(585\) −1.44892e17 −0.149463
\(586\) −6.67360e17 −0.680810
\(587\) 2.62939e17 0.265281 0.132641 0.991164i \(-0.457654\pi\)
0.132641 + 0.991164i \(0.457654\pi\)
\(588\) 6.56080e16 0.0654642
\(589\) −1.53761e18 −1.51739
\(590\) −1.01645e17 −0.0992083
\(591\) 5.44607e17 0.525732
\(592\) 1.61237e17 0.153948
\(593\) 1.03795e18 0.980213 0.490107 0.871663i \(-0.336958\pi\)
0.490107 + 0.871663i \(0.336958\pi\)
\(594\) 2.69177e17 0.251435
\(595\) 1.29693e18 1.19827
\(596\) −2.40896e17 −0.220156
\(597\) 5.08767e17 0.459924
\(598\) −1.42355e17 −0.127296
\(599\) −1.10082e18 −0.973740 −0.486870 0.873475i \(-0.661861\pi\)
−0.486870 + 0.873475i \(0.661861\pi\)
\(600\) −4.68820e16 −0.0410226
\(601\) −7.27854e17 −0.630028 −0.315014 0.949087i \(-0.602009\pi\)
−0.315014 + 0.949087i \(0.602009\pi\)
\(602\) 8.92636e17 0.764358
\(603\) 5.05015e17 0.427801
\(604\) −6.29028e17 −0.527145
\(605\) 2.65764e18 2.20336
\(606\) 6.40784e17 0.525581
\(607\) −1.40498e18 −1.14011 −0.570053 0.821608i \(-0.693077\pi\)
−0.570053 + 0.821608i \(0.693077\pi\)
\(608\) 1.40887e18 1.13109
\(609\) −6.27913e17 −0.498755
\(610\) 2.67511e17 0.210232
\(611\) 8.28125e16 0.0643914
\(612\) 2.64196e17 0.203256
\(613\) 8.32972e17 0.634070 0.317035 0.948414i \(-0.397313\pi\)
0.317035 + 0.948414i \(0.397313\pi\)
\(614\) −4.35290e17 −0.327857
\(615\) 7.49030e17 0.558227
\(616\) 2.23439e18 1.64773
\(617\) −2.11893e18 −1.54619 −0.773095 0.634290i \(-0.781292\pi\)
−0.773095 + 0.634290i \(0.781292\pi\)
\(618\) 3.79654e17 0.274134
\(619\) −1.45912e17 −0.104256 −0.0521280 0.998640i \(-0.516600\pi\)
−0.0521280 + 0.998640i \(0.516600\pi\)
\(620\) 7.36030e17 0.520415
\(621\) 1.09250e17 0.0764407
\(622\) −5.78776e17 −0.400749
\(623\) 2.12103e18 1.45336
\(624\) 1.24722e17 0.0845749
\(625\) −1.58217e18 −1.06178
\(626\) 2.12143e18 1.40895
\(627\) 2.13162e18 1.40111
\(628\) −7.79411e17 −0.507024
\(629\) 9.49238e17 0.611148
\(630\) −3.45447e17 −0.220124
\(631\) −4.40838e17 −0.278028 −0.139014 0.990290i \(-0.544393\pi\)
−0.139014 + 0.990290i \(0.544393\pi\)
\(632\) −1.09013e18 −0.680486
\(633\) −1.12937e18 −0.697769
\(634\) −1.84686e17 −0.112942
\(635\) 1.97723e18 1.19682
\(636\) −7.82079e17 −0.468575
\(637\) 1.82340e17 0.108137
\(638\) 2.21858e18 1.30239
\(639\) 1.48057e17 0.0860348
\(640\) −2.27511e17 −0.130868
\(641\) −2.84230e18 −1.61842 −0.809212 0.587517i \(-0.800106\pi\)
−0.809212 + 0.587517i \(0.800106\pi\)
\(642\) 4.53098e17 0.255396
\(643\) 1.88114e18 1.04966 0.524832 0.851206i \(-0.324128\pi\)
0.524832 + 0.851206i \(0.324128\pi\)
\(644\) 2.83734e17 0.156730
\(645\) −1.30288e18 −0.712472
\(646\) −2.50263e18 −1.35483
\(647\) −3.13644e18 −1.68096 −0.840482 0.541839i \(-0.817728\pi\)
−0.840482 + 0.541839i \(0.817728\pi\)
\(648\) −2.24917e17 −0.119340
\(649\) −4.38741e17 −0.230472
\(650\) −4.07662e16 −0.0212014
\(651\) 1.07557e18 0.553810
\(652\) −3.38323e17 −0.172473
\(653\) 1.64408e18 0.829829 0.414914 0.909860i \(-0.363812\pi\)
0.414914 + 0.909860i \(0.363812\pi\)
\(654\) −5.98322e17 −0.299006
\(655\) −2.67480e18 −1.32350
\(656\) −6.44755e17 −0.315878
\(657\) 3.00061e17 0.145557
\(658\) 1.97438e17 0.0948338
\(659\) −2.42234e18 −1.15207 −0.576036 0.817425i \(-0.695401\pi\)
−0.576036 + 0.817425i \(0.695401\pi\)
\(660\) −1.02038e18 −0.480535
\(661\) −1.73436e18 −0.808778 −0.404389 0.914587i \(-0.632516\pi\)
−0.404389 + 0.914587i \(0.632516\pi\)
\(662\) 1.26208e18 0.582789
\(663\) 7.34264e17 0.335749
\(664\) −2.09317e18 −0.947788
\(665\) −2.73561e18 −1.22663
\(666\) −2.52837e17 −0.112268
\(667\) 9.00446e17 0.395949
\(668\) 1.59154e18 0.693058
\(669\) −1.09890e18 −0.473903
\(670\) 2.28993e18 0.977995
\(671\) 1.15469e18 0.488391
\(672\) −9.85511e17 −0.412820
\(673\) −1.75908e16 −0.00729772 −0.00364886 0.999993i \(-0.501161\pi\)
−0.00364886 + 0.999993i \(0.501161\pi\)
\(674\) 1.82625e17 0.0750363
\(675\) 3.12859e16 0.0127313
\(676\) 9.16713e17 0.369471
\(677\) 5.81829e17 0.232257 0.116129 0.993234i \(-0.462952\pi\)
0.116129 + 0.993234i \(0.462952\pi\)
\(678\) 1.17709e18 0.465388
\(679\) −2.38247e18 −0.932982
\(680\) 3.82893e18 1.48515
\(681\) 2.85826e18 1.09811
\(682\) −3.80026e18 −1.44616
\(683\) 3.50818e18 1.32235 0.661176 0.750230i \(-0.270057\pi\)
0.661176 + 0.750230i \(0.270057\pi\)
\(684\) −5.57268e17 −0.208065
\(685\) 1.56621e18 0.579244
\(686\) 2.18049e18 0.798818
\(687\) 1.00085e18 0.363205
\(688\) 1.12151e18 0.403159
\(689\) −2.17358e18 −0.774018
\(690\) 4.95381e17 0.174751
\(691\) −2.68406e18 −0.937961 −0.468981 0.883208i \(-0.655379\pi\)
−0.468981 + 0.883208i \(0.655379\pi\)
\(692\) 1.12486e18 0.389410
\(693\) −1.49109e18 −0.511371
\(694\) 2.95877e18 1.00525
\(695\) −2.41330e18 −0.812289
\(696\) −1.85379e18 −0.618159
\(697\) −3.79582e18 −1.25399
\(698\) −1.16509e18 −0.381328
\(699\) −2.57754e18 −0.835803
\(700\) 8.12531e16 0.0261037
\(701\) −1.57761e18 −0.502148 −0.251074 0.967968i \(-0.580784\pi\)
−0.251074 + 0.967968i \(0.580784\pi\)
\(702\) −1.95577e17 −0.0616774
\(703\) −2.00222e18 −0.625609
\(704\) 5.41103e18 1.67517
\(705\) −2.88179e17 −0.0883962
\(706\) 3.13129e18 0.951683
\(707\) −3.54958e18 −1.06893
\(708\) 1.14700e17 0.0342252
\(709\) −1.16804e18 −0.345348 −0.172674 0.984979i \(-0.555241\pi\)
−0.172674 + 0.984979i \(0.555241\pi\)
\(710\) 6.71350e17 0.196684
\(711\) 7.27482e17 0.211188
\(712\) 6.26192e18 1.80131
\(713\) −1.54239e18 −0.439657
\(714\) 1.75060e18 0.494481
\(715\) −2.83587e18 −0.793774
\(716\) −9.95523e17 −0.276132
\(717\) 2.50035e18 0.687268
\(718\) 2.69116e17 0.0733045
\(719\) −5.83232e18 −1.57436 −0.787180 0.616724i \(-0.788460\pi\)
−0.787180 + 0.616724i \(0.788460\pi\)
\(720\) −4.34019e17 −0.116104
\(721\) −2.10307e18 −0.557538
\(722\) 2.46975e18 0.648876
\(723\) 2.58554e18 0.673213
\(724\) −1.44918e18 −0.373958
\(725\) 2.57861e17 0.0659461
\(726\) 3.58730e18 0.909243
\(727\) 3.99779e17 0.100426 0.0502131 0.998739i \(-0.484010\pi\)
0.0502131 + 0.998739i \(0.484010\pi\)
\(728\) −1.62345e18 −0.404190
\(729\) 1.50095e17 0.0370370
\(730\) 1.36059e18 0.332759
\(731\) 6.60257e18 1.60048
\(732\) −3.01868e17 −0.0725263
\(733\) −5.86421e18 −1.39648 −0.698238 0.715866i \(-0.746032\pi\)
−0.698238 + 0.715866i \(0.746032\pi\)
\(734\) −8.64709e17 −0.204101
\(735\) −6.34526e17 −0.148451
\(736\) 1.41325e18 0.327728
\(737\) 9.88427e18 2.27199
\(738\) 1.01105e18 0.230359
\(739\) 2.01623e18 0.455357 0.227679 0.973736i \(-0.426886\pi\)
0.227679 + 0.973736i \(0.426886\pi\)
\(740\) 9.58435e17 0.214564
\(741\) −1.54878e18 −0.343694
\(742\) −5.18217e18 −1.13995
\(743\) 7.56368e18 1.64932 0.824661 0.565627i \(-0.191366\pi\)
0.824661 + 0.565627i \(0.191366\pi\)
\(744\) 3.17540e18 0.686395
\(745\) 2.32982e18 0.499238
\(746\) −4.78343e18 −1.01610
\(747\) 1.39684e18 0.294146
\(748\) 5.17091e18 1.07946
\(749\) −2.50990e18 −0.519427
\(750\) −2.00257e18 −0.410855
\(751\) 7.77646e18 1.58169 0.790847 0.612014i \(-0.209641\pi\)
0.790847 + 0.612014i \(0.209641\pi\)
\(752\) 2.48061e17 0.0500199
\(753\) 1.99356e18 0.398530
\(754\) −1.61196e18 −0.319478
\(755\) 6.08363e18 1.19538
\(756\) 3.89813e17 0.0759390
\(757\) −6.02493e18 −1.16367 −0.581834 0.813308i \(-0.697665\pi\)
−0.581834 + 0.813308i \(0.697665\pi\)
\(758\) −5.20560e18 −0.996830
\(759\) 2.13826e18 0.405965
\(760\) −8.07634e18 −1.52029
\(761\) 5.12637e18 0.956775 0.478388 0.878149i \(-0.341221\pi\)
0.478388 + 0.878149i \(0.341221\pi\)
\(762\) 2.66888e18 0.493881
\(763\) 3.31436e18 0.608122
\(764\) −1.29915e18 −0.236348
\(765\) −2.55517e18 −0.460914
\(766\) −1.56391e18 −0.279720
\(767\) 3.18777e17 0.0565350
\(768\) −3.41381e18 −0.600333
\(769\) −1.48785e18 −0.259440 −0.129720 0.991551i \(-0.541408\pi\)
−0.129720 + 0.991551i \(0.541408\pi\)
\(770\) −6.76117e18 −1.16905
\(771\) 4.48795e18 0.769475
\(772\) −4.74459e18 −0.806653
\(773\) 1.00543e19 1.69506 0.847529 0.530749i \(-0.178089\pi\)
0.847529 + 0.530749i \(0.178089\pi\)
\(774\) −1.75864e18 −0.294009
\(775\) −4.41697e17 −0.0732256
\(776\) −7.03376e18 −1.15634
\(777\) 1.40057e18 0.228333
\(778\) −8.31644e18 −1.34453
\(779\) 8.00652e18 1.28366
\(780\) 7.41379e17 0.117876
\(781\) 2.89781e18 0.456918
\(782\) −2.51042e18 −0.392556
\(783\) 1.23710e18 0.191845
\(784\) 5.46192e17 0.0840023
\(785\) 7.53806e18 1.14976
\(786\) −3.61046e18 −0.546156
\(787\) 1.08288e19 1.62459 0.812296 0.583245i \(-0.198217\pi\)
0.812296 + 0.583245i \(0.198217\pi\)
\(788\) −2.78662e18 −0.414627
\(789\) −5.76490e18 −0.850729
\(790\) 3.29869e18 0.482798
\(791\) −6.52038e18 −0.946511
\(792\) −4.40213e18 −0.633796
\(793\) −8.38964e17 −0.119803
\(794\) 3.47029e18 0.491511
\(795\) 7.56386e18 1.06257
\(796\) −2.60324e18 −0.362726
\(797\) 1.20554e19 1.66610 0.833051 0.553197i \(-0.186592\pi\)
0.833051 + 0.553197i \(0.186592\pi\)
\(798\) −3.69254e18 −0.506182
\(799\) 1.46039e18 0.198571
\(800\) 4.04714e17 0.0545837
\(801\) −4.17879e18 −0.559035
\(802\) −3.33377e18 −0.442387
\(803\) 5.87286e18 0.773035
\(804\) −2.58404e18 −0.337392
\(805\) −2.74413e18 −0.355411
\(806\) 2.76117e18 0.354744
\(807\) 3.64721e18 0.464818
\(808\) −1.04794e19 −1.32484
\(809\) 2.12593e18 0.266614 0.133307 0.991075i \(-0.457440\pi\)
0.133307 + 0.991075i \(0.457440\pi\)
\(810\) 6.80588e17 0.0846704
\(811\) −4.63622e18 −0.572174 −0.286087 0.958204i \(-0.592355\pi\)
−0.286087 + 0.958204i \(0.592355\pi\)
\(812\) 3.21288e18 0.393351
\(813\) 4.45498e18 0.541074
\(814\) −4.94858e18 −0.596241
\(815\) 3.27208e18 0.391111
\(816\) 2.19946e18 0.260813
\(817\) −1.39268e19 −1.63835
\(818\) −1.17748e18 −0.137422
\(819\) 1.08338e18 0.125440
\(820\) −3.83260e18 −0.440254
\(821\) −8.98267e18 −1.02371 −0.511853 0.859073i \(-0.671041\pi\)
−0.511853 + 0.859073i \(0.671041\pi\)
\(822\) 2.11408e18 0.239032
\(823\) 7.07899e18 0.794094 0.397047 0.917798i \(-0.370035\pi\)
0.397047 + 0.917798i \(0.370035\pi\)
\(824\) −6.20889e18 −0.691015
\(825\) 6.12335e17 0.0676143
\(826\) 7.60016e17 0.0832631
\(827\) 9.08590e17 0.0987603 0.0493801 0.998780i \(-0.484275\pi\)
0.0493801 + 0.998780i \(0.484275\pi\)
\(828\) −5.59003e17 −0.0602861
\(829\) 1.79622e19 1.92201 0.961005 0.276532i \(-0.0891850\pi\)
0.961005 + 0.276532i \(0.0891850\pi\)
\(830\) 6.33382e18 0.672447
\(831\) 8.42550e17 0.0887542
\(832\) −3.93151e18 −0.410921
\(833\) 3.21556e18 0.333476
\(834\) −3.25749e18 −0.335200
\(835\) −1.53925e19 −1.57162
\(836\) −1.09070e19 −1.10500
\(837\) −2.11905e18 −0.213022
\(838\) −9.13366e18 −0.911084
\(839\) −8.03402e18 −0.795207 −0.397603 0.917557i \(-0.630158\pi\)
−0.397603 + 0.917557i \(0.630158\pi\)
\(840\) 5.64946e18 0.554870
\(841\) −6.43673e16 −0.00627323
\(842\) −7.76053e18 −0.750521
\(843\) −1.17730e19 −1.12982
\(844\) 5.77870e18 0.550306
\(845\) −8.86597e18 −0.837833
\(846\) −3.88987e17 −0.0364777
\(847\) −1.98716e19 −1.84923
\(848\) −6.51087e18 −0.601265
\(849\) 2.57807e18 0.236262
\(850\) −7.18910e17 −0.0653810
\(851\) −2.00846e18 −0.181268
\(852\) −7.57573e17 −0.0678527
\(853\) −1.05725e18 −0.0939740 −0.0469870 0.998896i \(-0.514962\pi\)
−0.0469870 + 0.998896i \(0.514962\pi\)
\(854\) −2.00022e18 −0.176442
\(855\) 5.38961e18 0.471821
\(856\) −7.40999e18 −0.643781
\(857\) −6.94534e18 −0.598850 −0.299425 0.954120i \(-0.596795\pi\)
−0.299425 + 0.954120i \(0.596795\pi\)
\(858\) −3.82788e18 −0.327560
\(859\) 2.23388e18 0.189716 0.0948580 0.995491i \(-0.469760\pi\)
0.0948580 + 0.995491i \(0.469760\pi\)
\(860\) 6.66654e18 0.561902
\(861\) −5.60062e18 −0.468506
\(862\) −1.33701e19 −1.11003
\(863\) 1.73634e19 1.43076 0.715378 0.698737i \(-0.246254\pi\)
0.715378 + 0.698737i \(0.246254\pi\)
\(864\) 1.94162e18 0.158791
\(865\) −1.08790e19 −0.883049
\(866\) 1.30838e19 1.05407
\(867\) 5.72827e18 0.458036
\(868\) −5.50341e18 −0.436771
\(869\) 1.42385e19 1.12159
\(870\) 5.60948e18 0.438578
\(871\) −7.18165e18 −0.557322
\(872\) 9.78500e18 0.753709
\(873\) 4.69386e18 0.358870
\(874\) 5.29521e18 0.401846
\(875\) 1.10931e19 0.835602
\(876\) −1.53534e18 −0.114796
\(877\) 1.75887e19 1.30538 0.652690 0.757625i \(-0.273641\pi\)
0.652690 + 0.757625i \(0.273641\pi\)
\(878\) −5.24886e18 −0.386679
\(879\) −7.28330e18 −0.532599
\(880\) −8.49472e18 −0.616612
\(881\) −1.52042e19 −1.09552 −0.547761 0.836635i \(-0.684520\pi\)
−0.547761 + 0.836635i \(0.684520\pi\)
\(882\) −8.56488e17 −0.0612598
\(883\) 8.94666e18 0.635209 0.317604 0.948223i \(-0.397122\pi\)
0.317604 + 0.948223i \(0.397122\pi\)
\(884\) −3.75705e18 −0.264794
\(885\) −1.10931e18 −0.0776110
\(886\) −1.00882e19 −0.700639
\(887\) 6.60815e18 0.455592 0.227796 0.973709i \(-0.426848\pi\)
0.227796 + 0.973709i \(0.426848\pi\)
\(888\) 4.13491e18 0.282997
\(889\) −1.47841e19 −1.00446
\(890\) −1.89483e19 −1.27801
\(891\) 2.93769e18 0.196698
\(892\) 5.62281e18 0.373751
\(893\) −3.08040e18 −0.203270
\(894\) 3.14481e18 0.206016
\(895\) 9.62818e18 0.626173
\(896\) 1.70113e18 0.109834
\(897\) −1.55360e18 −0.0995839
\(898\) −1.45760e19 −0.927559
\(899\) −1.74654e19 −1.10342
\(900\) −1.60082e17 −0.0100408
\(901\) −3.83310e19 −2.38693
\(902\) 1.97884e19 1.22340
\(903\) 9.74187e18 0.597960
\(904\) −1.92501e19 −1.17311
\(905\) 1.40158e19 0.848009
\(906\) 8.21173e18 0.493289
\(907\) 6.83270e18 0.407517 0.203758 0.979021i \(-0.434684\pi\)
0.203758 + 0.979021i \(0.434684\pi\)
\(908\) −1.46250e19 −0.866041
\(909\) 6.99327e18 0.411164
\(910\) 4.91249e18 0.286769
\(911\) 4.40333e18 0.255218 0.127609 0.991825i \(-0.459270\pi\)
0.127609 + 0.991825i \(0.459270\pi\)
\(912\) −4.63931e18 −0.266985
\(913\) 2.73393e19 1.56217
\(914\) 1.26825e19 0.719540
\(915\) 2.91951e18 0.164465
\(916\) −5.12113e18 −0.286448
\(917\) 1.99999e19 1.11078
\(918\) −3.44899e18 −0.190201
\(919\) −1.14720e19 −0.628188 −0.314094 0.949392i \(-0.601701\pi\)
−0.314094 + 0.949392i \(0.601701\pi\)
\(920\) −8.10149e18 −0.440498
\(921\) −4.75058e18 −0.256483
\(922\) 1.66387e19 0.892009
\(923\) −2.10547e18 −0.112083
\(924\) 7.62952e18 0.403301
\(925\) −5.75164e17 −0.0301905
\(926\) −2.10726e19 −1.09836
\(927\) 4.14340e18 0.214456
\(928\) 1.60030e19 0.822509
\(929\) 1.33511e19 0.681418 0.340709 0.940169i \(-0.389333\pi\)
0.340709 + 0.940169i \(0.389333\pi\)
\(930\) −9.60860e18 −0.486991
\(931\) −6.78257e18 −0.341367
\(932\) 1.31886e19 0.659169
\(933\) −6.31653e18 −0.313508
\(934\) −1.74610e19 −0.860628
\(935\) −5.00104e19 −2.44785
\(936\) 3.19848e18 0.155471
\(937\) 3.33608e19 1.61039 0.805193 0.593013i \(-0.202062\pi\)
0.805193 + 0.593013i \(0.202062\pi\)
\(938\) −1.71222e19 −0.820807
\(939\) 2.31524e19 1.10222
\(940\) 1.47454e18 0.0697150
\(941\) −1.45632e18 −0.0683792 −0.0341896 0.999415i \(-0.510885\pi\)
−0.0341896 + 0.999415i \(0.510885\pi\)
\(942\) 1.01749e19 0.474461
\(943\) 8.03145e18 0.371936
\(944\) 9.54884e17 0.0439170
\(945\) −3.77007e18 −0.172204
\(946\) −3.44206e19 −1.56144
\(947\) −2.86414e19 −1.29038 −0.645192 0.764021i \(-0.723222\pi\)
−0.645192 + 0.764021i \(0.723222\pi\)
\(948\) −3.72235e18 −0.166557
\(949\) −4.26707e18 −0.189627
\(950\) 1.51639e18 0.0669282
\(951\) −2.01559e18 −0.0883546
\(952\) −2.86295e19 −1.24645
\(953\) 1.06857e19 0.462063 0.231031 0.972946i \(-0.425790\pi\)
0.231031 + 0.972946i \(0.425790\pi\)
\(954\) 1.02097e19 0.438481
\(955\) 1.25647e19 0.535956
\(956\) −1.27937e19 −0.542024
\(957\) 2.42127e19 1.01886
\(958\) 1.27927e18 0.0534670
\(959\) −1.17108e19 −0.486145
\(960\) 1.36813e19 0.564110
\(961\) 5.49936e18 0.225222
\(962\) 3.59551e18 0.146259
\(963\) 4.94493e18 0.199797
\(964\) −1.32296e19 −0.530940
\(965\) 4.58872e19 1.82921
\(966\) −3.70404e18 −0.146664
\(967\) 1.65593e19 0.651284 0.325642 0.945493i \(-0.394420\pi\)
0.325642 + 0.945493i \(0.394420\pi\)
\(968\) −5.86670e19 −2.29194
\(969\) −2.73127e19 −1.05989
\(970\) 2.12838e19 0.820414
\(971\) −4.50154e19 −1.72360 −0.861799 0.507250i \(-0.830662\pi\)
−0.861799 + 0.507250i \(0.830662\pi\)
\(972\) −7.67997e17 −0.0292098
\(973\) 1.80447e19 0.681734
\(974\) 5.90413e17 0.0221576
\(975\) −4.44907e17 −0.0165859
\(976\) −2.51308e18 −0.0930642
\(977\) −1.62274e19 −0.596944 −0.298472 0.954418i \(-0.596477\pi\)
−0.298472 + 0.954418i \(0.596477\pi\)
\(978\) 4.41668e18 0.161396
\(979\) −8.17882e19 −2.96895
\(980\) 3.24672e18 0.117078
\(981\) −6.52985e18 −0.233913
\(982\) 1.34860e19 0.479910
\(983\) 5.11823e18 0.180935 0.0904674 0.995899i \(-0.471164\pi\)
0.0904674 + 0.995899i \(0.471164\pi\)
\(984\) −1.65347e19 −0.580669
\(985\) 2.69507e19 0.940232
\(986\) −2.84269e19 −0.985211
\(987\) 2.15476e18 0.0741888
\(988\) 7.92473e18 0.271059
\(989\) −1.39701e19 −0.474706
\(990\) 1.33206e19 0.449672
\(991\) 2.02170e19 0.678012 0.339006 0.940784i \(-0.389909\pi\)
0.339006 + 0.940784i \(0.389909\pi\)
\(992\) −2.74120e19 −0.913303
\(993\) 1.37739e19 0.455918
\(994\) −5.01979e18 −0.165072
\(995\) 2.51772e19 0.822539
\(996\) −7.14728e18 −0.231982
\(997\) −2.06510e19 −0.665921 −0.332960 0.942941i \(-0.608048\pi\)
−0.332960 + 0.942941i \(0.608048\pi\)
\(998\) −1.95452e19 −0.626169
\(999\) −2.75936e18 −0.0878279
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.14.a.c.1.19 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.19 31 1.1 even 1 trivial