Properties

Label 177.14.a.a.1.15
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $30$
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: \(1\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-17.8149 q^{2} +729.000 q^{3} -7874.63 q^{4} +5823.96 q^{5} -12987.1 q^{6} -495710. q^{7} +286225. q^{8} +531441. q^{9} +O(q^{10})\) \(q-17.8149 q^{2} +729.000 q^{3} -7874.63 q^{4} +5823.96 q^{5} -12987.1 q^{6} -495710. q^{7} +286225. q^{8} +531441. q^{9} -103753. q^{10} +4.50618e6 q^{11} -5.74060e6 q^{12} +2.28397e7 q^{13} +8.83102e6 q^{14} +4.24566e6 q^{15} +5.94099e7 q^{16} -1.25892e8 q^{17} -9.46757e6 q^{18} -1.03025e8 q^{19} -4.58615e7 q^{20} -3.61372e8 q^{21} -8.02772e7 q^{22} -1.20045e9 q^{23} +2.08658e8 q^{24} -1.18678e9 q^{25} -4.06886e8 q^{26} +3.87420e8 q^{27} +3.90353e9 q^{28} +4.62707e9 q^{29} -7.56361e7 q^{30} +8.13029e9 q^{31} -3.40314e9 q^{32} +3.28500e9 q^{33} +2.24275e9 q^{34} -2.88699e9 q^{35} -4.18490e9 q^{36} -7.22768e9 q^{37} +1.83538e9 q^{38} +1.66501e10 q^{39} +1.66696e9 q^{40} +9.28321e9 q^{41} +6.43781e9 q^{42} +3.44773e10 q^{43} -3.54845e10 q^{44} +3.09509e9 q^{45} +2.13859e10 q^{46} +3.11971e10 q^{47} +4.33098e10 q^{48} +1.48839e11 q^{49} +2.11425e10 q^{50} -9.17753e10 q^{51} -1.79854e11 q^{52} +6.65705e10 q^{53} -6.90186e9 q^{54} +2.62438e10 q^{55} -1.41885e11 q^{56} -7.51053e10 q^{57} -8.24309e10 q^{58} +4.21805e10 q^{59} -3.34330e10 q^{60} +6.87416e11 q^{61} -1.44840e11 q^{62} -2.63440e11 q^{63} -4.26059e11 q^{64} +1.33017e11 q^{65} -5.85220e10 q^{66} +5.94901e11 q^{67} +9.91353e11 q^{68} -8.75129e11 q^{69} +5.14315e10 q^{70} +6.97722e11 q^{71} +1.52112e11 q^{72} -1.61175e12 q^{73} +1.28760e11 q^{74} -8.65166e11 q^{75} +8.11284e11 q^{76} -2.23376e12 q^{77} -2.96620e11 q^{78} -3.41655e12 q^{79} +3.46001e11 q^{80} +2.82430e11 q^{81} -1.65380e11 q^{82} +2.41715e12 q^{83} +2.84567e12 q^{84} -7.33189e11 q^{85} -6.14210e11 q^{86} +3.37314e12 q^{87} +1.28978e12 q^{88} +3.97254e12 q^{89} -5.51387e10 q^{90} -1.13218e13 q^{91} +9.45311e12 q^{92} +5.92698e12 q^{93} -5.55774e11 q^{94} -6.00014e11 q^{95} -2.48089e12 q^{96} -7.61457e12 q^{97} -2.65155e12 q^{98} +2.39477e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −17.8149 −0.196829 −0.0984144 0.995146i \(-0.531377\pi\)
−0.0984144 + 0.995146i \(0.531377\pi\)
\(3\) 729.000 0.577350
\(4\) −7874.63 −0.961258
\(5\) 5823.96 0.166691 0.0833457 0.996521i \(-0.473439\pi\)
0.0833457 + 0.996521i \(0.473439\pi\)
\(6\) −12987.1 −0.113639
\(7\) −495710. −1.59254 −0.796269 0.604942i \(-0.793196\pi\)
−0.796269 + 0.604942i \(0.793196\pi\)
\(8\) 286225. 0.386032
\(9\) 531441. 0.333333
\(10\) −103753. −0.0328097
\(11\) 4.50618e6 0.766930 0.383465 0.923555i \(-0.374731\pi\)
0.383465 + 0.923555i \(0.374731\pi\)
\(12\) −5.74060e6 −0.554983
\(13\) 2.28397e7 1.31237 0.656187 0.754598i \(-0.272168\pi\)
0.656187 + 0.754598i \(0.272168\pi\)
\(14\) 8.83102e6 0.313457
\(15\) 4.24566e6 0.0962393
\(16\) 5.94099e7 0.885276
\(17\) −1.25892e8 −1.26497 −0.632485 0.774573i \(-0.717965\pi\)
−0.632485 + 0.774573i \(0.717965\pi\)
\(18\) −9.46757e6 −0.0656096
\(19\) −1.03025e8 −0.502394 −0.251197 0.967936i \(-0.580824\pi\)
−0.251197 + 0.967936i \(0.580824\pi\)
\(20\) −4.58615e7 −0.160233
\(21\) −3.61372e8 −0.919453
\(22\) −8.02772e7 −0.150954
\(23\) −1.20045e9 −1.69088 −0.845442 0.534067i \(-0.820663\pi\)
−0.845442 + 0.534067i \(0.820663\pi\)
\(24\) 2.08658e8 0.222876
\(25\) −1.18678e9 −0.972214
\(26\) −4.06886e8 −0.258313
\(27\) 3.87420e8 0.192450
\(28\) 3.90353e9 1.53084
\(29\) 4.62707e9 1.44451 0.722253 0.691629i \(-0.243107\pi\)
0.722253 + 0.691629i \(0.243107\pi\)
\(30\) −7.56361e7 −0.0189427
\(31\) 8.13029e9 1.64534 0.822669 0.568521i \(-0.192484\pi\)
0.822669 + 0.568521i \(0.192484\pi\)
\(32\) −3.40314e9 −0.560280
\(33\) 3.28500e9 0.442788
\(34\) 2.24275e9 0.248982
\(35\) −2.88699e9 −0.265462
\(36\) −4.18490e9 −0.320419
\(37\) −7.22768e9 −0.463114 −0.231557 0.972821i \(-0.574382\pi\)
−0.231557 + 0.972821i \(0.574382\pi\)
\(38\) 1.83538e9 0.0988856
\(39\) 1.66501e10 0.757700
\(40\) 1.66696e9 0.0643482
\(41\) 9.28321e9 0.305213 0.152607 0.988287i \(-0.451233\pi\)
0.152607 + 0.988287i \(0.451233\pi\)
\(42\) 6.43781e9 0.180975
\(43\) 3.44773e10 0.831742 0.415871 0.909424i \(-0.363477\pi\)
0.415871 + 0.909424i \(0.363477\pi\)
\(44\) −3.54845e10 −0.737218
\(45\) 3.09509e9 0.0555638
\(46\) 2.13859e10 0.332815
\(47\) 3.11971e10 0.422161 0.211081 0.977469i \(-0.432302\pi\)
0.211081 + 0.977469i \(0.432302\pi\)
\(48\) 4.33098e10 0.511114
\(49\) 1.48839e11 1.53618
\(50\) 2.11425e10 0.191360
\(51\) −9.17753e10 −0.730331
\(52\) −1.79854e11 −1.26153
\(53\) 6.65705e10 0.412561 0.206281 0.978493i \(-0.433864\pi\)
0.206281 + 0.978493i \(0.433864\pi\)
\(54\) −6.90186e9 −0.0378797
\(55\) 2.62438e10 0.127841
\(56\) −1.41885e11 −0.614771
\(57\) −7.51053e10 −0.290057
\(58\) −8.24309e10 −0.284320
\(59\) 4.21805e10 0.130189
\(60\) −3.34330e10 −0.0925108
\(61\) 6.87416e11 1.70835 0.854173 0.519989i \(-0.174064\pi\)
0.854173 + 0.519989i \(0.174064\pi\)
\(62\) −1.44840e11 −0.323850
\(63\) −2.63440e11 −0.530846
\(64\) −4.26059e11 −0.774997
\(65\) 1.33017e11 0.218761
\(66\) −5.85220e10 −0.0871533
\(67\) 5.94901e11 0.803449 0.401724 0.915761i \(-0.368411\pi\)
0.401724 + 0.915761i \(0.368411\pi\)
\(68\) 9.91353e11 1.21596
\(69\) −8.75129e11 −0.976232
\(70\) 5.14315e10 0.0522506
\(71\) 6.97722e11 0.646403 0.323201 0.946330i \(-0.395241\pi\)
0.323201 + 0.946330i \(0.395241\pi\)
\(72\) 1.52112e11 0.128677
\(73\) −1.61175e12 −1.24652 −0.623258 0.782016i \(-0.714191\pi\)
−0.623258 + 0.782016i \(0.714191\pi\)
\(74\) 1.28760e11 0.0911541
\(75\) −8.65166e11 −0.561308
\(76\) 8.11284e11 0.482931
\(77\) −2.23376e12 −1.22137
\(78\) −2.96620e11 −0.149137
\(79\) −3.41655e12 −1.58129 −0.790645 0.612275i \(-0.790254\pi\)
−0.790645 + 0.612275i \(0.790254\pi\)
\(80\) 3.46001e11 0.147568
\(81\) 2.82430e11 0.111111
\(82\) −1.65380e11 −0.0600747
\(83\) 2.41715e12 0.811513 0.405757 0.913981i \(-0.367008\pi\)
0.405757 + 0.913981i \(0.367008\pi\)
\(84\) 2.84567e12 0.883832
\(85\) −7.33189e11 −0.210860
\(86\) −6.14210e11 −0.163711
\(87\) 3.37314e12 0.833986
\(88\) 1.28978e12 0.296060
\(89\) 3.97254e12 0.847292 0.423646 0.905828i \(-0.360750\pi\)
0.423646 + 0.905828i \(0.360750\pi\)
\(90\) −5.51387e10 −0.0109366
\(91\) −1.13218e13 −2.09001
\(92\) 9.45311e12 1.62538
\(93\) 5.92698e12 0.949936
\(94\) −5.55774e11 −0.0830935
\(95\) −6.00014e11 −0.0837448
\(96\) −2.48089e12 −0.323478
\(97\) −7.61457e12 −0.928174 −0.464087 0.885790i \(-0.653617\pi\)
−0.464087 + 0.885790i \(0.653617\pi\)
\(98\) −2.65155e12 −0.302364
\(99\) 2.39477e12 0.255643
\(100\) 9.34549e12 0.934549
\(101\) 2.64783e12 0.248200 0.124100 0.992270i \(-0.460396\pi\)
0.124100 + 0.992270i \(0.460396\pi\)
\(102\) 1.63497e12 0.143750
\(103\) −1.04265e13 −0.860394 −0.430197 0.902735i \(-0.641556\pi\)
−0.430197 + 0.902735i \(0.641556\pi\)
\(104\) 6.53729e12 0.506619
\(105\) −2.10462e12 −0.153265
\(106\) −1.18595e12 −0.0812039
\(107\) −6.83692e10 −0.00440419 −0.00220209 0.999998i \(-0.500701\pi\)
−0.00220209 + 0.999998i \(0.500701\pi\)
\(108\) −3.05079e12 −0.184994
\(109\) 1.22444e13 0.699301 0.349651 0.936880i \(-0.386300\pi\)
0.349651 + 0.936880i \(0.386300\pi\)
\(110\) −4.67531e11 −0.0251627
\(111\) −5.26898e12 −0.267379
\(112\) −2.94500e13 −1.40984
\(113\) −3.21032e13 −1.45057 −0.725286 0.688448i \(-0.758292\pi\)
−0.725286 + 0.688448i \(0.758292\pi\)
\(114\) 1.33799e12 0.0570916
\(115\) −6.99138e12 −0.281856
\(116\) −3.64365e13 −1.38854
\(117\) 1.21379e13 0.437458
\(118\) −7.51442e11 −0.0256249
\(119\) 6.24059e13 2.01451
\(120\) 1.21522e12 0.0371515
\(121\) −1.42171e13 −0.411818
\(122\) −1.22463e13 −0.336252
\(123\) 6.76746e12 0.176215
\(124\) −6.40230e13 −1.58159
\(125\) −1.40211e13 −0.328751
\(126\) 4.69317e12 0.104486
\(127\) −5.98520e13 −1.26577 −0.632884 0.774246i \(-0.718129\pi\)
−0.632884 + 0.774246i \(0.718129\pi\)
\(128\) 3.54687e13 0.712822
\(129\) 2.51340e13 0.480207
\(130\) −2.36969e12 −0.0430585
\(131\) 3.92221e13 0.678059 0.339029 0.940776i \(-0.389901\pi\)
0.339029 + 0.940776i \(0.389901\pi\)
\(132\) −2.58682e13 −0.425633
\(133\) 5.10705e13 0.800082
\(134\) −1.05981e13 −0.158142
\(135\) 2.25632e12 0.0320798
\(136\) −3.60335e13 −0.488319
\(137\) −1.30617e14 −1.68778 −0.843888 0.536520i \(-0.819739\pi\)
−0.843888 + 0.536520i \(0.819739\pi\)
\(138\) 1.55903e13 0.192151
\(139\) −3.81902e13 −0.449113 −0.224556 0.974461i \(-0.572093\pi\)
−0.224556 + 0.974461i \(0.572093\pi\)
\(140\) 2.27340e13 0.255178
\(141\) 2.27427e13 0.243735
\(142\) −1.24299e13 −0.127231
\(143\) 1.02920e14 1.00650
\(144\) 3.15728e13 0.295092
\(145\) 2.69479e13 0.240787
\(146\) 2.87131e13 0.245350
\(147\) 1.08504e14 0.886914
\(148\) 5.69153e13 0.445172
\(149\) −1.06117e14 −0.794464 −0.397232 0.917718i \(-0.630029\pi\)
−0.397232 + 0.917718i \(0.630029\pi\)
\(150\) 1.54129e13 0.110482
\(151\) 2.68008e14 1.83992 0.919958 0.392018i \(-0.128223\pi\)
0.919958 + 0.392018i \(0.128223\pi\)
\(152\) −2.94884e13 −0.193940
\(153\) −6.69042e13 −0.421657
\(154\) 3.97941e13 0.240400
\(155\) 4.73505e13 0.274264
\(156\) −1.31113e14 −0.728345
\(157\) −5.26124e13 −0.280376 −0.140188 0.990125i \(-0.544771\pi\)
−0.140188 + 0.990125i \(0.544771\pi\)
\(158\) 6.08655e13 0.311243
\(159\) 4.85299e13 0.238192
\(160\) −1.98197e13 −0.0933938
\(161\) 5.95075e14 2.69280
\(162\) −5.03146e12 −0.0218699
\(163\) −2.09132e14 −0.873375 −0.436687 0.899613i \(-0.643848\pi\)
−0.436687 + 0.899613i \(0.643848\pi\)
\(164\) −7.31018e13 −0.293389
\(165\) 1.91317e13 0.0738088
\(166\) −4.30613e13 −0.159729
\(167\) −6.41900e13 −0.228987 −0.114493 0.993424i \(-0.536524\pi\)
−0.114493 + 0.993424i \(0.536524\pi\)
\(168\) −1.03434e14 −0.354938
\(169\) 2.18775e14 0.722326
\(170\) 1.30617e13 0.0415032
\(171\) −5.47518e13 −0.167465
\(172\) −2.71496e14 −0.799519
\(173\) 3.25761e14 0.923846 0.461923 0.886920i \(-0.347160\pi\)
0.461923 + 0.886920i \(0.347160\pi\)
\(174\) −6.00921e13 −0.164152
\(175\) 5.88300e14 1.54829
\(176\) 2.67712e14 0.678945
\(177\) 3.07496e13 0.0751646
\(178\) −7.07704e13 −0.166772
\(179\) −3.21077e14 −0.729565 −0.364783 0.931093i \(-0.618857\pi\)
−0.364783 + 0.931093i \(0.618857\pi\)
\(180\) −2.43727e13 −0.0534112
\(181\) −4.10482e14 −0.867727 −0.433864 0.900979i \(-0.642850\pi\)
−0.433864 + 0.900979i \(0.642850\pi\)
\(182\) 2.01697e14 0.411373
\(183\) 5.01126e14 0.986314
\(184\) −3.43600e14 −0.652735
\(185\) −4.20937e13 −0.0771971
\(186\) −1.05589e14 −0.186975
\(187\) −5.67292e14 −0.970144
\(188\) −2.45666e14 −0.405806
\(189\) −1.92048e14 −0.306484
\(190\) 1.06892e13 0.0164834
\(191\) −1.00717e15 −1.50102 −0.750510 0.660859i \(-0.770192\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(192\) −3.10597e14 −0.447445
\(193\) 4.24901e14 0.591787 0.295893 0.955221i \(-0.404383\pi\)
0.295893 + 0.955221i \(0.404383\pi\)
\(194\) 1.35653e14 0.182691
\(195\) 9.69695e13 0.126302
\(196\) −1.17205e15 −1.47667
\(197\) −5.01772e14 −0.611612 −0.305806 0.952094i \(-0.598926\pi\)
−0.305806 + 0.952094i \(0.598926\pi\)
\(198\) −4.26626e13 −0.0503180
\(199\) −9.86515e14 −1.12605 −0.563026 0.826439i \(-0.690363\pi\)
−0.563026 + 0.826439i \(0.690363\pi\)
\(200\) −3.39688e14 −0.375306
\(201\) 4.33683e14 0.463871
\(202\) −4.71708e13 −0.0488528
\(203\) −2.29368e15 −2.30043
\(204\) 7.22696e14 0.702036
\(205\) 5.40650e13 0.0508764
\(206\) 1.85748e14 0.169350
\(207\) −6.37969e14 −0.563628
\(208\) 1.35690e15 1.16181
\(209\) −4.64249e14 −0.385301
\(210\) 3.74935e13 0.0301669
\(211\) −2.84359e13 −0.0221835 −0.0110918 0.999938i \(-0.503531\pi\)
−0.0110918 + 0.999938i \(0.503531\pi\)
\(212\) −5.24218e14 −0.396578
\(213\) 5.08640e14 0.373201
\(214\) 1.21799e12 0.000866870 0
\(215\) 2.00794e14 0.138644
\(216\) 1.10890e14 0.0742919
\(217\) −4.03026e15 −2.62026
\(218\) −2.18132e14 −0.137643
\(219\) −1.17496e15 −0.719677
\(220\) −2.06660e14 −0.122888
\(221\) −2.87533e15 −1.66011
\(222\) 9.38663e13 0.0526278
\(223\) −2.22345e15 −1.21073 −0.605364 0.795949i \(-0.706972\pi\)
−0.605364 + 0.795949i \(0.706972\pi\)
\(224\) 1.68697e15 0.892267
\(225\) −6.30706e14 −0.324071
\(226\) 5.71916e14 0.285514
\(227\) 2.23256e15 1.08301 0.541507 0.840696i \(-0.317854\pi\)
0.541507 + 0.840696i \(0.317854\pi\)
\(228\) 5.91426e14 0.278820
\(229\) 3.04475e15 1.39515 0.697575 0.716512i \(-0.254263\pi\)
0.697575 + 0.716512i \(0.254263\pi\)
\(230\) 1.24551e14 0.0554773
\(231\) −1.62841e15 −0.705156
\(232\) 1.32439e15 0.557626
\(233\) −4.29493e15 −1.75850 −0.879251 0.476359i \(-0.841956\pi\)
−0.879251 + 0.476359i \(0.841956\pi\)
\(234\) −2.16236e14 −0.0861043
\(235\) 1.81691e14 0.0703707
\(236\) −3.32156e14 −0.125145
\(237\) −2.49066e15 −0.912958
\(238\) −1.11175e15 −0.396514
\(239\) −5.94158e14 −0.206213 −0.103106 0.994670i \(-0.532878\pi\)
−0.103106 + 0.994670i \(0.532878\pi\)
\(240\) 2.52234e14 0.0851984
\(241\) −1.69537e15 −0.557384 −0.278692 0.960380i \(-0.589901\pi\)
−0.278692 + 0.960380i \(0.589901\pi\)
\(242\) 2.53276e14 0.0810576
\(243\) 2.05891e14 0.0641500
\(244\) −5.41315e15 −1.64216
\(245\) 8.66831e14 0.256068
\(246\) −1.20562e14 −0.0346842
\(247\) −2.35306e15 −0.659329
\(248\) 2.32710e15 0.635153
\(249\) 1.76210e15 0.468528
\(250\) 2.49785e14 0.0647077
\(251\) 6.00464e15 1.51568 0.757841 0.652439i \(-0.226254\pi\)
0.757841 + 0.652439i \(0.226254\pi\)
\(252\) 2.07450e15 0.510280
\(253\) −5.40945e15 −1.29679
\(254\) 1.06626e15 0.249140
\(255\) −5.34495e14 −0.121740
\(256\) 2.85840e15 0.634693
\(257\) −1.37803e15 −0.298326 −0.149163 0.988813i \(-0.547658\pi\)
−0.149163 + 0.988813i \(0.547658\pi\)
\(258\) −4.47759e14 −0.0945185
\(259\) 3.58283e15 0.737527
\(260\) −1.04746e15 −0.210286
\(261\) 2.45902e15 0.481502
\(262\) −6.98738e14 −0.133461
\(263\) −4.10341e15 −0.764597 −0.382299 0.924039i \(-0.624867\pi\)
−0.382299 + 0.924039i \(0.624867\pi\)
\(264\) 9.40252e14 0.170930
\(265\) 3.87703e14 0.0687704
\(266\) −9.09816e14 −0.157479
\(267\) 2.89598e15 0.489185
\(268\) −4.68462e15 −0.772322
\(269\) −2.14891e15 −0.345802 −0.172901 0.984939i \(-0.555314\pi\)
−0.172901 + 0.984939i \(0.555314\pi\)
\(270\) −4.01961e13 −0.00631422
\(271\) −6.32922e15 −0.970622 −0.485311 0.874342i \(-0.661294\pi\)
−0.485311 + 0.874342i \(0.661294\pi\)
\(272\) −7.47923e15 −1.11985
\(273\) −8.25362e15 −1.20667
\(274\) 2.32692e15 0.332203
\(275\) −5.34786e15 −0.745621
\(276\) 6.89132e15 0.938411
\(277\) −1.08935e16 −1.44893 −0.724464 0.689312i \(-0.757913\pi\)
−0.724464 + 0.689312i \(0.757913\pi\)
\(278\) 6.80355e14 0.0883984
\(279\) 4.32077e15 0.548446
\(280\) −8.26330e14 −0.102477
\(281\) 2.55877e15 0.310056 0.155028 0.987910i \(-0.450453\pi\)
0.155028 + 0.987910i \(0.450453\pi\)
\(282\) −4.05159e14 −0.0479741
\(283\) −1.77363e15 −0.205235 −0.102618 0.994721i \(-0.532722\pi\)
−0.102618 + 0.994721i \(0.532722\pi\)
\(284\) −5.49430e15 −0.621360
\(285\) −4.37410e14 −0.0483501
\(286\) −1.83350e15 −0.198108
\(287\) −4.60178e15 −0.486064
\(288\) −1.80857e15 −0.186760
\(289\) 5.94422e15 0.600148
\(290\) −4.80074e14 −0.0473937
\(291\) −5.55102e15 −0.535881
\(292\) 1.26919e16 1.19822
\(293\) 2.09932e16 1.93838 0.969192 0.246307i \(-0.0792171\pi\)
0.969192 + 0.246307i \(0.0792171\pi\)
\(294\) −1.93298e15 −0.174570
\(295\) 2.45658e14 0.0217014
\(296\) −2.06875e15 −0.178777
\(297\) 1.74579e15 0.147596
\(298\) 1.89046e15 0.156373
\(299\) −2.74179e16 −2.21907
\(300\) 6.81286e15 0.539562
\(301\) −1.70907e16 −1.32458
\(302\) −4.77454e15 −0.362148
\(303\) 1.93027e15 0.143298
\(304\) −6.12071e15 −0.444758
\(305\) 4.00348e15 0.284766
\(306\) 1.19189e15 0.0829941
\(307\) −3.18012e15 −0.216792 −0.108396 0.994108i \(-0.534571\pi\)
−0.108396 + 0.994108i \(0.534571\pi\)
\(308\) 1.75900e16 1.17405
\(309\) −7.60094e15 −0.496749
\(310\) −8.43544e14 −0.0539830
\(311\) −3.43922e15 −0.215535 −0.107767 0.994176i \(-0.534370\pi\)
−0.107767 + 0.994176i \(0.534370\pi\)
\(312\) 4.76569e15 0.292496
\(313\) 1.43474e16 0.862453 0.431227 0.902244i \(-0.358081\pi\)
0.431227 + 0.902244i \(0.358081\pi\)
\(314\) 9.37286e14 0.0551860
\(315\) −1.53427e15 −0.0884875
\(316\) 2.69040e16 1.52003
\(317\) −1.44462e15 −0.0799594 −0.0399797 0.999200i \(-0.512729\pi\)
−0.0399797 + 0.999200i \(0.512729\pi\)
\(318\) −8.64555e14 −0.0468831
\(319\) 2.08504e16 1.10784
\(320\) −2.48135e15 −0.129185
\(321\) −4.98411e13 −0.00254276
\(322\) −1.06012e16 −0.530020
\(323\) 1.29700e16 0.635513
\(324\) −2.22403e15 −0.106806
\(325\) −2.71058e16 −1.27591
\(326\) 3.72566e15 0.171905
\(327\) 8.92615e15 0.403742
\(328\) 2.65709e15 0.117822
\(329\) −1.54647e16 −0.672308
\(330\) −3.40830e14 −0.0145277
\(331\) 1.70816e16 0.713914 0.356957 0.934121i \(-0.383814\pi\)
0.356957 + 0.934121i \(0.383814\pi\)
\(332\) −1.90341e16 −0.780074
\(333\) −3.84109e15 −0.154371
\(334\) 1.14354e15 0.0450712
\(335\) 3.46468e15 0.133928
\(336\) −2.14691e16 −0.813970
\(337\) −2.15042e16 −0.799705 −0.399852 0.916580i \(-0.630939\pi\)
−0.399852 + 0.916580i \(0.630939\pi\)
\(338\) −3.89745e15 −0.142175
\(339\) −2.34033e16 −0.837488
\(340\) 5.77360e15 0.202690
\(341\) 3.66365e16 1.26186
\(342\) 9.75397e14 0.0329619
\(343\) −2.57521e16 −0.853886
\(344\) 9.86829e15 0.321079
\(345\) −5.09671e15 −0.162729
\(346\) −5.80341e15 −0.181840
\(347\) −5.59137e16 −1.71940 −0.859699 0.510801i \(-0.829349\pi\)
−0.859699 + 0.510801i \(0.829349\pi\)
\(348\) −2.65622e16 −0.801676
\(349\) 1.77625e16 0.526184 0.263092 0.964771i \(-0.415258\pi\)
0.263092 + 0.964771i \(0.415258\pi\)
\(350\) −1.04805e16 −0.304748
\(351\) 8.84855e15 0.252567
\(352\) −1.53352e16 −0.429696
\(353\) −3.20503e16 −0.881651 −0.440825 0.897593i \(-0.645314\pi\)
−0.440825 + 0.897593i \(0.645314\pi\)
\(354\) −5.47801e14 −0.0147946
\(355\) 4.06350e15 0.107750
\(356\) −3.12823e16 −0.814467
\(357\) 4.54939e16 1.16308
\(358\) 5.71995e15 0.143599
\(359\) −5.13535e16 −1.26606 −0.633032 0.774125i \(-0.718190\pi\)
−0.633032 + 0.774125i \(0.718190\pi\)
\(360\) 8.85893e14 0.0214494
\(361\) −3.14388e16 −0.747600
\(362\) 7.31270e15 0.170794
\(363\) −1.03642e16 −0.237763
\(364\) 8.91552e16 2.00904
\(365\) −9.38674e15 −0.207783
\(366\) −8.92752e15 −0.194135
\(367\) −4.56541e16 −0.975327 −0.487663 0.873032i \(-0.662151\pi\)
−0.487663 + 0.873032i \(0.662151\pi\)
\(368\) −7.13187e16 −1.49690
\(369\) 4.93348e15 0.101738
\(370\) 7.49895e14 0.0151946
\(371\) −3.29996e16 −0.657020
\(372\) −4.66728e16 −0.913134
\(373\) 2.56728e16 0.493589 0.246795 0.969068i \(-0.420623\pi\)
0.246795 + 0.969068i \(0.420623\pi\)
\(374\) 1.01063e16 0.190952
\(375\) −1.02214e16 −0.189804
\(376\) 8.92941e15 0.162968
\(377\) 1.05681e17 1.89573
\(378\) 3.42132e15 0.0603249
\(379\) 2.01093e16 0.348532 0.174266 0.984699i \(-0.444245\pi\)
0.174266 + 0.984699i \(0.444245\pi\)
\(380\) 4.72488e15 0.0805004
\(381\) −4.36321e16 −0.730792
\(382\) 1.79427e16 0.295444
\(383\) −1.79861e16 −0.291170 −0.145585 0.989346i \(-0.546506\pi\)
−0.145585 + 0.989346i \(0.546506\pi\)
\(384\) 2.58567e16 0.411548
\(385\) −1.30093e16 −0.203591
\(386\) −7.56957e15 −0.116481
\(387\) 1.83227e16 0.277247
\(388\) 5.99619e16 0.892215
\(389\) 2.11128e16 0.308940 0.154470 0.987998i \(-0.450633\pi\)
0.154470 + 0.987998i \(0.450633\pi\)
\(390\) −1.72750e15 −0.0248599
\(391\) 1.51127e17 2.13892
\(392\) 4.26015e16 0.593015
\(393\) 2.85929e16 0.391477
\(394\) 8.93902e15 0.120383
\(395\) −1.98978e16 −0.263587
\(396\) −1.88579e16 −0.245739
\(397\) 1.03371e17 1.32514 0.662569 0.749001i \(-0.269466\pi\)
0.662569 + 0.749001i \(0.269466\pi\)
\(398\) 1.75747e16 0.221639
\(399\) 3.72304e16 0.461928
\(400\) −7.05067e16 −0.860678
\(401\) −5.08166e16 −0.610334 −0.305167 0.952299i \(-0.598712\pi\)
−0.305167 + 0.952299i \(0.598712\pi\)
\(402\) −7.72601e15 −0.0913032
\(403\) 1.85693e17 2.15930
\(404\) −2.08507e16 −0.238584
\(405\) 1.64486e15 0.0185213
\(406\) 4.08618e16 0.452791
\(407\) −3.25692e16 −0.355176
\(408\) −2.62684e16 −0.281931
\(409\) 1.31002e16 0.138381 0.0691903 0.997603i \(-0.477958\pi\)
0.0691903 + 0.997603i \(0.477958\pi\)
\(410\) −9.63163e14 −0.0100139
\(411\) −9.52195e16 −0.974438
\(412\) 8.21050e16 0.827061
\(413\) −2.09093e16 −0.207331
\(414\) 1.13654e16 0.110938
\(415\) 1.40774e16 0.135272
\(416\) −7.77266e16 −0.735297
\(417\) −2.78406e16 −0.259296
\(418\) 8.27056e15 0.0758384
\(419\) 2.02887e17 1.83174 0.915868 0.401480i \(-0.131504\pi\)
0.915868 + 0.401480i \(0.131504\pi\)
\(420\) 1.65731e16 0.147327
\(421\) 6.73135e16 0.589208 0.294604 0.955619i \(-0.404812\pi\)
0.294604 + 0.955619i \(0.404812\pi\)
\(422\) 5.06582e14 0.00436636
\(423\) 1.65794e16 0.140720
\(424\) 1.90542e16 0.159262
\(425\) 1.49407e17 1.22982
\(426\) −9.06137e15 −0.0734567
\(427\) −3.40759e17 −2.72061
\(428\) 5.38382e14 0.00423356
\(429\) 7.50284e16 0.581103
\(430\) −3.57713e15 −0.0272892
\(431\) −1.62884e17 −1.22399 −0.611993 0.790863i \(-0.709632\pi\)
−0.611993 + 0.790863i \(0.709632\pi\)
\(432\) 2.30166e16 0.170371
\(433\) −1.79440e17 −1.30842 −0.654210 0.756313i \(-0.726999\pi\)
−0.654210 + 0.756313i \(0.726999\pi\)
\(434\) 7.17988e16 0.515743
\(435\) 1.96450e16 0.139018
\(436\) −9.64199e16 −0.672209
\(437\) 1.23677e17 0.849490
\(438\) 2.09319e16 0.141653
\(439\) 7.31787e16 0.487939 0.243969 0.969783i \(-0.421550\pi\)
0.243969 + 0.969783i \(0.421550\pi\)
\(440\) 7.51164e15 0.0493506
\(441\) 7.90991e16 0.512060
\(442\) 5.12237e16 0.326758
\(443\) 1.60047e17 1.00606 0.503030 0.864269i \(-0.332219\pi\)
0.503030 + 0.864269i \(0.332219\pi\)
\(444\) 4.14912e16 0.257020
\(445\) 2.31359e16 0.141236
\(446\) 3.96106e16 0.238306
\(447\) −7.73593e16 −0.458684
\(448\) 2.11202e17 1.23421
\(449\) 1.47310e17 0.848458 0.424229 0.905555i \(-0.360545\pi\)
0.424229 + 0.905555i \(0.360545\pi\)
\(450\) 1.12360e16 0.0637866
\(451\) 4.18318e16 0.234077
\(452\) 2.52801e17 1.39437
\(453\) 1.95378e17 1.06228
\(454\) −3.97728e16 −0.213168
\(455\) −6.59379e16 −0.348386
\(456\) −2.14970e16 −0.111971
\(457\) −1.44949e17 −0.744321 −0.372161 0.928168i \(-0.621383\pi\)
−0.372161 + 0.928168i \(0.621383\pi\)
\(458\) −5.42419e16 −0.274606
\(459\) −4.87731e16 −0.243444
\(460\) 5.50545e16 0.270936
\(461\) 3.92089e17 1.90252 0.951258 0.308395i \(-0.0997918\pi\)
0.951258 + 0.308395i \(0.0997918\pi\)
\(462\) 2.90099e16 0.138795
\(463\) −1.53392e17 −0.723648 −0.361824 0.932246i \(-0.617846\pi\)
−0.361824 + 0.932246i \(0.617846\pi\)
\(464\) 2.74894e17 1.27879
\(465\) 3.45185e16 0.158346
\(466\) 7.65138e16 0.346124
\(467\) −3.07378e17 −1.37124 −0.685620 0.727959i \(-0.740469\pi\)
−0.685620 + 0.727959i \(0.740469\pi\)
\(468\) −9.55817e16 −0.420510
\(469\) −2.94898e17 −1.27952
\(470\) −3.23680e15 −0.0138510
\(471\) −3.83545e16 −0.161875
\(472\) 1.20731e16 0.0502571
\(473\) 1.55361e17 0.637888
\(474\) 4.43709e16 0.179696
\(475\) 1.22269e17 0.488435
\(476\) −4.91423e17 −1.93647
\(477\) 3.53783e16 0.137520
\(478\) 1.05849e16 0.0405886
\(479\) 3.09329e17 1.17015 0.585073 0.810981i \(-0.301066\pi\)
0.585073 + 0.810981i \(0.301066\pi\)
\(480\) −1.44486e16 −0.0539209
\(481\) −1.65078e17 −0.607779
\(482\) 3.02029e16 0.109709
\(483\) 4.33810e17 1.55469
\(484\) 1.11954e17 0.395863
\(485\) −4.43469e16 −0.154719
\(486\) −3.66793e15 −0.0126266
\(487\) −4.72135e17 −1.60372 −0.801858 0.597514i \(-0.796155\pi\)
−0.801858 + 0.597514i \(0.796155\pi\)
\(488\) 1.96756e17 0.659476
\(489\) −1.52457e17 −0.504243
\(490\) −1.54425e16 −0.0504015
\(491\) −4.75203e17 −1.53056 −0.765278 0.643700i \(-0.777398\pi\)
−0.765278 + 0.643700i \(0.777398\pi\)
\(492\) −5.32912e16 −0.169388
\(493\) −5.82511e17 −1.82726
\(494\) 4.19195e16 0.129775
\(495\) 1.39470e16 0.0426136
\(496\) 4.83020e17 1.45658
\(497\) −3.45868e17 −1.02942
\(498\) −3.13917e16 −0.0922197
\(499\) −9.98967e16 −0.289666 −0.144833 0.989456i \(-0.546264\pi\)
−0.144833 + 0.989456i \(0.546264\pi\)
\(500\) 1.10411e17 0.316015
\(501\) −4.67945e16 −0.132206
\(502\) −1.06972e17 −0.298330
\(503\) −1.48123e17 −0.407786 −0.203893 0.978993i \(-0.565359\pi\)
−0.203893 + 0.978993i \(0.565359\pi\)
\(504\) −7.54033e16 −0.204924
\(505\) 1.54208e16 0.0413727
\(506\) 9.63688e16 0.255246
\(507\) 1.59487e17 0.417035
\(508\) 4.71312e17 1.21673
\(509\) 4.66800e17 1.18978 0.594888 0.803809i \(-0.297196\pi\)
0.594888 + 0.803809i \(0.297196\pi\)
\(510\) 9.52198e15 0.0239619
\(511\) 7.98958e17 1.98513
\(512\) −3.41482e17 −0.837747
\(513\) −3.99140e16 −0.0966858
\(514\) 2.45494e16 0.0587192
\(515\) −6.07236e16 −0.143420
\(516\) −1.97921e17 −0.461603
\(517\) 1.40580e17 0.323768
\(518\) −6.38278e16 −0.145166
\(519\) 2.37480e17 0.533383
\(520\) 3.80729e16 0.0844489
\(521\) −2.93718e17 −0.643406 −0.321703 0.946841i \(-0.604255\pi\)
−0.321703 + 0.946841i \(0.604255\pi\)
\(522\) −4.38071e16 −0.0947734
\(523\) 2.20371e17 0.470861 0.235431 0.971891i \(-0.424350\pi\)
0.235431 + 0.971891i \(0.424350\pi\)
\(524\) −3.08859e17 −0.651790
\(525\) 4.28871e17 0.893905
\(526\) 7.31019e16 0.150495
\(527\) −1.02354e18 −2.08130
\(528\) 1.95162e17 0.391989
\(529\) 9.37048e17 1.85909
\(530\) −6.90690e15 −0.0135360
\(531\) 2.24165e16 0.0433963
\(532\) −4.02161e17 −0.769086
\(533\) 2.12025e17 0.400554
\(534\) −5.15917e16 −0.0962856
\(535\) −3.98179e14 −0.000734140 0
\(536\) 1.70276e17 0.310157
\(537\) −2.34065e17 −0.421215
\(538\) 3.82826e16 0.0680639
\(539\) 6.70695e17 1.17814
\(540\) −1.77677e16 −0.0308369
\(541\) −1.02405e17 −0.175606 −0.0878029 0.996138i \(-0.527985\pi\)
−0.0878029 + 0.996138i \(0.527985\pi\)
\(542\) 1.12755e17 0.191046
\(543\) −2.99241e17 −0.500983
\(544\) 4.28428e17 0.708737
\(545\) 7.13107e16 0.116567
\(546\) 1.47037e17 0.237507
\(547\) −4.00721e17 −0.639624 −0.319812 0.947481i \(-0.603620\pi\)
−0.319812 + 0.947481i \(0.603620\pi\)
\(548\) 1.02856e18 1.62239
\(549\) 3.65321e17 0.569449
\(550\) 9.52717e16 0.146760
\(551\) −4.76705e17 −0.725711
\(552\) −2.50484e17 −0.376857
\(553\) 1.69361e18 2.51826
\(554\) 1.94066e17 0.285191
\(555\) −3.06863e16 −0.0445697
\(556\) 3.00734e17 0.431714
\(557\) 4.72473e17 0.670376 0.335188 0.942151i \(-0.391200\pi\)
0.335188 + 0.942151i \(0.391200\pi\)
\(558\) −7.69741e16 −0.107950
\(559\) 7.87450e17 1.09156
\(560\) −1.71516e17 −0.235008
\(561\) −4.13556e17 −0.560113
\(562\) −4.55842e16 −0.0610278
\(563\) −1.37459e18 −1.81915 −0.909574 0.415542i \(-0.863592\pi\)
−0.909574 + 0.415542i \(0.863592\pi\)
\(564\) −1.79090e17 −0.234292
\(565\) −1.86968e17 −0.241798
\(566\) 3.15971e16 0.0403962
\(567\) −1.40003e17 −0.176949
\(568\) 1.99706e17 0.249532
\(569\) 5.06442e17 0.625605 0.312802 0.949818i \(-0.398732\pi\)
0.312802 + 0.949818i \(0.398732\pi\)
\(570\) 7.79242e15 0.00951668
\(571\) −1.25224e18 −1.51200 −0.756002 0.654569i \(-0.772850\pi\)
−0.756002 + 0.654569i \(0.772850\pi\)
\(572\) −8.10453e17 −0.967506
\(573\) −7.34228e17 −0.866614
\(574\) 8.19802e16 0.0956713
\(575\) 1.42468e18 1.64390
\(576\) −2.26425e17 −0.258332
\(577\) 3.91117e17 0.441229 0.220615 0.975361i \(-0.429194\pi\)
0.220615 + 0.975361i \(0.429194\pi\)
\(578\) −1.05896e17 −0.118126
\(579\) 3.09753e17 0.341668
\(580\) −2.12204e17 −0.231458
\(581\) −1.19820e18 −1.29237
\(582\) 9.88910e16 0.105477
\(583\) 2.99978e17 0.316406
\(584\) −4.61323e17 −0.481195
\(585\) 7.06908e16 0.0729205
\(586\) −3.73992e17 −0.381530
\(587\) −1.38275e17 −0.139507 −0.0697537 0.997564i \(-0.522221\pi\)
−0.0697537 + 0.997564i \(0.522221\pi\)
\(588\) −8.54425e17 −0.852553
\(589\) −8.37624e17 −0.826608
\(590\) −4.37637e15 −0.00427145
\(591\) −3.65792e17 −0.353114
\(592\) −4.29396e17 −0.409984
\(593\) −7.41382e17 −0.700143 −0.350072 0.936723i \(-0.613843\pi\)
−0.350072 + 0.936723i \(0.613843\pi\)
\(594\) −3.11010e16 −0.0290511
\(595\) 3.63449e17 0.335802
\(596\) 8.35632e17 0.763685
\(597\) −7.19169e17 −0.650127
\(598\) 4.88447e17 0.436777
\(599\) −5.07866e17 −0.449236 −0.224618 0.974447i \(-0.572113\pi\)
−0.224618 + 0.974447i \(0.572113\pi\)
\(600\) −2.47633e17 −0.216683
\(601\) 4.57309e17 0.395845 0.197923 0.980218i \(-0.436580\pi\)
0.197923 + 0.980218i \(0.436580\pi\)
\(602\) 3.04470e17 0.260716
\(603\) 3.16155e17 0.267816
\(604\) −2.11046e18 −1.76863
\(605\) −8.27995e16 −0.0686464
\(606\) −3.43875e16 −0.0282052
\(607\) 1.23098e17 0.0998904 0.0499452 0.998752i \(-0.484095\pi\)
0.0499452 + 0.998752i \(0.484095\pi\)
\(608\) 3.50609e17 0.281481
\(609\) −1.67210e18 −1.32815
\(610\) −7.13216e16 −0.0560502
\(611\) 7.12532e17 0.554034
\(612\) 5.26846e17 0.405321
\(613\) 1.47113e18 1.11985 0.559923 0.828545i \(-0.310831\pi\)
0.559923 + 0.828545i \(0.310831\pi\)
\(614\) 5.66535e16 0.0426709
\(615\) 3.94134e16 0.0293735
\(616\) −6.39358e17 −0.471487
\(617\) −2.51258e18 −1.83344 −0.916719 0.399532i \(-0.869172\pi\)
−0.916719 + 0.399532i \(0.869172\pi\)
\(618\) 1.35410e17 0.0977745
\(619\) −2.12558e18 −1.51876 −0.759379 0.650649i \(-0.774497\pi\)
−0.759379 + 0.650649i \(0.774497\pi\)
\(620\) −3.72867e17 −0.263638
\(621\) −4.65080e17 −0.325411
\(622\) 6.12694e16 0.0424235
\(623\) −1.96923e18 −1.34935
\(624\) 9.89181e17 0.670774
\(625\) 1.36705e18 0.917414
\(626\) −2.55598e17 −0.169756
\(627\) −3.38438e17 −0.222454
\(628\) 4.14303e17 0.269514
\(629\) 9.09907e17 0.585825
\(630\) 2.73328e16 0.0174169
\(631\) −5.79679e16 −0.0365592 −0.0182796 0.999833i \(-0.505819\pi\)
−0.0182796 + 0.999833i \(0.505819\pi\)
\(632\) −9.77903e17 −0.610428
\(633\) −2.07297e16 −0.0128077
\(634\) 2.57358e16 0.0157383
\(635\) −3.48575e17 −0.210993
\(636\) −3.82155e17 −0.228964
\(637\) 3.39943e18 2.01604
\(638\) −3.71448e17 −0.218054
\(639\) 3.70798e17 0.215468
\(640\) 2.06568e17 0.118821
\(641\) 8.34332e17 0.475075 0.237537 0.971378i \(-0.423660\pi\)
0.237537 + 0.971378i \(0.423660\pi\)
\(642\) 8.87915e14 0.000500488 0
\(643\) 2.66018e18 1.48436 0.742180 0.670201i \(-0.233792\pi\)
0.742180 + 0.670201i \(0.233792\pi\)
\(644\) −4.68600e18 −2.58847
\(645\) 1.46379e17 0.0800463
\(646\) −2.31060e17 −0.125087
\(647\) 3.58040e18 1.91891 0.959453 0.281869i \(-0.0909544\pi\)
0.959453 + 0.281869i \(0.0909544\pi\)
\(648\) 8.08385e16 0.0428925
\(649\) 1.90073e17 0.0998458
\(650\) 4.82886e17 0.251136
\(651\) −2.93806e18 −1.51281
\(652\) 1.64684e18 0.839539
\(653\) −1.59955e18 −0.807352 −0.403676 0.914902i \(-0.632268\pi\)
−0.403676 + 0.914902i \(0.632268\pi\)
\(654\) −1.59019e17 −0.0794680
\(655\) 2.28428e17 0.113027
\(656\) 5.51514e17 0.270198
\(657\) −8.56548e17 −0.415505
\(658\) 2.75502e17 0.132330
\(659\) 1.68722e18 0.802447 0.401223 0.915980i \(-0.368585\pi\)
0.401223 + 0.915980i \(0.368585\pi\)
\(660\) −1.50655e17 −0.0709494
\(661\) −2.36990e18 −1.10515 −0.552575 0.833463i \(-0.686355\pi\)
−0.552575 + 0.833463i \(0.686355\pi\)
\(662\) −3.04307e17 −0.140519
\(663\) −2.09612e18 −0.958467
\(664\) 6.91850e17 0.313270
\(665\) 2.97432e17 0.133367
\(666\) 6.84286e16 0.0303847
\(667\) −5.55458e18 −2.44249
\(668\) 5.05473e17 0.220115
\(669\) −1.62090e18 −0.699014
\(670\) −6.17229e16 −0.0263609
\(671\) 3.09762e18 1.31018
\(672\) 1.22980e18 0.515151
\(673\) 2.89363e18 1.20045 0.600226 0.799831i \(-0.295077\pi\)
0.600226 + 0.799831i \(0.295077\pi\)
\(674\) 3.83096e17 0.157405
\(675\) −4.59785e17 −0.187103
\(676\) −1.72277e18 −0.694342
\(677\) −2.12791e18 −0.849428 −0.424714 0.905328i \(-0.639625\pi\)
−0.424714 + 0.905328i \(0.639625\pi\)
\(678\) 4.16927e17 0.164842
\(679\) 3.77462e18 1.47815
\(680\) −2.09858e17 −0.0813985
\(681\) 1.62753e18 0.625279
\(682\) −6.52677e17 −0.248370
\(683\) −5.01423e18 −1.89004 −0.945018 0.327019i \(-0.893956\pi\)
−0.945018 + 0.327019i \(0.893956\pi\)
\(684\) 4.31150e17 0.160977
\(685\) −7.60705e17 −0.281338
\(686\) 4.58770e17 0.168069
\(687\) 2.21962e18 0.805490
\(688\) 2.04829e18 0.736322
\(689\) 1.52045e18 0.541435
\(690\) 9.07975e16 0.0320298
\(691\) −2.64832e18 −0.925473 −0.462736 0.886496i \(-0.653132\pi\)
−0.462736 + 0.886496i \(0.653132\pi\)
\(692\) −2.56525e18 −0.888055
\(693\) −1.18711e18 −0.407122
\(694\) 9.96097e17 0.338427
\(695\) −2.22418e17 −0.0748632
\(696\) 9.65478e17 0.321945
\(697\) −1.16868e18 −0.386085
\(698\) −3.16437e17 −0.103568
\(699\) −3.13101e18 −1.01527
\(700\) −4.63265e18 −1.48831
\(701\) 3.12315e18 0.994090 0.497045 0.867725i \(-0.334418\pi\)
0.497045 + 0.867725i \(0.334418\pi\)
\(702\) −1.57636e17 −0.0497124
\(703\) 7.44632e17 0.232666
\(704\) −1.91990e18 −0.594369
\(705\) 1.32453e17 0.0406285
\(706\) 5.70973e17 0.173534
\(707\) −1.31255e18 −0.395268
\(708\) −2.42142e17 −0.0722526
\(709\) 3.53911e18 1.04639 0.523195 0.852213i \(-0.324740\pi\)
0.523195 + 0.852213i \(0.324740\pi\)
\(710\) −7.23909e16 −0.0212083
\(711\) −1.81569e18 −0.527096
\(712\) 1.13704e18 0.327082
\(713\) −9.76002e18 −2.78208
\(714\) −8.10469e17 −0.228928
\(715\) 5.99399e17 0.167775
\(716\) 2.52836e18 0.701301
\(717\) −4.33141e17 −0.119057
\(718\) 9.14857e17 0.249198
\(719\) −3.87900e18 −1.04708 −0.523542 0.852000i \(-0.675390\pi\)
−0.523542 + 0.852000i \(0.675390\pi\)
\(720\) 1.83879e17 0.0491893
\(721\) 5.16853e18 1.37021
\(722\) 5.60080e17 0.147149
\(723\) −1.23593e18 −0.321806
\(724\) 3.23239e18 0.834110
\(725\) −5.49134e18 −1.40437
\(726\) 1.84638e17 0.0467986
\(727\) −5.85872e18 −1.47173 −0.735866 0.677127i \(-0.763225\pi\)
−0.735866 + 0.677127i \(0.763225\pi\)
\(728\) −3.24060e18 −0.806810
\(729\) 1.50095e17 0.0370370
\(730\) 1.67224e17 0.0408978
\(731\) −4.34042e18 −1.05213
\(732\) −3.94618e18 −0.948103
\(733\) −2.14921e17 −0.0511804 −0.0255902 0.999673i \(-0.508146\pi\)
−0.0255902 + 0.999673i \(0.508146\pi\)
\(734\) 8.13323e17 0.191972
\(735\) 6.31920e17 0.147841
\(736\) 4.08531e18 0.947368
\(737\) 2.68073e18 0.616189
\(738\) −8.78895e16 −0.0200249
\(739\) −4.67683e17 −0.105624 −0.0528121 0.998604i \(-0.516818\pi\)
−0.0528121 + 0.998604i \(0.516818\pi\)
\(740\) 3.31472e17 0.0742063
\(741\) −1.71538e18 −0.380664
\(742\) 5.87885e17 0.129320
\(743\) 2.89660e18 0.631629 0.315814 0.948821i \(-0.397722\pi\)
0.315814 + 0.948821i \(0.397722\pi\)
\(744\) 1.69645e18 0.366706
\(745\) −6.18021e17 −0.132430
\(746\) −4.57358e17 −0.0971526
\(747\) 1.28457e18 0.270504
\(748\) 4.46721e18 0.932559
\(749\) 3.38912e16 0.00701384
\(750\) 1.82093e17 0.0373590
\(751\) −2.86710e18 −0.583154 −0.291577 0.956547i \(-0.594180\pi\)
−0.291577 + 0.956547i \(0.594180\pi\)
\(752\) 1.85342e18 0.373729
\(753\) 4.37739e18 0.875079
\(754\) −1.88269e18 −0.373135
\(755\) 1.56087e18 0.306698
\(756\) 1.51231e18 0.294611
\(757\) 3.95257e18 0.763407 0.381703 0.924285i \(-0.375338\pi\)
0.381703 + 0.924285i \(0.375338\pi\)
\(758\) −3.58245e17 −0.0686011
\(759\) −3.94349e18 −0.748702
\(760\) −1.71739e17 −0.0323282
\(761\) 1.05752e18 0.197373 0.0986866 0.995119i \(-0.468536\pi\)
0.0986866 + 0.995119i \(0.468536\pi\)
\(762\) 7.77301e17 0.143841
\(763\) −6.06965e18 −1.11366
\(764\) 7.93110e18 1.44287
\(765\) −3.89647e17 −0.0702865
\(766\) 3.20421e17 0.0573106
\(767\) 9.63389e17 0.170857
\(768\) 2.08378e18 0.366440
\(769\) −2.34180e18 −0.408346 −0.204173 0.978935i \(-0.565450\pi\)
−0.204173 + 0.978935i \(0.565450\pi\)
\(770\) 2.31759e17 0.0400726
\(771\) −1.00458e18 −0.172239
\(772\) −3.34594e18 −0.568860
\(773\) 6.14843e18 1.03657 0.518284 0.855209i \(-0.326571\pi\)
0.518284 + 0.855209i \(0.326571\pi\)
\(774\) −3.26417e17 −0.0545703
\(775\) −9.64891e18 −1.59962
\(776\) −2.17948e18 −0.358305
\(777\) 2.61188e18 0.425811
\(778\) −3.76123e17 −0.0608082
\(779\) −9.56404e17 −0.153337
\(780\) −7.63599e17 −0.121409
\(781\) 3.14406e18 0.495746
\(782\) −2.69232e18 −0.421000
\(783\) 1.79262e18 0.277995
\(784\) 8.84250e18 1.35994
\(785\) −3.06412e17 −0.0467362
\(786\) −5.09380e17 −0.0770540
\(787\) 1.71869e18 0.257847 0.128924 0.991655i \(-0.458848\pi\)
0.128924 + 0.991655i \(0.458848\pi\)
\(788\) 3.95127e18 0.587917
\(789\) −2.99139e18 −0.441440
\(790\) 3.54478e17 0.0518815
\(791\) 1.59139e19 2.31009
\(792\) 6.85444e17 0.0986866
\(793\) 1.57003e19 2.24199
\(794\) −1.84155e18 −0.260825
\(795\) 2.82636e17 0.0397046
\(796\) 7.76844e18 1.08243
\(797\) −5.26477e18 −0.727613 −0.363806 0.931475i \(-0.618523\pi\)
−0.363806 + 0.931475i \(0.618523\pi\)
\(798\) −6.63256e17 −0.0909206
\(799\) −3.92747e18 −0.534021
\(800\) 4.03880e18 0.544712
\(801\) 2.11117e18 0.282431
\(802\) 9.05293e17 0.120131
\(803\) −7.26282e18 −0.955991
\(804\) −3.41509e18 −0.445900
\(805\) 3.46569e18 0.448866
\(806\) −3.30810e18 −0.425012
\(807\) −1.56655e18 −0.199649
\(808\) 7.57877e17 0.0958130
\(809\) 3.65111e18 0.457888 0.228944 0.973440i \(-0.426473\pi\)
0.228944 + 0.973440i \(0.426473\pi\)
\(810\) −2.93030e16 −0.00364552
\(811\) 3.66951e18 0.452869 0.226434 0.974026i \(-0.427293\pi\)
0.226434 + 0.974026i \(0.427293\pi\)
\(812\) 1.80619e19 2.21131
\(813\) −4.61400e18 −0.560389
\(814\) 5.80218e17 0.0699089
\(815\) −1.21797e18 −0.145584
\(816\) −5.45236e18 −0.646544
\(817\) −3.55203e18 −0.417862
\(818\) −2.33378e17 −0.0272373
\(819\) −6.01689e18 −0.696669
\(820\) −4.25742e17 −0.0489054
\(821\) −5.29791e18 −0.603774 −0.301887 0.953344i \(-0.597616\pi\)
−0.301887 + 0.953344i \(0.597616\pi\)
\(822\) 1.69633e18 0.191797
\(823\) 1.46955e19 1.64848 0.824241 0.566239i \(-0.191602\pi\)
0.824241 + 0.566239i \(0.191602\pi\)
\(824\) −2.98434e18 −0.332140
\(825\) −3.89859e18 −0.430484
\(826\) 3.72497e17 0.0408087
\(827\) −1.44513e19 −1.57081 −0.785403 0.618985i \(-0.787544\pi\)
−0.785403 + 0.618985i \(0.787544\pi\)
\(828\) 5.02377e18 0.541792
\(829\) 3.73464e18 0.399618 0.199809 0.979835i \(-0.435968\pi\)
0.199809 + 0.979835i \(0.435968\pi\)
\(830\) −2.50787e17 −0.0266255
\(831\) −7.94133e18 −0.836539
\(832\) −9.73104e18 −1.01709
\(833\) −1.87376e19 −1.94322
\(834\) 4.95979e17 0.0510368
\(835\) −3.73840e17 −0.0381701
\(836\) 3.65579e18 0.370374
\(837\) 3.14984e18 0.316645
\(838\) −3.61441e18 −0.360538
\(839\) −1.12147e18 −0.111003 −0.0555016 0.998459i \(-0.517676\pi\)
−0.0555016 + 0.998459i \(0.517676\pi\)
\(840\) −6.02395e17 −0.0591651
\(841\) 1.11492e19 1.08660
\(842\) −1.19918e18 −0.115973
\(843\) 1.86534e18 0.179011
\(844\) 2.23922e17 0.0213241
\(845\) 1.27413e18 0.120406
\(846\) −2.95361e17 −0.0276978
\(847\) 7.04753e18 0.655836
\(848\) 3.95494e18 0.365231
\(849\) −1.29298e18 −0.118493
\(850\) −2.66167e18 −0.242064
\(851\) 8.67648e18 0.783071
\(852\) −4.00535e18 −0.358743
\(853\) 2.67783e18 0.238020 0.119010 0.992893i \(-0.462028\pi\)
0.119010 + 0.992893i \(0.462028\pi\)
\(854\) 6.07058e18 0.535494
\(855\) −3.18872e17 −0.0279149
\(856\) −1.95690e16 −0.00170016
\(857\) −6.61516e18 −0.570381 −0.285191 0.958471i \(-0.592057\pi\)
−0.285191 + 0.958471i \(0.592057\pi\)
\(858\) −1.33662e18 −0.114378
\(859\) 2.83552e18 0.240811 0.120406 0.992725i \(-0.461580\pi\)
0.120406 + 0.992725i \(0.461580\pi\)
\(860\) −1.58118e18 −0.133273
\(861\) −3.35469e18 −0.280629
\(862\) 2.90176e18 0.240916
\(863\) −8.70517e18 −0.717311 −0.358655 0.933470i \(-0.616765\pi\)
−0.358655 + 0.933470i \(0.616765\pi\)
\(864\) −1.31845e18 −0.107826
\(865\) 1.89722e18 0.153997
\(866\) 3.19670e18 0.257535
\(867\) 4.33333e18 0.346496
\(868\) 3.17368e19 2.51875
\(869\) −1.53956e19 −1.21274
\(870\) −3.49974e17 −0.0273628
\(871\) 1.35873e19 1.05443
\(872\) 3.50465e18 0.269953
\(873\) −4.04670e18 −0.309391
\(874\) −2.20329e18 −0.167204
\(875\) 6.95039e18 0.523549
\(876\) 9.25240e18 0.691795
\(877\) 1.21686e19 0.903114 0.451557 0.892242i \(-0.350869\pi\)
0.451557 + 0.892242i \(0.350869\pi\)
\(878\) −1.30367e18 −0.0960404
\(879\) 1.53041e19 1.11913
\(880\) 1.55914e18 0.113174
\(881\) −4.97522e18 −0.358483 −0.179242 0.983805i \(-0.557364\pi\)
−0.179242 + 0.983805i \(0.557364\pi\)
\(882\) −1.40914e18 −0.100788
\(883\) 1.82648e19 1.29679 0.648396 0.761303i \(-0.275440\pi\)
0.648396 + 0.761303i \(0.275440\pi\)
\(884\) 2.26422e19 1.59580
\(885\) 1.79084e17 0.0125293
\(886\) −2.85122e18 −0.198021
\(887\) −4.48217e18 −0.309018 −0.154509 0.987991i \(-0.549380\pi\)
−0.154509 + 0.987991i \(0.549380\pi\)
\(888\) −1.50812e18 −0.103217
\(889\) 2.96692e19 2.01578
\(890\) −4.12164e17 −0.0277994
\(891\) 1.27268e18 0.0852145
\(892\) 1.75089e19 1.16382
\(893\) −3.21409e18 −0.212091
\(894\) 1.37815e18 0.0902822
\(895\) −1.86994e18 −0.121612
\(896\) −1.75822e19 −1.13520
\(897\) −1.99876e19 −1.28118
\(898\) −2.62431e18 −0.167001
\(899\) 3.76195e19 2.37670
\(900\) 4.96658e18 0.311516
\(901\) −8.38069e18 −0.521877
\(902\) −7.45230e17 −0.0460731
\(903\) −1.24592e19 −0.764748
\(904\) −9.18877e18 −0.559967
\(905\) −2.39063e18 −0.144643
\(906\) −3.48064e18 −0.209086
\(907\) −2.93556e19 −1.75083 −0.875414 0.483374i \(-0.839411\pi\)
−0.875414 + 0.483374i \(0.839411\pi\)
\(908\) −1.75806e19 −1.04106
\(909\) 1.40717e18 0.0827332
\(910\) 1.17468e18 0.0685724
\(911\) −2.54876e19 −1.47727 −0.738635 0.674105i \(-0.764529\pi\)
−0.738635 + 0.674105i \(0.764529\pi\)
\(912\) −4.46200e18 −0.256781
\(913\) 1.08921e19 0.622374
\(914\) 2.58226e18 0.146504
\(915\) 2.91854e18 0.164410
\(916\) −2.39763e19 −1.34110
\(917\) −1.94428e19 −1.07983
\(918\) 8.68889e17 0.0479167
\(919\) 2.13951e19 1.17156 0.585779 0.810471i \(-0.300789\pi\)
0.585779 + 0.810471i \(0.300789\pi\)
\(920\) −2.00111e18 −0.108805
\(921\) −2.31830e18 −0.125165
\(922\) −6.98503e18 −0.374470
\(923\) 1.59357e19 0.848323
\(924\) 1.28231e19 0.677837
\(925\) 8.57770e18 0.450246
\(926\) 2.73267e18 0.142435
\(927\) −5.54108e18 −0.286798
\(928\) −1.57466e19 −0.809328
\(929\) 1.54861e19 0.790388 0.395194 0.918598i \(-0.370677\pi\)
0.395194 + 0.918598i \(0.370677\pi\)
\(930\) −6.14944e17 −0.0311671
\(931\) −1.53341e19 −0.771768
\(932\) 3.38210e19 1.69037
\(933\) −2.50719e18 −0.124439
\(934\) 5.47592e18 0.269900
\(935\) −3.30388e18 −0.161715
\(936\) 3.47418e18 0.168873
\(937\) −1.07879e18 −0.0520752 −0.0260376 0.999661i \(-0.508289\pi\)
−0.0260376 + 0.999661i \(0.508289\pi\)
\(938\) 5.25358e18 0.251847
\(939\) 1.04593e19 0.497938
\(940\) −1.43075e18 −0.0676444
\(941\) −1.61059e19 −0.756226 −0.378113 0.925759i \(-0.623427\pi\)
−0.378113 + 0.925759i \(0.623427\pi\)
\(942\) 6.83281e17 0.0318617
\(943\) −1.11440e19 −0.516080
\(944\) 2.50594e18 0.115253
\(945\) −1.11848e18 −0.0510883
\(946\) −2.76774e18 −0.125555
\(947\) 1.64926e19 0.743042 0.371521 0.928425i \(-0.378836\pi\)
0.371521 + 0.928425i \(0.378836\pi\)
\(948\) 1.96130e19 0.877588
\(949\) −3.68117e19 −1.63590
\(950\) −2.17820e18 −0.0961380
\(951\) −1.05313e18 −0.0461646
\(952\) 1.78621e19 0.777667
\(953\) 3.53366e19 1.52799 0.763995 0.645222i \(-0.223235\pi\)
0.763995 + 0.645222i \(0.223235\pi\)
\(954\) −6.30261e17 −0.0270680
\(955\) −5.86572e18 −0.250207
\(956\) 4.67877e18 0.198224
\(957\) 1.52000e19 0.639609
\(958\) −5.51067e18 −0.230318
\(959\) 6.47479e19 2.68785
\(960\) −1.80890e18 −0.0745852
\(961\) 4.16841e19 1.70714
\(962\) 2.94084e18 0.119628
\(963\) −3.63342e16 −0.00146806
\(964\) 1.33504e19 0.535790
\(965\) 2.47461e18 0.0986458
\(966\) −7.72828e18 −0.306007
\(967\) −1.56512e19 −0.615566 −0.307783 0.951457i \(-0.599587\pi\)
−0.307783 + 0.951457i \(0.599587\pi\)
\(968\) −4.06929e18 −0.158975
\(969\) 9.45515e18 0.366914
\(970\) 7.90036e17 0.0304531
\(971\) 1.94259e19 0.743801 0.371901 0.928273i \(-0.378706\pi\)
0.371901 + 0.928273i \(0.378706\pi\)
\(972\) −1.62132e18 −0.0616648
\(973\) 1.89312e19 0.715230
\(974\) 8.41104e18 0.315658
\(975\) −1.97601e19 −0.736646
\(976\) 4.08393e19 1.51236
\(977\) −5.14788e19 −1.89371 −0.946855 0.321660i \(-0.895759\pi\)
−0.946855 + 0.321660i \(0.895759\pi\)
\(978\) 2.71601e18 0.0992496
\(979\) 1.79010e19 0.649814
\(980\) −6.82597e18 −0.246147
\(981\) 6.50716e18 0.233100
\(982\) 8.46569e18 0.301257
\(983\) −4.53291e19 −1.60243 −0.801216 0.598376i \(-0.795813\pi\)
−0.801216 + 0.598376i \(0.795813\pi\)
\(984\) 1.93702e18 0.0680246
\(985\) −2.92230e18 −0.101950
\(986\) 1.03774e19 0.359657
\(987\) −1.12738e19 −0.388157
\(988\) 1.85295e19 0.633786
\(989\) −4.13884e19 −1.40638
\(990\) −2.48465e17 −0.00838757
\(991\) −1.51168e19 −0.506970 −0.253485 0.967339i \(-0.581577\pi\)
−0.253485 + 0.967339i \(0.581577\pi\)
\(992\) −2.76685e19 −0.921850
\(993\) 1.24525e19 0.412178
\(994\) 6.16160e18 0.202620
\(995\) −5.74542e18 −0.187703
\(996\) −1.38759e19 −0.450376
\(997\) 3.60190e18 0.116148 0.0580742 0.998312i \(-0.481504\pi\)
0.0580742 + 0.998312i \(0.481504\pi\)
\(998\) 1.77965e18 0.0570146
\(999\) −2.80015e18 −0.0891263
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.a.1.15 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.15 30 1.1 even 1 trivial