Properties

Label 177.14.a.a.1.13
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 1.13
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-41.9317 q^{2} +729.000 q^{3} -6433.74 q^{4} -10428.5 q^{5} -30568.2 q^{6} -484911. q^{7} +613281. q^{8} +531441. q^{9} +O(q^{10})\) \(q-41.9317 q^{2} +729.000 q^{3} -6433.74 q^{4} -10428.5 q^{5} -30568.2 q^{6} -484911. q^{7} +613281. q^{8} +531441. q^{9} +437283. q^{10} -5.22450e6 q^{11} -4.69019e6 q^{12} -2.63123e7 q^{13} +2.03331e7 q^{14} -7.60235e6 q^{15} +2.69892e7 q^{16} +5.55106e7 q^{17} -2.22842e7 q^{18} +2.91313e8 q^{19} +6.70939e7 q^{20} -3.53500e8 q^{21} +2.19072e8 q^{22} +4.45190e8 q^{23} +4.47082e8 q^{24} -1.11195e9 q^{25} +1.10332e9 q^{26} +3.87420e8 q^{27} +3.11979e9 q^{28} +1.14421e9 q^{29} +3.18779e8 q^{30} +1.75609e9 q^{31} -6.15571e9 q^{32} -3.80866e9 q^{33} -2.32765e9 q^{34} +5.05687e9 q^{35} -3.41915e9 q^{36} +1.94584e10 q^{37} -1.22152e10 q^{38} -1.91817e10 q^{39} -6.39558e9 q^{40} +4.10675e10 q^{41} +1.48228e10 q^{42} -6.68796e10 q^{43} +3.36130e10 q^{44} -5.54211e9 q^{45} -1.86676e10 q^{46} +1.07923e11 q^{47} +1.96752e10 q^{48} +1.38250e11 q^{49} +4.66259e10 q^{50} +4.04673e10 q^{51} +1.69287e11 q^{52} +1.14657e11 q^{53} -1.62452e10 q^{54} +5.44834e10 q^{55} -2.97387e11 q^{56} +2.12367e11 q^{57} -4.79788e10 q^{58} +4.21805e10 q^{59} +4.89115e10 q^{60} -3.36859e11 q^{61} -7.36359e10 q^{62} -2.57702e11 q^{63} +3.70231e10 q^{64} +2.74397e11 q^{65} +1.59703e11 q^{66} -2.42464e11 q^{67} -3.57141e11 q^{68} +3.24544e11 q^{69} -2.12043e11 q^{70} +4.15485e11 q^{71} +3.25923e11 q^{72} -1.88437e12 q^{73} -8.15925e11 q^{74} -8.10612e11 q^{75} -1.87423e12 q^{76} +2.53342e12 q^{77} +8.04320e11 q^{78} -1.69099e12 q^{79} -2.81456e11 q^{80} +2.82430e11 q^{81} -1.72203e12 q^{82} -1.99354e12 q^{83} +2.27433e12 q^{84} -5.78890e11 q^{85} +2.80437e12 q^{86} +8.34133e11 q^{87} -3.20409e12 q^{88} +2.92261e12 q^{89} +2.32390e11 q^{90} +1.27591e13 q^{91} -2.86423e12 q^{92} +1.28019e12 q^{93} -4.52538e12 q^{94} -3.03794e12 q^{95} -4.48751e12 q^{96} +1.31868e13 q^{97} -5.79704e12 q^{98} -2.77651e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −41.9317 −0.463284 −0.231642 0.972801i \(-0.574410\pi\)
−0.231642 + 0.972801i \(0.574410\pi\)
\(3\) 729.000 0.577350
\(4\) −6433.74 −0.785368
\(5\) −10428.5 −0.298480 −0.149240 0.988801i \(-0.547683\pi\)
−0.149240 + 0.988801i \(0.547683\pi\)
\(6\) −30568.2 −0.267477
\(7\) −484911. −1.55785 −0.778923 0.627119i \(-0.784234\pi\)
−0.778923 + 0.627119i \(0.784234\pi\)
\(8\) 613281. 0.827132
\(9\) 531441. 0.333333
\(10\) 437283. 0.138281
\(11\) −5.22450e6 −0.889184 −0.444592 0.895733i \(-0.646651\pi\)
−0.444592 + 0.895733i \(0.646651\pi\)
\(12\) −4.69019e6 −0.453432
\(13\) −2.63123e7 −1.51192 −0.755958 0.654620i \(-0.772829\pi\)
−0.755958 + 0.654620i \(0.772829\pi\)
\(14\) 2.03331e7 0.721725
\(15\) −7.60235e6 −0.172327
\(16\) 2.69892e7 0.402171
\(17\) 5.55106e7 0.557774 0.278887 0.960324i \(-0.410035\pi\)
0.278887 + 0.960324i \(0.410035\pi\)
\(18\) −2.22842e7 −0.154428
\(19\) 2.91313e8 1.42057 0.710283 0.703917i \(-0.248567\pi\)
0.710283 + 0.703917i \(0.248567\pi\)
\(20\) 6.70939e7 0.234417
\(21\) −3.53500e8 −0.899423
\(22\) 2.19072e8 0.411945
\(23\) 4.45190e8 0.627068 0.313534 0.949577i \(-0.398487\pi\)
0.313534 + 0.949577i \(0.398487\pi\)
\(24\) 4.47082e8 0.477545
\(25\) −1.11195e9 −0.910910
\(26\) 1.10332e9 0.700446
\(27\) 3.87420e8 0.192450
\(28\) 3.11979e9 1.22348
\(29\) 1.14421e9 0.357207 0.178604 0.983921i \(-0.442842\pi\)
0.178604 + 0.983921i \(0.442842\pi\)
\(30\) 3.18779e8 0.0798365
\(31\) 1.75609e9 0.355383 0.177691 0.984086i \(-0.443137\pi\)
0.177691 + 0.984086i \(0.443137\pi\)
\(32\) −6.15571e9 −1.01345
\(33\) −3.80866e9 −0.513371
\(34\) −2.32765e9 −0.258408
\(35\) 5.05687e9 0.464986
\(36\) −3.41915e9 −0.261789
\(37\) 1.94584e10 1.24680 0.623400 0.781903i \(-0.285751\pi\)
0.623400 + 0.781903i \(0.285751\pi\)
\(38\) −1.22152e10 −0.658125
\(39\) −1.91817e10 −0.872905
\(40\) −6.39558e9 −0.246882
\(41\) 4.10675e10 1.35022 0.675108 0.737719i \(-0.264097\pi\)
0.675108 + 0.737719i \(0.264097\pi\)
\(42\) 1.48228e10 0.416688
\(43\) −6.68796e10 −1.61342 −0.806712 0.590945i \(-0.798755\pi\)
−0.806712 + 0.590945i \(0.798755\pi\)
\(44\) 3.36130e10 0.698337
\(45\) −5.54211e9 −0.0994933
\(46\) −1.86676e10 −0.290510
\(47\) 1.07923e11 1.46042 0.730209 0.683224i \(-0.239423\pi\)
0.730209 + 0.683224i \(0.239423\pi\)
\(48\) 1.96752e10 0.232194
\(49\) 1.38250e11 1.42689
\(50\) 4.66259e10 0.422010
\(51\) 4.04673e10 0.322031
\(52\) 1.69287e11 1.18741
\(53\) 1.14657e11 0.710573 0.355286 0.934758i \(-0.384383\pi\)
0.355286 + 0.934758i \(0.384383\pi\)
\(54\) −1.62452e10 −0.0891590
\(55\) 5.44834e10 0.265404
\(56\) −2.97387e11 −1.28855
\(57\) 2.12367e11 0.820164
\(58\) −4.79788e10 −0.165488
\(59\) 4.21805e10 0.130189
\(60\) 4.89115e10 0.135340
\(61\) −3.36859e11 −0.837152 −0.418576 0.908182i \(-0.637471\pi\)
−0.418576 + 0.908182i \(0.637471\pi\)
\(62\) −7.36359e10 −0.164643
\(63\) −2.57702e11 −0.519282
\(64\) 3.70231e10 0.0673446
\(65\) 2.74397e11 0.451276
\(66\) 1.59703e11 0.237836
\(67\) −2.42464e11 −0.327461 −0.163731 0.986505i \(-0.552353\pi\)
−0.163731 + 0.986505i \(0.552353\pi\)
\(68\) −3.57141e11 −0.438058
\(69\) 3.24544e11 0.362038
\(70\) −2.12043e11 −0.215420
\(71\) 4.15485e11 0.384925 0.192463 0.981304i \(-0.438353\pi\)
0.192463 + 0.981304i \(0.438353\pi\)
\(72\) 3.25923e11 0.275711
\(73\) −1.88437e12 −1.45736 −0.728682 0.684852i \(-0.759867\pi\)
−0.728682 + 0.684852i \(0.759867\pi\)
\(74\) −8.15925e11 −0.577623
\(75\) −8.10612e11 −0.525914
\(76\) −1.87423e12 −1.11567
\(77\) 2.53342e12 1.38521
\(78\) 8.04320e11 0.404403
\(79\) −1.69099e12 −0.782647 −0.391324 0.920253i \(-0.627983\pi\)
−0.391324 + 0.920253i \(0.627983\pi\)
\(80\) −2.81456e11 −0.120040
\(81\) 2.82430e11 0.111111
\(82\) −1.72203e12 −0.625533
\(83\) −1.99354e12 −0.669293 −0.334647 0.942344i \(-0.608617\pi\)
−0.334647 + 0.942344i \(0.608617\pi\)
\(84\) 2.27433e12 0.706378
\(85\) −5.78890e11 −0.166484
\(86\) 2.80437e12 0.747473
\(87\) 8.34133e11 0.206234
\(88\) −3.20409e12 −0.735473
\(89\) 2.92261e12 0.623356 0.311678 0.950188i \(-0.399109\pi\)
0.311678 + 0.950188i \(0.399109\pi\)
\(90\) 2.32390e11 0.0460936
\(91\) 1.27591e13 2.35533
\(92\) −2.86423e12 −0.492479
\(93\) 1.28019e12 0.205180
\(94\) −4.52538e12 −0.676588
\(95\) −3.03794e12 −0.424010
\(96\) −4.48751e12 −0.585117
\(97\) 1.31868e13 1.60739 0.803697 0.595038i \(-0.202863\pi\)
0.803697 + 0.595038i \(0.202863\pi\)
\(98\) −5.79704e12 −0.661054
\(99\) −2.77651e12 −0.296395
\(100\) 7.15399e12 0.715399
\(101\) 1.44784e13 1.35716 0.678582 0.734524i \(-0.262595\pi\)
0.678582 + 0.734524i \(0.262595\pi\)
\(102\) −1.69686e12 −0.149192
\(103\) −1.26142e13 −1.04092 −0.520462 0.853885i \(-0.674240\pi\)
−0.520462 + 0.853885i \(0.674240\pi\)
\(104\) −1.61369e13 −1.25055
\(105\) 3.68646e12 0.268460
\(106\) −4.80777e12 −0.329197
\(107\) 1.85559e13 1.19533 0.597665 0.801746i \(-0.296095\pi\)
0.597665 + 0.801746i \(0.296095\pi\)
\(108\) −2.49256e12 −0.151144
\(109\) −1.64035e13 −0.936839 −0.468420 0.883506i \(-0.655176\pi\)
−0.468420 + 0.883506i \(0.655176\pi\)
\(110\) −2.28458e12 −0.122957
\(111\) 1.41852e13 0.719841
\(112\) −1.30874e13 −0.626521
\(113\) 1.96811e13 0.889283 0.444642 0.895709i \(-0.353331\pi\)
0.444642 + 0.895709i \(0.353331\pi\)
\(114\) −8.90490e12 −0.379969
\(115\) −4.64265e12 −0.187167
\(116\) −7.36157e12 −0.280539
\(117\) −1.39835e13 −0.503972
\(118\) −1.76870e12 −0.0603144
\(119\) −2.69177e13 −0.868926
\(120\) −4.66238e12 −0.142538
\(121\) −7.22736e12 −0.209351
\(122\) 1.41251e13 0.387839
\(123\) 2.99382e13 0.779548
\(124\) −1.12982e13 −0.279106
\(125\) 2.43260e13 0.570368
\(126\) 1.08059e13 0.240575
\(127\) −4.59428e13 −0.971612 −0.485806 0.874067i \(-0.661474\pi\)
−0.485806 + 0.874067i \(0.661474\pi\)
\(128\) 4.88751e13 0.982252
\(129\) −4.87552e13 −0.931511
\(130\) −1.15059e13 −0.209069
\(131\) −7.21311e13 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(132\) 2.45039e13 0.403185
\(133\) −1.41261e14 −2.21302
\(134\) 1.01669e13 0.151708
\(135\) −4.04020e12 −0.0574425
\(136\) 3.40436e13 0.461353
\(137\) 1.19310e14 1.54168 0.770841 0.637028i \(-0.219836\pi\)
0.770841 + 0.637028i \(0.219836\pi\)
\(138\) −1.36086e13 −0.167726
\(139\) 1.11346e14 1.30942 0.654710 0.755880i \(-0.272791\pi\)
0.654710 + 0.755880i \(0.272791\pi\)
\(140\) −3.25346e13 −0.365185
\(141\) 7.86757e13 0.843173
\(142\) −1.74220e13 −0.178330
\(143\) 1.37469e14 1.34437
\(144\) 1.43432e13 0.134057
\(145\) −1.19324e13 −0.106619
\(146\) 7.90149e13 0.675174
\(147\) 1.00784e14 0.823814
\(148\) −1.25191e14 −0.979197
\(149\) −7.98647e13 −0.597922 −0.298961 0.954265i \(-0.596640\pi\)
−0.298961 + 0.954265i \(0.596640\pi\)
\(150\) 3.39903e13 0.243647
\(151\) 2.22450e13 0.152715 0.0763575 0.997081i \(-0.475671\pi\)
0.0763575 + 0.997081i \(0.475671\pi\)
\(152\) 1.78657e14 1.17500
\(153\) 2.95006e13 0.185925
\(154\) −1.06230e14 −0.641747
\(155\) −1.83133e13 −0.106075
\(156\) 1.23410e14 0.685552
\(157\) −1.49092e14 −0.794525 −0.397262 0.917705i \(-0.630040\pi\)
−0.397262 + 0.917705i \(0.630040\pi\)
\(158\) 7.09062e13 0.362588
\(159\) 8.35852e13 0.410249
\(160\) 6.41945e13 0.302495
\(161\) −2.15878e14 −0.976876
\(162\) −1.18427e13 −0.0514760
\(163\) 1.43831e14 0.600665 0.300333 0.953835i \(-0.402902\pi\)
0.300333 + 0.953835i \(0.402902\pi\)
\(164\) −2.64218e14 −1.06042
\(165\) 3.97184e13 0.153231
\(166\) 8.35923e13 0.310073
\(167\) 1.10771e14 0.395156 0.197578 0.980287i \(-0.436692\pi\)
0.197578 + 0.980287i \(0.436692\pi\)
\(168\) −2.16795e14 −0.743942
\(169\) 3.89464e14 1.28589
\(170\) 2.42738e13 0.0771295
\(171\) 1.54816e14 0.473522
\(172\) 4.30285e14 1.26713
\(173\) −4.81517e14 −1.36556 −0.682782 0.730622i \(-0.739230\pi\)
−0.682782 + 0.730622i \(0.739230\pi\)
\(174\) −3.49766e13 −0.0955448
\(175\) 5.39197e14 1.41906
\(176\) −1.41005e14 −0.357604
\(177\) 3.07496e13 0.0751646
\(178\) −1.22550e14 −0.288791
\(179\) 7.45116e14 1.69309 0.846544 0.532320i \(-0.178680\pi\)
0.846544 + 0.532320i \(0.178680\pi\)
\(180\) 3.56565e13 0.0781389
\(181\) −1.39421e14 −0.294725 −0.147362 0.989083i \(-0.547078\pi\)
−0.147362 + 0.989083i \(0.547078\pi\)
\(182\) −5.35012e14 −1.09119
\(183\) −2.45570e14 −0.483330
\(184\) 2.73027e14 0.518668
\(185\) −2.02922e14 −0.372145
\(186\) −5.36806e13 −0.0950568
\(187\) −2.90015e14 −0.495964
\(188\) −6.94347e14 −1.14697
\(189\) −1.87864e14 −0.299808
\(190\) 1.27386e14 0.196437
\(191\) −3.13121e14 −0.466654 −0.233327 0.972398i \(-0.574961\pi\)
−0.233327 + 0.972398i \(0.574961\pi\)
\(192\) 2.69898e13 0.0388814
\(193\) −8.97607e14 −1.25016 −0.625078 0.780563i \(-0.714933\pi\)
−0.625078 + 0.780563i \(0.714933\pi\)
\(194\) −5.52944e14 −0.744680
\(195\) 2.00035e14 0.260545
\(196\) −8.89462e14 −1.12063
\(197\) −3.94105e14 −0.480377 −0.240188 0.970726i \(-0.577209\pi\)
−0.240188 + 0.970726i \(0.577209\pi\)
\(198\) 1.16424e14 0.137315
\(199\) 5.70291e13 0.0650956 0.0325478 0.999470i \(-0.489638\pi\)
0.0325478 + 0.999470i \(0.489638\pi\)
\(200\) −6.81939e14 −0.753443
\(201\) −1.76756e14 −0.189060
\(202\) −6.07105e14 −0.628752
\(203\) −5.54842e14 −0.556475
\(204\) −2.60356e14 −0.252913
\(205\) −4.28271e14 −0.403012
\(206\) 5.28936e14 0.482243
\(207\) 2.36592e14 0.209023
\(208\) −7.10150e14 −0.608049
\(209\) −1.52196e15 −1.26314
\(210\) −1.54579e14 −0.124373
\(211\) 1.73039e14 0.134992 0.0674961 0.997720i \(-0.478499\pi\)
0.0674961 + 0.997720i \(0.478499\pi\)
\(212\) −7.37675e14 −0.558061
\(213\) 3.02889e14 0.222237
\(214\) −7.78080e14 −0.553777
\(215\) 6.97451e14 0.481575
\(216\) 2.37598e14 0.159182
\(217\) −8.51549e14 −0.553632
\(218\) 6.87827e14 0.434022
\(219\) −1.37371e15 −0.841410
\(220\) −3.50532e14 −0.208440
\(221\) −1.46061e15 −0.843307
\(222\) −5.94809e14 −0.333491
\(223\) 7.48625e14 0.407646 0.203823 0.979008i \(-0.434663\pi\)
0.203823 + 0.979008i \(0.434663\pi\)
\(224\) 2.98497e15 1.57880
\(225\) −5.90936e14 −0.303637
\(226\) −8.25263e14 −0.411991
\(227\) −2.46575e15 −1.19614 −0.598068 0.801445i \(-0.704065\pi\)
−0.598068 + 0.801445i \(0.704065\pi\)
\(228\) −1.36631e15 −0.644130
\(229\) 8.33539e13 0.0381940 0.0190970 0.999818i \(-0.493921\pi\)
0.0190970 + 0.999818i \(0.493921\pi\)
\(230\) 1.94674e14 0.0867115
\(231\) 1.84686e15 0.799753
\(232\) 7.01726e14 0.295458
\(233\) 1.25130e15 0.512326 0.256163 0.966634i \(-0.417542\pi\)
0.256163 + 0.966634i \(0.417542\pi\)
\(234\) 5.86349e14 0.233482
\(235\) −1.12547e15 −0.435905
\(236\) −2.71378e14 −0.102246
\(237\) −1.23274e15 −0.451862
\(238\) 1.12870e15 0.402560
\(239\) −2.29876e15 −0.797823 −0.398912 0.916989i \(-0.630612\pi\)
−0.398912 + 0.916989i \(0.630612\pi\)
\(240\) −2.05182e14 −0.0693051
\(241\) −3.05920e15 −1.00577 −0.502883 0.864355i \(-0.667727\pi\)
−0.502883 + 0.864355i \(0.667727\pi\)
\(242\) 3.03055e14 0.0969889
\(243\) 2.05891e14 0.0641500
\(244\) 2.16726e15 0.657473
\(245\) −1.44173e15 −0.425897
\(246\) −1.25536e15 −0.361152
\(247\) −7.66512e15 −2.14777
\(248\) 1.07698e15 0.293949
\(249\) −1.45329e15 −0.386417
\(250\) −1.02003e15 −0.264242
\(251\) 6.63415e14 0.167458 0.0837290 0.996489i \(-0.473317\pi\)
0.0837290 + 0.996489i \(0.473317\pi\)
\(252\) 1.65798e15 0.407828
\(253\) −2.32589e15 −0.557579
\(254\) 1.92646e15 0.450132
\(255\) −4.22011e14 −0.0961197
\(256\) −2.35271e15 −0.522406
\(257\) −2.29163e15 −0.496111 −0.248056 0.968746i \(-0.579792\pi\)
−0.248056 + 0.968746i \(0.579792\pi\)
\(258\) 2.04439e15 0.431554
\(259\) −9.43562e15 −1.94232
\(260\) −1.76540e15 −0.354418
\(261\) 6.08083e14 0.119069
\(262\) 3.02458e15 0.577706
\(263\) 1.59259e15 0.296750 0.148375 0.988931i \(-0.452596\pi\)
0.148375 + 0.988931i \(0.452596\pi\)
\(264\) −2.33578e15 −0.424626
\(265\) −1.19570e15 −0.212092
\(266\) 5.92330e15 1.02526
\(267\) 2.13058e15 0.359895
\(268\) 1.55995e15 0.257178
\(269\) 5.54351e15 0.892063 0.446031 0.895017i \(-0.352837\pi\)
0.446031 + 0.895017i \(0.352837\pi\)
\(270\) 1.69412e14 0.0266122
\(271\) −8.05173e15 −1.23478 −0.617389 0.786658i \(-0.711810\pi\)
−0.617389 + 0.786658i \(0.711810\pi\)
\(272\) 1.49819e15 0.224321
\(273\) 9.30141e15 1.35985
\(274\) −5.00289e15 −0.714236
\(275\) 5.80938e15 0.809967
\(276\) −2.08803e15 −0.284333
\(277\) −3.58336e15 −0.476620 −0.238310 0.971189i \(-0.576593\pi\)
−0.238310 + 0.971189i \(0.576593\pi\)
\(278\) −4.66893e15 −0.606633
\(279\) 9.33260e14 0.118461
\(280\) 3.10129e15 0.384605
\(281\) −1.62922e16 −1.97419 −0.987096 0.160127i \(-0.948810\pi\)
−0.987096 + 0.160127i \(0.948810\pi\)
\(282\) −3.29900e15 −0.390628
\(283\) −4.04402e15 −0.467953 −0.233976 0.972242i \(-0.575174\pi\)
−0.233976 + 0.972242i \(0.575174\pi\)
\(284\) −2.67312e15 −0.302308
\(285\) −2.21466e15 −0.244802
\(286\) −5.76429e15 −0.622826
\(287\) −1.99141e16 −2.10343
\(288\) −3.27139e15 −0.337817
\(289\) −6.82315e15 −0.688888
\(290\) 5.00345e14 0.0493950
\(291\) 9.61316e15 0.928030
\(292\) 1.21236e16 1.14457
\(293\) −2.80853e15 −0.259322 −0.129661 0.991558i \(-0.541389\pi\)
−0.129661 + 0.991558i \(0.541389\pi\)
\(294\) −4.22604e15 −0.381660
\(295\) −4.39878e14 −0.0388588
\(296\) 1.19335e16 1.03127
\(297\) −2.02408e15 −0.171124
\(298\) 3.34886e15 0.277007
\(299\) −1.17140e16 −0.948074
\(300\) 5.21526e15 0.413036
\(301\) 3.24306e16 2.51347
\(302\) −9.32769e14 −0.0707504
\(303\) 1.05548e16 0.783559
\(304\) 7.86231e15 0.571310
\(305\) 3.51292e15 0.249873
\(306\) −1.23701e15 −0.0861359
\(307\) −1.24621e16 −0.849554 −0.424777 0.905298i \(-0.639647\pi\)
−0.424777 + 0.905298i \(0.639647\pi\)
\(308\) −1.62993e16 −1.08790
\(309\) −9.19577e15 −0.600977
\(310\) 7.67909e14 0.0491427
\(311\) 1.54773e16 0.969959 0.484979 0.874526i \(-0.338827\pi\)
0.484979 + 0.874526i \(0.338827\pi\)
\(312\) −1.17638e16 −0.722008
\(313\) −3.84420e15 −0.231083 −0.115541 0.993303i \(-0.536860\pi\)
−0.115541 + 0.993303i \(0.536860\pi\)
\(314\) 6.25169e15 0.368090
\(315\) 2.68743e15 0.154995
\(316\) 1.08794e16 0.614666
\(317\) −1.20939e16 −0.669395 −0.334697 0.942326i \(-0.608634\pi\)
−0.334697 + 0.942326i \(0.608634\pi\)
\(318\) −3.50487e15 −0.190062
\(319\) −5.97794e15 −0.317623
\(320\) −3.86093e14 −0.0201010
\(321\) 1.35273e16 0.690124
\(322\) 9.05210e15 0.452571
\(323\) 1.61710e16 0.792354
\(324\) −1.81708e15 −0.0872631
\(325\) 2.92580e16 1.37722
\(326\) −6.03106e15 −0.278278
\(327\) −1.19582e16 −0.540884
\(328\) 2.51859e16 1.11681
\(329\) −5.23329e16 −2.27511
\(330\) −1.66546e15 −0.0709894
\(331\) −1.26292e16 −0.527829 −0.263915 0.964546i \(-0.585014\pi\)
−0.263915 + 0.964546i \(0.585014\pi\)
\(332\) 1.28259e16 0.525641
\(333\) 1.03410e16 0.415600
\(334\) −4.64481e15 −0.183069
\(335\) 2.52852e15 0.0977407
\(336\) −9.54070e15 −0.361722
\(337\) −3.65154e16 −1.35794 −0.678972 0.734165i \(-0.737574\pi\)
−0.678972 + 0.734165i \(0.737574\pi\)
\(338\) −1.63309e16 −0.595732
\(339\) 1.43475e16 0.513428
\(340\) 3.72443e15 0.130751
\(341\) −9.17470e15 −0.316001
\(342\) −6.49167e15 −0.219375
\(343\) −2.00562e16 −0.665025
\(344\) −4.10160e16 −1.33451
\(345\) −3.38449e15 −0.108061
\(346\) 2.01908e16 0.632644
\(347\) 7.54050e15 0.231877 0.115939 0.993256i \(-0.463012\pi\)
0.115939 + 0.993256i \(0.463012\pi\)
\(348\) −5.36659e15 −0.161969
\(349\) 4.18243e16 1.23898 0.619488 0.785006i \(-0.287340\pi\)
0.619488 + 0.785006i \(0.287340\pi\)
\(350\) −2.26094e16 −0.657427
\(351\) −1.01939e16 −0.290968
\(352\) 3.21605e16 0.901145
\(353\) 5.81122e16 1.59857 0.799285 0.600952i \(-0.205212\pi\)
0.799285 + 0.600952i \(0.205212\pi\)
\(354\) −1.28938e15 −0.0348225
\(355\) −4.33287e15 −0.114892
\(356\) −1.88033e16 −0.489564
\(357\) −1.96230e16 −0.501675
\(358\) −3.12440e16 −0.784380
\(359\) −5.56531e16 −1.37207 −0.686034 0.727570i \(-0.740650\pi\)
−0.686034 + 0.727570i \(0.740650\pi\)
\(360\) −3.39887e15 −0.0822941
\(361\) 4.28102e16 1.01801
\(362\) 5.84615e15 0.136541
\(363\) −5.26875e15 −0.120869
\(364\) −8.20889e16 −1.84980
\(365\) 1.96511e16 0.434994
\(366\) 1.02972e16 0.223919
\(367\) 6.40933e16 1.36925 0.684625 0.728895i \(-0.259966\pi\)
0.684625 + 0.728895i \(0.259966\pi\)
\(368\) 1.20153e16 0.252189
\(369\) 2.18250e16 0.450072
\(370\) 8.50884e15 0.172409
\(371\) −5.55986e16 −1.10696
\(372\) −8.23642e15 −0.161142
\(373\) −8.30832e16 −1.59737 −0.798685 0.601749i \(-0.794471\pi\)
−0.798685 + 0.601749i \(0.794471\pi\)
\(374\) 1.21608e16 0.229772
\(375\) 1.77336e16 0.329302
\(376\) 6.61870e16 1.20796
\(377\) −3.01070e16 −0.540068
\(378\) 7.87747e15 0.138896
\(379\) 7.40374e16 1.28320 0.641602 0.767037i \(-0.278270\pi\)
0.641602 + 0.767037i \(0.278270\pi\)
\(380\) 1.95453e16 0.333004
\(381\) −3.34923e16 −0.560960
\(382\) 1.31297e16 0.216193
\(383\) −1.15582e17 −1.87110 −0.935552 0.353190i \(-0.885097\pi\)
−0.935552 + 0.353190i \(0.885097\pi\)
\(384\) 3.56299e16 0.567103
\(385\) −2.64196e16 −0.413458
\(386\) 3.76382e16 0.579177
\(387\) −3.55425e16 −0.537808
\(388\) −8.48403e16 −1.26240
\(389\) −1.06005e16 −0.155115 −0.0775576 0.996988i \(-0.524712\pi\)
−0.0775576 + 0.996988i \(0.524712\pi\)
\(390\) −8.38782e15 −0.120706
\(391\) 2.47128e16 0.349762
\(392\) 8.47860e16 1.18022
\(393\) −5.25836e16 −0.719944
\(394\) 1.65255e16 0.222551
\(395\) 1.76345e16 0.233605
\(396\) 1.78633e16 0.232779
\(397\) 2.54679e16 0.326479 0.163239 0.986586i \(-0.447806\pi\)
0.163239 + 0.986586i \(0.447806\pi\)
\(398\) −2.39133e15 −0.0301578
\(399\) −1.02979e17 −1.27769
\(400\) −3.00107e16 −0.366342
\(401\) 1.11895e17 1.34392 0.671960 0.740588i \(-0.265453\pi\)
0.671960 + 0.740588i \(0.265453\pi\)
\(402\) 7.41167e15 0.0875884
\(403\) −4.62069e16 −0.537309
\(404\) −9.31504e16 −1.06587
\(405\) −2.94530e15 −0.0331644
\(406\) 2.32655e16 0.257806
\(407\) −1.01661e17 −1.10864
\(408\) 2.48178e16 0.266362
\(409\) 8.23815e15 0.0870218 0.0435109 0.999053i \(-0.486146\pi\)
0.0435109 + 0.999053i \(0.486146\pi\)
\(410\) 1.79581e16 0.186709
\(411\) 8.69773e16 0.890090
\(412\) 8.11566e16 0.817508
\(413\) −2.04538e16 −0.202814
\(414\) −9.92071e15 −0.0968368
\(415\) 2.07895e16 0.199771
\(416\) 1.61971e17 1.53225
\(417\) 8.11713e16 0.755994
\(418\) 6.38184e16 0.585194
\(419\) 1.24414e17 1.12325 0.561626 0.827391i \(-0.310176\pi\)
0.561626 + 0.827391i \(0.310176\pi\)
\(420\) −2.37177e16 −0.210840
\(421\) 1.47476e17 1.29088 0.645442 0.763809i \(-0.276673\pi\)
0.645442 + 0.763809i \(0.276673\pi\)
\(422\) −7.25582e15 −0.0625397
\(423\) 5.73546e16 0.486806
\(424\) 7.03172e16 0.587738
\(425\) −6.17251e16 −0.508082
\(426\) −1.27006e16 −0.102959
\(427\) 1.63347e17 1.30416
\(428\) −1.19384e17 −0.938774
\(429\) 1.00215e17 0.776173
\(430\) −2.92453e16 −0.223106
\(431\) 1.59550e17 1.19893 0.599465 0.800401i \(-0.295380\pi\)
0.599465 + 0.800401i \(0.295380\pi\)
\(432\) 1.04562e16 0.0773979
\(433\) 6.91743e16 0.504398 0.252199 0.967675i \(-0.418846\pi\)
0.252199 + 0.967675i \(0.418846\pi\)
\(434\) 3.57069e16 0.256489
\(435\) −8.69872e15 −0.0615567
\(436\) 1.05536e17 0.735763
\(437\) 1.29690e17 0.890791
\(438\) 5.76019e16 0.389812
\(439\) 8.97220e16 0.598246 0.299123 0.954215i \(-0.403306\pi\)
0.299123 + 0.954215i \(0.403306\pi\)
\(440\) 3.34137e16 0.219524
\(441\) 7.34716e16 0.475629
\(442\) 6.12460e16 0.390691
\(443\) −1.47931e17 −0.929896 −0.464948 0.885338i \(-0.653927\pi\)
−0.464948 + 0.885338i \(0.653927\pi\)
\(444\) −9.12639e16 −0.565340
\(445\) −3.04783e16 −0.186059
\(446\) −3.13911e16 −0.188856
\(447\) −5.82214e16 −0.345210
\(448\) −1.79529e16 −0.104913
\(449\) 1.58665e17 0.913860 0.456930 0.889503i \(-0.348949\pi\)
0.456930 + 0.889503i \(0.348949\pi\)
\(450\) 2.47789e16 0.140670
\(451\) −2.14557e17 −1.20059
\(452\) −1.26623e17 −0.698415
\(453\) 1.62166e16 0.0881700
\(454\) 1.03393e17 0.554151
\(455\) −1.33058e17 −0.703020
\(456\) 1.30241e17 0.678384
\(457\) −9.53833e16 −0.489798 −0.244899 0.969549i \(-0.578755\pi\)
−0.244899 + 0.969549i \(0.578755\pi\)
\(458\) −3.49517e15 −0.0176947
\(459\) 2.15060e16 0.107344
\(460\) 2.98696e16 0.146995
\(461\) −7.63684e16 −0.370559 −0.185280 0.982686i \(-0.559319\pi\)
−0.185280 + 0.982686i \(0.559319\pi\)
\(462\) −7.74419e16 −0.370513
\(463\) −1.08628e17 −0.512464 −0.256232 0.966615i \(-0.582481\pi\)
−0.256232 + 0.966615i \(0.582481\pi\)
\(464\) 3.08815e16 0.143659
\(465\) −1.33504e16 −0.0612422
\(466\) −5.24689e16 −0.237352
\(467\) −3.17982e17 −1.41854 −0.709272 0.704935i \(-0.750976\pi\)
−0.709272 + 0.704935i \(0.750976\pi\)
\(468\) 8.99658e16 0.395803
\(469\) 1.17573e17 0.510135
\(470\) 4.71928e16 0.201948
\(471\) −1.08688e17 −0.458719
\(472\) 2.58685e16 0.107683
\(473\) 3.49412e17 1.43463
\(474\) 5.16906e16 0.209340
\(475\) −3.23925e17 −1.29401
\(476\) 1.73181e17 0.682427
\(477\) 6.09336e16 0.236858
\(478\) 9.63907e16 0.369619
\(479\) −4.89415e17 −1.85138 −0.925692 0.378277i \(-0.876517\pi\)
−0.925692 + 0.378277i \(0.876517\pi\)
\(480\) 4.67978e16 0.174646
\(481\) −5.11997e17 −1.88506
\(482\) 1.28277e17 0.465955
\(483\) −1.57375e17 −0.563999
\(484\) 4.64989e16 0.164418
\(485\) −1.37518e17 −0.479775
\(486\) −8.63336e15 −0.0297197
\(487\) 2.63271e17 0.894261 0.447131 0.894469i \(-0.352446\pi\)
0.447131 + 0.894469i \(0.352446\pi\)
\(488\) −2.06590e17 −0.692436
\(489\) 1.04853e17 0.346794
\(490\) 6.04542e16 0.197311
\(491\) 3.20068e17 1.03089 0.515445 0.856923i \(-0.327627\pi\)
0.515445 + 0.856923i \(0.327627\pi\)
\(492\) −1.92615e17 −0.612232
\(493\) 6.35161e16 0.199241
\(494\) 3.21411e17 0.995029
\(495\) 2.89547e16 0.0884679
\(496\) 4.73956e16 0.142925
\(497\) −2.01473e17 −0.599654
\(498\) 6.09388e16 0.179021
\(499\) −4.56082e17 −1.32248 −0.661241 0.750174i \(-0.729970\pi\)
−0.661241 + 0.750174i \(0.729970\pi\)
\(500\) −1.56507e17 −0.447949
\(501\) 8.07520e16 0.228143
\(502\) −2.78181e16 −0.0775806
\(503\) 5.91424e17 1.62820 0.814099 0.580726i \(-0.197231\pi\)
0.814099 + 0.580726i \(0.197231\pi\)
\(504\) −1.58044e17 −0.429515
\(505\) −1.50988e17 −0.405086
\(506\) 9.75286e16 0.258317
\(507\) 2.83919e17 0.742408
\(508\) 2.95584e17 0.763073
\(509\) 7.16767e17 1.82689 0.913445 0.406963i \(-0.133412\pi\)
0.913445 + 0.406963i \(0.133412\pi\)
\(510\) 1.76956e16 0.0445307
\(511\) 9.13753e17 2.27035
\(512\) −3.01732e17 −0.740230
\(513\) 1.12861e17 0.273388
\(514\) 9.60918e16 0.229840
\(515\) 1.31547e17 0.310695
\(516\) 3.13678e17 0.731579
\(517\) −5.63842e17 −1.29858
\(518\) 3.95651e17 0.899848
\(519\) −3.51026e17 −0.788409
\(520\) 1.68283e17 0.373265
\(521\) 6.37395e16 0.139625 0.0698126 0.997560i \(-0.477760\pi\)
0.0698126 + 0.997560i \(0.477760\pi\)
\(522\) −2.54979e16 −0.0551628
\(523\) 3.40594e17 0.727739 0.363869 0.931450i \(-0.381455\pi\)
0.363869 + 0.931450i \(0.381455\pi\)
\(524\) 4.64073e17 0.979338
\(525\) 3.93075e17 0.819294
\(526\) −6.67799e16 −0.137480
\(527\) 9.74819e16 0.198223
\(528\) −1.02793e17 −0.206463
\(529\) −3.05842e17 −0.606786
\(530\) 5.01376e16 0.0982586
\(531\) 2.24165e16 0.0433963
\(532\) 9.08835e17 1.73804
\(533\) −1.08058e18 −2.04141
\(534\) −8.93390e16 −0.166733
\(535\) −1.93510e17 −0.356782
\(536\) −1.48698e17 −0.270854
\(537\) 5.43190e17 0.977504
\(538\) −2.32449e17 −0.413278
\(539\) −7.22285e17 −1.26877
\(540\) 2.59936e16 0.0451135
\(541\) 3.19418e16 0.0547743 0.0273872 0.999625i \(-0.491281\pi\)
0.0273872 + 0.999625i \(0.491281\pi\)
\(542\) 3.37622e17 0.572053
\(543\) −1.01638e17 −0.170160
\(544\) −3.41707e17 −0.565277
\(545\) 1.71063e17 0.279628
\(546\) −3.90024e17 −0.629998
\(547\) −6.84332e17 −1.09232 −0.546159 0.837682i \(-0.683911\pi\)
−0.546159 + 0.837682i \(0.683911\pi\)
\(548\) −7.67612e17 −1.21079
\(549\) −1.79021e17 −0.279051
\(550\) −2.43597e17 −0.375245
\(551\) 3.33324e17 0.507437
\(552\) 1.99037e17 0.299453
\(553\) 8.19982e17 1.21924
\(554\) 1.50256e17 0.220810
\(555\) −1.47930e17 −0.214858
\(556\) −7.16371e17 −1.02838
\(557\) −1.24182e16 −0.0176198 −0.00880990 0.999961i \(-0.502804\pi\)
−0.00880990 + 0.999961i \(0.502804\pi\)
\(558\) −3.91331e16 −0.0548811
\(559\) 1.75976e18 2.43936
\(560\) 1.36481e17 0.187004
\(561\) −2.11421e17 −0.286345
\(562\) 6.83161e17 0.914612
\(563\) 2.43031e17 0.321630 0.160815 0.986985i \(-0.448588\pi\)
0.160815 + 0.986985i \(0.448588\pi\)
\(564\) −5.06179e17 −0.662201
\(565\) −2.05244e17 −0.265433
\(566\) 1.69573e17 0.216795
\(567\) −1.36953e17 −0.173094
\(568\) 2.54809e17 0.318384
\(569\) 4.46432e17 0.551475 0.275737 0.961233i \(-0.411078\pi\)
0.275737 + 0.961233i \(0.411078\pi\)
\(570\) 9.28644e16 0.113413
\(571\) −1.45138e16 −0.0175245 −0.00876224 0.999962i \(-0.502789\pi\)
−0.00876224 + 0.999962i \(0.502789\pi\)
\(572\) −8.84437e17 −1.05583
\(573\) −2.28265e17 −0.269423
\(574\) 8.35031e17 0.974485
\(575\) −4.95029e17 −0.571202
\(576\) 1.96756e16 0.0224482
\(577\) −1.03181e18 −1.16401 −0.582004 0.813186i \(-0.697731\pi\)
−0.582004 + 0.813186i \(0.697731\pi\)
\(578\) 2.86106e17 0.319151
\(579\) −6.54356e17 −0.721777
\(580\) 7.67699e16 0.0837354
\(581\) 9.66687e17 1.04266
\(582\) −4.03096e17 −0.429941
\(583\) −5.99026e17 −0.631830
\(584\) −1.15565e18 −1.20543
\(585\) 1.45826e17 0.150425
\(586\) 1.17766e17 0.120140
\(587\) −1.61946e18 −1.63389 −0.816945 0.576716i \(-0.804334\pi\)
−0.816945 + 0.576716i \(0.804334\pi\)
\(588\) −6.48418e17 −0.646997
\(589\) 5.11572e17 0.504845
\(590\) 1.84448e16 0.0180026
\(591\) −2.87303e17 −0.277346
\(592\) 5.25169e17 0.501427
\(593\) 1.83507e18 1.73300 0.866498 0.499181i \(-0.166366\pi\)
0.866498 + 0.499181i \(0.166366\pi\)
\(594\) 8.48729e16 0.0792788
\(595\) 2.80710e17 0.259357
\(596\) 5.13828e17 0.469589
\(597\) 4.15742e16 0.0375830
\(598\) 4.91187e17 0.439227
\(599\) −5.61954e17 −0.497080 −0.248540 0.968622i \(-0.579951\pi\)
−0.248540 + 0.968622i \(0.579951\pi\)
\(600\) −4.97133e17 −0.435000
\(601\) 9.46428e17 0.819226 0.409613 0.912259i \(-0.365664\pi\)
0.409613 + 0.912259i \(0.365664\pi\)
\(602\) −1.35987e18 −1.16445
\(603\) −1.28855e17 −0.109154
\(604\) −1.43118e17 −0.119937
\(605\) 7.53703e16 0.0624871
\(606\) −4.42579e17 −0.363010
\(607\) 1.56184e18 1.26739 0.633696 0.773582i \(-0.281537\pi\)
0.633696 + 0.773582i \(0.281537\pi\)
\(608\) −1.79324e18 −1.43967
\(609\) −4.04480e17 −0.321281
\(610\) −1.47303e17 −0.115762
\(611\) −2.83970e18 −2.20803
\(612\) −1.89799e17 −0.146019
\(613\) 1.54590e18 1.17676 0.588379 0.808585i \(-0.299766\pi\)
0.588379 + 0.808585i \(0.299766\pi\)
\(614\) 5.22555e17 0.393584
\(615\) −3.12209e17 −0.232679
\(616\) 1.55370e18 1.14575
\(617\) −1.38383e17 −0.100979 −0.0504895 0.998725i \(-0.516078\pi\)
−0.0504895 + 0.998725i \(0.516078\pi\)
\(618\) 3.85594e17 0.278423
\(619\) 1.99704e18 1.42691 0.713456 0.700700i \(-0.247129\pi\)
0.713456 + 0.700700i \(0.247129\pi\)
\(620\) 1.17823e17 0.0833077
\(621\) 1.72476e17 0.120679
\(622\) −6.48990e17 −0.449366
\(623\) −1.41721e18 −0.971093
\(624\) −5.17699e17 −0.351057
\(625\) 1.10368e18 0.740666
\(626\) 1.61194e17 0.107057
\(627\) −1.10951e18 −0.729277
\(628\) 9.59220e17 0.623994
\(629\) 1.08015e18 0.695433
\(630\) −1.12688e17 −0.0718068
\(631\) −1.78543e18 −1.12603 −0.563017 0.826445i \(-0.690360\pi\)
−0.563017 + 0.826445i \(0.690360\pi\)
\(632\) −1.03706e18 −0.647353
\(633\) 1.26146e17 0.0779377
\(634\) 5.07119e17 0.310120
\(635\) 4.79112e17 0.290007
\(636\) −5.37765e17 −0.322197
\(637\) −3.63767e18 −2.15733
\(638\) 2.50665e17 0.147150
\(639\) 2.20806e17 0.128308
\(640\) −5.09692e17 −0.293182
\(641\) −4.96522e17 −0.282723 −0.141362 0.989958i \(-0.545148\pi\)
−0.141362 + 0.989958i \(0.545148\pi\)
\(642\) −5.67220e17 −0.319723
\(643\) −3.55250e18 −1.98227 −0.991134 0.132863i \(-0.957583\pi\)
−0.991134 + 0.132863i \(0.957583\pi\)
\(644\) 1.38890e18 0.767207
\(645\) 5.08442e17 0.278037
\(646\) −6.78075e17 −0.367085
\(647\) −1.84037e18 −0.986340 −0.493170 0.869933i \(-0.664162\pi\)
−0.493170 + 0.869933i \(0.664162\pi\)
\(648\) 1.73209e17 0.0919036
\(649\) −2.20372e17 −0.115762
\(650\) −1.22684e18 −0.638043
\(651\) −6.20779e17 −0.319640
\(652\) −9.25369e17 −0.471743
\(653\) −1.07637e18 −0.543283 −0.271641 0.962399i \(-0.587566\pi\)
−0.271641 + 0.962399i \(0.587566\pi\)
\(654\) 5.01426e17 0.250583
\(655\) 7.52217e17 0.372198
\(656\) 1.10838e18 0.543018
\(657\) −1.00143e18 −0.485788
\(658\) 2.19441e18 1.05402
\(659\) 1.13582e18 0.540201 0.270100 0.962832i \(-0.412943\pi\)
0.270100 + 0.962832i \(0.412943\pi\)
\(660\) −2.55538e17 −0.120343
\(661\) 1.99757e18 0.931522 0.465761 0.884911i \(-0.345781\pi\)
0.465761 + 0.884911i \(0.345781\pi\)
\(662\) 5.29563e17 0.244535
\(663\) −1.06479e18 −0.486884
\(664\) −1.22260e18 −0.553594
\(665\) 1.47313e18 0.660543
\(666\) −4.33616e17 −0.192541
\(667\) 5.09393e17 0.223993
\(668\) −7.12671e17 −0.310343
\(669\) 5.45748e17 0.235354
\(670\) −1.06025e17 −0.0452817
\(671\) 1.75992e18 0.744383
\(672\) 2.17604e18 0.911522
\(673\) 1.38797e17 0.0575814 0.0287907 0.999585i \(-0.490834\pi\)
0.0287907 + 0.999585i \(0.490834\pi\)
\(674\) 1.53115e18 0.629113
\(675\) −4.30792e17 −0.175305
\(676\) −2.50571e18 −1.00990
\(677\) −6.61948e17 −0.264239 −0.132120 0.991234i \(-0.542178\pi\)
−0.132120 + 0.991234i \(0.542178\pi\)
\(678\) −6.01616e17 −0.237863
\(679\) −6.39441e18 −2.50407
\(680\) −3.55023e17 −0.137705
\(681\) −1.79753e18 −0.690590
\(682\) 3.84710e17 0.146398
\(683\) 2.19099e18 0.825857 0.412929 0.910763i \(-0.364506\pi\)
0.412929 + 0.910763i \(0.364506\pi\)
\(684\) −9.96042e17 −0.371889
\(685\) −1.24422e18 −0.460161
\(686\) 8.40992e17 0.308095
\(687\) 6.07650e16 0.0220513
\(688\) −1.80503e18 −0.648873
\(689\) −3.01690e18 −1.07433
\(690\) 1.41917e17 0.0500629
\(691\) 2.88496e18 1.00817 0.504084 0.863655i \(-0.331830\pi\)
0.504084 + 0.863655i \(0.331830\pi\)
\(692\) 3.09795e18 1.07247
\(693\) 1.34636e18 0.461738
\(694\) −3.16186e17 −0.107425
\(695\) −1.16117e18 −0.390835
\(696\) 5.11558e17 0.170583
\(697\) 2.27968e18 0.753116
\(698\) −1.75376e18 −0.573998
\(699\) 9.12194e17 0.295792
\(700\) −3.46905e18 −1.11448
\(701\) −3.57673e18 −1.13846 −0.569232 0.822177i \(-0.692759\pi\)
−0.569232 + 0.822177i \(0.692759\pi\)
\(702\) 4.27449e17 0.134801
\(703\) 5.66850e18 1.77116
\(704\) −1.93427e17 −0.0598817
\(705\) −8.20466e17 −0.251670
\(706\) −2.43674e18 −0.740592
\(707\) −7.02075e18 −2.11425
\(708\) −1.97835e17 −0.0590319
\(709\) −3.26567e18 −0.965542 −0.482771 0.875747i \(-0.660370\pi\)
−0.482771 + 0.875747i \(0.660370\pi\)
\(710\) 1.81684e17 0.0532278
\(711\) −8.98664e17 −0.260882
\(712\) 1.79238e18 0.515598
\(713\) 7.81795e17 0.222849
\(714\) 8.22826e17 0.232418
\(715\) −1.43359e18 −0.401268
\(716\) −4.79388e18 −1.32970
\(717\) −1.67579e18 −0.460624
\(718\) 2.33363e18 0.635657
\(719\) −3.22106e18 −0.869484 −0.434742 0.900555i \(-0.643160\pi\)
−0.434742 + 0.900555i \(0.643160\pi\)
\(720\) −1.49577e17 −0.0400133
\(721\) 6.11678e18 1.62160
\(722\) −1.79510e18 −0.471625
\(723\) −2.23016e18 −0.580679
\(724\) 8.96997e17 0.231468
\(725\) −1.27231e18 −0.325384
\(726\) 2.20927e17 0.0559966
\(727\) 3.16803e18 0.795821 0.397911 0.917424i \(-0.369735\pi\)
0.397911 + 0.917424i \(0.369735\pi\)
\(728\) 7.82494e18 1.94817
\(729\) 1.50095e17 0.0370370
\(730\) −8.24004e17 −0.201526
\(731\) −3.71253e18 −0.899926
\(732\) 1.57993e18 0.379592
\(733\) 4.06683e18 0.968458 0.484229 0.874941i \(-0.339100\pi\)
0.484229 + 0.874941i \(0.339100\pi\)
\(734\) −2.68754e18 −0.634352
\(735\) −1.05102e18 −0.245892
\(736\) −2.74046e18 −0.635503
\(737\) 1.26675e18 0.291174
\(738\) −9.15157e17 −0.208511
\(739\) 3.29847e18 0.744944 0.372472 0.928044i \(-0.378510\pi\)
0.372472 + 0.928044i \(0.378510\pi\)
\(740\) 1.30554e18 0.292271
\(741\) −5.58787e18 −1.24002
\(742\) 2.33134e18 0.512838
\(743\) −2.79284e18 −0.609002 −0.304501 0.952512i \(-0.598490\pi\)
−0.304501 + 0.952512i \(0.598490\pi\)
\(744\) 7.85118e17 0.169711
\(745\) 8.32866e17 0.178468
\(746\) 3.48382e18 0.740036
\(747\) −1.05945e18 −0.223098
\(748\) 1.86588e18 0.389514
\(749\) −8.99796e18 −1.86214
\(750\) −7.43601e17 −0.152560
\(751\) −6.31465e18 −1.28437 −0.642184 0.766550i \(-0.721972\pi\)
−0.642184 + 0.766550i \(0.721972\pi\)
\(752\) 2.91276e18 0.587338
\(753\) 4.83629e17 0.0966819
\(754\) 1.26243e18 0.250205
\(755\) −2.31981e17 −0.0455824
\(756\) 1.20867e18 0.235459
\(757\) −2.12986e18 −0.411365 −0.205683 0.978619i \(-0.565941\pi\)
−0.205683 + 0.978619i \(0.565941\pi\)
\(758\) −3.10451e18 −0.594488
\(759\) −1.69558e18 −0.321918
\(760\) −1.86311e18 −0.350712
\(761\) −1.07384e18 −0.200419 −0.100210 0.994966i \(-0.531951\pi\)
−0.100210 + 0.994966i \(0.531951\pi\)
\(762\) 1.40439e18 0.259884
\(763\) 7.95425e18 1.45945
\(764\) 2.01454e18 0.366495
\(765\) −3.07646e17 −0.0554948
\(766\) 4.84654e18 0.866852
\(767\) −1.10987e18 −0.196835
\(768\) −1.71512e18 −0.301611
\(769\) −9.62435e18 −1.67823 −0.839113 0.543957i \(-0.816925\pi\)
−0.839113 + 0.543957i \(0.816925\pi\)
\(770\) 1.10782e18 0.191549
\(771\) −1.67060e18 −0.286430
\(772\) 5.77497e18 0.981832
\(773\) 6.61677e18 1.11553 0.557763 0.830001i \(-0.311660\pi\)
0.557763 + 0.830001i \(0.311660\pi\)
\(774\) 1.49036e18 0.249158
\(775\) −1.95269e18 −0.323722
\(776\) 8.08721e18 1.32953
\(777\) −6.87856e18 −1.12140
\(778\) 4.44497e17 0.0718623
\(779\) 1.19635e19 1.91807
\(780\) −1.28698e18 −0.204623
\(781\) −2.17070e18 −0.342269
\(782\) −1.03625e18 −0.162039
\(783\) 4.43292e17 0.0687446
\(784\) 3.73126e18 0.573853
\(785\) 1.55480e18 0.237150
\(786\) 2.20492e18 0.333538
\(787\) 8.44091e18 1.26635 0.633175 0.774009i \(-0.281751\pi\)
0.633175 + 0.774009i \(0.281751\pi\)
\(788\) 2.53557e18 0.377272
\(789\) 1.16100e18 0.171329
\(790\) −7.39443e17 −0.108225
\(791\) −9.54360e18 −1.38537
\(792\) −1.70278e18 −0.245158
\(793\) 8.86355e18 1.26570
\(794\) −1.06791e18 −0.151252
\(795\) −8.71664e17 −0.122451
\(796\) −3.66910e17 −0.0511240
\(797\) −7.37903e18 −1.01981 −0.509906 0.860230i \(-0.670320\pi\)
−0.509906 + 0.860230i \(0.670320\pi\)
\(798\) 4.31809e18 0.591933
\(799\) 5.99086e18 0.814583
\(800\) 6.84484e18 0.923163
\(801\) 1.55320e18 0.207785
\(802\) −4.69195e18 −0.622616
\(803\) 9.84490e18 1.29587
\(804\) 1.13720e18 0.148482
\(805\) 2.25127e18 0.291578
\(806\) 1.93753e18 0.248927
\(807\) 4.04122e18 0.515033
\(808\) 8.87935e18 1.12255
\(809\) −5.15112e18 −0.646006 −0.323003 0.946398i \(-0.604692\pi\)
−0.323003 + 0.946398i \(0.604692\pi\)
\(810\) 1.23502e17 0.0153645
\(811\) 1.50635e19 1.85905 0.929524 0.368761i \(-0.120218\pi\)
0.929524 + 0.368761i \(0.120218\pi\)
\(812\) 3.56971e18 0.437037
\(813\) −5.86971e18 −0.712899
\(814\) 4.26280e18 0.513613
\(815\) −1.49993e18 −0.179286
\(816\) 1.09218e18 0.129512
\(817\) −1.94829e19 −2.29197
\(818\) −3.45439e17 −0.0403158
\(819\) 6.78073e18 0.785111
\(820\) 2.75538e18 0.316513
\(821\) −2.51846e18 −0.287015 −0.143508 0.989649i \(-0.545838\pi\)
−0.143508 + 0.989649i \(0.545838\pi\)
\(822\) −3.64710e18 −0.412365
\(823\) 8.82032e18 0.989431 0.494715 0.869055i \(-0.335272\pi\)
0.494715 + 0.869055i \(0.335272\pi\)
\(824\) −7.73607e18 −0.860981
\(825\) 4.23504e18 0.467635
\(826\) 8.57662e17 0.0939606
\(827\) 3.27336e18 0.355802 0.177901 0.984048i \(-0.443069\pi\)
0.177901 + 0.984048i \(0.443069\pi\)
\(828\) −1.52217e18 −0.164160
\(829\) 6.05713e18 0.648131 0.324065 0.946035i \(-0.394950\pi\)
0.324065 + 0.946035i \(0.394950\pi\)
\(830\) −8.71738e17 −0.0925505
\(831\) −2.61227e18 −0.275177
\(832\) −9.74163e17 −0.101819
\(833\) 7.67433e18 0.795880
\(834\) −3.40365e18 −0.350240
\(835\) −1.15517e18 −0.117946
\(836\) 9.79190e18 0.992033
\(837\) 6.80347e17 0.0683935
\(838\) −5.21688e18 −0.520385
\(839\) 3.44143e18 0.340632 0.170316 0.985389i \(-0.445521\pi\)
0.170316 + 0.985389i \(0.445521\pi\)
\(840\) 2.26084e18 0.222052
\(841\) −8.95140e18 −0.872403
\(842\) −6.18391e18 −0.598046
\(843\) −1.18770e19 −1.13980
\(844\) −1.11329e18 −0.106018
\(845\) −4.06151e18 −0.383812
\(846\) −2.40497e18 −0.225529
\(847\) 3.50463e18 0.326137
\(848\) 3.09451e18 0.285772
\(849\) −2.94809e18 −0.270173
\(850\) 2.58823e18 0.235386
\(851\) 8.66271e18 0.781828
\(852\) −1.94871e18 −0.174538
\(853\) −9.61437e18 −0.854579 −0.427289 0.904115i \(-0.640531\pi\)
−0.427289 + 0.904115i \(0.640531\pi\)
\(854\) −6.84940e18 −0.604194
\(855\) −1.61449e18 −0.141337
\(856\) 1.13800e19 0.988696
\(857\) −1.78667e19 −1.54053 −0.770263 0.637726i \(-0.779875\pi\)
−0.770263 + 0.637726i \(0.779875\pi\)
\(858\) −4.20217e18 −0.359589
\(859\) 1.24841e19 1.06023 0.530116 0.847925i \(-0.322148\pi\)
0.530116 + 0.847925i \(0.322148\pi\)
\(860\) −4.48721e18 −0.378213
\(861\) −1.45174e19 −1.21442
\(862\) −6.69019e18 −0.555445
\(863\) 1.05396e18 0.0868472 0.0434236 0.999057i \(-0.486173\pi\)
0.0434236 + 0.999057i \(0.486173\pi\)
\(864\) −2.38485e18 −0.195039
\(865\) 5.02148e18 0.407593
\(866\) −2.90059e18 −0.233679
\(867\) −4.97407e18 −0.397730
\(868\) 5.47864e18 0.434805
\(869\) 8.83459e18 0.695918
\(870\) 3.64752e17 0.0285182
\(871\) 6.37978e18 0.495094
\(872\) −1.00600e19 −0.774890
\(873\) 7.00800e18 0.535798
\(874\) −5.43810e18 −0.412689
\(875\) −1.17959e19 −0.888546
\(876\) 8.83807e18 0.660817
\(877\) 1.28385e19 0.952834 0.476417 0.879220i \(-0.341935\pi\)
0.476417 + 0.879220i \(0.341935\pi\)
\(878\) −3.76219e18 −0.277158
\(879\) −2.04742e18 −0.149719
\(880\) 1.47047e18 0.106738
\(881\) 2.18015e19 1.57088 0.785439 0.618939i \(-0.212437\pi\)
0.785439 + 0.618939i \(0.212437\pi\)
\(882\) −3.08078e18 −0.220351
\(883\) 1.33672e19 0.949063 0.474532 0.880238i \(-0.342617\pi\)
0.474532 + 0.880238i \(0.342617\pi\)
\(884\) 9.39721e18 0.662306
\(885\) −3.20671e17 −0.0224351
\(886\) 6.20298e18 0.430806
\(887\) −1.95495e19 −1.34782 −0.673912 0.738812i \(-0.735387\pi\)
−0.673912 + 0.738812i \(0.735387\pi\)
\(888\) 8.69953e18 0.595403
\(889\) 2.22781e19 1.51362
\(890\) 1.27801e18 0.0861982
\(891\) −1.47555e18 −0.0987983
\(892\) −4.81646e18 −0.320152
\(893\) 3.14393e19 2.07462
\(894\) 2.44132e18 0.159930
\(895\) −7.77041e18 −0.505352
\(896\) −2.37001e19 −1.53020
\(897\) −8.53950e18 −0.547371
\(898\) −6.65308e18 −0.423376
\(899\) 2.00935e18 0.126945
\(900\) 3.80193e18 0.238466
\(901\) 6.36470e18 0.396339
\(902\) 8.99673e18 0.556215
\(903\) 2.36419e19 1.45115
\(904\) 1.20701e19 0.735555
\(905\) 1.45394e18 0.0879695
\(906\) −6.79988e17 −0.0408478
\(907\) −8.49574e18 −0.506703 −0.253352 0.967374i \(-0.581533\pi\)
−0.253352 + 0.967374i \(0.581533\pi\)
\(908\) 1.58640e19 0.939408
\(909\) 7.69443e18 0.452388
\(910\) 5.57935e18 0.325698
\(911\) −2.21168e18 −0.128190 −0.0640949 0.997944i \(-0.520416\pi\)
−0.0640949 + 0.997944i \(0.520416\pi\)
\(912\) 5.73163e18 0.329846
\(913\) 1.04152e19 0.595125
\(914\) 3.99958e18 0.226915
\(915\) 2.56092e18 0.144264
\(916\) −5.36277e17 −0.0299964
\(917\) 3.49772e19 1.94260
\(918\) −9.01781e17 −0.0497306
\(919\) −3.31535e18 −0.181542 −0.0907712 0.995872i \(-0.528933\pi\)
−0.0907712 + 0.995872i \(0.528933\pi\)
\(920\) −2.84725e18 −0.154812
\(921\) −9.08485e18 −0.490490
\(922\) 3.20225e18 0.171674
\(923\) −1.09324e19 −0.581974
\(924\) −1.18822e19 −0.628101
\(925\) −2.16368e19 −1.13572
\(926\) 4.55493e18 0.237416
\(927\) −6.70372e18 −0.346975
\(928\) −7.04345e18 −0.362012
\(929\) −4.98587e18 −0.254472 −0.127236 0.991873i \(-0.540610\pi\)
−0.127236 + 0.991873i \(0.540610\pi\)
\(930\) 5.59806e17 0.0283725
\(931\) 4.02739e19 2.02699
\(932\) −8.05050e18 −0.402365
\(933\) 1.12830e19 0.560006
\(934\) 1.33335e19 0.657189
\(935\) 3.02441e18 0.148035
\(936\) −8.57579e18 −0.416851
\(937\) −1.45978e19 −0.704660 −0.352330 0.935876i \(-0.614610\pi\)
−0.352330 + 0.935876i \(0.614610\pi\)
\(938\) −4.93004e18 −0.236337
\(939\) −2.80242e18 −0.133416
\(940\) 7.24097e18 0.342346
\(941\) −2.94295e19 −1.38182 −0.690908 0.722942i \(-0.742789\pi\)
−0.690908 + 0.722942i \(0.742789\pi\)
\(942\) 4.55748e18 0.212517
\(943\) 1.82828e19 0.846677
\(944\) 1.13842e18 0.0523582
\(945\) 1.95914e18 0.0894866
\(946\) −1.46514e19 −0.664642
\(947\) 1.32549e19 0.597173 0.298587 0.954383i \(-0.403485\pi\)
0.298587 + 0.954383i \(0.403485\pi\)
\(948\) 7.93109e18 0.354878
\(949\) 4.95822e19 2.20341
\(950\) 1.35827e19 0.599492
\(951\) −8.81648e18 −0.386475
\(952\) −1.65081e19 −0.718717
\(953\) −2.18343e19 −0.944139 −0.472069 0.881561i \(-0.656493\pi\)
−0.472069 + 0.881561i \(0.656493\pi\)
\(954\) −2.55505e18 −0.109732
\(955\) 3.26537e18 0.139287
\(956\) 1.47896e19 0.626585
\(957\) −4.35792e18 −0.183380
\(958\) 2.05220e19 0.857717
\(959\) −5.78550e19 −2.40170
\(960\) −2.81462e17 −0.0116053
\(961\) −2.13337e19 −0.873703
\(962\) 2.14689e19 0.873317
\(963\) 9.86137e18 0.398443
\(964\) 1.96821e19 0.789896
\(965\) 9.36066e18 0.373146
\(966\) 6.59898e18 0.261292
\(967\) 2.52961e19 0.994906 0.497453 0.867491i \(-0.334269\pi\)
0.497453 + 0.867491i \(0.334269\pi\)
\(968\) −4.43241e18 −0.173161
\(969\) 1.17886e19 0.457466
\(970\) 5.76635e18 0.222272
\(971\) 6.40939e18 0.245410 0.122705 0.992443i \(-0.460843\pi\)
0.122705 + 0.992443i \(0.460843\pi\)
\(972\) −1.32465e18 −0.0503814
\(973\) −5.39930e19 −2.03988
\(974\) −1.10394e19 −0.414297
\(975\) 2.13291e19 0.795138
\(976\) −9.09158e18 −0.336679
\(977\) −1.73549e19 −0.638423 −0.319211 0.947684i \(-0.603418\pi\)
−0.319211 + 0.947684i \(0.603418\pi\)
\(978\) −4.39665e18 −0.160664
\(979\) −1.52692e19 −0.554279
\(980\) 9.27572e18 0.334486
\(981\) −8.71751e18 −0.312280
\(982\) −1.34210e19 −0.477594
\(983\) −4.87986e19 −1.72508 −0.862541 0.505988i \(-0.831128\pi\)
−0.862541 + 0.505988i \(0.831128\pi\)
\(984\) 1.83606e19 0.644789
\(985\) 4.10991e18 0.143383
\(986\) −2.66334e18 −0.0923051
\(987\) −3.81507e19 −1.31353
\(988\) 4.93154e19 1.68679
\(989\) −2.97741e19 −1.01173
\(990\) −1.21412e18 −0.0409857
\(991\) −1.35291e19 −0.453722 −0.226861 0.973927i \(-0.572846\pi\)
−0.226861 + 0.973927i \(0.572846\pi\)
\(992\) −1.08100e19 −0.360163
\(993\) −9.20667e18 −0.304742
\(994\) 8.44811e18 0.277810
\(995\) −5.94726e17 −0.0194297
\(996\) 9.35007e18 0.303479
\(997\) −5.49885e19 −1.77318 −0.886591 0.462555i \(-0.846933\pi\)
−0.886591 + 0.462555i \(0.846933\pi\)
\(998\) 1.91243e19 0.612684
\(999\) 7.53860e18 0.239947
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.1.13 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.13 30 1.1 even 1 trivial