Properties

Label 177.12.a.b.1.8
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-47.2991 q^{2} +243.000 q^{3} +189.204 q^{4} +4204.59 q^{5} -11493.7 q^{6} +8235.98 q^{7} +87919.4 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-47.2991 q^{2} +243.000 q^{3} +189.204 q^{4} +4204.59 q^{5} -11493.7 q^{6} +8235.98 q^{7} +87919.4 q^{8} +59049.0 q^{9} -198873. q^{10} +281821. q^{11} +45976.7 q^{12} -286281. q^{13} -389554. q^{14} +1.02171e6 q^{15} -4.54600e6 q^{16} +5.87036e6 q^{17} -2.79296e6 q^{18} -8.24249e6 q^{19} +795526. q^{20} +2.00134e6 q^{21} -1.33299e7 q^{22} -1.83373e7 q^{23} +2.13644e7 q^{24} -3.11496e7 q^{25} +1.35408e7 q^{26} +1.43489e7 q^{27} +1.55828e6 q^{28} -3.47171e7 q^{29} -4.83262e7 q^{30} +3.33154e7 q^{31} +3.49627e7 q^{32} +6.84824e7 q^{33} -2.77663e8 q^{34} +3.46289e7 q^{35} +1.11723e7 q^{36} -6.02333e8 q^{37} +3.89862e8 q^{38} -6.95664e7 q^{39} +3.69665e8 q^{40} +1.14101e9 q^{41} -9.46617e7 q^{42} -9.42291e8 q^{43} +5.33217e7 q^{44} +2.48277e8 q^{45} +8.67338e8 q^{46} -1.01733e9 q^{47} -1.10468e9 q^{48} -1.90950e9 q^{49} +1.47335e9 q^{50} +1.42650e9 q^{51} -5.41657e7 q^{52} -1.59817e9 q^{53} -6.78690e8 q^{54} +1.18494e9 q^{55} +7.24102e8 q^{56} -2.00292e9 q^{57} +1.64209e9 q^{58} -7.14924e8 q^{59} +1.93313e8 q^{60} -5.49619e9 q^{61} -1.57579e9 q^{62} +4.86326e8 q^{63} +7.65650e9 q^{64} -1.20369e9 q^{65} -3.23915e9 q^{66} -9.28126e9 q^{67} +1.11070e9 q^{68} -4.45597e9 q^{69} -1.63791e9 q^{70} +5.67711e9 q^{71} +5.19155e9 q^{72} -3.15638e9 q^{73} +2.84898e10 q^{74} -7.56935e9 q^{75} -1.55951e9 q^{76} +2.32107e9 q^{77} +3.29043e9 q^{78} +3.09935e10 q^{79} -1.91140e10 q^{80} +3.48678e9 q^{81} -5.39688e10 q^{82} +6.71075e9 q^{83} +3.78663e8 q^{84} +2.46825e10 q^{85} +4.45695e10 q^{86} -8.43625e9 q^{87} +2.47775e10 q^{88} +8.36957e10 q^{89} -1.17433e10 q^{90} -2.35781e9 q^{91} -3.46950e9 q^{92} +8.09565e9 q^{93} +4.81190e10 q^{94} -3.46563e10 q^{95} +8.49593e9 q^{96} +1.29155e11 q^{97} +9.03174e10 q^{98} +1.66412e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −47.2991 −1.04517 −0.522586 0.852587i \(-0.675033\pi\)
−0.522586 + 0.852587i \(0.675033\pi\)
\(3\) 243.000 0.577350
\(4\) 189.204 0.0923849
\(5\) 4204.59 0.601712 0.300856 0.953670i \(-0.402728\pi\)
0.300856 + 0.953670i \(0.402728\pi\)
\(6\) −11493.7 −0.603430
\(7\) 8235.98 0.185215 0.0926074 0.995703i \(-0.470480\pi\)
0.0926074 + 0.995703i \(0.470480\pi\)
\(8\) 87919.4 0.948614
\(9\) 59049.0 0.333333
\(10\) −198873. −0.628892
\(11\) 281821. 0.527610 0.263805 0.964576i \(-0.415022\pi\)
0.263805 + 0.964576i \(0.415022\pi\)
\(12\) 45976.7 0.0533385
\(13\) −286281. −0.213848 −0.106924 0.994267i \(-0.534100\pi\)
−0.106924 + 0.994267i \(0.534100\pi\)
\(14\) −389554. −0.193581
\(15\) 1.02171e6 0.347398
\(16\) −4.54600e6 −1.08385
\(17\) 5.87036e6 1.00276 0.501379 0.865228i \(-0.332826\pi\)
0.501379 + 0.865228i \(0.332826\pi\)
\(18\) −2.79296e6 −0.348391
\(19\) −8.24249e6 −0.763684 −0.381842 0.924228i \(-0.624710\pi\)
−0.381842 + 0.924228i \(0.624710\pi\)
\(20\) 795526. 0.0555891
\(21\) 2.00134e6 0.106934
\(22\) −1.33299e7 −0.551443
\(23\) −1.83373e7 −0.594063 −0.297031 0.954868i \(-0.595997\pi\)
−0.297031 + 0.954868i \(0.595997\pi\)
\(24\) 2.13644e7 0.547683
\(25\) −3.11496e7 −0.637943
\(26\) 1.35408e7 0.223508
\(27\) 1.43489e7 0.192450
\(28\) 1.55828e6 0.0171111
\(29\) −3.47171e7 −0.314307 −0.157154 0.987574i \(-0.550232\pi\)
−0.157154 + 0.987574i \(0.550232\pi\)
\(30\) −4.83262e7 −0.363091
\(31\) 3.33154e7 0.209005 0.104502 0.994525i \(-0.466675\pi\)
0.104502 + 0.994525i \(0.466675\pi\)
\(32\) 3.49627e7 0.184196
\(33\) 6.84824e7 0.304616
\(34\) −2.77663e8 −1.04805
\(35\) 3.46289e7 0.111446
\(36\) 1.11723e7 0.0307950
\(37\) −6.02333e8 −1.42800 −0.713999 0.700147i \(-0.753118\pi\)
−0.713999 + 0.700147i \(0.753118\pi\)
\(38\) 3.89862e8 0.798181
\(39\) −6.95664e7 −0.123465
\(40\) 3.69665e8 0.570792
\(41\) 1.14101e9 1.53808 0.769039 0.639202i \(-0.220735\pi\)
0.769039 + 0.639202i \(0.220735\pi\)
\(42\) −9.46617e7 −0.111764
\(43\) −9.42291e8 −0.977482 −0.488741 0.872429i \(-0.662544\pi\)
−0.488741 + 0.872429i \(0.662544\pi\)
\(44\) 5.33217e7 0.0487432
\(45\) 2.48277e8 0.200571
\(46\) 8.67338e8 0.620898
\(47\) −1.01733e9 −0.647032 −0.323516 0.946223i \(-0.604865\pi\)
−0.323516 + 0.946223i \(0.604865\pi\)
\(48\) −1.10468e9 −0.625761
\(49\) −1.90950e9 −0.965695
\(50\) 1.47335e9 0.666761
\(51\) 1.42650e9 0.578942
\(52\) −5.41657e7 −0.0197563
\(53\) −1.59817e9 −0.524935 −0.262467 0.964941i \(-0.584536\pi\)
−0.262467 + 0.964941i \(0.584536\pi\)
\(54\) −6.78690e8 −0.201143
\(55\) 1.18494e9 0.317469
\(56\) 7.24102e8 0.175697
\(57\) −2.00292e9 −0.440913
\(58\) 1.64209e9 0.328505
\(59\) −7.14924e8 −0.130189
\(60\) 1.93313e8 0.0320944
\(61\) −5.49619e9 −0.833196 −0.416598 0.909091i \(-0.636778\pi\)
−0.416598 + 0.909091i \(0.636778\pi\)
\(62\) −1.57579e9 −0.218446
\(63\) 4.86326e8 0.0617383
\(64\) 7.65650e9 0.891334
\(65\) −1.20369e9 −0.128675
\(66\) −3.23915e9 −0.318376
\(67\) −9.28126e9 −0.839838 −0.419919 0.907562i \(-0.637942\pi\)
−0.419919 + 0.907562i \(0.637942\pi\)
\(68\) 1.11070e9 0.0926397
\(69\) −4.45597e9 −0.342982
\(70\) −1.63791e9 −0.116480
\(71\) 5.67711e9 0.373428 0.186714 0.982414i \(-0.440216\pi\)
0.186714 + 0.982414i \(0.440216\pi\)
\(72\) 5.19155e9 0.316205
\(73\) −3.15638e9 −0.178203 −0.0891013 0.996023i \(-0.528399\pi\)
−0.0891013 + 0.996023i \(0.528399\pi\)
\(74\) 2.84898e10 1.49250
\(75\) −7.56935e9 −0.368317
\(76\) −1.55951e9 −0.0705529
\(77\) 2.32107e9 0.0977212
\(78\) 3.29043e9 0.129042
\(79\) 3.09935e10 1.13324 0.566619 0.823980i \(-0.308251\pi\)
0.566619 + 0.823980i \(0.308251\pi\)
\(80\) −1.91140e10 −0.652165
\(81\) 3.48678e9 0.111111
\(82\) −5.39688e10 −1.60756
\(83\) 6.71075e9 0.187000 0.0935001 0.995619i \(-0.470194\pi\)
0.0935001 + 0.995619i \(0.470194\pi\)
\(84\) 3.78663e8 0.00987908
\(85\) 2.46825e10 0.603371
\(86\) 4.45695e10 1.02164
\(87\) −8.43625e9 −0.181465
\(88\) 2.47775e10 0.500498
\(89\) 8.36957e10 1.58876 0.794379 0.607422i \(-0.207796\pi\)
0.794379 + 0.607422i \(0.207796\pi\)
\(90\) −1.17433e10 −0.209631
\(91\) −2.35781e9 −0.0396078
\(92\) −3.46950e9 −0.0548825
\(93\) 8.09565e9 0.120669
\(94\) 4.81190e10 0.676260
\(95\) −3.46563e10 −0.459517
\(96\) 8.49593e9 0.106346
\(97\) 1.29155e11 1.52710 0.763551 0.645748i \(-0.223454\pi\)
0.763551 + 0.645748i \(0.223454\pi\)
\(98\) 9.03174e10 1.00932
\(99\) 1.66412e10 0.175870
\(100\) −5.89363e9 −0.0589363
\(101\) −6.81221e10 −0.644941 −0.322471 0.946579i \(-0.604513\pi\)
−0.322471 + 0.946579i \(0.604513\pi\)
\(102\) −6.74721e10 −0.605094
\(103\) −1.61545e11 −1.37306 −0.686528 0.727103i \(-0.740866\pi\)
−0.686528 + 0.727103i \(0.740866\pi\)
\(104\) −2.51697e10 −0.202859
\(105\) 8.41482e9 0.0643433
\(106\) 7.55919e10 0.548647
\(107\) 2.70987e11 1.86783 0.933916 0.357493i \(-0.116368\pi\)
0.933916 + 0.357493i \(0.116368\pi\)
\(108\) 2.71488e9 0.0177795
\(109\) 1.06839e11 0.665093 0.332546 0.943087i \(-0.392092\pi\)
0.332546 + 0.943087i \(0.392092\pi\)
\(110\) −5.60465e10 −0.331810
\(111\) −1.46367e11 −0.824455
\(112\) −3.74407e10 −0.200745
\(113\) −2.41918e11 −1.23520 −0.617599 0.786493i \(-0.711894\pi\)
−0.617599 + 0.786493i \(0.711894\pi\)
\(114\) 9.47365e10 0.460830
\(115\) −7.71008e10 −0.357455
\(116\) −6.56863e9 −0.0290373
\(117\) −1.69046e10 −0.0712826
\(118\) 3.38153e10 0.136070
\(119\) 4.83482e10 0.185726
\(120\) 8.98285e10 0.329547
\(121\) −2.05889e11 −0.721628
\(122\) 2.59965e11 0.870834
\(123\) 2.77266e11 0.888010
\(124\) 6.30342e9 0.0193089
\(125\) −3.36273e11 −0.985569
\(126\) −2.30028e10 −0.0645272
\(127\) 1.39360e11 0.374298 0.187149 0.982332i \(-0.440075\pi\)
0.187149 + 0.982332i \(0.440075\pi\)
\(128\) −4.33749e11 −1.11579
\(129\) −2.28977e11 −0.564349
\(130\) 5.69337e10 0.134487
\(131\) −7.67488e11 −1.73812 −0.869059 0.494708i \(-0.835275\pi\)
−0.869059 + 0.494708i \(0.835275\pi\)
\(132\) 1.29572e10 0.0281419
\(133\) −6.78849e10 −0.141446
\(134\) 4.38995e11 0.877776
\(135\) 6.03312e10 0.115799
\(136\) 5.16118e11 0.951230
\(137\) 4.82437e11 0.854039 0.427020 0.904242i \(-0.359564\pi\)
0.427020 + 0.904242i \(0.359564\pi\)
\(138\) 2.10763e11 0.358476
\(139\) 5.67488e11 0.927630 0.463815 0.885932i \(-0.346480\pi\)
0.463815 + 0.885932i \(0.346480\pi\)
\(140\) 6.55194e9 0.0102959
\(141\) −2.47212e11 −0.373564
\(142\) −2.68522e11 −0.390296
\(143\) −8.06799e10 −0.112828
\(144\) −2.68437e11 −0.361283
\(145\) −1.45971e11 −0.189122
\(146\) 1.49294e11 0.186252
\(147\) −4.64007e11 −0.557545
\(148\) −1.13964e11 −0.131925
\(149\) 1.25807e12 1.40340 0.701699 0.712474i \(-0.252425\pi\)
0.701699 + 0.712474i \(0.252425\pi\)
\(150\) 3.58023e11 0.384954
\(151\) −1.00010e11 −0.103674 −0.0518370 0.998656i \(-0.516508\pi\)
−0.0518370 + 0.998656i \(0.516508\pi\)
\(152\) −7.24674e11 −0.724441
\(153\) 3.46639e11 0.334252
\(154\) −1.09784e11 −0.102135
\(155\) 1.40078e11 0.125761
\(156\) −1.31623e10 −0.0114063
\(157\) −2.12968e12 −1.78183 −0.890914 0.454171i \(-0.849935\pi\)
−0.890914 + 0.454171i \(0.849935\pi\)
\(158\) −1.46596e12 −1.18443
\(159\) −3.88355e11 −0.303071
\(160\) 1.47004e11 0.110833
\(161\) −1.51026e11 −0.110029
\(162\) −1.64922e11 −0.116130
\(163\) −9.65551e11 −0.657269 −0.328635 0.944457i \(-0.606588\pi\)
−0.328635 + 0.944457i \(0.606588\pi\)
\(164\) 2.15884e11 0.142095
\(165\) 2.87940e11 0.183291
\(166\) −3.17413e11 −0.195447
\(167\) −2.58660e12 −1.54095 −0.770477 0.637468i \(-0.779982\pi\)
−0.770477 + 0.637468i \(0.779982\pi\)
\(168\) 1.75957e11 0.101439
\(169\) −1.71020e12 −0.954269
\(170\) −1.16746e12 −0.630626
\(171\) −4.86711e11 −0.254561
\(172\) −1.78286e11 −0.0903046
\(173\) 2.46099e12 1.20741 0.603707 0.797207i \(-0.293690\pi\)
0.603707 + 0.797207i \(0.293690\pi\)
\(174\) 3.99027e11 0.189663
\(175\) −2.56547e11 −0.118157
\(176\) −1.28116e12 −0.571850
\(177\) −1.73727e11 −0.0751646
\(178\) −3.95873e12 −1.66053
\(179\) −3.79982e12 −1.54551 −0.772755 0.634705i \(-0.781122\pi\)
−0.772755 + 0.634705i \(0.781122\pi\)
\(180\) 4.69750e10 0.0185297
\(181\) −3.35194e12 −1.28252 −0.641260 0.767323i \(-0.721588\pi\)
−0.641260 + 0.767323i \(0.721588\pi\)
\(182\) 1.11522e11 0.0413969
\(183\) −1.33557e12 −0.481046
\(184\) −1.61220e12 −0.563536
\(185\) −2.53256e12 −0.859243
\(186\) −3.82917e11 −0.126120
\(187\) 1.65439e12 0.529065
\(188\) −1.92484e11 −0.0597760
\(189\) 1.18177e11 0.0356446
\(190\) 1.63921e12 0.480275
\(191\) −4.77645e12 −1.35963 −0.679816 0.733382i \(-0.737941\pi\)
−0.679816 + 0.733382i \(0.737941\pi\)
\(192\) 1.86053e12 0.514612
\(193\) 8.03275e11 0.215923 0.107962 0.994155i \(-0.465568\pi\)
0.107962 + 0.994155i \(0.465568\pi\)
\(194\) −6.10893e12 −1.59608
\(195\) −2.92498e11 −0.0742903
\(196\) −3.61285e11 −0.0892157
\(197\) −4.58933e12 −1.10201 −0.551004 0.834502i \(-0.685755\pi\)
−0.551004 + 0.834502i \(0.685755\pi\)
\(198\) −7.87115e11 −0.183814
\(199\) −5.47173e12 −1.24289 −0.621445 0.783458i \(-0.713454\pi\)
−0.621445 + 0.783458i \(0.713454\pi\)
\(200\) −2.73865e12 −0.605162
\(201\) −2.25535e12 −0.484881
\(202\) 3.22211e12 0.674075
\(203\) −2.85929e11 −0.0582144
\(204\) 2.69900e11 0.0534855
\(205\) 4.79748e12 0.925480
\(206\) 7.64093e12 1.43508
\(207\) −1.08280e12 −0.198021
\(208\) 1.30143e12 0.231779
\(209\) −2.32290e12 −0.402927
\(210\) −3.98013e11 −0.0672499
\(211\) 2.55759e12 0.420996 0.210498 0.977594i \(-0.432492\pi\)
0.210498 + 0.977594i \(0.432492\pi\)
\(212\) −3.02380e11 −0.0484960
\(213\) 1.37954e12 0.215598
\(214\) −1.28174e13 −1.95221
\(215\) −3.96195e12 −0.588162
\(216\) 1.26155e12 0.182561
\(217\) 2.74385e11 0.0387108
\(218\) −5.05337e12 −0.695136
\(219\) −7.67001e11 −0.102885
\(220\) 2.24196e11 0.0293293
\(221\) −1.68058e12 −0.214437
\(222\) 6.92303e12 0.861697
\(223\) 1.33635e12 0.162271 0.0811357 0.996703i \(-0.474145\pi\)
0.0811357 + 0.996703i \(0.474145\pi\)
\(224\) 2.87952e11 0.0341158
\(225\) −1.83935e12 −0.212648
\(226\) 1.14425e13 1.29099
\(227\) −7.63779e12 −0.841057 −0.420528 0.907279i \(-0.638155\pi\)
−0.420528 + 0.907279i \(0.638155\pi\)
\(228\) −3.78962e11 −0.0407337
\(229\) 1.86050e13 1.95225 0.976123 0.217219i \(-0.0696985\pi\)
0.976123 + 0.217219i \(0.0696985\pi\)
\(230\) 3.64680e12 0.373602
\(231\) 5.64019e11 0.0564194
\(232\) −3.05230e12 −0.298156
\(233\) −7.86554e12 −0.750362 −0.375181 0.926951i \(-0.622420\pi\)
−0.375181 + 0.926951i \(0.622420\pi\)
\(234\) 7.99573e11 0.0745026
\(235\) −4.27747e12 −0.389326
\(236\) −1.35267e11 −0.0120275
\(237\) 7.53141e12 0.654275
\(238\) −2.28682e12 −0.194115
\(239\) −4.25283e12 −0.352768 −0.176384 0.984321i \(-0.556440\pi\)
−0.176384 + 0.984321i \(0.556440\pi\)
\(240\) −4.64471e12 −0.376528
\(241\) −1.92766e13 −1.52734 −0.763672 0.645605i \(-0.776605\pi\)
−0.763672 + 0.645605i \(0.776605\pi\)
\(242\) 9.73836e12 0.754225
\(243\) 8.47289e11 0.0641500
\(244\) −1.03990e12 −0.0769748
\(245\) −8.02864e12 −0.581070
\(246\) −1.31144e13 −0.928123
\(247\) 2.35967e12 0.163312
\(248\) 2.92907e12 0.198265
\(249\) 1.63071e12 0.107965
\(250\) 1.59054e13 1.03009
\(251\) 8.11676e12 0.514254 0.257127 0.966378i \(-0.417224\pi\)
0.257127 + 0.966378i \(0.417224\pi\)
\(252\) 9.20150e10 0.00570369
\(253\) −5.16783e12 −0.313433
\(254\) −6.59160e12 −0.391206
\(255\) 5.99784e12 0.348356
\(256\) 4.83543e12 0.274862
\(257\) 4.14442e12 0.230585 0.115293 0.993332i \(-0.463219\pi\)
0.115293 + 0.993332i \(0.463219\pi\)
\(258\) 1.08304e13 0.589842
\(259\) −4.96080e12 −0.264486
\(260\) −2.27744e11 −0.0118876
\(261\) −2.05001e12 −0.104769
\(262\) 3.63015e13 1.81663
\(263\) −3.40304e10 −0.00166767 −0.000833835 1.00000i \(-0.500265\pi\)
−0.000833835 1.00000i \(0.500265\pi\)
\(264\) 6.02093e12 0.288963
\(265\) −6.71964e12 −0.315859
\(266\) 3.21090e12 0.147835
\(267\) 2.03380e13 0.917270
\(268\) −1.75606e12 −0.0775884
\(269\) −5.28454e12 −0.228754 −0.114377 0.993437i \(-0.536487\pi\)
−0.114377 + 0.993437i \(0.536487\pi\)
\(270\) −2.85361e12 −0.121030
\(271\) 4.46026e13 1.85366 0.926828 0.375485i \(-0.122524\pi\)
0.926828 + 0.375485i \(0.122524\pi\)
\(272\) −2.66866e13 −1.08684
\(273\) −5.72947e11 −0.0228676
\(274\) −2.28189e13 −0.892618
\(275\) −8.77859e12 −0.336585
\(276\) −8.43088e11 −0.0316864
\(277\) −2.25119e13 −0.829419 −0.414709 0.909954i \(-0.636117\pi\)
−0.414709 + 0.909954i \(0.636117\pi\)
\(278\) −2.68416e13 −0.969533
\(279\) 1.96724e12 0.0696682
\(280\) 3.04455e12 0.105719
\(281\) 2.16093e13 0.735792 0.367896 0.929867i \(-0.380078\pi\)
0.367896 + 0.929867i \(0.380078\pi\)
\(282\) 1.16929e13 0.390439
\(283\) 5.07251e13 1.66111 0.830553 0.556940i \(-0.188025\pi\)
0.830553 + 0.556940i \(0.188025\pi\)
\(284\) 1.07413e12 0.0344991
\(285\) −8.42147e12 −0.265302
\(286\) 3.81609e12 0.117925
\(287\) 9.39734e12 0.284875
\(288\) 2.06451e12 0.0613986
\(289\) 1.89263e11 0.00552241
\(290\) 6.90430e12 0.197665
\(291\) 3.13848e13 0.881673
\(292\) −5.97202e11 −0.0164632
\(293\) −3.09748e13 −0.837986 −0.418993 0.907989i \(-0.637617\pi\)
−0.418993 + 0.907989i \(0.637617\pi\)
\(294\) 2.19471e13 0.582730
\(295\) −3.00596e12 −0.0783362
\(296\) −5.29568e13 −1.35462
\(297\) 4.04382e12 0.101539
\(298\) −5.95056e13 −1.46679
\(299\) 5.24963e12 0.127039
\(300\) −1.43215e12 −0.0340269
\(301\) −7.76069e12 −0.181044
\(302\) 4.73038e12 0.108357
\(303\) −1.65537e13 −0.372357
\(304\) 3.74703e13 0.827719
\(305\) −2.31092e13 −0.501344
\(306\) −1.63957e13 −0.349351
\(307\) −1.07004e13 −0.223944 −0.111972 0.993711i \(-0.535717\pi\)
−0.111972 + 0.993711i \(0.535717\pi\)
\(308\) 4.39156e11 0.00902797
\(309\) −3.92554e13 −0.792735
\(310\) −6.62554e12 −0.131441
\(311\) −7.06656e13 −1.37729 −0.688646 0.725098i \(-0.741794\pi\)
−0.688646 + 0.725098i \(0.741794\pi\)
\(312\) −6.11623e12 −0.117121
\(313\) 6.79714e12 0.127889 0.0639444 0.997953i \(-0.479632\pi\)
0.0639444 + 0.997953i \(0.479632\pi\)
\(314\) 1.00732e14 1.86232
\(315\) 2.04480e12 0.0371486
\(316\) 5.86410e12 0.104694
\(317\) −8.25941e12 −0.144918 −0.0724591 0.997371i \(-0.523085\pi\)
−0.0724591 + 0.997371i \(0.523085\pi\)
\(318\) 1.83688e13 0.316761
\(319\) −9.78399e12 −0.165832
\(320\) 3.21924e13 0.536326
\(321\) 6.58499e13 1.07839
\(322\) 7.14338e12 0.115000
\(323\) −4.83864e13 −0.765789
\(324\) 6.59715e11 0.0102650
\(325\) 8.91754e12 0.136423
\(326\) 4.56697e13 0.686960
\(327\) 2.59618e13 0.383991
\(328\) 1.00317e14 1.45904
\(329\) −8.37875e12 −0.119840
\(330\) −1.36193e13 −0.191570
\(331\) 1.06786e14 1.47728 0.738638 0.674102i \(-0.235469\pi\)
0.738638 + 0.674102i \(0.235469\pi\)
\(332\) 1.26970e12 0.0172760
\(333\) −3.55672e13 −0.475999
\(334\) 1.22344e14 1.61056
\(335\) −3.90239e13 −0.505340
\(336\) −9.09810e12 −0.115900
\(337\) 8.51744e13 1.06744 0.533721 0.845661i \(-0.320793\pi\)
0.533721 + 0.845661i \(0.320793\pi\)
\(338\) 8.08911e13 0.997376
\(339\) −5.87860e13 −0.713142
\(340\) 4.67003e12 0.0557424
\(341\) 9.38897e12 0.110273
\(342\) 2.30210e13 0.266060
\(343\) −3.20118e13 −0.364076
\(344\) −8.28456e13 −0.927253
\(345\) −1.87355e13 −0.206376
\(346\) −1.16403e14 −1.26195
\(347\) −2.09947e13 −0.224025 −0.112013 0.993707i \(-0.535730\pi\)
−0.112013 + 0.993707i \(0.535730\pi\)
\(348\) −1.59618e12 −0.0167647
\(349\) −1.57991e14 −1.63340 −0.816702 0.577059i \(-0.804200\pi\)
−0.816702 + 0.577059i \(0.804200\pi\)
\(350\) 1.21344e13 0.123494
\(351\) −4.10782e12 −0.0411550
\(352\) 9.85320e12 0.0971835
\(353\) −1.49722e13 −0.145386 −0.0726931 0.997354i \(-0.523159\pi\)
−0.0726931 + 0.997354i \(0.523159\pi\)
\(354\) 8.21711e12 0.0785600
\(355\) 2.38699e13 0.224696
\(356\) 1.58356e13 0.146777
\(357\) 1.17486e13 0.107229
\(358\) 1.79728e14 1.61532
\(359\) −1.43233e14 −1.26772 −0.633859 0.773448i \(-0.718530\pi\)
−0.633859 + 0.773448i \(0.718530\pi\)
\(360\) 2.18283e13 0.190264
\(361\) −4.85517e13 −0.416787
\(362\) 1.58544e14 1.34046
\(363\) −5.00310e13 −0.416632
\(364\) −4.46107e11 −0.00365916
\(365\) −1.32713e13 −0.107227
\(366\) 6.31714e13 0.502776
\(367\) −1.84151e14 −1.44382 −0.721908 0.691989i \(-0.756735\pi\)
−0.721908 + 0.691989i \(0.756735\pi\)
\(368\) 8.33613e13 0.643875
\(369\) 6.73755e13 0.512693
\(370\) 1.19788e14 0.898057
\(371\) −1.31625e13 −0.0972257
\(372\) 1.53173e12 0.0111480
\(373\) 5.36309e13 0.384607 0.192303 0.981336i \(-0.438404\pi\)
0.192303 + 0.981336i \(0.438404\pi\)
\(374\) −7.82511e13 −0.552964
\(375\) −8.17144e13 −0.569019
\(376\) −8.94434e13 −0.613783
\(377\) 9.93886e12 0.0672139
\(378\) −5.58968e12 −0.0372548
\(379\) 7.87457e13 0.517263 0.258631 0.965976i \(-0.416728\pi\)
0.258631 + 0.965976i \(0.416728\pi\)
\(380\) −6.55712e12 −0.0424525
\(381\) 3.38645e13 0.216101
\(382\) 2.25922e14 1.42105
\(383\) 1.66808e14 1.03425 0.517123 0.855911i \(-0.327003\pi\)
0.517123 + 0.855911i \(0.327003\pi\)
\(384\) −1.05401e14 −0.644203
\(385\) 9.75913e12 0.0588000
\(386\) −3.79942e13 −0.225677
\(387\) −5.56414e13 −0.325827
\(388\) 2.44368e13 0.141081
\(389\) 4.34698e13 0.247437 0.123719 0.992317i \(-0.460518\pi\)
0.123719 + 0.992317i \(0.460518\pi\)
\(390\) 1.38349e13 0.0776462
\(391\) −1.07647e14 −0.595701
\(392\) −1.67882e14 −0.916072
\(393\) −1.86500e14 −1.00350
\(394\) 2.17071e14 1.15179
\(395\) 1.30315e14 0.681882
\(396\) 3.14859e12 0.0162477
\(397\) 2.89431e13 0.147298 0.0736492 0.997284i \(-0.476535\pi\)
0.0736492 + 0.997284i \(0.476535\pi\)
\(398\) 2.58808e14 1.29903
\(399\) −1.64960e13 −0.0816636
\(400\) 1.41606e14 0.691435
\(401\) −3.82520e14 −1.84230 −0.921149 0.389211i \(-0.872748\pi\)
−0.921149 + 0.389211i \(0.872748\pi\)
\(402\) 1.06676e14 0.506784
\(403\) −9.53758e12 −0.0446952
\(404\) −1.28890e13 −0.0595829
\(405\) 1.46605e13 0.0668568
\(406\) 1.35242e13 0.0608441
\(407\) −1.69750e14 −0.753426
\(408\) 1.25417e14 0.549193
\(409\) 1.21169e14 0.523494 0.261747 0.965136i \(-0.415701\pi\)
0.261747 + 0.965136i \(0.415701\pi\)
\(410\) −2.26916e14 −0.967285
\(411\) 1.17232e14 0.493080
\(412\) −3.05650e13 −0.126850
\(413\) −5.88810e12 −0.0241129
\(414\) 5.12154e13 0.206966
\(415\) 2.82160e13 0.112520
\(416\) −1.00092e13 −0.0393899
\(417\) 1.37899e14 0.535568
\(418\) 1.09871e14 0.421128
\(419\) −1.03303e14 −0.390784 −0.195392 0.980725i \(-0.562598\pi\)
−0.195392 + 0.980725i \(0.562598\pi\)
\(420\) 1.59212e12 0.00594436
\(421\) 3.23588e13 0.119245 0.0596225 0.998221i \(-0.481010\pi\)
0.0596225 + 0.998221i \(0.481010\pi\)
\(422\) −1.20972e14 −0.440013
\(423\) −6.00726e13 −0.215677
\(424\) −1.40510e14 −0.497960
\(425\) −1.82859e14 −0.639702
\(426\) −6.52509e13 −0.225338
\(427\) −4.52665e13 −0.154320
\(428\) 5.12719e13 0.172560
\(429\) −1.96052e13 −0.0651414
\(430\) 1.87396e14 0.614731
\(431\) 2.59343e14 0.839941 0.419970 0.907538i \(-0.362040\pi\)
0.419970 + 0.907538i \(0.362040\pi\)
\(432\) −6.52301e13 −0.208587
\(433\) 3.06156e14 0.966629 0.483314 0.875447i \(-0.339433\pi\)
0.483314 + 0.875447i \(0.339433\pi\)
\(434\) −1.29782e13 −0.0404594
\(435\) −3.54710e13 −0.109190
\(436\) 2.02143e13 0.0614445
\(437\) 1.51145e14 0.453676
\(438\) 3.62785e13 0.107533
\(439\) 8.75264e12 0.0256203 0.0128101 0.999918i \(-0.495922\pi\)
0.0128101 + 0.999918i \(0.495922\pi\)
\(440\) 1.04179e14 0.301155
\(441\) −1.12754e14 −0.321898
\(442\) 7.94897e13 0.224124
\(443\) 3.44516e14 0.959376 0.479688 0.877439i \(-0.340750\pi\)
0.479688 + 0.877439i \(0.340750\pi\)
\(444\) −2.76933e13 −0.0761672
\(445\) 3.51906e14 0.955974
\(446\) −6.32079e13 −0.169602
\(447\) 3.05711e14 0.810252
\(448\) 6.30587e13 0.165088
\(449\) 9.04044e11 0.00233795 0.00116897 0.999999i \(-0.499628\pi\)
0.00116897 + 0.999999i \(0.499628\pi\)
\(450\) 8.69996e13 0.222254
\(451\) 3.21560e14 0.811505
\(452\) −4.57719e13 −0.114114
\(453\) −2.43024e13 −0.0598562
\(454\) 3.61260e14 0.879049
\(455\) −9.91360e12 −0.0238325
\(456\) −1.76096e14 −0.418256
\(457\) 3.24415e13 0.0761311 0.0380656 0.999275i \(-0.487880\pi\)
0.0380656 + 0.999275i \(0.487880\pi\)
\(458\) −8.80000e14 −2.04043
\(459\) 8.42333e13 0.192981
\(460\) −1.45878e13 −0.0330234
\(461\) 4.71969e14 1.05574 0.527871 0.849324i \(-0.322990\pi\)
0.527871 + 0.849324i \(0.322990\pi\)
\(462\) −2.66776e13 −0.0589679
\(463\) −4.86816e14 −1.06333 −0.531666 0.846954i \(-0.678434\pi\)
−0.531666 + 0.846954i \(0.678434\pi\)
\(464\) 1.57824e14 0.340662
\(465\) 3.40389e13 0.0726079
\(466\) 3.72033e14 0.784258
\(467\) −5.28154e14 −1.10032 −0.550158 0.835060i \(-0.685433\pi\)
−0.550158 + 0.835060i \(0.685433\pi\)
\(468\) −3.19843e12 −0.00658544
\(469\) −7.64403e13 −0.155551
\(470\) 2.02321e14 0.406913
\(471\) −5.17512e14 −1.02874
\(472\) −6.28557e13 −0.123499
\(473\) −2.65557e14 −0.515729
\(474\) −3.56229e14 −0.683830
\(475\) 2.56750e14 0.487187
\(476\) 9.14769e12 0.0171582
\(477\) −9.43702e13 −0.174978
\(478\) 2.01155e14 0.368703
\(479\) −1.62930e14 −0.295227 −0.147613 0.989045i \(-0.547159\pi\)
−0.147613 + 0.989045i \(0.547159\pi\)
\(480\) 3.57219e13 0.0639893
\(481\) 1.72437e14 0.305374
\(482\) 9.11766e14 1.59634
\(483\) −3.66992e13 −0.0635254
\(484\) −3.89551e13 −0.0666676
\(485\) 5.43045e14 0.918875
\(486\) −4.00760e13 −0.0670478
\(487\) −5.50531e14 −0.910694 −0.455347 0.890314i \(-0.650485\pi\)
−0.455347 + 0.890314i \(0.650485\pi\)
\(488\) −4.83221e14 −0.790382
\(489\) −2.34629e14 −0.379475
\(490\) 3.79747e14 0.607318
\(491\) −8.05489e14 −1.27383 −0.636915 0.770934i \(-0.719790\pi\)
−0.636915 + 0.770934i \(0.719790\pi\)
\(492\) 5.24599e13 0.0820388
\(493\) −2.03802e14 −0.315174
\(494\) −1.11610e14 −0.170689
\(495\) 6.99695e13 0.105823
\(496\) −1.51452e14 −0.226530
\(497\) 4.67565e13 0.0691643
\(498\) −7.71313e13 −0.112842
\(499\) −7.88458e14 −1.14084 −0.570421 0.821352i \(-0.693220\pi\)
−0.570421 + 0.821352i \(0.693220\pi\)
\(500\) −6.36244e13 −0.0910518
\(501\) −6.28545e14 −0.889670
\(502\) −3.83916e14 −0.537484
\(503\) −3.07198e14 −0.425398 −0.212699 0.977118i \(-0.568225\pi\)
−0.212699 + 0.977118i \(0.568225\pi\)
\(504\) 4.27575e13 0.0585658
\(505\) −2.86425e14 −0.388069
\(506\) 2.44434e14 0.327592
\(507\) −4.15579e14 −0.550948
\(508\) 2.63675e13 0.0345795
\(509\) 1.05222e15 1.36508 0.682540 0.730849i \(-0.260875\pi\)
0.682540 + 0.730849i \(0.260875\pi\)
\(510\) −2.83692e14 −0.364092
\(511\) −2.59959e13 −0.0330058
\(512\) 6.59607e14 0.828515
\(513\) −1.18271e14 −0.146971
\(514\) −1.96027e14 −0.241001
\(515\) −6.79229e14 −0.826184
\(516\) −4.33234e13 −0.0521374
\(517\) −2.86706e14 −0.341380
\(518\) 2.34642e14 0.276434
\(519\) 5.98020e14 0.697100
\(520\) −1.05828e14 −0.122063
\(521\) 5.34501e14 0.610015 0.305008 0.952350i \(-0.401341\pi\)
0.305008 + 0.952350i \(0.401341\pi\)
\(522\) 9.69636e13 0.109502
\(523\) 2.58752e14 0.289151 0.144575 0.989494i \(-0.453818\pi\)
0.144575 + 0.989494i \(0.453818\pi\)
\(524\) −1.45212e14 −0.160576
\(525\) −6.23410e13 −0.0682177
\(526\) 1.60961e12 0.00174300
\(527\) 1.95574e14 0.209581
\(528\) −3.11321e14 −0.330158
\(529\) −6.16553e14 −0.647089
\(530\) 3.17833e14 0.330127
\(531\) −4.22156e13 −0.0433963
\(532\) −1.28441e13 −0.0130674
\(533\) −3.26650e14 −0.328915
\(534\) −9.61971e14 −0.958705
\(535\) 1.13939e15 1.12390
\(536\) −8.16003e14 −0.796682
\(537\) −9.23357e14 −0.892300
\(538\) 2.49954e14 0.239088
\(539\) −5.38135e14 −0.509510
\(540\) 1.14149e13 0.0106981
\(541\) 7.12237e14 0.660753 0.330377 0.943849i \(-0.392824\pi\)
0.330377 + 0.943849i \(0.392824\pi\)
\(542\) −2.10966e15 −1.93739
\(543\) −8.14522e14 −0.740464
\(544\) 2.05244e14 0.184704
\(545\) 4.49212e14 0.400194
\(546\) 2.70999e13 0.0239005
\(547\) −9.55842e14 −0.834557 −0.417278 0.908779i \(-0.637016\pi\)
−0.417278 + 0.908779i \(0.637016\pi\)
\(548\) 9.12793e13 0.0789004
\(549\) −3.24544e14 −0.277732
\(550\) 4.15219e14 0.351789
\(551\) 2.86155e14 0.240031
\(552\) −3.91766e14 −0.325358
\(553\) 2.55261e14 0.209892
\(554\) 1.06479e15 0.866885
\(555\) −6.15413e14 −0.496084
\(556\) 1.07371e14 0.0856991
\(557\) −1.03837e15 −0.820634 −0.410317 0.911943i \(-0.634582\pi\)
−0.410317 + 0.911943i \(0.634582\pi\)
\(558\) −9.30488e13 −0.0728153
\(559\) 2.69760e14 0.209032
\(560\) −1.57423e14 −0.120791
\(561\) 4.02016e14 0.305456
\(562\) −1.02210e15 −0.769029
\(563\) 3.89162e14 0.289958 0.144979 0.989435i \(-0.453689\pi\)
0.144979 + 0.989435i \(0.453689\pi\)
\(564\) −4.67737e13 −0.0345117
\(565\) −1.01716e15 −0.743233
\(566\) −2.39925e15 −1.73614
\(567\) 2.87171e13 0.0205794
\(568\) 4.99128e14 0.354239
\(569\) 1.80300e15 1.26730 0.633649 0.773621i \(-0.281556\pi\)
0.633649 + 0.773621i \(0.281556\pi\)
\(570\) 3.98328e14 0.277287
\(571\) 8.23896e12 0.00568033 0.00284017 0.999996i \(-0.499096\pi\)
0.00284017 + 0.999996i \(0.499096\pi\)
\(572\) −1.52650e13 −0.0104236
\(573\) −1.16068e15 −0.784984
\(574\) −4.44486e14 −0.297743
\(575\) 5.71199e14 0.378978
\(576\) 4.52109e14 0.297111
\(577\) −1.90100e15 −1.23741 −0.618706 0.785622i \(-0.712343\pi\)
−0.618706 + 0.785622i \(0.712343\pi\)
\(578\) −8.95199e12 −0.00577187
\(579\) 1.95196e14 0.124663
\(580\) −2.76184e13 −0.0174721
\(581\) 5.52696e13 0.0346352
\(582\) −1.48447e15 −0.921500
\(583\) −4.50397e14 −0.276961
\(584\) −2.77507e14 −0.169046
\(585\) −7.10770e13 −0.0428915
\(586\) 1.46508e15 0.875840
\(587\) −4.79622e14 −0.284047 −0.142023 0.989863i \(-0.545361\pi\)
−0.142023 + 0.989863i \(0.545361\pi\)
\(588\) −8.77922e13 −0.0515087
\(589\) −2.74602e14 −0.159613
\(590\) 1.42179e14 0.0818748
\(591\) −1.11521e15 −0.636245
\(592\) 2.73821e15 1.54774
\(593\) 2.57962e15 1.44462 0.722312 0.691568i \(-0.243080\pi\)
0.722312 + 0.691568i \(0.243080\pi\)
\(594\) −1.91269e14 −0.106125
\(595\) 2.03284e14 0.111753
\(596\) 2.38033e14 0.129653
\(597\) −1.32963e15 −0.717583
\(598\) −2.48303e14 −0.132778
\(599\) 6.39537e14 0.338858 0.169429 0.985542i \(-0.445808\pi\)
0.169429 + 0.985542i \(0.445808\pi\)
\(600\) −6.65492e14 −0.349390
\(601\) 1.81544e14 0.0944436 0.0472218 0.998884i \(-0.484963\pi\)
0.0472218 + 0.998884i \(0.484963\pi\)
\(602\) 3.67074e14 0.189222
\(603\) −5.48049e14 −0.279946
\(604\) −1.89223e13 −0.00957792
\(605\) −8.65678e14 −0.434212
\(606\) 7.82973e14 0.389177
\(607\) −1.87669e15 −0.924387 −0.462194 0.886779i \(-0.652937\pi\)
−0.462194 + 0.886779i \(0.652937\pi\)
\(608\) −2.88179e14 −0.140667
\(609\) −6.94808e13 −0.0336101
\(610\) 1.09304e15 0.523991
\(611\) 2.91244e14 0.138366
\(612\) 6.55856e13 0.0308799
\(613\) 2.34801e13 0.0109564 0.00547820 0.999985i \(-0.498256\pi\)
0.00547820 + 0.999985i \(0.498256\pi\)
\(614\) 5.06120e14 0.234060
\(615\) 1.16579e15 0.534326
\(616\) 2.04067e14 0.0926997
\(617\) −2.75414e15 −1.23999 −0.619993 0.784607i \(-0.712865\pi\)
−0.619993 + 0.784607i \(0.712865\pi\)
\(618\) 1.85675e15 0.828544
\(619\) 1.04827e15 0.463631 0.231816 0.972760i \(-0.425533\pi\)
0.231816 + 0.972760i \(0.425533\pi\)
\(620\) 2.65033e13 0.0116184
\(621\) −2.63120e14 −0.114327
\(622\) 3.34242e15 1.43951
\(623\) 6.89316e14 0.294262
\(624\) 3.16248e14 0.133818
\(625\) 1.07085e14 0.0449148
\(626\) −3.21499e14 −0.133666
\(627\) −5.64465e14 −0.232630
\(628\) −4.02944e14 −0.164614
\(629\) −3.53592e15 −1.43194
\(630\) −9.67172e13 −0.0388267
\(631\) −1.74350e15 −0.693841 −0.346921 0.937894i \(-0.612773\pi\)
−0.346921 + 0.937894i \(0.612773\pi\)
\(632\) 2.72492e15 1.07501
\(633\) 6.21495e14 0.243062
\(634\) 3.90662e14 0.151464
\(635\) 5.85951e14 0.225219
\(636\) −7.34784e13 −0.0279992
\(637\) 5.46653e14 0.206512
\(638\) 4.62774e14 0.173323
\(639\) 3.35228e14 0.124476
\(640\) −1.82374e15 −0.671385
\(641\) −4.25280e15 −1.55223 −0.776114 0.630593i \(-0.782812\pi\)
−0.776114 + 0.630593i \(0.782812\pi\)
\(642\) −3.11464e15 −1.12711
\(643\) 3.10107e15 1.11263 0.556315 0.830971i \(-0.312215\pi\)
0.556315 + 0.830971i \(0.312215\pi\)
\(644\) −2.85747e13 −0.0101651
\(645\) −9.62753e14 −0.339576
\(646\) 2.28863e15 0.800382
\(647\) 5.81472e13 0.0201630 0.0100815 0.999949i \(-0.496791\pi\)
0.0100815 + 0.999949i \(0.496791\pi\)
\(648\) 3.06556e14 0.105402
\(649\) −2.01480e14 −0.0686889
\(650\) −4.21792e14 −0.142585
\(651\) 6.66756e13 0.0223497
\(652\) −1.82686e14 −0.0607218
\(653\) −2.69946e15 −0.889722 −0.444861 0.895600i \(-0.646747\pi\)
−0.444861 + 0.895600i \(0.646747\pi\)
\(654\) −1.22797e15 −0.401337
\(655\) −3.22697e15 −1.04585
\(656\) −5.18703e15 −1.66705
\(657\) −1.86381e14 −0.0594009
\(658\) 3.96307e14 0.125253
\(659\) 3.01895e15 0.946205 0.473103 0.881007i \(-0.343134\pi\)
0.473103 + 0.881007i \(0.343134\pi\)
\(660\) 5.44795e13 0.0169333
\(661\) 1.80854e15 0.557469 0.278735 0.960368i \(-0.410085\pi\)
0.278735 + 0.960368i \(0.410085\pi\)
\(662\) −5.05090e15 −1.54401
\(663\) −4.08380e14 −0.123805
\(664\) 5.90005e14 0.177391
\(665\) −2.85428e14 −0.0851094
\(666\) 1.68230e15 0.497501
\(667\) 6.36618e14 0.186718
\(668\) −4.89397e14 −0.142361
\(669\) 3.24732e14 0.0936874
\(670\) 1.84579e15 0.528168
\(671\) −1.54894e15 −0.439602
\(672\) 6.99723e13 0.0196968
\(673\) 1.28360e15 0.358381 0.179191 0.983814i \(-0.442652\pi\)
0.179191 + 0.983814i \(0.442652\pi\)
\(674\) −4.02867e15 −1.11566
\(675\) −4.46962e14 −0.122772
\(676\) −3.23578e14 −0.0881601
\(677\) 5.87526e15 1.58778 0.793888 0.608064i \(-0.208054\pi\)
0.793888 + 0.608064i \(0.208054\pi\)
\(678\) 2.78053e15 0.745356
\(679\) 1.06372e15 0.282842
\(680\) 2.17007e15 0.572366
\(681\) −1.85598e15 −0.485584
\(682\) −4.44090e14 −0.115254
\(683\) −2.70362e15 −0.696037 −0.348018 0.937488i \(-0.613145\pi\)
−0.348018 + 0.937488i \(0.613145\pi\)
\(684\) −9.20878e13 −0.0235176
\(685\) 2.02845e15 0.513885
\(686\) 1.51413e15 0.380522
\(687\) 4.52101e15 1.12713
\(688\) 4.28365e15 1.05944
\(689\) 4.57526e14 0.112256
\(690\) 8.86172e14 0.215699
\(691\) 3.12375e15 0.754305 0.377152 0.926151i \(-0.376903\pi\)
0.377152 + 0.926151i \(0.376903\pi\)
\(692\) 4.65630e14 0.111547
\(693\) 1.37057e14 0.0325737
\(694\) 9.93029e14 0.234145
\(695\) 2.38605e15 0.558166
\(696\) −7.41710e14 −0.172141
\(697\) 6.69815e15 1.54232
\(698\) 7.47285e15 1.70719
\(699\) −1.91133e15 −0.433222
\(700\) −4.85398e13 −0.0109159
\(701\) 3.98398e15 0.888930 0.444465 0.895796i \(-0.353394\pi\)
0.444465 + 0.895796i \(0.353394\pi\)
\(702\) 1.94296e14 0.0430141
\(703\) 4.96473e15 1.09054
\(704\) 2.15776e15 0.470276
\(705\) −1.03943e15 −0.224778
\(706\) 7.08169e14 0.151954
\(707\) −5.61052e14 −0.119453
\(708\) −3.28698e13 −0.00694408
\(709\) −5.06410e15 −1.06157 −0.530784 0.847507i \(-0.678103\pi\)
−0.530784 + 0.847507i \(0.678103\pi\)
\(710\) −1.12902e15 −0.234846
\(711\) 1.83013e15 0.377746
\(712\) 7.35847e15 1.50712
\(713\) −6.10915e14 −0.124162
\(714\) −5.55698e14 −0.112072
\(715\) −3.39226e14 −0.0678900
\(716\) −7.18943e14 −0.142782
\(717\) −1.03344e15 −0.203671
\(718\) 6.77478e15 1.32498
\(719\) −5.40287e15 −1.04861 −0.524307 0.851529i \(-0.675676\pi\)
−0.524307 + 0.851529i \(0.675676\pi\)
\(720\) −1.12866e15 −0.217388
\(721\) −1.33048e15 −0.254311
\(722\) 2.29645e15 0.435614
\(723\) −4.68421e15 −0.881812
\(724\) −6.34202e14 −0.118486
\(725\) 1.08142e15 0.200510
\(726\) 2.36642e15 0.435452
\(727\) 5.20866e15 0.951232 0.475616 0.879653i \(-0.342225\pi\)
0.475616 + 0.879653i \(0.342225\pi\)
\(728\) −2.07297e14 −0.0375725
\(729\) 2.05891e14 0.0370370
\(730\) 6.27720e14 0.112070
\(731\) −5.53159e15 −0.980177
\(732\) −2.52696e14 −0.0444414
\(733\) 1.03525e16 1.80706 0.903529 0.428527i \(-0.140967\pi\)
0.903529 + 0.428527i \(0.140967\pi\)
\(734\) 8.71020e15 1.50904
\(735\) −1.95096e15 −0.335481
\(736\) −6.41121e14 −0.109424
\(737\) −2.61565e15 −0.443107
\(738\) −3.18680e15 −0.535852
\(739\) 7.37617e15 1.23108 0.615540 0.788105i \(-0.288938\pi\)
0.615540 + 0.788105i \(0.288938\pi\)
\(740\) −4.79172e14 −0.0793811
\(741\) 5.73400e14 0.0942882
\(742\) 6.22573e14 0.101618
\(743\) 1.70163e15 0.275693 0.137846 0.990454i \(-0.455982\pi\)
0.137846 + 0.990454i \(0.455982\pi\)
\(744\) 7.11764e14 0.114468
\(745\) 5.28967e15 0.844440
\(746\) −2.53670e15 −0.401980
\(747\) 3.96263e14 0.0623334
\(748\) 3.13018e14 0.0488776
\(749\) 2.23184e15 0.345950
\(750\) 3.86502e15 0.594723
\(751\) −1.60833e15 −0.245672 −0.122836 0.992427i \(-0.539199\pi\)
−0.122836 + 0.992427i \(0.539199\pi\)
\(752\) 4.62480e15 0.701285
\(753\) 1.97237e15 0.296905
\(754\) −4.70099e14 −0.0702501
\(755\) −4.20501e14 −0.0623819
\(756\) 2.23597e13 0.00329303
\(757\) 2.14689e15 0.313893 0.156947 0.987607i \(-0.449835\pi\)
0.156947 + 0.987607i \(0.449835\pi\)
\(758\) −3.72460e15 −0.540629
\(759\) −1.25578e15 −0.180961
\(760\) −3.04696e15 −0.435905
\(761\) 5.84822e15 0.830631 0.415316 0.909677i \(-0.363671\pi\)
0.415316 + 0.909677i \(0.363671\pi\)
\(762\) −1.60176e15 −0.225863
\(763\) 8.79920e14 0.123185
\(764\) −9.03725e14 −0.125610
\(765\) 1.45747e15 0.201124
\(766\) −7.88987e15 −1.08097
\(767\) 2.04669e14 0.0278406
\(768\) 1.17501e15 0.158692
\(769\) −1.22144e16 −1.63787 −0.818934 0.573888i \(-0.805435\pi\)
−0.818934 + 0.573888i \(0.805435\pi\)
\(770\) −4.61598e14 −0.0614561
\(771\) 1.00709e15 0.133128
\(772\) 1.51983e14 0.0199480
\(773\) 1.07268e16 1.39792 0.698959 0.715162i \(-0.253647\pi\)
0.698959 + 0.715162i \(0.253647\pi\)
\(774\) 2.63179e15 0.340546
\(775\) −1.03776e15 −0.133333
\(776\) 1.13553e16 1.44863
\(777\) −1.20548e15 −0.152701
\(778\) −2.05608e15 −0.258615
\(779\) −9.40477e15 −1.17461
\(780\) −5.53419e13 −0.00686331
\(781\) 1.59993e15 0.197024
\(782\) 5.09159e15 0.622610
\(783\) −4.98152e14 −0.0604885
\(784\) 8.68056e15 1.04667
\(785\) −8.95442e15 −1.07215
\(786\) 8.82126e15 1.04883
\(787\) −5.89767e15 −0.696337 −0.348169 0.937432i \(-0.613196\pi\)
−0.348169 + 0.937432i \(0.613196\pi\)
\(788\) −8.68321e14 −0.101809
\(789\) −8.26938e12 −0.000962829 0
\(790\) −6.16377e15 −0.712684
\(791\) −1.99243e15 −0.228777
\(792\) 1.46309e15 0.166833
\(793\) 1.57346e15 0.178177
\(794\) −1.36898e15 −0.153952
\(795\) −1.63287e15 −0.182361
\(796\) −1.03528e15 −0.114824
\(797\) −1.19466e16 −1.31590 −0.657949 0.753062i \(-0.728576\pi\)
−0.657949 + 0.753062i \(0.728576\pi\)
\(798\) 7.80248e14 0.0853526
\(799\) −5.97212e15 −0.648816
\(800\) −1.08907e15 −0.117506
\(801\) 4.94214e15 0.529586
\(802\) 1.80928e16 1.92552
\(803\) −8.89534e14 −0.0940215
\(804\) −4.26722e14 −0.0447957
\(805\) −6.35000e14 −0.0662059
\(806\) 4.51119e14 0.0467141
\(807\) −1.28414e15 −0.132071
\(808\) −5.98925e15 −0.611800
\(809\) −6.72785e15 −0.682589 −0.341295 0.939956i \(-0.610865\pi\)
−0.341295 + 0.939956i \(0.610865\pi\)
\(810\) −6.93428e14 −0.0698769
\(811\) 9.15322e15 0.916134 0.458067 0.888918i \(-0.348542\pi\)
0.458067 + 0.888918i \(0.348542\pi\)
\(812\) −5.40990e13 −0.00537813
\(813\) 1.08384e16 1.07021
\(814\) 8.02902e15 0.787459
\(815\) −4.05974e15 −0.395486
\(816\) −6.48486e15 −0.627487
\(817\) 7.76683e15 0.746487
\(818\) −5.73116e15 −0.547142
\(819\) −1.39226e14 −0.0132026
\(820\) 9.07704e14 0.0855004
\(821\) −1.32950e16 −1.24395 −0.621973 0.783039i \(-0.713669\pi\)
−0.621973 + 0.783039i \(0.713669\pi\)
\(822\) −5.54498e15 −0.515353
\(823\) 3.17979e15 0.293562 0.146781 0.989169i \(-0.453109\pi\)
0.146781 + 0.989169i \(0.453109\pi\)
\(824\) −1.42029e16 −1.30250
\(825\) −2.13320e15 −0.194327
\(826\) 2.78502e14 0.0252022
\(827\) 2.13503e16 1.91921 0.959606 0.281346i \(-0.0907810\pi\)
0.959606 + 0.281346i \(0.0907810\pi\)
\(828\) −2.04870e14 −0.0182942
\(829\) −1.86561e16 −1.65489 −0.827447 0.561543i \(-0.810208\pi\)
−0.827447 + 0.561543i \(0.810208\pi\)
\(830\) −1.33459e15 −0.117603
\(831\) −5.47040e15 −0.478865
\(832\) −2.19191e15 −0.190610
\(833\) −1.12094e16 −0.968358
\(834\) −6.52252e15 −0.559760
\(835\) −1.08756e16 −0.927209
\(836\) −4.39503e14 −0.0372244
\(837\) 4.78040e14 0.0402230
\(838\) 4.88615e15 0.408436
\(839\) −8.22682e15 −0.683190 −0.341595 0.939847i \(-0.610967\pi\)
−0.341595 + 0.939847i \(0.610967\pi\)
\(840\) 7.39825e14 0.0610370
\(841\) −1.09952e16 −0.901211
\(842\) −1.53054e15 −0.124632
\(843\) 5.25105e15 0.424810
\(844\) 4.83907e14 0.0388937
\(845\) −7.19070e15 −0.574195
\(846\) 2.84138e15 0.225420
\(847\) −1.69570e15 −0.133656
\(848\) 7.26527e15 0.568950
\(849\) 1.23262e16 0.959040
\(850\) 8.64908e15 0.668599
\(851\) 1.10452e16 0.848321
\(852\) 2.61015e14 0.0199181
\(853\) −1.84247e16 −1.39695 −0.698474 0.715635i \(-0.746137\pi\)
−0.698474 + 0.715635i \(0.746137\pi\)
\(854\) 2.14106e15 0.161291
\(855\) −2.04642e15 −0.153172
\(856\) 2.38250e16 1.77185
\(857\) −1.62127e16 −1.19801 −0.599004 0.800746i \(-0.704437\pi\)
−0.599004 + 0.800746i \(0.704437\pi\)
\(858\) 9.27309e14 0.0680839
\(859\) −1.84274e16 −1.34431 −0.672157 0.740408i \(-0.734632\pi\)
−0.672157 + 0.740408i \(0.734632\pi\)
\(860\) −7.49618e14 −0.0543373
\(861\) 2.28355e15 0.164473
\(862\) −1.22667e16 −0.877883
\(863\) 2.70048e15 0.192036 0.0960179 0.995380i \(-0.469389\pi\)
0.0960179 + 0.995380i \(0.469389\pi\)
\(864\) 5.01676e14 0.0354485
\(865\) 1.03474e16 0.726514
\(866\) −1.44809e16 −1.01029
\(867\) 4.59910e13 0.00318836
\(868\) 5.19148e13 0.00357629
\(869\) 8.73459e15 0.597907
\(870\) 1.67774e15 0.114122
\(871\) 2.65705e15 0.179597
\(872\) 9.39317e15 0.630916
\(873\) 7.62650e15 0.509034
\(874\) −7.14902e15 −0.474170
\(875\) −2.76954e15 −0.182542
\(876\) −1.45120e14 −0.00950506
\(877\) −2.01065e15 −0.130870 −0.0654349 0.997857i \(-0.520843\pi\)
−0.0654349 + 0.997857i \(0.520843\pi\)
\(878\) −4.13992e14 −0.0267776
\(879\) −7.52688e15 −0.483812
\(880\) −5.38673e15 −0.344089
\(881\) −1.38461e16 −0.878939 −0.439469 0.898258i \(-0.644833\pi\)
−0.439469 + 0.898258i \(0.644833\pi\)
\(882\) 5.33315e15 0.336439
\(883\) 2.49585e16 1.56471 0.782357 0.622830i \(-0.214017\pi\)
0.782357 + 0.622830i \(0.214017\pi\)
\(884\) −3.17972e14 −0.0198108
\(885\) −7.30449e14 −0.0452274
\(886\) −1.62953e16 −1.00271
\(887\) −1.78428e16 −1.09115 −0.545574 0.838063i \(-0.683688\pi\)
−0.545574 + 0.838063i \(0.683688\pi\)
\(888\) −1.28685e16 −0.782089
\(889\) 1.14777e15 0.0693256
\(890\) −1.66448e16 −0.999158
\(891\) 9.82647e14 0.0586233
\(892\) 2.52842e14 0.0149914
\(893\) 8.38537e15 0.494128
\(894\) −1.44599e16 −0.846853
\(895\) −1.59767e16 −0.929951
\(896\) −3.57235e15 −0.206661
\(897\) 1.27566e15 0.0733460
\(898\) −4.27605e13 −0.00244356
\(899\) −1.15661e15 −0.0656917
\(900\) −3.48013e14 −0.0196454
\(901\) −9.38183e15 −0.526382
\(902\) −1.52095e16 −0.848163
\(903\) −1.88585e15 −0.104526
\(904\) −2.12693e16 −1.17173
\(905\) −1.40935e16 −0.771708
\(906\) 1.14948e15 0.0625601
\(907\) 1.58086e16 0.855174 0.427587 0.903974i \(-0.359364\pi\)
0.427587 + 0.903974i \(0.359364\pi\)
\(908\) −1.44510e15 −0.0777010
\(909\) −4.02254e15 −0.214980
\(910\) 4.68904e14 0.0249090
\(911\) 2.08974e15 0.110342 0.0551711 0.998477i \(-0.482430\pi\)
0.0551711 + 0.998477i \(0.482430\pi\)
\(912\) 9.10529e15 0.477884
\(913\) 1.89123e15 0.0986631
\(914\) −1.53446e15 −0.0795702
\(915\) −5.61553e15 −0.289451
\(916\) 3.52015e15 0.180358
\(917\) −6.32101e15 −0.321925
\(918\) −3.98416e15 −0.201698
\(919\) −2.87166e16 −1.44510 −0.722551 0.691318i \(-0.757030\pi\)
−0.722551 + 0.691318i \(0.757030\pi\)
\(920\) −6.77865e15 −0.339086
\(921\) −2.60020e15 −0.129294
\(922\) −2.23237e16 −1.10343
\(923\) −1.62525e15 −0.0798566
\(924\) 1.06715e14 0.00521230
\(925\) 1.87624e16 0.910981
\(926\) 2.30259e16 1.11137
\(927\) −9.53906e15 −0.457686
\(928\) −1.21380e15 −0.0578941
\(929\) 1.56332e16 0.741243 0.370621 0.928784i \(-0.379145\pi\)
0.370621 + 0.928784i \(0.379145\pi\)
\(930\) −1.61001e15 −0.0758877
\(931\) 1.57390e16 0.737486
\(932\) −1.48819e15 −0.0693222
\(933\) −1.71717e16 −0.795179
\(934\) 2.49812e16 1.15002
\(935\) 6.95602e15 0.318344
\(936\) −1.48624e15 −0.0676196
\(937\) −3.51956e16 −1.59192 −0.795958 0.605351i \(-0.793033\pi\)
−0.795958 + 0.605351i \(0.793033\pi\)
\(938\) 3.61556e15 0.162577
\(939\) 1.65171e15 0.0738367
\(940\) −8.09316e14 −0.0359679
\(941\) 3.43286e15 0.151675 0.0758373 0.997120i \(-0.475837\pi\)
0.0758373 + 0.997120i \(0.475837\pi\)
\(942\) 2.44778e16 1.07521
\(943\) −2.09231e16 −0.913715
\(944\) 3.25004e15 0.141105
\(945\) 4.96887e14 0.0214478
\(946\) 1.25606e16 0.539026
\(947\) 1.10249e16 0.470380 0.235190 0.971949i \(-0.424429\pi\)
0.235190 + 0.971949i \(0.424429\pi\)
\(948\) 1.42498e15 0.0604452
\(949\) 9.03614e14 0.0381082
\(950\) −1.21440e16 −0.509194
\(951\) −2.00704e15 −0.0836686
\(952\) 4.25074e15 0.176182
\(953\) 2.73506e15 0.112708 0.0563542 0.998411i \(-0.482052\pi\)
0.0563542 + 0.998411i \(0.482052\pi\)
\(954\) 4.46363e15 0.182882
\(955\) −2.00830e16 −0.818107
\(956\) −8.04653e14 −0.0325904
\(957\) −2.37751e15 −0.0957429
\(958\) 7.70644e15 0.308563
\(959\) 3.97334e15 0.158181
\(960\) 7.82276e15 0.309648
\(961\) −2.42986e16 −0.956317
\(962\) −8.15611e15 −0.319168
\(963\) 1.60015e16 0.622611
\(964\) −3.64722e15 −0.141104
\(965\) 3.37744e15 0.129923
\(966\) 1.73584e15 0.0663950
\(967\) −3.35304e16 −1.27524 −0.637622 0.770350i \(-0.720082\pi\)
−0.637622 + 0.770350i \(0.720082\pi\)
\(968\) −1.81016e16 −0.684546
\(969\) −1.17579e16 −0.442129
\(970\) −2.56855e16 −0.960382
\(971\) 3.35993e16 1.24918 0.624590 0.780953i \(-0.285266\pi\)
0.624590 + 0.780953i \(0.285266\pi\)
\(972\) 1.60311e14 0.00592650
\(973\) 4.67381e15 0.171811
\(974\) 2.60396e16 0.951833
\(975\) 2.16696e15 0.0787637
\(976\) 2.49856e16 0.903060
\(977\) 2.84370e16 1.02203 0.511016 0.859571i \(-0.329269\pi\)
0.511016 + 0.859571i \(0.329269\pi\)
\(978\) 1.10977e16 0.396616
\(979\) 2.35872e16 0.838245
\(980\) −1.51905e15 −0.0536821
\(981\) 6.30871e15 0.221698
\(982\) 3.80989e16 1.33137
\(983\) 2.38776e16 0.829749 0.414875 0.909879i \(-0.363825\pi\)
0.414875 + 0.909879i \(0.363825\pi\)
\(984\) 2.43770e16 0.842379
\(985\) −1.92962e16 −0.663091
\(986\) 9.63965e15 0.329411
\(987\) −2.03604e15 −0.0691896
\(988\) 4.46460e14 0.0150876
\(989\) 1.72791e16 0.580686
\(990\) −3.30949e15 −0.110603
\(991\) −4.58544e16 −1.52397 −0.761984 0.647596i \(-0.775774\pi\)
−0.761984 + 0.647596i \(0.775774\pi\)
\(992\) 1.16480e15 0.0384978
\(993\) 2.59491e16 0.852906
\(994\) −2.21154e15 −0.0722886
\(995\) −2.30064e16 −0.747861
\(996\) 3.08538e14 0.00997430
\(997\) 8.37516e15 0.269259 0.134629 0.990896i \(-0.457016\pi\)
0.134629 + 0.990896i \(0.457016\pi\)
\(998\) 3.72934e16 1.19238
\(999\) −8.64283e15 −0.274818
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.12.a.b.1.8 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.b.1.8 27 1.1 even 1 trivial