Properties

Label 177.12.a.b.1.17
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 1.17
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+13.5218 q^{2} +243.000 q^{3} -1865.16 q^{4} -12002.6 q^{5} +3285.79 q^{6} -19689.8 q^{7} -52912.9 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+13.5218 q^{2} +243.000 q^{3} -1865.16 q^{4} -12002.6 q^{5} +3285.79 q^{6} -19689.8 q^{7} -52912.9 q^{8} +59049.0 q^{9} -162297. q^{10} +275762. q^{11} -453234. q^{12} +260615. q^{13} -266242. q^{14} -2.91664e6 q^{15} +3.10438e6 q^{16} +2.78427e6 q^{17} +798447. q^{18} +1.56707e7 q^{19} +2.23868e7 q^{20} -4.78463e6 q^{21} +3.72879e6 q^{22} -5.51728e7 q^{23} -1.28578e7 q^{24} +9.52349e7 q^{25} +3.52397e6 q^{26} +1.43489e7 q^{27} +3.67247e7 q^{28} -4.30019e7 q^{29} -3.94381e7 q^{30} +1.37545e7 q^{31} +1.50342e8 q^{32} +6.70102e7 q^{33} +3.76483e7 q^{34} +2.36330e8 q^{35} -1.10136e8 q^{36} +2.61056e8 q^{37} +2.11896e8 q^{38} +6.33294e7 q^{39} +6.35094e8 q^{40} +1.38214e9 q^{41} -6.46967e7 q^{42} +4.91328e8 q^{43} -5.14341e8 q^{44} -7.08743e8 q^{45} -7.46034e8 q^{46} +9.26195e8 q^{47} +7.54363e8 q^{48} -1.58964e9 q^{49} +1.28774e9 q^{50} +6.76579e8 q^{51} -4.86089e8 q^{52} -5.11389e9 q^{53} +1.94023e8 q^{54} -3.30987e9 q^{55} +1.04185e9 q^{56} +3.80799e9 q^{57} -5.81463e8 q^{58} -7.14924e8 q^{59} +5.44000e9 q^{60} +5.97047e9 q^{61} +1.85985e8 q^{62} -1.16267e9 q^{63} -4.32487e9 q^{64} -3.12806e9 q^{65} +9.06096e8 q^{66} +1.02331e10 q^{67} -5.19312e9 q^{68} -1.34070e10 q^{69} +3.19560e9 q^{70} -2.24186e10 q^{71} -3.12445e9 q^{72} -2.72185e10 q^{73} +3.52995e9 q^{74} +2.31421e10 q^{75} -2.92285e10 q^{76} -5.42971e9 q^{77} +8.56325e8 q^{78} -2.62365e10 q^{79} -3.72607e10 q^{80} +3.48678e9 q^{81} +1.86890e10 q^{82} -4.00527e10 q^{83} +8.92411e9 q^{84} -3.34186e10 q^{85} +6.64363e9 q^{86} -1.04495e10 q^{87} -1.45914e10 q^{88} +6.06398e10 q^{89} -9.58346e9 q^{90} -5.13146e9 q^{91} +1.02906e11 q^{92} +3.34235e9 q^{93} +1.25238e10 q^{94} -1.88090e11 q^{95} +3.65332e10 q^{96} +1.53603e11 q^{97} -2.14947e10 q^{98} +1.62835e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.5218 0.298792 0.149396 0.988777i \(-0.452267\pi\)
0.149396 + 0.988777i \(0.452267\pi\)
\(3\) 243.000 0.577350
\(4\) −1865.16 −0.910723
\(5\) −12002.6 −1.71768 −0.858838 0.512247i \(-0.828813\pi\)
−0.858838 + 0.512247i \(0.828813\pi\)
\(6\) 3285.79 0.172508
\(7\) −19689.8 −0.442795 −0.221398 0.975184i \(-0.571062\pi\)
−0.221398 + 0.975184i \(0.571062\pi\)
\(8\) −52912.9 −0.570908
\(9\) 59049.0 0.333333
\(10\) −162297. −0.513228
\(11\) 275762. 0.516267 0.258134 0.966109i \(-0.416892\pi\)
0.258134 + 0.966109i \(0.416892\pi\)
\(12\) −453234. −0.525806
\(13\) 260615. 0.194675 0.0973376 0.995251i \(-0.468967\pi\)
0.0973376 + 0.995251i \(0.468967\pi\)
\(14\) −266242. −0.132304
\(15\) −2.91664e6 −0.991701
\(16\) 3.10438e6 0.740141
\(17\) 2.78427e6 0.475601 0.237801 0.971314i \(-0.423574\pi\)
0.237801 + 0.971314i \(0.423574\pi\)
\(18\) 798447. 0.0995973
\(19\) 1.56707e7 1.45193 0.725964 0.687733i \(-0.241394\pi\)
0.725964 + 0.687733i \(0.241394\pi\)
\(20\) 2.23868e7 1.56433
\(21\) −4.78463e6 −0.255648
\(22\) 3.72879e6 0.154256
\(23\) −5.51728e7 −1.78740 −0.893700 0.448665i \(-0.851900\pi\)
−0.893700 + 0.448665i \(0.851900\pi\)
\(24\) −1.28578e7 −0.329614
\(25\) 9.52349e7 1.95041
\(26\) 3.52397e6 0.0581673
\(27\) 1.43489e7 0.192450
\(28\) 3.67247e7 0.403264
\(29\) −4.30019e7 −0.389313 −0.194657 0.980871i \(-0.562359\pi\)
−0.194657 + 0.980871i \(0.562359\pi\)
\(30\) −3.94381e7 −0.296312
\(31\) 1.37545e7 0.0862891 0.0431446 0.999069i \(-0.486262\pi\)
0.0431446 + 0.999069i \(0.486262\pi\)
\(32\) 1.50342e8 0.792056
\(33\) 6.70102e7 0.298067
\(34\) 3.76483e7 0.142106
\(35\) 2.36330e8 0.760579
\(36\) −1.10136e8 −0.303574
\(37\) 2.61056e8 0.618906 0.309453 0.950915i \(-0.399854\pi\)
0.309453 + 0.950915i \(0.399854\pi\)
\(38\) 2.11896e8 0.433824
\(39\) 6.33294e7 0.112396
\(40\) 6.35094e8 0.980636
\(41\) 1.38214e9 1.86312 0.931562 0.363582i \(-0.118446\pi\)
0.931562 + 0.363582i \(0.118446\pi\)
\(42\) −6.46967e7 −0.0763855
\(43\) 4.91328e8 0.509677 0.254839 0.966984i \(-0.417978\pi\)
0.254839 + 0.966984i \(0.417978\pi\)
\(44\) −5.14341e8 −0.470177
\(45\) −7.08743e8 −0.572559
\(46\) −7.46034e8 −0.534061
\(47\) 9.26195e8 0.589066 0.294533 0.955641i \(-0.404836\pi\)
0.294533 + 0.955641i \(0.404836\pi\)
\(48\) 7.54363e8 0.427320
\(49\) −1.58964e9 −0.803932
\(50\) 1.28774e9 0.582767
\(51\) 6.76579e8 0.274589
\(52\) −4.86089e8 −0.177295
\(53\) −5.11389e9 −1.67971 −0.839855 0.542811i \(-0.817360\pi\)
−0.839855 + 0.542811i \(0.817360\pi\)
\(54\) 1.94023e8 0.0575025
\(55\) −3.30987e9 −0.886780
\(56\) 1.04185e9 0.252796
\(57\) 3.80799e9 0.838271
\(58\) −5.81463e8 −0.116324
\(59\) −7.14924e8 −0.130189
\(60\) 5.44000e9 0.903165
\(61\) 5.97047e9 0.905096 0.452548 0.891740i \(-0.350515\pi\)
0.452548 + 0.891740i \(0.350515\pi\)
\(62\) 1.85985e8 0.0257825
\(63\) −1.16267e9 −0.147598
\(64\) −4.32487e9 −0.503481
\(65\) −3.12806e9 −0.334389
\(66\) 9.06096e8 0.0890600
\(67\) 1.02331e10 0.925971 0.462985 0.886366i \(-0.346778\pi\)
0.462985 + 0.886366i \(0.346778\pi\)
\(68\) −5.19312e9 −0.433141
\(69\) −1.34070e10 −1.03196
\(70\) 3.19560e9 0.227255
\(71\) −2.24186e10 −1.47464 −0.737322 0.675541i \(-0.763910\pi\)
−0.737322 + 0.675541i \(0.763910\pi\)
\(72\) −3.12445e9 −0.190303
\(73\) −2.72185e10 −1.53670 −0.768348 0.640032i \(-0.778921\pi\)
−0.768348 + 0.640032i \(0.778921\pi\)
\(74\) 3.52995e9 0.184924
\(75\) 2.31421e10 1.12607
\(76\) −2.92285e10 −1.32230
\(77\) −5.42971e9 −0.228601
\(78\) 8.56325e8 0.0335829
\(79\) −2.62365e10 −0.959305 −0.479652 0.877459i \(-0.659237\pi\)
−0.479652 + 0.877459i \(0.659237\pi\)
\(80\) −3.72607e10 −1.27132
\(81\) 3.48678e9 0.111111
\(82\) 1.86890e10 0.556686
\(83\) −4.00527e10 −1.11610 −0.558048 0.829808i \(-0.688450\pi\)
−0.558048 + 0.829808i \(0.688450\pi\)
\(84\) 8.92411e9 0.232825
\(85\) −3.34186e10 −0.816929
\(86\) 6.64363e9 0.152287
\(87\) −1.04495e10 −0.224770
\(88\) −1.45914e10 −0.294741
\(89\) 6.06398e10 1.15110 0.575549 0.817767i \(-0.304788\pi\)
0.575549 + 0.817767i \(0.304788\pi\)
\(90\) −9.58346e9 −0.171076
\(91\) −5.13146e9 −0.0862013
\(92\) 1.02906e11 1.62783
\(93\) 3.34235e9 0.0498191
\(94\) 1.25238e10 0.176008
\(95\) −1.88090e11 −2.49394
\(96\) 3.65332e10 0.457294
\(97\) 1.53603e11 1.81617 0.908085 0.418786i \(-0.137544\pi\)
0.908085 + 0.418786i \(0.137544\pi\)
\(98\) −2.14947e10 −0.240208
\(99\) 1.62835e10 0.172089
\(100\) −1.77629e11 −1.77629
\(101\) −1.19648e11 −1.13276 −0.566380 0.824144i \(-0.691657\pi\)
−0.566380 + 0.824144i \(0.691657\pi\)
\(102\) 9.14854e9 0.0820448
\(103\) 1.93441e10 0.164416 0.0822081 0.996615i \(-0.473803\pi\)
0.0822081 + 0.996615i \(0.473803\pi\)
\(104\) −1.37899e10 −0.111142
\(105\) 5.74282e10 0.439121
\(106\) −6.91489e10 −0.501883
\(107\) −2.44523e11 −1.68543 −0.842713 0.538363i \(-0.819043\pi\)
−0.842713 + 0.538363i \(0.819043\pi\)
\(108\) −2.67630e10 −0.175269
\(109\) 1.67972e11 1.04566 0.522830 0.852437i \(-0.324876\pi\)
0.522830 + 0.852437i \(0.324876\pi\)
\(110\) −4.47553e10 −0.264963
\(111\) 6.34367e10 0.357326
\(112\) −6.11247e10 −0.327731
\(113\) 2.72254e11 1.39009 0.695046 0.718966i \(-0.255384\pi\)
0.695046 + 0.718966i \(0.255384\pi\)
\(114\) 5.14908e10 0.250468
\(115\) 6.62218e11 3.07017
\(116\) 8.02056e10 0.354557
\(117\) 1.53890e10 0.0648917
\(118\) −9.66704e9 −0.0388994
\(119\) −5.48219e10 −0.210594
\(120\) 1.54328e11 0.566170
\(121\) −2.09267e11 −0.733468
\(122\) 8.07314e10 0.270435
\(123\) 3.35861e11 1.07568
\(124\) −2.56544e10 −0.0785855
\(125\) −5.57003e11 −1.63250
\(126\) −1.57213e10 −0.0441012
\(127\) −2.86551e11 −0.769630 −0.384815 0.922994i \(-0.625735\pi\)
−0.384815 + 0.922994i \(0.625735\pi\)
\(128\) −3.66381e11 −0.942492
\(129\) 1.19393e11 0.294262
\(130\) −4.22969e10 −0.0999126
\(131\) 1.47330e11 0.333656 0.166828 0.985986i \(-0.446647\pi\)
0.166828 + 0.985986i \(0.446647\pi\)
\(132\) −1.24985e11 −0.271457
\(133\) −3.08555e11 −0.642907
\(134\) 1.38370e11 0.276673
\(135\) −1.72225e11 −0.330567
\(136\) −1.47324e11 −0.271525
\(137\) 1.04473e12 1.84945 0.924723 0.380641i \(-0.124297\pi\)
0.924723 + 0.380641i \(0.124297\pi\)
\(138\) −1.81286e11 −0.308340
\(139\) −6.22647e11 −1.01780 −0.508898 0.860827i \(-0.669947\pi\)
−0.508898 + 0.860827i \(0.669947\pi\)
\(140\) −4.40793e11 −0.692677
\(141\) 2.25065e11 0.340098
\(142\) −3.03139e11 −0.440612
\(143\) 7.18677e10 0.100504
\(144\) 1.83310e11 0.246714
\(145\) 5.16136e11 0.668714
\(146\) −3.68042e11 −0.459152
\(147\) −3.86282e11 −0.464151
\(148\) −4.86912e11 −0.563652
\(149\) −3.33149e10 −0.0371633 −0.0185816 0.999827i \(-0.505915\pi\)
−0.0185816 + 0.999827i \(0.505915\pi\)
\(150\) 3.12922e11 0.336461
\(151\) −1.10725e12 −1.14781 −0.573906 0.818921i \(-0.694573\pi\)
−0.573906 + 0.818921i \(0.694573\pi\)
\(152\) −8.29184e11 −0.828918
\(153\) 1.64409e11 0.158534
\(154\) −7.34193e10 −0.0683041
\(155\) −1.65090e11 −0.148217
\(156\) −1.18120e11 −0.102361
\(157\) 1.68694e12 1.41141 0.705703 0.708507i \(-0.250631\pi\)
0.705703 + 0.708507i \(0.250631\pi\)
\(158\) −3.54764e11 −0.286632
\(159\) −1.24268e12 −0.969781
\(160\) −1.80450e12 −1.36050
\(161\) 1.08634e12 0.791453
\(162\) 4.71475e10 0.0331991
\(163\) −7.59126e11 −0.516752 −0.258376 0.966044i \(-0.583187\pi\)
−0.258376 + 0.966044i \(0.583187\pi\)
\(164\) −2.57792e12 −1.69679
\(165\) −8.04298e11 −0.511983
\(166\) −5.41583e11 −0.333481
\(167\) 4.25956e11 0.253761 0.126880 0.991918i \(-0.459504\pi\)
0.126880 + 0.991918i \(0.459504\pi\)
\(168\) 2.53169e11 0.145952
\(169\) −1.72424e12 −0.962102
\(170\) −4.51879e11 −0.244092
\(171\) 9.25342e11 0.483976
\(172\) −9.16407e11 −0.464175
\(173\) −2.13312e12 −1.04655 −0.523277 0.852163i \(-0.675291\pi\)
−0.523277 + 0.852163i \(0.675291\pi\)
\(174\) −1.41295e11 −0.0671595
\(175\) −1.87516e12 −0.863633
\(176\) 8.56069e11 0.382111
\(177\) −1.73727e11 −0.0751646
\(178\) 8.19957e11 0.343939
\(179\) 2.26706e12 0.922087 0.461043 0.887378i \(-0.347475\pi\)
0.461043 + 0.887378i \(0.347475\pi\)
\(180\) 1.32192e12 0.521443
\(181\) −3.99086e11 −0.152698 −0.0763492 0.997081i \(-0.524326\pi\)
−0.0763492 + 0.997081i \(0.524326\pi\)
\(182\) −6.93865e10 −0.0257562
\(183\) 1.45083e12 0.522557
\(184\) 2.91935e12 1.02044
\(185\) −3.13336e12 −1.06308
\(186\) 4.51945e10 0.0148855
\(187\) 7.67797e11 0.245537
\(188\) −1.72750e12 −0.536476
\(189\) −2.82528e11 −0.0852160
\(190\) −2.54331e12 −0.745169
\(191\) 2.56305e12 0.729582 0.364791 0.931089i \(-0.381140\pi\)
0.364791 + 0.931089i \(0.381140\pi\)
\(192\) −1.05094e12 −0.290685
\(193\) 1.45814e12 0.391953 0.195976 0.980609i \(-0.437212\pi\)
0.195976 + 0.980609i \(0.437212\pi\)
\(194\) 2.07699e12 0.542657
\(195\) −7.60119e11 −0.193059
\(196\) 2.96493e12 0.732160
\(197\) 2.70562e11 0.0649684 0.0324842 0.999472i \(-0.489658\pi\)
0.0324842 + 0.999472i \(0.489658\pi\)
\(198\) 2.20181e11 0.0514188
\(199\) −1.19094e12 −0.270520 −0.135260 0.990810i \(-0.543187\pi\)
−0.135260 + 0.990810i \(0.543187\pi\)
\(200\) −5.03915e12 −1.11351
\(201\) 2.48665e12 0.534610
\(202\) −1.61785e12 −0.338460
\(203\) 8.46702e11 0.172386
\(204\) −1.26193e12 −0.250074
\(205\) −1.65894e13 −3.20024
\(206\) 2.61567e11 0.0491262
\(207\) −3.25790e12 −0.595800
\(208\) 8.09046e11 0.144087
\(209\) 4.32140e12 0.749583
\(210\) 7.76530e11 0.131206
\(211\) −5.22030e12 −0.859295 −0.429647 0.902997i \(-0.641362\pi\)
−0.429647 + 0.902997i \(0.641362\pi\)
\(212\) 9.53823e12 1.52975
\(213\) −5.44772e12 −0.851386
\(214\) −3.30639e12 −0.503591
\(215\) −5.89723e12 −0.875460
\(216\) −7.59242e11 −0.109871
\(217\) −2.70824e11 −0.0382084
\(218\) 2.27128e12 0.312435
\(219\) −6.61409e12 −0.887212
\(220\) 6.17344e12 0.807612
\(221\) 7.25623e11 0.0925877
\(222\) 8.57777e11 0.106766
\(223\) −4.06546e11 −0.0493666 −0.0246833 0.999695i \(-0.507858\pi\)
−0.0246833 + 0.999695i \(0.507858\pi\)
\(224\) −2.96022e12 −0.350719
\(225\) 5.62353e12 0.650137
\(226\) 3.68136e12 0.415348
\(227\) −4.75664e12 −0.523791 −0.261895 0.965096i \(-0.584348\pi\)
−0.261895 + 0.965096i \(0.584348\pi\)
\(228\) −7.10252e12 −0.763433
\(229\) 6.57938e12 0.690383 0.345192 0.938532i \(-0.387814\pi\)
0.345192 + 0.938532i \(0.387814\pi\)
\(230\) 8.95437e12 0.917343
\(231\) −1.31942e12 −0.131983
\(232\) 2.27536e12 0.222262
\(233\) −1.62372e13 −1.54900 −0.774502 0.632571i \(-0.782000\pi\)
−0.774502 + 0.632571i \(0.782000\pi\)
\(234\) 2.08087e11 0.0193891
\(235\) −1.11168e13 −1.01182
\(236\) 1.33345e12 0.118566
\(237\) −6.37547e12 −0.553855
\(238\) −7.41290e11 −0.0629238
\(239\) 3.09555e12 0.256773 0.128387 0.991724i \(-0.459020\pi\)
0.128387 + 0.991724i \(0.459020\pi\)
\(240\) −9.05434e12 −0.733998
\(241\) −1.74669e11 −0.0138395 −0.00691976 0.999976i \(-0.502203\pi\)
−0.00691976 + 0.999976i \(0.502203\pi\)
\(242\) −2.82966e12 −0.219154
\(243\) 8.47289e11 0.0641500
\(244\) −1.11359e13 −0.824292
\(245\) 1.90798e13 1.38090
\(246\) 4.54143e12 0.321403
\(247\) 4.08403e12 0.282654
\(248\) −7.27791e11 −0.0492632
\(249\) −9.73280e12 −0.644379
\(250\) −7.53167e12 −0.487777
\(251\) 1.34968e13 0.855119 0.427559 0.903987i \(-0.359373\pi\)
0.427559 + 0.903987i \(0.359373\pi\)
\(252\) 2.16856e12 0.134421
\(253\) −1.52146e13 −0.922777
\(254\) −3.87468e12 −0.229959
\(255\) −8.12072e12 −0.471654
\(256\) 3.90321e12 0.221872
\(257\) −2.22213e13 −1.23634 −0.618169 0.786045i \(-0.712125\pi\)
−0.618169 + 0.786045i \(0.712125\pi\)
\(258\) 1.61440e12 0.0879231
\(259\) −5.14016e12 −0.274049
\(260\) 5.83434e12 0.304536
\(261\) −2.53922e12 −0.129771
\(262\) 1.99216e12 0.0996938
\(263\) −3.72334e13 −1.82464 −0.912318 0.409482i \(-0.865710\pi\)
−0.912318 + 0.409482i \(0.865710\pi\)
\(264\) −3.54570e12 −0.170169
\(265\) 6.13801e13 2.88520
\(266\) −4.17220e12 −0.192095
\(267\) 1.47355e13 0.664587
\(268\) −1.90865e13 −0.843303
\(269\) 2.24861e13 0.973367 0.486683 0.873578i \(-0.338207\pi\)
0.486683 + 0.873578i \(0.338207\pi\)
\(270\) −2.32878e12 −0.0987707
\(271\) 7.64713e12 0.317810 0.158905 0.987294i \(-0.449204\pi\)
0.158905 + 0.987294i \(0.449204\pi\)
\(272\) 8.64343e12 0.352012
\(273\) −1.24695e12 −0.0497683
\(274\) 1.41266e13 0.552599
\(275\) 2.62622e13 1.00693
\(276\) 2.50062e13 0.939827
\(277\) −3.50920e13 −1.29291 −0.646457 0.762951i \(-0.723750\pi\)
−0.646457 + 0.762951i \(0.723750\pi\)
\(278\) −8.41929e12 −0.304109
\(279\) 8.12191e11 0.0287630
\(280\) −1.25049e13 −0.434221
\(281\) −1.11107e13 −0.378319 −0.189159 0.981946i \(-0.560576\pi\)
−0.189159 + 0.981946i \(0.560576\pi\)
\(282\) 3.04328e12 0.101618
\(283\) 2.58545e13 0.846664 0.423332 0.905975i \(-0.360860\pi\)
0.423332 + 0.905975i \(0.360860\pi\)
\(284\) 4.18143e13 1.34299
\(285\) −4.57059e13 −1.43988
\(286\) 9.71778e11 0.0300299
\(287\) −2.72142e13 −0.824983
\(288\) 8.87756e12 0.264019
\(289\) −2.65197e13 −0.773803
\(290\) 6.97908e12 0.199806
\(291\) 3.73256e13 1.04857
\(292\) 5.07669e13 1.39951
\(293\) 2.80373e13 0.758514 0.379257 0.925291i \(-0.376180\pi\)
0.379257 + 0.925291i \(0.376180\pi\)
\(294\) −5.22321e12 −0.138684
\(295\) 8.58097e12 0.223622
\(296\) −1.38132e13 −0.353339
\(297\) 3.95688e12 0.0993557
\(298\) −4.50477e11 −0.0111041
\(299\) −1.43788e13 −0.347962
\(300\) −4.31637e13 −1.02554
\(301\) −9.67418e12 −0.225683
\(302\) −1.49719e13 −0.342957
\(303\) −2.90745e13 −0.654000
\(304\) 4.86479e13 1.07463
\(305\) −7.16614e13 −1.55466
\(306\) 2.22310e12 0.0473686
\(307\) −6.77354e13 −1.41760 −0.708802 0.705408i \(-0.750764\pi\)
−0.708802 + 0.705408i \(0.750764\pi\)
\(308\) 1.01273e13 0.208192
\(309\) 4.70062e12 0.0949257
\(310\) −2.23231e12 −0.0442860
\(311\) −7.60898e13 −1.48301 −0.741506 0.670947i \(-0.765888\pi\)
−0.741506 + 0.670947i \(0.765888\pi\)
\(312\) −3.35094e12 −0.0641677
\(313\) 7.52366e13 1.41558 0.707791 0.706422i \(-0.249692\pi\)
0.707791 + 0.706422i \(0.249692\pi\)
\(314\) 2.28105e13 0.421717
\(315\) 1.39550e13 0.253526
\(316\) 4.89353e13 0.873661
\(317\) −7.02133e13 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(318\) −1.68032e13 −0.289762
\(319\) −1.18583e13 −0.200990
\(320\) 5.19098e13 0.864817
\(321\) −5.94192e13 −0.973081
\(322\) 1.46893e13 0.236480
\(323\) 4.36317e13 0.690538
\(324\) −6.50342e12 −0.101191
\(325\) 2.48196e13 0.379697
\(326\) −1.02647e13 −0.154401
\(327\) 4.08172e13 0.603713
\(328\) −7.31332e13 −1.06367
\(329\) −1.82366e13 −0.260836
\(330\) −1.08755e13 −0.152976
\(331\) 1.01064e14 1.39812 0.699058 0.715065i \(-0.253603\pi\)
0.699058 + 0.715065i \(0.253603\pi\)
\(332\) 7.47047e13 1.01646
\(333\) 1.54151e13 0.206302
\(334\) 5.75968e12 0.0758216
\(335\) −1.22825e14 −1.59052
\(336\) −1.48533e13 −0.189216
\(337\) −1.51730e13 −0.190155 −0.0950776 0.995470i \(-0.530310\pi\)
−0.0950776 + 0.995470i \(0.530310\pi\)
\(338\) −2.33148e13 −0.287468
\(339\) 6.61578e13 0.802570
\(340\) 6.23311e13 0.743996
\(341\) 3.79297e12 0.0445483
\(342\) 1.25123e13 0.144608
\(343\) 7.02330e13 0.798773
\(344\) −2.59976e13 −0.290979
\(345\) 1.60919e14 1.77257
\(346\) −2.88436e13 −0.312702
\(347\) −1.73746e14 −1.85397 −0.926985 0.375099i \(-0.877609\pi\)
−0.926985 + 0.375099i \(0.877609\pi\)
\(348\) 1.94900e13 0.204703
\(349\) −1.91317e13 −0.197794 −0.0988972 0.995098i \(-0.531532\pi\)
−0.0988972 + 0.995098i \(0.531532\pi\)
\(350\) −2.53555e13 −0.258046
\(351\) 3.73954e12 0.0374653
\(352\) 4.14587e13 0.408913
\(353\) 1.50374e14 1.46020 0.730098 0.683342i \(-0.239474\pi\)
0.730098 + 0.683342i \(0.239474\pi\)
\(354\) −2.34909e12 −0.0224586
\(355\) 2.69082e14 2.53296
\(356\) −1.13103e14 −1.04833
\(357\) −1.33217e13 −0.121587
\(358\) 3.06547e13 0.275512
\(359\) 1.51510e14 1.34097 0.670487 0.741921i \(-0.266085\pi\)
0.670487 + 0.741921i \(0.266085\pi\)
\(360\) 3.75016e13 0.326879
\(361\) 1.29082e14 1.10809
\(362\) −5.39635e12 −0.0456250
\(363\) −5.08519e13 −0.423468
\(364\) 9.57101e12 0.0785055
\(365\) 3.26693e14 2.63955
\(366\) 1.96177e13 0.156136
\(367\) −3.23653e13 −0.253756 −0.126878 0.991918i \(-0.540496\pi\)
−0.126878 + 0.991918i \(0.540496\pi\)
\(368\) −1.71277e14 −1.32293
\(369\) 8.16142e13 0.621041
\(370\) −4.23686e13 −0.317640
\(371\) 1.00692e14 0.743767
\(372\) −6.23402e12 −0.0453714
\(373\) −9.05386e12 −0.0649285 −0.0324642 0.999473i \(-0.510336\pi\)
−0.0324642 + 0.999473i \(0.510336\pi\)
\(374\) 1.03820e13 0.0733646
\(375\) −1.35352e14 −0.942524
\(376\) −4.90076e13 −0.336303
\(377\) −1.12069e13 −0.0757896
\(378\) −3.82028e12 −0.0254618
\(379\) −2.36249e14 −1.55186 −0.775932 0.630816i \(-0.782720\pi\)
−0.775932 + 0.630816i \(0.782720\pi\)
\(380\) 3.50818e14 2.27129
\(381\) −6.96320e13 −0.444346
\(382\) 3.46570e13 0.217993
\(383\) 2.62138e13 0.162531 0.0812657 0.996692i \(-0.474104\pi\)
0.0812657 + 0.996692i \(0.474104\pi\)
\(384\) −8.90305e13 −0.544148
\(385\) 6.51708e13 0.392662
\(386\) 1.97166e13 0.117112
\(387\) 2.90124e13 0.169892
\(388\) −2.86495e14 −1.65403
\(389\) 1.45020e14 0.825476 0.412738 0.910850i \(-0.364573\pi\)
0.412738 + 0.910850i \(0.364573\pi\)
\(390\) −1.02782e13 −0.0576846
\(391\) −1.53616e14 −0.850090
\(392\) 8.41123e13 0.458972
\(393\) 3.58012e13 0.192637
\(394\) 3.65847e12 0.0194120
\(395\) 3.14907e14 1.64777
\(396\) −3.03713e13 −0.156726
\(397\) 2.53779e14 1.29154 0.645771 0.763531i \(-0.276536\pi\)
0.645771 + 0.763531i \(0.276536\pi\)
\(398\) −1.61037e13 −0.0808292
\(399\) −7.49788e13 −0.371182
\(400\) 2.95645e14 1.44358
\(401\) −1.23162e14 −0.593173 −0.296587 0.955006i \(-0.595848\pi\)
−0.296587 + 0.955006i \(0.595848\pi\)
\(402\) 3.36239e13 0.159737
\(403\) 3.58463e12 0.0167983
\(404\) 2.23163e14 1.03163
\(405\) −4.18506e13 −0.190853
\(406\) 1.14489e13 0.0515075
\(407\) 7.19895e13 0.319521
\(408\) −3.57997e13 −0.156765
\(409\) 8.02377e13 0.346657 0.173329 0.984864i \(-0.444548\pi\)
0.173329 + 0.984864i \(0.444548\pi\)
\(410\) −2.24317e14 −0.956207
\(411\) 2.53870e14 1.06778
\(412\) −3.60799e13 −0.149738
\(413\) 1.40767e13 0.0576470
\(414\) −4.40526e13 −0.178020
\(415\) 4.80737e14 1.91709
\(416\) 3.91814e13 0.154194
\(417\) −1.51303e14 −0.587624
\(418\) 5.84329e13 0.223969
\(419\) 2.61467e14 0.989099 0.494550 0.869149i \(-0.335333\pi\)
0.494550 + 0.869149i \(0.335333\pi\)
\(420\) −1.07113e14 −0.399917
\(421\) −1.48199e14 −0.546127 −0.273064 0.961996i \(-0.588037\pi\)
−0.273064 + 0.961996i \(0.588037\pi\)
\(422\) −7.05877e13 −0.256750
\(423\) 5.46909e13 0.196355
\(424\) 2.70591e14 0.958960
\(425\) 2.65160e14 0.927618
\(426\) −7.36628e13 −0.254387
\(427\) −1.17558e14 −0.400772
\(428\) 4.56076e14 1.53496
\(429\) 1.74638e13 0.0580263
\(430\) −7.97410e13 −0.261580
\(431\) −2.49802e14 −0.809042 −0.404521 0.914529i \(-0.632562\pi\)
−0.404521 + 0.914529i \(0.632562\pi\)
\(432\) 4.45444e13 0.142440
\(433\) 3.87508e13 0.122348 0.0611740 0.998127i \(-0.480516\pi\)
0.0611740 + 0.998127i \(0.480516\pi\)
\(434\) −3.66203e12 −0.0114164
\(435\) 1.25421e14 0.386082
\(436\) −3.13295e14 −0.952308
\(437\) −8.64599e14 −2.59518
\(438\) −8.94342e13 −0.265092
\(439\) −2.17907e14 −0.637847 −0.318923 0.947781i \(-0.603321\pi\)
−0.318923 + 0.947781i \(0.603321\pi\)
\(440\) 1.75135e14 0.506270
\(441\) −9.38665e13 −0.267977
\(442\) 9.81171e12 0.0276645
\(443\) −3.80522e14 −1.05964 −0.529821 0.848109i \(-0.677741\pi\)
−0.529821 + 0.848109i \(0.677741\pi\)
\(444\) −1.18320e14 −0.325425
\(445\) −7.27837e14 −1.97721
\(446\) −5.49723e12 −0.0147503
\(447\) −8.09552e12 −0.0214562
\(448\) 8.51560e13 0.222939
\(449\) −2.61303e14 −0.675754 −0.337877 0.941190i \(-0.609709\pi\)
−0.337877 + 0.941190i \(0.609709\pi\)
\(450\) 7.60401e13 0.194256
\(451\) 3.81143e14 0.961871
\(452\) −5.07798e14 −1.26599
\(453\) −2.69061e14 −0.662690
\(454\) −6.43182e13 −0.156504
\(455\) 6.15910e13 0.148066
\(456\) −2.01492e14 −0.478576
\(457\) −1.74585e14 −0.409702 −0.204851 0.978793i \(-0.565671\pi\)
−0.204851 + 0.978793i \(0.565671\pi\)
\(458\) 8.89649e13 0.206281
\(459\) 3.99513e13 0.0915295
\(460\) −1.23514e15 −2.79608
\(461\) −1.56304e14 −0.349636 −0.174818 0.984601i \(-0.555934\pi\)
−0.174818 + 0.984601i \(0.555934\pi\)
\(462\) −1.78409e13 −0.0394354
\(463\) −2.02023e14 −0.441272 −0.220636 0.975356i \(-0.570813\pi\)
−0.220636 + 0.975356i \(0.570813\pi\)
\(464\) −1.33494e14 −0.288147
\(465\) −4.01170e13 −0.0855730
\(466\) −2.19555e14 −0.462830
\(467\) 5.86324e14 1.22150 0.610752 0.791822i \(-0.290867\pi\)
0.610752 + 0.791822i \(0.290867\pi\)
\(468\) −2.87030e13 −0.0590984
\(469\) −2.01489e14 −0.410016
\(470\) −1.50318e14 −0.302325
\(471\) 4.09927e14 0.814876
\(472\) 3.78287e13 0.0743260
\(473\) 1.35490e14 0.263130
\(474\) −8.62076e13 −0.165487
\(475\) 1.49240e15 2.83186
\(476\) 1.02252e14 0.191793
\(477\) −3.01970e14 −0.559903
\(478\) 4.18573e13 0.0767217
\(479\) 2.05544e14 0.372442 0.186221 0.982508i \(-0.440376\pi\)
0.186221 + 0.982508i \(0.440376\pi\)
\(480\) −4.38494e14 −0.785483
\(481\) 6.80351e13 0.120486
\(482\) −2.36183e12 −0.00413513
\(483\) 2.63982e14 0.456945
\(484\) 3.90317e14 0.667986
\(485\) −1.84364e15 −3.11959
\(486\) 1.14568e13 0.0191675
\(487\) 3.73028e14 0.617066 0.308533 0.951214i \(-0.400162\pi\)
0.308533 + 0.951214i \(0.400162\pi\)
\(488\) −3.15915e14 −0.516727
\(489\) −1.84468e14 −0.298347
\(490\) 2.57993e14 0.412600
\(491\) −9.58708e14 −1.51614 −0.758068 0.652176i \(-0.773856\pi\)
−0.758068 + 0.652176i \(0.773856\pi\)
\(492\) −6.26435e14 −0.979643
\(493\) −1.19729e14 −0.185158
\(494\) 5.52233e13 0.0844547
\(495\) −1.95444e14 −0.295593
\(496\) 4.26992e13 0.0638661
\(497\) 4.41418e14 0.652966
\(498\) −1.31605e14 −0.192535
\(499\) −4.42684e14 −0.640532 −0.320266 0.947328i \(-0.603772\pi\)
−0.320266 + 0.947328i \(0.603772\pi\)
\(500\) 1.03890e15 1.48675
\(501\) 1.03507e14 0.146509
\(502\) 1.82501e14 0.255502
\(503\) −7.53097e14 −1.04286 −0.521431 0.853293i \(-0.674602\pi\)
−0.521431 + 0.853293i \(0.674602\pi\)
\(504\) 6.15200e13 0.0842652
\(505\) 1.43609e15 1.94572
\(506\) −2.05728e14 −0.275718
\(507\) −4.18990e14 −0.555470
\(508\) 5.34465e14 0.700920
\(509\) 8.61451e12 0.0111759 0.00558795 0.999984i \(-0.498221\pi\)
0.00558795 + 0.999984i \(0.498221\pi\)
\(510\) −1.09807e14 −0.140926
\(511\) 5.35928e14 0.680442
\(512\) 8.03126e14 1.00879
\(513\) 2.24858e14 0.279424
\(514\) −3.00471e14 −0.369408
\(515\) −2.32180e14 −0.282414
\(516\) −2.22687e14 −0.267992
\(517\) 2.55409e14 0.304116
\(518\) −6.95041e13 −0.0818835
\(519\) −5.18348e14 −0.604228
\(520\) 1.65515e14 0.190905
\(521\) −1.10177e15 −1.25743 −0.628716 0.777635i \(-0.716419\pi\)
−0.628716 + 0.777635i \(0.716419\pi\)
\(522\) −3.43348e13 −0.0387745
\(523\) −7.11378e14 −0.794952 −0.397476 0.917613i \(-0.630114\pi\)
−0.397476 + 0.917613i \(0.630114\pi\)
\(524\) −2.74795e14 −0.303869
\(525\) −4.55664e14 −0.498619
\(526\) −5.03462e14 −0.545186
\(527\) 3.82964e13 0.0410392
\(528\) 2.08025e14 0.220612
\(529\) 2.09123e15 2.19480
\(530\) 8.29968e14 0.862073
\(531\) −4.22156e13 −0.0433963
\(532\) 5.75504e14 0.585510
\(533\) 3.60207e14 0.362704
\(534\) 1.99250e14 0.198573
\(535\) 2.93492e15 2.89502
\(536\) −5.41465e14 −0.528645
\(537\) 5.50896e14 0.532367
\(538\) 3.04052e14 0.290834
\(539\) −4.38362e14 −0.415044
\(540\) 3.21227e14 0.301055
\(541\) −1.15844e14 −0.107470 −0.0537351 0.998555i \(-0.517113\pi\)
−0.0537351 + 0.998555i \(0.517113\pi\)
\(542\) 1.03403e14 0.0949589
\(543\) −9.69779e13 −0.0881604
\(544\) 4.18594e14 0.376703
\(545\) −2.01610e15 −1.79611
\(546\) −1.68609e13 −0.0148704
\(547\) −3.52231e14 −0.307537 −0.153769 0.988107i \(-0.549141\pi\)
−0.153769 + 0.988107i \(0.549141\pi\)
\(548\) −1.94859e15 −1.68433
\(549\) 3.52550e14 0.301699
\(550\) 3.55111e14 0.300864
\(551\) −6.73873e14 −0.565254
\(552\) 7.09402e14 0.589152
\(553\) 5.16592e14 0.424776
\(554\) −4.74506e14 −0.386312
\(555\) −7.61407e14 −0.613770
\(556\) 1.16134e15 0.926930
\(557\) −2.35408e15 −1.86045 −0.930224 0.366992i \(-0.880388\pi\)
−0.930224 + 0.366992i \(0.880388\pi\)
\(558\) 1.09823e13 0.00859416
\(559\) 1.28047e14 0.0992215
\(560\) 7.33657e14 0.562936
\(561\) 1.86575e14 0.141761
\(562\) −1.50237e14 −0.113039
\(563\) −2.47912e15 −1.84714 −0.923572 0.383424i \(-0.874745\pi\)
−0.923572 + 0.383424i \(0.874745\pi\)
\(564\) −4.19783e14 −0.309735
\(565\) −3.26777e15 −2.38773
\(566\) 3.49599e14 0.252976
\(567\) −6.86542e13 −0.0491995
\(568\) 1.18623e15 0.841887
\(569\) 1.55307e15 1.09163 0.545814 0.837906i \(-0.316221\pi\)
0.545814 + 0.837906i \(0.316221\pi\)
\(570\) −6.18025e14 −0.430224
\(571\) 1.84361e15 1.27107 0.635537 0.772071i \(-0.280779\pi\)
0.635537 + 0.772071i \(0.280779\pi\)
\(572\) −1.34045e14 −0.0915318
\(573\) 6.22822e14 0.421224
\(574\) −3.67984e14 −0.246498
\(575\) −5.25438e15 −3.48617
\(576\) −2.55379e14 −0.167827
\(577\) −2.95570e15 −1.92395 −0.961973 0.273145i \(-0.911936\pi\)
−0.961973 + 0.273145i \(0.911936\pi\)
\(578\) −3.58594e14 −0.231206
\(579\) 3.54328e14 0.226294
\(580\) −9.62678e14 −0.609014
\(581\) 7.88631e14 0.494202
\(582\) 5.04709e14 0.313303
\(583\) −1.41022e15 −0.867179
\(584\) 1.44021e15 0.877313
\(585\) −1.84709e14 −0.111463
\(586\) 3.79114e14 0.226638
\(587\) −1.49815e15 −0.887252 −0.443626 0.896212i \(-0.646308\pi\)
−0.443626 + 0.896212i \(0.646308\pi\)
\(588\) 7.20478e14 0.422713
\(589\) 2.15544e14 0.125286
\(590\) 1.16030e14 0.0668165
\(591\) 6.57465e13 0.0375095
\(592\) 8.10417e14 0.458078
\(593\) 5.87200e14 0.328841 0.164420 0.986390i \(-0.447425\pi\)
0.164420 + 0.986390i \(0.447425\pi\)
\(594\) 5.35041e13 0.0296867
\(595\) 6.58007e14 0.361732
\(596\) 6.21377e13 0.0338455
\(597\) −2.89399e14 −0.156185
\(598\) −1.94427e14 −0.103968
\(599\) −1.76609e15 −0.935764 −0.467882 0.883791i \(-0.654983\pi\)
−0.467882 + 0.883791i \(0.654983\pi\)
\(600\) −1.22451e15 −0.642883
\(601\) 2.22109e15 1.15546 0.577732 0.816226i \(-0.303938\pi\)
0.577732 + 0.816226i \(0.303938\pi\)
\(602\) −1.30812e14 −0.0674321
\(603\) 6.04256e14 0.308657
\(604\) 2.06519e15 1.04534
\(605\) 2.51175e15 1.25986
\(606\) −3.93138e14 −0.195410
\(607\) 1.63236e15 0.804042 0.402021 0.915630i \(-0.368308\pi\)
0.402021 + 0.915630i \(0.368308\pi\)
\(608\) 2.35597e15 1.15001
\(609\) 2.05749e14 0.0995272
\(610\) −9.68989e14 −0.464520
\(611\) 2.41380e14 0.114677
\(612\) −3.06649e14 −0.144380
\(613\) −3.89084e15 −1.81556 −0.907779 0.419448i \(-0.862224\pi\)
−0.907779 + 0.419448i \(0.862224\pi\)
\(614\) −9.15903e14 −0.423568
\(615\) −4.03121e15 −1.84766
\(616\) 2.87302e14 0.130510
\(617\) −9.90339e14 −0.445878 −0.222939 0.974832i \(-0.571565\pi\)
−0.222939 + 0.974832i \(0.571565\pi\)
\(618\) 6.35608e13 0.0283630
\(619\) 2.76711e15 1.22385 0.611925 0.790916i \(-0.290396\pi\)
0.611925 + 0.790916i \(0.290396\pi\)
\(620\) 3.07920e14 0.134984
\(621\) −7.91669e14 −0.343985
\(622\) −1.02887e15 −0.443112
\(623\) −1.19399e15 −0.509701
\(624\) 1.96598e14 0.0831887
\(625\) 2.03536e15 0.853693
\(626\) 1.01733e15 0.422964
\(627\) 1.05010e15 0.432772
\(628\) −3.14642e15 −1.28540
\(629\) 7.26853e14 0.294353
\(630\) 1.88697e14 0.0757516
\(631\) −2.50972e14 −0.0998768 −0.0499384 0.998752i \(-0.515902\pi\)
−0.0499384 + 0.998752i \(0.515902\pi\)
\(632\) 1.38825e15 0.547675
\(633\) −1.26853e15 −0.496114
\(634\) −9.49408e14 −0.368097
\(635\) 3.43937e15 1.32198
\(636\) 2.31779e15 0.883202
\(637\) −4.14283e14 −0.156506
\(638\) −1.60345e14 −0.0600541
\(639\) −1.32379e15 −0.491548
\(640\) 4.39753e15 1.61890
\(641\) −3.72092e15 −1.35810 −0.679049 0.734093i \(-0.737607\pi\)
−0.679049 + 0.734093i \(0.737607\pi\)
\(642\) −8.03453e14 −0.290749
\(643\) 3.78590e15 1.35834 0.679171 0.733980i \(-0.262339\pi\)
0.679171 + 0.733980i \(0.262339\pi\)
\(644\) −2.02621e15 −0.720794
\(645\) −1.43303e15 −0.505447
\(646\) 5.89977e14 0.206327
\(647\) 9.53679e14 0.330696 0.165348 0.986235i \(-0.447125\pi\)
0.165348 + 0.986235i \(0.447125\pi\)
\(648\) −1.84496e14 −0.0634343
\(649\) −1.97149e14 −0.0672123
\(650\) 3.35605e14 0.113450
\(651\) −6.58103e13 −0.0220596
\(652\) 1.41589e15 0.470618
\(653\) −2.88986e15 −0.952477 −0.476238 0.879316i \(-0.658000\pi\)
−0.476238 + 0.879316i \(0.658000\pi\)
\(654\) 5.51921e14 0.180384
\(655\) −1.76835e15 −0.573114
\(656\) 4.29069e15 1.37897
\(657\) −1.60722e15 −0.512232
\(658\) −2.46592e14 −0.0779356
\(659\) −8.02108e14 −0.251399 −0.125699 0.992068i \(-0.540117\pi\)
−0.125699 + 0.992068i \(0.540117\pi\)
\(660\) 1.50015e15 0.466275
\(661\) 5.04397e15 1.55476 0.777381 0.629030i \(-0.216548\pi\)
0.777381 + 0.629030i \(0.216548\pi\)
\(662\) 1.36657e15 0.417746
\(663\) 1.76326e14 0.0534556
\(664\) 2.11930e15 0.637189
\(665\) 3.70347e15 1.10431
\(666\) 2.08440e14 0.0616414
\(667\) 2.37254e15 0.695859
\(668\) −7.94477e14 −0.231106
\(669\) −9.87907e13 −0.0285018
\(670\) −1.66081e15 −0.475234
\(671\) 1.64643e15 0.467272
\(672\) −7.19332e14 −0.202488
\(673\) 1.54943e15 0.432604 0.216302 0.976327i \(-0.430600\pi\)
0.216302 + 0.976327i \(0.430600\pi\)
\(674\) −2.05167e14 −0.0568168
\(675\) 1.36652e15 0.375357
\(676\) 3.21599e15 0.876208
\(677\) −5.29648e15 −1.43136 −0.715682 0.698426i \(-0.753884\pi\)
−0.715682 + 0.698426i \(0.753884\pi\)
\(678\) 8.94571e14 0.239801
\(679\) −3.02443e15 −0.804192
\(680\) 1.76827e15 0.466392
\(681\) −1.15586e15 −0.302411
\(682\) 5.12877e13 0.0133107
\(683\) 3.87697e14 0.0998110 0.0499055 0.998754i \(-0.484108\pi\)
0.0499055 + 0.998754i \(0.484108\pi\)
\(684\) −1.72591e15 −0.440768
\(685\) −1.25395e16 −3.17675
\(686\) 9.49674e14 0.238667
\(687\) 1.59879e15 0.398593
\(688\) 1.52527e15 0.377233
\(689\) −1.33276e15 −0.326998
\(690\) 2.17591e15 0.529628
\(691\) 4.47093e15 1.07961 0.539807 0.841789i \(-0.318497\pi\)
0.539807 + 0.841789i \(0.318497\pi\)
\(692\) 3.97861e15 0.953122
\(693\) −3.20619e14 −0.0762003
\(694\) −2.34935e15 −0.553951
\(695\) 7.47340e15 1.74824
\(696\) 5.52912e14 0.128323
\(697\) 3.84827e15 0.886104
\(698\) −2.58695e14 −0.0590994
\(699\) −3.94563e15 −0.894318
\(700\) 3.49748e15 0.786531
\(701\) 1.29897e15 0.289835 0.144918 0.989444i \(-0.453708\pi\)
0.144918 + 0.989444i \(0.453708\pi\)
\(702\) 5.05652e13 0.0111943
\(703\) 4.09095e15 0.898607
\(704\) −1.19263e15 −0.259931
\(705\) −2.70138e15 −0.584177
\(706\) 2.03332e15 0.436295
\(707\) 2.35585e15 0.501581
\(708\) 3.24028e14 0.0684542
\(709\) −1.07935e15 −0.226261 −0.113130 0.993580i \(-0.536088\pi\)
−0.113130 + 0.993580i \(0.536088\pi\)
\(710\) 3.63846e15 0.756828
\(711\) −1.54924e15 −0.319768
\(712\) −3.20863e15 −0.657172
\(713\) −7.58875e14 −0.154233
\(714\) −1.80133e14 −0.0363291
\(715\) −8.62601e14 −0.172634
\(716\) −4.22844e15 −0.839766
\(717\) 7.52219e14 0.148248
\(718\) 2.04868e15 0.400672
\(719\) −2.21158e14 −0.0429234 −0.0214617 0.999770i \(-0.506832\pi\)
−0.0214617 + 0.999770i \(0.506832\pi\)
\(720\) −2.20020e15 −0.423774
\(721\) −3.80883e14 −0.0728027
\(722\) 1.74542e15 0.331089
\(723\) −4.24445e13 −0.00799025
\(724\) 7.44360e14 0.139066
\(725\) −4.09529e15 −0.759321
\(726\) −6.87607e14 −0.126529
\(727\) −7.51766e14 −0.137292 −0.0686458 0.997641i \(-0.521868\pi\)
−0.0686458 + 0.997641i \(0.521868\pi\)
\(728\) 2.71521e14 0.0492130
\(729\) 2.05891e14 0.0370370
\(730\) 4.41747e15 0.788675
\(731\) 1.36799e15 0.242403
\(732\) −2.70602e15 −0.475905
\(733\) 8.71820e14 0.152179 0.0760895 0.997101i \(-0.475757\pi\)
0.0760895 + 0.997101i \(0.475757\pi\)
\(734\) −4.37636e14 −0.0758202
\(735\) 4.63640e15 0.797260
\(736\) −8.29480e15 −1.41572
\(737\) 2.82191e15 0.478049
\(738\) 1.10357e15 0.185562
\(739\) −5.79111e15 −0.966535 −0.483267 0.875473i \(-0.660550\pi\)
−0.483267 + 0.875473i \(0.660550\pi\)
\(740\) 5.84423e15 0.968172
\(741\) 9.92419e14 0.163190
\(742\) 1.36153e15 0.222232
\(743\) 5.60750e15 0.908513 0.454256 0.890871i \(-0.349905\pi\)
0.454256 + 0.890871i \(0.349905\pi\)
\(744\) −1.76853e14 −0.0284421
\(745\) 3.99866e14 0.0638345
\(746\) −1.22424e14 −0.0194001
\(747\) −2.36507e15 −0.372032
\(748\) −1.43207e15 −0.223617
\(749\) 4.81463e15 0.746299
\(750\) −1.83020e15 −0.281618
\(751\) 8.69603e15 1.32832 0.664158 0.747592i \(-0.268790\pi\)
0.664158 + 0.747592i \(0.268790\pi\)
\(752\) 2.87526e15 0.435992
\(753\) 3.27973e15 0.493703
\(754\) −1.51538e14 −0.0226453
\(755\) 1.32899e16 1.97157
\(756\) 5.26960e14 0.0776082
\(757\) −7.35887e15 −1.07593 −0.537965 0.842967i \(-0.680807\pi\)
−0.537965 + 0.842967i \(0.680807\pi\)
\(758\) −3.19450e15 −0.463684
\(759\) −3.69714e15 −0.532765
\(760\) 9.95239e15 1.42381
\(761\) −1.22298e16 −1.73702 −0.868511 0.495670i \(-0.834923\pi\)
−0.868511 + 0.495670i \(0.834923\pi\)
\(762\) −9.41548e14 −0.132767
\(763\) −3.30734e15 −0.463014
\(764\) −4.78051e15 −0.664448
\(765\) −1.97334e15 −0.272310
\(766\) 3.54457e14 0.0485630
\(767\) −1.86320e14 −0.0253445
\(768\) 9.48480e14 0.128098
\(769\) 8.90388e15 1.19395 0.596973 0.802262i \(-0.296370\pi\)
0.596973 + 0.802262i \(0.296370\pi\)
\(770\) 8.81225e14 0.117324
\(771\) −5.39978e15 −0.713800
\(772\) −2.71966e15 −0.356960
\(773\) −1.26441e16 −1.64778 −0.823890 0.566749i \(-0.808201\pi\)
−0.823890 + 0.566749i \(0.808201\pi\)
\(774\) 3.92300e14 0.0507624
\(775\) 1.30991e15 0.168299
\(776\) −8.12760e15 −1.03687
\(777\) −1.24906e15 −0.158222
\(778\) 1.96092e15 0.246645
\(779\) 2.16592e16 2.70512
\(780\) 1.41774e15 0.175824
\(781\) −6.18219e15 −0.761311
\(782\) −2.07716e15 −0.254000
\(783\) −6.17031e14 −0.0749234
\(784\) −4.93483e15 −0.595023
\(785\) −2.02477e16 −2.42434
\(786\) 4.84096e14 0.0575582
\(787\) −4.60899e15 −0.544183 −0.272091 0.962271i \(-0.587715\pi\)
−0.272091 + 0.962271i \(0.587715\pi\)
\(788\) −5.04641e14 −0.0591682
\(789\) −9.04772e15 −1.05345
\(790\) 4.25810e15 0.492342
\(791\) −5.36064e15 −0.615526
\(792\) −8.61606e14 −0.0982472
\(793\) 1.55599e15 0.176200
\(794\) 3.43155e15 0.385902
\(795\) 1.49154e16 1.66577
\(796\) 2.22130e15 0.246369
\(797\) −6.16784e15 −0.679379 −0.339690 0.940538i \(-0.610322\pi\)
−0.339690 + 0.940538i \(0.610322\pi\)
\(798\) −1.01385e15 −0.110906
\(799\) 2.57878e15 0.280161
\(800\) 1.43178e16 1.54484
\(801\) 3.58072e15 0.383700
\(802\) −1.66536e15 −0.177235
\(803\) −7.50583e15 −0.793347
\(804\) −4.63801e15 −0.486881
\(805\) −1.30390e16 −1.35946
\(806\) 4.84706e13 0.00501921
\(807\) 5.46412e15 0.561973
\(808\) 6.33092e15 0.646703
\(809\) 7.04742e15 0.715012 0.357506 0.933911i \(-0.383627\pi\)
0.357506 + 0.933911i \(0.383627\pi\)
\(810\) −5.65894e14 −0.0570253
\(811\) 3.60876e15 0.361196 0.180598 0.983557i \(-0.442197\pi\)
0.180598 + 0.983557i \(0.442197\pi\)
\(812\) −1.57924e15 −0.156996
\(813\) 1.85825e15 0.183488
\(814\) 9.73425e14 0.0954703
\(815\) 9.11151e15 0.887613
\(816\) 2.10035e15 0.203234
\(817\) 7.69948e15 0.740014
\(818\) 1.08496e15 0.103578
\(819\) −3.03008e14 −0.0287338
\(820\) 3.09418e16 2.91454
\(821\) −1.54106e16 −1.44189 −0.720947 0.692990i \(-0.756293\pi\)
−0.720947 + 0.692990i \(0.756293\pi\)
\(822\) 3.43277e15 0.319043
\(823\) 1.29390e16 1.19454 0.597272 0.802039i \(-0.296251\pi\)
0.597272 + 0.802039i \(0.296251\pi\)
\(824\) −1.02355e15 −0.0938666
\(825\) 6.38171e15 0.581354
\(826\) 1.90343e14 0.0172245
\(827\) 7.51765e15 0.675774 0.337887 0.941187i \(-0.390288\pi\)
0.337887 + 0.941187i \(0.390288\pi\)
\(828\) 6.07651e15 0.542609
\(829\) −6.61848e15 −0.587095 −0.293547 0.955945i \(-0.594836\pi\)
−0.293547 + 0.955945i \(0.594836\pi\)
\(830\) 6.50042e15 0.572812
\(831\) −8.52736e15 −0.746464
\(832\) −1.12712e15 −0.0980152
\(833\) −4.42599e15 −0.382351
\(834\) −2.04589e15 −0.175577
\(835\) −5.11259e15 −0.435879
\(836\) −8.06010e15 −0.682663
\(837\) 1.97362e14 0.0166064
\(838\) 3.53550e15 0.295535
\(839\) 1.22395e16 1.01642 0.508210 0.861233i \(-0.330307\pi\)
0.508210 + 0.861233i \(0.330307\pi\)
\(840\) −3.03869e15 −0.250698
\(841\) −1.03513e16 −0.848435
\(842\) −2.00391e15 −0.163178
\(843\) −2.69991e15 −0.218422
\(844\) 9.73671e15 0.782580
\(845\) 2.06954e16 1.65258
\(846\) 7.39518e14 0.0586694
\(847\) 4.12043e15 0.324776
\(848\) −1.58754e16 −1.24322
\(849\) 6.28265e15 0.488822
\(850\) 3.58544e15 0.277165
\(851\) −1.44032e16 −1.10623
\(852\) 1.01609e16 0.775377
\(853\) −1.16615e16 −0.884166 −0.442083 0.896974i \(-0.645760\pi\)
−0.442083 + 0.896974i \(0.645760\pi\)
\(854\) −1.58959e15 −0.119747
\(855\) −1.11065e16 −0.831314
\(856\) 1.29384e16 0.962224
\(857\) −2.36642e16 −1.74863 −0.874313 0.485363i \(-0.838687\pi\)
−0.874313 + 0.485363i \(0.838687\pi\)
\(858\) 2.36142e14 0.0173378
\(859\) −1.04372e16 −0.761415 −0.380707 0.924696i \(-0.624319\pi\)
−0.380707 + 0.924696i \(0.624319\pi\)
\(860\) 1.09993e16 0.797302
\(861\) −6.61305e15 −0.476304
\(862\) −3.37777e15 −0.241735
\(863\) 1.50730e16 1.07187 0.535933 0.844261i \(-0.319960\pi\)
0.535933 + 0.844261i \(0.319960\pi\)
\(864\) 2.15725e15 0.152431
\(865\) 2.56030e16 1.79764
\(866\) 5.23979e14 0.0365566
\(867\) −6.44429e15 −0.446756
\(868\) 5.05131e14 0.0347973
\(869\) −7.23503e15 −0.495258
\(870\) 1.69592e15 0.115358
\(871\) 2.66691e15 0.180264
\(872\) −8.88788e15 −0.596977
\(873\) 9.07013e15 0.605390
\(874\) −1.16909e16 −0.775417
\(875\) 1.09673e16 0.722863
\(876\) 1.23363e16 0.808005
\(877\) 2.11962e16 1.37962 0.689811 0.723989i \(-0.257693\pi\)
0.689811 + 0.723989i \(0.257693\pi\)
\(878\) −2.94649e15 −0.190583
\(879\) 6.81306e15 0.437929
\(880\) −1.02751e16 −0.656342
\(881\) −2.88353e16 −1.83045 −0.915223 0.402947i \(-0.867986\pi\)
−0.915223 + 0.402947i \(0.867986\pi\)
\(882\) −1.26924e15 −0.0800695
\(883\) −1.45222e16 −0.910433 −0.455217 0.890381i \(-0.650438\pi\)
−0.455217 + 0.890381i \(0.650438\pi\)
\(884\) −1.35340e15 −0.0843218
\(885\) 2.08518e15 0.129108
\(886\) −5.14533e15 −0.316612
\(887\) −1.17547e16 −0.718838 −0.359419 0.933176i \(-0.617025\pi\)
−0.359419 + 0.933176i \(0.617025\pi\)
\(888\) −3.35662e15 −0.204000
\(889\) 5.64215e15 0.340789
\(890\) −9.84164e15 −0.590775
\(891\) 9.61523e14 0.0573631
\(892\) 7.58274e14 0.0449593
\(893\) 1.45142e16 0.855281
\(894\) −1.09466e14 −0.00641095
\(895\) −2.72107e16 −1.58385
\(896\) 7.21398e15 0.417331
\(897\) −3.49406e15 −0.200896
\(898\) −3.53327e15 −0.201910
\(899\) −5.91471e14 −0.0335935
\(900\) −1.04888e16 −0.592095
\(901\) −1.42385e16 −0.798872
\(902\) 5.15372e15 0.287399
\(903\) −2.35082e15 −0.130298
\(904\) −1.44058e16 −0.793615
\(905\) 4.79008e15 0.262286
\(906\) −3.63818e15 −0.198006
\(907\) −1.11488e16 −0.603100 −0.301550 0.953450i \(-0.597504\pi\)
−0.301550 + 0.953450i \(0.597504\pi\)
\(908\) 8.87190e15 0.477029
\(909\) −7.06510e15 −0.377587
\(910\) 8.32820e14 0.0442409
\(911\) 2.30479e16 1.21697 0.608485 0.793565i \(-0.291777\pi\)
0.608485 + 0.793565i \(0.291777\pi\)
\(912\) 1.18214e16 0.620438
\(913\) −1.10450e16 −0.576204
\(914\) −2.36070e15 −0.122416
\(915\) −1.74137e16 −0.897584
\(916\) −1.22716e16 −0.628748
\(917\) −2.90091e15 −0.147742
\(918\) 5.40212e14 0.0273483
\(919\) 2.16392e15 0.108895 0.0544473 0.998517i \(-0.482660\pi\)
0.0544473 + 0.998517i \(0.482660\pi\)
\(920\) −3.50399e16 −1.75279
\(921\) −1.64597e16 −0.818454
\(922\) −2.11351e15 −0.104468
\(923\) −5.84261e15 −0.287077
\(924\) 2.46093e15 0.120200
\(925\) 2.48617e16 1.20712
\(926\) −2.73172e15 −0.131848
\(927\) 1.14225e15 0.0548054
\(928\) −6.46501e15 −0.308358
\(929\) 8.94797e15 0.424266 0.212133 0.977241i \(-0.431959\pi\)
0.212133 + 0.977241i \(0.431959\pi\)
\(930\) −5.42452e14 −0.0255685
\(931\) −2.49108e16 −1.16725
\(932\) 3.02849e16 1.41072
\(933\) −1.84898e16 −0.856217
\(934\) 7.92814e15 0.364975
\(935\) −9.21558e15 −0.421754
\(936\) −8.14278e14 −0.0370472
\(937\) −3.28664e15 −0.148657 −0.0743283 0.997234i \(-0.523681\pi\)
−0.0743283 + 0.997234i \(0.523681\pi\)
\(938\) −2.72449e15 −0.122509
\(939\) 1.82825e16 0.817287
\(940\) 2.07346e16 0.921493
\(941\) −4.18818e15 −0.185047 −0.0925235 0.995710i \(-0.529493\pi\)
−0.0925235 + 0.995710i \(0.529493\pi\)
\(942\) 5.54294e15 0.243478
\(943\) −7.62567e16 −3.33015
\(944\) −2.21939e15 −0.0963581
\(945\) 3.39108e15 0.146374
\(946\) 1.83206e15 0.0786210
\(947\) −2.66126e16 −1.13543 −0.567717 0.823223i \(-0.692173\pi\)
−0.567717 + 0.823223i \(0.692173\pi\)
\(948\) 1.18913e16 0.504409
\(949\) −7.09354e15 −0.299157
\(950\) 2.01799e16 0.846135
\(951\) −1.70618e16 −0.711267
\(952\) 2.90079e15 0.120230
\(953\) −2.30224e16 −0.948723 −0.474362 0.880330i \(-0.657321\pi\)
−0.474362 + 0.880330i \(0.657321\pi\)
\(954\) −4.08317e15 −0.167294
\(955\) −3.07634e16 −1.25319
\(956\) −5.77370e15 −0.233849
\(957\) −2.88157e15 −0.116041
\(958\) 2.77932e15 0.111283
\(959\) −2.05706e16 −0.818926
\(960\) 1.26141e16 0.499302
\(961\) −2.52193e16 −0.992554
\(962\) 9.19956e14 0.0360001
\(963\) −1.44389e16 −0.561809
\(964\) 3.25785e14 0.0126040
\(965\) −1.75015e16 −0.673248
\(966\) 3.56950e15 0.136532
\(967\) 3.88914e16 1.47914 0.739568 0.673082i \(-0.235030\pi\)
0.739568 + 0.673082i \(0.235030\pi\)
\(968\) 1.10729e16 0.418743
\(969\) 1.06025e16 0.398683
\(970\) −2.49293e16 −0.932108
\(971\) −1.59903e16 −0.594500 −0.297250 0.954800i \(-0.596069\pi\)
−0.297250 + 0.954800i \(0.596069\pi\)
\(972\) −1.58033e15 −0.0584229
\(973\) 1.22598e16 0.450675
\(974\) 5.04400e15 0.184374
\(975\) 6.03117e15 0.219218
\(976\) 1.85346e16 0.669898
\(977\) 1.52326e16 0.547461 0.273731 0.961806i \(-0.411742\pi\)
0.273731 + 0.961806i \(0.411742\pi\)
\(978\) −2.49433e15 −0.0891436
\(979\) 1.67221e16 0.594275
\(980\) −3.55869e16 −1.25761
\(981\) 9.91857e15 0.348554
\(982\) −1.29634e16 −0.453009
\(983\) 1.62788e16 0.565689 0.282845 0.959166i \(-0.408722\pi\)
0.282845 + 0.959166i \(0.408722\pi\)
\(984\) −1.77714e16 −0.614112
\(985\) −3.24745e15 −0.111595
\(986\) −1.61895e15 −0.0553236
\(987\) −4.43150e15 −0.150594
\(988\) −7.61737e15 −0.257420
\(989\) −2.71079e16 −0.910997
\(990\) −2.64276e15 −0.0883209
\(991\) −4.42759e16 −1.47151 −0.735753 0.677250i \(-0.763171\pi\)
−0.735753 + 0.677250i \(0.763171\pi\)
\(992\) 2.06789e15 0.0683459
\(993\) 2.45586e16 0.807203
\(994\) 5.96876e15 0.195101
\(995\) 1.42945e16 0.464666
\(996\) 1.81532e16 0.586851
\(997\) −3.68966e16 −1.18621 −0.593107 0.805123i \(-0.702099\pi\)
−0.593107 + 0.805123i \(0.702099\pi\)
\(998\) −5.98587e15 −0.191386
\(999\) 3.74587e15 0.119109
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.1.17 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.b.1.17 27 1.1 even 1 trivial